diff --git "a/all/mathqa_general.json" "b/all/mathqa_general.json" new file mode 100644--- /dev/null +++ "b/all/mathqa_general.json" @@ -0,0 +1,160892 @@ +{ + "Source": "https://arxiv.org/pdf/2108.07732.pdf", + "Categories": [ + { + "Math complexity": 3, + "Language complexity": 7, + "Domain knowledge complexity": 0 + } + ], + "Instances": [ + { + "Input": "sophia finished 2 / 3 of a book . she calculated that she finished 90 more pages than she has yet to read . how long is her book ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 90.0\nt0 = n0 / n1\nt1 = 1.0 - t0\nanswer = n2 / t1\nprint(answer)" + ], + "Output Answer": [ + "269.99999999999994" + ], + "split": "train" + }, + { + "Input": "a student was asked to find 4 / 5 of a number . but the student divided the number by 4 / 5 , thus the student got 36 more than the correct answer . find the number .", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 4.0\nn3 = 5.0\nn4 = 36.0\nt0 = n0 / n1\nt1 = n4 * t0\nt2 = t0 * t0\nt3 = t0 * t1\nt4 = 1.0 - t2\nt5 = t3 / t4\nanswer = t5 / t0\nprint(answer)" + ], + "Output Answer": [ + "80.00000000000003" + ], + "split": "train" + }, + { + "Input": "a vessel of capacity 2 litre has 30 % of alcohol and another vessel of capacity 6 litre had 40 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?", + "Output Program": [ + "n0 = 2.0\nn1 = 30.0\nn2 = 6.0\nn3 = 40.0\nn4 = 8.0\nn5 = 10.0\nt0 = n1 / 100.0\nt1 = n3 / 100.0\nt2 = n0 * t0\nt3 = n2 * t1\nt4 = t2 + t3\nt5 = t4 / n5\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "30.000000000000004" + ], + "split": "train" + }, + { + "Input": "the total of 324 of 20 paise and 25 paise make a sum of rs . 70 . the no of 20 paise coins is", + "Output Program": [ + "n0 = 324.0\nn1 = 20.0\nn2 = 25.0\nn3 = 70.0\nn4 = 20.0\nt0 = n0 * n2\nt1 = n3 * 100.0\nt2 = n2 - n1\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "220" + ], + "split": "train" + }, + { + "Input": "mark bought a set of 6 flower pots of different sizes at a total cost of $ 8.25 . each pot cost 0.1 more than the next one below it in size . what was the cost , in dollars , of the largest pot ?", + "Output Program": [ + "n0 = 6.0\nn1 = 8.25\nn2 = 0.1\nt0 = n0 - 1.0\nt1 = n0 * t0\nt2 = n2 * t0\nt3 = t1 / 2.0\nt4 = n2 * t3\nt5 = n1 - t4\nt6 = t5 / n0\nanswer = t6 + t2\nprint(answer)" + ], + "Output Answer": [ + "1.625" + ], + "split": "train" + }, + { + "Input": "if a bicyclist in motion increases his speed by 30 percent and then increases this speed by 10 percent , what percent of the original speed is the total increase in speed ?", + "Output Program": [ + "n0 = 30.0\nn1 = 10.0\nt0 = n0 + 100.0\nt1 = n1 / 100.0\nt2 = t0 * t1\nt3 = t0 + t2\nanswer = t3 - 100.0\nprint(answer)" + ], + "Output Answer": [ + "43" + ], + "split": "train" + }, + { + "Input": "what is the greatest number that divides 263 , 935 and 1383 leaving a remainder of 7 in each case ?", + "Output Program": [ + "n0 = 263.0\nn1 = 935.0\nn2 = 1383.0\nn3 = 7.0\nt0 = n2 - n3\nt1 = n1 - n3\nt2 = n0 - n3\nt3 = t0 - t1\nt4 = t3 - t2\nt5 = t4 / 3.0\nanswer = t5 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "find the average of all the numbers between 6 and 38 which are divisible by 4 .", + "Output Program": [ + "n0 = 6.0\nn1 = 38.0\nn2 = 4.0\nt0 = n0 + 4.0\nt1 = n1 - 4.0\nt2 = t0 + t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "a man has some hens and cows . if the number of heads be 50 and the number of feet equals 144 , then the number of hens will be", + "Output Program": [ + "n0 = 50.0\nn1 = 144.0\nt0 = n0 * 4.0\nt1 = t0 - n1\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "if p / q = 4 / 5 , then the value of 11 / 7 + { ( 2 q - p ) / ( 2 q + p ) } is ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 11.0\nn3 = 7.0\nn4 = 2.0\nn5 = 2.0\nt0 = n2 / n3\nt1 = n0 / n1\nt2 = n4 + t1\nt3 = n4 - t1\nt4 = t3 / t2\nanswer = t0 + t4\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a big container is 40 % full with water . if 14 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container in liters ?", + "Output Program": [ + "n0 = 40.0\nn1 = 14.0\nn2 = 3.0\nn3 = 4.0\nt0 = n2 / n3\nt1 = n0 / 100.0\nt2 = t0 - t1\nanswer = n1 / t2\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "the total cost of a vacation was divided among 3 people . if the total cost of the vacation had been divided equally among 5 people , the cost per person would have been $ 50 less . what was the total cost cost of the vacation ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 50.0\nt0 = n0 * n1\nt1 = n1 - n0\nt2 = n2 / t1\nanswer = t2 * t0\nprint(answer)" + ], + "Output Answer": [ + "375" + ], + "split": "train" + }, + { + "Input": "if y > 0 , ( 1 y ) / 20 + ( 3 y ) / 10 is what percent of y ?", + "Output Program": [ + "n0 = 0.0\nn1 = 1.0\nn2 = 20.0\nn3 = 3.0\nn4 = 10.0\nt0 = n1 / n2\nt1 = n3 / n4\nt2 = t0 + t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "for every even positive integer m , f ( m ) represents the product of all even integers from 2 to m , inclusive . for example , f ( 12 ) = 2 x 4 x 6 x 8 x 10 x 12 . what is the greatest prime factor of f ( 36 ) ?", + "Output Program": [ + "n0 = 2.0\nn1 = 12.0\nn2 = 2.0\nn3 = 4.0\nn4 = 6.0\nn5 = 8.0\nn6 = 10.0\nn7 = 12.0\nn8 = 36.0\nt0 = n8 / n0\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "the average age of 19 persons in a office is 15 years . out of these , the average age of 5 of them is 14 years and that of the other 9 persons is 16 years . the age of the 15 th person is ?", + "Output Program": [ + "n0 = 19.0\nn1 = 15.0\nn2 = 5.0\nn3 = 14.0\nn4 = 9.0\nn5 = 16.0\nn6 = 15.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n4 * n5\nt3 = t0 - t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "71" + ], + "split": "train" + }, + { + "Input": "if \u221a 10 = 3.16 , find the value of if \u221a 5 / 2", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 3.16\nn2 = 5.0\nn3 = 2.0\nt0 = n2 / n3\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "1.5811388300841898" + ], + "split": "train" + }, + { + "Input": "carrie likes to buy t - shirts at the local clothing store . they cost $ 9.65 each . one day , she bought 12 t - shirts . how much money did she spend ?", + "Output Program": [ + "import math\nn0 = 9.65\nn1 = 12.0\nt0 = n0 * n1\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "115" + ], + "split": "train" + }, + { + "Input": "how many 1 / 10 s are there in 37 1 / 2 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 10.0\nn2 = 37.0\nn3 = 1.0\nn4 = 2.0\nt0 = n0 / n4\nt1 = n0 / n1\nt2 = n2 + t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "375" + ], + "split": "train" + }, + { + "Input": "in a box of 8 pens , a total of 3 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?", + "Output Program": [ + "n0 = 8.0\nn1 = 3.0\nn2 = 2.0\nt0 = n0 - n1\nt1 = n0 - 1.0\nt2 = t0 / n0\nt3 = t0 - 1.0\nt4 = t3 / t1\nanswer = t2 * t4\nprint(answer)" + ], + "Output Answer": [ + "0.3571428571428571" + ], + "split": "train" + }, + { + "Input": "if k is an integer and 0.0010101 x 10 ^ k is greater than 10 , what is the least possible value of k ?", + "Output Program": [ + "import math\nn0 = 0.0010101\nn1 = 10.0\nn2 = 10.0\nt0 = n2 / n0\nt1 = math.log(max(1e-5, n1), 2)\nt2 = math.log(max(1e-5, t0), 2)\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "3.9956356288922485" + ], + "split": "train" + }, + { + "Input": "if a and b are positive integers and ( 3 ^ a ) ^ b = 3 ^ 3 , what is the value of 3 ^ a * 3 ^ b ?", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 3.0\nn3 = 3.0\nn4 = 3.0\nt0 = n0**min(n0, 5)\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "81" + ], + "split": "train" + }, + { + "Input": "a number exceeds by 35 from its 3 / 8 part . then the number is ?", + "Output Program": [ + "n0 = 35.0\nn1 = 3.0\nn2 = 8.0\nt0 = n0 * n2\nt1 = n2 - n1\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "train" + }, + { + "Input": "if 0.75 : x : : 5 : 6 , then x is equal to :", + "Output Program": [ + "n0 = 0.75\nn1 = 5.0\nn2 = 6.0\nt0 = n0 * n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.9" + ], + "split": "train" + }, + { + "Input": "the sum of the first 50 positive even integers is 2550 . what is the sum of the even integers from 602 to 700 inclusive ?", + "Output Program": [ + "n0 = 50.0\nn1 = 2550.0\nn2 = 602.0\nn3 = 700.0\nt0 = n2 + n3\nt1 = n3 - n2\nt2 = t1 / 2.0\nt3 = t0 / 2.0\nt4 = t2 + 1.0\nanswer = t4 * t3\nprint(answer)" + ], + "Output Answer": [ + "32550" + ], + "split": "train" + }, + { + "Input": "the average runs scored by a batsman in 10 matches is 40 . in the next 10 matches the batsman scored an average of 30 runs . find his average in all the 20 matches ?", + "Output Program": [ + "n0 = 10.0\nn1 = 40.0\nn2 = 10.0\nn3 = 30.0\nn4 = 20.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "there are 300 giraffes at a large zoo . the number of giraffes is 3 times the number of all the other animals combined . how many more giraffes are there than non giraffes animals at the zoo ?", + "Output Program": [ + "n0 = 300.0\nn1 = 3.0\nt0 = n0 / n1\nt1 = t0 / 10.0\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "290" + ], + "split": "train" + }, + { + "Input": "bucket a is 1 / 4 full of sand , and bucket b , which has one - half the capacity of bucket a , is 3 / 8 full of sand . jana pours the contents of bucket b into bucket a . bucket a is now filled to what fraction of its capacity ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 3.0\nn3 = 8.0\nt0 = n1 + n2\nt1 = n3 * 2.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.4375" + ], + "split": "train" + }, + { + "Input": "if n is an integer , f ( n ) = f ( n - 1 ) - n and f ( 4 ) = 15 . what is the value of f ( 6 ) ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 15.0\nn3 = 6.0\nt0 = n0 + n1\nt1 = n2 - t0\nanswer = t1 - n3\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "andy solves problems 78 to 125 inclusive in a math exercise . how many problems does he solve ?", + "Output Program": [ + "n0 = 78.0\nn1 = 125.0\nt0 = n1 - n0\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "a fair 2 sided coin is flipped 3 times . what is the probability that tails will be the result at least twice , but not more than 3 times ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 3.0\nt0 = n0**min(n1, 5)\nt1 = 1 / t0\nt2 = t1 + t1\nt3 = n1 * t1\nt4 = t2 + t3\nanswer = 1.0 - t4\nprint(answer)" + ], + "Output Answer": [ + "0.375" + ], + "split": "train" + }, + { + "Input": "3 / 5 of all married couples have more than one child . 2 / 5 of all married couples have more than 3 children . what fraction of all married couples have 2 or 3 children ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 2.0\nn3 = 5.0\nn4 = 3.0\nn5 = 2.0\nn6 = 3.0\nt0 = n0 / n1\nt1 = n2 / n1\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "0.19999999999999996" + ], + "split": "train" + }, + { + "Input": "if 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 18 , then n =", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 2.0\nn3 = 2.0\nn4 = 2.0\nn5 = 2.0\nn6 = 2.0\nn7 = 2.0\nn8 = 4.0\nn9 = 18.0\nt0 = n0 * n9\nt1 = t0 - n0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "a car traveled 35 % of the way from town x to town y at an average speed of 35 mph . the car traveled at an average speed of v mph for the remaining part of the trip . the average speed for the entire trip was 50 mph . what is v in mph ?", + "Output Program": [ + "n0 = 35.0\nn1 = 35.0\nn2 = 50.0\nt0 = n0 / n0\nt1 = 100.0 - n0\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "65" + ], + "split": "train" + }, + { + "Input": "hammers and wrenches are manufactured at a uniform weight per hammer and a uniform weight per wrench . if the total weight of two hammers and two wrenches is one - third that of 8 hammers and 5 wrenches , then the total weight of one wrench is how many times that of one hammer ?", + "Output Program": [ + "n0 = 8.0\nn1 = 5.0\nt0 = 2.0 * 3.0\nt1 = n0 - t0\nt2 = t0 - n1\nanswer = t1 / t2\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a certain pair of used shoes can be repaired for $ 10.50 and will last for 1 year . a pair of the same kind of shoes can be purchased new for $ 30.00 and will last for 2 years . the average cost per year of the new shoes is what percent greater than the cost of repairing the used shoes ?", + "Output Program": [ + "n0 = 10.5\nn1 = 1.0\nn2 = 30.0\nn3 = 2.0\nt0 = n0 * n3\nt1 = n2 - t0\nt2 = t1 / t0\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "42.857142857142854" + ], + "split": "train" + }, + { + "Input": "solution for 2.12 + . 004 + . 345", + "Output Program": [ + "n0 = 2.12\nn1 = 4.0\nn2 = 345.0\nt0 = n1 / 1000.0\nt1 = n2 / 1000.0\nt2 = n0 + t0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "2.4690000000000003" + ], + "split": "train" + }, + { + "Input": "how many paying stones , each measuring 2 1 / 2 m * 2 m are required to pave a rectangular court yard 30 m long and 16 1 / 2 m board ?", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 2.0\nn3 = 2.0\nn4 = 30.0\nn5 = 16.0\nn6 = 1.0\nn7 = 2.0\nt0 = n1 / n0\nt1 = n5 + t0\nt2 = n0 + t0\nt3 = n4 * t1\nt4 = n0 * t2\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "99" + ], + "split": "train" + }, + { + "Input": "20 liters of a mixture is created by mixing liquid p and liquid q in the ratio 3 : 2 . how many liters of liquid q must be added to make the ratio 4 : 3 ?", + "Output Program": [ + "n0 = 20.0\nn1 = 3.0\nn2 = 2.0\nn3 = 4.0\nn4 = 3.0\nt0 = n3 + n4\nt1 = n1 + n2\nt2 = n0 * n1\nt3 = n0 * n2\nt4 = t2 / t1\nt5 = t3 / t1\nt6 = t0 * t4\nt7 = t6 / n3\nt8 = n4 * t7\nt9 = t8 / t0\nanswer = t9 - t5\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "in a boat there are 8 men whose average weight is increased by 1 kg when 1 man of 60 kg is replaced by a new man . what is weight of new comer ?", + "Output Program": [ + "n0 = 8.0\nn1 = 1.0\nn2 = 1.0\nn3 = 60.0\n\nanswer = n0 + n3\nprint(answer)" + ], + "Output Answer": [ + "68" + ], + "split": "train" + }, + { + "Input": "if the probability of rain on any given day in chicago during the summer is 50 % , independent of what happens on any other day , what is the probability of having exactly 3 rainy days from july 4 through july 7 , inclusive ?", + "Output Program": [ + "n0 = 50.0\nn1 = 3.0\nn2 = 4.0\nn3 = 7.0\nt0 = 1.0 / 2.0\nt1 = t0**min(n2, 5)\nanswer = n2 * t1\nprint(answer)" + ], + "Output Answer": [ + "0.25" + ], + "split": "train" + }, + { + "Input": "every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 51200 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 8.0\nn2 = 51200.0\nt0 = n0 / n1\nt1 = n2 * t0\nt2 = n2 + t1\nt3 = t2 * t0\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "64800" + ], + "split": "train" + }, + { + "Input": "set s contains exactly 10 numbers and has an average ( arithmetic mean ) of 6.2 . if one of the numbers in set s is increased by 4 , while all other numbers remain the same , what is the new average of set s ?", + "Output Program": [ + "n0 = 10.0\nn1 = 6.2\nn2 = 4.0\nt0 = n0 * n1\nt1 = n2 + t0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "6.6" + ], + "split": "train" + }, + { + "Input": "if a person walks at 14 km / hr instead of 10 km / hr , he would have walked 20 km more . what is the actual distance travelled by him ?", + "Output Program": [ + "n0 = 14.0\nn1 = 10.0\nn2 = 20.0\nt0 = n0 - n1\nt1 = n2 / t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "a worker ' s take - home pay last year was the same each month , and she saved the same fraction of her take - home pay each month . the total amount of money that she had saved at the end of the year was 5 times the amount of that portion of her monthly take - home pay that she did not save . if all the money that she saved last year was from her take - home pay , what fraction of her take - home pay did she save each month ?", + "Output Program": [ + "n0 = 5.0\nt0 = 12.0 / n0\nt1 = t0 + 1.0\nanswer = 1 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.29411764705882354" + ], + "split": "train" + }, + { + "Input": "how many times will the digit 8 be written when listing the integers from 1 to 1000 ?", + "Output Program": [ + "n0 = 8.0\nn1 = 1.0\nn2 = 1000.0\nt0 = n1 * 10.0\nt1 = t0 * 10.0\nanswer = t1 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "on dividing 136 by a number , the quotient is 9 and the remainder is 1 . find the divisor ?", + "Output Program": [ + "import math\nn0 = 136.0\nn1 = 9.0\nn2 = 1.0\nt0 = n0 / n1\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "a 72 gallon solution of salt and water is 10 % salt . how many gallons of water must be added to the solution in order to decrease the salt to 8 % of the volume ?", + "Output Program": [ + "n0 = 72.0\nn1 = 10.0\nn2 = 8.0\nt0 = n1 - n2\nt1 = n0 * t0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "the simple interest on a sum of money will be rs . 600 after 10 years . if the principal is trebled after 5 years what will be the total interest at the end of the tenth year ?", + "Output Program": [ + "n0 = 600.0\nn1 = 10.0\nn2 = 5.0\nt0 = n0 / n1\nt1 = n2 * t0\nt2 = t1 * 3.0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "1200" + ], + "split": "train" + }, + { + "Input": "what least number must be subtracted from 427751 so that remaining no . is divisible by 10", + "Output Program": [ + "import math\nn0 = 427751.0\nn1 = 10.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "average monthly income of a family of 3 earning members was rs . 735 . one of the earning members died and therefore , the average income came down to rs 650 . the income of the deceased was ?", + "Output Program": [ + "n0 = 3.0\nn1 = 735.0\nn2 = 650.0\nt0 = n0 * n1\nt1 = n0 - 1.0\nt2 = n2 * t1\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "905" + ], + "split": "train" + }, + { + "Input": "a committee is reviewing a total of 20 x black - and - white films and 6 y color films for a festival . if the committee selects y / x % of the black - and - white films and all of the color films , what fraction x of the selected films are in color ?", + "Output Program": [ + "n0 = 20.0\nn1 = 6.0\nt0 = n0 / 100.0\nt1 = n1 + t0\nanswer = n1 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.9677419354838709" + ], + "split": "train" + }, + { + "Input": "for how many integers pair ( x , y ) satisfies the result ( 1 / x ) + ( ( 1 / y ) = 1 / 16", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 1.0\nn3 = 16.0\nt0 = n0 + n3\nt1 = n0 + t0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "a certain clock marks every hour by striking a number of times equal to the hour , and the time require for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stoke and the end of the last stroke is 22 seconds . at 7 : 00 , how many seconds elapse between the beginning of the first stroke and the end of the last stroke ?", + "Output Program": [ + "n0 = 6.0\nn1 = 0.0\nn2 = 22.0\nn3 = 7.0\nn4 = 0.0\nt0 = n3 - 1.0\nt1 = n0 - 1.0\nt2 = n3 + t0\nt3 = n0 + t1\nt4 = n2 / t3\nanswer = t2 * t4\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "the price of commodity x increases by 30 cents every year , while the price of commodity y increases by 20 cents every year . if in 2001 , the price of commodity x was $ 4.20 and the price of commodity y was $ 4.40 , in which year will commodity x cost 40 cents more than the commodity y ?", + "Output Program": [ + "n0 = 30.0\nn1 = 20.0\nn2 = 2001.0\nn3 = 4.2\nn4 = 4.4\nn5 = 40.0\nt0 = n5 / 100.0\nt1 = n0 / 100.0\nt2 = n4 - n3\nt3 = t0 + t2\nt4 = t1 - t2\nt5 = t3 / t4\nanswer = n2 + t5\nprint(answer)" + ], + "Output Answer": [ + "2007" + ], + "split": "train" + }, + { + "Input": "1 / 0.04 is equal to", + "Output Program": [ + "n0 = 1.0\nn1 = 0.04\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "if an integer n is to be chosen at random from the integers 1 to 92 , inclusive , what is the probability that n ( n + 1 ) ( n + 2 ) will be divisible by 8 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 92.0\nn2 = 1.0\nn3 = 2.0\nn4 = 8.0\nt0 = n1 / n3\nt1 = n1 / n4\nt2 = t0 + t1\nanswer = t2 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.625" + ], + "split": "train" + }, + { + "Input": "a , b and c have rs . 300 between them , a and c together have rs . 200 and b and c rs . 350 . how much does c have ?", + "Output Program": [ + "n0 = 300.0\nn1 = 200.0\nn2 = 350.0\nt0 = n1 + n2\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "250" + ], + "split": "train" + }, + { + "Input": "united telephone charges a base rate of $ 7.00 for service , plus an additional charge of $ 0.25 per minute . atlantic call charges a base rate of $ 12.00 for service , plus an additional charge of $ 0.20 per minute . for what number of minutes would the bills for each telephone company be the same ?", + "Output Program": [ + "n0 = 7.0\nn1 = 0.25\nn2 = 12.0\nn3 = 0.2\nt0 = n2 - n0\nt1 = n1 - n3\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "100.00000000000003" + ], + "split": "train" + }, + { + "Input": "how many gallons of milk that is 10 percent butter - fat must be added to 8 gallons of milk that is 50 percent butterfat to obtain milk that is 20 percent butterfat ?", + "Output Program": [ + "n0 = 10.0\nn1 = 8.0\nn2 = 50.0\nn3 = 20.0\nt0 = n2 - n3\nt1 = n1 * t0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "a certain family has 3 sons : richard is 6 years older than david , and david is 8 years older than scott . if in 8 years , richard will be twice as old as scott , then how old was david 3 years ago ?", + "Output Program": [ + "n0 = 3.0\nn1 = 6.0\nn2 = 8.0\nn3 = 8.0\nn4 = 3.0\nt0 = n1 + n2\nanswer = t0 - n4\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "if 60 % of ( x - y ) = 20 % of ( x + y ) , then what percent of x is y ?", + "Output Program": [ + "n0 = 60.0\nn1 = 20.0\nt0 = n0 + n1\nt1 = n0 - n1\nt2 = t1 / t0\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "how many even integers n , such that 20 < = n < = 220 are of the form 3 k + 4 , where k is any natural number ?", + "Output Program": [ + "n0 = 20.0\nn1 = 220.0\nn2 = 3.0\nn3 = 4.0\nt0 = n0 + 2.0\nt1 = 2.0 + n3\nt2 = n1 - 2.0\nt3 = t2 - t0\nt4 = t3 / t1\nanswer = t4 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "33.666666666666664" + ], + "split": "train" + }, + { + "Input": "of the final grades received by the students in a certain math course , 1 / 5 are a ' s , 1 / 4 are b ' s , 1 / 2 are c ' s , and the remaining 20 grades are d ' s . what is the number of students in the course ?", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 1.0\nn3 = 4.0\nn4 = 1.0\nn5 = 2.0\nn6 = 20.0\nt0 = n0 / n1\nt1 = n0 / n3\nt2 = n0 / n5\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n0 - t4\nanswer = n6 / t5\nprint(answer)" + ], + "Output Answer": [ + "399.99999999999966" + ], + "split": "train" + }, + { + "Input": "set a consists of all the prime numbers between 62 and 85 . what is the range of set a ?", + "Output Program": [ + "n0 = 62.0\nn1 = 85.0\nt0 = n0 + 4.0\nt1 = n1 - 2.0\nt2 = t0 + 1.0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "s ( n ) is a n - digit number formed by attaching the first n perfect squares , in order , into one integer . for example , s ( 1 ) = 1 , s ( 2 ) = 14 , s ( 3 ) = 149 , s ( 4 ) = 14916 , s ( 5 ) = 1491625 , etc . how many digits w are in s ( 99 ) ?", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 2.0\nn3 = 14.0\nn4 = 3.0\nn5 = 149.0\nn6 = 4.0\nn7 = 14916.0\nn8 = 5.0\nn9 = 1491625.0\nn10 = 99.0\nt0 = n6 + 60.0\nt1 = n0 * n4\nt2 = n2 * n4\nt3 = n6 + t0\nt4 = n2 * t2\nt5 = t1 + t4\nt6 = n6 * t3\nt7 = t3 + t6\nanswer = t7 + t5\nprint(answer)" + ], + "Output Answer": [ + "355" + ], + "split": "train" + }, + { + "Input": "the total age of a and b is 10 years more than the total age of b and c . c is how many years younger than a . ?", + "Output Program": [ + "n0 = 10.0\n\nanswer = n0 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the average runs of a cricket player of 8 innings was 24 . how many runs must he make in his next innings so as to increase his average of runs by 8 ?", + "Output Program": [ + "n0 = 8.0\nn1 = 24.0\nn2 = 8.0\nt0 = n0 + 1.0\nt1 = n1 + n2\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "96" + ], + "split": "train" + }, + { + "Input": "a number consists of 3 digits whose sum is 10 . the middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed . the number is :", + "Output Program": [ + "n0 = 3.0\nn1 = 10.0\nn2 = 99.0\nt0 = n1 / 2.0\nt1 = n1 * t0\nt2 = t0 - n0\nt3 = t2 * 100.0\nt4 = t3 + t1\nanswer = n0 + t4\nprint(answer)" + ], + "Output Answer": [ + "253" + ], + "split": "train" + }, + { + "Input": "if 213 \u00d7 16 = 3408 , then 1.6 \u00d7 213.0 is equal to :", + "Output Program": [ + "n0 = 213.0\nn1 = 16.0\nn2 = 3408.0\nn3 = 1.6\nn4 = 213.0\n\nanswer = n0 * n3\nprint(answer)" + ], + "Output Answer": [ + "340.8" + ], + "split": "train" + }, + { + "Input": "{ 5 , 6 , 3 , 8 , 4 } if we want to get the median value of the set to be 10 which value should be inserted in the set of 5 values ?", + "Output Program": [ + "n0 = 5.0\nn1 = 6.0\nn2 = 3.0\nn3 = 8.0\nn4 = 4.0\nn5 = 10.0\nn6 = 5.0\nt0 = n0 + n1\nt1 = t0 - n5\nt2 = t1 + 1.0\nt3 = t2 + t1\nt4 = t3 + t1\nt5 = t4 + t1\nt6 = t5 + t1\nanswer = t6 + t1\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "a positive number when decreased by 4 is equal to 21 times the reciprocal of the number . the number is", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 21.0\nt0 = n0 * n1\nt1 = n0**min(2.0, 5)\nt2 = t0 + t1\nt3 = math.sqrt(max(0, t2))\nt4 = n0 + t3\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "a = { 0 , 1 , - 3 , 6 , - 8 } b = { - 1 , 2 , - 4 , 7 } if a is a number that is randomly selected from set a , and b is a number that is randomly selected from set b , what is the probability that ab > 0 ?", + "Output Program": [ + "n0 = 0.0\nn1 = 1.0\nn2 = 3.0\nn3 = 6.0\nn4 = 8.0\nn5 = 1.0\nn6 = 2.0\nn7 = 4.0\nn8 = 7.0\nn9 = 0.0\nt0 = n1 + n7\nt1 = n6 / n7\nt2 = n6 / t0\nt3 = t2 * t1\nanswer = t3 + t3\nprint(answer)" + ], + "Output Answer": [ + "0.4" + ], + "split": "train" + }, + { + "Input": "for the positive integers x , x + 2 , x + 4 , x + 7 , and x + 17 , the mean is how much greater than the median ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 7.0\nn3 = 17.0\nt0 = n0 + n1\nt1 = 1.0 + n1\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = t3 / t1\nanswer = t4 - n1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "jar y has 10 % more marbles than jar x . what percent of marbles from jar y need to be moved into x so that both jars have equal marbles", + "Output Program": [ + "n0 = 10.0\nt0 = n0 + 100.0\nt1 = t0 + 100.0\nt2 = t1 / 2.0\nt3 = t0 - t2\nt4 = t3 / t0\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "4.545454545454546" + ], + "split": "train" + }, + { + "Input": "the price of a cycle is reduced by 25 per cent . the new price is reduced by a further 50 per cent . the two reductions together are equal to a single reduction of", + "Output Program": [ + "n0 = 25.0\nn1 = 50.0\nt0 = 100.0 - n1\nt1 = 100.0 - n0\nt2 = t0 / 100.0\nt3 = t2 * t1\nanswer = 100.0 - t3\nprint(answer)" + ], + "Output Answer": [ + "62.5" + ], + "split": "train" + }, + { + "Input": "shreehari has 125 pencils . there are 25 students are studying in his class . he would like to give each student the same amount of pencils , how much should he give to each student ?", + "Output Program": [ + "n0 = 125.0\nn1 = 25.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "there are 17 teams in the hockey league , and each team faces all the other teams 10 times each . how many games are played in the season ?", + "Output Program": [ + "n0 = 17.0\nn1 = 10.0\nt0 = n0 - 1.0\nt1 = n0 * t0\nt2 = n1 * t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "1360" + ], + "split": "train" + }, + { + "Input": "30 carrots on a scale weigh 5.94 kg . when 3 carrots are removed from the scale , the average weight of the 27 carrots is 200 grams . what is the average weight ( in grams ) of the 3 carrots which were removed ?", + "Output Program": [ + "n0 = 30.0\nn1 = 5.94\nn2 = 3.0\nn3 = 27.0\nn4 = 200.0\nn5 = 3.0\nt0 = n3 * n4\nt1 = t0 / 1000.0\nt2 = n1 - t1\nt3 = t2 / n2\nanswer = t3 * 1000.0\nprint(answer)" + ], + "Output Answer": [ + "180.00000000000003" + ], + "split": "train" + }, + { + "Input": "two trains start at same time from two stations and proceed towards each other at the rate of 20 km / hr and 25 km / hr respectively . when they meet , it is found that one train has traveled 75 km more than the other . what is the distance between the two stations ?", + "Output Program": [ + "n0 = 20.0\nn1 = 25.0\nn2 = 75.0\nt0 = n0 + n1\nt1 = n1 - n0\nt2 = n2 / t1\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "675" + ], + "split": "train" + }, + { + "Input": "two ants , arthur and amy , have discovered a picnic and are bringing crumbs back to the anthill . amy makes twice as many trips and carries one and a half times as many crumbs per trip as arthur . if arthur carries a total of c crumbs to the anthill , how many crumbs will amy bring to the anthill , in terms of c ?", + "Output Program": [ + "t0 = 1.0 / 2.0\nt1 = t0 + 1.0\nanswer = t1 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "the average weight of 20 persons sitting in a boat had some value . a new person added to them whose weight was 47 kg only . due to his arrival , the average weight of all the persons decreased by 5 kg . find the average weight of first 20 persons ?", + "Output Program": [ + "n0 = 20.0\nn1 = 47.0\nn2 = 5.0\nn3 = 20.0\nt0 = n0 + 1.0\nt1 = n2 * t0\nanswer = t1 - n1\nprint(answer)" + ], + "Output Answer": [ + "58" + ], + "split": "train" + }, + { + "Input": "what is the difference between the c . i . on rs . 8000 for 1 1 / 2 years at 4 % per annum compounded yearly and half - yearly ?", + "Output Program": [ + "n0 = 8000.0\nn1 = 1.0\nn2 = 1.0\nn3 = 2.0\nn4 = 4.0\nt0 = n3 / 100.0\nt1 = n4 / 100.0\nt2 = t0 + n1\nt3 = t1 + n1\nt4 = t2 * t2\nt5 = t2 * t3\nt6 = t2 * t4\nt7 = n0 * t5\nt8 = n0 * t6\nanswer = t8 - t7\nprint(answer)" + ], + "Output Answer": [ + "3.263999999999214" + ], + "split": "train" + }, + { + "Input": "on dividing 13698 by a certain number , we get 89 as quotient and 14 as remainder . what is the divisor ?", + "Output Program": [ + "n0 = 13698.0\nn1 = 89.0\nn2 = 14.0\nt0 = n0 - n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "153.75280898876406" + ], + "split": "train" + }, + { + "Input": "a father said his son , ` ` i was as old as you are at present at the time of your birth . ` ` if the father age is 38 now , the son age 5 years back was", + "Output Program": [ + "n0 = 38.0\nn1 = 5.0\nt0 = n0 / 2.0\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "the number of people who purchased book a is twice the number of people who purchased book b . the number of people who purchased both books a and b is 500 , which is twice the number of people who purchased only book b . what is the number of people x who purchased only book a ?", + "Output Program": [ + "n0 = 500.0\nt0 = n0 / 2.0\nt1 = n0 + t0\nt2 = t1 * 2.0\nanswer = t2 - n0\nprint(answer)" + ], + "Output Answer": [ + "1000" + ], + "split": "train" + }, + { + "Input": "in a certain game , each player scores either 2 points or 5 points . if n players score 2 points and m players score 5 points , and the total number of points scored is 50 , what is the least possible positive e difference between n and m ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 2.0\nn3 = 5.0\nn4 = 50.0\n\nanswer = n1 - n0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "a palindrome is a word or a number that reads the same forward and backward . for example , 2442 and 111 are palindromes . if 5 - digit palindromes are formed using one or more of the digits 1 , 2 , 3 , 4 , and 5 , how many palindromes are possible ?", + "Output Program": [ + "n0 = 2442.0\nn1 = 111.0\nn2 = 5.0\nn3 = 1.0\nn4 = 2.0\nn5 = 3.0\nn6 = 4.0\nn7 = 5.0\n\nanswer = n2**min(3.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "125" + ], + "split": "train" + }, + { + "Input": "joe \u2019 s average ( arithmetic mean ) test score across 4 equally weighted tests was 90 . he was allowed to drop his lowest score . after doing so , his average test score improved to 85 . what is the lowest test score that was dropped ?", + "Output Program": [ + "n0 = 4.0\nn1 = 90.0\nn2 = 95.0\nt0 = n0 * n1\nt1 = n2 * 3.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "the average age of 6 men increases by 2 years when two women are included in place of two men of ages 10 and 12 years . find the average age of the women ?", + "Output Program": [ + "n0 = 6.0\nn1 = 2.0\nn2 = 10.0\nn3 = 12.0\nt0 = n2 + n3\nt1 = n0 * n1\nt2 = t0 + t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "3639 + 11.95 - x = 3054 . find the value of x .", + "Output Program": [ + "n0 = 3639.0\nn1 = 11.95\nn2 = 3054.0\nt0 = n0 + n1\nanswer = t0 - n2\nprint(answer)" + ], + "Output Answer": [ + "596.9499999999998" + ], + "split": "train" + }, + { + "Input": "the cost per pound of milk powder and coffee were the same in june . in july , the price of coffee shot up by 300 % and that of milk powder dropped by 80 % . if in july , a mixture containing equal quantities of milk powder and coffee costs $ 6.30 for 3 lbs , how much did a pound of milk powder cost in july ?", + "Output Program": [ + "n0 = 300.0\nn1 = 80.0\nn2 = 6.3\nn3 = 3.0\nt0 = n1 / 100.0\nanswer = 1.0 - t0\nprint(answer)" + ], + "Output Answer": [ + "0.19999999999999996" + ], + "split": "train" + }, + { + "Input": "a certain class of students is being divided into teams . the class can either be divided into 18 teams with an equal number of players on each team or 24 teams with an equal number of players on each team . what is the lowest possible number of students in the class ?", + "Output Program": [ + "import scipy\nn0 = 18.0\nn1 = 24.0\n\nanswer = scipy.lcm(int(n0), int(n1))\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "train" + }, + { + "Input": "3 buffaloes eat as much as 4 cows or 2 oxen . at a farm , there are 15 buffaloes , 8 oxen , and 24 cows . the fodder for these cattle is available for 48 days . if 60 more cows and 30 more buffaloes are brought in , how many days will the fodder last ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 2.0\nn3 = 15.0\nn4 = 8.0\nn5 = 24.0\nn6 = 48.0\nn7 = 60.0\nn8 = 30.0\nt0 = n3 + n8\nt1 = n5 + n7\nt2 = n5 / n1\nt3 = n4 / n2\nt4 = t1 / n1\nt5 = n0 * t2\nt6 = n0 * t3\nt7 = n3 + t5\nt8 = n0 * t4\nt9 = t7 + t6\nt10 = t0 + t8\nt11 = t10 + t6\nt12 = n6 * t9\nanswer = t12 / t11\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "in a urban village of india named ` ` owlna ' ' , 70 % people have refrigerator , 75 % people have television , 65 % people got computers and 95 % got air - conditionor . how many people ( minimum ) got all these luxury .", + "Output Program": [ + "n0 = 70.0\nn1 = 75.0\nn2 = 65.0\nn3 = 95.0\nt0 = 100.0 - n0\nt1 = 100.0 - n1\nt2 = 100.0 - n2\nt3 = 100.0 - n3\nt4 = t0 + t1\nt5 = t4 + t2\nt6 = t5 + t3\nanswer = 100.0 - t6\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "having scored 96 runs in the 19 th inning , a cricketer increases his average score by 4 . what will be his average score after 19 innings ?", + "Output Program": [ + "n0 = 96.0\nn1 = 19.0\nn2 = 4.0\nn3 = 19.0\nt0 = n1 * n2\nt1 = n0 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "what least number should be added to 1019 , so that the sum is completely divisible by 25 ?", + "Output Program": [ + "n0 = 1019.0\nn1 = 25.0\nt0 = n0 % n1\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "there are 6 people in the elevator . their average weight is 156 lbs . another person enters the elevator , and increases the average weight to 151 lbs . what is the weight of the 7 th person .", + "Output Program": [ + "n0 = 6.0\nn1 = 156.0\nn2 = 151.0\nn3 = 7.0\nt0 = n2 * n3\nt1 = n0 * n1\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "121" + ], + "split": "train" + }, + { + "Input": "each child has 2 pencils and 13 skittles . if there are 15 children , how many pencils are there in total ?", + "Output Program": [ + "n0 = 2.0\nn1 = 13.0\nn2 = 15.0\n\nanswer = n0 * n2\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "if a certain number x is divided by 62 , the reminder is 7 . what is the reminder when x + 11 is divided by 31 ?", + "Output Program": [ + "n0 = 62.0\nn1 = 7.0\nn2 = 11.0\nn3 = 31.0\n\nanswer = n1 + n2\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "if 7 ^ w is a factor of the product of the integers from 1 to 100 , inclusive , what is the largest value of w ?", + "Output Program": [ + "import math\nn0 = 7.0\nn1 = 1.0\nn2 = 100.0\nt0 = n2 / n0\nt1 = n0**min(2.0, 5)\nt2 = n2 / t1\nt3 = t0 + t2\nanswer = math.floor(t3)\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "a women purchased 3 towels @ rs . 100 each , 5 towels @ rs . 150 each and two towels at a certain rate which is now slipped off from his memory . but she remembers that the average price of the towels was rs . 145 . find the unknown rate of two towels ?", + "Output Program": [ + "n0 = 3.0\nn1 = 100.0\nn2 = 5.0\nn3 = 150.0\nn4 = 145.0\nt0 = n0 + n2\nt1 = n2 * n3\nt2 = n0 * n1\nt3 = t0 + 2.0\nt4 = n4 * t3\nt5 = t4 - t1\nanswer = t5 - t2\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "train" + }, + { + "Input": "there are 6 chess amateurs playing in villa ' s chess club tournament . if each chess amateur plays with exactly 4 other amateurs , what is the total number of chess games possible to be played in the tournament ?", + "Output Program": [ + "n0 = 6.0\nn1 = 4.0\nt0 = n0 * n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "in a maths test , students were asked to find 5 / 16 of a certain number . one of the students by mistake found 5 / 6 th of that number and his answer was 100 more than the correct answer . find the number .", + "Output Program": [ + "n0 = 5.0\nn1 = 16.0\nn2 = 5.0\nn3 = 6.0\nn4 = 100.0\nt0 = n1 * n4\nt1 = n0 * n1\nt2 = n0 * n3\nt3 = n3 * t0\nt4 = t1 - t2\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "192" + ], + "split": "train" + }, + { + "Input": "there are 4 more women than there are men on a local co - ed softball team . if there are a total of 14 players on the team , what is the ratio of men to women ?", + "Output Program": [ + "n0 = 4.0\nn1 = 14.0\nt0 = 1.0 + 1.0\nt1 = n1 - n0\nt2 = t1 / t0\nt3 = n0 + t2\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.5555555555555556" + ], + "split": "train" + }, + { + "Input": "8900 \u00f7 6 \u00f7 4 = ?", + "Output Program": [ + "n0 = 8900.0\nn1 = 6.0\nn2 = 4.0\nt0 = n0 / n1\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "370.8333333333333" + ], + "split": "train" + }, + { + "Input": "the markup on a box of apples is 10 percent of the cost . the markup is what percent of the selling price ? ( markup = selling price - cost )", + "Output Program": [ + "n0 = 10.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "9.09090909090909" + ], + "split": "train" + }, + { + "Input": "a man saves 10 % of his monthly salary . if an account of dearness of things he is to increase his monthly expenses by 5 % , he is only able to save rs . 400 per month . what is his monthly salary ?", + "Output Program": [ + "n0 = 10.0\nn1 = 5.0\nn2 = 400.0\nt0 = n1 / 100.0\nt1 = n2 * 100.0\nt2 = 100.0 - n0\nt3 = t0 * t2\nt4 = t3 + t2\nt5 = 100.0 - t4\nanswer = t1 / t5\nprint(answer)" + ], + "Output Answer": [ + "7272.727272727273" + ], + "split": "train" + }, + { + "Input": "the average weight of d , e and f is 42 kg . if the average weight of d and e be 35 kg and that of e and f be 41 kg , what is the weight of e ?", + "Output Program": [ + "n0 = 42.0\nn1 = 35.0\nn2 = 41.0\nt0 = n1 * 2.0\nt1 = n2 * 2.0\nt2 = n0 * 3.0\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "a batsman in his 20 th innings makes a score of 90 , and thereby increases his average by 2 . what is his average after the 20 th innings ? he had never been \u2019 not out \u2019 .", + "Output Program": [ + "n0 = 20.0\nn1 = 90.0\nn2 = 2.0\nn3 = 20.0\nt0 = n0 * n2\nt1 = n1 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "52" + ], + "split": "train" + }, + { + "Input": "s ( n ) is a n - digit number formed by attaching the first n perfect squares , in order , into one integer . for example , s ( 1 ) = 1 , s ( 2 ) = 14 , s ( 3 ) = 149 , s ( 4 ) = 14916 , s ( 5 ) = 1491625 , etc . how many digits are in s ( 99 ) ?", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 2.0\nn3 = 14.0\nn4 = 3.0\nn5 = 149.0\nn6 = 4.0\nn7 = 14916.0\nn8 = 5.0\nn9 = 1491625.0\nn10 = 99.0\nt0 = n6 + 60.0\nt1 = n0 * n4\nt2 = n2 * n4\nt3 = n6 + t0\nt4 = n2 * t2\nt5 = t1 + t4\nt6 = n6 * t3\nt7 = t3 + t6\nanswer = t7 + t5\nprint(answer)" + ], + "Output Answer": [ + "355" + ], + "split": "train" + }, + { + "Input": "a and b are mixed together in the ratio 9 : 11 . what is the weight of mixture , if 26.1 kg of a has been consumed in it ?", + "Output Program": [ + "n0 = 9.0\nn1 = 11.0\nn2 = 26.1\nt0 = n2 / n0\nt1 = n1 * t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "58.00000000000001" + ], + "split": "train" + }, + { + "Input": "find the constant k so that : - x 2 - ( k + 12 ) x - 8 = - ( x - 2 ) ( x - 4 )", + "Output Program": [ + "n0 = 2.0\nn1 = 12.0\nn2 = 8.0\nn3 = 2.0\nn4 = 4.0\nt0 = n0 + n4\nanswer = n1 + t0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "3 maths classes : a , b and c take an algebra test . the average score of class a is 83 . the average score of class b is 76 . the average score of class c is 85 . the average score of class a and b is 79 and average score of class b and c is 81 . what is the average score of classes a , b , c ?", + "Output Program": [ + "n0 = 3.0\nn1 = 83.0\nn2 = 76.0\nn3 = 85.0\nn4 = 79.0\nn5 = 81.0\nt0 = 1.0 / 2.0\nanswer = n5 + t0\nprint(answer)" + ], + "Output Answer": [ + "81.5" + ], + "split": "train" + }, + { + "Input": "the product of two numbers is 120 and the sum of their squares is 289 . find the sum ?", + "Output Program": [ + "import math\nn0 = 120.0\nn1 = 289.0\nt0 = n0 * 4.0\nt1 = n0 * 2.0\nt2 = n1 - t1\nt3 = math.sqrt(max(0, t2))\nt4 = t3**min(2.0, 5)\nt5 = t0 + t4\nanswer = math.sqrt(max(0, t5))\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "x + ( 1 / x ) = 3 find x ^ 2 + ( 1 / x ^ 2 )", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 2.0\nn3 = 1.0\nn4 = 2.0\nt0 = n1**min(n2, 5)\nanswer = t0 - n2\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "a certain debt will be paid in 52 installments from january 1 to december 31 of a certain year . each of the first 8 payments is to be $ 410 ; each of the remaining payments is to be $ 65 more than each of the first 8 payments . what is the average ( arithmetic mean ) payment that will be made on the debt for the year ?", + "Output Program": [ + "n0 = 52.0\nn1 = 1.0\nn2 = 31.0\nn3 = 8.0\nn4 = 410.0\nn5 = 65.0\nn6 = 8.0\nt0 = n4 + n5\nt1 = n3 * n4\nt2 = n0 - n3\nt3 = t0 * t2\nt4 = t1 + t3\nanswer = t4 / n0\nprint(answer)" + ], + "Output Answer": [ + "465" + ], + "split": "train" + }, + { + "Input": "the sum of the fourth and twelfth term of an arithmetic progression is 20 . what is the sum of the first 20 terms of the arithmetic progression ?", + "Output Program": [ + "n0 = 20.0\nn1 = 20.0\nt0 = n0 * n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "train" + }, + { + "Input": "crazy eddie has a key chain factory . eddie managed to decrease the cost of manufacturing his key chains while keeping the same selling price , and thus increased the profit from the sale of each key chain from 40 % of the selling price to 50 % of the selling price . if the manufacturing cost is now $ 50 , what was it before the decrease ?", + "Output Program": [ + "n0 = 40.0\nn1 = 50.0\nn2 = 50.0\nt0 = n1 / 100.0\nt1 = n0 / 100.0\nt2 = n1 / t0\nt3 = t2 * t1\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "if the average of 1 , 2 , 4 , 5 , 6 , 9 , 9 , 10 , 12 and x is 7 , what is the value of x ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 4.0\nn3 = 5.0\nn4 = 6.0\nn5 = 9.0\nn6 = 9.0\nn7 = 10.0\nn8 = 12.0\nn9 = 7.0\nt0 = n0 + n1\nt1 = n9 * 10.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nt5 = n5 + t4\nt6 = n5 + t5\nt7 = n7 + t6\nt8 = n8 + t7\nanswer = t1 - t8\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "a jogger running at 9 km / hr along side a railway track is 200 m ahead of the engine of a 200 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?", + "Output Program": [ + "n0 = 9.0\nn1 = 200.0\nn2 = 200.0\nn3 = 45.0\nt0 = n1 + n2\nt1 = 10.0 / 2.0\nt2 = n3 - n0\nt3 = t2 / 2.0\nt4 = t1 / t3\nt5 = t4 * t2\nanswer = t0 / t5\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "what is the average of 1200 , 1300 , 1400 , 1510 , 1520 , 1530 , and 1200 ?", + "Output Program": [ + "n0 = 1200.0\nn1 = 1300.0\nn2 = 1400.0\nn3 = 1510.0\nn4 = 1520.0\nn5 = 1530.0\nn6 = 1200.0\nt0 = n0 + n1\nt1 = 3.0 + 4.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nt5 = n5 + t4\nt6 = n0 + t5\nanswer = t6 / t1\nprint(answer)" + ], + "Output Answer": [ + "1380" + ], + "split": "train" + }, + { + "Input": "a student took 5 papers in an examination , where the full marks were the same for each paper . his marks in these papers were in the proportion of 5 : 6 : 7 : 8 : 9 . in all papers together , the candidate obtained 60 % of the total marks . then the number of papers in which he got more than 50 % marks is", + "Output Program": [ + "n0 = 5.0\nn1 = 5.0\nn2 = 6.0\nn3 = 7.0\nn4 = 8.0\nn5 = 9.0\nn6 = 60.0\nn7 = 50.0\n\nanswer = 1.0 + 4.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "if x \u00a4 y = ( x + y ) ^ 2 - ( x - y ) ^ 2 . then \u221a 6 \u00a4 \u221a 6 =", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 2.0\nn2 = 6.0\nn3 = 6.0\nt0 = math.sqrt(max(0, n2))\nt1 = t0 + t0\nanswer = t1**min(n0, 5)\nprint(answer)" + ], + "Output Answer": [ + "23.999999999999996" + ], + "split": "train" + }, + { + "Input": "the average speed of a car is 1 4 / 5 times the avg speed of a bike . a tractor covers 575 km in 25 hrs . how much distance will the car cover in 4 hrs if the speed of the bike is twice speed of the tractor ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 5.0\nn3 = 575.0\nn4 = 25.0\nn5 = 4.0\nt0 = n1 / n2\nt1 = n3 / n4\nt2 = n0 + t0\nt3 = t1 * 2.0\nt4 = t2 * t3\nanswer = n5 * t4\nprint(answer)" + ], + "Output Answer": [ + "331.2" + ], + "split": "train" + }, + { + "Input": "there are 56 lights which are functional and each is controlled by a separate on / off switch . two children x and y start playing with the switches . x starts by pressing every third switch till he reaches the end . y , thereafter , presses every fifth switch till he too reaches the end . if all switches were in off position at the beggining , how many lights are switched on by the end of this operation ?", + "Output Program": [ + "n0 = 56.0\nt0 = 10.0 * 4.0\nt1 = n0 - t0\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "the difference between the local value and face value of 7 in the numeral 657903 is :", + "Output Program": [ + "n0 = 7.0\nn1 = 657903.0\nt0 = n0 * 1000.0\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "6993" + ], + "split": "train" + }, + { + "Input": "find the value of b from ( 15 ) ^ 2 x 9 ^ 2 \u00e3 \u00b7 356 = b .", + "Output Program": [ + "n0 = 15.0\nn1 = 2.0\nn2 = 9.0\nn3 = 2.0\nn4 = 356.0\nt0 = n0**min(n1, 5)\nt1 = n2**min(n1, 5)\nt2 = t0 * t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "51.193820224719104" + ], + "split": "train" + }, + { + "Input": "simplify : 0.2 * 0.4 + 0.6 * 0.8", + "Output Program": [ + "n0 = 0.2\nn1 = 0.4\nn2 = 0.6\nn3 = 0.8\nt0 = n0 * n1\nt1 = n2 * n3\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "0.56" + ], + "split": "train" + }, + { + "Input": "15 lts are taken of from a container full of liquid a and replaced with liquid b . again 15 more lts of the mixture is taken and replaced with liquid b . after this process , if the container contains liquid a and b in the ratio 9 : 16 , what is the capacity of the container s ?", + "Output Program": [ + "import math\nn0 = 15.0\nn1 = 15.0\nn2 = 9.0\nn3 = 16.0\nt0 = n2 + n3\nt1 = n2 / t0\nt2 = math.sqrt(max(0, t1))\nt3 = 1.0 - t2\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "37.5" + ], + "split": "train" + }, + { + "Input": "a 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2 . 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more . at the end of the two removal and replacement , what is the ratio e of milk and water in the resultant mixture ?", + "Output Program": [ + "n0 = 20.0\nn1 = 3.0\nn2 = 2.0\nn3 = 10.0\nt0 = n1 + n2\nt1 = n0 - n3\nt2 = n1 / t0\nt3 = n2 / t0\nt4 = t2 * t1\nt5 = t3 * t1\nt6 = n3 + t4\nt7 = t5 / n0\nt8 = t6 / n0\nt9 = t7 * t1\nt10 = t8 * t1\nt11 = n3 + t10\nanswer = t11 / t9\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "when greenville state university decided to move its fine arts collection to a new library , it had to package the collection in 20 - inch by 20 - inch by 15 - inch boxes . if the university pays $ 0.50 for every box , and if the university needs 3.06 million cubic inches to package the collection , what is the minimum amount the university must spend on boxes ?", + "Output Program": [ + "n0 = 20.0\nn1 = 20.0\nn2 = 15.0\nn3 = 0.5\nn4 = 3.06\nt0 = 1000.0 * 1000.0\nt1 = n0 * n0\nt2 = n4 * t0\nt3 = n2 * t1\nt4 = t2 / t3\nanswer = n3 * t4\nprint(answer)" + ], + "Output Answer": [ + "255" + ], + "split": "train" + }, + { + "Input": "the mean of 50 observations was 36 . it was found later that an observation 30 was wrongly taken as 23 . the corrected new mean is :", + "Output Program": [ + "n0 = 50.0\nn1 = 36.0\nn2 = 30.0\nn3 = 23.0\nt0 = n0 * n1\nt1 = n0 - 2.0\nt2 = t1 - n3\nt3 = t0 + t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "36.5" + ], + "split": "train" + }, + { + "Input": "a , b and c invest in the ratio of 3 : 4 : 5 . the percentage of return on their investments are in the ratio of 6 : 5 : 4 . find the total earnings , if b earns rs . 200 more than a :", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 5.0\nn3 = 6.0\nn4 = 5.0\nn5 = 4.0\nn6 = 200.0\nt0 = n0 * n3\nt1 = n1 * n2\nt2 = t0 + t1\nt3 = t1 - t0\nt4 = t2 + t1\nt5 = n6 / t3\nanswer = t4 * t5\nprint(answer)" + ], + "Output Answer": [ + "5800" + ], + "split": "train" + }, + { + "Input": "the average of first 14 even numbers is ?", + "Output Program": [ + "n0 = 14.0\n\nanswer = n0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "for what values of k will the pair of equations 4 ( 3 x + 4 y ) = 48 and kx + 12 y = 30 does not have a unique solution ?", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 4.0\nn3 = 48.0\nn4 = 12.0\nn5 = 30.0\nt0 = n1 * n4\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "a couple married in 1980 had two children , one in 1982 and the other in 1984 . their combined ages will equal the years of the marriage in ?", + "Output Program": [ + "n0 = 1980.0\nn1 = 1982.0\nn2 = 1984.0\nt0 = n1 - n0\nt1 = n2 - n0\nt2 = t0 + t1\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "1986" + ], + "split": "train" + }, + { + "Input": "the average weight of 8 people increases by 2.5 kg when a new person comes in place of one of them weighing 55 kg . what is the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.5\nn2 = 55.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "what is the least number which should be added to 5432 so that the sum is exactly divisible by 5 , 6 , 4 , and 3 ?", + "Output Program": [ + "n0 = 5432.0\nn1 = 5.0\nn2 = 6.0\nn3 = 4.0\nn4 = 3.0\nt0 = n1 * 2.0\nt1 = n1 + t0\nt2 = n2 + t1\nt3 = n3 + t2\nanswer = n4 + t3\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "a man can swim in still water at 6 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ?", + "Output Program": [ + "n0 = 6.0\n\nanswer = n0 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a certain roller coaster has 4 cars , and a passenger is equally likely to ride in any 1 of the 4 cars each time that passenger rides the roller coaster . if a certain passenger is to ride the roller coaster 4 times , what is the probability that the passenger will ride in each of the 4 cars ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 1.0\nn2 = 4.0\nn3 = 4.0\nn4 = 4.0\nt0 = n1 / n0\nt1 = math.factorial(min(15, int(n0)))\nt2 = t0**min(n0, 5)\nanswer = t1 * t2\nprint(answer)" + ], + "Output Answer": [ + "0.09375" + ], + "split": "train" + }, + { + "Input": "the average age of a , b and c is 25 years . if the average age of a and c is 29 years , what is the age of b in years ?", + "Output Program": [ + "n0 = 25.0\nn1 = 29.0\nt0 = n0 * 3.0\nt1 = n1 * 2.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "the mean of 40 observations was 100 . it was found later that an observation 50 was wrongly taken as 75 the corrected new mean is", + "Output Program": [ + "n0 = 40.0\nn1 = 100.0\nn2 = 50.0\nn3 = 75.0\nt0 = n0 * n1\nt1 = n0 - 2.0\nt2 = t1 - n3\nt3 = t0 + t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "99.075" + ], + "split": "train" + }, + { + "Input": "the entrance fee for a fair is $ 5 for persons under the age of 18 , and 20 % more for persons older . each ride at the fair costs $ 0.50 . if joe goes with her 6 years old twin brothers , and they each took 3 rides in total . how much money does joe end up spending at the fair ?", + "Output Program": [ + "n0 = 5.0\nn1 = 18.0\nn2 = 20.0\nn3 = 0.5\nn4 = 6.0\nn5 = 3.0\nt0 = n2 / 100.0\nt1 = n0 * 2.0\nt2 = n5 * 3.0\nt3 = t0 + 1.0\nt4 = n3 * t2\nt5 = n0 * t3\nt6 = t1 + t5\nanswer = t6 + t4\nprint(answer)" + ], + "Output Answer": [ + "20.5" + ], + "split": "train" + }, + { + "Input": "in what ratio p : q should the mixture p of milk and water in the ratio of 5 : 4 be mixed with another mixture q of milk and water in the ratio 2 : 7 so that the resultant mixture contains equal quantities of milk and water ?", + "Output Program": [ + "n0 = 5.0\nn1 = 4.0\nn2 = 2.0\nn3 = 7.0\nt0 = n1 + n3\nt1 = n0 + n2\nt2 = t0 - t1\nanswer = t2 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "a certain company expects quarterly earnings of $ 0.80 per share of stock , half of which will be distributed as dividends to shareholders while the rest will be used for research and development . if earnings are greater than expected , shareholders will receive an additional $ 0.04 per share for each additional $ 0.10 of per share earnings . if quarterly earnings are $ 1.10 per share , what will be the dividend paid to a person who owns 500 shares of the company ' s stock ?", + "Output Program": [ + "n0 = 0.8\nn1 = 0.04\nn2 = 0.1\nn3 = 1.1\nn4 = 500.0\nt0 = n0 / 2.0\nt1 = n3 - n0\nt2 = t1 * 10.0\nt3 = n1 * t2\nt4 = t0 + t3\nanswer = n4 * t4\nprint(answer)" + ], + "Output Answer": [ + "260" + ], + "split": "train" + }, + { + "Input": "the positive integers s and t leave remainders of 2 and 3 , respectively , when divided by 6 . s > t . what is the remainder when s \u2013 t is divided by 6 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 6.0\nn3 = 6.0\nt0 = n0 + n2\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "the sum of ages of 5 children born 2 years different each is 40 years . what is the age of the elder child ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 40.0\nt0 = n1 + 4.0\nt1 = 4.0 + 4.0\nt2 = t0 + t0\nt3 = t2 + t1\nt4 = n2 + t3\nanswer = t4 / n0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "find large number from below question the difference of two no . is 1365 . on dividing the larger no . by the smaller , we get 6 as quotient and the 15 as remainder ?", + "Output Program": [ + "n0 = 1365.0\nn1 = 6.0\nn2 = 15.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nt2 = t0 / t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "1620" + ], + "split": "train" + }, + { + "Input": "if the sum of the 4 th term and the 12 th term of an arithmetic progression is 16 , what is the sum of the first 15 terms of the progression ?", + "Output Program": [ + "n0 = 4.0\nn1 = 12.0\nn2 = 16.0\nn3 = 15.0\nt0 = n3 / 2.0\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "if x = 1 - 2 t and y = 2 t - 2 , then for what value of t does x = y ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 2.0\nn3 = 2.0\nt0 = n0 + n2\nt1 = n1 + n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.75" + ], + "split": "train" + }, + { + "Input": "if a - b = 3 and a ( power 2 ) + b ( power 2 ) = 21 , find the value of ab .", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 2.0\nn3 = 21.0\nt0 = n0**min(n1, 5)\nt1 = n3 - t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "in a 8 x 8 chess board what is the total number of squares .", + "Output Program": [ + "n0 = 8.0\nn1 = 8.0\nt0 = n0 + 1.0\nt1 = n0 * 2.0\nt2 = n0 - 2.0\nt3 = t1 + 1.0\nt4 = n0 * t0\nt5 = t3 * t4\nanswer = t5 / t2\nprint(answer)" + ], + "Output Answer": [ + "204" + ], + "split": "train" + }, + { + "Input": "in a division , divident is 686 , divisior is 36 and quotient is 19 . find the remainder .", + "Output Program": [ + "n0 = 686.0\nn1 = 36.0\nn2 = 19.0\n\nanswer = n0 % n1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "the average marks of a class of 24 students is 40 and that of another class of 50 students is 60 . find the average marks of all the students ?", + "Output Program": [ + "n0 = 24.0\nn1 = 40.0\nn2 = 50.0\nn3 = 60.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "53.513513513513516" + ], + "split": "train" + }, + { + "Input": "if x gets 25 % more than y and y gets 20 % more than z , the share of z out of rs . 555 will be :", + "Output Program": [ + "n0 = 25.0\nn1 = 20.0\nn2 = 555.0\nt0 = n1 / 100.0\nt1 = n0 / 100.0\nt2 = t0 + 1.0\nt3 = t1 + 1.0\nt4 = t3 * t2\nt5 = t2 + t4\nt6 = t5 + 1.0\nanswer = n2 / t6\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "train" + }, + { + "Input": "a grocer has a sale of rs . 2500 , rs . 6500 , rs . 9855 , rs . 7230 and rs . 7000 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 7500 ?", + "Output Program": [ + "n0 = 2500.0\nn1 = 6500.0\nn2 = 9855.0\nn3 = 7230.0\nn4 = 7000.0\nn5 = 5.0\nn6 = 7500.0\nt0 = n5 + 1.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n6 * t0\nt4 = n3 + t2\nt5 = n4 + t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "11915" + ], + "split": "train" + }, + { + "Input": "if a is an integer greater than 6 but less than 17 and b is an integer greater than 3 but less than 29 , what is the range of a / b ?", + "Output Program": [ + "n0 = 6.0\nn1 = 17.0\nn2 = 3.0\nn3 = 29.0\nt0 = n2 + 1.0\nt1 = n0 + 1.0\nt2 = n1 - 1.0\nt3 = n3 - 1.0\nt4 = t2 / t0\nt5 = t1 / t3\nanswer = t4 - t5\nprint(answer)" + ], + "Output Answer": [ + "3.75" + ], + "split": "train" + }, + { + "Input": "there are 1200 jelly beans divided between two jars , jar x and jar y . if there are 400 fewer jelly beans in jar x than 3 times the number of beans in jar y , how many beans are in jar x ?", + "Output Program": [ + "n0 = 1200.0\nn1 = 400.0\nn2 = 3.0\nt0 = n0 + n1\nt1 = t0 / 4.0\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "800" + ], + "split": "train" + }, + { + "Input": "if x is 20 percent more than y and y is 70 percent less than z , then x is what percent of z ?", + "Output Program": [ + "n0 = 20.0\nn1 = 70.0\nt0 = n0 / 100.0\nt1 = 100.0 - n1\nt2 = t0 + 1.0\nanswer = t2 * t1\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "how many alphabets need to be there in a language if one were to make 1 million distinct 3 digit initials using the alphabets of the language ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nt0 = n0 * 1000.0\nt1 = 10.0 * 1000.0\nt2 = t0 * 1000.0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "a 56 gallon solution of salt and water is 10 % salt . how many gallons of water must be added to the solution in order to decrease the salt to 8 % of the volume ?", + "Output Program": [ + "n0 = 56.0\nn1 = 10.0\nn2 = 8.0\nt0 = n1 - n2\nt1 = n0 * t0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "a , b and c invest in the ratio of 3 : 4 : 5 . the percentage of return on their investments are in the ratio of 6 : 5 : 4 . find the total earnings , if b earns rs . 120 more than a :", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 5.0\nn3 = 6.0\nn4 = 5.0\nn5 = 4.0\nn6 = 120.0\nt0 = n0 * n3\nt1 = n1 * n2\nt2 = t0 + t1\nt3 = t1 - t0\nt4 = t2 + t1\nt5 = n6 / t3\nanswer = t4 * t5\nprint(answer)" + ], + "Output Answer": [ + "3480" + ], + "split": "train" + }, + { + "Input": "in an examination , there were 2,000 candidates , out of which 900 candidates were girls and rest were boys . if 38 % of the boys and 32 % of the girls passed , then the total percentage of failed candidates is ?", + "Output Program": [ + "n0 = 2000.0\nn1 = 900.0\nn2 = 38.0\nn3 = 32.0\nt0 = n2 / 100.0\nt1 = n3 / 100.0\nt2 = 10.0 * 100.0\nt3 = t2 * 2.0\nt4 = n1 * t1\nt5 = t3 - n1\nt6 = t0 * t5\nt7 = t3 - t6\nt8 = t7 - t4\nt9 = t8 / t3\nanswer = t9 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "64.7" + ], + "split": "train" + }, + { + "Input": "the ratio of the amount of the oil bill for the month of february to the amount of the oil bill for the month of january was 3 : 2 . if the oil bill for february had been $ 10 more , the corresponding ratio would have been 5 : 3 . how much was the oil bill for january ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 10.0\nn3 = 5.0\nn4 = 3.0\nt0 = n3 / n4\nt1 = n0 / n1\nt2 = t0 - t1\nanswer = n2 / t2\nprint(answer)" + ], + "Output Answer": [ + "59.99999999999997" + ], + "split": "train" + }, + { + "Input": "what is the average ( arithmetic mean ) of all multiples of 10 from 10 to 600 inclusive ?", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 600.0\nt0 = n0 + n2\nt1 = n2 - n0\nt2 = t1 / n0\nt3 = t2 + 1.0\nt4 = t0 * t3\nt5 = t4 / 2.0\nanswer = t5 / t3\nprint(answer)" + ], + "Output Answer": [ + "305" + ], + "split": "train" + }, + { + "Input": "a $ 74.95 lawn chair was sold for $ 59.95 at a special sale . by approximately what percent was the price decreased ?", + "Output Program": [ + "n0 = 74.95\nn1 = 59.95\nt0 = n0 - n1\nt1 = t0 / n0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "20.0133422281521" + ], + "split": "train" + }, + { + "Input": "if rs . 595 be divided among a , b , c in such a way that a gets 2 / 3 of what b gets and b gets 1 / 4 of what c gets , then their shares are respectively ?", + "Output Program": [ + "n0 = 595.0\nn1 = 2.0\nn2 = 3.0\nn3 = 1.0\nn4 = 4.0\nt0 = n3 / n4\nt1 = n1 / n2\nt2 = t1 * t0\nt3 = t0 + t2\nt4 = t3 + n3\nanswer = n0 / t4\nprint(answer)" + ], + "Output Answer": [ + "420.00000000000006" + ], + "split": "train" + }, + { + "Input": "a part - time employee \u2019 s hourly wage was increased by 50 % . she decided to decrease the number of hours worked per week so that her total income did not change . by approximately what percent should the number of hours worked be decreased ?", + "Output Program": [ + "n0 = 50.0\nt0 = n0 + 100.0\nt1 = n0 / 100.0\nt2 = t0 / 100.0\nt3 = t1 / t2\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "33.33333333333333" + ], + "split": "train" + }, + { + "Input": "a room is 6 meters 24 centimeters in length and 4 meters 32 centimeters in width . find the least number of square tiles of equal size required to cover the entire floor of the room .", + "Output Program": [ + "import scipy\nn0 = 6.0\nn1 = 24.0\nn2 = 4.0\nn3 = 32.0\nt0 = n0 * 100.0\nt1 = n2 * 100.0\nt2 = n1 + t0\nt3 = n3 + t1\nt4 = scipy.gcd(int(t2), int(t3))\nt5 = t2 * t3\nt6 = t4 * t4\nanswer = t5 / t6\nprint(answer)" + ], + "Output Answer": [ + "117" + ], + "split": "train" + }, + { + "Input": "there are 60 supermarkets in the fgh chain . all of them are either in the us or canada . if there are 14 more fgh supermarkets in the us than in canada , how many fgh supermarkets are there in the us ?", + "Output Program": [ + "n0 = 60.0\nn1 = 14.0\nt0 = n0 + n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "37" + ], + "split": "train" + }, + { + "Input": "the cricket team of 11 members is 26 yrs old & the wicket keeper is 3 yrs older . if the ages ofthese 2 are excluded , the average age of the remainingplayers is 1 year less than the average age of the whole team . what is the average age of the team ?", + "Output Program": [ + "n0 = 11.0\nn1 = 26.0\nn2 = 3.0\nn3 = 2.0\nn4 = 1.0\nt0 = n1 + n2\nt1 = n0 - n3\nt2 = n1 + t0\nt3 = n0 - t1\nt4 = t2 - t1\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "a certain class of students is being divided into teams . the class can either be divided into 12 teams with an equal number of players on each team or 24 teams with an equal number of players on each team . what is the lowest possible number of students in the class ?", + "Output Program": [ + "import scipy\nn0 = 12.0\nn1 = 24.0\n\nanswer = scipy.lcm(int(n0), int(n1))\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "a group of 6 children and 10 adults are going to the zoo . child tickets cost $ 10 , and adult tickets cost $ 16 . how much will the zoo tickets cost in all ?", + "Output Program": [ + "n0 = 6.0\nn1 = 10.0\nn2 = 10.0\nn3 = 16.0\nt0 = n0 * n1\nt1 = n1 * n3\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "220" + ], + "split": "train" + }, + { + "Input": "tourist purchased a total of 30 travelers checks in $ 50 and $ 100 denominations . the total worth of the travelers checks is $ 1800 . how many checks of $ 50 denominations can he spend so that average amount ( arithmetic mean ) of the remaining travelers checks is $ 62.5 ?", + "Output Program": [ + "n0 = 30.0\nn1 = 50.0\nn2 = 100.0\nn3 = 1800.0\nn4 = 50.0\nn5 = 62.5\nt0 = n0 * n5\nt1 = n5 - n1\nt2 = t0 - n3\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "working alone , printers x , y , and z can do a certain printing job , consisting of a large number of pages , in 16 , 10 , and 20 hours , respectively . what is the ratio of the time it takes printer x to do the job , working alone at its rate , to the time it takes printers y and z to do the job , working together at their individual rates ?", + "Output Program": [ + "n0 = 16.0\nn1 = 10.0\nn2 = 20.0\nt0 = 1.0 / n1\nt1 = 1.0 / n2\nt2 = t0 + t1\nt3 = 1.0 / t2\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "2.4000000000000004" + ], + "split": "train" + }, + { + "Input": "the average weight of 10 oarsmen in a boat is increased by 1.8 kg when one of the crew , who weight 53 kg is replaced by a new man . find the weight of the new man .", + "Output Program": [ + "n0 = 10.0\nn1 = 1.8\nn2 = 53.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "71" + ], + "split": "train" + }, + { + "Input": "average expenditure of a person for the first 3 days of a week is rs . 350 and for the next 4 days is rs . 420 . average expenditure of the man for the whole week is :", + "Output Program": [ + "n0 = 3.0\nn1 = 350.0\nn2 = 4.0\nn3 = 420.0\nt0 = n0 + n2\nt1 = n3 - n1\nt2 = n2 * t1\nt3 = t2 / t0\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "390" + ], + "split": "train" + }, + { + "Input": "if 25 % of x is 15 less than 15 % of 1500 , then x is ?", + "Output Program": [ + "n0 = 25.0\nn1 = 15.0\nn2 = 15.0\nn3 = 1500.0\nt0 = n2 / 100.0\nt1 = n0 / 100.0\nt2 = n3 * t0\nt3 = t2 - n1\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "840" + ], + "split": "train" + }, + { + "Input": "45 % of major airline companies equip their planes with wireless internet access . 70 % of major airlines offer passengers free on - board snacks . what is the greatest possible percentage of major airline companies that offer both wireless internet and free on - board snacks ?", + "Output Program": [ + "n0 = 45.0\nn1 = 70.0\n\nanswer = n0 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "a card game called \u201c high - low \u201d divides a deck of 52 playing cards into 2 types , \u201c high \u201d cards and \u201c low \u201d cards . there are an equal number of \u201c high \u201d cards and \u201c low \u201d cards in the deck and \u201c high \u201d cards are worth 2 points , while \u201c low \u201d cards are worth 1 point . if you draw cards one at a time , how many ways can you draw \u201c high \u201d and \u201c low \u201d cards to earn 5 points if you must draw exactly 3 \u201c low \u201d cards ?", + "Output Program": [ + "n0 = 52.0\nn1 = 2.0\nn2 = 2.0\nn3 = 1.0\nn4 = 5.0\nn5 = 3.0\nt0 = n5 * 4.0\nt1 = n1 * n5\nt2 = n1 * t0\nt3 = n3 * t1\nt4 = n3 * t2\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "in 10 years , a will be twice as old 5 as b was 10 years ago . if a is now 8 years older than b , the present age of b is", + "Output Program": [ + "n0 = 10.0\nn1 = 5.0\nn2 = 10.0\nn3 = 8.0\nt0 = n0 + n3\nt1 = n0 * 2.0\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "38" + ], + "split": "train" + }, + { + "Input": "an assembly line produces 36 cogs per hour until an initial order of 60 cogs is completed . the speed of the assembly line is then immediately increased so that it can produce 60 cogs per hour until another 60 cogs are produced . what is the overall average output , in cogs per hour , for the assembly line during this whole time ?", + "Output Program": [ + "n0 = 36.0\nn1 = 60.0\nn2 = 60.0\nn3 = 60.0\nt0 = n1 / n0\nt1 = n1 * 2.0\nt2 = t0 + 1.0\nanswer = t1 / t2\nprint(answer)" + ], + "Output Answer": [ + "44.99999999999999" + ], + "split": "train" + }, + { + "Input": "if the number is decreased by 5 and divided by 7 the result is 7 . what would be the result if 2 is subtracted and divided by 13 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 7.0\nn2 = 7.0\nn3 = 2.0\nn4 = 13.0\nt0 = n1 * n1\nt1 = n0 + t0\nt2 = t1 - n3\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "a , b and c rents a pasture for rs . 870 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should b pay ?", + "Output Program": [ + "n0 = 870.0\nn1 = 12.0\nn2 = 8.0\nn3 = 16.0\nn4 = 9.0\nn5 = 18.0\nn6 = 6.0\nt0 = n1 * n2\nt1 = n3 * n4\nt2 = n5 * n6\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n0 / t4\nanswer = t5 * t1\nprint(answer)" + ], + "Output Answer": [ + "360" + ], + "split": "train" + }, + { + "Input": "average of money that group of 4 friends pay for rent each month is $ 800 . after one persons rent is increased by 20 % the new mean is $ 870 . what was original rent of friend whose rent is increased ?", + "Output Program": [ + "n0 = 4.0\nn1 = 800.0\nn2 = 20.0\nn3 = 870.0\nt0 = n2 / 100.0\nt1 = n3 - n1\nt2 = n0 * t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "1400" + ], + "split": "train" + }, + { + "Input": "if n = 2 ^ 0.3 and n ^ b = 16 , b must equal", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 0.3\nn2 = 16.0\nt0 = math.log(max(1e-5, n2), 2)\nt1 = n0**min(n1, 5)\nt2 = math.log(max(1e-5, t1), 2)\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "13.333333333333332" + ], + "split": "train" + }, + { + "Input": "the average mark of the students of a class in a particular exam is 90 . if 3 students whose average mark in that exam is 40 are excluded , the average mark of the remaining will be 95 . find the number of students who wrote the exam ?", + "Output Program": [ + "n0 = 90.0\nn1 = 3.0\nn2 = 40.0\nn3 = 95.0\nt0 = n1 * n3\nt1 = n1 * n2\nt2 = n3 - n0\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "in a company the manager wants to give some gifts to all of the workers . in each block there are about 200 workers are there . the total amount for giving the gifts for all the workers is $ 6000 . the worth of the gift is 2 $ . how many blocks are there in the company ?", + "Output Program": [ + "n0 = 200.0\nn1 = 6000.0\nn2 = 2.0\nt0 = n1 / n2\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "a student is ranked 6 th from right and 5 th from left . how many students are there in totality ?", + "Output Program": [ + "n0 = 6.0\nn1 = 5.0\nt0 = n0 + n1\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "solve for x and check : 15 x = 165", + "Output Program": [ + "n0 = 15.0\nn1 = 165.0\nt0 = n1 / n0\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "165" + ], + "split": "train" + }, + { + "Input": "company x sells a selection of products at various price points . listed below are unit sales made for one particular day . how many unit sales on that day were greater than the mean sale price but less than the median sale price ? $ 50 , $ 50 , $ 97 , $ 97 , $ 97 , $ 120 , $ 125 , $ 155 , $ 199 , $ 199 , $ 239", + "Output Program": [ + "n0 = 50.0\nn1 = 50.0\nn2 = 97.0\nn3 = 97.0\nn4 = 97.0\nn5 = 120.0\nn6 = 125.0\nn7 = 155.0\nn8 = 199.0\nn9 = 199.0\nn10 = 239.0\nt0 = n0 + n0\nt1 = 1.0 + 10.0\nt2 = n2 + t0\nt3 = n2 + t2\nt4 = n2 + t3\nt5 = n5 + t4\nt6 = n6 + t5\nt7 = n7 + t6\nt8 = n8 + t7\nt9 = n8 + t8\nt10 = n10 + t9\nt11 = t10 / t1\nanswer = t11 / t11\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "the average age of an adult class is 40 years . 15 new students with an avg age of 32 years join the class . therefore decreasing the average by 4 year . find what was theoriginal strength of class ?", + "Output Program": [ + "n0 = 40.0\nn1 = 15.0\nn2 = 32.0\nn3 = 4.0\nt0 = n1 * n2\nt1 = n0 - n3\nt2 = n1 * t1\nt3 = t2 - t0\nanswer = t3 / n3\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "if log 10 2 = 0.3010 , then log 2 10 is equal to :", + "Output Program": [ + "n0 = 10.0\nn1 = 2.0\nn2 = 0.301\nn3 = 2.0\nn4 = 10.0\n\nanswer = 1.0 / n2\nprint(answer)" + ], + "Output Answer": [ + "3.3222591362126246" + ], + "split": "train" + }, + { + "Input": "find two integers , neither of which ends in a zero , and whose product is exactly 00000", + "Output Program": [ + "n0 = 1.0\nn1 = 0.0\nt0 = 100.0 * 100.0\nt1 = 12.0 * 3.0\nt2 = t0 * 100.0\nt3 = t1 - 4.0\nt4 = t2 / t3\nanswer = t2 / t4\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "john want to buy a $ 100 trouser at the store , but he think it \u2019 s too expensive . finally , it goes on sale for $ 20 . what is the percent decrease ?", + "Output Program": [ + "n0 = 100.0\nn1 = 20.0\n\nanswer = n0 - n1\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "a soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price . during the annual summer sale , everything in the store is an additional 20 percent off the original list price . if a replica jersey ' s list price is $ 80 , approximately what percent q of the list price is the lowest possible sale price ?", + "Output Program": [ + "n0 = 30.0\nn1 = 50.0\nn2 = 20.0\nn3 = 80.0\n\nanswer = n3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "how many two - digit numbers yield a remainder of 1 when divided by both 4 and 17 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 17.0\nt0 = n1 * n2\nt1 = n0 + t0\nanswer = t1 - t0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "8 k 8 + k 88 - - - - - - - - 16 y 6 if k and y represent non - zero digits within the integers above , what is y ?", + "Output Program": [ + "import math\nn0 = 8.0\nn1 = 8.0\nn2 = 88.0\nn3 = 16.0\nn4 = 6.0\nt0 = 1.0 + 10.0\nt1 = n3 * 100.0\nt2 = n0 * 100.0\nt3 = n4 + t1\nt4 = n0 + t2\nt5 = n2 + t4\nt6 = t3 - t5\nt7 = t6 / 10.0\nt8 = t7 / t0\nanswer = math.floor(t8)\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "at the beginning of the year , the ratio of boys to girls in high school x was 3 to 4 . during the year , 10 boys and twice as many girls transferred to another high school , while no new students joined high school x . if , at the end of the year , the ratio of boys to girls was 4 to 5 , how many boys were there in high school x at the beginning of the year ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 10.0\nn3 = 4.0\nn4 = 5.0\nt0 = n1 * n2\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "the total number of digits used in numbering the pages of a book having 360 pages is", + "Output Program": [ + "n0 = 360.0\nt0 = n0 * 3.0\nt1 = 100.0 - 1.0\nt2 = 10.0 - 1.0\nt3 = t0 - t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "972" + ], + "split": "train" + }, + { + "Input": "the cost of 10 kg of mangos is equal to the cost of 24 kg of rice . the cost of 6 kg of flour equals the cost of 2 kg of rice . the cost of each kg of flour is $ 20.50 . find the total cost of 4 kg of mangos , 3 kg of rice and 5 kg of flour ?", + "Output Program": [ + "n0 = 10.0\nn1 = 24.0\nn2 = 6.0\nn3 = 2.0\nn4 = 20.5\nn5 = 4.0\nn6 = 3.0\nn7 = 5.0\nt0 = n1 / n0\nt1 = n2 * n4\nt2 = n4 * n7\nt3 = t1 / n3\nt4 = t0 * t3\nt5 = n6 * t3\nt6 = n5 * t4\nt7 = t6 + t5\nanswer = t7 + t2\nprint(answer)" + ], + "Output Answer": [ + "877.4" + ], + "split": "train" + }, + { + "Input": "an integer n between 1 and 100 , inclusive , is to be chosen at random . what is the probability that n ( n + 1 ) will be divisible by 5 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 100.0\nn2 = 1.0\nn3 = 5.0\nt0 = n1 / n3\nt1 = t0 / n1\nanswer = 2.0 * t1\nprint(answer)" + ], + "Output Answer": [ + "0.4" + ], + "split": "train" + }, + { + "Input": "jane started baby - sitting when she was 18 years old . whenever she baby - sat for a child , that child was no more than half her age at the time . jane is currently 34 years old , and she stopped baby - sitting 12 years ago . what is the current age of the oldest person for whom jane could have baby - sat ?", + "Output Program": [ + "n0 = 18.0\nn1 = 34.0\nn2 = 12.0\nt0 = n0 / 2.0\nt1 = n1 - n0\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "of the total amount that jill spent on a shopping trip , excluding taxes , she spent 50 percent on clothing , 20 percent on food , and 30 percent on other items . if jill paid a 4 percent tax on the clothing , no tax on the food , and an 10 percent tax on all other items , then the total tax that she paid was what percent of the total amount that she spent , excluding taxes ?", + "Output Program": [ + "n0 = 50.0\nn1 = 20.0\nn2 = 30.0\nn3 = 4.0\nn4 = 10.0\nt0 = n3 / 100.0\nt1 = n4 / 100.0\nt2 = n0 * t0\nt3 = n2 * t1\nt4 = t2 + t3\nt5 = t4 / 100.0\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "jeff has 252 ounces of peanut butter in 16 , 28 . and 40 ounce jars . he has an equal number of each sized jar . how many jars of peanut butter does jeff have ?", + "Output Program": [ + "n0 = 252.0\nn1 = 16.0\nn2 = 28.0\nn3 = 40.0\nt0 = n1 + n2\nt1 = n3 + t0\nt2 = n0 / t1\nanswer = t2 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "the average of 6 no . ' s is 2.5 . the average of 2 of them is 1.1 , while the average of the other 2 is 1.4 . what is the average of the remaining 2 no ' s ?", + "Output Program": [ + "n0 = 6.0\nn1 = 2.5\nn2 = 2.0\nn3 = 1.1\nn4 = 2.0\nn5 = 1.4\nn6 = 2.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n2 * n5\nt3 = t1 + t2\nt4 = t0 - t3\nanswer = t4 / n2\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "a is an integer greater than 9 but less than 21 , b is an integer greater than 19 but less than 31 , what is the range of a / b ?", + "Output Program": [ + "n0 = 9.0\nn1 = 21.0\nn2 = 19.0\nn3 = 31.0\nt0 = n2 + 1.0\nt1 = n0 + 1.0\nt2 = n1 - 1.0\nt3 = n3 - 1.0\nt4 = t2 / t0\nt5 = t1 / t3\nanswer = t4 - t5\nprint(answer)" + ], + "Output Answer": [ + "0.6666666666666667" + ], + "split": "train" + }, + { + "Input": "if 18 percent of the students at a certain school went to a camping trip and took more than $ 100 , and 75 percent of the students who went to the camping trip did not take more than $ 100 , what percentage of the students at the school went to the camping trip ?", + "Output Program": [ + "n0 = 18.0\nn1 = 100.0\nn2 = 75.0\nn3 = 100.0\nt0 = n1 - n2\nt1 = t0 / n1\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "train" + }, + { + "Input": "a computer manufacturer produces a certain electronic component at a cost of $ 80 per component . shipping costs for delivering the components are $ 5 per unit . further , the manufacturer has costs of $ 16,500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 150 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?", + "Output Program": [ + "n0 = 80.0\nn1 = 5.0\nn2 = 16500.0\nn3 = 150.0\nt0 = n0 + n1\nt1 = 4.0 * 4.0\nt2 = n1 * 100.0\nt3 = t1 * 1000.0\nt4 = n3 * t0\nt5 = t3 + t2\nt6 = t5 + t4\nanswer = t6 / n3\nprint(answer)" + ], + "Output Answer": [ + "195" + ], + "split": "train" + }, + { + "Input": "the average age of an adult class is 50 years . 12 new students with an avg age of 32 years join the class . therefore decreasing the average by 4 years . find what was the original average age of the class ?", + "Output Program": [ + "n0 = 50.0\nn1 = 12.0\nn2 = 32.0\nn3 = 4.0\nt0 = n1 * n2\nt1 = n0 - n3\nt2 = n1 * t1\nt3 = t2 - t0\nanswer = t3 / n3\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "anne and katherine are both saving money from their summer jobs to buy bicycles . if anne had $ 150 less , she would have exactly 1 / 3 as much as katherine . and if katherine had twice as much , she would have exactly 3 times as much as anne . how much money have they saved together ? (", + "Output Program": [ + "n0 = 150.0\nn1 = 1.0\nn2 = 3.0\nn3 = 3.0\nt0 = 2.0 / n2\nt1 = n0 * n2\nt2 = t0 * t1\nanswer = t1 + t2\nprint(answer)" + ], + "Output Answer": [ + "750" + ], + "split": "train" + }, + { + "Input": "a \u2019 s speed is 32 / 27 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?", + "Output Program": [ + "n0 = 32.0\nn1 = 27.0\nt0 = n0 - n1\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.15625" + ], + "split": "train" + }, + { + "Input": "a batsman in his 12 th innings makes a score of 55 and thereby increases his average by 1 runs . what is his average after the 12 th innings if he had never been \u2018 not out \u2019 ?", + "Output Program": [ + "n0 = 12.0\nn1 = 55.0\nn2 = 1.0\nn3 = 12.0\nt0 = n0 * n2\nt1 = n1 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "44" + ], + "split": "train" + }, + { + "Input": "find large number from below question the difference of two numbers is 2415 . on dividing the larger number by the smaller , we get 21 as quotient and the 15 as remainder", + "Output Program": [ + "n0 = 2415.0\nn1 = 21.0\nn2 = 15.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nt2 = t0 / t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "2520" + ], + "split": "train" + }, + { + "Input": "we bought 85 hats at the store . blue hats cost $ 6 and green hats cost $ 7 . the total price was $ 600 . how many green hats did we buy ?", + "Output Program": [ + "n0 = 85.0\nn1 = 6.0\nn2 = 7.0\nn3 = 600.0\nt0 = n0 * n1\nanswer = n3 - t0\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "if the price of 357 apples is rs . 1517.25 , what will be the approximate price of 49 dozens of such apples", + "Output Program": [ + "n0 = 357.0\nn1 = 1517.25\nn2 = 49.0\nt0 = n1 / n0\nt1 = n2 * 12.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "2499" + ], + "split": "train" + }, + { + "Input": "two trains of equal length are running on parallel lines in the same directions at 46 km / hr . and 36 km / hr . the faster trains pass the slower train in 144 seconds . the length of each train is :", + "Output Program": [ + "n0 = 46.0\nn1 = 36.0\nn2 = 144.0\nt0 = n0 - n1\nt1 = t0 * 1000.0\nt2 = t1 / 3600.0\nt3 = n2 * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "train" + }, + { + "Input": "for each color copy , print shop x charges $ 1.25 and print shop y charges $ 2.75 . how much greater is the charge for 60 color copies at print shop y than at print shop x ?", + "Output Program": [ + "n0 = 1.25\nn1 = 2.75\nn2 = 60.0\nt0 = n1 * n2\nt1 = n0 * n2\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "if a person walks at 16 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance traveled by him is :", + "Output Program": [ + "n0 = 16.0\nn1 = 10.0\nn2 = 20.0\nt0 = n0 - n1\nt1 = n2 / t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "33.333333333333336" + ], + "split": "train" + }, + { + "Input": "the two lines y = x and x = - 8 intersect on the coordinate plane . what is the value of the area of the figure formed by the intersecting lines and the x - axis ?", + "Output Program": [ + "n0 = 8.0\nt0 = n0 * n0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "a school has received 60 % of the amount it needs for a new building by receiving a donation of $ 400 each from people already solicited . people already solicited represent 40 % of the people from whom the school will solicit donations . how much average contribution is requited from the remaining targeted people to complete the fund raising exercise ?", + "Output Program": [ + "n0 = 60.0\nn1 = 400.0\nn2 = 40.0\nt0 = n2 / 100.0\nt1 = n0 / 100.0\nt2 = n1 * t0\nt3 = t2 / t1\nt4 = t3 * t0\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "177.77777777777783" + ], + "split": "train" + }, + { + "Input": "the average of 11 numbers is 60 . out of 11 numbers the average of first 6 no . is 58 , and last 6 numbers is 65 then find 6 th number ?", + "Output Program": [ + "n0 = 11.0\nn1 = 60.0\nn2 = 11.0\nn3 = 6.0\nn4 = 58.0\nn5 = 6.0\nn6 = 65.0\nn7 = 6.0\nt0 = n3 * n4\nt1 = n3 * n6\nt2 = n0 * n1\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "78" + ], + "split": "train" + }, + { + "Input": "jim \u2019 s taxi service charges an initial fee of $ 2.25 at the beginning of a trip and an additional charge of $ 0.15 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?", + "Output Program": [ + "n0 = 2.25\nn1 = 0.15\nn2 = 2.0\nn3 = 5.0\nn4 = 3.6\nt0 = n2 / n3\nt1 = n4 / t0\nt2 = n1 * t1\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "3.5999999999999996" + ], + "split": "train" + }, + { + "Input": "the average age of 8 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men . the average age of the two new men is", + "Output Program": [ + "n0 = 8.0\nn1 = 21.0\nn2 = 23.0\nt0 = n1 + n2\nt1 = n0 * 1.0\nt2 = t0 / 2.0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "an integer n between 1 and 99 , inclusive , is to be chosen at random . what is the probability that n ( n + 2 ) will be divisible by 3 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 99.0\nn2 = 2.0\nn3 = 3.0\nt0 = n1 / 3.0\nt1 = t0 / n1\nanswer = n2 * t1\nprint(answer)" + ], + "Output Answer": [ + "0.6666666666666666" + ], + "split": "train" + }, + { + "Input": "find the total number of prime factors in the expression ( 4 ) ^ 11 x ( 7 ) ^ 3 x ( 11 ) ^ 2", + "Output Program": [ + "n0 = 4.0\nn1 = 11.0\nn2 = 7.0\nn3 = 3.0\nn4 = 11.0\nn5 = 2.0\nt0 = n1 * n5\nt1 = n3 + t0\nanswer = n5 + t1\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "train" + }, + { + "Input": "for a group of n people , k of whom are of the same sex , the ( n - k ) / n expression yields an index for a certain phenomenon in group dynamics for members of that sex . for a group that consists of 20 people , 7 of whom are females , by how much does the index for the females exceed the index for the males in the group ?", + "Output Program": [ + "n0 = 20.0\nn1 = 7.0\nt0 = n1 / n0\nt1 = n0 - n1\nt2 = t1 / n0\nanswer = t2 - t0\nprint(answer)" + ], + "Output Answer": [ + "0.30000000000000004" + ], + "split": "train" + }, + { + "Input": "in a graduating class , the difference between the highest and lowest salaries is $ 100000 . the median salary is $ 50000 higher than the lowest salary and the average salary is $ 20000 higher than the median . what is the minimum number of students e in the class ?", + "Output Program": [ + "n0 = 100000.0\nn1 = 50000.0\nn2 = 20000.0\nt0 = n0 / n2\nt1 = n1 / n2\nt2 = t1 * 3.0\nt3 = t0 + t2\nanswer = t3 + t1\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "a car travels first 160 km at 64 km / hr and the next 160 km at 80 km / hr . what is the average speed for the first 320 km of the tour ?", + "Output Program": [ + "n0 = 160.0\nn1 = 64.0\nn2 = 160.0\nn3 = 80.0\nn4 = 320.0\nt0 = n0 / n1\nt1 = n0 / n3\nt2 = t0 + t1\nt3 = 1.0 / t2\nanswer = n4 * t3\nprint(answer)" + ], + "Output Answer": [ + "71.11111111111111" + ], + "split": "train" + }, + { + "Input": "a prize of $ 800 is to be distributed among 20 winners , each of whom must be awarded at least $ 20 . if 2 / 5 of the prize will be distributed to 3 / 5 of the winners , what is the greatest possible individual award ?", + "Output Program": [ + "n0 = 800.0\nn1 = 20.0\nn2 = 20.0\nn3 = 2.0\nn4 = 5.0\nn5 = 3.0\nn6 = 5.0\nt0 = n0 * n3\nt1 = n1 * n5\nt2 = t0 / n4\nt3 = t1 / n4\nt4 = n0 - t2\nt5 = n1 - t3\nt6 = t5 - 1.0\nt7 = n1 * t6\nanswer = t4 - t7\nprint(answer)" + ], + "Output Answer": [ + "340" + ], + "split": "train" + }, + { + "Input": "if the sum of two numbers is 42 and their product is 437 , then find the absolute difference between the numbers .", + "Output Program": [ + "import math\nn0 = 42.0\nn1 = 437.0\nt0 = n1 * 4.0\nt1 = n0**min(2.0, 5)\nt2 = t1 - t0\nanswer = math.sqrt(max(0, t2))\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "for dinner , cara ate 240 grams of bread which was 8 times as much bread as she ate for lunch , and 6 times as much bread as she ate for breakfast . how much bread did cara eat in total ?", + "Output Program": [ + "n0 = 240.0\nn1 = 8.0\nn2 = 6.0\nt0 = n0 / n1\nt1 = n0 / n2\nt2 = t0 + t1\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "310" + ], + "split": "train" + }, + { + "Input": "for a particular american football game , the probability of a team ' s quarterback throwing a completed pass on each throw is 3 / 10 . what is the least number of times that the quarterback should throw the ball that will increase the probability of getting a completed pass at least once to more than 50 % .", + "Output Program": [ + "n0 = 3.0\nn1 = 10.0\nn2 = 50.0\nt0 = n2 / 100.0\nt1 = n1 * t0\nanswer = t1 - n0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "in a weight - lifting competition , the total weight of joe ' s two lifts was 1800 pounds . if twice the weight of his first lift was 300 pounds more than the weight of his second lift , what was the weight , in pounds , of his first lift ?", + "Output Program": [ + "n0 = 1800.0\nn1 = 300.0\nt0 = n0 + n1\nanswer = t0 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "700" + ], + "split": "train" + }, + { + "Input": "in a division , divident is 729 , divisior is 38 and quotient is 19 . find the remainder .", + "Output Program": [ + "n0 = 729.0\nn1 = 38.0\nn2 = 19.0\n\nanswer = n0 % n1\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "the average salary of all the workers in a workshop is rs . 9000 . the average salary of 7 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is ?", + "Output Program": [ + "n0 = 9000.0\nn1 = 7.0\nn2 = 12000.0\nn3 = 6000.0\nt0 = n2 - n0\nt1 = n0 - n3\nt2 = n1 * t0\nt3 = t2 / t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "average of 10 matches is 34 , how many runs one should should score to increase his average by 4 runs .", + "Output Program": [ + "n0 = 10.0\nn1 = 34.0\nn2 = 4.0\nt0 = n1 + n2\nt1 = n0 + 1.0\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "78" + ], + "split": "train" + }, + { + "Input": "what least number should be added to 1021 , so that the sum is completely divisible by 25 ?", + "Output Program": [ + "n0 = 1021.0\nn1 = 25.0\nt0 = n0 % n1\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "17 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ?", + "Output Program": [ + "n0 = 17.0\nt0 = n0 - 1.0\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "272" + ], + "split": "train" + }, + { + "Input": "what will be the reminder when ( 13 ^ 13 + 13 ) is divided by 14 ?", + "Output Program": [ + "import math\nn0 = 13.0\nn1 = 13.0\nn2 = 13.0\nn3 = 14.0\nt0 = n0**min(n0, 5)\nt1 = n0 + t0\nt2 = t1 / n3\nt3 = math.floor(t2)\nt4 = n3 * t3\nanswer = t1 - t4\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "the remainder when positive integer nn ( n > 1 n > 1 ) is divided by 25 is 1 and the remainder when nn is divided by 7 is also 1 . what is the least value of nn ?", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 25.0\nn3 = 1.0\nn4 = 7.0\nn5 = 1.0\n\nanswer = n2 * n4\nprint(answer)" + ], + "Output Answer": [ + "175" + ], + "split": "train" + }, + { + "Input": "a tank is filled in sixteen hours by 3 pipes a , b and c . pipe a is twice as fast as pipe b , and b is twice as fast as c . how much time will pipe b alone take to fill the tank ?", + "Output Program": [ + "n0 = 3.0\nt0 = 2.0 + 4.0\nt1 = n0 * 4.0\nt2 = t1 + 4.0\nt3 = t0 + 1.0\nt4 = t3 / 2.0\nanswer = t2 * t4\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "train" + }, + { + "Input": "of the 3,600 employees of company x , 1 / 6 are clerical . if the clerical staff were to be reduced by 1 / 3 , what percent of the total number of the remaining employees would then be clerical ?", + "Output Program": [ + "n0 = 3600.0\nn1 = 1.0\nn2 = 6.0\nn3 = 1.0\nn4 = 3.0\nt0 = n1 / n2\nt1 = n3 / n4\nt2 = n3 - t1\nt3 = n3 - t0\nt4 = t0 * t2\nt5 = t4 + t3\nt6 = t4 / t5\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "11.76470588235294" + ], + "split": "train" + }, + { + "Input": "let the least number of 6 digits , which when divided by 4 , 610 and 15 leaves in each case the same remainder of 2 , be n . the sum of the digits in n is :", + "Output Program": [ + "n0 = 6.0\nn1 = 4.0\nn2 = 610.0\nn3 = 15.0\nn4 = 2.0\nt0 = n4 + 1.0\nt1 = t0 + 1.0\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "if a = 105 and a ^ 3 = 21 * 25 * 35 * b , what is the value of b ?", + "Output Program": [ + "n0 = 105.0\nn1 = 3.0\nn2 = 21.0\nn3 = 25.0\nn4 = 35.0\nt0 = n2 * n3\nt1 = n0**min(n1, 5)\nt2 = n4 * t0\nanswer = t1 / t2\nprint(answer)" + ], + "Output Answer": [ + "63" + ], + "split": "train" + }, + { + "Input": "a car was driving at 60 km / h for 20 minutes , and then at 90 km / h for another 40 minutes . what was its average speed ?", + "Output Program": [ + "n0 = 60.0\nn1 = 20.0\nn2 = 90.0\nn3 = 40.0\nt0 = n1 + n3\nt1 = n1 / t0\nt2 = n3 / t0\nt3 = t0 / 60.0\nt4 = n0 * t1\nt5 = n2 * t2\nt6 = t4 + t5\nanswer = t6 / t3\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "if - 3 / ( a - 3 ) = 3 / ( a + 2 ) , then a = ?", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 3.0\nn3 = 2.0\nt0 = n0 * n3\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "if rs . 782 be divided into 3 parts , proportional to 1 / 2 : 1 / 3 : 3 / 4 , then the second part is ?", + "Output Program": [ + "n0 = 782.0\nn1 = 3.0\nn2 = 1.0\nn3 = 2.0\nn4 = 1.0\nn5 = 3.0\nn6 = 3.0\nn7 = 4.0\nt0 = n2 / n3\nt1 = n2 / n1\nt2 = n1 / n7\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n0 / t4\nanswer = t5 * t1\nprint(answer)" + ], + "Output Answer": [ + "164.6315789473684" + ], + "split": "train" + }, + { + "Input": "a number is doubled and 5 is added . if the resultant is trebled , it becomes 117 . what is that number ?", + "Output Program": [ + "n0 = 5.0\nn1 = 117.0\nt0 = n0 * 3.0\nt1 = 2.0 * 3.0\nt2 = n1 - t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "in a division , divident is 760 , divisior is 36 and quotient is 21 . find the remainder .", + "Output Program": [ + "n0 = 760.0\nn1 = 36.0\nn2 = 21.0\n\nanswer = n0 % n1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "a 100 - litre mixture of milk and water contains 49 litres of milk . ' x ' litres of this mixture is removed and replaced with an equal quantum of water . if the process is repeated once , then the concentration of the milk stands reduced at 25 % . what is the value of x ?", + "Output Program": [ + "import math\nn0 = 100.0\nn1 = 49.0\nn2 = 25.0\nt0 = n2 / n1\nt1 = math.sqrt(max(0, t0))\nt2 = 1.0 - t1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "28.57142857142857" + ], + "split": "train" + }, + { + "Input": "4 friends a , b , c and d decided to share a lot of apples . each of them had half of the total plus half an apple in order . after each of them took their share 3 time , no apples were left . how many apples were there ?", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nt0 = 2.0 + 3.0\nt1 = n0 * 1000.0\nt2 = 10.0 * 10.0\nt3 = t1 + t2\nanswer = t3 - t0\nprint(answer)" + ], + "Output Answer": [ + "4095" + ], + "split": "train" + }, + { + "Input": "a certain family has 3 sons : richard is 6 years older than david , and david is 8 years older than scott . if in 8 years , richard will be twice as old as scott , then how old was david 2 years ago ?", + "Output Program": [ + "n0 = 3.0\nn1 = 6.0\nn2 = 8.0\nn3 = 8.0\nn4 = 2.0\nt0 = n1 + n2\nanswer = t0 - n4\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "a drink vendor has 40 liters of maaza , 144 liters of pepsi and 368 liters of sprite . he wants to pack them in cans , so that each can contains the same number of liters of a drink , and does n ' t want to mix any two drinks in a can . what is the least number of cans required ?", + "Output Program": [ + "import scipy\nn0 = 40.0\nn1 = 144.0\nn2 = 368.0\nt0 = scipy.gcd(int(n0), int(n1))\nt1 = scipy.gcd(int(n2), int(t0))\nt2 = n0 / t1\nt3 = n1 / t1\nt4 = n2 / t1\nt5 = t2 + t3\nanswer = t5 + t4\nprint(answer)" + ], + "Output Answer": [ + "69" + ], + "split": "train" + }, + { + "Input": "if x is 3 times larger than n , and if 2 n + 3 is 20 % of 25 , what is the value of ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 3.0\nn3 = 20.0\nn4 = 25.0\nt0 = n3 * n4\nt1 = t0 / 100.0\nt2 = t1 - n0\nt3 = t2 / n1\nanswer = n0 * t3\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "a one - foot stick is marked in 1 / 3 and 1 / 5 portion . how many total markings will there be , including the end points ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 5.0\n\nanswer = n1 + n3\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "in arun ' s opinion , his weight is greater than 64 kg but leas than 72 kg . his brother does not agree with arun and he thinks that arun ' s weight is greater than 60 kg but less than 70 kg . his mother ' s view is that his weight can not be greater than 67 kg . if all of them are correct in their estimation , what is the average of diferent probable weights of arun ?", + "Output Program": [ + "n0 = 64.0\nn1 = 72.0\nn2 = 60.0\nn3 = 70.0\nn4 = 67.0\nt0 = n0 + 1.0\nt1 = n4 + t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "66" + ], + "split": "train" + }, + { + "Input": "pat , kate and mark charged a total of 198 hours to a certain project . if pat charged twice as much time to the project as kate and 1 / 3 as much times as mark , how many more hours did mark charge to the project than kate .", + "Output Program": [ + "n0 = 198.0\nn1 = 1.0\nn2 = 3.0\nt0 = n1 + 2.0\nt1 = n2 * 2.0\nt2 = t0 + t1\nt3 = t1 - n1\nt4 = n0 / t2\nanswer = t4 * t3\nprint(answer)" + ], + "Output Answer": [ + "110" + ], + "split": "train" + }, + { + "Input": "how many 5 digit ( digit = 0 - 9 ) zip codes can exist in which at least one digit is repeated ?", + "Output Program": [ + "n0 = 5.0\nn1 = 0.0\nn2 = 9.0\nt0 = n0 + 1.0\nt1 = n0 + 2.0\nt2 = n0 + 3.0\nt3 = n2 * 10.0\nt4 = 10.0**min(n0, 5)\nt5 = t2 * t3\nt6 = t1 * t5\nt7 = t0 * t6\nanswer = t4 - t7\nprint(answer)" + ], + "Output Answer": [ + "69760" + ], + "split": "train" + }, + { + "Input": "g ( x ) is defined as the product of all even integers k such that 0 < k \u2264 x . for example , g ( 14 ) = 2 \u00d7 4 \u00d7 6 \u00d7 8 \u00d7 10 \u00d7 12 \u00d7 14 . if g ( e ) is divisible by 4 ^ 11 , what is the smallest possible value for e ?", + "Output Program": [ + "n0 = 0.0\nn1 = 14.0\nn2 = 2.0\nn3 = 4.0\nn4 = 6.0\nn5 = 8.0\nn6 = 10.0\nn7 = 12.0\nn8 = 14.0\nn9 = 4.0\nn10 = 11.0\n\nanswer = n2 * n7\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "what will be the result of 7 ^ 8 - 6 / 2 + 9 ^ 3 + 3 + 12 ?", + "Output Program": [ + "n0 = 7.0\nn1 = 8.0\nn2 = 6.0\nn3 = 2.0\nn4 = 9.0\nn5 = 3.0\nn6 = 3.0\nn7 = 12.0\nt0 = n0 * n1\nt1 = t0 - n2\nt2 = t1 / n3\nt3 = n4 + t2\nt4 = n5 * t3\nanswer = t4 - n0\nprint(answer)" + ], + "Output Answer": [ + "95" + ], + "split": "train" + }, + { + "Input": "erik ' s mother gave him $ 86 to go to the store . erik bought 3 loaves of bread and 3 cartons of orange juice . each loaf of bread cost $ 3 and each carton of orange juice cost $ 6 . how much money does erik have left ?", + "Output Program": [ + "n0 = 86.0\nn1 = 3.0\nn2 = 3.0\nn3 = 3.0\nn4 = 6.0\nt0 = n1 * n1\nt1 = n1 * n4\nt2 = t0 + t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "59" + ], + "split": "train" + }, + { + "Input": "1 ltr of water is added with 3 ltr of a solution containing 33 % of alcohol in the water . the % of alcohol in the new mixture is ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 33.0\nt0 = n0 + n1\nt1 = n2 / 100.0\nt2 = n1 * t1\nt3 = t2 / t0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "24.75" + ], + "split": "train" + }, + { + "Input": "a \u2019 s speed is 20 / 15 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?", + "Output Program": [ + "n0 = 20.0\nn1 = 15.0\nt0 = n0 - n1\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.25" + ], + "split": "train" + }, + { + "Input": "the sum of the even numbers between 1 and n is 81 * 82 , where n is an odd number , then n = ?", + "Output Program": [ + "n0 = 1.0\nn1 = 81.0\nn2 = 82.0\nt0 = n1 * 2.0\nanswer = t0 + n0\nprint(answer)" + ], + "Output Answer": [ + "163" + ], + "split": "train" + }, + { + "Input": "saleem bought 4 baskets with the average cost of $ 4 . if saleem also buys the fifth basket with the price of $ 8 , what is the average ( arithmetic mean ) price of those 5 baskets ?", + "Output Program": [ + "n0 = 4.0\nn1 = 4.0\nn2 = 8.0\nn3 = 5.0\nt0 = n0 * n0\nt1 = n2 + t0\nanswer = t1 / n3\nprint(answer)" + ], + "Output Answer": [ + "4.8" + ], + "split": "train" + }, + { + "Input": "when n is divided by 5 the remainder is 3 . what is the remainder when n ^ 2 is divided by 5 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nn2 = 2.0\nn3 = 5.0\nt0 = n0 + n1\nt1 = t0**min(n2, 5)\nanswer = t1 % n0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "if k is a non - negative integer and 15 ^ k is a divisor of 823,435 then 5 ^ k - k ^ 5 =", + "Output Program": [ + "n0 = 15.0\nn1 = 823435.0\nn2 = 5.0\nn3 = 5.0\nt0 = 1.0 - 1.0\nt1 = n2**min(t0, 5)\nt2 = t0**min(n2, 5)\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "the number of the members of a club is more than 10 and less than 40 . when 3 people sit at a table , other people exactly divided to 6 - people groups ( 6 people sit at a table ) or 5 - people groups ( 5 people sit at a table ) . if the members are divided to 7 - people groups , how many people will be left ?", + "Output Program": [ + "import scipy\nn0 = 10.0\nn1 = 40.0\nn2 = 3.0\nn3 = 6.0\nn4 = 6.0\nn5 = 5.0\nn6 = 5.0\nn7 = 7.0\nt0 = scipy.lcm(int(n3), int(n5))\nt1 = n2 + t0\nanswer = t1 % n7\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "find the number , difference between number and its 3 / 5 is 64 .", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 64.0\nt0 = n2 / 2.0\nanswer = n1 * t0\nprint(answer)" + ], + "Output Answer": [ + "160" + ], + "split": "train" + }, + { + "Input": "the mean proportional between 234 and 104 is :", + "Output Program": [ + "import math\nn0 = 234.0\nn1 = 104.0\nt0 = n0 * n1\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "156" + ], + "split": "train" + }, + { + "Input": "x and y are two towns . ganesh covers the distance from x to y at an average speed of 43 km / hr . however , he covers the distance from y to x at an average speed of 35 km / hr . his average speed during the whole journey in km / hr . is :", + "Output Program": [ + "n0 = 43.0\nn1 = 35.0\nt0 = n0 - 10.0\nt1 = t0 + 100.0\nt2 = t1 + t1\nt3 = t1 / n0\nt4 = t1 / n1\nt5 = t3 + t4\nanswer = t2 / t5\nprint(answer)" + ], + "Output Answer": [ + "38.58974358974359" + ], + "split": "train" + }, + { + "Input": "the hcf and lcm of two numbers m and n are respectively 6 and 210 . if m + n = 60 , then 1 / m + 1 / n is equal to", + "Output Program": [ + "n0 = 6.0\nn1 = 210.0\nn2 = 60.0\nn3 = 1.0\nn4 = 1.0\nt0 = n0 * n1\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.047619047619047616" + ], + "split": "train" + }, + { + "Input": "marketing executives for a certain chewing gum company projected a 25 percent increase in revenue this year over that of last year , but revenue this year actually decreased by 25 % . what percent of the projected revenue was the actual revenue ?", + "Output Program": [ + "n0 = 25.0\nn1 = 25.0\nt0 = n0 + 100.0\nt1 = 100.0 - n1\nt2 = t1 / t0\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "a container holds 4 quarts of diesel and 4 quarts of petrol . how many quarts of water must be added to the container to create a mixture that is 3 parts dieselto 5 parts water by petrol ?", + "Output Program": [ + "n0 = 4.0\nn1 = 4.0\nn2 = 3.0\nn3 = 5.0\nt0 = n2 / n3\nt1 = n0 * t0\nt2 = n0 - t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "2.666666666666667" + ], + "split": "train" + }, + { + "Input": "if x + y = - 4 , and x = 6 / y , what is the value of x ^ 2 + y ^ 2 ?", + "Output Program": [ + "n0 = 4.0\nn1 = 6.0\nn2 = 2.0\nn3 = 2.0\nt0 = n1 * n2\nt1 = n0**min(2.0, 5)\nanswer = t1 - t0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "an amount of money is to be divided between p , q and r in the ratio of 3 : 7 : 12 . if the difference between the shares of p and q is rs . 2400 , what will be the difference between q and r ' s share ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 12.0\nn3 = 2400.0\nt0 = n1 - n0\nt1 = n2 - n1\nt2 = n3 / t0\nanswer = t2 * t1\nprint(answer)" + ], + "Output Answer": [ + "3000" + ], + "split": "train" + }, + { + "Input": "a volunteer organization is recruiting new members . in the fall they manage to increase their number by 4 % . by the spring however membership falls by 19 % . what is the total change in percentage from fall to spring ?", + "Output Program": [ + "n0 = 4.0\nn1 = 19.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = t0 + 1.0\nt3 = 1.0 - t1\nt4 = t2 * t3\nt5 = t4 * 100.0\nanswer = 100.0 - t5\nprint(answer)" + ], + "Output Answer": [ + "15.759999999999991" + ], + "split": "train" + }, + { + "Input": "find the value of ( \u221a 1.21 ) / ( \u221a 0.81 ) + ( \u221a 0.81 ) / ( \u221a 0.49 ) is", + "Output Program": [ + "import math\nn0 = 1.21\nn1 = 0.81\nn2 = 0.81\nn3 = 0.49\nt0 = math.sqrt(max(0, n0))\nt1 = math.sqrt(max(0, n1))\nt2 = math.sqrt(max(0, n2))\nt3 = math.sqrt(max(0, n3))\nt4 = t0 / t1\nt5 = t2 / t3\nanswer = t4 + t5\nprint(answer)" + ], + "Output Answer": [ + "2.507936507936508" + ], + "split": "train" + }, + { + "Input": "in august , a cricket team that played 120 matches won 20 % of the games it played . after a continuous winning streak , this team raised its average to 52 % . how many matches did the team win to attain this average ?", + "Output Program": [ + "n0 = 120.0\nn1 = 20.0\nn2 = 52.0\nt0 = n2 / 100.0\nt1 = n1 / 100.0\nt2 = n0 * t0\nt3 = n0 * t1\nt4 = 1.0 - t0\nt5 = t2 - t3\nanswer = t5 / t4\nprint(answer)" + ], + "Output Answer": [ + "80.00000000000001" + ], + "split": "train" + }, + { + "Input": "dacid obtained 72 , 45 , 72 , 77 and 75 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?", + "Output Program": [ + "n0 = 72.0\nn1 = 45.0\nn2 = 72.0\nn3 = 77.0\nn4 = 75.0\nn5 = 100.0\nt0 = n0 + n1\nt1 = 10.0 / 2.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "68.2" + ], + "split": "train" + }, + { + "Input": "if a - b = 4 and a 2 + b 2 = 18 , find the value of ab .", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\nn2 = 2.0\nn3 = 18.0\nt0 = n0**min(n1, 5)\nt1 = n3 - t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "a batsman makes a score of 88 runs in the 17 th inning and thus increases his averages by 3 . find his average after 17 th inning ?", + "Output Program": [ + "n0 = 88.0\nn1 = 17.0\nn2 = 3.0\nn3 = 17.0\nt0 = n1 * n2\nt1 = n0 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "john want to buy a $ 100 trouser at the store , but he think it \u2019 s too expensive . finally , it goes on sale for $ 10 . what is the percent decrease ?", + "Output Program": [ + "n0 = 100.0\nn1 = 10.0\n\nanswer = n0 - n1\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "the price of 3 pants and 6 t - shirts is rs . 2250 . with the same money one can buy 1 pant and 12 t - shirts . if one wants to buy 8 t - shirts , how much shall she have to pay ?", + "Output Program": [ + "n0 = 3.0\nn1 = 6.0\nn2 = 2250.0\nn3 = 1.0\nn4 = 12.0\nn5 = 8.0\nt0 = n4 - n1\nt1 = n0 - n3\nt2 = t0 / t1\nt3 = n0 * t2\nt4 = n1 + t3\nt5 = n2 / t4\nanswer = n5 * t5\nprint(answer)" + ], + "Output Answer": [ + "1200" + ], + "split": "train" + }, + { + "Input": "- - - - - - - - - - - - - - - - yes - - - - - - - - - no - - - - unsure subject m - - - - 500 - - - - - - - - 200 - - - - - 100 subject r - - - - 400 - - - - - - - - 100 - - - - - 300 a total of 800 students were asked whether they found two subjects , m and r , interesting . each answer was either yes or no or unsure , and the numbers of students who gave these answers are listed in the table above . if 190 students answered yes only for subject m , how many of the students did not answer yes for either subject ?", + "Output Program": [ + "n0 = 500.0\nn1 = 200.0\nn2 = 100.0\nn3 = 400.0\nn4 = 100.0\nn5 = 300.0\nn6 = 800.0\nn7 = 190.0\nt0 = n0 - n7\nt1 = n7 + t0\nt2 = n3 - t0\nt3 = t1 + t2\nanswer = n6 - t3\nprint(answer)" + ], + "Output Answer": [ + "210" + ], + "split": "train" + }, + { + "Input": "the positive number z is divisible by 4 . what is the remainder of dividing z ( 2 + 4 + z ) + 3 by 2 ?", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\nn2 = 4.0\nn3 = 3.0\nn4 = 2.0\n\nanswer = n3 % n1\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "the total age of a and b is 11 years more than the total age of b and c . c is how many years younger than a . ?", + "Output Program": [ + "n0 = 11.0\n\nanswer = n0 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "lagaan is levied on the 60 percent of the cultivated land . the revenue department collected total rs . 3 , 44,000 through the lagaan from the village of mutter . mutter , a very rich farmer , paid only rs . 480 as lagaan . the percentage of total land of mutter over the total taxable land of the village is :", + "Output Program": [ + "n0 = 60.0\nn1 = 3.0\nn2 = 44000.0\nn3 = 480.0\nt0 = n0 / 100.0\nt1 = n1 * 100.0\nt2 = 10.0 * 4.0\nt3 = t2 + 4.0\nt4 = n3 / t0\nt5 = t1 * 1000.0\nt6 = t3 * 1000.0\nt7 = t5 + t6\nt8 = t4 / t7\nanswer = t8 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "0.23255813953488372" + ], + "split": "train" + }, + { + "Input": "s = { 2 , 3 , 4 , 5 } b = { 4 , 5 , 6 , 7 , 8 } two integers will be randomly selected from the sets above , one integer from set s and one integer from set b . what is the probability that the sum of the two integers will equal 9 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 4.0\nn3 = 5.0\nn4 = 4.0\nn5 = 5.0\nn6 = 6.0\nn7 = 7.0\nn8 = 8.0\nn9 = 9.0\nt0 = n3 * 4.0\nanswer = 4.0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.2" + ], + "split": "train" + }, + { + "Input": "given that 100.48 = x , 100.70 = y and xz = y \u00b2 , then the value of z is close to", + "Output Program": [ + "n0 = 100.48\nn1 = 100.7\nt0 = n1 - 100.0\nt1 = n0 - 100.0\nt2 = t0 * 2.0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "2.9166666666666545" + ], + "split": "train" + }, + { + "Input": "a certain car traveled twice as many miles from town a to town b as it did from town b to town c . from town a to town b , the car averaged 20 miles per gallon , and from town b to town c , the car averaged 25 miles per gallon . what is the average miles per gallon that the car achieved on its trip from town a through town b to town c ?", + "Output Program": [ + "n0 = 20.0\nn1 = 25.0\nt0 = n1 * 10.0\nt1 = t0 / 2.0\nt2 = t0 / n0\nt3 = t1 + t0\nt4 = t1 / n1\nt5 = t2 + t4\nanswer = t3 / t5\nprint(answer)" + ], + "Output Answer": [ + "21.428571428571427" + ], + "split": "train" + }, + { + "Input": "sum of the squares of 3 no . ' s is 267 and the sum of their products taken two at a time is 131 . find the sum ?", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 267.0\nn2 = 131.0\nt0 = n2 * 2.0\nt1 = n1 + t0\nanswer = math.sqrt(max(0, t1))\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "the average age of 10 students in a class is 15 years . if the age of teacher is also included , the average becomes 16 years , find the age of the teacher .", + "Output Program": [ + "n0 = 10.0\nn1 = 15.0\nn2 = 16.0\nt0 = n0 * n1\nt1 = n2 + t0\nt2 = n0 + t1\nanswer = t2 - t0\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "3550 - ( 1002 / 20.04 ) = ?", + "Output Program": [ + "n0 = 3550.0\nn1 = 1002.0\nn2 = 20.04\nt0 = n1 / n2\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "3500" + ], + "split": "train" + }, + { + "Input": "two ants , arthur and amy , have discovered a picnic and are bringing crumbs back to the anthill . amy makes twice as many trips and carries one and a half times as many crumbs per trip as arthur . if arthur carries a total of z crumbs to the anthill , how many crumbs will amy bring to the anthill , in terms of z ?", + "Output Program": [ + "t0 = 1.0 / 2.0\nt1 = t0 + 1.0\nanswer = t1 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "a waiter ' s salary consists of his salary and tips . during one week his tips were 3 / 4 of his salary . what fraction of his income came from tips ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nt0 = n0 / n1\nt1 = t0 + 1.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.42857142857142855" + ], + "split": "train" + }, + { + "Input": "the least number which must be subtracted from 509 to make it exactly divisible by 9 is :", + "Output Program": [ + "n0 = 509.0\nn1 = 9.0\nt0 = 2.0 + 4.0\nt1 = 1.0 + 4.0\nt2 = t1 * 10.0\nt3 = t0 + t2\nt4 = n1 * t3\nanswer = n0 - t4\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "in a certain brick wall , each row of bricks above the bottom row contains one less brick than the row just below it . if there are 5 rows in all and a total of 50 bricks in the wall , how many bricks does the bottom row contain ?", + "Output Program": [ + "n0 = 5.0\nn1 = 50.0\nt0 = n1 - 1.0\nt1 = t0 - 2.0\nt2 = t1 - 3.0\nt3 = t2 - 4.0\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "mark bought a set of 6 flower pots of different sizes at a total cost of $ 8.25 . each pot cost 0.15 more than the next one below it in size . what was the cost , in dollars , of the largest pot ?", + "Output Program": [ + "n0 = 6.0\nn1 = 8.25\nn2 = 0.15\nt0 = n0 - 1.0\nt1 = n0 * t0\nt2 = n2 * t0\nt3 = t1 / 2.0\nt4 = n2 * t3\nt5 = n1 - t4\nt6 = t5 / n0\nanswer = t6 + t2\nprint(answer)" + ], + "Output Answer": [ + "1.75" + ], + "split": "train" + }, + { + "Input": "on dividing 23 by a number , the quotient is 4 and the remainder is 3 . find the divisor .", + "Output Program": [ + "import math\nn0 = 23.0\nn1 = 4.0\nn2 = 3.0\nt0 = n0 / n1\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "plaudia can choose any two of 4 different candles and any 8 of 9 different flowers for a centerpiece arrangement . given these choices , how many candle + flower groupings can she select ?", + "Output Program": [ + "n0 = 4.0\nn1 = 8.0\nn2 = 9.0\nt0 = 10.0 - n0\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "train" + }, + { + "Input": "for an agricultural experiment , 300 seeds were planted in one plot and 200 were planted in a second plot . if exactly 30 percent of the seeds in the first plot germinated and exactly 35 percent of the seeds in the second plot germinated , what percent of the total number of seeds germinated ?", + "Output Program": [ + "n0 = 300.0\nn1 = 200.0\nn2 = 30.0\nn3 = 35.0\nt0 = n0 + n1\nt1 = n2 / 100.0\nt2 = n3 / 100.0\nt3 = n0 * t1\nt4 = n1 * t2\nt5 = t3 + t4\nt6 = t5 / t0\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "a batsman in his 17 th innings makes a score of 85 and their by increasing his average by 3 . what is his average after the 17 th innings ?", + "Output Program": [ + "n0 = 17.0\nn1 = 85.0\nn2 = 3.0\nn3 = 17.0\nt0 = n0 * n2\nt1 = n1 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "37" + ], + "split": "train" + }, + { + "Input": "p , q and r have $ 9000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?", + "Output Program": [ + "n0 = 9000.0\nt0 = 2.0 * 2.0\nt1 = 1.0 * 3.0\nt2 = t0 / 3.0\nt3 = n0 * t0\nt4 = t2 * 3.0\nt5 = t4 + t1\nt6 = t5 + t1\nanswer = t3 / t6\nprint(answer)" + ], + "Output Answer": [ + "3600" + ], + "split": "train" + }, + { + "Input": "a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 42 , the how old is b ?", + "Output Program": [ + "n0 = 42.0\nt0 = 1.0 + 4.0\nt1 = n0 - 2.0\nt2 = t1 * 2.0\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "the product of 3 consecutive numbers is 210 . then the sum of the smallest two numbers is ?", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 210.0\nt0 = n1**min(0.33, 5)\nt1 = math.floor(t0)\nt2 = t1 + 1.0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "ashok secured average of 75 marks in 6 subjects . if the average of marks in 5 subjects is 74 , how many marks did he secure in the 6 th subject ?", + "Output Program": [ + "n0 = 75.0\nn1 = 6.0\nn2 = 5.0\nn3 = 74.0\nn4 = 6.0\nt0 = n0 * n1\nt1 = n2 * n3\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "the sum of number of boys and girls in a school is 400 . if the number of boys is x , then the number of girls becomes x % of the total number of students . the number of boys is ?", + "Output Program": [ + "n0 = 400.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "a customer bought a product at the shop . however , the shopkeeper increased the price of the product by 15 % so that the customer could not buy the required amount of the product . the customer managed to buy only 60 % of the required amount . what is the difference in the amount of money that the customer paid for the second purchase compared to the first purchase ?", + "Output Program": [ + "n0 = 15.0\nn1 = 60.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = t0 + 1.0\nt3 = t2 * t1\nt4 = 1.0 - t3\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "31.000000000000007" + ], + "split": "train" + }, + { + "Input": "if xy = 1 , x / y = 36 , for positive numbers x and y , y = ?", + "Output Program": [ + "import math\nn0 = 1.0\nn1 = 36.0\nt0 = n0 / n1\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "0.16666666666666666" + ], + "split": "train" + }, + { + "Input": "for covering 88 km a wheel revolve 1000 times . what is the radius of wheel ?", + "Output Program": [ + "n0 = 88.0\nn1 = 1000.0\nt0 = 3.0 + 4.0\nt1 = n0 / n1\nt2 = 10.0 * 2.0\nt3 = t2 + 2.0\nt4 = t0 * t1\nt5 = t4 / 2.0\nt6 = t5 / t3\nt7 = t6 * 1000.0\nanswer = t7 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "find the least number must be subtracted from 427398 so that remaining no . is divisible by 15 ?", + "Output Program": [ + "import math\nn0 = 427398.0\nn1 = 15.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "if 15 students in a class average 73 % on an exam and 10 students average 88 % on the same exam , what is the average in percent for all 25 students ?", + "Output Program": [ + "n0 = 15.0\nn1 = 73.0\nn2 = 10.0\nn3 = 88.0\nn4 = 25.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = t0 + t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "79" + ], + "split": "train" + }, + { + "Input": "if the price of a tv is first decreased by 10 % and then increased by 30 % , then the net change in the price will be :", + "Output Program": [ + "n0 = 10.0\nn1 = 30.0\nt0 = n1 + 100.0\nt1 = 100.0 - n0\nt2 = t0 * t1\nt3 = t2 / 100.0\nanswer = t3 - 100.0\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "a soft drink company had 6000 small and 10000 big bottles in storage . if 12 % of small 15 % of big bottles have been sold , then the total bottles remaining in storage is", + "Output Program": [ + "n0 = 6000.0\nn1 = 10000.0\nn2 = 12.0\nn3 = 15.0\nt0 = n0 + n1\nt1 = n2 / 100.0\nt2 = n3 / 100.0\nt3 = n0 * t1\nt4 = n1 * t2\nt5 = t3 + t4\nanswer = t0 - t5\nprint(answer)" + ], + "Output Answer": [ + "13780" + ], + "split": "train" + }, + { + "Input": "in a race where 18 cars are running , the chance that car x will win is 1 / 8 , that y will win is 1 / 12 and that z will win is 1 / 6 . assuming that a dead heat is impossible , find the chance that one of them will win .", + "Output Program": [ + "n0 = 18.0\nn1 = 1.0\nn2 = 8.0\nn3 = 1.0\nn4 = 12.0\nn5 = 1.0\nn6 = 6.0\nt0 = n1 / n2\nt1 = n1 / n4\nt2 = n1 / n6\nt3 = t0 + t1\nanswer = t3 + t2\nprint(answer)" + ], + "Output Answer": [ + "0.375" + ], + "split": "train" + }, + { + "Input": "the average marks of 25 students in a class is 100 . but a student mark is wrongly noted as 60 instead of 10 then find the correct average marks ?", + "Output Program": [ + "n0 = 25.0\nn1 = 100.0\nn2 = 60.0\nn3 = 10.0\nt0 = n0 * n1\nt1 = t0 - n2\nt2 = n3 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "98" + ], + "split": "train" + }, + { + "Input": "what is the sum of the local values of the digits 2 , 3 , 4 , 5 in the number 2345 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 4.0\nn3 = 5.0\nn4 = 2345.0\nt0 = n0 * 1000.0\nt1 = n1 * 100.0\nt2 = n2 * 10.0\nt3 = t0 + t1\nt4 = t3 + t2\nanswer = n3 + t4\nprint(answer)" + ], + "Output Answer": [ + "2345" + ], + "split": "train" + }, + { + "Input": "if p and q are positive integers each greater than 1 , and 17 ( p + 1 ) = 28 ( q + 1 ) , what is the least possible value of p + q ?", + "Output Program": [ + "n0 = 1.0\nn1 = 17.0\nn2 = 1.0\nn3 = 28.0\nn4 = 1.0\nt0 = n1 + n3\nanswer = t0 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "43" + ], + "split": "train" + }, + { + "Input": "when a number is divided by 4 & then multiply by 12 the answer is 9 what is the no . ?", + "Output Program": [ + "n0 = 4.0\nn1 = 12.0\nn2 = 9.0\nt0 = n2 / n1\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "of the goose eggs laid at a certain pond , 1 / 4 hatched and 4 / 5 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 2 / 5 did not survive the first year . if 120 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 4.0\nn3 = 5.0\nn4 = 2.0\nn5 = 5.0\nn6 = 120.0\nt0 = n4 / n5\nt1 = n1 / n3\nt2 = n0 / n1\nt3 = 1.0 - t0\nt4 = n6 / t3\nt5 = t4 / t1\nanswer = t5 / t2\nprint(answer)" + ], + "Output Answer": [ + "1000" + ], + "split": "train" + }, + { + "Input": "calculate the average of first 18 even numbers is ?", + "Output Program": [ + "n0 = 18.0\n\nanswer = n0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "given that p is a positive even integer with a positive units digit , if the units digit of p ^ 3 minus the units digit of p ^ 2 is equal to 0 , what is the units digit of p + 2 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 0.0\nn3 = 2.0\nt0 = n0 + n0\nanswer = n3 + t0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "dan ' s age after 18 years will be 5 times his age 6 years ago . what is the present age of dan ?", + "Output Program": [ + "n0 = 18.0\nn1 = 5.0\nn2 = 6.0\nt0 = n1 * n2\nt1 = n1 - 1.0\nt2 = n0 + t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "the proportion of water to alcohol in solution a is 5 : 4 and the proportion of water to alcohol in solution b is 6 : 5 . if an equal amount of each solution is mixed together , what is the concentration of alcohol in the new solution ?", + "Output Program": [ + "n0 = 5.0\nn1 = 4.0\nn2 = 6.0\nn3 = 5.0\nt0 = n1 + n3\nt1 = n0 + n2\nt2 = t1 + t0\nt3 = t0 / t2\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "the sum of digits of a two digit number is 10 , the difference between the digits is 6 . find the number", + "Output Program": [ + "n0 = 10.0\nn1 = 6.0\nt0 = n0 + n1\nt1 = t0 / 2.0\nt2 = n0 * t1\nt3 = n0 - t1\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "82" + ], + "split": "train" + }, + { + "Input": "tough and tricky questions : word problems . a salesman ' s income consists of commission and base salary . his weekly income totals over the past 5 weeks have been $ 406 , $ 413 , $ 420 , $ 436 and $ 395 . what must his average ( arithmetic mean ) income over the next two weeks be to decrease his average weekly income to $ 400 over the 7 - week period ?", + "Output Program": [ + "n0 = 5.0\nn1 = 406.0\nn2 = 413.0\nn3 = 420.0\nn4 = 436.0\nn5 = 395.0\nn6 = 400.0\nn7 = 7.0\nt0 = n1 + n2\nt1 = n6 * n7\nt2 = n3 + t0\nt3 = n4 + t2\nt4 = n5 + t3\nt5 = t1 - t4\nanswer = t5 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "365" + ], + "split": "train" + }, + { + "Input": "let s be the set of all positive integers that , when divided by 8 , have a remainder of 5 . what is the 72 th number in this set ?", + "Output Program": [ + "n0 = 8.0\nn1 = 5.0\nn2 = 72.0\nt0 = n2 - 1.0\nt1 = n0 * t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "573" + ], + "split": "train" + }, + { + "Input": "how many positive integers will divide evenly into 190 ?", + "Output Program": [ + "n0 = 190.0\nt0 = 1.0 + 1.0\nt1 = t0 * t0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 50 milliliters of solution x to create a solution that is 25 percent alcohol by volume ?", + "Output Program": [ + "n0 = 10.0\nn1 = 30.0\nn2 = 50.0\nn3 = 25.0\nt0 = n3 - n0\nt1 = n1 - n3\nt2 = t0 / t1\nanswer = n2 * t2\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "train" + }, + { + "Input": "shipment - - - no . of defective chips / shipment - - - total chips in shipment s 1 - - - - - - - - - - - - - - - - - - - - - - 2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 5000 s 2 - - - - - - - - - - - - - - - - - - - - - - 4 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 12000 s 3 - - - - - - - - - - - - - - - - - - - - - - 2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 15000 s 4 - - - - - - - - - - - - - - - - - - - - - - 4 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 16000 a computer chip manufacturer expects the ratio of the number of defective chips to the total number of chips in all future shipments to equal the corresponding ratio for shipments s 1 , s 2 , s 3 , and s 4 combined , as shown in the table above . what \u2019 s the expected number of defective chips in a shipment of 60000 chips ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 5000.0\nn3 = 2.0\nn4 = 4.0\nn5 = 12000.0\nn6 = 3.0\nn7 = 2.0\nn8 = 15000.0\nn9 = 4.0\nn10 = 4.0\nn11 = 16000.0\nn12 = 1.0\nn13 = 2.0\nn14 = 3.0\nn15 = 4.0\nn16 = 60000.0\nt0 = n2 + n5\nt1 = n1 + n4\nt2 = n8 + t0\nt3 = n1 + t1\nt4 = n11 + t2\nt5 = n4 + t3\nt6 = t4 / t5\nanswer = n16 / t6\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "3 / 4 of 1 / 2 of 2 / 5 of 5020 = ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 1.0\nn3 = 2.0\nn4 = 2.0\nn5 = 5.0\nn6 = 5020.0\nt0 = n3 / n5\nt1 = n0 / n1\nt2 = n2 / n3\nt3 = t1 * t2\nt4 = t0 * t3\nanswer = n6 * t4\nprint(answer)" + ], + "Output Answer": [ + "753.0000000000001" + ], + "split": "train" + }, + { + "Input": "an auto assembly plant performs 6 functions with each frame that arrives : add axles , add wheels to the axles , install the windshield to the frame , install the instrument panel , install the steering wheel , and install the interior seating . once those 6 tasks are performed , each car goes to a separate building for finishing touches . if these tasks can be arranged along a linear assembly line in any order , except that the axles must be installed before the wheels can be added , how many t ways can the assembly line be arranged ?", + "Output Program": [ + "import math\nn0 = 6.0\nn1 = 6.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(4.0)))\nt2 = math.factorial(min(15, int(2.0)))\nt3 = t0 / t1\nt4 = t3 / t2\nanswer = t4 * t1\nprint(answer)" + ], + "Output Answer": [ + "360" + ], + "split": "train" + }, + { + "Input": "the average marks of a class of 30 students is 30 and that of another class of 50 students is 60 . find the average marks of all the students ?", + "Output Program": [ + "n0 = 30.0\nn1 = 30.0\nn2 = 50.0\nn3 = 60.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "48.75" + ], + "split": "train" + }, + { + "Input": "john purchased 1300 large bottles at $ 1.89 per bottle and 750 small bottles at $ 1.38 per bottle . what was the approximate average price paid per bottle ?", + "Output Program": [ + "n0 = 1300.0\nn1 = 1.89\nn2 = 750.0\nn3 = 1.38\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "1.7034146341463414" + ], + "split": "train" + }, + { + "Input": "a sports equipment store sold ping pong rackets for a total of $ 735 . if the average ( arithmetic mean ) price of a pair of rackets is $ 9.8 , how many pairs were sold ?", + "Output Program": [ + "n0 = 735.0\nn1 = 9.8\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "the mean of 50 observations is 200 . but later he found that there is decrements of 15 from each observations . what is the the updated mean is ?", + "Output Program": [ + "n0 = 50.0\nn1 = 200.0\nn2 = 15.0\n\nanswer = n1 - n2\nprint(answer)" + ], + "Output Answer": [ + "185" + ], + "split": "train" + }, + { + "Input": "the average of 10 numbers was calculated as 18 . it is discovered later on that while calculating the average , one number , namely 66 , was incorrectly read as 26 . what is the correct average ?", + "Output Program": [ + "n0 = 10.0\nn1 = 18.0\nn2 = 66.0\nn3 = 26.0\nt0 = n0 * n1\nt1 = n2 - n3\nt2 = t0 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "each child has 5 crayons and 14 apples . if there are 10 children , how many crayons are there in total ?", + "Output Program": [ + "n0 = 5.0\nn1 = 14.0\nn2 = 10.0\n\nanswer = n0 * n2\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "how many integers between 1 and 1050 are divisible by 10 , 25 , and 35 ?", + "Output Program": [ + "import scipy\nn0 = 1.0\nn1 = 1050.0\nn2 = 10.0\nn3 = 25.0\nn4 = 35.0\nt0 = scipy.lcm(int(n2), int(n3))\nt1 = scipy.lcm(int(n4), int(t0))\nanswer = n1 / t1\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "if the average ( arithmetic mean ) of ( 2 a + 16 ) and ( 3 a - 8 ) is 79 , what is the value of a ?", + "Output Program": [ + "n0 = 2.0\nn1 = 16.0\nn2 = 3.0\nn3 = 8.0\nn4 = 79.0\nt0 = n0 + n2\nt1 = n0 * n4\nt2 = n1 - n3\nt3 = t1 - t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "we run a business that rents out canoes and kayaks . a canoe rental costs $ 12 per day , and a kayak rental costs $ 18 dollars per day . one day , our business rents out 3 canoes for every 2 kayaks and receives a total of $ 504 in revenue . how many more canoes than kayaks were rented out ?", + "Output Program": [ + "n0 = 12.0\nn1 = 18.0\nn2 = 3.0\nn3 = 2.0\nn4 = 504.0\nt0 = n0 * n2\nt1 = n1 * n3\nt2 = n2 - n3\nt3 = t0 + t1\nt4 = n4 / t3\nanswer = t4 * t2\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "the average of runs of a cricket player of 20 innings was 32 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?", + "Output Program": [ + "n0 = 20.0\nn1 = 32.0\nn2 = 4.0\nt0 = n0 + 1.0\nt1 = n1 + n2\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "116" + ], + "split": "train" + }, + { + "Input": "a cube with its sides numbered 1 through 6 is rolled twice , first landing on a and then landing on b . if any roll of the cube yields an equal chance of landing on any of the numbers 1 through 6 , what is the probability r that a + b is prime ?", + "Output Program": [ + "n0 = 1.0\nn1 = 6.0\nn2 = 1.0\nn3 = 6.0\nt0 = 12.0 + 3.0\nt1 = n0 / n1\nt2 = t1**min(2.0, 5)\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "0.41666666666666663" + ], + "split": "train" + }, + { + "Input": "dacid obtained 51 , 65 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?", + "Output Program": [ + "n0 = 51.0\nn1 = 65.0\nn2 = 82.0\nn3 = 67.0\nn4 = 85.0\nn5 = 100.0\nt0 = n0 + n1\nt1 = 10.0 / 2.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "train" + }, + { + "Input": "in a mixture of 45 litres the ratio of milk to water is 4 : 1 . additional 23 litres of water is added to the mixture . find the ratio of milk to water in the resulting mixture .", + "Output Program": [ + "n0 = 45.0\nn1 = 4.0\nn2 = 1.0\nn3 = 23.0\nt0 = n1 + n2\nt1 = n0 / t0\nt2 = n3 + t1\nt3 = n0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "1.125" + ], + "split": "train" + }, + { + "Input": "the total marks obtained by a student in physics , chemistry and mathematics is 150 more than the marks obtained by him in physics . what is the average mark obtained by him in chemistry and mathematics ?", + "Output Program": [ + "n0 = 150.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "at a contest with 3000 participants , 1 / 2 of the people are aged 8 to 14 . next year , the number of people aged 8 to 14 will increase by 1 / 6 . after this change , what percentage of the total 3000 people will the 8 - to 14 - year - olds represent ?", + "Output Program": [ + "n0 = 3000.0\nn1 = 1.0\nn2 = 2.0\nn3 = 8.0\nn4 = 14.0\nn5 = 8.0\nn6 = 14.0\nn7 = 1.0\nn8 = 6.0\nn9 = 3000.0\nn10 = 8.0\nn11 = 14.0\nt0 = n1 / n8\nt1 = n0 / n2\nt2 = t0 + n1\nt3 = t2 * t1\nt4 = t3 / n0\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "58.333333333333336" + ], + "split": "train" + }, + { + "Input": "if henry were to add 7 gallons of water to a tank that is already 3 / 4 full of water , the tank would be 7 / 8 full . how many gallons of water would the tank hold if it were full ?", + "Output Program": [ + "n0 = 7.0\nn1 = 3.0\nn2 = 4.0\nn3 = 7.0\nn4 = 8.0\nt0 = n3 / n4\nt1 = n1 / n2\nt2 = t0 - t1\nt3 = 1.0 / t2\nanswer = n0 * t3\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "train" + }, + { + "Input": "the average weight of 16 boys in a class is 50.25 kgs and that of the remaining 8 boys is 45.15 kgs . find the average weight of all the boys in the class .", + "Output Program": [ + "n0 = 16.0\nn1 = 50.25\nn2 = 8.0\nn3 = 45.15\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "48.550000000000004" + ], + "split": "train" + }, + { + "Input": "from 4 officers and 8 jawans in how many can 6 be chosen to include exactly one officer ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 8.0\nn2 = 6.0\nt0 = math.factorial(min(15, int(n1)))\nt1 = math.factorial(min(15, int(3.0)))\nt2 = n2 - 1.0\nt3 = math.factorial(min(15, int(t2)))\nt4 = t0 / t3\nt5 = t4 / t1\nanswer = n0 * t5\nprint(answer)" + ], + "Output Answer": [ + "224" + ], + "split": "train" + }, + { + "Input": "if an integer n is to be chosen at random from the integers 1 to 96 , inclusive , what is the probability that n ( n + 1 ) ( n + 2 ) will be divisible by 16 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 96.0\nn2 = 1.0\nn3 = 2.0\nn4 = 16.0\nt0 = n1 / n3\nt1 = n1 / n4\nt2 = t0 + t1\nanswer = t2 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.5625" + ], + "split": "train" + }, + { + "Input": "a football player scores 4 goals in his fifth match thus increasing his average goals score by 0.2 . the total number of goals in his 5 matches would be", + "Output Program": [ + "n0 = 4.0\nn1 = 0.2\nn2 = 5.0\nt0 = n0 * 4.0\nt1 = n2 * 4.0\nt2 = n1 * t1\nt3 = t0 - t2\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "what is the smallest positive integer that leaves a remainder of 1 when divided by 2 , remainder of 2 when divided by 3 , a remainder of 3 when divided by 4 , and a remainder of 9 when divided by 10 ?", + "Output Program": [ + "import scipy\nn0 = 1.0\nn1 = 2.0\nn2 = 2.0\nn3 = 3.0\nn4 = 3.0\nn5 = 4.0\nn6 = 9.0\nn7 = 10.0\nt0 = scipy.lcm(int(n1), int(n3))\nt1 = scipy.lcm(int(n5), int(t0))\nt2 = scipy.lcm(int(n7), int(t1))\nanswer = t2 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "59" + ], + "split": "train" + }, + { + "Input": "if bill can buy 3 pairs of jeans and 2 shirts for $ 69 or 2 pairs of jeans and 3 shirts for $ 66 , how much does one shirt cost ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 69.0\nn3 = 2.0\nn4 = 3.0\nn5 = 66.0\nt0 = n0 * n5\nt1 = n1 * n2\nt2 = n0 * n0\nt3 = n1 * n1\nt4 = t0 - t1\nt5 = t2 - t3\nanswer = t4 / t5\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "the greatest number which on dividing 1657 and 2037 leaves remainders 10 and 7 respectively , is :", + "Output Program": [ + "import scipy\nn0 = 1657.0\nn1 = 2037.0\nn2 = 10.0\nn3 = 7.0\nt0 = n1 - n3\nt1 = n0 - n2\nanswer = scipy.gcd(int(t0), int(t1))\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "if @ is a binary operation defined as the difference between an integer n and the product of n and 5 , then what is the largest positive integer n such that the outcome of the binary operation of n is less than 21 ?", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 21.0\nt0 = n0 - 1.0\nt1 = n1 / t0\nanswer = math.floor(t1)\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "the average runs of a cricket player of 13 innings was 22 . how many runs must he make in his next innings so as to increase his average of runs by 5 ?", + "Output Program": [ + "n0 = 13.0\nn1 = 22.0\nn2 = 5.0\nt0 = n0 + 1.0\nt1 = n1 + n2\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "92" + ], + "split": "train" + }, + { + "Input": "3 students appear at an examination of mathematics . the probability of their success are 1 / 2 , 1 / 4 , 1 / 5 respectively . find the probability of success of at least two .", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 2.0\nn3 = 1.0\nn4 = 4.0\nn5 = 1.0\nn6 = 5.0\nt0 = n1 / n2\nt1 = n1 / n6\nt2 = n1 / n4\nt3 = t0 * t1\nt4 = t2 * t1\nt5 = t0 * t2\nt6 = n1 - t2\nt7 = n1 - t0\nt8 = t3 * t6\nt9 = t4 * t7\nt10 = t1 * t5\nt11 = t8 + t3\nt12 = t11 + t9\nanswer = t12 + t10\nprint(answer)" + ], + "Output Answer": [ + "0.225" + ], + "split": "train" + }, + { + "Input": "if a / b = 1 / 3 , b / c = 2 , c / d = 1 / 2 , d / e = 3 and e / f = 1 / 2 , then what is the value of abc / def ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 2.0\nn3 = 1.0\nn4 = 2.0\nn5 = 3.0\nn6 = 1.0\nn7 = 2.0\nt0 = n1 * n1\nt1 = n1 * n7\nt2 = n2 * t1\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.75" + ], + "split": "train" + }, + { + "Input": "the average of 7 consecutive numbers is 33 . the highest of these numbers is :", + "Output Program": [ + "n0 = 7.0\nn1 = 33.0\nt0 = 1.0 + 2.0\nt1 = n0 * n1\nt2 = t0 + 1.0\nt3 = t2 + 1.0\nt4 = t3 + 1.0\nt5 = t4 + 1.0\nt6 = t5 + 1.0\nt7 = t6 + 1.0\nt8 = t7 + 1.0\nt9 = t8 + 1.0\nt10 = t8 + t9\nt11 = t1 - t10\nt12 = t11 / n0\nanswer = t4 + t12\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "a number x is multiplied by 5 , and this product is then divided by 7 . if the positive square root of the result of these two operations equals x , what is the value of x if x \u2260 0 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 7.0\nn2 = 0.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.7142857142857143" + ], + "split": "train" + }, + { + "Input": "each week , harry is paid x dollars per hour for the first 15 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 41 hours if harry and james were paid the same amount last week , how many hours did harry work last week ?", + "Output Program": [ + "n0 = 15.0\nn1 = 1.5\nn2 = 40.0\nn3 = 2.0\nn4 = 41.0\nt0 = n2 + n3\nt1 = t0 - n0\nt2 = t1 / n1\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "at a bank , the service charges for transactions were us dollar 1 for every 5 transactions . the bank recently revised the charges to us dollar 0.75 for every 3 transactions . by approximately what percent did the ratio of price to transactions increase from the previous charge ?", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 0.75\nn3 = 3.0\nt0 = n2 / n3\nt1 = n0 / n1\nt2 = t0 / t1\nt3 = t2 * 100.0\nanswer = t3 - 100.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "how many real solutions does the equation x 5 + 2 x 3 + 8 x 2 + 16 = 0 have ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 3.0\nn3 = 8.0\nn4 = 2.0\nn5 = 16.0\nn6 = 0.0\nt0 = n0 * 1.0\nt1 = t0 - 1.0\nt2 = t1 - 1.0\nt3 = t2 - 1.0\nanswer = t3 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "a man is 20 years older than his son . in two years , his age will be twice the age of his son . what is the present age of his son ?", + "Output Program": [ + "n0 = 20.0\nt0 = 2.0 * 2.0\nt1 = 2.0 - 1.0\nt2 = t0 - 2.0\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "if ( 18 ^ a ) * 9 ^ ( 3 a \u2013 1 ) = ( 2 ^ 7 ) ( 3 ^ b ) and a and b are positive integers , what is the value of a ?", + "Output Program": [ + "n0 = 18.0\nn1 = 9.0\nn2 = 3.0\nn3 = 1.0\nn4 = 2.0\nn5 = 7.0\nn6 = 3.0\n\nanswer = n5 * n3\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "the average weight of 8 people increases by 2.5 kg when a new person comes in place of one of them weighing 85 kg . what is the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.5\nn2 = 85.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "105" + ], + "split": "train" + }, + { + "Input": "the average of 10 numbers is 60 . out of 10 numbers the average of first 6 no . is 68 , and last 6 numbers is 75 then find 7 th number ?", + "Output Program": [ + "n0 = 10.0\nn1 = 60.0\nn2 = 10.0\nn3 = 6.0\nn4 = 68.0\nn5 = 6.0\nn6 = 75.0\nn7 = 7.0\nt0 = n3 * n4\nt1 = n3 * n6\nt2 = n0 * n1\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "258" + ], + "split": "train" + }, + { + "Input": "for a certain exam , a score of 42 was 5 standard deviations below mean and a score of 67 was 2.5 standard deviations above mean . what was the mean score for the exam ?", + "Output Program": [ + "n0 = 42.0\nn1 = 5.0\nn2 = 67.0\nn3 = 2.5\nt0 = n1 + n3\nt1 = n0 * n3\nt2 = n1 * n2\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "58.666666666666664" + ], + "split": "train" + }, + { + "Input": "15 lts are taken of from a container full of liquid a and replaced with liquid b . again 15 more lts of the mixture is taken and replaced with liquid b . after this process , if the container contains liquid a and b in the ratio 9 : 16 , what is the capacity of the container q ?", + "Output Program": [ + "import math\nn0 = 15.0\nn1 = 15.0\nn2 = 9.0\nn3 = 16.0\nt0 = n2 + n3\nt1 = n2 / t0\nt2 = math.sqrt(max(0, t1))\nt3 = 1.0 - t2\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "37.5" + ], + "split": "train" + }, + { + "Input": "after playing 40 games , the lesley basketball team had won 50 % of the games . the additional games played gave the team a 20 % total winning average . how many additional games must the team have won to obtain this average ?", + "Output Program": [ + "n0 = 40.0\nn1 = 50.0\nn2 = 20.0\nt0 = n1 - n2\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "a doctor prescribed 12 cubic centimeters of a certain drug to a patient whose body weight was 120 pounds . if the typical dosage is 2 cubic centimeters per 15 pounds of the body weight , by what percent was the prescribed dosage lesser than the typical dosage ?", + "Output Program": [ + "n0 = 12.0\nn1 = 120.0\nn2 = 2.0\nn3 = 15.0\nt0 = n2 / n3\nt1 = n1 * t0\nt2 = t1 - n0\nt3 = t2 / t1\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "mr . smith calculated the average of 10 3 digit numbers . but due to a mistake he reversed the digits of a number and thus his average increased by 19.8 the difference between the unit digit and hundreds digit of that number is :", + "Output Program": [ + "n0 = 10.0\nn1 = 3.0\nn2 = 19.8\nt0 = n0 * n2\nt1 = 100.0 - 1.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a certain family has 3 sons : richard is 6 years older than david , and david is 8 years older than scott . if in 8 years , richard will be twice as old as scott , then how old was david 4 years ago ?", + "Output Program": [ + "n0 = 3.0\nn1 = 6.0\nn2 = 8.0\nn3 = 8.0\nn4 = 4.0\nt0 = n1 + n2\nanswer = t0 - n4\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "in an examination , there are 100 questions divided into 3 groups a , b and c such that each group contains at least one question . each question in group a carries 1 mark , each question in group b carries 2 marks and each question in group c carries 3 marks . it is known that the questions in group a together carry at least 60 % of the total marks . if group b contains 23 questions , then how many questions are there in group c ?", + "Output Program": [ + "import math\nn0 = 100.0\nn1 = 3.0\nn2 = 1.0\nn3 = 2.0\nn4 = 3.0\nn5 = 60.0\nn6 = 23.0\nt0 = n5 / 100.0\nt1 = n3 * n6\nt2 = n0 - n6\nt3 = 1 / t0\nt4 = t3 - 1.0\nt5 = n1 + t4\nt6 = t4 * t2\nt7 = t6 - t1\nt8 = t7 / t5\nanswer = math.floor(t8)\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "following an increase in prices , the price of a candy box was 10 pounds and the price of a can of soda was 9 pounds . if the price of a candy box was raised by 25 % , and the price of a can of soda was raised by 50 % . what was the price of a box of candy plus a can of soda before prices were raised ?", + "Output Program": [ + "n0 = 10.0\nn1 = 9.0\nn2 = 25.0\nn3 = 50.0\nt0 = n2 + 100.0\nt1 = n3 + 100.0\nt2 = n0 * 100.0\nt3 = n1 * 100.0\nt4 = t2 / t0\nt5 = t3 / t1\nanswer = t4 + t5\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "in a factory , an average of 65 tv ' s are produced per day for the fist 25 days of the months . a few workers fell ill for the next 5 days reducing the daily avg for the month to 60 sets / day . the average production per day for day last 5 days is ?", + "Output Program": [ + "n0 = 65.0\nn1 = 25.0\nn2 = 5.0\nn3 = 60.0\nn4 = 5.0\nt0 = n1 + n2\nt1 = n0 * n1\nt2 = n3 * t0\nt3 = t2 - t1\nanswer = t3 / n2\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "how many integers k greater than 100 and less than 1000 are there such that if the hundreds and the unit digits of k are reversed , the resulting integer is k + 99 ?", + "Output Program": [ + "n0 = 100.0\nn1 = 1000.0\nn2 = 99.0\nt0 = 10.0 - 2.0\nanswer = t0 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "if 225 / 999 = 0.225 , what is the 81 st digit to the right of the decimal point in the decimal equivalent of the fraction ?", + "Output Program": [ + "n0 = 225.0\nn1 = 999.0\nn2 = 0.225\nn3 = 81.0\n\nanswer = 2.0 + 3.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "if the numerator of a fraction is increased by 20 % and its denominator is diminished by 25 % value of the fraction is 2 / 15 . find the original fraction .", + "Output Program": [ + "n0 = 20.0\nn1 = 25.0\nn2 = 2.0\nn3 = 15.0\nt0 = n0 + 100.0\nt1 = n2 / n3\nt2 = 100.0 - n1\nt3 = t0 / 100.0\nt4 = t2 / 100.0\nt5 = t3 / t4\nanswer = t1 / t5\nprint(answer)" + ], + "Output Answer": [ + "0.08333333333333334" + ], + "split": "train" + }, + { + "Input": "4 ! / ( 4 - 3 ) ! = ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 4.0\nn2 = 3.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = n0 - n2\nt2 = math.factorial(min(15, int(t1)))\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "in a zoo there are 30 penguins , 22 zebras , and 8 tigers with some zookeepers . if the total number of heads are 132 less than the number of feet , the number of zookeepers is", + "Output Program": [ + "n0 = 30.0\nn1 = 22.0\nn2 = 8.0\nn3 = 132.0\nt0 = n0 * 2.0\nt1 = n1 * 4.0\nt2 = n2 * 4.0\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = t4 - n3\nanswer = t0 - t5\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "what is the greatest number of identical bouquets that can be made out of 21 white and 91 red tulips if no flowers are to be left out ? ( two bouquets are identical whenever the number of red tulips in the two bouquets is equal and the number of white tulips in the two bouquets is equal )", + "Output Program": [ + "n0 = 21.0\nn1 = 91.0\n\nanswer = n0 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "what least number must be added to 1049 , so that the sum is completely divisible by 25 ?", + "Output Program": [ + "n0 = 1049.0\nn1 = 25.0\nt0 = 10.0 * 4.0\nt1 = t0 + 2.0\nt2 = n1 * t1\nanswer = t2 - n0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 percent of the distribution lies within one standard deviation d of the mean , what percent w of the distribution is less than m + d ?", + "Output Program": [ + "n0 = 68.0\nt0 = 100.0 - n0\nt1 = t0 / 2.0\nanswer = 100.0 - t1\nprint(answer)" + ], + "Output Answer": [ + "84" + ], + "split": "train" + }, + { + "Input": "the manager at a health foods store mixes a unique superfruit juice cocktail that costs $ 1399.45 per litre to make . the cocktail includes mixed fruit juice and a \u00e7 ai berry juice , which cost $ 262.85 per litre and $ 3104.35 per litre , respectively . the manager has already opened 37 litres of the mixed fruit juice . how many litres of the a \u00e7 ai berry juice does he need to add ?", + "Output Program": [ + "n0 = 1399.45\nn1 = 262.85\nn2 = 3104.35\nn3 = 37.0\nt0 = n0 * n3\nt1 = n1 * n3\nt2 = n2 - n0\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "24.666666666666668" + ], + "split": "train" + }, + { + "Input": "subtracting 7 % of a from a is equivalent to multiplying a by how much ?", + "Output Program": [ + "n0 = 7.0\nt0 = 100.0 - n0\nanswer = t0 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "0.93" + ], + "split": "train" + }, + { + "Input": "the ratio of the present age of sandy to that of molly is 7 : 2 . sixteen years from now , the ratio of the ages of sandy to molly will be 5 : 2 . what was sandy ' s age 6 years ago ?", + "Output Program": [ + "n0 = 7.0\nn1 = 2.0\nn2 = 5.0\nn3 = 2.0\nn4 = 6.0\nt0 = n4 + 10.0\nt1 = n1 + n1\nt2 = n2 * t0\nt3 = n1 * t0\nt4 = t2 - t3\nt5 = n0 * t4\nt6 = t5 / t1\nanswer = t6 - n4\nprint(answer)" + ], + "Output Answer": [ + "78" + ], + "split": "train" + }, + { + "Input": "the average of the first 5 multiples of 9 is :", + "Output Program": [ + "n0 = 5.0\nn1 = 9.0\nt0 = n1 * 2.0\nt1 = n1 * 3.0\nt2 = n1 * 4.0\nt3 = n0 * n1\nt4 = n1 + t0\nt5 = t4 + t1\nt6 = t5 + t2\nt7 = t6 + t3\nanswer = t7 / n0\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "train" + }, + { + "Input": "calculate the share of y , if rs . 690 is divided among x , y and z in the ratio 5 : 7 : 11 ?", + "Output Program": [ + "n0 = 690.0\nn1 = 5.0\nn2 = 7.0\nn3 = 11.0\nt0 = n1 + n2\nt1 = n3 + t0\nt2 = n0 / t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "train" + }, + { + "Input": "robert ate 12 chocolates , nickel ate 3 chocolates . how many more chocolates did robert ate than nickel ?", + "Output Program": [ + "n0 = 12.0\nn1 = 3.0\n\nanswer = n0 - n1\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "if the average of 10 consecutive integers is 20.5 then the 10 th integer is : -", + "Output Program": [ + "n0 = 10.0\nn1 = 20.5\nn2 = 10.0\nt0 = n0 * 2.0\nt1 = n1 - t0\nt2 = n0 * t1\nanswer = t0 + t2\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "sandy gets 3 marks for each correct sum and loses 2 marks for each incorrect sum . sandy attempts 30 sums and obtains 55 marks . how many sums did sandy get correct ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 30.0\nn3 = 55.0\nt0 = n0 + n1\nt1 = n1 * n2\nt2 = n3 + t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "when x is multiplied by 3 , the result is 4 more than the result of subtracting x from 16 . what is the value of x ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 16.0\nt0 = n1 + n2\nt1 = 1.0 + n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "in a certain school , 25 % of students are below 8 years of age . the number of students above 8 years of age is 2 / 3 of the number of students of 8 years of age which is 36 . what is the total number of students in the school ?", + "Output Program": [ + "n0 = 25.0\nn1 = 8.0\nn2 = 8.0\nn3 = 2.0\nn4 = 3.0\nn5 = 8.0\nn6 = 36.0\nt0 = n3 / n4\nt1 = n0 / 100.0\nt2 = n6 * t0\nt3 = 1.0 - t1\nt4 = n6 + t2\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "what is the difference between the place value and face value of 4 in the numeral 46 ?", + "Output Program": [ + "n0 = 4.0\nn1 = 46.0\nt0 = n0 * 10.0\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "a person travels from p to q a speed of 30 km / hr and returns by increasing his speed by 30 % . what is his average speed for both the trips ?", + "Output Program": [ + "n0 = 30.0\nn1 = 30.0\nt0 = n1 / 100.0\nt1 = t0 + 1.0\nt2 = n0 * t1\nt3 = n0 + t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "34.5" + ], + "split": "train" + }, + { + "Input": "the average expenditure of a labourer for 6 months was 70 and he fell into debt . in the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30 . his monthly income i", + "Output Program": [ + "n0 = 6.0\nn1 = 70.0\nn2 = 4.0\nn3 = 60.0\nn4 = 30.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nt4 = n4 + t3\nanswer = t4 / t0\nprint(answer)" + ], + "Output Answer": [ + "69" + ], + "split": "train" + }, + { + "Input": "a student chose a number , multiplied it by 8 , then subtracted 138 from the result and got 102 . what was the number he chose ?", + "Output Program": [ + "n0 = 8.0\nn1 = 138.0\nn2 = 102.0\nt0 = n1 + n2\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "a man has rs . 192 in the denominations of one - rupee notes , 5 - rupee notes and 10 - rupee notes . the number of notes of each denomination is equal . what is the total number of notes that he has ?", + "Output Program": [ + "n0 = 192.0\nn1 = 5.0\nn2 = 10.0\nt0 = n1 + 1.0\nt1 = n2 + t0\nt2 = n0 / t1\nt3 = t2 + t2\nanswer = t3 + t2\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "how many gallons of milk that is 10 percent butter - fat must be added to 8 gallons of milk that is 40 percent butterfat to obtain milk that is 20 percent butterfat ?", + "Output Program": [ + "n0 = 10.0\nn1 = 8.0\nn2 = 40.0\nn3 = 20.0\nt0 = n2 - n3\nt1 = n1 * t0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "two trains start at same time from two stations and proceed towards each other at the rate of 20 km / hr and 25 km / hr respectively . when they meet , it is found that one train has traveled 70 km more than the other . what is the distance between the two stations ?", + "Output Program": [ + "n0 = 20.0\nn1 = 25.0\nn2 = 70.0\nt0 = n0 + n1\nt1 = n1 - n0\nt2 = n2 / t1\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "630" + ], + "split": "train" + }, + { + "Input": "the average age of 10 men increases by 2 years when two women are included in place of two men of ages 10 and 12 years . find the average age of the women ?", + "Output Program": [ + "n0 = 10.0\nn1 = 2.0\nn2 = 10.0\nn3 = 12.0\nt0 = n2 + n3\nt1 = n0 * n1\nt2 = t0 + t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "a , b , c subscribe rs . 50000 for a business , a subscribes rs . 4000 more than b and b rs . 5000 more than c . out of a total profit of rs . 35000 , c receives :", + "Output Program": [ + "n0 = 50000.0\nn1 = 4000.0\nn2 = 5000.0\nn3 = 35000.0\nt0 = n1 + n2\nt1 = n2 + t0\nt2 = n0 - t1\nt3 = t2 / 3.0\nt4 = t3 / n0\nanswer = n3 * t4\nprint(answer)" + ], + "Output Answer": [ + "8400" + ], + "split": "train" + }, + { + "Input": "a driver would have reduced the time it took to drive from home to the store by 1 / 3 if the average speed had been increased by 21 miles per hour . what was the actual average speed , in miles per hour , when the driver drove from home to the store ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 21.0\nt0 = n0 / n1\nt1 = n0 - t0\nt2 = t1 * n2\nt3 = n0 - t1\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "42.000000000000014" + ], + "split": "train" + }, + { + "Input": "find a number such that when 15 is subtracted from 7 times the number , the result is 10 more than twice the number .", + "Output Program": [ + "n0 = 15.0\nn1 = 7.0\nn2 = 10.0\nt0 = n0 + n2\nt1 = n1 - 2.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "the average monthly income of a and b is rs . 4050 . the average monthly income of b and c is rs . 5250 and the average monthly income of a and c is rs . 4200 . what is the monthly income of a ?", + "Output Program": [ + "n0 = 4050.0\nn1 = 5250.0\nn2 = 4200.0\nt0 = n0 * 2.0\nt1 = n1 * 2.0\nt2 = n2 * 2.0\nt3 = t1 - t2\nt4 = t0 + t3\nt5 = t4 / 2.0\nanswer = t0 - t5\nprint(answer)" + ], + "Output Answer": [ + "3000" + ], + "split": "train" + }, + { + "Input": "the product x of two prime numbers is between 15 and 70 . if one of the prime numbers is greater than 2 but less than 6 and the other is greater than 13 but less than 25 , then x =", + "Output Program": [ + "n0 = 15.0\nn1 = 70.0\nn2 = 2.0\nn3 = 6.0\nn4 = 13.0\nn5 = 25.0\nt0 = n2 + 1.0\nt1 = n5 - n2\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "69" + ], + "split": "train" + }, + { + "Input": "we define that k @ j is the product of j number from k in increasing order for positive integers k , j . for example , 6 @ 4 = 6 * 7 * 8 * 9 . if a = 2020 and b = 2120 , what is the value r of the ratio a / b ?", + "Output Program": [ + "n0 = 6.0\nn1 = 4.0\nn2 = 6.0\nn3 = 7.0\nn4 = 8.0\nn5 = 9.0\nn6 = 2020.0\nn7 = 2120.0\nt0 = n6 / n6\nt1 = t0 + t0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "two employees a and b are paid a total of rs . 560 per week by their employer . if a is paid 150 percent of the sum paid to b , how much is b paid per week ?", + "Output Program": [ + "n0 = 560.0\nn1 = 150.0\nt0 = n1 / 100.0\nt1 = t0 + 1.0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "224" + ], + "split": "train" + }, + { + "Input": "find the lowest common multiple of 10 , 14 and 20 .", + "Output Program": [ + "import scipy\nn0 = 10.0\nn1 = 14.0\nn2 = 20.0\nt0 = scipy.lcm(int(n0), int(n1))\nanswer = scipy.lcm(int(n2), int(t0))\nprint(answer)" + ], + "Output Answer": [ + "140" + ], + "split": "train" + }, + { + "Input": "3034 - ( 1002 / 200.4 ) = ?", + "Output Program": [ + "n0 = 3034.0\nn1 = 1002.0\nn2 = 200.4\nt0 = n1 / n2\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "3029" + ], + "split": "train" + }, + { + "Input": "if jake loses 8 pounds , he will weigh twice as much as his sister kendra . together they now weigh 290 pounds . what is jake \u2019 s present weight , in pounds ?", + "Output Program": [ + "n0 = 8.0\nn1 = 290.0\nt0 = n1 - n0\nt1 = t0 / 3.0\nt2 = t1 * 2.0\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "196" + ], + "split": "train" + }, + { + "Input": "find the sum the difference between the compound and s . i . on a certain sum of money for 2 years at 10 % per annum is rs . 13 of money ?", + "Output Program": [ + "n0 = 2.0\nn1 = 10.0\nn2 = 13.0\nt0 = n0 * n1\nt1 = n2 / t0\nt2 = t1 * 100.0\nanswer = t2 * t0\nprint(answer)" + ], + "Output Answer": [ + "1300" + ], + "split": "train" + }, + { + "Input": "kamal obtained 76 , 65 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?", + "Output Program": [ + "n0 = 76.0\nn1 = 65.0\nn2 = 82.0\nn3 = 67.0\nn4 = 85.0\nn5 = 100.0\nt0 = n0 + n1\nt1 = 1.0 + 4.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "find the number of factors of 180 that are in the form ( 4 * k + 2 ) , where k is a non - negative integer ?", + "Output Program": [ + "n0 = 180.0\nn1 = 4.0\nn2 = 2.0\nt0 = 2.0 + 3.0\nt1 = n0 / 3.0\nt2 = t1 / n2\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "every student of a certain school must play an instrument . in last year , 1 / 2 of the students picked a woodwind instrument , 2 / 5 of the students picked a brass instrument , and all of the other students took percussion . in this year , 1 / 2 of the students who play woodwind and 1 / 4 of the students who play brass instruments left school , other students did not leave , and no fresh student come in . what fraction of all students play either a woodwind or brass instrument ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 2.0\nn3 = 5.0\nn4 = 1.0\nn5 = 2.0\nn6 = 1.0\nn7 = 4.0\nt0 = 1.0 / 2.0\nt1 = 2.0 / n3\nt2 = t0 / n1\nt3 = t1 / n7\nt4 = n0 - t0\nt5 = t4 - t2\nt6 = t1 - t3\nt7 = t4 - t1\nt8 = t5 + t6\nt9 = n0 - t5\nt10 = t9 - t7\nanswer = t8 / t10\nprint(answer)" + ], + "Output Answer": [ + "0.8461538461538461" + ], + "split": "train" + }, + { + "Input": "| 16 - 5 | - | 5 - 12 | = ?", + "Output Program": [ + "n0 = 16.0\nn1 = 5.0\nn2 = 5.0\nn3 = 12.0\nt0 = n0 - n1\nt1 = n3 - n2\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "the population of a town increased from 1 , 75000 to 2 , 62500 in a decade . what is the average percent increase of population per year ?", + "Output Program": [ + "n0 = 1.0\nn1 = 75000.0\nn2 = 2.0\nn3 = 62500.0\nt0 = 100.0 * 1000.0\nt1 = n3 / t0\nt2 = n1 / t0\nt3 = n2 + t1\nt4 = n0 + t2\nt5 = t3 - t4\nt6 = t5 / 10.0\nt7 = t6 / t4\nanswer = t7 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "if x is equal to the sum of the integers from 20 to 40 , inclusive , and y is the number of even integers from 20 to 40 , inclusive , what is the value of x + y ?", + "Output Program": [ + "n0 = 20.0\nn1 = 40.0\nn2 = 20.0\nn3 = 40.0\nt0 = n0 + n1\nt1 = n1 - n0\nt2 = t1 + 1.0\nt3 = t1 / 2.0\nt4 = t0 / 2.0\nt5 = t3 + 1.0\nt6 = t2 * t4\nanswer = t5 + t6\nprint(answer)" + ], + "Output Answer": [ + "641" + ], + "split": "train" + }, + { + "Input": "the youngest of 4 children has siblings who are 2 , 7 , and 11 years older than she is . if the average ( arithmetic mean ) age of the 4 siblings is 25 , what is the age of the youngest sibling ?", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\nn2 = 7.0\nn3 = 11.0\nn4 = 4.0\nn5 = 25.0\nt0 = n1 + n2\nt1 = n0 * n5\nt2 = n3 + t0\nt3 = t1 - t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "in a can , there is a mixture of milk and water in the ratio 1 : 5 . if it is filled with an additional 2 litres of milk the can would be full and ratio of milk and water would become 3 : 5 . find the capacity of the can ?", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 2.0\nn3 = 3.0\nn4 = 5.0\nt0 = n3 / n4\nt1 = n1 * t0\nt2 = t1 - n0\nt3 = n2 / t2\nt4 = n1 * t3\nt5 = t3 + t4\nanswer = n2 + t5\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "each child has 6 crayons and 12 apples . if there are 12 children , how many crayons are there in total ?", + "Output Program": [ + "n0 = 6.0\nn1 = 12.0\nn2 = 12.0\n\nanswer = n0 * n2\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "train" + }, + { + "Input": "f ( 1 ) = 1 , where f ( x + y ) = f ( x ) + f ( y ) + 8 xy - 2 . then f ( 7 ) = ?", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 8.0\nn3 = 2.0\nn4 = 7.0\nt0 = n0 + n0\nt1 = 2.0 + 3.0\nt2 = 3.0 + 3.0\nt3 = n2 * 2.0\nt4 = n2 * 3.0\nt5 = n2 * 4.0\nt6 = n2 + t0\nt7 = n2 * t1\nt8 = n2 * t2\nt9 = t6 - n3\nt10 = n0 + t9\nt11 = t10 + t3\nt12 = t11 - n3\nt13 = n0 + t12\nt14 = t13 + t4\nt15 = t14 - n3\nt16 = n0 + t15\nt17 = t16 + t5\nt18 = t17 - n3\nt19 = n0 + t18\nt20 = t19 + t7\nt21 = t20 - n3\nt22 = n0 + t21\nt23 = t22 + t8\nanswer = t23 - n3\nprint(answer)" + ], + "Output Answer": [ + "163" + ], + "split": "train" + }, + { + "Input": "what is the largest possible value of cc if 5 c + ( d \u2212 12 ) ^ 2 = 235 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 12.0\nn2 = 2.0\nn3 = 235.0\n\nanswer = n3 / n0\nprint(answer)" + ], + "Output Answer": [ + "47" + ], + "split": "train" + }, + { + "Input": "if the operation \u00f8 is defined for all positive integers x and w by x \u00f8 w = ( 2 ^ x ) / ( 2 ^ w ) then ( 4 \u00f8 2 ) \u00f8 2 = ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 4.0\nn3 = 2.0\nn4 = 2.0\nt0 = n0**min(n2, 5)\nt1 = n0**min(n0, 5)\nt2 = n0**min(n4, 5)\nt3 = t0 / t1\nt4 = n0**min(t3, 5)\nanswer = t4 / t2\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "one - third less than 20 % of 180 is equal to :", + "Output Program": [ + "n0 = 20.0\nn1 = 180.0\nt0 = n0 / 100.0\nt1 = 1.0 / 3.0\nt2 = n1 * t0\nt3 = t1 * t2\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "a cricketer scored 132 runs which included 12 boundaries and 2 sixes . what percent of his total score did he make by running between the wickets .", + "Output Program": [ + "n0 = 132.0\nn1 = 12.0\nn2 = 2.0\nt0 = n1 * 4.0\nt1 = n2 * 3.0\nt2 = n2 * t1\nt3 = t0 + t2\nt4 = n0 - t3\nt5 = t4 / n0\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "54.54545454545454" + ], + "split": "train" + }, + { + "Input": "if the number 98348 * 0 is exactly divisible by 72 , then the minimum value of * is ?", + "Output Program": [ + "n0 = 98348.0\nn1 = 0.0\nn2 = 72.0\nt0 = n0 * 100.0\nt1 = t0 % n2\nt2 = n2 - t1\nanswer = t2 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "the average of temperatures at noontime from monday to friday is 40 ; the lowest one is 30 , what is the possible maximum range of the temperatures ?", + "Output Program": [ + "n0 = 40.0\nn1 = 30.0\nt0 = 2.0 + 3.0\nt1 = n1 * 4.0\nt2 = n0 * t0\nt3 = t2 - t1\nanswer = t3 - n1\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "find large number from below question the difference of two numbers is 1370 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder", + "Output Program": [ + "n0 = 1370.0\nn1 = 6.0\nn2 = 15.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nt2 = t0 / t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "1626" + ], + "split": "train" + }, + { + "Input": "the average monthly salary of 18 employees in an organisation is rs . 2000 . if the manager ' s salary is added , then the average salary increases by rs . 200 . what is the manager ' s monthly salary ?", + "Output Program": [ + "n0 = 18.0\nn1 = 2000.0\nn2 = 200.0\nt0 = n1 + n2\nt1 = n0 + 1.0\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "5800" + ], + "split": "train" + }, + { + "Input": "what is the leastvalue of x . so that 23 x 57 is divisible by 3 ?", + "Output Program": [ + "import math\nn0 = 23.0\nn1 = 57.0\nn2 = 3.0\nt0 = n0 / 10.0\nt1 = n1 / 10.0\nt2 = n0 % 10.0\nt3 = n1 % 10.0\nt4 = math.floor(t0)\nt5 = math.floor(t1)\nt6 = t4 + t2\nt7 = t6 + t5\nt8 = t7 + t3\nt9 = t8 % n2\nanswer = n2 - t9\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "s is a set of 45 consecutive multiples of 5 . if the smallest number in s is 55 , then the greatest number in s is", + "Output Program": [ + "n0 = 45.0\nn1 = 5.0\nn2 = 55.0\nt0 = n0 - 1.0\nt1 = n1 * t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "275" + ], + "split": "train" + }, + { + "Input": "a man \u00e2 \u20ac \u2122 s current age is ( 2 / 5 ) of the age of his father . after 14 years , he will be ( 1 / 2 ) of the age of his father . what is the age of father at now ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 14.0\nn3 = 1.0\nn4 = 2.0\nt0 = n3 / n0\nt1 = n0 / n1\nt2 = n2 * t0\nt3 = t0 - t1\nt4 = n2 - t2\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "70.00000000000001" + ], + "split": "train" + }, + { + "Input": "at a certain committee meeting only associate professors and assistant professors are present . each associate professor has brought 2 pencils and 1 chart to the meeting , while each assistant professor has brought 1 pencil and 2 charts . if a total of 10 pencils and 5 charts have been brought to the meeting , how many people are present ?", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 1.0\nn3 = 2.0\nn4 = 10.0\nn5 = 5.0\nt0 = n4 + n5\nt1 = n0 + n1\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "a set of consecutive positive integers beginning with 1 is written on the blackboard . a student came along and erased one number . the average of the remaining numbers is 35 7 / 17 . what was the number erased ?", + "Output Program": [ + "import math\nn0 = 1.0\nn1 = 35.0\nn2 = 7.0\nn3 = 17.0\nt0 = n2 / n3\nt1 = n1 + t0\nt2 = t1 * 2.0\nt3 = math.floor(t2)\nt4 = t3 / 2.0\nt5 = t3 - n0\nt6 = t4 * t5\nt7 = t5 - n0\nt8 = t1 * t7\nanswer = t6 - t8\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "the arithmetic mean and standard deviation of a certain normal distribution are 10.5 and 1 , respectively . what value is exactly 2 standard deviations less than the mean ?", + "Output Program": [ + "n0 = 10.5\nn1 = 1.0\nn2 = 2.0\nt0 = n1 * n2\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "8.5" + ], + "split": "train" + }, + { + "Input": "in expressing a length 810472 km as nearly as possible with 3 significant digits , find the percentage error .", + "Output Program": [ + "n0 = 810472.0\nn1 = 3.0\nt0 = n1 * 10.0\nt1 = t0 + 4.0\nt2 = t1 / 100.0\nanswer = t2 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "0.034" + ], + "split": "train" + }, + { + "Input": "there are 5 more women than there are men on a local co - ed softball team . if there are a total of 15 players on the team , what is the ratio of men to women ?", + "Output Program": [ + "n0 = 5.0\nn1 = 15.0\nt0 = 1.0 + 1.0\nt1 = n1 - n0\nt2 = t1 / t0\nt3 = n0 + t2\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "an analysis of the monthly incentives received by 5 salesmen : the mean and median of the incentives is $ 7000 . the only mode among the observations is $ 12000 . incentives paid to each salesman were in full thousands . what is the difference z between the highest and the lowest incentive received by the 5 salesmen in the month ?", + "Output Program": [ + "n0 = 5.0\nn1 = 7000.0\nn2 = 12000.0\nn3 = 5.0\n\nanswer = n2 - 1000.0\nprint(answer)" + ], + "Output Answer": [ + "11000" + ], + "split": "train" + }, + { + "Input": "3.5 can be expressed in terms of percentage as ?", + "Output Program": [ + "n0 = 3.5\n\nanswer = n0 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "350" + ], + "split": "train" + }, + { + "Input": "the average of 10 numbers is calculated as 16 . it is discovered later on that while calculating the average , the number 35 was incorrectly read as 25 , and this incorrect number was used in the calculation . what is the correct average ?", + "Output Program": [ + "n0 = 10.0\nn1 = 16.0\nn2 = 35.0\nn3 = 25.0\nt0 = n0 * n1\nt1 = t0 - n3\nt2 = n2 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "a library has an average of 510 visitors on sundays and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is ?", + "Output Program": [ + "import math\nn0 = 510.0\nn1 = 240.0\nn2 = 30.0\nt0 = 3.0 + 4.0\nt1 = n2 / t0\nt2 = math.floor(t1)\nt3 = t2 + 1.0\nt4 = n0 * t3\nt5 = n2 - t3\nt6 = n1 * t5\nt7 = t4 + t6\nanswer = t7 / n2\nprint(answer)" + ], + "Output Answer": [ + "285" + ], + "split": "train" + }, + { + "Input": "laura took out a charge account at the general store and agreed to pay 7 % simple annual interest . if she charges $ 35 on her account in january , how much will she owe a year later , assuming she does not make any additional charges or payments ?", + "Output Program": [ + "n0 = 7.0\nn1 = 35.0\nt0 = n0 / 100.0\nt1 = n1 * t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "37.45" + ], + "split": "train" + }, + { + "Input": "if the average of 10 digits is 80 and the average of 6 of them is 58 , calculate the average of the remaining 4 numbers ?", + "Output Program": [ + "n0 = 10.0\nn1 = 80.0\nn2 = 6.0\nn3 = 58.0\nn4 = 4.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = t0 - t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "113" + ], + "split": "train" + }, + { + "Input": "for a certain art exhibit , a museum sold admission tickets to a group of 30 people every 5 minutes from 9 : 00 in the morning to 5 : 55 in the afternoon , inclusive . the price of a regular admission ticket was $ 8 and the price of a student ticket was $ 4 . if on one day 3 times as many regular admission tickets were sold as student tickets , what was the total revenue from ticket sales that day ?", + "Output Program": [ + "n0 = 30.0\nn1 = 5.0\nn2 = 9.0\nn3 = 0.0\nn4 = 5.0\nn5 = 55.0\nn6 = 8.0\nn7 = 4.0\nn8 = 3.0\nt0 = 12.0 + n4\nt1 = n8 + 1.0\nt2 = t0 - n2\nt3 = t2 + 1.0\nt4 = t3 * 12.0\nt5 = n0 * t4\nt6 = t5 / t1\nt7 = n8 * t6\nt8 = n7 * t6\nt9 = n6 * t7\nanswer = t9 + t8\nprint(answer)" + ], + "Output Answer": [ + "22680" + ], + "split": "train" + }, + { + "Input": "a train ride from two p to town q costs $ 6.85 more than does a bus ride from town p to town q . together , the cost of one train ride and one bus ride is $ 9.85 . what is the cost of a bus ride from town p to town q ?", + "Output Program": [ + "n0 = 6.85\nn1 = 9.85\nt0 = n1 - n0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "1.5" + ], + "split": "train" + }, + { + "Input": "find k if 32 / k = 4 .", + "Output Program": [ + "n0 = 32.0\nn1 = 4.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "exactly 3 / 7 of the people in the room are under the age of 21 , and exactly 5 / 14 of the people in the room are over the age of 65 . if the total number of the people in the room is greater than 50 and less than 100 , how many people in the room are under the age of 21 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 21.0\nn3 = 5.0\nn4 = 14.0\nn5 = 65.0\nn6 = 50.0\nn7 = 100.0\nn8 = 21.0\nt0 = n1 * n4\nt1 = n0 * t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "in a group of ducks and cows , the total number of legs are 36 more than twice the number of heads . find the total number of cows .", + "Output Program": [ + "n0 = 36.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "the total age of a and b is 12 years more than the total age of b and c . c is how many years younger than a . ?", + "Output Program": [ + "n0 = 12.0\n\nanswer = n0 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "the average salary of a person for the months of january , february , march and april is rs . 8000 and that for the months february , march , april and may is rs . 8600 . if his salary for the month of may is rs . 6500 , find his salary for the month of january ?", + "Output Program": [ + "n0 = 8000.0\nn1 = 8600.0\nn2 = 6500.0\nt0 = n0 * 4.0\nt1 = n1 * 4.0\nt2 = t1 - n2\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "4100" + ], + "split": "train" + }, + { + "Input": "rahim bought 55 books for rs . 1500 from one shop and 60 books for rs . 340 from another . what is the average price he paid per book ?", + "Output Program": [ + "n0 = 55.0\nn1 = 1500.0\nn2 = 60.0\nn3 = 340.0\nt0 = n1 + n3\nt1 = n0 + n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "the average of 10 numbers was calculated as 16 . it is discovered later on that while calculating the average , one number , namely 46 , was incorrectly read as 26 . what is the correct average ?", + "Output Program": [ + "n0 = 10.0\nn1 = 16.0\nn2 = 46.0\nn3 = 26.0\nt0 = n0 * n1\nt1 = n2 - n3\nt2 = t0 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "an equal number of desks and bookcases are to be placed along a library wall that is 15 meters long . each desk is 2 meters long , and each bookshelf is 1.5 meters long . if the maximum possible number of desks and bookcases are to be placed along the wall , then the space along the wall that is left over will be how many meters w long ?", + "Output Program": [ + "n0 = 15.0\nn1 = 2.0\nn2 = 1.5\nt0 = n1 * 4.0\nt1 = n2 * 4.0\nt2 = t0 + t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "if 45 - [ 28 - { 37 - ( 15 - * ) } ] = 55 , then * is equal to :", + "Output Program": [ + "n0 = 45.0\nn1 = 28.0\nn2 = 37.0\nn3 = 15.0\nn4 = 55.0\nt0 = n1 - n2\nt1 = n3 + t0\nt2 = n0 - t1\nanswer = n4 - t2\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "what is the remainder of q = 3 ^ 19 when divided by 10 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 19.0\nn2 = 10.0\nt0 = n1 % 4.0\nt1 = n0**min(t0, 5)\nanswer = t1 % n2\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "in a class of 27 students in an examination in maths 5 students scored 95 marks each , 3 get zero each and the average of the rest was 45 . what is the average of the whole class ?", + "Output Program": [ + "n0 = 27.0\nn1 = 5.0\nn2 = 95.0\nn3 = 3.0\nn4 = 45.0\nt0 = n1 + n3\nt1 = n1 * n2\nt2 = n0 - t0\nt3 = n4 * t2\nt4 = t3 + t1\nanswer = t4 / n0\nprint(answer)" + ], + "Output Answer": [ + "49.25925925925926" + ], + "split": "train" + }, + { + "Input": "in a river flowing at 2 km / hr , a boat travels 64 km upstream and then returns downstream to the starting point . if its speed in still water be 6 km / hr , find the total journey time .", + "Output Program": [ + "n0 = 2.0\nn1 = 64.0\nn2 = 6.0\nt0 = n0 + n2\nt1 = n2 - n0\nt2 = n1 / t1\nt3 = n1 / t0\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "if ( m - 8 ) is a factor of m ^ 2 - pm - 24 , then p =", + "Output Program": [ + "n0 = 8.0\nn1 = 2.0\nn2 = 24.0\nt0 = n2 / n0\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "you and your friend spent a total of $ 15 for lunch . your friend spent $ 1 more than you . how much did your friend spend on their lunch ?", + "Output Program": [ + "n0 = 15.0\nn1 = 1.0\nt0 = n0 - n1\nt1 = t0 / 2.0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "what are the total number of divisors of 600 ( including 1 and 600 ) ?", + "Output Program": [ + "n0 = 600.0\nn1 = 1.0\nn2 = 600.0\nt0 = 0.25 * 100.0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "set # 1 = { a , b } set # 2 = { k , l , m , n , o , p } there are these two sets of letters , and you are going to pick exactly one letter from each set . what is the probability of picking at least one vowel ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nt0 = 1.0 + 4.0\nt1 = 1.0 / 2.0\nt2 = t0 + 1.0\nt3 = t0 / t2\nt4 = t1 * t3\nanswer = n0 - t4\nprint(answer)" + ], + "Output Answer": [ + "0.5833333333333333" + ], + "split": "train" + }, + { + "Input": "in digging a pond 20 m * 12 m * 5 m the volumes of the soil extracted will be ?", + "Output Program": [ + "n0 = 20.0\nn1 = 12.0\nn2 = 5.0\nt0 = n0 * n1\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "1200" + ], + "split": "train" + }, + { + "Input": "define a = the sum of digits of the number 7 ^ 100 and b = the sum of the digits of a . what is the sum of the digits of b ?", + "Output Program": [ + "n0 = 7.0\nn1 = 100.0\nt0 = 2.0 + 4.0\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "when 2 / 9 of the votes on a certain resolution have been counted , 3 / 4 of those counted are in favor of the resolution . what fraction w of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution ?", + "Output Program": [ + "n0 = 2.0\nn1 = 9.0\nn2 = 3.0\nn3 = 4.0\nn4 = 2.0\nn5 = 1.0\nt0 = n0 + n5\nt1 = n0 / n1\nt2 = n2 / n3\nt3 = n1 - n0\nt4 = n0 / t0\nt5 = t3 / n1\nt6 = t1 * t2\nt7 = t1 - t6\nt8 = t4 - t7\nanswer = t8 / t5\nprint(answer)" + ], + "Output Answer": [ + "0.7857142857142856" + ], + "split": "train" + }, + { + "Input": "the total age of a and b is 17 years more than the total age of b and c . c is how many years younger than a ?", + "Output Program": [ + "n0 = 17.0\n\nanswer = n0 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "if a = ( 10 ^ 10 ) - 47 , what is the sum of all the digit of a ?", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 47.0\nt0 = n0 * n0\nt1 = t0 + 60.0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "two sets of 7 consecutive positive integers have exactly one integer in common . the sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set ?", + "Output Program": [ + "n0 = 7.0\nt0 = n0 * 10.0\nt1 = n0 * 4.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "12 . what is the dividend . divisor 17 , the quotient is 9 and the remainder is 9 .", + "Output Program": [ + "n0 = 12.0\nn1 = 17.0\nn2 = 9.0\nn3 = 9.0\nt0 = n1 * n2\nanswer = n3 + t0\nprint(answer)" + ], + "Output Answer": [ + "162" + ], + "split": "train" + }, + { + "Input": "the average salary of all the workers in a workshop is rs . 6750 . the average salary of 7 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is ?", + "Output Program": [ + "n0 = 6750.0\nn1 = 7.0\nn2 = 12000.0\nn3 = 6000.0\nt0 = n2 - n0\nt1 = n0 - n3\nt2 = n1 * t0\nt3 = t2 / t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "train" + }, + { + "Input": "on dividinng 109 by a number , the quotient is 9 and the remainder is 1 . find the divisor .", + "Output Program": [ + "import math\nn0 = 109.0\nn1 = 9.0\nn2 = 1.0\nt0 = n0 / n1\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "in a fuel station the service costs $ 2.20 per vehicle and every liter of fuel costs $ 0.70 . assuming that you fill up 4 mini - vans and 2 trucks , what will be the total cost , if a mini - van ' s tank is 65 liters and a truck ' s tank is 120 % bigger and they are all empty ?", + "Output Program": [ + "n0 = 2.2\nn1 = 0.7\nn2 = 4.0\nn3 = 2.0\nn4 = 65.0\nn5 = 120.0\nt0 = n2 + n3\nt1 = n4 * n5\nt2 = n2 * n4\nt3 = t1 / 100.0\nt4 = n1 * t2\nt5 = n0 * t0\nt6 = n4 + t3\nt7 = n3 * t6\nt8 = n1 * t7\nt9 = t8 + t4\nanswer = t9 + t5\nprint(answer)" + ], + "Output Answer": [ + "395.4" + ], + "split": "train" + }, + { + "Input": "a group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 7 with 4 students left over . what is the sum of the two smallest possible values of n ?", + "Output Program": [ + "n0 = 4.0\nn1 = 1.0\nn2 = 7.0\nn3 = 4.0\nt0 = n2 * 2.0\nt1 = 2.0 * n3\nt2 = n3 + t0\nt3 = n2 * t1\nt4 = n3 + t3\nanswer = t2 + t4\nprint(answer)" + ], + "Output Answer": [ + "78" + ], + "split": "train" + }, + { + "Input": "an auto assembly plant performs 6 functions with each frame that arrives : add axles , add wheels to the axles , install the windshield to the frame , install the instrument panel , install the steering wheel , and install the interior seating . once those 6 tasks are performed , each car goes to a separate building for finishing touches . if these tasks can be arranged along a linear assembly line in any order , except that the axles must be installed before the wheels can be added , how many y ways can the assembly line be arranged ?", + "Output Program": [ + "import math\nn0 = 6.0\nn1 = 6.0\nt0 = 3.0 + 4.0\nt1 = math.factorial(min(15, int(4.0)))\nt2 = n0 - 1.0\nt3 = t0 + 2.0\nt4 = math.factorial(min(15, int(t2)))\nt5 = t3 + 1.0\nt6 = t5 * t1\nanswer = t4 + t6\nprint(answer)" + ], + "Output Answer": [ + "360" + ], + "split": "train" + }, + { + "Input": "if the function q is defined by the formula q = 5 e / ( 4 x ( z ^ 2 ) ) , by what factor will q be multiplied if e is quadrupled , x is doubled , and z is tripled ?", + "Output Program": [ + "n0 = 5.0\nn1 = 4.0\nn2 = 2.0\nt0 = n0 + n1\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.2222222222222222" + ], + "split": "train" + }, + { + "Input": "if a farmer sells 20 of his chickens , his stock of feed will last for 3 more days than planned , but if he buys 15 more chickens , he will run out of feed 4 days earlier than planned . if no chickens are sold or bought , the farmer will be exactly on schedule . how many chickens does the farmer have ?", + "Output Program": [ + "n0 = 20.0\nn1 = 3.0\nn2 = 15.0\nn3 = 4.0\nt0 = 2.0 + 3.0\nt1 = n1 * n3\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "which number can we add to 987654 to get a number exactly divisible by 456 ?", + "Output Program": [ + "n0 = 987654.0\nn1 = 456.0\nt0 = n0 % n1\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "the sum of the even numbers between 1 and n is 105 * 106 , where n is an odd number , then n = ?", + "Output Program": [ + "n0 = 1.0\nn1 = 105.0\nn2 = 106.0\nt0 = n1 * 2.0\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "211" + ], + "split": "train" + }, + { + "Input": "o mow a grass field a team of mowers planned to cover 15 hectares a day . after 4 working days they increased the daily productivity by 33 \u00d7 13 % 33 \u00d7 13 % , and finished the work 1 day earlier than it was planned . a ) what is the area of the grass field ? b ) how many days did it take to mow the whole field ? c ) how many days were scheduled initially for this job ?", + "Output Program": [ + "n0 = 15.0\nn1 = 4.0\nn2 = 33.0\nn3 = 13.0\nn4 = 33.0\nn5 = 13.0\nn6 = 1.0\nt0 = n1 + n6\nt1 = n0 / 3.0\nt2 = n0 * n1\nt3 = n0 + t1\nt4 = t3 * t0\nt5 = t3 - n0\nt6 = t4 - t2\nt7 = t6 / t5\nt8 = n0 * t7\nanswer = t8 % 100.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "the average monthly income of p and q is rs . 5050 . the average monthly income of q and r is rs . 6250 and the average monthly income of p and r is rs . 5200 . the monthly income of p is :", + "Output Program": [ + "n0 = 5050.0\nn1 = 6250.0\nn2 = 5200.0\nt0 = n0 + n2\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "4000" + ], + "split": "train" + }, + { + "Input": "if ( 1 / 2 ) ^ 23 ( 1 / 81 ) ^ k = 1 / 18 ^ 23 , then k =", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 23.0\nn3 = 1.0\nn4 = 81.0\nn5 = 1.0\nn6 = 18.0\nn7 = 23.0\nt0 = n1 * n2\nanswer = t0 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "11.5" + ], + "split": "train" + }, + { + "Input": "a certain company expects quarterly earnings of $ 0.80 per share of stock , half of which will be distributed as dividends to shareholders while the rest will be used for research and development . if earnings are greater than expected , shareholders will receive an additional $ 0.04 per share for each additional $ 0.10 of per share earnings . if quarterly earnings are $ 1.10 per share , what will be the dividend paid to a person who owns 400 shares of the company ' s stock ?", + "Output Program": [ + "n0 = 0.8\nn1 = 0.04\nn2 = 0.1\nn3 = 1.1\nn4 = 400.0\nt0 = n0 / 2.0\nt1 = n3 - n0\nt2 = t1 * 10.0\nt3 = n1 * t2\nt4 = t0 + t3\nanswer = n4 * t4\nprint(answer)" + ], + "Output Answer": [ + "208" + ], + "split": "train" + }, + { + "Input": "if n is a positive integer and the product of all integers from 1 to n , inclusive , is a multiple of 840 , what is the least possible value of n ?", + "Output Program": [ + "n0 = 1.0\nn1 = 840.0\nt0 = n1 / 2.0\nt1 = 10.0 / 2.0\nt2 = t0 / 3.0\nt3 = t2 / 4.0\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "calculate 469158 x 9999 = ?", + "Output Program": [ + "n0 = 469158.0\nn1 = 9999.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "4691110842" + ], + "split": "train" + }, + { + "Input": "a man has some hens and cows . if the number of heads be 48 and the number of feet equals 136 , then the number of hens will be :", + "Output Program": [ + "n0 = 48.0\nn1 = 136.0\nt0 = n0 * 4.0\nt1 = t0 - n1\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "in a division sum , the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 2 to the thrice of the remainder . the dividend is :", + "Output Program": [ + "n0 = 6.0\nn1 = 5.0\nn2 = 2.0\nt0 = n0 * 3.0\nt1 = n2 + t0\nt2 = t1 / n1\nt3 = t1 * t2\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "86" + ], + "split": "train" + }, + { + "Input": "a man is 22 years older than his son . in two years , his age will be twice the age of his son . the present age of this son is", + "Output Program": [ + "n0 = 22.0\nt0 = 2.0 * 2.0\nt1 = 2.0 - 1.0\nt2 = t0 - 2.0\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 6 eggs . if the cost of each pound of rice is $ 0.24 , then how many cents does a liter of kerosene cost ? [ one dollar has 100 cents . ]", + "Output Program": [ + "n0 = 6.0\nn1 = 0.24\nn2 = 100.0\nt0 = 1.0 / 2.0\nt1 = n1 * n2\nt2 = n0 / t0\nt3 = t2 / 12.0\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "a \u2019 s speed is 30 / 17 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?", + "Output Program": [ + "n0 = 30.0\nn1 = 17.0\nt0 = n0 - n1\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.43333333333333335" + ], + "split": "train" + }, + { + "Input": "the cost of 10 kg of mangos is equal to the cost of 24 kg of rice . the cost of 6 kg of flour equals the cost of 2 kg of rice . the cost of each kg of flour is $ 22 . find the total cost of 4 kg of mangos , 3 kg of rice and 5 kg of flour ?", + "Output Program": [ + "n0 = 10.0\nn1 = 24.0\nn2 = 6.0\nn3 = 2.0\nn4 = 22.0\nn5 = 4.0\nn6 = 3.0\nn7 = 5.0\nt0 = n1 / n0\nt1 = n2 * n4\nt2 = n4 * n7\nt3 = t1 / n3\nt4 = t0 * t3\nt5 = n6 * t3\nt6 = n5 * t4\nt7 = t6 + t5\nanswer = t7 + t2\nprint(answer)" + ], + "Output Answer": [ + "941.6" + ], + "split": "train" + }, + { + "Input": "765 chairs are to be arranged in a column in such a way that the number of chairs in each column should be equal to the columns . how many chairs will be excluded to make this arrangement possible ?", + "Output Program": [ + "n0 = 765.0\nt0 = n0 - 12.0\nt1 = t0 - 12.0\nt2 = t1 - 12.0\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "in a group of ducks and cows , the total number of legs are 30 more than twice the no . of heads . find the total no . of buffaloes .", + "Output Program": [ + "n0 = 30.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "there are 780 male and female participants in a meeting . half the female participants and one - quarter of the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?", + "Output Program": [ + "n0 = 780.0\nt0 = n0 / 3.0\nt1 = t0 * 4.0\nt2 = t1 - n0\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "130" + ], + "split": "train" + }, + { + "Input": "a man is 34 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ?", + "Output Program": [ + "n0 = 34.0\nt0 = 2.0 * 2.0\nt1 = 2.0 - 1.0\nt2 = t0 - 2.0\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "a jogger running at 9 km / hr along side a railway track is 240 m ahead of the engine of a 130 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?", + "Output Program": [ + "n0 = 9.0\nn1 = 240.0\nn2 = 130.0\nn3 = 45.0\nt0 = n1 + n2\nt1 = 10.0 / 2.0\nt2 = n3 - n0\nt3 = t2 / 2.0\nt4 = t1 / t3\nt5 = t4 * t2\nanswer = t0 / t5\nprint(answer)" + ], + "Output Answer": [ + "37" + ], + "split": "train" + }, + { + "Input": "if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer m that must divide n is ?", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 72.0\nt0 = n1 / n0\nt1 = math.sqrt(max(0, t0))\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "one - fourth of the workers in palabras bookstore have read the latest book by j . saramago , and 5 / 8 of the workers have read the latest book by h . kureishi . the number of workers that have read neither book is one less than the number of the workers that have read the latest saramago book and have not read the latest kureishi book . if there are 72 workers in the palabras bookstore , how many of them have read both books ?", + "Output Program": [ + "n0 = 5.0\nn1 = 8.0\nn2 = 72.0\nt0 = n2 / 4.0\nt1 = n2 / n1\nt2 = t0 + t0\nt3 = n0 * t1\nt4 = t2 + t3\nt5 = t4 - n2\nt6 = t5 - 1.0\nanswer = t6 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "sakshi invests a part of rs . 12000 in 12 % stock at rs . 120 and the remainder in 15 % stock at rs . 125 . if his total dividend per annum is rs . 1360 , how much does he invest in 12 % stock at rs . 120 ?", + "Output Program": [ + "n0 = 12000.0\nn1 = 12.0\nn2 = 120.0\nn3 = 15.0\nn4 = 125.0\nn5 = 1360.0\nn6 = 12.0\nn7 = 120.0\nt0 = n3 / n4\nt1 = n1 / n2\nt2 = n0 * t0\nt3 = t1 - t0\nt4 = n5 - t2\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "4000.000000000002" + ], + "split": "train" + }, + { + "Input": "xavier , yvonne , and zelda each try independently to solve a problem . if their individual probabilities for success are 1 / 5 , 1 / 2 and 5 / 8 , respectively , what is the probability that xavier and yvonne , but not zelda , will solve the problem ?", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 1.0\nn3 = 2.0\nn4 = 5.0\nn5 = 8.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = n4 / n5\nt3 = t0 * t1\nt4 = n0 - t2\nanswer = t3 * t4\nprint(answer)" + ], + "Output Answer": [ + "0.037500000000000006" + ], + "split": "train" + }, + { + "Input": "the tax on a commodity is diminished by 18 % and its consumption increased by 15 % . the effect on revenue is ?", + "Output Program": [ + "n0 = 18.0\nn1 = 15.0\nt0 = n1 / 100.0\nt1 = n0 / 100.0\nt2 = t0 + 1.0\nt3 = 1.0 - t1\nt4 = t2 * t3\nt5 = t4 * 100.0\nanswer = 100.0 - t5\nprint(answer)" + ], + "Output Answer": [ + "5.700000000000003" + ], + "split": "train" + }, + { + "Input": "on thrusday mabel handled 90 transactions . anthony handled 10 % more transaction than mabel , cal handled 2 / 3 rds of the transactions that anthony handled and jade handled 16 more transaction than cal . how much transaction did jade handled ?", + "Output Program": [ + "n0 = 90.0\nn1 = 10.0\nn2 = 2.0\nn3 = 3.0\nn4 = 16.0\nt0 = n0 / n1\nt1 = n0 + t0\nt2 = n2 * t1\nt3 = t2 / n3\nanswer = n4 + t3\nprint(answer)" + ], + "Output Answer": [ + "82" + ], + "split": "train" + }, + { + "Input": "a cement mixture is composed of 3 elements . by weight , 1 / 3 of the mixture is sand , 1 / 4 of the mixture is water , and the remaining 10 pounds of the mixture is gravel . what is the weight of the entire mixture in pounds ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 3.0\nn3 = 1.0\nn4 = 4.0\nn5 = 10.0\nt0 = n1 / n2\nt1 = n3 / n4\nt2 = t0 + t1\nt3 = n1 - t2\nanswer = n5 / t3\nprint(answer)" + ], + "Output Answer": [ + "23.999999999999996" + ], + "split": "train" + }, + { + "Input": "9 persons went to a hotel for taking their meals . 8 of them spent rs 12 each on their meals and the ninth spent rs . 8 more than the average expenditure of all the 9 . what was the total money spent by them ?", + "Output Program": [ + "n0 = 9.0\nn1 = 8.0\nn2 = 12.0\nn3 = 8.0\nn4 = 9.0\nt0 = n1 * n2\nt1 = n0 - 1.0\nt2 = n1 + t0\nt3 = t2 / t1\nanswer = n0 * t3\nprint(answer)" + ], + "Output Answer": [ + "117" + ], + "split": "train" + }, + { + "Input": "3 buffaloes eat as much as 4 cows or 2 oxen . at a farm , there are 15 buffaloes , 8 oxen , and 24 cows . the fodder for these cattle is available for 36 days . if 40 more cows and 15 more buffaloes are brought in , how many days will the fodder last ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 2.0\nn3 = 15.0\nn4 = 8.0\nn5 = 24.0\nn6 = 36.0\nn7 = 40.0\nn8 = 15.0\nt0 = n3 + n8\nt1 = n5 + n7\nt2 = n5 / n1\nt3 = n4 / n2\nt4 = t1 / n1\nt5 = n0 * t2\nt6 = n0 * t3\nt7 = n3 + t5\nt8 = n0 * t4\nt9 = t7 + t6\nt10 = t0 + t8\nt11 = t10 + t6\nt12 = n6 * t9\nanswer = t12 / t11\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "the greatest common divisor of ( b - 2 ) ! , ( b + 1 ) ! , and ( b + 4 ) ! is 5040 . what is the value of b ?", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 4.0\nn3 = 5040.0\nt0 = n2 + n2\nanswer = n1 + t0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "if a : b = 1 : 4 , b : c = 13 : 9 , c : d = 5 : 13 , find a : d ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 13.0\nn3 = 9.0\nn4 = 5.0\nn5 = 13.0\nt0 = n0 * n2\nt1 = n1 * n3\nt2 = n4 * t0\nt3 = n2 * t1\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.1388888888888889" + ], + "split": "train" + }, + { + "Input": "what is the smallest integer z for which 27 ^ z > 3 ^ 24 ?", + "Output Program": [ + "import math\nn0 = 27.0\nn1 = 3.0\nn2 = 24.0\nt0 = n2 / 3.0\nt1 = math.floor(t0)\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "the sum of two numbers is 21 and the sum of their squares is 527 . find the product of the numbers .", + "Output Program": [ + "n0 = 21.0\nn1 = 527.0\nt0 = n0**min(2.0, 5)\nt1 = n1 - t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "43" + ], + "split": "train" + }, + { + "Input": "thabo owns exactly 280 books , and each book is either paperback fiction , paperback nonfiction , or hardcover nonfiction . if he owns 20 more paperback nonfiction books than hardcover nonfiction books , and twice as many paperback fiction books as paperback nonfiction books , how many hardcover books nonfiction books does thabo own ?", + "Output Program": [ + "n0 = 280.0\nn1 = 20.0\nt0 = n0 + n1\nt1 = t0 / 4.0\nanswer = t1 - n1\nprint(answer)" + ], + "Output Answer": [ + "55" + ], + "split": "train" + }, + { + "Input": "in the number 100 ab , a and b represent the tens and units digits , respectively . if 110 ab is divisible by 55 , what is the greatest possible value of b \u00d7 a ?", + "Output Program": [ + "n0 = 100.0\nn1 = 110.0\nn2 = 55.0\nt0 = n1 / 10.0\nt1 = n2 / t0\nt2 = t1 - 2.0\nanswer = t1 * t2\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "the average weight of a , b and c is 30 kg . if the average weight of a and b be 25 kg and that of b and c be 28 kg , then the weight of b is :", + "Output Program": [ + "n0 = 30.0\nn1 = 25.0\nn2 = 28.0\nt0 = n1 * 2.0\nt1 = n2 * 2.0\nt2 = n0 * 3.0\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "the cost of a one - family home was $ 120000 in 1980 . in 1988 , the price had increased to $ 192000 . what was the percent increase in the cost of the home ?", + "Output Program": [ + "n0 = 120000.0\nn1 = 1980.0\nn2 = 1988.0\nn3 = 192000.0\nt0 = n3 / n0\nt1 = t0 - 1.0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "60.00000000000001" + ], + "split": "train" + }, + { + "Input": "how much water should be added to 11 liters of a 20 % - solution of alcohol to reduce the concentration of alcohol in the solution by 75 % ?", + "Output Program": [ + "n0 = 11.0\nn1 = 20.0\nn2 = 75.0\nt0 = n2 / 100.0\nt1 = 100.0 * 2.0\nt2 = n1 * t0\nt3 = n1 - t2\nt4 = t1 / t3\nanswer = t4 - n0\nprint(answer)" + ], + "Output Answer": [ + "29" + ], + "split": "train" + }, + { + "Input": "10 camels cost as much as 24 horses , 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants . if the cost of 10 elephants is rs . 130000 , find the cost of a camel ?", + "Output Program": [ + "n0 = 10.0\nn1 = 24.0\nn2 = 16.0\nn3 = 4.0\nn4 = 6.0\nn5 = 4.0\nn6 = 10.0\nn7 = 130000.0\nt0 = n1 * n3\nt1 = n0 * n2\nt2 = n3 * t0\nt3 = n4 * t1\nt4 = n7 * t2\nt5 = n0 * t3\nanswer = t4 / t5\nprint(answer)" + ], + "Output Answer": [ + "5200" + ], + "split": "train" + }, + { + "Input": "if an amount of rs 42,900 is distributed equally amongst 22 persons , how much amount would each person get ?", + "Output Program": [ + "n0 = 42900.0\nn1 = 22.0\nt0 = 10.0 * 4.0\nt1 = t0 + 3.0\nt2 = t1 * 1000.0\nt3 = t2 - 100.0\nanswer = t3 / n1\nprint(answer)" + ], + "Output Answer": [ + "1950" + ], + "split": "train" + }, + { + "Input": "a dozen eggs and 10 pounds of oranges are currently at the same price . if the price of a dozen eggs rises by 9 percent and the price of oranges rises by 6 % . how much more will it cost to buy a dozen eggs and 10 pounds of oranges .", + "Output Program": [ + "n0 = 10.0\nn1 = 9.0\nn2 = 6.0\nn3 = 10.0\nt0 = n3 + n3\nt1 = n1 / 100.0\nt2 = n2 / 100.0\nt3 = t1 * n3\nt4 = n3 * t2\nt5 = n3 + t3\nt6 = n3 + t4\nt7 = t5 + t6\nt8 = t7 - t0\nt9 = t8 * 100.0\nt10 = t9 / t0\nanswer = t10 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "in a river flowing at 2 km / hr , a boat travels 48 km upstream and then returns downstream to the starting point . if its speed in still water be 6 km / hr , find the total journey time .", + "Output Program": [ + "n0 = 2.0\nn1 = 48.0\nn2 = 6.0\nt0 = n0 + n2\nt1 = n2 - n0\nt2 = n1 / t1\nt3 = n1 / t0\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "in smithtown , the ratio of right - handed people to left - handed people is 3 to 1 and the ratio of men to women is 3 to 2 . if the number of right - handed men is maximized , then what x percent of all the people in smithtown are left - handed women ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 3.0\nn3 = 2.0\nt0 = n0 + n1\nt1 = n0 + n3\nt2 = t0 / t1\nt3 = n3 * t2\nt4 = n0 * t2\nt5 = n0 - t4\nt6 = t3 - t5\nt7 = t6 / t0\nanswer = t7 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "25.00000000000001" + ], + "split": "train" + }, + { + "Input": "a row of ants comprised of 102 ants . a man walked upon it and all except 42 were crushed beneath his foot . how many ants are left alive ?", + "Output Program": [ + "n0 = 102.0\nn1 = 42.0\n\nanswer = n1 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "at a certain food stand , the price of each apple is 40 \u00a2 and the price of each orange is 60 \u00a2 . mary selects a total of 10 apples and oranges from the food stand , and the average ( arithmetic mean ) price of the 10 pieces of fruit is 54 \u00a2 . how many oranges must mary put back so that the average price of the pieces of fruit that she keeps is 45 \u00a2 ?", + "Output Program": [ + "n0 = 40.0\nn1 = 60.0\nn2 = 10.0\nn3 = 10.0\nn4 = 54.0\nn5 = 45.0\nt0 = n1 * n2\nt1 = n2 * n4\nt2 = n2 * n5\nt3 = n1 - n0\nt4 = n1 - n5\nt5 = t0 - t1\nt6 = t5 / t3\nt7 = n0 * t6\nt8 = n2 - t6\nt9 = n1 * t8\nt10 = t7 + t9\nt11 = t10 - t2\nanswer = t11 / t4\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "for all integers x > 1 . < x > = 2 x + ( 2 x - 1 ) + ( 2 x - 2 ) + . . . . . . 2 + 1 . what is the value of < 2 > * < 4 > ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 2.0\nn3 = 1.0\nn4 = 2.0\nn5 = 2.0\nn6 = 2.0\nn7 = 1.0\nn8 = 2.0\nn9 = 4.0\nt0 = n1 * 4.0\nt1 = n1 * 2.0\nt2 = t0 - 1.0\nt3 = t0 - 2.0\nt4 = t0 - 3.0\nt5 = t0 - 4.0\nt6 = t1 - 1.0\nt7 = t1 - 2.0\nt8 = t1 - 3.0\nt9 = t0 + t2\nt10 = t1 + t6\nt11 = t0 - t4\nt12 = t0 - t3\nt13 = t0 - t2\nt14 = t9 + t3\nt15 = t10 + t7\nt16 = t14 + t4\nt17 = t15 + t8\nt18 = t16 + t5\nt19 = t18 + t11\nt20 = t19 + t12\nt21 = t20 + t13\nanswer = t21 * t17\nprint(answer)" + ], + "Output Answer": [ + "360" + ], + "split": "train" + }, + { + "Input": "pradeep has to obtain 35 % of the total marks to pass . he got 150 marks and failed by 25 marks . the maximum marks are", + "Output Program": [ + "n0 = 35.0\nn1 = 150.0\nn2 = 25.0\nt0 = n1 + n2\nt1 = n0 / 100.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "500.00000000000006" + ], + "split": "train" + }, + { + "Input": "rs . 1210 were divided among 3 person p , q , r so that p : q = 5 : 4 and q : r = 9 : 10 . then r gets the amount .", + "Output Program": [ + "n0 = 1210.0\nn1 = 3.0\nn2 = 5.0\nn3 = 4.0\nn4 = 9.0\nn5 = 10.0\nt0 = n2 / n3\nt1 = n5 / n4\nt2 = t0 + t1\nt3 = t2 + 1.0\nt4 = n0 / t3\nanswer = t4 * t1\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "train" + }, + { + "Input": "if a 2 + b 2 + c 2 = 390 and ab + bc + ca = 5 , then a + b + c is", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 2.0\nn2 = 2.0\nn3 = 390.0\nn4 = 5.0\nt0 = n4 * 2.0\nt1 = n3 + t0\nanswer = math.sqrt(max(0, t1))\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "a man has some hens and cows . if the number of heads be 48 and the number of feet equals 140 , then the number of hens will be", + "Output Program": [ + "n0 = 48.0\nn1 = 140.0\nt0 = n0 * 4.0\nt1 = t0 - n1\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "the cash realised on selling a 14 % stock is rs . 120.50 , brokerage being 1 / 4 % is", + "Output Program": [ + "n0 = 14.0\nn1 = 120.5\nn2 = 1.0\nn3 = 4.0\nt0 = n2 / n3\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "120.25" + ], + "split": "train" + }, + { + "Input": "a trained covered x km at 40 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 4 x km .", + "Output Program": [ + "n0 = 40.0\nn1 = 2.0\nn2 = 20.0\nn3 = 4.0\nt0 = n0 / n0\nt1 = n0 * n3\nt2 = n0 * n1\nt3 = t2 / n2\nt4 = t0 + t3\nanswer = t1 / t4\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "find the sum lend at c . i . at 5 p . c per annum will amount to rs . 240 in 2 years ?", + "Output Program": [ + "n0 = 5.0\nn1 = 240.0\nn2 = 2.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nt2 = t1**min(n2, 5)\nanswer = n1 / t2\nprint(answer)" + ], + "Output Answer": [ + "217.68707482993196" + ], + "split": "train" + }, + { + "Input": "average of money that group of 4 friends pay for rent each month is $ 800 . after one persons rent is increased by 20 % the new mean is $ 880 . what was original rent of friend whose rent is increased ?", + "Output Program": [ + "n0 = 4.0\nn1 = 800.0\nn2 = 20.0\nn3 = 880.0\nt0 = n2 / 100.0\nt1 = n3 - n1\nt2 = n0 * t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "1600" + ], + "split": "train" + }, + { + "Input": "when a student joe , weighing 43 kg , joins a group of students whose average weight is 30 kg , the average weight goes up by 1 kg . subsequently , if two students , excluding joe , leave the group the average weight comes back to 30 kg . what is the difference between the average weight of the two students who left and the weight of joe ?", + "Output Program": [ + "n0 = 43.0\nn1 = 30.0\nn2 = 1.0\nn3 = 30.0\nt0 = n1 + n2\nt1 = n0 - t0\nt2 = n1 * t1\nt3 = t1 - n2\nt4 = n0 + t2\nt5 = n1 * t3\nt6 = t4 - t5\nt7 = t6 / 2.0\nanswer = n0 - t7\nprint(answer)" + ], + "Output Answer": [ + "6.5" + ], + "split": "train" + }, + { + "Input": "in a certain diving competition , 5 judges score each dive on a scale from 1 to 10 . the point value of the dive is obtained by dropping the highest score and the lowest score and multiplying the sum of the remaining scores by the degree of difficulty . if a dive with a degree of difficulty of 3.2 received scores of 7.5 , 8.3 , 9.0 , 6.0 , and 8.6 , what was the point value of the dive ?", + "Output Program": [ + "n0 = 5.0\nn1 = 1.0\nn2 = 10.0\nn3 = 3.2\nn4 = 7.5\nn5 = 8.3\nn6 = 9.0\nn7 = 6.0\nn8 = 8.6\nt0 = n4 + n5\nt1 = n8 + t0\nanswer = n3 * t1\nprint(answer)" + ], + "Output Answer": [ + "78.08" + ], + "split": "train" + }, + { + "Input": "the 3 digits of a number add up to 11 . the number is divisible by 5 . the leftmost digit is double the middle digit . what is the product of the 3 digits ?", + "Output Program": [ + "n0 = 3.0\nn1 = 11.0\nn2 = 5.0\nn3 = 3.0\nt0 = n1 - n2\nt1 = t0 / n0\nt2 = t1 * 2.0\nt3 = t1 * t2\nanswer = n2 * t3\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "if a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20 , what is the probability t that this product will be a multiple of 45 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 20.0\nn2 = 45.0\nt0 = n1 + 4.0\nanswer = 1.0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.041666666666666664" + ], + "split": "train" + }, + { + "Input": "10 ^ ( 655 ) \u00e3 \u00b7 10 ^ ( 650 ) = ?", + "Output Program": [ + "n0 = 10.0\nn1 = 655.0\nn2 = 10.0\nn3 = 650.0\nt0 = n1 - n3\nanswer = n0**min(t0, 5)\nprint(answer)" + ], + "Output Answer": [ + "100000" + ], + "split": "train" + }, + { + "Input": "the average ( arithmetic mean ) of 16 students first quiz scores in a difficult english class is 62.5 . when one student dropped the class , the average of the remaining scores increased to 62.0 . what is the quiz score of the student who dropped the class ?", + "Output Program": [ + "n0 = 16.0\nn1 = 62.5\nn2 = 62.0\nt0 = n0 * n1\nt1 = n0 - 1.0\nt2 = n2 * t1\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "train" + }, + { + "Input": "what is the least number that should be added to 1076 , so the sum of the number is divisible by 23 ?", + "Output Program": [ + "import math\nn0 = 1076.0\nn1 = 23.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = t1 + 1.0\nt3 = t2 - t0\nanswer = n1 * t3\nprint(answer)" + ], + "Output Answer": [ + "5.000000000000043" + ], + "split": "train" + }, + { + "Input": "the sum of two numbers is 40 and their product is 375 . what will be the sum of their reciprocals ?", + "Output Program": [ + "n0 = 40.0\nn1 = 375.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.10666666666666667" + ], + "split": "train" + }, + { + "Input": "how many quarters are equal to 5 dollars ?", + "Output Program": [ + "n0 = 5.0\n\nanswer = n0 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "during a particular baseball game , the probability of a team ' s pitcher throwing a strike on each throw is 2 / 5 . what is the least number of times that the pitcher should pitch the ball that will increase the probability of getting a strike at least once to more than 50 % .", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 50.0\nt0 = n2 / 100.0\nt1 = n0 / n1\nt2 = t0 * t1\nanswer = t2 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a batsman scored 120 runs which included 5 boundaries and 5 sixes . what percent of his total score did he make by running between the wickets ?", + "Output Program": [ + "n0 = 120.0\nn1 = 5.0\nn2 = 5.0\nt0 = n1 * n2\nt1 = n1 * n2\nt2 = t0 + t1\nt3 = n0 - t2\nt4 = t3 / n0\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "58.333333333333336" + ], + "split": "train" + }, + { + "Input": "in a certain egg - processing plant , every egg must be inspected , and is either accepted for processing or rejected . for every 96 eggs accepted for processing , 4 eggs are rejected . if , on a particular day , 12 additional eggs were accepted , but the overall number of eggs inspected remained the same , the ratio of those accepted to those rejected would be 99 to 1 . how many r eggs does the plant process per day ?", + "Output Program": [ + "n0 = 96.0\nn1 = 4.0\nn2 = 12.0\nn3 = 99.0\nn4 = 1.0\nt0 = n3 - n0\nt1 = n2 / t0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "train" + }, + { + "Input": "if 2 x + y = 7 and x + 2 y = 5 , then 2 xy / 3 = ?", + "Output Program": [ + "n0 = 2.0\nn1 = 7.0\nn2 = 2.0\nn3 = 5.0\nn4 = 2.0\nn5 = 3.0\nt0 = n0 * n1\nt1 = n0 * n0\nt2 = t0 - n3\nt3 = t1 - 1.0\nt4 = t2 / t3\nt5 = n0 * t4\nt6 = n1 - t5\nt7 = t4 + t6\nanswer = t7 / n4\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a container contains 40 litres of milk . from this container 4 litres of milk was taken out and replaced by water . this process was repeated further two times . how much milk is now contained by the container ?", + "Output Program": [ + "n0 = 40.0\nn1 = 4.0\nt0 = n1 / n0\nt1 = 1.0 - t0\nt2 = t1**min(3.0, 5)\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "29.160000000000004" + ], + "split": "train" + }, + { + "Input": "if 3 a \u2013 2 b \u2013 2 c = 30 and \u221a 3 a - \u221a ( 2 b + 2 c ) = 4 , what is the value of a + b + c ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 2.0\nn3 = 30.0\nn4 = 3.0\nn5 = 2.0\nn6 = 2.0\nn7 = 4.0\nt0 = n3 - n7\nt1 = t0 - n7\nt2 = t1 - n2\nt3 = t2 - n2\nt4 = t3 - 1.0\nt5 = t4 - n1\nt6 = t5 - 1.0\nt7 = n2 + t6\nt8 = t7 - n1\nanswer = t8 - n7\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "a , b and c have rs . 350 between them , a and c together have rs . 200 and b and c rs . 350 . how much does c have ?", + "Output Program": [ + "n0 = 350.0\nn1 = 200.0\nn2 = 350.0\nt0 = n1 + n2\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "train" + }, + { + "Input": "linda spent 2 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 300 , what were her original savings ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 300.0\nt0 = n0 / n1\nt1 = 1.0 - t0\nanswer = n2 / t1\nprint(answer)" + ], + "Output Answer": [ + "600" + ], + "split": "train" + }, + { + "Input": "point ( m , n ) is on the circle represented by m ^ 2 + n ^ 2 = 10 , and m , n are integers . how many such points are possible ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 10.0\nt0 = n0**min(n0, 5)\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a soft drink company had 5000 small and 12000 big bottles in storage . if 15 % of small 18 % of big bottles have been sold , then the total bottles remaining in storage is", + "Output Program": [ + "n0 = 5000.0\nn1 = 12000.0\nn2 = 15.0\nn3 = 18.0\nt0 = n0 + n1\nt1 = n2 / 100.0\nt2 = n3 / 100.0\nt3 = n0 * t1\nt4 = n1 * t2\nt5 = t3 + t4\nanswer = t0 - t5\nprint(answer)" + ], + "Output Answer": [ + "14090" + ], + "split": "train" + }, + { + "Input": "4 - fifths of 3 - eighths of a number is 24 . what is 250 per cent of that number ?", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 24.0\nn3 = 250.0\nt0 = 1.0 + 4.0\nt1 = 4.0 + 4.0\nt2 = n3 / 100.0\nt3 = n0 / t0\nt4 = n1 / t1\nt5 = t3 * t4\nt6 = n2 / t5\nanswer = t6 * t2\nprint(answer)" + ], + "Output Answer": [ + "199.99999999999997" + ], + "split": "train" + }, + { + "Input": "find the mean proportional between 7921 & 9409 ?", + "Output Program": [ + "n0 = 7921.0\nn1 = 9409.0\nt0 = n0 + n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "8665" + ], + "split": "train" + }, + { + "Input": "martin bought 5 packet milk at an average price ( arithmetic mean ) of 20 \u00a2 . if martin returned two packet to the retailer , and the average price of the remaining millk packet was 12 \u00a2 , then what is the average price , in cents , of the two returned milk packets ?", + "Output Program": [ + "n0 = 5.0\nn1 = 20.0\nn2 = 12.0\nt0 = n0 * n1\nt1 = n0 - 2.0\nt2 = n2 * t1\nt3 = t0 - t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "diana is painting statues . she has 7 / 8 of a gallon of paint remaining . each statue requires 1 / 8 gallon of paint . how many statues can she paint ?", + "Output Program": [ + "n0 = 7.0\nn1 = 8.0\nn2 = 1.0\nn3 = 8.0\nt0 = n0 / n1\nt1 = n2 / n3\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "a cyclist rides a bicycle 8 km at an average speed of 11 km / hr and again travels 11 km at an average speed of 8 km / hr . what is the average speed for the entire trip ?", + "Output Program": [ + "n0 = 8.0\nn1 = 11.0\nn2 = 11.0\nn3 = 8.0\nt0 = n0 + n1\nt1 = n0 / n1\nt2 = n1 / n0\nt3 = t1 + t2\nanswer = t0 / t3\nprint(answer)" + ], + "Output Answer": [ + "9.037837837837836" + ], + "split": "train" + }, + { + "Input": "how many numbers from 13 to 76 are exactly divisible by 10 ?", + "Output Program": [ + "import math\nn0 = 13.0\nn1 = 76.0\nn2 = 10.0\nt0 = n1 / n2\nt1 = n0 / n2\nt2 = math.floor(t0)\nt3 = math.floor(t1)\nt4 = t3 + 1.0\nt5 = n2 * t2\nt6 = n2 * t4\nt7 = t5 - t6\nt8 = t7 / n2\nanswer = t8 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "among all sales staff at listco corporation , college graduates and those without college degrees are equally represented . each sales staff member is either a level - 1 or level - 2 employee . level - 1 college graduates account for 15 % of listco ' s sales staff . listco employs 60 level - 1 employees , 30 of whom are college graduates . how many sales staff members without college degrees are level - 2 employees ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 1.0\nn3 = 15.0\nn4 = 60.0\nn5 = 1.0\nn6 = 30.0\nn7 = 2.0\nt0 = n3 / 100.0\nt1 = n6 / t0\nt2 = t1 - n4\nanswer = t2 / n1\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "train" + }, + { + "Input": "90 % of the population of a village is 8100 . the total population of the village is ?", + "Output Program": [ + "n0 = 90.0\nn1 = 8100.0\nt0 = 100.0 / n0\nanswer = n1 * t0\nprint(answer)" + ], + "Output Answer": [ + "9000" + ], + "split": "train" + }, + { + "Input": "a certain psychologist charges $ 40 more for the first hour of therapy than for each additional hour . if the total charge to a patient who receives 5 hours of therapy is $ 375 , what is the total charge to a patient who receives only 2 hours of therapy ?", + "Output Program": [ + "n0 = 40.0\nn1 = 5.0\nn2 = 375.0\nn3 = 2.0\nt0 = n2 - n0\nt1 = t0 / n1\nt2 = n3 * t1\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "174" + ], + "split": "train" + }, + { + "Input": "if the product 4864 * 9 p 2 is divisible by 12 , the value of p ?", + "Output Program": [ + "n0 = 4864.0\nn1 = 9.0\nn2 = 2.0\nn3 = 12.0\nt0 = n0 * n1\nt1 = n2 * t0\nt2 = t1 / n3\nanswer = t2 / t2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "how many multiples of 4 are there between 20 and 112 , inclusive ?", + "Output Program": [ + "n0 = 4.0\nn1 = 20.0\nn2 = 112.0\nt0 = n2 - n1\nt1 = t0 / n0\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "for any number z , z * is defined as the greatest positive even integer less than or equal to y . what is the value of 6.32 \u2013 6.32 * ?", + "Output Program": [ + "import math\nn0 = 6.32\nn1 = 6.32\nt0 = math.floor(n0)\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "0.3200000000000003" + ], + "split": "train" + }, + { + "Input": "the total age of a and b is 18 years more than the total age of b and c . c is how many years younger than a ?", + "Output Program": [ + "n0 = 18.0\n\nanswer = n0 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "if x is divided by 7 , the remainder is 5 . what is the remainder if 4 x is divided by 7 ?", + "Output Program": [ + "n0 = 7.0\nn1 = 5.0\nn2 = 4.0\nn3 = 7.0\nt0 = n0 * n2\nt1 = t0 + 10.0\nt2 = t1 + 10.0\nt3 = t2 / n2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "the average weight of 4 person ' s increases by 3 kg when a new person comes in place of one of them weighing 70 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 70.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "82" + ], + "split": "train" + }, + { + "Input": "the no . of girls in a class are 7 times the no . of boys , which value cannever be the of total students ?", + "Output Program": [ + "n0 = 7.0\nt0 = n0 + 1.0\nt1 = t0 * 4.0\nanswer = t1 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "john want to buy a $ 100 trouser at the store , but he think it \u2019 s too expensive . finally , it goes on sale for $ 50 . what is the percent decrease ?", + "Output Program": [ + "n0 = 100.0\nn1 = 50.0\n\nanswer = n0 - n1\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "what least number should be subtracted from 2590 so that the remainder when divided by 9 , 11 , and 13 will leave in each case the same remainder 6 ?", + "Output Program": [ + "n0 = 2590.0\nn1 = 9.0\nn2 = 11.0\nn3 = 13.0\nn4 = 6.0\nt0 = n1 * n2\nt1 = n3 * t0\nt2 = t1 * 2.0\nt3 = n4 + t2\nanswer = n0 - t3\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "for each of her sales , a saleswoman receives a commission equal to 20 percent of the first $ 500 of the total amount of the sale , plus 25 percent of the total amount in excess of $ 500 . if the total amount of one of her sales was $ 800 , the saleswoman \u2019 s commission was approximately what percent of the total amount of the sale ?", + "Output Program": [ + "n0 = 20.0\nn1 = 500.0\nn2 = 25.0\nn3 = 500.0\nn4 = 800.0\nt0 = n0 / 100.0\nt1 = n2 / 100.0\nt2 = n4 - n1\nt3 = n1 * t0\nt4 = t1 * t2\nt5 = t3 + t4\nt6 = t5 / n4\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "21.875" + ], + "split": "train" + }, + { + "Input": "in the youth summer village there are 100 people , 50 of them are not working , 25 of them have families and 75 of them like to sing in the shower . what is the largest possible number of people in the village , which are working , that do n ' t have families and that are singing in the shower ?", + "Output Program": [ + "n0 = 100.0\nn1 = 50.0\nn2 = 25.0\nn3 = 75.0\nt0 = n1 + n2\nt1 = n3 + t0\nanswer = t1 - n0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 percent of the distribution lies within one standard deviation d of the mean , what percent j of the distribution is less than m + d ?", + "Output Program": [ + "n0 = 68.0\nt0 = 100.0 - n0\nt1 = t0 / 2.0\nanswer = 100.0 - t1\nprint(answer)" + ], + "Output Answer": [ + "84" + ], + "split": "train" + }, + { + "Input": "in a 4 person race , medals are awarded to the fastest 3 runners . the first - place runner receives a gold medal , the second - place runner receives a silver medal , and the third - place runner receives a bronze medal . in the event of a tie , the tied runners receive the same color medal . ( for example , if there is a two - way tie for first - place , the top two runners receive gold medals , the next - fastest runner receives a silver medal , and no bronze medal is awarded ) . assuming that exactly 3 medals are awarded , and that the 3 medal winners stand together with their medals to form a victory circle , how many z different victory circles are possible ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 3.0\nn2 = 3.0\nn3 = 3.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(2.0)))\nt2 = math.factorial(min(15, int(n1)))\nt3 = t0 / t1\nt4 = t0 / t2\nt5 = t3 + t0\nt6 = t5 + t3\nanswer = t6 + t4\nprint(answer)" + ], + "Output Answer": [ + "52" + ], + "split": "train" + }, + { + "Input": "in the hillside summer camp there are 50 children . 90 % of the children are boys and the rest are girls . the camp administrator decided to make the number of girls only 5 % of the total number of children in the camp . how many more boys must she bring to make that happen ?", + "Output Program": [ + "n0 = 50.0\nn1 = 90.0\nn2 = 5.0\nt0 = n2 / 100.0\nt1 = 100.0 - n2\nt2 = t1 / 100.0\nt3 = n0 * t0\nt4 = n0 * t2\nanswer = t4 + t3\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "the sum of 3 consecutive multiples of 3 is 72 . what is the larget number ?", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 72.0\nt0 = n2 / n0\nanswer = n0 + t0\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "train" + }, + { + "Input": "a certain school implemented a reading program for its students , with the goal of getting each student to read 7 books per month year - round . if the school has c classes made up of s students in each class , how many books will the entire student body read in one year ?", + "Output Program": [ + "n0 = 7.0\n\nanswer = n0 * 12.0\nprint(answer)" + ], + "Output Answer": [ + "84" + ], + "split": "train" + }, + { + "Input": "george is 8 years more than christopher and ford is 2 years younger than christopher . the sum of their ages is 60 . find the ages of christopher .", + "Output Program": [ + "n0 = 8.0\nn1 = 2.0\nn2 = 60.0\nt0 = n0 - n1\nt1 = n2 - t0\nanswer = t1 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "10 ^ ( 65 ) \u00e3 \u00b7 10 ^ ( 64 ) = ?", + "Output Program": [ + "n0 = 10.0\nn1 = 65.0\nn2 = 10.0\nn3 = 64.0\nt0 = n1 - n3\nanswer = n0**min(t0, 5)\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the average of the marks of 11 students in a class is 36 . if the marks of each student are doubled , find the new average ?", + "Output Program": [ + "n0 = 11.0\nn1 = 36.0\n\nanswer = n1 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "train" + }, + { + "Input": "a large box contains 18 small boxes and each small box contains 28 chocolate bars . how many chocolate bars are in the large box ?", + "Output Program": [ + "n0 = 18.0\nn1 = 28.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "504" + ], + "split": "train" + }, + { + "Input": "if one root of the equation 2 x ^ 2 + 3 x \u2013 k = 0 is 5 , what is the value of k ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 3.0\nn3 = 0.0\nn4 = 5.0\nt0 = n2 * n4\nt1 = n4**min(n0, 5)\nt2 = n0 * t1\nanswer = t2 + t0\nprint(answer)" + ], + "Output Answer": [ + "65" + ], + "split": "train" + }, + { + "Input": "the closest approximation of q = ( 69.28 \u00d7 0.004 ) / 0.03 is", + "Output Program": [ + "n0 = 69.28\nn1 = 0.004\nn2 = 0.03\nt0 = n1 / n2\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "9.237333333333334" + ], + "split": "train" + }, + { + "Input": "in an office , totally there are 800 employees and 25 % of the total employees are males . 40 % of the males in the office are at - least 50 years old . find the number of males aged below 50 years ?", + "Output Program": [ + "n0 = 800.0\nn1 = 25.0\nn2 = 40.0\nn3 = 50.0\nn4 = 50.0\nt0 = n0 * n1\nt1 = 100.0 - n2\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nanswer = t2 * t3\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "if a certain number x is divided by 82 , the reminder is 5 . what is the reminder when x + 13 is divided by 41 ?", + "Output Program": [ + "n0 = 82.0\nn1 = 5.0\nn2 = 13.0\nn3 = 41.0\n\nanswer = n1 + n2\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "find the sum lend at c . i . at 5 p . c per annum will amount to rs . 341 in 2 years ?", + "Output Program": [ + "n0 = 5.0\nn1 = 341.0\nn2 = 2.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nt2 = t1**min(n2, 5)\nanswer = n1 / t2\nprint(answer)" + ], + "Output Answer": [ + "309.297052154195" + ], + "split": "train" + }, + { + "Input": "in a factory , an average of 50 tv ' s are produced per day for the fist 25 days of the months . a few workers fell ill for the next 5 days reducing the daily avg for the month to 45 sets / day . the average production per day for day last 5 days is ?", + "Output Program": [ + "n0 = 50.0\nn1 = 25.0\nn2 = 5.0\nn3 = 45.0\nn4 = 5.0\nt0 = n1 + n2\nt1 = n0 * n1\nt2 = n3 * t0\nt3 = t2 - t1\nanswer = t3 / n2\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "( 1.2 ) ( power 3 ) - ( 0.9 ) ( power 3 ) / ( 1.2 ) ( power 2 ) + 1.08 + ( 0.9 ) ( power 2 ) is :", + "Output Program": [ + "n0 = 1.2\nn1 = 3.0\nn2 = 0.9\nn3 = 3.0\nn4 = 1.2\nn5 = 2.0\nn6 = 1.08\nn7 = 0.9\nn8 = 2.0\nt0 = n0**min(n1, 5)\nt1 = n2**min(n1, 5)\nt2 = n0**min(n5, 5)\nt3 = n2**min(n5, 5)\nt4 = n6 + t2\nt5 = t0 - t1\nt6 = t4 + t3\nanswer = t5 / t6\nprint(answer)" + ], + "Output Answer": [ + "0.2999999999999999" + ], + "split": "train" + }, + { + "Input": "linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 200 , what were her original savings ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 200.0\nt0 = n0 / n1\nt1 = 1.0 - t0\nanswer = n2 / t1\nprint(answer)" + ], + "Output Answer": [ + "800" + ], + "split": "train" + }, + { + "Input": "at a restaurant , glasses are stored in two different - sized boxes . one box contains 12 glasses , and the other contains 16 glasses . if the average number of glasses per box is 15 , and there are 16 more of the larger boxes , what is the total number of glasses q at the restaurant ? ( assume that all boxes are filled to capacity . )", + "Output Program": [ + "n0 = 12.0\nn1 = 16.0\nn2 = 15.0\nn3 = 16.0\nt0 = n1 * 2.0\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "480" + ], + "split": "train" + }, + { + "Input": "a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 % of the distribution lies one standard deviation h of the mean , what percent of the distribution is less than m + h ?", + "Output Program": [ + "n0 = 68.0\nt0 = 100.0 - n0\nt1 = t0 / 2.0\nanswer = 100.0 - t1\nprint(answer)" + ], + "Output Answer": [ + "84" + ], + "split": "train" + }, + { + "Input": "what is the 4 digit number whose second digit is thrice the first digit and 3 rd digit is sum of 1 st and 2 nd and last digit is thrice the second digit .", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 1.0\nn3 = 2.0\nt0 = 10.0 * 100.0\nt1 = n2 * 3.0\nt2 = n2 + t1\nt3 = t1 * 100.0\nt4 = t1 * 3.0\nt5 = t0 + t3\nt6 = t2 * 10.0\nt7 = t5 + t6\nanswer = t7 + t4\nprint(answer)" + ], + "Output Answer": [ + "1349" + ], + "split": "train" + }, + { + "Input": "rs . 525 among a , b and c such that b may get 2 / 3 of a and c together get . find the share of c ?", + "Output Program": [ + "n0 = 525.0\nn1 = 2.0\nn2 = 3.0\nt0 = n0 / n2\nt1 = t0 - 100.0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "train" + }, + { + "Input": "the difference in compound interest earned on a deposit ( compounded annually ) in year 1 and year 2 is $ 40 . had the interest rate been 3 times its present value , the difference c would have been how much ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 40.0\nn3 = 3.0\nt0 = n3 * n3\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "360" + ], + "split": "train" + }, + { + "Input": "the sum of the squares of two consecutive positive integers exceeds their product by 91 . find the integers ?", + "Output Program": [ + "import math\nn0 = 91.0\nt0 = n0 - 1.0\nt1 = t0 * 4.0\nt2 = t1 + 1.0\nt3 = math.sqrt(max(0, t2))\nt4 = t3 - 1.0\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "if a / b = 1 / 3 , b / c = 2 , c / d = 1 / 2 , d / e = 3 and e / f = 1 / 6 , then what is the value of abc / def ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 2.0\nn3 = 1.0\nn4 = 2.0\nn5 = 3.0\nn6 = 1.0\nn7 = 6.0\nt0 = n1 * n1\nt1 = n1 * n7\nt2 = n2 * t1\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.25" + ], + "split": "train" + }, + { + "Input": "in a maths test , students were asked to find 5 / 16 of a certain number . one of the students by mistake found 5 / 6 th of that number and his answer was 200 more than the correct answer . find the number .", + "Output Program": [ + "n0 = 5.0\nn1 = 16.0\nn2 = 5.0\nn3 = 6.0\nn4 = 200.0\nt0 = n1 * n4\nt1 = n0 * n1\nt2 = n0 * n3\nt3 = n3 * t0\nt4 = t1 - t2\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "384" + ], + "split": "train" + }, + { + "Input": "if 50 % of x is 20 less than 5 % of 500 , then x is ?", + "Output Program": [ + "n0 = 50.0\nn1 = 20.0\nn2 = 5.0\nn3 = 500.0\nt0 = n2 / 100.0\nt1 = n0 / 100.0\nt2 = n3 * t0\nt3 = t2 - n1\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "calculate the largest 4 digit number which is exactly divisible by 98 ?", + "Output Program": [ + "n0 = 4.0\nn1 = 98.0\nt0 = 100.0 + 2.0\nanswer = n1 * t0\nprint(answer)" + ], + "Output Answer": [ + "9996" + ], + "split": "train" + }, + { + "Input": "20 6 years ago , a father was 3 times as old as his son . now the father is only twice as old as his son . then the sum of the present ages of the son and the father is :", + "Output Program": [ + "n0 = 20.0\nn1 = 6.0\nn2 = 3.0\nt0 = n0 * n1\nt1 = n1 * n2\nt2 = t1 * 2.0\nanswer = t0 + t2\nprint(answer)" + ], + "Output Answer": [ + "156" + ], + "split": "train" + }, + { + "Input": "x varies inversely as square of y . given that y = 3 for x = 1 . the value of x for y = 6 will be equal to :", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 6.0\nt0 = n0**min(2.0, 5)\nt1 = n2**min(2.0, 5)\nt2 = n1 * t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.25" + ], + "split": "train" + }, + { + "Input": "each child has 3 crayons and 12 apples . if there are 6 children , how many crayons are there in total ?", + "Output Program": [ + "n0 = 3.0\nn1 = 12.0\nn2 = 6.0\n\nanswer = n0 * n2\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "find out the square of a number which when doubled exceeds its one fifth by 9 ?", + "Output Program": [ + "n0 = 9.0\nt0 = 1.0 + 4.0\nt1 = 1.0 / t0\nt2 = 2.0 - t1\nt3 = n0 / t2\nanswer = t3**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 50 paisa . if the share of y is rs . 18 , what is the total amount ?", + "Output Program": [ + "n0 = 45.0\nn1 = 50.0\nn2 = 18.0\nt0 = 100.0 / n0\nt1 = n1 / n0\nt2 = n2 * t0\nt3 = n2 * t1\nt4 = t2 + t3\nanswer = n2 + t4\nprint(answer)" + ], + "Output Answer": [ + "78" + ], + "split": "train" + }, + { + "Input": "in a certain game , each player scores either 2 points or 5 points . if n players score 2 points and m players score 5 points , and the total number of points scored is 50 , what is the least possible positive t difference between n and m ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 2.0\nn3 = 5.0\nn4 = 50.0\n\nanswer = n1 - n0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "if the average of 201 , 202 , 204 , 205 , 206 , 209 , 209 , 210 , 212 and x is 207 , what is the value of x ?", + "Output Program": [ + "n0 = 201.0\nn1 = 202.0\nn2 = 204.0\nn3 = 205.0\nn4 = 206.0\nn5 = 209.0\nn6 = 209.0\nn7 = 210.0\nn8 = 212.0\nn9 = 207.0\nt0 = n0 + n1\nt1 = n9 * 10.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nt5 = n5 + t4\nt6 = n5 + t5\nt7 = n7 + t6\nt8 = n8 + t7\nanswer = t1 - t8\nprint(answer)" + ], + "Output Answer": [ + "212" + ], + "split": "train" + }, + { + "Input": "in a group of cows and chickens , the number of legs was 20 more than twice the number of heads . the number of cows was :", + "Output Program": [ + "n0 = 20.0\nt0 = 4.0 - 2.0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the average marks in mathematics scored by the pupils of a school at the public examination were 39 . if 4 of these pupils who actually scored 25 , 12 , 15 and 19 marks at the examination had not been sent up , the average marks for the school would have been 44 . find the number of pupils sent up for examination from the school ?", + "Output Program": [ + "n0 = 39.0\nn1 = 4.0\nn2 = 25.0\nn3 = 12.0\nn4 = 15.0\nn5 = 19.0\nn6 = 44.0\nt0 = n2 + n3\nt1 = n1 * n6\nt2 = n6 - n0\nt3 = n4 + t0\nt4 = n5 + t3\nt5 = t1 - t4\nanswer = t5 / t2\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "a certain company has records stored with a record storage firm in 15 - inch by 12 - inch by 10 - inch boxes . the boxes occupy 1.08 million cubic inches of space . if the company pays $ 0.8 per box per month for the record storage , what is the total amount that the company pays each month for record storage ?", + "Output Program": [ + "n0 = 15.0\nn1 = 12.0\nn2 = 10.0\nn3 = 1.08\nn4 = 0.8\nt0 = n0 * n1\nt1 = n2 * t0\nt2 = t1 / 100.0\nt3 = t2 / 100.0\nt4 = t3 / 100.0\nt5 = n3 / t4\nanswer = n4 * t5\nprint(answer)" + ], + "Output Answer": [ + "480" + ], + "split": "train" + }, + { + "Input": "two trains of equal length are running on parallel lines in the same directions at 46 km / hr . and 36 km / hr . the faster trains pass the slower train in 108 seconds . the length of each train is :", + "Output Program": [ + "n0 = 46.0\nn1 = 36.0\nn2 = 108.0\nt0 = n0 - n1\nt1 = t0 * 1000.0\nt2 = t1 / 3600.0\nt3 = n2 * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "train" + }, + { + "Input": "the avg weight of a , b & c is 80 kg . if d joins the group , the avg weight of the group becomes 82 kg . if another man e who weights is 3 kg more than d replaces a , then the avgof b , c , d & e becomes 81 kg . what is the weight of a ?", + "Output Program": [ + "n0 = 80.0\nn1 = 82.0\nn2 = 3.0\nn3 = 81.0\nt0 = n1 * 4.0\nt1 = n3 * 4.0\nt2 = n0 * 3.0\nt3 = t0 - t2\nt4 = n2 + t3\nt5 = t1 - t4\nanswer = t0 - t5\nprint(answer)" + ], + "Output Answer": [ + "95" + ], + "split": "train" + }, + { + "Input": "if x is 30 percent more than y and y is 40 percent less than z , then x is what percent of z ?", + "Output Program": [ + "n0 = 30.0\nn1 = 40.0\nt0 = n0 / 100.0\nt1 = 100.0 - n1\nt2 = t0 + 1.0\nanswer = t2 * t1\nprint(answer)" + ], + "Output Answer": [ + "78" + ], + "split": "train" + }, + { + "Input": "if y > 0 , ( 7 y ) / 20 + ( 3 y ) / 10 is what percent of y ?", + "Output Program": [ + "n0 = 0.0\nn1 = 7.0\nn2 = 20.0\nn3 = 3.0\nn4 = 10.0\nt0 = n1 / n2\nt1 = n3 / n4\nt2 = t0 + t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "64.99999999999999" + ], + "split": "train" + }, + { + "Input": "the average of 15 numbers is 75 . average of the first 8 of them is 68 and that of the last 8.00001 is 77 . find the 8.000001 th number ?", + "Output Program": [ + "n0 = 15.0\nn1 = 75.0\nn2 = 8.0\nn3 = 68.0\nn4 = 8.00001\nn5 = 77.0\nn6 = 8.000001\nt0 = n5 * n6\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 - t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "35.00007699999992" + ], + "split": "train" + }, + { + "Input": "mr yadav spends 60 % of his monthly salary on consumable items and 50 % of the remaining on clothes and transport . he saves the remaining amount . if his savings at the end of the year were 48456 , how much amount per month would he have spent on clothes and transport ?", + "Output Program": [ + "n0 = 60.0\nn1 = 50.0\nn2 = 48456.0\nt0 = 3.0 * 4.0\nt1 = 100.0 - n0\nt2 = n1 * t1\nt3 = t2 / 100.0\nt4 = t3 / 100.0\nt5 = n2 / t4\nt6 = t5 / t0\nanswer = t6 * t4\nprint(answer)" + ], + "Output Answer": [ + "4038" + ], + "split": "train" + }, + { + "Input": "mother , her daughter and her grand child weighs 110 kg . daughter and her daughter ( child ) weighs 60 kg . child is 1 / 5 th of her grand mother . what is the age of the daughter ?", + "Output Program": [ + "n0 = 110.0\nn1 = 60.0\nn2 = 1.0\nn3 = 5.0\nt0 = n0 - n1\nt1 = t0 / n3\nanswer = n1 - t1\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "when a student joe , weighing 42 kg , joins a group of students whose average weight is 30 kg , the average weight goes up by 1 kg . subsequently , if two students , excluding joe , leave the group the average weight comes back to 30 kg . what is the difference between the average weight of the two students who left and the weight of joe ?", + "Output Program": [ + "n0 = 42.0\nn1 = 30.0\nn2 = 1.0\nn3 = 30.0\nt0 = n1 + n2\nt1 = n0 - t0\nt2 = n1 * t1\nt3 = t1 - 1.0\nt4 = n0 + t2\nt5 = n1 * t3\nt6 = t4 - t5\nt7 = t6 / 2.0\nanswer = n0 - t7\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "the sum of two numbers is 44 . 5 times one number is equal to 6 times the other . the smaller of the two numbers is", + "Output Program": [ + "n0 = 44.0\nn1 = 5.0\nn2 = 6.0\nt0 = n1 + n2\nt1 = n0 / t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "the average of temperatures at noontime from monday to friday is 50 ; the lowest one is 40 , what is the possible maximum range of the temperatures ?", + "Output Program": [ + "n0 = 50.0\nn1 = 40.0\nt0 = 2.0 + 3.0\nt1 = n1 * 4.0\nt2 = n0 * t0\nt3 = t2 - t1\nanswer = t3 - n1\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 30 paisa . if the share of y is rs . 36 , what is the total amount ?", + "Output Program": [ + "n0 = 45.0\nn1 = 30.0\nn2 = 36.0\nt0 = 100.0 / n0\nt1 = n1 / n0\nt2 = n2 * t0\nt3 = n2 * t1\nt4 = t2 + t3\nanswer = n2 + t4\nprint(answer)" + ], + "Output Answer": [ + "140" + ], + "split": "train" + }, + { + "Input": "a whale goes on a feeding frenzy that lasts for 9 hours . for the first hour he catches and eats x kilos of plankton . in every hour after the first , it consumes 3 kilos of plankton more than it consumed in the previous hour . if by the end of the frenzy the whale will have consumed a whopping accumulated total 270 kilos of plankton , how many kilos did he consume on the sixth hour ?", + "Output Program": [ + "n0 = 9.0\nn1 = 3.0\nn2 = 270.0\nt0 = n2 / n0\nanswer = n1 + t0\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "the ratio 15 : 25 expressed as percent equals to", + "Output Program": [ + "n0 = 15.0\nn1 = 25.0\nt0 = n0 / n1\nanswer = t0 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "a sum of money is sufficient to pay x ' s wages for 36 days and y ' s wages for 45 days . the same money is sufficient to pay the wages of both for ?", + "Output Program": [ + "n0 = 36.0\nn1 = 45.0\nt0 = 1.0 / n0\nt1 = 1.0 / n1\nt2 = t0 + t1\nanswer = 1 / t2\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "each week , harry is paid x dollars per hour for the first 12 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 41 hours if harry and james were paid the same amount last week , how many hours did harry work last week ?", + "Output Program": [ + "n0 = 12.0\nn1 = 1.5\nn2 = 40.0\nn3 = 2.0\nn4 = 41.0\nt0 = n2 + n3\nt1 = t0 - n0\nt2 = t1 / n1\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "in a mixture 60 litres , the ratio of milk and water 2 : 1 . if this ratio is to be 1 : 2 , then the quanity of water to be further added is :", + "Output Program": [ + "n0 = 60.0\nn1 = 2.0\nn2 = 1.0\nn3 = 1.0\nn4 = 2.0\nt0 = n1 + n2\nt1 = n0 / t0\nt2 = n0 - t1\nt3 = n1 * t2\nanswer = t3 - t1\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "the average of 10 consecutive integers is 16 . then , 9 is deducted from the first consecutive number , 8 is deducted from the second , 7 is deducted form the third , and so on until the last number which remains unchanged . what is the new average ?", + "Output Program": [ + "n0 = 10.0\nn1 = 16.0\nn2 = 9.0\nn3 = 8.0\nn4 = 7.0\nt0 = 1.0 + 4.0\nt1 = n0 * n1\nt2 = n2 * t0\nt3 = t1 - t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "11.5" + ], + "split": "train" + }, + { + "Input": "after 2 games , team b had an average of 61.5 points per game . if it got only 47 points in game 3 , how many more points does it need to score to get its total above 500 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 61.5\nn2 = 47.0\nn3 = 3.0\nn4 = 500.0\nt0 = n0 * n1\nt1 = n2 + t0\nanswer = n4 - t1\nprint(answer)" + ], + "Output Answer": [ + "330" + ], + "split": "train" + }, + { + "Input": "a millionaire bought a job lot of hats 1 / 4 of which were brown . the millionaire sold 2 / 3 of the hats including 4 / 5 of the brown hats . what fraction of the unsold hats were brown .", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 2.0\nn3 = 3.0\nn4 = 4.0\nn5 = 5.0\nt0 = n0 / n1\nt1 = n1 / n5\nt2 = n2 / n3\nt3 = 1.0 - t1\nt4 = 1.0 - t2\nt5 = t0 * t3\nanswer = t5 / t4\nprint(answer)" + ], + "Output Answer": [ + "0.14999999999999994" + ], + "split": "train" + }, + { + "Input": "{ ( 481 + 426 ) 2 - 4 x 481 x 426 } = ?", + "Output Program": [ + "n0 = 481.0\nn1 = 426.0\nn2 = 2.0\nn3 = 4.0\nn4 = 481.0\nn5 = 426.0\nt0 = n0 + n1\nt1 = n0 * n3\nt2 = n1 * t1\nt3 = t0**min(n2, 5)\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "3025" + ], + "split": "train" + }, + { + "Input": "sum of the squares of 3 no . ' s is 138 and the sum of their products taken two at a time is 131 . find the sum ?", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 138.0\nn2 = 131.0\nt0 = n2 * 2.0\nt1 = n1 + t0\nanswer = math.sqrt(max(0, t1))\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "if the number is decreased by 5 and divided by 7 the result is 7 . what would be the result if 6 is subtracted and divided by 8 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 7.0\nn2 = 7.0\nn3 = 6.0\nn4 = 8.0\nt0 = n1 * n1\nt1 = n0 + t0\nt2 = t1 - n3\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "( x + 5 ) is a factor in x ^ 2 - mx - 40 . what is the value of m ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 40.0\nt0 = n2 / n0\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "a sum is divided among b , c and d in such a way that for each rupee b gets , c gets 150 paisa and d gets 50 paisa . if the share of c is rs . 40 , what is the total amount ?", + "Output Program": [ + "n0 = 150.0\nn1 = 50.0\nn2 = 40.0\nt0 = 100.0 / n1\nt1 = n0 / n1\nt2 = n1 / n1\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = t4 / t1\nanswer = n2 * t5\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "find the average marks of all the students in 2 separate classes , if the average marks of students in the first class of 58 students is 67 and that of another class of 52 students is 82 .", + "Output Program": [ + "n0 = 2.0\nn1 = 58.0\nn2 = 67.0\nn3 = 52.0\nn4 = 82.0\nt0 = n1 + n3\nt1 = n1 * n2\nt2 = n3 * n4\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "74.0909090909091" + ], + "split": "train" + }, + { + "Input": "mixture contains alcohol and water in the ratio 4 : 3 . if 7 liters of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture .", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 7.0\nn3 = 4.0\nn4 = 5.0\nt0 = n0 * n4\nt1 = n0 * n2\nt2 = n0 * n1\nt3 = t1 - t2\nt4 = t0 / t3\nanswer = n0 * t4\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "find the value of 1 / ( 3 + 1 / ( 3 + 1 / ( 3 - 1 / 3 ) ) ) ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 3.0\nn4 = 1.0\nn5 = 3.0\nn6 = 1.0\nn7 = 3.0\nt0 = n0 / n1\nt1 = n1 - t0\nt2 = n0 / t1\nt3 = n1 + t2\nt4 = n0 / t3\nt5 = n1 + t4\nanswer = n0 / t5\nprint(answer)" + ], + "Output Answer": [ + "0.30337078651685395" + ], + "split": "train" + }, + { + "Input": "if a 10 percent deposit that has been paid toward the purchase of a certain product is $ 55 , how much more remains to be paid ?", + "Output Program": [ + "n0 = 10.0\nn1 = 55.0\nt0 = 100.0 / n0\nt1 = n1 * t0\nanswer = t1 - n1\nprint(answer)" + ], + "Output Answer": [ + "495" + ], + "split": "train" + }, + { + "Input": "if two times of the daughter \u2019 s age in years is included to the mother \u2019 s age , the total is 70 and if two times of the mother \u2019 s age is included to the daughter \u2019 s age , the total is 95 . so the mother \u2019 s age is ,", + "Output Program": [ + "n0 = 70.0\nn1 = 95.0\nt0 = n1 * 2.0\nt1 = t0 - n0\nanswer = t1 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "an auto assembly plant performs 6 functions with each frame that arrives : add axles , add wheels to the axles , install the windshield to the frame , install the instrument panel , install the steering wheel , and install the interior seating . once those 6 tasks are performed , each car goes to a separate building for finishing touches . if these tasks can be arranged along a linear assembly line in any order , except that the axles must be installed before the wheels can be added , how many r ways can the assembly line be arranged ?", + "Output Program": [ + "import math\nn0 = 6.0\nn1 = 6.0\nt0 = math.factorial(min(15, int(n0)))\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "360" + ], + "split": "train" + }, + { + "Input": "what is the smallest number which when diminished by 16 , is divisible 4 , 6 , 8 and 10 ?", + "Output Program": [ + "import scipy\nn0 = 16.0\nn1 = 4.0\nn2 = 6.0\nn3 = 8.0\nn4 = 10.0\nt0 = scipy.lcm(int(n1), int(n2))\nt1 = scipy.lcm(int(n3), int(n4))\nt2 = scipy.lcm(int(t0), int(t1))\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "136" + ], + "split": "train" + }, + { + "Input": "there are 4 people of different heights standing in order of increasing height . the difference is 2 inches between the first person and the second person , and also between the second person and the third person . the difference between the third person and the fourth person is 6 inches and the average height is 79 . how tall is the fourth person ?", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\nn2 = 6.0\nn3 = 79.0\nt0 = n0 + n2\nt1 = n0 * n3\nt2 = n2 + t0\nt3 = t1 - t2\nt4 = t3 / n0\nanswer = t0 + t4\nprint(answer)" + ], + "Output Answer": [ + "85" + ], + "split": "train" + }, + { + "Input": "3 people each took 5 tests . if the ranges of their scores in the 5 practice tests were 15 , 25 and 30 , what is the minimum possible range in scores of the 3 test - takers ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 5.0\nn3 = 15.0\nn4 = 25.0\nn5 = 30.0\nn6 = 3.0\n\nanswer = n5 - n1\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "rebecca ' s annual income is $ 15000 and jimmy ' s annual income is $ 18000 . by how much must rebecca ' s annual income increase so that it constitutes 50 % of rebecca and jimmy ' s combined income ?", + "Output Program": [ + "n0 = 15000.0\nn1 = 18000.0\nn2 = 50.0\nt0 = 100.0 - n2\nt1 = t0 / 100.0\nt2 = n1 / t1\nt3 = t2 - n1\nanswer = t3 - n0\nprint(answer)" + ], + "Output Answer": [ + "3000" + ], + "split": "train" + }, + { + "Input": "3 * 13 + 3 * 14 + 3 * 17 + 11 = ?", + "Output Program": [ + "n0 = 3.0\nn1 = 13.0\nn2 = 3.0\nn3 = 14.0\nn4 = 3.0\nn5 = 17.0\nn6 = 11.0\nt0 = n0 * n1\nt1 = n0 * n3\nt2 = n0 * n5\nt3 = t0 + t1\nt4 = t3 + t2\nanswer = n6 + t4\nprint(answer)" + ], + "Output Answer": [ + "143" + ], + "split": "train" + }, + { + "Input": "in mrs . susna ' s class , 1 / 4 of her students are getting an a , 1 / 2 are getting a b , 1 / 8 are getting a c , 1 / 12 are getting a d , and 1 / 24 are getting a f . what fraction of mrs . susna ' s class getting a passing grade of c or higher .", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 1.0\nn3 = 2.0\nn4 = 1.0\nn5 = 8.0\nn6 = 1.0\nn7 = 12.0\nn8 = 1.0\nn9 = 24.0\nt0 = n0 / n1\nt1 = n0 / n3\nt2 = n0 / n5\nt3 = t0 + t1\nanswer = t3 + t2\nprint(answer)" + ], + "Output Answer": [ + "0.875" + ], + "split": "train" + }, + { + "Input": "the sum of first 45 natural numbers is :", + "Output Program": [ + "n0 = 45.0\nt0 = n0 + 1.0\nt1 = n0 * t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "1035" + ], + "split": "train" + }, + { + "Input": "the total price of a basic computer and printer are $ 2500 . if the same printer had been purchased with an enhanced computer whose price was $ 500 more than the price of the basic computer , then the price of the printer would have been 1 / 6 of that total . what was the price of the basic computer ?", + "Output Program": [ + "n0 = 2500.0\nn1 = 500.0\nn2 = 1.0\nn3 = 6.0\nt0 = n0 + n1\nt1 = t0 / n3\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "2000" + ], + "split": "train" + }, + { + "Input": "company a ' s workforce consists of 10 percent managers and 90 percent software engineers . company b ' s workforce consists of 30 percent managers , 10 percent software engineers , and 60 percent support staff . the two companies merge , every employee stays with the resulting company , and no new employees are added . if the resulting company \u00ed s workforce consists of 25 percent managers , what percent of the workforce originated from company a ?", + "Output Program": [ + "n0 = 10.0\nn1 = 90.0\nn2 = 30.0\nn3 = 10.0\nn4 = 60.0\nn5 = 25.0\nt0 = n4 / n2\nt1 = n5 * t0\nt2 = t1 / n0\nt3 = n1 + t2\nt4 = t3 - n4\nanswer = t4 - n0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "there are 14 teams in a certain league and each team plays each of the other teams exactly once . what is the total number of games played ?", + "Output Program": [ + "n0 = 14.0\nt0 = n0 - 1.0\nt1 = n0 * t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "91" + ], + "split": "train" + }, + { + "Input": "a number is doubled and 9 is added . if the resultant is trebled , it becomes 63 . what is that number ?", + "Output Program": [ + "n0 = 9.0\nn1 = 63.0\nt0 = n0 * 3.0\nt1 = 2.0 * 3.0\nt2 = n1 - t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "a cab driver 5 days income was $ 300 , $ 150 , $ 750 , $ 400 , $ 500 . then his average income is ?", + "Output Program": [ + "n0 = 5.0\nn1 = 300.0\nn2 = 150.0\nn3 = 750.0\nn4 = 400.0\nn5 = 500.0\nt0 = n1 + n2\nt1 = n3 + t0\nt2 = n4 + t1\nt3 = n5 + t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "420" + ], + "split": "train" + }, + { + "Input": "if 12401 is divided by any no . then quotient is 76 and remainder is 13 . what is divisor ?", + "Output Program": [ + "n0 = 12401.0\nn1 = 76.0\nn2 = 13.0\nt0 = n0 - n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "163" + ], + "split": "train" + }, + { + "Input": "if 15 students in a class average 70 % on an exam and 10 students average 90 % on the same exam , what is the average in percent for all 25 students ?", + "Output Program": [ + "n0 = 15.0\nn1 = 70.0\nn2 = 10.0\nn3 = 90.0\nn4 = 25.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = t0 + t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "78" + ], + "split": "train" + }, + { + "Input": "the average ( arithmetic mean ) of all scores on a certain algebra test was 90 . if the average of the 8 male students \u2019 grades was 87 , and the average of the female students \u2019 grades was 92 , how many female students took the test ?", + "Output Program": [ + "n0 = 90.0\nn1 = 8.0\nn2 = 87.0\nn3 = 92.0\nt0 = n0 * n1\nt1 = n1 * n2\nt2 = n3 - n0\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "working simultaneously and independently at an identical constant rate , 30 machines of a certain type can produce a total of x units of product p in 3 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 5 x units of product p in 10 days ?", + "Output Program": [ + "n0 = 30.0\nn1 = 3.0\nn2 = 5.0\nn3 = 10.0\nt0 = n1 / n3\nt1 = n0 * n2\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "30 men shake hands with each other . maximum no of handshakes without cyclic handshakes .", + "Output Program": [ + "n0 = 30.0\nt0 = n0 / 2.0\nt1 = n0 - 1.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "435" + ], + "split": "train" + }, + { + "Input": "if the number is decreased by 5 and divided by 7 the result is 7 . what would be the result if 34 is subtracted and divided by 10 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 7.0\nn2 = 7.0\nn3 = 34.0\nn4 = 10.0\nt0 = n1 * n1\nt1 = n0 + t0\nt2 = t1 - n3\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "sum of the squares of 3 no . ' s is 179 and the sum of their products taken two at a time is 131 . find the sum ?", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 179.0\nn2 = 131.0\nt0 = n2 * 2.0\nt1 = n1 + t0\nanswer = math.sqrt(max(0, t1))\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "suzie \u2019 s discount footwear sells all pairs of shoes for one price and all pairs of boots for another price . on monday the store sold 22 pairs of shoes and 16 pairs of boots for $ 460 . on tuesday the store sold 8 pairs of shoes and 32 pairs of boots for $ 560 . how much more do pairs of boots cost than pairs of shoes at suzie \u2019 s discount footwear ?", + "Output Program": [ + "n0 = 22.0\nn1 = 16.0\nn2 = 460.0\nn3 = 8.0\nn4 = 32.0\nn5 = 560.0\nt0 = n2 * 2.0\nt1 = n0 * 2.0\nt2 = t0 - n5\nt3 = t1 - n3\nt4 = t2 / t3\nt5 = n0 * t4\nt6 = n2 - t5\nanswer = t6 / n1\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 27 , then how old is b ?", + "Output Program": [ + "n0 = 27.0\nt0 = 1.0 + 4.0\nt1 = n0 - 2.0\nt2 = t1 * 2.0\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "there are 225 female managers in a certain company . find the total number of female employees in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers .", + "Output Program": [ + "n0 = 225.0\nn1 = 2.0\nn2 = 5.0\nn3 = 2.0\nn4 = 5.0\nt0 = n1 / n2\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "562.5" + ], + "split": "train" + }, + { + "Input": "the cost of manufacturing a popular model car is made up of 3 items : cost of raw material , labour and overheads - in a year the cost of 3 items were in the ration of 4 : 3 : 2 . next year the cost of the raw material rose by 10 % , labour cost increased by 8 % but overhead reduced by 5 % . then % increase int the price of the car ?", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 4.0\nn3 = 3.0\nn4 = 2.0\nn5 = 10.0\nn6 = 8.0\nn7 = 5.0\nt0 = n5 + 100.0\nt1 = n0 + n2\nt2 = n6 + 100.0\nt3 = 100.0 - n7\nt4 = n4 + t1\nt5 = n2 / t4\nt6 = n0 / t4\nt7 = n4 / t4\nt8 = t0 * t5\nt9 = t2 * t6\nt10 = t7 * t3\nt11 = t8 + t9\nt12 = t11 + t10\nanswer = t12 - 100.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "377 \u00f7 13 \u00f7 29 \u00d7 1 / 4 \u00f7 2 = ?", + "Output Program": [ + "n0 = 377.0\nn1 = 13.0\nn2 = 29.0\nn3 = 1.0\nn4 = 4.0\nn5 = 2.0\nt0 = n0 / n1\nt1 = t0 / n2\nt2 = n3 * t1\nt3 = t2 / n4\nanswer = t3 / n5\nprint(answer)" + ], + "Output Answer": [ + "0.125" + ], + "split": "train" + }, + { + "Input": "david obtained 70 , 60 , 78 , 60 and 65 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology what are his average marks ?", + "Output Program": [ + "n0 = 70.0\nn1 = 60.0\nn2 = 78.0\nn3 = 60.0\nn4 = 65.0\nn5 = 100.0\nt0 = n0 + n1\nt1 = 2.0 + 3.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "66.6" + ], + "split": "train" + }, + { + "Input": "of 3 numbers , the third is 4 times the second and the second is two times the first . if their average is 165 , the second number of the 3 numbers is :", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 165.0\nn3 = 3.0\nt0 = n2 * 3.0\nt1 = 2.0 * 4.0\nt2 = n0 + t1\nt3 = t2 / 2.0\nanswer = t0 / t3\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "how many unique positive odd integers less than 80 are equal to the product of a positive multiple of 5 and an odd number ?", + "Output Program": [ + "n0 = 80.0\nn1 = 5.0\nt0 = n0 / n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a jogger running at 9 km / hr along side a railway track is 200 m ahead of the engine of a 210 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?", + "Output Program": [ + "n0 = 9.0\nn1 = 200.0\nn2 = 210.0\nn3 = 45.0\nt0 = n1 + n2\nt1 = 10.0 / 2.0\nt2 = n3 - n0\nt3 = t2 / 2.0\nt4 = t1 / t3\nt5 = t4 * t2\nanswer = t0 / t5\nprint(answer)" + ], + "Output Answer": [ + "41" + ], + "split": "train" + }, + { + "Input": "a box contain the number of balls which is as much greater than 20 is less than 30 . the number of balls is ?", + "Output Program": [ + "n0 = 20.0\nn1 = 30.0\nt0 = n0 + n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "a group of 3 investors and 3 clients recently frequented the chinese luyang restaurant . the total bill for the meal , including 20 % gratuity , came to $ 720 . on average , how much did the meal of each individual cost before gratuity ?", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 20.0\nn3 = 720.0\nt0 = n2 + 100.0\nt1 = n0 + n0\nt2 = t0 / 100.0\nt3 = n3 / t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "the average score of 35 students in a class is 37 . if every student is given 3 grace marks , the new average of the class is :", + "Output Program": [ + "n0 = 35.0\nn1 = 37.0\nn2 = 3.0\nt0 = n0 * n2\nt1 = t0 / n0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "chris mixed 3 pounds of raisins with 4 pounds of nuts . if a pound of nuts costs 2 times as much as a pound of raisins , then the total cost of the raisins was what fraction of the total cost of the mixture ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 2.0\nt0 = n1 * n2\nt1 = n0 + t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.2727272727272727" + ], + "split": "train" + }, + { + "Input": "there are 17 students in a certain class . on the day the test was given , taqeesha was absent . the other 16 students took the test , and their average was 77 . the next day , taqeesha took the test , and with her grade included , the new average is 78 . what is taqeesha \u2019 s grade on the test ?", + "Output Program": [ + "n0 = 17.0\nn1 = 16.0\nn2 = 77.0\nn3 = 78.0\n\nanswer = n1 + n3\nprint(answer)" + ], + "Output Answer": [ + "94" + ], + "split": "train" + }, + { + "Input": "a , b , c and d are 4 consecutive numbers . if the sum of a and dis 109 , what is the product of b and c ?", + "Output Program": [ + "n0 = 4.0\nn1 = 109.0\nt0 = n0 - 1.0\nt1 = n1 - t0\nt2 = t1 / 2.0\nt3 = t2 + 1.0\nt4 = t3 + 1.0\nanswer = t3 * t4\nprint(answer)" + ], + "Output Answer": [ + "2970" + ], + "split": "train" + }, + { + "Input": "of all the students in a certain dormitory , 1 / 2 are first - year students and the rest are second - year students . if 4 / 5 of the first - year students have not declared a major and if the fraction of second - year students who have declared a major is 4 times the fraction of first - year students who have declared a major , what fraction of all the students in the dormitory are second - year students who have not declared a major ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 4.0\nn3 = 5.0\nn4 = 4.0\nt0 = n2 / n3\nanswer = 1.0 - t0\nprint(answer)" + ], + "Output Answer": [ + "0.19999999999999996" + ], + "split": "train" + }, + { + "Input": "the positive integers a and b leave remainders of 2 and 3 , respectively , when divided by 6 . a > b . what is the remainder when a \u2013 b is divided by 6 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 6.0\nn3 = 6.0\nt0 = n0 % n2\nt1 = n1 % n2\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "the average ( arithmetic mean ) of 20 , 40 , and 60 is 9 more than the average of 10 , 70 , and what number ?", + "Output Program": [ + "n0 = 20.0\nn1 = 40.0\nn2 = 60.0\nn3 = 9.0\nn4 = 10.0\nn5 = 70.0\nt0 = n0 + n1\nt1 = n3 * 3.0\nt2 = n2 + t0\nt3 = n4 + t1\nt4 = n5 + t3\nanswer = t2 - t4\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "if 4 xz + yw = 3 and xw + yz = 6 , what is the value of the expression ( 2 x + y ) ( 2 z + w ) ?", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 6.0\nn3 = 2.0\nn4 = 2.0\nt0 = n2 * n3\nanswer = n1 + t0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "3 * 14 + 3 * 15 + 3 * 18 + 11 = ?", + "Output Program": [ + "n0 = 3.0\nn1 = 14.0\nn2 = 3.0\nn3 = 15.0\nn4 = 3.0\nn5 = 18.0\nn6 = 11.0\nt0 = n0 * n1\nt1 = n0 * n3\nt2 = n0 * n5\nt3 = t0 + t1\nt4 = t3 + t2\nanswer = n6 + t4\nprint(answer)" + ], + "Output Answer": [ + "152" + ], + "split": "train" + }, + { + "Input": "550 \u2212 ( 104 \u00f7 20.8 ) = ?", + "Output Program": [ + "n0 = 550.0\nn1 = 104.0\nn2 = 20.8\nt0 = n1 / n2\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "545" + ], + "split": "train" + }, + { + "Input": "a worker ' s take - home pay last year was the same each month , and she saved the same fraction of her take - home pay each month . the total amount of money that she had saved at the end of the year was 4 times the amount of that portion of her monthly take - home pay that she did not save . if all the money that she saved last year was from her take - home pay , what fraction of her take - home pay did she save each month ?", + "Output Program": [ + "n0 = 4.0\nt0 = 12.0 / n0\nt1 = t0 + 1.0\nanswer = 1 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.25" + ], + "split": "train" + }, + { + "Input": "if 0.60 : x : : 6 : 4 , then x is equal to", + "Output Program": [ + "n0 = 0.6\nn1 = 6.0\nn2 = 4.0\nt0 = n0 * n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.39999999999999997" + ], + "split": "train" + }, + { + "Input": "in a small snack shop , the average ( arithmetic mean ) revenue was $ 400 per day over a 10 - day period . during this period , if the average daily revenue was $ 360 for the first 6 days , what was the average daily revenue for the last 4 days ?", + "Output Program": [ + "n0 = 400.0\nn1 = 10.0\nn2 = 360.0\nn3 = 6.0\nn4 = 4.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = t0 - t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "460" + ], + "split": "train" + }, + { + "Input": "louie takes out a 3 - month loan of $ 1000 . the lender charges him 10 % interest per month compunded monthly . the terms of the loan state that louie must repay the loan in 3 equal monthly payments . to the nearest dollar , how much does louie have to pay each month ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1000.0\nn2 = 10.0\nn3 = 3.0\nt0 = n2 / 100.0\nt1 = t0 + 1.0\nt2 = t1 + 1.0\nt3 = n1 * t1\nt4 = t1 * t3\nt5 = t2 * t1\nt6 = t5 + 1.0\nt7 = t1 * t4\nanswer = t7 / t6\nprint(answer)" + ], + "Output Answer": [ + "402.1148036253776" + ], + "split": "train" + }, + { + "Input": "rahim bought 4 pillows with the average cost of $ 5 . if rahim also buys the fifth pillow with the price of $ 10 , what is the average ( arithmetic mean ) price of those 5 pillows ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 10.0\nn3 = 5.0\nt0 = n0 * n1\nt1 = n2 + t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "for an agricultural experiment , 300 seeds were planted in one plot and 200 were planted in a second plot . if exactly 20 percent of the seeds in the first plot germinated and exactly 35 percent of the seeds in the second plot germinated , what percent of the total number of seeds germinated ?", + "Output Program": [ + "n0 = 300.0\nn1 = 200.0\nn2 = 20.0\nn3 = 35.0\nt0 = n0 + n1\nt1 = n2 / 100.0\nt2 = n3 / 100.0\nt3 = n0 * t1\nt4 = n1 * t2\nt5 = t3 + t4\nt6 = t5 / t0\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "if p = 125 \u00d7 243 \u00d7 16 / 405 , how many digits are in p ?", + "Output Program": [ + "n0 = 125.0\nn1 = 243.0\nn2 = 16.0\nn3 = 405.0\nt0 = 1.0 + 4.0\nt1 = 100.0 * 3.0\nt2 = n0 / t0\nt3 = n3 / t0\nt4 = n1 / t3\nt5 = n2 * t4\nt6 = t2 * t5\nanswer = t6 / t1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "jane started baby - sitting when she was 18 years old . whenever she baby - sat for a child , that child was no more than half her age at the time . jane is currently 34 years old , and she stopped baby - sitting 10 years ago . what is the current age of the oldest person for whom jane could have baby - sat ?", + "Output Program": [ + "n0 = 18.0\nn1 = 34.0\nn2 = 10.0\nt0 = n0 / 2.0\nt1 = n1 - n0\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "in a certain diving competition , 5 judges score each dive on a scale from 1 to 10 . the point value of the dive is obtained by dropping the highest score and the lowest score and multiplying the sum of the remaining scores by the degree of difficulty . if a dive with a degree of difficulty of 3.2 received scores of 7.5 , 8.0 , 9.0 , 6.0 , and 8.8 , what was the point value of the dive ?", + "Output Program": [ + "n0 = 5.0\nn1 = 1.0\nn2 = 10.0\nn3 = 3.2\nn4 = 7.5\nn5 = 8.0\nn6 = 9.0\nn7 = 6.0\nn8 = 8.8\nt0 = n4 + n5\nt1 = n8 + t0\nanswer = n3 * t1\nprint(answer)" + ], + "Output Answer": [ + "77.76" + ], + "split": "train" + }, + { + "Input": "a 5 digit number divisible by 3 is to be formed using the digits 0 , 1 , 2 , 3 , 4 and 5 without repetitions . that total no of ways it can be done is ?", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 3.0\nn2 = 0.0\nn3 = 1.0\nn4 = 2.0\nn5 = 3.0\nn6 = 4.0\nn7 = 5.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = n0 - 1.0\nt2 = math.factorial(min(15, int(t1)))\nt3 = t2 * t1\nanswer = t0 + t3\nprint(answer)" + ], + "Output Answer": [ + "216" + ], + "split": "train" + }, + { + "Input": "right now , al and eliot have bank accounts , and al has more money than eliot . the difference between their two accounts is 1 / 12 of the sum of their two accounts . if al \u2019 s account were to increase by 10 % and eliot \u2019 s account were to increase by 15 % , then al would have exactly $ 22 more than eliot in his account . how much money does eliot have in his account right now ?", + "Output Program": [ + "n0 = 1.0\nn1 = 12.0\nn2 = 10.0\nn3 = 15.0\nn4 = 22.0\nt0 = n0 + n1\nt1 = n3 + 100.0\nt2 = n4 * 100.0\nt3 = t0 * 10.0\nt4 = t3 - t1\nanswer = t2 / t4\nprint(answer)" + ], + "Output Answer": [ + "146.66666666666666" + ], + "split": "train" + }, + { + "Input": "in a urban village of india named ` ` owlna ' ' , 80 % people have refrigerator , 82 % people have television , 70 % people got computers and 75 % got air - conditionor . how many people ( minimum ) got all these luxury .", + "Output Program": [ + "n0 = 80.0\nn1 = 82.0\nn2 = 70.0\nn3 = 75.0\nt0 = 100.0 - n0\nt1 = 100.0 - n1\nt2 = 100.0 - n2\nt3 = 100.0 - n3\nt4 = t0 + t1\nt5 = t4 + t2\nt6 = t5 + t3\nanswer = 100.0 - t6\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "if a , b , c , d , e and f are integers and ( ab + cdef ) < 0 , then what is the maximum number w of integers that can be negative ?", + "Output Program": [ + "n0 = 0.0\nt0 = 10.0 / 2.0\nanswer = n0 + t0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "rajan is sixth from the left end and vinay is tenth from the right end in a row of boys . if there are 8 boys between rajan and vinay , how many boys are there in the row ?", + "Output Program": [ + "n0 = 8.0\nt0 = 2.0 * 3.0\nt1 = n0 + t0\nanswer = t1 + 10.0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "find k if 64 / k = 8 .", + "Output Program": [ + "n0 = 64.0\nn1 = 8.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same . if there are 4 rows or 5 rows or 6 rows , then no tree will be left . find the least number of trees required .", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 6.0\nt0 = n1 * n2\nt1 = n0 * t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "find the greatest number which leaves the same remainder when it divides 20 , 40 and 90 .", + "Output Program": [ + "n0 = 20.0\nn1 = 40.0\nn2 = 90.0\nt0 = n1 - n0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "a grocer has a sale of rs . 7435 , rs . 7927 , rs . 7855 , rs . 8230 and rs . 7562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 7500 ?", + "Output Program": [ + "n0 = 7435.0\nn1 = 7927.0\nn2 = 7855.0\nn3 = 8230.0\nn4 = 7562.0\nn5 = 5.0\nn6 = 7500.0\nt0 = n5 + 1.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n6 * t0\nt4 = n3 + t2\nt5 = n4 + t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "5991" + ], + "split": "train" + }, + { + "Input": "when positive integer x is divided by positive integer y , the remainder is 9 . if x / y = 86.12 , what is the value of y ?", + "Output Program": [ + "import math\nn0 = 9.0\nn1 = 86.12\nt0 = math.floor(n1)\nt1 = n1 - t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "74.99999999999716" + ], + "split": "train" + }, + { + "Input": "a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 57.76 , the number of the member is the group is :", + "Output Program": [ + "import math\nn0 = 57.76\nt0 = n0 * 100.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "76" + ], + "split": "train" + }, + { + "Input": "village x has a population of 76000 , which is decreasing at the rate of 1200 per year . village y has a population of 42000 , which is increasing at the rate of 800 per year . in how many years will the population of the two villages be equal ?", + "Output Program": [ + "n0 = 76000.0\nn1 = 1200.0\nn2 = 42000.0\nn3 = 800.0\nt0 = n1 + n3\nt1 = n0 - n2\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "average of 10 matches is 34 , how many runs one should should score to increase his average by 5 runs .", + "Output Program": [ + "n0 = 10.0\nn1 = 34.0\nn2 = 5.0\nt0 = n1 + n2\nt1 = n0 + 1.0\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "89" + ], + "split": "train" + }, + { + "Input": "a customer bought a product at the shop . however , the shopkeeper increased the price of the product by 10 % so that the customer could not buy the required amount of the product . the customer managed to buy only 80 % of the required amount . what is the difference in the amount of money that the customer paid for the second purchase compared to the first purchase ?", + "Output Program": [ + "n0 = 10.0\nn1 = 80.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = t0 + 1.0\nt3 = t2 * t1\nt4 = 1.0 - t3\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "11.99999999999999" + ], + "split": "train" + }, + { + "Input": "of 3 numbers , the third is twice the second and the second is 4 times the first . if their average is 78 , the smallest of the 3 numbers is :", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 78.0\nn3 = 3.0\nt0 = n0 * n2\nt1 = n1 * 2.0\nt2 = n1 + t1\nt3 = t2 + 1.0\nanswer = t0 / t3\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "naomi drives to the beauty parlor in 60 minutes . on the way back , her average speed is half the average speed as it was to the way to the parlor . how much time will it take naomi to travel two round trips to the beauty parlor ?", + "Output Program": [ + "n0 = 60.0\n\nanswer = n0 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "a man has some hens and cows . if the number of heads be 48 and the number of feet equals 140 , then the number of hens will be :", + "Output Program": [ + "n0 = 48.0\nn1 = 140.0\nt0 = n0 * 4.0\nt1 = t0 - n1\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "a number is doubled and 9 is added . if the resultant is trebled , it becomes 51 . what is that number ?", + "Output Program": [ + "n0 = 9.0\nn1 = 51.0\nt0 = n0 * 3.0\nt1 = 2.0 * 3.0\nt2 = n1 - t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "9000 + 16 2 / 3 % of ? = 10500", + "Output Program": [ + "n0 = 9000.0\nn1 = 16.0\nn2 = 2.0\nn3 = 3.0\nn4 = 10500.0\nt0 = n3 / 3.0\nt1 = n1 * n2\nt2 = t1 / t0\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "9032" + ], + "split": "train" + }, + { + "Input": "10 is 6 % of a , and 6 is 10 % of b . c equals b / a . what is the value of c ?", + "Output Program": [ + "n0 = 10.0\nn1 = 6.0\nn2 = 6.0\nn3 = 10.0\nt0 = n1 / n0\nt1 = n0 / n1\nt2 = t0 * 100.0\nt3 = t1 * 100.0\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.36" + ], + "split": "train" + }, + { + "Input": "which no . need to add to 859622 to get a no . exactly divisible by 456 ?", + "Output Program": [ + "n0 = 859622.0\nn1 = 456.0\nt0 = n0 % n1\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "859560" + ], + "split": "train" + }, + { + "Input": "how many digits 2 ^ 400 has ?", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 400.0\nt0 = math.log(max(1e-5, n0), 2)\nt1 = math.log(max(1e-5, 10.0), 2)\nt2 = t0 / t1\nt3 = n1 * t2\nt4 = t3 + 1.0\nanswer = math.floor(t4)\nprint(answer)" + ], + "Output Answer": [ + "121" + ], + "split": "train" + }, + { + "Input": "a committee is reviewing a total of 40 x black - and - white films and 4 y color films for a festival . if the committee selects y / x % of the black - and - white films and all of the color films , what fraction of the selected films are in color ?", + "Output Program": [ + "n0 = 40.0\nn1 = 4.0\nt0 = n0 / 100.0\nt1 = n1 + t0\nanswer = n1 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.9090909090909091" + ], + "split": "train" + }, + { + "Input": "a worker ' s take - home pay last year was the same each month , and she saved the same fraction of her take - home pay each month . the total amount of money that she had saved at the end of the year was 8 times the amount of that portion of her monthly take - home pay that she did not save . if all the money that she saved last year was from her take - home pay , what fraction of her take - home pay did she save each month ?", + "Output Program": [ + "n0 = 8.0\nt0 = 12.0 / n0\nt1 = t0 + 1.0\nanswer = 1 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.4" + ], + "split": "train" + }, + { + "Input": "if x is equal to the sum of the integers from 50 to 70 , inclusive , and y is the number of even integers from 50 to 70 , inclusive , what is the value of x + y ?", + "Output Program": [ + "n0 = 50.0\nn1 = 70.0\nn2 = 50.0\nn3 = 70.0\nt0 = n0 + n1\nt1 = n1 - n0\nt2 = t1 + 1.0\nt3 = t1 / 2.0\nt4 = t0 / 2.0\nt5 = t3 + 1.0\nt6 = t2 * t4\nanswer = t5 + t6\nprint(answer)" + ], + "Output Answer": [ + "1271" + ], + "split": "train" + }, + { + "Input": "12 times a positive integer is more than its square by 36 , then the positive integer is", + "Output Program": [ + "n0 = 12.0\nn1 = 36.0\nt0 = n1 * 4.0\nt1 = n0**min(2.0, 5)\nt2 = t1 - t0\nt3 = n0 + t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "x and y started a business by investing rs . 5000 / - and rs . 15000 / - respectively . find the x \u2019 s share out of a total profit of rs . 1600 :", + "Output Program": [ + "n0 = 5000.0\nn1 = 15000.0\nn2 = 1600.0\nt0 = n0 + n1\nt1 = n2 / t0\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "train" + }, + { + "Input": "5 men are equal to as many women as are equal to 7 boys . all of them earn rs . 90 only . men \u2019 s wages are ?", + "Output Program": [ + "n0 = 5.0\nn1 = 7.0\nn2 = 90.0\nt0 = n0 * 3.0\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "if p ( a ) = 8 / 15 , p ( b ) = 4 / 15 , and p ( a \u00e2 \u02c6 \u00aa b ) = 16 / 15 find p ( b | a )", + "Output Program": [ + "n0 = 8.0\nn1 = 15.0\nn2 = 4.0\nn3 = 15.0\nn4 = 16.0\nn5 = 15.0\nt0 = n4 / n1\nt1 = n0 / n1\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "if w is 40 percent less than x , x is 40 percent less than y , and z is 46 percent less than y , then z is greater than w by what percent of w ?", + "Output Program": [ + "n0 = 40.0\nn1 = 40.0\nn2 = 46.0\nt0 = n2 / 100.0\nt1 = n0 / 100.0\nt2 = 100.0 - n0\nt3 = t1 * t2\nt4 = 1.0 - t0\nt5 = t4 * 100.0\nt6 = t2 - t3\nt7 = t5 - t6\nt8 = t7 / t6\nanswer = t8 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "arnold and danny are two twin brothers that are celebrating their birthday . the product of their ages today is smaller by 5 from the product of their ages a year from today . what is their age today ?", + "Output Program": [ + "n0 = 5.0\nt0 = n0 - 1.0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "the ages of ashley and mary are in the ratio 4 : 7 . the sum of their ages is 22 . find the ages of ashley .", + "Output Program": [ + "n0 = 4.0\nn1 = 7.0\nn2 = 22.0\nt0 = n0 + n1\nt1 = n2 / t0\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "if the price of a certain computer increased 30 percent from y dollars to 351 dollars , then 2 y =", + "Output Program": [ + "n0 = 30.0\nn1 = 351.0\nn2 = 2.0\nt0 = n0 + 100.0\nt1 = t0 / 100.0\nt2 = n1 / t1\nanswer = n2 * t2\nprint(answer)" + ], + "Output Answer": [ + "540" + ], + "split": "train" + }, + { + "Input": "a retailer bought a hat at wholesale and marked it up 60 % to its initial price of $ 24 . by how many more dollars does he need to increase the price to achieve a 100 % markup ?", + "Output Program": [ + "n0 = 60.0\nn1 = 24.0\nn2 = 100.0\nt0 = n0 + n2\nt1 = t0 / n2\nt2 = n1 / t1\nt3 = t2 * 2.0\nanswer = t3 - n1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "find last digits of ( 1023 ^ 3923 ) + ( 3081 ^ 3921 )", + "Output Program": [ + "n0 = 1023.0\nn1 = 3923.0\nn2 = 3081.0\nn3 = 3921.0\nt0 = n1 % 4.0\nt1 = 10.0 - t0\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "with an average speed of 40 km / hr a car reaches its destination on time . if it goes with an average speed of 35 km / h , it is late by 15 minutes . the total journey is ?", + "Output Program": [ + "import scipy\nn0 = 40.0\nn1 = 35.0\nn2 = 15.0\nt0 = n2 / 60.0\nt1 = scipy.gcd(int(n0), int(n1))\nt2 = n0 / t1\nt3 = t2 * t0\nanswer = n1 * t3\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "train" + }, + { + "Input": "find the remainder q when 12 ^ 190 is divided by 1729 ?", + "Output Program": [ + "n0 = 12.0\nn1 = 190.0\nn2 = 1729.0\n\nanswer = n2 - n0\nprint(answer)" + ], + "Output Answer": [ + "1717" + ], + "split": "train" + }, + { + "Input": "at the end of year x , automobile installment credit accounted for 43 % of all outstanding consumer installment credit . at that time automobile finance companies extended $ 50 billion of credit , or 1 / 4 of the automobile installment credit . how many billion dollars of consumer installment credit was outstanding at that time ?", + "Output Program": [ + "n0 = 43.0\nn1 = 50.0\nn2 = 1.0\nn3 = 4.0\nt0 = n0 / 100.0\nt1 = n1 * n3\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "465.1162790697675" + ], + "split": "train" + }, + { + "Input": "if 21 / 22 = 0 . 95.45 , what is the 57 th digit to the right of the decimal point of the fraction ?", + "Output Program": [ + "n0 = 21.0\nn1 = 22.0\nn2 = 0.0\nn3 = 95.45\nn4 = 57.0\n\nanswer = 2.0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "if * stands for / , / stands for - , + stands for * and - stands for + , then 9 / 8 * 7 + 5 - 10 = ?", + "Output Program": [ + "n0 = 9.0\nn1 = 8.0\nn2 = 7.0\nn3 = 5.0\nn4 = 10.0\nt0 = n1 / n2\nt1 = n3 * t0\nt2 = n0 - t1\nanswer = n4 + t2\nprint(answer)" + ], + "Output Answer": [ + "13.285714285714286" + ], + "split": "train" + }, + { + "Input": "a 4 digit number is such that the product of all of its digits is 126 . the sum of all the digits is equal to the 2 digit number formed by using thousands digit and tens digit ( 1000 digit in tens place & 10 digit in units place ) which in turn is equal to 19 . then difference of units and 1000 place of the number is , given that this difference is positive .", + "Output Program": [ + "n0 = 4.0\nn1 = 126.0\nn2 = 2.0\nn3 = 1000.0\nn4 = 10.0\nn5 = 19.0\nn6 = 1000.0\nt0 = n5 - 10.0\nt1 = n1 / t0\nt2 = t0 * 10.0\nt3 = t1 / n2\nt4 = t3 * 100.0\nt5 = t4 + 1000.0\nt6 = t5 + t2\nanswer = n2 + t6\nprint(answer)" + ], + "Output Answer": [ + "1792" + ], + "split": "train" + }, + { + "Input": "a man loses 1 / 3 rd of his money , then wins rs . 10 loses 1 / 3 rd of what he has and wins rs . 20 and finds that he has exactly what be had at the beginning . what was the amount he originally bad ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 10.0\nn3 = 1.0\nn4 = 3.0\nn5 = 20.0\nt0 = n0 / n1\nt1 = 1.0 - t0\nt2 = n2 * t1\nt3 = t1 * t1\nt4 = n5 + t2\nt5 = 1.0 - t3\nanswer = t4 / t5\nprint(answer)" + ], + "Output Answer": [ + "48.00000000000001" + ], + "split": "train" + }, + { + "Input": "for an agricultural experiment , 300 seeds were planted in one plot and 200 were planted in a second plot . if exactly 25 percent of the seeds in the first plot germinated and exactly 35 percent of the seeds in the second plot germinated , what percent of the total number of seeds germinated ?", + "Output Program": [ + "n0 = 300.0\nn1 = 200.0\nn2 = 25.0\nn3 = 35.0\nt0 = n0 + n1\nt1 = n2 / 100.0\nt2 = n3 / 100.0\nt3 = n0 * t1\nt4 = n1 * t2\nt5 = t3 + t4\nt6 = t5 / t0\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "28.999999999999996" + ], + "split": "train" + }, + { + "Input": "the number of positive integers n in the range 12 \u2264 n \u2264 40 such that the product ( n \u2212 1 ) ( n \u2212 2 ) . . . 3 . 2.1 is not divisible by n is", + "Output Program": [ + "n0 = 12.0\nn1 = 40.0\nn2 = 1.0\nn3 = 2.0\nn4 = 3.0\nn5 = 2.1\nt0 = n3 + n4\nanswer = n3 + t0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "find large number from below question the difference of 2 no ' s is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder", + "Output Program": [ + "n0 = 1365.0\nn1 = 6.0\nn2 = 15.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nt2 = t0 / t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "1620" + ], + "split": "train" + }, + { + "Input": "a man is 26 years older than his studen . in two years , his age will be twice the age of his student . the present age of his student is :", + "Output Program": [ + "n0 = 26.0\n\nanswer = n0 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "a = { 2 , 3 , 4 , 5 } b = { 4 , 5 , 6 , 7 , 8 } two integers will be randomly selected from the sets above , one integer from set a and one integer from set b . what is the probability t that the sum of the two integers will equal 9 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 4.0\nn3 = 5.0\nn4 = 4.0\nn5 = 5.0\nn6 = 6.0\nn7 = 7.0\nn8 = 8.0\nn9 = 9.0\nt0 = n2 * n3\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.2" + ], + "split": "train" + }, + { + "Input": "the population of a bacteria culture doubles every 4 minutes . approximately how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 1000.0\nn2 = 500000.0\nt0 = 1.0 + 4.0\nt1 = t0 * n1\nt2 = t1 * 100.0\nt3 = t2 / n1\nt4 = math.log(max(1e-5, t3), 2)\nanswer = n0 * t4\nprint(answer)" + ], + "Output Answer": [ + "35.86313713864835" + ], + "split": "train" + }, + { + "Input": "we bought orange juice and apple juice at the store . a bottle of orange juice costs 70 cents and a bottle of apple juice costs 60 cents . we bought a total of 70 bottles for $ 46.20 . how many bottles of orange juice did we buy ?", + "Output Program": [ + "n0 = 70.0\nn1 = 60.0\nn2 = 70.0\nn3 = 46.2\nt0 = n3 * 100.0\nt1 = n0 * n1\nt2 = n0 - n1\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "a basketball player practices 2 hours a day monday through friday . how many hours must he practice saturday and sunday combined if he wants to practice an average ( arithmetic mean ) of 3 hours a day for the 7 day week ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 7.0\nt0 = n0 + n1\nt1 = n1 * n2\nt2 = n0 * t0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "if the average ( arithmetic mean ) of a and b is 80 , and the average of b and c is 180 , what is the value of a \u2212 c ?", + "Output Program": [ + "n0 = 80.0\nn1 = 180.0\nt0 = n1 * 2.0\nt1 = n0 * 2.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "train" + }, + { + "Input": "exactly 3 / 7 of the people in the room are under the age of 21 , and exactly 5 / 8 of the people in the room are over the age of 65 . if the total number of the people in the room is greater than 50 and less than 100 , how many people in the room are under the age of 21 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 21.0\nn3 = 5.0\nn4 = 8.0\nn5 = 65.0\nn6 = 50.0\nn7 = 100.0\nn8 = 21.0\nt0 = n1 * n4\nt1 = n0 * t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "alice picked a number of pears , each of which she sold , canned , or poached . she canned 20 percent more than she poached , and she poached 50 percent less than she sold . if there were a total of 42 pears , then how many pears did she sell ?", + "Output Program": [ + "n0 = 20.0\nn1 = 50.0\nn2 = 42.0\nt0 = n1 / 100.0\nt1 = n0 / 100.0\nt2 = t1 + 1.0\nt3 = t2 * t0\nt4 = t0 + t3\nt5 = t4 + 1.0\nanswer = n2 / t5\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "if k is a non - negative integer and 30 ^ k is a divisor of 929260 then 3 ^ k - k ^ 3 =", + "Output Program": [ + "n0 = 30.0\nn1 = 929260.0\nn2 = 3.0\nn3 = 3.0\n\nanswer = n2 / n2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "a vending machine randomly dispenses 4 different types of fruit candy . there are twice as many apple candies as orange candies , twice as many strawberry candies as grape candies , and twice as many apple candies as strawberry candies . if each candy cost $ 0.1 , and there are exactly 90 candies , what is the minimum amount of money required to guarantee that you would buy at least 3 of each type of candy ?", + "Output Program": [ + "n0 = 4.0\nn1 = 0.1\nn2 = 90.0\nn3 = 3.0\nt0 = 1.0 / 2.0\nt1 = n0 + t0\nt2 = n2 / t1\nt3 = t2 * 2.0\nt4 = t2 + t3\nt5 = t4 + t2\nt6 = n3 + t5\nanswer = n1 * t6\nprint(answer)" + ], + "Output Answer": [ + "8.3" + ], + "split": "train" + }, + { + "Input": "if x / ( 12 p ) is an odd prime number , where x is a positive integer and p is a prime number , what is the least value of x ?", + "Output Program": [ + "n0 = 12.0\nt0 = n0 * 3.0\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "train" + }, + { + "Input": "given f ( x ) = 3 x \u2013 5 , for what value of x does 2 * [ f ( x ) ] \u2013 16 = f ( x \u2013 6 ) ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 2.0\nn3 = 16.0\nn4 = 6.0\nt0 = n1 * n2\nt1 = n4 * n0\nt2 = n0 * n2\nt3 = n0 * 1.0\nt4 = n3 + t0\nt5 = n1 + t1\nt6 = t2 - t3\nt7 = t4 - t5\nanswer = t7 / t6\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "a batsman in his 12 th innings makes a score of 80 and thereby increases his average by 3 runs . what is his average after the 12 th innings if he had never been \u2018 not out \u2019 ?", + "Output Program": [ + "n0 = 12.0\nn1 = 80.0\nn2 = 3.0\nn3 = 12.0\nt0 = n0 * n2\nt1 = n1 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "47" + ], + "split": "train" + }, + { + "Input": "a student multiplied a number by 3 / 5 instead of 5 / 3 . what is the percentage error .", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 5.0\nn3 = 3.0\nt0 = n1 / n0\nt1 = n0 / n1\nt2 = t0 - t1\nt3 = t2 / t0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "64.00000000000001" + ], + "split": "train" + }, + { + "Input": "solve the given equation 9 ^ y = 3 ^ 12 , what is y ?", + "Output Program": [ + "import math\nn0 = 9.0\nn1 = 3.0\nn2 = 12.0\nt0 = math.log(max(1e-5, n0), 2)\nt1 = math.log(max(1e-5, n1), 2)\nt2 = t0 / t1\nanswer = n2 / t2\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "if the number is decreased by 5 and divided by 7 the result is 7 . what would be the result if 4 is subtracted and divided by 10 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 7.0\nn2 = 7.0\nn3 = 4.0\nn4 = 10.0\nt0 = n1 * n1\nt1 = n0 + t0\nt2 = t1 - n3\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "if x ^ 2 + ( 1 / x ^ 2 ) = 5 , x ^ 4 + ( 1 / x ^ 4 ) = ?", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 2.0\nn3 = 5.0\nn4 = 4.0\nn5 = 1.0\nn6 = 4.0\nt0 = n3**min(n0, 5)\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "in arun ' s opinion , his weight is greater than 62 kg but leas than 72 kg . his brother does not agree with arun and he thinks that arun ' s weight is greater than 60 kg but less than 70 kg . his mother ' s view is that his weight can not be greater than 65 kg . if all of them are correct in their estimation , what is the average of diferent probable weights of arun ?", + "Output Program": [ + "n0 = 62.0\nn1 = 72.0\nn2 = 60.0\nn3 = 70.0\nn4 = 65.0\nt0 = n0 + 1.0\nt1 = n4 + t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "train" + }, + { + "Input": "x and y are two towns . ganesh covers the distance from x to y at an average speed of 60 km / hr . however , he covers the distance from y to x at an average speed of 36 km / hr . his average speed during the whole journey in km / hr . is :", + "Output Program": [ + "n0 = 60.0\nn1 = 36.0\nt0 = n0 - 10.0\nt1 = t0 + 100.0\nt2 = t1 + t1\nt3 = t1 / n0\nt4 = t1 / n1\nt5 = t3 + t4\nanswer = t2 / t5\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "a grocer has a sale of rs . 2500 , rs . 4000 , rs . 3540 for 3 consecutive months . how much sale must he have in the fourth month so that he gets an average sale of rs . 2890 ?", + "Output Program": [ + "n0 = 2500.0\nn1 = 4000.0\nn2 = 3540.0\nn3 = 3.0\nn4 = 2890.0\nt0 = n4 * 4.0\nt1 = t0 - n0\nt2 = t1 - n1\nanswer = t2 - n2\nprint(answer)" + ], + "Output Answer": [ + "1520" + ], + "split": "train" + }, + { + "Input": "( 0.76 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.76 ) ( power 2 ) + 0.076 + ( 0.1 ) ( power 2 ) is :", + "Output Program": [ + "n0 = 0.76\nn1 = 3.0\nn2 = 0.1\nn3 = 3.0\nn4 = 0.76\nn5 = 2.0\nn6 = 0.076\nn7 = 0.1\nn8 = 2.0\nt0 = n0**min(n1, 5)\nt1 = n2**min(n1, 5)\nt2 = n0**min(n5, 5)\nt3 = n2**min(n5, 5)\nt4 = n6 + t2\nt5 = t0 - t1\nt6 = t4 + t3\nanswer = t5 / t6\nprint(answer)" + ], + "Output Answer": [ + "0.66" + ], + "split": "train" + }, + { + "Input": "the digit sum of the year 2007 is 2 + 0 + 0 + 7 = 9 , which is a square number . how many years during the 20 - first century have a square digital sum ?", + "Output Program": [ + "n0 = 2007.0\nn1 = 2.0\nn2 = 0.0\nn3 = 0.0\nn4 = 7.0\nn5 = 9.0\nn6 = 20.0\n\nanswer = n4 + n5\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "if 525 / 999 = 0.525 , what is the 81 st digit to the right of the decimal point in the decimal equivalent of the fraction ?", + "Output Program": [ + "n0 = 525.0\nn1 = 999.0\nn2 = 0.525\nn3 = 81.0\n\nanswer = 2.0 + 3.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "the average weight of 24 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg . find the average weights of all the boys in the class .", + "Output Program": [ + "n0 = 24.0\nn1 = 50.25\nn2 = 8.0\nn3 = 45.15\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "48.975" + ], + "split": "train" + }, + { + "Input": "if ' y ' is a positive integer exactly divisible by 4 or 5 but not divisible by 8 . what could possibly be the value of ' y ' ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 8.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "the value of a scooter depreciates in such a way that its value of the end of each year is 3 / 4 of its value of the beginning of the same year . if the initial value of the scooter is rs . 40,000 , what is the value at the end of 1 year ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 40000.0\nn3 = 1.0\nt0 = n0 / n1\nt1 = 100.0 * 100.0\nt2 = n1 * t1\nt3 = t0**min(n3, 5)\nanswer = t2 * t3\nprint(answer)" + ], + "Output Answer": [ + "30000" + ], + "split": "train" + }, + { + "Input": "the greatest number by which the product of 3 consecutive multiples of 4 is always divisible is", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nt0 = n1 * 2.0\nt1 = n0 * n1\nt2 = n1 * t0\nanswer = t2 * t1\nprint(answer)" + ], + "Output Answer": [ + "384" + ], + "split": "train" + }, + { + "Input": "the average ( arithmetic mean ) of 14 , 32 , and 53 is 3 more than the average of 21 , 47 , and x . what is x ?", + "Output Program": [ + "n0 = 14.0\nn1 = 32.0\nn2 = 53.0\nn3 = 3.0\nn4 = 21.0\nn5 = 47.0\nt0 = n0 + n1\nt1 = n3 * 3.0\nt2 = n2 + t0\nt3 = n4 + t1\nt4 = n5 + t3\nanswer = t2 - t4\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "if \u221a 2 n = 64 , then the value of n is :", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 64.0\nt0 = math.log(max(1e-5, n1), 2)\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "a & b started a partnership business . a ' s investment was thrice the investment of b and the period of his investment was two times the period of investments of b . if b received rs 4500 as profit , what is their total profit ?", + "Output Program": [ + "n0 = 4500.0\nt0 = 1.0 * 1.0\nt1 = 2.0 * 3.0\nt2 = t1 + t0\nt3 = t0 / t2\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "31500" + ], + "split": "train" + }, + { + "Input": "robert ' s salary was decreased by 30 % and subsequently increased by 30 % . how much percentage does he lose ?", + "Output Program": [ + "n0 = 30.0\nn1 = 30.0\nt0 = n0 + 100.0\nt1 = 100.0 * 100.0\nt2 = 100.0 - n0\nt3 = t0 * t2\nt4 = t1 - t3\nt5 = t4 / t1\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "the total age of a and b is 20 years more than the total age of b and c . c is how many years younger than a . ?", + "Output Program": [ + "n0 = 20.0\n\nanswer = n0 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "3 friends a , b , c went for week end party to mcdonald \u2019 s restaurant and there they measure there weights in some order in 7 rounds . a , b , c , ab , bc , ac , abc . final round measure is 175 kg then find the average weight of all the 7 rounds ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 175.0\nn3 = 7.0\nt0 = 1.0 + n0\nt1 = n2 * t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "solution for 4.75 + . 303 + . 432", + "Output Program": [ + "n0 = 4.75\nn1 = 303.0\nn2 = 432.0\nt0 = n1 / 1000.0\nt1 = n2 / 1000.0\nt2 = n0 + t0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "5.485" + ], + "split": "train" + }, + { + "Input": "what number is 70 more than one - fourth of itself ?", + "Output Program": [ + "n0 = 70.0\nt0 = 1.0 / 4.0\nt1 = 1.0 - t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "93.33333333333333" + ], + "split": "train" + }, + { + "Input": "2 / 3 rd of the boys and 3 / 4 th of the girls of a school participate in a function . if the no . of participating students is 550 , out of which 150 are girls , what is the total no . of students in the school ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 3.0\nn3 = 4.0\nn4 = 550.0\nn5 = 150.0\nt0 = n3 * n5\nt1 = n4 - n5\nt2 = t0 / n1\nt3 = n1 * t1\nt4 = t3 / n0\nanswer = t4 + t2\nprint(answer)" + ], + "Output Answer": [ + "800" + ], + "split": "train" + }, + { + "Input": "if an average hard drive had a capacity of 0.2 tb in 2000 , and average hard drive capacities double every 5 years , what will be the average hard drive capacity in 2050 ?", + "Output Program": [ + "n0 = 0.2\nn1 = 2000.0\nn2 = 5.0\nn3 = 2050.0\nt0 = n0 * 2.0\nt1 = t0 * 2.0\nt2 = t1 * 2.0\nt3 = t2 * 2.0\nt4 = t3 * 2.0\nt5 = t4 * 2.0\nt6 = t5 * 2.0\nt7 = t6 * 2.0\nt8 = t7 * 2.0\nt9 = t8 * 2.0\nt10 = n0 + t9\nanswer = t10 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "2050" + ], + "split": "train" + }, + { + "Input": "the cricket team of 11 members is 24 yrs old & the wicket keeper is 3 yrs older . if the ages ofthese 2 are excluded , the average age of theremaining players is 1 year less than the average age of the whole team . what is the average age of the team ?", + "Output Program": [ + "n0 = 11.0\nn1 = 24.0\nn2 = 3.0\nn3 = 2.0\nn4 = 1.0\nt0 = n1 + n2\nt1 = n0 - n3\nt2 = n1 + t0\nt3 = n0 - t1\nt4 = t2 - t1\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "what is the least number . which should be added to 0.0320 to make it a perfect square ?", + "Output Program": [ + "n0 = 0.032\nt0 = 12.0 + 4.0\nt1 = t0 + 2.0\nt2 = t1 / 100.0\nt3 = t2 * t2\nanswer = t3 - n0\nprint(answer)" + ], + "Output Answer": [ + "0.0003999999999999976" + ], + "split": "train" + }, + { + "Input": "a , b and c have rs . 500 between them , a and c together have rs . 200 and b and c rs . 340 . how much does c have ?", + "Output Program": [ + "n0 = 500.0\nn1 = 200.0\nn2 = 340.0\nt0 = n1 + n2\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "if [ [ x ] ] = x ^ 2 + 2 x + 4 , what is the value of [ [ 2 ] ] ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 4.0\nn3 = 2.0\nt0 = n0 * n0\nt1 = n0**min(n0, 5)\nt2 = t0 + t1\nanswer = n2 + t2\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 62000 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 8.0\nn2 = 62000.0\nt0 = n0 / n1\nt1 = n2 * t0\nt2 = n2 + t1\nt3 = t2 * t0\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "78468.75" + ], + "split": "train" + }, + { + "Input": "in a class , 20 % of the students were absent for an exam . 30 % failed by 20 marks and 10 % just passed . find the average score of the class if the remaining students scored an average of 65 marks and the cut off for passing the exam is 40 .", + "Output Program": [ + "n0 = 20.0\nn1 = 30.0\nn2 = 20.0\nn3 = 10.0\nn4 = 65.0\nn5 = 40.0\nt0 = n0 * n1\nt1 = n3 * n5\nt2 = n4 * n5\nt3 = t0 + t1\nt4 = t3 + t2\nanswer = t4 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "a library has an average of 510 visitors on sundays and 240 on other days . the avearge number of visitors per day in a month of 30 days beginning with a sunday is ?", + "Output Program": [ + "import math\nn0 = 510.0\nn1 = 240.0\nn2 = 30.0\nt0 = 3.0 + 4.0\nt1 = n2 / t0\nt2 = math.floor(t1)\nt3 = t2 + 1.0\nt4 = n0 * t3\nt5 = n2 - t3\nt6 = n1 * t5\nt7 = t4 + t6\nanswer = t7 / n2\nprint(answer)" + ], + "Output Answer": [ + "285" + ], + "split": "train" + }, + { + "Input": "the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 40 kg . what is the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.5\nn2 = 40.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "an amount of rs . 1000 is to be distributed amongst p , q , r and s such that \u201c p \u201d gets twice as that of \u201c q \u201d and \u201c s \u201d gets 4 times as that of \u201c r \u201d . if \u201c q \u201d and \u201c r \u201d are to receive equal amount , what is the difference between the amounts received by s and p ?", + "Output Program": [ + "n0 = 1000.0\nn1 = 4.0\nt0 = 1.0 + 2.0\nt1 = t0 + 1.0\nt2 = t1 + 4.0\nt3 = n0 / t2\nt4 = n1 * t3\nt5 = t3 * 2.0\nanswer = t4 - t5\nprint(answer)" + ], + "Output Answer": [ + "250" + ], + "split": "train" + }, + { + "Input": "n 10 years , a will be twice as old as b was 10 years ago . if a is now 9 years older than b the present age of b is", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 9.0\nt0 = n0 * 2.0\nt1 = n0 + t0\nt2 = n2 + t1\nanswer = n2 + t2\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "rs . 700 is divided among a , b , c so that a receives half as much as b and b half as much as c . then c ' s share is", + "Output Program": [ + "n0 = 700.0\nt0 = 1.0 + 2.0\nt1 = t0 + 4.0\nt2 = 4.0 / t1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "train" + }, + { + "Input": "a number exceeds by 15 from its 3 / 8 part . then the number is ?", + "Output Program": [ + "n0 = 15.0\nn1 = 3.0\nn2 = 8.0\nt0 = n0 * n2\nt1 = n2 - n1\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "yearly subscription to professional magazines cost a company $ 940.00 . to make a 20 % cut in the magazine budget , how much less must be spent ?", + "Output Program": [ + "n0 = 940.0\nn1 = 20.0\nt0 = 100.0 - n1\nt1 = t0 / 100.0\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "752" + ], + "split": "train" + }, + { + "Input": "a student has to obtain 33 % of the total marks to pass . he got 125 marks and failed by 40 marks . the maximum marks are", + "Output Program": [ + "n0 = 33.0\nn1 = 125.0\nn2 = 40.0\nt0 = n1 + n2\nt1 = n0 / 100.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "train" + }, + { + "Input": "1 / 0.08 is equal to", + "Output Program": [ + "n0 = 1.0\nn1 = 0.08\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "12.5" + ], + "split": "train" + }, + { + "Input": "when a certain number x is divided by 52 , the remainder is 19 . what is the remainder when x is divided by 7 ?", + "Output Program": [ + "n0 = 52.0\nn1 = 19.0\nn2 = 7.0\n\nanswer = n1 % n2\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "if a , b , c , and d are integers ; w , x , y , and z are prime numbers ; w < x < y < z ; and ( wa ) ( xb ) ( yc ) ( zd ) = 660 ( wa ) ( xb ) ( yc ) ( zd ) = 660 , what is the value of ( a + b ) \u2013 ( c + d ) ?", + "Output Program": [ + "n0 = 660.0\nn1 = 660.0\nt0 = 3.0 + 4.0\nt1 = t0 + 4.0\nt2 = n0 / t1\nt3 = t2 / 10.0\nt4 = t3 / 2.0\nanswer = t4 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "| 14 - 5 | - | 8 - 12 | = ?", + "Output Program": [ + "n0 = 14.0\nn1 = 5.0\nn2 = 8.0\nn3 = 12.0\nt0 = n0 - n1\nt1 = n3 - n2\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "in kaya ' s teacher ' s desk there are 3 pink highlighters , 7 yellow highlighters , and 5 blue highlighters . how many highlighters are there in all ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 5.0\nt0 = n0 + n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "the sum of all the digits of the integers from 18 to 21 inclusive is 24 ( 1 + 8 + 1 + 9 + 2 + 0 + 2 + 1 = 24 ) . what is the sum w of all the digits of the integers from 0 to 99 inclusive ?", + "Output Program": [ + "n0 = 18.0\nn1 = 21.0\nn2 = 24.0\nn3 = 1.0\nn4 = 8.0\nn5 = 1.0\nn6 = 9.0\nn7 = 2.0\nn8 = 0.0\nn9 = 2.0\nn10 = 1.0\nn11 = 24.0\nn12 = 0.0\nn13 = 99.0\nt0 = n6 + n3\nt1 = 10.0 * n7\nt2 = n6 * t0\nt3 = t2 / n7\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "900" + ], + "split": "train" + }, + { + "Input": "in a basketball game , tim scored 20 points more than joe , but only half as many points as ken . if the 3 players scored a combined total of 100 points , how many points did tim score ?", + "Output Program": [ + "n0 = 20.0\nn1 = 3.0\nn2 = 100.0\nt0 = n0 * n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "if taxi fares were $ 2.00 for the first 1 / 5 mile and $ 0.60 for each 1 / 5 mile there after , then the taxi fare for a 8 - mile ride was", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 5.0\nn3 = 0.6\nn4 = 1.0\nn5 = 5.0\nn6 = 8.0\nt0 = n1 / n2\nt1 = n6 / t0\nt2 = t1 - n1\nt3 = n3 * t2\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "25.4" + ], + "split": "train" + }, + { + "Input": "40 % of the population of a village is 23040 . the total population of the village is ?", + "Output Program": [ + "n0 = 40.0\nn1 = 23040.0\nt0 = 100.0 / n0\nanswer = n1 * t0\nprint(answer)" + ], + "Output Answer": [ + "57600" + ], + "split": "train" + }, + { + "Input": "if ( 1 / 2 ) ^ 22 ( 1 / 81 ) ^ k = 1 / 18 ^ 22 , then k =", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 22.0\nn3 = 1.0\nn4 = 81.0\nn5 = 1.0\nn6 = 18.0\nn7 = 22.0\nt0 = n1 * n2\nanswer = t0 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "product of two natural numbers is 11 . then , the sum of reciprocals of their squares is", + "Output Program": [ + "n0 = 11.0\nt0 = 1.0 / 1.0\nt1 = 1.0 / n0\nt2 = t0**min(2.0, 5)\nt3 = t1**min(2.0, 5)\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "1.0082644628099173" + ], + "split": "train" + }, + { + "Input": "sandy gets 3 marks for each correct sum and loses 2 marks for each incorrect sum . sandy attempts 30 sums and obtains 45 marks . how many sums did sandy get correct ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 30.0\nn3 = 45.0\nt0 = n0 + n1\nt1 = n1 * n2\nt2 = n3 + t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "a student is ranked 21 th from right and 11 th from left . how many students are there in totality ?", + "Output Program": [ + "n0 = 21.0\nn1 = 11.0\nt0 = n0 + n1\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "31" + ], + "split": "train" + }, + { + "Input": "find the sum of the number of combinations possible by using 12 , 34 such that no number is repeated ( ex : - 12234322 are invalid 12344321 are valid ) more than once .", + "Output Program": [ + "n0 = 12.0\nn1 = 34.0\nn2 = 12234322.0\nn3 = 12344321.0\nt0 = 1.0 + 2.0\nt1 = n1 % 10.0\nt2 = t0 + 3.0\nt3 = t2 + t1\nt4 = t2 * t3\nt5 = t4 * 1000.0\nt6 = t4 * 100.0\nt7 = t4 * 10.0\nt8 = t5 + t6\nt9 = t8 + t7\nanswer = t9 + t4\nprint(answer)" + ], + "Output Answer": [ + "66660" + ], + "split": "train" + }, + { + "Input": "linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 240 , what were her original savings ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 240.0\nt0 = n0 / n1\nt1 = 1.0 - t0\nanswer = n2 / t1\nprint(answer)" + ], + "Output Answer": [ + "960" + ], + "split": "train" + }, + { + "Input": "the student manager of the university theater estimated that for every 6 movie tickets sold on valentine ' s weekend , the theater will sell 3 packs of grain crackers at $ 2.25 each , 4 bottles of a beverage at $ 1.50 each , and 4 chocolate bars at $ 1.00 each . find the approximate average ( arithmetic mean ) amount of estimated snack sales per movie ticket sold .", + "Output Program": [ + "n0 = 6.0\nn1 = 3.0\nn2 = 2.25\nn3 = 4.0\nn4 = 1.5\nn5 = 4.0\nn6 = 1.0\nt0 = n1 * n2\nt1 = n3 * n4\nt2 = n3 * n6\nt3 = t0 + t1\nt4 = t3 + t2\nanswer = t4 / n0\nprint(answer)" + ], + "Output Answer": [ + "2.7916666666666665" + ], + "split": "train" + }, + { + "Input": "eighteen years ago , a father was 3 times as old as his son . now the father is only twice as old as his son . then the sum of the present ages of the son and the father is :", + "Output Program": [ + "n0 = 3.0\nt0 = 2.0 * 3.0\nt1 = t0 * 3.0\nt2 = n0 * t1\nt3 = t2 - t1\nt4 = t3 * 2.0\nanswer = t4 + t3\nprint(answer)" + ], + "Output Answer": [ + "108" + ], + "split": "train" + }, + { + "Input": "if a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land heads up exectly twice in 3 consecutive flips ?", + "Output Program": [ + "n0 = 3.0\nt0 = 1.0 / 2.0\nt1 = t0**min(n0, 5)\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "0.375" + ], + "split": "train" + }, + { + "Input": "of the 160 people at a party , 70 were women , and 50 women tried the appetizer . if 50 people did not try the appetizer , what is the total number of men who tried the appetizer ?", + "Output Program": [ + "n0 = 160.0\nn1 = 70.0\nn2 = 50.0\nn3 = 50.0\nt0 = n0 - n3\nanswer = t0 - n2\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "if 20 liters of chemical x are added to 80 liters of a mixture that is 20 % chemical x and 80 % chemical y , then what percentage of the resulting mixture is chemical x ?", + "Output Program": [ + "n0 = 20.0\nn1 = 80.0\nn2 = 20.0\nn3 = 80.0\nt0 = n2 / 100.0\nt1 = n1 * t0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "he total marks obtained by a student in physics , chemistry and mathematics is 180 more than the marks obtained by him in physics . what is the average mark obtained by him in chemistry and mathematics ?", + "Output Program": [ + "n0 = 180.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "rahim bought 27 books for rs . 581 from one shop and 20 books for rs . 594 from another . what is the average price he paid per book ?", + "Output Program": [ + "n0 = 27.0\nn1 = 581.0\nn2 = 20.0\nn3 = 594.0\nt0 = n1 + n3\nt1 = n0 + n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "the smallest number which when diminished by 4 , is divisible by 12 , 16 , 18 , 21 and 28 is", + "Output Program": [ + "n0 = 4.0\nn1 = 12.0\nn2 = 16.0\nn3 = 18.0\nn4 = 21.0\nn5 = 28.0\nt0 = 3.0 + 4.0\nt1 = 3.0**min(2.0, 5)\nt2 = 2.0**min(4.0, 5)\nt3 = t1 * t2\nt4 = t0 * t3\nanswer = t4 + n0\nprint(answer)" + ], + "Output Answer": [ + "1012" + ], + "split": "train" + }, + { + "Input": "in a division sum , the remainder is 8 and the divisor is 3 times the quotient and is obtained by adding 3 to the thrice of the remainder . the dividend is :", + "Output Program": [ + "n0 = 8.0\nn1 = 3.0\nn2 = 3.0\nt0 = n0 * 3.0\nt1 = n2 + t0\nt2 = t1 / n1\nt3 = t1 * t2\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "251" + ], + "split": "train" + }, + { + "Input": "if x = - 5 and y = 8 , what is the value of 2 ( x - y ) ^ 2 - xy ?", + "Output Program": [ + "n0 = 5.0\nn1 = 8.0\nn2 = 2.0\nn3 = 2.0\nt0 = -n0\nt1 = n1 * t0\nt2 = t0 - n1\nt3 = t2**min(2.0, 5)\nt4 = n2 * t3\nanswer = t4 - t1\nprint(answer)" + ], + "Output Answer": [ + "378" + ], + "split": "train" + }, + { + "Input": "in an xy - coordinate plane , a line is defined by y = kx + 1 . if ( 4 , b ) , ( a , 5 ) , and ( a , b + 1 ) are 3 points on the line , where a and b are unknown , then k = ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 5.0\nn3 = 1.0\nn4 = 3.0\nt0 = n2 - n1\nt1 = t0 * 3.0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.75" + ], + "split": "train" + }, + { + "Input": "david has $ 1,500 at the beginning of his trip , after spending money , he still has exactly $ 500 less than he spent on the trip . how much money does john still have ?", + "Output Program": [ + "n0 = 1500.0\nn1 = 500.0\nt0 = 10.0 * 100.0\nt1 = n1 + t0\nt2 = n1 + t1\nt3 = t2 / 2.0\nanswer = t3 - n1\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "train" + }, + { + "Input": "a student was asked to find 4 / 5 of a number . but the student divided the number by 4 / 5 , thus the student got 18 more than the correct answer . find the number .", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 4.0\nn3 = 5.0\nn4 = 18.0\nt0 = n0 / n1\nt1 = n4 * t0\nt2 = t0 * t0\nt3 = t0 * t1\nt4 = 1.0 - t2\nt5 = t3 / t4\nanswer = t5 / t0\nprint(answer)" + ], + "Output Answer": [ + "40.000000000000014" + ], + "split": "train" + }, + { + "Input": "if a - b = 3 and a ^ 2 + b ^ 2 = 35 , find the value of ab .", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 2.0\nn2 = 2.0\nn3 = 35.0\nt0 = math.sqrt(max(0, n3))\nt1 = t0 - n0\nt2 = t1 / n1\nt3 = n0 + t2\nt4 = t3 * t2\nanswer = n1 * t4\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 320 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?", + "Output Program": [ + "n0 = 320.0\n\nanswer = n0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "640" + ], + "split": "train" + }, + { + "Input": "simplify 586645 * 9999", + "Output Program": [ + "n0 = 586645.0\nn1 = 9999.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "5865863355" + ], + "split": "train" + }, + { + "Input": "if the price of petrol increases by 30 , by how much must a user cut down his consumption so that his expenditure on petrol remains constant ?", + "Output Program": [ + "n0 = 30.0\nt0 = n0 + 100.0\nt1 = 100.0 / t0\nt2 = 1.0 - t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "23.076923076923073" + ], + "split": "train" + }, + { + "Input": "the least common multiple of positive integer e and 3 - digit integer n is 690 . if n is not divisible by 3 and e is not divisible by 2 , what is the value of n ?", + "Output Program": [ + "n0 = 3.0\nn1 = 690.0\nn2 = 3.0\nn3 = 2.0\nt0 = 2.0 + 3.0\nt1 = n0 * 10.0\nt2 = n1 / t1\nt3 = n3 * t0\nanswer = t2 * t3\nprint(answer)" + ], + "Output Answer": [ + "230" + ], + "split": "train" + }, + { + "Input": "half a number plus 5 is 15 . what is the number ?", + "Output Program": [ + "n0 = 5.0\nn1 = 15.0\nt0 = n1 - n0\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "the ratio 5 : 20 expressed as percent equals to", + "Output Program": [ + "n0 = 5.0\nn1 = 20.0\nt0 = n0 / n1\nanswer = t0 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "jennifer had $ 150 to spend on herself . she spent 1 / 5 of the money on a sandwich , 1 / 6 for a ticket to a museum , and 1 / 2 of it on a book . how much money does jennifer have left over ?", + "Output Program": [ + "n0 = 150.0\nn1 = 1.0\nn2 = 5.0\nn3 = 1.0\nn4 = 6.0\nn5 = 1.0\nn6 = 2.0\nt0 = n1 / n2\nt1 = n1 / n4\nt2 = n1 / n6\nt3 = n0 * t0\nt4 = n0 * t1\nt5 = n0 * t2\nt6 = t3 + t4\nt7 = t6 + t5\nanswer = n0 - t7\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "having scored 95 runs in the 19 th inning , a cricketer increases his average score by 4 . what will be his average score after 19 innings ?", + "Output Program": [ + "n0 = 95.0\nn1 = 19.0\nn2 = 4.0\nn3 = 19.0\nt0 = n1 * n2\nt1 = n0 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "5 x + y = 19 , and x + 3 y = 1 . find the value of 3 x + 2 y", + "Output Program": [ + "n0 = 5.0\nn1 = 19.0\nn2 = 3.0\nn3 = 1.0\nn4 = 3.0\nn5 = 2.0\nt0 = n1 + n3\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "if 0.75 : x : : 5 : 8 , then x is equal to :", + "Output Program": [ + "n0 = 0.75\nn1 = 5.0\nn2 = 8.0\nt0 = n0 * n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "1.2" + ], + "split": "train" + }, + { + "Input": "if 50 % of ( x - y ) = 20 % of ( x + y ) then what percent of x is y ?", + "Output Program": [ + "n0 = 50.0\nn1 = 20.0\nt0 = n0 + n1\nt1 = n0 - n1\nt2 = t1 / t0\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "42.857142857142854" + ], + "split": "train" + }, + { + "Input": "ashwin rented a power tool from a rental shop . the rent for the tool was $ 25 for the first hour and $ 10 for each additional hour . if ashwin paid a total of $ 125 , excluding sales tax , to rent the tool , for how many hours did she rent it ?", + "Output Program": [ + "n0 = 25.0\nn1 = 10.0\nn2 = 125.0\n\nanswer = n1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "b as a percentage of a is equal to a as a percentage of ( a + b ) . find b as a percentage of a .", + "Output Program": [ + "import math\nt0 = -1.0\nt1 = -4.0\nt2 = t0 * t1\nt3 = t2 + 1.0\nt4 = math.sqrt(max(0, t3))\nt5 = t0 + t4\nt6 = t5 / 2.0\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "61.80339887498949" + ], + "split": "train" + }, + { + "Input": "on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 390 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?", + "Output Program": [ + "n0 = 390.0\n\nanswer = n0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "780" + ], + "split": "train" + }, + { + "Input": "in goshawk - eurasian nature reserve 30 percent of the birds are hawks , and 40 percent of the non - hawks are paddyfield - warblers . if there are 25 percent as many kingfishers as paddyfield - warblers in the reserve , then what percent of the birds b in the nature reserve are not hawks , paddyfield - warblers , or kingfishers ?", + "Output Program": [ + "n0 = 30.0\nn1 = 40.0\nn2 = 25.0\nt0 = n2 + n2\nt1 = t0 / 2.0\nanswer = t1 + 10.0\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "the average age of a group of 10 persons was decreased by 3 years when one person , whose age was 42 years , was replaced by a new person . find the age of the new person ?", + "Output Program": [ + "n0 = 10.0\nn1 = 3.0\nn2 = 42.0\nt0 = n0 * n1\nanswer = n2 - t0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "the guests at a football banquet consumed a total of 319 pounds of food . if no individual guest consumed more than 2 pounds of food , what is the minimum number of guests that could have attended the banquet ?", + "Output Program": [ + "import math\nn0 = 319.0\nn1 = 2.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "160" + ], + "split": "train" + }, + { + "Input": "the compound interest on a sum of money for 2 years is rs . 832 and the simple interest on the same sum for the same period is rs . 800 . the difference between the compound interest and simple interest for 3 years", + "Output Program": [ + "n0 = 2.0\nn1 = 832.0\nn2 = 800.0\nn3 = 3.0\nt0 = n2 / n0\nt1 = n1 - t0\nt2 = t1 - t0\nt3 = t2 * 100.0\nt4 = t3 / t0\nt5 = n1 * t4\nt6 = t5 / 100.0\nanswer = t6 + t2\nprint(answer)" + ], + "Output Answer": [ + "98.56" + ], + "split": "train" + }, + { + "Input": "each child has 2 pencils and 13 skittles . if there are 11 children , how many pencils are there in total ?", + "Output Program": [ + "n0 = 2.0\nn1 = 13.0\nn2 = 11.0\n\nanswer = n0 * n2\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "find the sum of all 3 digit natural numbers , which are divisible by 8", + "Output Program": [ + "n0 = 3.0\nn1 = 8.0\nt0 = 100.0 + 4.0\nt1 = 10.0 * 100.0\nt2 = t1 - n1\nt3 = t0 + t2\nt4 = t2 - t0\nt5 = t4 / n1\nt6 = t5 + 1.0\nt7 = t6 / 2.0\nanswer = t3 * t7\nprint(answer)" + ], + "Output Answer": [ + "61376" + ], + "split": "train" + }, + { + "Input": "a textile manufacturing firm employees 70 looms . it makes fabrics for a branded company . the aggregate sales value of the output of the 70 looms is rs 00000 and the monthly manufacturing expenses is rs 1 , 50000 . assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms . monthly establishment charges are rs 75000 . if one loom breaks down and remains idle for one month , the decrease in profit is :", + "Output Program": [ + "n0 = 70.0\nn1 = 70.0\nn2 = 0.0\nn3 = 1.0\nn4 = 50000.0\nn5 = 75000.0\nt0 = 2.0 + 3.0\nt1 = n5 - n4\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "5000" + ], + "split": "train" + }, + { + "Input": "for a 3 - digit number xyz , where x , y , and z are the digits of the number , f ( xyz ) = 5 ^ x 2 ^ y 3 ^ z . if f ( abc ) = 3 * f ( def ) , what is the value of abc - def ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 2.0\nn3 = 3.0\nn4 = 3.0\n\nanswer = n0 - n2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "a no . when divided by the sum of 555 and 445 gives 2 times their difference as quotient & 70 as remainder . find the no . is ?", + "Output Program": [ + "n0 = 555.0\nn1 = 445.0\nn2 = 2.0\nn3 = 70.0\nt0 = n0 + n1\nt1 = n0 - n1\nt2 = n2 * t0\nt3 = t2 * t1\nanswer = n3 + t3\nprint(answer)" + ], + "Output Answer": [ + "220070" + ], + "split": "train" + }, + { + "Input": "if a 10 percent deposit that has been paid toward the purchase of a certain product is $ 140 , how much more remains to be paid ?", + "Output Program": [ + "n0 = 10.0\nn1 = 140.0\nt0 = 100.0 / n0\nt1 = n1 * t0\nanswer = t1 - n1\nprint(answer)" + ], + "Output Answer": [ + "1260" + ], + "split": "train" + }, + { + "Input": "a professional janitor can clean a certain high school in ( 4 + 4 ) hours , working at a constant rate . a student sentenced to detention can clean that same high school in 20 hours , also working at a constant rate . if the student is paid $ 7 total per hour and the janitor is paid $ 21 per hour , how much more would it cost the school to pay the janitor to do the job himself than it would to pay the student and the janitor to do the job together ?", + "Output Program": [ + "n0 = 4.0\nn1 = 4.0\nn2 = 20.0\nn3 = 7.0\nn4 = 21.0\nt0 = n0 + n0\nt1 = n3 + n4\nt2 = 1.0 / n2\nt3 = 1.0 / t0\nt4 = n4 * t0\nt5 = t3 + t2\nt6 = 1.0 / t5\nt7 = t1 * t6\nanswer = t4 - t7\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "the least number which when increased by 8 each divisible by each one of 24 , 32 , 36 and 54 is :", + "Output Program": [ + "import scipy\nn0 = 8.0\nn1 = 24.0\nn2 = 32.0\nn3 = 36.0\nn4 = 54.0\nt0 = scipy.lcm(int(n1), int(n2))\nt1 = scipy.lcm(int(n3), int(t0))\nt2 = scipy.lcm(int(n4), int(t1))\nanswer = t2 - n0\nprint(answer)" + ], + "Output Answer": [ + "856" + ], + "split": "train" + }, + { + "Input": "the number of the members of a club is more than 20 and less than 50 . when 4 people sit at a table , other people exactly divided to 6 - people groups ( 6 people sit at a table ) or 7 - people groups ( 7 people sit at a table ) . if the members are divided to 8 - people groups , how many people will be left ?", + "Output Program": [ + "import scipy\nn0 = 20.0\nn1 = 50.0\nn2 = 4.0\nn3 = 6.0\nn4 = 6.0\nn5 = 7.0\nn6 = 7.0\nn7 = 8.0\nt0 = scipy.lcm(int(n3), int(n5))\nt1 = n2 + t0\nanswer = t1 % n7\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "when 242 is divided by a certain divisor the remainder obtained is 11 . when 698 is divided by the same divisor the remainder obtained is 18 . however , when the sum of the two numbers 242 and 698 is divided by the divisor , the remainder obtained is 9 . what is the value of the divisor ?", + "Output Program": [ + "n0 = 242.0\nn1 = 11.0\nn2 = 698.0\nn3 = 18.0\nn4 = 242.0\nn5 = 698.0\nn6 = 9.0\nt0 = n1 + n3\nanswer = t0 - n6\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "the cost per pound of green tea and coffee were the same in june . in july , the price of coffee shot up by 100 % and that of green tea dropped by 90 % . if in july , a mixture containing equal quantities of green tea and coffee costs $ 3.15 for 3 lbs , how much did a pound of green tea cost in july ?", + "Output Program": [ + "n0 = 100.0\nn1 = 90.0\nn2 = 3.15\nn3 = 3.0\nt0 = n0 + n0\nt1 = n3 / 2.0\nt2 = n0 - n1\nt3 = t0 / n0\nt4 = t2 / n0\nt5 = t3 * t1\nt6 = t1 * t4\nt7 = t5 + t6\nt8 = t7 / n2\nanswer = t8 * t4\nprint(answer)" + ], + "Output Answer": [ + "0.1" + ], + "split": "train" + }, + { + "Input": "a case of 12 rolls of paper towels sells for $ 9 . the cost of one roll sold individually is $ 1 . what is the percent e of savings per roll for the 12 - roll package over the cost of 12 rolls purchased individually ?", + "Output Program": [ + "n0 = 12.0\nn1 = 9.0\nn2 = 1.0\nn3 = 12.0\nn4 = 12.0\nt0 = n1 / n0\nt1 = t0 * 100.0\nanswer = 100.0 - t1\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "for what values of k will the pair of equations 3 ( 3 x + 4 y ) = 36 and kx + 12 y = 30 does not have a unique solution ?", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 4.0\nn3 = 36.0\nn4 = 12.0\nn5 = 30.0\nt0 = n1 * n4\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "on rainy mornings , mo drinks exactly n cups of hot chocolate ( assume that n is an integer ) . on mornings that are not rainy , mo drinks exactly 5 cups of tea . last week mo drank a total of 36 cups of tea and hot chocolate together . if during that week mo drank 14 more tea cups than hot chocolate cups , then how many rainy days were there last week ?", + "Output Program": [ + "n0 = 5.0\nn1 = 36.0\nn2 = 14.0\nt0 = 3.0 + 4.0\nt1 = n1 + n2\nt2 = t1 / 2.0\nt3 = t2 / n0\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a retailer bought a shirt at wholesale and marked it up 80 % to its initial price of $ 27 . by how many more dollars does he need to increase the price to achieve a 100 % markup ?", + "Output Program": [ + "n0 = 80.0\nn1 = 27.0\nn2 = 100.0\nt0 = n0 / n2\nt1 = t0 + 1.0\nt2 = n1 / t1\nt3 = t2 * 2.0\nanswer = t3 - n1\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "the total of the ages of amar , akbar and anthony is 66 years . what was the total of their ages 4 years ago ?", + "Output Program": [ + "n0 = 66.0\nn1 = 4.0\nt0 = n1 * 3.0\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "train" + }, + { + "Input": "a certain country is divided into 8 provinces . each province consists entirely of progressives and traditionalists . if each province contains the same number of traditionalists and the number of traditionalists in any given province is 1 / 12 the total number of progressives in the entire country , what fraction of the country is traditionalist ?", + "Output Program": [ + "n0 = 8.0\nn1 = 1.0\nn2 = 12.0\nt0 = n0 / n2\nt1 = n1 + t0\nt2 = t0 / t1\nanswer = n1 - t2\nprint(answer)" + ], + "Output Answer": [ + "0.6" + ], + "split": "train" + }, + { + "Input": "5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 90 only . men \u00e2 \u20ac \u2122 s wages are ?", + "Output Program": [ + "n0 = 5.0\nn1 = 8.0\nn2 = 90.0\nt0 = n0 * 3.0\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "the smallest value of n , for which 2 n + 1 is not a prime number , is", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\n\nanswer = n0 + n0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "what sum of money put at c . i amounts in 2 years to rs . 7000 and in 3 years to rs . 9261 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 7000.0\nn2 = 3.0\nn3 = 9261.0\nt0 = n3 / n1\nt1 = t0 - 1.0\nt2 = t1 + 1.0\nt3 = t2**min(n0, 5)\nanswer = n1 / t3\nprint(answer)" + ], + "Output Answer": [ + "3999.248141349427" + ], + "split": "train" + }, + { + "Input": "two employees m and n are paid a total of $ 583 per week by their employer . if m is paid 120 percent of the salary paid to n , how much is n paid per week ?", + "Output Program": [ + "n0 = 583.0\nn1 = 120.0\nt0 = n1 / 100.0\nt1 = t0 + 1.0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "265" + ], + "split": "train" + }, + { + "Input": "if remainder is 1 , quotient is 54 and dividend is 217 then what is divisor ?", + "Output Program": [ + "n0 = 1.0\nn1 = 54.0\nn2 = 217.0\nt0 = n2 - n0\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "find the least number that must be subtracted from 1387 so that the remaining number is divisible by 15 .", + "Output Program": [ + "n0 = 1387.0\nn1 = 15.0\nt0 = 2.0 * 4.0\nt1 = 100.0 - t0\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "what is the 99 th digit after the decimal point in the decimal expansion of 2 / 9 + 3 / 11 ?", + "Output Program": [ + "import math\nn0 = 99.0\nn1 = 2.0\nn2 = 9.0\nn3 = 3.0\nn4 = 11.0\nt0 = n0 / n2\nt1 = n0 / n4\nt2 = n1 * t0\nt3 = n3 * t1\nt4 = t2 + t3\nt5 = t4 / n0\nt6 = t5 * 10.0\nanswer = math.floor(t6)\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "the ratio of ages of aman , bren , and charlie are in the ratio 5 : 8 : 7 respectively . if 8 years ago , the sum of their ages was 76 , what will be the age of bren 10 years from now ?", + "Output Program": [ + "n0 = 5.0\nn1 = 8.0\nn2 = 7.0\nn3 = 8.0\nn4 = 76.0\nn5 = 10.0\nt0 = n0 + n1\nt1 = n1 * 3.0\nt2 = n4 + t1\nt3 = n2 + t0\nt4 = t2 / t3\nt5 = n1 * t4\nanswer = n5 + t5\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "machine m , n , o working simultaneously machine m can produce x units in 3 / 4 of the time it takes machine n to produce the same amount of units . machine n can produce x units in 2 / 7 the time it takes machine o to produce that amount of units . if all 3 machines are working simultaneously , what fraction of the total output is produced by machine n ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 2.0\nn3 = 7.0\nn4 = 3.0\nt0 = n2 * n3\nt1 = t0 - 1.0\nanswer = n3 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.5384615384615384" + ], + "split": "train" + }, + { + "Input": "a man is 18 years older than his son . in two years , his age will be twice the age of his son . the present age of this son is", + "Output Program": [ + "n0 = 18.0\nt0 = 2.0 * 2.0\nt1 = 2.0 - 1.0\nt2 = t0 - 2.0\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "( 0.0088 ) ( 4.5 ) / ( 0.05 ) ( 0.1 ) ( 0.008 ) =", + "Output Program": [ + "n0 = 0.0088\nn1 = 4.5\nn2 = 0.05\nn3 = 0.1\nn4 = 0.008\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n4 * t1\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "989.9999999999999" + ], + "split": "train" + }, + { + "Input": "a batsman in his 12 th innings makes a score of 65 and thereby increases his average by 3 runs . what is his average after the 12 th innings if he had never been \u2018 not out \u2019 ?", + "Output Program": [ + "n0 = 12.0\nn1 = 65.0\nn2 = 3.0\nn3 = 12.0\nt0 = n0 * n2\nt1 = n1 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "find the number which when multiplied by 15 is increased by 196", + "Output Program": [ + "n0 = 15.0\nn1 = 196.0\nt0 = n0 - 1.0\nanswer = n1 / t0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 100 milliliters of solution x to create a solution that is 25 percent alcohol by volume ?", + "Output Program": [ + "n0 = 10.0\nn1 = 30.0\nn2 = 100.0\nn3 = 25.0\nt0 = n3 - n0\nt1 = n1 - n3\nt2 = t0 / t1\nanswer = n2 * t2\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "one millisecond is 0.001 of a second . the costs for a single run of a computer program are $ 1.07 for operating - system overhead , $ 0.023 per millisecond of computer time , and $ 5.35 for the mounting of a data tape . what is the total of these 3 costs for 1 run of a program that requires 1.5 seconds of computer time ?", + "Output Program": [ + "n0 = 0.001\nn1 = 1.07\nn2 = 0.023\nn3 = 5.35\nn4 = 3.0\nn5 = 1.0\nn6 = 1.5\nt0 = n1 + n3\nt1 = n6 / n0\nt2 = n2 * t1\nanswer = t0 + t2\nprint(answer)" + ], + "Output Answer": [ + "40.92" + ], + "split": "train" + }, + { + "Input": "if 4 x + y = 34 , 2 x - y = 20 , for integers of x and y , y ^ 2 = ?", + "Output Program": [ + "n0 = 4.0\nn1 = 34.0\nn2 = 2.0\nn3 = 20.0\nn4 = 2.0\nt0 = n1 + n3\nt1 = n0 + n2\nt2 = t0 / t1\nt3 = n2 * t2\nt4 = t3 - n3\nanswer = t4**min(n2, 5)\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "if a / b = 5 / 2 , b / c = 1 / 2 , c / d = 1 , d / e = 3 / 2 and e / f = 4 / 3 , then what is the value of abc / def ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 1.0\nn3 = 2.0\nn4 = 1.0\nn5 = 3.0\nn6 = 2.0\nn7 = 4.0\nn8 = 3.0\nt0 = n2 * n5\nt1 = n1 * n2\nt2 = n0 * n2\nt3 = n1 * n1\nt4 = n2 * n2\nt5 = n7 * t0\nt6 = n5 * t1\nt7 = n2 * t2\nt8 = n2 * t3\nt9 = n5 * t4\nt10 = n1 * t1\nt11 = t5 / t6\nt12 = t7 / t8\nt13 = t9 / t10\nt14 = t12 * t13\nanswer = t11 * t14\nprint(answer)" + ], + "Output Answer": [ + "1.875" + ], + "split": "train" + }, + { + "Input": "the price of a certain painting increased by 20 % during the first year and decreased by 15 % during the second year . the price of the painting at the end of the 2 - year period was what percent of the original price ?", + "Output Program": [ + "n0 = 20.0\nn1 = 15.0\nn2 = 2.0\nt0 = n0 * n1\nt1 = n0 - n1\nt2 = t0 / 100.0\nt3 = t1 - t2\nanswer = t3 + 100.0\nprint(answer)" + ], + "Output Answer": [ + "102" + ], + "split": "train" + }, + { + "Input": "for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today ' s production of 60 units raises the average to 55 units per day , what is the value of n ?", + "Output Program": [ + "n0 = 50.0\nn1 = 60.0\nn2 = 55.0\nt0 = n1 - n0\nt1 = n2 - n0\nt2 = t0 / t1\nanswer = t2 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "think of a number , divide it by 4 and add 9 to it . the result is 15 . what is the number thought of ?", + "Output Program": [ + "n0 = 6.0\nn1 = 5.0\nn2 = 2.0\nn3 = 19.0\nt0 = n0 * n1\nt1 = n2 * t0\nt2 = t1 / n2\nanswer = t2 + 3.0\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "let n be the greatest number that will divide 1305 , 4665 and 6905 , leaving the game remainder in each case . then sum of the digits in n is :", + "Output Program": [ + "n0 = 1305.0\nn1 = 4665.0\nn2 = 6905.0\nt0 = 1.0 + 1.0\nanswer = t0 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "the sum of the first 70 positive even integers is 4,970 . what is the sum of the first 70 odd integers ?", + "Output Program": [ + "n0 = 70.0\nn1 = 4970.0\nn2 = 70.0\nt0 = n0 / 2.0\nt1 = n0 * 2.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "4900" + ], + "split": "train" + }, + { + "Input": "a family consists of two grandparents , two parents , and 3 grandchildren . the average age of the grandparents is 64 years , the average age of the parents is 39 years , and the average age of the grandchildren is 6 years . what is the average age ( in years ) of the family ?", + "Output Program": [ + "n0 = 3.0\nn1 = 64.0\nn2 = 39.0\nn3 = 6.0\nt0 = n0 + 4.0\nt1 = n1 * 2.0\nt2 = n2 * 2.0\nt3 = n0 * n3\nt4 = t1 + t2\nt5 = t4 + t3\nanswer = t5 / t0\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "how many numbers from 49 to 79 are exactly divisible by 11 ?", + "Output Program": [ + "import math\nn0 = 49.0\nn1 = 79.0\nn2 = 11.0\nt0 = n1 / n2\nt1 = n0 / n2\nt2 = math.floor(t0)\nt3 = math.floor(t1)\nt4 = t3 + 1.0\nt5 = n2 * t2\nt6 = n2 * t4\nt7 = t5 - t6\nt8 = t7 / n2\nanswer = t8 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "the jogging track in a sports complex is 640 m in circumference . lata and geeta start from the same point and walk in opposite directions at 4.2 km / hr and 3.8 km / hr respectively . they will meet for the first time in ?", + "Output Program": [ + "n0 = 640.0\nn1 = 4.2\nn2 = 3.8\nt0 = 1.0 * 60.0\nt1 = n1 * 1000.0\nt2 = n2 * 1000.0\nt3 = t1 + t2\nt4 = n0 * t0\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "4.8" + ], + "split": "train" + }, + { + "Input": "village x has a population of 68000 , which is decreasing at the rate of 1200 per year . village y has a population of 42000 , which is increasing at the rate of 800 per year . in how many years will the population of the two villages be equal ?", + "Output Program": [ + "n0 = 68000.0\nn1 = 1200.0\nn2 = 42000.0\nn3 = 800.0\nt0 = n1 + n3\nt1 = n0 - n2\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "if x ^ 2 + ( 1 / x ^ 2 ) = 2 , x ^ 4 + ( 1 / x ^ 4 ) = ?", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 2.0\nn3 = 2.0\nn4 = 4.0\nn5 = 1.0\nn6 = 4.0\nt0 = n0**min(n0, 5)\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "in the x - y plane , point ( x , y ) is a lattice point if both x and y are integers . a square has a center at ( 0 , 0 ) and side = 4 . some points , such as the center ( 0 , 0 ) , are inside the square , but a point such as ( 0 , 2 ) is on the square but not in the square . how many lattice points are in the square ?", + "Output Program": [ + "n0 = 0.0\nn1 = 0.0\nn2 = 4.0\nn3 = 0.0\nn4 = 0.0\nn5 = 0.0\nn6 = 2.0\nt0 = n2 * n6\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "mary ' s income is 50 percent more than tim ' s income , and tim ' s income is 40 percent less than juan ' s income . what percent of juan ' s income is mary ' s income ?", + "Output Program": [ + "n0 = 50.0\nn1 = 40.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = t0 + 1.0\nt3 = 1.0 - t1\nt4 = t2 * t3\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "89.99999999999999" + ], + "split": "train" + }, + { + "Input": "a girl was asked to multiply a certain number by 43 . she multiplied it by 34 and got his answer less than the correct one by 1242 . find the number to be multiplied .", + "Output Program": [ + "n0 = 43.0\nn1 = 34.0\nn2 = 1242.0\nt0 = n0 - n1\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "138" + ], + "split": "train" + }, + { + "Input": "find out the c . i on rs . 5000 at 4 % p . a . compound half - yearly for 1 1 / 2 years", + "Output Program": [ + "n0 = 5000.0\nn1 = 4.0\nn2 = 1.0\nn3 = 1.0\nn4 = 2.0\nt0 = n1 / 100.0\nt1 = 3.0 / n4\nt2 = t0 + n2\nt3 = t2**min(t1, 5)\nt4 = n0 * t3\nanswer = t4 - n0\nprint(answer)" + ], + "Output Answer": [ + "302.9802941364969" + ], + "split": "train" + }, + { + "Input": "how much water should be added to 14 liters of a 20 % - solution of alcohol to reduce the concentration of alcohol in the solution by 75 % ?", + "Output Program": [ + "n0 = 14.0\nn1 = 20.0\nn2 = 75.0\nt0 = n2 / 100.0\nt1 = 100.0 * 2.0\nt2 = n1 * t0\nt3 = n1 - t2\nt4 = t1 / t3\nanswer = t4 - n0\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 20 are excluded , the average mark of the remaining will be 92 . find the number of students who wrote the exam .", + "Output Program": [ + "n0 = 80.0\nn1 = 5.0\nn2 = 20.0\nn3 = 92.0\nt0 = n1 * n3\nt1 = n1 * n2\nt2 = n3 - n0\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "the average weight of 8 students decreases by 5 kg when one of them weighing 86 kg is replaced by a new student . the weight of the student is", + "Output Program": [ + "n0 = 8.0\nn1 = 5.0\nn2 = 86.0\nt0 = n0 * n1\nanswer = n2 - t0\nprint(answer)" + ], + "Output Answer": [ + "46" + ], + "split": "train" + }, + { + "Input": "80 % of the population of a village is 23040 . the total population of the village is ?", + "Output Program": [ + "n0 = 80.0\nn1 = 23040.0\nt0 = 100.0 / n0\nanswer = n1 * t0\nprint(answer)" + ], + "Output Answer": [ + "28800" + ], + "split": "train" + }, + { + "Input": "solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 300 milliliters of solution x to create a solution that is 18 percent alcohol by volume ?", + "Output Program": [ + "n0 = 10.0\nn1 = 30.0\nn2 = 300.0\nn3 = 18.0\nt0 = n3 - n0\nt1 = n1 - n3\nt2 = t0 / t1\nanswer = n2 * t2\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "train" + }, + { + "Input": "if p is a prime number greater than 5 , what is the remainder when p ^ 2 is divided by 6 .", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 6.0\nt0 = n0 + n1\nt1 = t0**min(2.0, 5)\nanswer = t1 % n2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "lagaan is levied on the 60 percent of the cultivated land . the revenue department collected total rs . 3 , 44000 through the lagaan from the village of mutter . mutter , a very rich farmer , paid only rs . 480 as lagaan . the percentage of total land of mutter over the total taxable land of the village is :", + "Output Program": [ + "n0 = 60.0\nn1 = 3.0\nn2 = 44000.0\nn3 = 480.0\nt0 = n0 / 100.0\nt1 = n1 * 100.0\nt2 = 10.0 * 4.0\nt3 = t2 + 4.0\nt4 = n3 / t0\nt5 = t1 * 1000.0\nt6 = t3 * 1000.0\nt7 = t5 + t6\nt8 = t4 / t7\nanswer = t8 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "0.23255813953488372" + ], + "split": "train" + }, + { + "Input": "how many positive integer solutions does the equation 5 x + 10 y = 100 have ?", + "Output Program": [ + "n0 = 5.0\nn1 = 10.0\nn2 = 100.0\n\nanswer = n1 / n0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "in the annual cultural programme of indra prastha there was this math quiz going on . yudhisthir faced this last question that will bring the champion ' s trophy . what will be thesolution for the given problem ? the function f is defined is defined asf ( 2 x + 3 ) = ( x - 3 ) ( x + 4 ) what is f ( 29 ) ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 3.0\nn3 = 4.0\nn4 = 29.0\nt0 = n4 - n1\nt1 = t0 / n0\nt2 = n3 + t1\nt3 = t1 - n1\nanswer = t2 * t3\nprint(answer)" + ], + "Output Answer": [ + "170" + ], + "split": "train" + }, + { + "Input": "if 183 is divisible by 11 , find the value of the smallest natural no . n ?", + "Output Program": [ + "n0 = 183.0\nn1 = 11.0\nt0 = 2.0 * 4.0\nt1 = t0 - 3.0\nt2 = t1 - 1.0\nanswer = n1 - t2\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "in smithtown , the ratio of right - handed people to left - handed people is 3 to 1 and the ratio of men to women is 3 to 2 . if the number of right - handed men is maximized , then what z percent of all the people in smithtown are left - handed women ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 3.0\nn3 = 2.0\nt0 = n0 + n1\nt1 = n0 + n3\nt2 = t0 / t1\nt3 = n3 * t2\nt4 = n0 * t2\nt5 = n0 - t4\nt6 = t3 - t5\nt7 = t6 / t0\nanswer = t7 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "25.00000000000001" + ], + "split": "train" + }, + { + "Input": "a palindrome is a number that reads the same forward and backward . for example . 2442 and 111 are palindromes . if 5 - digit palindromes are formed using one or more of the digits , 1 , 2 , 3 , how many such palindromes are possible ?", + "Output Program": [ + "n0 = 2442.0\nn1 = 111.0\nn2 = 5.0\nn3 = 1.0\nn4 = 2.0\nn5 = 3.0\nt0 = n5 * 3.0\nanswer = n5 * t0\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "train" + }, + { + "Input": "if 20 % of ( x - y ) = 14 % of ( x + y ) , then what percent of x is y ?", + "Output Program": [ + "n0 = 20.0\nn1 = 14.0\nt0 = n0 + n1\nt1 = n0 - n1\nt2 = t1 / t0\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "17.647058823529413" + ], + "split": "train" + }, + { + "Input": "if rs . 510 be divided among a , b , c in such a way that a gets 2 / 3 of what b gets and b gets 1 / 4 of what c gets , then their shares are respectively :", + "Output Program": [ + "n0 = 510.0\nn1 = 2.0\nn2 = 3.0\nn3 = 1.0\nn4 = 4.0\nt0 = n3 / n4\nt1 = n1 / n2\nt2 = t1 * t0\nt3 = t0 + t2\nt4 = t3 + n3\nanswer = n0 / t4\nprint(answer)" + ], + "Output Answer": [ + "360.00000000000006" + ], + "split": "train" + }, + { + "Input": "what is the dividend . divisor 15 , the quotient is 9 and the remainder is 5 ?", + "Output Program": [ + "n0 = 15.0\nn1 = 9.0\nn2 = 5.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "140" + ], + "split": "train" + }, + { + "Input": "if n is an integer from 1 to 96 ( inclusive ) , what is the probability for n * ( n + 1 ) * ( n + 2 ) being divisible by 8 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 96.0\nn2 = 1.0\nn3 = 2.0\nn4 = 8.0\nt0 = n1 + n3\nt1 = n0 + n0\nt2 = t0 + t1\nt3 = t2 * t1\nanswer = t3 / n4\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "claire has a total of 90 pets consisting of gerbils and hamsters only . one - quarter of the gerbils are male , and one - third of the hamsters are male . if there are 25 males altogether , how many gerbils does claire have ?", + "Output Program": [ + "n0 = 90.0\nn1 = 25.0\nt0 = n0 - n1\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "66" + ], + "split": "train" + }, + { + "Input": "if the product of 12 integers is negative , at most how many of the integers can be negative ?", + "Output Program": [ + "n0 = 12.0\n\nanswer = n0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "there are 20 players in a chess group , and each player plays each of the others once . given that each game is played by two players , how many total games will be played ?", + "Output Program": [ + "n0 = 20.0\nt0 = n0 - 1.0\nt1 = n0 * t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "190" + ], + "split": "train" + }, + { + "Input": "if a person walks at 14 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance travelled by him is :", + "Output Program": [ + "n0 = 14.0\nn1 = 10.0\nn2 = 20.0\nt0 = n0 - n1\nt1 = n2 / t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "there are 50 players in a chess group , and each player plays each of the others once . given that each game is played by two players , how many total games will be played ?", + "Output Program": [ + "n0 = 50.0\nt0 = n0 - 1.0\nt1 = n0 * t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "1225" + ], + "split": "train" + }, + { + "Input": "if a , b , c , d , e and f are integers and ( ab + cdef ) < 0 , then what is the maximum number e of integers that can be negative ?", + "Output Program": [ + "n0 = 0.0\nt0 = 10.0 / 2.0\nanswer = n0 + t0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "a certain bus driver is paid a regular rate of $ 14 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 998 in total compensation , how many total hours did he work that week ?", + "Output Program": [ + "n0 = 14.0\nn1 = 40.0\nn2 = 40.0\nn3 = 75.0\nn4 = 998.0\nt0 = n3 + 100.0\nt1 = n0 * n1\nt2 = n0 * t0\nt3 = n4 - t1\nt4 = t2 / 100.0\nt5 = t3 / t4\nanswer = n1 + t5\nprint(answer)" + ], + "Output Answer": [ + "57.87755102040816" + ], + "split": "train" + }, + { + "Input": "a certain debt will be paid in 40 installments from january 1 to december 31 of a certain year . each of the first 20 payments is to be $ 410 ; each of the remaining payments is to be $ 65 more than each of the first 20 payments . what is the average ( arithmetic mean ) payment that will be made on the debt for the year ?", + "Output Program": [ + "n0 = 40.0\nn1 = 1.0\nn2 = 31.0\nn3 = 20.0\nn4 = 410.0\nn5 = 65.0\nn6 = 20.0\nt0 = n4 + n5\nt1 = n3 * n4\nt2 = n0 - n3\nt3 = t0 * t2\nt4 = t1 + t3\nanswer = t4 / n0\nprint(answer)" + ], + "Output Answer": [ + "442.5" + ], + "split": "train" + }, + { + "Input": "a man owns 2 / 3 of market reserch beauro buzness , and sells 3 / 4 of his shares for 6500 rs , what is the value of buzness ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 3.0\nn3 = 4.0\nn4 = 6500.0\nt0 = n0 / n1\nt1 = n1 / n3\nt2 = t0 * t1\nanswer = n4 / t2\nprint(answer)" + ], + "Output Answer": [ + "13000" + ], + "split": "train" + }, + { + "Input": "on july 1 of last year , total employees at company e was decreased by 10 percent . without any change in the salaries of the remaining employees , the average ( arithmetic mean ) employee salary was 10 percent more after the decrease in the number of employees than before the decrease . the total of the combined salaries of all the employees at company e after july 1 last year was what percent r of thatbeforejuly 1 last year ?", + "Output Program": [ + "n0 = 1.0\nn1 = 10.0\nn2 = 10.0\nn3 = 1.0\nn4 = 1.0\n\nanswer = n1 * n1\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "3 friends a , b , c went for week end party to mcdonald \u2019 s restaurant and there they measure there weights in some order in 7 rounds . a , b , c , ab , bc , ac , abc . final round measure is 140 kg then find the average weight of all the 7 rounds ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 140.0\nn3 = 7.0\nt0 = 1.0 + n0\nt1 = n2 * t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "if ( 27 / 4 ) x - 18 = 3 x + 27 what is the value of x ?", + "Output Program": [ + "n0 = 27.0\nn1 = 4.0\nn2 = 18.0\nn3 = 3.0\nn4 = 27.0\nt0 = n0 + n2\nt1 = n0 / n1\nt2 = t1 - n3\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "the batting average of a particular batsman is 63 runs in 46 innings . if the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs , find his highest score .", + "Output Program": [ + "n0 = 63.0\nn1 = 46.0\nn2 = 150.0\nn3 = 58.0\nt0 = n0 * n1\nt1 = n1 - 2.0\nt2 = n3 * t1\nt3 = t0 - t2\nt4 = n2 + t3\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "248" + ], + "split": "train" + }, + { + "Input": "when 2 + 3 = 65 , 3 + 4 = 125 , 4 + 5 = 205 , then 5 + 6 = ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 65.0\nn3 = 3.0\nn4 = 4.0\nn5 = 125.0\nn6 = 4.0\nn7 = 5.0\nn8 = 205.0\nn9 = 5.0\nn10 = 6.0\nt0 = n7 * n10\nt1 = t0 * 10.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "302" + ], + "split": "train" + }, + { + "Input": "q ' = 3 q - 3 , what is the value of ( 7 ' ) ' ?", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 7.0\nt0 = n0 * n2\nt1 = n2 - 1.0\nt2 = t0 - n0\nt3 = n0 * t2\nt4 = t3 - n0\nanswer = t4 * t1\nprint(answer)" + ], + "Output Answer": [ + "306" + ], + "split": "train" + }, + { + "Input": "a grocer has a sale of rs . 5400 , rs . 9000 , rs . 6300 , rs . 7200 and rs . 4500 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 5600 ?", + "Output Program": [ + "n0 = 5400.0\nn1 = 9000.0\nn2 = 6300.0\nn3 = 7200.0\nn4 = 4500.0\nn5 = 5.0\nn6 = 5600.0\nt0 = n5 + 1.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n6 * t0\nt4 = n3 + t2\nt5 = n4 + t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "1200" + ], + "split": "train" + }, + { + "Input": "marginal cost is the cost of increasing the quantity produced ( or purchased ) by one unit . if the fixed cost for n products is $ 12000 and the marginal cost is $ 200 , and the total cost is $ 16000 , what is the value of n ?", + "Output Program": [ + "n0 = 12000.0\nn1 = 200.0\nn2 = 16000.0\nt0 = n2 - n0\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "$ 392 is divided among a , b , and c so that a receives half as much as b , and b receives half as much as c . how much money is c ' s share ?", + "Output Program": [ + "n0 = 392.0\nt0 = 1.0 / 2.0\nt1 = t0 + 1.0\nt2 = t1 + 2.0\nt3 = n0 / t2\nanswer = t3 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "224" + ], + "split": "train" + }, + { + "Input": "the value for d = ( 0.889 \u00d7 55 ) / 9.97 to the nearest tenth is", + "Output Program": [ + "import math\nn0 = 0.889\nn1 = 55.0\nn2 = 9.97\nt0 = n0 * n1\nt1 = t0 / n2\nt2 = t1 * 10.0\nt3 = math.floor(t2)\nanswer = t3 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "4.9" + ], + "split": "train" + }, + { + "Input": "find the least number which when divided by 37 and 7 leaves a remainder of 2 in each case .", + "Output Program": [ + "import scipy\nn0 = 37.0\nn1 = 7.0\nn2 = 2.0\nt0 = scipy.lcm(int(n0), int(n1))\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "261" + ], + "split": "train" + }, + { + "Input": "a furniture store owner decided to drop the price of her recliners by 20 % to spur business . by the end of the week she had sold 60 % more recliners . what is the percentage increase of the gross ?", + "Output Program": [ + "n0 = 20.0\nn1 = 60.0\nt0 = n1 / 100.0\nt1 = n0 / 100.0\nt2 = t0 + 1.0\nt3 = 1.0 - t1\nt4 = t2 * t3\nt5 = t4 * 100.0\nanswer = t5 - 100.0\nprint(answer)" + ], + "Output Answer": [ + "28.00000000000003" + ], + "split": "train" + }, + { + "Input": "10 play kabadi , 25 play kho kho only , 5 play both gmaes . then how many in total ?", + "Output Program": [ + "n0 = 10.0\nn1 = 25.0\nn2 = 5.0\nt0 = n1 + n2\nt1 = n0 + t0\nanswer = t1 - n2\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "on dividing a number by 5 , we get 5 as quotient and 0 as remainder . on dividing the same number by 11 , what will be the remainder ?", + "Output Program": [ + "n0 = 5.0\nn1 = 5.0\nn2 = 0.0\nn3 = 11.0\nt0 = n0 * n1\nanswer = t0 % n3\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "two brothers took the gmat exam , the higher score is u and the lower one is v . if the difference between the two scores is equal to their average , what is the value of v / u ?", + "Output Program": [ + "\nanswer = 1.0 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "0.3333333333333333" + ], + "split": "train" + }, + { + "Input": "in the rectangular coordinate system , if the line x = 6 y + 5 passes through points ( m , n ) and ( m + 2 , n + p ) , what is the value of p ?", + "Output Program": [ + "n0 = 6.0\nn1 = 5.0\nn2 = 2.0\n\nanswer = n2 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.3333333333333333" + ], + "split": "train" + }, + { + "Input": "2.09 can be expressed in terms of percentage as", + "Output Program": [ + "n0 = 2.09\n\nanswer = n0 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "209" + ], + "split": "train" + }, + { + "Input": "johnny bought 6 peanut butter cans at an average price ( arithmetic mean ) of 36.5 \u00a2 . if johnny returned two cans to the retailer , and the average price of the remaining cans was 30 \u00a2 , then what is the average price , in cents , of the two returned peanut butter cans ?", + "Output Program": [ + "n0 = 6.0\nn1 = 36.5\nn2 = 30.0\nt0 = n0 * n1\nt1 = n0 - 2.0\nt2 = n2 * t1\nt3 = t0 - t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "49.5" + ], + "split": "train" + }, + { + "Input": "what should be the least number to be added to the 1202 number to make it divisible by 4 ?", + "Output Program": [ + "n0 = 1202.0\nn1 = 4.0\nt0 = n0 % n1\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a man is 24 years older than his son . in two years , his age will be twice the age of his son . what is the present age of his son ?", + "Output Program": [ + "n0 = 24.0\nt0 = 2.0 * 2.0\nt1 = 2.0 - 1.0\nt2 = t0 - 2.0\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "in the hillside summer camp there are 60 children . 90 % of the children are boys and the rest are girls . the camp administrator decided to make the number of girls only 5 % of the total number of children in the camp . how many more boys must she bring to make that happen ?", + "Output Program": [ + "n0 = 60.0\nn1 = 90.0\nn2 = 5.0\nt0 = n2 / 100.0\nt1 = 100.0 - n2\nt2 = t1 / 100.0\nt3 = n0 * t0\nt4 = n0 * t2\nanswer = t4 + t3\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "in a certain brick wall , each row of bricks above the bottom row contains one less brick than the row just below it . if there are 5 rows in all and a total of 200 bricks in the wall , how many bricks does the bottom row contain ?", + "Output Program": [ + "n0 = 5.0\nn1 = 200.0\nt0 = n1 - 1.0\nt1 = t0 - 2.0\nt2 = t1 - 3.0\nt3 = t2 - 4.0\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "38" + ], + "split": "train" + }, + { + "Input": "when positive integer k is divided by 5 , the remainder is 2 . when k is divided by 6 , the remainder is 5 . if k is less than 41 , what is the remainder when k is divided by 7 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 6.0\nn3 = 5.0\nn4 = 41.0\nn5 = 7.0\nt0 = n0 + 12.0\nanswer = t0 % n5\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "find the value of 4 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ]", + "Output Program": [ + "n0 = 4.0\nn1 = 3.6\nn2 = 0.48\nn3 = 2.5\nn4 = 0.12\nn5 = 0.09\nn6 = 0.5\nt0 = n1 * n2\nt1 = n4 * n5\nt2 = n3 * t0\nt3 = n6 * t1\nt4 = t2 / t3\nanswer = n0 * t4\nprint(answer)" + ], + "Output Answer": [ + "3200.0000000000005" + ], + "split": "train" + }, + { + "Input": "an army \u2019 s recruitment process included n rounds of selection tasks . for the first a rounds , the rejection percentage was 60 percent per round . for the next b rounds , the rejection percentage was 50 percent per round and for the remaining rounds , the selection percentage was 70 percent per round . if there were 100000 people who applied for the army and 175 were finally selected , what was the value of n ?", + "Output Program": [ + "n0 = 60.0\nn1 = 50.0\nn2 = 70.0\nn3 = 100000.0\nn4 = 175.0\nt0 = 1.0 + 4.0\nt1 = t0 + 2.0\nanswer = t1 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "3 distinct single - digit numbers . a , b , c are in gp . if abs ( x ) for real x is the absolute value of x ( x if x is + ve or 0 and - x if x is - ve ) , then the number of different possible values of abs ( a + b + c ) is", + "Output Program": [ + "n0 = 3.0\nn1 = 0.0\n\nanswer = n0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "a batch of cookies was divided among 3 tins : 2 / 3 of all the cookies were placed in either the blue tin or the green tin , and the rest were placed in the red tin . if 1 / 4 of all the cookies were placed in the blue tin , what fraction w of the cookies that were placed in the other tins were placed in the green tin ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 3.0\nn3 = 1.0\nn4 = 4.0\nt0 = n1 / n0\nt1 = n3 / n4\nt2 = n3 / n0\nt3 = t0 - t1\nt4 = t2 + t3\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "0.5555555555555555" + ], + "split": "train" + }, + { + "Input": "40 % of major airline companies equip their planes with wireless internet access . 70 % of major airlines offer passengers free on - board snacks . what is the greatest possible percentage of major airline companies that offer both wireless internet and free on - board snacks ?", + "Output Program": [ + "n0 = 40.0\nn1 = 70.0\n\nanswer = n0 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "the population of a city increases by 8 % per year but due to migration it decrease by 1 % per years . what will be the percentage increase in population in 3 years ?", + "Output Program": [ + "n0 = 8.0\nn1 = 1.0\nn2 = 3.0\nt0 = n0 - n1\nt1 = t0 + 100.0\nt2 = t1 * t0\nt3 = t2 / 100.0\nt4 = t3 + t0\nt5 = t4 + 100.0\nt6 = t5 * t0\nt7 = t6 / 100.0\nanswer = t4 + t7\nprint(answer)" + ], + "Output Answer": [ + "22.5043" + ], + "split": "train" + }, + { + "Input": "how many 3 - digit numerals end with a digit that represents a prime number ?", + "Output Program": [ + "n0 = 3.0\nt0 = n0 * 100.0\nanswer = t0 + 100.0\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "train" + }, + { + "Input": "# p is defined as 2 p - 20 for any number p . what is p , if # ( # ( # p ) ) = 6 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 20.0\nn2 = 6.0\nt0 = n1 * n2\nt1 = n0 * 4.0\nt2 = n1 + t0\nt3 = n2 + t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "18.25" + ], + "split": "train" + }, + { + "Input": "when the price of sugar was increased by 32 % , a family reduced its consumption in such a way that the expenditure on sugar was only 10 % more than before . if 30 kg were consumed per month before , find the new monthly consumption .", + "Output Program": [ + "n0 = 32.0\nn1 = 10.0\nn2 = 30.0\nt0 = n1 + 100.0\nt1 = n0 + 100.0\nt2 = t0 / t1\nanswer = n2 * t2\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "find the 25 th term of an arithmetic progression whose first term is 5 and the common difference is 7 .", + "Output Program": [ + "n0 = 25.0\nn1 = 5.0\nn2 = 7.0\nt0 = n0 - 1.0\nt1 = n2 * t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "173" + ], + "split": "train" + }, + { + "Input": "in a graduating class , 40 percent of the students are male . in this class , 50 percent of the male students and 30 percent of the female students are 25 years old or older . if one student in the class is randomly selected , approximately what is the probability that he or she will be less than 25 years old ?", + "Output Program": [ + "n0 = 40.0\nn1 = 50.0\nn2 = 30.0\nn3 = 25.0\nn4 = 25.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = n2 / 100.0\nt3 = t0 * t1\nt4 = 1.0 - t0\nt5 = t2 * t4\nt6 = t3 + t5\nanswer = 1.0 - t6\nprint(answer)" + ], + "Output Answer": [ + "0.62" + ], + "split": "train" + }, + { + "Input": "the function g ( a ) is defined for integers a such that if a is even , g ( a ) = a / 2 and if a is odd , g ( a ) = a + 5 . given that g ( g ( g ( g ( g ( a ) ) ) ) ) = 19 , how many possible values for a would satisfy this equation ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 19.0\nt0 = n0 + n1\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "there are 16 bees in the hive , then 9 more fly . how many bees are there in all ?", + "Output Program": [ + "n0 = 16.0\nn1 = 9.0\n\nanswer = n0 + n1\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "seller selling an apple for rs . 20 , a seller loses 1 / 6 th of what it costs him . the cp of the apple is ?", + "Output Program": [ + "n0 = 20.0\nn1 = 1.0\nn2 = 6.0\n\nanswer = n0 + n1\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "nina has exactly enough money to purchase 6 widgets . if the cost of each widget were reduced by $ 1.15 , then nina would have exactly enough money to purchase 8 widgets . how much money does nina have ?", + "Output Program": [ + "n0 = 6.0\nn1 = 1.15\nn2 = 8.0\nt0 = n1 * n2\nt1 = n2 - n0\nt2 = t0 / t1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "27.599999999999998" + ], + "split": "train" + }, + { + "Input": "zoey won the lottery and got $ 7 , 348340 . she wants to split it among herself and 5 friends evenly . how much money must she add if she wants to split it evenly ?", + "Output Program": [ + "n0 = 7.0\nn1 = 348340.0\nn2 = 5.0\nt0 = n2 + 1.0\nt1 = 1000.0 * 1000.0\nt2 = n0 * t1\nt3 = n1 + t2\nt4 = t3 % t0\nanswer = t4 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "in a certain code language , ' book ' is coded as ' pencil ' , ' pencil ' is coded as ' mirror ' , ' mirror ' is coded as ' board ' . then what is useful to write on a paper ?", + "Output Program": [ + "\nanswer = 1.0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "if 50 % of ( x - y ) = 30 % of ( x + y ) , then what percent of x is y ?", + "Output Program": [ + "n0 = 50.0\nn1 = 30.0\nt0 = n0 + n1\nt1 = n0 - n1\nt2 = t1 / t0\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "an army \u2019 s recruitment process included n rounds of selection tasks . for the first a rounds , the rejection percentage was 60 percent per round . for the next b rounds , the rejection percentage was 50 percent per round and for the remaining rounds , the selection percentage was 70 percent per round . if there were 100000 people who applied for the army and 245 were finally selected , what was the value of n ?", + "Output Program": [ + "n0 = 60.0\nn1 = 50.0\nn2 = 70.0\nn3 = 100000.0\nn4 = 245.0\nt0 = 1.0 + 4.0\nt1 = t0 + 2.0\nanswer = t1 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "the average of 11 results is 60 . if the average of first 6 results is 58 and that of the last 6 is 63 , find the sixth result ?", + "Output Program": [ + "n0 = 11.0\nn1 = 60.0\nn2 = 6.0\nn3 = 58.0\nn4 = 6.0\nn5 = 63.0\nt0 = n2 * n3\nt1 = n2 * n5\nt2 = n0 * n1\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "66" + ], + "split": "train" + }, + { + "Input": "if there are 4 peanuts in a box and mary puts 8 more peanuts inside , how many peanuts are in the box ?", + "Output Program": [ + "n0 = 4.0\nn1 = 8.0\n\nanswer = n0 + n1\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "if rs . 1440 / - are divided among a , b and c so that a receives 1 / 3 rd as much as b and b receives 1 / 4 th as much as c . the amount b received is ?", + "Output Program": [ + "n0 = 1440.0\nn1 = 1.0\nn2 = 3.0\nn3 = 1.0\nn4 = 4.0\nt0 = n1 / n4\nt1 = n2 * n4\nt2 = n1 / t1\nt3 = t2 + t0\nt4 = n1 + t3\nt5 = n0 / t4\nanswer = t5 / n4\nprint(answer)" + ], + "Output Answer": [ + "270" + ], + "split": "train" + }, + { + "Input": "when toys are grouped into 12 and 18 , always 3 toys remain ungrouped . what is the minimum number of toys to be added so that when they are grouped into 7 , no toys will remain ungrouped ?", + "Output Program": [ + "import scipy\nn0 = 12.0\nn1 = 18.0\nn2 = 3.0\nn3 = 7.0\nt0 = 2.0 + 4.0\nt1 = scipy.lcm(int(n0), int(n1))\nt2 = n2 + t1\nt3 = n3 * t0\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "the average temperature for monday , tuesday , wednesday and thursday was 48 degrees and for tuesday , wednesday , thursday and friday was 46 degrees . if the temperature on monday was 41 degrees . find the temperature on friday ?", + "Output Program": [ + "n0 = 48.0\nn1 = 46.0\nn2 = 41.0\nt0 = n0 * 4.0\nt1 = n1 * 4.0\nt2 = t0 - t1\nanswer = n2 - t2\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "month average price per dozen april $ 1.2 may $ 1.20 june $ 3.00 the table above shows the average ( arithmetic mean ) price per dozen of the large grade a eggs sold in a certain store during 3 successive months . if 2 / 3 as many dozen were sold in april as in may , and twice as many were sold in june as in april , what was the average price per dozen of the eggs sold over the 3 - month period ?", + "Output Program": [ + "n0 = 1.2\nn1 = 1.2\nn2 = 3.0\nn3 = 3.0\nn4 = 2.0\nn5 = 3.0\nn6 = 3.0\nt0 = n4 / n2\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a company received $ 2 million in royalties on the first $ 10 million in sales and then $ 8 million in royalties on the next $ 100 million in sales . by what percent did the ratio of royalties to sales decrease from the first $ 10 million in sales to the next $ 100 million in sales ?", + "Output Program": [ + "n0 = 2.0\nn1 = 10.0\nn2 = 8.0\nn3 = 100.0\nn4 = 10.0\nn5 = 100.0\nt0 = n0 / 10.0\nt1 = n2 / n3\nt2 = t0 - t1\nt3 = t2 / t0\nanswer = n3 * t3\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "zinc and copper are melted together in the ratio 9 : 11 . what is the weight of melted mixture , if 35.1 kg of zinc has been consumed in it ?", + "Output Program": [ + "n0 = 9.0\nn1 = 11.0\nn2 = 35.1\nt0 = n1 / n0\nt1 = n2 * t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "78" + ], + "split": "train" + }, + { + "Input": "find the lowest common multiple of 15 , 25 and 35 .", + "Output Program": [ + "import scipy\nn0 = 15.0\nn1 = 25.0\nn2 = 35.0\nt0 = scipy.lcm(int(n0), int(n1))\nanswer = scipy.lcm(int(n2), int(t0))\nprint(answer)" + ], + "Output Answer": [ + "525" + ], + "split": "train" + }, + { + "Input": "a charitable woman gave one penny more than half pennies in her purse to a farmer . afterwards she came across a beggar whom she gave 2 pennies more than half of what she had in her purse . in the end she gave 3 pennies more than half of what she had in her purse and left with a penny with her to a boy . find what she had in the beginning ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nt0 = n1 + 1.0\nt1 = n0 * t0\nt2 = n0 + t1\nt3 = n0 * t2\nt4 = t3 + 1.0\nanswer = n0 * t4\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "if x , y , and z are positive integers , and 2 x = 5 y = 6 z , then the least possible value of x + y + z is", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 6.0\nt0 = n0 * n1\nt1 = n2 * t0\nt2 = t1 / 2.0\nt3 = t2 / n0\nt4 = t2 / n1\nt5 = t2 / n2\nt6 = t3 + t4\nanswer = t6 + t5\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "one - third of rahul ' s savings in national savings certificate is equal to one - half of his savings in public provident fund . if he has rs . 1 , 80000 as total savings , how much has he saved in public provident fund ?", + "Output Program": [ + "n0 = 1.0\nn1 = 80000.0\nt0 = 2.0 + 3.0\nt1 = 2.0 * 3.0\nt2 = 10.0**min(4.0, 5)\nt3 = t2 * 10.0\nt4 = n1 + t3\nt5 = t4 / 2.0\nt6 = t5 * t1\nt7 = t6 / t0\nanswer = t4 - t7\nprint(answer)" + ], + "Output Answer": [ + "72000" + ], + "split": "train" + }, + { + "Input": "there are 408 boys and 192 girls in a school which are to be divided into equal sections of either boys or girls alone . find the total number of sections thus formed .", + "Output Program": [ + "n0 = 408.0\nn1 = 192.0\nt0 = n0 + n1\nt1 = 2.0 * 2.0\nt2 = t1 * 2.0\nt3 = t2 * 3.0\nanswer = t0 / t3\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "at deluxe paint store , fuchsia paint is made by mixing 5 parts of red paint with 3 parts of blue paint . mauve paint is made by mixing 3 parts of red paint with 5 parts blue paint . how many liters of blue paint must be added to 40 liters of fuchsia to change it to mauve paint ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nn2 = 3.0\nn3 = 5.0\nn4 = 40.0\nt0 = n0 + n1\nt1 = n0 / t0\nt2 = n2 / t0\nt3 = n3 / t0\nt4 = n4 * t1\nt5 = t4 / t2\nt6 = n4 - t4\nt7 = t5 * t3\nanswer = t7 - t6\nprint(answer)" + ], + "Output Answer": [ + "26.66666666666667" + ], + "split": "train" + }, + { + "Input": "according to the directions on the can of frozen orange juice concentrate , 1 can of concentrate is to be mixed with 3 cans of water to make orange juice . how many 12 ounces cans of the concentrate are required to prepare 320 6 ounces servings of orange juice ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 12.0\nn3 = 320.0\nn4 = 6.0\nt0 = n3 * n4\nt1 = t0 / n2\nanswer = t1 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "the largest natural number which exactly divides the product of any 4 consecutive natural numbers is", + "Output Program": [ + "import math\nn0 = 4.0\n\nanswer = math.factorial(min(15, int(n0)))\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "9873 + x = 13800 , then x is ?", + "Output Program": [ + "n0 = 9873.0\nn1 = 13800.0\n\nanswer = n1 - n0\nprint(answer)" + ], + "Output Answer": [ + "3927" + ], + "split": "train" + }, + { + "Input": "a grocer is storing soap boxes in cartons that measure 25 inches by 42 inches by 60 inches . if the measurement of each soap box is 7 inches by 6 inches by 5 inches , then what is the maximum number of soap boxes that can be placed in each carton ?", + "Output Program": [ + "n0 = 25.0\nn1 = 42.0\nn2 = 60.0\nn3 = 7.0\nn4 = 6.0\nn5 = 5.0\nt0 = n0 * n1\nt1 = n3 * n4\nt2 = n2 * t0\nt3 = n5 * t1\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "two employees x and y are paid a total of rs . 572 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?", + "Output Program": [ + "n0 = 572.0\nn1 = 120.0\nt0 = 1.0 + 4.0\nt1 = t0 * 2.0\nt2 = t1 + 1.0\nt3 = n0 * t1\nt4 = t2 * 2.0\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "260" + ], + "split": "train" + }, + { + "Input": "the product of a and b is equal to 11 more than twice the sum of a and b . if b = 7 , what is the value of b - a ?", + "Output Program": [ + "n0 = 11.0\nn1 = 7.0\nt0 = n1 * 2.0\nt1 = n1 - 2.0\nt2 = n0 + t0\nt3 = t2 / t1\nanswer = n1 - t3\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "9 men are equal to as many women as are equal to 7 boys . all of them earn rs . 216 only . men \u2019 s wages are ?", + "Output Program": [ + "n0 = 9.0\nn1 = 7.0\nn2 = 216.0\nt0 = n0 * 3.0\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "3 buffaloes eat as much as 4 cows or 2 oxen . at a farm , there are 15 buffaloes , 8 oxen , and 24 cows . the fodder for these cattle is available for 48 days . if 40 more cows and 15 more buffaloes are brought in , how many days will the fodder last ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 2.0\nn3 = 15.0\nn4 = 8.0\nn5 = 24.0\nn6 = 48.0\nn7 = 40.0\nn8 = 15.0\nt0 = n3 + n8\nt1 = n5 + n7\nt2 = n5 / n1\nt3 = n4 / n2\nt4 = t1 / n1\nt5 = n0 * t2\nt6 = n0 * t3\nt7 = n3 + t5\nt8 = n0 * t4\nt9 = t7 + t6\nt10 = t0 + t8\nt11 = t10 + t6\nt12 = n6 * t9\nanswer = t12 / t11\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "find the least number must be subtracted from 378461 so that remaining no . is divisible by 13 ?", + "Output Program": [ + "import math\nn0 = 378461.0\nn1 = 13.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "a certain pair of used shoes can be repaired for $ 11.50 and will last for 1 year . a pair of the same kind of shoes can be purchased new for $ 28.00 and will last for 2 years . the average cost per year of the new shoes is what percent greater than the cost of repairing the used shoes ?", + "Output Program": [ + "n0 = 11.5\nn1 = 1.0\nn2 = 28.0\nn3 = 2.0\nt0 = n0 * n3\nt1 = n2 - t0\nt2 = t1 / t0\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "21.73913043478261" + ], + "split": "train" + }, + { + "Input": "if sharon ' s weekly salary increased by 10 percent , she would earn $ 330 per week . if instead , her weekly salary were to increase by 8 percent , how much would she earn per week ?", + "Output Program": [ + "n0 = 10.0\nn1 = 330.0\nn2 = 8.0\nt0 = n0 / 100.0\nt1 = n2 / 100.0\nt2 = t0 + 1.0\nt3 = n1 / t2\nt4 = t1 * t3\nanswer = t3 + t4\nprint(answer)" + ], + "Output Answer": [ + "324" + ], + "split": "train" + }, + { + "Input": "a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 1200 in total compensation , how many total hours did he work that week ?", + "Output Program": [ + "n0 = 16.0\nn1 = 40.0\nn2 = 40.0\nn3 = 75.0\nn4 = 1200.0\nt0 = n3 + 100.0\nt1 = n0 * n1\nt2 = n0 * t0\nt3 = n4 - t1\nt4 = t2 / 100.0\nt5 = t3 / t4\nanswer = n1 + t5\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "if 5 ^ 29 * 4 ^ 15 = 2 * 10 ^ n , what is the value of n ?", + "Output Program": [ + "n0 = 5.0\nn1 = 29.0\nn2 = 4.0\nn3 = 15.0\nn4 = 2.0\nn5 = 10.0\nt0 = n3 * 2.0\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "29" + ], + "split": "train" + }, + { + "Input": "if 2 ^ k = 4 , then 2 ^ ( 2 k + 2 ) =", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 2.0\nn3 = 2.0\nn4 = 2.0\nt0 = n1**min(n3, 5)\nt1 = n0**min(n4, 5)\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "train" + }, + { + "Input": "the average marks of a class of 28 students is 40 and that of another class of 50 students is 60 . find the average marks of all the students ?", + "Output Program": [ + "n0 = 28.0\nn1 = 40.0\nn2 = 50.0\nn3 = 60.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "52.82051282051282" + ], + "split": "train" + }, + { + "Input": "free notebooks were distributed equally among children of a class . the number of notebooks each child got was one - eighth of the number of children . had the number of children been half , each child would have got 16 notebooks . total how many notebooks were distributed ?", + "Output Program": [ + "n0 = 16.0\nt0 = n0 / 2.0\nt1 = t0 * t0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "512" + ], + "split": "train" + }, + { + "Input": "find the greatest number which on dividing 1661 and 2045 , leaves a reminder of 10 and 13 respectively", + "Output Program": [ + "import scipy\nn0 = 1661.0\nn1 = 2045.0\nn2 = 10.0\nn3 = 13.0\nt0 = n0 - n2\nt1 = n1 - n3\nanswer = scipy.gcd(int(t0), int(t1))\nprint(answer)" + ], + "Output Answer": [ + "127" + ], + "split": "train" + }, + { + "Input": "find the number of terms in an arithmetic progression with the first term 2 and the last term being 62 , given that common difference is 2 .", + "Output Program": [ + "n0 = 2.0\nn1 = 62.0\nn2 = 2.0\nt0 = n1 - n0\nt1 = t0 / n0\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "31" + ], + "split": "train" + }, + { + "Input": "a , b , c , d , and e are positive consecutive integers and a < b < c < d < e . if the sum of a + b is one less than e , and the product of ab is one more than d , then what is the value of c ?", + "Output Program": [ + "import math\nt0 = 2.0 * 4.0\nt1 = -2.0\nt2 = -t1\nt3 = -t0\nt4 = t1**min(2.0, 5)\nt5 = t3 * t4\nt6 = t4 - t5\nt7 = math.sqrt(max(0, t6))\nt8 = t2 + t7\nanswer = t8 / t2\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "15 times a positive integer is more than its square by 56 , then the positive integer is", + "Output Program": [ + "n0 = 15.0\nn1 = 56.0\nt0 = n1 * 4.0\nt1 = n0**min(2.0, 5)\nt2 = t1 - t0\nt3 = n0 + t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a line that passes through ( \u2013 1 , \u2013 4 ) and ( 3 , k ) has a slope = k . what is the value of k ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 3.0\n\nanswer = n1 / n2\nprint(answer)" + ], + "Output Answer": [ + "1.3333333333333333" + ], + "split": "train" + }, + { + "Input": "the faces of storage box are to be painted by 6 different colors . in how many ways can be this be done ?", + "Output Program": [ + "n0 = 6.0\nt0 = n0 - 1.0\nt1 = n0 * t0\nt2 = t1 * 4.0\nt3 = t2 * 3.0\nt4 = t3 * 2.0\nanswer = t4 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "720" + ], + "split": "train" + }, + { + "Input": "in n is a positive integer less than 200 , and 14 n / 60 is an integer , then n has how many different positive prime factors r ?", + "Output Program": [ + "n0 = 200.0\nn1 = 14.0\nn2 = 60.0\nt0 = 1.0 + 4.0\nt1 = n2 / 2.0\nt2 = t1 / 2.0\nt3 = t2 / 3.0\nt4 = t0 / t3\nanswer = t4 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 35 kg . what is the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.5\nn2 = 35.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "55" + ], + "split": "train" + }, + { + "Input": "if x + y = 2 x + z , x - 2 y = 4 z and x + y + z = 21 , what is the value of y / z ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 4.0\nn3 = 21.0\nt0 = n3 / n0\nt1 = n3 / 10.0\nt2 = -t1\nt3 = t0 / t2\nt4 = -t3\nanswer = t4 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "12 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ?", + "Output Program": [ + "n0 = 12.0\nt0 = n0 - 1.0\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "132" + ], + "split": "train" + }, + { + "Input": "in a division , a student took 48 as divisor instead of 36 . his answer was 24 . the correct answer is -", + "Output Program": [ + "n0 = 48.0\nn1 = 36.0\nn2 = 24.0\nt0 = n0 * n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 160 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?", + "Output Program": [ + "n0 = 160.0\n\nanswer = n0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "320" + ], + "split": "train" + }, + { + "Input": "a number whose fifth part increased by 6 is equal to its fourth part diminished by 6 is ?", + "Output Program": [ + "n0 = 6.0\nn1 = 6.0\nt0 = n0 + n1\nt1 = 1.0 + 4.0\nt2 = 1.0 / 4.0\nt3 = 1.0 / t1\nt4 = t2 - t3\nanswer = t0 / t4\nprint(answer)" + ], + "Output Answer": [ + "240.00000000000006" + ], + "split": "train" + }, + { + "Input": "robert ate 7 chocolates , nickel ate 3 chocolates . how many more chocolates did robert ate than nickel ?", + "Output Program": [ + "n0 = 7.0\nn1 = 3.0\n\nanswer = n0 - n1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "what is the sum of the digits of integer k , if k = ( 10 ^ 30 - 54 )", + "Output Program": [ + "n0 = 10.0\nn1 = 30.0\nn2 = 54.0\nt0 = n0 - 1.0\nt1 = n1 - 2.0\nt2 = t0 * t1\nanswer = t2 + n0\nprint(answer)" + ], + "Output Answer": [ + "262" + ], + "split": "train" + }, + { + "Input": "a batsman makes a score of 90 runs in the 11 th inning and thus increases his average by 5 . find his average after 11 th inning .", + "Output Program": [ + "n0 = 90.0\nn1 = 11.0\nn2 = 5.0\nn3 = 11.0\nt0 = n1 * n2\nt1 = n0 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 72 , then how old is b ?", + "Output Program": [ + "n0 = 72.0\nt0 = 1.0 + 4.0\nt1 = n0 - 2.0\nt2 = t1 * 2.0\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "dick and jane each saved $ 1,000 in 1989 . in 1990 dick saved 15 percent more than in 1989 , and together he and jane saved a total of $ 2,000 . approximately what percent less did jane save in 1990 than in 1989 ?", + "Output Program": [ + "n0 = 1000.0\nn1 = 1989.0\nn2 = 1990.0\nn3 = 15.0\nn4 = 1989.0\nn5 = 2000.0\nn6 = 1990.0\nn7 = 1989.0\nt0 = n3 / 100.0\nt1 = t0 + 1.0\nt2 = 2.0 - t1\nt3 = 1.0 - t2\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "14.999999999999991" + ], + "split": "train" + }, + { + "Input": "a certain library assesses fines for overdue books as follows . on the first day that a book is overdue , the total fine is $ 0.07 . for each additional day that the book is overdue , the total fine is either increased by $ 0.30 or doubled , whichever results in the lesser amount . what is the total for a book on the fifth day it is overdue ?", + "Output Program": [ + "n0 = 0.07\nn1 = 0.3\nt0 = n0 * 2.0\nt1 = t0 * 2.0\nt2 = t1 * 2.0\nanswer = n1 + t2\nprint(answer)" + ], + "Output Answer": [ + "0.8600000000000001" + ], + "split": "train" + }, + { + "Input": "how many numbers from 19 to 79 are exactly divisible by 11 ?", + "Output Program": [ + "import math\nn0 = 19.0\nn1 = 79.0\nn2 = 11.0\nt0 = n1 / n2\nt1 = n0 / n2\nt2 = math.floor(t0)\nt3 = math.floor(t1)\nt4 = t3 + 1.0\nt5 = n2 * t2\nt6 = n2 * t4\nt7 = t5 - t6\nt8 = t7 / n2\nanswer = t8 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "if the sum and difference of two numbers are 10 and 8 respectively , then the difference of their square is :", + "Output Program": [ + "n0 = 10.0\nn1 = 8.0\nt0 = n0 + n1\nt1 = t0 / 2.0\nt2 = t1**min(2.0, 5)\nt3 = n0 - t1\nt4 = t3**min(2.0, 5)\nanswer = t2 - t4\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "how many times will the digit 5 be written when listing the integers from 1 to 1000 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 1.0\nn2 = 1000.0\nt0 = n1 * 10.0\nt1 = t0 * 10.0\nanswer = t1 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "a cab driver 5 days income was $ 200 , $ 150 , $ 750 , $ 400 , $ 500 . then his average income is ?", + "Output Program": [ + "n0 = 5.0\nn1 = 200.0\nn2 = 150.0\nn3 = 750.0\nn4 = 400.0\nn5 = 500.0\nt0 = n1 + n2\nt1 = n3 + t0\nt2 = n4 + t1\nt3 = n5 + t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "train" + }, + { + "Input": "a tightrope approximately 320 m long is suspended between two poles . during a performance , a break occurs in the line . assume that the line has an equal chance of breaking anywhere along its length . what is the probability that the break happened in the first 50 meters of the rope ?", + "Output Program": [ + "n0 = 320.0\nn1 = 50.0\n\nanswer = n1 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.15625" + ], + "split": "train" + }, + { + "Input": "on thursday mabel handled 90 transactions . anthony handled 10 % more transactions than mabel , cal handled 2 / 3 rds of the transactions that anthony handled , and jade handled 18 more transactions than cal . how much transactions did jade handled ?", + "Output Program": [ + "n0 = 90.0\nn1 = 10.0\nn2 = 2.0\nn3 = 3.0\nn4 = 18.0\nt0 = n1 + 100.0\nt1 = n0 / 100.0\nt2 = t0 * t1\nt3 = n2 * t2\nt4 = t3 / n3\nanswer = n4 + t4\nprint(answer)" + ], + "Output Answer": [ + "84" + ], + "split": "train" + }, + { + "Input": "a , b and c rent a pasture . if a puts 10 oxen for 7 months , b puts 12 oxen for 5 months and c puts 15 oxen for 3 months for grazing and the rent of the pasture is rs . 140 , then how much amount should c pay as his share of rent ?", + "Output Program": [ + "n0 = 10.0\nn1 = 7.0\nn2 = 12.0\nn3 = 5.0\nn4 = 15.0\nn5 = 3.0\nn6 = 140.0\nt0 = n4 * n5\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nt4 = t3 + t0\nt5 = t0 / t4\nanswer = n6 * t5\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "by how much is 12 % of 24.2 more than 10 % of 14.2 ?", + "Output Program": [ + "n0 = 12.0\nn1 = 24.2\nn2 = 10.0\nn3 = 14.2\nt0 = n0 / 100.0\nt1 = n2 / 100.0\nt2 = n1 * t0\nt3 = n3 * t1\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "1.484" + ], + "split": "train" + }, + { + "Input": "the jogging track in a sports complex is 627 m in circumference . deepak and his wife start from the same point and walk in opposite directions at 4.5 km / hr and 3.75 km / hr respectively . they will meet for the first time in ?", + "Output Program": [ + "n0 = 627.0\nn1 = 4.5\nn2 = 3.75\nt0 = n1 + n2\nt1 = n0 / 1000.0\nt2 = t1 / t0\nanswer = t2 * 60.0\nprint(answer)" + ], + "Output Answer": [ + "4.56" + ], + "split": "train" + }, + { + "Input": "a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 50 paisa . if the share of y is rs . 36 , what is the total amount ?", + "Output Program": [ + "n0 = 45.0\nn1 = 50.0\nn2 = 36.0\nt0 = 100.0 / n0\nt1 = n1 / n0\nt2 = n2 * t0\nt3 = n2 * t1\nt4 = t2 + t3\nanswer = n2 + t4\nprint(answer)" + ], + "Output Answer": [ + "156" + ], + "split": "train" + }, + { + "Input": "a certain company retirement plan has arule of 70 provision that allows an employee to retire when the employee ' s age plus years of employment with the company total at least 70 . in what year could a female employee hired in 1989 on her 32 nd birthday first be eligible to retire under this provision ?", + "Output Program": [ + "n0 = 70.0\nn1 = 70.0\nn2 = 1989.0\nn3 = 32.0\nt0 = n0 - n3\nt1 = t0 / 2.0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "2008" + ], + "split": "train" + }, + { + "Input": "carina has 115 ounces of coffee divided into 5 - and 10 - ounce packages . if she has 2 more 5 - ounce packages than 10 - ounce packages , how many 10 - ounce packages does she have ?", + "Output Program": [ + "n0 = 115.0\nn1 = 5.0\nn2 = 10.0\nn3 = 2.0\nn4 = 5.0\nn5 = 10.0\nn6 = 10.0\nt0 = n1 + n2\nt1 = n1 * n3\nt2 = n0 - t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "what is the sum of 100 consecutive integers from - 49 inclusive , in a increasing order ?", + "Output Program": [ + "n0 = 100.0\nn1 = 49.0\n\nanswer = n1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "if the average ( arithmetic mean ) of ( 2 a + 16 ) and ( 3 a - 8 ) is 84 , what is the value of a ?", + "Output Program": [ + "n0 = 2.0\nn1 = 16.0\nn2 = 3.0\nn3 = 8.0\nn4 = 84.0\nt0 = n0 + n2\nt1 = n0 * n4\nt2 = n1 - n3\nt3 = t1 - t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "if the sum and difference of two numbers are 10 and 19 respectively , then the difference of their square is :", + "Output Program": [ + "n0 = 10.0\nn1 = 19.0\nt0 = n0 + n1\nt1 = t0 / 2.0\nt2 = t1**min(2.0, 5)\nt3 = n0 - t1\nt4 = t3**min(2.0, 5)\nanswer = t2 - t4\nprint(answer)" + ], + "Output Answer": [ + "190" + ], + "split": "train" + }, + { + "Input": "if 14 percent of the students at a certain school went to a camping trip and took more than $ 100 , and 75 percent of the students who went to the camping trip did not take more than $ 100 , what percentage of the students at the school went to the camping trip ?", + "Output Program": [ + "n0 = 14.0\nn1 = 100.0\nn2 = 75.0\nn3 = 100.0\nt0 = 100.0 - n2\nt1 = t0 / 100.0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "train" + }, + { + "Input": "a vessel of capacity 2 litre has 40 % of alcohol and another vessel of capacity 6 litre had 60 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?", + "Output Program": [ + "n0 = 2.0\nn1 = 40.0\nn2 = 6.0\nn3 = 60.0\nn4 = 8.0\nn5 = 10.0\nt0 = n1 / 100.0\nt1 = n3 / 100.0\nt2 = n0 * t0\nt3 = n2 * t1\nt4 = t2 + t3\nt5 = t4 / n5\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "43.99999999999999" + ], + "split": "train" + }, + { + "Input": "65 % of x = 20 % of 422.50 . find the value of x ?", + "Output Program": [ + "n0 = 65.0\nn1 = 20.0\nn2 = 422.5\nt0 = n2 / 100.0\nt1 = n1 * t0\nt2 = t1 * 100.0\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "130" + ], + "split": "train" + }, + { + "Input": "on increasing the number of lines in a page by 80 , they become 240 . what is the % of increase in the no . of lines in the page ?", + "Output Program": [ + "n0 = 80.0\nn1 = 240.0\nt0 = n1 - n0\nt1 = n1 / t0\nt2 = t1 * 100.0\nanswer = t2 - 100.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "a batsman scored 120 runs whichincluded 3 boundaries and 8 sixes . what % of his total score did he make by running between the wickets", + "Output Program": [ + "n0 = 120.0\nn1 = 3.0\nn2 = 8.0\nt0 = n1 + 3.0\nt1 = n1 * 4.0\nt2 = n2 * t0\nt3 = t1 + t2\nt4 = t3 / n0\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "in a group of 86 students , each student is registered for at least one of 3 classes \u2013 history , math and english . 20 - 8 students are registered for history , 20 - 3 students are registered for math , and forty - 4 students are registered for english . if only 3 students are registered for all 3 classes , how many students are registered for exactly two classes ?", + "Output Program": [ + "n0 = 86.0\nn1 = 3.0\nn2 = 20.0\nn3 = 8.0\nn4 = 20.0\nn5 = 3.0\nn6 = 4.0\nn7 = 3.0\nn8 = 3.0\nt0 = n1 + n2\nt1 = n2 + n3\nt2 = n6 * 10.0\nt3 = n1 * n1\nt4 = n0 - n1\nt5 = t0 + t1\nt6 = n6 + t2\nt7 = t5 + t6\nt8 = t7 - t3\nanswer = t8 - t4\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "there were totally 100 men . 82 are married . 75 have t . v , 85 have radio , 70 have a . c . how many men have t . v , radio , a . c and also married ?", + "Output Program": [ + "n0 = 100.0\nn1 = 82.0\nn2 = 75.0\nn3 = 85.0\nn4 = 70.0\nt0 = n0 - n1\nt1 = n0 - n2\nt2 = n0 - n3\nt3 = n0 - n4\nt4 = t0 + t1\nt5 = t4 + t2\nt6 = t5 + t3\nanswer = n0 - t6\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "average monthly income of a family of 4 earning members was rs . 735 . one of the earning members died and therefore , the average income came down to rs 590 . the income of the deceased was ?", + "Output Program": [ + "n0 = 4.0\nn1 = 735.0\nn2 = 590.0\nt0 = n0 * n1\nt1 = n0 - 1.0\nt2 = n2 * t1\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "1170" + ], + "split": "train" + }, + { + "Input": "two nascar stock cars take off from the starting line at the exact same time , heading in opposite directions . the budweiser car travels at 145 miles per hour , while the stella artois car travels at 150 miles per hour . at this rate , and ignoring other variable , how long will the cars have to drive in order to be 500 miles , in total , from each other ?", + "Output Program": [ + "n0 = 145.0\nn1 = 150.0\nn2 = 500.0\nt0 = n0 + n1\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "1.694915254237288" + ], + "split": "train" + }, + { + "Input": "find the average of all numbers between 6 and 36 which are divisible by 7", + "Output Program": [ + "n0 = 6.0\nn1 = 36.0\nn2 = 7.0\nt0 = 1.0 + 4.0\nt1 = n2 * 2.0\nt2 = n2 * 3.0\nt3 = n2 * 4.0\nt4 = n2 + t1\nt5 = n2 * t0\nt6 = t4 + t2\nt7 = t6 + t3\nt8 = t7 + t5\nanswer = t8 / n2\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "a straight line in the xy - plane has slope 4 . on this line the x - coordinate of the point is 50 and y - coordinate is 300 then what is the y intercept of the plane ?", + "Output Program": [ + "n0 = 4.0\nn1 = 50.0\nn2 = 300.0\nt0 = n0 * n1\nanswer = n2 - t0\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "the ratio 4 : 20 expressed as percent equals to", + "Output Program": [ + "n0 = 4.0\nn1 = 20.0\nt0 = n0 / n1\nanswer = t0 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "the area of one square is x ^ 2 + 8 x + 16 and the area of another square is 4 x ^ 2 \u2212 12 x + 9 . if the sum of the perimeters of both squares is 32 , what is the value of x ?", + "Output Program": [ + "n0 = 2.0\nn1 = 8.0\nn2 = 16.0\nn3 = 4.0\nn4 = 2.0\nn5 = 12.0\nn6 = 9.0\nn7 = 32.0\nt0 = n1 / n0\nt1 = t0 * n3\nt2 = t1 - n5\nt3 = n7 - t2\nanswer = t3 / n5\nprint(answer)" + ], + "Output Answer": [ + "2.3333333333333335" + ], + "split": "train" + }, + { + "Input": "evaluate 45 / . 05", + "Output Program": [ + "n0 = 45.0\nn1 = 5.0\nt0 = n1 / 100.0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "900" + ], + "split": "train" + }, + { + "Input": "how many 3 - digit even numbers are possible such that if one of the digits is 5 , the next / succeeding digit to it should be 1 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 1.0\nt0 = n0 + n2\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "gopi gives rs . 90 plus one turban as salary to his servant for one year . the servant leaves after 9 months and receives rs . 40 and the turban . find the price of the turban .", + "Output Program": [ + "n0 = 90.0\nn1 = 9.0\nn2 = 40.0\nt0 = n0 - n2\nt1 = 12.0 - n1\nt2 = t0 / t1\nt3 = t2 * 12.0\nanswer = t3 - n0\nprint(answer)" + ], + "Output Answer": [ + "110" + ], + "split": "train" + }, + { + "Input": "in a class there are a total of 8 rows of desks and each desk can seat one student . there are 10 desks in the first row . in each subsequent row there are 2 more desks than in the previous row . find the maximum number of students seated in the class ?", + "Output Program": [ + "n0 = 8.0\nn1 = 10.0\nn2 = 2.0\nt0 = n0 + n1\nt1 = n0 * n2\nt2 = t0 + t1\nt3 = t2 / n2\nanswer = n0 * t3\nprint(answer)" + ], + "Output Answer": [ + "136" + ], + "split": "train" + }, + { + "Input": "solve for x and check : - 200 x = 1600", + "Output Program": [ + "n0 = 200.0\nn1 = 1600.0\nt0 = n1 / n0\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "1600" + ], + "split": "train" + }, + { + "Input": "there are 450 birds at a small zoo . the number of birds is 5 times the number of all the other animals combined . how many more birds are there than non bird animals at the zoo ?", + "Output Program": [ + "n0 = 450.0\nn1 = 5.0\nt0 = n0 / n1\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "360" + ], + "split": "train" + }, + { + "Input": "if 16 ^ y = 4 ^ 16 , what is y ?", + "Output Program": [ + "n0 = 16.0\nn1 = 4.0\nn2 = 16.0\n\nanswer = n2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a library has an average of 510 visitors on sundays and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is", + "Output Program": [ + "import math\nn0 = 510.0\nn1 = 240.0\nn2 = 30.0\nt0 = 3.0 + 4.0\nt1 = n2 / t0\nt2 = math.floor(t1)\nt3 = t2 + 1.0\nt4 = n0 * t3\nt5 = n2 - t3\nt6 = n1 * t5\nt7 = t4 + t6\nanswer = t7 / n2\nprint(answer)" + ], + "Output Answer": [ + "285" + ], + "split": "train" + }, + { + "Input": "the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 50 kg . what is the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.5\nn2 = 50.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "train" + }, + { + "Input": "the average of 10 numbers is calculated as 15 . it is discovered later on that while calculating the average one number , namely 36 was wrongly read as 26 . the correct average is :", + "Output Program": [ + "n0 = 10.0\nn1 = 15.0\nn2 = 36.0\nn3 = 26.0\nt0 = n2 - n3\nt1 = t0 / n0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "if z is not equal to zero , and z = 6 zs \u2212 9 s 2 \u2212 \u2212 \u2212 \u2212 \u2212 \u2212 \u2212 \u2212 \u221a z = 6 zs \u2212 9 s 2 , then z equals :", + "Output Program": [ + "import scipy\nn0 = 6.0\nn1 = 9.0\nn2 = 2.0\nn3 = 6.0\nn4 = 9.0\nn5 = 2.0\nt0 = scipy.gcd(int(n0), int(n1))\nt1 = n1 / t0\nt2 = n0 / t0\nt3 = t1 + t0\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "each machine of type a has 2 steel parts and 3 chrome parts . each machine of type b has 3 steel parts and 5 chrome parts . if a certain group of type a and type b machines has a total of 40 steel parts and 32 chrome parts , how many machines are in the group", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 3.0\nn3 = 5.0\nn4 = 40.0\nn5 = 32.0\nt0 = n1 + n3\nt1 = n0 + n1\nt2 = n5 / t0\nt3 = n4 / t1\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "find the average of all the numbers between 6 and 34 which are divisible by 5 ?", + "Output Program": [ + "n0 = 6.0\nn1 = 34.0\nn2 = 5.0\nt0 = n0 + 4.0\nt1 = n1 - 4.0\nt2 = t0 + t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "set # 1 = { a , b , c , d , e } set # 2 = { k , l , m , n , o , p } there are these two sets of letters , and you are going to pick exactly one letter from each set . what is the probability of picking at least one vowel ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nt0 = n1 + 3.0\nt1 = n0 + t0\nt2 = 3.0 / t0\nt3 = t0 / t1\nanswer = t2 * t3\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "a student is ranked 17 th from right and 5 th from left . how many students are there in totality ?", + "Output Program": [ + "n0 = 17.0\nn1 = 5.0\nt0 = n0 + n1\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "what should be the least number to be added to the 11002 number to make it divisible by 11 ?", + "Output Program": [ + "n0 = 11002.0\nn1 = 11.0\nt0 = n0 % n1\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "the average age of an adult class is 40 years . 12 new students with an avg age of 34 years join the class . therefore decreasing the average by 4 years . find what was the original average age of the class ?", + "Output Program": [ + "n0 = 40.0\nn1 = 12.0\nn2 = 34.0\nn3 = 4.0\nt0 = n1 * n2\nt1 = n0 - n3\nt2 = n1 * t1\nt3 = t2 - t0\nanswer = t3 / n3\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "there were totally 100 men . 85 are married . 75 have t . v , 85 have radio , 70 have a . c . how many men have t . v , radio , a . c and also married ?", + "Output Program": [ + "n0 = 100.0\nn1 = 85.0\nn2 = 75.0\nn3 = 85.0\nn4 = 70.0\nt0 = n0 - n1\nt1 = n0 - n2\nt2 = n0 - n3\nt3 = n0 - n4\nt4 = t0 + t1\nt5 = t4 + t2\nt6 = t5 + t3\nanswer = n0 - t6\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "virginia , adrienne , and dennis have taught history for a combined total of 102 years . if virginia has taught for 9 more years than adrienne and for 9 fewer years than dennis , for how many years has dennis taught ?", + "Output Program": [ + "n0 = 102.0\nn1 = 9.0\nn2 = 9.0\nt0 = n1 + n2\nt1 = n1 + t0\nt2 = n0 - t1\nt3 = t2 / 3.0\nanswer = t0 + t3\nprint(answer)" + ], + "Output Answer": [ + "43" + ], + "split": "train" + }, + { + "Input": "g ( x ) is defined as the product of all even integers k such that 0 < k \u2264 x . for example , g ( 14 ) = 2 \u00d7 4 \u00d7 6 \u00d7 8 \u00d7 10 \u00d7 12 \u00d7 14 . if g ( r ) is divisible by 4 ^ 11 , what is the smallest possible value for r ?", + "Output Program": [ + "n0 = 0.0\nn1 = 14.0\nn2 = 2.0\nn3 = 4.0\nn4 = 6.0\nn5 = 8.0\nn6 = 10.0\nn7 = 12.0\nn8 = 14.0\nn9 = 4.0\nn10 = 11.0\n\nanswer = n2 * n7\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "if 1 / 12 of the passengers on a ship are from north america , 1 / 8 are europeans , 1 / 3 are from africa , 1 / 6 are from asia and the remaining 35 people are citizens of other continents , then how many passengers are on board the ship ?", + "Output Program": [ + "n0 = 1.0\nn1 = 12.0\nn2 = 1.0\nn3 = 8.0\nn4 = 1.0\nn5 = 3.0\nn6 = 1.0\nn7 = 6.0\nn8 = 35.0\nt0 = n0 / n1\nt1 = n0 / n3\nt2 = n0 / n5\nt3 = n0 / n7\nt4 = t0 + t1\nt5 = t4 + t2\nt6 = t5 + t3\nt7 = 1.0 - t6\nanswer = n8 / t7\nprint(answer)" + ], + "Output Answer": [ + "119.99999999999997" + ], + "split": "train" + }, + { + "Input": "a gambler bought $ 3,000 worth of chips at a casino in denominations of $ 20 and $ 100 . that evening , the gambler lost 13 chips , and then cashed in the remainder . if the number of $ 20 chips lost was 3 more or 3 less than the number of $ 100 chips lost , what is the largest amount of money that the gambler could have received back ?", + "Output Program": [ + "n0 = 3000.0\nn1 = 20.0\nn2 = 100.0\nn3 = 13.0\nn4 = 20.0\nn5 = 3.0\nn6 = 3.0\nn7 = 100.0\nt0 = n3 + n5\nt1 = 1000.0 * 3.0\nt2 = t0 / 2.0\nt3 = n1 * t2\nt4 = t2 - 2.0\nt5 = n2 * t4\nt6 = t3 + t5\nanswer = t1 - t6\nprint(answer)" + ], + "Output Answer": [ + "2240" + ], + "split": "train" + }, + { + "Input": "the ages of two person differ by 20 years . if 7 years ago , the elder one be 5 times as old as the younger one , their present ages ( in years ) are respectively", + "Output Program": [ + "n0 = 20.0\nn1 = 7.0\nn2 = 5.0\nt0 = n1 * n2\nt1 = n0 - n1\nt2 = n2 - 1.0\nt3 = t0 + t1\nt4 = t3 / t2\nanswer = n0 + t4\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "shekar scored 76 , 65 , 82 , 67 and 55 marks in mathematics , science , social studies , english and biology respectively . what are his average marks ?", + "Output Program": [ + "n0 = 76.0\nn1 = 65.0\nn2 = 82.0\nn3 = 67.0\nn4 = 55.0\nt0 = n0 + n1\nt1 = 1.0 + 4.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "69" + ], + "split": "train" + }, + { + "Input": "if a person has two rectangular fields . the larger field has thrice the length and 4 times the width of the smaller field . if the smaller field has a length 50 % more than the width . if a person takes 20 minutes to complete one round of a smaller field then what is the time required to complete one round of a larger field ?", + "Output Program": [ + "n0 = 4.0\nn1 = 50.0\nn2 = 20.0\nt0 = n1 / 100.0\nt1 = n0 * t0\nt2 = n2 * t1\nt3 = n2 + t2\nt4 = n0 + t3\nanswer = n0 + t4\nprint(answer)" + ], + "Output Answer": [ + "68" + ], + "split": "train" + }, + { + "Input": "linda bought 3 notebooks at $ 1.20 each ; a box of pencils at $ 1.50 and a box of pens at $ 1.70 . how much did linda spend ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.2\nn2 = 1.5\nn3 = 1.7\nt0 = n0 * n1\nt1 = n2 + t0\nanswer = n3 + t1\nprint(answer)" + ], + "Output Answer": [ + "6.8" + ], + "split": "train" + }, + { + "Input": "an amount at compound interest sums to rs . 17640 / - in 2 years and to rs . 22932 / - in 3 years at the same rate of interest . find the rate percentage ?", + "Output Program": [ + "n0 = 17640.0\nn1 = 2.0\nn2 = 22932.0\nn3 = 3.0\nt0 = n2 - n0\nt1 = t0 / n0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "for how many integer values of n will the value of the expression 4 n + 7 be an integer greater than 1 and less than 60 ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 7.0\nn2 = 1.0\nn3 = 60.0\nt0 = n3 - n1\nt1 = n2 - n1\nt2 = t0 / n0\nt3 = t1 / n0\nt4 = math.floor(t2)\nt5 = math.floor(t3)\nanswer = t4 - t5\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "r = { 2 , 3 , 4 , 5 } b = { 4 , 5 , 6 , 7 , 8 } two integers will be randomly selected from the sets above , one integer from set r and one integer from set b . what is the probability that the sum of the two integers will equal 9 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 4.0\nn3 = 5.0\nn4 = 4.0\nn5 = 5.0\nn6 = 6.0\nn7 = 7.0\nn8 = 8.0\nn9 = 9.0\nt0 = n2 / n2\nt1 = 1.0 / n3\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "0.2" + ], + "split": "train" + }, + { + "Input": "a $ 79.95 lawn chair was sold for $ 59.95 at a special sale . by approximately what percent was the price decreased ?", + "Output Program": [ + "n0 = 79.95\nn1 = 59.95\nt0 = n0 - n1\nt1 = t0 / n0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "25.01563477173233" + ], + "split": "train" + }, + { + "Input": "5 drainage pipes , each draining water from a pool at the same constant rate , together can drain a certain pool in 16 days . how many additional pipes , each draining water at the same constant rate , will be needed to drain the pool in 4 days ?", + "Output Program": [ + "n0 = 5.0\nn1 = 16.0\nn2 = 4.0\nt0 = n0 * n2\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "a heap of grapes is divided into groups of 3 , 5 and 7 and each time one coconut is left over . the least number of grapes in the heap is ? a . 31 b . 41 c . 51 d . 61", + "Output Program": [ + "import scipy\nn0 = 3.0\nn1 = 5.0\nn2 = 7.0\nn3 = 31.0\nn4 = 41.0\nn5 = 51.0\nn6 = 61.0\nt0 = scipy.lcm(int(n0), int(n1))\nanswer = scipy.lcm(int(n2), int(t0))\nprint(answer)" + ], + "Output Answer": [ + "105" + ], + "split": "train" + }, + { + "Input": "find the greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively .", + "Output Program": [ + "import scipy\nn0 = 1657.0\nn1 = 2037.0\nn2 = 6.0\nn3 = 5.0\nt0 = n0 - n2\nt1 = n1 - n3\nanswer = scipy.gcd(int(t0), int(t1))\nprint(answer)" + ], + "Output Answer": [ + "127" + ], + "split": "train" + }, + { + "Input": "ram - leela has $ 100 in her piggy bank . how much will she have in her bank 52 weeks from now if she puts $ 1 in the bank next week , $ 2 two weeks from now , $ 3 3 weeks from now , and continues to increase the amount that she puts in by $ 1 each week ?", + "Output Program": [ + "n0 = 100.0\nn1 = 52.0\nn2 = 1.0\nn3 = 2.0\nn4 = 3.0\nn5 = 3.0\nn6 = 1.0\nt0 = n0 / n3\nt1 = n4 + t0\nt2 = n1 * t1\nt3 = t2 / n3\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "1478" + ], + "split": "train" + }, + { + "Input": "a certain mixture of nuts consists of 5 parts almonds to 2 parts walnuts , by weight . what is the number of pounds of almonds in 350 pounds of the mixture ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 350.0\nt0 = n0 + n1\nt1 = n0 * n2\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "250" + ], + "split": "train" + }, + { + "Input": "if x = - 5 / 4 and y = - 3 / 2 , what is the value of the expression - 2 x \u2013 y ^ 2 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 4.0\nn2 = 3.0\nn3 = 2.0\nn4 = 2.0\nn5 = 2.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = n3 * t0\nt3 = t1**min(n3, 5)\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "0.25" + ], + "split": "train" + }, + { + "Input": "which expression is the greatest", + "Output Program": [ + "t0 = 3.0 * 3.0\nt1 = 3600.0 - 4.0\nt2 = 3600.0 - t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.9986095661846496" + ], + "split": "train" + }, + { + "Input": "jerry \u2019 s average ( arithmetic mean ) score on the first 3 of 4 tests is 78 . if jerry wants to raise his average by 2 points , what score must he earn on the fourth test ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 78.0\nn3 = 2.0\nt0 = n2 + n3\nt1 = n0 * n2\nt2 = n1 * t0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "86" + ], + "split": "train" + }, + { + "Input": "15 years hence , rohan will be just 4 times as old as he was 15 years ago . how old is rohan at present ?", + "Output Program": [ + "n0 = 15.0\nn1 = 4.0\nn2 = 15.0\nt0 = n0 * n1\nt1 = n1 - 1.0\nt2 = n0 + t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "subash can copy 50 pages in 10 hrs . subash and prakash together can copy 300 pages in 40 hours . in how much time prakash can copy 18 pages .", + "Output Program": [ + "import math\nn0 = 50.0\nn1 = 10.0\nn2 = 300.0\nn3 = 40.0\nn4 = 18.0\nt0 = n2 / n3\nt1 = n0 / n1\nt2 = t0 - t1\nanswer = math.floor(t2)\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "in a hostel , the number of students decreased by 8 % and the price of food increased by 20 % over the previous year . if each student consumes the same amount of food then by how much should the consumption of food be cut short by every student , so that the total cost of the food remains the same as that of the previous year ?", + "Output Program": [ + "n0 = 8.0\nn1 = 20.0\nt0 = n1 + 100.0\nt1 = 100.0 * 100.0\nt2 = 100.0 - n0\nt3 = t0 * t2\nt4 = t1 / t3\nt5 = 1.0 - t4\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "9.420289855072461" + ], + "split": "train" + }, + { + "Input": "how many multiples of 2 are there between 101 and 999 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 101.0\nn2 = 999.0\nt0 = n2 - n1\nt1 = t0 / n0\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "450" + ], + "split": "train" + }, + { + "Input": "find the smallest number which when divided by 13 and 16 leaves respective remainders of 2 and 5 .", + "Output Program": [ + "n0 = 13.0\nn1 = 16.0\nn2 = 2.0\nn3 = 5.0\nt0 = 1.0 + 10.0\nt1 = n0 * n1\nanswer = t1 - t0\nprint(answer)" + ], + "Output Answer": [ + "197" + ], + "split": "train" + }, + { + "Input": "how much is 80 % of 40 is greater than 4 / 5 of 20 ?", + "Output Program": [ + "n0 = 80.0\nn1 = 40.0\nn2 = 4.0\nn3 = 5.0\nn4 = 20.0\nt0 = n0 / 100.0\nt1 = n2 / n3\nt2 = n1 * t0\nt3 = n4 * t1\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "if the price of sugar rises from rs . 10 per kg to rs . 13 per kg , a person , to have no increase in the expenditure on sugar , will have to reduce his consumption of sugar by", + "Output Program": [ + "n0 = 10.0\nn1 = 13.0\nt0 = n0 * 1.0\nt1 = t0 / n1\nt2 = 1.0 - t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "23.076923076923073" + ], + "split": "train" + }, + { + "Input": "when a certain tree was first planted , it was 4 feet tall , and the height of the tree increased by a constant amount each year for the next 6 years . at the end of the 6 th year , the tree was 1 / 3 taller than it was at the end of the 4 th year . by how many feet did the height of the tree increase each year ?", + "Output Program": [ + "n0 = 4.0\nn1 = 6.0\nn2 = 6.0\nn3 = 1.0\nn4 = 3.0\nn5 = 4.0\nt0 = n1 - n0\nt1 = n4 * t0\nt2 = t1 - n0\nanswer = n0 / t2\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2 . 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more . at the end of the two removal and replacement , what is the ratio w of milk and water in the resultant mixture ?", + "Output Program": [ + "n0 = 20.0\nn1 = 3.0\nn2 = 2.0\nn3 = 10.0\nt0 = n1 + n2\nt1 = n0 - n3\nt2 = n1 / t0\nt3 = n2 / t0\nt4 = t2 * t1\nt5 = t3 * t1\nt6 = n3 + t4\nt7 = t5 / n0\nt8 = t6 / n0\nt9 = t7 * t1\nt10 = t8 * t1\nt11 = n3 + t10\nanswer = t11 / t9\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "of the families in city x in 1992 , 60 percent owned a personal computer . the number of families in city x owning a computer in 1993 was 50 percent greater than it was in 1992 , and the total number of families in city x was 3 percent greater in 1993 than it was in 1992 . what percent of the families in city x owned a personal computer in 1993 ?", + "Output Program": [ + "n0 = 1992.0\nn1 = 60.0\nn2 = 1993.0\nn3 = 50.0\nn4 = 1992.0\nn5 = 3.0\nn6 = 1993.0\nn7 = 1992.0\nn8 = 1993.0\nt0 = n3 + 100.0\nt1 = n5 + 100.0\nt2 = n1 * t0\nt3 = t2 / 100.0\nt4 = t3 / t1\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "87.37864077669903" + ], + "split": "train" + }, + { + "Input": "find the value of ( \u221a 1.21 ) / ( \u221a 0.81 ) + ( \u221a 1.00 ) / ( \u221a 0.49 ) is", + "Output Program": [ + "import math\nn0 = 1.21\nn1 = 0.81\nn2 = 1.0\nn3 = 0.49\nt0 = math.sqrt(max(0, n0))\nt1 = math.sqrt(max(0, n1))\nt2 = math.sqrt(max(0, n2))\nt3 = math.sqrt(max(0, n3))\nt4 = t0 / t1\nt5 = t2 / t3\nanswer = t4 + t5\nprint(answer)" + ], + "Output Answer": [ + "2.650793650793651" + ], + "split": "train" + }, + { + "Input": "louie takes out a 3 - month loan of $ 1000 . the lender charges him 10 % interest per month compounded monthly . the terms of the loan state that louie must repay the loan in 3 equal monthly payments . to the nearest dollar , how much does louis have to pay each month ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1000.0\nn2 = 10.0\nn3 = 3.0\nt0 = n2 / 100.0\nt1 = n0 * n1\nt2 = t0 * t1\nt3 = t0 * t2\nt4 = t2 + t3\nt5 = t4 + 1.0\nt6 = n1 + t5\nt7 = t5 / 100.0\nanswer = t6 / t7\nprint(answer)" + ], + "Output Answer": [ + "402.11480362537765" + ], + "split": "train" + }, + { + "Input": "find the maximum value of n such that 50 ! is perfectly divisible by 2520 ^ n", + "Output Program": [ + "n0 = 50.0\nn1 = 2520.0\nt0 = n0 / 10.0\nanswer = t0 + 3.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a number exceeds by 30 from its 3 / 8 part . then the number is ?", + "Output Program": [ + "n0 = 30.0\nn1 = 3.0\nn2 = 8.0\nt0 = n0 * n2\nt1 = n2 - n1\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "the average weight of 10 men is increased by 2 \u00bd kg when one of the men who weighs 58 kg is replaced by a new man . what is the weight of the new man ?", + "Output Program": [ + "n0 = 10.0\nn1 = 2.0\nn2 = 58.0\nt0 = 1.0 / 2.0\nt1 = n1 + t0\nt2 = n0 * t1\nanswer = n2 + t2\nprint(answer)" + ], + "Output Answer": [ + "83" + ], + "split": "train" + }, + { + "Input": "in the rectangular coordinate system , what is the x - intercept of a line passing through ( 10 , 3 ) and ( \u2212 10 , \u2212 7 ) ?", + "Output Program": [ + "n0 = 10.0\nn1 = 3.0\nn2 = 10.0\nn3 = 7.0\nt0 = -n3\nt1 = -n2\nt2 = t0 - n1\nt3 = t1 - n0\nt4 = t2 / t3\nt5 = n0 * t4\nt6 = t5 - n1\nanswer = t6 / t4\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "when greenville state university decided to move its fine arts collection to a new library , it had to package the collection in 20 - inch by 20 - inch by 12 - inch boxes . if the university pays $ 0.50 for every box , and if the university needs 2.4 million cubic inches to package the collection , what is the minimum amount the university must spend on boxes ?", + "Output Program": [ + "n0 = 20.0\nn1 = 20.0\nn2 = 12.0\nn3 = 0.5\nn4 = 2.4\nt0 = 1000.0 * 1000.0\nt1 = n0 * n0\nt2 = n4 * t0\nt3 = n2 * t1\nt4 = t2 / t3\nanswer = n3 * t4\nprint(answer)" + ], + "Output Answer": [ + "250" + ], + "split": "train" + }, + { + "Input": "a batsman makes a score of 84 runs in the 17 th inning and thus increases his averages by 3 . find his average after 17 th inning ?", + "Output Program": [ + "n0 = 84.0\nn1 = 17.0\nn2 = 3.0\nn3 = 17.0\nt0 = n1 * n2\nt1 = n0 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "the maximum numbers of students among them 451 pens and 410 toys can be distributed in such a way that each student gets the same number of pens and same number of toys is", + "Output Program": [ + "n0 = 451.0\nn1 = 410.0\n\nanswer = n0 - n1\nprint(answer)" + ], + "Output Answer": [ + "41" + ], + "split": "train" + }, + { + "Input": "if @ is a binary operation defined as the difference between an integer n and the product of n and 5 , then what is the largest positive integer n such that the outcome of the binary operation of n is less than 18 ?", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 18.0\nt0 = n0 - 1.0\nt1 = n1 / t0\nanswer = math.floor(t1)\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "the price of commodity x increases by 45 cents every year , while the price of commodity y increases by 20 cents every year . in 2001 , the price of commodity x was $ 5.20 and the price of commodity y was $ 7.30 . in which year will the price of commodity x be 35 cents less than the price of commodity y ?", + "Output Program": [ + "n0 = 45.0\nn1 = 20.0\nn2 = 2001.0\nn3 = 5.2\nn4 = 7.3\nn5 = 35.0\nt0 = n5 / 100.0\nt1 = n0 / 100.0\nt2 = n4 - n3\nt3 = t0 + t2\nt4 = t1 - t2\nt5 = t3 / t4\nanswer = n2 + t5\nprint(answer)" + ], + "Output Answer": [ + "1999.5151515151515" + ], + "split": "train" + }, + { + "Input": "what is the greatest positive integer x such that 3 ^ x is a factor of 9 ^ 7 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 9.0\nn2 = 7.0\nt0 = n1 - n2\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "each machine of type a has 3 steel parts and 2 chrome parts . each machine of type b has 2 steel parts and 4 chrome parts . if a certain group of type a and type b machines has a total of 50 steel parts and 66 chrome parts , how many machines are in the group", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 2.0\nn3 = 4.0\nn4 = 50.0\nn5 = 66.0\nt0 = n1 + n3\nt1 = n0 + n1\nt2 = n5 / t0\nt3 = n4 / t1\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "a batsman in his 12 th innings makes a score of 75 and thereby increases his average by 1 runs . what is his average after the 12 th innings if he had never been \u2018 not out \u2019 ?", + "Output Program": [ + "n0 = 12.0\nn1 = 75.0\nn2 = 1.0\nn3 = 12.0\nt0 = n0 * n2\nt1 = n1 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "train" + }, + { + "Input": "if the price of gasoline increases by 25 % and ron intends to spend only 15 % more on gasoline , by how much percent should he reduce the quantity of gasoline that he buys ?", + "Output Program": [ + "n0 = 25.0\nn1 = 15.0\nt0 = n1 / 100.0\nt1 = n0 / 100.0\nt2 = t0 + 1.0\nt3 = t1 + 1.0\nt4 = t2 / t3\nt5 = 1.0 - t4\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "8.000000000000007" + ], + "split": "train" + }, + { + "Input": "25.25 / 1500 is equal to :", + "Output Program": [ + "n0 = 25.25\nn1 = 1500.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.016833333333333332" + ], + "split": "train" + }, + { + "Input": "if jake loses 20 pounds , he will weigh twice as much as his sister . together they now weigh 224 pounds . what is jake \u2019 s present weight , in pounds ?", + "Output Program": [ + "n0 = 20.0\nn1 = 224.0\nt0 = n1 - n0\nt1 = t0 / 3.0\nt2 = t1 * 2.0\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "156" + ], + "split": "train" + }, + { + "Input": "evaluate : | 7 - 8 ( 3 - 12 ) | - | 5 - 11 | = ?", + "Output Program": [ + "n0 = 7.0\nn1 = 8.0\nn2 = 3.0\nn3 = 12.0\nn4 = 5.0\nn5 = 11.0\nt0 = n2 - n3\nt1 = n4 - n5\nt2 = n1 * t0\nt3 = -t1\nt4 = n0 - t2\nanswer = t4 - t3\nprint(answer)" + ], + "Output Answer": [ + "73" + ], + "split": "train" + }, + { + "Input": "if | x - 25 | = 50 what is the sum of all the values of x .", + "Output Program": [ + "n0 = 25.0\nn1 = 50.0\nt0 = n0 + n1\nt1 = n1 - n0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "product of two co - prime numbers is 117 . their l . c . m should be :", + "Output Program": [ + "n0 = 117.0\n\nanswer = n0 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "117" + ], + "split": "train" + }, + { + "Input": "terry is having lunch at a salad bar . there are two types of lettuce to choose from , as well as 3 types of tomatoes , and 4 types of olives . he must also choose whether or not to have one of the two types of soup on the side . if terry has decided to have the salad and soup combo and he picks one type of lettuce , one type of tomato , and one type of olive for his salad , how many total options does he have for his lunch combo ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nt0 = n1 * 2.0\nt1 = n0 * 2.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "what will be the reminder when ( 31 ^ 31 + 31 ) is divided by 32 ?", + "Output Program": [ + "import math\nn0 = 31.0\nn1 = 31.0\nn2 = 31.0\nn3 = 32.0\nt0 = n0**min(n0, 5)\nt1 = n0 + t0\nt2 = t1 / n3\nt3 = math.floor(t2)\nt4 = n3 * t3\nanswer = t1 - t4\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "if m equals the sum of the odd integers from 1 to 111 , inclusive , and t equals the sum of the even integers from 2 to 50 , inclusive , what is the value of m + t ?", + "Output Program": [ + "n0 = 1.0\nn1 = 111.0\nn2 = 2.0\nn3 = 50.0\nt0 = n0 + n1\nt1 = n3 / n2\nt2 = t1 + 1.0\nt3 = t0 / n2\nt4 = t2 * t1\nt5 = t3**min(2.0, 5)\nanswer = t4 + t5\nprint(answer)" + ], + "Output Answer": [ + "3786" + ], + "split": "train" + }, + { + "Input": "in a division sum , the quotient is 36 , the divisor 85 and the remainder 26 , find the dividend ?", + "Output Program": [ + "n0 = 36.0\nn1 = 85.0\nn2 = 26.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "3086" + ], + "split": "train" + }, + { + "Input": "a pharmaceutical company received $ 6 million in royalties on the first $ 20 million in sales of the generic equivalent of one of its products and then $ 9 million in royalties on the next $ 108 million in sales . by approximately what percent did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 108 million in sales ?", + "Output Program": [ + "n0 = 6.0\nn1 = 20.0\nn2 = 9.0\nn3 = 108.0\nn4 = 20.0\nn5 = 108.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = t0 * 100.0\nt3 = t1 * 100.0\nt4 = t2 - t3\nt5 = t4 / t2\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "72.22222222222221" + ], + "split": "train" + }, + { + "Input": "the cost of 10 kg of mangos is equal to the cost of 24 kg of rice . the cost of 6 kg of flour equals the cost of 2 kg of rice . the cost of each kg of flour is $ 21 . find the total cost of 4 kg of mangos , 3 kg of rice and 5 kg of flour ?", + "Output Program": [ + "n0 = 10.0\nn1 = 24.0\nn2 = 6.0\nn3 = 2.0\nn4 = 21.0\nn5 = 4.0\nn6 = 3.0\nn7 = 5.0\nt0 = n1 / n0\nt1 = n2 * n4\nt2 = n4 * n7\nt3 = t1 / n3\nt4 = t0 * t3\nt5 = n6 * t3\nt6 = n5 * t4\nt7 = t6 + t5\nanswer = t7 + t2\nprint(answer)" + ], + "Output Answer": [ + "898.8" + ], + "split": "train" + }, + { + "Input": "a father is 4 times as old as his son . in 20 years , he ' ll be twice as old . how old are they now ?", + "Output Program": [ + "n0 = 4.0\nn1 = 20.0\nt0 = n1 / 2.0\nt1 = n0 * t0\nanswer = t1 + 1000.0\nprint(answer)" + ], + "Output Answer": [ + "1040" + ], + "split": "train" + }, + { + "Input": "how many positive integers h less than 10000 are such that the product of their digits is 210 ?", + "Output Program": [ + "import math\nn0 = 10000.0\nn1 = 210.0\nt0 = 1.0 + 4.0\nt1 = n1 / t0\nt2 = t1 / 3.0\nt3 = t2 / 2.0\nt4 = t3 - 3.0\nt5 = math.factorial(min(15, int(t4)))\nt6 = t3 - t4\nt7 = t5 + t5\nt8 = math.factorial(min(15, int(t6)))\nanswer = t7 + t8\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "train" + }, + { + "Input": "rounded to 3 decimal places , 1.003 ^ 4 =", + "Output Program": [ + "n0 = 3.0\nn1 = 1.003\nn2 = 4.0\nt0 = n0 / 1000.0\nt1 = n0 * t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "1.0119999999999998" + ], + "split": "train" + }, + { + "Input": "dawson is going with 14 friends on a trip to washington d . c for spring break . airfare and hotel costs a total of $ 13500.00 for the group of 15 friends . how much does each person have to pay for their hotel and airfare ?", + "Output Program": [ + "n0 = 14.0\nn1 = 13500.0\nn2 = 15.0\n\nanswer = n1 / n2\nprint(answer)" + ], + "Output Answer": [ + "900" + ], + "split": "train" + }, + { + "Input": "the batting average of a particular batsman is 60 runs in 46 innings . if the difference in his highest and lowest score is 190 runs and his average excluding these two innings is 58 runs , find his highest score .", + "Output Program": [ + "n0 = 60.0\nn1 = 46.0\nn2 = 190.0\nn3 = 58.0\nt0 = n0 * n1\nt1 = n1 - 2.0\nt2 = n3 * t1\nt3 = t0 - t2\nt4 = n2 + t3\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "199" + ], + "split": "train" + }, + { + "Input": "a sum of rs . 312 was divided among 100 boys and girls in such a way that each boy gets rs . 3.60 and each girl rs . 2.40 .", + "Output Program": [ + "n0 = 312.0\nn1 = 100.0\nn2 = 3.6\nn3 = 2.4\nt0 = n3 * 100.0\nt1 = n2 - n3\nt2 = n0 - t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "59.99999999999999" + ], + "split": "train" + }, + { + "Input": "if the average ( arithmetic mean ) of a and b is 30 and the average of b and c is 60 , what is the value of c \u2212 a ?", + "Output Program": [ + "n0 = 30.0\nn1 = 60.0\nt0 = n1 * 2.0\nt1 = n0 * 2.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "what is the minimum percentage increase in the mean of set f { - 4 , - 1 , 0 , 6 , 9 } if its two smallest elements are replaced with two different primes ?", + "Output Program": [ + "n0 = 4.0\nn1 = 1.0\nn2 = 0.0\nn3 = 6.0\nn4 = 9.0\nt0 = 2.0 + 3.0\nt1 = n0 + n1\nt2 = -n0\nt3 = -n1\nt4 = n3 + t0\nt5 = t2 + t3\nt6 = n4 + t4\nt7 = n3 + t5\nt8 = n4 + t7\nt9 = t6 / t1\nt10 = t8 / t1\nt11 = t9 - t10\nt12 = t11 / t10\nanswer = t12 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "when a certain tree was first planted , it was 4 feet tall , and the height of the tree increased by a constant amount each year for the next 6 years . at the end of the 6 th year , the tree was 1 / 6 taller than it was at the end of the 4 th year . by how many feet did the height of the tree increase each year ?", + "Output Program": [ + "n0 = 4.0\nn1 = 6.0\nn2 = 6.0\nn3 = 1.0\nn4 = 6.0\nn5 = 4.0\nt0 = n1 - n0\nt1 = n4 * t0\nt2 = t1 - n0\nanswer = n0 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "a waitress ' s income consists of her salary and tips . during one week , her tips were 9 / 4 of her salary . what fraction of her income for the week came from tips ?", + "Output Program": [ + "n0 = 9.0\nn1 = 4.0\nt0 = n0 + n1\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.6923076923076923" + ], + "split": "train" + }, + { + "Input": "find the value of m 62519 x 9999 = m ?", + "Output Program": [ + "n0 = 62519.0\nn1 = 9999.0\nt0 = n1 - 4.0\nanswer = t0 * n0\nprint(answer)" + ], + "Output Answer": [ + "624877405" + ], + "split": "train" + }, + { + "Input": "an italian sausage is 8 inches long . how many pieces of sausage can be cut from the 8 - inch piece of sausage if each piece is to be 2 / 3 of an inch ?", + "Output Program": [ + "n0 = 8.0\nn1 = 8.0\nn2 = 2.0\nn3 = 3.0\nt0 = n2 / n3\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "what is the dividend . divisor 20 , the quotient is 8 and the remainder is 6", + "Output Program": [ + "n0 = 20.0\nn1 = 8.0\nn2 = 6.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "166" + ], + "split": "train" + }, + { + "Input": "given that 268 x 74 = 19732 , find the value of 2.68 x . 74 .", + "Output Program": [ + "n0 = 268.0\nn1 = 74.0\nn2 = 19732.0\nn3 = 2.68\nn4 = 74.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "1.9832" + ], + "split": "train" + }, + { + "Input": "bill made a profit of 10 % by selling a product . if he had purchased that product for 10 % less and sold it at a profit of 30 % , he would have received $ 70 more . what was his original selling price ?", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 30.0\nn3 = 70.0\nt0 = n0 / 100.0\nt1 = n2 / 100.0\nt2 = t0 + 1.0\nt3 = t1 + 1.0\nt4 = 1.0 - t0\nt5 = t3 * t4\nt6 = t5 - t2\nt7 = n3 / t6\nanswer = t2 * t7\nprint(answer)" + ], + "Output Answer": [ + "1099.999999999999" + ], + "split": "train" + }, + { + "Input": "george baked a total of 50 pizzas for 5 straight days , beginning on saturday . he baked 3 / 5 of the pizzas the first day , and 3 / 5 of the remaining pizzas the second day . if each successive day he baked fewer pizzas than the previous day , what is the maximum number of pizzas he could have baked on wednesday ?", + "Output Program": [ + "n0 = 50.0\nn1 = 5.0\nn2 = 3.0\nn3 = 5.0\nn4 = 3.0\nn5 = 5.0\nt0 = n2 / n1\nt1 = n0 * t0\nt2 = n0 - t1\nt3 = t0 * t2\nt4 = t2 - t3\nt5 = t4 - n2\nanswer = t5 / t5\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "the difference between the value of a number increased by 12.5 % and the value of the original number decreased by 25 % is 30 . what is the original number ?", + "Output Program": [ + "n0 = 12.5\nn1 = 25.0\nn2 = 30.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = t0 + 1.0\nt3 = 1.0 - t1\nt4 = t2 - t3\nanswer = n2 / t4\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "dames school has 2000 boys and 5000 girls . what is the percentage increase from boys to total attendance and girls to total attendance ?", + "Output Program": [ + "n0 = 2000.0\nn1 = 5000.0\nt0 = n0 / n1\nanswer = t0 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 16000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is", + "Output Program": [ + "n0 = 8000.0\nn1 = 7.0\nn2 = 16000.0\nn3 = 6000.0\nt0 = n2 - n0\nt1 = n0 - n3\nt2 = n1 * t0\nt3 = t2 / t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "n = 1 / 3 + 1 / 4 what is the value of n ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 4.0\nt0 = n0 / n1\nt1 = n0 / n3\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "0.5833333333333333" + ], + "split": "train" + }, + { + "Input": "how many even multiples of 55 are there between 549 and 1101 ?", + "Output Program": [ + "n0 = 55.0\nn1 = 549.0\nn2 = 1101.0\nt0 = n0 * 2.0\nt1 = n2 - n1\nt2 = t1 / t0\nanswer = t2 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "6.0181818181818185" + ], + "split": "train" + }, + { + "Input": "25.25 / 2000 is equal to :", + "Output Program": [ + "n0 = 25.25\nn1 = 2000.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.012625" + ], + "split": "train" + }, + { + "Input": "the original price of a suit is $ 200 . the price increased 30 % , and after this increase , the store published a 30 % off coupon for a one - day sale . given that the consumers who used the coupon on sale day were getting 30 % off the increased price , how much did these consumers pay for the suit ?", + "Output Program": [ + "n0 = 200.0\nn1 = 30.0\nn2 = 30.0\nn3 = 30.0\nt0 = n0 * n1\nt1 = t0 / 100.0\nt2 = n0 + t1\nt3 = n1 * t2\nt4 = t3 / 100.0\nanswer = t2 - t4\nprint(answer)" + ], + "Output Answer": [ + "182" + ], + "split": "train" + }, + { + "Input": "if x + y = 2 and x 2 y 3 + y 2 x 3 = 32 , what is the value of xy ?", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 2.0\nn2 = 3.0\nn3 = 2.0\nn4 = 3.0\nn5 = 32.0\nt0 = n5 / n0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "if the price of a book is first decreased by 20 % and then increased by 10 % , then the net change in the price will be :", + "Output Program": [ + "n0 = 20.0\nn1 = 10.0\nt0 = n0 * 100.0\nt1 = n1 * 100.0\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = t3 + 100.0\nt5 = 100.0 - t2\nt6 = t5 / 100.0\nt7 = t4 / 100.0\nt8 = t6 * t7\nt9 = t8 * 100.0\nanswer = 100.0 - t9\nprint(answer)" + ], + "Output Answer": [ + "11.999999999999986" + ], + "split": "train" + }, + { + "Input": "mr yadav spends 60 % of his monthly salary on consumable items and 50 % of the remaining on clothes and transport . he saves the remaining amount . if his savings at the end of the year were 19008 , how much amount per month would he have spent on clothes and transport ?", + "Output Program": [ + "n0 = 60.0\nn1 = 50.0\nn2 = 19008.0\nt0 = 3.0 * 4.0\nt1 = 100.0 - n0\nt2 = n1 * t1\nt3 = t2 / 100.0\nt4 = t3 / 100.0\nt5 = n2 / t4\nt6 = t5 / t0\nanswer = t6 * t4\nprint(answer)" + ], + "Output Answer": [ + "1584" + ], + "split": "train" + }, + { + "Input": "a number is doubled and 9 is added . if resultant is trebled , it becomes 51 . what is that number", + "Output Program": [ + "n0 = 9.0\nn1 = 51.0\nt0 = n0 * 3.0\nt1 = 2.0 * 3.0\nt2 = n1 - t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "the expenditure of an woman increase consistently by 30 % per year . if her present expenditure is rs . 1000 then what will her expenditure be after 3 years ?", + "Output Program": [ + "n0 = 30.0\nn1 = 1000.0\nn2 = 3.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nt2 = t1**min(n2, 5)\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "2197" + ], + "split": "train" + }, + { + "Input": "in the xy - coordinate system , if ( m , n ) and ( m + 3 , n + k ) are two points on the line with the equation x = 2 y + 5 , then k =", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 5.0\nt0 = n0 + n2\nt1 = t0 - n2\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "1.5" + ], + "split": "train" + }, + { + "Input": "the product of 4 consecutive even numbers is always divisible by :", + "Output Program": [ + "import math\nn0 = 4.0\nt0 = math.factorial(min(15, int(4.0)))\nt1 = 2.0**min(n0, 5)\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "384" + ], + "split": "train" + }, + { + "Input": "a trailer carries 3 , 4 and 5 crates on a trip . each crate weighs no less than 1250 kg . what is the maximum weight of the crates on a single trip ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 5.0\nn3 = 1250.0\n\nanswer = n2 * n3\nprint(answer)" + ], + "Output Answer": [ + "6250" + ], + "split": "train" + }, + { + "Input": "the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 196 , what is the difference between the ages of patrick and monica ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 3.0\nn3 = 5.0\nn4 = 196.0\nt0 = n0 * n0\nt1 = n1 * n0\nt2 = n1 * n3\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n4 / t4\nt6 = t5 * t2\nt7 = t5 * t0\nanswer = t6 - t7\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "train" + }, + { + "Input": "s ( n ) is a n - digit number formed by attaching the first n perfect squares , in order , into one integer . for example , s ( 1 ) = 1 , s ( 2 ) = 14 , s ( 3 ) = 149 , s ( 4 ) = 14916 , s ( 5 ) = 1491625 , etc . how many digits y are in s ( 99 ) ?", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 2.0\nn3 = 14.0\nn4 = 3.0\nn5 = 149.0\nn6 = 4.0\nn7 = 14916.0\nn8 = 5.0\nn9 = 1491625.0\nn10 = 99.0\nt0 = n6 + 60.0\nt1 = n0 * n4\nt2 = n2 * n4\nt3 = n6 + t0\nt4 = n2 * t2\nt5 = t1 + t4\nt6 = n6 * t3\nt7 = t3 + t6\nanswer = t7 + t5\nprint(answer)" + ], + "Output Answer": [ + "355" + ], + "split": "train" + }, + { + "Input": "in track last week , the boys ran 34 laps . the girls ran 20 more laps . each lap is a 1 / 6 th of a mile . how many miles did the girls run ?", + "Output Program": [ + "n0 = 34.0\nn1 = 20.0\nn2 = 1.0\nn3 = 6.0\nt0 = n0 + n1\nanswer = t0 / n3\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "find the minimum value of n such that 50 ! is perfectly divisible by 2520 ^ n .", + "Output Program": [ + "n0 = 50.0\nn1 = 2520.0\nt0 = n0 / 100.0\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "fog + fog + fog + fog = 1464 . if f , o and g are digits in a 3 - digit number in the preceding equation the f + o + g = ?", + "Output Program": [ + "n0 = 1464.0\nn1 = 3.0\nt0 = 2.0 * 3.0\nt1 = n1 + t0\nanswer = t1 + t0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "a is an integer greater than 39 but less than 51 , b is an integer greater than 49 but less than 61 , what is the range of a / b ?", + "Output Program": [ + "n0 = 39.0\nn1 = 51.0\nn2 = 49.0\nn3 = 61.0\nt0 = n2 + 1.0\nt1 = n0 + 1.0\nt2 = n1 - 1.0\nt3 = n3 - 1.0\nt4 = t2 / t0\nt5 = t1 / t3\nanswer = t4 - t5\nprint(answer)" + ], + "Output Answer": [ + "0.33333333333333337" + ], + "split": "train" + }, + { + "Input": "how many paying stones , each measuring 2 1 / 2 m * 2 m are required to pave a rectangular court yard 50 m long and 16 1 / 2 m board ?", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 2.0\nn3 = 2.0\nn4 = 50.0\nn5 = 16.0\nn6 = 1.0\nn7 = 2.0\nt0 = n1 / n0\nt1 = n5 + t0\nt2 = n0 + t0\nt3 = n4 * t1\nt4 = n0 * t2\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "165" + ], + "split": "train" + }, + { + "Input": "how many digits are required to number a book containing 260 pages ?", + "Output Program": [ + "n0 = 260.0\nt0 = 10.0 - 1.0\nt1 = n0 - 100.0\nt2 = t1 + 1.0\nt3 = t0 * 10.0\nt4 = t3 * 2.0\nt5 = t2 * 3.0\nt6 = t4 + t0\nanswer = t6 + t5\nprint(answer)" + ], + "Output Answer": [ + "672" + ], + "split": "train" + }, + { + "Input": "the maximum number of students among them 1340 pens and 1280 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils ?", + "Output Program": [ + "import scipy\nn0 = 1340.0\nn1 = 1280.0\n\nanswer = scipy.gcd(int(n0), int(n1))\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "if the remainder is 10 when the integer n is divided by 18 , what is the remainder when 2 n is divided by 9 ?", + "Output Program": [ + "n0 = 10.0\nn1 = 18.0\nn2 = 2.0\nn3 = 9.0\nt0 = n0 * n2\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "in the land of oz only one or two - letter words are used . the local language has 67 different letters . the parliament decided to forbid the use of the seventh letter . how many words have the people of oz lost because of the prohibition ?", + "Output Program": [ + "n0 = 67.0\nt0 = n0 + 1.0\nanswer = n0 + t0\nprint(answer)" + ], + "Output Answer": [ + "135" + ], + "split": "train" + }, + { + "Input": "$ 500 is divided amongst a , b and c so that a may get 2 / 3 as much as b and c together , b may get 6 / 9 as much as a and c together , then the share of a is", + "Output Program": [ + "n0 = 500.0\nn1 = 2.0\nn2 = 3.0\nn3 = 6.0\nn4 = 9.0\nt0 = n1 / n2\nt1 = t0 + 1.0\nt2 = n0 / t1\nanswer = t2 * t0\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "train" + }, + { + "Input": "in an election between two candidates a and b , the number of valid votes received by a exceeds those received by b by 15 % of the total number of votes polled . if 20 % of the votes polled were invalid and a total of 5720 votes were polled , then how many valid votes did b get ?", + "Output Program": [ + "n0 = 15.0\nn1 = 20.0\nn2 = 5720.0\nt0 = n1 / 100.0\nt1 = n0 * n2\nt2 = t1 / 100.0\nt3 = 1.0 - t0\nt4 = n2 * t3\nt5 = t4 - t2\nanswer = t5 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "1859" + ], + "split": "train" + }, + { + "Input": "10 x 1.8 - 2 x 1.5 / 0.3 = ?", + "Output Program": [ + "n0 = 10.0\nn1 = 1.8\nn2 = 2.0\nn3 = 1.5\nn4 = 0.3\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = t0 - t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "an object thrown directly upward is at a height of h feet after t seconds , where h = - 15 ( t - 2 ) ^ 2 + 150 . at what height , in feet , is the object 2 seconds after it reaches its maximum height ?", + "Output Program": [ + "n0 = 15.0\nn1 = 2.0\nn2 = 2.0\nn3 = 150.0\nn4 = 2.0\nt0 = n1 + n2\nt1 = -n0\nt2 = t0 - n1\nt3 = t2**min(n2, 5)\nt4 = t1 * t3\nanswer = n3 + t4\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "what is the sum of the first 15 terms of an a . p whose 11 th and 7 th terms are 5.25 and 3.25 respectively", + "Output Program": [ + "n0 = 15.0\nn1 = 11.0\nn2 = 7.0\nn3 = 5.25\nn4 = 3.25\nt0 = n0 / 2.0\nanswer = t0 * t0\nprint(answer)" + ], + "Output Answer": [ + "56.25" + ], + "split": "train" + }, + { + "Input": "the average marks of a class of 30 students is 40 and that of another class of 50 students is 70 . find the average marks of all the students ?", + "Output Program": [ + "n0 = 30.0\nn1 = 40.0\nn2 = 50.0\nn3 = 70.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "58.75" + ], + "split": "train" + }, + { + "Input": "rates for having a manuscript typed at a certain typing service are $ 5 per page for the first time a page is typed and $ 3 per page each time a page is revised . if a certain manuscript has 100 pages , of which 30 were revised only once , 20 were revised twice , and the rest required no revisions , what was the total cost of having the manuscript typed ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nn2 = 100.0\nn3 = 30.0\nn4 = 20.0\nt0 = n0 * n2\nt1 = n1 * n3\nt2 = n1 * n4\nt3 = t0 + t1\nt4 = t2 * 2.0\nanswer = t3 + t4\nprint(answer)" + ], + "Output Answer": [ + "710" + ], + "split": "train" + }, + { + "Input": "if josh , doug , and brad have a total of $ 68 between them , and josh has two times as much money as brad but only 3 - fourths as much as doug , how much money does brad have ?", + "Output Program": [ + "n0 = 68.0\nn1 = 3.0\nt0 = 1.0 + 2.0\nt1 = n1 / 4.0\nt2 = 2.0 / t1\nt3 = t0 + t2\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "12.000000000000002" + ], + "split": "train" + }, + { + "Input": "find the remainder when 6 ^ 23 is divided by 5 ?", + "Output Program": [ + "n0 = 6.0\nn1 = 23.0\nn2 = 5.0\nt0 = n0**min(n1, 5)\nanswer = t0 % n2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "the product of two successive numbers is 9506 . which is the smaller of the two numbers ?", + "Output Program": [ + "import math\nn0 = 9506.0\n\nanswer = math.sqrt(max(0, n0))\nprint(answer)" + ], + "Output Answer": [ + "97.49871794028884" + ], + "split": "train" + }, + { + "Input": "the difference between a positive proper fraction and its reciprocal is 9 / 20 . the fraction is :", + "Output Program": [ + "n0 = 9.0\nn1 = 20.0\nt0 = n0 - 4.0\nanswer = 4.0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.8" + ], + "split": "train" + }, + { + "Input": "a man is 20 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is :", + "Output Program": [ + "n0 = 20.0\nt0 = 2.0 * 2.0\nt1 = 2.0 - 1.0\nt2 = t0 - 2.0\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "a big container is 50 % full with water . if 20 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container in liters ?", + "Output Program": [ + "n0 = 50.0\nn1 = 20.0\nn2 = 3.0\nn3 = 4.0\nt0 = n2 / n3\nt1 = n0 / 100.0\nt2 = t0 - t1\nanswer = n1 / t2\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "a certain lab experiments with white and brown mice only . in one experiment , 2 / 3 of the mice are white . if there are 14 white mice in the experiment , how many brown mice are in the experiment ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 14.0\nt0 = n0 / n1\nt1 = n2 / t0\nanswer = t1 - n2\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "? x 48 = 173 x 240", + "Output Program": [ + "n0 = 48.0\nn1 = 173.0\nn2 = 240.0\nt0 = n1 * n2\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "865" + ], + "split": "train" + }, + { + "Input": "of the total amount that rose spent on a shopping trip , excluding taxes , she spent 50 percent on clothing , 20 percent on food , and 30 percent on other items . if rose paid a 4 percent tax on the clothing , no tax on the food , and an 8 percent tax on all other items , then the total tax that she paid was what percent of the total amount that she spent , excluding taxes ?", + "Output Program": [ + "n0 = 50.0\nn1 = 20.0\nn2 = 30.0\nn3 = 4.0\nn4 = 8.0\nt0 = n3 / 100.0\nt1 = n4 / 100.0\nt2 = n0 * t0\nt3 = n2 * t1\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "4.4" + ], + "split": "train" + }, + { + "Input": "in a certain game of dice , the player \u2019 s score is determined as a sum of 3 throws of a single die . the player with the highest score wins the round . if more than one player has the highest score , the winnings of the round are divided equally among these players . if john plays this game against 22 other players , what is the probability of the minimum score that will guarantee john some monetary payoff ?", + "Output Program": [ + "n0 = 3.0\nn1 = 22.0\nt0 = n0 * 2.0\nt1 = 1.0 / t0\nanswer = t1**min(n0, 5)\nprint(answer)" + ], + "Output Answer": [ + "0.0046296296296296285" + ], + "split": "train" + }, + { + "Input": "if the product of the integers w , x , y and z is 68 , and if 0 < w < x < y < z , what is the value of w + z ?", + "Output Program": [ + "n0 = 68.0\nn1 = 0.0\nt0 = n0 / 2.0\nt1 = t0 / 2.0\nt2 = t1 - 1.0\nt3 = t2 - 1.0\nt4 = t3 - 1.0\nt5 = t4 - 1.0\nt6 = t5 - 1.0\nt7 = t6 - 1.0\nt8 = t7 - 1.0\nt9 = t8 - 1.0\nt10 = t9 - 1.0\nt11 = t10 - 1.0\nt12 = t11 - 1.0\nanswer = t12 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "what is the least number which when divided by 5 , 6 , 9 and 18 leaves remainder 4 in each care ?", + "Output Program": [ + "import scipy\nn0 = 5.0\nn1 = 6.0\nn2 = 9.0\nn3 = 18.0\nn4 = 4.0\nt0 = scipy.lcm(int(n0), int(n1))\nt1 = scipy.lcm(int(n2), int(n3))\nt2 = scipy.lcm(int(t0), int(t1))\nanswer = n4 + t2\nprint(answer)" + ], + "Output Answer": [ + "94" + ], + "split": "train" + }, + { + "Input": "a vessel of capacity 2 litre has 35 % of alcohol and another vessel of capacity 6 litre had 50 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?", + "Output Program": [ + "n0 = 2.0\nn1 = 35.0\nn2 = 6.0\nn3 = 50.0\nn4 = 8.0\nn5 = 10.0\nt0 = n1 / 100.0\nt1 = n3 / 100.0\nt2 = n0 * t0\nt3 = n2 * t1\nt4 = t2 + t3\nt5 = t4 / n5\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "37" + ], + "split": "train" + }, + { + "Input": "find the unknown term 8 , x , 62 , - 4 , - 12", + "Output Program": [ + "n0 = 8.0\nn1 = 62.0\nn2 = 4.0\nn3 = 12.0\nt0 = n1 + 2.0\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "what is the local value of 6 in the product of face value of 7 and local value of 8 in 7098060", + "Output Program": [ + "n0 = 6.0\nn1 = 7.0\nn2 = 8.0\nn3 = 7098060.0\nt0 = 10.0 * 1000.0\nt1 = n3 % 1000.0\nt2 = n3 - t1\nt3 = t2 % t0\nt4 = n1 * t3\nanswer = t4 % t0\nprint(answer)" + ], + "Output Answer": [ + "6000" + ], + "split": "train" + }, + { + "Input": "what is the unit digit in 12 ^ 100 ?", + "Output Program": [ + "n0 = 12.0\nn1 = 100.0\nt0 = 4.0**min(2.0, 5)\nanswer = t0 % 10.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "for the symbol , m \u201d n = n ^ 2 \u2212 m for all values of m and n . what is the value of 4 \u201d 3 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 3.0\nt0 = n2**min(n0, 5)\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "if a no . when divided by 44 , gives 432 as quotient and 0 as remainder . what will be the remainder when dividing the same no . by 38", + "Output Program": [ + "n0 = 44.0\nn1 = 432.0\nn2 = 0.0\nn3 = 38.0\nt0 = n0 * n1\nanswer = t0 % n3\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "300 first - time customers of a fashion store were surveyed for their shopping experience right after leaving the store . 60 % of the customers in the survey had purchased clothes for less than $ 100 . 40 % of the customers in the survey reported they were overall satisfied with their purchase . 55 % of the customers that had purchased clothes for less than $ 100 reported they were overall satisfied with their purchase . what percent of the customers surveyed purchased clothes for at least $ 100 and reported that they were not overall satisfied with their purchase ?", + "Output Program": [ + "n0 = 300.0\nn1 = 60.0\nn2 = 100.0\nn3 = 40.0\nn4 = 55.0\nn5 = 100.0\nn6 = 100.0\nt0 = n3 / n2\nt1 = n4 / n2\nt2 = n1 / n2\nt3 = n0 * t0\nt4 = n0 * t2\nt5 = t1 * t4\nt6 = t3 - t5\nt7 = t6 / n0\nanswer = t7 * n2\nprint(answer)" + ], + "Output Answer": [ + "6.999999999999995" + ], + "split": "train" + }, + { + "Input": "the average age of 9 men increases by 4 years when two women are included in place of two men of ages 36 and 32 years . find the average age of the women ?", + "Output Program": [ + "n0 = 9.0\nn1 = 4.0\nn2 = 36.0\nn3 = 32.0\nt0 = n2 + n3\nt1 = n0 * n1\nt2 = t0 + t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "52" + ], + "split": "train" + }, + { + "Input": "there are 59 people that own pets . 15 people own only dogs , 10 people own only cats , 5 people own only cats and dogs , 3 people own cats , dogs and snakes . how many total snakes are there ?", + "Output Program": [ + "n0 = 59.0\nn1 = 15.0\nn2 = 10.0\nn3 = 5.0\nn4 = 3.0\nt0 = n1 + n2\nt1 = n3 + t0\nt2 = n4 + t1\nt3 = n0 - t2\nanswer = n4 + t3\nprint(answer)" + ], + "Output Answer": [ + "29" + ], + "split": "train" + }, + { + "Input": "a sum of salary is distributed among a , b , c , d in the proportion of 2 : 3 : 4 : 6 . if d gets $ 700 more than c , what is the b ' s share ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 4.0\nn3 = 6.0\nn4 = 700.0\nt0 = n3 - n2\nt1 = n4 / t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "1050" + ], + "split": "train" + }, + { + "Input": "if { x } is the product of all even integers from 1 to x inclusive , what is the greatest prime factor of { 26 } + { 24 } ?", + "Output Program": [ + "n0 = 1.0\nn1 = 26.0\nn2 = 24.0\nt0 = n1 + n2\nt1 = n0 * 2.0\nt2 = t0 / 2.0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "train" + }, + { + "Input": "what is the product between the place values of two 8 ' s in the numeral 780.38", + "Output Program": [ + "import math\nn0 = 8.0\nn1 = 780.38\nt0 = n1 / 100.0\nt1 = n1 * 10.0\nt2 = math.floor(t1)\nt3 = math.floor(t0)\nt4 = t3 * 100.0\nt5 = t1 - t2\nt6 = t5 / 10.0\nt7 = n1 - t4\nt8 = math.floor(t7)\nanswer = t6 * t8\nprint(answer)" + ], + "Output Answer": [ + "6.400000000001455" + ], + "split": "train" + }, + { + "Input": "the total car population in a chennai is 9000 out of which 5000 are made by honda . out of every 100 honda cars , 90 are red in color , but only 60 % of the total car population is red . find the % of non - honda cars that are red", + "Output Program": [ + "n0 = 9000.0\nn1 = 5000.0\nn2 = 100.0\nn3 = 90.0\nn4 = 60.0\nt0 = 12.0 + 12.0\nt1 = n3 * 1.0\nt2 = t1 + 3.0\nt3 = t2 - t1\nt4 = t3 / 2.0\nanswer = t0 - t4\nprint(answer)" + ], + "Output Answer": [ + "22.5" + ], + "split": "train" + }, + { + "Input": "the average of 7 consecutive numbers a , b , c , d , e , f and g is 9 . what percent of g is a ?", + "Output Program": [ + "import math\nn0 = 7.0\nn1 = 9.0\nt0 = n0 / 2.0\nt1 = math.floor(t0)\nt2 = n1 + t1\nt3 = n1 - t1\nt4 = t2 - t3\nt5 = t4 / t2\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "if 204 \u00f7 12.75 = 16 , then 2.04 \u00f7 1.275 = ?", + "Output Program": [ + "n0 = 204.0\nn1 = 12.75\nn2 = 16.0\nn3 = 2.04\nn4 = 1.275\n\nanswer = n3 / n4\nprint(answer)" + ], + "Output Answer": [ + "1.6" + ], + "split": "train" + }, + { + "Input": "if n is an integer and 101 n ^ 2 is less than or equal to 3600 , what is the greatest possible value of n ?", + "Output Program": [ + "import math\nn0 = 101.0\nn1 = 2.0\nn2 = 3600.0\nt0 = n2 / n0\nt1 = math.sqrt(max(0, t0))\nanswer = math.floor(t1)\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "find the number , difference between number and its 3 / 5 is 62 .", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 62.0\nt0 = n2 / 2.0\nanswer = n1 * t0\nprint(answer)" + ], + "Output Answer": [ + "155" + ], + "split": "train" + }, + { + "Input": "two trains of equal length are running on parallel lines in the same directions at 46 km / hr . and 36 km / hr . the faster trains pass the slower train in 54 seconds . the length of each train is :", + "Output Program": [ + "n0 = 46.0\nn1 = 36.0\nn2 = 54.0\nt0 = n0 - n1\nt1 = t0 * 1000.0\nt2 = t1 / 3600.0\nt3 = n2 * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "if x ^ 2 + ( 1 / x ^ 2 ) = 7 , x ^ 4 + ( 1 / x ^ 4 ) = ?", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 2.0\nn3 = 7.0\nn4 = 4.0\nn5 = 1.0\nn6 = 4.0\nt0 = n3**min(n0, 5)\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "47" + ], + "split": "train" + }, + { + "Input": "of 64 players on a cricket team , 37 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?", + "Output Program": [ + "n0 = 64.0\nn1 = 37.0\nt0 = 1.0 / 3.0\nt1 = n0 - n1\nt2 = 1.0 - t0\nt3 = t2 * t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "55" + ], + "split": "train" + }, + { + "Input": "if the average of 5 positive integers is 45 and the difference between the largest and the smallest of these 5 numbers is 10 , what is the maximum value possible for the largest of these 5 integers ?", + "Output Program": [ + "n0 = 5.0\nn1 = 45.0\nn2 = 5.0\nn3 = 10.0\nn4 = 5.0\nt0 = n0 * n1\nt1 = t0 - n3\nt2 = t1 / n0\nanswer = n3 + t2\nprint(answer)" + ], + "Output Answer": [ + "53" + ], + "split": "train" + }, + { + "Input": "find the lowest common multiple of 24 , 30 and 40 .", + "Output Program": [ + "import scipy\nn0 = 24.0\nn1 = 30.0\nn2 = 40.0\nt0 = scipy.lcm(int(n0), int(n1))\nanswer = scipy.lcm(int(n2), int(t0))\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "a certain number when divided by 39 leaves a remainder 15 , what is the remainder when the same number is divided by 13 ?", + "Output Program": [ + "n0 = 39.0\nn1 = 15.0\nn2 = 13.0\n\nanswer = n1 % n2\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a , b , and c are integers and a < b < c . s is the set of all integers from a to b , inclusive . q is the set of all integers from b to c , inclusive . the median of set s is ( 3 / 4 ) * b . the median of set q is ( 4 / 8 ) * c . if r is the set of all integers from a to c , inclusive , what fraction of c is the median of set r ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 4.0\nn3 = 8.0\nt0 = n2 / n3\nt1 = n0 / n1\nt2 = t0 * 2.0\nt3 = t1 * 2.0\nt4 = t2 - 1.0\nt5 = t3 - 1.0\nt6 = 1.0 / t5\nt7 = t4 / t6\nt8 = t7 + 1.0\nanswer = t8 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "a pupil ' s marks were wrongly entered as 73 instead of 45 . due to that the average marks for the class got increased by half . the number of pupils in the class is :", + "Output Program": [ + "n0 = 73.0\nn1 = 45.0\nt0 = n0 - n1\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "train" + }, + { + "Input": "the average of 6 no . ' s is 5.40 . the average of 2 of them is 5.2 , while the average of the other 2 is 5.80 . what is the average of the remaining 2 no ' s ?", + "Output Program": [ + "n0 = 6.0\nn1 = 5.4\nn2 = 2.0\nn3 = 5.2\nn4 = 2.0\nn5 = 5.8\nn6 = 2.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n2 * n5\nt3 = t1 + t2\nt4 = t0 - t3\nanswer = t4 / n2\nprint(answer)" + ], + "Output Answer": [ + "5.200000000000003" + ], + "split": "train" + }, + { + "Input": "in a group of ducks and cows , the total number of legs are 16 more than twice the no . of heads . find the total no . of buffaloes .", + "Output Program": [ + "n0 = 16.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "3 friends a , b , c went for week end party to mcdonald \u2019 s restaurant and there they measure there weights in some order in 7 rounds . a , b , c , ab , bc , ac , abc . final round measure is 155 kg then find the average weight of all the 7 rounds ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 155.0\nn3 = 7.0\nt0 = 1.0 + n0\nt1 = n2 * t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "88.57142857142857" + ], + "split": "train" + }, + { + "Input": "set j consists of 18 consecutive even numbers . if the smallest term in the set is - 12 , what is the range of the positive integers in set j ?", + "Output Program": [ + "n0 = 18.0\nn1 = 12.0\nt0 = -2.0\nt1 = n0 - 1.0\nt2 = 2.0 * t1\nt3 = t2 + t0\nanswer = t3 - n1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "having received his weekly allowance , a student spent 2 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 1.20 at the candy store . what is this student \u2019 s weekly allowance ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 1.2\nt0 = n0 * n1\nt1 = n2 * t0\nanswer = t1 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "at deluxe paint store , fuchsia paint is made by mixing 5 parts of red paint with 3 parts of blue paint . mauve paint is made by mixing 3 parts of red paint with 6 parts blue paint . how many liters of blue paint must be added to 16 liters of fuchsia to change it to mauve paint ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nn2 = 3.0\nn3 = 6.0\nn4 = 16.0\nt0 = n0 + n1\nt1 = n0 / t0\nt2 = n2 / t0\nt3 = n3 / t0\nt4 = n4 * t1\nt5 = t4 / t2\nt6 = n4 - t4\nt7 = t5 * t3\nanswer = t7 - t6\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "a contractor undertakes to do a piece of work in 40 days . he engages 100 men at the begining and 100 more after 35 days and completes the work in stipulated time . if he had not engaged the additional men , how many days behind schedule would it be finished ?", + "Output Program": [ + "n0 = 40.0\nn1 = 100.0\nn2 = 100.0\nn3 = 35.0\nt0 = 2.0 + 3.0\nt1 = n1 * n3\nt2 = n1 * 2.0\nt3 = t0 * t2\nt4 = t1 + t3\nt5 = t4 / 100.0\nanswer = t5 - n0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "if jake loses 8 pounds , he will weigh twice as much as his sister . together they now weigh 278 pounds . what is jake \u2019 s present weight , in pounds ?", + "Output Program": [ + "n0 = 8.0\nn1 = 278.0\nt0 = n1 - n0\nt1 = t0 / 3.0\nt2 = t1 * 2.0\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "188" + ], + "split": "train" + }, + { + "Input": "find the value of y from ( 12 ) ^ 2 x 6 ^ 3 \u00f7 432 = y ?", + "Output Program": [ + "n0 = 12.0\nn1 = 2.0\nn2 = 6.0\nn3 = 3.0\nn4 = 432.0\nt0 = n0**min(n1, 5)\nt1 = n2**min(n3, 5)\nt2 = t0 * t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "train" + }, + { + "Input": "the instructions state that cheryl needs 2 / 9 square yards of one type of material and 1 / 8 square yards of another type of material for a project . she buys exactly that amount . after finishing the project , however , she has 4 / 18 square yards left that she did not use . what is the total amount of square yards of material cheryl used ?", + "Output Program": [ + "n0 = 2.0\nn1 = 9.0\nn2 = 1.0\nn3 = 8.0\nn4 = 4.0\nn5 = 18.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = n4 / n5\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "0.125" + ], + "split": "train" + }, + { + "Input": "the average age of 17 students of a class is 17 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years , the age of the 17 th student is", + "Output Program": [ + "n0 = 17.0\nn1 = 17.0\nn2 = 5.0\nn3 = 14.0\nn4 = 9.0\nn5 = 16.0\nn6 = 17.0\nt0 = n0 * n0\nt1 = n2 * n3\nt2 = n4 * n5\nt3 = t1 + t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "the average ( arithmetic mean ) of 4 different integers is 68 . if the largest integer is 90 , what is the least possible value of the smallest integer ?", + "Output Program": [ + "n0 = 4.0\nn1 = 68.0\nn2 = 90.0\nt0 = n0 * n1\nt1 = n2 - 1.0\nt2 = n2 - 2.0\nt3 = t0 - n2\nt4 = t3 - t1\nanswer = t4 - t2\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "the instructions state that cheryl needs 4 / 9 square yards of one type of material and 2 / 3 square yards of another type of material for a project . she buys exactly that amount . after finishing the project , however , she has 8 / 18 square yards left that she did not use . what is the total amount of square yards of material cheryl used ?", + "Output Program": [ + "n0 = 4.0\nn1 = 9.0\nn2 = 2.0\nn3 = 3.0\nn4 = 8.0\nn5 = 18.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = n4 / n5\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "0.6666666666666667" + ], + "split": "train" + }, + { + "Input": "3 people have $ 28 , $ 72 , and $ 98 , respectively . if they pool their money then redistribute it among them , what is the maximum value for the median amount of money ?", + "Output Program": [ + "n0 = 3.0\nn1 = 28.0\nn2 = 72.0\nn3 = 98.0\nt0 = n1 + n2\nt1 = n3 + t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "99" + ], + "split": "train" + }, + { + "Input": "if a is an integer greater than 2 but less than 11 and b is an integer greater than 11 but less than 21 , what is the range of a / b ?", + "Output Program": [ + "n0 = 2.0\nn1 = 11.0\nn2 = 11.0\nn3 = 21.0\nt0 = n2 + 1.0\nt1 = n0 + 1.0\nt2 = n1 - 1.0\nt3 = n3 - 1.0\nt4 = t2 / t0\nt5 = t1 / t3\nanswer = t4 - t5\nprint(answer)" + ], + "Output Answer": [ + "0.6833333333333333" + ], + "split": "train" + }, + { + "Input": "in an election , candidate x got 75 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favour of candidate ?", + "Output Program": [ + "n0 = 75.0\nn1 = 15.0\nn2 = 560000.0\nt0 = n2 / 100.0\nt1 = 100.0 - n1\nt2 = t0 / 100.0\nt3 = n0 * t1\nanswer = t2 * t3\nprint(answer)" + ], + "Output Answer": [ + "357000" + ], + "split": "train" + }, + { + "Input": "a no . when divided by the sum of 555 and 445 gives 2 times their difference as quotient & 20 as remainder . find the no . is ?", + "Output Program": [ + "n0 = 555.0\nn1 = 445.0\nn2 = 2.0\nn3 = 20.0\nt0 = n0 + n1\nt1 = n0 - n1\nt2 = n2 * t0\nt3 = t2 * t1\nanswer = n3 + t3\nprint(answer)" + ], + "Output Answer": [ + "220020" + ], + "split": "train" + }, + { + "Input": "a case contains c cartons . each carton contains b boxes , and each box contains 300 paper clips . how many paper clips are contained in 2 cases ?", + "Output Program": [ + "n0 = 300.0\nn1 = 2.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "600" + ], + "split": "train" + }, + { + "Input": "for the positive integers x , x + 2 , x + 4 , x + 7 , and x + 32 , the mean is how much greater than the median ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 7.0\nn3 = 32.0\nt0 = n0 + n1\nt1 = 1.0 + n1\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = t3 / t1\nanswer = t4 - n1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "a driver would have reduced the time it took to drive from home to the store by 1 / 3 if the average speed had been increased by 18 miles per hour . what was the actual average speed , in miles per hour , when the driver drove from home to the store ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 18.0\nt0 = n0 / n1\nt1 = n0 - t0\nt2 = t1 * n2\nt3 = n0 - t1\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "36.000000000000014" + ], + "split": "train" + }, + { + "Input": "how many numbers from 9 to 79 are exactly divisible by 11 ?", + "Output Program": [ + "import math\nn0 = 9.0\nn1 = 79.0\nn2 = 11.0\nt0 = n1 / n2\nt1 = n0 / n2\nt2 = math.floor(t0)\nt3 = math.floor(t1)\nt4 = t3 + 1.0\nt5 = n2 * t2\nt6 = n2 * t4\nt7 = t5 - t6\nt8 = t7 / n2\nanswer = t8 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "what least number should be added to 1053 , so that the sum is completely divisible by 23", + "Output Program": [ + "n0 = 1053.0\nn1 = 23.0\nt0 = n0 % n1\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "the average weight of 6 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 6.0\nn1 = 2.5\nn2 = 65.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "in a class of students , 1 / 2 of the number of girls is equal to 1 / 6 of the total number of students . what is the ratio of boys to girls in the class ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 1.0\nn3 = 6.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = t0 - t1\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "2.0000000000000004" + ], + "split": "train" + }, + { + "Input": "if x is less than y by 45 % then y exceed x by :", + "Output Program": [ + "n0 = 45.0\nt0 = 100.0 - n0\nt1 = 100.0 / t0\nt2 = t1 - 1.0\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "81.81818181818181" + ], + "split": "train" + }, + { + "Input": "in a flight of 600 km , an aircraft was slowed down due to bad weather . its average speed for the trip was reduced by 200 km / hr and the time of flight increased by 30 minutes . the duration of the flight is ?", + "Output Program": [ + "n0 = 600.0\nn1 = 200.0\nn2 = 30.0\nt0 = n1 * n2\nt1 = t0 / 10.0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "s is a set of 64 consecutive multiples of 4 . if the smallest number in s is 68 , then the greatest number in s is", + "Output Program": [ + "n0 = 64.0\nn1 = 4.0\nn2 = 68.0\nt0 = n0 - 1.0\nt1 = n1 * t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "320" + ], + "split": "train" + }, + { + "Input": "the \u201c s - number \u201d of a number x is defined as the ones digit of 2 ^ x . antony rolls a die with 6 sides labeled with the integers from 1 to 6 , each of which has an equal probability of landing face - up . he then takes 3 ^ s , where s is the s - number of the result of his die roll , and plots 3 ^ s on a number line as the point a . finally , he repeats this entire process , this time plotting the result as the point b . what is the probability that the distance between a and b is greater than the value of b ?", + "Output Program": [ + "n0 = 2.0\nn1 = 6.0\nn2 = 1.0\nn3 = 6.0\nn4 = 3.0\nn5 = 3.0\nt0 = n1 + n2\nt1 = n1 * n1\nt2 = n4 + t0\nt3 = n4 + t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.3611111111111111" + ], + "split": "train" + }, + { + "Input": "a waiter ' s salary consists of his salary and tips . during one week his tips were 5 / 2 of his salary . what fraction of his income came from tips ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nt0 = n0 / n1\nt1 = t0 + 1.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.7142857142857143" + ], + "split": "train" + }, + { + "Input": "if a certain number x is divided by 82 , the reminder is 5 . what is the reminder when x + 7 is divided by 41 ?", + "Output Program": [ + "n0 = 82.0\nn1 = 5.0\nn2 = 7.0\nn3 = 41.0\n\nanswer = n1 + n2\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "cindy has her eye on a sundress but thinks it is too expensive . it goes on sale for 15 % less than the original price . before cindy can buy the dress , however , the store raises the new price by 25 % . if the dress cost $ 85 after it went on sale for 15 % off , what is the difference between the original price and the final price ?", + "Output Program": [ + "n0 = 15.0\nn1 = 25.0\nn2 = 85.0\nn3 = 15.0\nt0 = n1 + 100.0\nt1 = 100.0 - n0\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = n2 / t3\nt5 = n2 * t2\nanswer = t5 - t4\nprint(answer)" + ], + "Output Answer": [ + "6.25" + ], + "split": "train" + }, + { + "Input": "a committee is reviewing a total of 20 x black - and - white films and 6 y color films for a festival . if the committee selects y / x % of the black - and - white films and all of the color films , what fraction q of the selected films are in color ?", + "Output Program": [ + "n0 = 20.0\nn1 = 6.0\nt0 = n0 / 100.0\nt1 = n1 + t0\nanswer = n1 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.9677419354838709" + ], + "split": "train" + }, + { + "Input": "at the end of year x , automobile installment credit accounted for 20 % of all outstanding consumer installment credit . at that time automobile finance companies extended $ 57 billion of credit , or 1 / 3 of the automobile installment credit . how many billion dollars of consumer installment credit was outstanding at that time ?", + "Output Program": [ + "n0 = 20.0\nn1 = 57.0\nn2 = 1.0\nn3 = 3.0\nt0 = n0 / 100.0\nt1 = n1 * n3\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "855" + ], + "split": "train" + }, + { + "Input": "3 buffaloes eat as much as 4 cows or 2 oxen . at a farm , there are 15 buffaloes , 8 oxen , and 24 cows . the fodder for these cattle is available for 24 days . if 60 more cows and 30 more buffaloes are brought in , how many days will the fodder last ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 2.0\nn3 = 15.0\nn4 = 8.0\nn5 = 24.0\nn6 = 24.0\nn7 = 60.0\nn8 = 30.0\nt0 = n3 + n8\nt1 = n5 + n7\nt2 = n5 / n1\nt3 = n4 / n2\nt4 = t1 / n1\nt5 = n0 * t2\nt6 = n0 * t3\nt7 = n3 + t5\nt8 = n0 * t4\nt9 = t7 + t6\nt10 = t0 + t8\nt11 = t10 + t6\nt12 = n6 * t9\nanswer = t12 / t11\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "a cuboidal block 6 cm x 9 cm x 12 cm is cut up into an exact number of equal cubes . the least possible number of equal cubes will be", + "Output Program": [ + "n0 = 6.0\nn1 = 9.0\nn2 = 12.0\nt0 = n0 / 2.0\nt1 = n0 * n1\nt2 = n2 * t1\nt3 = t0 * t0\nt4 = t0 * t3\nanswer = t2 / t4\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "in a class of 25 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 4 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?", + "Output Program": [ + "n0 = 25.0\nn1 = 2.0\nn2 = 12.0\nn3 = 1.0\nn4 = 4.0\nn5 = 2.0\nn6 = 3.0\nn7 = 2.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n1 * n4\nt3 = t1 + t2\nt4 = n4 + t1\nt5 = n1 + t4\nt6 = n0 - t5\nt7 = t6 - n3\nt8 = n6 * t7\nt9 = t3 + t8\nanswer = t0 - t9\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "a bowl of nuts is prepared for a party . brand p mixed nuts are 20 % almonds and brand q ' s deluxe nuts are 25 % almonds . if a bowl contains a total of 68 ounces of nuts , representing a mixture of both brands , and 15 ounces of the mixture are almonds , how many ounces of brand q ' s deluxe mixed nuts are used ?", + "Output Program": [ + "n0 = 20.0\nn1 = 25.0\nn2 = 68.0\nn3 = 15.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = n2 * t0\nt3 = t1 - t0\nt4 = n3 - t2\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "27.99999999999998" + ], + "split": "train" + }, + { + "Input": "a is the hundreds digit of the 3 digit integer x , b is the tens digit of x , and c is the units digit of x . 2 a = b = 4 c , and a > 0 . what is the difference between the two greatest possible values of x ? tip : dont stop till you have exhausted all answer choices to arrive at the correct one .", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 4.0\nn3 = 0.0\nt0 = n2 * 1.0\nt1 = n1 * n2\nt2 = t0 / n1\nt3 = t0 * 100.0\nt4 = t1 * 10.0\nt5 = t0 * 10.0\nt6 = t3 + t4\nt7 = t2 * 100.0\nt8 = t6 + t2\nt9 = t7 + t5\nt10 = t9 + 1.0\nanswer = t8 - t10\nprint(answer)" + ], + "Output Answer": [ + "241" + ], + "split": "train" + }, + { + "Input": "65 % of a number is 21 less than 4 / 5 th of that number . what is the number ?", + "Output Program": [ + "n0 = 65.0\nn1 = 21.0\nn2 = 4.0\nn3 = 5.0\nt0 = 100.0 / n3\nt1 = n1 * n3\nt2 = t0 * t1\nt3 = n2 * t0\nt4 = t3 - n0\nanswer = t2 / t4\nprint(answer)" + ], + "Output Answer": [ + "140" + ], + "split": "train" + }, + { + "Input": "a vendor sells 60 percent of the apples he had and throws away 40 percent of the remainder . the next day , the vendor sells 50 percent of the remaining apples and throws away the rest . in total , what percent of his apples does the vendor throw away ?", + "Output Program": [ + "n0 = 60.0\nn1 = 40.0\nn2 = 50.0\nt0 = n1 / 100.0\nt1 = 100.0 - n0\nt2 = t0 * t1\nt3 = t1 - t2\nt4 = t3 / 2.0\nanswer = t4 + t2\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "a vendor sells 80 percent of the pears he had and throws away 50 percent of the remainder . the next day , the vendor sells 80 percent of the remaining pears and throws away the rest . in total , what percent of his pears does the vendor throw away ?", + "Output Program": [ + "n0 = 80.0\nn1 = 50.0\nn2 = 80.0\nt0 = n1 / 100.0\nt1 = n0 / 100.0\nt2 = 1.0 - t1\nt3 = t0 * t2\nt4 = t2 - t3\nt5 = t1 * t4\nt6 = t4 - t5\nt7 = t3 + t6\nanswer = t7 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "11.999999999999996" + ], + "split": "train" + }, + { + "Input": "the average weight of 8 persons increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 3.5\nn2 = 65.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "93" + ], + "split": "train" + }, + { + "Input": "a certain taxi company charges $ 2.80 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ?", + "Output Program": [ + "n0 = 2.8\nn1 = 1.0\nn2 = 5.0\nn3 = 0.4\nn4 = 1.0\nn5 = 5.0\nn6 = 8.0\nt0 = n1 / n2\nt1 = n6 / t0\nt2 = t1 - n1\nt3 = n3 * t2\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "18.400000000000002" + ], + "split": "train" + }, + { + "Input": "of the 3 - digit integers greater than 200 , how many have two digits that are equal to each other and the remaining digit different from the other two ?", + "Output Program": [ + "n0 = 3.0\nn1 = 200.0\nt0 = n1 / 2.0\nt1 = t0 - 1.0\nt2 = t1 / n0\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "the tax on a commodity is diminished by 40 % but its consumption is increased by 25 % . find the decrease percent in the revenue derived from it ?", + "Output Program": [ + "n0 = 40.0\nn1 = 25.0\nt0 = n1 + 100.0\nt1 = 100.0 - n0\nt2 = t0 * t1\nt3 = t2 / 100.0\nanswer = 100.0 - t3\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "out of 40 applicants to a law school , 15 majored in political science , 20 had a grade point average higher than 3.0 , and 10 did not major in political science and had a gpa equal to or lower than 3.0 . how many of q applicants majored in political science and had a gpa higher than 3.0 ?", + "Output Program": [ + "n0 = 40.0\nn1 = 15.0\nn2 = 20.0\nn3 = 3.0\nn4 = 10.0\nn5 = 3.0\nn6 = 3.0\nt0 = n1 + n4\nt1 = n0 - t0\nanswer = n2 - t1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "the sum of the squares of the first 15 positive integers ( 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + . . . + 15 ^ 2 ) is equal to 1270 . what is the sum of the squares of the second 15 positive integers ( 16 ^ 2 + 17 ^ 2 + 18 ^ 2 + . . . + 30 ^ 2 ) ?", + "Output Program": [ + "n0 = 15.0\nn1 = 1.0\nn2 = 2.0\nn3 = 2.0\nn4 = 2.0\nn5 = 3.0\nn6 = 2.0\nn7 = 15.0\nn8 = 2.0\nn9 = 1270.0\nn10 = 15.0\nn11 = 16.0\nn12 = 2.0\nn13 = 17.0\nn14 = 2.0\nn15 = 18.0\nn16 = 2.0\nn17 = 30.0\nn18 = 2.0\nt0 = n17 + n1\nt1 = n5 + n5\nt2 = n17 * n2\nt3 = t2 + n1\nt4 = n17 * t0\nt5 = t3 * t4\nt6 = t5 / t1\nanswer = t6 - n9\nprint(answer)" + ], + "Output Answer": [ + "8185" + ], + "split": "train" + }, + { + "Input": "last week vartan spent 15 percent of his wages on recreation . this week , his wages are 10 percent less than last week \u02bc s wages and he spent 30 percent of his wages on recreation . the amount he spends on recreation this week is what percent of the amount he spent on recreation last week ?", + "Output Program": [ + "n0 = 15.0\nn1 = 10.0\nn2 = 30.0\nt0 = 100.0 - n1\nt1 = n2 * t0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "180" + ], + "split": "train" + }, + { + "Input": "the ages of old and young total 48 . old is twice as old as young was when old was half as old as young will be when young is 3 times as old was when old was 3 times as old as young . how old is old ?", + "Output Program": [ + "n0 = 48.0\nn1 = 3.0\nn2 = 3.0\nt0 = n1 + n1\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "keats library purchases a number of new books , all in the category of biography , and the library does not acquire any other books . with the addition of the new biographies , the biography collection of the library amounts to 32 % of the total number of books in the library . if prior to the purchase , only 20 % of the books in keats library were biographies , by what percent has the number of biographies in the library increased ?", + "Output Program": [ + "n0 = 32.0\nn1 = 20.0\nt0 = n0 * 100.0\nt1 = n1 * 100.0\nt2 = 100.0 - n0\nt3 = t0 - t1\nt4 = t3 / t2\nt5 = t4 / n1\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "88.23529411764707" + ], + "split": "train" + }, + { + "Input": "in a class of 20 students in an examination in mathematics 2 students scored 100 marks each , 3 get zero each and the average of the rest was 40 . what is the average of the whole class ?", + "Output Program": [ + "n0 = 20.0\nn1 = 2.0\nn2 = 100.0\nn3 = 3.0\nn4 = 40.0\nt0 = n1 * n2\nt1 = n0 - n1\nt2 = t1 - n3\nt3 = n4 * t2\nt4 = t3 + t0\nanswer = t4 / n0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "the average weight of 29 students is 28 kg . by the admission of a new student , the average weight is reduced to 27.4 kg . the weight of the new student is", + "Output Program": [ + "n0 = 29.0\nn1 = 28.0\nn2 = 27.4\nt0 = n0 + 1.0\nt1 = n0 * n1\nt2 = n2 * t0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number ?", + "Output Program": [ + "import scipy\nn0 = 17.0\nn1 = 60.0\nt0 = scipy.gcd(int(n0), int(n1))\nanswer = t0 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "the arithmetic mean and standard deviation of a certain normal distribution are 17.5 and 2.5 , respectively . what value is exactly 2 standard deviations less than the mean ?", + "Output Program": [ + "n0 = 17.5\nn1 = 2.5\nn2 = 2.0\nt0 = n1 * n2\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "12.5" + ], + "split": "train" + }, + { + "Input": "in a group of 130 people , 90 have an age of more 30 years , and the others have an age of less than 20 years . if a person is selected at random from this group , what is the probability the person ' s age is less than 20 ?", + "Output Program": [ + "n0 = 130.0\nn1 = 90.0\nn2 = 30.0\nn3 = 20.0\nn4 = 20.0\nt0 = n0 - n1\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.3076923076923077" + ], + "split": "train" + }, + { + "Input": "if a = { 17 , 27 , 31 , 53 , 61 } , what is the sum of mean and median of the numbers in a ?", + "Output Program": [ + "n0 = 17.0\nn1 = 27.0\nn2 = 31.0\nn3 = 53.0\nn4 = 61.0\nt0 = n0 + n1\nt1 = 1.0 + 4.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nt5 = t4 / t1\nanswer = n2 + t5\nprint(answer)" + ], + "Output Answer": [ + "68.8" + ], + "split": "train" + }, + { + "Input": "a ' s speed is 15 / 13 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that b beats a by 40 % of the length of the race ?", + "Output Program": [ + "n0 = 15.0\nn1 = 13.0\nn2 = 40.0\nt0 = n1 / n0\nt1 = 100.0 - n2\nt2 = t1 / 100.0\nt3 = t2 * t0\nt4 = 1.0 - t3\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "at the opening of a trading day at a certain stock exchange , the price per share of stock k was $ 8 . if the price per share of stock k was $ 9 at the closing of the day , what was the percent increase in the price per share of stock k for that day ?", + "Output Program": [ + "n0 = 8.0\nn1 = 9.0\nt0 = n1 / n0\nt1 = t0 - 1.0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "12.5" + ], + "split": "train" + }, + { + "Input": "the standard deviation of a normal distribution of data is 2 , and 3 standard deviations below the mean is greater than 45 . what is a possible value for the mean of the distribution ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 45.0\nt0 = n0 * n1\nt1 = n2 + t0\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "52" + ], + "split": "train" + }, + { + "Input": "evaluate : 10010 - 12 * 3 * 2 = ?", + "Output Program": [ + "n0 = 10010.0\nn1 = 12.0\nn2 = 3.0\nn3 = 2.0\nt0 = n1 * n2\nt1 = n3 * t0\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "9938" + ], + "split": "train" + }, + { + "Input": "find large number from below question the difference of two numbers is 1345 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder", + "Output Program": [ + "n0 = 1345.0\nn1 = 6.0\nn2 = 15.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nt2 = t0 / t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "1596" + ], + "split": "train" + }, + { + "Input": "if there are 10 peanuts in a box and mary puts 8 more peanuts inside , how many peanuts are in the box ?", + "Output Program": [ + "n0 = 10.0\nn1 = 8.0\n\nanswer = n0 + n1\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "the average runs of a cricket player of 10 innings was 32 . how many runs must he makes ih his next innings so as to increase his average of runs by 4 ?", + "Output Program": [ + "n0 = 10.0\nn1 = 32.0\nn2 = 4.0\nt0 = n0 + 1.0\nt1 = n1 + n2\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "76" + ], + "split": "train" + }, + { + "Input": "the average monthly income of p and q is rs . 5050 . the average monthly income of q and r is rs . 6250 and the average monthly income of p and r is rs . 5200 . the monthly income of p is ?", + "Output Program": [ + "n0 = 5050.0\nn1 = 6250.0\nn2 = 5200.0\nt0 = n0 + n2\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "4000" + ], + "split": "train" + }, + { + "Input": "if p and q are prime numbers , how many divisors does the product p ^ 3 * q ^ 6 have ?", + "Output Program": [ + "n0 = 3.0\nn1 = 6.0\nt0 = n0 + 1.0\nt1 = n1 + 1.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "in a renowned city , the average birth rate is 6 people every two seconds and the death rate is 2 people every two seconds . estimate the size of the population net increase that occurs in one day .", + "Output Program": [ + "n0 = 6.0\nn1 = 2.0\nt0 = n0 - n1\nt1 = t0 * 3600.0\nanswer = t1 * 12.0\nprint(answer)" + ], + "Output Answer": [ + "172800" + ], + "split": "train" + }, + { + "Input": "for every x , the action [ x ] is defined : [ x ] is the greatest integer less than or equal to x . what is the value of [ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.3 ] - 6.6 ?", + "Output Program": [ + "n0 = 6.5\nn1 = 2.0\nn2 = 3.0\nn3 = 2.0\nn4 = 7.2\nn5 = 8.3\nn6 = 6.6\nt0 = 4.0 / 10.0\nt1 = n1 * n4\nt2 = n5 - t0\nt3 = t1 + t2\nanswer = t3 - n6\nprint(answer)" + ], + "Output Answer": [ + "15.700000000000001" + ], + "split": "train" + }, + { + "Input": "in the rectangular coordinate system , if the line x = 8 y + 5 passes through points ( m , n ) and ( m + 2 , n + p ) , what is the value of p ?", + "Output Program": [ + "n0 = 8.0\nn1 = 5.0\nn2 = 2.0\n\nanswer = n2 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.25" + ], + "split": "train" + }, + { + "Input": "the difference between a two - digit number and the number obtained by interchanging the positions of its digits is 81 . what is the difference between the two digits of that number ?", + "Output Program": [ + "n0 = 81.0\nt0 = 10.0 - 1.0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "the average marks of a class of 35 students is 45 and that of another class of 55 students is 65 . find the average marks of all the students ?", + "Output Program": [ + "n0 = 35.0\nn1 = 45.0\nn2 = 55.0\nn3 = 65.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "57.22222222222222" + ], + "split": "train" + }, + { + "Input": "a and b together have $ 100 . if 3 / 10 of a ' s amount is equal to 1 / 5 of b ' s amount , how much amount does b have ?", + "Output Program": [ + "n0 = 100.0\nn1 = 3.0\nn2 = 10.0\nn3 = 1.0\nn4 = 5.0\nt0 = n3 / n4\nt1 = n1 / n2\nt2 = t0 / t1\nt3 = t2 + 1.0\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "virginia , adrienne , and dennis have taught history for a combined total of 93 years . if virginia has taught for 9 more years than adrienne and for 9 fewer years than dennis , for how many years has dennis taught ?", + "Output Program": [ + "n0 = 93.0\nn1 = 9.0\nn2 = 9.0\nt0 = n1 + n2\nt1 = n1 + t0\nt2 = n0 - t1\nt3 = t2 / 3.0\nanswer = t0 + t3\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "a customer bought a product at the shop . however , the shopkeeper increased the price of the product by 10 % so that the customer could not buy the required amount of the product . the customer managed to buy only 90 % of the required amount . what is the difference in the amount of money that the customer paid for the second purchase compared to the first purchase ?", + "Output Program": [ + "n0 = 10.0\nn1 = 90.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = t0 + 1.0\nt3 = t2 * t1\nt4 = 1.0 - t3\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "0.9999999999999898" + ], + "split": "train" + }, + { + "Input": "the expression ( 11.98 \u00d7 11.98 + 11.98 \u00d7 x + 0.02 \u00d7 0.02 ) will be a perfect square for x equal to", + "Output Program": [ + "n0 = 11.98\nn1 = 11.98\nn2 = 11.98\nn3 = 0.02\nn4 = 0.02\n\nanswer = n3 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "0.04" + ], + "split": "train" + }, + { + "Input": "the average height of 35 boys in a class was calculated as 180 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ) .", + "Output Program": [ + "import math\nn0 = 35.0\nn1 = 180.0\nn2 = 166.0\nn3 = 106.0\nt0 = n0 * n1\nt1 = t0 - n2\nt2 = n3 + t1\nt3 = t2 / n0\nanswer = math.floor(t3)\nprint(answer)" + ], + "Output Answer": [ + "178" + ], + "split": "train" + }, + { + "Input": "a + 2 b = 6 , ab = 4 2 / a + 1 / b = ?", + "Output Program": [ + "n0 = 2.0\nn1 = 6.0\nn2 = 4.0\nn3 = 2.0\nn4 = 1.0\nt0 = n0 + n4\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "1.5" + ], + "split": "train" + }, + { + "Input": "a man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses . next year his income increases by 20 % but his savings increase by 100 % . if his total expenditure in 2 years is double his expenditure in 1 st year , what % age of his income in the first year did he save ?", + "Output Program": [ + "n0 = 20.0\nn1 = 100.0\nn2 = 2.0\nn3 = 1.0\nt0 = n0 + n1\nt1 = n1 * n2\nt2 = n1 + t0\nt3 = t2 - t1\nt4 = t3 / n1\nanswer = t4 * n1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "how many digits will be there to the right of the decimal point in the product of 95 and . 02554 ?", + "Output Program": [ + "n0 = 95.0\nn1 = 2554.0\nt0 = 100.0 - n0\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "dacid obtained 86 , 85 , 92 , 87 and 95 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?", + "Output Program": [ + "n0 = 86.0\nn1 = 85.0\nn2 = 92.0\nn3 = 87.0\nn4 = 95.0\nn5 = 100.0\nt0 = n0 + n1\nt1 = 10.0 / 2.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "89" + ], + "split": "train" + }, + { + "Input": "if grapes are 92 % water and raisins are 20 % water , then how many kilograms did a quantity of raisins , which currently weighs 5 kilograms , weigh when all the raisins were grapes ? ( assume that the only difference between their raisin - weight and their grape - weight is water that evaporated during their transformation . )", + "Output Program": [ + "n0 = 92.0\nn1 = 20.0\nn2 = 5.0\nt0 = 100.0 - n1\nt1 = 100.0 - n0\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = n2 * t2\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "a teacher grades students \u2019 tests by subtracting twice the number of incorrect responses from the number of correct responses . if student a answers each of the 100 questions on her test and receives a score of 70 , how many questions did student a answer correctly ?", + "Output Program": [ + "n0 = 100.0\nn1 = 70.0\nt0 = n0 - n1\nt1 = t0 / 3.0\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "18 men shake hands with each other . maximum no of handshakes without cyclic handshakes .", + "Output Program": [ + "n0 = 18.0\nt0 = n0 / 2.0\nt1 = n0 - 1.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "153" + ], + "split": "train" + }, + { + "Input": "? x 120 = 173 x 240", + "Output Program": [ + "n0 = 120.0\nn1 = 173.0\nn2 = 240.0\nt0 = n1 * n2\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "346" + ], + "split": "train" + }, + { + "Input": "in a survey of parents , exactly 3 / 4 of the mothers and 9 / 10 of the fathers held full - time jobs . if 40 percent of the parents surveyed were women , what percent of the parents did not hold full - time jobs ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 9.0\nn3 = 10.0\nn4 = 40.0\nt0 = n2 / n3\nt1 = n0 / n1\nt2 = 100.0 - n4\nt3 = t0 * t2\nt4 = n4 * t1\nt5 = t2 - t3\nt6 = n4 - t4\nanswer = t5 + t6\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "workers decided to raise rs . 3 lacs by equal contribution from each . had they contributed rs . 50 eachextra , the contribution would have been rs . 3.60 lacs . how many workers were they ?", + "Output Program": [ + "n0 = 3.0\nn1 = 50.0\nn2 = 3.6\nt0 = n2 - n0\nt1 = t0 * 1000.0\nt2 = t1 * 100.0\nanswer = t2 / n1\nprint(answer)" + ], + "Output Answer": [ + "1200.0000000000002" + ], + "split": "train" + }, + { + "Input": "if a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land tails up exectly twice in 3 consecutive flips ?", + "Output Program": [ + "n0 = 3.0\nt0 = 1.0 / 2.0\nt1 = t0**min(n0, 5)\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "0.375" + ], + "split": "train" + }, + { + "Input": "if the average ( arithmetic mean ) of 10 consecutive odd integers is 154 , then the least of these integers is", + "Output Program": [ + "n0 = 10.0\nn1 = 154.0\nt0 = n1 - n0\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "145" + ], + "split": "train" + }, + { + "Input": "each of 3 investments has a 20 % of becoming worthless within a year of purchase , independently of what happens to the other two investments . if simone invests an equal sum v in each of these 3 investments on january 1 , the approximate chance that by the end of the year , she loses no more than 1 / 3 of her original investment is", + "Output Program": [ + "n0 = 3.0\nn1 = 20.0\nn2 = 3.0\nn3 = 1.0\nn4 = 1.0\nn5 = 3.0\nt0 = n1 / 100.0\nt1 = t0**min(n0, 5)\nt2 = 1.0 - t0\nt3 = t0 * t2\nt4 = t0 * t3\nt5 = n0 * t4\nt6 = t5 + t1\nt7 = -t6\nt8 = n3 + t7\nanswer = t8 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "89.6" + ], + "split": "train" + }, + { + "Input": "a man owns 2 / 3 of market reserch beauro buzness , and sells 3 / 4 of his shares for 75000 rs , what is the value of buzness ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 3.0\nn3 = 4.0\nn4 = 75000.0\nt0 = n0 / n1\nt1 = n1 / n3\nt2 = t0 * t1\nanswer = n4 / t2\nprint(answer)" + ], + "Output Answer": [ + "150000" + ], + "split": "train" + }, + { + "Input": "on a certain day , joey , the ice - cream seller sold his ice creams to 4 different kids in a manner that each of the kids purchased half of the remaining ice creams and half ice - cream more . if we tell you that the fourth kid bought just a single ice cream , can you find out how many ice creams were sold by joey that day ?", + "Output Program": [ + "n0 = 4.0\nt0 = n0 * 2.0\nt1 = t0 + t0\nanswer = t1 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "the total cost of a vacation was divided among 3 people . if the total cost of the vacation had been divided equally among 4 people , the cost per person would have been $ 40 less . what was the total cost cost of the vacation ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 40.0\nt0 = n0 * n1\nt1 = n1 - n0\nt2 = n2 / t1\nanswer = t2 * t0\nprint(answer)" + ], + "Output Answer": [ + "480" + ], + "split": "train" + }, + { + "Input": "a certain mixture of nuts consists of 5 parts almonds to 2 parts walnuts , by weight . what is the number of pounds of almonds in 150 pounds of the mixture ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 150.0\nt0 = n0 + n1\nt1 = n0 * n2\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "107.14285714285714" + ], + "split": "train" + }, + { + "Input": "in the coordinate plane , points ( x , 1 ) and ( 5 , y ) are on line k . if line k passes through the origin and has slope 1 / 5 , then what are the values of x and y respectively ?", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 1.0\nn3 = 5.0\nt0 = n0 / n3\nt1 = n1 * n3\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "5020 \u2212 ( 502 \u00f7 100.4 ) = ?", + "Output Program": [ + "n0 = 5020.0\nn1 = 502.0\nn2 = 100.4\nt0 = n1 / n2\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "5015" + ], + "split": "train" + }, + { + "Input": "the average of 10 numbers is calculated as 46 . it is discovered later on that while calculating the average , the number 65 was incorrectly read as 25 , and this incorrect number was used in the calculation . what is the correct average ?", + "Output Program": [ + "n0 = 10.0\nn1 = 46.0\nn2 = 65.0\nn3 = 25.0\nt0 = n0 * n1\nt1 = t0 - n3\nt2 = n2 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "a part - time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee ' s total income did not change . by what percent w should the number of hours worked be increased ?", + "Output Program": [ + "n0 = 20.0\nt0 = 10.0 * 4.0\nt1 = 100.0 - n0\nt2 = t1 / 100.0\nt3 = t2 * 10.0\nt4 = t0 / t3\nt5 = t4 - 4.0\nt6 = t5 / 4.0\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "john spends $ 320 buying his favorite dolls . if he buys only small monkey dolls , which are $ 4 cheaper than the large monkey dolls , he could buy 40 more dolls than if he were to buy only large monkey dolls . how much does a large monkey doll cost ?", + "Output Program": [ + "n0 = 320.0\nn1 = 4.0\nn2 = 40.0\nt0 = n1 * n2\nt1 = n0 - t0\nt2 = t1 / n1\nt3 = n2 + t2\nt4 = n0 / t3\nanswer = n1 + t4\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a profit of rs . 1000 is divided between x and y in the ratio of 1 / 2 : 1 / 3 . what is the difference between their profit shares ?", + "Output Program": [ + "n0 = 1000.0\nn1 = 1.0\nn2 = 2.0\nn3 = 1.0\nn4 = 3.0\nt0 = n1 / n2\nt1 = n1 / n4\nt2 = t0 + t1\nt3 = n0 / t2\nt4 = t3 / n2\nt5 = t3 / n4\nanswer = t4 - t5\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "train" + }, + { + "Input": "there is a total of 120 marbles in a box , each of which is red , green , blue , or white . if one marble is drawn from the box at random , the probability that it will be white is 1 / 4 and the probability that it will be green is 1 / 3 . what is the probability that the marble will be either red or blue ?", + "Output Program": [ + "n0 = 120.0\nn1 = 1.0\nn2 = 4.0\nn3 = 1.0\nn4 = 3.0\nt0 = n1 / n2\nt1 = n3 / n4\nt2 = t0 + t1\nanswer = n1 - t2\nprint(answer)" + ], + "Output Answer": [ + "0.41666666666666674" + ], + "split": "train" + }, + { + "Input": "if a 2 + b 2 + c 2 = 941 and ab + bc + ca = 10 , then a + b + c is", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 2.0\nn2 = 2.0\nn3 = 941.0\nn4 = 10.0\nt0 = n4 * n0\nt1 = n3 + t0\nanswer = math.sqrt(max(0, t1))\nprint(answer)" + ], + "Output Answer": [ + "31" + ], + "split": "train" + }, + { + "Input": "what is the tens digit of 6 ^ 18 ?", + "Output Program": [ + "import math\nn0 = 6.0\nn1 = 18.0\nt0 = 1.0 + 4.0\nt1 = n1 % t0\nt2 = n0**min(t1, 5)\nt3 = t2 % 100.0\nt4 = t3 / 10.0\nanswer = math.floor(t4)\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "the average of 10 consecutive integers is 20 . then , 9 is deducted from the first consecutive number , 8 is deducted from the second , 7 is deducted form the third , and so on until the last number which remains unchanged . what is the new average ?", + "Output Program": [ + "n0 = 10.0\nn1 = 20.0\nn2 = 9.0\nn3 = 8.0\nn4 = 7.0\nt0 = 1.0 + 4.0\nt1 = n0 * n1\nt2 = n2 * t0\nt3 = t1 - t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "15.5" + ], + "split": "train" + }, + { + "Input": "a person decided to build a house in 100 days . he employed 100 men in the beginning and 100 more after 10 days and completed the construction in stipulated time . if he had not employed the additional men , how many days behind schedule would it have been finished ?", + "Output Program": [ + "n0 = 100.0\nn1 = 100.0\nn2 = 100.0\nn3 = 10.0\n\nanswer = n0 - n3\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "there are 2 sections a and b in a class , consisting of 36 and 24 students respectively . if the average weight of section a is 30 kg and that of section b is 30 kg , find the average of the whole class ?", + "Output Program": [ + "n0 = 2.0\nn1 = 36.0\nn2 = 24.0\nn3 = 30.0\nn4 = 30.0\nt0 = n1 + n2\nt1 = n1 * n3\nt2 = n2 * n4\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "a train ride from two p to town q costs $ 6.35 more than does a bus ride from town p to town q . together , the cost of one train ride and one bus ride is $ 9.85 . what is the cost of a bus ride from town p to town q ?", + "Output Program": [ + "n0 = 6.35\nn1 = 9.85\nt0 = n1 - n0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "1.75" + ], + "split": "train" + }, + { + "Input": "a drink vendor has 10 liters of maaza , 144 liters of pepsi and 368 liters of sprite . he wants to pack them in cans , so that each can contains the same number of liters of a drink , and does n ' t want to mix any two drinks in a can . what is the least number of cans required ?", + "Output Program": [ + "import scipy\nn0 = 10.0\nn1 = 144.0\nn2 = 368.0\nt0 = scipy.gcd(int(n0), int(n1))\nt1 = scipy.gcd(int(n2), int(t0))\nt2 = n0 / t1\nt3 = n1 / t1\nt4 = n2 / t1\nt5 = t2 + t3\nanswer = t5 + t4\nprint(answer)" + ], + "Output Answer": [ + "261" + ], + "split": "train" + }, + { + "Input": "if the sum of two numbers is 45 and the l . c . m and sum of the reciprocal of the numbers are 120 and 11 / 120 then hcf of numbers is equal to :", + "Output Program": [ + "import math\nn0 = 45.0\nn1 = 120.0\nn2 = 11.0\nn3 = 120.0\nt0 = n0 / n2\nt1 = math.floor(t0)\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "there has been successive increases of 25 % and then 10 % in the price of gas from the previous month . by what percentage should a driver reduce gas consumption so that the expenditure does not change ?", + "Output Program": [ + "n0 = 25.0\nn1 = 10.0\nt0 = n0 + 100.0\nt1 = n1 * t0\nt2 = t1 / 100.0\nt3 = t0 + t2\nt4 = 100.0 / t3\nt5 = 1.0 - t4\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "27.27272727272727" + ], + "split": "train" + }, + { + "Input": "a dishonest dealer claims to sell a product at its cost price . he uses a counterfeit weight which is 20 % less than the real weight . further greed overtook him and he added 35 % impurities to the product . find the net profit percentage of the dealer ?", + "Output Program": [ + "n0 = 20.0\nn1 = 35.0\nt0 = n1 + 100.0\nt1 = 100.0 - n0\nt2 = t0 / t1\nt3 = t2 - 1.0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "68.75" + ], + "split": "train" + }, + { + "Input": "nina has exactly enough money to purchase 6 widgets . if the cost of each widget were reduced by $ 2 , then nina would have exactly enough money to purchase 8 widgets . how much money does nina have ?", + "Output Program": [ + "n0 = 6.0\nn1 = 2.0\nn2 = 8.0\nt0 = n1 * n2\nt1 = n2 - n0\nt2 = t0 / t1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "of the final grades received by the students in a certain math course , 1 / 5 are a ' s , 1 / 4 are b ' s , 1 / 2 are c ' s , and the remaining 5 grades are d ' s . what is the number of students in the course ?", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 1.0\nn3 = 4.0\nn4 = 1.0\nn5 = 2.0\nn6 = 5.0\nt0 = n0 / n1\nt1 = n0 / n3\nt2 = n0 / n5\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n0 - t4\nanswer = n6 / t5\nprint(answer)" + ], + "Output Answer": [ + "99.99999999999991" + ], + "split": "train" + }, + { + "Input": "the area of one square is x ^ 2 + 12 x + 36 and the area of another square is 4 x ^ 2 \u2212 12 x + 9 . if the sum of the perimeters of both squares is 64 , what is the value of x ?", + "Output Program": [ + "n0 = 2.0\nn1 = 12.0\nn2 = 36.0\nn3 = 4.0\nn4 = 2.0\nn5 = 12.0\nn6 = 9.0\nn7 = 64.0\nt0 = n1 / 2.0\nt1 = t0 * 4.0\nt2 = t1 - n1\nt3 = n7 - t2\nanswer = t3 / n1\nprint(answer)" + ], + "Output Answer": [ + "4.333333333333333" + ], + "split": "train" + }, + { + "Input": "if rs . 578 be divided among a , b , c in such a way that a gets 2 / 3 of what b gets and b gets 1 / 4 of what c gets , then their shares are respectively ?", + "Output Program": [ + "n0 = 578.0\nn1 = 2.0\nn2 = 3.0\nn3 = 1.0\nn4 = 4.0\nt0 = n3 / n4\nt1 = n1 / n2\nt2 = t1 * t0\nt3 = t0 + t2\nt4 = t3 + n3\nanswer = n0 / t4\nprint(answer)" + ], + "Output Answer": [ + "408.00000000000006" + ], + "split": "train" + }, + { + "Input": "the average weight of 29 students is 28 kg . by the admission of a new student , the average weight is reduced to 27.8 kg . the weight of the new student is", + "Output Program": [ + "n0 = 29.0\nn1 = 28.0\nn2 = 27.8\nt0 = n0 + 1.0\nt1 = n0 * n1\nt2 = n2 * t0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "in a group of 150 people , 90 have an age of more 30 years , and the others have an age of less than 20 years . if a person is selected at random from this group , what is the probability the person ' s age is less than 20 ?", + "Output Program": [ + "n0 = 150.0\nn1 = 90.0\nn2 = 30.0\nn3 = 20.0\nn4 = 20.0\nt0 = n0 - n1\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.4" + ], + "split": "train" + }, + { + "Input": "the sum of the first 50 positive even integers is 2550 . what is the sum of the even integers from 202 to 300 inclusive ?", + "Output Program": [ + "n0 = 50.0\nn1 = 2550.0\nn2 = 202.0\nn3 = 300.0\nt0 = n2 + n3\nt1 = n3 - n2\nt2 = t1 / 2.0\nt3 = t0 / 2.0\nt4 = t2 + 1.0\nanswer = t4 * t3\nprint(answer)" + ], + "Output Answer": [ + "12550" + ], + "split": "train" + }, + { + "Input": "the average weight of 8 person ' s increases by 3 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 3.0\nn2 = 65.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "89" + ], + "split": "train" + }, + { + "Input": "a dishonest dealer claims to sell a product at its cost price . he uses a counterfeit weight which is 20 % less than the real weight . further greed overtook him and he added 15 % impurities to the product . find the net profit percentage of the dealer ?", + "Output Program": [ + "n0 = 20.0\nn1 = 15.0\nt0 = n1 + 100.0\nt1 = 100.0 - n0\nt2 = t0 / t1\nt3 = t2 - 1.0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "43.75" + ], + "split": "train" + }, + { + "Input": "if a dozen of oranges cost $ 5 , what would be the cost of 10 oranges ?", + "Output Program": [ + "n0 = 5.0\nn1 = 10.0\nt0 = n1 + 2.0\nt1 = n0 * n1\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "4.166666666666667" + ], + "split": "train" + }, + { + "Input": "every letter in the alphabet has a number value that is equal to its place in the alphabet . thus , the letter a has a value of 1 , the letter b has a value of 2 , the letter c has a value of 3 , etc . . . the number value of a word is obtained by adding up the value of the letters in the word and then multiplying that sum by the length of the word . what is the number value of the word ` ` rat ' ' ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 3.0\nt0 = n1 * 10.0\nt1 = t0 - n1\nt2 = n0 + t1\nt3 = t2 + t0\nanswer = n2 * t3\nprint(answer)" + ], + "Output Answer": [ + "117" + ], + "split": "train" + }, + { + "Input": "\u221a ( 9 ) ^ 2", + "Output Program": [ + "import math\nn0 = 9.0\nn1 = 2.0\nt0 = n0**min(n1, 5)\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "moli buys 3 ribbons , 7 clips and 1 soap for rs . 120 exactly . at the same place it would cost rs . 164 for 4 ribbons , 10 clips and one soap . how much would it cost for one ribbon , one clip and one soap ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 1.0\nn3 = 120.0\nn4 = 164.0\nn5 = 4.0\nn6 = 10.0\nt0 = n6 + 2.0\nt1 = n4 - n3\nanswer = t1 - t0\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "if ( m - 8 ) is a factor of m ^ 2 - km - 24 , then k =", + "Output Program": [ + "n0 = 8.0\nn1 = 2.0\nn2 = 24.0\nt0 = n2 / n0\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "a box contains either blue or red flags . the total number of flags in the box is an even number . a group of children are asked to pick up two flags each . if all the flags are used up in the process such that 60 % of the children have blue flags , and 70 % have red flags , what percentage of children have flags of both the colors ?", + "Output Program": [ + "n0 = 60.0\nn1 = 70.0\nt0 = n0 + n1\nanswer = t0 - 100.0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "how many of the integers between 25 and 95 are even ?", + "Output Program": [ + "n0 = 25.0\nn1 = 95.0\nt0 = n1 - n0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "village x has a population of 78000 , which is decreasing at the rate of 1200 per year . village y has a population of 42000 , which is increasing at the rate of 800 per year . in how many years will the population of the two villages be equal ?", + "Output Program": [ + "n0 = 78000.0\nn1 = 1200.0\nn2 = 42000.0\nn3 = 800.0\nt0 = n1 + n3\nt1 = n0 - n2\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "if a whole number n is divided by 4 , we will get 3 as remainder . what will be the remainder if 2 n is divided by 4 ?", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 2.0\nn3 = 4.0\nt0 = n0 * 1.0\nt1 = n1 + t0\nt2 = n2 * t1\nanswer = t2 % n0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a grocer has a sale of rs . 5124 , rs . 5366 , rs . 5808 , rs . 5399 and rs . 6124 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 5400 ?", + "Output Program": [ + "n0 = 5124.0\nn1 = 5366.0\nn2 = 5808.0\nn3 = 5399.0\nn4 = 6124.0\nn5 = 5.0\nn6 = 5400.0\nt0 = n5 + 1.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n6 * t0\nt4 = n3 + t2\nt5 = n4 + t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "4579" + ], + "split": "train" + }, + { + "Input": "xavier , yvonne , and zelda each try independently to solve a problem . if their individual probabilities for success are 1 / 4 , 1 / 3 and 5 / 8 , respectively , what is the probability that xavier and yvonne , but not zelda , will solve the problem ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 1.0\nn3 = 3.0\nn4 = 5.0\nn5 = 8.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = n4 / n5\nt3 = t0 * t1\nt4 = n0 - t2\nanswer = t3 * t4\nprint(answer)" + ], + "Output Answer": [ + "0.03125" + ], + "split": "train" + }, + { + "Input": "a rope of which a calf is tied is increased from 10 m to 20 m , how much additional grassy ground shall it graze ?", + "Output Program": [ + "n0 = 10.0\nn1 = 20.0\nt0 = 3.0 + 4.0\nt1 = n0 * 2.0\nt2 = n1**min(2.0, 5)\nt3 = n0**min(2.0, 5)\nt4 = t1 + 2.0\nt5 = t2 - t3\nt6 = t4 / t0\nanswer = t6 * t5\nprint(answer)" + ], + "Output Answer": [ + "942.8571428571429" + ], + "split": "train" + }, + { + "Input": "if 5 < x < 8 < y < 13 , then what is the greatest possible positive integer difference of x and y ?", + "Output Program": [ + "n0 = 5.0\nn1 = 8.0\nn2 = 13.0\nt0 = n2 - n0\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "12 + 6 = 792 10 + 2 = 110 1 + 9 = 9 2 + 7 = 16 11 + 4 = ? ? solve it ?", + "Output Program": [ + "n0 = 12.0\nn1 = 6.0\nn2 = 792.0\nn3 = 10.0\nn4 = 2.0\nn5 = 110.0\nn6 = 1.0\nn7 = 9.0\nn8 = 9.0\nn9 = 2.0\nn10 = 7.0\nn11 = 16.0\nn12 = 11.0\nn13 = 4.0\nt0 = n12 + n13\nt1 = n3 * t0\nanswer = n13 + t1\nprint(answer)" + ], + "Output Answer": [ + "154" + ], + "split": "train" + }, + { + "Input": "at a certain high school , the senior class is 3 times the size of the junior class . if 1 / 3 of the seniors and 3 / 4 of the juniors study japanese , what fraction of the students in both classes study japanese ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 3.0\nn3 = 3.0\nn4 = 4.0\nt0 = n0 + n1\nt1 = n0 / n4\nt2 = t1 + 1.0\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.4375" + ], + "split": "train" + }, + { + "Input": "the least number which when increased by 7 each divisible by each one of 24 , 32 , 36 and 54 is :", + "Output Program": [ + "import scipy\nn0 = 7.0\nn1 = 24.0\nn2 = 32.0\nn3 = 36.0\nn4 = 54.0\nt0 = scipy.lcm(int(n1), int(n2))\nt1 = scipy.lcm(int(n3), int(t0))\nt2 = scipy.lcm(int(n4), int(t1))\nanswer = t2 - n0\nprint(answer)" + ], + "Output Answer": [ + "857" + ], + "split": "train" + }, + { + "Input": "at a contest with 3,500 participants , 1 / 2 of the people are aged 18 to 22 . next year , the number of people aged 18 to 22 will increase by 1 / 7 . after this change , what percentage of the total 3,500 people will the 18 - to 22 - year - olds represent ?", + "Output Program": [ + "n0 = 3500.0\nn1 = 1.0\nn2 = 2.0\nn3 = 18.0\nn4 = 22.0\nn5 = 18.0\nn6 = 22.0\nn7 = 1.0\nn8 = 7.0\nn9 = 3500.0\nn10 = 18.0\nn11 = 22.0\nt0 = n1 / n8\nt1 = n0 / n2\nt2 = t0 + n1\nt3 = t2 * t1\nt4 = t3 / n0\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "57.14285714285714" + ], + "split": "train" + }, + { + "Input": "the sum of the present age of henry and jill is 40 . what is their present ages if 11 years ago henry was twice the age of jill ?", + "Output Program": [ + "n0 = 40.0\nn1 = 11.0\nt0 = n0 + n1\nt1 = t0 / 3.0\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "you and your friend spent a total of $ 15 for lunch . your friend spent $ 5 more than you . how much did your friend spend on their lunch ?", + "Output Program": [ + "n0 = 15.0\nn1 = 5.0\nt0 = n0 - n1\nt1 = t0 / 2.0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "2 men and 2 women are lined up in a row . what is the number of cases where they stand with each other in turn ? ( the number of cases in which men ( or women ) do not stand next to each other )", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 2.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(n1)))\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "how many paying stones , each measuring 2 1 / 2 m * 2 m are required to pave a rectangular court yard 70 m long and 16 1 / 2 m board ?", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 2.0\nn3 = 2.0\nn4 = 70.0\nn5 = 16.0\nn6 = 1.0\nn7 = 2.0\nt0 = n1 / n0\nt1 = n5 + t0\nt2 = n0 + t0\nt3 = n4 * t1\nt4 = n0 * t2\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "231" + ], + "split": "train" + }, + { + "Input": "solution for 3.15 + . 014 + . 458", + "Output Program": [ + "n0 = 3.15\nn1 = 14.0\nn2 = 458.0\nt0 = n1 / 1000.0\nt1 = n2 / 1000.0\nt2 = n0 + t0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "3.622" + ], + "split": "train" + }, + { + "Input": "if 60 % of ( x - y ) = 30 % of ( x + y ) then what percent of x is y ?", + "Output Program": [ + "n0 = 60.0\nn1 = 30.0\nt0 = n0 + n1\nt1 = n0 - n1\nt2 = t1 / t0\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "33.33333333333333" + ], + "split": "train" + }, + { + "Input": "a multiple choice test consists of 4 questions , and each question has 5 answer choices . in how many q ways can the test be completed if every question is unanswered ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\n\nanswer = n1**min(n0, 5)\nprint(answer)" + ], + "Output Answer": [ + "625" + ], + "split": "train" + }, + { + "Input": "a is an integer greater than 49 but less than 61 , b is an integer greater than 59 but less than 71 , what is the range of a / b ?", + "Output Program": [ + "n0 = 49.0\nn1 = 61.0\nn2 = 59.0\nn3 = 71.0\nt0 = n2 + 1.0\nt1 = n0 + 1.0\nt2 = n1 - 1.0\nt3 = n3 - 1.0\nt4 = t2 / t0\nt5 = t1 / t3\nanswer = t4 - t5\nprint(answer)" + ], + "Output Answer": [ + "0.2857142857142857" + ], + "split": "train" + }, + { + "Input": "find the value of x , y by solving the below equations x + y = 15 x - y = 5", + "Output Program": [ + "n0 = 15.0\nn1 = 5.0\nt0 = n0 - n1\nt1 = t0 / 2.0\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "in a urban village of india named ` ` owlna ' ' , 90 % people have refrigerator , 86 % people have television , 80 % people got computers and 80 % got air - conditionor . how many people ( minimum ) got all these luxury .", + "Output Program": [ + "n0 = 90.0\nn1 = 86.0\nn2 = 80.0\nn3 = 80.0\nt0 = 100.0 - n0\nt1 = 100.0 - n1\nt2 = 100.0 - n2\nt3 = 100.0 - n3\nt4 = t0 + t1\nt5 = t4 + t2\nt6 = t5 + t3\nanswer = 100.0 - t6\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "the proportion of water to alcohol in solution a is 4 : 1 and the proportion of water to alcohol in solution b is 2 : 3 . if an equal amount of each solution is mixed together , what is the concentration of alcohol in the new solution ?", + "Output Program": [ + "n0 = 4.0\nn1 = 1.0\nn2 = 2.0\nn3 = 3.0\nt0 = n1 + n3\nt1 = n0 + n2\nt2 = t1 + t0\nt3 = t0 / t2\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "the price of a cycle is reduced by 25 per cent . the new price is reduced by a further 20 per cent . the two reductions together are equal to a single reduction of", + "Output Program": [ + "n0 = 25.0\nn1 = 20.0\nt0 = 100.0 - n1\nt1 = 100.0 - n0\nt2 = t0 / 100.0\nt3 = t2 * t1\nanswer = 100.0 - t3\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "if a number p is prime , and 2 p + 5 = q , where q is also prime , then the decimal expansion of 1 / q will produce a decimal with q - 1 digits . if this method produces a decimal with 166 digits , what is the units digit of the product of p and q ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 1.0\nn3 = 1.0\nn4 = 166.0\nt0 = n2 + n4\nt1 = t0 - n1\nt2 = t1 / n0\nt3 = t2 - n2\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "father is aged 3 times more than his son ronit . after 8 years , he would be two and half times if ronit ' s age . after further 8 years , how many times would he be of ronit ' s age ?", + "Output Program": [ + "n0 = 3.0\nn1 = 8.0\nn2 = 8.0\nt0 = n1 + n1\nt1 = n1 * 4.0\nt2 = t0 + t1\nt3 = n1 + t0\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "what is the greatest number of 4 digits which is divisible by 15 , 25 , 40 and 75 ?", + "Output Program": [ + "import math\nimport scipy\nn0 = 4.0\nn1 = 15.0\nn2 = 25.0\nn3 = 40.0\nn4 = 75.0\nt0 = scipy.lcm(int(n1), int(n2))\nt1 = 100.0 * 100.0\nt2 = scipy.lcm(int(n3), int(t0))\nt3 = scipy.lcm(int(n4), int(t2))\nt4 = t1 / t3\nt5 = math.floor(t4)\nanswer = t5 * t3\nprint(answer)" + ], + "Output Answer": [ + "9600" + ], + "split": "train" + }, + { + "Input": "a one - foot stick is marked in 1 / 3 and 1 / 4 portion . how many total markings will there be , including the end points ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 4.0\n\nanswer = n1 + n3\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "if a * b denotes the greatest common divisor of a and b , then ( ( 20 * 16 ) * ( 18 * 24 ) ) = ?", + "Output Program": [ + "n0 = 20.0\nn1 = 16.0\nn2 = 18.0\nn3 = 24.0\nt0 = n2 / 3.0\nanswer = t0 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "how many quarters are equal to 2 dollars ?", + "Output Program": [ + "n0 = 2.0\n\nanswer = n0 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "david obtained 86 , 85 , 82 , 87 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology what are his average marks ?", + "Output Program": [ + "n0 = 86.0\nn1 = 85.0\nn2 = 82.0\nn3 = 87.0\nn4 = 85.0\nn5 = 100.0\nt0 = n0 + n1\nt1 = 2.0 + 3.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "85" + ], + "split": "train" + }, + { + "Input": "a business executive and his client are charging their dinner tab on the executive ' s expense account . the company will only allow them to spend a total of 50 $ for the meal . assuming that they will pay 7 % in sales tax for the meal and leave a 15 % tip , what is the most their food can cost ?", + "Output Program": [ + "n0 = 50.0\nn1 = 7.0\nn2 = 15.0\nt0 = n1 + n2\nt1 = t0 / 100.0\nt2 = t1 + 1.0\nanswer = n0 / t2\nprint(answer)" + ], + "Output Answer": [ + "40.98360655737705" + ], + "split": "train" + }, + { + "Input": "the sum of present age of abe and the age before 7 years is 37 . find the present age of abe . what will be his age after 7 years ?", + "Output Program": [ + "n0 = 7.0\nn1 = 37.0\nn2 = 7.0\nt0 = n0 + n1\nt1 = t0 / 2.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "29" + ], + "split": "train" + }, + { + "Input": "find the value of ( 55 + 113 / 78 ) \u00d7 78", + "Output Program": [ + "n0 = 55.0\nn1 = 113.0\nn2 = 78.0\nn3 = 78.0\nt0 = n1 / n2\nt1 = n0 + t0\nanswer = t1 * n2\nprint(answer)" + ], + "Output Answer": [ + "4403" + ], + "split": "train" + }, + { + "Input": "the total age of a and b is 11 years more than the total age of b and c . c is how many year younger than", + "Output Program": [ + "n0 = 11.0\n\nanswer = n0 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "n ^ ( n / 2 ) = 2 is true when n = 2 in the same way what is the value of n if n ^ ( n / 2 ) = 12 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 2.0\nn3 = 2.0\nn4 = 12.0\nt0 = n4**min(n0, 5)\nanswer = t0 / n4\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "if p and q are positive integers each greater than 1 , and 17 ( p + 1 ) = 20 ( q + 1 ) , what is the least possible value of p + q ?", + "Output Program": [ + "n0 = 1.0\nn1 = 17.0\nn2 = 1.0\nn3 = 20.0\nn4 = 1.0\nt0 = n1 + n3\nanswer = t0 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "the maximum number of students among them 1008 pens and 928 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils ?", + "Output Program": [ + "import scipy\nn0 = 1008.0\nn1 = 928.0\n\nanswer = scipy.gcd(int(n0), int(n1))\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "lilly has 10 fish and rosy has 12 fish . in total , how many fish do they have in all ?", + "Output Program": [ + "n0 = 10.0\nn1 = 12.0\n\nanswer = n0 + n1\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "15 lts are taken of from a container full of liquid a and replaced with liquid b . again 15 more lts of the mixture is taken and replaced with liquid b . after this process , if the container contains liquid a and b in the ratio 9 : 16 , what is the capacity of the container m ?", + "Output Program": [ + "import math\nn0 = 15.0\nn1 = 15.0\nn2 = 9.0\nn3 = 16.0\nt0 = n2 + n3\nt1 = n2 / t0\nt2 = math.sqrt(max(0, t1))\nt3 = 1.0 - t2\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "37.5" + ], + "split": "train" + }, + { + "Input": "list k consists of 12 consecutive integers . if - 3 is the least integer in list k , what is the range of the positive integers in list k ?", + "Output Program": [ + "n0 = 12.0\nn1 = 3.0\nt0 = n0 - n1\nt1 = t0 - 1.0\nanswer = t1 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "let a , b , c be distinct digits . consider a two - digit number \u2018 ab \u2019 and a 3 - digit number \u2018 ccb \u2019 , both defined under the usual decimal number system , if ( ab ) 2 = ccb > 300 , then the value of b is", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 300.0\nt0 = n1 * 10.0\nt1 = t0 + 1.0\nt2 = t1**min(2.0, 5)\nanswer = t2 % 10.0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "instead of multiplying a number by 7 , the number is divided by 7 . what is the percentage of error obtained ?", + "Output Program": [ + "n0 = 7.0\nn1 = 7.0\nt0 = n1 / n1\nt1 = n0 * n1\nt2 = t0 / t1\nt3 = t2 * 100.0\nanswer = 100.0 - t3\nprint(answer)" + ], + "Output Answer": [ + "97.95918367346938" + ], + "split": "train" + }, + { + "Input": "find how many 4 digits no . is less then 1239 such that all 4 digits are distinct .", + "Output Program": [ + "n0 = 4.0\nn1 = 1239.0\nn2 = 4.0\nt0 = n1 % 10.0\nt1 = t0 - 1.0\nt2 = t0 - 2.0\nt3 = t0 - 3.0\nt4 = t1 - 1.0\nt5 = t1 * t4\nt6 = t5 + t2\nanswer = t6 + t3\nprint(answer)" + ], + "Output Answer": [ + "69" + ], + "split": "train" + }, + { + "Input": "a whale goes on a feeding frenzy that lasts for 9 hours . for the first hour he catches and eats x kilos of plankton . in every hour after the first , it consumes 3 kilos of plankton more than it consumed in the previous hour . if by the end of the frenzy the whale will have consumed a whopping accumulated total 360 kilos of plankton , how many kilos did he consume on the sixth hour ?", + "Output Program": [ + "n0 = 9.0\nn1 = 3.0\nn2 = 360.0\nt0 = n2 / n0\nanswer = n1 + t0\nprint(answer)" + ], + "Output Answer": [ + "43" + ], + "split": "train" + }, + { + "Input": "the mean of 50 observations was 36 . it was found later that an observation 34 was wrongly taken as 23 . the corrected new mean is :", + "Output Program": [ + "n0 = 50.0\nn1 = 36.0\nn2 = 34.0\nn3 = 23.0\nt0 = n0 * n1\nt1 = n0 - 2.0\nt2 = t1 - n3\nt3 = t0 + t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "36.5" + ], + "split": "train" + }, + { + "Input": "if - 11 and - 8 are negative integers , then - 11 * - 8 + 5 is", + "Output Program": [ + "n0 = 11.0\nn1 = 8.0\nn2 = 11.0\nn3 = 8.0\nn4 = 5.0\nt0 = -n0\nt1 = -n1\nt2 = t0 * t1\nanswer = n4 + t2\nprint(answer)" + ], + "Output Answer": [ + "93" + ], + "split": "train" + }, + { + "Input": "if there are 20 apples and the apples have to be shared equally among 3 babies . what number of apples are to be added ?", + "Output Program": [ + "n0 = 20.0\nn1 = 3.0\nt0 = 3.0 + 4.0\nt1 = n1 * t0\nanswer = t1 - n0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "8 people are planning to share equally the cost of a rental car . if one person withdraws from the arrangement and the others share equally the entire rest of the car , then the share of each of the remaining persons increased by ?", + "Output Program": [ + "n0 = 8.0\n\nanswer = 1.0 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.125" + ], + "split": "train" + }, + { + "Input": "in kaya ' s teacher ' s desk there are 4 pink highlighters , 2 yellow highlighters , and 5 blue highlighters . how many highlighters are there in all ?", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\nn2 = 5.0\nt0 = n0 + n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "the average weight of 10 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg . what is the weight of the new person ?", + "Output Program": [ + "n0 = 10.0\nn1 = 2.5\nn2 = 65.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "10 % people of a village in sri lanka died by bombardment , 15 % of the remainder left the village on account of fear . if now the population is reduced to 6514 , how much was it in the beginning ?", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 15.0\nn2 = 6514.0\nt0 = 100.0 - n0\nt1 = 100.0 - n1\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = t2 * t3\nt5 = n2 / t4\nanswer = math.floor(t5)\nprint(answer)" + ], + "Output Answer": [ + "8515" + ], + "split": "train" + }, + { + "Input": "a part - time employee \u2019 s hourly wage was increased by 15 % . she decided to decrease the number of hours worked per week so that her total income did not change . by approximately what percent should the number of hours worked be decreased ?", + "Output Program": [ + "n0 = 15.0\nt0 = n0 + 100.0\nt1 = n0 / 100.0\nt2 = t0 / 100.0\nt3 = t1 / t2\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "13.043478260869565" + ], + "split": "train" + }, + { + "Input": "if y is 60 % greater than x , than x is what % less than y ?", + "Output Program": [ + "n0 = 60.0\nt0 = n0 + 100.0\nt1 = n0 / t0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "37.5" + ], + "split": "train" + }, + { + "Input": "the product of two successive numbers is 2652 . which is the smaller of the two numbers ?", + "Output Program": [ + "import math\nn0 = 2652.0\n\nanswer = math.sqrt(max(0, n0))\nprint(answer)" + ], + "Output Answer": [ + "51.49757275833493" + ], + "split": "train" + }, + { + "Input": "if k is a non - negative integer and 30 ^ k is a divisor of 929,260 then 3 ^ k - k ^ 3 =", + "Output Program": [ + "n0 = 30.0\nn1 = 929260.0\nn2 = 3.0\nn3 = 3.0\n\nanswer = n2 / n2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "there are 7 players in a bowling team with an average weight of 103 kg . if two new players join the team , one weighs 110 kg and the second weighs 60 kg , what will be the new average weight ?", + "Output Program": [ + "n0 = 7.0\nn1 = 103.0\nn2 = 110.0\nn3 = 60.0\nt0 = n2 + n3\nt1 = n0 + 2.0\nt2 = n0 * n1\nt3 = t0 + t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "99" + ], + "split": "train" + }, + { + "Input": "the average of 21 numbers is 44 . average of the first 11 of them is 48 and that of the last 11 is 41 . find the 11 th number ?", + "Output Program": [ + "n0 = 21.0\nn1 = 44.0\nn2 = 11.0\nn3 = 48.0\nn4 = 11.0\nn5 = 41.0\nn6 = 11.0\nt0 = n5 * n6\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 - t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "55" + ], + "split": "train" + }, + { + "Input": "when x is multiplied by 3 , the result is 18 more than the result of subtracting x from 26 . what is the value of x ?", + "Output Program": [ + "n0 = 3.0\nn1 = 18.0\nn2 = 26.0\nt0 = n1 + n2\nt1 = 1.0 + n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "the maximum number of students among them 100 pens and 50 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils ?", + "Output Program": [ + "import scipy\nn0 = 100.0\nn1 = 50.0\n\nanswer = scipy.gcd(int(n0), int(n1))\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "if 5 x * x + 14 * x + k = 0 having two reciprocal roots find the value of k .", + "Output Program": [ + "n0 = 5.0\nn1 = 14.0\nn2 = 0.0\nt0 = n1 - n0\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "two employees x and y are paid a total of rs . 770 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?", + "Output Program": [ + "n0 = 770.0\nn1 = 120.0\nt0 = 1.0 + 4.0\nt1 = t0 * 2.0\nt2 = t1 + 1.0\nt3 = n0 * t1\nt4 = t2 * 2.0\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "350" + ], + "split": "train" + }, + { + "Input": "arnold and danny are two twin brothers that are celebrating their birthday . the product of their ages today is smaller by 17 from the product of their ages a year from today . what is their age today ?", + "Output Program": [ + "n0 = 17.0\nt0 = n0 - 1.0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a bowl contains equal numbers of red , orange , green , blue , and yellow candies . kaz eats all of the green candies and half of the orange ones . next , he eats half of the remaining pieces of each color . finally , he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 30 % of the original number . what percent of the red candies remain ?", + "Output Program": [ + "n0 = 30.0\nt0 = 2.0 + 3.0\nt1 = 100.0 / t0\nt2 = t1 / 2.0\nt3 = t2 / 2.0\nt4 = t2 + t3\nt5 = n0 - t4\nt6 = t5 / 2.0\nt7 = t6 / t1\nanswer = t7 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "37.5" + ], + "split": "train" + }, + { + "Input": "he total marks obtained by a student in physics , chemistry and mathematics is 130 more than the marks obtained by him in physics . what is the average mark obtained by him in chemistry and mathematics ?", + "Output Program": [ + "n0 = 130.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "65" + ], + "split": "train" + }, + { + "Input": "a salesman gets commission on total sales at 9 % . if the sale is exceeded rs . 10000 he gets an additional commission as bonus of 3 % on the excess of sales over rs . 10000 . if he gets total commission of rs . 1380 , then the bonus he received is :", + "Output Program": [ + "n0 = 9.0\nn1 = 10000.0\nn2 = 3.0\nn3 = 10000.0\nn4 = 1380.0\nt0 = 1.0 / 4.0\nt1 = n0 * n1\nt2 = t1 / 100.0\nt3 = n4 - t2\nanswer = t0 * t3\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "if equation | x / 2 | + | y / 2 | = 2 encloses a certain region on the coordinate plane , what is the area of this region ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 2.0\nt0 = n0 * n0\nt1 = t0**min(2.0, 5)\nanswer = t1 + t1\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "what is the smallest integer k for which 64 ^ k > 4 ^ 22 ?", + "Output Program": [ + "import math\nn0 = 64.0\nn1 = 4.0\nn2 = 22.0\nt0 = n2 / 3.0\nt1 = math.floor(t0)\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "the number 0.8 is how much greater than 1 / 8 ?", + "Output Program": [ + "n0 = 0.8\nn1 = 1.0\nn2 = 8.0\nt0 = n1 / n2\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "0.675" + ], + "split": "train" + }, + { + "Input": "in a two - digit , if it is known that its unit ' s digit exceeds its 10 ' s digit by 2 and that the product of the given number and the sum of its digits is equal to 144 , then the number is ?", + "Output Program": [ + "n0 = 10.0\nn1 = 2.0\nn2 = 144.0\nt0 = n0 * n1\nanswer = t0 + 4.0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "what is the smallest number which when diminished by 12 , is divisible 8 , 12 , 22 and 24 ?", + "Output Program": [ + "import scipy\nn0 = 12.0\nn1 = 8.0\nn2 = 12.0\nn3 = 22.0\nn4 = 24.0\nt0 = scipy.lcm(int(n1), int(n2))\nt1 = scipy.lcm(int(n3), int(n4))\nt2 = scipy.lcm(int(t0), int(t1))\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "276" + ], + "split": "train" + }, + { + "Input": "k is a 3 digit number such that the the ratio of the number to the sum of its digits is least . what is the difference between the hundreds and tens digit ?", + "Output Program": [ + "n0 = 3.0\nt0 = n0 + 4.0\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "niharika covers a distance in 30 min , if she drives at a speed of 60 km / h on an average . find the speed at which she must drive at to reduce the time of the journey by 30 % .", + "Output Program": [ + "n0 = 30.0\nn1 = 60.0\nn2 = 30.0\nt0 = 100.0 - 10.0\nanswer = t0 - 4.0\nprint(answer)" + ], + "Output Answer": [ + "86" + ], + "split": "train" + }, + { + "Input": "a vessel of capacity 2 litre has 20 % of alcohol and another vessel of capacity 6 litre had 55 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?", + "Output Program": [ + "n0 = 2.0\nn1 = 20.0\nn2 = 6.0\nn3 = 55.0\nn4 = 8.0\nn5 = 10.0\nt0 = n1 / 100.0\nt1 = n3 / 100.0\nt2 = n0 * t0\nt3 = n2 * t1\nt4 = t2 + t3\nt5 = t4 / n5\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "37" + ], + "split": "train" + }, + { + "Input": "the total number of digits used in numbering the pages of a book having 346 pages is", + "Output Program": [ + "n0 = 346.0\nt0 = n0 * 3.0\nt1 = 100.0 - 1.0\nt2 = 10.0 - 1.0\nt3 = t0 - t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "930" + ], + "split": "train" + }, + { + "Input": "at joes steakhouse the hourly wage for a chef is 20 % greater than that of a dishwasher , and the hourly wage of a dishwasher is half as much as the hourly wage of a manager . if a managers wage is $ 8.50 per hour , how much less than a manager does a chef earn each hour ?", + "Output Program": [ + "n0 = 20.0\nn1 = 8.5\nt0 = n0 + 100.0\nt1 = 1.0 / 2.0\nt2 = t0 / 100.0\nt3 = t2 * t1\nt4 = 1.0 - t3\nanswer = n1 * t4\nprint(answer)" + ], + "Output Answer": [ + "3.4000000000000004" + ], + "split": "train" + }, + { + "Input": "101 \u00e3 \u2014 101 + 99 \u00e3 \u2014 99 = ?", + "Output Program": [ + "n0 = 101.0\nn1 = 101.0\nn2 = 99.0\nn3 = 99.0\nt0 = n0**min(2.0, 5)\nt1 = n2**min(2.0, 5)\nt2 = t0 - n0\nt3 = t1 - n2\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "19802" + ], + "split": "train" + }, + { + "Input": "a case contains c cartons . each carton contains b boxes , and each box contains 500 paper clips . how many paper clips are contained in 2 cases ?", + "Output Program": [ + "n0 = 500.0\nn1 = 2.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "1000" + ], + "split": "train" + }, + { + "Input": "vishal invested 10 % more than trishul . trishul invested 10 % less than raghu . if the total sum of their investments is rs . 6647 , how much amount did raghu invest ?", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 6647.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nt2 = 1.0 - t0\nt3 = t1 * t2\nt4 = t3 + t2\nt5 = t4 + 1.0\nanswer = n2 / t5\nprint(answer)" + ], + "Output Answer": [ + "2300" + ], + "split": "train" + }, + { + "Input": "in a weight - lifting competition , the total weight of joe ' s two lifts was 600 pounds . if twice the weight of his first lift was 300 pounds more than the weight of his second lift , what was the weight , in pounds , of his first lift ?", + "Output Program": [ + "n0 = 600.0\nn1 = 300.0\nt0 = n0 + n1\nanswer = t0 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "a is two years older than b who is twice as old as c . the total of the ages of a , b and c is 27 . how old is b ?", + "Output Program": [ + "n0 = 27.0\nt0 = 1.0 + 4.0\nt1 = n0 - 2.0\nt2 = t1 * 2.0\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "a student scored an average of 75 marks in 3 subjects : physics , chemistry and mathematics . if the average marks in physics and mathematics is 90 and that in physics and chemistry is 70 , what are the marks in physics ?", + "Output Program": [ + "n0 = 75.0\nn1 = 3.0\nn2 = 90.0\nn3 = 70.0\nt0 = n2 * 2.0\nt1 = n3 * 2.0\nt2 = n0 * n1\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "95" + ], + "split": "train" + }, + { + "Input": "a positive number x is multiplied by 8 , and this product is then divided by 3 . if the positive square root of the result of these two operations equals x , what is the value of x ?", + "Output Program": [ + "n0 = 8.0\nn1 = 3.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "2.6666666666666665" + ], + "split": "train" + }, + { + "Input": "two employees x and y are paid a total of rs . 590 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?", + "Output Program": [ + "n0 = 590.0\nn1 = 120.0\nt0 = 1.0 + 4.0\nt1 = t0 * 2.0\nt2 = t1 + 1.0\nt3 = n0 * t1\nt4 = t2 * 2.0\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "268.1818181818182" + ], + "split": "train" + }, + { + "Input": "if 10 % of x = 20 % of y , then x : y is equal to ?", + "Output Program": [ + "n0 = 10.0\nn1 = 20.0\n\nanswer = n1 / n0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "let the number which when multiplied by 12 is increased by 198 .", + "Output Program": [ + "n0 = 12.0\nn1 = 198.0\nt0 = n0 - 1.0\nanswer = n1 / t0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "what is the smallest no . that should be added to 27452 to make it exactly divisible by 9 ?", + "Output Program": [ + "n0 = 27452.0\nn1 = 9.0\nt0 = n0 % n1\nt1 = n1 - t0\nanswer = t1 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "if a ^ 3 is divisible by 240 what is the least possible value of integer a ?", + "Output Program": [ + "n0 = 3.0\nn1 = 240.0\nt0 = 2.0**min(3.0, 5)\nt1 = n1 / t0\nanswer = t1 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "the average of temperatures at noontime from monday to friday is 60 ; the lowest one is 50 , what is the possible maximum range of the temperatures ?", + "Output Program": [ + "n0 = 60.0\nn1 = 50.0\nt0 = 2.0 + 3.0\nt1 = n1 * 4.0\nt2 = n0 * t0\nt3 = t2 - t1\nanswer = t3 - n1\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "what are the last two digits of ( 301 * 402 * 503 * 604 * 646 * 547 * 448 * 349 ) ^ 2", + "Output Program": [ + "n0 = 301.0\nn1 = 402.0\nn2 = 503.0\nn3 = 604.0\nn4 = 646.0\nn5 = 547.0\nn6 = 448.0\nn7 = 349.0\nn8 = 2.0\nt0 = 100.0 / 4.0\nt1 = n8 * 3.0\nt2 = 1.0 - n8\nt3 = t1 * t2\nt4 = t3 * t2\nt5 = t4 * t2\nt6 = t0 + t5\nanswer = t6 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "76" + ], + "split": "train" + }, + { + "Input": "list f consists of 12 consecutive integers . if - 4 is the least integer in list f , what is the range of positive integers in list f ?", + "Output Program": [ + "n0 = 12.0\nn1 = 4.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "a man is 32 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ?", + "Output Program": [ + "n0 = 32.0\nt0 = 2.0 * 2.0\nt1 = 2.0 - 1.0\nt2 = t0 - 2.0\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "the tax on a commodity is diminished by 20 % but its consumption is increased by 5 % . find the decrease percent in the revenue derived from it ?", + "Output Program": [ + "n0 = 20.0\nn1 = 5.0\nt0 = n1 + 100.0\nt1 = 100.0 - n0\nt2 = t0 * t1\nt3 = t2 / 100.0\nanswer = 100.0 - t3\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "we have boxes colored either red or blue . in each blue box there is a fixed number of blueberries . in each red box there is a fixed number of strawberries . if we dispose of one blue box for one additional red box , the total number of berries would increase by 20 , and the difference between the total number of strawberries and the total number of blueberries would increase by 80 . each blue box contains how many blueberries ?", + "Output Program": [ + "n0 = 20.0\nn1 = 80.0\nt0 = n1 - n0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "in smithtown , the ratio of right - handed people to left - handed people is 3 to 1 and the ratio of men to women is 3 to 2 . if the number of right - handed men is maximized , then what s percent of all the people in smithtown are left - handed women ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 3.0\nn3 = 2.0\nt0 = n0 + n1\nt1 = n0 + n3\nt2 = t0 / t1\nt3 = n3 * t2\nt4 = n0 * t2\nt5 = n0 - t4\nt6 = t3 - t5\nt7 = t6 / t0\nanswer = t7 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "25.00000000000001" + ], + "split": "train" + }, + { + "Input": "a man is 24 years older than his son . in two years , his age will be twice the age of his son . the present age of this son is", + "Output Program": [ + "n0 = 24.0\nt0 = 2.0 * 2.0\nt1 = 2.0 - 1.0\nt2 = t0 - 2.0\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "each of the integers from 1 to 14 is written on the a seperate index card and placed in a box . if the cards are drawn from the box at random without replecement , how many cards must be drawn to ensure that the product of all the integers drawn is even ?", + "Output Program": [ + "n0 = 1.0\nn1 = 14.0\nt0 = n1 / 2.0\nanswer = n0 + t0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "i chose a number and divide it by 6 . then i subtracted 15 from the result and got 5 . what was the number i chose ?", + "Output Program": [ + "n0 = 6.0\nn1 = 15.0\nn2 = 5.0\nt0 = n1 + n2\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 16 - meter platform and caught it after it had traveled 44.5 meters . how many times did the ball bounce ?", + "Output Program": [ + "n0 = 16.0\nn1 = 44.5\nt0 = n0 / 2.0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "of 70 players on a cricket team , 37 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?", + "Output Program": [ + "n0 = 70.0\nn1 = 37.0\nt0 = 1.0 / 3.0\nt1 = n0 - n1\nt2 = 1.0 - t0\nt3 = t2 * t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "59" + ], + "split": "train" + }, + { + "Input": "an integer n between 1 and 100 , inclusive , is to be chosen at random . what is the probability that n ( n + 1 ) will be divisible by 4 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 100.0\nn2 = 1.0\nn3 = 4.0\nt0 = n1 / n3\nt1 = t0 / n1\nanswer = 2.0 * t1\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "the product of two numbers is 120 and the sum of their squares is 289 . the sum of the number is ?", + "Output Program": [ + "import math\nn0 = 120.0\nn1 = 289.0\nt0 = n0 * 4.0\nt1 = n0 * 2.0\nt2 = n1 - t1\nt3 = math.sqrt(max(0, t2))\nt4 = t3**min(2.0, 5)\nt5 = t0 + t4\nanswer = math.sqrt(max(0, t5))\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "out of 9 persons , 8 persons spent rs . 30 each for their meals . the ninth one spent rs . 20 more than the average expenditure of all the 9 . the total money spent by all of them was", + "Output Program": [ + "n0 = 9.0\nn1 = 8.0\nn2 = 30.0\nn3 = 20.0\nn4 = 9.0\nt0 = n1 * n2\nt1 = n0 * n3\nt2 = t0 + t1\nt3 = t2 / n1\nanswer = t3 + t0\nprint(answer)" + ], + "Output Answer": [ + "292.5" + ], + "split": "train" + }, + { + "Input": "a driver just filled the car ' s gas tank with 36 liters of gasohol , a mixture consisting of 5 % ethanol and 95 % gasoline . if the car runs best on a mixture consisting of 10 % ethanol and 90 % gasoline , how many liters of ethanol must be added into the gas tank for the car to achieve optimum performance ?", + "Output Program": [ + "n0 = 36.0\nn1 = 5.0\nn2 = 95.0\nn3 = 10.0\nn4 = 90.0\nt0 = n0 * n1\nt1 = 100.0 - n3\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "the average of 10 numbers is calculated as 16 . it is discovered later on that while calculating the average , the number 45 was incorrectly read as 25 , and this incorrect number was used in the calculation . what is the correct average ?", + "Output Program": [ + "n0 = 10.0\nn1 = 16.0\nn2 = 45.0\nn3 = 25.0\nt0 = n0 * n1\nt1 = t0 - n3\nt2 = n2 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "in a urban village of india named ` ` owlna ' ' , 70 % people have refrigerator , 75 % people have television , 90 % people got computers and 85 % got air - conditionor . how many people ( minimum ) got all these luxury .", + "Output Program": [ + "n0 = 70.0\nn1 = 75.0\nn2 = 90.0\nn3 = 85.0\nt0 = 100.0 - n0\nt1 = 100.0 - n1\nt2 = 100.0 - n2\nt3 = 100.0 - n3\nt4 = t0 + t1\nt5 = t4 + t2\nt6 = t5 + t3\nanswer = 100.0 - t6\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "a merchant has selected two items to be placed on sale , one of which currently sells for 20 percent less than the other . if he wishes to raise the price of the cheaper item so that the two items are equally priced , by what percentage must he raise the price of the less expensive item ?", + "Output Program": [ + "n0 = 20.0\nt0 = n0 / 100.0\nt1 = 1.0 - t0\nt2 = t0 / t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "what must be added to each term of the ratio 4 : 15 , so that it may become equal to 3 : 4 ?", + "Output Program": [ + "n0 = 4.0\nn1 = 15.0\nn2 = 3.0\nn3 = 4.0\nt0 = n1 * n2\nt1 = n0 * n3\nt2 = n3 - n2\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "29" + ], + "split": "train" + }, + { + "Input": "what is the greatest prime factor of ( 11 ! \u00d7 10 ! \u2009 + 10 ! \u00d7 9 ! ) / 111 ?", + "Output Program": [ + "n0 = 11.0\nn1 = 10.0\nn2 = 10.0\nn3 = 9.0\nn4 = 111.0\nt0 = n0 * n1\nt1 = t0 + 1.0\nt2 = t1 / n4\nt3 = t2 + 3.0\nanswer = t3 + 3.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "there are 11 teams in a soccer league and each team plays each of the other teams once . how many games will be played in total ?", + "Output Program": [ + "import math\nn0 = 11.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(2.0)))\nt2 = n0 - 2.0\nt3 = math.factorial(min(15, int(t2)))\nt4 = t3 * t1\nanswer = t0 / t4\nprint(answer)" + ], + "Output Answer": [ + "55" + ], + "split": "train" + }, + { + "Input": "the average of 10 numbers was calculated as 17 . it is discovered later on that while calculating the average , one number , namely 56 , was incorrectly read as 26 . what is the correct average ?", + "Output Program": [ + "n0 = 10.0\nn1 = 17.0\nn2 = 56.0\nn3 = 26.0\nt0 = n0 * n1\nt1 = n2 - n3\nt2 = t0 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "the average of 6 observations is 15 . a new observation is included and the new average is decreased by 1 . the seventh observation is ?", + "Output Program": [ + "n0 = 6.0\nn1 = 15.0\nn2 = 1.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n1 - n2\nt3 = t0 * t2\nanswer = t3 - t1\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "if 25 % of x is 30 less than 15 % of 1500 , then x is ?", + "Output Program": [ + "n0 = 25.0\nn1 = 30.0\nn2 = 15.0\nn3 = 1500.0\nt0 = n2 / 100.0\nt1 = n0 / 100.0\nt2 = n3 * t0\nt3 = t2 - n1\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "780" + ], + "split": "train" + }, + { + "Input": "albert is 2 times mary \u2019 s age and 4 times as old as betty . mary is 22 years younger than albert . how old is betty ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 22.0\nt0 = n0 * n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "two brother x and y appeared for an exam . the probability of selection of x is 1 / 5 and that of b is 2 / 3 . find the probability that both of them are selected .", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 2.0\nn3 = 3.0\nt0 = n0 / n1\nt1 = n2 / n3\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "0.13333333333333333" + ], + "split": "train" + }, + { + "Input": "what is the smallest number which when increased by 7 is divisible by 25 , 49 , 15 , and 21 ?", + "Output Program": [ + "import scipy\nn0 = 7.0\nn1 = 25.0\nn2 = 49.0\nn3 = 15.0\nn4 = 21.0\nt0 = scipy.lcm(int(n1), int(n2))\nt1 = scipy.lcm(int(n3), int(n4))\nt2 = scipy.lcm(int(t0), int(t1))\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "3682" + ], + "split": "train" + }, + { + "Input": "at the opening of a trading day at a certain stock exchange , the price per share of stock k was $ 10 . if the price per share of stock k was $ 15 at the closing of the day , what was the percent increase in the price per share of stock k for that day ?", + "Output Program": [ + "n0 = 10.0\nn1 = 15.0\nt0 = n1 / n0\nt1 = t0 - 1.0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "if 213 \u00d7 16 = 3408 , then 1.6 \u00d7 2.13 is equal to :", + "Output Program": [ + "n0 = 213.0\nn1 = 16.0\nn2 = 3408.0\nn3 = 1.6\nn4 = 2.13\n\nanswer = n4 * n3\nprint(answer)" + ], + "Output Answer": [ + "3.408" + ], + "split": "train" + }, + { + "Input": "everyone shakes hands with everyone else in a room . total number of handshakes is 78 . number of persons = ?", + "Output Program": [ + "n0 = 78.0\nt0 = n0 * 2.0\nt1 = t0 / 3.0\nanswer = t1 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "if 50 % of x equals the sum of y and 20 , then what is the value of x \u2013 2 y ?", + "Output Program": [ + "n0 = 50.0\nn1 = 20.0\nn2 = 2.0\nt0 = n0 / 100.0\nanswer = n1 / t0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "weights of two friends ram and shyam are in the ratio of 4 : 5 . ram \u2019 s weight increases by 10 % and the total weight of ram and shyam together becomes 82.8 kg , with an increase of 15 % . by what per cent did the weight of shyam increase ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 10.0\nn3 = 82.8\nn4 = 15.0\nt0 = n0 / n1\nt1 = n4 - n2\nt2 = t0 * t1\nanswer = n4 + t2\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "barbata invests $ 2400 in the national bank at 4 % . how much additional money must she invest at 8 % so that the total annual income will be equal to 6 % of her entire investment ?", + "Output Program": [ + "n0 = 2400.0\nn1 = 4.0\nn2 = 8.0\nn3 = 6.0\nt0 = n3 / 100.0\nt1 = n1 / 100.0\nt2 = n2 / 100.0\nt3 = n0 * t0\nt4 = n0 * t1\nt5 = t2 - t0\nt6 = t3 - t4\nanswer = t6 / t5\nprint(answer)" + ], + "Output Answer": [ + "2399.9999999999995" + ], + "split": "train" + }, + { + "Input": "if m is an integer such that ( - 2 ) ^ 2 m = 2 ^ ( 12 - m ) then m = ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 2.0\nn3 = 12.0\nt0 = n0 + 1.0\nanswer = n3 / t0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "p and q are the only two applicants qualified for a short - term research project that pays 540 dollars in total . candidate p has more experience and , if hired , would be paid 50 percent more per hour than candidate q would be paid . candidate q , if hired , would require 10 hours more than candidate p to do the job . candidate p \u2019 s hourly wage is how many dollars greater than candidate q \u2019 s hourly wage ?", + "Output Program": [ + "n0 = 540.0\nn1 = 50.0\nn2 = 10.0\nt0 = 3.0 / 2.0\nt1 = t0 - 1.0\nt2 = n2 / t1\nt3 = n2 + t2\nt4 = n0 / t2\nt5 = n0 / t3\nanswer = t4 - t5\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "the average of the marks of 12 students in a class is 50 . if the marks of each student are doubled , find the new average ?", + "Output Program": [ + "n0 = 12.0\nn1 = 50.0\n\nanswer = n1 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "if the sum of two numbers is 55 and the h . c . f . and l . c . m . of these numbers are 5 and 120 respectively , then the sum of the reciprocals of the numbers is equal to :", + "Output Program": [ + "n0 = 55.0\nn1 = 5.0\nn2 = 120.0\nt0 = n0 / n1\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "0.09166666666666666" + ], + "split": "train" + }, + { + "Input": "the average salary of a person for the months of january , february , march and april is rs . 8000 and that for the months february , march , april and may is rs . 8200 . if his salary for the month of may is rs . 6500 , find his salary for the month of january ?", + "Output Program": [ + "n0 = 8000.0\nn1 = 8200.0\nn2 = 6500.0\nt0 = n0 * 4.0\nt1 = n1 * 4.0\nt2 = t1 - n2\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "5700" + ], + "split": "train" + }, + { + "Input": "the average age of 15 students of a class is 15 years . out of these , the average age of 5 students is 12 years and that of the other 9 students is 16 years . the age of the 15 th student is ?", + "Output Program": [ + "n0 = 15.0\nn1 = 15.0\nn2 = 5.0\nn3 = 12.0\nn4 = 9.0\nn5 = 16.0\nn6 = 15.0\nt0 = n0 * n0\nt1 = n2 * n3\nt2 = n4 * n5\nt3 = t1 + t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "the average ( arithmetic mean ) of 16 students first quiz scores in a difficult english class is 60.5 . when one student dropped the class , the average of the remaining scores increased to 64.0 . what is the quiz score of the student who dropped the class ?", + "Output Program": [ + "n0 = 16.0\nn1 = 60.5\nn2 = 64.0\nt0 = n0 * n1\nt1 = n0 - 1.0\nt2 = n2 * t1\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "median w of price of the car is 52000 . which could be the median of the other two . 35000 , 44000 , x , y , 57000 .", + "Output Program": [ + "n0 = 52000.0\nn1 = 35000.0\nn2 = 44000.0\nn3 = 57000.0\nt0 = 10.0 * 100.0\nanswer = n3 - t0\nprint(answer)" + ], + "Output Answer": [ + "56000" + ], + "split": "train" + }, + { + "Input": "find the least number must be subtracted from 568219 so that remaining no . is divisible by 5 ?", + "Output Program": [ + "import math\nn0 = 568219.0\nn1 = 5.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "the numbers 272738 and 232342 , when divided by n , a two digit number , leave a remainder of 13 and 17 respectively . find the sum of the digits of n ?", + "Output Program": [ + "import scipy\nn0 = 272738.0\nn1 = 232342.0\nn2 = 13.0\nn3 = 17.0\nt0 = n0 - n2\nt1 = n1 - n3\nt2 = scipy.gcd(int(t0), int(t1))\nt3 = t2 % 10.0\nanswer = t3 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "if the number is divided by 3 , it reduced by 42 . the number is", + "Output Program": [ + "n0 = 3.0\nn1 = 42.0\nt0 = n0 * n1\nt1 = n0 - 1.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "63" + ], + "split": "train" + }, + { + "Input": "when y is divided by 288 , the remainder is 45 . what is the remainder when the same y is divided by 24 ?", + "Output Program": [ + "n0 = 288.0\nn1 = 45.0\nn2 = 24.0\n\nanswer = n1 % n2\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "what is the sum of all 3 digit numbers that leave a remainder of ' 2 ' when divided by 6 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 6.0\nt0 = n0 * n0\nt1 = 1000.0 - n0\nt2 = t0 * 10.0\nt3 = t2 + t0\nt4 = n0 + t3\nt5 = t4 + t1\nt6 = t1 - t4\nt7 = t6 / n2\nt8 = t7 + 1.0\nt9 = t8 / n1\nanswer = t5 * t9\nprint(answer)" + ], + "Output Answer": [ + "82516.58333333333" + ], + "split": "train" + }, + { + "Input": "how many numbers between 190 and 580 are divisible by 45 and 6 ?", + "Output Program": [ + "import math\nn0 = 190.0\nn1 = 580.0\nn2 = 45.0\nn3 = 6.0\nt0 = n1 - n0\nt1 = t0 / n2\nt2 = math.floor(t1)\nanswer = t2 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "in a certain company , the ratio of the number of managers to the number of non - managers in any department must always be greater than 5 : 24 . in the company , what is the maximum number of non - managers in a department that has 8 managers :", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 24.0\nn2 = 8.0\nt0 = n1 * n2\nt1 = t0 / n0\nanswer = math.floor(t1)\nprint(answer)" + ], + "Output Answer": [ + "38" + ], + "split": "train" + }, + { + "Input": "the average runs scored by a batsman in 15 matches is 30 . in the next 20 matches the batsman scored an average of 15 runs . find his average in all the 30 matches ?", + "Output Program": [ + "n0 = 15.0\nn1 = 30.0\nn2 = 20.0\nn3 = 15.0\nn4 = 30.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "21.428571428571427" + ], + "split": "train" + }, + { + "Input": "jacob is now 12 years younger than michael . if 11 years from now michael will be twice as old as jacob , how old will jacob be in 4 years ?", + "Output Program": [ + "n0 = 12.0\nn1 = 11.0\nn2 = 4.0\nt0 = n0 + n1\nt1 = n1 * 2.0\nt2 = t0 - t1\nanswer = n2 + t2\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "a soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price . during the annual summer sale , everything in the store is an additional 20 percent off the original list price . if a replica jersey ' s list price is $ 80 , approximately what percent e of the list price is the lowest possible sale price ?", + "Output Program": [ + "n0 = 30.0\nn1 = 50.0\nn2 = 20.0\nn3 = 80.0\n\nanswer = n3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "chris mixed 3 pounds of raisins with 4 pounds of nuts . if a pound of nuts costs 4 times as much as a pound of raisins , then the total cost of the raisins was what fraction of the total cost of the mixture ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 4.0\nt0 = n1 * n2\nt1 = n0 + t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.15789473684210525" + ], + "split": "train" + }, + { + "Input": "45 x ? = 45 % of 900", + "Output Program": [ + "n0 = 45.0\nn1 = 45.0\nn2 = 900.0\nt0 = n1 / 100.0\nt1 = n2 * t0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "if 6 years are subtracted from the present age of arun and the remainder is divided by 18 , then the present age of his grandson gokul is obtained . if gokul is 2 years younger to madan whose age is 5 years , then what is the age of arun ?", + "Output Program": [ + "n0 = 6.0\nn1 = 18.0\nn2 = 2.0\nn3 = 5.0\nt0 = n3 - n2\nt1 = n1 * t0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "solve for the given equation 121 x 54 = ?", + "Output Program": [ + "n0 = 121.0\nn1 = 54.0\nt0 = 1.0 + 4.0\nt1 = t0**min(4.0, 5)\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "75625" + ], + "split": "train" + }, + { + "Input": "{ - 10 , - 6 , - 5 , - 4 , - 2.5 , - 1 , 0 , 2.5 , 4 , 6 , 7 , 10 } a number is to be selected at random from the set above . what is the probability that the number will be a solution to the equation ( x 3 ) ( x + 14 ) ( 2 x + 5 ) = 0 ?", + "Output Program": [ + "n0 = 10.0\nn1 = 6.0\nn2 = 5.0\nn3 = 4.0\nn4 = 2.5\nn5 = 1.0\nn6 = 0.0\nn7 = 2.5\nn8 = 4.0\nn9 = 6.0\nn10 = 7.0\nn11 = 10.0\nn12 = 3.0\nn13 = 14.0\nn14 = 2.0\nn15 = 5.0\nn16 = 0.0\nt0 = n0 + n14\nanswer = n5 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.08333333333333333" + ], + "split": "train" + }, + { + "Input": "the average of 10 numbers is 40.2 . later it is found that two numbers have been wrongly copied . the first is 19 greater than the actual number and the second number added is 13 instead of 31 . find the correct average .", + "Output Program": [ + "n0 = 10.0\nn1 = 40.2\nn2 = 19.0\nn3 = 13.0\nn4 = 31.0\nt0 = n2 + n3\nt1 = n0 * n1\nt2 = t0 + t1\nt3 = t2 - n4\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "40.3" + ], + "split": "train" + }, + { + "Input": "for each 6 - month period during a light bulb ' s life span , the odds of it not burning out from over - use are half what they were in the previous 6 - month period . if the odds of a light bulb burning out during the first 6 - month period following its purchase are 1 / 3 , what are the odds of it burning out during the period from 6 months to 1 year following its purchase ?", + "Output Program": [ + "n0 = 6.0\nn1 = 6.0\nn2 = 6.0\nn3 = 1.0\nn4 = 3.0\nn5 = 6.0\nn6 = 1.0\nt0 = n3 / n4\nt1 = n6 - t0\nt2 = t1 / 2.0\nt3 = n6 - t2\nanswer = t1 * t3\nprint(answer)" + ], + "Output Answer": [ + "0.4444444444444445" + ], + "split": "train" + }, + { + "Input": "a grocer has a sale of rs . 5921 , rs . 5468 , rs . 5568 , rs . 6088 and rs . 6433 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 5900 ?", + "Output Program": [ + "n0 = 5921.0\nn1 = 5468.0\nn2 = 5568.0\nn3 = 6088.0\nn4 = 6433.0\nn5 = 5.0\nn6 = 5900.0\nt0 = n5 + 1.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n6 * t0\nt4 = n3 + t2\nt5 = n4 + t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "5922" + ], + "split": "train" + }, + { + "Input": "nelly made a part payment of $ 875 toward buying a brand new refrigerator , which represents 25 % of the total cost of the refrigerator , how much remains to be paid ?", + "Output Program": [ + "n0 = 875.0\nn1 = 25.0\nt0 = n1 / 100.0\nt1 = n0 / t0\nanswer = t1 - n0\nprint(answer)" + ], + "Output Answer": [ + "2625" + ], + "split": "train" + }, + { + "Input": "when a certain number x is divided by 63 , the remainder is 25 . what is the remainder when x is divided by 8 ?", + "Output Program": [ + "n0 = 63.0\nn1 = 25.0\nn2 = 8.0\n\nanswer = n1 % n2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "5.02 can be expressed in terms of percentage as", + "Output Program": [ + "n0 = 5.02\n\nanswer = n0 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "501.99999999999994" + ], + "split": "train" + }, + { + "Input": "the mean of 50 observations was 36 . it was found later that an observation 48 was wrongly taken as 23 . the corrected new mean is ?", + "Output Program": [ + "n0 = 50.0\nn1 = 36.0\nn2 = 48.0\nn3 = 23.0\nt0 = n0 * n1\nt1 = n0 - 2.0\nt2 = t1 - n3\nt3 = t0 + t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "36.5" + ], + "split": "train" + }, + { + "Input": "what is x if x + 3 y = 33 and y = 10 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 33.0\nn2 = 10.0\nt0 = n0 * n2\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "jerry \u2019 s average ( arithmetic mean ) score on the first 3 of 4 tests is 85 . if jerry wants to raise his average by 3 points , what score must he earn on the fourth test ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 85.0\nn3 = 3.0\nt0 = n2 + n3\nt1 = n0 * n2\nt2 = n1 * t0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "97" + ], + "split": "train" + }, + { + "Input": "the sum of ages of 5 children born at the intervals of 3 years each is 50 years . find out the age of the youngest child ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nn2 = 50.0\nt0 = n2 / n0\nt1 = t0 - n1\nanswer = t1 - n1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "a trained covered x km at 40 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 6 x km .", + "Output Program": [ + "n0 = 40.0\nn1 = 2.0\nn2 = 20.0\nn3 = 6.0\nt0 = n0 / n0\nt1 = n0 * n3\nt2 = n0 * n1\nt3 = t2 / n2\nt4 = t0 + t3\nanswer = t1 / t4\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "when n is divided by 5 the remainder is 3 . what is the remainder when ( n - 1 ) ^ 2 is divided by 5 ?", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 3.0\nn2 = 1.0\nn3 = 2.0\nn4 = 5.0\nt0 = n0 + n1\nt1 = t0 - n2\nt2 = t1**min(n3, 5)\nt3 = t2 / n0\nt4 = math.floor(t3)\nt5 = n0 * t4\nanswer = t2 - t5\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "how many 1 / 12 s are there in 37 1 / 2 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 12.0\nn2 = 37.0\nn3 = 1.0\nn4 = 2.0\nt0 = n0 / n4\nt1 = n0 / n1\nt2 = n2 + t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "450" + ], + "split": "train" + }, + { + "Input": ". the price of commodity p increases by 40 paise every year , while the price of commodity q increases by 15 paise every year . if in 2001 , the price of commodity p was rs . 4.20 and that of q was rs . 6.30 , in which year commodity p will cost 40 paise more than the commodity q ?", + "Output Program": [ + "n0 = 40.0\nn1 = 15.0\nn2 = 2001.0\nn3 = 4.2\nn4 = 6.3\nn5 = 40.0\nt0 = n4 - n3\nt1 = n0 - n1\nt2 = n0 + t0\nt3 = t2 / t1\nanswer = n2 + t3\nprint(answer)" + ], + "Output Answer": [ + "2002.684" + ], + "split": "train" + }, + { + "Input": "in an office , totally there are 2200 employees and 40 % of the total employees are males . 30 % of the males in the office are at - least 50 years old . find the number of males aged below 50 years ?", + "Output Program": [ + "n0 = 2200.0\nn1 = 40.0\nn2 = 30.0\nn3 = 50.0\nn4 = 50.0\nt0 = n0 * n1\nt1 = 100.0 - n2\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nanswer = t2 * t3\nprint(answer)" + ], + "Output Answer": [ + "616" + ], + "split": "train" + }, + { + "Input": "the sum of ages of 5 children born at theintervals of 3 years each is 50 years . what is the age of the youngest child ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nn2 = 50.0\nt0 = n2 / n0\nt1 = t0 - n1\nanswer = t1 - n1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "find the greatest number that will divide 54 , 87 and 172 so as to leave the same remainder in each case", + "Output Program": [ + "import scipy\nn0 = 54.0\nn1 = 87.0\nn2 = 172.0\nt0 = n2 - n1\nt1 = n1 - n0\nt2 = t0 - n0\nt3 = scipy.gcd(int(t2), int(t1))\nanswer = scipy.gcd(int(t3), int(t0))\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "sally has a gold credit card with a certain spending limit , and a platinum card with twice the spending limit of the gold card . currently , she has a balance on her gold card that is 1 / 3 of the spending limit on that card , and she has a balance on her platinum card that is 1 / 9 of the spending limit on that card . if sally transfers the entire balance on her gold card to her platinum card , what portion of her limit on the platinum card will remain unspent ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 9.0\nt0 = 1 / n3\nt1 = 1 / n1\nt2 = 1 / 2.0\nt3 = t1 * t2\nt4 = t0 + t3\nanswer = n0 - t4\nprint(answer)" + ], + "Output Answer": [ + "0.7222222222222222" + ], + "split": "train" + }, + { + "Input": "according to the directions on the can of frozen orange juice concentrate , 1 can of concentrate is to be mixed with 3 cans of water to make orange juice . how many 12 ounces cans of the concentrate are required to prepare 360 6 ounces servings of orange juice ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 12.0\nn3 = 360.0\nn4 = 6.0\nt0 = n3 * n4\nt1 = t0 / n2\nanswer = t1 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "a student scored an average of 65 marks in 3 subjects : physics , chemistry and mathematics . if the average marks in physics and mathematics is 90 and that in physics and chemistry is 70 , what are the marks in physics ?", + "Output Program": [ + "n0 = 65.0\nn1 = 3.0\nn2 = 90.0\nn3 = 70.0\nt0 = n2 * 2.0\nt1 = n3 * 2.0\nt2 = n0 * n1\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "125" + ], + "split": "train" + }, + { + "Input": "find the number of trailing zeros in the product of ( 1 ^ 1 ) * ( 5 ^ 5 ) * ( 10 ^ 10 ) * ( 15 ^ 15 ) * ( 20 ^ 20 ) * ( 25 ^ 25 ) \u2026 \u2026 \u2026 . * ( 50 ^ 50 ) .", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 5.0\nn3 = 5.0\nn4 = 10.0\nn5 = 10.0\nn6 = 15.0\nn7 = 15.0\nn8 = 20.0\nn9 = 20.0\nn10 = 25.0\nn11 = 25.0\nn12 = 50.0\nn13 = 50.0\nt0 = n6 * n6\nanswer = n10 + t0\nprint(answer)" + ], + "Output Answer": [ + "250" + ], + "split": "train" + }, + { + "Input": "on a partly cloudy day , derek decides to walk back from work . when it is sunny , he walks at a speed of s miles / hr ( s is an integer ) and when it gets cloudy , he increases his speed to ( s + 1 ) miles / hr . if his average speed for the entire distance is 2.8 miles / hr , what fraction t of the total distance did he cover while the sun was shining on him ?", + "Output Program": [ + "import scipy\nn0 = 1.0\nn1 = 2.8\nt0 = scipy.lcm(int(2.0), int(3.0))\nt1 = t0 / n1\nanswer = t1 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "0.1428571428571428" + ], + "split": "train" + }, + { + "Input": "a man spend 1 / 5 of his salary on food , 1 / 10 of his salary on house rent and 3 / 5 salary on clothes . he still has $ 17000 left with him . find salary . .", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 1.0\nn3 = 10.0\nn4 = 3.0\nn5 = 5.0\nn6 = 17000.0\nt0 = n0 / n1\nt1 = n0 / n3\nt2 = n4 / n1\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n0 - t4\nanswer = n6 / t5\nprint(answer)" + ], + "Output Answer": [ + "170000.00000000003" + ], + "split": "train" + }, + { + "Input": "tara bought 19 cartons of ice cream and 4 cartons of yoghurt . each carton of ice cream cost $ 7 and each carton of yoghurt cost $ 1 . how much more did tara spend on ice cream than on yoghurt ?", + "Output Program": [ + "n0 = 19.0\nn1 = 4.0\nn2 = 7.0\nn3 = 1.0\nt0 = n0 * n2\nt1 = n1 * n3\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "129" + ], + "split": "train" + }, + { + "Input": "if 9 boys meet at a reunion and each boy shakes hands exactly once with each of the others , then what is the total number of handshakes", + "Output Program": [ + "import math\nn0 = 9.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(2.0)))\nt2 = n0 - 2.0\nt3 = math.factorial(min(15, int(t2)))\nt4 = t3 * t1\nanswer = t0 / t4\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "a grocer is storing soap boxes in cartons that measure 25 inches by 48 inches by 60 inches . if the measurement of each soap box is 8 inches by 6 inches by 5 inches , then what is the maximum number of soap boxes that can be placed in each carton ?", + "Output Program": [ + "n0 = 25.0\nn1 = 48.0\nn2 = 60.0\nn3 = 8.0\nn4 = 6.0\nn5 = 5.0\nt0 = n0 * n1\nt1 = n3 * n4\nt2 = n2 * t0\nt3 = n5 * t1\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "a collection of books went on sale , and 2 / 3 of them were sold for $ 5 each . if none of the 50 remaining books were sold , what was the total amount received for the books that were sold ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 5.0\nn3 = 50.0\nt0 = n2 / n1\nt1 = 1.0 / n1\nt2 = n3 * t0\nt3 = t2 / t1\nanswer = n0 * t3\nprint(answer)" + ], + "Output Answer": [ + "500.00000000000006" + ], + "split": "train" + }, + { + "Input": "5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 75 only . men \u00e2 \u20ac \u2122 s wages are ?", + "Output Program": [ + "n0 = 5.0\nn1 = 8.0\nn2 = 75.0\nt0 = n0 * 3.0\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "elvin ' s monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for internet service . elvin ' s total telephone bill for january was $ 40 and elvin ' s total telephone bill for february was 76 $ . if elvin ' s charge for the calls he made in february was twice the charge for the calls he made in january , what is elvin ' s fixed monthly charge for internet service ?", + "Output Program": [ + "n0 = 40.0\nn1 = 76.0\nt0 = n0 * 2.0\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "the sum of the ages 4 members of a family 5 years ago was 94 . today , when the daughter has been married off and replaced by a daughter - in - law , the sum of their ages is 100 . assuming that there has been no other change in the family structure and all members are alive , what is the difference in the ages of daughter and daughter - in - law ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 94.0\nn3 = 100.0\nt0 = n0 * n1\nt1 = n2 + t0\nanswer = t1 - n3\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "40 \u00d7 ? + ( 12 + 8 ) \u00d7 3 / 5 = 1212", + "Output Program": [ + "n0 = 40.0\nn1 = 12.0\nn2 = 8.0\nn3 = 3.0\nn4 = 5.0\nn5 = 1212.0\nt0 = n1 + n2\nt1 = n3 / n4\nt2 = t0 * t1\nt3 = n5 - t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "f ( x ) is a function such that f ( x ) + 3 f ( 8 - x ) = x for all real numbers x . find the value of f ( 2 )", + "Output Program": [ + "n0 = 3.0\nn1 = 8.0\nn2 = 2.0\nt0 = n0 * n0\nt1 = t0 * n2\nt2 = 1.0 - t0\nt3 = n2 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a teacher grades students \u2019 tests by subtracting twice the number of incorrect responses from the number of correct responses . if student b answers each of the 100 questions on her test and receives a score of 73 , how many questions did student b answer correctly ?", + "Output Program": [ + "n0 = 100.0\nn1 = 73.0\nt0 = n0 - n1\nt1 = t0 / 3.0\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "91" + ], + "split": "train" + }, + { + "Input": "the average weight of 5 persons increases by 1.5 kg . if a person weighing 65 kg is replaced by a new person , what could be the weight of the new person ?", + "Output Program": [ + "n0 = 5.0\nn1 = 1.5\nn2 = 65.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "72.5" + ], + "split": "train" + }, + { + "Input": "on july 1 of last year , total employees at company e was decreased by 10 percent . without any change in the salaries of the remaining employees , the average ( arithmetic mean ) employee salary was 10 percent more after the decrease in the number of employees than before the decrease . the total of the combined salaries of all the employees at company e after july 1 last year was what percent e of thatbeforejuly 1 last year ?", + "Output Program": [ + "n0 = 1.0\nn1 = 10.0\nn2 = 10.0\nn3 = 1.0\nn4 = 1.0\n\nanswer = n1 * n1\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "find the last digit of 322 ^ 369", + "Output Program": [ + "n0 = 322.0\nn1 = 369.0\nt0 = n0 % 10.0\nt1 = n1 % 10.0\nt2 = t0**min(t1, 5)\nanswer = t2 % 10.0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "if x is equal to the sum of the even integers from 40 to 60 inclusive , and y is the number of even integers from 40 to 60 inclusive , what is the value of x + y ?", + "Output Program": [ + "n0 = 40.0\nn1 = 60.0\nn2 = 40.0\nn3 = 60.0\nt0 = n0 * 2.0\nt1 = n1 - n0\nt2 = t1 / 2.0\nt3 = t2 + 1.0\nt4 = t2 * 2.0\nt5 = t0 + t4\nt6 = t3 * t5\nt7 = t6 / 2.0\nanswer = t3 + t7\nprint(answer)" + ], + "Output Answer": [ + "561" + ], + "split": "train" + }, + { + "Input": "in a competitive examination in state a , 6 % candidates got selected from the total appeared candidates . state b had an equal number of candidates appeared and 7 % candidates got selected with 79 more candidates got selected than a . what was the number of candidates appeared from each state ?", + "Output Program": [ + "n0 = 6.0\nn1 = 7.0\nn2 = 79.0\nt0 = n1 - n0\nt1 = t0 / 100.0\nanswer = n2 / t1\nprint(answer)" + ], + "Output Answer": [ + "7900" + ], + "split": "train" + }, + { + "Input": "20 carrots on a scale weigh 3.64 kg . when 4 carrots are removed from the scale , the average weight of the 16 carrots is 180 grams . what is the average weight ( in grams ) of the 4 carrots which were removed ?", + "Output Program": [ + "n0 = 20.0\nn1 = 3.64\nn2 = 4.0\nn3 = 16.0\nn4 = 180.0\nn5 = 4.0\nt0 = n3 * n4\nt1 = t0 / 1000.0\nt2 = n1 - t1\nt3 = t2 / n2\nanswer = t3 * 1000.0\nprint(answer)" + ], + "Output Answer": [ + "190.00000000000006" + ], + "split": "train" + }, + { + "Input": "if a * b * c = 130 , b * c * d = 65 , c * d * e = 750 and d * e * f = 250 the ( a * f ) / ( c * d ) = ?", + "Output Program": [ + "n0 = 130.0\nn1 = 65.0\nn2 = 750.0\nn3 = 250.0\nt0 = n0 * n3\nt1 = n1 * n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.6666666666666666" + ], + "split": "train" + }, + { + "Input": "in a class of students , 2 / 3 of the number of girls is equal to 1 / 4 of the total number of students . what is the ratio of boys to girls in the class ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 1.0\nn3 = 4.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = t0 - t1\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "1.6666666666666665" + ], + "split": "train" + }, + { + "Input": "the greatest number which on dividing 1442 and 1816 leaves remainders 12 and 6 respectively , is :", + "Output Program": [ + "import scipy\nn0 = 1442.0\nn1 = 1816.0\nn2 = 12.0\nn3 = 6.0\nt0 = n1 - n3\nt1 = n0 - n2\nanswer = scipy.gcd(int(t0), int(t1))\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "joe went on a diet 3 months ago when he weighed 222 pounds . if he now weighs 198 pounds and continues to lose at the same average monthly rate , in approximately how many months will he weigh 170 pounds ?", + "Output Program": [ + "n0 = 3.0\nn1 = 222.0\nn2 = 198.0\nn3 = 170.0\nt0 = n2 - n3\nt1 = n1 - n2\nt2 = t1 / n0\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "3.5" + ], + "split": "train" + }, + { + "Input": "given f ( x ) = 2 x \u2013 3 , for what value of x does 2 * [ f ( x ) ] \u2013 11 = f ( x \u2013 2 ) ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 2.0\nn3 = 11.0\nn4 = 2.0\nt0 = n1 * n2\nt1 = n4 * n0\nt2 = n0 * n2\nt3 = n0 * 1.0\nt4 = n3 + t0\nt5 = n1 + t1\nt6 = t2 - t3\nt7 = t4 - t5\nanswer = t7 / t6\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "all the milk in container a which was filled to its brim was poured into two containers b and c . the quantity of milk in container b was 62.5 % less than the capacity of container a . if 150 liters was now transferred from c to b , then both the containers would have equal quantities of milk . what was the initial quantity of milk in container a ?", + "Output Program": [ + "n0 = 62.5\nn1 = 150.0\nt0 = n0 / 100.0\nt1 = 1 / 2.0\nt2 = 1.0 - t0\nt3 = t1 - t2\nanswer = n1 / t3\nprint(answer)" + ], + "Output Answer": [ + "1200" + ], + "split": "train" + }, + { + "Input": "let the number which when multiplied by 13 is increased by 180 .", + "Output Program": [ + "n0 = 13.0\nn1 = 180.0\nt0 = n0 - 1.0\nanswer = n1 / t0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "10 ^ ( 655 ) \u00e3 \u00b7 10 ^ ( 652 ) = ?", + "Output Program": [ + "n0 = 10.0\nn1 = 655.0\nn2 = 10.0\nn3 = 652.0\nt0 = n1 - n3\nanswer = n0**min(t0, 5)\nprint(answer)" + ], + "Output Answer": [ + "1000" + ], + "split": "train" + }, + { + "Input": "the jogging track in a sports complex is 1000 meters in circumference . deepak and his wife start from the same point and walk in opposite directions at 20 km / hr and 12 km / hr respectively . they will meet for the first time in ?", + "Output Program": [ + "n0 = 1000.0\nn1 = 20.0\nn2 = 12.0\n\nanswer = n1 + n2\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "jean drew a gumball at random from a jar of pink and blue gumballs . since the gumball she selected was blue and she wanted a pink one , she replaced it and drew another . the second gumball also happened to be blue and she replaced it as well . if the probability of her drawing the two blue gumballs was 16 / 49 what is the probability that the next one she draws will be pink ?", + "Output Program": [ + "import math\nn0 = 16.0\nn1 = 49.0\nt0 = n0 / n1\nt1 = math.sqrt(max(0, t0))\nanswer = 1.0 - t1\nprint(answer)" + ], + "Output Answer": [ + "0.4285714285714286" + ], + "split": "train" + }, + { + "Input": "if x is 25 percent greater than 88 , then x =", + "Output Program": [ + "n0 = 25.0\nn1 = 88.0\nt0 = n0 / 100.0\nt1 = n1 * t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "110" + ], + "split": "train" + }, + { + "Input": "at a certain food stand , the price of each apple is 40 \u00a2 and the price of each orange is 60 \u00a2 . mary selects a total of 10 apples and oranges from the food stand , and the average ( arithmetic mean ) price of the 10 pieces of fruit is 54 \u00a2 . how many oranges must mary put back so that the average price of the pieces of fruit that she keeps is 48 \u00a2 ?", + "Output Program": [ + "n0 = 40.0\nn1 = 60.0\nn2 = 10.0\nn3 = 10.0\nn4 = 54.0\nn5 = 48.0\nt0 = n1 * n2\nt1 = n2 * n4\nt2 = n2 * n5\nt3 = n1 - n0\nt4 = n1 - n5\nt5 = t0 - t1\nt6 = t5 / t3\nt7 = n0 * t6\nt8 = n2 - t6\nt9 = n1 * t8\nt10 = t7 + t9\nt11 = t10 - t2\nanswer = t11 / t4\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "david has $ 1800 at the beginning of his trip , after spending money , he still has exactly $ 800 less than he spent on the trip . how much money does john still have ?", + "Output Program": [ + "n0 = 1800.0\nn1 = 800.0\nt0 = n0 - n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "train" + }, + { + "Input": "a 5 - digit number divisible by 3 is to be formed using numerical 0 , 1 , 2 , 3 , 4 and 5 without repetition . the total number e of ways this can be done is :", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 3.0\nn2 = 0.0\nn3 = 1.0\nn4 = 2.0\nn5 = 3.0\nn6 = 4.0\nn7 = 5.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(n6)))\nt2 = n6 * t1\nanswer = t0 + t2\nprint(answer)" + ], + "Output Answer": [ + "216" + ], + "split": "train" + }, + { + "Input": "at a supermarket , john spent 1 / 5 of his money on fresh fruits and vegetables , 1 / 3 on meat products , and 1 / 10 on bakery products . if he spent the remaining $ 11 on candy , how much did john spend at the supermarket ?", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 1.0\nn3 = 3.0\nn4 = 1.0\nn5 = 10.0\nn6 = 11.0\nt0 = n0 / n5\nt1 = n0 / n3\nt2 = n0 / n1\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n0 - t4\nanswer = n6 / t5\nprint(answer)" + ], + "Output Answer": [ + "29.999999999999996" + ], + "split": "train" + }, + { + "Input": "two kinds of vodka are mixed in the ratio 1 : 2 and 2 : 1 and they are sold fetching the profit 40 % and 20 % respectively . if the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4 / 3 and 5 / 3 times respectively , then the mixture will fetch the profit of", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 2.0\nn3 = 1.0\nn4 = 10.0\nn5 = 35.0\nn6 = 4.0\nn7 = 3.0\nn8 = 5.0\nn9 = 3.0\nt0 = n4 + n8\nt1 = n4 * n6\nt2 = t1 / n1\nanswer = t0 + t2\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "there are 280 female managers in a certain company . find the total number of female employees in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers .", + "Output Program": [ + "n0 = 280.0\nn1 = 2.0\nn2 = 5.0\nn3 = 2.0\nn4 = 5.0\nt0 = n1 / n2\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "700" + ], + "split": "train" + }, + { + "Input": "the average monthly income of p and q is rs . 2050 . the average monthly income of q and r is rs . 5250 and the average monthly income of p and r is rs . 6200 . the monthly income of p is :", + "Output Program": [ + "n0 = 2050.0\nn1 = 5250.0\nn2 = 6200.0\nt0 = n0 + n2\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "3000" + ], + "split": "train" + }, + { + "Input": "the events a and b are independent , the probability that event a occurs is greater than 0 , and the probability that event a occurs is twice the probability that event b occurs . the probability that at least one of events a and b occurs is 14 times the probability that both events a and b occur . what is the probability that event a occurs ?", + "Output Program": [ + "n0 = 0.0\nn1 = 14.0\nt0 = 1.0 + 2.0\nt1 = n1 * 2.0\nt2 = t1 + 2.0\nt3 = t0 / t2\nanswer = t3 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "0.2" + ], + "split": "train" + }, + { + "Input": "in a classroom , the average age of boys ( b ) is g and the average age of girls ( g ) is b . the average age of all is b + g . at the time of calculation , the class teacher , who is 42 years old was also present in the class . can you find the value of b + g ?", + "Output Program": [ + "import math\nn0 = 42.0\nt0 = n0 * 4.0\nt1 = t0 + 2.0\nt2 = math.sqrt(max(0, t1))\nt3 = t2 + 1.0\nt4 = t3 / 2.0\nt5 = math.floor(t4)\nt6 = t5**min(2.0, 5)\nt7 = t5 - 1.0\nt8 = t7 / 2.0\nt9 = t1 - t6\nt10 = math.sqrt(max(0, t9))\nt11 = t10 - 1.0\nt12 = t11 / 2.0\nanswer = t8 + t12\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "sushil got thrice as many marks in english as in science . his total marks in english , science and maths are 170 . if the ratio of his marks in english and maths is 1 : 4 , find his marks in science ?", + "Output Program": [ + "n0 = 170.0\nn1 = 1.0\nn2 = 4.0\nt0 = n1 * 3.0\nt1 = n1 + t0\nt2 = t1 * t0\nt3 = t1 + t2\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "what is the remainder if 7 ^ 8 is divided by 100 ?", + "Output Program": [ + "n0 = 7.0\nn1 = 8.0\nn2 = 100.0\nt0 = n2 / 2.0\nt1 = n0 * n0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "65 % of x = 20 % of 617.50 . find the value of x ?", + "Output Program": [ + "n0 = 65.0\nn1 = 20.0\nn2 = 617.5\nt0 = n2 / 100.0\nt1 = n1 * t0\nt2 = t1 * 100.0\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "190" + ], + "split": "train" + }, + { + "Input": "how many numbers from 12 to 82 are exactly divisible by 6 ?", + "Output Program": [ + "import math\nn0 = 12.0\nn1 = 82.0\nn2 = 6.0\nt0 = n1 / n2\nt1 = n0 / n2\nt2 = math.floor(t0)\nt3 = math.floor(t1)\nt4 = t3 + 1.0\nt5 = n2 * t2\nt6 = n2 * t4\nt7 = t5 - t6\nt8 = t7 / n2\nanswer = t8 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "a certain quantity is measured on two different scales , the r - scale and the s - scale , that are related linearly . measurements on the r - scale of 6 and 24 correspond to measurements on the s - scale of 30 and 60 , respectively . what measurement on the r - scale corresponds to a measurement of 100 on the s - scale ?", + "Output Program": [ + "n0 = 6.0\nn1 = 24.0\nn2 = 30.0\nn3 = 60.0\nn4 = 100.0\nt0 = n4 - n3\nt1 = n1 - n0\nt2 = t0 * t1\nt3 = t2 / n2\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "a family x went for a vacation . unfortunately it rained for 13 days when they were there . but whenever it rained in the mornings , they had clear afternoons and vice versa . in all they enjoyed 11 mornings and 12 afternoons . how many days did they stay there totally ?", + "Output Program": [ + "n0 = 13.0\nn1 = 11.0\nn2 = 12.0\nt0 = n1 + n2\nt1 = t0 - n0\nt2 = t1 / 2.0\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "a textile manufacturing firm employees 125 looms . it makes fabrics for a branded company . the aggregate sales value of the output of the 125 looms is rs 5 , 00,000 and the monthly manufacturing expenses is rs 1 , 50,000 . assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms . monthly establishment charges are rs 75000 . if one loom breaks down and remains idle for one month , the decrease in profit is :", + "Output Program": [ + "n0 = 125.0\nn1 = 125.0\nn2 = 5.0\nn3 = 0.0\nn4 = 1.0\nn5 = 50000.0\nn6 = 75000.0\nt0 = n2 * 1000.0\nt1 = n6 * 2.0\nt2 = n0 - n4\nt3 = n6 + t1\nt4 = t2 / n0\nt5 = t0 * 100.0\nt6 = t4 * t5\nt7 = t4 * t1\nt8 = t5 - t3\nt9 = t6 - t7\nt10 = t9 - n6\nanswer = t8 - t10\nprint(answer)" + ], + "Output Answer": [ + "2800" + ], + "split": "train" + }, + { + "Input": "what is the decimal equivalent of ( 1 / 4 ) ^ 4 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 4.0\nt0 = n0 / n1\nanswer = t0**min(n2, 5)\nprint(answer)" + ], + "Output Answer": [ + "0.00390625" + ], + "split": "train" + }, + { + "Input": "( ( a + b ) / c ) / 2 in the expression above , a , b , and c are different numbers and each is one of the numbers 2 , 3 , or 5 . what is the least possible value of the expression ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 3.0\nn3 = 5.0\n\nanswer = n3 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "if the median of a list of numbers is m , the first quartile of the list is the median of the numbers in the list that are less than m . what is the first quartile of the list of numbers 42 , 24 , 30 , 22 , 26 , 27 , 33 and 35 ?", + "Output Program": [ + "n0 = 42.0\nn1 = 24.0\nn2 = 30.0\nn3 = 22.0\nn4 = 26.0\nn5 = 27.0\nn6 = 33.0\nn7 = 35.0\nt0 = n1 + n4\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "14 . the sum and the product of two numbers are 25 and 144 respectively , the difference of the number is ?", + "Output Program": [ + "n0 = 14.0\nn1 = 25.0\nn2 = 144.0\nt0 = n2 * 2.0\nt1 = n1**min(2.0, 5)\nt2 = t1 - t0\nt3 = t2 - t0\nt4 = t3 - 4.0\nt5 = t4 - 3.0\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "the rate at which a sum becomes 4 times of itself in 15 years at s . i . , will be :", + "Output Program": [ + "n0 = 4.0\nn1 = 15.0\nt0 = 100.0 * 3.0\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.60 per glass on the first day , what was the price q per glass on the second day ?", + "Output Program": [ + "n0 = 0.6\nt0 = 1.0 + 1.0\nt1 = 1.0 + 2.0\nt2 = n0 * t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.39999999999999997" + ], + "split": "train" + }, + { + "Input": "9 people decided to split the restaurant bill evenly . if the bill was $ 314.16 dollars , how much money did they 1 cent is the smallest unit ?", + "Output Program": [ + "n0 = 9.0\nn1 = 314.16\nn2 = 1.0\nt0 = 3.0 / 100.0\nanswer = n1 + t0\nprint(answer)" + ], + "Output Answer": [ + "314.19" + ], + "split": "train" + }, + { + "Input": "x \u00f7 4 \u00d7 5 + 10 \u2013 12 = 48 , then x =", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 10.0\nn3 = 12.0\nn4 = 48.0\nt0 = n4 - n2\nt1 = n3 + t0\nt2 = n0 * t1\nanswer = t2 / n1\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "find the value of a / b + b / a , if a and b are the roots of the quadratic equation x 2 + 10 x + 5 = 0 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 10.0\nn2 = 5.0\nn3 = 0.0\nt0 = -n1\nt1 = t0**min(2.0, 5)\nt2 = t1 / n2\nanswer = t2 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "to be considered for \u201c movie of the year , \u201d a film must appear in at least 1 / 4 of the top - 10 - movies lists submitted by the cinematic academy \u2019 s 795 members . what is the smallest number of top - 10 lists a film can appear on and still be considered for \u201c movie of the year \u201d ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 10.0\nn3 = 795.0\nn4 = 10.0\n\nanswer = n3 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "198.75" + ], + "split": "train" + }, + { + "Input": "a man can swim in still water at 9 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ?", + "Output Program": [ + "n0 = 9.0\n\nanswer = n0 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "the distance from the x - axis to point p is half the distance from the y - axis to point p . if the coordinates of p are ( x , - 6 ) , how many units is p from the y - axis ?", + "Output Program": [ + "n0 = 6.0\n\nanswer = n0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "a , b , c subscribe rs . 50000 for a business . if a subscribes rs . 4000 more than b and b rs . 5000 more than c , out of a total profit of rs . 36000 , what will be the amount a receives ?", + "Output Program": [ + "n0 = 50000.0\nn1 = 4000.0\nn2 = 5000.0\nn3 = 36000.0\nt0 = n1 + n2\nt1 = n2 + t0\nt2 = n0 - t1\nt3 = t2 / 3.0\nt4 = t0 + t3\nt5 = t4 / n0\nanswer = n3 * t5\nprint(answer)" + ], + "Output Answer": [ + "15120" + ], + "split": "train" + }, + { + "Input": "an integer n between 1 and 99 , inclusive , is to be chosen at random . what is the probability that n ( n + 1 ) will be divisible by 2 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 99.0\nn2 = 1.0\nn3 = 2.0\nt0 = n1 / 3.0\nt1 = t0 / n1\nanswer = 2.0 * t1\nprint(answer)" + ], + "Output Answer": [ + "0.6666666666666666" + ], + "split": "train" + }, + { + "Input": "of the 80 people in a room , 1 / 4 are women . if 3 / 4 of the people are married , what is the maximum number of women in the room who could be unmarried ?", + "Output Program": [ + "n0 = 80.0\nn1 = 1.0\nn2 = 4.0\nn3 = 3.0\nn4 = 4.0\nt0 = n1 / n2\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "if the mean of numbers 12 , x , 42 , 78 and 104 is 62 , then what is the mean of 128 , 255 , 511 , 1023 and x ?", + "Output Program": [ + "n0 = 12.0\nn1 = 42.0\nn2 = 78.0\nn3 = 104.0\nn4 = 62.0\nn5 = 128.0\nn6 = 255.0\nn7 = 511.0\nn8 = 1023.0\nt0 = 1.0 + 4.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n4 * t0\nt4 = n3 + t2\nt5 = t3 - t4\nt6 = n5 + t5\nt7 = n6 + t6\nt8 = n7 + t7\nt9 = n8 + t8\nanswer = t9 / t0\nprint(answer)" + ], + "Output Answer": [ + "398.2" + ], + "split": "train" + }, + { + "Input": "the ratio of the present ages of ramesh and mahesh is 2 : 5 . 10 years hence , the ratio of their ages will be 10 : 15 . find the difference in their present ages ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 10.0\nn3 = 10.0\nn4 = 15.0\n\nanswer = n4 / n0\nprint(answer)" + ], + "Output Answer": [ + "7.5" + ], + "split": "train" + }, + { + "Input": "one boss decided to increase the salary of an employee by 5 % . how much will he get if his salary was rs . 2000 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2000.0\nt0 = n0 / 100.0\nt1 = n1 * t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "2100" + ], + "split": "train" + }, + { + "Input": "in a certain accounting class of 100 students , 70 % of the students took the final exam on the assigned day while the rest of the students took the exam on a make - up date . if the students on the assigned day had an average score of 60 % , and the students on the make - up date had an average score of 80 % , what was the average score for the entire class ?", + "Output Program": [ + "n0 = 100.0\nn1 = 70.0\nn2 = 60.0\nn3 = 80.0\nt0 = n1 * n2\nt1 = n0 - n1\nt2 = n3 * t1\nt3 = t0 + t2\nanswer = t3 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "66" + ], + "split": "train" + }, + { + "Input": "if p ( 32 , 6 ) = kc ( 32 , 6 ) , then what is the value of k ?", + "Output Program": [ + "import math\nn0 = 32.0\nn1 = 6.0\nn2 = 32.0\nn3 = 6.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(n1)))\nt2 = n0 - n1\nt3 = math.factorial(min(15, int(t2)))\nt4 = t0 / t3\nt5 = t1 * t3\nt6 = t0 / t5\nanswer = t4 / t6\nprint(answer)" + ], + "Output Answer": [ + "720" + ], + "split": "train" + }, + { + "Input": "for how many values of q , is | | | q - 5 | - 10 | - 5 | = 2 ? ( those ls are mods )", + "Output Program": [ + "n0 = 5.0\nn1 = 10.0\nn2 = 5.0\nn3 = 2.0\nt0 = n1 - n0\nt1 = n0 + t0\nanswer = t1 - n3\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "at joes steakhouse the hourly wage for a chef is 25 % greater than that of a dishwasher , and the hourly wage of a dishwasher is half as much as the hourly wage of a manager . if a managers wage is $ 8.50 per hour , how much less than a manager does a chef earn each hour ?", + "Output Program": [ + "n0 = 25.0\nn1 = 8.5\nt0 = n0 + 100.0\nt1 = 1.0 / 2.0\nt2 = t0 / 100.0\nt3 = t2 * t1\nt4 = 1.0 - t3\nanswer = n1 * t4\nprint(answer)" + ], + "Output Answer": [ + "3.1875" + ], + "split": "train" + }, + { + "Input": "in 10 years , a will be twice as old as b was 10 years ago . if a is now 9 years older than b , the present age of b is ?", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 9.0\nt0 = n0 * 2.0\nt1 = n0 + t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "39" + ], + "split": "train" + }, + { + "Input": "little krish had $ 200.50 . he spent $ 35.25 on sweets and gave to his two friends $ 25.20 each . how much money was left ?", + "Output Program": [ + "n0 = 200.5\nn1 = 35.25\nn2 = 25.2\nt0 = n2 * 2.0\nt1 = n0 - n1\nanswer = t1 - t0\nprint(answer)" + ], + "Output Answer": [ + "114.85" + ], + "split": "train" + }, + { + "Input": "pat , kate , and mark charged a total of 117 hours to a certain project . if pat charged twice as much time to the project as kate and 1 / 3 as much time as mark , how many more hours did mark charge to the project than kate ?", + "Output Program": [ + "n0 = 117.0\nn1 = 1.0\nn2 = 3.0\nt0 = n1 / n2\nt1 = n2 * 2.0\nt2 = n1 + t0\nt3 = n1 / t1\nt4 = t2 + t3\nt5 = n0 / t4\nt6 = t5 / t1\nanswer = t5 - t6\nprint(answer)" + ], + "Output Answer": [ + "65" + ], + "split": "train" + }, + { + "Input": "a school has 4 section of chemistry in class x having 65 , 35 , 45 and 42 students . the mean marks obtained in chemistry test are 50 , 60 , 55 and 45 respectively for the 4 sections . determine the overall average of marks per student .", + "Output Program": [ + "n0 = 4.0\nn1 = 65.0\nn2 = 35.0\nn3 = 45.0\nn4 = 42.0\nn5 = 50.0\nn6 = 60.0\nn7 = 55.0\nn8 = 45.0\nn9 = 4.0\nt0 = n1 + n2\nt1 = n1 * n5\nt2 = n2 * n6\nt3 = n3 * n7\nt4 = n3 * n4\nt5 = t1 + t2\nt6 = n3 + t0\nt7 = t5 + t3\nt8 = n4 + t6\nt9 = t7 + t4\nanswer = t9 / t8\nprint(answer)" + ], + "Output Answer": [ + "51.95187165775401" + ], + "split": "train" + }, + { + "Input": "a basket of 1430 apples is divided equally among a group of apple lovers . if 45 people join the group , each apple lover would receive 9 apples less . how many apples did each person get before 45 people joined the feast ?", + "Output Program": [ + "n0 = 1430.0\nn1 = 45.0\nn2 = 9.0\nn3 = 45.0\nt0 = 10.0 + 10.0\nt1 = t0 + 2.0\nt2 = n0 / t1\nt3 = n1 + t2\nt4 = n0 / t3\nanswer = n2 + t4\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "running at their respective constant rate , machine x takes 2 days longer to produce w widgets than machines y . at these rates , if the two machines together produce 5 w / 4 widgets in 3 days , how many days would it take machine x alone to produce 5 w widgets .", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 4.0\nn3 = 3.0\nn4 = 5.0\nt0 = n0 * n4\nanswer = n3 * t0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "two employees x and y are paid a total of rs . 616 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?", + "Output Program": [ + "n0 = 616.0\nn1 = 120.0\nt0 = 1.0 + 4.0\nt1 = t0 * 2.0\nt2 = t1 + 1.0\nt3 = n0 * t1\nt4 = t2 * 2.0\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "280" + ], + "split": "train" + }, + { + "Input": "jacob is now 14 years younger than michael . if 9 years from now michael will be twice as old as jacob , how old will jacob be in 4 years ?", + "Output Program": [ + "n0 = 14.0\nn1 = 9.0\nn2 = 4.0\nt0 = n0 + n1\nt1 = n1 * 2.0\nt2 = t0 - t1\nanswer = n2 + t2\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "when a certain number x is divided by 95 , the remainder is 31 . what is the remainder when x is divided by 19 ?", + "Output Program": [ + "n0 = 95.0\nn1 = 31.0\nn2 = 19.0\n\nanswer = n1 % n2\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "a number is doubled and 5 is added . if the resultant is trebled , it becomes 135 . what is that number ?", + "Output Program": [ + "n0 = 5.0\nn1 = 135.0\nt0 = n0 * 3.0\nt1 = 2.0 * 3.0\nt2 = n1 - t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "the average ( arithmetic mean ) of 10 , 30 , and 50 is 8 more than the average of 20 , 40 , and x . what is x ?", + "Output Program": [ + "n0 = 10.0\nn1 = 30.0\nn2 = 50.0\nn3 = 8.0\nn4 = 20.0\nn5 = 40.0\nt0 = n0 + n1\nt1 = n3 * 3.0\nt2 = n2 + t0\nt3 = n4 + t1\nt4 = n5 + t3\nanswer = t2 - t4\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "calculate the sum of first 39 natural numbers .", + "Output Program": [ + "n0 = 39.0\nt0 = n0 + 1.0\nt1 = n0 / 2.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "780" + ], + "split": "train" + }, + { + "Input": "of the 150 people at a party , 70 were women , and 40 women tried the appetizer . if 50 people did not try the appetizer , what is the total number of men who tried the appetizer ?", + "Output Program": [ + "n0 = 150.0\nn1 = 70.0\nn2 = 40.0\nn3 = 50.0\nt0 = n0 - n3\nanswer = t0 - n2\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "a trained covered x km at 40 kmph and another 4 x km at 20 kmph . find the average speed of the train in covering the entire 3 x km .", + "Output Program": [ + "n0 = 40.0\nn1 = 4.0\nn2 = 20.0\nn3 = 3.0\nt0 = n0 / n0\nt1 = n0 * n3\nt2 = n0 * n1\nt3 = t2 / n2\nt4 = t0 + t3\nanswer = t1 / t4\nprint(answer)" + ], + "Output Answer": [ + "13.333333333333334" + ], + "split": "train" + }, + { + "Input": "a box contains 100 balls , numbered from 1 to 100 . if 3 balls are selected at random and with replacement from the box , what is the probability that the sum of the 3 numbers on the balls selected from the box will be odd ?", + "Output Program": [ + "n0 = 100.0\nn1 = 1.0\nn2 = 100.0\nn3 = 3.0\nn4 = 3.0\nt0 = n1 / 2.0\nt1 = t0**min(2.0, 5)\nt2 = t0**min(3.0, 5)\nt3 = n3 * t1\nt4 = t0 * t3\nanswer = t4 + t2\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "if 4 ( p ' s capital ) = 6 ( q ' s capital ) = 10 ( r ' s capital ) , then out of the total profit of rs 4650 , how much r will receive ?", + "Output Program": [ + "n0 = 4.0\nn1 = 6.0\nn2 = 10.0\nn3 = 4650.0\nt0 = n0 + 1.0\nt1 = n2 + t0\nt2 = n2 + t1\nt3 = n1 + t2\nt4 = n1 / t3\nanswer = n3 * t4\nprint(answer)" + ], + "Output Answer": [ + "900" + ], + "split": "train" + }, + { + "Input": "when greenville state university decided to move its fine arts collection to a new library , it had to package the collection in 20 - inch by 20 - inch by 15 - inch boxes . if the university pays $ 0.70 for every box , and if the university needs 3.06 million cubic inches to package the collection , what is the minimum amount the university must spend on boxes ?", + "Output Program": [ + "n0 = 20.0\nn1 = 20.0\nn2 = 15.0\nn3 = 0.7\nn4 = 3.06\nt0 = 1000.0 * 1000.0\nt1 = n0 * n0\nt2 = n4 * t0\nt3 = n2 * t1\nt4 = t2 / t3\nanswer = n3 * t4\nprint(answer)" + ], + "Output Answer": [ + "357" + ], + "split": "train" + }, + { + "Input": "on a race track a maximum of 5 horses can race together at a time . there are a total of 25 horses . there is no way of timing the races . what is the minimum number y of races we need to conduct to get the top 3 fastest horses ?", + "Output Program": [ + "n0 = 5.0\nn1 = 25.0\nn2 = 3.0\nt0 = n1 / n0\nanswer = t0 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "the average weight of 5 person ' s increases by 4 kg when a new person comes in place of one of them weighing 50 kg . what is the weight of the new person ?", + "Output Program": [ + "n0 = 5.0\nn1 = 4.0\nn2 = 50.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "train" + }, + { + "Input": "the average age of 15 students of a class is 15 years . out of these , the average age of 8 students is 14 years and that of the other 6 students is 16 years . the age of the 15 th student is", + "Output Program": [ + "n0 = 15.0\nn1 = 15.0\nn2 = 8.0\nn3 = 14.0\nn4 = 6.0\nn5 = 16.0\nn6 = 15.0\nt0 = n0 * n0\nt1 = n2 * n3\nt2 = n4 * n5\nt3 = t1 + t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "the average ( arithmetic mean ) of 4 positive integers is 50 . if the average of 2 of these integers is 35 , what is the greatest possible value that one of the other 2 integers can have ?", + "Output Program": [ + "n0 = 4.0\nn1 = 50.0\nn2 = 2.0\nn3 = 35.0\nn4 = 2.0\nt0 = n0 * n1\nt1 = n2 * n3\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "130" + ], + "split": "train" + }, + { + "Input": "a customer bought a product at the shop . however , the shopkeeper increased the price of the product by 20 % so that the customer could not buy the required amount of the product . the customer managed to buy only 70 % of the required amount . what is the difference in the amount of money that the customer paid for the second purchase compared to the first purchase ?", + "Output Program": [ + "n0 = 20.0\nn1 = 70.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = t0 + 1.0\nt3 = t2 * t1\nt4 = 1.0 - t3\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "16.000000000000004" + ], + "split": "train" + }, + { + "Input": "the number of diagonals of a polygon of n sides is given by the formula c = n ( n - 3 ) / 2 . if a polygon has twice as many diagonals as sides , how many sides does it have ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\n\nanswer = n0 + n1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "the total age of a and b is 12 years more than the total age of b and c . c is how many years younger than a ?", + "Output Program": [ + "n0 = 12.0\n\nanswer = n0 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "harold works at a resort from the beginning of march to the end of september . during the month of august this past year , he made 6 times the average ( arithmetic mean ) of his monthly totals in tips for the other months . his total tips for august were what fraction of his total tips for all of the months he worked ?", + "Output Program": [ + "n0 = 6.0\nt0 = n0 * 1.0\nt1 = t0 + t0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "for how many values of n , is | | | n - 5 | - 10 | - 5 | = 2 ? ( those ls are mods )", + "Output Program": [ + "n0 = 5.0\nn1 = 10.0\nn2 = 5.0\nn3 = 2.0\n\nanswer = n3**min(3.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a certain bus driver is paid a regular rate of $ 15 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 976 in total compensation , how many total hours did he work that week ?", + "Output Program": [ + "n0 = 15.0\nn1 = 40.0\nn2 = 40.0\nn3 = 75.0\nn4 = 976.0\nt0 = n3 + 100.0\nt1 = n0 * n1\nt2 = n0 * t0\nt3 = n4 - t1\nt4 = t2 / 100.0\nt5 = t3 / t4\nanswer = n1 + t5\nprint(answer)" + ], + "Output Answer": [ + "54.32380952380952" + ], + "split": "train" + }, + { + "Input": "what should be the least number to be added to the 3198 number to make it divisible by 8 ?", + "Output Program": [ + "n0 = 3198.0\nn1 = 8.0\nt0 = n0 % n1\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "10 % people of a village in sri lanka died by bombardment , 20 % of the remainder left the village on account of fear . if now the population is reduced to 3168 , how much was it in the beginning ?", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 20.0\nn2 = 3168.0\nt0 = 100.0 - n0\nt1 = 100.0 - n1\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = t2 * t3\nt5 = n2 / t4\nanswer = math.floor(t5)\nprint(answer)" + ], + "Output Answer": [ + "4399" + ], + "split": "train" + }, + { + "Input": "60 men shake hands with each other . maximum no of handshakes without cyclic handshakes .", + "Output Program": [ + "n0 = 60.0\nt0 = n0 / 2.0\nt1 = n0 - 1.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "1770" + ], + "split": "train" + }, + { + "Input": "what is the difference between the c . i . on rs . 4000 for 1 1 / 2 years at 4 % per annum compounded yearly and half - yearly ?", + "Output Program": [ + "n0 = 4000.0\nn1 = 1.0\nn2 = 1.0\nn3 = 2.0\nn4 = 4.0\nt0 = n3 / 100.0\nt1 = n4 / 100.0\nt2 = t0 + n1\nt3 = t1 + n1\nt4 = t2 * t2\nt5 = t2 * t3\nt6 = t2 * t4\nt7 = n0 * t5\nt8 = n0 * t6\nanswer = t8 - t7\nprint(answer)" + ], + "Output Answer": [ + "1.631999999999607" + ], + "split": "train" + }, + { + "Input": "approximately what percentage of the world \u2019 s forested area is represented by finland given that finland has 53.42 million hectares of forested land of the world \u2019 s 8.076 billion hectares of forested land .", + "Output Program": [ + "n0 = 53.42\nn1 = 8.076\nt0 = n0 / 3.0\nt1 = 10.0 - 1.0\nt2 = t0 / 3.0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.6595061728395062" + ], + "split": "train" + }, + { + "Input": "the total age of a and b is 13 years more than the total age of b and c . c is how many years younger than a . ?", + "Output Program": [ + "n0 = 13.0\n\nanswer = n0 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "a pupil ' s marks were wrongly entered as 67 instead of 45 . due to that the average marks for the class got increased by half . the number of pupils in the class is :", + "Output Program": [ + "n0 = 67.0\nn1 = 45.0\nt0 = n0 - n1\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "44" + ], + "split": "train" + }, + { + "Input": "what is the smallest number which when increased by 3 is divisible by 12 , 15 , 35 , and 40 ?", + "Output Program": [ + "import scipy\nn0 = 3.0\nn1 = 12.0\nn2 = 15.0\nn3 = 35.0\nn4 = 40.0\nt0 = scipy.lcm(int(n1), int(n2))\nt1 = scipy.lcm(int(n3), int(n4))\nt2 = scipy.lcm(int(t0), int(t1))\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "843" + ], + "split": "train" + }, + { + "Input": "on a race track a maximum of 5 horses can race together at a time . there are a total of 25 horses . there is no way of timing the races . what is the minimum number r of races we need to conduct to get the top 3 fastest horses ?", + "Output Program": [ + "n0 = 5.0\nn1 = 25.0\nn2 = 3.0\nt0 = n1 / n0\nanswer = t0 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "if a certain toy store ' s revenue in november was 2 / 5 of its revenue in december and its revenue in january was 1 / 2 of its revenue in november , then the store ' s revenue in december was how many times the average ( arithmetic mean ) of its revenues in november and january ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 1.0\nn3 = 2.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = t0 * t1\nt3 = t0 + t2\nt4 = t3 / 2.0\nanswer = n2 / t4\nprint(answer)" + ], + "Output Answer": [ + "3.333333333333333" + ], + "split": "train" + }, + { + "Input": "7 people average age is 30 . youngest person age is 5 . find average of the people when youngest was born .", + "Output Program": [ + "n0 = 7.0\nn1 = 30.0\nn2 = 5.0\nt0 = n0 * n1\nt1 = n0 * n2\nt2 = t0 - t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "linda spent 3 / 5 of her savings on furniture and the rest on a tv . if the tv cost her $ 400 , what were her original savings ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 400.0\nt0 = n0 / n1\nt1 = 1.0 - t0\nanswer = n2 / t1\nprint(answer)" + ], + "Output Answer": [ + "1000" + ], + "split": "train" + }, + { + "Input": "a sum of money lent out at s . i . amounts to rs . 850 after 2 years and to rs . 1020 after a further period of 5 years . the sum is ?", + "Output Program": [ + "n0 = 850.0\nn1 = 2.0\nn2 = 1020.0\nn3 = 5.0\nt0 = n2 - n0\nt1 = t0 / n3\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "782" + ], + "split": "train" + }, + { + "Input": "on dividing 15698 by a certain number , we get 89 as quotient and 14 as remainder . what is the divisor ?", + "Output Program": [ + "n0 = 15698.0\nn1 = 89.0\nn2 = 14.0\nt0 = n0 - n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "176.22471910112358" + ], + "split": "train" + }, + { + "Input": "given that 268 x 74 = 19832 , find the value of 2.68 x . 74 .", + "Output Program": [ + "n0 = 268.0\nn1 = 74.0\nn2 = 19832.0\nn3 = 2.68\nn4 = 74.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "1.9832" + ], + "split": "train" + }, + { + "Input": "a salt manufacturing company produced a total of 1000 tonnes of salt in january of a particular year . starting from february its production increased by 100 tonnes every month over the previous months until the end of the year . find its average monthly production for that year ?", + "Output Program": [ + "n0 = 1000.0\nn1 = 100.0\nt0 = 1.0 + 10.0\nt1 = n1 * t0\nt2 = n0 + t1\nt3 = n0 + t2\nt4 = t3 * 12.0\nt5 = t4 / 2.0\nanswer = t5 / 12.0\nprint(answer)" + ], + "Output Answer": [ + "1550" + ], + "split": "train" + }, + { + "Input": "a batsman in his 11 th inning makes a score of 69 and their by increasing his average by 1 . what is his average after the 11 th inning ?", + "Output Program": [ + "n0 = 11.0\nn1 = 69.0\nn2 = 1.0\nn3 = 11.0\nt0 = n0 * n2\nt1 = n1 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "59" + ], + "split": "train" + }, + { + "Input": "what is the smallest integer b for which 27 ^ b > 3 ^ 24 ?", + "Output Program": [ + "import math\nn0 = 27.0\nn1 = 3.0\nn2 = 24.0\nt0 = n2 / 3.0\nt1 = math.floor(t0)\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "if 9 ^ y = 3 ^ 16 , what is y ?", + "Output Program": [ + "n0 = 9.0\nn1 = 3.0\nn2 = 16.0\n\nanswer = n2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "the average age of 3 boys is 15 years and their ages are in proportion 3 : 5 : 7 . what is the age in years of the eldest boy ?", + "Output Program": [ + "n0 = 3.0\nn1 = 15.0\nn2 = 3.0\nn3 = 5.0\nn4 = 7.0\nt0 = n0 * n1\nt1 = t0 / n1\nanswer = n4 * t1\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "the average weight of 10 persons increases by 7.2 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 10.0\nn1 = 7.2\nn2 = 65.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "137" + ], + "split": "train" + }, + { + "Input": "a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 50 paisa . if the share of y is rs . 45 , what is the total amount ?", + "Output Program": [ + "n0 = 45.0\nn1 = 50.0\nn2 = 45.0\nt0 = 100.0 / n0\nt1 = n1 / n0\nt2 = n2 * t0\nt3 = n2 * t1\nt4 = t2 + t3\nanswer = n2 + t4\nprint(answer)" + ], + "Output Answer": [ + "195" + ], + "split": "train" + }, + { + "Input": "if x + y = 4 , x - y = 36 , for integers of x and y , x = ?", + "Output Program": [ + "n0 = 4.0\nn1 = 36.0\nt0 = n0 + n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 864 in total compensation , how many total hours did he work that week ?", + "Output Program": [ + "n0 = 16.0\nn1 = 40.0\nn2 = 40.0\nn3 = 75.0\nn4 = 864.0\nt0 = n3 + 100.0\nt1 = n0 * n1\nt2 = n0 * t0\nt3 = n4 - t1\nt4 = t2 / 100.0\nt5 = t3 / t4\nanswer = n1 + t5\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 200 milliliters of solution x to create a solution that is 14 percent alcohol by volume ?", + "Output Program": [ + "n0 = 10.0\nn1 = 30.0\nn2 = 200.0\nn3 = 14.0\nt0 = n3 - n0\nt1 = n1 - n3\nt2 = t0 / t1\nanswer = n2 * t2\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "patrick purchased 80 pencils and sold them at a loss equal to the selling price of 16 pencils . the cost of 80 pencils is how many times the selling price of 80 pencils ?", + "Output Program": [ + "n0 = 80.0\nn1 = 16.0\nn2 = 80.0\nn3 = 80.0\nt0 = n0 + n1\nt1 = n0 / t0\nanswer = 1 / t1\nprint(answer)" + ], + "Output Answer": [ + "1.2" + ], + "split": "train" + }, + { + "Input": "if the price of a book is first decreased by 50 % and then increased by 60 % , then the net change in the price will be ?", + "Output Program": [ + "n0 = 50.0\nn1 = 60.0\nt0 = n0 * 100.0\nt1 = n1 * 100.0\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = t3 + 100.0\nt5 = 100.0 - t2\nt6 = t5 / 100.0\nt7 = t4 / 100.0\nt8 = t6 * t7\nt9 = t8 * 100.0\nanswer = 100.0 - t9\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "find the value of x from this equation ? 7 ( x - 1 ) = 21", + "Output Program": [ + "n0 = 7.0\nn1 = 1.0\nn2 = 21.0\nt0 = n2 / n0\nanswer = n1 + t0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 30 paisa . if the share of y is rs . 27 , what is the total amount ?", + "Output Program": [ + "n0 = 45.0\nn1 = 30.0\nn2 = 27.0\nt0 = 100.0 / n0\nt1 = n1 / n0\nt2 = n2 * t0\nt3 = n2 * t1\nt4 = t2 + t3\nanswer = n2 + t4\nprint(answer)" + ], + "Output Answer": [ + "105" + ], + "split": "train" + }, + { + "Input": "albert is 2 times mary \u2019 s age and 4 times as old as betty . mary is 10 years younger than albert . how old is betty ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 10.0\nt0 = n0 * n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "a worker is paid rs . 20 / - for a full days work . he works 11 / 32 / 31 / 8.3 / 4 days in a week . what is the total amount paid for that worker ?", + "Output Program": [ + "n0 = 20.0\nn1 = 11.0\nn2 = 32.0\nn3 = 31.0\nn4 = 8.3\nn5 = 4.0\nt0 = 1.0 / 3.0\nt1 = 2.0 / 3.0\nt2 = 3.0 / n5\nt3 = 2.0 * 4.0\nt4 = t0 + 1.0\nt5 = 1.0 / t3\nt6 = t4 + t1\nt7 = t6 + t5\nt8 = t7 + t2\nanswer = n0 * t8\nprint(answer)" + ], + "Output Answer": [ + "57.5" + ], + "split": "train" + }, + { + "Input": "find a number such that when 15 is subtracted from 7 times the number , the results is more than twice the number ?", + "Output Program": [ + "n0 = 15.0\nn1 = 7.0\nt0 = n0 + 10.0\nt1 = n1 - 2.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "having received his weekly allowance , a student spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 1.00 at the candy store . what is this student \u2019 s weekly allowance ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 1.0\nt0 = n0 * n1\nt1 = n2 * t0\nanswer = t1 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "3.75" + ], + "split": "train" + }, + { + "Input": "if 2 | 2 \u2013 e | = 5 , what is the sum of all the possible values for e ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 5.0\nt0 = n2 / n0\nt1 = n0 + t0\nt2 = n0 - t0\nanswer = t1 + t2\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "if jake loses 33 pounds , he will weigh twice as much as his sister . together they now weigh 153 pounds . what is jake ' s present weight , in pounds ?", + "Output Program": [ + "n0 = 33.0\nn1 = 153.0\nt0 = n1 - n0\nt1 = t0 / 3.0\nt2 = t1 * 2.0\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "113" + ], + "split": "train" + }, + { + "Input": "a certain sum of money is divided among a , b and c so that for each rs . a has , b has 65 paisa and c 40 paisa . if c ' s share is rs . 48 , find the sum of money ?", + "Output Program": [ + "n0 = 65.0\nn1 = 40.0\nn2 = 48.0\nt0 = n0 + 100.0\nt1 = n2 / n1\nt2 = n1 + t0\nanswer = t2 * t1\nprint(answer)" + ], + "Output Answer": [ + "246" + ], + "split": "train" + }, + { + "Input": "rahim bought 65 books for rs . 1150 from one shop and 50 books for rs . 920 from another . what is the average price he paid per book ?", + "Output Program": [ + "n0 = 65.0\nn1 = 1150.0\nn2 = 50.0\nn3 = 920.0\nt0 = n1 + n3\nt1 = n0 + n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "3 pig \u2019 s and 10 hens are brought for rs . 1200 . if the average price of a hen be rs . 30 . what is the average price of a pig .", + "Output Program": [ + "n0 = 3.0\nn1 = 10.0\nn2 = 1200.0\nn3 = 30.0\nt0 = n1 * n3\nt1 = n2 - t0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "mr yadav spends 60 % of his monthly salary on consumable items and 50 % of the remaining on clothes and transport . he saves the remaining amount . if his savings at the end of the year were 46800 , how much amount per month would he have spent on clothes and transport ?", + "Output Program": [ + "n0 = 60.0\nn1 = 50.0\nn2 = 46800.0\nt0 = 3.0 * 4.0\nt1 = 100.0 - n0\nt2 = n1 * t1\nt3 = t2 / 100.0\nt4 = t3 / 100.0\nt5 = n2 / t4\nt6 = t5 / t0\nanswer = t6 * t4\nprint(answer)" + ], + "Output Answer": [ + "3900" + ], + "split": "train" + }, + { + "Input": "if x < y < z and y - x > 5 , where x is an even integer and y and z are odd integers , what is the least possible value s of z - x ?", + "Output Program": [ + "n0 = 5.0\nt0 = n0 + 2.0\nanswer = t0 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "if renee earns a raise of between 5 % and 10 % , non - inclusive , by what fraction could her salary have increased ?", + "Output Program": [ + "n0 = 5.0\nn1 = 10.0\nt0 = n0 * 10.0\nt1 = n0 - 1.0\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.08" + ], + "split": "train" + }, + { + "Input": "dacid obtained 73 , 69 , 92 , 64 and 82 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?", + "Output Program": [ + "n0 = 73.0\nn1 = 69.0\nn2 = 92.0\nn3 = 64.0\nn4 = 82.0\nn5 = 100.0\nt0 = n0 + n1\nt1 = 10.0 / 2.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "76" + ], + "split": "train" + }, + { + "Input": "36 is divided in 2 parts such that 8 times the first part added to 3 times the second part makes 203 . what is the first part ?", + "Output Program": [ + "n0 = 36.0\nn1 = 2.0\nn2 = 8.0\nn3 = 3.0\nn4 = 203.0\nt0 = n0 * n3\nt1 = n2 - n3\nt2 = n4 - t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "roy is now 8 years older than julia and half of that amount older than kelly . if in 2 years , roy will be twice as old as julia , then in 2 years what would be roy \u2019 s age multiplied by kelly \u2019 s age ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.0\nn2 = 2.0\nt0 = n0 / 2.0\nt1 = n0 - n1\nt2 = n0 + t1\nt3 = n1 + t2\nt4 = t2 - t0\nt5 = n1 + t4\nanswer = t3 * t5\nprint(answer)" + ], + "Output Answer": [ + "192" + ], + "split": "train" + }, + { + "Input": "the arithmetic mean and standard deviation of a certain normal distribution are 14.5 and 1.5 , respectively . what value is exactly 2 standard deviations less than the mean ?", + "Output Program": [ + "n0 = 14.5\nn1 = 1.5\nn2 = 2.0\nt0 = n1 * n2\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "11.5" + ], + "split": "train" + }, + { + "Input": "the average age of 15 students of a class is 15 years . out of these , the average age of 4 students is 14 years and that of the other 9 students is 16 years . tee age of the 15 th student is ?", + "Output Program": [ + "n0 = 15.0\nn1 = 15.0\nn2 = 4.0\nn3 = 14.0\nn4 = 9.0\nn5 = 16.0\nn6 = 15.0\nt0 = n0 * n0\nt1 = n2 * n3\nt2 = n4 * n5\nt3 = t1 + t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "in a class of 25 students in an examination in maths 5 students scored 95 marks each , 3 get zero each and the average of the rest was 45 . what is the average of the whole class ?", + "Output Program": [ + "n0 = 25.0\nn1 = 5.0\nn2 = 95.0\nn3 = 3.0\nn4 = 45.0\nt0 = n1 + n3\nt1 = n1 * n2\nt2 = n0 - t0\nt3 = n4 * t2\nt4 = t3 + t1\nanswer = t4 / n0\nprint(answer)" + ], + "Output Answer": [ + "49.6" + ], + "split": "train" + }, + { + "Input": "how many positive integers between 1 and 400 are there such that they are multiples of 25 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 400.0\nn2 = 25.0\nt0 = n1 - n0\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "15.96" + ], + "split": "train" + }, + { + "Input": "if the range w of the 6 numbers 4 , 314 , 710 and x is 12 , what is the difference between the greatest possible value of x and least possible value of x ?", + "Output Program": [ + "n0 = 6.0\nn1 = 4.0\nn2 = 314.0\nn3 = 710.0\nn4 = 12.0\nt0 = n4 + 3.0\nt1 = n1 + 10.0\nt2 = t1 - n4\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "if x is an integer and 2.134 \u00d7 10 ^ x is less than 220,000 , what is the greatest possible value for x ?", + "Output Program": [ + "import math\nn0 = 2.134\nn1 = 10.0\nn2 = 220000.0\nt0 = n2 / n0\nt1 = math.log(max(1e-5, n1), 2)\nt2 = math.log(max(1e-5, t0), 2)\nt3 = t2 / t1\nanswer = math.floor(t3)\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "calculate 469157 x 9999 = ?", + "Output Program": [ + "n0 = 469157.0\nn1 = 9999.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "4691100843" + ], + "split": "train" + }, + { + "Input": "there are 10 dozen mangoes in a box . if there are 36 such boxes , how many mangoes are there in all the boxes together ?", + "Output Program": [ + "n0 = 10.0\nn1 = 36.0\nt0 = 10.0 + 2.0\nt1 = n0 * n1\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "4320" + ], + "split": "train" + }, + { + "Input": "the sum of a number and the number preceding it is 33 . by how much is two less than 6 times the number ?", + "Output Program": [ + "n0 = 33.0\nn1 = 6.0\nt0 = 4.0 * 4.0\nt1 = n0 - t0\nt2 = n1 * t1\nanswer = t2 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "what is the smallest integer x for which 27 ^ x > 3 ^ 24 ?", + "Output Program": [ + "import math\nn0 = 27.0\nn1 = 3.0\nn2 = 24.0\nt0 = n2 / 3.0\nt1 = math.floor(t0)\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "solve ( 0.76 \u00d7 0.76 \u00d7 0.76 \u2212 0.008 ) / ( 0.76 \u00d7 0.76 + 0.76 \u00d7 0.2 + 0.04 )", + "Output Program": [ + "n0 = 0.76\nn1 = 0.76\nn2 = 0.76\nn3 = 0.008\nn4 = 0.76\nn5 = 0.76\nn6 = 0.76\nn7 = 0.2\nn8 = 0.04\nt0 = n0 * n0\nt1 = n0 * n7\nt2 = t0 + t1\nt3 = n0 * t0\nt4 = n8 + t2\nt5 = t3 - n3\nanswer = t5 / t4\nprint(answer)" + ], + "Output Answer": [ + "0.5599999999999999" + ], + "split": "train" + }, + { + "Input": "find the value of 80641 x 9999 = m ?", + "Output Program": [ + "n0 = 80641.0\nn1 = 9999.0\nt0 = n1 - 4.0\nanswer = t0 * n0\nprint(answer)" + ], + "Output Answer": [ + "806006795" + ], + "split": "train" + }, + { + "Input": "3889 + 12.952 \u2013 ? = 3854.002", + "Output Program": [ + "n0 = 3889.0\nn1 = 12.952\nn2 = 3854.002\nt0 = n0 + n1\nanswer = t0 - n2\nprint(answer)" + ], + "Output Answer": [ + "47.95000000000027" + ], + "split": "train" + }, + { + "Input": "there are 2 sections a and b in a class , consisting of 24 and 16 students respectively . if the average weight of section a is 40 kg and that of section b is 35 kg , find the average of the whole class ?", + "Output Program": [ + "n0 = 2.0\nn1 = 24.0\nn2 = 16.0\nn3 = 40.0\nn4 = 35.0\nt0 = n1 + n2\nt1 = n1 * n3\nt2 = n2 * n4\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "38" + ], + "split": "train" + }, + { + "Input": "if x + 4 y = 5 and 5 x + 6 y = 7 , then 3 x + 5 y = ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 5.0\nn3 = 6.0\nn4 = 7.0\nn5 = 3.0\nn6 = 5.0\nt0 = n1 * n1\nt1 = n0 * n1\nt2 = t0 - n4\nt3 = t1 - n3\nt4 = t2 / t3\nt5 = n1 * t4\nt6 = n0 * t4\nt7 = n1 - t6\nt8 = n5 * t7\nanswer = t5 + t8\nprint(answer)" + ], + "Output Answer": [ + "5.999999999999999" + ], + "split": "train" + }, + { + "Input": "300 first - time customers of a fashion store were surveyed for their shopping experience right after leaving the store . 60 % of the customers in the survey had purchased clothes for less than $ 100 . 40 % of the customers in the survey reported they were overall satisfied with their purchase . 35 % of the customers that had purchased clothes for less than $ 100 reported they were overall satisfied with their purchase . what percent of the customers surveyed purchased clothes for at least $ 100 and reported that they were not overall satisfied with their purchase ?", + "Output Program": [ + "n0 = 300.0\nn1 = 60.0\nn2 = 100.0\nn3 = 40.0\nn4 = 35.0\nn5 = 100.0\nn6 = 100.0\nt0 = n3 / n2\nt1 = n4 / n2\nt2 = n1 / n2\nt3 = n0 * t0\nt4 = n0 * t2\nt5 = t1 * t4\nt6 = t3 - t5\nt7 = t6 / n0\nanswer = t7 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "19.000000000000004" + ], + "split": "train" + }, + { + "Input": "the average weight of 10 persons increases by 6.3 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 10.0\nn1 = 6.3\nn2 = 65.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "128" + ], + "split": "train" + }, + { + "Input": "a charitable association sold an average of 66 raffle tickets per member . among the female members , the average was 70 raffle tickets . the male to female ratio of the association is 1 : 2 . what was the average number t of tickets sold by the male members of the association", + "Output Program": [ + "n0 = 66.0\nn1 = 70.0\nn2 = 1.0\nn3 = 2.0\nt0 = n2 + n3\nt1 = n1 * n3\nt2 = n0 * t0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "58" + ], + "split": "train" + }, + { + "Input": "what is the least whole number that should be added to 625573 if it is to be divisible by 3 ?", + "Output Program": [ + "n0 = 625573.0\nn1 = 3.0\nt0 = n0 - 1.0\nt1 = n1 + t0\nanswer = t1 - n0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "what least number must be subtracted from 2000 to get a number exactly divisible by 17 ?", + "Output Program": [ + "import math\nn0 = 2000.0\nn1 = 17.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "at an upscale fast - food restaurant , shin can buy 3 burgers , 7 shakes , and one cola for $ 120 . at the same place it would cost $ 162.50 for 4 burgers , 10 shakes , and one cola . how much would it cost for a meal of one burger , one shake , and one cola ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 120.0\nn3 = 162.5\nn4 = 4.0\nn5 = 10.0\nt0 = n3 - n2\nt1 = n2 + t0\nt2 = t0 * n0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "simplify : ( 4 + 3 ) + ( 8 - 3 - 1 )", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 8.0\nn3 = 3.0\nn4 = 1.0\nt0 = n0 + n1\nt1 = n2 - n1\nt2 = t1 - n4\nanswer = t0 + t2\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "how many 9 - digits number are palindromic numbers ? a palindromic number reads the same forward and backward , example 123454321 .", + "Output Program": [ + "n0 = 9.0\nn1 = 123454321.0\nt0 = n0 * 10.0\nt1 = t0 * 10.0\nt2 = t1 * 10.0\nanswer = t2 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "90000" + ], + "split": "train" + }, + { + "Input": "on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 305 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?", + "Output Program": [ + "n0 = 305.0\n\nanswer = n0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "610" + ], + "split": "train" + }, + { + "Input": "two pots are in side - by - side . one pot , which is 20 inches tall , casts a shadow that is 10 inches long . the other pot is 40 inches tall . compute , in inches , the length of the shadow that the taller pot casts .", + "Output Program": [ + "n0 = 20.0\nn1 = 10.0\nn2 = 40.0\nt0 = n1 / n0\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "if n is an integer , f ( n ) = f ( n - 1 ) - n and f ( 4 ) = 12 . what is the value of f ( 6 ) ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 12.0\nn3 = 6.0\nt0 = n0 + n1\nt1 = n2 - t0\nanswer = t1 - n3\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "if the charge of staying in a student youth hostel $ 18.00 / day for the first week , and $ 12.00 / day for each additional week , how much does it cost to stay for 23 days ?", + "Output Program": [ + "n0 = 18.0\nn1 = 12.0\nn2 = 23.0\nt0 = 3.0 + 4.0\nt1 = n0 * t0\nt2 = n2 - t0\nt3 = n1 * t2\nanswer = t1 + t3\nprint(answer)" + ], + "Output Answer": [ + "318" + ], + "split": "train" + }, + { + "Input": "when a number is divided by 3 & then multiply by 12 the answer is 9 what is the no . ?", + "Output Program": [ + "n0 = 3.0\nn1 = 12.0\nn2 = 9.0\nt0 = n2 / n1\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "2.25" + ], + "split": "train" + }, + { + "Input": "lucia ' s sells kale at x dollar per pound for the first 20 pounds and . 8 x for every subsequent pound . amby ' s price is x per pound for the first 14 pounds and . 9 x for subsequent pounds . what is the minimum number of pounds over 15 for which lucia ' s becomes an equal or better deal ?", + "Output Program": [ + "n0 = 20.0\nn1 = 8.0\nn2 = 14.0\nn3 = 9.0\nn4 = 15.0\nt0 = n1 / 10.0\nt1 = n3 / 10.0\nt2 = 1.0 / 10.0\nt3 = n0 * t0\nt4 = n2 * t1\nt5 = n0 - t3\nt6 = n2 - t4\nt7 = t5 - t6\nanswer = t7 / t2\nprint(answer)" + ], + "Output Answer": [ + "25.999999999999996" + ], + "split": "train" + }, + { + "Input": "when positive integer x is divided by 11 , the quotient is y and the remainder is 4 . when 2 x is divided by 6 , the quotient is 3 y and the remainder is 1 . what is the value of 7 y \u2013 x ?", + "Output Program": [ + "n0 = 11.0\nn1 = 4.0\nn2 = 2.0\nn3 = 6.0\nn4 = 3.0\nn5 = 1.0\nn6 = 7.0\nt0 = n1 * n2\nt1 = n3 * n4\nt2 = n0 * n2\nt3 = t0 - n5\nt4 = t1 - t2\nt5 = t3 / t4\nt6 = n6 * t5\nt7 = n0 * t5\nt8 = n1 + t7\nanswer = t6 - t8\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "in a certain game , a large bag is filled with blue , green , purple and red chips worth 1 , 5 , x and 11 points each , respectively . the purple chips are worth more than the green chips , but less than the red chips . a certain number of chips are then selected from the bag . if the product of the point values of the selected chips is 140800 , how many purple chips were selected ?", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 11.0\nn3 = 140800.0\n\nanswer = n1 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "evaluate 49 / . 07", + "Output Program": [ + "n0 = 49.0\nn1 = 7.0\nt0 = n1 / 100.0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "699.9999999999999" + ], + "split": "train" + }, + { + "Input": "( 1000 ) 7 \u00f7 ( 10 ) 17 = ?", + "Output Program": [ + "n0 = 1000.0\nn1 = 7.0\nn2 = 10.0\nn3 = 17.0\n\nanswer = n0 * n2\nprint(answer)" + ], + "Output Answer": [ + "10000" + ], + "split": "train" + }, + { + "Input": "a mixture of 200 liters of wine and water contains 20 % water . how much more water should be added so that water becomes 25 % of the new mixture ?", + "Output Program": [ + "n0 = 200.0\nn1 = 20.0\nn2 = 25.0\nt0 = n2 / 100.0\nt1 = n1 / 100.0\nt2 = n0 * t0\nt3 = n0 * t1\nt4 = 1.0 - t0\nt5 = t2 - t3\nanswer = t5 / t4\nprint(answer)" + ], + "Output Answer": [ + "13.333333333333334" + ], + "split": "train" + }, + { + "Input": "the average ( arithmetic mean ) of 5 numbers is 5 . if 2 is subtracted from each of 4 of the numbers , what is the new average ?", + "Output Program": [ + "n0 = 5.0\nn1 = 5.0\nn2 = 2.0\nn3 = 4.0\nt0 = n0 * n0\nt1 = n2 * n3\nt2 = t0 - t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "3.4" + ], + "split": "train" + }, + { + "Input": "one ton has 2300 pounds , and one pound has 16 ounces . how many packets containing wheat weighing 16 pounds and 4 ounces each would totally fill a gunny bag of capacity 13 tons ?", + "Output Program": [ + "n0 = 2300.0\nn1 = 16.0\nn2 = 16.0\nn3 = 4.0\nn4 = 13.0\nt0 = n0 * n4\nt1 = n1 * n1\nt2 = n3 + t1\nt3 = n1 * t0\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "1840" + ], + "split": "train" + }, + { + "Input": "total dinning bill for 10 people was $ 211.00 . if they add 15 % tip and divided the bill evenly , approximate . what was each persons find share", + "Output Program": [ + "n0 = 10.0\nn1 = 211.0\nn2 = 15.0\nt0 = n1 * n2\nt1 = t0 / 100.0\nt2 = n1 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "24.265" + ], + "split": "train" + }, + { + "Input": "on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 330 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?", + "Output Program": [ + "n0 = 330.0\n\nanswer = n0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "660" + ], + "split": "train" + }, + { + "Input": "tourist purchased a total of 30 travelers checks in $ 50 and $ 100 denominations . the total worth of the travelers checks is $ 1800 . how many checks of $ 50 denominations can he spend so that average amount ( arithmetic mean ) of the remaining travelers checks is $ 75 ?", + "Output Program": [ + "n0 = 30.0\nn1 = 50.0\nn2 = 100.0\nn3 = 1800.0\nn4 = 50.0\nn5 = 75.0\nt0 = n0 * n5\nt1 = n5 - n1\nt2 = t0 - n3\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "if x is an integer and 2.134 \u00d7 10 ^ x is less than 21000 , what is the greatest possible value for x ?", + "Output Program": [ + "import math\nn0 = 2.134\nn1 = 10.0\nn2 = 21000.0\nt0 = n2 / n0\nt1 = math.log(max(1e-5, n1), 2)\nt2 = math.log(max(1e-5, t0), 2)\nt3 = t2 / t1\nanswer = math.floor(t3)\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "if there are 200 questions in a 3 hr examination . among these questions are 15 type a problems , which requires twice as much as time be spent than the rest of the type b problems . how many minutes should be spent on type a problems ?", + "Output Program": [ + "n0 = 200.0\nn1 = 3.0\nn2 = 15.0\nt0 = n1 * 60.0\nt1 = n2 * 2.0\nt2 = n0 - n2\nt3 = t1 + t2\nt4 = t0 / t3\nt5 = t4 * 2.0\nanswer = n2 * t5\nprint(answer)" + ], + "Output Answer": [ + "25.116279069767444" + ], + "split": "train" + }, + { + "Input": "of the 3,600 employees of company x , 1 / 3 are clerical . if the clerical staff were to be reduced by 1 / 2 , what percent of the total number of the remaining employees would then be clerical ?", + "Output Program": [ + "n0 = 3600.0\nn1 = 1.0\nn2 = 3.0\nn3 = 1.0\nn4 = 2.0\nt0 = n1 / n2\nt1 = n3 / n4\nt2 = n3 - t1\nt3 = n3 - t0\nt4 = t0 * t2\nt5 = t4 + t3\nt6 = t4 / t5\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "john is 3 times as old as sam . if john will be twice as old as sam in 9 years , how old was sam two years ago ?", + "Output Program": [ + "n0 = 3.0\nn1 = 9.0\nt0 = n1 * 2.0\nt1 = t0 - n1\nanswer = t1 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "\u221a ( 49 ) 2", + "Output Program": [ + "import math\nn0 = 49.0\nn1 = 2.0\nt0 = n0**min(n1, 5)\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "49" + ], + "split": "train" + }, + { + "Input": "8 cups of water are to be poured into a 4 - cup bottle and a 8 - cup bottle . if each bottle is to be filled to the same fraction of its capacity , how many cups of water should be poured into the 8 - cup bottle ?", + "Output Program": [ + "n0 = 8.0\nn1 = 4.0\nn2 = 8.0\nn3 = 8.0\nt0 = n1 + 2.0\nt1 = n0 * 2.0\nt2 = t1 / t0\nanswer = t2 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "5.333333333333333" + ], + "split": "train" + }, + { + "Input": "the average age of a group of n people is 14 years old . one more person aged 32 joins the group and the new average is 15 years old . what is the value of n ?", + "Output Program": [ + "n0 = 14.0\nn1 = 32.0\nn2 = 15.0\nt0 = n1 - n2\nt1 = n2 - n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "the average of 7 numbers is 26 . if each number be multiplied by 5 . find the average of new set of numbers ?", + "Output Program": [ + "n0 = 7.0\nn1 = 26.0\nn2 = 5.0\n\nanswer = n1 * n2\nprint(answer)" + ], + "Output Answer": [ + "130" + ], + "split": "train" + }, + { + "Input": "the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 4 . if the sum of their ages is 88 , what is the difference between the ages of patrick and monica ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 3.0\nn3 = 4.0\nn4 = 88.0\nt0 = n0 * n0\nt1 = n1 * n0\nt2 = n1 * n3\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n4 / t4\nt6 = t5 * t2\nt7 = t5 * t0\nanswer = t6 - t7\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "what is 3 / 7 of 7 / 8 of 1 / 3 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 7.0\nn3 = 8.0\nn4 = 1.0\nn5 = 3.0\nt0 = n0 / n1\nt1 = n1 / n3\nt2 = n4 / n0\nt3 = t1 * t2\nanswer = t0 * t3\nprint(answer)" + ], + "Output Answer": [ + "0.12499999999999997" + ], + "split": "train" + }, + { + "Input": "in a competitive examination in state a , 6 % candidates got selected from the total appeared candidates . state b had an equal number of candidates appeared and 7 % candidates got selected with 82 more candidates got selected than a . what was the number of candidates appeared from each state ?", + "Output Program": [ + "n0 = 6.0\nn1 = 7.0\nn2 = 82.0\nt0 = n1 - n0\nt1 = t0 / 100.0\nanswer = n2 / t1\nprint(answer)" + ], + "Output Answer": [ + "8200" + ], + "split": "train" + }, + { + "Input": "a jogger running at 9 km / hr along side a railway track is 240 m ahead of the engine of a 100 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?", + "Output Program": [ + "n0 = 9.0\nn1 = 240.0\nn2 = 100.0\nn3 = 45.0\nt0 = n1 + n2\nt1 = 10.0 / 2.0\nt2 = n3 - n0\nt3 = t2 / 2.0\nt4 = t1 / t3\nt5 = t4 * t2\nanswer = t0 / t5\nprint(answer)" + ], + "Output Answer": [ + "34" + ], + "split": "train" + }, + { + "Input": "in an election between two candidates a and b , the number of valid votes received by a exceeds those received by b by 15 % of the total number of votes polled . if 20 % of the votes polled were invalid and a total of 8720 votes were polled , then how many valid votes did b get ?", + "Output Program": [ + "n0 = 15.0\nn1 = 20.0\nn2 = 8720.0\nt0 = n1 / 100.0\nt1 = n0 * n2\nt2 = t1 / 100.0\nt3 = 1.0 - t0\nt4 = n2 * t3\nt5 = t4 - t2\nanswer = t5 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "2834" + ], + "split": "train" + }, + { + "Input": "the value of ( 4.7 \u00d7 13.26 + 4.7 \u00d7 9.43 + 4.7 \u00d7 77.31 ) is", + "Output Program": [ + "n0 = 4.7\nn1 = 13.26\nn2 = 4.7\nn3 = 9.43\nn4 = 4.7\nn5 = 77.31\nt0 = n1 + n3\nt1 = n5 + t0\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "470" + ], + "split": "train" + }, + { + "Input": "a , b , c and d enter into partnership . a subscribes 1 / 3 of the capital b 1 / 4 , c 1 / 5 and d the rest . how much share did a get in a profit of rs . 2445 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 4.0\nn4 = 1.0\nn5 = 5.0\nn6 = 2445.0\nt0 = n0 / n1\nanswer = n6 * t0\nprint(answer)" + ], + "Output Answer": [ + "815" + ], + "split": "train" + }, + { + "Input": "the average salary / head of all the workers in a workshop is rs . 1000 , if the average salary / head of 10 technician is rs . 1200 and the average salary / head of the rest is rs . 820 , the total no . of workers in the work - shop is ?", + "Output Program": [ + "n0 = 1000.0\nn1 = 10.0\nn2 = 1200.0\nn3 = 820.0\nt0 = n1 * n2\nt1 = n1 * n3\nt2 = n0 - n3\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "21.11111111111111" + ], + "split": "train" + }, + { + "Input": "the maximum number of student amoung them 1080 pens and 920 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :", + "Output Program": [ + "import scipy\nn0 = 1080.0\nn1 = 920.0\n\nanswer = scipy.gcd(int(n0), int(n1))\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "76 ^ 77 / 7 remainder is ?", + "Output Program": [ + "n0 = 76.0\nn1 = 77.0\nn2 = 7.0\nt0 = n0 - n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "20 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ?", + "Output Program": [ + "n0 = 20.0\nt0 = n0 - 1.0\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "380" + ], + "split": "train" + }, + { + "Input": "the price of commodity x increases by 40 cents every year , while the price of commodity y increases by 15 cents every year . in 2001 , the price of commodity x was $ 4.20 and the price of commodity y was $ 6.30 . in which year will the price of commodity x be 15 cents more than the price of commodity y ?", + "Output Program": [ + "n0 = 40.0\nn1 = 15.0\nn2 = 2001.0\nn3 = 4.2\nn4 = 6.3\nn5 = 15.0\nt0 = n5 / 100.0\nt1 = n0 / 100.0\nt2 = n4 - n3\nt3 = t0 + t2\nt4 = t1 - t2\nt5 = t3 / t4\nanswer = n2 + t5\nprint(answer)" + ], + "Output Answer": [ + "1999.6764705882354" + ], + "split": "train" + }, + { + "Input": "a wholesaler wishes to sell 100 pounds of mixed nuts at $ 2.50 a pound . she mixes peanuts worth $ 3.50 a pound with cashews worth $ 4.00 a pound . how many pounds of cashews must she use ?", + "Output Program": [ + "n0 = 100.0\nn1 = 2.5\nn2 = 3.5\nn3 = 4.0\nt0 = n3 - n1\nt1 = n0 * t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "in a competitive examination in state a , 6 % candidates got selected from the total appeared candidates . state b had an equal number of candidates appeared and 7 % candidates got selected with 83 more candidates got selected than a . what was the number of candidates appeared from each state ?", + "Output Program": [ + "n0 = 6.0\nn1 = 7.0\nn2 = 83.0\nt0 = n1 - n0\nt1 = t0 / 100.0\nanswer = n2 / t1\nprint(answer)" + ], + "Output Answer": [ + "8300" + ], + "split": "train" + }, + { + "Input": "for any integer k > 1 , the term \u201c length of an integer \u201d refers to the number of positive prime factors , not necessarily distinct , whose product is equal to k . for example , if k = 24 , the length of k is equal to 4 , since 24 = 2 \u00d7 2 \u00d7 2 \u00d7 3 . if x and y are positive integers such that x > 1 , y > 1 , and x + 3 y < 902 , what is the maximum possible sum of the length of x and the length of y ?", + "Output Program": [ + "n0 = 1.0\nn1 = 24.0\nn2 = 4.0\nn3 = 24.0\nn4 = 2.0\nn5 = 2.0\nn6 = 2.0\nn7 = 3.0\nn8 = 1.0\nn9 = 1.0\nn10 = 3.0\nn11 = 902.0\nt0 = n2 + n7\nt1 = n2 + n2\nt2 = n0 + t1\nanswer = t0 + t2\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "alice is now 10 years older than bob . if in 6 years alice will be twice as old as bob , how old will alice be in 5 years ?", + "Output Program": [ + "n0 = 10.0\nn1 = 6.0\nn2 = 5.0\nt0 = n0 * 2.0\nt1 = n2 + t0\nanswer = t1 - n1\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "thabo owns exactly 180 books , and each book is either paperback fiction , paperback nonfiction , or hardcover nonfiction . if he owns 20 more paperback nonfiction books than hardcover nonfiction books , and twice as many paperback fiction books as paperback nonfiction books , how many hardcover books nonfiction books does thabo own ?", + "Output Program": [ + "n0 = 180.0\nn1 = 20.0\nt0 = n0 + n1\nt1 = t0 / 4.0\nanswer = t1 - n1\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "a school has 7 maths 6 physics and 5 chemistry teachers each teacher can teach 3 subjects max what is he minimum number of teachers required", + "Output Program": [ + "n0 = 7.0\nn1 = 6.0\nn2 = 5.0\nn3 = 3.0\nt0 = n0 + n1\nt1 = n2 + t0\nanswer = t1 / n3\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 8 eggs . if the cost of each pound of rice is $ 0.36 , then how many cents does a liter of kerosene cost ? [ one dollar has 100 cents . ]", + "Output Program": [ + "n0 = 8.0\nn1 = 0.36\nn2 = 100.0\nt0 = 1.0 / 2.0\nt1 = n1 * n2\nt2 = n0 / t0\nt3 = t2 / 12.0\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "at a certain high school , the senior class is twice the size of the junior class . if 3 / 8 of the seniors and 1 / 4 of the juniors study japanese , what fraction of the students in both classes study japanese ?", + "Output Program": [ + "n0 = 3.0\nn1 = 8.0\nn2 = 1.0\nn3 = 4.0\nt0 = n1 + n3\nanswer = n3 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.3333333333333333" + ], + "split": "train" + }, + { + "Input": "in a school with 604 students , the average age of the boys is 12 years and that of the girls is 11 years . if the average age of the school is 11 years 9 months , then the number of girls in the school is", + "Output Program": [ + "n0 = 604.0\nn1 = 12.0\nn2 = 11.0\nn3 = 11.0\nn4 = 9.0\nt0 = n4 / n1\nt1 = n0 * n1\nt2 = n2 + t0\nt3 = n0 * t2\nanswer = t1 - t3\nprint(answer)" + ], + "Output Answer": [ + "151" + ], + "split": "train" + }, + { + "Input": "a dishonest dealer claims to sell a product at its cost price . he uses a counterfeit weight which is 20 % less than the real weight . further greed overtook him and he added 25 % impurities to the product . find the net profit percentage of the dealer ?", + "Output Program": [ + "n0 = 20.0\nn1 = 25.0\nt0 = n1 + 100.0\nt1 = 100.0 - n0\nt2 = t0 / t1\nt3 = t2 - 1.0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "56.25" + ], + "split": "train" + }, + { + "Input": "in 30 years , a will be twice as old as b was 30 years ago . if a is now 5 years older than b , the present age of b is ?", + "Output Program": [ + "n0 = 30.0\nn1 = 30.0\nn2 = 5.0\nt0 = n0 * 2.0\nt1 = n0 + t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "95" + ], + "split": "train" + }, + { + "Input": "if remainder is 8 , quotient is 43 and dividend is 997 then what is divisor ?", + "Output Program": [ + "n0 = 8.0\nn1 = 43.0\nn2 = 997.0\nt0 = n2 - n0\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "q and r are two - digit positive integers that have the same digits but in reverse order . if the positive difference between q and r is less than 60 , what is the greatest possible value of q minus r ?", + "Output Program": [ + "n0 = 60.0\nt0 = 10.0 - 1.0\nt1 = n0 % t0\nanswer = t1 * t0\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "train" + }, + { + "Input": "there were 35 students in a hostel . due to the admission of 7 new students the expenses of the mess were increased by rs . 84 per day while the average expenditure per head diminished by re 1 . what was the original expenditure of the mess ?", + "Output Program": [ + "n0 = 35.0\nn1 = 7.0\nn2 = 84.0\nn3 = 1.0\nt0 = n0 + n1\nt1 = n2 + t0\nt2 = t1 / n1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "630" + ], + "split": "train" + }, + { + "Input": "if the sum and difference of two numbers are 15 and 10 respectively , then the difference of their square is :", + "Output Program": [ + "n0 = 15.0\nn1 = 10.0\nt0 = n0 + n1\nt1 = t0 / 2.0\nt2 = t1**min(2.0, 5)\nt3 = n0 - t1\nt4 = t3**min(2.0, 5)\nanswer = t2 - t4\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "train" + }, + { + "Input": "in a group of ducks and cows , the total number of legs are 22 more than twice the no . of heads . find the total no . of buffaloes .", + "Output Program": [ + "n0 = 22.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "on dividing 23 by a number , the quotient is 5 and the remainder is 3 . find the divisor .", + "Output Program": [ + "import math\nn0 = 23.0\nn1 = 5.0\nn2 = 3.0\nt0 = n0 / n1\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "( 2 ^ 2 + 4 ^ 2 + 6 ^ 2 + . . . . . + 14 ^ 2 ) = ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 4.0\nn3 = 2.0\nn4 = 6.0\nn5 = 2.0\nn6 = 14.0\nn7 = 2.0\nt0 = n6 + 1.0\nt1 = n4 + 1.0\nt2 = t1 + 1.0\nt3 = n0 * t1\nt4 = t2 * t3\nt5 = t0 * t4\nanswer = t5 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "560" + ], + "split": "train" + }, + { + "Input": "the function f ( x ) = x + 4 is given . solve the equation : [ 3 . f ( x - 2 ) ] / f ( 0 ) + 4 = f ( 2 x + 1 )", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 2.0\nn3 = 0.0\nn4 = 4.0\nn5 = 2.0\nn6 = 1.0\nt0 = n0 + n6\nt1 = n0 * n0\nt2 = n0 * n2\nt3 = n0 - n2\nt4 = n1 * t3\nt5 = n0 * t0\nt6 = t2 - n1\nt7 = t4 + t1\nt8 = t7 - t5\nanswer = t8 / t6\nprint(answer)" + ], + "Output Answer": [ + "0.4" + ], + "split": "train" + }, + { + "Input": "find the largest 6 digit number which is exactly divisible by 88 ?", + "Output Program": [ + "n0 = 6.0\nn1 = 88.0\nt0 = 100.0 * 100.0\nt1 = 10.0 * 100.0\nt2 = 100.0 * 3.0\nt3 = n0 * 10.0\nt4 = t0 + t1\nt5 = t4 + t2\nt6 = t5 + t3\nt7 = t6 + 3.0\nanswer = n1 * t7\nprint(answer)" + ], + "Output Answer": [ + "999944" + ], + "split": "train" + }, + { + "Input": "if the sum of two numbers is 18 and the sum of their squares is 220 , then the product of the numbers is", + "Output Program": [ + "n0 = 18.0\nn1 = 220.0\nt0 = n0**min(2.0, 5)\nt1 = t0 - n1\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "52" + ], + "split": "train" + }, + { + "Input": "how many positive integers less than 10,000 are there in which the sum of the digits equals 5 ?", + "Output Program": [ + "import math\nn0 = 10000.0\nn1 = 5.0\nt0 = n1 + 4.0\nt1 = math.factorial(min(15, int(n1)))\nt2 = 4.0 - 1.0\nt3 = math.factorial(min(15, int(t2)))\nt4 = t0 - 1.0\nt5 = math.factorial(min(15, int(t4)))\nt6 = t1 * t3\nanswer = t5 / t6\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "train" + }, + { + "Input": "if the remainder is 7 when positive integer n is divided by 10 , what is the remainder when n is divided by 5 ?", + "Output Program": [ + "n0 = 7.0\nn1 = 10.0\nn2 = 5.0\n\nanswer = n1 / n2\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "what must be added to each term of the ratio 7 : 11 , so as to make it equal to 3 : 4 ?", + "Output Program": [ + "n0 = 7.0\nn1 = 11.0\nn2 = 3.0\nn3 = 4.0\nt0 = n1 * n2\nt1 = n0 * n3\nt2 = n3 - n2\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "3 friends alice , bond and charlie divide $ 1105 amongs them in such a way that if $ 10 , $ 20 and $ 15 are removed from the sums that alice , bond and charlie received respectively , then the share of the sums that they got will be in the ratio of 11 : 18 : 24 . how much did charlie receive ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1105.0\nn2 = 10.0\nn3 = 20.0\nn4 = 15.0\nn5 = 11.0\nn6 = 18.0\nn7 = 24.0\nt0 = n2 + n3\nt1 = n5 + n6\nt2 = n4 + t0\nt3 = n7 + t1\nt4 = n1 - t2\nt5 = t4 / t3\nt6 = n7 * t5\nanswer = n4 + t6\nprint(answer)" + ], + "Output Answer": [ + "495" + ], + "split": "train" + }, + { + "Input": "mother , her daughter and her grand child weighs 150 kg . daughter and her daughter ( child ) weighs 60 kg . child is 1 / 5 th of her grand mother . what is the age of the daughter ?", + "Output Program": [ + "n0 = 150.0\nn1 = 60.0\nn2 = 1.0\nn3 = 5.0\nt0 = n0 - n1\nt1 = t0 / n3\nanswer = n1 - t1\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "in a weight - lifting competition , the total weight of joe ' s two lifts was 900 pounds . if twice the weight of his first lift was 300 pounds more than the weight of his second lift , what was the weight , in pounds , of his first lift ?", + "Output Program": [ + "n0 = 900.0\nn1 = 300.0\nt0 = n0 + n1\nanswer = t0 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "train" + }, + { + "Input": "if 30 % of ( x - y ) = 20 % of ( x + y ) , then what percent of x is y ?", + "Output Program": [ + "n0 = 30.0\nn1 = 20.0\nt0 = n0 + n1\nt1 = n0 - n1\nt2 = t1 / t0\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "if x is an integer and 2.134 \u00d7 10 ^ x is less than 210,000 , what is the greatest possible value for x ?", + "Output Program": [ + "import math\nn0 = 2.134\nn1 = 10.0\nn2 = 210000.0\nt0 = n2 / n0\nt1 = math.log(max(1e-5, n1), 2)\nt2 = math.log(max(1e-5, t0), 2)\nt3 = t2 / t1\nanswer = math.floor(t3)\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "in a renowned city , the average birth rate is 4 people every two seconds and the death rate is 3 people every two seconds . estimate the size of the population net increase that occurs in one day .", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nt0 = n0 - n1\nt1 = t0 * 3600.0\nanswer = t1 * 12.0\nprint(answer)" + ], + "Output Answer": [ + "43200" + ], + "split": "train" + }, + { + "Input": "in an examination , 300 students appeared . out of these students ; 25 % got first division , 54 % got second division and the remaining just passed . assuming that no student failed ; find the number of students who just passed .", + "Output Program": [ + "n0 = 300.0\nn1 = 25.0\nn2 = 54.0\nt0 = n1 + n2\nt1 = 100.0 - t0\nt2 = n0 * t1\nanswer = t2 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "63" + ], + "split": "train" + }, + { + "Input": "a no . when divided by the sum of 555 and 445 gives 2 times their difference as quotient & 25 as remainder . find the no . is ?", + "Output Program": [ + "n0 = 555.0\nn1 = 445.0\nn2 = 2.0\nn3 = 25.0\nt0 = n0 + n1\nt1 = n0 - n1\nt2 = n2 * t0\nt3 = t2 * t1\nanswer = n3 + t3\nprint(answer)" + ], + "Output Answer": [ + "220025" + ], + "split": "train" + }, + { + "Input": "a father said his son , ` ` i was as old as you are at present at the time of your birth . ` ` if the father age is 32 now , the son age 5 years back was", + "Output Program": [ + "n0 = 32.0\nn1 = 5.0\nt0 = n0 / 2.0\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "in a division sum , the remainder is 0 . as student mistook the divisor by 12 instead of 21 and obtained 56 as quotient . what is the correct quotient ?", + "Output Program": [ + "n0 = 0.0\nn1 = 12.0\nn2 = 21.0\nn3 = 56.0\nt0 = n1 * n3\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "a group of 55 adults and 70 children go for trekking . if there is meal for either 70 adults or 90 children and if 21 adults have their meal , find the total number of children that can be catered with the remaining food .", + "Output Program": [ + "n0 = 55.0\nn1 = 70.0\nn2 = 70.0\nn3 = 90.0\nn4 = 21.0\nt0 = n3 / n1\nt1 = n1 - n4\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "63.00000000000001" + ], + "split": "train" + }, + { + "Input": "rahim bought 42 books for rs . 520 from one shop and 22 books for rs . 248 from another . what is the average price he paid per book ?", + "Output Program": [ + "n0 = 42.0\nn1 = 520.0\nn2 = 22.0\nn3 = 248.0\nt0 = n1 + n3\nt1 = n0 + n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "the smallest number which when diminished by 3 , is divisible by 12 , 16 , 18 , 21 and 28 is", + "Output Program": [ + "n0 = 3.0\nn1 = 12.0\nn2 = 16.0\nn3 = 18.0\nn4 = 21.0\nn5 = 28.0\nt0 = 3.0 + 4.0\nt1 = 3.0**min(2.0, 5)\nt2 = 2.0**min(4.0, 5)\nt3 = t1 * t2\nt4 = t0 * t3\nanswer = t4 + n0\nprint(answer)" + ], + "Output Answer": [ + "1011" + ], + "split": "train" + }, + { + "Input": "the average age of students of a class is 15.8 years . the average age of boys in the class is 16.4 years and that of the girls is 15.2 years , the ratio of the number of boys to the number of girls in the class is", + "Output Program": [ + "n0 = 15.8\nn1 = 16.4\nn2 = 15.2\nt0 = n0 - n2\nt1 = n1 - n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "1.000000000000006" + ], + "split": "train" + }, + { + "Input": "the ratio of the amount of the oil bill for the month of february to the amount of the oil bill for the month of january was 3 : 2 . if the oil bill for february had been $ 20 more , the corresponding ratio would have been 5 : 3 . how much was the oil bill for january ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 20.0\nn3 = 5.0\nn4 = 3.0\nt0 = n3 / n4\nt1 = n0 / n1\nt2 = t0 - t1\nanswer = n2 / t2\nprint(answer)" + ], + "Output Answer": [ + "119.99999999999994" + ], + "split": "train" + }, + { + "Input": "papaya , a popular soft drink , contains only 4 ingredients . soda water comprise 4 / 7 of papaya and natural lemon juice makes 1 / 3 of papaya . the amounts of sugar and papaya puree in papaya are equal . due to a malfunction , the mixing machine mixes double the regular amount of lemon juice and 3 times the regular amount of papaya puree . if no other changes were made to the relative quantities of the ingredients , what is the fractional portion of soda water in the drink that comes out of the malfunctioning machine ?", + "Output Program": [ + "n0 = 4.0\nn1 = 4.0\nn2 = 7.0\nn3 = 1.0\nn4 = 3.0\nn5 = 3.0\nt0 = n0 / n2\nt1 = n2 * n4\nt2 = n2 * 2.0\nt3 = n3 * n4\nt4 = t0 * t1\nt5 = t2 + t4\nt6 = t5 + t3\nt7 = n3 + t6\nanswer = t4 / t7\nprint(answer)" + ], + "Output Answer": [ + "0.4" + ], + "split": "train" + }, + { + "Input": "in an office , totally there are 5200 employees and 45 % of the total employees are males . 50 % of the males in the office are at - least 50 years old . find the number of males aged below 50 years ?", + "Output Program": [ + "n0 = 5200.0\nn1 = 45.0\nn2 = 50.0\nn3 = 50.0\nn4 = 50.0\nt0 = n0 * n1\nt1 = 100.0 - n2\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nanswer = t2 * t3\nprint(answer)" + ], + "Output Answer": [ + "1170" + ], + "split": "train" + }, + { + "Input": "if you write down all the numbers from 1 to 100 , then how many multiples of 3 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 100.0\nn2 = 3.0\nt0 = n1 - 1.0\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "if x + ( 1 / x ) = 5 , what is the value q of x ^ 2 + ( 1 / x ) ^ 2 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 2.0\nn3 = 1.0\nn4 = 2.0\nt0 = n1**min(n2, 5)\nanswer = t0 - n2\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "if 2 ^ 4 , 3 ^ 3 , and 13 ^ 3 are factors of the product of 1452 and w , where w is a positive integer , what is the smallest possible value of w ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 3.0\nn3 = 3.0\nn4 = 13.0\nn5 = 3.0\nn6 = 1452.0\nt0 = n0**min(n0, 5)\nt1 = n2**min(n0, 5)\nt2 = t0 * t1\nanswer = n4 * t2\nprint(answer)" + ], + "Output Answer": [ + "468" + ], + "split": "train" + }, + { + "Input": "in a certain egg - processing plant , every egg must be inspected , and is either accepted for processing or rejected . for every 96 eggs accepted for processing , 4 eggs are rejected . if , on a particular day , 12 additional eggs were accepted , but the overall number of eggs inspected remained the same , the ratio of those accepted to those rejected would be 99 to 1 . how many w eggs does the plant process per day ?", + "Output Program": [ + "n0 = 96.0\nn1 = 4.0\nn2 = 12.0\nn3 = 99.0\nn4 = 1.0\nt0 = n3 - n0\nt1 = n2 / t0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "train" + }, + { + "Input": "when anunfaircoin is tossed twice , the probability of getting one tails and one heads is 1 / 2 . what is the probability of getting two heads and two tails if the coin is tossed 4 times ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 4.0\nt0 = n0 / 1.0\nt1 = n0 * 1.0\nt2 = n1 + t1\nt3 = t2 * 3.0\nanswer = t0 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.1111111111111111" + ], + "split": "train" + }, + { + "Input": "two employees x and y are paid a total of rs . 570 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?", + "Output Program": [ + "n0 = 570.0\nn1 = 120.0\nt0 = 1.0 + 4.0\nt1 = t0 * 2.0\nt2 = t1 + 1.0\nt3 = n0 * t1\nt4 = t2 * 2.0\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "259.09090909090907" + ], + "split": "train" + }, + { + "Input": "the average of 6 number is 3.95 . the average of two of them is 3.8 , while the average of the other two is 3.85 . what is the average of the remaining two number ?", + "Output Program": [ + "n0 = 6.0\nn1 = 3.95\nn2 = 3.8\nn3 = 3.85\nt0 = n0 * n1\nt1 = n2 * 2.0\nt2 = n3 * 2.0\nt3 = t1 + t2\nt4 = t0 - t3\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "4.200000000000001" + ], + "split": "train" + }, + { + "Input": "a basketball team composed of 12 players scored 100 points in a particular contest . if none of the individual players scored fewer than 7 points , what is the greatest number of points q that an individual player might have scored ?", + "Output Program": [ + "n0 = 12.0\nn1 = 100.0\nn2 = 7.0\nt0 = n0 * n2\nt1 = n1 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "jill has 7 gallons of water stored in quart , half - gallon , and one gallon jars . she has equal numbers of each size jar holding the liquid . what is the total number of water filled jars ?", + "Output Program": [ + "n0 = 7.0\nt0 = 1.0 / 2.0\nt1 = t0 + 0.25\nt2 = t1 + 1.0\nt3 = n0 / t2\nanswer = t3 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "the sum of ages of 5 children born 2 years different each is 50 yrs . what is the age of the elder child ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 50.0\nt0 = n1 + 4.0\nt1 = 4.0 + 4.0\nt2 = t0 + t0\nt3 = t2 + t1\nt4 = n2 + t3\nanswer = t4 / n0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "we bought a total of 80 books at the store . math books cost $ 4 and history books cost $ 5 . the total price was $ 390 . how many math books did we buy ?", + "Output Program": [ + "n0 = 80.0\nn1 = 4.0\nn2 = 5.0\nn3 = 390.0\nt0 = n0 * n1\nt1 = n3 - t0\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the price of a certain painting increased by 10 % during the first year and decreased by 15 % during the second year . the price of the painting at the end of the 2 - year period was what percent of the original price ?", + "Output Program": [ + "n0 = 10.0\nn1 = 15.0\nn2 = 2.0\nt0 = n0 * n1\nt1 = n0 - n1\nt2 = t0 / 100.0\nt3 = t1 - t2\nanswer = t3 + 100.0\nprint(answer)" + ], + "Output Answer": [ + "93.5" + ], + "split": "train" + }, + { + "Input": "dacid obtained 86 , 89 , 82 , 87 and 81 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?", + "Output Program": [ + "n0 = 86.0\nn1 = 89.0\nn2 = 82.0\nn3 = 87.0\nn4 = 81.0\nn5 = 100.0\nt0 = n0 + n1\nt1 = 10.0 / 2.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "85" + ], + "split": "train" + }, + { + "Input": "how many different 3 - digit multiples of 5 can be composed of digits 1 , 2 , 3 , 4 , and 5 if none of the digits is repeated ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 1.0\nn3 = 2.0\nn4 = 3.0\nn5 = 4.0\nn6 = 5.0\nt0 = n0 * n5\nanswer = t0 - n5\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a student finds the sum 1 + 2 + 3 + . . . as his patience runs out . he found the sum as 575 . when the teacher declared the result wrong , the student realized that he missed a number . what was the number the student missed ?", + "Output Program": [ + "import math\nn0 = 1.0\nn1 = 2.0\nn2 = 3.0\nn3 = 575.0\nt0 = n1 * n3\nt1 = t0 * 4.0\nt2 = n0 + t1\nt3 = math.sqrt(max(0, t2))\nt4 = t3 - n0\nt5 = t4 / 2.0\nt6 = math.floor(t5)\nt7 = n0 + t6\nt8 = n0 + t7\nt9 = t7 * t8\nt10 = t9 / n1\nanswer = t10 - n3\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "dhoni spends $ 300 buying his favorite dolls . if he buys only small monkey dolls , which are $ 2 cheaper than the large monkey dolls , he could buy 25 more dolls than if he were to buy only large monkey dolls . how much does a large monkey doll cost ?", + "Output Program": [ + "n0 = 300.0\nn1 = 2.0\nn2 = 25.0\nt0 = n0 / n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "find the principle on a certain sum of money at 8 % per annum for 2 2 / 5 years if the amount being rs . 1120 ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.0\nn2 = 2.0\nn3 = 5.0\nn4 = 1120.0\nt0 = n1 * n3\nt1 = n1 + t0\nt2 = t1 / n3\nt3 = n0 * t2\nt4 = t3 / 100.0\nt5 = t4 + 1.0\nanswer = n4 / t5\nprint(answer)" + ], + "Output Answer": [ + "939.5973154362416" + ], + "split": "train" + }, + { + "Input": "the average salary of all the workers in a workshop is rs . 8000 . the average salary of 10 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is :", + "Output Program": [ + "n0 = 8000.0\nn1 = 10.0\nn2 = 12000.0\nn3 = 6000.0\nt0 = n2 - n0\nt1 = n0 - n3\nt2 = n1 * t0\nt3 = t2 / t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "what is the remainder when 14452 \u00d7 15652 \u00d7 16781 is divided by 5 ?", + "Output Program": [ + "n0 = 14452.0\nn1 = 15652.0\nn2 = 16781.0\nn3 = 5.0\nt0 = n0 * n1\nt1 = n2 * t0\nanswer = t1 % n3\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "there are 2 friends peter and paul . peter age is twice as old as paul when peter was as old as paul is now . sum of the present ages of peter and paul is 35 . what is the present age of peter ?", + "Output Program": [ + "n0 = 2.0\nn1 = 35.0\nt0 = 3.0 + 4.0\nt1 = n1 / t0\nanswer = t1 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "8 % people of a village in sri lanka died by bombardment , 15 % of the remainder left the village on account of fear . if now the population is reduced to 3553 , how much was it in the beginning ?", + "Output Program": [ + "import math\nn0 = 8.0\nn1 = 15.0\nn2 = 3553.0\nt0 = 100.0 - n0\nt1 = 100.0 - n1\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = t2 * t3\nt5 = n2 / t4\nanswer = math.floor(t5)\nprint(answer)" + ], + "Output Answer": [ + "4543" + ], + "split": "train" + }, + { + "Input": "how many different values of positive integer x , for which | x + 4 | < x , are there ?", + "Output Program": [ + "n0 = 4.0\n\nanswer = n0 + 4.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a car travels uphill at 30 km / hr and downhill at 70 km / hr . it goes 100 km uphill and 50 km downhill . find the average speed of the car ?", + "Output Program": [ + "n0 = 30.0\nn1 = 70.0\nn2 = 100.0\nn3 = 50.0\nt0 = n2 + n3\nt1 = n2 / n0\nt2 = n3 / n1\nt3 = t1 + t2\nanswer = t0 / t3\nprint(answer)" + ], + "Output Answer": [ + "37.05882352941177" + ], + "split": "train" + }, + { + "Input": "vlaudia can choose any two of 4 different candles and any 8 of 9 different flowers for a centerpiece arrangement . given these choices , how many candle + flower groupings can she select ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 8.0\nn2 = 9.0\nt0 = math.factorial(min(15, int(n2)))\nt1 = math.factorial(min(15, int(n1)))\nt2 = math.factorial(min(15, int(n0)))\nt3 = 2.0 * 2.0\nt4 = t0 / t1\nt5 = t2 / t3\nanswer = t4 * t5\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "train" + }, + { + "Input": "there are 15 teams in a soccer league and each team plays each of the other teams once . how many games will be played in total ?", + "Output Program": [ + "import math\nn0 = 15.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(2.0)))\nt2 = n0 - 2.0\nt3 = math.factorial(min(15, int(t2)))\nt4 = t3 * t1\nanswer = t0 / t4\nprint(answer)" + ], + "Output Answer": [ + "105" + ], + "split": "train" + }, + { + "Input": "rahim bought 65 books for rs . 6500 from one shop and 35 books for rs . 2000 from another . what is the average price he paid per book ?", + "Output Program": [ + "n0 = 65.0\nn1 = 6500.0\nn2 = 35.0\nn3 = 2000.0\nt0 = n1 + n3\nt1 = n0 + n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "85" + ], + "split": "train" + }, + { + "Input": "a man engaged a servant on the condition that he would pay him rs . 800 and a uniform after one year service . he served only for 9 months and received uniform and rs . 400 , find the price of the uniform ?", + "Output Program": [ + "n0 = 800.0\nn1 = 9.0\nn2 = 400.0\nt0 = n0 * n1\nt1 = 3.0 * 4.0\nt2 = n2 * t1\nt3 = t1 * 1.0\nt4 = t0 - t2\nt5 = t4 / t3\nanswer = t5 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "800" + ], + "split": "train" + }, + { + "Input": "a computer manufacturer produces a certain electronic component at a cost of $ 80 per component . shipping costs for delivering the components are $ 7 per unit . further , the manufacturer has costs of $ 16,500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 150 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?", + "Output Program": [ + "n0 = 80.0\nn1 = 7.0\nn2 = 16500.0\nn3 = 150.0\nt0 = n0 + n1\nt1 = 4.0 * 4.0\nt2 = n1 * 100.0\nt3 = t1 * 1000.0\nt4 = n3 * t0\nt5 = t3 + t2\nt6 = t5 + t4\nanswer = t6 / n3\nprint(answer)" + ], + "Output Answer": [ + "198.33333333333334" + ], + "split": "train" + }, + { + "Input": "in a race where 12 cars are running , the chance that car x will win is 1 / 6 , that y will win is 1 / 10 and that z will win is 1 / 8 . assuming that a dead heat is impossible , find the chance that one of them will win .", + "Output Program": [ + "n0 = 12.0\nn1 = 1.0\nn2 = 6.0\nn3 = 1.0\nn4 = 10.0\nn5 = 1.0\nn6 = 8.0\nt0 = n1 / n2\nt1 = n1 / n4\nt2 = n1 / n6\nt3 = t0 + t1\nanswer = t3 + t2\nprint(answer)" + ], + "Output Answer": [ + "0.39166666666666666" + ], + "split": "train" + }, + { + "Input": "mary ' s income is 60 % more than tim ' s income and tim ' s income is 30 % less than juan ' s income . what % of juan ' s income is mary ' s income .", + "Output Program": [ + "n0 = 60.0\nn1 = 30.0\nt0 = n0 / 100.0\nt1 = 100.0 - n1\nt2 = t0 * t1\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "112" + ], + "split": "train" + }, + { + "Input": "a telephone company needs to create a set of 3 - digit area codes . the company is entitled to use only digits 2 , 4 and 5 , which can be repeated . if the product of the digits in the area code must be even , how many different codes can be created ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 4.0\nn3 = 5.0\nt0 = n0**min(3.0, 5)\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "which no . need to add to 859622 to get a number exactly divisible by 456 ?", + "Output Program": [ + "n0 = 859622.0\nn1 = 456.0\nt0 = n0 % n1\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "859560" + ], + "split": "train" + }, + { + "Input": "a part - time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee ' s total income did not change . by what percent e should the number of hours worked be increased ?", + "Output Program": [ + "n0 = 20.0\nt0 = 10.0 * 4.0\nt1 = 100.0 - n0\nt2 = t1 / 100.0\nt3 = t2 * 10.0\nt4 = t0 / t3\nt5 = t4 - 4.0\nt6 = t5 / 4.0\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "a number when divided by 221 gives a remainder 43 , what remainder will be obtained by dividing the same number 17 ?", + "Output Program": [ + "n0 = 221.0\nn1 = 43.0\nn2 = 17.0\nt0 = n2 * 2.0\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "in a bus left side are 15 seats available , 3 few seats in right side because in rear exit door . each seat hold 3 people . in addition , there is a seat back can sit 7 people all together . how many people can sit in a bus ?", + "Output Program": [ + "n0 = 15.0\nn1 = 3.0\nn2 = 3.0\nn3 = 7.0\nt0 = n0 - n1\nt1 = n0 + t0\nt2 = n1 * t1\nanswer = n3 + t2\nprint(answer)" + ], + "Output Answer": [ + "88" + ], + "split": "train" + }, + { + "Input": "a worker ' s take - home pay last year was the same each month , and she saved the same fraction of her take - home pay each month . the total amount of money that she had saved at the end of the year was 2 times the amount of that portion of her monthly take - home pay that she did not save . if all the money that she saved last year was from her take - home pay , what fraction of her take - home pay did she save each month ?", + "Output Program": [ + "n0 = 2.0\nt0 = 12.0 / n0\nt1 = t0 + 1.0\nanswer = 1 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.14285714285714285" + ], + "split": "train" + }, + { + "Input": "a sum of money lent out at s . i . amounts to a total of $ 520 after 2 years and to $ 820 after a further period of 5 years . what was the initial sum of money that was invested ?", + "Output Program": [ + "n0 = 520.0\nn1 = 2.0\nn2 = 820.0\nn3 = 5.0\nt0 = n1 / n3\nt1 = n2 - n0\nt2 = t0 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "train" + }, + { + "Input": "what is the average of first 21 multiples of 5 ?", + "Output Program": [ + "n0 = 21.0\nn1 = 5.0\nt0 = n0 + 1.0\nt1 = n0 * t0\nt2 = t1 / 2.0\nt3 = t2 / n0\nanswer = n1 * t3\nprint(answer)" + ], + "Output Answer": [ + "55" + ], + "split": "train" + }, + { + "Input": "given that e and f are events such that p ( e ) = 25 , p ( f ) = 75 and p ( e n f ) = 75 , find p ( e | f ) and p ( f | e )", + "Output Program": [ + "n0 = 25.0\nn1 = 75.0\nn2 = 75.0\n\nanswer = n1 / n0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "if 360 is divided into 4 parts proportional to 5 , 7 , 4 , 8 then the smallest part is :", + "Output Program": [ + "n0 = 360.0\nn1 = 4.0\nn2 = 5.0\nn3 = 7.0\nn4 = 4.0\nn5 = 8.0\nt0 = n2 + n3\nt1 = n1 + t0\nt2 = n5 + t1\nt3 = n1 / t2\nanswer = n0 * t3\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "a scale 10 ft . 5 inches long is divided into 5 equal parts . find the length of each part .", + "Output Program": [ + "n0 = 10.0\nn1 = 5.0\nn2 = 5.0\nt0 = n0 * 12.0\nt1 = n1 + t0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "the value of ( 4.7 \u00d7 13.26 + 4.7 \u00d7 9.43 + 4.7 \u00d7 77.31 ) is :", + "Output Program": [ + "n0 = 4.7\nn1 = 13.26\nn2 = 4.7\nn3 = 9.43\nn4 = 4.7\nn5 = 77.31\nt0 = n1 + n3\nt1 = n5 + t0\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "470" + ], + "split": "train" + }, + { + "Input": "an ant walks an average of 500 meters in 60 minutes . a beetle walks 15 % less distance at the same time on the average . assuming the beetle walks at her regular rate , what is its speed in km / h ?", + "Output Program": [ + "n0 = 500.0\nn1 = 60.0\nn2 = 15.0\nt0 = n0 / 1000.0\nt1 = n1 / 60.0\nt2 = n2 / 100.0\nt3 = t0 / t1\nt4 = 1.0 - t2\nanswer = t3 * t4\nprint(answer)" + ], + "Output Answer": [ + "0.425" + ], + "split": "train" + }, + { + "Input": "a tank holds x gallons of a saltwater solution that is 20 % salt by volume . one fourth of the water is evaporated , leaving all of the salt . when 10 gallons of water and 20 gallons of salt are added , the resulting mixture is 33 1 / 3 % salt by volume . what is the value of x ?", + "Output Program": [ + "n0 = 20.0\nn1 = 10.0\nn2 = 20.0\nn3 = 33.0\nn4 = 1.0\nn5 = 3.0\nt0 = n0 / 100.0\nt1 = n4 / 4.0\nt2 = n2 * 2.0\nt3 = t0 * 2.0\nt4 = t2 - n1\nt5 = n4 - t0\nt6 = t1 * t5\nt7 = t5 - t6\nt8 = t7 - t3\nanswer = t4 / t8\nprint(answer)" + ], + "Output Answer": [ + "149.99999999999994" + ], + "split": "train" + }, + { + "Input": "roses can be purchased individually for $ 2.30 , one dozen for $ 36 , or two dozen for $ 50 . what is the greatest number of roses that can be purchased for $ 680 ?", + "Output Program": [ + "import math\nn0 = 2.3\nn1 = 36.0\nn2 = 50.0\nn3 = 680.0\nt0 = n3 / n2\nt1 = 12.0 * 2.0\nt2 = math.floor(t0)\nt3 = n2 * t2\nt4 = t2 * t1\nt5 = n3 - t3\nt6 = t5 / n0\nt7 = math.floor(t6)\nanswer = t7 + t4\nprint(answer)" + ], + "Output Answer": [ + "325" + ], + "split": "train" + }, + { + "Input": "in the land of oz only one or two - letter words are used . the local language has 65 different letters . the parliament decided to forbid the use of the seventh letter . how many words have the people of oz lost because of the prohibition ?", + "Output Program": [ + "n0 = 65.0\nt0 = n0 + 1.0\nanswer = n0 + t0\nprint(answer)" + ], + "Output Answer": [ + "131" + ], + "split": "train" + }, + { + "Input": "baker ram is storing cake boxes in cartons that measure 25 inches by 42 inches by 60 inches . if the measurement of each cake box is 8 inches by 7 inches by 5 inches , then what is the maximum number of cake boxes that can be placed in each carton ?", + "Output Program": [ + "n0 = 25.0\nn1 = 42.0\nn2 = 60.0\nn3 = 8.0\nn4 = 7.0\nn5 = 5.0\nt0 = 2.0 + 4.0\nt1 = n4 * t0\nanswer = n5 * t1\nprint(answer)" + ], + "Output Answer": [ + "210" + ], + "split": "train" + }, + { + "Input": "a 40 - liter solution of alcohol and water is 5 percent alcohol . if 4.5 liters of alcohol and 5.5 liters of water are added to this solution , what percent of the solution produced is alcohol ?", + "Output Program": [ + "n0 = 40.0\nn1 = 5.0\nn2 = 4.5\nn3 = 5.5\nt0 = n2 + n3\nt1 = n1 / 100.0\nt2 = n0 + t0\nt3 = n0 * t1\nt4 = n2 + t3\nt5 = t4 / t2\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "the average of the marks of 12 students in a class is 36 . if the marks of each student are doubled , find the new average ?", + "Output Program": [ + "n0 = 12.0\nn1 = 36.0\n\nanswer = n1 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "train" + }, + { + "Input": "if 3 ^ x * 4 ^ y = 19683 and x \u2013 y = 9 , then x = ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 19683.0\nn3 = 9.0\n\nanswer = n3 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 210 only . men \u00e2 \u20ac \u2122 s wages are ?", + "Output Program": [ + "n0 = 5.0\nn1 = 8.0\nn2 = 210.0\nt0 = n0 * 3.0\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "a person decided to build a house in 100 days . he employed 100 men in the beginning and 100 more after 50 days and completed the construction in stipulated time . if he had not employed the additional men , how many days behind schedule would it have been finished ?", + "Output Program": [ + "n0 = 100.0\nn1 = 100.0\nn2 = 100.0\nn3 = 50.0\n\nanswer = n0 - n3\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "if x + y = 24 , x - y = 40 , for integers of x and y , x = ?", + "Output Program": [ + "n0 = 24.0\nn1 = 40.0\nt0 = n0 + n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "if 222 = 6 333 = 12 444 = 20 then , 555 = ? ?", + "Output Program": [ + "n0 = 222.0\nn1 = 6.0\nn2 = 333.0\nn3 = 12.0\nn4 = 444.0\nn5 = 20.0\nn6 = 555.0\nt0 = 2.0 + 3.0\nanswer = n1 * t0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "if f ( x ) = 5 - 2 x , then f - 1 ( - 3 ) = ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 1.0\nn3 = 3.0\nt0 = n3 - n2\nt1 = t0 / n1\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "joan and karl each bought a telescopes and the sum of their purchases was $ 400 . if twice of what joan paid was $ 74 more than what karl paid , what did joan pay for her telescope ?", + "Output Program": [ + "n0 = 400.0\nn1 = 74.0\nt0 = n0 * 2.0\nt1 = t0 - n1\nt2 = t1 / 3.0\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "158" + ], + "split": "train" + }, + { + "Input": "a parking garage rents parking spaces for $ 10 per week or $ 40 per month . how much does a person save in a year by renting by the month rather than by the week ?", + "Output Program": [ + "n0 = 10.0\nn1 = 40.0\nt0 = 2.0 + 3.0\nt1 = n1 * 12.0\nt2 = t0 * n0\nt3 = t2 + 2.0\nt4 = n0 * t3\nanswer = t4 - t1\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "10 play kabadi , 20 play kho kho only , 5 play both gmaes . then how many in total ?", + "Output Program": [ + "n0 = 10.0\nn1 = 20.0\nn2 = 5.0\nt0 = n1 + n2\nt1 = n0 + t0\nanswer = t1 - n2\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 210 games will be played during the tournament . what is the number of participants ?", + "Output Program": [ + "import math\nn0 = 210.0\nt0 = n0 * 2.0\nt1 = t0 * 4.0\nt2 = t1 + 1.0\nt3 = math.sqrt(max(0, t2))\nt4 = t3 + 1.0\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "if a ( a - 6 ) = 7 and b ( b - 6 ) = 7 , where a \u2260 b , then a + b =", + "Output Program": [ + "n0 = 6.0\nn1 = 7.0\nn2 = 6.0\nn3 = 7.0\nt0 = 4.0 + n1\nt1 = n0 - n1\nt2 = t0 + t1\nt3 = t2 - 1.0\nt4 = t3 - 1.0\nt5 = t4 - 1.0\nanswer = t5 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "the average of 13 numbers is 60 . average of the first 6 of them is 57 and that of the last 8 is 61 . find the 8 th number ?", + "Output Program": [ + "n0 = 13.0\nn1 = 60.0\nn2 = 6.0\nn3 = 57.0\nn4 = 8.0\nn5 = 61.0\nn6 = 8.0\nt0 = n5 * n6\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 - t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 22 , then how old is b ?", + "Output Program": [ + "n0 = 22.0\nt0 = 2.0 + 3.0\nt1 = n0 - 2.0\nt2 = t1 / t0\nanswer = t2 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "in a fuel station the service costs $ 2.20 per vehicle and every liter of fuel costs $ 0.70 . assuming that you fill up 3 mini - vans and 2 trucks , what will be the total cost , if a mini - van ' s tank is 65 liters and a truck ' s tank is 120 % bigger and they are all empty ?", + "Output Program": [ + "n0 = 2.2\nn1 = 0.7\nn2 = 3.0\nn3 = 2.0\nn4 = 65.0\nn5 = 120.0\nt0 = n2 + n3\nt1 = n4 * n5\nt2 = n2 * n4\nt3 = t1 / 100.0\nt4 = n1 * t2\nt5 = n0 * t0\nt6 = n4 + t3\nt7 = n3 * t6\nt8 = n1 * t7\nt9 = t8 + t4\nanswer = t9 + t5\nprint(answer)" + ], + "Output Answer": [ + "347.7" + ], + "split": "train" + }, + { + "Input": "john want to buy a $ 100 trouser at the store , but he think it \u2019 s too expensive . finally , it goes on sale for $ 30 . what is the percent decrease ?", + "Output Program": [ + "n0 = 100.0\nn1 = 30.0\n\nanswer = n0 - n1\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "train" + }, + { + "Input": "for the symbol , m \u201d n = n ^ 2 \u2212 m for all values of m and n . what is the value of 5 \u201d 3 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 3.0\nt0 = n2**min(n0, 5)\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "there are 408 boys and 312 girls in a school which are to be divided into equal sections of either boys or girls alone . find the total number of sections thus formed .", + "Output Program": [ + "n0 = 408.0\nn1 = 312.0\nt0 = n0 + n1\nt1 = 2.0 * 2.0\nt2 = t1 * 2.0\nt3 = t2 * 3.0\nanswer = t0 / t3\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "in 20 years , a will be twice as old as b was 20 years ago . if a is now 10 years older than b , the present age of b is ?", + "Output Program": [ + "n0 = 20.0\nn1 = 20.0\nn2 = 10.0\nt0 = n0 * 2.0\nt1 = n0 + t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "train" + }, + { + "Input": "if a 10 percent deposit that has been paid toward the purchase of a certain product is $ 105 , how much more remains to be paid ?", + "Output Program": [ + "n0 = 10.0\nn1 = 105.0\nt0 = 100.0 / n0\nt1 = n1 * t0\nanswer = t1 - n1\nprint(answer)" + ], + "Output Answer": [ + "945" + ], + "split": "train" + }, + { + "Input": "in the biology lab of ` ` jefferson ' ' high school there are 5.4 * 10 ^ 6 germs , equally divided among 10,800 petri dishes . how many germs live happily in a single dish ?", + "Output Program": [ + "n0 = 5.4\nn1 = 10.0\nn2 = 6.0\nn3 = 10800.0\nt0 = 100.0 * 100.0\nt1 = 2.0 * 4.0\nt2 = t0 * 100.0\nt3 = t1 * 100.0\nt4 = t0 + t3\nt5 = n0 * t2\nanswer = t5 / t4\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "train" + }, + { + "Input": "a part - time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee ' s total income did not change . by what percent r should the number of hours worked be increased ?", + "Output Program": [ + "n0 = 20.0\nt0 = 10.0 * 4.0\nt1 = 100.0 - n0\nt2 = t1 / 100.0\nt3 = t2 * 10.0\nt4 = t0 / t3\nt5 = t4 - 4.0\nt6 = t5 / 4.0\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "a grocery shop has a sale of rs . 6535 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ?", + "Output Program": [ + "n0 = 6535.0\nn1 = 6927.0\nn2 = 6855.0\nn3 = 7230.0\nn4 = 6562.0\nn5 = 5.0\nn6 = 6500.0\nt0 = n5 + 1.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n6 * t0\nt4 = n3 + t2\nt5 = n4 + t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "4891" + ], + "split": "train" + }, + { + "Input": "how many times will the digit 7 be written when listing the integers from 1 to 1000 ?", + "Output Program": [ + "n0 = 7.0\nn1 = 1.0\nn2 = 1000.0\nt0 = n1 * 10.0\nt1 = t0 * 10.0\nanswer = t1 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "the average salary of a person for the months of january , february , march and april is rs . 8000 and that for the months february , march , april and may is rs . 8450 . if his salary for the month of may is rs . 6500 , find his salary for the month of january ?", + "Output Program": [ + "n0 = 8000.0\nn1 = 8450.0\nn2 = 6500.0\nt0 = n0 * 4.0\nt1 = n1 * 4.0\nt2 = t1 - n2\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "4700" + ], + "split": "train" + }, + { + "Input": "a student was asked to find 4 / 5 of a number . but the student divided the number by 4 / 5 , thus the student got 45 more than the correct answer . find the number .", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 4.0\nn3 = 5.0\nn4 = 45.0\nt0 = n0 / n1\nt1 = n4 * t0\nt2 = t0 * t0\nt3 = t0 * t1\nt4 = 1.0 - t2\nt5 = t3 / t4\nanswer = t5 / t0\nprint(answer)" + ], + "Output Answer": [ + "100.00000000000003" + ], + "split": "train" + }, + { + "Input": "if 2 + 7 = 57 ; 3 + 6 = 63 ; 5 + 9 = 206 then 4 + 8 = ?", + "Output Program": [ + "n0 = 2.0\nn1 = 7.0\nn2 = 57.0\nn3 = 3.0\nn4 = 6.0\nn5 = 63.0\nn6 = 5.0\nn7 = 9.0\nn8 = 206.0\nn9 = 4.0\nn10 = 8.0\nt0 = n9**min(3.0, 5)\nt1 = n10**min(2.0, 5)\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "128" + ], + "split": "train" + }, + { + "Input": "if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer q that must divide n is ?", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 72.0\nt0 = n1 / n0\nt1 = math.sqrt(max(0, t0))\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "the value of ( 2.502 + 0.064 ) ^ 2 - ( 2.502 - 0.064 ) ^ 2 / 2.502 * 0.064", + "Output Program": [ + "n0 = 2.502\nn1 = 0.064\nn2 = 2.0\nn3 = 2.502\nn4 = 0.064\nn5 = 2.0\nn6 = 2.502\nn7 = 0.064\nt0 = n0 + n1\nt1 = n0 * n1\nt2 = n0 - n1\nt3 = t0**min(2.0, 5)\nt4 = t2**min(2.0, 5)\nt5 = t3 - t4\nanswer = t5 / t1\nprint(answer)" + ], + "Output Answer": [ + "4.000000000000002" + ], + "split": "train" + }, + { + "Input": "a , b and c have rs . 500 between them , a and c together have rs . 200 and b and c rs . 320 . how much does c have ?", + "Output Program": [ + "n0 = 500.0\nn1 = 200.0\nn2 = 320.0\nt0 = n1 + n2\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "sally has a gold credit card with a certain spending limit , and a platinum card with twice the spending limit of the gold card . currently , she has a balance on her gold card that is 1 / 3 of the spending limit on that card , and she has a balance on her platinum card that is 1 / 6 of the spending limit on that card . if sally transfers the entire balance on her gold card to her platinum card , what portion of her limit on the platinum card will remain unspent ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 6.0\nt0 = 1 / n3\nt1 = 1 / n1\nt2 = 1 / 2.0\nt3 = t1 * t2\nt4 = t0 + t3\nanswer = n0 - t4\nprint(answer)" + ], + "Output Answer": [ + "0.6666666666666667" + ], + "split": "train" + }, + { + "Input": "the average weight of a , b and c is 45 kg . if the average weight of a and b be 40 kg and that of b and c be 44 kg , then the weight of b is :", + "Output Program": [ + "n0 = 45.0\nn1 = 40.0\nn2 = 44.0\nt0 = n1 * 2.0\nt1 = n2 * 2.0\nt2 = n0 * 3.0\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "a car salesman earns a base salary of $ 1000 per month plus a commission of $ 200 for each car he sells . if the car salesman earned $ 1800 in january , how many cars does he need to sell in february in order to double his january earnings ?", + "Output Program": [ + "n0 = 1000.0\nn1 = 200.0\nn2 = 1800.0\nt0 = n2 * 2.0\nt1 = t0 - n0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "a \u2019 s speed is 22 / 19 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?", + "Output Program": [ + "n0 = 22.0\nn1 = 19.0\nt0 = n0 - n1\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.13636363636363635" + ], + "split": "train" + }, + { + "Input": "the average weight of 8 girls increases by 3 kg when a new girl comes in place of one of them weighing 70 kg . what might be the weight of the new girl ?", + "Output Program": [ + "n0 = 8.0\nn1 = 3.0\nn2 = 70.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "94" + ], + "split": "train" + }, + { + "Input": "if t = 5 / 9 * ( k - 32 ) , and if t = 35 , then what is the value of k ?", + "Output Program": [ + "n0 = 5.0\nn1 = 9.0\nn2 = 32.0\nn3 = 35.0\nt0 = n1 * n3\nt1 = t0 / n0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "95" + ], + "split": "train" + }, + { + "Input": "a certain number of horses and an equal number of men are going somewhere . half of the owners are on their horses ' back while the remaining ones are walking along leading their horses . if the number of legs walking on the ground is 50 , how many horses are there ?", + "Output Program": [ + "n0 = 50.0\nt0 = 2.0 / 2.0\nt1 = t0 + 4.0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "in 1990 the budgets for projects q and v were $ 540000 and $ 780000 , respectively . in each of the next 10 years , the budget for q was increased by $ 30000 and the budget for v was decreased by $ 10000 . in which year was the budget for q equal to the budget for v ?", + "Output Program": [ + "n0 = 1990.0\nn1 = 540000.0\nn2 = 780000.0\nn3 = 10.0\nn4 = 30000.0\nn5 = 10000.0\n\nanswer = n0 + 4.0\nprint(answer)" + ], + "Output Answer": [ + "1994" + ], + "split": "train" + }, + { + "Input": "in a colony the municipality decided to number the houses and the shops . they want to number the shops with the numbers containing 3 between 1 - 100 . the houses are 10 - 20 floored and at the back of the houses 8 feet is left for fire exit . how many shops can be numbered ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 100.0\nn3 = 10.0\nn4 = 20.0\nn5 = 8.0\nt0 = n0 * n3\nt1 = t0 - n3\nanswer = t1 - n1\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "a sporting goods store sold 64 frisbees in one week , some for $ 3 and the rest for $ 4 each . if receipts from frisbee sales for the week totaled $ 196 what is the fewest number of $ 4 frisbees that could have been sold ?", + "Output Program": [ + "n0 = 64.0\nn1 = 3.0\nn2 = 4.0\nn3 = 196.0\nn4 = 4.0\nt0 = n0 * n1\nanswer = n3 - t0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "the average ( arithmetic man ) of 3 integers a , b , and c is exactly half the median . if a < b < c and a = 0 , what is the value of c / b ?", + "Output Program": [ + "n0 = 3.0\nn1 = 0.0\nt0 = 1.0 / 2.0\nt1 = n0 * t0\nt2 = t1 - 1.0\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "1.5" + ], + "split": "train" + }, + { + "Input": "an object thrown directly upward is at a height of h feet after t seconds , where h = - 12 ( t - 3 ) ^ 2 + 120 . at what height , in feet , is the object 2 seconds after it reaches its maximum height ?", + "Output Program": [ + "n0 = 12.0\nn1 = 3.0\nn2 = 2.0\nn3 = 120.0\nn4 = 2.0\nt0 = n1 + n2\nt1 = -n0\nt2 = t0 - n1\nt3 = t2**min(n2, 5)\nt4 = t1 * t3\nanswer = n3 + t4\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "train" + }, + { + "Input": "if | x - 5 | = 23 what is the sum of all the values of x .", + "Output Program": [ + "n0 = 5.0\nn1 = 23.0\nt0 = n0 + n1\nt1 = n1 - n0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "find \u221a ? / 11 = 4 ?", + "Output Program": [ + "n0 = 11.0\nn1 = 4.0\nt0 = n0 * n1\nanswer = t0**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "1936" + ], + "split": "train" + }, + { + "Input": "on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.60 per glass on the first day , what was the price w per glass on the second day ?", + "Output Program": [ + "n0 = 0.6\nt0 = 1.0 + 1.0\nt1 = 1.0 + 2.0\nt2 = n0 * t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.39999999999999997" + ], + "split": "train" + }, + { + "Input": "a man has some hens and cows . if the number of heads be 44 and the number of feet equals 128 , then the number of hens will be", + "Output Program": [ + "n0 = 44.0\nn1 = 128.0\nt0 = n0 * 4.0\nt1 = t0 - n1\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "on a test average ( arithmetic mean ) test score for 4 students is 85 . what must be 5 th student ' s score that average score for 5 students to be 86 ?", + "Output Program": [ + "n0 = 4.0\nn1 = 85.0\nn2 = 5.0\nn3 = 5.0\nn4 = 86.0\nt0 = n2 * n4\nt1 = n0 * n1\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "( 0.86 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.86 ) ( power 2 ) + 0.086 + ( 0.1 ) ( power 2 ) is :", + "Output Program": [ + "n0 = 0.86\nn1 = 3.0\nn2 = 0.1\nn3 = 3.0\nn4 = 0.86\nn5 = 2.0\nn6 = 0.086\nn7 = 0.1\nn8 = 2.0\nt0 = n0**min(n1, 5)\nt1 = n2**min(n1, 5)\nt2 = n0**min(n5, 5)\nt3 = n2**min(n5, 5)\nt4 = n6 + t2\nt5 = t0 - t1\nt6 = t4 + t3\nanswer = t5 / t6\nprint(answer)" + ], + "Output Answer": [ + "0.76" + ], + "split": "train" + }, + { + "Input": "- - - - - - - - - - - - - - - - yes - - - - - - - - - no - - - - unsure subject m - - - - 500 - - - - - - - - 200 - - - - - 100 subject r - - - - 400 - - - - - - - - 100 - - - - - 300 a total of 800 students were asked whether they found two subjects , m and r , interesting . each answer was either yes or no or unsure , and the numbers of students who gave these answers are listed in the table above . if 150 students answered yes only for subject m , how many of the students did not answer yes for either subject ?", + "Output Program": [ + "n0 = 500.0\nn1 = 200.0\nn2 = 100.0\nn3 = 400.0\nn4 = 100.0\nn5 = 300.0\nn6 = 800.0\nn7 = 150.0\nt0 = n0 - n7\nt1 = n7 + t0\nt2 = n3 - t0\nt3 = t1 + t2\nanswer = n6 - t3\nprint(answer)" + ], + "Output Answer": [ + "250" + ], + "split": "train" + }, + { + "Input": "if x and y are the two digits of the number 653 xy . such that this number is divisible by 80 , then x + y is equal to", + "Output Program": [ + "n0 = 653.0\nn1 = 80.0\nt0 = n0 * 100.0\nt1 = t0 % n1\nanswer = t1 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "if n is a positive integer and n ^ 2 is divisible by 450 , then what is the largest positive integer that must divide n ?", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 450.0\nt0 = n1 / n0\nt1 = math.sqrt(max(0, t0))\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "a trailer carries 3 , 4 and 6 crates on a trip . each crate weighs no less than 120 kg . what is the maximum weight of the crates on a single trip ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 6.0\nn3 = 120.0\n\nanswer = n2 * n3\nprint(answer)" + ], + "Output Answer": [ + "720" + ], + "split": "train" + }, + { + "Input": "the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 45 kg . what is the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.5\nn2 = 45.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "65" + ], + "split": "train" + }, + { + "Input": "if ( 10 ^ 4 * 3.456789 ) ^ 10 is written as a single term , how many digits would be to the right of the decimal place ?", + "Output Program": [ + "n0 = 10.0\nn1 = 4.0\nn2 = 3.456789\nn3 = 10.0\n\nanswer = n3 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "a certain drink of type a is prepared by mixing 4 parts milk with 3 parts fruit juice . another drink of type b is prepared by mixing 4 parts of fruit juice and 3 parts of milk . how many liters of fruit juice must be added to 63 liters of drink a to convert it to drink b ?", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 4.0\nn3 = 3.0\nn4 = 63.0\nt0 = n0 + n1\nt1 = n0 / t0\nt2 = n1 / t0\nt3 = n4 * t1\nt4 = n4 * t2\nt5 = n0 * t3\nt6 = t5 / n1\nanswer = t6 - t4\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "james went on a diet 12 months ago when he weighed 222 pounds . if he now weighs 198 pounds and continues to lose at the same average monthly rate , in approximately how many months will he weigh 190 pounds ?", + "Output Program": [ + "n0 = 12.0\nn1 = 222.0\nn2 = 198.0\nn3 = 190.0\nt0 = n1 - n2\nt1 = n2 - n3\nt2 = t0 / t1\nanswer = n0 / t2\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "elvin ' s monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for internet service . elvin ' s total telephone bill for january was $ 50 and elvin ' s total telephone bill for february was 76 $ . if elvin ' s charge for the calls he made in february was twice the charge for the calls he made in january , what is elvin ' s fixed monthly charge for internet service ?", + "Output Program": [ + "n0 = 50.0\nn1 = 76.0\nt0 = n0 * 2.0\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "a salesman \u2019 s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1300 plus 2.5 % commission on all sales exceeding rs . 4,000 . if his remuneration as per new scheme was rs . 600 more than that by the previous schema , his sales were worth ?", + "Output Program": [ + "n0 = 5.0\nn1 = 1300.0\nn2 = 2.5\nn3 = 4000.0\nn4 = 600.0\nt0 = n0 / 100.0\nanswer = n4 / t0\nprint(answer)" + ], + "Output Answer": [ + "12000" + ], + "split": "train" + }, + { + "Input": "suppose you want to buy 3 loaves of bread that cost $ 2.25 each and a jar of peanut butter that costs $ 2 . a jar of jelly is $ 2.75 , but you don \u00e2 \u20ac \u2122 t need any jelly . you have $ 14 . how much money will you have left over ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.25\nn2 = 2.0\nn3 = 2.75\nn4 = 14.0\nt0 = n0 * n1\nt1 = n4 - t0\nanswer = t1 - n2\nprint(answer)" + ], + "Output Answer": [ + "5.25" + ], + "split": "train" + }, + { + "Input": "a man can row 3.6 km / hr in still water . it takes him twice as long to row upstream as to row downstream . what is the rate of the current ?", + "Output Program": [ + "n0 = 3.6\nt0 = n0 * 2.0\nt1 = t0 - n0\nanswer = t1 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "1.2" + ], + "split": "train" + }, + { + "Input": "united telephone charges a base rate of $ 11.00 for service , plus an additional charge of $ 0.25 per minute . atlantic call charges a base rate of $ 12.00 for service , plus an additional charge of $ 0.20 per minute . for what number of minutes would the bills for each telephone company be the same ?", + "Output Program": [ + "n0 = 11.0\nn1 = 0.25\nn2 = 12.0\nn3 = 0.2\nt0 = n2 - n0\nt1 = n1 - n3\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "20.000000000000004" + ], + "split": "train" + }, + { + "Input": "the least number which when divided by 5 , 67 and 8 leaves a remainder 3 , but when divided by 9 leaves no remainder , is :", + "Output Program": [ + "n0 = 5.0\nn1 = 67.0\nn2 = 8.0\nn3 = 3.0\nn4 = 9.0\nt0 = n0 + 2.0\nt1 = n0 + 1.0\nt2 = n0 * t1\nt3 = t0 * t2\nt4 = n2 * t3\nanswer = n3 + t4\nprint(answer)" + ], + "Output Answer": [ + "1683" + ], + "split": "train" + }, + { + "Input": "a theater charges $ 12 for seats in the orchestra and $ 8 for seats in the balcony . on a certain night , a total of 380 tickets were sold for a total cost of $ 3,320 . how many more tickets were sold that night for seats in the balcony than for seats in the orchestra ?", + "Output Program": [ + "n0 = 12.0\nn1 = 8.0\nn2 = 380.0\nn3 = 3320.0\nt0 = n0 * n2\nt1 = 1000.0 * 3.0\nt2 = 100.0 * 3.0\nt3 = 10.0 * 2.0\nt4 = n0 - n1\nt5 = t1 + t2\nt6 = t5 + t3\nt7 = t0 - t6\nt8 = t7 / t4\nt9 = n2 - t8\nanswer = t8 - t9\nprint(answer)" + ], + "Output Answer": [ + "240" + ], + "split": "train" + }, + { + "Input": "in an electric circuit , two resistors with resistances x and y are connected in parallel . if r is the combined resistance of these two resistors , then the reciprocal of r is equal to the sum of the reciprocals of x and y . what is r if x is 5 ohms and y is 6 ohms ?", + "Output Program": [ + "n0 = 5.0\nn1 = 6.0\nt0 = n0 + n1\nt1 = n0 * n1\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "2.727272727272727" + ], + "split": "train" + }, + { + "Input": "in a practice paper at 2 iim . com , questions were given from 5 topics . out of the appearing students , 10 % passed in all topics while 10 % did not pass in any . of the remaining , 20 % passed in one topic only and 25 % in two topics only . if 24 % of the total students passed 4 topics only and 500 students passed in 3 topics only , find the total number of students who appeared in the examination ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 10.0\nn3 = 10.0\nn4 = 20.0\nn5 = 25.0\nn6 = 24.0\nn7 = 4.0\nn8 = 500.0\nn9 = 3.0\nt0 = n4 + n5\nt1 = 100.0 - n2\nt2 = t1 - n2\nt3 = t0 * t2\nt4 = t3 / 100.0\nt5 = n6 + t4\nt6 = n2 + t5\nt7 = n2 + t6\nt8 = 100.0 - t7\nt9 = t8 / 100.0\nanswer = n8 / t9\nprint(answer)" + ], + "Output Answer": [ + "2500" + ], + "split": "train" + }, + { + "Input": "a mixture contains milk and water in the ratio 3 : 2 . on adding 10 litters of water , the ratio of milk to water becomes 2 : 3 . total quantity of milk & water before adding water to it ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 10.0\nn3 = 2.0\nn4 = 3.0\nt0 = n0 + n1\nt1 = n1 / n0\nt2 = n0 / t0\nt3 = n1 / t0\nt4 = n2 * t1\nt5 = t3 * t1\nt6 = t2 - t5\nanswer = t4 / t6\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "a drink vendor has 80 liters of maaza , 144 liters of pepsi and 368 liters of sprite . he wants to pack them in cans , so that each can contains the same number of liters of a drink , and does n ' t want to mix any two drinks in a can . what is the least number of cans required ?", + "Output Program": [ + "import scipy\nn0 = 80.0\nn1 = 144.0\nn2 = 368.0\nt0 = scipy.gcd(int(n0), int(n1))\nt1 = scipy.gcd(int(n2), int(t0))\nt2 = n0 / t1\nt3 = n1 / t1\nt4 = n2 / t1\nt5 = t2 + t3\nanswer = t5 + t4\nprint(answer)" + ], + "Output Answer": [ + "37" + ], + "split": "train" + }, + { + "Input": "( 112 % of 2348 ) \u00f7 4.98 = ?", + "Output Program": [ + "n0 = 112.0\nn1 = 2348.0\nn2 = 4.98\nt0 = n0 / 100.0\nt1 = n1 * t0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "528.0642570281125" + ], + "split": "train" + }, + { + "Input": "find the sum lend at c . i . at 5 p . c per annum will amount to rs . 441 in 2 years ?", + "Output Program": [ + "n0 = 5.0\nn1 = 441.0\nn2 = 2.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nt2 = t1**min(n2, 5)\nanswer = n1 / t2\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "train" + }, + { + "Input": "if an integer n is to be selected at random from 1 to 100 , inclusive , what is probability n ( n + 1 ) will be divisible by 5 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 100.0\nn2 = 1.0\nn3 = 5.0\n\nanswer = 2.0 / n3\nprint(answer)" + ], + "Output Answer": [ + "0.4" + ], + "split": "train" + }, + { + "Input": "5100 \u2212 ( 102 \u00f7 20.4 ) = ?", + "Output Program": [ + "n0 = 5100.0\nn1 = 102.0\nn2 = 20.4\nt0 = n1 / n2\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "5095" + ], + "split": "train" + }, + { + "Input": "what least number should be subtracted from 13603 such that the remainder is divisible by 87 ?", + "Output Program": [ + "n0 = 13603.0\nn1 = 87.0\n\nanswer = n0 % n1\nprint(answer)" + ], + "Output Answer": [ + "31" + ], + "split": "train" + }, + { + "Input": "in 40 litres of a mixture , the ratio of milk to water is 7 : 1 . in order to make the ratio of milk to water as 3 : 1 , the quantity of water that should be added to the mixture will be ?", + "Output Program": [ + "n0 = 40.0\nn1 = 7.0\nn2 = 1.0\nn3 = 3.0\nn4 = 1.0\nt0 = n3 / n2\nt1 = n1 / n2\nt2 = n0 * 2.0\nt3 = t0 * t1\nt4 = n0 * t3\nt5 = t4 * 2.0\nanswer = t5 - t2\nprint(answer)" + ], + "Output Answer": [ + "1600" + ], + "split": "train" + }, + { + "Input": "rates for having a manuscript typed at a certain typing service are $ 6 per page for the first time a page is typed and $ 4 per page each time a page is revised . if a certain manuscript has 100 pages , of which 35 were revised only once , 15 were revised twice , and the rest required no revisions , what was the total cost of having the manuscript typed ?", + "Output Program": [ + "n0 = 6.0\nn1 = 4.0\nn2 = 100.0\nn3 = 35.0\nn4 = 15.0\nt0 = n0 * n2\nt1 = n1 * n3\nt2 = n1 * n4\nt3 = t0 + t1\nt4 = t2 * 2.0\nanswer = t3 + t4\nprint(answer)" + ], + "Output Answer": [ + "860" + ], + "split": "train" + }, + { + "Input": "the events a and b are independent , the probability that event a occurs is greater than 0 , and the probability that event a occurs is twice the probability that event b occurs . the probability that at least one of events a and b occurs is 18 times the probability that both events a and b occur . what is the probability that event a occurs ?", + "Output Program": [ + "n0 = 0.0\nn1 = 18.0\nt0 = 1.0 + 2.0\nt1 = n1 * 2.0\nt2 = t1 + 2.0\nt3 = t0 / t2\nanswer = t3 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "0.15789473684210525" + ], + "split": "train" + }, + { + "Input": "a student got twice as many sums wrong as he got right . if he attempted 24 sums in all , how many did he solve correctly ?", + "Output Program": [ + "n0 = 24.0\nt0 = 1.0 + 2.0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "there are 2 sections a and b in a class , consisting of 30 and 20 students respectively . if the average weight of section a is 40 kg and that of section b is 35 kg , find the average of the whole class ?", + "Output Program": [ + "n0 = 2.0\nn1 = 30.0\nn2 = 20.0\nn3 = 40.0\nn4 = 35.0\nt0 = n1 + n2\nt1 = n1 * n3\nt2 = n2 * n4\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "38" + ], + "split": "train" + }, + { + "Input": "the closest approximation of d ( 69.28 \u00d7 0.004 ) / 0.03 is", + "Output Program": [ + "n0 = 69.28\nn1 = 0.004\nn2 = 0.03\nt0 = n1 / n2\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "9.237333333333334" + ], + "split": "train" + }, + { + "Input": "robert ' s salary was decreased by 50 % and subsequently increased by 50 % . how much percentage does he lose ?", + "Output Program": [ + "n0 = 50.0\nn1 = 50.0\nt0 = n0 + 100.0\nt1 = 100.0 * 100.0\nt2 = 100.0 - n0\nt3 = t0 * t2\nt4 = t1 - t3\nt5 = t4 / t1\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "the average age of 10 members of a committee is the same as it was 4 years ago , because an old member has been replaced by a young member . find how much younger is the new member ?", + "Output Program": [ + "n0 = 10.0\nn1 = 4.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "if 75 percent of 600 is 50 percent of x , then x = ?", + "Output Program": [ + "n0 = 75.0\nn1 = 600.0\nn2 = 50.0\nt0 = n0 * n1\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "900" + ], + "split": "train" + }, + { + "Input": "there were 35 students in a hostel . due to the admission of 7 new students , the expenses of mess were increased by 42 per day while the average expenditure per head diminished by 1 . what was the original expenditure of the mess ?", + "Output Program": [ + "n0 = 35.0\nn1 = 7.0\nn2 = 42.0\nn3 = 1.0\nt0 = n2 + n2\nt1 = n2 - n0\nt2 = t0 / t1\nt3 = n0 * t2\nt4 = n2 - t2\nt5 = t4 - t2\nt6 = t5 + 2.0\nanswer = t3 - t6\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "train" + }, + { + "Input": "a tour group of 25 people paid a total of $ 945 for entrance to a museum . if this price included a 5 % sales tax , and all the tickets cost the same amount , what was the face value of each ticket price without the sales tax ? choices", + "Output Program": [ + "n0 = 25.0\nn1 = 945.0\nn2 = 5.0\nt0 = n1 / n0\nt1 = 100.0 - n2\nt2 = t0 * t1\nanswer = t2 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "35.91" + ], + "split": "train" + }, + { + "Input": "what is the average of the first 10 multiples of 11 ?", + "Output Program": [ + "n0 = 10.0\nn1 = 11.0\nt0 = n0 + 1.0\nt1 = n0 * t0\nt2 = t1 / 2.0\nt3 = t2 / n0\nanswer = n1 * t3\nprint(answer)" + ], + "Output Answer": [ + "60.5" + ], + "split": "train" + }, + { + "Input": "the avg weight of a , b & c is 84 kg . if d joins the group , the avg weight of the group becomes 80 kg . if another man e who weights is 5 kg more than d replaces a , then the avgof b , c , d & e becomes 79 kg . what is the weight of a ?", + "Output Program": [ + "n0 = 84.0\nn1 = 80.0\nn2 = 5.0\nn3 = 79.0\nt0 = n1 * 4.0\nt1 = n3 * 4.0\nt2 = n0 * 3.0\nt3 = t0 - t2\nt4 = n2 + t3\nt5 = t1 - t4\nanswer = t0 - t5\nprint(answer)" + ], + "Output Answer": [ + "77" + ], + "split": "train" + }, + { + "Input": "at golds gym class can be divided into 8 teams with an equal number of players on each team or into 12 teams with an equal number of players on each team . what is the lowest possible number of students in the class ?", + "Output Program": [ + "import scipy\nn0 = 8.0\nn1 = 12.0\n\nanswer = scipy.lcm(int(n0), int(n1))\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "find the principle on a certain sum of money at 5 % per annum for 2 2 / 5 years if the amount being rs . 1568 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 2.0\nn3 = 5.0\nn4 = 1568.0\nt0 = n1 * n3\nt1 = n1 + t0\nt2 = t1 / n3\nt3 = n0 * t2\nt4 = t3 / 100.0\nt5 = t4 + 1.0\nanswer = n4 / t5\nprint(answer)" + ], + "Output Answer": [ + "1399.9999999999998" + ], + "split": "train" + }, + { + "Input": "solve the equation for x : 19 ( x + y ) + 17 = 19 ( - x + y ) - 21", + "Output Program": [ + "n0 = 19.0\nn1 = 17.0\nn2 = 19.0\nn3 = 21.0\nt0 = n1 + n3\nt1 = n0 + n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "if each digit in the set a = { 1 , 2 , 3 , 4 , 5 , 6 } is used exactly once , in how many ways can the digits be arranged ?", + "Output Program": [ + "import math\nn0 = 1.0\nn1 = 2.0\nn2 = 3.0\nn3 = 4.0\nn4 = 5.0\nn5 = 6.0\n\nanswer = math.factorial(min(15, int(n5)))\nprint(answer)" + ], + "Output Answer": [ + "720" + ], + "split": "train" + }, + { + "Input": "a \u2019 s speed is 20 / 19 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?", + "Output Program": [ + "n0 = 20.0\nn1 = 19.0\nt0 = n0 - n1\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.05" + ], + "split": "train" + }, + { + "Input": "if 1 = 6 , 2 = 12 , 3 = 18 , 4 = 24 , 5 = 30 , then 6 = ?", + "Output Program": [ + "n0 = 1.0\nn1 = 6.0\nn2 = 2.0\nn3 = 12.0\nn4 = 3.0\nn5 = 18.0\nn6 = 4.0\nn7 = 24.0\nn8 = 5.0\nn9 = 30.0\nn10 = 6.0\n\nanswer = n2 - n0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "3 partners a , b , c start a business . twice a \u2019 s capital is equal to thrice b \u2019 s capital and b \u2019 s capital is 4 times c \u2019 s capital . out of a total profit of rs . 16500 at the end of the year , b \u2019 share is :", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 16500.0\nt0 = 3.0 / 2.0\nt1 = 1.0 / n1\nt2 = t0 + 1.0\nt3 = t2 + t1\nanswer = n2 / t3\nprint(answer)" + ], + "Output Answer": [ + "6000" + ], + "split": "train" + }, + { + "Input": "the average weight of 10 students decreases by 6 kg when one of them weighing 120 kg is replaced by a new student . the weight of the student is", + "Output Program": [ + "n0 = 10.0\nn1 = 6.0\nn2 = 120.0\nt0 = n0 * n1\nanswer = n2 - t0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "each week , harry is paid x dollars per hour for the first 30 hours and 2 x dollars for each additional hour worked that week . each week , james is paid x dollars per per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 41 hours if harry and james were paid the same amount last week , how many hours did harry work last week ?", + "Output Program": [ + "n0 = 30.0\nn1 = 2.0\nn2 = 40.0\nn3 = 2.0\nn4 = 41.0\nt0 = n2 + n3\nt1 = t0 - n0\nt2 = t1 / n1\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "the sum of 3 numbers is 98 . the ratio of the first to the second is 2 / 3 , and the ratio of the second to the third is 5 / 8 . the second number is :", + "Output Program": [ + "n0 = 3.0\nn1 = 98.0\nn2 = 2.0\nn3 = 3.0\nn4 = 5.0\nn5 = 8.0\nt0 = n0 * n4\nt1 = n2 * n4\nt2 = n0 * n5\nt3 = t0 + t1\nt4 = n1 * t0\nt5 = t3 + t2\nanswer = t4 / t5\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "what is the remainder when ( 55 ) ( 57 ) is divided by 7 ?", + "Output Program": [ + "n0 = 55.0\nn1 = 57.0\nn2 = 7.0\nt0 = n0 * n1\nanswer = t0 % n2\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "there is a total of 100 marbles in a box , each of which is red , green , blue , or white . if one marble is drawn from the box at random , the probability that it will be white is 1 / 4 and the probability that it will be green is 1 / 5 . what is the probability that the marble will be either red or blue ?", + "Output Program": [ + "n0 = 100.0\nn1 = 1.0\nn2 = 4.0\nn3 = 1.0\nn4 = 5.0\nt0 = n1 / n2\nt1 = n3 / n4\nt2 = t0 + t1\nanswer = n1 - t2\nprint(answer)" + ], + "Output Answer": [ + "0.55" + ], + "split": "train" + }, + { + "Input": "you and your friend spent a total of $ 11 for lunch . your friend spent $ 3 more than you . how much did your friend spend on their lunch ?", + "Output Program": [ + "n0 = 11.0\nn1 = 3.0\nt0 = n0 - n1\nt1 = t0 / 2.0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "haresh went to buy fruits . she bought 1 apple , 3 bananas , 5 oranges and paid 21 rupees . another person bought 7 apple , 5 bananas , 3 oranges and paid 51 rupees . if i want to buy 1 apple , 1 banana , 1 orange then how much i have to pay ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 5.0\nn3 = 21.0\nn4 = 7.0\nn5 = 5.0\nn6 = 3.0\nn7 = 51.0\nn8 = 1.0\nn9 = 1.0\nn10 = 1.0\nt0 = n3 + n7\nt1 = n0 + n4\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "if a = 105 and a ^ 3 = 21 \u00d7 25 \u00d7 45 \u00d7 q , what is the value of q ?", + "Output Program": [ + "n0 = 105.0\nn1 = 3.0\nn2 = 21.0\nn3 = 25.0\nn4 = 45.0\nt0 = n2 * n3\nt1 = n0**min(n1, 5)\nt2 = n4 * t0\nanswer = t1 / t2\nprint(answer)" + ], + "Output Answer": [ + "49" + ], + "split": "train" + }, + { + "Input": "the average ( arithmetic mean ) of 4 different integers is 72 . if the largest integer is 90 , what is the least possible value of the smallest integer ?", + "Output Program": [ + "n0 = 4.0\nn1 = 72.0\nn2 = 90.0\nt0 = n0 * n1\nt1 = n2 - 1.0\nt2 = n2 - 2.0\nt3 = t0 - n2\nt4 = t3 - t1\nanswer = t4 - t2\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "diana took out a charge account at the general store and agreed to pay 7 % simple annual interest . if she charges $ 75 on her account in january , how much will she owe a year later , assuming she does not make any additional charges or payments ?", + "Output Program": [ + "n0 = 7.0\nn1 = 75.0\nt0 = n0 / 100.0\nt1 = n1 * t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "80.25" + ], + "split": "train" + }, + { + "Input": "a football player scores 2 goals in his fifth match thus increasing his average goals score by 0.1 . the total number of goals in his 5 matches would be", + "Output Program": [ + "n0 = 2.0\nn1 = 0.1\nn2 = 5.0\nt0 = n0 * 4.0\nt1 = n2 * 4.0\nt2 = n1 * t1\nt3 = t0 - t2\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "if x is equal to the sum of the integers from 30 to 50 , inclusive , and y is the number of even integers from 30 to 50 , inclusive , what is the value of x + y ?", + "Output Program": [ + "n0 = 30.0\nn1 = 50.0\nn2 = 30.0\nn3 = 50.0\nt0 = n0 + n1\nt1 = n1 - n0\nt2 = t1 + 1.0\nt3 = t1 / 2.0\nt4 = t0 / 2.0\nt5 = t3 + 1.0\nt6 = t2 * t4\nanswer = t5 + t6\nprint(answer)" + ], + "Output Answer": [ + "851" + ], + "split": "train" + }, + { + "Input": "of the 100 people in a room , 2 / 5 are women . if 1 / 4 of the people are married , what is the maximum number of women in the room who could be unmarried ?", + "Output Program": [ + "n0 = 100.0\nn1 = 2.0\nn2 = 5.0\nn3 = 1.0\nn4 = 4.0\nt0 = n1 / n2\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "if a certain toy store ' s revenue in november was 2 / 5 of its revenue in december and its revenue in january was 1 / 5 of its revenue in november , then the store ' s revenue in december was how many times the average ( arithmetic mean ) of its revenues in november and january ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 1.0\nn3 = 5.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = t0 * t1\nt3 = t0 + t2\nt4 = t3 / 2.0\nanswer = n2 / t4\nprint(answer)" + ], + "Output Answer": [ + "4.166666666666666" + ], + "split": "train" + }, + { + "Input": "if rs . 510 be divided among a , b , c in such a way that a gets 2 / 3 of what b gets and b gets 1 / 4 of what c gets , then their shares are respectively ?", + "Output Program": [ + "n0 = 510.0\nn1 = 2.0\nn2 = 3.0\nn3 = 1.0\nn4 = 4.0\nt0 = n3 / n4\nt1 = n1 / n2\nt2 = t1 * t0\nt3 = t0 + t2\nt4 = t3 + n3\nanswer = n0 / t4\nprint(answer)" + ], + "Output Answer": [ + "360.00000000000006" + ], + "split": "train" + }, + { + "Input": "if p # q denotes the least common multiple of p and q , then p = ( ( 12 # 16 ) # ( 18 # 24 ) ) = ?", + "Output Program": [ + "n0 = 12.0\nn1 = 16.0\nn2 = 18.0\nn3 = 24.0\nt0 = n2 * n3\nt1 = n0 * n1\nt2 = t0 - t1\nt3 = t2 / 2.0\nanswer = n3 + t3\nprint(answer)" + ], + "Output Answer": [ + "144" + ], + "split": "train" + }, + { + "Input": "if ( 18 ^ a ) * 9 ^ ( 3 a \u2013 1 ) = ( 2 ^ 6 ) ( 3 ^ b ) and a and b are positive integers , what is the value of a ?", + "Output Program": [ + "n0 = 18.0\nn1 = 9.0\nn2 = 3.0\nn3 = 1.0\nn4 = 2.0\nn5 = 6.0\nn6 = 3.0\n\nanswer = n5 * n3\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "keats library purchases a number of new books , all in the category of biography , and the library does not acquire any other books . with the addition of the new biographies , the biography collection of the library amounts to 55 % of the total number of books in the library . if prior to the purchase , only 20 % of the books in keats library were biographies , by what percent has the number of biographies in the library increased ?", + "Output Program": [ + "n0 = 55.0\nn1 = 20.0\nt0 = n0 * 100.0\nt1 = n1 * 100.0\nt2 = 100.0 - n0\nt3 = t0 - t1\nt4 = t3 / t2\nt5 = t4 / n1\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "388.88888888888886" + ], + "split": "train" + }, + { + "Input": "in a weight - lifting competition , the total weight of joe ' s two lifts was 1500 pounds . if twice the weight of his first lift was 300 pounds more than the weight of his second lift , what was the weight , in pounds , of his first lift ?", + "Output Program": [ + "n0 = 1500.0\nn1 = 300.0\nt0 = n0 + n1\nanswer = t0 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "600" + ], + "split": "train" + }, + { + "Input": "the cash realised on selling a 14 % stock is rs . 109.25 , brokerage being 1 / 4 % is", + "Output Program": [ + "n0 = 14.0\nn1 = 109.25\nn2 = 1.0\nn3 = 4.0\nt0 = n2 / n3\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "109" + ], + "split": "train" + }, + { + "Input": "a ' and ' b ' are positive integers such that their lcm is 20 and their hcf is 1 . what is the difference between the maximum and minimum possible values of ' a - b ' ?", + "Output Program": [ + "n0 = 20.0\nn1 = 1.0\nt0 = n0 + n0\nt1 = n1 + n1\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "38" + ], + "split": "train" + }, + { + "Input": "find the principle on a certain sum of money at 5 % per annum for 2 2 / 5 years if the amount being rs . 1456 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 2.0\nn3 = 5.0\nn4 = 1456.0\nt0 = n1 * n3\nt1 = n1 + t0\nt2 = t1 / n3\nt3 = n0 * t2\nt4 = t3 / 100.0\nt5 = t4 + 1.0\nanswer = n4 / t5\nprint(answer)" + ], + "Output Answer": [ + "1299.9999999999998" + ], + "split": "train" + }, + { + "Input": "what is the 4 digit no . in which the 1 st digit is 1 / 3 of the second , the 3 rd is the sum of the 1 st and 2 nd , and the last is 3 times the second ?", + "Output Program": [ + "n0 = 4.0\nn1 = 1.0\nn2 = 1.0\nn3 = 3.0\nn4 = 3.0\nn5 = 1.0\nn6 = 2.0\nn7 = 3.0\nt0 = n0 + n3\nt1 = 10.0 * 100.0\nt2 = 100.0 * 3.0\nt3 = t1 + t2\nt4 = t0 * t0\nanswer = t3 + t4\nprint(answer)" + ], + "Output Answer": [ + "1349" + ], + "split": "train" + }, + { + "Input": "what number is 76 more than one - fourth of itself ?", + "Output Program": [ + "n0 = 76.0\nt0 = 1.0 / 4.0\nt1 = 1.0 - t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "101.33333333333333" + ], + "split": "train" + }, + { + "Input": "the tax on a commodity is diminished by 20 % and its consumption increased by 15 % . the effect on revenue is ?", + "Output Program": [ + "n0 = 20.0\nn1 = 15.0\nt0 = n1 / 100.0\nt1 = n0 / 100.0\nt2 = t0 + 1.0\nt3 = 1.0 - t1\nt4 = t2 * t3\nt5 = t4 * 100.0\nanswer = 100.0 - t5\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "90 % of the population of a village is 23040 . the total population of the village is ?", + "Output Program": [ + "n0 = 90.0\nn1 = 23040.0\nt0 = 100.0 / n0\nanswer = n1 * t0\nprint(answer)" + ], + "Output Answer": [ + "25600" + ], + "split": "train" + }, + { + "Input": "a tourist does not have to pay tax on the first $ 600 of goods he purchases in country b , but does have to pay a 12 percent tax on the portion of the total value that is in excess of $ 600 . what tax must be paid by a tourist if he buys goods with a total value of $ 1720 ?", + "Output Program": [ + "n0 = 600.0\nn1 = 12.0\nn2 = 600.0\nn3 = 1720.0\nt0 = n3 - n0\nt1 = n1 * t0\nanswer = t1 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "134.4" + ], + "split": "train" + }, + { + "Input": "how many of the integers between 45 and 105 are even ?", + "Output Program": [ + "n0 = 45.0\nn1 = 105.0\nt0 = n1 - n0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "yearly subscription to professional magazines cost a company $ 940.00 . to make a 50 % cut in the magazine budget , how much less must be spent ?", + "Output Program": [ + "n0 = 940.0\nn1 = 50.0\nt0 = 100.0 - n1\nt1 = t0 / 100.0\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "470" + ], + "split": "train" + }, + { + "Input": "price of a book increases 15 % successively ( 2 times ) what is the new price of the book more compared to that of the old price :", + "Output Program": [ + "n0 = 15.0\nn1 = 2.0\nt0 = n0 + 100.0\nt1 = t0 / 100.0\nt2 = t1 * t1\nt3 = t2 - 1.0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "32.24999999999998" + ], + "split": "train" + }, + { + "Input": "3 / 4 of 1 / 2 of 2 / 5 of 5040 = ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 1.0\nn3 = 2.0\nn4 = 2.0\nn5 = 5.0\nn6 = 5040.0\nt0 = n3 / n5\nt1 = n0 / n1\nt2 = n2 / n3\nt3 = t1 * t2\nt4 = t0 * t3\nanswer = n6 * t4\nprint(answer)" + ], + "Output Answer": [ + "756.0000000000001" + ], + "split": "train" + }, + { + "Input": "the average of 10 numbers is 40.2 . later it is found that two numbers have been wrongly copied . the first is 16 greater than the actual number and the second number added is 13 instead of 31 . find the correct average .", + "Output Program": [ + "n0 = 10.0\nn1 = 40.2\nn2 = 16.0\nn3 = 13.0\nn4 = 31.0\nt0 = n2 + n3\nt1 = n0 * n1\nt2 = t0 + t1\nt3 = t2 - n4\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "the average salary of all the workers in a workshop is rs . 9500 . the average salary of 7 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is ?", + "Output Program": [ + "n0 = 9500.0\nn1 = 7.0\nn2 = 12000.0\nn3 = 6000.0\nt0 = n2 - n0\nt1 = n0 - n3\nt2 = n1 * t0\nt3 = t2 / t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "1 / 0.06 is equal to", + "Output Program": [ + "n0 = 1.0\nn1 = 0.06\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "16.666666666666668" + ], + "split": "train" + }, + { + "Input": "the average of 1 st 3 of 4 numbers is 6 and of the last 3 are 3 . if the sum of the first and the last number is 13 . what is the last numbers ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 4.0\nn3 = 6.0\nn4 = 3.0\nn5 = 3.0\nn6 = 13.0\nt0 = n1 * n3\nt1 = n6 - n3\nt2 = n1 + t1\nt3 = t0 - t2\nanswer = t3 - n3\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a classroom has equal number of boys and girls . 8 girls left to play kho - kho , leaving twice as many boys as girls in the classroom . what was the total number of girls and boys present initially ?", + "Output Program": [ + "n0 = 8.0\nt0 = n0 * 2.0\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "when a number is divided by 6 & then multiply by 12 the answer is 10 what is the no . ?", + "Output Program": [ + "n0 = 6.0\nn1 = 12.0\nn2 = 10.0\nt0 = n2 / n1\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "the circulation for magazine p in 1971 was 4 times the average ( arithmetic mean ) yearly circulation for magazine p for the years 1972 - 1980 . what is the ratio of the circulation in 1971 to the total circulation during 1971 - 1980 for magazine p ?", + "Output Program": [ + "n0 = 1971.0\nn1 = 4.0\nn2 = 1972.0\nn3 = 1980.0\nn4 = 1971.0\nn5 = 1971.0\nn6 = 1980.0\nt0 = n3 - n2\nt1 = t0 + 1.0\nt2 = n1 + t1\nt3 = t2 + 1.0\nanswer = n1 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.2857142857142857" + ], + "split": "train" + }, + { + "Input": "the average marks of a class of 26 students is 40 and that of another class of 50 students is 60 . find the average marks of all the students ?", + "Output Program": [ + "n0 = 26.0\nn1 = 40.0\nn2 = 50.0\nn3 = 60.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "53.1578947368421" + ], + "split": "train" + }, + { + "Input": "each of the integers from 1 to 18 is written on the a seperate index card and placed in a box . if the cards are drawn from the box at random without replecement , how many cards must be drawn to ensure that the product of all the integers drawn is even", + "Output Program": [ + "n0 = 1.0\nn1 = 18.0\nt0 = n1 / 2.0\nanswer = n0 + t0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "suppose f ( x ) is an odd function for which f ( x + 2 ) = f ( x ) for all x , and f ( x ) = x 2 for x 2 ( 0 , 1 ) . compute f ( - 3 / 2 ) + f ( 1 ) .", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 2.0\nn3 = 0.0\nn4 = 1.0\nn5 = 3.0\nn6 = 2.0\nn7 = 1.0\nt0 = n0 + n0\nanswer = n4 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.25" + ], + "split": "train" + }, + { + "Input": "a car travels first 160 km at 75 km / hr and the next 160 km at 80 km / hr . what is the average speed for the first 320 km of the tour ?", + "Output Program": [ + "n0 = 160.0\nn1 = 75.0\nn2 = 160.0\nn3 = 80.0\nn4 = 320.0\nt0 = n0 / n1\nt1 = n0 / n3\nt2 = t0 + t1\nt3 = 1.0 / t2\nanswer = n4 * t3\nprint(answer)" + ], + "Output Answer": [ + "77.4193548387097" + ], + "split": "train" + }, + { + "Input": "if y is 70 % greater than x , than x is what % less than y ?", + "Output Program": [ + "n0 = 70.0\nt0 = n0 + 100.0\nt1 = n0 / t0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "41.17647058823529" + ], + "split": "train" + }, + { + "Input": "jim \u00e2 \u20ac \u2122 s taxi service charges an initial fee of $ 2.35 at the beginning of a trip and an additional charge of $ 0.35 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?", + "Output Program": [ + "n0 = 2.35\nn1 = 0.35\nn2 = 2.0\nn3 = 5.0\nn4 = 3.6\nt0 = n2 / n3\nt1 = n4 / t0\nt2 = n1 * t1\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "5.5" + ], + "split": "train" + }, + { + "Input": "a special municipal payroll tax charges not tax on a payroll less than $ 200,000 and only 0.2 % on a company \u2019 s payroll above $ 200,000 . if belfried industries paid $ 400 in this special municipal payroll tax , then they must have had a payroll of", + "Output Program": [ + "n0 = 200000.0\nn1 = 0.2\nn2 = 200000.0\nn3 = 400.0\nt0 = n3 * 100.0\nanswer = t0 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "400000" + ], + "split": "train" + }, + { + "Input": "what is remainder of the division ( 1225 * 1227 * 1229 ) / 12 ?", + "Output Program": [ + "n0 = 1225.0\nn1 = 1227.0\nn2 = 1229.0\nn3 = 12.0\nt0 = n0 * n1\nt1 = n2 * t0\nt2 = t1 - 3.0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "what number should replace the question mark ? 2 , 16 , 4 , 14 , 6 , 12 , - - - ?", + "Output Program": [ + "n0 = 2.0\nn1 = 16.0\nn2 = 4.0\nn3 = 14.0\nn4 = 6.0\nn5 = 12.0\nt0 = n0 + n0\nt1 = n0 + t0\nanswer = t1 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a father said his son , ` ` i was as old as you are at present at the time of your birth . ` ` if the father age is 62 now , the son age 5 years back was", + "Output Program": [ + "n0 = 62.0\nn1 = 5.0\nt0 = n0 / 2.0\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "calculate the average of all the numbers between 7 and 49 which are divisible by 6 .", + "Output Program": [ + "import math\nn0 = 7.0\nn1 = 49.0\nn2 = 6.0\nt0 = n0 / n2\nt1 = n1 / n2\nt2 = math.floor(t0)\nt3 = math.floor(t1)\nt4 = t2 + 1.0\nt5 = t4 + t3\nt6 = t5 / 2.0\nanswer = n2 * t6\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "a certain sum of money is divided among a , b and c such that a gets one - third of what b and c together get and b gets two - seventh of what a and c together get . if the amount received by a is $ 35 more than that received by b , find the total amount shared by a , b and c .", + "Output Program": [ + "n0 = 35.0\nt0 = n0 * 3.0\nt1 = n0 * 2.0\nt2 = t0 * 2.0\nt3 = t2 + t1\nt4 = n0 + t3\nt5 = t3 + t4\nt6 = t4 * 3.0\nt7 = t6 - t3\nanswer = t5 + t7\nprint(answer)" + ], + "Output Answer": [ + "1260" + ], + "split": "train" + }, + { + "Input": "if 4 ( p ' s capital ) = 6 ( q ' s capital ) = 10 ( r ' s capital ) , then out of the total profit of rs 4960 , r will receive", + "Output Program": [ + "n0 = 4.0\nn1 = 6.0\nn2 = 10.0\nn3 = 4960.0\nt0 = n0 + 1.0\nt1 = n2 + t0\nt2 = n2 + t1\nt3 = n1 + t2\nt4 = n1 / t3\nanswer = n3 * t4\nprint(answer)" + ], + "Output Answer": [ + "960" + ], + "split": "train" + }, + { + "Input": "n is an 80 - digit positive integer ( in the decimal scale ) . all digits except the 44 th digit ( from the left ) are 2 . if n is divisible by 13 , find the 26 th digit ?", + "Output Program": [ + "n0 = 80.0\nn1 = 44.0\nn2 = 2.0\nn3 = 13.0\nn4 = 26.0\nt0 = 12.0 / 2.0\nanswer = t0 / 1.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "the average weight of 3 packets a , b and c is 84 kg . another packet d added into the group and the average now becomes 80 kg . if another packet e , whose weight is 3 kg more than that of d , replaces a then the average weight of b , c , d and e becomes 79 kg . the weight of a is :", + "Output Program": [ + "n0 = 3.0\nn1 = 84.0\nn2 = 80.0\nn3 = 3.0\nn4 = 79.0\nt0 = n0 * n1\nt1 = n4 * 4.0\nt2 = n2 * 4.0\nt3 = t2 - t0\nt4 = n0 + t3\nt5 = t4 + t3\nt6 = t1 - t5\nanswer = t0 - t6\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "in a office work is distribute between p persons . if 1 / 5 members are absent then work increased for each person is ?", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nt0 = n1 * 100.0\nt1 = n1 - n0\nt2 = t0 / t1\nanswer = t2 - 100.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "a gambler bought $ 3,000 worth of chips at a casino in denominations of $ 20 and $ 100 . that evening , the gambler lost 16 chips , and then cashed in the remainder . if the number of $ 20 chips lost was 2 more or 2 less than the number of $ 100 chips lost , what is the largest amount of money that the gambler could have received back ?", + "Output Program": [ + "n0 = 3000.0\nn1 = 20.0\nn2 = 100.0\nn3 = 16.0\nn4 = 20.0\nn5 = 2.0\nn6 = 2.0\nn7 = 100.0\nt0 = n3 + n5\nt1 = 1000.0 * 3.0\nt2 = t0 / n5\nt3 = n1 * t2\nt4 = t2 - n5\nt5 = n2 * t4\nt6 = t3 + t5\nanswer = t1 - t6\nprint(answer)" + ], + "Output Answer": [ + "2120" + ], + "split": "train" + }, + { + "Input": "the sum of the first 100 numbers , 1 to 100 is always divisible by", + "Output Program": [ + "n0 = 100.0\nn1 = 1.0\nn2 = 100.0\nt0 = n0 + n1\nt1 = n0 / 2.0\nt2 = t0 * t1\nt3 = t2 / 2.0\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a man spends 1 / 3 rd of his salary on food . he spends 1 / 4 th on rent and 1 / 5 th on cloths . if he is left with 1760 , then who much salary does he earn", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 4.0\nn4 = 1.0\nn5 = 5.0\nn6 = 1760.0\nt0 = n0 / n1\nt1 = n0 / n3\nt2 = n0 / n5\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = 1.0 - t4\nanswer = n6 / t5\nprint(answer)" + ], + "Output Answer": [ + "8123.076923076918" + ], + "split": "train" + }, + { + "Input": "what is the largest 4 digit number exactly divisible by 48 ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 48.0\nt0 = 10.0**min(n0, 5)\nt1 = t0 / n1\nt2 = math.floor(t1)\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "9984" + ], + "split": "train" + }, + { + "Input": "he number of times a bucket of capacity 4 liters to be used to fill up a tank is less than number of ties another bucket of capacity 3 liters used for the same purpose by 4 . what is the capacity of the tank ?", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 4.0\nt0 = n0 * n1\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "find the last 3 digit of 443 ^ 443 .", + "Output Program": [ + "n0 = 3.0\nn1 = 443.0\nn2 = 443.0\nt0 = n1 % 4.0\nt1 = n1**min(t0, 5)\nanswer = t1 % 1000.0\nprint(answer)" + ], + "Output Answer": [ + "307" + ], + "split": "train" + }, + { + "Input": "the average of 11 numbers is 60 . out of 11 numbers the average of first 6 no . is 78 , and last 6 numbers is 75 then find 6 th number ?", + "Output Program": [ + "n0 = 11.0\nn1 = 60.0\nn2 = 11.0\nn3 = 6.0\nn4 = 78.0\nn5 = 6.0\nn6 = 75.0\nn7 = 6.0\nt0 = n3 * n4\nt1 = n3 * n6\nt2 = n0 * n1\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "258" + ], + "split": "train" + }, + { + "Input": "marts income is 60 percent more than tims income and tims income is 50 percent less than juans income . what percentage of juans income is marts income", + "Output Program": [ + "n0 = 60.0\nn1 = 50.0\nt0 = n0 + 100.0\nt1 = 100.0 - n1\nt2 = 100.0 / t1\nt3 = t2 * 100.0\nt4 = t0 / t3\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "155 liters of a mixture of milk and water contains in the ratio 3 : 2 . how much water should now be added so that the ratio of milk and water becomes 3 : 4 ?", + "Output Program": [ + "n0 = 155.0\nn1 = 3.0\nn2 = 2.0\nn3 = 3.0\nn4 = 4.0\nt0 = n1 + n2\nt1 = n0 / t0\nanswer = n2 * t1\nprint(answer)" + ], + "Output Answer": [ + "62" + ], + "split": "train" + }, + { + "Input": "if 821562 is to be divisible by 5 , what is the least whole number that should be added to it ?", + "Output Program": [ + "import math\nn0 = 821562.0\nn1 = 5.0\nt0 = math.floor(n1)\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "what is the unit digit of 3 ^ 58 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 58.0\nt0 = n0**min(2.0, 5)\nanswer = t0 % 10.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "if the average ( arithmetic mean ) of a and b is 35 and the average of b and c is 80 , what is the value of c \u2212 a ?", + "Output Program": [ + "n0 = 35.0\nn1 = 80.0\nt0 = n1 * 2.0\nt1 = n0 * 2.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "in an apartment building that has 490 units , 4 out of every 7 units are currently rented , including 1 / 6 of the one - bedroom units . if , of the rented apartments , there is a 6 : 1 ratio of two - bedroom units to one - bedroom units , and the building only consists of two - bedroom and one - bedroom units , how many two - bedroom units are not rented ?", + "Output Program": [ + "n0 = 490.0\nn1 = 4.0\nn2 = 7.0\nn3 = 1.0\nn4 = 6.0\nn5 = 6.0\nn6 = 1.0\nt0 = n3 + n4\nt1 = n0 / n2\nt2 = n3 / n4\nt3 = n1 * t1\nt4 = t3 / t0\nt5 = n4 * t4\nt6 = t3 - t5\nt7 = t6 / t2\nt8 = n0 - t7\nanswer = t8 - t5\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 976 in total compensation , how many total hours did he work that week ?", + "Output Program": [ + "n0 = 16.0\nn1 = 40.0\nn2 = 40.0\nn3 = 75.0\nn4 = 976.0\nt0 = n3 + 100.0\nt1 = n0 * n1\nt2 = n0 * t0\nt3 = n4 - t1\nt4 = t2 / 100.0\nt5 = t3 / t4\nanswer = n1 + t5\nprint(answer)" + ], + "Output Answer": [ + "52" + ], + "split": "train" + }, + { + "Input": "he average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.5\nn2 = 65.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "85" + ], + "split": "train" + }, + { + "Input": "if f ( f ( n ) ) + f ( n ) = 2 n + 3 , f ( 0 ) = 1 then f ( 2013 ) = ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 0.0\nn3 = 1.0\nn4 = 2013.0\n\nanswer = n3 + n4\nprint(answer)" + ], + "Output Answer": [ + "2014" + ], + "split": "train" + }, + { + "Input": "of the final grades received by the students in a certain math course , 1 / 5 are a ' s , 1 / 4 are b ' s , 1 / 2 are c ' s , and the remaining 30 grades are d ' s . what is the number of students in the course ?", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 1.0\nn3 = 4.0\nn4 = 1.0\nn5 = 2.0\nn6 = 30.0\nt0 = n0 / n1\nt1 = n0 / n3\nt2 = n0 / n5\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n0 - t4\nanswer = n6 / t5\nprint(answer)" + ], + "Output Answer": [ + "599.9999999999994" + ], + "split": "train" + }, + { + "Input": "the salary of a , b , c , d , e is rs . 8000 , rs . 5000 , rs . 14000 , rs . 7000 , rs . 9000 per month respectively , then the average salary of a , b , c , d , and e per month is", + "Output Program": [ + "n0 = 8000.0\nn1 = 5000.0\nn2 = 14000.0\nn3 = 7000.0\nn4 = 9000.0\nt0 = n0 + n1\nt1 = 1.0 + 4.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "8600" + ], + "split": "train" + }, + { + "Input": "if 0.75 : x : : 7 : 8 , then x is equal to :", + "Output Program": [ + "n0 = 0.75\nn1 = 7.0\nn2 = 8.0\nt0 = n0 * n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.8571428571428571" + ], + "split": "train" + }, + { + "Input": "of the 3,600 employees of company x , 1 / 3 are clerical . if the clerical staff were to be reduced by 1 / 3 , what percent of the total number of the remaining employees would then be clerical ?", + "Output Program": [ + "n0 = 3600.0\nn1 = 1.0\nn2 = 3.0\nn3 = 1.0\nn4 = 3.0\nt0 = n1 / n2\nt1 = n3 / n4\nt2 = n3 - t1\nt3 = n3 - t0\nt4 = t0 * t2\nt5 = t4 + t3\nt6 = t4 / t5\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "pat , kate and mark charged a total of 216 hours to a certain project . if pat charged twice as much time to the project as kate and 1 / 3 as much times as mark , how many more hours did mark charge to the project than kate .", + "Output Program": [ + "n0 = 216.0\nn1 = 1.0\nn2 = 3.0\nt0 = n1 + 2.0\nt1 = n2 * 2.0\nt2 = t0 + t1\nt3 = t1 - n1\nt4 = n0 / t2\nanswer = t4 * t3\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "a 40 - liter solution of alcohol and water is 5 percent alcohol . if 6.5 liters of alcohol and 3.5 liters of water are added to this solution , what percent of the solution produced is alcohol ?", + "Output Program": [ + "n0 = 40.0\nn1 = 5.0\nn2 = 6.5\nn3 = 3.5\nt0 = n2 + n3\nt1 = n1 / 100.0\nt2 = n0 + t0\nt3 = n0 * t1\nt4 = n2 + t3\nt5 = t4 / t2\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "rs . 730 were divided among punith , michael , suresh in such a way that if punith gets rs . 3 , then michael gets rs . 4 and if michael gets rs . 3.50 then suresh gets rs . 3 . the share of michael exceeds that of suresh by", + "Output Program": [ + "n0 = 730.0\nn1 = 3.0\nn2 = 4.0\nn3 = 3.5\nn4 = 3.0\nt0 = n1 * n3\nt1 = n2 * n3\nt2 = n1 * n2\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n0 / t4\nt6 = t5 * t1\nt7 = t5 * t2\nanswer = t6 - t7\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "for any number z , z * is defined as the greatest positive even integer less than or equal to y . what is the value of 6.35 \u2013 6.35 * ?", + "Output Program": [ + "import math\nn0 = 6.35\nn1 = 6.35\nt0 = math.floor(n0)\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "0.34999999999999964" + ], + "split": "train" + }, + { + "Input": "12 . what is the dividend . divisor 17 , the quotient is 9 and the remainder is 8 .", + "Output Program": [ + "n0 = 12.0\nn1 = 17.0\nn2 = 9.0\nn3 = 8.0\nt0 = n1 * n2\nanswer = n3 + t0\nprint(answer)" + ], + "Output Answer": [ + "161" + ], + "split": "train" + }, + { + "Input": "what is the sum of all possible 3 - digit numbers that can be constructed using the digits 2 , 4 , and 5 if each digit can be used only once in each number ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 4.0\nn3 = 5.0\nt0 = n2 + n3\nt1 = n1 + t0\nt2 = t1 * 100.0\nt3 = t1 * 10.0\nt4 = t2 + t3\nt5 = t4 + t1\nanswer = t5 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "2442" + ], + "split": "train" + }, + { + "Input": "the difference between the ages of two persons is 20 years . fifteen years ago , the elder one was twice as old as the younger one . the present age of the younger person is ?", + "Output Program": [ + "n0 = 20.0\nt0 = 2.0 + 3.0\nt1 = n0 - t0\nt2 = t1 * 2.0\nt3 = n0 - t1\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "if 70 percent of 600 is 40 percent of x , then x = ?", + "Output Program": [ + "n0 = 70.0\nn1 = 600.0\nn2 = 40.0\nt0 = n0 * n1\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "1050" + ], + "split": "train" + }, + { + "Input": "if john makes a contribution to a charity fund at school , the average contribution size will increase by 50 % reaching $ 75 per person . if there were 6 other contributions made before john ' s , what is the size of his donation ?", + "Output Program": [ + "n0 = 50.0\nn1 = 75.0\nn2 = 6.0\nt0 = n2 + 1.0\nt1 = n1 * t0\nt2 = n0 * t0\nt3 = t1 - t2\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "225" + ], + "split": "train" + }, + { + "Input": "if p represents the product of the first 14 positive integers , then p is not a multiple of :", + "Output Program": [ + "n0 = 14.0\nt0 = n0 + 3.0\nanswer = t0 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "51" + ], + "split": "train" + }, + { + "Input": "the average weight of 10 girls increases by 5 kg when a new girl comes in place of one of them weighing 50 kg . what might be the weight of the new girl ?", + "Output Program": [ + "n0 = 10.0\nn1 = 5.0\nn2 = 50.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "on dividing 144 by a number , the quotient is 13 and the remainder is 1 . find the divisor .", + "Output Program": [ + "import math\nn0 = 144.0\nn1 = 13.0\nn2 = 1.0\nt0 = n0 / n1\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "an old man distributed all the gold coins he had to his two sons into two different numbers such that the difference between the squares of the two numbers is 25 times the difference between the two numbers . how many coins did the old man have ?", + "Output Program": [ + "import math\nn0 = 25.0\n\nanswer = math.floor(n0)\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "the last two - digits in the multiplication 122 \u00d7 123 \u00d7 125 \u00d7 127 \u00d7 129 will be", + "Output Program": [ + "n0 = 122.0\nn1 = 123.0\nn2 = 125.0\nn3 = 127.0\nn4 = 129.0\nt0 = 1.0 + 4.0\nanswer = t0 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "the population of a bacteria culture doubles every 5 minutes . approximately how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 1000.0\nn2 = 500000.0\nt0 = 1.0 + 4.0\nt1 = t0 * n1\nt2 = t1 * 100.0\nt3 = t2 / n1\nt4 = math.log(max(1e-5, t3), 2)\nanswer = n0 * t4\nprint(answer)" + ], + "Output Answer": [ + "44.82892142331043" + ], + "split": "train" + }, + { + "Input": "set j consists of 10 consecutive even numbers . if the smallest term in the set is - 4 , what is the range of the positive integers in set j ?", + "Output Program": [ + "n0 = 10.0\nn1 = 4.0\nt0 = -2.0\nt1 = n0 - 1.0\nt2 = 2.0 * t1\nt3 = t2 + t0\nanswer = t3 - n1\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "if p / q = 4 / 5 , then the value of 18 / 7 + { ( 2 q - p ) / ( 2 q + p ) } is ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 18.0\nn3 = 7.0\nn4 = 2.0\nn5 = 2.0\nt0 = n2 / n3\nt1 = n0 / n1\nt2 = n4 + t1\nt3 = n4 - t1\nt4 = t3 / t2\nanswer = t0 + t4\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "how many prime numbers are between 26 / 3 and 85 / 6 ?", + "Output Program": [ + "import math\nn0 = 26.0\nn1 = 3.0\nn2 = 85.0\nn3 = 6.0\n\nanswer = math.floor(2.0)\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "average of 10 matches is 32 , how many runs one should should score to increase his average by 5 runs .", + "Output Program": [ + "n0 = 10.0\nn1 = 32.0\nn2 = 5.0\nt0 = n1 + n2\nt1 = n0 + 1.0\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "87" + ], + "split": "train" + }, + { + "Input": "if there are 4 peanuts in a box and mary puts 2 more peanuts inside , how many peanuts are in the box ?", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\n\nanswer = n0 + n1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "in august , a cricket team that played 120 matches won 22 % of the games it played . after a continuous winning streak , this team raised its average to 52 % . how many matches did the team win to attain this average ?", + "Output Program": [ + "n0 = 120.0\nn1 = 22.0\nn2 = 52.0\nt0 = n2 / 100.0\nt1 = n1 / 100.0\nt2 = n0 * t0\nt3 = n0 * t1\nt4 = 1.0 - t0\nt5 = t2 - t3\nanswer = t5 / t4\nprint(answer)" + ], + "Output Answer": [ + "75.00000000000001" + ], + "split": "train" + }, + { + "Input": "jane started baby - sitting when she was 16 years old . whenever she baby - sat for a child , that child was no more than half her age at the time . jane is currently 32 years old , and she stopped baby - sitting 10 years ago . what is the current age of the oldest person for whom jane could have baby - sat ?", + "Output Program": [ + "n0 = 16.0\nn1 = 32.0\nn2 = 10.0\nt0 = n0 / 2.0\nt1 = n1 - n0\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "there are 3 boats b 1 , b 2 and b 3 working together they carry 60 people in each trip . one day an early morning b 1 carried 50 people in few trips alone . when it stopped carrying the passengers b 2 and b 3 started carrying the people together . it took a total of 10 trips to carry 300 people by b 1 , b 2 and b 3 . it is known that each day on an average 300 people cross the river using only one of the 3 boats b 1 , b 2 and b 3 . how many trips it would take to b 1 , to carry 150 passengers alone ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 2.0\nn3 = 3.0\nn4 = 60.0\nn5 = 1.0\nn6 = 50.0\nn7 = 2.0\nn8 = 3.0\nn9 = 10.0\nn10 = 300.0\nn11 = 1.0\nn12 = 2.0\nn13 = 3.0\nn14 = 300.0\nn15 = 3.0\nn16 = 1.0\nn17 = 2.0\nn18 = 3.0\nn19 = 1.0\nn20 = 150.0\nt0 = n10 / n2\nanswer = t0 / n9\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "the average age of 12 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men . the average age of the two new men is", + "Output Program": [ + "n0 = 12.0\nn1 = 21.0\nn2 = 23.0\nt0 = n1 + n2\nt1 = n0 * 1.0\nt2 = t0 / 2.0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "34" + ], + "split": "train" + }, + { + "Input": "the average of 10 numbers is calculated as 16 . it is discovered later on that while calculating the average , the number 55 was incorrectly read as 25 , and this incorrect number was used in the calculation . what is the correct average ?", + "Output Program": [ + "n0 = 10.0\nn1 = 16.0\nn2 = 55.0\nn3 = 25.0\nt0 = n0 * n1\nt1 = t0 - n3\nt2 = n2 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "the average of 6 no . ' s is 6.40 . the average of 2 of them is 6.2 , while the average of the other 2 is 6.1 . what is the average of the remaining 2 no ' s ?", + "Output Program": [ + "n0 = 6.0\nn1 = 6.4\nn2 = 2.0\nn3 = 6.2\nn4 = 2.0\nn5 = 6.1\nn6 = 2.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n2 * n5\nt3 = t1 + t2\nt4 = t0 - t3\nanswer = t4 / n2\nprint(answer)" + ], + "Output Answer": [ + "6.900000000000002" + ], + "split": "train" + }, + { + "Input": "a school has 6 maths 5 physics and 5 chemistry teachers each teacher can teach 4 subjects max what is he minimum number of teachers required", + "Output Program": [ + "n0 = 6.0\nn1 = 5.0\nn2 = 5.0\nn3 = 4.0\nt0 = n0 + n1\nt1 = n2 + t0\nanswer = t1 / n3\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "the cash realised on selling a 14 % stock is rs . 104.25 , brokerage being 1 / 4 % is ?", + "Output Program": [ + "n0 = 14.0\nn1 = 104.25\nn2 = 1.0\nn3 = 4.0\nt0 = n2 / n3\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "104" + ], + "split": "train" + }, + { + "Input": "a dog has 15 bones , then he finds 8 more bones . now how many bones does he have .", + "Output Program": [ + "n0 = 15.0\nn1 = 8.0\n\nanswer = n0 + n1\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "last year manfred received 26 paychecks . each of his first 6 paychecks was $ 750 ; each of his remaining paychecks was $ 20 more than each of his first 6 paychecks . to the nearest dollar , what was the average ( arithmetic mean ) amount of his pay checks for the year ?", + "Output Program": [ + "n0 = 26.0\nn1 = 6.0\nn2 = 750.0\nn3 = 20.0\nn4 = 6.0\nt0 = n2 + n3\nt1 = n1 * n2\nt2 = n3 * t0\nt3 = t2 + t1\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "765.3846153846154" + ], + "split": "train" + }, + { + "Input": "the denominator of a fraction is 5 greater than the numerator . if the numerator and the denominator are increased by 1 , the resulting fraction is equal to 7 \u00e2 \u0081 \u201e 12 . what is the value of the original fraction ?", + "Output Program": [ + "n0 = 5.0\nn1 = 1.0\nn2 = 7.0\nn3 = 12.0\nt0 = n0 + n1\nt1 = n3 - n2\nt2 = n2 * t0\nt3 = t2 - n3\nt4 = t3 / t1\nt5 = n0 + t4\nanswer = t4 / t5\nprint(answer)" + ], + "Output Answer": [ + "0.5454545454545454" + ], + "split": "train" + }, + { + "Input": "if the sum of two positive integers is 22 and the difference of their squares is 44 , what is the product of the two integers ?", + "Output Program": [ + "n0 = 22.0\nn1 = 44.0\nt0 = n1 / n0\nt1 = n0 - t0\nt2 = t1 / t0\nt3 = t2 + t0\nanswer = t3 * t2\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "a waitress ' s income consists of her salary and tips . during one week , her tips were 11 / 4 of her salary . what fraction of her income for the week came from tips ?", + "Output Program": [ + "n0 = 11.0\nn1 = 4.0\nt0 = n0 + n1\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.7333333333333333" + ], + "split": "train" + }, + { + "Input": "the price of commodity x increases by 45 cents every year , while the price of commodity y increases by 20 cents every year . in 2001 , the price of commodity x was $ 5.20 and the price of commodity y was $ 7.30 . in which year will the price of commodity x be 90 cents more than the price of commodity y ?", + "Output Program": [ + "n0 = 45.0\nn1 = 20.0\nn2 = 2001.0\nn3 = 5.2\nn4 = 7.3\nn5 = 90.0\nt0 = n5 / 100.0\nt1 = n0 / 100.0\nt2 = n4 - n3\nt3 = t0 + t2\nt4 = t1 - t2\nt5 = t3 / t4\nanswer = n2 + t5\nprint(answer)" + ], + "Output Answer": [ + "1999.1818181818182" + ], + "split": "train" + }, + { + "Input": "of 3 numbers , the third is 4 times the second and the second is two times the first . if their average is 165 , the smallest of the 3 numbers is :", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 165.0\nn3 = 3.0\nt0 = n0 * n2\nt1 = n1 * 2.0\nt2 = n0 + t1\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "two mixers and one t . v . cost rs . 7000 , while two t . v . s and a mixer cost rs , 9800 . the value of one t . v . is :", + "Output Program": [ + "n0 = 7000.0\nn1 = 9800.0\nt0 = n1 * 2.0\nt1 = n0 - t0\nt2 = t1 / 3.0\nanswer = -t2\nprint(answer)" + ], + "Output Answer": [ + "4200" + ], + "split": "train" + }, + { + "Input": "in a certain diving competition , 5 judges score each dive on a scale from 1 to 10 . the point value of the dive is obtained by dropping the highest score and the lowest score and multiplying the sum of the remaining scores by the degree of difficulty . if a dive with a degree of difficulty of 3.2 received scores of 7.5 , 7.8 , 9.0 , 6.0 , and 8.5 , what was the point value of the dive ?", + "Output Program": [ + "n0 = 5.0\nn1 = 1.0\nn2 = 10.0\nn3 = 3.2\nn4 = 7.5\nn5 = 7.8\nn6 = 9.0\nn7 = 6.0\nn8 = 8.5\nt0 = n4 + n5\nt1 = n8 + t0\nanswer = n3 * t1\nprint(answer)" + ], + "Output Answer": [ + "76.16000000000001" + ], + "split": "train" + }, + { + "Input": "15 times a number gives 150 . the number is", + "Output Program": [ + "n0 = 15.0\nn1 = 150.0\nt0 = n1 / n0\nanswer = n1 / t0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "for a certain exam , a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean . what was the mean score q for the exam ?", + "Output Program": [ + "n0 = 58.0\nn1 = 2.0\nn2 = 98.0\nn3 = 3.0\nt0 = n1 + n3\nt1 = n0 * n3\nt2 = n1 * n2\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "74" + ], + "split": "train" + }, + { + "Input": "the standard deviation of a normal distribution of data is 2 , and 3 standard deviations below the mean is greater than 47 . what is a possible value for the mean of the distribution ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 47.0\nt0 = n0 * n1\nt1 = n2 + t0\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "train" + }, + { + "Input": "the average of 35 numbers is 25 . if each number is multiplied by 5 , find the new average ?", + "Output Program": [ + "n0 = 35.0\nn1 = 25.0\nn2 = 5.0\n\nanswer = n1 * n2\nprint(answer)" + ], + "Output Answer": [ + "125" + ], + "split": "train" + }, + { + "Input": "the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 50 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam .", + "Output Program": [ + "n0 = 80.0\nn1 = 5.0\nn2 = 50.0\nn3 = 90.0\nt0 = n1 * n3\nt1 = n1 * n2\nt2 = n3 - n0\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "p , q and r have rs . 4000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?", + "Output Program": [ + "n0 = 4000.0\nt0 = 2.0 / 3.0\nt1 = t0 + 1.0\nt2 = n0 / t1\nanswer = t2 * t0\nprint(answer)" + ], + "Output Answer": [ + "1600" + ], + "split": "train" + }, + { + "Input": "at the end of the month , a certain ocean desalination plant \u2019 s reservoir contained 14 million gallons of water . this amount is twice the normal level . if this amount represents 70 % of the reservoir \u2019 s total capacity , how many million gallons short of total capacity is the normal level ?", + "Output Program": [ + "n0 = 14.0\nn1 = 70.0\nt0 = n0 / 2.0\nt1 = n1 / 100.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "what is the value of x ^ 2 yz \u2212 xyz ^ 2 , if x = 1 , y = 1 , and z = 3 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 1.0\nn3 = 1.0\nn4 = 3.0\nt0 = -n0\nt1 = n3 * t0\nt2 = t0 - n3\nt3 = n3 * t1\nanswer = t3 * t2\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "at the opening of a trading day at a certain stock exchange , the price per share of stock k was $ 6 . if the price per share of stock k was $ 8 at the closing of the day , what was the percent increase in the price per share of stock k for that day ?", + "Output Program": [ + "n0 = 6.0\nn1 = 8.0\nt0 = n1 / n0\nt1 = t0 - 1.0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "33.33333333333333" + ], + "split": "train" + }, + { + "Input": "a man engaged a servant on the condition that he would pay him rs . 900 and a uniform after one year service . he served only for 9 months and received uniform and rs . 650 , find the price of the uniform ?", + "Output Program": [ + "n0 = 900.0\nn1 = 9.0\nn2 = 650.0\nt0 = n0 * n1\nt1 = 3.0 * 4.0\nt2 = n2 * t1\nt3 = t1 * 1.0\nt4 = t0 - t2\nt5 = t4 / t3\nanswer = t5 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "in a office work is distribute between p persons . if 1 / 3 members are absent then work increased for each person is ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nt0 = n1 * 100.0\nt1 = n1 - n0\nt2 = t0 / t1\nanswer = t2 - 100.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "the average salary of a person for the months of january , february , march and april is rs . 8000 and that for the months february , march , april and may is rs . 8400 . if his salary for the month of may is rs . 6500 , find his salary for the month of january ?", + "Output Program": [ + "n0 = 8000.0\nn1 = 8400.0\nn2 = 6500.0\nt0 = n0 * 4.0\nt1 = n1 * 4.0\nt2 = t1 - n2\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "4900" + ], + "split": "train" + }, + { + "Input": "on a race track a maximum of 5 horses can race together at a time . there are a total of 25 horses . there is no way of timing the races . what is the minimum number w of races we need to conduct to get the top 3 fastest horses ?", + "Output Program": [ + "n0 = 5.0\nn1 = 25.0\nn2 = 3.0\nt0 = n1 / n0\nanswer = t0 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "simplify 80 \u00e2 \u02c6 \u2019 [ 5 \u00e2 \u02c6 \u2019 ( 6 + 2 ( 7 \u00e2 \u02c6 \u2019 8 \u00e2 \u02c6 \u2019 5 \u00e2 \u00af \u00e2 \u00af \u00e2 \u00af \u00e2 \u00af \u00e2 \u00af \u00e2 \u00af \u00e2 \u00af \u00e2 \u00af \u00e2 \u00af \u00e2 \u00af \u00e2 \u00af ) ) ]", + "Output Program": [ + "n0 = 80.0\nn1 = 5.0\nn2 = 6.0\nn3 = 2.0\nn4 = 7.0\nn5 = 8.0\nn6 = 5.0\nt0 = n2 - n1\nt1 = n4 - n3\nt2 = n5 - n1\nt3 = t0 + t1\nt4 = t3 + t2\nanswer = n0 + t4\nprint(answer)" + ], + "Output Answer": [ + "89" + ], + "split": "train" + }, + { + "Input": "solve the equation for x : 19 ( x + y ) + 17 = 19 ( - x + y ) - 21 ?", + "Output Program": [ + "n0 = 19.0\nn1 = 17.0\nn2 = 19.0\nn3 = 21.0\nt0 = n1 + n3\nt1 = n0 + n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "a farmer has an apple orchard consisting of fuji and gala apple trees . due to high winds this year 10 % of his trees cross pollinated . the number of his trees that are pure fuji plus the cross - pollinated ones totals 204 , while 3 / 4 of all his trees are pure fuji . how many of his trees are pure gala ?", + "Output Program": [ + "n0 = 10.0\nn1 = 204.0\nn2 = 3.0\nn3 = 4.0\nt0 = n0 / 100.0\nt1 = n2 / n3\nt2 = t0 + t1\nt3 = n1 / t2\nanswer = t3 - n1\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "the number 91 is equal to the sum of the cubes of two integers . what is the product of those integers ?", + "Output Program": [ + "import math\nn0 = 91.0\nt0 = n0 / 2.0\nt1 = 1.0 / 3.0\nt2 = t0**min(t1, 5)\nt3 = math.floor(t2)\nt4 = t3**min(3.0, 5)\nt5 = n0 - t4\nt6 = t5**min(t1, 5)\nanswer = t3 * t6\nprint(answer)" + ], + "Output Answer": [ + "11.999999999999998" + ], + "split": "train" + }, + { + "Input": "a student multiplied a number by 3 / 5 instead of 5 / 3 . what is the percentage error in the calculation ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 5.0\nn3 = 3.0\nt0 = n1 / n0\nt1 = n0 / n1\nt2 = t0 - t1\nt3 = t2 / t0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "64.00000000000001" + ], + "split": "train" + }, + { + "Input": "logx 16 = 0.8 then what is the value of x ?", + "Output Program": [ + "n0 = 16.0\nn1 = 0.8\nt0 = n1 * 4.0\nt1 = n1 + t0\nt2 = n0 * t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "find the sum the difference between the compound and s . i . on a certain sum of money for 2 years at 10 % per annum is rs . 12 of money ?", + "Output Program": [ + "n0 = 2.0\nn1 = 10.0\nn2 = 12.0\nt0 = n0 * n1\nt1 = n2 / t0\nt2 = t1 * 100.0\nanswer = t2 * t0\nprint(answer)" + ], + "Output Answer": [ + "1200" + ], + "split": "train" + }, + { + "Input": "a man whose bowling average is 12.4 , takes 3 wickets for 26 runs and there by decreases his average by 0.4 . the number of wickets taken by him before his last match is ?", + "Output Program": [ + "import math\nn0 = 12.4\nn1 = 3.0\nn2 = 26.0\nn3 = 0.4\nt0 = math.floor(n0)\nt1 = n1 * t0\nt2 = n0 - t0\nt3 = t1 - n2\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "24.99999999999998" + ], + "split": "train" + }, + { + "Input": "a 40 - liter solution of alcohol and water is 5 percent alcohol . if 3.5 liters of alcohol and 6.5 liters of water are added to this solution , what percent of the solution produced is alcohol ?", + "Output Program": [ + "n0 = 40.0\nn1 = 5.0\nn2 = 3.5\nn3 = 6.5\nt0 = n2 + n3\nt1 = n1 / 100.0\nt2 = n0 + t0\nt3 = n0 * t1\nt4 = n2 + t3\nt5 = t4 / t2\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "the sum of the first 50 positive even integers is 2550 . what is the sum e of even integers from 102 to 200 inclusive ?", + "Output Program": [ + "n0 = 50.0\nn1 = 2550.0\nn2 = 102.0\nn3 = 200.0\nt0 = n2 + n3\nt1 = n3 - n2\nt2 = t1 / 2.0\nt3 = t0 / 2.0\nt4 = t2 + 1.0\nanswer = t4 * t3\nprint(answer)" + ], + "Output Answer": [ + "7550" + ], + "split": "train" + }, + { + "Input": "in a class of 28 students in an examination in maths 4 students scored 95 marks each , 3 get zero each and the average of the rest was 45 . what is the average of the whole class ?", + "Output Program": [ + "n0 = 28.0\nn1 = 4.0\nn2 = 95.0\nn3 = 3.0\nn4 = 45.0\nt0 = n1 + n3\nt1 = n1 * n2\nt2 = n0 - t0\nt3 = n4 * t2\nt4 = t3 + t1\nanswer = t4 / n0\nprint(answer)" + ], + "Output Answer": [ + "47.32142857142857" + ], + "split": "train" + }, + { + "Input": "gopi gives rs . 90 plus one turban as salary to his servant for one year . the servant leaves after 9 months and receives rs . 65 and the turban . find the price of the turban .", + "Output Program": [ + "n0 = 90.0\nn1 = 9.0\nn2 = 65.0\nt0 = n0 - n2\nt1 = 12.0 - n1\nt2 = t0 / t1\nt3 = t2 * 12.0\nanswer = t3 - n0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "a cricketer scored 152 runs which included 12 boundaries and 2 sixes . what percent of his total score did he make by running between the wickets .", + "Output Program": [ + "n0 = 152.0\nn1 = 12.0\nn2 = 2.0\nt0 = n1 * 4.0\nt1 = n2 * 3.0\nt2 = n2 * t1\nt3 = t0 + t2\nt4 = n0 - t3\nt5 = t4 / n0\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "60.526315789473685" + ], + "split": "train" + }, + { + "Input": "paulson spends 75 % of his income . his income is increased by 20 % and he increased his expenditure by 10 % . find the percentage increase in his savings .", + "Output Program": [ + "n0 = 75.0\nn1 = 20.0\nn2 = 10.0\nt0 = n1 / 100.0\nt1 = n2 / 100.0\nt2 = n0 / 100.0\nt3 = t0 + 1.0\nt4 = t1 + 1.0\nt5 = 1.0 - t2\nt6 = t4 * t2\nt7 = t3 - t6\nt8 = t7 - t5\nt9 = t8 / t5\nanswer = t9 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "49.99999999999996" + ], + "split": "train" + }, + { + "Input": "on the average mr . jackson has 2 hours to plan for an long hour meeting he talk to his assistant 7 hours to prepare the paper work needed . how much hours should jackson and assistant has t plan for 30 min meeting ?", + "Output Program": [ + "n0 = 2.0\nn1 = 7.0\nn2 = 30.0\nt0 = n1 / 2.0\nt1 = n0 / 2.0\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "4.5" + ], + "split": "train" + }, + { + "Input": "the sum of the first 50 positive even integers is 2550 . what is the sum t of even integers from 102 to 200 inclusive ?", + "Output Program": [ + "n0 = 50.0\nn1 = 2550.0\nn2 = 102.0\nn3 = 200.0\nt0 = n2 + n3\nt1 = n3 - n2\nt2 = t1 / 2.0\nt3 = t0 / 2.0\nt4 = t2 + 1.0\nanswer = t4 * t3\nprint(answer)" + ], + "Output Answer": [ + "7550" + ], + "split": "train" + }, + { + "Input": "if y is 75 % greater than x , than x is what % less than y ?", + "Output Program": [ + "n0 = 75.0\nt0 = n0 + 100.0\nt1 = n0 / t0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "42.857142857142854" + ], + "split": "train" + }, + { + "Input": "arjun started a business with rs . 20,000 and is joined afterwards by anoop with rs . 40 , 000 . after how many months did anoop join if the profits at the end of the year are divided equally ?", + "Output Program": [ + "n0 = 20000.0\nn1 = 40.0\nn2 = 0.0\nt0 = 100.0 * 4.0\nt1 = 100.0 * 2.0\nt2 = n1 * 100.0\nt3 = t0 * 100.0\nt4 = t1 * 100.0\nt5 = t2 * 10.0\nt6 = t3 * 12.0\nt7 = t4 * 12.0\nt8 = t6 - t7\nanswer = t8 / t5\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "there are 14 teams in a soccer league and each team plays each of the other teams once . how many games will be played in total ?", + "Output Program": [ + "import math\nn0 = 14.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(2.0)))\nt2 = n0 - 2.0\nt3 = math.factorial(min(15, int(t2)))\nt4 = t3 * t1\nanswer = t0 / t4\nprint(answer)" + ], + "Output Answer": [ + "91" + ], + "split": "train" + }, + { + "Input": "two employees a and b are paid a total of rs . 450 per week by their employer . if a is paid 150 percent of the sum paid to b , how much is b paid per week ?", + "Output Program": [ + "n0 = 450.0\nn1 = 150.0\nt0 = n1 / 100.0\nt1 = t0 + 1.0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "180" + ], + "split": "train" + }, + { + "Input": "a jogger running at 9 km / hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?", + "Output Program": [ + "n0 = 9.0\nn1 = 240.0\nn2 = 120.0\nn3 = 45.0\nt0 = n1 + n2\nt1 = 10.0 / 2.0\nt2 = n3 - n0\nt3 = t2 / 2.0\nt4 = t1 / t3\nt5 = t4 * t2\nanswer = t0 / t5\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "for 6 - digit integer 46 x , y 12 , when x and y are drawn at random from { 3 , 58 } , what is the probability w that the integer drawn is divisible by 8 ? * a solution will be posted in two days .", + "Output Program": [ + "n0 = 6.0\nn1 = 46.0\nn2 = 12.0\nn3 = 3.0\nn4 = 58.0\nn5 = 8.0\nt0 = n4 - n1\nt1 = t0 / n0\nanswer = t1 / n3\nprint(answer)" + ], + "Output Answer": [ + "0.6666666666666666" + ], + "split": "train" + }, + { + "Input": "the average of 10 numbers is calculated as 46 . it is discovered later on that while calculating the average , the number 75 was incorrectly read as 25 , and this incorrect number was used in the calculation . what is the correct average ?", + "Output Program": [ + "n0 = 10.0\nn1 = 46.0\nn2 = 75.0\nn3 = 25.0\nt0 = n0 * n1\nt1 = t0 - n3\nt2 = n2 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "51" + ], + "split": "train" + }, + { + "Input": "all the students of class are told to sit in circle shape . here the boy at the 10 th position is exactly opposite to 40 th boy . total number of boys in the class ?", + "Output Program": [ + "n0 = 10.0\nn1 = 40.0\nt0 = n1 - n0\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "5 ltr of water is added with 15 ltr of a solution containing 26 % of alcohol in the water . the % of alcohol in the new mixture is ?", + "Output Program": [ + "n0 = 5.0\nn1 = 15.0\nn2 = 26.0\nt0 = n0 + n1\nt1 = n2 / 100.0\nt2 = n1 * t1\nt3 = t2 / t0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "19.5" + ], + "split": "train" + }, + { + "Input": "anne bought doughnuts for a class breakfast party . she bought 15 chocolate doughnuts , 12 coconut doughnuts , and 14 jam - filled doughnuts . how many doughnuts did anne buy in all ?", + "Output Program": [ + "n0 = 15.0\nn1 = 12.0\nn2 = 14.0\nt0 = n0 + n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "41" + ], + "split": "train" + }, + { + "Input": "following an increase in prices , the price of a candy box was 10 pounds and the price of a can of soda was 6 pounds . if the price of a candy box was raised by 25 % , and the price of a can of soda was raised by 50 % . what was the price of a box of candy plus a can of soda before prices were raised ?", + "Output Program": [ + "n0 = 10.0\nn1 = 6.0\nn2 = 25.0\nn3 = 50.0\nt0 = n2 + 100.0\nt1 = n3 + 100.0\nt2 = n0 * 100.0\nt3 = n1 * 100.0\nt4 = t2 / t0\nt5 = t3 / t1\nanswer = t4 + t5\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "set d consists of all the prime numbers between 10 and 25 . what is the range of set d ?", + "Output Program": [ + "n0 = 10.0\nn1 = 25.0\n\nanswer = n0 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "an amount of money is to be divided between p , q and r in the ratio of 3 : 7 : 12 . if the difference between the shares of p and q is rs . 2800 , what will be the difference between q and r ' s share ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 12.0\nn3 = 2800.0\nt0 = n1 - n0\nt1 = n2 - n1\nt2 = n3 / t0\nanswer = t2 * t1\nprint(answer)" + ], + "Output Answer": [ + "3500" + ], + "split": "train" + }, + { + "Input": "the price of a mobile was increased by 25 percent . the new price was then decreased by 10 percent . a single increase of what percent is equivalent to these two successive changes ?", + "Output Program": [ + "n0 = 25.0\nn1 = 10.0\nt0 = n0 + 100.0\nt1 = 100.0 - n1\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = t2 * t3\nt5 = t4 - 1.0\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "12.5" + ], + "split": "train" + }, + { + "Input": "caleb spends $ 64.50 on 50 hamburgers for the marching band . if single burgers cost $ 1.00 each and double burgers cost $ 1.50 each , how many double burgers did he buy ?", + "Output Program": [ + "n0 = 64.5\nn1 = 50.0\nn2 = 1.0\nn3 = 1.5\nt0 = n0 - n1\nt1 = n3 - n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "29" + ], + "split": "train" + }, + { + "Input": "the no 2.52 , when written as a fraction and reduced to lowest terms , the sum of the numeratr n denominator is :", + "Output Program": [ + "n0 = 2.52\nt0 = n0 * 100.0\nt1 = 100.0 - 1.0\nt2 = t0 - 2.0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "349" + ], + "split": "train" + }, + { + "Input": "if sharon ' s weekly salary increased by 15 percent , she would earn $ 575 per week . if instead , her weekly salary were to decreased by 12 percent , how much would she earn per week ?", + "Output Program": [ + "n0 = 15.0\nn1 = 575.0\nn2 = 12.0\nt0 = n0 / 100.0\nt1 = n2 / 100.0\nt2 = t0 + 1.0\nt3 = n1 / t2\nt4 = t1 * t3\nanswer = t3 + t4\nprint(answer)" + ], + "Output Answer": [ + "560.0000000000001" + ], + "split": "train" + }, + { + "Input": "what is the least common multiple of 812 , 3214", + "Output Program": [ + "n0 = 812.0\nn1 = 3214.0\nt0 = 2.0 + 3.0\nt1 = 100.0 * 2.0\nt2 = t0 * 12.0\nt3 = n0 - t1\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "672" + ], + "split": "train" + }, + { + "Input": "a student is ranked 13 th from right and 8 th from left . how many students are there in totality ?", + "Output Program": [ + "n0 = 13.0\nn1 = 8.0\nt0 = n0 + n1\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "how many gallons of milk that is 10 percent butter - fat must be added to 8 gallons of milk that is 30 percent butterfat to obtain milk that is 20 percent butterfat ?", + "Output Program": [ + "n0 = 10.0\nn1 = 8.0\nn2 = 30.0\nn3 = 20.0\nt0 = n2 - n3\nt1 = n1 * t0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a certain protective additive increases from 30 days to 60 days the time between required maintenance checks on an industrial vehicle . by what percent is the time between maintenance checks increased by using the additive ?", + "Output Program": [ + "n0 = 30.0\nn1 = 60.0\nt0 = n1 - n0\nt1 = t0 / n0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "a cab driver 5 days income was $ 600 , $ 250 , $ 450 , $ 400 , $ 800 . then his average income is ?", + "Output Program": [ + "n0 = 5.0\nn1 = 600.0\nn2 = 250.0\nn3 = 450.0\nn4 = 400.0\nn5 = 800.0\nt0 = n1 + n2\nt1 = n3 + t0\nt2 = n4 + t1\nt3 = n5 + t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "train" + }, + { + "Input": "two trains of equal are running on parallel lines in the same direction at 52 km / hr and 36 km / hr . the faster train passes the slower train in 36 sec . the length of each train is ?", + "Output Program": [ + "n0 = 52.0\nn1 = 36.0\nn2 = 36.0\nt0 = n0 - n1\nt1 = t0 * 1000.0\nt2 = t1 / 3600.0\nt3 = n2 * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "10 is added to a certain number , the sum is multiplied by 2 , the product is divided by 2 and 2 is subtracted from the quotient . the remainder left is half of 88 . what is the number ?", + "Output Program": [ + "n0 = 10.0\nn1 = 2.0\nn2 = 2.0\nn3 = 2.0\nn4 = 88.0\nt0 = n4 / 2.0\nt1 = n2 + t0\nt2 = n2 * t1\nt3 = t2 / n1\nanswer = t3 - n0\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "when jessica withdrew $ 200 from her bank account , her account balance decreased by 2 / 5 . if she deposits an amount equal to 1 / 2 of the remaining balance , what will be the final balance in her bank account ?", + "Output Program": [ + "n0 = 200.0\nn1 = 2.0\nn2 = 5.0\nn3 = 1.0\nn4 = 2.0\nt0 = n3 / n4\nt1 = 3.0 / n2\nt2 = n3 + t0\nt3 = n3 - t1\nt4 = n0 / t3\nt5 = t4 - n0\nanswer = t2 * t5\nprint(answer)" + ], + "Output Answer": [ + "450" + ], + "split": "train" + }, + { + "Input": "what is the least number should be added to 1100 , so the sum of the number is completely divisible by 23 ?", + "Output Program": [ + "import math\nn0 = 1100.0\nn1 = 23.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = t1 + 1.0\nt3 = n1 * t2\nanswer = t3 - n0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "if p ( a ) = 4 / 5 and p ( b ) = 2 / 5 , find p ( a n b ) if a and b are independent events .", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 2.0\nn3 = 5.0\nt0 = n0 / n1\nt1 = n2 / n3\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "0.32000000000000006" + ], + "split": "train" + }, + { + "Input": "how many 4 digit numbers have no repeat digits , do not contain zero , and have a sum of digits f equal to 28 ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 28.0\nt0 = math.factorial(min(15, int(n0)))\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "dacid obtained 81 , 65 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?", + "Output Program": [ + "n0 = 81.0\nn1 = 65.0\nn2 = 82.0\nn3 = 67.0\nn4 = 85.0\nn5 = 100.0\nt0 = n0 + n1\nt1 = 10.0 / 2.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "76" + ], + "split": "train" + }, + { + "Input": "he average of 30 numbers is zero . of them , at the most , how many may be greater than zero ?", + "Output Program": [ + "n0 = 30.0\n\nanswer = n0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "29" + ], + "split": "train" + }, + { + "Input": "a number when divided by 342 gives a remainder 47 . when the same number if it divided by 19 , what would be the remainder ?", + "Output Program": [ + "n0 = 342.0\nn1 = 47.0\nn2 = 19.0\nt0 = n2 * 2.0\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "\u221a ( 36 ) ^ 2", + "Output Program": [ + "import math\nn0 = 36.0\nn1 = 2.0\nt0 = n0**min(n1, 5)\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "he total marks obtained by a student in physics , chemistry and mathematics is 140 more than the marks obtained by him in physics . what is the average mark obtained by him in chemistry and mathematics ?", + "Output Program": [ + "n0 = 140.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "train" + }, + { + "Input": "given that p is a positive even integer with a positive units digit , if the units digit of p ^ 3 minus the units digit of p ^ 2 is equal to 0 , what is the units digit of p + 1 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 0.0\nn3 = 1.0\nt0 = n0 + n0\nanswer = n3 + t0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "a certain country is divided into 6 provinces . each province consists entirely of progressives and traditionalists . if each province contains the same number of traditionalists and the number of traditionalists in any given province is 1 / 9 the total number of progressives in the entire country , what fraction of the country is traditionalist ?", + "Output Program": [ + "n0 = 6.0\nn1 = 1.0\nn2 = 9.0\nt0 = n0 / n2\nt1 = n1 + t0\nt2 = t0 / t1\nanswer = n1 - t2\nprint(answer)" + ], + "Output Answer": [ + "0.6" + ], + "split": "train" + }, + { + "Input": "if f ( f ( n ) ) + f ( n ) = 2 n + 3 , f ( 0 ) = 1 then f ( 2015 ) = ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 0.0\nn3 = 1.0\nn4 = 2015.0\n\nanswer = n3 + n4\nprint(answer)" + ], + "Output Answer": [ + "2016" + ], + "split": "train" + }, + { + "Input": "if a and b are two events such that p ( a ) = 3 / 4 , p ( b ) = 1 / 2 and p ( a n b ) = 3 / 8 , find p ( not a and not b ) .", + "Output Program": [ + "import scipy\nn0 = 3.0\nn1 = 4.0\nn2 = 1.0\nn3 = 2.0\nn4 = 3.0\nn5 = 8.0\nt0 = n0 + n1\nt1 = scipy.lcm(int(n1), int(n3))\nt2 = n0 + t0\nt3 = scipy.lcm(int(n5), int(t1))\nt4 = t2 - n2\nt5 = t4 - t3\nanswer = t5 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.125" + ], + "split": "train" + }, + { + "Input": "what is the sum of all possible 3 - digit numbers that can be constructed using the digits 1 , 3 , and 4 if each digit can be used only once in each number ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 3.0\nn3 = 4.0\nt0 = n2 + n3\nt1 = n1 + t0\nt2 = t1 * 100.0\nt3 = t1 * 10.0\nt4 = t2 + t3\nt5 = t4 + t1\nanswer = t5 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "1776" + ], + "split": "train" + }, + { + "Input": "solve the equation for x : 14 ( - x + z ) + 18 = - 14 ( x - z ) - 10", + "Output Program": [ + "n0 = 14.0\nn1 = 18.0\nn2 = 14.0\nn3 = 10.0\nt0 = n1 + n3\nt1 = n0 + n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "if 1 / 3 of the passengers on a ship are from north america , 1 / 8 are europeans , 1 / 5 are from africa , 1 / 6 are from asia and the remaining 42 people are citizens of other continents , then how many passengers are on board the ship ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 8.0\nn4 = 1.0\nn5 = 5.0\nn6 = 1.0\nn7 = 6.0\nn8 = 42.0\nt0 = n0 / n1\nt1 = n0 / n3\nt2 = n0 / n5\nt3 = n0 / n7\nt4 = t0 + t1\nt5 = t4 + t2\nt6 = t5 + t3\nt7 = n0 - t6\nanswer = n8 / t7\nprint(answer)" + ], + "Output Answer": [ + "239.99999999999994" + ], + "split": "train" + }, + { + "Input": "in a mayoral election , candidate x received 1 / 2 more votes than candidate y , and candidate y received 2 / 5 fewer votes than z . if z received 25,000 votes how many votes did candidate x received ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 2.0\nn3 = 5.0\nn4 = 25000.0\nt0 = n0 / n1\nt1 = n1 / n3\nt2 = 0.25 * 100.0\nt3 = n0 + t0\nt4 = t2 * 100.0\nt5 = 1.0 - t1\nt6 = t4 * 10.0\nt7 = t6 * t5\nanswer = t3 * t7\nprint(answer)" + ], + "Output Answer": [ + "22500" + ], + "split": "train" + }, + { + "Input": "on july 1 of last year , total employees at company e was decreased by 10 percent . without any change in the salaries of the remaining employees , the average ( arithmetic mean ) employee salary was 10 percent more after the decrease in the number of employees than before the decrease . the total of the combined salaries of all the employees at company e after july 1 last year was what percent t of thatbeforejuly 1 last year ?", + "Output Program": [ + "n0 = 1.0\nn1 = 10.0\nn2 = 10.0\nn3 = 1.0\nn4 = 1.0\n\nanswer = n1 * n1\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "a small beaker is 1 / 2 filled with salt water . another beaker , which has 5 times the capacity of the small beaker , is 1 / 5 filled with fresh water . after dumping all of the salt water from the small beaker into the large beaker , to what fraction of its capacity will the large beaker be filled ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 5.0\nn3 = 1.0\nn4 = 5.0\nt0 = n0 + n1\nt1 = n1 * n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.3" + ], + "split": "train" + }, + { + "Input": "sum of the squares of 3 numbers is 222 and the sum of their products taken two at a time is 131 . find the sum ?", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 222.0\nn2 = 131.0\nt0 = n2 * 2.0\nt1 = n1 + t0\nanswer = math.sqrt(max(0, t1))\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "the total price of a basic computer and printer are $ 2,500 . if the same printer had been purchased with an enhanced computer whose price was $ 500 more than the price of the basic computer , then the price of the printer would have been 1 / 4 of that total . what was the price of the basic computer ?", + "Output Program": [ + "n0 = 2500.0\nn1 = 500.0\nn2 = 1.0\nn3 = 4.0\nt0 = 0.25 * 1000.0\nt1 = t0 * 10.0\nt2 = n1 + t1\nt3 = t2 / n3\nanswer = t1 - t3\nprint(answer)" + ], + "Output Answer": [ + "1750" + ], + "split": "train" + }, + { + "Input": "n ^ ( n / 2 ) = 6 is true when n = 6 in the same way what is the value of n if n ^ ( n / 2 ) = 9 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 6.0\nn2 = 6.0\nn3 = 2.0\nn4 = 9.0\nt0 = n4**min(n0, 5)\nanswer = t0 / n4\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "y and z are in a relay race . y runs the first leg of the course in 58 seconds . z runs the second leg of the course in 26 seconds . what was the average time they took to run a leg of the course ?", + "Output Program": [ + "n0 = 58.0\nn1 = 26.0\nt0 = n0 + n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "a , b , and c are integers and a < b < c . s is the set of all integers from a to b , inclusive . q is the set of all integers from b to c , inclusive . the median of set s is ( 3 / 4 ) * b . the median of set q is ( 5 / 8 ) * c . if r is the set of all integers from a to c , inclusive , what fraction of c is the median of set r ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 5.0\nn3 = 8.0\nt0 = n2 / n3\nt1 = n0 / n1\nt2 = t0 * 2.0\nt3 = t1 * 2.0\nt4 = t2 - 1.0\nt5 = t3 - 1.0\nt6 = 1.0 / t5\nt7 = t4 / t6\nt8 = t7 + 1.0\nanswer = t8 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "0.5625" + ], + "split": "train" + }, + { + "Input": "the mean of 30 values was 180 . it was detected on rechecking that one value 155 was wrongly copied as 135 for the computation of the mean . find the correct mean .", + "Output Program": [ + "n0 = 30.0\nn1 = 180.0\nn2 = 155.0\nn3 = 135.0\nt0 = n0 * n1\nt1 = n2 - n3\nt2 = t0 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "180.66666666666666" + ], + "split": "train" + }, + { + "Input": "the security gate at a storage facility requires a 5 - digit lock code . if the lock code must consist only of digits from 1 through 7 , inclusive , with no repeated digits , and the first and last digits of the code must be even , how many lock codes are possible ?", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 1.0\nn2 = 7.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(3.0)))\nt2 = t0 / 2.0\nanswer = t2 * t1\nprint(answer)" + ], + "Output Answer": [ + "360" + ], + "split": "train" + }, + { + "Input": "a group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 7 with 2 students left over . what is the sum of the two smallest possible values of n ?", + "Output Program": [ + "n0 = 4.0\nn1 = 1.0\nn2 = 7.0\nn3 = 2.0\nt0 = n2 * 2.0\nt1 = 2.0 * n3\nt2 = n3 + t0\nt3 = n2 * t1\nt4 = n3 + t3\nanswer = t2 + t4\nprint(answer)" + ], + "Output Answer": [ + "46" + ], + "split": "train" + }, + { + "Input": "in the rectangular coordinate system , what is the x - intercept of a line passing through ( 10 , 3 ) and ( \u2212 6 , \u2212 5 ) ?", + "Output Program": [ + "n0 = 10.0\nn1 = 3.0\nn2 = 6.0\nn3 = 5.0\nt0 = -n3\nt1 = -n2\nt2 = t0 - n1\nt3 = t1 - n0\nt4 = t2 / t3\nt5 = n0 * t4\nt6 = t5 - n1\nanswer = t6 / t4\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "in what ratio p : q should the mixture p of milk and water in the ratio of 5 : 3 be mixed with another mixture q of milk and water in the ratio 1 : 3 so that the resultant mixture contains equal quantities of milk and water ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nn2 = 1.0\nn3 = 3.0\nt0 = 4.0 + n3\nt1 = n0 + n2\nt2 = t0 - t1\nanswer = t2 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a person travels from p to q a speed of 80 km / hr and returns by increasing his speed by 10 % . what is his average speed for both the trips ?", + "Output Program": [ + "n0 = 80.0\nn1 = 10.0\nt0 = n1 / 100.0\nt1 = t0 + 1.0\nt2 = n0 * t1\nt3 = n0 + t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "84" + ], + "split": "train" + }, + { + "Input": "in a class of 38 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 10 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?", + "Output Program": [ + "n0 = 38.0\nn1 = 2.0\nn2 = 12.0\nn3 = 1.0\nn4 = 10.0\nn5 = 2.0\nn6 = 3.0\nn7 = 2.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n1 * n4\nt3 = t1 + t2\nt4 = n4 + t1\nt5 = n1 + t4\nt6 = n0 - t5\nt7 = t6 - n3\nt8 = n6 * t7\nt9 = t3 + t8\nanswer = t0 - t9\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "( 5 ) 1.25 \u00d7 ( 12 ) 0.25 \u00d7 ( 60 ) 0.75 = ?", + "Output Program": [ + "n0 = 5.0\nn1 = 1.25\nn2 = 12.0\nn3 = 0.25\nn4 = 60.0\nn5 = 0.75\nt0 = n0**min(n1, 5)\nt1 = n2**min(n3, 5)\nt2 = n4**min(n5, 5)\nt3 = t0 * t1\nanswer = t3 * t2\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "3 friends a , b , c went for week end party to mcdonald \u2019 s restaurant and there they measure there weights in some order in 7 rounds . a , b , c , ab , bc , ac , abc . final round measure is 170 kg then find the average weight of all the 7 rounds ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 170.0\nn3 = 7.0\nt0 = 1.0 + n0\nt1 = n2 * t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "97.14285714285714" + ], + "split": "train" + }, + { + "Input": "in digging a pond 28 m * 10 m * 5 m the volumes of the soil extracted will be ?", + "Output Program": [ + "n0 = 28.0\nn1 = 10.0\nn2 = 5.0\nt0 = n0 * n1\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "1400" + ], + "split": "train" + }, + { + "Input": "( 150 % of 1265 ) \u00f7 7 = ?", + "Output Program": [ + "n0 = 150.0\nn1 = 1265.0\nn2 = 7.0\nt0 = n0 / 100.0\nt1 = n1 * t0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "271.07142857142856" + ], + "split": "train" + }, + { + "Input": "if a is an integer greater than 2 but less than 7 and b is an integer greater than 4 but less than 13 , what is the range of a / b ?", + "Output Program": [ + "n0 = 2.0\nn1 = 7.0\nn2 = 4.0\nn3 = 13.0\nt0 = n2 + 1.0\nt1 = n0 + 1.0\nt2 = n1 - 1.0\nt3 = n3 - 1.0\nt4 = t2 / t0\nt5 = t1 / t3\nanswer = t4 - t5\nprint(answer)" + ], + "Output Answer": [ + "0.95" + ], + "split": "train" + }, + { + "Input": "all factors of a positive integer a are multiplied and the product obtained is a ^ 3 . if a is greater than 1 , how many factors does a have ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nt0 = 2.0 * 2.0\nt1 = t0 * 2.0\nt2 = t1 * 2.0\nt3 = n0 * t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today ' s production of 90 units raises the average to 58 units per day , what is the value of n ?", + "Output Program": [ + "n0 = 50.0\nn1 = 90.0\nn2 = 58.0\nt0 = n1 - n0\nt1 = n2 - n0\nt2 = t0 / t1\nanswer = t2 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "the manager at a health foods store mixes a unique superfruit juice cocktail that costs $ 1399.45 per litre to make . the cocktail includes mixed fruit juice and a \u00e7 ai berry juice , which cost $ 262.85 per litre and $ 3104.35 per litre , respectively . the manager has already opened 32 litres of the mixed fruit juice . how many litres of the a \u00e7 ai berry juice does he need to add ?", + "Output Program": [ + "n0 = 1399.45\nn1 = 262.85\nn2 = 3104.35\nn3 = 32.0\nt0 = n0 * n3\nt1 = n1 * n3\nt2 = n2 - n0\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "21.333333333333332" + ], + "split": "train" + }, + { + "Input": "the sum of the squares of 3 numbers is 241 , while the sum of their products taken two at a time is 100 . their sum is :", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 241.0\nn2 = 100.0\nt0 = n2 * 2.0\nt1 = n1 + t0\nanswer = math.sqrt(max(0, t1))\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "if w / x = 1 / 6 and w / y = 1 / 5 , then ( x + y ) / y =", + "Output Program": [ + "n0 = 1.0\nn1 = 6.0\nn2 = 1.0\nn3 = 5.0\nt0 = n2 / n0\nt1 = n3 / n1\nt2 = t0 / t1\nanswer = t2 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "2.2" + ], + "split": "train" + }, + { + "Input": "35 liters of a mixture is created by mixing liquid p and liquid q in the ratio 4 : 3 . how many liters of liquid q must be added to make the ratio 5 : 7 ?", + "Output Program": [ + "n0 = 35.0\nn1 = 4.0\nn2 = 3.0\nn3 = 5.0\nn4 = 7.0\nt0 = n3 + n4\nt1 = n1 + n2\nt2 = n0 * n1\nt3 = n0 * n2\nt4 = t2 / t1\nt5 = t3 / t1\nt6 = t0 * t4\nt7 = t6 / n3\nt8 = n4 * t7\nt9 = t8 / t0\nanswer = t9 - t5\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "for a certain exam , a score of 60 was 2 standard deviations below mean and a score of 100 was 3 standard deviations above mean . what was the mean score for the exam ?", + "Output Program": [ + "n0 = 60.0\nn1 = 2.0\nn2 = 100.0\nn3 = 3.0\nt0 = n1 + n3\nt1 = n0 * n3\nt2 = n1 * n2\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "76" + ], + "split": "train" + }, + { + "Input": "the sum of the present age of henry and jill is 48 . what is their present ages if 9 years ago henry was twice the age of jill ?", + "Output Program": [ + "n0 = 48.0\nn1 = 9.0\nt0 = n0 + n1\nt1 = t0 / 3.0\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "29" + ], + "split": "train" + }, + { + "Input": "the avg age of an adult class is 40 years . 12 new students with an avg age of 32 years join the class . therefore decreasingthe avg by 4 year . find what was the original strength of class ?", + "Output Program": [ + "n0 = 40.0\nn1 = 12.0\nn2 = 32.0\nn3 = 4.0\nt0 = n2 - n1\nt1 = n0 - n2\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "( 0.0048 ) ( 3.5 ) / ( 0.05 ) ( 0.1 ) ( 0.004 ) =", + "Output Program": [ + "n0 = 0.0048\nn1 = 3.5\nn2 = 0.05\nn3 = 0.1\nn4 = 0.004\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n4 * t1\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "839.9999999999998" + ], + "split": "train" + }, + { + "Input": "a batsman in his 17 th innings makes a score of 85 , and thereby increases his average by 3 . what is his average after the 17 th innings ? he had never been \u2019 not out \u2019 .", + "Output Program": [ + "n0 = 17.0\nn1 = 85.0\nn2 = 3.0\nn3 = 17.0\nt0 = n0 * n2\nt1 = n1 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "37" + ], + "split": "train" + }, + { + "Input": "of the total amount that jill spent on a shopping trip , excluding taxes , she spent 50 percent on clothing , 20 percent on food , and 30 percent on other items . if jill paid a 5 percent tax on the clothing , no tax on the food , and an 10 percent tax on all other items , then the total tax that she paid was what percent of the total amount that she spent , excluding taxes ?", + "Output Program": [ + "n0 = 50.0\nn1 = 20.0\nn2 = 30.0\nn3 = 5.0\nn4 = 10.0\nt0 = n3 / 100.0\nt1 = n4 / 100.0\nt2 = n0 * t0\nt3 = n2 * t1\nt4 = t2 + t3\nt5 = t4 / 100.0\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "5.5" + ], + "split": "train" + }, + { + "Input": "in a certain warehouse , 70 percent of the packages weigh less than 75 pounds , and a total of 48 packages weigh less than 25 pounds . if 80 percent of the packages weigh at least 25 pounds , how many of the packages weigh at least 25 pounds but less than 75 pounds ?", + "Output Program": [ + "n0 = 70.0\nn1 = 75.0\nn2 = 48.0\nn3 = 25.0\nn4 = 80.0\nn5 = 25.0\nn6 = 25.0\nn7 = 75.0\nt0 = 100.0 - n4\nt1 = n2 / t0\nt2 = t1 * 100.0\nt3 = n0 * t2\nt4 = t3 / 100.0\nanswer = t4 - n2\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "( 51 + 52 + 53 + \u2026 \u2026 \u2026 + 100 ) is equal to :", + "Output Program": [ + "n0 = 51.0\nn1 = 52.0\nn2 = 53.0\nn3 = 100.0\nt0 = n3 + 1.0\nt1 = n0 - 1.0\nt2 = n3 * t0\nt3 = n0 * t1\nt4 = t2 / 2.0\nt5 = t3 / 2.0\nanswer = t4 - t5\nprint(answer)" + ], + "Output Answer": [ + "3775" + ], + "split": "train" + }, + { + "Input": "the mean of 50 observations was 30 . it was found later that an observation 48 was wrongly taken as 23 . the corrected new mean is", + "Output Program": [ + "n0 = 50.0\nn1 = 30.0\nn2 = 48.0\nn3 = 23.0\nt0 = n0 * n1\nt1 = n0 - 2.0\nt2 = t1 - n3\nt3 = t0 + t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "30.5" + ], + "split": "train" + }, + { + "Input": "the average weight of 6 person ' s increases by 3.5 kg when a new person comes in place of one of them weighing 47 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 6.0\nn1 = 3.5\nn2 = 47.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "68" + ], + "split": "train" + }, + { + "Input": "a profit of rs . 800 is divided between x and y in the ratio of 1 / 2 : 1 / 3 . what is the difference between their profit shares ?", + "Output Program": [ + "n0 = 800.0\nn1 = 1.0\nn2 = 2.0\nn3 = 1.0\nn4 = 3.0\nt0 = n1 / n2\nt1 = n1 / n4\nt2 = t0 + t1\nt3 = n0 / t2\nt4 = t3 / n2\nt5 = t3 / n4\nanswer = t4 - t5\nprint(answer)" + ], + "Output Answer": [ + "160" + ], + "split": "train" + }, + { + "Input": "a is a positive integer and multiple of 2 ; p = 4 ^ a , what is the remainder when p is divided by 10 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 10.0\nt0 = 4.0**min(4.0, 5)\nanswer = t0 % n2\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "product of two natural numbers is 7 . then , the sum of reciprocals of their squares is", + "Output Program": [ + "n0 = 7.0\nt0 = 1.0 / 1.0\nt1 = 1.0 / n0\nt2 = t0**min(2.0, 5)\nt3 = t1**min(2.0, 5)\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "1.0204081632653061" + ], + "split": "train" + }, + { + "Input": "a telephone company needs to create a set of 3 - digit area codes . the company is entitled to use only digits 6 , 4 and 3 , which can be repeated . if the product of the digits in the area code must be even , how many different codes can be created ?", + "Output Program": [ + "n0 = 3.0\nn1 = 6.0\nn2 = 4.0\nn3 = 3.0\nt0 = n0**min(n0, 5)\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "you collect pens . suppose you start out with 5 . mike gives you another 20 pens . since her father makes pens , cindy decides to double your pens . since you ' re nice , you give sharon 10 pens . how many pens do you have at the end ?", + "Output Program": [ + "n0 = 5.0\nn1 = 20.0\nn2 = 10.0\nt0 = n0 + n1\nt1 = t0 * 2.0\nanswer = t1 - n2\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "of the total amount that jill spent on a shopping trip , excluding taxes , she spent 40 percent on clothing , 30 percent on food , and 30 percent on other items . if jill paid a 4 percent tax on the clothing , no tax on the food , and an 8 percent tax on all other items , then the total tax that she paid was what percent of the total amount that she spent , excluding taxes ?", + "Output Program": [ + "n0 = 40.0\nn1 = 30.0\nn2 = 30.0\nn3 = 4.0\nn4 = 8.0\nt0 = n3 / 100.0\nt1 = n4 / 100.0\nt2 = n0 * t0\nt3 = n2 * t1\nt4 = t2 + t3\nt5 = t4 / 100.0\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "a student chose a number , multiplied it by 5 , then subtracted 138 from the result and got 102 . what was the number he chose ?", + "Output Program": [ + "n0 = 5.0\nn1 = 138.0\nn2 = 102.0\nt0 = n1 + n2\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "sally has a gold credit card with a certain spending limit , and a platinum card with twice the spending limit of the gold card . currently , she has a balance on her gold card that is 1 / 3 of the spending limit on that card , and she has a balance on her platinum card that is 1 / 8 of the spending limit on that card . if sally transfers the entire balance on her gold card to her platinum card , what portion of her limit on the platinum card will remain unspent ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 8.0\nt0 = 1 / n3\nt1 = 1 / n1\nt2 = 1 / 2.0\nt3 = t1 * t2\nt4 = t0 + t3\nanswer = n0 - t4\nprint(answer)" + ], + "Output Answer": [ + "0.7083333333333334" + ], + "split": "train" + }, + { + "Input": "if { x } is the product of all even integers from 1 to x inclusive , what is the greatest prime factor of { 14 } + { 12 } ?", + "Output Program": [ + "n0 = 1.0\nn1 = 14.0\nn2 = 12.0\nt0 = n1 + n2\nt1 = n0 * 2.0\nt2 = t0 / 2.0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "if x + ( 1 / x ) = 5 , what is the value of w = x ^ 2 + ( 1 / x ) ^ 2 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 2.0\nn3 = 1.0\nn4 = 2.0\nt0 = n1**min(n2, 5)\nanswer = t0 - n2\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "if the price of a certain computer increased 30 percent from d dollars to 351 dollars , then 2 d =", + "Output Program": [ + "n0 = 30.0\nn1 = 351.0\nn2 = 2.0\nt0 = n0 + 100.0\nt1 = t0 / 100.0\nt2 = n1 / t1\nanswer = n2 * t2\nprint(answer)" + ], + "Output Answer": [ + "540" + ], + "split": "train" + }, + { + "Input": "a number when divided by 342 gives a remainder 47 . when the same number ift divided by 19 , what would be the remainder ?", + "Output Program": [ + "n0 = 342.0\nn1 = 47.0\nn2 = 19.0\nt0 = n2 * 2.0\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "1 / 2 + [ ( 2 / 3 * 3 / 8 ) + 4 ] - 8 / 16 =", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 2.0\nn3 = 3.0\nn4 = 3.0\nn5 = 8.0\nn6 = 4.0\nn7 = 8.0\nn8 = 16.0\nt0 = n1 / n3\nt1 = n3 / n5\nt2 = n0 / n1\nt3 = n5 / n8\nt4 = t0 * t1\nt5 = n6 + t4\nt6 = t5 + t2\nanswer = t6 - t3\nprint(answer)" + ], + "Output Answer": [ + "4.25" + ], + "split": "train" + }, + { + "Input": "a company producing fruit juice changed its packaging from boxes measuring 5 x 10 x 20 centimeters to boxes measuring 6 x 10 x 20 centimeters . if the price of a box did not change and all boxes are full of juice , by approximately what percent did the price of the juice decrease ?", + "Output Program": [ + "n0 = 5.0\nn1 = 10.0\nn2 = 20.0\nn3 = 6.0\nn4 = 10.0\nn5 = 20.0\nt0 = n0 * n1\nt1 = n1 * n3\nt2 = n2 * t0\nt3 = n2 * t1\nt4 = t2 / t3\nt5 = 1.0 - t4\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "16.666666666666664" + ], + "split": "train" + }, + { + "Input": "a man can row 4.2 km / hr in still water . it takes him twice as long to row upstream as to row downstream . what is the rate of the current ?", + "Output Program": [ + "n0 = 4.2\nt0 = n0 * 2.0\nt1 = t0 - n0\nanswer = t1 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "1.4000000000000001" + ], + "split": "train" + }, + { + "Input": "find the average of all the numbers between 11 and 21 which are divisible by 2 .", + "Output Program": [ + "n0 = 11.0\nn1 = 21.0\nn2 = 2.0\nt0 = n0 + 4.0\nt1 = n1 - 4.0\nt2 = t0 + t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "the events a and b are independent , the probability that event a occurs is greater than 0 , and the probability that event a occurs is twice the probability that event b occurs . the probability that at least one of events a and b occurs is 12 times the probability that both events a and b occur . what is the probability that event a occurs ?", + "Output Program": [ + "n0 = 0.0\nn1 = 12.0\nt0 = 1.0 + 2.0\nt1 = n1 * 2.0\nt2 = t1 + 2.0\nt3 = t0 / t2\nanswer = t3 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "0.23076923076923078" + ], + "split": "train" + }, + { + "Input": "a envelop weight 8.5 gm , if 800 of these envelop are sent with an advertisement mail . how much wieght ?", + "Output Program": [ + "n0 = 8.5\nn1 = 800.0\nt0 = n0 * n1\nanswer = t0 / 1000.0\nprint(answer)" + ], + "Output Answer": [ + "6.8" + ], + "split": "train" + }, + { + "Input": "a batsman scored 120 runs whichincluded 3 boundaries and 8 sixes . what % of his total score did he make by running between the wickets ?", + "Output Program": [ + "n0 = 120.0\nn1 = 3.0\nn2 = 8.0\nt0 = n1 + n1\nt1 = n1 * 4.0\nt2 = n2 * t0\nt3 = t1 + t2\nt4 = t3 / n0\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "the events a and b are independent , the probability that event a occurs is greater than 0 , and the probability that event a occurs is twice the probability that event b occurs . the probability that at least one of events a and b occurs is 3 times the probability that both events a and b occur . what is the probability that event a occurs ?", + "Output Program": [ + "n0 = 0.0\nn1 = 3.0\nt0 = 1.0 + 2.0\nt1 = n1 * 2.0\nt2 = t1 + 2.0\nt3 = t0 / t2\nanswer = t3 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "0.75" + ], + "split": "train" + }, + { + "Input": "3 photographers , lisa , mike and norm , take photos of a wedding . the total of lisa and mikes photos is 60 less than the sum of mike ' s and norms . if norms photos number 10 more than twice the number of lisa ' s photos , then how many photos did norm take ?", + "Output Program": [ + "n0 = 3.0\nn1 = 60.0\nn2 = 10.0\nt0 = n1 * 2.0\nanswer = t0 - n2\nprint(answer)" + ], + "Output Answer": [ + "110" + ], + "split": "train" + }, + { + "Input": "the average age of a group of 10 students is 14 years . if 5 more students join the group , the average age rises by 1 year . the average age of the new students is :", + "Output Program": [ + "n0 = 10.0\nn1 = 14.0\nn2 = 5.0\nn3 = 1.0\nt0 = n1 + n3\nt1 = n0 * n1\nt2 = t0 * t0\nt3 = t2 - t1\nanswer = t3 / n2\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "shekar scored 76 , 65 , 82 , 67 and 75 marks in mathematics , science , social studies , english and biology respectively . what are his average marks ?", + "Output Program": [ + "n0 = 76.0\nn1 = 65.0\nn2 = 82.0\nn3 = 67.0\nn4 = 75.0\nt0 = n0 + n1\nt1 = 1.0 + 4.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "73" + ], + "split": "train" + }, + { + "Input": "a student chose a number , multiplied it by 2 , then subtracted 152 from the result and got 102 . what was the number he chose ?", + "Output Program": [ + "n0 = 2.0\nn1 = 152.0\nn2 = 102.0\nt0 = n1 + n2\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "127" + ], + "split": "train" + }, + { + "Input": "if a is an integer greater than 9 but less than 26 and b is an integer greater than 14 but less than 31 , what is the range of a / b ?", + "Output Program": [ + "n0 = 9.0\nn1 = 26.0\nn2 = 14.0\nn3 = 31.0\nt0 = n2 + 1.0\nt1 = n0 + 1.0\nt2 = n1 - 1.0\nt3 = n3 - 1.0\nt4 = t2 / t0\nt5 = t1 / t3\nanswer = t4 - t5\nprint(answer)" + ], + "Output Answer": [ + "1.3333333333333335" + ], + "split": "train" + }, + { + "Input": "when positive integer x is divided by positive integer y , the remainder is 12 . if x / y = 75.12 , what is the value of y ?", + "Output Program": [ + "import math\nn0 = 12.0\nn1 = 75.12\nt0 = math.floor(n1)\nt1 = n1 - t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "99.9999999999962" + ], + "split": "train" + }, + { + "Input": "the cost to park a car in a certain parking garage is $ 20.00 for up to 2 hours of parking and $ 1.75 for each hour in excess of 2 hours . what is the average ( arithmetic mean ) cost per hour to park a car in the parking garage for 9 hours ?", + "Output Program": [ + "n0 = 20.0\nn1 = 2.0\nn2 = 1.75\nn3 = 2.0\nn4 = 9.0\nt0 = n4 - n1\nt1 = n2 * t0\nt2 = n0 + t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "3.5833333333333335" + ], + "split": "train" + }, + { + "Input": "if the sum and difference of two numbers are 20 and 10 respectively , then the difference of their square is :", + "Output Program": [ + "n0 = 20.0\nn1 = 10.0\nt0 = n0 + n1\nt1 = t0 / 2.0\nt2 = t1**min(2.0, 5)\nt3 = n0 - t1\nt4 = t3**min(2.0, 5)\nanswer = t2 - t4\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "train" + }, + { + "Input": "the average mark of the students of a class in a particular exam is 90 . if 2 students whose average mark in that exam is 45 are excluded , the average mark of the remaining will be 95 . find the number of students who wrote the exam ?", + "Output Program": [ + "n0 = 90.0\nn1 = 2.0\nn2 = 45.0\nn3 = 95.0\nt0 = n1 * n3\nt1 = n1 * n2\nt2 = n3 - n0\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "a , b and c invest in the ratio of 3 : 4 : 5 . the percentage of return on their investments are in the ratio of 6 : 5 : 4 . find the total earnings , if b earns rs . 250 more than a :", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 5.0\nn3 = 6.0\nn4 = 5.0\nn5 = 4.0\nn6 = 250.0\nt0 = n0 * n3\nt1 = n1 * n2\nt2 = t0 + t1\nt3 = t1 - t0\nt4 = t2 + t1\nt5 = n6 / t3\nanswer = t4 * t5\nprint(answer)" + ], + "Output Answer": [ + "7250" + ], + "split": "train" + }, + { + "Input": "find the value of x from the below equation ? : 3 x ^ 2 - 5 x + 2 = 0", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 2.0\nn2 = 5.0\nn3 = 2.0\nn4 = 0.0\nt0 = n2 * n2\nt1 = n1**min(n0, 5)\nt2 = t1 - t0\nt3 = math.sqrt(max(0, t2))\nt4 = n1 - t3\nanswer = t4 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.6666666666666666" + ], + "split": "train" + }, + { + "Input": "n ^ ( n / 2 ) = 4 is true when n = 4 in the same way what is the value of n if n ^ ( n / 2 ) = 8 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 4.0\nn3 = 2.0\nn4 = 8.0\nt0 = n4**min(n0, 5)\nanswer = t0 / n4\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "if n = 2 ^ 0.25 and n ^ b = 8 , b must equal", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 0.25\nn2 = 8.0\nt0 = math.log(max(1e-5, n2), 2)\nt1 = n0**min(n1, 5)\nt2 = math.log(max(1e-5, t1), 2)\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "12.000000000000002" + ], + "split": "train" + }, + { + "Input": "[ ( 3.242 x 15 ) / 100 ] = ?", + "Output Program": [ + "n0 = 3.242\nn1 = 15.0\nn2 = 100.0\nt0 = n0 * n1\nt1 = t0 / n2\nanswer = t1 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "0.04863" + ], + "split": "train" + }, + { + "Input": "find the total number of prime factors in the expression ( 4 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 2", + "Output Program": [ + "n0 = 4.0\nn1 = 11.0\nn2 = 7.0\nn3 = 5.0\nn4 = 11.0\nn5 = 2.0\nt0 = n1 * n5\nt1 = n3 + t0\nanswer = n5 + t1\nprint(answer)" + ], + "Output Answer": [ + "29" + ], + "split": "train" + }, + { + "Input": "xy = 1 then what is ( 6 ^ ( x + y ) ^ 2 ) / ( 6 ^ ( x - y ) ^ 2 )", + "Output Program": [ + "n0 = 1.0\nn1 = 6.0\nn2 = 2.0\nn3 = 6.0\nn4 = 2.0\nt0 = n0 * 4.0\nanswer = n1**min(t0, 5)\nprint(answer)" + ], + "Output Answer": [ + "1296" + ], + "split": "train" + }, + { + "Input": "\u221a ( 25 ) ^ 2", + "Output Program": [ + "import math\nn0 = 25.0\nn1 = 2.0\nt0 = n0**min(n1, 5)\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "what is the sum of 20 consecutive integers from - 9 inclusive , in a increasing order ?", + "Output Program": [ + "n0 = 20.0\nn1 = 9.0\n\nanswer = n1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "a soft drink company had 6000 small and 15000 big bottles in storage . if 12 % of small 14 % of big bottles have been sold , then the total bottles remaining in storage is", + "Output Program": [ + "n0 = 6000.0\nn1 = 15000.0\nn2 = 12.0\nn3 = 14.0\nt0 = n0 + n1\nt1 = n2 / 100.0\nt2 = n3 / 100.0\nt3 = n0 * t1\nt4 = n1 * t2\nt5 = t3 + t4\nanswer = t0 - t5\nprint(answer)" + ], + "Output Answer": [ + "18180" + ], + "split": "train" + }, + { + "Input": "in a box of 10 pencils , a total of 2 are defective . if a customer buys 3 pencils selected at random from the box , what is the probability that neither pencils will be defective ?", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 2.0\nn2 = 3.0\nt0 = math.factorial(min(15, int(n2)))\nt1 = math.factorial(min(15, int(n0)))\nt2 = n0 - n1\nt3 = n0 - n2\nt4 = math.factorial(min(15, int(t2)))\nt5 = math.factorial(min(15, int(t3)))\nt6 = t2 - n2\nt7 = math.factorial(min(15, int(t6)))\nt8 = t5 * t0\nt9 = t1 / t8\nt10 = t7 * t0\nt11 = t4 / t10\nanswer = t11 / t9\nprint(answer)" + ], + "Output Answer": [ + "0.4666666666666667" + ], + "split": "train" + }, + { + "Input": "company workers decided to raise rs . 3 lakhs by equal contribution from each . had they contributed rs . 50 each extra , the contribution would have been rs . 3.25 lakhs . how many workers were they ?", + "Output Program": [ + "n0 = 3.0\nn1 = 50.0\nn2 = 3.25\nt0 = 100.0 * 1000.0\nt1 = n2 * t0\nt2 = n0 * t0\nt3 = t1 - t2\nanswer = t3 / n1\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "train" + }, + { + "Input": "the average of 7 numbers is 20 . if each number be multiplied by 5 . find the average of new set of numbers ?", + "Output Program": [ + "n0 = 7.0\nn1 = 20.0\nn2 = 5.0\n\nanswer = n1 * n2\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "each of the positive integers a and c is a 4 - digit integer . if each of the digits 0 through 9 appears in one of these 3 integers , what is the maximum possible value of the sum of a and c ?", + "Output Program": [ + "n0 = 4.0\nn1 = 0.0\nn2 = 9.0\nn3 = 3.0\nt0 = n0 + n3\nt1 = n0 + 1.0\nt2 = n2 * 1000.0\nt3 = n0 * 2.0\nt4 = n3 * 2.0\nt5 = n0 * 10.0\nt6 = t0 * 100.0\nt7 = t1 * 10.0\nt8 = t3 * 1000.0\nt9 = t4 * 100.0\nt10 = t2 + t6\nt11 = t8 + t9\nt12 = t10 + t7\nt13 = t11 + t5\nt14 = n3 + t12\nt15 = t13 + 2.0\nanswer = t14 + t15\nprint(answer)" + ], + "Output Answer": [ + "18395" + ], + "split": "train" + }, + { + "Input": "a number when divided by 899 gives a remainder 63 . what remainder will be obtained by dividing the same number by 29", + "Output Program": [ + "n0 = 899.0\nn1 = 63.0\nn2 = 29.0\nt0 = n2 * 2.0\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "if xy = 9 , x / y = 36 , for positive numbers x and y , y = ?", + "Output Program": [ + "import math\nn0 = 9.0\nn1 = 36.0\nt0 = n0 / n1\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "in one year , the population , of a village increased by 20 % and in the next year , it decreased by 20 % . if at the end of 2 nd year , the population was 9600 , what was it in the beginning ?", + "Output Program": [ + "n0 = 20.0\nn1 = 20.0\nn2 = 2.0\nn3 = 9600.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nt2 = 1.0 - t0\nt3 = n3 / t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "10000" + ], + "split": "train" + }, + { + "Input": "ram get 450 marks in his exam which is 90 % of total marks . what is the total marks ?", + "Output Program": [ + "n0 = 450.0\nn1 = 90.0\nt0 = 2.0 + 3.0\nt1 = t0 * 10.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "train" + }, + { + "Input": "in a certain country 1 / 7 of 8 = 5 . assuming the same proportion , what would be the value of 1 / 5 of 40 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 7.0\nn2 = 8.0\nn3 = 5.0\nn4 = 1.0\nn5 = 5.0\nn6 = 40.0\nt0 = n1 / n2\nanswer = n6 * t0\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "in the junior basketball league there are 18 teams , 2 / 3 of them are bad and \u00bd are rich . what ca n ' t be the number of teams that are rich and bad ?", + "Output Program": [ + "n0 = 18.0\nn1 = 2.0\nn2 = 3.0\nt0 = 1.0 / 2.0\nt1 = n0 * t0\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the total of 344 of 20 paise and 25 paise make a sum of rs . 71 . the no of 20 paise coins is", + "Output Program": [ + "n0 = 344.0\nn1 = 20.0\nn2 = 25.0\nn3 = 71.0\nn4 = 20.0\nt0 = n0 * n2\nt1 = n3 * 100.0\nt2 = n2 - n1\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "if a * b * c = ( \u221a ( a + 2 ) ( b + 3 ) ) / ( c + 1 ) , find the value of 6 * 15 * 7 .", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 3.0\nn2 = 1.0\nn3 = 6.0\nn4 = 15.0\nn5 = 7.0\nt0 = n0 + n3\nt1 = n1 + n4\nt2 = n2 + n5\nt3 = t0 * t1\nt4 = math.sqrt(max(0, t3))\nanswer = t4 / t2\nprint(answer)" + ], + "Output Answer": [ + "1.5" + ], + "split": "train" + }, + { + "Input": "during a certain two - week period , 64 percent of the movies rented from a video store were comedies , and of the remaining movies rented , there were 5 times as many dramas as action movies . if no other movies were rented during that two - week period and there were a action movies rented , then how many comedies , in terms of a , were rented during that two - week period ?", + "Output Program": [ + "import math\nn0 = 64.0\nn1 = 5.0\nt0 = n1 + 1.0\nt1 = n0 / t0\nanswer = math.floor(t1)\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "find the greatest 4 digit number which leaves respective remainders of 2 and 5 when divided by 15 and 24 . a . 9974", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\nn2 = 5.0\nn3 = 15.0\nn4 = 24.0\nn5 = 9974.0\nt0 = n3 * n4\nt1 = n2 * n3\nt2 = t0 - t1\nanswer = t2 - 4.0\nprint(answer)" + ], + "Output Answer": [ + "281" + ], + "split": "train" + }, + { + "Input": "p has $ 35 more than what q and r together would have had if both b and c had 1 / 7 of what p has . how much does p have ?", + "Output Program": [ + "n0 = 35.0\nn1 = 1.0\nn2 = 7.0\nt0 = n1 / n2\nt1 = t0 * 2.0\nt2 = n1 - t1\nanswer = n0 / t2\nprint(answer)" + ], + "Output Answer": [ + "49" + ], + "split": "train" + }, + { + "Input": "a is the hundreds digit of the 3 digit integer x , b is the tens digit of x , and c is the units digit of x . 4 a = 2 b = c , and a > 0 . what is the difference between the two greatest possible values of x ? tip : dont stop till you have exhausted all answer choices to arrive at the correct one .", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 2.0\nn3 = 0.0\nt0 = n0 * n1\nt1 = t0 * 10.0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "124" + ], + "split": "train" + }, + { + "Input": "35 - [ 23 - { 15 - x } ] = 12 \u00d7 2 \u00f7 1 / 2", + "Output Program": [ + "n0 = 35.0\nn1 = 23.0\nn2 = 15.0\nn3 = 12.0\nn4 = 2.0\nn5 = 1.0\nn6 = 2.0\n\nanswer = n0 - 3.0\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "if n is an integer , f ( n ) = f ( n - 1 ) - n and f ( 4 ) = 20 . what is the value of f ( 6 ) ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 20.0\nn3 = 6.0\nt0 = n0 + n1\nt1 = n2 - t0\nanswer = t1 - n3\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "what is the smallest 5 digit number that is divisible by 15 , 32 , 45 , and 54 ?", + "Output Program": [ + "import scipy\nn0 = 5.0\nn1 = 15.0\nn2 = 32.0\nn3 = 45.0\nn4 = 54.0\nt0 = scipy.lcm(int(n0), int(n1))\nt1 = 100.0 * 100.0\nt2 = scipy.lcm(int(n2), int(t0))\nt3 = scipy.lcm(int(n3), int(t2))\nt4 = scipy.lcm(int(n4), int(t3))\nt5 = t1 % t4\nt6 = t4 - t5\nanswer = t1 + t6\nprint(answer)" + ], + "Output Answer": [ + "12960" + ], + "split": "train" + }, + { + "Input": "excluding stoppages , the average speed of a bus is 60 km / hr and including stoppages , the average speed of the bus is 45 km / hr . for how many minutes does the bus stop per hour ?", + "Output Program": [ + "n0 = 60.0\nn1 = 45.0\nt0 = n1 / n0\nt1 = 1.0 * 60.0\nt2 = t0 * 60.0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "there are 6 more women than there are men on a local co - ed softball team . if there are a total of 24 players on the team , what is the ratio of men to women ?", + "Output Program": [ + "n0 = 6.0\nn1 = 24.0\nt0 = 1.0 + 1.0\nt1 = n1 - n0\nt2 = t1 / t0\nt3 = n0 + t2\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.6" + ], + "split": "train" + }, + { + "Input": "( x + 6 ) is a factor in x ^ 2 - mx - 42 . what is the value of m ?", + "Output Program": [ + "n0 = 6.0\nn1 = 2.0\nn2 = 42.0\nt0 = n2 / n0\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "if a 10 percent deposit that has been paid toward the purchase of a certain product is $ 120 , how much more remains to be paid ?", + "Output Program": [ + "n0 = 10.0\nn1 = 120.0\nt0 = 100.0 / n0\nt1 = n1 * t0\nanswer = t1 - n1\nprint(answer)" + ], + "Output Answer": [ + "1080" + ], + "split": "train" + }, + { + "Input": "what least number should be added to 1101 , so that the sum is completely divisible by 24", + "Output Program": [ + "n0 = 1101.0\nn1 = 24.0\nt0 = n0 % n1\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "how many 3 digit no ' s are between 100 - 500 , where sum of two digit is 3 rd ?", + "Output Program": [ + "n0 = 3.0\nn1 = 100.0\nn2 = 500.0\nn3 = 3.0\nt0 = 4.0 + 4.0\nt1 = n2 / 100.0\nt2 = n0 - 1.0\nt3 = t0 - t1\nt4 = t3 + 1.0\nt5 = t4 + t0\nt6 = t5 * t1\nt7 = t6 / t2\nanswer = t7 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "in a mixture of 45 litres the ratio of milk to water is 4 : 1 . additional 21 litres of water is added to the mixture . find the ratio of milk to water in the resulting mixture .", + "Output Program": [ + "n0 = 45.0\nn1 = 4.0\nn2 = 1.0\nn3 = 21.0\nt0 = n1 + n2\nt1 = n0 / t0\nt2 = n3 + t1\nt3 = n0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "1.2" + ], + "split": "train" + }, + { + "Input": "the cost of 2 books and 2 magazines is $ 26 . the cost of 1 book and 3 magazines is $ 27 . how much does 1 magazine cost ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 26.0\nn3 = 1.0\nn4 = 3.0\nn5 = 27.0\nn6 = 1.0\nt0 = n0 * n5\nt1 = n0 * n4\nt2 = t0 - n2\nt3 = t1 - n0\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "the organizers of a fair projected a 25 percent increase in attendance this year over that of last year , but attendance this year actually decreased by 20 percent . what percent of the projected attendance was the actual attendance ?", + "Output Program": [ + "n0 = 25.0\nn1 = 20.0\nt0 = n0 + 100.0\nt1 = n1 * 4.0\nt2 = t1 / t0\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "train" + }, + { + "Input": "if x + y = 270 , x - y = 200 , for integers of x and y , y = ?", + "Output Program": [ + "n0 = 270.0\nn1 = 200.0\nt0 = n0 + n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "235" + ], + "split": "train" + }, + { + "Input": "the average weight of 22 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg . find the average weights of all the boys in the class .", + "Output Program": [ + "n0 = 22.0\nn1 = 50.25\nn2 = 8.0\nn3 = 45.15\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "48.89" + ], + "split": "train" + }, + { + "Input": "a sporting goods store sold 60 frisbees in one week , some for $ 3 and the rest for $ 4 each . if receipts from frisbee sales for the week totaled $ 204 , what is the fewest number of $ 4 frisbees that could have been sold ?", + "Output Program": [ + "n0 = 60.0\nn1 = 3.0\nn2 = 4.0\nn3 = 204.0\nn4 = 4.0\nt0 = n0 * n1\nanswer = n3 - t0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "patrick purchased 90 pencils and sold them at a loss equal to the selling price of 40 pencils . the cost of 90 pencils is how many times the selling price of 90 pencils ?", + "Output Program": [ + "n0 = 90.0\nn1 = 40.0\nn2 = 90.0\nn3 = 90.0\nt0 = n0 + n1\nt1 = n0 / t0\nanswer = 1 / t1\nprint(answer)" + ], + "Output Answer": [ + "1.4444444444444444" + ], + "split": "train" + }, + { + "Input": "if ( a - b - c + d = 18 ) and ( a + b - c - d = 6 ) , what is the value of ( b - d ) ^ 2 ?", + "Output Program": [ + "n0 = 18.0\nn1 = 6.0\nn2 = 2.0\nt0 = n0 + n1\nt1 = t0 / n2\nt2 = n1 - t1\nanswer = t2**min(n2, 5)\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "if the price of sugar rises from rs . 6 per kg to rs . 7.50 per kg , a person , to have no increase in the expenditure on sugar , will have to reduce his consumption of sugar by", + "Output Program": [ + "n0 = 6.0\nn1 = 7.5\nt0 = n0 * 1.0\nt1 = t0 / n1\nt2 = 1.0 - t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "19.999999999999996" + ], + "split": "train" + }, + { + "Input": "the number of the members of a club is more than 50 and less than 80 . when 5 people sit at a table , other people exactly divided to 8 - people groups ( 8 people sit at a table ) or 7 - people groups ( 7 people sit at a table ) . if the members are divided to 9 - people groups , how many people will be left ?", + "Output Program": [ + "import scipy\nn0 = 50.0\nn1 = 80.0\nn2 = 5.0\nn3 = 8.0\nn4 = 8.0\nn5 = 7.0\nn6 = 7.0\nn7 = 9.0\nt0 = scipy.lcm(int(n3), int(n5))\nt1 = n2 + t0\nanswer = t1 % n7\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "in a certain flower shop , which stocks 4 types of flowers , there are 1 / 3 as many violets as carnations , and 1 / 3 as many tulips as violets . if there are equal numbers of roses and tulips , what percent of the flowers in the shop are carnations ?", + "Output Program": [ + "n0 = 4.0\nn1 = 1.0\nn2 = 3.0\nn3 = 1.0\nn4 = 3.0\nt0 = n2 * n2\nt1 = 1.0 / t0\nt2 = t1 + t1\nt3 = t2 + 1.0\nt4 = t3 + 0.33\nanswer = 100.0 / t4\nprint(answer)" + ], + "Output Answer": [ + "64.42376521116678" + ], + "split": "train" + }, + { + "Input": "two brother x and y appeared for an exam . the probability of selection of x is 1 / 5 and that of b is 2 / 7 . find the probability that both of them are selected .", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 2.0\nn3 = 7.0\nt0 = n0 / n1\nt1 = n2 / n3\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "0.05714285714285714" + ], + "split": "train" + }, + { + "Input": "the average of runs of a cricket player of 10 innings was 42 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?", + "Output Program": [ + "n0 = 10.0\nn1 = 42.0\nn2 = 4.0\nt0 = n0 + 1.0\nt1 = n1 + n2\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "86" + ], + "split": "train" + }, + { + "Input": "in a survey of parents , exactly 9 / 10 of the mothers and 3 / 4 of the fathers held full - time jobs . if 40 percent of the parents surveyed were women , what percent of the parents did not hold full - time jobs ?", + "Output Program": [ + "n0 = 9.0\nn1 = 10.0\nn2 = 3.0\nn3 = 4.0\nn4 = 40.0\nt0 = n2 / n3\nt1 = n0 / n1\nt2 = 100.0 - n4\nt3 = t0 * t2\nt4 = n4 * t1\nt5 = t2 - t3\nt6 = n4 - t4\nanswer = t5 + t6\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "if josh , doug , and brad have a total of $ 68 between them , and josh has two times as much money as brad but only 3 - fourths as much as doug , how much money does doug have ?", + "Output Program": [ + "n0 = 68.0\nn1 = 3.0\nt0 = 4.0 / 3.0\nt1 = 1.0 / 2.0\nt2 = t0 + 1.0\nt3 = t2 + t1\nt4 = n0 / t3\nanswer = t4 * t0\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "if p / q = 5 / 4 , then 2 p + q = ?", + "Output Program": [ + "n0 = 5.0\nn1 = 4.0\nn2 = 2.0\nt0 = n0 * n2\nanswer = n1 + t0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "a box contains 9 pairs of shoes ( 18 shoes in total ) . if two shoes are selected at random , what it is the probability that they are matching shoes ?", + "Output Program": [ + "n0 = 9.0\nn1 = 18.0\nt0 = n1 - 1.0\nanswer = 1.0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.058823529411764705" + ], + "split": "train" + }, + { + "Input": "a marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each . there can be no less than 8 musicians per row and no more than 30 musicians per row . how many different rectangular formations x are possible ?", + "Output Program": [ + "n0 = 240.0\nn1 = 8.0\nn2 = 30.0\n\nanswer = n0 / n2\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "solve : - 666 x 666 x 666 + 555 x 555 x 555 = ? ( 666 x 666 - 666 x 555 + 555 x 555 )", + "Output Program": [ + "n0 = 666.0\nn1 = 666.0\nn2 = 666.0\nn3 = 555.0\nn4 = 555.0\nn5 = 555.0\nn6 = 666.0\nn7 = 666.0\nn8 = 666.0\nn9 = 555.0\nn10 = 555.0\nn11 = 555.0\nt0 = n0 * n0\nt1 = n3 * n3\nt2 = n0 * n3\nt3 = t0 + t1\nt4 = n0 * t0\nt5 = n3 * t1\nt6 = t4 + t5\nt7 = t3 - t2\nanswer = t6 / t7\nprint(answer)" + ], + "Output Answer": [ + "1221" + ], + "split": "train" + }, + { + "Input": "when positive integer x is divided by positive integer y , the remainder is 11.52 . if x / y = 96.12 , what is the value of y ?", + "Output Program": [ + "import math\nn0 = 11.52\nn1 = 96.12\nt0 = math.floor(n1)\nt1 = n1 - t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "95.99999999999636" + ], + "split": "train" + }, + { + "Input": "if 213 \u00d7 16 = 3408 , then 0.016 \u00d7 2.13 is equal to :", + "Output Program": [ + "n0 = 213.0\nn1 = 16.0\nn2 = 3408.0\nn3 = 0.016\nn4 = 2.13\n\nanswer = n4 * n3\nprint(answer)" + ], + "Output Answer": [ + "0.03408" + ], + "split": "train" + }, + { + "Input": "the number n is 76 h 4 , where h represents the 10 ' s digit . if n is divisible by 9 , what is the value of h ?", + "Output Program": [ + "n0 = 76.0\nn1 = 4.0\nn2 = 10.0\nn3 = 9.0\nt0 = n0 * 100.0\nt1 = n1 + t0\nt2 = t1 % n3\nanswer = n3 - t2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "what is the dividend . divisor 14 , the quotient is 9 and the remainder is 5 ?", + "Output Program": [ + "n0 = 14.0\nn1 = 9.0\nn2 = 5.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "131" + ], + "split": "train" + }, + { + "Input": "if q = { 1 , 7 , 18 , 20 , 29 , 33 } , how much less is the mean of the numbers in q than the median of the numbers in q ?", + "Output Program": [ + "n0 = 1.0\nn1 = 7.0\nn2 = 18.0\nn3 = 20.0\nn4 = 29.0\nn5 = 33.0\nt0 = n2 + n3\nt1 = n0 + n1\nt2 = 2.0 * 3.0\nt3 = n2 + t1\nt4 = t0 / 2.0\nt5 = n3 + t3\nt6 = n4 + t5\nt7 = n5 + t6\nt8 = t7 / t2\nanswer = t4 - t8\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "one ton has 2100 pounds , and one pound has 16 ounces . how many packets containing wheat weighing 16 pounds and 4 ounces each would totally fill a gunny bag of capacity 13 tons ?", + "Output Program": [ + "n0 = 2100.0\nn1 = 16.0\nn2 = 16.0\nn3 = 4.0\nn4 = 13.0\nt0 = n0 * n4\nt1 = n1 * n1\nt2 = n3 + t1\nt3 = n1 * t0\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "1680" + ], + "split": "train" + }, + { + "Input": "perimeter of front wheel = 30 , back wheel = 20 . if front wheel revolves 240 times . how many revolutions will the back wheel take ?", + "Output Program": [ + "n0 = 30.0\nn1 = 20.0\nn2 = 240.0\nt0 = n0 * n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "360" + ], + "split": "train" + }, + { + "Input": "if x is a positive integer , then the least value of x for which x ! is divisible by 100,000 is ? can someone please explain intuitively what the question is asking ?", + "Output Program": [ + "n0 = 100000.0\nt0 = 10.0 / 2.0\nanswer = t0 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "when x is multiplied by 3 , the result is 26 more than the result of subtracting x from 62 . what is the value of x ?", + "Output Program": [ + "n0 = 3.0\nn1 = 26.0\nn2 = 62.0\nt0 = n1 + n2\nt1 = 1.0 + n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "find the principle on a certain sum of money at 6 % per annum for 2 2 / 5 years if the amount being rs . 1120 ?", + "Output Program": [ + "n0 = 6.0\nn1 = 2.0\nn2 = 2.0\nn3 = 5.0\nn4 = 1120.0\nt0 = n1 * n3\nt1 = n1 + t0\nt2 = t1 / n3\nt3 = n0 * t2\nt4 = t3 / 100.0\nt5 = t4 + 1.0\nanswer = n4 / t5\nprint(answer)" + ], + "Output Answer": [ + "979.0209790209791" + ], + "split": "train" + }, + { + "Input": "a collection of books went on sale , and 2 / 3 of them were sold for $ 4 each . if none of the 36 remaining books were sold , what was the total amount received for the books that were sold ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 4.0\nn3 = 36.0\nt0 = n2 / n1\nt1 = 1.0 / n1\nt2 = n3 * t0\nt3 = t2 / t1\nanswer = n0 * t3\nprint(answer)" + ], + "Output Answer": [ + "288" + ], + "split": "train" + }, + { + "Input": "in a digital circuit which was to implement ( a b ) + ( a ) xor ( b ) , the designer implements ( a b ) ( a ) xor ( b ) what is the probability of error in it ?", + "Output Program": [ + "t0 = 3.0 / 4.0\nanswer = t0 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "if 20 gallons of grape juice are added to 40 gallons of a mixture , which contains 10 percent grape juice then what percent of the resulting mixture is grape juice ?", + "Output Program": [ + "n0 = 20.0\nn1 = 40.0\nn2 = 10.0\nt0 = n0 + n1\nt1 = n2 / 100.0\nt2 = n1 * t1\nt3 = n0 + t2\nt4 = t3 / t0\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "a box has exactly 100 balls , and each ball is either red , blue , or white . if the box has 12 more blue balls than white balls , and twice as many red balls as blue balls , how many white balls does the box has ?", + "Output Program": [ + "n0 = 100.0\nn1 = 12.0\nt0 = n1 * 3.0\nt1 = n0 - t0\nanswer = t1 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "the total age of a and b is 11 years more than the total age of b and c . c is how many year younger than a", + "Output Program": [ + "n0 = 11.0\n\nanswer = n0 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "( 6 ! - 4 ! ) / 5 ! = ?", + "Output Program": [ + "import math\nn0 = 6.0\nn1 = 4.0\nn2 = 5.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(n1)))\nt2 = math.factorial(min(15, int(n2)))\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "5.8" + ], + "split": "train" + }, + { + "Input": "a sum of money is sufficient to pay p ' s wages for 24 days and q ' s wages for 40 days . the same money is sufficient to pay the wages of both for ?", + "Output Program": [ + "n0 = 24.0\nn1 = 40.0\nt0 = 1.0 / n0\nt1 = 1.0 / n1\nt2 = t0 + t1\nanswer = 1.0 / t2\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "a certain family has 3 sons : richard is 6 years older than david , and david is 8 years older than scott . if in 8 years , richard will be twice as old as scott , then how old was david 7 years ago ?", + "Output Program": [ + "n0 = 3.0\nn1 = 6.0\nn2 = 8.0\nn3 = 8.0\nn4 = 7.0\nt0 = n1 + n2\nanswer = t0 - n4\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "in a competitive examination in state a , 6 % candidates got selected from the total appeared candidates . state b had an equal number of candidates appeared and 7 % candidates got selected with 84 more candidates got selected than a . what was the number of candidates appeared from each state ?", + "Output Program": [ + "n0 = 6.0\nn1 = 7.0\nn2 = 84.0\nt0 = n1 - n0\nt1 = t0 / 100.0\nanswer = n2 / t1\nprint(answer)" + ], + "Output Answer": [ + "8400" + ], + "split": "train" + }, + { + "Input": "on day one , a store sold 96 pens . on each of the next d days , the company sold 44 pens . if the average daily sales of pens over this time period ( including day one ) is 48 pens , what is the value of d ?", + "Output Program": [ + "n0 = 96.0\nn1 = 44.0\nn2 = 48.0\nt0 = n0 - n2\nt1 = n2 - n1\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "carrie likes to buy t - shirts at the local clothing store . they cost $ 9.15 each . one day , she bought 22 t - shirts . how much money did she spend ?", + "Output Program": [ + "import math\nn0 = 9.15\nn1 = 22.0\nt0 = n0 * n1\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "201" + ], + "split": "train" + }, + { + "Input": "the h . c . f . of two numbers is 12 and their difference is 12 . the numbers are :", + "Output Program": [ + "n0 = 12.0\nn1 = 12.0\nt0 = 3.0 + 4.0\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "84" + ], + "split": "train" + }, + { + "Input": "if a no . when divided by 44 , gives 432 as quotient and 0 as remainder . what will be the remainder when dividing the same no . by 39", + "Output Program": [ + "n0 = 44.0\nn1 = 432.0\nn2 = 0.0\nn3 = 39.0\nt0 = n0 * n1\nanswer = t0 % n3\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "a satellite is composed of 24 modular units , each of which is equipped with a set of sensors , some of which have been upgraded . each unit contains the same number of non - upgraded sensors . if the number of non - upgraded sensors on one unit is 1 / 8 the total number of upgraded sensors on the entire satellite , what fraction of the sensors on the satellite have been upgraded ?", + "Output Program": [ + "n0 = 24.0\nn1 = 1.0\nn2 = 8.0\nt0 = n1 / n2\nt1 = n0 * t0\nt2 = n0 * t1\nt3 = n0 + t2\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.25" + ], + "split": "train" + }, + { + "Input": "if the operation \u00f8 is defined for all positive integers x and w by x \u00f8 w = ( 2 ^ x ) / ( 2 ^ w ) then ( 4 \u00f8 2 ) \u00f8 1 = ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 4.0\nn3 = 2.0\nn4 = 1.0\nt0 = n0**min(n2, 5)\nt1 = n0**min(n0, 5)\nt2 = n0**min(n4, 5)\nt3 = t0 / t1\nt4 = n0**min(t3, 5)\nanswer = t4 / t2\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "if 3 ^ x * 4 ^ y = 531,441 and x \u2013 y = 12 , then x = ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 531441.0\nn3 = 12.0\n\nanswer = n3 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "ajay and vijay have some marbles with them . ajay told vijay ` ` if you give me ' x ' marbles , both of us will have equal number of marbles ' ' . vijay then told ajay ` ` if you give me twice as many marbles , i will have 30 more marbles than you would ' ' . find ' x ' ?", + "Output Program": [ + "n0 = 30.0\nt0 = 2.0 * 3.0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "the average of temperatures at noontime from monday to friday is 45 ; the lowest one is 42 , what is the possible maximum range of the temperatures ?", + "Output Program": [ + "n0 = 45.0\nn1 = 42.0\nt0 = 2.0 + 3.0\nt1 = n1 * 4.0\nt2 = n0 * t0\nt3 = t2 - t1\nanswer = t3 - n1\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "david is 12 years older than his daughter rosy . in 4 years david will be twice as old as rosy . what is rosy current age .", + "Output Program": [ + "n0 = 12.0\nn1 = 4.0\nt0 = n0 + n1\nt1 = n1 * 2.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "average age of students of an adult school is 48 years . 120 new students whose average age is 32 years joined the school . as a result the average age is decreased by 4 years . find the number of students of the school after joining of the new students .", + "Output Program": [ + "n0 = 48.0\nn1 = 120.0\nn2 = 32.0\nn3 = 4.0\nt0 = n2 + n3\nt1 = n1 * n2\nt2 = n1 * t0\nt3 = n0 - t0\nt4 = t2 - t1\nt5 = t4 / t3\nanswer = n3 * t5\nprint(answer)" + ], + "Output Answer": [ + "160" + ], + "split": "train" + }, + { + "Input": "if 9 - 4 / x = 7 + 8 / x , then x =", + "Output Program": [ + "n0 = 9.0\nn1 = 4.0\nn2 = 7.0\nn3 = 8.0\nt0 = n3 + 4.0\nt1 = n0 - n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "last week david spent 40 percent of his wages on recreation . this week , his wages are 5 percent less than last week \u02bc s wages and he spent 50 percent of his wages on recreation . the amount he spends on recreation this week is what percent of the amount he spent on recreation last week", + "Output Program": [ + "n0 = 40.0\nn1 = 5.0\nn2 = 50.0\nt0 = n2 / 100.0\nt1 = n1 / 100.0\nt2 = n0 / 100.0\nt3 = 1.0 - t1\nt4 = t0 * t3\nt5 = t4 / t2\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "118.74999999999997" + ], + "split": "train" + }, + { + "Input": "the data a and b are equal to the data subtracted c ; the data b is 3 times the data a ; if the data a is equal to 12 what is the sum of the data a , b and c ?", + "Output Program": [ + "n0 = 3.0\nn1 = 12.0\nt0 = n0 * n1\nt1 = n1 + t0\nt2 = t1 + t0\nanswer = n1 + t2\nprint(answer)" + ], + "Output Answer": [ + "96" + ], + "split": "train" + }, + { + "Input": "a , b and c invest in the ratio of 3 : 4 : 5 . the percentage of return on their investments are in the ratio of 6 : 5 : 4 . find the total earnings , if b earns rs . 150 more than a :", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 5.0\nn3 = 6.0\nn4 = 5.0\nn5 = 4.0\nn6 = 150.0\nt0 = n0 * n3\nt1 = n1 * n2\nt2 = t0 + t1\nt3 = t1 - t0\nt4 = t2 + t1\nt5 = n6 / t3\nanswer = t4 * t5\nprint(answer)" + ], + "Output Answer": [ + "4350" + ], + "split": "train" + }, + { + "Input": "the average salary of all the workers in a workshop is rs . 10000 . the average salary of 7 technicians is rs . 12000 and the average salary of the rest is rs . 8000 . the total number of workers in the workshop is :", + "Output Program": [ + "n0 = 10000.0\nn1 = 7.0\nn2 = 12000.0\nn3 = 8000.0\nt0 = n2 - n0\nt1 = n0 - n3\nt2 = n1 * t0\nt3 = t2 / t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "a salt manufacturing company produced a total of 4000 tonnes of salt in january of a particular year . starting from february its production increased by 100 tonnes every month over the previous months until the end of the year . find its ave 66 rage daily production for that year ?", + "Output Program": [ + "n0 = 4000.0\nn1 = 100.0\nn2 = 66.0\nt0 = 2.0 + 3.0\nt1 = n0 * 2.0\nt2 = n1 * 3.0\nt3 = 2.0 * 3.0\nt4 = 12.0 - 1.0\nt5 = n1 * t4\nt6 = t3 * 10.0\nt7 = t1 + t5\nt8 = t2 + t6\nt9 = t8 + t0\nt10 = t7 * 12.0\nt11 = t10 / 2.0\nanswer = t11 / t9\nprint(answer)" + ], + "Output Answer": [ + "149.58904109589042" + ], + "split": "train" + }, + { + "Input": "a batsman in his 17 th innings makes a score of 80 , and thereby increases his average by 2 . what is his average after the 17 th innings ? he had never been \u2019 not out \u2019 .", + "Output Program": [ + "n0 = 17.0\nn1 = 80.0\nn2 = 2.0\nn3 = 17.0\nt0 = n0 * n2\nt1 = n1 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "whats the reminder when 445876 , 985420 , 215546 , 656452 is divided by 8", + "Output Program": [ + "n0 = 445876.0\nn1 = 985420.0\nn2 = 215546.0\nn3 = 656452.0\nn4 = 8.0\n\nanswer = n0 % n4\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "the sum of two numbers is 64 , and one of them is 12 more than the other . what are the two numbers ?", + "Output Program": [ + "n0 = 64.0\nn1 = 12.0\nt0 = n0 - n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "a man is 24 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is", + "Output Program": [ + "n0 = 24.0\nt0 = 2.0 * 2.0\nt1 = 2.0 - 1.0\nt2 = t0 - 2.0\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "yearly subscription to professional magazines cost a company $ 940.00 . to make a 30 % cut in the magazine budget , how much less must be spent ?", + "Output Program": [ + "n0 = 940.0\nn1 = 30.0\nt0 = 100.0 - n1\nt1 = t0 / 100.0\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "658" + ], + "split": "train" + }, + { + "Input": "4 barrels of water have an average capacity of 8 gallons . what is the maximum possible capacity of the smallest barrel e if the median is 10 gallons ?", + "Output Program": [ + "n0 = 4.0\nn1 = 8.0\nn2 = 10.0\nt0 = n1 * 2.0\nt1 = n0 * 2.0\nt2 = t0 + t1\nt3 = t2 - 12.0\nanswer = t3 - n2\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "in a two - digit number , if it is known that its unit ' s digit exceeds its 10 ' s digit by 2 and that the product of the given number and the sum of its digits is equal to 144 , then the number is :", + "Output Program": [ + "n0 = 10.0\nn1 = 2.0\nn2 = 144.0\nt0 = n0 + 1.0\nt1 = n1 * t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "shekar scored 76 , 65 , 82 , 67 and 85 marks in mathematics , science , social studies , english and biology respectively . what are his average marks ?", + "Output Program": [ + "n0 = 76.0\nn1 = 65.0\nn2 = 82.0\nn3 = 67.0\nn4 = 85.0\nt0 = n0 + n1\nt1 = 1.0 + 4.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "two employees x and y are paid a total of rs . 800 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?", + "Output Program": [ + "n0 = 800.0\nn1 = 120.0\nt0 = 1.0 + 4.0\nt1 = t0 * 2.0\nt2 = t1 + 1.0\nt3 = n0 * t1\nt4 = t2 * 2.0\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "363.6363636363636" + ], + "split": "train" + }, + { + "Input": "elena \u2019 s bread recipe calls for 5 ounces of butter for each 7 cups of flour used . she needs to make 4 times the original recipe . if 12 ounces of butter is used , then how many cups of flour are needed ?", + "Output Program": [ + "n0 = 5.0\nn1 = 7.0\nn2 = 4.0\nn3 = 12.0\n\nanswer = n1 * n2\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "tom left a job paying $ 75000 per year to accept a sales job paying $ 45000 per year plus 15 percent commission . if each of his sales is for $ 750 , what is the least number of sales he must make per year if he is not to lose money because of the change ?", + "Output Program": [ + "n0 = 75000.0\nn1 = 45000.0\nn2 = 15.0\nn3 = 750.0\nt0 = n2 / 100.0\nt1 = n0 - n1\nt2 = n3 * t0\nanswer = t1 / t2\nprint(answer)" + ], + "Output Answer": [ + "266.6666666666667" + ], + "split": "train" + }, + { + "Input": "the average of 6 integers is 63 , and none of these integers is greater than 100 . if the average of 3 of the integers is 65 , what is the least possible value of one of the other two integers ?", + "Output Program": [ + "n0 = 6.0\nn1 = 63.0\nn2 = 100.0\nn3 = 3.0\nn4 = 65.0\nt0 = n0 * n1\nt1 = n3 * n4\nt2 = t0 - t1\nanswer = t2 - n2\nprint(answer)" + ], + "Output Answer": [ + "83" + ], + "split": "train" + }, + { + "Input": "in a flight of 600 km , an aircraft was slowed down due to bad weather . its average speed for the trip was reduced by 200 km / hr and the time of flight increased by 30 minutes . what is the duration of the flight ?", + "Output Program": [ + "n0 = 600.0\nn1 = 200.0\nn2 = 30.0\nt0 = n1 * n2\nt1 = t0 / 10.0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "if x is equal to the sum of the integers from 20 to 30 , inclusive , and y is the number of even integers from 20 to 30 , inclusive , what is the value of x + y ?", + "Output Program": [ + "n0 = 20.0\nn1 = 30.0\nn2 = 20.0\nn3 = 30.0\nt0 = n0 + n1\nt1 = n1 - n0\nt2 = t1 + 1.0\nt3 = t1 / 2.0\nt4 = t0 / 2.0\nt5 = t3 + 1.0\nt6 = t2 * t4\nanswer = t5 + t6\nprint(answer)" + ], + "Output Answer": [ + "281" + ], + "split": "train" + }, + { + "Input": "a departmental store has 9 managers and 18 associates . the 9 managers have an average salary of $ 1300 . the 18 associates have an average salary of $ 12000 . what is the average salary for the departmental store ?", + "Output Program": [ + "import math\nn0 = 9.0\nn1 = 18.0\nn2 = 9.0\nn3 = 1300.0\nn4 = 18.0\nn5 = 12000.0\nt0 = n0 + n1\nt1 = 1.0 + 10.0\nt2 = n0 * n3\nt3 = n1 * n5\nt4 = t2 + t3\nt5 = t4 / t0\nt6 = t5 / 2.0\nt7 = t6 / 1000.0\nt8 = math.floor(t7)\nt9 = t8 * 1000.0\nanswer = t9 - t1\nprint(answer)" + ], + "Output Answer": [ + "3989" + ], + "split": "train" + }, + { + "Input": "a furniture store owner decided to drop the price of her recliners by 20 % to spur business . by the end of the week she had sold 70 % more recliners . what is the percentage increase of the gross ?", + "Output Program": [ + "n0 = 20.0\nn1 = 70.0\nt0 = n1 / 100.0\nt1 = n0 / 100.0\nt2 = t0 + 1.0\nt3 = 1.0 - t1\nt4 = t2 * t3\nt5 = t4 * 100.0\nanswer = t5 - 100.0\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "timothy drove at an average speed of 10 mph for some time and then at an average speed of 50 mph for the rest of the journey . if he made no stops during the trip and his average speed for the entire journey was 40 mph , for what fraction of the total time did he drive at 50 mph ?", + "Output Program": [ + "n0 = 10.0\nn1 = 50.0\nn2 = 40.0\nn3 = 50.0\nt0 = n2 - n0\nt1 = n1 - n2\nt2 = t0 / t1\nanswer = t2 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "0.75" + ], + "split": "train" + }, + { + "Input": "in august , a cricket team that played 120 matches won 26 % of the games it played . after a continuous winning streak , this team raised its average to 52 % . how many matches did the team win to attain this average ?", + "Output Program": [ + "n0 = 120.0\nn1 = 26.0\nn2 = 52.0\nt0 = n2 / 100.0\nt1 = n1 / 100.0\nt2 = n0 * t0\nt3 = n0 * t1\nt4 = 1.0 - t0\nt5 = t2 - t3\nanswer = t5 / t4\nprint(answer)" + ], + "Output Answer": [ + "65.00000000000001" + ], + "split": "train" + }, + { + "Input": "a , b and c rent a pasture . if a puts 10 oxen for 7 months , b puts 12 oxen for 5 months and c puts 15 oxen for 3 months for grazing and the rent of the pasture is rs . 105 , then how much amount should c pay as his share of rent ?", + "Output Program": [ + "n0 = 10.0\nn1 = 7.0\nn2 = 12.0\nn3 = 5.0\nn4 = 15.0\nn5 = 3.0\nn6 = 105.0\nt0 = n4 * n5\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nt4 = t3 + t0\nt5 = t0 / t4\nanswer = n6 * t5\nprint(answer)" + ], + "Output Answer": [ + "26.999999999999996" + ], + "split": "train" + }, + { + "Input": "in a 20 litre mixture ratio of milk and water is 3 : 1 . how much milk should added so that mixture ratio become 4 : 1 ?", + "Output Program": [ + "n0 = 20.0\nn1 = 3.0\nn2 = 1.0\nn3 = 4.0\nn4 = 1.0\nt0 = n1 + n2\nt1 = n1 / n3\nt2 = n2 / t0\nt3 = n0 * t1\nt4 = n0 * t2\nt5 = n3 * t4\nanswer = t5 - t3\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "a certain taxi company charges $ 2.50 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ?", + "Output Program": [ + "n0 = 2.5\nn1 = 1.0\nn2 = 5.0\nn3 = 0.4\nn4 = 1.0\nn5 = 5.0\nn6 = 8.0\nt0 = n1 / n2\nt1 = n6 / t0\nt2 = t1 - n1\nt3 = n3 * t2\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "18.1" + ], + "split": "train" + }, + { + "Input": "a positive number x is multiplied by 7 , and this product is then divided by 3 . if the positive square root of the result of these two operations equals x , what is the value of x ?", + "Output Program": [ + "n0 = 7.0\nn1 = 3.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "2.3333333333333335" + ], + "split": "train" + }, + { + "Input": "the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 18000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is :", + "Output Program": [ + "n0 = 8000.0\nn1 = 7.0\nn2 = 18000.0\nn3 = 6000.0\nt0 = n2 - n0\nt1 = n0 - n3\nt2 = n1 * t0\nt3 = t2 / t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "a company charges a fixed rental of rs . 350 per month . it allows 200 calls free per month . each call is charge at rs . 1.4 when the number of calls exceed 200 per month and it charges rs . 1.6 when the number of calls exceeds 400 per month and so on . a customer made 150 calls in february and 250 calls in march . by how much percent each call is cheaper in march than each call in february .", + "Output Program": [ + "n0 = 350.0\nn1 = 200.0\nn2 = 1.4\nn3 = 200.0\nn4 = 1.6\nn5 = 400.0\nn6 = 150.0\nn7 = 250.0\nt0 = n0 / n6\nt1 = n7 - n1\nt2 = n2 * t1\nt3 = n0 + t2\nt4 = t3 / n7\nt5 = t0 - t4\nt6 = t5 / t0\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "28.000000000000007" + ], + "split": "train" + }, + { + "Input": "3 * 12 + 3 * 13 + 3 * 16 + 11 = ?", + "Output Program": [ + "n0 = 3.0\nn1 = 12.0\nn2 = 3.0\nn3 = 13.0\nn4 = 3.0\nn5 = 16.0\nn6 = 11.0\nt0 = n0 * n1\nt1 = n0 * n3\nt2 = n0 * n5\nt3 = t0 + t1\nt4 = t3 + t2\nanswer = n6 + t4\nprint(answer)" + ], + "Output Answer": [ + "134" + ], + "split": "train" + }, + { + "Input": "there are 16 bees in the hive , then 8 more fly . how many bees are there in all ?", + "Output Program": [ + "n0 = 16.0\nn1 = 8.0\n\nanswer = n0 + n1\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "let raj be 3 years older than ravi and hema be two years younger than ravi . raj is 3 times as old as rahul who is hema \u2019 s brother . the ratio of the ages of hema and her brother is 3 : 2 . find by how much percentage raj \u2019 s age is more than hema \u2019 s when raj will be 20 years old .", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 3.0\nn3 = 2.0\nn4 = 20.0\nt0 = n0 + 2.0\nt1 = n0 / n3\nt2 = n0 - t1\nt3 = t0 / t2\nt4 = n0 * t3\nt5 = t4 - t0\nt6 = n4 - t4\nt7 = t5 + t6\nt8 = t0 / t7\nanswer = t8 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "33.33333333333333" + ], + "split": "train" + }, + { + "Input": "gopi gives rs . 90 plus one turban as salary to his servant for one year . the servant leaves after 9 months and receives rs . 50 and the turban . find the price of the turban .", + "Output Program": [ + "n0 = 90.0\nn1 = 9.0\nn2 = 50.0\nt0 = n0 - n2\nt1 = 12.0 - n1\nt2 = t0 / t1\nt3 = t2 * 12.0\nanswer = t3 - n0\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "train" + }, + { + "Input": "following an increase in prices , the price of a candy box was 10 pounds and the price of a can of soda was 12 pounds . if the price of a candy box was raised by 25 % , and the price of a can of soda was raised by 50 % . what was the price of a box of candy plus a can of soda before prices were raised ?", + "Output Program": [ + "n0 = 10.0\nn1 = 12.0\nn2 = 25.0\nn3 = 50.0\nt0 = n2 + 100.0\nt1 = n3 + 100.0\nt2 = n0 * 100.0\nt3 = n1 * 100.0\nt4 = t2 / t0\nt5 = t3 / t1\nanswer = t4 + t5\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "the mean of 30 values was 150 . it was detected on rechecking that one value 165 was wrongly copied as 135 for the computation of the mean . find the correct mean .", + "Output Program": [ + "n0 = 30.0\nn1 = 150.0\nn2 = 165.0\nn3 = 135.0\nt0 = n0 * n1\nt1 = n2 - n3\nt2 = t0 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "151" + ], + "split": "train" + }, + { + "Input": "a man spends rs . 1700 per month on an average for the first 3 months , rs 1550 for next 4 months and rs . 1800 per month for the last 5 months and saves rs . 5200 a year . what is his average monthly income ?", + "Output Program": [ + "n0 = 1700.0\nn1 = 3.0\nn2 = 1550.0\nn3 = 4.0\nn4 = 1800.0\nn5 = 5.0\nn6 = 5200.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n4 * n5\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n6 + t4\nanswer = t5 / 12.0\nprint(answer)" + ], + "Output Answer": [ + "2125" + ], + "split": "train" + }, + { + "Input": "in what proportion must rice at rs 3.10 per kg be mixed with rice at rs 3.60 per kg , so that the mixture be worth rs 3.25 a kg ?", + "Output Program": [ + "n0 = 3.1\nn1 = 3.6\nn2 = 3.25\nt0 = n1 - n2\nt1 = n2 - n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "2.3333333333333353" + ], + "split": "train" + }, + { + "Input": "of the families in city x in 1994 , 40 percent owned a personal computer . the number of families in city x owning a computer in 1998 was 30 percent greater than it was in 1994 , and the total number of families in city x was 4 percent greater in 1998 than it was in 1994 . what percent of the families in city x owned a personal computer in 1998 ?", + "Output Program": [ + "n0 = 1994.0\nn1 = 40.0\nn2 = 1998.0\nn3 = 30.0\nn4 = 1994.0\nn5 = 4.0\nn6 = 1998.0\nn7 = 1994.0\nn8 = 1998.0\nt0 = n3 + 100.0\nt1 = n5 + 100.0\nt2 = n1 * t0\nt3 = t2 / 100.0\nt4 = t3 / t1\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "one - third less than 35 % of 180 is equal to :", + "Output Program": [ + "n0 = 35.0\nn1 = 180.0\nt0 = n0 / 100.0\nt1 = 1.0 / 3.0\nt2 = n1 * t0\nt3 = t1 * t2\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "country x imported approximately $ 1.44 billion of goods in 1996 . if country x imported $ 420 million of goods in the first two months of 1997 and continued to import goods at the same rate for the rest of the year , by how much would country xs 1997 imports exceed those of 1996 ?", + "Output Program": [ + "n0 = 1.44\nn1 = 1996.0\nn2 = 420.0\nn3 = 1997.0\nn4 = 1997.0\nn5 = 1996.0\nt0 = 12.0 / 2.0\nt1 = n0 * 1000.0\nt2 = n2 * t0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "1080" + ], + "split": "train" + }, + { + "Input": "a certain mixture of nuts consists of 5 parts almonds to 2 parts walnuts , by weight . what is the number of pounds of almonds in 210 pounds of the mixture ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 210.0\nt0 = n0 + n1\nt1 = n0 * n2\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "train" + }, + { + "Input": "the simple interest on a sum of money will be rs . 1200 after 10 years . if the principal is trebled after 5 years what will be the total interest at the end of the tenth year ?", + "Output Program": [ + "n0 = 1200.0\nn1 = 10.0\nn2 = 5.0\nt0 = n0 / n1\nt1 = n2 * t0\nt2 = t1 * 3.0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "2400" + ], + "split": "train" + }, + { + "Input": "a number whose fifth part increased by 4 is equal to its fourth part diminished by 4 is ?", + "Output Program": [ + "n0 = 4.0\nn1 = 4.0\nt0 = n0 + n1\nt1 = 1.0 + n0\nt2 = 1.0 / n0\nt3 = 1.0 / t1\nt4 = t2 - t3\nanswer = t0 / t4\nprint(answer)" + ], + "Output Answer": [ + "160.00000000000003" + ], + "split": "train" + }, + { + "Input": "the average age of a class of 25 students is 26 years . the average increased by 1 when the teacher ' s age also included . what is the age of the teacher ?", + "Output Program": [ + "n0 = 25.0\nn1 = 26.0\nn2 = 1.0\nt0 = n0 + n2\nt1 = n1 + n2\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "52" + ], + "split": "train" + }, + { + "Input": "the difference between two numbers is 1356 . when the larger number is divided by the smaller one , the quotient is 6 and the remainder is 15 . the smaller number is", + "Output Program": [ + "n0 = 1356.0\nn1 = 6.0\nn2 = 15.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "268.2" + ], + "split": "train" + }, + { + "Input": "on a test , the boys in the class averaged 90 points and the girls in the class averaged 96 points . if the overall class average was 94 points , what is the ratio of boys to girls in the class ?", + "Output Program": [ + "n0 = 90.0\nn1 = 96.0\nn2 = 94.0\nt0 = n1 - n2\nt1 = n2 - n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "9 - 3 \u00f7 1 / 3 + 3 = ?", + "Output Program": [ + "n0 = 9.0\nn1 = 3.0\nn2 = 1.0\nn3 = 3.0\nn4 = 3.0\nt0 = n2 / n1\nt1 = n1 / t0\nt2 = n0 - t1\nanswer = n1 + t2\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "find the ones digit of 73 ^ 355", + "Output Program": [ + "import math\nn0 = 73.0\nn1 = 355.0\nt0 = 3.0 + 4.0\nt1 = n1 / 4.0\nt2 = 10.0 * 2.0\nt3 = math.floor(t1)\nt4 = t0 * 10.0\nt5 = t3 * 4.0\nt6 = n0 - t4\nt7 = n1 - t5\nt8 = t6**min(t7, 5)\nanswer = t8 - t2\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "by approximately what percent is x greater than 1 / 2 if ( 1 / 2 ) ( x ) = 1 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 1.0\nn3 = 2.0\nn4 = 1.0\nt0 = n0 / n1\nt1 = n1 - t0\nt2 = t1 / t0\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "set x consists of all two - digit primes and set y consists of all positive multiples of 6 less than 100 . if the two sets are combined into one , what will be the range of the new set ?", + "Output Program": [ + "n0 = 6.0\nn1 = 100.0\nt0 = n1 - 3.0\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "91" + ], + "split": "train" + }, + { + "Input": "a club wants to mix 30 pounds of candy worth $ 8.00 per pound with candy worth $ 5.00 per pound to reduce the cost of the mixture to $ 6.00 per pound . how many pounds of the $ 5.00 per pound candy should be used ?", + "Output Program": [ + "n0 = 30.0\nn1 = 8.0\nn2 = 5.0\nn3 = 6.0\nn4 = 5.0\nt0 = n0 * n1\nt1 = n0 * n3\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "nancy obtained 66 , 75 , 52 , 68 and 89 marks ( out of 100 ) in american literature , history , home economics , physical education and art . calculate her average marks ?", + "Output Program": [ + "n0 = 66.0\nn1 = 75.0\nn2 = 52.0\nn3 = 68.0\nn4 = 89.0\nn5 = 100.0\nt0 = n0 + n1\nt1 = 1.0 + 4.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "train" + }, + { + "Input": "a textile manufacturing firm employees 80 looms . it makes fabrics for a branded company . the aggregate sales value of the output of the 80 looms is rs 5 , 00,000 and the monthly manufacturing expenses is rs 1 , 50,000 . assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms . monthly establishment charges are rs 75000 . if one loom breaks down and remains idle for one month , the decrease in profit is :", + "Output Program": [ + "n0 = 80.0\nn1 = 80.0\nn2 = 5.0\nn3 = 0.0\nn4 = 1.0\nn5 = 50000.0\nn6 = 75000.0\nt0 = n2 * 1000.0\nt1 = n6 * 2.0\nt2 = n0 - n4\nt3 = n6 + t1\nt4 = t2 / n0\nt5 = t0 * 100.0\nt6 = t4 * t5\nt7 = t4 * t1\nt8 = t5 - t3\nt9 = t6 - t7\nt10 = t9 - n6\nanswer = t8 - t10\nprint(answer)" + ], + "Output Answer": [ + "4375" + ], + "split": "train" + }, + { + "Input": "of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 180 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 3.0\nn3 = 4.0\nn4 = 3.0\nn5 = 5.0\nn6 = 180.0\nt0 = n1 / n5\nt1 = n1 / n3\nt2 = n0 / n1\nt3 = 1.0 - t0\nt4 = n6 / t3\nt5 = t4 / t1\nanswer = t5 / t2\nprint(answer)" + ], + "Output Answer": [ + "900" + ], + "split": "train" + }, + { + "Input": "20 litres of mixture of acid and water contain 10 % water . how much water should be added so that percentage of water becomes 20 % in this mixture ?", + "Output Program": [ + "n0 = 20.0\nn1 = 10.0\nn2 = 20.0\nt0 = 10.0 / 100.0\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a certain telescope increases the visual range at a particular location from 80 kilometers to 150 kilometers . by what percent is the visual range increased by using the telescope ?", + "Output Program": [ + "n0 = 80.0\nn1 = 150.0\nt0 = n1 - n0\nt1 = t0 / n0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "87.5" + ], + "split": "train" + }, + { + "Input": "if the price of a book is first decreased by 25 % and then increased by 20 % , then the net change in the price will be :", + "Output Program": [ + "n0 = 25.0\nn1 = 20.0\nt0 = n0 * 100.0\nt1 = n1 * 100.0\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = t3 + 100.0\nt5 = 100.0 - t2\nt6 = t5 / 100.0\nt7 = t4 / 100.0\nt8 = t6 * t7\nt9 = t8 * 100.0\nanswer = 100.0 - t9\nprint(answer)" + ], + "Output Answer": [ + "10.000000000000014" + ], + "split": "train" + }, + { + "Input": "if a certain number is divided by 11 , the quotient , dividend , and divisor , added together , will amount to 71 . what is the number ?", + "Output Program": [ + "n0 = 11.0\nn1 = 71.0\nt0 = n0 + 1.0\nt1 = n1 - n0\nt2 = n0 * t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "55" + ], + "split": "train" + }, + { + "Input": "the number 0.127 is how much greater than 1 / 8 ?", + "Output Program": [ + "n0 = 0.127\nn1 = 1.0\nn2 = 8.0\nt0 = n1 / n2\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "0.0020000000000000018" + ], + "split": "train" + }, + { + "Input": "let p be a prime number . if n = 7 p , how many divisors does n have ?", + "Output Program": [ + "n0 = 7.0\nt0 = 1.0 / 2.0\nt1 = n0 / 2.0\nt2 = t1 - 2.0\nanswer = t0 + t2\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "in a factory there are 3 types of machine m 1 , m 2 and m which produces 25 % , 35 % and 40 % of the total products respectively . m 1 , m 2 and m 3 produces 2 % , 4 % and 5 % defective products , respectively . what is the percentage of non - defective products ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 2.0\nn3 = 25.0\nn4 = 35.0\nn5 = 40.0\nn6 = 1.0\nn7 = 2.0\nn8 = 3.0\nn9 = 2.0\nn10 = 4.0\nn11 = 5.0\nt0 = n2 / 100.0\nt1 = n10 / 100.0\nt2 = n11 / 100.0\nt3 = n3 * t0\nt4 = n4 * t1\nt5 = n5 * t2\nt6 = t3 + t4\nt7 = t6 + t5\nanswer = 100.0 - t7\nprint(answer)" + ], + "Output Answer": [ + "96.1" + ], + "split": "train" + }, + { + "Input": "in a class of 20 students , 3 students did not borrow any books from the library , 9 students each borrowed 1 book , 4 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?", + "Output Program": [ + "n0 = 20.0\nn1 = 3.0\nn2 = 9.0\nn3 = 1.0\nn4 = 4.0\nn5 = 2.0\nn6 = 3.0\nn7 = 2.0\nt0 = n0 * n5\nt1 = n2 * n3\nt2 = n5 * n4\nt3 = t1 + t2\nt4 = n4 + t1\nt5 = n1 + t4\nt6 = n0 - t5\nt7 = t6 - n3\nt8 = n6 * t7\nt9 = t3 + t8\nanswer = t0 - t9\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "on a partly cloudy day , derek decides to walk back from work . when it is sunny , he walks at a speed of s miles / hr ( s is an integer ) and when it gets cloudy , he increases his speed to ( s + 1 ) miles / hr . if his average speed for the entire distance is 2.8 miles / hr , what fraction r of the total distance did he cover while the sun was shining on him ?", + "Output Program": [ + "import scipy\nn0 = 1.0\nn1 = 2.8\nt0 = scipy.lcm(int(2.0), int(3.0))\nt1 = t0 / n1\nanswer = t1 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "0.1428571428571428" + ], + "split": "train" + }, + { + "Input": "the average weight of a , b and c is 45 kg . if the average weight of a and b be 40 kg and that of b and c be 43 kg , then the weight of b is ?", + "Output Program": [ + "n0 = 45.0\nn1 = 40.0\nn2 = 43.0\nt0 = n1 * 2.0\nt1 = n2 * 2.0\nt2 = n0 * 3.0\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "31" + ], + "split": "train" + }, + { + "Input": "400 students took a mock exam in delhi , 60 % of the boys and 80 % of the girls cleared the cut off in the examination . if the total percentage of students qualifying is 65 % , how many girls appeared in the examination ?", + "Output Program": [ + "n0 = 400.0\nn1 = 60.0\nn2 = 80.0\nn3 = 65.0\nt0 = n3 / 100.0\nt1 = n1 / 100.0\nt2 = n2 / 100.0\nt3 = n0 * t0\nt4 = n0 * t1\nt5 = t2 - t1\nt6 = t3 - t4\nanswer = t6 / t5\nprint(answer)" + ], + "Output Answer": [ + "99.99999999999997" + ], + "split": "train" + }, + { + "Input": "what is the greater of the two numbers whose product is 2688 , given that the sum of the two numbers exceeds their difference by 64 ?", + "Output Program": [ + "n0 = 2688.0\nn1 = 64.0\nt0 = 2.0**min(4.0, 5)\nt1 = t0 * 2.0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "84" + ], + "split": "train" + }, + { + "Input": "the proportion of copper and zinc in the brass is 3 : 7 . how much zinc will there be in 100 kg of brass ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 100.0\nt0 = n0 + n1\nt1 = n1 / t0\nanswer = n2 * t1\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "train" + }, + { + "Input": "find the value of c from ( 8 ) ^ 3 x 9 ^ 3 \u00e3 \u00b7 679 = c .", + "Output Program": [ + "n0 = 8.0\nn1 = 3.0\nn2 = 9.0\nn3 = 3.0\nn4 = 679.0\nt0 = n0**min(n1, 5)\nt1 = n2**min(n1, 5)\nt2 = t0 * t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "549.7025036818851" + ], + "split": "train" + }, + { + "Input": "in the quadratic equation x 2 - bx + 20 = 0 , if the product of two roots is 20 , what is the sum of the two roots ?", + "Output Program": [ + "n0 = 2.0\nn1 = 20.0\nn2 = 0.0\nn3 = 20.0\nt0 = n1 / n0\nanswer = n0 + t0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "if taxi fares were $ 10.00 for the first 1 / 5 mile and $ 1.00 for each 1 / 5 mile there after , then the taxi fare for a 10 - mile ride was", + "Output Program": [ + "n0 = 10.0\nn1 = 1.0\nn2 = 5.0\nn3 = 1.0\nn4 = 1.0\nn5 = 5.0\nn6 = 10.0\nt0 = n1 / n2\nt1 = n0 / t0\nt2 = t1 - n1\nt3 = n3 * t2\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "59" + ], + "split": "train" + }, + { + "Input": "for how many integer values of n will the value of the expression 4 n + 7 be an integer greater than 1 and less than 80 ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 7.0\nn2 = 1.0\nn3 = 80.0\nt0 = n3 - n1\nt1 = n2 - n1\nt2 = t0 / n0\nt3 = t1 / n0\nt4 = math.floor(t2)\nt5 = math.floor(t3)\nanswer = t4 - t5\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "in a box of 7 pencils , a total of 2 are defective . if a customer buys 3 pencils selected at random from the box , what is the probability that neither pencils will be defective ?", + "Output Program": [ + "import math\nn0 = 7.0\nn1 = 2.0\nn2 = 3.0\nt0 = math.factorial(min(15, int(n2)))\nt1 = math.factorial(min(15, int(n0)))\nt2 = n0 - n1\nt3 = n0 - n2\nt4 = math.factorial(min(15, int(t2)))\nt5 = math.factorial(min(15, int(t3)))\nt6 = t2 - n2\nt7 = math.factorial(min(15, int(t6)))\nt8 = t5 * t0\nt9 = t1 / t8\nt10 = t7 * t0\nt11 = t4 / t10\nanswer = t11 / t9\nprint(answer)" + ], + "Output Answer": [ + "0.2857142857142857" + ], + "split": "train" + }, + { + "Input": "there is a escalator and 2 persons move down it . a takes 50 steps and b takes 75 steps while the escalator is moving down . given that the time taken by a to take 1 step is equal to time taken by b to take 3 steps . find the no . of steps in the escalator while it is staionary ?", + "Output Program": [ + "n0 = 2.0\nn1 = 50.0\nn2 = 75.0\nn3 = 1.0\nn4 = 3.0\nt0 = n2 / n4\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "if 3 ^ x * 4 ^ y = 59,049 and x \u2013 y = 10 , then x = ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 59049.0\nn3 = 10.0\n\nanswer = n3 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "when you multiply a number by 4 and then subtract 3 , the result is the same as if you first subtracted 7 from the same number and then multiplied by 9 . what is the number ?", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 7.0\nn3 = 9.0\nt0 = n2 * n3\nt1 = n3 - n0\nt2 = t0 - n1\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 6400 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 8.0\nn2 = 6400.0\nt0 = n0 / n1\nt1 = n2 * t0\nt2 = n2 + t1\nt3 = t2 * t0\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "8100" + ], + "split": "train" + }, + { + "Input": "an art gallery has only paintings and sculptures . currently , 1 / 3 of the pieces of art are displayed , and 1 / 6 of the pieces on display are sculptures . if 1 / 3 of the pieces not on display are paintings , and 1200 sculptures are not on display , how many pieces of art does the gallery have ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 6.0\nn4 = 1.0\nn5 = 3.0\nn6 = 1200.0\nt0 = n0 / n1\nt1 = n0 - t0\nt2 = n6 / t1\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "2699.9999999999995" + ], + "split": "train" + }, + { + "Input": "if taxi fares were $ 1.00 for the first 1 / 5 mile and $ 0.45 for each 1 / 5 mile there after , then the taxi fare for a 3 - mile ride was", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 5.0\nn3 = 0.45\nn4 = 1.0\nn5 = 5.0\nn6 = 3.0\nt0 = n1 / n2\nt1 = n6 / t0\nt2 = t1 - n1\nt3 = n3 * t2\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "7.3" + ], + "split": "train" + }, + { + "Input": "find the lowest positive integer that can be divided by all the even numbers between 14 and 21 .", + "Output Program": [ + "import scipy\nn0 = 14.0\nn1 = 21.0\nt0 = n0 / 2.0\nt1 = t0 + 1.0\nt2 = t1 + 1.0\nt3 = scipy.lcm(int(t2), int(10.0))\nt4 = scipy.lcm(int(t0), int(t3))\nanswer = t1 * t4\nprint(answer)" + ], + "Output Answer": [ + "5040" + ], + "split": "train" + }, + { + "Input": "jacob is now 12 years younger than michael . if 3 years from now michael will be twice as old as jacob , how old will jacob be in 4 years ?", + "Output Program": [ + "n0 = 12.0\nn1 = 3.0\nn2 = 4.0\nt0 = n0 + n1\nt1 = n1 * 2.0\nt2 = t0 - t1\nanswer = n2 + t2\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "the sum of first n consecutive odd integers is n ^ 2 . what is the sum of all odd integers between 13 and 35 inclusive .", + "Output Program": [ + "n0 = 2.0\nn1 = 13.0\nn2 = 35.0\nt0 = n2 + 1.0\nt1 = n1 - n0\nt2 = t1 + 1.0\nt3 = t0 / n0\nt4 = t2 / n0\nt5 = t3**min(n0, 5)\nt6 = t4**min(n0, 5)\nanswer = t5 - t6\nprint(answer)" + ], + "Output Answer": [ + "288" + ], + "split": "train" + }, + { + "Input": "the function f ( n ) is defined as the product of all the consecutive positive integers between 4 and n ^ 2 , inclusive , whereas the function g ( n ) is defined as the product of the squares of all the consecutive positive integers between 1 and n , inclusive . the exponent on 2 in the prime factorization of f ( 3 ) / g ( 3 ) is", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\nn2 = 1.0\nn3 = 2.0\nn4 = 3.0\nn5 = 3.0\n\nanswer = n1**min(n1, 5)\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "for how many integer values of n will the value of the expression 4 n + 7 be an integer greater than 1 and less than 200 ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 7.0\nn2 = 1.0\nn3 = 200.0\nt0 = n3 - n1\nt1 = n2 - n1\nt2 = t0 / n0\nt3 = t1 / n0\nt4 = math.floor(t2)\nt5 = math.floor(t3)\nanswer = t4 - t5\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "a small pool filled only with water will require an additional 300 gallons of water in order to be filled to 70 % of its capacity . if pumping in these additional 300 gallons of water will increase the amount of water in the pool by 30 % , what is the total capacity of the pool in gallons ?", + "Output Program": [ + "n0 = 300.0\nn1 = 70.0\nn2 = 300.0\nn3 = 30.0\nt0 = n1 / 100.0\nt1 = n0 * 100.0\nt2 = t1 / n3\nt3 = n0 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "1857.1428571428573" + ], + "split": "train" + }, + { + "Input": "if money is invested at r percent interest , compounded annually , the amount of investment will double in approximately 70 / r years . if pat ' s parents invested $ 7000 in a long term bond that pays 8 percent interest , compounded annually , what will be the approximate total amount of investment 18 years later , when pat is ready for college ?", + "Output Program": [ + "n0 = 70.0\nn1 = 7000.0\nn2 = 8.0\nn3 = 18.0\nt0 = n1 * 2.0\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "28000" + ], + "split": "train" + }, + { + "Input": "in a group of cows and chickens , the number of legs was 16 more than twice the number of heads . the number of cows was :", + "Output Program": [ + "n0 = 16.0\nt0 = 4.0 - 2.0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "in a mixture of 45 litres the ratio of milk to water is 4 : 1 . additional 3 litres of water is added to the mixture . find the ratio of milk to water in the resulting mixture .", + "Output Program": [ + "n0 = 45.0\nn1 = 4.0\nn2 = 1.0\nn3 = 3.0\nt0 = n1 + n2\nt1 = n0 / t0\nt2 = n3 + t1\nt3 = n0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "how much water must be added to 60 litres of milk at 1.5 litres for rs . 20 so as to have a mixture worth rs . 32 / 3 a litre ?", + "Output Program": [ + "n0 = 60.0\nn1 = 1.5\nn2 = 20.0\nn3 = 32.0\nn4 = 3.0\nt0 = n3 / n4\nt1 = n2 / n1\nt2 = t1 - t0\nt3 = t0 / t2\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "15.000000000000007" + ], + "split": "train" + }, + { + "Input": "if greg buys 3 shirts , 4 trousers and 2 ties , the total cost is $ 40 . if greg buys 7 shirts , 2 trousers and 2 ties , the total cost is $ 60 . how much will it cost him to buy 3 trousers , 5 shirts and 2 ties ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 2.0\nn3 = 40.0\nn4 = 7.0\nn5 = 2.0\nn6 = 2.0\nn7 = 60.0\nn8 = 3.0\nn9 = 5.0\nn10 = 2.0\nt0 = n3 + n7\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "the heights of 3 individuals are in the ratio 4 : 5 : 6 . if the sum of the heights of the heaviest and the lightest boy is 150 cm more than the height of the third boy , what is the weight of the lightest boy ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 5.0\nn3 = 6.0\nn4 = 150.0\nt0 = n1 + n3\nt1 = t0 - n2\nt2 = n4 / t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "on a game show , there are 3 tables . each table has 3 boxes ( one zonk ! , one cash prize , and one grand prize ) . the contestant can choose one box from each table for a total of 3 boxes . if any of the boxes are a zonk ! , the contestant loses everything . what is the probability of getting no zonk ! from any of the 3 boxes chosen ?", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 3.0\nn3 = 3.0\nt0 = 2.0**min(n0, 5)\nt1 = n0**min(3.0, 5)\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.2962962962962963" + ], + "split": "train" + }, + { + "Input": "the average weight of a , b and c is 42 kg . if the average weight of a and b be 40 kg and that of b and c be 43 kg , then the weight of b is :", + "Output Program": [ + "n0 = 42.0\nn1 = 40.0\nn2 = 43.0\nt0 = n1 * 2.0\nt1 = n2 * 2.0\nt2 = n0 * 3.0\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "dividing by 3 \u2044 8 and then multiplying by 5 \u2044 9 is the same as dividing by what number ?", + "Output Program": [ + "n0 = 3.0\nn1 = 8.0\nn2 = 5.0\nn3 = 9.0\nt0 = n1 / n0\nt1 = n2 / n3\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "1.4814814814814814" + ], + "split": "train" + }, + { + "Input": "how many integers n greater than and less than 100 are there such that , if the digits of n are reversed , the resulting integer is n + 9 ?", + "Output Program": [ + "n0 = 100.0\nn1 = 9.0\nt0 = n0 / 10.0\nanswer = t0 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "reeya obtained 65 , 67 , 76 , 80 and 95 out of 100 in different subjects , what will be the average", + "Output Program": [ + "n0 = 65.0\nn1 = 67.0\nn2 = 76.0\nn3 = 80.0\nn4 = 95.0\nn5 = 100.0\nt0 = n0 + n1\nt1 = 1.0 + 4.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "76.6" + ], + "split": "train" + }, + { + "Input": "an ant walks an average of 600 meters in 12 minutes . a beetle walks 15 % less distance at the same time on the average . assuming the beetle walks at her regular rate , what is its speed in km / h ?", + "Output Program": [ + "n0 = 600.0\nn1 = 12.0\nn2 = 15.0\nt0 = n0 / 1000.0\nt1 = n1 / 60.0\nt2 = n2 / 100.0\nt3 = t0 / t1\nt4 = 1.0 - t2\nanswer = t3 * t4\nprint(answer)" + ], + "Output Answer": [ + "2.5499999999999994" + ], + "split": "train" + }, + { + "Input": "a 12 month project had a total budget of $ 42000 . after 8 months , the project had spent $ 23700 . at this point , how much was the project under budget ?", + "Output Program": [ + "n0 = 12.0\nn1 = 42000.0\nn2 = 8.0\nn3 = 23700.0\nt0 = n3 / n2\nt1 = n0 * t0\nt2 = n1 - t1\nt3 = t2 / n0\nanswer = n2 * t3\nprint(answer)" + ], + "Output Answer": [ + "4300" + ], + "split": "train" + }, + { + "Input": "a is the average ( arithmetic mean ) of the first 7 positive multiples of 4 and b is the median of the first 3 positive multiples of positive integer n . if the value of a ^ 2 \u2013 b ^ 2 is zero , what is the value of n ?", + "Output Program": [ + "n0 = 7.0\nn1 = 4.0\nn2 = 3.0\nn3 = 2.0\nn4 = 2.0\nt0 = n1 * 4.0\nanswer = t0 / n3\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "what is the dividend . divisor 19 , the quotient is 7 and the remainder is 6", + "Output Program": [ + "n0 = 19.0\nn1 = 7.0\nn2 = 6.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "139" + ], + "split": "train" + }, + { + "Input": "if 50 % of ( x - y ) = 20 % of ( x + y ) , then what percent of x is y ?", + "Output Program": [ + "n0 = 50.0\nn1 = 20.0\nt0 = n0 + n1\nt1 = n0 - n1\nt2 = t1 / t0\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "42.857142857142854" + ], + "split": "train" + }, + { + "Input": "165 liters of a mixture of milk and water contains in the ratio 3 : 2 . how much water should now be added so that the ratio of milk and water becomes 3 : 4 ?", + "Output Program": [ + "n0 = 165.0\nn1 = 3.0\nn2 = 2.0\nn3 = 3.0\nn4 = 4.0\nt0 = n1 + n2\nt1 = n0 / t0\nanswer = n2 * t1\nprint(answer)" + ], + "Output Answer": [ + "66" + ], + "split": "train" + }, + { + "Input": "average of money that group of 4 friends pay for rent each month is $ 800 . after one persons rent is increased by 25 % the new mean is $ 850 . what was original rent of friend whose rent is increased ?", + "Output Program": [ + "n0 = 4.0\nn1 = 800.0\nn2 = 25.0\nn3 = 850.0\nt0 = n2 / 100.0\nt1 = n3 - n1\nt2 = n0 * t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "800" + ], + "split": "train" + }, + { + "Input": "company m produces two kinds of stereos : basic and deluxe . of the stereos produced by company m last month , 2 / 3 were basic and the rest were deluxe . if it takes 7 / 5 as many hours to produce a deluxe stereo as it does to produce a basic stereo , then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 7.0\nn3 = 5.0\nt0 = n1 * n3\nt1 = n0 * t0\nt2 = t1 / n1\nt3 = n2 + t2\nt4 = n3 + t3\nanswer = n2 / t4\nprint(answer)" + ], + "Output Answer": [ + "0.3181818181818182" + ], + "split": "train" + }, + { + "Input": "find large number from below question the difference of two numbers is 1395 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder", + "Output Program": [ + "n0 = 1395.0\nn1 = 6.0\nn2 = 15.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nt2 = t0 / t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "1656" + ], + "split": "train" + }, + { + "Input": "the average of temperatures at noontime from monday to friday is 50 ; the lowest one is 45 , what is the possible maximum range of the temperatures ?", + "Output Program": [ + "n0 = 50.0\nn1 = 45.0\nt0 = 2.0 + 3.0\nt1 = n1 * 4.0\nt2 = n0 * t0\nt3 = t2 - t1\nanswer = t3 - n1\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "a grocer has a sale of rs . 800 , rs . 900 , rs . 1000 , rs . 700 and rs . 800 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 850 ?", + "Output Program": [ + "n0 = 800.0\nn1 = 900.0\nn2 = 1000.0\nn3 = 700.0\nn4 = 800.0\nn5 = 5.0\nn6 = 850.0\nt0 = n5 + 1.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n6 * t0\nt4 = n3 + t2\nt5 = n4 + t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "900" + ], + "split": "train" + }, + { + "Input": "the least common multiple of positive integer d and 3 - digit integer n is 690 . if n is not divisible by 3 and d is not divisible by 2 , what is the value of n ?", + "Output Program": [ + "n0 = 3.0\nn1 = 690.0\nn2 = 3.0\nn3 = 2.0\nt0 = 2.0 + 3.0\nt1 = n1 / 2.0\nt2 = t1 / 3.0\nt3 = n3 * t0\nt4 = t2 / t0\nanswer = t4 * t3\nprint(answer)" + ], + "Output Answer": [ + "230" + ], + "split": "train" + }, + { + "Input": "in a renowned city , the average birth rate is 7 people every two seconds and the death rate is 3 people every two seconds . estimate the size of the population net increase that occurs in one day .", + "Output Program": [ + "n0 = 7.0\nn1 = 3.0\nt0 = n0 - n1\nt1 = t0 * 3600.0\nanswer = t1 * 12.0\nprint(answer)" + ], + "Output Answer": [ + "172800" + ], + "split": "train" + }, + { + "Input": "two trains of equal are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train passes the slower train in 54 sec . the length of each train is ?", + "Output Program": [ + "n0 = 46.0\nn1 = 36.0\nn2 = 54.0\nt0 = n0 - n1\nt1 = t0 * 1000.0\nt2 = t1 / 3600.0\nt3 = n2 * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "a number is doubled and 8 is added . if the resultant is trebled , it becomes 84 . what is that number ?", + "Output Program": [ + "n0 = 8.0\nn1 = 84.0\nt0 = n0 * 3.0\nt1 = 2.0 * 3.0\nt2 = n1 - t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the average of 10 numbers is calculated as 5 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?", + "Output Program": [ + "n0 = 10.0\nn1 = 5.0\nn2 = 36.0\nn3 = 26.0\nt0 = n2 - n3\nt1 = t0 / n0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "if ( 10 ^ 4 * 3.456789 ) ^ 14 is written as a single term , how many digits would be to the right of the decimal place ?", + "Output Program": [ + "n0 = 10.0\nn1 = 4.0\nn2 = 3.456789\nn3 = 14.0\n\nanswer = n3 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "certain stocks in january were 10 % less than they were in february and 20 % greater than they were in march . what was the percentage decrease in the stocks from february to march ?", + "Output Program": [ + "n0 = 10.0\nn1 = 20.0\nt0 = n1 + 100.0\nt1 = 100.0 - n0\nt2 = t1 / 100.0\nt3 = t0 / 100.0\nt4 = 100.0 / t2\nt5 = 100.0 / t3\nt6 = t4 - t5\nt7 = t6 / t4\nanswer = t7 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "24.999999999999993" + ], + "split": "train" + }, + { + "Input": "a positive number x is multiplied by 4 , and this product is then divided by 3 . if the positive square root of the result of these two operations equals x , what is the value of x ?", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "1.3333333333333333" + ], + "split": "train" + }, + { + "Input": "pradeep has to obtain 20 % of the total marks to pass . he got 160 marks and failed by 25 marks . the maximum marks are", + "Output Program": [ + "n0 = 20.0\nn1 = 160.0\nn2 = 25.0\nt0 = n1 + n2\nt1 = n0 / 100.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "925" + ], + "split": "train" + }, + { + "Input": "what is the difference between the c . i . on rs . 5000 for 1 1 / 2 years at 4 % per annum compounded yearly and half - yearly ?", + "Output Program": [ + "n0 = 5000.0\nn1 = 1.0\nn2 = 1.0\nn3 = 2.0\nn4 = 4.0\nt0 = n3 / 100.0\nt1 = n4 / 100.0\nt2 = t0 + n1\nt3 = t1 + n1\nt4 = t2 * t2\nt5 = t2 * t3\nt6 = t2 * t4\nt7 = n0 * t5\nt8 = n0 * t6\nanswer = t8 - t7\nprint(answer)" + ], + "Output Answer": [ + "2.0399999999999636" + ], + "split": "train" + }, + { + "Input": "6 friends went to a hotel and decided to pay the bill amount equally . but 5 of them could pay rs . 100 each as a result 6 th has to pay rs . 100 extra than his share . find the amount paid by him .", + "Output Program": [ + "n0 = 6.0\nn1 = 5.0\nn2 = 100.0\nn3 = 6.0\nn4 = 100.0\nt0 = n1 * n2\nt1 = n4 + t0\nt2 = t1 / n1\nanswer = n4 + t2\nprint(answer)" + ], + "Output Answer": [ + "220" + ], + "split": "train" + }, + { + "Input": "there are 18 teams in the hockey league , and each team faces all the other teams 10 times each . how many games are played in the season ?", + "Output Program": [ + "n0 = 18.0\nn1 = 10.0\nt0 = n0 - 1.0\nt1 = n0 * t0\nt2 = n1 * t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "1530" + ], + "split": "train" + }, + { + "Input": "how is 1 / 2 % expressed as a decimal fraction ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nt0 = n0 / n1\nanswer = t0 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "0.005" + ], + "split": "train" + }, + { + "Input": "the ratio of a to b is 4 to 5 , where a and b are positive . if x equals a increased by 25 percent of a , and m equals b decreased by 20 percent of b , what is the value of m / x ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 25.0\nn3 = 20.0\nt0 = n2 + 100.0\nt1 = n1 / n0\nt2 = 100.0 - n3\nt3 = t2 / t0\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "0.8" + ], + "split": "train" + }, + { + "Input": "a house wife saved $ 2.75 in buying an item on sale . if she spent $ 20 for the item , approximately how much percent she saved in the transaction ?", + "Output Program": [ + "n0 = 2.75\nn1 = 20.0\nt0 = n0 + n1\nt1 = n0 / t0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "12.087912087912088" + ], + "split": "train" + }, + { + "Input": "the average age of 7 men increases by 3 years when two women are included in place of two men of ages 18 and 22 years . find the average age of the women ?", + "Output Program": [ + "n0 = 7.0\nn1 = 3.0\nn2 = 18.0\nn3 = 22.0\nt0 = n2 + n3\nt1 = n0 * n1\nt2 = t0 + t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "30.5" + ], + "split": "train" + }, + { + "Input": "barbata invests $ 2400 in the national bank at 5 % . how much additional money must she invest at 10 % so that the total annual income will be equal to 6 % of her entire investment ?", + "Output Program": [ + "n0 = 2400.0\nn1 = 5.0\nn2 = 10.0\nn3 = 6.0\nt0 = n3 / 100.0\nt1 = n1 / 100.0\nt2 = n2 / 100.0\nt3 = n0 * t0\nt4 = n0 * t1\nt5 = t2 - t0\nt6 = t3 - t4\nanswer = t6 / t5\nprint(answer)" + ], + "Output Answer": [ + "599.9999999999999" + ], + "split": "train" + }, + { + "Input": "a miniature roulette wheel is divided into 10 equal sectors , each bearing a distinct integer from 1 to 10 , inclusive . each time the wheel is spun , a ball randomly determines the winning sector by settling in that sector . if the wheel is spun two times , approximately what is the probability that the product of the two winning sectors \u2019 integers will be even ?", + "Output Program": [ + "n0 = 10.0\nn1 = 1.0\nn2 = 10.0\nt0 = n0 / 2.0\nt1 = t0 / n0\nt2 = t1**min(2.0, 5)\nt3 = n1 - t2\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "jill has 28 gallons of water stored in quart , half - gallon , and one gallon jars . she has equal numbers of each size jar holding the liquid . what is the total number of water filled jars ?", + "Output Program": [ + "n0 = 28.0\nt0 = 1.0 / 2.0\nt1 = t0 + 0.25\nt2 = t1 + 1.0\nt3 = n0 / t2\nanswer = t3 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "11 friends went to a hotel and decided to pay the bill amount equally . but 10 of them could pay rs . 60 each as a result 11 th has to pay rs . 50 extra than his share . find the amount paid by him .", + "Output Program": [ + "n0 = 11.0\nn1 = 10.0\nn2 = 60.0\nn3 = 11.0\nn4 = 50.0\nt0 = n1 * n2\nt1 = n4 + t0\nt2 = t1 / n1\nanswer = n4 + t2\nprint(answer)" + ], + "Output Answer": [ + "115" + ], + "split": "train" + }, + { + "Input": "what is the remainder when 7 ^ 700 is divided by 100 ?", + "Output Program": [ + "n0 = 7.0\nn1 = 700.0\nn2 = 100.0\nt0 = n2 / 2.0\nt1 = n0 * n0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "a teacher gave the same test to 3 history classes : a , b , and c . the average ( arithmetic mean ) scores for the 3 classes were 65 , 90 , and 77 , respectively . the ratio of the numbers of students in each class who took the test was 4 to 6 to 5 , respectively . what was the average score for the 3 classes combined ?", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 65.0\nn3 = 90.0\nn4 = 77.0\nn5 = 4.0\nn6 = 6.0\nn7 = 5.0\nn8 = 3.0\nt0 = n5 + n6\nt1 = n2 * n5\nt2 = n3 * n6\nt3 = n4 * n7\nt4 = t1 + t2\nt5 = n7 + t0\nt6 = t4 + t3\nanswer = t6 / t5\nprint(answer)" + ], + "Output Answer": [ + "79" + ], + "split": "train" + }, + { + "Input": "the ages of two persons differ by 16 years . 6 years ago , the elder one was 3 times as old as the younger one . what are their present ages of the elder person ?", + "Output Program": [ + "n0 = 16.0\nn1 = 6.0\nn2 = 3.0\nt0 = n1 * n2\nt1 = n0 - n1\nt2 = t0 + t1\nt3 = t2 / 2.0\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "in a mixture of 45 litres the ratio of milk to water is 4 : 1 . additional 9 litres of water is added to the mixture . find the ratio of milk to water in the resulting mixture .", + "Output Program": [ + "n0 = 45.0\nn1 = 4.0\nn2 = 1.0\nn3 = 9.0\nt0 = n1 + n2\nt1 = n0 / t0\nt2 = n3 + t1\nt3 = n0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "what is the sum of all possible solutions to | x - 5 | ^ 2 + | x - 5 | = 20 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 5.0\nn3 = 20.0\nt0 = n0 + 4.0\nt1 = n0 - 4.0\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "anil had to do a multiplication . instead of taking 35 as one of the multipliers , he took 53 . as a result , the product went up by 540 . what is the new product ?", + "Output Program": [ + "n0 = 35.0\nn1 = 53.0\nn2 = 540.0\nt0 = n0 * n1\nt1 = 10.0 * 3.0\nt2 = 100.0 * 4.0\nt3 = t0 + t1\nt4 = t3 - t2\nanswer = t4 + 100.0\nprint(answer)" + ], + "Output Answer": [ + "1585" + ], + "split": "train" + }, + { + "Input": "one - tenth of the students at a nursery school are 4 years old or older . if 20 students have not yet reached their third birthday , and a total of 25 students are not between 3 years old and 4 years old , how many children are in the nursery school ?", + "Output Program": [ + "n0 = 4.0\nn1 = 20.0\nn2 = 25.0\nn3 = 3.0\nn4 = 4.0\nt0 = n2 - n1\nanswer = t0 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "the overall age of x and y is 18 year greater than the overall age of y and z . z is how many decades younger that x ?", + "Output Program": [ + "n0 = 18.0\n\nanswer = n0 / 1.0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "a boy rides his bicycle 10 km at an average sped of 12 km / hr and again travels 12 km at an average speed of 10 km / hr . his average speed for the entire trip is approximately .", + "Output Program": [ + "n0 = 10.0\nn1 = 12.0\nn2 = 12.0\nn3 = 10.0\nt0 = n0 + n1\nt1 = n0 / n1\nt2 = n1 / n0\nt3 = t1 + t2\nanswer = t0 / t3\nprint(answer)" + ], + "Output Answer": [ + "10.819672131147541" + ], + "split": "train" + }, + { + "Input": "( a / 2 ) / ( b / c ) in the expression above , a , b , and c are different numbers and each is one of the numbers 1 , 2 , or 4 . what is the largest possible value of the expression ?", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 2.0\nn3 = 4.0\nt0 = n0 * n3\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "if the numerator of a fraction be increased by 15 % and its denominator be diminished by 8 % , the value of the fraction is 15 / 16 . find the original fraction ?", + "Output Program": [ + "n0 = 15.0\nn1 = 8.0\nn2 = 15.0\nn3 = 16.0\nt0 = n0 + 100.0\nt1 = 100.0 - n1\nt2 = n2 * t1\nt3 = n3 * t0\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.75" + ], + "split": "train" + }, + { + "Input": "a tank holds x gallons of a saltwater solution that is 20 % salt by volume . one fourth of the water is evaporated , leaving all of the salt . when 5 gallons of water and 10 gallons of salt are added , the resulting mixture is 33 1 / 3 % salt by volume . what is the value of x ?", + "Output Program": [ + "n0 = 20.0\nn1 = 5.0\nn2 = 10.0\nn3 = 33.0\nn4 = 1.0\nn5 = 3.0\nt0 = n0 / 100.0\nt1 = n4 / 4.0\nt2 = n2 * 2.0\nt3 = t0 * 2.0\nt4 = t2 - n1\nt5 = n4 - t0\nt6 = t1 * t5\nt7 = t5 - t6\nt8 = t7 - t3\nanswer = t4 / t8\nprint(answer)" + ], + "Output Answer": [ + "74.99999999999997" + ], + "split": "train" + }, + { + "Input": "the tax on a commodity is diminished by 32 % but its consumption is increased by 12 % . find the decrease percent in the revenue derived from it ?", + "Output Program": [ + "n0 = 32.0\nn1 = 12.0\nt0 = n1 + 100.0\nt1 = 100.0 - n0\nt2 = t0 * t1\nt3 = t2 / 100.0\nanswer = 100.0 - t3\nprint(answer)" + ], + "Output Answer": [ + "23.840000000000003" + ], + "split": "train" + }, + { + "Input": "when x is multiplied by 3 , the result is 26 more than the result of subtracting x from 26 . what is the value of x ?", + "Output Program": [ + "n0 = 3.0\nn1 = 26.0\nn2 = 26.0\nt0 = n1 + n2\nt1 = 1.0 + n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "a sports retailer ordered white and yellow tennis balls in equal number but the dispatch clerk of the tennis ball company erred and dispatched 90 extra yellow balls and making ratio of white balls to yellow balls 8 / 13 . how many tennis balls did the retailer order originally .", + "Output Program": [ + "n0 = 90.0\nn1 = 8.0\nn2 = 13.0\nt0 = n0 * n1\nt1 = n2 - n1\nt2 = t0 / t1\nanswer = t2 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "288" + ], + "split": "train" + }, + { + "Input": "find the least number which when divided by 5 , 67 , and 8 leaves a remainder 3 , but when divided by 9 leaves no remainder", + "Output Program": [ + "import scipy\nn0 = 5.0\nn1 = 67.0\nn2 = 8.0\nn3 = 3.0\nn4 = 9.0\nt0 = 3.0 + 4.0\nt1 = 2.0 * 3.0\nt2 = scipy.lcm(int(n0), int(t1))\nt3 = scipy.lcm(int(t0), int(t2))\nt4 = scipy.lcm(int(n2), int(t3))\nt5 = t4 * 2.0\nanswer = n3 + t5\nprint(answer)" + ], + "Output Answer": [ + "1683" + ], + "split": "train" + }, + { + "Input": "xavier , yvonne , and zelda each try independently to solve a problem . if their individual probabilities for success are 1 / 6 , 1 / 2 and 5 / 8 , respectively , what is the probability that xavier and yvonne , but not zelda , will solve the problem ?", + "Output Program": [ + "n0 = 1.0\nn1 = 6.0\nn2 = 1.0\nn3 = 2.0\nn4 = 5.0\nn5 = 8.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = n4 / n5\nt3 = t0 * t1\nt4 = n0 - t2\nanswer = t3 * t4\nprint(answer)" + ], + "Output Answer": [ + "0.03125" + ], + "split": "train" + }, + { + "Input": "zinc and copper are melted together in the ratio 9 : 11 . what is the weight of melted mixture , if 27 kg of zinc has been consumed in it ?", + "Output Program": [ + "n0 = 9.0\nn1 = 11.0\nn2 = 27.0\nt0 = n1 / n0\nt1 = n2 * t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "if x is an integer such that 3 < x < 10 , 5 < x < 18 , 9 > x > \u2013 2 , 8 > x > 0 , and x + 1 < 9 , then x is", + "Output Program": [ + "n0 = 3.0\nn1 = 10.0\nn2 = 5.0\nn3 = 18.0\nn4 = 9.0\nn5 = 2.0\nn6 = 8.0\nn7 = 0.0\nn8 = 1.0\nn9 = 9.0\nt0 = n4 - n8\nanswer = t0 - n8\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "if n is a positive integer greater than 1 , then p ( n ) represents the product of all the prime numbers less than or equal to n . the second smallest prime factor of p ( 12 ) + 11 is", + "Output Program": [ + "n0 = 1.0\nn1 = 12.0\nn2 = 11.0\nt0 = 1.0 + 4.0\nt1 = 3.0 + 4.0\nt2 = n2 * t1\nt3 = t0 * t2\nt4 = t3 * 3.0\nt5 = t4 * 2.0\nt6 = n2 + t5\nanswer = t6 / n2\nprint(answer)" + ], + "Output Answer": [ + "211" + ], + "split": "train" + }, + { + "Input": "the average ( arithmetic mean ) of 4 different integers is 70 . if the largest integer is 90 , what is the least possible value of the smallest integer ?", + "Output Program": [ + "n0 = 4.0\nn1 = 70.0\nn2 = 90.0\nt0 = n0 * n1\nt1 = n2 - 1.0\nt2 = n2 - 2.0\nt3 = t0 - n2\nt4 = t3 - t1\nanswer = t4 - t2\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "a salesman ` s commission is 5 % on all sales upto rs . 10000 and 4 % on all sales exceeding this . he remits rs . 31100 to his parent company after deducing his commission . find the total sales .", + "Output Program": [ + "n0 = 5.0\nn1 = 10000.0\nn2 = 4.0\nn3 = 31100.0\nt0 = n3 + 100.0\nt1 = 12.0 + 12.0\nt2 = 100.0 / 4.0\nt3 = t0 * t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "32500" + ], + "split": "train" + }, + { + "Input": "approximately how many revolutions will be made by a car tire with a 15 - inch diameter if the car travels 1 \u2044 2 mile ?", + "Output Program": [ + "n0 = 15.0\nn1 = 1.0\nn2 = 2.0\nt0 = n1 / n2\nt1 = 2.0 * 3.0\nt2 = t1 / 10.0\nt3 = t1 * 10.0\nt4 = t2 + 1.0\nt5 = t3 + 3.0\nt6 = t4 / 10.0\nt7 = t5 * 10.0\nt8 = t6 + 4.0\nt9 = t7 + 3.0\nt10 = t8 / 10.0\nt11 = t9 * 10.0\nt12 = t10 + 1.0\nt13 = t11 + 3.0\nt14 = t13 + 2.0\nt15 = t12 / 10.0\nt16 = t15 + 3.0\nt17 = t14 * 10.0\nt18 = n0 * t16\nt19 = t18 / t17\nanswer = t0 / t19\nprint(answer)" + ], + "Output Answer": [ + "672.1628045157456" + ], + "split": "train" + }, + { + "Input": "16 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ?", + "Output Program": [ + "n0 = 16.0\nt0 = n0 - 1.0\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "240" + ], + "split": "train" + }, + { + "Input": "the grade point average of one third of the classroom is 30 ; the grade point average of the rest is 33 . what is the grade point average of the whole class ?", + "Output Program": [ + "n0 = 30.0\nn1 = 33.0\nt0 = n0 / 3.0\nt1 = n1 / 3.0\nt2 = t1 * 2.0\nanswer = t0 + t2\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "what approximate value will come in place of the question mark ( ? ) in the below question ? ( 47 % of 1442 - 36 % of 1412 ) + 63 = ?", + "Output Program": [ + "n0 = 47.0\nn1 = 1442.0\nn2 = 36.0\nn3 = 1412.0\nn4 = 63.0\nt0 = 10.0 + 4.0\nt1 = n2 + 10.0\nt2 = n0 / 100.0\nt3 = n2 / 100.0\nt4 = t0 + 4.0\nt5 = t1 + 12.0\nt6 = n1 * t2\nt7 = n3 * t3\nt8 = t4 + 1.0\nt9 = t5 / 100.0\nt10 = t6 - t7\nt11 = t8 + t9\nt12 = n4 + t10\nanswer = t11 + t12\nprint(answer)" + ], + "Output Answer": [ + "252" + ], + "split": "train" + }, + { + "Input": "multiplication of 2 numbers is 9375 and the quotient , when the larger one is divided by the smalleris 15 . find the sum of the numbers ?", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 9375.0\nn2 = 15.0\nt0 = n1 / n2\nt1 = math.sqrt(max(0, t0))\nt2 = n1 / t1\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "train" + }, + { + "Input": "for any number z , z * is defined as the greatest positive even integer less than or equal to y . what is the value of 6.45 \u2013 6.45 * ?", + "Output Program": [ + "import math\nn0 = 6.45\nn1 = 6.45\nt0 = math.floor(n0)\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "0.4500000000000002" + ], + "split": "train" + }, + { + "Input": "find the total number of prime factors in the expression ( 4 ) ^ 11 x ( 7 ) ^ 7 x ( 11 ) ^ 2", + "Output Program": [ + "n0 = 4.0\nn1 = 11.0\nn2 = 7.0\nn3 = 7.0\nn4 = 11.0\nn5 = 2.0\nt0 = n1 * n5\nt1 = n3 + t0\nanswer = n5 + t1\nprint(answer)" + ], + "Output Answer": [ + "31" + ], + "split": "train" + }, + { + "Input": "at a certain fruit stand , the price of each apple is 40 cents and the price of each orange is 60 cents . mary selects a total of 10 apples and oranges from the fruit stand , and the average ( arithmetic mean ) price of the 10 pieces of fruit is 48 cents . how many oranges must mary put back so that the average price of the pieces of fruit that she keeps is 45 cents ?", + "Output Program": [ + "n0 = 40.0\nn1 = 60.0\nn2 = 10.0\nn3 = 10.0\nn4 = 48.0\nn5 = 45.0\nt0 = n2 * n4\nt1 = n2 * n5\nt2 = n1 - n5\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a soft drink company had 6000 small and 15000 big bottles in storage . if 11 % of small 12 % of big bottles have been sold , then the total bottles remaining in storage is", + "Output Program": [ + "n0 = 6000.0\nn1 = 15000.0\nn2 = 11.0\nn3 = 12.0\nt0 = n0 + n1\nt1 = n2 / 100.0\nt2 = n3 / 100.0\nt3 = n0 * t1\nt4 = n1 * t2\nt5 = t3 + t4\nanswer = t0 - t5\nprint(answer)" + ], + "Output Answer": [ + "18540" + ], + "split": "train" + }, + { + "Input": "if sharon ' s weekly salary increased by 16 percent , she would earn $ 348 per week . if instead , her weekly salary were to increase by 25 percent , how much would she earn per week ?", + "Output Program": [ + "n0 = 16.0\nn1 = 348.0\nn2 = 25.0\nt0 = n0 / 100.0\nt1 = n2 / 100.0\nt2 = t0 + 1.0\nt3 = n1 / t2\nt4 = t1 * t3\nanswer = t3 + t4\nprint(answer)" + ], + "Output Answer": [ + "375" + ], + "split": "train" + }, + { + "Input": "5 % people of a village in sri lanka died by bombardment , 15 % of the remainder left the village on account of fear . if now the population is reduced to 2553 , how much was it in the beginning ?", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 15.0\nn2 = 2553.0\nt0 = 100.0 - n0\nt1 = 100.0 - n1\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = t2 * t3\nt5 = n2 / t4\nanswer = math.floor(t5)\nprint(answer)" + ], + "Output Answer": [ + "3161" + ], + "split": "train" + }, + { + "Input": "in an election between two candidates a and b , the number of valid votes received by a exceeds those received by b by 15 % of the total number of votes polled . if 20 % of the votes polled were invalid and a total of 7720 votes were polled , then how many valid votes did b get ?", + "Output Program": [ + "n0 = 15.0\nn1 = 20.0\nn2 = 7720.0\nt0 = n1 / 100.0\nt1 = n0 * n2\nt2 = t1 / 100.0\nt3 = 1.0 - t0\nt4 = n2 * t3\nt5 = t4 - t2\nanswer = t5 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "2509" + ], + "split": "train" + }, + { + "Input": "lisa and robert have taken the same number of photos on their school trip . lisa has taken 3 times as many photos as claire and robert has taken 16 more photos than claire . how many photos has claire taken ?", + "Output Program": [ + "n0 = 3.0\nn1 = 16.0\nt0 = n0 - 1.0\nanswer = n1 / t0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "the unit digit in the product 7858 * 1086 * 4582 * 9783 is ?", + "Output Program": [ + "n0 = 7858.0\nn1 = 1086.0\nn2 = 4582.0\nn3 = 9783.0\nt0 = 4.0 + 4.0\nt1 = n0 * n1\nt2 = n2 * t1\nt3 = n3 * t2\nt4 = t3 - t0\nanswer = t3 - t4\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "20 - 8 percent of the programmers in a startup company weigh 200 pounds or more . 20 - 5 percent of the programmers that are under 200 pounds in that same company weigh 100 pounds or less . what percent of the programmers in the startup company weigh between 100 and 200 pounds ?", + "Output Program": [ + "n0 = 20.0\nn1 = 8.0\nn2 = 200.0\nn3 = 20.0\nn4 = 5.0\nn5 = 200.0\nn6 = 100.0\nn7 = 100.0\nn8 = 200.0\nt0 = n0 + n4\nt1 = n0 + n1\nt2 = 100.0 - t0\nt3 = 100.0 - t1\nt4 = t2 / 100.0\nanswer = t4 * t3\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "train" + }, + { + "Input": "what is the unit \u2019 s digit of 7 ^ 6", + "Output Program": [ + "n0 = 7.0\nn1 = 6.0\nt0 = n0**min(2.0, 5)\nanswer = t0 % 10.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "the telephone company wants to add an area code composed of 2 letters to every phone number . in order to do so , the company chose a special sign language containing 424 different signs . if the company used 422 of the signs fully and two remained unused , how many additional area codes can be created if the company uses all 424 signs ?", + "Output Program": [ + "n0 = 2.0\nn1 = 424.0\nn2 = 422.0\nn3 = 424.0\nt0 = n1 - n2\nt1 = n2 * t0\nanswer = t1 * t0\nprint(answer)" + ], + "Output Answer": [ + "1688" + ], + "split": "train" + }, + { + "Input": "on sunday , bill ran 4 more miles than he ran on saturday . julia did not run on saturday , but she ran twice the number of miles on sunday that bill ran on sunday . if bill and julia ran a total of 28 miles on saturday and sunday , how many miles did bill run on sunday ?", + "Output Program": [ + "n0 = 4.0\nn1 = 28.0\nt0 = n0 * 2.0\nt1 = n0 + t0\nt2 = n1 - t1\nt3 = t2 / n0\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "operation # is defined as : a # b = 4 a ^ 2 + 4 b ^ 2 + 8 ab for all non - negative integers . what is the value of ( a + b ) + 5 , when a # b = 100 ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 2.0\nn2 = 4.0\nn3 = 2.0\nn4 = 8.0\nn5 = 5.0\nn6 = 100.0\nt0 = n6 / n0\nt1 = math.sqrt(max(0, t0))\nanswer = n5 + t1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "a student got 72 % in math and 84 % in history . to get an overall average of 75 % , how much should the student get in the third subject ?", + "Output Program": [ + "n0 = 72.0\nn1 = 84.0\nn2 = 75.0\nt0 = n0 + n1\nt1 = n2 * 3.0\nanswer = t1 - t0\nprint(answer)" + ], + "Output Answer": [ + "69" + ], + "split": "train" + }, + { + "Input": "what is the sum r of all 3 digit numbers that leave a remainder of ' 2 ' when divided by 3 ?", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 2.0\nn2 = 3.0\nt0 = 10.0**min(n0, 5)\nt1 = t0 / 10.0\nt2 = t1 - n1\nt3 = t2 / n0\nt4 = math.floor(t3)\nt5 = t4 + 1.0\nt6 = n0 * t5\nt7 = n1 + t6\nt8 = t0 - t7\nt9 = t8 / n0\nt10 = math.floor(t9)\nt11 = n0 * t10\nt12 = t7 + t11\nt13 = t7 + t12\nt14 = t13 * t10\nanswer = t14 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "164300.5" + ], + "split": "train" + }, + { + "Input": "each week a restaurant serving mexican food uses the same volume of chili paste , which comes in either 25 - ounce cans or 15 - ounce cans of chili paste . if the restaurant must order 30 more of the smaller cans than the larger cans to fulfill its weekly needs , then how many larger cans are required to fulfill its weekly needs ?", + "Output Program": [ + "n0 = 25.0\nn1 = 15.0\nn2 = 30.0\n\nanswer = n1 + n2\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "the tax on a commodity is diminished by 16 % and its consumption increased by 15 % . the effect on revenue is ?", + "Output Program": [ + "n0 = 16.0\nn1 = 15.0\nt0 = n1 / 100.0\nt1 = n0 / 100.0\nt2 = t0 + 1.0\nt3 = 1.0 - t1\nt4 = t2 * t3\nt5 = t4 * 100.0\nanswer = 100.0 - t5\nprint(answer)" + ], + "Output Answer": [ + "3.40000000000002" + ], + "split": "train" + }, + { + "Input": "the maximum number of student amoung them 2010 pens and 1050 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :", + "Output Program": [ + "import scipy\nn0 = 2010.0\nn1 = 1050.0\n\nanswer = scipy.gcd(int(n0), int(n1))\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "a cricketer scored 134 runs which included 12 boundaries and 2 sixes . what percent of his total score did he make by running between the wickets .", + "Output Program": [ + "n0 = 134.0\nn1 = 12.0\nn2 = 2.0\nt0 = n1 * 4.0\nt1 = n2 * 3.0\nt2 = n2 * t1\nt3 = t0 + t2\nt4 = n0 - t3\nt5 = t4 / n0\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "55.223880597014926" + ], + "split": "train" + }, + { + "Input": "? x 40 = 173 x 240", + "Output Program": [ + "n0 = 40.0\nn1 = 173.0\nn2 = 240.0\nt0 = n1 * n2\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "1038" + ], + "split": "train" + }, + { + "Input": "rose made a part payment of $ 300 toward buying a brand new car , which represents 5 % of the total cost of the car , how much remains to be paid ?", + "Output Program": [ + "n0 = 300.0\nn1 = 5.0\nt0 = n0 * 100.0\nt1 = t0 / n1\nanswer = t1 - n0\nprint(answer)" + ], + "Output Answer": [ + "5700" + ], + "split": "train" + }, + { + "Input": "n is the greatest number which divides 1305 , 4665 and 6905 and gives the same remainder in each case . what is the sum of the digits in n ?", + "Output Program": [ + "import scipy\nn0 = 1305.0\nn1 = 4665.0\nn2 = 6905.0\nt0 = n1 - n0\nt1 = n2 - n1\nt2 = n2 - n0\nt3 = scipy.gcd(int(t0), int(t1))\nt4 = scipy.gcd(int(t3), int(t2))\nt5 = t4 / 10.0\nt6 = t5 % 10.0\nt7 = t5 - t6\nt8 = t7 / 10.0\nt9 = t8 % 10.0\nt10 = t8 - t9\nt11 = t10 / 10.0\nt12 = t11 + t9\nanswer = t12 + t6\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "mid intended to type a 7 - digit number , but the two 3 ' s he meant to type did not appear . what appeared instead was the 5 - digit number 52115 . how many different 7 - digit numbers could mid have meant to type ?", + "Output Program": [ + "import math\nn0 = 7.0\nn1 = 3.0\nn2 = 5.0\nn3 = 52115.0\nn4 = 7.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(n2)))\nt2 = n0 - n2\nt3 = math.factorial(min(15, int(t2)))\nt4 = t1 * t3\nanswer = t0 / t4\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "in a clothing store , there are 6 different colored neckties ( red , orange , yellow , green , blue , and indigo ) and 4 different colored shirts ( red , orange , yellow , green , blue , and indigo ) that must be packed into boxes for gifts . if each box can only fit one necktie and one shirt , what is the probability that all of the boxes will contain a necktie and a shirt of the same color ?", + "Output Program": [ + "import math\nn0 = 6.0\nn1 = 4.0\nt0 = math.factorial(min(15, int(n1)))\nanswer = 1.0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.041666666666666664" + ], + "split": "train" + }, + { + "Input": "a , b , c subscribe rs . 50000 for a business , a subscribes rs . 4000 more than b and b rs . 5000 more than c . out of a total profit of rs . 70000 , a receives :", + "Output Program": [ + "n0 = 50000.0\nn1 = 4000.0\nn2 = 5000.0\nn3 = 70000.0\nt0 = n1 + n2\nt1 = n2 + t0\nt2 = n0 - t1\nt3 = t2 / 3.0\nt4 = t0 + t3\nt5 = n3 * t4\nanswer = t5 / n0\nprint(answer)" + ], + "Output Answer": [ + "29400" + ], + "split": "train" + }, + { + "Input": "a canoe has two oars , left and right . each oar either works or breaks . the failure or non - failure of each oar is independent of the failure or non - failure of the other . you can still row the canoe with one oar . the probability that the left oar works is 3 / 5 . the probability that the right oar works is also 3 / 5 . what is the probability q that you can still row the canoe ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 3.0\nn3 = 5.0\nt0 = n0 / n1\nt1 = 2.0 / n1\nt2 = t0 * t1\nt3 = t0 * t0\nt4 = t2 + t2\nanswer = t4 + t3\nprint(answer)" + ], + "Output Answer": [ + "0.84" + ], + "split": "train" + }, + { + "Input": "if the price of sugar rises from rs . 6 per kg to rs . 7.50 per kg , a person , to have no increase in his expenditure on sugar , will have to reduce his consumption of sugar by", + "Output Program": [ + "n0 = 6.0\nn1 = 7.5\nt0 = n0 * 1.0\nt1 = t0 / n1\nt2 = 1.0 - t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "19.999999999999996" + ], + "split": "train" + }, + { + "Input": "if p and q are positive integers each greater than 1 , and 15 ( p + 1 ) = 29 ( q + 1 ) , what is the least possible value of p + q ?", + "Output Program": [ + "n0 = 1.0\nn1 = 15.0\nn2 = 1.0\nn3 = 29.0\nn4 = 1.0\nt0 = n1 + n3\nanswer = t0 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "how many numbers from 10 to 50 are exactly divisible by 3 ?", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 50.0\nn2 = 3.0\nt0 = n1 / n2\nt1 = n0 / n2\nt2 = math.floor(t0)\nt3 = math.floor(t1)\nt4 = t3 + 1.0\nt5 = n2 * t2\nt6 = n2 * t4\nt7 = t5 - t6\nt8 = t7 / n2\nanswer = t8 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "if the remainder is 3 when positive integer n is divided by 18 , what is the remainder when n is divided by 6 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 18.0\nn2 = 6.0\n\nanswer = n1 / n2\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "farm tax is levied on the 40 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . willam . mr . willam paid only $ 480 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :", + "Output Program": [ + "n0 = 40.0\nn1 = 3840.0\nn2 = 480.0\nt0 = n2 / n1\nt1 = t0 * 100.0\nt2 = t1 * 100.0\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "31.25" + ], + "split": "train" + }, + { + "Input": "( 7.5 \u00d7 7.5 + 37.5 + 2.5 \u00d7 2.5 ) is equal to :", + "Output Program": [ + "n0 = 7.5\nn1 = 7.5\nn2 = 37.5\nn3 = 2.5\nn4 = 2.5\nt0 = n0 * n0\nt1 = n3 * n3\nt2 = t0 + t1\nanswer = n2 + t2\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "a theater charges $ 12 for seats in the orchestra and $ 8 for seats in the balcony . on a certain night , a total of 350 tickets were sold for a total cost of $ 3,320 . how many more tickets were sold that night for seats in the balcony than for seats in the orchestra ?", + "Output Program": [ + "n0 = 12.0\nn1 = 8.0\nn2 = 350.0\nn3 = 3320.0\nt0 = n0 * n2\nt1 = 1000.0 * 3.0\nt2 = 100.0 * 3.0\nt3 = 10.0 * 2.0\nt4 = n0 - n1\nt5 = t1 + t2\nt6 = t5 + t3\nt7 = t0 - t6\nt8 = t7 / t4\nt9 = n2 - t8\nanswer = t8 - t9\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "if a - b = 3 and a 2 + b 2 = 29 , find the value of ab .", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 2.0\nn3 = 29.0\nt0 = n0**min(n1, 5)\nt1 = n3 - t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "each child has 4 pencils and 13 skittles . if there are 8 children , how many pencils are there in total ?", + "Output Program": [ + "n0 = 4.0\nn1 = 13.0\nn2 = 8.0\n\nanswer = n0 * n2\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "the average of 5 quantities is 6 . the average of 3 of them is 4 . what is the average of remaining 2 numbers ?", + "Output Program": [ + "n0 = 6.0\nn1 = 5.0\nn2 = 2.0\nn3 = 19.0\nt0 = n0 * n1\nt1 = n2 * t0\nt2 = t1 / n2\nanswer = t2 + 3.0\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.40 at the candy store . what is john \u2019 s weekly allowance ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 0.4\nt0 = n0 / n1\nt1 = 1.0 / n0\nt2 = 1.0 - t0\nt3 = t1 * t2\nt4 = t0 + t3\nt5 = 1.0 - t4\nanswer = n2 / t5\nprint(answer)" + ], + "Output Answer": [ + "1.4999999999999998" + ], + "split": "train" + }, + { + "Input": "in an examination , there were 2,000 candidates , out of which 900 candidates were girls and rest were boys . if 32 % of the boys and 32 % of the girls passed , then the total percentage of failed candidates is ?", + "Output Program": [ + "n0 = 2000.0\nn1 = 900.0\nn2 = 32.0\nn3 = 32.0\nt0 = n2 / 100.0\nt1 = n3 / 100.0\nt2 = 10.0 * 100.0\nt3 = t2 * 2.0\nt4 = n1 * t1\nt5 = t3 - n1\nt6 = t0 * t5\nt7 = t3 - t6\nt8 = t7 - t4\nt9 = t8 / t3\nanswer = t9 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "68" + ], + "split": "train" + }, + { + "Input": "find ( 7 x + 5 y ) / ( x - 2 y ) if x / 2 y = 3 / 2 ?", + "Output Program": [ + "n0 = 7.0\nn1 = 5.0\nn2 = 2.0\nn3 = 2.0\nn4 = 3.0\nn5 = 2.0\nt0 = n4 / n2\nt1 = n2 * t0\nt2 = n0 * t1\nt3 = t1 - n2\nt4 = n1 + t2\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "when a student weighing 45 kgs left a class , the average weight of the remaining 59 students increased by 200 g . what is the average weight of the remaining 59 students", + "Output Program": [ + "n0 = 45.0\nn1 = 59.0\nn2 = 200.0\nn3 = 59.0\nt0 = n1 + 1.0\nt1 = n2 / 1000.0\nt2 = t0 * t1\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "57" + ], + "split": "train" + }, + { + "Input": "if f ( x ) = 12 - x ^ 2 / 2 and f ( 2 k ) = 3 k , what is one possible value for k ?", + "Output Program": [ + "n0 = 12.0\nn1 = 2.0\nn2 = 2.0\nn3 = 2.0\nn4 = 3.0\nt0 = n1**min(n1, 5)\nt1 = t0 / n1\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "there are 19 teams in the hockey league , and each team faces all the other teams 10 times each . how many games are played in the season ?", + "Output Program": [ + "n0 = 19.0\nn1 = 10.0\nt0 = n0 - 1.0\nt1 = n0 * t0\nt2 = n1 * t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "1710" + ], + "split": "train" + }, + { + "Input": "a cyclist climbs a hill with a length of 400 m with a speed of 7.2 km / h . when descending , the speed is two times greater . how much time is necessary for the cyclist to climb and descend the hill ?", + "Output Program": [ + "n0 = 400.0\nn1 = 7.2\nt0 = n1 * 1000.0\nt1 = t0 / 3600.0\nt2 = n0 / t1\nt3 = t2 / 2.0\nt4 = t3 + t2\nanswer = t4 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "the present age of the father is 4 years more than 4 times the age of his son . 4 years hence , father ' s age will be 20 years more than twice the age of the son . find the present age of the father ?", + "Output Program": [ + "n0 = 4.0\nn1 = 4.0\nn2 = 4.0\nn3 = 20.0\nt0 = 2.0 * 4.0\nt1 = n3 + t0\nt2 = t1 - n0\nt3 = t2 - n0\nt4 = t3 / 2.0\nt5 = n0 * t4\nanswer = n0 + t5\nprint(answer)" + ], + "Output Answer": [ + "44" + ], + "split": "train" + }, + { + "Input": "in a certain company , the ratio of the number of managers to the number of non - managers in any department must always be greater than 7 : 32 . in the company , what is the maximum number of non - managers in a department that has 8 managers ?", + "Output Program": [ + "import math\nn0 = 7.0\nn1 = 32.0\nn2 = 8.0\nt0 = n1 * n2\nt1 = t0 / n0\nanswer = math.floor(t1)\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "a paint store mixes 3 / 4 pint of red paint and 2 / 3 pint of white paint to make a new paint color called perfect pink . how many pints of red paint would be needed to make 30 pints of perfect pink paint ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 2.0\nn3 = 3.0\nn4 = 30.0\nt0 = n0 * n2\nt1 = n0 * n1\nt2 = t0 / t1\nanswer = n4 * t2\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "each year for 4 years , a farmer increased the number of trees in a certain orchard by 1 / 4 of the number of trees in the orchard of the preceding year . if all of the trees thrived and there were 5625 trees in the orchard at the end of 4 year period , how many trees were in the orchard at the beginning of the 4 year period .", + "Output Program": [ + "n0 = 4.0\nn1 = 1.0\nn2 = 4.0\nn3 = 5625.0\nn4 = 4.0\nn5 = 4.0\nt0 = n1 / n0\nt1 = n1 + t0\nt2 = t1**min(n0, 5)\nanswer = n3 / t2\nprint(answer)" + ], + "Output Answer": [ + "2304" + ], + "split": "train" + }, + { + "Input": "what is the largest 4 digit number exactly divisible by 88", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 88.0\nt0 = 10.0**min(n0, 5)\nt1 = t0 / n1\nt2 = math.floor(t1)\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "9944" + ], + "split": "train" + }, + { + "Input": "a certain protective additive increases from 25 days to 30 days the time between required maintenance checks on an industrial vehicle . by what percent is the time between maintenance checks increased by using the additive ?", + "Output Program": [ + "n0 = 25.0\nn1 = 30.0\nt0 = n1 - n0\nt1 = t0 / n0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "working simultaneously and independently at an identical constant rate , 4 machines of a certain type can produce a total of x units of product p in 6 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 2 x units of product p in 6 days ?", + "Output Program": [ + "n0 = 4.0\nn1 = 6.0\nn2 = 2.0\nn3 = 6.0\nt0 = n1 / n3\nt1 = n0 * n2\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "product of two natural numbers is 19 . then , the sum of reciprocals of their squares is", + "Output Program": [ + "n0 = 19.0\nt0 = 1.0 / 1.0\nt1 = 1.0 / n0\nt2 = t0**min(2.0, 5)\nt3 = t1**min(2.0, 5)\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "1.002770083102493" + ], + "split": "train" + }, + { + "Input": "a basket of 1430 apples is divided equally among a group of apple lovers . if 45 people join the group , each apple lover would receive 9 apples less . how many u apples did each person get before 45 people joined the feast ?", + "Output Program": [ + "n0 = 1430.0\nn1 = 45.0\nn2 = 9.0\nn3 = 45.0\nt0 = 10.0 + 10.0\nt1 = t0 + 2.0\nt2 = n0 / t1\nt3 = n1 + t2\nt4 = n0 / t3\nanswer = n2 + t4\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "what is the smallest number which when increased by 3 is divisible by 18 , 70 , 100 and 21 ?", + "Output Program": [ + "import scipy\nn0 = 3.0\nn1 = 18.0\nn2 = 70.0\nn3 = 100.0\nn4 = 21.0\nt0 = scipy.lcm(int(n1), int(n2))\nt1 = scipy.lcm(int(n3), int(n4))\nt2 = scipy.lcm(int(t0), int(t1))\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "6303" + ], + "split": "train" + }, + { + "Input": "if a ( k ) = ( 2 k + 1 ) ^ k , and k = 0 , what is the value of a ( a ( a ( k ) ) ) ?", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 0.0\nt0 = n0 * n2\nt1 = n1 + t0\nt2 = t1**min(n2, 5)\nt3 = n0 * t2\nt4 = n1 + t3\nt5 = t4**min(n1, 5)\nt6 = n0 * t5\nt7 = n1 + t6\nanswer = t7**min(t5, 5)\nprint(answer)" + ], + "Output Answer": [ + "343" + ], + "split": "train" + }, + { + "Input": "the cricket team of 11 members is 27 yrs old & the wicket keeper is 3 yrs older . if the ages ofthese 2 are excluded , the average age of theremaining players is 1 year less than the average age of the whole team . what is the average age of the team ?", + "Output Program": [ + "n0 = 11.0\nn1 = 27.0\nn2 = 3.0\nn3 = 2.0\nn4 = 1.0\nt0 = n1 + n2\nt1 = n0 - n3\nt2 = n1 + t0\nt3 = n0 - t1\nt4 = t2 - t1\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "the scoring system in a certain football competition goes as follows : 3 points for victory , 1 point for a draw , and 0 points for defeat . each team plays 20 matches . if a team scored 12 points after 5 games , what is the least number of the remaining matches it has to win to reach the 40 - point mark by the end of the tournament ?", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 1.0\nn2 = 0.0\nn3 = 20.0\nn4 = 12.0\nn5 = 5.0\nn6 = 40.0\nt0 = n6 - n4\nt1 = n3 - n5\nt2 = t0 - t1\nt3 = t2 / 2.0\nt4 = math.floor(t3)\nanswer = t4 + n1\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "if x is an integer and 3.134 \u00d7 10 ^ x is less than 31,000 what is the greatest possible value for x ?", + "Output Program": [ + "import math\nn0 = 3.134\nn1 = 10.0\nn2 = 31000.0\nt0 = n2 / n0\nt1 = math.log(max(1e-5, n1), 2)\nt2 = math.log(max(1e-5, t0), 2)\nt3 = t2 / t1\nanswer = math.floor(t3)\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "in a river flowing at 2 km / hr , a boat travels 40 km upstream and then returns downstream to the starting point . if its speed in still water be 6 km / hr , find the total journey time .", + "Output Program": [ + "n0 = 2.0\nn1 = 40.0\nn2 = 6.0\nt0 = n0 + n2\nt1 = n2 - n0\nt2 = n1 / t1\nt3 = n1 / t0\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "ifaequals the sum of the even integers from 2 to 100 , inclusive , andbequals the sum of the odd integers from 1 to 99 , inclusive , what is the value of a - b ?", + "Output Program": [ + "n0 = 2.0\nn1 = 100.0\nn2 = 1.0\nn3 = 99.0\nt0 = n2 + n3\nt1 = n1 / n0\nt2 = n3 - n2\nt3 = n2 + t1\nt4 = t2 / n0\nt5 = t0 / n0\nt6 = n2 + t4\nt7 = t3 * t1\nt8 = t6 * t5\nanswer = t7 - t8\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "the sum of all possible two digit numbers formed from 3 different one digit natural numbers when divided by the sum of the original 3 numbers is equal to ?", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nt0 = n0 * 10.0\nt1 = t0 + 3.0\nt2 = t1 / n0\nanswer = t2 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "john is going with 10 friends on a trip to sidney for spring break . airfare and hotel costs a total of $ 12100.00 for the group of 11 friends . how much does each person have to pay for their hotel and airfare ?", + "Output Program": [ + "n0 = 10.0\nn1 = 12100.0\nn2 = 11.0\n\nanswer = n1 / n2\nprint(answer)" + ], + "Output Answer": [ + "1100" + ], + "split": "train" + }, + { + "Input": "a soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price . during the annual summer sale , everything in the store is an additional 20 percent off the original list price . if a replica jersey ' s list price is $ 80 , approximately what r percent of the list price is the lowest possible sale price ?", + "Output Program": [ + "n0 = 30.0\nn1 = 50.0\nn2 = 20.0\nn3 = 80.0\n\nanswer = n3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "a certain drink of type a is prepared by mixing 4 parts milk with 3 parts fruit juice . another drink of type b is prepared by mixing 4 parts of fruit juice and 3 parts of milk . how many liters of fruit juice must be added to 42 liters of drink a to convert it to drink b ?", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 4.0\nn3 = 3.0\nn4 = 42.0\nt0 = n0 + n1\nt1 = n0 / t0\nt2 = n1 / t0\nt3 = n4 * t1\nt4 = n4 * t2\nt5 = n0 * t3\nt6 = t5 / n1\nanswer = t6 - t4\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "machine \u2013 a produces 40 % of the total output and machine - b produces 60 % of the total output . an average of 9 units out of a 1000 goods manufactured by machine - a and one unit of 50 units produced by machine - b prove to be defective . what is the probability that a unit chosen at random from the total daily output of the factory is defective ?", + "Output Program": [ + "n0 = 40.0\nn1 = 60.0\nn2 = 9.0\nn3 = 1000.0\nn4 = 50.0\nt0 = n1 * n3\nt1 = t0 / n0\nt2 = n3 + t1\nt3 = t1 / n4\nt4 = n2 + t3\nanswer = t4 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.0156" + ], + "split": "train" + }, + { + "Input": "gold is 10 times as heavy as water and copper is 5 times as heavy as water . in what ratio should these be mixed to get an alloy 9 times as heavy as water ?", + "Output Program": [ + "n0 = 10.0\nn1 = 5.0\nn2 = 9.0\nt0 = n2 - n1\nt1 = n0 - n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "every student of a certain school must take one and only one elective course . in last year , 1 / 2 of the students took p . e . as an elective , 1 / 3 of the students took theatre as an elective , and all of the other students took music . in this year , 1 / 3 of the students who took p . e . and 1 / 4 of the students who took theatre left school , other students did not leave , and no fresh student come in . what fraction of all students took p . e . or music ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 1.0\nn3 = 3.0\nn4 = 1.0\nn5 = 3.0\nn6 = 1.0\nn7 = 4.0\nt0 = n0 / n1\nt1 = n0 / n3\nt2 = n0 / n7\nt3 = t0 + t1\nt4 = 1.0 - t1\nt5 = 1.0 - t2\nt6 = t0 * t4\nt7 = t1 * t5\nt8 = 1.0 - t3\nt9 = t6 + t8\nt10 = t9 + t7\nanswer = t9 / t10\nprint(answer)" + ], + "Output Answer": [ + "0.6666666666666667" + ], + "split": "train" + }, + { + "Input": "if sharon ' s weekly salary increased by 20 percent , she would earn $ 600 per week . if instead , her weekly salary were to increase by 15 percent , how much would she earn per week ?", + "Output Program": [ + "n0 = 20.0\nn1 = 600.0\nn2 = 15.0\nt0 = n0 / 100.0\nt1 = n2 / 100.0\nt2 = t0 + 1.0\nt3 = n1 / t2\nt4 = t1 * t3\nanswer = t3 + t4\nprint(answer)" + ], + "Output Answer": [ + "575" + ], + "split": "train" + }, + { + "Input": "patrick purchased 80 pencils and sold them at a loss equal to the selling price of 30 pencils . the cost of 80 pencils is how many times the selling price of 80 pencils ?", + "Output Program": [ + "n0 = 80.0\nn1 = 30.0\nn2 = 80.0\nn3 = 80.0\nt0 = n0 + n1\nt1 = n0 / t0\nanswer = 1 / t1\nprint(answer)" + ], + "Output Answer": [ + "1.375" + ], + "split": "train" + }, + { + "Input": "the average of 9 numbers is 104 . average of the first 5 of them is 99 and that of the last 5 is 100 . find the 5 th number ?", + "Output Program": [ + "n0 = 9.0\nn1 = 104.0\nn2 = 5.0\nn3 = 99.0\nn4 = 5.0\nn5 = 100.0\nn6 = 5.0\nt0 = n5 * n6\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 - t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "59" + ], + "split": "train" + }, + { + "Input": "the cash realised on selling a 14 % stock is rs . 101.25 , brokerage being 1 / 4 % is", + "Output Program": [ + "n0 = 14.0\nn1 = 101.25\nn2 = 1.0\nn3 = 4.0\nt0 = n2 / n3\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "101" + ], + "split": "train" + }, + { + "Input": "farm tax is levied on the 75 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . william . mr . william paid only $ 480 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :", + "Output Program": [ + "n0 = 75.0\nn1 = 3840.0\nn2 = 480.0\nt0 = n2 / n1\nt1 = t0 * 100.0\nt2 = t1 * 100.0\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "16.666666666666668" + ], + "split": "train" + }, + { + "Input": "what is x if 2 x - y = 14 and y = 2 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 14.0\nn2 = 2.0\nt0 = n0 * n0\nt1 = n1 - n0\nanswer = t1 - t0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a pupil ' s marks were wrongly entered as 83 instead of 70 . due to the average marks for the class got increased by half . the number of pupils in the class is ?", + "Output Program": [ + "n0 = 83.0\nn1 = 70.0\nt0 = n0 - n1\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "calculate the average of all the numbers between 18 and 57 which are divisible by 7 .", + "Output Program": [ + "import math\nn0 = 18.0\nn1 = 57.0\nn2 = 7.0\nt0 = n0 / n2\nt1 = n1 / n2\nt2 = math.floor(t0)\nt3 = math.floor(t1)\nt4 = t2 + 1.0\nt5 = t4 + t3\nt6 = t5 / 2.0\nanswer = n2 * t6\nprint(answer)" + ], + "Output Answer": [ + "38.5" + ], + "split": "train" + }, + { + "Input": "a trained covered x km at 50 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 3 x km .", + "Output Program": [ + "n0 = 50.0\nn1 = 2.0\nn2 = 20.0\nn3 = 3.0\nt0 = n0 / n0\nt1 = n0 * n3\nt2 = n0 * n1\nt3 = t2 / n2\nt4 = t0 + t3\nanswer = t1 / t4\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "a drink vendor has 60 liters of maaza , 144 liters of pepsi and 368 liters of sprite . he wants to pack them in cans , so that each can contains the same number of liters of a drink , and does n ' t want to mix any two drinks in a can . what is the least number of cans required ?", + "Output Program": [ + "import scipy\nn0 = 60.0\nn1 = 144.0\nn2 = 368.0\nt0 = scipy.gcd(int(n0), int(n1))\nt1 = scipy.gcd(int(n2), int(t0))\nt2 = n0 / t1\nt3 = n1 / t1\nt4 = n2 / t1\nt5 = t2 + t3\nanswer = t5 + t4\nprint(answer)" + ], + "Output Answer": [ + "143" + ], + "split": "train" + }, + { + "Input": "a retailer sells 5 shirts . he sells first 2 shirts for $ 30 and $ 20 . if the retailer wishes to sell the 5 shirts for an overall average price of over $ 30 , what must be the minimum average price of the remaining 3 shirts ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 30.0\nn3 = 20.0\nn4 = 5.0\nn5 = 30.0\nn6 = 3.0\nt0 = n2 + n3\nt1 = n0 * n2\nt2 = t1 - t0\nanswer = t2 / n6\nprint(answer)" + ], + "Output Answer": [ + "33.333333333333336" + ], + "split": "train" + }, + { + "Input": "a farmer has an apple orchard consisting of fuji and gala apple trees . due to high winds this year 10 % of his trees cross pollinated . the number of his trees that are pure fuji plus the cross - pollinated ones totals 170 , while 3 / 4 of all his trees are pure fuji . how many of his trees are pure gala ?", + "Output Program": [ + "n0 = 10.0\nn1 = 170.0\nn2 = 3.0\nn3 = 4.0\nt0 = n0 / 100.0\nt1 = n2 / n3\nt2 = t0 + t1\nt3 = n1 / t2\nanswer = t3 - n1\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "a man is 46 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is :", + "Output Program": [ + "n0 = 46.0\nt0 = 2.0 * 2.0\nt1 = 2.0 - 1.0\nt2 = t0 - 2.0\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "44" + ], + "split": "train" + }, + { + "Input": "what is the maximum value of vx - yz . if the value of v , x , y , z have to be chosen from the set a where a ( - 3 , - 2 , - 1 , 01 , 23 )", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 1.0\nn3 = 1.0\nn4 = 23.0\nt0 = -n0\nt1 = n1 * t0\nt2 = t0**min(n1, 5)\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "x and y are two towns . ganesh covers the distance from x to y at an average speed of 54 km / hr . however , he covers the distance from y to x at an average speed of 36 km / hr . his average speed during the whole journey in km / hr . is :", + "Output Program": [ + "n0 = 54.0\nn1 = 36.0\nt0 = n0 - 10.0\nt1 = t0 + 100.0\nt2 = t1 + t1\nt3 = t1 / n0\nt4 = t1 / n1\nt5 = t3 + t4\nanswer = t2 / t5\nprint(answer)" + ], + "Output Answer": [ + "43.2" + ], + "split": "train" + }, + { + "Input": "if p is a prime number greater than 3 , find the remainder when p ^ 2 + 12 is divided by 12 .", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 12.0\nn3 = 12.0\nt0 = 1.0 + 4.0\nt1 = n0 * n3\nt2 = t0**min(n1, 5)\nt3 = n2 + t2\nanswer = t3 - t1\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "in 1979 approximately 1 / 3 of the 37.3 million airline passengers traveling to or from the united states used kennedy airport . if the number of such passengers that used miami airport was 1 / 4 the number that used kennedy airport and 3 times the number that used logan airport , approximately how many millions of these passengers used logan airport that year ?", + "Output Program": [ + "n0 = 1979.0\nn1 = 1.0\nn2 = 3.0\nn3 = 37.3\nn4 = 1.0\nn5 = 4.0\nn6 = 3.0\nt0 = n3 / n2\nt1 = n5 * n6\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "1.036111111111111" + ], + "split": "train" + }, + { + "Input": "if a ( a - 4 ) = 5 and b ( b - 4 ) = 5 , where a \u2260 b , then a + b =", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 4.0\nn3 = 5.0\nt0 = n0 + n1\nt1 = n0 - n1\nt2 = t0 + t1\nt3 = t2 - 1.0\nt4 = t3 - 1.0\nt5 = t4 - 1.0\nanswer = t5 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "in a software company 4 / 10 of people know c + + , 2 / 4 of them know java , 2 / 8 of them know neither , find the total possibility to know c + + ?", + "Output Program": [ + "n0 = 4.0\nn1 = 10.0\nn2 = 2.0\nn3 = 4.0\nn4 = 2.0\nn5 = 8.0\nt0 = n2 / n5\nt1 = n2 / n0\nt2 = 1.0 - t0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "0.25" + ], + "split": "train" + }, + { + "Input": "the average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 10 years . find the average age of the women ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.0\nn2 = 20.0\nn3 = 10.0\nt0 = n2 + n3\nt1 = n0 * n1\nt2 = t0 + t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "the number 0.8 is how much greater than 1 / 2 ?", + "Output Program": [ + "n0 = 0.8\nn1 = 1.0\nn2 = 2.0\nt0 = n1 / n2\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "0.30000000000000004" + ], + "split": "train" + }, + { + "Input": "cindy has her eye on a sundress but thinks it is too expensive . it goes on sale for 15 % less than the original price . before cindy can buy the dress , however , the store raises the new price by 25 % . if the dress cost $ 68 after it went on sale for 15 % off , what is the difference between the original price and the final price ?", + "Output Program": [ + "n0 = 15.0\nn1 = 25.0\nn2 = 68.0\nn3 = 15.0\nt0 = n1 + 100.0\nt1 = 100.0 - n0\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = n2 / t3\nt5 = n2 * t2\nanswer = t5 - t4\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "the cost per pound of milk powder and coffee were the same in june . in july , the price of coffee shot up by 200 % and that of milk powder dropped by 60 % . if in july , a mixture containing equal quantities of milk powder and coffee costs $ 5.10 for 3 lbs , how much did a pound of milk powder cost in july ?", + "Output Program": [ + "n0 = 200.0\nn1 = 60.0\nn2 = 5.1\nn3 = 3.0\nt0 = n1 / 100.0\nanswer = 1.0 - t0\nprint(answer)" + ], + "Output Answer": [ + "0.4" + ], + "split": "train" + }, + { + "Input": "for any number z , z * is defined as the greatest positive even integer less than or equal to y . what is the value of 6.30 \u2013 6.30 * ?", + "Output Program": [ + "import math\nn0 = 6.3\nn1 = 6.3\nt0 = math.floor(n0)\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "0.2999999999999998" + ], + "split": "train" + }, + { + "Input": "the guests at a football banquet consumed a total of 406 pounds of food . if no individual guest consumed more than 2.5 pounds of food , what is the minimum number of guests that could have attended the banquet ?", + "Output Program": [ + "import math\nn0 = 406.0\nn1 = 2.5\nt0 = n0 / n1\nt1 = math.floor(t0)\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "163" + ], + "split": "train" + }, + { + "Input": "an equal number of desks and bookcases are to be placed along a library wall that is 15 meters long . each desk is 2 meters long , and each bookshelf is 1.5 meters long . if the maximum possible number of desks and bookcases are to be placed along the wall , then the space along the wall that is left over will be how many g meters long ?", + "Output Program": [ + "n0 = 15.0\nn1 = 2.0\nn2 = 1.5\nt0 = n1 * 4.0\nt1 = n2 * 4.0\nt2 = t0 + t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "if 2 x + y = 7 and x + 2 y = 8 , then ( x + y ) / 3 =", + "Output Program": [ + "n0 = 2.0\nn1 = 7.0\nn2 = 2.0\nn3 = 8.0\nn4 = 3.0\nt0 = n0 * n1\nt1 = n0 * n0\nt2 = t0 - n3\nt3 = t1 - 1.0\nt4 = t2 / t3\nt5 = n0 * t4\nt6 = n1 - t5\nt7 = t4 + t6\nanswer = t7 / n4\nprint(answer)" + ], + "Output Answer": [ + "1.6666666666666667" + ], + "split": "train" + }, + { + "Input": "farm tax is levied on the 90 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . william . mr . william paid only $ 480 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :", + "Output Program": [ + "n0 = 90.0\nn1 = 3840.0\nn2 = 480.0\nt0 = n2 / n1\nt1 = t0 * 100.0\nt2 = t1 * 100.0\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "13.88888888888889" + ], + "split": "train" + }, + { + "Input": "the average salary of a person for the months of january , february , march and april is rs . 8000 and that for the months february , march , april and may is rs . 8500 . if his salary for the month of may is rs . 6500 , find his salary for the month of january ?", + "Output Program": [ + "n0 = 8000.0\nn1 = 8500.0\nn2 = 6500.0\nt0 = n0 * 4.0\nt1 = n1 * 4.0\nt2 = t1 - n2\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "4500" + ], + "split": "train" + }, + { + "Input": "if x + y = 300 , x - y = 200 , for integers of x and y , y = ?", + "Output Program": [ + "n0 = 300.0\nn1 = 200.0\nt0 = n0 + n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "250" + ], + "split": "train" + }, + { + "Input": "the average ( arithmetic mean ) of all scores on a certain algebra test was 90 . if the average of the 8 male students \u2019 grades was 82 , and the average of the female students \u2019 grades was 92 , how many female students took the test ?", + "Output Program": [ + "n0 = 90.0\nn1 = 8.0\nn2 = 82.0\nn3 = 92.0\nt0 = n0 * n1\nt1 = n1 * n2\nt2 = n3 - n0\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "the class mean score on a test was 60 , and the standard deviation was 10 . if jack ' s score was within 2 standard deviations of the mean , what is the lowest score he could have received ?", + "Output Program": [ + "n0 = 60.0\nn1 = 10.0\nn2 = 2.0\n\nanswer = n1 * n2\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "a certain roller coaster has 5 cars , and a passenger is equally likely to ride in any 1 of the 5 cars each time that passenger rides the roller coaster . if a certain passenger is to ride the roller coaster 5 times , what is the probability that the passenger will ride in each of the 5 cars ?", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 1.0\nn2 = 5.0\nn3 = 5.0\nn4 = 5.0\nt0 = n1 / n0\nt1 = math.factorial(min(15, int(n0)))\nt2 = t0**min(n0, 5)\nanswer = t1 * t2\nprint(answer)" + ], + "Output Answer": [ + "0.03840000000000001" + ], + "split": "train" + }, + { + "Input": "a certain no . when divided by 35 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ?", + "Output Program": [ + "n0 = 35.0\nn1 = 25.0\nn2 = 15.0\nt0 = n0 - n1\nt1 = t0 - 4.0\nanswer = t1 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 40 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam ?", + "Output Program": [ + "n0 = 80.0\nn1 = 5.0\nn2 = 40.0\nn3 = 90.0\nt0 = n1 * n3\nt1 = n1 * n2\nt2 = n3 - n0\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "evaluate : 13 + sqrt ( - 4 + 5 \u00e3 \u2014 3 \u00e3 \u00b7 3 ) = ?", + "Output Program": [ + "import math\nn0 = 13.0\nn1 = 4.0\nn2 = 5.0\nn3 = 3.0\nn4 = 3.0\nt0 = n3 * n2\nt1 = t0 / n4\nt2 = t1 - n1\nt3 = math.sqrt(max(0, t2))\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "if two positive numbers are in the ratio 1 / 6 : 1 / 5 , then by what percent is the second number more than the first ?", + "Output Program": [ + "n0 = 1.0\nn1 = 6.0\nn2 = 1.0\nn3 = 5.0\nt0 = n0 / n3\nanswer = t0 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "what is the largest 4 digit number exactly divisible by 24 ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 24.0\nt0 = 10.0**min(n0, 5)\nt1 = t0 / n1\nt2 = math.floor(t1)\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "9984" + ], + "split": "train" + }, + { + "Input": "the average weight of 8 persons increases by 1.5 kg when a person weighting 65 kg is replaced by a new person . what could be the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 1.5\nn2 = 65.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "77" + ], + "split": "train" + }, + { + "Input": "what is the remainder when ( 71 ) ( 73 ) is divided by 8 ?", + "Output Program": [ + "n0 = 71.0\nn1 = 73.0\nn2 = 8.0\nt0 = n0 * n1\nanswer = t0 % n2\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "if the product of 8 integers is negative , at most how many of the integers can be negative ?", + "Output Program": [ + "n0 = 8.0\n\nanswer = n0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "a briefcase has a number - lock system containing a combination of 3 digits ( each digit can be of numbers 0 to 8 ) . if the correct combination is unknown , how much maximum time would be required to open the bag if each \u201c trial \u201d of combination takes 3 seconds ?", + "Output Program": [ + "n0 = 3.0\nn1 = 0.0\nn2 = 8.0\nn3 = 3.0\nt0 = n2 + 1.0\nt1 = t0 * t0\nt2 = t0 * t1\nt3 = n0 * t2\nanswer = t3 / 60.0\nprint(answer)" + ], + "Output Answer": [ + "36.45" + ], + "split": "train" + }, + { + "Input": "a driver just filled the car ' s gas tank with 27 liters of gasohol , a mixture consisting of 5 % ethanol and 95 % gasoline . if the car runs best on a mixture consisting of 10 % ethanol and 90 % gasoline , how many liters of ethanol must be added into the gas tank for the car to achieve optimum performance ?", + "Output Program": [ + "n0 = 27.0\nn1 = 5.0\nn2 = 95.0\nn3 = 10.0\nn4 = 90.0\nt0 = n0 * n1\nt1 = 100.0 - n3\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "1.5" + ], + "split": "train" + }, + { + "Input": "if money is invested at r percent interest , compounded annually , the amount of investment will double in approximately 70 / r years . if pat ' s parents invested $ 8000 in a long term bond that pays 4 percent interest , compounded annually , what will be the approximate total amount of investment 36 years later , when pat is ready for college ?", + "Output Program": [ + "n0 = 70.0\nn1 = 8000.0\nn2 = 4.0\nn3 = 36.0\nt0 = n1 * 2.0\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "32000" + ], + "split": "train" + }, + { + "Input": "in a division sum , the remainder is 0 . as student mistook the divisor by 12 instead of 21 and obtained 42 as quotient . what is the correct quotient ?", + "Output Program": [ + "n0 = 0.0\nn1 = 12.0\nn2 = 21.0\nn3 = 42.0\nt0 = n1 * n3\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "what is the sum of the 1 st 6 prime numbers greater than 10 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 6.0\nn2 = 10.0\nt0 = n0 + n2\nt1 = t0 + 2.0\nt2 = t0 + t1\nt3 = t1 + 4.0\nt4 = t2 + t3\nt5 = t3 + 2.0\nt6 = t4 + t5\nt7 = t5 + 4.0\nt8 = t6 + t7\nt9 = n1 + t7\nanswer = t8 + t9\nprint(answer)" + ], + "Output Answer": [ + "112" + ], + "split": "train" + }, + { + "Input": "to be considered for \u201c movie of the year , \u201d a film must appear in at least 1 / 4 of the top - 10 - movies lists submitted by the cinematic academy \u2019 s 775 members . what is the smallest number of top - 10 lists a film can appear on and still be considered for \u201c movie of the year \u201d ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 10.0\nn3 = 775.0\nn4 = 10.0\n\nanswer = n3 / n1\nprint(answer)" + ], + "Output Answer": [ + "193.75" + ], + "split": "train" + }, + { + "Input": "a certain characteristic in a large population has a distribution that is symmetric about the mean a . if 68 % of the distribution lies one standard deviation d of the mean , what percent of the distribution is less than a + d ?", + "Output Program": [ + "n0 = 68.0\nt0 = 100.0 - n0\nt1 = t0 / 2.0\nanswer = 100.0 - t1\nprint(answer)" + ], + "Output Answer": [ + "84" + ], + "split": "train" + }, + { + "Input": "if a / b = 1 / 3 , b / c = 2 , c / d = 1 / 2 , d / e = 3 and e / f = 1 / 8 , then what is the value of abc / def ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 2.0\nn3 = 1.0\nn4 = 2.0\nn5 = 3.0\nn6 = 1.0\nn7 = 8.0\nt0 = n1 * n1\nt1 = n1 * n7\nt2 = n2 * t1\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.1875" + ], + "split": "train" + }, + { + "Input": "a camera lens filter kit containing 5 filters sells for $ 87.50 . if the filters are purchased individually , 2 of them are priced at $ 16.45 each , 2 at $ 14.05 each , 1 at $ 19.50 . the amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually ?", + "Output Program": [ + "n0 = 5.0\nn1 = 87.5\nn2 = 2.0\nn3 = 16.45\nn4 = 2.0\nn5 = 14.05\nn6 = 1.0\nn7 = 19.5\nn8 = 5.0\nt0 = n2 * n3\nt1 = n2 * n5\nt2 = t0 + t1\nt3 = n7 + t2\nt4 = n1 - t3\nt5 = t4 * 100.0\nanswer = t5 / n1\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "what is the dividend . divisor 16 , the quotient is 9 and the remainder is 5 ?", + "Output Program": [ + "n0 = 16.0\nn1 = 9.0\nn2 = 5.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "149" + ], + "split": "train" + }, + { + "Input": "if a certain number is divided by 5 , the quotient , dividend , and divisor , added together , will amount to 65 . what is the number ?", + "Output Program": [ + "n0 = 5.0\nn1 = 65.0\nt0 = n0 + 1.0\nt1 = n1 - n0\nt2 = n0 * t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "if t = 5 / 9 * ( k - 32 ) , and if t = 105 , then what is the value of k ?", + "Output Program": [ + "n0 = 5.0\nn1 = 9.0\nn2 = 32.0\nn3 = 105.0\nt0 = n1 * n3\nt1 = t0 / n0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "221" + ], + "split": "train" + }, + { + "Input": "if 170 ! / 10 ^ n is an integer , what is the largest possible value of n ?", + "Output Program": [ + "n0 = 170.0\nn1 = 10.0\nt0 = 1.0 + 4.0\nt1 = n0 / t0\nt2 = t1 / t0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "40.8" + ], + "split": "train" + }, + { + "Input": "chris mixed 3 pounds of raisins with 3 pounds of nuts . if a pound of nuts costs 3 times as much as a pound of raisins , then the total cost of the raisins was what fraction of the total cost of the mixture ?", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 3.0\nt0 = n1 * n2\nt1 = n0 + t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.25" + ], + "split": "train" + }, + { + "Input": "a theater charges $ 12 for seats in the orchestra and $ 8 for seats in the balcony . on a certain night , a total of 370 tickets were sold for a total cost of $ 3320 . how many more tickets were sold that night for seats in the balcony than for seats in the orchestra ?", + "Output Program": [ + "n0 = 12.0\nn1 = 8.0\nn2 = 370.0\nn3 = 3320.0\nt0 = n1 * n2\nt1 = n0 - n1\nt2 = n3 - t0\nt3 = t2 / t1\nt4 = n2 - t3\nanswer = t4 - t3\nprint(answer)" + ], + "Output Answer": [ + "190" + ], + "split": "train" + }, + { + "Input": "a meal cost $ 37.25 adn there was no tax . if the tip was more than 10 pc but less than 15 pc of the price , then the total amount paid should be :", + "Output Program": [ + "n0 = 37.25\nn1 = 10.0\nn2 = 15.0\nt0 = n0 * n1\nt1 = t0 / 100.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "40.975" + ], + "split": "train" + }, + { + "Input": "at a certain high school , the senior class is twice the size of the junior class . if 1 / 8 of the seniors and 3 / 4 of the juniors study japanese , what fraction of the students in both classes study japanese ?", + "Output Program": [ + "n0 = 1.0\nn1 = 8.0\nn2 = 3.0\nn3 = 4.0\nt0 = n1 + n3\nanswer = n3 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.3333333333333333" + ], + "split": "train" + }, + { + "Input": "carol is 5 times alice \u2019 s age but only twice as old as betty . alice is 12 years younger than carol . how old is betty ?", + "Output Program": [ + "n0 = 5.0\nn1 = 12.0\n\nanswer = n0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "in a box of 10 pens , a total of 2 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?", + "Output Program": [ + "n0 = 10.0\nn1 = 2.0\nn2 = 2.0\nt0 = n0 - n1\nt1 = n0 - 1.0\nt2 = t0 / n0\nt3 = t0 - 1.0\nt4 = t3 / t1\nanswer = t2 * t4\nprint(answer)" + ], + "Output Answer": [ + "0.6222222222222222" + ], + "split": "train" + }, + { + "Input": "if the sum of the 4 th term and the 12 th term of an arithmetic progression is 30 , what is the sum of the first 15 terms of the progression ?", + "Output Program": [ + "n0 = 4.0\nn1 = 12.0\nn2 = 30.0\nn3 = 15.0\nt0 = n3 / 2.0\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "225" + ], + "split": "train" + }, + { + "Input": "if x and y are numbers such that ( x + 5 ) ( y - 5 ) = 0 , what is the smallest possible value of x ^ 2 + y ^ 2", + "Output Program": [ + "n0 = 5.0\nn1 = 5.0\nn2 = 0.0\nn3 = 2.0\nn4 = 2.0\n\nanswer = n0**min(n3, 5)\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "find the value of ( 19 + 43 / 151 ) \u00d7 151", + "Output Program": [ + "n0 = 19.0\nn1 = 43.0\nn2 = 151.0\nn3 = 151.0\nt0 = n1 / n2\nt1 = n0 + t0\nanswer = t1 * n2\nprint(answer)" + ], + "Output Answer": [ + "2912" + ], + "split": "train" + }, + { + "Input": "a , b and c have rs . 250 between them , a and c together have rs . 200 and b and c rs . 350 . how much does c have ?", + "Output Program": [ + "n0 = 250.0\nn1 = 200.0\nn2 = 350.0\nt0 = n1 + n2\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "a computer is programmed to multiply consecutive even integers 2 * 4 * 6 * 8 * \u2026 * n until the product is divisible by 1947 , what is the value of n ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 6.0\nn3 = 8.0\nn4 = 1947.0\nt0 = 1.0 + 10.0\nt1 = n4 / t0\nt2 = t1 / 3.0\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "118" + ], + "split": "train" + }, + { + "Input": "if x is equal to the sum of the integers from 40 to 60 , inclusive , and y is the number of even integers from 40 to 60 , inclusive , what is the value of x + y ?", + "Output Program": [ + "n0 = 40.0\nn1 = 60.0\nn2 = 40.0\nn3 = 60.0\nt0 = n0 + n1\nt1 = n1 - n0\nt2 = t1 + 1.0\nt3 = t1 / 2.0\nt4 = t0 / 2.0\nt5 = t3 + 1.0\nt6 = t2 * t4\nanswer = t5 + t6\nprint(answer)" + ], + "Output Answer": [ + "1061" + ], + "split": "train" + }, + { + "Input": "the average weight of a , b and c is 45 kg . if the average weight of a and b be 40 kg and that of b and c be 46 kg , then the weight of b is :", + "Output Program": [ + "n0 = 45.0\nn1 = 40.0\nn2 = 46.0\nt0 = n1 * 2.0\nt1 = n2 * 2.0\nt2 = n0 * 3.0\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "37" + ], + "split": "train" + }, + { + "Input": "what is the least number should be added to 1156 , so the sum of the number is completely divisible by 25 ?", + "Output Program": [ + "import math\nn0 = 1156.0\nn1 = 25.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = t1 + 1.0\nt3 = n1 * t2\nanswer = t3 - n0\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "the youngest of 4 children has siblings who are 4 , 5 , and 7 years older than she is . if the average ( arithmetic mean ) age of the 4 siblings is 21 , what is the age of the youngest sibling ?", + "Output Program": [ + "n0 = 4.0\nn1 = 4.0\nn2 = 5.0\nn3 = 7.0\nn4 = 4.0\nn5 = 21.0\nt0 = n0 + n2\nt1 = n0 * n5\nt2 = n3 + t0\nt3 = t1 - t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "the average of 8 numbers is 25 , that of the first 2 is 20 and of the next 3 is 26 . the sixth number is less than the seventh by 4 , and less than the eighth by 6 . the last number is", + "Output Program": [ + "n0 = 8.0\nn1 = 25.0\nn2 = 2.0\nn3 = 20.0\nn4 = 3.0\nn5 = 26.0\nn6 = 4.0\nn7 = 6.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n4 * n5\nt3 = t1 + t2\nt4 = t0 - t3\nt5 = n0 + t4\nanswer = t5 / n4\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "if a - b = 3 and a ( power 2 ) + b ( power 2 ) = 27 , find the value of ab .", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 2.0\nn3 = 27.0\nt0 = n0**min(n1, 5)\nt1 = n3 - t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "kamal ' s salary was decreased by 50 % and subsequently increased by 30 % . how much percent does he lose ?", + "Output Program": [ + "n0 = 50.0\nn1 = 30.0\nt0 = n1 / 100.0\nt1 = n0 / 100.0\nt2 = t0 + 1.0\nt3 = t2 * t1\nt4 = 1.0 - t3\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "the ratio of a to b to c is 2 to 3 to 4 , and a , b , c are positive integers . if the average ( arithmetic mean ) of the 3 numbers is 42 , what is the value of a ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 4.0\nn3 = 3.0\nn4 = 42.0\nt0 = n0 + n1\nt1 = n1 * n4\nt2 = n2 + t0\nt3 = t1 / t2\nanswer = n0 * t3\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "what is the dividend . divisor 18 , the quotient is 9 and the remainder is 4", + "Output Program": [ + "n0 = 18.0\nn1 = 9.0\nn2 = 4.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "166" + ], + "split": "train" + }, + { + "Input": "1 / [ ( 1 / 0.03 ) + ( 1 / 0.37 ) ] = ?", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 0.03\nn3 = 1.0\nn4 = 0.37\nt0 = n0 / n2\nt1 = n0 / n4\nt2 = t0 + t1\nanswer = 1 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.02775" + ], + "split": "train" + }, + { + "Input": "which number need to add to 956734 to get a number exactly divisible by 412 ?", + "Output Program": [ + "import math\nn0 = 956734.0\nn1 = 412.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = t1 + 1.0\nt3 = t2 - t0\nanswer = n1 * t3\nprint(answer)" + ], + "Output Answer": [ + "342.00000000007276" + ], + "split": "train" + }, + { + "Input": "find the highest value of ' a ' so that 365 a 24 is divisible by 8 .", + "Output Program": [ + "import scipy\nn0 = 365.0\nn1 = 24.0\nn2 = 8.0\nt0 = scipy.gcd(int(n2), int(100.0))\nt1 = scipy.lcm(int(n2), int(100.0))\nt2 = t0 * t1\nanswer = t2 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "in a division sum , the remainder is 0 . as student mistook the divisor by 12 instead of 21 and obtained 70 as quotient . what is the correct quotient ?", + "Output Program": [ + "n0 = 0.0\nn1 = 12.0\nn2 = 21.0\nn3 = 70.0\nt0 = n1 * n3\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "a box contains 10 tablets of medicine a and 13 tablets of medicine b . what is the least number of tablets that should be taken from the box to ensure that at least two tablets of each kind are among the extracted .", + "Output Program": [ + "n0 = 10.0\nn1 = 13.0\n\nanswer = n1 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "find large number from below question the difference of 2 no . ' s is 1365 . on dividing the larger no . by the smaller , we get 6 as quotient and the 15 as remainder ?", + "Output Program": [ + "n0 = 1365.0\nn1 = 6.0\nn2 = 15.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nt2 = t0 / t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "1620" + ], + "split": "train" + }, + { + "Input": "of 70 players on a football team , 28 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?", + "Output Program": [ + "n0 = 70.0\nn1 = 28.0\nt0 = 1.0 / 3.0\nt1 = n0 - n1\nt2 = 1.0 - t0\nt3 = t2 * t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "train" + }, + { + "Input": "if the average of 8 digits is 20 and the average of 5 of them is 12 , calculate the average of the remaining 3 numbers ?", + "Output Program": [ + "n0 = 8.0\nn1 = 20.0\nn2 = 5.0\nn3 = 12.0\nn4 = 3.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = t0 - t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "33.333333333333336" + ], + "split": "train" + }, + { + "Input": "a man purchased 3 blankets @ rs . 100 each , 5 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ?", + "Output Program": [ + "n0 = 3.0\nn1 = 100.0\nn2 = 5.0\nn3 = 150.0\nn4 = 150.0\nt0 = n3 * 10.0\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "450" + ], + "split": "train" + }, + { + "Input": "in goshawk - eurasian nature reserve 30 percent of the birds are hawks , and 40 percent of the non - hawks are paddyfield - warblers . if there are 25 percent as many kingfishers as paddyfield - warblers in the reserve , then what percent of the birds x in the nature reserve are not hawks , paddyfield - warblers , or kingfishers ?", + "Output Program": [ + "n0 = 30.0\nn1 = 40.0\nn2 = 25.0\nt0 = n2 + n2\nt1 = t0 / 2.0\nanswer = t1 + 10.0\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "country x taxes each of its citizens an amount equal to 15 percent of the first $ 40,000 of income , plus 20 percent of all income in excess of $ 40,000 . if a citizen of country x is taxed a total of $ 8,000 , what is her income ?", + "Output Program": [ + "n0 = 15.0\nn1 = 40000.0\nn2 = 20.0\nn3 = 40000.0\nn4 = 8000.0\nt0 = n0 / 100.0\nt1 = n2 / 100.0\nt2 = 2.0 * 4.0\nt3 = 10.0 * 4.0\nt4 = t2 * 1000.0\nt5 = t3 * 1000.0\nt6 = t0 * t5\nt7 = t4 - t6\nt8 = t7 / t1\nanswer = t8 + t5\nprint(answer)" + ], + "Output Answer": [ + "50000" + ], + "split": "train" + }, + { + "Input": "in the faculty of reverse - engineering , 250 second year students study numeric methods , 423 second year students study automatic control of airborne vehicles and 134 second year students study them both . how many students are there in the faculty if the second year students are approximately 80 % of the total ?", + "Output Program": [ + "n0 = 250.0\nn1 = 423.0\nn2 = 134.0\nn3 = 80.0\n\nanswer = n0 + n1\nprint(answer)" + ], + "Output Answer": [ + "673" + ], + "split": "train" + }, + { + "Input": "the price of 10 chairs is equal to that of 4 tables . the price of 15 chairs and 2 tables together is rs . 4000 . the total price of 12 chairs and 3 tables is", + "Output Program": [ + "n0 = 10.0\nn1 = 4.0\nn2 = 15.0\nn3 = 2.0\nn4 = 4000.0\nn5 = 12.0\nn6 = 3.0\nt0 = n1 / n0\nt1 = n2 * t0\nt2 = n3 + t1\nt3 = n4 / t2\nt4 = n6 * t3\nt5 = t0 * t3\nt6 = n5 * t5\nanswer = t4 + t6\nprint(answer)" + ], + "Output Answer": [ + "3900" + ], + "split": "train" + }, + { + "Input": "instead of multiplying a number by 2 , the number is divided by 10 . what is the percentage of error obtained ?", + "Output Program": [ + "n0 = 2.0\nn1 = 10.0\nt0 = n1 / n1\nt1 = n0 * 10.0\nt2 = t0 / t1\nt3 = t2 * 100.0\nanswer = 100.0 - t3\nprint(answer)" + ], + "Output Answer": [ + "95" + ], + "split": "train" + }, + { + "Input": "for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today ' s production of 90 units raises the average to 54 units per day , what is the value of n ?", + "Output Program": [ + "n0 = 50.0\nn1 = 90.0\nn2 = 54.0\nt0 = n1 - n0\nt1 = n2 - n0\nt2 = t0 / t1\nanswer = t2 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "the year next to 1991 having the same calendar as that of 1990 is \u2013", + "Output Program": [ + "n0 = 1991.0\nn1 = 1990.0\nt0 = n0 - n1\nanswer = n0 + t0\nprint(answer)" + ], + "Output Answer": [ + "1992" + ], + "split": "train" + }, + { + "Input": "find ( 7 x + 6 y ) / ( x - 2 y ) if x / 2 y = 3 / 2 ?", + "Output Program": [ + "n0 = 7.0\nn1 = 6.0\nn2 = 2.0\nn3 = 2.0\nn4 = 3.0\nn5 = 2.0\nt0 = n4 / n2\nt1 = n2 * t0\nt2 = n0 * t1\nt3 = t1 - n2\nt4 = n1 + t2\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "train" + }, + { + "Input": "what is the largest integral value of ' k ' for which the quadratic equation x 2 - 6 x + k = 0 will have two real and distinct roots ?", + "Output Program": [ + "n0 = 2.0\nn1 = 6.0\nn2 = 0.0\nt0 = n1**min(2.0, 5)\nt1 = n0**min(2.0, 5)\nt2 = t0 / t1\nanswer = t2 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a certain sum of money is divided among a , b and c such that a gets one - third of what b and c together get and b gets two - seventh of what a and c together get . if the amount received by a is $ 20 more than that received by b , find the total amount shared by a , b and c .", + "Output Program": [ + "n0 = 20.0\nt0 = n0 * 3.0\nt1 = n0 * 2.0\nt2 = t0 * 2.0\nt3 = t2 + t1\nt4 = n0 + t3\nt5 = t3 + t4\nt6 = t4 * 3.0\nt7 = t6 - t3\nanswer = t5 + t7\nprint(answer)" + ], + "Output Answer": [ + "720" + ], + "split": "train" + }, + { + "Input": "the average of runs of a cricket player of 10 innings was 35 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?", + "Output Program": [ + "n0 = 10.0\nn1 = 35.0\nn2 = 4.0\nt0 = n0 + 1.0\nt1 = n1 + n2\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "79" + ], + "split": "train" + }, + { + "Input": "on dividing 161 by a number , the quotient is 10 and the remainder is 1 . find the divisor .", + "Output Program": [ + "import math\nn0 = 161.0\nn1 = 10.0\nn2 = 1.0\nt0 = n0 / n1\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "the average of 11 numbers is 10.7 . if the average of first 6 is 10.5 and that of the last 6.00001 is 11.4 the sixth number is ?", + "Output Program": [ + "n0 = 11.0\nn1 = 10.7\nn2 = 6.0\nn3 = 10.5\nn4 = 6.00001\nn5 = 11.4\nt0 = n2 * n5\nt1 = n2 * n3\nt2 = n0 * n1\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "13.700000000000017" + ], + "split": "train" + }, + { + "Input": "tom and jerry enter into a partnership by investing $ 700 and $ 300 respectively . at the end of one year , they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business . if tom received $ 800 more than jerry did , what was the profit made by their business in that year ?", + "Output Program": [ + "n0 = 700.0\nn1 = 300.0\nn2 = 800.0\nt0 = n0 + n1\nt1 = 1.0 / 3.0\nt2 = t1 / 2.0\nt3 = 1.0 - t1\nt4 = t3 / t0\nt5 = n0 * t4\nt6 = n1 * t4\nt7 = t2 + t5\nt8 = t2 + t6\nt9 = t7 - t8\nanswer = n2 / t9\nprint(answer)" + ], + "Output Answer": [ + "2999.9999999999995" + ], + "split": "train" + }, + { + "Input": "simplify : 0.72 * 0.43 + 0.12 * 0.34", + "Output Program": [ + "n0 = 0.72\nn1 = 0.43\nn2 = 0.12\nn3 = 0.34\nt0 = n0 * n1\nt1 = n2 * n3\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "0.3504" + ], + "split": "train" + }, + { + "Input": "what sum of money put at c . i amounts in 2 years to rs . 8880 and in 3 years to rs . 9261 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 8880.0\nn2 = 3.0\nn3 = 9261.0\nt0 = n3 / n1\nt1 = t0 - 1.0\nt2 = t1 + 1.0\nt3 = t2**min(n0, 5)\nanswer = n1 / t3\nprint(answer)" + ], + "Output Answer": [ + "8164.378472940381" + ], + "split": "train" + }, + { + "Input": "in a class , 6 students can speak gujarati , 15 can speak hindi and 6 can speak marathi . if two students can speak two languages and one student can speak all the 3 languages , then how many students are there in the class", + "Output Program": [ + "n0 = 6.0\nn1 = 15.0\nn2 = 6.0\nn3 = 3.0\nt0 = n0 + n1\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "find a number such that it exceeds 18 by 3 times the number by which it is less than 86 ?", + "Output Program": [ + "n0 = 18.0\nn1 = 3.0\nn2 = 86.0\nt0 = n1 * n2\nt1 = n0 + t0\nanswer = t1 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "69" + ], + "split": "train" + }, + { + "Input": "for an agricultural experiment , 300 seeds were planted in one plot and 200 were planted in a second plot . if exactly 25 percent of the seeds in the first plot germinated and exactly 40 percent of the seeds in the second plot germinated , what percent of the total number of seeds germinated ?", + "Output Program": [ + "n0 = 300.0\nn1 = 200.0\nn2 = 25.0\nn3 = 40.0\nt0 = n0 + n1\nt1 = n2 / 100.0\nt2 = n3 / 100.0\nt3 = n0 * t1\nt4 = n1 * t2\nt5 = t3 + t4\nt6 = t5 / t0\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "31" + ], + "split": "train" + }, + { + "Input": "in an election , candidate douglas won 66 percent of the total vote in counties x and y . he won 74 percent of the vote in county x . if the ratio of people who voted in county x to county y is 2 : 1 , what percent of the vote did candidate douglas win in county y ?", + "Output Program": [ + "n0 = 66.0\nn1 = 74.0\nn2 = 2.0\nn3 = 1.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = n2 / 3.0\nt3 = n3 / 3.0\nt4 = t1 * t2\nt5 = t0 - t4\nt6 = t5 / t3\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "50.00000000000002" + ], + "split": "train" + }, + { + "Input": "amithab ' s average expenditure for the january to june is rs . 4200 and he spends rs . 1200 in january and rs . 1500 in july . the average expenditure for the months of febraury to july is", + "Output Program": [ + "n0 = 4200.0\nn1 = 1200.0\nn2 = 1500.0\nt0 = 2.0 * 3.0\nt1 = n2 - n1\nt2 = t1 / t0\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "4250" + ], + "split": "train" + }, + { + "Input": "neha ' s mother was 4 times her age 12 years ago . she will be twice as old as neha 12 years from now . what is the present age of neha ' s mother ?", + "Output Program": [ + "n0 = 4.0\nn1 = 12.0\nn2 = 12.0\nt0 = n1 + n1\nt1 = n0 - 2.0\nt2 = t0 * 2.0\nt3 = t2 - t0\nt4 = t3 / t1\nt5 = n0 * t4\nanswer = n1 + t5\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "a student multiplied a number by 3 / 5 instead of 5 / 3 , what is the percentage error in the calculation ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 5.0\nn3 = 3.0\nt0 = n1 / n0\nt1 = n0 / n1\nt2 = t0 - t1\nt3 = t2 / t0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "64.00000000000001" + ], + "split": "train" + }, + { + "Input": "a team of 6 entered for a shooting competition . the best marks man scored 85 points . if he had scored 92 points , the average scores for . the team would have been 84 . how many points altogether did the team score ?", + "Output Program": [ + "n0 = 6.0\nn1 = 85.0\nn2 = 92.0\nn3 = 84.0\nt0 = n0 * n3\nt1 = n2 - n1\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "497" + ], + "split": "train" + }, + { + "Input": "if 60 percent of 500 is 50 percent of x , then x = ?", + "Output Program": [ + "n0 = 60.0\nn1 = 500.0\nn2 = 50.0\nt0 = n0 * n1\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "600" + ], + "split": "train" + }, + { + "Input": "if x = 1 - 3 t and y = 2 t - 3 , then for what value of t does x = y ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 2.0\nn3 = 3.0\nt0 = n0 + n3\nt1 = n1 + n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.8" + ], + "split": "train" + }, + { + "Input": "a person was asked to state his age in years . his reply was , ` ` take my age 5 years hence , multiply it by 3 and subtract 3 times my age 5 years ago and you will know how old i am . ' ' what was the age of the person ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nn2 = 3.0\nn3 = 5.0\nt0 = n0 * n1\nanswer = t0 + t0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "the mean of 50 observations was 40 . it was found later that an observation 45 was wrongly taken as 15 the corrected new mean is", + "Output Program": [ + "n0 = 50.0\nn1 = 40.0\nn2 = 45.0\nn3 = 15.0\nt0 = n0 * n1\nt1 = n0 - 2.0\nt2 = t1 - n3\nt3 = t0 + t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "40.66" + ], + "split": "train" + }, + { + "Input": "caleb spends $ 70.50 on 50 hamburgers for the marching band . if single burgers cost $ 1.00 each and double burgers cost $ 1.50 each , how many double burgers did he buy ?", + "Output Program": [ + "n0 = 70.5\nn1 = 50.0\nn2 = 1.0\nn3 = 1.5\nt0 = n0 - n1\nt1 = n3 - n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "41" + ], + "split": "train" + }, + { + "Input": "you and your friend spent a total of $ 19 for lunch . your friend spent $ 3 more than you . how much did your friend spend on their lunch ?", + "Output Program": [ + "n0 = 19.0\nn1 = 3.0\nt0 = n0 - n1\nt1 = t0 / 2.0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "the average age of 3 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men . the average age of the two new men is", + "Output Program": [ + "n0 = 3.0\nn1 = 21.0\nn2 = 23.0\nt0 = n1 + n2\nt1 = n0 * 1.0\nt2 = t0 / 2.0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "last year , for every 100 million vehicles that traveled on a certain highway , 75 vehicles were involved in accidents . if 6 billion vehicles traveled on the highway last year , how many of those vehicles were involved in accidents ? ( 1 billion = 1,000 , 000,000 )", + "Output Program": [ + "n0 = 100.0\nn1 = 75.0\nn2 = 6.0\nn3 = 1.0\nn4 = 1000.0\nn5 = 0.0\nt0 = n2 * 10.0\nanswer = n1 * t0\nprint(answer)" + ], + "Output Answer": [ + "4500" + ], + "split": "train" + }, + { + "Input": "if x is an integer such that 1 < x < 9 , 2 < x < 15 , 7 > x > \u2013 1 , 4 > x > 0 , and x + 1 < 5 , then x is", + "Output Program": [ + "n0 = 1.0\nn1 = 9.0\nn2 = 2.0\nn3 = 15.0\nn4 = 7.0\nn5 = 1.0\nn6 = 4.0\nn7 = 0.0\nn8 = 1.0\nn9 = 5.0\nt0 = n9 - n8\nanswer = t0 - n8\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "the average of marks obtained by 120 candidates was 35 . if the avg of marks of passed candidates was 39 & that of failed candidates was 39 and that of failed candidates was 15 , the no . of candidateswho passed the examination is ?", + "Output Program": [ + "n0 = 120.0\nn1 = 35.0\nn2 = 39.0\nn3 = 39.0\nn4 = 15.0\nt0 = n0 * n1\nt1 = n0 * n4\nt2 = n2 - n4\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 8 eggs . if the cost of each pound of rice is $ 0.33 , then how many f cents does a liter of kerosene cost ? [ one dollar has 100 cents . ]", + "Output Program": [ + "n0 = 8.0\nn1 = 0.33\nn2 = 100.0\nt0 = 1.0 / 2.0\nt1 = n1 * n2\nt2 = n0 / t0\nt3 = t2 / 12.0\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "44" + ], + "split": "train" + }, + { + "Input": "paulson spends 75 % of his income . his income is increased by 20 % and he increased his expenditure by 10 % . find the percentage increase in his savings", + "Output Program": [ + "n0 = 75.0\nn1 = 20.0\nn2 = 10.0\nt0 = n1 / 100.0\nt1 = n2 / 100.0\nt2 = n0 / 100.0\nt3 = t0 + 1.0\nt4 = t1 + 1.0\nt5 = 1.0 - t2\nt6 = t4 * t2\nt7 = t3 - t6\nt8 = t7 - t5\nt9 = t8 / t5\nanswer = t9 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "49.99999999999996" + ], + "split": "train" + }, + { + "Input": "the average weight of 5 students decreases by 12 kg when one of them weighing 72 kg is replaced by a new student . the weight of the student is", + "Output Program": [ + "n0 = 5.0\nn1 = 12.0\nn2 = 72.0\nt0 = n0 * n1\nanswer = n2 - t0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "find the least multiple of 23 , which when divided by 1821 and 24 leaves remainders 710 and 13 respectively .", + "Output Program": [ + "n0 = 23.0\nn1 = 1821.0\nn2 = 24.0\nn3 = 710.0\nn4 = 13.0\nt0 = 4.0 + 4.0\nt1 = n2 * 10.0\nt2 = n4 - 10.0\nt3 = t1 + t1\nt4 = t2 + 3.0\nt5 = t0 * 3.0\nt6 = t3 + t5\nanswer = t6 * t4\nprint(answer)" + ], + "Output Answer": [ + "3024" + ], + "split": "train" + }, + { + "Input": "{ - 10 , - 6 , - 5 , - 4 , - 2.5 , - 1 , 0 , 2.5 , 4 , 6 , 7 , 10 } a number is to be selected at random from the set above . what is the probability that the number selected will be a solution of the equation ( x - 5 ) ( x + 10 ) ( 2 x - 5 ) = 0 ?", + "Output Program": [ + "n0 = 10.0\nn1 = 6.0\nn2 = 5.0\nn3 = 4.0\nn4 = 2.5\nn5 = 1.0\nn6 = 0.0\nn7 = 2.5\nn8 = 4.0\nn9 = 6.0\nn10 = 7.0\nn11 = 10.0\nn12 = 5.0\nn13 = 10.0\nn14 = 2.0\nn15 = 5.0\nn16 = 0.0\nt0 = n1 * n14\nanswer = n14 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.16666666666666666" + ], + "split": "train" + }, + { + "Input": "when processing flower - nectar into honey bees ' extract , a considerable amount of water gets reduced . how much flower - nectar must be processed to yield 1 kg of honey , if nectar contains 50 % water , and the honey obtained from this nectar contains 40 % water ?", + "Output Program": [ + "n0 = 1.0\nn1 = 50.0\nn2 = 40.0\nt0 = n1 / 100.0\nt1 = 100.0 - n2\nt2 = t1 / 100.0\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "1.2" + ], + "split": "train" + }, + { + "Input": "in the x - y plane , there are 4 points ( 0,0 ) , ( 0,4 ) , ( 5,4 ) , and ( 5,0 ) . if these 4 points makes a rectangle , what is the probability that x + y < 4 ?", + "Output Program": [ + "n0 = 4.0\nn1 = 0.0\nn2 = 0.0\nn3 = 0.0\nn4 = 4.0\nn5 = 5.0\nn6 = 4.0\nn7 = 5.0\nn8 = 0.0\nn9 = 4.0\nn10 = 4.0\nt0 = 1.0 + 4.0\nt1 = n0 * n0\nt2 = t1 / 2.0\nt3 = n0 * t0\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.4" + ], + "split": "train" + }, + { + "Input": "we define that k @ j is the product of j number from k in increasing order for positive integers k , j . for example , 6 @ 4 = 6 * 7 * 8 * 9 . if a = 2020 and b = 2120 , what is the value q of the ratio a / b ?", + "Output Program": [ + "n0 = 6.0\nn1 = 4.0\nn2 = 6.0\nn3 = 7.0\nn4 = 8.0\nn5 = 9.0\nn6 = 2020.0\nn7 = 2120.0\nt0 = n6 / n6\nt1 = t0 + t0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "3 numbers are in the ratio of 2 : 3 : 4 . if the sum of the squares of the extremes is 180 , then the middle number is :", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 2.0\nn2 = 3.0\nn3 = 4.0\nn4 = 180.0\nt0 = n1**min(2.0, 5)\nt1 = n3**min(2.0, 5)\nt2 = t0 + t1\nt3 = n4 / t2\nt4 = math.sqrt(max(0, t3))\nanswer = n0 * t4\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "if xy denotes x is raised to the power y , find the last two digits of 19413846 + 19614181", + "Output Program": [ + "import math\nn0 = 19413846.0\nn1 = 19614181.0\nt0 = 100.0**min(2.0, 5)\nt1 = n0 / t0\nt2 = n1 % t0\nt3 = math.floor(t1)\nt4 = t2 % 100.0\nt5 = t3 % 100.0\nt6 = t4 - 10.0\nt7 = t6 - 10.0\nt8 = t5 + t7\nt9 = t8 - 10.0\nanswer = t9 - 10.0\nprint(answer)" + ], + "Output Answer": [ + "82" + ], + "split": "train" + }, + { + "Input": "all the milk in container a which was filled to its brim was poured into two containers b and c . the quantity of milk in container b was 62.5 % less than the capacity of container a . if 156 liters was now transferred from c to b , then both the containers would have equal quantities of milk . what was the initial quantity of milk in container a ?", + "Output Program": [ + "n0 = 62.5\nn1 = 156.0\nt0 = n0 / 100.0\nt1 = 1 / 2.0\nt2 = 1.0 - t0\nt3 = t1 - t2\nanswer = n1 / t3\nprint(answer)" + ], + "Output Answer": [ + "1248" + ], + "split": "train" + }, + { + "Input": "of 67 players on a cricket team , 37 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?", + "Output Program": [ + "n0 = 67.0\nn1 = 37.0\nt0 = 1.0 / 3.0\nt1 = n0 - n1\nt2 = 1.0 - t0\nt3 = t2 * t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "57" + ], + "split": "train" + }, + { + "Input": "a grocery shop has a sale of rs . 6635 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ?", + "Output Program": [ + "n0 = 6635.0\nn1 = 6927.0\nn2 = 6855.0\nn3 = 7230.0\nn4 = 6562.0\nn5 = 5.0\nn6 = 6500.0\nt0 = n5 + 1.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n6 * t0\nt4 = n3 + t2\nt5 = n4 + t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "4791" + ], + "split": "train" + }, + { + "Input": "in a certain country 1 / 3 of 4 = 8 . assuming the same proportion , what would be the value of 1 / 8 of 4 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 4.0\nn3 = 8.0\nn4 = 1.0\nn5 = 8.0\nn6 = 4.0\nt0 = n1 / n2\nanswer = n6 * t0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "a number x is 8 times another number y . the percentage that y is less than x is", + "Output Program": [ + "n0 = 8.0\nt0 = n0 - 1.0\nt1 = t0 / n0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "87.5" + ], + "split": "train" + }, + { + "Input": "amithab ' s average expenditure for the january to june is rs . 4200 and he spends rs . 1200 in january and rs . 1500 in july . the average expenditure for the months of febraury to july is :", + "Output Program": [ + "n0 = 4200.0\nn1 = 1200.0\nn2 = 1500.0\nt0 = 2.0 * 3.0\nt1 = n2 - n1\nt2 = t1 / t0\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "4250" + ], + "split": "train" + }, + { + "Input": "when f is divided by 5 , the remainder is 3 . when y is divided by 5 , the remainder is 4 . what is the remainder when f + y is divided by 5 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nn2 = 5.0\nn3 = 4.0\nn4 = 5.0\nt0 = n1 + n3\nanswer = t0 % n0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is :", + "Output Program": [ + "n0 = 8000.0\nn1 = 7.0\nn2 = 12000.0\nn3 = 6000.0\nt0 = n2 - n0\nt1 = n0 - n3\nt2 = n1 * t0\nt3 = t2 / t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "the present age of a father is 3 years more than 3 times the age of his son . 3 years hence , father \u2019 s age will be 10 years more than twice athe age of the son . find the present age of the father .", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 3.0\nn3 = 10.0\nt0 = n0 * n3\nanswer = n0 + t0\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "the total age of a and b is 13 years more than the total age of b and c . c is how many year younger than a", + "Output Program": [ + "n0 = 13.0\n\nanswer = n0 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "a , b and c rent a pasture . if a puts 10 oxen for 7 months , b puts 12 oxen for 5 months and c puts 15 oxen for 3 months for grazing and the rent of the pasture is rs . 175 , then how much amount should c pay as his share of rent ?", + "Output Program": [ + "n0 = 10.0\nn1 = 7.0\nn2 = 12.0\nn3 = 5.0\nn4 = 15.0\nn5 = 3.0\nn6 = 175.0\nt0 = n4 * n5\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nt4 = t3 + t0\nt5 = t0 / t4\nanswer = n6 * t5\nprint(answer)" + ], + "Output Answer": [ + "44.99999999999999" + ], + "split": "train" + }, + { + "Input": "96 % of the population of a village is 23040 . the total population of the village is ?", + "Output Program": [ + "n0 = 96.0\nn1 = 23040.0\nt0 = 100.0 / n0\nanswer = n1 * t0\nprint(answer)" + ], + "Output Answer": [ + "24000" + ], + "split": "train" + }, + { + "Input": "the average monthly salary of 20 employees in an organisation is rs . 1200 . if the manager ' s salary is added , then the average salary increases by rs . 100 . what is the manager ' s monthly salary ?", + "Output Program": [ + "n0 = 20.0\nn1 = 1200.0\nn2 = 100.0\nt0 = n1 + n2\nt1 = n0 + 1.0\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "3300" + ], + "split": "train" + }, + { + "Input": "there are 408 boys and 288 girls in a school which are to be divided into equal sections of either boys or girls alone . find the total number of sections thus formed .", + "Output Program": [ + "n0 = 408.0\nn1 = 288.0\nt0 = n0 + n1\nt1 = 2.0 * 2.0\nt2 = t1 * 2.0\nt3 = t2 * 3.0\nanswer = t0 / t3\nprint(answer)" + ], + "Output Answer": [ + "29" + ], + "split": "train" + }, + { + "Input": "if a no . when divided by 44 , gives 432 as quotient and 0 as remainder . what will be the remainder when dividing the same no . by 35", + "Output Program": [ + "n0 = 44.0\nn1 = 432.0\nn2 = 0.0\nn3 = 35.0\nt0 = n0 * n1\nanswer = t0 % n3\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "a car travels first 160 km at 70 km / hr and the next 160 km at 80 km / hr . what is the average speed for the first 320 km of the tour ?", + "Output Program": [ + "n0 = 160.0\nn1 = 70.0\nn2 = 160.0\nn3 = 80.0\nn4 = 320.0\nt0 = n0 / n1\nt1 = n0 / n3\nt2 = t0 + t1\nt3 = 1.0 / t2\nanswer = n4 * t3\nprint(answer)" + ], + "Output Answer": [ + "74.66666666666667" + ], + "split": "train" + }, + { + "Input": "joe \u2019 s average ( arithmetic mean ) test score across 4 equally weighted tests was 90 . he was allowed to drop his lowest score . after doing so , his average test score improved to 95 . what is the lowest test score that was dropped ?", + "Output Program": [ + "n0 = 4.0\nn1 = 90.0\nn2 = 95.0\nt0 = n0 * n1\nt1 = n2 * 3.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "john found that the average of 15 numbers is 40 . if 15 is added to each number then the mean of number is ?", + "Output Program": [ + "n0 = 15.0\nn1 = 40.0\nn2 = 15.0\n\nanswer = n1 + n2\nprint(answer)" + ], + "Output Answer": [ + "55" + ], + "split": "train" + }, + { + "Input": "scott ' s average ( arithmetic mean ) golf score on his first 4 rounds was 78 . what score does he need on his fifth round to drop his average score by 2 points ?", + "Output Program": [ + "n0 = 4.0\nn1 = 78.0\nn2 = 2.0\nt0 = n0 + 1.0\nt1 = n0 * n1\nt2 = n1 - n2\nt3 = t0 * t2\nanswer = t3 - t1\nprint(answer)" + ], + "Output Answer": [ + "68" + ], + "split": "train" + }, + { + "Input": "a , b and c have rs . 600 between them , a and c together have rs . 250 and b and c rs . 450 . how much does c have ?", + "Output Program": [ + "n0 = 600.0\nn1 = 250.0\nn2 = 450.0\nt0 = n1 + n2\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "an equal number of desks and bookcases are to be placed along a library wall that is 15 meters long . each desk is 2 meters long , and each bookshelf is 1.5 meters long . if the maximum possible number of desks and bookcases are to be placed along the wall , then the space along the wall that is left over will be how many meters k long ?", + "Output Program": [ + "n0 = 15.0\nn1 = 2.0\nn2 = 1.5\nt0 = n1 * 4.0\nt1 = n2 * 4.0\nt2 = t0 + t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "how many kg of pure salt must be added to 100 kg of 10 % solution of salt and water to increase it to a 25 % solution ?", + "Output Program": [ + "n0 = 100.0\nn1 = 10.0\nn2 = 25.0\nt0 = n2 / n0\nt1 = n2 - n1\nt2 = 1.0 - t0\nanswer = t1 / t2\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "in arun ' s company 60 % of the employees earn less than $ 50000 a year , 60 % of the employees earn more than $ 40000 a year , 11 % of the employees earn $ 43000 a year and 5 % of the employees earn $ 49000 a year . what is the median salary for the company ?", + "Output Program": [ + "n0 = 60.0\nn1 = 50000.0\nn2 = 60.0\nn3 = 40000.0\nn4 = 11.0\nn5 = 43000.0\nn6 = 5.0\nn7 = 49000.0\nt0 = n5 * 2.0\nt1 = t0 / 2.0\nt2 = t1 / 100.0\nanswer = t2 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "43" + ], + "split": "train" + }, + { + "Input": "the number of the members of a club is more than 20 and less than 50 . when 5 people sit at a table , other people exactly divided to 6 - people groups ( 6 people sit at a table ) or 7 - people groups ( 7 people sit at a table ) . if the members are divided to 8 - people groups , how many people will be left ?", + "Output Program": [ + "import scipy\nn0 = 20.0\nn1 = 50.0\nn2 = 5.0\nn3 = 6.0\nn4 = 6.0\nn5 = 7.0\nn6 = 7.0\nn7 = 8.0\nt0 = scipy.lcm(int(n3), int(n5))\nt1 = n2 + t0\nanswer = t1 % n7\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "at the store opening , larry ' s grocery had 50 lemons and 60 oranges . by closing , the store at 20 lemons and 40 oranges left . by approximately what percent did the ratio of lemons to orange decrease from opening to closing .", + "Output Program": [ + "n0 = 50.0\nn1 = 60.0\nn2 = 20.0\nn3 = 40.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = t0 - t1\nt3 = t2 / t0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "if x is a positive integer with fewer than 3 digits , what is the probability that z x * ( x + 1 ) is a multiple of either 4 or 5 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 4.0\nn3 = 5.0\nt0 = 100.0 / n2\nt1 = 100.0 / n3\nt2 = 100.0 - n1\nt3 = t0 * 2.0\nt4 = t1 * 2.0\nt5 = t3 + t4\nt6 = t5 - n2\nanswer = t6 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.8686868686868687" + ], + "split": "train" + }, + { + "Input": "the cash realised on selling a 14 % stock is rs . 108.25 , brokerage being 1 / 4 % is", + "Output Program": [ + "n0 = 14.0\nn1 = 108.25\nn2 = 1.0\nn3 = 4.0\nt0 = n2 / n3\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "108" + ], + "split": "train" + }, + { + "Input": "if y is 40 % greater than x , than x is what % less than y ?", + "Output Program": [ + "n0 = 40.0\nt0 = n0 + 100.0\nt1 = n0 / t0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "28.57142857142857" + ], + "split": "train" + }, + { + "Input": "a luxury liner , queen marry ii , is transporting several cats as well as the crew ( sailors , a cook , and one - legged captain ) to a nearby port . altogether , these passengers have 16 heads and 41 legs . how many cats does the ship host ?", + "Output Program": [ + "n0 = 16.0\nn1 = 41.0\nt0 = n1 - 1.0\nt1 = n0 - 1.0\nt2 = t1 * 2.0\nt3 = t1 * 4.0\nt4 = t0 - t2\nt5 = t3 - t2\nt6 = t4 / t5\nanswer = t6 * t1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "two brothers ram and ravi appeared for an exam . the probability of selection of ram is 1 / 7 and that of ravi is 1 / 5 . find the probability that both of them are selected .", + "Output Program": [ + "n0 = 1.0\nn1 = 7.0\nn2 = 1.0\nn3 = 5.0\nt0 = n0 / n1\nt1 = n2 / n3\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "0.02857142857142857" + ], + "split": "train" + }, + { + "Input": "when 242 is divided by a certain divisor the remainder obtained is 6 . when 698 is divided by the same divisor the remainder obtained is 13 . however , when the sum of the two numbers 242 and 698 is divided by the divisor , the remainder obtained is 5 . what is the value of the divisor ?", + "Output Program": [ + "n0 = 242.0\nn1 = 6.0\nn2 = 698.0\nn3 = 13.0\nn4 = 242.0\nn5 = 698.0\nn6 = 5.0\nt0 = n1 + n3\nanswer = t0 - n6\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "in a river flowing at 2 km / hr , a boat travels 56 km upstream and then returns downstream to the starting point . if its speed in still water be 6 km / hr , find the total journey time .", + "Output Program": [ + "n0 = 2.0\nn1 = 56.0\nn2 = 6.0\nt0 = n0 + n2\nt1 = n2 - n0\nt2 = n1 / t1\nt3 = n1 / t0\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "what is the least number that should be added to 1055 , so the sum of the number is divisible by 23 ?", + "Output Program": [ + "import math\nn0 = 1055.0\nn1 = 23.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = t1 + 1.0\nt3 = t2 - t0\nanswer = n1 * t3\nprint(answer)" + ], + "Output Answer": [ + "2.999999999999993" + ], + "split": "train" + }, + { + "Input": "a man has rs . 400 in the denominations of one - rupee notes , 5 - rupee notes and 10 rupee notes . the number of notes of each denomination is equal . what is the total number of notes that he has ?", + "Output Program": [ + "n0 = 400.0\nn1 = 5.0\nn2 = 10.0\nt0 = n1 + 1.0\nt1 = n2 + t0\nt2 = n0 / t1\nanswer = t2 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "3 / 4 of 1 / 2 of 2 / 5 of 5000 = ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 1.0\nn3 = 2.0\nn4 = 2.0\nn5 = 5.0\nn6 = 5000.0\nt0 = n3 / n5\nt1 = n0 / n1\nt2 = n2 / n3\nt3 = t1 * t2\nt4 = t0 * t3\nanswer = n6 * t4\nprint(answer)" + ], + "Output Answer": [ + "750.0000000000001" + ], + "split": "train" + }, + { + "Input": "in a sample of associates at a law firm , 25 percent are second - year associates , and 75 percent are not first - year associates . what percentage of the associates at the law firm have been there for more than two years ?", + "Output Program": [ + "n0 = 25.0\nn1 = 75.0\n\nanswer = n1 - n0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "if ( 2 to the x ) - ( 2 to the ( x - 2 ) ) = 3 ( 2 to the 10 ) , what is the value of x ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 2.0\nn3 = 3.0\nn4 = 2.0\nn5 = 10.0\n\nanswer = n0 + n5\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "if a / b = 5 / 4 , then ( 4 a + 3 b ) / ( 4 a - 3 b ) = ?", + "Output Program": [ + "n0 = 5.0\nn1 = 4.0\nn2 = 4.0\nn3 = 3.0\nn4 = 4.0\nn5 = 3.0\nt0 = n0 * n1\nt1 = n1 * n3\nt2 = t0 + t1\nt3 = t0 - t1\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "total 63 matches are conducted in knockout match type . how many players will be participated in that tournament ?", + "Output Program": [ + "n0 = 63.0\n\nanswer = n0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "train" + }, + { + "Input": "if f ( f ( n ) ) + f ( n ) = 2 n + 3 , f ( 0 ) = 1 then f ( 2012 ) = ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 0.0\nn3 = 1.0\nn4 = 2012.0\n\nanswer = n3 + n4\nprint(answer)" + ], + "Output Answer": [ + "2013" + ], + "split": "train" + }, + { + "Input": "if 102 x = 25 , then 10 - x equals :", + "Output Program": [ + "n0 = 102.0\nn1 = 25.0\nn2 = 10.0\nt0 = n0 * 100.0\nt1 = t0 / 2.0\nt2 = t1 + 2.0\nt3 = t1 - 2.0\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.9992159937279498" + ], + "split": "train" + }, + { + "Input": "it takes 30 days to fill a laboratory dish with bacteria . if the size of the bacteria doubles each day , how long did it take for the bacteria to fill 1 / 32 of the dish ?", + "Output Program": [ + "import math\nn0 = 30.0\nn1 = 1.0\nn2 = 32.0\nt0 = math.log(max(1e-5, n2), 2)\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "rahim bought 32 books for rs . 1500 from one shop and 60 books for rs . 340 from another . what is the average price he paid per book ?", + "Output Program": [ + "n0 = 32.0\nn1 = 1500.0\nn2 = 60.0\nn3 = 340.0\nt0 = n1 + n3\nt1 = n0 + n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "sandy bought 65 books for $ 1480 from one shop and 55 books for $ 920 from another shop . what is the average price that sandy paid per book ?", + "Output Program": [ + "n0 = 65.0\nn1 = 1480.0\nn2 = 55.0\nn3 = 920.0\nt0 = n1 + n3\nt1 = n0 + n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "calculate 1307 x 1307 = ?", + "Output Program": [ + "n0 = 1307.0\nn1 = 1307.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "1708249" + ], + "split": "train" + }, + { + "Input": "the hcf and lcm of two numbers m and n are respectively 6 and 210 . if m + n = 80 , then 1 / m + 1 / n is equal to", + "Output Program": [ + "n0 = 6.0\nn1 = 210.0\nn2 = 80.0\nn3 = 1.0\nn4 = 1.0\nt0 = n0 * n1\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.06349206349206349" + ], + "split": "train" + }, + { + "Input": "if 3 a = 4 b and ab \u2260 0 , what is the ratio of a / 4 to b / 3 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 0.0\nn3 = 4.0\nn4 = 3.0\nt0 = n0 * n1\nanswer = t0 / t0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "what is the smallest integer x such that 2 x + 2 is divisible by 33 , 44 , 55 , and 666 ?", + "Output Program": [ + "import scipy\nn0 = 2.0\nn1 = 2.0\nn2 = 33.0\nn3 = 44.0\nn4 = 55.0\nn5 = 666.0\nt0 = scipy.lcm(int(n2), int(n3))\nt1 = scipy.lcm(int(n4), int(t0))\nt2 = scipy.lcm(int(n5), int(t1))\nt3 = t2 - n0\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "36629" + ], + "split": "train" + }, + { + "Input": "there are 6 chess amateurs playing in villa ' s chess club tournament . if each chess amateur plays with exactly 15 other amateurs , what is the total number of chess games possible to be played in the tournament ?", + "Output Program": [ + "n0 = 6.0\nn1 = 15.0\nt0 = n0 * n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "tough and tricky questions : probability . medical analysts predict that a quarter of all people who are infected by a certain biological agent could be expected to be killed for each day that passes during which they have not received an antidote . what fraction of a group of 1000 people could be expected to be killed if infected and not treated for 3 full days ?", + "Output Program": [ + "n0 = 1000.0\nn1 = 3.0\nt0 = n1 + 1.0\nt1 = 1.0 / t0\nt2 = 1.0 - t1\nt3 = t1 * t2\nt4 = t1 + t3\nt5 = 1.0 - t4\nt6 = t1 * t5\nanswer = t4 + t6\nprint(answer)" + ], + "Output Answer": [ + "0.578125" + ], + "split": "train" + }, + { + "Input": "if the sales tax reduced from 3 1 / 2 % to 3 1 / 3 % , then what difference does it make to a person who purchases an article with market price of rs . 10800 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 2.0\nn3 = 3.0\nn4 = 1.0\nn5 = 3.0\nn6 = 10800.0\nt0 = n1 / n2\nt1 = n1 / n0\nt2 = n0 + t0\nt3 = n0 + t1\nt4 = t2 - t3\nt5 = n6 * t4\nanswer = t5 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "17.999999999999986" + ], + "split": "train" + }, + { + "Input": "find the number , difference between number and its 3 / 5 is 50 .", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 50.0\nt0 = n2 / 2.0\nanswer = n1 * t0\nprint(answer)" + ], + "Output Answer": [ + "125" + ], + "split": "train" + }, + { + "Input": "in a coconut grove , ( x + 3 ) trees yield 60 nuts per year , x trees yield 120 nuts per year and ( x \u2013 3 ) trees yield 180 nuts per year . if the average yield per year per tree be 100 , find x .", + "Output Program": [ + "n0 = 3.0\nn1 = 60.0\nn2 = 120.0\nn3 = 3.0\nn4 = 180.0\nn5 = 100.0\nt0 = n1 + n2\nt1 = n0 * n4\nt2 = n0 * n1\nt3 = n5 * 3.0\nt4 = n4 + t0\nt5 = t1 - t2\nt6 = t4 - t3\nanswer = t5 / t6\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "find the average of all prime numbers between 4 and 15 .", + "Output Program": [ + "n0 = 4.0\nn1 = 15.0\nt0 = n0 + 1.0\nt1 = n1 - n0\nt2 = n1 - 2.0\nt3 = t0 + 2.0\nt4 = t1 + t2\nt5 = t0 + t3\nt6 = t5 + t4\nanswer = t6 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "what sum of money put at c . i amounts in 2 years to rs . 8800 and in 3 years to rs . 9261 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 8800.0\nn2 = 3.0\nn3 = 9261.0\nt0 = n3 / n1\nt1 = t0 - 1.0\nt2 = t1 + 1.0\nt3 = t2**min(n0, 5)\nanswer = n1 / t3\nprint(answer)" + ], + "Output Answer": [ + "7945.70154338681" + ], + "split": "train" + }, + { + "Input": "find the value of x . ( 47 % of 1442 - 36 % of 1412 ) + 63 = x ?", + "Output Program": [ + "import math\nn0 = 47.0\nn1 = 1442.0\nn2 = 36.0\nn3 = 1412.0\nn4 = 63.0\nt0 = n0 / 100.0\nt1 = n2 / 100.0\nt2 = n1 * t0\nt3 = n3 * t1\nt4 = t2 - t3\nt5 = n4 + t4\nt6 = t5 % 10.0\nt7 = t6 + 1.0\nanswer = math.floor(t7)\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "if henry were to add 4 gallons of water to a tank that is already 3 / 4 full of water , the tank would be 7 / 8 full . how many gallons of water would the tank hold if it were full ?", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 4.0\nn3 = 7.0\nn4 = 8.0\nt0 = n3 / n4\nt1 = n1 / n2\nt2 = t0 - t1\nt3 = 1.0 / t2\nanswer = n0 * t3\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 146 , what is the difference between the ages of patrick and monica ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 3.0\nn3 = 5.0\nn4 = 146.0\nt0 = n0 * n0\nt1 = n1 * n0\nt2 = n1 * n3\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n4 / t4\nt6 = t5 * t2\nt7 = t5 * t0\nanswer = t6 - t7\nprint(answer)" + ], + "Output Answer": [ + "47.673469387755105" + ], + "split": "train" + }, + { + "Input": "mark bought a set of 6 flower pots of different sizes at a total cost of $ 8.25 . each pot cost 0.3 more than the next one below it in size . what was the cost , in dollars , of the largest pot ?", + "Output Program": [ + "n0 = 6.0\nn1 = 8.25\nn2 = 0.3\nt0 = n0 - 1.0\nt1 = n0 * t0\nt2 = n2 * t0\nt3 = t1 / 2.0\nt4 = n2 * t3\nt5 = n1 - t4\nt6 = t5 / n0\nanswer = t6 + t2\nprint(answer)" + ], + "Output Answer": [ + "2.125" + ], + "split": "train" + }, + { + "Input": "a trained covered x km at 65 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 3 x km .", + "Output Program": [ + "n0 = 65.0\nn1 = 2.0\nn2 = 20.0\nn3 = 3.0\nt0 = n0 / n0\nt1 = n0 * n3\nt2 = n0 * n1\nt3 = t2 / n2\nt4 = t0 + t3\nanswer = t1 / t4\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "the value of ( ( x \u2013 y ) \u00b3 + ( y - z ) \u00b3 + ( z \u2013 x ) \u00b3 ) / ( 15 ( x \u2013 y ) ( y \u2013 z ) ( z \u2013 x ) ) is equal to :", + "Output Program": [ + "n0 = 15.0\n\nanswer = 3.0 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.2" + ], + "split": "train" + }, + { + "Input": "a is the product of each integer from 1 to 50 , inclusive and b = 100 ^ k , where k is an integer . what is the greatest value of k for which y is a factor of a ?", + "Output Program": [ + "n0 = 1.0\nn1 = 50.0\nn2 = 100.0\nt0 = 10.0 / 2.0\nt1 = n1 / t0\nt2 = t1 + 2.0\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "an art gallery has only paintings and sculptures . currently , 1 / 3 of the pieces of art are displayed , and 1 / 6 of the pieces on display are sculptures . if 1 / 3 of the pieces not on display are paintings , and 1400 sculptures are not on display , how many pieces of art does the gallery have ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 6.0\nn4 = 1.0\nn5 = 3.0\nn6 = 1400.0\nt0 = n0 / n1\nt1 = n0 - t0\nt2 = n6 / t1\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "3149.999999999999" + ], + "split": "train" + }, + { + "Input": "the grade point average of one third of the classroom is 60 ; the grade point average of the rest is 66 . what is the grade point average of the whole class ?", + "Output Program": [ + "n0 = 60.0\nn1 = 66.0\nt0 = n0 / 3.0\nt1 = n1 / 3.0\nt2 = t1 * 2.0\nanswer = t0 + t2\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "train" + }, + { + "Input": "if the digits 33 in the decimal 0.00033 repeat indefinitely , what is the value of ( 10 ^ 5 - 10 ^ 3 ) ( 0.00033 ) ?", + "Output Program": [ + "n0 = 33.0\nn1 = 0.00033\nn2 = 10.0\nn3 = 5.0\nn4 = 10.0\nn5 = 3.0\nn6 = 0.00033\nt0 = n2 * n2\nt1 = t0 - 1.0\nt2 = n0 / t1\nt3 = t0 * t1\nt4 = t2 * t3\nt5 = t4 / 1000.0\nanswer = n2 * t5\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "sum of two numbers is 10 . two times of the first exceeds by 5 from the 3 times of the other . then the numbers will be ?", + "Output Program": [ + "n0 = 10.0\nn1 = 5.0\nn2 = 3.0\nt0 = n2 + 2.0\nt1 = n0 * n2\nt2 = n1 + t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "in how many no . between 10 and 30 exactly two of the digits is 3 ?", + "Output Program": [ + "n0 = 10.0\nn1 = 30.0\nn2 = 3.0\nt0 = n1 / n0\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "( 208 % of 1265 ) \u00f7 6 = ?", + "Output Program": [ + "n0 = 208.0\nn1 = 1265.0\nn2 = 6.0\nt0 = n0 / 100.0\nt1 = n1 * t0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "438.53333333333336" + ], + "split": "train" + }, + { + "Input": "the average score of a cricketer in 2 matches is 40 and in other 3 matches is 10 . then find the average score in all the 5 matches ?", + "Output Program": [ + "n0 = 2.0\nn1 = 40.0\nn2 = 3.0\nn3 = 10.0\nn4 = 5.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = t0 + t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "which number need to add to 8679921 to get a number exactly divisible by 330 ?", + "Output Program": [ + "import math\nn0 = 8679921.0\nn1 = 330.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = t1 + 1.0\nt3 = t2 - t0\nanswer = n1 * t3\nprint(answer)" + ], + "Output Answer": [ + "69.00000000008731" + ], + "split": "train" + }, + { + "Input": "at a certain college , 60 percent of the total number of students are freshmen . if 40 percent of the fresh - men are enrolled in the school of liberal arts and , of these , 20 percent are psychology majors , what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts ?", + "Output Program": [ + "n0 = 60.0\nn1 = 40.0\nn2 = 20.0\nt0 = n0 * n1\nt1 = t0 / 100.0\nt2 = n2 * t1\nanswer = t2 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "4.8" + ], + "split": "train" + }, + { + "Input": "what is the smallest integer k for which 64 ^ k > 4 ^ 16 ?", + "Output Program": [ + "import math\nn0 = 64.0\nn1 = 4.0\nn2 = 16.0\nt0 = n2 / 3.0\nt1 = math.floor(t0)\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "if t = 5 / 9 * ( k - 32 ) , and if t = 50 , then what is the value of k ?", + "Output Program": [ + "n0 = 5.0\nn1 = 9.0\nn2 = 32.0\nn3 = 50.0\nt0 = n1 * n3\nt1 = t0 / n0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "122" + ], + "split": "train" + }, + { + "Input": "let q represent a set of 7 distinct prime numbers . if the sum of the numbers in q is even and x is a member of q , then what is the least possible value that x can be ?", + "Output Program": [ + "n0 = 7.0\nt0 = n0 / n0\nanswer = t0 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "how many digits are in the number 50 ^ 8 \u00d7 8 ^ 3 \u00d7 11 ^ 2 x 10 ^ 4 ?", + "Output Program": [ + "n0 = 50.0\nn1 = 8.0\nn2 = 8.0\nn3 = 3.0\nn4 = 11.0\nn5 = 2.0\nn6 = 10.0\nn7 = 4.0\nt0 = n5 * n6\nanswer = t0 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "x , y , and z are consecutive numbers and x > y > z . also , 2 x + 3 y + 3 z = 5 y + 11 . what is the value of z ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 3.0\nn3 = 5.0\nn4 = 11.0\nt0 = n0 * 4.0\nt1 = n0 * n1\nt2 = t0 - t1\nt3 = n4 - t2\nanswer = t3 / n1\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "[ ( 3.242 x 10 ) / 100 ] = ?", + "Output Program": [ + "n0 = 3.242\nn1 = 10.0\nn2 = 100.0\nt0 = n0 * n1\nt1 = t0 / n2\nanswer = t1 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "0.032420000000000004" + ], + "split": "train" + }, + { + "Input": "find a positive number , which when increased by 8 is equal to 128 times reciprocal of the number .", + "Output Program": [ + "import math\nn0 = 8.0\nn1 = 128.0\nt0 = n1 * 4.0\nt1 = n0**min(2.0, 5)\nt2 = t0 + t1\nt3 = math.sqrt(max(0, t2))\nt4 = t3 - n0\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "when a person aged 39 is added to a group of n people , the average age increases by 2 . when a person aged 15 is added instead , the average age decreases by 1 . what is the value of r ?", + "Output Program": [ + "n0 = 39.0\nn1 = 2.0\nn2 = 15.0\nn3 = 1.0\nt0 = n1 + n3\nt1 = n0 - n2\nt2 = t1 / t0\nanswer = t2 - n3\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "a number when multiplied by 3 is odd and divisible by 9 . this number when multiplied by 4 is 108 . what is the original number ?", + "Output Program": [ + "n0 = 3.0\nn1 = 9.0\nn2 = 4.0\nn3 = 108.0\n\nanswer = n3 / n2\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "train" + }, + { + "Input": "four numbers are in the ratio 2 : 3 : 4 : 5 add up to give a sum of 1344 . find the biggest number .", + "Output Program": [ + "n0 = 6.0\nn1 = 5.0\nn2 = 2.0\nn3 = 19.0\nt0 = n0 * n1\nt1 = n2 * t0\nt2 = t1 / n2\nanswer = t2 + 3.0\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "find ( 7 x + 4 y ) / ( x - 2 y ) if x / 2 y = 5 / 2 ?", + "Output Program": [ + "n0 = 7.0\nn1 = 4.0\nn2 = 2.0\nn3 = 2.0\nn4 = 5.0\nn5 = 2.0\nt0 = n4 / n2\nt1 = n2 * t0\nt2 = n0 * t1\nt3 = t1 - n2\nt4 = n1 + t2\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "find value of x ( 11 ^ 2 + 12 ^ 2 + 13 ^ 2 + . . . + 20 ^ 2 ) = x", + "Output Program": [ + "n0 = 11.0\nn1 = 2.0\nn2 = 12.0\nn3 = 2.0\nn4 = 13.0\nn5 = 2.0\nn6 = 20.0\nn7 = 2.0\nt0 = n6 + 1.0\nt1 = 1.0 + 10.0\nt2 = n1 * n6\nt3 = 2.0 * 3.0\nt4 = n1 * 10.0\nt5 = t2 + 1.0\nt6 = t4 + 1.0\nt7 = n6 * t0\nt8 = t1 * 10.0\nt9 = t5 * t7\nt10 = t6 * t8\nt11 = t9 / t3\nt12 = t10 / t3\nanswer = t11 - t12\nprint(answer)" + ], + "Output Answer": [ + "2485" + ], + "split": "train" + }, + { + "Input": "in a mixture 60 litres , the ratio of milk and water 2 : 1 . if the this ratio is to be 1 : 2 , then the quanity of water to be further added is", + "Output Program": [ + "n0 = 60.0\nn1 = 2.0\nn2 = 1.0\nn3 = 1.0\nn4 = 2.0\nt0 = n1 + n2\nt1 = n0 / t0\nt2 = n0 - t1\nt3 = n1 * t2\nanswer = t3 - t1\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "rahim bought 65 books for rs . 1160 from one shop and 50 books for rs . 920 from another . what is the average price he paid per book ?", + "Output Program": [ + "n0 = 65.0\nn1 = 1160.0\nn2 = 50.0\nn3 = 920.0\nt0 = n1 + n3\nt1 = n0 + n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "18.08695652173913" + ], + "split": "train" + }, + { + "Input": "if rs . 782 be divided into 3 parts , proportional to 1 / 2 : 1 / 3 : 3 / 4 , then the first part is ?", + "Output Program": [ + "n0 = 782.0\nn1 = 3.0\nn2 = 1.0\nn3 = 2.0\nn4 = 1.0\nn5 = 3.0\nn6 = 3.0\nn7 = 4.0\nt0 = n2 / n3\nt1 = n2 / n1\nt2 = n1 / n7\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = t0 / t4\nanswer = n0 * t5\nprint(answer)" + ], + "Output Answer": [ + "246.94736842105266" + ], + "split": "train" + }, + { + "Input": "in a class of 30 students , 5 students did not borrow any books from the library , 12 students each borrowed 1 book , 8 students each borrowed 2 books , and the rest of the students each borrowed at least 3 books . if the average ( arithmetic mean ) number of books borrowed per student was 2 , what is the maximum number of books that any single student could have borrowed ?", + "Output Program": [ + "n0 = 30.0\nn1 = 5.0\nn2 = 12.0\nn3 = 1.0\nn4 = 8.0\nn5 = 2.0\nn6 = 3.0\nn7 = 2.0\nt0 = n0 * n5\nt1 = n4 * n5\nt2 = n1 * n6\nt3 = n2 + t1\nt4 = t3 + t2\nt5 = t0 - t4\nanswer = n6 + t5\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "if 35 percent of 400 is 20 percent of x , then x =", + "Output Program": [ + "n0 = 35.0\nn1 = 400.0\nn2 = 20.0\nt0 = n0 * n1\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "700" + ], + "split": "train" + }, + { + "Input": "10 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ?", + "Output Program": [ + "n0 = 10.0\nt0 = n0 - 1.0\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "a certain car uses one gallon of gasoline every 36 miles when it travels on highway , and one gallon of gasoline every 20 miles when it travels in the city . when a car travels 4 miles on highway and 4 additional miles in the city , it uses what percent more gasoline than if it travels 8 miles on the highway ?", + "Output Program": [ + "n0 = 36.0\nn1 = 20.0\nn2 = 4.0\nn3 = 4.0\nn4 = 8.0\nt0 = 1.0 / n1\nt1 = 1.0 / n0\nt2 = n2 * t0\nt3 = n2 * t1\nt4 = n4 * t1\nt5 = t2 + t3\nt6 = t5 - t4\nt7 = t6 / t4\nanswer = t7 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "40.00000000000001" + ], + "split": "train" + }, + { + "Input": "p and q are the only two applicants qualified for a short - term research project that pays 480 dollars in total . candidate p has more experience and , if hired , would be paid 50 percent more per hour than candidate q would be paid . candidate q , if hired , would require 10 hours more than candidate p to do the job . candidate p \u2019 s hourly wage is how many dollars greater than candidate q \u2019 s hourly wage ?", + "Output Program": [ + "n0 = 480.0\nn1 = 50.0\nn2 = 10.0\nt0 = 3.0 / 2.0\nt1 = t0 - 1.0\nt2 = n2 / t1\nt3 = n2 + t2\nt4 = n0 / t2\nt5 = n0 / t3\nanswer = t4 - t5\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "if 3 < x < 6 < y < 8 , then what is the greatest possible positive integer difference of x and y ?", + "Output Program": [ + "n0 = 3.0\nn1 = 6.0\nn2 = 8.0\nt0 = n2 - n0\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "having received his weekly allowance , a student spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.40 at the candy store . what is this student \u2019 s weekly allowance ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 0.4\nt0 = n0 * n1\nt1 = n2 * t0\nanswer = t1 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "1.5" + ], + "split": "train" + }, + { + "Input": "how much is 75 % of 40 is greater than 4 / 5 of 25 ?", + "Output Program": [ + "n0 = 75.0\nn1 = 40.0\nn2 = 4.0\nn3 = 5.0\nn4 = 25.0\nt0 = n0 / 100.0\nt1 = n2 / n3\nt2 = n1 * t0\nt3 = n4 * t1\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "a number is doubled and 5 is added . if the resultant is trebled , it becomes 105 . what is that number ?", + "Output Program": [ + "n0 = 5.0\nn1 = 105.0\nt0 = n0 * 3.0\nt1 = 2.0 * 3.0\nt2 = n1 - t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "10 play kabadi , 35 play kho kho only , 5 play both gmaes . then how many in total ?", + "Output Program": [ + "n0 = 10.0\nn1 = 35.0\nn2 = 5.0\nt0 = n1 + n2\nt1 = n0 + t0\nanswer = t1 - n2\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "in a certain company , the ratio of the number of managers to the number of non - managers in any department must always be greater than 7 : 24 . in the company , what is the maximum number of non - managers in a department that has 8 managers ?", + "Output Program": [ + "import math\nn0 = 7.0\nn1 = 24.0\nn2 = 8.0\nt0 = n1 * n2\nt1 = t0 / n0\nanswer = math.floor(t1)\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "train" + }, + { + "Input": "one pack of cake mix is being stirred before being poured into two separate baking trays . the first tray can hold a certain amount of cups of the mix while the other holds 20 cups less than the first . if the total number of cups poured is 500 , how many cups of batter does the second tray hold ?", + "Output Program": [ + "n0 = 20.0\nn1 = 500.0\nt0 = n1 - n0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "240" + ], + "split": "train" + }, + { + "Input": "how many integers between 500 and 1000 are there such that their unit digit is even ?", + "Output Program": [ + "n0 = 500.0\nn1 = 1000.0\nt0 = n0 / 2.0\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "251" + ], + "split": "train" + }, + { + "Input": "a man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses . next year his income increases by 50 % but his savings increase by 100 % . if his total expenditure in 2 years is double his expenditure in 1 st year , what % age of his income in the first year did he save ?", + "Output Program": [ + "n0 = 50.0\nn1 = 100.0\nn2 = 2.0\nn3 = 1.0\nt0 = n0 + n1\nt1 = n1 * n2\nt2 = n1 + t0\nt3 = t2 - t1\nt4 = t3 / n1\nanswer = t4 * n1\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "on increasing the number of lines in a page by 110 , they become 240 . what is the % of increase in the no . of lines in the page ?", + "Output Program": [ + "n0 = 110.0\nn1 = 240.0\nt0 = n1 - n0\nt1 = n1 / t0\nt2 = t1 * 100.0\nanswer = t2 - 100.0\nprint(answer)" + ], + "Output Answer": [ + "84.61538461538461" + ], + "split": "train" + }, + { + "Input": "what is the total number of d integers between 100 and 200 that are divisible by 3 ?", + "Output Program": [ + "import math\nn0 = 100.0\nn1 = 200.0\nn2 = 3.0\nt0 = n1 / n2\nt1 = n0 / n2\nt2 = math.floor(t0)\nt3 = math.floor(t1)\nt4 = n2 * t2\nt5 = n2 * t3\nt6 = n2 + t5\nt7 = t4 - t6\nt8 = n2 + t7\nanswer = t8 / n2\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "a club wants to mix 15 pounds of candy worth $ 8.00 per pound with candy worth $ 5.00 per pound to reduce the cost of the mixture to $ 6.00 per pound . how many pounds of the $ 5.00 per pound candy should be used ?", + "Output Program": [ + "n0 = 15.0\nn1 = 8.0\nn2 = 5.0\nn3 = 6.0\nn4 = 5.0\nt0 = n0 * n1\nt1 = n0 * n3\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "300 + 5 \u00d7 8 = ?", + "Output Program": [ + "n0 = 300.0\nn1 = 5.0\nn2 = 8.0\nt0 = n1 * n2\nanswer = n0 + t0\nprint(answer)" + ], + "Output Answer": [ + "340" + ], + "split": "train" + }, + { + "Input": "a trained covered x km at 40 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 3 x km .", + "Output Program": [ + "n0 = 40.0\nn1 = 2.0\nn2 = 20.0\nn3 = 3.0\nt0 = n0 / n0\nt1 = n0 * n3\nt2 = n0 * n1\nt3 = t2 / n2\nt4 = t0 + t3\nanswer = t1 / t4\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "the avg weight of a , b & c is 70 kg . if d joins the group , the avg weight of the group becomes 70 kg . if another man e who weights is 3 kg more than d replaces a , then the avgof b , c , d & e becomes 68 kg . what is the weight of a ?", + "Output Program": [ + "n0 = 70.0\nn1 = 70.0\nn2 = 3.0\nn3 = 68.0\nt0 = n1 * 4.0\nt1 = n3 * 4.0\nt2 = n0 * n2\nt3 = t0 - t2\nt4 = n2 + t3\nt5 = t1 - t4\nanswer = t0 - t5\nprint(answer)" + ], + "Output Answer": [ + "81" + ], + "split": "train" + }, + { + "Input": "1 / 0.025 is equal to", + "Output Program": [ + "n0 = 1.0\nn1 = 0.025\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "evaluate : | 4 - 8 ( 3 - 12 ) | - | 5 - 11 | =", + "Output Program": [ + "n0 = 4.0\nn1 = 8.0\nn2 = 3.0\nn3 = 12.0\nn4 = 5.0\nn5 = 11.0\nt0 = n2 - n3\nt1 = n4 - n5\nt2 = n1 * t0\nt3 = -t1\nt4 = n0 - t2\nanswer = t4 - t3\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "train" + }, + { + "Input": "if i equals the sum of the even integers from 2 to 224 , inclusive , and k equals the sum of the even integers from 8 to 80 , inclusive , what is the value of i - k ?", + "Output Program": [ + "n0 = 2.0\nn1 = 224.0\nn2 = 8.0\nn3 = 80.0\nt0 = n0 + n0\nt1 = n0 + n3\nt2 = n2 + t0\nt3 = n1 + t1\nt4 = n1 - t1\nt5 = t4 / 2.0\nt6 = t3 * t5\nt7 = t3 + t6\nt8 = t7 / 2.0\nanswer = t2 + t8\nprint(answer)" + ], + "Output Answer": [ + "11028" + ], + "split": "train" + }, + { + "Input": "if 25 % of x is 15 less than 12 % of 1500 , then x is ?", + "Output Program": [ + "n0 = 25.0\nn1 = 15.0\nn2 = 12.0\nn3 = 1500.0\nt0 = n2 / 100.0\nt1 = n0 / 100.0\nt2 = n3 * t0\nt3 = t2 - n1\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "660" + ], + "split": "train" + }, + { + "Input": "evaluate : 11 + sqrt ( - 4 + 6 \u00d7 4 \u00f7 3 ) = . . . .", + "Output Program": [ + "import math\nn0 = 11.0\nn1 = 4.0\nn2 = 6.0\nn3 = 4.0\nn4 = 3.0\nt0 = n1 * n2\nt1 = t0 / n4\nt2 = t1 - n1\nt3 = math.sqrt(max(0, t2))\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "sum of 49 odd numbers is ?", + "Output Program": [ + "n0 = 49.0\nt0 = n0 / 2.0\nt1 = n0 * 2.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "2401" + ], + "split": "train" + }, + { + "Input": "the product of x and y is a constant . if the value of x is increased by 20 % , by what percentage must the value of y be decreased ?", + "Output Program": [ + "n0 = 20.0\nt0 = n0 + 100.0\nt1 = 100.0 / t0\nt2 = 1.0 - t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "16.666666666666664" + ], + "split": "train" + }, + { + "Input": "how many trucks are there if each truck carrying 70 packages and total of 490 packages ?", + "Output Program": [ + "n0 = 70.0\nn1 = 490.0\n\nanswer = n1 / n0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "the average of 6 observations is 14 . a new observation is included and the new average is decreased by 1 . the seventh observation is ?", + "Output Program": [ + "n0 = 6.0\nn1 = 14.0\nn2 = 1.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n1 - n2\nt3 = t0 * t2\nanswer = t3 - t1\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "find the value of ( 50 + 20 / 90 ) \u00d7 90", + "Output Program": [ + "n0 = 50.0\nn1 = 20.0\nn2 = 90.0\nn3 = 90.0\nt0 = n1 / n2\nt1 = n0 + t0\nanswer = t1 * n2\nprint(answer)" + ], + "Output Answer": [ + "4520" + ], + "split": "train" + }, + { + "Input": "if sharon ' s weekly salary increased by 16 percent , she would earn $ 348 per week . if instead , her weekly salary were to increase by 20 percent , how much would she earn per week ?", + "Output Program": [ + "n0 = 16.0\nn1 = 348.0\nn2 = 20.0\nt0 = n0 / 100.0\nt1 = n2 / 100.0\nt2 = t0 + 1.0\nt3 = n1 / t2\nt4 = t1 * t3\nanswer = t3 + t4\nprint(answer)" + ], + "Output Answer": [ + "360" + ], + "split": "train" + }, + { + "Input": "what should be the least number to be added to the 2496 number to make it divisible by 5 ?", + "Output Program": [ + "n0 = 2496.0\nn1 = 5.0\nt0 = n0 % n1\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "1 \u2044 5 of a number is equal to 5 \u2044 8 of the second number . if 35 is added to the first number then it becomes 4 times of second number . what is the value of the second number ?", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 5.0\nn3 = 8.0\nn4 = 35.0\nn5 = 4.0\nt0 = n3 * n4\nt1 = n3 * n5\nt2 = n1 * n1\nt3 = t1 - t2\nanswer = t0 / t3\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 4 . if the sum of their ages is 132 , what is the difference between the ages of patrick and monica ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 3.0\nn3 = 4.0\nn4 = 132.0\nt0 = n0 * 3.0\nt1 = n1 * 3.0\nt2 = n1 * n3\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n4 / t4\nt6 = t5 * t2\nt7 = t5 * t0\nanswer = t6 - t7\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "ashok secured average of 80 marks in 6 subjects . if the average of marks in 5 subjects is 74 , how many marks did he secure in the 6 th subject ?", + "Output Program": [ + "n0 = 80.0\nn1 = 6.0\nn2 = 5.0\nn3 = 74.0\nn4 = 6.0\nt0 = n0 * n1\nt1 = n2 * n3\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "110" + ], + "split": "train" + }, + { + "Input": "a number consists of 3 digit whose sum is 10 . the middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed . the number is :", + "Output Program": [ + "n0 = 3.0\nn1 = 10.0\nn2 = 99.0\nt0 = n1 + 2.0\nt1 = t0 / 4.0\nt2 = t1 - 1.0\nt3 = t1 + t2\nt4 = t2 * 100.0\nt5 = t3 * 10.0\nt6 = t4 + t5\nanswer = t6 + t1\nprint(answer)" + ], + "Output Answer": [ + "253" + ], + "split": "train" + }, + { + "Input": "of the 3,600 employees of company x , 1 / 4 are clerical . if the clerical staff were to be reduced by 1 / 4 , what percent of the total number of the remaining employees would then be clerical ?", + "Output Program": [ + "n0 = 3600.0\nn1 = 1.0\nn2 = 4.0\nn3 = 1.0\nn4 = 4.0\nt0 = n1 / n2\nt1 = n3 / n4\nt2 = n3 - t1\nt3 = n3 - t0\nt4 = t0 * t2\nt5 = t4 + t3\nt6 = t4 / t5\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "there are 12 teams in a certain league and each team plays each of the other teams exactly once . what is the total number of games played ?", + "Output Program": [ + "n0 = 12.0\nt0 = n0 - 1.0\nt1 = n0 * t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "66" + ], + "split": "train" + }, + { + "Input": "tough and tricky questions : statistics . set x consists of prime numbers { 3 , 11 , 7 , a , 17 , 19 } . if integer y represents the product of all elements in set x and if 11 y is an even number , what is the range of set x ?", + "Output Program": [ + "n0 = 3.0\nn1 = 11.0\nn2 = 7.0\nn3 = 17.0\nn4 = 19.0\nn5 = 11.0\n\nanswer = n4 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "of the families in city x in 1992 , 30 percent owned a personal computer . the number of families in city x owning a computer in 1999 was 50 percent greater than it was in 1992 , and the total number of families in city x was 5 percent greater in 1999 than it was in 1994 . what percent of the families in city x owned a personal computer in 1999 ?", + "Output Program": [ + "n0 = 1992.0\nn1 = 30.0\nn2 = 1999.0\nn3 = 50.0\nn4 = 1992.0\nn5 = 5.0\nn6 = 1999.0\nn7 = 1994.0\nn8 = 1999.0\nt0 = n3 + 100.0\nt1 = n5 + 100.0\nt2 = n1 * t0\nt3 = t2 / 100.0\nt4 = t3 / t1\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "42.857142857142854" + ], + "split": "train" + }, + { + "Input": "a , b and c have rs . 400 between them , a and c together have rs . 300 and b and c rs . 150 . how much does c have ?", + "Output Program": [ + "n0 = 400.0\nn1 = 300.0\nn2 = 150.0\nt0 = n1 + n2\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "city x has a population 8 times as great as the population of city y , which has a population twice as great as the population of city z . what is the ratio of the population of city x to the population of city z ?", + "Output Program": [ + "n0 = 8.0\n\nanswer = n0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "in digging a pond 20 m * 10 m * 8 m the volumes of the soil extracted will be ?", + "Output Program": [ + "n0 = 20.0\nn1 = 10.0\nn2 = 8.0\nt0 = n0 * n1\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "1600" + ], + "split": "train" + }, + { + "Input": "in a bus left side are 15 seats available , 3 few seats in right side because in rear exit door . each seat hold 3 people . in addition , there is a seat back can sit 8 people all together . how many people can sit in a bus ?", + "Output Program": [ + "n0 = 15.0\nn1 = 3.0\nn2 = 3.0\nn3 = 8.0\nt0 = n0 - n1\nt1 = n0 + t0\nt2 = n1 * t1\nanswer = n3 + t2\nprint(answer)" + ], + "Output Answer": [ + "89" + ], + "split": "train" + }, + { + "Input": "a computer wholesaler sells 10 different computers and each is priced differently . if the wholesaler chooses 3 computers for display at a trade show , what is the probability ( all things being equal ) that the two most expensive computers will be among the 3 chosen for display ?", + "Output Program": [ + "n0 = 10.0\nn1 = 3.0\nn2 = 3.0\nt0 = n1 - 1.0\nt1 = n0 - 1.0\nt2 = t0 / n0\nt3 = 1.0 / t1\nt4 = t2 * t3\nanswer = n1 * t4\nprint(answer)" + ], + "Output Answer": [ + "0.06666666666666667" + ], + "split": "train" + }, + { + "Input": "on thursday mabel handled 90 transactions . anthony handled 10 % more transactions than mabel , cal handled 2 / 3 rds of the transactions that anthony handled , and jade handled 17 more transactions than cal . how much transactions did jade handled ?", + "Output Program": [ + "n0 = 90.0\nn1 = 10.0\nn2 = 2.0\nn3 = 3.0\nn4 = 17.0\nt0 = n1 + 100.0\nt1 = n0 / 100.0\nt2 = t0 * t1\nt3 = n2 * t2\nt4 = t3 / n3\nanswer = n4 + t4\nprint(answer)" + ], + "Output Answer": [ + "83" + ], + "split": "train" + }, + { + "Input": "the sum of number of boys and girls in a school is 900 . if the number of boys is x , then the number of girls becomes x % of the total number of students . the number of boys is ?", + "Output Program": [ + "n0 = 900.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "one half of a two digit number exceeds its one fourth by 3 . what is the sum of the digits of the number ?", + "Output Program": [ + "n0 = 3.0\nt0 = n0 * 4.0\nt1 = t0 % 10.0\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "a student chose a number , multiplied it by 2 , then subtracted 200 from the result and got 110 . what was the number he chose ?", + "Output Program": [ + "n0 = 2.0\nn1 = 200.0\nn2 = 110.0\nt0 = n1 + n2\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "155" + ], + "split": "train" + }, + { + "Input": "the average expenditure of a labourer for 6 months was 90 and he fell into debt . in the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30 . his monthly income i", + "Output Program": [ + "n0 = 6.0\nn1 = 90.0\nn2 = 4.0\nn3 = 60.0\nn4 = 30.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nt4 = n4 + t3\nanswer = t4 / t0\nprint(answer)" + ], + "Output Answer": [ + "81" + ], + "split": "train" + }, + { + "Input": "find the value of ( \u221a 1.1 ) / ( \u221a 0.81 ) + ( \u221a 1.44 ) / ( \u221a 0.49 ) is", + "Output Program": [ + "import math\nn0 = 1.1\nn1 = 0.81\nn2 = 1.44\nn3 = 0.49\nt0 = math.sqrt(max(0, n0))\nt1 = math.sqrt(max(0, n1))\nt2 = math.sqrt(max(0, n2))\nt3 = math.sqrt(max(0, n3))\nt4 = t0 / t1\nt5 = t2 / t3\nanswer = t4 + t5\nprint(answer)" + ], + "Output Answer": [ + "2.879628878919216" + ], + "split": "train" + }, + { + "Input": "if x ^ 2 + y ^ 2 = 15 and xy = 3 , then ( x \u2212 y ) ^ 2 =", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 15.0\nn3 = 3.0\nn4 = 2.0\n\nanswer = n3**min(n0, 5)\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "if h = { 1 , 7 , 18 , 20 , 29 , 33 } , how much less is the mean of the numbers in h than the median of the numbers in h ?", + "Output Program": [ + "n0 = 1.0\nn1 = 7.0\nn2 = 18.0\nn3 = 20.0\nn4 = 29.0\nn5 = 33.0\nt0 = n2 + n3\nt1 = n0 + n1\nt2 = 2.0 * 3.0\nt3 = n2 + t1\nt4 = t0 / 2.0\nt5 = n3 + t3\nt6 = n4 + t5\nt7 = n5 + t6\nt8 = t7 / t2\nanswer = t4 - t8\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "x varies inversely as square of y . given that y = 2 for x = 1 . the value of x for y = 6 will be equal to ?", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 6.0\nt0 = n0**min(2.0, 5)\nt1 = n2**min(2.0, 5)\nt2 = n1 * t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.1111111111111111" + ], + "split": "train" + }, + { + "Input": "there are , in a certain league , 50 teams , and each team face another team for a total of 4 times . how many games are played in the season ?", + "Output Program": [ + "n0 = 50.0\nn1 = 4.0\nt0 = n0 / 2.0\nt1 = n0 - 1.0\nt2 = t1 * 4.0\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "4900" + ], + "split": "train" + }, + { + "Input": "5 x 1.6 - 2 x 1.4 / 1.3 = ?", + "Output Program": [ + "n0 = 5.0\nn1 = 1.6\nn2 = 2.0\nn3 = 1.4\nn4 = 1.3\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = t0 - t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "david works at a resort from the beginning of march to the end of september . during the month of august this past year , he made 4 times the average ( arithmetic mean ) of his monthly totals in tips for the other months . his total tips for august were what fraction of his total tips for all of the months he worked ?", + "Output Program": [ + "n0 = 4.0\nt0 = 10.0 - n0\nt1 = n0 + t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.4" + ], + "split": "train" + }, + { + "Input": "the population of a city increases by 9 % per year but due to migration it decrease by 1 % per years . what will be the percentage increase in population in 3 years ?", + "Output Program": [ + "n0 = 9.0\nn1 = 1.0\nn2 = 3.0\nt0 = n0 - n1\nt1 = t0 + 100.0\nt2 = t1 * t0\nt3 = t2 / 100.0\nt4 = t3 + t0\nt5 = t4 + 100.0\nt6 = t5 * t0\nt7 = t6 / 100.0\nanswer = t4 + t7\nprint(answer)" + ], + "Output Answer": [ + "25.971200000000003" + ], + "split": "train" + }, + { + "Input": "if 18888 \u2013 n is divisible by 11 , and 0 < n < 11 , what is n ?", + "Output Program": [ + "import scipy\nn0 = 18888.0\nn1 = 11.0\nn2 = 0.0\nn3 = 11.0\n\nanswer = scipy.gcd(int(n0), int(n1))\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "a number is 4 less than 6 times the other number . if the sum of both the number is 38 , what are the numbers ?", + "Output Program": [ + "n0 = 4.0\nn1 = 6.0\nn2 = 38.0\nt0 = n2 - n1\nt1 = n2 - t0\nt2 = t1 * 100.0\nanswer = t2 + t0\nprint(answer)" + ], + "Output Answer": [ + "632" + ], + "split": "train" + }, + { + "Input": "if the largest 3 digit number is subtracted from the smallest 5 digit number , then the remainder is", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nt0 = n1 * 100.0\nt1 = t0 + t0\nt2 = t1 * 10.0\nt3 = t1 - 1.0\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "9001" + ], + "split": "train" + }, + { + "Input": "what is the sum of 80 consecutive integers from - 39 inclusive , in a increasing order ?", + "Output Program": [ + "n0 = 80.0\nn1 = 39.0\n\nanswer = n1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "a man has some hens and cows . if the number of heads be 46 and the number of feet equals 136 , then the number of hens will be", + "Output Program": [ + "n0 = 46.0\nn1 = 136.0\nt0 = n0 * 4.0\nt1 = t0 - n1\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "find the smallest number which when divided by 13 and 17 leaves respective remainders of 3 and 7 .", + "Output Program": [ + "n0 = 13.0\nn1 = 17.0\nn2 = 3.0\nn3 = 7.0\nt0 = 1.0 + 10.0\nt1 = n0 * n1\nanswer = t1 - t0\nprint(answer)" + ], + "Output Answer": [ + "210" + ], + "split": "train" + }, + { + "Input": "find the constant k so that : - x 2 - ( k + 11 ) x - 8 = - ( x - 2 ) ( x - 4 )", + "Output Program": [ + "n0 = 2.0\nn1 = 11.0\nn2 = 8.0\nn3 = 2.0\nn4 = 4.0\nt0 = n0 + n4\nanswer = n1 + t0\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "at a restaurant , glasses are stored in two different - sized boxes . one box contains 12 glasses , and the other contains 16 glasses . if the average number of glasses per box is 15 , and there are 16 more of the larger boxes , what is the total number of glasses r at the restaurant ? ( assume that all boxes are filled to capacity . )", + "Output Program": [ + "n0 = 12.0\nn1 = 16.0\nn2 = 15.0\nn3 = 16.0\nt0 = n1 * 2.0\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "480" + ], + "split": "train" + }, + { + "Input": "on increasing the number of lines in a page by 60 , they become 240 . what is the % of increase in the no . of lines in the page ?", + "Output Program": [ + "n0 = 60.0\nn1 = 240.0\nt0 = n1 - n0\nt1 = n1 / t0\nt2 = t1 * 100.0\nanswer = t2 - 100.0\nprint(answer)" + ], + "Output Answer": [ + "33.333333333333314" + ], + "split": "train" + }, + { + "Input": "two kinds of vodka are mixed in the ratio 1 : 2 and 2 : 1 and they are sold fetching the profit 10 % and 35 % respectively . if the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4 / 3 and 5 / 3 times respectively , then the mixture will fetch the profit of", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 2.0\nn3 = 1.0\nn4 = 10.0\nn5 = 35.0\nn6 = 4.0\nn7 = 3.0\nn8 = 5.0\nn9 = 3.0\nt0 = n4 + n8\nt1 = n4 * n6\nt2 = t1 / n1\nanswer = t0 + t2\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "evaluate 75 / . 05", + "Output Program": [ + "n0 = 75.0\nn1 = 5.0\nt0 = n1 / 100.0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "1500" + ], + "split": "train" + }, + { + "Input": "a house wife saved $ 4 in buying an item on sale . if she spent $ 29 for the item , approximately how much percent she saved in the transaction ?", + "Output Program": [ + "n0 = 4.0\nn1 = 29.0\nt0 = n0 + n1\nt1 = n0 / t0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "12.121212121212121" + ], + "split": "train" + }, + { + "Input": "if a + b = \u2212 6 , and a = 10 / b , what is the value of a ^ 2 + b ^ 2 ?", + "Output Program": [ + "n0 = 6.0\nn1 = 10.0\nn2 = 2.0\nn3 = 2.0\nt0 = n1 * 2.0\nt1 = n0**min(2.0, 5)\nanswer = t1 - t0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "a large box contains 15 small boxes and each small box contains 20 chocolate bars . how many chocolate bars are in the large box ?", + "Output Program": [ + "n0 = 15.0\nn1 = 20.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "if a # b = ab \u2013 b + b ^ 2 , then 3 # 6 =", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 6.0\nt0 = n1 * n2\nt1 = n2**min(n0, 5)\nt2 = t0 - n2\nanswer = t1 + t2\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "a man engaged a servant on a condition that he ' ll pay rs 90 and also give him a bag at the end of the yr . he served for 9 months and was given a turban and rs 65 . so the price of turban is", + "Output Program": [ + "n0 = 90.0\nn1 = 9.0\nn2 = 65.0\nt0 = n0 / 12.0\nt1 = t0 * 10.0\nanswer = t1 - n2\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "for a certain exam , a score of 86 was 7 standard deviations below mean and a score of 90 was 3 standard deviations above mean . what was the mean score for the exam ?", + "Output Program": [ + "n0 = 86.0\nn1 = 7.0\nn2 = 90.0\nn3 = 3.0\nt0 = n1 + n3\nt1 = n0 * n3\nt2 = n1 * n2\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "88.8" + ], + "split": "train" + }, + { + "Input": "in a division , a student took 72 as divisor instead of 36 . his answer was 24 . the correct answer is -", + "Output Program": [ + "n0 = 72.0\nn1 = 36.0\nn2 = 24.0\nt0 = n0 * n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "a scientist used a unique two - color code to identify each of the test subjects involved in a certain study . if the scientist found that choosing from among 5 colors produced enough color codes to identify all but 6 of the test subjects , how many test subjects were in the study ? ( assume that the order of the colors in the codes does not matter . )", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 6.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(2.0)))\nt2 = n0 - 2.0\nt3 = math.factorial(min(15, int(t2)))\nt4 = t3 * t1\nt5 = t0 / t4\nanswer = n1 + t5\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "enrollment in city college in 1980 was 85 / 3 percent of enrollment in 1990 . what was the percent increase in the college \u2019 s enrollment from 1980 to 1990 ?", + "Output Program": [ + "n0 = 1980.0\nn1 = 85.0\nn2 = 3.0\nn3 = 1990.0\nn4 = 1980.0\nn5 = 1990.0\nt0 = n1 / n2\nt1 = 100.0 - t0\nt2 = t1 / t0\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "252.94117647058826" + ], + "split": "train" + }, + { + "Input": "lisa and robert have taken the same number of photos on their school trip . lisa has taken 3 times as many photos as claire and robert has taken 10 more photos than claire . how many photos has claire taken ?", + "Output Program": [ + "n0 = 3.0\nn1 = 10.0\nt0 = n0 - 1.0\nanswer = n1 / t0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "how many even multiples of 45 are there between 449 and 901 ?", + "Output Program": [ + "n0 = 45.0\nn1 = 449.0\nn2 = 901.0\nt0 = n0 * 2.0\nt1 = n2 - n1\nt2 = t1 / t0\nanswer = t2 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "6.022222222222222" + ], + "split": "train" + }, + { + "Input": "19 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ?", + "Output Program": [ + "n0 = 19.0\nt0 = n0 - 1.0\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "342" + ], + "split": "train" + }, + { + "Input": "rs . 585 is divided amongst a , b , c so that 4 times a ' s share , 6 times b ' s share and 3 times c ' s share are all equal . find c ' s share ?", + "Output Program": [ + "n0 = 585.0\nn1 = 4.0\nn2 = 6.0\nn3 = 3.0\nt0 = n3 / n1\nt1 = n3 / n2\nt2 = t0 + t1\nt3 = t2 + 1.0\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "260" + ], + "split": "train" + }, + { + "Input": "in 10 years , a will be twice as old as b was 10 years ago . if a is now 8 years older than b the present age of b is", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 8.0\nt0 = n0 * 2.0\nt1 = n0 + t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "38" + ], + "split": "train" + }, + { + "Input": "cost is expressed by the formula tb ^ 4 . if b is doubled , the new cost is what percent t of the original cost ?", + "Output Program": [ + "n0 = 4.0\nt0 = 2.0**min(n0, 5)\nanswer = t0 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "1600" + ], + "split": "train" + }, + { + "Input": "in a certain egg - processing plant , every egg must be inspected , and is either accepted for processing or rejected . for every 96 eggs accepted for processing , 4 eggs are rejected . if , on a particular day , 12 additional eggs were accepted , but the overall number of eggs inspected remained the same , the ratio of those accepted to those rejected would be 99 to 1 . how many q eggs does the plant process per day ?", + "Output Program": [ + "n0 = 96.0\nn1 = 4.0\nn2 = 12.0\nn3 = 99.0\nn4 = 1.0\nt0 = n3 - n0\nt1 = n2 / t0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "train" + }, + { + "Input": "two students appeared at an examination . one of them secured 9 marks more than the other and his marks was 56 % of the sum of their marks . the marks obtained by them are :", + "Output Program": [ + "n0 = 9.0\nn1 = 56.0\nt0 = n0 * 100.0\nt1 = n0 * n1\nt2 = n1 * 2.0\nt3 = t0 - t1\nt4 = t2 - 100.0\nt5 = t3 / t4\nanswer = n0 + t5\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "if x is the product of the positive integers from 1 to 8 , inclusive , and if i , k , m , and p are positive integers such that x = 2 ^ i \u2217 3 ^ k \u2217 5 ^ m \u2217 7 ^ p , then i + k + m + p =", + "Output Program": [ + "n0 = 1.0\nn1 = 8.0\nn2 = 2.0\nn3 = 3.0\nn4 = 5.0\nn5 = 7.0\nt0 = n2 + n5\nt1 = n4 / n4\nt2 = n3 / n3\nt3 = t0 + t1\nanswer = t3 + t2\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "the average of 10 numbers is calculated as 14 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?", + "Output Program": [ + "n0 = 10.0\nn1 = 14.0\nn2 = 36.0\nn3 = 26.0\nt0 = n2 - n3\nt1 = t0 / n0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "the average of 6 quantities is 8 . the average of 4 of them is 5 . what is the avg . of the remaining 2 numbers ?", + "Output Program": [ + "n0 = 6.0\nn1 = 8.0\nn2 = 4.0\nn3 = 5.0\nn4 = 2.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = t0 - t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "a man has rs . 10350 in the form of rs . 50 notes and rs . 500 notes . the total number of notes are 90 . find the number of notes of rs . 50 denomination .", + "Output Program": [ + "n0 = 10350.0\nn1 = 50.0\nn2 = 500.0\nn3 = 90.0\nn4 = 50.0\nt0 = n2 * n3\nt1 = n2 - n1\nt2 = t0 - n0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "77" + ], + "split": "train" + }, + { + "Input": "the average age of an adult class is 40 years . 12 new students with an avg age of 32 years join the class . thereforedecreasing the average by 4 year . find what was theoriginal strength of class ?", + "Output Program": [ + "n0 = 40.0\nn1 = 12.0\nn2 = 32.0\nn3 = 4.0\nt0 = n1 * n2\nt1 = n0 - n3\nt2 = n1 * t1\nt3 = t2 - t0\nanswer = t3 / n3\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "the distance from the x - axis to point p is half the distance from the y - axis to point p . if the coordinates of p are ( x , - 5 ) , how many units is p from the y - axis ?", + "Output Program": [ + "n0 = 5.0\n\nanswer = n0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "we bought a total of 90 books at the store . math books cost $ 4 and history books cost $ 5 . the total price was $ 397 . how many math books did we buy ?", + "Output Program": [ + "n0 = 90.0\nn1 = 4.0\nn2 = 5.0\nn3 = 397.0\nt0 = n0 * n1\nt1 = n3 - t0\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "53" + ], + "split": "train" + }, + { + "Input": "two employees a and b are paid a total of rs . 580 per week by their employer . if a is paid 150 percent of the sum paid to b , how much is b paid per week ?", + "Output Program": [ + "n0 = 580.0\nn1 = 150.0\nt0 = n1 / 100.0\nt1 = t0 + 1.0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "232" + ], + "split": "train" + }, + { + "Input": "at a certain committee meeting only associate professors and assistant professors are present . each associate professor has brought 2 pencils and 1 chart to the meeting , while each assistant professor has brought 1 pencil and 2 charts . if a total of 7 pencils and 11 charts have been brought to the meeting , how many people are present ?", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 1.0\nn3 = 2.0\nn4 = 7.0\nn5 = 11.0\nt0 = n4 + n5\nt1 = n0 + n1\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "the difference between the value of a number increased by 12.5 % and the value of the original number decreased by 25 % is 30 . what is the original number r ?", + "Output Program": [ + "n0 = 12.5\nn1 = 25.0\nn2 = 30.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = t0 + 1.0\nt3 = 1.0 - t1\nt4 = t2 - t3\nanswer = n2 / t4\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "the average height of 35 boys in a class was calculated as 182 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ) . ?", + "Output Program": [ + "import math\nn0 = 35.0\nn1 = 182.0\nn2 = 166.0\nn3 = 106.0\nt0 = n0 * n1\nt1 = t0 - n2\nt2 = n3 + t1\nt3 = t2 / n0\nanswer = math.floor(t3)\nprint(answer)" + ], + "Output Answer": [ + "180" + ], + "split": "train" + }, + { + "Input": "if solomon distributes his toys in the ratio of 1 / 4 : 1 / 6 : 1 / 10 : 1 / 9 between his 4 friends a , b , c and d , then find the total number of toys solomon should have ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 1.0\nn3 = 6.0\nn4 = 1.0\nn5 = 10.0\nn6 = 1.0\nn7 = 9.0\nn8 = 4.0\nt0 = n3 * n5\nt1 = n1 * n5\nt2 = n3 * 3.0\nt3 = t0 + t1\nanswer = t3 + t2\nprint(answer)" + ], + "Output Answer": [ + "118" + ], + "split": "train" + }, + { + "Input": "a room is 8 meters 16 centimeters in length and 4 meters 32 centimeters in width . find the least number of square tiles of equal size required to cover the entire floor of the room .", + "Output Program": [ + "import scipy\nn0 = 8.0\nn1 = 16.0\nn2 = 4.0\nn3 = 32.0\nt0 = n0 * 100.0\nt1 = n2 * 100.0\nt2 = n1 + t0\nt3 = n3 + t1\nt4 = scipy.gcd(int(t2), int(t3))\nt5 = t2 * t3\nt6 = t4 * t4\nanswer = t5 / t6\nprint(answer)" + ], + "Output Answer": [ + "153" + ], + "split": "train" + }, + { + "Input": "max planned to buy bike , sales man advised him to buy within this month , if he purchase next month means state tax will be increasing 10 % than its cost and it would be 82500 . what is the bike ' s selling price in this month", + "Output Program": [ + "n0 = 10.0\nn1 = 82500.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nanswer = n1 / t1\nprint(answer)" + ], + "Output Answer": [ + "75000" + ], + "split": "train" + }, + { + "Input": "a , b and c rent a pasture . if a puts 10 oxen for 7 months , b puts 12 oxen for 5 months and c puts 15 oxen for 3 months for grazing and the rent of the pasture is rs . 280 , then how much amount should c pay as his share of rent ?", + "Output Program": [ + "n0 = 10.0\nn1 = 7.0\nn2 = 12.0\nn3 = 5.0\nn4 = 15.0\nn5 = 3.0\nn6 = 280.0\nt0 = n4 * n5\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nt4 = t3 + t0\nt5 = t0 / t4\nanswer = n6 * t5\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "train" + }, + { + "Input": "after 4 games , team b had an average of 61.5 points per game . if it got only 47 points in game 5 , how many more points does it need to score to get its total above 500 ?", + "Output Program": [ + "n0 = 4.0\nn1 = 61.5\nn2 = 47.0\nn3 = 5.0\nn4 = 500.0\nt0 = n0 * n1\nt1 = n2 + t0\nanswer = n4 - t1\nprint(answer)" + ], + "Output Answer": [ + "207" + ], + "split": "train" + }, + { + "Input": "the jogging track in a sports complex is 726 m in circumference . deepak and his wife start from the same point and walk in opposite directions at 4.5 km / hr and 3.75 km / hr respectively . they will meet for the first time in ?", + "Output Program": [ + "n0 = 726.0\nn1 = 4.5\nn2 = 3.75\nt0 = n1 + n2\nt1 = n0 / 1000.0\nt2 = t1 / t0\nanswer = t2 * 60.0\nprint(answer)" + ], + "Output Answer": [ + "5.279999999999999" + ], + "split": "train" + }, + { + "Input": "a , b , c and d enter into partnership . a subscribes 1 / 3 of the capital b 1 / 4 , c 1 / 5 and d the rest . how much share did a get in a profit of rs . 2415 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 4.0\nn4 = 1.0\nn5 = 5.0\nn6 = 2415.0\nt0 = n0 / n1\nanswer = n6 * t0\nprint(answer)" + ], + "Output Answer": [ + "805" + ], + "split": "train" + }, + { + "Input": "a student has to obtain 45 % of the total marks to pass . he got 150 marks and failed by 30 marks . the maximum marks are ?", + "Output Program": [ + "n0 = 45.0\nn1 = 150.0\nn2 = 30.0\nt0 = n1 + n2\nt1 = n0 / 100.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "train" + }, + { + "Input": "if f ( x ) = 2 x ^ 2 + y , and f ( 2 ) = 30 , what is the value of f ( 10 ) ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 2.0\nn3 = 30.0\nn4 = 10.0\nt0 = n4**min(n0, 5)\nt1 = n0**min(n0, 5)\nt2 = n0 * t0\nt3 = n0 * t1\nt4 = n3 - t3\nanswer = t2 + t4\nprint(answer)" + ], + "Output Answer": [ + "222" + ], + "split": "train" + }, + { + "Input": "when tossed , a certain coin has equal probability of landing on either side . if the coin is tossed 3 times , what is the probability that it will land twice on heads and once on tails ?", + "Output Program": [ + "n0 = 3.0\nt0 = 2.0**min(n0, 5)\nanswer = 1.0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.125" + ], + "split": "train" + }, + { + "Input": "[ ( 5 / 2 \u00f7 1 / 2 \u00d7 5 / 2 ) ] / [ ( 5 / 2 \u00d7 1 / 2 \u00f7 5 / 2 ) ] = ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 1.0\nn3 = 2.0\nn4 = 5.0\nn5 = 2.0\nn6 = 5.0\nn7 = 2.0\nn8 = 1.0\nn9 = 2.0\nn10 = 5.0\nn11 = 2.0\nt0 = n0 / n1\nt1 = n2 / n1\nt2 = t0 / t1\nt3 = t0 * t1\nt4 = t3 / t0\nt5 = t2 * t0\nanswer = t5 / t4\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "find the value of ( 85 + 32 / 113 ) \u00d7 113", + "Output Program": [ + "n0 = 85.0\nn1 = 32.0\nn2 = 113.0\nn3 = 113.0\nt0 = n1 / n2\nt1 = n0 + t0\nanswer = t1 * n2\nprint(answer)" + ], + "Output Answer": [ + "9637" + ], + "split": "train" + }, + { + "Input": "the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 20000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is :", + "Output Program": [ + "n0 = 8000.0\nn1 = 7.0\nn2 = 20000.0\nn3 = 6000.0\nt0 = n2 - n0\nt1 = n0 - n3\nt2 = n1 * t0\nt3 = t2 / t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "49" + ], + "split": "train" + }, + { + "Input": "in 70 liters of a mixture of milk and water , the quantity of water is 10 % . how much water should be added so that new mixture may 25 % water .", + "Output Program": [ + "n0 = 70.0\nn1 = 10.0\nn2 = 25.0\nt0 = 100.0 - n2\nt1 = n2 - n1\nt2 = t0 / t1\nanswer = n0 / t2\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "which expression has the greatest value ?", + "Output Program": [ + "t0 = 3.0 * 3.0\nt1 = 3600.0 - 4.0\nt2 = 3600.0 - t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.9986095661846496" + ], + "split": "train" + }, + { + "Input": "what is the greatest prime factor of 4 ^ 17 - 2 ^ 29 ?", + "Output Program": [ + "n0 = 4.0\nn1 = 17.0\nn2 = 2.0\nn3 = 29.0\n\nanswer = n2 + n3\nprint(answer)" + ], + "Output Answer": [ + "31" + ], + "split": "train" + }, + { + "Input": "a student , after his teacher ' s question , chose a number , multiplied it by 2 , then subtracted 138 from the result and got 102 . what was the number he chose ?", + "Output Program": [ + "n0 = 2.0\nn1 = 138.0\nn2 = 102.0\nt0 = n1 + n2\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "lisa and robert have taken the same number of photos on their school trip . lisa has taken 3 times as many photos as claire and robert has taken 28 more photos than claire . how many photos has claire taken ?", + "Output Program": [ + "n0 = 3.0\nn1 = 28.0\nt0 = n0 - 1.0\nanswer = n1 / t0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "when a certain number x is divided by 66 , the remainder is 14 . what is the remainder when x is divided by 11 ?", + "Output Program": [ + "n0 = 66.0\nn1 = 14.0\nn2 = 11.0\n\nanswer = n1 % n2\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "a 40 - liter solution of alcohol and water is 5 percent alcohol . if 5.5 liters of alcohol and 4.5 liters of water are added to this solution , what percent of the solution produced is alcohol ?", + "Output Program": [ + "n0 = 40.0\nn1 = 5.0\nn2 = 5.5\nn3 = 4.5\nt0 = n2 + n3\nt1 = n1 / 100.0\nt2 = n0 + t0\nt3 = n0 * t1\nt4 = n2 + t3\nt5 = t4 / t2\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "in the first round of the elections , the only two candidates got exactly the same number of votes . during the second round , 16000 votes switched from the first candidate to the second one . the total number of votes remained the same in both rounds , and no other votes switched sides . if , in the second round , the winning candidate got 5 times as many votes as the other candidate , how many people have voted in each round ?", + "Output Program": [ + "n0 = 16000.0\nn1 = 5.0\nt0 = n0 * n1\nt1 = n0 + t0\nt2 = t1 / 4.0\nanswer = t2 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "48000" + ], + "split": "train" + }, + { + "Input": "what is the largest 4 digit number exactly divisible by 35 ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 35.0\nt0 = 10.0**min(n0, 5)\nt1 = t0 / n1\nt2 = math.floor(t1)\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "9975" + ], + "split": "train" + }, + { + "Input": "the sum of the average ( arithmetic mean ) of the even integers from 0 to 100 inclusive and the average ( arithmetic mean ) of the even integers from 0 to 50 inclusive ?", + "Output Program": [ + "n0 = 0.0\nn1 = 100.0\nn2 = 0.0\nn3 = 50.0\nt0 = n1 / 2.0\nt1 = n3 / 2.0\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "when greenville state university decided to move its fine arts collection to a new library , it had to package the collection in 20 - inch by 20 - inch by 12 - inch boxes . if the university pays $ 0.50 for every box , and if the university needs 1.92 million cubic inches to package the collection , what is the minimum amount the university must spend on boxes ?", + "Output Program": [ + "n0 = 20.0\nn1 = 20.0\nn2 = 12.0\nn3 = 0.5\nn4 = 1.92\nt0 = 1000.0 * 1000.0\nt1 = n0 * n0\nt2 = n4 * t0\nt3 = n2 * t1\nt4 = t2 / t3\nanswer = n3 * t4\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "train" + }, + { + "Input": "in the list 1 , 2 , 3 , 4 , 5 , 5 , 5 , 5 , 7 , 11 , 21 , what fraction of the data is less than the mode ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 3.0\nn3 = 4.0\nn4 = 5.0\nn5 = 5.0\nn6 = 5.0\nn7 = 5.0\nn8 = 7.0\nn9 = 11.0\nn10 = 21.0\n\nanswer = n3 / n9\nprint(answer)" + ], + "Output Answer": [ + "0.36363636363636365" + ], + "split": "train" + }, + { + "Input": "a soft drink company had 6000 small and 14000 big bottles in storage . if 20 % of small 23 % of big bottles have been sold , then the total bottles remaining in storage is", + "Output Program": [ + "n0 = 6000.0\nn1 = 14000.0\nn2 = 20.0\nn3 = 23.0\nt0 = n0 + n1\nt1 = n2 / 100.0\nt2 = n3 / 100.0\nt3 = n0 * t1\nt4 = n1 * t2\nt5 = t3 + t4\nanswer = t0 - t5\nprint(answer)" + ], + "Output Answer": [ + "15580" + ], + "split": "train" + }, + { + "Input": "there are 10 teams in a soccer league and each team plays each of the other teams once . how many games will be played in total ?", + "Output Program": [ + "import math\nn0 = 10.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(2.0)))\nt2 = n0 - 2.0\nt3 = math.factorial(min(15, int(t2)))\nt4 = t3 * t1\nanswer = t0 / t4\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "if two of the 4 expressions x + y , x + 5 y , x - y , 5 x + y are chosen at random , what is the probability that their product will be of the form of x ^ 2 - ( by ) ^ 2 , where b is an integer ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 5.0\nn3 = 2.0\nn4 = 2.0\nt0 = n0 + n3\nt1 = n1 - n0\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.16666666666666666" + ], + "split": "train" + }, + { + "Input": "find large number from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 7 as quotient and the 15 as remainder", + "Output Program": [ + "n0 = 1365.0\nn1 = 7.0\nn2 = 15.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nt2 = t0 / t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "1575" + ], + "split": "train" + }, + { + "Input": "when a person aged 39 is added to a group of n people , the average age increases by 2 . when a person aged 15 is added instead , the average age decreases by 1 . what is the value of q ?", + "Output Program": [ + "n0 = 39.0\nn1 = 2.0\nn2 = 15.0\nn3 = 1.0\nt0 = n1 + n3\nt1 = n0 - n2\nt2 = t1 / t0\nanswer = t2 - n3\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "how many paying stones , each measuring 2 1 / 2 m * 2 m are required to pave a rectangular court yard 60 m long and 16 1 / 2 m board ?", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 2.0\nn3 = 2.0\nn4 = 60.0\nn5 = 16.0\nn6 = 1.0\nn7 = 2.0\nt0 = n1 / n0\nt1 = n5 + t0\nt2 = n0 + t0\nt3 = n4 * t1\nt4 = n0 * t2\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "198" + ], + "split": "train" + }, + { + "Input": "10 % people of a village in sri lanka died by bombardment , 15 % of the remainder left the village on account of fear . if now the population is reduced to 3213 , how much was it in the beginning ?", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 15.0\nn2 = 3213.0\nt0 = 100.0 - n0\nt1 = 100.0 - n1\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = t2 * t3\nt5 = n2 / t4\nanswer = math.floor(t5)\nprint(answer)" + ], + "Output Answer": [ + "4200" + ], + "split": "train" + }, + { + "Input": "a jogger running at 9 km / hr along side a railway track is 180 m ahead of the engine of a 120 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?", + "Output Program": [ + "n0 = 9.0\nn1 = 180.0\nn2 = 120.0\nn3 = 45.0\nt0 = n1 + n2\nt1 = 10.0 / 2.0\nt2 = n3 - n0\nt3 = t2 / 2.0\nt4 = t1 / t3\nt5 = t4 * t2\nanswer = t0 / t5\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "x + ( 1 / x ) = 1.5 find x ^ 2 + ( 1 / x ^ 2 )", + "Output Program": [ + "n0 = 1.0\nn1 = 1.5\nn2 = 2.0\nn3 = 1.0\nn4 = 2.0\nt0 = n1**min(n2, 5)\nanswer = t0 - n2\nprint(answer)" + ], + "Output Answer": [ + "0.25" + ], + "split": "train" + }, + { + "Input": "the total age of a and b is 12 years more than the total age of b and c . c is how many year younger than a ?", + "Output Program": [ + "n0 = 12.0\n\nanswer = n0 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "the temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees fahrenheit . if the temperature f of the coffee t minutes after it was poured can be determined by the formula f = 120 ( 2 ^ - at ) + 60 , where f is in degrees fahrenheit and a is a constant . then the temperature of the coffee 60 minutes after it was poured was how many degrees fahrenheit ?", + "Output Program": [ + "n0 = 10.0\nn1 = 120.0\nn2 = 120.0\nn3 = 2.0\nn4 = 60.0\nn5 = 60.0\nt0 = n4 / n0\nt1 = 1.0 - 2.0\nt2 = t0 * t1\nt3 = n3**min(t2, 5)\nt4 = n1 * t3\nanswer = n4 + t4\nprint(answer)" + ], + "Output Answer": [ + "61.875" + ], + "split": "train" + }, + { + "Input": "the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.5\nn2 = 65.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "85" + ], + "split": "train" + }, + { + "Input": "a bucket contains 2 mixtures a and b in the ratio 7 : 5 . if 9 liters of the mixture is replaced by 9 liters of liquid b , then the ratio of the two liquids becomes 7 : 9 . how much of the liquid a was there in the bucket ?", + "Output Program": [ + "n0 = 2.0\nn1 = 7.0\nn2 = 5.0\nn3 = 9.0\nn4 = 9.0\nn5 = 7.0\nn6 = 9.0\nt0 = n1 + n2\nt1 = n1 * n3\nt2 = n1 * n2\nt3 = n1 / t0\nt4 = n2 / t0\nt5 = t1 - t2\nt6 = n3 * t3\nt7 = n3 * t4\nt8 = n3 * t6\nt9 = n3 - t7\nt10 = n1 * t9\nt11 = t8 + t10\nt12 = t11 / t5\nanswer = n1 * t12\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "the cost to park a car in a certain parking garage is $ 12.00 for up to 2 hours of parking and $ 1.75 for each hour in excess of 2 hours . what is the average ( arithmetic mean ) cost per hour to park a car in the parking garage for 9 hours ?", + "Output Program": [ + "n0 = 12.0\nn1 = 2.0\nn2 = 1.75\nn3 = 2.0\nn4 = 9.0\nt0 = n4 - n1\nt1 = n2 * t0\nt2 = n0 + t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "2.6944444444444446" + ], + "split": "train" + }, + { + "Input": "a man purchased 3 blankets @ rs . 100 each , 5 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 160 . find the unknown rate of two blankets ?", + "Output Program": [ + "n0 = 3.0\nn1 = 100.0\nn2 = 5.0\nn3 = 150.0\nn4 = 160.0\nt0 = n4 * 10.0\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "550" + ], + "split": "train" + }, + { + "Input": "two trains of equal length are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . if the faster train passes the slower train in 36 seconds , what is the length of each train ?", + "Output Program": [ + "n0 = 46.0\nn1 = 36.0\nn2 = 36.0\nt0 = n0 - n1\nt1 = t0 * 1000.0\nt2 = t1 / 3600.0\nt3 = n2 * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "marketing executives for a certain chewing gum company projected a 30 percent increase in revenue this year over that of last year , but revenue this year actually decreased by 25 % . what percent of the projected revenue was the actual revenue ?", + "Output Program": [ + "n0 = 30.0\nn1 = 25.0\nt0 = n0 + 100.0\nt1 = 100.0 - n1\nt2 = t1 / t0\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "57.692307692307686" + ], + "split": "train" + }, + { + "Input": "find large number from below question the difference of two numbers is 2500 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder", + "Output Program": [ + "n0 = 2500.0\nn1 = 6.0\nn2 = 15.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nt2 = t0 / t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "2982" + ], + "split": "train" + }, + { + "Input": "which number should replace both the asterisks in ( * / 18 ) x ( * / 72 ) = 1 ?", + "Output Program": [ + "import math\nn0 = 18.0\nn1 = 72.0\nn2 = 1.0\nt0 = n0 * n1\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "last year department store x had a sales total for december that was 3 times the average ( arithmetic mean ) of the monthly sales totals for january through november . the sales total for december was what fraction of the sales total for the year ?", + "Output Program": [ + "n0 = 3.0\nt0 = 12.0 - 1.0\nt1 = n0 + t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.21428571428571427" + ], + "split": "train" + }, + { + "Input": "if a - b = 3 and a ^ 2 + b ^ 2 = 29 , find the value of ab", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 2.0\nn2 = 2.0\nn3 = 29.0\nt0 = math.sqrt(max(0, n3))\nt1 = t0 - n0\nt2 = t1 / n1\nt3 = n0 + t2\nt4 = t3 * t2\nanswer = n1 * t4\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "farm tax is levied on the 50 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . willam . mr . willam paid only $ 480 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :", + "Output Program": [ + "n0 = 50.0\nn1 = 3840.0\nn2 = 480.0\nt0 = n2 / n1\nt1 = t0 * 100.0\nt2 = t1 * 100.0\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "how many even 4 - digit numbers can be formed , so that the numbers are divisible by 4 and no two digits are repeated ?", + "Output Program": [ + "n0 = 4.0\nn1 = 4.0\nt0 = 100.0 / n0\nt1 = 2.0 * 3.0\nt2 = 10.0 - 2.0\nt3 = t2 - 1.0\nt4 = t0 - 3.0\nt5 = t3 * t3\nt6 = t2 * t3\nt7 = t4 - t1\nt8 = t5 * t7\nt9 = t6 * t1\nanswer = t8 + t9\nprint(answer)" + ], + "Output Answer": [ + "1120" + ], + "split": "train" + }, + { + "Input": "how many two - element subsets of { 6,7 , 8,9 } are there that do not contain the pair of elements 8 and 9 ?", + "Output Program": [ + "n0 = 6.0\nn1 = 7.0\nn2 = 8.0\nn3 = 9.0\nn4 = 8.0\nn5 = 9.0\n\nanswer = n3 - 4.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "there are 69 people that own pets . 15 people own only dogs , 10 people own only cats , 5 people own only cats and dogs , 3 people own cats , dogs and snakes . how many total snakes are there ?", + "Output Program": [ + "n0 = 69.0\nn1 = 15.0\nn2 = 10.0\nn3 = 5.0\nn4 = 3.0\nt0 = n1 + n2\nt1 = n3 + t0\nt2 = n4 + t1\nt3 = n0 - t2\nanswer = n4 + t3\nprint(answer)" + ], + "Output Answer": [ + "39" + ], + "split": "train" + }, + { + "Input": "an employee \u2019 s annual salary was increased $ 25,000 . if her new annual salary now equals $ 90,000 , what was the percent increase ?", + "Output Program": [ + "n0 = 25000.0\nn1 = 90000.0\nt0 = 0.25 * 100.0\nt1 = 100.0 - 10.0\nt2 = t1 * 1000.0\nt3 = t0 * 1000.0\nt4 = t2 - t3\nt5 = t2 / t4\nt6 = t5 - 1.0\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "38.46153846153846" + ], + "split": "train" + }, + { + "Input": "a car averages 70 mph for the first 4 hours of a trip and averages 60 mph for each additional hour . the average speed for the entire trip was 65 mph . how many hours long is the trip ?", + "Output Program": [ + "n0 = 70.0\nn1 = 4.0\nn2 = 60.0\nn3 = 65.0\nt0 = n3 * n1\nt1 = n0 * n1\nt2 = n2 - n3\nt3 = t0 - t1\nt4 = t3 / t2\nanswer = n1 + t4\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "the product of two numbers is 120 and the sum of their squares is 289 . the sum of the number is :", + "Output Program": [ + "import math\nn0 = 120.0\nn1 = 289.0\nt0 = n0 * 4.0\nt1 = n0 * 2.0\nt2 = n1 - t1\nt3 = math.sqrt(max(0, t2))\nt4 = t3**min(2.0, 5)\nt5 = t0 + t4\nanswer = math.sqrt(max(0, t5))\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "according to the formula f = 9 / 5 ( c ) + 32 , if the temperature in degrees farenheit ( f ) increases by 25 , by how much does the temperature in degrees celsius ( c ) increase ?", + "Output Program": [ + "n0 = 9.0\nn1 = 5.0\nn2 = 32.0\nn3 = 25.0\nt0 = n1 * n3\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "13.88888888888889" + ], + "split": "train" + }, + { + "Input": "kamal obtained 76 , 60 , 72 , 65 and 82 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?", + "Output Program": [ + "n0 = 76.0\nn1 = 60.0\nn2 = 72.0\nn3 = 65.0\nn4 = 82.0\nn5 = 100.0\nt0 = n0 + n1\nt1 = 1.0 + 4.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "71" + ], + "split": "train" + }, + { + "Input": "the number of natural numbers n such that ( n + 1 ) ^ 2 / ( n + 7 ) is an integer , is ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 7.0\n\nanswer = n2 - 3.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "total dinning bill of 8 people was $ 139.00 and 10 % tip divided the bill evenly ? what is the bill amount each person shared .", + "Output Program": [ + "n0 = 8.0\nn1 = 139.0\nn2 = 10.0\nt0 = 1.0 / n2\nt1 = t0 + 1.0\nt2 = n1 * t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "19.1125" + ], + "split": "train" + }, + { + "Input": "3 / 4 of 1 / 2 of 2 / 5 of 5060 = ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 1.0\nn3 = 2.0\nn4 = 2.0\nn5 = 5.0\nn6 = 5060.0\nt0 = n3 / n5\nt1 = n0 / n1\nt2 = n2 / n3\nt3 = t1 * t2\nt4 = t0 * t3\nanswer = n6 * t4\nprint(answer)" + ], + "Output Answer": [ + "759.0000000000001" + ], + "split": "train" + }, + { + "Input": "the average of 10 numbers is 40.2 . later it is found that two numbers have been wrongly copied . the first is 18 greater than the actual number and the second number added is 13 instead of 31 . find the correct average .", + "Output Program": [ + "n0 = 10.0\nn1 = 40.2\nn2 = 18.0\nn3 = 13.0\nn4 = 31.0\nt0 = n2 + n3\nt1 = n0 * n1\nt2 = t0 + t1\nt3 = t2 - n4\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "40.2" + ], + "split": "train" + }, + { + "Input": "$ 300 is divided amongst a , b and c so that a may get 2 / 3 as much as b and c together , b may get 6 / 9 as much as a and c together , then the share of a is", + "Output Program": [ + "n0 = 300.0\nn1 = 2.0\nn2 = 3.0\nn3 = 6.0\nn4 = 9.0\nt0 = n1 / n2\nt1 = t0 + 1.0\nt2 = n0 / t1\nanswer = t2 * t0\nprint(answer)" + ], + "Output Answer": [ + "120.00000000000001" + ], + "split": "train" + }, + { + "Input": "how many x ways can you group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nt0 = 2.0**min(n0, 5)\nanswer = n1 * t0\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "in the game of dubblefud , yellow chips , blue chips and green chips are each worth 2 , 4 and 5 points respectively . in a certain selection of chips , the product of the point values of the chips is 16000 . if the number of blue chips in this selection equals the number of green chips , how many yellow chips are in the selection ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 5.0\nn3 = 16000.0\nt0 = n0 * n1\nt1 = 10.0**min(2.0, 5)\nt2 = n2 * t0\nt3 = n3 / t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "if a - b = 3 and a ( power 2 ) + b ( power 2 ) = 25 , find the value of ab .", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 2.0\nn3 = 25.0\nt0 = n0**min(n1, 5)\nt1 = n3 - t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "the cash realised on selling a 14 % stock is rs . 106.25 , brokerage being 1 / 4 % is", + "Output Program": [ + "n0 = 14.0\nn1 = 106.25\nn2 = 1.0\nn3 = 4.0\nt0 = n2 / n3\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "106" + ], + "split": "train" + }, + { + "Input": "rice weighing 25 / 4 pounds was divided equally and placed in 4 containers . how many ounces of rice were in each container ? ( note that 1 pound = 16 ounces )", + "Output Program": [ + "n0 = 25.0\nn1 = 4.0\nn2 = 4.0\nn3 = 1.0\nn4 = 16.0\nt0 = n0 / n1\nt1 = n4 * t0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "when a number is divided by 13 , the remainder is 11 . when the same number is divided by 17 , then remainder is 9 . what is the number ?", + "Output Program": [ + "n0 = 13.0\nn1 = 11.0\nn2 = 17.0\nn3 = 9.0\nt0 = 10.0 + 12.0\nt1 = t0 + 4.0\nt2 = n0 * t1\nanswer = n1 + t2\nprint(answer)" + ], + "Output Answer": [ + "349" + ], + "split": "train" + }, + { + "Input": "a football player scores 3 goals in his fifth match thus increasing his average goals score by 0.2 . the total number of goals in his 5 matches would be", + "Output Program": [ + "n0 = 3.0\nn1 = 0.2\nn2 = 5.0\nt0 = n0 * 4.0\nt1 = n2 * 4.0\nt2 = n1 * t1\nt3 = t0 - t2\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "if k is an integer and 0.00010101 x 10 ^ k is greater than 10 , what is the least possible value of k ?", + "Output Program": [ + "import math\nn0 = 0.00010101\nn1 = 10.0\nn2 = 10.0\nt0 = n2 / n0\nt1 = math.log(max(1e-5, n1), 2)\nt2 = math.log(max(1e-5, t0), 2)\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "4.9956356288922485" + ], + "split": "train" + }, + { + "Input": "what least number must be subtracted from 42398 so that remaining no . is divisible by 15", + "Output Program": [ + "import math\nn0 = 42398.0\nn1 = 15.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a man is 24 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is :", + "Output Program": [ + "n0 = 24.0\nt0 = 2.0 * 2.0\nt1 = 2.0 - 1.0\nt2 = t0 - 2.0\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "pat , kate and mark charged a total of 180 hours to a certain project . if pat charged twice as much time to the project as kate and 1 / 3 as much times as mark , how many more hours did mark charge to the project than kate .", + "Output Program": [ + "n0 = 180.0\nn1 = 1.0\nn2 = 3.0\nt0 = n1 + 2.0\nt1 = n2 * 2.0\nt2 = t0 + t1\nt3 = t1 - n1\nt4 = n0 / t2\nanswer = t4 * t3\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "the difference between the squares of two consecutive odd integers is a square < 1000 whose root equals the combined sum of the digits of the two integers . what is the sum of the digits m of the larger integer ?", + "Output Program": [ + "import math\nn0 = 1000.0\nt0 = n0 / 10.0\nt1 = t0 + 1.0\nt2 = t1**min(2.0, 5)\nt3 = t1 - 2.0\nt4 = t3**min(2.0, 5)\nt5 = t2 - t4\nt6 = math.sqrt(max(0, t5))\nanswer = t6 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "if f ( x ) = 2 x + 3 , & g ( x ) = ( x - 3 ) / 2 , then what is the value of , fo ( fo ( go ( go ( fo ( fo ( go ( go . . . . . . . . . . . . . . . . ( fo ( fo ( go ( gof ( x ) ) ) ) ) . . . . . ) ) ) ) ) ) ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 3.0\nn3 = 2.0\nt0 = n1 * 4.0\nt1 = n0 + t0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "find the number which is nearest to 3105 and is exactly divisible by 21", + "Output Program": [ + "n0 = 3105.0\nn1 = 21.0\nt0 = n0 % n1\nt1 = n1 - t0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "3108" + ], + "split": "train" + }, + { + "Input": "p is 3 times as old as q . in 11 years , p will be twice as old as q . how old was p 3 years ago ?", + "Output Program": [ + "n0 = 3.0\nn1 = 11.0\nn2 = 3.0\nt0 = n0 * n1\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "in a class of 40 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 13 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?", + "Output Program": [ + "n0 = 40.0\nn1 = 2.0\nn2 = 12.0\nn3 = 1.0\nn4 = 13.0\nn5 = 2.0\nn6 = 3.0\nn7 = 2.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n1 * n4\nt3 = t1 + t2\nt4 = n4 + t1\nt5 = n1 + t4\nt6 = n0 - t5\nt7 = t6 - n3\nt8 = n6 * t7\nt9 = t3 + t8\nanswer = t0 - t9\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "on rainy mornings , mo drinks exactly n cups of hot chocolate ( assume that n is an integer ) . on mornings that are not rainy , mo drinks exactly 3 cups of tea . last week mo drank a total of 26 cups of tea and hot chocolate together . if during that week mo drank 10 more tea cups than hot chocolate cups , then how many rainy days were there last week ?", + "Output Program": [ + "n0 = 3.0\nn1 = 26.0\nn2 = 10.0\nt0 = n0 + 4.0\nt1 = n1 + n2\nt2 = t1 / 2.0\nt3 = t2 / n0\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "the mean of 50 observations was 36 . it was found later that an observation 45 was wrongly taken as 23 . the corrected new mean is ?", + "Output Program": [ + "n0 = 50.0\nn1 = 36.0\nn2 = 45.0\nn3 = 23.0\nt0 = n0 * n1\nt1 = n0 - 2.0\nt2 = t1 - n3\nt3 = t0 + t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "36.5" + ], + "split": "train" + }, + { + "Input": "an individual deposited 20 % of 25 % of 30 % of what he had into his account with a bank . if he deposited rs . 750 , how much was he having initially with him before depositing ?", + "Output Program": [ + "n0 = 20.0\nn1 = 25.0\nn2 = 30.0\nn3 = 750.0\nt0 = n2 / 100.0\nt1 = n0 / 100.0\nt2 = n1 / 100.0\nt3 = t1 * t2\nt4 = t0 * t3\nanswer = n3 / t4\nprint(answer)" + ], + "Output Answer": [ + "50000" + ], + "split": "train" + }, + { + "Input": "in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 8 eggs . if the cost of each pound of rice is $ 0.33 , then how many r cents does a liter of kerosene cost ? [ one dollar has 100 cents . ]", + "Output Program": [ + "n0 = 8.0\nn1 = 0.33\nn2 = 100.0\nt0 = 1.0 / 2.0\nt1 = n1 * n2\nt2 = n0 / t0\nt3 = t2 / 12.0\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "44" + ], + "split": "train" + }, + { + "Input": "dacid obtained 96 , 98 , 99 , 100 and 98 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?", + "Output Program": [ + "n0 = 96.0\nn1 = 98.0\nn2 = 99.0\nn3 = 100.0\nn4 = 98.0\nn5 = 100.0\nt0 = n0 + n1\nt1 = 10.0 / 2.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "98.2" + ], + "split": "train" + }, + { + "Input": "a lemonade stand sold only small and large cups of lemonade on tuesday . 3 / 5 of the cups sold were small and the rest were large . if the large cups were sold for 1 / 6 as much as the small cups , what fraction of tuesday ' s total revenue was from the sale of large cups ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 1.0\nn3 = 6.0\nt0 = n2 / n3\nt1 = n0 / n1\nt2 = t1 * 10.0\nt3 = t0 * t2\nt4 = t2 * t2\nt5 = 10.0 - t2\nt6 = t3 * t5\nt7 = t4 + t6\nanswer = t6 / t7\nprint(answer)" + ], + "Output Answer": [ + "0.1" + ], + "split": "train" + }, + { + "Input": "what is difference between biggest and smallest fraction among 2 / 3 , 3 / 4 , 4 / 5 and 5 / 7", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 3.0\nn3 = 4.0\nn4 = 4.0\nn5 = 5.0\nn6 = 5.0\nn7 = 7.0\nt0 = n3 / n5\nt1 = n0 / n1\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "0.13333333333333341" + ], + "split": "train" + }, + { + "Input": "last year department store x had a sales total for december that was 5 times the average ( arithmetic mean ) of the monthly sales totals for january through november . the sales total for december was what fraction of the sales total for the year ?", + "Output Program": [ + "n0 = 5.0\nt0 = 12.0 - 1.0\nt1 = n0 + t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.3125" + ], + "split": "train" + }, + { + "Input": "the vertex of a rectangle are ( 1 , 0 ) , ( 5 , 0 ) , ( 1 , 2 ) and ( 5 , 2 ) respectively . if line l passes through the origin and divided the rectangle into two identical quadrilaterals , what is the slope of line l ?", + "Output Program": [ + "n0 = 1.0\nn1 = 0.0\nn2 = 5.0\nn3 = 0.0\nn4 = 1.0\nn5 = 2.0\nn6 = 5.0\nn7 = 2.0\nt0 = n2 - n0\nt1 = t0 + n5\nt2 = t1 / n5\nanswer = n0 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.3333333333333333" + ], + "split": "train" + }, + { + "Input": "if a 10 percent deposit that has been paid toward the purchase of a certain product is $ 80 , how much more remains to be paid ?", + "Output Program": [ + "n0 = 10.0\nn1 = 80.0\nt0 = 100.0 / n0\nt1 = n1 * t0\nanswer = t1 - n1\nprint(answer)" + ], + "Output Answer": [ + "720" + ], + "split": "train" + }, + { + "Input": "in the xy - plane , the point ( 2 , 1 ) is the center of a circle . the point ( - 2 , 1 ) lies inside the circle and the point ( 2 , - 5 ) lies outside the circle . if the radius r of the circle is an integer , then r =", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 2.0\nn3 = 1.0\nn4 = 2.0\nn5 = 5.0\nt0 = n0 + n0\nanswer = n1 + t0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "if k is the greatest positive integer such that 4 ^ k is a divisor of 16 ! then k =", + "Output Program": [ + "n0 = 4.0\nn1 = 16.0\nt0 = n1 / n0\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "the difference between the value of a number increased by 12.5 % and the value of the original number decreased by 25 % is 30 . what is the original number t ?", + "Output Program": [ + "n0 = 12.5\nn1 = 25.0\nn2 = 30.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = t0 + 1.0\nt3 = 1.0 - t1\nt4 = t2 - t3\nanswer = n2 / t4\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "evaluate : | 4 - 8 ( 3 - 12 ) | - | 5 - 11 | = ?", + "Output Program": [ + "n0 = 4.0\nn1 = 8.0\nn2 = 3.0\nn3 = 12.0\nn4 = 5.0\nn5 = 11.0\nt0 = n2 - n3\nt1 = n4 - n5\nt2 = n1 * t0\nt3 = -t1\nt4 = n0 - t2\nanswer = t4 - t3\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "train" + }, + { + "Input": "( 168 % of 1265 ) \u00f7 6 = ?", + "Output Program": [ + "n0 = 168.0\nn1 = 1265.0\nn2 = 6.0\nt0 = n0 / 100.0\nt1 = n1 * t0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "354.2" + ], + "split": "train" + }, + { + "Input": "there are 15 teams in the hockey league , and each team faces all the other teams 10 times each . how many games are played in the season ?", + "Output Program": [ + "n0 = 15.0\nn1 = 10.0\nt0 = n0 - 1.0\nt1 = n0 * t0\nt2 = n1 * t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "1050" + ], + "split": "train" + }, + { + "Input": "if 3 : 12 : : x : 16 , then find the value of x", + "Output Program": [ + "n0 = 3.0\nn1 = 12.0\nn2 = 16.0\nt0 = n0 * n1\nt1 = n1 + t0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "in cliff \u2019 s impressive rock collection , there are half as many igneous rocks as sedimentary rocks . of the igneous rocks , 1 / 3 are shiny and the rest are matte , while 1 / 5 of the sedimentary rocks are shiny . if there are 30 shiny igneous rocks , how many total rocks does cliff have ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 5.0\nn4 = 30.0\nt0 = n0 * n1\nt1 = n4 * t0\nt2 = t1 / n0\nt3 = n1 * t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "270" + ], + "split": "train" + }, + { + "Input": "a man has some hens and cows . if the number of heads be 50 and the number of feet equals 140 , then the number of hens will be :", + "Output Program": [ + "n0 = 50.0\nn1 = 140.0\nt0 = n0 * 4.0\nt1 = t0 - n1\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "if p / q = 6 / 7 , then 2 p + q = ?", + "Output Program": [ + "n0 = 6.0\nn1 = 7.0\nn2 = 2.0\nt0 = n0 * n2\nanswer = n1 + t0\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "mary and mike enter into a partnership by investing $ 800 and $ 200 respectively . at the end of one year , they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business . if mary received $ 1200 more than mike did , what was the profit made by their business in that year ?", + "Output Program": [ + "n0 = 800.0\nn1 = 200.0\nn2 = 1200.0\nt0 = n0 / 1000.0\nt1 = n1 / 1000.0\nt2 = 1.0 / 3.0\nt3 = t0 - t1\nt4 = 1.0 - t2\nt5 = t3 * t4\nanswer = n2 / t5\nprint(answer)" + ], + "Output Answer": [ + "2999.9999999999995" + ], + "split": "train" + }, + { + "Input": "an owner of a pizza stand sold small slices of pizza for rs . 150 each and large slices for rs . 250 each . one night he sold 5000 slices , for a total of rs . 10.50 lakh . how many small slices were sold ?", + "Output Program": [ + "n0 = 150.0\nn1 = 250.0\nn2 = 5000.0\nn3 = 10.5\nt0 = 1000.0 * 3.0\nanswer = n2 - t0\nprint(answer)" + ], + "Output Answer": [ + "2000" + ], + "split": "train" + }, + { + "Input": "light glows for every 21 seconds . how many max . times did it glow between 1 : 57 : 58 and 3 : 20 : 47 am .", + "Output Program": [ + "n0 = 21.0\nn1 = 1.0\nn2 = 57.0\nn3 = 58.0\nn4 = 3.0\nn5 = 20.0\nn6 = 47.0\nt0 = n6 + 2.0\nt1 = 2.0 + 60.0\nt2 = n5 + t1\nt3 = t2 * 60.0\nt4 = t0 + t3\nanswer = t4 / n0\nprint(answer)" + ], + "Output Answer": [ + "236.61904761904762" + ], + "split": "train" + }, + { + "Input": "2 , 3 , 6 , 15 , _ , 123 ?", + "Output Program": [ + "n0 = 6.0\nn1 = 5.0\nn2 = 2.0\nn3 = 19.0\nt0 = n0 * n1\nt1 = n2 * t0\nt2 = t1 / n2\nanswer = t2 + 3.0\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "canister c is 1 / 2 full of water and canister d , which has twice the capacity of canister c , is 1 / 3 full of water . if the water in canister d is poured in canister c until canister c is completely full of water , canister d will still contain what fraction of its capacity of water ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 1.0\nn3 = 3.0\nt0 = n0 / n3\nt1 = n0 / n1\nt2 = t1 * t1\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "0.08333333333333331" + ], + "split": "train" + }, + { + "Input": "the average monthly salary of 20 employees in an organisation is rs . 1600 . if the manager ' s salary is added , then the average salary increases by rs . 100 . what is the manager ' s monthly salary ?", + "Output Program": [ + "n0 = 20.0\nn1 = 1600.0\nn2 = 100.0\nt0 = n1 + n2\nt1 = n0 + 1.0\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "3700" + ], + "split": "train" + }, + { + "Input": "a man spend 1 / 5 of his salary on food , 1 / 10 of his salary on house rent and 3 / 5 salary on clothes . he still has $ 19000 left with him . find salary . .", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 1.0\nn3 = 10.0\nn4 = 3.0\nn5 = 5.0\nn6 = 19000.0\nt0 = n0 / n1\nt1 = n0 / n3\nt2 = n4 / n1\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n0 - t4\nanswer = n6 / t5\nprint(answer)" + ], + "Output Answer": [ + "190000.00000000003" + ], + "split": "train" + }, + { + "Input": "in an examination , there were 2,000 candidates , out of which 900 candidates were girls and rest were boys . if 30 % of the boys and 32 % of the girls passed , then the total percentage of failed candidates is ?", + "Output Program": [ + "n0 = 2000.0\nn1 = 900.0\nn2 = 30.0\nn3 = 32.0\nt0 = n2 / 100.0\nt1 = n3 / 100.0\nt2 = 10.0 * 100.0\nt3 = t2 * 2.0\nt4 = n1 * t1\nt5 = t3 - n1\nt6 = t0 * t5\nt7 = t3 - t6\nt8 = t7 - t4\nt9 = t8 / t3\nanswer = t9 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "69.1" + ], + "split": "train" + }, + { + "Input": "if 2 x + y = 7 and x + 2 y = 10 , then ( x + y ) / 3 =", + "Output Program": [ + "n0 = 2.0\nn1 = 7.0\nn2 = 2.0\nn3 = 10.0\nn4 = 3.0\nt0 = n0 * n1\nt1 = n0 * n0\nt2 = t0 - n3\nt3 = t1 - 1.0\nt4 = t2 / t3\nt5 = n0 * t4\nt6 = n1 - t5\nt7 = t4 + t6\nanswer = t7 / n4\nprint(answer)" + ], + "Output Answer": [ + "1.888888888888889" + ], + "split": "train" + }, + { + "Input": "christine selects an item at a 25 % off ticket price sale . the item is ticket priced at $ 25 . how much should christine expect to pay at the register ?", + "Output Program": [ + "n0 = 25.0\nn1 = 25.0\nt0 = n0 * n0\nt1 = t0 / 100.0\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "18.75" + ], + "split": "train" + }, + { + "Input": "two employees x and y are paid a total of rs . 500 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?", + "Output Program": [ + "n0 = 500.0\nn1 = 120.0\nt0 = 1.0 + 4.0\nt1 = t0 * 2.0\nt2 = t1 + 1.0\nt3 = n0 * t1\nt4 = t2 * 2.0\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "227.27272727272728" + ], + "split": "train" + }, + { + "Input": "calculate the average of all the numbers between 11 and 27 which are divisible by 2 .", + "Output Program": [ + "import math\nn0 = 11.0\nn1 = 27.0\nn2 = 2.0\nt0 = n0 / n2\nt1 = n1 / n2\nt2 = math.floor(t0)\nt3 = math.floor(t1)\nt4 = t2 + 1.0\nt5 = t4 + t3\nt6 = t5 / 2.0\nanswer = n2 * t6\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "a gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same . if there are 7 rows or 6 rows or 4 rows , then no tree will be left . find the least number of trees required", + "Output Program": [ + "n0 = 7.0\nn1 = 6.0\nn2 = 4.0\nt0 = n1 * n2\nt1 = n0 * t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "84" + ], + "split": "train" + }, + { + "Input": "if { x } is the product of all even integers from 1 to x inclusive , what is the greatest prime factor of { 22 } + { 20 } ?", + "Output Program": [ + "n0 = 1.0\nn1 = 22.0\nn2 = 20.0\nt0 = n1 + n2\nt1 = n0 * 2.0\nt2 = t0 / 2.0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "if x gets 25 % more than y and y gets 20 % more than z , the share of z out of rs . 1480 will be :", + "Output Program": [ + "n0 = 25.0\nn1 = 20.0\nn2 = 1480.0\nt0 = n1 / 100.0\nt1 = n0 / 100.0\nt2 = t0 + 1.0\nt3 = t1 + 1.0\nt4 = t3 * t2\nt5 = t2 + t4\nt6 = t5 + 1.0\nanswer = n2 / t6\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "train" + }, + { + "Input": "find the least number must be subtracted from 724946 so that remaining no . is divisible by 10 ?", + "Output Program": [ + "import math\nn0 = 724946.0\nn1 = 10.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "if x is 20 percent more than y and y is 30 percent less than z , then x is what percent of z ?", + "Output Program": [ + "n0 = 20.0\nn1 = 30.0\nt0 = n0 / 100.0\nt1 = 100.0 - n1\nt2 = t0 + 1.0\nanswer = t2 * t1\nprint(answer)" + ], + "Output Answer": [ + "84" + ], + "split": "train" + }, + { + "Input": "a mixture of 180 liters of wine and water contains 20 % water . how much more water should be added so that water becomes 25 % of the new mixture ?", + "Output Program": [ + "n0 = 180.0\nn1 = 20.0\nn2 = 25.0\nt0 = n2 / 100.0\nt1 = n1 / 100.0\nt2 = n0 * t0\nt3 = n0 * t1\nt4 = 1.0 - t0\nt5 = t2 - t3\nanswer = t5 / t4\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "what is the sum between the place values of three 7 ' s in the numeral 87953.0727", + "Output Program": [ + "n0 = 7.0\nn1 = 87953.0727\nt0 = n0 * 10.0\nt1 = n0 * 1000.0\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "7070" + ], + "split": "train" + }, + { + "Input": "the average salary of all the workers in a workshop is rs . 8000 . the average salary of 6 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is ?", + "Output Program": [ + "n0 = 8000.0\nn1 = 6.0\nn2 = 12000.0\nn3 = 6000.0\nt0 = n2 - n0\nt1 = n0 - n3\nt2 = n1 * t0\nt3 = t2 / t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "in a tree , 2 / 5 of the birds are robins while the rest are bluejays . if 1 / 3 of the robins are female and 2 / 3 of the bluejays are female , what fraction of the birds in the tree are male ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 1.0\nn3 = 3.0\nn4 = 2.0\nn5 = 3.0\nt0 = n0 / n1\nt1 = n0 / n3\nt2 = 3.0 / n1\nt3 = n2 / n3\nt4 = t0 * t1\nt5 = t2 * t3\nanswer = t4 + t5\nprint(answer)" + ], + "Output Answer": [ + "0.4666666666666667" + ], + "split": "train" + }, + { + "Input": "the simple interest on a sum of money will be rs . 700 after 10 years . if the principal is trebled after 5 years what will be the total interest at the end of the tenth year ?", + "Output Program": [ + "n0 = 700.0\nn1 = 10.0\nn2 = 5.0\nt0 = n0 / n1\nt1 = n2 * t0\nt2 = t1 * 3.0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "1400" + ], + "split": "train" + }, + { + "Input": "barbata invests $ 2000 in the national bank at 5 % . how much additional money must she invest at 8 % so that the total annual income will be equal to 6 % of her entire investment ?", + "Output Program": [ + "n0 = 2000.0\nn1 = 5.0\nn2 = 8.0\nn3 = 6.0\nt0 = n3 / 100.0\nt1 = n1 / 100.0\nt2 = n2 / 100.0\nt3 = n0 * t0\nt4 = n0 * t1\nt5 = t2 - t0\nt6 = t3 - t4\nanswer = t6 / t5\nprint(answer)" + ], + "Output Answer": [ + "999.9999999999998" + ], + "split": "train" + }, + { + "Input": "( ( 1 ^ ( m + 1 ) ) / ( 5 ^ ( m + 1 ) ) ) ( ( 1 ^ 18 ) / ( 4 ^ 18 ) ) = 1 / ( 2 ( 10 ) ^ 35 ) what is m ?", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 5.0\nn3 = 1.0\nn4 = 1.0\nn5 = 18.0\nn6 = 4.0\nn7 = 18.0\nn8 = 1.0\nn9 = 2.0\nn10 = 10.0\nn11 = 35.0\nt0 = n5 * n9\nt1 = t0 - 1.0\nanswer = t1 - n0\nprint(answer)" + ], + "Output Answer": [ + "34" + ], + "split": "train" + }, + { + "Input": "a student chose a number , multiplied it by 2 , then subtracted 138 from the result and got 106 . what was the number he chose ?", + "Output Program": [ + "n0 = 2.0\nn1 = 138.0\nn2 = 106.0\nt0 = n1 + n2\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "122" + ], + "split": "train" + }, + { + "Input": "a charitable association sold an average of 66 raffle tickets per member . among the female members , the average was 70 raffle tickets . the male to female ratio of the association is 1 : 2 . what was the average number q of tickets sold by the male members of the association", + "Output Program": [ + "n0 = 66.0\nn1 = 70.0\nn2 = 1.0\nn3 = 2.0\nt0 = n2 + n3\nt1 = n1 * n3\nt2 = n0 * t0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "58" + ], + "split": "train" + }, + { + "Input": "subtract the absolute value from the local value of 4 in 564823", + "Output Program": [ + "n0 = 4.0\nn1 = 564823.0\nt0 = n0 * 100.0\nanswer = t0 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "4000" + ], + "split": "train" + }, + { + "Input": "machine x and machine b are each used to manufacture 660 sprockets . it takes machine x 10 hours longer to produce 660 sprockets than machine b . machine b produces 10 percent more sprockets per hour than machine x . how many sprockets per hour does machine x produces ?", + "Output Program": [ + "n0 = 660.0\nn1 = 10.0\nn2 = 660.0\nn3 = 10.0\nt0 = n1 / 100.0\nt1 = t0 + 1.0\nt2 = t1 * 100.0\nanswer = n0 / t2\nprint(answer)" + ], + "Output Answer": [ + "5.999999999999999" + ], + "split": "train" + }, + { + "Input": "the ages of two persons differ by 16 years . 6 years ago , the elder one was 3 times as old as the younger one . what are their present ages of the elder person", + "Output Program": [ + "n0 = 16.0\nn1 = 6.0\nn2 = 3.0\nt0 = n1 * n2\nt1 = n0 - n1\nt2 = t0 + t1\nt3 = t2 / 2.0\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "the average of 5 quantities is 10 . the average of 3 of them is 4 . what is the average of remaining 2 numbers ?", + "Output Program": [ + "n0 = 5.0\nn1 = 10.0\nn2 = 3.0\nn3 = 4.0\nn4 = 2.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = t0 - t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "if the sum of two numbers is 22 and the sum of their squares is 460 , then the product of the numbers is", + "Output Program": [ + "n0 = 22.0\nn1 = 460.0\nt0 = n0**min(2.0, 5)\nt1 = t0 - n1\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "what is the value of n if the sum of the consecutive odd integers from 1 to n equals 169 ?", + "Output Program": [ + "import math\nn0 = 1.0\nn1 = 169.0\nt0 = n0 * 2.0\nt1 = math.sqrt(max(0, n1))\nt2 = t1 * 2.0\nt3 = t2 - t0\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "the total number of plums that grew during each year on a certain plum tree was equal to the number of plums that grew during the previous year , less the age of the tree in years ( rounded to the nearest lower integer . ) during its 3 rd year , this plum tree grew 50 plums . how many plums did it grow during its 6 th year ?", + "Output Program": [ + "n0 = 3.0\nn1 = 50.0\nn2 = 6.0\nt0 = 1.0 + 4.0\nt1 = n1 - 4.0\nt2 = t1 - t0\nanswer = t2 - n2\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "in a group of 68 students , each student is registered for at least one of 3 classes \u2013 history , math and english . 20 - one students are registered for history , 20 - 6 students are registered for math , and thirty - 4 students are registered for english . if only 3 students are registered for all 3 classes , how many students are registered for exactly two classes ?", + "Output Program": [ + "n0 = 68.0\nn1 = 3.0\nn2 = 20.0\nn3 = 20.0\nn4 = 6.0\nn5 = 4.0\nn6 = 3.0\nn7 = 3.0\nt0 = n2 + 1.0\nt1 = n2 + n4\nt2 = n2 + 10.0\nt3 = n1 * 2.0\nt4 = t0 + t1\nt5 = n5 + t2\nt6 = t4 + t5\nt7 = t6 - n0\nanswer = t7 - t3\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "in march mrs bil ' s earnings were 80 percent of the bil family ' s total income . in april mrs bil earned 10 percent more than in may . if the rest of the family ' s income was the same both months , then , in june , mrs bil ' s earnings were approximately what percent of the bil family ' s total income ?", + "Output Program": [ + "n0 = 80.0\nn1 = 10.0\nt0 = 100.0 - n1\nt1 = 100.0 - n0\nt2 = t0 / 100.0\nt3 = n0 * t2\nt4 = t3 + t1\nt5 = t3 / t4\nt6 = t5 * 100.0\nanswer = t6 + 4.0\nprint(answer)" + ], + "Output Answer": [ + "82.26086956521739" + ], + "split": "train" + }, + { + "Input": "how many prime numbers are between 29 / 4 and 87 / 5 ?", + "Output Program": [ + "import math\nn0 = 29.0\nn1 = 4.0\nn2 = 87.0\nn3 = 5.0\n\nanswer = math.floor(2.0)\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a will was written such that an estate would be divided among 4 beneficiaries with the remainder donated to charity . one stipulation in the will is that no one beneficiary can receive an amount within 20 % of another ' s amount . if one of the beneficiaries received $ 40000 , what is the smallest possible range between the highest and lowest amounts ( rounded to the nearest dollar ) among the 4 beneficiaries ?", + "Output Program": [ + "n0 = 4.0\nn1 = 20.0\nn2 = 40000.0\nn3 = 4.0\nt0 = n1 / 100.0\nt1 = 1.0 - t0\nt2 = n2 * t1\nt3 = t2 * t1\nt4 = t3 * t1\nanswer = n2 - t4\nprint(answer)" + ], + "Output Answer": [ + "19520" + ], + "split": "train" + }, + { + "Input": "the sum of the present ages of a , b , c is 57 years . 3 years ago their ages were in the ratio 1 : 2 : 3 . what is the present age of a ?", + "Output Program": [ + "n0 = 57.0\nn1 = 3.0\nn2 = 1.0\nn3 = 2.0\nn4 = 3.0\nt0 = n2 + n3\nt1 = n1 * 3.0\nt2 = n1 + t0\nt3 = n0 - t1\nt4 = t3 / t2\nanswer = n1 + t4\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "1 , 1 , 2 , 1 , 2 , 3 , 1 , 2 , 3 , 4 , 1 , 2 , __ ?", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 2.0\nn3 = 1.0\nn4 = 2.0\nn5 = 3.0\nn6 = 1.0\nn7 = 2.0\nn8 = 3.0\nn9 = 4.0\nn10 = 1.0\nn11 = 2.0\n\nanswer = n5 * n0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "in a party every person shakes hands with every other person . if there were a total of 153 handshakes in the party then what is the number of persons present in the party ?", + "Output Program": [ + "import math\nn0 = 153.0\nt0 = n0 * 2.0\nt1 = t0 * 4.0\nt2 = t1 + 1.0\nt3 = math.sqrt(max(0, t2))\nt4 = t3 + 1.0\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "in the xy - coordinate system , if ( m , n ) and ( m + 1 , n + k ) are two points on the line with the equation x = 2 y + 5 , then k =", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 5.0\nt0 = n0 + n2\nt1 = t0 - n2\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "the least number by which 72 must be multiplied in order to produce a multiple of 112 , is", + "Output Program": [ + "import scipy\nn0 = 72.0\nn1 = 112.0\nt0 = scipy.gcd(int(n0), int(n1))\nanswer = n1 / t0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "find the number , difference between number and its 3 / 5 is 58 .", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 58.0\nt0 = n2 / 2.0\nanswer = n1 * t0\nprint(answer)" + ], + "Output Answer": [ + "145" + ], + "split": "train" + }, + { + "Input": "find the value of 3 + 2 . ( 8 - 3 )", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 8.0\nn3 = 3.0\nt0 = n1 / 100.0\nt1 = n0 + t0\nanswer = t1 * n2\nprint(answer)" + ], + "Output Answer": [ + "24.16" + ], + "split": "train" + }, + { + "Input": "when jessica withdrew $ 200 from her bank account , her account balance decreased by 2 / 5 . if she deposits an amount equal to 1 / 5 of the remaining balance , what will be the final balance in her bank account ?", + "Output Program": [ + "n0 = 200.0\nn1 = 2.0\nn2 = 5.0\nn3 = 1.0\nn4 = 5.0\nt0 = n3 / n4\nt1 = 3.0 / n2\nt2 = n3 + t0\nt3 = n3 - t1\nt4 = n0 / t3\nt5 = t4 - n0\nanswer = t2 * t5\nprint(answer)" + ], + "Output Answer": [ + "360" + ], + "split": "train" + }, + { + "Input": "in a certain company , the ratio of the number of managers to the number of non - managers in any department must always be greater than 7 : 32 . in the company , what is the maximum number of non - managers in a department that has 9 managers ?", + "Output Program": [ + "import math\nn0 = 7.0\nn1 = 32.0\nn2 = 9.0\nt0 = n1 * n2\nt1 = t0 / n0\nanswer = math.floor(t1)\nprint(answer)" + ], + "Output Answer": [ + "41" + ], + "split": "train" + }, + { + "Input": "a certain pair of used shoes can be repaired for $ 13.50 and will last for 1 year . a pair of the same kind of shoes can be purchased new for $ 32.00 and will last for 2 years . the average cost per year of the new shoes is what percent greater than the cost of repairing the used shoes ?", + "Output Program": [ + "n0 = 13.5\nn1 = 1.0\nn2 = 32.0\nn3 = 2.0\nt0 = n0 * n3\nt1 = n2 - t0\nt2 = t1 / t0\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "18.51851851851852" + ], + "split": "train" + }, + { + "Input": "if x = 55 + 2 q and y = 4 q + 41 , then for what value of q , x is equal to y ?", + "Output Program": [ + "n0 = 55.0\nn1 = 2.0\nn2 = 4.0\nn3 = 41.0\nt0 = 3.0 + 4.0\nt1 = n1 * t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "if one person completes a journey in 10 hrs . he travels 1 st half of the journey at the rate of 21 km / hr and 2 nd half at therate of 24 km / hr . find the total journey in km .", + "Output Program": [ + "n0 = 10.0\nn1 = 1.0\nn2 = 21.0\nn3 = 2.0\nn4 = 24.0\nt0 = n0 / n3\nt1 = n2 * t0\nt2 = n4 * t0\nanswer = t1 + t2\nprint(answer)" + ], + "Output Answer": [ + "225" + ], + "split": "train" + }, + { + "Input": "m = { - 6 , - 5 , - 4 , - 3 , - 2 , - 1 } t = { - 5 , - 4 , - 3 , - 2 , - 1 , 0 , 1 , 2 } if an integer is to be randomly selected from set m above and an integer is to be randomly selected from set t above , what is the probability that the product of the two integers will be negative ?", + "Output Program": [ + "n0 = 6.0\nn1 = 5.0\nn2 = 4.0\nn3 = 3.0\nn4 = 2.0\nn5 = 1.0\nn6 = 5.0\nn7 = 4.0\nn8 = 3.0\nn9 = 2.0\nn10 = 1.0\nn11 = 0.0\nn12 = 1.0\nn13 = 2.0\nt0 = n2 * n4\nanswer = n4 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.25" + ], + "split": "train" + }, + { + "Input": "what is the tenth digit of ( 5 ! * 5 ! - 5 ! * 3 ! ) / 5 ?", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 5.0\nn2 = 5.0\nn3 = 3.0\nn4 = 5.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(n3)))\nt2 = 10.0 * 100.0\nt3 = t0 * t0\nt4 = t0 * t1\nt5 = t3 - t4\nt6 = t5 / n0\nt7 = t6 / t2\nanswer = math.floor(t7)\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "30 pens and 75 pencils were purchased for 570 . if the average price of a pencil was 2.00 , find the average price of a pen .", + "Output Program": [ + "n0 = 30.0\nn1 = 75.0\nn2 = 570.0\nn3 = 2.0\nt0 = n1 * n3\nt1 = n2 - t0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "two trains of equal are running on parallel lines in the same direction at 42 km / hr and 36 km / hr . the faster train passes the slower train in 36 sec . the length of each train is ?", + "Output Program": [ + "n0 = 42.0\nn1 = 36.0\nn2 = 36.0\nt0 = n0 - n1\nt1 = t0 * 1000.0\nt2 = t1 / 3600.0\nt3 = n2 * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 16000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is :", + "Output Program": [ + "n0 = 8000.0\nn1 = 7.0\nn2 = 16000.0\nn3 = 6000.0\nt0 = n2 - n0\nt1 = n0 - n3\nt2 = n1 * t0\nt3 = t2 / t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "when positive integer w is divided by 13 , the remainder is 2 . when n is divided by 8 , the remainder is 5 . how many such values are less than 180 ?", + "Output Program": [ + "n0 = 13.0\nn1 = 2.0\nn2 = 8.0\nn3 = 5.0\nn4 = 180.0\nt0 = n1 + n3\nt1 = n0 * t0\nt2 = t1 % n2\nanswer = t2 - n1\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "a certain box has 11 cards and each card has one of the integers from 1 to 11 inclusive . each card has a different number . if 2 different cards are selected at random , what is the probability that the sum of the numbers written on the 2 cards is less than the average ( arithmetic mean ) of all the numbers written on the 11 cards ?", + "Output Program": [ + "import math\nn0 = 11.0\nn1 = 1.0\nn2 = 11.0\nn3 = 2.0\nn4 = 2.0\nn5 = 11.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(n3)))\nt2 = n0 - n3\nt3 = math.factorial(min(15, int(t2)))\nt4 = t1 * t3\nt5 = t0 / t4\nanswer = 4.0 / t5\nprint(answer)" + ], + "Output Answer": [ + "0.07272727272727272" + ], + "split": "train" + }, + { + "Input": "if a 2 + b 2 + c 2 = 281 and ab + bc + ca = 4 , then a + b + c is", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 2.0\nn2 = 2.0\nn3 = 281.0\nn4 = 4.0\nt0 = n4 * n0\nt1 = n3 + t0\nanswer = math.sqrt(max(0, t1))\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "pradeep has to obtain 25 % of the total marks to pass . he got 185 marks and failed by 25 marks . the maximum marks are", + "Output Program": [ + "n0 = 25.0\nn1 = 185.0\nn2 = 25.0\nt0 = n1 + n2\nt1 = n0 / 100.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "840" + ], + "split": "train" + }, + { + "Input": "9 men went to a theater . 8 of them spent rs . 3 each over their tickets and the ninth spent rs . 2 more than the average expenditure of all the 9 . determine the total money spent by them ?", + "Output Program": [ + "n0 = 9.0\nn1 = 8.0\nn2 = 3.0\nn3 = 2.0\nn4 = 9.0\nt0 = n1 * n2\nt1 = n3 + t0\nt2 = t1 / n1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "29.25" + ], + "split": "train" + }, + { + "Input": "a runs 1 2 / 3 times as fast as b . if a gives b a start of 80 m , how far must the winning post be so that a and b might reach it at the same time ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 3.0\nn3 = 80.0\nt0 = n0 * n2\nt1 = n1 + t0\nt2 = n3 * t1\nanswer = t2 / n1\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "train" + }, + { + "Input": "farm tax is levied on the 60 % of the cultivated land . the tax department collected total $ 5000 through the farm tax from the village of mr . william . mr . william paid only $ 480 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :", + "Output Program": [ + "n0 = 60.0\nn1 = 5000.0\nn2 = 480.0\nt0 = n2 / n1\nt1 = t0 * 100.0\nt2 = t1 * 100.0\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "in company j , the total monthly payroll for the 15 factory workers is $ 30000 and the total monthly payroll for the 30 office workers is $ 75000 . by how much does the average ( arithmetic mean ) monthly salary of an office worker exceed that of a factory worker in this company ?", + "Output Program": [ + "n0 = 15.0\nn1 = 30000.0\nn2 = 30.0\nn3 = 75000.0\nt0 = n1 / n2\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "train" + }, + { + "Input": "the average mark of the students of a class in a particular exam is 70 . if 5 students whose average mark in that exam is 50 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam ?", + "Output Program": [ + "n0 = 70.0\nn1 = 5.0\nn2 = 50.0\nn3 = 90.0\nt0 = n1 * n3\nt1 = n1 * n2\nt2 = n3 - n0\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the average temperature for monday , tuesday , wednesday and thursday was 48 degrees and for tuesday , wednesday , thursday and friday was 46 degrees . if the temperature on monday was 39 degrees . find the temperature on friday ?", + "Output Program": [ + "n0 = 48.0\nn1 = 46.0\nn2 = 39.0\nt0 = n0 * 4.0\nt1 = n1 * 4.0\nt2 = t0 - t1\nanswer = n2 - t2\nprint(answer)" + ], + "Output Answer": [ + "31" + ], + "split": "train" + }, + { + "Input": "a man is 16 years older than his son . in two years , his age will be twice the age of his son . the present age of this son is", + "Output Program": [ + "n0 = 16.0\nt0 = 2.0 * 2.0\nt1 = 2.0 - 1.0\nt2 = t0 - 2.0\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "1 + 3 = 2 2 + 3 = 10 3 + 3 = 30 4 + 3 = 68 5 + 3 = ? ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 2.0\nn3 = 2.0\nn4 = 3.0\nn5 = 10.0\nn6 = 3.0\nn7 = 3.0\nn8 = 30.0\nn9 = 4.0\nn10 = 3.0\nn11 = 68.0\nn12 = 5.0\nn13 = 3.0\nt0 = n12 * n12\nt1 = n0 + t0\nanswer = n12 * t1\nprint(answer)" + ], + "Output Answer": [ + "130" + ], + "split": "train" + }, + { + "Input": "what is the difference between the place value of 2 in the numeral 7669 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 7669.0\nt0 = n0 * 3.0\nt1 = t0 * 100.0\nt2 = t0 * 10.0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "540" + ], + "split": "train" + }, + { + "Input": "if x gets 25 % more than y and y gets 20 % more than z , the share of z out of rs . 370 will be :", + "Output Program": [ + "n0 = 25.0\nn1 = 20.0\nn2 = 370.0\nt0 = n1 / 100.0\nt1 = n0 / 100.0\nt2 = t0 + 1.0\nt3 = t1 + 1.0\nt4 = t3 * t2\nt5 = t2 + t4\nt6 = t5 + 1.0\nanswer = n2 / t6\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "village x has a population of 70000 , which is decreasing at the rate of 1200 per year . village y has a population of 42000 , which is increasing at the rate of 800 per year . in how many years will the population of the two villages be equal ?", + "Output Program": [ + "n0 = 70000.0\nn1 = 1200.0\nn2 = 42000.0\nn3 = 800.0\nt0 = n1 + n3\nt1 = n0 - n2\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "? x 24 = 173 x 240", + "Output Program": [ + "n0 = 24.0\nn1 = 173.0\nn2 = 240.0\nt0 = n1 * n2\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "1730" + ], + "split": "train" + }, + { + "Input": "after a storm deposits 115 billion gallons of water into the city reservoir , the reservoir is 80 % full . if the original contents of the reservoir totaled 245 billion gallons , the reservoir was approximately what percentage full before the storm ?", + "Output Program": [ + "n0 = 115.0\nn1 = 80.0\nn2 = 245.0\nt0 = n0 + n2\nt1 = n1 / 100.0\nt2 = t0 / t1\nt3 = n2 / t2\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "54.44444444444444" + ], + "split": "train" + }, + { + "Input": "the sum of the ages of 5 children born at the intervals of 2 years each is 50 years . what is the age of the youngest child ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 50.0\nt0 = n0 / 2.0\nt1 = n0 - 1.0\nt2 = n2 / t0\nt3 = n1 * t1\nt4 = t2 - t3\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "jean drew a gumball at random from a jar of pink and blue gumballs . since the gumball she selected was blue and she wanted a pink one , she replaced it and drew another . the second gumball also happened to be blue and she replaced it as well . if the probability of her drawing the two blue gumballs was 36 / 49 , what is the probability that the next one she draws will be pink ?", + "Output Program": [ + "import math\nn0 = 36.0\nn1 = 49.0\nt0 = n0 / n1\nt1 = math.sqrt(max(0, t0))\nanswer = 1.0 - t1\nprint(answer)" + ], + "Output Answer": [ + "0.1428571428571428" + ], + "split": "train" + }, + { + "Input": "on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 370 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?", + "Output Program": [ + "n0 = 370.0\n\nanswer = n0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "740" + ], + "split": "train" + }, + { + "Input": "if ( 2 to the x ) - ( 2 to the ( x - 2 ) ) = 3 ( 2 to the 11 ) , what is the value of x ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 2.0\nn3 = 3.0\nn4 = 2.0\nn5 = 11.0\n\nanswer = n0 + n5\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "the vertex of a rectangle are ( 1 , 0 ) , ( 9 , 0 ) , ( 1 , 2 ) and ( 9 , 2 ) respectively . if line l passes through the origin and divided the rectangle into two identical quadrilaterals , what is the slope of line l ?", + "Output Program": [ + "n0 = 1.0\nn1 = 0.0\nn2 = 9.0\nn3 = 0.0\nn4 = 1.0\nn5 = 2.0\nn6 = 9.0\nn7 = 2.0\nt0 = n2 - n0\nt1 = t0 + 2.0\nt2 = t1 / 2.0\nanswer = 1.0 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.2" + ], + "split": "train" + }, + { + "Input": "if x is 11 percent greater than 70 , then x =", + "Output Program": [ + "n0 = 11.0\nn1 = 70.0\nt0 = n0 / 100.0\nt1 = n1 * t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "77.7" + ], + "split": "train" + }, + { + "Input": "the expression ( 12.86 \u00d7 12.86 + 12.86 \u00d7 p + 0.14 \u00d7 0.14 ) will be a perfect square for p equal to", + "Output Program": [ + "n0 = 12.86\nn1 = 12.86\nn2 = 12.86\nn3 = 0.14\nn4 = 0.14\n\nanswer = n3 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "0.28" + ], + "split": "train" + }, + { + "Input": "a pupil ' s marks were wrongly entered as 83 instead of 63 . due to that the average marks for the class got increased by half . the number of pupils in the class is", + "Output Program": [ + "n0 = 83.0\nn1 = 63.0\nt0 = n0 - n1\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "a volunteer organization is recruiting new members . in the fall they manage to increase their number by 8 % . by the spring however membership falls by 19 % . what is the total change in percentage from fall to spring ?", + "Output Program": [ + "n0 = 8.0\nn1 = 19.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = t0 + 1.0\nt3 = 1.0 - t1\nt4 = t2 * t3\nt5 = t4 * 100.0\nanswer = 100.0 - t5\nprint(answer)" + ], + "Output Answer": [ + "12.519999999999982" + ], + "split": "train" + }, + { + "Input": "5 + 8", + "Output Program": [ + "n0 = 280.0\nn1 = 254.0\nn2 = 280.0\nn3 = 97.0\nn4 = 138.0\nn5 = 152.0\nn6 = 73.0\nn7 = 3.0\nt0 = n0 + n1\nt1 = n0 + t0\nt2 = t1 - n3\nt3 = t2 - n4\nt4 = t3 - n5\nanswer = n6 + t4\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "train" + }, + { + "Input": "a couple spent $ 158.40 in total while dining out and paid this amount using a credit card . the $ 158.40 figure included a 20 percent tip which was paid on top of the price which already included a sales tax of 10 percent on top of the price of the food . what was the actual price of the food before tax and tip ?", + "Output Program": [ + "n0 = 158.4\nn1 = 158.4\nn2 = 20.0\nn3 = 10.0\nt0 = n2 + 100.0\nt1 = n3 + 100.0\nt2 = n0 * 100.0\nt3 = t2 / t0\nt4 = t3 * 100.0\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "in the xy - coordinate system , if ( m , n ) and ( m + 2 , n + k ) are two points on the line with the equation x = 2 y + 3 , then k =", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 3.0\nt0 = n0 + n2\nt1 = t0 - n2\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "when positive integer x is divided by positive integer y , the remainder is 5 . if x / y = 96.2 , what is the value of y ?", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 96.2\nt0 = math.floor(n1)\nt1 = n1 - t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "24.999999999999645" + ], + "split": "train" + }, + { + "Input": "what is the greater of the two numbers whose product is 2048 , given that the sum of the two numbers exceeds their difference by 64 ?", + "Output Program": [ + "n0 = 2048.0\nn1 = 64.0\nt0 = 2.0**min(4.0, 5)\nt1 = t0 * 2.0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "train" + }, + { + "Input": "a number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34 . such a least possible number m is", + "Output Program": [ + "n0 = 5.0\nn1 = 8.0\nn2 = 34.0\nt0 = n2 * 2.0\nt1 = n0 * n1\nt2 = n0 - 1.0\nt3 = t0 - t1\nt4 = t3 / t2\nanswer = t4 + t0\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "when asked what the time is , a person answered that the amount of time left is 1 / 2 of the time already completed . what is the time .", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nt0 = n0 / n1\nt1 = 12.0 * n0\nt2 = t0 + 1.0\nt3 = t1 / t2\nanswer = t1 - t3\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "in a renowned city , the average birth rate is 10 people every two seconds and the death rate is 2 people every two seconds . estimate the size of the population net increase that occurs in one day .", + "Output Program": [ + "n0 = 10.0\nn1 = 2.0\nt0 = n0 - n1\nt1 = t0 * 3600.0\nanswer = t1 * 12.0\nprint(answer)" + ], + "Output Answer": [ + "345600" + ], + "split": "train" + }, + { + "Input": "two employees m and n are paid a total of $ 616 per week by their employer . if m is paid 120 percent of the salary paid to n , how much is n paid per week ?", + "Output Program": [ + "n0 = 616.0\nn1 = 120.0\nt0 = n1 / 100.0\nt1 = t0 + 1.0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "280" + ], + "split": "train" + }, + { + "Input": "5 friends adi , brian , close , derek and eli appeared in two aptitude tests . in the first aptitude test , derek score 50 % less than the average score of the 5 people . in the second aptitude test , derek score 50 % more than what he scored on the first aptitude test . if the score of his friend in the second aptitude test were same as their score in the first test , by approximately what percentage was derek ' s score less than the average score of the 5 people in the second aptitude ?", + "Output Program": [ + "n0 = 5.0\nn1 = 50.0\nn2 = 5.0\nn3 = 50.0\nn4 = 5.0\nt0 = n0 * n0\nt1 = n1 * t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "$ 700 is divided amongst a , b and c so that a may get 2 / 3 as much as b and c together , b may get 6 / 9 as much as a and c together , then the share of a is", + "Output Program": [ + "n0 = 700.0\nn1 = 2.0\nn2 = 3.0\nn3 = 6.0\nn4 = 9.0\nt0 = 2.0 / 3.0\nt1 = t0 + 1.0\nt2 = n0 / t1\nanswer = t2 * t0\nprint(answer)" + ], + "Output Answer": [ + "280" + ], + "split": "train" + }, + { + "Input": "the average age of applicants for a new job is 31 , with a standard deviation of 5 . the hiring manager is only willing to accept applications whose age is within one standard deviation of the average age . what is the maximum number of different ages of the applicants ?", + "Output Program": [ + "n0 = 31.0\nn1 = 5.0\nt0 = n1 * 2.0\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "tough and tricky questions : word problems . a salesman ' s income consists of commission and base salary . his weekly income totals over the past 7 weeks have been $ 406 , $ 413 , $ 420 , $ 436 , $ 395 , $ 410 , $ 360 . what must his average ( arithmetic mean ) income over the next two weeks be to decrease his average weekly income to $ 400 over the 9 - week period ?", + "Output Program": [ + "n0 = 7.0\nn1 = 406.0\nn2 = 413.0\nn3 = 420.0\nn4 = 436.0\nn5 = 395.0\nn6 = 410.0\nn7 = 360.0\nn8 = 400.0\nn9 = 9.0\nt0 = n1 + n2\nt1 = n8 * n9\nt2 = n3 + t0\nt3 = n4 + t2\nt4 = n5 + t3\nt5 = n6 + t4\nt6 = n7 + t5\nt7 = t1 - t6\nanswer = t7 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "380" + ], + "split": "train" + }, + { + "Input": "a teacher grades students \u2019 tests by subtracting twice the number of incorrect responses from the number of correct responses . if student a answers each of the 100 questions on her test and receives a score of 79 , how many questions did student a answer correctly ?", + "Output Program": [ + "n0 = 100.0\nn1 = 79.0\nt0 = n0 - n1\nt1 = t0 / 3.0\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "93" + ], + "split": "train" + }, + { + "Input": "rahim bought 50 books for rs . 1000 from one shop and 40 books for rs . 800 from another . what is the average price he paid per book ?", + "Output Program": [ + "n0 = 50.0\nn1 = 1000.0\nn2 = 40.0\nn3 = 800.0\nt0 = n1 + n3\nt1 = n0 + n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "the average age of applicants for a new job is 31 , with a standard deviation of 9 . the hiring manager is only willing to accept applications whose age is within one standard deviation of the average age . what is the maximum number of different ages of the applicants ?", + "Output Program": [ + "n0 = 31.0\nn1 = 9.0\nt0 = n1 * 2.0\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "ms . mary sold two properties , x and y , for $ 25000 each . she sold property x for 20 % more than she paid for it and sold property y for 20 % less than she paid for it . if expenses are disregarded , what was her total net gain or loss , if any , on the two properties ?", + "Output Program": [ + "n0 = 25000.0\nn1 = 20.0\nn2 = 20.0\nt0 = n1 / 100.0\nt1 = 100.0 - n1\nt2 = t1 + 3.0\nt3 = n0 * t0\nt4 = t2 + 0.33\nt5 = t3 - 1000.0\nt6 = t5 / 2.0\nanswer = t4 + t6\nprint(answer)" + ], + "Output Answer": [ + "2083.33" + ], + "split": "train" + }, + { + "Input": "what is the difference between the place values of two 1 ' s in the numeral 135.21", + "Output Program": [ + "n0 = 1.0\nn1 = 135.21\nt0 = n0 / 100.0\nt1 = n0 * 100.0\nanswer = t1 - t0\nprint(answer)" + ], + "Output Answer": [ + "99.99" + ], + "split": "train" + }, + { + "Input": "if x + ( 1 / x ) = 5 , what is the value of e = x ^ 2 + ( 1 / x ) ^ 2 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 2.0\nn3 = 1.0\nn4 = 2.0\nt0 = n1**min(n2, 5)\nanswer = t0 - n2\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "8 is 4 % of a , and 4 is 8 % of b . c equals b / a . what is the value of c ?", + "Output Program": [ + "n0 = 8.0\nn1 = 4.0\nn2 = 4.0\nn3 = 8.0\nt0 = n1 / n0\nt1 = n0 / n1\nt2 = t0 * 100.0\nt3 = t1 * 100.0\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.25" + ], + "split": "train" + }, + { + "Input": "the average weight of a group of 30 friends increases by 10 kg when the weight of additional 30 friends was added . if average weight of the whole group after including the additional 30 members is 40 kg , what is the average weight of the additional friends ?", + "Output Program": [ + "n0 = 30.0\nn1 = 10.0\nn2 = 30.0\nn3 = 30.0\nn4 = 40.0\nt0 = n0 + n0\nt1 = n4 - n1\nt2 = n4 * t0\nt3 = n0 * t1\nt4 = t2 - t3\nanswer = t4 / n0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "sum of two numbers is 50 . two times of the difference of first and seceond is 20 . then the numbers will be ?", + "Output Program": [ + "n0 = 50.0\nn1 = 20.0\nt0 = n1 / 2.0\nt1 = n0 - t0\nt2 = t1 / 2.0\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "if a and b are the roots of the equation x 2 - 7 x + 7 = 0 , then the value of a 2 + b 2 is :", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 7.0\nn2 = 7.0\nn3 = 0.0\nn4 = 2.0\nn5 = 2.0\nt0 = n1 * 4.0\nt1 = n1**min(2.0, 5)\nt2 = t1 - t0\nt3 = math.sqrt(max(0, t2))\nt4 = n1 + t3\nt5 = n1 - t3\nt6 = t5 / 2.0\nt7 = t4 / 2.0\nt8 = t6**min(n0, 5)\nt9 = t7**min(n0, 5)\nanswer = t8 + t9\nprint(answer)" + ], + "Output Answer": [ + "34.99999999999999" + ], + "split": "train" + }, + { + "Input": "each machine of type a has 4 steel parts and 2 chrome parts . each machine of type b has 2 steel parts and 1 chrome parts . if a certain group of type a and type b machines has a total of 30 steel parts and 33 chrome parts , how many machines are in the group", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\nn2 = 2.0\nn3 = 1.0\nn4 = 30.0\nn5 = 33.0\nt0 = n1 + n3\nt1 = n0 + n1\nt2 = n5 / t0\nt3 = n4 / t1\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "there are 750 male and female participants in a meeting . half the female participants and one - quarter of the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?", + "Output Program": [ + "n0 = 750.0\nt0 = n0 / 3.0\nt1 = t0 * 4.0\nt2 = t1 - n0\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "125" + ], + "split": "train" + }, + { + "Input": "if 25 % of x is 5 less than 10 % of 500 , then x is ?", + "Output Program": [ + "n0 = 25.0\nn1 = 5.0\nn2 = 10.0\nn3 = 500.0\nt0 = n2 / 100.0\nt1 = n0 / 100.0\nt2 = n3 * t0\nt3 = t2 - n1\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "180" + ], + "split": "train" + }, + { + "Input": "what is the least possible value of expression e = ( x - 1 ) ( x - 3 ) ( x - 4 ) ( x - 6 ) + 10 for real values of x ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 4.0\nn3 = 6.0\nn4 = 10.0\nt0 = n0 + n4\nt1 = n2 + n3\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "a jogger running at 9 km / hr along side a railway track is 200 m ahead of the engine of a 120 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?", + "Output Program": [ + "n0 = 9.0\nn1 = 200.0\nn2 = 120.0\nn3 = 45.0\nt0 = n1 + n2\nt1 = 10.0 / 2.0\nt2 = n3 - n0\nt3 = t2 / 2.0\nt4 = t1 / t3\nt5 = t4 * t2\nanswer = t0 / t5\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "x , a , z , and b are single digit positive integers . x = 1 / 6 a . z = 1 / 6 b . ( 10 a + b ) \u2013 ( 10 x + z ) could not equal", + "Output Program": [ + "n0 = 1.0\nn1 = 6.0\nn2 = 1.0\nn3 = 6.0\nn4 = 10.0\nn5 = 10.0\nt0 = n1 * n1\nt1 = n1 * n4\nt2 = t0 + t1\nt3 = n1 + t1\nt4 = t2 - t3\nt5 = n4 + t4\nanswer = t5 + 3.0\nprint(answer)" + ], + "Output Answer": [ + "43" + ], + "split": "train" + }, + { + "Input": "if jake loses 8 pounds , he will weigh twice as much as his sister . together they now weigh 290 pounds . what is jake \u2019 s present weight , in pounds ?", + "Output Program": [ + "n0 = 8.0\nn1 = 290.0\nt0 = n1 - n0\nt1 = t0 / 3.0\nt2 = t1 * 2.0\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "196" + ], + "split": "train" + }, + { + "Input": "the greatest number which on dividing 1642 and 1856 leaves remainders 6 and 4 respectively , is :", + "Output Program": [ + "import scipy\nn0 = 1642.0\nn1 = 1856.0\nn2 = 6.0\nn3 = 4.0\nt0 = n1 - n3\nt1 = n0 - n2\nanswer = scipy.gcd(int(t0), int(t1))\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "marcella has 27 pairs of shoes . if she loses 9 individual shoes , what is the greatest number of matching pairs she could have left ?", + "Output Program": [ + "import math\nn0 = 27.0\nn1 = 9.0\nt0 = n1 / 2.0\nt1 = math.floor(t0)\nt2 = t1 + 1.0\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "how many 3 - digit numbers can be formed from the digits 2 , 3 , 5 , 6 , 7 and 9 , which are divisible by 5 and none of the digits is repeated ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 3.0\nn3 = 5.0\nn4 = 6.0\nn5 = 7.0\nn6 = 9.0\nn7 = 5.0\n\nanswer = n3 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "the average age of applicants for a new job is 20 , with a standard deviation of 8 . the hiring manager is only willing to accept applicants whose age is within one standard deviation of the average age . assuming that all applicants ' ages are integers and that the endpoints of the range are included , what is the maximum number of different ages of the applicants ?", + "Output Program": [ + "n0 = 20.0\nn1 = 8.0\nt0 = n0 + n1\nt1 = n0 - n1\nt2 = t0 - t1\nanswer = t2 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "p , q and r have $ 7000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?", + "Output Program": [ + "n0 = 7000.0\nt0 = 2.0 * 2.0\nt1 = 1.0 * 3.0\nt2 = t0 / 3.0\nt3 = n0 * t0\nt4 = t2 * 3.0\nt5 = t4 + t1\nt6 = t5 + t1\nanswer = t3 / t6\nprint(answer)" + ], + "Output Answer": [ + "2800" + ], + "split": "train" + }, + { + "Input": "if x is 30 percent greater than 88 , then x =", + "Output Program": [ + "n0 = 30.0\nn1 = 88.0\nt0 = n0 / 100.0\nt1 = n1 * t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "114.4" + ], + "split": "train" + }, + { + "Input": "find value for x from below equation ? x + 1 = 5", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\n\nanswer = n1 - n0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "what least number should be added to 1015 , so that the sum is completely divisible by 25 ?", + "Output Program": [ + "n0 = 1015.0\nn1 = 25.0\nt0 = n0 % n1\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the sum of even numbers between 1 and 31 is :", + "Output Program": [ + "import math\nn0 = 1.0\nn1 = 31.0\nt0 = n0 + n1\nt1 = n1 / 2.0\nt2 = math.floor(t1)\nt3 = t2 / 2.0\nanswer = t0 * t3\nprint(answer)" + ], + "Output Answer": [ + "240" + ], + "split": "train" + }, + { + "Input": "a whale goes on a feeding frenzy that lasts for 9 hours . for the first hour he catches and eats x kilos of plankton . in every hour after the first , it consumes 3 kilos of plankton more than it consumed in the previous hour . if by the end of the frenzy the whale will have consumed a whopping accumulated total 450 kilos of plankton , how many kilos did he consume on the sixth hour ?", + "Output Program": [ + "n0 = 9.0\nn1 = 3.0\nn2 = 450.0\nt0 = n2 / n0\nanswer = n1 + t0\nprint(answer)" + ], + "Output Answer": [ + "53" + ], + "split": "train" + }, + { + "Input": "the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 55 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.5\nn2 = 55.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "when processing flower - nectar into honey bees ' extract , a considerable amount of water gets reduced . how much flower - nectar must be processed to yield 1 kg of honey , if nectar contains 50 % water , and the honey obtained from this nectar contains 30 % water ?", + "Output Program": [ + "n0 = 1.0\nn1 = 50.0\nn2 = 30.0\nt0 = n1 / 100.0\nt1 = 100.0 - n2\nt2 = t1 / 100.0\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "1.4" + ], + "split": "train" + }, + { + "Input": "find the constant k so that : - x 2 - ( k + 9 ) x - 8 = - ( x - 2 ) ( x - 4 )", + "Output Program": [ + "n0 = 2.0\nn1 = 9.0\nn2 = 8.0\nn3 = 2.0\nn4 = 4.0\nt0 = n0 + n4\nanswer = n1 + t0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "we bought 85 hats at the store . blue hats cost $ 6 and green hats cost $ 7 . the total price was $ 550 . how many green hats did we buy ?", + "Output Program": [ + "n0 = 85.0\nn1 = 6.0\nn2 = 7.0\nn3 = 550.0\nt0 = n0 * n1\nanswer = n3 - t0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "one - fourth of a number is greater than one - fifth of the number succeeding it by 1 . find the number .", + "Output Program": [ + "n0 = 1.0\nt0 = 2.0 / 10.0\nt1 = n0 / 4.0\nt2 = n0 + t0\nt3 = t1 - t0\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "24.000000000000004" + ], + "split": "train" + }, + { + "Input": "a vessel of capacity 2 litre has 25 % of alcohol and another vessel of capacity 6 litre had 40 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?", + "Output Program": [ + "n0 = 2.0\nn1 = 25.0\nn2 = 6.0\nn3 = 40.0\nn4 = 8.0\nn5 = 10.0\nt0 = n1 / 100.0\nt1 = n3 / 100.0\nt2 = n0 * t0\nt3 = n2 * t1\nt4 = t2 + t3\nt5 = t4 / n5\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "29.000000000000004" + ], + "split": "train" + }, + { + "Input": "find the value of m 32519 x 9999 = m ?", + "Output Program": [ + "n0 = 32519.0\nn1 = 9999.0\nt0 = n1 - 4.0\nanswer = t0 * n0\nprint(answer)" + ], + "Output Answer": [ + "325027405" + ], + "split": "train" + }, + { + "Input": "a & b started a partnership business . a ' s investment was thrice the investment of b and the period of his investment was two times the period of investments of b . if b received rs 6000 as profit , what is their total profit ?", + "Output Program": [ + "n0 = 6000.0\nt0 = 1.0 * 1.0\nt1 = 2.0 * 3.0\nt2 = t1 + t0\nt3 = t0 / t2\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "42000" + ], + "split": "train" + }, + { + "Input": "the average of 5 quantities is 11 . the average of 3 of them is 4 . what is the average of remaining 2 numbers ?", + "Output Program": [ + "n0 = 5.0\nn1 = 11.0\nn2 = 3.0\nn3 = 4.0\nn4 = 2.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = t0 - t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "21.5" + ], + "split": "train" + }, + { + "Input": "if 4 x + y + z = 80 , 2 x - y - z = 4003 x + y - z = 20 for integers of x , y and z , find x = ?", + "Output Program": [ + "n0 = 4.0\nn1 = 80.0\nn2 = 2.0\nn3 = 4003.0\nn4 = 20.0\n\nanswer = n1 / n0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "a batsman in his 12 th innings makes a score of 48 and thereby increases his average by 2 runs . what is his average after the 12 th innings if he had never been \u2018 not out \u2019 ?", + "Output Program": [ + "n0 = 12.0\nn1 = 48.0\nn2 = 2.0\nn3 = 12.0\nt0 = n0 * n2\nt1 = n1 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "the average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.5\nn2 = 65.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "85" + ], + "split": "train" + }, + { + "Input": "a , b , and c are integers and a < b < c . s is the set of all integers from a to b , inclusive . q is the set of all integers from b to c , inclusive . the median of set s is ( 3 / 4 ) * b . the median of set q is ( 6 / 8 ) * c . if r is the set of all integers from a to c , inclusive , what fraction of c is the median of set r ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 6.0\nn3 = 8.0\nt0 = n2 / n3\nt1 = n0 / n1\nt2 = t0 * 2.0\nt3 = t1 * 2.0\nt4 = t2 - 1.0\nt5 = t3 - 1.0\nt6 = 1.0 / t5\nt7 = t4 / t6\nt8 = t7 + 1.0\nanswer = t8 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "0.625" + ], + "split": "train" + }, + { + "Input": "x is a positive number which when increased by 17 is equal to 60 times the reciprocal of the number . find value of x ?", + "Output Program": [ + "import math\nn0 = 17.0\nn1 = 60.0\nt0 = -n0\nt1 = -n1\nt2 = n0**min(2.0, 5)\nt3 = t1 * 1.0\nt4 = t3 * 4.0\nt5 = t2 - t4\nt6 = math.sqrt(max(0, t5))\nt7 = t0 + t6\nanswer = t7 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "the average mark of the students of a class in a particular exam is 65 . if 5 students whose average mark in that exam is 20 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam .", + "Output Program": [ + "n0 = 65.0\nn1 = 5.0\nn2 = 20.0\nn3 = 90.0\nt0 = n1 * n3\nt1 = n1 * n2\nt2 = n3 - n0\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "a camera lens filter kit containing 5 filters sells for $ 72.50 . if the filters are purchased individually , 2 of them are priced at $ 12.45 each , 2 at $ 14.05 each , 1 at $ 11.50 . the amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually ?", + "Output Program": [ + "n0 = 5.0\nn1 = 72.5\nn2 = 2.0\nn3 = 12.45\nn4 = 2.0\nn5 = 14.05\nn6 = 1.0\nn7 = 11.5\nn8 = 5.0\nt0 = n2 * n3\nt1 = n2 * n5\nt2 = t0 + t1\nt3 = n7 + t2\nt4 = n1 - t3\nt5 = t4 * 100.0\nanswer = t5 / n1\nprint(answer)" + ], + "Output Answer": [ + "11.03448275862069" + ], + "split": "train" + }, + { + "Input": "every student in a room is either a junior or a senior . there is at least one junior and at least one senior in the room . if 1 / 2 of the juniors is equal to 2 / 3 of the seniors , what fraction of the students in the room are juniors ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 2.0\nn3 = 3.0\nt0 = n1 * n1\nt1 = n3 + t0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.5714285714285714" + ], + "split": "train" + }, + { + "Input": "the smallest number when increased by ` ` 2 ` ` is exactly divisible by 12 , 30 , 48 , 74 and 100 is :", + "Output Program": [ + "import scipy\nn0 = 2.0\nn1 = 12.0\nn2 = 30.0\nn3 = 48.0\nn4 = 74.0\nn5 = 100.0\nt0 = scipy.lcm(int(n1), int(n2))\nt1 = scipy.lcm(int(n3), int(n4))\nt2 = scipy.lcm(int(t0), int(t1))\nt3 = scipy.lcm(int(n5), int(t2))\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "44402" + ], + "split": "train" + }, + { + "Input": "how many integers between 1 and 1400 are divisible by 25 , and 35 ?", + "Output Program": [ + "import scipy\nn0 = 1.0\nn1 = 1400.0\nn2 = 25.0\nn3 = 35.0\nt0 = scipy.lcm(int(n2), int(n3))\nanswer = n1 / t0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a batsman makes a score of 92 runs in the 17 th inning and thus increases his average by 3 . find his average after 17 th inning .", + "Output Program": [ + "n0 = 92.0\nn1 = 17.0\nn2 = 3.0\nn3 = 17.0\nt0 = n1 * n2\nt1 = n0 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "44" + ], + "split": "train" + }, + { + "Input": "in a division sum , the quotient is 65 , the divisor 24 and the remainder 5 , find the dividend ?", + "Output Program": [ + "n0 = 65.0\nn1 = 24.0\nn2 = 5.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "1565" + ], + "split": "train" + }, + { + "Input": "at a certain committee meeting only associate professors and assistant professors are present . each associate professor has brought 2 pencils and 1 chart to the meeting , while each assistant professor has brought 1 pencil and 2 charts . if a total of 10 pencils and 8 charts have been brought to the meeting , how many people are present ?", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 1.0\nn3 = 2.0\nn4 = 10.0\nn5 = 8.0\nt0 = n4 + n5\nt1 = n0 + n1\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "jim \u00e2 \u20ac \u2122 s taxi service charges an initial fee of $ 2.25 at the beginning of a trip and an additional charge of $ 0.4 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?", + "Output Program": [ + "n0 = 2.25\nn1 = 0.4\nn2 = 2.0\nn3 = 5.0\nn4 = 3.6\nt0 = n2 / n3\nt1 = n4 / t0\nt2 = n1 * t1\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "5.85" + ], + "split": "train" + }, + { + "Input": "in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 8 eggs . if the cost of each pound of rice is $ 0.33 , then how many w cents does a liter of kerosene cost ? [ one dollar has 100 cents . ]", + "Output Program": [ + "n0 = 8.0\nn1 = 0.33\nn2 = 100.0\nt0 = 1.0 / 2.0\nt1 = n1 * n2\nt2 = n0 / t0\nt3 = t2 / 12.0\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "44" + ], + "split": "train" + }, + { + "Input": "a two digit number is 18 less than the square of the sum of its digits . how many such numbers are there ?", + "Output Program": [ + "n0 = 18.0\nt0 = 100.0 / 2.0\nt1 = n0**min(3.0, 5)\nt2 = t0 * 10.0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "6332" + ], + "split": "train" + }, + { + "Input": "( 26.3 * 12 * 20 ) / 3 + 125 = ?", + "Output Program": [ + "n0 = 26.3\nn1 = 12.0\nn2 = 20.0\nn3 = 3.0\nn4 = 125.0\nt0 = n0 * n1\nt1 = n2 * t0\nt2 = t1 / 3.0\nanswer = n4 + t2\nprint(answer)" + ], + "Output Answer": [ + "2229" + ], + "split": "train" + }, + { + "Input": "if 15 people contributed a total of $ 30.00 toward a gift and each of them contributed at least $ 1.00 , then the maximum possible amount any one person could have contributed is", + "Output Program": [ + "n0 = 15.0\nn1 = 30.0\nn2 = 1.0\nt0 = n0 - n2\nt1 = n2 * t0\nanswer = n1 - t1\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "the difference between a two - digit number and the number obtained by interchanging the positions of its digits is 72 . what is the difference between the two digits of that number ?", + "Output Program": [ + "n0 = 72.0\nt0 = 10.0 - 1.0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a \u2019 s speed is 16 / 15 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?", + "Output Program": [ + "n0 = 16.0\nn1 = 15.0\nt0 = n0 - n1\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.0625" + ], + "split": "train" + }, + { + "Input": "when xyz co discontinued an agency arrangement with john , management held his commission of rs . 25000 / - for one month . earlier john had availed an advance agency fees of 8280 / - from company . but robert forgot that . after one month john asked his fees and accountant gives rs . 18500 / - to him . what is the incentive amount given to john ?", + "Output Program": [ + "n0 = 25000.0\nn1 = 8280.0\nn2 = 18500.0\nt0 = n1 + n2\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "1780" + ], + "split": "train" + }, + { + "Input": "jean drew a gumball at random from a jar of pink and blue gumballs . since the gumball she selected was blue and she wanted a pink one , she replaced it and drew another . the second gumball also happened to be blue and she replaced it as well . if the probability of her drawing the two blue gumballs was 9 / 49 , what is the probability that the next one she draws will be pink ?", + "Output Program": [ + "import math\nn0 = 9.0\nn1 = 49.0\nt0 = n0 / n1\nt1 = math.sqrt(max(0, t0))\nanswer = 1.0 - t1\nprint(answer)" + ], + "Output Answer": [ + "0.5714285714285714" + ], + "split": "train" + }, + { + "Input": "a grocer has a sale of rs . 2435 , rs . 2920 , rs . 2855 , rs . 3230 and rs . 2560 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 2500 ?", + "Output Program": [ + "n0 = 2435.0\nn1 = 2920.0\nn2 = 2855.0\nn3 = 3230.0\nn4 = 2560.0\nn5 = 5.0\nn6 = 2500.0\nt0 = n5 + 1.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n6 * t0\nt4 = n3 + t2\nt5 = n4 + t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "1000" + ], + "split": "train" + }, + { + "Input": "what sum of money put at c . i amounts in 2 years to rs . 8840 and in 3 years to rs . 9261 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 8840.0\nn2 = 3.0\nn3 = 9261.0\nt0 = n3 / n1\nt1 = t0 - 1.0\nt2 = t1 + 1.0\nt3 = t2**min(n0, 5)\nanswer = n1 / t3\nprint(answer)" + ], + "Output Answer": [ + "8054.545267355626" + ], + "split": "train" + }, + { + "Input": "if square - root of 15 is 3.87 . then find the value of square - root of ( 5 / 3 )", + "Output Program": [ + "import math\nn0 = 15.0\nn1 = 3.87\nn2 = 5.0\nn3 = 3.0\nt0 = n2 / n3\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "1.2909944487358056" + ], + "split": "train" + }, + { + "Input": "on rainy mornings , mo drinks exactly n cups of hot chocolate ( assume that n is an integer ) . on mornings that are not rainy , mo drinks exactly 3 cups of tea . last week mo drank a total of 20 cups of tea and hot chocolate together . if during that week mo drank 10 more tea cups than hot chocolate cups , then how many rainy days were there last week ?", + "Output Program": [ + "n0 = 3.0\nn1 = 20.0\nn2 = 10.0\nt0 = 3.0 + 4.0\nt1 = n1 + n2\nt2 = t1 / 2.0\nt3 = t2 / n0\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a grocery shop has a sale of rs . 6235 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ?", + "Output Program": [ + "n0 = 6235.0\nn1 = 6927.0\nn2 = 6855.0\nn3 = 7230.0\nn4 = 6562.0\nn5 = 5.0\nn6 = 6500.0\nt0 = n5 + 1.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n6 * t0\nt4 = n3 + t2\nt5 = n4 + t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "5191" + ], + "split": "train" + }, + { + "Input": "the average age of a group of 10 persons was decreased by 3 years when one person , whose age was 45 years , was replaced by a new person . find the age of the new person ?", + "Output Program": [ + "n0 = 10.0\nn1 = 3.0\nn2 = 45.0\nt0 = n0 * n1\nanswer = n2 - t0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.60 per glass on the first day , what was the price per glass on the second day ?", + "Output Program": [ + "n0 = 0.6\nt0 = 1.0 + 1.0\nt1 = 1.0 + 2.0\nt2 = n0 * t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.39999999999999997" + ], + "split": "train" + }, + { + "Input": "the number 1254 is divisible by which number ?", + "Output Program": [ + "n0 = 1254.0\nt0 = 100.0 + 100.0\nt1 = 10.0 - 1.0\nt2 = t0 + t1\nanswer = n0 / t2\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "a certain no . when divided by 35 leaves aremainder 25 , what is the remainder if the same no . be divided by 15 ?", + "Output Program": [ + "n0 = 35.0\nn1 = 25.0\nn2 = 15.0\nt0 = n0 - n1\nt1 = t0 - 4.0\nanswer = t1 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "if x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year , the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $ 56 . if $ 2,000 is the total amount invested , how much is invested at 8 percent ?", + "Output Program": [ + "n0 = 10.0\nn1 = 8.0\nn2 = 10.0\nn3 = 8.0\nn4 = 56.0\nn5 = 2000.0\nn6 = 8.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = n0 * 100.0\nt3 = n0 * n1\nt4 = t0 + t1\nt5 = t2 * 2.0\nt6 = t3 * 2.0\nt7 = n4 + t6\nt8 = t7 / t4\nanswer = t5 - t8\nprint(answer)" + ], + "Output Answer": [ + "800" + ], + "split": "train" + }, + { + "Input": "54 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780 . the bigger part is", + "Output Program": [ + "n0 = 54.0\nn1 = 10.0\nn2 = 22.0\nn3 = 780.0\nt0 = n0 * n1\nt1 = n2 - n1\nt2 = n3 - t0\nt3 = t2 / t1\nanswer = n0 - t3\nprint(answer)" + ], + "Output Answer": [ + "34" + ], + "split": "train" + }, + { + "Input": "the average age of one class strength 32 students is 16 yrs . if the staff ' s age is also included , the average increases by one year . find the age of the staff", + "Output Program": [ + "n0 = 32.0\nn1 = 16.0\nt0 = n0 + 1.0\nt1 = n1 + 1.0\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "49" + ], + "split": "train" + }, + { + "Input": "a man purchased 5 blankets @ rs . 100 each , 5 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ?", + "Output Program": [ + "n0 = 5.0\nn1 = 100.0\nn2 = 5.0\nn3 = 150.0\nn4 = 150.0\nt0 = n3 * 10.0\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "250" + ], + "split": "train" + }, + { + "Input": "working simultaneously and independently at an identical constant rate , 5 machines of a certain type can produce a total of x units of product p in 8 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 3 x units of product p in 4 days ?", + "Output Program": [ + "n0 = 5.0\nn1 = 8.0\nn2 = 3.0\nn3 = 4.0\nt0 = n1 / n3\nt1 = n0 * n2\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "3 litre of water is added to 11 litre of a solution containing 42 % of alcohol in the water . the percentage of alcohol in the new mixture is ?", + "Output Program": [ + "n0 = 3.0\nn1 = 11.0\nn2 = 42.0\nt0 = n0 + n1\nt1 = n1 * n2\nt2 = t1 / 100.0\nt3 = t2 / t0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "a trailer carries 3 , 4 and 5 crates on a trip . each crate weighs no less than 120 kg . what is the maximum weight of the crates on a single trip ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 5.0\nn3 = 120.0\n\nanswer = n2 * n3\nprint(answer)" + ], + "Output Answer": [ + "600" + ], + "split": "train" + }, + { + "Input": "the average of first 3 prime numbers greater than 20 is ?", + "Output Program": [ + "n0 = 3.0\nn1 = 20.0\nt0 = n1 + 3.0\nt1 = t0 + 4.0\nt2 = t1 + 2.0\nt3 = t0 + t2\nt4 = t2 + 2.0\nt5 = t3 + t4\nanswer = t5 / n0\nprint(answer)" + ], + "Output Answer": [ + "27.666666666666668" + ], + "split": "train" + }, + { + "Input": "if x and y are integers , what is the least positive number of 24 x + 16 y ?", + "Output Program": [ + "n0 = 24.0\nn1 = 16.0\n\nanswer = n0 - n1\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a certain company retirement plan has arule of 70 provision that allows an employee to retire when the employee ' s age plus years of employment with the company total at least 70 . in what year could a female employee hired in 1987 on her 32 nd birthday first be eligible to retire under this provision ?", + "Output Program": [ + "n0 = 70.0\nn1 = 70.0\nn2 = 1987.0\nn3 = 32.0\nt0 = n0 - n3\nt1 = t0 / 2.0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "2006" + ], + "split": "train" + }, + { + "Input": "if 10 boys meet at a reunion and each boy shakes hands exactly once with each of the others , then what is the total number of handshakes", + "Output Program": [ + "import math\nn0 = 10.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(2.0)))\nt2 = n0 - 2.0\nt3 = math.factorial(min(15, int(t2)))\nt4 = t3 * t1\nanswer = t0 / t4\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "6 x \u2013 5 y + 3 z = 22 4 x + 8 y \u2013 11 z = 7 5 x \u2013 6 y + 2 z = 12 given the equations above , x + y + z = ?", + "Output Program": [ + "n0 = 6.0\nn1 = 5.0\nn2 = 3.0\nn3 = 22.0\nn4 = 4.0\nn5 = 8.0\nn6 = 11.0\nn7 = 7.0\nn8 = 5.0\nn9 = 6.0\nn10 = 2.0\nn11 = 12.0\n\nanswer = n1 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the output of a factory is increased by 10 % to keep up with rising demand . to handle the holiday rush , this new output is increased by 60 % . by approximately what percent would the output of the factory now have to be decreased in order to restore the original output ?", + "Output Program": [ + "n0 = 10.0\nn1 = 60.0\nt0 = n0 + 100.0\nt1 = n1 + 100.0\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = t2 * t3\nt5 = t4 - 1.0\nt6 = t5 / t4\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "43.18181818181819" + ], + "split": "train" + }, + { + "Input": "average of money that group of 4 friends pay for rent each month is $ 800 . after one persons rent is increased by 16 % the new mean is $ 850 . what was original rent of friend whose rent is increased ?", + "Output Program": [ + "n0 = 4.0\nn1 = 800.0\nn2 = 16.0\nn3 = 850.0\nt0 = n2 / 100.0\nt1 = n3 - n1\nt2 = n0 * t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "1250" + ], + "split": "train" + }, + { + "Input": "which number should replace both the asterisks in ( * / 18 ) x ( * / 162 ) = 1 ?", + "Output Program": [ + "import math\nn0 = 18.0\nn1 = 162.0\nn2 = 1.0\nt0 = n0 * n1\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "train" + }, + { + "Input": "anne bought doughnuts for a class breakfast party . she bought 5 chocolate doughnuts , 6 coconut doughnuts , and 11 jam - filled doughnuts . how many doughnuts did anne buy in all ?", + "Output Program": [ + "n0 = 5.0\nn1 = 6.0\nn2 = 11.0\nt0 = n0 + n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "gopi gives rs . 90 plus one turban as salary to his servant for one year . the servant leaves after 9 months and receives rs . 55 and the turban . find the price of the turban .", + "Output Program": [ + "n0 = 90.0\nn1 = 9.0\nn2 = 55.0\nt0 = n0 - n2\nt1 = 12.0 - n1\nt2 = t0 / t1\nt3 = t2 * 12.0\nanswer = t3 - n0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "the average of 50 numbers is 38 . if two numbers 45 and 55 are discarded , the average of the remaining set of numbers is", + "Output Program": [ + "n0 = 50.0\nn1 = 38.0\nn2 = 45.0\nn3 = 55.0\nt0 = n0 * n1\nt1 = n0 - 2.0\nt2 = t0 - n2\nt3 = t2 - n3\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "37.5" + ], + "split": "train" + }, + { + "Input": "if the price of petrol increases by 20 , by how much must a user cut down his consumption so that his expenditure on petrol remains constant ?", + "Output Program": [ + "n0 = 20.0\nt0 = n0 + 100.0\nt1 = 100.0 / t0\nt2 = 1.0 - t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "16.666666666666664" + ], + "split": "train" + }, + { + "Input": "a cargo ship carrying 4 kinds of items , doohickies , geegaws , widgets , and yamyams , arrives at the port . each item weighs 2 , 11 , 5 , and 7 pounds , respectively , and each item is weighed as it is unloaded . if , in the middle of the unloading process , the product of the individual weights of the unloaded items equals 104 , 350400 pounds , how many widgets have been unloaded ?", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\nn2 = 11.0\nn3 = 5.0\nn4 = 7.0\nn5 = 104.0\nn6 = 350400.0\n\nanswer = 1.0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "bert left the house with n dollars . he spent 1 / 4 of this at the hardware store , then $ 9 at the dry cleaners , and then half of what was left at the grocery store . when he got home , he had $ 15 left in his pocket . what was the value of n ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 9.0\nn3 = 15.0\nt0 = n2 / 2.0\nt1 = n0 / n1\nt2 = n3 + t0\nt3 = n0 - t1\nt4 = 1 / t3\nt5 = t2 * t4\nanswer = t5 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "52" + ], + "split": "train" + }, + { + "Input": "a company has $ 329864 in its account . what is the least amount of money ( in whole number of dollars ) that it must add to the account if the money is paid evenly among 9 of its vendors ?", + "Output Program": [ + "n0 = 329864.0\nn1 = 9.0\nt0 = n0 % n1\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "in a group of ducks and cows , the total number of legs are 34 more than twice the no . of heads . find the total no . of buffaloes .", + "Output Program": [ + "n0 = 34.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "in a division sum , the remainder is 0 . as student mistook the divisor by 12 instead of 21 and obtained 63 as quotient . what is the correct quotient ?", + "Output Program": [ + "n0 = 0.0\nn1 = 12.0\nn2 = 21.0\nn3 = 63.0\nt0 = n1 * n3\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "the difference between a positive proper fraction and its reciprocal is 9 / 20 . then the fraction is :", + "Output Program": [ + "n0 = 9.0\nn1 = 20.0\nt0 = n0 - 4.0\nanswer = 4.0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.8" + ], + "split": "train" + }, + { + "Input": "a sum of money is to be distributed among a , b , c , d in the proportion of 6 : 3 : 5 : 4 . if c gets rs . 1000 more than d , what is b ' s share ?", + "Output Program": [ + "n0 = 6.0\nn1 = 3.0\nn2 = 5.0\nn3 = 4.0\nn4 = 1000.0\nt0 = n2 - n3\nt1 = n4 * t0\nanswer = 3.0 * t1\nprint(answer)" + ], + "Output Answer": [ + "3000" + ], + "split": "train" + }, + { + "Input": "a sports equipment store sold ping pong rackets for a total of $ 686 . if the average ( arithmetic mean ) price of a pair of rackets is $ 9.8 , how many pairs were sold ?", + "Output Program": [ + "n0 = 686.0\nn1 = 9.8\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "train" + }, + { + "Input": "the average weight of 8 person ' s increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 3.5\nn2 = 65.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "93" + ], + "split": "train" + }, + { + "Input": "if xy > 0 , 1 / x + 1 / y = 15 , and 1 / xy = 5 , then ( x + y ) / 5 = ?", + "Output Program": [ + "n0 = 0.0\nn1 = 1.0\nn2 = 1.0\nn3 = 15.0\nn4 = 1.0\nn5 = 5.0\nn6 = 5.0\nt0 = n3 / n5\nanswer = t0 / n5\nprint(answer)" + ], + "Output Answer": [ + "0.6" + ], + "split": "train" + }, + { + "Input": "there are 60 doors marked with numbers 1 to 60 . there are 60 individuals marked 1 to 60 . an operation on a door is defined as changing the status of the door from open to closed or vice versa . all the doors are closed to start with . one at a time , one randomly chosen individual goes and operates the doors . the individual however operates only those doors which are a multiple of the number he / she is carrying . for example , the individual marked with number 5 operates the doors marked with 5 , 10 , 15 , 20 , 25 , 30 , 35 , 40 , 45 , 50 , 55 , and 60 . if every individual in the group gets one turn , then how many doors are open at the end ?", + "Output Program": [ + "n0 = 60.0\nn1 = 1.0\nn2 = 60.0\nn3 = 60.0\nn4 = 1.0\nn5 = 60.0\nn6 = 5.0\nn7 = 5.0\nn8 = 10.0\nn9 = 15.0\nn10 = 20.0\nn11 = 25.0\nn12 = 30.0\nn13 = 35.0\nn14 = 40.0\nn15 = 45.0\nn16 = 50.0\nn17 = 55.0\nn18 = 60.0\nt0 = n0 / 10.0\nanswer = n1 + t0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "a call center has two teams . each member of team a was able to process 3 / 5 calls as compared to each member of team b . if team a has 5 / 8 as many number of call center agents as team b , what fraction of the total calls was processed by team b ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 5.0\nn3 = 8.0\nt0 = n1 * n3\nt1 = n0 * n1\nt2 = t0 + t1\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.7272727272727273" + ], + "split": "train" + }, + { + "Input": "cindy has her eye on a sundress but thinks it is too expensive . it goes on sale for 15 % less than the original price . before cindy can buy the dress , however , the store raises the new price by 25 % . if the dress cost $ 71.4 after it went on sale for 15 % off , what is the difference between the original price and the final price ?", + "Output Program": [ + "n0 = 15.0\nn1 = 25.0\nn2 = 71.4\nn3 = 15.0\nt0 = n1 + 100.0\nt1 = 100.0 - n0\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = n2 / t3\nt5 = n2 * t2\nanswer = t5 - t4\nprint(answer)" + ], + "Output Answer": [ + "5.249999999999986" + ], + "split": "train" + }, + { + "Input": "( 1 / 5 ) ^ e * ( 1 / 4 ) ^ 18 = 1 / ( 2 ( 10 ) ^ 35 ) . what is e ?", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 1.0\nn3 = 4.0\nn4 = 18.0\nn5 = 1.0\nn6 = 2.0\nn7 = 10.0\nn8 = 35.0\n\nanswer = n8 / n0\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "| 13 - 3 | - | 4 - 10 | = ?", + "Output Program": [ + "n0 = 13.0\nn1 = 3.0\nn2 = 4.0\nn3 = 10.0\nt0 = n0 - n1\nt1 = n3 - n2\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "the monthly salaries of 6 employees in a company are $ 1000 , $ 2500 , $ 3100 , $ 3650 , $ 1500 , $ 2000 . what is the mean of the salaries of 6 employees .", + "Output Program": [ + "n0 = 6.0\nn1 = 1000.0\nn2 = 2500.0\nn3 = 3100.0\nn4 = 3650.0\nn5 = 1500.0\nn6 = 2000.0\nn7 = 6.0\nt0 = n1 + n2\nt1 = n3 + t0\nt2 = n4 + t1\nt3 = n5 + t2\nt4 = n6 + t3\nanswer = t4 / n0\nprint(answer)" + ], + "Output Answer": [ + "2291.6666666666665" + ], + "split": "train" + }, + { + "Input": "when positive integer x is divided by positive integer y , the remainder is 6 . if x / y = 6.12 , what is the value of y ?", + "Output Program": [ + "import math\nn0 = 6.0\nn1 = 6.12\nt0 = math.floor(n1)\nt1 = n1 - t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "49.99999999999996" + ], + "split": "train" + }, + { + "Input": "two identical trains aa and bb running in opposite direction at same speed tale 2 min to cross each other completely . the number of bogies of aa are increased from 12 to 16 . how much more time would they now require to cross each other ?", + "Output Program": [ + "n0 = 2.0\nn1 = 12.0\nn2 = 16.0\nt0 = n1 + n1\nt1 = n0 * 60.0\nt2 = n2 - n1\nt3 = t1 / t0\nanswer = t3 * t2\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "a person starting with rs . 64 and making 6 bets , wins 3 times and loses 3 times , the wins and loses occurring in random order . the chance for a win is equal to the chance for a loss . if each wager is for 1 / 2 the money remaining at the time of the bet , then the final result is ?", + "Output Program": [ + "n0 = 64.0\nn1 = 6.0\nn2 = 3.0\nn3 = 3.0\nn4 = 1.0\nn5 = 2.0\nt0 = n4 / n5\nt1 = t0 + 1.0\nt2 = t0**min(3.0, 5)\nt3 = t1**min(3.0, 5)\nt4 = n0 * t3\nt5 = t4 * t2\nanswer = n0 - t5\nprint(answer)" + ], + "Output Answer": [ + "37" + ], + "split": "train" + }, + { + "Input": "a canoe has two oars , left and right . each oar either works or breaks . the failure or non - failure of each oar is independent of the failure or non - failure of the other . you can still row the canoe with one oar . the probability that the left oar works is 3 / 5 . the probability that the right oar works is also 3 / 5 . what is the probability y that you can still row the canoe ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 3.0\nn3 = 5.0\nt0 = n0 / n1\nt1 = 2.0 / n1\nt2 = t0 * t1\nt3 = t0 * t0\nt4 = t2 + t2\nanswer = t4 + t3\nprint(answer)" + ], + "Output Answer": [ + "0.84" + ], + "split": "train" + }, + { + "Input": "if jake loses 15 pounds , he will weigh twice as much as his sister . together they now weigh 132 pounds . what is jake \u2019 s present weight , in pounds ?", + "Output Program": [ + "n0 = 15.0\nn1 = 132.0\nt0 = n1 - n0\nt1 = t0 / 3.0\nt2 = t1 * 2.0\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "93" + ], + "split": "train" + }, + { + "Input": "what is the decimal equivalent of ( 1 / 5 ) ^ 2 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 2.0\nt0 = n0 / n1\nanswer = t0**min(n2, 5)\nprint(answer)" + ], + "Output Answer": [ + "0.04000000000000001" + ], + "split": "train" + }, + { + "Input": "the average salary / head of allthe workers in a workshop is rs . 750 , if the average salary / head of 5 technician is rs . 900 and the average salary / head of the rest is rs . 700 , the total no . of workers in the work - shop is ?", + "Output Program": [ + "n0 = 750.0\nn1 = 5.0\nn2 = 900.0\nn3 = 700.0\nt0 = n1 * n2\nt1 = n1 * n3\nt2 = n0 - n3\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "the average age of 10 men increases by 6 years when two women are included in place of two men of ages 18 and 22 years . find the average age of the women ?", + "Output Program": [ + "n0 = 10.0\nn1 = 6.0\nn2 = 18.0\nn3 = 22.0\nt0 = n2 + n3\nt1 = n0 * n1\nt2 = t0 + t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "in a group of ducks and cows , the total number of legs are 48 more than twice the no . of heads . find the total no . of buffaloes .", + "Output Program": [ + "n0 = 48.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "two - third of a positive number and 64 / 216 of its reciprocal are equal . the number is :", + "Output Program": [ + "import math\nn0 = 64.0\nn1 = 216.0\nt0 = n0 * 3.0\nt1 = n1 * 2.0\nt2 = t0 / t1\nanswer = math.sqrt(max(0, t2))\nprint(answer)" + ], + "Output Answer": [ + "0.6666666666666666" + ], + "split": "train" + }, + { + "Input": "when positive integer m is divided by positive integer n , the remainder is 12 . if m / n = 24.2 , what is the value of n ?", + "Output Program": [ + "n0 = 12.0\nn1 = 24.2\nt0 = n1 % 1.0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "60.00000000000021" + ], + "split": "train" + }, + { + "Input": "if doubling a number and adding 20 to the result gives the same answer as multiplying the number by 8 and taking away 4 from the product , the number is", + "Output Program": [ + "n0 = 20.0\nn1 = 8.0\nn2 = 4.0\nt0 = n0 + n2\nt1 = n1 - 2.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "x + ( 1 / x ) = 3.5 find x ^ 2 + ( 1 / x ^ 2 )", + "Output Program": [ + "n0 = 1.0\nn1 = 3.5\nn2 = 2.0\nn3 = 1.0\nn4 = 2.0\nt0 = n1**min(n2, 5)\nanswer = t0 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "10.25" + ], + "split": "train" + }, + { + "Input": "what is the difference between the largest number and the least number written with the digits 9 , 2 , 1 , 5 ?", + "Output Program": [ + "n0 = 9.0\nn1 = 2.0\nn2 = 1.0\nn3 = 5.0\nt0 = n0 * 100.0\nt1 = n3 * 100.0\nt2 = n1 * 10.0\nt3 = n1 * 100.0\nt4 = n3 * 10.0\nt5 = t3 + 1000.0\nt6 = t0 * 10.0\nt7 = t6 + t1\nt8 = t5 + t4\nt9 = t7 + t2\nt10 = n0 + t8\nt11 = n2 + t9\nanswer = t11 - t10\nprint(answer)" + ], + "Output Answer": [ + "8262" + ], + "split": "train" + }, + { + "Input": "a school has 4 section of chemistry in class x having 70 , 35 , 45 and 42 students . the mean marks obtained in chemistry test are 50 , 60 , 55 and 45 respectively for the 4 sections . determine the overall average of marks per student .", + "Output Program": [ + "n0 = 4.0\nn1 = 70.0\nn2 = 35.0\nn3 = 45.0\nn4 = 42.0\nn5 = 50.0\nn6 = 60.0\nn7 = 55.0\nn8 = 45.0\nn9 = 4.0\nt0 = n1 + n2\nt1 = n1 * n5\nt2 = n2 * n6\nt3 = n3 * n7\nt4 = n3 * n4\nt5 = t1 + t2\nt6 = n3 + t0\nt7 = t5 + t3\nt8 = n4 + t6\nt9 = t7 + t4\nanswer = t9 / t8\nprint(answer)" + ], + "Output Answer": [ + "51.901041666666664" + ], + "split": "train" + }, + { + "Input": "how much is 40 % of 60 is greater than 4 / 5 of 25 ?", + "Output Program": [ + "n0 = 40.0\nn1 = 60.0\nn2 = 4.0\nn3 = 5.0\nn4 = 25.0\nt0 = n0 / 100.0\nt1 = n2 / n3\nt2 = n1 * t0\nt3 = n4 * t1\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "ashok borrowed some money at the rate of 6 % p . a . for the first two years , at the rate of 9 % p . a . for the next 3 years and at the rate of 14 % p . a . for the period beyond 5 years . if he pays a total interest of 11400 / - at the end of 9 years , how much money did he borrow ?", + "Output Program": [ + "n0 = 6.0\nn1 = 9.0\nn2 = 3.0\nn3 = 14.0\nn4 = 5.0\nn5 = 11400.0\nn6 = 9.0\nt0 = n0 * 2.0\nt1 = n1 * n2\nt2 = n1 - 3.0\nt3 = t0 / 100.0\nt4 = t1 / 100.0\nt5 = t2 - 2.0\nt6 = t3 + t4\nt7 = n3 * t5\nt8 = t7 / 100.0\nt9 = t6 + t8\nanswer = n5 / t9\nprint(answer)" + ], + "Output Answer": [ + "12000" + ], + "split": "train" + }, + { + "Input": "` ` i am 8 times as old as you were when i was as old as you are ` ` , said a man to his son . find out their present ages if the sum of the their ages is 75 years .", + "Output Program": [ + "n0 = 8.0\nn1 = 75.0\nt0 = n0 + 1.0\nt1 = n0 * 2.0\nt2 = t0 / t1\nt3 = t2 + 1.0\nt4 = n1 / t3\nanswer = n1 - t4\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "train" + }, + { + "Input": "ada and paul received their scores on 3 tests . on the first test , ada ' s score was 10 points higher than paul ' s score . on the second test , ada ' s score was 4 points higher than paul ' s score . if paul ' s average ( arithmetic mean ) score on the 3 tests was 4 points higher than ada ' s average score on the 3 tests , then paul ' s score on the third test was how many points higher than ada ' s score ?", + "Output Program": [ + "n0 = 3.0\nn1 = 10.0\nn2 = 4.0\nn3 = 3.0\nn4 = 4.0\nn5 = 3.0\nt0 = n0 * n2\nt1 = n1 + t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "in a company with 48 employees , some part - time and some full - time , exactly ( 1 / 3 ) of the part - time employees and ( 1 / 4 ) of the full - time employees take the subway to work . what is the greatest possible number of employees who take the subway to work ?", + "Output Program": [ + "n0 = 48.0\nn1 = 1.0\nn2 = 3.0\nn3 = 1.0\nn4 = 4.0\nt0 = n0 * n2\nt1 = n2 * n4\nt2 = t0 / t1\nt3 = n0 - t1\nt4 = t3 / t2\nanswer = t2 + t4\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "in a certain company , the ratio of the number of managers to the number of non - managers in any department must always be greater than 7 : 37 . in the company , what is the maximum number of non - managers in a department that has 9 managers ?", + "Output Program": [ + "import math\nn0 = 7.0\nn1 = 37.0\nn2 = 9.0\nt0 = n1 * n2\nt1 = t0 / n0\nanswer = math.floor(t1)\nprint(answer)" + ], + "Output Answer": [ + "47" + ], + "split": "train" + }, + { + "Input": "joe \u2019 s average ( arithmetic mean ) test score across 4 equally weighted tests was 60 . he was allowed to drop his lowest score . after doing so , his average test score improved to 65 . what is the lowest test score that was dropped ?", + "Output Program": [ + "n0 = 4.0\nn1 = 60.0\nn2 = 65.0\nt0 = n0 * n1\nt1 = n2 * 3.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "in kaya ' s teacher ' s desk there are 9 pink highlighters , 8 yellow highlighters , and 5 blue highlighters . how many highlighters are there in all ?", + "Output Program": [ + "n0 = 9.0\nn1 = 8.0\nn2 = 5.0\nt0 = n0 + n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "the average age of 20 students of a class is 20 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years , the age of the 20 th student is", + "Output Program": [ + "n0 = 20.0\nn1 = 20.0\nn2 = 5.0\nn3 = 14.0\nn4 = 9.0\nn5 = 16.0\nn6 = 20.0\nt0 = n0 * n0\nt1 = n2 * n3\nt2 = n4 * n5\nt3 = t1 + t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "186" + ], + "split": "train" + }, + { + "Input": "little roshini had $ 10.50 . he spent some money on sweets and gave to his two friends $ 3.40 each . how much money was spent for sweets ?", + "Output Program": [ + "n0 = 10.5\nn1 = 3.4\nt0 = n1 * 2.0\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "3.7" + ], + "split": "train" + }, + { + "Input": "a batsman makes a score of 110 runs in the 11 th inning and thus increases his average by 5 . find his average after 11 th inning .", + "Output Program": [ + "n0 = 110.0\nn1 = 11.0\nn2 = 5.0\nn3 = 11.0\nt0 = n1 * n2\nt1 = n0 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "the difference of two numbers is 8 and one - fourth of their sum is 6 . find the numbers .", + "Output Program": [ + "n0 = 8.0\nn1 = 6.0\nt0 = 10.0 / 2.0\nt1 = n1 * t0\nt2 = n0 + t1\nt3 = t2 / 2.0\nt4 = t1 - t3\nanswer = t0 + t4\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "a retailer bought a shirt at wholesale and marked it up 80 % to its initial price of $ 45 . by how many more dollars does he need to increase the price to achieve a 100 % markup ?", + "Output Program": [ + "n0 = 80.0\nn1 = 45.0\nn2 = 100.0\nt0 = n0 / n2\nt1 = t0 + 1.0\nt2 = n1 / t1\nt3 = t2 * 2.0\nanswer = t3 - n1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "at a certain company , each employee has a salary grade s that is at least 1 and at most 5 . each employee receives an hourly wage p , in dollars , determined by the formula p = 7.50 + 0.25 ( s \u2013 1 ) . an employee with a salary grade of 5 receives how many more dollars per hour than an employee with a salary grade of 1 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 7.5\nn3 = 0.25\nn4 = 1.0\nn5 = 5.0\nn6 = 1.0\nt0 = n1 - n0\nt1 = n3 * t0\nanswer = n3 + t1\nprint(answer)" + ], + "Output Answer": [ + "1.25" + ], + "split": "train" + }, + { + "Input": "a car traveled 40 % of the way from town x to town y at an average speed of 40 mph . the car traveled at an average speed of v mph for the remaining part of the trip . the average speed for the entire trip was 50 mph . what is v in mph ?", + "Output Program": [ + "n0 = 40.0\nn1 = 40.0\nn2 = 50.0\nt0 = n0 / n0\nt1 = 100.0 - n0\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "the average weight of a , b and c is 45 kg . if the average weight of a and b be 40 kg and that of b and c be 43 kg , what is the weight of b ?", + "Output Program": [ + "n0 = 45.0\nn1 = 40.0\nn2 = 43.0\nt0 = n1 * 2.0\nt1 = n2 * 2.0\nt2 = n0 * 3.0\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "31" + ], + "split": "train" + }, + { + "Input": "if 4 < x < 6 < y < 10 , then what is the greatest possible positive integer difference of x and y ?", + "Output Program": [ + "n0 = 4.0\nn1 = 6.0\nn2 = 10.0\nt0 = n2 - n0\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "there are 7 players in a chess group , and each player plays each of the others once . given that each game is played by two players , how many total games will be played ?", + "Output Program": [ + "n0 = 7.0\nt0 = n0 - 1.0\nt1 = n0 * t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "find the total average marks of all the students in 2 separate classes , if the average marks of students in the first class of 39 students is 45 and that of another class of 35 students is 70 .", + "Output Program": [ + "n0 = 2.0\nn1 = 39.0\nn2 = 45.0\nn3 = 35.0\nn4 = 70.0\nt0 = n2 * 1.0\nt1 = t0 + 4.0\nt2 = t1 + 12.0\nt3 = t2 - 4.0\nt4 = t3 - 0.25\nt5 = t4 + 1.0\nanswer = t5 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "56.75" + ], + "split": "train" + }, + { + "Input": "in an examination , 300 students appeared . out of these students ; 27 % got first division , 54 % got second division and the remaining just passed . assuming that no student failed ; find the number of students who just passed .", + "Output Program": [ + "n0 = 300.0\nn1 = 27.0\nn2 = 54.0\nt0 = n1 + n2\nt1 = 100.0 - t0\nt2 = n0 * t1\nanswer = t2 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "57" + ], + "split": "train" + }, + { + "Input": "there are 9 cities numbered 1 to 9 . from how many cities the flight can start so as to reach the city 8 either directly or indirectly such that the path formed is divisible by 3 .", + "Output Program": [ + "n0 = 9.0\nn1 = 1.0\nn2 = 9.0\nn3 = 8.0\nn4 = 3.0\n\nanswer = n0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "find the sum lend at c . i . at 5 p . c per annum will amount to rs . 740 in 2 years ?", + "Output Program": [ + "n0 = 5.0\nn1 = 740.0\nn2 = 2.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nt2 = t1**min(n2, 5)\nanswer = n1 / t2\nprint(answer)" + ], + "Output Answer": [ + "671.2018140589569" + ], + "split": "train" + }, + { + "Input": "when a number is divided by 6 & then multiply by 12 the answer is 18 what is the no . ?", + "Output Program": [ + "n0 = 6.0\nn1 = 12.0\nn2 = 18.0\nt0 = n2 / n1\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "what is the median of a set of consecutive integers if the sum of nth number from the beginning and nth number from the end is 200 ?", + "Output Program": [ + "n0 = 200.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "57 + 58 = 115 . how many such 2 consecutive numbers are there less than 1500 when added gives a sum which is divisible by 5 ?", + "Output Program": [ + "n0 = 57.0\nn1 = 58.0\nn2 = 115.0\nn3 = 2.0\nn4 = 1500.0\nn5 = 5.0\n\nanswer = n4 / n5\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "the diameter of a garden roller is 1.4 m and it is 2 m long . how much area will it cover in 5 revolutions ? ( use \u03c0 = 22 \u2044 7 )", + "Output Program": [ + "n0 = 1.4\nn1 = 2.0\nn2 = 5.0\nn3 = 22.0\nn4 = 7.0\nt0 = n0 / n1\nt1 = n3 / n4\nt2 = t1 * n1\nt3 = t0 * t2\nt4 = n1 * t3\nanswer = n2 * t4\nprint(answer)" + ], + "Output Answer": [ + "43.99999999999999" + ], + "split": "train" + }, + { + "Input": "what is the dividend . divisor 16 , the quotient is 8 and the remainder is 4", + "Output Program": [ + "n0 = 16.0\nn1 = 8.0\nn2 = 4.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "132" + ], + "split": "train" + }, + { + "Input": "in a coconut grove , ( x + 1 ) trees yield 60 nuts per year , x trees yield 120 nuts per year and ( x \u2013 1 ) trees yield 180 nuts per year . if the average yield per year per tree be 100 , find x .", + "Output Program": [ + "n0 = 1.0\nn1 = 60.0\nn2 = 120.0\nn3 = 1.0\nn4 = 180.0\nn5 = 100.0\nt0 = n1 + n2\nt1 = n0 * n4\nt2 = n0 * n1\nt3 = n5 * 3.0\nt4 = n4 + t0\nt5 = t1 - t2\nt6 = t4 - t3\nanswer = t5 / t6\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a certain no . whendivided by 35 leaves a remainder 25 , what is the remainder if the same no . be dividedby 15 ?", + "Output Program": [ + "n0 = 35.0\nn1 = 25.0\nn2 = 15.0\nt0 = n0 + n1\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": ". on dividing a number by 357 , we get 36 as remainder . on dividing the same number 17 , what will be the remainder ?", + "Output Program": [ + "import math\nn0 = 357.0\nn1 = 36.0\nn2 = 17.0\nt0 = n1 / n2\nanswer = math.factorial(min(15, int(t0)))\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "carina has 55 ounces of coffee divided into 5 - and 10 - ounce packages . if she has 2 more 5 - ounce packages than 10 - ounce packages , how many 10 - ounce packages does she have ?", + "Output Program": [ + "n0 = 55.0\nn1 = 5.0\nn2 = 10.0\nn3 = 2.0\nn4 = 5.0\nn5 = 10.0\nn6 = 10.0\nt0 = n1 + n2\nt1 = n1 * n3\nt2 = n0 - t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "notebooks are sold in packages of 4 or 7 only . if wilson bought 69 notebooks exactly , what could be the number of large packs wilson bought ?", + "Output Program": [ + "n0 = 4.0\nn1 = 7.0\nn2 = 69.0\nt0 = n2 - n0\nt1 = t0 - n0\nt2 = t1 - n0\nt3 = t2 - n0\nt4 = t3 - n0\nanswer = t4 / n1\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "the ages of two person differ by 20 years . if 4 years ago , the elder one be 5 times as old as the younger one , their present ages ( in years ) are respectively", + "Output Program": [ + "n0 = 20.0\nn1 = 4.0\nn2 = 5.0\nt0 = n1 * n2\nt1 = n0 - n1\nt2 = n2 - 1.0\nt3 = t0 + t1\nt4 = t3 / t2\nanswer = n0 + t4\nprint(answer)" + ], + "Output Answer": [ + "29" + ], + "split": "train" + }, + { + "Input": "how many 3 - digit integers exist such that all their digits are odd ?", + "Output Program": [ + "n0 = 3.0\nt0 = n0 + 2.0\nanswer = t0**min(n0, 5)\nprint(answer)" + ], + "Output Answer": [ + "125" + ], + "split": "train" + }, + { + "Input": "matt gets a $ 1,300 commission on a big sale . this commission alone raises his average commission by $ 150 . if matt ' s new average commission is $ 400 , how many sales has matt made ?", + "Output Program": [ + "n0 = 1300.0\nn1 = 150.0\nn2 = 400.0\nt0 = 1000.0 - 100.0\nt1 = n2 - n1\nt2 = n2 - t1\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "a student is ranked 13 th from right and 8 th from left . how many are there ?", + "Output Program": [ + "n0 = 13.0\nn1 = 8.0\nt0 = n0 + n1\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "a is older than b by 5 years . 7 years hence , thrice a ' s age shall be equal to 4 times that of b . find their present ages .", + "Output Program": [ + "n0 = 5.0\nn1 = 7.0\nn2 = 4.0\nt0 = n0 * 3.0\nt1 = n1 * 3.0\nt2 = n1 * n2\nt3 = t0 + t1\nt4 = t3 - t2\nanswer = n0 + t4\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "what is x if x + 2 y = 20 and y = 5 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 20.0\nn2 = 5.0\nt0 = n0 * n2\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "if 2 x + y = 4 and x + 2 y = 5 , then ( x + y ) / 3 =", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 2.0\nn3 = 5.0\nn4 = 3.0\nt0 = n0 * n1\nt1 = n0 * n0\nt2 = t0 - n3\nt3 = t1 - 1.0\nt4 = t2 / t3\nt5 = n0 * t4\nt6 = n1 - t5\nt7 = t4 + t6\nanswer = t7 / n4\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "the least number which when increased by 6 each divisible by each one of 24 , 32 , 36 and 54 is :", + "Output Program": [ + "import scipy\nn0 = 6.0\nn1 = 24.0\nn2 = 32.0\nn3 = 36.0\nn4 = 54.0\nt0 = scipy.lcm(int(n1), int(n2))\nt1 = scipy.lcm(int(n3), int(t0))\nt2 = scipy.lcm(int(n4), int(t1))\nanswer = t2 - n0\nprint(answer)" + ], + "Output Answer": [ + "858" + ], + "split": "train" + }, + { + "Input": "find the mean proportional between 81 & 100 ?", + "Output Program": [ + "n0 = 81.0\nn1 = 100.0\nt0 = n0 + n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "90.5" + ], + "split": "train" + }, + { + "Input": "evaluate : 1234562 - 12 * 3 * 2 = ?", + "Output Program": [ + "n0 = 1234562.0\nn1 = 12.0\nn2 = 3.0\nn3 = 2.0\nt0 = n1 * n2\nt1 = n3 * t0\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "1234490" + ], + "split": "train" + }, + { + "Input": "if k is a non - negative integer and 12 ^ k is a divisor of 856,736 then 3 ^ k - k ^ 3 =", + "Output Program": [ + "n0 = 12.0\nn1 = 856736.0\nn2 = 3.0\nn3 = 3.0\nt0 = 1.0 - 1.0\nt1 = n2**min(t0, 5)\nt2 = t0**min(n2, 5)\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "the maximum number of students among them 1230 pens and 920 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :", + "Output Program": [ + "import scipy\nn0 = 1230.0\nn1 = 920.0\n\nanswer = scipy.gcd(int(n0), int(n1))\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "3889 + 12.808 - ? = 3854.002", + "Output Program": [ + "n0 = 3889.0\nn1 = 12.808\nn2 = 3854.002\nt0 = n0 + n1\nanswer = t0 - n2\nprint(answer)" + ], + "Output Answer": [ + "47.80600000000004" + ], + "split": "train" + }, + { + "Input": "a sum of money is sufficient to pay a ' s wages for 20 days and b ' s wages for 30 days . the same money is sufficient to pay the wages of both for ?", + "Output Program": [ + "n0 = 20.0\nn1 = 30.0\nt0 = 1.0 / n0\nt1 = 1.0 / n1\nt2 = t0 + t1\nanswer = 1.0 / t2\nprint(answer)" + ], + "Output Answer": [ + "11.999999999999998" + ], + "split": "train" + }, + { + "Input": "what will be the reminder when ( 43 ^ 43 + 43 ) is divided by 44 ?", + "Output Program": [ + "import math\nn0 = 43.0\nn1 = 43.0\nn2 = 43.0\nn3 = 44.0\nt0 = n0**min(n0, 5)\nt1 = n0 + t0\nt2 = t1 / n3\nt3 = math.floor(t2)\nt4 = n3 * t3\nanswer = t1 - t4\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "the total of 342 of 20 paise and 25 paise make a sum of rs . 71 . the no of 20 paise coins is", + "Output Program": [ + "n0 = 342.0\nn1 = 20.0\nn2 = 25.0\nn3 = 71.0\nn4 = 20.0\nt0 = n0 * n2\nt1 = n3 * 100.0\nt2 = n2 - n1\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "290" + ], + "split": "train" + }, + { + "Input": "in a group of ducks and cows , the total number of legs are 20 more than twice the no . of heads . find the total no . of buffaloes .", + "Output Program": [ + "n0 = 20.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the average weight of a , b and c is 45 kg . if the average weight of a and b be 40 kg and that of b and c be 41 kg , then the weight of b is :", + "Output Program": [ + "n0 = 45.0\nn1 = 40.0\nn2 = 41.0\nt0 = n1 * 2.0\nt1 = n2 * 2.0\nt2 = n0 * 3.0\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "train" + }, + { + "Input": "the product of two positive integers is 323 and their difference is 2 . what is the smaller number ?", + "Output Program": [ + "n0 = 323.0\nn1 = 2.0\nt0 = n0 / n1\nt1 = n0 / t0\nt2 = t1 * 4.0\nt3 = t2 + 10.0\nanswer = t3 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "3034 \u2212 ( 1002 \u00f7 20.04 ) = ?", + "Output Program": [ + "n0 = 3034.0\nn1 = 1002.0\nn2 = 20.04\nt0 = n1 / n2\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "2984" + ], + "split": "train" + }, + { + "Input": "a number is doubled and 9 is added . if the resultant is trebled , it becomes 57 . what is that number ?", + "Output Program": [ + "n0 = 9.0\nn1 = 57.0\nt0 = n0 * 3.0\nt1 = 2.0 * 3.0\nt2 = n1 - t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "mark and ann together were allocated n boxes of cookies to sell for a club project . mark sold 9 boxes less than n and ann sold 2 boxes less than n . if mark and ann have each sold at least one box of cookies , but together they have sold less than n boxes , what is the value of n ?", + "Output Program": [ + "n0 = 9.0\nn1 = 2.0\n\nanswer = n0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "135 liters of a mixture of milk and water contains in the ratio 3 : 2 . how much water should now be added so that the ratio of milk and water becomes 3 : 4 ?", + "Output Program": [ + "n0 = 135.0\nn1 = 3.0\nn2 = 2.0\nn3 = 3.0\nn4 = 4.0\nt0 = n1 + n2\nt1 = n0 / t0\nanswer = n2 * t1\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "train" + }, + { + "Input": "90 is divided into two parts in such a way that seventh part of first and ninth part of second are equal . find the smallest part ?", + "Output Program": [ + "n0 = 90.0\nt0 = 3.0 + 4.0\nt1 = t0 + 2.0\nt2 = t0 / t1\nt3 = n0 * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "two persons raj and ramu started working for a company in similar jobs on january 1 , 1991 . raj ' s initial monthly salary was rs 400 , which increases by rs 40 after every year . ramu ' s initial monthly salary was rs 500 which increases by rs 20 after every 6 months . if these arrangements continue till december 31 , 200 . find the total salary they received during that period .", + "Output Program": [ + "n0 = 1.0\nn1 = 1991.0\nn2 = 400.0\nn3 = 40.0\nn4 = 500.0\nn5 = 20.0\nn6 = 6.0\nn7 = 31.0\nn8 = 200.0\nt0 = 2.0 + 3.0\nt1 = n2 * 2.0\nt2 = n4 * 2.0\nt3 = 10.0 - 1.0\nt4 = n5 - 1.0\nt5 = n3 * t3\nt6 = n5 * t4\nt7 = t1 + t5\nt8 = t2 + t6\nt9 = t7 * 12.0\nt10 = n6 * t8\nt11 = t0 * t9\nt12 = t10 * 10.0\nanswer = t11 + t12\nprint(answer)" + ], + "Output Answer": [ + "152400" + ], + "split": "train" + }, + { + "Input": "at a certain college , 80 percent of the total number of students are freshmen . if 60 percent of the fresh - men are enrolled in the school of liberal arts and , of these , 50 percent are psychology majors , what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts ?", + "Output Program": [ + "n0 = 80.0\nn1 = 60.0\nn2 = 50.0\nt0 = n0 * n1\nt1 = t0 / 100.0\nt2 = n2 * t1\nanswer = t2 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "craig sells major appliances . for each appliance he sells , craig receives a commission of $ 50 plus 10 percent of the selling price . during one particular week craig sold 6 appliances for selling prices totaling $ 3620 . what was the total of craig ' s commissions for that week ?", + "Output Program": [ + "n0 = 50.0\nn1 = 10.0\nn2 = 6.0\nn3 = 3620.0\nt0 = n3 / n1\nt1 = n0 * n2\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "662" + ], + "split": "train" + }, + { + "Input": "if 8 ^ x = 2 ^ 9 , what is x ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.0\nn2 = 9.0\n\nanswer = n2 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "i chose a number and divide it by 8 . then i subtracted 100 from the result and got 6 . what was the number i chose ?", + "Output Program": [ + "n0 = 8.0\nn1 = 100.0\nn2 = 6.0\nt0 = n1 + n2\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "848" + ], + "split": "train" + }, + { + "Input": "light glows for every 32 seconds . how many max . times did it glow between 1 : 57 : 58 and 3 : 20 : 47 am .", + "Output Program": [ + "n0 = 32.0\nn1 = 1.0\nn2 = 57.0\nn3 = 58.0\nn4 = 3.0\nn5 = 20.0\nn6 = 47.0\nt0 = n6 + 2.0\nt1 = 2.0 + 60.0\nt2 = n5 + t1\nt3 = t2 * 60.0\nt4 = t0 + t3\nanswer = t4 / n0\nprint(answer)" + ], + "Output Answer": [ + "155.28125" + ], + "split": "train" + }, + { + "Input": "the maximum numbers of students among them 781 pens and 710 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is", + "Output Program": [ + "n0 = 781.0\nn1 = 710.0\n\nanswer = n0 - n1\nprint(answer)" + ], + "Output Answer": [ + "71" + ], + "split": "train" + }, + { + "Input": "the sum of the present ages of two persons a and b is 60 . if the age of a is twice that of b , find the sum of their ages 3 years hence ?", + "Output Program": [ + "n0 = 60.0\nn1 = 3.0\nt0 = n0 / n1\nt1 = t0 + 3.0\nt2 = t0 * 2.0\nt3 = t2 + 3.0\nanswer = t3 + t1\nprint(answer)" + ], + "Output Answer": [ + "66" + ], + "split": "train" + }, + { + "Input": "two brothers ram and ravi appeared for an exam . the probability of selection of ram is 2 / 7 and that of ravi is 1 / 5 . find the probability that both of them are selected .", + "Output Program": [ + "n0 = 2.0\nn1 = 7.0\nn2 = 1.0\nn3 = 5.0\nt0 = n0 / n1\nt1 = n2 / n3\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "0.05714285714285714" + ], + "split": "train" + }, + { + "Input": "if 4 ^ ( 2 x + 2 ) = 16 ^ ( 3 x \u2212 1 ) , what is the value of x ?", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\nn2 = 2.0\nn3 = 16.0\nn4 = 3.0\nn5 = 1.0\nt0 = n1 + n1\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "you collect pens . suppose you start out with 25 . mike gives you another 22 pens . since her father makes pens , cindy decides to double your pens . since you ' re nice , you give sharon 19 pens . how many pens do you have at the end ?", + "Output Program": [ + "n0 = 25.0\nn1 = 22.0\nn2 = 19.0\nt0 = n0 + n1\nt1 = t0 * 2.0\nanswer = t1 - n2\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "the number 523 fbc is divisible by 7 , 89 . then what is the value of f * b * c", + "Output Program": [ + "n0 = 523.0\nn1 = 7.0\nn2 = 89.0\nt0 = 1.0 + 4.0\nt1 = n0 / 4.0\nt2 = t1 + t1\nt3 = t0 * 10.0\nt4 = t2 / 2.0\nanswer = t4 + t3\nprint(answer)" + ], + "Output Answer": [ + "180.75" + ], + "split": "train" + }, + { + "Input": "the toll t , in dollars , for a truck using a certain bridge is given by the formula t = 1.50 + 0.50 ( x \u2212 2 ) , where x is the number of axles on the truck . what is the toll for an 18 - wheel truck that has 2 wheels on its front axle and 2 wheels on each of its other axles ?", + "Output Program": [ + "n0 = 1.5\nn1 = 0.5\nn2 = 2.0\nn3 = 18.0\nn4 = 2.0\nn5 = 2.0\nt0 = n3 - n2\nt1 = t0 / n5\nt2 = t1 + 1.0\nt3 = t2 - n2\nt4 = n1 * t3\nanswer = n0 + t4\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "on a partly cloudy day , derek decides to walk back from work . when it is sunny , he walks at a speed of s miles / hr ( s is an integer ) and when it gets cloudy , he increases his speed to ( s + 1 ) miles / hr . if his average speed for the entire distance is 2.8 miles / hr , what fraction w of the total distance did he cover while the sun was shining on him ?", + "Output Program": [ + "import scipy\nn0 = 1.0\nn1 = 2.8\nt0 = scipy.lcm(int(2.0), int(3.0))\nt1 = t0 / n1\nanswer = t1 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "0.1428571428571428" + ], + "split": "train" + }, + { + "Input": "the sum of the fourth and twelfth term of an arithmetic progression is 20 . what is the sum of the first 17 terms of the arithmetic progression ?", + "Output Program": [ + "n0 = 20.0\nn1 = 17.0\nt0 = n0 * n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "170" + ], + "split": "train" + }, + { + "Input": "a cab driver 5 days income was $ 400 , $ 250 , $ 650 , $ 400 , $ 500 . then his average income is ?", + "Output Program": [ + "n0 = 5.0\nn1 = 400.0\nn2 = 250.0\nn3 = 650.0\nn4 = 400.0\nn5 = 500.0\nt0 = n1 + n2\nt1 = n3 + t0\nt2 = n4 + t1\nt3 = n5 + t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "440" + ], + "split": "train" + }, + { + "Input": "how many numbers between 190 and 580 are divisible by 4,5 and 6 ?", + "Output Program": [ + "import math\nn0 = 190.0\nn1 = 580.0\nn2 = 45.0\nn3 = 6.0\nt0 = n1 - n0\nt1 = t0 / n2\nt2 = math.floor(t1)\nanswer = t2 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "kamal obtained 76 , 60 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?", + "Output Program": [ + "n0 = 76.0\nn1 = 60.0\nn2 = 82.0\nn3 = 67.0\nn4 = 85.0\nn5 = 100.0\nt0 = n0 + n1\nt1 = 1.0 + 4.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "74" + ], + "split": "train" + }, + { + "Input": "if x + y = 14 , x - y = 60 , for integers of x and y , x = ?", + "Output Program": [ + "n0 = 14.0\nn1 = 60.0\nt0 = n0 + n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "37" + ], + "split": "train" + }, + { + "Input": "( \u221a 27 + \u221a 243 ) / \u221a 48 = ?", + "Output Program": [ + "import math\nn0 = 27.0\nn1 = 243.0\nn2 = 48.0\nt0 = math.sqrt(max(0, n0))\nt1 = math.sqrt(max(0, n1))\nt2 = math.sqrt(max(0, n2))\nt3 = t0 + t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "3.0000000000000004" + ], + "split": "train" + }, + { + "Input": "in a certain company , the ratio of male to female employees is 7 : 8 . if 3 more men were hired , this ratio would increase to 8 : 9 . how many male employees are there in the company ?", + "Output Program": [ + "n0 = 7.0\nn1 = 8.0\nn2 = 3.0\nn3 = 8.0\nn4 = 9.0\nt0 = n1 / n4\nt1 = n0 / n1\nt2 = t0 - t1\nt3 = n2 / t2\nt4 = n0 * t3\nanswer = t4 / n1\nprint(answer)" + ], + "Output Answer": [ + "189.00000000000068" + ], + "split": "train" + }, + { + "Input": "a guy was asked to specify his age in years . he said , \u201c take my age 5 years hence , multiply it by 5 and subtract 5 times of my age 5 years ago and you will know my age . \u201d what was the age of that guy ?", + "Output Program": [ + "n0 = 5.0\nn1 = 5.0\nn2 = 5.0\nn3 = 5.0\nt0 = n0 * n0\nanswer = t0 + t0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "a person travels from p to q a speed of 60 km / hr and returns by increasing his speed by 50 % . what is his average speed for both the trips ?", + "Output Program": [ + "n0 = 60.0\nn1 = 50.0\nt0 = n1 / 100.0\nt1 = t0 + 1.0\nt2 = n0 * t1\nt3 = n0 + t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "how much is 85 % of 40 is greater than 4 / 5 of 25 ?", + "Output Program": [ + "n0 = 85.0\nn1 = 40.0\nn2 = 4.0\nn3 = 5.0\nn4 = 25.0\nt0 = n0 / 100.0\nt1 = n2 / n3\nt2 = n1 * t0\nt3 = n4 * t1\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "in a fuel station the service costs $ 2.10 per vehicle and every liter of fuel costs $ 0.70 . assuming that you fill up 3 mini - vans and 2 trucks , what will be the total cost , if a mini - van ' s tank is 65 liters and a truck ' s tank is 120 % bigger and they are all empty ?", + "Output Program": [ + "n0 = 2.1\nn1 = 0.7\nn2 = 3.0\nn3 = 2.0\nn4 = 65.0\nn5 = 120.0\nt0 = n2 + n3\nt1 = n4 * n5\nt2 = n2 * n4\nt3 = t1 / 100.0\nt4 = n1 * t2\nt5 = n0 * t0\nt6 = n4 + t3\nt7 = n3 * t6\nt8 = n1 * t7\nt9 = t8 + t4\nanswer = t9 + t5\nprint(answer)" + ], + "Output Answer": [ + "347.2" + ], + "split": "train" + }, + { + "Input": "following an increase in prices , the price of a candy box was 10 pounds and the price of a can of soda was 15 pounds . if the price of a candy box was raised by 25 % , and the price of a can of soda was raised by 50 % . what was the price of a box of candy plus a can of soda before prices were raised ?", + "Output Program": [ + "n0 = 10.0\nn1 = 15.0\nn2 = 25.0\nn3 = 50.0\nt0 = n2 + 100.0\nt1 = n3 + 100.0\nt2 = n0 * 100.0\nt3 = n1 * 100.0\nt4 = t2 / t0\nt5 = t3 / t1\nanswer = t4 + t5\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "in how many ways can an answer key for a quiz be written if the quiz contains 4 true - false questions followed by 2 multiples - choice questions with 4 answer choices each , if the correct answers to all true - false questions can not be the same ?", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\nn2 = 4.0\nt0 = n2 * n2\nt1 = n1**min(n0, 5)\nt2 = t1 - n1\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "224" + ], + "split": "train" + }, + { + "Input": "the average age of 30 students in a class is 14 years . if the age of teacher is also included , the average becomes 15 years , find the age of the teacher .", + "Output Program": [ + "n0 = 30.0\nn1 = 14.0\nn2 = 15.0\nt0 = n0 * n1\nt1 = n2 + t0\nt2 = n0 + t1\nanswer = t2 - t0\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "the average weight of 8 persons increases by 3 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 3.0\nn2 = 65.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "89" + ], + "split": "train" + }, + { + "Input": "in a village of 100 households , 85 have at least one dvd player , 90 have at least one cell phone , and 55 have at least one mp 3 player . if x and y are respectively the greatest and lowest possible number of households that have all 3 of these devices , x \u2013 y is :", + "Output Program": [ + "n0 = 100.0\nn1 = 85.0\nn2 = 90.0\nn3 = 55.0\nn4 = 3.0\nn5 = 3.0\nt0 = n0 - n1\nt1 = n0 - n2\nt2 = n0 - n3\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n0 - t4\nanswer = n3 - t5\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "the total marks obtained by a student in mathematics and physics is 40 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together .", + "Output Program": [ + "n0 = 40.0\nn1 = 20.0\nt0 = n0 + n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "the average monthly salary of 20 employees in an organisation is rs . 1500 . if the manager ' s salary is added , then the average salary increases by rs . 100 . what is the manager ' s monthly salary ?", + "Output Program": [ + "n0 = 20.0\nn1 = 1500.0\nn2 = 100.0\nt0 = n1 + n2\nt1 = n0 + 1.0\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "3600" + ], + "split": "train" + }, + { + "Input": "a call center has two teams . each member of team a was able to process 6 / 5 calls as compared to each member of team b . if team a has 5 / 8 as many number of call center agents as team b , what fraction of the total calls was processed by team b ?", + "Output Program": [ + "n0 = 6.0\nn1 = 5.0\nn2 = 5.0\nn3 = 8.0\nt0 = n1 * n3\nt1 = n0 * n1\nt2 = t0 + t1\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.5714285714285714" + ], + "split": "train" + }, + { + "Input": "300 \u00d7 ? + ( 12 + 4 ) \u00d7 1 / 8 = 602", + "Output Program": [ + "n0 = 300.0\nn1 = 12.0\nn2 = 4.0\nn3 = 1.0\nn4 = 8.0\nn5 = 602.0\nt0 = n1 + n2\nt1 = n3 / n4\nt2 = t0 * t1\nt3 = n5 - t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "the average ( arithmetic mean ) of the 5 positive integers k , m , r , s , and t is 16 , and k < m < r < s < t . if t is 42 , what is the greatest possible value of the median of the 5 integers ?", + "Output Program": [ + "n0 = 5.0\nn1 = 16.0\nn2 = 42.0\nn3 = 5.0\nt0 = n0 * n1\nt1 = t0 - n2\nt2 = t1 / 2.0\nanswer = t2 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "if 12 people contributed a total of $ 20.00 toward a gift and each of them contributed at least $ 1.00 , then the maximum possible amount any one person could have contributed is", + "Output Program": [ + "n0 = 12.0\nn1 = 20.0\nn2 = 1.0\nt0 = n0 - 1.0\nt1 = n2 * t0\nanswer = n1 - t1\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "if the number is divided by 3 , it reduced by 48 . the number is", + "Output Program": [ + "n0 = 3.0\nn1 = 48.0\nt0 = n0 * n1\nt1 = n0 - 1.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "train" + }, + { + "Input": "if 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 26 , then n =", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 2.0\nn3 = 2.0\nn4 = 2.0\nn5 = 2.0\nn6 = 2.0\nn7 = 2.0\nn8 = 4.0\nn9 = 26.0\nt0 = n0 * n9\nt1 = t0 - n0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "if a - b = 5 and a 2 + b 2 = 34 , find the value of ab .", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 2.0\nn3 = 34.0\nt0 = n0**min(n1, 5)\nt1 = n3 - t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "4.5" + ], + "split": "train" + }, + { + "Input": "in the formula a = ( 2 r ) ^ 3 , if r is halved , then a is multiplied by ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nt0 = n0**min(n1, 5)\nanswer = 1.0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.125" + ], + "split": "train" + }, + { + "Input": "all the students of class are told to sit in circle shape . here the boy at the 8 th position is exactly opposite to 33 th boy . total number of boys in the class ?", + "Output Program": [ + "n0 = 8.0\nn1 = 33.0\nt0 = n1 - n0\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "ifaequals the sum of the even integers from 2 to 40 , inclusive , andbequals the sum of the odd integers from 1 to 39 , inclusive , what is the value of a - b ?", + "Output Program": [ + "n0 = 2.0\nn1 = 40.0\nn2 = 1.0\nn3 = 39.0\nt0 = n2 + n3\nt1 = n1 / 2.0\nt2 = n3 - n2\nt3 = n2 + t1\nt4 = t2 / n0\nt5 = t0 / 2.0\nt6 = n2 + t4\nt7 = t3 * t1\nt8 = t6 * t5\nanswer = t7 - t8\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "on a race track a maximum of 5 horses can race together at a time . there are a total of 25 horses . there is no way of timing the races . what is the minimum number t of races we need to conduct to get the top 3 fastest horses ?", + "Output Program": [ + "n0 = 5.0\nn1 = 25.0\nn2 = 3.0\nt0 = n1 / n0\nanswer = t0 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "set s consists of integers { 6 , 7 , 10 , 12 , 15 } . if integer n is included in the set , the average ( arithmetic mean ) of set s will increase by 40 % . what is the value of integer n ?", + "Output Program": [ + "n0 = 6.0\nn1 = 7.0\nn2 = 10.0\nn3 = 12.0\nn4 = 15.0\nn5 = 40.0\nt0 = n2 + n3\nanswer = n3 + t0\nprint(answer)" + ], + "Output Answer": [ + "34" + ], + "split": "train" + }, + { + "Input": "a girl was asked to multiply a certain number by 43 . she multiplied it by 34 and got his answer less than the correct one by 1224 . find the number to be multiplied .", + "Output Program": [ + "n0 = 43.0\nn1 = 34.0\nn2 = 1224.0\nt0 = n0 - n1\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "136" + ], + "split": "train" + }, + { + "Input": "martins made a part payment of $ 650 toward buying a brand new washing machine , which represents 15 % of the total cost of the washing machine , how much remains to be paid ?", + "Output Program": [ + "n0 = 650.0\nn1 = 15.0\nt0 = n1 / 100.0\nt1 = n0 / t0\nanswer = t1 - n0\nprint(answer)" + ], + "Output Answer": [ + "3683.333333333334" + ], + "split": "train" + }, + { + "Input": "in the storage room of a certain bakery , the ratio of sugar to flour is 5 to 6 , and the ratio of flour to baking soda is 10 to 1 . if there were 60 more pounds of baking soda in the room , the ratio of flour to baking soda would be 8 to 1 . how many pounds of sugar are stored in the room ?", + "Output Program": [ + "n0 = 5.0\nn1 = 6.0\nn2 = 10.0\nn3 = 1.0\nn4 = 60.0\nn5 = 8.0\nn6 = 1.0\nt0 = n0 / n1\nt1 = n4 * n5\nt2 = n2 - n5\nt3 = t1 / t2\nt4 = n2 * t3\nanswer = t0 * t4\nprint(answer)" + ], + "Output Answer": [ + "2000" + ], + "split": "train" + }, + { + "Input": "what number times ( 1 \u2044 4 ) ^ 2 will give the value of 4 ^ 3 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 2.0\nn3 = 4.0\nn4 = 3.0\nt0 = n2**min(n1, 5)\nt1 = n1**min(n4, 5)\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "1024" + ], + "split": "train" + }, + { + "Input": "the mean of 30 values was 250 . it was detected on rechecking that one value 165 was wrongly copied as 135 for the computation of the mean . find the correct mean .", + "Output Program": [ + "n0 = 30.0\nn1 = 250.0\nn2 = 165.0\nn3 = 135.0\nt0 = n0 * n1\nt1 = n2 - n3\nt2 = t0 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "251" + ], + "split": "train" + }, + { + "Input": "a cyclist rides a bicycle 9 km at an average speed of 11 km / hr and again travels 11 km at an average speed of 9 km / hr . what is the average speed for the entire trip ?", + "Output Program": [ + "n0 = 9.0\nn1 = 11.0\nn2 = 11.0\nn3 = 9.0\nt0 = n0 + n1\nt1 = n0 / n1\nt2 = n1 / n0\nt3 = t1 + t2\nanswer = t0 / t3\nprint(answer)" + ], + "Output Answer": [ + "9.8019801980198" + ], + "split": "train" + }, + { + "Input": "if a 2 - b 2 = 10 and a * b = 8 , find a 4 + b 4 .", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 10.0\nn3 = 8.0\nn4 = 4.0\nn5 = 4.0\nt0 = n3**min(n0, 5)\nt1 = n2**min(n0, 5)\nt2 = t0 * n0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "228" + ], + "split": "train" + }, + { + "Input": "of 58 players on a cricket team , 37 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?", + "Output Program": [ + "n0 = 58.0\nn1 = 37.0\nt0 = 1.0 / 3.0\nt1 = n0 - n1\nt2 = 1.0 - t0\nt3 = t2 * t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "51" + ], + "split": "train" + }, + { + "Input": "there are 660 male and female participants in a meeting . half the female participants and one - quarter of the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?", + "Output Program": [ + "n0 = 660.0\nt0 = n0 / 3.0\nt1 = t0 * 4.0\nt2 = t1 - n0\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "110" + ], + "split": "train" + }, + { + "Input": "if the operation @ is defined for all a and b by the equation a @ b = ( a ^ b ) / 2 , then ( 3 @ 2 ) = ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 2.0\nt0 = n1**min(n0, 5)\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "4.5" + ], + "split": "train" + }, + { + "Input": "if a * b * c = ( \u221a ( a + 2 ) ( b + 3 ) ) / ( c + 1 ) , find the value of 6 * 15 * 3 .", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 3.0\nn2 = 1.0\nn3 = 6.0\nn4 = 15.0\nn5 = 3.0\nt0 = n0 + n3\nt1 = n1 + n4\nt2 = n2 + n5\nt3 = t0 * t1\nt4 = math.sqrt(max(0, t3))\nanswer = t4 / t2\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "ifaequals the sum of the even integers from 2 to 80 , inclusive , andbequals the sum of the odd integers from 1 to 79 , inclusive , what is the value of a - b ?", + "Output Program": [ + "n0 = 2.0\nn1 = 80.0\nn2 = 1.0\nn3 = 79.0\nt0 = n2 + n3\nt1 = n1 / n0\nt2 = n3 - n2\nt3 = n2 + t1\nt4 = t2 / n0\nt5 = t0 / n0\nt6 = n2 + t4\nt7 = t3 * t1\nt8 = t6 * t5\nanswer = t7 - t8\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "if an average hard drive had a capacity of 0.6 tb in 2000 , and average hard drive capacities double every 5 years , what will be the average hard drive capacity in 2050 ?", + "Output Program": [ + "n0 = 0.6\nn1 = 2000.0\nn2 = 5.0\nn3 = 2050.0\nt0 = n0 * 2.0\nt1 = t0 * 2.0\nt2 = t1 * 2.0\nt3 = t2 * 2.0\nt4 = t3 * 2.0\nt5 = t4 * 2.0\nt6 = t5 * 2.0\nt7 = t6 * 2.0\nt8 = t7 * 2.0\nt9 = t8 * 2.0\nt10 = n0 + t9\nanswer = t10 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "6150" + ], + "split": "train" + }, + { + "Input": "two digits in father ' s age are the same as the digit in the son ' s age , but in reverse order . in 5 years father will be twice as old as son will be then . what is the difference in their current age ?", + "Output Program": [ + "n0 = 5.0\nt0 = n0 * 4.0\nanswer = t0 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "the average monthly income of a and b is rs . 5050 . the average monthly income of b and c is rs . 6250 and the average monthly income of a and c is rs . 5200 . what is the monthly income of a ?", + "Output Program": [ + "n0 = 5050.0\nn1 = 6250.0\nn2 = 5200.0\nt0 = n0 * 2.0\nt1 = n1 * 2.0\nt2 = n2 * 2.0\nt3 = t1 - t2\nt4 = t0 + t3\nt5 = t4 / 2.0\nanswer = t0 - t5\nprint(answer)" + ], + "Output Answer": [ + "4000" + ], + "split": "train" + }, + { + "Input": "the captain of a cricket team of 11 members is 25 years old and the wicket keeper is 5 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ?", + "Output Program": [ + "n0 = 11.0\nn1 = 25.0\nn2 = 5.0\nt0 = n1 + n2\nt1 = 3.0 * 3.0\nt2 = n1 + t0\nt3 = t2 - t1\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "there are 3 girls and 6 boys . how many kids are there ?", + "Output Program": [ + "n0 = 8.0\nt0 = n0 - 1.0\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "if y > 0 , ( 2 y ) / 5 + ( 3 y ) / 10 is what percent of y ?", + "Output Program": [ + "n0 = 0.0\nn1 = 2.0\nn2 = 5.0\nn3 = 3.0\nn4 = 10.0\nt0 = n1 / n2\nt1 = n3 / n4\nt2 = t0 + t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "train" + }, + { + "Input": "the product of x and y is a constant . if the value of x is increased by 80 % , by what percentage must the value of y be decreased ?", + "Output Program": [ + "n0 = 80.0\nt0 = n0 + 100.0\nt1 = 100.0 / t0\nt2 = 1.0 - t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "44.44444444444444" + ], + "split": "train" + }, + { + "Input": "the average age of 15 students of a class is 15 years . out of these , the average age of 4 students is 14 years and that of the other 10 students is 16 years , the age of the 15 th student is", + "Output Program": [ + "n0 = 15.0\nn1 = 15.0\nn2 = 4.0\nn3 = 14.0\nn4 = 10.0\nn5 = 16.0\nn6 = 15.0\nt0 = n0 * n0\nt1 = n2 * n3\nt2 = n4 * n5\nt3 = t1 + t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "a club wants to mix 20 pounds of candy worth $ 10.00 per pound with candy worth $ 5.00 per pound to reduce the cost of the mixture to $ 6.00 per pound . how many pounds of the $ 5.00 per pound candy should be used ?", + "Output Program": [ + "n0 = 20.0\nn1 = 10.0\nn2 = 5.0\nn3 = 6.0\nn4 = 5.0\nt0 = n0 * n1\nt1 = n0 * n3\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "the total age of a and b is 18 years more than the total age of b and c . c is how many years younger than a . ?", + "Output Program": [ + "n0 = 18.0\n\nanswer = n0 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "a jewelry store purchased a pair of earrings for $ 240 and was selling it at a price that equaled the purchase price of the earrings plus a markup that was 25 percent of the selling price . after some time a jewelry store owner decided to decrease the selling price by 20 percent . what was the jewelry store ' s gross profit on this sale ?", + "Output Program": [ + "n0 = 240.0\nn1 = 25.0\nn2 = 20.0\nt0 = n1 / 100.0\nt1 = n2 / 100.0\nt2 = n0 * t0\nt3 = 1.0 - t0\nt4 = 1.0 - t1\nt5 = t2 / t3\nt6 = n0 + t5\nt7 = t6 * t4\nanswer = t7 - n0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "if 1 / 4 of the passengers on a ship are from north america , 1 / 8 are europeans , 1 / 12 are from africa , 1 / 6 are from asia and the remaining 36 people are citizens of other continents , then how many passengers are on board the ship ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 1.0\nn3 = 8.0\nn4 = 1.0\nn5 = 12.0\nn6 = 1.0\nn7 = 6.0\nn8 = 36.0\nt0 = n0 / n1\nt1 = n0 / n3\nt2 = n0 / n5\nt3 = n0 / n7\nt4 = t0 + t1\nt5 = t4 + t2\nt6 = t5 + t3\nt7 = n0 - t6\nanswer = n8 / t7\nprint(answer)" + ], + "Output Answer": [ + "96" + ], + "split": "train" + }, + { + "Input": "jack got paid today for his part - time job as a juggler , and noticed that 20 % of his paycheck went to taxes . jack wants to spend 80 % of what ' s left on a new bike , and put the rest into savings . if jack puts $ 20 into savings , how much was his original paycheck before taxes ?", + "Output Program": [ + "n0 = 20.0\nn1 = 80.0\nn2 = 20.0\nt0 = n1 / 100.0\nt1 = 100.0 - n1\nt2 = t1 / 100.0\nt3 = n0 / t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "125" + ], + "split": "train" + }, + { + "Input": "a canoe has two oars , left and right . each oar either works or breaks . the failure or non - failure of each oar is independent of the failure or non - failure of the other . you can still row the canoe with one oar . the probability that the left oar works is 3 / 5 . the probability that the right oar works is also 3 / 5 . what is the probability w that you can still row the canoe ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 3.0\nn3 = 5.0\nt0 = n0 / n1\nt1 = 2.0 / n1\nt2 = t0 * t1\nt3 = t0 * t0\nt4 = t2 + t2\nanswer = t4 + t3\nprint(answer)" + ], + "Output Answer": [ + "0.84" + ], + "split": "train" + }, + { + "Input": "karthik read 7 / 13 th of a book in 1 st week and 5 / 9 th of the remaining book in 2 nd week . if there were 96 pages unread after 2 nd week , how many pages were there in the book ?", + "Output Program": [ + "n0 = 7.0\nn1 = 13.0\nn2 = 1.0\nn3 = 5.0\nn4 = 9.0\nn5 = 2.0\nn6 = 96.0\nn7 = 2.0\nt0 = n3 / n4\nt1 = n0 - n2\nt2 = n2 - t0\nt3 = n6 / t2\nt4 = n1 * t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "468" + ], + "split": "train" + }, + { + "Input": "find the quotient : 0.0204 / 17", + "Output Program": [ + "n0 = 0.0204\nn1 = 17.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.0012000000000000001" + ], + "split": "train" + }, + { + "Input": "a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 59.29 , the number of the member is the group is :", + "Output Program": [ + "import math\nn0 = 59.29\nt0 = n0 * 100.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "77" + ], + "split": "train" + }, + { + "Input": "3 x ^ 2 - 6 x + 3 = 0 find the above equation find the value of x", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 6.0\nn3 = 3.0\nn4 = 0.0\nt0 = n2 / 3.0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "how many gallons of milk that is 10 percent butter - fat must be added to 8 gallons of milk that is 45 percent butterfat to obtain milk that is 20 percent butterfat ?", + "Output Program": [ + "n0 = 10.0\nn1 = 8.0\nn2 = 45.0\nn3 = 20.0\nt0 = n2 - n3\nt1 = n1 * t0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "18 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ?", + "Output Program": [ + "n0 = 18.0\nt0 = n0 - 1.0\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "306" + ], + "split": "train" + }, + { + "Input": "a 6 - liter solution is 40 % alcohol . how many liters of pure alcohol must be added to produce a solution that is 50 % alcohol ?", + "Output Program": [ + "n0 = 6.0\nn1 = 40.0\nn2 = 50.0\nt0 = n0 * n1\nt1 = t0 / 100.0\nt2 = t1 * 2.0\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "1.2000000000000002" + ], + "split": "train" + }, + { + "Input": "when the positive integer x is divided by 9 , the remainder is 5 . what is the remainder when 7 x is divided by 9 ?", + "Output Program": [ + "n0 = 9.0\nn1 = 5.0\nn2 = 7.0\nn3 = 9.0\nt0 = n1 * n2\nanswer = t0 % n0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "when positive integer k is divided by 5 , the remainder is 2 . when k is divided by 6 , the remainder is 5 . if k is less than 42 , what is the remainder when k is divided by 7 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 6.0\nn3 = 5.0\nn4 = 42.0\nn5 = 7.0\nt0 = n0 + 12.0\nanswer = t0 % n5\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "a student chose a number , multiplied it by 6 , then subtracted 138 from the result and got 102 . what was the number he chose ?", + "Output Program": [ + "n0 = 6.0\nn1 = 138.0\nn2 = 102.0\nt0 = n1 + n2\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "10 years ago , the average age of a family of 4 members was 24 years . two children having been born ( with age diference of 2 years ) , the present average age of the family is the same . the present age of the youngest child is :", + "Output Program": [ + "n0 = 10.0\nn1 = 4.0\nn2 = 24.0\nn3 = 2.0\nt0 = n1 + n3\nt1 = n1 * n2\nt2 = n0 * n1\nt3 = t1 + t2\nt4 = n2 * t0\nt5 = t4 - t3\nt6 = t5 - n3\nanswer = t6 / n3\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "the average monthly salary of 8 workers and one supervisor in a factory was 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . whenthesupervisor , whosesalarywas 430 . when the supervisor , whose salary was 870 per month , retired , a new person was appointed and then the average salary of 9 people was $ $ 390 per month . the salary of the new supervisor is :", + "Output Program": [ + "n0 = 8.0\nn1 = 430.0\nn2 = 430.0\nn3 = 430.0\nn4 = 430.0\nn5 = 870.0\nn6 = 9.0\nn7 = 390.0\nt0 = n6 * n7\nt1 = n1 * n6\nt2 = t1 - n5\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "510" + ], + "split": "train" + }, + { + "Input": "a \u2019 s speed is 17 / 15 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?", + "Output Program": [ + "n0 = 17.0\nn1 = 15.0\nt0 = n0 - n1\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.11764705882352941" + ], + "split": "train" + }, + { + "Input": "if 1 + 2 + 3 + . . . + n = n ( n + 1 ) , then 3 ( 1 + 3 + 5 + . . . . + 89 ) = ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 3.0\nn3 = 1.0\nn4 = 3.0\nn5 = 1.0\nn6 = 3.0\nn7 = 5.0\nn8 = 89.0\nt0 = n8 + n0\nt1 = n8 - n0\nt2 = t1 / n1\nt3 = n8 * t0\nt4 = t2 + n0\nt5 = t3 / n1\nt6 = t4 * t2\nt7 = t5 - t6\nanswer = t7 * n2\nprint(answer)" + ], + "Output Answer": [ + "6075" + ], + "split": "train" + }, + { + "Input": "a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 percent of the distribution lies within one standard deviation d of the mean , what percent q of the distribution is less than m + d ?", + "Output Program": [ + "n0 = 68.0\nt0 = 100.0 - n0\nt1 = t0 / 2.0\nanswer = 100.0 - t1\nprint(answer)" + ], + "Output Answer": [ + "84" + ], + "split": "train" + }, + { + "Input": "find the smallest positive integer n such that 11 n - 1 is divisible by 105 .", + "Output Program": [ + "n0 = 11.0\nn1 = 1.0\nn2 = 105.0\nt0 = 2.0 * 3.0\nt1 = n2 * t0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "there are 89 people that own pets . 15 people own only dogs , 10 people own only cats , 5 people own only cats and dogs , 3 people own cats , dogs and snakes . how many total snakes are there ?", + "Output Program": [ + "n0 = 89.0\nn1 = 15.0\nn2 = 10.0\nn3 = 5.0\nn4 = 3.0\nt0 = n1 + n2\nt1 = n3 + t0\nt2 = n4 + t1\nt3 = n0 - t2\nanswer = n4 + t3\nprint(answer)" + ], + "Output Answer": [ + "59" + ], + "split": "train" + }, + { + "Input": "when greenville state university decided to move its fine arts collection to a new library , it had to package the collection in 20 - inch by 20 - inch by 12 - inch boxes . if the university pays $ 0.50 for every box , and if the university needs 2.16 million cubic inches to package the collection , what is the minimum amount the university must spend on boxes ?", + "Output Program": [ + "n0 = 20.0\nn1 = 20.0\nn2 = 12.0\nn3 = 0.5\nn4 = 2.16\nt0 = 1000.0 * 1000.0\nt1 = n0 * n0\nt2 = n4 * t0\nt3 = n2 * t1\nt4 = t2 / t3\nanswer = n3 * t4\nprint(answer)" + ], + "Output Answer": [ + "225" + ], + "split": "train" + }, + { + "Input": "a mixture contains milk and water in the ratio 6 : 3 . on adding 10 litters of water , the ratio of milk to water becomes 6 : 5 . the quantity of milk in the original mixture is ?", + "Output Program": [ + "n0 = 6.0\nn1 = 3.0\nn2 = 10.0\nn3 = 6.0\nn4 = 5.0\nt0 = n0 + n1\nt1 = n3 / n4\nt2 = n0 / t0\nt3 = n1 / t0\nt4 = n2 * t1\nt5 = t3 * t1\nt6 = t2 - t5\nanswer = t4 / t6\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "if the numerator of a fraction be increased by 20 % and its denominator be diminished by 10 % , the value of the fraction is 20 / 21 . find the original fraction ?", + "Output Program": [ + "n0 = 20.0\nn1 = 10.0\nn2 = 20.0\nn3 = 21.0\nt0 = n0 + 100.0\nt1 = 100.0 - n1\nt2 = n2 * t1\nt3 = n3 * t0\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.7142857142857143" + ], + "split": "train" + }, + { + "Input": "the ratio of a to b is 4 to 5 , where a and b are positive . if x equals a increased by 25 percent of a , and m equals b decreased by 80 percent of b , what is the value of m / x ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 25.0\nn3 = 80.0\nt0 = n2 + 100.0\nt1 = n1 / n0\nt2 = 100.0 - n3\nt3 = t2 / t0\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "0.2" + ], + "split": "train" + }, + { + "Input": "a man saves 10 % of his monthly salary . if an account of dearness of things he is to increase his monthly expenses by 10 % , he is only able to save rs . 200 per month . what is his monthly salary ?", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 200.0\nt0 = n1 / 100.0\nt1 = n2 * 100.0\nt2 = 100.0 - n0\nt3 = t0 * t2\nt4 = t3 + t2\nt5 = 100.0 - t4\nanswer = t1 / t5\nprint(answer)" + ], + "Output Answer": [ + "20000" + ], + "split": "train" + }, + { + "Input": "4 different children have jelly beans : aaron has 5 , bianca has 7 , callie has 8 , and dante has 9 . how many jelly beans must dante give to aaron to ensure that no child has more than 1 fewer jelly beans than any other child ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 7.0\nn3 = 8.0\nn4 = 9.0\nn5 = 1.0\n\nanswer = n4 - n3\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "when 2 / 9 of the votes on a certain resolution have been counted , 3 / 4 of those counted are in favor of the resolution . what fraction f of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution ?", + "Output Program": [ + "n0 = 2.0\nn1 = 9.0\nn2 = 3.0\nn3 = 4.0\nn4 = 2.0\nn5 = 1.0\nt0 = n0 + n5\nt1 = n0 / n1\nt2 = n2 / n3\nt3 = n1 - n0\nt4 = n0 / t0\nt5 = t3 / n1\nt6 = t1 * t2\nt7 = t1 - t6\nt8 = t4 - t7\nanswer = t8 / t5\nprint(answer)" + ], + "Output Answer": [ + "0.7857142857142856" + ], + "split": "train" + }, + { + "Input": "when 1 / 20 % of 8000 is subtracted from 1 / 10 of 8000 , the difference is", + "Output Program": [ + "n0 = 1.0\nn1 = 20.0\nn2 = 8000.0\nn3 = 1.0\nn4 = 10.0\nn5 = 8000.0\nt0 = n2 / n4\nt1 = n1 * 100.0\nt2 = n2 / t1\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "796" + ], + "split": "train" + }, + { + "Input": "if the median of a list of numbers is m , the first quartile of the list is the median of the numbers in the list that are less than m . what is the first quartile of the list of numbers 42 , 24 , 30 , 28 , 26 , 19 , 33 and 35 ?", + "Output Program": [ + "n0 = 42.0\nn1 = 24.0\nn2 = 30.0\nn3 = 28.0\nn4 = 26.0\nn5 = 19.0\nn6 = 33.0\nn7 = 35.0\nt0 = n1 + n4\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "how many 3 digit positive integers r exist that when divided by 7 leave a remainder of 5 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 5.0\nt0 = 10.0 + 4.0\nt1 = 10.0 * 100.0\nt2 = n1 * t0\nt3 = t1 - 1.0\nt4 = n2 + t2\nt5 = t3 - t4\nanswer = t5 / n1\nprint(answer)" + ], + "Output Answer": [ + "128" + ], + "split": "train" + }, + { + "Input": "the price of 3 chudi and 6 tops is rs . 1500 . with the same money one can buy 1 chudi and 12 tops . if one wants to buy 5 tops , how much shall she have to pay ?", + "Output Program": [ + "n0 = 3.0\nn1 = 6.0\nn2 = 1500.0\nn3 = 1.0\nn4 = 12.0\nn5 = 5.0\n\nanswer = n5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "train" + }, + { + "Input": "when a certain number x is divided by 63 , the remainder is 27 . what is the remainder when x is divided by 8 ?", + "Output Program": [ + "n0 = 63.0\nn1 = 27.0\nn2 = 8.0\n\nanswer = n1 % n2\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "on dividing 100 by a number , the quotient is 9 and the remainder is 1 . find the divisor ?", + "Output Program": [ + "import math\nn0 = 100.0\nn1 = 9.0\nn2 = 1.0\nt0 = n0 / n1\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "what will be the reminder when ( 67 ^ 67 + 67 ) is divided by 68 ?", + "Output Program": [ + "import math\nn0 = 67.0\nn1 = 67.0\nn2 = 67.0\nn3 = 68.0\nt0 = n0**min(n0, 5)\nt1 = n0 + t0\nt2 = t1 / n3\nt3 = math.floor(t2)\nt4 = n3 * t3\nanswer = t1 - t4\nprint(answer)" + ], + "Output Answer": [ + "66" + ], + "split": "train" + }, + { + "Input": "aunt marge is giving candy to each of her nephews and nieces . she has 20 pieces of candy and she gives all the candy to the children according to her wish . if robert gets 2 more pieces than kate , bill gets 6 less than mary , mary gets 2 more pieces than robert , and kate gets 2 more pieces than bill , how many pieces of candy does kate get ?", + "Output Program": [ + "n0 = 20.0\nn1 = 2.0\nn2 = 6.0\nn3 = 2.0\nn4 = 2.0\nt0 = n2 / n1\nt1 = n0 - n2\nt2 = n1 + t0\nt3 = n1 * t2\nanswer = t1 - t3\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "in the list 3 , 3 , 4 , 4 , 5 , 5 , 5 , 5 , 7 , 11 , 21 , what fraction of the data is less than the mode ?", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 4.0\nn3 = 4.0\nn4 = 5.0\nn5 = 5.0\nn6 = 5.0\nn7 = 5.0\nn8 = 7.0\nn9 = 11.0\nn10 = 21.0\n\nanswer = n2 / n9\nprint(answer)" + ], + "Output Answer": [ + "0.36363636363636365" + ], + "split": "train" + }, + { + "Input": "the average runs scored by a batsman in 22 matches is 28 . in the next 13 matches the batsman scored an average of 15 runs . find his average in all the 35 matches ?", + "Output Program": [ + "n0 = 22.0\nn1 = 28.0\nn2 = 13.0\nn3 = 15.0\nn4 = 35.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "23.17142857142857" + ], + "split": "train" + }, + { + "Input": "the sum of the numbers is 330 . if the first number be twice the second and third number be one - third of the first , then the second number is :", + "Output Program": [ + "n0 = 330.0\nt0 = 1.0 + 10.0\nt1 = n0 * 3.0\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "a trailer carries 3 , 4 and 5 crates on a trip . each crate weighs no less than 150 kg . what is the maximum weight of the crates on a single trip ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 5.0\nn3 = 150.0\n\nanswer = n2 * n3\nprint(answer)" + ], + "Output Answer": [ + "750" + ], + "split": "train" + }, + { + "Input": "a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 22 , then how old is b ?", + "Output Program": [ + "n0 = 22.0\nt0 = 1.0 + 4.0\nt1 = n0 - 2.0\nt2 = t1 * 2.0\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "all the students of class are told to sit in circle shape . here the boy at the 6 th position is exactly opposite to 16 th boy . total number of boys in the class ?", + "Output Program": [ + "n0 = 6.0\nn1 = 16.0\nt0 = n1 - n0\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "find the principle on a certain sum of money at 5 % per annum for 2 2 / 5 years if the amount being rs . 2120 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 2.0\nn3 = 5.0\nn4 = 2120.0\nt0 = n1 * n3\nt1 = n1 + t0\nt2 = t1 / n3\nt3 = n0 * t2\nt4 = t3 / 100.0\nt5 = t4 + 1.0\nanswer = n4 / t5\nprint(answer)" + ], + "Output Answer": [ + "1892.8571428571427" + ], + "split": "train" + }, + { + "Input": "the average age of an adult class is 40 years . 8 new students with an avg age of 32 years join the class . therefore decreasing the average by 4 year . find what was theoriginal strength of class ?", + "Output Program": [ + "n0 = 40.0\nn1 = 8.0\nn2 = 32.0\nn3 = 4.0\nt0 = n1 * n2\nt1 = n0 - n3\nt2 = n1 * t1\nt3 = t2 - t0\nanswer = t3 / n3\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "what least number should be added to 1056 , so that the sum is completely divisible by 23 ?", + "Output Program": [ + "n0 = 1056.0\nn1 = 23.0\nt0 = n0 % n1\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "at a restaurant , glasses are stored in two different - sized boxes . one box contains 12 glasses , and the other contains 16 glasses . if the average number of glasses per box is 15 , and there are 16 more of the larger boxes , what is the total number of glasses t at the restaurant ? ( assume that all boxes are filled to capacity . )", + "Output Program": [ + "n0 = 12.0\nn1 = 16.0\nn2 = 15.0\nn3 = 16.0\nt0 = n1 * 2.0\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "480" + ], + "split": "train" + }, + { + "Input": "how many digits are used to number a book containg 300 pages .", + "Output Program": [ + "n0 = 300.0\nt0 = n0 * 2.0\nt1 = 100.0 - 4.0\nt2 = t0 + 100.0\nt3 = t1 - 4.0\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "792" + ], + "split": "train" + }, + { + "Input": "barbata invests $ 2800 in the national bank at 5 % . how much additional money must she invest at 8 % so that the total annual income will be equal to 6 % of her entire investment ?", + "Output Program": [ + "n0 = 2800.0\nn1 = 5.0\nn2 = 8.0\nn3 = 6.0\nt0 = n3 / 100.0\nt1 = n1 / 100.0\nt2 = n2 / 100.0\nt3 = n0 * t0\nt4 = n0 * t1\nt5 = t2 - t0\nt6 = t3 - t4\nanswer = t6 / t5\nprint(answer)" + ], + "Output Answer": [ + "1399.9999999999998" + ], + "split": "train" + }, + { + "Input": "mother , her daughter and her grand child weighs 120 kg . daughter and her daughter ( child ) weighs 60 kg . child is 1 / 5 th of her grand mother . what is the age of the daughter ?", + "Output Program": [ + "n0 = 120.0\nn1 = 60.0\nn2 = 1.0\nn3 = 5.0\nt0 = n0 - n1\nt1 = t0 / n3\nanswer = n1 - t1\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "in a class of students , 1 / 2 of the number of girls is equal to 1 / 5 of the total number of students . what is the ratio of boys to girls in the class ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 1.0\nn3 = 5.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = t0 - t1\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "1.4999999999999998" + ], + "split": "train" + }, + { + "Input": "what is x if x + 2 y = 10 and y = 3 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 10.0\nn2 = 3.0\nt0 = n0 * n2\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "if 10 a = 6 b = 20 , then 120 ab =", + "Output Program": [ + "n0 = 10.0\nn1 = 6.0\nn2 = 20.0\nn3 = 120.0\nt0 = n2 / n0\nt1 = n2 / n1\nt2 = t0 * t1\nanswer = n3 * t2\nprint(answer)" + ], + "Output Answer": [ + "800" + ], + "split": "train" + }, + { + "Input": "which number need to add to 7844213 to get a number exactly divisible by 549 ?", + "Output Program": [ + "import math\nn0 = 7844213.0\nn1 = 549.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = t1 + 1.0\nt3 = t2 - t0\nanswer = n1 * t3\nprint(answer)" + ], + "Output Answer": [ + "448.0000000000291" + ], + "split": "train" + }, + { + "Input": "a scale 7 ft . 12 inches long is divided into 4 equal parts . find the length of each part .", + "Output Program": [ + "n0 = 7.0\nn1 = 12.0\nn2 = 4.0\nt0 = n0 * 12.0\nt1 = n1 + t0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "one week , a certain truck rental lot had a total of 20 trucks , all of which were on the lot monday morning . if 50 % of the trucks that were rented out during the week were returned to the lot on or before saturday morning of that week , and if there were at least 10 trucks on the lot that saturday morning , what is the greatest number of different trucks that could have been rented out during the week ?", + "Output Program": [ + "n0 = 20.0\nn1 = 50.0\nn2 = 10.0\nt0 = n1 / 100.0\nt1 = n0 * t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "the mean of 50 observations was 36 . it was found later that an observation 48 was wrongly taken as 47 . the corrected new mean is ?", + "Output Program": [ + "n0 = 50.0\nn1 = 36.0\nn2 = 48.0\nn3 = 47.0\nt0 = n0 * n1\nt1 = n0 - 2.0\nt2 = t1 - n3\nt3 = t0 + t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "36.02" + ], + "split": "train" + }, + { + "Input": "hillary and eddy are climbing to the summit of mt . everest from a base camp 5000 ft from the summit . when they depart for the summit at 06 : 00 , hillary climbs at a rate of 800 ft / hr with eddy lagging behind at a slower rate of 500 ft / hr . if hillary stops 1000 ft short of the summit and then descends at a rate of 1000 ft / hr , at what time do hillary and eddy pass each other on her return trip ?", + "Output Program": [ + "n0 = 5000.0\nn1 = 6.0\nn2 = 0.0\nn3 = 800.0\nn4 = 500.0\nn5 = 1000.0\nn6 = 1000.0\nt0 = n0 - n5\nt1 = t0 / n3\nt2 = n1 + t1\nanswer = t2 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "$ 200 is divided amongst a , b and c so that a may get 2 / 3 as much as b and c together , b may get 6 / 9 as much as a and c together , then the share of a is", + "Output Program": [ + "n0 = 200.0\nn1 = 2.0\nn2 = 3.0\nn3 = 6.0\nn4 = 9.0\nt0 = n1 / n2\nt1 = t0 + 1.0\nt2 = n0 / t1\nanswer = t2 * t0\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "a man whose bowling average is 12.4 , takes 8 wickets for 26 runs and there by decreases his average by 0.4 . the number of wickets taken by him before his last match is ?", + "Output Program": [ + "import math\nn0 = 12.4\nn1 = 8.0\nn2 = 26.0\nn3 = 0.4\nt0 = math.floor(n0)\nt1 = n1 * t0\nt2 = n0 - t0\nt3 = t1 - n2\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "174.99999999999986" + ], + "split": "train" + }, + { + "Input": "a number when divided by 342 gives a remainder 47 . when the same number is divided by 19 what would be the remainder ?", + "Output Program": [ + "n0 = 342.0\nn1 = 47.0\nn2 = 19.0\n\nanswer = n1 % n2\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "the average ( arithmetic mean ) of 24 , 35 , and 58 is 6 more than the average of 19 , 51 , and x . what is x ?", + "Output Program": [ + "n0 = 24.0\nn1 = 35.0\nn2 = 58.0\nn3 = 6.0\nn4 = 19.0\nn5 = 51.0\nt0 = n0 + n1\nt1 = n3 * 3.0\nt2 = n2 + t0\nt3 = n4 + t1\nt4 = n5 + t3\nanswer = t2 - t4\nprint(answer)" + ], + "Output Answer": [ + "29" + ], + "split": "train" + }, + { + "Input": "instead of multiplying a number by 5 , the number is divided by 5 . what is the percentage of error obtained ?", + "Output Program": [ + "n0 = 5.0\nn1 = 5.0\nt0 = n1 / n1\nt1 = n0 * n1\nt2 = t0 / t1\nt3 = t2 * 100.0\nanswer = 100.0 - t3\nprint(answer)" + ], + "Output Answer": [ + "96" + ], + "split": "train" + }, + { + "Input": "a car travels first 160 km at 90 km / hr and the next 160 km at 80 km / hr . what is the average speed for the first 320 km of the tour ?", + "Output Program": [ + "n0 = 160.0\nn1 = 90.0\nn2 = 160.0\nn3 = 80.0\nn4 = 320.0\nt0 = n0 / n1\nt1 = n0 / n3\nt2 = t0 + t1\nt3 = 1.0 / t2\nanswer = n4 * t3\nprint(answer)" + ], + "Output Answer": [ + "84.70588235294117" + ], + "split": "train" + }, + { + "Input": "country x taxes each of its citizens an amount equal to 10 percent of the first $ 40,000 of income , plus 20 percent of all income in excess of $ 40,000 . if a citizen of country x is taxed a total of $ 8,000 , what is her income ?", + "Output Program": [ + "n0 = 10.0\nn1 = 40000.0\nn2 = 20.0\nn3 = 40000.0\nn4 = 8000.0\nt0 = n0 / 100.0\nt1 = n2 / 100.0\nt2 = 2.0 * 4.0\nt3 = 10.0 * 4.0\nt4 = t2 * 1000.0\nt5 = t3 * 1000.0\nt6 = t0 * t5\nt7 = t4 - t6\nt8 = t7 / t1\nanswer = t8 + t5\nprint(answer)" + ], + "Output Answer": [ + "60000" + ], + "split": "train" + }, + { + "Input": "peter ' s average ( arithmetic mean ) test score on 4 tests is 78 . what must be the student ' s score on a 5 th test for the peter ' s average score on the 5 tests to be 80 ?", + "Output Program": [ + "n0 = 4.0\nn1 = 78.0\nn2 = 5.0\nn3 = 5.0\nn4 = 80.0\nt0 = n2 * n4\nt1 = n0 * n1\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "88" + ], + "split": "train" + }, + { + "Input": "a type of extra - large suv averages 12.2 miles per gallon ( mpg ) on the highway , but only 7.6 mpg in the city . what is the maximum distance , in miles , that this suv could be driven on 21 gallons of gasoline ?", + "Output Program": [ + "n0 = 12.2\nn1 = 7.6\nn2 = 21.0\n\nanswer = n0 * n2\nprint(answer)" + ], + "Output Answer": [ + "256.2" + ], + "split": "train" + }, + { + "Input": "find the 15 th term of an arithmetic progression whose first term is 2 and the common difference is 3 .", + "Output Program": [ + "n0 = 15.0\nn1 = 2.0\nn2 = 3.0\nt0 = n0 - 1.0\nt1 = n2 * t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "44" + ], + "split": "train" + }, + { + "Input": "kiran has 85 currency notes in all , some of which were of rs . 100 denomination and the remaining of rs . 50 denomination . the total amount of all these currency notes was rs . 5000 . how much amount did she have in the denomination of rs . 50 ?", + "Output Program": [ + "n0 = 85.0\nn1 = 100.0\nn2 = 50.0\nn3 = 5000.0\nn4 = 50.0\nt0 = n0 * n2\nt1 = n3 - t0\nt2 = t1 / n2\nt3 = n0 - t2\nanswer = n2 * t3\nprint(answer)" + ], + "Output Answer": [ + "3500" + ], + "split": "train" + }, + { + "Input": "in a 4 person race , medals are awarded to the fastest 3 runners . the first - place runner receives a gold medal , the second - place runner receives a silver medal , and the third - place runner receives a bronze medal . in the event of a tie , the tied runners receive the same color medal . ( for example , if there is a two - way tie for first - place , the top two runners receive gold medals , the next - fastest runner receives a silver medal , and no bronze medal is awarded ) . assuming that exactly 3 medals are awarded , and that the 3 medal winners stand together with their medals to form a victory circle , how many different victory circles are possible ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 3.0\nn2 = 3.0\nn3 = 3.0\nt0 = math.factorial(min(15, int(n0)))\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "96" + ], + "split": "train" + }, + { + "Input": "in a hostel , the number of students decreased by 15 % and the price of food increased by 20 % over the previous year . if each student consumes the same amount of food then by how much should the consumption of food be cut short by every student , so that the total cost of the food remains the same as that of the previous year ?", + "Output Program": [ + "n0 = 15.0\nn1 = 20.0\nt0 = n1 + 100.0\nt1 = 100.0 * 100.0\nt2 = 100.0 - n0\nt3 = t0 * t2\nt4 = t1 / t3\nt5 = 1.0 - t4\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "1.9607843137254943" + ], + "split": "train" + }, + { + "Input": "a , b , c , d , e , f are the only 6 families in indira nagar . a , b , c , d , e and f has 7 , 8 , 10 , 13 , 6 , and 10 member in their families respectively . if 1 member from all the 6 families left their respective families to accommodate themselves in the hostel of iim lucknow , then the average number of member now in each family of indira nagar is", + "Output Program": [ + "n0 = 6.0\nn1 = 7.0\nn2 = 8.0\nn3 = 10.0\nn4 = 13.0\nn5 = 6.0\nn6 = 10.0\nn7 = 1.0\nn8 = 6.0\n\nanswer = n3 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "in a river flowing at 2 km / hr , a boat travels 72 km upstream and then returns downstream to the starting point . if its speed in still water be 6 km / hr , find the total journey time .", + "Output Program": [ + "n0 = 2.0\nn1 = 72.0\nn2 = 6.0\nt0 = n0 + n2\nt1 = n2 - n0\nt2 = n1 / t1\nt3 = n1 / t0\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "train" + }, + { + "Input": "if a - b = 5 and a 2 + b 2 = 29 , find the value of ab .", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 2.0\nn3 = 29.0\nt0 = n0**min(n1, 5)\nt1 = n3 - t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "the average score of a cricketer for 10 matches is 38.9 runs . if the average for the first 6 matches is 42 , then find the average for the last 4 matches .", + "Output Program": [ + "n0 = 10.0\nn1 = 38.9\nn2 = 6.0\nn3 = 42.0\nn4 = 4.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = t0 - t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "34.25" + ], + "split": "train" + }, + { + "Input": "of 55 players on a cricket team , 37 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?", + "Output Program": [ + "n0 = 55.0\nn1 = 37.0\nt0 = 1.0 / 3.0\nt1 = n0 - n1\nt2 = 1.0 - t0\nt3 = t2 * t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "49" + ], + "split": "train" + }, + { + "Input": "if a and b are the two values of t that satisfy the equation t ^ 2 \u00e2 \u20ac \u201c 12 t + 20 = 0 , with a > b , what is the value of a \u00e2 \u20ac \u201c b ?", + "Output Program": [ + "n0 = 2.0\nn1 = 12.0\nn2 = 20.0\nn3 = 0.0\nt0 = n2 / n0\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "the average ( arithmetic mean ) of 4 different integers is 74 . if the largest integer is 90 , what is the least possible value of the smallest integer ?", + "Output Program": [ + "n0 = 4.0\nn1 = 74.0\nn2 = 90.0\nt0 = n0 * n1\nt1 = n2 - 1.0\nt2 = n2 - 2.0\nt3 = t0 - n2\nt4 = t3 - t1\nanswer = t4 - t2\nprint(answer)" + ], + "Output Answer": [ + "29" + ], + "split": "train" + }, + { + "Input": "4 milkmen rented a pasture . a grazed 24 cows for 3 months ; b 10 for 5 months ; c 35 cows for 4 months and d 21 cows for 3 months . if a ' s share of rent is rs . 1440 , find the total rent of the field .", + "Output Program": [ + "n0 = 4.0\nn1 = 24.0\nn2 = 3.0\nn3 = 10.0\nn4 = 5.0\nn5 = 35.0\nn6 = 4.0\nn7 = 21.0\nn8 = 3.0\nn9 = 1440.0\nt0 = n1 * n2\nt1 = n3 * n4\nt2 = n0 * n5\nt3 = n2 * n7\nt4 = t0 + t1\nt5 = t4 + t2\nt6 = t5 + t3\nt7 = t6 / t0\nanswer = n9 * t7\nprint(answer)" + ], + "Output Answer": [ + "6500.000000000001" + ], + "split": "train" + }, + { + "Input": "how many multiples of 4 are there between 12 and 108 , inclusive ?", + "Output Program": [ + "n0 = 4.0\nn1 = 12.0\nn2 = 108.0\nt0 = n2 - n1\nt1 = t0 / n0\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "if a - b = 10 and a ^ 2 + b ^ 2 = 150 , find the value of ab", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 2.0\nn2 = 2.0\nn3 = 150.0\nt0 = math.sqrt(max(0, n3))\nt1 = t0 - n0\nt2 = t1 / n1\nt3 = n0 + t2\nt4 = t3 * t2\nanswer = n1 * t4\nprint(answer)" + ], + "Output Answer": [ + "24.999999999999996" + ], + "split": "train" + }, + { + "Input": "of the families in city x in 2001 , 25 percent owned a personal computer . the number of families in city x owning a computer in 2008 was 15 percent greater than it was in 2001 , and the total number of families in city x was 6 percent greater in 2008 than it was in 2001 . what percent of the families in city x owned a personal computer in 2008 ?", + "Output Program": [ + "n0 = 2001.0\nn1 = 25.0\nn2 = 2008.0\nn3 = 15.0\nn4 = 2001.0\nn5 = 6.0\nn6 = 2008.0\nn7 = 2001.0\nn8 = 2008.0\nt0 = n3 + 100.0\nt1 = n5 + 100.0\nt2 = n1 * t0\nt3 = t2 / 100.0\nt4 = t3 / t1\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "27.122641509433965" + ], + "split": "train" + }, + { + "Input": "the sum of number of boys and girls in a school is 100 . if the number of boys is x , then the number of girls becomes x % of the total number of students . the number of boys is ?", + "Output Program": [ + "n0 = 100.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "in a class of students , 1 / 2 of the number of girls is equal to 1 / 3 of the total number of students . what is the ratio of boys to girls in the class ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 1.0\nn3 = 3.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = t0 - t1\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.5000000000000001" + ], + "split": "train" + }, + { + "Input": "an = 2 an - 1 + 4 and qn = 4 qn - 1 + 8 for all n > 1 . if a 5 = q 4 and a 7 = 316 , what is the first value of n for which qn is an integer ?", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 4.0\nn3 = 4.0\nn4 = 1.0\nn5 = 8.0\nn6 = 1.0\nn7 = 5.0\nn8 = 4.0\nn9 = 7.0\nn10 = 316.0\n\nanswer = n9 - n2\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "tough and tricky questions : word problems . a salesman ' s income consists of commission and base salary . his weekly income totals over the past 5 weeks have been $ 406 , $ 413 , $ 420 , $ 436 and $ 395 . what must his average ( arithmetic mean ) income over the next 5 weeks be to increase his average weekly income to $ 500 over the 10 - week period ?", + "Output Program": [ + "n0 = 5.0\nn1 = 406.0\nn2 = 413.0\nn3 = 420.0\nn4 = 436.0\nn5 = 395.0\nn6 = 5.0\nn7 = 500.0\nn8 = 10.0\nt0 = n1 + n2\nt1 = n3 + t0\nt2 = n4 + t1\nt3 = n5 + t2\nt4 = t3 / n0\nt5 = n7 - t4\nanswer = n7 + t5\nprint(answer)" + ], + "Output Answer": [ + "586" + ], + "split": "train" + }, + { + "Input": "a certain number when divided by 39 leaves a remainder 19 , what is the remainder when the same number is divided by 13 ?", + "Output Program": [ + "n0 = 39.0\nn1 = 19.0\nn2 = 13.0\n\nanswer = n1 % n2\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "if the price of gasoline increases by 20 % and a driver intends to spend only 8 % more on gasoline , by how much percent should the driver reduce the quantity of gasoline that he buys ?", + "Output Program": [ + "n0 = 20.0\nn1 = 8.0\nt0 = n0 + 100.0\nt1 = n1 + 100.0\nt2 = t0 - t1\nt3 = t2 / t0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 50 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.5\nn2 = 50.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "train" + }, + { + "Input": "a sum of rs . 427 is to be divided among a , b and c in such a way that 3 times a \u2019 s share , 4 times b \u2019 s share and 7 times c \u2019 s share are all equal . the share of c is", + "Output Program": [ + "n0 = 427.0\nn1 = 3.0\nn2 = 4.0\nn3 = 7.0\nt0 = n3 / n1\nt1 = n3 / n2\nt2 = n3 / n3\nt3 = t0 + t1\nt4 = t3 + t2\nanswer = n0 / t4\nprint(answer)" + ], + "Output Answer": [ + "83.99999999999999" + ], + "split": "train" + }, + { + "Input": "if 15 students in a class average 80 % on an english exam and 10 students average 90 % on the same exam , what is the average in percent for all 25 students ?", + "Output Program": [ + "n0 = 15.0\nn1 = 80.0\nn2 = 10.0\nn3 = 90.0\nn4 = 25.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = t0 + t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "84" + ], + "split": "train" + }, + { + "Input": "in a room filled with 7 people , 4 people have exactly 1 sibling in the room and 3 people have exactly 2 siblings in the room . if two individuals are selected from the room at random , what is the probability that those two individuals are not siblings ?", + "Output Program": [ + "n0 = 7.0\nn1 = 4.0\nn2 = 1.0\nn3 = 3.0\nn4 = 2.0\nt0 = n1 / n0\nt1 = n0 - n4\nt2 = n0 - n2\nt3 = n0 - n1\nt4 = t1 / t2\nt5 = t3 / t2\nt6 = t0 * t4\nt7 = t0 * t5\nanswer = t6 + t7\nprint(answer)" + ], + "Output Answer": [ + "0.7619047619047619" + ], + "split": "train" + }, + { + "Input": "which number can we add to 897326 to get a number exactly divisible by 456 ?", + "Output Program": [ + "n0 = 897326.0\nn1 = 456.0\nt0 = n0 % n1\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "82" + ], + "split": "train" + }, + { + "Input": "after spending rs . 5000 on rent , rs . 1500 on milk , rs . 4500 on groceries , rs . 2500 on childrens education rs . 2000 on petrol and rs . 3940 on miscellaneous expenses , mr . kishore saved 10 % of his monthly salary . how much did he save in rs . ?", + "Output Program": [ + "n0 = 5000.0\nn1 = 1500.0\nn2 = 4500.0\nn3 = 2500.0\nn4 = 2000.0\nn5 = 3940.0\nn6 = 10.0\nt0 = n0 + n1\nt1 = 100.0 - n6\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nt5 = n5 + t4\nt6 = t5 * 100.0\nt7 = t6 / t1\nanswer = t7 - t5\nprint(answer)" + ], + "Output Answer": [ + "2160" + ], + "split": "train" + }, + { + "Input": "the standard deviation of a normal distribution of data is 2 , and 3 standard deviations below the mean is greater than 44 . what is a possible value for the mean of the distribution ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 44.0\nt0 = n0 * n1\nt1 = n2 + t0\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "51" + ], + "split": "train" + }, + { + "Input": "the set x = { 78 , 910 } . the set y = { 23 , 45 } . we will randomly choose one element x from set x and one element y from set y . what is the probability that x / y will be an integer ?", + "Output Program": [ + "import math\nn0 = 78.0\nn1 = 910.0\nn2 = 23.0\nn3 = 45.0\nt0 = n0 / n2\nt1 = n1 / n3\nt2 = math.floor(t0)\nt3 = math.floor(t1)\nt4 = t2 + 2.0\nt5 = t3 - t2\nt6 = t5 - 1.0\nanswer = t4 / t6\nprint(answer)" + ], + "Output Answer": [ + "0.3125" + ], + "split": "train" + }, + { + "Input": "for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today ' s production of 115 units raises the average to 55 units per day , what is the value of n ?", + "Output Program": [ + "n0 = 50.0\nn1 = 115.0\nn2 = 55.0\nt0 = n1 - n0\nt1 = n2 - n0\nt2 = t0 / t1\nanswer = t2 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "the average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 65 kg . what is the correct weight ?", + "Output Program": [ + "n0 = 20.0\nn1 = 58.4\nn2 = 56.0\nn3 = 65.0\nt0 = n0 * n1\nt1 = n3 - n2\nt2 = t0 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "58.85" + ], + "split": "train" + }, + { + "Input": "a box contains 13 apples , 12 of which are red . an apple is drawn from the box and its color is noted before it is eaten . this is done a total of n times , and the probability that a red apple is drawn each time is less than 0.5 . what is the smallest possible value of n ?", + "Output Program": [ + "n0 = 13.0\nn1 = 12.0\nn2 = 0.5\nt0 = n2 * n1\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "a = { 2 , 3 , 5 , 7 , 11 } b = { 2 , 4 , 6 , 19 } two integers will be randomly selected from sets a and b , one integer from set a and one from set b , and then multiplied together . how many different products can be obtained ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 5.0\nn3 = 7.0\nn4 = 11.0\nn5 = 2.0\nn6 = 4.0\nn7 = 6.0\nn8 = 19.0\n\nanswer = n6 * n7\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "if one - seventh of a number exceeds its eleventh part by 100 then the number is \u2026", + "Output Program": [ + "n0 = 100.0\nt0 = 3.0 + 4.0\nt1 = 1.0 + 10.0\nt2 = n0 * t1\nt3 = t1 - t0\nt4 = t0 * t2\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "1925" + ], + "split": "train" + }, + { + "Input": "list i : 3 , 4 , 8 , 19 list ii : x , 3 , 4 , 8 , 19", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 8.0\nn3 = 19.0\nn4 = 3.0\nn5 = 4.0\nn6 = 8.0\nn7 = 19.0\nt0 = 3.0 - 1.0\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "there are 4 more women than there are men on a local co - ed softball team . if there are a total of 20 players on the team , what is the ratio of men to women ?", + "Output Program": [ + "n0 = 4.0\nn1 = 20.0\nt0 = 1.0 + 1.0\nt1 = n1 - n0\nt2 = t1 / t0\nt3 = n0 + t2\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.6666666666666666" + ], + "split": "train" + }, + { + "Input": "6 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ?", + "Output Program": [ + "n0 = 6.0\nt0 = n0 - 1.0\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "the average ( arithmetic man ) of 3 integers a , b , and c is exactly 4 times the median . if a < b < c and a = 0 , what is the value of c / b ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 0.0\nt0 = n0 * n1\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "a 6 - liter solution is 30 % alcohol . how many liters of pure alcohol must be added to produce a solution that is 50 % alcohol ?", + "Output Program": [ + "n0 = 6.0\nn1 = 30.0\nn2 = 50.0\nt0 = n0 * n1\nt1 = t0 / 100.0\nt2 = t1 * 2.0\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "2.4" + ], + "split": "train" + }, + { + "Input": "if you add all the numbers on your mobile phone , what is the answer ?", + "Output Program": [ + "t0 = 10.0 - 1.0\nt1 = t0 + 1.0\nt2 = t1 / 2.0\nanswer = t2 * t0\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "the jogging track in a sports complex is 561 m in circumference . deepak and his wife start from the same point and walk in opposite directions at 4.5 km / hr and 3.75 km / hr respectively . they will meet for the first time in ?", + "Output Program": [ + "n0 = 561.0\nn1 = 4.5\nn2 = 3.75\nt0 = n1 + n2\nt1 = n0 / 1000.0\nt2 = t1 / t0\nanswer = t2 * 60.0\nprint(answer)" + ], + "Output Answer": [ + "4.08" + ], + "split": "train" + }, + { + "Input": "a certain protective additive increases from 20 days to 25 days the time between required maintenance checks on an industrial vehicle . by what percent is the time between maintenance checks increased by using the additive ?", + "Output Program": [ + "n0 = 20.0\nn1 = 25.0\nt0 = n1 - n0\nt1 = t0 / n0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "75 % of x is greater than 1 / 3 rd of x by 110 . what is x ?", + "Output Program": [ + "n0 = 75.0\nn1 = 1.0\nn2 = 3.0\nn3 = 110.0\nt0 = n0 / 100.0\nt1 = n1 / n2\nt2 = t0 - t1\nanswer = n3 / t2\nprint(answer)" + ], + "Output Answer": [ + "264" + ], + "split": "train" + }, + { + "Input": "there are 8 stores in town that had a total of 21 visitors on a particular day . however , only 12 people went shopping that day ; some people visited more than one store . if 8 people visited exactly two stores each , and everyone visited at least one store , what is the largest number of stores anyone could have visited ?", + "Output Program": [ + "n0 = 8.0\nn1 = 21.0\nn2 = 12.0\nn3 = 8.0\nt0 = n0 * 2.0\nt1 = n2 - n0\nt2 = n1 - t0\nt3 = t1 - 1.0\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "7 people average age is 30 . youngest person age is 7 . find average of the people when youngest was born .", + "Output Program": [ + "n0 = 7.0\nn1 = 30.0\nn2 = 7.0\nt0 = n0 * n1\nt1 = n0 * n2\nt2 = t0 - t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "jim needs $ 1000 to buy a new flat - screen tv . since he has only $ 7 , he borrows the remaining balance from his sister mary . the loan will be repaid in 3 annual installments at an interest rate of 10 % , compounded annually . the formula for calculating the monthly payment p is p = ( l x c x r ) / ( c \u2013 1 ) where l = amount of the loan , r = annual interest rate , and c = compounding factor = ( 1 + r ) ^ n where n = number of annual payments . how much does jim have to pay mary at the end of each of the next 3 years ( rounded to the nearest penny ) ?", + "Output Program": [ + "n0 = 1000.0\nn1 = 7.0\nn2 = 3.0\nn3 = 10.0\nn4 = 1.0\nn5 = 1.0\nn6 = 3.0\nt0 = n3 / 100.0\nt1 = n0 - n1\nt2 = n4 + t0\nt3 = t0 * t1\nt4 = t2**min(n2, 5)\nt5 = t3 * t4\nt6 = t4 - 1.0\nanswer = t5 / t6\nprint(answer)" + ], + "Output Answer": [ + "399.29999999999967" + ], + "split": "train" + }, + { + "Input": "the two lines y = x and x = - 5 intersect on the coordinate plane . what is the value of the area of the figure formed by the intersecting lines and the x - axis ?", + "Output Program": [ + "n0 = 5.0\nt0 = n0 * n0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "12.5" + ], + "split": "train" + }, + { + "Input": "in a 100 - mile trip , the first 30 miles were completed at 60 mph . if the average speed for the whole trip was 40 mph , what was the average speed in the last 70 miles ?", + "Output Program": [ + "n0 = 100.0\nn1 = 30.0\nn2 = 60.0\nn3 = 40.0\nn4 = 70.0\nt0 = n0 / n3\nt1 = n1 / n2\nt2 = t0 - t1\nanswer = n4 / t2\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "diana took out a charge account at the general store and agreed to pay 6 % simple annual interest . if she charges $ 60 on her account in january , how much will she owe a year later , assuming she does not make any additional charges or payments ?", + "Output Program": [ + "n0 = 6.0\nn1 = 60.0\nt0 = n0 / 100.0\nt1 = n1 * t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "63.6" + ], + "split": "train" + }, + { + "Input": "which number can we add to 722425 to get a number exactly divisible by 456 ?", + "Output Program": [ + "n0 = 722425.0\nn1 = 456.0\nt0 = n0 % n1\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "335" + ], + "split": "train" + }, + { + "Input": "if x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year , the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $ 65 . if $ 2,000 is the total amount invested , how much is invested at 8 percent ?", + "Output Program": [ + "n0 = 10.0\nn1 = 8.0\nn2 = 10.0\nn3 = 8.0\nn4 = 65.0\nn5 = 2000.0\nn6 = 8.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = n0 * 100.0\nt3 = n0 * n1\nt4 = t0 + t1\nt5 = t2 * 2.0\nt6 = t3 * 2.0\nt7 = n4 + t6\nt8 = t7 / t4\nanswer = t5 - t8\nprint(answer)" + ], + "Output Answer": [ + "750" + ], + "split": "train" + }, + { + "Input": "how many 3 digit positive integers q exist that when divided by 7 leave a remainder of 5 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 5.0\nt0 = 10.0 + 4.0\nt1 = 10.0 * 100.0\nt2 = n1 * t0\nt3 = t1 - 1.0\nt4 = n2 + t2\nt5 = t3 - t4\nanswer = t5 / n1\nprint(answer)" + ], + "Output Answer": [ + "128" + ], + "split": "train" + }, + { + "Input": "alice , benjamin , and carol each try independently to win a carnival game . if their individual probabilities for success are 1 / 5 , 3 / 8 , and 2 / 7 , respectively , what is the probability that exactly two of the 3 players will win but one will lose ?", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 3.0\nn3 = 8.0\nn4 = 2.0\nn5 = 7.0\nn6 = 3.0\nt0 = n4 / n5\nt1 = 4.0 / n1\nt2 = n2 / n3\nt3 = n0 / n1\nt4 = n1 / n3\nt5 = n1 / n5\nt6 = t1 * t2\nt7 = t3 * t4\nt8 = t3 * t2\nt9 = t0 * t6\nt10 = t0 * t7\nt11 = t5 * t8\nt12 = t9 + t10\nanswer = t12 + t11\nprint(answer)" + ], + "Output Answer": [ + "0.17500000000000002" + ], + "split": "train" + }, + { + "Input": "for any integer k > 1 , the term \u201c length of an integer \u201d refers to the number of positive prime factors , not necessarily distinct , whose product is equal to k . for example , if k = 24 , the length of k is equal to 4 , since 24 = 2 \u00d7 2 \u00d7 2 \u00d7 3 . if x and y are positive integers such that x > 1 , y > 1 , and x + 3 y < 1000 , what is the maximum possible sum of the length of x and the length of y ?", + "Output Program": [ + "n0 = 1.0\nn1 = 24.0\nn2 = 4.0\nn3 = 24.0\nn4 = 2.0\nn5 = 2.0\nn6 = 2.0\nn7 = 3.0\nn8 = 1.0\nn9 = 1.0\nn10 = 3.0\nn11 = 1000.0\nt0 = n2 + n7\nt1 = n2 + n2\nt2 = n0 + t1\nanswer = t0 + t2\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 100 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 3.0\nn3 = 4.0\nn4 = 3.0\nn5 = 5.0\nn6 = 100.0\nt0 = n1 / n5\nt1 = n1 / n3\nt2 = n0 / n1\nt3 = 1.0 - t0\nt4 = n6 / t3\nt5 = t4 / t1\nanswer = t5 / t2\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "train" + }, + { + "Input": "a cave is going to explode . a family is trapped inside that cave . the only way to get outside is a narrow tunnel . but the tunnel is weak and thus only two people can go at one time . also , everybody is afraid of going alone . the father takes one minute to go through till the end , the mother takes two , the son takes 4 and the daughter takes 5 . the cave and tunnel will explode in 12 minutes . can they make it to the other end in that time frame ? ps : keep in mind that when two people are moving , the total time taken will be as per the slower one .", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 12.0\nt0 = n2 / n0\nt1 = n1 * t0\nanswer = t1 - 3.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "a bag contains 10 balls numbered from 0 to 9 . the balls are such that the person picking a ball out of the bag is equally likely to pick anyone of them . a person picked a ball and replaced it in the bag after noting its number . he repeated this process 2 more times . what is the probability that the ball picked first is numbered higher than the ball picked second and the ball picked second is numbered higher than the ball picked third ?", + "Output Program": [ + "n0 = 10.0\nn1 = 0.0\nn2 = 9.0\nn3 = 2.0\nt0 = 4.0 + 4.0\nt1 = 2.0 + 4.0\nt2 = n0 * n2\nt3 = 10.0**min(3.0, 5)\nt4 = t0 * t2\nt5 = t4 / t1\nanswer = t5 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.12" + ], + "split": "train" + }, + { + "Input": "there are 16 teams in the hockey league , and each team faces all the other teams 10 times each . how many games are played in the season ?", + "Output Program": [ + "n0 = 16.0\nn1 = 10.0\nt0 = n0 - 1.0\nt1 = n0 * t0\nt2 = n1 * t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "1200" + ], + "split": "train" + }, + { + "Input": "in an examination , the percentage of students qualified to the number of students appeared from school a is 70 % . in school b , the number of students appeared is 20 % more than the students appeared from school a and the number of students qualified from school b is 50 % more than the students qualified from school a . what is the percentage of students qualified to the number of students appeared from school b ?", + "Output Program": [ + "n0 = 70.0\nn1 = 20.0\nn2 = 50.0\nt0 = 0.25 * 2.0\nt1 = n0 - n1\nt2 = n2 - t0\nt3 = t2 - 12.0\nanswer = t1 + t3\nprint(answer)" + ], + "Output Answer": [ + "87.5" + ], + "split": "train" + }, + { + "Input": "if 45 - [ 28 - { 37 - ( 15 - * ) } ] = 56 , then * is equal to :", + "Output Program": [ + "n0 = 45.0\nn1 = 28.0\nn2 = 37.0\nn3 = 15.0\nn4 = 56.0\nt0 = n1 - n2\nt1 = n3 + t0\nt2 = n0 - t1\nanswer = n4 - t2\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "how much percentage 80 is of 480 ?", + "Output Program": [ + "n0 = 80.0\nn1 = 480.0\nt0 = n0 * 100.0\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "16.666666666666668" + ], + "split": "train" + }, + { + "Input": "the numbers { 1 , 3 , 6 , 7 , 7 , 7 } are used to form 3 2 - digit numbers . if the sum of these 3 numbers is a prime number p , what is the largest possible value of p ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 6.0\nn3 = 7.0\nn4 = 7.0\nn5 = 7.0\nn6 = 3.0\nn7 = 2.0\nn8 = 3.0\nt0 = n3 * 10.0\nt1 = n2 * 10.0\nt2 = n3 + t0\nt3 = n1 + t0\nt4 = n0 + t1\nt5 = t2 + t3\nanswer = t5 + t4\nprint(answer)" + ], + "Output Answer": [ + "211" + ], + "split": "train" + }, + { + "Input": "what is the sum of the digits of integer k , if k = ( 10 ^ 40 - 46 )", + "Output Program": [ + "n0 = 10.0\nn1 = 40.0\nn2 = 46.0\nt0 = n0 - 1.0\nt1 = n1 - 2.0\nt2 = t0 * t1\nanswer = t2 + n0\nprint(answer)" + ], + "Output Answer": [ + "352" + ], + "split": "train" + }, + { + "Input": "let s be the set of all positive integers that , when divided by 8 , have a remainder of 5 . what is the 81 th number in this set ?", + "Output Program": [ + "n0 = 8.0\nn1 = 5.0\nn2 = 81.0\nt0 = n2 - 1.0\nt1 = n0 * t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "645" + ], + "split": "train" + }, + { + "Input": "company z has 61 employees . if the number of employees having birthdays on wednesday is more than the number of employees having birthdays on any other day of the week , each of which have same number of birth - days , what is the minimum number of employees having birthdays on wednesday .", + "Output Program": [ + "import math\nn0 = 61.0\nt0 = 3.0 + 4.0\nt1 = n0 / t0\nt2 = math.floor(t1)\nt3 = t2 + 1.0\nanswer = t3 + 4.0\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "a women purchased 3 towels @ rs . 100 each , 5 towels @ rs . 150 each and two towels at a certain rate which is now slipped off from his memory . but she remembers that the average price of the towels was rs . 155 . find the unknown rate of two towels ?", + "Output Program": [ + "n0 = 3.0\nn1 = 100.0\nn2 = 5.0\nn3 = 150.0\nn4 = 155.0\nt0 = n0 + n2\nt1 = n2 * n3\nt2 = n0 * n1\nt3 = t0 + 2.0\nt4 = n4 * t3\nt5 = t4 - t1\nanswer = t5 - t2\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "train" + }, + { + "Input": "the avg weight of a , b & c is 84 kg . if d joins the group , the avg weight of the group becomes 80 kg . if another man e who weights is 7 kg more than d replaces a , then the avgof b , c , d & e becomes 79 kg . what is the weight of a ?", + "Output Program": [ + "n0 = 84.0\nn1 = 80.0\nn2 = 7.0\nn3 = 79.0\nt0 = n1 * 4.0\nt1 = n3 * 4.0\nt2 = n0 * 3.0\nt3 = t0 - t2\nt4 = n2 + t3\nt5 = t1 - t4\nanswer = t0 - t5\nprint(answer)" + ], + "Output Answer": [ + "79" + ], + "split": "train" + }, + { + "Input": "if there are 4 peanuts in a box and mary puts 4 more peanuts inside , how many peanuts are in the box ?", + "Output Program": [ + "n0 = 4.0\nn1 = 4.0\n\nanswer = n0 + n1\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "the average marks of 30 students in a class is 60 . but a student mark is wrongly noted as 90 instead of 15 then find the correct average marks ?", + "Output Program": [ + "n0 = 30.0\nn1 = 60.0\nn2 = 90.0\nn3 = 15.0\nt0 = n0 * n1\nt1 = t0 - n2\nt2 = n3 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "57.5" + ], + "split": "train" + }, + { + "Input": "we bought a total of 80 books at the store . math books cost $ 4 and history books cost $ 5 . the total price was $ 368 . how many math books did we buy ?", + "Output Program": [ + "n0 = 80.0\nn1 = 4.0\nn2 = 5.0\nn3 = 368.0\nt0 = n0 * n1\nt1 = n3 - t0\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "if x + y = 25 and x 2 y 3 + y 2 x 3 = 25 , what is the value of xy ?", + "Output Program": [ + "import math\nn0 = 25.0\nn1 = 2.0\nn2 = 3.0\nn3 = 2.0\nn4 = 3.0\nn5 = 25.0\nt0 = n0 / n0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "if p ( a ) = 2 / 5 and p ( b ) = 2 / 5 , find p ( a n b ) if a and b are independent events .", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 2.0\nn3 = 5.0\nt0 = n0 / n1\nt1 = n2 / n3\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "0.16000000000000003" + ], + "split": "train" + }, + { + "Input": "the mean of 50 observations was 36 . it was found later that an observation 45 was wrongly taken as 23 . the corrected new mean is", + "Output Program": [ + "n0 = 50.0\nn1 = 36.0\nn2 = 45.0\nn3 = 23.0\nt0 = n0 * n1\nt1 = n0 - 2.0\nt2 = t1 - n3\nt3 = t0 + t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "36.5" + ], + "split": "train" + }, + { + "Input": "a luxury liner , queen marry ii , is transporting several cats as well as the crew ( sailors , a cook , and one - legged captain ) to a nearby port . altogether , these passengers have 15 heads and 43 legs . how many cats does the ship host ?", + "Output Program": [ + "n0 = 15.0\nn1 = 43.0\nt0 = n1 - 1.0\nt1 = n0 - 1.0\nt2 = t1 * 2.0\nt3 = t1 * 4.0\nt4 = t0 - t2\nt5 = t3 - t2\nt6 = t4 / t5\nanswer = t6 * t1\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "the average age of a group of n people is 15 years old . one more person aged 35 joins the group and the new average is 17 years old . what is the value of n ?", + "Output Program": [ + "n0 = 15.0\nn1 = 35.0\nn2 = 17.0\nt0 = n1 - n2\nt1 = n2 - n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "what is x if x + 2 y = 10 and y = 4 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 10.0\nn2 = 4.0\nt0 = n0 * n2\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "we bought a total of 90 books at the store . math books cost $ 4 and history books cost $ 5 . the total price was $ 396 . how many math books did we buy ?", + "Output Program": [ + "n0 = 90.0\nn1 = 4.0\nn2 = 5.0\nn3 = 396.0\nt0 = n0 * n1\nt1 = n3 - t0\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "train" + }, + { + "Input": "8 x 5.4 - 0.6 x 10 / 1.2 = ?", + "Output Program": [ + "n0 = 8.0\nn1 = 5.4\nn2 = 0.6\nn3 = 10.0\nn4 = 1.2\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = t0 - t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "31.000000000000004" + ], + "split": "train" + }, + { + "Input": "there were 36000 hardback copies of a certain novel sold before the paperback version was issued . from the time the first paperback copy was sold until the last copy of the novel was sold 9 times as many paperback copies as hardback copies were sold . if a total of 440000 copies of the novel were sold in all , how many paperback copies were sold ?", + "Output Program": [ + "n0 = 36000.0\nn1 = 9.0\nn2 = 440000.0\nt0 = n1 + 1.0\nt1 = n2 - n0\nt2 = t1 / t0\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "363600" + ], + "split": "train" + }, + { + "Input": "in a group of ducks and cows , the total number of legs are 24 more than twice the no . of heads . find the total no . of buffaloes .", + "Output Program": [ + "n0 = 24.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "the probability of a student possessing a ball point pen in exam is 3 / 5 & possessing an ink pen is 2 / 3 . find his probability of possessing at least one of them", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 2.0\nn3 = 3.0\nt0 = 1.0 + 12.0\nt1 = n0 * n1\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.8666666666666667" + ], + "split": "train" + }, + { + "Input": "evaluate 248 + 64 \u2212 \u2212 \u221a \u2212 \u2212 \u2212 \u2212 \u2212 \u2212 \u2212 \u2212 \u2212 \u221a", + "Output Program": [ + "n0 = 248.0\nn1 = 64.0\nt0 = n1 * 4.0\nt1 = t0 - n0\nanswer = t1 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "two employees x and y are paid a total of rs . 638 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?", + "Output Program": [ + "n0 = 638.0\nn1 = 120.0\nt0 = 1.0 + 4.0\nt1 = t0 * 2.0\nt2 = t1 + 1.0\nt3 = n0 * t1\nt4 = t2 * 2.0\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "290" + ], + "split": "train" + }, + { + "Input": "for any integer k > 1 , the term \u201c length of an integer \u201d refers to the number of positive prime factors , not necessarily distinct , whose product is equal to k . for example , if k = 24 , the length of k is equal to 4 , since 24 = 2 \u00d7 2 \u00d7 2 \u00d7 3 . if x and y are positive integers such that x > 1 , y > 1 , and x + 3 y < 920 , what is the maximum possible sum of the length of x and the length of y ?", + "Output Program": [ + "n0 = 1.0\nn1 = 24.0\nn2 = 4.0\nn3 = 24.0\nn4 = 2.0\nn5 = 2.0\nn6 = 2.0\nn7 = 3.0\nn8 = 1.0\nn9 = 1.0\nn10 = 3.0\nn11 = 920.0\nt0 = n2 + n7\nt1 = n2 + n2\nt2 = n0 + t1\nanswer = t0 + t2\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "the average of marks obtained by 120 candidates was 35 . if the avg of marks of passed candidates was 39 and that of failed candidates was 39 and that of failed candidates was 15 , the no . of candidates who passed the examination is ?", + "Output Program": [ + "n0 = 120.0\nn1 = 35.0\nn2 = 39.0\nn3 = 39.0\nn4 = 15.0\nt0 = n0 * n1\nt1 = n0 * n4\nt2 = n2 - n4\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "workers decided to raise rs . 3 lacs by equal contribution from each . had they contributed rs . 50 eachextra , the contribution would have been rs . 3.15 lacs . how many workers were they ?", + "Output Program": [ + "n0 = 3.0\nn1 = 50.0\nn2 = 3.15\nt0 = n2 - n0\nt1 = t0 * 1000.0\nt2 = t1 * 100.0\nanswer = t2 / n1\nprint(answer)" + ], + "Output Answer": [ + "299.99999999999983" + ], + "split": "train" + }, + { + "Input": "there are 7 players in a bowling team with an average weight of 112 kg . if two new players join the team , one weighs 110 kg and the second weighs 60 kg , what will be the new average weight ?", + "Output Program": [ + "n0 = 7.0\nn1 = 112.0\nn2 = 110.0\nn3 = 60.0\nt0 = n2 + n3\nt1 = n0 + 2.0\nt2 = n0 * n1\nt3 = t0 + t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "106" + ], + "split": "train" + }, + { + "Input": "in a group of ducks and cows , the total number of legs are 26 more than thrice the number of heads . find the total number of cows .", + "Output Program": [ + "n0 = 26.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "the total price of a basic computer and printer are $ 2,500 . if the same printer had been purchased with an enhanced computer whose price was $ 500 more than the price of the basic computer , then the price of the printer would have been 1 / 3 of that total . what was the price of the basic computer ?", + "Output Program": [ + "n0 = 2500.0\nn1 = 500.0\nn2 = 1.0\nn3 = 3.0\nt0 = 0.25 * 1000.0\nt1 = t0 * 10.0\nt2 = n1 + t1\nt3 = t2 / n3\nanswer = t1 - t3\nprint(answer)" + ], + "Output Answer": [ + "1500" + ], + "split": "train" + }, + { + "Input": "the contents of a certain box consist of 14 apples and 26 oranges . how many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples ?", + "Output Program": [ + "n0 = 14.0\nn1 = 26.0\nn2 = 70.0\nt0 = n0 + n1\nt1 = n2 / 100.0\nt2 = n0 / t1\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "light glows for every 20 seconds . how many max . times did it glow between 1 : 57 : 58 and 3 : 20 : 47 am .", + "Output Program": [ + "n0 = 20.0\nn1 = 1.0\nn2 = 57.0\nn3 = 58.0\nn4 = 3.0\nn5 = 20.0\nn6 = 47.0\nt0 = n6 + 2.0\nt1 = 2.0 + 60.0\nt2 = n5 + t1\nt3 = t2 * 60.0\nt4 = t0 + t3\nanswer = t4 / n0\nprint(answer)" + ], + "Output Answer": [ + "248.45" + ], + "split": "train" + }, + { + "Input": "each week , harry is paid x dollars per hour for the first 18 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 41 hours if harry and james were paid the same amount last week , how many hours did harry work last week ?", + "Output Program": [ + "n0 = 18.0\nn1 = 1.5\nn2 = 40.0\nn3 = 2.0\nn4 = 41.0\nt0 = n2 + n3\nt1 = t0 - n0\nt2 = t1 / n1\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "34" + ], + "split": "train" + }, + { + "Input": "if x + | x | + y = 5 and x + | y | - y = 6 what is x + y = ?", + "Output Program": [ + "n0 = 5.0\nn1 = 6.0\n\nanswer = n1 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "a certain clock rings two notes at quarter past the hour , 4 notes at half past , and 6 notes at 3 - quarters past . on the hour , it rings 8 notes plus an additional number of notes equal to whatever hour it is . how many notes will the clock ring from 1 : 00 p . m . through 5 : 00 p . m . , including the rings at 1 : 00 and 5 : 00 ?", + "Output Program": [ + "n0 = 4.0\nn1 = 6.0\nn2 = 3.0\nn3 = 8.0\nn4 = 1.0\nn5 = 0.0\nn6 = 5.0\nn7 = 0.0\nn8 = 1.0\nn9 = 0.0\nn10 = 5.0\nn11 = 0.0\nt0 = n3 + n4\nt1 = n4 + t0\nt2 = t0 + t1\nt3 = n4 + t1\nt4 = t2 + t3\nt5 = n4 + t3\nt6 = t4 + t5\nt7 = n4 + t5\nt8 = t5 + t5\nt9 = t6 + t7\nt10 = t8 + t5\nt11 = t10 + t5\nanswer = t9 + t11\nprint(answer)" + ], + "Output Answer": [ + "103" + ], + "split": "train" + }, + { + "Input": "the total age of a and b is 13 years more than the total age of b and c . c is how many years younger than a ?", + "Output Program": [ + "n0 = 13.0\n\nanswer = n0 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "if the product of 6 integers is negative , at most how many of the integers can be negative ?", + "Output Program": [ + "n0 = 6.0\n\nanswer = n0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "at chennai it rained as much on tuesday as on all the others days of the week combined . if the average rainfall for the whole week was 3 cm . how much did it rain on tuesday ?", + "Output Program": [ + "n0 = 3.0\nt0 = 3.0 + 4.0\nt1 = n0 * t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "10.5" + ], + "split": "train" + }, + { + "Input": "( 3 * 10 ^ 2 ) * ( 4 * 10 ^ - 2 ) = ?", + "Output Program": [ + "n0 = 3.0\nn1 = 10.0\nn2 = 2.0\nn3 = 4.0\nn4 = 10.0\nn5 = 2.0\nt0 = -n2\nt1 = n1**min(n2, 5)\nt2 = n0 * t1\nt3 = n1**min(t0, 5)\nt4 = n3 * t3\nanswer = t2 * t4\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "the annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years k in which the population would be doubled assuming there is no emigration or immigration is", + "Output Program": [ + "n0 = 1000.0\nn1 = 39.4\nn2 = 19.4\nt0 = 10.0 * 3.0\nt1 = n1 - n2\nt2 = t1 / n0\nt3 = 100.0 - t0\nt4 = t2 * 100.0\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "a pupil ' s marks were wrongly entered as 83 instead of 63 . due to that the average marks for the class got increased by half ( 1 / 2 ) . the number of pupils in the class is :", + "Output Program": [ + "n0 = 83.0\nn1 = 63.0\nn2 = 1.0\nn3 = 2.0\nt0 = n0 - n1\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "4.036 divided by 0.02 gives :", + "Output Program": [ + "n0 = 4.036\nn1 = 0.02\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "201.79999999999998" + ], + "split": "train" + }, + { + "Input": "in the rectangular coordinate system , what is the x - intercept of a line passing through ( 10 , 3 ) and ( \u2212 8 , \u2212 6 ) ?", + "Output Program": [ + "n0 = 10.0\nn1 = 3.0\nn2 = 8.0\nn3 = 6.0\nt0 = -n3\nt1 = -n2\nt2 = t0 - n1\nt3 = t1 - n0\nt4 = t2 / t3\nt5 = n0 * t4\nt6 = t5 - n1\nanswer = t6 / t4\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "set a contains all the even numbers between 6 and 50 inclusive . set b contains all the even numbers between 106 and 150 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ?", + "Output Program": [ + "n0 = 6.0\nn1 = 50.0\nn2 = 106.0\nn3 = 150.0\nt0 = n1 - n0\nt1 = n2 - n0\nt2 = t0 / 2.0\nt3 = t2 + 1.0\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "2300" + ], + "split": "train" + }, + { + "Input": "when positive integer x is divided by 11 , the quotient is y and the remainder is 4 . when 2 x is divided by 8 , the quotient is 3 y and the remainder is 3 . what is the value of 13 y \u2013 x ?", + "Output Program": [ + "n0 = 11.0\nn1 = 4.0\nn2 = 2.0\nn3 = 8.0\nn4 = 3.0\nn5 = 3.0\nn6 = 13.0\nt0 = n1 * n2\nt1 = n3 * n4\nt2 = n0 * n2\nt3 = t0 - n5\nt4 = t1 - t2\nt5 = t3 / t4\nt6 = n6 * t5\nt7 = n0 * t5\nt8 = n1 + t7\nanswer = t6 - t8\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "if 3 x \u2013 5 y = 5 and x / x + y = 5 / 7 , then what is the value of x \u2013 y ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 5.0\nn3 = 5.0\nn4 = 7.0\nt0 = n1 / n4\nt1 = 1 / t0\nt2 = t1 - 1.0\nt3 = n1 * t2\nt4 = n0 - t3\nt5 = n1 / t4\nt6 = t5 * t2\nanswer = t5 - t6\nprint(answer)" + ], + "Output Answer": [ + "2.999999999999999" + ], + "split": "train" + }, + { + "Input": "he average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 75 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.5\nn2 = 75.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "95" + ], + "split": "train" + }, + { + "Input": "a garden center sells a certain grass seed in 5 - pound bags at $ 13.85 per bag , 10 - pound bags at $ 20.40 per bag , and 25 - pound bags $ 32.25 per bag . if a customer is to buy at least 65 pounds of the grass seed , but no more than 80 pounds , what is the least possible cost of the grass seed that the customer will buy ?", + "Output Program": [ + "n0 = 5.0\nn1 = 13.85\nn2 = 10.0\nn3 = 20.4\nn4 = 25.0\nn5 = 32.25\nn6 = 65.0\nn7 = 80.0\nt0 = n5 * 2.0\nt1 = n3 * 1.0\nt2 = n1 * 1.0\nt3 = t0 + t1\nanswer = t3 + t2\nprint(answer)" + ], + "Output Answer": [ + "98.75" + ], + "split": "train" + }, + { + "Input": "if the sales tax reduced from 3 1 / 2 % to 3 1 / 3 % , then what difference does it make to a person who purchases an article with market price of rs . 8400 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 2.0\nn3 = 3.0\nn4 = 1.0\nn5 = 3.0\nn6 = 8400.0\nt0 = n1 / n2\nt1 = n1 / n0\nt2 = n0 + t0\nt3 = n0 + t1\nt4 = t2 - t3\nt5 = n6 * t4\nanswer = t5 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "13.99999999999999" + ], + "split": "train" + }, + { + "Input": "find ( 7 x + 8 y ) / ( x - 2 y ) if x / 2 y = 3 / 2 ?", + "Output Program": [ + "n0 = 7.0\nn1 = 8.0\nn2 = 2.0\nn3 = 2.0\nn4 = 3.0\nn5 = 2.0\nt0 = n4 / n2\nt1 = n2 * t0\nt2 = n0 * t1\nt3 = t1 - n2\nt4 = n1 + t2\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "29" + ], + "split": "train" + }, + { + "Input": "list d consists of 12 consecutive integers . if - 4 is the least integer in list d , what is the range of positive integers in list d ?", + "Output Program": [ + "n0 = 12.0\nn1 = 4.0\nt0 = n0 - 1.0\nt1 = t0 - n1\nanswer = t1 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "the average weight of 9 person ' s increases by 5.5 kg when a new person comes in place of one of them weighing 86 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 9.0\nn1 = 5.5\nn2 = 86.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "135.5" + ], + "split": "train" + }, + { + "Input": "in a maths test , students were asked to find 5 / 16 of a certain number . one of the students by mistake found 5 / 6 th of that number and his answer was 50 more than the correct answer . find the number .", + "Output Program": [ + "n0 = 5.0\nn1 = 16.0\nn2 = 5.0\nn3 = 6.0\nn4 = 50.0\nt0 = n1 * n4\nt1 = n0 * n1\nt2 = n0 * n3\nt3 = n3 * t0\nt4 = t1 - t2\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "96" + ], + "split": "train" + }, + { + "Input": "find the 12 th term of an arithmetic progression whose first term is 2 and the common difference is 8 .", + "Output Program": [ + "n0 = 12.0\nn1 = 2.0\nn2 = 8.0\nt0 = n0 - 1.0\nt1 = n2 * t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "united telephone charges a base rate of $ 6.00 for service , plus an additional charge of $ 0.25 per minute . atlantic call charges a base rate of $ 12.00 for service , plus an additional charge of $ 0.20 per minute . for what number of minutes would the bills for each telephone company be the same ?", + "Output Program": [ + "n0 = 6.0\nn1 = 0.25\nn2 = 12.0\nn3 = 0.2\nt0 = n2 - n0\nt1 = n1 - n3\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "120.00000000000003" + ], + "split": "train" + }, + { + "Input": "the contents of a certain box consist of 14 apples and 20 oranges . how many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples ?", + "Output Program": [ + "n0 = 14.0\nn1 = 20.0\nn2 = 70.0\nt0 = n0 + n1\nt1 = n2 / 100.0\nt2 = n0 / t1\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "3 people decided to put a down payment on a car for 3500 dollars . how much money do they each have to pay , given that that they have to pay the same amount , and they can not use any bills below $ 1 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 3500.0\nn2 = 1.0\n\nanswer = n1 / n0\nprint(answer)" + ], + "Output Answer": [ + "1166.6666666666667" + ], + "split": "train" + }, + { + "Input": "on dividing 16698 by a certain number , we get 89 as quotient and 14 as remainder . what is the divisor ?", + "Output Program": [ + "n0 = 16698.0\nn1 = 89.0\nn2 = 14.0\nt0 = n0 - n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "187.46067415730337" + ], + "split": "train" + }, + { + "Input": "when an amount was distributed among 14 boys , each of them got rs 80 more than the amount received by each boy when the same amount is distributed equally among 18 boys . what was the amount ?", + "Output Program": [ + "n0 = 14.0\nn1 = 80.0\nn2 = 18.0\nt0 = 1.0 / n0\nt1 = 1.0 / n2\nt2 = t0 - t1\nanswer = n1 / t2\nprint(answer)" + ], + "Output Answer": [ + "5040" + ], + "split": "train" + }, + { + "Input": "sum of the squares of 3 no . is 156 and the sum of their products taken two at a time is 50 . find the sum ?", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 156.0\nn2 = 50.0\nt0 = n2 * 2.0\nt1 = n1 + t0\nanswer = math.sqrt(max(0, t1))\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "farm tax is levied on the 60 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . willam . mr . willam paid only $ 500 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :", + "Output Program": [ + "n0 = 60.0\nn1 = 3840.0\nn2 = 500.0\nt0 = n2 / n1\nt1 = t0 * 100.0\nt2 = t1 * 100.0\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "21.701388888888893" + ], + "split": "train" + }, + { + "Input": "a batsman makes a score of 83 runs in the 17 th inning and thus increases his averages by 3 . find his average after 17 th inning ?", + "Output Program": [ + "n0 = 83.0\nn1 = 17.0\nn2 = 3.0\nn3 = 17.0\nt0 = n1 * n2\nt1 = n0 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "when x is multiplied by 3 , the result is 20 more than the result of subtracting x from 20 . what is the value of x ?", + "Output Program": [ + "n0 = 3.0\nn1 = 20.0\nn2 = 20.0\nt0 = n1 + n2\nt1 = 1.0 + n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "solution for 2.75 + . 003 + . 158", + "Output Program": [ + "n0 = 2.75\nn1 = 3.0\nn2 = 158.0\nt0 = n1 / 1000.0\nt1 = n2 / 1000.0\nt2 = n0 + t0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "2.911" + ], + "split": "train" + }, + { + "Input": "a farmer has an apple orchard consisting of fuji and gala apple trees . due to high winds this year 10 % of his trees cross pollinated . the number of his trees that are pure fuji plus the cross - pollinated ones totals 238 , while 3 / 4 of all his trees are pure fuji . how many of his trees are pure gala ?", + "Output Program": [ + "n0 = 10.0\nn1 = 238.0\nn2 = 3.0\nn3 = 4.0\nt0 = n0 / 100.0\nt1 = n2 / n3\nt2 = t0 + t1\nt3 = n1 / t2\nanswer = t3 - n1\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "what should be the least number to be added to the 51234 number to make it divisible by 9 ?", + "Output Program": [ + "n0 = 51234.0\nn1 = 9.0\nt0 = n0 % n1\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "8 k 8 + k 88 - - - - - - - - 16 t 6 if k and t represent non - zero digits within the integers above , what is t ?", + "Output Program": [ + "n0 = 8.0\nn1 = 8.0\nn2 = 88.0\nn3 = 16.0\nn4 = 6.0\nt0 = n0 + 1.0\nt1 = n3 - t0\nanswer = t1 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "the value of a scooter depreciates in such a way that its value of the end of each year is 3 / 4 of its value of the beginning of the same year . if the initial value of the scooter is rs . 40,000 , what is the value at the end of 4 years ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 40000.0\nn3 = 4.0\nt0 = n0 / n1\nt1 = 100.0 * 100.0\nt2 = n1 * t1\nt3 = t0**min(n3, 5)\nanswer = t2 * t3\nprint(answer)" + ], + "Output Answer": [ + "12656.25" + ], + "split": "train" + }, + { + "Input": "the simple interest on a sum of money will be rs . 400 after 10 years . if the principal is trebled after 5 years what will be the total interest at the end of the tenth year ?", + "Output Program": [ + "n0 = 400.0\nn1 = 10.0\nn2 = 5.0\nt0 = n0 / n1\nt1 = n2 * t0\nt2 = t1 * 3.0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "800" + ], + "split": "train" + }, + { + "Input": "when greenville state university decided to move its fine arts collection to a new library , it had to package the collection in 20 - inch by 20 - inch by 15 - inch boxes . if the university pays $ 0.90 for every box , and if the university needs 3.06 million cubic inches to package the collection , what is the minimum amount the university must spend on boxes ?", + "Output Program": [ + "n0 = 20.0\nn1 = 20.0\nn2 = 15.0\nn3 = 0.9\nn4 = 3.06\nt0 = 1000.0 * 1000.0\nt1 = n0 * n0\nt2 = n4 * t0\nt3 = n2 * t1\nt4 = t2 / t3\nanswer = n3 * t4\nprint(answer)" + ], + "Output Answer": [ + "459" + ], + "split": "train" + }, + { + "Input": "for any number y , y * is defined as the greatest positive even integer less than or equal to y . what is the value of 5.0 \u2013 5.0 * ?", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 5.0\nt0 = math.floor(n0)\nt1 = t0 - 1.0\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "if the average ( arithmetic mean ) of 102 consecutive odd integers is 414 , then the least of these integers is", + "Output Program": [ + "n0 = 102.0\nn1 = 414.0\nt0 = n1 - n0\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "313" + ], + "split": "train" + }, + { + "Input": "10 play kabadi , 40 play kho kho only , 5 play both gmaes . then how many in total ?", + "Output Program": [ + "n0 = 10.0\nn1 = 40.0\nn2 = 5.0\nt0 = n1 + n2\nt1 = n0 + t0\nanswer = t1 - n2\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "1 + 2 = 10 2 + 3 = 26 3 + 4 = 50 then 4 + 5 = ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 10.0\nn3 = 2.0\nn4 = 3.0\nn5 = 26.0\nn6 = 3.0\nn7 = 4.0\nn8 = 50.0\nn9 = 4.0\nn10 = 5.0\nt0 = n7 + n10\nt1 = t0**min(2.0, 5)\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "82" + ], + "split": "train" + }, + { + "Input": "in the list 3 , 4 , 5 , 5 , 5 , 5 , 7 , 11 , 21 , what fraction of the data is less than the mode ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 5.0\nn3 = 5.0\nn4 = 5.0\nn5 = 5.0\nn6 = 7.0\nn7 = 11.0\nn8 = 21.0\nt0 = n1 + n2\nanswer = 2.0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.2222222222222222" + ], + "split": "train" + }, + { + "Input": "56 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780 . the bigger part is :", + "Output Program": [ + "n0 = 56.0\nn1 = 10.0\nn2 = 22.0\nn3 = 780.0\nt0 = n0 * n1\nt1 = n2 - n1\nt2 = n3 - t0\nt3 = t2 / t1\nanswer = n0 - t3\nprint(answer)" + ], + "Output Answer": [ + "37.66666666666667" + ], + "split": "train" + }, + { + "Input": "what is the lowest positive integer that is divisible by 1 through 2 , inclusive ?", + "Output Program": [ + "import scipy\nn0 = 1.0\nn1 = 2.0\n\nanswer = scipy.lcm(int(n0), int(n1))\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "each year for 4 years , a farmer increased the number of trees in a certain orchard by 1 / 4 of the number of trees in the orchard of the preceding year . if all of the trees thrived and there were 1250 trees in the orchard at the end of 4 year period , how many trees were in the orchard at the beginning of the 4 year period .", + "Output Program": [ + "n0 = 4.0\nn1 = 1.0\nn2 = 4.0\nn3 = 1250.0\nn4 = 4.0\nn5 = 4.0\nt0 = n1 / n0\nt1 = n1 + t0\nt2 = t1**min(n0, 5)\nanswer = n3 / t2\nprint(answer)" + ], + "Output Answer": [ + "512" + ], + "split": "train" + }, + { + "Input": "45 x ? = 60 % of 900", + "Output Program": [ + "n0 = 45.0\nn1 = 60.0\nn2 = 900.0\nt0 = n1 / 100.0\nt1 = n2 * t0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "set s contains exactly 10 numbers and has an average ( arithmetic mean ) of 6.2 . if one of the numbers in set s is increased by 6 , while all other numbers remain the same , what is the new average of set s ?", + "Output Program": [ + "n0 = 10.0\nn1 = 6.2\nn2 = 6.0\nt0 = n0 * n1\nt1 = n2 + t0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "6.8" + ], + "split": "train" + }, + { + "Input": "what is the greatest 6 - digit number when divided by 8 , 9 , and 10 leaves a remainder of 6 , 7 , and 8 respectively ?", + "Output Program": [ + "import scipy\nn0 = 6.0\nn1 = 8.0\nn2 = 9.0\nn3 = 10.0\nn4 = 6.0\nn5 = 7.0\nn6 = 8.0\nt0 = scipy.lcm(int(n1), int(n2))\nt1 = scipy.lcm(int(n2), int(n3))\nt2 = 1000.0 * 1000.0\nt3 = scipy.lcm(int(t0), int(t1))\nt4 = t2 - 1.0\nt5 = t3 * t1\nt6 = n3 * t5\nanswer = t4 - t6\nprint(answer)" + ], + "Output Answer": [ + "675999" + ], + "split": "train" + }, + { + "Input": "the average of runs of a cricket player of 20 innings was 36 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?", + "Output Program": [ + "n0 = 20.0\nn1 = 36.0\nn2 = 4.0\nt0 = n0 + 1.0\nt1 = n1 + n2\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "the product of a and b is equal to 14 more than twice the sum of a and b . if b = 8 , what is the value of b - a ?", + "Output Program": [ + "n0 = 14.0\nn1 = 8.0\nt0 = n1 * 2.0\nt1 = n1 - 2.0\nt2 = n0 + t0\nt3 = t2 / t1\nanswer = n1 - t3\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "the smallest number when increased by ` ` 1 ` ` is exactly divisible by 618 , 3648 , 60 is :", + "Output Program": [ + "n0 = 1.0\nn1 = 618.0\nn2 = 3648.0\nn3 = 60.0\nt0 = n0 + n1\nanswer = t0 + 100.0\nprint(answer)" + ], + "Output Answer": [ + "719" + ], + "split": "train" + }, + { + "Input": "having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.96 at the candy store . what is john \u2019 s weekly allowance ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 0.96\nt0 = n0 / n1\nt1 = 1.0 / n0\nt2 = 1.0 - t0\nt3 = t1 * t2\nt4 = t0 + t3\nt5 = 1.0 - t4\nanswer = n2 / t5\nprint(answer)" + ], + "Output Answer": [ + "3.599999999999999" + ], + "split": "train" + }, + { + "Input": "what is x if x + 3 y = 10 and y = 3 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 10.0\nn2 = 3.0\nt0 = n0 * n2\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "arun borrowed a sum of money from jayant at the rate of 8 % per annum simple interest for the first 4 years , 10 % per annum for the next 6 years and 12 % per annum for the period beyond 10 years . if he pays a total of 12160 as interest only at the end of 15 years , how much money did he borrow ?", + "Output Program": [ + "n0 = 8.0\nn1 = 4.0\nn2 = 10.0\nn3 = 6.0\nn4 = 12.0\nn5 = 10.0\nn6 = 12160.0\nn7 = 15.0\nt0 = n6 * 100.0\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = n7 - n2\nt4 = t1 + t2\nt5 = n4 * t3\nt6 = t4 + t5\nanswer = t0 / t6\nprint(answer)" + ], + "Output Answer": [ + "8000" + ], + "split": "train" + }, + { + "Input": "what is the largest 4 digit number exactly divisible by 88 ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 88.0\nt0 = 10.0**min(n0, 5)\nt1 = t0 / n1\nt2 = math.floor(t1)\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "9944" + ], + "split": "train" + }, + { + "Input": "a vendor sells 20 percent of the pears he had and throws away 50 percent of the remainder . the next day , the vendor sells 20 percent of the remaining pears and throws away the rest . in total , what percent of his pears does the vendor throw away ?", + "Output Program": [ + "n0 = 20.0\nn1 = 50.0\nn2 = 20.0\nt0 = n1 / 100.0\nt1 = n0 / 100.0\nt2 = 1.0 - t1\nt3 = t0 * t2\nt4 = t2 - t3\nt5 = t1 * t4\nt6 = t4 - t5\nt7 = t3 + t6\nanswer = t7 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "train" + }, + { + "Input": "john want to buy a $ 100 trouser at the store , but he think it \u00e2 \u20ac \u2122 s too expensive . finally , it goes on sale for $ 80 . what is the percent decrease ?", + "Output Program": [ + "n0 = 100.0\nn1 = 80.0\n\nanswer = n0 - n1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "a number is doubled and 9 is added . if the resultant is trebled , it becomes 75 . what is that number ?", + "Output Program": [ + "n0 = 9.0\nn1 = 75.0\nt0 = n0 * 3.0\nt1 = 2.0 * 3.0\nt2 = n1 - t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "on teacher ' s day , sweets were to be equally distributed among 190 children in a school . actually , on the teacher ' s day , 70 children were absent and therefore each child got 14 sweets extra . how many sweets did each child get on that day ?", + "Output Program": [ + "n0 = 190.0\nn1 = 70.0\nn2 = 14.0\nt0 = n0 * n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "38" + ], + "split": "train" + }, + { + "Input": "x , a , z , and b are single digit positive integers . x = \u00bc a . z = \u00bc b . ( 10 a + b ) \u2013 ( 10 x + z ) could not equal", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nt0 = n0 * 4.0\nanswer = t0 + 4.0\nprint(answer)" + ], + "Output Answer": [ + "44" + ], + "split": "train" + }, + { + "Input": "on a two - dimensional coordinate plane , the line z = x ^ 2 - x ^ 3 touches the x - axis in how many places ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nt0 = max(n0,n1)\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "find the value of 72514 x 9999 = m ?", + "Output Program": [ + "n0 = 72514.0\nn1 = 9999.0\nt0 = n1 - 4.0\nanswer = t0 * n0\nprint(answer)" + ], + "Output Answer": [ + "724777430" + ], + "split": "train" + }, + { + "Input": "if | x - 12 | = 100 , what is the sum of all the possible values of x ?", + "Output Program": [ + "n0 = 12.0\nn1 = 100.0\nt0 = n0 + n1\nt1 = n1 - n0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "the sum of all solutions for x in the equation x ^ 2 \u2013 8 x + 21 = | x \u2013 5 | + 4 is equal to :", + "Output Program": [ + "n0 = 2.0\nn1 = 8.0\nn2 = 21.0\nn3 = 5.0\nn4 = 4.0\n\nanswer = n3 * n4\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "1.20 can be expressed in terms of percentage as", + "Output Program": [ + "n0 = 1.2\n\nanswer = n0 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "in a group of ducks and cows , the total number of legs are 24 more than twice the number of heads . find the total number of cows .", + "Output Program": [ + "n0 = 24.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "the average weight of a , b and c is 45 kg . if the average weight of a and b be 40 kg and that of b and c be 45 kg , then the weight of b is :", + "Output Program": [ + "n0 = 45.0\nn1 = 40.0\nn2 = 45.0\nt0 = n1 * 2.0\nt1 = n2 * 2.0\nt2 = n0 * 3.0\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "a waiter ' s salary consists of his salary and tips . during one week his tips were 5 / 4 of his salary . what fraction of his income came from tips ?", + "Output Program": [ + "n0 = 5.0\nn1 = 4.0\nt0 = n0 / n1\nt1 = t0 + 1.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.5555555555555556" + ], + "split": "train" + }, + { + "Input": "in a fort , there are 1200 soldiers . if each soldier consumes 3 kg per day , the provisions available in the fort will last for 30 days . if some more soldiers join , the provisions available will last for 25 days given each soldier consumes 2.5 kg per day . find the number of soldiers joining the fort in that case ?", + "Output Program": [ + "n0 = 1200.0\nn1 = 3.0\nn2 = 30.0\nn3 = 25.0\nn4 = 2.5\nt0 = n0 * n1\nt1 = n2 * t0\nt2 = t1 / n3\nt3 = t2 / n4\nanswer = t3 - n0\nprint(answer)" + ], + "Output Answer": [ + "528" + ], + "split": "train" + }, + { + "Input": "in a competitive examination in state a , 6 % candidates got selected from the total appeared candidates . state b had an equal number of candidates appeared and 7 % candidates got selected with 81 more candidates got selected than a . what was the number of candidates appeared from each state ?", + "Output Program": [ + "n0 = 6.0\nn1 = 7.0\nn2 = 81.0\nt0 = n1 - n0\nt1 = t0 / 100.0\nanswer = n2 / t1\nprint(answer)" + ], + "Output Answer": [ + "8100" + ], + "split": "train" + }, + { + "Input": "a man \u00e2 \u20ac \u2122 s current age is ( 2 / 5 ) of the age of his father . after 10 years , he will be ( 1 / 2 ) of the age of his father . what is the age of father at now ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 10.0\nn3 = 1.0\nn4 = 2.0\nt0 = n3 / n0\nt1 = n0 / n1\nt2 = n2 * t0\nt3 = t0 - t1\nt4 = n2 - t2\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "50.000000000000014" + ], + "split": "train" + }, + { + "Input": "a cricketer whose bowling average is 12.4 runs per wicket takes 5 wickets for 26 runs and thereby decreases his average by 0.4 . the number of wickets taken by him till the last match was :", + "Output Program": [ + "n0 = 12.4\nn1 = 5.0\nn2 = 26.0\nn3 = 0.4\nt0 = n0 - n3\nt1 = n1 * t0\nt2 = t1 - n2\nanswer = t2 / n3\nprint(answer)" + ], + "Output Answer": [ + "85" + ], + "split": "train" + }, + { + "Input": "in a bus left side are 15 seats available , 3 few seats in right side because in rear exit door . each seat hold 3 people . in addition , there is a seat back can sit 9 people all together . how many people can sit in a bus ?", + "Output Program": [ + "n0 = 15.0\nn1 = 3.0\nn2 = 3.0\nn3 = 9.0\nt0 = n0 - n1\nt1 = n0 + t0\nt2 = n1 * t1\nanswer = n3 + t2\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "the average of temperatures at noontime from monday to friday is 25 ; the lowest one is 15 , what is the possible maximum range of the temperatures ?", + "Output Program": [ + "n0 = 25.0\nn1 = 15.0\nt0 = 2.0 + 3.0\nt1 = n1 * 4.0\nt2 = n0 * t0\nt3 = t2 - t1\nanswer = t3 - n1\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "a grocery shop has a sale of rs . 6335 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ?", + "Output Program": [ + "n0 = 6335.0\nn1 = 6927.0\nn2 = 6855.0\nn3 = 7230.0\nn4 = 6562.0\nn5 = 5.0\nn6 = 6500.0\nt0 = n5 + 1.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n6 * t0\nt4 = n3 + t2\nt5 = n4 + t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "5091" + ], + "split": "train" + }, + { + "Input": "in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 4 eggs . if the cost of each pound of rice is $ 0.33 , then how many cents does a liter of kerosene cost ? [ one dollar has 100 cents . ]", + "Output Program": [ + "n0 = 4.0\nn1 = 0.33\nn2 = 100.0\nt0 = 1.0 / 2.0\nt1 = n1 * n2\nt2 = n0 / t0\nt3 = t2 / 12.0\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 14000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is", + "Output Program": [ + "n0 = 8000.0\nn1 = 7.0\nn2 = 14000.0\nn3 = 6000.0\nt0 = n2 - n0\nt1 = n0 - n3\nt2 = n1 * t0\nt3 = t2 / t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "elena \u2019 s bread recipe calls for 8 ounces of butter for each 14 cups of flour used . she needs to make 4 times the original recipe . if 12 ounces of butter is used , then how many cups of flour are needed ?", + "Output Program": [ + "n0 = 8.0\nn1 = 14.0\nn2 = 4.0\nn3 = 12.0\n\nanswer = n1 * n2\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "train" + }, + { + "Input": "5 kilograms of oranges contained 95 % of water . if the next day the concentration of water decreased by 5 % , what was the new weight of the oranges , in kilograms ?", + "Output Program": [ + "n0 = 5.0\nn1 = 95.0\nn2 = 5.0\n\nanswer = n0 * n0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "the mean of 20 values was 150 . it was detected on rechecking that one value 160 was wrongly copied as 135 for the computation of the mean . find the correct mean .", + "Output Program": [ + "n0 = 20.0\nn1 = 150.0\nn2 = 160.0\nn3 = 135.0\nt0 = n0 * n1\nt1 = n2 - n3\nt2 = t0 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "151.25" + ], + "split": "train" + }, + { + "Input": "a rich aristocrat decided that he would give every man rs . 45 and every women rs . 60 . only one nineth of the man and only one twelfth of the women collected their dues . can u tell me how much money thath aristocrat spent if their were 3552 people in total", + "Output Program": [ + "n0 = 45.0\nn1 = 60.0\nn2 = 3552.0\nt0 = 100.0 * 100.0\nt1 = 2.0 * 3600.0\nt2 = 10.0 * 4.0\nt3 = 10.0 * 2.0\nt4 = t0 + t1\nt5 = t2 * 10.0\nt6 = t4 + t2\nt7 = t6 + t5\nt8 = t7 + 100.0\nt9 = t8 + t3\nanswer = t9 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "17760" + ], + "split": "train" + }, + { + "Input": "for the positive integers x , x + 2 , x + 4 , x + 7 , and x + 37 , the mean is how much greater than the median ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 7.0\nn3 = 37.0\nt0 = n0 + n1\nt1 = 1.0 + n1\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = t3 / t1\nanswer = t4 - n1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "the flow of water through a drainage pipe was monitored for a 3 - hour period . in the second hour , the rate of flow was 36 gallons per hour , which was 50 percent faster than the rate of flow for the first hour . if 25 percent more water flowed through the pipe in the third hour than it did in the second , how many gallons of water flowed through the pipe during the entire 3 hours ?", + "Output Program": [ + "n0 = 3.0\nn1 = 36.0\nn2 = 50.0\nn3 = 25.0\nn4 = 3.0\nt0 = n0 / 2.0\nt1 = n1 * 0.25\nt2 = n1 + t1\nt3 = n1 / t0\nt4 = t2 + t3\nanswer = n1 + t4\nprint(answer)" + ], + "Output Answer": [ + "105" + ], + "split": "train" + }, + { + "Input": "can you find a 6 digit number under 5 lakh such that the sum of it ' s digits is 43 ?", + "Output Program": [ + "n0 = 6.0\nn1 = 5.0\nn2 = 43.0\nt0 = n0 + 1.0\nt1 = t0 * 100.0\nt2 = t0 + t1\nanswer = t2**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "499849" + ], + "split": "train" + }, + { + "Input": "there is a total of 84 marbles in a box , each of which is red , green , blue , or white . if one marble is drawn from the box at random , the probability that it will be white is 1 / 4 and the probability that it will be green is 2 / 7 . what is the probability that the marble will be either red or blue ?", + "Output Program": [ + "n0 = 84.0\nn1 = 1.0\nn2 = 4.0\nn3 = 2.0\nn4 = 7.0\nt0 = n1 / n2\nt1 = n3 / n4\nt2 = t0 + t1\nanswer = n1 - t2\nprint(answer)" + ], + "Output Answer": [ + "0.4642857142857143" + ], + "split": "train" + }, + { + "Input": "at a certain pizza parlor , the diameter of a large pizza is 40 % larger than the diameter of a small pizza . what is the percent increase in total amount of pizza , from a small to a large ?", + "Output Program": [ + "n0 = 40.0\nt0 = n0 + 100.0\nt1 = 100.0**min(2.0, 5)\nt2 = t0**min(2.0, 5)\nt3 = t2 - t1\nanswer = t3 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "96" + ], + "split": "train" + }, + { + "Input": "the average weight of 20 persons sitting in a boat had some value . a new person added to them whose weight was 48 kg only . due to his arrival , the average weight of all the persons decreased by 5 kg . find the average weight of first 20 persons ?", + "Output Program": [ + "n0 = 20.0\nn1 = 48.0\nn2 = 5.0\nn3 = 20.0\nt0 = n0 + 1.0\nt1 = n2 * t0\nanswer = t1 - n1\nprint(answer)" + ], + "Output Answer": [ + "57" + ], + "split": "train" + }, + { + "Input": "rs . 120 are divided among a , b , c such that a ' s share is rs . 20 more than b ' s and rs . 20 less than c ' s . what is b ' s share", + "Output Program": [ + "n0 = 120.0\nn1 = 20.0\nn2 = 20.0\nt0 = n1 + n1\nt1 = n0 - n1\nt2 = t1 - t0\nanswer = t2 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "a sum of money lent out at s . i . amounts to rs . 660 after 2 years and to rs . 1020 after a further period of 5 years . the sum is ?", + "Output Program": [ + "n0 = 660.0\nn1 = 2.0\nn2 = 1020.0\nn3 = 5.0\nt0 = n2 - n0\nt1 = t0 / n3\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "516" + ], + "split": "train" + }, + { + "Input": "for an agricultural experiment , 500 seeds were planted in one plot and 200 were planted in a second plot . if exactly 30 percent of the seeds in the first plot germinated and exactly 50 percent of the seeds in the second plot germinated , what percent of the total number of seeds germinated ?", + "Output Program": [ + "n0 = 500.0\nn1 = 200.0\nn2 = 30.0\nn3 = 50.0\nt0 = n0 + n1\nt1 = n2 / 100.0\nt2 = n3 / 100.0\nt3 = n0 * t1\nt4 = n1 * t2\nt5 = t3 + t4\nt6 = t5 / t0\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "35.714285714285715" + ], + "split": "train" + }, + { + "Input": "what is the total number of prime numbers less than 70 ?", + "Output Program": [ + "n0 = 70.0\nt0 = 10.0 + 3.0\nt1 = t0 + 4.0\nt2 = t1 + 2.0\nanswer = max(t1,t2)\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "3 / 5 of all married couples have more than one child . 1 / 2 of all married couples have more than 3 children . what fraction of all married couples have 2 or 3 children ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 1.0\nn3 = 2.0\nn4 = 3.0\nn5 = 2.0\nn6 = 3.0\nt0 = n0 / n1\nt1 = n2 / n3\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "0.09999999999999998" + ], + "split": "train" + }, + { + "Input": "a 4 - digit code can consist of the digits 0 ~ 9 except that it does not contain the digits 1 , 2 , 4 , and 6 at all . if repeated digits are allowed , what is the probability that it has at least one even digit ?", + "Output Program": [ + "n0 = 4.0\nn1 = 0.0\nn2 = 9.0\nn3 = 1.0\nn4 = 2.0\nn5 = 4.0\nn6 = 6.0\nt0 = 4.0**min(n0, 5)\nt1 = 10.0 - 4.0\nt2 = t1**min(n0, 5)\nt3 = t2 - t0\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.8024691358024691" + ], + "split": "train" + }, + { + "Input": "find the greatest number that exactly divides 35 , 91 and 840 ?", + "Output Program": [ + "import scipy\nn0 = 35.0\nn1 = 91.0\nn2 = 840.0\nt0 = n2 - n1\nt1 = n1 - n0\nt2 = t0 - n0\nt3 = scipy.gcd(int(t2), int(t1))\nanswer = scipy.gcd(int(t3), int(t0))\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "when a number is divided by 6 & then multiply by 12 the answer is 11 what is the no . ?", + "Output Program": [ + "n0 = 6.0\nn1 = 12.0\nn2 = 11.0\nt0 = n2 / n1\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "5.5" + ], + "split": "train" + }, + { + "Input": "if 3 x + 4 y = 60 and 6 x - 4 y = 12 , what is the product of x and y ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 60.0\nn3 = 6.0\nn4 = 4.0\nn5 = 12.0\nt0 = n2 + n5\nt1 = n0 + n3\nt2 = t0 / t1\nt3 = n3 * t2\nt4 = t3 - n5\nt5 = t4 / n1\nanswer = t2 * t5\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "train" + }, + { + "Input": "a seller of used cars has 18 cars to sell and each of his clients selected 3 cars that he liked most . if each car was selected exactly thrice , how many clients visited the garage ?", + "Output Program": [ + "n0 = 18.0\nn1 = 3.0\nt0 = n0 / n1\nanswer = t0 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "if a 5 percent deposit that has been paid toward the purchase of a certain product is $ 50 , how much more remains to be paid ?", + "Output Program": [ + "n0 = 5.0\nn1 = 50.0\nt0 = 100.0 / n0\nt1 = n1 * t0\nanswer = t1 - n1\nprint(answer)" + ], + "Output Answer": [ + "950" + ], + "split": "train" + }, + { + "Input": "a , b and c have rs . 700 between them , a and c together have rs . 300 and b and c rs . 600 . how much does c have ?", + "Output Program": [ + "n0 = 700.0\nn1 = 300.0\nn2 = 600.0\nt0 = n1 + n2\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "train" + }, + { + "Input": "find the lowest common multiple of 24 , 36 and 42 .", + "Output Program": [ + "import scipy\nn0 = 24.0\nn1 = 36.0\nn2 = 42.0\nt0 = scipy.lcm(int(n0), int(n1))\nanswer = scipy.lcm(int(n2), int(t0))\nprint(answer)" + ], + "Output Answer": [ + "504" + ], + "split": "train" + }, + { + "Input": "if 7 / 10 of a pencil is green , 4 / 5 of the remaining is gold and the remaining 1 / 2 is white , what is the total length of the pencil ?", + "Output Program": [ + "n0 = 7.0\nn1 = 10.0\nn2 = 4.0\nn3 = 5.0\nn4 = 1.0\nn5 = 2.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = n4 / n5\nt3 = t0 + t1\nanswer = t3 + t2\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "the average salary of a person for the months of january , february , march and april is rs . 8000 and that for the months february , march , april and may is rs . 9500 . if his salary for the month of may is rs . 6500 , find his salary for the month of january ?", + "Output Program": [ + "n0 = 8000.0\nn1 = 9500.0\nn2 = 6500.0\nt0 = n0 * 4.0\nt1 = n1 * 4.0\nt2 = t1 - n2\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "train" + }, + { + "Input": "last week david spent 20 percent of his wages on recreation . this week , his wages are 30 percent less than last week \u02bc s wages and he spent 20 percent of his wages on recreation . the amount he spends on recreation this week is what percent of the amount he spent on recreation last week", + "Output Program": [ + "n0 = 20.0\nn1 = 30.0\nn2 = 20.0\nt0 = n2 / 100.0\nt1 = n1 / 100.0\nt2 = n0 / 100.0\nt3 = 1.0 - t1\nt4 = t0 * t3\nt5 = t4 / t2\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "69.99999999999999" + ], + "split": "train" + }, + { + "Input": "in a can , there is a mixture of milk and water in the ratio 4 : 3 . if the can is filled with an additional 10 liters of milk , the can would be full and the ratio of milk and water would become 5 : 2 . find the capacity of the can ?", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 10.0\nn3 = 5.0\nn4 = 2.0\nt0 = n2 * n4\nt1 = n1 * n3\nt2 = n0 * n4\nt3 = t1 - t2\nt4 = t0 / t3\nt5 = n0 * t4\nt6 = n1 * t4\nt7 = n2 + t5\nanswer = t7 + t6\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "a certain kind of fuel is 1515 high octane and 4545 regular octane . if high octane costs 3 times as much as regular octane , what fraction of the cost of the fuel is due to the high octane ?", + "Output Program": [ + "n0 = 1515.0\nn1 = 4545.0\nn2 = 3.0\nt0 = 3.0 + 4.0\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.42857142857142855" + ], + "split": "train" + }, + { + "Input": "if x is 20 percent greater than 12 , then x =", + "Output Program": [ + "n0 = 20.0\nn1 = 12.0\nt0 = n0 / 100.0\nt1 = n1 * t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "14.4" + ], + "split": "train" + }, + { + "Input": "a student got 74 % in math and 81 % in history . to get an overall average of 75 % , how much should the student get in the third subject ?", + "Output Program": [ + "n0 = 74.0\nn1 = 81.0\nn2 = 75.0\nt0 = n0 + n1\nt1 = n2 * 3.0\nanswer = t1 - t0\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "train" + }, + { + "Input": "the jogging track in a sports complex is 1000 meters in circumference . deepak and his wife start from the same point and walk in opposite directions at 20 km / hr and 16 km / hr respectively . they will meet for the first time in ?", + "Output Program": [ + "n0 = 1000.0\nn1 = 20.0\nn2 = 16.0\n\nanswer = n1 + n2\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "two brother x and y appeared for an exam . the probability of selection of x is 1 / 3 and that of b is 2 / 5 . find the probability that both of them are selected .", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 2.0\nn3 = 5.0\nt0 = n0 / n1\nt1 = n2 / n3\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "0.13333333333333333" + ], + "split": "train" + }, + { + "Input": "20 % of major airline companies equip their planes with wireless internet access . 70 % of major airlines offer passengers free on - board snacks . what is the greatest possible percentage of major airline companies that offer both wireless internet and free on - board snacks ?", + "Output Program": [ + "n0 = 20.0\nn1 = 70.0\n\nanswer = n0 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "david obtained 74 , 65 , 82 , 67 and 90 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?", + "Output Program": [ + "n0 = 74.0\nn1 = 65.0\nn2 = 82.0\nn3 = 67.0\nn4 = 90.0\nn5 = 100.0\nt0 = n0 + n1\nt1 = 2.0 + 3.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "75.6" + ], + "split": "train" + }, + { + "Input": "if the product of 2 integers is negative , at most how many of the integers can be negative ?", + "Output Program": [ + "n0 = 2.0\n\nanswer = n0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "find k if 16 / k = 4 .", + "Output Program": [ + "n0 = 16.0\nn1 = 4.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "the simple interest on a sum of money will be rs . 800 after 10 years . if the principal is trebled after 5 years what will be the total interest at the end of the tenth year ?", + "Output Program": [ + "n0 = 800.0\nn1 = 10.0\nn2 = 5.0\nt0 = n0 / n1\nt1 = n2 * t0\nt2 = t1 * 3.0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "1600" + ], + "split": "train" + }, + { + "Input": "a certain clock marks every hour by striking a number of times equal to the hour , and the time required for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stroke and the end of the last stroke is 66 seconds . at 12 : 00 , how many seconds elapse between the beginning of the first stroke and the end of the last stroke ?", + "Output Program": [ + "n0 = 6.0\nn1 = 0.0\nn2 = 66.0\nn3 = 12.0\nn4 = 0.0\nt0 = 1.0 + 4.0\nt1 = n0 + t0\nt2 = n3 + t1\nt3 = n2 / t1\nanswer = t2 * t3\nprint(answer)" + ], + "Output Answer": [ + "138" + ], + "split": "train" + }, + { + "Input": "mr . kramer , the losing candidate in a two - candidate election , received 942,568 votes , which was exactly 35 percent of all votes cast . approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast ?", + "Output Program": [ + "n0 = 942568.0\nn1 = 35.0\nn2 = 50.0\nt0 = n2 / 100.0\nt1 = n1 / 100.0\nt2 = t0 - t1\nt3 = 1.0 - t1\nt4 = t2 / t3\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "23.076923076923077" + ], + "split": "train" + }, + { + "Input": "at 1 : 00 pm , there were 10.0 grams of bacteria . the bacteria increased to x grams at 4 : 00 pm , and 28.9 grams at 7 : 00 pm . if the amount of bacteria present increased by the same fraction during each of the 3 - hour periods , how many grams of bacteria were present at 4 : 00 pm ?", + "Output Program": [ + "import math\nn0 = 1.0\nn1 = 0.0\nn2 = 10.0\nn3 = 4.0\nn4 = 0.0\nn5 = 28.9\nn6 = 7.0\nn7 = 0.0\nn8 = 3.0\nn9 = 4.0\nn10 = 0.0\nt0 = n5 / n2\nt1 = math.sqrt(max(0, t0))\nanswer = t1 * n2\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "rahul played weel in this season . his current batting averagge is 53 . if he score 78 runs in today match . his batting average will become 58 . how many matches had he played in this season .", + "Output Program": [ + "n0 = 53.0\nn1 = 78.0\nn2 = 58.0\nt0 = n1 - n2\nt1 = n2 - n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "the average weight of 19 students is 15 kg . by the admission of a new student the average weight is reduced to 14.9 kg . the weight of the new student is ?", + "Output Program": [ + "n0 = 19.0\nn1 = 15.0\nn2 = 14.9\nt0 = n0 + 1.0\nt1 = n0 * n1\nt2 = n2 * t0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "the difference between a two - digit number and the number obtained by interchanging the digits is 36 . what is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?", + "Output Program": [ + "n0 = 36.0\nn1 = 1.0\nn2 = 2.0\nt0 = n2 * 10.0\nt1 = n1 + t0\nt2 = t1 - 10.0\nt3 = t2 - n2\nt4 = n0 / t3\nt5 = n2 * t4\nt6 = t4 + t5\nt7 = t5 - t4\nanswer = t6 - t7\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "excluding stoppages , the average speed of a bus is 80 km / hr and including stoppages , the average speed of the bus is 40 km / hr . for how many minutes does the bus stop per hour ?", + "Output Program": [ + "n0 = 80.0\nn1 = 40.0\nt0 = n1 / n0\nt1 = 1.0 * 60.0\nt2 = t0 * 60.0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "find the smallest number of 6 digits which is exactly divisible by 111 .", + "Output Program": [ + "n0 = 6.0\nn1 = 111.0\nt0 = 100.0 * 100.0\nt1 = t0 * 10.0\nt2 = t1 - 100.0\nanswer = n1 + t2\nprint(answer)" + ], + "Output Answer": [ + "100011" + ], + "split": "train" + }, + { + "Input": "the greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively , is :", + "Output Program": [ + "import scipy\nn0 = 1657.0\nn1 = 2037.0\nn2 = 6.0\nn3 = 5.0\nt0 = n1 - n3\nt1 = n0 - n2\nanswer = scipy.gcd(int(t0), int(t1))\nprint(answer)" + ], + "Output Answer": [ + "127" + ], + "split": "train" + }, + { + "Input": "in an examination , 300 students appeared . out of these students ; 28 % got first division , 54 % got second division and the remaining just passed . assuming that no student failed ; find the number of students who just passed .", + "Output Program": [ + "n0 = 300.0\nn1 = 28.0\nn2 = 54.0\nt0 = n1 + n2\nt1 = 100.0 - t0\nt2 = n0 * t1\nanswer = t2 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "train" + }, + { + "Input": "the average of first 13 even numbers is ?", + "Output Program": [ + "n0 = 13.0\n\nanswer = n0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "in plutarch enterprises , 70 % of the employees are marketers , 10 % are engineers , and the rest are managers . marketers make an average salary of $ 50,000 a year , and engineers make an average of $ 80,000 . what is the average salary for managers if the average for all employees is also $ 80,000 ?", + "Output Program": [ + "n0 = 70.0\nn1 = 10.0\nn2 = 50000.0\nn3 = 80000.0\nn4 = 80000.0\nt0 = n0 + n1\nt1 = 10.0 / 2.0\nt2 = t0 * 1000.0\nt3 = t1 * 10.0\nt4 = t2 * 100.0\nt5 = t2 * 10.0\nt6 = t3 * 1000.0\nt7 = n0 * t6\nt8 = t4 - t5\nt9 = t8 - t7\nanswer = t9 / n1\nprint(answer)" + ], + "Output Answer": [ + "370000" + ], + "split": "train" + }, + { + "Input": "company s produces two kinds of stereos : basic and deluxe . of the stereos produced by company s last month , 2 / 3 were basic and the rest were deluxe . if it takes 1.6 as many hours to produce a deluxe stereo as it does to produce a basic stereo , then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 1.6\nt0 = n0 + n1\nanswer = t0 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "the average score of a cricketer in 2 matches is 20 and in other 3 matches is 30 . then find the average score in all the 5 matches ?", + "Output Program": [ + "n0 = 2.0\nn1 = 20.0\nn2 = 3.0\nn3 = 30.0\nn4 = 5.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = t0 + t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "rahul played weel in this season . his current batting averagge is 51 . if he score 78 runs in today match . his batting average will become 54 . how many matches had he played in this season .", + "Output Program": [ + "n0 = 51.0\nn1 = 78.0\nn2 = 54.0\nt0 = n1 - n2\nt1 = n2 - n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "if 7 a = 2 b = 15 , then 42 ab =", + "Output Program": [ + "n0 = 7.0\nn1 = 2.0\nn2 = 15.0\nn3 = 42.0\nt0 = n2 / n0\nt1 = n2 / n1\nt2 = t0 * t1\nanswer = n3 * t2\nprint(answer)" + ], + "Output Answer": [ + "674.9999999999999" + ], + "split": "train" + }, + { + "Input": "if 0.75 : x : : 5 : 7 , then x is equal to :", + "Output Program": [ + "n0 = 0.75\nn1 = 5.0\nn2 = 7.0\nt0 = n0 * n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "1.05" + ], + "split": "train" + }, + { + "Input": "there are certain number of hats and gloves in a box . they are of 41 red , 23 green , 11 orange . power gone but a woman can differentiate between hats and gloves . how many draws are required to obtain a pair of each color ?", + "Output Program": [ + "n0 = 41.0\nn1 = 23.0\nn2 = 11.0\nt0 = n0 + n1\nanswer = t0 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "66" + ], + "split": "train" + }, + { + "Input": "the average weight of 20 persons sitting in a boat had some value . a new person added to them whose weight was 49 kg only . due to his arrival , the average weight of all the persons decreased by 5 kg . find the average weight of first 20 persons ?", + "Output Program": [ + "n0 = 20.0\nn1 = 49.0\nn2 = 5.0\nn3 = 20.0\nt0 = n0 + 1.0\nt1 = n2 * t0\nanswer = t1 - n1\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "train" + }, + { + "Input": "the average age of a group of n people is 15 years old . one more person aged 37 joins the group and the new average is 17 years old . what is the value of n ?", + "Output Program": [ + "n0 = 15.0\nn1 = 37.0\nn2 = 17.0\nt0 = n1 - n2\nt1 = n2 - n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the average of first 18 even numbers is ?", + "Output Program": [ + "n0 = 18.0\n\nanswer = n0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "for every integer n \u2265 3 , the function g ( n ) is defined as the product of all the odd integers from 1 to n , inclusive . what is the value of g ( 99 ) \u2013 g ( 97 ) ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 99.0\nn3 = 97.0\n\nanswer = n2 - n1\nprint(answer)" + ], + "Output Answer": [ + "98" + ], + "split": "train" + }, + { + "Input": "a theater charges $ 12 for seats in the orchestra and $ 8 for seats in the balcony . on a certain night , a total of 370 tickets were sold for a total cost of $ 3,320 . how many more tickets were sold that night for seats in the balcony than for seats in the orchestra ?", + "Output Program": [ + "n0 = 12.0\nn1 = 8.0\nn2 = 370.0\nn3 = 3320.0\nt0 = n1 * n2\nt1 = n0 - n1\nt2 = n3 - t0\nt3 = t2 / t1\nt4 = n2 - t3\nanswer = t4 - t3\nprint(answer)" + ], + "Output Answer": [ + "190" + ], + "split": "train" + }, + { + "Input": "if bill can buy 3 pairs of jeans and 2 shirts for $ 69 or 2 pairs of jeans and 3 shirts for $ 81 , how much does one shirt cost ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 69.0\nn3 = 2.0\nn4 = 3.0\nn5 = 81.0\nt0 = n0 * n5\nt1 = n1 * n2\nt2 = n0 * n0\nt3 = n1 * n1\nt4 = t0 - t1\nt5 = t2 - t3\nanswer = t4 / t5\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "how many zeroes are there at the end of the number n , if n = 60 ! + 120 ! ?", + "Output Program": [ + "n0 = 60.0\nn1 = 120.0\nt0 = 1.0 + 4.0\nt1 = n0 / t0\nanswer = t1 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "on dividing 265 by a number , the quotient is 12 and the remainder is 1 . find the divisor .", + "Output Program": [ + "import math\nn0 = 265.0\nn1 = 12.0\nn2 = 1.0\nt0 = n0 / n1\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "given two sets a = { 11 , 44 , 55 } and b = { 01 } , if one number is chosen from each set at random , what is the probability that the sum of both numbers is an even number", + "Output Program": [ + "n0 = 11.0\nn1 = 44.0\nn2 = 55.0\nn3 = 1.0\nt0 = n0 + n1\nt1 = t0 / 2.0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "a man saves 20 % of his monthly salary . if an account of dearness of things he is to increase his monthly expenses by 20 % , he is only able to save rs . 230 per month . what is his monthly salary ?", + "Output Program": [ + "n0 = 20.0\nn1 = 20.0\nn2 = 230.0\nt0 = n1 / 100.0\nt1 = n2 * 100.0\nt2 = 100.0 - n0\nt3 = t0 * t2\nt4 = t3 + t2\nt5 = 100.0 - t4\nanswer = t1 / t5\nprint(answer)" + ], + "Output Answer": [ + "5750" + ], + "split": "train" + }, + { + "Input": "john found that the average of 15 numbers is 40 . if 14 is added to each number then the mean of number is ?", + "Output Program": [ + "n0 = 15.0\nn1 = 40.0\nn2 = 14.0\n\nanswer = n1 + n2\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "train" + }, + { + "Input": "when 6 is added to half of one - third of one - fifth of a number , the result is one - fifteenth of the number . find the number ?", + "Output Program": [ + "n0 = 6.0\nt0 = 2.0 + 3.0\nt1 = t0 * 3.0\nt2 = 1.0 / t1\nt3 = t2 / 2.0\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "180" + ], + "split": "train" + }, + { + "Input": "a rope of which a calf is tied is increased from 12 m to 21 m , how much additional grassy ground shall it graze ?", + "Output Program": [ + "n0 = 12.0\nn1 = 21.0\nt0 = 3.0 + 4.0\nt1 = 10.0 * 2.0\nt2 = n1**min(2.0, 5)\nt3 = n0**min(2.0, 5)\nt4 = t1 + 2.0\nt5 = t2 - t3\nt6 = t4 / t0\nanswer = t6 * t5\nprint(answer)" + ], + "Output Answer": [ + "933.4285714285714" + ], + "split": "train" + }, + { + "Input": "in a school with 640 students , the average age of the boys is 12 years and that of the girls is 11 years . if the average age of the school is 11 years 9 months , then the number of girls in the school is", + "Output Program": [ + "n0 = 640.0\nn1 = 12.0\nn2 = 11.0\nn3 = 11.0\nn4 = 9.0\nt0 = n4 / n1\nt1 = n0 * n1\nt2 = n2 + t0\nt3 = n0 * t2\nanswer = t1 - t3\nprint(answer)" + ], + "Output Answer": [ + "160" + ], + "split": "train" + }, + { + "Input": "30 pens and 75 pencils were purchased for 690 . if the average price of a pencil was 2.00 , find the average price of a pen .", + "Output Program": [ + "n0 = 30.0\nn1 = 75.0\nn2 = 690.0\nn3 = 2.0\nt0 = n1 * n3\nt1 = n2 - t0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "if the price of a tv is first decreased by 20 % and then increased by 45 % , then the net change in the price will be :", + "Output Program": [ + "n0 = 20.0\nn1 = 45.0\nt0 = n1 + 100.0\nt1 = 100.0 - n0\nt2 = t0 * t1\nt3 = t2 / 100.0\nanswer = t3 - 100.0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "how many numbers from 10 to 43 are exactly divisible by 3 ?", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 43.0\nn2 = 3.0\nt0 = n1 / n2\nt1 = n0 / n2\nt2 = math.floor(t0)\nt3 = math.floor(t1)\nt4 = t3 + 1.0\nt5 = n2 * t2\nt6 = n2 * t4\nt7 = t5 - t6\nt8 = t7 / n2\nanswer = t8 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "300 first - time customers of a fashion store were surveyed for their shopping experience right after leaving the store . 60 % of the customers in the survey had purchased clothes for less than $ 100 . 40 % of the customers in the survey reported they were overall satisfied with their purchase . 65 % of the customers that had purchased clothes for less than $ 100 reported they were overall satisfied with their purchase . what percent of the customers surveyed purchased clothes for at least $ 100 and reported that they were not overall satisfied with their purchase ?", + "Output Program": [ + "n0 = 300.0\nn1 = 60.0\nn2 = 100.0\nn3 = 40.0\nn4 = 65.0\nn5 = 100.0\nn6 = 100.0\nt0 = n3 / n2\nt1 = n4 / n2\nt2 = n1 / n2\nt3 = n0 * t0\nt4 = n0 * t2\nt5 = t1 * t4\nt6 = t3 - t5\nt7 = t6 / n0\nanswer = t7 * n2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "if the price of a certain computer increased 30 percent from d dollars to 364 dollars , then 2 d =", + "Output Program": [ + "n0 = 30.0\nn1 = 364.0\nn2 = 2.0\nt0 = n0 + 100.0\nt1 = t0 / 100.0\nt2 = n1 / t1\nanswer = n2 * t2\nprint(answer)" + ], + "Output Answer": [ + "560" + ], + "split": "train" + }, + { + "Input": "find the value of 72518 x 9999 = m ?", + "Output Program": [ + "n0 = 72518.0\nn1 = 9999.0\nt0 = n1 - 4.0\nanswer = t0 * n0\nprint(answer)" + ], + "Output Answer": [ + "724817410" + ], + "split": "train" + }, + { + "Input": "if 6 a = 7 b = 20 , then 84 ab =", + "Output Program": [ + "n0 = 6.0\nn1 = 7.0\nn2 = 20.0\nn3 = 84.0\nt0 = n2 / n0\nt1 = n2 / n1\nt2 = t0 * t1\nanswer = n3 * t2\nprint(answer)" + ], + "Output Answer": [ + "800" + ], + "split": "train" + }, + { + "Input": "the ratio 9 : 5 expressed as a percent equals", + "Output Program": [ + "n0 = 9.0\nn1 = 5.0\nt0 = n0 / n1\nanswer = t0 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "180" + ], + "split": "train" + }, + { + "Input": "a number when divided by a certain divisor left remainder 241 , when twice the number was divided by the same divisor , the remainder was 115 . find the divisor ?", + "Output Program": [ + "n0 = 241.0\nn1 = 115.0\nt0 = n0 * 2.0\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "367" + ], + "split": "train" + }, + { + "Input": "find the value of x . ( 47 % of 1442 - 36 % of 1412 ) + 65 = x ?", + "Output Program": [ + "import math\nn0 = 47.0\nn1 = 1442.0\nn2 = 36.0\nn3 = 1412.0\nn4 = 65.0\nt0 = n0 / 100.0\nt1 = n2 / 100.0\nt2 = n1 * t0\nt3 = n3 * t1\nt4 = t2 - t3\nt5 = n4 + t4\nt6 = t5 % 10.0\nt7 = t6 + 1.0\nanswer = math.floor(t7)\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "what is the positive difference between the sum of the squares of the first 6 positive integers and the sum of the prime numbers between the first square and fourth square ?", + "Output Program": [ + "n0 = 6.0\nt0 = 1.0 + 4.0\nt1 = 3.0 + 4.0\nt2 = 2.0 + 3.0\nt3 = 2.0**min(2.0, 5)\nt4 = 3.0**min(2.0, 5)\nt5 = 4.0**min(2.0, 5)\nt6 = n0**min(2.0, 5)\nt7 = t3 + 1.0\nt8 = n0 + t1\nt9 = t2 + t0\nt10 = n0 + t2\nt11 = t0**min(2.0, 5)\nt12 = t7 + t4\nt13 = t9 + t1\nt14 = t12 + t5\nt15 = t13 + t10\nt16 = t14 + t11\nt17 = t8 + t15\nt18 = t16 + t6\nanswer = t18 - t17\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "a man can swim in still water at 15 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ?", + "Output Program": [ + "n0 = 15.0\n\nanswer = n0 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "there are 134 toys coloured red and white in a box . two red toys are removed from the lot and now there are twice as many red ones as white ones . how many of red colour toys are there now ?", + "Output Program": [ + "n0 = 134.0\nt0 = n0 * 2.0\nt1 = t0 + 2.0\nt2 = t1 / 3.0\nanswer = t2 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "88" + ], + "split": "train" + }, + { + "Input": "a pharmaceutical company received $ 2 million in royalties on the first $ 12 ; million in sales of generic equivalent of one of its products and then $ 4 million in royalties on the next $ 48 million in sales . by approximately what percent did the ratio of royalties to sales decrease from the first $ 12 million in sales to the next $ 48 million in sales ?", + "Output Program": [ + "n0 = 2.0\nn1 = 12.0\nn2 = 4.0\nn3 = 48.0\nn4 = 12.0\nn5 = 48.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = t0 - t1\nt3 = t2 / t0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "the average temperature for monday , tuesday , wednesday and thursday was 48 degrees and for tuesday , wednesday , thursday and friday was 46 degrees . if the temperature on monday was 43 degrees . find the temperature on friday ?", + "Output Program": [ + "n0 = 48.0\nn1 = 46.0\nn2 = 43.0\nt0 = n0 * 4.0\nt1 = n1 * 4.0\nt2 = t0 - t1\nanswer = n2 - t2\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "albert father was 48 years of age when she was born while her mother was 46 years old when her brother 2 years younger to her was born . what is the difference between the ages of her parents ?", + "Output Program": [ + "n0 = 48.0\nn1 = 46.0\nn2 = 2.0\nt0 = 2.0 + 3.0\nt1 = t0 + 4.0\nanswer = t1 - t0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "on thursday mabel handled 90 transactions . anthony handled 10 % more transactions than mabel , cal handled 2 / 3 rds of the transactions that anthony handled , and jade handled 14 more transactions than cal . how much transactions did jade handled ?", + "Output Program": [ + "n0 = 90.0\nn1 = 10.0\nn2 = 2.0\nn3 = 3.0\nn4 = 14.0\nt0 = n1 + 100.0\nt1 = n0 / 100.0\nt2 = t0 * t1\nt3 = n2 * t2\nt4 = t3 / n3\nanswer = n4 + t4\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.60 per glass on the first day , what was the price r per glass on the second day ?", + "Output Program": [ + "n0 = 0.6\nt0 = 1.0 + 1.0\nt1 = 1.0 + 2.0\nt2 = n0 * t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.39999999999999997" + ], + "split": "train" + }, + { + "Input": "in a certain accounting class of 100 students , 70 % of the students took the final exam on the assigned day while the rest of the students took the exam on a make - up date . if the students on the assigned day had an average score of 55 % , and the students on the make - up date had an average score of 95 % , what was the average score for the entire class ?", + "Output Program": [ + "n0 = 100.0\nn1 = 70.0\nn2 = 55.0\nn3 = 95.0\nt0 = n1 * n2\nt1 = n0 - n1\nt2 = n3 * t1\nt3 = t0 + t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "67" + ], + "split": "train" + }, + { + "Input": "what is the sum of the digits of integer k , if k = ( 10 ^ 30 - 36 )", + "Output Program": [ + "n0 = 10.0\nn1 = 30.0\nn2 = 36.0\nt0 = n0 - 1.0\nt1 = n1 - 2.0\nt2 = t0 * t1\nanswer = t2 + 10.0\nprint(answer)" + ], + "Output Answer": [ + "262" + ], + "split": "train" + }, + { + "Input": "if a # b = ab \u2013 b + b ^ 2 , then 3 # 7 =", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 7.0\nt0 = n1 * n2\nt1 = n2**min(2.0, 5)\nt2 = t0 - n2\nanswer = t1 + t2\nprint(answer)" + ], + "Output Answer": [ + "63" + ], + "split": "train" + }, + { + "Input": "a certain list consists of 21 different numbers . if n is in the list and n is 4 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction w of the sum of the 21 numbers in the list ?", + "Output Program": [ + "n0 = 21.0\nn1 = 4.0\nn2 = 20.0\nn3 = 21.0\nt0 = n2 / n1\nt1 = 1.0 * 1.0\nt2 = n0 + t0\nt3 = t2 / n1\nt4 = t3 * 2.0\nt5 = t4 - n1\nt6 = t5 - 3.0\nanswer = t1 / t6\nprint(answer)" + ], + "Output Answer": [ + "0.16666666666666666" + ], + "split": "train" + }, + { + "Input": "a no . when divided by 142 gives a remainder 110 , what remainder will be obtainedby dividingthe same no . 14 ?", + "Output Program": [ + "n0 = 142.0\nn1 = 110.0\nn2 = 14.0\nt0 = n0 + n1\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "a scale 6 ft . 8 inches long is divided into 5 equal parts . find the length of each part .", + "Output Program": [ + "n0 = 6.0\nn1 = 8.0\nn2 = 5.0\nt0 = n0 * 12.0\nt1 = n1 + t0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "after spending rs . 5000 on rent , rs . 1500 on milk , rs . 4500 on groceries , rs . 2500 on childrens education rs . 2000 on petrol and rs . 700 on miscellaneous expenses , mr . kishore saved 10 % of his monthly salary . how much did he save in rs . ?", + "Output Program": [ + "n0 = 5000.0\nn1 = 1500.0\nn2 = 4500.0\nn3 = 2500.0\nn4 = 2000.0\nn5 = 700.0\nn6 = 10.0\nt0 = n0 + n1\nt1 = 100.0 - n6\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nt5 = n5 + t4\nt6 = t5 * 100.0\nt7 = t6 / t1\nanswer = t7 - t5\nprint(answer)" + ], + "Output Answer": [ + "1800" + ], + "split": "train" + }, + { + "Input": "when 2 / 9 of the votes on a certain resolution have been counted , 3 / 4 of those counted are in favor of the resolution . what fraction e of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution ?", + "Output Program": [ + "n0 = 2.0\nn1 = 9.0\nn2 = 3.0\nn3 = 4.0\nn4 = 2.0\nn5 = 1.0\nt0 = n0 + n5\nt1 = n0 / n1\nt2 = n2 / n3\nt3 = n1 - n0\nt4 = n0 / t0\nt5 = t3 / n1\nt6 = t1 * t2\nt7 = t1 - t6\nt8 = t4 - t7\nanswer = t8 / t5\nprint(answer)" + ], + "Output Answer": [ + "0.7857142857142856" + ], + "split": "train" + }, + { + "Input": "john found that the average of 15 numbers is 40 . if 13 is added to each number then the mean of number is ?", + "Output Program": [ + "n0 = 15.0\nn1 = 40.0\nn2 = 13.0\n\nanswer = n1 + n2\nprint(answer)" + ], + "Output Answer": [ + "53" + ], + "split": "train" + }, + { + "Input": "a straight line in the xy - plane has y - intercept of 10 . on this line the x - coordinate of the point is 100 and y - coordinate is 1000 then what is the slope of the line ?", + "Output Program": [ + "n0 = 10.0\nn1 = 100.0\nn2 = 1000.0\nt0 = n2 - n0\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "9.9" + ], + "split": "train" + }, + { + "Input": "if the price of a book is first decreased by 30 % and then increased by 40 % , then the net change in the price will be :", + "Output Program": [ + "n0 = 30.0\nn1 = 40.0\nt0 = n0 * 100.0\nt1 = n1 * 100.0\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = t3 + 100.0\nt5 = 100.0 - t2\nt6 = t5 / 100.0\nt7 = t4 / 100.0\nt8 = t6 * t7\nt9 = t8 * 100.0\nanswer = 100.0 - t9\nprint(answer)" + ], + "Output Answer": [ + "2.000000000000014" + ], + "split": "train" + }, + { + "Input": "all the milk in container a which was filled to its brim was poured into two containers b and c . the quantity of milk in container b was 62.5 % less than the capacity of container a . if 158 liters was now transferred from c to b , then both the containers would have equal quantities of milk . what was the initial quantity of milk in container a ?", + "Output Program": [ + "n0 = 62.5\nn1 = 158.0\nt0 = n0 / 100.0\nt1 = 1 / 2.0\nt2 = 1.0 - t0\nt3 = t1 - t2\nanswer = n1 / t3\nprint(answer)" + ], + "Output Answer": [ + "1264" + ], + "split": "train" + }, + { + "Input": "two spies agreed to meet at a gas station between noon and 1 pm , but they have both forgotten the arranged time . each arrives at a random time between noon and 1 pm and stays for 6 minutes unless the other is there before the 6 minutes are up . assuming all random times are equally likely , what is the probability that they will meet within the hour ( noon to 1 pm ) ?", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 6.0\nn3 = 6.0\nn4 = 1.0\nt0 = n2 * 3.0\nt1 = n0 + t0\nanswer = t1 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "0.19" + ], + "split": "train" + }, + { + "Input": "3 ltr of water is added with 11 ltr of a solution containing 42 % of alcohol in the water . the % of alcohol in the new mixture is ?", + "Output Program": [ + "n0 = 3.0\nn1 = 11.0\nn2 = 42.0\nt0 = n0 + n1\nt1 = n2 / 100.0\nt2 = n1 * t1\nt3 = t2 / t0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "when positive integer x is divided by positive integer y , the remainder is 1.44 . if x / y = 96.12 , what is the value of y ?", + "Output Program": [ + "import math\nn0 = 1.44\nn1 = 96.12\nt0 = math.floor(n1)\nt1 = n1 - t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "11.999999999999545" + ], + "split": "train" + }, + { + "Input": "sophia finished 23 of a book . she calculated that she finished 90 more pages than she has yet to read . how long is her book ?", + "Output Program": [ + "n0 = 23.0\nn1 = 90.0\nt0 = 2.0 / 3.0\nt1 = 1.0 - t0\nt2 = t0 - t1\nanswer = n1 / t2\nprint(answer)" + ], + "Output Answer": [ + "270.00000000000006" + ], + "split": "train" + }, + { + "Input": "a sports retailer ordered white and yellow tennis balls in equal number but the dispatch clerk of the tennis ball company erred and dispatched 50 extra yellow balls and making ratio of white balls to yellow balls 7 / 11 . how many tennis balls did the retailer order originally .", + "Output Program": [ + "n0 = 50.0\nn1 = 7.0\nn2 = 11.0\nt0 = n0 * n1\nt1 = n2 - n1\nt2 = t0 / t1\nanswer = t2 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "175" + ], + "split": "train" + }, + { + "Input": "the difference between a positive proper fraction and its reciprocal is 9 / 20 . the fraction is", + "Output Program": [ + "n0 = 9.0\nn1 = 20.0\nt0 = n0 - 4.0\nanswer = 4.0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.8" + ], + "split": "train" + }, + { + "Input": "each of the 30 boxes in a certain shipment weighs either 10 pounds or 20 pounds , and the average ( arithmetic mean ) weight of the boxes in the shipment is 18 pounds . if the average weight of the boxes in the shipment is to be reduced to 15 pounds by removing some of the 20 - pound boxes , how many 20 - pound boxes must be removed ?", + "Output Program": [ + "n0 = 30.0\nn1 = 10.0\nn2 = 20.0\nn3 = 18.0\nn4 = 15.0\nn5 = 20.0\nn6 = 20.0\nt0 = n0 * n2\nt1 = n0 * n3\nt2 = n0 * n4\nt3 = n2 - n1\nt4 = n2 - n4\nt5 = t0 - t1\nt6 = t5 / t3\nt7 = n1 * t6\nt8 = n0 - t6\nt9 = n2 * t8\nt10 = t7 + t9\nt11 = t10 - t2\nanswer = t11 / t4\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "in a coconut grove , ( x + 4 ) trees yield 60 nuts per year , x trees yield 120 nuts per year and ( x \u2013 4 ) trees yield 180 nuts per year . if the average yield per year per tree be 100 , find x .", + "Output Program": [ + "n0 = 4.0\nn1 = 60.0\nn2 = 120.0\nn3 = 4.0\nn4 = 180.0\nn5 = 100.0\nt0 = n1 + n2\nt1 = n0 * n4\nt2 = n0 * n1\nt3 = n5 * 3.0\nt4 = n4 + t0\nt5 = t1 - t2\nt6 = t4 - t3\nanswer = t5 / t6\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a palindrome is a number that reads the same forward and backward , such as 121 . how many odd , 4 - digit numbers are palindromes ?", + "Output Program": [ + "n0 = 121.0\nn1 = 4.0\nt0 = n1 / 2.0\nt1 = 10.0**min(t0, 5)\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "last year , for every 100 million vehicles that traveled on a certain highway , 100 vehicles were involved in accidents . if 2 billion vehicles traveled on the highway last year , how many of those vehicles were involved in accidents ? ( 1 billion = 1,000 , 000,000 )", + "Output Program": [ + "n0 = 100.0\nn1 = 100.0\nn2 = 2.0\nn3 = 1.0\nn4 = 1000.0\nn5 = 0.0\nt0 = n2 * 10.0\nanswer = n1 * t0\nprint(answer)" + ], + "Output Answer": [ + "2000" + ], + "split": "train" + }, + { + "Input": "the population of locusts in a certain swarm doubles every two hours . if 4 hours ago there were 1000 locusts in the swarm , in approximately how many hours will the swarm population exceed 128000 locusts ?", + "Output Program": [ + "n0 = 4.0\nn1 = 1000.0\nn2 = 128000.0\nt0 = 10.0 / 2.0\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "what is the tens digit of 36 ^ 12 ?", + "Output Program": [ + "import math\nn0 = 36.0\nn1 = 12.0\nt0 = 1.0 + 4.0\nt1 = n1 % t0\nt2 = n0**min(t1, 5)\nt3 = t2 % 100.0\nt4 = t3 / 10.0\nanswer = math.floor(t4)\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "calculate 469160 x 9999 = ?", + "Output Program": [ + "n0 = 469160.0\nn1 = 9999.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "4691130840" + ], + "split": "train" + }, + { + "Input": "joe went on a diet 4 months ago when he weighed 222 pounds . if he now weighs 198 pounds and continues to lose at the same average monthly rate , in approximately how many months will he weigh 180 pounds ?", + "Output Program": [ + "n0 = 4.0\nn1 = 222.0\nn2 = 198.0\nn3 = 180.0\nt0 = n2 - n3\nt1 = n1 - n2\nt2 = t1 / n0\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "the milk level in a rectangular box measuring 56 feet by 25 feet is to be lowered by 6 inches . how many gallons of milk must be removed ? ( 1 cu ft = 7.5 gallons )", + "Output Program": [ + "n0 = 56.0\nn1 = 25.0\nn2 = 6.0\nn3 = 1.0\nn4 = 7.5\nt0 = n3 / 2.0\nt1 = n0 * n1\nt2 = t0 * t1\nanswer = n4 * t2\nprint(answer)" + ], + "Output Answer": [ + "5250" + ], + "split": "train" + }, + { + "Input": "how many quarters are equal to 3 dollars ?", + "Output Program": [ + "n0 = 3.0\n\nanswer = n0 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "a no . when divided by the sum of 555 and 445 gives 2 times their difference as quotient & 30 as remainder . find the no . is ?", + "Output Program": [ + "n0 = 555.0\nn1 = 445.0\nn2 = 2.0\nn3 = 30.0\nt0 = n0 + n1\nt1 = n0 - n1\nt2 = n2 * t0\nt3 = t2 * t1\nanswer = n3 + t3\nprint(answer)" + ], + "Output Answer": [ + "220030" + ], + "split": "train" + }, + { + "Input": "there are some rabbits and peacocks in a zoo . the total number of their heads is 60 and total number of their legs is 192 . find the number of total rabbits ?", + "Output Program": [ + "n0 = 60.0\nn1 = 192.0\nt0 = n0 * 2.0\nt1 = 4.0 - 2.0\nt2 = n1 - t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "( 169 ) ^ 2 - ( 168 ) ^ 2 =", + "Output Program": [ + "n0 = 169.0\nn1 = 2.0\nn2 = 168.0\nn3 = 2.0\nt0 = n0**min(n1, 5)\nt1 = n2**min(n1, 5)\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "337" + ], + "split": "train" + }, + { + "Input": "what least number should be added to 1054 , so that the sum is completely divisible by 23", + "Output Program": [ + "n0 = 1054.0\nn1 = 23.0\nt0 = n0 % n1\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "the operation is defined for all integers a and b by the equation ab = ( a - 1 ) ( b - 1 ) . if y 10 = 90 , what is the value of y ?", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 10.0\nn3 = 90.0\nt0 = n2 - n0\nt1 = n3 / t0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "a high school has 400 students 1 / 2 attend the arithmetic club , 5 / 8 attend the biology club and 3 / 4 attend the chemistry club . 3 / 8 attend all 3 clubs . if every student attends at least one club how many students attend exactly 2 clubs .", + "Output Program": [ + "n0 = 400.0\nn1 = 1.0\nn2 = 2.0\nn3 = 5.0\nn4 = 8.0\nn5 = 3.0\nn6 = 4.0\nn7 = 3.0\nn8 = 8.0\nn9 = 3.0\nn10 = 2.0\nt0 = n0 * n1\nt1 = n0 * n3\nt2 = n0 * n5\nt3 = t0 / n2\nt4 = t1 / n4\nt5 = t2 / n6\nt6 = t2 / n4\nt7 = t3 + t4\nt8 = n2 * t6\nt9 = t7 + t5\nt10 = t9 - t8\nanswer = t10 - n0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "a person ' s present age is two - fifth of the age of his mother . after 10 years , he will be one - half of the age of his mother . how old is the mother at present ?", + "Output Program": [ + "n0 = 10.0\nt0 = 2.0 + 3.0\nt1 = 1.0 / 2.0\nt2 = 2.0 / t0\nt3 = n0 - t0\nt4 = t1 - t2\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "50.000000000000014" + ], + "split": "train" + }, + { + "Input": "when positive integer t is divided by 13 , the remainder is 2 . when n is divided by 8 , the remainder is 5 . how many such values are less than 180 ?", + "Output Program": [ + "n0 = 13.0\nn1 = 2.0\nn2 = 8.0\nn3 = 5.0\nn4 = 180.0\nt0 = n1 + n3\nt1 = n0 * t0\nt2 = n1 + t1\nanswer = t2 / t2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "in an exam 49 % candidates failed in english and 36 % failed in hindi and 15 % failed in both subjects . if the total number of candidates who passed in english alone is 630 . what is the total number of candidates appeared in exam ?", + "Output Program": [ + "n0 = 49.0\nn1 = 36.0\nn2 = 15.0\nn3 = 630.0\nt0 = n1 - n2\nt1 = 100.0 / t0\nanswer = n3 * t1\nprint(answer)" + ], + "Output Answer": [ + "3000" + ], + "split": "train" + }, + { + "Input": "in a box of 8 pens , a total of 2 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.0\nn2 = 2.0\nt0 = n0 - n1\nt1 = n0 - 1.0\nt2 = t0 / n0\nt3 = t0 - 1.0\nt4 = t3 / t1\nanswer = t2 * t4\nprint(answer)" + ], + "Output Answer": [ + "0.5357142857142857" + ], + "split": "train" + }, + { + "Input": "every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 2880 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 8.0\nn2 = 2880.0\nt0 = n0 / n1\nt1 = n2 * t0\nt2 = n2 + t1\nt3 = t2 * t0\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "3645" + ], + "split": "train" + }, + { + "Input": "linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 150 , what were her original savings ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 150.0\nt0 = n0 / n1\nt1 = 1.0 - t0\nanswer = n2 / t1\nprint(answer)" + ], + "Output Answer": [ + "600" + ], + "split": "train" + }, + { + "Input": "the sum of number of boys and girls in a school is 150 . if the number of boys is x , then the number of girls becomes x % of the total number of students . the number of boys is ?", + "Output Program": [ + "n0 = 150.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "if m is an integer such that ( - 2 ) ^ 2 m = 2 ^ ( 18 - m ) then m = ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 2.0\nn3 = 18.0\nt0 = n0 + 1.0\nanswer = n3 / t0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "in 10 years , a will be twice as old 5 as b was 10 years ago . if a is now 12 years older than b , the present age of b is", + "Output Program": [ + "n0 = 10.0\nn1 = 5.0\nn2 = 10.0\nn3 = 12.0\nt0 = n0 + n3\nt1 = n0 * 2.0\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "drum x is 1 / 2 full of oil and drum y , which has twice the capacity of drum x , is 1 / 5 full of oil . if all of the oil in drum x is poured into drum y , then drum y will be filled to what capacity ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 1.0\nn3 = 5.0\nt0 = n0 / n3\nt1 = 12.0 / n1\nt2 = n0 / n1\nt3 = t0 * 12.0\nt4 = t1 * t2\nt5 = t3 + t4\nanswer = t5 / 12.0\nprint(answer)" + ], + "Output Answer": [ + "0.45" + ], + "split": "train" + }, + { + "Input": "the average age of 3 boys is 120 years and their ages are in proportion 2 : 6 : 8 . what is the age in years of the youngest boy ?", + "Output Program": [ + "n0 = 3.0\nn1 = 120.0\nn2 = 2.0\nn3 = 6.0\nn4 = 8.0\nt0 = n2 + n3\nt1 = n4 + t0\nt2 = n1 / t1\nanswer = n2 * t2\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "rahul played weel in this season . his current batting averagge is 50 . if he score 78 runs in today match . his batting average will become 54 . how many matches had he played in this season .", + "Output Program": [ + "n0 = 50.0\nn1 = 78.0\nn2 = 54.0\nt0 = n1 - n2\nt1 = n2 - n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "the average salary of a person for the months of january , february , march and april is rs . 8000 and that for the months february , march , april and may is rs . 8900 . if his salary for the month of may is rs . 6500 , find his salary for the month of january ?", + "Output Program": [ + "n0 = 8000.0\nn1 = 8900.0\nn2 = 6500.0\nt0 = n0 * 4.0\nt1 = n1 * 4.0\nt2 = t1 - n2\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "2900" + ], + "split": "train" + }, + { + "Input": "3 * 15 + 3 * 16 + 3 * 19 + 11 = ?", + "Output Program": [ + "n0 = 3.0\nn1 = 15.0\nn2 = 3.0\nn3 = 16.0\nn4 = 3.0\nn5 = 19.0\nn6 = 11.0\nt0 = n0 * n1\nt1 = n0 * n3\nt2 = n0 * n5\nt3 = t0 + t1\nt4 = t3 + t2\nanswer = n6 + t4\nprint(answer)" + ], + "Output Answer": [ + "161" + ], + "split": "train" + }, + { + "Input": "right triangle pqr is to be constructed in the xy - plane so that the right angle is at p and pr is parallel to the x - axis . the x - and y - coordinates of p , q and r are to be integers that satisfy the inequalities - 4 < = x < = 5 and 6 < = y < = 16 . how many different triangles with these properties could be constructed ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 6.0\nn3 = 16.0\nt0 = n0 + n2\nt1 = n3 - n1\nt2 = 10.0 - 1.0\nt3 = t0 * t1\nt4 = t3 * t2\nanswer = t4 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "9900" + ], + "split": "train" + }, + { + "Input": "in arun ' s opinion , his weight is greater than 65 kg but leas than 72 kg . his brother does not agree with arun and he thinks that arun ' s weight is greater than 60 kg but less than 70 kg . his mother ' s view is that his weight can not be greater than 68 kg . if all of them are correct in their estimation , what is the average of diferent probable weights of arun ?", + "Output Program": [ + "n0 = 65.0\nn1 = 72.0\nn2 = 60.0\nn3 = 70.0\nn4 = 68.0\nt0 = n0 + 1.0\nt1 = n4 + t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "67" + ], + "split": "train" + }, + { + "Input": "how many numbers from 10 to 1000000 are exactly divisible by 9 ?", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 1000000.0\nn2 = 9.0\nt0 = n1 / n2\nt1 = n0 / n2\nt2 = math.floor(t0)\nt3 = math.floor(t1)\nt4 = t3 + 1.0\nt5 = n2 * t2\nt6 = n2 * t4\nt7 = t5 - t6\nt8 = t7 / n2\nanswer = t8 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "111110" + ], + "split": "train" + }, + { + "Input": "a certain list consists of 21 different numbers . if n is in the list and n is 4 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction of the sum of the 21 numbers in the list ?", + "Output Program": [ + "n0 = 21.0\nn1 = 4.0\nn2 = 20.0\nn3 = 21.0\nt0 = n2 / n1\nt1 = 1.0 * 1.0\nt2 = n0 + t0\nt3 = t2 / n1\nt4 = t3 * 2.0\nt5 = t4 - n1\nt6 = t5 - 3.0\nanswer = t1 / t6\nprint(answer)" + ], + "Output Answer": [ + "0.16666666666666666" + ], + "split": "train" + }, + { + "Input": "a batsman in his 12 th innings makes a score of 80 and thereby increases his average by 2 runs . what is his average after the 12 th innings if he had never been \u2018 not out \u2019 ?", + "Output Program": [ + "n0 = 12.0\nn1 = 80.0\nn2 = 2.0\nn3 = 12.0\nt0 = n0 * n2\nt1 = n1 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "58" + ], + "split": "train" + }, + { + "Input": "danny can divide his herd into 5 equal parts and also to 6 equal parts , but not to 9 equal parts . what could be the number of cows danny has in his herd ?", + "Output Program": [ + "n0 = 5.0\nn1 = 6.0\nn2 = 9.0\nt0 = n0 * 4.0\nanswer = t0 + 100.0\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "how much is 90 % of 40 is greater than 4 / 5 of 25 ?", + "Output Program": [ + "n0 = 90.0\nn1 = 40.0\nn2 = 4.0\nn3 = 5.0\nn4 = 25.0\nt0 = n0 / 100.0\nt1 = n2 / n3\nt2 = n1 * t0\nt3 = n4 * t1\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "a grocer is storing soap boxes in cartons that measure 25 inches by 42 inches by 60 inches . if the measurement of each soap box is 7 inches by 6 inches by 6 inches , then what is the maximum number of soap boxes that can be placed in each carton ?", + "Output Program": [ + "n0 = 25.0\nn1 = 42.0\nn2 = 60.0\nn3 = 7.0\nn4 = 6.0\nn5 = 6.0\nt0 = n0 * n1\nt1 = n3 * n4\nt2 = n2 * t0\nt3 = n5 * t1\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "250" + ], + "split": "train" + }, + { + "Input": "let n be the greatest number that will divide 1305 , 4665 and 6905 , leaving the same remainder in each case . then sum of the digits in n is :", + "Output Program": [ + "n0 = 1305.0\nn1 = 4665.0\nn2 = 6905.0\nt0 = 1.0 + 1.0\nanswer = t0 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "a driver would have reduced the time it took to drive from home to the store by 1 / 4 if the average speed had been increased by 12 miles per hour . what was the actual average speed , in miles per hour , when the driver drove from home to the store ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 12.0\nt0 = n0 / n1\nt1 = n0 - t0\nt2 = t1 * n2\nt3 = n0 - t1\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "a certain company expects quarterly earnings of $ 0.80 per share of stock , half of which will be distributed as dividends to shareholders while the rest will be used for research and development . if earnings are greater than expected , shareholders will receive an additional $ 0.04 per share for each additional $ 0.10 of per share earnings . if quarterly earnings are $ 1.10 per share , what will be the dividend paid to a person who owns 300 shares of the company ' s stock ?", + "Output Program": [ + "n0 = 0.8\nn1 = 0.04\nn2 = 0.1\nn3 = 1.1\nn4 = 300.0\nt0 = n0 / 2.0\nt1 = n3 - n0\nt2 = t1 * 10.0\nt3 = n1 * t2\nt4 = t0 + t3\nanswer = n4 * t4\nprint(answer)" + ], + "Output Answer": [ + "156" + ], + "split": "train" + }, + { + "Input": "on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.50 per glass on the first day , what was the price per glass on the second day ?", + "Output Program": [ + "n0 = 0.5\nt0 = 1.0 + 1.0\nt1 = 1.0 + 2.0\nt2 = n0 * t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.3333333333333333" + ], + "split": "train" + }, + { + "Input": "if 2 / z = 2 / ( z + 1 ) + 2 / ( z + 25 ) which of these integers could be the value of z ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 1.0\nn3 = 2.0\nn4 = 25.0\nt0 = n0 + n0\nt1 = n2 + t0\nanswer = n4 / t1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "the average student age of a certain class which has 45 students is 14 . if one student aged 15 go to another class and the age of the class teacher is included the average changes to 14.66 . what is the age of class teacher ?", + "Output Program": [ + "n0 = 45.0\nn1 = 14.0\nn2 = 15.0\nn3 = 14.66\nt0 = n0 * n3\nt1 = n0 * n1\nt2 = t1 - n2\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "44.700000000000045" + ], + "split": "train" + }, + { + "Input": "the mean of 50 observations was 41 . it was found later that an observation 48 was wrongly taken as 23 . the corrected new mean is", + "Output Program": [ + "n0 = 50.0\nn1 = 41.0\nn2 = 48.0\nn3 = 23.0\nt0 = n0 * n1\nt1 = n0 - 2.0\nt2 = t1 - n3\nt3 = t0 + t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "41.5" + ], + "split": "train" + }, + { + "Input": "ashok secured average of 70 marks in 6 subjects . if the average of marks in 5 subjects is 74 , how many marks did he secure in the 6 th subject ?", + "Output Program": [ + "n0 = 70.0\nn1 = 6.0\nn2 = 5.0\nn3 = 74.0\nn4 = 6.0\nt0 = n0 * n1\nt1 = n2 * n3\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "p , q and r have rs . 5000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?", + "Output Program": [ + "n0 = 5000.0\nt0 = 2.0 / 3.0\nt1 = t0 + 1.0\nt2 = n0 / t1\nanswer = t2 * t0\nprint(answer)" + ], + "Output Answer": [ + "2000.0000000000002" + ], + "split": "train" + }, + { + "Input": "a cab driver 5 days income was $ 250 , $ 400 , $ 750 , $ 400 , $ 500 . then his average income is ?", + "Output Program": [ + "n0 = 5.0\nn1 = 250.0\nn2 = 400.0\nn3 = 750.0\nn4 = 400.0\nn5 = 500.0\nt0 = n1 + n2\nt1 = n3 + t0\nt2 = n4 + t1\nt3 = n5 + t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "460" + ], + "split": "train" + }, + { + "Input": "a grocer has a sale of rs . 6435 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6700 ?", + "Output Program": [ + "n0 = 6435.0\nn1 = 6927.0\nn2 = 6855.0\nn3 = 7230.0\nn4 = 6562.0\nn5 = 5.0\nn6 = 6700.0\nt0 = n5 + 1.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n6 * t0\nt4 = n3 + t2\nt5 = n4 + t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "6191" + ], + "split": "train" + }, + { + "Input": "if p and q are prime numbers , how many divisors does the product p ^ 3 * q ^ 7 have ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nt0 = n0 + 1.0\nt1 = n1 + 1.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "a batsman makes a score of 87 runs in the 17 th inning and thus increases his averages by 3 . what is his average after 17 th inning ?", + "Output Program": [ + "n0 = 87.0\nn1 = 17.0\nn2 = 3.0\nn3 = 17.0\nt0 = n1 * n2\nt1 = n0 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "39" + ], + "split": "train" + }, + { + "Input": "nina has exactly enough money to purchase 5 widgets . if the cost of each widget were reduced by $ 1.25 , then nina would have exactly enough money to purchase 8 widgets . how much money does nina have ?", + "Output Program": [ + "n0 = 5.0\nn1 = 1.25\nn2 = 8.0\nt0 = n1 * n2\nt1 = n2 - n0\nt2 = t0 / t1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "16.666666666666668" + ], + "split": "train" + }, + { + "Input": "if the sales tax reduced from 3 1 / 2 % to 3 1 / 3 % , then what difference does it make to a person who purchases an article with market price of rs . 9000 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 2.0\nn3 = 3.0\nn4 = 1.0\nn5 = 3.0\nn6 = 9000.0\nt0 = n1 / n2\nt1 = n1 / n0\nt2 = n0 + t0\nt3 = n0 + t1\nt4 = t2 - t3\nt5 = n6 * t4\nanswer = t5 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "14.999999999999986" + ], + "split": "train" + }, + { + "Input": "a waitress ' s income consists of her salary and tips . during one week , her tips were 7 / 4 of her salary . what fraction of her income for the week came from tips ?", + "Output Program": [ + "n0 = 7.0\nn1 = 4.0\nt0 = n0 + n1\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.6363636363636364" + ], + "split": "train" + }, + { + "Input": "on dividing 83 by a number , the quotient is 9 and the remainder is 2 . find the divisor ?", + "Output Program": [ + "import math\nn0 = 83.0\nn1 = 9.0\nn2 = 2.0\nt0 = n0 / n1\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "if a ' s height is 35 % less than that of b , how much percent b ' s height is more than that of a ?", + "Output Program": [ + "n0 = 35.0\nt0 = 100.0 - n0\nt1 = n0 / t0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "53.84615384615385" + ], + "split": "train" + }, + { + "Input": "a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 77.44 , the number of the member is the group is :", + "Output Program": [ + "import math\nn0 = 77.44\nt0 = n0 * 100.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "88" + ], + "split": "train" + }, + { + "Input": "a library has an average of 510 visitors on sunday and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :", + "Output Program": [ + "n0 = 510.0\nn1 = 240.0\nn2 = 30.0\nt0 = 1.0 + 4.0\nt1 = n0 * t0\nt2 = t0 * t0\nt3 = n1 * t2\nt4 = t1 + t3\nanswer = t4 / n2\nprint(answer)" + ], + "Output Answer": [ + "285" + ], + "split": "train" + }, + { + "Input": "a fruit drink is made of orange , watermelon , and grape juice , where 15 percent of the drink is orange juice and 60 percent is watermelon juice . if the drink is made with 35 ounces of grape juice , how many ounces is the drink total ?", + "Output Program": [ + "n0 = 15.0\nn1 = 60.0\nn2 = 35.0\nt0 = n0 + n1\nt1 = n0 * n2\nt2 = n1 * n2\nt3 = 100.0 - t0\nt4 = t1 / t3\nt5 = t2 / t3\nt6 = n2 + t4\nanswer = t6 + t5\nprint(answer)" + ], + "Output Answer": [ + "140" + ], + "split": "train" + }, + { + "Input": "if the average ( arithmetic mean ) of ( 2 a + 16 ) and ( 3 a - 8 ) is 69 , what is the value of a ?", + "Output Program": [ + "n0 = 2.0\nn1 = 16.0\nn2 = 3.0\nn3 = 8.0\nn4 = 69.0\nt0 = n0 + n2\nt1 = n0 * n4\nt2 = n1 - n3\nt3 = t1 - t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "if the average of 55 , 48 , 507 , 2 , 684 and y is 223 , then what is y ?", + "Output Program": [ + "n0 = 55.0\nn1 = 48.0\nn2 = 507.0\nn3 = 2.0\nn4 = 684.0\nn5 = 223.0\nt0 = 2.0 + 4.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n5 * t0\nt4 = n3 + t2\nt5 = n4 + t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "in the xy - coordinate system , if ( m , n ) and ( m + 5 , n + k ) are two points on the line with the equation x = 2 y + 5 , then k =", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 5.0\nt0 = n0 + n2\nt1 = t0 - n2\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "2.5" + ], + "split": "train" + }, + { + "Input": "the sum of the first 70 positive even integers is 4970 . what is the sum of the first 70 odd integers ?", + "Output Program": [ + "n0 = 70.0\nn1 = 4970.0\nn2 = 70.0\nt0 = n0 / 2.0\nt1 = n0 * 2.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "4900" + ], + "split": "train" + }, + { + "Input": "a 40 - liter solution of alcohol and water is 5 percent alcohol . if 2.5 liters of alcohol and 7.5 liters of water are added to this solution , what percent of the solution produced is alcohol ?", + "Output Program": [ + "n0 = 40.0\nn1 = 5.0\nn2 = 2.5\nn3 = 7.5\nt0 = n2 + n3\nt1 = n1 / 100.0\nt2 = n0 + t0\nt3 = n0 * t1\nt4 = n2 + t3\nt5 = t4 / t2\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "in a consumer survey , 80 % of those surveyed liked at least one of 3 products : 1 , 2 , and 3 . 50 % of those asked liked product 1 , 30 % liked product 2 , and 20 % liked product 3 . if 5 % of the people in the survey liked all 3 of the products , what percentage of the survey participants liked more than one of the 3 products ?", + "Output Program": [ + "n0 = 80.0\nn1 = 3.0\nn2 = 1.0\nn3 = 2.0\nn4 = 3.0\nn5 = 50.0\nn6 = 1.0\nn7 = 30.0\nn8 = 2.0\nn9 = 20.0\nn10 = 3.0\nn11 = 5.0\nn12 = 3.0\nn13 = 3.0\nt0 = n5 + n7\nt1 = n9 + t0\nt2 = t1 - n0\nanswer = t2 - n11\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "find the greatest number which on dividing 1255 and 1490 , leaves a reminder of 8 and 11 respectively", + "Output Program": [ + "import scipy\nn0 = 1255.0\nn1 = 1490.0\nn2 = 8.0\nn3 = 11.0\nt0 = n0 - n2\nt1 = n1 - n3\nanswer = scipy.gcd(int(t0), int(t1))\nprint(answer)" + ], + "Output Answer": [ + "29" + ], + "split": "train" + }, + { + "Input": "there are 2 positive integers x and y . what is the probability that x + y is odd ?", + "Output Program": [ + "n0 = 2.0\n\nanswer = n0 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "solution x contains 20 % of material a and 80 % of material b . solution y contains 30 % of material a and 70 % of material b . a mixture of both these solutions contains 22 % of material a in the final product . how much solution x is present in the mixture ?", + "Output Program": [ + "n0 = 20.0\nn1 = 80.0\nn2 = 30.0\nn3 = 70.0\nn4 = 22.0\nt0 = n1 * 1000.0\nt1 = t0 / 100.0\nt2 = t1 / 100.0\nanswer = t2 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "let p be a prime number greater than 2 , and let n = 32 p . how many odd divisors does n have ?", + "Output Program": [ + "n0 = 2.0\nn1 = 32.0\n\nanswer = n0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "a women purchased 3 towels @ rs . 100 each , 5 towels @ rs . 150 each and two towels at a certain rate which is now slipped off from his memory . but she remembers that the average price of the towels was rs . 160 . find the unknown rate of two towels ?", + "Output Program": [ + "n0 = 3.0\nn1 = 100.0\nn2 = 5.0\nn3 = 150.0\nn4 = 160.0\nt0 = n0 + n2\nt1 = n2 * n3\nt2 = n0 * n1\nt3 = t0 + 2.0\nt4 = n4 * t3\nt5 = t4 - t1\nanswer = t5 - t2\nprint(answer)" + ], + "Output Answer": [ + "550" + ], + "split": "train" + }, + { + "Input": "a number a is squared and then multiplied by negative 6 . the result of this operation is equal to 3 times the sum of fourth times a and two . what is one possible value of a ?", + "Output Program": [ + "n0 = 6.0\nn1 = 3.0\nt0 = n0 / n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "how many liters of pure alcohol must be added to a 100 - liter solution that is 20 percent alcohol in order to produce a solution that is 30 percent alcohol ?", + "Output Program": [ + "n0 = 100.0\nn1 = 20.0\nn2 = 30.0\nt0 = 3.0 + 4.0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "14.285714285714286" + ], + "split": "train" + }, + { + "Input": "the average of non - zero number and its square is 5 times the number . the number is ?", + "Output Program": [ + "n0 = 5.0\nt0 = n0 * 2.0\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "the average weight of 2 person ' s increases by 4.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.5\nn2 = 65.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "74" + ], + "split": "train" + }, + { + "Input": "two kinds of vodka are mixed in the ratio 1 : 2 and 2 : 1 and they are sold fetching the profit 30 % and 20 % respectively . if the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4 / 3 and 5 / 3 times respectively , then the mixture will fetch the profit of", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 2.0\nn3 = 1.0\nn4 = 10.0\nn5 = 35.0\nn6 = 4.0\nn7 = 3.0\nn8 = 5.0\nn9 = 3.0\nt0 = n4 + n8\nt1 = n4 * n6\nt2 = t1 / n1\nanswer = t0 + t2\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "bert left the house with n dollars . he spent 1 / 3 of this at the hardware store , then $ 7 at the dry cleaners , and then half of what was left at the grocery store . when he got home , he had $ 10.50 left in his pocket . what was the value of n ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 7.0\nn3 = 10.5\nt0 = n2 / 2.0\nt1 = n0 / n1\nt2 = n3 + t0\nt3 = n0 - t1\nt4 = 1 / t3\nt5 = t2 * t4\nanswer = t5 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "41.99999999999999" + ], + "split": "train" + }, + { + "Input": "the average age of a group of 10 persons was decreased by 3 years when one person , whose age was 44 years , was replaced by a new person . find the age of the new person ?", + "Output Program": [ + "n0 = 10.0\nn1 = 3.0\nn2 = 44.0\nt0 = n0 * n1\nanswer = n2 - t0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "a = { 2 , 3 , 4 , 5 } b = { 4 , 5 , 6 , 7 , 8 } two integers will be randomly selected from the sets above , one integer from set a and one integer from set b . what is the probability q that the sum of the two integers will equal 9 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 4.0\nn3 = 5.0\nn4 = 4.0\nn5 = 5.0\nn6 = 6.0\nn7 = 7.0\nn8 = 8.0\nn9 = 9.0\nt0 = n2 / n3\nt1 = 1.0 / n2\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "0.2" + ], + "split": "train" + }, + { + "Input": "how many times will the digit 3 be written when listing the integers from 1 to 1000 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 1000.0\nt0 = n1 * 10.0\nt1 = t0 * 10.0\nanswer = t1 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "if the remainder is 11 when the integer n is divided by 20 , what is the remainder when 2 n is divided by 10 ?", + "Output Program": [ + "n0 = 11.0\nn1 = 20.0\nn2 = 2.0\nn3 = 10.0\nt0 = n0 * n2\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a basketball team composed of 12 players scored 100 points in a particular contest . if none of the individual players scored fewer than 7 points , what is the greatest number of points t that an individual player might have scored ?", + "Output Program": [ + "n0 = 12.0\nn1 = 100.0\nn2 = 7.0\nt0 = n0 * n2\nt1 = n1 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "the average of first 10 even numbers is ?", + "Output Program": [ + "n0 = 10.0\n\nanswer = n0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "there are 2 sections a and b in a class , consisting of 26 and 34 students respectively . if the average weight of section a is 50 kg and that of section b is 30 kg , find the average of the whole class ?", + "Output Program": [ + "n0 = 2.0\nn1 = 26.0\nn2 = 34.0\nn3 = 50.0\nn4 = 30.0\nt0 = n1 + n2\nt1 = n1 * n3\nt2 = n2 * n4\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "38.666666666666664" + ], + "split": "train" + }, + { + "Input": "john want to buy a $ 100 trouser at the store , but he think it \u00e2 \u20ac \u2122 s too expensive . finally , it goes on sale for $ 50 . what is the percent decrease ?", + "Output Program": [ + "n0 = 100.0\nn1 = 50.0\n\nanswer = n0 - n1\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "divide rs . 1800 among a , b and c so that a receives 2 / 5 as much as b and c together and b receives 1 / 5 as a and c together . a ' s share is ?", + "Output Program": [ + "n0 = 1800.0\nn1 = 2.0\nn2 = 5.0\nn3 = 1.0\nn4 = 5.0\n\nanswer = n0 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "600" + ], + "split": "train" + }, + { + "Input": "when the positive integer x is divided by 9 , the remainder is 5 . what is the remainder when 8 x is divided by 9 ?", + "Output Program": [ + "n0 = 9.0\nn1 = 5.0\nn2 = 8.0\nn3 = 9.0\nt0 = n1 * n2\nanswer = t0 % n0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "find the last term of a g . p whose first term is 9 and common ratio is ( 1 / 3 ) if the sum of the terms of the g . p is ( 40 / 3 )", + "Output Program": [ + "n0 = 9.0\nn1 = 1.0\nn2 = 3.0\nn3 = 40.0\nn4 = 3.0\n\nanswer = n1 / n2\nprint(answer)" + ], + "Output Answer": [ + "0.3333333333333333" + ], + "split": "train" + }, + { + "Input": "the average of marks obtained by 120 boys was 36 . if the average of marks of passed boys was 39 and that of failed boys was 15 , the number of boys who passed the examination is ?", + "Output Program": [ + "n0 = 120.0\nn1 = 36.0\nn2 = 39.0\nn3 = 15.0\nt0 = n0 * n1\nt1 = n0 * n3\nt2 = n2 - n3\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "105" + ], + "split": "train" + }, + { + "Input": "shekar scored 76 , 65 , 82 , 62 and 85 marks in mathematics , science , social studies , english and biology respectively . what are his average marks ?", + "Output Program": [ + "n0 = 76.0\nn1 = 65.0\nn2 = 82.0\nn3 = 62.0\nn4 = 85.0\nt0 = n0 + n1\nt1 = 1.0 + 4.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "74" + ], + "split": "train" + }, + { + "Input": "carina has 70 ounces of coffee divided into 5 - and 10 - ounce packages . if she has 2 more 5 - ounce packages than 10 - ounce packages , how many 10 - ounce packages does she have ?", + "Output Program": [ + "n0 = 70.0\nn1 = 5.0\nn2 = 10.0\nn3 = 2.0\nn4 = 5.0\nn5 = 10.0\nn6 = 10.0\nt0 = n1 + n2\nt1 = n1 * n3\nt2 = n0 - t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "the average weight of a , b and c is 45 kg . if the average weight of a and b be 42 kg and that of b and c be 43 kg , then the weight of b is :", + "Output Program": [ + "n0 = 45.0\nn1 = 42.0\nn2 = 43.0\nt0 = n1 * 2.0\nt1 = n2 * 2.0\nt2 = n0 * 3.0\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "john found that the average of 15 numbers is 40 . if 11 is added to each number then the mean of number is ?", + "Output Program": [ + "n0 = 15.0\nn1 = 40.0\nn2 = 11.0\n\nanswer = n1 + n2\nprint(answer)" + ], + "Output Answer": [ + "51" + ], + "split": "train" + }, + { + "Input": "x and y are positive integers . when x is divided by 9 , the remainder is 2 , and when x is divided by 7 , the remainder is 4 . when y is divided by 11 , the remainder is 3 , and when y is divided by 13 , the remainder is 12 . what is the least possible value of y - x ?", + "Output Program": [ + "n0 = 9.0\nn1 = 2.0\nn2 = 7.0\nn3 = 4.0\nn4 = 11.0\nn5 = 3.0\nn6 = 13.0\nn7 = 12.0\nt0 = n0 + n1\nt1 = n4 * 2.0\nt2 = n5 + t1\nanswer = t2 - t0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "at joes steakhouse the hourly wage for a chef is 22 % greater than that of a dishwasher , and the hourly wage of a dishwasher is half as much as the hourly wage of a manager . if a managers wage is $ 8.50 per hour , how much less than a manager does a chef earn each hour ?", + "Output Program": [ + "n0 = 22.0\nn1 = 8.5\nt0 = n0 + 100.0\nt1 = 1.0 / 2.0\nt2 = t0 / 100.0\nt3 = t2 * t1\nt4 = 1.0 - t3\nanswer = n1 * t4\nprint(answer)" + ], + "Output Answer": [ + "3.315" + ], + "split": "train" + }, + { + "Input": "if the sum of two positive integers is 18 and the difference of their squares is 36 , what is the product of the two integers ?", + "Output Program": [ + "n0 = 18.0\nn1 = 36.0\nt0 = n1 / n0\nt1 = n0 - t0\nt2 = t1 / t0\nt3 = t2 + t0\nanswer = t3 * t2\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "a student chose a number , multiplied it by 4 , then subtracted 138 from the result and got 102 . what was the number he chose ?", + "Output Program": [ + "n0 = 4.0\nn1 = 138.0\nn2 = 102.0\nt0 = n1 + n2\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "( 228 % of 1265 ) \u00f7 6 = ?", + "Output Program": [ + "n0 = 228.0\nn1 = 1265.0\nn2 = 6.0\nt0 = n0 / 100.0\nt1 = n1 * t0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "480.7" + ], + "split": "train" + }, + { + "Input": "the average height of 40 girls out of a class of 50 is 169 cm . and that of the remaining girls is 167 cm . the average height of the whole class is :", + "Output Program": [ + "n0 = 40.0\nn1 = 50.0\nn2 = 169.0\nn3 = 167.0\nt0 = n0 * n2\nt1 = n3 * 10.0\nt2 = t0 + t1\nanswer = t2 / n1\nprint(answer)" + ], + "Output Answer": [ + "168.6" + ], + "split": "train" + }, + { + "Input": "equal amount of water were poured into two empty jars of different capacities , which made one jar 1 / 7 full and other jar 1 / 6 full . if the water in the jar with lesser capacity is then poured into the jar with greater capacity , what fraction of the larger jar will be filled with water ?", + "Output Program": [ + "n0 = 1.0\nn1 = 7.0\nn2 = 1.0\nn3 = 6.0\n\nanswer = 2.0 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.2857142857142857" + ], + "split": "train" + }, + { + "Input": "given f ( x ) = 3 x \u2013 5 , for what value of x does 2 * [ f ( x ) ] \u2013 10 = f ( x \u2013 2 ) ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 2.0\nn3 = 10.0\nn4 = 2.0\nt0 = n1 * n2\nt1 = n4 * n0\nt2 = n0 * n2\nt3 = n0 * 1.0\nt4 = n3 + t0\nt5 = n1 + t1\nt6 = t2 - t3\nt7 = t4 - t5\nanswer = t7 / t6\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "a positive integer n is a perfect number provided that the sum of all the positive factors of n , including 1 and n , is equal to 2 n . what is the sum of the reciprocals of all the positive factors of the perfect number 28 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 28.0\nt0 = 1.0 / n2\nt1 = t0 * 2.0\nanswer = n2 * t1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a tank holds x gallons of a saltwater solution that is 20 % salt by volume . one fourth of the water is evaporated , leaving all of the salt . when 6 gallons of water and 12 gallons of salt are added , the resulting mixture is 33 1 / 3 % salt by volume . what is the value of x ?", + "Output Program": [ + "n0 = 20.0\nn1 = 6.0\nn2 = 12.0\nn3 = 33.0\nn4 = 1.0\nn5 = 3.0\nt0 = n0 / 100.0\nt1 = 1.0 / 4.0\nt2 = n2 * 2.0\nt3 = t0 * 2.0\nt4 = t2 - n1\nt5 = 1.0 - t0\nt6 = t1 * t5\nt7 = t5 - t6\nt8 = t7 - t3\nanswer = t4 / t8\nprint(answer)" + ], + "Output Answer": [ + "89.99999999999997" + ], + "split": "train" + }, + { + "Input": "there are 250 female managers in a certain company . find the total number of female employees in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers .", + "Output Program": [ + "n0 = 250.0\nn1 = 2.0\nn2 = 5.0\nn3 = 2.0\nn4 = 5.0\nt0 = n1 / n2\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "625" + ], + "split": "train" + }, + { + "Input": "ashok secured average of 78 marks in 6 subjects . if the average of marks in 5 subjects is 74 , how many marks did he secure in the 6 th subject ?", + "Output Program": [ + "n0 = 78.0\nn1 = 6.0\nn2 = 5.0\nn3 = 74.0\nn4 = 6.0\nt0 = n0 * n1\nt1 = n2 * n3\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "98" + ], + "split": "train" + }, + { + "Input": "if p / q = 3 / 5 , then 2 p + q = ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 2.0\nt0 = n0 * n2\nanswer = n1 + t0\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "the difference between a two digit number and the number obtained by interchanging the digits is 36 . what is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?", + "Output Program": [ + "n0 = 36.0\nn1 = 1.0\nn2 = 2.0\nt0 = n2 + 10.0\nt1 = n2 * 10.0\nt2 = 3.0 - n1\nt3 = n1 + t1\nt4 = t3 - t0\nt5 = n0 / t4\nanswer = t5 * t2\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "40 + 5 * 12 / ( 180 / 3 ) = ?", + "Output Program": [ + "n0 = 40.0\nn1 = 5.0\nn2 = 12.0\nn3 = 180.0\nn4 = 3.0\nt0 = n3 / n4\nt1 = n1 * n2\nt2 = t1 / t0\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "41" + ], + "split": "train" + }, + { + "Input": "on dividing 13787 by a certain number , we get 89 as quotient and 14 as remainder . what is the divisor ?", + "Output Program": [ + "n0 = 13787.0\nn1 = 89.0\nn2 = 14.0\nt0 = n0 - n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "154.75280898876406" + ], + "split": "train" + }, + { + "Input": "in a mixture 60 litres , the ra \u0275 o of milk and water 2 : 1 . if the this ra \u0275 o is to be 1 : 2 , then the quanity of water to be further added is", + "Output Program": [ + "n0 = 60.0\nn1 = 2.0\nn2 = 1.0\nn3 = 1.0\nn4 = 2.0\nt0 = n1 + n2\nt1 = n0 * n1\nt2 = t1 / t0\nt3 = n1 * t2\nt4 = n0 - t2\nanswer = t3 - t4\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "a scale 6 ft . 8 inches long is divided into 4 equal parts . find the length of each part", + "Output Program": [ + "n0 = 6.0\nn1 = 8.0\nn2 = 4.0\nt0 = n0 * 12.0\nt1 = n1 + t0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "there are 79 people that own pets . 15 people own only dogs , 10 people own only cats , 5 people own only cats and dogs , 3 people own cats , dogs and snakes . how many total snakes are there ?", + "Output Program": [ + "n0 = 79.0\nn1 = 15.0\nn2 = 10.0\nn3 = 5.0\nn4 = 3.0\nt0 = n1 + n2\nt1 = n3 + t0\nt2 = n4 + t1\nt3 = n0 - t2\nanswer = n4 + t3\nprint(answer)" + ], + "Output Answer": [ + "49" + ], + "split": "train" + }, + { + "Input": "the ages of two person differ by 20 years . if 10 years ago , the elder one be 5 times as old as the younger one , their present ages ( in years ) are respectively", + "Output Program": [ + "n0 = 20.0\nn1 = 10.0\nn2 = 5.0\nt0 = n1 * n2\nt1 = n0 - n1\nt2 = n2 - 1.0\nt3 = t0 + t1\nt4 = t3 / t2\nanswer = n0 + t4\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "a company has 15 managers and 75 associates . the 15 managers have an average salary of $ 90,000 . the 75 associates have an average salary of $ 30,000 . what is the average salary for the company ?", + "Output Program": [ + "n0 = 15.0\nn1 = 75.0\nn2 = 15.0\nn3 = 90000.0\nn4 = 75.0\nn5 = 30000.0\nt0 = n0 + n1\nt1 = n0 * n3\nt2 = n1 * n5\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "40000" + ], + "split": "train" + }, + { + "Input": "a straight line in the xy - plane has y - intercept of 20 . on this line the x - coordinate of the point is 150 and y - coordinate is 600 then what is the slope of the line ?", + "Output Program": [ + "n0 = 20.0\nn1 = 150.0\nn2 = 600.0\nt0 = n2 - n0\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "3.8666666666666667" + ], + "split": "train" + }, + { + "Input": "a case contains c cartons . each carton contains b boxes , and each box contains 400 paper clips . how many paper clips are contained in 2 cases ?", + "Output Program": [ + "n0 = 400.0\nn1 = 2.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "800" + ], + "split": "train" + }, + { + "Input": "what least number should be added to 1052 , so that the sum is completely divisible by 23", + "Output Program": [ + "n0 = 1052.0\nn1 = 23.0\nt0 = n0 % n1\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "a certain taxi company charges $ 3.00 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 5.0\nn3 = 0.4\nn4 = 1.0\nn5 = 5.0\nn6 = 8.0\nt0 = n1 / n2\nt1 = n6 / t0\nt2 = t1 - n1\nt3 = n3 * t2\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "18.6" + ], + "split": "train" + }, + { + "Input": "a waitress ' s income consists of her salary and tips . during one week , her tips were 2 / 4 of her salary . what fraction of her income for the week came from tips ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nt0 = n0 + n1\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.3333333333333333" + ], + "split": "train" + }, + { + "Input": "there are 990 male and female participants in a meeting . half the female participants and one - quarter of the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?", + "Output Program": [ + "n0 = 990.0\nt0 = n0 / 3.0\nt1 = t0 * 4.0\nt2 = t1 - n0\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "165" + ], + "split": "train" + }, + { + "Input": "5 years ago amith was 3 times as old as his daughter and 10 years hence , he will be two times as old as his daughter . then amith \u2019 s current age is ,", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nn2 = 10.0\nt0 = n0 * n1\nanswer = n0 + t0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "a batch of cookies was divided among 3 tins : 2 / 3 of all the cookies were placed in either the blue tin or the green tin , and the rest were placed in the red tin . if 1 / 4 of all the cookies were placed in the blue tin , what fraction q of the cookies that were placed in the other tins were placed in the green tin ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 3.0\nn3 = 1.0\nn4 = 4.0\nt0 = n1 / n0\nt1 = n3 / n4\nt2 = 12.0 / n0\nt3 = t0 - t1\nt4 = t3 * 12.0\nt5 = t2 + t4\nanswer = t4 / t5\nprint(answer)" + ], + "Output Answer": [ + "0.5555555555555556" + ], + "split": "train" + }, + { + "Input": "the cricket team of 11 members is 26 yrs old & the wicket keeper is 3 yrs older . if the ages ofthese 2 are excluded , the average age of theremaining players is 1 year less than the average age of the whole team . what is the average age of the team ?", + "Output Program": [ + "n0 = 11.0\nn1 = 26.0\nn2 = 3.0\nn3 = 2.0\nn4 = 1.0\nt0 = n1 + n2\nt1 = n0 - n3\nt2 = n1 + t0\nt3 = n0 - t1\nt4 = t2 - t1\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "a student has to obtain 33 % of the total marks to pass . he got 125 marks and failed by 73 marks . the maximum marks are ?", + "Output Program": [ + "n0 = 33.0\nn1 = 125.0\nn2 = 73.0\nt0 = n1 + n2\nt1 = n0 / 100.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "600" + ], + "split": "train" + }, + { + "Input": "two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs , x and y . now , jug x is 1 / 7 full , while jug y is 2 / 3 full . if water is poured from jug x into jug y until jug y is filled , what fraction of jug x then contains water ?", + "Output Program": [ + "n0 = 1.0\nn1 = 7.0\nn2 = 2.0\nn3 = 3.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = 1.0 - t1\nt3 = t2 / t1\nanswer = t0 * t3\nprint(answer)" + ], + "Output Answer": [ + "0.07142857142857144" + ], + "split": "train" + }, + { + "Input": "how many e ways can jason sit with his 5 friends in a row of 6 seats with an aisle on either side of the row , if jason insists on sitting next to one of the aisles ?", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 6.0\nt0 = math.factorial(min(15, int(n0)))\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "240" + ], + "split": "train" + }, + { + "Input": "in the biology lab of ` ` jefferson ' ' high school there are 0.037 * 10 ^ 5 germs , equally divided among 148000 * 10 ^ ( - 3 ) petri dishes . how many germs live happily in a single dish ?", + "Output Program": [ + "n0 = 0.037\nn1 = 10.0\nn2 = 5.0\nn3 = 148000.0\nn4 = 10.0\nn5 = 3.0\nt0 = n3 / 1000.0\nt1 = 100.0 * 1000.0\nt2 = n0 * t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "what is the average ( arithmetic mean ) of all multiples of 10 from 10 to 100 inclusive ?", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 100.0\nt0 = n0 + n2\nt1 = n2 - n0\nt2 = t1 / n0\nt3 = t2 + 1.0\nt4 = t0 * t3\nt5 = t4 / 2.0\nanswer = t5 / t3\nprint(answer)" + ], + "Output Answer": [ + "55" + ], + "split": "train" + }, + { + "Input": "what is the sum of all 3 digit numbers that leave a remainder of ' 2 ' when divided by 4 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 4.0\nt0 = n0 * n0\nt1 = 1000.0 - n0\nt2 = t0 * 10.0\nt3 = t2 + t0\nt4 = n0 + t3\nt5 = t4 + t1\nt6 = t1 - t4\nt7 = t6 / n2\nt8 = t7 + 1.0\nt9 = t8 / n1\nanswer = t5 * t9\nprint(answer)" + ], + "Output Answer": [ + "123500.125" + ], + "split": "train" + }, + { + "Input": "if money is invested at r percent interest , compounded annually , the amount of investment will double in approximately 70 / r years . if pat ' s parents invested $ 5000 in a long term bond that pays 8 percent interest , compounded annually , what will be the approximate total amount of investment 18 years later , when pat is ready for college ?", + "Output Program": [ + "n0 = 70.0\nn1 = 5000.0\nn2 = 8.0\nn3 = 18.0\nt0 = n1 * 2.0\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "20000" + ], + "split": "train" + }, + { + "Input": "a company has 15 managers and 75 associates . the 15 managers have an average salary of $ 90000 . the 75 associates have an average salary of $ 30000 . what is the average salary for the company ?", + "Output Program": [ + "n0 = 15.0\nn1 = 75.0\nn2 = 15.0\nn3 = 90000.0\nn4 = 75.0\nn5 = 30000.0\nt0 = n0 + n1\nt1 = n0 * n3\nt2 = n1 * n5\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "40000" + ], + "split": "train" + }, + { + "Input": "if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer t that must divide n is ?", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 72.0\nt0 = n1 / n0\nt1 = math.sqrt(max(0, t0))\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "the average age of 15 students of a class is 15 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years . tee age of the 15 th student is :", + "Output Program": [ + "n0 = 15.0\nn1 = 15.0\nn2 = 5.0\nn3 = 14.0\nn4 = 9.0\nn5 = 16.0\nn6 = 15.0\nt0 = n0 * n0\nt1 = n2 * n3\nt2 = n4 * n5\nt3 = t1 + t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "a certain company has records stored with a record storage firm in 15 - inch by 12 - inch by 10 - inch boxes . the boxes occupy 1.08 million cubic inches of space . if the company pays $ 0.6 per box per month for the record storage , what is the total amount that the company pays each month for record storage ?", + "Output Program": [ + "n0 = 15.0\nn1 = 12.0\nn2 = 10.0\nn3 = 1.08\nn4 = 0.6\nt0 = n0 * n1\nt1 = n2 * t0\nt2 = t1 / 100.0\nt3 = t2 / 100.0\nt4 = t3 / 100.0\nt5 = n3 / t4\nanswer = n4 * t5\nprint(answer)" + ], + "Output Answer": [ + "360" + ], + "split": "train" + }, + { + "Input": "if y > 0 , ( 8 y ) / 20 + ( 3 y ) / 10 is what percent of y ?", + "Output Program": [ + "n0 = 0.0\nn1 = 8.0\nn2 = 20.0\nn3 = 3.0\nn4 = 10.0\nt0 = n1 / n2\nt1 = n3 / n4\nt2 = t0 + t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "train" + }, + { + "Input": "on dividing 14698 by a certain number , we get 89 as quotient and 14 as remainder . what is the divisor ?", + "Output Program": [ + "n0 = 14698.0\nn1 = 89.0\nn2 = 14.0\nt0 = n0 - n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "164.98876404494382" + ], + "split": "train" + }, + { + "Input": "paulson spends 75 % of his income . his income is increased by 20 % and he increased his expenditure by 10 % . find the percentage increase in his savings ?", + "Output Program": [ + "n0 = 75.0\nn1 = 20.0\nn2 = 10.0\nt0 = n1 / 100.0\nt1 = n2 / 100.0\nt2 = n0 / 100.0\nt3 = t0 + 1.0\nt4 = t1 + 1.0\nt5 = 1.0 - t2\nt6 = t4 * t2\nt7 = t3 - t6\nt8 = t7 - t5\nt9 = t8 / t5\nanswer = t9 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "49.99999999999996" + ], + "split": "train" + }, + { + "Input": "rice weighing 33 / 4 pounds was divided equally and placed in 4 containers . how many ounces of rice were in each container ? ( note that 1 pound = 16 ounces )", + "Output Program": [ + "n0 = 33.0\nn1 = 4.0\nn2 = 4.0\nn3 = 1.0\nn4 = 16.0\nt0 = n0 / n1\nt1 = n4 * t0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "on a race track a maximum of 5 horses can race together at a time . there are a total of 25 horses . there is no way of timing the races . what is the minimum number q of races we need to conduct to get the top 3 fastest horses ?", + "Output Program": [ + "n0 = 5.0\nn1 = 25.0\nn2 = 3.0\nt0 = n1 / n0\nanswer = t0 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "if ( 2 to the x ) - ( 2 to the ( x - 2 ) ) = 3 ( 2 to the 12 ) , what is the value of x ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 2.0\nn3 = 3.0\nn4 = 2.0\nn5 = 12.0\n\nanswer = n0 + n5\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "jean drew a gumball at random from a jar of pink and blue gumballs . since the gumball she selected was blue and she wanted a pink one , she replaced it and drew another . the second gumball also happened to be blue and she replaced it as well . if the probability of her drawing the two blue gumballs was 25 / 49 , what is the probability that the next one she draws will be pink ?", + "Output Program": [ + "import math\nn0 = 25.0\nn1 = 49.0\nt0 = n0 / n1\nt1 = math.sqrt(max(0, t0))\nanswer = 1.0 - t1\nprint(answer)" + ], + "Output Answer": [ + "0.2857142857142857" + ], + "split": "train" + }, + { + "Input": "m and n are the x and y coordinates , respectively , of a point in the coordinate plane . if the points ( m , n ) and ( m + p , n + 18 ) both lie on the line defined by the equation x = ( y / 6 ) - ( 2 / 5 ) , what is the value of p ?", + "Output Program": [ + "n0 = 18.0\nn1 = 6.0\nn2 = 2.0\nn3 = 5.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "if w is the product of the integers from 1 to 30 , inclusive , what is the greatest integer k for which 3 ^ k is a factor of w ?", + "Output Program": [ + "n0 = 1.0\nn1 = 30.0\nn2 = 3.0\nt0 = n1 - 2.0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "if ( a + b ) = 4 , ( b + c ) = 5 and ( c + d ) = 3 , what is the value of ( a + d ) ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 3.0\nt0 = n0 + n2\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 920 in total compensation , how many total hours did he work that week ?", + "Output Program": [ + "n0 = 16.0\nn1 = 40.0\nn2 = 40.0\nn3 = 75.0\nn4 = 920.0\nt0 = n3 + 100.0\nt1 = n0 * n1\nt2 = n0 * t0\nt3 = n4 - t1\nt4 = t2 / 100.0\nt5 = t3 / t4\nanswer = n1 + t5\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "the average age of a class of 20 students is 21 years . the average increased by 1 when the teacher ' s age also included . what is the age of the teacher ?", + "Output Program": [ + "n0 = 20.0\nn1 = 21.0\nn2 = 1.0\nt0 = n0 + n2\nt1 = n1 + n2\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "when the positive integer k is divided by the positive integer n , the remainder is 11 . if k / n = 71.2 , what is the value of n ?", + "Output Program": [ + "n0 = 11.0\nn1 = 81.1\nt0 = 2.0 / 10.0\nt1 = n1 * 10.0\nt2 = n0 / t0\nt3 = t1 - 2.0\nt4 = t3 / 10.0\nt5 = t4 * t2\nt6 = n0 + t5\nanswer = t6 / t2\nprint(answer)" + ], + "Output Answer": [ + "81.1" + ], + "split": "train" + }, + { + "Input": "if a and b are integers and ( a * b ) ^ 5 = 128 y , y could be :", + "Output Program": [ + "n0 = 5.0\nn1 = 128.0\nt0 = 2.0**min(n0, 5)\nt1 = n1 / t0\nanswer = t1 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "jacob is now 12 years younger than michael . if 5 years from now michael will be twice as old as jacob , how old will jacob be in 4 years ?", + "Output Program": [ + "n0 = 12.0\nn1 = 5.0\nn2 = 4.0\nt0 = n0 + n1\nt1 = n1 * 2.0\nt2 = t0 - t1\nanswer = n2 + t2\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "mixture a is 20 % oil and 80 % material b by weight . if 2 more kilograms of oil are added to the 8 kilograms mixture a , how many kilograms of mixture a must be added to make a 70 % material b in the new mixture ?", + "Output Program": [ + "n0 = 20.0\nn1 = 80.0\nn2 = 2.0\nn3 = 8.0\nn4 = 70.0\nt0 = 100.0 - n4\nt1 = t0 - n0\nt2 = n4 / t1\nt3 = n2 * t2\nanswer = t3 - n3\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "in a theater , the first row has 15 seats and each row has 2 more seats than previous row . if the last row has 53 seats , what is the total number of seats in the theater ?", + "Output Program": [ + "n0 = 15.0\nn1 = 2.0\nn2 = 53.0\nt0 = n0 + n2\nt1 = n2 - n0\nt2 = n1 + t1\nt3 = t0 / 2.0\nt4 = t2 / n1\nanswer = t3 * t4\nprint(answer)" + ], + "Output Answer": [ + "680" + ], + "split": "train" + }, + { + "Input": "shipment - - - no . of defective chips / shipment - - - total chips in shipment s 1 - - - - - - - - - - - - - - - - - - - - - - 2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 5,000 s 2 - - - - - - - - - - - - - - - - - - - - - - 4 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 12,000 s 3 - - - - - - - - - - - - - - - - - - - - - - 2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 15,000 s 4 - - - - - - - - - - - - - - - - - - - - - - 4 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 16,000 a computer chip manufacturer expects the ratio of the number of defective chips to the total number of chips in all future shipments to equal the corresponding ratio for shipments s 1 , s 2 , s 3 , and s 4 combined , as shown in the table above . what \u2019 s the expected number of defective chips in a shipment of 60,000 chips ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 5000.0\nn3 = 2.0\nn4 = 4.0\nn5 = 12000.0\nn6 = 3.0\nn7 = 2.0\nn8 = 15000.0\nn9 = 4.0\nn10 = 4.0\nn11 = 16000.0\nn12 = 1.0\nn13 = 2.0\nn14 = 3.0\nn15 = 4.0\nn16 = 60000.0\nt0 = n2 + n5\nt1 = n1 + n4\nt2 = n8 + t0\nt3 = n1 + t1\nt4 = n11 + t2\nt5 = n4 + t3\nt6 = t4 / t5\nanswer = n16 / t6\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "x can give y 100 meters start and z 200 meters start in x kilometer race . how much start can y give z in x kilometer race ?", + "Output Program": [ + "n0 = 100.0\nn1 = 200.0\nt0 = n1 - n0\nt1 = 1000.0 - n0\nt2 = t0 * 1000.0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "111.11111111111111" + ], + "split": "train" + }, + { + "Input": "what is the least number that should be added to 1053 , so the sum of the number is divisible by 23 ?", + "Output Program": [ + "import math\nn0 = 1053.0\nn1 = 23.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = t1 + 1.0\nt3 = t2 - t0\nanswer = n1 * t3\nprint(answer)" + ], + "Output Answer": [ + "5.000000000000043" + ], + "split": "train" + }, + { + "Input": "the salary of a , b , c , d , e is rs . 8000 , rs . 5000 , rs . 16000 , rs . 7000 , rs . 9000 per month respectively , then the average salary of a , b , c , d , and e per month is", + "Output Program": [ + "n0 = 8000.0\nn1 = 5000.0\nn2 = 16000.0\nn3 = 7000.0\nn4 = 9000.0\nt0 = n0 + n1\nt1 = 1.0 + 4.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "9000" + ], + "split": "train" + }, + { + "Input": "find out the c . i on rs . 3000 at 4 % p . a . compound half - yearly for 1 1 / 2 years", + "Output Program": [ + "n0 = 3000.0\nn1 = 4.0\nn2 = 1.0\nn3 = 1.0\nn4 = 2.0\nt0 = n1 / 100.0\nt1 = 3.0 / n4\nt2 = t0 + n2\nt3 = t2**min(t1, 5)\nt4 = n0 * t3\nanswer = t4 - n0\nprint(answer)" + ], + "Output Answer": [ + "181.78817648189806" + ], + "split": "train" + }, + { + "Input": "a number when divided by 20 leaves 6 as a remainder . what will be the remainder if the number is divided by 19 ?", + "Output Program": [ + "n0 = 20.0\nn1 = 6.0\nn2 = 19.0\nt0 = n0 + n1\nanswer = t0 % n2\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "a number is doubled and 9 is added . if resultant is trebled , it becomes 57 . what is that number", + "Output Program": [ + "n0 = 9.0\nn1 = 57.0\nt0 = n0 * 3.0\nt1 = 2.0 * 3.0\nt2 = n1 - t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "2 pipes can separately fill a tank in 20 hrs and 30 hrs respectively . both the pipes are opened tofill the tank , a leak develops in the tank through which one - third of water supplied by both the pipes goes out . what is the total time taken to fill the tank ?", + "Output Program": [ + "n0 = 2.0\nn1 = 20.0\nn2 = 30.0\nt0 = 1.0 / 3.0\nt1 = 1 / n1\nt2 = 1 / n2\nt3 = t0 + 1.0\nt4 = t1 + t2\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "15.999999999999998" + ], + "split": "train" + }, + { + "Input": "there are 99 people that own pets . 15 people own only dogs , 10 people own only cats , 5 people own only cats and dogs , 3 people own cats , dogs and snakes . how many total snakes are there ?", + "Output Program": [ + "n0 = 99.0\nn1 = 15.0\nn2 = 10.0\nn3 = 5.0\nn4 = 3.0\nt0 = n1 + n2\nt1 = n3 + t0\nt2 = n4 + t1\nt3 = n0 - t2\nanswer = n4 + t3\nprint(answer)" + ], + "Output Answer": [ + "69" + ], + "split": "train" + }, + { + "Input": "if 12 % of x is equal to 6 % of y , then 18 % of x will be equal to how much % of y ?", + "Output Program": [ + "n0 = 12.0\nn1 = 6.0\nn2 = 18.0\nt0 = n1 * n2\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "on dividing 127 by a number , the quotient is 9 and the remainder is 1 . find the divisor .", + "Output Program": [ + "import math\nn0 = 127.0\nn1 = 9.0\nn2 = 1.0\nt0 = n0 / n1\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "if a ( k ) = ( k + 1 ) ^ 2 , and k = 1 , what is the value of a ( a ( a ( a ( k ) ) ) ) ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 1.0\nt0 = n0 + n0\nt1 = t0**min(n1, 5)\nt2 = n0 + t1\nt3 = t2**min(n1, 5)\nt4 = n0 + t3\nt5 = t4**min(n1, 5)\nt6 = n0 + t5\nanswer = t6**min(n1, 5)\nprint(answer)" + ], + "Output Answer": [ + "458329" + ], + "split": "train" + }, + { + "Input": "in a certain accounting class of 100 students , 70 % of the students took the final exam on the assigned day while the rest of the students took the exam on a make - up date . if the students on the assigned day had an average score of 65 % , and the students on the make - up date had an average score of 95 % , what was the average score for the entire class ?", + "Output Program": [ + "n0 = 100.0\nn1 = 70.0\nn2 = 65.0\nn3 = 95.0\nt0 = n1 * n2\nt1 = n0 - n1\nt2 = n3 * t1\nt3 = t0 + t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "74" + ], + "split": "train" + }, + { + "Input": "the maximum number of student amoung them 1020 pens and 860 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :", + "Output Program": [ + "import scipy\nn0 = 1020.0\nn1 = 860.0\n\nanswer = scipy.gcd(int(n0), int(n1))\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "there were totally 100 men . 80 are married . 75 have t . v , 85 have radio , 70 have a . c . how many men have t . v , radio , a . c and also married ?", + "Output Program": [ + "n0 = 100.0\nn1 = 80.0\nn2 = 75.0\nn3 = 85.0\nn4 = 70.0\nt0 = n0 - n1\nt1 = n0 - n2\nt2 = n0 - n3\nt3 = n0 - n4\nt4 = t0 + t1\nt5 = t4 + t2\nt6 = t5 + t3\nanswer = n0 - t6\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "how many integerskgreater than 100 and less than 1100 are there such that if the hundreds and the units digits ofkare reversed , the resulting integer is k + 99 ?", + "Output Program": [ + "n0 = 100.0\nn1 = 1100.0\nn2 = 99.0\nt0 = n0 / 10.0\nt1 = 2.0 * 4.0\nt2 = t0 * t1\nanswer = t0 + t2\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "in a function , every person shakes hand with every other person . if there was a total of 28 handshakes in the function , how many persons were present in the function ?", + "Output Program": [ + "n0 = 28.0\nt0 = n0 - 10.0\nanswer = t0 - 10.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "3 * 16 + 3 * 17 + 3 * 20 + 11 = ?", + "Output Program": [ + "n0 = 3.0\nn1 = 16.0\nn2 = 3.0\nn3 = 17.0\nn4 = 3.0\nn5 = 20.0\nn6 = 11.0\nt0 = n0 * n1\nt1 = n0 * n3\nt2 = n0 * n5\nt3 = t0 + t1\nt4 = t3 + t2\nanswer = n6 + t4\nprint(answer)" + ], + "Output Answer": [ + "170" + ], + "split": "train" + }, + { + "Input": "if x = - 2 and y = - 4 , what is the value of 5 ( x - y ) ^ 2 - xy ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 5.0\nn3 = 2.0\nt0 = -n0\nt1 = -n1\nt2 = t0 * t1\nt3 = t0 - t1\nt4 = t3**min(n3, 5)\nt5 = n2 * t4\nanswer = t5 - t2\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "a library has an average of 660 visitors on sundays and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :", + "Output Program": [ + "import math\nn0 = 660.0\nn1 = 240.0\nn2 = 30.0\nt0 = 3.0 + 4.0\nt1 = n2 / t0\nt2 = math.floor(t1)\nt3 = t2 + 1.0\nt4 = n0 * t3\nt5 = n2 - t3\nt6 = n1 * t5\nt7 = t4 + t6\nanswer = t7 / n2\nprint(answer)" + ], + "Output Answer": [ + "310" + ], + "split": "train" + }, + { + "Input": "at company x , senior sales representatives visit the home office once every 16 days , and junior sales representatives visit the home office once every 12 days . the number of visits that a junior sales representative makes in a 2 - year period is approximately what percent greater than the number of visits that a senior representative makes in the same period ?", + "Output Program": [ + "n0 = 16.0\nn1 = 12.0\nn2 = 2.0\nt0 = 1.0 + 10.0\nt1 = n0 - n1\nt2 = t1 - 1.0\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "in n is a positive integer less than 200 , and 14 n / 60 is an integer , then n has how many different positive prime factors q ?", + "Output Program": [ + "n0 = 200.0\nn1 = 14.0\nn2 = 60.0\nt0 = 1.0 + 4.0\nt1 = n2 / 2.0\nt2 = t1 / 2.0\nt3 = t2 / 3.0\nt4 = t0 / t3\nanswer = t4 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "the two lines y = x and x = - 9 intersect on the coordinate plane . what is the value of the area of the figure formed by the intersecting lines and the x - axis ?", + "Output Program": [ + "n0 = 9.0\nt0 = n0 * n0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "40.5" + ], + "split": "train" + }, + { + "Input": "at a certain food stand , the price of each apple is 40 \u00a2 and the price of each orange is 60 \u00a2 . mary selects a total of 10 apples and oranges from the food stand , and the average ( arithmetic mean ) price of the 10 pieces of fruit is 54 \u00a2 . how many oranges must mary put back so that the average price of the pieces of fruit that she keeps is 50 \u00a2 ?", + "Output Program": [ + "n0 = 40.0\nn1 = 60.0\nn2 = 10.0\nn3 = 10.0\nn4 = 54.0\nn5 = 50.0\nt0 = n1 * n2\nt1 = n2 * n4\nt2 = n2 * n5\nt3 = n1 - n0\nt4 = n1 - n5\nt5 = t0 - t1\nt6 = t5 / t3\nt7 = n0 * t6\nt8 = n2 - t6\nt9 = n1 * t8\nt10 = t7 + t9\nt11 = t10 - t2\nanswer = t11 / t4\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "m and n are the x and y coordinates , respectively , of a point in the coordinate plane . if the points ( m , n ) and ( m + p , n + 9 ) both lie on the line defined by the equation x = ( y / 3 ) - ( 2 / 5 ) , what is the value of p ?", + "Output Program": [ + "n0 = 9.0\nn1 = 3.0\nn2 = 2.0\nn3 = 5.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "1 + 2 + 3 + . . . + 12 = ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 3.0\nn3 = 12.0\nt0 = n0 + n3\nt1 = n3 * t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "78" + ], + "split": "train" + }, + { + "Input": "7 people average age is 30 . youngest person age is 6 . find average of the people when youngest was born .", + "Output Program": [ + "n0 = 7.0\nn1 = 30.0\nn2 = 6.0\nt0 = n0 * n1\nt1 = n0 * n2\nt2 = t0 - t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "in the excel manufacturing company , 46 percent of the employees are men . if 60 percent of the employees are unionized and 70 percent of these are men , what percent of the non - union employees are women ?", + "Output Program": [ + "n0 = 46.0\nn1 = 60.0\nn2 = 70.0\nt0 = n2 / 100.0\nt1 = 100.0 - n0\nt2 = 100.0 - n1\nt3 = n1 * t0\nt4 = n1 - t3\nt5 = t1 - t4\nt6 = t5 / t2\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "a man was asked to state his age in years . his reply was , ` ` take my age 6 years hence , multiply it by 6 and subtract 6 times my age 6 years ago and you will know how old i am . ' ' what was the age of the person ?", + "Output Program": [ + "n0 = 6.0\nn1 = 6.0\nn2 = 6.0\nn3 = 6.0\nt0 = n0 + n0\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "train" + }, + { + "Input": "of 70 players on a football team , 49 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?", + "Output Program": [ + "n0 = 70.0\nn1 = 49.0\nt0 = 1.0 / 3.0\nt1 = n0 - n1\nt2 = 1.0 - t0\nt3 = t2 * t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "63" + ], + "split": "train" + }, + { + "Input": "change the below lagarithm log 255 = 1 / 2 to exponential form", + "Output Program": [ + "n0 = 255.0\nn1 = 1.0\nn2 = 2.0\nt0 = 10.0 * 4.0\nt1 = n0 - 100.0\nt2 = t1 - 100.0\nt3 = t2 - t0\nanswer = t3 - 10.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "a batsman makes a score of 65 runs in the 17 th inning and thus increases his average by 3 . find his average after 17 th inning .", + "Output Program": [ + "n0 = 65.0\nn1 = 17.0\nn2 = 3.0\nn3 = 17.0\nt0 = n1 * n2\nt1 = n0 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "a student got twice as many sums wrong as he got right . if he attempted 54 sums in all , how many did he solve correctly ?", + "Output Program": [ + "n0 = 54.0\nt0 = 1.0 + 2.0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "the instructions state that deepthi needs 4 / 17 square yards of one type of material and 3 / 10 square yards of another type of material for a project . she buys exactly that amount . after finishing the project , however , she has 9 / 30 square yards left that she did not use . what is the total amount of square yards of material deepthi used ?", + "Output Program": [ + "n0 = 4.0\nn1 = 17.0\nn2 = 3.0\nn3 = 10.0\nn4 = 9.0\nn5 = 30.0\nt0 = n0 / n1\nt1 = 3.0 / 10.0\nt2 = n4 / n5\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "0.23529411764705882" + ], + "split": "train" + }, + { + "Input": "jerry \u2019 s average ( arithmetic mean ) score on the first 3 of 4 tests is 81 . if jerry wants to raise his average by 2 points , what score must he earn on the fourth test ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 81.0\nn3 = 2.0\nt0 = n2 + n3\nt1 = n0 * n2\nt2 = n1 * t0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "89" + ], + "split": "train" + }, + { + "Input": "a palindrome is a number that reads the same front - to - back as it does back - to - front ( e . g . 202 , 575 , 1991 , etc . ) p is the smallest integer greater than 300 that is both a prime and a palindrome . what is the sum of the digits of p ?", + "Output Program": [ + "n0 = 202.0\nn1 = 575.0\nn2 = 1991.0\nn3 = 300.0\n\nanswer = 3.0 + 3.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "if the number is decreased by 5 and divided by 7 the result is 7 . what would be the result if 24 is subtracted and divided by 10 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 7.0\nn2 = 7.0\nn3 = 24.0\nn4 = 10.0\nt0 = n1 * n1\nt1 = n0 + t0\nt2 = t1 - n3\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "45 x ? = 40 % of 900", + "Output Program": [ + "n0 = 45.0\nn1 = 40.0\nn2 = 900.0\nt0 = n1 / 100.0\nt1 = n2 * t0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "the sum of all two digit numbers divisible by 9 is", + "Output Program": [ + "n0 = 9.0\nt0 = n0 + n0\nt1 = n0 + t0\nt2 = t0 + t1\nt3 = n0 + t1\nt4 = t2 + t3\nt5 = n0 + t3\nt6 = t4 + t5\nt7 = n0 + t5\nt8 = t6 + t7\nt9 = n0 + t7\nt10 = t8 + t9\nt11 = n0 + t9\nt12 = t10 + t11\nt13 = n0 + t11\nt14 = t12 + t13\nt15 = n0 + t13\nt16 = t14 + t15\nt17 = n0 + t15\nanswer = t16 + t17\nprint(answer)" + ], + "Output Answer": [ + "585" + ], + "split": "train" + }, + { + "Input": "find the least number must be subtracted from 899830 so that remaining no . is divisible by 16 ?", + "Output Program": [ + "import math\nn0 = 899830.0\nn1 = 16.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "set a : { 1 , 3 , 4 , 6 , 9 , 12 , 15 } if 3 numbers are randomly selected from set a without replacement , what is the probability that the sum of the 3 numbers is divisible by 3 ?", + "Output Program": [ + "import math\nn0 = 1.0\nn1 = 3.0\nn2 = 4.0\nn3 = 6.0\nn4 = 9.0\nn5 = 12.0\nn6 = 15.0\nn7 = 3.0\nn8 = 3.0\nn9 = 3.0\nt0 = n0 + n2\nt1 = n1 + n2\nt2 = math.factorial(min(15, int(n1)))\nt3 = math.factorial(min(15, int(n2)))\nt4 = math.factorial(min(15, int(t0)))\nt5 = math.factorial(min(15, int(t1)))\nt6 = t3 * t2\nt7 = t0 - n1\nt8 = t5 / t6\nt9 = math.factorial(min(15, int(t7)))\nt10 = t9 * t2\nt11 = t4 / t10\nanswer = t11 / t8\nprint(answer)" + ], + "Output Answer": [ + "0.2857142857142857" + ], + "split": "train" + }, + { + "Input": "how many digits 2 ^ 200 has ?", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 200.0\nt0 = math.log(max(1e-5, n0), 2)\nt1 = math.log(max(1e-5, 10.0), 2)\nt2 = t0 / t1\nt3 = n1 * t2\nt4 = t3 + 1.0\nanswer = math.floor(t4)\nprint(answer)" + ], + "Output Answer": [ + "61" + ], + "split": "train" + }, + { + "Input": "the shopkeeper increased the price of a product by 25 % so that customer finds it difficult to purchase the required amount . but somehow the customer managed to purchase only 68 % of the required amount . what is the net difference in the expenditure on that product ?", + "Output Program": [ + "n0 = 25.0\nn1 = 68.0\nt0 = n0 + 100.0\nt1 = 100.0 * 100.0\nt2 = n1 * t0\nt3 = t1 - t2\nt4 = t3 * 100.0\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "if 25 % of ( x - y ) = 15 % of ( x + y ) , then what percent of x is y ?", + "Output Program": [ + "n0 = 25.0\nn1 = 15.0\nt0 = n0 + n1\nt1 = n0 - n1\nt2 = t1 / t0\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "the average weight of 3 men a , b and c is 84 kg . the average weight becomes 80 kg when d joins them . if e whose weight is 3 kg more than d joins the group replacing a , then the average weight of b , c , d and e becomes 79 kg . the weight of a is :", + "Output Program": [ + "n0 = 3.0\nn1 = 84.0\nn2 = 80.0\nn3 = 3.0\nn4 = 79.0\nt0 = n2 * 4.0\nt1 = n4 * 4.0\nt2 = n0 * n1\nt3 = t0 - t2\nt4 = n0 + t3\nt5 = t1 - t4\nanswer = t0 - t5\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "in 3 annual examinations , of which the aggregate marks of each was 500 , a student secured average marks 45 % and 55 % in the first and the second yearly examinations respectively . to secure 40 % average total marks , it is necessary for him in third yearly examination to secure marks :", + "Output Program": [ + "n0 = 3.0\nn1 = 500.0\nn2 = 45.0\nn3 = 55.0\nn4 = 40.0\nt0 = n0 * n1\nt1 = n1 * n3\nt2 = n1 * n2\nt3 = t1 / 100.0\nt4 = t2 / 100.0\nt5 = n4 * t0\nt6 = t3 + t4\nt7 = t5 / 100.0\nanswer = t7 - t6\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "a man has some hens and cows . if the number of heads be 46 and the number of feet equals 140 , then the number of hens will be :", + "Output Program": [ + "n0 = 46.0\nn1 = 140.0\nt0 = n0 * 4.0\nt1 = t0 - n1\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "if x is 20 percent greater than 52 , then x =", + "Output Program": [ + "n0 = 20.0\nn1 = 52.0\nt0 = n0 / 100.0\nt1 = n1 * t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "62.4" + ], + "split": "train" + }, + { + "Input": "a girl was asked to multiply a certain number by 43 . she multiplied it by 34 and got his answer less than the correct one by 1215 . find the number to be multiplied .", + "Output Program": [ + "n0 = 43.0\nn1 = 34.0\nn2 = 1215.0\nt0 = n0 - n1\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "135" + ], + "split": "train" + }, + { + "Input": "if x + y = - 10 , and x = 25 / y , what is the value of x ^ 2 + y ^ 2 ?", + "Output Program": [ + "n0 = 10.0\nn1 = 25.0\nn2 = 2.0\nn3 = 2.0\nt0 = n1 * n2\nt1 = n0**min(n2, 5)\nanswer = t1 - t0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "a basketball team composed of 12 players scored 100 points in a particular contest . if none of the individual players scored fewer than 7 points , what is the greatest number of points l that an individual player might have scored ?", + "Output Program": [ + "n0 = 12.0\nn1 = 100.0\nn2 = 7.0\nt0 = n0 * n2\nt1 = n1 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "find the value of log y ( x 4 ) if logx ( y 3 ) = 2", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 2.0\n\nanswer = n0 + n2\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "a 100 - litre mixture of milk and water contains 36 litres of milk . ' x ' litres of this mixture is removed and replaced with an equal quantum of water . if the process is repeated once , then the concentration of the milk stands reduced at 16 % . what is the value of x ?", + "Output Program": [ + "import math\nn0 = 100.0\nn1 = 36.0\nn2 = 16.0\nt0 = n2 / n1\nt1 = math.sqrt(max(0, t0))\nt2 = 1.0 - t1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "33.333333333333336" + ], + "split": "train" + }, + { + "Input": "a man \u00e2 \u20ac \u2122 s current age is ( 2 / 5 ) of the age of his father . after 5 years , he will be ( 1 / 2 ) of the age of his father . what is the age of father at now ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 5.0\nn3 = 1.0\nn4 = 2.0\nt0 = n3 / n0\nt1 = n0 / n1\nt2 = n2 * t0\nt3 = t0 - t1\nt4 = n2 - t2\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "25.000000000000007" + ], + "split": "train" + }, + { + "Input": "if taxi fares were $ 1.00 for the first 1 / 5 mile and $ 0.40 for each 1 / 5 mile there after , then the taxi fare for a 3 - mile ride was", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 5.0\nn3 = 0.4\nn4 = 1.0\nn5 = 5.0\nn6 = 3.0\nt0 = n1 / n2\nt1 = n6 / t0\nt2 = t1 - n1\nt3 = n3 * t2\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "6.6000000000000005" + ], + "split": "train" + }, + { + "Input": "the batting average of a particular batsman is 60 runs in 46 innings . if the difference in his highest and lowest score is 180 runs and his average excluding these two innings is 58 runs , find his highest score .", + "Output Program": [ + "n0 = 60.0\nn1 = 46.0\nn2 = 180.0\nn3 = 58.0\nt0 = n0 * n1\nt1 = n1 - 2.0\nt2 = n3 * t1\nt3 = t0 - t2\nt4 = n2 + t3\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "194" + ], + "split": "train" + }, + { + "Input": "the average weight of 19 students is 15 kg . by the admission of a new student the average weight is reduced to 14.8 kg . the weight of the new student is ?", + "Output Program": [ + "n0 = 19.0\nn1 = 15.0\nn2 = 14.8\nt0 = n0 + 1.0\nt1 = n0 * n1\nt2 = n2 * t0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "the total age of a and b is 16 years more than the total age of b and c . c is how many year younger than a", + "Output Program": [ + "n0 = 16.0\n\nanswer = n0 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "a batsman makes a score of 87 runs in the 17 th match and thus increases his average by 3 . find his average after 17 th match", + "Output Program": [ + "n0 = 87.0\nn1 = 17.0\nn2 = 3.0\nn3 = 17.0\nt0 = n1 * n2\nt1 = n0 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "39" + ], + "split": "train" + }, + { + "Input": "having received his weekly allowance , a student spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 1.20 at the candy store . what is this student \u2019 s weekly allowance ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 1.2\nt0 = n0 * n1\nt1 = n2 * t0\nanswer = t1 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "4.5" + ], + "split": "train" + }, + { + "Input": "$ 364 is divided among a , b , and c so that a receives half as much as b , and b receives half as much as c . how much money is c ' s share ?", + "Output Program": [ + "n0 = 364.0\nt0 = 1.0 / 2.0\nt1 = t0 + 1.0\nt2 = t1 + 2.0\nt3 = n0 / t2\nanswer = t3 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "208" + ], + "split": "train" + }, + { + "Input": "a man saves 20 % of his monthly salary . if an account of dearness of things he is to increase his monthly expenses by 10 % , he is only able to save rs . 500 per month . what is his monthly salary ?", + "Output Program": [ + "n0 = 20.0\nn1 = 10.0\nn2 = 500.0\nt0 = n1 / 100.0\nt1 = n2 * 100.0\nt2 = 100.0 - n0\nt3 = t0 * t2\nt4 = t3 + t2\nt5 = 100.0 - t4\nanswer = t1 / t5\nprint(answer)" + ], + "Output Answer": [ + "4166.666666666667" + ], + "split": "train" + }, + { + "Input": "what is the minimum value of | x - 4 | + | x + 7 | + | x - 5 | ?", + "Output Program": [ + "n0 = 4.0\nn1 = 7.0\nn2 = 5.0\n\nanswer = n1 + n2\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "kate and danny each have $ 10 . together , they flip a fair coin 5 times . every time the coin lands on heads , kate gives danny $ 1 . every time the coin lands on tails , danny gives kate $ 1 . after the 5 coin flips , what is the probability that kate has more than $ 10 but less than $ 15 ?", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 5.0\nn2 = 1.0\nn3 = 1.0\nn4 = 5.0\nn5 = 10.0\nn6 = 15.0\nt0 = math.factorial(min(15, int(n1)))\nt1 = math.factorial(min(15, int(4.0)))\nt2 = math.factorial(min(15, int(1.0)))\nt3 = math.factorial(min(15, int(3.0)))\nt4 = math.factorial(min(15, int(2.0)))\nt5 = 2.0**min(n1, 5)\nt6 = t1 * t2\nt7 = t3 * t4\nt8 = t0 / t6\nt9 = t0 / t7\nt10 = t8 + t9\nanswer = t10 / t5\nprint(answer)" + ], + "Output Answer": [ + "0.46875" + ], + "split": "train" + }, + { + "Input": "when 1 / 10 percent of 7000 is subtracted from 1 / 10 of 7000 , the difference is", + "Output Program": [ + "n0 = 1.0\nn1 = 10.0\nn2 = 7000.0\nn3 = 1.0\nn4 = 10.0\nn5 = 7000.0\nt0 = n1 * n2\nanswer = t0 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "700" + ], + "split": "train" + }, + { + "Input": "a line has a slope of 3 / 4 and intersects the point ( - 12 , - 39 ) . at which point e does this line intersect the x - axis ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 12.0\nn3 = 39.0\nt0 = n0 / n1\nt1 = -n3\nt2 = -n2\nt3 = t0 * t2\nt4 = t1 - t3\nt5 = t4 / t0\nt6 = -t5\nanswer = t6 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "train" + }, + { + "Input": "a , b and c invest in the ratio of 3 : 4 : 5 . the percentage of return on their investments are in the ratio of 6 : 5 : 4 . find the total earnings , if b earns rs . 100 more than a :", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 5.0\nn3 = 6.0\nn4 = 5.0\nn5 = 4.0\nn6 = 100.0\nt0 = n0 * n3\nt1 = n1 * n2\nt2 = t0 + t1\nt3 = t1 - t0\nt4 = t2 + t1\nt5 = n6 / t3\nanswer = t4 * t5\nprint(answer)" + ], + "Output Answer": [ + "2900" + ], + "split": "train" + }, + { + "Input": "what number times ( 1 \u2044 2 ) ^ 2 will give the value of 2 ^ 3 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 2.0\nn3 = 2.0\nn4 = 3.0\nt0 = n1**min(n1, 5)\nt1 = n1**min(n4, 5)\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "the average marks of a class of 20 students is 40 and that of another class of 50 students is 60 . find the average marks of all the students ?", + "Output Program": [ + "n0 = 20.0\nn1 = 40.0\nn2 = 50.0\nn3 = 60.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "54.285714285714285" + ], + "split": "train" + }, + { + "Input": "in shop there are 10 bulbs , a total of 4 are defective . if a customer buys 4 bulbs selected at random from the box , what is the probability that neither bulbs will be defective ?", + "Output Program": [ + "n0 = 10.0\nn1 = 4.0\nn2 = 4.0\nt0 = n0 - n1\nt1 = n1 / t0\nt2 = t0 / n0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "0.06666666666666665" + ], + "split": "train" + }, + { + "Input": "employees of a certain company are each to receive a unique 5 - digit identification code consisting of the digits 0 , 1 , 2 , 3 , and 4 such that no digit is used more than once in any given code . in valid codes , the second digit in the code is exactly twice the first digit . how many valid codes are there ?", + "Output Program": [ + "n0 = 5.0\nn1 = 0.0\nn2 = 1.0\nn3 = 2.0\nn4 = 3.0\nn5 = 4.0\nt0 = 2.0 * 3.0\nanswer = n3 * t0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "if p is the product of the integers from 1 to 34 , inclusive , what is the greatest integer k for which 3 ^ k is a factor of p ?", + "Output Program": [ + "n0 = 1.0\nn1 = 34.0\nn2 = 3.0\nt0 = n2 * 4.0\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "the sum of the squares of the first 15 positive integers ( 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + . . . + 15 ^ 2 ) is equal to 1280 . what is the sum of the squares of the second 15 positive integers ( 16 ^ 2 + 17 ^ 2 + 18 ^ 2 + . . . + 30 ^ 2 ) ?", + "Output Program": [ + "n0 = 15.0\nn1 = 1.0\nn2 = 2.0\nn3 = 2.0\nn4 = 2.0\nn5 = 3.0\nn6 = 2.0\nn7 = 15.0\nn8 = 2.0\nn9 = 1280.0\nn10 = 15.0\nn11 = 16.0\nn12 = 2.0\nn13 = 17.0\nn14 = 2.0\nn15 = 18.0\nn16 = 2.0\nn17 = 30.0\nn18 = 2.0\nt0 = n17 + n1\nt1 = n5 + n5\nt2 = n17 * n2\nt3 = t2 + n1\nt4 = n17 * t0\nt5 = t3 * t4\nt6 = t5 / t1\nanswer = t6 - n9\nprint(answer)" + ], + "Output Answer": [ + "8175" + ], + "split": "train" + }, + { + "Input": "a number exceeds by 25 from its 3 / 8 part . then the number is ?", + "Output Program": [ + "n0 = 25.0\nn1 = 3.0\nn2 = 8.0\nt0 = n0 * n2\nt1 = n2 - n1\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "in an it company , there are a total of 70 employees including 50 programmers . the number of male employees is 80 , including 35 male programmers . how many employees must be selected to guaranty that we have 3 programmers of the same sex ?", + "Output Program": [ + "n0 = 70.0\nn1 = 50.0\nn2 = 80.0\nn3 = 35.0\nn4 = 3.0\nt0 = n2 - n0\nt1 = n1 - n3\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "the age of somu is one - third his father ' s . 9 years back he was one - fifth of his father ' s age . what is his persent age ?", + "Output Program": [ + "n0 = 9.0\nt0 = 1.0 + 4.0\nt1 = n0 * t0\nt2 = t0 - 3.0\nt3 = t1 - n0\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "at a certain committee meeting only associate professors and assistant professors are present . each associate professor has brought 2 pencils and 1 chart to the meeting , while each assistant professor has brought 1 pencil and 2 charts . if a total of 11 pencils and 16 charts have been brought to the meeting , how many people are present ?", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 1.0\nn3 = 2.0\nn4 = 11.0\nn5 = 16.0\nt0 = n4 + n5\nt1 = n0 + n1\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "the element being searched for is not found in an array of 100 elements . what is the average number of comparisons needed in a sequential search to determine that the element is not there , if the elements are completely unordered ?", + "Output Program": [ + "import math\nn0 = 100.0\nt0 = n0 + 1.0\nt1 = n0 / 2.0\nt2 = t0 * t1\nt3 = t2 / n0\nt4 = math.floor(t3)\nanswer = t4 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "if a person walks at 12 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance traveled by him is :", + "Output Program": [ + "n0 = 12.0\nn1 = 10.0\nn2 = 20.0\nt0 = n0 - n1\nt1 = n2 / t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "an order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth . what be the cost of a carpet whose length and breadth are 40 % more and 25 % more respectively than the first carpet . given that the ratio of carpet is rs . 45 per sq . m ?", + "Output Program": [ + "n0 = 6.0\nn1 = 1.44\nn2 = 40.0\nn3 = 25.0\nn4 = 45.0\nt0 = n2 + 100.0\nt1 = n3 + 100.0\nt2 = n0 * n1\nt3 = t0 / 100.0\nt4 = t1 / 100.0\nt5 = t3 * t2\nt6 = n0 * t4\nt7 = t5 * t6\nanswer = n4 * t7\nprint(answer)" + ], + "Output Answer": [ + "4082.4" + ], + "split": "train" + }, + { + "Input": "in a office work is distribute between p persons . if 1 / 7 members are absent then work increased for each person is ?", + "Output Program": [ + "n0 = 1.0\nn1 = 7.0\nt0 = n1 * 100.0\nt1 = n1 - n0\nt2 = t0 / t1\nanswer = t2 - 100.0\nprint(answer)" + ], + "Output Answer": [ + "16.66666666666667" + ], + "split": "train" + }, + { + "Input": "the average marks of 10 students in a class is 100 . but a student mark is wrongly noted as 60 instead of 10 then find the correct average marks ?", + "Output Program": [ + "n0 = 10.0\nn1 = 100.0\nn2 = 60.0\nn3 = 10.0\nt0 = n0 * n1\nt1 = t0 - n2\nt2 = n3 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "95" + ], + "split": "train" + }, + { + "Input": "carrie likes to buy t - shirts at the local clothing store . they cost $ 9.95 each . one day , she bought 20 t - shirts . how much money did she spend ?", + "Output Program": [ + "import math\nn0 = 9.95\nn1 = 20.0\nt0 = n0 * n1\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "199" + ], + "split": "train" + }, + { + "Input": "in a mixed college 160 students are there in one class . out of this 160 students 5 / 8 students are girls . how many boys are there ?", + "Output Program": [ + "n0 = 160.0\nn1 = 160.0\nn2 = 5.0\nn3 = 8.0\nt0 = n0 / n3\nanswer = t0 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "if 10 gallons of grape juice are added to 50 gallons of a mixture , which contains 10 percent grape juice then what percent of the resulting mixture is grape juice ?", + "Output Program": [ + "n0 = 10.0\nn1 = 50.0\nn2 = 10.0\nt0 = n0 + n1\nt1 = n2 / 100.0\nt2 = n1 * t1\nt3 = n0 + t2\nt4 = t3 / t0\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "an artist who needs to buy only paint and canvas finds that the cost of canvas has decreased by 40 percent and the cost of paint has decreased by 60 percent . if paint previously accounted for 4 times as much of the expense of painting as did canvas , by what percent did the total cost for paint and canvas decrease ?", + "Output Program": [ + "n0 = 40.0\nn1 = 60.0\nn2 = 4.0\nt0 = n2 + 1.0\nt1 = n1 / 100.0\nt2 = n0 / 100.0\nt3 = n2 * t2\nt4 = t1 + t3\nt5 = t4 / t0\nt6 = 1.0 - t5\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "55.99999999999999" + ], + "split": "train" + }, + { + "Input": "if v is the product of the integers from 1 to 30 , inclusive , what is the greatest integer k for which 3 ^ k is a factor of v ?", + "Output Program": [ + "import math\nn0 = 1.0\nn1 = 30.0\nn2 = 3.0\nt0 = n1 / n2\nt1 = n2**min(2.0, 5)\nt2 = n2**min(n2, 5)\nt3 = n1 / t1\nt4 = n1 / t2\nt5 = math.floor(t3)\nt6 = math.floor(t4)\nt7 = t0 + t5\nanswer = t7 + t6\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "for a certain exam , a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean . what was the mean score e for the exam ?", + "Output Program": [ + "n0 = 58.0\nn1 = 2.0\nn2 = 98.0\nn3 = 3.0\nt0 = n1 + n3\nt1 = n0 * n3\nt2 = n1 * n2\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "74" + ], + "split": "train" + }, + { + "Input": "evaluate 35 / . 07", + "Output Program": [ + "n0 = 35.0\nn1 = 7.0\nt0 = n1 / 100.0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "499.99999999999994" + ], + "split": "train" + }, + { + "Input": "the average weight of 20 girls increases by 2 kg when a new girl comes in place of one of them weighing 40 kg . what might be the weight of the new girl ?", + "Output Program": [ + "n0 = 20.0\nn1 = 2.0\nn2 = 40.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "if k is an integer and 0.0010101 x 10 ^ k is greater than 100 , what is the least possible value of k ?", + "Output Program": [ + "import math\nn0 = 0.0010101\nn1 = 10.0\nn2 = 100.0\nt0 = n2 / n0\nt1 = math.log(max(1e-5, n1), 2)\nt2 = math.log(max(1e-5, t0), 2)\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "4.9956356288922485" + ], + "split": "train" + }, + { + "Input": "gold is 19 times as heavy as water and copper is 9 times as heavy as water . in what ratio should these be mixed to get an alloy 18 times as heavy as water ?", + "Output Program": [ + "n0 = 19.0\nn1 = 9.0\nn2 = 18.0\nt0 = n2 - n1\nt1 = n0 - n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "in the coordinate plane a slope of the line k is 0.5 times the y - intercept of the line k . what is the x - intercept of the line k ?", + "Output Program": [ + "n0 = 0.5\n\nanswer = 1.0 / n0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "the sum of all the digits of the integers from 18 to 21 inclusive is 24 ( 1 + 8 + 1 + 9 + 2 + 0 + 2 + 1 = 24 ) . what is the sum r of all the digits of the integers from 0 to 99 inclusive ?", + "Output Program": [ + "n0 = 18.0\nn1 = 21.0\nn2 = 24.0\nn3 = 1.0\nn4 = 8.0\nn5 = 1.0\nn6 = 9.0\nn7 = 2.0\nn8 = 0.0\nn9 = 2.0\nn10 = 1.0\nn11 = 24.0\nn12 = 0.0\nn13 = 99.0\nt0 = n6 + n3\nt1 = 10.0 * n7\nt2 = n6 * t0\nt3 = t2 / n7\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "900" + ], + "split": "train" + }, + { + "Input": "when positive integer x is divided by positive integer y , the remainder is 9 . if x / y = 96.12 , what is the value of y ?", + "Output Program": [ + "import math\nn0 = 9.0\nn1 = 96.12\nt0 = math.floor(n1)\nt1 = n1 - t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "74.99999999999716" + ], + "split": "train" + }, + { + "Input": "if the sum of the 4 th term and the 12 th term of an arithmetic progression is 24 , what is the sum of the first 15 terms of the progression ?", + "Output Program": [ + "n0 = 4.0\nn1 = 12.0\nn2 = 24.0\nn3 = 15.0\nt0 = n3 / 2.0\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "180" + ], + "split": "train" + }, + { + "Input": "how many 4 - digit positive integers are there , where each digit is positive , and no 3 adjacent digits are same ?", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nt0 = 3.0 + 4.0\nt1 = n0 + n0\nt2 = n1 * n1\nt3 = t0 * t0\nt4 = t1 * t2\nanswer = t3 * t4\nprint(answer)" + ], + "Output Answer": [ + "3528" + ], + "split": "train" + }, + { + "Input": "15 lts are taken of from a container full of liquid a and replaced with liquid b . again 15 more lts of the mixture is taken and replaced with liquid b . after this process , if the container contains liquid a and b in the ratio 9 : 16 , what is the capacity of the container w ?", + "Output Program": [ + "import math\nn0 = 15.0\nn1 = 15.0\nn2 = 9.0\nn3 = 16.0\nt0 = n2 + n3\nt1 = n2 / t0\nt2 = math.sqrt(max(0, t1))\nt3 = 1.0 - t2\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "37.5" + ], + "split": "train" + }, + { + "Input": "of the families in city x in 1904 , 50 percent owned a personal computer . the number of families in city x owning a computer in 1908 was 30 percent greater than it was in 1904 , and the total number of families in city x was 5 percent greater in 1908 than it was in 1904 . what percent of the families in city x owned a personal computer in 1908 ?", + "Output Program": [ + "n0 = 1904.0\nn1 = 50.0\nn2 = 1908.0\nn3 = 30.0\nn4 = 1904.0\nn5 = 5.0\nn6 = 1908.0\nn7 = 1904.0\nn8 = 1908.0\nt0 = n3 + 100.0\nt1 = n5 + 100.0\nt2 = n1 * t0\nt3 = t2 / 100.0\nt4 = t3 / t1\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "61.904761904761905" + ], + "split": "train" + }, + { + "Input": "4 / 15 of 5 / 7 of a number is greater than 4 / 9 of 2 / 5 of the same number by 8 . what is half of that number ?", + "Output Program": [ + "n0 = 4.0\nn1 = 15.0\nn2 = 5.0\nn3 = 7.0\nn4 = 4.0\nn5 = 9.0\nn6 = 2.0\nn7 = 5.0\nn8 = 8.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = n6 / n2\nt3 = n0 / n5\nt4 = t0 * t1\nt5 = t2 * t3\nt6 = t4 - t5\nt7 = n8 / t6\nanswer = t7 / n6\nprint(answer)" + ], + "Output Answer": [ + "315.00000000000045" + ], + "split": "train" + }, + { + "Input": "what is the total number of y integers between 100 and 200 that are divisible by 3 ?", + "Output Program": [ + "import math\nn0 = 100.0\nn1 = 200.0\nn2 = 3.0\nt0 = n1 / n2\nt1 = n0 / n2\nt2 = math.floor(t0)\nt3 = math.floor(t1)\nt4 = n2 * t2\nt5 = n2 * t3\nt6 = n2 + t5\nt7 = t4 - t6\nt8 = n2 + t7\nanswer = t8 / n2\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 136 games will be played during the tournament . find the number of participants .", + "Output Program": [ + "import math\nn0 = 136.0\nt0 = n0 * 2.0\nt1 = t0 * 4.0\nt2 = t1 + 1.0\nt3 = math.sqrt(max(0, t2))\nt4 = t3 + 1.0\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "for the past n days , the average ( arithmetic mean ) daily production at a company was 40 units . if today ' s production of 90 units raises the average to 45 units per day , what is the value of n ?", + "Output Program": [ + "n0 = 40.0\nn1 = 90.0\nn2 = 45.0\nt0 = n1 - n0\nt1 = n2 - n0\nt2 = t0 / t1\nanswer = t2 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "in the johnsons ' monthly budget , the dollar amounts allocated to household expenses , food , and miscellaneous items are in the ratio 5 : 4 : 1 , respectively . if the total amount allocated to these 3 categories is $ 1800 , what is the amount allocated to food ?", + "Output Program": [ + "n0 = 5.0\nn1 = 4.0\nn2 = 1.0\nn3 = 3.0\nn4 = 1800.0\nt0 = n0 + n1\nt1 = n2 + t0\nt2 = n4 / t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "720" + ], + "split": "train" + }, + { + "Input": "one ton has 2600 pounds , and one pound has 16 ounces . how many packets containing wheat weighing 16 pounds and 4 ounces each would totally fill a gunny bag of capacity 13 tons ?", + "Output Program": [ + "n0 = 2600.0\nn1 = 16.0\nn2 = 16.0\nn3 = 4.0\nn4 = 13.0\nt0 = n0 * n4\nt1 = n1 * n1\nt2 = n3 + t1\nt3 = n1 * t0\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "2080" + ], + "split": "train" + }, + { + "Input": "of the female students at barkely university , 5 / 6 are on the honor roll . of the male students , 2 / 3 are on the honor roll . if 2 / 5 of the students are female , what fraction of all the students are on the honor roll ?", + "Output Program": [ + "n0 = 5.0\nn1 = 6.0\nn2 = 2.0\nn3 = 3.0\nn4 = 2.0\nn5 = 5.0\nt0 = n0 * n2\nt1 = n0 * n3\nt2 = n2 * t0\nt3 = n2 * t1\nt4 = n2 + t2\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.7333333333333333" + ], + "split": "train" + }, + { + "Input": "if x is 20 percent greater than 88 , then x =", + "Output Program": [ + "n0 = 20.0\nn1 = 88.0\nt0 = n0 / 100.0\nt1 = n1 * t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "105.6" + ], + "split": "train" + }, + { + "Input": "set a consists of all the prime numbers between 15 and 36 . what is the range of set a ?", + "Output Program": [ + "n0 = 15.0\nn1 = 36.0\nt0 = n0 + 4.0\nt1 = n1 - 2.0\nt2 = t0 + 1.0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "5 % people of a village in sri lanka died by bombardment , 15 % of the remainder left the village on account of fear . if now the population is reduced to 3294 , how much was it in the beginning ?", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 15.0\nn2 = 3294.0\nt0 = 100.0 - n0\nt1 = 100.0 - n1\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = t2 * t3\nt5 = n2 / t4\nanswer = math.floor(t5)\nprint(answer)" + ], + "Output Answer": [ + "4079" + ], + "split": "train" + }, + { + "Input": "on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 350 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?", + "Output Program": [ + "n0 = 350.0\n\nanswer = n0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "700" + ], + "split": "train" + }, + { + "Input": "every digit of a number written in binary is either 0 or 1 . to translate a number from binary , multiply the nth digit ( reading from right to left ) by 2 ^ ( n - 1 ) what is the largest prime number ( written in binary ) that is a factor of both 10010000 and 100100000 ?", + "Output Program": [ + "n0 = 0.0\nn1 = 1.0\nn2 = 2.0\nn3 = 1.0\nn4 = 10010000.0\nn5 = 100100000.0\nt0 = n5 / n4\nanswer = t0 + 1000.0\nprint(answer)" + ], + "Output Answer": [ + "1010" + ], + "split": "train" + }, + { + "Input": "the product of a and b is equal to 1 more than twice the sum of a and b . if b = 7 , what is the value of b - a ?", + "Output Program": [ + "n0 = 1.0\nn1 = 7.0\nt0 = n1 * 2.0\nt1 = n1 - 2.0\nt2 = n0 + t0\nt3 = t2 / t1\nanswer = n1 - t3\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "12 is 6 % of a , and 6 is 12 % of b . c equals b / a . what is the value of c ?", + "Output Program": [ + "n0 = 12.0\nn1 = 6.0\nn2 = 6.0\nn3 = 12.0\nt0 = n1 / n0\nt1 = n0 / n1\nt2 = t0 * 100.0\nt3 = t1 * 100.0\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.25" + ], + "split": "train" + }, + { + "Input": "working alone , printers x , y , and z can do a certain printing job , consisting of a large number of pages , in 15 , 10 , and 20 hours , respectively . what is the ratio of the time it takes printer x to do the job , working alone at its rate , to the time it takes printers y and z to do the job , working together at their individual rates ?", + "Output Program": [ + "n0 = 15.0\nn1 = 10.0\nn2 = 20.0\nt0 = 1.0 / n1\nt1 = 1.0 / n2\nt2 = t0 + t1\nt3 = 1.0 / t2\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "2.25" + ], + "split": "train" + }, + { + "Input": "a team of 8 persons joins in a shooting competition . the best marksman scored 85 points . if he had scored 92 points , the average score for the team would have been 84 . the number of points , the team scored was", + "Output Program": [ + "n0 = 8.0\nn1 = 85.0\nn2 = 92.0\nn3 = 84.0\nt0 = n0 * n3\nt1 = n1 + t0\nanswer = t1 - n2\nprint(answer)" + ], + "Output Answer": [ + "665" + ], + "split": "train" + }, + { + "Input": "if ( x + 3 ) ^ 2 / ( 3 x + 65 ) = 2 , then the difference between the two possible values of x is :", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 2.0\nn2 = 3.0\nn3 = 65.0\nn4 = 2.0\nt0 = n4 * n3\nt1 = n0 * n0\nt2 = t0 - t1\nt3 = math.sqrt(max(0, t2))\nanswer = t3 * n1\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "if there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city , find the number of 4 wheelers parked there if the total number of wheels is 70 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 4.0\nn3 = 70.0\nt0 = n3 - n0\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "a dog is tied to a tree by a long nylon cord . if the dog runs from the due north side of the tree to the due south side of the tree with the cord extended to its full length at all items , and the dog ran approximately 30 feet , what was the approximate length of the nylon cord e , in feet ?", + "Output Program": [ + "n0 = 30.0\n\nanswer = n0 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "a will was written such that an estate would be divided among 3 guys with the remainder donated to charity . one stipulation in the will is that no one from the guys can receive an amount within 30 % of another ' s amount . if one of the guys received $ 20000 , what is the smallest possible range between the highest and lowest amounts ( rounded to the nearest dollar ) among the 3 guys ?", + "Output Program": [ + "n0 = 3.0\nn1 = 30.0\nn2 = 20000.0\nn3 = 3.0\n\nanswer = n2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "10000" + ], + "split": "train" + }, + { + "Input": "mukesh borrowed a sum of rs . 10000 at simple interest from a bank . after two years he takes rs . 12000 more as loan and discharge all the debt at the end of next 3 years depositing rs . 27160 to the bank . what is the rate of interest per annum ?", + "Output Program": [ + "n0 = 10000.0\nn1 = 12000.0\nn2 = 3.0\nn3 = 27160.0\nt0 = n0 + n1\nt1 = n2 + 2.0\nt2 = n1 * n2\nt3 = n0 * t1\nt4 = n3 - t0\nt5 = t3 + t2\nt6 = t4 / t5\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "here is a simple arithmetical puzzle in his own flowery , poetical language . if one - fifth of a hive of bees flew to the badamba flower , one - third flew to the slandbara , 3 times the difference of these two numbers flew to an arbour , and one bee continued to fly about , attracted on each side by the fragrant ketaki and malati , what was the total number of bees ?", + "Output Program": [ + "n0 = 3.0\nt0 = 1.0 + 4.0\nt1 = 1.0 / 3.0\nt2 = 1.0 / t0\nt3 = t2 + t1\nt4 = t1 - t2\nt5 = n0 * t4\nt6 = t3 + t5\nt7 = 1.0 - t6\nanswer = 1.0 / t7\nprint(answer)" + ], + "Output Answer": [ + "14.999999999999979" + ], + "split": "train" + }, + { + "Input": "product of two co - prime numbers is 117 . their l . c . m should be", + "Output Program": [ + "n0 = 117.0\n\nanswer = n0 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "117" + ], + "split": "train" + }, + { + "Input": "if to a certain number , 720 be added , and the sum be divided by 125 ; the quotient will be equal to 7392 divided by 462 . what is that number ?", + "Output Program": [ + "n0 = 720.0\nn1 = 125.0\nn2 = 7392.0\nn3 = 462.0\nt0 = n1 * n2\nt1 = n0 * n3\nt2 = t0 - t1\nanswer = t2 / n3\nprint(answer)" + ], + "Output Answer": [ + "1280" + ], + "split": "train" + }, + { + "Input": "a certain debt will be paid in 52 installments from january 1 to december 31 of a certain year . each of the first 25 payments is to be $ 500 ; each of the remaining payments is to be $ 100 more than each of the first 25 payments . what is the average ( arithmetic mean ) payment that will be made on the debt for the year ?", + "Output Program": [ + "n0 = 52.0\nn1 = 1.0\nn2 = 31.0\nn3 = 25.0\nn4 = 500.0\nn5 = 100.0\nn6 = 25.0\nt0 = n4 + n5\nt1 = n3 * n4\nt2 = n0 - n3\nt3 = t0 * t2\nt4 = t1 + t3\nanswer = t4 / n0\nprint(answer)" + ], + "Output Answer": [ + "551.9230769230769" + ], + "split": "train" + }, + { + "Input": "a certain school implemented a reading program for its students , with the goal of getting each student to read 4 books per month year - round . if the school has c classes made up of s students in each class , how many books will the entire student body read in one year ?", + "Output Program": [ + "n0 = 4.0\n\nanswer = n0 * 12.0\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "right triangle pqr is to be constructed in the xy - plane so that the right angle is at p and pr is parallel to the x - axis . the x - and y - coordinates of p , q , and r are to be integers that satisfy the inequalities - 4 < = x < = 5 and 6 < = y < = 16 . how many different triangles with these properties could be constructed ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 6.0\nn3 = 16.0\nt0 = n0 + n2\nt1 = n3 - n1\nt2 = 10.0 - 1.0\nt3 = t0 * t1\nt4 = t3 * t2\nanswer = t4 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "9900" + ], + "split": "train" + }, + { + "Input": "a batsman makes a score of 50 runs in the 17 th inning and thus increases his averages by 2 . what is his average after 17 th inning ?", + "Output Program": [ + "n0 = 50.0\nn1 = 17.0\nn2 = 2.0\nn3 = 17.0\nt0 = n1 * n2\nt1 = n0 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "if 0.12 \u00f7 x 2 = 12 , than x = ?", + "Output Program": [ + "import math\nn0 = 0.12\nn1 = 2.0\nn2 = 12.0\nt0 = n0 / n2\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "0.1" + ], + "split": "train" + }, + { + "Input": "a part - time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee ' s total income did not change . by what percent should the number of hours worked be increased ?", + "Output Program": [ + "n0 = 20.0\nt0 = 10.0 * 4.0\nt1 = 100.0 - n0\nt2 = t1 / 100.0\nt3 = t2 * 10.0\nt4 = t0 / t3\nt5 = t4 - 4.0\nt6 = t5 / 4.0\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "patrick purchased 60 pencils and sold them at a loss equal to the selling price of 20 pencils . the cost of 60 pencils is how many times the selling price of 60 pencils ?", + "Output Program": [ + "n0 = 60.0\nn1 = 20.0\nn2 = 60.0\nn3 = 60.0\nt0 = n0 + n1\nt1 = n0 / t0\nanswer = 1 / t1\nprint(answer)" + ], + "Output Answer": [ + "1.3333333333333333" + ], + "split": "train" + }, + { + "Input": "in a group of 800 people , 1 / 5 play at least one instrument , 128 play two or more . what is the probability that one student play exactly one instrument ?", + "Output Program": [ + "n0 = 800.0\nn1 = 1.0\nn2 = 5.0\nn3 = 128.0\nt0 = n0 * n1\nt1 = t0 / n2\nt2 = t1 - n3\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.04" + ], + "split": "train" + }, + { + "Input": "a pharmaceutical company received $ 7 million in royalties on the first $ 20 million in sales of the generic equivalent of one of its products and then $ 9 million in royalties on the next $ 108 million in sales . by approximately what percent did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 108 million in sales ?", + "Output Program": [ + "n0 = 7.0\nn1 = 20.0\nn2 = 9.0\nn3 = 108.0\nn4 = 20.0\nn5 = 108.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = t0 * 100.0\nt3 = t1 * 100.0\nt4 = t2 - t3\nt5 = t4 / t2\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "76.1904761904762" + ], + "split": "train" + }, + { + "Input": "what is the decimal equivalent of ( 1 / 9 ) ^ 2 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 9.0\nn2 = 2.0\nt0 = n0 / n1\nanswer = t0**min(n2, 5)\nprint(answer)" + ], + "Output Answer": [ + "0.012345679012345678" + ], + "split": "train" + }, + { + "Input": "elena \u2019 s bread recipe calls for 3 ounces of butter for each 4 cups of flour used . she needs to make 4 times the original recipe . if 12 ounces of butter is used , then how many cups of flour are needed ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 4.0\nn3 = 12.0\n\nanswer = n1 * n2\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "the average marks of 10 students in a class is 100 . but a student mark is wrongly noted as 50 instead of 10 then find the correct average marks ?", + "Output Program": [ + "n0 = 10.0\nn1 = 100.0\nn2 = 50.0\nn3 = 10.0\nt0 = n0 * n1\nt1 = t0 - n2\nt2 = n3 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "96" + ], + "split": "train" + }, + { + "Input": "if the price of petrol increases by 25 , by how much must a user cut down his consumption so that his expenditure on petrol remains constant ?", + "Output Program": [ + "n0 = 25.0\nt0 = n0 + 100.0\nt1 = 100.0 / t0\nt2 = 1.0 - t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "19.999999999999996" + ], + "split": "train" + }, + { + "Input": "there are 10 players in a chess group , and each player plays each of the others once . given that each game is played by two players , how many total games will be played ?", + "Output Program": [ + "n0 = 10.0\nt0 = n0 - 1.0\nt1 = n0 * t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "if the arithmetic mean of p and q is 10 and the arithmetic mean of q and r is 26 , what is the value of r - p ?", + "Output Program": [ + "n0 = 10.0\nn1 = 26.0\nt0 = n1 * 2.0\nt1 = n0 * 2.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "the number 189 is equal to the sum of the cubes of two integers . what is the product of those integers ?", + "Output Program": [ + "import math\nn0 = 189.0\nt0 = n0 / 2.0\nt1 = 1.0 / 3.0\nt2 = t0**min(t1, 5)\nt3 = math.floor(t2)\nt4 = t3**min(3.0, 5)\nt5 = n0 - t4\nt6 = t5**min(t1, 5)\nanswer = t3 * t6\nprint(answer)" + ], + "Output Answer": [ + "19.999999999999996" + ], + "split": "train" + }, + { + "Input": "in the biology lab of ` ` jefferson ' ' high school there are 0.036 * 10 ^ 5 germs , equally divided among 36000 * 10 ^ ( - 3 ) petri dishes . how many germs live happily in a single dish ?", + "Output Program": [ + "n0 = 0.036\nn1 = 10.0\nn2 = 5.0\nn3 = 36000.0\nn4 = 10.0\nn5 = 3.0\nt0 = n3 / 1000.0\nt1 = 100.0 * 1000.0\nt2 = n0 * t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "99.99999999999999" + ], + "split": "train" + }, + { + "Input": "the original price of a suit is $ 150 . the price increased 20 % , and after this increase , the store published a 20 % off coupon for a one - day sale . given that the consumers who used the coupon on sale day were getting 20 % off the increased price , how much did these consumers pay for the suit ?", + "Output Program": [ + "n0 = 150.0\nn1 = 20.0\nn2 = 20.0\nn3 = 20.0\nt0 = n0 * n1\nt1 = t0 / 100.0\nt2 = n0 + t1\nt3 = n1 * t2\nt4 = t3 / 100.0\nanswer = t2 - t4\nprint(answer)" + ], + "Output Answer": [ + "144" + ], + "split": "train" + }, + { + "Input": "how much time does a train 225 metres long running at 90 km / hr take to pass a pole ?", + "Output Program": [ + "n0 = 225.0\nn1 = 90.0\nt0 = n0 / 1000.0\nt1 = t0 / n1\nanswer = t1 * 3600.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "of the goose eggs laid at a certain pond , 1 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 120 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 3.0\nn3 = 4.0\nn4 = 3.0\nn5 = 5.0\nn6 = 120.0\nt0 = n1 / n5\nt1 = n1 / n3\nt2 = n0 / n1\nt3 = 1.0 - t0\nt4 = n6 / t3\nt5 = t4 / t1\nanswer = t5 / t2\nprint(answer)" + ], + "Output Answer": [ + "1200" + ], + "split": "train" + }, + { + "Input": "chris mixed 4 pounds of raisins with 4 pounds of nuts . if a pound of nuts costs 3 times as much as a pound of raisins , then the total cost of the raisins was what fraction of the total cost of the mixture ?", + "Output Program": [ + "n0 = 4.0\nn1 = 4.0\nn2 = 3.0\nt0 = n1 * n2\nt1 = n0 + t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.25" + ], + "split": "train" + }, + { + "Input": "if a * b * c = ( \u221a ( a + 2 ) ( b + 3 ) ) / ( c + 1 ) , find the value of 6 * 15 * 11 .", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 3.0\nn2 = 1.0\nn3 = 6.0\nn4 = 15.0\nn5 = 11.0\nt0 = n0 + n3\nt1 = n1 + n4\nt2 = n2 + n5\nt3 = t0 * t1\nt4 = math.sqrt(max(0, t3))\nanswer = t4 / t2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "in a caravan , in addition to 50 hens , there are 45 goats and 8 camels with some keepers . if the total number of feet be 224 more than the number of heads in the caravan , the number of keepers is", + "Output Program": [ + "n0 = 50.0\nn1 = 45.0\nn2 = 8.0\nn3 = 224.0\nt0 = n0 + n1\nt1 = n0 * 2.0\nt2 = n1 * 4.0\nt3 = n2 * 4.0\nt4 = n2 + t0\nt5 = t1 + t2\nt6 = n3 + t4\nt7 = t5 + t3\nanswer = t6 - t7\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "n is a positive integer . when n + 1 is divided by 6 , the remainder is 4 . what is the remainder when n is divided by 2 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 6.0\nn2 = 4.0\nn3 = 2.0\nt0 = n2 + n3\nanswer = n1 / t0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "if 9 / ( 5 + 3 / x ) = 1 , then x =", + "Output Program": [ + "n0 = 9.0\nn1 = 5.0\nn2 = 3.0\nn3 = 1.0\nt0 = n0 - n1\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.75" + ], + "split": "train" + }, + { + "Input": "in a hostel there were 100 students . to accommodate 20 more students the average is decreased by rupees 5 . but total expenditure increased by rs . 400 . find the total expenditure of the hostel now ?", + "Output Program": [ + "n0 = 100.0\nn1 = 20.0\nn2 = 5.0\nn3 = 400.0\nt0 = n0 + n1\nt1 = n2 * t0\nt2 = n3 + t1\nt3 = t2 / n1\nt4 = t3 - n2\nanswer = t0 * t4\nprint(answer)" + ], + "Output Answer": [ + "5400" + ], + "split": "train" + }, + { + "Input": "two employees x and y are paid a total of rs . 560 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?", + "Output Program": [ + "n0 = 560.0\nn1 = 120.0\nt0 = 1.0 + 4.0\nt1 = t0 * 2.0\nt2 = t1 + 1.0\nt3 = n0 * t1\nt4 = t2 * 2.0\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "254.54545454545453" + ], + "split": "train" + }, + { + "Input": "calculate the sum of first 28 natural numbers .", + "Output Program": [ + "n0 = 28.0\nt0 = n0 + 1.0\nt1 = n0 / 2.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "406" + ], + "split": "train" + }, + { + "Input": "a & b started a partnership business . a ' s investment was thrice the investment of b and the period of his investment was two times the period of investments of b . if b received rs 5000 as profit , what is their total profit ?", + "Output Program": [ + "n0 = 5000.0\nt0 = 1.0 * 1.0\nt1 = 2.0 * 3.0\nt2 = t1 + t0\nt3 = t0 / t2\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "35000" + ], + "split": "train" + }, + { + "Input": "for the positive integers x , x + 2 , x + 4 , x + 7 , and x + 22 , the mean is how much greater than the median ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 7.0\nn3 = 22.0\nt0 = n0 + n1\nt1 = 1.0 + 4.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = t3 / t1\nanswer = t4 - n1\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "3 / 4 of 1 / 2 of 2 / 5 of 5100 = ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 1.0\nn3 = 2.0\nn4 = 2.0\nn5 = 5.0\nn6 = 5100.0\nt0 = n3 / n5\nt1 = n0 / n1\nt2 = n2 / n3\nt3 = t1 * t2\nt4 = t0 * t3\nanswer = n6 * t4\nprint(answer)" + ], + "Output Answer": [ + "765.0000000000001" + ], + "split": "train" + }, + { + "Input": "find the principle on a certain sum of money at 5 % per annum for 2 2 / 5 years if the amount being rs . 1120 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 2.0\nn3 = 5.0\nn4 = 1120.0\nt0 = n1 * n3\nt1 = n1 + t0\nt2 = t1 / n3\nt3 = n0 * t2\nt4 = t3 / 100.0\nt5 = t4 + 1.0\nanswer = n4 / t5\nprint(answer)" + ], + "Output Answer": [ + "999.9999999999999" + ], + "split": "train" + }, + { + "Input": "seller selling an apple for rs . 15 , a seller loses 1 / 6 th of what it costs him . the cp of the apple is ?", + "Output Program": [ + "n0 = 15.0\nn1 = 1.0\nn2 = 6.0\n\nanswer = n0 + n1\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "how many words , with or without meaning , can be formed using all letters of the word red using each letter exactly once ?", + "Output Program": [ + "import math\n\nanswer = math.factorial(min(15, int(3.0)))\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "the average of 60 results is 40 and the average of other 40 results is 60 . what is the average of all the results ?", + "Output Program": [ + "n0 = 60.0\nn1 = 40.0\nn2 = 40.0\nn3 = 60.0\nt0 = n0 + n1\nt1 = n0 * n1\nt2 = t1 + t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "a person was asked to state his age in years . his reply was , ` ` take my age 3 years hence , multiply it by 4 and subtract 4 times my age 3 years ago and you will know how old i am . ' ' what was the age of the person ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 4.0\nn3 = 3.0\nt0 = n0 * n1\nanswer = t0 + t0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "a group of 55 adults and 70 children go for trekking . if there is meal for either 70 adults or 90 children and if 35 adults have their meal , find the total number of children that can be catered with the remaining food .", + "Output Program": [ + "n0 = 55.0\nn1 = 70.0\nn2 = 70.0\nn3 = 90.0\nn4 = 35.0\nt0 = n3 / n1\nt1 = n1 - n4\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "a man goes into a barbershop and gets a $ 15 haircut . he pays the barber with a $ 20 bill , but the barber does n ' t have change because it is an especially slow day . the barber goes to the flower shop next to his own and trades the $ 20 bill for a $ 10 dollar bill and two $ 5 bills . then he gives the man his $ 5 in change . later the lady from the flower shop confronts the barber and tells him that the $ 20 bill he gave her was counterfeit . the barber agrees and he gives the lady a different $ 20 bill . later that day he tries to figure out how much money he lost . what did he lose ?", + "Output Program": [ + "n0 = 15.0\nn1 = 20.0\nn2 = 20.0\nn3 = 10.0\nn4 = 5.0\nn5 = 5.0\nn6 = 20.0\nn7 = 20.0\n\nanswer = n1 - n0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "of all the homes on gotham street , 1 / 3 are termite - ridden , and 5 / 8 of these are collapsing . what fraction of the homes are termite - ridden , but not collapsing ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 5.0\nn3 = 8.0\nt0 = n0 + 2.0\nt1 = n1 * n3\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.125" + ], + "split": "train" + }, + { + "Input": "if a person walks at 16 km / hr instead of 12 km / hr , he would have walked 20 km more . the actual distance traveled by him is ?", + "Output Program": [ + "n0 = 16.0\nn1 = 12.0\nn2 = 20.0\nt0 = n0 - n1\nt1 = n2 / t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "a man is 29 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is :", + "Output Program": [ + "n0 = 29.0\nt0 = 2.0 * 2.0\nt1 = 2.0 - 1.0\nt2 = t0 - 2.0\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "train" + }, + { + "Input": "the average of 25 results is 18 . the average of first 12 of them is 10 and that of last 12 is 20 . find the 13 th result ?", + "Output Program": [ + "n0 = 25.0\nn1 = 18.0\nn2 = 12.0\nn3 = 10.0\nn4 = 12.0\nn5 = 20.0\nn6 = 13.0\nt0 = n0 * n1\nt1 = n2 * n5\nt2 = n2 * n3\nt3 = t0 - t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "of the 3 - digit integers greater than 700 , how many have two digits t that are equal to each other and the remaining digit different from the other two ?", + "Output Program": [ + "n0 = 3.0\nn1 = 700.0\nt0 = n1 / 100.0\nt1 = 1000.0 - n1\nt2 = 10.0 - 1.0\nt3 = 10.0 - 2.0\nt4 = t1 - 1.0\nt5 = 10.0 - t0\nt6 = t5 * t2\nt7 = t6 * t3\nt8 = t7 + 3.0\nanswer = t4 - t8\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "the ages of two person differ by 20 years . if 5 years ago , the elder one be 5 times as old as the younger one , their present ages ( in years ) are respectively", + "Output Program": [ + "n0 = 20.0\nn1 = 5.0\nn2 = 5.0\nt0 = n1 * n2\nt1 = n0 - n1\nt2 = n2 - 1.0\nt3 = t0 + t1\nt4 = t3 / t2\nanswer = n0 + t4\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "out of 40 applicants to a law school , 15 majored in political science , 20 had a grade point average higher than 3.0 , and 10 did not major in political science and had a gpa equal to or lower than 3.0 . how many w applicants majored in political science and had a gpa higher than 3.0 ?", + "Output Program": [ + "n0 = 40.0\nn1 = 15.0\nn2 = 20.0\nn3 = 3.0\nn4 = 10.0\nn5 = 3.0\nn6 = 3.0\nt0 = n1 + n4\nt1 = n0 - t0\nanswer = n2 - t1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "the cost per pound of green tea and coffee were the same in june . in july , the price of coffee shot up by 100 % and that of green tea dropped by 70 % . if in july , a mixture containing equal quantities of green tea and coffee costs $ 3.45 for 3 lbs , how much did a pound of green tea cost in july ?", + "Output Program": [ + "n0 = 100.0\nn1 = 70.0\nn2 = 3.45\nn3 = 3.0\nt0 = n0 + n0\nt1 = n3 / 2.0\nt2 = n0 - n1\nt3 = t0 / n0\nt4 = t2 / n0\nt5 = t3 * t1\nt6 = t1 * t4\nt7 = t5 + t6\nt8 = t7 / n2\nanswer = t8 * t4\nprint(answer)" + ], + "Output Answer": [ + "0.3" + ], + "split": "train" + }, + { + "Input": "the average weight of 10 oarsmen in a boat is increased by 1.8 kg when one of the crew , who weighs 53 kg is replaced by a new man . find the weight of the new man .", + "Output Program": [ + "n0 = 10.0\nn1 = 1.8\nn2 = 53.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "71" + ], + "split": "train" + }, + { + "Input": "bill made a profit of 10 % by selling a product . if he had purchased that product for 10 % less and sold it at a profit of 30 % , he would have received $ 49 more . what was his original selling price ?", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 30.0\nn3 = 49.0\nt0 = n0 / 100.0\nt1 = n2 / 100.0\nt2 = t0 + 1.0\nt3 = t1 + 1.0\nt4 = 1.0 - t0\nt5 = t3 * t4\nt6 = t5 - t2\nt7 = n3 / t6\nanswer = t2 * t7\nprint(answer)" + ], + "Output Answer": [ + "769.9999999999994" + ], + "split": "train" + }, + { + "Input": "3 numbers which are co - prime to each other are such that the product of the first two is 551 and that of the last two is 1073 . the sum of the 3 numbers is :", + "Output Program": [ + "import scipy\nn0 = 3.0\nn1 = 551.0\nn2 = 1073.0\nn3 = 3.0\nt0 = scipy.gcd(int(n1), int(n2))\nt1 = n1 / t0\nt2 = n2 / t0\nt3 = t1 + t0\nanswer = t3 + t2\nprint(answer)" + ], + "Output Answer": [ + "85" + ], + "split": "train" + }, + { + "Input": "the sum of the squares of the first 15 positive integers ( 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + . . . + 15 ^ 2 ) is equal to 1260 . what is the sum of the squares of the second 15 positive integers ( 16 ^ 2 + 17 ^ 2 + 18 ^ 2 + . . . + 30 ^ 2 ) ?", + "Output Program": [ + "n0 = 15.0\nn1 = 1.0\nn2 = 2.0\nn3 = 2.0\nn4 = 2.0\nn5 = 3.0\nn6 = 2.0\nn7 = 15.0\nn8 = 2.0\nn9 = 1260.0\nn10 = 15.0\nn11 = 16.0\nn12 = 2.0\nn13 = 17.0\nn14 = 2.0\nn15 = 18.0\nn16 = 2.0\nn17 = 30.0\nn18 = 2.0\nt0 = n17 + n1\nt1 = n5 + n5\nt2 = n17 * n2\nt3 = t2 + n1\nt4 = n17 * t0\nt5 = t3 * t4\nt6 = t5 / t1\nanswer = t6 - n9\nprint(answer)" + ], + "Output Answer": [ + "8195" + ], + "split": "train" + }, + { + "Input": "n is a whole number which when divided by 4 gives 3 as remainder . what will be the remainder when 2 n is divided by 4 ?", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 2.0\nn3 = 4.0\nt0 = n1 * n2\nanswer = t0 % n0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a sports retailer ordered white and yellow tennis balls in equal number but the dispatch clerk of the tennis ball company erred and dispatched 70 extra yellow balls and making ratio of white balls to yellow balls 8 / 13 . how many tennis balls did the retailer order originally .", + "Output Program": [ + "n0 = 70.0\nn1 = 8.0\nn2 = 13.0\nt0 = n0 * n1\nt1 = n2 - n1\nt2 = t0 / t1\nanswer = t2 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "224" + ], + "split": "train" + }, + { + "Input": "what could be the range of a set consisting of odd multiples of 11 ?", + "Output Program": [ + "n0 = 11.0\n\nanswer = n0 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "44" + ], + "split": "train" + }, + { + "Input": "a no . when divided by 242 gives a remainder 100 , what remainder will be obtainedby dividingthe same no . 18 ?", + "Output Program": [ + "n0 = 242.0\nn1 = 100.0\nn2 = 18.0\nt0 = n0 + n1\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "in a bus left side are 15 seats available , 3 few seats in right side because in rear exit door . each seat hold 3 people . in addition , there is a seat back can sit 11 people all together . how many people can sit in a bus ?", + "Output Program": [ + "n0 = 15.0\nn1 = 3.0\nn2 = 3.0\nn3 = 11.0\nt0 = n0 - n1\nt1 = n0 + t0\nt2 = n1 * t1\nanswer = n3 + t2\nprint(answer)" + ], + "Output Answer": [ + "92" + ], + "split": "train" + }, + { + "Input": "the scoring system in a certain football competition goes as follows : 3 points for victory , 1 point for a draw , and 0 points for defeat . each team plays 20 matches . if a team scored 14 points after 5 games , what is the least number of the remaining matches it has to win to reach the 40 - point mark by the end of the tournament ?", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 1.0\nn2 = 0.0\nn3 = 20.0\nn4 = 14.0\nn5 = 5.0\nn6 = 40.0\nt0 = n6 - n4\nt1 = n3 - n5\nt2 = t0 - t1\nt3 = t2 / 2.0\nt4 = math.floor(t3)\nanswer = t4 + n1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "find large number from below question the difference of two numbers is 1390 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder", + "Output Program": [ + "n0 = 1390.0\nn1 = 6.0\nn2 = 15.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nt2 = t0 / t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "1650" + ], + "split": "train" + }, + { + "Input": "for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today ' s production of 105 units raises the average to 55 units per day , what is the value of n ?", + "Output Program": [ + "n0 = 50.0\nn1 = 105.0\nn2 = 55.0\nt0 = n1 - n0\nt1 = n2 - n0\nt2 = t0 / t1\nanswer = t2 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "there are 10 teams in a certain league and each team plays each of the other teams exactly once . what is the total number of games played ?", + "Output Program": [ + "n0 = 10.0\nt0 = n0 - 1.0\nt1 = n0 * t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "if x is to be chosen at random from the integers between 1 to 5 , inclusive , and y is to be chosen at random from the integers between 7 and 10 , inclusive , what is the probability that x + y will be even ?", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 7.0\nn3 = 10.0\nt0 = 2.0 * 2.0\nt1 = 2.0 * 3.0\nt2 = n1 - 1.0\nt3 = t0 + t1\nt4 = n1 * t2\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "how much is 60 % of 40 is greater than 4 / 5 of 25 ?", + "Output Program": [ + "n0 = 60.0\nn1 = 40.0\nn2 = 4.0\nn3 = 5.0\nn4 = 25.0\nt0 = n0 / 100.0\nt1 = n2 / n3\nt2 = n1 * t0\nt3 = n4 * t1\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "if x and y are integers , what is the least positive number of 24 x + 18 y ?", + "Output Program": [ + "n0 = 24.0\nn1 = 18.0\n\nanswer = n0 - n1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "the jogging track in a sports complex is 726 m in circumference . suresh and his wife start from the same point and walk in opposite direction at 4.5 km / hr and 3.75 km / hr respectively . they will meet for the first time in ?", + "Output Program": [ + "n0 = 726.0\nn1 = 4.5\nn2 = 3.75\nt0 = n1 * 1000.0\nt1 = n2 * 1000.0\nt2 = t0 + t1\nt3 = t2 / 60.0\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "5.28" + ], + "split": "train" + }, + { + "Input": "the average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 24 years . find the average age of the women ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.0\nn2 = 20.0\nn3 = 24.0\nt0 = n2 + n3\nt1 = n0 * n1\nt2 = t0 + t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "how many paying stones , each measuring 2 1 / 2 m * 2 m are required to pave a rectangular court yard 20 m long and 16 1 / 2 m board ?", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 2.0\nn3 = 2.0\nn4 = 20.0\nn5 = 16.0\nn6 = 1.0\nn7 = 2.0\nt0 = n1 / n0\nt1 = n5 + t0\nt2 = n0 + t0\nt3 = n4 * t1\nt4 = n0 * t2\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "66" + ], + "split": "train" + }, + { + "Input": "a textile manufacturing firm employees 70 looms . it makes fabrics for a branded company . the aggregate sales value of the output of the 70 looms is rs 5 , 00,000 and the monthly manufacturing expenses is rs 1 , 50,000 . assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms . monthly establishment charges are rs 75000 . if one loom breaks down and remains idle for one month , the decrease in profit is :", + "Output Program": [ + "n0 = 70.0\nn1 = 70.0\nn2 = 0.0\nn3 = 1.0\nn4 = 50000.0\nn5 = 75000.0\nt0 = 2.0 + 3.0\nt1 = n5 - n4\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "5000" + ], + "split": "train" + }, + { + "Input": "there are 5 thieves , each loot a bakery one after the other such that the first one takes 1 / 2 of the total no . of the breads plus 1 / 2 of a bread . similarly 2 nd , 3 rd , 4 th and 5 fth also did the same . after the fifth one no . of breads remained are 3 . initially how many breads were there ?", + "Output Program": [ + "n0 = 5.0\nn1 = 1.0\nn2 = 2.0\nn3 = 1.0\nn4 = 2.0\nn5 = 2.0\nn6 = 3.0\nn7 = 4.0\nn8 = 5.0\nn9 = 3.0\nt0 = n0 * n7\nt1 = n0 * t0\nt2 = t1 + t0\nt3 = n0 + t2\nanswer = n2 + t3\nprint(answer)" + ], + "Output Answer": [ + "127" + ], + "split": "train" + }, + { + "Input": "average of 6 numbers comes out to be 3.95 . average of two of the numbers is 3.4 while the average of other two is 3.85 . determine the average of the two numbers left .", + "Output Program": [ + "n0 = 6.0\nn1 = 3.95\nn2 = 3.4\nn3 = 3.85\nt0 = 2.0 / n0\nt1 = n2 * t0\nt2 = n3 * t0\nt3 = t1 + t2\nt4 = n1 - t3\nanswer = t4 / t0\nprint(answer)" + ], + "Output Answer": [ + "4.600000000000001" + ], + "split": "train" + }, + { + "Input": "the average weight of 8 person ' s increases by 4 kg when a new person comes in place of one of them weighing 55 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 4.0\nn2 = 55.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "87" + ], + "split": "train" + }, + { + "Input": "reeya obtained 55 , 67 , 76 , 82 and 55 out of 100 in different subjects , what will be the average", + "Output Program": [ + "n0 = 55.0\nn1 = 67.0\nn2 = 76.0\nn3 = 82.0\nn4 = 55.0\nn5 = 100.0\nt0 = n0 + n1\nt1 = 1.0 + 4.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "67" + ], + "split": "train" + }, + { + "Input": "there are 100 freshmen at a particular college , all of whom must take at least one of the 3 core classes : art , biology , and calculus . of these freshmen , 17 take only biology , 10 take only calculus , 9 take all 3 classes , and 20 take art and exactly one of the other two core classes . if the number of freshmen who take only art is 3 times the number of freshmen who take every core class except art , how many freshmen take art ?", + "Output Program": [ + "n0 = 100.0\nn1 = 3.0\nn2 = 17.0\nn3 = 10.0\nn4 = 9.0\nn5 = 3.0\nn6 = 20.0\nn7 = 3.0\nt0 = n2 + n3\nt1 = n4 + t0\nt2 = n6 + t1\nt3 = n0 - t2\nt4 = n1 * t3\nt5 = t4 / 4.0\nt6 = n6 + t5\nanswer = n4 + t6\nprint(answer)" + ], + "Output Answer": [ + "62" + ], + "split": "train" + }, + { + "Input": "city x has a population 5 times as great as the population of city y , which has a population twice as great as the population of city z . what is the ratio of the population of city x to the population of city z ?", + "Output Program": [ + "n0 = 5.0\n\nanswer = n0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "thabo owns exactly 160 books , and each book is either paperback fiction , paperback nonfiction , or hardcover nonfiction . if he owns 20 more paperback nonfiction books than hardcover nonfiction books , and twice as many paperback fiction books as paperback nonfiction books , how many hardcover books nonfiction books does thabo own ?", + "Output Program": [ + "n0 = 160.0\nn1 = 20.0\nt0 = n0 + n1\nt1 = t0 / 4.0\nanswer = t1 - n1\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "evaluate 100 / . 25", + "Output Program": [ + "n0 = 100.0\nn1 = 25.0\nt0 = n1 / 100.0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "train" + }, + { + "Input": "what is the smallest integer that is the sum of 2 distinct prime integers , each greater than 70 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 70.0\nt0 = n1 + 1.0\nt1 = n1 + 3.0\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "144" + ], + "split": "train" + }, + { + "Input": "for any integer k > 1 , the term \u201c length of an integer \u201d refers to the number of positive prime factors , not necessarily distinct , whose product is equal to k . for example , if k = 24 , the length of k is equal to 4 , since 24 = 2 \u00d7 2 \u00d7 2 \u00d7 3 . if x and y are positive integers such that x > 1 , y > 1 , and x + 3 y < 940 , what is the maximum possible sum of the length of x and the length of y ?", + "Output Program": [ + "n0 = 1.0\nn1 = 24.0\nn2 = 4.0\nn3 = 24.0\nn4 = 2.0\nn5 = 2.0\nn6 = 2.0\nn7 = 3.0\nn8 = 1.0\nn9 = 1.0\nn10 = 3.0\nn11 = 940.0\nt0 = n2 + n7\nt1 = n2 + n2\nt2 = n0 + t1\nanswer = t0 + t2\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "the cricket team of 11 members is 28 yrs old & the wicket keeper is 3 yrs older . if the ages ofthese 2 are excluded , the average age of theremaining players is 1 year less than the average age of the whole team . what is the average age of the team ?", + "Output Program": [ + "n0 = 11.0\nn1 = 28.0\nn2 = 3.0\nn3 = 2.0\nn4 = 1.0\nt0 = n1 + n2\nt1 = n0 - n3\nt2 = n1 + t0\nt3 = n0 - t1\nt4 = t2 - t1\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "a certain psychologist charges $ 35 more for the first hour of therapy than for each additional hour . if the total charge to a patient who receives 5 hours of therapy is $ 350 , what is the total charge to a patient who receives only 2 hours of therapy ?", + "Output Program": [ + "n0 = 35.0\nn1 = 5.0\nn2 = 350.0\nn3 = 2.0\nt0 = n2 - n0\nt1 = t0 / n1\nt2 = n3 * t1\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "161" + ], + "split": "train" + }, + { + "Input": "the average length of 6 ropes is 80 cm . if the average length of one third of the ropes measure to 70 cm , what is the average of the other ropes ?", + "Output Program": [ + "n0 = 6.0\nn1 = 80.0\nn2 = 70.0\nt0 = n0 / 4.0\nt1 = n2 * 2.0\nt2 = t1 / n0\nt3 = n1 - t2\nanswer = t0 * t3\nprint(answer)" + ], + "Output Answer": [ + "85" + ], + "split": "train" + }, + { + "Input": "x and y are two towns . ganesh covers the distance from x to y at an average speed of 44 km / hr . however , he covers the distance from y to x at an average speed of 36 km / hr . his average speed during the whole journey in km / hr . is :", + "Output Program": [ + "n0 = 44.0\nn1 = 36.0\nt0 = n0 - 10.0\nt1 = t0 + 100.0\nt2 = t1 + t1\nt3 = t1 / n0\nt4 = t1 / n1\nt5 = t3 + t4\nanswer = t2 / t5\nprint(answer)" + ], + "Output Answer": [ + "39.599999999999994" + ], + "split": "train" + }, + { + "Input": "in a division sum , the quotient is 120 , the divisor 456 and the remainder 333 , find the dividend ?", + "Output Program": [ + "n0 = 120.0\nn1 = 456.0\nn2 = 333.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "55053" + ], + "split": "train" + }, + { + "Input": "what is the remainder when ( 71 ) ( 73 ) is divided by 9 ?", + "Output Program": [ + "n0 = 71.0\nn1 = 73.0\nn2 = 9.0\nt0 = n0 * n1\nanswer = t0 % n2\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "roses can be purchased individually for $ 5.30 , one dozen for $ 36 , or two dozen for $ 50 . what is the greatest number of roses that can be purchased for $ 680 ?", + "Output Program": [ + "import math\nn0 = 5.3\nn1 = 36.0\nn2 = 50.0\nn3 = 680.0\nt0 = n3 / n2\nt1 = 12.0 * 2.0\nt2 = math.floor(t0)\nt3 = n2 * t2\nt4 = t2 * t1\nt5 = n3 - t3\nt6 = t5 / n0\nt7 = math.floor(t6)\nanswer = t7 + t4\nprint(answer)" + ], + "Output Answer": [ + "317" + ], + "split": "train" + }, + { + "Input": "two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs , x and y . now , jug x is 1 / 6 full , while jug y is 2 / 3 full . if water is poured from jug x into jug y until jug y is filled , what fraction of jug x then contains water ?", + "Output Program": [ + "n0 = 1.0\nn1 = 6.0\nn2 = 2.0\nn3 = 3.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = n0 - t1\nt3 = t2 / t1\nanswer = t0 * t3\nprint(answer)" + ], + "Output Answer": [ + "0.08333333333333334" + ], + "split": "train" + }, + { + "Input": "the total price of a kilogram each of shimla apples and red delicious apples is 250 rupees more than the total price of a kilogram each of red delicious apples and fuji apples . fuji apples is how much cheaper than shimla apples ?", + "Output Program": [ + "n0 = 250.0\n\nanswer = n0 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "250" + ], + "split": "train" + }, + { + "Input": "a sum of money lent out at s . i . amounts to a total of $ 590 after 2 years and to $ 815 after a further period of 5 years . what was the initial sum of money that was invested ?", + "Output Program": [ + "n0 = 590.0\nn1 = 2.0\nn2 = 815.0\nn3 = 5.0\nt0 = n1 / n3\nt1 = n2 - n0\nt2 = t0 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "train" + }, + { + "Input": "\u00e2 \u02c6 \u0161 1.5625 = ?", + "Output Program": [ + "n0 = 1.5625\nt0 = n0 / n0\nanswer = t0 + 0.25\nprint(answer)" + ], + "Output Answer": [ + "1.25" + ], + "split": "train" + }, + { + "Input": "the tax on a commodity is diminished by 20 % but its consumption is increased by 20 % . find the decrease percent in the revenue derived from it ?", + "Output Program": [ + "n0 = 20.0\nn1 = 20.0\nt0 = n1 + 100.0\nt1 = 100.0 - n0\nt2 = t0 * t1\nt3 = t2 / 100.0\nanswer = 100.0 - t3\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "find ( 7 x + 4 y ) / ( x - 2 y ) if x / 2 y = 3 / 2 ?", + "Output Program": [ + "n0 = 7.0\nn1 = 4.0\nn2 = 2.0\nn3 = 2.0\nn4 = 3.0\nn5 = 2.0\nt0 = n4 / n2\nt1 = n2 * t0\nt2 = n0 * t1\nt3 = t1 - n2\nt4 = n1 + t2\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "a certain number of horses and an equal number of men are going somewhere . half of the owners are on their horses ' back while the remaining ones are walking along leading their horses . if the number of legs walking on the ground is 70 , how many horses are there ?", + "Output Program": [ + "n0 = 70.0\nt0 = 2.0 / 2.0\nt1 = t0 + 4.0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "a cube with its sides numbered 1 through 6 is rolled twice , first landing on a and then landing on b . if any roll of the cube yields an equal chance of landing on any of the numbers 1 through 6 , what is the probability t that a + b is prime ?", + "Output Program": [ + "n0 = 1.0\nn1 = 6.0\nn2 = 1.0\nn3 = 6.0\nt0 = 12.0 + 3.0\nt1 = n0 / n1\nt2 = t1**min(2.0, 5)\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "0.41666666666666663" + ], + "split": "train" + }, + { + "Input": "if ' a ' and ' b ' are non - zero numbers such that their sum is 6 times the product , what is the value of 1 / a + 1 / b ?", + "Output Program": [ + "n0 = 6.0\nn1 = 1.0\nn2 = 1.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "a worker ' s take - home pay last year was the same each month , and she saved the same fraction of her take - home pay each month . the total amount of money that she had saved at the end of the year was 6 times the amount of that portion of her monthly take - home pay that she did not save . if all the money that she saved last year was from her take - home pay , what fraction of her take - home pay did she save each month ?", + "Output Program": [ + "n0 = 6.0\nt0 = 12.0 / n0\nt1 = t0 + 1.0\nanswer = 1 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.3333333333333333" + ], + "split": "train" + }, + { + "Input": "marts income is 60 percent more than tims income and tims income is 40 percent less than juans income . what percentage of juans income is marts income", + "Output Program": [ + "n0 = 60.0\nn1 = 40.0\nt0 = n0 + 100.0\nt1 = 100.0 - n1\nt2 = 100.0 / t1\nt3 = t2 * 100.0\nt4 = t0 / t3\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "95.99999999999999" + ], + "split": "train" + }, + { + "Input": "joan took out a mortgage from hel local bank . each monthly mortgage payment she makes must be triple the amount of the previous month ' s payment . if her first payment is $ 100 , and the total amount she must pay back is $ 109300 , how many months will it take joan to pay back her mortgage ?", + "Output Program": [ + "import math\nn0 = 100.0\nn1 = 109300.0\nt0 = math.log(max(1e-5, 3.0), 2)\nt1 = n1 * 2.0\nt2 = t1 / n0\nt3 = t2 + 1.0\nt4 = math.log(max(1e-5, t3), 2)\nanswer = t4 / t0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "having scored 97 runs in the 19 th inning , a cricketer increases his average score by 4 . what will be his average score after 19 innings ?", + "Output Program": [ + "n0 = 97.0\nn1 = 19.0\nn2 = 4.0\nn3 = 19.0\nt0 = n1 * n2\nt1 = n0 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "working alone , printers x , y , and z can do a certain printing job , consisting of a large number of pages , in 12 , 10 , and 20 hours , respectively . what is the ratio of the time it takes printer x to do the job , working alone at its rate , to the time it takes printers y and z to do the job , working together at their individual rates ?", + "Output Program": [ + "n0 = 12.0\nn1 = 10.0\nn2 = 20.0\nt0 = 1.0 / n1\nt1 = 1.0 / n2\nt2 = t0 + t1\nt3 = 1.0 / t2\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "1.8000000000000003" + ], + "split": "train" + }, + { + "Input": "virginia , adrienne , and dennis have taught history for a combined total of 75 years . if virginia has taught for 9 more years than adrienne and for 9 fewer years than dennis , for how many years has dennis taught ?", + "Output Program": [ + "n0 = 75.0\nn1 = 9.0\nn2 = 9.0\nt0 = n1 + n2\nt1 = n1 + t0\nt2 = n0 - t1\nt3 = t2 / 3.0\nanswer = t0 + t3\nprint(answer)" + ], + "Output Answer": [ + "34" + ], + "split": "train" + }, + { + "Input": "a big container is 40 % full with water . if 28 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container in liters ?", + "Output Program": [ + "n0 = 40.0\nn1 = 28.0\nn2 = 3.0\nn3 = 4.0\nt0 = n2 / n3\nt1 = n0 / 100.0\nt2 = t0 - t1\nanswer = n1 / t2\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "a 3 - digit number 4 a 3 is added to another 3 - digit number 984 to give a 4 - digit number 13 b 7 , which is divisible by 11 . then , ( a + b ) = ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 3.0\nn3 = 3.0\nn4 = 984.0\nn5 = 4.0\nn6 = 13.0\nn7 = 7.0\nn8 = 11.0\nt0 = n0 * n0\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "if 3 ^ x * 4 ^ y = 19,683 and x \u2013 y = 9 , then x = ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 19683.0\nn3 = 9.0\n\nanswer = n3 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "find the principle on a certain sum of money at 5 % per annum for 2 2 / 5 years if the amount being rs . 1232 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 2.0\nn3 = 5.0\nn4 = 1232.0\nt0 = n1 * n3\nt1 = n1 + t0\nt2 = t1 / n3\nt3 = n0 * t2\nt4 = t3 / 100.0\nt5 = t4 + 1.0\nanswer = n4 / t5\nprint(answer)" + ], + "Output Answer": [ + "1100" + ], + "split": "train" + }, + { + "Input": "find the greatest number which on dividing 1428 and 2206 , leaves a reminder of 9 and 13 respectively", + "Output Program": [ + "import scipy\nn0 = 1428.0\nn1 = 2206.0\nn2 = 9.0\nn3 = 13.0\nt0 = n0 - n2\nt1 = n1 - n3\nanswer = scipy.gcd(int(t0), int(t1))\nprint(answer)" + ], + "Output Answer": [ + "129" + ], + "split": "train" + }, + { + "Input": "there are 2 sections a and b in a class , consisting of 40 and 20 students respectively . if the average weight of section a is 50 kg and that of section b is 40 kg , find the average of the whole class ?", + "Output Program": [ + "n0 = 2.0\nn1 = 40.0\nn2 = 20.0\nn3 = 50.0\nn4 = 40.0\nt0 = n1 + n2\nt1 = n1 * n3\nt2 = n2 * n4\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "46.666666666666664" + ], + "split": "train" + }, + { + "Input": "on dividing 15 by a number , the quotient is 4 and the remainder is 3 . find the divisor ?", + "Output Program": [ + "import math\nn0 = 15.0\nn1 = 4.0\nn2 = 3.0\nt0 = n0 / n1\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "a certain clock marks every hour by striking a number of times equal to the hour , and the time require for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stoke and the end of the last stroke is 22 seconds . at 8 : 00 , how many seconds elapse between the beginning of the first stroke and the end of the last stroke ?", + "Output Program": [ + "n0 = 6.0\nn1 = 0.0\nn2 = 22.0\nn3 = 8.0\nn4 = 0.0\nt0 = n3 - 1.0\nt1 = n0 - 1.0\nt2 = n3 + t0\nt3 = n0 + t1\nt4 = n2 / t3\nanswer = t2 * t4\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "if m and n are whole numbers such that mn = 121 , the value of ( m 1 ) n + 1 is :", + "Output Program": [ + "import math\nn0 = 121.0\nn1 = 1.0\nn2 = 1.0\nt0 = math.sqrt(max(0, n0))\nt1 = t0 - n1\nanswer = t1**min(3.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "1000" + ], + "split": "train" + }, + { + "Input": "a certain taxi company charges $ 3.50 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ?", + "Output Program": [ + "n0 = 3.5\nn1 = 1.0\nn2 = 5.0\nn3 = 0.4\nn4 = 1.0\nn5 = 5.0\nn6 = 8.0\nt0 = n1 / n2\nt1 = n6 / t0\nt2 = t1 - n1\nt3 = n3 * t2\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "19.1" + ], + "split": "train" + }, + { + "Input": "how much time does a train 125 metres long running at 60 km / hr take to pass a pole ?", + "Output Program": [ + "n0 = 125.0\nn1 = 60.0\nt0 = n0 / 1000.0\nt1 = t0 / n1\nanswer = t1 * 3600.0\nprint(answer)" + ], + "Output Answer": [ + "7.5" + ], + "split": "train" + }, + { + "Input": "if the number 517 * 324 is completely divisible by 7 , then the smallest whole number in the place of * will be :", + "Output Program": [ + "import math\nimport scipy\nn0 = 517.0\nn1 = 324.0\nn2 = 7.0\nt0 = 100.0**min(2.0, 5)\nt1 = 100.0 % n2\nt2 = 10.0 % n2\nt3 = 1000.0 % n2\nt4 = scipy.lcm(int(n2), int(t3))\nt5 = t0 * 10.0\nt6 = t1 * 3.0\nt7 = t2 * 2.0\nt8 = t0 % n2\nt9 = n2 * t8\nt10 = t5 % n2\nt11 = t10 * 1.0\nt12 = t11 + t11\nt13 = t12 + t9\nt14 = t13 + t6\nt15 = t14 + t7\nt16 = t15 + 4.0\nt17 = t16 / t4\nt18 = t17 + 1.0\nt19 = math.floor(t18)\nt20 = t19 * t4\nt21 = t20 - t16\nt22 = t21 / t3\nanswer = t22 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "what is the least number which when divided by 5 , 6 , 9 and 12 leaves remainder 4 in each care ?", + "Output Program": [ + "import scipy\nn0 = 5.0\nn1 = 6.0\nn2 = 9.0\nn3 = 12.0\nn4 = 4.0\nt0 = scipy.lcm(int(n0), int(n1))\nt1 = scipy.lcm(int(n2), int(n3))\nt2 = scipy.lcm(int(t0), int(t1))\nanswer = n4 + t2\nprint(answer)" + ], + "Output Answer": [ + "184" + ], + "split": "train" + }, + { + "Input": "a number is doubled and 9 is added . if the resultant is trebled , it becomes 69 . what is that number ?", + "Output Program": [ + "n0 = 9.0\nn1 = 69.0\nt0 = n0 * 3.0\nt1 = 2.0 * 3.0\nt2 = n1 - t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "n ^ ( n / 2 ) = 8 is true when n = 8 in the same way what is the value of n if n ^ ( n / 2 ) = 20 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 8.0\nn2 = 8.0\nn3 = 2.0\nn4 = 20.0\nt0 = n4**min(n0, 5)\nanswer = t0 / n4\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "find the unit \u2019 s digit in the product ( 76 ^ 41 ) * ( 41 ^ 14 ) * ( 14 ^ 87 ) * ( 87 ^ 76 )", + "Output Program": [ + "n0 = 76.0\nn1 = 41.0\nn2 = 41.0\nn3 = 14.0\nn4 = 14.0\nn5 = 87.0\nn6 = 87.0\nn7 = 76.0\nt0 = n3 / n3\nanswer = t0 + 3.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "what is the least value of x . so that 1894 x is divisible by 3 ?", + "Output Program": [ + "n0 = 1894.0\nn1 = 3.0\nt0 = n0 * 10.0\nt1 = t0 + 1.0\nt2 = t1 + 1.0\nanswer = t2 - t0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "on july 1 of last year , total employees at company e was decreased by 10 percent . without any change in the salaries of the remaining employees , the average ( arithmetic mean ) employee salary was 10 percent more after the decrease in the number of employees than before the decrease . the total of the combined salaries of all the employees at company e after july 1 last year was what percent w of thatbeforejuly 1 last year ?", + "Output Program": [ + "n0 = 1.0\nn1 = 10.0\nn2 = 10.0\nn3 = 1.0\nn4 = 1.0\n\nanswer = n1 * n1\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "a part - time employee whose hourly wage was increased by 10 percent decided to reduce the number of hours worked per week so that the employee ' s total weekly income would remain unchanged . by what percent should the number of hours worked be reduced ?", + "Output Program": [ + "n0 = 10.0\nt0 = n0 + 100.0\nt1 = t0 / 100.0\nt2 = t1 * 10.0\nt3 = 1.0 / t2\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "9.090909090909092" + ], + "split": "train" + }, + { + "Input": "in the above number , a and b represent the tens and units digits , respectively . if the above number is divisible by 35 , what is the greatest possible value of b x a ?", + "Output Program": [ + "n0 = 35.0\nt0 = 3.0 + 4.0\nt1 = 2.0 + 3.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "if 2 x - y = 4 then 6 x - 3 y = ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 6.0\nn3 = 3.0\nt0 = n0 * n3\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "find 3486 / 189", + "Output Program": [ + "n0 = 3486.0\nn1 = 189.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "18.444444444444443" + ], + "split": "train" + }, + { + "Input": "mary and mike enter into a partnership by investing $ 600 and $ 400 respectively . at the end of one year , they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business . if mary received $ 1000 more than mike did , what was the profit made by their business in that year ?", + "Output Program": [ + "n0 = 600.0\nn1 = 400.0\nn2 = 1000.0\nt0 = n0 / 1000.0\nt1 = n1 / 1000.0\nt2 = 1.0 / 3.0\nt3 = t0 - t1\nt4 = 1.0 - t2\nt5 = t3 * t4\nanswer = n2 / t5\nprint(answer)" + ], + "Output Answer": [ + "7500" + ], + "split": "train" + }, + { + "Input": "after a storm deposits 120 billion gallons of water into the city reservoir , the reservoir is 80 % full . if the original contents of the reservoir totaled 200 billion gallons , the reservoir was approximately what percentage full before the storm ?", + "Output Program": [ + "n0 = 120.0\nn1 = 80.0\nn2 = 200.0\nt0 = n0 + n2\nt1 = n1 / 100.0\nt2 = t0 / t1\nt3 = n2 / t2\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "4 numbers are in the ratio 2 : 3 : 4 : 5 add up to give a sum of 1344 . find the biggest number .", + "Output Program": [ + "n0 = 6.0\nn1 = 5.0\nn2 = 2.0\nn3 = 19.0\nt0 = n0 * n1\nt1 = n2 * t0\nt2 = t1 / n2\nanswer = t2 + 3.0\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "rs . 700 is divided among a , b , c so that a receives half as much as b and b half as much as c . then c ' s share is :", + "Output Program": [ + "n0 = 700.0\nt0 = 1.0 + 2.0\nt1 = t0 + 4.0\nt2 = 4.0 / t1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "train" + }, + { + "Input": "find the greatest number that will divide 150 , 230 and 175 leaving 50 , 5 and 25 as remainders respectively", + "Output Program": [ + "n0 = 150.0\nn1 = 230.0\nn2 = 175.0\nn3 = 50.0\nn4 = 5.0\nn5 = 25.0\nt0 = n4 * 4.0\nanswer = t0 + 12.0\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "in track last week , the boys ran 27 laps . the girls ran 9 more laps . each lap is a 3 - fourth of a mile . how many miles did the girls run ?", + "Output Program": [ + "n0 = 27.0\nn1 = 9.0\nn2 = 3.0\nt0 = n0 + n1\nt1 = n2 / 4.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "train" + }, + { + "Input": "if the operation \u20ac is defined for all x and y by the equation x \u20ac y = 2 * x * y , then 8 \u20ac ( 4 \u20ac 5 ) =", + "Output Program": [ + "n0 = 2.0\nn1 = 8.0\nn2 = 4.0\nn3 = 5.0\nt0 = n0 * n1\nt1 = n0 * n2\nt2 = n3 * t1\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "640" + ], + "split": "train" + }, + { + "Input": "every year an amount increases by 1 / 6 th of itself . how much will it be after two years if its present value is rs . 64000 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 6.0\nn2 = 64000.0\nt0 = n0 / n1\nt1 = n2 * t0\nt2 = n2 + t1\nt3 = t2 * t0\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "87111.11111111112" + ], + "split": "train" + }, + { + "Input": "a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 752 in total compensation , how many total hours did he work that week ?", + "Output Program": [ + "n0 = 16.0\nn1 = 40.0\nn2 = 40.0\nn3 = 75.0\nn4 = 752.0\nt0 = n3 + 100.0\nt1 = n0 * n1\nt2 = n0 * t0\nt3 = n4 - t1\nt4 = t2 / 100.0\nt5 = t3 / t4\nanswer = n1 + t5\nprint(answer)" + ], + "Output Answer": [ + "44" + ], + "split": "train" + }, + { + "Input": "david obtained 72 , 60 , 35 , 62 and 84 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology what are his average marks ?", + "Output Program": [ + "n0 = 72.0\nn1 = 60.0\nn2 = 35.0\nn3 = 62.0\nn4 = 84.0\nn5 = 100.0\nt0 = n0 + n1\nt1 = 2.0 + 3.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "62.6" + ], + "split": "train" + }, + { + "Input": "williams works at a resort from the beginning of march to the end of september . during the month of august this past year , he made 10 times the average ( arithmetic mean ) of his monthly totals in tips for the other months . his total tips for august were what fraction of his total tips for all of the months he worked ?", + "Output Program": [ + "n0 = 10.0\nt0 = 3.0 + 4.0\nt1 = t0 - 1.0\nt2 = n0 + t1\nanswer = n0 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.625" + ], + "split": "train" + }, + { + "Input": "find large number from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 asquotient and the 15 as remainder ?", + "Output Program": [ + "n0 = 1365.0\nn1 = 6.0\nn2 = 15.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nt2 = t0 / t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "1620" + ], + "split": "train" + }, + { + "Input": "in a coconut grove , ( x + 2 ) trees yield 40 nuts per year , x trees yield 120 nuts per year and ( x \u2013 2 ) trees yield 180 nuts per year . if the average yield per year per tree be 100 , find x .", + "Output Program": [ + "n0 = 2.0\nn1 = 40.0\nn2 = 120.0\nn3 = 2.0\nn4 = 180.0\nn5 = 100.0\nt0 = n1 + n2\nt1 = n0 * n4\nt2 = n0 * n1\nt3 = n5 * 3.0\nt4 = n4 + t0\nt5 = t1 - t2\nt6 = t4 - t3\nanswer = t5 / t6\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "of the 3,600 employees of company x , 1 / 6 are clerical . if the clerical staff were to be reduced by 1 / 4 , what percent of the total number of the remaining employees would then be clerical ?", + "Output Program": [ + "n0 = 3600.0\nn1 = 1.0\nn2 = 6.0\nn3 = 1.0\nn4 = 4.0\nt0 = n1 / n2\nt1 = n3 / n4\nt2 = n3 - t1\nt3 = n3 - t0\nt4 = t0 * t2\nt5 = t4 + t3\nt6 = t4 / t5\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "13.043478260869565" + ], + "split": "train" + }, + { + "Input": "shekar scored 76 , 65 , 82 , 67 and 95 marks in mathematics , science , social studies , english and biology respectively . what are his average marks ?", + "Output Program": [ + "n0 = 76.0\nn1 = 65.0\nn2 = 82.0\nn3 = 67.0\nn4 = 95.0\nt0 = n0 + n1\nt1 = 1.0 + 4.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "77" + ], + "split": "train" + }, + { + "Input": "the smallest number when increased by ` ` 3 ` ` is exactly divisible by 510 , 4590 , and 105 is :", + "Output Program": [ + "n0 = 3.0\nn1 = 510.0\nn2 = 4590.0\nn3 = 105.0\nt0 = n2 / n1\nt1 = n3 / n0\nt2 = t0 * t1\nt3 = t2 + t2\nanswer = t3 - 3.0\nprint(answer)" + ], + "Output Answer": [ + "627" + ], + "split": "train" + }, + { + "Input": "a waiter ' s salary consists of his salary and tips . during one week his tips were 5 / 3 of his salary . what fraction of his income came from tips ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nt0 = n0 / n1\nt1 = t0 + 1.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.625" + ], + "split": "train" + }, + { + "Input": "rachel and sarah spent $ 8 for gasoline , $ 15.65 for their lunch , and $ 5 apiece for gifts for grandma . grandma gave each of them $ 10 . if the girls left home with a total of $ 50 , how much do they have for the return trip ?", + "Output Program": [ + "n0 = 8.0\nn1 = 15.65\nn2 = 5.0\nn3 = 10.0\nn4 = 50.0\nt0 = n0 + n1\nt1 = n2 + t0\nt2 = t1 - n2\nt3 = n4 - t2\nanswer = n3 + t3\nprint(answer)" + ], + "Output Answer": [ + "36.35" + ], + "split": "train" + }, + { + "Input": "if ( m - 8 ) is a factor of m ^ 2 - qm - 24 , then q =", + "Output Program": [ + "n0 = 8.0\nn1 = 2.0\nn2 = 24.0\nt0 = n2 / n0\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "half a number plus 5 is 13 . what is the number ?", + "Output Program": [ + "n0 = 5.0\nn1 = 13.0\nt0 = n1 - n0\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "on dividing 109 by a number , the quotient is 9 and the remainder is 1 . find the divisor .", + "Output Program": [ + "import math\nn0 = 109.0\nn1 = 9.0\nn2 = 1.0\nt0 = n0 / n1\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "when a number is divided by 6 & then multiply by 12 the answer is 15 what is the no . ?", + "Output Program": [ + "n0 = 6.0\nn1 = 12.0\nn2 = 15.0\nt0 = n2 / n1\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "7.5" + ], + "split": "train" + }, + { + "Input": "aram \u2019 s car was fined when he gave joe and peter a ride , so they decided to help aram pay the fine . joe paid $ 3 more than 1 / 4 of the fine and peter paid $ 3 less than 1 / 3 of the fine , leaving pay $ 4 less than 1 / 2 the fine to complete the payment . what fraction of the fine did aram pay ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 4.0\nn3 = 3.0\nn4 = 1.0\nn5 = 3.0\nn6 = 4.0\nn7 = 1.0\nn8 = 2.0\nt0 = n0 + n2\nt1 = n1 / n2\nt2 = n1 / n0\nt3 = n1 / n8\nt4 = n0 + t0\nt5 = t1 + t2\nt6 = t5 + t3\nt7 = t6 - n1\nt8 = t4 / t7\nanswer = t8 - 100.0\nprint(answer)" + ], + "Output Answer": [ + "20.000000000000114" + ], + "split": "train" + }, + { + "Input": "the mean of 50 observations was 36 . it was found later that an observation 43 was wrongly taken as 23 . the corrected new mean is", + "Output Program": [ + "n0 = 50.0\nn1 = 36.0\nn2 = 43.0\nn3 = 23.0\nt0 = n0 * n1\nt1 = n0 - 2.0\nt2 = t1 - n3\nt3 = t0 + t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "36.5" + ], + "split": "train" + }, + { + "Input": "52 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780 . the bigger part is :", + "Output Program": [ + "n0 = 52.0\nn1 = 10.0\nn2 = 22.0\nn3 = 780.0\nt0 = n0 * n1\nt1 = n2 - n1\nt2 = n3 - t0\nt3 = t2 / t1\nanswer = n0 - t3\nprint(answer)" + ], + "Output Answer": [ + "30.333333333333332" + ], + "split": "train" + }, + { + "Input": "the price of 2 sarees and 4 shirts is $ 1600 . with the same money one can buy 1 saree and 6 shirts . if one wants to buy 12 shirts , how much shall he have to pay ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 1600.0\nn3 = 1.0\nn4 = 6.0\nn5 = 12.0\nt0 = n0 * n2\nt1 = n0 * n4\nt2 = t0 - n2\nt3 = t1 - n1\nt4 = t2 / t3\nanswer = n5 * t4\nprint(answer)" + ], + "Output Answer": [ + "2400" + ], + "split": "train" + }, + { + "Input": "on dividing 271 by a number , the quotient is 9 and the remainder is 1 . find the divisor ?", + "Output Program": [ + "import math\nn0 = 271.0\nn1 = 9.0\nn2 = 1.0\nt0 = n0 / n1\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "m and n are the x and y coordinates , respectively , of a point in the coordinate plane . if the points ( m , n ) and ( m + p , n + 15 ) both lie on the line defined by the equation x = ( y / 5 ) - ( 2 / 5 ) , what is the value of p ?", + "Output Program": [ + "n0 = 15.0\nn1 = 5.0\nn2 = 2.0\nn3 = 5.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "the \u201c connection \u201d between any two positive integers a and b is the ratio of the smallest common multiple of a and b to the product of a and b . for instance , the smallest common multiple of 8 and 12 is 24 , and the product of 8 and 12 is 96 , so the connection between 8 and 12 is 24 / 96 = 1 / 4 the positive integer y is less than 20 and the connection between y and 6 is equal to 1 / 1 . how many possible values of y are there ?", + "Output Program": [ + "n0 = 8.0\nn1 = 12.0\nn2 = 24.0\nn3 = 8.0\nn4 = 12.0\nn5 = 96.0\nn6 = 8.0\nn7 = 12.0\nn8 = 24.0\nn9 = 96.0\nn10 = 1.0\nn11 = 4.0\nn12 = 20.0\nn13 = 6.0\nn14 = 1.0\nn15 = 1.0\nt0 = n12 - 1.0\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "( 0.8 ) ( power 3 ) - ( 0.5 ) ( power 3 ) / ( 0.8 ) ( power 2 ) + 0.40 + ( 0.5 ) ( power 2 ) is :", + "Output Program": [ + "n0 = 0.8\nn1 = 3.0\nn2 = 0.5\nn3 = 3.0\nn4 = 0.8\nn5 = 2.0\nn6 = 0.4\nn7 = 0.5\nn8 = 2.0\nt0 = n0**min(n1, 5)\nt1 = n2**min(n1, 5)\nt2 = n0**min(n5, 5)\nt3 = n2**min(n5, 5)\nt4 = n6 + t2\nt5 = t0 - t1\nt6 = t4 + t3\nanswer = t5 / t6\nprint(answer)" + ], + "Output Answer": [ + "0.3000000000000001" + ], + "split": "train" + }, + { + "Input": "when a merchant imported a certain item , she paid a 7 percent import tax on the portion of the total value of the item in excess of $ 1,000 . if the amount of the import tax that the merchant paid was $ 110.60 , what was the total value of the item ?", + "Output Program": [ + "n0 = 7.0\nn1 = 1000.0\nn2 = 110.6\nt0 = n0 / 100.0\nt1 = n2 / t0\nanswer = t1 + n1\nprint(answer)" + ], + "Output Answer": [ + "2580" + ], + "split": "train" + }, + { + "Input": "eighteen years ago , a father was 3 times as old as his son . now the father is only twice as old his son . then the sum of the present ages of the son and the father is :", + "Output Program": [ + "n0 = 3.0\nt0 = 3.0 + 3.0\nt1 = n0 * t0\nt2 = n0 * t1\nt3 = t2 - t1\nt4 = t3 * 2.0\nanswer = t4 + t3\nprint(answer)" + ], + "Output Answer": [ + "108" + ], + "split": "train" + }, + { + "Input": "if x is a prime number , and x - 1 is the median of the set { x - 1 , 3 x + 3 , 2 x - 4 } , then what is the average ( arithmetic mean ) of the set ?", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 3.0\nn3 = 3.0\nn4 = 2.0\nn5 = 4.0\nt0 = n2 * n4\nt1 = n4 - n0\nt2 = n2 + t0\nt3 = t2 + t1\nanswer = t3 / n2\nprint(answer)" + ], + "Output Answer": [ + "3.3333333333333335" + ], + "split": "train" + }, + { + "Input": "the batting average of a particular batsman is 60 runs in 46 innings . if the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs , find his highest score .", + "Output Program": [ + "n0 = 60.0\nn1 = 46.0\nn2 = 150.0\nn3 = 58.0\nt0 = n0 * n1\nt1 = n1 - 2.0\nt2 = n3 * t1\nt3 = t0 - t2\nt4 = n2 + t3\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "179" + ], + "split": "train" + }, + { + "Input": "jancy had 100 currency notes in all , some of which are of rs 70 denomination and the remaining of rs 50 denomination . the total amount of all these currency notes was rs . 5000 . how much amount ( in rs ) did she have in the denomination of rs 50 ?", + "Output Program": [ + "n0 = 100.0\nn1 = 70.0\nn2 = 50.0\nn3 = 5000.0\nn4 = 50.0\n\nanswer = n3 / n2\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "a line that passes through ( \u2013 1 , \u2013 4 ) and ( 4 , k ) has a slope = k . what is the value of k ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 4.0\n\nanswer = n1 / n2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "a man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses . next year his income increases by 25 % but his savings increase by 100 % . if his total expenditure in 2 years is double his expenditure in 1 st year , what % age of his income in the first year did he save ?", + "Output Program": [ + "n0 = 25.0\nn1 = 100.0\nn2 = 2.0\nn3 = 1.0\nt0 = n0 + n1\nt1 = n1 * n2\nt2 = n1 + t0\nt3 = t2 - t1\nt4 = t3 / n1\nanswer = t4 * n1\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "in an examination , questions were asked in 5 sections . out of the total students , 5 % candidates cleared the cut - off in all the sections and 5 % cleared none . of the rest , 25 % cleared only one section and 20 % cleared 4 sections . if 24.5 % of the entire candidates cleared two sections and 300 candidates cleared 3 sections . find out how many candidates appeared at the examination ?", + "Output Program": [ + "n0 = 5.0\nn1 = 5.0\nn2 = 5.0\nn3 = 25.0\nn4 = 20.0\nn5 = 4.0\nn6 = 24.5\nn7 = 300.0\nn8 = 3.0\nt0 = n0 + n0\nt1 = 100.0 - t0\nt2 = n3 * t1\nt3 = n4 * t1\nt4 = t2 / 100.0\nt5 = t3 / 100.0\nt6 = t0 + t4\nt7 = t6 + t5\nt8 = n6 + t7\nt9 = 100.0 - t8\nt10 = n7 / t9\nanswer = t10 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "1200" + ], + "split": "train" + }, + { + "Input": "g ( x ) is defined as the product of all even integers k such that 0 < k \u2264 x . for example , g ( 14 ) = 2 \u00d7 4 \u00d7 6 \u00d7 8 \u00d7 10 \u00d7 12 \u00d7 14 . if g ( z ) is divisible by 4 ^ 11 , what is the smallest possible value for z ?", + "Output Program": [ + "n0 = 0.0\nn1 = 14.0\nn2 = 2.0\nn3 = 4.0\nn4 = 6.0\nn5 = 8.0\nn6 = 10.0\nn7 = 12.0\nn8 = 14.0\nn9 = 4.0\nn10 = 11.0\n\nanswer = n2 * n7\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "if ( a + b ) = 5 , ( b + c ) = 6 and ( c + d ) = 3 , what is the value of ( a + d ) ?", + "Output Program": [ + "n0 = 5.0\nn1 = 6.0\nn2 = 3.0\nt0 = n0 + n2\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a salesman commission is 10 % on all sales upto $ 5000 and 5 % on all sales exceeding this . he remits $ 15000 to his parent company after deducting his commission . find the total sales ?", + "Output Program": [ + "n0 = 10.0\nn1 = 5000.0\nn2 = 5.0\nn3 = 15000.0\nt0 = 4.0 / 100.0\nt1 = n0 * n1\nt2 = n1 * n2\nt3 = t1 / 100.0\nt4 = t2 / 100.0\nt5 = 1.0 - t0\nt6 = t3 - t4\nt7 = n3 + t6\nanswer = t7 / t5\nprint(answer)" + ], + "Output Answer": [ + "15885.416666666668" + ], + "split": "train" + }, + { + "Input": "a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 32.49 , the number of the member is the group is :", + "Output Program": [ + "import math\nn0 = 32.49\nt0 = n0 * 100.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "57" + ], + "split": "train" + }, + { + "Input": "q ' = 3 q - 3 , what is the value of ( 6 ' ) ' ?", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 6.0\nt0 = n0 * n2\nt1 = n2 - 1.0\nt2 = t0 - n0\nt3 = n0 * t2\nt4 = t3 - n0\nanswer = t4 * t1\nprint(answer)" + ], + "Output Answer": [ + "210" + ], + "split": "train" + }, + { + "Input": "in 1979 approximately 1 / 3 of the 38.3 million airline passengers traveling to or from the united states used kennedy airport . if the number of such passengers that used miami airport was 1 / 2 the number that used kennedy airport and 4 times the number that used logan airport , approximately how many millions of these passengers used logan airport that year ?", + "Output Program": [ + "n0 = 1979.0\nn1 = 1.0\nn2 = 3.0\nn3 = 38.3\nn4 = 1.0\nn5 = 2.0\nn6 = 4.0\nt0 = n3 / n2\nt1 = n5 * n6\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "1.5958333333333332" + ], + "split": "train" + }, + { + "Input": "a man spend 1 / 5 of his salary on food , 1 / 10 of his salary on house rent and 3 / 5 salary on clothes . he still has $ 16000 left with him . find salary . .", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 1.0\nn3 = 10.0\nn4 = 3.0\nn5 = 5.0\nn6 = 16000.0\nt0 = n0 / n1\nt1 = n0 / n3\nt2 = n4 / n1\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n0 - t4\nanswer = n6 / t5\nprint(answer)" + ], + "Output Answer": [ + "160000.00000000003" + ], + "split": "train" + }, + { + "Input": "a school has 4 section of chemistry in class x having 60 , 35 , 45 and 42 students . the mean marks obtained in chemistry test are 50 , 60 , 55 and 45 respectively for the 4 sections . determine the overall average of marks per student .", + "Output Program": [ + "n0 = 4.0\nn1 = 60.0\nn2 = 35.0\nn3 = 45.0\nn4 = 42.0\nn5 = 50.0\nn6 = 60.0\nn7 = 55.0\nn8 = 45.0\nn9 = 4.0\nt0 = n1 + n2\nt1 = n1 * n5\nt2 = n2 * n6\nt3 = n3 * n7\nt4 = n3 * n4\nt5 = t1 + t2\nt6 = n3 + t0\nt7 = t5 + t3\nt8 = n4 + t6\nt9 = t7 + t4\nanswer = t9 / t8\nprint(answer)" + ], + "Output Answer": [ + "52.005494505494504" + ], + "split": "train" + }, + { + "Input": "the average of 11 results is 52 , if the average of first 6 results is 49 and that of the last 6 is 52 . find the sixth result ?", + "Output Program": [ + "n0 = 11.0\nn1 = 52.0\nn2 = 6.0\nn3 = 49.0\nn4 = 6.0\nn5 = 52.0\nt0 = n1 * n2\nt1 = n2 * n3\nt2 = n0 * n1\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "34" + ], + "split": "train" + }, + { + "Input": "sum of the squares of 3 no . is 138 and the sum of their products taken two at a time is 131 . find the sum ?", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 138.0\nn2 = 131.0\nt0 = n2 * 2.0\nt1 = n1 + t0\nanswer = math.sqrt(max(0, t1))\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "the total of 324 of 20 paise and 25 paise make a sum of rs . 71 . the no of 20 paise coins is :", + "Output Program": [ + "n0 = 324.0\nn1 = 20.0\nn2 = 25.0\nn3 = 71.0\nn4 = 20.0\nt0 = n0 * n2\nt1 = n3 * 100.0\nt2 = n2 - n1\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "train" + }, + { + "Input": "the maximum number of student amoung them 1204 pens and 840 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :", + "Output Program": [ + "import scipy\nn0 = 1204.0\nn1 = 840.0\n\nanswer = scipy.gcd(int(n0), int(n1))\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "how many even number in the range between 10 to 140 inclusive are not divisible by 3", + "Output Program": [ + "n0 = 10.0\nn1 = 140.0\nn2 = 3.0\nt0 = n2 * 4.0\nt1 = n1 - n0\nt2 = n1 - 2.0\nt3 = t1 - 2.0\nt4 = t2 - t0\nt5 = t3 / 2.0\nt6 = t4 - n2\nt7 = t6 - n2\nt8 = t7 / n2\nt9 = t8 / 2.0\nanswer = t5 - t9\nprint(answer)" + ], + "Output Answer": [ + "44" + ], + "split": "train" + }, + { + "Input": "a cricketer scored 142 runs which included 12 boundaries and 2 sixes . what percent of his total score did he make by running between the wickets .", + "Output Program": [ + "n0 = 142.0\nn1 = 12.0\nn2 = 2.0\nt0 = n1 * 4.0\nt1 = n2 * 3.0\nt2 = n2 * t1\nt3 = t0 + t2\nt4 = n0 - t3\nt5 = t4 / n0\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "57.74647887323944" + ], + "split": "train" + }, + { + "Input": "a box contains 5 pairs of shoes ( 10 shoes in total ) . if two shoes are selected at random , what it is the probability that they are matching shoes ?", + "Output Program": [ + "n0 = 5.0\nn1 = 10.0\nt0 = n1 - 1.0\nanswer = 1.0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.1111111111111111" + ], + "split": "train" + }, + { + "Input": "if the price of petrol increases by 32 , by how much must a user cut down his consumption so that his expenditure on petrol remains constant ?", + "Output Program": [ + "n0 = 32.0\nt0 = n0 + 100.0\nt1 = 100.0 / t0\nt2 = 1.0 - t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "24.242424242424242" + ], + "split": "train" + }, + { + "Input": "the average ( arithmetic mean ) of 10 , 20 , and 60 is 5 more than the average of 10 , 40 , and what number ?", + "Output Program": [ + "n0 = 10.0\nn1 = 20.0\nn2 = 60.0\nn3 = 5.0\nn4 = 10.0\nn5 = 40.0\nt0 = n0 + n1\nt1 = n3 * 3.0\nt2 = n2 + t0\nt3 = n4 + t1\nt4 = n5 + t3\nanswer = t2 - t4\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "solution for 1.35 + . 123 + . 321", + "Output Program": [ + "n0 = 1.35\nn1 = 123.0\nn2 = 321.0\nt0 = n1 / 1000.0\nt1 = n2 / 1000.0\nt2 = n0 + t0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "1.794" + ], + "split": "train" + }, + { + "Input": "a student scored an average of 60 marks in 3 subjects : physics , chemistry and mathematics . if the average marks in physics and mathematics is 90 and that in physics and chemistry is 70 , what are the marks in physics ?", + "Output Program": [ + "n0 = 60.0\nn1 = 3.0\nn2 = 90.0\nn3 = 70.0\nt0 = n2 * 2.0\nt1 = n3 * 2.0\nt2 = n0 * n1\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "140" + ], + "split": "train" + }, + { + "Input": "if m is an integer such that ( - 2 ) ^ 2 m = 2 ^ ( 21 - m ) then m = ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 2.0\nn3 = 21.0\nt0 = n0 + 1.0\nanswer = n3 / t0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "set a contains all the even numbers between 42 and 90 inclusive . set b contains all the even numbers between 62 and 110 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ?", + "Output Program": [ + "n0 = 42.0\nn1 = 90.0\nn2 = 62.0\nn3 = 110.0\nt0 = n1 - n0\nt1 = n2 - n0\nt2 = t0 / 2.0\nt3 = t2 + 1.0\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "train" + }, + { + "Input": "of the 3,600 employees of company x , 1 / 3 are clerical . if the clerical staff were to be reduced by 1 / 6 , what percent of the total number of the remaining employees would then be clerical ?", + "Output Program": [ + "n0 = 3600.0\nn1 = 1.0\nn2 = 3.0\nn3 = 1.0\nn4 = 6.0\nt0 = n1 / n2\nt1 = n3 / n4\nt2 = n3 - t1\nt3 = n3 - t0\nt4 = t0 * t2\nt5 = t4 + t3\nt6 = t4 / t5\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "29.411764705882355" + ], + "split": "train" + }, + { + "Input": "if x is 20 percent greater than 80 , then x =", + "Output Program": [ + "n0 = 20.0\nn1 = 80.0\nt0 = n0 / 100.0\nt1 = n1 * t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "96" + ], + "split": "train" + }, + { + "Input": "a bag contains an equal number of one rupee , 50 paise and 25 paise coins respectively . if the total value is 70 , how many coins of each type are there ?", + "Output Program": [ + "n0 = 50.0\nn1 = 25.0\nn2 = 70.0\nt0 = 1 / 4.0\nt1 = 1 / 2.0\nt2 = t0 + t1\nt3 = t2 + 1.0\nanswer = n2 / t3\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "there are 30 players in a chess group , and each player plays each of the others once . given that each game is played by two players , how many total games will be played ?", + "Output Program": [ + "n0 = 30.0\nt0 = n0 - 1.0\nt1 = n0 * t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "435" + ], + "split": "train" + }, + { + "Input": "a certain number of horses and an equal number of men are going somewhere . half of the owners are on their horses ' back while the remaining ones are walking along leading their horses . if the number of legs walking on the ground is 90 , how many horses are there ?", + "Output Program": [ + "n0 = 90.0\nt0 = 2.0 / 2.0\nt1 = t0 + 4.0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "the average of 10 consecutive integers is 11 . then , 9 is deducted from the first consecutive number , 8 is deducted from the second , 7 is deducted form the third , and so on until the last number which remains unchanged . what is the new average ?", + "Output Program": [ + "n0 = 10.0\nn1 = 20.0\nn2 = 9.0\nn3 = 8.0\nn4 = 7.0\nt0 = 1.0 + 4.0\nt1 = n0 * n1\nt2 = n2 * t0\nt3 = t1 - t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "15.5" + ], + "split": "train" + }, + { + "Input": "let the number which when multiplied by 15 is increased by 196 .", + "Output Program": [ + "n0 = 15.0\nn1 = 196.0\nt0 = n0 - 1.0\nanswer = n1 / t0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "on day one , a store sold 86 cups . on each of the next d days , the company sold 50 cups . if the average daily sales of cups over this time period ( including day one ) is 53 cups , what is the value of d ?", + "Output Program": [ + "n0 = 86.0\nn1 = 50.0\nn2 = 53.0\nt0 = n0 + n1\nt1 = n2 + t0\nt2 = t1 / 3.0\nt3 = t2 + 1.0\nanswer = t3 - n2\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "a grocer has a sale of rs . 5420 , rs . 5660 , rs . 6200 , rs . 6350 and rs . 6500 for 5 consecutive months . find the sale he should have in the sixth month , so that he gets an average sale of rs . 6100 ?", + "Output Program": [ + "n0 = 5420.0\nn1 = 5660.0\nn2 = 6200.0\nn3 = 6350.0\nn4 = 6500.0\nn5 = 5.0\nn6 = 6100.0\nt0 = n5 + 1.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n6 * t0\nt4 = n3 + t2\nt5 = n4 + t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "6470" + ], + "split": "train" + }, + { + "Input": "eggs are sold in packages of 6 or 11 only . if doris bought 79 eggs exactly , what could be the number of large packs doris bought ?", + "Output Program": [ + "n0 = 6.0\nn1 = 11.0\nn2 = 79.0\nt0 = n0 * 4.0\nt1 = n2 - t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "find out the c . i on rs . 5000 at 4 % p . a . compound half - yearly for 1 1 / 2 year ?", + "Output Program": [ + "n0 = 5000.0\nn1 = 4.0\nn2 = 1.0\nn3 = 1.0\nn4 = 2.0\nt0 = n1 / 100.0\nt1 = 3.0 / n4\nt2 = t0 + n2\nt3 = t2**min(t1, 5)\nt4 = n0 * t3\nanswer = t4 - n0\nprint(answer)" + ], + "Output Answer": [ + "302.9802941364969" + ], + "split": "train" + }, + { + "Input": "a motorist knows 6 different routes from bristol to birmingham . from birmingham to sheffield he knows 3 different routes and from sheffield to carlisle he knows two different routes . how many routes does he know from bristol to carlisle ?", + "Output Program": [ + "n0 = 6.0\nn1 = 3.0\nt0 = n0 * n1\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "the grade point average of one third of the classroom is 54 ; the grade point average of the rest is 45 . what is the grade point average of the whole class ?", + "Output Program": [ + "n0 = 54.0\nn1 = 45.0\nt0 = n0 / 3.0\nt1 = n1 / 3.0\nt2 = t1 * 2.0\nanswer = t0 + t2\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "if x is an integer that has exactly 3 positive divisors ( these include 1 and x ) , how many positive divisors does x ^ 3 have ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 3.0\nt0 = n0 + n0\nanswer = n1 + t0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "60 % of the population of a village is 23040 . the total population of the village is ?", + "Output Program": [ + "n0 = 60.0\nn1 = 23040.0\nt0 = 100.0 / n0\nanswer = n1 * t0\nprint(answer)" + ], + "Output Answer": [ + "38400" + ], + "split": "train" + }, + { + "Input": "when positive integer x is divided by positive integer y , the remainder is 9 . if x / y = 96.25 , what is the value of y ?", + "Output Program": [ + "import math\nn0 = 9.0\nn1 = 96.25\nt0 = math.floor(n1)\nt1 = n1 - t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "what least number should be subtracted from 13605 such that the remainder is divisible by 87 ?", + "Output Program": [ + "n0 = 13605.0\nn1 = 87.0\n\nanswer = n0 % n1\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 20 kg . what is the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.5\nn2 = 20.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "there has been successive increases of 15 % and then 10 % in the price of gas from the previous month . by what percentage should a driver reduce gas consumption so that the expenditure does not change ?", + "Output Program": [ + "n0 = 15.0\nn1 = 10.0\nt0 = n0 + 100.0\nt1 = n1 * t0\nt2 = t1 / 100.0\nt3 = t0 + t2\nt4 = 100.0 / t3\nt5 = 1.0 - t4\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "20.948616600790515" + ], + "split": "train" + }, + { + "Input": "p and q are the only two applicants qualified for a short - term research project that pays 300 dollars in total . candidate p has more experience and , if hired , would be paid 50 percent more per hour than candidate q would be paid . candidate q , if hired , would require 10 hours more than candidate p to do the job . candidate p \u2019 s hourly wage is how many dollars greater than candidate q \u2019 s hourly wage ?", + "Output Program": [ + "n0 = 300.0\nn1 = 50.0\nn2 = 10.0\nt0 = 3.0 / 2.0\nt1 = t0 - 1.0\nt2 = n2 / t1\nt3 = n2 + t2\nt4 = n0 / t2\nt5 = n0 / t3\nanswer = t4 - t5\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "if one - third of one fourth of a number is 15 , then 3 - tenth of that number is :", + "Output Program": [ + "n0 = 15.0\nn1 = 3.0\nt0 = n0 * n1\nt1 = t0 + 12.0\nanswer = t1 - 3.0\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "train" + }, + { + "Input": "sandy gets 3 marks for each correct sum and loses 2 marks for each incorrect sum . sandy attempts 30 sums and obtains 60 marks . how many sums did sandy get correct ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 30.0\nn3 = 60.0\nt0 = n0 + n1\nt1 = n1 * n2\nt2 = n3 + t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "what is the product of all the possible values of x if x ^ 2 - 2 x - 8 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 8.0\n\nanswer = n2 / 1.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "in a office work is distribute between p persons . if 1 / 4 members are absent then work increased for each person is ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nt0 = n1 * 100.0\nt1 = n1 - n0\nt2 = t0 / t1\nanswer = t2 - 100.0\nprint(answer)" + ], + "Output Answer": [ + "33.33333333333334" + ], + "split": "train" + }, + { + "Input": "what least number should be subtracted from 13602 such that the remainder is divisible by 87 ?", + "Output Program": [ + "n0 = 13602.0\nn1 = 87.0\n\nanswer = n0 % n1\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "christine and siri have 21 rs between them . christine has 20 rs more than siri . how much does christine have .", + "Output Program": [ + "n0 = 21.0\nn1 = 20.0\nt0 = n0 - n1\nt1 = t0 / 2.0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "20.5" + ], + "split": "train" + }, + { + "Input": "in 10 years , a will be twice as old as b was 10 years ago . if a is now 4 years older than b the present age of b is", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 4.0\nt0 = n0 * 2.0\nt1 = n0 + t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "34" + ], + "split": "train" + }, + { + "Input": "the cost of 10 kg of mangos is equal to the cost of 24 kg of rice . the cost of 6 kg of flour equals the cost of 2 kg of rice . the cost of each kg of flour is $ 23 . find the total cost of 4 kg of mangos , 3 kg of rice and 5 kg of flour ?", + "Output Program": [ + "n0 = 10.0\nn1 = 24.0\nn2 = 6.0\nn3 = 2.0\nn4 = 23.0\nn5 = 4.0\nn6 = 3.0\nn7 = 5.0\nt0 = n1 / n0\nt1 = n2 * n4\nt2 = n4 * n7\nt3 = t1 / n3\nt4 = t0 * t3\nt5 = n6 * t3\nt6 = n5 * t4\nt7 = t6 + t5\nanswer = t7 + t2\nprint(answer)" + ], + "Output Answer": [ + "984.4" + ], + "split": "train" + }, + { + "Input": "if x is equal to the sum of the integers from 50 to 60 , inclusive , and y is the number of even integers from 50 to 60 , inclusive , what is the value of x + y ?", + "Output Program": [ + "n0 = 50.0\nn1 = 60.0\nn2 = 50.0\nn3 = 60.0\nt0 = n0 + n1\nt1 = n1 - n0\nt2 = t1 + 1.0\nt3 = t1 / 2.0\nt4 = t0 / 2.0\nt5 = t3 + 1.0\nt6 = t2 * t4\nanswer = t5 + t6\nprint(answer)" + ], + "Output Answer": [ + "611" + ], + "split": "train" + }, + { + "Input": "a number x is 7 times another number y . the percentage that y is less than x is", + "Output Program": [ + "n0 = 7.0\nt0 = n0 - 1.0\nt1 = t0 / n0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "85.71428571428571" + ], + "split": "train" + }, + { + "Input": "if the average ( arithmetic mean ) of 7 consecutive integers is 20 , then the product of the greatest and least integer is", + "Output Program": [ + "n0 = 7.0\nn1 = 20.0\nt0 = n0 * n1\nt1 = n0 * 3.0\nt2 = n0 - 1.0\nt3 = t0 - t1\nt4 = t3 / n0\nt5 = t4 + t2\nanswer = t5 * t4\nprint(answer)" + ], + "Output Answer": [ + "391" + ], + "split": "train" + }, + { + "Input": "the price of lunch for 15 people was $ 207.00 , including a 15 percent gratuity for service . what was the average price per person , excluding the gratuity ?", + "Output Program": [ + "n0 = 15.0\nn1 = 207.0\nn2 = 15.0\nt0 = n0 + 100.0\nt1 = 1.0 / n0\nt2 = n1 / t0\nt3 = t2 * 100.0\nanswer = t1 * t3\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "shipment - - - - - - no . of defective chips / shipment - - - total chips in shipment s 2 - - - - - - - - - - - - - - 5 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 12000 s 3 - - - - - - - - - - - - - - 6 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 18000 s 4 - - - - - - - - - - - - - - 4 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 16000 a computer chip manufacturer expects the ratio of the number of defective chips to be total number of chips in all future shipments equal to the corresponding ratio for shipmemts s 1 , s 2 , s 3 and s 4 comined as shown in the table above . what is the expected number q of defective chips in a shipment of 60000 chips ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 12000.0\nn3 = 3.0\nn4 = 6.0\nn5 = 18000.0\nn6 = 4.0\nn7 = 4.0\nn8 = 16000.0\nn9 = 1.0\nn10 = 2.0\nn11 = 3.0\nn12 = 4.0\nn13 = 60000.0\nt0 = n13 - n5\nt1 = t0 - n8\nt2 = t1 - n2\nt3 = n8 - t2\nanswer = t3 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "the maximum number of students among them 640 pens and 520 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils ?", + "Output Program": [ + "import scipy\nn0 = 640.0\nn1 = 520.0\n\nanswer = scipy.gcd(int(n0), int(n1))\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "the average of 50 numbers id 56 . if two numbers , namely 45 and 55 are discarded , the average of the remaining numbers is :", + "Output Program": [ + "n0 = 50.0\nn1 = 56.0\nn2 = 45.0\nn3 = 55.0\nt0 = n2 + n3\nt1 = n0 * n1\nt2 = n0 - 2.0\nt3 = t1 - t0\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "56.25" + ], + "split": "train" + }, + { + "Input": "sum of the squares of 3 no . is 149 and the sum of their products taken two at a time is 70 . find the sum ?", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 149.0\nn2 = 70.0\nt0 = n2 * 2.0\nt1 = n1 + t0\nanswer = math.sqrt(max(0, t1))\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "if , 1 * 3 * 5 = 16 3 * 5 * 7 = 38 5 * 7 * 9 = 68 then find , 7 * 9 * 11 = ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 5.0\nn3 = 16.0\nn4 = 3.0\nn5 = 5.0\nn6 = 7.0\nn7 = 38.0\nn8 = 5.0\nn9 = 7.0\nn10 = 9.0\nn11 = 68.0\nn12 = 7.0\nn13 = 9.0\nn14 = 11.0\nt0 = n10 * n14\nanswer = n6 + t0\nprint(answer)" + ], + "Output Answer": [ + "106" + ], + "split": "train" + }, + { + "Input": "if a 10 percent deposit that has been paid toward the purchase of a certain product is $ 110 , how much more remains to be paid ?", + "Output Program": [ + "n0 = 10.0\nn1 = 110.0\nt0 = 100.0 / n0\nt1 = n1 * t0\nanswer = t1 - n1\nprint(answer)" + ], + "Output Answer": [ + "990" + ], + "split": "train" + }, + { + "Input": "when 1 / 10 percent of 6,000 is subtracted from 1 / 10 of 6,000 , the difference is", + "Output Program": [ + "n0 = 1.0\nn1 = 10.0\nn2 = 6000.0\nn3 = 1.0\nn4 = 10.0\nn5 = 6000.0\nt0 = 3.0 + 4.0\nt1 = n0 / n1\nt2 = t1 / 100.0\nt3 = t0 * 1000.0\nt4 = t1 * t3\nt5 = t2 * t3\nanswer = t4 - t5\nprint(answer)" + ], + "Output Answer": [ + "693" + ], + "split": "train" + }, + { + "Input": "if there are 200 questions in a 3 hr examination . among these questions are 10 type a problems , which requires twice as much as time be spent than the rest of the type b problems . how many minutes should be spent on type a problems ?", + "Output Program": [ + "n0 = 200.0\nn1 = 3.0\nn2 = 10.0\nt0 = n1 * 60.0\nt1 = n2 * 2.0\nt2 = n0 - n2\nt3 = t1 + t2\nt4 = t0 / t3\nt5 = t4 * 2.0\nanswer = n2 * t5\nprint(answer)" + ], + "Output Answer": [ + "17.142857142857142" + ], + "split": "train" + }, + { + "Input": "carrie likes to buy t - shirts at the local clothing store . they cost $ 9.95 each . one day , she bought 25 t - shirts . how much money did she spend ?", + "Output Program": [ + "import math\nn0 = 9.95\nn1 = 25.0\nt0 = n0 * n1\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "248" + ], + "split": "train" + }, + { + "Input": "evaluate the sum 1 - 2 + 3 - 4 + 5 - 6 + . . . + 997 - 998 + 999 - 1000", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 3.0\nn3 = 4.0\nn4 = 5.0\nn5 = 6.0\nn6 = 997.0\nn7 = 998.0\nn8 = 999.0\nn9 = 1000.0\n\nanswer = n9 / n1\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "train" + }, + { + "Input": "find out the c . i on rs . 9000 at 4 % p . a . compound half - yearly for 1 1 / 2 years", + "Output Program": [ + "n0 = 9000.0\nn1 = 4.0\nn2 = 1.0\nn3 = 1.0\nn4 = 2.0\nt0 = n1 / 100.0\nt1 = 3.0 / n4\nt2 = t0 + n2\nt3 = t2**min(t1, 5)\nt4 = n0 * t3\nanswer = t4 - n0\nprint(answer)" + ], + "Output Answer": [ + "545.3645294456946" + ], + "split": "train" + }, + { + "Input": "in a flight of 600 km , an aircraft was slowed down due to bad weather . its average speed for the trip was reduced by 200 km / hr and the time of flight increased by 30 minutes . the duration of the flight is", + "Output Program": [ + "n0 = 600.0\nn1 = 200.0\nn2 = 30.0\nt0 = n1 * n2\nt1 = t0 / 10.0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "which number need to add to 859622 to get a no . exactly divisible by 456 ?", + "Output Program": [ + "n0 = 859622.0\nn1 = 456.0\nt0 = n0 % n1\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "859560" + ], + "split": "train" + }, + { + "Input": "a case of 12 rolls of paper towels sells for $ 9 . the cost of one roll sold individually is $ 1 . what is the percent r of savings per roll for the 12 - roll package over the cost of 12 rolls purchased individually ?", + "Output Program": [ + "n0 = 12.0\nn1 = 9.0\nn2 = 1.0\nn3 = 12.0\nn4 = 12.0\nt0 = n1 / n0\nt1 = t0 * 100.0\nanswer = 100.0 - t1\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "in a class of 20 students , 2 students did not borrow any books from the library , 8 students each borrowed 1 book , 3 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?", + "Output Program": [ + "n0 = 20.0\nn1 = 2.0\nn2 = 8.0\nn3 = 1.0\nn4 = 3.0\nn5 = 2.0\nn6 = 3.0\nn7 = 2.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n1 * n4\nt3 = t1 + t2\nt4 = n4 + t1\nt5 = n1 + t4\nt6 = n0 - t5\nt7 = t6 - n3\nt8 = n6 * t7\nt9 = t3 + t8\nanswer = t0 - t9\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a manufacturer produces a certain men ' s athletic shoe in integer sizes from 8 to 17 . for this particular shoe , each unit increase in size corresponds to a 1 / 4 - inch increase in the length of the shoe . if the largest size of this shoe is 30 % longer than the smallest size , how long , in inches , is the shoe in size 15 ?", + "Output Program": [ + "n0 = 8.0\nn1 = 17.0\nn2 = 1.0\nn3 = 4.0\nn4 = 30.0\nn5 = 15.0\nt0 = n2 / n3\nt1 = n4 / 100.0\nt2 = n1 - n0\nt3 = n5 - n0\nt4 = t0 * t2\nt5 = t0 * t3\nt6 = t4 / t1\nanswer = t6 + t5\nprint(answer)" + ], + "Output Answer": [ + "9.25" + ], + "split": "train" + }, + { + "Input": "xy = 1 then what is ( 5 ^ ( x + y ) ^ 2 ) / ( 5 ^ ( x - y ) ^ 2 )", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 2.0\nn3 = 5.0\nn4 = 2.0\nt0 = n0 * 4.0\nanswer = n1**min(t0, 5)\nprint(answer)" + ], + "Output Answer": [ + "625" + ], + "split": "train" + }, + { + "Input": "a baker charges n dollars for a birthday cake . next week , she intends to earn 320 dollars selling cakes . if she were to reduce the price of the cake by 20 percent , she would have to sell two more cakes to earn the same amount of revenue . how many cakes does she intend to sell next week ?", + "Output Program": [ + "n0 = 320.0\nn1 = 20.0\nt0 = 100.0 - n1\nt1 = t0 / 100.0\nt2 = n0 * t1\nt3 = t1 * 2.0\nt4 = n0 - t2\nt5 = t4 / t3\nanswer = n0 / t5\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "an assembly line produces 30 cogs per hour until an initial order of 60 cogs is completed . the speed of the assembly line is then immediately increased so that it can produce 60 cogs per hour until another 60 cogs are produced . what is the overall average output , in cogs per hour , for the assembly line during this whole time ?", + "Output Program": [ + "n0 = 30.0\nn1 = 60.0\nn2 = 60.0\nn3 = 60.0\nt0 = n1 / n0\nt1 = n1 * 2.0\nt2 = t0 + 1.0\nanswer = t1 / t2\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "if k is an integer and 0.00010101 x 10 ^ k is greater than 1000 , what is the least possible value of k ?", + "Output Program": [ + "import math\nn0 = 0.00010101\nn1 = 10.0\nn2 = 1000.0\nt0 = n2 / n0\nt1 = math.log(max(1e-5, n1), 2)\nt2 = math.log(max(1e-5, t0), 2)\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "6.995635628892249" + ], + "split": "train" + }, + { + "Input": "the average weight of a , b and c is 45 kg . if the average weight of a and b be 40 kg and that of b and c be 43 kg , then the weight of b is :", + "Output Program": [ + "n0 = 45.0\nn1 = 40.0\nn2 = 43.0\nt0 = n1 * 2.0\nt1 = n2 * 2.0\nt2 = n0 * 3.0\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "31" + ], + "split": "train" + }, + { + "Input": "5 is added to a certain number , the sum is multiplied by 2 , the product is divided by 5 and 5 is subtracted from the quotient . the remainder left is half of 44 . what is the number ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 5.0\nn3 = 5.0\nn4 = 44.0\nt0 = n4 / 2.0\nt1 = n0 + t0\nt2 = n0 * t1\nt3 = t2 / n1\nanswer = t3 - n0\nprint(answer)" + ], + "Output Answer": [ + "62.5" + ], + "split": "train" + }, + { + "Input": "find the number which when multiplied by 15 is increased by 196 .", + "Output Program": [ + "n0 = 15.0\nn1 = 196.0\nt0 = n0 - 1.0\nanswer = n1 / t0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "80 + 5 * 12 / ( 180 / 3 ) = ?", + "Output Program": [ + "n0 = 80.0\nn1 = 5.0\nn2 = 12.0\nn3 = 180.0\nn4 = 3.0\nt0 = n3 / n4\nt1 = n1 * n2\nt2 = t1 / t0\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "81" + ], + "split": "train" + }, + { + "Input": "tough and tricky questions : percents . over the course of a year , a certain microbrewery increased its beer output by 20 percent . at the same time , it decreased its total working hours by 30 percent . by what percent did this factory increase its output per hour ?", + "Output Program": [ + "n0 = 20.0\nn1 = 30.0\nt0 = n0 + 100.0\nt1 = 100.0 - n1\nt2 = t0 / t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "171.42857142857142" + ], + "split": "train" + }, + { + "Input": "a couple decides to have 3 children . if they succeed in having 3 children and each child is equally likely to be a boy or a girl , what is the probability that they will have exactly 1 girl and 2 boys ?", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 3.0\nn2 = 1.0\nn3 = 2.0\nt0 = n2 / n3\nt1 = math.factorial(min(15, int(n0)))\nt2 = math.factorial(min(15, int(n3)))\nt3 = t1 / t2\nt4 = t0**min(n0, 5)\nt5 = t3 * t4\nanswer = n2 - t5\nprint(answer)" + ], + "Output Answer": [ + "0.625" + ], + "split": "train" + }, + { + "Input": "the average of 55 results is 28 and the average of other 28 results is 55 . what is the average of all the results ?", + "Output Program": [ + "n0 = 55.0\nn1 = 28.0\nn2 = 28.0\nn3 = 55.0\nt0 = n0 + n1\nt1 = n0 * n1\nt2 = t1 + t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "37.10843373493976" + ], + "split": "train" + }, + { + "Input": "jerry \u2019 s average ( arithmetic mean ) score on the first 3 of 4 tests is 90 . if jerry wants to raise his average by 2 points , what score must he earn on the fourth test ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 90.0\nn3 = 2.0\nt0 = n2 + n3\nt1 = n0 * n2\nt2 = n1 * t0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "98" + ], + "split": "train" + }, + { + "Input": "what is the total cost of 2 sandwiches at $ 2.44 each and 4 sodas at $ 0.87 each ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.44\nn2 = 4.0\nn3 = 0.87\nt0 = n0 * n1\nt1 = n2 * n3\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "8.36" + ], + "split": "train" + }, + { + "Input": "average of 5 numbers is 12 . if one number is excluded the average becomes 10 . the excluded number is", + "Output Program": [ + "n0 = 5.0\nn1 = 12.0\nn2 = 10.0\nt0 = n0 * n1\nt1 = n2 * 4.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "set a contains all the even numbers between 12 and 60 inclusive . set b contains all the even numbers between 62 and 110 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ?", + "Output Program": [ + "n0 = 12.0\nn1 = 60.0\nn2 = 62.0\nn3 = 110.0\nt0 = n1 - n0\nt1 = n2 - n0\nt2 = t0 / 2.0\nt3 = t2 + 1.0\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "1250" + ], + "split": "train" + }, + { + "Input": "if 213 \u00d7 16 = 3408 , then 16 \u00d7 21.3 is equal to :", + "Output Program": [ + "n0 = 213.0\nn1 = 16.0\nn2 = 3408.0\nn3 = 16.0\nn4 = 21.3\n\nanswer = n4 * n3\nprint(answer)" + ], + "Output Answer": [ + "340.8" + ], + "split": "train" + }, + { + "Input": "if x and y are numbers such that ( x + 3 ) ( y - 3 ) = 0 , what is the smallest possible value of x ^ 2 + y ^ 2", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 0.0\nn3 = 2.0\nn4 = 2.0\n\nanswer = n0**min(n3, 5)\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "a man \u00e2 \u20ac \u2122 s current age is ( 2 / 5 ) of the age of his father . after 6 years , he will be ( 1 / 2 ) of the age of his father . what is the age of father at now ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 6.0\nn3 = 1.0\nn4 = 2.0\nt0 = n3 / n0\nt1 = n0 / n1\nt2 = n2 * t0\nt3 = t0 - t1\nt4 = n2 - t2\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "30.000000000000007" + ], + "split": "train" + }, + { + "Input": "the toll t , in dollars , for a truck using a certain bridge is given by the formula t = 1.50 + 1.50 ( x \u2212 2 ) , where x is the number of axles on the truck . what is the toll for an 18 - wheel truck that has 2 wheels on its front axle and 4 wheels on each of its other axles ?", + "Output Program": [ + "n0 = 1.5\nn1 = 1.5\nn2 = 2.0\nn3 = 18.0\nn4 = 2.0\nn5 = 4.0\nt0 = n3 - n2\nt1 = t0 / n5\nt2 = t1 + 1.0\nt3 = t2 - n2\nt4 = n1 * t3\nanswer = n0 + t4\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "a fraction in reduced form is such that when it is squared and then its numerator is reduced by 33 ( 1 / 3 ) % and denominator is reduced to 20 % , its result is twice the original fraction . the sum of numerator and denominator is :", + "Output Program": [ + "n0 = 33.0\nn1 = 1.0\nn2 = 3.0\nn3 = 20.0\nt0 = 100.0 / n3\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a computer is programmed to multiply consecutive even integers 2 * 4 * 6 * 8 * \u2026 * n until the product is divisible by 2211 , what is the value of n ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 6.0\nn3 = 8.0\nn4 = 2211.0\nt0 = 1.0 + 10.0\nt1 = n4 / t0\nt2 = t1 / 3.0\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "134" + ], + "split": "train" + }, + { + "Input": "a basket of 1430 apples is divided equally among a group of apple lovers . if 45 people join the group , each apple lover would receive 9 apples less . how many q apples did each person get before 45 people joined the feast ?", + "Output Program": [ + "n0 = 1430.0\nn1 = 45.0\nn2 = 9.0\nn3 = 45.0\nt0 = 10.0 + 10.0\nt1 = t0 + 2.0\nt2 = n0 / t1\nt3 = n1 + t2\nt4 = n0 / t3\nanswer = n2 + t4\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "the number of positive integers valued pairs ( x , y ) satisfying 4 x - 17 y = 1 and x < = 1000 ( x is less than or equal to 1000 ) is", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 17.0\nn2 = 1.0\nn3 = 1000.0\nn4 = 1000.0\nt0 = n0 * n3\nt1 = t0 - n2\nt2 = t1 / n1\nt3 = math.floor(t2)\nt4 = t3 + n2\nt5 = t4 / 2.0\nanswer = t5 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "59" + ], + "split": "train" + }, + { + "Input": "a retailer sells 10 shirts . the first 3 he sells for $ 20 , $ 22 and $ 25 . if the retailer wishes to sell the 10 shirts for an overall average price of over $ 20 , what must be the minimum average price of the remaining 7 shirts ?", + "Output Program": [ + "n0 = 10.0\nn1 = 3.0\nn2 = 20.0\nn3 = 22.0\nn4 = 25.0\nn5 = 10.0\nn6 = 20.0\nn7 = 7.0\nt0 = n2 + n3\nt1 = n0 * n6\nt2 = n4 + t0\nt3 = t1 - t2\nanswer = t3 / n7\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "a total of 50 percent of the geese included in a certain migration study were male . if some of the geese migrated during the study and 20 percent of the migrating geese were male , what was the ratio of the migration rate for the male geese to the migration rate for the female geese ? [ migration rate for geese of a certain sex = ( number of geese of that sex migrating ) / ( total number of geese of that sex ) ]", + "Output Program": [ + "n0 = 50.0\nn1 = 20.0\nt0 = n1 / 100.0\nt1 = n0 / 100.0\nt2 = 2.0 * 4.0\nt3 = t0 / t1\nt4 = t2 * 10.0\nt5 = t4 / 100.0\nt6 = t5 / t1\nanswer = t3 / t6\nprint(answer)" + ], + "Output Answer": [ + "0.25" + ], + "split": "train" + }, + { + "Input": "a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 13.69 , the number of the member is the group is :", + "Output Program": [ + "import math\nn0 = 13.69\nt0 = n0 * 100.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "37" + ], + "split": "train" + }, + { + "Input": "how many paying stones , each measuring 2 1 / 2 m * 2 m are required to pave a rectangular court yard 40 m long and 16 1 / 2 m board ?", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 2.0\nn3 = 2.0\nn4 = 40.0\nn5 = 16.0\nn6 = 1.0\nn7 = 2.0\nt0 = n1 / n0\nt1 = n5 + t0\nt2 = n0 + t0\nt3 = n4 * t1\nt4 = n0 * t2\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "132" + ], + "split": "train" + }, + { + "Input": "when a number is divided by 13 , the remainder is 11 . when the same number is divided by 17 , the remainder is 9 . what is the number ?", + "Output Program": [ + "n0 = 13.0\nn1 = 11.0\nn2 = 17.0\nn3 = 9.0\nt0 = 10.0 + 12.0\nt1 = t0 + 4.0\nt2 = n0 * t1\nanswer = n1 + t2\nprint(answer)" + ], + "Output Answer": [ + "349" + ], + "split": "train" + }, + { + "Input": "if 1 / ( x + 5 ) + 1 / ( x - 5 ) = 1 / ( x - 5 ) , what is the value of x ?", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 1.0\nn3 = 5.0\nn4 = 1.0\nn5 = 5.0\nt0 = n1 + n0\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "at the end of year x , automobile installment credit accounted for 36 % of all outstanding consumer installment credit . at that time automobile finance companies extended $ 35 billion of credit , or 1 / 3 of the automobile installment credit . how many billion dollars of consumer installment credit was outstanding at that time ?", + "Output Program": [ + "n0 = 36.0\nn1 = 35.0\nn2 = 1.0\nn3 = 3.0\nt0 = n0 / 100.0\nt1 = n1 * n3\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "291.6666666666667" + ], + "split": "train" + }, + { + "Input": "if j is the least positive integer that is divisible by every integer from 10 to 15 inclusive , then j / 26 is =", + "Output Program": [ + "n0 = 10.0\nn1 = 15.0\nn2 = 26.0\nt0 = n0 + 1.0\nt1 = t0 + 1.0\nt2 = n0 * t0\nt3 = t1 + 1.0\nt4 = t1 * t2\nt5 = t3 + 1.0\nt6 = t5 * t4\nt7 = t6 / 2.0\nanswer = t7 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "2310" + ], + "split": "train" + }, + { + "Input": "diana is painting statues . she has 1 / 2 of a gallon of paint remaining . each statue requires 1 / 4 gallon of paint . how many statues can she paint ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 1.0\nn3 = 4.0\nt0 = n0 / n1\nt1 = n2 / n3\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "find the average of first 15 natural numbers .", + "Output Program": [ + "n0 = 15.0\nt0 = 1.0 + 2.0\nt1 = 1.0 + 4.0\nt2 = 3.0 + 4.0\nt3 = 4.0 + 4.0\nt4 = 1.0 + 10.0\nt5 = 1.0 + 12.0\nt6 = t0 + 3.0\nt7 = t3 + 1.0\nt8 = t5 + 1.0\nt9 = t6 + 4.0\nt10 = t9 + t1\nt11 = t10 + t6\nt12 = t11 + t2\nt13 = t12 + t3\nt14 = t13 + t7\nt15 = t14 + 10.0\nt16 = t15 + t4\nt17 = t16 + 12.0\nt18 = t17 + t5\nt19 = t18 + t8\nt20 = n0 + t19\nanswer = t20 / n0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "the \u201c a - number \u201d of a number x is defined as the ones digit of 2 ^ x . antony rolls a die with 6 sides labeled with the integers from 1 to 6 , each of which has an equal probability of landing face - up . he then takes 3 ^ a , where a is the a - number of the result of his die roll , and plots 3 ^ a on a number line as the point a . finally , he repeats this entire process , this time plotting the result as the point b . what is the probability that the distance between a and b is greater than the value of b ?", + "Output Program": [ + "n0 = 2.0\nn1 = 6.0\nn2 = 1.0\nn3 = 6.0\nn4 = 3.0\nn5 = 3.0\nt0 = n0 + 4.0\nt1 = n1 * n1\nt2 = n2 + t0\nt3 = n0 + t2\nt4 = t3 + 4.0\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.3611111111111111" + ], + "split": "train" + }, + { + "Input": "you and your friend spent a total of $ 17 for lunch . your friend spent $ 3 more than you . how much did your friend spend on their lunch ?", + "Output Program": [ + "n0 = 17.0\nn1 = 3.0\nt0 = n0 - n1\nt1 = t0 / 2.0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the average of 7 numbers is 15 . if each number be multiplied by 5 . find the average of new set of numbers ?", + "Output Program": [ + "n0 = 7.0\nn1 = 15.0\nn2 = 5.0\n\nanswer = n1 * n2\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "a mixture of 40 liters of milk and water contains 10 % water . how much water should be added to this so that water may be 20 % in the new mixture ?", + "Output Program": [ + "n0 = 40.0\nn1 = 10.0\nn2 = 20.0\nt0 = n2 / 100.0\nt1 = n1 / 100.0\nt2 = 100.0 - n2\nt3 = t2 / 100.0\nt4 = n0 * t0\nt5 = n0 * t1\nt6 = t4 - t5\nanswer = t6 / t3\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "a trained covered x km at 40 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 5 x km .", + "Output Program": [ + "n0 = 40.0\nn1 = 2.0\nn2 = 20.0\nn3 = 5.0\nt0 = n0 / n0\nt1 = n0 * n3\nt2 = n0 * n1\nt3 = t2 / n2\nt4 = t0 + t3\nanswer = t1 / t4\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "a family had dinner in a restaurant and paid $ 30 for food . they also had to pay 9.5 % sale tax and 10 % for the tip . how much did they pay for the dinner ?", + "Output Program": [ + "n0 = 30.0\nn1 = 9.5\nn2 = 10.0\nt0 = n1 - 3.0\nt1 = n1 * t0\nt2 = t1 - 0.25\nt3 = t2 + 0.25\nt4 = t3 - 12.0\nt5 = t4 - 12.0\nanswer = t5 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "35.75" + ], + "split": "train" + }, + { + "Input": "a man is 26 years older than his son . in two years , his age will be twice the age of his son . the present age of this son is", + "Output Program": [ + "n0 = 26.0\nt0 = 2.0 * 2.0\nt1 = 2.0 - 1.0\nt2 = t0 - 2.0\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "the manager at a health foods store mixes a unique superfruit juice cocktail that costs $ 1399.45 per litre to make . the cocktail includes mixed fruit juice and a \u00e7 ai berry juice , which cost $ 262.85 per litre and $ 3104.35 per litre , respectively . the manager has already opened 35 litres of the mixed fruit juice . how many litres of the a \u00e7 ai berry juice does he need to add ?", + "Output Program": [ + "n0 = 1399.45\nn1 = 262.85\nn2 = 3104.35\nn3 = 35.0\nt0 = n0 * n3\nt1 = n1 * n3\nt2 = n2 - n0\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "23.333333333333336" + ], + "split": "train" + }, + { + "Input": "a number x is 18 times another number y . the percentage that y is less than x is", + "Output Program": [ + "n0 = 18.0\nt0 = n0 - 1.0\nt1 = t0 / n0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "94.44444444444444" + ], + "split": "train" + }, + { + "Input": "a dozen eggs and 5 pounds of oranges are currently at the same price . if the price of a dozen eggs rises by 3 percent and the price of oranges rises by 6 % . how much more will it cost to buy a dozen eggs and 10 pounds of oranges .", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nn2 = 6.0\nn3 = 10.0\nt0 = n3 + n3\nt1 = n1 / 100.0\nt2 = n2 / 100.0\nt3 = t1 * 10.0\nt4 = n3 * t2\nt5 = n3 + t3\nt6 = n3 + t4\nt7 = t5 + t6\nt8 = t7 - t0\nt9 = t8 * 100.0\nt10 = t9 / t0\nanswer = t10 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "8.999999999999986" + ], + "split": "train" + }, + { + "Input": "3 years ago the average age of a class of 6 members was 19 years . a boy have been added , the average age of the class is the same today . what is the age of the boy ?", + "Output Program": [ + "n0 = 3.0\nn1 = 6.0\nn2 = 19.0\nt0 = n1 + 1.0\nt1 = n1 * n2\nt2 = n0 * n1\nt3 = t1 + t2\nt4 = n2 * t0\nanswer = t4 - t3\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "if ( x + 3 ) ^ 2 / ( 3 x + 29 ) = 2 , then the difference between the two possible values of x is :", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 2.0\nn2 = 3.0\nn3 = 29.0\nn4 = 2.0\nt0 = n4 * n3\nt1 = n0 * n0\nt2 = t0 - t1\nt3 = math.sqrt(max(0, t2))\nanswer = t3 * n1\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "the price of 24 apples is equal to that of 28 oranges . the price of 45 apples and 60 oranges together is rs . 1350 . the total price of 30 apples and 40 oranges is", + "Output Program": [ + "n0 = 24.0\nn1 = 28.0\nn2 = 45.0\nn3 = 60.0\nn4 = 1350.0\nn5 = 30.0\nn6 = 40.0\nt0 = n0 / n1\nt1 = n3 * t0\nt2 = n2 + t1\nt3 = n4 / t2\nt4 = n5 * t3\nt5 = t3 * t0\nt6 = n6 * t5\nanswer = t4 + t6\nprint(answer)" + ], + "Output Answer": [ + "900" + ], + "split": "train" + }, + { + "Input": "the population of a town increased from 1 , 75000 to 2 , 97500 in a decade . the average percent increase of population per year is", + "Output Program": [ + "n0 = 1.0\nn1 = 75000.0\nn2 = 2.0\nn3 = 97500.0\nt0 = 100.0 * 1000.0\nt1 = n1 + t0\nt2 = n2 * t0\nt3 = n3 + t2\nt4 = t3 - t1\nt5 = t4 / 10.0\nt6 = t5 / t1\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "7.000000000000001" + ], + "split": "train" + }, + { + "Input": "a couple spent $ 132 in total while dining out and paid this amount using a credit card . the $ 132 figure included a 20 percent tip which was paid on top of the price which already included a sales tax of 10 percent on top of the price of the food . what was the actual price of the food before tax and tip ?", + "Output Program": [ + "n0 = 132.0\nn1 = 132.0\nn2 = 20.0\nn3 = 10.0\nt0 = n2 + 100.0\nt1 = n3 + 100.0\nt2 = n0 * 100.0\nt3 = t2 / t0\nt4 = t3 * 100.0\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 14000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is :", + "Output Program": [ + "n0 = 8000.0\nn1 = 7.0\nn2 = 14000.0\nn3 = 6000.0\nt0 = n2 - n0\nt1 = n0 - n3\nt2 = n1 * t0\nt3 = t2 / t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "in arun ' s opinion , his weight is greater than 61 kg but leas than 72 kg . his brother does not agree with arun and he thinks that arun ' s weight is greater than 60 kg but less than 70 kg . his mother ' s view is that his weight can not be greater than 64 kg . if all of them are correct in their estimation , what is the average of diferent probable weights of arun ?", + "Output Program": [ + "n0 = 61.0\nn1 = 72.0\nn2 = 60.0\nn3 = 70.0\nn4 = 64.0\nt0 = n0 + 1.0\nt1 = n4 + t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "63" + ], + "split": "train" + }, + { + "Input": "a and b together have $ 1210 . if of a ' s amount is equal to of b ' s amount , how much amount does b have ?", + "Output Program": [ + "n0 = 1210.0\nt0 = n0 * 2.0\nt1 = t0 * 2.0\nanswer = t1 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "484" + ], + "split": "train" + }, + { + "Input": "what is the minimum value of | x - 4 | + | x + 6 | + | x - 5 | ?", + "Output Program": [ + "n0 = 4.0\nn1 = 6.0\nn2 = 5.0\n\nanswer = n1 + n2\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "a man saves 20 % of his monthly salary . if an account of dearness of things he is to increase his monthly expenses by 20 % , he is only able to save rs . 200 per month . what is his monthly salary ?", + "Output Program": [ + "n0 = 20.0\nn1 = 20.0\nn2 = 200.0\nt0 = n1 / 100.0\nt1 = n2 * 100.0\nt2 = 100.0 - n0\nt3 = t0 * t2\nt4 = t3 + t2\nt5 = 100.0 - t4\nanswer = t1 / t5\nprint(answer)" + ], + "Output Answer": [ + "5000" + ], + "split": "train" + }, + { + "Input": "the average height of 20 students is 20 cm and the average height of 11 students is 20 cm . what is the average height of the 31 students ?", + "Output Program": [ + "n0 = 20.0\nn1 = 20.0\nn2 = 11.0\nn3 = 20.0\nn4 = 31.0\nt0 = n0 * n0\nt1 = n0 * n2\nt2 = t0 + t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "a certain ball team has an equal number of right - and left - handed players . on a certain day , two - thirds of the players were absent from practice . of the players at practice that day , two - third were left handed . what is the ratio of the number of right - handed players who were not at practice that day to the number of lefthanded players who were not at practice ?", + "Output Program": [ + "t0 = 1.0 / 2.0\nt1 = 2.0 / 3.0\nt2 = 1.0 - t1\nt3 = t1 * t2\nt4 = t2 - t3\nt5 = t0 - t3\nt6 = t0 - t4\nanswer = t6 / t5\nprint(answer)" + ], + "Output Answer": [ + "1.3999999999999997" + ], + "split": "train" + }, + { + "Input": "find the value of y from ( 12 ) ^ 2 x 6 ^ 4 \u00f7 432 = y ?", + "Output Program": [ + "n0 = 12.0\nn1 = 2.0\nn2 = 6.0\nn3 = 4.0\nn4 = 432.0\nt0 = n0**min(n1, 5)\nt1 = n2**min(n3, 5)\nt2 = t0 * t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "432" + ], + "split": "train" + }, + { + "Input": "in how many no . between 10 and 40 exactly two of the digits is 4 ?", + "Output Program": [ + "n0 = 10.0\nn1 = 40.0\nn2 = 4.0\nt0 = n1 / n0\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "10 people went to a hotel for combine dinner party 8 of them spent rs . 10 each on their dinner and rest spent 4 more than the average expenditure of all the 10 . what was the total money spent by them .", + "Output Program": [ + "n0 = 10.0\nn1 = 8.0\nn2 = 10.0\nn3 = 4.0\nn4 = 10.0\nt0 = n1 * n2\nt1 = n0 - n1\nt2 = n3 * t1\nt3 = n0 - t1\nt4 = t0 + t2\nt5 = t4 / t3\nanswer = n0 * t5\nprint(answer)" + ], + "Output Answer": [ + "110" + ], + "split": "train" + }, + { + "Input": "if x is a positive integer with fewer than 3 digits , what is the probability that c x * ( x + 1 ) is a multiple of either 4 or 5 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 4.0\nn3 = 5.0\nt0 = 100.0 / n2\nt1 = 100.0 / n3\nt2 = 100.0 - n1\nt3 = t0 * 2.0\nt4 = t1 * 2.0\nt5 = t3 + t4\nt6 = t5 - n2\nanswer = t6 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.8686868686868687" + ], + "split": "train" + }, + { + "Input": "the price of commodity x increases by 30 cents every year , while the price of commodity y increases by 20 cents every year . if in 2001 , the price of commodity x was $ 4.20 and the price of commodity y was $ 4.40 , in which year will commodity x cost 90 cents more than the commodity y ?", + "Output Program": [ + "n0 = 30.0\nn1 = 20.0\nn2 = 2001.0\nn3 = 4.2\nn4 = 4.4\nn5 = 90.0\nt0 = n5 / 100.0\nt1 = n0 / 100.0\nt2 = n4 - n3\nt3 = t0 + t2\nt4 = t1 - t2\nt5 = t3 / t4\nanswer = n2 + t5\nprint(answer)" + ], + "Output Answer": [ + "2012" + ], + "split": "train" + }, + { + "Input": "10 years ago , the age of anand was one - third the age of bala at that time . the present age of bala is 10 years more than the present age of anand . find the present age of anand ?", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nt0 = n0 * 3.0\nt1 = 3.0 - 1.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "the average of 10 numbers is 40.2 . later it is found that two numbers have been wrongly copied . the first is 17 greater than the actual number and the second number added is 13 instead of 31 . find the correct average .", + "Output Program": [ + "n0 = 10.0\nn1 = 40.2\nn2 = 17.0\nn3 = 13.0\nn4 = 31.0\nt0 = n2 + n3\nt1 = n0 * n1\nt2 = t0 + t1\nt3 = t2 - n4\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "40.1" + ], + "split": "train" + }, + { + "Input": "4 brothers adam , bill , charles and david together contributed certain amount of money and purchased a car . the contribution made by adam is half that of the total contribution made by the other 3 brothers , contribution made by bill is one - fourth of the total contribution made by the other 3 brothers and the contribution made by charles is two - third of the total contribution made by the other 3 brothers . if the total price of the car is $ 9750 , find the contribution made by david .", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 3.0\nn3 = 3.0\nn4 = 9750.0\nt0 = 1.0 + 2.0\nt1 = n0 + 1.0\nt2 = n1 / 2.0\nt3 = t2 + 1.0\nt4 = n4 / t0\nt5 = n4 / t1\nt6 = t4 + t5\nt7 = n4 / t3\nt8 = t6 + t7\nanswer = n4 - t8\nprint(answer)" + ], + "Output Answer": [ + "650" + ], + "split": "train" + }, + { + "Input": "there are , in a certain league , 20 teams , and each team face another team for a total of 4 times . how many games are played in the season ?", + "Output Program": [ + "n0 = 20.0\nn1 = 4.0\nt0 = n0 / 2.0\nt1 = n0 - 1.0\nt2 = t1 * n1\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "760" + ], + "split": "train" + }, + { + "Input": "if p ( a ) = 2 / 15 , p ( b ) = 4 / 15 , and p ( a \u00e2 \u02c6 \u00aa b ) = 12 / 15 find p ( b | a )", + "Output Program": [ + "n0 = 2.0\nn1 = 15.0\nn2 = 4.0\nn3 = 15.0\nn4 = 12.0\nn5 = 15.0\nt0 = n4 / n1\nt1 = n0 / n1\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "a car travels first 160 km at 75 km / hr and the next 160 km at 90 km / hr . what is the average speed for the first 320 km of the tour ?", + "Output Program": [ + "n0 = 160.0\nn1 = 75.0\nn2 = 160.0\nn3 = 90.0\nn4 = 320.0\nt0 = n0 / n1\nt1 = n0 / n3\nt2 = t0 + t1\nt3 = 1.0 / t2\nanswer = n4 * t3\nprint(answer)" + ], + "Output Answer": [ + "81.81818181818181" + ], + "split": "train" + }, + { + "Input": "a , b and c have rs . 500 between them , a and c together have rs . 200 and b and c rs . 360 . how much does c have ?", + "Output Program": [ + "n0 = 500.0\nn1 = 200.0\nn2 = 360.0\nt0 = n1 + n2\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 190 games will be played during the tournament . what is the number of participants ?", + "Output Program": [ + "import math\nn0 = 190.0\nt0 = n0 * 2.0\nt1 = t0 * 4.0\nt2 = t1 + 1.0\nt3 = math.sqrt(max(0, t2))\nt4 = t3 + 1.0\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "find the value of x in [ ( 17.28 / x ) / ( 3.6 * 0.2 ) ] = 2", + "Output Program": [ + "n0 = 17.28\nn1 = 3.6\nn2 = 0.2\nn3 = 2.0\nt0 = n1 * n2\nt1 = n3 * t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "set a contains all the even numbers between 22 and 70 inclusive . set b contains all the even numbers between 62 and 110 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ?", + "Output Program": [ + "n0 = 22.0\nn1 = 70.0\nn2 = 62.0\nn3 = 110.0\nt0 = n1 - n0\nt1 = n2 - n0\nt2 = t0 / 2.0\nt3 = t2 + 1.0\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "1000" + ], + "split": "train" + }, + { + "Input": "the average of 5 numbers is 6.8 . if one of the numbers is multiplied by a factor of 2 , the average of the numbers increases to 9.2 . what number is multiplied by 2 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 6.8\nn2 = 2.0\nn3 = 9.2\nn4 = 2.0\nt0 = n0 * n3\nt1 = n0 * n1\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "p and q are the only two applicants qualified for a short - term research project that pays 360 dollars in total . candidate p has more experience and , if hired , would be paid 50 percent more per hour than candidate q would be paid . candidate q , if hired , would require 10 hours more than candidate p to do the job . candidate p \u2019 s hourly wage is how many dollars greater than candidate q \u2019 s hourly wage ?", + "Output Program": [ + "n0 = 360.0\nn1 = 50.0\nn2 = 10.0\nt0 = 3.0 / 2.0\nt1 = t0 - 1.0\nt2 = n2 / t1\nt3 = n2 + t2\nt4 = n0 / t2\nt5 = n0 / t3\nanswer = t4 - t5\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 250 , what were her original savings ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 250.0\nt0 = n0 / n1\nt1 = 1.0 - t0\nanswer = n2 / t1\nprint(answer)" + ], + "Output Answer": [ + "1000" + ], + "split": "train" + }, + { + "Input": "bill made a profit of 10 % by selling a product . if he had purchased that product for 10 % less and sold it at a profit of 30 % , he would have received $ 56 more . what was his original selling price ?", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 30.0\nn3 = 56.0\nt0 = n0 / 100.0\nt1 = n2 / 100.0\nt2 = t0 + 1.0\nt3 = t1 + 1.0\nt4 = 1.0 - t0\nt5 = t3 * t4\nt6 = t5 - t2\nt7 = n3 / t6\nanswer = t2 * t7\nprint(answer)" + ], + "Output Answer": [ + "879.9999999999993" + ], + "split": "train" + }, + { + "Input": "suraj has a certain average of runs for 16 innings . in the 17 th innings he scores 112 runs thereby increasing his average by 6 runs . what is his average after the 17 th innings ?", + "Output Program": [ + "n0 = 16.0\nn1 = 17.0\nn2 = 112.0\nn3 = 6.0\nn4 = 17.0\nt0 = n0 * n3\nt1 = n1 - n0\nt2 = n2 - t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "the average of squares of first 11 consecutive even numbers is :", + "Output Program": [ + "n0 = 11.0\nt0 = n0 + 1.0\nt1 = n0 * 2.0\nt2 = t1 + 1.0\nt3 = t0 * 2.0\nt4 = t2 * t3\nanswer = t4 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "184" + ], + "split": "train" + }, + { + "Input": "rahul played weel in this season . his current batting averagge is 51 . if he score 69 runs in today match . his batting average will become 54 . how many matches had he played in this season .", + "Output Program": [ + "n0 = 51.0\nn1 = 69.0\nn2 = 54.0\nt0 = n1 - n2\nt1 = n2 - n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "mixture contains alcohol and water in the ratio 4 : 3 . if 8 liters of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture .", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 8.0\nn3 = 4.0\nn4 = 5.0\nt0 = n0 * n4\nt1 = n0 * n2\nt2 = n0 * n1\nt3 = t1 - t2\nt4 = t0 / t3\nanswer = n0 * t4\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "mary ' s income is 60 % more than tim ' s income and tim ' s income is 50 % less than juan ' s income . what % of juan ' s income is mary ' s income .", + "Output Program": [ + "n0 = 60.0\nn1 = 50.0\nt0 = n0 / 100.0\nt1 = 100.0 - n1\nt2 = t0 * t1\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "the average age of 15 students of a class is 15 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years . the age of the 15 th student is", + "Output Program": [ + "n0 = 15.0\nn1 = 15.0\nn2 = 5.0\nn3 = 14.0\nn4 = 9.0\nn5 = 16.0\nn6 = 15.0\nt0 = n0 * n0\nt1 = n2 * n3\nt2 = n4 * n5\nt3 = t1 + t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "what is the decimal equivalent of ( 1 / 4 ) ^ 3 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 3.0\nt0 = n0 / n1\nanswer = t0**min(3.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "0.015625" + ], + "split": "train" + }, + { + "Input": "a student took 6 courses last year and received an average ( arithmetic mean ) grade of 100 points . the year before , the student took 5 courses and received an average grade of 40 points . to the nearest tenth of a point , what was the student \u2019 s average grade for the entire two - year period ?", + "Output Program": [ + "import math\nn0 = 6.0\nn1 = 100.0\nn2 = 5.0\nn3 = 40.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nt4 = t3 / t0\nanswer = math.floor(t4)\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "train" + }, + { + "Input": "the smallest number which when diminished by 7 , is divisible 12 , 16 , 18 , 21 and 28 is :", + "Output Program": [ + "n0 = 7.0\nn1 = 12.0\nn2 = 16.0\nn3 = 18.0\nn4 = 21.0\nn5 = 28.0\nt0 = 3.0 + 4.0\nt1 = 3.0**min(2.0, 5)\nt2 = 2.0**min(4.0, 5)\nt3 = t1 * t2\nt4 = t0 * t3\nanswer = t4 + n0\nprint(answer)" + ], + "Output Answer": [ + "1015" + ], + "split": "train" + }, + { + "Input": "the average of first 15 even numbers is ?", + "Output Program": [ + "n0 = 15.0\n\nanswer = n0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "in 100 litres mixture milk and water are in the ratio 3 : 2 . after adding how many liters of water its ratio will become 3 : 4", + "Output Program": [ + "n0 = 100.0\nn1 = 3.0\nn2 = 2.0\nn3 = 3.0\nn4 = 4.0\nt0 = 10.0 + 2.0\nt1 = n1 + n2\nt2 = n1 + n4\nt3 = t0 / 10.0\nt4 = n1 / t1\nt5 = n1 / t2\nt6 = n0 * t4\nt7 = t6 / t5\nt8 = t7 - n0\nanswer = t3 * t8\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "a profit of rs . 500 is divided between x and y in the ratio of 1 / 2 : 1 / 3 . what is the difference between their profit shares ?", + "Output Program": [ + "n0 = 500.0\nn1 = 1.0\nn2 = 2.0\nn3 = 1.0\nn4 = 3.0\nt0 = n1 / n2\nt1 = n1 / n4\nt2 = t0 + t1\nt3 = n0 / t2\nt4 = t3 / n2\nt5 = t3 / n4\nanswer = t4 - t5\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "the cost per unit of electricity during a 4 year period is as follows : year 1 , $ 3 per unit ; year 2 , $ 4 per unit ; year 3 , $ 5 per unit ; year 4 , $ 6 per unit . if a factory spent equal dollars on electricity each year , what was the average cost of a unit of electricity during the 4 year period ?", + "Output Program": [ + "n0 = 4.0\nn1 = 1.0\nn2 = 3.0\nn3 = 2.0\nn4 = 4.0\nn5 = 3.0\nn6 = 5.0\nn7 = 4.0\nn8 = 6.0\nn9 = 4.0\nt0 = 1.0 / n2\nt1 = 1.0 / n0\nt2 = 1.0 / n6\nt3 = 1.0 / n8\nt4 = t0 + t1\nt5 = t4 + t2\nt6 = t5 + t3\nanswer = n0 / t6\nprint(answer)" + ], + "Output Answer": [ + "4.210526315789474" + ], + "split": "train" + }, + { + "Input": "two trains of equal are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train passes the slower train in 45 sec . the length of each train is ?", + "Output Program": [ + "n0 = 46.0\nn1 = 36.0\nn2 = 45.0\nt0 = n0 - n1\nt1 = t0 * 1000.0\nt2 = t1 / 3600.0\nt3 = n2 * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "62.5" + ], + "split": "train" + }, + { + "Input": "a batsman makes a score of 87 runs in the 17 th inning and thus increases his averages by 3 . find his average after 17 th inning ?", + "Output Program": [ + "n0 = 87.0\nn1 = 17.0\nn2 = 3.0\nn3 = 17.0\nt0 = n1 * n2\nt1 = n0 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "39" + ], + "split": "train" + }, + { + "Input": "a student took 6 courses last year and received an average ( arithmetic mean ) grade of 100 points . the year before , the student took 5 courses and received an average grade of 50 points . to the nearest tenth of a point , what was the student \u2019 s average grade for the entire two - year period ?", + "Output Program": [ + "import math\nn0 = 6.0\nn1 = 100.0\nn2 = 5.0\nn3 = 50.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nt4 = t3 / t0\nanswer = math.floor(t4)\nprint(answer)" + ], + "Output Answer": [ + "77" + ], + "split": "train" + }, + { + "Input": "jim \u2019 s taxi service charges an initial fee of $ 2.35 at the beginning of a trip and an additional charge of $ 0.35 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?", + "Output Program": [ + "n0 = 2.35\nn1 = 0.35\nn2 = 2.0\nn3 = 5.0\nn4 = 3.6\nt0 = n2 / n3\nt1 = n4 / t0\nt2 = n1 * t1\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "5.5" + ], + "split": "train" + }, + { + "Input": "10 camels cost as much as 24 horses , 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants . if the cost of 10 elephants is rs . 140000 , find the cost of a camel ?", + "Output Program": [ + "n0 = 10.0\nn1 = 24.0\nn2 = 16.0\nn3 = 4.0\nn4 = 6.0\nn5 = 4.0\nn6 = 10.0\nn7 = 140000.0\nt0 = n1 * n3\nt1 = n0 * n2\nt2 = n3 * t0\nt3 = n4 * t1\nt4 = n7 * t2\nt5 = n0 * t3\nanswer = t4 / t5\nprint(answer)" + ], + "Output Answer": [ + "5600" + ], + "split": "train" + }, + { + "Input": "how many positive integers less than 15 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3 ?", + "Output Program": [ + "n0 = 15.0\nn1 = 2.0\nn2 = 3.0\nt0 = n0 - 2.0\nt1 = t0 - 4.0\nanswer = t1 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a dog is tied to a tree by a long nylon cord . if the dog runs from the due north side of the tree to the due south side of the tree with the cord extended to its full length at all items , and the dog ran approximately 30 feet , what was the approximate length of the nylon cord w , in feet ?", + "Output Program": [ + "n0 = 30.0\n\nanswer = n0 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "in the rectangular coordinate system , if the line x = 5 y + 5 passes through points ( m , n ) and ( m + 2 , n + p ) , what is the value of p ?", + "Output Program": [ + "n0 = 5.0\nn1 = 5.0\nn2 = 2.0\n\nanswer = n2 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.4" + ], + "split": "train" + }, + { + "Input": "in digging a pond 20 m * 15 m * 5 m the volumes of the soil extracted will be ?", + "Output Program": [ + "n0 = 20.0\nn1 = 15.0\nn2 = 5.0\nt0 = n0 * n1\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "1500" + ], + "split": "train" + }, + { + "Input": "the jogging track in a sports complex is 726 m in circumference . suresh and his wife start from the same point and walk in opposite direction at 4.5 km / hr and 3.75 km / hr respectively . they will meet for the first time in :", + "Output Program": [ + "n0 = 726.0\nn1 = 4.5\nn2 = 3.75\nt0 = n1 * 1000.0\nt1 = n2 * 1000.0\nt2 = t0 + t1\nt3 = t2 / 60.0\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "5.28" + ], + "split": "train" + }, + { + "Input": "a sports equipment store sold ping pong rackets for a total of $ 539 . if the average ( arithmetic mean ) price of a pair of rackets is $ 9.8 , how many pairs were sold ?", + "Output Program": [ + "n0 = 539.0\nn1 = 9.8\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "54.99999999999999" + ], + "split": "train" + }, + { + "Input": "if x + y + z = 1 . then xy + yz + zx is", + "Output Program": [ + "n0 = 1.0\n\nanswer = n0 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "0.25" + ], + "split": "train" + }, + { + "Input": "in the storage room of a certain bakery , the ratio of sugar to flour is 5 to 2 , and the ratio of flour to baking soda is 10 to 1 . if there were 60 more pounds of baking soda in the room , the ratio of flour to baking soda would be 8 to 1 . how many pounds of sugar are stored in the room ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 10.0\nn3 = 1.0\nn4 = 60.0\nn5 = 8.0\nn6 = 1.0\nt0 = n0 / n1\nt1 = n4 * n5\nt2 = n2 - n5\nt3 = t1 / t2\nt4 = n2 * t3\nanswer = t0 * t4\nprint(answer)" + ], + "Output Answer": [ + "6000" + ], + "split": "train" + }, + { + "Input": "a student has to obtain 33 % of the total marks to pass . he got 125 marks and failed by 40 marks . the maximum mark is", + "Output Program": [ + "n0 = 33.0\nn1 = 125.0\nn2 = 40.0\nt0 = n1 + n2\nt1 = n0 / 100.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "train" + }, + { + "Input": "for the past n days , the average ( arithmetic mean ) daily production at a company was 60 units . if today ' s production of 90 units raises the average to 65 units per day , what is the value of n ?", + "Output Program": [ + "n0 = 60.0\nn1 = 90.0\nn2 = 65.0\nt0 = n1 - n0\nt1 = n2 - n0\nt2 = t0 / t1\nanswer = t2 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "a 7 - digit combination lock on a safe has zero exactly 3 times , does not have the digit 1 at all . what is the probability that exactly 3 of its digits are odd ?", + "Output Program": [ + "n0 = 7.0\nn1 = 3.0\nn2 = 1.0\nn3 = 3.0\nt0 = n0 - n1\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.25" + ], + "split": "train" + }, + { + "Input": "evaluate : 11 + sqrt ( - 4 + 6 \u00d7 4 \u00f7 3 ) = ?", + "Output Program": [ + "import math\nn0 = 11.0\nn1 = 4.0\nn2 = 6.0\nn3 = 4.0\nn4 = 3.0\nt0 = n1 * n2\nt1 = t0 / n4\nt2 = t1 - n1\nt3 = math.sqrt(max(0, t2))\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "the number of positive integer solutions for the equation x + y + z + t = 15 is", + "Output Program": [ + "import math\nn0 = 15.0\nt0 = n0 - 1.0\nt1 = 4.0 - 1.0\nt2 = math.factorial(min(15, int(t0)))\nt3 = math.factorial(min(15, int(t1)))\nt4 = t0 - t1\nt5 = math.factorial(min(15, int(t4)))\nt6 = t3 * t5\nanswer = t2 / t6\nprint(answer)" + ], + "Output Answer": [ + "364" + ], + "split": "train" + }, + { + "Input": "the salary of a , b , c , d , e is rs . 8000 , rs . 5000 , rs . 11000 , rs . 7000 , rs . 9000 per month respectively , then the average salary of a , b , c , d , and e per month is", + "Output Program": [ + "n0 = 8000.0\nn1 = 5000.0\nn2 = 11000.0\nn3 = 7000.0\nn4 = 9000.0\nt0 = n0 + n1\nt1 = 1.0 + 4.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "8000" + ], + "split": "train" + }, + { + "Input": "a car averages 75 mph for the first 4 hours of a trip and averages 60 mph for each additional hour . the average speed for the entire trip was 70 mph . how many hours long is the trip ?", + "Output Program": [ + "n0 = 75.0\nn1 = 4.0\nn2 = 60.0\nn3 = 70.0\nt0 = n3 * n1\nt1 = n0 * n1\nt2 = n2 - n3\nt3 = t0 - t1\nt4 = t3 / t2\nanswer = n1 + t4\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 210 , what were her original savings ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 210.0\nt0 = n0 / n1\nt1 = 1.0 - t0\nanswer = n2 / t1\nprint(answer)" + ], + "Output Answer": [ + "840" + ], + "split": "train" + }, + { + "Input": "the sum of the non - prime numbers between 60 and 70 , non - inclusive , is", + "Output Program": [ + "n0 = 60.0\nn1 = 70.0\nt0 = n0 + 1.0\nt1 = t0 + 1.0\nt2 = t0 + t1\nt3 = t1 + 2.0\nt4 = t2 + t3\nt5 = t3 + 1.0\nt6 = t4 + t5\nt7 = t5 + 1.0\nt8 = t6 + t7\nt9 = t7 + 1.0\nt10 = t8 + t9\nt11 = t9 + 1.0\nanswer = t10 + t11\nprint(answer)" + ], + "Output Answer": [ + "453" + ], + "split": "train" + }, + { + "Input": "ifaequals the sum of the even integers from 2 to 20 , inclusive , andbequals the sum of the odd integers from 1 to 19 , inclusive , what is the value of b - a ?", + "Output Program": [ + "n0 = 2.0\nn1 = 20.0\nn2 = 1.0\nn3 = 19.0\nt0 = n2 + n3\nt1 = n1 / n0\nt2 = n3 - n2\nt3 = n2 + t1\nt4 = t2 / n0\nt5 = t0 / n0\nt6 = n2 + t4\nt7 = t3 * t1\nt8 = t6 * t5\nanswer = t7 - t8\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "what is the minimum value of | x - 4 | + | x + 8 | + | x - 5 | ?", + "Output Program": [ + "n0 = 4.0\nn1 = 8.0\nn2 = 5.0\n\nanswer = n1 + n2\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "in 10 years , a will be twice as old as b was 10 years ago . if a is now 6 years older than b the present age of b is", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 6.0\nt0 = n0 * 2.0\nt1 = n0 + t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "a runs 1 2 \u2044 3 times as fast as b . if a gives b a start of 80 m , how far must the winning post be so that a and b might reach it at the same time ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 3.0\nn3 = 80.0\nt0 = n0 * n2\nt1 = n1 + t0\nt2 = t1 / n2\nt3 = n3 * t2\nt4 = t2 - 1.0\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "train" + }, + { + "Input": "hyderabad chennai mumbai delhi bangalore trivandram ; hyderabad chennai mumbai delhi bangalore trivandram in the table above , what is the least number of table entries that are needed to show the mileage between each city and each of the other 5 cities ?", + "Output Program": [ + "n0 = 5.0\n\nanswer = n0 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "the average weight of 8 person ' s increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg . what is the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 3.5\nn2 = 65.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "93" + ], + "split": "train" + }, + { + "Input": "if the number is divided by 3 , it reduced by 24 . the number is", + "Output Program": [ + "n0 = 3.0\nn1 = 24.0\nt0 = n0 * n1\nt1 = n0 - 1.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "at an upscale fast - food restaurant , shin can buy 3 burgers , 7 shakes , and one cola for $ 120 . at the same place it would cost $ 158.50 for 4 burgers , 10 shakes , and one cola . how much would it cost for a meal of one burger , one shake , and one cola ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 120.0\nn3 = 158.5\nn4 = 4.0\nn5 = 10.0\nt0 = n3 - n2\nt1 = n2 + t0\nt2 = t0 * n0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "43" + ], + "split": "train" + }, + { + "Input": "thabo owns exactly 220 books , and each book is either paperback fiction , paperback nonfiction , or hardcover nonfiction . if he owns 20 more paperback nonfiction books than hardcover nonfiction books , and twice as many paperback fiction books as paperback nonfiction books , how many hardcover books nonfiction books does thabo own ?", + "Output Program": [ + "n0 = 220.0\nn1 = 20.0\nt0 = n0 + n1\nt1 = t0 / 4.0\nanswer = t1 - n1\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "there are 84 supermarkets in the fgh chain . all of them are either in the us or canada . if there are 14 more fgh supermarkets in the us than in canada , how many fgh supermarkets are there in the us ?", + "Output Program": [ + "n0 = 84.0\nn1 = 14.0\nt0 = n0 + n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "49" + ], + "split": "train" + }, + { + "Input": "in a coconut grove , ( x + 2 ) trees yield 30 nuts per year , x trees yield 120 nuts per year and ( x \u2013 2 ) trees yield 180 nuts per year . if the average yield per year per tree be 100 , find x .", + "Output Program": [ + "n0 = 2.0\nn1 = 30.0\nn2 = 120.0\nn3 = 2.0\nn4 = 180.0\nn5 = 100.0\nt0 = n1 + n2\nt1 = n0 * n4\nt2 = n0 * n1\nt3 = n5 * 3.0\nt4 = n4 + t0\nt5 = t1 - t2\nt6 = t4 - t3\nanswer = t5 / t6\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "a football player scores 2 goals in his fifth match thus increasing his average goals score by 0.3 . the total number of goals in his 5 matches would be", + "Output Program": [ + "n0 = 2.0\nn1 = 0.3\nn2 = 5.0\nt0 = n0 * 4.0\nt1 = n2 * 4.0\nt2 = n1 * t1\nt3 = t0 - t2\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "jennifer had $ 120 to spend on herself . she spent 1 / 5 of the money on a sandwich , 1 / 6 for a ticket to a museum , and 1 / 2 of it on a book . how much money does jennifer have left over ?", + "Output Program": [ + "n0 = 120.0\nn1 = 1.0\nn2 = 5.0\nn3 = 1.0\nn4 = 6.0\nn5 = 1.0\nn6 = 2.0\nt0 = n1 / n2\nt1 = n1 / n4\nt2 = n1 / n6\nt3 = n0 * t0\nt4 = n0 * t1\nt5 = n0 * t2\nt6 = t3 + t4\nt7 = t6 + t5\nanswer = n0 - t7\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "if the sum of two numbers is 55 and the h . c . f . and l . c . m of these numbers are 5 and 120 respectively , then the sum of the reciprocals of the numbers is equal to :", + "Output Program": [ + "n0 = 55.0\nn1 = 5.0\nn2 = 120.0\nt0 = n0 / n1\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "0.09166666666666666" + ], + "split": "train" + }, + { + "Input": "the sum of 3 integers a , b and c is 60 . a is one third of the sum of b and c and b is one fifth of the sum of a and c . what is c ?", + "Output Program": [ + "n0 = 3.0\nn1 = 60.0\nt0 = 1.0 + 4.0\nt1 = 1 / 3.0\nt2 = 1 / t0\nt3 = n1 * t1\nt4 = n1 * t2\nt5 = t3 + t4\nanswer = n0 + t5\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "the instructions state that cheryl needs 5 / 11 square yards of one type of material and 2 / 3 square yards of another type of material for a project . she buys exactly that amount . after finishing the project , however , she has 25 / 55 square yards left that she did not use . what is the total amount of square yards of material cheryl used ?", + "Output Program": [ + "n0 = 5.0\nn1 = 11.0\nn2 = 2.0\nn3 = 3.0\nn4 = 25.0\nn5 = 55.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = n4 / n5\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "0.6666666666666665" + ], + "split": "train" + }, + { + "Input": "what is the least positive integer x for which ( x ^ 2 ) + 164 is divisible by 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , and 11 ?", + "Output Program": [ + "import math\nimport scipy\nn0 = 2.0\nn1 = 164.0\nn2 = 2.0\nn3 = 3.0\nn4 = 4.0\nn5 = 5.0\nn6 = 6.0\nn7 = 7.0\nn8 = 8.0\nn9 = 9.0\nn10 = 10.0\nn11 = 11.0\nt0 = scipy.lcm(int(n0), int(n3))\nt1 = scipy.lcm(int(n4), int(t0))\nt2 = scipy.lcm(int(n5), int(t1))\nt3 = scipy.lcm(int(n6), int(t2))\nt4 = scipy.lcm(int(n7), int(t3))\nt5 = scipy.lcm(int(n8), int(t4))\nt6 = scipy.lcm(int(n9), int(t5))\nt7 = scipy.lcm(int(n11), int(t6))\nt8 = t7 - n1\nanswer = math.sqrt(max(0, t8))\nprint(answer)" + ], + "Output Answer": [ + "166" + ], + "split": "train" + }, + { + "Input": "there is a total of 84 marbles in a box , each of which is red , green , blue , or white . if one marble is drawn from the box at random , the probability that it will be white is 1 / 4 and the probability that it will be green is 1 / 7 . what is the probability that the marble will be either red or blue ?", + "Output Program": [ + "n0 = 84.0\nn1 = 1.0\nn2 = 4.0\nn3 = 1.0\nn4 = 7.0\nt0 = n1 / n2\nt1 = n3 / n4\nt2 = t0 + t1\nanswer = n1 - t2\nprint(answer)" + ], + "Output Answer": [ + "0.6071428571428572" + ], + "split": "train" + }, + { + "Input": "two trains of equal are running on parallel lines in the same direction at 50 km / hr and 36 km / hr . the faster train passes the slower train in 36 sec . the length of each train is ?", + "Output Program": [ + "n0 = 50.0\nn1 = 36.0\nn2 = 36.0\nt0 = n0 - n1\nt1 = t0 * 1000.0\nt2 = t1 / 3600.0\nt3 = n2 * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "train" + }, + { + "Input": "what is the dividend . divisor 17 , the quotient is 9 and the remainder is 5 ?", + "Output Program": [ + "n0 = 17.0\nn1 = 9.0\nn2 = 5.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "158" + ], + "split": "train" + }, + { + "Input": "the average marks of a class of 25 students is 40 and that of another class of 30 students is 60 . find the average marks of all the students ?", + "Output Program": [ + "n0 = 25.0\nn1 = 40.0\nn2 = 30.0\nn3 = 60.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "50.90909090909091" + ], + "split": "train" + }, + { + "Input": "two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs , x and y . now , jug x is 1 / 3 full , while jug y is 2 / 3 full . if water is poured from jug x into jug y until jug y is filled , what fraction of jug x then contains water ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 2.0\nn3 = 3.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = n0 - t1\nt3 = t2 / t1\nanswer = t0 * t3\nprint(answer)" + ], + "Output Answer": [ + "0.16666666666666669" + ], + "split": "train" + }, + { + "Input": "the average ( arithmetic mean ) of 20 , 40 , and 60 is 5 more than the average of 10 , 60 , and what number ?", + "Output Program": [ + "n0 = 20.0\nn1 = 40.0\nn2 = 60.0\nn3 = 5.0\nn4 = 10.0\nn5 = 60.0\nt0 = n0 + n1\nt1 = n3 * 3.0\nt2 = n2 + t0\nt3 = n4 + t1\nt4 = n5 + t3\nanswer = t2 - t4\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "a man \u00e2 \u20ac \u2122 s current age is ( 2 / 5 ) of the age of his father . after 12 years , he will be ( 1 / 2 ) of the age of his father . what is the age of father at now ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 12.0\nn3 = 1.0\nn4 = 2.0\nt0 = n3 / n0\nt1 = n0 / n1\nt2 = n2 * t0\nt3 = t0 - t1\nt4 = n2 - t2\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "60.000000000000014" + ], + "split": "train" + }, + { + "Input": "a mixture of 50 litres of milk and water contains 10 % water . how many litres of water should be added to the mixture so that the mixture contains 15 % water ?", + "Output Program": [ + "n0 = 50.0\nn1 = 10.0\nn2 = 15.0\nt0 = n0 * n2\nt1 = t0 / n1\nanswer = t1 - n0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "each of the 20 boxes in a certain shipment weighs either 10 pounds or 20 pounds , and the average ( arithmetic mean ) weight of the boxes in the shipment is 18 pounds . if the average weight of the boxes in the shipment is to be reduced to 16 pounds by removing some of the 20 - pound boxes , how many 20 - pound boxes must be removed ?", + "Output Program": [ + "n0 = 20.0\nn1 = 10.0\nn2 = 20.0\nn3 = 18.0\nn4 = 16.0\nn5 = 20.0\nn6 = 20.0\nt0 = n0 * n2\nt1 = n0 * n3\nt2 = n0 * n4\nt3 = n2 - n1\nt4 = n2 - n4\nt5 = t0 - t1\nt6 = t5 / t3\nt7 = n1 * t6\nt8 = n0 - t6\nt9 = n2 * t8\nt10 = t7 + t9\nt11 = t10 - t2\nanswer = t11 / t4\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "a television have side 6 * 5 . its screen size is 5 * 4 . calculate the percentage of unscreened part t . v .", + "Output Program": [ + "n0 = 6.0\nn1 = 5.0\nn2 = 5.0\nn3 = 4.0\nt0 = n0 * n1\nt1 = n1 * n3\nt2 = t0 - t1\nt3 = t2 / t0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "33.33333333333333" + ], + "split": "train" + }, + { + "Input": "last week john spent 10 percent of his wages on recreation . this week , his wages are 10 percent less than last week \u02bc s wages and he spent 40 percent of his wages on recreation . the amount he spends on recreation this week is what percent of the amount he spent on recreation last week", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 40.0\nt0 = n2 / 100.0\nt1 = n0 / 100.0\nt2 = 100.0 - n1\nt3 = t2 / 100.0\nt4 = t1 * 100.0\nt5 = t3 * 100.0\nt6 = t0 * t5\nt7 = t6 / t4\nanswer = t7 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "360" + ], + "split": "train" + }, + { + "Input": "a line with slope 2 intersects a line with slope 6 at the point ( 40 , 30 ) . what is the distance between the x - intercepts of these lines ?", + "Output Program": [ + "n0 = 2.0\nn1 = 6.0\nn2 = 40.0\nn3 = 30.0\nt0 = n2 * n3\nt1 = n0 * n1\nt2 = t0 / t1\nanswer = t2 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 47 , then how old is b ?", + "Output Program": [ + "n0 = 47.0\nt0 = 2.0 + 3.0\nt1 = n0 - 2.0\nt2 = t1 / t0\nanswer = t2 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "right now , al and eliot have bank accounts , and al has more money than eliot . the difference between their two accounts is 1 / 12 of the sum of their two accounts . if al \u2019 s account were to increase by 10 % and eliot \u2019 s account were to increase by 20 % , then al would have exactly $ 20 more than eliot in his account . how much money does eliot have in his account right now ?", + "Output Program": [ + "n0 = 1.0\nn1 = 12.0\nn2 = 10.0\nn3 = 20.0\nn4 = 20.0\nt0 = n0 + n1\nt1 = n3 + 100.0\nt2 = n4 * 100.0\nt3 = t0 * n2\nt4 = t3 - t1\nanswer = t2 / t4\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "train" + }, + { + "Input": "tough and tricky questions : number properties . if ( z + 3 ) / 9 is an integer , what is remainder when z is divided by 9 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 9.0\nn2 = 9.0\n\nanswer = n1 - n0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "if x < y < z and y - x > 5 , where x is an even integer and y and z are odd integers , what is the least possible value d of z - x ?", + "Output Program": [ + "n0 = 5.0\nt0 = n0 + 2.0\nanswer = t0 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "if money is invested at r percent interest , compounded annually , the amount of the investment will double in approximately 70 / r years . if pat ' s parents invested $ 5,000 in a long - term bond that pays 8 percent interest , compounded annually , what will be the approximate total amount of the investment 18 years later , when pat is ready for college ?", + "Output Program": [ + "n0 = 70.0\nn1 = 5000.0\nn2 = 8.0\nn3 = 18.0\nt0 = 2.0 + 3.0\nt1 = t0 * 1000.0\nt2 = n2 * t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "20000" + ], + "split": "train" + }, + { + "Input": "instead of multiplying a number by 9 , the number is divided by 9 . what is the percentage of error obtained ?", + "Output Program": [ + "n0 = 9.0\nn1 = 9.0\nt0 = n1 / n1\nt1 = n0 * n1\nt2 = t0 / t1\nt3 = t2 * 100.0\nanswer = 100.0 - t3\nprint(answer)" + ], + "Output Answer": [ + "98.76543209876543" + ], + "split": "train" + }, + { + "Input": "in august , a cricket team that played 120 matches won 28 % of the games it played . after a continuous winning streak , this team raised its average to 52 % . how many matches did the team win to attain this average ?", + "Output Program": [ + "n0 = 120.0\nn1 = 28.0\nn2 = 52.0\nt0 = n2 / 100.0\nt1 = n1 / 100.0\nt2 = n0 * t0\nt3 = n0 * t1\nt4 = 1.0 - t0\nt5 = t2 - t3\nanswer = t5 / t4\nprint(answer)" + ], + "Output Answer": [ + "60.000000000000014" + ], + "split": "train" + }, + { + "Input": "the captain of a cricket team of 11 members is 26 years old and the wicket keeper is 5 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ?", + "Output Program": [ + "n0 = 11.0\nn1 = 26.0\nn2 = 5.0\nt0 = n1 + n2\nt1 = 3.0 * 3.0\nt2 = n1 + t0\nt3 = t2 - t1\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "joe \u2019 s average ( arithmetic mean ) test score across 4 equally weighted tests was 50 . he was allowed to drop his lowest score . after doing so , his average test score improved to 55 . what is the lowest test score that was dropped ?", + "Output Program": [ + "n0 = 4.0\nn1 = 50.0\nn2 = 55.0\nt0 = n0 * n1\nt1 = n2 * 3.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "jamshid and irwin decided to make up their own version of basketball . in addition to being able to score 2 - point baskets , they created ways to score 5 - , 11 - , and 13 - point baskets . if at halftime the product of the point values of irwin \u2019 s baskets was 2420 , how many 11 - point baskets e did irwin score ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 11.0\nn3 = 13.0\nn4 = 2420.0\nn5 = 11.0\nt0 = n4 / n2\nt1 = t0 / n2\nanswer = t1 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "when the positive integer x is divided by 9 , the remainder is 5 . what is the remainder when 5 x is divided by 9 ?", + "Output Program": [ + "n0 = 9.0\nn1 = 5.0\nn2 = 5.0\nn3 = 9.0\nt0 = n1 * n2\nanswer = t0 % n0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "when positive integer x is divided by positive integer y , the remainder is 7 . if x / y = 86.1 , what is the value of y ?", + "Output Program": [ + "import math\nn0 = 7.0\nn1 = 86.1\nt0 = math.floor(n1)\nt1 = n1 - t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "70.00000000000398" + ], + "split": "train" + }, + { + "Input": "if ( a + b ) = 11 , ( b + c ) = 9 and ( c + d ) = 3 , what is the value of ( a + d ) ?", + "Output Program": [ + "n0 = 11.0\nn1 = 9.0\nn2 = 3.0\nt0 = n0 + n2\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "the average of 6 numbers is 30 . if the average of first 4 is 25 and that of last 3 is 35 , the fourth number is :", + "Output Program": [ + "n0 = 6.0\nn1 = 30.0\nn2 = 4.0\nn3 = 25.0\nn4 = 3.0\nn5 = 35.0\nt0 = n4 * n5\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 - t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "in the faculty of reverse - engineering , 240 second year students study numeric methods , 423 second year students study automatic control of airborne vehicles and 134 second year students study them both . how many students are there in the faculty if the second year students are approximately 80 % of the total ?", + "Output Program": [ + "n0 = 240.0\nn1 = 423.0\nn2 = 134.0\nn3 = 80.0\n\nanswer = n0 + n1\nprint(answer)" + ], + "Output Answer": [ + "663" + ], + "split": "train" + }, + { + "Input": "the total marks obtained by a student in mathematics and physics is 60 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together .", + "Output Program": [ + "n0 = 60.0\nn1 = 20.0\nt0 = n0 + n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "a jogger running at 9 km / hr along side a railway track is 240 m ahead of the engine of a 210 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?", + "Output Program": [ + "n0 = 9.0\nn1 = 240.0\nn2 = 210.0\nn3 = 45.0\nt0 = n1 + n2\nt1 = 10.0 / 2.0\nt2 = n3 - n0\nt3 = t2 / 2.0\nt4 = t1 / t3\nt5 = t4 * t2\nanswer = t0 / t5\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "what is the units digit of the product of the first 100 odd numbers ?", + "Output Program": [ + "import scipy\nn0 = 100.0\nt0 = scipy.lcm(int(n0), int(1.0))\nt1 = t0 / 10.0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "caleb spends $ 68.50 on 50 hamburgers for the marching band . if single burgers cost $ 1.00 each and double burgers cost $ 1.50 each , how many double burgers did he buy ?", + "Output Program": [ + "n0 = 68.5\nn1 = 50.0\nn2 = 1.0\nn3 = 1.5\nt0 = n0 - n1\nt1 = n3 - n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "37" + ], + "split": "train" + }, + { + "Input": "if money is invested at r percent interest , compounded annually , the amount of investment will double in approximately 70 / r years . if pat ' s parents invested $ 8000 in a long term bond that pays 8 percent interest , compounded annually , what will be the approximate total amount of investment 18 years later , when pat is ready for college ?", + "Output Program": [ + "n0 = 70.0\nn1 = 8000.0\nn2 = 8.0\nn3 = 18.0\nt0 = n1 * 2.0\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "32000" + ], + "split": "train" + }, + { + "Input": "the average age of 6 men increases by 3 years when two women are included in place of two men of ages 24 and 26 years . find the average age of the women ?", + "Output Program": [ + "n0 = 6.0\nn1 = 3.0\nn2 = 24.0\nn3 = 26.0\nt0 = n2 + n3\nt1 = n0 * n1\nt2 = t0 + t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "34" + ], + "split": "train" + }, + { + "Input": "| 9 - 4 | - | 12 - 14 | = ?", + "Output Program": [ + "n0 = 9.0\nn1 = 4.0\nn2 = 12.0\nn3 = 14.0\nt0 = n0 - n1\nt1 = n3 - n2\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "if 4 ^ k = 5 , then 4 ^ ( 2 k + 2 ) =", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 4.0\nn3 = 2.0\nn4 = 2.0\nt0 = n1**min(n3, 5)\nt1 = n0**min(n4, 5)\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "train" + }, + { + "Input": "in the storage room of a certain bakery , the ratio of sugar to flour is 5 to 4 , and the ratio of flour to baking soda is 10 to 1 . if there were 60 more pounds of baking soda in the room , the ratio of flour to baking soda would be 8 to 1 . how many pounds of sugar are stored in the room ?", + "Output Program": [ + "n0 = 5.0\nn1 = 4.0\nn2 = 10.0\nn3 = 1.0\nn4 = 60.0\nn5 = 8.0\nn6 = 1.0\nt0 = n0 / n1\nt1 = n4 * n5\nt2 = n2 - n5\nt3 = t1 / t2\nt4 = n2 * t3\nanswer = t0 * t4\nprint(answer)" + ], + "Output Answer": [ + "3000" + ], + "split": "train" + }, + { + "Input": "tough and tricky questions : word problems . mike , sarah and david decided to club together to buy a present . each of them gave equal amount of money . luckily sarah negotiated a 20 % discount for the present so that each of them paid 4 dollars less . how much did they pay for a present ?", + "Output Program": [ + "n0 = 20.0\nn1 = 4.0\nt0 = n1 * 3.0\nt1 = n0 * n1\nt2 = t0 * 100.0\nt3 = t2 / n0\nt4 = t3 * t1\nanswer = t4 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "in a competitive examination in a state a , 6 % candidates got selected from the total appeared candidates . state b had an equal number of candidates appeared and 7 % candidates got selected with 80 more candidates got selected than a . what was the number of candidates appeared from each state ?", + "Output Program": [ + "n0 = 6.0\nn1 = 7.0\nn2 = 80.0\nt0 = n1 - n0\nt1 = t0 * 100.0\nanswer = n2 * t1\nprint(answer)" + ], + "Output Answer": [ + "8000" + ], + "split": "train" + }, + { + "Input": "how many natural numbers are there between 23 and 100 which are exactly divisible by 6 ?", + "Output Program": [ + "n0 = 23.0\nn1 = 100.0\nn2 = 6.0\nt0 = n0 + 1.0\nt1 = n1 - 4.0\nt2 = t1 - t0\nt3 = t2 / n2\nanswer = t3 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "if x \u00a4 y = ( x + y ) ^ 2 - ( x - y ) ^ 2 . then \u221a 5 \u00a4 \u221a 5 =", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 2.0\nn2 = 5.0\nn3 = 5.0\nt0 = math.sqrt(max(0, n2))\nt1 = t0 + t0\nanswer = t1**min(n0, 5)\nprint(answer)" + ], + "Output Answer": [ + "20.000000000000004" + ], + "split": "train" + }, + { + "Input": "which number should replace both the asterisks in ( * / 20 ) x ( * / 180 ) = 1 ?", + "Output Program": [ + "import math\nn0 = 20.0\nn1 = 180.0\nn2 = 1.0\nt0 = n0 * n1\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "a library has an average of 510 visitors on sundays and 240 on other days . what is the average number of visitors per day in a month of 30 days beginning with a sunday ?", + "Output Program": [ + "import math\nn0 = 510.0\nn1 = 240.0\nn2 = 30.0\nt0 = 3.0 + 4.0\nt1 = n2 / t0\nt2 = math.floor(t1)\nt3 = t2 + 1.0\nt4 = n0 * t3\nt5 = n2 - t3\nt6 = n1 * t5\nt7 = t4 + t6\nanswer = t7 / n2\nprint(answer)" + ], + "Output Answer": [ + "285" + ], + "split": "train" + }, + { + "Input": "if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 231 games will be played during the tournament . what is the number of participants ?", + "Output Program": [ + "import math\nn0 = 231.0\nt0 = n0 * 2.0\nt1 = t0 * 4.0\nt2 = t1 + 1.0\nt3 = math.sqrt(max(0, t2))\nt4 = t3 + 1.0\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "running at their respective constant rate , machine x takes 2 days longer to produce w widgets than machines y . at these rates , if the two machines together produce 5 w / 4 widgets in 3 days , how many days would it take machine x alone to produce 4 w widgets .", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 4.0\nn3 = 3.0\nn4 = 4.0\nt0 = n0 * n4\nanswer = n3 * t0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "a sum of money lent out at s . i . amounts to a total of $ 420 after 2 years and to $ 595 after a further period of 5 years . what was the initial sum of money that was invested ?", + "Output Program": [ + "n0 = 420.0\nn1 = 2.0\nn2 = 595.0\nn3 = 5.0\nt0 = n1 / n3\nt1 = n2 - n0\nt2 = t0 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "350" + ], + "split": "train" + }, + { + "Input": "the average age of a group of persons going for picnic is years . fifteen new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years . the number of persons initially going for picnic is", + "Output Program": [ + "n0 = 15.0\nn1 = 15.5\nt0 = n0 * n1\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "the average of 10 numbers was calculated as 19 . it is discovered later on that while calculating the average , one number , namely 76 , was incorrectly read as 26 . what is the correct average ?", + "Output Program": [ + "n0 = 10.0\nn1 = 19.0\nn2 = 76.0\nn3 = 26.0\nt0 = n0 * n1\nt1 = n2 - n3\nt2 = t0 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "when a merchant imported a certain item , she paid a 7 percent import tax on the portion of the total value of the item in excess of $ 1,000 . if the amount of the import tax that the merchant paid was $ 109.90 , what was the total value of the item ?", + "Output Program": [ + "n0 = 7.0\nn1 = 1000.0\nn2 = 109.9\nt0 = n0 / 100.0\nt1 = n2 / t0\nanswer = t1 + 1000.0\nprint(answer)" + ], + "Output Answer": [ + "2570" + ], + "split": "train" + }, + { + "Input": "a cyclist rides a bicycle 9 km at an average speed of 12 km / hr and again travels 12 km at an average speed of 9 km / hr . what is the average speed for the entire trip ?", + "Output Program": [ + "n0 = 9.0\nn1 = 12.0\nn2 = 12.0\nn3 = 9.0\nt0 = n0 + n1\nt1 = n0 / n1\nt2 = n1 / n0\nt3 = t1 + t2\nanswer = t0 / t3\nprint(answer)" + ], + "Output Answer": [ + "10.080000000000002" + ], + "split": "train" + }, + { + "Input": "a textile manufacturing firm employees 50 looms . it makes fabrics for a branded company . the aggregate sales value of the output of the 50 looms is rs 5 , 00,000 and the monthly manufacturing expenses is rs 1 , 50,000 . assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms . monthly establishment charges are rs 75000 . if one loom breaks down and remains idle for one month , the decrease in profit is :", + "Output Program": [ + "n0 = 50.0\nn1 = 50.0\nn2 = 5.0\nn3 = 0.0\nn4 = 1.0\nn5 = 50000.0\nn6 = 75000.0\nt0 = n2 * 1000.0\nt1 = n6 * 2.0\nt2 = n0 - n4\nt3 = n6 + t1\nt4 = t2 / n0\nt5 = t0 * 100.0\nt6 = t4 * t5\nt7 = t4 * t1\nt8 = t5 - t3\nt9 = t6 - t7\nt10 = t9 - n6\nanswer = t8 - t10\nprint(answer)" + ], + "Output Answer": [ + "7000" + ], + "split": "train" + }, + { + "Input": "find large number from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 4 as quotient and the 15 as remainder", + "Output Program": [ + "n0 = 1365.0\nn1 = 4.0\nn2 = 15.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nt2 = t0 / t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "1800" + ], + "split": "train" + }, + { + "Input": "the average weight of 4 pigs is 15 kg . weight less than 16 kg is considered as under weight . what maximum no . of pig can be under weight .", + "Output Program": [ + "n0 = 4.0\nn1 = 15.0\nn2 = 16.0\nt0 = n2 - n1\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "in a division sum , the remainder is 0 . as student mistook the divisor by 12 instead of 21 and obtained 35 as quotient . what is the correct quotient ?", + "Output Program": [ + "n0 = 0.0\nn1 = 12.0\nn2 = 21.0\nn3 = 35.0\nt0 = n1 * n3\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random . what is the probability that the ticket drawn bears a number which is a multiple of 3 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 20.0\nn2 = 3.0\n\nanswer = n2 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "0.3" + ], + "split": "train" + }, + { + "Input": "the sum of the digits of [ ( 10 ^ x ) ^ y ] - 64 = 279 . what is the value of xy ?", + "Output Program": [ + "n0 = 10.0\nn1 = 64.0\nn2 = 279.0\n\nanswer = n1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "15 % people of a village in sri lanka died by bombardment , 25 % of the remainder left the village on account of fear . if now the population is reduced to 4555 , how much was it in the beginning ?", + "Output Program": [ + "import math\nn0 = 15.0\nn1 = 25.0\nn2 = 4555.0\nt0 = 100.0 - n0\nt1 = 100.0 - n1\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = t2 * t3\nt5 = n2 / t4\nanswer = math.floor(t5)\nprint(answer)" + ], + "Output Answer": [ + "7145" + ], + "split": "train" + }, + { + "Input": "sum of the squares of 3 no . is 252 and the sum of their products taken two at a time is 116 . find the sum ?", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 252.0\nn2 = 116.0\nt0 = n2 * 2.0\nt1 = n1 + t0\nanswer = math.sqrt(max(0, t1))\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "evaluate : 22 + sqrt ( - 4 + 6 * 4 * 3 ) = ?", + "Output Program": [ + "import math\nn0 = 22.0\nn1 = 4.0\nn2 = 6.0\nn3 = 4.0\nn4 = 3.0\nt0 = n1 * n2\nt1 = t0 / n4\nt2 = t1 - n1\nt3 = math.sqrt(max(0, t2))\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "a retailer sells 10 shirts . the first 3 he sells for $ 82 , $ 100 and $ 90 . if the retailer wishes to sell the 10 shirts for an overall average price of over $ 100 , what must be the minimum average price of the remaining 7 shirts ?", + "Output Program": [ + "n0 = 10.0\nn1 = 3.0\nn2 = 82.0\nn3 = 100.0\nn4 = 90.0\nn5 = 10.0\nn6 = 100.0\nn7 = 7.0\nt0 = n2 + n3\nt1 = n0 * n3\nt2 = n4 + t0\nt3 = t1 - t2\nanswer = t3 / n7\nprint(answer)" + ], + "Output Answer": [ + "104" + ], + "split": "train" + }, + { + "Input": "a mixture of 85 kg contains milk and water in the ratio 27 : 7 . how much more water is to be added to get a new mixture containing milk and water in the ratio 3 : 1 ?", + "Output Program": [ + "n0 = 85.0\nn1 = 27.0\nn2 = 7.0\nn3 = 3.0\nn4 = 1.0\nt0 = n1 + n2\nt1 = n1 / t0\nt2 = n2 / t0\nt3 = n0 * t1\nt4 = n0 * t2\nt5 = n3 * t4\nt6 = t3 - t5\nanswer = t6 / n3\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "the product of a and b is equal to 12 more than twice the sum of a and b . if b = 10 , what is the value of b - a ?", + "Output Program": [ + "n0 = 12.0\nn1 = 10.0\nt0 = n1 * 2.0\nt1 = n1 - 2.0\nt2 = n0 + t0\nt3 = t2 / t1\nanswer = n1 - t3\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "there are 7 stores in town that had a total of 21 visitors on a particular day . however , only 11 people went shopping that day ; some people visited more than one store . if 7 people visited exactly two stores each , and everyone visited at least one store , what is the largest number of stores anyone could have visited ?", + "Output Program": [ + "n0 = 7.0\nn1 = 21.0\nn2 = 11.0\nn3 = 7.0\nt0 = n0 * 2.0\nt1 = n2 - n0\nt2 = n1 - t0\nt3 = t1 - 1.0\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "what is the largest 4 digit number exactly divisible by 12 ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 12.0\nt0 = 10.0**min(n0, 5)\nt1 = t0 / n1\nt2 = math.floor(t1)\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "9996" + ], + "split": "train" + }, + { + "Input": "if two positive numbers are in the ratio 1 / 8 : 1 / 7 , then by what percent is the second number more than the first ?", + "Output Program": [ + "n0 = 1.0\nn1 = 8.0\nn2 = 1.0\nn3 = 7.0\nt0 = n0 / n3\nanswer = t0 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "14.285714285714285" + ], + "split": "train" + }, + { + "Input": "ashok secured average of 79 marks in 6 subjects . if the average of marks in 5 subjects is 74 , how many marks did he secure in the 6 th subject ?", + "Output Program": [ + "n0 = 79.0\nn1 = 6.0\nn2 = 5.0\nn3 = 74.0\nn4 = 6.0\nt0 = n0 * n1\nt1 = n2 * n3\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "104" + ], + "split": "train" + }, + { + "Input": "a basketball player is shooting hoops . he shoots a free throw , a high school 3 - pointer , and then a professional 3 - pointer . the probability that he makes the free throw is 4 / 5 , the probability that he makes the high school 3 - pointer is 1 / 2 , and the probability that he makes the professional 3 - pointer is 1 / 3 . what is the probability that he makes at least one of the 3 shots ?", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 4.0\nn3 = 5.0\nn4 = 3.0\nn5 = 1.0\nn6 = 2.0\nn7 = 3.0\nn8 = 1.0\nn9 = 3.0\nn10 = 3.0\nt0 = n2 + 10.0\nt1 = n0 * n3\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.9333333333333333" + ], + "split": "train" + }, + { + "Input": "a confectioner decides to sell all of his pastry due to the coming holiday . his pastry goods are equally divided among a group of 28 regular customers . if only 49 customers come to the bakery , each one will receive 6 less pastry goods . how much pastry does the confectioner needs to sell ?", + "Output Program": [ + "n0 = 28.0\nn1 = 49.0\nn2 = 6.0\nt0 = n1 * n2\nt1 = n1 - n0\nt2 = t0 / t1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "392" + ], + "split": "train" + }, + { + "Input": "the average age of 20 students in a class is 15 years . if the age of teacher is also included , the average becomes 16 years , find the age of the teacher .", + "Output Program": [ + "n0 = 20.0\nn1 = 15.0\nn2 = 16.0\nt0 = n0 * n1\nt1 = n2 + t0\nt2 = n0 + t1\nanswer = t2 - t0\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "in how many t ways can 4 white and 3 black chess pieces be arranged in a row such that they occupy alternate places ? assume that the pieces are distinct .", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 3.0\nt0 = math.factorial(min(15, int(n1)))\nt1 = math.factorial(min(15, int(n0)))\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "144" + ], + "split": "train" + }, + { + "Input": "in the rectangular coordinate system , what is the x - intercept of a line passing through ( 10 , 3 ) and ( \u2212 4 , \u2212 4 ) ?", + "Output Program": [ + "n0 = 10.0\nn1 = 3.0\nn2 = 4.0\nn3 = 4.0\nt0 = -n3\nt1 = -n2\nt2 = t0 - n1\nt3 = t1 - n0\nt4 = t2 / t3\nt5 = n0 * t4\nt6 = t5 - n1\nanswer = t6 / t4\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "if x and y are numbers such that ( x + 8 ) ( y - 8 ) = 0 , what is the smallest possible value of x ^ 2 + y ^ 2", + "Output Program": [ + "n0 = 8.0\nn1 = 8.0\nn2 = 0.0\nn3 = 2.0\nn4 = 2.0\n\nanswer = n0**min(n3, 5)\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "train" + }, + { + "Input": "dick and jane each saved $ 1000 in 1989 . in 1990 dick saved 15 percent more than in 1989 , and together he and jane saved a total of $ 2000 . approximately what percent less did jane save in 1990 than in 1989 ?", + "Output Program": [ + "n0 = 1000.0\nn1 = 1989.0\nn2 = 1990.0\nn3 = 15.0\nn4 = 1989.0\nn5 = 2000.0\nn6 = 1990.0\nn7 = 1989.0\nt0 = n3 / 100.0\nt1 = t0 + 1.0\nt2 = 2.0 - t1\nt3 = 1.0 - t2\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "14.999999999999991" + ], + "split": "train" + }, + { + "Input": "a lemonade stand sold only small and large cups of lemonade on tuesday . 3 / 5 of the cups sold were small and the rest were large . if the large cups were sold for 5 / 6 as much as the small cups , what fraction of tuesday ' s total revenue was from the sale of large cups ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 5.0\nn3 = 6.0\nt0 = n2 / n3\nt1 = n0 / n1\nt2 = t1 * 10.0\nt3 = t0 * t2\nt4 = t2 * t2\nt5 = 10.0 - t2\nt6 = t3 * t5\nt7 = t4 + t6\nanswer = t6 / t7\nprint(answer)" + ], + "Output Answer": [ + "0.35714285714285715" + ], + "split": "train" + }, + { + "Input": "if rs . 10 be allowed as true discount on a bill of rs . 110 at the end of a certain time , then the discount allowed on the same sum due at the end of double the time is ?", + "Output Program": [ + "n0 = 10.0\nn1 = 110.0\nt0 = n0 + n1\nt1 = t0 - 100.0\nt2 = t1 / t0\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "18.333333333333332" + ], + "split": "train" + }, + { + "Input": "for the past n days , the average ( arithmetic mean ) daily production at a company was 60 units . if today ' s production of 90 units raises the average to 62 units per day , what is the value of n ?", + "Output Program": [ + "n0 = 60.0\nn1 = 90.0\nn2 = 62.0\nt0 = n1 - n0\nt1 = n2 - n0\nt2 = t0 / t1\nanswer = t2 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "the average weight of 8 persons increases by 1.5 kg . if a person weighing 65 kg is replaced by a new person , what could be the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 1.5\nn2 = 65.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "77" + ], + "split": "train" + }, + { + "Input": "two employees m and n are paid a total of $ 572 per week by their employer . if m is paid 120 percent of the salary paid to n , how much is n paid per week ?", + "Output Program": [ + "n0 = 572.0\nn1 = 120.0\nt0 = n1 / 100.0\nt1 = t0 + 1.0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "260" + ], + "split": "train" + }, + { + "Input": "if rs . 527 be divided among a , b , c in such a way that a gets 2 / 3 of what b gets and b gets 1 / 4 of what c gets , then their shares are respectively ?", + "Output Program": [ + "n0 = 527.0\nn1 = 2.0\nn2 = 3.0\nn3 = 1.0\nn4 = 4.0\nt0 = n3 / n4\nt1 = n1 / n2\nt2 = t1 * t0\nt3 = t0 + t2\nt4 = t3 + 1.0\nanswer = n0 / t4\nprint(answer)" + ], + "Output Answer": [ + "372.00000000000006" + ], + "split": "train" + }, + { + "Input": "we bought 85 hats at the store . blue hats cost $ 6 and green hats cost $ 7 . the total price was $ 540 . how many green hats did we buy ?", + "Output Program": [ + "n0 = 85.0\nn1 = 6.0\nn2 = 7.0\nn3 = 540.0\nt0 = n0 * n1\nanswer = n3 - t0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "a certain meter records voltage between 0 and 10 volts inclusive . if the average value of 3 recordings on the meter was 6 volts , what was the smallest possible recording in volts ?", + "Output Program": [ + "n0 = 0.0\nn1 = 10.0\nn2 = 3.0\nn3 = 6.0\nt0 = n2 * 4.0\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "find the last digit in the product 287 x 287 + 269 x 269 - 2 x 287 x 269 ?", + "Output Program": [ + "n0 = 287.0\nn1 = 287.0\nn2 = 269.0\nn3 = 269.0\nn4 = 2.0\nn5 = 287.0\nn6 = 269.0\nt0 = n0 * n0\nt1 = n2 * n2\nt2 = n0 * n4\nt3 = 10.0 * 2.0\nt4 = 100.0 * 3.0\nt5 = t0 + t1\nt6 = t3 + t4\nt7 = n2 * t2\nt8 = t5 - t7\nanswer = t8 - t6\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "at a monthly meeting , 2 / 3 of the attendees were males and 3 / 4 of the male attendees arrived on time . if 5 / 6 of the female attendees arrived on time , what fraction of the attendees at the monthly meeting did not arrive on time ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 3.0\nn3 = 4.0\nn4 = 5.0\nn5 = 6.0\nt0 = n4 / n5\nt1 = n0 / n1\nt2 = n2 / n3\nt3 = 1.0 - t0\nt4 = 1.0 - t1\nt5 = 1.0 - t2\nt6 = t3 * t4\nt7 = t1 * t5\nanswer = t6 + t7\nprint(answer)" + ], + "Output Answer": [ + "0.2222222222222222" + ], + "split": "train" + }, + { + "Input": "a school has 4 section of chemistry in class x having 50 , 35 , 45 and 42 students . the mean marks obtained in chemistry test are 50 , 60 , 55 and 45 respectively for the 4 sections . determine the overall average of marks per student .", + "Output Program": [ + "n0 = 4.0\nn1 = 50.0\nn2 = 35.0\nn3 = 45.0\nn4 = 42.0\nn5 = 50.0\nn6 = 60.0\nn7 = 55.0\nn8 = 45.0\nn9 = 4.0\nt0 = n1 + n2\nt1 = n1 * n5\nt2 = n2 * n6\nt3 = n3 * n7\nt4 = n3 * n4\nt5 = t1 + t2\nt6 = n3 + t0\nt7 = t5 + t3\nt8 = n4 + t6\nt9 = t7 + t4\nanswer = t9 / t8\nprint(answer)" + ], + "Output Answer": [ + "52.122093023255815" + ], + "split": "train" + }, + { + "Input": "what is the least integer that is a sum of 4 different prime numbers each greater than 10 ?", + "Output Program": [ + "n0 = 4.0\nn1 = 10.0\nt0 = n1 + 1.0\nt1 = t0 + 2.0\nt2 = t0 + t1\nt3 = n0 + t1\nt4 = t2 + t3\nt5 = t3 + 2.0\nanswer = t4 + t5\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "p , q and r have rs . 6000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?", + "Output Program": [ + "n0 = 6000.0\nt0 = 2.0 / 3.0\nt1 = t0 + 1.0\nt2 = n0 / t1\nanswer = t2 * t0\nprint(answer)" + ], + "Output Answer": [ + "2400" + ], + "split": "train" + }, + { + "Input": "on sunday , bill ran 4 more miles than he ran on saturday . julia did not run on saturday , but she ran twice the number of miles on sunday that bill ran on sunday . if bill and julia ran a total of 32 miles on saturday and sunday , how many miles did bill run on sunday ?", + "Output Program": [ + "n0 = 4.0\nn1 = 32.0\nt0 = n0 * 2.0\nt1 = n0 + t0\nt2 = n1 - t1\nt3 = t2 / n0\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "a man saves 20 % of his monthly salary . if an account of dearness of things he is to increase his monthly expenses by 20 % , he is only able to save rs . 260 per month . what is his monthly salary ?", + "Output Program": [ + "n0 = 20.0\nn1 = 20.0\nn2 = 260.0\nt0 = n1 / 100.0\nt1 = n2 * 100.0\nt2 = 100.0 - n0\nt3 = t0 * t2\nt4 = t3 + t2\nt5 = 100.0 - t4\nanswer = t1 / t5\nprint(answer)" + ], + "Output Answer": [ + "6500" + ], + "split": "train" + }, + { + "Input": "find the average marks of all the students in 2 separate classes , if the average marks of students in the first class of 55 students is 60 and that of another class of 48 students is 58", + "Output Program": [ + "n0 = 2.0\nn1 = 55.0\nn2 = 60.0\nn3 = 48.0\nn4 = 58.0\nt0 = n1 + n3\nt1 = n1 * n2\nt2 = n3 * n4\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "59.067961165048544" + ], + "split": "train" + }, + { + "Input": "on a game show , a contestant is given 3 keys , each of which opens exactly one of the 3 identical boxes . the contestant assigns each key to one of the boxes and wins the amount of money contained in any box that is opened by the key assigned to it . the first box contains $ 4 , the second $ 400 , and the third $ 4000 . what is the probability that a contestant will win more than $ 4000 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 4.0\nn3 = 400.0\nn4 = 4000.0\nn5 = 4000.0\nt0 = n0 * 2.0\nanswer = 1.0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.16666666666666666" + ], + "split": "train" + }, + { + "Input": "the average of 6 observations is 16 . a new observation is included and the new average is decreased by 1 . the seventh observation is ?", + "Output Program": [ + "n0 = 6.0\nn1 = 16.0\nn2 = 1.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n1 - n2\nt3 = t0 * t2\nanswer = t3 - t1\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "the total age of a and b is 16 years more than the total age of b and c . c is how many years younger than a ?", + "Output Program": [ + "n0 = 16.0\n\nanswer = n0 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "mary and harry enter into a partnership by investing $ 700 and $ 300 respectively . at the end of one year , they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business . if mary received $ 800 more than harry did , what was the profit made by their business in that year ?", + "Output Program": [ + "n0 = 700.0\nn1 = 300.0\nn2 = 800.0\nt0 = n0 + n1\nt1 = n2 * 3.0\nt2 = n0 - n1\nt3 = t1 / 2.0\nt4 = t2 / t0\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "3000" + ], + "split": "train" + }, + { + "Input": "the average of runs of a cricket player of 10 innings was 40 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?", + "Output Program": [ + "n0 = 10.0\nn1 = 40.0\nn2 = 4.0\nt0 = n0 + 1.0\nt1 = n1 + n2\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "84" + ], + "split": "train" + }, + { + "Input": "a certain school implemented a reading program for its students , with the goal of getting each student to read 3 books per month year - round . if the school has c classes made up of s students in each class , how many books will the entire student body read in one year ?", + "Output Program": [ + "n0 = 3.0\n\nanswer = n0 * 12.0\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "if x gets 25 % more than y and y gets 20 % more than z , the share of z out of rs . 740 will be :", + "Output Program": [ + "n0 = 25.0\nn1 = 20.0\nn2 = 740.0\nt0 = n1 / 100.0\nt1 = n0 / 100.0\nt2 = t0 + 1.0\nt3 = t1 + 1.0\nt4 = t3 * t2\nt5 = t2 + t4\nt6 = t5 + 1.0\nanswer = n2 / t6\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "train" + }, + { + "Input": "a number divided by 64 leaves remainder 37 what is the remainder when same number divided by 5", + "Output Program": [ + "n0 = 64.0\nn1 = 37.0\nn2 = 5.0\nt0 = n1 - n2\nanswer = t0 / t0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "a number when divided by 296 leaves 75 as remainder . when the same number is divided by 37 , the remainder will be :", + "Output Program": [ + "n0 = 296.0\nn1 = 75.0\nn2 = 37.0\nt0 = n0 + n1\nanswer = t0 % n2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "how many 3 digit positive integers w exist that when divided by 7 leave a remainder of 5 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 5.0\nt0 = 10.0 + 4.0\nt1 = 10.0 * 100.0\nt2 = n1 * t0\nt3 = t1 - 1.0\nt4 = n2 + t2\nt5 = t3 - t4\nanswer = t5 / n1\nprint(answer)" + ], + "Output Answer": [ + "128" + ], + "split": "train" + }, + { + "Input": "find the value of 18396 x 9999 = m ?", + "Output Program": [ + "n0 = 18396.0\nn1 = 9999.0\nt0 = n1 - 4.0\nanswer = t0 * n0\nprint(answer)" + ], + "Output Answer": [ + "183868020" + ], + "split": "train" + }, + { + "Input": "if , 1 * 3 * 5 = 16 3 * 5 * 7 = 38 then find , 13 * 15 * 17 = ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 5.0\nn3 = 16.0\nn4 = 3.0\nn5 = 5.0\nn6 = 7.0\nn7 = 38.0\nn8 = 13.0\nn9 = 15.0\nn10 = 17.0\nt0 = n9 * n10\nanswer = n8 + t0\nprint(answer)" + ], + "Output Answer": [ + "268" + ], + "split": "train" + }, + { + "Input": "3 partners a , b , c starts a business . twice a ' s capital is equal to thrice b ' s capital and b ' s capital is 4 times c ' s capital . out of a total profit of rs . 16500 at the end of the year , b ' s share is", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 16500.0\nt0 = n0 + n1\nt1 = n1 + t0\nt2 = n1 / t1\nanswer = n2 * t2\nprint(answer)" + ], + "Output Answer": [ + "6000" + ], + "split": "train" + }, + { + "Input": "a retailer sells 6 shirts . the first 2 he sells for $ 40 and $ 50 . if the retailer wishes to sell the 6 shirts for an overall average price of over $ 50 , what must be the minimum average price of the remaining 4 shirts ?", + "Output Program": [ + "n0 = 6.0\nn1 = 2.0\nn2 = 40.0\nn3 = 50.0\nn4 = 6.0\nn5 = 50.0\nn6 = 4.0\nt0 = n2 + n3\nt1 = n0 * n5\nt2 = n0 - n1\nt3 = t1 - t0\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "52.5" + ], + "split": "train" + }, + { + "Input": "the average salary of a person for the months of january , february , march and april is rs . 8000 and that for the months february , march , april and may is rs . 8800 . if his salary for the month of may is rs . 6500 , find his salary for the month of january ?", + "Output Program": [ + "n0 = 8000.0\nn1 = 8800.0\nn2 = 6500.0\nt0 = n0 * 4.0\nt1 = n1 * 4.0\nt2 = t1 - n2\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "3300" + ], + "split": "train" + }, + { + "Input": "every year taylor goes to the same carnival , and he attempts to shoot a basketball into a small hoop , hoping that he will win a 10 - foot tall teddy bear . if the probability that taylor does not make a basket is 1 / 3 , what is the probability that taylor makes exactly one basket in 3 tries ?", + "Output Program": [ + "n0 = 10.0\nn1 = 1.0\nn2 = 3.0\nn3 = 3.0\nt0 = n1 / n2\nt1 = n1 - t0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "0.22222222222222224" + ], + "split": "train" + }, + { + "Input": "find value for x from below equation ? x + 1 = 2", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\n\nanswer = n1 - n0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "little john had $ 10.50 . he spent $ 2.25 on sweets and gave to his two friends $ 2.20 each . how much money was left ?", + "Output Program": [ + "n0 = 10.5\nn1 = 2.25\nn2 = 2.2\nt0 = n2 + n2\nt1 = n1 + t0\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "3.8499999999999996" + ], + "split": "train" + }, + { + "Input": "a motorcycle importer is planning on increasing the price of a certain model by $ 1000 . at this new price 8 fewer motorcycles will be sold per month , but the total revenues will increase by $ 26000 to $ 594000 . what is the number of motorcycles the manufacturer will sell at this new price ?", + "Output Program": [ + "n0 = 1000.0\nn1 = 8.0\nn2 = 26000.0\nn3 = 594000.0\nt0 = n1 + 1.0\nt1 = n1 - 1.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "63" + ], + "split": "train" + }, + { + "Input": "1 / 0.02 is equal to", + "Output Program": [ + "n0 = 1.0\nn1 = 0.02\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 10000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is", + "Output Program": [ + "n0 = 8000.0\nn1 = 7.0\nn2 = 10000.0\nn3 = 6000.0\nt0 = n2 - n0\nt1 = n0 - n3\nt2 = n1 * t0\nt3 = t2 / t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "if the price of a certain computer increased 20 percent from d dollars to 351 dollars , then 2 d =", + "Output Program": [ + "n0 = 20.0\nn1 = 351.0\nn2 = 2.0\nt0 = n0 + 100.0\nt1 = t0 / 100.0\nt2 = n1 / t1\nanswer = n2 * t2\nprint(answer)" + ], + "Output Answer": [ + "585" + ], + "split": "train" + }, + { + "Input": "what must be added to each term of the ratio 2 : 3 , so that it may become equal to 4 : 5 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 4.0\nn3 = 5.0\nt0 = n1 * n2\nt1 = n0 * n3\nt2 = n3 - n2\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "the average of 8 numbers is 21 . if each of the number is multiplied by 8 , the average of the new set of numbers is :", + "Output Program": [ + "n0 = 8.0\nn1 = 21.0\nn2 = 8.0\n\nanswer = n1 * n2\nprint(answer)" + ], + "Output Answer": [ + "168" + ], + "split": "train" + }, + { + "Input": "for every x , the action [ x ] is defined : [ x ] is the greatest integer less than or equal to x . what is the value of [ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 9.8 ?", + "Output Program": [ + "n0 = 6.5\nn1 = 2.0\nn2 = 3.0\nn3 = 2.0\nn4 = 7.2\nn5 = 8.4\nn6 = 9.8\nt0 = 4.0 / 10.0\nt1 = n1 * n4\nt2 = n5 - t0\nt3 = t1 + t2\nanswer = t3 - n6\nprint(answer)" + ], + "Output Answer": [ + "12.599999999999998" + ], + "split": "train" + }, + { + "Input": "sixteen percent of the programmers in a startup company weigh 200 pounds or more . 20 - 5 percent of the programmers that are under 200 pounds in that same company weigh 100 pounds or less . what percent of the programmers in the startup company weigh between 100 and 200 pounds ?", + "Output Program": [ + "n0 = 200.0\nn1 = 20.0\nn2 = 5.0\nn3 = 200.0\nn4 = 100.0\nn5 = 100.0\nn6 = 200.0\nt0 = n1 + n2\nt1 = n1 - 4.0\nt2 = 100.0 - t0\nt3 = 100.0 - t1\nt4 = t2 / 100.0\nanswer = t4 * t3\nprint(answer)" + ], + "Output Answer": [ + "63" + ], + "split": "train" + }, + { + "Input": "in a graduating class , the difference between the highest and lowest salaries is $ 100000 . the median salary is $ 50000 higher than the lowest salary and the average salary is $ 20000 higher than the median . what is the minimum number of students r in the class ?", + "Output Program": [ + "n0 = 100000.0\nn1 = 50000.0\nn2 = 20000.0\nt0 = n0 / n2\nt1 = n1 / n2\nt2 = t1 * 3.0\nt3 = t0 + t2\nanswer = t3 + t1\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "if 10 people contributed a total of $ 20.00 toward a gift and each of them contributed at least $ 1.00 , then the maximum possible amount any one person could have contributed is", + "Output Program": [ + "n0 = 10.0\nn1 = 20.0\nn2 = 1.0\nt0 = n0 - n2\nt1 = n2 * t0\nanswer = n1 - t1\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "the product of two numbers is 120 and the sum of their squares is 289 . the sum is :", + "Output Program": [ + "import math\nn0 = 120.0\nn1 = 289.0\nt0 = n0 * 4.0\nt1 = n0 * 2.0\nt2 = n1 - t1\nt3 = math.sqrt(max(0, t2))\nt4 = t3**min(2.0, 5)\nt5 = t0 + t4\nanswer = math.sqrt(max(0, t5))\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "the average of runs of a cricket player of 10 innings was 32 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?", + "Output Program": [ + "n0 = 10.0\nn1 = 32.0\nn2 = 4.0\nt0 = n0 + 1.0\nt1 = n1 + n2\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "76" + ], + "split": "train" + }, + { + "Input": "the guests at a football banquet consumed a total of 323 pounds of food . if no individual guest consumed more than 2 pounds of food , what is the minimum number of guests that could have attended the banquet ?", + "Output Program": [ + "import math\nn0 = 323.0\nn1 = 2.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "162" + ], + "split": "train" + }, + { + "Input": "circles x and y are concentric . if the radius of circle x is 6 times that of circle y , what is the probability that a point selected inside circle x at random will be outside circle y ?", + "Output Program": [ + "n0 = 6.0\nt0 = n0**min(2.0, 5)\nt1 = t0 - 1.0\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.9722222222222222" + ], + "split": "train" + }, + { + "Input": "if x + y = 8 and y \u2212 3 x = 7 , then what is the value of y - x ?", + "Output Program": [ + "n0 = 8.0\nn1 = 3.0\nn2 = 7.0\nt0 = 1.0 + 3.0\nt1 = n0 * n1\nt2 = n2 + t1\nt3 = t2 / t0\nt4 = n0 - t3\nanswer = t3 - t4\nprint(answer)" + ], + "Output Answer": [ + "7.5" + ], + "split": "train" + }, + { + "Input": "if 6 / w + 6 / x = 6 / y and wx = y , then the average ( arithmetic mean ) of w and x is", + "Output Program": [ + "n0 = 6.0\nn1 = 6.0\nn2 = 6.0\nt0 = n0 + n0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "what is the sum of all 3 digit numbers that leave a remainder of ' 2 ' when divided by 3 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 3.0\nt0 = n0 * n0\nt1 = 1000.0 - n0\nt2 = t0 * 10.0\nt3 = t2 + t0\nt4 = n0 + t3\nt5 = t4 + t1\nt6 = t1 - t4\nt7 = t6 / n2\nt8 = t7 + 1.0\nt9 = t8 / n1\nanswer = t5 * t9\nprint(answer)" + ], + "Output Answer": [ + "164483.66666666666" + ], + "split": "train" + }, + { + "Input": "a grocer has a sale of rs . 5420 , rs . 5660 , rs . 6200 , rs . 6350 and rs . 6500 for 5 consecutive months . find the sale he should have in the sixth month , so that he gets an average sale of rs . 6300 ?", + "Output Program": [ + "n0 = 5420.0\nn1 = 5660.0\nn2 = 6200.0\nn3 = 6350.0\nn4 = 6500.0\nn5 = 5.0\nn6 = 6300.0\nt0 = n5 + 1.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n6 * t0\nt4 = n3 + t2\nt5 = n4 + t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "7670" + ], + "split": "train" + }, + { + "Input": "if 5 x = 6 y and xy \u2260 0 , what is the ratio of 1 / 3 * x to 1 / 5 * y ?", + "Output Program": [ + "n0 = 5.0\nn1 = 6.0\nn2 = 0.0\nn3 = 1.0\nn4 = 3.0\nn5 = 1.0\nn6 = 5.0\nt0 = n3 / n4\nt1 = n3 / n0\nt2 = n1 / n0\nt3 = t0 / t1\nanswer = t3 * t2\nprint(answer)" + ], + "Output Answer": [ + "1.9999999999999998" + ], + "split": "train" + }, + { + "Input": "the average marks of a class of 30 students is 50 and that of another class of 50 students is 60 . find the average marks of all the students ?", + "Output Program": [ + "n0 = 30.0\nn1 = 50.0\nn2 = 50.0\nn3 = 60.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "56.25" + ], + "split": "train" + }, + { + "Input": "andrea wants to fill in two sections of her backyard with sod that must be purchased in 2 - x - 2 - foot squares . if the two sections measure 30 x 40 feet and 60 x 80 feet , how many squares of sod does she need to buy ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 30.0\nn3 = 40.0\nn4 = 60.0\nn5 = 80.0\nt0 = n2 * n3\nt1 = n0 * n0\nt2 = n4 * n5\nt3 = t0 / t1\nt4 = t2 / t1\nanswer = t3 + t4\nprint(answer)" + ], + "Output Answer": [ + "1500" + ], + "split": "train" + }, + { + "Input": "if 4 b ^ 4 \u2212 41 b ^ 2 + 100 = 0 , then what is the sum of the two greatest possible values of b ?", + "Output Program": [ + "n0 = 4.0\nn1 = 4.0\nn2 = 41.0\nn3 = 2.0\nn4 = 100.0\nn5 = 0.0\nt0 = n0 + n0\nt1 = t0 + 1.0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "4.5" + ], + "split": "train" + }, + { + "Input": "having scored 99 runs in the 19 th inning , a cricketer increases his average score by 4 . what will be his average score after 19 innings ?", + "Output Program": [ + "n0 = 99.0\nn1 = 19.0\nn2 = 4.0\nn3 = 19.0\nt0 = n1 * 4.0\nt1 = n0 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "train" + }, + { + "Input": "a company decreased the price of its main product by 10 % . subsequently , the number of units sold increased such that the total revenue remained unchanged . what was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product ?", + "Output Program": [ + "n0 = 10.0\n\nanswer = 100.0 / n0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "of all the homes on gotham street , 1 / 3 are termite - ridden , and 7 / 10 of these are collapsing . what fraction of the homes are termite - ridden , but not collapsing ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 7.0\nn3 = 10.0\nt0 = n0 + 2.0\nt1 = n1 * n3\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.1" + ], + "split": "train" + }, + { + "Input": "how much is 80 % of 40 is greater than 4 / 5 of 15 ?", + "Output Program": [ + "n0 = 80.0\nn1 = 40.0\nn2 = 4.0\nn3 = 5.0\nn4 = 15.0\nt0 = n0 / 100.0\nt1 = n2 / n3\nt2 = n1 * t0\nt3 = n4 * t1\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 250 milliliters of solution x to create a solution that is 25 percent alcohol by volume ?", + "Output Program": [ + "n0 = 10.0\nn1 = 30.0\nn2 = 250.0\nn3 = 25.0\nt0 = n3 - n0\nt1 = n1 - n3\nt2 = t0 / t1\nanswer = n2 * t2\nprint(answer)" + ], + "Output Answer": [ + "750" + ], + "split": "train" + }, + { + "Input": "if jake loses 8 pounds , he will weigh twice as much as his sister kendra . together they now weigh 287 pounds . what is jake \u2019 s present weight , in pounds ?", + "Output Program": [ + "n0 = 8.0\nn1 = 287.0\nt0 = n1 - n0\nt1 = t0 / 3.0\nt2 = t1 * 2.0\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "194" + ], + "split": "train" + }, + { + "Input": "[ ( 3.242 x 14 ) / 100 ] = ?", + "Output Program": [ + "n0 = 3.242\nn1 = 14.0\nn2 = 100.0\nt0 = n0 * n1\nt1 = t0 / n2\nanswer = t1 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "0.045388" + ], + "split": "train" + }, + { + "Input": "i chose a number and divide it by 5 . then i subtracted 154 from the result and got 6 . what was the number i chose ?", + "Output Program": [ + "n0 = 5.0\nn1 = 154.0\nn2 = 6.0\nt0 = n1 + n2\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "800" + ], + "split": "train" + }, + { + "Input": "the least number of 4 digits which is divisible by 15 , 25 , 40 and 75 is :", + "Output Program": [ + "n0 = 4.0\nn1 = 15.0\nn2 = 25.0\nn3 = 40.0\nn4 = 75.0\nt0 = n0 * 2.0\nt1 = n4 * t0\nt2 = t1 * t0\nanswer = t2 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "9600" + ], + "split": "train" + }, + { + "Input": "in a fraction , if numerator is added by 2 and denominator by 1 it results 1 , and if numerator added again by 4 and denominator by 2 it results 1 / 2 . find the fraction ?", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 1.0\nn3 = 4.0\nn4 = 2.0\nn5 = 1.0\nn6 = 2.0\nt0 = n1 + n3\nanswer = t0 / n3\nprint(answer)" + ], + "Output Answer": [ + "1.25" + ], + "split": "train" + }, + { + "Input": "7 people average age is 30 . youngest person age is 4 . find average of the people when youngest was born .", + "Output Program": [ + "n0 = 7.0\nn1 = 30.0\nn2 = 4.0\nt0 = n0 * n1\nt1 = n0 * n2\nt2 = t0 - t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "in a group of cows and chickens , the number of legs was 10 more than twice the number of heads . the number of cows was :", + "Output Program": [ + "n0 = 10.0\nt0 = 4.0 - 2.0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "the total number of digits used in numbering the pages of a book having 356 pages is", + "Output Program": [ + "n0 = 356.0\nt0 = n0 * 3.0\nt1 = 100.0 - 1.0\nt2 = 10.0 - 1.0\nt3 = t0 - t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "960" + ], + "split": "train" + }, + { + "Input": "the average age of a group of 10 persons was decreased by 3 years when one person , whose age was 46 years , was replaced by a new person . find the age of the new person ?", + "Output Program": [ + "n0 = 10.0\nn1 = 3.0\nn2 = 46.0\nt0 = n0 * n1\nanswer = n2 - t0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "a number whose fifth part increased by 4 is equal to its fourth part diminished by 10 , is :", + "Output Program": [ + "n0 = 4.0\nn1 = 10.0\nt0 = n0 + n1\nt1 = 1.0 + 4.0\nt2 = 1.0 / 4.0\nt3 = 1.0 / t1\nt4 = t2 - t3\nanswer = t0 / t4\nprint(answer)" + ], + "Output Answer": [ + "280.00000000000006" + ], + "split": "train" + }, + { + "Input": "if 0.60 : x : : 6 : 2 , then x is equal to", + "Output Program": [ + "n0 = 0.6\nn1 = 6.0\nn2 = 2.0\nt0 = n0 * n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.19999999999999998" + ], + "split": "train" + }, + { + "Input": "find the number of elements in the power set of { 1,2 }", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\n\nanswer = 2.0 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "64 + 5 * 12 / ( 180 / 3 ) = ?", + "Output Program": [ + "n0 = 64.0\nn1 = 5.0\nn2 = 12.0\nn3 = 180.0\nn4 = 3.0\nt0 = n3 / n4\nt1 = n1 * n2\nt2 = t1 / t0\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "65" + ], + "split": "train" + }, + { + "Input": "alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 1021 . find the cost of each ice - cream cup ?", + "Output Program": [ + "n0 = 16.0\nn1 = 5.0\nn2 = 7.0\nn3 = 6.0\nn4 = 6.0\nn5 = 45.0\nn6 = 70.0\nn7 = 1021.0\nt0 = n0 * n3\nt1 = n1 * n5\nt2 = n2 * n6\nt3 = n7 - t0\nt4 = t3 - t1\nt5 = t4 - t2\nanswer = t5 / n3\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "jack went on a diet 6 months ago when he weighed 222 pounds . if he now weighs 198 pounds and continues to lose at the same average monthly rate , in approximately how many months will he weigh 180 pounds ?", + "Output Program": [ + "n0 = 6.0\nn1 = 222.0\nn2 = 198.0\nn3 = 180.0\nt0 = n1 - n2\nt1 = n2 - n3\nt2 = n0 / t0\nt3 = t2 * t1\nanswer = t3 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "5 pieces of wood have an average length of 128 cm and a median length of 140 cm . what is the maximum possible length , in cm , of the shortest piece of wood ?", + "Output Program": [ + "n0 = 5.0\nn1 = 128.0\nn2 = 140.0\nt0 = n0 * n1\nt1 = n2 * 3.0\nt2 = t0 - t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "110" + ], + "split": "train" + }, + { + "Input": "3 years ago , the average age of a family of 5 members was 17 . a baby having been born , the average age of the family is the same today . what is the age of the child ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 17.0\nt0 = n0 * n1\nanswer = n2 - t0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a , b , and c were to be paid in proportion to the part of work they did while working on the same piece of work . a and b individually can finish the piece of work in 12 days and 15 days respectively . they worked together for 5 days and then c completed the remaining work all alone . if $ 810 was the net sum to be paid for the entire work , what was the average daily wage of b ?", + "Output Program": [ + "n0 = 12.0\nn1 = 15.0\nn2 = 5.0\nn3 = 810.0\nt0 = 1.0 / n1\nt1 = n2 * t0\nt2 = n3 * t1\nanswer = t2 / n2\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "train" + }, + { + "Input": "how many numbers from 29 to 79 are exactly divisible by 11 ?", + "Output Program": [ + "import math\nn0 = 29.0\nn1 = 79.0\nn2 = 11.0\nt0 = n1 / n2\nt1 = n0 / n2\nt2 = math.floor(t0)\nt3 = math.floor(t1)\nt4 = t3 + 1.0\nt5 = n2 * t2\nt6 = n2 * t4\nt7 = t5 - t6\nt8 = t7 / n2\nanswer = t8 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "in a company with 48 employees , some part - time and some full - time , exactly ( 1 / 3 ) of the part - time employees and ( 1 / 4 ) of the full - time employees take the subway to work . what is the greatest possible number q of employees who take the subway to work ?", + "Output Program": [ + "n0 = 48.0\nn1 = 1.0\nn2 = 3.0\nn3 = 1.0\nn4 = 4.0\nt0 = n0 * n2\nt1 = n2 * n4\nt2 = t0 / t1\nt3 = n0 - t1\nt4 = t3 / t2\nanswer = t2 + t4\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "lilly has 10 fish and rosy has 8 fish . in total , how many fish do they have in all ?", + "Output Program": [ + "n0 = 10.0\nn1 = 8.0\n\nanswer = n0 + n1\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "a certain clock marks every hour by striking a number of times equal to the hour , and the time required for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stroke and the end of the last stroke is 55 seconds . at 12 : 00 , how many seconds elapse between the beginning of the first stroke and the end of the last stroke ?", + "Output Program": [ + "n0 = 6.0\nn1 = 0.0\nn2 = 55.0\nn3 = 12.0\nn4 = 0.0\nt0 = 1.0 + 4.0\nt1 = n0 + t0\nt2 = n3 + t1\nt3 = n2 / t1\nanswer = t2 * t3\nprint(answer)" + ], + "Output Answer": [ + "115" + ], + "split": "train" + }, + { + "Input": "the avearge score of a cricketer for 10 matches is 38.9 runs . if the average for the first 6 matches is 41 . then find the average for the last 4 matches ?", + "Output Program": [ + "n0 = 10.0\nn1 = 38.9\nn2 = 6.0\nn3 = 41.0\nn4 = 4.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = t0 - t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "35.75" + ], + "split": "train" + }, + { + "Input": "the greatest number that divides 60 and 190 leaving remainder 6 and 10 respectively is :", + "Output Program": [ + "import scipy\nn0 = 60.0\nn1 = 190.0\nn2 = 6.0\nn3 = 10.0\nt0 = scipy.gcd(int(n0), int(n1))\nt1 = n1 - n3\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "9 students bought burgers for $ 143 dollars . if the bill has to be divided among these students , how much amount should be added to the amound to make it divided amoung them equally in dollars ( in whole number of dollars )", + "Output Program": [ + "n0 = 9.0\nn1 = 143.0\nt0 = n1 % n0\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "b alone can do piece of work in 10 days . a alone can do it in 15 days . if the total wages for the work is rs 5000 , how much should b be paid if they work together for the entire duration of the work ?", + "Output Program": [ + "n0 = 6.0\nn1 = 5.0\nn2 = 2.0\nn3 = 19.0\nt0 = n0 * n1\nt1 = n2 * t0\nt2 = t1 / n2\nanswer = t2 + 3.0\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "how many numbers from 29 to 79 are exactly divisible by 11", + "Output Program": [ + "import math\nn0 = 29.0\nn1 = 79.0\nn2 = 11.0\nt0 = n1 / n2\nt1 = n0 / n2\nt2 = math.floor(t0)\nt3 = math.floor(t1)\nt4 = t3 + 1.0\nt5 = n2 * t2\nt6 = n2 * t4\nt7 = t5 - t6\nt8 = t7 / n2\nanswer = t8 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "a person travels from p to q a speed of 50 km / hr and returns by increasing his speed by 50 % . what is his average speed for both the trips ?", + "Output Program": [ + "n0 = 50.0\nn1 = 50.0\nt0 = n1 / 100.0\nt1 = t0 + 1.0\nt2 = n0 * t1\nt3 = n0 + t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "62.5" + ], + "split": "train" + }, + { + "Input": "find the greatest number which is such that when 794 , 858 and 1351 are divided by it , the remainders are all same .", + "Output Program": [ + "import scipy\nn0 = 794.0\nn1 = 858.0\nn2 = 1351.0\nt0 = n2 - n0\nt1 = n1 - n0\nanswer = scipy.gcd(int(t0), int(t1))\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "a man spend 1 / 5 of his salary on food , 1 / 10 of his salary on house rent and 3 / 5 salary on clothes . he still has $ 14000 left with him . find salary . .", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 1.0\nn3 = 10.0\nn4 = 3.0\nn5 = 5.0\nn6 = 14000.0\nt0 = n0 / n1\nt1 = n0 / n3\nt2 = n4 / n1\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n0 - t4\nanswer = n6 / t5\nprint(answer)" + ], + "Output Answer": [ + "140000.00000000003" + ], + "split": "train" + }, + { + "Input": "the equal amounts of money are deposited in two banks each at 15 % per annum for 3.5 years and 10 years respectively . if the difference between their interests is rs . 144 , find the each sum ?", + "Output Program": [ + "n0 = 15.0\nn1 = 3.5\nn2 = 10.0\nn3 = 144.0\nt0 = n0 * n2\nt1 = n0 * n1\nt2 = t0 - t1\nt3 = t2 / 100.0\nanswer = n3 / t3\nprint(answer)" + ], + "Output Answer": [ + "147.6923076923077" + ], + "split": "train" + }, + { + "Input": "what is the sum of the first 30 odd natural numbers", + "Output Program": [ + "n0 = 30.0\n\nanswer = n0**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "900" + ], + "split": "train" + }, + { + "Input": "a group of 55 adults and 70 children go for trekking . if there is meal for either 70 adults or 90 children and if 42 adults have their meal , find the total number of children that can be catered with the remaining food .", + "Output Program": [ + "n0 = 55.0\nn1 = 70.0\nn2 = 70.0\nn3 = 90.0\nn4 = 42.0\nt0 = n3 / n1\nt1 = n1 - n4\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "the units digit of ( 35 ) ^ ( 87 ) + ( 93 ) ^ ( 53 ) is :", + "Output Program": [ + "n0 = 35.0\nn1 = 87.0\nn2 = 93.0\nn3 = 53.0\nt0 = n3 % 4.0\nt1 = n0 % 10.0\nt2 = n2 * t0\nt3 = t2 % 10.0\nanswer = t3 + t1\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "in a graduating class , 40 percent of the students are male . in this class , 40 percent of the male students and 30 percent of the female students are 25 years old or older . if one student in the class is randomly selected , approximately what is the probability that he or she will be less than 25 years old ?", + "Output Program": [ + "n0 = 40.0\nn1 = 40.0\nn2 = 30.0\nn3 = 25.0\nn4 = 25.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = n2 / 100.0\nt3 = t0 * t1\nt4 = 1.0 - t0\nt5 = t2 * t4\nt6 = t3 + t5\nanswer = 1.0 - t6\nprint(answer)" + ], + "Output Answer": [ + "0.6599999999999999" + ], + "split": "train" + }, + { + "Input": "a number is doubled and 13 is added . if resultant is trebled , it becomes 93 . what is that number", + "Output Program": [ + "n0 = 13.0\nn1 = 93.0\nt0 = n0 * 3.0\nt1 = 2.0 * 3.0\nt2 = n1 - t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "we define that k @ j is the product of j number from k in increasing order for positive integers k , j . for example , 6 @ 4 = 6 * 7 * 8 * 9 . if a = 2020 and b = 2120 , what is the value t of the ratio a / b ?", + "Output Program": [ + "n0 = 6.0\nn1 = 4.0\nn2 = 6.0\nn3 = 7.0\nn4 = 8.0\nn5 = 9.0\nn6 = 2020.0\nn7 = 2120.0\nt0 = n6 / n6\nt1 = t0 + t0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "a type of extra - large suv averages 12.2 miles per gallon ( mpg ) on the highway , but only 7.6 mpg in the city . what is the maximum distance , in miles , that this suv could be driven on 22 gallons of gasoline ?", + "Output Program": [ + "n0 = 12.2\nn1 = 7.6\nn2 = 22.0\n\nanswer = n0 * n2\nprint(answer)" + ], + "Output Answer": [ + "268.4" + ], + "split": "train" + }, + { + "Input": "a library has an average of 1000 visitors on sundays and 700 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :", + "Output Program": [ + "import math\nn0 = 1000.0\nn1 = 700.0\nn2 = 30.0\nt0 = 3.0 + 4.0\nt1 = n2 / t0\nt2 = math.floor(t1)\nt3 = t2 + 1.0\nt4 = n0 * t3\nt5 = n2 - t3\nt6 = n1 * t5\nt7 = t4 + t6\nanswer = t7 / n2\nprint(answer)" + ], + "Output Answer": [ + "750" + ], + "split": "train" + }, + { + "Input": "the average weight of 19 students is 15 kg . by the admission of a new student the average weight is reduced to 14.6 kg . the weight of the new student is ?", + "Output Program": [ + "n0 = 19.0\nn1 = 15.0\nn2 = 14.6\nt0 = n0 + 1.0\nt1 = n0 * n1\nt2 = n2 * t0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "how many two digit numbers are there such that the product of their digits after reducing it to the smallest form is a prime number ? for example if we take 98 then 9 * 8 = 72 , 72 = 7 * 2 = 14 , 14 = 1 * 4 = 4 . consider only 4 prime no . s ( 23 , 57 )", + "Output Program": [ + "n0 = 98.0\nn1 = 9.0\nn2 = 8.0\nn3 = 72.0\nn4 = 72.0\nn5 = 7.0\nn6 = 2.0\nn7 = 14.0\nn8 = 14.0\nn9 = 1.0\nn10 = 4.0\nn11 = 4.0\nn12 = 4.0\nn13 = 23.0\nn14 = 57.0\n\nanswer = n1 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "each of the integers from 1 to 16 is written on the a seperate index card and placed in a box . if the cards are drawn from the box at random without replecement , how many cards must be drawn to ensure that the product of all the integers drawn is even ?", + "Output Program": [ + "n0 = 1.0\nn1 = 16.0\nt0 = n1 / 2.0\nanswer = n0 + t0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "a taxi owner buys diesel at rs . 8.50 , rs . 9 and rs . 9.50 per litre for 3 successive years . what approximately is the average cost per litre of diesel if he spends rs . 5000 each year ?", + "Output Program": [ + "n0 = 8.5\nn1 = 9.0\nn2 = 9.5\nn3 = 3.0\nn4 = 5000.0\nt0 = n4 / n0\nt1 = n4 / n1\nt2 = n4 / n2\nt3 = n3 * n4\nt4 = t0 + t1\nt5 = t4 + t2\nanswer = t3 / t5\nprint(answer)" + ], + "Output Answer": [ + "8.981462409886715" + ], + "split": "train" + }, + { + "Input": "the average of 10 numbers is 7 . if each number is multiplied by 10 , then what is the average of the new set of numbers ?", + "Output Program": [ + "n0 = 10.0\nn1 = 7.0\nn2 = 10.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "train" + }, + { + "Input": "if xy = 25 , x / y = 36 , for positive numbers x and y , y = ?", + "Output Program": [ + "import math\nn0 = 25.0\nn1 = 36.0\nt0 = n0 / n1\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "0.8333333333333334" + ], + "split": "train" + }, + { + "Input": "dacid obtained 70 , 63 , 80 , 63 and 65 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?", + "Output Program": [ + "n0 = 70.0\nn1 = 63.0\nn2 = 80.0\nn3 = 63.0\nn4 = 65.0\nn5 = 100.0\nt0 = n0 + n1\nt1 = 10.0 / 2.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "68.2" + ], + "split": "train" + }, + { + "Input": "the jogging track in a sports complex is 1000 meters in circumference . deepak and his wife start from the same point and walk in opposite directions at 20 km / hr and 13 km / hr respectively . they will meet for the first time in ?", + "Output Program": [ + "n0 = 1000.0\nn1 = 20.0\nn2 = 13.0\n\nanswer = n1 + n2\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "at a recent small town election for mayor a total of 979 votes were cast for the 4 candidates , the winner exceeding his opponents by 53 , 79 and 105 votes , respectively . how many votes were cast for the candidate in fourth place ?", + "Output Program": [ + "n0 = 979.0\nn1 = 4.0\nn2 = 53.0\nn3 = 79.0\nn4 = 105.0\nt0 = n2 + n3\nt1 = n4 + t0\nt2 = n0 + t1\nt3 = t2 / n1\nanswer = t3 - n4\nprint(answer)" + ], + "Output Answer": [ + "199" + ], + "split": "train" + }, + { + "Input": "a primitive village follows a strange custom . they have babies only to have a boy . whenever a boy is born in a family , they stop having babies and whenever a girl is born , they have a baby again and again till a boy is born . the probability of having a boy is same as the probability of having a girl . what will be the proportion of boys to girls in the village after some time ?", + "Output Program": [ + "t0 = 1.0 / 10.0\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "1.1" + ], + "split": "train" + }, + { + "Input": "a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 19.36 , the number of the member is the group is :", + "Output Program": [ + "import math\nn0 = 19.36\nt0 = n0 * 100.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "44" + ], + "split": "train" + }, + { + "Input": "a $ 77.95 lawn chair was sold for $ 59.95 at a special sale . by approximately what percent was the price decreased ?", + "Output Program": [ + "n0 = 77.95\nn1 = 59.95\nt0 = n0 - n1\nt1 = t0 / n0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "23.091725465041694" + ], + "split": "train" + }, + { + "Input": "in a division sum , the divisor is 10 times the quotient and 5 times the remainder . if the remainder is 46 , the divident is", + "Output Program": [ + "n0 = 10.0\nn1 = 5.0\nn2 = 46.0\nt0 = n1 * n2\nt1 = t0 / n0\nanswer = t1 * t0\nprint(answer)" + ], + "Output Answer": [ + "5290" + ], + "split": "train" + }, + { + "Input": "a teacher grades students \u2019 tests by subtracting twice the number of incorrect responses from the number of correct responses . if student a answers each of the 100 questions on her test and receives a score of 73 , how many questions did student a answer correctly ?", + "Output Program": [ + "n0 = 100.0\nn1 = 73.0\nt0 = n0 - n1\nt1 = t0 / 3.0\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "91" + ], + "split": "train" + }, + { + "Input": "find the value of 3 / 11 \u00d7 [ ( 1 + 1 / 3 ) ( 1 + 1 / 4 ) \u2026 \u2026 \u2026 \u2026 . ( 1 + 1 / 120 ) ] is", + "Output Program": [ + "n0 = 3.0\nn1 = 11.0\nn2 = 1.0\nn3 = 1.0\nn4 = 3.0\nn5 = 1.0\nn6 = 1.0\nn7 = 4.0\nn8 = 1.0\nn9 = 1.0\nn10 = 120.0\nt0 = n2 + n10\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "what is the sum of all possible 3 - digit numbers that can be constructed using the digits 2 , 3 , and 4 if each digit can be used only once in each number ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 3.0\nn3 = 4.0\nt0 = n2 + n3\nt1 = n1 + t0\nt2 = t1 * 100.0\nt3 = t1 * 10.0\nt4 = t2 + t3\nt5 = t4 + t1\nanswer = t5 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "1998" + ], + "split": "train" + }, + { + "Input": "how many even number in the range between 10 to 160 inclusive are not divisible by 3", + "Output Program": [ + "n0 = 10.0\nn1 = 160.0\nn2 = 3.0\nt0 = n2 * 4.0\nt1 = n1 - n0\nt2 = n1 - 2.0\nt3 = t1 - 2.0\nt4 = t2 - t0\nt5 = t3 / 2.0\nt6 = t4 - n2\nt7 = t6 - n2\nt8 = t7 / n2\nt9 = t8 / 2.0\nanswer = t5 - t9\nprint(answer)" + ], + "Output Answer": [ + "50.66666666666667" + ], + "split": "train" + }, + { + "Input": "if a is a positive integer and 10 ^ a \u2013 74 in decimal notation has digits whose sum is 440 , what is the value of a ?", + "Output Program": [ + "n0 = 10.0\nn1 = 74.0\nn2 = 440.0\nt0 = 2.0 + 3.0\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "if x = 7 and y = \u2212 2 , what is the value of ( x \u2212 2 y ) ^ y ?", + "Output Program": [ + "n0 = 7.0\nn1 = 2.0\nn2 = 2.0\nt0 = n1 / 2.0\nanswer = t0 / 1000.0\nprint(answer)" + ], + "Output Answer": [ + "0.001" + ], + "split": "train" + }, + { + "Input": "one ton has 2200 pounds , and one pound has 16 ounces . how many packets containing wheat weighing 16 pounds and 4 ounces each would totally fill a gunny bag of capacity 13 tons ?", + "Output Program": [ + "n0 = 2200.0\nn1 = 16.0\nn2 = 16.0\nn3 = 4.0\nn4 = 13.0\nt0 = n0 * n4\nt1 = n1 * n1\nt2 = n3 + t1\nt3 = n1 * t0\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "1760" + ], + "split": "train" + }, + { + "Input": "the value of a scooter depreciates in such a way that its value of the end of each year is 3 / 4 of its value of the beginning of the same year . if the initial value of the scooter is rs . 40,000 , what is the value at the end of 5 years ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 40000.0\nn3 = 5.0\nt0 = n0 / n1\nt1 = 100.0 * 100.0\nt2 = n1 * t1\nt3 = t0**min(n3, 5)\nanswer = t2 * t3\nprint(answer)" + ], + "Output Answer": [ + "9492.1875" + ], + "split": "train" + }, + { + "Input": "a cube with its sides numbered 1 through 6 is rolled twice , first landing on a and then landing on b . if any roll of the cube yields an equal chance of landing on any of the numbers 1 through 6 , what is the probability w that a + b is prime ?", + "Output Program": [ + "n0 = 1.0\nn1 = 6.0\nn2 = 1.0\nn3 = 6.0\nt0 = 12.0 + 3.0\nt1 = n0 / n1\nt2 = t1**min(2.0, 5)\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "0.41666666666666663" + ], + "split": "train" + }, + { + "Input": "in one year , the population , of a village increased by 25 % and in the next year , it decreased by 25 % . if at the end of 2 nd year , the population was 18750 , what was it in the beginning ?", + "Output Program": [ + "n0 = 25.0\nn1 = 25.0\nn2 = 2.0\nn3 = 18750.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nt2 = 1.0 - t0\nt3 = n3 / t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "20000" + ], + "split": "train" + }, + { + "Input": "a small pool filled only with water will require an additional 300 gallons of water in order to be filled to 85 % of its capacity . if pumping in these additional 300 gallons of water will increase the amount of water in the pool by 30 % , what is the total capacity of the pool in gallons ?", + "Output Program": [ + "n0 = 300.0\nn1 = 85.0\nn2 = 300.0\nn3 = 30.0\nt0 = n1 / 100.0\nt1 = n0 * 100.0\nt2 = t1 / n3\nt3 = n0 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "1529.4117647058824" + ], + "split": "train" + }, + { + "Input": "x , a , z , and b are single digit positive integers . x = 1 / 5 a . z = 1 / 5 b . ( 10 a + b ) \u2013 ( 10 x + z ) could not equal", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 1.0\nn3 = 5.0\nn4 = 10.0\nn5 = 10.0\nt0 = n1 * n1\nt1 = n1 * n4\nt2 = t0 + t1\nt3 = n1 + t1\nt4 = t2 - t3\nt5 = n4 + t4\nanswer = t5 + 3.0\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "how much water should be added to 10 liters of a 20 % - solution of alcohol to reduce the concentration of alcohol in the solution by 75 % ?", + "Output Program": [ + "n0 = 10.0\nn1 = 20.0\nn2 = 75.0\nt0 = n2 / 100.0\nt1 = 100.0 * 2.0\nt2 = n1 * t0\nt3 = n1 - t2\nt4 = t1 / t3\nanswer = t4 - n0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "on a game show , a contestant is given 3 keys , each of which opens exactly one of 3 identical boxes . the first box contains $ 5 , the second $ 500 , and the third $ 5000 . the contestant assigns each key to one of the boxes and wins the amount of money contained in any box that is opened by the key assigned to it . what is the probability that a contestant will win more than $ 5000 ?", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 3.0\nn2 = 5.0\nn3 = 500.0\nn4 = 5000.0\nn5 = 5000.0\nt0 = math.factorial(min(15, int(n0)))\nanswer = 1.0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.16666666666666666" + ], + "split": "train" + }, + { + "Input": "in a certain country 1 / 3 of 4 = 6 . assuming the same proportion , what would be the value of 1 / 6 of 20 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 4.0\nn3 = 6.0\nn4 = 1.0\nn5 = 6.0\nn6 = 20.0\nt0 = n1 / n2\nanswer = n6 * t0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "from below option 49 is divisible by which one ?", + "Output Program": [ + "import math\nn0 = 49.0\n\nanswer = math.sqrt(max(0, n0))\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "if x / ( 12 p ) is an even prime number , where x is a positive integer and p is a prime number , what is the least value of x ?", + "Output Program": [ + "n0 = 12.0\nt0 = n0 * 2.0\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "there are 8 players in a chess group , and each player plays each of the others once . given that each game is played by two players , how many total games will be played ?", + "Output Program": [ + "n0 = 8.0\nt0 = n0 - 1.0\nt1 = n0 * t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "a driver just filled the car ' s gas tank with 45 liters of gasohol , a mixture consisting of 5 % ethanol and 95 % gasoline . if the car runs best on a mixture consisting of 10 % ethanol and 90 % gasoline , how many liters of ethanol must be added into the gas tank for the car to achieve optimum performance ?", + "Output Program": [ + "n0 = 45.0\nn1 = 5.0\nn2 = 95.0\nn3 = 10.0\nn4 = 90.0\nt0 = n0 * n1\nt1 = 100.0 - n3\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "2.5" + ], + "split": "train" + }, + { + "Input": "think of a number , divide it by 5 and add 23 to it . the result is 42 . what is the number thought of ?", + "Output Program": [ + "n0 = 5.0\nn1 = 23.0\nn2 = 42.0\nt0 = n2 - n1\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "95" + ], + "split": "train" + }, + { + "Input": "here ' s an easy question of averages , but let ' s try to see innovative ways of solving this . a class has 12 boys and x girls . average score of boys and girls is 84 and 92 respectively . the average of the whole class is 86 , what is the value of x ?", + "Output Program": [ + "n0 = 12.0\nn1 = 84.0\nn2 = 92.0\nn3 = 86.0\nt0 = n0 * n3\nt1 = n0 * n1\nt2 = n2 - n3\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "a man is 30 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ?", + "Output Program": [ + "n0 = 30.0\nt0 = 2.0 * 2.0\nt1 = 2.0 - 1.0\nt2 = t0 - 2.0\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "q and r are two - digit positive integers that have the same digits but in reverse order . if the positive difference between q and r is less than 20 , what is the greatest possible value of q minus r ?", + "Output Program": [ + "n0 = 20.0\nt0 = 10.0 - 1.0\nt1 = n0 % t0\nanswer = t1 * t0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "if the sum of two positive integers is 20 and the difference of their squares is 40 , what is the product of the two integers ?", + "Output Program": [ + "n0 = 20.0\nn1 = 40.0\nt0 = n1 / n0\nt1 = n0 - t0\nt2 = t1 / t0\nt3 = t2 + t0\nanswer = t3 * t2\nprint(answer)" + ], + "Output Answer": [ + "99" + ], + "split": "train" + }, + { + "Input": "the average marks obtained by 100 candidates in an examination is 50 . find how many candidates have passed in the examination , if the average marks of candidates who passed is 70 and that of failed candidates is 20 .", + "Output Program": [ + "n0 = 100.0\nn1 = 50.0\nn2 = 70.0\nn3 = 20.0\nt0 = n0 * n1\nt1 = n0 * n3\nt2 = n2 - n3\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "in an office , totally there are 1800 employees and 60 % of the total employees are males . 30 % of the males in the office are at - least 50 years old . find the number of males aged below 50 years ?", + "Output Program": [ + "n0 = 1800.0\nn1 = 60.0\nn2 = 30.0\nn3 = 50.0\nn4 = 50.0\nt0 = n0 * n1\nt1 = 100.0 - n2\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nanswer = t2 * t3\nprint(answer)" + ], + "Output Answer": [ + "756" + ], + "split": "train" + }, + { + "Input": "in a renowned city , the average birth rate is 5 people every two seconds and the death rate is 3 people every two seconds . estimate the size of the population net increase that occurs in one day .", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nt0 = n0 - n1\nt1 = t0 * 3600.0\nanswer = t1 * 12.0\nprint(answer)" + ], + "Output Answer": [ + "86400" + ], + "split": "train" + }, + { + "Input": "a number is doubled and 9 is added . if resultant is trebled , it becomes 69 . what is that number", + "Output Program": [ + "n0 = 9.0\nn1 = 69.0\nt0 = n0 * 3.0\nt1 = 2.0 * 3.0\nt2 = n1 - t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "if x is a positive integer , then the least value of x for which x ! is divisible by 100000 is ? can someone please explain intuitively what the question is asking ?", + "Output Program": [ + "n0 = 100000.0\nt0 = 10.0 / 2.0\nanswer = t0 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "a certain sum of money is divided among a , b and c such that a gets one - third of what b and c together get and b gets two - seventh of what a and c together get . if the amount received by a is $ 30 more than that received by b , find the total amount shared by a , b and c .", + "Output Program": [ + "n0 = 30.0\nt0 = n0 * 3.0\nt1 = n0 * 2.0\nt2 = t0 * 2.0\nt3 = t2 + t1\nt4 = n0 + t3\nt5 = t3 + t4\nt6 = t4 * 3.0\nt7 = t6 - t3\nanswer = t5 + t7\nprint(answer)" + ], + "Output Answer": [ + "1080" + ], + "split": "train" + }, + { + "Input": "if x and g are integers and 2 x \u2013 g = 11 , then 4 x + g can not be", + "Output Program": [ + "n0 = 2.0\nn1 = 11.0\nn2 = 4.0\nt0 = n0 + n2\nt1 = t0 * 3.0\nanswer = t1 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "a fair 8 - sided dice labeled 1 to 8 is tossed 3 times . what is the probability the value of the dice shown is 3 at least once ?", + "Output Program": [ + "n0 = 8.0\nn1 = 1.0\nn2 = 8.0\nn3 = 3.0\nn4 = 3.0\nt0 = n0 * n3\nt1 = n0 * n0\nt2 = n3 * t0\nt3 = n0 * t1\nt4 = t2 - n0\nt5 = t4 - n3\nt6 = t5 - n3\nt7 = t6 - n1\nanswer = t7 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.111328125" + ], + "split": "train" + }, + { + "Input": "consider below info to be a table : amount of bacteria time - amount 1 pm - 10 gms 4 pm - x gms 7 pm - 12.1 gms data for a certain biology experiment are given in the table above . if the amount of bacteria present increased by the same factor during each of the two 3 - hour periods shown , how many grams of bacteria were present at 4 pm ?", + "Output Program": [ + "n0 = 1.0\nn1 = 10.0\nn2 = 4.0\nn3 = 7.0\nn4 = 12.1\nn5 = 3.0\nn6 = 4.0\nt0 = n1 + n4\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "11.05" + ], + "split": "train" + }, + { + "Input": "caleb spends $ 66.50 on 50 hamburgers for the marching band . if single burgers cost $ 1.00 each and double burgers cost $ 1.50 each , how many double burgers did he buy ?", + "Output Program": [ + "n0 = 66.5\nn1 = 50.0\nn2 = 1.0\nn3 = 1.5\nt0 = n0 - n1\nt1 = n3 - n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "if 7 gallons of gasoline are added to a tank that is already filled to 3 / 4 of its capacity , the tank is then filled to 9 / 10 of its capacity . how many gallons does the tank hold ?", + "Output Program": [ + "n0 = 7.0\nn1 = 3.0\nn2 = 4.0\nn3 = 9.0\nn4 = 10.0\nt0 = n3 / n4\nt1 = n1 / n2\nt2 = t0 - t1\nt3 = n0 / t2\nt4 = t3 * t1\nanswer = n0 + t4\nprint(answer)" + ], + "Output Answer": [ + "41.99999999999999" + ], + "split": "train" + }, + { + "Input": "the average of marks obtained by 120 boys was 37 . if the average of marks of passed boys was 39 and that of failed boys was 15 , the number of boys who passed the examination is ?", + "Output Program": [ + "n0 = 120.0\nn1 = 37.0\nn2 = 39.0\nn3 = 15.0\nt0 = n0 * n1\nt1 = n0 * n3\nt2 = n2 - n3\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "110" + ], + "split": "train" + }, + { + "Input": "a fruit drink is made of orange , watermelon , and grape juice , where 25 percent of the drink is orange juice and 40 percent is watermelon juice . if the drink is made with 105 ounces of grape juice , how many ounces is the drink total ?", + "Output Program": [ + "n0 = 25.0\nn1 = 40.0\nn2 = 105.0\nt0 = n0 + n1\nt1 = n0 * n2\nt2 = n1 * n2\nt3 = 100.0 - t0\nt4 = t1 / t3\nt5 = t2 / t3\nt6 = n2 + t4\nanswer = t6 + t5\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "gold is 11 times as heavy as water and copper is 5 times as heavy as water . in what ratio should these be mixed to get an alloy 8 times as heavy as water ?", + "Output Program": [ + "n0 = 11.0\nn1 = 5.0\nn2 = 8.0\nt0 = n2 - n1\nt1 = n0 - n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "all the milk in container a which was filled to its brim was poured into two containers b and c . the quantity of milk in container b was 62.5 % less than the capacity of container a . if 152 liters was now transferred from c to b , then both the containers would have equal quantities of milk . what was the initial quantity of milk in container a ?", + "Output Program": [ + "n0 = 62.5\nn1 = 152.0\nt0 = n0 / 100.0\nt1 = 1 / 2.0\nt2 = 1.0 - t0\nt3 = t1 - t2\nanswer = n1 / t3\nprint(answer)" + ], + "Output Answer": [ + "1216" + ], + "split": "train" + }, + { + "Input": "35 % of major airline companies equip their planes with wireless internet access . 70 % of major airlines offer passengers free on - board snacks . what is the greatest possible percentage of major airline companies that offer both wireless internet and free on - board snacks ?", + "Output Program": [ + "n0 = 35.0\nn1 = 70.0\n\nanswer = n0 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "the batting average of a particular batsman is 59 runs in 46 innings . if the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs , find his highest score .", + "Output Program": [ + "n0 = 59.0\nn1 = 46.0\nn2 = 150.0\nn3 = 58.0\nt0 = n0 * n1\nt1 = n1 - 2.0\nt2 = n3 * t1\nt3 = t0 - t2\nt4 = n2 + t3\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "156" + ], + "split": "train" + }, + { + "Input": "if 9 ^ y = 3 ^ 12 , what is y ?", + "Output Program": [ + "n0 = 9.0\nn1 = 3.0\nn2 = 12.0\n\nanswer = n2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "the average monthly salary of 8 workers and one supervisor in a factory was 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . whenthesupervisor , whosesalarywas 430 . when the supervisor , whose salary was 870 per month , retired , a new person was appointed and then the average salary of 9 people was $ $ 420 per month . the salary of the new supervisor is :", + "Output Program": [ + "n0 = 8.0\nn1 = 430.0\nn2 = 430.0\nn3 = 430.0\nn4 = 430.0\nn5 = 870.0\nn6 = 9.0\nn7 = 420.0\nt0 = n6 * n7\nt1 = n1 * n6\nt2 = t1 - n5\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "780" + ], + "split": "train" + }, + { + "Input": "the average of 6 no . ' s is 3.95 . the average of 2 of them is 3.6 , while the average of the other 2 is 3.85 . what is the average of the remaining 2 no ' s ?", + "Output Program": [ + "n0 = 6.0\nn1 = 3.95\nn2 = 2.0\nn3 = 3.6\nn4 = 2.0\nn5 = 3.85\nn6 = 2.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n2 * n5\nt3 = t1 + t2\nt4 = t0 - t3\nanswer = t4 / n2\nprint(answer)" + ], + "Output Answer": [ + "4.400000000000001" + ], + "split": "train" + }, + { + "Input": "a is an integer greater than 29 but less than 41 , b is an integer greater than 39 but less than 51 , what is the range of a / b ?", + "Output Program": [ + "n0 = 29.0\nn1 = 41.0\nn2 = 39.0\nn3 = 51.0\nt0 = n2 + 1.0\nt1 = n0 + 1.0\nt2 = n1 - 1.0\nt3 = n3 - 1.0\nt4 = t2 / t0\nt5 = t1 / t3\nanswer = t4 - t5\nprint(answer)" + ], + "Output Answer": [ + "0.4" + ], + "split": "train" + }, + { + "Input": "in one year , the population , of a village increased by 5 % and in the next year , it decreased by 5 % . if at the end of 2 nd year , the population was 9975 , what was it in the beginning ?", + "Output Program": [ + "n0 = 5.0\nn1 = 5.0\nn2 = 2.0\nn3 = 9975.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nt2 = 1.0 - t0\nt3 = n3 / t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "10000" + ], + "split": "train" + }, + { + "Input": "if k ^ 2 is divisible by 240 what is the least possible value of integer k ?", + "Output Program": [ + "n0 = 2.0\nn1 = 240.0\nt0 = n1 / 2.0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "a no . when divided by the sum of 555 and 445 gives 2 times their difference as quotient & 40 as remainder . find the no . is ?", + "Output Program": [ + "n0 = 555.0\nn1 = 445.0\nn2 = 2.0\nn3 = 40.0\nt0 = n0 + n1\nt1 = n0 - n1\nt2 = n2 * t0\nt3 = t2 * t1\nanswer = n3 + t3\nprint(answer)" + ], + "Output Answer": [ + "220040" + ], + "split": "train" + }, + { + "Input": "a cement mixture is composed of 3 elements . by weight , 1 / 3 of the mixture is sand , 1 / 2 of the mixture is water , and the remaining 8 pounds of the mixture is gravel . what is the weight of the entire mixture in pounds ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 3.0\nn3 = 1.0\nn4 = 2.0\nn5 = 8.0\nt0 = n1 / n2\nt1 = n3 / n4\nt2 = t0 + t1\nt3 = n1 - t2\nanswer = n5 / t3\nprint(answer)" + ], + "Output Answer": [ + "47.99999999999998" + ], + "split": "train" + }, + { + "Input": "albert is 2 times mary \u2019 s age and 4 times as old as betty . mary is 14 years younger than albert . how old is betty ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 14.0\nt0 = n0 * n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "how many kg of pure salt must be added to 100 kg of 10 % solution of salt and water to increase it to a 35 % solution ?", + "Output Program": [ + "n0 = 100.0\nn1 = 10.0\nn2 = 35.0\nt0 = n2 / n0\nt1 = n2 - n1\nt2 = 1.0 - t0\nanswer = t1 / t2\nprint(answer)" + ], + "Output Answer": [ + "38.46153846153846" + ], + "split": "train" + }, + { + "Input": "when y is divided by 276 , the remainder is 42 . what is the remainder when the same y is divided by 23 ?", + "Output Program": [ + "n0 = 276.0\nn1 = 42.0\nn2 = 23.0\n\nanswer = n1 % n2\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "when 200 is divided by positive integer x , the remainder is 2 . what is the remainder when 398 is divided by x ?", + "Output Program": [ + "n0 = 200.0\nn1 = 2.0\nn2 = 398.0\nt0 = n2 - n0\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "if it takes a tub 4 minutes to drain 5 / 7 of its content , how much more time will it take for the tub to be empty ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 7.0\nt0 = n1 / n2\nt1 = 1.0 - t0\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "a welder received an order to make a 1 million liter cube - shaped tank . if he has only 4 x 2 meter sheets of metal that can be cut , how many metal sheets will be required for this ordert ? ( 1 cubic meter = 1000 liters )", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 2.0\nn3 = 1.0\nn4 = 1000.0\nt0 = 1.0 / 3.0\nt1 = n1 * n2\nt2 = n4**min(t0, 5)\nt3 = t2**min(2.0, 5)\nt4 = t3 * 4.0\nt5 = t4 + t3\nt6 = t5 + t3\nanswer = t6 / t1\nprint(answer)" + ], + "Output Answer": [ + "74.99999999999997" + ], + "split": "train" + }, + { + "Input": "how many different 3 - digit multiples of 5 can be composed of digits 2 , 7 , 4 , and 5 if none of the digits is repeated ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 2.0\nn3 = 7.0\nn4 = 4.0\nn5 = 5.0\nt0 = n3 * n4\nt1 = t0 - n4\nanswer = t1 / n4\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "firm a ' s revenues are described by the equation ra = 17.12 x and its costs by ca = 12.87 x + 2400 . firm b ' s revenues are described by the equation rb = 13.27 x and its costs by cb = 8.77 x + 1500 . ( x denotes the quantity of sales ) . if a ' s volume of sales increases from 1000 to 3000 over the same period that b ' s volume increases from 2000 to 3000 , the percent increase in profits for the firm with the biggest dollar increase in profits is", + "Output Program": [ + "n0 = 17.12\nn1 = 12.87\nn2 = 2400.0\nn3 = 13.27\nn4 = 8.77\nn5 = 1500.0\nn6 = 1000.0\nn7 = 3000.0\nn8 = 2000.0\nn9 = 3000.0\nt0 = n3 - n4\nt1 = n6 * t0\nt2 = n8 * t0\nt3 = t2 - n5\nt4 = t1 / t3\nt5 = t4 * 100.0\nanswer = t5 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "if the average ( arithmetic mean ) of a and b is 45 and the average of b and c is 90 , what is the value of c \u00e2 \u02c6 \u2019 a ?", + "Output Program": [ + "n0 = 45.0\nn1 = 90.0\nt0 = n1 * 2.0\nt1 = n0 * 2.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "? x 240 = 173 x 240", + "Output Program": [ + "n0 = 240.0\nn1 = 173.0\nn2 = 240.0\nt0 = n1 * n2\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "173" + ], + "split": "train" + }, + { + "Input": "12 years ago , p was half of q in age . if the ratio of their present ages is 3 : 4 , what will be the total of their present ages", + "Output Program": [ + "n0 = 12.0\nn1 = 3.0\nn2 = 4.0\nt0 = n1 + n2\nt1 = n0 * 2.0\nt2 = n1 * 2.0\nt3 = t1 - n0\nt4 = t2 - n2\nt5 = t1 - t3\nt6 = t5 / t4\nanswer = t0 * t6\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "a number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34 . such a least possible number n is", + "Output Program": [ + "n0 = 5.0\nn1 = 8.0\nn2 = 34.0\nt0 = n2 * 2.0\nt1 = n0 * n1\nt2 = n0 - 1.0\nt3 = t0 - t1\nt4 = t3 / t2\nanswer = t4 + t0\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "if 3 / p = 6 and 3 / q = 15 then p \u2013 q = ?", + "Output Program": [ + "n0 = 3.0\nn1 = 6.0\nn2 = 3.0\nn3 = 15.0\nt0 = n0 / n1\nt1 = n0 / n3\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "0.3" + ], + "split": "train" + }, + { + "Input": "light glows for every 13 seconds . how many max . times did it glow between 1 : 57 : 58 and 3 : 20 : 47 am .", + "Output Program": [ + "n0 = 13.0\nn1 = 1.0\nn2 = 57.0\nn3 = 58.0\nn4 = 3.0\nn5 = 20.0\nn6 = 47.0\nt0 = n6 + 2.0\nt1 = 2.0 + 60.0\nt2 = n5 + t1\nt3 = t2 * 60.0\nt4 = t0 + t3\nanswer = t4 / n0\nprint(answer)" + ], + "Output Answer": [ + "382.2307692307692" + ], + "split": "train" + }, + { + "Input": "if n = 2 ^ 0.1 and n ^ b = 16 , b must equal", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 0.1\nn2 = 16.0\nt0 = math.log(max(1e-5, n2), 2)\nt1 = n0**min(n1, 5)\nt2 = math.log(max(1e-5, t1), 2)\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "40.00000000000002" + ], + "split": "train" + }, + { + "Input": "the maximum number of students among them 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :", + "Output Program": [ + "import scipy\nn0 = 1001.0\nn1 = 910.0\n\nanswer = scipy.gcd(int(n0), int(n1))\nprint(answer)" + ], + "Output Answer": [ + "91" + ], + "split": "train" + }, + { + "Input": "calculate 469111 x 9999 = ?", + "Output Program": [ + "n0 = 469111.0\nn1 = 9999.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "4690640889" + ], + "split": "train" + }, + { + "Input": "if a ' s salary is 20 % less than b ' s salary , by how much percentage is b ' s salary more than a ' s ?", + "Output Program": [ + "n0 = 20.0\nt0 = 100.0 - n0\nt1 = t0 / 100.0\nt2 = 100.0 - t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "if the price of sugar rises from rs . 2 per kg to rs . 5 per kg , a person , to have no increase in the expenditure on sugar , will have to reduce his consumption of sugar by", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nt0 = n0 * 1.0\nt1 = t0 / n1\nt2 = 1.0 - t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "when n is divided by 25 , the remainder is 4 . what is the remainder when n + 15 is divided by 5 ?", + "Output Program": [ + "n0 = 25.0\nn1 = 4.0\nn2 = 15.0\nn3 = 5.0\nt0 = n2 % n3\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "what is the average ( arithmetic mean ) of all multiples of 10 from 10 to 200 inclusive ?", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 200.0\nt0 = n0 + n2\nt1 = n2 - n0\nt2 = t1 / n0\nt3 = t2 + 1.0\nt4 = t0 * t3\nt5 = t4 / 2.0\nanswer = t5 / t3\nprint(answer)" + ], + "Output Answer": [ + "105" + ], + "split": "train" + }, + { + "Input": "if 4 a = 5 b = 30 , then 40 ab =", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 30.0\nn3 = 40.0\nt0 = n2 / n0\nt1 = n2 / n1\nt2 = t0 * t1\nanswer = n3 * t2\nprint(answer)" + ], + "Output Answer": [ + "1800" + ], + "split": "train" + }, + { + "Input": "x , y , and z are different prime numbers . the product x ^ 2 * y * z is divisible by how many different positive numbers ?", + "Output Program": [ + "n0 = 2.0\nt0 = n0**min(4.0, 5)\nanswer = t0 - 4.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "if 20 % of a class averages 80 % on a test , 50 % of the class averages 60 % on the test , and the remainder of the class averages 40 % on the test , what is the overall class average ?", + "Output Program": [ + "n0 = 20.0\nn1 = 80.0\nn2 = 50.0\nn3 = 60.0\nn4 = 40.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nt4 = 100.0 - t0\nt5 = n4 * t4\nt6 = t3 + t5\nanswer = t6 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "58" + ], + "split": "train" + }, + { + "Input": "a man whose bowling average is 12.4 , takes 6 wickets for 26 runs and there by decreases his average by 0.4 . the number of wickets taken by him before his last match is ?", + "Output Program": [ + "import math\nn0 = 12.4\nn1 = 6.0\nn2 = 26.0\nn3 = 0.4\nt0 = math.floor(n0)\nt1 = n1 * t0\nt2 = n0 - t0\nt3 = t1 - n2\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "114.9999999999999" + ], + "split": "train" + }, + { + "Input": "\u221a 289 - \u221a 625 \u00f7 \u221a 25 is equal to ?", + "Output Program": [ + "import math\nn0 = 289.0\nn1 = 625.0\nn2 = 25.0\nt0 = math.sqrt(max(0, n0))\nt1 = math.sqrt(max(0, n1))\nt2 = math.sqrt(max(0, t1))\nt3 = t1 / t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "the average ( arithmetic mean ) of all scores on a certain algebra test was 90 . if the average of the 8 male students \u2019 grades was 83 , and the average of the female students \u2019 grades was 92 , how many female students took the test ?", + "Output Program": [ + "n0 = 90.0\nn1 = 8.0\nn2 = 83.0\nn3 = 92.0\nt0 = n0 * n1\nt1 = n1 * n2\nt2 = n3 - n0\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "the population of a bacteria culture doubles every 6 minutes . approximately how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria", + "Output Program": [ + "import math\nn0 = 6.0\nn1 = 1000.0\nn2 = 500000.0\nt0 = 1.0 + 4.0\nt1 = t0 * n1\nt2 = t1 * 100.0\nt3 = t2 / n1\nt4 = math.log(max(1e-5, t3), 2)\nanswer = n0 * t4\nprint(answer)" + ], + "Output Answer": [ + "53.794705707972525" + ], + "split": "train" + }, + { + "Input": "can you solve it ? 2 + 3 = 8 , 3 + 7 = 27 , 4 + 5 = 32 , 5 + 8 = 60 , 6 + 7 = 72 , 7 + 8 = ? ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 8.0\nn3 = 3.0\nn4 = 7.0\nn5 = 27.0\nn6 = 4.0\nn7 = 5.0\nn8 = 32.0\nn9 = 5.0\nn10 = 8.0\nn11 = 60.0\nn12 = 6.0\nn13 = 7.0\nn14 = 72.0\nn15 = 7.0\nn16 = 8.0\nt0 = n4 - 1.0\nt1 = n2 + t0\nanswer = n4 * t1\nprint(answer)" + ], + "Output Answer": [ + "98" + ], + "split": "train" + }, + { + "Input": "if x ^ 2 + 1 / x ^ 2 = 2 , what is the value of x ^ 4 + 1 / x ^ 4 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 2.0\nn3 = 2.0\nn4 = 4.0\nn5 = 1.0\nn6 = 4.0\nt0 = n0**min(2.0, 5)\nanswer = t0 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a certain debt will be paid in 52 installments from january 1 to december 31 of a certain year . each of the first 12 payments is to be $ 410 ; each of the remaining payments is to be $ 65 more than each of the first 12 payments . what is the average ( arithmetic mean ) payment that will be made on the debt for the year ?", + "Output Program": [ + "n0 = 52.0\nn1 = 1.0\nn2 = 31.0\nn3 = 12.0\nn4 = 410.0\nn5 = 65.0\nn6 = 12.0\nt0 = n4 + n5\nt1 = n3 * n4\nt2 = n0 - n3\nt3 = t0 * t2\nt4 = t1 + t3\nanswer = t4 / n0\nprint(answer)" + ], + "Output Answer": [ + "460" + ], + "split": "train" + }, + { + "Input": "the tax on a commodity is diminished by 14 % and its consumption increased by 15 % . the effect on revenue is ?", + "Output Program": [ + "n0 = 14.0\nn1 = 15.0\nt0 = n1 / 100.0\nt1 = n0 / 100.0\nt2 = t0 + 1.0\nt3 = 1.0 - t1\nt4 = t2 * t3\nt5 = t4 * 100.0\nanswer = 100.0 - t5\nprint(answer)" + ], + "Output Answer": [ + "1.1000000000000085" + ], + "split": "train" + }, + { + "Input": "in a party every person shakes hands with every other person . if there were a total of 136 handshakes in the party then what is the number of persons present in the party ?", + "Output Program": [ + "import math\nn0 = 136.0\nt0 = n0 * 2.0\nt1 = t0 * 4.0\nt2 = t1 + 1.0\nt3 = math.sqrt(max(0, t2))\nt4 = t3 + 1.0\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "caleb spends $ 74.50 on 50 hamburgers for the marching band . if single burgers cost $ 1.00 each and double burgers cost $ 1.50 each , how many double burgers did he buy ?", + "Output Program": [ + "n0 = 74.5\nn1 = 50.0\nn2 = 1.0\nn3 = 1.5\nt0 = n0 - n1\nt1 = n3 - n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "49" + ], + "split": "train" + }, + { + "Input": "the average temperature for monday , tuesday , wednesday and thursday was 48 degrees and for tuesday , wednesday , thursday and friday was 40 degrees . if the temperature on monday was 42 degrees . find the temperature on friday ?", + "Output Program": [ + "n0 = 48.0\nn1 = 40.0\nn2 = 42.0\nt0 = n0 * 4.0\nt1 = n1 * 4.0\nt2 = t0 - t1\nanswer = n2 - t2\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "if the sum of the 4 th term and the 12 th term of an arithmetic progression is 8 , what is the sum of the first 15 terms of the progression ?", + "Output Program": [ + "n0 = 4.0\nn1 = 12.0\nn2 = 8.0\nn3 = 15.0\nt0 = n3 / 2.0\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "a satellite is composed of 24 modular units , each of which is equipped with a set of sensors , some of which have been upgraded . each unit contains the same number of non - upgraded sensors . if the number of non - upgraded sensors on one unit is 1 / 4 the total number of upgraded sensors on the entire satellite , what fraction of the sensors on the satellite have been upgraded ?", + "Output Program": [ + "n0 = 24.0\nn1 = 1.0\nn2 = 4.0\nt0 = n1 / n2\nt1 = n0 * t0\nt2 = n0 * t1\nt3 = n0 + t2\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.14285714285714285" + ], + "split": "train" + }, + { + "Input": "a group of 4 investment bankers and 5 clients recently frequented the bonbon ribs restaurant . the total bill for the meal , including 20 % gratuity , came to $ 756 . on average , how much did the meal of each individual cost before gratuity ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 20.0\nn3 = 756.0\nt0 = n2 + 100.0\nt1 = n0 + n1\nt2 = t0 / 100.0\nt3 = n3 / t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "train" + }, + { + "Input": "a salesman ' s income consists of a commission and a base salary of $ 370 per week . over the past 5 weeks , his weekly income totals have been $ 406 , $ 413 , $ 420 , $ 436 and $ 395 . what must his average ( arithmetic mean ) commission be per week over the next two weeks so that his average weekly income is $ 500 over the 7 - week period ?", + "Output Program": [ + "n0 = 370.0\nn1 = 5.0\nn2 = 406.0\nn3 = 413.0\nn4 = 420.0\nn5 = 436.0\nn6 = 395.0\nn7 = 500.0\nn8 = 7.0\nt0 = n2 + n3\nt1 = n4 + n5\nt2 = n7 * n8\nt3 = t0 + t1\nt4 = n6 + t3\nt5 = t2 - t4\nt6 = t5 / 2.0\nanswer = t6 - n0\nprint(answer)" + ], + "Output Answer": [ + "345" + ], + "split": "train" + }, + { + "Input": "a fruit drink is made of grapefruit , lemon , and orange juice , where 25 percent of the drink is grapefruit juice and 35 percent is lemon juice . if the drink is made with 20 ounces of orange juice , how many ounces is the drink total ?", + "Output Program": [ + "n0 = 25.0\nn1 = 35.0\nn2 = 20.0\nt0 = n0 + n1\nt1 = 100.0 - t0\nt2 = t1 / 100.0\nanswer = n2 / t2\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "` ` how old are you , alchemerion ? ' ' asked one of the wizards appearances the wizards answer with a riddle , ` ` i am still very young as wizards go . i am only 3 times my son ' s age . my father is 40 year more than twice of my age . together the 3 of us are a 1240 year old ' ' . how old is alchemerion", + "Output Program": [ + "n0 = 3.0\nn1 = 40.0\nn2 = 3.0\nn3 = 1240.0\nt0 = n3 - n1\nt1 = t0 / 10.0\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "360" + ], + "split": "train" + }, + { + "Input": "if a person walks at 14 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance travelled by him is", + "Output Program": [ + "n0 = 14.0\nn1 = 10.0\nn2 = 20.0\nt0 = n0 - n1\nt1 = n2 / t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "working simultaneously and independently at an identical constant rate , 4 machines of a certain type can produce a total of x units of product p in 6 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 2 x units of product p in 3 days ?", + "Output Program": [ + "n0 = 4.0\nn1 = 6.0\nn2 = 2.0\nn3 = 3.0\nt0 = n1 / n3\nt1 = n0 * n2\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "a bag of potatoes weighs 36 lbs divided by half of its weight . how much does the bag of potatoes weight ?", + "Output Program": [ + "n0 = 36.0\n\nanswer = n0 / 1.0\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "when 200 is divided by positive integer x , the remainder is 5 . what is the remainder when 395 is divided by x ?", + "Output Program": [ + "n0 = 200.0\nn1 = 5.0\nn2 = 395.0\nt0 = n2 - n0\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "xy = 1 then what is ( 7 ^ ( x + y ) ^ 2 ) / ( 7 ^ ( x - y ) ^ 2 )", + "Output Program": [ + "n0 = 1.0\nn1 = 7.0\nn2 = 2.0\nn3 = 7.0\nn4 = 2.0\nt0 = n0 * 4.0\nanswer = n1**min(t0, 5)\nprint(answer)" + ], + "Output Answer": [ + "2401" + ], + "split": "train" + }, + { + "Input": "let p be a prime number greater than 2 and let n = 14 p . how many even numbers divide n ?", + "Output Program": [ + "n0 = 2.0\nn1 = 14.0\n\nanswer = n0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "a train starts full of passengers . at the first station , it drops one - third of the passengers and takes 280 more . at the second station , it drops one - half of the new total and takes 12 more . on arriving at the third station , it is found to have 248 passengers . find the number of passengers in the beginning .", + "Output Program": [ + "n0 = 280.0\nn1 = 12.0\nn2 = 248.0\nt0 = n2 - n1\nt1 = t0 * 2.0\nt2 = t1 - n0\nt3 = t2 * 3.0\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "288" + ], + "split": "train" + }, + { + "Input": "if a 2 + b 2 + c 2 = 213 and ab + bc + ca = 6 , then a + b + c is", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 2.0\nn2 = 2.0\nn3 = 213.0\nn4 = 6.0\nt0 = n4 * n0\nt1 = n3 + t0\nanswer = math.sqrt(max(0, t1))\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "if a - b = 6 and a 2 + b 2 = 48 , find the value of ab .", + "Output Program": [ + "n0 = 6.0\nn1 = 2.0\nn2 = 2.0\nn3 = 48.0\nt0 = n0**min(n1, 5)\nt1 = n3 - t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "a committee is reviewing a total of 30 x black - and - white films and 6 y color films for a festival . if the committee selects y / x % of the black - and - white films and all of the color films , what fraction of the selected films are in color ?", + "Output Program": [ + "n0 = 30.0\nn1 = 6.0\nt0 = n0 / 100.0\nt1 = n1 + t0\nanswer = n1 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.9523809523809524" + ], + "split": "train" + }, + { + "Input": "half a number plus 5 is 11 . what is the number ?", + "Output Program": [ + "n0 = 5.0\nn1 = 11.0\nt0 = n1 - n0\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "in the coordinate plane a slope of the line k is 4 times the x - intercept of the line k . what is the y - intercept of the line k ?", + "Output Program": [ + "n0 = 4.0\n\nanswer = 1.0 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.25" + ], + "split": "train" + }, + { + "Input": "what no . should be subtracted from x ^ 3 + 4 x 2 \u2212 7 x + 12 x ^ 3 + 4 x ^ 2 \u2212 7 x + 12 , if it is to be perfectly divisible by x + 3 x + 3 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 2.0\nn3 = 7.0\nn4 = 12.0\nn5 = 3.0\nn6 = 4.0\nn7 = 2.0\nn8 = 7.0\nn9 = 12.0\nn10 = 3.0\nn11 = 3.0\nt0 = -n0\nt1 = n3 * t0\nt2 = t0**min(n2, 5)\nt3 = t0**min(n0, 5)\nt4 = n1 * t2\nt5 = t4 + t3\nt6 = t5 - t1\nanswer = n4 + t6\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "in a division sum , the quotient is 40 , the divisor 72 and the remainder 64 , find the dividend ?", + "Output Program": [ + "n0 = 40.0\nn1 = 72.0\nn2 = 64.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "2944" + ], + "split": "train" + }, + { + "Input": "the probability that a man will be alive for 10 more yrs is 1 / 4 & the probability that his wife will alive for 10 more yrs is 1 / 3 . the probability that none of them will be alive for 10 more yrs , is", + "Output Program": [ + "n0 = 10.0\nn1 = 1.0\nn2 = 4.0\nn3 = 10.0\nn4 = 1.0\nn5 = 3.0\nn6 = 10.0\nt0 = n1 / n2\nt1 = n1 / n5\nt2 = n1 - t0\nt3 = n1 - t1\nanswer = t2 * t3\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "amount of bacteria present time amount 1 : 00 p . m . 8.0 grams 4 : 00 p . m . x grams 7 : 00 p . m . 12.4 grams data for a certain biology experiment are given in the table above . if the amount of bacteria present increased by the same fraction during each of the two 3 - hour periods shown , how many grams of bacteria were present at 4 : 00 p . m . ?", + "Output Program": [ + "import math\nn0 = 1.0\nn1 = 0.0\nn2 = 8.0\nn3 = 4.0\nn4 = 0.0\nn5 = 7.0\nn6 = 0.0\nn7 = 12.4\nn8 = 3.0\nn9 = 4.0\nn10 = 0.0\nt0 = n2 * n7\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "9.959919678390985" + ], + "split": "train" + }, + { + "Input": "during the first week of performances of a certain play , 5400 tickets were sold , all at reduced price . during the remaining weeks of performances , 5 times as many tickets were sold at full price as were sold at reduced price . if the total number of tickets e sold was 25200 , how many of them were sold at full price ?", + "Output Program": [ + "n0 = 5400.0\nn1 = 5.0\nn2 = 25200.0\nt0 = 2.0 + 4.0\nt1 = n2 - n0\nt2 = n1 * t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "16500" + ], + "split": "train" + }, + { + "Input": "mary ' s income is 60 % more than tim ' s income and tim ' s income is 10 % less than juan ' s income . what % of juan ' s income is mary ' s income .", + "Output Program": [ + "n0 = 60.0\nn1 = 10.0\nt0 = n0 / 100.0\nt1 = 100.0 - n1\nt2 = t0 * t1\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "144" + ], + "split": "train" + }, + { + "Input": "let s be the set of all positive integers that , when divided by 8 , have a remainder of 5 . what is the 75 th number in this set ?", + "Output Program": [ + "n0 = 8.0\nn1 = 5.0\nn2 = 75.0\nt0 = n2 - 1.0\nt1 = n0 * t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "597" + ], + "split": "train" + }, + { + "Input": "if the operation \u20ac is defined for all x and y by the equation x \u20ac y = 2 * x * y , then 9 \u20ac ( 4 \u20ac 5 ) =", + "Output Program": [ + "n0 = 2.0\nn1 = 9.0\nn2 = 4.0\nn3 = 5.0\nt0 = n0 * n1\nt1 = n0 * n2\nt2 = n3 * t1\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "720" + ], + "split": "train" + }, + { + "Input": "if a no . when divided by 44 , gives 432 as quotient and 0 as remainder . what will be the remainder when dividing the same no . by 34", + "Output Program": [ + "n0 = 44.0\nn1 = 432.0\nn2 = 0.0\nn3 = 34.0\nt0 = n0 * n1\nanswer = t0 % n3\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "65 bags of nuts are to be divided among 13 students . each bag contains 15 nuts . how many nuts will each student receive ?", + "Output Program": [ + "n0 = 65.0\nn1 = 13.0\nn2 = 15.0\nt0 = n0 / n1\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "if x = 1 - 4 t and y = 2 t - 2 , then for what value of t does x = y ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 2.0\nn3 = 2.0\nt0 = n0 + n2\nt1 = n1 + n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "what is the last digit in ( 7 ^ 95 - 3 ^ 58 ) ?", + "Output Program": [ + "n0 = 7.0\nn1 = 95.0\nn2 = 3.0\nn3 = 58.0\nt0 = 4.0 * 4.0\nt1 = t0 / 2.0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "of 3 numbers , the third is twice the first and the second is 4 times the first . if their average is 77 , the smallest of the 3 numbers is :", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 77.0\nn3 = 3.0\nt0 = 1.0 + 2.0\nt1 = n0 * n2\nt2 = n1 + t0\nanswer = t1 / t2\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "a store reported total sales of $ 400 million for february of this year . if the total sales for the same month last year was $ 320 million , approximately what was the percent increase in sales ?", + "Output Program": [ + "n0 = 400.0\nn1 = 320.0\nt0 = n0 - n1\nt1 = t0 / n1\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "in a two digit number it is known that its unit ' s digit exceeds its 10 ' s digit by 4 and that the product of the given number and the sum of its digits is equal to 208 , what is the number ?", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 4.0\nn2 = 208.0\nt0 = 1.0 + 10.0\nt1 = 4.0 * 4.0\nt2 = n1 * 2.0\nt3 = t0 * 2.0\nt4 = n1 * t0\nt5 = n2 - t1\nt6 = t4 + t2\nt7 = n1 * t3\nt8 = t7 * t5\nt9 = t6**min(2.0, 5)\nt10 = t8 + t9\nt11 = math.sqrt(max(0, t10))\nt12 = t11 - t6\nt13 = t12 / t4\nt14 = n1 + t13\nt15 = n0 * t13\nanswer = t14 + t15\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "jennifer had $ 180 to spend on herself . she spent 1 / 5 of the money on a sandwich , 1 / 6 for a ticket to a museum , and 1 / 2 of it on a book . how much money does jennifer have left over ?", + "Output Program": [ + "n0 = 180.0\nn1 = 1.0\nn2 = 5.0\nn3 = 1.0\nn4 = 6.0\nn5 = 1.0\nn6 = 2.0\nt0 = n1 / n2\nt1 = n1 / n4\nt2 = n1 / n6\nt3 = n0 * t0\nt4 = n0 * t1\nt5 = n0 * t2\nt6 = t3 + t4\nt7 = t6 + t5\nanswer = n0 - t7\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "the greater of two numbers is twice the less , and the sum of the numbers is 96 . what are the numbers ?", + "Output Program": [ + "n0 = 96.0\nt0 = 1.0 + 2.0\nt1 = n0 / t0\nanswer = t1 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "train" + }, + { + "Input": "5 times a number equals one 100 . the number is", + "Output Program": [ + "n0 = 5.0\nn1 = 100.0\n\nanswer = n1 / n0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "a collection of books went on sale , and 2 / 3 of them were sold for $ 2.00 each . if none of the 36 remaining books were sold , what was the total amount received for the books that were sold ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 2.0\nn3 = 36.0\nt0 = n0 / n1\nt1 = 1.0 / 3.0\nt2 = n3 * t0\nt3 = t2 / t1\nanswer = n0 * t3\nprint(answer)" + ], + "Output Answer": [ + "144" + ], + "split": "train" + }, + { + "Input": "if a ( a - 4 ) = 21 and b ( b - 4 ) = 21 , where a \u2260 b , then a + b =", + "Output Program": [ + "n0 = 4.0\nn1 = 21.0\nn2 = 4.0\nn3 = 21.0\nt0 = n0 + n1\nt1 = n0 - n1\nt2 = t0 + t1\nt3 = t2 - 1.0\nt4 = t3 - 1.0\nt5 = t4 - 1.0\nanswer = t5 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "a survey reveals that the average income of a company \u2019 s customers is $ 45000 per year . if 50 customers respond to the survey and the average income of the wealthiest 10 of those customers is $ 55000 , what is the average income of the other 40 customers ? is there a way to solve this using weighted average concept instead of doing tedious calculations ?", + "Output Program": [ + "n0 = 45000.0\nn1 = 50.0\nn2 = 10.0\nn3 = 55000.0\nn4 = 40.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = t0 - t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "42500" + ], + "split": "train" + }, + { + "Input": "hcf of two numbers is 11 and the product of these numbers is 363 , what is the the greater number ?", + "Output Program": [ + "n0 = 11.0\nn1 = 363.0\n\nanswer = n1 / n0\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "there are 9 players in a chess group , and each player plays each of the others once . given that each game is played by two players , how many total games will be played ?", + "Output Program": [ + "n0 = 9.0\nt0 = n0 - 1.0\nt1 = n0 * t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "in a party every person shakes hands with every other person . if there are 105 hands shakes , find the number of person in the party", + "Output Program": [ + "import math\nn0 = 105.0\nt0 = n0 * 2.0\nt1 = t0 * 4.0\nt2 = t1 + 1.0\nt3 = math.sqrt(max(0, t2))\nt4 = t3 + 1.0\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "the average age of 20 persons in a office is 15 years . out of these , the average age of 5 of them is 14 years and that of the other 9 persons is 16 years . the age of the 15 th person is ?", + "Output Program": [ + "n0 = 20.0\nn1 = 15.0\nn2 = 5.0\nn3 = 14.0\nn4 = 9.0\nn5 = 16.0\nn6 = 15.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n4 * n5\nt3 = t0 - t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "86" + ], + "split": "train" + }, + { + "Input": "if a * b * c = 195 , b * c * d = 65 , c * d * e = 1000 and d * e * f = 250 the ( a * f ) / ( c * d ) = ?", + "Output Program": [ + "n0 = 195.0\nn1 = 65.0\nn2 = 1000.0\nn3 = 250.0\nt0 = n0 * n3\nt1 = n1 * n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.75" + ], + "split": "train" + }, + { + "Input": "the jogging track in a sports complex is 594 m in circumference . deepak and his wife start from the same point and walk in opposite directions at 4.5 km / hr and 3.75 km / hr respectively . they will meet for the first time in ?", + "Output Program": [ + "n0 = 594.0\nn1 = 4.5\nn2 = 3.75\nt0 = n1 + n2\nt1 = n0 / 1000.0\nt2 = t1 / t0\nanswer = t2 * 60.0\nprint(answer)" + ], + "Output Answer": [ + "4.319999999999999" + ], + "split": "train" + }, + { + "Input": "a certain car uses one gallon of gasoline every 34 miles when it travels on highway , and one gallon of gasoline every 20 miles when it travels in the city . when a car travels 4 miles on highway and 4 additional miles in the city , it uses what percent more gasoline than if it travels 8 miles on the highway ?", + "Output Program": [ + "n0 = 34.0\nn1 = 20.0\nn2 = 4.0\nn3 = 4.0\nn4 = 8.0\nt0 = 1.0 / n1\nt1 = 1.0 / n0\nt2 = n2 * t0\nt3 = n2 * t1\nt4 = n4 * t1\nt5 = t2 + t3\nt6 = t5 - t4\nt7 = t6 / t4\nanswer = t7 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "34.99999999999999" + ], + "split": "train" + }, + { + "Input": "find the length of the wire required to go 15 times round a square field containing 69696 m ^ 2 .", + "Output Program": [ + "import math\nn0 = 15.0\nn1 = 69696.0\nn2 = 2.0\nt0 = math.sqrt(n1) # square edge given area\nt1 = 4 * t0\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "15840" + ], + "split": "train" + }, + { + "Input": "the average of 5 quantities is 8 . the average of 3 of them is 4 . what is the average of remaining 2 numbers ?", + "Output Program": [ + "n0 = 5.0\nn1 = 8.0\nn2 = 3.0\nn3 = 4.0\nn4 = 2.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = t0 - t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "in a class of 40 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 14 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?", + "Output Program": [ + "n0 = 40.0\nn1 = 2.0\nn2 = 12.0\nn3 = 1.0\nn4 = 14.0\nn5 = 2.0\nn6 = 3.0\nn7 = 2.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n1 * n4\nt3 = t1 + t2\nt4 = n4 + t1\nt5 = n1 + t4\nt6 = n0 - t5\nt7 = t6 - n3\nt8 = n6 * t7\nt9 = t3 + t8\nanswer = t0 - t9\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "find the average of all the numbers between 40 and 80 which are divisible by 3 .", + "Output Program": [ + "n0 = 40.0\nn1 = 80.0\nn2 = 3.0\nt0 = n0 + 4.0\nt1 = n1 - 4.0\nt2 = t0 + t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "a theater charges $ 12 for seats in the orchestra and $ 8 for seats in the balcony . on a certain night , a total of 355 tickets were sold for a total cost of $ 3,320 . how many more tickets were sold that night for seats in the balcony than for seats in the orchestra ?", + "Output Program": [ + "n0 = 12.0\nn1 = 8.0\nn2 = 355.0\nn3 = 3320.0\nt0 = n0 * n2\nt1 = 1000.0 * 3.0\nt2 = 100.0 * 3.0\nt3 = 10.0 * 2.0\nt4 = n0 - n1\nt5 = t1 + t2\nt6 = t5 + t3\nt7 = t0 - t6\nt8 = t7 / t4\nt9 = n2 - t8\nanswer = t8 - t9\nprint(answer)" + ], + "Output Answer": [ + "115" + ], + "split": "train" + }, + { + "Input": "a certain family has 3 sons : richard is 6 years older than david , and david is 8 years older than scott . if in 8 years , richard will be twice as old as scott , then how old was david 6 years ago ?", + "Output Program": [ + "n0 = 3.0\nn1 = 6.0\nn2 = 8.0\nn3 = 8.0\nn4 = 6.0\nt0 = n1 + n2\nanswer = t0 - n4\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "if the sum of two numbers is 16 and the sum of their squares is 200 , then the product of the numbers is", + "Output Program": [ + "n0 = 16.0\nn1 = 200.0\nt0 = n0**min(2.0, 5)\nt1 = t0 - n1\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "an amount of money is to be divided between p , q and r in the ratio of 3 : 7 : 12 . if the difference between the shares of p and q is rs . 4000 , what will be the difference between q and r ' s share ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 12.0\nn3 = 4000.0\nt0 = n1 - n0\nt1 = n2 - n1\nt2 = n3 / t0\nanswer = t2 * t1\nprint(answer)" + ], + "Output Answer": [ + "5000" + ], + "split": "train" + }, + { + "Input": "a certain pair of used shoes can be repaired for $ 14.50 and will last for 1 year . a pair of the same kind of shoes can be purchased new for $ 32.00 and will last for 2 years . the average cost per year of the new shoes is what percent greater than the cost of repairing the used shoes ?", + "Output Program": [ + "n0 = 14.5\nn1 = 1.0\nn2 = 32.0\nn3 = 2.0\nt0 = n0 * n3\nt1 = n2 - t0\nt2 = t1 / t0\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "10.344827586206897" + ], + "split": "train" + }, + { + "Input": "each child has 8 crayons and 15 apples . if there are 7 children , how many crayons are there in total ?", + "Output Program": [ + "n0 = 8.0\nn1 = 15.0\nn2 = 7.0\n\nanswer = n0 * n2\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "train" + }, + { + "Input": "a student took 6 courses last year and received an average ( arithmetic mean ) grade of 100 points . the year before , the student took 5 courses and received an average grade of 60 points . to the nearest tenth of a point , what was the student \u2019 s average grade for the entire two - year period ?", + "Output Program": [ + "import math\nn0 = 6.0\nn1 = 100.0\nn2 = 5.0\nn3 = 60.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nt4 = t3 / t0\nanswer = math.floor(t4)\nprint(answer)" + ], + "Output Answer": [ + "81" + ], + "split": "train" + }, + { + "Input": "reduce 4128 / 4386 to its lowest terms", + "Output Program": [ + "n0 = 4128.0\nn1 = 4386.0\nt0 = n0 / 2.0\nt1 = n1 / 2.0\nt2 = t0 / 3.0\nt3 = t1 / 3.0\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.9411764705882353" + ], + "split": "train" + }, + { + "Input": "for how many integer values of n will the value of the expression 4 n + 7 be an integer greater than 1 and less than 40 ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 7.0\nn2 = 1.0\nn3 = 40.0\nt0 = n3 - n1\nt1 = n2 - n1\nt2 = t0 / n0\nt3 = t1 / n0\nt4 = math.floor(t2)\nt5 = math.floor(t3)\nanswer = t4 - t5\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the average of 11 results is 42 , if the average of first 5 results is 49 and that of the last 7 is 52 . find the fifth result ?", + "Output Program": [ + "n0 = 11.0\nn1 = 42.0\nn2 = 5.0\nn3 = 49.0\nn4 = 7.0\nn5 = 52.0\nt0 = n2 * n3\nt1 = n4 * n5\nt2 = n0 * n1\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "147" + ], + "split": "train" + }, + { + "Input": "initially two cups of same volume are present with milk filled upto 3 / 5 th and 4 / 5 th of their volumes . water is then filled . then two mixtures are mixed . find the ratio of water to milk in the mixture", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 4.0\nn3 = 5.0\nt0 = n2 / n1\nt1 = n0 / n1\nt2 = t1 + t0\nt3 = 1.0 - t0\nt4 = 1.0 - t1\nt5 = t3 + t4\nanswer = t5 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.4285714285714286" + ], + "split": "train" + }, + { + "Input": "if x < y < z and y - x > 3 , where x is an even integer and y and z are odd integers , what is the least possible value of z - x ?", + "Output Program": [ + "n0 = 3.0\nt0 = n0 + 2.0\nanswer = t0 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "if an amount of rs 42900 is distributed equally amongst 22 persons , how much amount would each person get ?", + "Output Program": [ + "n0 = 42900.0\nn1 = 22.0\nt0 = 10.0 * 4.0\nt1 = t0 + 3.0\nt2 = t1 * 1000.0\nt3 = t2 - 100.0\nanswer = t3 / n1\nprint(answer)" + ], + "Output Answer": [ + "1950" + ], + "split": "train" + }, + { + "Input": "what least number must be subtracted from 9671 so that the remaining number is divisible by 5 ?", + "Output Program": [ + "import math\nn0 = 9671.0\nn1 = 5.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "the sum of ages of 5 children born at the intervals of 3 years each is 70 years . what is the age of the youngest child ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nn2 = 70.0\nt0 = n2 / n0\nt1 = t0 - n1\nanswer = t1 - n1\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "for how many integer values of n will the value of the expression 4 n + 7 be an integer greater than 1 and less than 120 ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 7.0\nn2 = 1.0\nn3 = 120.0\nt0 = n3 - n1\nt1 = n2 - n1\nt2 = t0 / n0\nt3 = t1 / n0\nt4 = math.floor(t2)\nt5 = math.floor(t3)\nanswer = t4 - t5\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "the average of thirteen numbers is 9 . the average of first 6 numbers is 5 and the average of last 6 numbers is 7 . what is the middle number ?", + "Output Program": [ + "n0 = 9.0\nn1 = 6.0\nn2 = 5.0\nn3 = 6.0\nn4 = 7.0\nt0 = n1 + n1\nt1 = n1 * n2\nt2 = n1 * n4\nt3 = t0 + 1.0\nt4 = t1 + t2\nt5 = n0 * t3\nanswer = t5 - t4\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "two heavily loaded sixteen - wheeler transport trucks are 1025 kilometers apart , sitting at two rest stops on opposite sides of the same highway . driver a begins heading down the highway driving at an average speed of 90 kilometers per hour . exactly one hour later , driver b starts down the highway toward driver a , maintaining an average speed of 80 kilometers per hour . how many kilometers farther than driver b , will driver a have driven when they meet and pass each other on the highway ?", + "Output Program": [ + "n0 = 1025.0\nn1 = 90.0\nn2 = 80.0\nt0 = n1 + n2\nt1 = n0 - n1\nt2 = n1 - n2\nt3 = t1 / t0\nt4 = t3 * t2\nanswer = n1 + t4\nprint(answer)" + ], + "Output Answer": [ + "145" + ], + "split": "train" + }, + { + "Input": "two employees m and n are paid a total of $ 605 per week by their employer . if m is paid 120 percent of the salary paid to n , how much is n paid per week ?", + "Output Program": [ + "n0 = 605.0\nn1 = 120.0\nt0 = n1 / 100.0\nt1 = t0 + 1.0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "275" + ], + "split": "train" + }, + { + "Input": "the weight of 4 dogs is determined to be 25 pounds , 31 pounds , 35 pounds and 33 pounds respectively . the weight of a fifth dog is determined to be y pounds . if the average ( arithmetic mean ) weight of the first 4 dogs is the same as that of all 5 dogs what is the value of y ?", + "Output Program": [ + "n0 = 4.0\nn1 = 25.0\nn2 = 31.0\nn3 = 35.0\nn4 = 33.0\nn5 = 4.0\nn6 = 5.0\nt0 = n1 + n2\nt1 = n3 + n4\nt2 = t0 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "31" + ], + "split": "train" + }, + { + "Input": "if 3 x + y = 40 , 2 x - y = 20 , for integers of x and y , 3 y ^ 2 = ?", + "Output Program": [ + "n0 = 3.0\nn1 = 40.0\nn2 = 2.0\nn3 = 20.0\nn4 = 3.0\nn5 = 2.0\nt0 = n1 + n3\nt1 = n0 + n2\nt2 = t0 / t1\nt3 = n0 * t2\nt4 = n1 - t3\nt5 = t4**min(2.0, 5)\nanswer = n0 * t5\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "the average age of a group of persons going for picnic is 16 years . 20 new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years . the number of persons initially going for picnic is ?", + "Output Program": [ + "n0 = 16.0\nn1 = 20.0\nn2 = 15.0\nn3 = 15.5\nt0 = n1 * n3\nt1 = n1 * n2\nt2 = n0 - n3\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "if the operation \u20ac is defined for all x and y by the equation x \u20ac y = 3 * x * y , then 3 \u20ac ( 4 \u20ac 5 ) =", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 4.0\nn3 = 5.0\nt0 = n0 * n1\nt1 = n0 * n2\nt2 = n3 * t1\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "540" + ], + "split": "train" + }, + { + "Input": "if the integer n has exactly 5 positive divisors , including 1 and n , how many positive divisors does \u221a n have ?", + "Output Program": [ + "n0 = 5.0\nn1 = 1.0\nt0 = n1 + n1\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "a straight line in the xy - plane has a slope of 2 and a y - intercept of 2 . on this line , what is the x - coordinate of the point whose y - coordinate is 480 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 480.0\nt0 = n2 - n0\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "239" + ], + "split": "train" + }, + { + "Input": "if the sum of two positive integers is 26 and the difference of their squares is 52 , what is the product of the two integers ?", + "Output Program": [ + "n0 = 26.0\nn1 = 52.0\nt0 = n1 / n0\nt1 = n0 - t0\nt2 = t1 / t0\nt3 = t2 + t0\nanswer = t3 * t2\nprint(answer)" + ], + "Output Answer": [ + "168" + ], + "split": "train" + }, + { + "Input": "fonzie , aunt bee and lapis paid $ 7000 , $ 8000 and $ 9000 respectively to buy a map to capt . plaidstache ' s treasure . when they found it , the treasure turned out to be worth a cool $ 900000 . how much of it should lapis get ?", + "Output Program": [ + "n0 = 7000.0\nn1 = 8000.0\nn2 = 9000.0\nn3 = 900000.0\nt0 = n0 + n1\nt1 = n2 + t0\nt2 = n3 / t1\nanswer = n2 * t2\nprint(answer)" + ], + "Output Answer": [ + "337500" + ], + "split": "train" + }, + { + "Input": "the captain of a cricket team of 11 members is 27 years old and the wicket keeper is 1 year older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ?", + "Output Program": [ + "n0 = 11.0\nn1 = 27.0\nn2 = 1.0\nt0 = n1 + n2\nt1 = 3.0 * 3.0\nt2 = n1 + t0\nt3 = t2 - t1\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "two heavily loaded sixteen - wheeler transport trucks are 787 kilometers apart , sitting at two rest stops on opposite sides of the same highway . driver a begins heading down the highway driving at an average speed of 90 kilometers per hour . exactly one hour later , driver b starts down the highway toward driver a , maintaining an average speed of 80 kilometers per hour . how many kilometers farther than driver b , will driver a have driven when they meet and pass each other on the highway ?", + "Output Program": [ + "n0 = 787.0\nn1 = 90.0\nn2 = 80.0\nt0 = n1 + n2\nt1 = n0 - n1\nt2 = n1 - n2\nt3 = t1 / t0\nt4 = t3 * t2\nanswer = n1 + t4\nprint(answer)" + ], + "Output Answer": [ + "131" + ], + "split": "train" + }, + { + "Input": "in a group of 800 people , 1 / 5 play at least one instrument , 64 play two or more . what is the probability that one student play exactly one instrument ?", + "Output Program": [ + "n0 = 800.0\nn1 = 1.0\nn2 = 5.0\nn3 = 64.0\nt0 = n0 * n1\nt1 = t0 / n2\nt2 = t1 - n3\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.12" + ], + "split": "train" + }, + { + "Input": "in the xy - coordinate system , if ( m , n ) and ( m + 4 , n + k ) are two points on the line with the equation x = 2 y + 5 , then k =", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\nn2 = 5.0\nt0 = n0 + n2\nt1 = t0 - n2\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "during the first week of performances of a certain play , 5400 tickets were sold , all at reduced price . during the remaining weeks of performances , 5 times as many tickets were sold at full price as were sold at reduced price . if the total number of tickets r sold was 25200 , how many of them were sold at full price ?", + "Output Program": [ + "n0 = 5400.0\nn1 = 5.0\nn2 = 25200.0\nt0 = 2.0 + 4.0\nt1 = n2 - n0\nt2 = n1 * t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "16500" + ], + "split": "train" + }, + { + "Input": "two positive integers differ by 4 , and sum of their reciprocals is 1 . then one of the numbers is", + "Output Program": [ + "n0 = 4.0\nn1 = 1.0\n\nanswer = n1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "the price of food in the area where the sims family lives is scheduled to increase by 50 % next year . since the sims family can not afford an increase in their food bill , how much will they have to reduce consumption to keep their cost the same ?", + "Output Program": [ + "n0 = 50.0\nt0 = n0 + 100.0\nt1 = t0 / 100.0\nt2 = 1.0 / t1\nt3 = 1.0 - t2\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "33.333333333333336" + ], + "split": "train" + }, + { + "Input": "a pupil ' s marks were wrongly entered as 73 instead of 63 . due to the average marks for the class got increased by half . the number of pupils in the class is ?", + "Output Program": [ + "n0 = 73.0\nn1 = 63.0\nt0 = n0 - n1\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "a sports equipment store sold ping pong rackets for a total of $ 588 . if the average ( arithmetic mean ) price of a pair of rackets is $ 9.8 , how many pairs were sold ?", + "Output Program": [ + "n0 = 588.0\nn1 = 9.8\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "59.99999999999999" + ], + "split": "train" + }, + { + "Input": "find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number", + "Output Program": [ + "import scipy\nn0 = 17.0\nn1 = 60.0\nt0 = scipy.gcd(int(n0), int(n1))\nanswer = t0 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "we bought a total of 80 books at the store . math books cost $ 4 and history books cost $ 5 . the total price was $ 373 . how many math books did we buy ?", + "Output Program": [ + "n0 = 80.0\nn1 = 4.0\nn2 = 5.0\nn3 = 373.0\nt0 = n0 * n1\nt1 = n3 - t0\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "train" + }, + { + "Input": "if a , b , c , d , e and f are integers and ( ab + cdef ) < 0 , then what is the maximum number s of integers that can be negative ?", + "Output Program": [ + "n0 = 0.0\nt0 = 10.0 / 2.0\nanswer = n0 + t0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "on a test average ( arithmetic mean ) test score for 9 students is 80 . what must be 10 th student ' s score that average score for 10 students to be 82 ?", + "Output Program": [ + "n0 = 9.0\nn1 = 80.0\nn2 = 10.0\nn3 = 10.0\nn4 = 82.0\nt0 = n2 * n4\nt1 = n0 * n1\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "how many multiples of 7 are there between 21 and 343 , inclusive ?", + "Output Program": [ + "n0 = 7.0\nn1 = 21.0\nn2 = 343.0\nt0 = n2 - n1\nt1 = t0 / n0\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "47" + ], + "split": "train" + }, + { + "Input": "a charitable association sold an average of 66 raffle tickets per member . among the female members , the average was 70 raffle tickets . the male to female ratio of the association is 1 : 2 . what was the average number e of tickets sold by the male members of the association", + "Output Program": [ + "n0 = 66.0\nn1 = 70.0\nn2 = 1.0\nn3 = 2.0\nt0 = n2 + n3\nt1 = n1 * n3\nt2 = n0 * t0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "58" + ], + "split": "train" + }, + { + "Input": "107 \u00e3 \u2014 107 + 93 \u00e3 \u2014 93 = ?", + "Output Program": [ + "n0 = 107.0\nn1 = 107.0\nn2 = 93.0\nn3 = 93.0\nt0 = n0**min(2.0, 5)\nt1 = n2**min(2.0, 5)\nt2 = t0 - n0\nt3 = t1 - n2\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "19898" + ], + "split": "train" + }, + { + "Input": "at a certain college , 50 percent of the total number of students are freshmen . if 40 percent of the fresh - men are enrolled in the school of liberal arts and , of these , 20 percent are psychology majors , what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts ?", + "Output Program": [ + "n0 = 50.0\nn1 = 40.0\nn2 = 20.0\nt0 = n0 * n1\nt1 = t0 / 100.0\nt2 = n2 * t1\nanswer = t2 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "60 percent of movie theatres in town x have 3 screens or less . 20 % of those theatres sell an average of more than $ 300 worth of popcorn per showing . 50 percent of all the movie theatres in town x sell $ 300 or less of popcorn per showing . what percent of all the stores on the street have 4 or more screens and sell an average of more than $ 100 worth of popcorn per day ?", + "Output Program": [ + "n0 = 60.0\nn1 = 3.0\nn2 = 20.0\nn3 = 300.0\nn4 = 50.0\nn5 = 300.0\nn6 = 4.0\nn7 = 100.0\nt0 = n2 / 100.0\nt1 = n3 * t0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "two trains start at same time from two stations and proceed towards each other at the rate of 20 km / hr and 25 km / hr respectively . when they meet , it is found that one train has traveled 65 km more than the other . what is the distance between the two stations ?", + "Output Program": [ + "n0 = 20.0\nn1 = 25.0\nn2 = 65.0\nt0 = n0 + n1\nt1 = n1 - n0\nt2 = n2 / t1\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "585" + ], + "split": "train" + }, + { + "Input": "if 7 boys meet at a reunion and each boy shakes hands exactly once with each of the others , then what is the total number of handshakes", + "Output Program": [ + "import math\nn0 = 7.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(2.0)))\nt2 = n0 - 2.0\nt3 = math.factorial(min(15, int(t2)))\nt4 = t3 * t1\nanswer = t0 / t4\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "a certain car uses one gallon of gasoline every 40 miles when it travels on highway , and one gallon of gasoline every 20 miles when it travels in the city . when a car travels 4 miles on highway and 4 additional miles in the city , it uses what percent more gasoline than if it travels 8 miles on the highway ?", + "Output Program": [ + "n0 = 40.0\nn1 = 20.0\nn2 = 4.0\nn3 = 4.0\nn4 = 8.0\nt0 = 1.0 / n1\nt1 = 1.0 / n0\nt2 = n2 * t0\nt3 = n2 * t1\nt4 = n4 * t1\nt5 = t2 + t3\nt6 = t5 - t4\nt7 = t6 / t4\nanswer = t7 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "50.000000000000014" + ], + "split": "train" + }, + { + "Input": "find \u221a ? / 18 = 4 ?", + "Output Program": [ + "n0 = 18.0\nn1 = 4.0\nt0 = n0 * n1\nanswer = t0**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "5184" + ], + "split": "train" + }, + { + "Input": "the population of a city increases by 6 % per year but due to migration it decrease by 1 % per years . what will be the percentage increase in population in 3 years ?", + "Output Program": [ + "n0 = 6.0\nn1 = 1.0\nn2 = 3.0\nt0 = n0 - n1\nt1 = t0 + 100.0\nt2 = t1 * t0\nt3 = t2 / 100.0\nt4 = t3 + t0\nt5 = t4 + 100.0\nt6 = t5 * t0\nt7 = t6 / 100.0\nanswer = t4 + t7\nprint(answer)" + ], + "Output Answer": [ + "15.7625" + ], + "split": "train" + }, + { + "Input": "when leo imported a certain item , he paid a 7 percent import tax on the portion of the total value of the item in excess of $ 1000 . if the amount of the import tax that leo paid was $ 87.50 , what was the total value of the item ?", + "Output Program": [ + "n0 = 7.0\nn1 = 1000.0\nn2 = 87.5\nt0 = n0 / 100.0\nt1 = n2 / t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "2250" + ], + "split": "train" + }, + { + "Input": "i chose a number and divide it by 6 . then i subtracted 189 from the result and got 3 . what was the number i chose ?", + "Output Program": [ + "n0 = 6.0\nn1 = 189.0\nn2 = 3.0\nt0 = n1 + n2\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "1152" + ], + "split": "train" + }, + { + "Input": "in a group of ducks and cows , the total number of legs are 30 more than twice the number of heads . find the total number of cows .", + "Output Program": [ + "n0 = 30.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "two trains of equal length are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train passes the slower train in 36 seconds . the length of each train is ?", + "Output Program": [ + "n0 = 46.0\nn1 = 36.0\nn2 = 36.0\nt0 = n0 - n1\nt1 = t0 * 1000.0\nt2 = t1 / 3600.0\nt3 = n2 * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "if a ' s height is 25 % less than that of b , how much percent b ' s height is more than that of a ?", + "Output Program": [ + "n0 = 25.0\nt0 = 100.0 - n0\nt1 = n0 / t0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "33.33333333333333" + ], + "split": "train" + }, + { + "Input": "the tax on a commodity is diminished by 24 % but its consumption is increased by 12 % . find the decrease percent in the revenue derived from it ?", + "Output Program": [ + "n0 = 24.0\nn1 = 12.0\nt0 = n1 + 100.0\nt1 = 100.0 - n0\nt2 = t0 * t1\nt3 = t2 / 100.0\nanswer = 100.0 - t3\nprint(answer)" + ], + "Output Answer": [ + "14.879999999999995" + ], + "split": "train" + }, + { + "Input": "there is a total of 90 marbles in a box , each of which is red , green , blue , or white . if one marble is drawn from the box at random , the probability that it will be white is 1 / 6 and the probability that it will be green is 1 / 5 . what is the probability that the marble will be either red or blue ?", + "Output Program": [ + "n0 = 90.0\nn1 = 1.0\nn2 = 6.0\nn3 = 1.0\nn4 = 5.0\nt0 = n1 / n2\nt1 = n3 / n4\nt2 = t0 + t1\nanswer = n1 - t2\nprint(answer)" + ], + "Output Answer": [ + "0.6333333333333333" + ], + "split": "train" + }, + { + "Input": "what is the average of first 21 multiples of 7 ?", + "Output Program": [ + "n0 = 21.0\nn1 = 7.0\nt0 = n0 + 1.0\nt1 = n0 * t0\nt2 = t1 / 2.0\nt3 = t2 / n0\nanswer = n1 * t3\nprint(answer)" + ], + "Output Answer": [ + "77" + ], + "split": "train" + }, + { + "Input": "if a person walks at 14 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance traveled by him is :", + "Output Program": [ + "n0 = 14.0\nn1 = 10.0\nn2 = 20.0\nt0 = n0 - n1\nt1 = n2 / t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "300 first - time customers of a fashion store were surveyed for their shopping experience right after leaving the store . 60 % of the customers in the survey had purchased clothes for less than $ 100 . 40 % of the customers in the survey reported they were overall satisfied with their purchase . 15 % of the customers that had purchased clothes for less than $ 100 reported they were overall satisfied with their purchase . what percent of the customers surveyed purchased clothes for at least $ 100 and reported that they were not overall satisfied with their purchase ?", + "Output Program": [ + "n0 = 300.0\nn1 = 60.0\nn2 = 100.0\nn3 = 40.0\nn4 = 15.0\nn5 = 100.0\nn6 = 100.0\nt0 = n3 / n2\nt1 = n4 / n2\nt2 = n1 / n2\nt3 = n0 * t0\nt4 = n0 * t2\nt5 = t1 * t4\nt6 = t3 - t5\nt7 = t6 / n0\nanswer = t7 * n2\nprint(answer)" + ], + "Output Answer": [ + "31" + ], + "split": "train" + }, + { + "Input": "the average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 62 kg . what is the correct weight ?", + "Output Program": [ + "n0 = 20.0\nn1 = 58.4\nn2 = 56.0\nn3 = 62.0\nt0 = n0 * n1\nt1 = n3 - n2\nt2 = t0 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "58.7" + ], + "split": "train" + }, + { + "Input": "the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 60 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.5\nn2 = 60.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "if a certain number when divided by the numbers 5 , 32 one after other successively , leaves a remainder 0 , 21 then what will be the remainders if it is divided by the numbers 2 , 35", + "Output Program": [ + "n0 = 5.0\nn1 = 32.0\nn2 = 0.0\nn3 = 21.0\nn4 = 2.0\nn5 = 35.0\nt0 = n0 * n3\nanswer = t0 % n4\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "the difference between the value of a number increased by 12.5 % and the value of the original number decreased by 25 % is 30 . what is the original number q ?", + "Output Program": [ + "n0 = 12.5\nn1 = 25.0\nn2 = 30.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = t0 + 1.0\nt3 = 1.0 - t1\nt4 = t2 - t3\nanswer = n2 / t4\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "a man is 30 years older than his son . in two years , his age will be twice the age of his son . what is the present age of his son ?", + "Output Program": [ + "n0 = 30.0\nt0 = 2.0 * 2.0\nt1 = 2.0 - 1.0\nt2 = t0 - 2.0\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "machine x takes 60 hours longer than machine y to produce 1080 widgets . machine y produces 20 percent more widgets in an hour than machine x does in an hour . how many widgets per hour does machine x produce", + "Output Program": [ + "n0 = 60.0\nn1 = 1080.0\nn2 = 20.0\nt0 = n0 / 10.0\nt1 = n0 * t0\nanswer = n1 / t1\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 20 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam .", + "Output Program": [ + "n0 = 80.0\nn1 = 5.0\nn2 = 20.0\nn3 = 90.0\nt0 = n1 * n3\nt1 = n1 * n2\nt2 = n3 - n0\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "how many 1 / 4 s are there in 37 1 / 2 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 37.0\nn3 = 1.0\nn4 = 2.0\nt0 = n0 / n4\nt1 = n0 / n1\nt2 = n2 + t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "train" + }, + { + "Input": "a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 12 , the how old is b ?", + "Output Program": [ + "n0 = 12.0\nt0 = 1.0 + 4.0\nt1 = n0 - 2.0\nt2 = t1 * 2.0\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "how many digits are required to number a book containing 300 pages ?", + "Output Program": [ + "n0 = 300.0\nt0 = 10.0 - 1.0\nt1 = n0 - 100.0\nt2 = t1 + 1.0\nt3 = t0 * 10.0\nt4 = t3 * 2.0\nt5 = t2 * 3.0\nt6 = t4 + t0\nanswer = t6 + t5\nprint(answer)" + ], + "Output Answer": [ + "792" + ], + "split": "train" + }, + { + "Input": "if rs . 782 be divided into 3 parts , proportional to 1 / 2 : 2 / 3 : 3 / 4 , then the third part is ?", + "Output Program": [ + "n0 = 782.0\nn1 = 3.0\nn2 = 1.0\nn3 = 2.0\nn4 = 2.0\nn5 = 3.0\nn6 = 3.0\nn7 = 4.0\nt0 = n3 + 100.0\nt1 = 2.0 * 3.0\nt2 = n1 + t1\nt3 = n3 + t1\nt4 = t2 + t3\nt5 = t4 + t1\nt6 = t1 / t5\nt7 = n0 * t6\nanswer = t0 + t7\nprint(answer)" + ], + "Output Answer": [ + "306" + ], + "split": "train" + }, + { + "Input": "if t = 5 / 9 * ( k - 32 ) , and if t = 75 , then what is the value of k ?", + "Output Program": [ + "n0 = 5.0\nn1 = 9.0\nn2 = 32.0\nn3 = 75.0\nt0 = n1 * n3\nt1 = t0 / n0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "167" + ], + "split": "train" + }, + { + "Input": "( 0.0077 ) ( 4.5 ) / ( 0.05 ) ( 0.1 ) ( 0.007 ) =", + "Output Program": [ + "n0 = 0.0077\nn1 = 4.5\nn2 = 0.05\nn3 = 0.1\nn4 = 0.007\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n4 * t1\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "989.9999999999997" + ], + "split": "train" + }, + { + "Input": "of 70 players on a football team , 40 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?", + "Output Program": [ + "n0 = 70.0\nn1 = 40.0\nt0 = 1.0 / 3.0\nt1 = n0 - n1\nt2 = 1.0 - t0\nt3 = t2 * t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "average monthly income of a family of 4 earning members was rs . 735 . one of the earning members died and therefore , the average income came down to rs 650 . the income of the deceased was ?", + "Output Program": [ + "n0 = 4.0\nn1 = 735.0\nn2 = 650.0\nt0 = n0 * n1\nt1 = n0 - 1.0\nt2 = n2 * t1\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "990" + ], + "split": "train" + }, + { + "Input": "a car travels a certain distance taking 7 hrs in forward journey , during the return journey increased speed 12 km / hr takes the times 5 hrs . what is the distance traveled", + "Output Program": [ + "n0 = 7.0\nn1 = 12.0\nn2 = 5.0\nt0 = n1 * n2\nt1 = n0 - n2\nt2 = t0 / t1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "210" + ], + "split": "train" + }, + { + "Input": "the sum of first n consecutive odd integers is n ^ 2 . what is the sum of all odd integers between 11 and 41 inclusive .", + "Output Program": [ + "n0 = 2.0\nn1 = 11.0\nn2 = 41.0\nt0 = n2 + 1.0\nt1 = n1 - n0\nt2 = t1 + 1.0\nt3 = t0 / n0\nt4 = t2 / n0\nt5 = t3**min(n0, 5)\nt6 = t4**min(n0, 5)\nanswer = t5 - t6\nprint(answer)" + ], + "Output Answer": [ + "416" + ], + "split": "train" + }, + { + "Input": "if x is an integer and 6.1 \u00d7 10 ^ x is less than 620 what is the greatest possible value for x ?", + "Output Program": [ + "import math\nn0 = 6.1\nn1 = 10.0\nn2 = 620.0\nt0 = n2 / n0\nt1 = math.log(max(1e-5, n1), 2)\nt2 = math.log(max(1e-5, t0), 2)\nt3 = t2 / t1\nanswer = math.floor(t3)\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "in the game of dubblefud , red balls , blue balls and green balls are each worth 2 , 4 and 5 points respectively . in a certain selection of balls , the product of the point values of the balls is 16000 . if the number of blue balls in this selection equals the number of green balls , how many red balls are in the selection ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 5.0\nn3 = 16000.0\nt0 = n0 / n0\nt1 = n0 * t0\nt2 = t0 + t1\nanswer = t2 + t0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "a man can row 4.5 km / hr in still water . it takes him twice as long to row upstream as to row downstream . what is the rate of the current ?", + "Output Program": [ + "n0 = 4.5\nt0 = n0 * 2.0\nt1 = t0 - n0\nanswer = t1 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "1.5" + ], + "split": "train" + }, + { + "Input": "what is the smallest no . which must be added to 8261955 so as to obtain a sum which is divisible by 11 ?", + "Output Program": [ + "n0 = 8261955.0\nn1 = 11.0\nt0 = n0 * n1\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "a \u2019 s speed is 20 / 14 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?", + "Output Program": [ + "n0 = 20.0\nn1 = 14.0\nt0 = n0 - n1\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.3" + ], + "split": "train" + }, + { + "Input": "two employees m and n are paid a total of $ 594 per week by their employer . if m is paid 120 percent of the salary paid to n , how much is n paid per week ?", + "Output Program": [ + "n0 = 594.0\nn1 = 120.0\nt0 = n1 / 100.0\nt1 = t0 + 1.0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "270" + ], + "split": "train" + }, + { + "Input": "if the price of a book is first decreased by 20 % and then increased by 20 % , then the net change in the price will be :", + "Output Program": [ + "n0 = 20.0\nn1 = 20.0\nt0 = n0 * 100.0\nt1 = n1 * 100.0\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = t3 + 100.0\nt5 = 100.0 - t2\nt6 = t5 / 100.0\nt7 = t4 / 100.0\nt8 = t6 * t7\nt9 = t8 * 100.0\nanswer = 100.0 - t9\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "praveen age after 10 years will be 3 times his age 3 years back . what is the present age of chris ?", + "Output Program": [ + "n0 = 10.0\nn1 = 3.0\nn2 = 3.0\nt0 = n0 * n1\nt1 = n1 - 1.0\nt2 = n0 + t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "how many multiples of 2 are there between 10 and 52 , 10 and 52 inclusive ?", + "Output Program": [ + "n0 = 2.0\nn1 = 10.0\nn2 = 52.0\nn3 = 10.0\nn4 = 52.0\nt0 = n2 - n1\nt1 = t0 / n0\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "what is the next number 12 13 15 17 111 113 117 119 123 129 ?", + "Output Program": [ + "n0 = 12.0\nn1 = 13.0\nn2 = 15.0\nn3 = 17.0\nn4 = 111.0\nn5 = 113.0\nn6 = 117.0\nn7 = 119.0\nn8 = 123.0\nn9 = 129.0\nt0 = n9 % 100.0\nt1 = t0 + 2.0\nanswer = t1 + 100.0\nprint(answer)" + ], + "Output Answer": [ + "131" + ], + "split": "train" + }, + { + "Input": "david works at a resort from the beginning of march to the end of september . during the month of august this past year , he made 2 times the average ( arithmetic mean ) of his monthly totals in tips for the other months . his total tips for august were what fraction of his total tips for all of the months he worked ?", + "Output Program": [ + "n0 = 2.0\nt0 = 10.0 - 4.0\nt1 = n0 + t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.25" + ], + "split": "train" + }, + { + "Input": "when processing flower - nectar into honey bees ' extract , a considerable amount of water gets reduced . how much flower - nectar must be processed to yield 1 kg of honey , if nectar contains 50 % water , and the honey obtained from this nectar contains 35 % water ?", + "Output Program": [ + "n0 = 1.0\nn1 = 50.0\nn2 = 35.0\nt0 = n1 / 100.0\nt1 = 100.0 - n2\nt2 = t1 / 100.0\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "1.3" + ], + "split": "train" + }, + { + "Input": "cindy has her eye on a sundress but thinks it is too expensive . it goes on sale for 15 % less than the original price . before cindy can buy the dress , however , the store raises the new price by 25 % . if the dress cost $ 61.2 after it went on sale for 15 % off , what is the difference between the original price and the final price ?", + "Output Program": [ + "n0 = 15.0\nn1 = 25.0\nn2 = 61.2\nn3 = 15.0\nt0 = n1 + 100.0\nt1 = 100.0 - n0\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = n2 / t3\nt5 = n2 * t2\nanswer = t5 - t4\nprint(answer)" + ], + "Output Answer": [ + "4.5" + ], + "split": "train" + }, + { + "Input": "the smallest number which when diminished by 12 , is divisible 12 , 24 , 36 , 48 and 56 is :", + "Output Program": [ + "n0 = 12.0\nn1 = 12.0\nn2 = 24.0\nn3 = 36.0\nn4 = 48.0\nn5 = 56.0\nt0 = 3.0 + 4.0\nt1 = 3.0**min(2.0, 5)\nt2 = 2.0**min(4.0, 5)\nt3 = t1 * t2\nt4 = t0 * t3\nanswer = t4 + n0\nprint(answer)" + ], + "Output Answer": [ + "1020" + ], + "split": "train" + }, + { + "Input": "there are 100 students in 3 sections a , b and c of a class . the average marks of all the 3 sections was 84 . the average of b and c was 87.5 and the average marks of students in a section was ?", + "Output Program": [ + "n0 = 100.0\nn1 = 3.0\nn2 = 3.0\nn3 = 84.0\nn4 = 87.5\nt0 = 3.0 + 4.0\nt1 = n0 * n4\nt2 = n0 * n3\nt3 = t0 * 10.0\nt4 = t1 - t2\nt5 = n4 - t3\nanswer = t4 / t5\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "8 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ?", + "Output Program": [ + "n0 = 8.0\nt0 = n0 - 1.0\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "train" + }, + { + "Input": "if x + y = 250 , x - y = 200 , for integers of x and y , y = ?", + "Output Program": [ + "n0 = 250.0\nn1 = 200.0\nt0 = n0 + n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "225" + ], + "split": "train" + }, + { + "Input": "what is the least number which when divided by 5 , 9 , 12 and 18 leaves remainder 4 in each care ?", + "Output Program": [ + "import scipy\nn0 = 5.0\nn1 = 9.0\nn2 = 12.0\nn3 = 18.0\nn4 = 4.0\nt0 = scipy.lcm(int(n0), int(n1))\nt1 = scipy.lcm(int(n2), int(n3))\nt2 = scipy.lcm(int(t0), int(t1))\nanswer = n4 + t2\nprint(answer)" + ], + "Output Answer": [ + "184" + ], + "split": "train" + }, + { + "Input": "abhinav and bhupathi together have rs . 1210 . if 4 / 15 of abhinav ' s amount is equal to 2 / 5 of bhupathi ' s amount , how much amount does bhupathi have ?", + "Output Program": [ + "n0 = 1210.0\nn1 = 4.0\nn2 = 15.0\nn3 = 2.0\nn4 = 5.0\nt0 = n0 / n4\nanswer = t0 + t0\nprint(answer)" + ], + "Output Answer": [ + "484" + ], + "split": "train" + }, + { + "Input": "the value of a scooter depreciates in such a way that its value of the end of each year is 3 / 4 of its value of the beginning of the same year . if the initial value of the scooter is rs . 40,000 , what is the value at the end of 2 years ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 40000.0\nn3 = 2.0\nt0 = n0 / n1\nt1 = 100.0 * 100.0\nt2 = n1 * t1\nt3 = t0**min(n3, 5)\nanswer = t2 * t3\nprint(answer)" + ], + "Output Answer": [ + "22500" + ], + "split": "train" + }, + { + "Input": "a committee is reviewing a total of 20 x black - and - white films and 6 y color films for a festival . if the committee selects y / x % of the black - and - white films and all of the color films , what fraction e of the selected films are in color ?", + "Output Program": [ + "n0 = 20.0\nn1 = 6.0\nt0 = n0 / 100.0\nt1 = n1 + t0\nanswer = n1 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.9677419354838709" + ], + "split": "train" + }, + { + "Input": "a batsman makes a score of 200 runs in the 17 th inning and thus increases his averages by 10 what is his average after 17 th inning ?", + "Output Program": [ + "n0 = 200.0\nn1 = 17.0\nn2 = 10.0\nn3 = 17.0\nt0 = n1 * n2\nt1 = n0 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "in goshawk - eurasian nature reserve 30 percent of the birds are hawks , and 40 percent of the non - hawks are paddyfield - warblers . if there are 25 percent as many kingfishers as paddyfield - warblers in the reserve , then what percent of the birds r in the nature reserve are not hawks , paddyfield - warblers , or kingfishers ?", + "Output Program": [ + "n0 = 30.0\nn1 = 40.0\nn2 = 25.0\nt0 = n2 + n2\nt1 = t0 / 2.0\nanswer = t1 + 10.0\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 32000 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 8.0\nn2 = 32000.0\nt0 = n0 / n1\nt1 = n2 * t0\nt2 = n2 + t1\nt3 = t2 * t0\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "40500" + ], + "split": "train" + }, + { + "Input": "a number is doubled and 7 is added . if resultant is trebled , it becomes 99 . what is that number", + "Output Program": [ + "n0 = 7.0\nn1 = 99.0\nt0 = n0 * 3.0\nt1 = 2.0 * 3.0\nt2 = n1 - t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "find the value of a / b + b / a , if a and b are the roots of the quadratic equation x 2 + 8 x + 4 = 0 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 8.0\nn2 = 4.0\nn3 = 0.0\nt0 = -n1\nt1 = t0**min(n0, 5)\nt2 = t1 / n2\nanswer = t2 - n0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "darren bought 5 packs of white t - shirts and 3 packs of blue t - shirts for his basketball team . the white t - shirts come in packs of 6 , and the blue t - shirts come in packs of 9 . how many t - shirts did darren buy in all ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nn2 = 6.0\nn3 = 9.0\nt0 = n0 * n2\nt1 = n1 * n3\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "57" + ], + "split": "train" + }, + { + "Input": "a student chose a number , multiplied it by 7 , then subtracted 150 from the result and got 130 . what was the number he chose ?", + "Output Program": [ + "n0 = 7.0\nn1 = 150.0\nn2 = 130.0\nt0 = n1 + n2\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "evaluate : ( 1 - 1 / 10 ) ( 1 - 1 / 11 ) ( 1 - 1 / 12 ) . . . ( 1 - 1 / 99 ) ( 1 - 1 / 100 )", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 10.0\nn3 = 1.0\nn4 = 1.0\nn5 = 11.0\nn6 = 1.0\nn7 = 1.0\nn8 = 12.0\nn9 = 1.0\nn10 = 1.0\nn11 = 99.0\nn12 = 1.0\nn13 = 1.0\nn14 = 100.0\nt0 = n2 - n0\nanswer = t0 / n14\nprint(answer)" + ], + "Output Answer": [ + "0.09" + ], + "split": "train" + }, + { + "Input": "when a person aged 39 is added to a group of n people , the average age increases by 2 . when a person aged 15 is added instead , the average age decreases by 1 . what is the value of w ?", + "Output Program": [ + "n0 = 39.0\nn1 = 2.0\nn2 = 15.0\nn3 = 1.0\nt0 = n1 + n3\nt1 = n0 - n2\nt2 = t1 / t0\nanswer = t2 - n3\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "if the number is divided by 3 , it reduced by 30 . the number is", + "Output Program": [ + "n0 = 3.0\nn1 = 30.0\nt0 = n0 * n1\nt1 = n0 - 1.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "( 0.0077 ) ( 3.6 ) / ( 0.04 ) ( 0.1 ) ( 0.007 ) =", + "Output Program": [ + "n0 = 0.0077\nn1 = 3.6\nn2 = 0.04\nn3 = 0.1\nn4 = 0.007\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n4 * t1\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "990.0000000000001" + ], + "split": "train" + }, + { + "Input": "out of 4 numbers , the average of first 3 is 20 and that of the last 3 is 15 . if the last number is 18 , the first number is :", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 20.0\nn3 = 3.0\nn4 = 15.0\nn5 = 18.0\nt0 = n1 * n2\nt1 = n1 * n4\nt2 = t1 - n5\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "a driver would have reduced the time it took to drive from home to the store by 1 / 4 if the average speed had been increased by 10 miles per hour . what was the actual average speed , in miles per hour , when the driver drove from home to the store ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 10.0\nt0 = n0 / n1\nt1 = n0 - t0\nt2 = t1 * 10.0\nt3 = n0 - t1\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "at a supermarket , john spent 1 / 2 of his money on fresh fruits and vegetables , 1 / 3 on meat products , and 1 / 10 on bakery products . if he spent the remaining $ 10 on candy , how much did john spend at the supermarket ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 1.0\nn3 = 3.0\nn4 = 1.0\nn5 = 10.0\nn6 = 10.0\nt0 = n0 / n5\nt1 = n0 / n3\nt2 = n0 / n1\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n0 - t4\nanswer = n6 / t5\nprint(answer)" + ], + "Output Answer": [ + "150.00000000000003" + ], + "split": "train" + }, + { + "Input": "if the sum and difference of two numbers are 5 and 10 respectively , then the difference of their square is :", + "Output Program": [ + "n0 = 5.0\nn1 = 10.0\nt0 = n0 + n1\nt1 = t0 / 2.0\nt2 = t1**min(2.0, 5)\nt3 = n0 - t1\nt4 = t3**min(2.0, 5)\nanswer = t2 - t4\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "find the least number which when divided by 56 , 78 leaves a remainder 3 but when divided by 9 leaves no remainder", + "Output Program": [ + "n0 = 56.0\nn1 = 78.0\nn2 = 3.0\nn3 = 9.0\nt0 = 4.0 + 4.0\nt1 = n2 + 4.0\nt2 = 2.0 + 3.0\nt3 = n2 + n2\nt4 = t2 * t3\nt5 = t1 * t4\nanswer = t0 * t5\nprint(answer)" + ], + "Output Answer": [ + "1680" + ], + "split": "train" + }, + { + "Input": "what is the average of first 21 multiples of 8 ?", + "Output Program": [ + "n0 = 21.0\nn1 = 8.0\nt0 = n0 + 1.0\nt1 = n0 * t0\nt2 = t1 / 2.0\nt3 = t2 / n0\nanswer = n1 * t3\nprint(answer)" + ], + "Output Answer": [ + "88" + ], + "split": "train" + }, + { + "Input": "for any number y , y * is defined as the greatest positive even integer less than or equal to y . what is the value of 9.2 \u2013 9.2 * ?", + "Output Program": [ + "import math\nn0 = 9.2\nn1 = 9.2\nt0 = math.floor(n0)\nt1 = t0 - 1.0\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "1.1999999999999993" + ], + "split": "train" + }, + { + "Input": "$ 400 is divided amongst a , b and c so that a may get 2 / 3 as much as b and c together , b may get 6 / 9 as much as a and c together , then the share of a is", + "Output Program": [ + "n0 = 400.0\nn1 = 2.0\nn2 = 3.0\nn3 = 6.0\nn4 = 9.0\nt0 = n1 / n2\nt1 = t0 + 1.0\nt2 = n0 / t1\nanswer = t2 * t0\nprint(answer)" + ], + "Output Answer": [ + "160" + ], + "split": "train" + }, + { + "Input": "2 . the value of x + x ( xx ) when x = 2 is :", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nt0 = n0 * n0\nt1 = n0 * t0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "if the operation x is defined by a x b = ( b - a ) ^ 2 / a ^ 2 for all numbers a and b , and a \u2260 0 , then \u2212 1 x ( 1 x \u2212 1 ) =", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 0.0\nn3 = 1.0\nn4 = 1.0\nn5 = 1.0\nt0 = -n3\nt1 = t0 - n3\nt2 = t1**min(n0, 5)\nt3 = t2 - t0\nanswer = t3**min(n0, 5)\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "subtracting 4 % of a from a is equivalent to multiplying a by how much ?", + "Output Program": [ + "n0 = 4.0\nt0 = 100.0 - n0\nanswer = t0 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "0.96" + ], + "split": "train" + }, + { + "Input": "a number when divided by 296 leaves 75 as remainder when the same number is divided by 37 then the remainder will be ?", + "Output Program": [ + "n0 = 296.0\nn1 = 75.0\nn2 = 37.0\nt0 = n0 + n1\nanswer = t0 % n2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "860 % of 50 + 50 % of 860 = ?", + "Output Program": [ + "n0 = 860.0\nn1 = 50.0\nn2 = 50.0\nn3 = 860.0\nt0 = n0 * n1\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "860" + ], + "split": "train" + }, + { + "Input": "marcella has 20 pairs of shoes . if she loses 9 individual shoes , what is the greatest number of matching pairs she could have left ?", + "Output Program": [ + "import math\nn0 = 20.0\nn1 = 9.0\nt0 = n1 / 2.0\nt1 = math.floor(t0)\nt2 = t1 + 1.0\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "if 3 < x < 6 < y < 7 , then what is the greatest possible positive integer difference of x and y ?", + "Output Program": [ + "n0 = 3.0\nn1 = 6.0\nn2 = 7.0\nt0 = n2 - n0\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "the average age of 4 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men . the average age of the two new men is", + "Output Program": [ + "n0 = 4.0\nn1 = 21.0\nn2 = 23.0\nt0 = n1 + n2\nt1 = n0 * 1.0\nt2 = t0 / 2.0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "the largest natural number by which the product of 3 consecutive even natural numbers is always divisible , is", + "Output Program": [ + "n0 = 3.0\nt0 = n0 - 1.0\nt1 = t0 * t0\nt2 = t1 + t0\nt3 = t1 * t0\nanswer = t2 * t3\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "the captain of a cricket team of 11 members is 28 years old and the wicket keeper is 3 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ?", + "Output Program": [ + "n0 = 11.0\nn1 = 28.0\nn2 = 3.0\nt0 = n1 + n2\nt1 = n2 * n2\nt2 = n1 + t0\nt3 = t2 - t1\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "a library has an average of 510 visitors on sundays and 240 on other day . the average number of visitors in a month of 30 days starting with sunday is", + "Output Program": [ + "import math\nn0 = 510.0\nn1 = 240.0\nn2 = 30.0\nt0 = 3.0 + 4.0\nt1 = n2 / t0\nt2 = math.floor(t1)\nt3 = t2 + 1.0\nt4 = n0 * t3\nt5 = n2 - t3\nt6 = n1 * t5\nt7 = t4 + t6\nanswer = t7 / n2\nprint(answer)" + ], + "Output Answer": [ + "285" + ], + "split": "train" + }, + { + "Input": "there are 2 sections a and b in a class , consisting of 40 and 30 students respectively . if the average weight of section a is 50 kg and that of section b is 60 kg , find the average of the whole class ?", + "Output Program": [ + "n0 = 2.0\nn1 = 40.0\nn2 = 30.0\nn3 = 50.0\nn4 = 60.0\nt0 = n1 + n2\nt1 = n1 * n3\nt2 = n2 * n4\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "54.285714285714285" + ], + "split": "train" + }, + { + "Input": "the average ( arithmetic mean ) of the even integers from 16 to 44 inclusive is how much greater than the average ( arithmetic mean ) of the even integers from 14 to 56 inclusive ?", + "Output Program": [ + "n0 = 16.0\nn1 = 44.0\nn2 = 14.0\nn3 = 56.0\nt0 = n2 + n3\nt1 = n0 + n1\nt2 = t0 / 2.0\nt3 = t1 / 2.0\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "two employees a and b are paid a total of rs . 570 per week by their employer . if a is paid 150 percent of the sum paid to b , how much is b paid per week ?", + "Output Program": [ + "n0 = 570.0\nn1 = 150.0\nt0 = n1 / 100.0\nt1 = t0 + 1.0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "228" + ], + "split": "train" + }, + { + "Input": "a sporting goods store sold 60 frisbees in one week , some for $ 3 and the rest for $ 4 each . if receipts from frisbee sales for the week totaled $ 200 , what is the fewest number of $ 4 frisbees that could have been sold ?", + "Output Program": [ + "n0 = 60.0\nn1 = 3.0\nn2 = 4.0\nn3 = 200.0\nn4 = 4.0\nt0 = n0 * n1\nanswer = n3 - t0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "there are 16 bees in the hive , then 7 more fly . how many bees are there in all ?", + "Output Program": [ + "n0 = 16.0\nn1 = 7.0\n\nanswer = n0 + n1\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "laura took out a charge account at the general store and agreed to pay 6 % simple annual interest . if she charges $ 35 on her account in january , how much will she owe a year later , assuming she does not make any additional charges or payments ?", + "Output Program": [ + "n0 = 6.0\nn1 = 35.0\nt0 = n0 / 100.0\nt1 = n1 * t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "37.1" + ], + "split": "train" + }, + { + "Input": "if the price of a tv is first decreased by 20 % and then increased by 40 % , then the net change in the price will be :", + "Output Program": [ + "n0 = 20.0\nn1 = 40.0\nt0 = n1 + 100.0\nt1 = 100.0 - n0\nt2 = t0 * t1\nt3 = t2 / 100.0\nanswer = t3 - 100.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "two sets of 3 consecutive positive odd integers have exactly one integer in common . the sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set ?", + "Output Program": [ + "n0 = 3.0\nt0 = 2.0 + 3.0\nt1 = 2.0 + 4.0\nt2 = 3.0 + 4.0\nt3 = t0 - n0\nt4 = t2 - 1.0\nt5 = t1 - t3\nt6 = t3 + t5\nanswer = t6 + t4\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "a batsman makes a score of 64 runs in the 16 th innings and thus increased his average by 3 . find his average after the 16 th inning ?", + "Output Program": [ + "n0 = 64.0\nn1 = 16.0\nn2 = 3.0\nn3 = 16.0\nt0 = n1 * n2\nt1 = n0 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "how many positive integers , from 2 to 100 , inclusive , are not divisible by even integers greater than 1 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 100.0\nn2 = 1.0\nt0 = n0 * n0\nt1 = n0 * t0\nt2 = n0 * t1\nt3 = n0 * t2\nt4 = n0 * t3\nt5 = t4 - 4.0\nanswer = t5 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "two airplanes fly the same exact route from atlanta to chicago . plane a flies 200 mph while plane b flies 300 mph ( assume that simple model versus actual acceleration / deceleration near the airports ) . if plane a took off exactly 40 minutes before plane b , after how many minutes will plane b overtake plane a ?", + "Output Program": [ + "n0 = 200.0\nn1 = 300.0\nn2 = 40.0\nt0 = n0 * n2\nt1 = n1 - n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "find the least number which when divided by 20 , 2535 and 40 leaves remainders 14 , 1929 and 34 respectively .", + "Output Program": [ + "n0 = 20.0\nn1 = 2535.0\nn2 = 40.0\nn3 = 14.0\nn4 = 1929.0\nn5 = 34.0\nt0 = n3 / 2.0\nt1 = 2.0 * 3.0\nt2 = t0 * 100.0\nt3 = t2 * 2.0\nanswer = t3 - t1\nprint(answer)" + ], + "Output Answer": [ + "1394" + ], + "split": "train" + }, + { + "Input": "when average age of 22 members are 0 , how many members greater than 0 ?", + "Output Program": [ + "n0 = 22.0\nn1 = 0.0\nn2 = 0.0\n\nanswer = n0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "in a certain egg - processing plant , every egg must be inspected , and is either accepted for processing or rejected . for every 96 eggs accepted for processing , 4 eggs are rejected . if , on a particular day , 12 additional eggs were accepted , but the overall number of eggs inspected remained the same , the ratio of those accepted to those rejected would be 99 to 1 . how many e eggs does the plant process per day ?", + "Output Program": [ + "n0 = 96.0\nn1 = 4.0\nn2 = 12.0\nn3 = 99.0\nn4 = 1.0\nt0 = n3 - n0\nt1 = n2 / t0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "train" + }, + { + "Input": "the average expenditure of a labourer for 6 months was 75 and he fell into debt . in the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30 . his monthly income i", + "Output Program": [ + "n0 = 6.0\nn1 = 75.0\nn2 = 4.0\nn3 = 60.0\nn4 = 30.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nt4 = n4 + t3\nanswer = t4 / t0\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "train" + }, + { + "Input": "in a school with 600 students , the average age of the boys is 12 years and that of the girls is 11 years . if the average age of the school is 11 years 9 months , then the number of girls in the school is", + "Output Program": [ + "n0 = 600.0\nn1 = 12.0\nn2 = 11.0\nn3 = 11.0\nn4 = 9.0\nt0 = n4 / n1\nt1 = n0 * n1\nt2 = n2 + t0\nt3 = n0 * t2\nanswer = t1 - t3\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "train" + }, + { + "Input": "a batsman makes a score of 66 runs in the 17 th inning and thus increases his averages by 3 . what is his average after 17 th inning ?", + "Output Program": [ + "n0 = 66.0\nn1 = 17.0\nn2 = 3.0\nn3 = 17.0\nt0 = n1 * n2\nt1 = n0 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "find the value of e from ( 14 ) ^ 2 x 5 ^ 3 \u00e3 \u00b7 568 = e .", + "Output Program": [ + "n0 = 14.0\nn1 = 2.0\nn2 = 5.0\nn3 = 3.0\nn4 = 568.0\nt0 = n0**min(n1, 5)\nt1 = n2**min(n3, 5)\nt2 = t0 * t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "43.13380281690141" + ], + "split": "train" + }, + { + "Input": "mike earns $ 12 per hour and phil earns $ 6 per hour . approximately how much less , as a percentage , does phil earn than mike per hour ?", + "Output Program": [ + "n0 = 12.0\nn1 = 6.0\nt0 = n1 / n0\nanswer = t0 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "a certain bus driver is paid a regular rate of $ 14 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 982 in total compensation , how many total hours did he work that week ?", + "Output Program": [ + "n0 = 14.0\nn1 = 40.0\nn2 = 40.0\nn3 = 75.0\nn4 = 982.0\nt0 = n3 + 100.0\nt1 = n0 * n1\nt2 = n0 * t0\nt3 = n4 - t1\nt4 = t2 / 100.0\nt5 = t3 / t4\nanswer = n1 + t5\nprint(answer)" + ], + "Output Answer": [ + "57.224489795918366" + ], + "split": "train" + }, + { + "Input": "70 + 5 * 12 / ( 180 / 3 ) = ?", + "Output Program": [ + "n0 = 70.0\nn1 = 5.0\nn2 = 12.0\nn3 = 180.0\nn4 = 3.0\nt0 = n3 / n4\nt1 = n1 * n2\nt2 = t1 / t0\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "71" + ], + "split": "train" + }, + { + "Input": "reduce 368 / 598 to the lowest terms", + "Output Program": [ + "n0 = 368.0\nn1 = 598.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.6153846153846154" + ], + "split": "train" + }, + { + "Input": "what will be the reminder when ( 19 ^ 19 + 19 ) is divided by 20 ?", + "Output Program": [ + "import math\nn0 = 19.0\nn1 = 19.0\nn2 = 19.0\nn3 = 20.0\nt0 = n0**min(n0, 5)\nt1 = n0 + t0\nt2 = t1 / n3\nt3 = math.floor(t2)\nt4 = n3 * t3\nanswer = t1 - t4\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "a luxury liner , queen marry ii , is transporting several cats as well as the crew ( sailors , a cook , and one - legged captain ) to a nearby port . altogether , these passengers have 16 heads and 45 legs . how many cats does the ship host ?", + "Output Program": [ + "n0 = 16.0\nn1 = 45.0\nt0 = n1 - 1.0\nt1 = n0 - 1.0\nt2 = t1 * 2.0\nt3 = t1 * 4.0\nt4 = t0 - t2\nt5 = t3 - t2\nt6 = t4 / t5\nanswer = t6 * t1\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "what least number must be subtracted from 9671 so that the remaining number is divisible by 2 ?", + "Output Program": [ + "import math\nn0 = 9671.0\nn1 = 2.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "find the value of ( 200 + 200 / 90 ) \u00d7 90", + "Output Program": [ + "n0 = 200.0\nn1 = 200.0\nn2 = 90.0\nn3 = 90.0\nt0 = n1 / n2\nt1 = n0 + t0\nanswer = t1 * n2\nprint(answer)" + ], + "Output Answer": [ + "18200" + ], + "split": "train" + }, + { + "Input": "a beekeeper has 600000 bees living in 4 beehives . among these beehives , the sizes of the beehives are proportional to the numbers of bees living in them . no beehive has less than 80 % the number of bees of any other beehive . what is the maximum possible number of bees that the greatest beehive could have ?", + "Output Program": [ + "n0 = 600000.0\nn1 = 4.0\nn2 = 80.0\nt0 = n0 / n1\nt1 = n0 / 100.0\nt2 = 10.0 * 1000.0\nt3 = 100.0 * 4.0\nt4 = n2 - 10.0\nt5 = t0 + t2\nt6 = t5 + t2\nt7 = t6 + t1\nt8 = t7 + t3\nanswer = t8 + t4\nprint(answer)" + ], + "Output Answer": [ + "176470" + ], + "split": "train" + }, + { + "Input": "of the total amount that jill spent on a shopping trip , excluding taxes , she spent 50 percent on clothing , 10 percent on food , and 40 percent on other items . if jill paid a 4 percent tax on the clothing , no tax on the food , and an 8 percent tax on all other items , then the total tax that she paid was what percent of the total amount that she spent , excluding taxes ?", + "Output Program": [ + "n0 = 50.0\nn1 = 10.0\nn2 = 40.0\nn3 = 4.0\nn4 = 8.0\nt0 = n3 / 100.0\nt1 = n4 / 100.0\nt2 = n0 * t0\nt3 = n2 * t1\nt4 = t2 + t3\nt5 = t4 / 100.0\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "5.2" + ], + "split": "train" + }, + { + "Input": "a retailer bought a hat at wholesale and marked it up 70 % to its initial price of $ 34 . by how many more dollars does he need to increase the price to achieve a 100 % markup ?", + "Output Program": [ + "n0 = 70.0\nn1 = 34.0\nn2 = 100.0\nt0 = n0 + 100.0\nt1 = t0 / 100.0\nt2 = n1 / t1\nt3 = t2 * 2.0\nanswer = t3 - n1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "the average of 11 numbers is 60 . out of 11 numbers the average of first 6 no . is 88 , and last 6 numbers is 65 then find 6 th number ?", + "Output Program": [ + "n0 = 11.0\nn1 = 60.0\nn2 = 11.0\nn3 = 6.0\nn4 = 88.0\nn5 = 6.0\nn6 = 65.0\nn7 = 6.0\nt0 = n3 * n4\nt1 = n3 * n6\nt2 = n0 * n1\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "258" + ], + "split": "train" + }, + { + "Input": "set a contains all the even numbers between 4 and 50 inclusive . set b contains all the even numbers between 104 and 150 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ?", + "Output Program": [ + "n0 = 4.0\nn1 = 50.0\nn2 = 104.0\nn3 = 150.0\nt0 = n1 - n0\nt1 = n2 - n0\nt2 = t0 / 2.0\nt3 = t2 + 1.0\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "2400" + ], + "split": "train" + }, + { + "Input": "a number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34 . such a least possible number v is", + "Output Program": [ + "n0 = 5.0\nn1 = 8.0\nn2 = 34.0\nt0 = n2 * 2.0\nt1 = n0 * n1\nt2 = n0 - 1.0\nt3 = t0 - t1\nt4 = t3 / t2\nanswer = t4 + t0\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "in the hillside summer camp there are 50 children . 80 % of the children are boys and the rest are girls . the camp administrator decided to make the number of girls only 10 % of the total number of children in the camp . how many more boys must she bring to make that happen ?", + "Output Program": [ + "n0 = 50.0\nn1 = 80.0\nn2 = 10.0\nt0 = n2 / 100.0\nt1 = 100.0 - n2\nt2 = t1 / 100.0\nt3 = n0 * t0\nt4 = n0 * t2\nanswer = t4 + t3\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "if a number p is prime , and 2 p + 3 = q , where q is also prime , then the decimal expansion of 1 / q will produce a decimal with q - 1 digits . if this method produces a decimal with 166 digits , what is the units digit of the product of p and q ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 1.0\nn3 = 1.0\nn4 = 166.0\nt0 = n2 + n4\nt1 = t0 - n1\nt2 = t1 / n0\nt3 = t2 - n2\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "two brothers took the gmat exam , the higher score is x and the lower one is y . if the difference between the two scores is 1 / 3 , what is the value of x / y ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nt0 = n0 * n1\nt1 = t0 / n1\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "in a flight of 600 km , an aircraft was slowed down due to bad weather . its average speed for the trip was reduced by 200 km / hr and the time of flight increased by 30 minutes . the duration of the flight is :", + "Output Program": [ + "n0 = 600.0\nn1 = 200.0\nn2 = 30.0\nt0 = n1 * n2\nt1 = t0 / 10.0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "if 5 + 3 + 2 = 151022 , 9 + 2 + 4 = 183652 , then 7 + 2 + 5 = ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nn2 = 2.0\nn3 = 151022.0\nn4 = 9.0\nn5 = 2.0\nn6 = 4.0\nn7 = 183652.0\nn8 = 7.0\nn9 = 2.0\nn10 = 5.0\nt0 = n2 * n8\nt1 = n0 * n8\nt2 = t0 + t1\nt3 = t0 * 100.0\nt4 = t3 + t1\nt5 = t2 - n2\nt6 = t4 * 100.0\nanswer = t6 + t5\nprint(answer)" + ], + "Output Answer": [ + "143547" + ], + "split": "train" + }, + { + "Input": "find \u221a ? / 15 = 4 ?", + "Output Program": [ + "n0 = 15.0\nn1 = 4.0\nt0 = n0 * n1\nanswer = t0**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "3600" + ], + "split": "train" + }, + { + "Input": "10 % people of a village in sri lanka died by bombardment , 20 % of the remainder left the village on account of fear . if now the population is reduced to 3240 , how much was it in the beginning ?", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 20.0\nn2 = 3240.0\nt0 = 100.0 - n0\nt1 = 100.0 - n1\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = t2 * t3\nt5 = n2 / t4\nanswer = math.floor(t5)\nprint(answer)" + ], + "Output Answer": [ + "4499" + ], + "split": "train" + }, + { + "Input": "a meal cost $ 35.50 adn there was no tax . if the tip was more than 2 pc but less than 12 pc of the price , then the total amount paid should be :", + "Output Program": [ + "n0 = 35.5\nn1 = 2.0\nn2 = 12.0\nt0 = n0 * n1\nt1 = t0 / 100.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "36.21" + ], + "split": "train" + }, + { + "Input": "for each color copy , print shop x charges $ 1.20 and print shop y charges $ 1.70 . how much greater is the charge for 70 color copies at print shop y than at print shop x ?", + "Output Program": [ + "n0 = 1.2\nn1 = 1.7\nn2 = 70.0\nt0 = n1 * n2\nt1 = n0 * n2\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "a picnic attracts 240 persons . there are 80 more men than women , and 80 more adults than children . how many men are at this picnic ?", + "Output Program": [ + "n0 = 240.0\nn1 = 80.0\nn2 = 80.0\nt0 = n0 - n1\nt1 = t0 / 2.0\nt2 = n1 + t1\nt3 = t2 - n1\nt4 = t3 / 2.0\nanswer = n1 + t4\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "if 10 gallons of grape juice are added to 30 gallons of a mixture , which contains 10 percent grape juice then what percent of the resulting mixture is grape juice ?", + "Output Program": [ + "n0 = 10.0\nn1 = 30.0\nn2 = 10.0\nt0 = n0 + n1\nt1 = n2 / 100.0\nt2 = n1 * t1\nt3 = n0 + t2\nt4 = t3 / t0\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "32.5" + ], + "split": "train" + }, + { + "Input": "if ( 10 ^ 4 * 3.456789 ) ^ 12 is written as a single term , how many digits would be to the right of the decimal place ?", + "Output Program": [ + "n0 = 10.0\nn1 = 4.0\nn2 = 3.456789\nn3 = 12.0\n\nanswer = n3 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "a , b , c subscribe rs . 50,000 for a business . if a subscribes rs . 4000 more than b and b rs . 5000 more than c , out of a total profit of rs . 36,000 , what will be the amount a receives ?", + "Output Program": [ + "n0 = 50000.0\nn1 = 4000.0\nn2 = 5000.0\nn3 = 36000.0\nt0 = n1 + n2\nt1 = n2 + t0\nt2 = n0 - t1\nt3 = t2 / 3.0\nt4 = t0 + t3\nt5 = t4 / n0\nanswer = n3 * t5\nprint(answer)" + ], + "Output Answer": [ + "15120" + ], + "split": "train" + }, + { + "Input": "a shopping cart contains only apples , oranges , and pears . if there are 3 times as many oranges as apples , and 4 times as many pears as oranges , then the apples are equivalent to what fraction of the pears ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nt0 = n0 * n1\nanswer = 1.0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.08333333333333333" + ], + "split": "train" + }, + { + "Input": "q ' = 3 q - 3 , what is the value of ( 3 ' ) ' ?", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 3.0\nt0 = n0 * n2\nt1 = n2 - 1.0\nt2 = t0 - n0\nt3 = n0 * t2\nt4 = t3 - n0\nanswer = t4 * t1\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 110 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 3.0\nn3 = 4.0\nn4 = 3.0\nn5 = 5.0\nn6 = 110.0\nt0 = n1 / n5\nt1 = n1 / n3\nt2 = n0 / n1\nt3 = 1.0 - t0\nt4 = n6 / t3\nt5 = t4 / t1\nanswer = t5 / t2\nprint(answer)" + ], + "Output Answer": [ + "550.0000000000001" + ], + "split": "train" + }, + { + "Input": "a library has an average of 510 visitors on sundays and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :", + "Output Program": [ + "import math\nn0 = 510.0\nn1 = 240.0\nn2 = 30.0\nt0 = 3.0 + 4.0\nt1 = n2 / t0\nt2 = math.floor(t1)\nt3 = t2 + 1.0\nt4 = n0 * t3\nt5 = n2 - t3\nt6 = n1 * t5\nt7 = t4 + t6\nanswer = t7 / n2\nprint(answer)" + ], + "Output Answer": [ + "285" + ], + "split": "train" + }, + { + "Input": "crazy eddie has a key chain factory . eddie managed to decrease the cost of manufacturing his key chains while keeping the same selling price , and thus increased the profit from the sale of each key chain from 25 % of the selling price to 50 % of the selling price . if the manufacturing cost is now $ 50 , what was it before the decrease ?", + "Output Program": [ + "n0 = 25.0\nn1 = 50.0\nn2 = 50.0\nt0 = n1 / 100.0\nt1 = n0 / 100.0\nt2 = n1 / t0\nt3 = t2 * t1\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "the number of diagonals of a polygon of n sides is given by the formula z = n ( n - 3 ) / 2 . if a polygon has twice as many diagonals as sides , how many sides does it have ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\n\nanswer = n0 + n1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "what will be the remainder if 2 ^ 300 is divided by 4 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 300.0\nn2 = 4.0\n\nanswer = n0**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "a movie buff owns movies on dvd and on blu - ray in a ratio of 7 : 2 . if she buys 5 more blu - ray movies , that ratio would change to 13 : 4 . if she owns movies on no other medium , what was the original number of movies in her library before the extra purchase ?", + "Output Program": [ + "n0 = 7.0\nn1 = 2.0\nn2 = 5.0\nn3 = 13.0\nn4 = 4.0\nt0 = n0 + n1\nt1 = n2 + 1.0\nt2 = n0 * n4\nt3 = n1 * n3\nt4 = n3 * t1\nt5 = t2 - t3\nt6 = t4 / t5\nanswer = t0 * t6\nprint(answer)" + ], + "Output Answer": [ + "351" + ], + "split": "train" + }, + { + "Input": "10 % people of a village in sri lanka died by bombardment , 20 % of the remainder left the village on account of fear . if now the population is reduced to 4500 , how much was it in the beginning ?", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 20.0\nn2 = 4500.0\nt0 = 100.0 - n0\nt1 = 100.0 - n1\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = t2 * t3\nt5 = n2 / t4\nanswer = math.floor(t5)\nprint(answer)" + ], + "Output Answer": [ + "6249" + ], + "split": "train" + }, + { + "Input": "the tax on a commodity is diminished by 25 % but its consumption is increased by 10 % . find the decrease percent in the revenue derived from it ?", + "Output Program": [ + "n0 = 25.0\nn1 = 10.0\nt0 = n1 + 100.0\nt1 = 100.0 - n0\nt2 = t0 * t1\nt3 = t2 / 100.0\nanswer = 100.0 - t3\nprint(answer)" + ], + "Output Answer": [ + "17.5" + ], + "split": "train" + }, + { + "Input": "there are 16 bees in the hive , then 10 more fly . how many bees are there in all ?", + "Output Program": [ + "n0 = 16.0\nn1 = 10.0\n\nanswer = n0 + n1\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "if remainder is 19 , quotient is 61 and dividend is 507 then what is divisor ?", + "Output Program": [ + "n0 = 19.0\nn1 = 61.0\nn2 = 507.0\nt0 = n2 - n0\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "the average salary of raj and roshan is rs . 4000 but the average salary of raj , roshan and thomas is rs . 5000 . what is the salary of thomas ?", + "Output Program": [ + "n0 = 4000.0\nn1 = 5000.0\nt0 = n0 + n1\nt1 = 1000.0 * 2.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "7000" + ], + "split": "train" + }, + { + "Input": "gopi gives rs . 90 plus one turban as salary to his servant for one year . the servant leaves after 9 months and receives rs . 45 and the turban . find the price of the turban .", + "Output Program": [ + "n0 = 90.0\nn1 = 9.0\nn2 = 45.0\nt0 = n0 - n2\nt1 = 12.0 - n1\nt2 = t0 / t1\nt3 = t2 * 12.0\nanswer = t3 - n0\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "vishal invested 10 % more than trishul . trishul invested 10 % less than raghu . if the total sum of their investments is rs . 6936 , how much amount did raghu invest ?", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 6936.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nt2 = 1.0 - t0\nt3 = t1 * t2\nt4 = t3 + t2\nt5 = t4 + 1.0\nanswer = n2 / t5\nprint(answer)" + ], + "Output Answer": [ + "2400" + ], + "split": "train" + }, + { + "Input": "the maximum numbers of students among them 891 pens and 810 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is", + "Output Program": [ + "n0 = 891.0\nn1 = 810.0\n\nanswer = n0 - n1\nprint(answer)" + ], + "Output Answer": [ + "81" + ], + "split": "train" + }, + { + "Input": "the telephone company wants to add an area code composed of 2 letters to every phone number . in order to do so , the company chose a special sign language containing 124 different signs . if the company used 122 of the signs fully and two remained unused , how many additional area codes can be created if the company uses all 124 signs ?", + "Output Program": [ + "n0 = 2.0\nn1 = 124.0\nn2 = 122.0\nn3 = 124.0\nt0 = n1 - n2\nt1 = n2 * t0\nanswer = t1 * t0\nprint(answer)" + ], + "Output Answer": [ + "488" + ], + "split": "train" + }, + { + "Input": "a large box contains 20 small boxes and each small box contains 25 chocolate bars . how many chocolate bars are in the large box ?", + "Output Program": [ + "n0 = 20.0\nn1 = 25.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "train" + }, + { + "Input": "each week , harry is paid x dollars per hour for the first 30 hours and 2 x dollars for each additional hour worked that week . each week , james is paid x dollars per per hour for the first 40 hours and 1.5 x dollars for each additional hour worked that week . last week james worked a total of 41 hours if harry and james were paid the same amount last week , how many hours did harry work last week ?", + "Output Program": [ + "n0 = 30.0\nn1 = 2.0\nn2 = 40.0\nn3 = 1.5\nn4 = 41.0\nt0 = n2 + n3\nt1 = t0 - n0\nt2 = t1 / n1\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "35.75" + ], + "split": "train" + }, + { + "Input": "there are 70 supermarkets in the fgh chain . all of them are either in the us or canada . if there are 14 more fgh supermarkets in the us than in canada , how many fgh supermarkets are there in the us ?", + "Output Program": [ + "n0 = 70.0\nn1 = 14.0\nt0 = n0 + n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "find the least number must be subtracted from 165826 so that remaining no . is divisible by 4 ?", + "Output Program": [ + "import math\nn0 = 165826.0\nn1 = 4.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a trained covered x km at 40 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 2 x km .", + "Output Program": [ + "n0 = 40.0\nn1 = 2.0\nn2 = 20.0\nn3 = 2.0\nt0 = n0 / n0\nt1 = n0 * n3\nt2 = n0 * n1\nt3 = t2 / n2\nt4 = t0 + t3\nanswer = t1 / t4\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "if x and y are positive integers , and y = x ^ 2 + 8 , the greatest common divisor of a and b can not be", + "Output Program": [ + "n0 = 2.0\nn1 = 8.0\n\nanswer = n1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "there are 100 students in a certain geometry class . if one half of the students are boys and one fifth of the boys are under 6 feet tall , how many boys in the class are under 6 feet tall ?", + "Output Program": [ + "n0 = 100.0\nn1 = 6.0\nn2 = 6.0\nt0 = 1.0 + 4.0\nt1 = n0 / 2.0\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the wages earned by robin is 30 % more than that earned by erica . the wages earned by charles is 60 % more than that earned by erica . how much % is the wages earned by charles more than that earned by robin ?", + "Output Program": [ + "n0 = 30.0\nn1 = 60.0\nt0 = n1 + 100.0\nt1 = n0 + 100.0\nt2 = t0 - t1\nt3 = t2 / t1\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "23.076923076923077" + ], + "split": "train" + }, + { + "Input": "if henry were to add 5 gallons of water to a tank that is already 3 / 4 full of water , the tank would be 7 / 8 full . how many gallons of water would the tank hold if it were full ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nn2 = 4.0\nn3 = 7.0\nn4 = 8.0\nt0 = n3 / n4\nt1 = n1 / n2\nt2 = t0 - t1\nt3 = 1.0 / t2\nanswer = n0 * t3\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "in a box of 10 pens , a total of 3 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?", + "Output Program": [ + "n0 = 10.0\nn1 = 3.0\nn2 = 2.0\nt0 = n0 - n1\nt1 = n0 - 1.0\nt2 = t0 / n0\nt3 = t0 - 1.0\nt4 = t3 / t1\nanswer = t2 * t4\nprint(answer)" + ], + "Output Answer": [ + "0.4666666666666666" + ], + "split": "train" + }, + { + "Input": "in 10 years , a will be twice as old as b was 10 years ago . if a is now 9 years older than b , the present age of b is :", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 9.0\nt0 = n0 * 2.0\nt1 = n0 + t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "39" + ], + "split": "train" + }, + { + "Input": "the sum of the numbers is 660 . if the first number be twice the second and third number be one - third of the first , then the second number is :", + "Output Program": [ + "n0 = 660.0\nt0 = 1.0 + 10.0\nt1 = n0 * 3.0\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "180" + ], + "split": "train" + }, + { + "Input": "x and y are positive integers . when x is divided by 17 , the remainder is 3 , and when x is divided by 19 , the remainder is 1 . when y is divided by 14 , the remainder is 5 , and when y is divided by 21 , the remainder is 12 . what is the least possible value of y - x ?", + "Output Program": [ + "n0 = 17.0\nn1 = 3.0\nn2 = 19.0\nn3 = 1.0\nn4 = 14.0\nn5 = 5.0\nn6 = 21.0\nn7 = 12.0\nt0 = n0 + n1\nt1 = n4 * 2.0\nt2 = n5 + t1\nanswer = t2 - t0\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "brindavan express leave chennai central station every day at 07.50 am and goes to bangalore city railway station . this train is very popular among the travelers . on 25 th july 2012 number of passengers traveling by i class and ii class was in the ratio 1 : 4 . the fare for this travel is in the ratio 3 : 1 . the total fare collected was rs . 224000 / . ( rs . two lakhs 20 4 1000 only ) . what was the fare collected from i class passengers on that day ?", + "Output Program": [ + "n0 = 7.5\nn1 = 25.0\nn2 = 2012.0\nn3 = 1.0\nn4 = 4.0\nn5 = 3.0\nn6 = 1.0\nn7 = 224000.0\nn8 = 20.0\nn9 = 4.0\nn10 = 1000.0\nt0 = n4 + n5\nt1 = n5 / t0\nanswer = n7 * t1\nprint(answer)" + ], + "Output Answer": [ + "96000" + ], + "split": "train" + }, + { + "Input": "in a theater , the first row has 12 seats and each row has 2 more seats than previous row . if the last row has 48 seats , what is the total number of seats in the theater ?", + "Output Program": [ + "n0 = 12.0\nn1 = 2.0\nn2 = 48.0\nt0 = n0 + n2\nt1 = n2 - n0\nt2 = n1 + t1\nt3 = t0 / 2.0\nt4 = t2 / n1\nanswer = t3 * t4\nprint(answer)" + ], + "Output Answer": [ + "570" + ], + "split": "train" + }, + { + "Input": "in a certain diving competition , 5 judges score each dive on a scale from 1 to 10 . the point value of the dive is obtained by dropping the highest score and the lowest score and multiplying the sum of the remaining scores by the degree of difficulty . if a dive with a degree of difficulty of 3.2 received scores of 7.5 , 8.1 , 9.0 , 6.0 , and 8.5 , what was the point value of the dive ?", + "Output Program": [ + "n0 = 5.0\nn1 = 1.0\nn2 = 10.0\nn3 = 3.2\nn4 = 7.5\nn5 = 8.1\nn6 = 9.0\nn7 = 6.0\nn8 = 8.5\nt0 = n4 + n5\nt1 = n8 + t0\nanswer = n3 * t1\nprint(answer)" + ], + "Output Answer": [ + "77.12" + ], + "split": "train" + }, + { + "Input": "a man has rs . 10350 in the form of rs . 50 notes and rs . 500 notes . the total number of notes are 54 . find the number of notes of rs . 50 denomination .", + "Output Program": [ + "n0 = 10350.0\nn1 = 50.0\nn2 = 500.0\nn3 = 54.0\nn4 = 50.0\nt0 = n2 * n3\nt1 = n2 - n1\nt2 = t0 - n0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "37" + ], + "split": "train" + }, + { + "Input": "one - third less than 15 % of 180 is equal to :", + "Output Program": [ + "n0 = 15.0\nn1 = 180.0\nt0 = n0 / 100.0\nt1 = 1.0 / 3.0\nt2 = n1 * t0\nt3 = t1 * t2\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "if bill can buy 3 pairs of jeans and 2 shirts for $ 69 or 2 pairs of jeans and 3 shirts for $ 86 , how much does one shirt cost ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 69.0\nn3 = 2.0\nn4 = 3.0\nn5 = 86.0\nt0 = n0 * n5\nt1 = n1 * n2\nt2 = n0 * n0\nt3 = n1 * n1\nt4 = t0 - t1\nt5 = t2 - t3\nanswer = t4 / t5\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "tough and tricky questions : word problems . if bill ' s salary increased by 16 percent , he would earn $ 812 per month . if instead , his salary were to increase by only 10 percent , how much money r would he earn per month ?", + "Output Program": [ + "n0 = 16.0\nn1 = 812.0\nn2 = 10.0\nt0 = n2 / 100.0\nt1 = n0 / 100.0\nt2 = t0 + 1.0\nt3 = t1 + 1.0\nt4 = n1 / t3\nanswer = t2 * t4\nprint(answer)" + ], + "Output Answer": [ + "770.0000000000001" + ], + "split": "train" + }, + { + "Input": "tough and tricky questions : decimals . the value of x is derived by summing a , b , and c and then rounding the result to the tenths place . the value of y is derived by first rounding a , b , and c to the tenths place and then summing the resulting values . if a = 5.45 , b = 2.95 , and c = 3.74 , what is y \u2013 x ?", + "Output Program": [ + "import math\nn0 = 5.45\nn1 = 2.95\nn2 = 3.74\nt0 = n0 + n1\nt1 = n0 * 10.0\nt2 = n1 * 10.0\nt3 = n2 * 10.0\nt4 = n2 + t0\nt5 = math.floor(t1)\nt6 = math.floor(t2)\nt7 = math.floor(t3)\nt8 = t5 + 1.0\nt9 = t6 + 1.0\nt10 = t7 + 1.0\nt11 = t4 * 10.0\nt12 = t8 / 10.0\nt13 = t9 / 10.0\nt14 = t10 / 10.0\nt15 = math.floor(t11)\nt16 = t12 + t13\nt17 = t15 / 10.0\nt18 = t16 + t14\nanswer = t18 - t17\nprint(answer)" + ], + "Output Answer": [ + "0.20000000000000107" + ], + "split": "train" + }, + { + "Input": "[ 1 / ( 1 . 2.3 ) ] + [ 1 / ( 2 . 3.4 ) ] + [ 1 / ( 3 . 4.5 ) ] + [ 1 / ( 4 . 5.6 ) ] is equal to", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 2.3\nn3 = 1.0\nn4 = 2.0\nn5 = 3.4\nn6 = 1.0\nn7 = 3.0\nn8 = 4.5\nn9 = 1.0\nn10 = 4.0\nn11 = 5.6\nt0 = n7 + n10\nt1 = n0 + n4\nt2 = t1 * 10.0\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.23333333333333334" + ], + "split": "train" + }, + { + "Input": "a \u2019 s speed is 21 / 19 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?", + "Output Program": [ + "n0 = 21.0\nn1 = 19.0\nt0 = n0 - n1\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.09523809523809523" + ], + "split": "train" + }, + { + "Input": "the total population of city a and city b is 5000 more than the total population of city b and city c . how much lesser is the population in city c as compared to city a ?", + "Output Program": [ + "n0 = 5000.0\n\nanswer = n0 / 1.0\nprint(answer)" + ], + "Output Answer": [ + "5000" + ], + "split": "train" + }, + { + "Input": "if p ' s height is 40 % less than that of q , how much percent q ' s height is more than that of p ?", + "Output Program": [ + "n0 = 40.0\nt0 = 100.0 - n0\nt1 = n0 / t0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "66.66666666666666" + ], + "split": "train" + }, + { + "Input": "if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 120 games will be played during the tournament . find the number of participants .", + "Output Program": [ + "import math\nn0 = 120.0\nt0 = n0 * 2.0\nt1 = t0 * 4.0\nt2 = t1 + 1.0\nt3 = math.sqrt(max(0, t2))\nt4 = t3 + 1.0\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "a parking garage rents parking spaces for $ 10 per week or $ 35 per month . how much does a person save in a year by renting by the month rather than by the week ?", + "Output Program": [ + "n0 = 10.0\nn1 = 35.0\nt0 = 2.0 + 3.0\nt1 = n1 * 12.0\nt2 = t0 * 10.0\nt3 = t2 + 2.0\nt4 = n0 * t3\nanswer = t4 - t1\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "a train starts full of passengers at the first station it drops 1 / 3 of the passengers and takes 280 more at the second station it drops one half the new total and takes 12 more . on arriving at the third station it is found to have 242 passengers . find the no of passengers in the beginning ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 280.0\nn3 = 12.0\nn4 = 242.0\nt0 = n2 / 2.0\nt1 = n1 * 2.0\nt2 = n3 + t0\nt3 = n4 - t2\nt4 = t3 / 2.0\nanswer = t4 * t1\nprint(answer)" + ], + "Output Answer": [ + "270" + ], + "split": "train" + }, + { + "Input": "a mixture of 125 gallons of wine and water contains 20 % of water . how much water must be added to the mixture in order to increase the percentage of water to 25 % of the new mixture ?", + "Output Program": [ + "n0 = 125.0\nn1 = 20.0\nn2 = 25.0\nt0 = n1 / 100.0\nt1 = n0 * t0\nt2 = t1 / 100.0\nt3 = n0 * t2\nt4 = 1.0 - t2\nt5 = t3 - n2\nanswer = t5 / t4\nprint(answer)" + ], + "Output Answer": [ + "8.333333333333334" + ], + "split": "train" + }, + { + "Input": "barbata invests $ 3000 in the national bank at 5 % . how much additional money must she invest at 8 % so that the total annual income will be equal to 6 % of her entire investment ?", + "Output Program": [ + "n0 = 3000.0\nn1 = 5.0\nn2 = 8.0\nn3 = 6.0\nt0 = n3 / 100.0\nt1 = n1 / 100.0\nt2 = n2 / 100.0\nt3 = n0 * t0\nt4 = n0 * t1\nt5 = t2 - t0\nt6 = t3 - t4\nanswer = t6 / t5\nprint(answer)" + ], + "Output Answer": [ + "1499.9999999999998" + ], + "split": "train" + }, + { + "Input": "for integers x and y , if ( x + 2 ) ( y + 3 ) is even then 4 xy must be divisible by :", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 4.0\n\nanswer = n2 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "benny goes to the market for buying some apples to be distributed between her 9 kids equally . she takes 360 dollars with her . the cost of each apple is 2 dollars . how many apples does she buy to share them equally between her 6 kids ?", + "Output Program": [ + "n0 = 9.0\nn1 = 360.0\nn2 = 2.0\nn3 = 6.0\nt0 = n1 / n2\nanswer = t0 / n3\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "in one year , the population , of a village increased by 12 % and in the next year , it decreased by 12 % . if at the end of 2 nd year , the population was 14784 , what was it in the beginning ?", + "Output Program": [ + "n0 = 12.0\nn1 = 12.0\nn2 = 2.0\nn3 = 14784.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nt2 = 1.0 - t0\nt3 = n3 / t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "14999.999999999998" + ], + "split": "train" + }, + { + "Input": "a grocer has a sale of rs . 5266 , rs . 5744 , rs . 5864 , rs . 6122 and rs . 6588 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 5750 ?", + "Output Program": [ + "n0 = 5266.0\nn1 = 5744.0\nn2 = 5864.0\nn3 = 6122.0\nn4 = 6588.0\nn5 = 5.0\nn6 = 5750.0\nt0 = n5 + 1.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n6 * t0\nt4 = n3 + t2\nt5 = n4 + t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "4916" + ], + "split": "train" + }, + { + "Input": "in a house a hall is 20 m long , 15 m wide and 5 m high . its interior has to be covered with mat . what will be the total expenditure if it costs rs . 20 per square m ?", + "Output Program": [ + "n0 = 20.0\nn1 = 15.0\nn2 = 5.0\nn3 = 20.0\nt0 = n0 * n1\nt1 = n0 * n2\nt2 = n1 * n2\nt3 = t0 * 2.0\nt4 = t1 * 2.0\nt5 = t2 * 2.0\nt6 = n3 * t3\nt7 = n3 * t4\nt8 = n3 * t5\nt9 = t6 + t7\nanswer = t9 + t8\nprint(answer)" + ], + "Output Answer": [ + "19000" + ], + "split": "train" + }, + { + "Input": "the average score of a cricketer in 2 matches is 27 and in other 3 matches is 32 . then find the average score in all the 5 matches ?", + "Output Program": [ + "n0 = 2.0\nn1 = 27.0\nn2 = 3.0\nn3 = 32.0\nn4 = 5.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = t0 + t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "john found that the average of 15 numbers is 40 . if 12 is added to each number then the mean of number is ?", + "Output Program": [ + "n0 = 15.0\nn1 = 40.0\nn2 = 12.0\n\nanswer = n1 + n2\nprint(answer)" + ], + "Output Answer": [ + "52" + ], + "split": "train" + }, + { + "Input": "how many 4 - digit positive integers can be formed by using the digits from 1 to 9 so that two digits are equal to each other and the remaining two are also equal to each other but different from the other two ? .", + "Output Program": [ + "n0 = 4.0\nn1 = 1.0\nn2 = 9.0\nt0 = n0 * 3.0\nt1 = n2 - n1\nt2 = t0 / 2.0\nt3 = n2 * t1\nt4 = t3 / 2.0\nanswer = t4 * t2\nprint(answer)" + ], + "Output Answer": [ + "216" + ], + "split": "train" + }, + { + "Input": "0.009 / x = 0.03 . find the value of x", + "Output Program": [ + "n0 = 0.009\nn1 = 0.03\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.3" + ], + "split": "train" + }, + { + "Input": "if an integer n is to be selected at random from 1 to 400 , inclusive , what is probability n ( n + 1 ) will be divisible by 8 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 400.0\nn2 = 1.0\nn3 = 8.0\n\nanswer = 2.0 / n3\nprint(answer)" + ], + "Output Answer": [ + "0.25" + ], + "split": "train" + }, + { + "Input": "students at a school were on average 180 cm tall . the average female height was 170 cm , and the average male height was 185 cms . what was the ratio of men to women ?", + "Output Program": [ + "n0 = 180.0\nn1 = 170.0\nn2 = 185.0\nt0 = n0 - n1\nt1 = n2 - n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "find the least positive integer divisible by each of the integers between 5 through 10 ( including 10 ) .", + "Output Program": [ + "n0 = 5.0\nn1 = 10.0\nn2 = 10.0\nt0 = 3.0 + 4.0\nt1 = 2.0**min(3.0, 5)\nt2 = 3.0**min(2.0, 5)\nt3 = t1 * t2\nt4 = n0 * t3\nanswer = t0 * t4\nprint(answer)" + ], + "Output Answer": [ + "2520" + ], + "split": "train" + }, + { + "Input": "according to the directions on a packet of smoothie mix , 1 3 - ounce packet of smoothie mix is to be combined with 12 ounces of water to make a smoothie . how many 2 - ounce packets of smoothie mix are required to prepare 150 12 - ounce smoothies ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 12.0\nn3 = 2.0\nn4 = 150.0\nn5 = 12.0\nt0 = n1 * 10.0\nanswer = n4 + t0\nprint(answer)" + ], + "Output Answer": [ + "180" + ], + "split": "train" + }, + { + "Input": "the difference between a two - digit number and the number obtained by interchanging the positions of its digits is 54 . what is the difference between the two digits of that number ?", + "Output Program": [ + "n0 = 54.0\nt0 = 10.0 - 1.0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "a grocery shop has a sale of rs . 6435 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ?", + "Output Program": [ + "n0 = 6435.0\nn1 = 6927.0\nn2 = 6855.0\nn3 = 7230.0\nn4 = 6562.0\nn5 = 5.0\nn6 = 6500.0\nt0 = n5 + 1.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n6 * t0\nt4 = n3 + t2\nt5 = n4 + t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "4991" + ], + "split": "train" + }, + { + "Input": "workers decided to raise rs . 3 lacs by equal contribution from each . had they contributed rs . 50 eachextra , the contribution would have been rs . 3.20 lacs . how many workers were they ?", + "Output Program": [ + "n0 = 3.0\nn1 = 50.0\nn2 = 3.2\nt0 = n2 - n0\nt1 = t0 * 1000.0\nt2 = t1 * 100.0\nanswer = t2 / n1\nprint(answer)" + ], + "Output Answer": [ + "400.00000000000034" + ], + "split": "train" + }, + { + "Input": "find the greatest number which on dividing 3815 and 4521 , leaves a reminder of 31 and 33 respectively", + "Output Program": [ + "import scipy\nn0 = 3815.0\nn1 = 4521.0\nn2 = 31.0\nn3 = 33.0\nt0 = n0 - n2\nt1 = n1 - n3\nanswer = scipy.gcd(int(t0), int(t1))\nprint(answer)" + ], + "Output Answer": [ + "88" + ], + "split": "train" + }, + { + "Input": "what is the sum of all 3 digit numbers that leave a remainder of ' 2 ' when divided by 5 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 5.0\nt0 = n0 * n0\nt1 = 1000.0 - n0\nt2 = t0 * 10.0\nt3 = t2 + t0\nt4 = n0 + t3\nt5 = t4 + t1\nt6 = t1 - t4\nt7 = t6 / n2\nt8 = t7 + 1.0\nt9 = t8 / n1\nanswer = t5 * t9\nprint(answer)" + ], + "Output Answer": [ + "98910" + ], + "split": "train" + }, + { + "Input": "the total marks obtained by a student in mathematics and physics is 70 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together .", + "Output Program": [ + "n0 = 70.0\nn1 = 20.0\nt0 = n0 + n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "( 3 x + 2 ) ( 2 x - 7 ) = ax ^ 2 + kx + n . what is the value of a - n + k ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 2.0\nn3 = 7.0\nn4 = 2.0\nt0 = n0 * n1\nt1 = n1 * n3\nt2 = n1 * n1\nt3 = n0 * n3\nt4 = t0 + t1\nt5 = t2 - t3\nanswer = t4 + t5\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "for every even positive integer m , f ( m ) represents the product of all even integers from 2 to m , inclusive . for example , f ( 12 ) = 2 x 4 x 6 x 8 x 10 x 12 . what is the greatest prime factor of f ( 28 ) ?", + "Output Program": [ + "n0 = 2.0\nn1 = 12.0\nn2 = 2.0\nn3 = 4.0\nn4 = 6.0\nn5 = 8.0\nn6 = 10.0\nn7 = 12.0\nn8 = 28.0\nt0 = n8 / n0\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "following an increase in prices , the price of a candy box was 15 pounds and the price of a can of soda was 6 pounds . if the price of a candy box was raised by 25 % , and the price of a can of soda was raised by 50 % . what was the price of a box of candy plus a can of soda before prices were raised ?", + "Output Program": [ + "n0 = 15.0\nn1 = 6.0\nn2 = 25.0\nn3 = 50.0\nt0 = n2 + 100.0\nt1 = n3 + 100.0\nt2 = n0 * 100.0\nt3 = n1 * 100.0\nt4 = t2 / t0\nt5 = t3 / t1\nanswer = t4 + t5\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "a mathematics teacher tabulated the marks secured by 35 students of 8 th class . the average of their marks was 72 . if the marks secured by reema was written as 46 instead of 56 then find the correct average marks up to two decimal places .", + "Output Program": [ + "n0 = 35.0\nn1 = 8.0\nn2 = 72.0\nn3 = 46.0\nn4 = 56.0\nt0 = n0 * n2\nt1 = n4 - n3\nt2 = t0 - t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "71.71428571428571" + ], + "split": "train" + }, + { + "Input": "in an election between two candidates a and b , the number of valid votes received by a exceeds those received by b by 15 % of the total number of votes polled . if 20 % of the votes polled were invalid and a total of 6720 votes were polled , then how many valid votes did b get ?", + "Output Program": [ + "n0 = 15.0\nn1 = 20.0\nn2 = 6720.0\nt0 = n1 / 100.0\nt1 = n0 * n2\nt2 = t1 / 100.0\nt3 = 1.0 - t0\nt4 = n2 * t3\nt5 = t4 - t2\nanswer = t5 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "2184" + ], + "split": "train" + }, + { + "Input": "in a hostel there were 100 students . to accommodate some more students the average budget is decreased by rupees 10 . but total expenditure increased by rs . 400 . if the total expenditure of the hostel now 5400 , find the number of student joined ?", + "Output Program": [ + "n0 = 100.0\nn1 = 10.0\nn2 = 400.0\nn3 = 5400.0\nt0 = n3 - n2\nt1 = t0 / n0\nt2 = t1 - n1\nt3 = n3 / t2\nt4 = t3 - n0\nanswer = t4 - 3.0\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "a batsman makes a score of 87 runs in the 17 th inning and thus increases his average by 4 . find his average after 17 th inning .", + "Output Program": [ + "n0 = 87.0\nn1 = 17.0\nn2 = 4.0\nn3 = 17.0\nt0 = n1 * n2\nt1 = n0 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "when the positive integer x is divided by 9 , the remainder is 5 . what is the remainder when 6 x is divided by 9 ?", + "Output Program": [ + "n0 = 9.0\nn1 = 5.0\nn2 = 6.0\nn3 = 9.0\nt0 = n1 * n2\nanswer = t0 % n0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "tickets numbered 1 to 20 are mixed up and then a ticked is drawn at random . what is the probability that the ticket drawn bears a number which is a multiple of 3 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 20.0\nn2 = 3.0\n\nanswer = n2 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "0.3" + ], + "split": "train" + }, + { + "Input": "the average weight of 6 persons increases by 1.5 kg . if a person weighing 65 kg is replaced by a new person , what could be the weight of the new person ?", + "Output Program": [ + "n0 = 6.0\nn1 = 1.5\nn2 = 65.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "74" + ], + "split": "train" + }, + { + "Input": "a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 50 paisa . if the share of y is rs . 54 , what is the total amount ?", + "Output Program": [ + "n0 = 45.0\nn1 = 50.0\nn2 = 54.0\nt0 = 100.0 / n0\nt1 = n1 / n0\nt2 = n2 * t0\nt3 = n2 * t1\nt4 = t2 + t3\nanswer = n2 + t4\nprint(answer)" + ], + "Output Answer": [ + "234" + ], + "split": "train" + }, + { + "Input": "if x is 12 percent greater than 70 , then x =", + "Output Program": [ + "n0 = 12.0\nn1 = 70.0\nt0 = n0 / 100.0\nt1 = n1 * t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "78.4" + ], + "split": "train" + }, + { + "Input": "a man is 28 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is", + "Output Program": [ + "n0 = 28.0\nt0 = 2.0 * 2.0\nt1 = 2.0 - 1.0\nt2 = t0 - 2.0\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "a call center has two teams . each member of team a was able to process 7 / 5 calls as compared to each member of team b . if team a has 5 / 8 as many number of call center agents as team b , what fraction of the total calls was processed by team b ?", + "Output Program": [ + "n0 = 7.0\nn1 = 5.0\nn2 = 5.0\nn3 = 8.0\nt0 = n1 * n3\nt1 = n0 * n1\nt2 = t0 + t1\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.5333333333333333" + ], + "split": "train" + }, + { + "Input": "a committee is reviewing a total of 20 x black - and - white films and 4 y color films for a festival . if the committee selects y / x % of the black - and - white films and all of the color films , what fraction of the selected films are in color ?", + "Output Program": [ + "n0 = 20.0\nn1 = 4.0\nt0 = n0 / 100.0\nt1 = n1 + t0\nanswer = n1 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.9523809523809523" + ], + "split": "train" + }, + { + "Input": "each child has 2 pencils and 13 skittles . if there are 9 children , how many pencils are there in total ?", + "Output Program": [ + "n0 = 2.0\nn1 = 13.0\nn2 = 9.0\n\nanswer = n0 * n2\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "x is a positive integer less than 400 . when x is divided by 7 , the remainder is 1 ; when x is divided by 3 , the remainder is 2 . how many x are there ?", + "Output Program": [ + "n0 = 400.0\nn1 = 7.0\nn2 = 1.0\nn3 = 3.0\nn4 = 2.0\nt0 = n1 % n0\nt1 = n3 % n0\nt2 = n2 % n0\nt3 = n3 * t0\nt4 = t3 + t1\nanswer = t4 - t2\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "the rate of increase of the price of sugar is observed to be 3 percent more than the inflation rate expressed in percentage . the price of sugar , on january 1 , 1994 , is rs . 25 per kg . the inflation rate for the years 1994 and 1995 are expected to be 12 % each . the expected price of sugar on january 1 , 1996 would be", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 1994.0\nn3 = 25.0\nn4 = 1994.0\nn5 = 1995.0\nn6 = 12.0\nn7 = 1.0\nn8 = 1996.0\nt0 = n0 + n6\nt1 = 100.0 * 100.0\nt2 = t0 + 100.0\nt3 = n3 * t2\nt4 = t2 * t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "33.0625" + ], + "split": "train" + }, + { + "Input": "average weight of 10 people increased by 3 kg when one person of 45 kg is replaced by a new man . then weight of the new man is", + "Output Program": [ + "n0 = 10.0\nn1 = 3.0\nn2 = 45.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "marketing executives for a certain chewing gum company projected a 20 percent increase in revenue this year over that of last year , but revenue this year actually decreased by 10 % . what percent of the projected revenue was the actual revenue ?", + "Output Program": [ + "n0 = 20.0\nn1 = 10.0\nt0 = n0 + 100.0\nt1 = 100.0 - n1\nt2 = t1 / t0\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "a small pool filled only with water will require an additional 300 gallons of water in order to be filled to 75 % of its capacity . if pumping in these additional 300 gallons of water will increase the amount of water in the pool by 30 % , what is the total capacity of the pool in gallons ?", + "Output Program": [ + "n0 = 300.0\nn1 = 75.0\nn2 = 300.0\nn3 = 30.0\nt0 = n1 / 100.0\nt1 = n0 * 100.0\nt2 = t1 / n3\nt3 = n0 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "1733.3333333333333" + ], + "split": "train" + }, + { + "Input": "a motorist travels to a place 150 km away at an average speed of 50 km / hr and returns at 30 km / hr . his average speed for the whole journey in km / hr is ?", + "Output Program": [ + "n0 = 150.0\nn1 = 50.0\nn2 = 30.0\nt0 = n1 + n2\nt1 = n1 * n2\nt2 = t1 * 2.0\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "37.5" + ], + "split": "train" + }, + { + "Input": "a textile manufacturing firm employees 56 looms . it makes fabrics for a branded company . the aggregate sales value of the output of the 56 looms is rs 5 , 00,000 and the monthly manufacturing expenses is rs 1 , 50,000 . assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms . monthly establishment charges are rs 75000 . if one loom breaks down and remains idle for one month , the decrease in profit is :", + "Output Program": [ + "n0 = 56.0\nn1 = 56.0\nn2 = 5.0\nn3 = 0.0\nn4 = 1.0\nn5 = 50000.0\nn6 = 75000.0\nt0 = n2 * 1000.0\nt1 = n6 * 2.0\nt2 = n0 - n4\nt3 = n6 + t1\nt4 = t2 / n0\nt5 = t0 * 100.0\nt6 = t4 * t5\nt7 = t4 * t1\nt8 = t5 - t3\nt9 = t6 - t7\nt10 = t9 - n6\nanswer = t8 - t10\nprint(answer)" + ], + "Output Answer": [ + "6250" + ], + "split": "train" + }, + { + "Input": "a meal cost $ 48.75 adn there was no tax . if the tip was more than 5 pc but less than 20 pc of the price , then the total amount paid should be :", + "Output Program": [ + "n0 = 48.75\nn1 = 5.0\nn2 = 20.0\nt0 = n0 * n1\nt1 = t0 / 100.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "51.1875" + ], + "split": "train" + }, + { + "Input": "a basket of 1430 apples is divided equally among a group of apple lovers . if 45 people join the group , each apple lover would receive 9 apples less . how many apples f did each person get before 45 people joined the feast ?", + "Output Program": [ + "n0 = 1430.0\nn1 = 45.0\nn2 = 9.0\nn3 = 45.0\nt0 = 10.0 + 10.0\nt1 = t0 + 2.0\nt2 = n0 / t1\nt3 = n1 + t2\nt4 = n0 / t3\nanswer = n2 + t4\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "the average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 28 years . find the average age of the women ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.0\nn2 = 20.0\nn3 = 28.0\nt0 = n2 + n3\nt1 = n0 * n1\nt2 = t0 + t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "the captain of a cricket team of 11 members is 27 years old and the wicket keeper is 3 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ?", + "Output Program": [ + "n0 = 11.0\nn1 = 27.0\nn2 = 3.0\nt0 = n1 + n2\nt1 = n2 * n2\nt2 = n1 + t0\nt3 = t2 - t1\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "i have 150 pieces of cake . there are 50 friends in my house . i would like to give each friend the same amount of cake , how much should i give to each friend ?", + "Output Program": [ + "n0 = 150.0\nn1 = 50.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "find the value of y from ( 12 ) ^ 3 x 6 ^ 2 \u00f7 432 = y ?", + "Output Program": [ + "n0 = 12.0\nn1 = 3.0\nn2 = 6.0\nn3 = 2.0\nn4 = 432.0\nt0 = n0**min(n1, 5)\nt1 = n2**min(n3, 5)\nt2 = t0 * t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "144" + ], + "split": "train" + }, + { + "Input": "find value for x from below equation ? x + 1 = 4", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\n\nanswer = n1 - n0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "find large number from below question the difference of two numbers is 1325 . on dividing the larger number by the smaller , we get 5 as quotient and the 5 as remainder", + "Output Program": [ + "n0 = 1325.0\nn1 = 5.0\nn2 = 5.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nt2 = t0 / t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "1650" + ], + "split": "train" + }, + { + "Input": "if 11 boys meet at a reunion and each boy shakes hands exactly once with each of the others , then what is the total number of handshakes", + "Output Program": [ + "import math\nn0 = 11.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(2.0)))\nt2 = n0 - 2.0\nt3 = math.factorial(min(15, int(t2)))\nt4 = t3 * t1\nanswer = t0 / t4\nprint(answer)" + ], + "Output Answer": [ + "55" + ], + "split": "train" + }, + { + "Input": "workers decided to raise rs . 3 lacs by equal contribution from each . had they contributed rs . 50 eachextra , the contribution would have been rs . 3.50 lacs . how many workers were they ?", + "Output Program": [ + "n0 = 3.0\nn1 = 50.0\nn2 = 3.5\nt0 = n2 - n0\nt1 = t0 * 1000.0\nt2 = t1 * 100.0\nanswer = t2 / n1\nprint(answer)" + ], + "Output Answer": [ + "1000" + ], + "split": "train" + }, + { + "Input": "if 25 % of x is 30 less than 20 % of 1000 , then x is ?", + "Output Program": [ + "n0 = 25.0\nn1 = 30.0\nn2 = 20.0\nn3 = 1000.0\nt0 = n2 / 100.0\nt1 = n0 / 100.0\nt2 = n3 * t0\nt3 = t2 - n1\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "680" + ], + "split": "train" + }, + { + "Input": "a batsman in his 15 th inning makes a score of 75 and their by increasing his average by 3 . what is his average after the 15 th inning ?", + "Output Program": [ + "n0 = 15.0\nn1 = 75.0\nn2 = 3.0\nn3 = 15.0\nt0 = n0 * n2\nt1 = n1 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "a man purchased 3 blankets @ rs . 100 each , 1 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ?", + "Output Program": [ + "n0 = 3.0\nn1 = 100.0\nn2 = 1.0\nn3 = 150.0\nn4 = 150.0\nt0 = n3 * 10.0\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "1050" + ], + "split": "train" + }, + { + "Input": "the tax on a commodity is diminished by 15 % and its consumption increased by 10 % . the effect on revenue is ?", + "Output Program": [ + "n0 = 15.0\nn1 = 10.0\nt0 = n1 / 100.0\nt1 = n0 / 100.0\nt2 = t0 + 1.0\nt3 = 1.0 - t1\nt4 = t2 * t3\nt5 = t4 * 100.0\nanswer = 100.0 - t5\nprint(answer)" + ], + "Output Answer": [ + "6.5" + ], + "split": "train" + }, + { + "Input": "cindy has her eye on a sundress but thinks it is too expensive . it goes on sale for 15 % less than the original price . before cindy can buy the dress , however , the store raises the new price by 25 % . if the dress cost $ 78.2 after it went on sale for 15 % off , what is the difference between the original price and the final price ?", + "Output Program": [ + "n0 = 15.0\nn1 = 25.0\nn2 = 78.2\nn3 = 15.0\nt0 = n1 + 100.0\nt1 = 100.0 - n0\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = n2 / t3\nt5 = n2 * t2\nanswer = t5 - t4\nprint(answer)" + ], + "Output Answer": [ + "5.75" + ], + "split": "train" + }, + { + "Input": "if 20 liters of chemical x are added to 80 liters of a mixture that is 30 % chemical x and 70 % chemical y , then what percentage of the resulting mixture is chemical x ?", + "Output Program": [ + "n0 = 20.0\nn1 = 80.0\nn2 = 30.0\nn3 = 70.0\nt0 = n2 / 100.0\nt1 = n1 * t0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "44" + ], + "split": "train" + }, + { + "Input": "the total car population in a chennai is 900 out of which 500 are made by honda . out of every 100 honda cars , 90 are red in color , but only 60 % of the total car population is red . find the % of non - honda cars that are red", + "Output Program": [ + "n0 = 900.0\nn1 = 500.0\nn2 = 100.0\nn3 = 90.0\nn4 = 60.0\nt0 = 12.0 + 12.0\nt1 = n3 * 1.0\nt2 = t1 + 3.0\nt3 = t2 - t1\nt4 = t3 / 2.0\nanswer = t0 - t4\nprint(answer)" + ], + "Output Answer": [ + "22.5" + ], + "split": "train" + }, + { + "Input": "find the least number of 5 digits which is exactly divisible by 12 , 15 and 18 ?", + "Output Program": [ + "import scipy\nn0 = 5.0\nn1 = 12.0\nn2 = 15.0\nn3 = 18.0\nt0 = scipy.lcm(int(n1), int(n2))\nt1 = 2.0 * 4.0\nt2 = 12.0 * 4.0\nt3 = t1 + t2\nt4 = scipy.lcm(int(n3), int(t0))\nanswer = t3 * t4\nprint(answer)" + ], + "Output Answer": [ + "10080" + ], + "split": "train" + }, + { + "Input": "sandy gets 3 marks for each correct sum and loses 2 marks for each incorrect sum . sandy attempts 30 sums and obtains 65 marks . how many sums did sandy get correct ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 30.0\nn3 = 65.0\nt0 = n0 + n1\nt1 = n1 * n2\nt2 = n3 + t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "the average weight of 4 persons increases by 1.5 kg . if a person weighing 65 kg is replaced by a new person , what could be the weight of the new person ?", + "Output Program": [ + "n0 = 4.0\nn1 = 1.5\nn2 = 65.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "71" + ], + "split": "train" + }, + { + "Input": "the average of 10 numbers is 210 . the average of first 5 numbers is 40 and the average of last 4 numbers is 200 . what is the middle number ?", + "Output Program": [ + "n0 = 10.0\nn1 = 210.0\nn2 = 5.0\nn3 = 40.0\nn4 = 4.0\nn5 = 200.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n4 * n5\nt3 = t0 - t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "1100" + ], + "split": "train" + }, + { + "Input": "the overall age of x and y is 15 year greater than the overall age of y and z . z is how many decades younger that x ?", + "Output Program": [ + "n0 = 15.0\n\nanswer = n0 / 1.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "the average height of 30 students in a class was calculated as 175 cm . it has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 136 cm . what was the actual average height of the students in the class ?", + "Output Program": [ + "n0 = 30.0\nn1 = 175.0\nn2 = 151.0\nn3 = 136.0\nt0 = n0 * n1\nt1 = n2 - n3\nt2 = t0 - t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "174.5" + ], + "split": "train" + }, + { + "Input": "a certain sum of money is divided among a , b and c so that for each rs . a has , b has 65 paisa and c 40 paisa . if c ' s share is rs . 64 , find the sum of money ?", + "Output Program": [ + "n0 = 65.0\nn1 = 40.0\nn2 = 64.0\nt0 = n0 + 100.0\nt1 = n2 / n1\nt2 = n1 + t0\nanswer = t2 * t1\nprint(answer)" + ], + "Output Answer": [ + "328" + ], + "split": "train" + }, + { + "Input": "if x is equal to the sum of the integers from 60 to 80 , inclusive , and y is the number of even integers from 60 to 80 , inclusive , what is the value of x + y ?", + "Output Program": [ + "n0 = 60.0\nn1 = 80.0\nn2 = 60.0\nn3 = 80.0\nt0 = n0 + n1\nt1 = n1 - n0\nt2 = t1 + 1.0\nt3 = t1 / 2.0\nt4 = t0 / 2.0\nt5 = t3 + 1.0\nt6 = t2 * t4\nanswer = t5 + t6\nprint(answer)" + ], + "Output Answer": [ + "1481" + ], + "split": "train" + }, + { + "Input": "a mixture contains alcohol and water in the ratio 2 : 5 . if 10 liters of water is added to the mixture , the ratio becomes 2 : 7 . find the quality of alcohol in the given mixture .", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 10.0\nn3 = 2.0\nn4 = 7.0\n\nanswer = n2 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "in the biology lab of ` ` jefferson ' ' high school there are 5.4 * 10 ^ 6 germs , equally divided among 10800 petri dishes . how many germs live happily in a single dish ?", + "Output Program": [ + "n0 = 5.4\nn1 = 10.0\nn2 = 6.0\nn3 = 10800.0\nt0 = 100.0 * 100.0\nt1 = 2.0 * 4.0\nt2 = t0 * 100.0\nt3 = t1 * 100.0\nt4 = t0 + t3\nt5 = n0 * t2\nanswer = t5 / t4\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "train" + }, + { + "Input": "if x is 11 percent greater than 80 , then x =", + "Output Program": [ + "n0 = 11.0\nn1 = 80.0\nt0 = n0 / 100.0\nt1 = n1 * t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "88.8" + ], + "split": "train" + }, + { + "Input": "8 people decided to split the restaurant bill evenly . if the bill was $ 314.12 dollars , how much money did they 1 cent is the smallest unit ?", + "Output Program": [ + "n0 = 8.0\nn1 = 314.12\nn2 = 1.0\nt0 = 3.0 / 100.0\nanswer = n1 + t0\nprint(answer)" + ], + "Output Answer": [ + "314.15" + ], + "split": "train" + }, + { + "Input": "if the numerator of a fraction be increased by 15 % and its denominator be diminished by 8 % , the value of the fraction is 15 / 16 . find the original fraction .", + "Output Program": [ + "n0 = 15.0\nn1 = 8.0\nn2 = 15.0\nn3 = 16.0\nt0 = n0 + 100.0\nt1 = 100.0 - n1\nt2 = n2 * t1\nt3 = n3 * t0\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.75" + ], + "split": "train" + }, + { + "Input": "at a contest with 2,500 participants , 1 / 2 of the people are aged 10 to 12 . next year , the number of people aged 10 to 12 will increase by 1 / 5 . after this change , what percentage of the total 2,500 people will the 10 - to 12 - year - olds represent ?", + "Output Program": [ + "n0 = 2500.0\nn1 = 1.0\nn2 = 2.0\nn3 = 10.0\nn4 = 12.0\nn5 = 10.0\nn6 = 12.0\nn7 = 1.0\nn8 = 5.0\nn9 = 2500.0\nn10 = 10.0\nn11 = 12.0\nt0 = n1 / n8\nt1 = n0 / n2\nt2 = t0 + n1\nt3 = t2 * t1\nt4 = t3 / n0\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "a large box contains 17 small boxes and each small box contains 26 chocolate bars . how many chocolate bars are in the large box ?", + "Output Program": [ + "n0 = 17.0\nn1 = 26.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "442" + ], + "split": "train" + }, + { + "Input": "a student scored an average of 85 marks in 3 subjects : physics , chemistry and mathematics . if the average marks in physics and mathematics is 90 and that in physics and chemistry is 70 , what are the marks in physics ?", + "Output Program": [ + "n0 = 85.0\nn1 = 3.0\nn2 = 90.0\nn3 = 70.0\nt0 = n2 * 2.0\nt1 = n3 * 2.0\nt2 = n0 * n1\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "65" + ], + "split": "train" + }, + { + "Input": "at a certain college , 40 percent of the total number of students are freshmen . if 50 percent of the fresh - men are enrolled in the school of liberal arts and , of these , 50 percent are psychology majors , what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts ?", + "Output Program": [ + "n0 = 40.0\nn1 = 50.0\nn2 = 50.0\nt0 = n0 * n1\nt1 = t0 / 100.0\nt2 = n2 * t1\nanswer = t2 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "3500 \u2013 ( 1000 \u00f7 20.50 ) is equal to :", + "Output Program": [ + "n0 = 3500.0\nn1 = 1000.0\nn2 = 20.5\nt0 = n1 / n2\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "3451.2195121951218" + ], + "split": "train" + }, + { + "Input": "joan took out a mortgage from hel local bank . each monthly mortgage payment she makes must be triple the amount of the previous month ' s payment . if her first payment is $ 100 , and the total amount she must pay back is $ 12100 , how many months will it take joan to pay back her mortgage ?", + "Output Program": [ + "import math\nn0 = 100.0\nn1 = 12100.0\nt0 = math.log(max(1e-5, 3.0), 2)\nt1 = n1 * 2.0\nt2 = t1 / n0\nt3 = t2 + 1.0\nt4 = math.log(max(1e-5, t3), 2)\nanswer = t4 / t0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "s ( n ) is a n - digit number formed by attaching the first n perfect squares , in order , into one integer . for example , s ( 1 ) = 1 , s ( 2 ) = 14 , s ( 3 ) = 149 , s ( 4 ) = 14916 , s ( 5 ) = 1491625 , etc . how many digits q are in s ( 99 ) ?", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 2.0\nn3 = 14.0\nn4 = 3.0\nn5 = 149.0\nn6 = 4.0\nn7 = 14916.0\nn8 = 5.0\nn9 = 1491625.0\nn10 = 99.0\nt0 = 4.0 + 60.0\nt1 = n0 * n4\nt2 = n2 * n4\nt3 = n6 + t0\nt4 = n2 * t2\nt5 = t1 + t4\nt6 = n6 * t3\nt7 = t3 + t6\nanswer = t7 + t5\nprint(answer)" + ], + "Output Answer": [ + "355" + ], + "split": "train" + }, + { + "Input": "the average height of 35 boys in a class was calculated as 183 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ) . ?", + "Output Program": [ + "import math\nn0 = 35.0\nn1 = 183.0\nn2 = 166.0\nn3 = 106.0\nt0 = n0 * n1\nt1 = t0 - n2\nt2 = n3 + t1\nt3 = t2 / n0\nanswer = math.floor(t3)\nprint(answer)" + ], + "Output Answer": [ + "181" + ], + "split": "train" + }, + { + "Input": "65 + 5 * 12 / ( 180 / 3 ) = ?", + "Output Program": [ + "n0 = 65.0\nn1 = 5.0\nn2 = 12.0\nn3 = 180.0\nn4 = 3.0\nt0 = n3 / n4\nt1 = n1 * n2\nt2 = t1 / t0\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "66" + ], + "split": "train" + }, + { + "Input": "in the county of veenapaniville , there are a total of 50 high schools , of 3 kinds : 25 public schools , 16 parochial schools , and 9 private independent schools . these 50 schools are divided between 3 districts : a , b , and c . district a has 18 high schools total . district b has 17 high schools total , and only two of those are private independent schools . if district c has an equal number of each of the 3 kinds of schools , how many private independent schools are there in district a ?", + "Output Program": [ + "n0 = 50.0\nn1 = 3.0\nn2 = 25.0\nn3 = 16.0\nn4 = 9.0\nn5 = 50.0\nn6 = 3.0\nn7 = 18.0\nn8 = 17.0\nn9 = 3.0\nt0 = n7 + n8\nt1 = n0 - t0\nt2 = t1 / n1\nt3 = t2 + 2.0\nanswer = n4 - t3\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "the average weight of 19 students is 15 kg . by the admission of a new student the average weight is reduced to 14.4 kg . the weight of the new student is ?", + "Output Program": [ + "n0 = 19.0\nn1 = 15.0\nn2 = 14.4\nt0 = n0 + 1.0\nt1 = n0 * n1\nt2 = n2 * t0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "a new model car was not selling as expected and the base retail price was lowered by 5 % to increase sales . a customer haggled on the price and negotiated a final agreed price of 90 % of the retail price . how much did the customer save off the retail price ?", + "Output Program": [ + "n0 = 5.0\nn1 = 90.0\nt0 = n1 / 100.0\nt1 = 100.0 - n0\nt2 = t1 / 100.0\nt3 = t0 * t2\nt4 = t3 * 100.0\nanswer = 100.0 - t4\nprint(answer)" + ], + "Output Answer": [ + "14.5" + ], + "split": "train" + }, + { + "Input": "a welder received an order to make a 1 million liter cube - shaped tank . if he has only 4 x 2 meter sheets of metal that can be cut , how many metal sheets will be required for this order r ? ( 1 cubic meter = 1000 liters )", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 2.0\nn3 = 1.0\nn4 = 1000.0\nt0 = 2.0 + 4.0\nt1 = 1.0 / 3.0\nt2 = 2.0 * 4.0\nt3 = n4**min(t1, 5)\nt4 = t3**min(2.0, 5)\nt5 = t0 * t4\nanswer = t5 / t2\nprint(answer)" + ], + "Output Answer": [ + "74.99999999999997" + ], + "split": "train" + }, + { + "Input": "in a renowned city , the average birth rate is 7 people every two seconds and the death rate is 1 people every two seconds . estimate the size of the population net increase that occurs in one day .", + "Output Program": [ + "n0 = 7.0\nn1 = 1.0\nt0 = n0 - n1\nt1 = t0 * 3600.0\nanswer = t1 * 12.0\nprint(answer)" + ], + "Output Answer": [ + "259200" + ], + "split": "train" + }, + { + "Input": "how much time does a train 150 metres long running at 90 km / hr take to pass a pole ?", + "Output Program": [ + "n0 = 150.0\nn1 = 90.0\nt0 = n0 / 1000.0\nt1 = t0 / n1\nanswer = t1 * 3600.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 130 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?", + "Output Program": [ + "n0 = 130.0\n\nanswer = n0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "260" + ], + "split": "train" + }, + { + "Input": "working alone , printers x , y , and z can do a certain printing job , consisting of a large number of pages , in 16 , 12 , and 8 hours , respectively . what is the ratio of the time it takes printer x to do the job , working alone at its rate , to the time it takes printers y and z to do the job , working together at their individual rates ?", + "Output Program": [ + "n0 = 16.0\nn1 = 12.0\nn2 = 8.0\nt0 = 1.0 / n1\nt1 = 1.0 / n2\nt2 = t0 + t1\nt3 = 1.0 / t2\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "3.333333333333333" + ], + "split": "train" + }, + { + "Input": "what is the unit digit in 15 ^ 100 ?", + "Output Program": [ + "n0 = 15.0\nn1 = 100.0\nt0 = n0**min(2.0, 5)\nanswer = t0 % 10.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "a , b and c rents a pasture for rs . 435 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should b pay ?", + "Output Program": [ + "n0 = 435.0\nn1 = 12.0\nn2 = 8.0\nn3 = 16.0\nn4 = 9.0\nn5 = 18.0\nn6 = 6.0\nt0 = n1 * n2\nt1 = n3 * n4\nt2 = n5 * n6\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n0 / t4\nanswer = t5 * t1\nprint(answer)" + ], + "Output Answer": [ + "180" + ], + "split": "train" + }, + { + "Input": "a car traveled 80 % of the way from town x to town y at an average speed of 80 mph . the car traveled at an average speed of v mph for the remaining part of the trip . the average speed for the entire trip was 50 mph . what is v in mph ?", + "Output Program": [ + "n0 = 80.0\nn1 = 80.0\nn2 = 50.0\nt0 = n0 / n0\nt1 = 100.0 - n0\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "a guy was asked to specify his age in years . he said , \u201c take my age 8 years hence , multiply it by 8 and subtract 8 times of my age 8 years ago and get the half of the result and you will know my age . \u201d what was the age of that guy ?", + "Output Program": [ + "n0 = 8.0\nn1 = 8.0\nn2 = 8.0\nn3 = 8.0\n\nanswer = n0 * n0\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "train" + }, + { + "Input": "the average marks of a class of 30 students is 40 and that of another class of 50 students is 90 . find the average marks of all the students ?", + "Output Program": [ + "n0 = 30.0\nn1 = 40.0\nn2 = 50.0\nn3 = 90.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "71.25" + ], + "split": "train" + }, + { + "Input": "in the storage room of a certain bakery , the ratio of sugar to flour is 3 to 8 , and the ratio of flour to baking soda is 10 to 1 . if there were 60 more pounds of baking soda in the room , the ratio of flour to baking soda would be 8 to 1 . how many pounds of sugar are stored in the room ?", + "Output Program": [ + "n0 = 3.0\nn1 = 8.0\nn2 = 10.0\nn3 = 1.0\nn4 = 60.0\nn5 = 8.0\nn6 = 1.0\nt0 = n0 / n1\nt1 = n4 * n5\nt2 = n2 - n5\nt3 = t1 / t2\nt4 = n2 * t3\nanswer = t0 * t4\nprint(answer)" + ], + "Output Answer": [ + "900" + ], + "split": "train" + }, + { + "Input": "jacob is 18 years old . he is 2 times as old as his brother . how old will jacob be when he is twice as old ?", + "Output Program": [ + "n0 = 18.0\nn1 = 2.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "the average monthly salary of 20 employees in an organisation is rs . 1500 . if the manager ' s salary is added , then the average salary increases by rs . 600 . what is the manager ' s monthly salary ?", + "Output Program": [ + "n0 = 20.0\nn1 = 1500.0\nn2 = 600.0\nt0 = n1 + n2\nt1 = n0 + 1.0\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "14100" + ], + "split": "train" + }, + { + "Input": "for a recipe for triple berry pie calls for cups of strawberries , raspberries , and blueberries in a ratio of 1 : 2 : 3 . how many total cups of fruit will you need to make the pie ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 3.0\nt0 = n0 + n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "the batting average of a particular batsman is 58 runs in 46 innings . if the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs , find his highest score .", + "Output Program": [ + "n0 = 58.0\nn1 = 46.0\nn2 = 150.0\nn3 = 58.0\nt0 = n0 * n1\nt1 = n1 - 2.0\nt2 = n3 * t1\nt3 = t0 - t2\nt4 = n2 + t3\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "133" + ], + "split": "train" + }, + { + "Input": "the average monthly income of p and q is rs . 5050 . the average monthly income of q and r is 6250 and the average monthly income of p and r is rs . 5200 . the monthly income of p is ?", + "Output Program": [ + "n0 = 5050.0\nn1 = 6250.0\nn2 = 5200.0\nt0 = n0 + n2\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "4000" + ], + "split": "train" + }, + { + "Input": "the salary of a , b , c , d , e is rs . 10000 , rs . 5000 , rs . 11000 , rs . 7000 , rs . 9000 per month respectively , then the average salary of a , b , c , d , and e per month is", + "Output Program": [ + "n0 = 10000.0\nn1 = 5000.0\nn2 = 11000.0\nn3 = 7000.0\nn4 = 9000.0\nt0 = n0 + n1\nt1 = 1.0 + 4.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "8400" + ], + "split": "train" + }, + { + "Input": "find the value of m 72519 x 9999 = m ?", + "Output Program": [ + "n0 = 72519.0\nn1 = 9999.0\nt0 = n1 - 4.0\nanswer = t0 * n0\nprint(answer)" + ], + "Output Answer": [ + "724827405" + ], + "split": "train" + }, + { + "Input": "a sports retailer ordered white and yellow tennis balls in equal number but the dispatch clerk of the tennis ball company erred and dispatched 20 extra yellow balls and making ratio of white balls to yellow balls 8 / 13 . how many tennis balls did the retailer order originally .", + "Output Program": [ + "n0 = 20.0\nn1 = 8.0\nn2 = 13.0\nt0 = n0 * n1\nt1 = n2 - n1\nt2 = t0 / t1\nanswer = t2 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "train" + }, + { + "Input": "the youngest of 4 children has siblings who are 3 , 6 , and 7 years older than she is . if the average ( arithmetic mean ) age of the 4 siblings is 30 , what is the age of the youngest sibling ?", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 6.0\nn3 = 7.0\nn4 = 4.0\nn5 = 30.0\nt0 = n0 + n2\nt1 = n0 * n5\nt2 = n3 + t0\nt3 = t1 - t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "25.75" + ], + "split": "train" + }, + { + "Input": "when greenville state university decided to move its fine arts collection to a new library , it had to package the collection in 20 - inch by 20 - inch by 12 - inch boxes . if the university pays $ 0.40 for every box , and if the university needs 2.16 million cubic inches to package the collection , what is the minimum amount the university must spend on boxes ?", + "Output Program": [ + "n0 = 20.0\nn1 = 20.0\nn2 = 12.0\nn3 = 0.4\nn4 = 2.16\nt0 = 1000.0 * 1000.0\nt1 = n0 * n0\nt2 = n4 * t0\nt3 = n2 * t1\nt4 = t2 / t3\nanswer = n3 * t4\nprint(answer)" + ], + "Output Answer": [ + "180" + ], + "split": "train" + }, + { + "Input": "3 friends a , b , c went for week end party to mcdonald \u2019 s restaurant and there they measure there weights in some order in 7 rounds . a , b , c , ab , bc , ac , abc . final round measure is 160 kg then find the average weight of all the 7 rounds ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 160.0\nn3 = 7.0\nt0 = 1.0 + 3.0\nt1 = n2 * t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "91.42857142857143" + ], + "split": "train" + }, + { + "Input": "if p # q denotes the least common multiple of p and q , then t = ( ( 12 # 16 ) # ( 18 # 24 ) ) = ?", + "Output Program": [ + "n0 = 12.0\nn1 = 16.0\nn2 = 18.0\nn3 = 24.0\nt0 = n2 * n3\nt1 = n0 * n1\nt2 = t0 - t1\nt3 = t2 / 2.0\nanswer = n3 + t3\nprint(answer)" + ], + "Output Answer": [ + "144" + ], + "split": "train" + }, + { + "Input": "7 people went to a restaurant for dinner . 6 of them spent $ 11 each on their meals and the seventh person spent $ 6 more than the average expenditure of all 7 people . what was the total amount of money that the 7 people spent ?", + "Output Program": [ + "n0 = 7.0\nn1 = 6.0\nn2 = 11.0\nn3 = 6.0\nn4 = 7.0\nn5 = 7.0\nt0 = n1 * n2\nt1 = n0 - 1.0\nt2 = n1 + t0\nt3 = t2 / t1\nt4 = n1 + t3\nanswer = t4 + t0\nprint(answer)" + ], + "Output Answer": [ + "84" + ], + "split": "train" + }, + { + "Input": "a batsman makes a score of 100 runs in the 11 th inning and thus increases his average by 5 . find his average after 11 th inning .", + "Output Program": [ + "n0 = 100.0\nn1 = 11.0\nn2 = 5.0\nn3 = 11.0\nt0 = n1 * n2\nt1 = n0 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "sam wrote 7 letters on tuesday and 3 letters on wednesday . how many letters did he write on average per day ?", + "Output Program": [ + "n0 = 7.0\nn1 = 3.0\nt0 = n0 + n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "the mean of 20 observations was 36 . it was found later that an observation 25 was wrongly taken as 40 . the corrected new mean is", + "Output Program": [ + "n0 = 20.0\nn1 = 36.0\nn2 = 25.0\nn3 = 40.0\nt0 = n0 * n1\nt1 = n0 - 2.0\nt2 = t1 - n3\nt3 = t0 + t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "34.9" + ], + "split": "train" + }, + { + "Input": "he average weight of 6 persons increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 6.0\nn1 = 2.5\nn2 = 65.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "a company decreased the price of its main product by 30 % . subsequently , the number of units sold increased such that the total revenue remained unchanged . what was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product ?", + "Output Program": [ + "n0 = 30.0\n\nanswer = 100.0 / n0\nprint(answer)" + ], + "Output Answer": [ + "3.3333333333333335" + ], + "split": "train" + }, + { + "Input": "if 10 gallons of grape juice are added to 40 gallons of a mixture , which contains 10 percent grape juice then what percent of the resulting mixture is grape juice ?", + "Output Program": [ + "n0 = 10.0\nn1 = 40.0\nn2 = 10.0\nt0 = n0 + n1\nt1 = n2 / 100.0\nt2 = n1 * t1\nt3 = n0 + t2\nt4 = t3 / t0\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "28.000000000000004" + ], + "split": "train" + }, + { + "Input": "what is the average ( arithmetic mean ) of all multiples of 10 from 10 to 300 inclusive ?", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 300.0\nt0 = n0 + n2\nt1 = n2 - n0\nt2 = t1 / n0\nt3 = t2 + 1.0\nt4 = t0 * t3\nt5 = t4 / 2.0\nanswer = t5 / t3\nprint(answer)" + ], + "Output Answer": [ + "155" + ], + "split": "train" + }, + { + "Input": "if 0.75 : x : : 5 : 8 , then x is equal to", + "Output Program": [ + "n0 = 0.75\nn1 = 5.0\nn2 = 8.0\nt0 = n0 * n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "1.2" + ], + "split": "train" + }, + { + "Input": "the ratio of two no . addition and subtraction be 4 : 3 . the what is the ratio of numbers ?", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\n\nanswer = n0 + n1\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "in a can , there is a mixture of milk and water in the ratio 1 : 5 . if it is filled with an additional 2 litres of milk the can would be full and ratio of milk and water would become 2.00001 : 5.00001 . find the capacity of the can ?", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 2.0\nn3 = 2.00001\nn4 = 5.00001\nt0 = n3 / n4\nt1 = n1 * t0\nt2 = t1 - n0\nt3 = n2 / t2\nt4 = n1 * t3\nt5 = t3 + t4\nanswer = n2 + t5\nprint(answer)" + ], + "Output Answer": [ + "13.999928000575995" + ], + "split": "train" + }, + { + "Input": "45 x ? = 35 % of 900", + "Output Program": [ + "n0 = 45.0\nn1 = 35.0\nn2 = 900.0\nt0 = n1 / 100.0\nt1 = n2 * t0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "if the average of 54 , 55 , 57 , 58 , 59 , 62 , 62 , 63 , 65 and x is 60 , what is the value of x ?", + "Output Program": [ + "n0 = 54.0\nn1 = 55.0\nn2 = 57.0\nn3 = 58.0\nn4 = 59.0\nn5 = 62.0\nn6 = 62.0\nn7 = 63.0\nn8 = 65.0\nn9 = 60.0\nt0 = n0 + n1\nt1 = n9 * 10.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nt5 = n5 + t4\nt6 = n5 + t5\nt7 = n7 + t6\nt8 = n8 + t7\nanswer = t1 - t8\nprint(answer)" + ], + "Output Answer": [ + "65" + ], + "split": "train" + }, + { + "Input": "a ranch has both horses and ponies . exactly 5 / 6 of the ponies have horseshoes , and exactly 2 / 3 of the ponies with horseshoes are from iceland . if there are 4 more horses than ponies , what is the minimum possible combined number of horses and ponies on the ranch ?", + "Output Program": [ + "import scipy\nn0 = 5.0\nn1 = 6.0\nn2 = 2.0\nn3 = 3.0\nn4 = 4.0\nt0 = n1 / n2\nt1 = n3 * t0\nt2 = scipy.lcm(int(n1), int(t1))\nt3 = n4 + t2\nanswer = t3 + t2\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "what least number must be subtracted from 427398 so that remaining no . is divisible by 14", + "Output Program": [ + "import math\nn0 = 427398.0\nn1 = 14.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "the average monthly salary of laborers and supervisors in a factory is rs . 1250 per month ; where as the average monthly salary of 6 supervisors is rs . 2450 . if the average monthly salary of the laborers is rs . 950 find the number of laborers ?", + "Output Program": [ + "n0 = 1250.0\nn1 = 6.0\nn2 = 2450.0\nn3 = 950.0\nt0 = n1 * n2\nt1 = n0 * n1\nt2 = n0 - n3\nt3 = t0 - t1\nt4 = t3 / t2\nt5 = t4 * 2.0\nt6 = t5 - 4.0\nanswer = t6 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "the output of a factory is increased by 10 % to keep up with rising demand . to handle the holiday rush , this new output is increased by 40 % . by approximately what percent would the output of the factory now have to be decreased in order to restore the original output ?", + "Output Program": [ + "n0 = 10.0\nn1 = 40.0\nt0 = n0 + 100.0\nt1 = n1 + 100.0\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = t2 * t3\nt5 = t4 - 1.0\nt6 = t5 / t4\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "35.064935064935064" + ], + "split": "train" + }, + { + "Input": "balls of equal size are arranged in rows to form an equilateral triangle . the top most row consists of one ball , the 2 nd row of two balls and so on . if 424 balls are added , then all the balls can be arranged in the shape of square and each of the sides of the square contain 8 balls less than the each side of the triangle did . how many balls made up the triangle ?", + "Output Program": [ + "n0 = 2.0\nn1 = 424.0\nn2 = 8.0\nt0 = 100.0 * 4.0\nt1 = n1 - t0\nt2 = n0 * t1\nt3 = t2 + 1.0\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "1176" + ], + "split": "train" + }, + { + "Input": "laura took out a charge account at the general store and agreed to pay 5 % simple annual interest . if she charges $ 35 on her account in january , how much will she owe a year later , assuming she does not make any additional charges or payments ?", + "Output Program": [ + "n0 = 5.0\nn1 = 35.0\nt0 = n0 / 100.0\nt1 = n1 * t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "36.75" + ], + "split": "train" + }, + { + "Input": "a batsman makes a score of 90 runs in the 17 th inning and thus increases his averages by 3 . what is his average after 17 th inning ?", + "Output Program": [ + "n0 = 90.0\nn1 = 17.0\nn2 = 3.0\nn3 = 17.0\nt0 = n1 * n2\nt1 = n0 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "the captain of a cricket team of 11 members is 25 years old and the wicket keeper is 3 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ?", + "Output Program": [ + "n0 = 11.0\nn1 = 25.0\nn2 = 3.0\nt0 = n1 + n2\nt1 = n2 * n2\nt2 = n1 + t0\nt3 = t2 - t1\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.90 per glass on the first day , what was the price per glass on the second day ?", + "Output Program": [ + "n0 = 0.9\nt0 = 1.0 + 1.0\nt1 = 1.0 + 2.0\nt2 = n0 * t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.6" + ], + "split": "train" + }, + { + "Input": "if a person walks at 25 km / hr instead of 10 km / hr , he would have walked 31 km more . the actual distance traveled by him is ?", + "Output Program": [ + "n0 = 25.0\nn1 = 10.0\nn2 = 31.0\nt0 = n0 - n1\nt1 = n2 / t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "20.666666666666668" + ], + "split": "train" + }, + { + "Input": "if 90 percent of 600 is 50 percent of x , then x = ?", + "Output Program": [ + "n0 = 90.0\nn1 = 600.0\nn2 = 50.0\nt0 = n0 * n1\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "1080" + ], + "split": "train" + }, + { + "Input": "a seller of used cars has 15 cars to sell and each of his clients selected 3 cars that he liked most . if each car was selected exactly thrice , how many clients visited the garage ?", + "Output Program": [ + "n0 = 15.0\nn1 = 3.0\nt0 = n0 / n1\nanswer = t0 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "25.25 / 3000 is equal to :", + "Output Program": [ + "n0 = 25.25\nn1 = 3000.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.008416666666666666" + ], + "split": "train" + }, + { + "Input": "how many even number in the range between 10 to 170 inclusive are not divisible by 3", + "Output Program": [ + "n0 = 10.0\nn1 = 170.0\nn2 = 3.0\nt0 = n2 * 4.0\nt1 = n1 - n0\nt2 = n1 - 2.0\nt3 = t1 - 2.0\nt4 = t2 - t0\nt5 = t3 / 2.0\nt6 = t4 - n2\nt7 = t6 - n2\nt8 = t7 / n2\nt9 = t8 / 2.0\nanswer = t5 - t9\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "train" + }, + { + "Input": "when positive integer x is divided by positive integer y , the remainder is 8 . if x / y = 96.16 , what is the value of y ?", + "Output Program": [ + "import math\nn0 = 8.0\nn1 = 96.16\nt0 = math.floor(n1)\nt1 = n1 - t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "50.000000000001066" + ], + "split": "train" + }, + { + "Input": "the mean of 30 values was 140 . it was detected on rechecking that one value 145 was wrongly copied as 135 for the computation of the mean . find the correct mean .", + "Output Program": [ + "n0 = 30.0\nn1 = 140.0\nn2 = 145.0\nn3 = 135.0\nt0 = n0 * n1\nt1 = n2 - n3\nt2 = t0 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "140.33333333333334" + ], + "split": "train" + }, + { + "Input": "a large box contains 21 small boxes and each small box contains 25 chocolate bars . how many chocolate bars are in the large box ?", + "Output Program": [ + "n0 = 21.0\nn1 = 25.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "525" + ], + "split": "train" + }, + { + "Input": "a man is 26 years older than his son . in two years , his age will be twice the age of his son . what is the present age of his son ?", + "Output Program": [ + "n0 = 26.0\nt0 = 2.0 * 2.0\nt1 = 2.0 - 1.0\nt2 = t0 - 2.0\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "of all the students in a certain dormitory , 1 / 2 are first - year students and the rest are second - year students . if 4 / 5 of the first - year students have not declared a major and if the fraction of second - year students who have declared a major is 1 / 2 times the fraction of first - year students who have declared a major , what fraction of all the students in the dormitory are second - year students who have not declared a major ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 4.0\nn3 = 5.0\nn4 = 1.0\nn5 = 2.0\nt0 = n0 / n1\nt1 = n5 * 10.0\nt2 = n0 / t1\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "0.45" + ], + "split": "train" + }, + { + "Input": "a computer is programmed to multiply consecutive even integers 2 * 4 * 6 * 8 * \u2026 * n until the product is divisible by 1419 , what is the value of n ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 6.0\nn3 = 8.0\nn4 = 1419.0\nt0 = 1.0 + 10.0\nt1 = n4 / t0\nt2 = t1 / 3.0\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "86" + ], + "split": "train" + }, + { + "Input": "if f ( x ) = 2 x ^ 2 + y , and f ( 2 ) = 50 , what is the value of f ( 5 ) ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 2.0\nn3 = 50.0\nn4 = 5.0\nt0 = n4**min(n0, 5)\nt1 = n0**min(n0, 5)\nt2 = n0 * t0\nt3 = n0 * t1\nt4 = n3 - t3\nanswer = t2 + t4\nprint(answer)" + ], + "Output Answer": [ + "92" + ], + "split": "train" + }, + { + "Input": "a man has an investment of $ 3000 which yields a fixed 305 for every $ 500 invested . if the man takes out $ 12.6 for every $ 500 how long will it take for him to double his investment assuming no compounding of interest .", + "Output Program": [ + "n0 = 3000.0\nn1 = 305.0\nn2 = 500.0\nn3 = 12.6\nn4 = 500.0\nt0 = n0 / n1\nt1 = t0 * 3.0\nt2 = t1 + 3.0\nt3 = t2 + 1.0\nanswer = t3 + 4.0\nprint(answer)" + ], + "Output Answer": [ + "37.50819672131148" + ], + "split": "train" + }, + { + "Input": "2 x + y = 13 | y | < = 13 for how many ordered pairs ( x , y ) that are solutions of the system above are x and y both integers ?", + "Output Program": [ + "n0 = 2.0\nn1 = 13.0\nn2 = 13.0\nt0 = n1 + n1\nt1 = t0 / 2.0\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "mary decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month . if mary ' s savings by the end of the year from these monthly savings were 7 times the amount she spent per month , what should be the fraction of her salary that she spent each month ?", + "Output Program": [ + "n0 = 7.0\nt0 = 12.0 / n0\nt1 = t0 + 1.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.631578947368421" + ], + "split": "train" + }, + { + "Input": "9 men went to a hotel . 8 of them spent 3 each over their meals and the ninth spent 5 more than the average expenditure of all the 9 . the total money spent by all of them was", + "Output Program": [ + "n0 = 9.0\nn1 = 8.0\nn2 = 3.0\nn3 = 5.0\nn4 = 9.0\nt0 = n1 * n2\nt1 = n3 + t0\nt2 = t1 / n1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "32.625" + ], + "split": "train" + }, + { + "Input": "when a certain tree was first planted , it was 4 feet tall , and the height of the tree increased by a constant amount each year for the next 6 years . at the end of the 6 th year , the tree was 1 / 4 taller than it was at the end of the 4 th year . by how many feet did the height of the tree increase each year ?", + "Output Program": [ + "n0 = 4.0\nn1 = 6.0\nn2 = 6.0\nn3 = 1.0\nn4 = 4.0\nn5 = 4.0\nt0 = n1 - n0\nt1 = n4 * t0\nt2 = t1 - n0\nanswer = n0 / t2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "find the value of 72519 x 9999 = m .", + "Output Program": [ + "n0 = 72519.0\nn1 = 9999.0\nt0 = n1 - 4.0\nanswer = t0 * n0\nprint(answer)" + ], + "Output Answer": [ + "724827405" + ], + "split": "train" + }, + { + "Input": "one - third of rahul ' s savings in national savings certificate is equal to one - half of his savings in public provident fund . if he has rs . 1 , 80,000 as total savings , how much has he saved in public provident fund ?", + "Output Program": [ + "n0 = 1.0\nn1 = 80000.0\nt0 = 2.0 + 3.0\nt1 = 2.0 * 3.0\nt2 = 10.0**min(4.0, 5)\nt3 = t2 * 10.0\nt4 = n1 + t3\nt5 = t4 / 2.0\nt6 = t5 * t1\nt7 = t6 / t0\nanswer = t4 - t7\nprint(answer)" + ], + "Output Answer": [ + "72000" + ], + "split": "train" + }, + { + "Input": "in 10 years , a will be twice as old 5 as b was 10 years ago . if a is now 11 years older than b , the present age of b is", + "Output Program": [ + "n0 = 10.0\nn1 = 5.0\nn2 = 10.0\nn3 = 11.0\nt0 = n0 + n3\nt1 = n0 * 2.0\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "41" + ], + "split": "train" + }, + { + "Input": "the average of first 16 even numbers is ?", + "Output Program": [ + "n0 = 16.0\n\nanswer = n0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "if 5 a + 7 b = g , where a and b are positive integers , what is the largest possible value of g for which exactly one pair of integers ( a , b ) makes the equation true ?", + "Output Program": [ + "n0 = 5.0\nn1 = 7.0\nt0 = n0 * n1\nanswer = t0 + t0\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "train" + }, + { + "Input": "0.009 / x = 0.01 . find the value of x", + "Output Program": [ + "n0 = 0.009\nn1 = 0.01\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.8999999999999999" + ], + "split": "train" + }, + { + "Input": "if the mean of numbers 28 , x , 70 , 88 and 104 is 67 , what is the mean of 50 , 62 , 97 , 124 and x ?", + "Output Program": [ + "n0 = 28.0\nn1 = 70.0\nn2 = 88.0\nn3 = 104.0\nn4 = 67.0\nn5 = 50.0\nn6 = 62.0\nn7 = 97.0\nn8 = 124.0\nt0 = 1.0 + 4.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n4 * t0\nt4 = n3 + t2\nt5 = t3 - t4\nt6 = n5 + t5\nt7 = n6 + t6\nt8 = n7 + t7\nt9 = n8 + t8\nanswer = t9 / t0\nprint(answer)" + ], + "Output Answer": [ + "75.6" + ], + "split": "train" + }, + { + "Input": "total dinning bill for 5 people was $ 211.00 . if they add 15 % tip and divided the bill evenly , approximate . what was each persons find share", + "Output Program": [ + "n0 = 5.0\nn1 = 211.0\nn2 = 15.0\nt0 = n1 * n2\nt1 = t0 / 100.0\nt2 = n1 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "48.53" + ], + "split": "train" + }, + { + "Input": "the positive numbers w , x , y , and z are such that x is 20 percent greater than y , y is 20 percent greater than z , and w is 20 percent less than x . what percent greater than z is w ?", + "Output Program": [ + "n0 = 20.0\nn1 = 20.0\nn2 = 20.0\nt0 = n0 + 100.0\nt1 = 100.0 - n0\nt2 = t1 / 100.0\nt3 = t0 / 100.0\nt4 = t3 * t3\nt5 = t2 * t4\nt6 = t5 - 1.0\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "15.199999999999992" + ], + "split": "train" + }, + { + "Input": "if t = 5 / 9 * ( k - 32 ) , and if t = 20 , then what is the value of k ?", + "Output Program": [ + "n0 = 5.0\nn1 = 9.0\nn2 = 32.0\nn3 = 20.0\nt0 = n1 * n3\nt1 = t0 / n0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "68" + ], + "split": "train" + }, + { + "Input": "how many even integers n , such that 20 < = n < = 240 are of the form 3 k + 4 , where k is any natural number ?", + "Output Program": [ + "n0 = 20.0\nn1 = 240.0\nn2 = 3.0\nn3 = 4.0\nt0 = n0 + 2.0\nt1 = 2.0 + n3\nt2 = n1 - 2.0\nt3 = t2 - t0\nt4 = t3 / t1\nanswer = t4 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "37" + ], + "split": "train" + }, + { + "Input": "a train ride from two p to town q costs $ 2.35 more than does a bus ride from town p to town q . together , the cost of one train ride and one bus ride is $ 9.85 . what is the cost of a bus ride from town p to town q ?", + "Output Program": [ + "n0 = 2.35\nn1 = 9.85\nt0 = n1 - n0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "3.75" + ], + "split": "train" + }, + { + "Input": "in a can , there is a mixture of milk and water in the ratio 5 : 3 . if the can is filled with an additional 8 liters of milk , the can would be full and the ratio of milk and water would become 2 : 1 . find the capacity of the can ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nn2 = 8.0\nn3 = 2.0\nn4 = 1.0\nt0 = n2 * n4\nt1 = n1 * n3\nt2 = n0 * n4\nt3 = t1 - t2\nt4 = t0 / t3\nt5 = n0 * t4\nt6 = n1 * t4\nt7 = n2 + t5\nanswer = t7 + t6\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "train" + }, + { + "Input": "an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 16 - meter platform and caught it after it had traveled 46 meters . how many times did the ball bounce ?", + "Output Program": [ + "n0 = 16.0\nn1 = 46.0\nt0 = n0 / 2.0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "( 786 \u00d7 74 ) \u00f7 ? = 1938.8", + "Output Program": [ + "n0 = 786.0\nn1 = 74.0\nn2 = 1938.8\nt0 = n0 * n1\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "the average salary per head of the entire staff of an office including the officers and clerks is rs . 90 . the average salary of officers is rs . 600 and that of the clerks is rs . 84 . if the number of officers is 2 , find the number of officers in the office ?", + "Output Program": [ + "n0 = 90.0\nn1 = 600.0\nn2 = 84.0\nn3 = 2.0\nt0 = 3.0 + 3.0\nt1 = n2 + t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "the average salary of a person for the months of january , february , march and april is rs . 8000 and that for the months february , march , april and may is rs . 8700 . if his salary for the month of may is rs . 6500 , find his salary for the month of january ?", + "Output Program": [ + "n0 = 8000.0\nn1 = 8700.0\nn2 = 6500.0\nt0 = n0 * 4.0\nt1 = n1 * 4.0\nt2 = t1 - n2\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "3700" + ], + "split": "train" + }, + { + "Input": "if a jogger jogs 16 km / hr instead of 12 km / hr , he would have jogged 10 km more . the actual distance he jogged is", + "Output Program": [ + "n0 = 16.0\nn1 = 12.0\nn2 = 10.0\nt0 = n0 - n1\nt1 = n2 / t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "when a certain number x is divided by 84 , the remainder is 25 . what is the remainder when x is divided by 14 ?", + "Output Program": [ + "n0 = 84.0\nn1 = 25.0\nn2 = 14.0\n\nanswer = n1 % n2\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "marketing executives for a certain chewing gum company projected a 20 percent increase in revenue this year over that of last year , but revenue this year actually decreased by 25 % . what percent of the projected revenue was the actual revenue ?", + "Output Program": [ + "n0 = 20.0\nn1 = 25.0\nt0 = n0 + 100.0\nt1 = 100.0 - n1\nt2 = t1 / t0\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "62.5" + ], + "split": "train" + }, + { + "Input": "country x imported approximately $ 1.44 billion of goods in 1996 . if country x imported $ 360 million of goods in the first two months of 1997 and continued to import goods at the same rate for the rest of the year , by how much would country xs 1997 imports exceed those of 1996 ?", + "Output Program": [ + "n0 = 1.44\nn1 = 1996.0\nn2 = 360.0\nn3 = 1997.0\nn4 = 1997.0\nn5 = 1996.0\nt0 = 12.0 / 2.0\nt1 = n0 * 1000.0\nt2 = n2 * t0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "720" + ], + "split": "train" + }, + { + "Input": "if the arithmetic mean of p and q is 10 and the arithmetic mean of q and r is 27 , what is the value of r - p ?", + "Output Program": [ + "n0 = 10.0\nn1 = 27.0\nt0 = n1 * 2.0\nt1 = n0 * 2.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "34" + ], + "split": "train" + }, + { + "Input": "for any integer k > 1 , the term \u201c length of an integer \u201d refers to the number of positive prime factors , not necessarily distinct , whose product is equal to k . for example , if k = 24 , the length of k is equal to 4 , since 24 = 2 \u00d7 2 \u00d7 2 \u00d7 3 . if x and y are positive integers such that x > 1 , y > 1 , and x + 3 y < 960 , what is the maximum possible sum of the length of x and the length of y ?", + "Output Program": [ + "n0 = 1.0\nn1 = 24.0\nn2 = 4.0\nn3 = 24.0\nn4 = 2.0\nn5 = 2.0\nn6 = 2.0\nn7 = 3.0\nn8 = 1.0\nn9 = 1.0\nn10 = 3.0\nn11 = 960.0\nt0 = n2 + n7\nt1 = n2 + n2\nt2 = n0 + t1\nanswer = t0 + t2\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "what is the smallest positive integer k such that the product of 1575 x k is a perfect square ?", + "Output Program": [ + "n0 = 1575.0\n\nanswer = 3.0 + 4.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "a project scheduled to be carried out over a single fiscal year has a budget of $ 12600 , divided into 12 equal monthly allocations . at the end of the sixth month of that fiscal year , the total amount actually spent on the project was $ 6580 . by how much was the project over its budget ?", + "Output Program": [ + "n0 = 12600.0\nn1 = 12.0\nn2 = 6580.0\nt0 = 2.0 + 4.0\nt1 = n0 / n1\nt2 = t0 * t1\nanswer = n2 - t2\nprint(answer)" + ], + "Output Answer": [ + "280" + ], + "split": "train" + }, + { + "Input": "a cement mixture is composed of 3 elements . by weight , 1 / 4 of the mixture is sand , 2 / 5 of the mixture is water , and the remaining 14 pounds of the mixture is gravel . what is the weight of the entire mixture in pounds ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 4.0\nn3 = 2.0\nn4 = 5.0\nn5 = 14.0\nt0 = n1 / n2\nt1 = n3 / n4\nt2 = t0 + t1\nt3 = 1.0 - t2\nanswer = n5 / t3\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "working simultaneously and independently at an identical constant rate , 6 machines of a certain type can produce a total of x units of product p in 10 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 5 x units of product p in 6 days ?", + "Output Program": [ + "n0 = 6.0\nn1 = 10.0\nn2 = 5.0\nn3 = 6.0\nt0 = n1 / n3\nt1 = n0 * n2\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "each year for 4 years , a farmer increased the number of trees in a certain orchard by 1 / 4 of the number of trees in the orchard of the preceding year . if all of the trees thrived and there were 3125 trees in the orchard at the end of 4 year period , how many trees were in the orchard at the beginning of the 4 year period .", + "Output Program": [ + "n0 = 4.0\nn1 = 1.0\nn2 = 4.0\nn3 = 3125.0\nn4 = 4.0\nn5 = 4.0\nt0 = n1 / n0\nt1 = n1 + t0\nt2 = t1**min(n0, 5)\nanswer = n3 / t2\nprint(answer)" + ], + "Output Answer": [ + "1280" + ], + "split": "train" + }, + { + "Input": "there were 35 students in a hostel . if the number of students increases by 7 , the expenses of the mess increase by rs . 42 per day while the average expenditure per head diminishes by re 1 . find the original expenditure of the mess .", + "Output Program": [ + "n0 = 35.0\nn1 = 7.0\nn2 = 42.0\nn3 = 1.0\nt0 = n2 + n2\nt1 = n2 - n0\nt2 = t0 / t1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "420" + ], + "split": "train" + }, + { + "Input": "in a group of donkeys and pigs , the numbers of legs are 16 more than twice the number of heads . the number of donkeys is", + "Output Program": [ + "n0 = 16.0\nt0 = 2.0 + 2.0\nt1 = n0 / t0\nanswer = t1 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a mixture of 125 gallons of wine and water contains 20 % water . how much water must be added to the mixture in order to increase the percentage of water to 25 % of the new mixture ?", + "Output Program": [ + "n0 = 125.0\nn1 = 20.0\nn2 = 25.0\nt0 = n1 / 100.0\nt1 = n0 * t0\nt2 = t1 / 100.0\nt3 = n0 * t2\nt4 = 1.0 - t2\nt5 = t3 - n2\nanswer = t5 / t4\nprint(answer)" + ], + "Output Answer": [ + "8.333333333333334" + ], + "split": "train" + }, + { + "Input": "the average ( arithmetic mean ) of 16 students first quiz scores in a difficult english class is 61.5 . when one student dropped the class , the average of the remaining scores increased to 64.0 . what is the quiz score of the student who dropped the class ?", + "Output Program": [ + "n0 = 16.0\nn1 = 61.5\nn2 = 64.0\nt0 = n0 * n1\nt1 = n0 - 1.0\nt2 = n2 * t1\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "if a person walks at 15 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance traveled by him is :", + "Output Program": [ + "n0 = 15.0\nn1 = 10.0\nn2 = 20.0\nt0 = n0 - n1\nt1 = n2 / t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "nina has exactly enough money to purchase 6 widgets . if the cost of each widget were reduced by $ 1.5 , then nina would have exactly enough money to purchase 8 widgets . how much money does nina have ?", + "Output Program": [ + "n0 = 6.0\nn1 = 1.5\nn2 = 8.0\nt0 = n1 * n2\nt1 = n2 - n0\nt2 = t0 / t1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "there are 40 doors marked with numbers 1 to 40 . there are 40 individuals marked 1 to 40 . an operation on a door is defined as changing the status of the door from open to closed or vice versa . all the doors are closed to start with . one at a time , one randomly chosen individual goes and operates the doors . the individual however operates only those doors which are a multiple of the number he / she is carrying . for example , the individual marked with number 5 operates the doors marked with 5 , 10 , 15 , 20 , 25 , 30 , 35 , and 40 . if every individual in the group gets one turn , then how many doors are open at the end ?", + "Output Program": [ + "n0 = 40.0\nn1 = 1.0\nn2 = 40.0\nn3 = 40.0\nn4 = 1.0\nn5 = 40.0\nn6 = 5.0\nn7 = 5.0\nn8 = 10.0\nn9 = 15.0\nn10 = 20.0\nn11 = 25.0\nn12 = 30.0\nn13 = 35.0\nn14 = 40.0\n\nanswer = n8 - 4.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "for any number y , y * is defined as the greatest positive even integer less than or equal to y . what is the value of 7.2 \u2013 7.2 * ?", + "Output Program": [ + "import math\nn0 = 7.2\nn1 = 7.2\nt0 = math.floor(n0)\nt1 = t0 - 1.0\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "1.2000000000000002" + ], + "split": "train" + }, + { + "Input": "how many multiples of 3 are there between 81 and 358 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 81.0\nn2 = 358.0\nt0 = n2 - n1\nt1 = t0 / n0\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "93.33333333333333" + ], + "split": "train" + }, + { + "Input": "according to the formula f = 9 / 5 ( c ) + 32 , if the temperature in degrees farenheit ( f ) increases by 30 , by how much does the temperature in degrees celsius ( c ) increase ?", + "Output Program": [ + "n0 = 9.0\nn1 = 5.0\nn2 = 32.0\nn3 = 30.0\nt0 = n1 * n3\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "16.666666666666668" + ], + "split": "train" + }, + { + "Input": "9548 + 7314 = 3362 + ( ? )", + "Output Program": [ + "n0 = 9548.0\nn1 = 7314.0\nn2 = 3362.0\nt0 = n0 + n1\nanswer = t0 - n2\nprint(answer)" + ], + "Output Answer": [ + "13500" + ], + "split": "train" + }, + { + "Input": "a sum of money is distributed among w , x , y , z in the proportion of 1 : 6 : 2 : 4 . if x gets $ 1500 more than y , what is the w ' s share ?", + "Output Program": [ + "n0 = 1.0\nn1 = 6.0\nn2 = 2.0\nn3 = 4.0\nn4 = 1500.0\nt0 = n1 / n2\nt1 = t0 - 1.0\nt2 = n4 / t1\nanswer = t2 / n2\nprint(answer)" + ], + "Output Answer": [ + "375" + ], + "split": "train" + }, + { + "Input": "a student has to obtain 33 % of the total marks to pass . he got 125 marks and failed by 40 marks . the maximum marks are :", + "Output Program": [ + "n0 = 33.0\nn1 = 125.0\nn2 = 40.0\nt0 = n1 + n2\nt1 = n0 / 100.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "train" + }, + { + "Input": "a volunteer organization is recruiting new members . in the fall they manage to increase their number by 7 % . by the spring however membership falls by 19 % . what is the total change in percentage from fall to spring ?", + "Output Program": [ + "n0 = 7.0\nn1 = 19.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = t0 + 1.0\nt3 = 1.0 - t1\nt4 = t2 * t3\nt5 = t4 * 100.0\nanswer = 100.0 - t5\nprint(answer)" + ], + "Output Answer": [ + "13.329999999999984" + ], + "split": "train" + }, + { + "Input": "in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 8 eggs . if the cost of each pound of rice is $ 0.33 , then how many e cents does a liter of kerosene cost ? [ one dollar has 100 cents . ]", + "Output Program": [ + "n0 = 8.0\nn1 = 0.33\nn2 = 100.0\nt0 = 1.0 / 2.0\nt1 = n1 * n2\nt2 = n0 / t0\nt3 = t2 / 12.0\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "44" + ], + "split": "train" + }, + { + "Input": "if 144 / 0.144 = 14.4 / x , then the value of x is :", + "Output Program": [ + "n0 = 144.0\nn1 = 0.144\nn2 = 14.4\nt0 = n1 * n2\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.0144" + ], + "split": "train" + }, + { + "Input": "john want to buy a $ 100 trouser at the store , but he think it \u2019 s too expensive . finally , it goes on sale for $ 40 . what is the percent decrease ?", + "Output Program": [ + "n0 = 100.0\nn1 = 40.0\n\nanswer = n0 - n1\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "a mixture of 150 liters of wine and water contains 20 % water . how much more water should be added so that water becomes 25 % of the new mixture ?", + "Output Program": [ + "n0 = 150.0\nn1 = 20.0\nn2 = 25.0\nt0 = n2 / 100.0\nt1 = n1 / 100.0\nt2 = n0 * t0\nt3 = n0 * t1\nt4 = 1.0 - t0\nt5 = t2 - t3\nanswer = t5 / t4\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "jenny can divide her sweets equally to 5 people and also to 6 people equally but not to 12 people . what could be the number ?", + "Output Program": [ + "import scipy\nn0 = 5.0\nn1 = 6.0\nn2 = 12.0\n\nanswer = scipy.lcm(int(n0), int(n1))\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "at a certain committee meeting only associate professors and assistant professors are present . each associate professor has brought 2 pencils and 1 chart to the meeting , while each assistant professor has brought 1 pencil and 2 charts . if a total of 10 pencils and 11 charts have been brought to the meeting , how many people are present ?", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 1.0\nn3 = 2.0\nn4 = 10.0\nn5 = 11.0\nt0 = n4 + n5\nt1 = n0 + n1\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "if 522 x is a 3 digit no . with as a digit x . if the no . is divisible by 6 , what is the value of the digit x is ?", + "Output Program": [ + "n0 = 522.0\nn1 = 3.0\nn2 = 6.0\nt0 = n0 * 10.0\nt1 = n2 + t0\nt2 = t1 / n2\nanswer = t1 / t2\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "at deluxe paint store , fuchsia paint is made by mixing 6 parts of red paint with 3 parts of blue paint . mauve paint is made by mixing 4 parts of red paint with 5 parts blue paint . how many liters of blue paint must be added to 24 liters of fuchsia to change it to mauve paint ?", + "Output Program": [ + "n0 = 6.0\nn1 = 3.0\nn2 = 4.0\nn3 = 5.0\nn4 = 24.0\nt0 = n0 + n1\nt1 = n0 / t0\nt2 = n2 / t0\nt3 = n3 / t0\nt4 = n4 * t1\nt5 = t4 / t2\nt6 = n4 - t4\nt7 = t5 * t3\nanswer = t7 - t6\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "if x is a positive integer with fewer than 3 digits , what is the probability w that x * ( x + 1 ) is a multiple of either 4 or 5 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 4.0\nn3 = 5.0\nt0 = 100.0 / n2\nt1 = 100.0 / n3\nt2 = 100.0 - n1\nt3 = t0 * 2.0\nt4 = t1 * 2.0\nt5 = t3 + t4\nt6 = t5 - n2\nanswer = t6 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.8686868686868687" + ], + "split": "train" + }, + { + "Input": "two employees m and n are paid a total of rs . 550 per week by their employer . if m is paid 120 percent of the sum paid to n , how much is n paid per week ?", + "Output Program": [ + "n0 = 550.0\nn1 = 120.0\nt0 = 10.0 / 2.0\nt1 = n0 * 2.0\nt2 = t1 - n1\nt3 = t2 / 2.0\nt4 = t3 / 2.0\nanswer = t4 + t0\nprint(answer)" + ], + "Output Answer": [ + "250" + ], + "split": "train" + }, + { + "Input": "a certain bag of gemstones is composed of two - thirds diamonds and one - third rubies . if the probability of randomly selecting two diamonds from the bag , without replacement , is 5 / 12 , what is the probability of selecting two rubies from the bag , without replacement ?", + "Output Program": [ + "n0 = 5.0\nn1 = 12.0\nt0 = 1.0 / 2.0\nt1 = n0 / n1\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "0.08333333333333331" + ], + "split": "train" + }, + { + "Input": "in a certain school , 20 % of students are below 8 years of age . the number of students above 8 years of age is 2 / 3 of the number of students of 8 years of age which is 60 . what is the total number of students in the school ?", + "Output Program": [ + "n0 = 20.0\nn1 = 8.0\nn2 = 8.0\nn3 = 2.0\nn4 = 3.0\nn5 = 8.0\nn6 = 60.0\nt0 = n3 / n4\nt1 = n0 / 100.0\nt2 = n6 * t0\nt3 = 1.0 - t1\nt4 = n6 + t2\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "125" + ], + "split": "train" + }, + { + "Input": "robert ' s salary was decreased by 40 % and subsequently increased by 40 % . how much percentage does he lose ?", + "Output Program": [ + "n0 = 40.0\nn1 = 40.0\nt0 = n0 + 100.0\nt1 = 100.0 * 100.0\nt2 = 100.0 - n0\nt3 = t0 * t2\nt4 = t1 - t3\nt5 = t4 / t1\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "the average runs of a cricket player of 12 innings was 48 . how many runs must he make in his next innings so as to increase his average of runs by 10 ?", + "Output Program": [ + "n0 = 12.0\nn1 = 48.0\nn2 = 10.0\nt0 = n0 + 1.0\nt1 = n1 + n2\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "178" + ], + "split": "train" + }, + { + "Input": "of the goose eggs laid at a certain pond , 1 / 2 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 120 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 3.0\nn3 = 4.0\nn4 = 3.0\nn5 = 5.0\nn6 = 120.0\nt0 = n1 / n5\nt1 = n1 / n3\nt2 = n0 / n1\nt3 = 1.0 - t0\nt4 = n6 / t3\nt5 = t4 / t1\nanswer = t5 / t2\nprint(answer)" + ], + "Output Answer": [ + "800" + ], + "split": "train" + }, + { + "Input": "if x = 5 - q and y = 3 q - 1 , then for what value of q , x is three times to y ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nn2 = 1.0\nt0 = n2 - n0\nanswer = n0 + t0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 30 paisa . if the share of y is rs . 63 , what is the total amount ?", + "Output Program": [ + "n0 = 45.0\nn1 = 30.0\nn2 = 63.0\nt0 = 100.0 / n0\nt1 = n1 / n0\nt2 = n2 * t0\nt3 = n2 * t1\nt4 = t2 + t3\nanswer = n2 + t4\nprint(answer)" + ], + "Output Answer": [ + "245" + ], + "split": "train" + }, + { + "Input": "the average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 68 kg . what is the correct weight ?", + "Output Program": [ + "n0 = 20.0\nn1 = 58.4\nn2 = 56.0\nn3 = 68.0\nt0 = n0 * n1\nt1 = n3 - n2\nt2 = t0 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "59" + ], + "split": "train" + }, + { + "Input": "there are many numbers that can be expressed as the sum of 3 squares in 3 different ways . can you find out the smallest of such number ?", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nt0 = n0 * n0\nt1 = t0 * 4.0\nt2 = t1 + 12.0\nt3 = t2 + 4.0\nanswer = t3 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "train" + }, + { + "Input": "a basket of 1430 apples is divided equally among a group of apple lovers . if 45 people join the group , each apple lover would receive 9 apples less . how many w apples did each person get before 45 people joined the feast ?", + "Output Program": [ + "n0 = 1430.0\nn1 = 45.0\nn2 = 9.0\nn3 = 45.0\nt0 = 10.0 + 10.0\nt1 = t0 + 2.0\nt2 = n0 / t1\nt3 = n1 + t2\nt4 = n0 / t3\nanswer = n2 + t4\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "free notebooks were distributed equally among children of a class . the number of notebooks each child got was one - eighth of the number of children . had the number of children been half , each child would have got 16 notebooks . how many notebooks were distributed in all ?", + "Output Program": [ + "n0 = 16.0\nt0 = n0 / 2.0\nt1 = t0 * t0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "512" + ], + "split": "train" + }, + { + "Input": "( 0.5 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.5 ) ( power 2 ) + 0.05 + ( 0.1 ) ( power 2 ) is :", + "Output Program": [ + "n0 = 0.5\nn1 = 3.0\nn2 = 0.1\nn3 = 3.0\nn4 = 0.5\nn5 = 2.0\nn6 = 0.05\nn7 = 0.1\nn8 = 2.0\nt0 = n0**min(n1, 5)\nt1 = n2**min(n1, 5)\nt2 = n0**min(n5, 5)\nt3 = n2**min(n5, 5)\nt4 = n6 + t2\nt5 = t0 - t1\nt6 = t4 + t3\nanswer = t5 / t6\nprint(answer)" + ], + "Output Answer": [ + "0.4" + ], + "split": "train" + }, + { + "Input": "if p is a prime number greater than 3 , find the remainder when p ^ 2 + 17 is divided by 12 .", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 17.0\nn3 = 12.0\nt0 = 1.0 + 4.0\nt1 = n0 * n3\nt2 = t0**min(n1, 5)\nt3 = n2 + t2\nanswer = t3 - t1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "9.8 , 9.8 , 9.9 , 9.9 , 10.0 , 10.0 , 10.1 , 10.5 the mean and the standard deviation of the 8 numbers shown above is 10 and 0.212 respectively . what percent of the 8 numbers are within 1 standard deviation of the mean ?", + "Output Program": [ + "n0 = 9.8\nn1 = 9.8\nn2 = 9.9\nn3 = 9.9\nn4 = 10.0\nn5 = 10.0\nn6 = 10.1\nn7 = 10.5\nn8 = 8.0\nn9 = 10.0\nn10 = 0.212\nn11 = 8.0\nn12 = 1.0\nt0 = n8 - 1.0\nt1 = t0 / n8\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "87.5" + ], + "split": "train" + }, + { + "Input": "given f ( x ) = 2 x \u2013 3 , for what value of x does 2 * [ f ( x ) ] \u2013 21 = f ( x \u2013 4 ) ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 2.0\nn3 = 21.0\nn4 = 4.0\nt0 = n1 * n2\nt1 = n4 * n0\nt2 = n0 * n2\nt3 = n0 * 1.0\nt4 = n3 + t0\nt5 = n1 + t1\nt6 = t2 - t3\nt7 = t4 - t5\nanswer = t7 / t6\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "find the least number of 5 digits , which is exactly divisible by 89 .", + "Output Program": [ + "n0 = 6.0\nn1 = 5.0\nn2 = 2.0\nn3 = 19.0\nt0 = n0 * n1\nt1 = n2 * t0\nt2 = t1 / n2\nanswer = t2 + 3.0\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "a rope of which a calf is tied is increased from 16 m to 23 m , how much additional grassy ground shall it graze ?", + "Output Program": [ + "n0 = 16.0\nn1 = 23.0\nt0 = 3.0 + 4.0\nt1 = 10.0 * 2.0\nt2 = n1**min(2.0, 5)\nt3 = n0**min(2.0, 5)\nt4 = t1 + 2.0\nt5 = t2 - t3\nt6 = t4 / t0\nanswer = t6 * t5\nprint(answer)" + ], + "Output Answer": [ + "858" + ], + "split": "train" + }, + { + "Input": "david obtained 76 , 65 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology what are his average marks ?", + "Output Program": [ + "n0 = 76.0\nn1 = 65.0\nn2 = 82.0\nn3 = 67.0\nn4 = 85.0\nn5 = 100.0\nt0 = n0 + n1\nt1 = 2.0 + 3.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "the least number which when divided by 5 , 6 , 7 and 8 leaves a remainder 3 , but when divided by 9 leaves no remainder , is", + "Output Program": [ + "import scipy\nn0 = 5.0\nn1 = 6.0\nn2 = 7.0\nn3 = 8.0\nn4 = 3.0\nn5 = 9.0\nt0 = scipy.lcm(int(n0), int(n1))\nt1 = scipy.lcm(int(n2), int(t0))\nt2 = scipy.lcm(int(n3), int(t1))\nanswer = t2 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "1680" + ], + "split": "train" + }, + { + "Input": "what is the least number which when divided by 7 , 9 , 12 and 18 leaves remainder 4 in each care ?", + "Output Program": [ + "import scipy\nn0 = 7.0\nn1 = 9.0\nn2 = 12.0\nn3 = 18.0\nn4 = 4.0\nt0 = scipy.lcm(int(n0), int(n1))\nt1 = scipy.lcm(int(n2), int(n3))\nt2 = scipy.lcm(int(t0), int(t1))\nanswer = n4 + t2\nprint(answer)" + ], + "Output Answer": [ + "256" + ], + "split": "train" + }, + { + "Input": "how many points ( x , y ) lie on the line segment between ( 15 , 12 2 / 3 ) and ( 7 , 17 2 / 3 ) such that x and y are both integers ?", + "Output Program": [ + "n0 = 15.0\nn1 = 12.0\nn2 = 2.0\nn3 = 3.0\nn4 = 7.0\nn5 = 17.0\nn6 = 2.0\nn7 = 3.0\n\nanswer = n4 / n4\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "q is a set of 8 distinct prime numbers . if the sum of the integers in q is even and the number x is a member of q , then what is the least value that x can be ?", + "Output Program": [ + "n0 = 8.0\nt0 = n0 / 4.0\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "the average of 6 observations is 12 . a new observation is included and the new average is decreased by 1 . the seventh observation is ?", + "Output Program": [ + "n0 = 6.0\nn1 = 12.0\nn2 = 1.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n1 - n2\nt3 = t0 * t2\nanswer = t3 - t1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "for an agricultural experiment , 300 seeds were planted in one plot and 200 were planted in a second plot . if exactly 15 percent of the seeds in the first plot germinated and exactly 35 percent of the seeds in the second plot germinated , what percent of the total number of seeds germinated ?", + "Output Program": [ + "n0 = 300.0\nn1 = 200.0\nn2 = 15.0\nn3 = 35.0\nt0 = n0 + n1\nt1 = n2 / 100.0\nt2 = n3 / 100.0\nt3 = n0 * t1\nt4 = n1 * t2\nt5 = t3 + t4\nt6 = t5 / t0\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "how many numbers from 10 to 50 are exactly divisible by 3", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 50.0\nn2 = 3.0\nt0 = n1 / n2\nt1 = n0 / n2\nt2 = math.floor(t0)\nt3 = math.floor(t1)\nt4 = t3 + 1.0\nt5 = n2 * t2\nt6 = n2 * t4\nt7 = t5 - t6\nt8 = t7 / n2\nanswer = t8 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 30 paisa . if the share of y is rs . 18 , what is the total amount ?", + "Output Program": [ + "n0 = 45.0\nn1 = 30.0\nn2 = 18.0\nt0 = 100.0 / n0\nt1 = n1 / n0\nt2 = n2 * t0\nt3 = n2 * t1\nt4 = t2 + t3\nanswer = n2 + t4\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "train" + }, + { + "Input": "what is the sum of all 3 digit numbers that leave a remainder of ' 2 ' when divided by 8 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 8.0\nt0 = n0 * n0\nt1 = 1000.0 - n0\nt2 = t0 * 10.0\nt3 = t2 + t0\nt4 = n0 + t3\nt5 = t4 + t1\nt6 = t1 - t4\nt7 = t6 / n2\nt8 = t7 + 1.0\nt9 = t8 / n1\nanswer = t5 * t9\nprint(answer)" + ], + "Output Answer": [ + "62024.8125" + ], + "split": "train" + }, + { + "Input": "what least number should be subtracted from 1,439 so that the remainder when divided by 5 , 11 , and 13 will leave in each case the same remainder 3 ?", + "Output Program": [ + "n0 = 1439.0\nn1 = 5.0\nn2 = 11.0\nn3 = 13.0\nn4 = 3.0\nt0 = n1 * n2\nt1 = n3 * t0\nt2 = t1 * 2.0\nt3 = n4 + t2\nanswer = n0 - t3\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "what is the average of 12 , 13 , 14 , 510 , 520 , 530 , 1115 , 1120 , and 1 , 1252140 , 2345 ?", + "Output Program": [ + "n0 = 12.0\nn1 = 13.0\nn2 = 14.0\nn3 = 510.0\nn4 = 520.0\nn5 = 530.0\nn6 = 1115.0\nn7 = 1120.0\nn8 = 1.0\nn9 = 1252140.0\nn10 = 2345.0\nt0 = n0 + n1\nt1 = n6 + 10.0\nt2 = 1.0 + 10.0\nt3 = 100.0 * 2.0\nt4 = n2 + t0\nt5 = t3 + 4.0\nt6 = n3 + t4\nt7 = t5 + 1.0\nt8 = n4 + t6\nt9 = n10 - t7\nt10 = n5 + t8\nt11 = n6 + t10\nt12 = n7 + t11\nt13 = t12 + t1\nt14 = t13 + t9\nt15 = n10 + t14\nanswer = t15 / t2\nprint(answer)" + ], + "Output Answer": [ + "858.5454545454545" + ], + "split": "train" + }, + { + "Input": "the price of a certain painting increased by 20 % during the first year and decreased by 25 % during the second year . the price of the painting at the end of the 2 - year period was what percent of the original price ?", + "Output Program": [ + "n0 = 20.0\nn1 = 25.0\nn2 = 2.0\nt0 = n0 * n1\nt1 = n0 - n1\nt2 = t0 / 100.0\nt3 = t1 - t2\nanswer = t3 + 100.0\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "the average age of 15 students of a class is 15 years . out of these , the average age of 5 students is 13 years and that of the other 9 students is 16 years , the age of the 15 th student is", + "Output Program": [ + "n0 = 15.0\nn1 = 15.0\nn2 = 5.0\nn3 = 13.0\nn4 = 9.0\nn5 = 16.0\nn6 = 15.0\nt0 = n0 * n0\nt1 = n2 * n3\nt2 = n4 * n5\nt3 = t1 + t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "if the charge of staying in a student youth hostel $ 18.00 / day for the first week , and $ 13.00 / day for each additional week , how much does it cost to stay for 23 days ?", + "Output Program": [ + "n0 = 18.0\nn1 = 13.0\nn2 = 23.0\nt0 = 3.0 + 4.0\nt1 = n0 * t0\nt2 = n2 - t0\nt3 = n1 * t2\nanswer = t1 + t3\nprint(answer)" + ], + "Output Answer": [ + "334" + ], + "split": "train" + }, + { + "Input": "country x taxes each of its citizens an amount equal to 15 percent of the first $ 40000 of income , plus 20 percent of all income in excess of $ 40000 . if a citizen of country x is taxed a total of $ 8000 , what is her income ?", + "Output Program": [ + "n0 = 15.0\nn1 = 40000.0\nn2 = 20.0\nn3 = 40000.0\nn4 = 8000.0\nt0 = n0 / 100.0\nt1 = n2 / 100.0\nt2 = 2.0 * 4.0\nt3 = 10.0 * 4.0\nt4 = t2 * 1000.0\nt5 = t3 * 1000.0\nt6 = t0 * t5\nt7 = t4 - t6\nt8 = t7 / t1\nanswer = t8 + t5\nprint(answer)" + ], + "Output Answer": [ + "50000" + ], + "split": "train" + }, + { + "Input": "the sum of 3 consecutive odd numbers is 20 more than the first of these numbers . what is the middle number ?", + "Output Program": [ + "n0 = 3.0\nn1 = 20.0\nt0 = 2.0 + 4.0\nt1 = n0 - 1.0\nt2 = n1 - t0\nt3 = t2 / t1\nanswer = t3 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "the sum of ages of 4 children born 4 years different each is 48 yrs . what is the age of the elder child ?", + "Output Program": [ + "n0 = 4.0\nn1 = 4.0\nn2 = 48.0\nt0 = n1 + 4.0\nt1 = 4.0 + 4.0\nt2 = t0 + t0\nt3 = t2 + t1\nt4 = n2 + t3\nanswer = t4 / n0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "a bowl contains equal numbers of red , orange , green , blue , and yellow candies . kaz eats all of the green candies and half of the orange ones . next , he eats half of the remaining pieces of each color . finally , he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 32 % of the original number . what percent of the red candies remain ?", + "Output Program": [ + "n0 = 32.0\nt0 = 2.0 + 3.0\nt1 = 100.0 / t0\nt2 = t1 / 2.0\nt3 = t2 / 2.0\nt4 = t2 + t3\nt5 = n0 - t4\nt6 = t5 / 2.0\nt7 = t6 / t1\nanswer = t7 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "42.5" + ], + "split": "train" + }, + { + "Input": "the average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 61 kg . what is the correct weight ?", + "Output Program": [ + "n0 = 20.0\nn1 = 58.4\nn2 = 56.0\nn3 = 61.0\nt0 = n0 * n1\nt1 = n3 - n2\nt2 = t0 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "58.65" + ], + "split": "train" + }, + { + "Input": "in the floor of a particular kitchen owned by an abstract artist , each row of tiles to the right of the first row contains two fewer tiles than the row directly to its left . if there are 9 rows in all and a total of 405 tiles in the floor , how many tiles does the leftmost row contain ?", + "Output Program": [ + "n0 = 9.0\nn1 = 405.0\nt0 = n1 / n0\nt1 = n0 + t0\nanswer = t1 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "53" + ], + "split": "train" + }, + { + "Input": "each of 3 charities in novel grove estates has 8 persons serving on its board of directors . if exactly 4 persons serve on 3 boards each and each pair of charities has 5 persons in common on their boards of directors , then how many distinct persons serve on one or more boards of directors ? a . b . c . d . e .", + "Output Program": [ + "n0 = 3.0\nn1 = 8.0\nn2 = 4.0\nn3 = 3.0\nn4 = 5.0\nt0 = n0 * n1\nt1 = t0 - n1\nanswer = t1 - n0\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "a mixture of 20 kg of spirit and water contains 10 % water . how much water must be added to this mixture to raise the percentage of water to 25 %", + "Output Program": [ + "n0 = 20.0\nn1 = 10.0\nn2 = 25.0\nt0 = n2 / 100.0\nt1 = n0 / n1\nt2 = n0 * t0\nt3 = 1.0 - t0\nt4 = t2 - t1\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "for all even integers n , h ( n ) is defined to be the sum of the even integers between 2 and n , inclusive . what is the value of h ( 18 ) / h ( 10 ) ?", + "Output Program": [ + "n0 = 2.0\nn1 = 18.0\nn2 = 10.0\nt0 = n0 + n1\nt1 = n0 + n2\nt2 = n1 - n0\nt3 = n2 - n0\nt4 = t2 / 2.0\nt5 = t3 / 2.0\nt6 = t4 + 1.0\nt7 = t5 + 1.0\nt8 = t0 * t6\nt9 = t7 * t1\nt10 = t8 / 2.0\nt11 = t9 / 2.0\nanswer = t10 / t11\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "in how many ways can an answer key for a quiz be written if the quiz contains 5 true - false questions followed by 2 multiples - choice questions with 4 answer choices each , if the correct answers to all true - false questions can not be the same ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 4.0\nt0 = n2 * n2\nt1 = 2.0**min(n0, 5)\nt2 = t1 - n1\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "480" + ], + "split": "train" + }, + { + "Input": "a number when divided by a certain divisor left remainder 255 , when twice the number was divided by the same divisor , the remainder was 112 . find the divisor ?", + "Output Program": [ + "n0 = 255.0\nn1 = 112.0\nt0 = n0 * 2.0\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "398" + ], + "split": "train" + }, + { + "Input": "find the number , difference between number and its 3 / 5 is 60 .", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 60.0\nt0 = n2 / 2.0\nanswer = n1 * t0\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "train" + }, + { + "Input": "two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs , x and y . now , jug x is 1 / 4 full , while jug y is 2 / 3 full . if water is poured from jug x into jug y until jug y is filled , what fraction of jug x then contains water ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 2.0\nn3 = 3.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = n0 - t1\nt3 = t2 / t1\nanswer = t0 * t3\nprint(answer)" + ], + "Output Answer": [ + "0.12500000000000003" + ], + "split": "train" + }, + { + "Input": "the average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 60 kg . what is the correct weight ?", + "Output Program": [ + "n0 = 20.0\nn1 = 58.4\nn2 = 56.0\nn3 = 60.0\nt0 = n0 * n1\nt1 = n3 - n2\nt2 = t0 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "58.6" + ], + "split": "train" + }, + { + "Input": "hillary and eddy are climbing to the summit of mt . everest from a base camp 4,700 ft from the summit . when they depart for the summit at 06 : 00 , hillary climbs at a rate of 800 ft / hr with eddy lagging behind at a slower rate of 500 ft / hr . if hillary stops 700 ft short of the summit and then descends at a rate of 1,000 ft / hr , at what time do hillary and eddy pass each other on her return trip ?", + "Output Program": [ + "n0 = 4700.0\nn1 = 6.0\nn2 = 0.0\nn3 = 800.0\nn4 = 500.0\nn5 = 700.0\nn6 = 1000.0\nt0 = n4 / 100.0\nt1 = n3 / n6\nt2 = n4 / n6\nt3 = t2 + 1.0\nt4 = t0 - 1.0\nt5 = t1 - t2\nt6 = t4 / t1\nt7 = t6 * t5\nt8 = t7 / t3\nt9 = t8 + t6\nanswer = n1 + t9\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "p and q are the only two applicants qualified for a short - term research project that pays 420 dollars in total . candidate p has more experience and , if hired , would be paid 50 percent more per hour than candidate q would be paid . candidate q , if hired , would require 10 hours more than candidate p to do the job . candidate p \u2019 s hourly wage is how many dollars greater than candidate q \u2019 s hourly wage ?", + "Output Program": [ + "n0 = 420.0\nn1 = 50.0\nn2 = 10.0\nt0 = 3.0 / 2.0\nt1 = t0 - 1.0\nt2 = n2 / t1\nt3 = n2 + t2\nt4 = n0 / t2\nt5 = n0 / t3\nanswer = t4 - t5\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "log ( a ( a ( a ) ^ 1 / 4 ) ^ 1 / 4 ) ^ 1 / 4 here base is a .", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 1.0\nn3 = 4.0\nn4 = 1.0\nn5 = 4.0\nt0 = n0 / n1\nt1 = t0 + 1.0\nt2 = t1 / n1\nt3 = t2 + 1.0\nanswer = t3 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.328125" + ], + "split": "train" + }, + { + "Input": "rahul is 30 years older than his daughter mary . in 20 years rahul will be twice as old as mary . what is mary current age .", + "Output Program": [ + "n0 = 30.0\nn1 = 20.0\nt0 = n0 + n1\nt1 = n1 * 2.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "line m lies in the xy - plane . the y - intercept of line m is - 2 , and line m passes through the midpoint of the line segment whose endpoints are ( 2 , 8 ) and ( 8 , - 2 ) . what is the slope of line m ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 8.0\nn3 = 8.0\nn4 = 2.0\nt0 = n1 + n3\nt1 = n2 - n4\nt2 = t1 / n1\nt3 = t0 / n1\nt4 = t2 + n0\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "what is 5 + 7", + "Output Program": [ + "n0 = 8.0\nt0 = n0 - 1.0\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "if 0.75 : x : : 5 : 9 , then x is equal to :", + "Output Program": [ + "n0 = 0.75\nn1 = 5.0\nn2 = 9.0\nt0 = n0 * n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "1.35" + ], + "split": "train" + }, + { + "Input": "s ( n ) is a n - digit number formed by attaching the first n perfect squares , in order , into one integer . for example , s ( 1 ) = 1 , s ( 2 ) = 14 , s ( 3 ) = 149 , s ( 4 ) = 14916 , s ( 5 ) = 1491625 , etc . how many digits t are in s ( 99 ) ?", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 2.0\nn3 = 14.0\nn4 = 3.0\nn5 = 149.0\nn6 = 4.0\nn7 = 14916.0\nn8 = 5.0\nn9 = 1491625.0\nn10 = 99.0\nt0 = n6 + 60.0\nt1 = n0 * n4\nt2 = n2 * n4\nt3 = n6 + t0\nt4 = n2 * t2\nt5 = t1 + t4\nt6 = n6 * t3\nt7 = t3 + t6\nanswer = t7 + t5\nprint(answer)" + ], + "Output Answer": [ + "355" + ], + "split": "train" + }, + { + "Input": "the average age of 7 men increases by 4 years when two women are included in place of two men of ages 26 and 30 years . find the average age of the women ?", + "Output Program": [ + "n0 = 7.0\nn1 = 4.0\nn2 = 26.0\nn3 = 30.0\nt0 = n2 + n3\nt1 = n0 * n1\nt2 = t0 + t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "how many 3 - digit numerals begin with a digit that represents a prime number ?", + "Output Program": [ + "n0 = 3.0\nt0 = n0 * 100.0\nanswer = t0 + 100.0\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "train" + }, + { + "Input": "the average of 25 results is 18 . the average of first 12 of those is 14 and the average of last 12 is 17 . what is the 13 th result ?", + "Output Program": [ + "n0 = 25.0\nn1 = 18.0\nn2 = 12.0\nn3 = 14.0\nn4 = 12.0\nn5 = 17.0\nn6 = 13.0\nt0 = n0 * n1\nt1 = n2 * n5\nt2 = n2 * n3\nt3 = t0 - t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "78" + ], + "split": "train" + }, + { + "Input": "a number consists of 3 digits whose sum is 10 . the middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed . the number is", + "Output Program": [ + "n0 = 3.0\nn1 = 10.0\nn2 = 99.0\nt0 = n1 / 2.0\nt1 = n1 * t0\nt2 = t0 - n0\nt3 = t2 * 100.0\nt4 = t3 + t1\nanswer = n0 + t4\nprint(answer)" + ], + "Output Answer": [ + "253" + ], + "split": "train" + }, + { + "Input": "what least number must be subtracted from 7538 so that remaining no . is divisible by 14", + "Output Program": [ + "import math\nn0 = 7538.0\nn1 = 14.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "in a survey of parents , exactly 5 / 6 of the mothers and 3 / 4 of the fathers held full - time jobs . if 60 percent of the parents surveyed were women , what percent of the parents did not hold full - time jobs ?", + "Output Program": [ + "n0 = 5.0\nn1 = 6.0\nn2 = 3.0\nn3 = 4.0\nn4 = 60.0\nt0 = n2 / n3\nt1 = n0 / n1\nt2 = 100.0 - n4\nt3 = t0 * t2\nt4 = n4 * t1\nt5 = t2 - t3\nt6 = n4 - t4\nanswer = t5 + t6\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "the ratio w , by volume of soap to alcohol to water in a 76 litre solution is 2 : 50 : 100 . the solution is then altered by adding more soap , alcohol and water . after this alteration the ratio , by volume of soap to water in the solution doubles whereas the ratio , by volume of soap to water remains the same as before . what could be the resulting volume .", + "Output Program": [ + "n0 = 76.0\nn1 = 2.0\nn2 = 50.0\nn3 = 100.0\n\nanswer = n0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "77" + ], + "split": "train" + }, + { + "Input": "a manufacturer produces a certain men ' s athletic shoe in integer sizes from 8 to 17 . for this particular shoe , each unit increase in size corresponds to a 1 / 5 - inch increase in the length of the shoe . if the largest size of this shoe is 40 % longer than the smallest size , how long , in inches , is the shoe in size 15 ?", + "Output Program": [ + "n0 = 8.0\nn1 = 17.0\nn2 = 1.0\nn3 = 5.0\nn4 = 40.0\nn5 = 15.0\nt0 = n2 / n3\nt1 = n4 / 100.0\nt2 = n1 - n0\nt3 = n5 - n0\nt4 = t0 * t2\nt5 = t0 * t3\nt6 = t4 / t1\nanswer = t6 + t5\nprint(answer)" + ], + "Output Answer": [ + "5.9" + ], + "split": "train" + }, + { + "Input": "the average salary / head of allthe workers in a workshop is rs . 850 , if the average salary / head of 7 technician is rs . 1000 and the average salary / head of the rest is rs . 780 , the total no . of workers in the work - shop is ?", + "Output Program": [ + "n0 = 850.0\nn1 = 7.0\nn2 = 1000.0\nn3 = 780.0\nt0 = n1 * n2\nt1 = n1 * n3\nt2 = n0 - n3\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "15 people went to a hotel for combine dinner party 10 of them spent rs . 50 each on their dinner and rest spent 4 more than the average expenditure of all the 15 . what was the total money spent by them .", + "Output Program": [ + "n0 = 15.0\nn1 = 10.0\nn2 = 50.0\nn3 = 4.0\nn4 = 15.0\nt0 = n1 * n2\nt1 = n0 - n1\nt2 = n3 * t1\nt3 = n0 - t1\nt4 = t0 + t2\nt5 = t4 / t3\nanswer = n0 * t5\nprint(answer)" + ], + "Output Answer": [ + "780" + ], + "split": "train" + }, + { + "Input": "if p / q = 4 / 5 , then the value of 1 / 7 + { ( 2 q - p ) / ( 2 q + p ) } is ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 1.0\nn3 = 7.0\nn4 = 2.0\nn5 = 2.0\nt0 = n2 / n3\nt1 = n0 / n1\nt2 = n4 + t1\nt3 = n4 - t1\nt4 = t3 / t2\nanswer = t0 + t4\nprint(answer)" + ], + "Output Answer": [ + "0.5714285714285714" + ], + "split": "train" + }, + { + "Input": "when a natural number n is successively divided by 1020 , 3040 . the remainders are 5060 , 7080 . what will be the sum of the remainders if the order of the division is reversed ?", + "Output Program": [ + "import math\nn0 = 1020.0\nn1 = 3040.0\nn2 = 5060.0\nn3 = 7080.0\nt0 = 3.0 + 4.0\nt1 = 1.0 + 2.0\nt2 = n2 / n0\nt3 = n3 / n1\nt4 = t0 + t1\nt5 = math.floor(t2)\nt6 = math.floor(t3)\nt7 = t4 * 2.0\nt8 = t5 * t6\nanswer = t7 + t8\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "in the land of oz only one or two - letter words are used . the local language has 68 different letters . the parliament decided to forbid the use of the seventh letter . how many words have the people of oz lost because of the prohibition ?", + "Output Program": [ + "n0 = 68.0\nt0 = n0 + 1.0\nanswer = n0 + t0\nprint(answer)" + ], + "Output Answer": [ + "137" + ], + "split": "train" + }, + { + "Input": "how many positive 3 - digit integers are divisible by both 3 and 7 ?", + "Output Program": [ + "import math\nimport scipy\nn0 = 3.0\nn1 = 3.0\nn2 = 7.0\nt0 = scipy.lcm(int(n0), int(n2))\nt1 = 1000.0 / t0\nt2 = 100.0 / t0\nt3 = math.floor(t1)\nt4 = math.floor(t2)\nanswer = t3 - t4\nprint(answer)" + ], + "Output Answer": [ + "43" + ], + "split": "train" + }, + { + "Input": "the average of 50 numbers id 62 . if two numbers , namely 45 and 55 are discarded , the average of the remaining numbers is :", + "Output Program": [ + "n0 = 50.0\nn1 = 62.0\nn2 = 45.0\nn3 = 55.0\nt0 = n2 + n3\nt1 = n0 * n1\nt2 = n0 - 2.0\nt3 = t1 - t0\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "62.5" + ], + "split": "train" + }, + { + "Input": "mona and donald fly to rome for the weekend . they take cash only in notes of $ 10 and notes of \u20ac 10 . mona carries 3 times the amount of euros donald carries . she also carries as many dollars as donald carries . the number of \u20ac 10 notes they take is double the number of $ 10 notes they take . if donald carries a total of 39 notes ( of either $ 10 or \u20ac 10 , ) then what is the total number of notes ( of either $ 10 or \u20ac 10 , ) they take ?", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 3.0\nn3 = 10.0\nn4 = 10.0\nn5 = 39.0\nn6 = 10.0\nn7 = 10.0\nn8 = 10.0\nn9 = 10.0\nt0 = n5 / n2\nt1 = n2 * n5\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "130" + ], + "split": "train" + }, + { + "Input": "how many numbers from 39 to 79 are exactly divisible by 11 ?", + "Output Program": [ + "import math\nn0 = 39.0\nn1 = 79.0\nn2 = 11.0\nt0 = n1 / n2\nt1 = n0 / n2\nt2 = math.floor(t0)\nt3 = math.floor(t1)\nt4 = t3 + 1.0\nt5 = n2 * t2\nt6 = n2 * t4\nt7 = t5 - t6\nt8 = t7 / n2\nanswer = t8 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "when a number is divided by 6 & then multiply by 12 the answer is 8 what is the no . ?", + "Output Program": [ + "n0 = 6.0\nn1 = 12.0\nn2 = 8.0\nt0 = n2 / n1\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "in one year , the population , of a village increased by 30 % and in the next year , it decreased by 30 % . if at the end of 2 nd year , the population was 13650 , what was it in the beginning ?", + "Output Program": [ + "n0 = 30.0\nn1 = 30.0\nn2 = 2.0\nn3 = 13650.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nt2 = 1.0 - t0\nt3 = n3 / t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "15000" + ], + "split": "train" + }, + { + "Input": "company c sells a line of 25 products with an average retail price of $ 1,200 . if none of these products sells for less than $ 400 , and exactly 12 of the products sell for less than $ 1,000 , what is the greatest possible selling price of the most expensive product ?", + "Output Program": [ + "n0 = 25.0\nn1 = 1200.0\nn2 = 400.0\nn3 = 12.0\nn4 = 1000.0\nt0 = 100.0 * 12.0\nt1 = n2 * n3\nt2 = n0 - n3\nt3 = n0 * t0\nt4 = t2 - 1.0\nt5 = t4 * n4\nt6 = t1 + t5\nanswer = t3 - t6\nprint(answer)" + ], + "Output Answer": [ + "13200" + ], + "split": "train" + }, + { + "Input": "drum x is 1 / 2 full of oil and drum y , which has twice the capacity of drum x , is 1 / 2 full of oil . if all of the oil in drum x is poured into drum y , then drum y will be filled to what capacity ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 1.0\nn3 = 2.0\nt0 = n0 / n3\nt1 = 12.0 / n1\nt2 = n0 / n1\nt3 = t0 * 12.0\nt4 = t1 * t2\nt5 = t3 + t4\nanswer = t5 / 12.0\nprint(answer)" + ], + "Output Answer": [ + "0.75" + ], + "split": "train" + }, + { + "Input": "the average weight of 8 people increases by 2.5 kg when a new person comes in place of one of them weighing 45 kg . what is the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.5\nn2 = 45.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "65" + ], + "split": "train" + }, + { + "Input": "average of 10 matches is 32 , how many runs one should should score to increase his average by 3 runs .", + "Output Program": [ + "n0 = 10.0\nn1 = 32.0\nn2 = 3.0\nt0 = n1 + n2\nt1 = n0 + 1.0\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "65" + ], + "split": "train" + }, + { + "Input": "running at their respective constant rate , machine x takes 2 days longer to produce w widgets than machines y . at these rates , if the two machines together produce 5 w / 4 widgets in 3 days , how many days would it take machine x alone to produce 3 w widgets .", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 4.0\nn3 = 3.0\nn4 = 3.0\nt0 = n0 * n4\nanswer = n3 * t0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "on thursday mabel handled 90 transactions . anthony handled 10 % more transactions than mabel , cal handled 2 / 3 rds of the transactions that anthony handled , and jade handled 19 more transactions than cal . how much transactions did jade handled ?", + "Output Program": [ + "n0 = 90.0\nn1 = 10.0\nn2 = 2.0\nn3 = 3.0\nn4 = 19.0\nt0 = n1 + 100.0\nt1 = n0 / 100.0\nt2 = t0 * t1\nt3 = n2 * t2\nt4 = t3 / n3\nanswer = n4 + t4\nprint(answer)" + ], + "Output Answer": [ + "85" + ], + "split": "train" + }, + { + "Input": "if x is 13 percent greater than 80 , then x =", + "Output Program": [ + "n0 = 13.0\nn1 = 80.0\nt0 = n0 / 100.0\nt1 = n1 * t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "90.4" + ], + "split": "train" + }, + { + "Input": "an integer n between 1 and 99 , inclusive , is to be chosen at random . what is the probability that n ( n + 1 ) will be divisible by 3 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 99.0\nn2 = 1.0\nn3 = 3.0\nt0 = n1 / n3\nt1 = t0 / n1\nanswer = 2.0 * t1\nprint(answer)" + ], + "Output Answer": [ + "0.6666666666666666" + ], + "split": "train" + }, + { + "Input": "how many numbers from 10 to 40 are exactly divisible by 3 ?", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 40.0\nn2 = 3.0\nt0 = n1 / n2\nt1 = n0 / n2\nt2 = math.floor(t0)\nt3 = math.floor(t1)\nt4 = t3 + 1.0\nt5 = n2 * t2\nt6 = n2 * t4\nt7 = t5 - t6\nt8 = t7 / n2\nanswer = t8 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "in the land of oz only one or two - letter words are used . the local language has 64 different letters . the parliament decided to forbid the use of the seventh letter . how many words have the people of oz lost because of the prohibition ?", + "Output Program": [ + "n0 = 64.0\nt0 = n0 + 1.0\nanswer = n0 + t0\nprint(answer)" + ], + "Output Answer": [ + "129" + ], + "split": "train" + }, + { + "Input": "the average of 6 no . ' s is 3.95 . the average of 2 of them is 4.4 , while the average of theother 2 is 3.85 . what is the average of the remaining 2 no ' s ?", + "Output Program": [ + "n0 = 6.0\nn1 = 3.95\nn2 = 2.0\nn3 = 4.4\nn4 = 2.0\nn5 = 3.85\nn6 = 2.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n2 * n5\nt3 = t1 + t2\nt4 = t0 - t3\nanswer = t4 / n2\nprint(answer)" + ], + "Output Answer": [ + "3.6000000000000014" + ], + "split": "train" + }, + { + "Input": "the price of a cycle is reduced by 25 per cent . the new price is reduced by a further 30 per cent . the two reductions together are equal to a single reduction of", + "Output Program": [ + "n0 = 25.0\nn1 = 30.0\nt0 = 100.0 - n1\nt1 = 100.0 - n0\nt2 = t0 / 100.0\nt3 = t2 * t1\nanswer = 100.0 - t3\nprint(answer)" + ], + "Output Answer": [ + "47.5" + ], + "split": "train" + }, + { + "Input": "a seller of used cars has 10 cars to sell and each of his clients selected 2 cars that he liked most . if each car was selected exactly thrice , how many clients visited the garage ?", + "Output Program": [ + "n0 = 10.0\nn1 = 2.0\nt0 = n0 / n1\nanswer = t0 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "find the value of x in ( x / 5 ) + 3 = 4 .", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nn2 = 4.0\nt0 = n2 - n1\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "what is the least number should be added to 1056 , so the sum of the number is completely divisible by 26 ?", + "Output Program": [ + "import math\nn0 = 1056.0\nn1 = 26.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = t1 + 1.0\nt3 = n1 * t2\nanswer = t3 - n0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "abi decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month . if abi ' s savings by the end of the year from these monthly savings were 6 times the amount she spent per month , what should be the fraction of her salary that she spent each month ?", + "Output Program": [ + "n0 = 6.0\nt0 = n0 + 12.0\nt1 = n0 / t0\nanswer = 1.0 - t1\nprint(answer)" + ], + "Output Answer": [ + "0.6666666666666667" + ], + "split": "train" + }, + { + "Input": "3 people who work full - time are to work together on a project , but their total time on the project is to be equivalent to that of only one person working full - time . if one of the people is budgeted for 1 / 2 of his time to the project and a second person for 1 / 3 of her time , what part of the third worker ' s time should be budgeted to this project ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 2.0\nn3 = 1.0\nn4 = 3.0\nt0 = n1 / n0\nt1 = n1 / n2\nt2 = t0 + t1\nt3 = 1.0 - t2\nanswer = t3 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "0.3333333333333335" + ], + "split": "train" + }, + { + "Input": "the population of bacteria culture doubles every 2 minutes . approximately how many minutes will it take for the population to grow from 1000 to 500000 bacteria ?", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 1000.0\nn2 = 500000.0\nt0 = n2 / n1\nt1 = math.log(max(1e-5, t0), 2)\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "17.931568569324174" + ], + "split": "train" + }, + { + "Input": "a envelop weight 8.5 gm , if 880 of these envelop are sent with an advertisement mail . how much wieght ?", + "Output Program": [ + "n0 = 8.5\nn1 = 880.0\nt0 = n0 * n1\nanswer = t0 / 1000.0\nprint(answer)" + ], + "Output Answer": [ + "7.48" + ], + "split": "train" + }, + { + "Input": "the average weight of 20 persons sitting in a boat had some value . a new person added to them whose weight was 50 kg only . due to his arrival , the average weight of all the persons decreased by 5 kg . find the average weight of first 20 persons ?", + "Output Program": [ + "n0 = 20.0\nn1 = 50.0\nn2 = 5.0\nn3 = 20.0\nt0 = n0 + 1.0\nt1 = n2 * t0\nanswer = t1 - n1\nprint(answer)" + ], + "Output Answer": [ + "55" + ], + "split": "train" + }, + { + "Input": "in a school with 5 classes , each class has 2 students less than the previous class . how many students are there in the largest class if the total number of students at school is 120 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 120.0\nt0 = n1 + n1\nt1 = n1 + t0\nt2 = n1 + t1\nt3 = t1 + t1\nt4 = t3 + t2\nt5 = n2 - t4\nt6 = t5 / n0\nanswer = t2 + t6\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . how many workers are there in the workshop ?", + "Output Program": [ + "n0 = 8000.0\nn1 = 7.0\nn2 = 12000.0\nn3 = 6000.0\nt0 = n2 - n0\nt1 = n0 - n3\nt2 = n1 * t0\nt3 = t2 / t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "40 liters of a mixture is created by mixing liquid p and liquid q in the ratio 5 : 3 . how many liters of liquid q must be added to make the ratio 5 : 6 ?", + "Output Program": [ + "n0 = 40.0\nn1 = 5.0\nn2 = 3.0\nn3 = 5.0\nn4 = 6.0\nt0 = n3 + n4\nt1 = n1 + n2\nt2 = n0 * n1\nt3 = n0 * n2\nt4 = t2 / t1\nt5 = t3 / t1\nt6 = t0 * t4\nt7 = t6 / n3\nt8 = n4 * t7\nt9 = t8 / t0\nanswer = t9 - t5\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets $ 500 more than d , what is d ' s share ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 4.0\nn3 = 3.0\nn4 = 500.0\nt0 = n2 - n3\nt1 = n4 * t0\nanswer = n3 * t1\nprint(answer)" + ], + "Output Answer": [ + "1500" + ], + "split": "train" + }, + { + "Input": "if 45 - [ 28 - { 37 - ( 15 - * ) } ] = 59 , then * is equal to :", + "Output Program": [ + "n0 = 45.0\nn1 = 28.0\nn2 = 37.0\nn3 = 15.0\nn4 = 59.0\nt0 = n1 - n2\nt1 = n3 + t0\nt2 = n0 - t1\nanswer = n4 - t2\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "find the total number of prime factors in the expression ( 4 ) 11 x ( 7 ) 5 x ( 11 ) 2 .", + "Output Program": [ + "n0 = 4.0\nn1 = 11.0\nn2 = 7.0\nn3 = 5.0\nn4 = 11.0\nn5 = 2.0\nt0 = n1 * n5\nt1 = n3 + t0\nanswer = n5 + t1\nprint(answer)" + ], + "Output Answer": [ + "29" + ], + "split": "train" + }, + { + "Input": "the average salary of workers in an industry is rs . 300 the average salary of technicians being rs . 400 and that of non - technicians being rs . 125 . what is the total number of workers ?", + "Output Program": [ + "import math\nn0 = 300.0\nn1 = 400.0\nn2 = 125.0\nt0 = n1 / n0\nt1 = n0 - n2\nt2 = t0 * t1\nt3 = t2 + 1.0\nanswer = math.floor(t3)\nprint(answer)" + ], + "Output Answer": [ + "234" + ], + "split": "train" + }, + { + "Input": "a man can buy a new house in 4 years with all of his earnings . but he spend the same amount in household expenses in 8 years and for savings in 12 years . how many time needed for buying the house ?", + "Output Program": [ + "n0 = 4.0\nn1 = 8.0\nn2 = 12.0\nt0 = n2 / n0\nt1 = t0 * 2.0\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "andy solves problems 80 to 125 inclusive in a math exercise . how many problems does he solve ?", + "Output Program": [ + "n0 = 80.0\nn1 = 125.0\nt0 = n1 - n0\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "46" + ], + "split": "train" + }, + { + "Input": "set a of 8 positive integers may have the same element and have 39 . and set b of 8 positive integers must have different elements and have 39 . when m and n are the greatest possible differences between 39 and other elements \u2019 sums in set a and set b , respectively , m - n = ?", + "Output Program": [ + "n0 = 8.0\nn1 = 39.0\nn2 = 8.0\nn3 = 39.0\nn4 = 39.0\nt0 = n0 + 2.0\nt1 = n0 + t0\nanswer = n1 - t1\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "find the value of 1.5 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ]", + "Output Program": [ + "n0 = 1.5\nn1 = 3.6\nn2 = 0.48\nn3 = 2.5\nn4 = 0.12\nn5 = 0.09\nn6 = 0.5\nt0 = n1 * n2\nt1 = n4 * n5\nt2 = n3 * t0\nt3 = n6 * t1\nt4 = t2 / t3\nanswer = n0 * t4\nprint(answer)" + ], + "Output Answer": [ + "1200.0000000000002" + ], + "split": "train" + }, + { + "Input": "by how much does the larger root of the equation 2 z ^ 2 + 5 z = 12 exceed the smaller root ?", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 2.0\nn2 = 5.0\nn3 = 12.0\nt0 = n0 * n3\nt1 = n0 * n0\nt2 = n2**min(n0, 5)\nt3 = t0 * 4.0\nt4 = t3 + t2\nt5 = math.sqrt(max(0, t4))\nt6 = n2 + t5\nt7 = n2 - t5\nt8 = t6 / t1\nt9 = t7 / t1\nanswer = t8 - t9\nprint(answer)" + ], + "Output Answer": [ + "5.5" + ], + "split": "train" + }, + { + "Input": ". star question : if f ( 1 ) = 4 and f ( x + y ) = f ( x ) + f ( y ) + 7 xy + 4 , then f ( 2 ) + f ( 5 ) = ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 7.0\nn3 = 4.0\nn4 = 2.0\nn5 = 5.0\nt0 = n5 * n5\nanswer = n5 * t0\nprint(answer)" + ], + "Output Answer": [ + "125" + ], + "split": "train" + }, + { + "Input": "the average ( arithmetic mean ) of 20 , 40 , and 60 is 8 more than the average of 10 , 70 , and what number ?", + "Output Program": [ + "n0 = 20.0\nn1 = 40.0\nn2 = 60.0\nn3 = 8.0\nn4 = 10.0\nn5 = 70.0\nt0 = n0 + n1\nt1 = n3 * 3.0\nt2 = n2 + t0\nt3 = n4 + t1\nt4 = n5 + t3\nanswer = t2 - t4\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "a cement mixture is composed of 3 elements . by weight , 1 / 5 of the mixture is sand , 3 / 4 of the mixture is water , and the remaining 6 pounds of the mixture is gravel . what is the weight of the entire mixture in pounds ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 5.0\nn3 = 3.0\nn4 = 4.0\nn5 = 6.0\nt0 = n1 / n2\nt1 = n3 / n4\nt2 = t0 + t1\nt3 = n1 - t2\nanswer = n5 / t3\nprint(answer)" + ], + "Output Answer": [ + "119.9999999999999" + ], + "split": "train" + }, + { + "Input": "a die is rolled twice . what is the probability of getting a sum equal to 9 ?", + "Output Program": [ + "n0 = 9.0\n\nanswer = 1.0 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.1111111111111111" + ], + "split": "train" + }, + { + "Input": "the difference in compound interest earned on a deposit ( compounded annually ) in year 1 and year 2 is $ 40 . had the interest rate been 3 times its present value , the difference a would have been how much ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 40.0\nn3 = 3.0\nt0 = n3 * 100.0\nt1 = n1 * 10.0\nt2 = n2 + t0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "360" + ], + "split": "train" + }, + { + "Input": "a number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34 . such a least possible number k is", + "Output Program": [ + "n0 = 5.0\nn1 = 8.0\nn2 = 34.0\nt0 = n2 * 2.0\nt1 = n0 * n1\nt2 = n0 - 1.0\nt3 = t0 - t1\nt4 = t3 / t2\nanswer = t4 + t0\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "sanoop bought 8 t - shirts at an average price ( arithmetic mean ) of rs . 526 . if sanoop returned 1 t - shirts to the retailer , and the average price of the remaining t - shirts was rs . 505 , then what is the average price , of the 3 returned t - shirts ?", + "Output Program": [ + "n0 = 8.0\nn1 = 526.0\nn2 = 1.0\nn3 = 505.0\nn4 = 3.0\nt0 = n0 * n1\nt1 = n0 - n2\nt2 = n3 * t1\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "673" + ], + "split": "train" + }, + { + "Input": "a number is doubled and 6 is added . if resultant is trebled , it becomes 72 . what is that number", + "Output Program": [ + "n0 = 6.0\nn1 = 72.0\nt0 = n0 * 3.0\nt1 = 2.0 * 3.0\nt2 = n1 - t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "in a group of 800 people , 3 / 5 play at least one instrument , 96 play two or more . what is the probability that one student play exactly one instrument ?", + "Output Program": [ + "n0 = 800.0\nn1 = 3.0\nn2 = 5.0\nn3 = 96.0\nt0 = n0 * n1\nt1 = t0 / n2\nt2 = t1 - n3\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.48" + ], + "split": "train" + }, + { + "Input": "jar x is 1 / 2 full of water . jar y , which has half the capacity of jar x , is 1 / 2 full of water . if the water in jar y is poured into jar x , then jar x will be filled to what fraction of its capacity ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 1.0\nn3 = 2.0\nt0 = n0 / n1\nt1 = t0 * t0\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "0.75" + ], + "split": "train" + }, + { + "Input": "a certain ball team has an equal number of right - and left - handed players . on a certain day , one - third of the players were absent from practice . of the players at practice that day , one - third were left handed . what is the ratio of the number of right - handed players who were not at practice that day to the number of lefthanded players who were not at practice ?", + "Output Program": [ + "t0 = 1.0 / 2.0\nt1 = 1.0 / 3.0\nt2 = 1.0 - t1\nt3 = t1 * t2\nt4 = t2 - t3\nt5 = t0 - t3\nt6 = t0 - t4\nanswer = t6 / t5\nprint(answer)" + ], + "Output Answer": [ + "0.19999999999999968" + ], + "split": "train" + }, + { + "Input": "rates for having a manuscript typed at a certain typing service are $ 5 per page for the first time a page is typed and $ 3 per page each time a page is revised . if a certain manuscript has 200 pages , of which 80 were revised only once , 20 were revised twice , and the rest required no revisions , what was the total cost of having the manuscript typed ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nn2 = 200.0\nn3 = 80.0\nn4 = 20.0\nt0 = n0 * n2\nt1 = n1 * n3\nt2 = n1 * n4\nt3 = t0 + t1\nt4 = t2 * 2.0\nanswer = t3 + t4\nprint(answer)" + ], + "Output Answer": [ + "1360" + ], + "split": "train" + }, + { + "Input": "the average monthly salary of 20 employees in an organisation is rs . 1700 . if the manager ' s salary is added , then the average salary increases by rs . 100 . what is the manager ' s monthly salary ?", + "Output Program": [ + "n0 = 20.0\nn1 = 1700.0\nn2 = 100.0\nt0 = n1 + n2\nt1 = n0 + 1.0\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "3800" + ], + "split": "train" + }, + { + "Input": "on dividing 17698 by a certain number , we get 89 as quotient and 14 as remainder . what is the divisor ?", + "Output Program": [ + "n0 = 17698.0\nn1 = 89.0\nn2 = 14.0\nt0 = n0 - n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "198.69662921348313" + ], + "split": "train" + }, + { + "Input": "the total age of a and b is 10 years more than the total age of b and c . c is how many year younger than", + "Output Program": [ + "n0 = 10.0\n\nanswer = n0 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "at 1 : 00 pm , there were 10.0 grams of bacteria . the bacteria increased to x grams at 4 : 00 pm , and 22.5 grams at 7 : 00 pm . if the amount of bacteria present increased by the same fraction during each of the 3 - hour periods , how many grams of bacteria were present at 4 : 00 pm ?", + "Output Program": [ + "import math\nn0 = 1.0\nn1 = 0.0\nn2 = 10.0\nn3 = 4.0\nn4 = 0.0\nn5 = 22.5\nn6 = 7.0\nn7 = 0.0\nn8 = 3.0\nn9 = 4.0\nn10 = 0.0\nt0 = n5 / n2\nt1 = math.sqrt(max(0, t0))\nanswer = t1 * n2\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "if 6 x ^ 2 + x - 12 = ( ax + w ) ( cx + d ) , then | a | + | w | + | c | + | d | = for a complete solution and more practice problems , see this blog : http : / / magoosh . com / gmat / 2012 / algebra - on . . . to - factor /", + "Output Program": [ + "n0 = 6.0\nn1 = 2.0\nn2 = 12.0\nn3 = 2012.0\nt0 = n0 / 3.0\nt1 = n2 / 4.0\nt2 = t0 + t1\nt3 = t2 + t1\nanswer = t3 + 4.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "5 % people of a village in sri lanka died by bombardment , 15 % of the remainder left the village on account of fear . if now the population is reduced to 3553 , how much was it in the beginning ?", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 15.0\nn2 = 3553.0\nt0 = 100.0 - n0\nt1 = 100.0 - n1\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = t2 * t3\nt5 = n2 / t4\nanswer = math.floor(t5)\nprint(answer)" + ], + "Output Answer": [ + "4400" + ], + "split": "train" + }, + { + "Input": "the average of 5 numbers id 27 . if one number is excluded , the average becomes 25 . the excluded number is", + "Output Program": [ + "n0 = 5.0\nn1 = 27.0\nn2 = 25.0\nt0 = n0 * n1\nt1 = n2 * 4.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "a batsman makes a score of 86 runs in the 17 th inning and thus increases his averages by 3 . find his average after 17 th inning ?", + "Output Program": [ + "n0 = 86.0\nn1 = 17.0\nn2 = 3.0\nn3 = 17.0\nt0 = n1 * n2\nt1 = n0 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "38" + ], + "split": "train" + }, + { + "Input": "a person deposits 1 / 16 of his income as provident fund and 1 / 15 of the remaining as insurance premium . if he spends 5 / 7 of the balance on domestic needs and deposits an amount of rs . 50 in the bank , his total income would be", + "Output Program": [ + "n0 = 1.0\nn1 = 16.0\nn2 = 1.0\nn3 = 15.0\nn4 = 5.0\nn5 = 7.0\nn6 = 50.0\nt0 = n0 / n1\nt1 = n4 / n5\nt2 = n0 - t0\nt3 = t2 / n3\nt4 = t2 - t3\nt5 = t1 * t4\nt6 = t4 - t5\nanswer = n6 / t6\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "train" + }, + { + "Input": "what is 3 / 5 of 5 / 7 of 2 / 3 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 5.0\nn3 = 7.0\nn4 = 2.0\nn5 = 3.0\nt0 = n0 / n1\nt1 = n1 / n3\nt2 = n4 / n0\nt3 = t1 * t2\nanswer = t0 * t3\nprint(answer)" + ], + "Output Answer": [ + "0.2857142857142857" + ], + "split": "train" + }, + { + "Input": "two employees a and b are paid a total of rs . 550 per week by their employer . if a is paid 150 percent of the sum paid to b , how much is b paid per week ?", + "Output Program": [ + "n0 = 550.0\nn1 = 150.0\nt0 = n1 / 100.0\nt1 = t0 + 1.0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "220" + ], + "split": "train" + }, + { + "Input": "of the families in city x in 1991 , 60 percent owned a personal computer . the number of families in city x owning a computer in 1993 was 20 percent greater than it was in 1991 , and the total number of families in city x was 9 percent greater in 1993 than it was in 1991 . what percent of the families in city x owned a personal computer in 1993 ?", + "Output Program": [ + "n0 = 1991.0\nn1 = 60.0\nn2 = 1993.0\nn3 = 20.0\nn4 = 1991.0\nn5 = 9.0\nn6 = 1993.0\nn7 = 1991.0\nn8 = 1993.0\nt0 = n3 + 100.0\nt1 = n5 + 100.0\nt2 = n1 * t0\nt3 = t2 / 100.0\nt4 = t3 / t1\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "66.05504587155964" + ], + "split": "train" + }, + { + "Input": "in township k each property is taxed at 10 percent of its assessed value . if the assessed value of a property in township k is increased from $ 20,000 to $ 28,000 , by how much will the property tax increase ?", + "Output Program": [ + "n0 = 10.0\nn1 = 20000.0\nn2 = 28000.0\nt0 = 3.0 + 4.0\nt1 = 1.0 + 4.0\nt2 = t0 * 4.0\nt3 = t1 * 4.0\nt4 = t2 * 1000.0\nt5 = t3 * 1000.0\nt6 = t4 - t5\nt7 = n0 * t6\nanswer = t7 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "800" + ], + "split": "train" + }, + { + "Input": "if 0.25 : x : : 2 : 6 , then x is equal to", + "Output Program": [ + "n0 = 0.25\nn1 = 2.0\nn2 = 6.0\nt0 = n0 * n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.75" + ], + "split": "train" + }, + { + "Input": "287 x 287 + 269 x 269 - 2 x 287 x 269 = ?", + "Output Program": [ + "n0 = 287.0\nn1 = 287.0\nn2 = 269.0\nn3 = 269.0\nn4 = 2.0\nn5 = 287.0\nn6 = 269.0\nt0 = n0 * n0\nt1 = n2 * n2\nt2 = n0 * n4\nt3 = t0 + t1\nt4 = n2 * t2\nanswer = t3 - t4\nprint(answer)" + ], + "Output Answer": [ + "324" + ], + "split": "train" + }, + { + "Input": "the visitors of a modern art museum who watched a certain picasso painting were asked to fill in a short questionnaire indicating whether they had enjoyed looking at the picture and whether they felt they had understood it . according to the results of the survey , all 100 visitors who did not enjoy the painting also did not feel they had understood the painting , and the number of visitors who enjoyed the painting was equal to the number of visitors who felt they had understood the painting . if 3 / 4 of the visitors who answered the questionnaire both enjoyed the painting and felt they had understood the painting , then how many visitors answered the questionnaire ?", + "Output Program": [ + "n0 = 100.0\nn1 = 3.0\nn2 = 4.0\nt0 = n1 / n2\nt1 = 1.0 - t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "train" + }, + { + "Input": "| 8 - 3 | - | 4 - 6 | = ?", + "Output Program": [ + "n0 = 8.0\nn1 = 3.0\nn2 = 4.0\nn3 = 6.0\nt0 = n0 - n1\nt1 = n3 - n2\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "if x is an integer and 2.134 \u00d7 10 ^ x is less than 240,000 , what is the greatest possible value for x ?", + "Output Program": [ + "import math\nn0 = 2.134\nn1 = 10.0\nn2 = 240000.0\nt0 = n2 / n0\nt1 = math.log(max(1e-5, n1), 2)\nt2 = math.log(max(1e-5, t0), 2)\nt3 = t2 / t1\nanswer = math.floor(t3)\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "in a class of 40 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 10 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?", + "Output Program": [ + "n0 = 40.0\nn1 = 2.0\nn2 = 12.0\nn3 = 1.0\nn4 = 10.0\nn5 = 2.0\nn6 = 3.0\nn7 = 2.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n1 * n4\nt3 = t1 + t2\nt4 = n4 + t1\nt5 = n1 + t4\nt6 = n0 - t5\nt7 = t6 - n3\nt8 = n6 * t7\nt9 = t3 + t8\nanswer = t0 - t9\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "of the 20210 employees of the anvil factory , 2 / 7 are journeymen . if half of the journeymen were laid off , what percentage of the total remaining employees would be journeymen ?", + "Output Program": [ + "n0 = 20210.0\nn1 = 2.0\nn2 = 7.0\nt0 = n1 / n2\nt1 = t0 / n1\nt2 = 1.0 - t0\nt3 = t1 + t2\nt4 = t1 / t3\nt5 = t4 * 100.0\nanswer = t5 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "49.99999999999999" + ], + "split": "train" + }, + { + "Input": "find the total number of prime factors in the expression ( 4 ) ^ 13 x ( 7 ) ^ 5 x ( 11 ) ^ 2", + "Output Program": [ + "n0 = 4.0\nn1 = 13.0\nn2 = 7.0\nn3 = 5.0\nn4 = 11.0\nn5 = 2.0\nt0 = n1 * n5\nt1 = n3 + t0\nanswer = n5 + t1\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "a man is 22 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ?", + "Output Program": [ + "n0 = 22.0\nt0 = 2.0 * 2.0\nt1 = 2.0 - 1.0\nt2 = t0 - 2.0\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "two trains of equal length are running on parallel lines in the same directions at 46 km / hr . and 36 km / hr . the faster trains pass the slower train in 36 seconds . the length of each train is :", + "Output Program": [ + "n0 = 46.0\nn1 = 36.0\nn2 = 36.0\nt0 = n0 - n1\nt1 = t0 * 1000.0\nt2 = t1 / 3600.0\nt3 = n2 * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "a circular racetrack is 3 miles in length and has signs posted to indicate each 1 / 10 mile increment . if a race car starts at a random location on the track and travels exactly one half mile , what is the probability that the car ends within a half mile of the sign indicating 2 1 / 2 miles ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 10.0\nn3 = 2.0\nn4 = 1.0\nn5 = 2.0\nt0 = n0 * 10.0\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.3333333333333333" + ], + "split": "train" + }, + { + "Input": "the sum of 4 th and 20 th term of a . p . is equal to the sum of 8 th , 15 th and 12 th term . find the term which is 0", + "Output Program": [ + "n0 = 4.0\nn1 = 20.0\nn2 = 8.0\nn3 = 15.0\nn4 = 12.0\nn5 = 0.0\nt0 = n2 + n3\nt1 = n0 + n1\nt2 = n4 + t0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "a 6 - liter solution is 20 % alcohol . how many liters of pure alcohol must be added to produce a solution that is 50 % alcohol ?", + "Output Program": [ + "n0 = 6.0\nn1 = 20.0\nn2 = 50.0\nt0 = n0 * n1\nt1 = t0 / 100.0\nt2 = t1 * 2.0\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "3.6" + ], + "split": "train" + }, + { + "Input": "a box contains 10 tablets of medicine a and 14 tablets of medicine b . what is the least number of tablets that should be taken from the box to ensure that at least two tablets of each kind are among the extracted .", + "Output Program": [ + "n0 = 10.0\nn1 = 14.0\n\nanswer = n1 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "the sum of present age of abe and the age before 7 years is 27 . find the present age of abe . what will be his age after 7 years ?", + "Output Program": [ + "n0 = 7.0\nn1 = 27.0\nn2 = 7.0\nt0 = n0 + n1\nt1 = t0 / 2.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "find the principle on a certain sum of money at 5 % per annum for 2 2 / 5 years if the amount being rs . 896 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 2.0\nn3 = 5.0\nn4 = 896.0\nt0 = n1 * n3\nt1 = n1 + t0\nt2 = t1 / n3\nt3 = n0 * t2\nt4 = t3 / 100.0\nt5 = t4 + 1.0\nanswer = n4 / t5\nprint(answer)" + ], + "Output Answer": [ + "799.9999999999999" + ], + "split": "train" + }, + { + "Input": "a certain clock marks every hour by striking a number of times equal to the hour , and the time require for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stoke and the end of the last stroke is 22 seconds . at 11 : 00 , how many seconds elapse between the beginning of the first stroke and the end of the last stroke ?", + "Output Program": [ + "n0 = 6.0\nn1 = 0.0\nn2 = 22.0\nn3 = 11.0\nn4 = 0.0\nt0 = n3 - 1.0\nt1 = n0 - 1.0\nt2 = n3 + t0\nt3 = n0 + t1\nt4 = n2 / t3\nanswer = t2 * t4\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "if there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city , find the number of 4 wheelers parked there if the total number of wheels is 54 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 4.0\nn3 = 54.0\nt0 = n3 - n0\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "the difference between the value of a number increased by 12.5 % and the value of the original number decreased by 25 % is 30 . what is the original number w ?", + "Output Program": [ + "n0 = 12.5\nn1 = 25.0\nn2 = 30.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = t0 + 1.0\nt3 = 1.0 - t1\nt4 = t2 - t3\nanswer = n2 / t4\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "the arithmetic mean and standard deviation of a certain normal distribution are 12 and 1.2 , respectively . what value is exactly 2 standard deviations less than the mean ?", + "Output Program": [ + "n0 = 12.0\nn1 = 1.2\nn2 = 2.0\nt0 = n1 * n2\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "9.6" + ], + "split": "train" + }, + { + "Input": "for what value of \u00e2 \u20ac \u0153 k \u00e2 \u20ac \u009d will the equation ( 2 kx 2 + 4 kx + 2 ) = 0 have equal roots ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 4.0\nn3 = 2.0\nn4 = 0.0\nt0 = n0 + n0\nt1 = n2**min(n0, 5)\nt2 = n0**min(t0, 5)\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "a is the average ( arithmetic mean ) of the first 7 positive multiples of 7 and b is the median of the first 3 positive multiples of positive integer n . if the value of a ^ 2 \u2013 b ^ 2 is zero , what is the value of n ?", + "Output Program": [ + "n0 = 7.0\nn1 = 7.0\nn2 = 3.0\nn3 = 2.0\nn4 = 2.0\nt0 = n1 * 4.0\nanswer = t0 / n3\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "roses can be purchased individually for $ 4.50 , one dozen for $ 36 , or two dozen for $ 50 . what is the greatest number of roses that can be purchased for $ 680 ?", + "Output Program": [ + "import math\nn0 = 4.5\nn1 = 36.0\nn2 = 50.0\nn3 = 680.0\nt0 = n3 / n2\nt1 = 12.0 * 2.0\nt2 = math.floor(t0)\nt3 = n2 * t2\nt4 = t2 * t1\nt5 = n3 - t3\nt6 = t5 / n0\nt7 = math.floor(t6)\nanswer = t7 + t4\nprint(answer)" + ], + "Output Answer": [ + "318" + ], + "split": "train" + }, + { + "Input": "set a contains all the even numbers between 8 and 50 inclusive . set b contains all the even numbers between 108 and 150 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ?", + "Output Program": [ + "n0 = 8.0\nn1 = 50.0\nn2 = 108.0\nn3 = 150.0\nt0 = n1 - n0\nt1 = n2 - n0\nt2 = t0 / 2.0\nt3 = t2 + 1.0\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "2200" + ], + "split": "train" + }, + { + "Input": "find the highest value of ' a ' so that 365 a 16 is divisible by 8 .", + "Output Program": [ + "import scipy\nn0 = 365.0\nn1 = 16.0\nn2 = 8.0\nt0 = scipy.gcd(int(n2), int(100.0))\nt1 = scipy.lcm(int(n2), int(100.0))\nt2 = t0 * t1\nanswer = t2 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "in a office work is distribute between p persons . if 1 / 8 members are absent then work increased for each person is ?", + "Output Program": [ + "n0 = 1.0\nn1 = 8.0\nt0 = n1 * 100.0\nt1 = n1 - n0\nt2 = t0 / t1\nanswer = t2 - 100.0\nprint(answer)" + ], + "Output Answer": [ + "14.285714285714292" + ], + "split": "train" + }, + { + "Input": "if a * b * c = 65 , b * c * d = 65 , c * d * e = 1000 and d * e * f = 250 the ( a * f ) / ( c * d ) = ?", + "Output Program": [ + "n0 = 65.0\nn1 = 65.0\nn2 = 1000.0\nn3 = 250.0\nt0 = n0 * n3\nt1 = n1 * n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.25" + ], + "split": "train" + }, + { + "Input": "a satellite is composed of 24 modular units , each of which is equipped with a set of sensors , some of which have been upgraded . each unit contains the same number of non - upgraded sensors . if the number of non - upgraded sensors on one unit is 1 / 3 the total number of upgraded sensors on the entire satellite , what fraction of the sensors on the satellite have been upgraded ?", + "Output Program": [ + "n0 = 24.0\nn1 = 1.0\nn2 = 3.0\nt0 = n1 / n2\nt1 = n0 * t0\nt2 = n0 * t1\nt3 = n0 + t2\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.1111111111111111" + ], + "split": "train" + }, + { + "Input": "what is the decimal equivalent of ( 1 / 10 ) ^ 2 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 10.0\nn2 = 2.0\nt0 = n0 / n1\nanswer = t0**min(n2, 5)\nprint(answer)" + ], + "Output Answer": [ + "0.010000000000000002" + ], + "split": "train" + }, + { + "Input": "for a bake sale , simon baked 2 n more pies than theresa . theresa baked half as many pies as roger , who baked 1313 n pies . no other pies were baked for the sale . what fraction of the total pies for sale did roger bake ?", + "Output Program": [ + "n0 = 2.0\nn1 = 1313.0\nt0 = 1.0 / 3.0\nt1 = n0 * t0\nt2 = n0 * t1\nt3 = n0 * t2\nanswer = t0 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.125" + ], + "split": "train" + }, + { + "Input": "if x , y , and z are positive integers and x = 4 y = 7 z , then the least possible value of x - y - z is", + "Output Program": [ + "n0 = 4.0\nn1 = 7.0\nt0 = n0 * n1\nt1 = t0 - n1\nanswer = t1 - n0\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "in an election , candidate douglas won 60 percent of the total vote in counties x and y . he won 72 percent of the vote in county x . if the ratio of people who voted in county x to county y is 2 : 1 , what percent of the vote did candidate douglas win in county y ?", + "Output Program": [ + "n0 = 60.0\nn1 = 72.0\nn2 = 2.0\nn3 = 1.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = n2 / 3.0\nt3 = n3 / 3.0\nt4 = t1 * t2\nt5 = t0 - t4\nt6 = t5 / t3\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "a ferry can transport 50 tons of vehicles . automobiles range in weight from 1600 to 3200 pounds . what is the greatest number of automobiles that can be loaded onto the ferry ?", + "Output Program": [ + "n0 = 50.0\nn1 = 1600.0\nn2 = 3200.0\nt0 = 1000.0 * 2.0\nt1 = n1 / t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "62.5" + ], + "split": "train" + }, + { + "Input": "how much time does a train 150 metres long running at 54 km / hr take to pass a pole ?", + "Output Program": [ + "n0 = 150.0\nn1 = 54.0\nt0 = n0 / 1000.0\nt1 = t0 / n1\nanswer = t1 * 3600.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the cash realised on selling a 14 % stock is rs . 104.25 , brokerage being 1 / 4 % is", + "Output Program": [ + "n0 = 14.0\nn1 = 104.25\nn2 = 1.0\nn3 = 4.0\nt0 = n2 / n3\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "104" + ], + "split": "train" + }, + { + "Input": "a type of extra - large suv averages 12.2 miles per gallon ( mpg ) on the highway , but only 7.6 mpg in the city . what is the maximum distance , in miles , that this suv could be driven on 23 gallons of gasoline ?", + "Output Program": [ + "n0 = 12.2\nn1 = 7.6\nn2 = 23.0\n\nanswer = n0 * n2\nprint(answer)" + ], + "Output Answer": [ + "280.59999999999997" + ], + "split": "train" + }, + { + "Input": "how many integers from 0 to 50 inclusive have a remainder of 3 when divided by 11 ?", + "Output Program": [ + "n0 = 0.0\nn1 = 50.0\nn2 = 3.0\nn3 = 11.0\n\nanswer = n1 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number .", + "Output Program": [ + "import scipy\nn0 = 17.0\nn1 = 60.0\nt0 = scipy.gcd(int(n0), int(n1))\nanswer = t0 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "a no . when divided by the sum of 555 and 445 gives 2 times their difference as quotient & 80 as remainder . find the no . is ?", + "Output Program": [ + "n0 = 555.0\nn1 = 445.0\nn2 = 2.0\nn3 = 80.0\nt0 = n0 + n1\nt1 = n0 - n1\nt2 = n2 * t0\nt3 = t2 * t1\nanswer = n3 + t3\nprint(answer)" + ], + "Output Answer": [ + "220080" + ], + "split": "train" + }, + { + "Input": "there was a cycle race going on . 1 / 5 th of the those in front of a person and 5 / 6 th of those behind him gives the total number of participants . how many people took part in the race ?", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 5.0\nn3 = 6.0\nt0 = n1 * n3\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "31" + ], + "split": "train" + }, + { + "Input": "what is the difference between the largest number and the least number written with the digits 7 , 3 , 1 , 4 ?", + "Output Program": [ + "n0 = 7.0\nn1 = 3.0\nn2 = 1.0\nn3 = 4.0\nt0 = n0 * 100.0\nt1 = n3 * 100.0\nt2 = n1 * 10.0\nt3 = n1 * 100.0\nt4 = n3 * 10.0\nt5 = t3 + 1000.0\nt6 = t0 * 10.0\nt7 = t6 + t1\nt8 = t5 + t4\nt9 = t7 + t2\nt10 = n0 + t8\nt11 = n2 + t9\nanswer = t11 - t10\nprint(answer)" + ], + "Output Answer": [ + "6084" + ], + "split": "train" + }, + { + "Input": "if 2 / w + 2 / x = 2 / y and wx = y , then the average ( arithmetic mean ) of w and x is", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 2.0\nt0 = n0 + n0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "what least number must be subtracted from 427398 so that remaining no . is divisible by 11", + "Output Program": [ + "import math\nn0 = 427398.0\nn1 = 11.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "4 milkmen rented a pasture . a grazed 24 cows for 3 months , b 10 cows for 5 months , c 35 cows for 4 months and d 21 cows for 3 months . if a \u2019 s share of rent is rs . 720 , find the total rent of the field .", + "Output Program": [ + "n0 = 4.0\nn1 = 24.0\nn2 = 3.0\nn3 = 10.0\nn4 = 5.0\nn5 = 35.0\nn6 = 4.0\nn7 = 21.0\nn8 = 3.0\nn9 = 720.0\nt0 = n1 * n2\nt1 = n3 * n4\nt2 = n0 * n5\nt3 = n2 * n7\nt4 = t0 + t1\nt5 = t2 + t3\nt6 = t4 + t5\nt7 = n9 * t6\nanswer = t7 / t0\nprint(answer)" + ], + "Output Answer": [ + "3250" + ], + "split": "train" + }, + { + "Input": "if ( a - b - c + d = 12 ) and ( a + b - c - d = 6 ) , what is the value of ( b - d ) ^ 2 ?", + "Output Program": [ + "n0 = 12.0\nn1 = 6.0\nn2 = 2.0\nt0 = n0 + n1\nt1 = t0 / n2\nt2 = n1 - t1\nanswer = t2**min(n2, 5)\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "when a number is divided by 6 & then multiply by 12 the answer is 13 what is the no . ?", + "Output Program": [ + "n0 = 6.0\nn1 = 12.0\nn2 = 13.0\nt0 = n2 / n1\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "6.5" + ], + "split": "train" + }, + { + "Input": "in arun ' s opinion , his weight is greater than 66 kg but leas than 72 kg . his brother does not agree with arun and he thinks that arun ' s weight is greater than 60 kg but less than 70 kg . his mother ' s view is that his weight can not be greater than 69 kg . if all of them are correct in their estimation , what is the average of diferent probable weights of arun ?", + "Output Program": [ + "n0 = 66.0\nn1 = 72.0\nn2 = 60.0\nn3 = 70.0\nn4 = 69.0\nt0 = n0 + 1.0\nt1 = n4 + t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "68" + ], + "split": "train" + }, + { + "Input": "find large no . from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 20 as remainder", + "Output Program": [ + "n0 = 1365.0\nn1 = 6.0\nn2 = 20.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nt2 = t0 / t1\nt3 = n1 * t2\nanswer = n2 + t3\nprint(answer)" + ], + "Output Answer": [ + "1634" + ], + "split": "train" + }, + { + "Input": "50 boys and 100 girls are examined in a test ; 50 % of the boys and 40 % of the girls pass . the percentage of the total who failed is ?", + "Output Program": [ + "n0 = 50.0\nn1 = 100.0\nn2 = 50.0\nn3 = 40.0\nt0 = n0 + n1\nt1 = n2 / 100.0\nt2 = n3 / 100.0\nt3 = n0 * t1\nt4 = n1 * t2\nt5 = t3 + t4\nt6 = t0 - t5\nt7 = t6 / t0\nanswer = t7 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "56.666666666666664" + ], + "split": "train" + }, + { + "Input": "if ( 5 ^ 5 ) ( 9 ^ 3 ) = 3 ( 15 ^ x ) , what is the value of x ?", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 5.0\nn2 = 9.0\nn3 = 3.0\nn4 = 3.0\nn5 = 15.0\nt0 = math.log(max(1e-5, n5), 2)\nt1 = n0**min(n1, 5)\nt2 = n2**min(n3, 5)\nt3 = t1 * t2\nt4 = t3 / n4\nt5 = math.log(max(1e-5, t4), 2)\nanswer = t5 / t0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "marts income is 60 percent more than tims income and tims income is 60 percent less than juans income . what percentage of juans income is marts income", + "Output Program": [ + "n0 = 60.0\nn1 = 60.0\nt0 = n0 + 100.0\nt1 = 100.0 - n1\nt2 = 100.0 / t1\nt3 = t2 * 100.0\nt4 = t0 / t3\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "train" + }, + { + "Input": "how many 4 - digit numbers ( abcd ) can be formed such that | a \u2013 d | = 2 ?", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\nt0 = 10.0 * 10.0\nt1 = 10.0 - 1.0\nt2 = t0 * t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "1800" + ], + "split": "train" + }, + { + "Input": "if the mean of numbers 28 , x , 42 , 78 and 104 is 90 , then what is the mean of 128 , 255 , 511 , 1023 and x ?", + "Output Program": [ + "n0 = 28.0\nn1 = 42.0\nn2 = 78.0\nn3 = 104.0\nn4 = 90.0\nn5 = 128.0\nn6 = 255.0\nn7 = 511.0\nn8 = 1023.0\nt0 = 1.0 + 4.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n4 * t0\nt4 = n3 + t2\nt5 = t3 - t4\nt6 = n5 + t5\nt7 = n6 + t6\nt8 = n7 + t7\nt9 = n8 + t8\nanswer = t9 / t0\nprint(answer)" + ], + "Output Answer": [ + "423" + ], + "split": "train" + }, + { + "Input": "the average speed of a car is 1 4 / 5 times the avg speed of a bike . a tractor covers 575 km in 23 hrs . how much distance will the car cover in 7 hrs if the speed of the bike is twice speed of the tractor ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 5.0\nn3 = 575.0\nn4 = 23.0\nn5 = 7.0\nt0 = n1 / n2\nt1 = n3 / n4\nt2 = n0 + t0\nt3 = t1 * 2.0\nt4 = t2 * t3\nanswer = n5 * t4\nprint(answer)" + ], + "Output Answer": [ + "630" + ], + "split": "train" + }, + { + "Input": "a caterer ordered 125 ice - cream bars and 125 sundaes . if the total price was $ 250.00 and the price of each ice - cream bar was $ 0.60 , what was the price of each sundae ?", + "Output Program": [ + "n0 = 125.0\nn1 = 125.0\nn2 = 250.0\nn3 = 0.6\nt0 = n0 * n3\nt1 = n2 - t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "1.4" + ], + "split": "train" + }, + { + "Input": "the sum of ages of 5 children born at the intervals of 3 years each is 65 years . what is the age of the youngest child ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nn2 = 65.0\nt0 = n2 / n0\nt1 = t0 - n1\nanswer = t1 - n1\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "if a - b = 3 and a ^ 2 + b ^ 2 = 31 , find the value of ab .", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 2.0\nn2 = 2.0\nn3 = 31.0\nt0 = math.sqrt(max(0, n3))\nt1 = t0 - n0\nt2 = t1 / n1\nt3 = n0 + t2\nt4 = t3 * t2\nanswer = n1 * t4\nprint(answer)" + ], + "Output Answer": [ + "10.999999999999998" + ], + "split": "train" + }, + { + "Input": "if x , y , and z are positive real numbers such that x ( y + z ) = 132 , y ( z + x ) = 152 , and z ( x + y ) = 180 , then xyz is", + "Output Program": [ + "n0 = 132.0\nn1 = 152.0\nn2 = 180.0\nt0 = n1 - n0\nanswer = n2 - t0\nprint(answer)" + ], + "Output Answer": [ + "160" + ], + "split": "train" + }, + { + "Input": "what is the greatest integer m for which the number 40 ! / 14 ^ m is an integer ?", + "Output Program": [ + "import math\nn0 = 40.0\nn1 = 14.0\nt0 = n1 / 2.0\nt1 = n0 / t0\nanswer = math.floor(t1)\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "m and n are the x and y coordinates , respectively , of a point in the coordinate plane . if the points ( m , n ) and ( m + p , n + 21 ) both lie on the line defined by the equation x = ( y / 7 ) - ( 2 / 5 ) , what is the value of p ?", + "Output Program": [ + "n0 = 21.0\nn1 = 7.0\nn2 = 2.0\nn3 = 5.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "rates for having a manuscript typed at a certain typing service are $ 5 per page for the first time a page is typed and $ 4 per page each time a page is revised . if a certain manuscript has 100 pages , of which 30 were revised only once , 20 were revised twice , and the rest required no revisions , what was the total cost of having the manuscript typed ?", + "Output Program": [ + "n0 = 5.0\nn1 = 4.0\nn2 = 100.0\nn3 = 30.0\nn4 = 20.0\nt0 = n0 * n2\nt1 = n1 * n3\nt2 = n1 * n4\nt3 = t0 + t1\nt4 = t2 * 2.0\nanswer = t3 + t4\nprint(answer)" + ], + "Output Answer": [ + "780" + ], + "split": "train" + }, + { + "Input": "if 15 students in a class average 75 % on an exam and 10 students average 95 % on the same exam , what is the average in percent for all 25 students ?", + "Output Program": [ + "n0 = 15.0\nn1 = 75.0\nn2 = 10.0\nn3 = 95.0\nn4 = 25.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = t0 + t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "83" + ], + "split": "train" + }, + { + "Input": "a boat crossed a lake from north to west at the speed of 5 km / h , entered a river and covered twice as much distance going upstream at 4 km / h . it then turned around and stopped at the south shore of the lake . if it averaged 3.6 km / h that day , what was its approximate downstream speed ?", + "Output Program": [ + "n0 = 5.0\nn1 = 4.0\nn2 = 3.6\nt0 = n0 * 2.0\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 171 games will be played during the tournament . find the number of participants .", + "Output Program": [ + "import math\nn0 = 171.0\nt0 = n0 * 2.0\nt1 = t0 * 4.0\nt2 = t1 + 1.0\nt3 = math.sqrt(max(0, t2))\nt4 = t3 + 1.0\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "a contest will consist of n questions , each of which is to be answered eithertrueorfalse . anyone who answers all n questions correctly will be a winner . what is the least value of n for which the probability is less than 1 / 10 that a person who randomly guesses the answer to each question will be a winner ?", + "Output Program": [ + "n0 = 1.0\nn1 = 10.0\nt0 = n0 / n1\nanswer = t0 * 1000.0\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "a student got twice as many sums wrong as he got right . if he attempted 75 sums in all , how many did he solve correctly ?", + "Output Program": [ + "n0 = 75.0\nt0 = 1.0 + 2.0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "how much water should be added to 12 liters of a 20 % - solution of alcohol to reduce the concentration of alcohol in the solution by 75 % ?", + "Output Program": [ + "n0 = 12.0\nn1 = 20.0\nn2 = 75.0\nt0 = n2 / 100.0\nt1 = 100.0 * 2.0\nt2 = n1 * t0\nt3 = n1 - t2\nt4 = t1 / t3\nanswer = t4 - n0\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "a sum of money lent out at s . i . amounts to rs . 710 after 2 years and to rs . 1020 after a further period of 5 years . the sum is ?", + "Output Program": [ + "n0 = 710.0\nn1 = 2.0\nn2 = 1020.0\nn3 = 5.0\nt0 = n2 - n0\nt1 = t0 / n3\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "586" + ], + "split": "train" + }, + { + "Input": "the overall age of x and y is 10 year greater than the overall age of y and z . z is how many decades younger that x ?", + "Output Program": [ + "n0 = 10.0\n\nanswer = n0 / 1.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 52 , then how old is b ?", + "Output Program": [ + "n0 = 52.0\nt0 = 1.0 + 4.0\nt1 = n0 - 2.0\nt2 = t1 * 2.0\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "a man ' s age is 125 % of what it was 10 years ago , but 83 x 1 / 3 % of what it will be after 10 years . what is his present age ?", + "Output Program": [ + "n0 = 125.0\nn1 = 10.0\nn2 = 83.0\nn3 = 1.0\nn4 = 3.0\nn5 = 10.0\nt0 = n0 / 100.0\nt1 = t0 - 1.0\nt2 = n1 / t1\nanswer = n1 + t2\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "when average age of 20 members are 0 , how many members greater than 0 ?", + "Output Program": [ + "n0 = 20.0\nn1 = 0.0\nn2 = 0.0\n\nanswer = n0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "each of the 20 boxes in a certain shipment weighs either 10 pounds or 20 pounds , and the average ( arithmetic mean ) weight of the boxes in the shipment is 18 pounds . if the average weight of the boxes in the shipment is to be reduced to 12 pounds by removing some of the 20 - pound boxes , how many 20 - pound boxes must be removed ?", + "Output Program": [ + "n0 = 20.0\nn1 = 10.0\nn2 = 20.0\nn3 = 18.0\nn4 = 12.0\nn5 = 20.0\nn6 = 20.0\nt0 = n0 * n2\nt1 = n0 * n3\nt2 = n0 * n4\nt3 = n2 - n1\nt4 = n2 - n4\nt5 = t0 - t1\nt6 = t5 / t3\nt7 = n1 * t6\nt8 = n0 - t6\nt9 = n2 * t8\nt10 = t7 + t9\nt11 = t10 - t2\nanswer = t11 / t4\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "a soccer store typically sells replica jerseys at a discount of 30 percent to 70 percent off list price . during the annual summer sale , everything in the store is an additional 20 percent off the original list price . if a replica jersey ' s list price is $ 80 , approximately what percent of the list price is the lowest possible sale price ?", + "Output Program": [ + "n0 = 30.0\nn1 = 70.0\nn2 = 20.0\nn3 = 80.0\n\nanswer = n3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "q ' = 3 q - 3 , what is the value of ( 4 ' ) ' ?", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 4.0\nt0 = n0 * n2\nt1 = n2 - 1.0\nt2 = t0 - n0\nt3 = n0 * t2\nt4 = t3 - n0\nanswer = t4 * t1\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "train" + }, + { + "Input": "consider the word rotor . whichever way you read it , from left to right or from right to left , you get the same word . such a word is known as palindrome . find the maximum possible number of 5 - letter palindromes ?", + "Output Program": [ + "n0 = 5.0\nt0 = 10.0 + 10.0\nt1 = n0 - 2.0\nt2 = t0 + 3.0\nt3 = t2 + 3.0\nanswer = t3**min(t1, 5)\nprint(answer)" + ], + "Output Answer": [ + "17576" + ], + "split": "train" + }, + { + "Input": "a type of extra - large suv averages 12.2 miles per gallon ( mpg ) on the highway , but only 7.6 mpg in the city . what is the maximum distance , in miles , that this suv could be driven on 24 gallons of gasoline ?", + "Output Program": [ + "n0 = 12.2\nn1 = 7.6\nn2 = 24.0\n\nanswer = n0 * n2\nprint(answer)" + ], + "Output Answer": [ + "292.79999999999995" + ], + "split": "train" + }, + { + "Input": "what is the 20 - fourth decimal to the right in the fraction 35 / 36 ?", + "Output Program": [ + "n0 = 20.0\nn1 = 35.0\nn2 = 36.0\nt0 = 12.0 - 1.0\nt1 = t0 * 2.0\nanswer = t1 - n0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a regular hexagon is there . the mid points of the sides were joined and formed another hexagon . then what is the percentage reduction in area .", + "Output Program": [ + "t0 = 3.0 / 4.0\nt1 = 1.0 - t0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "a jogger running at 9 km / hr along side a railway track is 240 m ahead of the engine of a 110 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?", + "Output Program": [ + "n0 = 9.0\nn1 = 240.0\nn2 = 110.0\nn3 = 45.0\nt0 = n1 + n2\nt1 = 10.0 / 2.0\nt2 = n3 - n0\nt3 = t2 / 2.0\nt4 = t1 / t3\nt5 = t4 * t2\nanswer = t0 / t5\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "a marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each . there can be no less than 8 musicians per row and no more than 30 musicians per row . how many different rectangular formations f are possible ?", + "Output Program": [ + "n0 = 240.0\nn1 = 8.0\nn2 = 30.0\n\nanswer = n0 / n2\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "the average of 100 , 200300 and x is 250 and the average of 300 , 150100 , x and y is 200 . what is the value of y ?", + "Output Program": [ + "n0 = 100.0\nn1 = 200300.0\nn2 = 250.0\nn3 = 300.0\nn4 = 150100.0\nn5 = 200.0\nt0 = 2.0 + 3.0\nt1 = n2 * 4.0\nt2 = 100.0 * 2.0\nt3 = 100.0 * 3.0\nt4 = n2 - n0\nt5 = n3 + t4\nt6 = n5 * t0\nt7 = t1 - n0\nt8 = n0 + t5\nt9 = t7 - t2\nt10 = t9 - t3\nt11 = t8 + t10\nanswer = t6 - t11\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "a person spends 1 / 3 rd of the money with him on clothes , 1 / 5 th of the remaining on food and 1 / 4 th of the remaining on travel . now , he is left with rs 500 . how much did he have with him in the beginning ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 5.0\nn4 = 1.0\nn5 = 4.0\nn6 = 500.0\nt0 = n0 / n1\nt1 = n0 - t0\nt2 = t1 / n3\nt3 = t1 - t2\nt4 = t3 / n5\nt5 = t3 - t4\nanswer = n6 / t5\nprint(answer)" + ], + "Output Answer": [ + "1249.9999999999998" + ], + "split": "train" + }, + { + "Input": "the jogging track in a sports complex is 660 m in circumference . deepak and his wife start from the same point and walk in opposite directions at 4.5 km / hr and 3.75 km / hr respectively . they will meet for the first time in ?", + "Output Program": [ + "n0 = 660.0\nn1 = 4.5\nn2 = 3.75\nt0 = n1 + n2\nt1 = n0 / 1000.0\nt2 = t1 / t0\nanswer = t2 * 60.0\nprint(answer)" + ], + "Output Answer": [ + "4.8" + ], + "split": "train" + }, + { + "Input": "the average ( arithmetic mean ) of 20 , 40 , and 60 is 5 more than the average of 20 , 60 , and what number ?", + "Output Program": [ + "n0 = 20.0\nn1 = 40.0\nn2 = 60.0\nn3 = 5.0\nn4 = 20.0\nn5 = 60.0\nt0 = n0 + n1\nt1 = n3 * 3.0\nt2 = n2 + t0\nt3 = n4 + t1\nt4 = n5 + t3\nanswer = t2 - t4\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "what is the decimal equivalent of ( 1 / 4 ) ^ 1 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 1.0\nt0 = n0 / n1\nanswer = t0**min(n2, 5)\nprint(answer)" + ], + "Output Answer": [ + "0.25" + ], + "split": "train" + }, + { + "Input": "find the least number must be subtracted from 5474827 so that remaining no . is divisible by 12 ?", + "Output Program": [ + "import math\nn0 = 5474827.0\nn1 = 12.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "find the sum the difference between the compound and s . i . on a certain sum of money for 2 years at 10 % per annum is rs . 18 of money ?", + "Output Program": [ + "n0 = 2.0\nn1 = 10.0\nn2 = 18.0\nt0 = n0 * n1\nt1 = n2 / t0\nt2 = t1 * 100.0\nanswer = t2 * t0\nprint(answer)" + ], + "Output Answer": [ + "1800" + ], + "split": "train" + }, + { + "Input": "a vessel of capacity 2 litre has 30 % of alcohol and another vessel of capacity 6 litre had 45 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?", + "Output Program": [ + "n0 = 2.0\nn1 = 30.0\nn2 = 6.0\nn3 = 45.0\nn4 = 8.0\nn5 = 10.0\nt0 = n1 / 100.0\nt1 = n3 / 100.0\nt2 = n0 * t0\nt3 = n2 * t1\nt4 = t2 + t3\nt5 = t4 / n5\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "a \u2019 s speed is 51 / 44 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?", + "Output Program": [ + "n0 = 51.0\nn1 = 44.0\nt0 = n0 - n1\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.13725490196078433" + ], + "split": "train" + }, + { + "Input": "john and mike enter into a partnership by investing $ 700 and $ 300 respectively . at the end of one year , they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business . if john received $ 800 more than mike did , what was the profit made by their business in that year ?", + "Output Program": [ + "n0 = 700.0\nn1 = 300.0\nn2 = 800.0\nt0 = n0 + n1\nt1 = 2.0 / 3.0\nt2 = n0 / t0\nt3 = n1 / t0\nt4 = t1 * t2\nt5 = t1 * t3\nt6 = t4 - t5\nanswer = n2 / t6\nprint(answer)" + ], + "Output Answer": [ + "3000.0000000000005" + ], + "split": "train" + }, + { + "Input": "a positive number when decreased by 4 is equal to 21 times the reciprocal of the number . the number is :", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 21.0\nt0 = n0 * n1\nt1 = n0**min(2.0, 5)\nt2 = t0 + t1\nt3 = math.sqrt(max(0, t2))\nt4 = n0 + t3\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 1340 in total compensation , how many total hours did he work that week ?", + "Output Program": [ + "n0 = 16.0\nn1 = 40.0\nn2 = 40.0\nn3 = 75.0\nn4 = 1340.0\nt0 = n3 + 100.0\nt1 = n0 * n1\nt2 = n0 * t0\nt3 = n4 - t1\nt4 = t2 / 100.0\nt5 = t3 / t4\nanswer = n1 + t5\nprint(answer)" + ], + "Output Answer": [ + "65" + ], + "split": "train" + }, + { + "Input": "3 buffaloes eat as much as 4 cows or 2 oxen . at a farm , there are 15 buffaloes , 8 oxen , and 24 cows . the fodder for these cattle is available for 24 days . if 40 more cows and 15 more buffaloes are brought in , how many days will the fodder last ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 2.0\nn3 = 15.0\nn4 = 8.0\nn5 = 24.0\nn6 = 24.0\nn7 = 40.0\nn8 = 15.0\nt0 = n3 + n8\nt1 = n5 + n7\nt2 = n5 / n1\nt3 = n4 / n2\nt4 = t1 / n1\nt5 = n0 * t2\nt6 = n0 * t3\nt7 = n3 + t5\nt8 = n0 * t4\nt9 = t7 + t6\nt10 = t0 + t8\nt11 = t10 + t6\nt12 = n6 * t9\nanswer = t12 / t11\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "a grocer has a sale of rs . 5420 , rs . 5660 , rs . 6200 , rs . 6350 and rs . 6500 for 5 consecutive months . find the sale he should have in the sixth month , so that he gets an average sale of rs . 6000 ?", + "Output Program": [ + "n0 = 5420.0\nn1 = 5660.0\nn2 = 6200.0\nn3 = 6350.0\nn4 = 6500.0\nn5 = 5.0\nn6 = 6000.0\nt0 = n5 + 1.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n6 * t0\nt4 = n3 + t2\nt5 = n4 + t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "5870" + ], + "split": "train" + }, + { + "Input": "of the total amount that jill spent on a shopping trip , excluding taxes , she spent 60 percent on clothing , 10 percent on food , and 30 percent on other items . if jill paid a 4 percent tax on the clothing , no tax on the food , and an 8 percent tax on all other items , then the total tax that she paid was what percent of the total amount that she spent , excluding taxes ?", + "Output Program": [ + "n0 = 60.0\nn1 = 10.0\nn2 = 30.0\nn3 = 4.0\nn4 = 8.0\nt0 = n3 / 100.0\nt1 = n4 / 100.0\nt2 = n0 * t0\nt3 = n2 * t1\nt4 = t2 + t3\nt5 = t4 / 100.0\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "4.8" + ], + "split": "train" + }, + { + "Input": "x ^ 2 + sx + 72 = 0 has two distinct integer roots ; how many values are possible for s ?", + "Output Program": [ + "n0 = 2.0\nn1 = 72.0\nn2 = 0.0\nt0 = 1.0 + 3.0\nt1 = 1.0 + 2.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "a , b and c invest in the ratio of 3 : 4 : 5 . the percentage of return on their investments are in the ratio of 6 : 5 : 4 . find the total earnings , if b earns rs . 350 more than a :", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 5.0\nn3 = 6.0\nn4 = 5.0\nn5 = 4.0\nn6 = 350.0\nt0 = n0 * n3\nt1 = n1 * n2\nt2 = t0 + t1\nt3 = t1 - t0\nt4 = t2 + t1\nt5 = n6 / t3\nanswer = t4 * t5\nprint(answer)" + ], + "Output Answer": [ + "10150" + ], + "split": "train" + }, + { + "Input": "having scored 98 runs in the 19 th inning , a cricketer increases his average score by 4 . what will be his average score after 19 innings ?", + "Output Program": [ + "n0 = 98.0\nn1 = 19.0\nn2 = 4.0\nn3 = 19.0\nt0 = n1 * n2\nt1 = n0 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "a man whose bowling average is 12.4 , takes 7 wickets for 26 runs and there by decreases his average by 0.4 . the number of wickets taken by him before his last match is ?", + "Output Program": [ + "import math\nn0 = 12.4\nn1 = 7.0\nn2 = 26.0\nn3 = 0.4\nt0 = math.floor(n0)\nt1 = n1 * t0\nt2 = n0 - t0\nt3 = t1 - n2\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "144.99999999999986" + ], + "split": "train" + }, + { + "Input": "137 + 276 = 435 how much is 731 + 672 ?", + "Output Program": [ + "n0 = 137.0\nn1 = 276.0\nn2 = 435.0\nn3 = 731.0\nn4 = 672.0\nt0 = n2 % 10.0\nt1 = t0 * 100.0\nt2 = n2 - t0\nt3 = t2 / 10.0\nt4 = t3 % 10.0\nt5 = t4 * 10.0\nt6 = t3 - t4\nt7 = t1 + t5\nt8 = t6 / 10.0\nanswer = t7 + t8\nprint(answer)" + ], + "Output Answer": [ + "534" + ], + "split": "train" + }, + { + "Input": "a batsman scored 120 runs which included 6 boundaries and 4 sixes . what % of his total score did he make by running between the wickets", + "Output Program": [ + "n0 = 120.0\nn1 = 6.0\nn2 = 4.0\nt0 = n1 * 4.0\nt1 = n1 * n2\nt2 = t0 + t1\nt3 = n0 - t2\nt4 = t3 / n0\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "if x ^ 2 is divisible by 240 what is the least possible value of integer x ?", + "Output Program": [ + "n0 = 2.0\nn1 = 240.0\nt0 = n1 / n0\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "machine t can produce x units in 3 / 4 of the time it takes machine n to produce x units . machine n can produce x units in 2 / 3 the time it takes machine o to produce x units . if all 3 machines are working simultaneously , what fraction of the total output is produced by machine n ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 2.0\nn3 = 3.0\nn4 = 3.0\nt0 = n2 / n0\nt1 = n0 / n1\nt2 = t0 * t1\nt3 = t2 + 1.0\nt4 = t3 + t0\nt5 = 1 / t4\nanswer = t0 * t5\nprint(answer)" + ], + "Output Answer": [ + "0.3076923076923077" + ], + "split": "train" + }, + { + "Input": "( ( 1 ^ m ) / ( 5 ^ m ) ) ( ( 1 ^ 16 ) / ( 4 ^ 16 ) ) = 1 / ( 2 ( 10 ) ^ 31 ) what is m ?", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 1.0\nn3 = 16.0\nn4 = 4.0\nn5 = 16.0\nn6 = 1.0\nn7 = 2.0\nn8 = 10.0\nn9 = 31.0\nt0 = n0 / n3\nt1 = n4 / n3\nt2 = 1 / n9\nt3 = n7 * n8\nt4 = t0 / t1\nt5 = n0 / t3\nt6 = t4 / t5\nt7 = t6 / n1\nt8 = t7 * t2\nanswer = 1 / t8\nprint(answer)" + ], + "Output Answer": [ + "31" + ], + "split": "train" + }, + { + "Input": "the average age of an adult class is 40 years . 18 new students with an avg age of 32 years join the class . therefore decreasing the average by 4 year . find what was theoriginal strength of class ?", + "Output Program": [ + "n0 = 40.0\nn1 = 18.0\nn2 = 32.0\nn3 = 4.0\nt0 = n1 * n2\nt1 = n0 - n3\nt2 = n1 * t1\nt3 = t2 - t0\nanswer = t3 / n3\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "a number whose fifth part increased by 7 is equal to its fourth part diminished by 7 is ?", + "Output Program": [ + "n0 = 7.0\nn1 = 7.0\nt0 = n0 + n1\nt1 = 1.0 + 4.0\nt2 = 1.0 / 4.0\nt3 = 1.0 / t1\nt4 = t2 - t3\nanswer = t0 / t4\nprint(answer)" + ], + "Output Answer": [ + "280.00000000000006" + ], + "split": "train" + }, + { + "Input": "if 1.5 x = 0.04 y then the value of ( y - x ) / ( y + x ) is", + "Output Program": [ + "n0 = 1.5\nn1 = 0.04\nt0 = n0 * 100.0\nt1 = t0 / 2.0\nt2 = t1 + 2.0\nt3 = t1 - 2.0\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.948051948051948" + ], + "split": "train" + }, + { + "Input": "the distance from the x - axis to point p is half the distance from the y - axis to point p . if the coordinates of p are ( x , - 8 ) , how many units is p from the y - axis ?", + "Output Program": [ + "n0 = 8.0\n\nanswer = n0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "a bucket full of nuts was discovered by the crow living in the basement . the crow eats a fifth of the total number of nuts in 6 hours . how many hours in total will it take the crow to finish a quarter of the nuts ?", + "Output Program": [ + "n0 = 6.0\nt0 = 2.0 + 3.0\nt1 = 1.0 / 4.0\nt2 = 1.0 / t0\nt3 = t2 / n0\nanswer = t1 / t3\nprint(answer)" + ], + "Output Answer": [ + "7.5" + ], + "split": "train" + }, + { + "Input": "how much is 65 % of 40 is greater than 4 / 5 of 25 ?", + "Output Program": [ + "n0 = 65.0\nn1 = 40.0\nn2 = 4.0\nn3 = 5.0\nn4 = 25.0\nt0 = n0 / 100.0\nt1 = n2 / n3\nt2 = n1 * t0\nt3 = n4 * t1\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "if the numerator of a fraction be increased by 12 % and its denominator decreased by 2 % the value of the fraction becomes 6 / 7 . thus , the original fraction is :", + "Output Program": [ + "n0 = 12.0\nn1 = 2.0\nn2 = 6.0\nn3 = 7.0\nt0 = n0 + 100.0\nt1 = 100.0 - n1\nt2 = n2 * t1\nt3 = n3 * t0\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.75" + ], + "split": "train" + }, + { + "Input": "65 % of x = 20 % of 487.50 . find the value of x ?", + "Output Program": [ + "n0 = 65.0\nn1 = 20.0\nn2 = 487.5\nt0 = n2 / 100.0\nt1 = n1 * t0\nt2 = t1 * 100.0\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "train" + }, + { + "Input": "m = { - 6 , - 5 , - 4 , - 3 , - 2 } t = { - 3 , - 2 , - 1 , 0 , 1 , 2 , 3 , 4 , 5 } if an integer is to be randomly selected from set m above and an integer is to be randomly selected from set t above , what is the probability that the product of the two integers will be negative ?", + "Output Program": [ + "n0 = 6.0\nn1 = 5.0\nn2 = 4.0\nn3 = 3.0\nn4 = 2.0\nn5 = 3.0\nn6 = 2.0\nn7 = 1.0\nn8 = 0.0\nn9 = 1.0\nn10 = 2.0\nn11 = 3.0\nn12 = 4.0\nn13 = 5.0\nt0 = n1 + n2\nanswer = n1 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.5555555555555556" + ], + "split": "train" + }, + { + "Input": "if a * b * c = ( \u221a ( a + 2 ) ( b + 3 ) ) / ( c + 1 ) , find the value of 6 * 15 * 5 .", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 3.0\nn2 = 1.0\nn3 = 6.0\nn4 = 15.0\nn5 = 5.0\nt0 = n0 + n3\nt1 = n1 + n4\nt2 = n2 + n5\nt3 = t0 * t1\nt4 = math.sqrt(max(0, t3))\nanswer = t4 / t2\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "when a number is divided by 6 & then multiply by 12 the answer is 9 what is the no . ?", + "Output Program": [ + "n0 = 6.0\nn1 = 12.0\nn2 = 9.0\nt0 = n2 / n1\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "4.5" + ], + "split": "train" + }, + { + "Input": "the least number , which when divided by 12 , 15 , 20 and 54 leaves in each case a remainder of 5 is :", + "Output Program": [ + "n0 = 12.0\nn1 = 15.0\nn2 = 20.0\nn3 = 54.0\nn4 = 5.0\n\nanswer = n3 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "540" + ], + "split": "train" + }, + { + "Input": "a & b started a partnership business . a ' s investment was thrice the investment of b and the period of his investment was two times the period of investments of b . if b received rs 7000 as profit , what is their total profit ?", + "Output Program": [ + "n0 = 7000.0\nt0 = 1.0 * 1.0\nt1 = 2.0 * 3.0\nt2 = t1 + t0\nt3 = t0 / t2\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "49000" + ], + "split": "train" + }, + { + "Input": "a man has rs . 10350 in the form of rs . 50 notes and rs . 500 notes . the total number of notes are 36 . find the number of notes of rs . 50 denomination .", + "Output Program": [ + "n0 = 10350.0\nn1 = 50.0\nn2 = 500.0\nn3 = 36.0\nn4 = 50.0\nt0 = n2 * n3\nt1 = n2 - n1\nt2 = t0 - n0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "the product z of two prime numbers is between 15 and 36 . if one of the prime numbers is greater than 2 but less than 6 and the other prime number is greater than 8 but less than 24 , then what is z ?", + "Output Program": [ + "n0 = 15.0\nn1 = 36.0\nn2 = 2.0\nn3 = 6.0\nn4 = 8.0\nn5 = 24.0\nt0 = n0 - 4.0\nanswer = t0 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "in a certain company , the ratio of the number of managers to the number of non - managers in any department must always be greater than 7 : 37 . in the company , what is the maximum number of non - managers in a department that has 11 managers ?", + "Output Program": [ + "import math\nn0 = 7.0\nn1 = 37.0\nn2 = 11.0\nt0 = n1 * n2\nt1 = t0 / n0\nanswer = math.floor(t1)\nprint(answer)" + ], + "Output Answer": [ + "58" + ], + "split": "train" + }, + { + "Input": "rebecca ' s yearly income is $ 15000 and jimmy ' s annual income is $ 18000 . by how much must rebecca ' s yearly income increase so that it constitutes 55 % of rebecca and jimmy ' s combined income ?", + "Output Program": [ + "n0 = 15000.0\nn1 = 18000.0\nn2 = 55.0\nt0 = n1 - n0\nt1 = t0 * 2.0\nanswer = t1 + 1000.0\nprint(answer)" + ], + "Output Answer": [ + "7000" + ], + "split": "train" + }, + { + "Input": "in a group of ducks and cows , the total number of legs are 32 more than twice the number of heads . find the total number of cows .", + "Output Program": [ + "n0 = 32.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "find the value of x . ( 47 % of 1442 - 36 % of 1412 ) + 66 = x ?", + "Output Program": [ + "import math\nn0 = 47.0\nn1 = 1442.0\nn2 = 36.0\nn3 = 1412.0\nn4 = 66.0\nt0 = n0 / 100.0\nt1 = n2 / 100.0\nt2 = n1 * t0\nt3 = n3 * t1\nt4 = t2 - t3\nt5 = n4 + t4\nt6 = t5 % 10.0\nt7 = t6 + 1.0\nanswer = math.floor(t7)\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "9823 + x = 13200 , then x is ?", + "Output Program": [ + "n0 = 9823.0\nn1 = 13200.0\n\nanswer = n1 - n0\nprint(answer)" + ], + "Output Answer": [ + "3377" + ], + "split": "train" + }, + { + "Input": "in a soccer bet , we play 4 teams . first team odd 1.28 , second 5.23 , third 3.25 , fourth 2.05 . we place the bet with 5.00 euros . how much money we expect to win ?", + "Output Program": [ + "n0 = 4.0\nn1 = 1.28\nn2 = 5.23\nn3 = 3.25\nn4 = 2.05\nn5 = 5.0\nt0 = n4 * n5\nt1 = n3 * t0\nt2 = n2 * t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "223.0072" + ], + "split": "train" + }, + { + "Input": "linda spent 4 / 5 of her savings on furniture and the rest on a tv . if the tv cost her $ 100 , what were her original savings ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 100.0\nt0 = n0 / n1\nt1 = 1.0 - t0\nanswer = n2 / t1\nprint(answer)" + ], + "Output Answer": [ + "500.0000000000001" + ], + "split": "train" + }, + { + "Input": "solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 300 milliliters of solution x to create a solution that is 25 percent alcohol by volume ?", + "Output Program": [ + "n0 = 10.0\nn1 = 30.0\nn2 = 300.0\nn3 = 25.0\nt0 = n3 - n0\nt1 = n1 - n3\nt2 = t0 / t1\nanswer = n2 * t2\nprint(answer)" + ], + "Output Answer": [ + "900" + ], + "split": "train" + }, + { + "Input": "when 242 is divided by a certain divisor the remainder obtained is 8 . when 698 is divided by the same divisor the remainder obtained is 9 . when the sum of the two numbers 242 and 698 is divided by the divisor , the remainder obtained is 4 . what is the value of the divisor ?", + "Output Program": [ + "n0 = 242.0\nn1 = 8.0\nn2 = 698.0\nn3 = 9.0\nn4 = 242.0\nn5 = 698.0\nn6 = 4.0\nt0 = n1 + n3\nanswer = t0 - n6\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "the number of positive integer solutions for the equation x + y + z + t = 10 is", + "Output Program": [ + "import math\nn0 = 10.0\nt0 = n0 - 1.0\nt1 = 4.0 - 1.0\nt2 = math.factorial(min(15, int(t0)))\nt3 = math.factorial(min(15, int(t1)))\nt4 = t0 - t1\nt5 = math.factorial(min(15, int(t4)))\nt6 = t3 * t5\nanswer = t2 / t6\nprint(answer)" + ], + "Output Answer": [ + "84" + ], + "split": "train" + }, + { + "Input": "on dividing 122 by a number , the quotient is 6 and the remainder is 2 . find the divisor ?", + "Output Program": [ + "import math\nn0 = 122.0\nn1 = 6.0\nn2 = 2.0\nt0 = n0 / n1\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "a bucket full of nuts was discovered by the crow living in the basement . the crow eats a fifth of the total number of nuts in 4 hours . how many hours in total will it take the crow to finish a quarter of the nuts ?", + "Output Program": [ + "n0 = 4.0\nt0 = 2.0 + 3.0\nt1 = 1.0 / 4.0\nt2 = 1.0 / t0\nt3 = t2 / n0\nanswer = t1 / t3\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "there are 20 brown dogs , 10 white dogs , 15 black dogs . totally how many dogs are there in all ?", + "Output Program": [ + "n0 = 20.0\nn1 = 10.0\nn2 = 15.0\nt0 = n0 + n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "in an examination , there were 2000 candidates , out of which 900 candidates were girls and rest were boys . if 28 % of the boys and 32 % of the girls passed , then the total percentage of failed candidates is ?", + "Output Program": [ + "n0 = 2000.0\nn1 = 900.0\nn2 = 28.0\nn3 = 32.0\nt0 = n1 * n3\nt1 = n0 - n1\nt2 = t0 / 100.0\nt3 = n2 * t1\nt4 = t3 / 100.0\nt5 = t2 + t4\nt6 = n0 - t5\nt7 = t6 / n0\nanswer = t7 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "70.19999999999999" + ], + "split": "train" + }, + { + "Input": "at an upscale fast - food restaurant , shin can buy 3 burgers , 7 shakes , and one cola for $ 130 . at the same place it would cost $ 164.50 for 4 burgers , 10 shakes , and one cola . how much would it cost for a meal of one burger , one shake , and one cola ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 130.0\nn3 = 164.5\nn4 = 4.0\nn5 = 10.0\nt0 = n3 - n2\nt1 = n2 + t0\nt2 = t0 * n0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "61" + ], + "split": "train" + }, + { + "Input": "if @ is a binary operation defined as the difference between an integer n and the product of n and 5 , then what is the largest positive integer n such that the outcome of the binary operation of n is less than 10 ?", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 10.0\nt0 = n0 - 1.0\nt1 = n1 / t0\nanswer = math.floor(t1)\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "if a and b are the roots of the equation x 2 - 8 x + 8 = 0 , then the value of a 2 + b 2 is :", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 8.0\nn2 = 8.0\nn3 = 0.0\nn4 = 2.0\nn5 = 2.0\nt0 = n1 * 4.0\nt1 = n1**min(n0, 5)\nt2 = t1 - t0\nt3 = math.sqrt(max(0, t2))\nt4 = n1 + t3\nt5 = n1 - t3\nt6 = t5 / n0\nt7 = t4 / n0\nt8 = t6**min(n0, 5)\nt9 = t7**min(n0, 5)\nanswer = t8 + t9\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "country x taxes each of its citizens an amount equal to 12 percent of the first $ 40,000 of income , plus 20 percent of all income in excess of $ 40,000 . if a citizen of country x is taxed a total of $ 8,000 , what is her income ?", + "Output Program": [ + "n0 = 12.0\nn1 = 40000.0\nn2 = 20.0\nn3 = 40000.0\nn4 = 8000.0\nt0 = n0 / 100.0\nt1 = n2 / 100.0\nt2 = 2.0 * 4.0\nt3 = 10.0 * 4.0\nt4 = t2 * 1000.0\nt5 = t3 * 1000.0\nt6 = t0 * t5\nt7 = t4 - t6\nt8 = t7 / t1\nanswer = t8 + t5\nprint(answer)" + ], + "Output Answer": [ + "56000" + ], + "split": "train" + }, + { + "Input": "the average salary / head of all the workers in a workshop is rs . 700 , if the average salary / head of 5 technician is rs . 800 and the average salary / head of the rest is rs . 650 , the total no . of workers in the work - shop is ?", + "Output Program": [ + "n0 = 700.0\nn1 = 5.0\nn2 = 800.0\nn3 = 650.0\nt0 = n1 * n2\nt1 = n1 * n3\nt2 = n0 - n3\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "there are 720 male and female participants in a meeting . half the female participants and one - quarterof the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?", + "Output Program": [ + "n0 = 720.0\nt0 = n0 / 3.0\nt1 = t0 * 4.0\nt2 = t1 - n0\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "in the biology lab of ` ` jefferson ' ' high school there are 0.036 * 10 ^ 5 germs , equally divided among 45000 * 10 ^ ( - 3 ) petri dishes . how many germs live happily in a single dish ?", + "Output Program": [ + "n0 = 0.036\nn1 = 10.0\nn2 = 5.0\nn3 = 45000.0\nn4 = 10.0\nn5 = 3.0\nt0 = n3 / 1000.0\nt1 = 100.0 * 1000.0\nt2 = n0 * t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "79.99999999999999" + ], + "split": "train" + }, + { + "Input": "a large field of 500 hectares is divided into two parts . the difference of the areas of the two parts is one - fifth of the average of the two areas . what is the area of the smaller part in hectares ?", + "Output Program": [ + "n0 = 500.0\nt0 = 1.0 + 4.0\nt1 = n0 / 2.0\nt2 = 1.0 / t0\nt3 = t1 * t2\nt4 = n0 - t3\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "225" + ], + "split": "train" + }, + { + "Input": "a jogger running at 9 km / hr along side a railway track is 240 m ahead of the engine of a 150 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?", + "Output Program": [ + "n0 = 9.0\nn1 = 240.0\nn2 = 150.0\nn3 = 45.0\nt0 = n1 + n2\nt1 = 10.0 / 2.0\nt2 = n3 - n0\nt3 = t2 / 2.0\nt4 = t1 / t3\nt5 = t4 * t2\nanswer = t0 / t5\nprint(answer)" + ], + "Output Answer": [ + "39" + ], + "split": "train" + }, + { + "Input": "0 - - - : - | - - - : - - | - : - - : - | - - : - - - | - : - - - - 1 on the number line above , the segment from 0 to 1 has been divided into fifths , as indicated by the large tick marks , and also into sevenths , as indicated by the small tick marks . what is the least possible distance z between any two of the tick marks ?", + "Output Program": [ + "n0 = 0.0\nn1 = 1.0\nn2 = 0.0\nn3 = 1.0\nt0 = 1.0 + 4.0\nt1 = 10.0 * 3.0\nt2 = t0 + t1\nanswer = n1 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.02857142857142857" + ], + "split": "train" + }, + { + "Input": "david obtained 76 , 65 , 82 , 67 and 85 marks ( out in 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?", + "Output Program": [ + "n0 = 76.0\nn1 = 65.0\nn2 = 82.0\nn3 = 67.0\nn4 = 85.0\nn5 = 100.0\nt0 = n0 + n1\nt1 = 2.0 + 3.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "joan took out a mortgage from hel local bank . each monthly mortgage payment she makes must be triple the amount of the previous month ' s payment . if her first payment is $ 100 , and the total amount she must pay back is $ 2952400 , how many months will it take joan to pay back her mortgage ?", + "Output Program": [ + "import math\nn0 = 100.0\nn1 = 2952400.0\nt0 = math.log(max(1e-5, 3.0), 2)\nt1 = n1 * 2.0\nt2 = t1 / n0\nt3 = t2 + 1.0\nt4 = math.log(max(1e-5, t3), 2)\nanswer = t4 / t0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "a company decreased the price of its main product by 20 % . subsequently , the number of units sold increased such that the total revenue remained unchanged . what was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product ?", + "Output Program": [ + "n0 = 20.0\n\nanswer = 100.0 / n0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "the average age of an adult class is 40 years . 17 new students with an avg age of 32 years join the class . therefore decreasing the average by 4 year . find what was theoriginal strength of class ?", + "Output Program": [ + "n0 = 40.0\nn1 = 17.0\nn2 = 32.0\nn3 = 4.0\nt0 = n1 * n2\nt1 = n0 - n3\nt2 = n1 * t1\nt3 = t2 - t0\nanswer = t3 / n3\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "on dividing a number by 5 , we get 2 as quotient and 0 as remainder . on dividing the same number by 4 , what will be the remainder ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 0.0\nn3 = 4.0\nt0 = n0 * n1\nanswer = t0 % n3\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "the expression x # y denotes the product of the consecutive multiples of 3 between x and y , inclusive . what is the sum of the exponents in the prime factorization of 21 # 36 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 21.0\nn2 = 36.0\nt0 = 2.0 + 2.0\nt1 = n0 + t0\nt2 = t1 + t0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "a grocer has a sale of rs . 435 , rs . 927 , rs . 855 , rs . 230 and rs . 562 for 5 consecutive days . how much sale must he have in the sixth day so that he gets an average sale of rs . 625 ?", + "Output Program": [ + "n0 = 435.0\nn1 = 927.0\nn2 = 855.0\nn3 = 230.0\nn4 = 562.0\nn5 = 5.0\nn6 = 625.0\nt0 = n5 + 1.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n6 * t0\nt4 = n3 + t2\nt5 = n4 + t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "741" + ], + "split": "train" + }, + { + "Input": "in a group of 800 people , 1 / 5 play at least one instrument , 32 play two or more . what is the probability that one student play exactly one instrument ?", + "Output Program": [ + "n0 = 800.0\nn1 = 1.0\nn2 = 5.0\nn3 = 32.0\nt0 = n0 * n1\nt1 = t0 / n2\nt2 = t1 - n3\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.16" + ], + "split": "train" + }, + { + "Input": "teacher took exam for english , average for the entire class was 80 marks . if we say that 10 % of the students scored 95 marks and 20 % scored 90 marks then calcualte average marks of the remaining students of the class .", + "Output Program": [ + "n0 = 80.0\nn1 = 10.0\nn2 = 95.0\nn3 = 20.0\nn4 = 90.0\nt0 = n1 / 100.0\nt1 = n3 / 100.0\nt2 = t0 + t1\nt3 = n2 * t0\nt4 = n4 * t1\nt5 = n0 - t3\nt6 = 1.0 - t2\nt7 = t5 - t4\nanswer = t7 / t6\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "a and b together have rs . 1210 . if of a ' s amount is equal to of b ' s amount , how much amount does b have ?", + "Output Program": [ + "n0 = 1210.0\nt0 = 2.0 + 3.0\nt1 = 2.0 / t0\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "484" + ], + "split": "train" + }, + { + "Input": "robert ate 10 chocolates , nickel ate 5 chocolates . how many more chocolates did robert ate than nickel ?", + "Output Program": [ + "n0 = 10.0\nn1 = 5.0\n\nanswer = n0 - n1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "if a + b = \u2212 9 , and a = 30 / b , what is the value of a ^ 2 + b ^ 2 ?", + "Output Program": [ + "n0 = 9.0\nn1 = 30.0\nn2 = 2.0\nn3 = 2.0\nt0 = n1 * n2\nt1 = n0**min(n2, 5)\nanswer = t1 - t0\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "if f ( x ) = 2 x ^ 2 + y , and f ( 2 ) = 60 , what is the value of f ( 5 ) ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 2.0\nn3 = 60.0\nn4 = 5.0\nt0 = n4**min(n0, 5)\nt1 = n0**min(n0, 5)\nt2 = n0 * t0\nt3 = n0 * t1\nt4 = n3 - t3\nanswer = t2 + t4\nprint(answer)" + ], + "Output Answer": [ + "102" + ], + "split": "train" + }, + { + "Input": "if n divided by 7 has a remainder of 2 , what is the remainder when 2 times n is divided by 7 ?", + "Output Program": [ + "n0 = 7.0\nn1 = 2.0\nn2 = 2.0\nn3 = 7.0\n\nanswer = n1 * n2\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "if 60 percent of 600 is 50 percent of x , then x = ?", + "Output Program": [ + "n0 = 60.0\nn1 = 600.0\nn2 = 50.0\nt0 = n0 * n1\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "720" + ], + "split": "train" + }, + { + "Input": "a car averages 50 mph for the first 4 hours of a trip and averages 80 mph for each additional hour . the average speed for the entire trip was 65 mph . how many hours long is the trip ?", + "Output Program": [ + "n0 = 50.0\nn1 = 4.0\nn2 = 80.0\nn3 = 65.0\nt0 = n3 * 4.0\nt1 = n0 * n1\nt2 = n2 - n3\nt3 = t0 - t1\nt4 = t3 / t2\nanswer = n1 + t4\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "60 % of x is greater than 1 / 3 rd of x by 110 . what is x ?", + "Output Program": [ + "n0 = 60.0\nn1 = 1.0\nn2 = 3.0\nn3 = 110.0\nt0 = n0 / 100.0\nt1 = n1 / n2\nt2 = t0 - t1\nanswer = n3 / t2\nprint(answer)" + ], + "Output Answer": [ + "412.5" + ], + "split": "train" + }, + { + "Input": "if an integer n is to be selected at random from 1 to 900 , inclusive , what is probability n ( n + 1 ) will be divisible by 9 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 900.0\nn2 = 1.0\nn3 = 9.0\n\nanswer = 2.0 / n3\nprint(answer)" + ], + "Output Answer": [ + "0.2222222222222222" + ], + "split": "train" + }, + { + "Input": "if p / q = 4 / 5 , then the value of 4 / 7 + { ( 2 q - p ) / ( 2 q + p ) } is ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 4.0\nn3 = 7.0\nn4 = 2.0\nn5 = 2.0\nt0 = n2 / n3\nt1 = n0 / n1\nt2 = n4 + t1\nt3 = n4 - t1\nt4 = t3 / t2\nanswer = t0 + t4\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "patrick purchased 70 pencils and sold them at a loss equal to the selling price of 20 pencils . the cost of 70 pencils is how many times the selling price of 70 pencils ?", + "Output Program": [ + "n0 = 70.0\nn1 = 20.0\nn2 = 70.0\nn3 = 70.0\nt0 = n0 + n1\nt1 = n0 / t0\nanswer = 1 / t1\nprint(answer)" + ], + "Output Answer": [ + "1.2857142857142856" + ], + "split": "train" + }, + { + "Input": "40 % of x is greater than 1 / 3 rd of x by 110 . what is x ?", + "Output Program": [ + "n0 = 40.0\nn1 = 1.0\nn2 = 3.0\nn3 = 110.0\nt0 = n0 / 100.0\nt1 = n1 / n2\nt2 = t0 - t1\nanswer = n3 / t2\nprint(answer)" + ], + "Output Answer": [ + "1649.999999999999" + ], + "split": "train" + }, + { + "Input": "the sum of two numbers is 62 , and one of them is 12 more than the other . what are the two numbers ?", + "Output Program": [ + "n0 = 62.0\nn1 = 12.0\nt0 = n0 - n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "tickets numbered from 1 to 27 are mixed and then a ticket is selected randomly . what is the probability that the selected ticket bears a number which is a multiple of 3 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 27.0\nn2 = 3.0\nt0 = n1 / n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.3333333333333333" + ], + "split": "train" + }, + { + "Input": "if 2 ^ ( 2 w ) = 8 ^ ( w \u2212 4 ) , what is the value of w ?", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 2.0\nn2 = 8.0\nn3 = 4.0\nt0 = math.log(max(1e-5, n0), 2)\nt1 = t0 * 12.0\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "what is the local value of 7 in the difference of 100889 and local value of 3 in 28943712 ?", + "Output Program": [ + "n0 = 7.0\nn1 = 100889.0\nn2 = 3.0\nn3 = 28943712.0\nt0 = 10.0 * 1000.0\nt1 = n3 % 1000.0\nt2 = n3 - t1\nt3 = t2 % t0\nt4 = n1 * t3\nanswer = t4 % t0\nprint(answer)" + ], + "Output Answer": [ + "7000" + ], + "split": "train" + }, + { + "Input": "3 numbers are in the ratio 5 : 6 : 8 . the sum of its longest and smallest numbers equals the sum of the third number and 49 . find the third number ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 6.0\nn3 = 8.0\nn4 = 49.0\nt0 = n1 + n3\nt1 = t0 - n2\nt2 = n4 / t1\nanswer = n2 * t2\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "what is the next number : 3 , 11 , 83 , __", + "Output Program": [ + "n0 = 3.0\nn1 = 11.0\nn2 = 83.0\nt0 = n2 * 10.0\nt1 = t0 - 100.0\nt2 = t1 - n0\nanswer = t2 - n0\nprint(answer)" + ], + "Output Answer": [ + "724" + ], + "split": "train" + }, + { + "Input": "if the farmer sells 75 of his chickens , his stock of feed will last for 20 more days than planned , but if he buys 100 more chickens , he will run out of feed 15 days earlier than planned . if no chickens are sold or bought , the farmer will be exactly on schedule . how many chickens does the farmer have ?", + "Output Program": [ + "n0 = 75.0\nn1 = 20.0\nn2 = 100.0\nn3 = 15.0\nt0 = n2 - n0\nt1 = n1 - n3\nt2 = t0 / t1\nt3 = n0 / t2\nt4 = n1 * t3\nt5 = n1 - t3\nt6 = t4 / t5\nanswer = t6 * t2\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "if the average of t , b , c , 14 and 15 is 12 . what is the average value of t , b , c and 29", + "Output Program": [ + "n0 = 14.0\nn1 = 15.0\nn2 = 12.0\nn3 = 29.0\nt0 = 2.0 + 3.0\nt1 = n2 * t0\nanswer = t1 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "if p # q denotes the least common multiple of p and q , then q = ( ( 12 # 16 ) # ( 18 # 24 ) ) = ?", + "Output Program": [ + "n0 = 12.0\nn1 = 16.0\nn2 = 18.0\nn3 = 24.0\nt0 = n2 * n3\nt1 = n0 * n1\nt2 = t0 - t1\nt3 = t2 / 2.0\nanswer = n3 + t3\nprint(answer)" + ], + "Output Answer": [ + "144" + ], + "split": "train" + }, + { + "Input": "set x consists of all two - digit primes and set y consists of all positive odd multiples of 7 less than 100 . if the two sets are combined into one , what will be the range of the new set ?", + "Output Program": [ + "n0 = 7.0\nn1 = 100.0\nt0 = n1 - 3.0\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "a ranch has both horses and ponies . exactly 3 / 10 of the ponies have horseshoes , and exactly 5 / 8 of the ponies with horseshoes are from iceland . if there are 3 more horses than ponies , what is the minimum possible combined number of horses and ponies on the ranch ?", + "Output Program": [ + "import scipy\nn0 = 3.0\nn1 = 10.0\nn2 = 5.0\nn3 = 8.0\nn4 = 3.0\nt0 = n1 / n2\nt1 = n3 * t0\nt2 = scipy.lcm(int(n1), int(t1))\nt3 = n4 + t2\nanswer = t3 + t2\nprint(answer)" + ], + "Output Answer": [ + "163" + ], + "split": "train" + }, + { + "Input": "if the price of a tv is first decreased by 20 % and then increased by 55 % , then the net change in the price will be :", + "Output Program": [ + "n0 = 20.0\nn1 = 55.0\nt0 = n1 + 100.0\nt1 = 100.0 - n0\nt2 = t0 * t1\nt3 = t2 / 100.0\nanswer = t3 - 100.0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "what is the smallest integer c for which 27 ^ c > 3 ^ 24 ?", + "Output Program": [ + "import math\nn0 = 27.0\nn1 = 3.0\nn2 = 24.0\nt0 = n2 / 3.0\nt1 = math.floor(t0)\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "what is the average ( arithmetic mean ) of all multiples of 10 from 10 to 400 inclusive ?", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 400.0\nt0 = n0 + n2\nt1 = n2 - n0\nt2 = t1 / n0\nt3 = t2 + 1.0\nt4 = t0 * t3\nt5 = t4 / 2.0\nanswer = t5 / t3\nprint(answer)" + ], + "Output Answer": [ + "205" + ], + "split": "train" + }, + { + "Input": "if the digits 27 in the decimal 0.00027 repeat indefinitely , what is the value of ( 10 ^ 5 - 10 ^ 3 ) ( 0.00027 ) ?", + "Output Program": [ + "n0 = 27.0\nn1 = 0.00027\nn2 = 10.0\nn3 = 5.0\nn4 = 10.0\nn5 = 3.0\nn6 = 0.00027\nt0 = n2 * n2\nt1 = t0 - 1.0\nt2 = n0 / t1\nt3 = t0 * t1\nt4 = t2 * t3\nt5 = t4 / 1000.0\nanswer = n2 * t5\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "train" + }, + { + "Input": "in a school with 652 students , the average age of the boys is 12 years and that of the girls is 11 years . if the average age of the school is 11 years 9 months , then the number of girls in the school is", + "Output Program": [ + "n0 = 652.0\nn1 = 12.0\nn2 = 11.0\nn3 = 11.0\nn4 = 9.0\nt0 = n4 / n1\nt1 = n0 * n1\nt2 = n2 + t0\nt3 = n0 * t2\nanswer = t1 - t3\nprint(answer)" + ], + "Output Answer": [ + "163" + ], + "split": "train" + }, + { + "Input": "country x taxes each of its citizens an amount equal to 11 percent of the first $ 40,000 of income , plus 20 percent of all income in excess of $ 40,000 . if a citizen of country x is taxed a total of $ 8,000 , what is her income ?", + "Output Program": [ + "n0 = 11.0\nn1 = 40000.0\nn2 = 20.0\nn3 = 40000.0\nn4 = 8000.0\nt0 = n0 / 100.0\nt1 = n2 / 100.0\nt2 = 2.0 * 4.0\nt3 = 10.0 * 4.0\nt4 = t2 * 1000.0\nt5 = t3 * 1000.0\nt6 = t0 * t5\nt7 = t4 - t6\nt8 = t7 / t1\nanswer = t8 + t5\nprint(answer)" + ], + "Output Answer": [ + "58000" + ], + "split": "train" + }, + { + "Input": "list k consists of 14 consecutive integers . if - 4 is the least integer in list k , what is the range of the positive integers in list k ?", + "Output Program": [ + "n0 = 14.0\nn1 = 4.0\nt0 = n0 - n1\nt1 = t0 - 1.0\nanswer = t1 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "find the average of all the numbers between 6 and 34 which is divisible by 5", + "Output Program": [ + "n0 = 6.0\nn1 = 34.0\nn2 = 5.0\nt0 = n0 + 4.0\nt1 = n1 - 4.0\nt2 = t0 + t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": ". 3 + 33 + 333 + 3.33 = ?", + "Output Program": [ + "n0 = 3.0\nn1 = 33.0\nn2 = 333.0\nn3 = 3.33\nt0 = n1 + n2\nt1 = 3.0 / 10.0\nt2 = n3 + t0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "369.63" + ], + "split": "train" + }, + { + "Input": "find a sum for first 6 prime number ' ss ?", + "Output Program": [ + "n0 = 6.0\nt0 = n0 + n0\nt1 = n0 + 1.0\nt2 = t0 * 4.0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "41" + ], + "split": "train" + }, + { + "Input": "what least number should be subtracted from 3,381 so that the remainder when divided by 9 , 11 , and 17 will leave in each case the same remainder 8 ?", + "Output Program": [ + "n0 = 3381.0\nn1 = 9.0\nn2 = 11.0\nn3 = 17.0\nn4 = 8.0\nt0 = n1 * n2\nt1 = n3 * t0\nt2 = t1 * 2.0\nt3 = n4 + t2\nanswer = n0 - t3\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "diana is painting statues . she has 7 / 16 of a gallon of paint remaining . each statue requires 1 / 16 gallon of paint . how many statues can she paint ?", + "Output Program": [ + "n0 = 7.0\nn1 = 16.0\nn2 = 1.0\nn3 = 16.0\nt0 = n0 / n1\nt1 = n2 / n3\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "if 5 / ( 4 + 1 / x ) = 1 , then x =", + "Output Program": [ + "n0 = 5.0\nn1 = 4.0\nn2 = 1.0\nn3 = 1.0\nt0 = n0 - n1\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "the average age of a class of 22 students is 21 years . the average increased by 1 when the teacher ' s age also included . what is the age of the teacher ?", + "Output Program": [ + "n0 = 22.0\nn1 = 21.0\nn2 = 1.0\nt0 = n0 + n2\nt1 = n1 + n2\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "44" + ], + "split": "train" + }, + { + "Input": "if k is a non - negative integer and 18 ^ k is a divisor of 624,938 then 6 ^ k - k ^ 6 =", + "Output Program": [ + "n0 = 18.0\nn1 = 624938.0\nn2 = 6.0\nn3 = 6.0\nt0 = 1.0 - 1.0\nt1 = n2**min(t0, 5)\nt2 = t0**min(n2, 5)\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "two trains start at same time from two stations and proceed towards each other at the rate of 20 km / hr and 25 km / hr respectively . when they meet , it is found that one train has traveled 55 km more than the other . what is the distance between the two stations ?", + "Output Program": [ + "n0 = 20.0\nn1 = 25.0\nn2 = 55.0\nt0 = n0 + n1\nt1 = n1 - n0\nt2 = n2 / t1\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "495" + ], + "split": "train" + }, + { + "Input": "lilly has 10 fish and rosy has 9 fish . in total , how many fish do they have in all ?", + "Output Program": [ + "n0 = 10.0\nn1 = 9.0\n\nanswer = n0 + n1\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "of the goose eggs laid at a certain pond , 1 / 3 hatched and 4 / 5 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 120 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 4.0\nn3 = 5.0\nn4 = 3.0\nn5 = 5.0\nn6 = 120.0\nt0 = n1 / n5\nt1 = n2 / n3\nt2 = n0 / n1\nt3 = 1.0 - t0\nt4 = n6 / t3\nt5 = t4 / t1\nanswer = t5 / t2\nprint(answer)" + ], + "Output Answer": [ + "1125" + ], + "split": "train" + }, + { + "Input": "given that p is a positive even integer with a positive units digit , if the units digit of p ^ 3 minus the units digit of p ^ 2 is equal to 0 , what is the units digit of p + 5 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 0.0\nn3 = 5.0\nt0 = n0 + n0\nanswer = n3 + t0\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "if a / x = 1 / 3 and a / y = 1 / 4 , then ( x + y ) =", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 4.0\n\nanswer = n1 + n3\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "for the past n days , the average ( arithmetic mean ) daily production at a company was 70 units . if today ' s production of 90 units raises the average to 75 units per day , what is the value of n ?", + "Output Program": [ + "n0 = 70.0\nn1 = 90.0\nn2 = 75.0\nt0 = n1 - n0\nt1 = n2 - n0\nt2 = t0 / t1\nanswer = t2 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "if a @ b = a * b ^ ( 1 / 2 ) then 4 @ 9 = ? self made", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 4.0\nn3 = 9.0\nt0 = n0 / n1\nt1 = n3**min(t0, 5)\nanswer = n2 * t1\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "the equal amounts of money are deposited in two banks each at 15 % per annum for 3.5 years and 5 years respectively . if the difference between their interests is rs . 144 , find the each sum ?", + "Output Program": [ + "n0 = 15.0\nn1 = 3.5\nn2 = 5.0\nn3 = 144.0\nt0 = n0 * n2\nt1 = n0 * n1\nt2 = t0 - t1\nt3 = t2 / 100.0\nanswer = n3 / t3\nprint(answer)" + ], + "Output Answer": [ + "640" + ], + "split": "train" + }, + { + "Input": "a library has an average of 510 visitors on sunday and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is ?", + "Output Program": [ + "n0 = 510.0\nn1 = 240.0\nn2 = 30.0\nt0 = 1.0 + 4.0\nt1 = n0 * t0\nt2 = t0 * t0\nt3 = n1 * t2\nt4 = t1 + t3\nanswer = t4 / n2\nprint(answer)" + ], + "Output Answer": [ + "285" + ], + "split": "train" + }, + { + "Input": "the sum of present age of abe and the age before 7 years is 35 . find the present age of abe . what will be his age after 7 years ?", + "Output Program": [ + "n0 = 7.0\nn1 = 35.0\nn2 = 7.0\nt0 = n0 + n1\nt1 = t0 / 2.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "the two lines y = x and x = - 6 intersect on the coordinate plane . what is the value of the area of the figure formed by the intersecting lines and the x - axis ?", + "Output Program": [ + "n0 = 6.0\nt0 = n0 * n0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "the average weight of 29 students is 28 kg . by the admission of a new student , the average weight is reduced to 27.5 kg . the weight of the new student is", + "Output Program": [ + "n0 = 29.0\nn1 = 28.0\nn2 = 27.5\nt0 = n0 + 1.0\nt1 = n0 * n1\nt2 = n2 * t0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "the arithmetic mean and standard deviation of a certain normal distribution are 15 and 1.5 , respectively . what value is exactly 2 standard deviations less than the mean ?", + "Output Program": [ + "n0 = 15.0\nn1 = 1.5\nn2 = 2.0\nt0 = n1 * n2\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "if greg buys 5 shirts , 4 trousers and 2 ties , the total cost is $ 80 . if greg buys 7 shirts , 4 trousers and 2 ties , the total cost is $ 70 . how much will it cost him to buy 2 trousers , 3 shirts and 1 ties ?", + "Output Program": [ + "n0 = 5.0\nn1 = 4.0\nn2 = 2.0\nn3 = 80.0\nn4 = 7.0\nn5 = 4.0\nn6 = 2.0\nn7 = 70.0\nn8 = 2.0\nn9 = 3.0\nn10 = 1.0\nt0 = n3 + n7\nanswer = t0 / n5\nprint(answer)" + ], + "Output Answer": [ + "37.5" + ], + "split": "train" + }, + { + "Input": "80 % of the population of a village is 32000 . the total population of the village is ?", + "Output Program": [ + "n0 = 80.0\nn1 = 32000.0\nt0 = 100.0 / n0\nanswer = n1 * t0\nprint(answer)" + ], + "Output Answer": [ + "40000" + ], + "split": "train" + }, + { + "Input": "a number x is 4 times another number y . the percentage that y is less than x is", + "Output Program": [ + "n0 = 4.0\nt0 = n0 - 1.0\nt1 = t0 / n0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "if the remainder is 16 when the integer n is divided by 30 , what is the remainder when 2 n is divided by 15 ?", + "Output Program": [ + "n0 = 16.0\nn1 = 30.0\nn2 = 2.0\nn3 = 15.0\nt0 = n0 * n2\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a case of 12 rolls of paper towels sells for $ 9 . the cost of one roll sold individually is $ 1 . what is the percent t of savings per roll for the 12 - roll package over the cost of 12 rolls purchased individually ?", + "Output Program": [ + "n0 = 12.0\nn1 = 9.0\nn2 = 1.0\nn3 = 12.0\nn4 = 12.0\nt0 = n1 / n0\nt1 = t0 * 100.0\nanswer = 100.0 - t1\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "set x consists of 10 integers and has median of 30 and a range of 20 . what is the value of the greatest possible integer that can be present in the set ?", + "Output Program": [ + "n0 = 10.0\nn1 = 30.0\nn2 = 20.0\n\nanswer = n1 + n2\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "find the sum lend at c . i . at 5 p . c per annum will amount to rs . 650 in 2 years ?", + "Output Program": [ + "n0 = 5.0\nn1 = 650.0\nn2 = 2.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nt2 = t1**min(n2, 5)\nanswer = n1 / t2\nprint(answer)" + ], + "Output Answer": [ + "589.5691609977324" + ], + "split": "train" + }, + { + "Input": "a batsman scored 120 runs which included 3 boundaries and 8 sixes . what % of his total score did he make by running between the wickets", + "Output Program": [ + "n0 = 120.0\nn1 = 3.0\nn2 = 8.0\nt0 = n1 + n1\nt1 = n1 * 4.0\nt2 = n2 * t0\nt3 = t1 + t2\nt4 = t3 / n0\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "4.036 divided by 0.04 gives :", + "Output Program": [ + "n0 = 4.036\nn1 = 0.04\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "100.89999999999999" + ], + "split": "train" + }, + { + "Input": "find the constant k so that : - x 2 - ( k + 7 ) x - 8 = - ( x - 2 ) ( x - 4 )", + "Output Program": [ + "n0 = 2.0\nn1 = 7.0\nn2 = 8.0\nn3 = 2.0\nn4 = 4.0\nt0 = n0 + n4\nanswer = n1 + t0\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "the average age of a group of 10 persons was decreased by 3 years when one person , whose age was 48 years , was replaced by a new person . find the age of the new person ?", + "Output Program": [ + "n0 = 10.0\nn1 = 3.0\nn2 = 48.0\nt0 = n0 * n1\nanswer = n2 - t0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "what least no . must be subtracted from 10154 so that remaining no . is divisible by 30 ?", + "Output Program": [ + "import math\nn0 = 10154.0\nn1 = 30.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "a batsman makes a score of 74 runs in the 17 th inning and thus increases his averages by 3 . what is his average after 17 th inning ?", + "Output Program": [ + "n0 = 74.0\nn1 = 17.0\nn2 = 3.0\nn3 = 17.0\nt0 = n1 * n2\nt1 = n0 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "a 5 - digit number divisible by 3 is to be formed using numerical 0 , 1 , 2 , 3 , 4 and 5 without repetition . the total number q of ways this can be done is :", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 3.0\nn2 = 0.0\nn3 = 1.0\nn4 = 2.0\nn5 = 3.0\nn6 = 4.0\nn7 = 5.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(n6)))\nt2 = t0 * 2.0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "216" + ], + "split": "train" + }, + { + "Input": "the average height of 35 boys in a class was calculated as 180 cm . it has later found that the height of one of the boys in the class was wrongly written as 156 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ) .", + "Output Program": [ + "import math\nn0 = 35.0\nn1 = 180.0\nn2 = 156.0\nn3 = 106.0\nt0 = n0 * n1\nt1 = t0 - n2\nt2 = n3 + t1\nt3 = t2 / n0\nanswer = math.floor(t3)\nprint(answer)" + ], + "Output Answer": [ + "178" + ], + "split": "train" + }, + { + "Input": "john purchased 1365 large bottles at $ 1.89 per bottle and 720 small bottles at $ 1.42 per bottle . what was the approximate average price paid per bottle ?", + "Output Program": [ + "n0 = 1365.0\nn1 = 1.89\nn2 = 720.0\nn3 = 1.42\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "1.7276978417266187" + ], + "split": "train" + }, + { + "Input": "40 onions on a scale weigh 7.68 kg . when 5 onions are removed from the scale , the average weight of the 35 onions is 190 grams . what is the average weight ( in grams ) of the 5 onions which were removed ?", + "Output Program": [ + "n0 = 40.0\nn1 = 7.68\nn2 = 5.0\nn3 = 35.0\nn4 = 190.0\nn5 = 5.0\nt0 = n1 * 1000.0\nt1 = n3 * n4\nt2 = t0 - t1\nanswer = t2 / n2\nprint(answer)" + ], + "Output Answer": [ + "206" + ], + "split": "train" + }, + { + "Input": "mudit ' s age 16 years hence will be thrice his age 4 years ago . find mudit ' s present age ?", + "Output Program": [ + "n0 = 16.0\nn1 = 4.0\nt0 = n1 * 3.0\nt1 = n0 + t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "on a certain planet where people usually tend to live for more than a century , the ratio of present ages of father and son is 7 : 4 . 10 years later , the ratio of their ages will be 5 : 3 . what is the sum of their present ages ?", + "Output Program": [ + "n0 = 7.0\nn1 = 4.0\nn2 = 10.0\nn3 = 5.0\nn4 = 3.0\nt0 = n2 * n3\nt1 = n2 * n4\nt2 = t0 - t1\nt3 = n0 * t2\nt4 = n1 * t2\nanswer = t3 + t4\nprint(answer)" + ], + "Output Answer": [ + "220" + ], + "split": "train" + }, + { + "Input": "what is the value of x ^ 2 yz \u2212 xyz ^ 2 , if x = \u2212 2 , y = 1 , and z = 4 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 2.0\nn3 = 1.0\nn4 = 4.0\nt0 = -n0\nt1 = n4 * t0\nt2 = t0 - n4\nt3 = n3 * t1\nanswer = t3 * t2\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "on july 1 of last year , total employees at company e was decreased by 10 percent . without any change in the salaries of the remaining employees , the average ( arithmetic mean ) employee salary was 10 percent more after the decrease in the number of employees than before the decrease . the total of the combined salaries of all the employees at company e after july 1 last year was what percent q of thatbeforejuly 1 last year ?", + "Output Program": [ + "n0 = 1.0\nn1 = 10.0\nn2 = 10.0\nn3 = 1.0\nn4 = 1.0\n\nanswer = n1 * n1\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "a man spend 1 / 5 of his salary on food , 1 / 10 of his salary on house rent and 3 / 5 salary on clothes . he still has $ 18000 left with him . find salary . .", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 1.0\nn3 = 10.0\nn4 = 3.0\nn5 = 5.0\nn6 = 18000.0\nt0 = n0 / n1\nt1 = n0 / n3\nt2 = n4 / n1\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n0 - t4\nanswer = n6 / t5\nprint(answer)" + ], + "Output Answer": [ + "180000.00000000003" + ], + "split": "train" + }, + { + "Input": "bert left the house with n dollars . he spent 1 / 4 of this at the hardware store , then $ 9 at the dry cleaners , and then half of what was left at the grocery store . when he got home , he had $ 12 left in his pocket . what was the value of n ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 9.0\nn3 = 12.0\nt0 = n2 / 2.0\nt1 = n0 / n1\nt2 = n3 + t0\nt3 = n0 - t1\nt4 = 1 / t3\nt5 = t2 * t4\nanswer = t5 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "44" + ], + "split": "train" + }, + { + "Input": "if 13 = 13 w / ( 1 - w ) , then ( w ) 2 =", + "Output Program": [ + "n0 = 13.0\nn1 = 13.0\nn2 = 1.0\nn3 = 2.0\nt0 = n0 + n0\nt1 = n0 / t0\nanswer = n3 * t1\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "on dividing 15968 by a certain number , the quotient is 89 and the remainder is 37 . find the divisor .", + "Output Program": [ + "n0 = 15968.0\nn1 = 89.0\nn2 = 37.0\nt0 = n0 - n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "179" + ], + "split": "train" + }, + { + "Input": "a trained covered x km at 70 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 3 x km .", + "Output Program": [ + "n0 = 70.0\nn1 = 2.0\nn2 = 20.0\nn3 = 3.0\nt0 = n0 / n0\nt1 = n0 * n3\nt2 = n0 * n1\nt3 = t2 / n2\nt4 = t0 + t3\nanswer = t1 / t4\nprint(answer)" + ], + "Output Answer": [ + "26.25" + ], + "split": "train" + }, + { + "Input": "tim has 13 10 - dollar bills , 11 5 - dollar bills , and 17 one - dollar bills . if tim needs to pay exactly $ 128 , what is the least number of bills he will need to use ?", + "Output Program": [ + "n0 = 13.0\nn1 = 10.0\nn2 = 11.0\nn3 = 5.0\nn4 = 17.0\nn5 = 128.0\nt0 = n0 - 1.0\nt1 = t0 + 1.0\nanswer = t1 + 3.0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "the average of 10 consecutive integers is 25 . then , 9 is deducted from the first consecutive number , 8 is deducted from the second , 7 is deducted form the third , and so on until the last number which remains unchanged . what is the new average ?", + "Output Program": [ + "n0 = 10.0\nn1 = 20.0\nn2 = 9.0\nn3 = 8.0\nn4 = 7.0\nt0 = 1.0 + 4.0\nt1 = n0 * n1\nt2 = n2 * t0\nt3 = t1 - t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "15.5" + ], + "split": "train" + }, + { + "Input": "if 0.75 : x : : 5 : 11 , then x is equal to :", + "Output Program": [ + "n0 = 0.75\nn1 = 5.0\nn2 = 11.0\nt0 = n0 * n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "1.65" + ], + "split": "train" + }, + { + "Input": "there are 9 teams in a certain league and each team plays each of the other teams exactly once . what is the total number of games played ?", + "Output Program": [ + "n0 = 9.0\nt0 = n0 - 1.0\nt1 = n0 * t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "for each color copy , print shop x charges $ 1.25 and print shop y charges $ 2.75 . how much greater is the charge for 80 color copies at print shop y than at print shop x ?", + "Output Program": [ + "n0 = 1.25\nn1 = 2.75\nn2 = 80.0\nt0 = n1 * n2\nt1 = n0 * n2\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "bob is attempting to feed his pets . he feeds his pets as follows : - no dog receives more food than any other dog - no cat receives any less food than any other cat - the cats , as a group , receive exactly as much food as a single dog if bob has 7 dogs and 4 cats , approximately what percentage of the food bag does a cat receive ?", + "Output Program": [ + "n0 = 7.0\nn1 = 4.0\nt0 = n0 * n1\nt1 = n1 + t0\nt2 = 1.0 / t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "3.125" + ], + "split": "train" + }, + { + "Input": "in a cricket match , 5 batsmen a , b , c , d and e scored an average of 36 runs . d scored 5 more than e ; e scored 8 fewer than a ; b scored as many as d and e combined ; and b and c scored 107 between them . how many runs did e score ?", + "Output Program": [ + "n0 = 5.0\nn1 = 36.0\nn2 = 5.0\nn3 = 8.0\nn4 = 107.0\nt0 = n0 * n1\nt1 = n0 * 2.0\nt2 = t1 + 3.0\nt3 = n4 + t2\nt4 = t0 - t3\nanswer = t4 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "a manufacturing company has 15 % cobalt , 25 % led and 60 % of copper . if 5 kg of led is used in a mixture how much copper we need to use", + "Output Program": [ + "n0 = 15.0\nn1 = 25.0\nn2 = 60.0\nn3 = 5.0\nt0 = n2 / 100.0\nt1 = n3 * 4.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "in a simultaneous throw of pair of dice . find the probability of getting the total more than 7 ?", + "Output Program": [ + "n0 = 7.0\nt0 = n0 + 4.0\nt1 = 2.0 + 4.0\nt2 = t0 + 4.0\nt3 = t1 * t1\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.4166666666666667" + ], + "split": "train" + }, + { + "Input": "addison high school \u2019 s senior class has 160 boys and 200 girls . if 75 % of the boys attended the college and 40 % of the girls did not attend the college , what percentage of the total class attended college ?", + "Output Program": [ + "n0 = 160.0\nn1 = 200.0\nn2 = 75.0\nn3 = 40.0\nt0 = n0 + n1\nt1 = n2 / 100.0\nt2 = n3 / 100.0\nt3 = n0 * t1\nt4 = 1.0 - t2\nt5 = n1 * t4\nt6 = t3 + t5\nt7 = t6 / t0\nanswer = t7 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "66.66666666666666" + ], + "split": "train" + }, + { + "Input": "if x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year , the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $ 92 . if $ 2,000 is the total amount invested , how much is invested at 8 percent ?", + "Output Program": [ + "n0 = 10.0\nn1 = 8.0\nn2 = 10.0\nn3 = 8.0\nn4 = 92.0\nn5 = 2000.0\nn6 = 8.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = 10.0 * 100.0\nt3 = n0 * n1\nt4 = t0 + t1\nt5 = t2 * 2.0\nt6 = t3 * 2.0\nt7 = n4 + t6\nt8 = t7 / t4\nanswer = t5 - t8\nprint(answer)" + ], + "Output Answer": [ + "600" + ], + "split": "train" + }, + { + "Input": "danny obtained 76 , 65 , 82 , 67 and 75 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?", + "Output Program": [ + "n0 = 76.0\nn1 = 65.0\nn2 = 82.0\nn3 = 67.0\nn4 = 75.0\nn5 = 100.0\nt0 = n0 + n1\nt1 = 10.0 / 2.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "73" + ], + "split": "train" + }, + { + "Input": "in the land of oz only one or two - letter words are used . the local language has 69 different letters . the parliament decided to forbid the use of the seventh letter . how many words have the people of oz lost because of the prohibition ?", + "Output Program": [ + "n0 = 69.0\nt0 = n0 + 1.0\nanswer = n0 + t0\nprint(answer)" + ], + "Output Answer": [ + "139" + ], + "split": "train" + }, + { + "Input": "a , b and c started a business with a total investment of rs . 90000 . a invests rs . 6000 more than b and b invests rs . 3000 less than c . if the total profit at the end of a year is rs . 8640 , find a ' s share .", + "Output Program": [ + "n0 = 90000.0\nn1 = 6000.0\nn2 = 3000.0\nn3 = 8640.0\nt0 = n1 + n2\nt1 = n0 - t0\nt2 = t1 / 3.0\nt3 = n1 + t2\nt4 = t3 / n0\nanswer = n3 * t4\nprint(answer)" + ], + "Output Answer": [ + "3168" + ], + "split": "train" + }, + { + "Input": "a ' s speed is 20 / 13 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that b beats a by 60 % of the length of the race ?", + "Output Program": [ + "n0 = 20.0\nn1 = 13.0\nn2 = 60.0\nt0 = n1 / n0\nt1 = 100.0 - n2\nt2 = t1 / 100.0\nt3 = t2 * t0\nt4 = 1.0 - t3\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "74" + ], + "split": "train" + }, + { + "Input": "if ( n + 2 ) ! / n ! = 72 , n = ?", + "Output Program": [ + "n0 = 2.0\nn1 = 72.0\nt0 = 4.0 + 4.0\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "for all positive integers m and v , the expression m \u03b8 v represents the remainder when m is divided by v . what is the value of ( ( 90 \u03b8 33 ) \u03b8 17 ) - ( 99 \u03b8 ( 33 \u03b8 17 ) ) ?", + "Output Program": [ + "n0 = 90.0\nn1 = 33.0\nn2 = 17.0\nn3 = 99.0\nn4 = 33.0\nn5 = 17.0\nt0 = n0 % n1\nt1 = n1 % n2\nt2 = t0 % n2\nt3 = n3 % t1\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "if the price of gasoline increases by 25 % and a driver intends to spend only 10 % more on gasoline , by how much percent should the driver reduce the quantity of gasoline that he buys ?", + "Output Program": [ + "n0 = 25.0\nn1 = 10.0\nt0 = n0 + 100.0\nt1 = n1 + 100.0\nt2 = t0 - t1\nt3 = t2 / t0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "the average age of 16 students of a class is 16 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years , the age of the 12 th student is", + "Output Program": [ + "n0 = 16.0\nn1 = 16.0\nn2 = 5.0\nn3 = 14.0\nn4 = 9.0\nn5 = 16.0\nn6 = 12.0\nt0 = n0 * n0\nt1 = n2 * n3\nt2 = n4 * n5\nt3 = t1 + t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "the average speed of a car is 1 4 / 5 times the avg speed of a bike . a tractor covers 575 km in 23 hrs . how much distance will the car cover in 6 hrs if the speed of the bike is twice speed of the tractor ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 5.0\nn3 = 575.0\nn4 = 23.0\nn5 = 6.0\nt0 = n1 / n2\nt1 = n3 / n4\nt2 = n0 + t0\nt3 = t1 * 2.0\nt4 = t2 * t3\nanswer = n5 * t4\nprint(answer)" + ], + "Output Answer": [ + "540" + ], + "split": "train" + }, + { + "Input": "in kaya ' s teacher ' s desk there are 6 pink highlighters , 2 yellow highlighters , and 4 blue highlighters . how many highlighters are there in all ?", + "Output Program": [ + "n0 = 6.0\nn1 = 2.0\nn2 = 4.0\nt0 = n0 + n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "a batsman makes a score of 85 runs in the 17 th inning and thus increases his averages by 3 . find his average after 17 th inning ?", + "Output Program": [ + "n0 = 85.0\nn1 = 17.0\nn2 = 3.0\nn3 = 17.0\nt0 = n1 * n2\nt1 = n0 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "37" + ], + "split": "train" + }, + { + "Input": "of the families in city x in 1998 , 20 percent owned a personal computer . the number of families in city x owning a computer in 2002 was 40 percent greater than it was in 1998 , and the total number of families in city x was 8 percent greater in 2002 than it was in 1998 . what percent of the families in city x owned a personal computer in 2002 ?", + "Output Program": [ + "n0 = 1998.0\nn1 = 20.0\nn2 = 2002.0\nn3 = 40.0\nn4 = 1998.0\nn5 = 8.0\nn6 = 2002.0\nn7 = 1998.0\nn8 = 2002.0\nt0 = n3 + 100.0\nt1 = n5 + 100.0\nt2 = n1 * t0\nt3 = t2 / 100.0\nt4 = t3 / t1\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "25.925925925925924" + ], + "split": "train" + }, + { + "Input": "s is a set of 100 consecutive multiples of 8 . if the smallest number in s is 108 , then the greatest number in s is", + "Output Program": [ + "n0 = 100.0\nn1 = 8.0\nn2 = 108.0\nt0 = n0 - 1.0\nt1 = n1 * t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "900" + ], + "split": "train" + }, + { + "Input": "the batting average of a particular batsman is 62 runs in 46 innings . if the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs , find his highest score .", + "Output Program": [ + "n0 = 62.0\nn1 = 46.0\nn2 = 150.0\nn3 = 58.0\nt0 = n0 * n1\nt1 = n1 - 2.0\nt2 = n3 * t1\nt3 = t0 - t2\nt4 = n2 + t3\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "225" + ], + "split": "train" + }, + { + "Input": "if the price of a tv is first decreased by 20 % and then increased by 30 % , then the net change in the price will be :", + "Output Program": [ + "n0 = 20.0\nn1 = 30.0\nt0 = n1 + 100.0\nt1 = 100.0 - n0\nt2 = t0 * t1\nt3 = t2 / 100.0\nanswer = t3 - 100.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "equal amount of water were poured into two empty jars of different capacities , which made one jar 1 / 5 full and other jar 1 / 4 full . if the water in the jar with lesser capacity is then poured into the jar with greater capacity , what fraction of the larger jar will be filled with water ?", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 1.0\nn3 = 4.0\n\nanswer = 2.0 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.4" + ], + "split": "train" + }, + { + "Input": "when processing flower - nectar into honey bees ' extract , a considerable amount of water gets reduced . how much flower - nectar must be processed to yield 1 kg of honey , if nectar contains 50 % water , and the honey obtained from this nectar contains 20 % water ?", + "Output Program": [ + "n0 = 1.0\nn1 = 50.0\nn2 = 20.0\nt0 = n1 / 100.0\nt1 = 100.0 - n2\nt2 = t1 / 100.0\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "1.6" + ], + "split": "train" + }, + { + "Input": "a , b and c are partners . a receives 2 / 3 of profits , b and c dividing the remainder equally . a ' s income is increased by rs . 200 when the rate to profit rises from 5 to 7 percent . find the capital of a ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 200.0\nn3 = 5.0\nn4 = 7.0\nt0 = n2 * 100.0\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "10000" + ], + "split": "train" + }, + { + "Input": "a sports equipment store sold ping pong rackets for a total of $ 490 . if the average ( arithmetic mean ) price of a pair of rackets is $ 9.8 , how many pairs were sold ?", + "Output Program": [ + "n0 = 490.0\nn1 = 9.8\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "49.99999999999999" + ], + "split": "train" + }, + { + "Input": "a little girl went to the farm to buy fruits . she bought a bag of apples and grabbed a bag of oranges which was 5 times as heavy as the apples . she brought home a total of 12 pounds of fruits . how many pounds was the oranges ?", + "Output Program": [ + "n0 = 5.0\nn1 = 12.0\nt0 = n0 + 1.0\nt1 = n0 * n1\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "if 7 < x < 9 < y < 15 , then what is the greatest possible positive integer difference of x and y ?", + "Output Program": [ + "n0 = 7.0\nn1 = 9.0\nn2 = 15.0\nt0 = n2 - n0\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "when 100 is divided by positive integer x , the remainder is 3 . what is the remainder when 197 is divided by x ?", + "Output Program": [ + "n0 = 100.0\nn1 = 3.0\nn2 = 197.0\nt0 = n2 - n0\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "a batsman scored 125 runs which included 5 boundaries and 5 sixes . what percent of his total score did he make by running between the wickets ?", + "Output Program": [ + "n0 = 125.0\nn1 = 5.0\nn2 = 5.0\nt0 = n1 * n2\nt1 = n1 * n2\nt2 = t0 + t1\nt3 = n0 - t2\nt4 = t3 / n0\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "3 friends neha , sabi and mahi divide $ 1100 amongs them in such a way that if $ 5 , $ 8 and $ 4 are removed from the sums that neha , sabi and mahi received respectively , then the share of the sums that they got will be in the ratio of 2 : 8 : 6 . how much did mahi receive ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1100.0\nn2 = 5.0\nn3 = 8.0\nn4 = 4.0\nn5 = 2.0\nn6 = 8.0\nn7 = 6.0\nt0 = n3 + 12.0\nt1 = n4 * t0\nt2 = t1 + 12.0\nanswer = t2 + 10.0\nprint(answer)" + ], + "Output Answer": [ + "102" + ], + "split": "train" + }, + { + "Input": "the maximum number of girls among them 2923 bags and 3239 eyeliners can be distributed in such a way that each student gets the same number of bags and eyeliners .", + "Output Program": [ + "import scipy\nn0 = 2923.0\nn1 = 3239.0\n\nanswer = scipy.gcd(int(n0), int(n1))\nprint(answer)" + ], + "Output Answer": [ + "79" + ], + "split": "train" + }, + { + "Input": "on dividing 23 by a number , the quotient is 7 and the remainder is 2 . find the divisor .", + "Output Program": [ + "import math\nn0 = 23.0\nn1 = 7.0\nn2 = 2.0\nt0 = n0 / n1\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "a , b and c enter into a partnership and theirs shares are in the ratio 1 / 2 : 1 / 3 : 1 / 4 . after two months , a withdraws half of his capital and after 10 months , a profit of rs . 378 is divided among them . what is b \u2019 s share ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 1.0\nn3 = 3.0\nn4 = 1.0\nn5 = 4.0\nn6 = 10.0\nn7 = 378.0\nt0 = n3 + n5\nt1 = n1 * n5\nt2 = n7 * t1\nt3 = n3 * t0\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "144" + ], + "split": "train" + }, + { + "Input": "if 6 x ^ 2 + x - 12 = ( hx + b ) ( cx + d ) , then | h | + | b | + | c | + | d | = for a complete solution and more practice problems , see this blog : http : / / magoosh . com / gmat / 2012 / algebra - on . . . to - factor /", + "Output Program": [ + "n0 = 6.0\nn1 = 2.0\nn2 = 12.0\nn3 = 2012.0\nt0 = n1 + 3.0\nt1 = t0 + 3.0\nanswer = t1 + 4.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "p has $ 42 more than what q and r together would have had if both b and c had 1 / 8 of what p has . how much does p have ?", + "Output Program": [ + "n0 = 42.0\nn1 = 1.0\nn2 = 8.0\nt0 = n1 / n2\nt1 = t0 * 2.0\nt2 = n1 - t1\nanswer = n0 / t2\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "train" + }, + { + "Input": "the sum of the first 50 positive even integers is 2550 . what is the sum r of even integers from 102 to 200 inclusive ?", + "Output Program": [ + "n0 = 50.0\nn1 = 2550.0\nn2 = 102.0\nn3 = 200.0\nt0 = n2 + n3\nt1 = n3 - n2\nt2 = t1 / 2.0\nt3 = t0 / 2.0\nt4 = t2 + 1.0\nanswer = t4 * t3\nprint(answer)" + ], + "Output Answer": [ + "7550" + ], + "split": "train" + }, + { + "Input": "bipin is 6 times old as alok . bipin ' s age will be twice of chandan ' s age after 10 years . if chandan ' s 7 th birthday was celebrated 3 years ago , what is alok ' s present age ?", + "Output Program": [ + "n0 = 6.0\nn1 = 10.0\nn2 = 7.0\nn3 = 3.0\nt0 = n1 * 2.0\nt1 = n1 + t0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "a big container is 30 % full with water . if 36 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container ?", + "Output Program": [ + "n0 = 30.0\nn1 = 36.0\nn2 = 3.0\nn3 = 4.0\nt0 = n2 / n3\nt1 = n0 / 100.0\nt2 = t0 - t1\nanswer = n1 / t2\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "the average mark of the students of a class in a particular exam is 72 . if 5 students whose average mark in that exam is 40 are excluded , the average mark of the remaining will be 92 . find the number of students who wrote the exam ?", + "Output Program": [ + "n0 = 72.0\nn1 = 5.0\nn2 = 40.0\nn3 = 92.0\nt0 = n1 * n3\nt1 = n1 * n2\nt2 = n3 - n0\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "in a certain game of dice , the player \u2019 s score is determined as a sum of two throws of a single die . the player with the highest score wins the round . if more than one player has the highest score , the winnings of the round are divided equally among these players . if jim plays this game against 21 other players , what is the probability of the minimum score that will guarantee jim some monetary payoff ?", + "Output Program": [ + "n0 = 21.0\nt0 = n0 / 3.0\nt1 = t0 - 1.0\nt2 = t1**min(2.0, 5)\nanswer = 1.0 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.027777777777777776" + ], + "split": "train" + }, + { + "Input": "how many times will the digit 6 be written when listing the integers from 1 to 1000 ?", + "Output Program": [ + "n0 = 6.0\nn1 = 1.0\nn2 = 1000.0\nt0 = n1 * 10.0\nt1 = t0 * 10.0\nanswer = t1 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "an assembly line produces 20 cogs per hour until an initial order of 60 cogs is completed . the speed of the assembly line is then immediately increased so that it can produce 60 cogs per hour until another 60 cogs are produced . what is the overall average output , in cogs per hour , for the assembly line during this whole time ?", + "Output Program": [ + "n0 = 20.0\nn1 = 60.0\nn2 = 60.0\nn3 = 60.0\nt0 = n1 / n0\nt1 = n1 * 2.0\nt2 = t0 + 1.0\nanswer = t1 / t2\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "the sum of two numbers is 45 . sum of their quotient and reciprocal is 2.05 , find the product of the numbers .", + "Output Program": [ + "n0 = 45.0\nn1 = 2.05\nt0 = n1 + 2.0\nt1 = n0 * n0\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "train" + }, + { + "Input": "in smithtown , the ratio of right - handed people to left - handed people is 3 to 1 and the ratio of men to women is 3 to 2 . if the number of right - handed men is maximized , then what q percent of all the people in smithtown are left - handed women ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 3.0\nn3 = 2.0\nt0 = n0 + n1\nt1 = n0 + n3\nt2 = t0 / t1\nt3 = n3 * t2\nt4 = n0 * t2\nt5 = n0 - t4\nt6 = t3 - t5\nt7 = t6 / t0\nanswer = t7 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "25.00000000000001" + ], + "split": "train" + }, + { + "Input": "at a certain fruit stand , the price of each apple is 50 cents and the price of each orange is 60 cents . mary selects a total of 10 apples and oranges from the fruit stand , and the average ( arithmetic mean ) price of the 10 pieces of fruit is 56 cents . how many oranges must mary put back so that the average price of the pieces of fruit that she keeps is 52 cents ?", + "Output Program": [ + "n0 = 50.0\nn1 = 60.0\nn2 = 10.0\nn3 = 10.0\nn4 = 56.0\nn5 = 52.0\nt0 = n2 * n4\nt1 = n2 * n5\nt2 = n1 - n5\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "a certain number when divided by 39 leaves a remainder 18 , what is the remainder when the same number is divided by 13 ?", + "Output Program": [ + "n0 = 39.0\nn1 = 18.0\nn2 = 13.0\n\nanswer = n1 % n2\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "the average monthly salary of 24 employees in an organisation is rs . 1500 . if the manager ' s salary is added , then the average salary increases by rs . 400 . what is the manager ' s monthly salary ?", + "Output Program": [ + "n0 = 24.0\nn1 = 1500.0\nn2 = 400.0\nt0 = n1 + n2\nt1 = n0 + 1.0\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "11500" + ], + "split": "train" + }, + { + "Input": "in country x a returning tourist may import goods with a total value of $ 500 or less tax free , but must pay an 8 percent tax on the portion of the total value in excess of $ 500 . what tax must be paid by a returning tourist who imports goods with a total value of $ 730 ?", + "Output Program": [ + "n0 = 500.0\nn1 = 8.0\nn2 = 500.0\nn3 = 730.0\nt0 = n1 / 100.0\nt1 = n3 - n0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "18.400000000000002" + ], + "split": "train" + }, + { + "Input": "the averageincome of m and n is rs . 5050 . the average monthly income of n and o is rs . 6250 and the average monthly income of m and ois rs . 5200 . the income of m is ?", + "Output Program": [ + "n0 = 5050.0\nn1 = 6250.0\nn2 = 5200.0\nt0 = n0 + n1\nt1 = n1 * 2.0\nt2 = n2 + t0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "4000" + ], + "split": "train" + }, + { + "Input": "if x is 20 percent more than y and y is 50 percent less than z , then x is what percent of z ?", + "Output Program": [ + "n0 = 20.0\nn1 = 50.0\nt0 = n0 / 100.0\nt1 = 100.0 - n1\nt2 = t0 + 1.0\nanswer = t2 * t1\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "the difference between two numbers is 1365 . when the larger number is divided by the smaller one , the quotient is 6 and the remainder is 15 . the smaller number is :", + "Output Program": [ + "n0 = 1365.0\nn1 = 6.0\nn2 = 15.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "270" + ], + "split": "train" + }, + { + "Input": "lilly has 10 fish and rosy has 11 fish . in total , how many fish do they have in all ?", + "Output Program": [ + "n0 = 10.0\nn1 = 11.0\n\nanswer = n0 + n1\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "we run a business that rents out canoes and kayaks . a canoe rental costs $ 11 per day , and a kayak rental costs $ 16 dollars per day . one day , our business rents out 4 canoes for every 3 kayaks and receives a total of $ 460 in revenue . how many more canoes than kayaks were rented out ?", + "Output Program": [ + "n0 = 11.0\nn1 = 16.0\nn2 = 4.0\nn3 = 3.0\nn4 = 460.0\nt0 = n0 * n2\nt1 = n1 * n3\nt2 = n2 - n3\nt3 = t0 + t1\nt4 = n4 / t3\nanswer = t4 * t2\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "set w consists of all the prime numbers between 10 and 25 . what is the range of set w ?", + "Output Program": [ + "n0 = 10.0\nn1 = 25.0\nt0 = n0 + 1.0\nt1 = n1 - 2.0\nanswer = t1 - t0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "there are 11 teams in a certain league and each team plays each of the other teams exactly once . what is the total number of games played ?", + "Output Program": [ + "n0 = 11.0\nt0 = n0 - 1.0\nt1 = n0 * t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "55" + ], + "split": "train" + }, + { + "Input": "if greg buys 6 shirts , 4 trousers and 2 ties , the total cost is $ 80 . if greg buys 4 shirts , 2 trousers and 2 ties , the total cost is $ 140 . how much will it cost him to buy 3 trousers , 5 shirts and 2 ties ?", + "Output Program": [ + "n0 = 6.0\nn1 = 4.0\nn2 = 2.0\nn3 = 80.0\nn4 = 4.0\nn5 = 2.0\nn6 = 2.0\nn7 = 140.0\nn8 = 3.0\nn9 = 5.0\nn10 = 2.0\nt0 = n3 + n7\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "110" + ], + "split": "train" + }, + { + "Input": "if jenee earns a raise of between 5 % and 10 % , non - inclusive , by what fraction could her salary have increased ?", + "Output Program": [ + "n0 = 5.0\nn1 = 10.0\nt0 = n0 * n1\nanswer = 3.0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.06" + ], + "split": "train" + }, + { + "Input": "3 consecutive even numbers are such that thrice the first number exceeds double the third number by 7 . what is the third number ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nt0 = n0 * n1\nanswer = t0 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "last week vartan spent 20 percent of his wages on recreation . this week , his wages are 20 percent less than last week \u02bc s wages and he spent 40 percent of his wages on recreation . the amount he spends on recreation this week is what percent of the amount he spent on recreation last week ?", + "Output Program": [ + "n0 = 20.0\nn1 = 20.0\nn2 = 40.0\nt0 = 100.0 - n1\nt1 = n2 * t0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "160" + ], + "split": "train" + }, + { + "Input": "the ratio of two numbers is 2 : 3 and the sum of their cubes is 945 . the difference of number is ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 945.0\nt0 = n1 * n1\nt1 = n1**min(n1, 5)\nt2 = n0**min(3.0, 5)\nt3 = t1 + t2\nt4 = n2 / t3\nanswer = t4 / t0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "the mean of 1 ^ 22 ^ 23 ^ 24 ^ 25 ^ 26 ^ 27 ^ 2 is ?", + "Output Program": [ + "n0 = 1.0\nn1 = 22.0\nn2 = 23.0\nn3 = 24.0\nn4 = 25.0\nn5 = 26.0\nn6 = 27.0\nn7 = 2.0\nt0 = 2.0 + 3.0\nt1 = 2.0 + 4.0\nt2 = 3.0 + 4.0\nt3 = 2.0**min(2.0, 5)\nt4 = 3.0**min(2.0, 5)\nt5 = 4.0**min(2.0, 5)\nt6 = t3 + t4\nt7 = t0**min(2.0, 5)\nt8 = t1**min(2.0, 5)\nt9 = t2**min(2.0, 5)\nt10 = t5 + t7\nt11 = t8 + t9\nt12 = t6 + t10\nt13 = t12 + t11\nt14 = n0 + t13\nanswer = t14 / t2\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "if 25 % of x is 20 less than 15 % of 1500 , then x is ?", + "Output Program": [ + "n0 = 25.0\nn1 = 20.0\nn2 = 15.0\nn3 = 1500.0\nt0 = n2 / 100.0\nt1 = n0 / 100.0\nt2 = n3 * t0\nt3 = t2 - n1\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "820" + ], + "split": "train" + }, + { + "Input": "a number , x is chosen at random from the set of positive integers less than 10 . what is the probability that ( 8 / x ) > x ?", + "Output Program": [ + "n0 = 10.0\nn1 = 8.0\nt0 = n0 - n1\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.25" + ], + "split": "train" + }, + { + "Input": "x varies inversely as square of y . given that y = 3 for x = 1 . the value of x for y = 2 will be equal to :", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 2.0\nt0 = n0**min(2.0, 5)\nt1 = n2**min(2.0, 5)\nt2 = n1 * t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "2.25" + ], + "split": "train" + }, + { + "Input": "you collect pens . suppose you start out with 5 . mike gives you another 20 pens . since her father makes pens , cindy decides to double your pens . since you ' re nice , you give sharon 19 pens . how many pens do you have at the end ?", + "Output Program": [ + "n0 = 5.0\nn1 = 20.0\nn2 = 19.0\nt0 = n0 + n1\nt1 = t0 * 2.0\nanswer = t1 - n2\nprint(answer)" + ], + "Output Answer": [ + "31" + ], + "split": "train" + }, + { + "Input": "the average ( arithmetic mean ) of the integers from 200 to 400 , inclusive , is how much greater than the average of the integers from 100 to 200 , inclusive ?", + "Output Program": [ + "n0 = 200.0\nn1 = 400.0\nn2 = 100.0\nn3 = 200.0\nt0 = n0 + n1\nt1 = n2 + n3\nt2 = t0 / 2.0\nt3 = t1 / 2.0\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "train" + }, + { + "Input": "in a house a hall is 20 m long , 15 m wide and 5 m high . its interior has to be covered with mat . what will be the total expenditure if it costs rs . 30 per square m ?", + "Output Program": [ + "n0 = 20.0\nn1 = 15.0\nn2 = 5.0\nn3 = 30.0\nt0 = n0 * n1\nt1 = n0 * n2\nt2 = n1 * n2\nt3 = t0 * 2.0\nt4 = t1 * 2.0\nt5 = t2 * 2.0\nt6 = n3 * t3\nt7 = n3 * t4\nt8 = n3 * t5\nt9 = t6 + t7\nanswer = t9 + t8\nprint(answer)" + ], + "Output Answer": [ + "28500" + ], + "split": "train" + }, + { + "Input": "an old man distributed all the gold coins he had to his two sons into two different numbers such that the difference between the squares of the two numbers is 16 times the difference between the two numbers . how many coins did the old man have ?", + "Output Program": [ + "import math\nn0 = 16.0\n\nanswer = math.floor(n0)\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "the sum of the numbers is 220 . if the first number be twice the second and third number be one - third of the first , then the second number is :", + "Output Program": [ + "n0 = 220.0\nt0 = 1.0 + 10.0\nt1 = n0 * 3.0\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "for what value of \u00e2 \u20ac \u0153 k \u00e2 \u20ac \u009d will the equation ( 2 kx 2 + 6 kx + 2 ) = 0 have equal roots ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 6.0\nn3 = 2.0\nn4 = 0.0\nt0 = n0 + n0\nt1 = n2**min(n0, 5)\nt2 = n0**min(t0, 5)\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.4444444444444444" + ], + "split": "train" + }, + { + "Input": "$ 366 is divided amongst a , b and c so that a may get 1 / 2 as much as b and c together , b may get 2 / 3 as much as a and c together , then the share of a is", + "Output Program": [ + "n0 = 366.0\nn1 = 1.0\nn2 = 2.0\nn3 = 2.0\nn4 = 3.0\nt0 = n1 / n2\nt1 = t0 + 1.0\nt2 = n0 / t1\nanswer = t2 * t0\nprint(answer)" + ], + "Output Answer": [ + "122" + ], + "split": "train" + }, + { + "Input": "if 12 boys meet at a reunion and each boy shakes hands exactly once with each of the others , then what is the total number of handshakes", + "Output Program": [ + "import math\nn0 = 12.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(2.0)))\nt2 = n0 - 2.0\nt3 = math.factorial(min(15, int(t2)))\nt4 = t3 * t1\nanswer = t0 / t4\nprint(answer)" + ], + "Output Answer": [ + "66" + ], + "split": "train" + }, + { + "Input": "8 liters of a 25 percent solution of alcohol in water are mixed with 2 liters of a 12 percent alcohol in water solution . what is the percentage of alcohol in the new solution ?", + "Output Program": [ + "n0 = 8.0\nn1 = 25.0\nn2 = 2.0\nn3 = 12.0\nt0 = n0 + n2\nt1 = n1 / 100.0\nt2 = n3 / 100.0\nt3 = n0 * t1\nt4 = t2 * t3\nt5 = t3 + t4\nt6 = t5 / t0\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "22.400000000000002" + ], + "split": "train" + }, + { + "Input": "find the least number must be subtracted from 5264 so that remaining number is divisible by 17 .", + "Output Program": [ + "import math\nn0 = 5264.0\nn1 = 17.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "a salesman ' s income consists of a commission and a base salary of $ 400 per week . over the past 5 weeks , his weekly income totals have been $ 406 , $ 413 , $ 420 , $ 436 and $ 395 . what must his average ( arithmetic mean ) commission be per week over the next two weeks so that his average weekly income is $ 500 over the 7 - week period ?", + "Output Program": [ + "n0 = 400.0\nn1 = 5.0\nn2 = 406.0\nn3 = 413.0\nn4 = 420.0\nn5 = 436.0\nn6 = 395.0\nn7 = 500.0\nn8 = 7.0\nt0 = n2 + n3\nt1 = n4 + n5\nt2 = n7 * n8\nt3 = t0 + t1\nt4 = n6 + t3\nt5 = t2 - t4\nt6 = t5 / 2.0\nanswer = t6 - n0\nprint(answer)" + ], + "Output Answer": [ + "315" + ], + "split": "train" + }, + { + "Input": "for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today ' s production of 100 units raises the average to 55 units per day , what is the value of n ?", + "Output Program": [ + "n0 = 50.0\nn1 = 100.0\nn2 = 55.0\nt0 = n1 - n0\nt1 = n2 - n0\nt2 = t0 / t1\nanswer = t2 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "a batsman makes a score of 300 runs in the 17 th inning and thus increases his averages by 10 . what is his average after 17 th inning ?", + "Output Program": [ + "n0 = 300.0\nn1 = 17.0\nn2 = 10.0\nn3 = 17.0\nt0 = n1 * n2\nt1 = n0 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "140" + ], + "split": "train" + }, + { + "Input": "you make a cube that is made of 10 x 10 x 10 smaller cubes which sums up to a total of 1000 smaller cubes . now , if someone takes one layer of cubes , how many will remain ?", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 10.0\nn3 = 1000.0\nt0 = n0 - 2.0\nanswer = t0**min(3.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "512" + ], + "split": "train" + }, + { + "Input": "if a - b = 4 and a 2 + b 2 = 30 , find the value of ab .", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\nn2 = 2.0\nn3 = 30.0\nt0 = n0**min(n1, 5)\nt1 = n3 - t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "a batsman in his 12 th innings makes a score of 92 and thereby increases his average by 2 runs . what is his average after the 12 th innings if he had never been \u2018 not out \u2019 ?", + "Output Program": [ + "n0 = 12.0\nn1 = 92.0\nn2 = 2.0\nn3 = 12.0\nt0 = n0 * n2\nt1 = n1 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "train" + }, + { + "Input": "what is the least number by which 16800 must be divided to get a number perfect square", + "Output Program": [ + "n0 = 16800.0\nt0 = 10.0 * 2.0\nt1 = t0 * t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "addison high school \u2019 s senior class has 300 boys and 240 girls . if 30 % of the boys did not attend the college then 70 % of the total class attended college , what percentage of the girls class did not attend college ?", + "Output Program": [ + "n0 = 300.0\nn1 = 240.0\nn2 = 30.0\nn3 = 70.0\nt0 = n0 + n1\nt1 = n2 / 100.0\nt2 = n3 / 100.0\nt3 = n0 * t1\nt4 = 1.0 - t2\nt5 = n1 * t4\nt6 = t3 + t5\nt7 = t6 / t0\nanswer = t7 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "on dividing 95 by a number , the quotient is 6 and the remainder is 5 . find the divisor .", + "Output Program": [ + "import math\nn0 = 95.0\nn1 = 6.0\nn2 = 5.0\nt0 = n0 / n1\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "how many boxes do you need if you have to pack 1080 apples into cases that each hold one dozen apples ?", + "Output Program": [ + "n0 = 1080.0\n\nanswer = n0 / 12.0\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "a sum of money lent out at s . i . amounts to rs . 820 after 2 years and to rs . 1020 after a further period of 4 years . the sum is ?", + "Output Program": [ + "n0 = 820.0\nn1 = 2.0\nn2 = 1020.0\nn3 = 4.0\nt0 = n2 - n0\nt1 = t0 / n3\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "720" + ], + "split": "train" + }, + { + "Input": "there are 4 more women than there are men on a local co - ed softball team . if there are a total of 18 players on the team , what is the ratio of men to women ?", + "Output Program": [ + "n0 = 4.0\nn1 = 18.0\nt0 = 1.0 + 1.0\nt1 = n1 - n0\nt2 = t1 / t0\nt3 = n0 + t2\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.6363636363636364" + ], + "split": "train" + }, + { + "Input": "how much is 80 % of 40 is greater than 4 / 5 of 25 ?", + "Output Program": [ + "n0 = 80.0\nn1 = 40.0\nn2 = 4.0\nn3 = 5.0\nn4 = 25.0\nt0 = n0 / 100.0\nt1 = n2 / n3\nt2 = n1 * t0\nt3 = n4 * t1\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "a vessel of capacity 2 litre has 25 % of alcohol and another vessel of capacity 6 litre had 50 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?", + "Output Program": [ + "n0 = 2.0\nn1 = 25.0\nn2 = 6.0\nn3 = 50.0\nn4 = 8.0\nn5 = 10.0\nt0 = n1 / 100.0\nt1 = n3 / 100.0\nt2 = n0 * t0\nt3 = n2 * t1\nt4 = t2 + t3\nt5 = t4 / n5\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "how many different positive integers exist between 10 ^ 7 and 10 ^ 8 , the sum of whose digits is equal to 2 ?", + "Output Program": [ + "n0 = 10.0\nn1 = 7.0\nn2 = 10.0\nn3 = 8.0\nn4 = 2.0\nt0 = 3.0 + 4.0\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "zinc and copper are melted together in the ratio 9 : 11 . what is the weight of melted mixture , if 33.3 kg of zinc has been consumed in it ?", + "Output Program": [ + "n0 = 9.0\nn1 = 11.0\nn2 = 33.3\nt0 = n1 / n0\nt1 = n2 * t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "74" + ], + "split": "train" + }, + { + "Input": "a line that passes through ( \u2013 1 , \u2013 4 ) and ( 5 , k ) has a slope = k . what is the value of k ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 5.0\n\nanswer = n1 / n2\nprint(answer)" + ], + "Output Answer": [ + "0.8" + ], + "split": "train" + }, + { + "Input": "total dinning bill for 8 people was $ 211.00 . if they add 15 % tip and divided the bill evenly , approximate . what was each persons find share", + "Output Program": [ + "n0 = 8.0\nn1 = 211.0\nn2 = 15.0\nt0 = n1 * n2\nt1 = t0 / 100.0\nt2 = n1 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "30.33125" + ], + "split": "train" + }, + { + "Input": "in the rectangular coordinate system , what is the x - intercept of a line passing through ( 10 , 3 ) and ( \u2212 12 , \u2212 8 ) ?", + "Output Program": [ + "n0 = 10.0\nn1 = 3.0\nn2 = 12.0\nn3 = 8.0\nt0 = -n3\nt1 = -n2\nt2 = t0 - n1\nt3 = t1 - n0\nt4 = t2 / t3\nt5 = n0 * t4\nt6 = t5 - n1\nanswer = t6 / t4\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "in a group of ducks and cows , the total number of legs are 12 more than twice the no . of heads . find the total no . of buffaloes .", + "Output Program": [ + "n0 = 12.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "in a group of 800 people , 2 / 5 play at least one instrument , 96 play two or more . what is the probability that one student play exactly one instrument ?", + "Output Program": [ + "n0 = 800.0\nn1 = 2.0\nn2 = 5.0\nn3 = 96.0\nt0 = n0 * n1\nt1 = t0 / n2\nt2 = t1 - n3\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.28" + ], + "split": "train" + }, + { + "Input": "if bill can buy 3 pairs of jeans and 2 shirts for $ 69 or 2 pairs of jeans and 3 shirts for $ 76 , how much does one shirt cost ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 69.0\nn3 = 2.0\nn4 = 3.0\nn5 = 76.0\nt0 = n0 * n5\nt1 = n1 * n2\nt2 = n0 * n0\nt3 = n1 * n1\nt4 = t0 - t1\nt5 = t2 - t3\nanswer = t4 / t5\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "what is the least common multiple of 1227 and 40", + "Output Program": [ + "import scipy\nn0 = 1227.0\nn1 = 40.0\nt0 = n0 % 100.0\nt1 = n0 - t0\nt2 = t1 / 100.0\nt3 = scipy.lcm(int(t2), int(t0))\nanswer = scipy.lcm(int(n1), int(t3))\nprint(answer)" + ], + "Output Answer": [ + "1080" + ], + "split": "train" + }, + { + "Input": "there are 810 male and female participants in a meeting . half the female participants and one - quarterof the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?", + "Output Program": [ + "n0 = 810.0\nt0 = n0 / 3.0\nt1 = t0 * 4.0\nt2 = t1 - n0\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "135" + ], + "split": "train" + }, + { + "Input": "find the greatest number of 5 digits which is exactly divisible by 12 , 15 and 18 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 12.0\nn2 = 15.0\nn3 = 18.0\nt0 = n1 * n2\nt1 = n3 * t0\nanswer = t1 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "12960" + ], + "split": "train" + }, + { + "Input": "in an examination , 20 % of total students failed in hindi , 70 % failed in english and 10 % in both . the percentage of these who passed in both the subjects is :", + "Output Program": [ + "n0 = 20.0\nn1 = 70.0\nn2 = 10.0\nt0 = n0 + n1\nt1 = t0 - n2\nanswer = 100.0 - t1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "if p , q , and r are distinct positive digits and the product of the two - digit integers pq and pr is 221 , what is the sum of the digits p , q , and r ?", + "Output Program": [ + "n0 = 221.0\nt0 = 1.0 + 12.0\nt1 = n0 / t0\nt2 = t0 % 10.0\nt3 = t2 + 1.0\nt4 = t1 % 10.0\nanswer = t3 + t4\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "pat , kate and mark charged a total of 189 hours to a certain project . if pat charged twice as much time to the project as kate and 1 / 3 as much times as mark , how many more hours did mark charge to the project than kate .", + "Output Program": [ + "n0 = 189.0\nn1 = 1.0\nn2 = 3.0\nt0 = n1 + 2.0\nt1 = n2 * 2.0\nt2 = t0 + t1\nt3 = t1 - n1\nt4 = n0 / t2\nanswer = t4 * t3\nprint(answer)" + ], + "Output Answer": [ + "105" + ], + "split": "train" + }, + { + "Input": "working simultaneously and independently at an identical constant rate , 10 machines of a certain type can produce a total of x units of product p in 4 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 3 x units of product p in 6 days ?", + "Output Program": [ + "n0 = 10.0\nn1 = 4.0\nn2 = 3.0\nn3 = 6.0\nt0 = n1 / n3\nt1 = n0 * n2\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "robert ate 9 chocolates , nickel ate 2 chocolates . how many more chocolates did robert ate than nickel ?", + "Output Program": [ + "n0 = 9.0\nn1 = 2.0\n\nanswer = n0 - n1\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "3 boys are ages 4 , 6 and 7 respectively . 3 girls are ages 5 , 8 and 9 , respectively . if two of the boys and two of the girls are randomly selected and the sum of the selected children ' s ages is q , what is the difference between the probability that q is even and the probability that q is odd ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 6.0\nn3 = 7.0\nn4 = 3.0\nn5 = 5.0\nn6 = 8.0\nn7 = 9.0\nt0 = n5 / n7\nt1 = n1 / n7\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "0.11111111111111116" + ], + "split": "train" + }, + { + "Input": "if 4 xz + yw = 4 and xw + yz = 8 , what is the value of the expression ( 2 x + y ) ( 2 z + w ) ?", + "Output Program": [ + "n0 = 4.0\nn1 = 4.0\nn2 = 8.0\nn3 = 2.0\nn4 = 2.0\nt0 = n2 * n3\nanswer = n0 + t0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "in 10 years , a will be twice as old 5 as b was 10 years ago . if a is now 7 years older than b , the present age of b is", + "Output Program": [ + "n0 = 10.0\nn1 = 5.0\nn2 = 10.0\nn3 = 7.0\nt0 = n0 + n3\nt1 = n0 * 2.0\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "37" + ], + "split": "train" + }, + { + "Input": "what is the last digit in the product ( 3 ^ 65 x 6 ^ 59 x 7 ^ 71 )", + "Output Program": [ + "n0 = 3.0\nn1 = 65.0\nn2 = 6.0\nn3 = 59.0\nn4 = 7.0\nn5 = 71.0\nt0 = n0 * n2\nt1 = n5 % 4.0\nt2 = n4**min(t1, 5)\nt3 = t2 % 10.0\nt4 = t0 * t3\nanswer = t4 % 10.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "the average weight of 5 person ' s increases by 10.0 kg when a new person comes in place of one of them weighing 40 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 5.0\nn1 = 10.0\nn2 = 40.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "there are some people in party , 1 / 3 rd left the party . then 2 / 5 th of the remaining left the party , then 2 / 3 rd of the remaining left the party . at last 10 were remaining . how many people were in total ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 2.0\nn3 = 5.0\nn4 = 2.0\nn5 = 3.0\nn6 = 10.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = n2 / n1\nt3 = n0 - t0\nt4 = n0 - t1\nt5 = n0 - t2\nt6 = t3 * t4\nt7 = t6 * t5\nanswer = n6 / t7\nprint(answer)" + ], + "Output Answer": [ + "74.99999999999999" + ], + "split": "train" + }, + { + "Input": "in a school with 5 classes , each class has 2 students less than the previous class . how many students are there in the largest class if the total number of students at school is 115 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 115.0\nt0 = n1 + n1\nt1 = n1 + t0\nt2 = n1 + t1\nt3 = t1 + t1\nt4 = t3 + t2\nt5 = n2 - t4\nt6 = t5 / n0\nanswer = t2 + t6\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "train" + }, + { + "Input": "the length of 3 ropes are in the ratio 4 : 5 : 6 . if the sum of the weights of the longest and the shortest rope is 100 metres more than the length of the third rope , what is the length of the shortest rope ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 5.0\nn3 = 6.0\nn4 = 100.0\nt0 = n1 + n3\nt1 = t0 - n2\nt2 = n4 / t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "9 people decided to split the restaurant bill evenly . if the bill was $ 514.16 dollars , how much money did they 1 cent is the smallest unit ?", + "Output Program": [ + "n0 = 9.0\nn1 = 514.16\nn2 = 1.0\nt0 = 3.0 / 100.0\nanswer = n1 + t0\nprint(answer)" + ], + "Output Answer": [ + "514.1899999999999" + ], + "split": "train" + }, + { + "Input": "the grade point average of the entire class is 84 . if the average of one fourth of the class is 96 , what is the average of the rest of the class ?", + "Output Program": [ + "n0 = 84.0\nn1 = 96.0\nt0 = n0 * 4.0\nt1 = 4.0 - 1.0\nt2 = t0 - n1\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "an ant walks an average of 600 meters in 10 minutes . a beetle walks 25 % less distance at the same time on the average . assuming the beetle walks at her regular rate , what is its speed in km / h ?", + "Output Program": [ + "n0 = 600.0\nn1 = 10.0\nn2 = 25.0\nt0 = n0 / 1000.0\nt1 = n1 / 60.0\nt2 = n2 / 100.0\nt3 = t0 / t1\nt4 = 1.0 - t2\nanswer = t3 * t4\nprint(answer)" + ], + "Output Answer": [ + "2.7" + ], + "split": "train" + }, + { + "Input": "in a river flowing at 2 km / hr , a boat travels 32 km upstream and then returns downstream to the starting point . if its speed in still water be 6 km / hr , find the total journey time .", + "Output Program": [ + "n0 = 2.0\nn1 = 32.0\nn2 = 6.0\nt0 = n0 + n2\nt1 = n2 - n0\nt2 = n1 / t1\nt3 = n1 / t0\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "a bowl of nuts is prepared for a party . brand p mixed nuts are 20 % almonds and brand q ' s deluxe nuts are 25 % almonds . if a bowl contains a total of 66 ounces of nuts , representing a mixture of both brands , and 15 ounces of the mixture are almonds , how many ounces of brand q ' s deluxe mixed nuts are used ?", + "Output Program": [ + "n0 = 20.0\nn1 = 25.0\nn2 = 66.0\nn3 = 15.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = n2 * t0\nt3 = t1 - t0\nt4 = n3 - t2\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "35.999999999999986" + ], + "split": "train" + }, + { + "Input": "the mean of 50 observations was 36 . it was found later that an observation 48 was wrongly taken as 21 . the corrected new mean is :", + "Output Program": [ + "n0 = 50.0\nn1 = 36.0\nn2 = 48.0\nn3 = 21.0\nt0 = n0 * n1\nt1 = n0 - 2.0\nt2 = t1 - n3\nt3 = t0 + t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "36.54" + ], + "split": "train" + }, + { + "Input": "the output of a factory was increased by 10 % to keep up with rising demand . to handle the holiday rush , this new output was increased by 30 % . by approximately what percent would the output now have to be decreased in order to restore the original output ?", + "Output Program": [ + "n0 = 10.0\nn1 = 30.0\nt0 = n0 + 100.0\nt1 = n1 / 100.0\nt2 = t0 * t1\nt3 = t0 + t2\nt4 = t3 - 100.0\nt5 = t4 * 100.0\nanswer = t5 / t3\nprint(answer)" + ], + "Output Answer": [ + "30.06993006993007" + ], + "split": "train" + }, + { + "Input": "the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 20 are excluded , the average mark of the remaining will be 95 . find the number of students who wrote the exam .", + "Output Program": [ + "n0 = 80.0\nn1 = 5.0\nn2 = 20.0\nn3 = 95.0\nt0 = n1 * n3\nt1 = n1 * n2\nt2 = n3 - n0\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "a student has to obtain 33 % of the total marks to pass . he got 92 marks and failed by 40 marks . the maximum marks are ?", + "Output Program": [ + "n0 = 33.0\nn1 = 92.0\nn2 = 40.0\nt0 = n1 + n2\nt1 = n0 / 100.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "train" + }, + { + "Input": "each of the products produced yesterday was checked by worker x or worker y . 0.5 % of the products checked by worker x are defective and 0.8 % of the products checked by worker y are defective . if the total defective rate of all the products checked by worker x and worker y is 0.6 % , what fraction of the products was checked by worker y ?", + "Output Program": [ + "n0 = 0.5\nn1 = 0.8\nn2 = 0.6\nt0 = n2 - n0\nt1 = n1 - n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.3333333333333332" + ], + "split": "train" + }, + { + "Input": "linda spent 5 / 6 of her savings on furniture and the rest on a tv . if the tv cost her $ 500 , what were her original savings ?", + "Output Program": [ + "n0 = 5.0\nn1 = 6.0\nn2 = 500.0\nt0 = n0 / n1\nt1 = 1.0 - t0\nanswer = n2 / t1\nprint(answer)" + ], + "Output Answer": [ + "3000.0000000000005" + ], + "split": "train" + }, + { + "Input": "1 / 3 + 1 / 2 - 5 / 6 + 1 / 5 + 1 / 4 - 9 / 20 - 9 / 20 =", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 2.0\nn4 = 5.0\nn5 = 6.0\nn6 = 1.0\nn7 = 5.0\nn8 = 1.0\nn9 = 4.0\nn10 = 9.0\nn11 = 20.0\nn12 = 9.0\nn13 = 20.0\n\nanswer = n12 / n13\nprint(answer)" + ], + "Output Answer": [ + "0.45" + ], + "split": "train" + }, + { + "Input": "ashok secured average of 76 marks in 6 subjects . if the average of marks in 5 subjects is 74 , how many marks did he secure in the 6 th subject ?", + "Output Program": [ + "n0 = 76.0\nn1 = 6.0\nn2 = 5.0\nn3 = 74.0\nn4 = 6.0\nt0 = n0 * n1\nt1 = n2 * n3\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "86" + ], + "split": "train" + }, + { + "Input": "a man has a certain number of small boxes to pack into parcles . if he packs 3 , 4 , 5 or 6 in a parcel , he is left with one over ; if he packs 7 in a parcle , none is left over . what is the number of boxes , he may have to pack ?", + "Output Program": [ + "import scipy\nn0 = 3.0\nn1 = 4.0\nn2 = 5.0\nn3 = 6.0\nn4 = 7.0\nt0 = scipy.lcm(int(n0), int(n1))\nt1 = scipy.lcm(int(n2), int(t0))\nt2 = scipy.lcm(int(n3), int(t1))\nt3 = n2 * t2\nanswer = t3 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "301" + ], + "split": "train" + }, + { + "Input": "a call center has two teams . each member of team a was able to process 2 / 5 calls as compared to each member of team b . if team a has 5 / 8 as many number of call center agents as team b , what fraction of the total calls was processed by team b ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 5.0\nn3 = 8.0\nt0 = n1 * n3\nt1 = n0 * n1\nt2 = t0 + t1\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.8" + ], + "split": "train" + }, + { + "Input": "if each digit in the set a = { 1 , 2 , 3 , 4 , 5 } is used exactly once , in how many ways can the 5 digits be arranged ?", + "Output Program": [ + "import math\nn0 = 1.0\nn1 = 2.0\nn2 = 3.0\nn3 = 4.0\nn4 = 5.0\nn5 = 5.0\n\nanswer = math.factorial(min(15, int(n5)))\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "a man saves 20 % of his monthly salary . if an account of dearness of things he is to increase his monthly expenses by 20 % , he is only able to save rs . 220 per month . what is his monthly salary ?", + "Output Program": [ + "n0 = 20.0\nn1 = 20.0\nn2 = 220.0\nt0 = n1 / 100.0\nt1 = n2 * 100.0\nt2 = 100.0 - n0\nt3 = t0 * t2\nt4 = t3 + t2\nt5 = 100.0 - t4\nanswer = t1 / t5\nprint(answer)" + ], + "Output Answer": [ + "5500" + ], + "split": "train" + }, + { + "Input": "the toll t , in dollars , for a truck using a certain bridge is given by the formula t = 2.50 + 0.50 ( x \u2212 2 ) , where x is the number of axles on the truck . what is the toll for an 18 - wheel truck that has 2 wheels on its front axle and 4 wheels on each of its other axles ?", + "Output Program": [ + "n0 = 2.5\nn1 = 0.5\nn2 = 2.0\nn3 = 18.0\nn4 = 2.0\nn5 = 4.0\nt0 = n3 - n2\nt1 = t0 / n5\nt2 = t1 + 1.0\nt3 = t2 - n2\nt4 = n1 * t3\nanswer = n0 + t4\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "what is the difference between the c . i . on rs . 7000 for 1 1 / 2 years at 4 % per annum compounded yearly and half - yearly ?", + "Output Program": [ + "n0 = 7000.0\nn1 = 1.0\nn2 = 1.0\nn3 = 2.0\nn4 = 4.0\nt0 = n3 / 100.0\nt1 = n4 / 100.0\nt2 = t0 + n1\nt3 = t1 + n1\nt4 = t2 * t2\nt5 = t2 * t3\nt6 = t2 * t4\nt7 = n0 * t5\nt8 = n0 * t6\nanswer = t8 - t7\nprint(answer)" + ], + "Output Answer": [ + "2.855999999999767" + ], + "split": "train" + }, + { + "Input": "mary ' s income is 70 percent more than tim ' s income , and tim ' s income is 40 percent less than juan ' s income . what percent of juan ' s income is mary ' s income ?", + "Output Program": [ + "n0 = 70.0\nn1 = 40.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = t0 + 1.0\nt3 = 1.0 - t1\nt4 = t2 * t3\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "102" + ], + "split": "train" + }, + { + "Input": "a sum of money lent out at s . i . amounts to a total of $ 480 after 2 years and to $ 680 after a further period of 5 years . what was the initial sum of money that was invested ?", + "Output Program": [ + "n0 = 480.0\nn1 = 2.0\nn2 = 680.0\nn3 = 5.0\nt0 = n1 / n3\nt1 = n2 - n0\nt2 = t0 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "train" + }, + { + "Input": "a man is 24 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ?", + "Output Program": [ + "n0 = 24.0\nt0 = 2.0 * 2.0\nt1 = 2.0 - 1.0\nt2 = t0 - 2.0\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "if x < y < z and y - x > 5 , where x is an even integer and y and z are odd integers , what is the least possible value of z - x ?", + "Output Program": [ + "n0 = 5.0\nt0 = n0 + 2.0\nanswer = t0 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "reeya obtained 65 , 67 , 76 , 82 and 85 out of 100 in different subjects , what will be the average", + "Output Program": [ + "n0 = 65.0\nn1 = 67.0\nn2 = 76.0\nn3 = 82.0\nn4 = 85.0\nn5 = 100.0\nt0 = n0 + n1\nt1 = 1.0 + 4.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "a jar of 312 marbles is divided equally among a group of marble - players today . if 2 people joined the group in the future , each person would receive 1 marble less . how many people are there in the group today ?", + "Output Program": [ + "import math\nn0 = 312.0\nn1 = 2.0\nn2 = 1.0\nt0 = n0 * n1\nt1 = n1**min(n1, 5)\nt2 = t0 * 4.0\nt3 = t2 + t1\nt4 = math.sqrt(max(0, t3))\nt5 = t4 - n1\nanswer = t5 / n1\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "right now , al and eliot have bank accounts , and al has more money than eliot . the difference between their two accounts is 1 / 12 of the sum of their two accounts . if al \u2019 s account were to increase by 10 % and eliot \u2019 s account were to increase by 20 % , then al would have exactly $ 21 more than eliot in his account . how much money does eliot have in his account right now ?", + "Output Program": [ + "n0 = 1.0\nn1 = 12.0\nn2 = 10.0\nn3 = 20.0\nn4 = 21.0\nt0 = n0 + n1\nt1 = n3 + 100.0\nt2 = n4 * 100.0\nt3 = t0 * n2\nt4 = t3 - t1\nanswer = t2 / t4\nprint(answer)" + ], + "Output Answer": [ + "210" + ], + "split": "train" + }, + { + "Input": "the product of x and y is a constant . if the value of x is increased by 30 % , by what percentage must the value of y be decreased ?", + "Output Program": [ + "n0 = 30.0\nt0 = n0 + 100.0\nt1 = 100.0 / t0\nt2 = 1.0 - t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "23.076923076923073" + ], + "split": "train" + }, + { + "Input": "two employees a and b are paid a total of rs . 550 per week by their employer . if a is paid 120 percent of the sum paid to b , how much is b paid per week ?", + "Output Program": [ + "n0 = 550.0\nn1 = 120.0\nt0 = n1 / 100.0\nt1 = t0 + 1.0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "249.99999999999997" + ], + "split": "train" + }, + { + "Input": "in an election between two candidates a and b , the number of valid votes received by a exceeds those received by b by 15 % of the total number of votes polled . if 20 % of the votes polled were invalid and a total of 9720 votes were polled , then how many valid votes did b get ?", + "Output Program": [ + "n0 = 15.0\nn1 = 20.0\nn2 = 9720.0\nt0 = n1 / 100.0\nt1 = n0 * n2\nt2 = t1 / 100.0\nt3 = 1.0 - t0\nt4 = n2 * t3\nt5 = t4 - t2\nanswer = t5 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "3159" + ], + "split": "train" + }, + { + "Input": "the average runs scored by a batsman in 20 matches is 30 . in the next 10 matches the batsman scored an average of 15 runs . find his average in all the 30 matches ?", + "Output Program": [ + "n0 = 20.0\nn1 = 30.0\nn2 = 10.0\nn3 = 15.0\nn4 = 30.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "a luxury liner , queen marry ii , is transporting several cats as well as the crew ( sailors , a cook , and one - legged captain ) to a nearby port . altogether , these passengers have 14 heads and 41 legs . how many cats does the ship host ?", + "Output Program": [ + "n0 = 14.0\nn1 = 41.0\nt0 = n1 - 1.0\nt1 = n0 - 1.0\nt2 = t1 * 2.0\nt3 = t1 * 4.0\nt4 = t0 - t2\nt5 = t3 - t2\nt6 = t4 / t5\nanswer = t6 * t1\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "if x + ( 1 / x ) = 5 , what is the value of t = x ^ 2 + ( 1 / x ) ^ 2 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 2.0\nn3 = 1.0\nn4 = 2.0\nt0 = n1**min(n2, 5)\nanswer = t0 - n2\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "on dividing 181 by a number , the quotient is 9 and the remainder is 1 . find the divisor ?", + "Output Program": [ + "import math\nn0 = 181.0\nn1 = 9.0\nn2 = 1.0\nt0 = n0 / n1\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "the average speed of a car is 1 4 / 5 times the avg speed of a bike . a tractor covers 575 km in 23 hrs . how much distance will the car cover in 5 hrs if the speed of the bike is twice speed of the tractor ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 5.0\nn3 = 575.0\nn4 = 23.0\nn5 = 5.0\nt0 = n1 / n2\nt1 = n3 / n4\nt2 = n0 + t0\nt3 = t1 * 2.0\nt4 = t2 * t3\nanswer = n5 * t4\nprint(answer)" + ], + "Output Answer": [ + "450" + ], + "split": "train" + }, + { + "Input": "a woodworker normally makes a certain number of parts in 24 days . but he was able to increase his productivity by 5 parts per day , and so he not only finished the job in only 22 days but also he made 80 extra parts . how many parts does the woodworker normally makes per day and how many pieces does he make in 24 days ?", + "Output Program": [ + "n0 = 24.0\nn1 = 5.0\nn2 = 22.0\nn3 = 80.0\nn4 = 24.0\nt0 = n1 * n2\nt1 = n0 - n2\nt2 = t0 - n3\nt3 = t2 / t1\nanswer = n0 * t3\nprint(answer)" + ], + "Output Answer": [ + "360" + ], + "split": "train" + }, + { + "Input": "julian owes his classmate jenny 20 dollars . if he borrows 8 dollars how much will he owe her ?", + "Output Program": [ + "n0 = 20.0\nn1 = 8.0\n\nanswer = n0 + n1\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "the sum of ages of 5 children born at the intervals of 8 years each is 90 years . what is the age of the youngest child ?", + "Output Program": [ + "n0 = 5.0\nn1 = 8.0\nn2 = 90.0\nt0 = n2 / n0\nt1 = t0 - n1\nanswer = t1 - n1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "how many even 4 - digit integers greater than 8000 are there such that all their digits are different ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 8000.0\nt0 = n0 + 1.0\nt1 = 3.0 + 4.0\nt2 = n0 * 2.0\nt3 = math.factorial(min(15, int(t2)))\nt4 = t0 * t1\nt5 = t2 - 2.0\nt6 = math.factorial(min(15, int(t5)))\nt7 = t3 / t6\nt8 = n0 * t7\nt9 = t0 * t7\nt10 = t8 + t9\nanswer = t10 - t4\nprint(answer)" + ], + "Output Answer": [ + "469" + ], + "split": "train" + }, + { + "Input": "what is x if x + 2 y = 100 and y = 25 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 100.0\nn2 = 25.0\nt0 = n0 * n2\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "last year department store x had a sales total for december that was 2 times the average ( arithmetic mean ) of the monthly sales totals for january through november . the sales total for december was what fraction of the sales total for the year ?", + "Output Program": [ + "n0 = 2.0\nt0 = 12.0 - 1.0\nt1 = n0 + t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.15384615384615385" + ], + "split": "train" + }, + { + "Input": "in a class of students , 2 / 3 of the number of girls is equal to 1 / 5 of the total number of students . what is the ratio of boys to girls in the class ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 1.0\nn3 = 5.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = t0 - t1\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "2.333333333333333" + ], + "split": "train" + }, + { + "Input": "jaya two digits age when appended with the two digits age of amitabh the 4 digits number formed is a perfect square . what is the the sum of the 4 digits no . ?", + "Output Program": [ + "n0 = 4.0\nn1 = 4.0\nt0 = 1.0 + 2.0\nanswer = n0 + t0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "pure milk costs 3.60 per litre . a milkman adds water to 25 litres of pure milk and sells the mixture at 3 per litre . how many litres of water does he add ?", + "Output Program": [ + "n0 = 3.6\nn1 = 25.0\nn2 = 3.0\nt0 = n0 * n1\nt1 = n1 * n2\nt2 = t0 - t1\nanswer = t2 / n2\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "the avg weight of a , b & c is 84 kg . if d joins the group , the avg weight of the group becomes 80 kg . if another man e who weights is 6 kg more than d replaces a , then the avgof b , c , d & e becomes 79 kg . what is the weight of a ?", + "Output Program": [ + "n0 = 84.0\nn1 = 80.0\nn2 = 6.0\nn3 = 79.0\nt0 = n1 * 4.0\nt1 = n3 * 4.0\nt2 = n0 * 3.0\nt3 = t0 - t2\nt4 = n2 + t3\nt5 = t1 - t4\nanswer = t0 - t5\nprint(answer)" + ], + "Output Answer": [ + "78" + ], + "split": "train" + }, + { + "Input": "the ratio of the amount of the oil bill for the month of february to the amount of the oil bill for the month of january was 5 : 4 . if the oil bill for february had been $ 45 more , the corresponding ratio would have been 3 : 2 . how much was the oil bill for january ?", + "Output Program": [ + "n0 = 5.0\nn1 = 4.0\nn2 = 45.0\nn3 = 3.0\nn4 = 2.0\nt0 = n3 / n4\nt1 = n0 / n1\nt2 = t0 - t1\nanswer = n2 / t2\nprint(answer)" + ], + "Output Answer": [ + "180" + ], + "split": "train" + }, + { + "Input": "what is the least number should be added to 1056 , so the sum of the number is completely divisible by 28 ?", + "Output Program": [ + "import math\nn0 = 1056.0\nn1 = 28.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = t1 + 1.0\nt3 = n1 * t2\nanswer = t3 - n0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "# p is defined as 2 p + 20 for any number p . what is p , if # ( # ( # p ) ) = - 4 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 20.0\nn2 = 4.0\nt0 = n1 * 2.0\nt1 = n2 * 2.0\nt2 = n0 * t0\nt3 = t2 + t0\nt4 = n1 + t3\nt5 = n2 + t4\nanswer = t5 / t1\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "the average student age of a certain class which has 30 students is 10 . if one student aged 11 go to another class and the age of the class teacher is included the average changes to 11 . what is the age of class teacher ?", + "Output Program": [ + "n0 = 30.0\nn1 = 10.0\nn2 = 11.0\nn3 = 11.0\nt0 = n0 * n3\nt1 = n0 * n1\nt2 = t1 - n2\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "41" + ], + "split": "train" + }, + { + "Input": "ifaequals the sum of the even integers from 2 to 60 , inclusive , andbequals the sum of the odd integers from 1 to 59 , inclusive , what is the value of a - b ?", + "Output Program": [ + "n0 = 2.0\nn1 = 60.0\nn2 = 1.0\nn3 = 59.0\nt0 = n2 + n3\nt1 = n1 / n0\nt2 = n3 - n2\nt3 = n2 + t1\nt4 = t2 / n0\nt5 = t0 / n0\nt6 = n2 + t4\nt7 = t3 * t1\nt8 = t6 * t5\nanswer = t7 - t8\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "a , b and c have rs . 500 between them , a and c together have rs . 200 and b and c rs . 310 . how much does c have ?", + "Output Program": [ + "n0 = 500.0\nn1 = 200.0\nn2 = 310.0\nt0 = n1 + n2\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "of the total amount that jill spent on a shopping trip , excluding taxes , she spent 50 percent on clothing , 20 percent on food , and 30 percent on other items . if jill paid a 4 percent tax on the clothing , no tax on the food , and an 8 percent tax on all other items , then the total tax that she paid was what percent of the total amount that she spent , excluding taxes ?", + "Output Program": [ + "n0 = 50.0\nn1 = 20.0\nn2 = 30.0\nn3 = 4.0\nn4 = 8.0\nt0 = n3 / 100.0\nt1 = n4 / 100.0\nt2 = n0 * t0\nt3 = n2 * t1\nt4 = t2 + t3\nt5 = t4 / 100.0\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "4.4" + ], + "split": "train" + }, + { + "Input": "united telephone charges a base rate of $ 8.00 for service , plus an additional charge of $ 0.25 per minute . atlantic call charges a base rate of $ 12.00 for service , plus an additional charge of $ 0.20 per minute . for what number of minutes would the bills for each telephone company be the same ?", + "Output Program": [ + "n0 = 8.0\nn1 = 0.25\nn2 = 12.0\nn3 = 0.2\nt0 = n2 - n0\nt1 = n1 - n3\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "80.00000000000001" + ], + "split": "train" + }, + { + "Input": "the tax on a commodity is diminished by 30 % but its consumption is increased by 20 % . find the decrease percent in the revenue derived from it ?", + "Output Program": [ + "n0 = 30.0\nn1 = 20.0\nt0 = n1 + 100.0\nt1 = 100.0 - n0\nt2 = t0 * t1\nt3 = t2 / 100.0\nanswer = 100.0 - t3\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "when throwing 2 dices , and looking at the sum of numbers on the dices - what is the probability to have a sum which is smaller than 5 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nt0 = n1 + 1.0\nt1 = n0 / 2.0\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.16666666666666666" + ], + "split": "train" + }, + { + "Input": "a man is 24 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is :", + "Output Program": [ + "n0 = 24.0\nt0 = 2.0 * 2.0\nt1 = 2.0 - 1.0\nt2 = t0 - 2.0\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "in a mixed college 160 students are there in one class . out of this 160 students 1 / 4 students are girls . how many boys are there ?", + "Output Program": [ + "n0 = 160.0\nn1 = 160.0\nn2 = 1.0\nn3 = 4.0\nt0 = n0 / n3\nanswer = t0 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "a \u2019 s speed is 20 / 16 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?", + "Output Program": [ + "n0 = 20.0\nn1 = 16.0\nt0 = n0 - n1\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.2" + ], + "split": "train" + }, + { + "Input": "for any integer k > 1 , the term \u201c length of an integer \u201d refers to the number of positive prime factors , not necessarily distinct , whose product is equal to k . for example , if k = 24 , the length of k is equal to 4 , since 24 = 2 \u00d7 2 \u00d7 2 \u00d7 3 . if x and y are positive integers such that x > 1 , y > 1 , and x + 3 y < 980 , what is the maximum possible sum of the length of x and the length of y ?", + "Output Program": [ + "n0 = 1.0\nn1 = 24.0\nn2 = 4.0\nn3 = 24.0\nn4 = 2.0\nn5 = 2.0\nn6 = 2.0\nn7 = 3.0\nn8 = 1.0\nn9 = 1.0\nn10 = 3.0\nn11 = 980.0\nt0 = n2 + n7\nt1 = n2 + n2\nt2 = n0 + t1\nanswer = t0 + t2\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "the temperature of a certain cup of coffee 2 minutes after it was poured was 120 degrees fahrenheit . if the temperature f of the coffee t minutes after it was poured can be determined by the formula f = 120 * 2 ^ ( - at ) + 60 , where f is in degrees fahrenheit and a is a constant . then the temperature of the coffee 30 minutes after it was poured was how many degrees fahrenheit ?", + "Output Program": [ + "n0 = 2.0\nn1 = 120.0\nn2 = 120.0\nn3 = 2.0\nn4 = 60.0\nn5 = 30.0\nt0 = n4 / n0\nt1 = 1.0 - n3\nt2 = t0 * t1\nt3 = n3**min(t2, 5)\nt4 = n1 * t3\nanswer = n4 + t4\nprint(answer)" + ], + "Output Answer": [ + "60.00000011175871" + ], + "split": "train" + }, + { + "Input": "if p is a prime number greater than 3 , find the remainder when p ^ 2 + 13 is divided by 12 .", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 13.0\nn3 = 12.0\nt0 = 1.0 + 4.0\nt1 = n0 * n3\nt2 = t0**min(n1, 5)\nt3 = n2 + t2\nanswer = t3 - t1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "on dividing 127 by a number , the quotient is 5 and the remainder is 2 . find the divisor .", + "Output Program": [ + "import math\nn0 = 127.0\nn1 = 5.0\nn2 = 2.0\nt0 = n0 / n1\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "if 15 students in a class average 70 % on an exam and 10 students average 95 % on the same exam , what is the average in percent for all 25 students ?", + "Output Program": [ + "n0 = 15.0\nn1 = 70.0\nn2 = 10.0\nn3 = 95.0\nn4 = 25.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = t0 + t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "in how many ways can a 5 - letter password be chosen , using the letters a , b , c , d , e , f , g , and / or h such that at least one letter is repeated within the password ?", + "Output Program": [ + "import math\nn0 = 5.0\nt0 = n0 + 3.0\nt1 = math.factorial(min(15, int(3.0)))\nt2 = math.factorial(min(15, int(t0)))\nt3 = t0**min(n0, 5)\nt4 = t2 / t1\nanswer = t3 - t4\nprint(answer)" + ], + "Output Answer": [ + "26048" + ], + "split": "train" + }, + { + "Input": "find the greatest number which on dividing 4351 and 5161 , leaves a reminder of 8 and 10 respectively", + "Output Program": [ + "import scipy\nn0 = 4351.0\nn1 = 5161.0\nn2 = 8.0\nn3 = 10.0\nt0 = n0 - n2\nt1 = n1 - n3\nanswer = scipy.gcd(int(t0), int(t1))\nprint(answer)" + ], + "Output Answer": [ + "101" + ], + "split": "train" + }, + { + "Input": "a scale 6 ft . 8 inches long is divided into 4 equal parts . find the length of each part .", + "Output Program": [ + "n0 = 6.0\nn1 = 8.0\nn2 = 4.0\nt0 = n0 * 12.0\nt1 = n1 + t0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "what least no . must be subtracted from 50248 so that remaining no . is divisible by 20 ?", + "Output Program": [ + "import math\nn0 = 50248.0\nn1 = 20.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a man has some hens and cows . if the number of heads be 48 and the number of feet equals 144 , then the number of hens will be :", + "Output Program": [ + "n0 = 48.0\nn1 = 144.0\nt0 = n0 * 4.0\nt1 = t0 - n1\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "a batsman in his 10 th innings makes a score of 60 , and thereby increases his average by 3 . what is his average after the 10 th innings ? he had never been \u2019 not out \u2019 .", + "Output Program": [ + "n0 = 10.0\nn1 = 60.0\nn2 = 3.0\nn3 = 10.0\nt0 = n0 * n2\nt1 = n1 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "8.036 divided by 0.04 gives :", + "Output Program": [ + "n0 = 8.036\nn1 = 0.04\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "200.89999999999998" + ], + "split": "train" + }, + { + "Input": "tom has travelling to 7 cities . gasoline prices varied from city to city . what is the median gasoline price ?", + "Output Program": [ + "n0 = 7.0\nt0 = n0 + 1.0\nt1 = t0 * 10.0\nt2 = t1 + 4.0\nt3 = t2 + 100.0\nanswer = t3 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "1.84" + ], + "split": "train" + }, + { + "Input": "if n is an integer and 102 n ^ 2 is less than or equal to 8100 , what is the greatest possible value of n ?", + "Output Program": [ + "import math\nn0 = 102.0\nn1 = 2.0\nn2 = 8100.0\nt0 = n2 / n0\nt1 = math.sqrt(max(0, t0))\nanswer = math.floor(t1)\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "in x - y plane , there is a right triangle abc ( \u2220 b = 90 o ) . if the length of ac is 100 and the slope of line segment ac is 4 / 3 , what is the length of ab ?", + "Output Program": [ + "import math\nn0 = 90.0\nn1 = 100.0\nn2 = 4.0\nn3 = 3.0\nt0 = n2**min(2.0, 5)\nt1 = n3**min(2.0, 5)\nt2 = t0 + t1\nt3 = math.sqrt(max(0, t2))\nt4 = n1 / t3\nanswer = n2 * t4\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "it costs a publishing company 50000 dollars to make books . the 50000 is a fixed cost or a cost that can not change . to help the publishing company sell the books , a marketing company charges 4 dollars for each book sold . if the company charges 9 dollars per book , how many books should they sell to break even ?", + "Output Program": [ + "n0 = 50000.0\nn1 = 50000.0\nn2 = 4.0\nn3 = 9.0\nt0 = n3 - n2\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "10000" + ], + "split": "train" + }, + { + "Input": "a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 % of the distribution lies one standard deviation s of the mean , what percent of the distribution is less than m + s ?", + "Output Program": [ + "n0 = 68.0\nt0 = 100.0 - n0\nt1 = t0 / 2.0\nanswer = 100.0 - t1\nprint(answer)" + ], + "Output Answer": [ + "84" + ], + "split": "train" + }, + { + "Input": "for any real number x , the operatoris defined as : ( x ) = x ( 2 \u2212 x ) if p + 1 = ( p + 1 ) , then p =", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 1.0\nt0 = n1 * 2.0\nt1 = -n0\nt2 = t1 / t0\nanswer = -t2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "on average , the bottle - nosed dolphin comes up for air once every 3 minutes ; the beluga whale , a close relative , comes up for air on average once every 6 minutes . the number of times a bottle - nosed dolphin would come up for air in a 24 hour period is approximately what percent greater than the number of times a beluga whale would come up for air in that same period ?", + "Output Program": [ + "n0 = 3.0\nn1 = 6.0\nn2 = 24.0\nt0 = n1 - n0\nt1 = t0 / 2.0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "train" + }, + { + "Input": "the average of 25 results is 50 . the average of first 12 of those is 14 and the average of last 12 is 17 . what is the 13 th result ?", + "Output Program": [ + "n0 = 25.0\nn1 = 50.0\nn2 = 12.0\nn3 = 14.0\nn4 = 12.0\nn5 = 17.0\nn6 = 13.0\nt0 = n0 * n1\nt1 = n2 * n5\nt2 = n2 * n3\nt3 = t0 - t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "878" + ], + "split": "train" + }, + { + "Input": "10 camels cost as much as 24 horses , 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants . if the cost of 10 elephants is rs . 110000 , find the cost of a camel ?", + "Output Program": [ + "n0 = 10.0\nn1 = 24.0\nn2 = 16.0\nn3 = 4.0\nn4 = 6.0\nn5 = 4.0\nn6 = 10.0\nn7 = 110000.0\nt0 = n1 * n3\nt1 = n0 * n2\nt2 = n3 * t0\nt3 = n4 * t1\nt4 = n7 * t2\nt5 = n0 * t3\nanswer = t4 / t5\nprint(answer)" + ], + "Output Answer": [ + "4400" + ], + "split": "train" + }, + { + "Input": "kyle , david , and catherine each try independently to solve a problem . if their individual probabilities for success are 1 / 3 , 2 / 7 and 5 / 9 , respectively , what is the probability that kyle and catherine , but not david will solve the problem ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 2.0\nn3 = 7.0\nn4 = 5.0\nn5 = 9.0\nt0 = n4 * n4\nt1 = 3.0 * 60.0\nt2 = 3.0 * 3.0\nt3 = t1 + t2\nanswer = t0 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.13227513227513227" + ], + "split": "train" + }, + { + "Input": "a car travels uphill at 30 km / hr and downhill at 60 km / hr . it goes 100 km uphill and 50 km downhill . find the average speed of the car ?", + "Output Program": [ + "n0 = 30.0\nn1 = 60.0\nn2 = 100.0\nn3 = 50.0\nt0 = n2 + n3\nt1 = n2 / n0\nt2 = n3 / n1\nt3 = t1 + t2\nanswer = t0 / t3\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "if the average ( arithmetic mean ) of a and b is 50 and the average of b and c is 70 , what is the value of c \u2212 a ?", + "Output Program": [ + "n0 = 50.0\nn1 = 70.0\nt0 = n1 * 2.0\nt1 = n0 * 2.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "if p ( a ) = 0.18 , p ( b ) = 0.5 and p ( b | a ) = 0.2 , find p ( a n b ) ?", + "Output Program": [ + "n0 = 0.18\nn1 = 0.5\nn2 = 0.2\nt0 = n0 * n2\nanswer = t0 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "0.36" + ], + "split": "train" + }, + { + "Input": "there are 4 people of different heights standing in order of increasing height . the difference is 2 inches between the first person and the second person , and also between the second person and the third person . the difference between the third person and the fourth person is 6 inches and the average height is 77 . how tall is the fourth person ?", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\nn2 = 6.0\nn3 = 77.0\nt0 = n0 + n2\nt1 = n0 * n3\nt2 = n2 + t0\nt3 = t1 - t2\nt4 = t3 / n0\nanswer = t0 + t4\nprint(answer)" + ], + "Output Answer": [ + "83" + ], + "split": "train" + }, + { + "Input": "t = { 2 , 3 , 4 , 5 } b = { 4 , 5 , 6 , 7 , 8 } two integers will be randomly selected from the sets above , one integer from set t and one integer from set b . what is the probability that the sum of the two integers will equal 9 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 4.0\nn3 = 5.0\nn4 = 4.0\nn5 = 5.0\nn6 = 6.0\nn7 = 7.0\nn8 = 8.0\nn9 = 9.0\nt0 = n3 + n6\nt1 = n9 + t0\nanswer = t1 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "0.2" + ], + "split": "train" + }, + { + "Input": "the average salary of the employees in a office is rs . 120 / month . the avg salary of officers is rs . 420 and of non officers is rs 110 . if the no . of officers is 15 , then find the no of nonofficers in the office .", + "Output Program": [ + "n0 = 120.0\nn1 = 420.0\nn2 = 110.0\nn3 = 15.0\nt0 = n1 * n3\nt1 = n0 * n3\nt2 = n0 - n2\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "450" + ], + "split": "train" + }, + { + "Input": "if ( a - b - c + d = 13 ) and ( a + b - c - d = 9 ) , what is the value of ( b - d ) ^ 2 ?", + "Output Program": [ + "n0 = 13.0\nn1 = 9.0\nn2 = 2.0\nt0 = n0 + n1\nt1 = t0 / n2\nt2 = n1 - t1\nanswer = t2**min(n2, 5)\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "9873 + x = 13200 , then x is ?", + "Output Program": [ + "n0 = 9873.0\nn1 = 13200.0\n\nanswer = n1 - n0\nprint(answer)" + ], + "Output Answer": [ + "3327" + ], + "split": "train" + }, + { + "Input": "a certain number of horses and an equal number of men are going somewhere . half of the owners are on their horses ' back while the remaining ones are walking along leading their horses . if the number of legs walking on the ground is 60 , how many horses are there ?", + "Output Program": [ + "n0 = 60.0\nt0 = 2.0 / 2.0\nt1 = t0 + 4.0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 985 . find the cost of each ice - cream cup ?", + "Output Program": [ + "n0 = 16.0\nn1 = 5.0\nn2 = 7.0\nn3 = 6.0\nn4 = 6.0\nn5 = 45.0\nn6 = 70.0\nn7 = 985.0\nt0 = n0 * n3\nt1 = n1 * n5\nt2 = n2 * n6\nt3 = n7 - t0\nt4 = t3 - t1\nt5 = t4 - t2\nanswer = t5 / n3\nprint(answer)" + ], + "Output Answer": [ + "29" + ], + "split": "train" + }, + { + "Input": "the age of somu is one - third his father ' s . 5 years back he was one - fifth of his father ' s age . what is his persent age ?", + "Output Program": [ + "n0 = 5.0\nt0 = 1.0 + 4.0\nt1 = n0 * t0\nt2 = t0 - 3.0\nt3 = t1 - n0\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "a charitable association sold an average of 66 raffle tickets per member . among the female members , the average was 70 raffle tickets . the male to female ratio of the association is 1 : 2 . what was the average number w of tickets sold by the male members of the association", + "Output Program": [ + "n0 = 66.0\nn1 = 70.0\nn2 = 1.0\nn3 = 2.0\nt0 = n2 + n3\nt1 = n1 * n3\nt2 = n0 * t0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "58" + ], + "split": "train" + }, + { + "Input": "city x has a population 6 times as great as the population of city y , which has a population twice as great as the population of city z . what is the ratio of the population of city x to the population of city z ?", + "Output Program": [ + "n0 = 6.0\n\nanswer = n0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "the maximum number of students among them 1001 pens and 910 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils ?", + "Output Program": [ + "import scipy\nn0 = 1001.0\nn1 = 910.0\n\nanswer = scipy.gcd(int(n0), int(n1))\nprint(answer)" + ], + "Output Answer": [ + "91" + ], + "split": "train" + }, + { + "Input": "how many even integers n , such that 20 < = n < = 250 are of the form 3 k + 4 , where k is any natural number ?", + "Output Program": [ + "n0 = 20.0\nn1 = 250.0\nn2 = 3.0\nn3 = 4.0\nt0 = n0 + 2.0\nt1 = 2.0 + n3\nt2 = n1 - 2.0\nt3 = t2 - t0\nt4 = t3 / t1\nanswer = t4 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "38.666666666666664" + ], + "split": "train" + }, + { + "Input": "a fruit - salad mixture consists of apples , peaches , and grapes in the ratio 12 : 8 : 7 , respectively , by weight . if 54 pounds of the mixture is prepared , the mixture includes how many more pounds of apples than grapes ?", + "Output Program": [ + "n0 = 12.0\nn1 = 8.0\nn2 = 7.0\nn3 = 54.0\nt0 = n0 * 2.0\nt1 = n2 * 2.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "two employees x and y are paid a total of rs . 330 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?", + "Output Program": [ + "n0 = 330.0\nn1 = 120.0\nt0 = 1.0 + 4.0\nt1 = t0 * 2.0\nt2 = t1 + 1.0\nt3 = n0 * t1\nt4 = t2 * 2.0\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "train" + }, + { + "Input": "if the price of a certain computer increased 30 percent from d dollars to 338 dollars , then 2 d =", + "Output Program": [ + "n0 = 30.0\nn1 = 338.0\nn2 = 2.0\nt0 = n0 + 100.0\nt1 = t0 / 100.0\nt2 = n1 / t1\nanswer = n2 * t2\nprint(answer)" + ], + "Output Answer": [ + "520" + ], + "split": "train" + }, + { + "Input": "a pupil ' s marks were wrongly entered as 79 instead of 45 . due to that the average marks for the class got increased by half . the number of pupils in the class is :", + "Output Program": [ + "n0 = 79.0\nn1 = 45.0\nt0 = n0 - n1\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "68" + ], + "split": "train" + }, + { + "Input": "90 % of the population of a village is 45000 . the total population of the village is ?", + "Output Program": [ + "n0 = 90.0\nn1 = 45000.0\nt0 = 100.0 / n0\nanswer = n1 * t0\nprint(answer)" + ], + "Output Answer": [ + "50000" + ], + "split": "train" + }, + { + "Input": "there are 12 teams in a soccer league and each team plays each of the other teams once . how many games will be played in total ?", + "Output Program": [ + "import math\nn0 = 12.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(2.0)))\nt2 = n0 - 2.0\nt3 = math.factorial(min(15, int(t2)))\nt4 = t3 * t1\nanswer = t0 / t4\nprint(answer)" + ], + "Output Answer": [ + "66" + ], + "split": "train" + }, + { + "Input": "michael cashed a check for $ 1270 and received only $ 10 and $ 50 bills in return . during the course of a day , he used 15 bills and then lost the rest of the money . if the number of $ 10 bills used was either one more or one less than the number of $ 50 bills used , what is the minimum possible amount of money that was lost ?", + "Output Program": [ + "import math\nn0 = 1270.0\nn1 = 10.0\nn2 = 50.0\nn3 = 15.0\nn4 = 10.0\nn5 = 50.0\nt0 = n3 / 2.0\nt1 = math.floor(t0)\nt2 = n1 * t1\nt3 = n3 - t1\nt4 = n2 * t3\nt5 = t4 + t2\nanswer = n0 - t5\nprint(answer)" + ], + "Output Answer": [ + "800" + ], + "split": "train" + }, + { + "Input": "if a farmer sells 5 of his goats , his stock of feed will last for 4 more days than planned , but if he buys 10 more goats , he will run out of feed 3 days earlier than planned . if no goats are sold or bought , the farmer will be exactly on schedule . how many goats does the farmer have ?", + "Output Program": [ + "n0 = 5.0\nn1 = 4.0\nn2 = 10.0\nn3 = 3.0\nt0 = n1 * n3\nt1 = t0 - n2\nanswer = n2 * t1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "what is the smallest integer y for which 27 ^ y > 3 ^ 24 ?", + "Output Program": [ + "import math\nn0 = 27.0\nn1 = 3.0\nn2 = 24.0\nt0 = n2 / 3.0\nt1 = math.floor(t0)\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "1 / 3 + 1 / 2 - 5 / 6 + 1 / 5 + 1 / 4 - 9 / 20 - 2 / 15 =", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 2.0\nn4 = 5.0\nn5 = 6.0\nn6 = 1.0\nn7 = 5.0\nn8 = 1.0\nn9 = 4.0\nn10 = 9.0\nn11 = 20.0\nn12 = 2.0\nn13 = 15.0\n\nanswer = n12 / n13\nprint(answer)" + ], + "Output Answer": [ + "0.13333333333333333" + ], + "split": "train" + }, + { + "Input": "tourist purchased a total of 30 travelers checks in $ 50 and $ 100 denominations . the total worth of the travelers checks is $ 1800 . how many checks of $ 50 denominations can he spend so that average amount ( arithmetic mean ) of the remaining travelers checks is $ 70 ?", + "Output Program": [ + "n0 = 30.0\nn1 = 50.0\nn2 = 100.0\nn3 = 1800.0\nn4 = 50.0\nn5 = 70.0\nt0 = n0 * n5\nt1 = n5 - n1\nt2 = t0 - n3\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "in a graduating class , 40 percent of the students are male . in this class , 50 percent of the male students and 40 percent of the female students are 25 years old or older . if one student in the class is randomly selected , approximately what is the probability that he or she will be less than 25 years old ?", + "Output Program": [ + "n0 = 40.0\nn1 = 50.0\nn2 = 40.0\nn3 = 25.0\nn4 = 25.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = n2 / 100.0\nt3 = t0 * t1\nt4 = 1.0 - t0\nt5 = t2 * t4\nt6 = t3 + t5\nanswer = 1.0 - t6\nprint(answer)" + ], + "Output Answer": [ + "0.56" + ], + "split": "train" + }, + { + "Input": "the events a and b are independent , the probability that event a occurs is greater than 0 , and the probability that event a occurs is twice the probability that event b occurs . the probability that at least one of events a and b occurs is 5 times the probability that both events a and b occur . what is the probability that event a occurs ?", + "Output Program": [ + "n0 = 0.0\nn1 = 5.0\nt0 = 1.0 + 2.0\nt1 = n1 * 2.0\nt2 = t1 + 2.0\nt3 = t0 / t2\nanswer = t3 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "a , b , and c are integers and a < b < c . s is the set of all integers from a to b , inclusive . q is the set of all integers from b to c , inclusive . the median of set s is ( 3 / 4 ) * b . the median of set q is ( 7.5 / 8 ) * c . if r is the set of all integers from a to c , inclusive , what fraction of c is the median of set r ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 7.5\nn3 = 8.0\nt0 = n2 / n3\nt1 = n0 / n1\nt2 = t0 * 2.0\nt3 = t1 * 2.0\nt4 = t2 - 1.0\nt5 = t3 - 1.0\nt6 = 1.0 / t5\nt7 = t4 / t6\nt8 = t7 + 1.0\nanswer = t8 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "0.71875" + ], + "split": "train" + }, + { + "Input": "barbata invests $ 1400 in the national bank at 5 % . how much additional money must she invest at 8 % so that the total annual income will be equal to 6 % of her entire investment ?", + "Output Program": [ + "n0 = 1400.0\nn1 = 5.0\nn2 = 8.0\nn3 = 6.0\nt0 = n3 / 100.0\nt1 = n1 / 100.0\nt2 = n2 / 100.0\nt3 = n0 * t0\nt4 = n0 * t1\nt5 = t2 - t0\nt6 = t3 - t4\nanswer = t6 / t5\nprint(answer)" + ], + "Output Answer": [ + "699.9999999999999" + ], + "split": "train" + }, + { + "Input": "a person has 12004 coins of silver . how much would he need to add so that he can distribute equally among his 7 children in whole numbers ?", + "Output Program": [ + "import math\nn0 = 12004.0\nn1 = 7.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = t1 + 1.0\nt3 = n1 * t2\nanswer = t3 - n0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "a man purchased 3 blankets @ rs . 100 each , 5 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 162 . find the unknown rate of two blankets ?", + "Output Program": [ + "n0 = 3.0\nn1 = 100.0\nn2 = 5.0\nn3 = 150.0\nn4 = 162.0\nt0 = n4 * 10.0\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "570" + ], + "split": "train" + }, + { + "Input": "two trains of equal are running on parallel lines in the same direction at 49 km / hr and 36 km / hr . the faster train passes the slower train in 36 sec . the length of each train is ?", + "Output Program": [ + "n0 = 49.0\nn1 = 36.0\nn2 = 36.0\nt0 = n0 - n1\nt1 = t0 * 1000.0\nt2 = t1 / 3600.0\nt3 = n2 * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "65" + ], + "split": "train" + }, + { + "Input": "in an examination , a pupil \u2019 s average marks were 63 per paper . if he had obtained 20 more marks for his geography paper and 2 more marks for his history paper , his average per paper would have been 65 . how many papers were there in the examination ?", + "Output Program": [ + "n0 = 63.0\nn1 = 20.0\nn2 = 2.0\nn3 = 65.0\nt0 = n1 + n2\nt1 = n3 - n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "if p / q = 2 / 7 , then 2 p + q = ?", + "Output Program": [ + "n0 = 2.0\nn1 = 7.0\nn2 = 2.0\nt0 = n0 * n2\nanswer = n1 + t0\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "the sum of the non - prime numbers between 50 and 60 , non - inclusive , is", + "Output Program": [ + "n0 = 50.0\nn1 = 60.0\nt0 = n0 + 1.0\nt1 = t0 + 1.0\nt2 = t0 + t1\nt3 = t1 + 2.0\nt4 = t2 + t3\nt5 = t3 + 1.0\nt6 = t4 + t5\nt7 = t5 + 1.0\nt8 = t6 + t7\nt9 = t7 + 1.0\nt10 = t8 + t9\nt11 = t9 + 1.0\nanswer = t10 + t11\nprint(answer)" + ], + "Output Answer": [ + "383" + ], + "split": "train" + }, + { + "Input": "the average weight of 10 person ' s increases by 5 kg when a new person comes in place of one of them weighing 60 kg . what is the weight of the new person ?", + "Output Program": [ + "n0 = 10.0\nn1 = 5.0\nn2 = 60.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "110" + ], + "split": "train" + }, + { + "Input": "if p ( a ) = 2 / 15 , p ( b ) = 4 / 15 , and p ( a \u00e2 \u02c6 \u00aa b ) = 6 / 15 find p ( b | a )", + "Output Program": [ + "n0 = 2.0\nn1 = 15.0\nn2 = 4.0\nn3 = 15.0\nn4 = 6.0\nn5 = 15.0\nt0 = n4 / n1\nt1 = n0 / n1\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "if x + y = 9 and x \u2013 y = 3 , then x ^ 2 - y ^ 2 =", + "Output Program": [ + "n0 = 9.0\nn1 = 3.0\nn2 = 2.0\nn3 = 2.0\nt0 = 3.0**min(2.0, 5)\nt1 = n0 - n1\nt2 = t1**min(n2, 5)\nanswer = t2 - t0\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "train" + }, + { + "Input": "a box contains 10 apples , 9 of which are red . an apple is drawn from the box and its color is noted before it is eaten . this is done a total of n times , and the probability that a red apple is drawn each time is less than 0.5 . what is the smallest possible value of n ?", + "Output Program": [ + "n0 = 10.0\nn1 = 9.0\nn2 = 0.5\nt0 = n2 * 10.0\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "if a - b = 10 and a 2 + b 2 = 210 , find the value of ab .", + "Output Program": [ + "n0 = 10.0\nn1 = 2.0\nn2 = 2.0\nn3 = 210.0\nt0 = n0**min(n1, 5)\nt1 = n3 - t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "55" + ], + "split": "train" + }, + { + "Input": "in a 150 member association consisting of men and women , exactly 10 % of men and exactly 20 % women are homeowners . what is the least number of members who are homeowners ?", + "Output Program": [ + "n0 = 150.0\nn1 = 10.0\nn2 = 20.0\nt0 = n2 / 100.0\nt1 = n0 - n1\nt2 = t1 / n1\nt3 = n1 * t0\nt4 = t3 * t3\nanswer = t2 + t4\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "7 people average age is 30 . youngest person age is 8 . find average of the people when youngest was born .", + "Output Program": [ + "n0 = 7.0\nn1 = 30.0\nn2 = 8.0\nt0 = n0 * n1\nt1 = n0 * n2\nt2 = t0 - t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "at a supermarket , john spent 1 / 2 of his money on fresh fruits and vegetables , 1 / 3 on meat products , and 1 / 10 on bakery products . if he spent the remaining $ 5 on candy , how much did john spend at the supermarket ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 1.0\nn3 = 3.0\nn4 = 1.0\nn5 = 10.0\nn6 = 5.0\nt0 = n0 / n5\nt1 = n0 / n3\nt2 = n0 / n1\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n0 - t4\nanswer = n6 / t5\nprint(answer)" + ], + "Output Answer": [ + "75.00000000000001" + ], + "split": "train" + }, + { + "Input": "in a certain school , 20 % of students are below 8 years of age . the number of students above 8 years of age is 2 / 3 of the number of students of 8 years of age which is 12 . what is the total number of students in the school ?", + "Output Program": [ + "n0 = 20.0\nn1 = 8.0\nn2 = 8.0\nn3 = 2.0\nn4 = 3.0\nn5 = 8.0\nn6 = 12.0\nt0 = n3 / n4\nt1 = n0 / 100.0\nt2 = n6 * t0\nt3 = 1.0 - t1\nt4 = n6 + t2\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "if w is a positive integer and 10 ^ w \u2013 74 in decimal notation has digits whose sum is 440 , what is the value of w ?", + "Output Program": [ + "n0 = 10.0\nn1 = 74.0\nn2 = 440.0\nt0 = n2 / n0\nt1 = n0 * 2.0\nt2 = n1 - t0\nanswer = t1 + t2\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "think of a number , divide it by 5 and add 6 to it . the result is 65 . what is the number thought of ?", + "Output Program": [ + "n0 = 5.0\nn1 = 6.0\nn2 = 65.0\nt0 = n2 - n1\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "295" + ], + "split": "train" + }, + { + "Input": "in a two digit number , the digit in the units place is 6 times the digit in 10 ' s place and sum of the digits is equal to 7 . what is the number ?", + "Output Program": [ + "n0 = 6.0\nn1 = 10.0\nn2 = 7.0\nt0 = n0 + 1.0\nt1 = n2 / t0\nt2 = n1 * t1\nt3 = n0 * t1\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "in an exam , amar scored 64 percent , bhavan scored 36 percent and chetan 44 percent . the maximum score awarded in the exam is 900 . find the average mark scored by all the 3 boys ?", + "Output Program": [ + "n0 = 64.0\nn1 = 36.0\nn2 = 44.0\nn3 = 900.0\nn4 = 3.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = n2 / 100.0\nt3 = n3 * t0\nt4 = n3 * t1\nt5 = n3 * t2\nt6 = t3 + t4\nt7 = t6 + t5\nanswer = t7 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "432" + ], + "split": "train" + }, + { + "Input": "when a certain number x is divided by 63 , the remainder is 11 . what is the remainder when x is divided by 9 ?", + "Output Program": [ + "n0 = 63.0\nn1 = 11.0\nn2 = 9.0\n\nanswer = n1 % n2\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "[ ( 3.242 x 12 ) / 100 ] = ?", + "Output Program": [ + "n0 = 3.242\nn1 = 12.0\nn2 = 100.0\nt0 = n0 * n1\nt1 = t0 / 100.0\nanswer = t1 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "0.038903999999999994" + ], + "split": "train" + }, + { + "Input": "for all positive integers m , [ m ] = 3 m when m is odd and [ m ] = ( 1 / 2 ) * m when m is even . what is [ 5 ] * [ 6 ] equivalent to ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 2.0\nn3 = 5.0\nn4 = 6.0\nt0 = n4 / n2\nt1 = n0 * n3\nt2 = t0 * t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "the price of commodity x increases by 40 paise every year , while the price of commodity y increases by 15 paise every year . if in 1988 , the price of commodity x was 4.20 and that of y was 6.30 , in which year will commodity x cost 40 paise more than commodity y ?", + "Output Program": [ + "n0 = 40.0\nn1 = 15.0\nn2 = 1988.0\nn3 = 4.2\nn4 = 6.3\nn5 = 40.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = n4 - n3\nt3 = t0 + t2\nt4 = t0 - t1\nt5 = t3 / t4\nanswer = n2 + t5\nprint(answer)" + ], + "Output Answer": [ + "1998" + ], + "split": "train" + }, + { + "Input": "of the total amount that jill spent on a shopping trip , excluding taxes , she spent 45 percent on clothing , 45 percent on food , and 10 percent on other items . if jill paid a 5 percent tax on the clothing , no tax on the food , and an 10 percent tax on all other items , then the total tax that she paid was what percent of the total amount that she spent , excluding taxes ?", + "Output Program": [ + "n0 = 45.0\nn1 = 45.0\nn2 = 10.0\nn3 = 5.0\nn4 = 10.0\nt0 = n3 / 100.0\nt1 = n4 / 100.0\nt2 = n0 * t0\nt3 = n2 * t1\nt4 = t2 + t3\nt5 = t4 / 100.0\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "3.25" + ], + "split": "train" + }, + { + "Input": "if the price of gasoline increases by 25 % and ron intends to spend only 15 % more on gasoline , by how much % should he reduce the quantity of gasoline that he buys ?", + "Output Program": [ + "n0 = 25.0\nn1 = 15.0\nt0 = n1 / 100.0\nt1 = n0 / 100.0\nt2 = t0 + 1.0\nt3 = t1 + 1.0\nt4 = t2 / t3\nt5 = 1.0 - t4\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "8.000000000000007" + ], + "split": "train" + }, + { + "Input": "if x gets 25 % more than y and y gets 20 % more than z , the share of z out of rs . 925 will be :", + "Output Program": [ + "n0 = 25.0\nn1 = 20.0\nn2 = 925.0\nt0 = n1 / 100.0\nt1 = n0 / 100.0\nt2 = t0 + 1.0\nt3 = t1 + 1.0\nt4 = t3 * t2\nt5 = t2 + t4\nt6 = t5 + 1.0\nanswer = n2 / t6\nprint(answer)" + ], + "Output Answer": [ + "250" + ], + "split": "train" + }, + { + "Input": "5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 60 only . men \u00e2 \u20ac \u2122 s wages are ?", + "Output Program": [ + "n0 = 5.0\nn1 = 8.0\nn2 = 60.0\nt0 = n0 * 3.0\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "3034 - ( 1002 / 20.04 ) = ?", + "Output Program": [ + "n0 = 3034.0\nn1 = 1002.0\nn2 = 20.04\nt0 = n1 / n2\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "2984" + ], + "split": "train" + }, + { + "Input": "what will be the reminder when ( 27 ^ 27 + 27 ) is divided by 28 ?", + "Output Program": [ + "import math\nn0 = 27.0\nn1 = 27.0\nn2 = 27.0\nn3 = 28.0\nt0 = n0**min(n0, 5)\nt1 = n0 + t0\nt2 = t1 / n3\nt3 = math.floor(t2)\nt4 = n3 * t3\nanswer = t1 - t4\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "ram ' s salary is 25 % more than raja ' s . how much percent is raja ' s salary less than ram ' s ?", + "Output Program": [ + "n0 = 25.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nt2 = 1 / t1\nt3 = t2 * 100.0\nanswer = 100.0 - t3\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "0.009 / x = 0.1 . find the value of x", + "Output Program": [ + "n0 = 0.009\nn1 = 0.1\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.08999999999999998" + ], + "split": "train" + }, + { + "Input": "the average runs of a cricket player of 15 innings was 25 . how many runs must he make in his next innings so as to increase his average of runs by 6 ?", + "Output Program": [ + "n0 = 15.0\nn1 = 25.0\nn2 = 6.0\nt0 = n0 + 1.0\nt1 = n1 + n2\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "121" + ], + "split": "train" + }, + { + "Input": "( x ) + 1315 + 9211 - 1569 = 11901 . calculate the value of x", + "Output Program": [ + "n0 = 1315.0\nn1 = 9211.0\nn2 = 1569.0\nn3 = 11901.0\nt0 = n2 + n3\nt1 = 60.0 / 2.0\nt2 = t0 - n1\nt3 = t2 - n0\nanswer = t1 * t3\nprint(answer)" + ], + "Output Answer": [ + "88320" + ], + "split": "train" + }, + { + "Input": "a man can row 3.9 km / hr in still water . it takes him twice as long to row upstream as to row downstream . what is the rate of the current ?", + "Output Program": [ + "n0 = 3.9\nt0 = n0 * 2.0\nt1 = t0 - n0\nanswer = t1 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "1.3" + ], + "split": "train" + }, + { + "Input": "a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 50 paisa . if the share of y is rs . 27 , what is the total amount ?", + "Output Program": [ + "n0 = 45.0\nn1 = 50.0\nn2 = 27.0\nt0 = 100.0 / n0\nt1 = n1 / n0\nt2 = n2 * t0\nt3 = n2 * t1\nt4 = t2 + t3\nanswer = n2 + t4\nprint(answer)" + ], + "Output Answer": [ + "117" + ], + "split": "train" + }, + { + "Input": "the average weight of 7 person ' s increases by 6.2 kg when a new person comes in place of one of them weighing 76 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 7.0\nn1 = 6.2\nn2 = 76.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "119.4" + ], + "split": "train" + }, + { + "Input": "10 camels cost as much as 24 horses , 26 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants . if the cost of 10 elephants is rs . 170000 , find the cost of a camel ?", + "Output Program": [ + "n0 = 10.0\nn1 = 24.0\nn2 = 26.0\nn3 = 4.0\nn4 = 6.0\nn5 = 4.0\nn6 = 10.0\nn7 = 170000.0\nt0 = n1 * n3\nt1 = n0 * n2\nt2 = n3 * t0\nt3 = n4 * t1\nt4 = n7 * t2\nt5 = n0 * t3\nanswer = t4 / t5\nprint(answer)" + ], + "Output Answer": [ + "4184.615384615385" + ], + "split": "train" + }, + { + "Input": "the average score of a cricketer for 7 matches is 56 runs . if the average for first 4 matches is 46 , then average for last 3 matches is", + "Output Program": [ + "n0 = 7.0\nn1 = 56.0\nn2 = 4.0\nn3 = 46.0\nn4 = 3.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = t0 - t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "69.33333333333333" + ], + "split": "train" + }, + { + "Input": "how many multiples of 10 are there between 11 and 1001 ?", + "Output Program": [ + "n0 = 10.0\nn1 = 11.0\nn2 = 1001.0\nt0 = n2 - n1\nt1 = t0 / n0\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "a 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2 . 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more . at the end of the two removal and replacement , what is the ratio of milk and water in the resultant mixture ?", + "Output Program": [ + "n0 = 20.0\nn1 = 3.0\nn2 = 2.0\nn3 = 10.0\nt0 = n1 + n2\nt1 = n0 - n3\nt2 = n1 / t0\nt3 = n2 / t0\nt4 = t2 * t1\nt5 = t3 * t1\nt6 = n3 + t4\nt7 = t5 / n0\nt8 = t6 / n0\nt9 = t7 * t1\nt10 = t8 * t1\nt11 = n3 + t10\nanswer = t11 / t9\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "a \u201c sophie germain \u201d prime is any positive prime number p for which 2 p + 1 is also prime . the product of all the possible units digits of sophie germain primes greater than 6 is", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 6.0\nt0 = n0 + n1\nt1 = n0 * 10.0\nt2 = n2 - n1\nt3 = t0 + t2\nt4 = t3 + t0\nt5 = n0 * t3\nt6 = n1 + t5\nt7 = t4 + t0\nt8 = t4 - 10.0\nt9 = n0 * t7\nt10 = t6 - 10.0\nt11 = n1 + t9\nt12 = t8 * t10\nt13 = t0 * t12\nt14 = t11 - t1\nanswer = t13 * t14\nprint(answer)" + ], + "Output Answer": [ + "189" + ], + "split": "train" + }, + { + "Input": "if the price of a book is first decreased by 15 % and then increased by 10 % , then the net change in the price will be :", + "Output Program": [ + "n0 = 15.0\nn1 = 10.0\nt0 = n0 * 100.0\nt1 = n1 * 100.0\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = t3 + 100.0\nt5 = 100.0 - t2\nt6 = t5 / 100.0\nt7 = t4 / 100.0\nt8 = t6 * t7\nt9 = t8 * 100.0\nanswer = 100.0 - t9\nprint(answer)" + ], + "Output Answer": [ + "6.5" + ], + "split": "train" + }, + { + "Input": "a warehouse is labeling computer inventory with 5 - digit codes . each code is to consist of 4 digits between the numbers 0 and 9 . the manager is debating whether to allow any 5 - digit codes to have leading zero ' s before a non - zero number is used . if not allowed , then numbers like 0025 cannot be used . the manager wants to measure the magnitude of the number of 5 - digit code possibilities that are lost if he disallows the use of leading zero ' s . how many such codes would be lost ?", + "Output Program": [ + "n0 = 5.0\nn1 = 4.0\nn2 = 0.0\nn3 = 9.0\nn4 = 5.0\nn5 = 25.0\nn6 = 5.0\nt0 = 10.0**min(n0, 5)\nt1 = 10.0**min(n1, 5)\nt2 = n3 * t1\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "10000" + ], + "split": "train" + }, + { + "Input": "every year an amount increases by 1 / 9 th of itself . how much will it be after two years if its present value is rs . 64000 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 9.0\nn2 = 64000.0\nt0 = n0 / n1\nt1 = n2 * t0\nt2 = n2 + t1\nt3 = t2 * t0\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "79012.34567901235" + ], + "split": "train" + }, + { + "Input": "an amount of money is to be divided between p , q and r in the ratio of 3 : 7 : 12 . if the difference between the shares of p and q is rs . 3600 , what will be the difference between q and r ' s share ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 12.0\nn3 = 3600.0\nt0 = n1 - n0\nt1 = n2 - n1\nt2 = n3 / t0\nanswer = t2 * t1\nprint(answer)" + ], + "Output Answer": [ + "4500" + ], + "split": "train" + }, + { + "Input": "a number is doubled and 9 is added . if resultant is trebled , it becomes 81 . what is that number", + "Output Program": [ + "n0 = 9.0\nn1 = 81.0\nt0 = n0 * 3.0\nt1 = 2.0 * 3.0\nt2 = n1 - t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "10 camels cost as much as 24 horses , 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants . if the cost of 10 elephants is rs . 120000 , find the cost of a camel ?", + "Output Program": [ + "n0 = 10.0\nn1 = 24.0\nn2 = 16.0\nn3 = 4.0\nn4 = 6.0\nn5 = 4.0\nn6 = 10.0\nn7 = 120000.0\nt0 = n1 * n3\nt1 = n0 * n2\nt2 = n3 * t0\nt3 = n4 * t1\nt4 = n7 * t2\nt5 = n0 * t3\nanswer = t4 / t5\nprint(answer)" + ], + "Output Answer": [ + "4800" + ], + "split": "train" + }, + { + "Input": "a man is 24 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is", + "Output Program": [ + "n0 = 24.0\nt0 = 2.0 * 2.0\nt1 = 2.0 - 1.0\nt2 = t0 - 2.0\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "a number when divided by 100 leaves 11 as a remainder . what will be the remainder if the number is divided by 11 ?", + "Output Program": [ + "n0 = 100.0\nn1 = 11.0\nn2 = 11.0\nt0 = n0 + n1\nanswer = t0 % n2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is", + "Output Program": [ + "n0 = 8000.0\nn1 = 7.0\nn2 = 12000.0\nn3 = 6000.0\nt0 = n2 - n0\nt1 = n0 - n3\nt2 = n1 * t0\nt3 = t2 / t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "a straight line in the xy - plane has a slope of 2 and a y - intercept of 2 . on this line , what is the x - coordinate of the point whose y - coordinate is 520 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 520.0\nt0 = n2 - n0\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "259" + ], + "split": "train" + }, + { + "Input": "john purchased 1325 large bottles at $ 1.89 per bottle and 750 small bottles at $ 1.38 per bottle . what was the approximate average price paid per bottle ?", + "Output Program": [ + "n0 = 1325.0\nn1 = 1.89\nn2 = 750.0\nn3 = 1.38\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "1.7056626506024097" + ], + "split": "train" + }, + { + "Input": "find the smallest number of six digits exactly divisible by 25 , 35,45 and 15 .", + "Output Program": [ + "n0 = 25.0\nn1 = 35.0\nn2 = 45.0\nn3 = 15.0\nt0 = 100.0 * 100.0\nt1 = t0 * 10.0\nt2 = t1 - 100.0\nanswer = n1 + t2\nprint(answer)" + ], + "Output Answer": [ + "99935" + ], + "split": "train" + }, + { + "Input": "a whale goes on a feeding frenzy that lasts for 9 hours . for the first hour he catches and eats x kilos of plankton . in every hour after the first , it consumes 3 kilos of plankton more than it consumed in the previous hour . if by the end of the frenzy the whale will have consumed a whopping accumulated total 540 kilos of plankton , how many kilos did he consume on the sixth hour ?", + "Output Program": [ + "n0 = 9.0\nn1 = 3.0\nn2 = 540.0\nt0 = n2 / n0\nanswer = n1 + t0\nprint(answer)" + ], + "Output Answer": [ + "63" + ], + "split": "train" + }, + { + "Input": "two employees x and y are paid a total of rs . 880 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?", + "Output Program": [ + "n0 = 880.0\nn1 = 120.0\nt0 = 1.0 + 4.0\nt1 = t0 * 2.0\nt2 = t1 + 1.0\nt3 = n0 * t1\nt4 = t2 * 2.0\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "train" + }, + { + "Input": "in a box of 11 pencils , a total of 2 are defective . if a customer buys 3 pencils selected at random from the box , what is the probability that neither pencils will be defective ?", + "Output Program": [ + "import math\nn0 = 11.0\nn1 = 2.0\nn2 = 3.0\nt0 = math.factorial(min(15, int(n2)))\nt1 = math.factorial(min(15, int(n0)))\nt2 = n0 - n1\nt3 = n0 - n2\nt4 = math.factorial(min(15, int(t2)))\nt5 = math.factorial(min(15, int(t3)))\nt6 = t2 - n2\nt7 = math.factorial(min(15, int(t6)))\nt8 = t5 * t0\nt9 = t1 / t8\nt10 = t7 * t0\nt11 = t4 / t10\nanswer = t11 / t9\nprint(answer)" + ], + "Output Answer": [ + "0.509090909090909" + ], + "split": "train" + }, + { + "Input": "the average salary of a person for the months of january , february , march and april is rs . 8000 and that for the months february , march , april and may is rs . 8300 . if his salary for the month of may is rs . 6500 , find his salary for the month of january ?", + "Output Program": [ + "n0 = 8000.0\nn1 = 8300.0\nn2 = 6500.0\nt0 = n0 * 4.0\nt1 = n1 * 4.0\nt2 = t1 - n2\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "5300" + ], + "split": "train" + }, + { + "Input": "65 % of x = 20 % of 552.50 . find the value of x ?", + "Output Program": [ + "n0 = 65.0\nn1 = 20.0\nn2 = 552.5\nt0 = n2 / 100.0\nt1 = n1 * t0\nt2 = t1 * 100.0\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "170" + ], + "split": "train" + }, + { + "Input": "find the value of y from ( 12 ) ^ 3 x 6 ^ 3 \u00f7 432 = y ?", + "Output Program": [ + "n0 = 12.0\nn1 = 3.0\nn2 = 6.0\nn3 = 3.0\nn4 = 432.0\nt0 = n0**min(n1, 5)\nt1 = n2**min(n3, 5)\nt2 = t0 * t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "864" + ], + "split": "train" + }, + { + "Input": "the total price of a basic computer and printer are $ 2,500 . if the same printer had been purchased with an enhanced computer whose price was $ 500 more than the price of the basic computer , then the price of the printer would have been 1 / 6 of that total . what was the price of the basic computer ?", + "Output Program": [ + "n0 = 2500.0\nn1 = 500.0\nn2 = 1.0\nn3 = 6.0\nt0 = n0 + n1\nt1 = t0 / n3\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "2000" + ], + "split": "train" + }, + { + "Input": "last week john spent 30 percent of his wages on recreation . this week , his wages are 25 percent less than last week \u02bc s wages and he spent 20 percent of his wages on recreation . the amount he spends on recreation this week is what percent of the amount he spent on recreation last week ?", + "Output Program": [ + "n0 = 30.0\nn1 = 25.0\nn2 = 20.0\nt0 = n2 / 100.0\nt1 = n0 / 100.0\nt2 = 100.0 - n1\nt3 = t2 / 100.0\nt4 = t1 * 100.0\nt5 = t3 * 100.0\nt6 = t0 * t5\nt7 = t6 / t4\nanswer = t7 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "in 2000 there were 10000 women stockbrokers in the united states . by 2005 the number had increased to 20000 . approximately what was the percent increase ?", + "Output Program": [ + "n0 = 2000.0\nn1 = 10000.0\nn2 = 2005.0\nn3 = 20000.0\nt0 = n3 - n1\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "if \u2018 + \u2019 means \u2018 \u00d7 \u2019 , \u2018 - \u2018 means \u2018 + \u2019 , \u2018 \u00d7 \u2019 means \u2018 \u00f7 \u2019 and \u2018 \u00f7 \u2019 means \u2018 - \u2018 then find the value of ; 6 \u2013 9 + 8 \u00d7 3 \u00f7 25 =", + "Output Program": [ + "n0 = 6.0\nn1 = 9.0\nn2 = 8.0\nn3 = 3.0\nn4 = 25.0\nt0 = n1 * n2\nt1 = t0 / n3\nt2 = n0 + t1\nanswer = t2 - n4\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "a grocer has a sale of rs . 5700 , rs . 8550 , rs . 6855 , rs . 3850 for 4 consecutive months . how much sale must he have in the fifth month so that he gets an average sale of rs . 7800 ?", + "Output Program": [ + "n0 = 5700.0\nn1 = 8550.0\nn2 = 6855.0\nn3 = 3850.0\nn4 = 4.0\nn5 = 7800.0\nt0 = n4 + 1.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n5 * t0\nt4 = n3 + t2\nanswer = t3 - t4\nprint(answer)" + ], + "Output Answer": [ + "14045" + ], + "split": "train" + }, + { + "Input": "suraj has a certain average of runs for 14 innings . in the 15 th innings he scores 140 runs thereby increasing his average by 8 runs . what is his average after the 15 th innings ?", + "Output Program": [ + "n0 = 14.0\nn1 = 15.0\nn2 = 140.0\nn3 = 8.0\nn4 = 15.0\nt0 = n0 * n3\nt1 = n1 - n0\nt2 = n2 - t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "how many points ( x , y ) lie on the line segment between ( 22 , 12 2 / 3 ) and ( 16 , 17 2 / 3 ) such that x and y are both integers ?", + "Output Program": [ + "n0 = 22.0\nn1 = 12.0\nn2 = 2.0\nn3 = 3.0\nn4 = 16.0\nn5 = 17.0\nn6 = 2.0\nn7 = 3.0\n\nanswer = n4 / n4\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "a certain class of students is being divided into teams . the class can either be divided into 15 teams with an equal number of players on each team or 24 teams with an equal number of players on each team . what is the lowest possible number of students in the class ?", + "Output Program": [ + "import scipy\nn0 = 15.0\nn1 = 24.0\n\nanswer = scipy.lcm(int(n0), int(n1))\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "a department store perceived a run on a lower priced garment and raised the price by 20 % to keep stock available until another shipment arrived . customers fumed and the department store manager allowed them to purchase the garments at 80 % of the new price to save face . what was the difference in the new retail price and the price the customers were allowed to pay instead ?", + "Output Program": [ + "n0 = 20.0\nn1 = 80.0\nt0 = n0 + 100.0\nt1 = n1 / 100.0\nt2 = t0 / 100.0\nt3 = t1 * t2\nt4 = 1.0 - t3\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "4.0000000000000036" + ], + "split": "train" + }, + { + "Input": "the price of a mobile was increased by 40 percent . the new price was then decreased by 15 percent . a single increase of what percent is equivalent to these two successive changes ?", + "Output Program": [ + "n0 = 40.0\nn1 = 15.0\nt0 = n0 + 100.0\nt1 = 100.0 - n1\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = t2 * t3\nt5 = t4 - 1.0\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "18.999999999999993" + ], + "split": "train" + }, + { + "Input": "the closest approximation of w ( 69.28 \u00d7 0.004 ) / 0.03 is", + "Output Program": [ + "n0 = 69.28\nn1 = 0.004\nn2 = 0.03\nt0 = n1 / n2\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "9.237333333333334" + ], + "split": "train" + }, + { + "Input": "the least number by which 72 must be multiplied in order to produce a multiple of 112 , is :", + "Output Program": [ + "import scipy\nn0 = 72.0\nn1 = 112.0\nt0 = scipy.gcd(int(n0), int(n1))\nanswer = n1 / t0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "if there are 200 questions in a 3 hr examination . among these questions are 50 type a problems , which requires twice as much as time be spent than the rest of the type b problems . how many minutes should be spent on type a problems ?", + "Output Program": [ + "n0 = 200.0\nn1 = 3.0\nn2 = 50.0\nt0 = n1 * 60.0\nt1 = n2 * 2.0\nt2 = n0 - n2\nt3 = t1 + t2\nt4 = t0 / t3\nt5 = t4 * 2.0\nanswer = n2 * t5\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "train" + }, + { + "Input": "a person spends 1 / 3 rd of the money with him on clothes , 1 / 5 th of the remaining on food and 1 / 4 th of the remaining on travel . now , he is left with rs 100 . how much did he have with him in the beginning ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 5.0\nn4 = 1.0\nn5 = 4.0\nn6 = 100.0\nt0 = n0 / n1\nt1 = n0 - t0\nt2 = t1 / n3\nt3 = t1 - t2\nt4 = t3 / n5\nt5 = t3 - t4\nanswer = n6 / t5\nprint(answer)" + ], + "Output Answer": [ + "249.99999999999994" + ], + "split": "train" + }, + { + "Input": "sam taken a loan rs . 15000 / - from co - operative society with an interest @ 11.5 % per month . at the same time he deposited rs . 10000 / - as fixed deposit with an interest @ 9.5 % per month . after one week sam asked the manager to calculate the interest to be paid . what is the interest amount for 7 days ?", + "Output Program": [ + "n0 = 15000.0\nn1 = 11.5\nn2 = 10000.0\nn3 = 9.5\nn4 = 7.0\nt0 = n1 / 100.0\nt1 = n3 / 100.0\nt2 = 10.0 * 3.0\nt3 = n0 * t0\nt4 = n2 * t1\nt5 = t3 - t4\nt6 = t5 / t2\nanswer = n4 * t6\nprint(answer)" + ], + "Output Answer": [ + "180.83333333333331" + ], + "split": "train" + }, + { + "Input": "on a two - dimensional coordinate plane , the line d = x ^ 2 - x ^ 3 touches the x - axis in how many places ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nt0 = max(n0,n1)\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "when the price of an article is reduced by 30 % , the sales increases by 50 % . the percentage change in the total amount of receipts is ?", + "Output Program": [ + "n0 = 30.0\nn1 = 50.0\nt0 = n1 + 100.0\nt1 = 100.0 - n0\nt2 = t0 * t1\nt3 = t2 / 100.0\nanswer = t3 - 100.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 20000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is", + "Output Program": [ + "n0 = 8000.0\nn1 = 7.0\nn2 = 20000.0\nn3 = 6000.0\nt0 = n2 - n0\nt1 = n0 - n3\nt2 = n1 * t0\nt3 = t2 / t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "49" + ], + "split": "train" + }, + { + "Input": "if a mixture is 3 \u2044 5 alcohol by volume and 4 \u2044 5 water by volume , what is the ratio of the volume of alcohol to the volume of water in this mixture ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 4.0\nn3 = 5.0\nt0 = n0 / n1\nt1 = n2 / n1\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.7499999999999999" + ], + "split": "train" + }, + { + "Input": "of the 150 people at a party , 70 were women , and 30 women tried the appetizer . if 60 people did not try the appetizer , what is the total number of men who tried the appetizer ?", + "Output Program": [ + "n0 = 150.0\nn1 = 70.0\nn2 = 30.0\nn3 = 60.0\nt0 = n0 - n3\nanswer = t0 - n2\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "in the biology lab of ` ` jefferson ' ' high school there are 0.036 * 10 ^ 5 germs , equally divided among 75000 * 10 ^ ( - 3 ) petri dishes . how many germs live happily in a single dish ?", + "Output Program": [ + "n0 = 0.036\nn1 = 10.0\nn2 = 5.0\nn3 = 75000.0\nn4 = 10.0\nn5 = 3.0\nt0 = n3 / 1000.0\nt1 = 100.0 * 1000.0\nt2 = n0 * t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "47.99999999999999" + ], + "split": "train" + }, + { + "Input": "the difference b / w the compound interest payble half yearly and the simple interest on a certain sum lent out at 10 % p . a for 1 year is rs 25 . what is the sum ?", + "Output Program": [ + "n0 = 10.0\nn1 = 1.0\nn2 = 25.0\nt0 = 10.0 / 2.0\nt1 = n0 / 100.0\nt2 = t0 / 100.0\nt3 = n1 + t2\nt4 = t3**min(2.0, 5)\nt5 = t4 - 1.0\nt6 = t5 - t1\nanswer = n2 / t6\nprint(answer)" + ], + "Output Answer": [ + "9999.99999999988" + ], + "split": "train" + }, + { + "Input": "the sum of the squares of the first 15 positive integers ( 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + . . . + 15 ^ 2 ) is equal to 1250 . what is the sum of the squares of the second 15 positive integers ( 16 ^ 2 + 17 ^ 2 + 18 ^ 2 + . . . + 30 ^ 2 ) ?", + "Output Program": [ + "n0 = 15.0\nn1 = 1.0\nn2 = 2.0\nn3 = 2.0\nn4 = 2.0\nn5 = 3.0\nn6 = 2.0\nn7 = 15.0\nn8 = 2.0\nn9 = 1250.0\nn10 = 15.0\nn11 = 16.0\nn12 = 2.0\nn13 = 17.0\nn14 = 2.0\nn15 = 18.0\nn16 = 2.0\nn17 = 30.0\nn18 = 2.0\nt0 = n17 + n1\nt1 = n5 + n5\nt2 = n17 * n2\nt3 = t2 + n1\nt4 = n17 * t0\nt5 = t3 * t4\nt6 = t5 / t1\nanswer = t6 - n9\nprint(answer)" + ], + "Output Answer": [ + "8205" + ], + "split": "train" + }, + { + "Input": "what is the probability for a family with 5 children to have two boys and 3 girls ( assuming the probability of having a boy or a girl is equal ) ?", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 3.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(n1)))\nt2 = 2.0**min(n0, 5)\nt3 = n0 - n1\nt4 = math.factorial(min(15, int(t3)))\nt5 = t1 * t4\nt6 = t0 / t5\nanswer = t6 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.3125" + ], + "split": "train" + }, + { + "Input": "the ratio of sodium chloride to ammonium in 100 kg of mixed ammonium normally used by 3 chemists is 1 : 4 . the amount of sodium chloride to be added to 100 kg of mixed ammonium to make the ratio 9 : 25 is", + "Output Program": [ + "n0 = 100.0\nn1 = 3.0\nn2 = 1.0\nn3 = 4.0\nn4 = 100.0\nn5 = 9.0\nn6 = 25.0\nt0 = 1.0 + 4.0\nt1 = n5 / n6\nt2 = n3 / t0\nt3 = 1.0 / t0\nt4 = n0 * t2\nt5 = n0 * t3\nt6 = t1 * t4\nanswer = t6 - t5\nprint(answer)" + ], + "Output Answer": [ + "8.799999999999997" + ], + "split": "train" + }, + { + "Input": "think of a number , divide it by 6 and add 5 to it . the result is 17 . what is the number thought of ?", + "Output Program": [ + "n0 = 6.0\nn1 = 5.0\nn2 = 17.0\nt0 = n2 - n1\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "train" + }, + { + "Input": "$ 406 is divided among a , b , and c so that a receives half as much as b , and b receives half as much as c . how much money is c ' s share ?", + "Output Program": [ + "n0 = 406.0\nt0 = 1.0 / 2.0\nt1 = t0 + 1.0\nt2 = t1 + 2.0\nt3 = n0 / t2\nanswer = t3 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "232" + ], + "split": "train" + }, + { + "Input": "what is the dividend . divisor 18 , the quotient is 9 and the remainder is 5 ?", + "Output Program": [ + "n0 = 18.0\nn1 = 9.0\nn2 = 5.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "167" + ], + "split": "train" + }, + { + "Input": "a 15 lt mixture contains water with 20 % of alcohol . if 5 more lts of water added to the mixture what is the percentage of alcohol ?", + "Output Program": [ + "n0 = 15.0\nn1 = 20.0\nn2 = 5.0\nt0 = n0 + n2\nt1 = n1 / 100.0\nt2 = n0 * t1\nt3 = t2 / t0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "by how much does the larger root of the equation 2 c ^ 2 + 5 c = 12 exceed the smaller root ?", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 2.0\nn2 = 5.0\nn3 = 12.0\nt0 = n0 * n3\nt1 = n0 * n0\nt2 = n2**min(n0, 5)\nt3 = t0 * 4.0\nt4 = t3 + t2\nt5 = math.sqrt(max(0, t4))\nt6 = n2 + t5\nt7 = n2 - t5\nt8 = t6 / t1\nt9 = t7 / t1\nanswer = t8 - t9\nprint(answer)" + ], + "Output Answer": [ + "5.5" + ], + "split": "train" + }, + { + "Input": "a certain sum of money is divided among a , b and c such that a gets one - third of what b and c together get and b gets two - seventh of what a and c together get . if the amount received by a is $ 10 more than that received by b , find the total amount shared by a , b and c .", + "Output Program": [ + "n0 = 10.0\nt0 = n0 * 3.0\nt1 = n0 * 2.0\nt2 = t0 * 2.0\nt3 = t2 + t1\nt4 = n0 + t3\nt5 = t3 + t4\nt6 = t4 * 3.0\nt7 = t6 - t3\nanswer = t5 + t7\nprint(answer)" + ], + "Output Answer": [ + "360" + ], + "split": "train" + }, + { + "Input": "in a can , there is a mixture of milk and water in the ratio 5 : 3 . if the can is filled with an additional 20 liters of milk , the can would be full and the ratio of milk and water would become 3 : 1 . find the capacity of the can ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nn2 = 20.0\nn3 = 3.0\nn4 = 1.0\nt0 = n2 * n4\nt1 = n1 * n3\nt2 = n0 * n4\nt3 = t1 - t2\nt4 = t0 / t3\nt5 = n0 * t4\nt6 = n1 * t4\nt7 = n2 + t5\nanswer = t7 + t6\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "the greatest number that exactly divided 105 , 1001 and 2436 is :", + "Output Program": [ + "n0 = 105.0\nn1 = 1001.0\nn2 = 2436.0\nt0 = 1.0 + 4.0\nt1 = n0 / 3.0\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "the average age of a group of persons going for picnic is 16 years . 12 new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years . the number of persons initially going for picnic is", + "Output Program": [ + "n0 = 16.0\nn1 = 12.0\nn2 = 15.0\nn3 = 15.5\nt0 = n1 * n3\nt1 = n1 * n2\nt2 = n0 - n3\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "if ( c - a ) / ( c - b ) = 1 , then ( 5 b - 2 a ) / ( c - a ) =", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 2.0\nt0 = n1 - n2\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "when greenville state university decided to move its fine arts collection to a new library , it had to package the collection in 20 - inch by 20 - inch by 15 - inch boxes . if the university pays $ 1.20 for every box , and if the university needs 3.06 million cubic inches to package the collection , what is the minimum amount the university must spend on boxes ?", + "Output Program": [ + "n0 = 20.0\nn1 = 20.0\nn2 = 15.0\nn3 = 1.2\nn4 = 3.06\nt0 = 1000.0 * 1000.0\nt1 = n0 * n0\nt2 = n4 * t0\nt3 = n2 * t1\nt4 = t2 / t3\nanswer = n3 * t4\nprint(answer)" + ], + "Output Answer": [ + "612" + ], + "split": "train" + }, + { + "Input": "what is the remainder when 1274 * 1275 * 1277 * 1285 is divided by 12 ?", + "Output Program": [ + "n0 = 1274.0\nn1 = 1275.0\nn2 = 1277.0\nn3 = 1285.0\nn4 = 12.0\nt0 = n0 * n1\nanswer = t0 % n2\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "yearly subscription to professional magazines cost a company $ 940.00 . to make a 35 % cut in the magazine budget , how much less must be spent ?", + "Output Program": [ + "n0 = 940.0\nn1 = 35.0\nt0 = 100.0 - n1\nt1 = t0 / 100.0\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "611" + ], + "split": "train" + }, + { + "Input": "rates for having a manuscript typed at a certain typing service are $ 10 per page for the first time a page is typed and $ 5 per page each time a page is revised . if a certain manuscript has 100 pages , of which 20 were revised only once , 30 were revised twice , and the rest required no revisions , what was the total cost of having the manuscript typed ?", + "Output Program": [ + "n0 = 10.0\nn1 = 5.0\nn2 = 100.0\nn3 = 20.0\nn4 = 30.0\nt0 = n0 * n2\nt1 = n1 * n3\nt2 = n1 * n4\nt3 = t0 + t1\nt4 = t2 * 2.0\nanswer = t3 + t4\nprint(answer)" + ], + "Output Answer": [ + "1400" + ], + "split": "train" + }, + { + "Input": "the average ( arithmetic mean ) of 20 , 40 , and 60 is 7 more than the average of 10 , 70 , and what number ?", + "Output Program": [ + "n0 = 20.0\nn1 = 40.0\nn2 = 60.0\nn3 = 7.0\nn4 = 10.0\nn5 = 70.0\nt0 = n0 + n1\nt1 = n3 * 3.0\nt2 = n2 + t0\nt3 = n4 + t1\nt4 = n5 + t3\nanswer = t2 - t4\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "there are 2 sections a and b in a class , consisting of 50 and 40 students respectively . if the average weight of section a is 50 kg and that of section b is 70 kg , find the average of the whole class ?", + "Output Program": [ + "n0 = 2.0\nn1 = 50.0\nn2 = 40.0\nn3 = 50.0\nn4 = 70.0\nt0 = n1 + n2\nt1 = n1 * n3\nt2 = n2 * n4\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "58.888888888888886" + ], + "split": "train" + }, + { + "Input": "dan ' s age after 20 years will be 7 times his age 4 years ago . what is the present age of dan ?", + "Output Program": [ + "n0 = 20.0\nn1 = 7.0\nn2 = 4.0\nt0 = n1 * n2\nt1 = n1 - 1.0\nt2 = n0 + t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a man \u2019 s current age is ( 2 / 5 ) of the age of his father . after 8 years , he will be ( 1 / 2 ) of the age of his father . what is the age of father at now ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 8.0\nn3 = 1.0\nn4 = 2.0\nt0 = n0 / n3\nt1 = n0 / n1\nt2 = n2 * t0\nt3 = t1 * t0\nt4 = t2 - n2\nt5 = 1.0 - t3\nanswer = t4 / t5\nprint(answer)" + ], + "Output Answer": [ + "40.00000000000001" + ], + "split": "train" + }, + { + "Input": "the average age of a group of 10 persons was decreased by 3 years when one person , whose age was 40 years , was replaced by a new person . find the age of the new person ?", + "Output Program": [ + "n0 = 10.0\nn1 = 3.0\nn2 = 40.0\nt0 = n0 * n1\nanswer = n2 - t0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "if an integer n is to be selected at random from 1 to 105 , inclusive , what is probability n ( n + 1 ) will be divisible by 7 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 105.0\nn2 = 1.0\nn3 = 7.0\n\nanswer = 2.0 / n3\nprint(answer)" + ], + "Output Answer": [ + "0.2857142857142857" + ], + "split": "train" + }, + { + "Input": "the average height of 35 boys in a class was calculated as 184 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ) . ?", + "Output Program": [ + "import math\nn0 = 35.0\nn1 = 184.0\nn2 = 166.0\nn3 = 106.0\nt0 = n0 * n1\nt1 = t0 - n2\nt2 = n3 + t1\nt3 = t2 / n0\nanswer = math.floor(t3)\nprint(answer)" + ], + "Output Answer": [ + "182" + ], + "split": "train" + }, + { + "Input": "all the students of class are told to sit in circle shape . here the boy at the 7 th position is exactly opposite to 27 th boy . total number of boys in the class ?", + "Output Program": [ + "n0 = 7.0\nn1 = 27.0\nt0 = n1 - n0\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "a $ 72.95 lawn chair was sold for $ 59.95 at a special sale . by approximately what percent was the price decreased ?", + "Output Program": [ + "n0 = 72.95\nn1 = 59.95\nt0 = n0 - n1\nt1 = t0 / n0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "17.820424948594926" + ], + "split": "train" + }, + { + "Input": "( 0.96 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.96 ) ( power 2 ) + 0.096 + ( 0.1 ) ( power 2 ) is :", + "Output Program": [ + "n0 = 0.96\nn1 = 3.0\nn2 = 0.1\nn3 = 3.0\nn4 = 0.96\nn5 = 2.0\nn6 = 0.096\nn7 = 0.1\nn8 = 2.0\nt0 = n0**min(n1, 5)\nt1 = n2**min(n1, 5)\nt2 = n0**min(n5, 5)\nt3 = n2**min(n5, 5)\nt4 = n6 + t2\nt5 = t0 - t1\nt6 = t4 + t3\nanswer = t5 / t6\nprint(answer)" + ], + "Output Answer": [ + "0.8599999999999998" + ], + "split": "train" + }, + { + "Input": "a jogger running at 9 km / hr along side a railway track is 150 m ahead of the engine of a 100 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?", + "Output Program": [ + "n0 = 9.0\nn1 = 150.0\nn2 = 100.0\nn3 = 45.0\nt0 = n1 + n2\nt1 = 10.0 / 2.0\nt2 = n3 - n0\nt3 = t2 / 2.0\nt4 = t1 / t3\nt5 = t4 * t2\nanswer = t0 / t5\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "there are 2 white plates , 6 green plates , 8 red plates , 4 pink plates , and 10 purple plates in the cabinet . what is the least number of plates that you have to pull out to make sure that you will have a matching pair ? ( assume that all the plates are identical except for the color )", + "Output Program": [ + "n0 = 2.0\nn1 = 6.0\nn2 = 8.0\nn3 = 4.0\nn4 = 10.0\n\nanswer = n0 + n3\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "the smallest number which when diminished by 7 , is divisible by 12 , 16 , 18 , 21 and 28 is", + "Output Program": [ + "n0 = 7.0\nn1 = 12.0\nn2 = 16.0\nn3 = 18.0\nn4 = 21.0\nn5 = 28.0\nt0 = 3.0 + 4.0\nt1 = 3.0**min(2.0, 5)\nt2 = 2.0**min(4.0, 5)\nt3 = t1 * t2\nt4 = t0 * t3\nanswer = t4 + n0\nprint(answer)" + ], + "Output Answer": [ + "1015" + ], + "split": "train" + }, + { + "Input": "what is the dividend . divisor 14 , the quotient is 12 and the remainder is 8", + "Output Program": [ + "n0 = 14.0\nn1 = 12.0\nn2 = 8.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "176" + ], + "split": "train" + }, + { + "Input": "if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 171 games will be played during the tournament . what is the number of participants ?", + "Output Program": [ + "import math\nn0 = 171.0\nt0 = n0 * 2.0\nt1 = t0 * 4.0\nt2 = t1 + 1.0\nt3 = math.sqrt(max(0, t2))\nt4 = t3 + 1.0\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "if the mean of numbers 28 , x , 50 , 78 and 104 is 62 , what is the mean of 48 , 62 , 98 , 124 and x ?", + "Output Program": [ + "n0 = 28.0\nn1 = 50.0\nn2 = 78.0\nn3 = 104.0\nn4 = 62.0\nn5 = 48.0\nn6 = 62.0\nn7 = 98.0\nn8 = 124.0\nt0 = 1.0 + 4.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n4 * t0\nt4 = n3 + t2\nt5 = t3 - t4\nt6 = n5 + t5\nt7 = n6 + t6\nt8 = n7 + t7\nt9 = n8 + t8\nanswer = t9 / t0\nprint(answer)" + ], + "Output Answer": [ + "76.4" + ], + "split": "train" + }, + { + "Input": "to be considered for \u201c movie of the year , \u201d a film must appear in at least 1 / 4 of the top - 10 - movies lists submitted by the cinematic academy \u2019 s 765 members . what is the smallest number of top - 10 lists a film can appear on and still be considered for \u201c movie of the year \u201d ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 10.0\nn3 = 765.0\nn4 = 10.0\n\nanswer = n3 / n1\nprint(answer)" + ], + "Output Answer": [ + "191.25" + ], + "split": "train" + }, + { + "Input": "there are 11 baskets numbered from 1 to 11 and filled with apples . 10 children are asked to pick apples one by one from each basket such that the number of apples picked by each child from each basket is equal to the number marked on the basket . if there were 1000 apples in total and the baskets were filled in such a way that none of the basket became empty in the process , how many apples were left in the end ?", + "Output Program": [ + "n0 = 11.0\nn1 = 1.0\nn2 = 11.0\nn3 = 10.0\nn4 = 1000.0\nt0 = n0 + n1\nt1 = n3 / 2.0\nt2 = t0 * t1\nt3 = t1 + t2\nt4 = t3 + 1.0\nt5 = t4 * 10.0\nanswer = n4 - t5\nprint(answer)" + ], + "Output Answer": [ + "340" + ], + "split": "train" + }, + { + "Input": "if a number n is chosen at random from the set of two - digit integers whose digits are both prime numbers , what is the probability t that n is divisible by 3 ?", + "Output Program": [ + "n0 = 3.0\nt0 = n0 + 2.0\nt1 = 4.0 * 4.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.3125" + ], + "split": "train" + }, + { + "Input": "raj invests a part of rs . 12000 in 12 % stock at rs . 120 and the remainder in 15 % stock at rs . 125 . if his total dividend per annum is rs . 1360 , how much does he invest in 12 % stock at rs . 120 ?", + "Output Program": [ + "n0 = 12000.0\nn1 = 12.0\nn2 = 120.0\nn3 = 15.0\nn4 = 125.0\nn5 = 1360.0\nn6 = 12.0\nn7 = 120.0\nt0 = n3 / n4\nt1 = n1 / n2\nt2 = n0 * t0\nt3 = t0 - t1\nt4 = t2 - n5\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "4000.000000000002" + ], + "split": "train" + }, + { + "Input": "if 42.24 = k ( 14 + m / 50 ) , where k and m are positive integers and m < 50 , then what is the value of k + m ?", + "Output Program": [ + "n0 = 42.24\nn1 = 14.0\nn2 = 50.0\nn3 = 50.0\nt0 = 1.0 / 100.0\nt1 = 0.25 - t0\nt2 = n2 * t1\nt3 = n0 - t1\nt4 = t3 / n1\nt5 = t2 / t4\nanswer = t5 + t4\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 30 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam .", + "Output Program": [ + "n0 = 80.0\nn1 = 5.0\nn2 = 30.0\nn3 = 90.0\nt0 = n1 * n3\nt1 = n1 * n2\nt2 = n3 - n0\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "a , b and c have rs . 450 between them , a and c together have rs . 200 and b and c rs . 350 . how much does c have ?", + "Output Program": [ + "n0 = 450.0\nn1 = 200.0\nn2 = 350.0\nt0 = n1 + n2\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "linda spent 2 / 3 of her savings on furniture and the rest on a tv . if the tv cost her $ 250 , what were her original savings ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 250.0\nt0 = n0 / n1\nt1 = 1.0 - t0\nanswer = n2 / t1\nprint(answer)" + ], + "Output Answer": [ + "749.9999999999999" + ], + "split": "train" + }, + { + "Input": "the average ( arithmetic mean ) of the even integers from 20 to 60 inclusive is how much greater than the average ( arithmetic mean ) of the even integers from 10 to 140 inclusive ?", + "Output Program": [ + "n0 = 20.0\nn1 = 60.0\nn2 = 10.0\nn3 = 140.0\nt0 = n2 + n3\nt1 = n0 + n1\nt2 = t0 / 2.0\nt3 = t1 / 2.0\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "if | x + 10 | = 10 what is the sum of all the values of x .", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\n\nanswer = n0 + n1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "anne bought doughnuts for a class breakfast party . she bought 12 chocolate doughnuts , 12 coconut doughnuts , and 10 jam - filled doughnuts . how many doughnuts did anne buy in all ?", + "Output Program": [ + "n0 = 12.0\nn1 = 12.0\nn2 = 10.0\nt0 = n0 + n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "34" + ], + "split": "train" + }, + { + "Input": "of the final grades received by the students in a certain math course , 1 / 5 are a ' s , 1 / 4 are b ' s , 1 / 2 are c ' s , and the remaining 40 grades are d ' s . what is the number of students in the course ?", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 1.0\nn3 = 4.0\nn4 = 1.0\nn5 = 2.0\nn6 = 40.0\nt0 = n0 / n1\nt1 = n0 / n3\nt2 = n0 / n5\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = 1.0 - t4\nanswer = n6 / t5\nprint(answer)" + ], + "Output Answer": [ + "799.9999999999993" + ], + "split": "train" + }, + { + "Input": "the scoring system in a certain football competition goes as follows : 3 points for victory , 1 point for a draw , and 0 points for defeat . each team plays 20 matches . if a team scored 8 points after 5 games , what is the least number of the remaining matches it has to win to reach the 40 - point mark by the end of the tournament ?", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 1.0\nn2 = 0.0\nn3 = 20.0\nn4 = 8.0\nn5 = 5.0\nn6 = 40.0\nt0 = n6 - n4\nt1 = n3 - n5\nt2 = t0 - t1\nt3 = t2 / 2.0\nt4 = math.floor(t3)\nanswer = t4 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "what least number must be subtracted from 427398 so that remaining no . is divisible by 12", + "Output Program": [ + "import math\nn0 = 427398.0\nn1 = 12.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "charges made by two companies for the same a / c company xcompany y price $ 575 $ 530 surcharge as a percent of price 4 % 3 % installation charge $ 82.50 $ 93.00 the table above shows the various charges made by two companies for the same air conditioner . what is the total amount that can be saved on the purchase and installation of the air conditioner by dealing with the company that offers the lower total charge ?", + "Output Program": [ + "n0 = 575.0\nn1 = 530.0\nn2 = 4.0\nn3 = 3.0\nn4 = 82.5\nn5 = 93.0\nt0 = n2 / 100.0\nt1 = n3 / 100.0\nt2 = n0 * t0\nt3 = n1 * t1\nt4 = n0 + t2\nt5 = n1 + t3\nt6 = n4 + t4\nt7 = n5 + t5\nanswer = t6 - t7\nprint(answer)" + ], + "Output Answer": [ + "41.60000000000002" + ], + "split": "train" + }, + { + "Input": "total dinning bill for 6 people was $ 211.00 . if they add 15 % tip and divided the bill evenly , approximate . what was each persons find share", + "Output Program": [ + "n0 = 6.0\nn1 = 211.0\nn2 = 15.0\nt0 = n1 * n2\nt1 = t0 / 100.0\nt2 = n1 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "40.44166666666667" + ], + "split": "train" + }, + { + "Input": "there are 400 female managers in a certain company . find the total number of female employees in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers .", + "Output Program": [ + "n0 = 400.0\nn1 = 2.0\nn2 = 5.0\nn3 = 2.0\nn4 = 5.0\nt0 = n1 / n2\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "1000" + ], + "split": "train" + }, + { + "Input": "a bucket full of nuts was discovered by the crow living in the basement . the crow eats a fifth of the total number of nuts in 8 hours . how many hours in total will it take the crow to finish a quarter of the nuts ?", + "Output Program": [ + "n0 = 8.0\nt0 = 2.0 + 3.0\nt1 = 1.0 / 4.0\nt2 = 1.0 / t0\nt3 = t2 / n0\nanswer = t1 / t3\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "when asked what the time is , a person answered that the amount of time left is 2 / 6 of the time already completed . what is the time .", + "Output Program": [ + "n0 = 2.0\nn1 = 6.0\nt0 = n0 / n1\nt1 = 12.0 * 2.0\nt2 = t0 + 1.0\nt3 = t1 / t2\nanswer = t1 - t3\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "if a = 105 and a ^ 3 = 21 * 35 * 45 * b , what is the value of b ?", + "Output Program": [ + "n0 = 105.0\nn1 = 3.0\nn2 = 21.0\nn3 = 35.0\nn4 = 45.0\nt0 = n2 * n3\nt1 = n0**min(n1, 5)\nt2 = n4 * t0\nanswer = t1 / t2\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "a prize of $ 400 is to be distributed among 20 winners , each of whom must be awarded at least $ 20 . if 2 / 5 of the prize will be distributed to 3 / 5 of the winners , what is the greatest possible individual award ?", + "Output Program": [ + "n0 = 400.0\nn1 = 20.0\nn2 = 20.0\nn3 = 2.0\nn4 = 5.0\nn5 = 3.0\nn6 = 5.0\nt0 = n0 * n3\nt1 = n1 * n5\nt2 = t0 / n4\nt3 = t1 / n4\nt4 = n0 - t2\nt5 = n1 - t3\nt6 = t5 - 1.0\nt7 = n1 * t6\nanswer = t4 - t7\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "the average height of 35 boys in a class was calculated as 181 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ) . ?", + "Output Program": [ + "import math\nn0 = 35.0\nn1 = 181.0\nn2 = 166.0\nn3 = 106.0\nt0 = n0 * n1\nt1 = t0 - n2\nt2 = n3 + t1\nt3 = t2 / n0\nanswer = math.floor(t3)\nprint(answer)" + ], + "Output Answer": [ + "179" + ], + "split": "train" + }, + { + "Input": ". 3 + 33 + 333 + 33.3 = ?", + "Output Program": [ + "n0 = 3.0\nn1 = 33.0\nn2 = 333.0\nn3 = 33.3\nt0 = n1 + n2\nt1 = n0 / 10.0\nt2 = n3 + t0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "399.6" + ], + "split": "train" + }, + { + "Input": "if a certain number x is divided by 82 , the reminder is 5 . what is the reminder when x + 17 is divided by 41 ?", + "Output Program": [ + "n0 = 82.0\nn1 = 5.0\nn2 = 17.0\nn3 = 41.0\n\nanswer = n1 + n2\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "at a certain fruit stand , the price of each apple is 40 cents and the price of each orange is 60 cents . mary selects a total of 15 apples and oranges from the fruit stand , and the average ( arithmetic mean ) price of the 15 pieces of fruit is 48 cents . how many oranges must mary put back so that the average price of the pieces of fruit that she keeps is 45 cents ?", + "Output Program": [ + "n0 = 40.0\nn1 = 60.0\nn2 = 15.0\nn3 = 15.0\nn4 = 48.0\nn5 = 45.0\nt0 = n2 * n4\nt1 = n2 * n5\nt2 = n1 - n5\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "on the richter scale , which measures the total amount of energy released during an earthquake , a reading of x - 1 indicates one - tenth the released energy as is indicated by a reading of x . on that scale , the frequency corresponding to a reading of 5 is how many times as great as the frequency corresponding to a reading of 3 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 3.0\nt0 = n1 - n2\nanswer = 10.0**min(t0, 5)\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "115 liters of a mixture of milk and water contains in the ratio 3 : 2 . how much water should now be added so that the ratio of milk and water becomes 3 : 4 ?", + "Output Program": [ + "n0 = 115.0\nn1 = 3.0\nn2 = 2.0\nn3 = 3.0\nn4 = 4.0\nt0 = n1 + n2\nt1 = n0 / t0\nanswer = n2 * t1\nprint(answer)" + ], + "Output Answer": [ + "46" + ], + "split": "train" + }, + { + "Input": "if p ( a ) = 4 / 7 and p ( b ) = 2 / 5 , find p ( a n b ) if a and b are independent events .", + "Output Program": [ + "n0 = 4.0\nn1 = 7.0\nn2 = 2.0\nn3 = 5.0\nt0 = n0 / n1\nt1 = n2 / n3\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "0.22857142857142856" + ], + "split": "train" + }, + { + "Input": "bottle r contains 250 capsules and costs $ 6.25 . bottle t contains 100 capsules and costs $ 3.0 . what is the difference between the cost per capsule for bottle r and the cost per capsule for bottle t ?", + "Output Program": [ + "n0 = 250.0\nn1 = 6.25\nn2 = 100.0\nn3 = 3.0\nt0 = n3 / n2\nt1 = n1 / n0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "0.0049999999999999975" + ], + "split": "train" + }, + { + "Input": "for what value of \u201c k \u201d will the equation ( 2 kx 2 + 5 kx + 2 ) = 0 have equal roots ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 5.0\nn3 = 2.0\nn4 = 0.0\nt0 = n0 * n0\nt1 = n2 * n2\nt2 = n0 * t0\nt3 = n0 * t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.64" + ], + "split": "train" + }, + { + "Input": "it takes 30 days to fill a laboratory dish with bacteria . if the size of the bacteria doubles each day , how long did it take for the bacteria to fill one sixteenth of the dish ?", + "Output Program": [ + "n0 = 30.0\n\nanswer = n0 - 4.0\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "if a certain toy store ' s revenue in november was 3 / 5 of its revenue in december and its revenue in january was 1 / 6 of its revenue in november , then the store ' s revenue in december was how many times the average ( arithmetic mean ) of its revenues in november and january ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 1.0\nn3 = 6.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = t0 * t1\nt3 = t0 + t2\nt4 = t3 / 2.0\nanswer = 1.0 / t4\nprint(answer)" + ], + "Output Answer": [ + "2.857142857142857" + ], + "split": "train" + }, + { + "Input": "the greatest number which on dividing 1557 and 2037 leaves remainders 7 and 5 respectively , is :", + "Output Program": [ + "import scipy\nn0 = 1557.0\nn1 = 2037.0\nn2 = 7.0\nn3 = 5.0\nt0 = n1 - n3\nt1 = n0 - n2\nanswer = scipy.gcd(int(t0), int(t1))\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "david is 18 years older than his daughter rosy . in 6 years david will be twice as old as rosy . what is rosy current age .", + "Output Program": [ + "n0 = 18.0\nn1 = 6.0\nt0 = n0 + n1\nt1 = n1 * 2.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "you collect pens . suppose you start out with 20 . mike gives you another 22 pens . since her father makes pens , cindy decides to double your pens . since you ' re nice , you give sharon 19 pens . how many pens do you have at the end ?", + "Output Program": [ + "n0 = 20.0\nn1 = 22.0\nn2 = 19.0\nt0 = n0 + n1\nt1 = t0 * 2.0\nanswer = t1 - n2\nprint(answer)" + ], + "Output Answer": [ + "65" + ], + "split": "train" + }, + { + "Input": "the sum of the 1 st and 3 rd of 3 consecutive odd integers is 131 less than 3 times the second integer . find the 3 integers ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 3.0\nn3 = 131.0\nn4 = 3.0\nn5 = 3.0\nt0 = n1 + n1\nt1 = n3 - n1\nt2 = t0 - n0\nanswer = t1 + t2\nprint(answer)" + ], + "Output Answer": [ + "133" + ], + "split": "train" + }, + { + "Input": "for a certain exam , a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean . what was the mean score t for the exam ?", + "Output Program": [ + "n0 = 58.0\nn1 = 2.0\nn2 = 98.0\nn3 = 3.0\nt0 = n1 + n3\nt1 = n0 * n3\nt2 = n1 * n2\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "74" + ], + "split": "train" + }, + { + "Input": "how many numbers from 10 to 31 are exactly divisible by 3 ?", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 31.0\nn2 = 3.0\nt0 = n1 / n2\nt1 = n0 / n2\nt2 = math.floor(t0)\nt3 = math.floor(t1)\nt4 = t3 + 1.0\nt5 = n2 * t2\nt6 = n2 * t4\nt7 = t5 - t6\nt8 = t7 / n2\nanswer = t8 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "the average ( arithmetic mean ) of 20 , 40 , and 60 is 4 more than the average of 10 , 70 , and what number ?", + "Output Program": [ + "n0 = 20.0\nn1 = 40.0\nn2 = 60.0\nn3 = 4.0\nn4 = 10.0\nn5 = 70.0\nt0 = n0 + n1\nt1 = n3 * 3.0\nt2 = n2 + t0\nt3 = n4 + t1\nt4 = n5 + t3\nanswer = t2 - t4\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "121 x 5 ^ 4 = ?", + "Output Program": [ + "n0 = 121.0\nn1 = 5.0\nn2 = 4.0\nt0 = n1**min(n2, 5)\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "75625" + ], + "split": "train" + }, + { + "Input": "the number n is h , 284 , where h represents the 10 ' s digit . if n is divisible by 6 , what is the value of h ?", + "Output Program": [ + "n0 = 284.0\nn1 = 10.0\nn2 = 6.0\nt0 = n1 * n2\nanswer = t0 / t0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "if s = { 8 , 16 , 24 , 32 , 40 , 48 } , what is the product of mean and median of the numbers in s ?", + "Output Program": [ + "n0 = 8.0\nn1 = 16.0\nn2 = 24.0\nn3 = 32.0\nn4 = 40.0\nn5 = 48.0\nt0 = n0 + n1\nt1 = 2.0 + 4.0\nt2 = n2 + n3\nt3 = n2 + t0\nt4 = t2 / 2.0\nt5 = n3 + t3\nt6 = n4 + t5\nt7 = n5 + t6\nt8 = t7 / t1\nanswer = t8 * t4\nprint(answer)" + ], + "Output Answer": [ + "784" + ], + "split": "train" + }, + { + "Input": "if 2994 \u00e3 \u00b7 14.5 = 171 , then 29.94 \u00e3 \u00b7 1.45 = ?", + "Output Program": [ + "n0 = 2994.0\nn1 = 14.5\nn2 = 171.0\nn3 = 29.94\nn4 = 1.45\nt0 = n1 / n4\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "17.1" + ], + "split": "train" + }, + { + "Input": "there are 840 male and female participants in a meeting . half the female participants and one - quarter of the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?", + "Output Program": [ + "n0 = 840.0\nt0 = n0 / 3.0\nt1 = t0 * 4.0\nt2 = t1 - n0\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "140" + ], + "split": "train" + }, + { + "Input": "there are 4 members in a family . their average income is rs . 10000 per month . 3 members get rs . 8000 , rs . 15000 , rs . 6000 respectively . therefore what is the income of the fourth member of the family ?", + "Output Program": [ + "n0 = 4.0\nn1 = 10000.0\nn2 = 3.0\nn3 = 8000.0\nn4 = 15000.0\nn5 = 6000.0\nt0 = n3 + n4\nt1 = n0 * n1\nt2 = n5 + t0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "11000" + ], + "split": "train" + }, + { + "Input": "if ( 3 / 2 ) x - 3 = 15 what is the value of x ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 3.0\nn3 = 15.0\nt0 = n0 + n3\nt1 = n1 * t0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "the price of a bushel of corn is currently $ 3.20 , and the price of a peck of wheat is $ 9.80 . the price of corn is increasing at a constant rate of 5 x cents per day while the price of wheat is decreasing at a constant rate of x ( 2 ^ 1 / 2 ) - x cents per day . what is the approximate price when a bushel of corn costs the same amount as a peck of wheat ?", + "Output Program": [ + "import math\nn0 = 3.2\nn1 = 9.8\nn2 = 5.0\nn3 = 2.0\nn4 = 1.0\nn5 = 2.0\nt0 = math.sqrt(max(0, n3))\nt1 = n1 - n0\nt2 = t0 - n4\nt3 = n2 + t2\nt4 = t1 / t3\nt5 = n2 * t4\nanswer = n0 + t5\nprint(answer)" + ], + "Output Answer": [ + "9.295068031549134" + ], + "split": "train" + }, + { + "Input": "the average monthly salary of 8 workers and one supervisor in a factory was 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . whenthesupervisor , whosesalarywas 430 . when the supervisor , whose salary was 870 per month , retired , a new person was appointed and then the average salary of 9 people was $ $ 410 per month . the salary of the new supervisor is :", + "Output Program": [ + "n0 = 8.0\nn1 = 430.0\nn2 = 430.0\nn3 = 430.0\nn4 = 430.0\nn5 = 870.0\nn6 = 9.0\nn7 = 410.0\nt0 = n6 * n7\nt1 = n1 * n6\nt2 = t1 - n5\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "690" + ], + "split": "train" + }, + { + "Input": "if there are 4 peanuts in a box and mary puts 6 more peanuts inside , how many peanuts are in the box ?", + "Output Program": [ + "n0 = 4.0\nn1 = 6.0\n\nanswer = n0 + n1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "how many 3 digit positive integers exist that when divided by 7 leave a remainder of 5 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 5.0\nt0 = 10.0 + 4.0\nt1 = 10.0 * 100.0\nt2 = n1 * t0\nt3 = t1 - 1.0\nt4 = n2 + t2\nt5 = t3 - t4\nanswer = t5 / n1\nprint(answer)" + ], + "Output Answer": [ + "128" + ], + "split": "train" + }, + { + "Input": "if ( 10 ^ 4 * 3.456789 ) ^ 9 is written as a single term , how many digits would be to the right of the decimal place ?", + "Output Program": [ + "n0 = 10.0\nn1 = 4.0\nn2 = 3.456789\nn3 = 9.0\n\nanswer = n3 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "according to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . how many 5 - ounce cans of the concentrate are required to prepare 200 6 - ounce servings of orange juice ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 200.0\nn3 = 6.0\nt0 = n2 / 10.0\nt1 = n2 * n3\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "each of the 30 boxes in a certain shipment weighs either 10 pounds or 20 pounds , and the average ( arithmetic mean ) weight of the boxes in the shipment is 18 pounds . if the average weight of the boxes in the shipment is to be reduced to 16 pounds by removing some of the 20 - pound boxes , how many 20 - pound boxes must be removed ?", + "Output Program": [ + "n0 = 30.0\nn1 = 10.0\nn2 = 20.0\nn3 = 18.0\nn4 = 16.0\nn5 = 20.0\nn6 = 20.0\nt0 = n0 * n2\nt1 = n0 * n3\nt2 = n0 * n4\nt3 = n2 - n1\nt4 = n2 - n4\nt5 = t0 - t1\nt6 = t5 / t3\nt7 = n1 * t6\nt8 = n0 - t6\nt9 = n2 * t8\nt10 = t7 + t9\nt11 = t10 - t2\nanswer = t11 / t4\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "a prize of $ 500 is to be distributed among 20 winners , each of whom must be awarded at least $ 20 . if 2 / 5 of the prize will be distributed to 3 / 5 of the winners , what is the greatest possible individual award ?", + "Output Program": [ + "n0 = 500.0\nn1 = 20.0\nn2 = 20.0\nn3 = 2.0\nn4 = 5.0\nn5 = 3.0\nn6 = 5.0\nt0 = n0 * n3\nt1 = n1 * n5\nt2 = t0 / n4\nt3 = t1 / n4\nt4 = n0 - t2\nt5 = n1 - t3\nt6 = t5 - 1.0\nt7 = n1 * t6\nanswer = t4 - t7\nprint(answer)" + ], + "Output Answer": [ + "160" + ], + "split": "train" + }, + { + "Input": "for the symbol , m \u201d n = n ^ 2 \u2212 m for all values of m and n . what is the value of 3 \u201d 3 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 3.0\nt0 = n2**min(n0, 5)\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "a student chose a number , multiplied it by 4 , then subtracted 142 from the result and got 110 . what was the number he chose ?", + "Output Program": [ + "n0 = 4.0\nn1 = 142.0\nn2 = 110.0\nt0 = n1 + n2\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "63" + ], + "split": "train" + }, + { + "Input": "a jar of 144 marbles is divided equally among a group of marble - players today . if 2 people joined the group in the future , each person would receive 1 marble less . how many people are there in the group today ?", + "Output Program": [ + "import math\nn0 = 144.0\nn1 = 2.0\nn2 = 1.0\nt0 = n0 * n1\nt1 = n1**min(n1, 5)\nt2 = t0 * 4.0\nt3 = t2 + t1\nt4 = math.sqrt(max(0, t3))\nt5 = t4 - n1\nanswer = t5 / n1\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "a cyclist rides a bicycle 7 km at an average speed of 10 km / hr and again travels 10 km at an average speed of 7 km / hr . what is the average speed for the entire trip ?", + "Output Program": [ + "n0 = 7.0\nn1 = 10.0\nn2 = 10.0\nn3 = 7.0\nt0 = n0 + n1\nt1 = n0 / n1\nt2 = n1 / n0\nt3 = t1 + t2\nanswer = t0 / t3\nprint(answer)" + ], + "Output Answer": [ + "7.9865771812080535" + ], + "split": "train" + }, + { + "Input": "marcella has 23 pairs of shoes . if she loses 9 individual shoes , what is the greatest number of matching pairs she could have left ?", + "Output Program": [ + "import math\nn0 = 23.0\nn1 = 9.0\nt0 = n1 / 2.0\nt1 = math.floor(t0)\nt2 = t1 + 1.0\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "the price of 2 saris and 4 shirts is rs . 1600 . with the same money one can buy 1 saree and 6 shirts . if one wants to buy 12 shirts , how much shall he have to pay ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 1600.0\nn3 = 1.0\nn4 = 6.0\nn5 = 12.0\nt0 = n0 * n4\nt1 = t0 - n1\nt2 = n2 / t1\nanswer = n5 * t2\nprint(answer)" + ], + "Output Answer": [ + "2400" + ], + "split": "train" + }, + { + "Input": "a tourist does not have to pay tax on the first $ 600 of goods he purchases in country b , but does have to pay a 8 percent tax on the portion of the total value that is in excess of $ 600 . what tax must be paid by a tourist if he buys goods with a total value of $ 1720 ?", + "Output Program": [ + "n0 = 600.0\nn1 = 8.0\nn2 = 600.0\nn3 = 1720.0\nt0 = n3 - n0\nt1 = n1 * t0\nanswer = t1 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "89.6" + ], + "split": "train" + }, + { + "Input": "what is the remainder of g = 3 ^ 19 when divided by 10 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 19.0\nn2 = 10.0\nt0 = n1 % 4.0\nt1 = n0**min(t0, 5)\nanswer = t1 % n2\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "find large number from below question the difference of two no . ' s is 1365 . on dividing the larger no . by the smaller , we get 6 as quotient and the 15 as remainder ?", + "Output Program": [ + "n0 = 1365.0\nn1 = 6.0\nn2 = 15.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nt2 = t0 / t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "1620" + ], + "split": "train" + }, + { + "Input": "in a group of cows and chickens , the number of legs was 18 more than twice the number of heads . the number of cows was :", + "Output Program": [ + "n0 = 18.0\nt0 = 4.0 - 2.0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "what least number should be subtracted from 642 so that the remainder when divided by 5 , 7 , and 9 will leave in each case the same remainder 4 ?", + "Output Program": [ + "n0 = 642.0\nn1 = 5.0\nn2 = 7.0\nn3 = 9.0\nn4 = 4.0\nt0 = n1 * n2\nt1 = n3 * t0\nt2 = t1 * 2.0\nt3 = n4 + t2\nanswer = n0 - t3\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "4 friends , peter , john , quincy , and andrew , are pooling their money to buy a $ 1200 item . peter has twice as much money as john . quincy has $ 20 more than peter . andrew has 15 % more than quincy . if they put all their money together and spend the $ 1200 , they will have $ 11 left . how much money does peter have ?", + "Output Program": [ + "n0 = 4.0\nn1 = 1200.0\nn2 = 20.0\nn3 = 15.0\nn4 = 1200.0\nn5 = 11.0\nt0 = n1 + n5\nt1 = n3 + 100.0\nt2 = 1.0 / 2.0\nt3 = t2 + 1.0\nt4 = t1 / 100.0\nt5 = t0 - n2\nt6 = t3 + 1.0\nt7 = n2 * t4\nt8 = t6 + t4\nt9 = t5 - t7\nanswer = t9 / t8\nprint(answer)" + ], + "Output Answer": [ + "320" + ], + "split": "train" + }, + { + "Input": "find the value of ( \u221a 1.21 ) / ( \u221a 0.81 ) + ( \u221a 1.44 ) / ( \u221a 0.49 ) is", + "Output Program": [ + "import math\nn0 = 1.21\nn1 = 0.81\nn2 = 1.44\nn3 = 0.49\nt0 = math.sqrt(max(0, n0))\nt1 = math.sqrt(max(0, n1))\nt2 = math.sqrt(max(0, n2))\nt3 = math.sqrt(max(0, n3))\nt4 = t0 / t1\nt5 = t2 / t3\nanswer = t4 + t5\nprint(answer)" + ], + "Output Answer": [ + "2.9365079365079367" + ], + "split": "train" + }, + { + "Input": "the units digit of ( 35 ) ^ ( 87 ) + ( 93 ) ^ ( 49 ) is :", + "Output Program": [ + "n0 = 35.0\nn1 = 87.0\nn2 = 93.0\nn3 = 49.0\nt0 = n3 % 4.0\nt1 = n0 % 10.0\nt2 = n2 * t0\nt3 = t2 % 10.0\nanswer = t3 + t1\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a manufacturer produces a certain men ' s athletic shoe in integer sizes from 8 to 17 . for this particular shoe , each unit increase in size corresponds to a 1 / 5 - inch increase in the length of the shoe . if the largest size of this shoe is 20 % longer than the smallest size , how long , in inches , is the shoe in size 15 ?", + "Output Program": [ + "n0 = 8.0\nn1 = 17.0\nn2 = 1.0\nn3 = 5.0\nn4 = 20.0\nn5 = 15.0\nt0 = n2 / n3\nt1 = n4 / 100.0\nt2 = n1 - n0\nt3 = n5 - n0\nt4 = t0 * t2\nt5 = t0 * t3\nt6 = t4 / t1\nanswer = t6 + t5\nprint(answer)" + ], + "Output Answer": [ + "10.4" + ], + "split": "train" + }, + { + "Input": "a 6 - liter solution is 35 % alcohol . how many liters of pure alcohol must be added to produce a solution that is 50 % alcohol ?", + "Output Program": [ + "n0 = 6.0\nn1 = 35.0\nn2 = 50.0\nt0 = n0 * n1\nt1 = t0 / 100.0\nt2 = t1 * 2.0\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "1.7999999999999998" + ], + "split": "train" + }, + { + "Input": "if a * b * c = 130 , b * c * d = 65 , c * d * e = 1000 and d * e * f = 250 the ( a * f ) / ( c * d ) = ?", + "Output Program": [ + "n0 = 130.0\nn1 = 65.0\nn2 = 1000.0\nn3 = 250.0\nt0 = n0 * n3\nt1 = n1 * n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "free notebooks were distributed in a class among all the students . each student got notebooks which were 1 / 8 th of the number of student . if number of student been half , then each child would have received 16 notebooks in total . find the total number of books distributed among students ?", + "Output Program": [ + "n0 = 1.0\nn1 = 8.0\nn2 = 16.0\nt0 = 1.0 / 2.0\nt1 = n2 * t0\nt2 = n1 * t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "512" + ], + "split": "train" + }, + { + "Input": "jean drew a gumball at random from a jar of pink and blue gumballs . since the gumball she selected was blue and she wanted a pink one , she replaced it and drew another . the second gumball also happened to be blue and she replaced it as well . if the probability of her drawing the two blue gumballs was 16 / 36 , what is the probability that the next one she draws will be pink ?", + "Output Program": [ + "import math\nn0 = 16.0\nn1 = 36.0\nt0 = n0 / n1\nt1 = math.sqrt(max(0, t0))\nanswer = 1.0 - t1\nprint(answer)" + ], + "Output Answer": [ + "0.33333333333333337" + ], + "split": "train" + }, + { + "Input": "if f ( x ) = 2 x ^ 2 + y , and f ( 2 ) = 100 , what is the value of f ( 5 ) ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 2.0\nn3 = 100.0\nn4 = 5.0\nt0 = n4**min(n0, 5)\nt1 = n0**min(n0, 5)\nt2 = n0 * t0\nt3 = n0 * t1\nt4 = n3 - t3\nanswer = t2 + t4\nprint(answer)" + ], + "Output Answer": [ + "142" + ], + "split": "train" + }, + { + "Input": "on a certain island , 5 % of the 10000 inhabitants are one - legged and half of the others go barefooted . what is the least number of shoes needed in the island ?", + "Output Program": [ + "n0 = 5.0\nn1 = 10000.0\nt0 = n0 / 100.0\nt1 = n1 * t0\nt2 = t1 * 1.0\nt3 = n1 - t1\nt4 = t3 / 2.0\nt5 = t4 * 2.0\nanswer = t5 + t2\nprint(answer)" + ], + "Output Answer": [ + "10000" + ], + "split": "train" + }, + { + "Input": "a tank holds x gallons of a saltwater solution that is 20 % salt by volume . one fourth of the water is evaporated , leaving all of the salt . when 7 gallons of water and 14 gallons of salt are added , the resulting mixture is 33 1 / 3 % salt by volume . what is the value of x ?", + "Output Program": [ + "n0 = 20.0\nn1 = 7.0\nn2 = 14.0\nn3 = 33.0\nn4 = 1.0\nn5 = 3.0\nt0 = n0 / 100.0\nt1 = n4 / 4.0\nt2 = n2 * 2.0\nt3 = t0 * 2.0\nt4 = t2 - n1\nt5 = n4 - t0\nt6 = t1 * t5\nt7 = t5 - t6\nt8 = t7 - t3\nanswer = t4 / t8\nprint(answer)" + ], + "Output Answer": [ + "104.99999999999997" + ], + "split": "train" + }, + { + "Input": "the telephone company wants to add an area code composed of 2 letters to every phone number . in order to do so , the company chose a special sign language containing 224 different signs . if the company used 222 of the signs fully and two remained unused , how many additional area codes can be created if the company uses all 224 signs ?", + "Output Program": [ + "n0 = 2.0\nn1 = 224.0\nn2 = 222.0\nn3 = 224.0\nt0 = n1 - n2\nt1 = n2 * t0\nanswer = t1 * t0\nprint(answer)" + ], + "Output Answer": [ + "888" + ], + "split": "train" + }, + { + "Input": "in 6 successive games , a baseball team scored 1 runs once , 4 runs twice , and 5 runs 3 times . what was the average ( arithmetic mean ) number of runs the team scored per game over the 6 - game period ?", + "Output Program": [ + "n0 = 6.0\nn1 = 1.0\nn2 = 4.0\nn3 = 5.0\nn4 = 3.0\nn5 = 6.0\nt0 = n1 * n1\nt1 = n2 * 2.0\nt2 = n3 * n4\nt3 = t0 + t1\nt4 = t3 + t2\nanswer = t4 / n0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "in an electric circuit , two resistors with resistances x and y are connected in parallel . if r is the combined resistance of these two resistors , then the reciprocal of r is equal to the sum of the reciprocals of x and y . what is r if x is 4 ohms and y is 5 ohms ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nt0 = n0 + n1\nt1 = n0 * n1\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "2.2222222222222223" + ], + "split": "train" + }, + { + "Input": "in a fort , there are 1200 soldiers . if each soldier consumes 3 kg per day , the provisions available in the fort will last for 30 days . if some more soldiers join , the provisions available will last for 25 days given each soldier consumes 2.5 kg per day . find the number of soldiers joining the fort in that case .", + "Output Program": [ + "n0 = 1200.0\nn1 = 3.0\nn2 = 30.0\nn3 = 25.0\nn4 = 2.5\nt0 = n0 * n1\nt1 = n2 * t0\nt2 = t1 / n3\nt3 = t2 / n4\nanswer = t3 - n0\nprint(answer)" + ], + "Output Answer": [ + "528" + ], + "split": "train" + }, + { + "Input": "find the number , difference between number and its 3 / 5 is 56 .", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 56.0\nt0 = n2 / 2.0\nanswer = n1 * t0\nprint(answer)" + ], + "Output Answer": [ + "140" + ], + "split": "train" + }, + { + "Input": "jerry \u2019 s average ( arithmetic mean ) score on the first 3 of 4 tests is 85 . if jerry wants to raise his average by 2 points , what score must he earn on the fourth test ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 85.0\nn3 = 2.0\nt0 = n2 + n3\nt1 = n0 * n2\nt2 = n1 * t0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "93" + ], + "split": "train" + }, + { + "Input": "a number exceeds by 20 from its 3 / 8 part . then the number is ?", + "Output Program": [ + "n0 = 20.0\nn1 = 3.0\nn2 = 8.0\nt0 = n0 * n2\nt1 = n2 - n1\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "find the lowest common multiple of 25 , 35 and 50 .", + "Output Program": [ + "import scipy\nn0 = 25.0\nn1 = 35.0\nn2 = 50.0\nt0 = scipy.lcm(int(n0), int(n1))\nanswer = scipy.lcm(int(n2), int(t0))\nprint(answer)" + ], + "Output Answer": [ + "350" + ], + "split": "train" + }, + { + "Input": "country x imported approximately $ 1.20 billion of goods in 1996 . if country x imported $ 288 million of goods in the first two months of 1997 and continued to import goods at the same rate for the rest of the year , by how much would country xs 1997 imports exceed those of 1996 ?", + "Output Program": [ + "n0 = 1.2\nn1 = 1996.0\nn2 = 288.0\nn3 = 1997.0\nn4 = 1997.0\nn5 = 1996.0\nt0 = 12.0 / 2.0\nt1 = n0 * 1000.0\nt2 = n2 * t0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "528" + ], + "split": "train" + }, + { + "Input": "25 liters of a mixture is created by mixing liquid p and liquid q in the ratio 3 : 2 . how many liters of liquid q must be added to make the ratio 5 : 4 ?", + "Output Program": [ + "n0 = 25.0\nn1 = 3.0\nn2 = 2.0\nn3 = 5.0\nn4 = 4.0\nt0 = n3 + n4\nt1 = n1 + n2\nt2 = n0 * n1\nt3 = n0 * n2\nt4 = t2 / t1\nt5 = t3 / t1\nt6 = t0 * t4\nt7 = t6 / n3\nt8 = n4 * t7\nt9 = t8 / t0\nanswer = t9 - t5\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "elena purchased brand x pens for $ 4.00 apiece and brand y for $ 2.20 apiece . if elena purchased a total of 12 of these pens for $ 42.00 , how many brand x pens did she purchase ?", + "Output Program": [ + "n0 = 4.0\nn1 = 2.2\nn2 = 12.0\nn3 = 42.0\nt0 = n0 * n2\nanswer = t0 - n3\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "what is the least number which when divided by 6 , 9 , 12 and 18 leaves remainder 4 in each care ?", + "Output Program": [ + "import scipy\nn0 = 6.0\nn1 = 9.0\nn2 = 12.0\nn3 = 18.0\nn4 = 4.0\nt0 = scipy.lcm(int(n0), int(n1))\nt1 = scipy.lcm(int(n2), int(n3))\nt2 = scipy.lcm(int(t0), int(t1))\nanswer = n4 + t2\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "a club wants to mix 20 pounds of candy worth $ 8.00 per pound with candy worth $ 5.00 per pound to reduce the cost of the mixture to $ 6.00 per pound . how many pounds of the $ 5.00 per pound candy should be used ?", + "Output Program": [ + "n0 = 20.0\nn1 = 8.0\nn2 = 5.0\nn3 = 6.0\nn4 = 5.0\nt0 = n0 * n1\nt1 = n0 * n3\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "if a ' s height is 30 % less than that of b , how much percent b ' s height is more than that of a ?", + "Output Program": [ + "n0 = 30.0\nt0 = 100.0 - n0\nt1 = n0 / t0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "42.857142857142854" + ], + "split": "train" + }, + { + "Input": "a large field of 700 hectares is divided into two parts . the difference of the areas of the two parts is one - fifth of the average of the two areas . what is the area of the smaller part in hectares ?", + "Output Program": [ + "n0 = 700.0\nt0 = 1.0 + 4.0\nt1 = n0 / 2.0\nt2 = 1.0 / t0\nt3 = t1 * t2\nt4 = n0 - t3\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "315" + ], + "split": "train" + }, + { + "Input": "if 2994 \u00e3 \u00b7 14.5 = 177 , then 29.94 \u00e3 \u00b7 1.45 = ?", + "Output Program": [ + "n0 = 2994.0\nn1 = 14.5\nn2 = 177.0\nn3 = 29.94\nn4 = 1.45\nt0 = n1 / n4\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "17.7" + ], + "split": "train" + }, + { + "Input": "a part - time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee ' s total income did not change . by what percent t should the number of hours worked be increased ?", + "Output Program": [ + "n0 = 20.0\nt0 = 10.0 * 4.0\nt1 = 100.0 - n0\nt2 = t1 / 100.0\nt3 = t2 * 10.0\nt4 = t0 / t3\nt5 = t4 - 4.0\nt6 = t5 / 4.0\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random . what is the probability that the ticket drawn has a number which is a multiple of 4 or 15 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 20.0\nn2 = 4.0\nn3 = 15.0\n\nanswer = 3.0 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "0.3" + ], + "split": "train" + }, + { + "Input": "in the xy - coordinate system , if ( m , n ) and ( m + 2 , n + k ) are two points on the line with the equation x = 2 y + 5 , then k =", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 5.0\nt0 = n0 + n2\nt1 = t0 - n2\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "$ 600 is divided amongst a , b and c so that a may get 2 / 3 as much as b and c together , b may get 6 / 9 as much as a and c together , then the share of a is", + "Output Program": [ + "n0 = 600.0\nn1 = 2.0\nn2 = 3.0\nn3 = 6.0\nn4 = 9.0\nt0 = n1 / n2\nt1 = t0 + 1.0\nt2 = n0 / t1\nanswer = t2 * t0\nprint(answer)" + ], + "Output Answer": [ + "240.00000000000003" + ], + "split": "train" + }, + { + "Input": "what least no . must be subtracted from 427398 so that remaining no . is divisible by 10 ?", + "Output Program": [ + "import math\nn0 = 427398.0\nn1 = 10.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "the number of students enrolled at school xx this year is 7 percent more than it was last year . the number of students enrolled at school yy this year is 3 percent more than it was last year . if school xx grew by 40 more students than school yy did , and if there were 4000 total enrolled students last year at both schools , how many students were enrolled at school yy last year ?", + "Output Program": [ + "n0 = 7.0\nn1 = 3.0\nn2 = 40.0\nn3 = 4000.0\nt0 = n0 + n1\nt1 = n0 * n3\nt2 = t1 - n3\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "2400" + ], + "split": "train" + }, + { + "Input": "a 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2 . 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more . at the end of the two removal and replacement , what is the ratio t of milk and water in the resultant mixture ?", + "Output Program": [ + "n0 = 20.0\nn1 = 3.0\nn2 = 2.0\nn3 = 10.0\nt0 = n1 + n2\nt1 = n0 - n3\nt2 = n1 / t0\nt3 = n2 / t0\nt4 = t2 * t1\nt5 = t3 * t1\nt6 = n3 + t4\nt7 = t5 / n0\nt8 = t6 / n0\nt9 = t7 * t1\nt10 = t8 * t1\nt11 = n3 + t10\nanswer = t11 / t9\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "a collection of books went on sale , and 2 / 3 of them were sold for $ 3.50 each . if none of the 36 remaining books were sold , what was the total amount received for the books that were sold ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 3.5\nn3 = 36.0\nt0 = n2 / n1\nt1 = 1.0 / n1\nt2 = n3 * t0\nt3 = t2 / t1\nanswer = n0 * t3\nprint(answer)" + ], + "Output Answer": [ + "252" + ], + "split": "train" + }, + { + "Input": "the average runs scored by a batsman in 35 matches is 36 . in the next 14 matches the batsman scored an average of 15 runs . find his average in all the 30 matches ?", + "Output Program": [ + "n0 = 35.0\nn1 = 36.0\nn2 = 14.0\nn3 = 15.0\nn4 = 30.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "the average ( arithmetic mean ) of the 5 positive integers k , m , r , s , and t is 18 , and k < m < r < s < t . if t is 40 , what is the greatest possible value of the median of the 5 integers ?", + "Output Program": [ + "n0 = 5.0\nn1 = 18.0\nn2 = 40.0\nn3 = 5.0\nt0 = n0 * n1\nt1 = t0 - n2\nt2 = t1 / 2.0\nanswer = t2 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "how many positive integers less than 7,000 are there in which the sum of the digits equals 5 ?", + "Output Program": [ + "import math\nn0 = 7000.0\nn1 = 5.0\nt0 = n1 + 4.0\nt1 = math.factorial(min(15, int(n1)))\nt2 = 4.0 - 1.0\nt3 = math.factorial(min(15, int(t2)))\nt4 = t0 - 1.0\nt5 = math.factorial(min(15, int(t4)))\nt6 = t1 * t3\nanswer = t5 / t6\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "train" + }, + { + "Input": "a parking garage rents parking spaces for $ 10 per week or $ 24 per month . how much does a person save in a year by renting by the month rather than by the week ?", + "Output Program": [ + "n0 = 10.0\nn1 = 24.0\nt0 = 2.0 + 3.0\nt1 = n1 * 12.0\nt2 = t0 * n0\nt3 = t2 + 2.0\nt4 = n0 * t3\nanswer = t4 - t1\nprint(answer)" + ], + "Output Answer": [ + "232" + ], + "split": "train" + }, + { + "Input": "3 friends are planning to attend a concert . if another friend also goes with them , they will get a group discount on their tickets . if the new total price of the tickets with the group discount is the same as the original total price of the tickets without the group discount , how much is the discount ?", + "Output Program": [ + "n0 = 3.0\nt0 = n0 + 1.0\nt1 = 3.0 / t0\nt2 = 1.0 - t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "when positive integer x is divided by positive integer y , the remainder is 3 . if x / y = 96.15 , what is the value of y ?", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 96.15\nt0 = math.floor(n1)\nt1 = n1 - t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "19.999999999999243" + ], + "split": "train" + }, + { + "Input": "the average of 10 numbers is calculated as 15 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?", + "Output Program": [ + "n0 = 10.0\nn1 = 15.0\nn2 = 36.0\nn3 = 26.0\nt0 = n2 - n3\nt1 = t0 / n0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "if x is 20 percent greater than 98 , then x =", + "Output Program": [ + "n0 = 20.0\nn1 = 98.0\nt0 = n0 / 100.0\nt1 = n1 * t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "117.6" + ], + "split": "train" + }, + { + "Input": "30 pens and 75 pencils were purchased for 450 . if the average price of a pencil was 2.00 , find the average price of a pen .", + "Output Program": [ + "n0 = 30.0\nn1 = 75.0\nn2 = 450.0\nn3 = 2.0\nt0 = n1 * 2.0\nt1 = n2 - t0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "what is the smallest number h which when increased by 5 is completely divisible by 8 , 11 and 24 ?", + "Output Program": [ + "import scipy\nn0 = 5.0\nn1 = 8.0\nn2 = 11.0\nn3 = 24.0\nt0 = scipy.lcm(int(n1), int(n2))\nt1 = scipy.lcm(int(n3), int(t0))\nanswer = t1 - n0\nprint(answer)" + ], + "Output Answer": [ + "259" + ], + "split": "train" + }, + { + "Input": "calculate the value of n from the below equation : y ^ 4 \u00e2 \u02c6 \u2019 20 y + 1 = 22", + "Output Program": [ + "n0 = 4.0\nn1 = 20.0\nn2 = 1.0\nn3 = 22.0\nt0 = n1 + n2\nt1 = n3 - n2\nt2 = t1 / t0\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "a lemonade stand sold only small and large cups of lemonade on tuesday . 1 / 5 of the cups sold were small and the rest were large . if the large cups were sold for 7 / 6 as much as the small cups , what fraction of tuesday ' s total revenue was from the sale of large cups ?", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 7.0\nn3 = 6.0\nt0 = n2 / n3\nt1 = n0 / n1\nt2 = t1 * 10.0\nt3 = t0 * t2\nt4 = t2 * t2\nt5 = 10.0 - t2\nt6 = t3 * t5\nt7 = t4 + t6\nanswer = t6 / t7\nprint(answer)" + ], + "Output Answer": [ + "0.8235294117647058" + ], + "split": "train" + }, + { + "Input": "12 is 4 % of a , and 4 is 12 % of b . c equals b / a . what is the value of c ?", + "Output Program": [ + "n0 = 12.0\nn1 = 4.0\nn2 = 4.0\nn3 = 12.0\nt0 = n1 / n0\nt1 = n0 / n1\nt2 = t0 * 100.0\nt3 = t1 * 100.0\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.11111111111111109" + ], + "split": "train" + }, + { + "Input": "find the least number of complete years in which a sum of money put out at 33.3 % compound interest will be more than double of itself ?", + "Output Program": [ + "import math\nn0 = 33.3\nt0 = n0 / 100.0\nt1 = math.log(max(1e-5, 2.0), 2)\nt2 = t0 + 1.0\nt3 = math.log(max(1e-5, t2), 2)\nt4 = t1 / t3\nt5 = t4 + 1.0\nanswer = math.floor(t5)\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "if a number n is chosen at random from the set of two - digit integers whose digits are both prime numbers , what is the probability w that n is divisible by 3 ?", + "Output Program": [ + "n0 = 3.0\nt0 = n0 + 2.0\nt1 = 4.0 * 4.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.3125" + ], + "split": "train" + }, + { + "Input": "a women purchased 3 towels @ rs . 100 each , 5 towels @ rs . 150 each and two towels at a certain rate which is now slipped off from his memory . but she remembers that the average price of the towels was rs . 170 . find the unknown rate of two towels ?", + "Output Program": [ + "n0 = 3.0\nn1 = 100.0\nn2 = 5.0\nn3 = 150.0\nn4 = 170.0\nt0 = n0 + n2\nt1 = n2 * n3\nt2 = n0 * n1\nt3 = t0 + 2.0\nt4 = n4 * t3\nt5 = t4 - t1\nanswer = t5 - t2\nprint(answer)" + ], + "Output Answer": [ + "650" + ], + "split": "train" + }, + { + "Input": "a grocer has a sale of rs . 5266 , rs . 5768 , rs . 5922 , rs . 5678 and rs . 6029 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 5600 ?", + "Output Program": [ + "n0 = 5266.0\nn1 = 5768.0\nn2 = 5922.0\nn3 = 5678.0\nn4 = 6029.0\nn5 = 5.0\nn6 = 5600.0\nt0 = n5 + 1.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n6 * t0\nt4 = n3 + t2\nt5 = n4 + t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "4937" + ], + "split": "train" + }, + { + "Input": "the guests at a football banquet consumed a total of 327 pounds of food . if no individual guest consumed more than 2 pounds of food , what is the minimum number of guests that could have attended the banquet ?", + "Output Program": [ + "import math\nn0 = 327.0\nn1 = 2.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "164" + ], + "split": "train" + }, + { + "Input": "the average salary / head of all the workers ina workshop is rs . 850 , if the average salary / head of 7 technician is rs . 1000 and the average salary / head of the rest is rs . 780 , the total no . of workers in the work - shop is ?", + "Output Program": [ + "n0 = 850.0\nn1 = 7.0\nn2 = 1000.0\nn3 = 780.0\nt0 = n1 * n2\nt1 = n1 * n3\nt2 = n0 - n3\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "the average weight of 6 students decreases by 3 kg when one of them weighing 80 kg is replaced by a new student . the weight of the student is", + "Output Program": [ + "n0 = 6.0\nn1 = 3.0\nn2 = 80.0\nt0 = n0 * n1\nanswer = n2 - t0\nprint(answer)" + ], + "Output Answer": [ + "62" + ], + "split": "train" + }, + { + "Input": "out of 3 consecutive odd numbers 9 times the first number is equal to addition of twice the third number and adding 9 to twice the second . what is the first number ?", + "Output Program": [ + "n0 = 3.0\nn1 = 9.0\nn2 = 9.0\nt0 = n0 + 2.0\nt1 = n0 * n1\nt2 = 2.0 * 3.0\nt3 = t1 - t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "4.2" + ], + "split": "train" + }, + { + "Input": "if x / ( 9 p ) is an odd prime number , where x is a positive integer and p is a prime number , what is the least value of x ?", + "Output Program": [ + "n0 = 9.0\nt0 = n0 * 3.0\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "train" + }, + { + "Input": "rs . 900 is divided among maya , annie , saiji so that maya receives half as much as annie and annie half as much as saiji . then saiji \u2019 s share is :", + "Output Program": [ + "n0 = 900.0\nt0 = n0 / 100.0\nt1 = 4.0 / t0\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "train" + }, + { + "Input": "in a school with 5 classes , each class has 2 students less than the previous class . how many students are there in the largest class if the total number of students at school is 100 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 100.0\nt0 = n1 + n1\nt1 = n1 + t0\nt2 = n1 + t1\nt3 = t1 + t1\nt4 = t3 + t2\nt5 = n2 - t4\nt6 = t5 / n0\nanswer = t2 + t6\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "mark and ann together were allocated n boxes of cookies to sell for a club project . mark sold 7 boxes less than n and ann sold 2 boxes less than n . if mark and ann have each sold at least one box of cookies , but together they have sold less than n boxes , what is the value of n ?", + "Output Program": [ + "n0 = 7.0\nn1 = 2.0\n\nanswer = n0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "given f ( x ) = 3 x \u2013 5 , for what value of x does 2 * [ f ( x ) ] \u2013 19 = f ( x \u2013 4 ) ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 2.0\nn3 = 19.0\nn4 = 4.0\nt0 = n1 * n2\nt1 = n4 * 3.0\nt2 = n0 * n2\nt3 = n0 * 1.0\nt4 = n3 + t0\nt5 = n1 + t1\nt6 = t2 - t3\nt7 = t4 - t5\nanswer = t7 / t6\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "a committee is reviewing a total of 20 x black - and - white films and 8 y color films for a festival . if the committee selects y / x % of the black - and - white films and all of the color films , what fraction of the selected films are in color ?", + "Output Program": [ + "n0 = 20.0\nn1 = 8.0\nt0 = n0 / 100.0\nt1 = n1 + t0\nanswer = n1 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.9756097560975611" + ], + "split": "train" + }, + { + "Input": "there are 780 male and female participants in a meeting . half the female participants and one - quarterof the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?", + "Output Program": [ + "n0 = 780.0\nt0 = n0 / 3.0\nt1 = t0 * 4.0\nt2 = t1 - n0\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "130" + ], + "split": "train" + }, + { + "Input": "in a clothing store , there are 6 different colored neckties ( orange , yellow , green , blue , and indigo ) and 5 different colored shirts ( orange , yellow , green , blue , and indigo ) that must be packed into boxes for gifts . if each box can only fit one necktie and one shirt , what is the probability that all of the boxes will contain a necktie and a shirt of the same color ?", + "Output Program": [ + "n0 = 6.0\nn1 = 5.0\nt0 = n0 * n1\nt1 = t0 * 4.0\nanswer = 1.0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.008333333333333333" + ], + "split": "train" + }, + { + "Input": "the average weight of 20 persons sitting in a boat had some value . a new person added to them whose weight was 45 kg only . due to his arrival , the average weight of all the persons decreased by 5 kg . find the average weight of first 20 persons ?", + "Output Program": [ + "n0 = 20.0\nn1 = 45.0\nn2 = 5.0\nn3 = 20.0\nt0 = n0 + 1.0\nt1 = n2 * t0\nanswer = t1 - n1\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "q and f represent two distinct digits . if the number 457 q 89 f is divisible by 36 , what is the value of ( q + f ) ?", + "Output Program": [ + "n0 = 457.0\nn1 = 89.0\nn2 = 36.0\nt0 = n1 % 10.0\nt1 = n0 % 10.0\nt2 = t1 + 1.0\nt3 = t2 + t1\nt4 = t3 - t0\nanswer = t0 - t4\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "the ratio 25 : 50 expressed as percent equals to", + "Output Program": [ + "n0 = 25.0\nn1 = 50.0\nt0 = n0 / n1\nanswer = t0 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "a man is 22 years older than his son . in two years , his age will be twice the age of his son . what is the present age of his son ?", + "Output Program": [ + "n0 = 22.0\nt0 = 2.0 * 2.0\nt1 = 2.0 - 1.0\nt2 = t0 - 2.0\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "2 + 4", + "Output Program": [ + "n0 = 8.0\nt0 = n0 - 1.0\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "10 people went to a hotel for combine dinner party 5 of them spent rs . 20 each on their dinner and rest spent 4 more than the average expenditure of all the 10 . what was the total money spent by them .", + "Output Program": [ + "n0 = 10.0\nn1 = 5.0\nn2 = 20.0\nn3 = 4.0\nn4 = 10.0\nt0 = n1 * n2\nt1 = n0 - n1\nt2 = n3 * t1\nt3 = n0 - t1\nt4 = t0 + t2\nt5 = t4 / t3\nanswer = n0 * t5\nprint(answer)" + ], + "Output Answer": [ + "240" + ], + "split": "train" + }, + { + "Input": "a sum is divided among w , x and y in such a way that for each rupee w gets , x gets 30 paisa and y gets 20 paisa . if the share of w is rs . 10 , what is the total amount ?", + "Output Program": [ + "n0 = 30.0\nn1 = 20.0\nn2 = 10.0\nt0 = n1 / n2\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "if the price of a book is first decreased by 30 % and then increased by 20 % , then the net change in the price will be :", + "Output Program": [ + "n0 = 30.0\nn1 = 20.0\nt0 = n0 * 100.0\nt1 = n1 * 100.0\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = t3 + 100.0\nt5 = 100.0 - t2\nt6 = t5 / 100.0\nt7 = t4 / 100.0\nt8 = t6 * t7\nt9 = t8 * 100.0\nanswer = 100.0 - t9\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "in the coordinate plane , points ( x , 8 ) and ( 20 , y ) are on line k . if line k passes through the origin and has slope 1 / 4 , then x * y =", + "Output Program": [ + "n0 = 8.0\nn1 = 20.0\nn2 = 1.0\nn3 = 4.0\nt0 = n0 / n3\nt1 = n1 * n3\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "160" + ], + "split": "train" + }, + { + "Input": "bill is golfing with 3 friends and can either buy generic golf tees that are packaged by the dozen or the higher quality aero flight tees that come by the pair . what is the minimum number of packages of aero flight tees bill must purchase to ensure that he has at least 20 golf tees for each member of his foursome , if he will buy no more than 2 packages of the generic golf tees ?", + "Output Program": [ + "n0 = 3.0\nn1 = 20.0\nn2 = 2.0\nt0 = n0 + 1.0\nt1 = n2 * 12.0\nt2 = n1 * t0\nt3 = t2 - t1\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "country x imported approximately $ 1.44 billion of goods in 1996 . if country x imported $ 388 million of goods in the first two months of 1997 and continued to import goods at the same rate for the rest of the year , by how much would country xs 1997 imports exceed those of 1996 ?", + "Output Program": [ + "n0 = 1.44\nn1 = 1996.0\nn2 = 388.0\nn3 = 1997.0\nn4 = 1997.0\nn5 = 1996.0\nt0 = 12.0 / 2.0\nt1 = n0 * 1000.0\nt2 = n2 * t0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "888" + ], + "split": "train" + }, + { + "Input": "two - third of a positive number and 25 / 216 of its reciprocal are equal . the number is :", + "Output Program": [ + "import math\nn0 = 25.0\nn1 = 216.0\nt0 = n0 * 3.0\nt1 = n1 * 2.0\nt2 = t0 / t1\nanswer = math.sqrt(max(0, t2))\nprint(answer)" + ], + "Output Answer": [ + "0.4166666666666667" + ], + "split": "train" + }, + { + "Input": "if 50 % of ( x - y ) = 40 % of ( x + y ) then what percent of x is y ?", + "Output Program": [ + "n0 = 50.0\nn1 = 40.0\nt0 = n0 + n1\nt1 = n0 - n1\nt2 = t1 / t0\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "11.11111111111111" + ], + "split": "train" + }, + { + "Input": "x + ( 1 / x ) = 2.5 find x ^ 2 + ( 1 / x ^ 2 )", + "Output Program": [ + "n0 = 1.0\nn1 = 2.5\nn2 = 2.0\nn3 = 1.0\nn4 = 2.0\nt0 = n1**min(n2, 5)\nanswer = t0 - n2\nprint(answer)" + ], + "Output Answer": [ + "4.25" + ], + "split": "train" + }, + { + "Input": "a = { 0 , 1 , - 3 , 6 , - 8 , - 10 } b = { - 1 , 2 , - 4 , 7 , 6 , - 9 } if a is a number that is randomly selected from set a , and b is a number that is randomly selected from set b , what is the probability that ab < 0 ?", + "Output Program": [ + "n0 = 0.0\nn1 = 1.0\nn2 = 3.0\nn3 = 6.0\nn4 = 8.0\nn5 = 10.0\nn6 = 1.0\nn7 = 2.0\nn8 = 4.0\nn9 = 7.0\nn10 = 6.0\nn11 = 9.0\nn12 = 0.0\nt0 = n2 / n3\nt1 = n7 / n3\nt2 = 3.0 / n3\nt3 = t0 * t0\nt4 = t1 * t2\nanswer = t3 + t4\nprint(answer)" + ], + "Output Answer": [ + "0.41666666666666663" + ], + "split": "train" + }, + { + "Input": "which number need to add to 172835 to get a number exactly divisible by 136 ?", + "Output Program": [ + "import math\nn0 = 172835.0\nn1 = 136.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = t1 + 1.0\nt3 = t2 - t0\nanswer = n1 * t3\nprint(answer)" + ], + "Output Answer": [ + "20.999999999996362" + ], + "split": "train" + }, + { + "Input": "how many even integers n , such that 20 < = n < = 180 are of the form 3 k + 4 , where k is any natural number ?", + "Output Program": [ + "n0 = 20.0\nn1 = 180.0\nn2 = 3.0\nn3 = 4.0\nt0 = n0 + 2.0\nt1 = 2.0 + 4.0\nt2 = n1 - 2.0\nt3 = t2 - t0\nt4 = t3 / t1\nanswer = t4 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "train" + }, + { + "Input": "in a hostel , the number of students decreased by 9 % and the price of food increased by 20 % over the previous year . if each student consumes the same amount of food then by how much should the consumption of food be cut short by every student , so that the total cost of the food remains the same as that of the previous year ?", + "Output Program": [ + "n0 = 9.0\nn1 = 20.0\nt0 = n1 + 100.0\nt1 = 100.0 * 100.0\nt2 = 100.0 - n0\nt3 = t0 * t2\nt4 = t1 / t3\nt5 = 1.0 - t4\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "8.424908424908429" + ], + "split": "train" + }, + { + "Input": "a company produces on an average 4000 items per month for the first 3 months . how many items it must produce on an average per month over the next 9 months , to average of 4375 items per month over the whole ?", + "Output Program": [ + "n0 = 4000.0\nn1 = 3.0\nn2 = 9.0\nn3 = 4375.0\nt0 = n1 + n2\nt1 = n0 * n1\nt2 = n3 * t0\nt3 = t2 - t1\nanswer = t3 / n2\nprint(answer)" + ], + "Output Answer": [ + "4500" + ], + "split": "train" + }, + { + "Input": "pat , kate and mark charged a total of 144 hours to a certain project . if pat charged twice as much time to the project as kate and 1 / 3 as much times as mark , how many more hours did mark charge to the project than kate .", + "Output Program": [ + "n0 = 144.0\nn1 = 1.0\nn2 = 3.0\nt0 = n1 + 2.0\nt1 = n2 * 2.0\nt2 = t0 + t1\nt3 = t1 - n1\nt4 = n0 / t2\nanswer = t4 * t3\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "divide $ 5000 among x , y in the ratio 2 : 8 . how many $ that x get ?", + "Output Program": [ + "n0 = 5000.0\nn1 = 2.0\nn2 = 8.0\nt0 = 1000.0 * 4.0\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "1000" + ], + "split": "train" + }, + { + "Input": "a teacher gave the same test to 3 history classes : u , b , and c . the average ( arithmetic mean ) scores for the 3 classes were 65 , 80 , and 77 , respectively . the ratio of the numbers of students in each class who took the test was 4 to 6 to 5 , respectively . what was the average score for the 3 classes combined ?", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 65.0\nn3 = 80.0\nn4 = 77.0\nn5 = 4.0\nn6 = 6.0\nn7 = 5.0\nn8 = 3.0\nt0 = n5 + n6\nt1 = n2 * n5\nt2 = n3 * n6\nt3 = n4 * n7\nt4 = t1 + t2\nt5 = n7 + t0\nt6 = t4 + t3\nanswer = t6 / t5\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "what are the last two digits of 63 * 35 * 37 * 82 * 71 * 41 * 53 ?", + "Output Program": [ + "n0 = 63.0\nn1 = 35.0\nn2 = 37.0\nn3 = 82.0\nn4 = 71.0\nn5 = 41.0\nn6 = 53.0\n\nanswer = n3 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "the population of a city increases by 5 % per year but due to migration it decrease by 1 % per years . what will be the percentage increase in population in 3 years ?", + "Output Program": [ + "n0 = 5.0\nn1 = 1.0\nn2 = 3.0\nt0 = n0 - n1\nt1 = t0 + 100.0\nt2 = t1 * t0\nt3 = t2 / 100.0\nt4 = t3 + t0\nt5 = t4 + 100.0\nt6 = t5 * t0\nt7 = t6 / 100.0\nanswer = t4 + t7\nprint(answer)" + ], + "Output Answer": [ + "12.4864" + ], + "split": "train" + }, + { + "Input": "the sum of the present age of henry and jill is 33 . what is their present ages if 6 years ago henry was twice the age of jill ?", + "Output Program": [ + "n0 = 33.0\nn1 = 6.0\nt0 = n0 + n1\nt1 = t0 / 3.0\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "in a division sum , the remainder is 5 and the divisor is 3 times the quotient and is obtained by adding 3 to the thrice of the remainder . the dividend is :", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nn2 = 3.0\nt0 = n0 * 3.0\nt1 = n2 + t0\nt2 = t1 / n1\nt3 = t1 * t2\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "113" + ], + "split": "train" + }, + { + "Input": "what is the sum of the multiples of 4 between 34 and 135 inclusive ?", + "Output Program": [ + "n0 = 4.0\nn1 = 34.0\nn2 = 135.0\nt0 = n1 + 2.0\nt1 = n2 - 3.0\nt2 = t0 + t1\nt3 = t1 - t0\nt4 = t3 / n0\nt5 = t2 / 2.0\nt6 = t4 + 1.0\nanswer = t6 * t5\nprint(answer)" + ], + "Output Answer": [ + "2100" + ], + "split": "train" + }, + { + "Input": "( 3 x + 2 ) ( 2 x - 3 ) = ax ^ 2 + kx + n . what is the value of a - n + k ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 2.0\nn3 = 3.0\nn4 = 2.0\nt0 = n0 * n1\nt1 = n1 * n3\nt2 = n1 * n1\nt3 = n0 * n3\nt4 = t0 + t1\nt5 = t2 - t3\nanswer = t4 + t5\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "a vendor sells 50 percent of the apples he had and throws away 20 percent of the remainder . the next day , the vendor sells 50 percent of the remaining apples and throws away the rest . in total , what percent of his apples does the vendor throw away ?", + "Output Program": [ + "n0 = 50.0\nn1 = 20.0\nn2 = 50.0\nt0 = n1 / 100.0\nt1 = 100.0 - n0\nt2 = t0 * t1\nt3 = t1 - t2\nt4 = t3 / 2.0\nanswer = t4 + t2\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "x ^ y + y ^ x = 2408 find the values of x ?", + "Output Program": [ + "n0 = 2408.0\n\nanswer = n0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "2407" + ], + "split": "train" + }, + { + "Input": "alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 1111 . find the cost of each ice - cream cup ?", + "Output Program": [ + "n0 = 16.0\nn1 = 5.0\nn2 = 7.0\nn3 = 6.0\nn4 = 6.0\nn5 = 45.0\nn6 = 70.0\nn7 = 1111.0\nt0 = n0 * n3\nt1 = n1 * n5\nt2 = n2 * n6\nt3 = n7 - t0\nt4 = t3 - t1\nt5 = t4 - t2\nanswer = t5 / n3\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "the average of 3 numbers is 48 . the average of two of these numbers is 56 % . what is the third number ?", + "Output Program": [ + "n0 = 3.0\nn1 = 48.0\nn2 = 56.0\nt0 = n0 * n1\nt1 = n2 * 2.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "what is 2 / 5 of 5 / 9 of 1 / 2 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 5.0\nn3 = 9.0\nn4 = 1.0\nn5 = 2.0\nt0 = n0 / n1\nt1 = n1 / n3\nt2 = n4 / n0\nt3 = t1 * t2\nanswer = t0 * t3\nprint(answer)" + ], + "Output Answer": [ + "0.11111111111111112" + ], + "split": "train" + }, + { + "Input": "106 \u00e3 \u2014 106 + 94 \u00e3 \u2014 94 = ?", + "Output Program": [ + "n0 = 106.0\nn1 = 106.0\nn2 = 94.0\nn3 = 94.0\nt0 = n0**min(2.0, 5)\nt1 = n2**min(2.0, 5)\nt2 = t0 - n0\nt3 = t1 - n2\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "19872" + ], + "split": "train" + }, + { + "Input": "in an office , totally there are 6400 employees and 65 % of the total employees are males . 25 % of the males in the office are at - least 50 years old . find the number of males aged below 50 years ?", + "Output Program": [ + "n0 = 6400.0\nn1 = 65.0\nn2 = 25.0\nn3 = 50.0\nn4 = 50.0\nt0 = n0 * n1\nt1 = 100.0 - n2\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nanswer = t2 * t3\nprint(answer)" + ], + "Output Answer": [ + "3120" + ], + "split": "train" + }, + { + "Input": "the ratio of a to b is 4 to 5 , where a and b are positive . if x equals a increased by 75 percent of a , and m equals b decreased by 80 percent of b , what is the value of m / x ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 75.0\nn3 = 80.0\nt0 = n2 + 100.0\nt1 = n1 / n0\nt2 = 100.0 - n3\nt3 = t2 / t0\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "0.14285714285714285" + ], + "split": "train" + }, + { + "Input": "9 . the least number which should be added to 28523 so that the sum is exactly divisible by 3 , 5 , 7 and 8 is", + "Output Program": [ + "import scipy\nn0 = 9.0\nn1 = 28523.0\nn2 = 3.0\nn3 = 5.0\nn4 = 7.0\nn5 = 8.0\nt0 = scipy.lcm(int(n2), int(n3))\nt1 = scipy.lcm(int(n4), int(t0))\nt2 = scipy.lcm(int(n5), int(t1))\nt3 = n1 % t2\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "37" + ], + "split": "train" + }, + { + "Input": "alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 1051 . find the cost of each ice - cream cup ?", + "Output Program": [ + "n0 = 16.0\nn1 = 5.0\nn2 = 7.0\nn3 = 6.0\nn4 = 6.0\nn5 = 45.0\nn6 = 70.0\nn7 = 1051.0\nt0 = n0 * n3\nt1 = n1 * n5\nt2 = n2 * n6\nt3 = n7 - t0\nt4 = t3 - t1\nt5 = t4 - t2\nanswer = t5 / n3\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "the cost of painting the 4 walls of a room is rs . 350 . the cost of painting a room 3 times in length , breadth and height will be :", + "Output Program": [ + "n0 = 4.0\nn1 = 350.0\nn2 = 3.0\nt0 = n2**min(2.0, 5)\nanswer = n1 * t0\nprint(answer)" + ], + "Output Answer": [ + "3150" + ], + "split": "train" + }, + { + "Input": "a number is doubled and 5 is added . if the resultant is trebled , it becomes 123 . what is that number ?", + "Output Program": [ + "n0 = 5.0\nn1 = 123.0\nt0 = n0 * 3.0\nt1 = 2.0 * 3.0\nt2 = n1 - t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "a certain number when divided by 899 leaves the remainder 63 . find the remainder when the same number is divided by 29 .", + "Output Program": [ + "n0 = 899.0\nn1 = 63.0\nn2 = 29.0\n\nanswer = n1 % n2\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "sandy bought 65 books for $ 1280 from one shop and 55 books for $ 880 from another shop . what is the average price that sandy paid per book ?", + "Output Program": [ + "n0 = 65.0\nn1 = 1280.0\nn2 = 55.0\nn3 = 880.0\nt0 = n1 + n3\nt1 = n0 + n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "find large number from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 8 as quotient and the 15 as remainder", + "Output Program": [ + "n0 = 1365.0\nn1 = 8.0\nn2 = 15.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nt2 = t0 / t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "1542.857142857143" + ], + "split": "train" + }, + { + "Input": "a is the average ( arithmetic mean ) of the first 7 positive multiples of 6 and b is the median of the first 3 positive multiples of positive integer n . if the value of a ^ 2 \u2013 b ^ 2 is zero , what is the value of n ?", + "Output Program": [ + "n0 = 7.0\nn1 = 6.0\nn2 = 3.0\nn3 = 2.0\nn4 = 2.0\nt0 = n1 * 4.0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "in a class of 20 students , 2 students did not borrow any books from the library , 10 students each borrowed 1 book , 5 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?", + "Output Program": [ + "n0 = 20.0\nn1 = 2.0\nn2 = 10.0\nn3 = 1.0\nn4 = 5.0\nn5 = 2.0\nn6 = 3.0\nn7 = 2.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n1 * n4\nt3 = t1 + t2\nt4 = n4 + t1\nt5 = n1 + t4\nt6 = n0 - t5\nt7 = t6 - n3\nt8 = n6 * t7\nt9 = t3 + t8\nanswer = t0 - t9\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "a marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each . there can be no less than 8 musicians per row and no more than 30 musicians per row . how many different rectangular formations g are possible ?", + "Output Program": [ + "n0 = 240.0\nn1 = 8.0\nn2 = 30.0\n\nanswer = n0 / n2\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "set x consists of 10 integers and has median of 10 and a range of 10 . what is the value of the greatest possible integer that can be present in the set ?", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 10.0\n\nanswer = n1 + n2\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "a student chose a number , multiplied it by 2 , then subtracted 140 from the result and got 102 . what was the number he chose ?", + "Output Program": [ + "n0 = 2.0\nn1 = 140.0\nn2 = 102.0\nt0 = n1 + n2\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "121" + ], + "split": "train" + }, + { + "Input": "a certain quantity is measured on two different scales , the p - scale and the s - scale , that are related linearly . measurements on the p - scale of 6 and 24 correspond to measurements on the s - scale of 30 and 60 , respectively . what measurement on the p - scale corresponds to a measurement of 100 on the s - scale ?", + "Output Program": [ + "n0 = 6.0\nn1 = 24.0\nn2 = 30.0\nn3 = 60.0\nn4 = 100.0\nt0 = n4 - n2\nt1 = n1 - n0\nt2 = t0 / n2\nt3 = t2 * t1\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "set a contains all the even numbers between 2 and 50 inclusive . set b contains all the even numbers between 102 and 150 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ?", + "Output Program": [ + "n0 = 2.0\nn1 = 50.0\nn2 = 102.0\nn3 = 150.0\nt0 = n1 - n0\nt1 = n2 - n0\nt2 = t0 / 2.0\nt3 = t2 + 1.0\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "2500" + ], + "split": "train" + }, + { + "Input": "machine x takes 10 hours longer than machine y to produce 1080 widgets . machine y produces 20 percent more widgets in an hour than machine x does in an hour . how many widgets per hour does machine x produce", + "Output Program": [ + "n0 = 10.0\nn1 = 1080.0\nn2 = 20.0\nt0 = 60.0 / 10.0\nt1 = n0 * t0\nanswer = n1 / t1\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "[ ( 3.241 x 14 ) / 100 ] = ?", + "Output Program": [ + "n0 = 3.241\nn1 = 14.0\nn2 = 100.0\nt0 = n0 * n1\nt1 = t0 / n2\nanswer = t1 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "0.045374000000000005" + ], + "split": "train" + }, + { + "Input": "let p and q be the root of the quadratic equation x 2 - ( \u221d - 2 ) x - \u221d - 1 = 0 . what is the minimum possible value of p 2 + q 2 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 1.0\nn3 = 0.0\nn4 = 2.0\nn5 = 2.0\nt0 = n0 + n0\nt1 = n0 + t0\nanswer = t1 - n2\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "6 years ago , p was half of q in age . if the ratio of their present ages is 3 : 4 , what will be the total of their present ages", + "Output Program": [ + "n0 = 6.0\nn1 = 3.0\nn2 = 4.0\nt0 = n0 * 2.0\nt1 = n1 * t0\nt2 = t1 / n2\nanswer = t2 + t0\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "the average mark obtained by 22 candidates in an examination is 48 . the average of the first 10 is 55 while the last 11 is 40 . the marks obtained by the 11 th candidate is ?", + "Output Program": [ + "n0 = 22.0\nn1 = 48.0\nn2 = 10.0\nn3 = 55.0\nn4 = 11.0\nn5 = 40.0\nn6 = 11.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n4 * n5\nt3 = t1 + t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "66" + ], + "split": "train" + }, + { + "Input": "if a person walks at 12 km / hr instead of 8 km / hr , he would have walked 20 km more . the actual distance traveled by him is ?", + "Output Program": [ + "n0 = 12.0\nn1 = 8.0\nn2 = 20.0\nt0 = n0 - n1\nt1 = n2 / t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "a certain country is divided into 4 provinces . each province consists entirely of progressives and traditionalists . if each province contains the same number of traditionalists and the number of traditionalists in any given province is 1 / 12 the total number of progressives in the entire country , what fraction of the country is traditionalist ?", + "Output Program": [ + "n0 = 4.0\nn1 = 1.0\nn2 = 12.0\nt0 = n0 / n2\nt1 = n1 + t0\nt2 = t0 / t1\nanswer = n1 - t2\nprint(answer)" + ], + "Output Answer": [ + "0.75" + ], + "split": "train" + }, + { + "Input": "vishal invested 10 % more than trishul . trishul invested 10 % less than raghu . if the total sum of their investments is rs . 6069 , how much amount did raghu invest ?", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 6069.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nt2 = 1.0 - t0\nt3 = t1 * t2\nt4 = t3 + t2\nt5 = t4 + 1.0\nanswer = n2 / t5\nprint(answer)" + ], + "Output Answer": [ + "2100" + ], + "split": "train" + }, + { + "Input": "the sum of two numbers is 45 . the sum of their quotient and is reciprocal is 2.05 , the product of the numbers is ?", + "Output Program": [ + "n0 = 45.0\nn1 = 2.05\nt0 = 2.0 + 3.0\nt1 = n0 * 100.0\nt2 = t1 / 10.0\nt3 = n0 + t2\nanswer = t0 + t3\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "train" + }, + { + "Input": "joe \u2019 s average ( arithmetic mean ) test score across 4 equally weighted tests was 40 . he was allowed to drop his lowest score . after doing so , his average test score improved to 45 . what is the lowest test score that was dropped ?", + "Output Program": [ + "n0 = 4.0\nn1 = 40.0\nn2 = 45.0\nt0 = n0 * n1\nt1 = n2 * 3.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 147 , what is the difference between the ages of patrick and monica ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 3.0\nn3 = 5.0\nn4 = 147.0\nt0 = n0 * n0\nt1 = n1 * n0\nt2 = n1 * n3\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n4 / t4\nt6 = t5 * t2\nt7 = t5 * t0\nanswer = t6 - t7\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "how many even multiples of 25 are there between 249 and 501 ?", + "Output Program": [ + "n0 = 25.0\nn1 = 249.0\nn2 = 501.0\nt0 = n0 * 2.0\nt1 = n2 - n1\nt2 = t1 / t0\nanswer = t2 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "6.04" + ], + "split": "train" + }, + { + "Input": "in n is a positive integer less than 200 , and 14 n / 60 is an integer , then n has how many different positive prime factors c ?", + "Output Program": [ + "n0 = 200.0\nn1 = 14.0\nn2 = 60.0\nt0 = 1.0 + 4.0\nt1 = n2 / 2.0\nt2 = t1 / 2.0\nt3 = t2 / 3.0\nt4 = t0 / t3\nanswer = t4 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "if the average ( arithmetic mean ) of a and b is 110 , and the average of b and c is 150 , what is the value of a \u2212 c ?", + "Output Program": [ + "n0 = 110.0\nn1 = 150.0\nt0 = n1 * 2.0\nt1 = n0 * 2.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "the average of marks obtained by 120 boys was 40 . if the average of marks of passed boys was 39 and that of failed boys was 15 , the number of boys who passed the examination is ?", + "Output Program": [ + "n0 = 120.0\nn1 = 40.0\nn2 = 39.0\nn3 = 15.0\nt0 = n0 * n1\nt1 = n0 * n3\nt2 = n2 - n3\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "125" + ], + "split": "train" + }, + { + "Input": "a man is 26 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ?", + "Output Program": [ + "n0 = 26.0\nt0 = 2.0 * 2.0\nt1 = 2.0 - 1.0\nt2 = t0 - 2.0\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "if a 2 + b 2 + c 2 = 250 and ab + bc + ca = 3 , then a + b + c is", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 2.0\nn2 = 2.0\nn3 = 250.0\nn4 = 3.0\nt0 = n4 * n0\nt1 = n3 + t0\nanswer = math.sqrt(max(0, t1))\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "if sales tax is reduced from 5 % to 4 % , then what difference it will make if you purchase an item of rs . 1000", + "Output Program": [ + "n0 = 5.0\nn1 = 4.0\nn2 = 1000.0\nt0 = n0 * n2\nt1 = n1 * n2\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "of all the homes on gotham street , 1 / 3 are termite - ridden , and 1 / 4 of these are collapsing . what fraction of the homes are termite - ridden , but not collapsing ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 4.0\nt0 = n0 + 2.0\nt1 = n1 * n3\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.25" + ], + "split": "train" + }, + { + "Input": "take number 1000 and then add 20 to it . now add 1000 one more time . now add 30 . now add 1000 one more time . now add 40 . now add 1000 one more time . now add 10 . what is the total ?", + "Output Program": [ + "n0 = 1000.0\nn1 = 20.0\nn2 = 1000.0\nn3 = 30.0\nn4 = 1000.0\nn5 = 40.0\nn6 = 1000.0\nn7 = 10.0\nt0 = n0 + n0\nt1 = n1 + n3\nt2 = n0 + t0\nt3 = n5 + t1\nt4 = n0 + t2\nt5 = n7 + t3\nanswer = t4 + t5\nprint(answer)" + ], + "Output Answer": [ + "4100" + ], + "split": "train" + }, + { + "Input": "elena \u2019 s bread recipe calls for 2 ounces of butter for each 5 cups of flour used . she needs to make 4 times the original recipe . if 12 ounces of butter is used , then how many cups of flour are needed ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 4.0\nn3 = 12.0\n\nanswer = n1 * n2\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "a dog is tied to a tree by a long nylon cord . if the dog runs from the due north side of the tree to the due south side of the tree with the cord extended to its full length at all items , and the dog ran approximately 30 feet , what was the approximate length of the nylon cord l in feet ?", + "Output Program": [ + "n0 = 30.0\n\nanswer = n0 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "all factors of a positive integer x are multiplied and the product obtained is x ^ 3 . if x is greater than 1 , how many factors does x have ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\n\nanswer = n0 + 3.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 47 , the how old is b ?", + "Output Program": [ + "n0 = 47.0\nt0 = 1.0 + 4.0\nt1 = n0 - 2.0\nt2 = t1 * 2.0\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "the mean of 50 observations was 36 . it was found later that an observation 44 was wrongly taken as 23 . the corrected new mean is", + "Output Program": [ + "n0 = 50.0\nn1 = 36.0\nn2 = 44.0\nn3 = 23.0\nt0 = n0 * n1\nt1 = n0 - 2.0\nt2 = t1 - n3\nt3 = t0 + t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "36.5" + ], + "split": "train" + }, + { + "Input": "is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 27 , then how old is b ?", + "Output Program": [ + "n0 = 27.0\nt0 = 2.0 + 3.0\nt1 = n0 - 2.0\nt2 = t1 / t0\nanswer = t2 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "a whale goes on a feeding frenzy that lasts for 9 hours . for the first hour he catches and eats x kilos of plankton . in every hour after the first , it consumes 4 kilos of plankton more than it consumed in the previous hour . if by the end of the frenzy the whale will have consumed a whopping accumulated total 450 kilos of plankton , how many kilos did he consume on the sixth hour ?", + "Output Program": [ + "n0 = 9.0\nn1 = 4.0\nn2 = 450.0\nt0 = n2 / n0\nanswer = n1 + t0\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "train" + }, + { + "Input": "a waiter ' s salary consists of his salary and tips . during one week his tips were 9 / 4 of his salary . what fraction of his income came from tips ?", + "Output Program": [ + "n0 = 9.0\nn1 = 4.0\nt0 = n0 / n1\nt1 = t0 + 1.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.6923076923076923" + ], + "split": "train" + }, + { + "Input": "the average age of a husband and his wife was 23 years at the time of their marriage . after 5 years they have a one - year old child . the average age of the family now is :", + "Output Program": [ + "n0 = 23.0\nn1 = 5.0\nt0 = n0 * 2.0\nt1 = n1 + t0\nt2 = n1 + t1\nt3 = t2 + 1.0\nanswer = t3 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "what sum of money put at c . i amounts in 2 years to rs . 8820 and in 3 years to rs . 9261 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 8820.0\nn2 = 3.0\nn3 = 9261.0\nt0 = n3 / n1\nt1 = t0 - 1.0\nt2 = t1 + 1.0\nt3 = t2**min(n0, 5)\nanswer = n1 / t3\nprint(answer)" + ], + "Output Answer": [ + "8000" + ], + "split": "train" + }, + { + "Input": "when a number is divided by 6 & then multiply by 12 the answer is 12 what is the no . ?", + "Output Program": [ + "n0 = 6.0\nn1 = 12.0\nn2 = 12.0\nt0 = n2 / n1\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "running at their respective constant rate , machine x takes 2 days longer to produce w widgets than machines y . at these rates , if the two machines together produce 5 w / 4 widgets in 3 days , how many days would it take machine x alone to produce 2 w widgets .", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 4.0\nn3 = 3.0\nn4 = 2.0\nt0 = n0 * n4\nanswer = n3 * t0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "if the arithmetic mean of p and q is 10 and the arithmetic mean of q and r is 20 , what is the value of r - p ?", + "Output Program": [ + "n0 = 10.0\nn1 = 20.0\nt0 = n1 * 2.0\nt1 = n0 * 2.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "the total age of a and b is 10 years more than the total age of b and c . c is how many years younger than a ?", + "Output Program": [ + "n0 = 10.0\n\nanswer = n0 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "how many halves are there in 9 - fourth ?", + "Output Program": [ + "n0 = 9.0\nt0 = n0 / 4.0\nt1 = 1.0 / 2.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "4.5" + ], + "split": "train" + }, + { + "Input": "what is the population standard deviation for the numbers : 75 , 83 , 96 , 100 , 121 and 125 ?", + "Output Program": [ + "n0 = 75.0\nn1 = 83.0\nn2 = 96.0\nn3 = 100.0\nn4 = 121.0\nn5 = 125.0\nt0 = n4 + n5\nt1 = n1 / 3.0\nt2 = t0 - n3\nt3 = t2 - n2\nt4 = t3 - t1\nanswer = t4 - 4.0\nprint(answer)" + ], + "Output Answer": [ + "18.333333333333332" + ], + "split": "train" + }, + { + "Input": "find the average of all the numbers between 6 and 30 which are divisible by 4 .", + "Output Program": [ + "n0 = 6.0\nn1 = 30.0\nn2 = 4.0\nt0 = n0 + 4.0\nt1 = n1 - 4.0\nt2 = t0 + t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "in a renowned city , the average birth rate is 8 people every two seconds and the death rate is 6 people every two seconds . estimate the size of the population net increase that occurs in one day .", + "Output Program": [ + "n0 = 8.0\nn1 = 6.0\nt0 = n0 - n1\nt1 = t0 * 3600.0\nanswer = t1 * 12.0\nprint(answer)" + ], + "Output Answer": [ + "86400" + ], + "split": "train" + }, + { + "Input": "7 years ago , paula was 3 times as old as karl . in 2 years , paula will be twice as old as karl . what is the sum of their ages now ?", + "Output Program": [ + "n0 = 7.0\nn1 = 3.0\nn2 = 2.0\nt0 = n2 * 2.0\nt1 = n0 * n1\nt2 = n2 - t0\nt3 = t1 - n0\nt4 = -t2\nt5 = t4 + t3\nt6 = t5 * n1\nt7 = t6 - t3\nanswer = t5 + t7\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "what number times ( 1 \u2044 7 ) ^ 2 will give the value of 7 ^ 3 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 7.0\nn2 = 2.0\nn3 = 7.0\nn4 = 3.0\nt0 = n1**min(n2, 5)\nt1 = n1**min(n4, 5)\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "16807" + ], + "split": "train" + }, + { + "Input": "the ratio 2 : 10 expressed as percent equals to", + "Output Program": [ + "n0 = 2.0\nn1 = 10.0\nt0 = n0 / n1\nanswer = t0 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "if a - b = 3 and a ( power 2 ) + b ( power 2 ) = 39 , find the value of ab .", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 2.0\nn3 = 39.0\nt0 = n0**min(n1, 5)\nt1 = n3 - t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "a big container is 30 % full with water . if 54 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container ?", + "Output Program": [ + "n0 = 30.0\nn1 = 54.0\nn2 = 3.0\nn3 = 4.0\nt0 = n2 / n3\nt1 = n0 / 100.0\nt2 = t0 - t1\nanswer = n1 / t2\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "how much is 80 % of 60 is greater than 4 / 5 of 25 ?", + "Output Program": [ + "n0 = 80.0\nn1 = 60.0\nn2 = 4.0\nn3 = 5.0\nn4 = 25.0\nt0 = n0 / 100.0\nt1 = n2 / n3\nt2 = n1 * t0\nt3 = n4 * t1\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "if r is a positive integer , and r / 15 = 8.2 , what is the remainder when r is divided by 15 ?", + "Output Program": [ + "n0 = 15.0\nn1 = 8.2\nn2 = 15.0\nt0 = n0 * n1\nanswer = t0 % n0\nprint(answer)" + ], + "Output Answer": [ + "2.999999999999986" + ], + "split": "train" + }, + { + "Input": "working alone , printers x , y , and z can do a certain printing job , consisting of a large number of pages , in 15 , 12 , and 18 hours , respectively . what is the ratio of the time it takes printer x to do the job , working alone at its rate , to the time it takes printers y and z to do the job , working together at their individual rates ?", + "Output Program": [ + "n0 = 15.0\nn1 = 12.0\nn2 = 18.0\nt0 = 1.0 / n1\nt1 = 1.0 / n2\nt2 = t0 + t1\nt3 = 1.0 / t2\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "2.0833333333333335" + ], + "split": "train" + }, + { + "Input": "what is the 20 - fifth decimal to the right in the fraction 10 / 11 ?", + "Output Program": [ + "import math\nn0 = 20.0\nn1 = 10.0\nn2 = 11.0\nt0 = n1 / n2\nt1 = t0 * 10.0\nanswer = math.floor(t1)\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "the sum of 5 th and 21 th term of a . p . is equal to the sum of 8 th , 15 th and 13 th term . find the term which is 0", + "Output Program": [ + "n0 = 5.0\nn1 = 21.0\nn2 = 8.0\nn3 = 15.0\nn4 = 13.0\nn5 = 0.0\nt0 = n2 + n3\nt1 = n0 + n1\nt2 = n4 + t0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "in 5 football games thus far this season , barry has run for 98 , 107 , 85 , 89 , and 91 yards . at a minimum , how many yards n will he need to gain this sunday if he wants to keep his season average above 100 yards ?", + "Output Program": [ + "n0 = 5.0\nn1 = 98.0\nn2 = 107.0\nn3 = 85.0\nn4 = 89.0\nn5 = 91.0\nn6 = 100.0\nt0 = n0 + 1.0\nt1 = n1 + n2\nt2 = n3 + t1\nt3 = n6 * t0\nt4 = n4 + t2\nt5 = n5 + t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "130" + ], + "split": "train" + }, + { + "Input": "ab + cd = jjj , where ab and cd are two - digit numbers and jjj is a 3 digit number ; a , b , c , and d are distinct positive integers . in the addition problem above , what is the value of c ?", + "Output Program": [ + "n0 = 3.0\n\nanswer = n0 * n0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "8 friends went to a hotel and decided to pay the bill amount equally . but 7 of them could pay rs . 80 each as a result 8 th has to pay rs . 70 extra than his share . find the amount paid by him .", + "Output Program": [ + "n0 = 8.0\nn1 = 7.0\nn2 = 80.0\nn3 = 8.0\nn4 = 70.0\nt0 = n1 * n2\nt1 = n4 + t0\nt2 = t1 / n1\nanswer = n4 + t2\nprint(answer)" + ], + "Output Answer": [ + "160" + ], + "split": "train" + }, + { + "Input": "if a : b = 4 : 1 , then find ( a - 3 b ) / ( 2 a - b ) ?", + "Output Program": [ + "n0 = 4.0\nn1 = 1.0\nn2 = 3.0\nn3 = 2.0\nt0 = n0 * n3\nt1 = n0 - n2\nt2 = t0 - n1\nanswer = t1 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.14285714285714285" + ], + "split": "train" + }, + { + "Input": "the average weight of a , b , c is 45 kg . the avgwgt of a & b be 40 kg & that of b , c be 43 kg . find the wgt of b .", + "Output Program": [ + "n0 = 45.0\nn1 = 40.0\nn2 = 43.0\nt0 = n1 * 2.0\nt1 = n2 * 2.0\nt2 = n0 * 3.0\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "31" + ], + "split": "train" + }, + { + "Input": "if two integers x , y ( x > y ) are selected from - 3 to 4 ( inclusive ) , how many cases are there ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nt0 = n0 + n1\nt1 = n1 + 2.0\nt2 = n1 + 1.0\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = t4 + 4.0\nt6 = t5 + 3.0\nt7 = t6 + 2.0\nanswer = t7 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "20 is added to a certain number , the sum is multiplied by 2 , the product is divided by 2 and 2 is subtracted from the quotient . the remainder left is half of 88 . what is the number ?", + "Output Program": [ + "n0 = 20.0\nn1 = 2.0\nn2 = 2.0\nn3 = 2.0\nn4 = 88.0\nt0 = n4 / 2.0\nt1 = n2 + t0\nt2 = n2 * t1\nt3 = t2 / n1\nanswer = t3 - n0\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "on a partly cloudy day , derek decides to walk back from work . when it is sunny , he walks at a speed of s miles / hr ( s is an integer ) and when it gets cloudy , he increases his speed to ( s + 1 ) miles / hr . if his average speed for the entire distance is 2.8 miles / hr , what fraction e of the total distance did he cover while the sun was shining on him ?", + "Output Program": [ + "import scipy\nn0 = 1.0\nn1 = 2.8\nt0 = scipy.lcm(int(2.0), int(3.0))\nt1 = t0 / n1\nanswer = t1 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "0.1428571428571428" + ], + "split": "train" + }, + { + "Input": "instead of multiplying a number by 5 , the number is divided by 10 . what is the percentage of error obtained ?", + "Output Program": [ + "n0 = 5.0\nn1 = 10.0\nt0 = n1 / n1\nt1 = n0 * n1\nt2 = t0 / t1\nt3 = t2 * 100.0\nanswer = 100.0 - t3\nprint(answer)" + ], + "Output Answer": [ + "98" + ], + "split": "train" + }, + { + "Input": "if 325 / 999 = 0.125 , what is the 81 st digit to the right of the decimal point in the decimal equivalent of the fraction ?", + "Output Program": [ + "n0 = 325.0\nn1 = 999.0\nn2 = 0.125\nn3 = 81.0\n\nanswer = 2.0 + 3.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "if d is the standard deviation a , b , and c , what is the standard deviation of a + 2 , b + 2 , c + 2 ?", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 2.0\nn2 = 2.0\nt0 = n0**min(n0, 5)\nt1 = t0 * 3.0\nt2 = t1 / 3.0\nanswer = math.sqrt(max(0, t2))\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "at the end of year x , automobile installment credit accounted for 36 % of all outstanding consumer installment credit . at that time automobile finance companies extended $ 75 billion of credit , or 1 / 2 of the automobile installment credit . how many billion dollars of consumer installment credit was outstanding at that time ?", + "Output Program": [ + "n0 = 36.0\nn1 = 75.0\nn2 = 1.0\nn3 = 2.0\nt0 = n0 / 100.0\nt1 = n1 * n3\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "416.6666666666667" + ], + "split": "train" + }, + { + "Input": "nr books bought nr of people 6 3 7 1 8 5 9 2 what is the median of books bought per person ?", + "Output Program": [ + "n0 = 6.0\nn1 = 3.0\nn2 = 7.0\nn3 = 1.0\nn4 = 8.0\nn5 = 5.0\nn6 = 9.0\nn7 = 2.0\n\nanswer = n4 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "find 62976 \u00f7 ? = 123", + "Output Program": [ + "n0 = 62976.0\nn1 = 123.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "512" + ], + "split": "train" + }, + { + "Input": "a caterer ordered 200 ice - cream bars and 200 sundaes . if the total price was $ 200.00 and the price of each ice - cream bar was $ 0.40 , what was the price of each sundae ?", + "Output Program": [ + "n0 = 200.0\nn1 = 200.0\nn2 = 200.0\nn3 = 0.4\nt0 = n0 * n3\nt1 = n2 - t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.6" + ], + "split": "train" + }, + { + "Input": "a man purchased 4 blankets @ rs . 100 each , 5 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ?", + "Output Program": [ + "n0 = 4.0\nn1 = 100.0\nn2 = 5.0\nn3 = 150.0\nn4 = 150.0\nt0 = n3 * 10.0\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "350" + ], + "split": "train" + }, + { + "Input": "of 70 players on a football team , 31 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?", + "Output Program": [ + "n0 = 70.0\nn1 = 31.0\nt0 = 1.0 / 3.0\nt1 = n0 - n1\nt2 = 1.0 - t0\nt3 = t2 * t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "57" + ], + "split": "train" + }, + { + "Input": "a 75 m long train is running at 54 km / hr . in how much time will it cross an electric pole ?", + "Output Program": [ + "n0 = 75.0\nn1 = 54.0\nt0 = n1 * 1000.0\nt1 = t0 / 3600.0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "what is the least number that should be added to 1077 , so the sum of the number is divisible by 23 ?", + "Output Program": [ + "import math\nn0 = 1077.0\nn1 = 23.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = t1 + 1.0\nt3 = t2 - t0\nanswer = n1 * t3\nprint(answer)" + ], + "Output Answer": [ + "3.999999999999936" + ], + "split": "train" + }, + { + "Input": "gold is 19 times as heavy as water and copper is 9 times as heavy as water . in what ratio should these be mixed to get an alloy 17 times as heavy as water ?", + "Output Program": [ + "n0 = 19.0\nn1 = 9.0\nn2 = 17.0\nt0 = n2 - n1\nt1 = n0 - n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "two trains of equal are running on parallel lines in the same direction at 47 km / hr and 36 km / hr . the faster train passes the slower train in 36 sec . the length of each train is ?", + "Output Program": [ + "n0 = 47.0\nn1 = 36.0\nn2 = 36.0\nt0 = n0 - n1\nt1 = t0 * 1000.0\nt2 = t1 / 3600.0\nt3 = n2 * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "55" + ], + "split": "train" + }, + { + "Input": "the average weight of 8 person ' s increases by 6 kg when a new person comes in place of one of them weighing 45 kg . what is the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 6.0\nn2 = 45.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "93" + ], + "split": "train" + }, + { + "Input": "how many digits 2 ^ 300 has ?", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 300.0\nt0 = math.log(max(1e-5, n0), 2)\nt1 = math.log(max(1e-5, 10.0), 2)\nt2 = t0 / t1\nt3 = n1 * t2\nt4 = t3 + 1.0\nanswer = math.floor(t4)\nprint(answer)" + ], + "Output Answer": [ + "91" + ], + "split": "train" + }, + { + "Input": "after distributing the sweets equally among 25 children , 8 sweets remain . had the number of children been 28 , 22 sweets would have been left after equal distribution . what was the total number of sweets ?", + "Output Program": [ + "n0 = 25.0\nn1 = 8.0\nn2 = 28.0\nn3 = 22.0\nt0 = n0 - 1.0\nt1 = t0 / 2.0\nt2 = n2 * t1\nanswer = n3 + t2\nprint(answer)" + ], + "Output Answer": [ + "358" + ], + "split": "train" + }, + { + "Input": "the average age of a class of 23 students is 22 years . the average increased by 1 when the teacher ' s age also included . what is the age of the teacher ?", + "Output Program": [ + "n0 = 23.0\nn1 = 22.0\nn2 = 1.0\nt0 = n0 + n2\nt1 = n1 + n2\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "46" + ], + "split": "train" + }, + { + "Input": "in the coordinate plane , line a has a slope of - 1 and an x - intercept of 2 . line b has a slope of 5 and a y - intercept of - 10 . if the two lines intersect at the point ( a , b ) , what is the sum a + b ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 5.0\nn3 = 10.0\nt0 = n3 - n2\nt1 = t0 - n0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "by how much does the larger root of the equation 2 q ^ 2 + 5 q = 12 exceed the smaller root ?", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 2.0\nn2 = 5.0\nn3 = 12.0\nt0 = n0 * n3\nt1 = n0 * n0\nt2 = n2**min(n0, 5)\nt3 = t0 * 4.0\nt4 = t3 + t2\nt5 = math.sqrt(max(0, t4))\nt6 = n2 + t5\nt7 = n2 - t5\nt8 = t6 / t1\nt9 = t7 / t1\nanswer = t8 - t9\nprint(answer)" + ], + "Output Answer": [ + "5.5" + ], + "split": "train" + }, + { + "Input": "for the positive integers x , x + 2 , x + 4 , x + 7 , and x + 27 , the mean is how much greater than the median ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 7.0\nn3 = 27.0\nt0 = n0 + n1\nt1 = 1.0 + n1\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = t3 / t1\nanswer = t4 - n1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 % of the distribution lies one standard deviation g of the mean , what percent of the distribution is less than m + g ?", + "Output Program": [ + "n0 = 68.0\nt0 = 100.0 - n0\nt1 = t0 / 2.0\nanswer = 100.0 - t1\nprint(answer)" + ], + "Output Answer": [ + "84" + ], + "split": "train" + }, + { + "Input": "pradeep has to obtain 35 % of the total marks to pass . he got 185 marks and failed by 25 marks . the maximum marks are", + "Output Program": [ + "n0 = 35.0\nn1 = 185.0\nn2 = 25.0\nt0 = n1 + n2\nt1 = n0 / 100.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "600" + ], + "split": "train" + }, + { + "Input": "a man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses . next year his income increases by 35 % but his savings increase by 100 % . if his total expenditure in 2 years is double his expenditure in 1 st year , what % age of his income in the first year did he save ?", + "Output Program": [ + "n0 = 35.0\nn1 = 100.0\nn2 = 2.0\nn3 = 1.0\nt0 = n0 + n1\nt1 = n1 * n2\nt2 = n1 + t0\nt3 = t2 - t1\nt4 = t3 / n1\nanswer = t4 * n1\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "p , q , r enter into a partnership & their share are in the ratio 1 / 2 : 1 / 3 : 1 / 4 , after two months , p withdraws half of the capitals & after 10 months , a profit of rs 378 is divided among them . what is q ' s share ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 1.0\nn3 = 3.0\nn4 = 1.0\nn5 = 4.0\nn6 = 10.0\nn7 = 378.0\nt0 = n1 * n5\nt1 = n1 * n6\nt2 = n0 + t1\nt3 = n7 * t0\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "144" + ], + "split": "train" + }, + { + "Input": "a computer is programmed to multiply consecutive even integers 2 * 4 * 6 * 8 * \u2026 * n until the product is divisible by 2013 , what is the value of n ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 6.0\nn3 = 8.0\nn4 = 2013.0\nt0 = 1.0 + 10.0\nt1 = n4 / t0\nt2 = t1 / 3.0\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "122" + ], + "split": "train" + }, + { + "Input": "for what value of \u00e2 \u20ac \u0153 k \u00e2 \u20ac \u009d will the equation ( 2 kx 2 + 3 kx + 2 ) = 0 have equal roots ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 3.0\nn3 = 2.0\nn4 = 0.0\nt0 = n0 + n0\nt1 = n2**min(n0, 5)\nt2 = n0**min(t0, 5)\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "1.7777777777777777" + ], + "split": "train" + }, + { + "Input": "entry fee in an examination was re . 1 . later , this was reduced by 25 % which increased the sale by 20 % . the percentage increase in the number of visitors is", + "Output Program": [ + "n0 = 1.0\nn1 = 25.0\nn2 = 20.0\nt0 = n1 / 100.0\nt1 = n2 * 100.0\nt2 = t1 / 100.0\nt3 = 1.0 - t0\nt4 = t2 + 100.0\nt5 = t4 / t3\nanswer = t5 - 100.0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "if rs . 10 be allowed as true discount on a bill of rs . 110 at the end of a certain time , then the discount allowed on the same sum due at the end of double the time is", + "Output Program": [ + "n0 = 10.0\nn1 = 110.0\nt0 = n0 + n1\nt1 = t0 - 100.0\nt2 = t1 / t0\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "18.333333333333332" + ], + "split": "train" + }, + { + "Input": "keats library purchases a number of new books , all in the category of biography , and the library does not acquire any other books . with the addition of the new biographies , the biography collection of the library amounts to 35 % of the total number of books in the library . if prior to the purchase , only 20 % of the books in keats library were biographies , by what percent has the number of biographies in the library increased ?", + "Output Program": [ + "n0 = 35.0\nn1 = 20.0\nt0 = n0 * 100.0\nt1 = n1 * 100.0\nt2 = 100.0 - n0\nt3 = t0 - t1\nt4 = t3 / t2\nt5 = t4 / n1\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "115.38461538461537" + ], + "split": "train" + }, + { + "Input": "if the average marks of 3 batches of 40 , 50 and 60 students respectively is 45 , 55 , 65 , what is the average marks of all the students ?", + "Output Program": [ + "n0 = 3.0\nn1 = 40.0\nn2 = 50.0\nn3 = 60.0\nn4 = 45.0\nn5 = 55.0\nn6 = 65.0\nt0 = n1 + n2\nt1 = n1 * n4\nt2 = n2 * n5\nt3 = n3 * n6\nt4 = t1 + t2\nt5 = n3 + t0\nt6 = t4 + t3\nanswer = t6 / t5\nprint(answer)" + ], + "Output Answer": [ + "56.333333333333336" + ], + "split": "train" + }, + { + "Input": "in a bus left side are 15 seats available , 3 few seats in right side because in rear exit door . each seat hold 3 people . in addition , there is a seat back can sit 10 people all together . how many people can sit in a bus ?", + "Output Program": [ + "n0 = 15.0\nn1 = 3.0\nn2 = 3.0\nn3 = 10.0\nt0 = n0 - n1\nt1 = n0 + t0\nt2 = n1 * t1\nanswer = n3 + t2\nprint(answer)" + ], + "Output Answer": [ + "91" + ], + "split": "train" + }, + { + "Input": "if 4 < x < 8 < y < 12 , then what is the greatest possible positive integer difference of x and y ?", + "Output Program": [ + "n0 = 4.0\nn1 = 8.0\nn2 = 12.0\nt0 = n2 - n0\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 70 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam .", + "Output Program": [ + "n0 = 80.0\nn1 = 5.0\nn2 = 70.0\nn3 = 90.0\nt0 = n1 * n3\nt1 = n1 * n2\nt2 = n3 - n0\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "when y is divided by 276 , the remainder is 44 . what is the remainder when the same y is divided by 23 ?", + "Output Program": [ + "n0 = 276.0\nn1 = 44.0\nn2 = 23.0\n\nanswer = n1 % n2\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "the cricket team of 11 members is 29 yrs old & the wicket keeper is 3 yrs older . if the ages ofthese 2 are excluded , the average age of theremaining players is 1 year less than the average age of the whole team . what is the average age of the team ?", + "Output Program": [ + "n0 = 11.0\nn1 = 29.0\nn2 = 3.0\nn3 = 2.0\nn4 = 1.0\nt0 = n1 + n2\nt1 = n0 - n3\nt2 = n1 + t0\nt3 = n0 - t1\nt4 = t2 - t1\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "find value for x from below equation ? x + 1 = 3", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\n\nanswer = n1 - n0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "jane started baby - sitting when she was 18 years old . whenever she baby - sat for a child , that child was no more than half her age at the time . jane is currently 32 years old , and she stopped baby - sitting 12 years ago . what is the current age of the oldest person for whom jane could have baby - sat ?", + "Output Program": [ + "n0 = 18.0\nn1 = 32.0\nn2 = 12.0\nt0 = n0 / 2.0\nt1 = n1 - n0\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "what is the remainder of r = 3 ^ 19 when divided by 10 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 19.0\nn2 = 10.0\nt0 = n1 % 4.0\nt1 = n0**min(t0, 5)\nanswer = t1 % n2\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "line m lies in the xy - plane . the y - intercept of line m is - 2 , and line m passes through the midpoint of the line segment whose endpoints are ( 2 , 8 ) and ( 6 , - 4 ) . what is the slope of line m ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 8.0\nn3 = 6.0\nn4 = 4.0\nt0 = n1 + n3\nt1 = n2 - n4\nt2 = t1 / n1\nt3 = t0 / n1\nt4 = t2 + n0\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "the annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years b in which the population would be doubled assuming there is no emigration or immigration is", + "Output Program": [ + "n0 = 1000.0\nn1 = 39.4\nn2 = 19.4\nt0 = 10.0 * 3.0\nt1 = n1 - n2\nt2 = t1 / n0\nt3 = 100.0 - t0\nt4 = t2 * 100.0\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "a teacher grades students \u2019 tests by subtracting twice the number of incorrect responses from the number of correct responses . if student a answers each of the 100 questions on her test and receives a score of 64 , how many questions did student a answer correctly ?", + "Output Program": [ + "n0 = 100.0\nn1 = 64.0\nt0 = n0 - n1\nt1 = t0 / 3.0\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "88" + ], + "split": "train" + }, + { + "Input": "a wildlife preserve is being planned for 8000 rhinoceroses . the preserve is to contain a total of 10000 acres of watering area , plus 100 acres of grazing area for each rhinoceros . if the number of rhinoceroses is expected to increase by 10 percent , how many 1000 acres should the preserve have in order to provide for the increased population ?", + "Output Program": [ + "n0 = 8000.0\nn1 = 10000.0\nn2 = 100.0\nn3 = 10.0\nn4 = 1000.0\nt0 = n0 * n2\nt1 = t0 / n3\nt2 = t1 + t0\nt3 = n1 + t2\nanswer = t3 / n4\nprint(answer)" + ], + "Output Answer": [ + "890" + ], + "split": "train" + }, + { + "Input": "a tourist does not have to pay tax on the first $ 600 of goods he purchases in country b , but does have to pay a 10 percent tax on the portion of the total value that is in excess of $ 600 . what tax must be paid by a tourist if he buys goods with a total value of $ 1720 ?", + "Output Program": [ + "n0 = 600.0\nn1 = 10.0\nn2 = 600.0\nn3 = 1720.0\nt0 = n3 - n0\nt1 = n1 * t0\nanswer = t1 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "112" + ], + "split": "train" + }, + { + "Input": "a man is 37 years older than his son . in two years , his age will be twice the age of his son . the present age of this son is", + "Output Program": [ + "n0 = 37.0\nt0 = 2.0 * 2.0\nt1 = 2.0 - 1.0\nt2 = t0 - 2.0\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "if 80 percent of 600 is 50 percent of x , then x = ?", + "Output Program": [ + "n0 = 80.0\nn1 = 600.0\nn2 = 50.0\nt0 = n0 * n1\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "960" + ], + "split": "train" + }, + { + "Input": "if a 2 + b 2 + c 2 = 560 and ab + bc + ca = 8 , then a + b + c is", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 2.0\nn2 = 2.0\nn3 = 560.0\nn4 = 8.0\nt0 = n4 * n0\nt1 = n3 + t0\nanswer = math.sqrt(max(0, t1))\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "the arithmetic mean and standard deviation of a certain normal distribution are 15.5 and 1.5 , respectively . what value is exactly 2 standard deviations less than the mean ?", + "Output Program": [ + "n0 = 15.5\nn1 = 1.5\nn2 = 2.0\nt0 = n1 * n2\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "12.5" + ], + "split": "train" + }, + { + "Input": "all the milk in container a which was filled to its brim was poured into two containers b and c . the quantity of milk in container b was 62.5 % less than the capacity of container a . if 148 liters was now transferred from c to b , then both the containers would have equal quantities of milk . what was the initial quantity of milk in container a ?", + "Output Program": [ + "n0 = 62.5\nn1 = 148.0\nt0 = n0 / 100.0\nt1 = 1 / 2.0\nt2 = 1.0 - t0\nt3 = t1 - t2\nanswer = n1 / t3\nprint(answer)" + ], + "Output Answer": [ + "1184" + ], + "split": "train" + }, + { + "Input": "in a division sum , the divisor is 10 times the quotient and 5 times the remainder . if the remainder is 46 , the dividend is", + "Output Program": [ + "n0 = 10.0\nn1 = 5.0\nn2 = 46.0\nt0 = n1 * n2\nt1 = t0 / n0\nanswer = t1 * t0\nprint(answer)" + ], + "Output Answer": [ + "5290" + ], + "split": "train" + }, + { + "Input": "of 70 players on a football team , 46 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?", + "Output Program": [ + "n0 = 70.0\nn1 = 46.0\nt0 = 1.0 / 3.0\nt1 = n0 - n1\nt2 = 1.0 - t0\nt3 = t2 * t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "62" + ], + "split": "train" + }, + { + "Input": "5 ^ 100 is divided by 18 then what is the remainder ?", + "Output Program": [ + "n0 = 5.0\nn1 = 100.0\nn2 = 18.0\n\nanswer = n2 - n0\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "if ( a + b ) = 4 , ( b + c ) = 7 and ( c + d ) = 5 , what is the value of ( a + d ) ?", + "Output Program": [ + "n0 = 4.0\nn1 = 7.0\nn2 = 5.0\nt0 = n0 + n2\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "3 cannons are firing at a target . if their individual probabilities to hit the target are 0.5 , 0.2 , and 0.3 respectively , what is the probability that none of the cannons will hit the target after one round of fire ? prob . that all the cannons will hit the target = . 06 prob . that none of the cannons will hit = 1 - . 06 = . 94", + "Output Program": [ + "n0 = 3.0\nn1 = 0.5\nn2 = 0.2\nn3 = 0.3\nn4 = 6.0\nn5 = 1.0\nn6 = 6.0\nn7 = 94.0\nt0 = 1.0 - n3\nt1 = 1.0 - n2\nt2 = 1.0 - n1\nt3 = t0 * t1\nanswer = t3 * t2\nprint(answer)" + ], + "Output Answer": [ + "0.27999999999999997" + ], + "split": "train" + }, + { + "Input": "if money is invested at r percent interest , compounded annually , the amount of investment will double in approximately 70 / r years . if pat ' s parents invested $ 5000 in a long term bond that pays 4 percent interest , compounded annually , what will be the approximate total amount of investment 36 years later , when pat is ready for college ?", + "Output Program": [ + "n0 = 70.0\nn1 = 5000.0\nn2 = 4.0\nn3 = 36.0\nt0 = n1 * 2.0\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "20000" + ], + "split": "train" + }, + { + "Input": "if a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20 , what is the probability that this product will be a multiple of 45 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 20.0\nn2 = 45.0\nt0 = n1 + 4.0\nanswer = 1.0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.041666666666666664" + ], + "split": "train" + }, + { + "Input": "if p ^ 2 \u2013 13 p + 40 = h , and p is a positive integer between 1 and 10 , inclusive , what is the probability that h < 0 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 13.0\nn2 = 40.0\nn3 = 1.0\nn4 = 10.0\nn5 = 0.0\n\nanswer = 2.0 / n4\nprint(answer)" + ], + "Output Answer": [ + "0.2" + ], + "split": "train" + }, + { + "Input": "two - third of a positive number and 16 / 216 of its reciprocal are equal . the number is :", + "Output Program": [ + "import math\nn0 = 16.0\nn1 = 216.0\nt0 = n0 * 3.0\nt1 = n1 * 2.0\nt2 = t0 / t1\nanswer = math.sqrt(max(0, t2))\nprint(answer)" + ], + "Output Answer": [ + "0.3333333333333333" + ], + "split": "train" + }, + { + "Input": "if x < y < z and y - x > 9 , where x is an even integer and y and z are odd integers , what is the least possible value of z - x ?", + "Output Program": [ + "n0 = 9.0\nt0 = n0 + 2.0\nanswer = t0 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "3 times the first of 3 consecutive odd integers is 3 more than twice the third . the third integer is ?", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 3.0\nt0 = 2.0 * 4.0\nt1 = n0 + t0\nanswer = t1 + 4.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "if a certain number is divided by 9 , the quotient , dividend , and divisor , added together , will amount to 69 . what is the number ?", + "Output Program": [ + "n0 = 9.0\nn1 = 69.0\nt0 = n0 + 1.0\nt1 = n1 - n0\nt2 = n0 * t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "train" + }, + { + "Input": "if the price of a book is first decreased by 25 % and then increased by 20 % , then the decrease in the price will be ?", + "Output Program": [ + "n0 = 25.0\nn1 = 20.0\nt0 = n0 * 100.0\nt1 = n1 * 100.0\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = t3 + 100.0\nt5 = 100.0 - t2\nt6 = t5 / 100.0\nt7 = t4 / 100.0\nt8 = t6 * t7\nt9 = t8 * 100.0\nanswer = 100.0 - t9\nprint(answer)" + ], + "Output Answer": [ + "10.000000000000014" + ], + "split": "train" + }, + { + "Input": "the average weight of 8 people increases by 2.5 kg when a new person comes in place of one of them weighing 35 kg . what is the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.5\nn2 = 35.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "55" + ], + "split": "train" + }, + { + "Input": "in a renowned city , the average birth rate is 4 people every two seconds and the death rate is 2 people every two seconds . estimate the size of the population net increase that occurs in one day .", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\nt0 = n0 - n1\nt1 = t0 * 3600.0\nanswer = t1 * 12.0\nprint(answer)" + ], + "Output Answer": [ + "86400" + ], + "split": "train" + }, + { + "Input": "a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 22 , the how old is b ?", + "Output Program": [ + "n0 = 22.0\nt0 = 1.0 + 4.0\nt1 = n0 - 2.0\nt2 = t1 * 2.0\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "the price of 3 pants and 6 t - shirts is rs . 1500 . with the same money one can buy 1 pant and 12 t - shirts . if one wants to buy 8 t - shirts , how much shall she have to pay ?", + "Output Program": [ + "n0 = 3.0\nn1 = 6.0\nn2 = 1500.0\nn3 = 1.0\nn4 = 12.0\nn5 = 8.0\nt0 = n4 - n1\nt1 = n0 - n3\nt2 = t0 / t1\nt3 = n0 * t2\nt4 = n1 + t3\nt5 = n2 / t4\nanswer = n5 * t5\nprint(answer)" + ], + "Output Answer": [ + "800" + ], + "split": "train" + }, + { + "Input": "rs . 770 were divided among a , b , c in such a way that a had rs . 40 more than b and c had rs 30 more than a . how much was b \u00e2 \u20ac \u2122 s share ?", + "Output Program": [ + "n0 = 770.0\nn1 = 40.0\nn2 = 30.0\nt0 = n1 + n1\nt1 = n2 + t0\nt2 = n0 - t1\nt3 = t2 / 3.0\nt4 = n2 + t3\nanswer = n1 + t4\nprint(answer)" + ], + "Output Answer": [ + "290" + ], + "split": "train" + }, + { + "Input": "village x has a population of 74000 , which is decreasing at the rate of 1200 per year . village y has a population of 42000 , which is increasing at the rate of 800 per year . in how many years will the population of the two villages be equal ?", + "Output Program": [ + "n0 = 74000.0\nn1 = 1200.0\nn2 = 42000.0\nn3 = 800.0\nt0 = n1 + n3\nt1 = n0 - n2\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "a number x is 3 times another number y . the percentage that y is less than x is", + "Output Program": [ + "n0 = 3.0\nt0 = n0 - 1.0\nt1 = t0 / n0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "66.66666666666666" + ], + "split": "train" + }, + { + "Input": "a student has to obtain 33 % of the total marks to pass . he got 59 marks and failed by 40 marks . the maximum marks are ?", + "Output Program": [ + "n0 = 33.0\nn1 = 59.0\nn2 = 40.0\nt0 = n1 + n2\nt1 = n0 / 100.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "if the price of gasoline increases by 25 % and a driver intends to spend only 5 % more on gasoline , by how much percent should the driver reduce the quantity of gasoline that he buys ?", + "Output Program": [ + "n0 = 25.0\nn1 = 5.0\nt0 = n0 + 100.0\nt1 = n1 + 100.0\nt2 = t0 - t1\nt3 = t2 / t0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "a person saved $ 10 in buying an item on sale . if he spent $ 100 for the item , approximately how much percent he saved in the transaction ?", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 100.0\nt0 = n0 + n1\nt1 = n0 / t0\nt2 = t1 * 100.0\nt3 = math.floor(t2)\nanswer = t3 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "roy is now 8 years older than julia and half of that amount older than kelly . if in 2 years , roy will be 3 times as old as julia , then in 2 years what would be roy \u2019 s age multiplied by kelly \u2019 s age ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.0\nn2 = 3.0\nn3 = 2.0\nt0 = n0 + n1\nt1 = n0 / 2.0\nt2 = n1 * n2\nt3 = n2 - 1.0\nt4 = t0 - t2\nt5 = t4 / t3\nt6 = t0 + t5\nt7 = t6 - t1\nanswer = t6 * t7\nprint(answer)" + ], + "Output Answer": [ + "96" + ], + "split": "train" + }, + { + "Input": "a mixture of 120 liters of wine and water contains 20 % water . how much more water should be added so that water becomes 25 % of the new mixture ?", + "Output Program": [ + "n0 = 120.0\nn1 = 20.0\nn2 = 25.0\nt0 = n2 / 100.0\nt1 = n1 / 100.0\nt2 = n0 * t0\nt3 = n0 * t1\nt4 = 1.0 - t0\nt5 = t2 - t3\nanswer = t5 / t4\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "5 friends visited a fruit stall , and everyone decided to contribute equally to the total bill of $ 100 . if one of the friends had a coupon for 6 % off the total bill , and if each friend still contributed equally after the coupon was applied to the bill , how much did each friend pay ?", + "Output Program": [ + "n0 = 5.0\nn1 = 100.0\nn2 = 6.0\nt0 = n1 * n2\nt1 = t0 / 100.0\nt2 = n1 - t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "18.8" + ], + "split": "train" + }, + { + "Input": "a certain country is divided into 5 provinces . each province consists entirely of progressives and traditionalists . if each province contains the same number of traditionalists and the number of traditionalists in any given province is 1 / 15 the total number of progressives in the entire country , what fraction of the country is traditionalist ?", + "Output Program": [ + "n0 = 5.0\nn1 = 1.0\nn2 = 15.0\nt0 = n0 / n2\nt1 = n1 + t0\nt2 = t0 / t1\nanswer = n1 - t2\nprint(answer)" + ], + "Output Answer": [ + "0.75" + ], + "split": "train" + }, + { + "Input": "an amount at compound interest sums to rs . 17640 / - in 2 years and to rs . 22050 / - in 3 years at the same rate of interest . find the rate percentage ?", + "Output Program": [ + "n0 = 17640.0\nn1 = 2.0\nn2 = 22050.0\nn3 = 3.0\nt0 = n2 - n0\nt1 = t0 / n0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "which number can we add to 859722 to get a number exactly divisible by 456 ?", + "Output Program": [ + "n0 = 859722.0\nn1 = 456.0\nt0 = n0 % n1\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "294" + ], + "split": "train" + }, + { + "Input": "in the hillside summer camp there are 100 children . 90 % of the children are boys and the rest are girls . the camp administrator decided to make the number of girls only 5 % of the total number of children in the camp . how many more boys must she bring to make that happen ?", + "Output Program": [ + "n0 = 100.0\nn1 = 90.0\nn2 = 5.0\nt0 = n2 / 100.0\nt1 = 100.0 - n2\nt2 = t1 / 100.0\nt3 = n0 * t0\nt4 = n0 * t2\nanswer = t4 + t3\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "10 years ago , the average age of a family of 4 members was 24 years . two children having been born ( with age diference of 2 years ) , the present average age of the family is the same . the present age of the youngest child is ?", + "Output Program": [ + "n0 = 10.0\nn1 = 4.0\nn2 = 24.0\nn3 = 2.0\nt0 = n1 + n3\nt1 = n1 * n2\nt2 = n0 * n1\nt3 = t1 + t2\nt4 = n2 * t0\nt5 = t4 - t3\nt6 = t5 - n3\nanswer = t6 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "f 1 ( x ) f 1 ( x ) = 2 x - 1 and fn ( x ) = f 1 ( fn \u2212 1 ( x ) ) fn ( x ) = f 1 ( fn \u2212 1 ( x ) ) for n \u2265 \u2265 2 . find f 5 ( 2 )", + "Output Program": [ + "n0 = 6.0\nn1 = 5.0\nn2 = 2.0\nn3 = 19.0\nt0 = n0 * n1\nt1 = n2 * t0\nt2 = t1 / n2\nanswer = t2 + 3.0\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "in a sample of associates at a law firm , 30 percent are second - year associates , and 60 percent are not first - year associates . what percentage of the associates at the law firm have been there for more than two years ?", + "Output Program": [ + "n0 = 30.0\nn1 = 60.0\n\nanswer = n1 - n0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "the average ( arithmetic mean ) of 20 , 40 , and 60 is 5 more than the average of 10 , 50 , and what number ?", + "Output Program": [ + "n0 = 20.0\nn1 = 40.0\nn2 = 60.0\nn3 = 5.0\nn4 = 10.0\nn5 = 50.0\nt0 = n0 + n1\nt1 = n3 * 3.0\nt2 = n2 + t0\nt3 = n4 + t1\nt4 = n5 + t3\nanswer = t2 - t4\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "an old man distributed all the gold coins he had to his two sons into two different numbers such that the difference between the squares of the two numbers is 49 times the difference between the two numbers . how many coins did the old man have ?", + "Output Program": [ + "import math\nn0 = 49.0\n\nanswer = math.floor(n0)\nprint(answer)" + ], + "Output Answer": [ + "49" + ], + "split": "train" + }, + { + "Input": "how many times will the digit 4 be written when listing the integers from 1 to 1000 ?", + "Output Program": [ + "n0 = 4.0\nn1 = 1.0\nn2 = 1000.0\nt0 = n1 * 10.0\nt1 = t0 * 10.0\nanswer = t1 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "a rope of which a calf is tied is increased from 12 m to 18 m , how much additional grassy ground shall it graze ?", + "Output Program": [ + "n0 = 12.0\nn1 = 18.0\nt0 = 3.0 + 4.0\nt1 = 10.0 * 2.0\nt2 = n1**min(2.0, 5)\nt3 = n0**min(2.0, 5)\nt4 = t1 + 2.0\nt5 = t2 - t3\nt6 = t4 / t0\nanswer = t6 * t5\nprint(answer)" + ], + "Output Answer": [ + "565.7142857142857" + ], + "split": "train" + }, + { + "Input": "lisa and robert have taken the same number of photos on their school trip . lisa has taken 3 times as many photos as claire and robert has taken 24 more photos than claire . how many photos has claire taken ?", + "Output Program": [ + "n0 = 3.0\nn1 = 24.0\nt0 = n0 - 1.0\nanswer = n1 / t0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "for an agricultural experiment , 300 seeds were planted in one plot and 200 were planted in a second plot . if exactly 25 percent of the seeds in the first plot germinated and exactly 30 percent of the seeds in the second plot germinated , what percent of the total number of seeds germinated ?", + "Output Program": [ + "n0 = 300.0\nn1 = 200.0\nn2 = 25.0\nn3 = 30.0\nt0 = n0 + n1\nt1 = n2 / 100.0\nt2 = n3 / 100.0\nt3 = n0 * t1\nt4 = n1 * t2\nt5 = t3 + t4\nt6 = t5 / t0\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "train" + }, + { + "Input": "john want to buy a $ 100 trouser at the store , but he think it \u00e2 \u20ac \u2122 s too expensive . finally , it goes on sale for $ 55 . what is the percent decrease ?", + "Output Program": [ + "n0 = 100.0\nn1 = 55.0\n\nanswer = n0 - n1\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "the average age of a , b and c is 28 years . if the average age of a and c is 29 years , what is the age of b in years ?", + "Output Program": [ + "n0 = 28.0\nn1 = 29.0\nt0 = n0 * 3.0\nt1 = n1 * 2.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "a multiple choice test consists of 4 questions , and each question has 5 answer choices . in how many f ways can the test be completed if every question is unanswered ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\n\nanswer = n1**min(n0, 5)\nprint(answer)" + ], + "Output Answer": [ + "625" + ], + "split": "train" + }, + { + "Input": "a store reported total sales of $ 480 million for february of this year . if the total sales for the same month last year was $ 320 million , approximately what was the percent increase in sales ?", + "Output Program": [ + "n0 = 480.0\nn1 = 320.0\nt0 = n0 - n1\nt1 = t0 / n1\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "a cyclist rides a bicycle 8 km at an average speed of 10 km / hr and again travels 10 km at an average speed of 8 km / hr . what is the average speed for the entire trip ?", + "Output Program": [ + "n0 = 8.0\nn1 = 10.0\nn2 = 10.0\nn3 = 8.0\nt0 = n0 + n1\nt1 = n0 / n1\nt2 = n1 / n0\nt3 = t1 + t2\nanswer = t0 / t3\nprint(answer)" + ], + "Output Answer": [ + "8.78048780487805" + ], + "split": "train" + }, + { + "Input": "find the value of 72516 x 9999 = m ?", + "Output Program": [ + "n0 = 72516.0\nn1 = 9999.0\nt0 = n1 - 4.0\nanswer = t0 * n0\nprint(answer)" + ], + "Output Answer": [ + "724797420" + ], + "split": "train" + }, + { + "Input": "a meal cost $ 35.50 adn there was no tax . if the tip was more than 15 pc but less than 25 pc of the price , then the total amount paid should be :", + "Output Program": [ + "n0 = 35.5\nn1 = 15.0\nn2 = 25.0\nt0 = n0 * n1\nt1 = t0 / 100.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "40.825" + ], + "split": "train" + }, + { + "Input": "the sum of the even numbers between 1 and n is 95 * 96 , where n is an odd number , then n = ?", + "Output Program": [ + "n0 = 1.0\nn1 = 95.0\nn2 = 96.0\nt0 = n1 * 2.0\nanswer = t0 + n0\nprint(answer)" + ], + "Output Answer": [ + "191" + ], + "split": "train" + }, + { + "Input": "julie decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month . if julie ' s savings by the end of the year from these monthly savings were 4 times the amount she spent per month , what should be the fraction of her salary that she spent each month ?", + "Output Program": [ + "n0 = 4.0\n\nanswer = 3.0 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.75" + ], + "split": "train" + }, + { + "Input": "how many positive integers less than 6,000 are there in which the sum of the digits equals 5 ?", + "Output Program": [ + "import math\nn0 = 6000.0\nn1 = 5.0\nt0 = n1 + 4.0\nt1 = math.factorial(min(15, int(n1)))\nt2 = 4.0 - 1.0\nt3 = math.factorial(min(15, int(t2)))\nt4 = t0 - 1.0\nt5 = math.factorial(min(15, int(t4)))\nt6 = t1 * t3\nanswer = t5 / t6\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "train" + }, + { + "Input": "the average ( arithmetic mean ) of 8 numbers is 8 . if 4 is added from each of 5 of the numbers , what is the new average ?", + "Output Program": [ + "n0 = 8.0\nn1 = 8.0\nn2 = 4.0\nn3 = 5.0\nt0 = n0 * n0\nt1 = n2 * n3\nt2 = t0 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "10.5" + ], + "split": "train" + }, + { + "Input": "list k consists of 10 consecutive integers . if - 3 is the least integer in list k , what is the range of the positive integers in list k ?", + "Output Program": [ + "n0 = 10.0\nn1 = 3.0\nt0 = n0 - n1\nt1 = t0 - 1.0\nanswer = t1 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "we run a business that rents out canoes and kayaks . a canoe rental costs $ 14 per day , and a kayak rental costs $ 15 dollars per day . one day , our business rents out 3 canoes for every 2 kayaks and receives a total of $ 288 in revenue . how many more canoes than kayaks were rented out ?", + "Output Program": [ + "n0 = 14.0\nn1 = 15.0\nn2 = 3.0\nn3 = 2.0\nn4 = 288.0\nt0 = n0 * n2\nt1 = n1 * n3\nt2 = n2 - n3\nt3 = t0 + t1\nt4 = n4 / t3\nanswer = t4 * t2\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "the average weight of 9 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg . what is the weight of the new person ?", + "Output Program": [ + "n0 = 9.0\nn1 = 2.5\nn2 = 65.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "87.5" + ], + "split": "train" + }, + { + "Input": "find the least number which when divided by 38 and 3 leaves a remainder of 1 in each case .", + "Output Program": [ + "import scipy\nn0 = 38.0\nn1 = 3.0\nn2 = 1.0\nt0 = scipy.lcm(int(n0), int(n1))\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "115" + ], + "split": "train" + }, + { + "Input": "in a certain supermarket , a triangular display of cans is arranged in 10 rows , numbered 1 through 10 from top to bottom . each successively numbered row contains 3 more cans than the row immediately above it . if there are fewer than 150 cans in the entire display , how many cans are in the seventh row ?", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 1.0\nn2 = 10.0\nn3 = 3.0\nn4 = 150.0\nt0 = n3 + n3\nt1 = n0 - n1\nt2 = n3 * t1\nt3 = n3 * t0\nt4 = t2 / 2.0\nt5 = n0 * t4\nt6 = n4 - t5\nt7 = t6 / n0\nt8 = math.floor(t7)\nanswer = t8 + t3\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "q ' = 3 q - 3 , what is the value of ( 5 ' ) ' ?", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 5.0\nt0 = n0 * n2\nt1 = n2 - 1.0\nt2 = t0 - n0\nt3 = n0 * t2\nt4 = t3 - n0\nanswer = t4 * t1\nprint(answer)" + ], + "Output Answer": [ + "132" + ], + "split": "train" + }, + { + "Input": "the smallest number when increased by ` ` 1 ` ` is exactly divisible by 12 , 18 , 24 , 32 and 40 is :", + "Output Program": [ + "import scipy\nn0 = 1.0\nn1 = 12.0\nn2 = 18.0\nn3 = 24.0\nn4 = 32.0\nn5 = 40.0\nt0 = scipy.lcm(int(n1), int(n2))\nt1 = scipy.lcm(int(n3), int(n4))\nt2 = scipy.lcm(int(t0), int(t1))\nt3 = scipy.lcm(int(n5), int(t2))\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "1441" + ], + "split": "train" + }, + { + "Input": "from given equation find the value of x : 2 x \u00b2 + 9 x \u2212 5", + "Output Program": [ + "n0 = 2.0\nn1 = 9.0\nn2 = 5.0\n\nanswer = 1.0 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "how many positive integers between 100 and 500 are there such that they are multiples of 19 ?", + "Output Program": [ + "n0 = 100.0\nn1 = 500.0\nn2 = 19.0\nt0 = n1 - n0\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "21.05263157894737" + ], + "split": "train" + }, + { + "Input": "p says to q ` ` i am thrice as old as you were when i was as old as you are ' ' . if the sum of their present age is 100 years , then the present age of q ?", + "Output Program": [ + "n0 = 100.0\nt0 = n0 * 3.0\nt1 = 3.0 * 3.0\nt2 = t1 - 1.0\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "37.5" + ], + "split": "train" + }, + { + "Input": "a committee is reviewing a total of 20 x black - and - white films and 6 y color films for a festival . if the committee selects y / x % of the black - and - white films and all of the color films , what fraction r of the selected films are in color ?", + "Output Program": [ + "n0 = 20.0\nn1 = 6.0\nt0 = n0 / 100.0\nt1 = n1 + t0\nanswer = n1 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.9677419354838709" + ], + "split": "train" + }, + { + "Input": "at 1 : 00 pm , there were 10.0 grams of bacteria . the bacteria increased to x grams at 4 : 00 pm , and 16.9 grams at 7 : 00 pm . if the amount of bacteria present increased by the same fraction during each of the 3 - hour periods , how many grams of bacteria were present at 4 : 00 pm ?", + "Output Program": [ + "import math\nn0 = 1.0\nn1 = 0.0\nn2 = 10.0\nn3 = 4.0\nn4 = 0.0\nn5 = 16.9\nn6 = 7.0\nn7 = 0.0\nn8 = 3.0\nn9 = 4.0\nn10 = 0.0\nt0 = n5 / n2\nt1 = math.sqrt(max(0, t0))\nanswer = t1 * n2\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "if ( 1 / 2 ) ^ 25 ( 1 / 81 ) ^ k = 1 / 18 ^ 25 , then k =", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 25.0\nn3 = 1.0\nn4 = 81.0\nn5 = 1.0\nn6 = 18.0\nn7 = 25.0\nt0 = n1 * n2\nanswer = t0 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "12.5" + ], + "split": "train" + }, + { + "Input": "the difference between a positive proper fraction and its reciprocal is 9 / 20 . the fraction is ?", + "Output Program": [ + "n0 = 9.0\nn1 = 20.0\nt0 = n0 - 4.0\nanswer = 4.0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.8" + ], + "split": "train" + }, + { + "Input": "a man can swim in still water at 1.5 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ?", + "Output Program": [ + "n0 = 1.5\n\nanswer = n0 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "there are 2 more women than there are men on a local co - ed softball team . if there are a total of 16 players on the team , what is the ratio of men to women ?", + "Output Program": [ + "n0 = 2.0\nn1 = 16.0\nt0 = 1.0 + 1.0\nt1 = n1 - n0\nt2 = t1 / t0\nt3 = n0 + t2\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.7777777777777778" + ], + "split": "train" + }, + { + "Input": "a large field of 900 hectares is divided into two parts . the difference of the areas of the two parts is one - fifth of the average of the two areas . what is the area of the smaller part in hectares ?", + "Output Program": [ + "n0 = 900.0\nt0 = 1.0 + 4.0\nt1 = n0 / 2.0\nt2 = 1.0 / t0\nt3 = t1 * t2\nt4 = n0 - t3\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "405" + ], + "split": "train" + }, + { + "Input": "a batsman makes a score of 82 runs in the 17 th inning and thus increases his averages by 3 . what is his average after 17 th inning ?", + "Output Program": [ + "n0 = 82.0\nn1 = 17.0\nn2 = 3.0\nn3 = 17.0\nt0 = n1 * n2\nt1 = n0 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "34" + ], + "split": "train" + }, + { + "Input": "what is the remainder if 7 ^ 4 is divided by 100 ?", + "Output Program": [ + "n0 = 7.0\nn1 = 4.0\nn2 = 100.0\nt0 = n2 / 2.0\nt1 = n0 * n0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "find value of x : ( 422 + 404 ) ^ 2 \u2212 ( 4 \u00d7 422 \u00d7 404 ) = x .", + "Output Program": [ + "n0 = 422.0\nn1 = 404.0\nn2 = 2.0\nn3 = 4.0\nn4 = 422.0\nn5 = 404.0\nt0 = n0 + n1\nt1 = n0 * n3\nt2 = n1 * t1\nt3 = t0**min(2.0, 5)\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "324" + ], + "split": "train" + }, + { + "Input": "every disk in a bag is either blue , yellow or green . the ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8 . if the total number of disks in the bag is 54 , how many more green disks than blue disks are in the bag ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 8.0\nn3 = 54.0\nt0 = n0 + n1\nt1 = n2 - n0\nt2 = n2 + t0\nt3 = n3 / t2\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "among 250 viewers interviewed who watch at least one of the 3 tv channels namely a , bc . 116 watch a , 127 watch c , while 107 watch b . if 90 watch exactly two channels . how many watch exactly one channel ?", + "Output Program": [ + "n0 = 250.0\nn1 = 3.0\nn2 = 116.0\nn3 = 127.0\nn4 = 107.0\nn5 = 90.0\nt0 = n2 + n3\nt1 = n0 - n5\nt2 = n4 + t0\nt3 = t2 - n5\nt4 = t3 - n0\nt5 = t4 / 2.0\nanswer = t1 - t5\nprint(answer)" + ], + "Output Answer": [ + "155" + ], + "split": "train" + }, + { + "Input": "working simultaneously and independently at an identical constant rate , 6 machines of a certain type can produce a total of x units of product p in 5 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 4 x units of product p in 10 days ?", + "Output Program": [ + "n0 = 6.0\nn1 = 5.0\nn2 = 4.0\nn3 = 10.0\nt0 = n1 / n3\nt1 = n0 * n2\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "what is the minimum percentage increase in the mean of set s { - 4 , - 1 , 0 , 6 , 9 } if its two smallest elements are replaced with two different primes ?", + "Output Program": [ + "n0 = 4.0\nn1 = 1.0\nn2 = 0.0\nn3 = 6.0\nn4 = 9.0\nt0 = 100.0 * 2.0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "in a renowned city , the average birth rate is 6 people every two seconds and the death rate is 3 people every two seconds . estimate the size of the population net increase that occurs in one day .", + "Output Program": [ + "n0 = 6.0\nn1 = 3.0\nt0 = n0 - n1\nt1 = t0 * 3600.0\nanswer = t1 * 12.0\nprint(answer)" + ], + "Output Answer": [ + "129600" + ], + "split": "train" + }, + { + "Input": "in a certain quiz that consists of 8 questions , each question after the first is worth 4 points more than the preceding question . if the 10 questions on the quiz are worth a total of 360 points , how many points is the third question worth ?", + "Output Program": [ + "n0 = 8.0\nn1 = 4.0\nn2 = 10.0\nn3 = 360.0\nt0 = n3 / n2\nt1 = n0 - n1\nt2 = t1 - 1.0\nanswer = t0 + t2\nprint(answer)" + ], + "Output Answer": [ + "39" + ], + "split": "train" + }, + { + "Input": "a certain school implemented a reading program for its students , with the goal of getting each student to read 6 books per month year - round . if the school has c classes made up of s students in each class , how many books will the entire student body read in one year ?", + "Output Program": [ + "n0 = 6.0\n\nanswer = n0 * 12.0\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "train" + }, + { + "Input": "if the average ( arithmetic mean ) of a and b is 40 and the average of b and c is 60 , what is the value of c \u2212 a ?", + "Output Program": [ + "n0 = 40.0\nn1 = 60.0\nt0 = n1 * 2.0\nt1 = n0 * 2.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "a 6 - liter solution is 25 % alcohol . how many liters of pure alcohol must be added to produce a solution that is 50 % alcohol ?", + "Output Program": [ + "n0 = 6.0\nn1 = 25.0\nn2 = 50.0\nt0 = n0 * n1\nt1 = t0 / 100.0\nt2 = t1 * 2.0\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "the sum of the first 50 positive even integers is 2550 . what is the sum of even integers from 102 to 200 inclusive ?", + "Output Program": [ + "n0 = 50.0\nn1 = 2550.0\nn2 = 102.0\nn3 = 200.0\nt0 = n2 + n3\nt1 = n3 - n2\nt2 = t1 / 2.0\nt3 = t0 / 2.0\nt4 = t2 + 1.0\nanswer = t4 * t3\nprint(answer)" + ], + "Output Answer": [ + "7550" + ], + "split": "train" + }, + { + "Input": "which of the options is a two - digit number , which has a unit ' s digit that exceeds its 10 ' s digit by 4 and the product of the given number and the sum of its digits is equal to 208 .", + "Output Program": [ + "n0 = 10.0\nn1 = 4.0\nn2 = 208.0\nt0 = n1 * 2.0\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "the hcf and lcm of two numbers m and n are respectively 5 and 210 . if m + n = 75 , then 1 / m + 1 / n is equal to", + "Output Program": [ + "n0 = 5.0\nn1 = 210.0\nn2 = 75.0\nn3 = 1.0\nn4 = 1.0\nt0 = n0 * n1\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.07142857142857142" + ], + "split": "train" + }, + { + "Input": "drum x is 1 / 2 full of oil and drum y , which has twice the capacity of drum x , is 1 / 4 full of oil . if all of the oil in drum x is poured into drum y , then drum y will be filled to what capacity ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 1.0\nn3 = 4.0\nt0 = n0 / n3\nt1 = 12.0 / 2.0\nt2 = n0 / n1\nt3 = t0 * 12.0\nt4 = t1 * t2\nt5 = t3 + t4\nanswer = t5 / 12.0\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "( 0.66 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.66 ) ( power 2 ) + 0.066 + ( 0.1 ) ( power 2 ) is :", + "Output Program": [ + "n0 = 0.66\nn1 = 3.0\nn2 = 0.1\nn3 = 3.0\nn4 = 0.66\nn5 = 2.0\nn6 = 0.066\nn7 = 0.1\nn8 = 2.0\nt0 = n0**min(n1, 5)\nt1 = n2**min(n1, 5)\nt2 = n0**min(n5, 5)\nt3 = n2**min(n5, 5)\nt4 = n6 + t2\nt5 = t0 - t1\nt6 = t4 + t3\nanswer = t5 / t6\nprint(answer)" + ], + "Output Answer": [ + "0.5599999999999999" + ], + "split": "train" + }, + { + "Input": "when the no . 7 y 86038 is exactly divisible by 11 , then the smallest whole no . in place of y ?", + "Output Program": [ + "n0 = 7.0\nn1 = 86038.0\nn2 = 11.0\nt0 = 2.0 * 4.0\nt1 = 2.0 * 3.0\nt2 = n0 + t0\nt3 = t1 + 3.0\nt4 = t2 + t0\nt5 = t4 - t3\nanswer = t5 - n2\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "65 % of x = 20 % of 747.50 . find the value of x ?", + "Output Program": [ + "n0 = 65.0\nn1 = 20.0\nn2 = 747.5\nt0 = n2 / 100.0\nt1 = n1 * t0\nt2 = t1 * 100.0\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "230" + ], + "split": "train" + }, + { + "Input": "the average monthly salary of 20 employees in an organisation is rs . 1300 . if the manager ' s salary is added , then the average salary increases by rs . 100 . what is the manager ' s monthly salary ?", + "Output Program": [ + "n0 = 20.0\nn1 = 1300.0\nn2 = 100.0\nt0 = n1 + n2\nt1 = n0 + 1.0\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "3400" + ], + "split": "train" + }, + { + "Input": "seller selling an apple for rs . 19 , a seller loses 1 / 6 th of what it costs him . the cp of the apple is ?", + "Output Program": [ + "n0 = 19.0\nn1 = 1.0\nn2 = 6.0\n\nanswer = n0 + n1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "if a certain toy store ' s revenue in november was 2 / 5 of its revenue in december and its revenue in january was 1 / 3 of its revenue in november , then the store ' s revenue in december was how many times the average ( arithmetic mean ) of its revenues in november and january ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 1.0\nn3 = 3.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = t0 * t1\nt3 = t0 + t2\nt4 = t3 / 2.0\nanswer = n2 / t4\nprint(answer)" + ], + "Output Answer": [ + "3.75" + ], + "split": "train" + }, + { + "Input": "a sum of money lent out at s . i . amounts to rs . 720 after 2 years and to rs . 1020 after a further period of 5 years . the sum is ?", + "Output Program": [ + "n0 = 720.0\nn1 = 2.0\nn2 = 1020.0\nn3 = 5.0\nt0 = n2 - n0\nt1 = t0 / n3\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "600" + ], + "split": "train" + }, + { + "Input": "how many integers between 1000 and 10000 have no digits other than 4 , 5 or 6 ?", + "Output Program": [ + "n0 = 1000.0\nn1 = 10000.0\nn2 = 4.0\nn3 = 5.0\nn4 = 6.0\nt0 = n2 - 1.0\nt1 = t0 * t0\nanswer = t1 * t1\nprint(answer)" + ], + "Output Answer": [ + "81" + ], + "split": "train" + }, + { + "Input": "in kaya ' s teacher ' s desk there are 10 pink highlighters , 15 yellow highlighters , and 8 blue highlighters . how many highlighters are there in all ?", + "Output Program": [ + "n0 = 10.0\nn1 = 15.0\nn2 = 8.0\nt0 = n0 + n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "x , y , and z are consecutive numbers and x > y > z . also , 2 x + 3 y + 3 z = 5 y + 8 . what is the value of z ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 3.0\nn3 = 5.0\nn4 = 8.0\nt0 = 2.0 * 4.0\nt1 = 2.0 * 3.0\nt2 = t0 - t1\nt3 = n4 - t2\nanswer = t3 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "in the coordinate plane , points ( x , 6 ) and ( 10 , y ) are on line k . if line k passes through the origin and has slope 1 / 2 , then x * y =", + "Output Program": [ + "n0 = 6.0\nn1 = 10.0\nn2 = 1.0\nn3 = 2.0\nt0 = n0 / n3\nt1 = n1 * n3\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "a vessel of capacity 3 litre has 25 % of alcohol and another vessel of capacity 5 litre had 40 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?", + "Output Program": [ + "n0 = 3.0\nn1 = 25.0\nn2 = 5.0\nn3 = 40.0\nn4 = 8.0\nn5 = 10.0\nt0 = n1 / 100.0\nt1 = n3 / 100.0\nt2 = n0 * t0\nt3 = n2 * t1\nt4 = t2 + t3\nt5 = t4 / n5\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "27.500000000000004" + ], + "split": "train" + }, + { + "Input": "if x is 40 percent greater than 88 , then x =", + "Output Program": [ + "n0 = 40.0\nn1 = 88.0\nt0 = n0 / 100.0\nt1 = n1 * t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "123.2" + ], + "split": "train" + }, + { + "Input": "30 pens and 75 pencils were purchased for 630 . if the average price of a pencil was 2.00 , find the average price of a pen .", + "Output Program": [ + "n0 = 30.0\nn1 = 75.0\nn2 = 630.0\nn3 = 2.0\nt0 = n1 * n3\nt1 = n2 - t0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "if x + y = 280 , x - y = 200 , for integers of x and y , y = ?", + "Output Program": [ + "n0 = 280.0\nn1 = 200.0\nt0 = n0 + n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "240" + ], + "split": "train" + }, + { + "Input": "if $ 10 be allowed as true discount on a bill of $ 110 due at the end of a certain time , then the discount allowed on the same sum due at the end of double the time is :", + "Output Program": [ + "n0 = 10.0\nn1 = 110.0\nt0 = n0 + n1\nt1 = n0 * 2.0\nt2 = t1 / t0\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "18.333333333333332" + ], + "split": "train" + }, + { + "Input": "if you multiply two integers together and then add 4 , the result is 40 . which of the following could not be the sum of the two numbers ?", + "Output Program": [ + "n0 = 4.0\nn1 = 40.0\nt0 = n1 - n0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 45 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.5\nn2 = 45.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "65" + ], + "split": "train" + }, + { + "Input": "a cricketer makes a score of 134 runs in the 22 nd inning and thus increases his average by 3.5 . find his average after 22 nd inning .", + "Output Program": [ + "n0 = 134.0\nn1 = 22.0\nn2 = 3.5\nn3 = 22.0\nt0 = n1 * n2\nt1 = n0 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "60.5" + ], + "split": "train" + }, + { + "Input": "the average marks of a class of 25 students is 50 and that of another class of 40 students is 65 . find the average marks of all the students ?", + "Output Program": [ + "n0 = 25.0\nn1 = 50.0\nn2 = 40.0\nn3 = 65.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "59.23076923076923" + ], + "split": "train" + }, + { + "Input": "what least number must be subtracted from 12702 to get number exactly 99 ?", + "Output Program": [ + "import math\nn0 = 12702.0\nn1 = 99.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "if x is 20 percent greater than 40 , then x =", + "Output Program": [ + "n0 = 20.0\nn1 = 40.0\nt0 = n0 / 100.0\nt1 = n1 * t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "in a theater , the first row has 14 seats and each row has 2 more seats than previous row . if the last row has 56 seats , what is the total number of seats in the theater ?", + "Output Program": [ + "n0 = 14.0\nn1 = 2.0\nn2 = 56.0\nt0 = n0 + n2\nt1 = n2 - n0\nt2 = n1 + t1\nt3 = t0 / 2.0\nt4 = t2 / n1\nanswer = t3 * t4\nprint(answer)" + ], + "Output Answer": [ + "770" + ], + "split": "train" + }, + { + "Input": "a bag of potatoes weighs 12 lbs divided by half of its weight . how much does the bag of potatoes weight ?", + "Output Program": [ + "n0 = 12.0\n\nanswer = n0 / 1.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "the price of 80 apples is equal to that of 120 oranges . the price of 60 apples and 75 oranges together is rs . 1320 . the total price of 25 apples and 40 oranges is", + "Output Program": [ + "n0 = 80.0\nn1 = 120.0\nn2 = 60.0\nn3 = 75.0\nn4 = 1320.0\nn5 = 25.0\nn6 = 40.0\nt0 = n0 / n1\nt1 = n3 * t0\nt2 = n2 + t1\nt3 = n4 / t2\nt4 = n5 * t3\nt5 = t3 * t0\nt6 = n6 * t5\nanswer = t4 + t6\nprint(answer)" + ], + "Output Answer": [ + "620" + ], + "split": "train" + }, + { + "Input": "a scale 7 ft . 6 inches long is divided into 5 equal parts . find the length of each part .", + "Output Program": [ + "n0 = 7.0\nn1 = 6.0\nn2 = 5.0\nt0 = n0 * 12.0\nt1 = n1 + t0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "having received his weekly allowance , a student spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.60 at the candy store . what is this student \u2019 s weekly allowance ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 0.6\nt0 = n0 * n1\nt1 = n2 * t0\nanswer = t1 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "2.25" + ], + "split": "train" + }, + { + "Input": "there are 14 players in a chess group , and each player plays each of the others once . given that each game is played by two players , how many total games will be played ?", + "Output Program": [ + "n0 = 14.0\nt0 = n0 - 1.0\nt1 = n0 * t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "91" + ], + "split": "train" + }, + { + "Input": "10 years ago a was half of b in age . if the ratio of their present ages is 3 : 4 , what will be the total of their present ages", + "Output Program": [ + "n0 = 10.0\nn1 = 3.0\nn2 = 4.0\nt0 = n0 / 2.0\nt1 = n2 / 2.0\nt2 = n0 - t0\nt3 = n1 - t1\nt4 = t2 / t3\nt5 = n1 * t4\nt6 = n2 * t4\nanswer = t5 + t6\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "if a * b denotes the greatest common divisor of a and b , then ( ( 12 * 16 ) * ( 18 * 12 ) ) = ?", + "Output Program": [ + "n0 = 12.0\nn1 = 16.0\nn2 = 18.0\nn3 = 12.0\nt0 = n2 / 3.0\nanswer = t0 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "the average of runs of a cricket player of 10 innings was 36 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?", + "Output Program": [ + "n0 = 10.0\nn1 = 36.0\nn2 = 4.0\nt0 = n0 + 1.0\nt1 = n1 + n2\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "a girl was asked to multiply a certain number by 43 . she multiplied it by 34 and got his answer less than the correct one by 1206 . find the number to be multiplied .", + "Output Program": [ + "n0 = 43.0\nn1 = 34.0\nn2 = 1206.0\nt0 = n0 - n1\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "134" + ], + "split": "train" + }, + { + "Input": "3 math classes : x , y , and z , take an algebra test . the average score in class x is 83 . the average score in class y is 76 . the average score in class z is 85 . the average score of all students in classes x and y together is 79 . the average score of all students in classes y and z together is 81 . what is the average score for all the 3 classes , taken together ?", + "Output Program": [ + "n0 = 3.0\nn1 = 83.0\nn2 = 76.0\nn3 = 85.0\nn4 = 79.0\nn5 = 81.0\nn6 = 3.0\nt0 = n5 - n2\nt1 = n1 - n4\nt2 = n4 - n2\nt3 = t1 + t2\nt4 = n3 * t0\nt5 = n2 * t1\nt6 = n1 * t2\nt7 = t4 + t5\nt8 = t3 + t0\nt9 = t7 + t6\nanswer = t9 / t8\nprint(answer)" + ], + "Output Answer": [ + "81.5" + ], + "split": "train" + }, + { + "Input": "if r is the product of the integers from 1 to 30 , inclusive , what is the greatest integer k for which 3 ^ k is a factor of r ?", + "Output Program": [ + "n0 = 1.0\nn1 = 30.0\nn2 = 3.0\nt0 = n1 / 2.0\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "rs . 460 was divided among 41 boys and girls such that each boy rs . 12 and each girl got rs . 8 . what is the number of boys ?", + "Output Program": [ + "n0 = 460.0\nn1 = 41.0\nn2 = 12.0\nn3 = 8.0\nt0 = n1 * n3\nt1 = n0 - t0\nanswer = t1 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "find the total number of prime factors in the expression ( 4 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 2 .", + "Output Program": [ + "n0 = 4.0\nn1 = 11.0\nn2 = 7.0\nn3 = 5.0\nn4 = 11.0\nn5 = 2.0\nt0 = n1 * n5\nt1 = n3 + t0\nanswer = n5 + t1\nprint(answer)" + ], + "Output Answer": [ + "29" + ], + "split": "train" + }, + { + "Input": "what is the largest 4 digit number exactly divisible by 50 ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 50.0\nt0 = 10.0**min(n0, 5)\nt1 = t0 / n1\nt2 = math.floor(t1)\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "10000" + ], + "split": "train" + }, + { + "Input": "in a division sum , the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 2 to the thrice of the remainder . the dividend is", + "Output Program": [ + "n0 = 6.0\nn1 = 5.0\nn2 = 2.0\nt0 = n0 * 3.0\nt1 = n2 + t0\nt2 = t1 / n1\nt3 = t1 * t2\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "86" + ], + "split": "train" + }, + { + "Input": "a , b are positive integers . the remainder of a to be divided by 8 is 3 and the remainder of b to be divided by 6 is 5 . which is possible to be the remainder of a * b to be divided by 48", + "Output Program": [ + "n0 = 8.0\nn1 = 3.0\nn2 = 6.0\nn3 = 5.0\nn4 = 48.0\n\nanswer = n1 * n3\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "the revenue from sales items in 1996 increases by x percent , compared in 1995 and the revenue in 1997 decreases by x percent , compared in 1996 . if the revenue from sales items in 1997 decreases by 4 percent , compared in 1995 , what is the value of x ?", + "Output Program": [ + "import math\nn0 = 1996.0\nn1 = 1995.0\nn2 = 1997.0\nn3 = 1996.0\nn4 = 1997.0\nn5 = 4.0\nn6 = 1995.0\nt0 = n5 * 100.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "peter has $ 642986 in his savings account . what is the least amount of money ( in whole number of dollars ) that he must add to his account if he wants to split this money evenly among his 9 children ?", + "Output Program": [ + "n0 = 642986.0\nn1 = 9.0\nt0 = n1 / n1\nanswer = n0 + t0\nprint(answer)" + ], + "Output Answer": [ + "642987" + ], + "split": "train" + }, + { + "Input": "a car travels first 160 km at 75 km / hr and the next 160 km at 70 km / hr . what is the average speed for the first 320 km of the tour ?", + "Output Program": [ + "n0 = 160.0\nn1 = 75.0\nn2 = 160.0\nn3 = 70.0\nn4 = 320.0\nt0 = n0 / n1\nt1 = n0 / n3\nt2 = t0 + t1\nt3 = 1.0 / t2\nanswer = n4 * t3\nprint(answer)" + ], + "Output Answer": [ + "72.41379310344827" + ], + "split": "train" + }, + { + "Input": "if a - b = 2 and a 2 + b 2 = 25 , find the value of ab .", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 2.0\nn3 = 25.0\nt0 = n0**min(n1, 5)\nt1 = n3 - t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "10.5" + ], + "split": "train" + }, + { + "Input": "set # 1 = { a , b , o , d , e } set # 2 = { k , l , m , n , u , p } there are these two sets of letters , and you are going to pick exactly one letter from each set . what is the probability of picking at least one vowel ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nt0 = 2.0 + 3.0\nt1 = t0 + 1.0\nt2 = 2.0 / t0\nt3 = t0 / t1\nt4 = t2 * t3\nanswer = n0 - t4\nprint(answer)" + ], + "Output Answer": [ + "0.6666666666666666" + ], + "split": "train" + }, + { + "Input": "the value of x + ( xx ) when x = 3 is :", + "Output Program": [ + "n0 = 3.0\nt0 = n0 * n0\nanswer = n0 + t0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "roy is now 6 years older than julia and half of that amount older than kelly . if in 2 years , roy will be twice as old as julia , then in 2 years what would be roy \u2019 s age multiplied by kelly \u2019 s age ?", + "Output Program": [ + "n0 = 6.0\nn1 = 2.0\nn2 = 2.0\nt0 = n0 / 2.0\nt1 = n0 - n1\nt2 = n0 + t1\nt3 = n1 + t2\nt4 = t2 - t0\nt5 = n1 + t4\nanswer = t3 * t5\nprint(answer)" + ], + "Output Answer": [ + "108" + ], + "split": "train" + }, + { + "Input": "if x is equal to the sum of the integers from 30 to 40 , inclusive , and y is the number of even integers from 30 to 40 , inclusive , what is the value of x + y ?", + "Output Program": [ + "n0 = 30.0\nn1 = 40.0\nn2 = 30.0\nn3 = 40.0\nt0 = n0 + n1\nt1 = n1 - n0\nt2 = t1 + 1.0\nt3 = t1 / 2.0\nt4 = t0 / 2.0\nt5 = t3 + 1.0\nt6 = t2 * t4\nanswer = t5 + t6\nprint(answer)" + ], + "Output Answer": [ + "391" + ], + "split": "train" + }, + { + "Input": "the average age of a , b and c is 27 years . if the average age of a and c is 29 years , what is the age of b in years ?", + "Output Program": [ + "n0 = 27.0\nn1 = 29.0\nt0 = n0 * 3.0\nt1 = n1 * 2.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "for every x , the action [ x ] is defined : [ x ] is the greatest integer less than or equal to x . what is the value of [ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 6.0 ?", + "Output Program": [ + "n0 = 6.5\nn1 = 2.0\nn2 = 3.0\nn3 = 2.0\nn4 = 7.2\nn5 = 8.4\nn6 = 6.0\nt0 = 4.0 / 10.0\nt1 = n1 * n4\nt2 = n5 - t0\nt3 = t1 + t2\nanswer = t3 - n6\nprint(answer)" + ], + "Output Answer": [ + "16.4" + ], + "split": "train" + }, + { + "Input": "a parking garage rents parking spaces for $ 10 per week or $ 42 per month . how much does a person save in a year by renting by the month rather than by the week ?", + "Output Program": [ + "n0 = 10.0\nn1 = 42.0\nt0 = 2.0 + 3.0\nt1 = n1 * 12.0\nt2 = t0 * n0\nt3 = t2 + 2.0\nt4 = n0 * t3\nanswer = t4 - t1\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "what is the least number which when divided by 8 , 12 , 15 and 20 leaves in each case a remainder of 5", + "Output Program": [ + "import scipy\nn0 = 8.0\nn1 = 12.0\nn2 = 15.0\nn3 = 20.0\nn4 = 5.0\nt0 = scipy.lcm(int(n0), int(n1))\nt1 = scipy.lcm(int(n2), int(n3))\nt2 = scipy.lcm(int(t0), int(t1))\nanswer = n4 + t2\nprint(answer)" + ], + "Output Answer": [ + "125" + ], + "split": "train" + }, + { + "Input": "if xy = 4 , x / y = 81 , for positive numbers x and y , y = ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 81.0\nt0 = n0 / n1\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "0.2222222222222222" + ], + "split": "train" + }, + { + "Input": "maximun number of identical pieces ( of same size ) of a cake by making only 3 cuts ?", + "Output Program": [ + "n0 = 3.0\nt0 = 1.0 + 4.0\nt1 = n0 * 2.0\nt2 = n0**min(3.0, 5)\nt3 = 1 / t1\nt4 = n0 * t0\nt5 = t4 + t2\nt6 = t5 + t1\nanswer = t6 * t3\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "the average of runs of a cricket player of 10 innings was 15 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?", + "Output Program": [ + "n0 = 10.0\nn1 = 15.0\nn2 = 4.0\nt0 = n0 + 1.0\nt1 = n1 + n2\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "59" + ], + "split": "train" + }, + { + "Input": "the total age of a and b is 15 years more than the total age of b and c . c is how many years younger than a ?", + "Output Program": [ + "n0 = 15.0\n\nanswer = n0 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "mother , her daughter and her grand child weighs 160 kg . daughter and her daughter ( child ) weighs 60 kg . child is 1 / 5 th of her grand mother . what is the age of the daughter ?", + "Output Program": [ + "n0 = 160.0\nn1 = 60.0\nn2 = 1.0\nn3 = 5.0\nt0 = n0 - n1\nt1 = t0 / n3\nanswer = n1 - t1\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "a batsman makes a score of 100 runs in the 17 th inning and thus increases his averages by 5 . what is his average after 17 th inning ?", + "Output Program": [ + "n0 = 100.0\nn1 = 17.0\nn2 = 5.0\nn3 = 17.0\nt0 = n1 * n2\nt1 = n0 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "john want to buy a $ 100 trouser at the store , but he think it \u2019 s too expensive . finally , it goes on sale for $ 60 . what is the percent decrease ?", + "Output Program": [ + "n0 = 100.0\nn1 = 60.0\n\nanswer = n0 - n1\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "if rs . 561 be divided among a , b , c in such a way that a gets 2 / 3 of what b gets and b gets 1 / 4 of what c gets , then their shares are respectively ?", + "Output Program": [ + "n0 = 561.0\nn1 = 2.0\nn2 = 3.0\nn3 = 1.0\nn4 = 4.0\nt0 = n3 / n4\nt1 = n1 / n2\nt2 = t1 * t0\nt3 = t0 + t2\nt4 = t3 + n3\nanswer = n0 / t4\nprint(answer)" + ], + "Output Answer": [ + "396.00000000000006" + ], + "split": "train" + }, + { + "Input": "total of the ages of a , b ahd c at present is 90 years . 10 years ago , the ratio of their ages was 1 : 2 : 3 . what is the age of b at present", + "Output Program": [ + "n0 = 90.0\nn1 = 10.0\nn2 = 1.0\nn3 = 2.0\nn4 = 3.0\nt0 = n1 + n1\nt1 = n3 + n4\nt2 = n1 + t0\nt3 = n2 + t1\nt4 = n0 - t2\nt5 = t4 / t3\nt6 = n3 * t5\nanswer = t5 + t6\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "a cube with its sides numbered 1 through 6 is rolled twice , first landing on a and then landing on b . if any roll of the cube yields an equal chance of landing on any of the numbers 1 through 6 , what is the probability e that a + b is prime ?", + "Output Program": [ + "n0 = 1.0\nn1 = 6.0\nn2 = 1.0\nn3 = 6.0\nt0 = 12.0 + 3.0\nt1 = n0 / n1\nt2 = t1**min(2.0, 5)\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "0.41666666666666663" + ], + "split": "train" + }, + { + "Input": "replace x with the appropriate number in 4 , 5 , 14 , 15 , 24 , 25 , x", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 14.0\nn3 = 15.0\nn4 = 24.0\nn5 = 25.0\nt0 = n2 - n1\nanswer = n5 + t0\nprint(answer)" + ], + "Output Answer": [ + "34" + ], + "split": "train" + }, + { + "Input": "if bill can buy 3 pairs of jeans and 2 shirts for $ 69 or 2 pairs of jeans and 3 shirts for $ 71 , how much does one shirt cost ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 69.0\nn3 = 2.0\nn4 = 3.0\nn5 = 71.0\nt0 = n0 * n5\nt1 = n1 * n2\nt2 = n0 * n0\nt3 = n1 * n1\nt4 = t0 - t1\nt5 = t2 - t3\nanswer = t4 / t5\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "3 friends a , b , c went for week end party to mcdonald \u2019 s restaurant and there they measure there weights in some order in 7 rounds . a , b , c , ab , bc , ac , abc . final round measure is 165 kg then find the average weight of all the 7 rounds ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 165.0\nn3 = 7.0\nt0 = 1.0 + n0\nt1 = n2 * t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "94.28571428571429" + ], + "split": "train" + }, + { + "Input": "lisa and robert have taken the same number of photos on their school trip . lisa has taken 3 times as many photos as claire and robert has taken 20 more photos than claire . how many photos has claire taken ?", + "Output Program": [ + "n0 = 3.0\nn1 = 20.0\nt0 = n0 - 1.0\nanswer = n1 / t0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "an object thrown directly upward is at a height of h feet after t seconds , where h = - 14 ( t - 3 ) ^ 2 + 140 . at what height , in feet , is the object 2 seconds after it reaches its maximum height ?", + "Output Program": [ + "n0 = 14.0\nn1 = 3.0\nn2 = 2.0\nn3 = 140.0\nn4 = 2.0\nt0 = n1 + n2\nt1 = -n0\nt2 = t0 - n1\nt3 = t2**min(n2, 5)\nt4 = t1 * t3\nanswer = n3 + t4\nprint(answer)" + ], + "Output Answer": [ + "84" + ], + "split": "train" + }, + { + "Input": "rani bought more apples than oranges . she sells apples at \u20b9 23 apiece and makes 15 % profit . she sells oranges at \u20b9 10 apiece and makes 25 % profit . if she gets \u20b9 653 after selling all the apples and oranges , find her profit percentage x .", + "Output Program": [ + "n0 = 23.0\nn1 = 15.0\nn2 = 10.0\nn3 = 25.0\nn4 = 653.0\nt0 = n1 + 2.0\nt1 = n3 / 100.0\nt2 = n2 * 2.0\nt3 = t2 + 1.0\nt4 = t1 + 1.0\nt5 = n2 / t4\nt6 = t3 * t2\nt7 = t0 * t5\nt8 = t6 + t7\nt9 = n4 - t8\nt10 = t9 / t8\nanswer = t10 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "17.446043165467625" + ], + "split": "train" + }, + { + "Input": "there are 7 thieves . they stole diamonds from a diamond merchant and ran away . while running , night sets in and they decide to rest in the jungle . when everybody was sleeping , two of them woke up and decided to divide the diamonds equally among themselves . but when they divided the diamonds equally , one diamond is left . so they woke up the 3 rd thief and tried to divide the diamonds equally again but still one diamond was left . then they woke up the 4 th thief to divide the diamonds equally again , and again one diamond was left . this happened with the 5 th and 6 th thief \u2013 one diamond was still left . finally , they woke up the 7 th thief and this time the diamonds were divided equally . how many diamonds did they steal in total ?", + "Output Program": [ + "n0 = 7.0\nn1 = 3.0\nn2 = 4.0\nn3 = 5.0\nn4 = 6.0\nn5 = 7.0\nt0 = n0 + n1\nt1 = n2 * n3\nt2 = t0 * t1\nt3 = t2 + t1\nt4 = n1 + t3\nanswer = n0 * t4\nprint(answer)" + ], + "Output Answer": [ + "1561" + ], + "split": "train" + }, + { + "Input": "in a race where 15 cars are running , the chance that car x will win is 1 / 4 , that y will win is 1 / 8 and that z will win is 1 / 12 . assuming that a dead heat is impossible , find the chance that one of them will win .", + "Output Program": [ + "n0 = 15.0\nn1 = 1.0\nn2 = 4.0\nn3 = 1.0\nn4 = 8.0\nn5 = 1.0\nn6 = 12.0\nt0 = n1 / n2\nt1 = n1 / n4\nt2 = n1 / n6\nt3 = t0 + t1\nanswer = t3 + t2\nprint(answer)" + ], + "Output Answer": [ + "0.4583333333333333" + ], + "split": "train" + }, + { + "Input": "to be considered for \u201c movie of the year , \u201d a film must appear in at least 1 / 4 of the top - 10 - movies lists submitted by the cinematic academy \u2019 s 770 members . what is the smallest number of top - 10 lists a film can appear on and still be considered for \u201c movie of the year \u201d ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 10.0\nn3 = 770.0\nn4 = 10.0\n\nanswer = n3 / n1\nprint(answer)" + ], + "Output Answer": [ + "192.5" + ], + "split": "train" + }, + { + "Input": "suraj has a certain average of runs for 9 innings . in the 10 th innings he scores 200 runs thereby increasing his average by 8 runs . what is his average after the 10 th innings ?", + "Output Program": [ + "n0 = 9.0\nn1 = 10.0\nn2 = 200.0\nn3 = 8.0\nn4 = 10.0\nt0 = n0 * n3\nt1 = n1 - n0\nt2 = n2 - t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "128" + ], + "split": "train" + }, + { + "Input": "if n divided by 7 has a remainder of 1 , what is the remainder when 3 times n is divided by 7 ?", + "Output Program": [ + "n0 = 7.0\nn1 = 1.0\nn2 = 3.0\nn3 = 7.0\n\nanswer = n1 * n2\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "in a house , there are 4 birds , 3 dogs , and 18 cats living with the human family . if the total number of feet in the house are 74 more than the number of heads in the house , how many family members are there ?", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 18.0\nn3 = 74.0\nt0 = n2 / n1\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "the h . c . f . of two numbers is 12 and their difference is 12 . the numbers are", + "Output Program": [ + "n0 = 12.0\nn1 = 12.0\nt0 = 3.0 + 4.0\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "84" + ], + "split": "train" + }, + { + "Input": "if the sum of the 4 th term and the 12 th term of an arithmetic progression is 10 , what is the sum of the first 15 terms of the progression ?", + "Output Program": [ + "n0 = 4.0\nn1 = 12.0\nn2 = 10.0\nn3 = 15.0\nt0 = n3 / 2.0\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "one ton has 2500 pounds , and one pound has 16 ounces . how many packets containing wheat weighing 16 pounds and 4 ounces each would totally fill a gunny bag of capacity 13 tons ?", + "Output Program": [ + "n0 = 2500.0\nn1 = 16.0\nn2 = 16.0\nn3 = 4.0\nn4 = 13.0\nt0 = n0 * n4\nt1 = n1 * n1\nt2 = n3 + t1\nt3 = n1 * t0\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "2000" + ], + "split": "train" + }, + { + "Input": "in an examination , there were 2,000 candidates , out of which 900 candidates were girls and rest were boys . if 28 % of the boys and 32 % of the girls passed , then the total percentage of failed candidates is ?", + "Output Program": [ + "n0 = 2000.0\nn1 = 900.0\nn2 = 28.0\nn3 = 32.0\nt0 = n1 * n3\nt1 = n0 - n1\nt2 = t0 / 100.0\nt3 = n2 * t1\nt4 = t3 / 100.0\nt5 = t2 + t4\nt6 = n0 - t5\nt7 = t6 / n0\nanswer = t7 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "70.19999999999999" + ], + "split": "train" + }, + { + "Input": "a , b and c are employed to do apiece of work for rs . 529 . a and c are supposed to finish 19 / 23 of the work together . how much shall be paid to b ?", + "Output Program": [ + "n0 = 529.0\nn1 = 19.0\nn2 = 23.0\nt0 = 4.0 + 4.0\nt1 = n1 / n2\nt2 = n0 * t1\nt3 = n0 - t2\nt4 = t3 + 4.0\nanswer = t4 / t0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "find the value of ( 28 + 48 / 69 ) \u00d7 69", + "Output Program": [ + "n0 = 28.0\nn1 = 48.0\nn2 = 69.0\nn3 = 69.0\nt0 = n1 / n2\nt1 = n0 + t0\nanswer = t1 * n2\nprint(answer)" + ], + "Output Answer": [ + "1980" + ], + "split": "train" + }, + { + "Input": "if jake loses 32 pounds , he will weigh twice as much as his sister . together they now weigh 212 pounds . what is jake \u2019 s present weight , in pounds ?", + "Output Program": [ + "n0 = 32.0\nn1 = 212.0\nt0 = n1 - n0\nt1 = t0 / 3.0\nt2 = t1 * 2.0\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "152" + ], + "split": "train" + }, + { + "Input": "there are 36 students in a certain geometry class . if one third of the students are boys and one fourth of the boys are under 6 feet tall , how many boys in the class are under 6 feet tall ?", + "Output Program": [ + "n0 = 36.0\nn1 = 6.0\nn2 = 6.0\nt0 = n0 / 3.0\nanswer = t0 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "a cricketer scored 138 runs which included 12 boundaries and 2 sixes . what percent of his total score did he make by running between the wickets .", + "Output Program": [ + "n0 = 138.0\nn1 = 12.0\nn2 = 2.0\nt0 = n1 * 4.0\nt1 = 2.0 * 3.0\nt2 = n2 * t1\nt3 = t0 + t2\nt4 = n0 - t3\nt5 = t4 / n0\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "56.52173913043478" + ], + "split": "train" + }, + { + "Input": "if taxi fares were $ 8.00 for the first 1 / 5 mile and $ 0.8 for each 1 / 5 mile there after , then the taxi fare for a 8 - mile ride was", + "Output Program": [ + "n0 = 8.0\nn1 = 1.0\nn2 = 5.0\nn3 = 0.8\nn4 = 1.0\nn5 = 5.0\nn6 = 8.0\nt0 = n1 / n2\nt1 = n0 / t0\nt2 = t1 - 1.0\nt3 = n3 * t2\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "39.2" + ], + "split": "train" + }, + { + "Input": "in a graduating class , the difference between the highest and lowest salaries is $ 100000 . the median salary is $ 50000 higher than the lowest salary and the average salary is $ 20000 higher than the median . what is the minimum number of students t in the class ?", + "Output Program": [ + "n0 = 100000.0\nn1 = 50000.0\nn2 = 20000.0\nt0 = n0 / n2\nt1 = n1 / n2\nt2 = t1 * 3.0\nt3 = t0 + t2\nanswer = t3 + t1\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "mike took a taxi to the airport and paid $ 2.50 to start plus $ 0.25 per mile . annie took a different route to the airport and paid $ 2.50 plus $ 5.00 in bridge toll fees plus $ 0.25 per mile . if each was charged exactly the same amount , and annie ' s ride was 22 miles , how many miles was mike ' s ride ?", + "Output Program": [ + "n0 = 2.5\nn1 = 0.25\nn2 = 2.5\nn3 = 5.0\nn4 = 0.25\nn5 = 22.0\nt0 = n0 + n3\nt1 = n1 * n5\nt2 = t0 + t1\nt3 = t2 - n0\nanswer = t3 / n1\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "a computer is programmed to multiply consecutive even integers 2 * 4 * 6 * 8 * \u2026 * n until the product is divisible by 1551 , what is the value of n ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 6.0\nn3 = 8.0\nn4 = 1551.0\nt0 = 1.0 + 10.0\nt1 = n4 / t0\nt2 = t1 / 3.0\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "94" + ], + "split": "train" + }, + { + "Input": "if 70 % of ( x - y ) = 30 % of ( x + y ) then what percent of x is y ?", + "Output Program": [ + "n0 = 70.0\nn1 = 30.0\nt0 = n0 + n1\nt1 = n0 - n1\nt2 = t1 / t0\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "a man spends 1 / 3 rd of his salary on food . he spends 1 / 4 th on rent and 1 / 5 th on cloths . if he is left with 1760 , then who much salary does he earn .", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 4.0\nn4 = 1.0\nn5 = 5.0\nn6 = 1760.0\nt0 = n0 / n1\nt1 = n0 / n3\nt2 = n0 / n5\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n0 - t4\nanswer = n6 / t5\nprint(answer)" + ], + "Output Answer": [ + "8123.076923076918" + ], + "split": "train" + }, + { + "Input": "a man engaged a servant on the condition that he would pay him rs . 600 and a uniform after one year service . he served only for 9 months and received uniform and rs . 400 , find the price of the uniform ?", + "Output Program": [ + "n0 = 600.0\nn1 = 9.0\nn2 = 400.0\nt0 = n0 * n1\nt1 = 3.0 * 4.0\nt2 = n2 * t1\nt3 = t1 * 1.0\nt4 = t0 - t2\nt5 = t4 / t3\nanswer = t5 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "train" + }, + { + "Input": "find the value of y from ( 12 ) ^ 1 x 6 ^ 4 \u00f7 432 = y ?", + "Output Program": [ + "n0 = 12.0\nn1 = 1.0\nn2 = 6.0\nn3 = 4.0\nn4 = 432.0\nt0 = n0**min(n1, 5)\nt1 = n2**min(n3, 5)\nt2 = t0 * t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "if 1 / 8 of a pencil is black , 1 / 2 of the remaining is white and the remaining 3 1 / 2 cm is blue , find the total length of the pencil .", + "Output Program": [ + "n0 = 1.0\nn1 = 8.0\nn2 = 1.0\nn3 = 2.0\nn4 = 3.0\nn5 = 1.0\nn6 = 2.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "marcella has 25 pairs of shoes . if she loses 9 individual shoes , what is the greatest number of matching pairs she could have left ?", + "Output Program": [ + "import math\nn0 = 25.0\nn1 = 9.0\nt0 = n1 / 2.0\nt1 = math.floor(t0)\nt2 = t1 + 1.0\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "a fruit drink is made of orange , watermelon , and grape juice , where 25 percent of the drink is orange juice and 40 percent is watermelon juice . if the drink is made with 70 ounces of grape juice , how many ounces is the drink total ?", + "Output Program": [ + "n0 = 25.0\nn1 = 40.0\nn2 = 70.0\nt0 = n0 + n1\nt1 = n0 * n2\nt2 = n1 * n2\nt3 = 100.0 - t0\nt4 = t1 / t3\nt5 = t2 / t3\nt6 = n2 + t4\nanswer = t6 + t5\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "train" + }, + { + "Input": "the wages earned by robin is 30 % more than that earned by erica . the wages earned by charles is 60 % more than that earned by erica . how much percent is the wages earned by charles more than that earned by robin ?", + "Output Program": [ + "n0 = 30.0\nn1 = 60.0\nt0 = n1 + 100.0\nt1 = n0 + 100.0\nt2 = t0 - t1\nt3 = t2 / t1\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "23.076923076923077" + ], + "split": "train" + }, + { + "Input": "the sum of ages of 5 children born at the intervals of 3 years each is 60 years . what is the age of the youngest child ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nn2 = 60.0\nt0 = n2 / n0\nt1 = t0 - n1\nanswer = t1 - n1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "a 100 - litre mixture of milk and water contains 36 litres of milk . ' x ' litres of this mixture is removed and replaced with an equal quantum of water . if the process is repeated once , then the concentration of the milk stands reduced at 9 % . what is the value of x ?", + "Output Program": [ + "import math\nn0 = 100.0\nn1 = 36.0\nn2 = 9.0\nt0 = n2 / n1\nt1 = math.sqrt(max(0, t0))\nt2 = 1.0 - t1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "the average monthly salary of 20 employees in an organisation is rs . 1500 . if the manager ' s salary is added , then the average salary increases by rs . 150 . what is the manager ' s monthly salary ?", + "Output Program": [ + "n0 = 20.0\nn1 = 1500.0\nn2 = 150.0\nt0 = n1 + n2\nt1 = n0 + 1.0\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "4650" + ], + "split": "train" + }, + { + "Input": "a camera lens filter kit containing 5 filters sells for $ 75.50 . if the filters are purchased individually , 3 of them are priced at $ 7.35 each , 3 at $ 12.05 each , 1 at $ 12.50 . the amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually ?", + "Output Program": [ + "n0 = 5.0\nn1 = 75.5\nn2 = 3.0\nn3 = 7.35\nn4 = 3.0\nn5 = 12.05\nn6 = 1.0\nn7 = 12.5\nn8 = 5.0\nt0 = n2 * n3\nt1 = n2 * n5\nt2 = t0 + t1\nt3 = n7 + t2\nt4 = n1 - t3\nt5 = t4 * 100.0\nanswer = t5 / n1\nprint(answer)" + ], + "Output Answer": [ + "6.357615894039731" + ], + "split": "train" + }, + { + "Input": "if a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20 , what is the probability e that this product will be a multiple of 45 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 20.0\nn2 = 45.0\nt0 = n1 + 4.0\nanswer = 1.0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.041666666666666664" + ], + "split": "train" + }, + { + "Input": "find the lowest common multiple of 24 , 36 and 40 .", + "Output Program": [ + "import scipy\nn0 = 24.0\nn1 = 36.0\nn2 = 40.0\nt0 = scipy.lcm(int(n0), int(n1))\nanswer = scipy.lcm(int(n2), int(t0))\nprint(answer)" + ], + "Output Answer": [ + "360" + ], + "split": "train" + }, + { + "Input": "among the members of the malmo family , there are 3 times as many members who do not wear glasses as members who do . half of the malmo family members have blue eyes , and 4 / 5 of the family members who have blue eyes do not wear glasses . what percent of the malmo family members wear glasses and do not have blue eyes ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 5.0\nt0 = n0 / n2\nt1 = t0 / n1\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "a theater charges $ 12 for seats in the orchestra and $ 8 for seats in the balcony . on a certain night , a total of 360 tickets were sold for a total cost of $ 3,320 . how many more tickets were sold that night for seats in the balcony than for seats in the orchestra ?", + "Output Program": [ + "n0 = 12.0\nn1 = 8.0\nn2 = 360.0\nn3 = 3320.0\nt0 = n0 * n2\nt1 = 1000.0 * 3.0\nt2 = 100.0 * 3.0\nt3 = 10.0 * 2.0\nt4 = n0 - n1\nt5 = t1 + t2\nt6 = t5 + t3\nt7 = t0 - t6\nt8 = t7 / t4\nt9 = n2 - t8\nanswer = t8 - t9\nprint(answer)" + ], + "Output Answer": [ + "140" + ], + "split": "train" + }, + { + "Input": "tough and tricky questions : arithmetic . ( 56 ^ 2 + 56 ^ 2 ) / 28 ^ 2 =", + "Output Program": [ + "n0 = 56.0\nn1 = 2.0\nn2 = 56.0\nn3 = 2.0\nn4 = 28.0\nn5 = 2.0\nt0 = n0**min(n1, 5)\nt1 = n4**min(n1, 5)\nt2 = t0 + t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a boy has rs . 480 in the denominations of one - rupee notes , 5 - rupee notes and 10 - rupee notes . the number of notes of each denomination is equal . what is the total number of notes that he has ?", + "Output Program": [ + "n0 = 480.0\nn1 = 5.0\nn2 = 10.0\nt0 = 4.0 * 4.0\nt1 = n0 / t0\nanswer = t1 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "the output of a factory was increased by 10 % to keep up with rising demand . to handle the holiday rush , this new output was increased by 20 % . by approximately what percent would the output now have to be decreased in order to restore the original output ?", + "Output Program": [ + "n0 = 10.0\nn1 = 20.0\nt0 = n0 + 100.0\nt1 = n1 / 100.0\nt2 = t0 * t1\nt3 = t0 + t2\nt4 = t3 - 100.0\nt5 = t4 * 100.0\nanswer = t5 / t3\nprint(answer)" + ], + "Output Answer": [ + "24.242424242424242" + ], + "split": "train" + }, + { + "Input": "integer d is the product of the integers a , b , and c and 1 < a < b < c . if the remainder when 233 is divided by d is 79 , what is the value of a + c ?", + "Output Program": [ + "n0 = 1.0\nn1 = 233.0\nn2 = 79.0\nt0 = 3.0 + 4.0\nt1 = n1 - n2\nt2 = t1 / 2.0\nt3 = t2 / t0\nanswer = t3 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "each of the 20 boxes in a certain shipment weighs either 10 pounds or 20 pounds , and the average ( arithmetic mean ) weight of the boxes in the shipment is 18 pounds . if the average weight of the boxes in the shipment is to be reduced to 15 pounds by removing some of the 20 - pound boxes , how many 20 - pound boxes must be removed ?", + "Output Program": [ + "n0 = 20.0\nn1 = 10.0\nn2 = 20.0\nn3 = 18.0\nn4 = 15.0\nn5 = 20.0\nn6 = 20.0\nt0 = n0 * n2\nt1 = n0 * n3\nt2 = n0 * n4\nt3 = n2 - n1\nt4 = n2 - n4\nt5 = t0 - t1\nt6 = t5 / t3\nt7 = n1 * t6\nt8 = n0 - t6\nt9 = n2 * t8\nt10 = t7 + t9\nt11 = t10 - t2\nanswer = t11 / t4\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "country x taxes each of its citizens an amount equal to 14 percent of the first $ 40,000 of income , plus 20 percent of all income in excess of $ 40,000 . if a citizen of country x is taxed a total of $ 8,000 , what is her income ?", + "Output Program": [ + "n0 = 14.0\nn1 = 40000.0\nn2 = 20.0\nn3 = 40000.0\nn4 = 8000.0\nt0 = n0 / 100.0\nt1 = n2 / 100.0\nt2 = 2.0 * 4.0\nt3 = 10.0 * 4.0\nt4 = t2 * 1000.0\nt5 = t3 * 1000.0\nt6 = t0 * t5\nt7 = t4 - t6\nt8 = t7 / t1\nanswer = t8 + t5\nprint(answer)" + ], + "Output Answer": [ + "51999.99999999999" + ], + "split": "train" + }, + { + "Input": "a tank holds x gallons of a saltwater solution that is 20 % salt by volume . one fourth of the water is evaporated , leaving all of the salt . when 8 gallons of water and 16 gallons of salt are added , the resulting mixture is 33 1 / 3 % salt by volume . what is the value of x ?", + "Output Program": [ + "n0 = 20.0\nn1 = 8.0\nn2 = 16.0\nn3 = 33.0\nn4 = 1.0\nn5 = 3.0\nt0 = n0 / 100.0\nt1 = n4 / 4.0\nt2 = n2 * 2.0\nt3 = t0 * 2.0\nt4 = t2 - n1\nt5 = n4 - t0\nt6 = t1 * t5\nt7 = t5 - t6\nt8 = t7 - t3\nanswer = t4 / t8\nprint(answer)" + ], + "Output Answer": [ + "119.99999999999996" + ], + "split": "train" + }, + { + "Input": "subtracting 6 % of a from a is equivalent to multiplying a by how much ?", + "Output Program": [ + "n0 = 6.0\nt0 = 100.0 - n0\nanswer = t0 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "0.94" + ], + "split": "train" + }, + { + "Input": "the visitors of a modern art museum who watched a certain picasso painting were asked to fill in a short questionnaire indicating whether they had enjoyed looking at the picture and whether they felt they had understood it . according to the results of the survey , all 140 visitors who did not enjoy the painting also did not feel they had understood the painting , and the number of visitors who enjoyed the painting was equal to the number of visitors who felt they had understood the painting . if 3 / 4 of the visitors who answered the questionnaire both enjoyed the painting and felt they had understood the painting , then how many visitors answered the questionnaire ?", + "Output Program": [ + "n0 = 140.0\nn1 = 3.0\nn2 = 4.0\nt0 = n1 / n2\nt1 = 1.0 - t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "560" + ], + "split": "train" + }, + { + "Input": "the average monthly salary of 8 workers and one supervisor in a factory was 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . whenthesupervisor , whosesalarywas 430 . when the supervisor , whose salary was 870 per month , retired , a new person was appointed and then the average salary of 9 people was $ $ 430 per month . the salary of the new supervisor is :", + "Output Program": [ + "n0 = 8.0\nn1 = 430.0\nn2 = 430.0\nn3 = 430.0\nn4 = 430.0\nn5 = 870.0\nn6 = 9.0\nn7 = 430.0\nt0 = n6 * n7\nt1 = n1 * n6\nt2 = t1 - n5\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "870" + ], + "split": "train" + }, + { + "Input": "3 men and 2 women are lined up in a row . what is the number of cases where they stand with each other in turn ? ( the number of cases in which men ( or women ) do not stand next to each other )", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 2.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(n1)))\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "a prize of $ 600 is to be distributed among 15 winners , each of whom must be awarded at least $ 15 . if 2 / 5 of the prize will be distributed to 3 / 5 of the winners , what is the greatest possible individual award ?", + "Output Program": [ + "n0 = 600.0\nn1 = 15.0\nn2 = 15.0\nn3 = 2.0\nn4 = 5.0\nn5 = 3.0\nn6 = 5.0\nt0 = n0 * n3\nt1 = n1 * n5\nt2 = t0 / n4\nt3 = t1 / n4\nt4 = n0 - t2\nt5 = n1 - t3\nt6 = t5 - 1.0\nt7 = n1 * t6\nanswer = t4 - t7\nprint(answer)" + ], + "Output Answer": [ + "285" + ], + "split": "train" + }, + { + "Input": "evaluate ( 51 + 52 + 53 + . . . + 100 )", + "Output Program": [ + "n0 = 51.0\nn1 = 52.0\nn2 = 53.0\nn3 = 100.0\nt0 = n0 + n3\nt1 = n0 - 1.0\nt2 = t0 / 2.0\nanswer = t2 * t1\nprint(answer)" + ], + "Output Answer": [ + "3775" + ], + "split": "train" + }, + { + "Input": "in an examination , 34 % of total students failed in hindi , 44 % failed in english and 22 % in both . the percentage of these who passed in both the subjects is :", + "Output Program": [ + "n0 = 34.0\nn1 = 44.0\nn2 = 22.0\nt0 = n0 + n1\nt1 = t0 - n2\nanswer = 100.0 - t1\nprint(answer)" + ], + "Output Answer": [ + "44" + ], + "split": "train" + }, + { + "Input": "in 1990 the budgets for projects q and v were $ 540,000 and $ 780,000 , respectively . in each of the next 10 years , the budget for q was increased by $ 30,000 and the budget for v was decreased by $ 10,000 . in which year was the budget for q equal to the budget for v ?", + "Output Program": [ + "n0 = 1990.0\nn1 = 540000.0\nn2 = 780000.0\nn3 = 10.0\nn4 = 30000.0\nn5 = 10000.0\n\nanswer = n0 + 4.0\nprint(answer)" + ], + "Output Answer": [ + "1994" + ], + "split": "train" + }, + { + "Input": "of all the students in a certain dormitory , 1 / 2 are first - year students and the rest are second - year students . if 4 / 5 of the first - year students have not declared a major and if the fraction of second - year students who have declared a major is 1 / 3 times the fraction of first - year students who have declared a major , what fraction of all the students in the dormitory are second - year students who have not declared a major ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 4.0\nn3 = 5.0\nn4 = 1.0\nn5 = 3.0\nt0 = n0 / n1\nt1 = n5 * 10.0\nt2 = 1.0 / t1\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "0.4666666666666667" + ], + "split": "train" + }, + { + "Input": "in a maths test , students were asked to find 5 / 16 of a certain number . one of the students by mistake found 5 / 6 th of that number and his answer was 250 more than the correct answer . find the number .", + "Output Program": [ + "n0 = 5.0\nn1 = 16.0\nn2 = 5.0\nn3 = 6.0\nn4 = 250.0\nt0 = n1 * n4\nt1 = n0 * n1\nt2 = n0 * n3\nt3 = n3 * t0\nt4 = t1 - t2\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "480" + ], + "split": "train" + }, + { + "Input": "if 2 ^ 5 , 3 ^ 3 , and 11 ^ 2 are all factors of the product of 936 and w where w is a positive integer , what is the smallest possible value of w ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 3.0\nn3 = 3.0\nn4 = 11.0\nn5 = 2.0\nn6 = 936.0\nt0 = n4 / n0\nt1 = n0**min(n0, 5)\nt2 = n2 * t1\nt3 = t0 * t2\nanswer = n0 * t3\nprint(answer)" + ], + "Output Answer": [ + "132" + ], + "split": "train" + }, + { + "Input": "xy = 1 then what is ( 4 ^ ( x + y ) ^ 2 ) / ( 4 ^ ( x - y ) ^ 2 )", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 2.0\nn3 = 4.0\nn4 = 2.0\nt0 = n0 * 4.0\nanswer = n1**min(t0, 5)\nprint(answer)" + ], + "Output Answer": [ + "256" + ], + "split": "train" + }, + { + "Input": "if x is a positive integer with fewer than 3 digits , what is the probability r that x * ( x + 1 ) is a multiple of either 4 or 5 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 4.0\nn3 = 5.0\nt0 = 100.0 / n2\nt1 = 100.0 / n3\nt2 = 100.0 - n1\nt3 = t0 * 2.0\nt4 = t1 * 2.0\nt5 = t3 + t4\nt6 = t5 - n2\nanswer = t6 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.8686868686868687" + ], + "split": "train" + }, + { + "Input": "there are 12 pieces of radioactive metal a that look identical . 11 of the pieces give the same radiation count when measured , the 12 th piece is a counterfeit and gives a different radiation level , which may be more or less than the other 11 . we are given a radiation scale , which can take 2 sets of samples and compare their added up radiation levels to tell us if the sums are the same or if different , which set has the higher level of radiation . what is the minimum number of comparisons we need on this scale to identify the counterfeit sample and to also determine whether it has more or less radiation than the other samples ?", + "Output Program": [ + "n0 = 12.0\nn1 = 11.0\nn2 = 12.0\nn3 = 11.0\nn4 = 2.0\nt0 = n0 - n1\nanswer = n4 + t0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "a certain school implemented a reading program for its students , with the goal of getting each student to read 5 books per month year - round . if the school has c classes made up of s students in each class , how many books will the entire student body read in one year ?", + "Output Program": [ + "n0 = 5.0\n\nanswer = n0 * 12.0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "a father said his son , ` ` i was as old as you are at present at the time of your birth . ` ` if the father age is 44 now , the son age 5 years back was", + "Output Program": [ + "n0 = 44.0\nn1 = 5.0\nt0 = n0 / 2.0\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "a bowl of nuts is prepared for a party . brand p mixed nuts are 20 % almonds and brand q ' s deluxe nuts are 25 % almonds . if a bowl contains a total of 65 ounces of nuts , representing a mixture of both brands , and 15 ounces of the mixture are almonds , how many ounces of brand q ' s deluxe mixed nuts are used ?", + "Output Program": [ + "n0 = 20.0\nn1 = 25.0\nn2 = 65.0\nn3 = 15.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = n2 * t0\nt3 = t1 - t0\nt4 = n3 - t2\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "40.00000000000001" + ], + "split": "train" + }, + { + "Input": "if a number n is chosen at random from the set of two - digit integers whose digits are both prime numbers , what is the probability q that n is divisible by 3 ?", + "Output Program": [ + "n0 = 3.0\nt0 = n0 + 2.0\nt1 = 4.0 * 4.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.3125" + ], + "split": "train" + }, + { + "Input": "if 3 < x < 6 < y < 10 , then what is the greatest possible positive integer difference of x and y ?", + "Output Program": [ + "n0 = 3.0\nn1 = 6.0\nn2 = 10.0\nt0 = n2 - n0\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "the average monthly salary of 20 employees in an organisation is rs . 1500 . if the manager ' s salary is added , then the average salary increases by rs . 1000 . what is the manager ' s monthly salary ?", + "Output Program": [ + "n0 = 20.0\nn1 = 1500.0\nn2 = 1000.0\nt0 = n1 + n2\nt1 = n0 + 1.0\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "22500" + ], + "split": "train" + }, + { + "Input": "the average age of an adult class is 40 years . 12 new students with an avg age of 32 years join the class . therefore decreasing the average by 6 year . find what was the original average age of the class ?", + "Output Program": [ + "n0 = 40.0\nn1 = 12.0\nn2 = 32.0\nn3 = 6.0\nt0 = n1 * n2\nt1 = n0 - n3\nt2 = n1 * t1\nt3 = t2 - t0\nanswer = t3 / n3\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "the price of a consumer good increased by pp % during 20122012 and decreased by 1212 % during 20132013 . if no other change took place in the price of the good and the price of the good at the end of 20132013 was 1010 % higher than the price at the beginning of 20122012 , what was the value of pp ?", + "Output Program": [ + "n0 = 20122012.0\nn1 = 1212.0\nn2 = 20132013.0\nn3 = 20132013.0\nn4 = 1010.0\nn5 = 20122012.0\nt0 = 10.0 / 100.0\nt1 = 12.0 / 100.0\nt2 = t0 + 1.0\nt3 = 1.0 - t1\nt4 = t2 / t3\nt5 = t4 - 1.0\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "what is the unit digit in ( 4137 ) 754 ?", + "Output Program": [ + "n0 = 4137.0\nn1 = 754.0\nt0 = n0**min(2.0, 5)\nanswer = t0 % 10.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "a certain number of horses and an equal number of men are going somewhere . half of the owners are on their horses ' back while the remaining ones are walking along leading their horses . if the number of legs walking on the ground is 80 , how many horses are there ?", + "Output Program": [ + "n0 = 80.0\nt0 = 2.0 / 2.0\nt1 = t0 + 4.0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "54 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780 . the bigger part is :", + "Output Program": [ + "n0 = 54.0\nn1 = 10.0\nn2 = 22.0\nn3 = 780.0\nt0 = n0 * n1\nt1 = n2 - n1\nt2 = n3 - t0\nt3 = t2 / t1\nanswer = n0 - t3\nprint(answer)" + ], + "Output Answer": [ + "34" + ], + "split": "train" + }, + { + "Input": "all the students of class are told to sit in circle shape . here the boy at the 10 th position is exactly opposite to 45 th boy . total number of boys in the class ?", + "Output Program": [ + "n0 = 10.0\nn1 = 45.0\nt0 = n1 - n0\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "train" + }, + { + "Input": "how many integers between 2000 and 3000 that have distinct digits and increase from left to right ?", + "Output Program": [ + "import math\nn0 = 2000.0\nn1 = 3000.0\nt0 = n0 / 1000.0\nt1 = n1 / 1000.0\nt2 = math.factorial(min(15, int(t1)))\nt3 = t0 * t1\nt4 = math.factorial(min(15, int(t3)))\nt5 = t2 * t2\nanswer = t4 / t5\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "a no . when divided by 125 gives a remainder 40 , what remainder will be obtainedby dividingthe same no . 15 ?", + "Output Program": [ + "n0 = 125.0\nn1 = 40.0\nn2 = 15.0\nt0 = n0 + n1\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "a certain company has records stored with a record storage firm in 15 - inch by 12 - inch by 10 - inch boxes . the boxes occupy 1.08 million cubic inches of space . if the company pays $ 0.5 per box per month for the record storage , what is the total amount that the company pays each month for record storage ?", + "Output Program": [ + "n0 = 15.0\nn1 = 12.0\nn2 = 10.0\nn3 = 1.08\nn4 = 0.5\nt0 = n0 * n1\nt1 = n2 * t0\nt2 = t1 / 100.0\nt3 = t2 / 100.0\nt4 = t3 / 100.0\nt5 = n3 / t4\nanswer = n4 * t5\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "on dividing number by 357 , we get 39 as remainder . on dividing the same number by 17 , what will be the remainder ?", + "Output Program": [ + "n0 = 357.0\nn1 = 39.0\nn2 = 17.0\n\nanswer = n1 % n2\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "how many even number in the range between 10 to 150 inclusive are not divisible by 3", + "Output Program": [ + "n0 = 10.0\nn1 = 150.0\nn2 = 3.0\nt0 = n2 * 4.0\nt1 = n1 - n0\nt2 = n1 - 2.0\nt3 = t1 - 2.0\nt4 = t2 - t0\nt5 = t3 / 2.0\nt6 = t4 - n2\nt7 = t6 - n2\nt8 = t7 / n2\nt9 = t8 / 2.0\nanswer = t5 - t9\nprint(answer)" + ], + "Output Answer": [ + "47.33333333333333" + ], + "split": "train" + }, + { + "Input": "suppose a , b , and c are positive integers with a < b < c such that 1 / a + 1 / b + 1 / c = 1 . what is a + b + c ?", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 1.0\nn3 = 1.0\nt0 = n0 + n0\nt1 = n0 + t0\nt2 = t0 + t1\nt3 = t1 * t0\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "what is the smallest number which when diminished by 24 , is divisible 5 , 10 , 15 and 20 ?", + "Output Program": [ + "import scipy\nn0 = 24.0\nn1 = 5.0\nn2 = 10.0\nn3 = 15.0\nn4 = 20.0\nt0 = scipy.lcm(int(n1), int(n2))\nt1 = scipy.lcm(int(n3), int(n4))\nt2 = scipy.lcm(int(t0), int(t1))\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "84" + ], + "split": "train" + }, + { + "Input": "the average mark of the students of a class in a particular exam is 60 . if 5 students whose average mark in that exam is 44 are excluded , the average mark of the remaining will be 80 . find the number of students who wrote the exam ?", + "Output Program": [ + "n0 = 60.0\nn1 = 5.0\nn2 = 44.0\nn3 = 80.0\nt0 = n1 * n3\nt1 = n1 * n2\nt2 = n3 - n0\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "joe \u2019 s average ( arithmetic mean ) test score across 4 equally weighted tests was 35 . he was allowed to drop his lowest score . after doing so , his average test score improved to 40 . what is the lowest test score that was dropped ?", + "Output Program": [ + "n0 = 4.0\nn1 = 35.0\nn2 = 40.0\nt0 = n0 * n1\nt1 = n2 * 3.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "how many positive integers less than 5,000 are there in which the sum of the digits equals 5 ?", + "Output Program": [ + "import math\nn0 = 5000.0\nn1 = 5.0\nt0 = n1 + 4.0\nt1 = math.factorial(min(15, int(n1)))\nt2 = 4.0 - 1.0\nt3 = math.factorial(min(15, int(t2)))\nt4 = t0 - 1.0\nt5 = math.factorial(min(15, int(t4)))\nt6 = t1 * t3\nanswer = t5 / t6\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "train" + }, + { + "Input": "on a partly cloudy day , derek decides to walk back from work . when it is sunny , he walks at a speed of s miles / hr ( s is an integer ) and when it gets cloudy , he increases his speed to ( s + 1 ) miles / hr . if his average speed for the entire distance is 2.8 miles / hr , what fraction q of the total distance did he cover while the sun was shining on him ?", + "Output Program": [ + "import scipy\nn0 = 1.0\nn1 = 2.8\nt0 = scipy.lcm(int(2.0), int(3.0))\nt1 = t0 / n1\nanswer = t1 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "0.1428571428571428" + ], + "split": "train" + }, + { + "Input": "given the two equations 3 x + 2 y = 16 and 5 x + 3 y = 26 , by how much does r exceed s ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 16.0\nn3 = 5.0\nn4 = 3.0\nn5 = 26.0\nt0 = n1 * n2\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "how many integers are divisible by 5 between 10 ! and 10 ! + 20 inclusive ?", + "Output Program": [ + "n0 = 5.0\nn1 = 10.0\nn2 = 10.0\nn3 = 20.0\nt0 = n3 / n0\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "if 3 / p = 6 & 3 / q = 18 then p - q = ?", + "Output Program": [ + "n0 = 3.0\nn1 = 6.0\nn2 = 3.0\nn3 = 18.0\nt0 = n0 / n1\nt1 = n0 / n3\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "0.33333333333333337" + ], + "split": "train" + }, + { + "Input": "a company that ships boxes to a total of 12 distribution centers uses color coding to identify each center . if either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors , what is the minimum number of colors needed for the coding ? ( assume that the order of colors in a pair does not matter )", + "Output Program": [ + "import math\nn0 = 12.0\nt0 = n0 / 2.0\nt1 = math.factorial(min(15, int(3.0)))\nt2 = math.factorial(min(15, int(2.0)))\nt3 = t1 * t2\nt4 = t0 - 1.0\nt5 = math.factorial(min(15, int(t4)))\nt6 = t5 / t3\nanswer = t6 - t4\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "the average of 5 numbers is 27 . if one number is excluded the average become 25 . the excluded number is :", + "Output Program": [ + "n0 = 5.0\nn1 = 27.0\nn2 = 25.0\nt0 = n0 * n1\nt1 = n0 - 1.0\nt2 = n2 * t1\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "the captain of a cricket team of 11 members is 24 years old and the wicket keeper is 7 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ?", + "Output Program": [ + "n0 = 11.0\nn1 = 24.0\nn2 = 7.0\nt0 = n1 + n2\nt1 = 3.0 * 3.0\nt2 = n1 + t0\nt3 = t2 - t1\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "in a box of 16 pens , a total of 3 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?", + "Output Program": [ + "n0 = 16.0\nn1 = 3.0\nn2 = 2.0\nt0 = n0 - n1\nt1 = n0 - 1.0\nt2 = t0 / n0\nt3 = t0 - 1.0\nt4 = t3 / t1\nanswer = t2 * t4\nprint(answer)" + ], + "Output Answer": [ + "0.65" + ], + "split": "train" + }, + { + "Input": "during a pizza buffet where a eats more times 2.6 than b , and b eats 4 times less than c . find the least number of times all the 3 has to eat", + "Output Program": [ + "import scipy\nn0 = 2.6\nn1 = 4.0\nn2 = 3.0\nt0 = n0 * 10.0\nt1 = n1 * 10.0\nt2 = t0 / 2.0\nt3 = t1 / 2.0\nanswer = scipy.lcm(int(t2), int(t3))\nprint(answer)" + ], + "Output Answer": [ + "260" + ], + "split": "train" + }, + { + "Input": "if the mean of numbers 28 , x , 42 , 78 and 104 is 62 , what is the mean of 48 , 62 , 98 , 124 and x ?", + "Output Program": [ + "n0 = 28.0\nn1 = 42.0\nn2 = 78.0\nn3 = 104.0\nn4 = 62.0\nn5 = 48.0\nn6 = 62.0\nn7 = 98.0\nn8 = 124.0\nt0 = 1.0 + 4.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n4 * t0\nt4 = n3 + t2\nt5 = t3 - t4\nt6 = n5 + t5\nt7 = n6 + t6\nt8 = n7 + t7\nt9 = n8 + t8\nanswer = t9 / t0\nprint(answer)" + ], + "Output Answer": [ + "78" + ], + "split": "train" + }, + { + "Input": "5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 150 only . men \u00e2 \u20ac \u2122 s wages are ?", + "Output Program": [ + "n0 = 5.0\nn1 = 8.0\nn2 = 150.0\nt0 = n0 * 3.0\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "if x > 0 , x / 10 + x / 25 is what percent of x ?", + "Output Program": [ + "n0 = 0.0\nn1 = 10.0\nn2 = 25.0\nt0 = 1.0 / n1\nt1 = 1.0 / n2\nt2 = t0 + t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "14.000000000000002" + ], + "split": "train" + }, + { + "Input": "if 50 % of x is 30 less than 25 % of 1500 , then x is ?", + "Output Program": [ + "n0 = 50.0\nn1 = 30.0\nn2 = 25.0\nn3 = 1500.0\nt0 = n2 / 100.0\nt1 = n0 / 100.0\nt2 = n3 * t0\nt3 = t2 - n1\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "690" + ], + "split": "train" + }, + { + "Input": "an investor can sell her microtron stock for 36 $ per share and her dynaco stock for 44 $ per share , if she sells 300 shares altogether , some of each stock , at an average price per share of 40 $ , how many shares of dynaco stock has she sold ?", + "Output Program": [ + "n0 = 36.0\nn1 = 44.0\nn2 = 300.0\nn3 = 40.0\nt0 = n0 + n1\nt1 = n1 - n0\nt2 = n3 / t1\nt3 = t0 / t1\nt4 = n2 * t2\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "train" + }, + { + "Input": "a man is 35 years older than his son . in two years , his age will be twice the age of his son . the present age of this son is", + "Output Program": [ + "n0 = 35.0\nt0 = 2.0 * 2.0\nt1 = 2.0 - 1.0\nt2 = t0 - 2.0\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "a jogger running at 9 km / hr along side a railway track is 120 m ahead of the engine of a 120 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?", + "Output Program": [ + "n0 = 9.0\nn1 = 120.0\nn2 = 120.0\nn3 = 45.0\nt0 = n1 + n2\nt1 = 10.0 / 2.0\nt2 = n3 - n0\nt3 = t2 / 2.0\nt4 = t1 / t3\nt5 = t4 * t2\nanswer = t0 / t5\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "if n is an integer and 101 n ^ 2 is less than or equal to 12100 , what is the greatest possible value of n ?", + "Output Program": [ + "import math\nn0 = 101.0\nn1 = 2.0\nn2 = 12100.0\nt0 = n2 / n0\nt1 = math.sqrt(max(0, t0))\nanswer = math.floor(t1)\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "if k ^ 3 is divisible by 120 , what is the least possible value of integer k ?", + "Output Program": [ + "n0 = 3.0\nn1 = 120.0\nt0 = n1 / 2.0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "sony and johnny caught 40 fishes . sony caught 4 times as many as johnny . how many fishes did johnny catch ?", + "Output Program": [ + "n0 = 40.0\nn1 = 4.0\nt0 = n1 + 1.0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "two digits in brother ' s age are the same as the digit in the sister ' s age , but in reverse order . in 20 9 years brother will be twice as old as sister will be then . what is the difference in their current age ?", + "Output Program": [ + "n0 = 20.0\nn1 = 9.0\nt0 = n0 + n0\nt1 = n1 - 4.0\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "a man owns 1 / 3 of market reserch beauro buzness , and sells 3 / 5 of his shares for 2000 rs , what is the value of buzness ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 3.0\nn3 = 5.0\nn4 = 2000.0\nt0 = n0 / n1\nt1 = n1 / n3\nt2 = t0 * t1\nanswer = n4 / t2\nprint(answer)" + ], + "Output Answer": [ + "10000" + ], + "split": "train" + }, + { + "Input": "what is the smallest number which when increased by 3 is divisible by 18 , 70 , 100 and 84 ?", + "Output Program": [ + "import scipy\nn0 = 3.0\nn1 = 18.0\nn2 = 70.0\nn3 = 100.0\nn4 = 21.0\nt0 = scipy.lcm(int(n1), int(n2))\nt1 = scipy.lcm(int(n3), int(n4))\nt2 = scipy.lcm(int(t0), int(t1))\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "6303" + ], + "split": "train" + }, + { + "Input": "the arithmetic mean and standard deviation of a certain normal distribution are 16.5 and 1.5 , respectively . what value is exactly 2 standard deviations less than the mean ?", + "Output Program": [ + "n0 = 16.5\nn1 = 1.5\nn2 = 2.0\nt0 = n1 * n2\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "13.5" + ], + "split": "train" + }, + { + "Input": "find the value of 3 / 11 \u00d7 [ ( 1 + 1 / 3 ) ( 1 + 1 / 4 ) \u2026 \u2026 \u2026 \u2026 . ( 1 + 1 / 120 ) ] is ?", + "Output Program": [ + "n0 = 3.0\nn1 = 11.0\nn2 = 1.0\nn3 = 1.0\nn4 = 3.0\nn5 = 1.0\nn6 = 1.0\nn7 = 4.0\nn8 = 1.0\nn9 = 1.0\nn10 = 120.0\nt0 = n2 + n10\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "which fraction should be added to : 1 / ( 2 \u00e3 \u2014 3 ) + 1 / ( 3 \u00e3 \u2014 4 ) + 1 / ( 4 \u00e3 \u2014 5 ) + . . . . . . . + 1 / ( 23 \u00e3 \u2014 24 ) so that the result is equal to 1 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 3.0\nn3 = 1.0\nn4 = 3.0\nn5 = 4.0\nn6 = 1.0\nn7 = 4.0\nn8 = 5.0\nn9 = 1.0\nn10 = 23.0\nn11 = 24.0\nn12 = 1.0\nt0 = n2 + 10.0\nanswer = t0 / n11\nprint(answer)" + ], + "Output Answer": [ + "0.5416666666666666" + ], + "split": "train" + }, + { + "Input": "if one positive integer is greater than another positive integer by 3 , and the difference of their cubes is 63 , what is their sum ?", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 63.0\nt0 = n0**min(3.0, 5)\nt1 = n0**min(2.0, 5)\nt2 = t1 * 2.0\nt3 = t0**min(2.0, 5)\nt4 = n1 - t0\nt5 = t4**min(2.0, 5)\nt6 = t3 + t5\nt7 = math.sqrt(max(0, t6))\nt8 = t0 + t7\nt9 = t8 / t2\nt10 = t9 - n0\nanswer = t9 + t10\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 76800 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 8.0\nn2 = 76800.0\nt0 = n0 / n1\nt1 = n2 * t0\nt2 = n2 + t1\nt3 = t2 * t0\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "97200" + ], + "split": "train" + }, + { + "Input": "kamal obtained 96 , 65 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?", + "Output Program": [ + "n0 = 96.0\nn1 = 65.0\nn2 = 82.0\nn3 = 67.0\nn4 = 85.0\nn5 = 100.0\nt0 = n0 + n1\nt1 = 1.0 + 4.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "79" + ], + "split": "train" + }, + { + "Input": "a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 32 , then how old is b ?", + "Output Program": [ + "n0 = 32.0\nt0 = 1.0 + 4.0\nt1 = n0 - 2.0\nt2 = t1 * 2.0\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "a man spends 2 / 5 of his salary on house rent , 3 / 10 of his salary on food , and 1 / 8 of his salary on conveyance . if he has rs 1400 left with him , find his expenditure on food and conveyance", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 3.0\nn3 = 10.0\nn4 = 1.0\nn5 = 8.0\nn6 = 1400.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = n4 / n5\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n4 - t4\nt6 = n6 / t5\nt7 = t6 * t1\nt8 = t6 * t2\nanswer = t7 + t8\nprint(answer)" + ], + "Output Answer": [ + "3399.999999999999" + ], + "split": "train" + }, + { + "Input": "the sum of two numbers is 8 and the sum of their squares is 120 . find the product of the two numbers .", + "Output Program": [ + "n0 = 8.0\nn1 = 120.0\nt0 = n0**min(2.0, 5)\nt1 = n1 - t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "a library has an average of 500 visitors on sundays and 140 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :", + "Output Program": [ + "import math\nn0 = 500.0\nn1 = 140.0\nn2 = 30.0\nt0 = 3.0 + 4.0\nt1 = n2 / t0\nt2 = math.floor(t1)\nt3 = t2 + 1.0\nt4 = n0 * t3\nt5 = n2 - t3\nt6 = n1 * t5\nt7 = t4 + t6\nanswer = t7 / n2\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "train" + }, + { + "Input": "he average weight of 8 persons increases by 3.5 kg when a new person comes in place of one of them weighing 62 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 3.5\nn2 = 62.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 98 , what is the difference between the ages of patrick and monica ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 3.0\nn3 = 5.0\nn4 = 98.0\nt0 = n0 * n0\nt1 = n1 * n0\nt2 = n1 * n3\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n4 / t4\nt6 = t5 * t2\nt7 = t5 * t0\nanswer = t6 - t7\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "if all the 6 are replaced by 9 , then the algebraic sum of all the numbers from 1 to 100 ( both inclusive ) varies by how much ?", + "Output Program": [ + "n0 = 6.0\nn1 = 9.0\nn2 = 1.0\nn3 = 100.0\nt0 = n1 - n0\nt1 = t0 * 10.0\nt2 = t1 * 10.0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "330" + ], + "split": "train" + }, + { + "Input": "if y is 80 % greater than x , than x is what % less than y ?", + "Output Program": [ + "n0 = 80.0\nt0 = n0 + 100.0\nt1 = n0 / t0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "44.44444444444444" + ], + "split": "train" + }, + { + "Input": "every disk in a bag is either blue , yellow or green . the ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8 . if the total number of disks in the bag is 108 , how many more green disks than blue disks are in the bag ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 8.0\nn3 = 108.0\nt0 = n0 + n1\nt1 = n2 - n0\nt2 = n2 + t0\nt3 = n3 / t2\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "a room is 7 meters 20 centimeters in length and 4 meters 32 centimeters in width . find the least number of square tiles of equal size required to cover the entire floor of the room .", + "Output Program": [ + "import scipy\nn0 = 7.0\nn1 = 20.0\nn2 = 4.0\nn3 = 32.0\nt0 = n0 * 100.0\nt1 = n2 * 100.0\nt2 = n1 + t0\nt3 = n3 + t1\nt4 = scipy.gcd(int(t2), int(t3))\nt5 = t2 * t3\nt6 = t4 * t4\nanswer = t5 / t6\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "a number is greater than 3 but less than 8 . also the number is greater than 6 but less than 10 . what is the number ?", + "Output Program": [ + "n0 = 3.0\nn1 = 8.0\nn2 = 6.0\nn3 = 10.0\n\nanswer = n1 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "( 178 % of 1265 ) \u00f7 5.96 = ?", + "Output Program": [ + "n0 = 178.0\nn1 = 1265.0\nn2 = 5.96\nt0 = n0 / 100.0\nt1 = n1 * t0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "377.8020134228188" + ], + "split": "train" + }, + { + "Input": "after spending rs . 5000 on rent , rs . 1500 on milk , rs . 4500 on groceries , rs . 2500 on childrens education rs . 2000 on petrol and rs . 6100 on miscellaneous expenses , mr . kishore saved 10 % of his monthly salary . how much did he save in rs . ?", + "Output Program": [ + "n0 = 5000.0\nn1 = 1500.0\nn2 = 4500.0\nn3 = 2500.0\nn4 = 2000.0\nn5 = 6100.0\nn6 = 10.0\nt0 = n0 + n1\nt1 = 100.0 - n6\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nt5 = n5 + t4\nt6 = t5 * 100.0\nt7 = t6 / t1\nanswer = t7 - t5\nprint(answer)" + ], + "Output Answer": [ + "2400" + ], + "split": "train" + }, + { + "Input": "in a hostel , the number of students decreased by 10 % and the price of food increased by 20 % over the previous year . if each student consumes the same amount of food then by how much should the consumption of food be cut short by every student , so that the total cost of the food remains the same as that of the previous year ?", + "Output Program": [ + "n0 = 10.0\nn1 = 20.0\nt0 = n1 + 100.0\nt1 = 100.0 * 100.0\nt2 = 100.0 - n0\nt3 = t0 * t2\nt4 = t1 / t3\nt5 = 1.0 - t4\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "7.4074074074074066" + ], + "split": "train" + }, + { + "Input": "if the sales tax reduced from 3 1 / 2 % to 3 1 / 3 % , then what difference does it make to a person who purchases an article with market price of rs . 6600 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 2.0\nn3 = 3.0\nn4 = 1.0\nn5 = 3.0\nn6 = 6600.0\nt0 = n1 / n2\nt1 = n1 / n0\nt2 = n0 + t0\nt3 = n0 + t1\nt4 = t2 - t3\nt5 = n6 * t4\nanswer = t5 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "10.999999999999991" + ], + "split": "train" + }, + { + "Input": "from the digits 2 , 3 , 4 , 5 , 6 and 7 , how many 5 - digit numbers can be formed that have distinct digits and are multiples of 12 ?", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 3.0\nn2 = 4.0\nn3 = 5.0\nn4 = 6.0\nn5 = 7.0\nn6 = 5.0\nn7 = 12.0\nt0 = 2.0 * 3.0\nt1 = n3 - 2.0\nt2 = math.factorial(min(15, int(t1)))\nt3 = t2 * t0\nt4 = t2 * 4.0\nanswer = t3 + t4\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "the difference between the local value and the face value of 8 in the numeral 96348621 is", + "Output Program": [ + "n0 = 8.0\nn1 = 96348621.0\nt0 = n0 * 1000.0\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "7992" + ], + "split": "train" + }, + { + "Input": "if n = 2 ^ 0.15 and n ^ b = 32 , b must equal", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 0.15\nn2 = 32.0\nt0 = math.log(max(1e-5, n2), 2)\nt1 = n0**min(n1, 5)\nt2 = math.log(max(1e-5, t1), 2)\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "33.333333333333314" + ], + "split": "train" + }, + { + "Input": "a man is 25 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is", + "Output Program": [ + "n0 = 25.0\nt0 = 2.0 * 2.0\nt1 = 2.0 - 1.0\nt2 = t0 - 2.0\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "if m is a positive integer and m ^ 2 is divisible by 54 , then the largest positive integer that must divide m is ?", + "Output Program": [ + "n0 = 2.0\nn1 = 54.0\nt0 = n1 / 3.0\nt1 = t0 / 3.0\nanswer = t1 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "a marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each . there can be no less than 8 musicians per row and no more than 30 musicians per row . how many different rectangular formations p are possible ?", + "Output Program": [ + "n0 = 240.0\nn1 = 8.0\nn2 = 30.0\n\nanswer = n0 / n2\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "for every x , the action [ x ] is defined : [ x ] is the greatest integer less than or equal to x . what is the value of [ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 6.2 ?", + "Output Program": [ + "n0 = 6.5\nn1 = 2.0\nn2 = 3.0\nn3 = 2.0\nn4 = 7.2\nn5 = 8.4\nn6 = 6.2\nt0 = 4.0 / 10.0\nt1 = n1 * n4\nt2 = n5 - t0\nt3 = t1 + t2\nanswer = t3 - n6\nprint(answer)" + ], + "Output Answer": [ + "16.2" + ], + "split": "train" + }, + { + "Input": "we have boxes colored either red or blue . in each blue box there is a fixed number of blueberries . in each red box there is a fixed number of strawberries . if we dispose of one blue box for one additional red box , the total number of berries would increase by 15 , and the difference between the total number of strawberries and the total number of blueberries would increase by 87 . each blue box contains how many blueberries ?", + "Output Program": [ + "n0 = 15.0\nn1 = 87.0\nt0 = n1 - n0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "a rope of which a calf is tied is increased from 12 m to 25 m , how much additional grassy ground shall it graze ?", + "Output Program": [ + "n0 = 12.0\nn1 = 25.0\nt0 = 3.0 + 4.0\nt1 = 10.0 * 2.0\nt2 = n1**min(2.0, 5)\nt3 = n0**min(2.0, 5)\nt4 = t1 + 2.0\nt5 = t2 - t3\nt6 = t4 / t0\nanswer = t6 * t5\nprint(answer)" + ], + "Output Answer": [ + "1511.7142857142858" + ], + "split": "train" + }, + { + "Input": "patty ran a marathon at an average speed of 3 mph for some time and then at an average speed of 6 mph for the rest of the marathon . if she made no stops during the run and her average speed for the entire marathon was 5 mph , for what fraction of the total time did she run at 3 mph ?", + "Output Program": [ + "n0 = 3.0\nn1 = 6.0\nn2 = 5.0\nn3 = 3.0\nt0 = n1 - n2\nt1 = n1 - n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.3333333333333333" + ], + "split": "train" + }, + { + "Input": "kamal obtained 66 , 65 , 77 , 62 and 75 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?", + "Output Program": [ + "n0 = 66.0\nn1 = 65.0\nn2 = 77.0\nn3 = 62.0\nn4 = 75.0\nn5 = 100.0\nt0 = n0 + n1\nt1 = 1.0 + 4.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "69" + ], + "split": "train" + }, + { + "Input": "if a number p is prime , and 2 p + 4 = q , where q is also prime , then the decimal expansion of 1 / q will produce a decimal with q - 1 digits . if this method produces a decimal with 166 digits , what is the units digit of the product of p and q ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 1.0\nn3 = 1.0\nn4 = 166.0\nt0 = n2 + n4\nt1 = t0 - n1\nt2 = t1 / n0\nt3 = t2 - n2\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 32 , the how old is b ?", + "Output Program": [ + "n0 = 32.0\nt0 = 1.0 + 4.0\nt1 = n0 - 2.0\nt2 = t1 * 2.0\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "a man owns 2 / 3 of market reserch beauro buzness , and sells 3 / 4 of his shares for 45000 rs , what is the value of buzness ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 3.0\nn3 = 4.0\nn4 = 45000.0\nt0 = n0 / n1\nt1 = n1 / n3\nt2 = t0 * t1\nanswer = n4 / t2\nprint(answer)" + ], + "Output Answer": [ + "90000" + ], + "split": "train" + }, + { + "Input": "in a certain company , the formula for maximizing profits is p = - 25 x ^ 2 + 7500 x , , where p is profit and x is the number of machines the company operates in its factory . what value for x will maximize p ? this one is from integratedlearning . here ' s what i did : the oa states : to find a maximum or minimum value of an equation with an exponent in it , you take the derivative of the equation , set it to zero , and solve . i dont really get what that means . so whoever solves it , could you plz post explanation of what the above sentence mean as well ?", + "Output Program": [ + "import math\nn0 = 25.0\nn1 = 2.0\nn2 = 7500.0\nt0 = math.sqrt(max(0, n0))\nt1 = t0 * 2.0\nt2 = n2 / t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "train" + }, + { + "Input": "what is the smallest number which when diminished by 18 , is divisible 8 , 14 , 26 and 28 ?", + "Output Program": [ + "import scipy\nn0 = 18.0\nn1 = 8.0\nn2 = 14.0\nn3 = 26.0\nn4 = 28.0\nt0 = scipy.lcm(int(n1), int(n2))\nt1 = scipy.lcm(int(n3), int(n4))\nt2 = scipy.lcm(int(t0), int(t1))\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "746" + ], + "split": "train" + }, + { + "Input": "in a mixture of 45 litres the ratio of milk to water is 4 : 1 . additional 11 litres of water is added to the mixture . find the ratio of milk to water in the resulting mixture .", + "Output Program": [ + "n0 = 45.0\nn1 = 4.0\nn2 = 1.0\nn3 = 11.0\nt0 = n1 + n2\nt1 = n0 / t0\nt2 = n3 + t1\nt3 = n0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "1.8" + ], + "split": "train" + }, + { + "Input": "p , q , r enter into a partnership & their share are in the ratio 1 / 2 : 1 / 3 : 1 / 4 , after two months , p withdraws half of the capitals & after 10 months , a profit of rs 378 is divided among them . what is r ' s share ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 1.0\nn3 = 3.0\nn4 = 1.0\nn5 = 4.0\nn6 = 10.0\nn7 = 378.0\nt0 = n3 + n5\nt1 = n1 * n3\nt2 = n7 * t1\nt3 = n3 * t0\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "108" + ], + "split": "train" + }, + { + "Input": "find the smallest number which leaves 2235 , 48 and 61 as remainders when divided by 26 , 39 , 52 and 65 respectively .", + "Output Program": [ + "n0 = 2235.0\nn1 = 48.0\nn2 = 61.0\nn3 = 26.0\nn4 = 39.0\nn5 = 52.0\nn6 = 65.0\nt0 = n1 / 2.0\nanswer = t0 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "if k ^ 3 is divisible by 168 , what is the least possible value of integer k ?", + "Output Program": [ + "n0 = 3.0\nn1 = 168.0\nt0 = n1 / 2.0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "what is the unit digit in 14 ^ 100 ?", + "Output Program": [ + "n0 = 14.0\nn1 = 100.0\nt0 = n0**min(2.0, 5)\nanswer = t0 % 10.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "a container contains 40 litres of milk . from this container 4 litres of milk was taken out and replaced by water . this process was repeated further two times . how much milk is now contained by the container .", + "Output Program": [ + "n0 = 40.0\nn1 = 4.0\nt0 = n1 / n0\nt1 = 1.0 - t0\nt2 = t1**min(3.0, 5)\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "29.160000000000004" + ], + "split": "train" + }, + { + "Input": "if grapes are 90 % water and raisins are 17 % water , then how many kilograms did a quantity of raisins , which currently weighs 14 kilograms , weigh when all the raisins were grapes ? ( assume that the only difference between their raisin - weight and their grape - weight is water that evaporated during their transformation . )", + "Output Program": [ + "n0 = 90.0\nn1 = 17.0\nn2 = 14.0\nt0 = 100.0 - n1\nt1 = 100.0 - n0\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = n2 * t2\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "116.19999999999999" + ], + "split": "train" + }, + { + "Input": "a father said his son , ` ` i was as old as you are at present at the time of your birth . ` ` if the father age is 38 now , the son age 5 years back was :", + "Output Program": [ + "n0 = 38.0\nn1 = 5.0\nt0 = n0 / 2.0\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "in x - y plane , there is a right triangle abc ( \u2220 b = 90 o ) . if the length of ac is 225 and the slope of line segment ac is 4 / 3 , what is the length of ab ?", + "Output Program": [ + "import math\nn0 = 90.0\nn1 = 225.0\nn2 = 4.0\nn3 = 3.0\nt0 = n2**min(2.0, 5)\nt1 = n3**min(2.0, 5)\nt2 = t0 + t1\nt3 = math.sqrt(max(0, t2))\nt4 = n1 / t3\nanswer = n2 * t4\nprint(answer)" + ], + "Output Answer": [ + "180" + ], + "split": "train" + }, + { + "Input": "what is the total cost of 2 sandwiches at $ 3.49 each and 4 sodas at $ 0.87 each ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.49\nn2 = 4.0\nn3 = 0.87\nt0 = n0 * n1\nt1 = n2 * n3\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "10.46" + ], + "split": "train" + }, + { + "Input": "for all real numbers v , an operation is defined by the equation v * = v - v / 3 . if ( v * ) * = 4 , then v =", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nt0 = 1.0 / n0\nt1 = 1.0 - t0\nt2 = n1 / t1\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "8.999999999999998" + ], + "split": "train" + }, + { + "Input": "on dividing 12401 by a certain number , we get 76 as quotient and 13 as remainder . what is the divisor ?", + "Output Program": [ + "n0 = 12401.0\nn1 = 76.0\nn2 = 13.0\nt0 = n0 - n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "163" + ], + "split": "train" + }, + { + "Input": "the average of the marks of 10 students in a class is 40 . if the marks of each student are doubled , find the new average ?", + "Output Program": [ + "n0 = 10.0\nn1 = 40.0\n\nanswer = n1 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "at 1 : 00 pm , there were 10.0 grams of bacteria . the bacteria increased to x grams at 4 : 00 pm , and 19.6 grams at 7 : 00 pm . if the amount of bacteria present increased by the same fraction during each of the 3 - hour periods , how many grams of bacteria were present at 4 : 00 pm ?", + "Output Program": [ + "import math\nn0 = 1.0\nn1 = 0.0\nn2 = 10.0\nn3 = 4.0\nn4 = 0.0\nn5 = 19.6\nn6 = 7.0\nn7 = 0.0\nn8 = 3.0\nn9 = 4.0\nn10 = 0.0\nt0 = n5 / n2\nt1 = math.sqrt(max(0, t0))\nanswer = t1 * n2\nprint(answer)" + ], + "Output Answer": [ + "14.000000000000002" + ], + "split": "train" + }, + { + "Input": "light glows for every 30 seconds . how many max . times did it glow between 1 : 57 : 58 and 3 : 20 : 47 am .", + "Output Program": [ + "n0 = 30.0\nn1 = 1.0\nn2 = 57.0\nn3 = 58.0\nn4 = 3.0\nn5 = 20.0\nn6 = 47.0\nt0 = n6 + 2.0\nt1 = 2.0 + 60.0\nt2 = n5 + t1\nt3 = t2 * 60.0\nt4 = t0 + t3\nanswer = t4 / n0\nprint(answer)" + ], + "Output Answer": [ + "165.63333333333333" + ], + "split": "train" + }, + { + "Input": "a man is 35 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is :", + "Output Program": [ + "n0 = 35.0\nt0 = 2.0 * 2.0\nt1 = 2.0 - 1.0\nt2 = t0 - 2.0\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "on charlie ' s cell phone plan , he signed up for 8 gb of data per 4 week period . if he went over the 8 gb per month , it would cost him an extra $ 10.00 per gb . in the first week , he used 2 gb ; in the 2 nd week , he used 3 gb ; in the 3 rd week , he used 5 gb ; and in the 4 th week , he used a whopping 10 gb . how much extra did charlie need to pay on his cell phone bill ?", + "Output Program": [ + "n0 = 8.0\nn1 = 4.0\nn2 = 8.0\nn3 = 10.0\nn4 = 2.0\nn5 = 2.0\nn6 = 3.0\nn7 = 3.0\nn8 = 5.0\nn9 = 4.0\nn10 = 10.0\nt0 = n4 + n6\nt1 = n8 + t0\nt2 = n3 + t1\nt3 = t2 - n0\nanswer = n3 * t3\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "how many numbers between 100 and 600 are divisible by 2 , 3 , and 7 together ?", + "Output Program": [ + "n0 = 100.0\nn1 = 600.0\nn2 = 2.0\nn3 = 3.0\nn4 = 7.0\nt0 = n2 * n3\nt1 = n4 * t0\nt2 = n1 / t1\nt3 = n0 / t1\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "11.904761904761905" + ], + "split": "train" + }, + { + "Input": "in a house a hall is 20 m long , 15 m wide and 5 m high . its interior has to be covered with mat . what will be the total expenditure if it costs rs . 50 per square m ?", + "Output Program": [ + "n0 = 20.0\nn1 = 15.0\nn2 = 5.0\nn3 = 50.0\nt0 = n0 * n1\nt1 = n0 * n2\nt2 = n1 * n2\nt3 = t0 * 2.0\nt4 = t1 * 2.0\nt5 = t2 * 2.0\nt6 = n3 * t3\nt7 = n3 * t4\nt8 = n3 * t5\nt9 = t6 + t7\nanswer = t9 + t8\nprint(answer)" + ], + "Output Answer": [ + "47500" + ], + "split": "train" + }, + { + "Input": "at a certain committee meeting only associate professors and assistant professors are present . each associate professor has brought 2 pencils and 1 chart to the meeting , while each assistant professor has brought 1 pencil and 2 charts . if a total of 10 pencils and 14 charts have been brought to the meeting , how many people are present ?", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 1.0\nn3 = 2.0\nn4 = 10.0\nn5 = 14.0\nt0 = n4 + n5\nt1 = n0 + n1\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "{ 8 , 46 , 53 , 127 } what number should be inserted in the set of 7 values to get a median of 9 ?", + "Output Program": [ + "n0 = 8.0\nn1 = 46.0\nn2 = 53.0\nn3 = 127.0\nn4 = 7.0\nn5 = 9.0\n\nanswer = n3 / n5\nprint(answer)" + ], + "Output Answer": [ + "14.11111111111111" + ], + "split": "train" + }, + { + "Input": "the ratio 2 : 3 expressed as a percent equals", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nt0 = n0 / n1\nanswer = t0 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "66.66666666666666" + ], + "split": "train" + }, + { + "Input": "two brother x and y appeared for an exam . the probability of selection of x is 1 / 7 and that of b is 2 / 5 . find the probability that both of them are selected .", + "Output Program": [ + "n0 = 1.0\nn1 = 7.0\nn2 = 2.0\nn3 = 5.0\nt0 = n0 / n1\nt1 = n2 / n3\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "0.05714285714285714" + ], + "split": "train" + }, + { + "Input": "3 consecutive odd integers are in increasing order such that the sum of the last two integers is 17 more than the first integer . find the 3 integers ?", + "Output Program": [ + "n0 = 3.0\nn1 = 17.0\nn2 = 3.0\nt0 = n0 + 1.0\nt1 = n1 - 1.0\nt2 = t1 - t0\nt3 = t2 / 2.0\nt4 = t3 * 2.0\nanswer = t4 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "there are 6 people in the elevator . their average weight is 154 lbs . another person enters the elevator , and increases the average weight to 151 lbs . what is the weight of the 7 th person .", + "Output Program": [ + "n0 = 6.0\nn1 = 154.0\nn2 = 151.0\nn3 = 7.0\nt0 = n2 * n3\nt1 = n0 * n1\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "133" + ], + "split": "train" + }, + { + "Input": "for any number z , z * is defined as the greatest positive even integer less than or equal to y . what is the value of 6.25 \u2013 6.25 * ?", + "Output Program": [ + "import math\nn0 = 6.25\nn1 = 6.25\nt0 = math.floor(n0)\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "0.25" + ], + "split": "train" + }, + { + "Input": "6 friends visited a book stall and brought 6 books , and everyone decided to contribute equally to the total bill of $ 400 . if one of the friends had a coupon for 5 % off the total bill , and if each friend still contributed equally after the coupon was applied to the bill , how much did each friend pay ?", + "Output Program": [ + "n0 = 6.0\nn1 = 6.0\nn2 = 400.0\nn3 = 5.0\nt0 = n0 + n0\nt1 = n3 + t0\nt2 = n2 / t1\nt3 = t2 * 3.0\nt4 = t3 - 4.0\nanswer = t4 - 3.0\nprint(answer)" + ], + "Output Answer": [ + "63.58823529411765" + ], + "split": "train" + }, + { + "Input": "the average weight of 8 person ' s increases by 5 kg when a new person comes in place of one of them weighing 35 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 5.0\nn2 = 35.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "the average marks of a class of 22 students is 40 and that of another class of 28 students is 60 . find the average marks of all the students ?", + "Output Program": [ + "n0 = 22.0\nn1 = 40.0\nn2 = 28.0\nn3 = 60.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "51.2" + ], + "split": "train" + }, + { + "Input": "if 45 - [ 28 - { 37 - ( 15 - * ) } ] = 57 , then * is equal to :", + "Output Program": [ + "n0 = 45.0\nn1 = 28.0\nn2 = 37.0\nn3 = 15.0\nn4 = 57.0\nt0 = n1 - n2\nt1 = n3 + t0\nt2 = n0 - t1\nanswer = n4 - t2\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "the sum of 3 consecutive odd natural numbers , each divisible by 3 is 72 . what is the largest among them ?", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 72.0\nt0 = 3.0 + 3.0\nt1 = n0 + t0\nt2 = n2 - t1\nt3 = t2 / n0\nanswer = t0 + t3\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "train" + }, + { + "Input": "if n = 3 ^ 0.15 and n ^ b = 9 , b must equal", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 0.15\nn2 = 9.0\nt0 = math.log(max(1e-5, n2), 2)\nt1 = n0**min(n1, 5)\nt2 = math.log(max(1e-5, t1), 2)\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "13.33333333333333" + ], + "split": "train" + }, + { + "Input": "the price of commodity x increases by 30 cents every year , while the price of commodity y increases by 20 cents every year . if in 2001 , the price of commodity x was $ 4.20 and the price of commodity y was $ 4.40 , in which year will commodity x cost 70 cents more than the commodity y ?", + "Output Program": [ + "n0 = 30.0\nn1 = 20.0\nn2 = 2001.0\nn3 = 4.2\nn4 = 4.4\nn5 = 70.0\nt0 = n5 / 100.0\nt1 = n0 / 100.0\nt2 = n4 - n3\nt3 = t0 + t2\nt4 = t1 - t2\nt5 = t3 / t4\nanswer = n2 + t5\nprint(answer)" + ], + "Output Answer": [ + "2010" + ], + "split": "train" + }, + { + "Input": "suppose that f ( x ) is a function such that for every real number x , i ) f ( x ) + f ( 1 - x ) = 10 and ( ii ) f ( 1 + x ) = 3 + f ( x ) . then f ( x ) + f ( - x ) must equal", + "Output Program": [ + "n0 = 1.0\nn1 = 10.0\nn2 = 1.0\nn3 = 3.0\n\nanswer = 10.0 - n3\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "each child has 12 crayons and 24 apples . if there are 18 children , how many crayons are there in total ?", + "Output Program": [ + "n0 = 12.0\nn1 = 24.0\nn2 = 18.0\n\nanswer = n0 * n2\nprint(answer)" + ], + "Output Answer": [ + "216" + ], + "split": "train" + }, + { + "Input": "in a certain warehouse , 90 percent of the packages weigh less than 75 pounds , and a total of 48 packages weigh less than 25 pounds . if 80 percent of the packages weigh at least 25 pounds , how many of the packages weigh at least 25 pounds but less than 75 pounds ?", + "Output Program": [ + "n0 = 90.0\nn1 = 75.0\nn2 = 48.0\nn3 = 25.0\nn4 = 80.0\nn5 = 25.0\nn6 = 25.0\nn7 = 75.0\nt0 = 100.0 - n4\nt1 = n2 / t0\nt2 = t1 * 100.0\nt3 = n0 * t2\nt4 = t3 / 100.0\nanswer = t4 - n2\nprint(answer)" + ], + "Output Answer": [ + "168" + ], + "split": "train" + }, + { + "Input": "if 425 / 999 = 0.125 , what is the 81 st digit to the right of the decimal point in the decimal equivalent of the fraction ?", + "Output Program": [ + "n0 = 425.0\nn1 = 999.0\nn2 = 0.125\nn3 = 81.0\n\nanswer = 2.0 + 3.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "if p and q are prime numbers , how many divisors does the product p ^ 2 * q ^ 5 have ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nt0 = n0 + 1.0\nt1 = n1 + 1.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "the average of a batsman for 40 innings is 50 runs . his highest score exceeds his lowest score by 172 runs . if these two innings are excluded , his average drops by 2 runs . find his highest score .", + "Output Program": [ + "n0 = 40.0\nn1 = 50.0\nn2 = 172.0\nn3 = 2.0\nt0 = n0 * n1\nt1 = n0 - n3\nt2 = n1 - n3\nt3 = t1 * t2\nt4 = t0 - t3\nt5 = t4 - n2\nt6 = t5 / n3\nanswer = n2 + t6\nprint(answer)" + ], + "Output Answer": [ + "174" + ], + "split": "train" + }, + { + "Input": "the number of years of service of the 8 employees in a production department are 15 , 10 , 9 , 17 , 6 , 3 , 14 and 16 . what is the range in the number of years of service of the 8 employees ?", + "Output Program": [ + "n0 = 8.0\nn1 = 15.0\nn2 = 10.0\nn3 = 9.0\nn4 = 17.0\nn5 = 6.0\nn6 = 3.0\nn7 = 14.0\nn8 = 16.0\nn9 = 8.0\n\nanswer = n4 - n6\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "the instructions state that cheryl needs 4 / 19 square yards of one type of material and 2 / 13 square yards of another type of material for a project . she buys exactly that amount . after finishing the project , however , she has 4 / 26 square yards left that she did not use . what is the total amount of square yards of material cheryl used ?", + "Output Program": [ + "n0 = 4.0\nn1 = 19.0\nn2 = 2.0\nn3 = 13.0\nn4 = 4.0\nn5 = 26.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = n4 / n5\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "0.21052631578947367" + ], + "split": "train" + }, + { + "Input": "all the milk in container a which was filled to its brim was poured into two containers b and c . the quantity of milk in container b was 62.5 % less than the capacity of container a . if 154 liters was now transferred from c to b , then both the containers would have equal quantities of milk . what was the initial quantity of milk in container a ?", + "Output Program": [ + "n0 = 62.5\nn1 = 154.0\nt0 = n0 / 100.0\nt1 = 1 / 2.0\nt2 = 1.0 - t0\nt3 = t1 - t2\nanswer = n1 / t3\nprint(answer)" + ], + "Output Answer": [ + "1232" + ], + "split": "train" + }, + { + "Input": "of the 170 people at a party , 70 were women , and 30 women tried the appetizer . if 60 people did not try the appetizer , what is the total number of men who tried the appetizer ?", + "Output Program": [ + "n0 = 170.0\nn1 = 70.0\nn2 = 30.0\nn3 = 60.0\nt0 = n0 - n3\nanswer = t0 - n2\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "on dividing a number by 7 , we get 5 as quotient and 0 as remainder . on dividing the same number by 11 , what will be the remainder ?", + "Output Program": [ + "n0 = 7.0\nn1 = 5.0\nn2 = 0.0\nn3 = 11.0\nt0 = n0 * n1\nanswer = t0 % n3\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "if a 10 percent deposit that has been paid toward the purchase of a certain product is $ 130 , how much more remains to be paid ?", + "Output Program": [ + "n0 = 10.0\nn1 = 130.0\nt0 = 100.0 / n0\nt1 = n1 * t0\nanswer = t1 - n1\nprint(answer)" + ], + "Output Answer": [ + "1170" + ], + "split": "train" + }, + { + "Input": "( ? ) + 3699 + 1985 - 2047 = 31111", + "Output Program": [ + "n0 = 3699.0\nn1 = 1985.0\nn2 = 2047.0\nn3 = 31111.0\nt0 = n0 + n1\nt1 = t0 - n2\nanswer = n3 - t1\nprint(answer)" + ], + "Output Answer": [ + "27474" + ], + "split": "train" + }, + { + "Input": "how many digits are in ( 8 \u00d7 10 ^ 10 ) ( 10 \u00d7 10 ^ 5 ) ?", + "Output Program": [ + "n0 = 8.0\nn1 = 10.0\nn2 = 10.0\nn3 = 10.0\nn4 = 10.0\nn5 = 5.0\nt0 = 3.0 + 4.0\nanswer = t0 + 10.0\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "the shopkeeper increased the price of a product by 25 % so that customer finds it difficult to purchase the required amount . but somehow the customer managed to purchase only 72 % of the required amount . what is the net difference in the expenditure on that product ?", + "Output Program": [ + "n0 = 25.0\nn1 = 72.0\nt0 = n0 + 100.0\nt1 = 100.0 * 100.0\nt2 = n1 * t0\nt3 = t1 - t2\nt4 = t3 * 100.0\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "in a class of 25 students , 3 students did not borrow any books from the library , 11 students each borrowed 1 book , 6 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?", + "Output Program": [ + "n0 = 25.0\nn1 = 3.0\nn2 = 11.0\nn3 = 1.0\nn4 = 6.0\nn5 = 2.0\nn6 = 3.0\nn7 = 2.0\nt0 = n0 * n5\nt1 = n2 * n3\nt2 = n5 * n4\nt3 = t1 + t2\nt4 = n4 + t1\nt5 = n1 + t4\nt6 = n0 - t5\nt7 = t6 - n3\nt8 = n6 * t7\nt9 = t3 + t8\nanswer = t0 - t9\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "a and b together have $ 1210 . if 4 / 15 of a ' s amount is equal to 2 / 5 of b ' s amount , how much amount does b have ?", + "Output Program": [ + "n0 = 1210.0\nn1 = 4.0\nn2 = 15.0\nn3 = 2.0\nn4 = 5.0\nt0 = n3 / n4\nt1 = n1 / n2\nt2 = t0 / t1\nt3 = t2 + 1.0\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "484" + ], + "split": "train" + }, + { + "Input": "a gambler bought $ 3000 worth of chips at a casino in denominations of $ 20 and $ 100 . that evening , the gambler lost 16 chips , and then cashed in the remainder . if the number of $ 20 chips lost was 2 more or 2 less than the number of $ 100 chips lost , what is the largest amount of money that the gambler could have received back ?", + "Output Program": [ + "n0 = 3000.0\nn1 = 20.0\nn2 = 100.0\nn3 = 16.0\nn4 = 20.0\nn5 = 2.0\nn6 = 2.0\nn7 = 100.0\nt0 = n3 + n5\nt1 = 1000.0 * 3.0\nt2 = t0 / n5\nt3 = n1 * t2\nt4 = t2 - n5\nt5 = n2 * t4\nt6 = t3 + t5\nanswer = t1 - t6\nprint(answer)" + ], + "Output Answer": [ + "2120" + ], + "split": "train" + }, + { + "Input": "simplify : 0.3 * 0.8 + 0.1 * 0.5", + "Output Program": [ + "n0 = 0.3\nn1 = 0.8\nn2 = 0.1\nn3 = 0.5\nt0 = n0 * n1\nt1 = n2 * n3\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "0.29" + ], + "split": "train" + }, + { + "Input": "if p ( a ) = 6 / 17 , p ( b ) = 5 / 17 , and p ( a \u222a b ) = 4 / 17 find p ( b | a ) ?", + "Output Program": [ + "n0 = 6.0\nn1 = 17.0\nn2 = 5.0\nn3 = 17.0\nn4 = 4.0\nn5 = 17.0\nt0 = n4 / n1\nt1 = n0 / n1\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.6666666666666666" + ], + "split": "train" + }, + { + "Input": "given a spinner with 4 sections of equal size labeled e , b , c , and d , what is the probability of not getting an e after spinning the spinner two times ?", + "Output Program": [ + "n0 = 4.0\nt0 = 3.0 / n0\nanswer = t0**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "0.5625" + ], + "split": "train" + }, + { + "Input": "the sum of the fourth and twelfth term of an arithmetic progression is 20 . what is the sum of the first 10 terms of the arithmetic progression ?", + "Output Program": [ + "n0 = 20.0\nn1 = 10.0\nt0 = n0 * n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "a salt manufacturing company produced a total of 3000 tonnes of salt in january of a particular year . starting from february its production increased by 100 tonnes every month over the previous months until the end of the year . find its ave 66 rage daily production for that year ?", + "Output Program": [ + "n0 = 3000.0\nn1 = 100.0\nn2 = 66.0\nt0 = 2.0 + 3.0\nt1 = n0 * 2.0\nt2 = n1 * 3.0\nt3 = 2.0 * 3.0\nt4 = 12.0 - 1.0\nt5 = n1 * t4\nt6 = t3 * 10.0\nt7 = t1 + t5\nt8 = t2 + t6\nt9 = t8 + t0\nt10 = t7 * 12.0\nt11 = t10 / 2.0\nanswer = t11 / t9\nprint(answer)" + ], + "Output Answer": [ + "116.71232876712328" + ], + "split": "train" + }, + { + "Input": "what least number must be subtracted from 652543 so that remaining no . is divisible by 12", + "Output Program": [ + "import math\nn0 = 652543.0\nn1 = 12.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "a , b , c and d enter into partnership . a subscribes 1 / 3 of the capital b 1 / 4 , c 1 / 5 and d the rest . how much share did a get in a profit of rs . 2475 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 4.0\nn4 = 1.0\nn5 = 5.0\nn6 = 2475.0\nt0 = n0 / n1\nanswer = n6 * t0\nprint(answer)" + ], + "Output Answer": [ + "825" + ], + "split": "train" + }, + { + "Input": "a batsman makes a score of 80 runs in the 11 th inning and thus increases his average by 5 . find his average after 11 th inning .", + "Output Program": [ + "n0 = 80.0\nn1 = 11.0\nn2 = 5.0\nn3 = 11.0\nt0 = n1 * n2\nt1 = n0 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "on a two - dimensional coordinate plane , the line s = x ^ 2 - x ^ 3 touches the x - axis in how many places ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nt0 = max(n0,n1)\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a batsman makes a score of 95 runs in the 11 th inning and thus increases his average by 5 . find his average after 11 th inning .", + "Output Program": [ + "n0 = 95.0\nn1 = 11.0\nn2 = 5.0\nn3 = 11.0\nt0 = n1 * n2\nt1 = n0 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "16.036 divided by 0.04 gives :", + "Output Program": [ + "n0 = 16.036\nn1 = 0.04\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "400.90000000000003" + ], + "split": "train" + }, + { + "Input": "a canoe has two oars , left and right . each oar either works or breaks . the failure or non - failure of each oar is independent of the failure or non - failure of the other . you can still row the canoe with one oar . the probability that the left oar works is 3 / 5 . the probability that the right oar works is also 3 / 5 . what is the probability r that you can still row the canoe ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 3.0\nn3 = 5.0\nt0 = n0 / n1\nt1 = 2.0 / n1\nt2 = t0 * t1\nt3 = t0 * t0\nt4 = t2 + t2\nanswer = t4 + t3\nprint(answer)" + ], + "Output Answer": [ + "0.84" + ], + "split": "train" + }, + { + "Input": "a is the average ( arithmetic mean ) of the first 7 positive multiples of 8 and b is the median of the first 3 positive multiples of positive integer n . if the value of a ^ 2 \u2013 b ^ 2 is zero , what is the value of n ?", + "Output Program": [ + "n0 = 7.0\nn1 = 8.0\nn2 = 3.0\nn3 = 2.0\nn4 = 2.0\nt0 = n1 * 4.0\nanswer = t0 / n3\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "the population of a bacteria culture doubles every 3 minutes . approximately how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 1000.0\nn2 = 500000.0\nt0 = 1.0 + 4.0\nt1 = t0 * 1000.0\nt2 = t1 * 100.0\nt3 = t2 / 1000.0\nt4 = math.log(max(1e-5, t3), 2)\nanswer = n0 * t4\nprint(answer)" + ], + "Output Answer": [ + "26.897352853986263" + ], + "split": "train" + }, + { + "Input": "8 ! / ( 8 - 2 ) ! = ?", + "Output Program": [ + "import math\nn0 = 8.0\nn1 = 8.0\nn2 = 2.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = n0 - n2\nt2 = math.factorial(min(15, int(t1)))\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "train" + }, + { + "Input": "sally , mark , sarah , steve and jim are inheriting the money from their grandmother . she left them $ 527500 to split equally between all of them . if the money is split equally , how much money will each person receive ?", + "Output Program": [ + "n0 = 527500.0\nt0 = 1.0 + 4.0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "105500" + ], + "split": "train" + }, + { + "Input": "s ( n ) is a n - digit number formed by attaching the first n perfect squares , in order , into one integer . for example , s ( 1 ) = 1 , s ( 2 ) = 14 , s ( 3 ) = 149 , s ( 4 ) = 14916 , s ( 5 ) = 1491625 , etc . how many digits r are in s ( 99 ) ?", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 2.0\nn3 = 14.0\nn4 = 3.0\nn5 = 149.0\nn6 = 4.0\nn7 = 14916.0\nn8 = 5.0\nn9 = 1491625.0\nn10 = 99.0\nt0 = n6 + 60.0\nt1 = n0 * n4\nt2 = n2 * n4\nt3 = n6 + t0\nt4 = n2 * t2\nt5 = t1 + t4\nt6 = n6 * t3\nt7 = t3 + t6\nanswer = t7 + t5\nprint(answer)" + ], + "Output Answer": [ + "355" + ], + "split": "train" + }, + { + "Input": "if a and b are positive integers and ( 2 ^ a ) ^ b = 2 ^ 2 , what is the value of 2 ^ a * 2 ^ b ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 2.0\nn3 = 2.0\nn4 = 2.0\nt0 = n0**min(n0, 5)\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "when 242 is divided by a certain divisor the remainder obtained is 4 . when 698 is divided by the same divisor the remainder obtained is 8 . however , when the sum of the two numbers 242 and 698 is divided by the divisor , the remainder obtained is 7 . what is the value of the divisor ?", + "Output Program": [ + "n0 = 242.0\nn1 = 4.0\nn2 = 698.0\nn3 = 8.0\nn4 = 242.0\nn5 = 698.0\nn6 = 7.0\nt0 = n1 + n3\nanswer = t0 - n6\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "p , q and r have rs . 8000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?", + "Output Program": [ + "n0 = 8000.0\nt0 = 2.0 / 3.0\nt1 = t0 + 1.0\nt2 = n0 / t1\nanswer = t2 * t0\nprint(answer)" + ], + "Output Answer": [ + "3200" + ], + "split": "train" + }, + { + "Input": "how many positive integers between 1 and 300 are there such that they are multiples of 9 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 300.0\nn2 = 9.0\nt0 = n1 - n0\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "33.22222222222222" + ], + "split": "train" + }, + { + "Input": "the average weight of 16 girls in a class is 50.25 kg and that of the remaining 8 girls is 45.15 kg . find the average weights of all the girls in the class .", + "Output Program": [ + "n0 = 16.0\nn1 = 50.25\nn2 = 8.0\nn3 = 45.15\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "48.550000000000004" + ], + "split": "train" + }, + { + "Input": "if rs . 782 is divided into 3 parts , proportional to 1 / 2 : 2 / 3 : 3 / 4 find the first part .", + "Output Program": [ + "n0 = 782.0\nn1 = 3.0\nn2 = 1.0\nn3 = 2.0\nn4 = 2.0\nn5 = 3.0\nn6 = 3.0\nn7 = 4.0\nt0 = 12.0 / n3\nt1 = 12.0 / n1\nt2 = 12.0 / n7\nt3 = t1 * 2.0\nt4 = t2 * 3.0\nt5 = t0 + t3\nt6 = t5 + t4\nt7 = t0 / t6\nanswer = n0 * t7\nprint(answer)" + ], + "Output Answer": [ + "204" + ], + "split": "train" + }, + { + "Input": "find the value for m ? 21 ( m + n ) + 21 = 21 ( - m + n ) + 21", + "Output Program": [ + "n0 = 21.0\nn1 = 21.0\nn2 = 21.0\nn3 = 21.0\nt0 = 10.0 * 2.0\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "a certain telescope increases the visual range at a particular location from 50 kilometers to 150 kilometers . by what percent is the visual range increased by using the telescope ?", + "Output Program": [ + "n0 = 50.0\nn1 = 150.0\nt0 = n1 - n0\nt1 = t0 / n0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "train" + }, + { + "Input": "excluding stoppages , the average speed of a bus is 50 km / hr and including stoppages , the average speed of the bus is 40 km / hr . for how many minutes does the bus stop per hour ?", + "Output Program": [ + "n0 = 50.0\nn1 = 40.0\nt0 = n1 / n0\nt1 = 1.0 * 60.0\nt2 = t0 * 60.0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "the total marks obtained by a student in mathematics and physics is 20 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together .", + "Output Program": [ + "n0 = 20.0\nn1 = 20.0\nt0 = n0 + n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "how many numbers from 10 to 10000 are exactly divisible by 9 ?", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 10000.0\nn2 = 9.0\nt0 = n1 / n2\nt1 = n0 / n2\nt2 = math.floor(t0)\nt3 = math.floor(t1)\nt4 = t3 + 1.0\nt5 = n2 * t2\nt6 = n2 * t4\nt7 = t5 - t6\nt8 = t7 / n2\nanswer = t8 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "1110" + ], + "split": "train" + }, + { + "Input": "if the price of sugar rises from rs . 3 per kg to rs . 5 per kg , a person , to have no increase in the expenditure on sugar , will have to reduce his consumption of sugar by", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nt0 = n0 * 1.0\nt1 = t0 / n1\nt2 = 1.0 - t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "find the average of all prime numbers between 30 and 50 .", + "Output Program": [ + "n0 = 30.0\nn1 = 50.0\nt0 = n0 + 1.0\nt1 = n1 - 4.0\nt2 = n1 - 2.0\nt3 = t0 + 2.0\nt4 = t1 + t2\nt5 = t0 + t3\nt6 = t5 + t4\nanswer = t6 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "39.5" + ], + "split": "train" + }, + { + "Input": "a gambler bought $ 3,000 worth of chips at a casino in denominations of $ 30 and $ 100 . that evening , the gambler lost 16 chips , and then cashed in the remainder . if the number of $ 30 chips lost was 2 more or 2 less than the number of $ 100 chips lost , what is the largest amount of money that the gambler could have received back ?", + "Output Program": [ + "n0 = 3000.0\nn1 = 30.0\nn2 = 100.0\nn3 = 16.0\nn4 = 30.0\nn5 = 2.0\nn6 = 2.0\nn7 = 100.0\nt0 = n3 + n5\nt1 = 1000.0 * 3.0\nt2 = t0 / n5\nt3 = n1 * t2\nt4 = t2 - n5\nt5 = n2 * t4\nt6 = t3 + t5\nanswer = t1 - t6\nprint(answer)" + ], + "Output Answer": [ + "2030" + ], + "split": "train" + }, + { + "Input": "if 20 percent of the students at a certain school went to a camping trip and took more than $ 100 , and 75 percent of the students who went to the camping trip did not take more than $ 100 , what percentage of the students at the school went to the camping trip ?", + "Output Program": [ + "n0 = 20.0\nn1 = 100.0\nn2 = 75.0\nn3 = 100.0\nt0 = n1 - n2\nt1 = t0 / n1\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "a certain bus driver is paid a regular rate of $ 12 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 976 in total compensation , how many total hours did he work that week ?", + "Output Program": [ + "n0 = 12.0\nn1 = 40.0\nn2 = 40.0\nn3 = 75.0\nn4 = 976.0\nt0 = n3 + 100.0\nt1 = n0 * n1\nt2 = n0 * t0\nt3 = n4 - t1\nt4 = t2 / 100.0\nt5 = t3 / t4\nanswer = n1 + t5\nprint(answer)" + ], + "Output Answer": [ + "63.61904761904762" + ], + "split": "train" + }, + { + "Input": "the tax on a commodity is diminished by 19 % and its consumption increased by 15 % . the effect on revenue is ?", + "Output Program": [ + "n0 = 19.0\nn1 = 15.0\nt0 = n1 / 100.0\nt1 = n0 / 100.0\nt2 = t0 + 1.0\nt3 = 1.0 - t1\nt4 = t2 * t3\nt5 = t4 * 100.0\nanswer = 100.0 - t5\nprint(answer)" + ], + "Output Answer": [ + "6.849999999999994" + ], + "split": "train" + }, + { + "Input": "if x is less than y by 40 % then y exceed x by :", + "Output Program": [ + "n0 = 40.0\nt0 = 100.0 - n0\nt1 = 100.0 / t0\nt2 = t1 - 1.0\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "66.66666666666667" + ], + "split": "train" + }, + { + "Input": "a school has 4 section of chemistry in class x having 55 , 35 , 45 and 42 students . the mean marks obtained in chemistry test are 50 , 60 , 55 and 45 respectively for the 4 sections . determine the overall average of marks per student .", + "Output Program": [ + "n0 = 4.0\nn1 = 55.0\nn2 = 35.0\nn3 = 45.0\nn4 = 42.0\nn5 = 50.0\nn6 = 60.0\nn7 = 55.0\nn8 = 45.0\nn9 = 4.0\nt0 = n1 + n2\nt1 = n1 * n5\nt2 = n2 * n6\nt3 = n3 * n7\nt4 = n3 * n4\nt5 = t1 + t2\nt6 = n3 + t0\nt7 = t5 + t3\nt8 = n4 + t6\nt9 = t7 + t4\nanswer = t9 / t8\nprint(answer)" + ], + "Output Answer": [ + "52.06214689265537" + ], + "split": "train" + }, + { + "Input": "if a person cover 3 / 5 part of his journey by train , 7 / 20 part of his journey by bus and rest 6.5 km . by walk . what is total distance of his journey ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 7.0\nn3 = 20.0\nn4 = 6.5\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = t0 + t1\nt3 = 1.0 - t2\nanswer = n4 / t3\nprint(answer)" + ], + "Output Answer": [ + "129.9999999999999" + ], + "split": "train" + }, + { + "Input": "calculate the average of all the numbers between 15 and 55 which are divisible by 4 .", + "Output Program": [ + "import math\nn0 = 15.0\nn1 = 55.0\nn2 = 4.0\nt0 = n0 / n2\nt1 = n1 / n2\nt2 = math.floor(t0)\nt3 = math.floor(t1)\nt4 = t2 + 1.0\nt5 = t4 + t3\nt6 = t5 / 2.0\nanswer = n2 * t6\nprint(answer)" + ], + "Output Answer": [ + "34" + ], + "split": "train" + }, + { + "Input": "if ( a + b ) = 16 , ( b + c ) = 9 and ( c + d ) = 3 , what is the value of ( a + d ) ?", + "Output Program": [ + "n0 = 16.0\nn1 = 9.0\nn2 = 3.0\nt0 = n0 + n2\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "rs . 880 is divided amongst a , b , c so that 4 times a ' s share , 5 times b ' s share and 10 times c ' s share are all equal . find c ' s share ?", + "Output Program": [ + "n0 = 880.0\nn1 = 4.0\nn2 = 5.0\nn3 = 10.0\nt0 = n3 / n1\nt1 = n3 / n2\nt2 = t0 + t1\nt3 = t2 + 1.0\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "160" + ], + "split": "train" + }, + { + "Input": "in a mixture of 45 litres the ratio of milk to water is 4 : 1 . additional 18 litres of water is added to the mixture . find the ratio of milk to water in the resulting mixture .", + "Output Program": [ + "n0 = 45.0\nn1 = 4.0\nn2 = 1.0\nn3 = 18.0\nt0 = n1 + n2\nt1 = n0 / t0\nt2 = n3 + t1\nt3 = n0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "1.3333333333333333" + ], + "split": "train" + }, + { + "Input": "what is the least number should be added to 1056 , so the sum of the number is completely divisible by 25 ?", + "Output Program": [ + "import math\nn0 = 1056.0\nn1 = 25.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = t1 + 1.0\nt3 = n1 * t2\nanswer = t3 - n0\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "if 853845 bars of chocolate need to be placed in little boxes and each box can contain at most 9 bars of chocolate . how many bars of chocolate will be in the last unfilled box ?", + "Output Program": [ + "import math\nn0 = 853845.0\nn1 = 9.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "a class is 6 meters 24 centimeters in length and 4 meters 32 centimeters in width . find the least number of square tiles of equal size required to cover the entire floor of the class room ?", + "Output Program": [ + "n0 = 6.0\nn1 = 24.0\nn2 = 4.0\nn3 = 32.0\nt0 = n1 + n1\nt1 = n0 * 100.0\nt2 = n2 * 100.0\nt3 = n1 + t1\nt4 = n3 + t2\nt5 = t0 * t0\nt6 = t3 * t4\nanswer = t6 / t5\nprint(answer)" + ], + "Output Answer": [ + "117" + ], + "split": "train" + }, + { + "Input": "mixture contains alcohol and water in the ratio 4 : 3 . if 4 liters of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture .", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 4.0\nn3 = 4.0\nn4 = 5.0\nt0 = n0 * n4\nt1 = n0 * n2\nt2 = n0 * n1\nt3 = t1 - t2\nt4 = t0 / t3\nanswer = n0 * t4\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "the sum of the fourth and twelfth term of an arithmetic progression is 20 . what is the sum of the first 12 terms of the arithmetic progression ?", + "Output Program": [ + "n0 = 20.0\nn1 = 12.0\nt0 = n0 * n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "soja finished 2 / 3 of a book . she calculated that she finished 100 more pages than she has yet to read . how long is her book ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 100.0\n\nanswer = n1 * n2\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "the average score of a cricketer in 10 matches is 60 and in other 15 matches is 70 . then find the average score in all the 25 matches ?", + "Output Program": [ + "n0 = 10.0\nn1 = 60.0\nn2 = 15.0\nn3 = 70.0\nn4 = 25.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = t0 + t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "66" + ], + "split": "train" + }, + { + "Input": "one - third less than 30 % of 180 is equal to :", + "Output Program": [ + "n0 = 30.0\nn1 = 180.0\nt0 = n0 / 100.0\nt1 = 1.0 / 3.0\nt2 = n1 * t0\nt3 = t1 * t2\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "the average of marks obtained by 120 boys was 35 . if the average of marks of passed boys was 39 and that of failed boys was 15 , the number of boys who passed the examination is ?", + "Output Program": [ + "n0 = 120.0\nn1 = 35.0\nn2 = 39.0\nn3 = 15.0\nt0 = n0 * n1\nt1 = n0 * n3\nt2 = n2 - n3\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "a whale goes on a feeding frenzy that lasts for 5 hours . for the first hour he catches and eats x kilos of plankton . in every hour after the first , it consumes 3 kilos of plankton more than it consumed in the previous hour . if by the end of the frenzy the whale will have consumed a whopping accumulated total 450 kilos of plankton , how many kilos did he consume on the third hour ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nn2 = 450.0\nt0 = n2 / n0\nanswer = n1 + t0\nprint(answer)" + ], + "Output Answer": [ + "93" + ], + "split": "train" + }, + { + "Input": "10 camels cost as much as 24 horses , 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants . if the cost of 10 elephants is rs . 150000 , find the cost of a camel ?", + "Output Program": [ + "n0 = 10.0\nn1 = 24.0\nn2 = 16.0\nn3 = 4.0\nn4 = 6.0\nn5 = 4.0\nn6 = 10.0\nn7 = 150000.0\nt0 = n1 * n3\nt1 = n0 * n2\nt2 = n3 * t0\nt3 = n4 * t1\nt4 = n7 * t2\nt5 = n0 * t3\nanswer = t4 / t5\nprint(answer)" + ], + "Output Answer": [ + "6000" + ], + "split": "train" + }, + { + "Input": "7 people average age is 30 . youngest person age is 3 . find average of the people when youngest was born .", + "Output Program": [ + "n0 = 7.0\nn1 = 30.0\nn2 = 3.0\nt0 = n0 * n1\nt1 = n0 * n2\nt2 = t0 - t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "train" + }, + { + "Input": "what is value of ( ( 2 ^ 5 ) * ( 9 ^ 2 ) ) / ( ( 8 ^ 2 ) * ( 3 ^ 5 ) ) = ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 9.0\nn3 = 2.0\nn4 = 8.0\nn5 = 2.0\nn6 = 3.0\nn7 = 5.0\nt0 = n0**min(n1, 5)\nt1 = n2**min(n0, 5)\nt2 = n4**min(n0, 5)\nt3 = n6**min(n1, 5)\nt4 = t0 * t1\nt5 = t2 * t3\nanswer = t4 / t5\nprint(answer)" + ], + "Output Answer": [ + "0.16666666666666666" + ], + "split": "train" + }, + { + "Input": "when a natural number n is successively divided by 12 , 34 the remainders are 56 , 78 . what will be the sum of the remainders if the order of the division is reversed ?", + "Output Program": [ + "n0 = 12.0\nn1 = 34.0\nn2 = 56.0\nn3 = 78.0\nt0 = n0 + n1\nanswer = n2 - t0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the shopkeeper increased the price of a product by 25 % so that customer finds it difficult to purchase the required amount . but somehow the customer managed to purchase only 64 % of the required amount . what is the net difference in the expenditure on that product ?", + "Output Program": [ + "n0 = 25.0\nn1 = 64.0\nt0 = n0 + 100.0\nt1 = 100.0 * 100.0\nt2 = n1 * t0\nt3 = t1 - t2\nt4 = t3 * 100.0\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "two digits in john ' s age are the same as the digit in the wilson ' s age , but in reverse order . in 21 years john will be twice as old as wilson will be then . what is the difference in their current age ?", + "Output Program": [ + "n0 = 21.0\nt0 = n0 + 3.0\nt1 = 3.0 * 4.0\nt2 = t0 * 2.0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "a cab driver 5 days income was $ 45 , $ 50 , $ 60 , $ 65 , $ 70 . then his average income is ?", + "Output Program": [ + "n0 = 5.0\nn1 = 45.0\nn2 = 50.0\nn3 = 60.0\nn4 = 65.0\nn5 = 70.0\nt0 = n1 + n2\nt1 = n3 + t0\nt2 = n4 + t1\nt3 = n5 + t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "58" + ], + "split": "train" + }, + { + "Input": "in a box of 9 pencils , a total of 2 are defective . if a customer buys 3 pencils selected at random from the box , what is the probability that neither pencils will be defective ?", + "Output Program": [ + "import math\nn0 = 9.0\nn1 = 2.0\nn2 = 3.0\nt0 = math.factorial(min(15, int(n2)))\nt1 = math.factorial(min(15, int(n0)))\nt2 = n0 - n1\nt3 = n0 - n2\nt4 = math.factorial(min(15, int(t2)))\nt5 = math.factorial(min(15, int(t3)))\nt6 = t2 - n2\nt7 = math.factorial(min(15, int(t6)))\nt8 = t5 * t0\nt9 = t1 / t8\nt10 = t7 * t0\nt11 = t4 / t10\nanswer = t11 / t9\nprint(answer)" + ], + "Output Answer": [ + "0.4166666666666667" + ], + "split": "train" + }, + { + "Input": "at a monthly meeting , 3 / 5 of the attendees were males and 7 / 8 of the male attendees arrived on time . if 9 / 10 of the female attendees arrived on time , what fraction of the attendees at the monthly meeting did not arrive on time ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 7.0\nn3 = 8.0\nn4 = 9.0\nn5 = 10.0\nt0 = n4 / n5\nt1 = n0 / n1\nt2 = n2 / n3\nt3 = 1.0 - t0\nt4 = 1.0 - t1\nt5 = 1.0 - t2\nt6 = t3 * t4\nt7 = t1 * t5\nanswer = t6 + t7\nprint(answer)" + ], + "Output Answer": [ + "0.11499999999999999" + ], + "split": "train" + }, + { + "Input": "how many pages do you need if you have to write 150 lines of information into pages that each hold 30 lines ?", + "Output Program": [ + "n0 = 150.0\nn1 = 30.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "a sum of money lent out at s . i . amounts to rs . 780 after 2 years and to rs . 1020 after a further period of 5 years . the sum is ?", + "Output Program": [ + "n0 = 780.0\nn1 = 2.0\nn2 = 1020.0\nn3 = 5.0\nt0 = n2 - n0\nt1 = t0 / n3\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "684" + ], + "split": "train" + }, + { + "Input": "the average salary of the employees in a office is rs . 120 / month . the avg salary of officers is rs . 440 and of non officers is rs 110 . if the no . of officers is 15 , then find the no of nonofficers in the office .", + "Output Program": [ + "n0 = 120.0\nn1 = 440.0\nn2 = 110.0\nn3 = 15.0\nt0 = n1 * n3\nt1 = n0 * n3\nt2 = n0 - n2\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "480" + ], + "split": "train" + }, + { + "Input": "farm tax is levied on the 50 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . william . mr . william paid only $ 480 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :", + "Output Program": [ + "n0 = 50.0\nn1 = 3840.0\nn2 = 480.0\nt0 = n2 / n1\nt1 = t0 * 100.0\nt2 = t1 * 100.0\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "the total number of digits used in numbering the pages of a book having 266 pages is", + "Output Program": [ + "n0 = 266.0\nt0 = n0 * 3.0\nt1 = 100.0 - 1.0\nt2 = 10.0 - 1.0\nt3 = t0 - t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "690" + ], + "split": "train" + }, + { + "Input": "a mixture of 150 liters of wine and water contains 10 % water . how much more water should be added so that water becomes 25 % of the new mixture ?", + "Output Program": [ + "n0 = 150.0\nn1 = 10.0\nn2 = 25.0\nt0 = n2 / 100.0\nt1 = n1 / 100.0\nt2 = n0 * t0\nt3 = n0 * t1\nt4 = 1.0 - t0\nt5 = t2 - t3\nanswer = t5 / t4\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "what is the difference between the local values of 8 in the number 58408 ?", + "Output Program": [ + "n0 = 8.0\nn1 = 58408.0\nt0 = n0 * 1000.0\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "7992" + ], + "split": "train" + }, + { + "Input": "if there are 4 peanuts in a box and mary puts 12 more peanuts inside , how many peanuts are in the box ?", + "Output Program": [ + "n0 = 4.0\nn1 = 12.0\n\nanswer = n0 + n1\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "total dinning bill of 7 people was $ 139.00 and 10 % tip divided the bill evenly ? what is the bill amount each person shared .", + "Output Program": [ + "n0 = 7.0\nn1 = 139.0\nn2 = 10.0\nt0 = 1.0 / n2\nt1 = t0 + 1.0\nt2 = n1 * t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "21.842857142857145" + ], + "split": "train" + }, + { + "Input": "city x has a population 3 times as great as the population of city y , which has a population twice as great as the population of city z . what is the ratio of the population of city x to the population of city z ?", + "Output Program": [ + "n0 = 3.0\n\nanswer = n0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "what is the dividend ? the divisor is 800 , the quotient is 594 , and the remainder is - 968 .", + "Output Program": [ + "n0 = 800.0\nn1 = 594.0\nn2 = 968.0\nt0 = n0 * n1\nanswer = t0 - n2\nprint(answer)" + ], + "Output Answer": [ + "474232" + ], + "split": "train" + }, + { + "Input": "sum of 24 odd numbers is ?", + "Output Program": [ + "n0 = 24.0\nt0 = n0 / 2.0\nt1 = n0 * 2.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "576" + ], + "split": "train" + }, + { + "Input": "find 4 + 7 + 10 + 13 + 16 + . . . up to 20 terms", + "Output Program": [ + "n0 = 4.0\nn1 = 7.0\nn2 = 10.0\nn3 = 13.0\nn4 = 16.0\nn5 = 20.0\nt0 = n4 * n5\nt1 = n2 * n3\nt2 = n0 * n1\nt3 = n2 - 2.0\nt4 = t0 + t1\nt5 = t2 - t3\nt6 = t5 * 10.0\nanswer = t4 + t6\nprint(answer)" + ], + "Output Answer": [ + "650" + ], + "split": "train" + }, + { + "Input": "10 play kabadi , 15 play kho kho only , 5 play both gmaes . then how many in total ?", + "Output Program": [ + "n0 = 10.0\nn1 = 15.0\nn2 = 5.0\nt0 = n1 + n2\nt1 = n0 + t0\nanswer = t1 - n2\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "the number 523 rbc is divisible by 7 , 89 . then what is the value of r * b * c", + "Output Program": [ + "n0 = 523.0\nn1 = 7.0\nn2 = 89.0\nt0 = 2.0 + 3.0\nt1 = 2.0 * 3.0\nt2 = t0 * t1\nanswer = t2 * t1\nprint(answer)" + ], + "Output Answer": [ + "180" + ], + "split": "train" + }, + { + "Input": "in a certain game , a large bag is filled with blue , green , purple and red chips worth 1 , 5 , x and 11 points each , respectively . the purple chips are worth more than the green chips , but less than the red chips . a certain number of chips are then selected from the bag . if the product of the point values of the selected chips is 28160 , how many purple chips were selected ?", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 11.0\nn3 = 28160.0\n\nanswer = n1 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "if a - b = 9 and a ^ 2 + b ^ 2 = 281 , find the value of ab", + "Output Program": [ + "import math\nn0 = 9.0\nn1 = 2.0\nn2 = 2.0\nn3 = 281.0\nt0 = math.sqrt(max(0, n3))\nt1 = t0 - n0\nt2 = t1 / n1\nt3 = n0 + t2\nt4 = t3 * t2\nanswer = n1 * t4\nprint(answer)" + ], + "Output Answer": [ + "100.00000000000001" + ], + "split": "train" + }, + { + "Input": "there are 2 sections a and b in a class , consisting of 60 and 70 students respectively . if the average weight of section a is 60 kg and that of section b is 80 kg , find the average of the whole class ?", + "Output Program": [ + "n0 = 2.0\nn1 = 60.0\nn2 = 70.0\nn3 = 60.0\nn4 = 80.0\nt0 = n1 + n2\nt1 = n1 * n3\nt2 = n2 * n4\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "70.76923076923077" + ], + "split": "train" + }, + { + "Input": "a furniture store owner decided to drop the price of her recliners by 20 % to spur business . by the end of the week she had sold 80 % more recliners . what is the percentage increase of the gross ?", + "Output Program": [ + "n0 = 20.0\nn1 = 80.0\nt0 = n1 / 100.0\nt1 = n0 / 100.0\nt2 = t0 + 1.0\nt3 = 1.0 - t1\nt4 = t2 * t3\nt5 = t4 * 100.0\nanswer = t5 - 100.0\nprint(answer)" + ], + "Output Answer": [ + "44.00000000000003" + ], + "split": "train" + }, + { + "Input": "if k is an integer and 121 < k ^ 2 < 225 , then k can have at most how many values ?", + "Output Program": [ + "import math\nn0 = 121.0\nn1 = 2.0\nn2 = 225.0\nt0 = math.sqrt(max(0, n2))\nt1 = math.sqrt(max(0, n0))\nt2 = t0 - t1\nt3 = t2 - 1.0\nanswer = t3 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "the mean of 40 observations was 36 . it was found later that an observation 34 was wrongly taken as 20 . the corrected new mean is", + "Output Program": [ + "n0 = 40.0\nn1 = 36.0\nn2 = 34.0\nn3 = 20.0\nt0 = n0 * n1\nt1 = n0 - 2.0\nt2 = t1 - n3\nt3 = t0 + t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "36.45" + ], + "split": "train" + }, + { + "Input": "a small pool filled only with water will require an additional 300 gallons of water in order to be filled to 80 % of its capacity . if pumping in these additional 300 gallons of water will increase the amount of water in the pool by 40 % , what is the total capacity of the pool in gallons ?", + "Output Program": [ + "n0 = 300.0\nn1 = 80.0\nn2 = 300.0\nn3 = 40.0\nt0 = n1 / 100.0\nt1 = n0 * 100.0\nt2 = t1 / n3\nt3 = n0 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "1312.5" + ], + "split": "train" + }, + { + "Input": "total dinning bill of 5 people was $ 139.00 and 10 % tip divided the bill evenly ? what is the bill amount each person shared .", + "Output Program": [ + "n0 = 5.0\nn1 = 139.0\nn2 = 10.0\nt0 = 1.0 / n2\nt1 = t0 + 1.0\nt2 = n1 * t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "30.580000000000002" + ], + "split": "train" + }, + { + "Input": "at a monthly meeting , 3 / 5 of the attendees were males and 4 / 5 of the male attendees arrived on time . if 5 / 6 of the female attendees arrived on time , what fraction of the attendees at the monthly meeting did not arrive on time ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 4.0\nn3 = 5.0\nn4 = 5.0\nn5 = 6.0\nt0 = n4 / n5\nt1 = n0 / n1\nt2 = n2 / n3\nt3 = 1.0 - t0\nt4 = 1.0 - t1\nt5 = 1.0 - t2\nt6 = t3 * t4\nt7 = t1 * t5\nanswer = t6 + t7\nprint(answer)" + ], + "Output Answer": [ + "0.18666666666666662" + ], + "split": "train" + }, + { + "Input": "when positive integer x is divided by 7 , the quotient is y and the remainder is 3 . when 2 x is divided by 6 , the quotient is 3 y and the remainder is 2 . what is the value of 11 y \u2013 x ?", + "Output Program": [ + "n0 = 7.0\nn1 = 3.0\nn2 = 2.0\nn3 = 6.0\nn4 = 3.0\nn5 = 2.0\nn6 = 11.0\nt0 = n1 * n2\nt1 = n3 * n4\nt2 = n0 * n2\nt3 = t0 - n5\nt4 = t1 - t2\nt5 = t3 / t4\nt6 = n6 * t5\nt7 = n0 * t5\nt8 = n1 + t7\nanswer = t6 - t8\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "two brothers ram and ravi appeared for an exam . the probability of selection of ram is 6 / 7 and that of ravi is 1 / 5 . find the probability that both of them are selected .", + "Output Program": [ + "n0 = 6.0\nn1 = 7.0\nn2 = 1.0\nn3 = 5.0\nt0 = n0 / n1\nt1 = n2 / n3\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "0.17142857142857143" + ], + "split": "train" + }, + { + "Input": "a volunteer organization is recruiting new members . in the fall they manage to increase their number by 6 % . by the spring however membership falls by 19 % . what is the total change in percentage from fall to spring ?", + "Output Program": [ + "n0 = 6.0\nn1 = 19.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = t0 + 1.0\nt3 = 1.0 - t1\nt4 = t2 * t3\nt5 = t4 * 100.0\nanswer = 100.0 - t5\nprint(answer)" + ], + "Output Answer": [ + "14.139999999999986" + ], + "split": "train" + }, + { + "Input": "if 8 boys meet at a reunion and each boy shakes hands exactly once with each of the others , then what is the total number of handshakes", + "Output Program": [ + "import math\nn0 = 8.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(2.0)))\nt2 = n0 - 2.0\nt3 = math.factorial(min(15, int(t2)))\nt4 = t3 * t1\nanswer = t0 / t4\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "for all real numbers v , an operation is defined by the equation v * = v - v / 3 . if ( v * ) * = 12 , then v =", + "Output Program": [ + "n0 = 3.0\nn1 = 12.0\nt0 = 1.0 / n0\nt1 = 1.0 - t0\nt2 = n1 / t1\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "26.999999999999993" + ], + "split": "train" + }, + { + "Input": "a grocer has a sale of rs . 8435 , rs . 8927 , rs . 8855 , rs . 9230 and rs . 8562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 8500 ?", + "Output Program": [ + "n0 = 8435.0\nn1 = 8927.0\nn2 = 8855.0\nn3 = 9230.0\nn4 = 8562.0\nn5 = 5.0\nn6 = 8500.0\nt0 = n5 + 1.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n6 * t0\nt4 = n3 + t2\nt5 = n4 + t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "6991" + ], + "split": "train" + }, + { + "Input": "7 does not occur in 1000 . so we have to count the number of times it appears between 1 and 999 . any number between 1 and 999 can be expressed in the form of xyz where 0 < x , y , z < 9 .", + "Output Program": [ + "n0 = 7.0\nn1 = 1000.0\nn2 = 1.0\nn3 = 999.0\nn4 = 1.0\nn5 = 999.0\nn6 = 0.0\nn7 = 9.0\nt0 = n7 * n7\nt1 = n7 * 3.0\nt2 = t0 * 3.0\nt3 = t1 * 2.0\nt4 = t2 + t3\nanswer = t4 + 3.0\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "dacid obtained 76 , 65 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?", + "Output Program": [ + "n0 = 76.0\nn1 = 65.0\nn2 = 82.0\nn3 = 67.0\nn4 = 85.0\nn5 = 100.0\nt0 = n0 + n1\nt1 = 10.0 / 2.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "16 ltr of water is added with 24 ltr of a solution containing 90 % of alcohol in the water . the % of alcohol in the new mixture is ?", + "Output Program": [ + "n0 = 16.0\nn1 = 24.0\nn2 = 90.0\nt0 = n0 + n1\nt1 = n2 / 100.0\nt2 = n1 * t1\nt3 = t2 / t0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "train" + }, + { + "Input": "in karthik ' s opinion , his weight is greater than 55 kg but less than 62 kg . his brother does not agree with karthik and he thinks that karthik ' s weight is greater than 50 kg but less than 60 kg . his father ' s view is that his weight can not be greater than 58 kg . if all of them are correct in their estimation , what is the average of different probable weights of karthik ?", + "Output Program": [ + "n0 = 55.0\nn1 = 62.0\nn2 = 50.0\nn3 = 60.0\nn4 = 58.0\nt0 = n0 + n4\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "56.5" + ], + "split": "train" + }, + { + "Input": "a garden center sells a certain grass seed in 5 - pound bags at $ 13.85 per bag , 10 - pound bags at $ 20.43 per bag , and 25 - pound bags $ 32.20 per bag . if a customer is to buy at least 65 pounds of the grass seed , but no more than 80 pounds , what is the least possible cost of the grass seed that the customer will buy ?", + "Output Program": [ + "n0 = 5.0\nn1 = 13.85\nn2 = 10.0\nn3 = 20.43\nn4 = 25.0\nn5 = 32.2\nn6 = 65.0\nn7 = 80.0\nt0 = n5 * 2.0\nt1 = n3 * 1.0\nt2 = n1 * 1.0\nt3 = t0 + t1\nanswer = t3 + t2\nprint(answer)" + ], + "Output Answer": [ + "98.68" + ], + "split": "train" + }, + { + "Input": "a certain clock marks every hour by striking a number of times equal to the hour , and the time require for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stoke and the end of the last stroke is 22 seconds . at 10 : 00 , how many seconds elapse between the beginning of the first stroke and the end of the last stroke ?", + "Output Program": [ + "n0 = 6.0\nn1 = 0.0\nn2 = 22.0\nn3 = 10.0\nn4 = 0.0\nt0 = n3 - 1.0\nt1 = n0 - 1.0\nt2 = n3 + t0\nt3 = n0 + t1\nt4 = n2 / t3\nanswer = t2 * t4\nprint(answer)" + ], + "Output Answer": [ + "38" + ], + "split": "train" + }, + { + "Input": "on dividing 171 by a number , the quotient is 8 and the remainder is 3 . find the divisor .", + "Output Program": [ + "import math\nn0 = 171.0\nn1 = 8.0\nn2 = 3.0\nt0 = n0 / n1\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "40 men shake hands with each other . maximum no of handshakes without cyclic handshakes .", + "Output Program": [ + "n0 = 40.0\nt0 = n0 / 2.0\nt1 = n0 - 1.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "780" + ], + "split": "train" + }, + { + "Input": "the two lines y = x and x = - 7 intersect on the coordinate plane . what is the value of the area of the figure formed by the intersecting lines and the x - axis ?", + "Output Program": [ + "n0 = 7.0\nt0 = n0 * n0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "24.5" + ], + "split": "train" + }, + { + "Input": "if 16 ^ y = 4 ^ 14 , what is y ?", + "Output Program": [ + "n0 = 16.0\nn1 = 4.0\nn2 = 14.0\n\nanswer = n2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 105 games will be played during the tournament . find the number of participants .", + "Output Program": [ + "import math\nn0 = 105.0\nt0 = n0 * 2.0\nt1 = t0 * 4.0\nt2 = t1 + 1.0\nt3 = math.sqrt(max(0, t2))\nt4 = t3 + 1.0\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "jen has a jar of jam , and she ate 1 / 3 of the jam for lunch . if jen ate 1 / 7 of the remaining jam for dinner , what fraction of the jam was left after dinner ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 7.0\nt0 = n3 - n1\nanswer = t0 / n3\nprint(answer)" + ], + "Output Answer": [ + "0.5714285714285714" + ], + "split": "train" + }, + { + "Input": "a garden center sells a certain grass seed in 5 - pound bags at $ 13.85 per bag , 10 - pound bags at $ 20.42 per bag , and 25 - pound bags $ 32.25 per bag . if a customer is to buy at least 65 pounds of the grass seed , but no more than 80 pounds , what is the least possible cost of the grass seed that the customer will buy ?", + "Output Program": [ + "n0 = 5.0\nn1 = 13.85\nn2 = 10.0\nn3 = 20.42\nn4 = 25.0\nn5 = 32.25\nn6 = 65.0\nn7 = 80.0\nt0 = n5 * 2.0\nt1 = n3 * 1.0\nt2 = n1 * 1.0\nt3 = t0 + t1\nanswer = t3 + t2\nprint(answer)" + ], + "Output Answer": [ + "98.77" + ], + "split": "train" + }, + { + "Input": "if p ^ 2 \u2013 13 p + 40 = s , and p is a positive integer between 1 and 10 , inclusive , what is the probability that s < 0 ?", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 13.0\nn2 = 40.0\nn3 = 1.0\nn4 = 10.0\nn5 = 0.0\nt0 = n2 * 4.0\nt1 = n1**min(2.0, 5)\nt2 = t1 - t0\nt3 = math.sqrt(max(0, t2))\nt4 = n1 + t3\nt5 = t4 / 2.0\nt6 = n1 - t5\nt7 = t5 - t6\nt8 = t7 - 1.0\nanswer = t8 / n4\nprint(answer)" + ], + "Output Answer": [ + "0.2" + ], + "split": "train" + }, + { + "Input": "5 * 2 is a 3 digit number with * is a missing digit . if the number is divisible by 6 , the missing digit is", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 3.0\nn3 = 6.0\nt0 = n0 * 100.0\nt1 = 1.0 * 10.0\nt2 = n1 + t0\nt3 = t2 + t1\nt4 = t3 + t1\nt5 = t4 - t2\nanswer = t5 / t1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "the security gate at a storage facility requires a 4 - digit lock code . if the lock code must consist only of digits from 1 through 7 , inclusive , with no repeated digits , and the first and last digits of the code must be odd , how many lock codes are possible ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 1.0\nn2 = 7.0\nt0 = n0 + 1.0\nt1 = math.factorial(min(15, int(3.0)))\nt2 = n0 * 3.0\nt3 = math.factorial(min(15, int(t0)))\nt4 = t3 / t1\nanswer = t4 * t2\nprint(answer)" + ], + "Output Answer": [ + "240" + ], + "split": "train" + }, + { + "Input": "in the new budget the price of milk rose by 20 % . by how much percent must a person reduce his consumption so that his expenditure on it does not increase ?", + "Output Program": [ + "n0 = 20.0\nt0 = n0 + 100.0\nt1 = n0 / t0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "16.666666666666664" + ], + "split": "train" + }, + { + "Input": "evaluate 64 / . 08", + "Output Program": [ + "n0 = 64.0\nn1 = 8.0\nt0 = n1 / 100.0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "800" + ], + "split": "train" + }, + { + "Input": "( ab ) x \u2212 2 = ( ba ) x \u2212 7 . what is the value of x ?", + "Output Program": [ + "n0 = 2.0\nn1 = 7.0\nt0 = n0 + n1\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "4.5" + ], + "split": "train" + }, + { + "Input": "jerry \u2019 s average ( arithmetic mean ) score on the first 3 of 4 tests is 94 . if jerry wants to raise his average by 2 points , what score must he earn on the fourth test ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 94.0\nn3 = 2.0\nt0 = n2 + n3\nt1 = n0 * n2\nt2 = n1 * t0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "102" + ], + "split": "train" + }, + { + "Input": "in the biology lab of ` ` jefferson ' ' high school there are 0.036 * 10 ^ 5 germs , equally divided among 18000 * 10 ^ ( - 3 ) petri dishes . how many germs live happily in a single dish ?", + "Output Program": [ + "n0 = 0.036\nn1 = 10.0\nn2 = 5.0\nn3 = 18000.0\nn4 = 10.0\nn5 = 3.0\nt0 = n3 / 1000.0\nt1 = 100.0 * 1000.0\nt2 = n0 * t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "199.99999999999997" + ], + "split": "train" + }, + { + "Input": "an amount of money is to be divided between p , q and r in the ratio of 3 : 7 : 12 . if the difference between the shares of p and q is rs . 4400 , what will be the difference between q and r ' s share ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 12.0\nn3 = 4400.0\nt0 = n1 - n0\nt1 = n2 - n1\nt2 = n3 / t0\nanswer = t2 * t1\nprint(answer)" + ], + "Output Answer": [ + "5500" + ], + "split": "train" + }, + { + "Input": "the average monthly salary of 15 employees in an organisation is rs . 1800 . if the manager ' s salary is added , then the average salary increases by rs . 150 . what is the manager ' s monthly salary ?", + "Output Program": [ + "n0 = 15.0\nn1 = 1800.0\nn2 = 150.0\nt0 = n1 + n2\nt1 = n0 + 1.0\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "4200" + ], + "split": "train" + }, + { + "Input": "if p is a prime number greater than 3 , find the remainder when p ^ 2 + 15 is divided by 12 .", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 15.0\nn3 = 12.0\nt0 = 1.0 + 4.0\nt1 = n0 * n3\nt2 = t0**min(n1, 5)\nt3 = n2 + t2\nanswer = t3 - t1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "the average age of 18 persons in a office is 15 years . out of these , the average age of 5 of them is 14 years and that of the other 9 persons is 16 years . the age of the 15 th person is ?", + "Output Program": [ + "n0 = 18.0\nn1 = 15.0\nn2 = 5.0\nn3 = 14.0\nn4 = 9.0\nn5 = 16.0\nn6 = 15.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n4 * n5\nt3 = t0 - t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "train" + }, + { + "Input": "a profit of rs . 700 is divided between x and y in the ratio of 1 / 2 : 1 / 3 . what is the difference between their profit shares ?", + "Output Program": [ + "n0 = 700.0\nn1 = 1.0\nn2 = 2.0\nn3 = 1.0\nn4 = 3.0\nt0 = n1 / n2\nt1 = n1 / n4\nt2 = t0 + t1\nt3 = n0 / t2\nt4 = t3 / n2\nt5 = t3 / n4\nanswer = t4 - t5\nprint(answer)" + ], + "Output Answer": [ + "140" + ], + "split": "train" + }, + { + "Input": "a container holds 4 quarts of alcohol and 4 quarts of water . how many quarts of water must be added to the container to create a mixture that is 3 parts alcohol to 5 parts water by volume ?", + "Output Program": [ + "n0 = 4.0\nn1 = 4.0\nn2 = 3.0\nn3 = 5.0\nt0 = n2 / n3\nt1 = n0 / t0\nanswer = t1 - n0\nprint(answer)" + ], + "Output Answer": [ + "2.666666666666667" + ], + "split": "train" + }, + { + "Input": "an equal number of desks and bookcases are to be placed along a library wall that is 15 meters long . each desk is 2 meters long , and each bookshelf is 1.5 meters long . if the maximum possible number of desks and bookcases are to be placed along the wall , then the space along the wall that is left over will be how many meters q long ?", + "Output Program": [ + "n0 = 15.0\nn1 = 2.0\nn2 = 1.5\nt0 = n1 * 4.0\nt1 = n2 * 4.0\nt2 = t0 + t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "when positive integer k is divided by 5 , the remainder is 2 . when k is divided by 6 , the remainder is 5 . if k is less than 39 , what is the remainder when k is divided by 7 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 6.0\nn3 = 5.0\nn4 = 39.0\nn5 = 7.0\nt0 = n0 + 12.0\nanswer = t0 % n5\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "the batting average of a particular batsman is 61 runs in 46 innings . if the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs , find his highest score .", + "Output Program": [ + "n0 = 61.0\nn1 = 46.0\nn2 = 150.0\nn3 = 58.0\nt0 = n0 * n1\nt1 = n1 - 2.0\nt2 = n3 * t1\nt3 = t0 - t2\nt4 = n2 + t3\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "202" + ], + "split": "train" + }, + { + "Input": "there are 408 boys and 216 girls in a school which are to be divided into equal sections of either boys or girls alone . find the total number of sections thus formed .", + "Output Program": [ + "n0 = 408.0\nn1 = 216.0\nt0 = n0 + n1\nt1 = 2.0 * 2.0\nt2 = t1 * 2.0\nt3 = t2 * 3.0\nanswer = t0 / t3\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "13 ltr of water is added with 11 ltr of a solution containing 16 % of alcohol in the water . the % of alcohol in the new mixture is ?", + "Output Program": [ + "n0 = 13.0\nn1 = 11.0\nn2 = 16.0\nt0 = n0 + n1\nt1 = n2 / 100.0\nt2 = n1 * t1\nt3 = t2 / t0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "7.333333333333333" + ], + "split": "train" + }, + { + "Input": "a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 1116 in total compensation , how many total hours did he work that week ?", + "Output Program": [ + "n0 = 16.0\nn1 = 40.0\nn2 = 40.0\nn3 = 75.0\nn4 = 1116.0\nt0 = n3 + 100.0\nt1 = n0 * n1\nt2 = n0 * t0\nt3 = n4 - t1\nt4 = t2 / 100.0\nt5 = t3 / t4\nanswer = n1 + t5\nprint(answer)" + ], + "Output Answer": [ + "57" + ], + "split": "train" + }, + { + "Input": "a man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses . next year his income increases by 30 % but his savings increase by 100 % . if his total expenditure in 2 years is double his expenditure in 1 st year , what % age of his income in the first year did he save ?", + "Output Program": [ + "n0 = 30.0\nn1 = 100.0\nn2 = 2.0\nn3 = 1.0\nt0 = n0 + n1\nt1 = n1 * n2\nt2 = n1 + t0\nt3 = t2 - t1\nt4 = t3 / n1\nanswer = t4 * n1\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "the average age of applicants for a new job is 31 , with a standard deviation of 8 . the hiring manager is only willing to accept applications whose age is within one standard deviation of the average age . what is the maximum number of different ages of the applicants ?", + "Output Program": [ + "n0 = 31.0\nn1 = 8.0\nt0 = n1 * 2.0\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "a 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2 . 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more . at the end of the two removal and replacement , what is the ratio q of milk and water in the resultant mixture ?", + "Output Program": [ + "n0 = 20.0\nn1 = 3.0\nn2 = 2.0\nn3 = 10.0\nt0 = n1 + n2\nt1 = n0 - n3\nt2 = n1 / t0\nt3 = n2 / t0\nt4 = t2 * t1\nt5 = t3 * t1\nt6 = n3 + t4\nt7 = t5 / n0\nt8 = t6 / n0\nt9 = t7 * t1\nt10 = t8 * t1\nt11 = n3 + t10\nanswer = t11 / t9\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "the average age of 16 persons in a office is 15 years . out of these , the average age of 5 of them is 14 years and that of the other 9 persons is 16 years . the age of the 15 th person is ?", + "Output Program": [ + "n0 = 16.0\nn1 = 15.0\nn2 = 5.0\nn3 = 14.0\nn4 = 9.0\nn5 = 16.0\nn6 = 15.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n4 * n5\nt3 = t0 - t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "a train ride from two p to town q costs $ 6.85 more than does a bus ride from town p to town q . together , the cost of one train ride and one bus ride is $ 9.65 . what is the cost of a bus ride from town p to town q ?", + "Output Program": [ + "n0 = 6.85\nn1 = 9.65\nt0 = n1 - n0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "1.4000000000000004" + ], + "split": "train" + }, + { + "Input": "matt gets a $ 1,000 commission on a big sale . this commission alone raises his average commission by $ 150 . if matt ' s new average commission is $ 250 , how many sales has matt made ?", + "Output Program": [ + "n0 = 1000.0\nn1 = 150.0\nn2 = 250.0\nt0 = 1000.0 - 100.0\nt1 = n2 - n1\nt2 = n2 - t1\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "the average age of an adult class is 40 years . 10 new students with an avg age of 32 years join the class . therefore decreasing the average by 4 year . find what was theoriginal strength of class ?", + "Output Program": [ + "n0 = 40.0\nn1 = 10.0\nn2 = 32.0\nn3 = 4.0\nt0 = n1 * n2\nt1 = n0 - n3\nt2 = n1 * t1\nt3 = t2 - t0\nanswer = t3 / n3\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "if a = 105 and a ^ 3 = 21 \u00d7 25 \u00d7 45 \u00d7 b , what is the value of b ?", + "Output Program": [ + "n0 = 105.0\nn1 = 3.0\nn2 = 21.0\nn3 = 25.0\nn4 = 45.0\nt0 = n2 * n3\nt1 = n0**min(n1, 5)\nt2 = n4 * t0\nanswer = t1 / t2\nprint(answer)" + ], + "Output Answer": [ + "49" + ], + "split": "train" + }, + { + "Input": "a man purchased 3 blankets @ rs . 100 each , 6 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ?", + "Output Program": [ + "n0 = 3.0\nn1 = 100.0\nn2 = 6.0\nn3 = 150.0\nn4 = 150.0\nt0 = n3 * 10.0\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "for a group of n people , k of whom are of the same sex , the ( n - k ) / n expression yields an index for a certain phenomenon in group dynamics for members of that sex . for a group that consists of 25 people , 8 of whom are females , by how much does the index for the females exceed the index for the males in the group ?", + "Output Program": [ + "n0 = 25.0\nn1 = 8.0\nt0 = n1 / n0\nt1 = n0 - n1\nt2 = t1 / n0\nanswer = t2 - t0\nprint(answer)" + ], + "Output Answer": [ + "0.36000000000000004" + ], + "split": "train" + }, + { + "Input": "at the end of year x , automobile installment credit accounted for 36 % of all outstanding consumer installment credit . at that time automobile finance companies extended $ 57 billion of credit , or 1 / 3 of the automobile installment credit . how many billion dollars of consumer installment credit was outstanding at that time ?", + "Output Program": [ + "n0 = 36.0\nn1 = 57.0\nn2 = 1.0\nn3 = 3.0\nt0 = n0 / 100.0\nt1 = n1 * n3\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "475" + ], + "split": "train" + }, + { + "Input": "claire has a total of 92 pets consisting of gerbils and hamsters only . one - quarter of the gerbils are male , and one - third of the hamsters are male . if there are 25 males altogether , how many gerbils does claire have ?", + "Output Program": [ + "n0 = 92.0\nn1 = 25.0\nt0 = n0 - n1\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "68" + ], + "split": "train" + }, + { + "Input": "what is the sum of all even integers between 99 and 301 ?", + "Output Program": [ + "n0 = 99.0\nn1 = 301.0\nt0 = n1 - n0\nt1 = t0 + 2.0\nt2 = t0 - 2.0\nt3 = t2 / 2.0\nt4 = t1 / 2.0\nt5 = n0 + t3\nanswer = t5 * t4\nprint(answer)" + ], + "Output Answer": [ + "20298" + ], + "split": "train" + }, + { + "Input": "a person was asked to state his age in years . his reply was , ` ` take my age 4 years hence , multiply it by 4 and subtract 4 times my age 4 years ago and you will know how old i am . ' ' what was the age of the person ?", + "Output Program": [ + "n0 = 4.0\nn1 = 4.0\nn2 = 4.0\nn3 = 4.0\nt0 = n0 * n1\nanswer = t0 + t0\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "2 friends a and b running up hill and then to get down length of road - 440 yads a on his return journey met b going up at 20 yards from top if a has finished race 5 minute earlier than b then how much time a had taken to complete the race ?", + "Output Program": [ + "n0 = 2.0\nn1 = 440.0\nn2 = 20.0\nn3 = 5.0\nt0 = n1 / 10.0\nt1 = n0 * n1\nt2 = t0 - 4.0\nt3 = n3 / t2\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "110" + ], + "split": "train" + }, + { + "Input": "the average age of 40 students in a class is 15 years . if the age of teacher is also included , the average becomes 16 years , find the age of the teacher .", + "Output Program": [ + "n0 = 40.0\nn1 = 15.0\nn2 = 16.0\nt0 = n0 * n1\nt1 = n2 + t0\nt2 = n0 + t1\nanswer = t2 - t0\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "train" + }, + { + "Input": "the average of non - zero number and its square is 5 times the number . the number is :", + "Output Program": [ + "n0 = 5.0\nt0 = n0 * 2.0\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "the sum and the product of two numbers are 24 and 23 respectively , the difference of the number is ?", + "Output Program": [ + "import math\nn0 = 24.0\nn1 = 23.0\nt0 = n1 * 2.0\nt1 = n0**min(2.0, 5)\nt2 = t1 - t0\nt3 = t2 - t0\nanswer = math.sqrt(max(0, t3))\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "7 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ?", + "Output Program": [ + "n0 = 7.0\nt0 = n0 - 1.0\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "the average age of a , b and c is 29 years . if the average age of a and c is 32 years , what is the age of b in years ?", + "Output Program": [ + "n0 = 29.0\nn1 = 32.0\nt0 = n0 * 3.0\nt1 = n1 * 2.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "at deluxe paint store , fuchsia paint is made by mixing 5 parts of red paint with 3 parts of blue paint . mauve paint is made by mixing 3 parts of red paint with 5 parts blue paint . how many liters of blue paint must be added to 24 liters of fuchsia to change it to mauve paint ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nn2 = 3.0\nn3 = 5.0\nn4 = 24.0\nt0 = n0 + n1\nt1 = n0 / t0\nt2 = n2 / t0\nt3 = n3 / t0\nt4 = n4 * t1\nt5 = t4 / t2\nt6 = n4 - t4\nt7 = t5 * t3\nanswer = t7 - t6\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "the manager at a health foods store mixes a unique superfruit juice cocktail that costs $ 1399.45 per litre to make . the cocktail includes mixed fruit juice and a \u00e7 ai berry juice , which cost $ 262.85 per litre and $ 3104.35 per litre , respectively . the manager has already opened 33 litres of the mixed fruit juice . how many litres of the a \u00e7 ai berry juice does he need to add ?", + "Output Program": [ + "n0 = 1399.45\nn1 = 262.85\nn2 = 3104.35\nn3 = 33.0\nt0 = n0 * n3\nt1 = n1 * n3\nt2 = n2 - n0\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "if the sales tax reduced from 3 1 / 2 % to 3 1 / 3 % , then what difference does it make to a person who purchases an article with market price of rs . 7800 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 2.0\nn3 = 3.0\nn4 = 1.0\nn5 = 3.0\nn6 = 7800.0\nt0 = n1 / n2\nt1 = n1 / n0\nt2 = n0 + t0\nt3 = n0 + t1\nt4 = t2 - t3\nt5 = n6 * t4\nanswer = t5 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "12.99999999999999" + ], + "split": "train" + }, + { + "Input": "in an entrance exam , 3 marks is awarded for every correct answer and ( - 1 ) for every wrong answer . if a student gets 38 marks after attempting all questions , find the number of questions answered correctly if the total questions were 70 .", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 38.0\nn3 = 70.0\nt0 = n0 + n1\nt1 = n0 * n3\nt2 = t1 - n2\nt3 = t2 / t0\nanswer = n3 - t3\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "train" + }, + { + "Input": "a meal cost $ 35.50 adn there was no tax . if the tip was more than 5 pc but less than 8 pc of the price , then the total amount paid should be :", + "Output Program": [ + "n0 = 35.5\nn1 = 5.0\nn2 = 8.0\nt0 = n0 * n1\nt1 = t0 / 100.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "37.275" + ], + "split": "train" + }, + { + "Input": "if the operation \u20ac is defined for all x and y by the equation x \u20ac y = 2 * x * y , then 6 \u20ac ( 4 \u20ac 5 ) =", + "Output Program": [ + "n0 = 2.0\nn1 = 6.0\nn2 = 4.0\nn3 = 5.0\nt0 = n0 * n1\nt1 = n0 * n2\nt2 = n3 * t1\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "480" + ], + "split": "train" + }, + { + "Input": "the average height of 20 students in a class was calculated as 175 cm . it has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 111 cm . what was the actual average height of the students in the class ?", + "Output Program": [ + "n0 = 20.0\nn1 = 175.0\nn2 = 151.0\nn3 = 111.0\nt0 = n0 * n1\nt1 = n2 - n3\nt2 = t0 - t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "173" + ], + "split": "train" + }, + { + "Input": "john was thrice as old as tom 6 years ago . john will be 2 times as old as tom in 4 years . how old is tom today ?", + "Output Program": [ + "n0 = 6.0\nn1 = 2.0\nn2 = 4.0\nt0 = n0 * n1\nt1 = n1 * n2\nt2 = t0 + t1\nanswer = t2 - n2\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "mary and mike enter into a partnership by investing $ 700 and $ 300 respectively . at the end of one year , they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business . if mary received $ 800 more than mike did , what was the profit made by their business in that year ?", + "Output Program": [ + "n0 = 700.0\nn1 = 300.0\nn2 = 800.0\nt0 = n0 / 1000.0\nt1 = n1 / 1000.0\nt2 = 1.0 / 3.0\nt3 = t0 - t1\nt4 = 1.0 - t2\nt5 = t3 * t4\nanswer = n2 / t5\nprint(answer)" + ], + "Output Answer": [ + "3000" + ], + "split": "train" + }, + { + "Input": "in goshawk - eurasian nature reserve 30 percent of the birds are hawks , and 40 percent of the non - hawks are paddyfield - warblers . if there are 25 percent as many kingfishers as paddyfield - warblers in the reserve , then what percent of the birds w in the nature reserve are not hawks , paddyfield - warblers , or kingfishers ?", + "Output Program": [ + "n0 = 30.0\nn1 = 40.0\nn2 = 25.0\nt0 = n2 + n2\nt1 = t0 / 2.0\nanswer = t1 + 10.0\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "if 5 gallons of gasoline are added to a tank that is already filled to 3 / 4 of its capacity , the tank is then filled to 9 / 10 of its capacity . how many gallons does the tank hold ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nn2 = 4.0\nn3 = 9.0\nn4 = 10.0\nt0 = n3 / n4\nt1 = n1 / n2\nt2 = t0 - t1\nt3 = n0 / t2\nt4 = t3 * t1\nanswer = n0 + t4\nprint(answer)" + ], + "Output Answer": [ + "29.999999999999996" + ], + "split": "train" + }, + { + "Input": "on dividing number by 56 , we get 29 as remainder . on dividing the same number by 8 , what will be the remainder ?", + "Output Program": [ + "n0 = 56.0\nn1 = 29.0\nn2 = 8.0\n\nanswer = n1 % n2\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "given that g and h are events such that q ( g ) = 0.30 q ( h ) = 0.9 q ( gnh ) = 0.9 find q ( g | h ) and q ( g | h )", + "Output Program": [ + "n0 = 0.3\nn1 = 0.9\nn2 = 0.9\nt0 = n1 / n0\nt1 = n0 * 4.0\nt2 = n0 + t1\nt3 = t2 - 0.25\nt4 = t3 - 0.25\nanswer = t4 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.3333333333333333" + ], + "split": "train" + }, + { + "Input": "6000 \u2212 ( 105 \u00f7 21.0 ) = ?", + "Output Program": [ + "n0 = 6000.0\nn1 = 105.0\nn2 = 21.0\nt0 = n1 / n2\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "5995" + ], + "split": "train" + }, + { + "Input": "there are 4 people of different heights standing in order of increasing height . the difference is 2 inches between the first person and the second person , and also between the second person and the third person . the difference between the third person and the fourth person is 6 inches and the average height is 76 . how tall is the fourth person ?", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\nn2 = 6.0\nn3 = 76.0\nt0 = n0 + n2\nt1 = n0 * n3\nt2 = n2 + t0\nt3 = t1 - t2\nt4 = t3 / n0\nanswer = t0 + t4\nprint(answer)" + ], + "Output Answer": [ + "82" + ], + "split": "train" + }, + { + "Input": "by how much is 3 - fifth of 390 greater than 4 - seventh of 210 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 390.0\nn2 = 4.0\nn3 = 210.0\nt0 = 2.0 + 3.0\nt1 = 3.0 + 4.0\nt2 = n0 / t0\nt3 = n2 / t1\nt4 = n1 * t2\nt5 = n3 * t3\nanswer = t4 - t5\nprint(answer)" + ], + "Output Answer": [ + "114" + ], + "split": "train" + }, + { + "Input": "if x is 30 percent more than y and y is 50 percent less than z , then x is what percent of z ?", + "Output Program": [ + "n0 = 30.0\nn1 = 50.0\nt0 = n0 / 100.0\nt1 = 100.0 - n1\nt2 = t0 + 1.0\nanswer = t2 * t1\nprint(answer)" + ], + "Output Answer": [ + "65" + ], + "split": "train" + }, + { + "Input": "if 10000 microns = 1 decimeter , and 1000000000 angstroms = 1 decimeter , how many angstroms equal 1 micron ?", + "Output Program": [ + "n0 = 10000.0\nn1 = 1.0\nn2 = 1000000000.0\nn3 = 1.0\nn4 = 1.0\n\nanswer = n1 / n1\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "if the arithmetic mean of p and q is 10 and the arithmetic mean of q and r is 24 , what is the value of r - p ?", + "Output Program": [ + "n0 = 10.0\nn1 = 24.0\nt0 = n1 * 2.0\nt1 = n0 * 2.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "a room is 6 meters 24 centimeters in length and 4 meters 32 centimeters in width . find the least number of square tiles of equal size required to cover the entire floor of the room ?", + "Output Program": [ + "import scipy\nn0 = 6.0\nn1 = 24.0\nn2 = 4.0\nn3 = 32.0\nt0 = n0 * 100.0\nt1 = n2 * 100.0\nt2 = n1 + t0\nt3 = n3 + t1\nt4 = scipy.gcd(int(t2), int(t3))\nt5 = t2 * t3\nt6 = t4 * t4\nanswer = t5 / t6\nprint(answer)" + ], + "Output Answer": [ + "117" + ], + "split": "train" + }, + { + "Input": "if f ( f ( n ) ) + f ( n ) = 2 n + 3 , f ( 0 ) = 1 then f ( 2016 ) = ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 0.0\nn3 = 1.0\nn4 = 2016.0\n\nanswer = n3 + n4\nprint(answer)" + ], + "Output Answer": [ + "2017" + ], + "split": "train" + }, + { + "Input": "there are 408 boys and 264 girls in a school which are to be divided into equal sections of either boys or girls alone . find the total number of sections thus formed .", + "Output Program": [ + "n0 = 408.0\nn1 = 264.0\nt0 = n0 + n1\nt1 = 2.0 * 2.0\nt2 = t1 * 2.0\nt3 = t2 * 3.0\nanswer = t0 / t3\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "we have boxes colored either red or blue . in each blue box there is a fixed number of blueberries . in each red box there is a fixed number of strawberries . if we dispose of one blue box for one additional red box , the total number of berries would increase by 12 , and the difference between the total number of strawberries and the total number of blueberries would increase by 76 . each blue box contains how many blueberries ?", + "Output Program": [ + "n0 = 12.0\nn1 = 76.0\nt0 = n1 - n0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "in a competitive examination in state a , 6 % candidates got selected from the total appeared candidates . states b had an equal number of candidates appeared and 7 % candidates got selected with 80 more candidates got selected than a . what was the number of candidates appeared from each state ?", + "Output Program": [ + "n0 = 6.0\nn1 = 7.0\nn2 = 80.0\nt0 = n1 - n0\nt1 = t0 / 100.0\nanswer = n2 / t1\nprint(answer)" + ], + "Output Answer": [ + "8000" + ], + "split": "train" + }, + { + "Input": "a person spends 1 / 3 rd of the money with him on clothes , 1 / 5 th of the remaining on food and 1 / 4 th of the remaining on travel . now , he is left with rs 600 . how much did he have with him in the beginning ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 5.0\nn4 = 1.0\nn5 = 4.0\nn6 = 600.0\nt0 = n0 / n1\nt1 = n0 - t0\nt2 = t1 / n3\nt3 = t1 - t2\nt4 = t3 / n5\nt5 = t3 - t4\nanswer = n6 / t5\nprint(answer)" + ], + "Output Answer": [ + "1499.9999999999998" + ], + "split": "train" + }, + { + "Input": "a fruit drink is made of orange , watermelon , and grape juice , where 15 percent of the drink is orange juice and 60 percent is watermelon juice . if the drink is made with 30 ounces of grape juice , how many ounces is the drink total ?", + "Output Program": [ + "n0 = 15.0\nn1 = 60.0\nn2 = 30.0\nt0 = n0 + n1\nt1 = n0 * n2\nt2 = n1 * n2\nt3 = 100.0 - t0\nt4 = t1 / t3\nt5 = t2 / t3\nt6 = n2 + t4\nanswer = t6 + t5\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "if 213 \u00d7 16 = 3408 , then 0.16 \u00d7 2.13 is equal to :", + "Output Program": [ + "n0 = 213.0\nn1 = 16.0\nn2 = 3408.0\nn3 = 0.16\nn4 = 2.13\n\nanswer = n4 * n3\nprint(answer)" + ], + "Output Answer": [ + "0.3408" + ], + "split": "train" + }, + { + "Input": "the salary of a , b , c , d , e is rs . 8000 , rs . 5000 , rs . 15000 , rs . 7000 , rs . 9000 per month respectively , then the average salary of a , b , c , d , and e per month is", + "Output Program": [ + "n0 = 8000.0\nn1 = 5000.0\nn2 = 15000.0\nn3 = 7000.0\nn4 = 9000.0\nt0 = n0 + n1\nt1 = 1.0 + 4.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "8800" + ], + "split": "train" + }, + { + "Input": "total number of 4 digit number do not having the digit 3 or 6 .", + "Output Program": [ + "n0 = 2235.0\nn1 = 48.0\nn2 = 61.0\nn3 = 26.0\nn4 = 39.0\nn5 = 52.0\nn6 = 65.0\nt0 = n1 / 2.0\nanswer = t0 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "the average weight of a , b and c is 43 kg . if the average weight of a and b be 40 kg and that of b and c be 43 kg , then the weight of b is :", + "Output Program": [ + "n0 = 43.0\nn1 = 40.0\nn2 = 43.0\nt0 = n1 * 2.0\nt1 = n2 * 2.0\nt2 = n0 * 3.0\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "37" + ], + "split": "train" + }, + { + "Input": "what is x if x + 2 y = 12 and y = 3 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 12.0\nn2 = 3.0\nt0 = n0 * n2\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "out of 3 given numbers , the first one is twice the second and 3 times the third . if the average of these numbers is 88 , then the difference between first and third is .", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 88.0\nt0 = 4.0 + 4.0\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "96" + ], + "split": "train" + }, + { + "Input": "the cost to park a car in a certain parking garage is $ 9.00 for up to 2 hours of parking and $ 1.75 for each hour in excess of 2 hours . what is the average ( arithmetic mean ) cost per hour to park a car in the parking garage for 9 hours ?", + "Output Program": [ + "n0 = 9.0\nn1 = 2.0\nn2 = 1.75\nn3 = 2.0\nn4 = 9.0\nt0 = n4 - n1\nt1 = n2 * t0\nt2 = n0 + t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "2.361111111111111" + ], + "split": "train" + }, + { + "Input": "the average waight of a , b , c is 45 kg . the avg wgt of a & b be 40 kg & that of b , c be 43 kg . find the wgt of b .", + "Output Program": [ + "n0 = 45.0\nn1 = 40.0\nn2 = 43.0\nt0 = n1 * 2.0\nt1 = n0 * 3.0\nt2 = n2 * 2.0\nt3 = t1 - t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "31" + ], + "split": "train" + }, + { + "Input": "john ' s marks wrongly entered as 82 instead of 62 . due to that the average marks for the class got increased by half ( 1 / 2 ) . the number of john in the class is ?", + "Output Program": [ + "n0 = 82.0\nn1 = 62.0\nn2 = 1.0\nn3 = 2.0\nt0 = n2 / n3\nt1 = n0 - n1\nt2 = t1 / t0\nanswer = n3 * t2\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "the difference between the place value and the face value of 7 in the numeral 856973 is", + "Output Program": [ + "n0 = 7.0\nn1 = 856973.0\nt0 = n0 * 10.0\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "63" + ], + "split": "train" + }, + { + "Input": "if a person walks at 15 km / hr instead of 5 km / hr , he would have walked 20 km more . the actual distance traveled by him is ?", + "Output Program": [ + "n0 = 15.0\nn1 = 5.0\nn2 = 20.0\nt0 = n0 - n1\nt1 = n2 / t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the average weight of 8 person ' s increases by 2 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.0\nn2 = 65.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "81" + ], + "split": "train" + }, + { + "Input": "the average weight of 29 students is 28 kg . by the admission of a new student , the average weight is reduced to 27.2 kg . the weight of the new student is", + "Output Program": [ + "n0 = 29.0\nn1 = 28.0\nn2 = 27.2\nt0 = n0 + 1.0\nt1 = n0 * n1\nt2 = n2 * t0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "the average expenditure of a labourer for 6 months was 80 and he fell into debt . in the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30 . his monthly income i", + "Output Program": [ + "n0 = 6.0\nn1 = 80.0\nn2 = 4.0\nn3 = 60.0\nn4 = 30.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nt4 = n4 + t3\nanswer = t4 / t0\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "a man saves 25 % of his monthly salary . if an account of dearness of things he is to increase his monthly expenses by 10 % , he is only able to save rs . 175 per month . what is his monthly salary ?", + "Output Program": [ + "n0 = 25.0\nn1 = 10.0\nn2 = 175.0\nt0 = n1 / 100.0\nt1 = n2 * 100.0\nt2 = 100.0 - n0\nt3 = t0 * t2\nt4 = t3 + t2\nt5 = 100.0 - t4\nanswer = t1 / t5\nprint(answer)" + ], + "Output Answer": [ + "1000" + ], + "split": "train" + }, + { + "Input": "having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.92 at the candy store . what is john \u2019 s weekly allowance ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 0.92\nt0 = n0 / n1\nt1 = 1.0 / n0\nt2 = 1.0 - t0\nt3 = t1 * t2\nt4 = t0 + t3\nt5 = 1.0 - t4\nanswer = n2 / t5\nprint(answer)" + ], + "Output Answer": [ + "3.4499999999999993" + ], + "split": "train" + }, + { + "Input": "a salesman \u2019 s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1300 plus 2.5 % commission on all sales exceeding rs . 4000 . if his remuneration as per new scheme was rs . 600 more than that by the previous schema , his sales were worth ?", + "Output Program": [ + "n0 = 5.0\nn1 = 1300.0\nn2 = 2.5\nn3 = 4000.0\nn4 = 600.0\nt0 = n0 / 100.0\nanswer = n4 / t0\nprint(answer)" + ], + "Output Answer": [ + "12000" + ], + "split": "train" + }, + { + "Input": "exactly 3 / 7 of the people in the room are under the age of 21 , and exactly 5 / 11 of the people in the room are over the age of 65 . if the total number of the people in the room is greater than 50 and less than 100 , how many people in the room are under the age of 21 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 21.0\nn3 = 5.0\nn4 = 11.0\nn5 = 65.0\nn6 = 50.0\nn7 = 100.0\nn8 = 21.0\nt0 = n1 * n4\nt1 = n0 * t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "with # andeach representing different digits in the problem below , the difference between # and # # is 801 . what is the value of ? # - # # ____ 812", + "Output Program": [ + "n0 = 801.0\nn1 = 812.0\nt0 = n1 - n0\nanswer = t0 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "( \u221a 97 + \u221a 486 ) / \u221a 54 = ?", + "Output Program": [ + "import math\nn0 = 97.0\nn1 = 486.0\nn2 = 54.0\nt0 = math.sqrt(max(0, n0))\nt1 = math.sqrt(max(0, n1))\nt2 = math.sqrt(max(0, n2))\nt3 = t0 + t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "4.340259786868312" + ], + "split": "train" + }, + { + "Input": "find the smallest number which when divided by 13 and 15 leaves respective remainders of 2 and 4", + "Output Program": [ + "n0 = 13.0\nn1 = 15.0\nn2 = 2.0\nn3 = 4.0\nt0 = 1.0 + 10.0\nt1 = n0 * n1\nanswer = t1 - t0\nprint(answer)" + ], + "Output Answer": [ + "184" + ], + "split": "train" + }, + { + "Input": "if sharon ' s weekly salary increased by 16 percent , she would earn $ 406 per week . if instead , her weekly salary were to increase by 20 percent , how much would she earn per week ?", + "Output Program": [ + "n0 = 16.0\nn1 = 406.0\nn2 = 20.0\nt0 = n0 / 100.0\nt1 = n2 / 100.0\nt2 = t0 + 1.0\nt3 = n1 / t2\nt4 = t1 * t3\nanswer = t3 + t4\nprint(answer)" + ], + "Output Answer": [ + "420" + ], + "split": "train" + }, + { + "Input": "a student has to obtain 60 % of the total marks to pass . he got 160 marks and failed by 20 marks . the maximum marks are ?", + "Output Program": [ + "n0 = 60.0\nn1 = 160.0\nn2 = 20.0\nt0 = n1 + n2\nt1 = n0 / 100.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "in a renowned city , the average birth rate is 7 people every two seconds and the death rate is 2 people every two seconds . estimate the size of the population net increase that occurs in one day .", + "Output Program": [ + "n0 = 7.0\nn1 = 2.0\nt0 = n0 - 2.0\nt1 = t0 * 3600.0\nanswer = t1 * 12.0\nprint(answer)" + ], + "Output Answer": [ + "216000" + ], + "split": "train" + }, + { + "Input": "two trains of equal are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train passes the slower train in 36.00001 sec . the length of each train is ?", + "Output Program": [ + "n0 = 46.0\nn1 = 36.0\nn2 = 36.00001\nt0 = n0 - n1\nt1 = t0 * 1000.0\nt2 = t1 / 3600.0\nt3 = n2 * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "50.000013888888894" + ], + "split": "train" + }, + { + "Input": "when average age of 23 members are 0 , how many members greater than 0 ?", + "Output Program": [ + "n0 = 23.0\nn1 = 0.0\nn2 = 0.0\n\nanswer = n0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "during the first two weeks of january , the total rainfall in springdale was 35 inches . if the rainfall during the second week was 1.5 times the rainfall during the first week , what was the rainfall during the second week of january ?", + "Output Program": [ + "n0 = 35.0\nn1 = 1.5\nt0 = n1 + 1.0\nt1 = n1 / t0\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "40 persons like apple . 7 like orange and mango dislike apple . 10 like mango and apple and dislike orange . 4 like all . how many people like apple ?", + "Output Program": [ + "n0 = 40.0\nn1 = 7.0\nn2 = 10.0\nn3 = 4.0\nt0 = n0 - 3.0\nt1 = n2 - n1\nt2 = n1 + t0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "47" + ], + "split": "train" + }, + { + "Input": "if x = - 6 and y = - 3 , what is the value of 4 ( x - y ) ^ 2 - xy ?", + "Output Program": [ + "n0 = 6.0\nn1 = 3.0\nn2 = 4.0\nn3 = 2.0\nt0 = -n0\nt1 = -n1\nt2 = t0 * t1\nt3 = t0 - t1\nt4 = t3**min(n3, 5)\nt5 = n2 * t4\nanswer = t5 - t2\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "if the sum of the 4 th term and the 12 th term of an arithmetic progression is 12 , what is the sum of the first 15 terms of the progression ?", + "Output Program": [ + "n0 = 4.0\nn1 = 12.0\nn2 = 12.0\nn3 = 15.0\nt0 = n3 / 2.0\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "the telephone company wants to add an area code composed of 2 letters to every phone number . in order to do so , the company chose a special sign language containing 324 different signs . if the company used 322 of the signs fully and two remained unused , how many additional area codes can be created if the company uses all 324 signs ?", + "Output Program": [ + "n0 = 2.0\nn1 = 324.0\nn2 = 322.0\nn3 = 324.0\nt0 = n1 - n2\nt1 = n2 * t0\nanswer = t1 * t0\nprint(answer)" + ], + "Output Answer": [ + "1288" + ], + "split": "train" + }, + { + "Input": "the toll t , in dollars , for a truck using a certain bridge is given by the formula t = 3.50 + 0.50 ( x \u2212 2 ) , where x is the number of axles on the truck . what is the toll for an 18 - wheel truck that has 2 wheels on its front axle and 4 wheels on each of its other axles ?", + "Output Program": [ + "n0 = 3.5\nn1 = 0.5\nn2 = 2.0\nn3 = 18.0\nn4 = 2.0\nn5 = 4.0\nt0 = n3 - n2\nt1 = t0 / n5\nt2 = t1 + 1.0\nt3 = t2 - n2\nt4 = n1 * t3\nanswer = n0 + t4\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "in feb mrs bil ' s earnings were 70 percent of the bil family ' s total income . in june mrs bil earned 10 percent more than in may . if the rest of the family ' s income was the same both months , then , in june , mrs bil ' s earnings were approximately what percent of the bil family ' s total income ?", + "Output Program": [ + "n0 = 70.0\nn1 = 10.0\nt0 = n0 / n1\nt1 = n0 + t0\nt2 = t0 + 100.0\nt3 = t1 / t2\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "71.96261682242991" + ], + "split": "train" + }, + { + "Input": "if 7125 \u00b8 1.25 = 5700 < the value of 712.5 \u00f7 12.5 is :", + "Output Program": [ + "n0 = 7125.0\nn1 = 1.25\nn2 = 5700.0\nn3 = 712.5\nn4 = 12.5\n\nanswer = n3 / n4\nprint(answer)" + ], + "Output Answer": [ + "57" + ], + "split": "train" + }, + { + "Input": "when 1 / 10 percent of 7,000 is subtracted from 1 / 10 of 7,000 , the difference is", + "Output Program": [ + "n0 = 1.0\nn1 = 10.0\nn2 = 7000.0\nn3 = 1.0\nn4 = 10.0\nn5 = 7000.0\nt0 = n1 * n2\nanswer = t0 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "700" + ], + "split": "train" + }, + { + "Input": "the milk level in a rectangular box measuring 64 feet by 25 feet is to be lowered by 6 inches . how many gallons of milk must be removed ? ( 1 cu ft = 7.5 gallons )", + "Output Program": [ + "n0 = 64.0\nn1 = 25.0\nn2 = 6.0\nn3 = 1.0\nn4 = 7.5\nt0 = n3 / 2.0\nt1 = n0 * n1\nt2 = t0 * t1\nanswer = n4 * t2\nprint(answer)" + ], + "Output Answer": [ + "6000" + ], + "split": "train" + }, + { + "Input": "a man whose bowling average is 12.4 , takes 4 wickets for 26 runs and there by decreases his average by 0.4 . the number of wickets taken by him before his last match is ?", + "Output Program": [ + "import math\nn0 = 12.4\nn1 = 4.0\nn2 = 26.0\nn3 = 0.4\nt0 = math.floor(n0)\nt1 = n1 * t0\nt2 = n0 - t0\nt3 = t1 - n2\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "54.99999999999995" + ], + "split": "train" + }, + { + "Input": "in an ngo the daily average wages of 20 illiterate employees is decreased from rs . 25 to rs . 10 , thus the average salary of all the literate and illiterate employees is decreased rs . 10 per day . the no . of educated employees working in the ngo is :", + "Output Program": [ + "n0 = 20.0\nn1 = 25.0\nn2 = 10.0\nn3 = 10.0\n\nanswer = n0 - n2\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "find unit digit of n when n = 63 ^ 1 ! + 2 ! + . . . + 63 ! + 18 ^ 1 ! + 2 ! + . . . + 18 ! + 37 ^ 1 ! + 2 ! + . . . 37 !", + "Output Program": [ + "n0 = 63.0\nn1 = 1.0\nn2 = 2.0\nn3 = 63.0\nn4 = 18.0\nn5 = 1.0\nn6 = 2.0\nn7 = 18.0\nn8 = 37.0\nn9 = 1.0\nn10 = 2.0\nn11 = 37.0\nt0 = n0 + n4\nt1 = n8 + t0\nt2 = t1 - 100.0\nanswer = t2 - 10.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "find the value of ( \u221a 1.5 ) / ( \u221a 0.81 ) + ( \u221a 1.44 ) / ( \u221a 0.49 ) is", + "Output Program": [ + "import math\nn0 = 1.5\nn1 = 0.81\nn2 = 1.44\nn3 = 0.49\nt0 = math.sqrt(max(0, n0))\nt1 = math.sqrt(max(0, n1))\nt2 = math.sqrt(max(0, n2))\nt3 = math.sqrt(max(0, n3))\nt4 = t0 / t1\nt5 = t2 / t3\nanswer = t4 + t5\nprint(answer)" + ], + "Output Answer": [ + "3.0751133491652576" + ], + "split": "train" + }, + { + "Input": "a completes a piece of work in 3 / 4 of the time in b does , b takes 4 / 5 of the time in c does . they got a profit of rs . 40000 how much b gets ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 4.0\nn3 = 5.0\nn4 = 40000.0\nt0 = 1000.0 + 1000.0\nt1 = n3 + 60.0\nt2 = n4 / n1\nt3 = 10.0 * 60.0\nt4 = t0 + t2\nt5 = t3 + 100.0\nt6 = t5 + t1\nanswer = t4 + t6\nprint(answer)" + ], + "Output Answer": [ + "12765" + ], + "split": "train" + }, + { + "Input": "when a student joe , weighing 40 kg , joins a group of students whose average weight is 30 kg , the average weight goes up by 1 kg . subsequently , if two students , excluding joe , leave the group the average weight comes back to 30 kg . what is the difference between the average weight of the two students who left and the weight of joe ?", + "Output Program": [ + "n0 = 40.0\nn1 = 30.0\nn2 = 1.0\nn3 = 30.0\nt0 = n1 + n2\nt1 = n0 - t0\nt2 = n1 * t1\nt3 = t1 - n2\nt4 = n0 + t2\nt5 = n1 * t3\nt6 = t4 - t5\nt7 = t6 / 2.0\nanswer = n0 - t7\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "a certain clock marks every hour by striking a number of times equal to the hour , and the time required for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stroke and the end of the last stroke is 33 seconds . at 12 : 00 , how many seconds elapse between the beginning of the first stroke and the end of the last stroke ?", + "Output Program": [ + "n0 = 6.0\nn1 = 0.0\nn2 = 33.0\nn3 = 12.0\nn4 = 0.0\nt0 = 1.0 + 4.0\nt1 = n0 + t0\nt2 = n3 + t1\nt3 = n2 / t1\nanswer = t2 * t3\nprint(answer)" + ], + "Output Answer": [ + "69" + ], + "split": "train" + }, + { + "Input": "the ratio of petrol and kerosene in the container is 3 : 2 when 10 liters of the mixture is taken out and is replaced by the kerosene , the ratio become 2 : 3 . then total quantity of the mixture in the container is :", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 10.0\nn3 = 2.0\nn4 = 3.0\nt0 = n1 / n0\nt1 = 1.0 - t0\nanswer = n2 / t1\nprint(answer)" + ], + "Output Answer": [ + "29.999999999999996" + ], + "split": "train" + }, + { + "Input": "a part - time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee ' s total income did not change . by what percent q should the number of hours worked be increased ?", + "Output Program": [ + "n0 = 20.0\nt0 = 10.0 * 4.0\nt1 = 100.0 - n0\nt2 = t1 / 100.0\nt3 = t2 * 10.0\nt4 = t0 / t3\nt5 = t4 - 4.0\nt6 = t5 / 4.0\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "roy is now 8 years older than julia and half of that amount older than kelly . if in 4 years , roy will be twice as old as julia , then in 4 years what would be roy \u2019 s age multiplied by kelly \u2019 s age ?", + "Output Program": [ + "n0 = 8.0\nn1 = 4.0\nn2 = 4.0\nt0 = n0 / 2.0\nt1 = n0 - n1\nt2 = n0 + t1\nt3 = n1 + t2\nt4 = t2 - t0\nt5 = n1 + t4\nanswer = t3 * t5\nprint(answer)" + ], + "Output Answer": [ + "192" + ], + "split": "train" + }, + { + "Input": "if l is the least positive integer that is divisible by every integer from 1 to 9 inclusive , then l / 2 is =", + "Output Program": [ + "n0 = 1.0\nn1 = 9.0\nn2 = 2.0\nt0 = n0 + n2\nt1 = n2 + t0\nt2 = n2**min(t0, 5)\nt3 = t0**min(n2, 5)\nt4 = n2 + t1\nt5 = t2 * t3\nt6 = t4 * t5\nt7 = t1 * t6\nanswer = t7 / n2\nprint(answer)" + ], + "Output Answer": [ + "1260" + ], + "split": "train" + }, + { + "Input": "if the average ( arithmetic mean ) of a and b is 115 , and the average of b and c is 160 , what is the value of a \u2212 c ?", + "Output Program": [ + "n0 = 115.0\nn1 = 160.0\nt0 = n1 * 2.0\nt1 = n0 * 2.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "a batsman in his 12 th innings makes a score of 70 and thereby increases his average by 3 runs . what is his average after the 12 th innings if he had never been \u2018 not out \u2019 ?", + "Output Program": [ + "n0 = 12.0\nn1 = 70.0\nn2 = 3.0\nn3 = 12.0\nt0 = n0 * n2\nt1 = n1 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "37" + ], + "split": "train" + }, + { + "Input": "5 ^ 100 is divided by 18 . then what is the remainder ?", + "Output Program": [ + "n0 = 5.0\nn1 = 100.0\nn2 = 18.0\n\nanswer = n2 - n0\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "a , b and c have rs . 900 between them , a and c together have rs . 400 and b and c rs . 750 . how much does c have ?", + "Output Program": [ + "n0 = 900.0\nn1 = 400.0\nn2 = 750.0\nt0 = n1 + n2\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "250" + ], + "split": "train" + }, + { + "Input": "there are 84 supermarkets in the fgh chain . all of them are either in the us or canada . if there are 10 more fgh supermarkets in the us than in canada , how many fgh supermarkets are there in the us ?", + "Output Program": [ + "n0 = 84.0\nn1 = 10.0\nt0 = n0 + n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "47" + ], + "split": "train" + }, + { + "Input": "a positive integer , which when added to 1000 , gives a sum which is greater than when it is multiplied by 1000 . this positive integer is", + "Output Program": [ + "n0 = 1000.0\nn1 = 1000.0\nt0 = n0 + 1.0\nt1 = n0 * 1.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "the average of 11 numbers is 22 . average of the first 6 of them is 19 and that of the last 6 is 27 . find the 6 th number ?", + "Output Program": [ + "n0 = 11.0\nn1 = 22.0\nn2 = 6.0\nn3 = 19.0\nn4 = 6.0\nn5 = 27.0\nn6 = 6.0\nt0 = n5 * n6\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 - t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "34" + ], + "split": "train" + }, + { + "Input": "a sporting goods store sold 64 frisbees in one week , some for $ 3 and the rest for $ 4 each . if receipts from frisbee sales for the week totaled $ 200 , what is the fewest number of $ 4 frisbees that could have been sold ?", + "Output Program": [ + "n0 = 64.0\nn1 = 3.0\nn2 = 4.0\nn3 = 200.0\nn4 = 4.0\nt0 = n0 * n1\nanswer = n3 - t0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "when average age of 24 members are 0 , how many members greater than 0 ?", + "Output Program": [ + "n0 = 24.0\nn1 = 0.0\nn2 = 0.0\n\nanswer = n0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "marcella has 26 pairs of shoes . if she loses 9 individual shoes , what is the greatest number of matching pairs she could have left ?", + "Output Program": [ + "import math\nn0 = 26.0\nn1 = 9.0\nt0 = n1 / 2.0\nt1 = math.floor(t0)\nt2 = t1 + 1.0\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "a large box contains 16 small boxes and each small box contains 25 chocolate bars . how many chocolate bars are in the large box ?", + "Output Program": [ + "n0 = 16.0\nn1 = 25.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "train" + }, + { + "Input": "in a caravan , in addition to 60 hens , there are 35 goats and 6 camels with some keepers . if the total number of feet be 193 more than the number of heads in the caravan , the number of keepers is", + "Output Program": [ + "n0 = 60.0\nn1 = 35.0\nn2 = 6.0\nn3 = 193.0\nt0 = n0 + n1\nt1 = n0 * 2.0\nt2 = n1 * 4.0\nt3 = n2 * 4.0\nt4 = n2 + t0\nt5 = t1 + t2\nt6 = n3 + t4\nt7 = t5 + t3\nanswer = t6 - t7\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "two kinds of vodka are mixed in the ratio 1 : 2 and 2 : 1 and they are sold fetching the profit 25 % and 20 % respectively . if the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4 / 3 and 5 / 3 times respectively , then the mixture will fetch the profit of", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 2.0\nn3 = 1.0\nn4 = 10.0\nn5 = 35.0\nn6 = 4.0\nn7 = 3.0\nn8 = 5.0\nn9 = 3.0\nt0 = n4 + n8\nt1 = n4 * n6\nt2 = t1 / n1\nanswer = t0 + t2\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "in a division , divident is 725 , divisior is 36 and quotient is 20 . find the remainder .", + "Output Program": [ + "n0 = 725.0\nn1 = 36.0\nn2 = 20.0\n\nanswer = n0 % n1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "at deluxe paint store , fuchsia paint is made by mixing 5 parts of red paint with 3 parts of blue paint . mauve paint is made by mixing 4 parts of red paint with 5 parts blue paint . how many liters of blue paint must be added to 32 liters of fuchsia to change it to mauve paint ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nn2 = 4.0\nn3 = 5.0\nn4 = 32.0\nt0 = n0 + n1\nt1 = n0 / t0\nt2 = n2 / t0\nt3 = n3 / t0\nt4 = n4 * t1\nt5 = t4 / t2\nt6 = n4 - t4\nt7 = t5 * t3\nanswer = t7 - t6\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "if 5 / w + 5 / x = 5 / y and wx = y , then the average ( arithmetic mean ) of w and x is", + "Output Program": [ + "n0 = 5.0\nn1 = 5.0\nn2 = 5.0\nt0 = n0 + n0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.60 per glass on the first day , what was the price e per glass on the second day ?", + "Output Program": [ + "n0 = 0.6\nt0 = 1.0 + 1.0\nt1 = 1.0 + 2.0\nt2 = n0 * t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.39999999999999997" + ], + "split": "train" + }, + { + "Input": "in an examination , 25 % of total students failed in hindi , 48 % failed in english and 27 % in both . the percentage of these who passed in both the subjects is :", + "Output Program": [ + "n0 = 25.0\nn1 = 48.0\nn2 = 27.0\nt0 = n0 + n1\nt1 = t0 - n2\nanswer = 100.0 - t1\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "train" + }, + { + "Input": "if john makes a contribution to a charity fund at school , the average contribution size will increase by 50 % reaching $ 75 per person . if there were 2 other contributions made before john ' s , what is the size of his donation ?", + "Output Program": [ + "n0 = 50.0\nn1 = 75.0\nn2 = 2.0\nt0 = n2 + 1.0\nt1 = n1 * t0\nt2 = n0 * t0\nt3 = t1 - t2\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "125" + ], + "split": "train" + }, + { + "Input": "n and m are each 3 - digit integers . each of the numbers 2 , 34 , 6 , 7 , and 8 is a digit of either n or m . what is the smallest possible positive difference between n and m ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 34.0\nn3 = 6.0\nn4 = 7.0\nn5 = 8.0\nt0 = n1 - n5\nt1 = t0 * 10.0\nt2 = t1 + 100.0\nanswer = t2 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "39" + ], + "split": "train" + }, + { + "Input": "rebecca ' s annual income is $ 20 , and jimmy ' s annual income is $ 10 , . by how much must rebecca ' s annual income increase so that it constitutes 55 % of rebecca and jimmy ' s combined income ?", + "Output Program": [ + "n0 = 20.0\nn1 = 10.0\nn2 = 55.0\nt0 = n0 + n1\nt1 = n2 / 100.0\nt2 = t0 * t1\nt3 = 1.0 - t1\nt4 = t2 - n0\nt5 = t4 / t3\nanswer = -t5\nprint(answer)" + ], + "Output Answer": [ + "7.777777777777779" + ], + "split": "train" + }, + { + "Input": "if x , y , and z are positive integers , and 4 x = 5 y = 6 z , then the least possible value of x + y + z is", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 6.0\nt0 = n0 * n1\nt1 = n2 * t0\nt2 = t1 / 2.0\nt3 = t2 / n0\nt4 = t2 / n1\nt5 = t2 / n2\nt6 = t3 + t4\nanswer = t6 + t5\nprint(answer)" + ], + "Output Answer": [ + "37" + ], + "split": "train" + }, + { + "Input": "during the first two weeks of january , the total rainfall in springdale was 40 inches . if the rainfall during the second week was 1.5 times the rainfall during the first week , what was the rainfall during the second week of january ?", + "Output Program": [ + "n0 = 40.0\nn1 = 1.5\nt0 = n1 + 1.0\nt1 = n1 / t0\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "on rainy mornings , mo drinks exactly n cups of hot chocolate ( assume that n is an integer ) . on mornings that are not rainy , mo drinks exactly 5 cups of tea . last week mo drank a total of 22 cups of tea and hot chocolate together . if during that week mo drank 8 more tea cups than hot chocolate cups , then how many rainy days were there last week ?", + "Output Program": [ + "n0 = 5.0\nn1 = 22.0\nn2 = 8.0\nt0 = 3.0 + 4.0\nt1 = n1 + n2\nt2 = t1 / 2.0\nt3 = t2 / n0\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "mary and mike enter into a partnership by investing $ 650 and $ 350 respectively . at the end of one year , they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business . if mary received $ 600 more than mike did , what was the profit made by their business in that year ?", + "Output Program": [ + "n0 = 650.0\nn1 = 350.0\nn2 = 600.0\nt0 = n0 / 1000.0\nt1 = n1 / 1000.0\nt2 = 1.0 / 3.0\nt3 = t0 - t1\nt4 = 1.0 - t2\nt5 = t3 * t4\nanswer = n2 / t5\nprint(answer)" + ], + "Output Answer": [ + "2999.9999999999995" + ], + "split": "train" + }, + { + "Input": "on a certain date , pat invested $ 6000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 10 years will be $ 24000 , in how many years total will the total value of the investment plus interest increase to $ 48000 ?", + "Output Program": [ + "n0 = 6000.0\nn1 = 10.0\nn2 = 24000.0\nn3 = 48000.0\nt0 = n2 + n3\nt1 = t0 / n0\nanswer = t1 + 3.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "equal amount of water were poured into two empty jars of different capacities , which made one jar 1 / 6 full and other jar 1 / 5 full . if the water in the jar with lesser capacity is then poured into the jar with greater capacity , what fraction of the larger jar will be filled with water ?", + "Output Program": [ + "n0 = 1.0\nn1 = 6.0\nn2 = 1.0\nn3 = 5.0\n\nanswer = 2.0 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.3333333333333333" + ], + "split": "train" + }, + { + "Input": "if x is less than y by 20 % then y exceed x by :", + "Output Program": [ + "n0 = 20.0\nt0 = 100.0 - n0\nt1 = 100.0 / t0\nt2 = t1 - 1.0\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "a picnic attracts 200 persons . there are 20 more men than women , and 20 more adults than children . how many men are at this picnic ?", + "Output Program": [ + "n0 = 200.0\nn1 = 20.0\nn2 = 20.0\nt0 = n0 - n1\nt1 = t0 / 2.0\nt2 = n1 + t1\nt3 = t2 - n1\nt4 = t3 / 2.0\nanswer = n1 + t4\nprint(answer)" + ], + "Output Answer": [ + "65" + ], + "split": "train" + }, + { + "Input": "the smallest fraction , which each of 6 / 7 , 5 / 14 , 10 / 21 will divide exactly is :", + "Output Program": [ + "n0 = 6.0\nn1 = 7.0\nn2 = 5.0\nn3 = 14.0\nn4 = 10.0\nn5 = 21.0\nt0 = n0 * n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "4.285714285714286" + ], + "split": "train" + }, + { + "Input": "a box contains either blue or red flags . the total number of flags in the box is an even number . a group of children are asked to pick up two flags each . if all the flags are used up in the process such that 60 % of the children have blue flags , and 50 % have red flags , what percentage of children have flags of both the colors ?", + "Output Program": [ + "n0 = 60.0\nn1 = 50.0\nt0 = n0 + n1\nanswer = t0 - 100.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 200 milliliters of solution x to create a solution that is 20 percent alcohol by volume ?", + "Output Program": [ + "n0 = 10.0\nn1 = 30.0\nn2 = 200.0\nn3 = 20.0\nt0 = n3 - n0\nt1 = n1 - n3\nt2 = t0 / t1\nanswer = n2 * t2\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "train" + }, + { + "Input": "the ratio 6 : 3 expressed as a percent equals", + "Output Program": [ + "n0 = 6.0\nn1 = 3.0\nt0 = n0 / n1\nanswer = t0 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "train" + }, + { + "Input": "the average weight of 8 person ' s increases by 6 kg when a new person comes in place of one of them weighing 40 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 6.0\nn2 = 40.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "88" + ], + "split": "train" + }, + { + "Input": "if a no . when divided by 44 , gives 432 as quotient and 0 as remainder . what will be the remainder when dividing the same no . by 30", + "Output Program": [ + "n0 = 44.0\nn1 = 432.0\nn2 = 0.0\nn3 = 30.0\nt0 = n0 * n1\nanswer = t0 % n3\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "among 7 numbers the average of first 4 numbers is 13 and the average of last 4 numbers is 15 . the sum of last 3 numbers is 55 . the square of the fourth number is equal to the last number then what is the last number ?", + "Output Program": [ + "n0 = 7.0\nn1 = 4.0\nn2 = 13.0\nn3 = 4.0\nn4 = 15.0\nn5 = 3.0\nn6 = 55.0\nt0 = n1 * n4\nt1 = t0 - n6\nanswer = t1**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "a driver would have reduced the time it took to drive from home to the store by 1 / 3 if the average speed had been increased by 12 miles per hour . what was the actual average speed , in miles per hour , when the driver drove from home to the store ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 12.0\nt0 = n0 / n1\nt1 = n0 - t0\nt2 = t1 * n2\nt3 = n0 - t1\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "24.000000000000007" + ], + "split": "train" + }, + { + "Input": "the sum of all the digits of the integers from 18 to 21 inclusive is 24 ( 1 + 8 + 1 + 9 + 2 + 0 + 2 + 1 = 24 ) . what is the sum q of all the digits of the integers from 0 to 99 inclusive ?", + "Output Program": [ + "n0 = 18.0\nn1 = 21.0\nn2 = 24.0\nn3 = 1.0\nn4 = 8.0\nn5 = 1.0\nn6 = 9.0\nn7 = 2.0\nn8 = 0.0\nn9 = 2.0\nn10 = 1.0\nn11 = 24.0\nn12 = 0.0\nn13 = 99.0\nt0 = n6 + n3\nt1 = 10.0 * n7\nt2 = n6 * t0\nt3 = t2 / n7\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "900" + ], + "split": "train" + }, + { + "Input": "a man has rs . 10350 in the form of rs . 50 notes and rs . 500 notes . the total number of notes are 126 . find the number of notes of rs . 50 denomination .", + "Output Program": [ + "n0 = 10350.0\nn1 = 50.0\nn2 = 500.0\nn3 = 126.0\nn4 = 50.0\nt0 = n2 * n3\nt1 = n2 - n1\nt2 = t0 - n0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "117" + ], + "split": "train" + }, + { + "Input": "there are 870 male and female participants in a meeting . half the female participants and one - quarterof the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?", + "Output Program": [ + "n0 = 870.0\nt0 = n0 / 3.0\nt1 = t0 * 4.0\nt2 = t1 - n0\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "145" + ], + "split": "train" + }, + { + "Input": "is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 37 , then how old is b ?", + "Output Program": [ + "n0 = 37.0\nt0 = 2.0 + 3.0\nt1 = n0 - 2.0\nt2 = t1 / t0\nanswer = t2 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "a batsman scored 150 runs which included 5 boundaries and 5 sixes . what percent of his total score did he make by running between the wickets .", + "Output Program": [ + "n0 = 150.0\nn1 = 5.0\nn2 = 5.0\nt0 = n1 * n2\nt1 = n1 * n2\nt2 = t0 + t1\nt3 = n0 - t2\nt4 = t3 / n0\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "66.66666666666666" + ], + "split": "train" + }, + { + "Input": "a jar of 220 marbles is divided equally among a group of marble - players today . if 2 people joined the group in the future , each person would receive 1 marble less . how many people are there in the group today ?", + "Output Program": [ + "import math\nn0 = 220.0\nn1 = 2.0\nn2 = 1.0\nt0 = n0 * n1\nt1 = n1**min(n1, 5)\nt2 = t0 * 4.0\nt3 = t2 + t1\nt4 = math.sqrt(max(0, t3))\nt5 = t4 - n1\nanswer = t5 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "if a and b are the roots of the equation x 2 - 4 x + 4 = 0 , then the value of a 2 + b 2 is :", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 4.0\nn2 = 4.0\nn3 = 0.0\nn4 = 2.0\nn5 = 2.0\nt0 = n1 * 4.0\nt1 = n1**min(n0, 5)\nt2 = t1 - t0\nt3 = math.sqrt(max(0, t2))\nt4 = n1 + t3\nt5 = n1 - t3\nt6 = t5 / n0\nt7 = t4 / n0\nt8 = t6**min(n0, 5)\nt9 = t7**min(n0, 5)\nanswer = t8 + t9\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "if ( m - 8 ) is a factor of m ^ 2 - sm - 24 , then s =", + "Output Program": [ + "n0 = 8.0\nn1 = 2.0\nn2 = 24.0\nt0 = n2 / n0\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "each of the products produced yesterday was checked by worker x or worker y . 0.5 % of the products checked by worker x are defective and 0.8 % of the products checked by worker y are defective . if the total defective rate of all the products checked by worker x and worker y is 0.7 % , what fraction of the products was checked by worker y ?", + "Output Program": [ + "n0 = 0.5\nn1 = 0.8\nn2 = 0.7\nt0 = n2 - n0\nt1 = n1 - n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.6666666666666664" + ], + "split": "train" + }, + { + "Input": "what is the average of first 21 multiples of 4 ?", + "Output Program": [ + "n0 = 21.0\nn1 = 4.0\nt0 = n0 + 1.0\nt1 = n0 * t0\nt2 = t1 / 2.0\nt3 = t2 / n0\nanswer = n1 * t3\nprint(answer)" + ], + "Output Answer": [ + "44" + ], + "split": "train" + }, + { + "Input": "g ( a ) is defined as the product of all even integers k such that 0 < k \u2264 x . for example , g ( 14 ) = 2 \u00d7 4 \u00d7 6 \u00d7 8 \u00d7 10 \u00d7 12 \u00d7 14 . if g ( y ) is divisible by 4 ^ 11 , what is the smallest possible value for a ?", + "Output Program": [ + "n0 = 0.0\nn1 = 14.0\nn2 = 2.0\nn3 = 4.0\nn4 = 6.0\nn5 = 8.0\nn6 = 10.0\nn7 = 12.0\nn8 = 14.0\nn9 = 4.0\nn10 = 11.0\nt0 = n3 / 2.0\nt1 = n10 * t0\nanswer = t1 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "last year department store x had a sales total for december that was 7 times the average ( arithmetic mean ) of the monthly sales totals for january through november . the sales total for december was what fraction of the sales total for the year ?", + "Output Program": [ + "n0 = 7.0\nt0 = 12.0 - 1.0\nt1 = n0 + t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.3888888888888889" + ], + "split": "train" + }, + { + "Input": "the average age of 15 students of a class is 15 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years . the age of the 15 th student is ?", + "Output Program": [ + "n0 = 15.0\nn1 = 15.0\nn2 = 5.0\nn3 = 14.0\nn4 = 9.0\nn5 = 16.0\nn6 = 15.0\nt0 = n0 * n0\nt1 = n2 * n3\nt2 = n4 * n5\nt3 = t1 + t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "if x + y = 20 , x - y = 10 , for integers of x and y , x = ?", + "Output Program": [ + "n0 = 20.0\nn1 = 10.0\nt0 = n0 + n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "molly ' s age in 18 years will be 5 times her age 6 years ago . what is molly ' s present age ?", + "Output Program": [ + "n0 = 18.0\nn1 = 5.0\nn2 = 6.0\n\nanswer = n0 - n2\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "4 / 15 of 5 / 7 of a number is greater than 4 / 9 of 2 / 5 of the same number by 24 . what is half of that number ?", + "Output Program": [ + "n0 = 4.0\nn1 = 15.0\nn2 = 5.0\nn3 = 7.0\nn4 = 4.0\nn5 = 9.0\nn6 = 2.0\nn7 = 5.0\nn8 = 24.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = n6 / n2\nt3 = n0 / n5\nt4 = t0 * t1\nt5 = t2 * t3\nt6 = t4 - t5\nt7 = n8 / t6\nanswer = t7 / n6\nprint(answer)" + ], + "Output Answer": [ + "945.0000000000013" + ], + "split": "train" + }, + { + "Input": "a driver just filled the car ' s gas tank with 54 liters of gasohol , a mixture consisting of 5 % ethanol and 95 % gasoline . if the car runs best on a mixture consisting of 10 % ethanol and 90 % gasoline , how many liters of ethanol must be added into the gas tank for the car to achieve optimum performance ?", + "Output Program": [ + "n0 = 54.0\nn1 = 5.0\nn2 = 95.0\nn3 = 10.0\nn4 = 90.0\nt0 = n0 * n1\nt1 = 100.0 - n3\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "the average weight of 10 person ' s increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 10.0\nn1 = 3.5\nn2 = 65.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "the average marks of 10 students in a class is 100 . but a student mark is wrongly noted as 90 instead of 10 then find the correct average marks ?", + "Output Program": [ + "n0 = 10.0\nn1 = 100.0\nn2 = 90.0\nn3 = 10.0\nt0 = n0 * n1\nt1 = t0 - n2\nt2 = n3 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "92" + ], + "split": "train" + }, + { + "Input": "what will be remainder when ( 67 ^ 67 + 67 ) is divided by 68 ?", + "Output Program": [ + "n0 = 67.0\nn1 = 67.0\nn2 = 67.0\nn3 = 68.0\nt0 = n0 - n3\nt1 = t0**min(n0, 5)\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "66" + ], + "split": "train" + }, + { + "Input": "- - - - - - - - - - - - - - - - yes - - - - - - - - - no - - - - unsure subject m - - - - 500 - - - - - - - - 200 - - - - - 100 subject r - - - - 400 - - - - - - - - 100 - - - - - 300 a total of 800 students were asked whether they found two subjects , m and r , interesting . each answer was either yes or no or unsure , and the numbers of students who gave these answers are listed in the table above . if 170 students answered yes only for subject m , how many of the students did not answer yes for either subject ?", + "Output Program": [ + "n0 = 500.0\nn1 = 200.0\nn2 = 100.0\nn3 = 400.0\nn4 = 100.0\nn5 = 300.0\nn6 = 800.0\nn7 = 170.0\nt0 = n0 - n7\nt1 = n7 + t0\nt2 = n3 - t0\nt3 = t1 + t2\nanswer = n6 - t3\nprint(answer)" + ], + "Output Answer": [ + "230" + ], + "split": "train" + }, + { + "Input": "the average expenditure of a labourer for 6 months was 85 and he fell into debt . in the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30 . his monthly income i", + "Output Program": [ + "n0 = 6.0\nn1 = 85.0\nn2 = 4.0\nn3 = 60.0\nn4 = 30.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nt4 = n4 + t3\nanswer = t4 / t0\nprint(answer)" + ], + "Output Answer": [ + "78" + ], + "split": "train" + }, + { + "Input": "of 30 applicants for a job , 10 had at least 4 years ' experience , 18 had degrees , and 3 had less than 4 years ' experience and did not have a degree . how many of the applicants had at least 4 years ' experience and a degree ?", + "Output Program": [ + "n0 = 30.0\nn1 = 10.0\nn2 = 4.0\nn3 = 18.0\nn4 = 3.0\nn5 = 4.0\nn6 = 4.0\nt0 = n1 + n3\nt1 = n0 - n4\nt2 = n3 - n1\nt3 = t0 - t1\nanswer = t3 + t2\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "of 70 players on a football team , 34 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?", + "Output Program": [ + "n0 = 70.0\nn1 = 34.0\nt0 = 1.0 / 3.0\nt1 = n0 - n1\nt2 = 1.0 - t0\nt3 = t2 * t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "58" + ], + "split": "train" + }, + { + "Input": "if the digits 31 in the decimal 0.00031 repeat indefinitely , what is the value of ( 10 ^ 5 - 10 ^ 3 ) ( 0.00031 ) ?", + "Output Program": [ + "n0 = 31.0\nn1 = 0.00031\nn2 = 10.0\nn3 = 5.0\nn4 = 10.0\nn5 = 3.0\nn6 = 0.00031\nt0 = n2 * n2\nt1 = t0 - 1.0\nt2 = n0 / t1\nt3 = t0 * t1\nt4 = t2 * t3\nt5 = t4 / 1000.0\nanswer = n2 * t5\nprint(answer)" + ], + "Output Answer": [ + "31" + ], + "split": "train" + }, + { + "Input": "if the sum of two numbers is 30 and the sum of their squares is 840 , then the product of the numbers is", + "Output Program": [ + "n0 = 30.0\nn1 = 840.0\nt0 = n0**min(2.0, 5)\nt1 = t0 - n1\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "if 6 x ^ 2 + x - 12 = ( ax + b ) ( cx + d ) , then | a | + | b | + | c | + | d |", + "Output Program": [ + "n0 = 6.0\nn1 = 2.0\nn2 = 12.0\nt0 = n1 + 3.0\nt1 = 3.0 + 4.0\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "the sum of two numbers is 30 and their difference is 10 . find their product .", + "Output Program": [ + "n0 = 30.0\nn1 = 10.0\nt0 = n0 + n1\nt1 = 1.0 + 1.0\nt2 = t0 / t1\nt3 = t2 - n1\nanswer = t2 * t3\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "train" + }, + { + "Input": "simplify 3 / 4 of 6 0 \u2013 8 / 5 of 60 + ? = 12", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 6.0\nn3 = 0.0\nn4 = 8.0\nn5 = 5.0\nn6 = 60.0\nn7 = 12.0\nt0 = n0 / n1\nt1 = n4 / n5\nt2 = n6 * t0\nt3 = n6 * t1\nt4 = t2 - t3\nt5 = -t4\nanswer = n7 + t5\nprint(answer)" + ], + "Output Answer": [ + "63" + ], + "split": "train" + }, + { + "Input": "what is the average ( arithmetic mean ) of all the multiples of 10 from 10 to 160 inclusive ?", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 160.0\nt0 = n0 * 2.0\nt1 = n2 - t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "train" + }, + { + "Input": "pat , kate , and mark charged a total of 153 hours to a certain project . if pat charged twice as much time to the project as kate and 1 / 3 as much time as mark , how many more hours did mark charge to the project than kate ?", + "Output Program": [ + "n0 = 153.0\nn1 = 1.0\nn2 = 3.0\nt0 = n1 / n2\nt1 = n2 * 2.0\nt2 = n1 + t0\nt3 = n1 / t1\nt4 = t2 + t3\nt5 = n0 / t4\nt6 = t5 / t1\nanswer = t5 - t6\nprint(answer)" + ], + "Output Answer": [ + "85" + ], + "split": "train" + }, + { + "Input": "evaluate : | 9 - 8 ( 3 - 12 ) | - | 5 - 11 | = ?", + "Output Program": [ + "n0 = 9.0\nn1 = 8.0\nn2 = 3.0\nn3 = 12.0\nn4 = 5.0\nn5 = 11.0\nt0 = n2 - n3\nt1 = n4 - n5\nt2 = n1 * t0\nt3 = -t1\nt4 = n0 - t2\nanswer = t4 - t3\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "dacid obtained 96 , 95 , 82 , 97 and 95 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?", + "Output Program": [ + "n0 = 96.0\nn1 = 95.0\nn2 = 82.0\nn3 = 97.0\nn4 = 95.0\nn5 = 100.0\nt0 = n0 + n1\nt1 = 10.0 / 2.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "93" + ], + "split": "train" + }, + { + "Input": "the number 0.5 is how much greater than 1 / 6 ?", + "Output Program": [ + "n0 = 0.5\nn1 = 1.0\nn2 = 6.0\nt0 = n1 / n2\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "0.33333333333333337" + ], + "split": "train" + }, + { + "Input": "the ratio 10 : 20 expressed as percent equals to", + "Output Program": [ + "n0 = 10.0\nn1 = 20.0\nt0 = n0 / n1\nanswer = t0 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "in the junior basketball league there are 18 teams , 2 / 3 of them are bad and \u00bd are rich . what ca n ' t be the number of teams that are rich and bad", + "Output Program": [ + "n0 = 18.0\nn1 = 2.0\nn2 = 3.0\nt0 = 1.0 / n1\nt1 = n0 * t0\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the sum of the present age of henry and jill is 43 . what is their present ages if 5 years ago henry was twice the age of jill ?", + "Output Program": [ + "n0 = 43.0\nn1 = 5.0\nt0 = n0 + n1\nt1 = t0 / 3.0\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "train" + }, + { + "Input": "a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 84 percent of the distribution lies within one standard deviation d of the mean , what percent of the distribution is less than m + d ?", + "Output Program": [ + "n0 = 84.0\nt0 = 100.0 - n0\nt1 = t0 / 2.0\nanswer = 100.0 - t1\nprint(answer)" + ], + "Output Answer": [ + "92" + ], + "split": "train" + }, + { + "Input": "cost is expressed by the formula tb ^ 4 . if b is doubled , the new cost r is what percent of the original cost ?", + "Output Program": [ + "n0 = 4.0\nt0 = 2.0**min(n0, 5)\nanswer = t0 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "1600" + ], + "split": "train" + }, + { + "Input": "there are 6 positive and 8 negative numbers . 4 numbers are choosen at random and multiplied . the probability that the product is positive is :", + "Output Program": [ + "import math\nn0 = 6.0\nn1 = 8.0\nn2 = 4.0\nt0 = n0 + n1\nt1 = math.factorial(min(15, int(n0)))\nt2 = math.factorial(min(15, int(n2)))\nt3 = math.factorial(min(15, int(2.0)))\nt4 = math.factorial(min(15, int(n1)))\nt5 = math.factorial(min(15, int(t0)))\nt6 = t2 * t3\nt7 = t2 * t2\nt8 = t1 * t3\nt9 = t0 - n2\nt10 = t1 / t6\nt11 = t4 / t7\nt12 = t4 / t8\nt13 = math.factorial(min(15, int(t9)))\nt14 = t10 + t11\nt15 = t10 * t12\nt16 = t13 * t2\nt17 = t14 + t15\nt18 = t5 / t16\nanswer = t17 / t18\nprint(answer)" + ], + "Output Answer": [ + "0.5044955044955045" + ], + "split": "train" + }, + { + "Input": "f ( x ) is a function such that f ( x ) + 3 f ( 8 - x ) = x for all real numbers x . find the value of f ( 2 ) .", + "Output Program": [ + "n0 = 3.0\nn1 = 8.0\nn2 = 2.0\nt0 = n0 * n0\nt1 = t0 * 2.0\nt2 = 1.0 - t0\nt3 = n2 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a bag contains an equal number of one rupee , 50 paise and 25 paise coins respectively . if the total value is 105 , how many coins of each type are there ?", + "Output Program": [ + "n0 = 50.0\nn1 = 25.0\nn2 = 105.0\nt0 = 1 / 4.0\nt1 = 1 / 2.0\nt2 = t0 + t1\nt3 = t2 + 1.0\nanswer = n2 / t3\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "list k consists of 10 consecutive integers . if - 4 is the least integer in list k , what is the range of the positive integers in list k ?", + "Output Program": [ + "n0 = 10.0\nn1 = 4.0\nt0 = n0 - n1\nt1 = t0 - 1.0\nanswer = t1 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "a , b , c weighted separately 1 st like a , b , c , then a & b , then b & c , then c & a at last a & b & c , the last weight was 167 , then what will be the average weight of the 7 reading ?", + "Output Program": [ + "n0 = 1.0\nn1 = 167.0\nn2 = 7.0\nt0 = n1 * 4.0\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "95.42857142857143" + ], + "split": "train" + }, + { + "Input": "john want to buy a $ 100 trouser at the store , but he think it \u00e2 \u20ac \u2122 s too expensive . finally , it goes on sale for $ 70 . what is the percent decrease ?", + "Output Program": [ + "n0 = 100.0\nn1 = 70.0\n\nanswer = n0 - n1\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 10000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is :", + "Output Program": [ + "n0 = 8000.0\nn1 = 7.0\nn2 = 10000.0\nn3 = 6000.0\nt0 = n2 - n0\nt1 = n0 - n3\nt2 = n1 * t0\nt3 = t2 / t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "the total cost of a vacation was divided among 3 people . if the total cost of the vacation had been divided equally among 4 people , the cost per person would have been $ 30 less . what was the total cost cost of the vacation ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 30.0\nt0 = n0 * n1\nt1 = n1 - n0\nt2 = n2 / t1\nanswer = t2 * t0\nprint(answer)" + ], + "Output Answer": [ + "360" + ], + "split": "train" + }, + { + "Input": "mary ' s income is 60 % more than tim ' s income and tim ' s income is 20 % less than juan ' s income . what % of juan ' s income is mary ' s income .", + "Output Program": [ + "n0 = 60.0\nn1 = 20.0\nt0 = n0 / 100.0\nt1 = 100.0 - n1\nt2 = t0 * t1\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "128" + ], + "split": "train" + }, + { + "Input": "if there are 200 questions in a 3 hr examination . among these questions are 25 type a problems , which requires twice as much as time be spent than the rest of the type b problems . how many minutes should be spent on type a problems ?", + "Output Program": [ + "n0 = 200.0\nn1 = 3.0\nn2 = 25.0\nt0 = n1 * 60.0\nt1 = n2 * 2.0\nt2 = n0 - n2\nt3 = t1 + t2\nt4 = t0 / t3\nt5 = t4 * 2.0\nanswer = n2 * t5\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "8 is 2 % of a , and 2 is 8 % of b . c equals b / a . what is the value of c ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.0\nn2 = 2.0\nn3 = 8.0\nt0 = n1 / n0\nt1 = n0 / n1\nt2 = t0 * 100.0\nt3 = t1 * 100.0\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.0625" + ], + "split": "train" + }, + { + "Input": "a certain psychologist charges $ 30 more for the first hour of therapy than for each additional hour . if the total charge to a patient who receives 5 hours of therapy is $ 400 , what is the total charge to a patient who receives only 3 hours of therapy ?", + "Output Program": [ + "n0 = 30.0\nn1 = 5.0\nn2 = 400.0\nn3 = 3.0\nt0 = n2 - n0\nt1 = t0 / n1\nt2 = n3 * t1\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "252" + ], + "split": "train" + }, + { + "Input": "x is the product of each integer from 1 to 50 , inclusive and y = 100 ^ k , where k is an integer . what is the greatest value of k for which y is a factor of x ?", + "Output Program": [ + "n0 = 1.0\nn1 = 50.0\nn2 = 100.0\nt0 = n1 / 10.0\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "dawson and henry are in a relay race . dawson runs the first leg of the course in 38 seconds . henry runs the second leg of the course in 7 seconds . what was the average time they took to run a leg of the course ?", + "Output Program": [ + "n0 = 38.0\nn1 = 7.0\nt0 = n0 + n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "22.5" + ], + "split": "train" + }, + { + "Input": "we have boxes colored either red or blue . in each blue box there is a fixed number of blueberries . in each red box there is a fixed number of strawberries . if we dispose of one blue box for one additional red box , the total number of berries would increase by 30 , and the difference between the total number of strawberries and the total number of blueberries would increase by 100 . each blue box contains how many blueberries ?", + "Output Program": [ + "n0 = 30.0\nn1 = 100.0\nt0 = n1 - n0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "there are an average of 117 jellybeans in each of 34 bags of various sizes . after adding another bag , the average number of jellybeans per bag increases by 7 . how many jellybeans are in the new bag ?", + "Output Program": [ + "n0 = 117.0\nn1 = 34.0\nn2 = 7.0\nt0 = n1 + 1.0\nt1 = n2 * t0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "362" + ], + "split": "train" + }, + { + "Input": "a student has to obtain 33 % of the total marks to pass . he got 175 marks and failed by 89 marks . the maximum marks are ?", + "Output Program": [ + "n0 = 33.0\nn1 = 175.0\nn2 = 89.0\nt0 = n1 + n2\nt1 = n0 / 100.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "800" + ], + "split": "train" + }, + { + "Input": "a large box contains 19 small boxes and each small box contains 25 chocolate bars . how many chocolate bars are in the large box ?", + "Output Program": [ + "n0 = 19.0\nn1 = 25.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "475" + ], + "split": "train" + }, + { + "Input": "of 70 players on a football team , 52 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?", + "Output Program": [ + "n0 = 70.0\nn1 = 52.0\nt0 = 1.0 / 3.0\nt1 = n0 - n1\nt2 = 1.0 - t0\nt3 = t2 * t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "train" + }, + { + "Input": "there were totally 100 men . 84 are married . 75 have t . v , 85 have radio , 70 have a . c . how many men have t . v , radio , a . c and also married ?", + "Output Program": [ + "n0 = 100.0\nn1 = 84.0\nn2 = 75.0\nn3 = 85.0\nn4 = 70.0\nt0 = n0 - n1\nt1 = n0 - n2\nt2 = n0 - n3\nt3 = n0 - n4\nt4 = t0 + t1\nt5 = t4 + t2\nt6 = t5 + t3\nanswer = n0 - t6\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "one paper sheet can be used to create 8 paper boats or 6 paper planes . if total exact 80 paper toys are to be made , minimum how many sheets need to be used to make paper boats ?", + "Output Program": [ + "n0 = 8.0\nn1 = 6.0\nn2 = 80.0\nt0 = n2 / n0\nanswer = t0 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "a bag of potatoes weighs 16 kg divided by a quarter of its weight . how much does the bag weigh ?", + "Output Program": [ + "n0 = 16.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "what is the least number should be added to 1056 , so the sum of the number is completely divisible by 27 ?", + "Output Program": [ + "import math\nn0 = 1056.0\nn1 = 27.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = t1 + 1.0\nt3 = n1 * t2\nanswer = t3 - n0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "denominator of a number is 4 less than the numerator . if 6 is added to the numerator , it becomes 3 times the denominator . find the denominator .", + "Output Program": [ + "n0 = 4.0\nn1 = 6.0\nn2 = 3.0\nt0 = n0 + n1\nt1 = n2 - 1.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "if m is an integer such that ( - 2 ) ^ 2 m = 2 ^ ( 3 - m ) then m = ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 2.0\nn3 = 3.0\nt0 = n0 + 1.0\nanswer = n3 / t0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "a gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same . if there are 4 rows or 5 rows or 6 rows , then no tree will be left . find the least number of trees required", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 6.0\nt0 = n1 * n2\nt1 = n0 * t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "a batsman ' s avg in 12 innings is 24.00 . if his avg is to be double of the no of innings ( 15 innings ) , what should he score in the remaining 3 innings ( avg ) ?", + "Output Program": [ + "n0 = 12.0\nn1 = 24.0\nn2 = 15.0\nn3 = 3.0\nt0 = n1 * 2.0\nt1 = n0 * n1\nt2 = n2 * t0\nt3 = t2 - t1\nanswer = t3 / n3\nprint(answer)" + ], + "Output Answer": [ + "144" + ], + "split": "train" + }, + { + "Input": "if the sum of two numbers is 20 and the sum of their squares is 200 , then the product of the numbers is", + "Output Program": [ + "n0 = 20.0\nn1 = 200.0\nt0 = n0**min(2.0, 5)\nt1 = t0 - n1\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "a certain number when divided by 39 leaves a remainder 16 , what is the remainder when the same number is divided by 13 ?", + "Output Program": [ + "n0 = 39.0\nn1 = 16.0\nn2 = 13.0\n\nanswer = n1 % n2\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "rahul played weel in this season . his current batting averagge is 52 . if he score 78 runs in today match . his batting average will become 54 . how many matches had he played in this season .", + "Output Program": [ + "n0 = 52.0\nn1 = 78.0\nn2 = 54.0\nt0 = n1 - n2\nt1 = n2 - n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "the maximum number of students among them 1048 pens and 828 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :", + "Output Program": [ + "import scipy\nn0 = 1048.0\nn1 = 828.0\n\nanswer = scipy.gcd(int(n0), int(n1))\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "marts income is 40 percent more than tims income and tims income is 40 percent less than juans income . what percentage of juans income is marts income", + "Output Program": [ + "n0 = 40.0\nn1 = 40.0\nt0 = n0 + 100.0\nt1 = 100.0 - n1\nt2 = 100.0 / t1\nt3 = t2 * 100.0\nt4 = t0 / t3\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "83.99999999999999" + ], + "split": "train" + }, + { + "Input": "a gold purification process cycle , is able to remove 1 / 16 of impurities in gold . if we have a 10 grams of gold ore dust containing 16 / 24 pure gold . how much impurities would have been removed from that old after 4 cycles of purification using that method ?", + "Output Program": [ + "n0 = 1.0\nn1 = 16.0\nn2 = 10.0\nn3 = 16.0\nn4 = 24.0\nn5 = 4.0\nt0 = n4 - n1\nt1 = n2 * t0\nt2 = t1 / n4\nt3 = t2 / n1\nt4 = t2 - t3\nt5 = t4 / n1\nt6 = t4 - t5\nt7 = t6 / n1\nt8 = t6 - t7\nt9 = t8 / n1\nt10 = t8 - t9\nanswer = t2 - t10\nprint(answer)" + ], + "Output Answer": [ + "0.7584126790364585" + ], + "split": "train" + }, + { + "Input": "if f ( x ) = 2 x ^ 2 + y , and f ( 2 ) = 20 , what is the value of f ( 5 ) ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 2.0\nn3 = 20.0\nn4 = 5.0\nt0 = n4**min(n0, 5)\nt1 = n0**min(n0, 5)\nt2 = n0 * t0\nt3 = n0 * t1\nt4 = n3 - t3\nanswer = t2 + t4\nprint(answer)" + ], + "Output Answer": [ + "62" + ], + "split": "train" + }, + { + "Input": "david obtained 36 , 35 , 42 , 57 and 55 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology what are his average marks ?", + "Output Program": [ + "n0 = 36.0\nn1 = 35.0\nn2 = 42.0\nn3 = 57.0\nn4 = 55.0\nn5 = 100.0\nt0 = n0 + n1\nt1 = 2.0 + 3.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "the average score in an examination of 10 students of a class is 60 . if the scores of the top 5 students are not considered , the average score of the remaining students falls by 5 . the pass mark was 40 and the maximum mark was 100 . it is also known that none of the students failed . if each of the top 5 scorers had distinct integral scores , the maximum possible score of the topper is . . . . . .", + "Output Program": [ + "n0 = 10.0\nn1 = 60.0\nn2 = 5.0\nn3 = 5.0\nn4 = 40.0\nn5 = 100.0\nn6 = 5.0\nt0 = n0 * n1\nt1 = n1 - n2\nt2 = t1 + 1.0\nt3 = t1 + 2.0\nt4 = t1 + 3.0\nt5 = n2 * t1\nt6 = t0 - t5\nt7 = t6 - t1\nt8 = t7 - t2\nt9 = t8 - t3\nanswer = t9 - t4\nprint(answer)" + ], + "Output Answer": [ + "99" + ], + "split": "train" + }, + { + "Input": "5 + 3 + 2 = 151022 9 + 2 + 4 = 183652 8 + 6 + 3 = 482466 5 + 4 + 5 = 202541 then ; 7 + 2 + 5 = ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nn2 = 2.0\nn3 = 151022.0\nn4 = 9.0\nn5 = 2.0\nn6 = 4.0\nn7 = 183652.0\nn8 = 8.0\nn9 = 6.0\nn10 = 3.0\nn11 = 482466.0\nn12 = 5.0\nn13 = 4.0\nn14 = 5.0\nn15 = 202541.0\nn16 = 7.0\nn17 = 2.0\nn18 = 5.0\nt0 = n2 * n16\nt1 = n0 * 100.0\nt2 = n0 * n16\nt3 = t2 + t0\nt4 = t0 * 10.0\nt5 = n1 + t4\nt6 = t3 - n2\nt7 = t5 * 1000.0\nt8 = t7 + t1\nanswer = t8 + t6\nprint(answer)" + ], + "Output Answer": [ + "143547" + ], + "split": "train" + }, + { + "Input": "calculate the ratio between x and y if 80 % of x equal to 20 % of y ?", + "Output Program": [ + "n0 = 80.0\nn1 = 20.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "a certain psychologist charges $ 25 more for the first hour of therapy than for each additional hour . if the total charge to a patient who receives 5 hours of therapy is $ 250 , what is the total charge to a patient who receives only 2 hours of therapy ?", + "Output Program": [ + "n0 = 25.0\nn1 = 5.0\nn2 = 250.0\nn3 = 2.0\nt0 = n2 - n0\nt1 = t0 / n1\nt2 = n3 * t1\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "115" + ], + "split": "train" + }, + { + "Input": "there are 8 stores in town that had a total of 23 visitors on a particular day . however , only 12 people went shopping that day ; some people visited more than one store . if 8 people visited exactly two stores each , and everyone visited at least one store , what is the largest number of stores anyone could have visited ?", + "Output Program": [ + "n0 = 8.0\nn1 = 23.0\nn2 = 12.0\nn3 = 8.0\nt0 = n0 * 2.0\nt1 = n2 - n0\nt2 = n1 - t0\nt3 = t1 - 1.0\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "according to the directions on a can of frozen orange juice concentrate , 1 can of concentrate is to be mixed with 4 cans of water to make orange juice . how many 12 ounce cans of concentrate are required to prepare 120 6 - ounce servings of orange juice ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 12.0\nn3 = 120.0\nn4 = 6.0\nt0 = n0 + n1\nt1 = n3 * n4\nt2 = t1 / t0\nanswer = t2 / n2\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "if a , b , c , d , e and f are integers and ( ab + cdef ) < 0 , then what is the maximum number a of integers that can be negative ?", + "Output Program": [ + "n0 = 0.0\nt0 = 10.0 / 2.0\nanswer = n0 + t0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "calculate the average marks of a student who obtained 56 , 60 , 72 , 85 and 80 marks ( out of 100 ) in geography , history and government , art , computer science and modern literature ?", + "Output Program": [ + "n0 = 56.0\nn1 = 60.0\nn2 = 72.0\nn3 = 85.0\nn4 = 80.0\nn5 = 100.0\nt0 = n0 + n1\nt1 = n2 + n3\nt2 = 2.0 + 3.0\nt3 = t0 + t1\nt4 = n4 + t3\nanswer = t4 / t2\nprint(answer)" + ], + "Output Answer": [ + "70.6" + ], + "split": "train" + }, + { + "Input": "find the 21 th term of an arithmetic progression whose first term is 3 and the common difference is 5 .", + "Output Program": [ + "n0 = 21.0\nn1 = 3.0\nn2 = 5.0\nt0 = n0 - 1.0\nt1 = n2 * t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "103" + ], + "split": "train" + }, + { + "Input": "a committee is reviewing a total of 20 x black - and - white films and 6 y color films for a festival . if the committee selects y / x % of the black - and - white films and all of the color films , what fraction w of the selected films are in color ?", + "Output Program": [ + "n0 = 20.0\nn1 = 6.0\nt0 = n0 / 100.0\nt1 = n1 + t0\nanswer = n1 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.9677419354838709" + ], + "split": "train" + }, + { + "Input": "a person spends 1 / 3 rd of the money with him on clothes , 1 / 5 th of the remaining on food and 1 / 4 th of the remaining on travel . now , he is left with rs 400 . how much did he have with him in the beginning ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 5.0\nn4 = 1.0\nn5 = 4.0\nn6 = 400.0\nt0 = n0 / n1\nt1 = n0 - t0\nt2 = t1 / n3\nt3 = t1 - t2\nt4 = t3 / n5\nt5 = t3 - t4\nanswer = n6 / t5\nprint(answer)" + ], + "Output Answer": [ + "999.9999999999998" + ], + "split": "train" + }, + { + "Input": "when 100 is divided by positive integer x , the remainder is 4 . what is the remainder when 196 is divided by x ?", + "Output Program": [ + "n0 = 100.0\nn1 = 4.0\nn2 = 196.0\nt0 = n2 - n0\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "\u221a ( 14 ) ^ 2", + "Output Program": [ + "import math\nn0 = 14.0\nn1 = 2.0\nt0 = n0**min(n1, 5)\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "paul ' s salary was decreased by 50 % and subsequently increased by 50 % . how much percent does he lose ?", + "Output Program": [ + "n0 = 50.0\nn1 = 50.0\nt0 = n0 * n0\nt1 = t0 / 100.0\nt2 = n0 + t1\nanswer = 100.0 - t2\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "a certain list consists of 21 different numbers . if n is in the list and n is 4 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction u of the sum of the 21 numbers in the list ?", + "Output Program": [ + "n0 = 21.0\nn1 = 4.0\nn2 = 20.0\nn3 = 21.0\nt0 = n2 / n1\nt1 = 1.0 * 1.0\nt2 = n0 + t0\nt3 = t2 / n1\nt4 = t3 * 2.0\nt5 = t4 - n1\nt6 = t5 - 3.0\nanswer = t1 / t6\nprint(answer)" + ], + "Output Answer": [ + "0.16666666666666666" + ], + "split": "train" + }, + { + "Input": "if a - b = 4 and a ^ 2 + b ^ 2 = 80 , find the value of ab", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 2.0\nn2 = 2.0\nn3 = 80.0\nt0 = math.sqrt(max(0, n3))\nt1 = t0 - n0\nt2 = t1 / n1\nt3 = n0 + t2\nt4 = t3 * t2\nanswer = n1 * t4\nprint(answer)" + ], + "Output Answer": [ + "32.00000000000001" + ], + "split": "train" + }, + { + "Input": "in the xy - plane the point ( - 2 - 3 ) is the centre of a circle , the point ( - 2 , 3 ) lies inside the circle and the point ( 6 , - 3 ) lies outside the circle . if the radius r of the circle r is an integer then r =", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 2.0\nn3 = 3.0\nn4 = 6.0\nn5 = 3.0\nt0 = -n0\nt1 = n4 - t0\nt2 = n4 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "a man performs 3 / 5 of the total journey by rail , 17 / 20 by bus and the remaining 6.5 km on foot . his total journey is ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 17.0\nn3 = 20.0\nn4 = 6.5\n\nanswer = n3 * n4\nprint(answer)" + ], + "Output Answer": [ + "130" + ], + "split": "train" + }, + { + "Input": "the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 70 kg . what is the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.5\nn2 = 70.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "the function f ( y ) represents the number of ways that prime numbers can be uniquely summed to form a certain number y such that y = a + b + c + d \u2026 where those summed variables are each prime and a \u2264 b \u2264 c \u2264 d . . . for instance f ( 8 ) = 3 and the unique ways are 2 + 2 + 2 + 2 and 2 + 3 + 3 and 3 + 5 . what is f ( 12 ) ?", + "Output Program": [ + "n0 = 8.0\nn1 = 3.0\nn2 = 2.0\nn3 = 2.0\nn4 = 2.0\nn5 = 2.0\nn6 = 2.0\nn7 = 3.0\nn8 = 3.0\nn9 = 3.0\nn10 = 5.0\nn11 = 12.0\nt0 = n2 + n2\nanswer = n1 + t0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "a person was asked to state his age in years . his reply was , ` ` take my age 3 years hence , multiply it by 3 and subtract 3 times my age 3 years ago and you will know how old i am . ' ' what was the age of the person ?", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 3.0\nn3 = 3.0\nt0 = n0 * n1\nanswer = t0 + t0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "if the average of 744 , 745 , 747 , 748 , 749 , 752 , 752 , 753 , 755 and x is 750 , what is the value of x ?", + "Output Program": [ + "n0 = 744.0\nn1 = 745.0\nn2 = 747.0\nn3 = 748.0\nn4 = 749.0\nn5 = 752.0\nn6 = 752.0\nn7 = 753.0\nn8 = 755.0\nn9 = 750.0\nt0 = n0 + n1\nt1 = n9 * 10.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nt5 = n5 + t4\nt6 = n5 + t5\nt7 = n7 + t6\nt8 = n8 + t7\nanswer = t1 - t8\nprint(answer)" + ], + "Output Answer": [ + "755" + ], + "split": "train" + }, + { + "Input": "if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer that must divide n is", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 72.0\nt0 = n1 / n0\nt1 = math.sqrt(max(0, t0))\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "little john had $ 20.10 . he spent $ 1.05 on sweets and gave to his two friends $ 1.00 each . how much money was left ?", + "Output Program": [ + "n0 = 20.1\nn1 = 1.05\nn2 = 1.0\nt0 = n2 + n2\nt1 = n1 + t0\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "17.05" + ], + "split": "train" + }, + { + "Input": "a small pool filled only with water will require an additional 300 gallons of water in order to be filled to 80 % of its capacity . if pumping in these additional 300 gallons of water will increase the amount of water in the pool by 30 % , what is the total capacity of the pool in gallons ?", + "Output Program": [ + "n0 = 300.0\nn1 = 80.0\nn2 = 300.0\nn3 = 30.0\nt0 = n1 / 100.0\nt1 = n0 * 100.0\nt2 = t1 / n3\nt3 = n0 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "1625" + ], + "split": "train" + }, + { + "Input": "there are 200 female managers in a certain company . find the total number t of female employees in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers .", + "Output Program": [ + "n0 = 200.0\nn1 = 2.0\nn2 = 5.0\nn3 = 2.0\nn4 = 5.0\nt0 = n1 / n2\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "train" + }, + { + "Input": "60 + 5 * 12 / ( 180 / 3 ) = ?", + "Output Program": [ + "n0 = 60.0\nn1 = 5.0\nn2 = 12.0\nn3 = 180.0\nn4 = 3.0\nt0 = n3 / n4\nt1 = n1 * n2\nt2 = t1 / t0\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "61" + ], + "split": "train" + }, + { + "Input": "there are 200 female managers in a certain company . find the total number y of female employees in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers .", + "Output Program": [ + "n0 = 200.0\nn1 = 2.0\nn2 = 5.0\nn3 = 2.0\nn4 = 5.0\nt0 = n1 / n2\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "train" + }, + { + "Input": "if the operation \u00f8 is defined for all positive integers x and w by x \u00f8 w = ( 2 ^ x ) / ( 2 ^ w ) then ( 4 \u00f8 2 ) \u00f8 3 = ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 4.0\nn3 = 2.0\nn4 = 3.0\nt0 = n0**min(n2, 5)\nt1 = n0**min(n0, 5)\nt2 = n0**min(n4, 5)\nt3 = t0 / t1\nt4 = n0**min(t3, 5)\nanswer = t4 / t2\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "in a rectangular box measuring 12 inches by 14 inches by 16 inches if small rectangular boxes measuring 3 inches by 7 inches by 2 inches are arranged in it , what is the max number of boxes that fit into it ?", + "Output Program": [ + "n0 = 12.0\nn1 = 14.0\nn2 = 16.0\nn3 = 3.0\nn4 = 7.0\nn5 = 2.0\nt0 = n2 / n5\nt1 = n0 / n3\nt2 = n1 / n4\nt3 = t1 * t2\nanswer = t0 * t3\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "train" + }, + { + "Input": "ashis ' s height is 25 % more than babji , by how much percent babji ' s height is less than ashis .", + "Output Program": [ + "n0 = 25.0\nt0 = n0 + 100.0\nt1 = n0 / t0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "in a graduating class , 40 percent of the students are male . in this class , 40 percent of the male students and 20 percent of the female students are 25 years old or older . if one student in the class is randomly selected , approximately what is the probability that he or she will be less than 25 years old ?", + "Output Program": [ + "n0 = 40.0\nn1 = 40.0\nn2 = 20.0\nn3 = 25.0\nn4 = 25.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = n2 / 100.0\nt3 = t0 * t1\nt4 = 1.0 - t0\nt5 = t2 * t4\nt6 = t3 + t5\nanswer = 1.0 - t6\nprint(answer)" + ], + "Output Answer": [ + "0.72" + ], + "split": "train" + }, + { + "Input": "if the remainder is 12 when the integer n is divided by 22 , what is the remainder when 2 n is divided by 11 ?", + "Output Program": [ + "n0 = 12.0\nn1 = 22.0\nn2 = 2.0\nn3 = 11.0\nt0 = n0 * n2\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "the average marks of a class of 30 students is 40 and that of another class of 50 students is 80 . find the average marks of all the students ?", + "Output Program": [ + "n0 = 30.0\nn1 = 40.0\nn2 = 50.0\nn3 = 80.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "65" + ], + "split": "train" + }, + { + "Input": "if x is a sum of all even integers on the interval 13 . . . 63 and y is their number , what is the gcd ( x , y ) ?", + "Output Program": [ + "n0 = 13.0\nn1 = 63.0\nt0 = n0 - 10.0\nt1 = t0 + 2.0\nanswer = t1 * t1\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "a company decreased the price of its main product by 25 % . subsequently , the number of units sold increased such that the total revenue remained unchanged . what was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product ?", + "Output Program": [ + "n0 = 25.0\n\nanswer = 100.0 / n0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "the average of runs of a cricket player of 10 innings was 30 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?", + "Output Program": [ + "n0 = 10.0\nn1 = 30.0\nn2 = 4.0\nt0 = n0 + 1.0\nt1 = n1 + n2\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "74" + ], + "split": "train" + }, + { + "Input": "when a student joe , weighing 44 kg , joins a group of students whose average weight is 30 kg , the average weight goes up by 1 kg . subsequently , if two students , excluding joe , leave the group the average weight comes back to 30 kg . what is the difference between the average weight of the two students who left and the weight of joe ?", + "Output Program": [ + "n0 = 44.0\nn1 = 30.0\nn2 = 1.0\nn3 = 30.0\nt0 = n1 + n2\nt1 = n0 - t0\nt2 = n1 * t1\nt3 = t1 - n2\nt4 = n0 + t2\nt5 = n1 * t3\nt6 = t4 - t5\nt7 = t6 / 2.0\nanswer = n0 - t7\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "if a 2 - b 2 = 8 and a * b = 2 , find a 4 + b 4 .", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 8.0\nn3 = 2.0\nn4 = 4.0\nn5 = 4.0\nt0 = n3**min(n0, 5)\nt1 = n2**min(n0, 5)\nt2 = t0 * n0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "train" + }, + { + "Input": "when positive integer x is divided by positive integer y , the remainder is 5.76 . if x / y = 96.12 , what is the value of y ?", + "Output Program": [ + "import math\nn0 = 5.76\nn1 = 96.12\nt0 = math.floor(n1)\nt1 = n1 - t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "47.99999999999818" + ], + "split": "train" + }, + { + "Input": "the instructions state that cheryl needs 5 / 9 square yards of one type of material and 1 / 3 square yards of another type of material for a project . she buys exactly that amount . after finishing the project , however , she has 8 / 24 square yards left that she did not use . what is the total amount of square yards of material cheryl used ?", + "Output Program": [ + "n0 = 5.0\nn1 = 9.0\nn2 = 1.0\nn3 = 3.0\nn4 = 8.0\nn5 = 24.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = n4 / n5\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "0.5555555555555556" + ], + "split": "train" + }, + { + "Input": "what is the value of n if the sum of the consecutive odd intergers q from 1 to n equals 169 ?", + "Output Program": [ + "import math\nn0 = 1.0\nn1 = 169.0\nt0 = n0 * 2.0\nt1 = math.sqrt(max(0, n1))\nt2 = t1 * 2.0\nt3 = t2 - t0\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "how many kg of pure salt must be added to 100 kg of 10 % solution of salt and water to increase it to a 30 % solution ?", + "Output Program": [ + "n0 = 100.0\nn1 = 10.0\nn2 = 30.0\nt0 = n2 / n0\nt1 = n2 - n1\nt2 = 1.0 - t0\nanswer = t1 / t2\nprint(answer)" + ], + "Output Answer": [ + "28.571428571428573" + ], + "split": "train" + }, + { + "Input": "in how many ways can the integer 15 be expressed as a product of two different positive integers ?", + "Output Program": [ + "n0 = 15.0\nt0 = n0 / 1.0\nt1 = t0 / 3.0\nanswer = t1 - 3.0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "if 5 x + 3 = 10 x \u2013 17 , what is the value of x ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nn2 = 10.0\nn3 = 17.0\nt0 = n1 + n3\nt1 = n2 - n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "1 / 216 , 415 , 356 , _ ?", + "Output Program": [ + "n0 = 1.0\nn1 = 216.0\nn2 = 415.0\nn3 = 356.0\nt0 = 2.0 * 4.0\nt1 = 10.0 * 2.0\nt2 = t0 + t1\nanswer = t2 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "9.333333333333334" + ], + "split": "train" + }, + { + "Input": "two trains start at same time from two stations and proceed towards each other at the rate of 20 km / hr and 25 km / hr respectively . when they meet , it is found that one train has traveled 50 km more than the other . what is the distance between the two stations ?", + "Output Program": [ + "n0 = 20.0\nn1 = 25.0\nn2 = 50.0\nt0 = n0 + n1\nt1 = n1 - n0\nt2 = n2 / t1\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "450" + ], + "split": "train" + }, + { + "Input": "the cost of 10 kg of mangos is equal to the cost of 24 kg of rice . the cost of 6 kg of flour equals the cost of 2 kg of rice . the cost of each kg of flour is $ 24 . find the total cost of 4 kg of mangos , 3 kg of rice and 5 kg of flour ?", + "Output Program": [ + "n0 = 10.0\nn1 = 24.0\nn2 = 6.0\nn3 = 2.0\nn4 = 24.0\nn5 = 4.0\nn6 = 3.0\nn7 = 5.0\nt0 = n1 / n0\nt1 = n2 * n4\nt2 = n4 * n7\nt3 = t1 / n3\nt4 = t0 * t3\nt5 = n6 * t3\nt6 = n5 * t4\nt7 = t6 + t5\nanswer = t7 + t2\nprint(answer)" + ], + "Output Answer": [ + "1027.1999999999998" + ], + "split": "train" + }, + { + "Input": "if n is the product of integers from 1 to 20 inclusive what is the greatest integer k for which 2 ^ k is a factor of n ?", + "Output Program": [ + "import math\nn0 = 1.0\nn1 = 20.0\nn2 = 2.0\nt0 = n1 / n2\nt1 = n2**min(n2, 5)\nt2 = n2**min(3.0, 5)\nt3 = n1 / t1\nt4 = n1 / t2\nt5 = t1**min(n2, 5)\nt6 = t0 + t3\nt7 = n1 / t5\nt8 = math.floor(t4)\nt9 = math.floor(t7)\nt10 = t6 + t9\nanswer = t10 + t8\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "find the value of 72519 x 9999 = m ?", + "Output Program": [ + "n0 = 72519.0\nn1 = 9999.0\nt0 = n1 - 4.0\nanswer = t0 * n0\nprint(answer)" + ], + "Output Answer": [ + "724827405" + ], + "split": "train" + }, + { + "Input": "3 , 15 , x , 51 , 53 , 159161 value of x ?", + "Output Program": [ + "n0 = 3.0\nn1 = 15.0\nn2 = 51.0\nn3 = 53.0\nn4 = 159161.0\n\nanswer = n1 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "a , b and c are partners . a receives 2 / 3 of profits , b and c dividing the remainder equally . a ' s income is increased by rs . 300 when the rate to profit rises from 5 to 7 percent . find the capital of a ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 300.0\nn3 = 5.0\nn4 = 7.0\nt0 = n2 * 100.0\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "15000" + ], + "split": "train" + }, + { + "Input": "how many two - digit numbers yield a remainder of 3 when divided by both 4 and 14 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 14.0\nt0 = n1 * n2\nt1 = n0 + t0\nanswer = t1 - t0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "a certain roller coaster has 2 cars , and a passenger is equally likely to ride in any 1 of the 2 cars each time that passenger rides the roller coaster . if a certain passenger is to ride the roller coaster 2 times , what is the probability that the passenger will ride in each of the 2 cars ?", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 1.0\nn2 = 2.0\nn3 = 2.0\nn4 = 2.0\nt0 = n1 / n0\nt1 = math.factorial(min(15, int(n0)))\nt2 = t0**min(n0, 5)\nanswer = t1 * t2\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "a man can swim in still water at 7.5 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ?", + "Output Program": [ + "n0 = 7.5\n\nanswer = n0 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "2.5" + ], + "split": "train" + }, + { + "Input": "little john had $ 10.10 . he spent $ 3.25 on sweets and gave to his two friends $ 2.20 each . how much money was left ?", + "Output Program": [ + "n0 = 10.1\nn1 = 3.25\nn2 = 2.2\nt0 = n2 + n2\nt1 = n1 + t0\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "2.4499999999999993" + ], + "split": "train" + }, + { + "Input": "if a and b are the roots of the equation x 2 - 5 x + 5 = 0 , then the value of a 2 + b 2 is :", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 5.0\nn2 = 5.0\nn3 = 0.0\nn4 = 2.0\nn5 = 2.0\nt0 = n1 * 4.0\nt1 = n1**min(n0, 5)\nt2 = t1 - t0\nt3 = math.sqrt(max(0, t2))\nt4 = n1 + t3\nt5 = n1 - t3\nt6 = t5 / n0\nt7 = t4 / n0\nt8 = t6**min(n0, 5)\nt9 = t7**min(n0, 5)\nanswer = t8 + t9\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "a chocolate manufacturer produces 400 units of a certain model each month at a cost to the manufacturer of \u00a3 40 per unit and all of the produced units are sold each month . what is the minimum selling price per unit that will ensure that the monthly profit ( revenue from sales minus production costs ) on the sales of these units will be at least \u00a3 40000 ?", + "Output Program": [ + "n0 = 400.0\nn1 = 40.0\nn2 = 40000.0\n\nanswer = n0 + n1\nprint(answer)" + ], + "Output Answer": [ + "440" + ], + "split": "train" + }, + { + "Input": "1,000 ^ 2 + 1,001 ^ 2 + 1,002 ^ 2 + 1,003 ^ 2 + 1,004 ^ 2 + 1,005 ^ 2 + 1,006 ^ 2 =", + "Output Program": [ + "n0 = 1000.0\nn1 = 2.0\nn2 = 1001.0\nn3 = 2.0\nn4 = 1002.0\nn5 = 2.0\nn6 = 1003.0\nn7 = 2.0\nn8 = 1004.0\nn9 = 2.0\nn10 = 1005.0\nn11 = 2.0\nn12 = 1006.0\nn13 = 2.0\n\nanswer = n1 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "( 112 x 54 ) = ?", + "Output Program": [ + "n0 = 112.0\nn1 = 54.0\nt0 = 1.0 + 4.0\nt1 = t0**min(4.0, 5)\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "70000" + ], + "split": "train" + }, + { + "Input": "an amount at compound interest sums to rs . 17640 / - in 2 years and to rs . 21168 / - in 3 years at the same rate of interest . find the rate percentage ?", + "Output Program": [ + "n0 = 17640.0\nn1 = 2.0\nn2 = 21168.0\nn3 = 3.0\nt0 = n2 - n0\nt1 = t0 / n0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "in the above number , a and b represent the tens and units digits , respectively . if the above number is divisible by 25 , what is the greatest possible value of b x a ?", + "Output Program": [ + "n0 = 25.0\nt0 = 3.0 + 4.0\nt1 = 2.0 + 3.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "( 0.15 ) ( power 3 ) - ( 0.06 ) ( power 3 ) / ( 0.15 ) ( power 2 ) + 0.009 + ( 0.06 ) ( power 2 ) is :", + "Output Program": [ + "n0 = 0.15\nn1 = 3.0\nn2 = 0.06\nn3 = 3.0\nn4 = 0.15\nn5 = 2.0\nn6 = 0.009\nn7 = 0.06\nn8 = 2.0\nt0 = n0**min(n1, 5)\nt1 = n2**min(n1, 5)\nt2 = n0**min(n5, 5)\nt3 = n2**min(n5, 5)\nt4 = n6 + t2\nt5 = t0 - t1\nt6 = t4 + t3\nanswer = t5 / t6\nprint(answer)" + ], + "Output Answer": [ + "0.08999999999999998" + ], + "split": "train" + }, + { + "Input": "if the remainder is 8 when positive integer n is divided by 12 , what is the remainder when n is divided by 6 ?", + "Output Program": [ + "n0 = 8.0\nn1 = 12.0\nn2 = 6.0\n\nanswer = n1 / n2\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "x varies inversely as square of y . given that y = 2 for x = 1 . the value of x for y = 6 will be equal to :", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 6.0\nt0 = n0**min(2.0, 5)\nt1 = n2**min(2.0, 5)\nt2 = n1 * t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.1111111111111111" + ], + "split": "train" + }, + { + "Input": "how many positive integers less than 9,000 are there in which the sum of the digits equals 5 ?", + "Output Program": [ + "import math\nn0 = 9000.0\nn1 = 5.0\nt0 = n1 + 4.0\nt1 = math.factorial(min(15, int(n1)))\nt2 = 4.0 - 1.0\nt3 = math.factorial(min(15, int(t2)))\nt4 = t0 - 1.0\nt5 = math.factorial(min(15, int(t4)))\nt6 = t1 * t3\nanswer = t5 / t6\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "train" + }, + { + "Input": "two employees x and y are paid a total of rs . 550 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?", + "Output Program": [ + "n0 = 550.0\nn1 = 120.0\nt0 = 1.0 + 4.0\nt1 = t0 * 2.0\nt2 = t1 + 1.0\nt3 = n0 * t1\nt4 = t2 * 2.0\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "250" + ], + "split": "train" + }, + { + "Input": "set a contains all the even numbers between 32 and 80 inclusive . set b contains all the even numbers between 62 and 110 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ?", + "Output Program": [ + "n0 = 32.0\nn1 = 80.0\nn2 = 62.0\nn3 = 110.0\nt0 = n1 - n0\nt1 = n2 - n0\nt2 = t0 / 2.0\nt3 = t2 + 1.0\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "750" + ], + "split": "train" + }, + { + "Input": "in a maths test , students were asked to find 5 / 16 of a certain number . one of the students by mistake found 5 / 6 th of that number and his answer was 300 more than the correct answer . find the number .", + "Output Program": [ + "n0 = 5.0\nn1 = 16.0\nn2 = 5.0\nn3 = 6.0\nn4 = 300.0\nt0 = n1 * n4\nt1 = n0 * n1\nt2 = n0 * n3\nt3 = n3 * t0\nt4 = t1 - t2\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "576" + ], + "split": "train" + }, + { + "Input": "a factory producing tennis balls stores them in either big boxes , 25 balls per box , or small boxes , 20 balls per box . if 104 freshly manufactured balls are to be stored , what is the least number of balls that can be left unboxed ?", + "Output Program": [ + "n0 = 25.0\nn1 = 20.0\nn2 = 104.0\n\nanswer = n0 - n1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "if x / y = 7 / 3 , then ( x + y ) / ( x - y ) = ?", + "Output Program": [ + "n0 = 7.0\nn1 = 3.0\nt0 = n0 + n1\nt1 = n0 - n1\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "2.5" + ], + "split": "train" + }, + { + "Input": "calculate the sum of first 19 natural numbers .", + "Output Program": [ + "n0 = 19.0\nt0 = n0 + 1.0\nt1 = n0 / 2.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "190" + ], + "split": "train" + }, + { + "Input": "in a division , divident is 689 , divisior is 36 and quotient is 19 . find the remainder .", + "Output Program": [ + "n0 = 689.0\nn1 = 36.0\nn2 = 19.0\n\nanswer = n0 % n1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "the product of two numbers is 120 and the sum of their squares is 289 . the sum of the number is", + "Output Program": [ + "import math\nn0 = 120.0\nn1 = 289.0\nt0 = n0 * 4.0\nt1 = n0 * 2.0\nt2 = n1 - t1\nt3 = math.sqrt(max(0, t2))\nt4 = t3**min(2.0, 5)\nt5 = t0 + t4\nanswer = math.sqrt(max(0, t5))\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "what is the dividend . divisor 18 , the quotient is 9 and the remainder is 3", + "Output Program": [ + "n0 = 18.0\nn1 = 9.0\nn2 = 3.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "165" + ], + "split": "train" + }, + { + "Input": "each child has 2 pencils and 13 skittles . if there are 8 children , how many pencils are there in total ?", + "Output Program": [ + "n0 = 2.0\nn1 = 13.0\nn2 = 8.0\n\nanswer = n0 * n2\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "a , b and c rent a pasture . if a puts 10 oxen for 7 months , b puts 12 oxen for 5 months and c puts 15 oxen for 3 months for grazing and the rent of the pasture is rs . 245 , then how much amount should c pay as his share of rent ?", + "Output Program": [ + "n0 = 10.0\nn1 = 7.0\nn2 = 12.0\nn3 = 5.0\nn4 = 15.0\nn5 = 3.0\nn6 = 245.0\nt0 = n4 * n5\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nt4 = t3 + t0\nt5 = t0 / t4\nanswer = n6 * t5\nprint(answer)" + ], + "Output Answer": [ + "62.99999999999999" + ], + "split": "train" + }, + { + "Input": "a and b started a business jointly a ' s investment was thrice the investment of b and the period of his investment was two times the period of investment of b . if b received rs . 4000 as profit , then their total profit is ?", + "Output Program": [ + "n0 = 4000.0\nt0 = 2.0 * 3.0\nt1 = t0 + 1.0\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "28000" + ], + "split": "train" + }, + { + "Input": "there is a total of 90 marbles in a box , each of which is red , green , blue , or white . if one marble is drawn from the box at random , the probability that it will be white is 1 / 3 and the probability that it will be green is 1 / 5 . what is the probability that the marble will be either red or blue ?", + "Output Program": [ + "n0 = 90.0\nn1 = 1.0\nn2 = 3.0\nn3 = 1.0\nn4 = 5.0\nt0 = n1 / n2\nt1 = n3 / n4\nt2 = t0 + t1\nanswer = n1 - t2\nprint(answer)" + ], + "Output Answer": [ + "0.4666666666666667" + ], + "split": "train" + }, + { + "Input": "a boat crossed a lake from north to east at the speed of 10 km / h , entered a river and covered twice as much distance going upstream at 9 km / h . it then turned around and stopped at the south shore of the lake . if it averaged 3.8 km / h that day , what was its approximate downstream speed ?", + "Output Program": [ + "n0 = 10.0\nn1 = 9.0\nn2 = 3.8\nt0 = n0 - n1\nanswer = n0 + t0\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "the avg weight of a , b & c is 50 kg . if d joins the group , the avg weight of the group becomes 53 kg . if another man e who weights is 3 kg more than d replaces a , then the avgof b , c , d & e becomes 51 kg . what is the weight of a ?", + "Output Program": [ + "n0 = 50.0\nn1 = 53.0\nn2 = 3.0\nn3 = 51.0\nt0 = n1 * 4.0\nt1 = n3 * 4.0\nt2 = n0 * n2\nt3 = t0 - t2\nt4 = n2 + t3\nt5 = t1 - t4\nanswer = t0 - t5\nprint(answer)" + ], + "Output Answer": [ + "73" + ], + "split": "train" + }, + { + "Input": "p , q and r have $ 5000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?", + "Output Program": [ + "n0 = 5000.0\nt0 = 2.0 * 2.0\nt1 = 1.0 * 3.0\nt2 = t0 / 3.0\nt3 = n0 * t0\nt4 = t2 * 3.0\nt5 = t4 + t1\nt6 = t5 + t1\nanswer = t3 / t6\nprint(answer)" + ], + "Output Answer": [ + "2000" + ], + "split": "train" + }, + { + "Input": "you have a 6 - sided cube and 6 cans of paint , each a different color . you may not mix colors of paint . how many distinct ways can you paint the cube using a different color for each side ? ( if you can reorient a cube to look like another cube , then the two cubes are not distinct . )", + "Output Program": [ + "import math\nn0 = 6.0\nn1 = 6.0\nt0 = n0 / 2.0\nt1 = n0 - 1.0\nt2 = math.factorial(min(15, int(t0)))\nanswer = t2 * t1\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "laura took out a charge account at the general store and agreed to pay 4 % simple annual interest . if she charges $ 35 on her account in january , how much will she owe a year later , assuming she does not make any additional charges or payments ?", + "Output Program": [ + "n0 = 4.0\nn1 = 35.0\nt0 = n0 / 100.0\nt1 = n1 * t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "36.4" + ], + "split": "train" + }, + { + "Input": "how many of the integers between 10 and 40 are even ?", + "Output Program": [ + "n0 = 10.0\nn1 = 40.0\nt0 = n1 - n0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "in a class of 35 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 10 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?", + "Output Program": [ + "n0 = 35.0\nn1 = 2.0\nn2 = 12.0\nn3 = 1.0\nn4 = 10.0\nn5 = 2.0\nn6 = 3.0\nn7 = 2.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n1 * n4\nt3 = t1 + t2\nt4 = n4 + t1\nt5 = n1 + t4\nt6 = n0 - t5\nt7 = t6 - n3\nt8 = n6 * t7\nt9 = t3 + t8\nanswer = t0 - t9\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "crazy eddie has a key chain factory . eddie managed to decrease the cost of manufacturing his key chains while keeping the same selling price , and thus increased the profit from the sale of each key chain from 35 % of the selling price to 50 % of the selling price . if the manufacturing cost is now $ 50 , what was it before the decrease ?", + "Output Program": [ + "n0 = 35.0\nn1 = 50.0\nn2 = 50.0\nt0 = n1 / 100.0\nt1 = n0 / 100.0\nt2 = n1 / t0\nt3 = t2 * t1\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "65" + ], + "split": "train" + }, + { + "Input": "mike earns $ 14 per hour and phil earns $ 7 per hour . approximately how much less , as a percentage , does phil earn than mike per hour ?", + "Output Program": [ + "n0 = 14.0\nn1 = 7.0\nt0 = n1 / n0\nanswer = t0 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "albert is 2 times mary \u2019 s age and 4 times as old as betty . mary is 8 years younger than albert . how old is betty ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 8.0\nt0 = n0 * n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "crazy eddie has a key chain factory . eddie managed to decrease the cost of manufacturing his key chains while keeping the same selling price , and thus increased the profit from the sale of each key chain from 30 % of the selling price to 50 % of the selling price . if the manufacturing cost is now $ 50 , what was it before the decrease ?", + "Output Program": [ + "n0 = 30.0\nn1 = 50.0\nn2 = 50.0\nt0 = n1 / 100.0\nt1 = n0 / 100.0\nt2 = n1 / t0\nt3 = t2 * t1\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "train" + }, + { + "Input": "if ( 1 / 2 ) ^ 16 ( 1 / 81 ) ^ k = 1 / 18 ^ 16 , then k =", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 16.0\nn3 = 1.0\nn4 = 81.0\nn5 = 1.0\nn6 = 18.0\nn7 = 16.0\nt0 = n1 * n2\nanswer = t0 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "the average age of 25 students of a class is 25 years . out of these , the average age of 10 students is 22 years and that of the other 14 students is 28 years . the age of the 25 th student is ?", + "Output Program": [ + "n0 = 25.0\nn1 = 25.0\nn2 = 10.0\nn3 = 22.0\nn4 = 14.0\nn5 = 28.0\nn6 = 25.0\nt0 = n0 * n0\nt1 = n2 * n3\nt2 = n4 * n5\nt3 = t1 + t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "anita has 360 apples . there are 60 students are studying in her class . she would like to give each student the same amount of apples , how much should she give to each student ?", + "Output Program": [ + "n0 = 360.0\nn1 = 60.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "6 persons standing in queue with different age group , after two years their average age will be 43 and seventh person joined with them . hence the current average age has become 45 . find the age of seventh person ?", + "Output Program": [ + "n0 = 6.0\nn1 = 43.0\nn2 = 45.0\nt0 = n0 + 1.0\nt1 = n1 - 2.0\nt2 = n2 * t0\nt3 = n0 * t1\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "69" + ], + "split": "train" + }, + { + "Input": "every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 1600 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 8.0\nn2 = 1600.0\nt0 = n0 / n1\nt1 = n2 * t0\nt2 = n2 + t1\nt3 = t2 * t0\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "2025" + ], + "split": "train" + }, + { + "Input": "how many unique positive odd integers less than 110 are equal to the product of a positive multiple of 5 and an odd number ?", + "Output Program": [ + "n0 = 110.0\nn1 = 5.0\nt0 = n0 / n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "every disk in a bag is either blue , yellow or green . the ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8 . if the total number of disks in the bag is 72 , how many more green disks than blue disks are in the bag ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 8.0\nn3 = 72.0\nt0 = n0 + n1\nt1 = n2 - n0\nt2 = n2 + t0\nt3 = n3 / t2\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "if 5 x + 3 = 10 x \u2013 22 , what is the value of x ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nn2 = 10.0\nn3 = 22.0\nt0 = n1 + n3\nt1 = n2 - n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "a jogger running at 9 km / hr along side a railway track is 270 m ahead of the engine of a 120 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?", + "Output Program": [ + "n0 = 9.0\nn1 = 270.0\nn2 = 120.0\nn3 = 45.0\nt0 = n1 + n2\nt1 = 10.0 / 2.0\nt2 = n3 - n0\nt3 = t2 / 2.0\nt4 = t1 / t3\nt5 = t4 * t2\nanswer = t0 / t5\nprint(answer)" + ], + "Output Answer": [ + "39" + ], + "split": "train" + }, + { + "Input": "add : + 47 and - 27", + "Output Program": [ + "n0 = 47.0\nn1 = 27.0\n\nanswer = n1 + 3.0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "last year , for every 100 million vehicles that traveled on a certain highway , 40 vehicles were involved in accidents . if 2 billion vehicles traveled on the highway last year , how many of those vehicles were involved in accidents ? ( 1 billion = 1,000 , 000,000 )", + "Output Program": [ + "n0 = 100.0\nn1 = 40.0\nn2 = 2.0\nn3 = 1.0\nn4 = 1000.0\nn5 = 0.0\nt0 = n2 * 10.0\nanswer = n1 * t0\nprint(answer)" + ], + "Output Answer": [ + "800" + ], + "split": "train" + }, + { + "Input": "find the value of ( \u221a 1.21 ) / ( \u221a 0.64 ) + ( \u221a 1.44 ) / ( \u221a 0.49 ) is", + "Output Program": [ + "import math\nn0 = 1.21\nn1 = 0.64\nn2 = 1.44\nn3 = 0.49\nt0 = math.sqrt(max(0, n0))\nt1 = math.sqrt(max(0, n1))\nt2 = math.sqrt(max(0, n2))\nt3 = math.sqrt(max(0, n3))\nt4 = t0 / t1\nt5 = t2 / t3\nanswer = t4 + t5\nprint(answer)" + ], + "Output Answer": [ + "3.0892857142857144" + ], + "split": "train" + }, + { + "Input": "set r is composed of 9 numbers , labeled r 1 through r 9 . set s is also composed of 9 numbers , labeled s 1 through s 9 . set s is defined as follows : s 1 = 1 + r 1 ; s 2 = 2 + r 2 ; and so on , including s 9 = 9 + r 9 . how much larger is the sum of set s ' s mean and range than the sum of set r ' s mean and range ?", + "Output Program": [ + "n0 = 9.0\nn1 = 1.0\nn2 = 9.0\nn3 = 9.0\nn4 = 1.0\nn5 = 9.0\nn6 = 1.0\nn7 = 1.0\nn8 = 1.0\nn9 = 2.0\nn10 = 2.0\nn11 = 2.0\nn12 = 9.0\nn13 = 9.0\nn14 = 9.0\nt0 = n0 - n1\nanswer = t0 - 4.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "the average of temperatures at noontime from monday to friday is 60 ; the lowest one is 45 , what is the possible maximum range of the temperatures ?", + "Output Program": [ + "n0 = 60.0\nn1 = 45.0\nt0 = 2.0 + 3.0\nt1 = n1 * 4.0\nt2 = n0 * t0\nt3 = t2 - t1\nanswer = t3 - n1\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "if the average of 9 digits is 18 and the average of 4 of them is 8 , calculate the average of the remaining 5 numbers ?", + "Output Program": [ + "n0 = 9.0\nn1 = 18.0\nn2 = 4.0\nn3 = 8.0\nn4 = 5.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = t0 - t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "the units digit of ( 35 ) ^ ( 87 ) + ( 3 ) ^ ( 45 ) is :", + "Output Program": [ + "n0 = 35.0\nn1 = 87.0\nn2 = 3.0\nn3 = 45.0\nt0 = n3 % 4.0\nt1 = n0 % 10.0\nt2 = n2 * t0\nt3 = t2 % 10.0\nanswer = t3 + t1\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "mr yadav spends 60 % of his monthly salary on consumable items and 50 % of the remaining on clothes and transport . he saves the remaining amount . if his savings at the end of the year were 24624 , how much amount per month would he have spent on clothes and transport ?", + "Output Program": [ + "n0 = 60.0\nn1 = 50.0\nn2 = 24624.0\nt0 = 3.0 * 4.0\nt1 = 100.0 - n0\nt2 = n1 * t1\nt3 = t2 / 100.0\nt4 = t3 / 100.0\nt5 = n2 / t4\nt6 = t5 / t0\nanswer = t6 * t4\nprint(answer)" + ], + "Output Answer": [ + "2052" + ], + "split": "train" + }, + { + "Input": "drum x is 1 / 2 full of oil and drum y , which has twice the capacity of drum x , is 2 / 5 full of oil . if all of the oil in drum x is poured into drum y , then drum y will be filled to what capacity ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 2.0\nn3 = 5.0\nt0 = n2 / n3\nt1 = 12.0 / n1\nt2 = n0 / n1\nt3 = t0 * 12.0\nt4 = t1 * t2\nt5 = t3 + t4\nanswer = t5 / 12.0\nprint(answer)" + ], + "Output Answer": [ + "0.65" + ], + "split": "train" + }, + { + "Input": "a volunteer organization is recruiting new members . in the fall they manage to increase their number by 9 % . by the spring however membership falls by 19 % . what is the total change in percentage from fall to spring ?", + "Output Program": [ + "n0 = 9.0\nn1 = 19.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = t0 + 1.0\nt3 = 1.0 - t1\nt4 = t2 * t3\nt5 = t4 * 100.0\nanswer = 100.0 - t5\nprint(answer)" + ], + "Output Answer": [ + "11.709999999999994" + ], + "split": "train" + }, + { + "Input": "in an examination , there were 2,000 candidates , out of which 900 candidates were girls and rest were boys . if 34 % of the boys and 32 % of the girls passed , then the total percentage of failed candidates is ?", + "Output Program": [ + "n0 = 2000.0\nn1 = 900.0\nn2 = 34.0\nn3 = 32.0\nt0 = n2 / 100.0\nt1 = n3 / 100.0\nt2 = 10.0 * 100.0\nt3 = t2 * 2.0\nt4 = n1 * t1\nt5 = t3 - n1\nt6 = t0 * t5\nt7 = t3 - t6\nt8 = t7 - t4\nt9 = t8 / t3\nanswer = t9 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "66.9" + ], + "split": "train" + }, + { + "Input": "a , b and c have rs . 500 between them , a and c together have rs . 200 and b and c rs . 330 . how much does c have ?", + "Output Program": [ + "n0 = 500.0\nn1 = 200.0\nn2 = 330.0\nt0 = n1 + n2\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "when positive integer x is divided by positive integer y , the remainder is 4 . if x / y = 96.16 , what is the value of y ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 96.16\nt0 = math.floor(n1)\nt1 = n1 - t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "25.000000000000533" + ], + "split": "train" + }, + { + "Input": "a bucket contains 2 mixtures a and b in the ratio 3 : 2 . if 5 liters of the mixture is replaced by 5 liters of liquid b , then the ratio of the two liquids becomes 3 : 5 . how much of the liquid a was there in the bucket ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 2.0\nn3 = 5.0\nn4 = 5.0\nn5 = 3.0\nn6 = 5.0\nt0 = n1 + n2\nt1 = n1 * n3\nt2 = n1 * n2\nt3 = n1 / t0\nt4 = n2 / t0\nt5 = t1 - t2\nt6 = n3 * t3\nt7 = n3 * t4\nt8 = n3 * t6\nt9 = n3 - t7\nt10 = n1 * t9\nt11 = t8 + t10\nt12 = t11 / t5\nanswer = n1 * t12\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "if n is a positive integer and n ^ 2 is divisible by 50 , then what is the largest positive integer that must divide n ?", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 50.0\nt0 = n1 / n0\nt1 = math.sqrt(max(0, t0))\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the sum of present age of abe and the age before 7 years is 29 . find the present age of abe . what will be his age after 7 years ?", + "Output Program": [ + "n0 = 7.0\nn1 = 29.0\nn2 = 7.0\nt0 = n0 + n1\nt1 = t0 / 2.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "if the function q is defined by the formula q = 5 w / ( 4 d ( z ^ 2 ) ) , by what factor will q be multiplied if w is quadrupled , d is doubled , and z is tripled ?", + "Output Program": [ + "n0 = 5.0\nn1 = 4.0\nn2 = 2.0\nt0 = 3.0**min(n2, 5)\nt1 = n2 * t0\nanswer = n1 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.2222222222222222" + ], + "split": "train" + }, + { + "Input": "a total of 3000 chocolates were distributed among 120 boys and girls such that each boy received 2 chocolates and each girl received 3 chocolates . find the respective number of boys and girls ?", + "Output Program": [ + "n0 = 3000.0\nn1 = 120.0\nn2 = 2.0\nn3 = 3.0\nt0 = n0 / 10.0\nt1 = n1 * n3\nanswer = t1 - t0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "a mixture contains milk and water in the ratio 3 : 2 . on adding 10 liters of water , the ratio of milk to water becomes 2 : 3 . total quantity of milk & water before adding water to it ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 10.0\nn3 = 2.0\nn4 = 3.0\nt0 = n0 + n1\nt1 = n1 / n0\nt2 = n0 / t0\nt3 = n1 / t0\nt4 = n2 * t1\nt5 = t3 * t1\nt6 = t2 - t5\nanswer = t4 / t6\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "if p is the product of the integers from 1 to 35 , inclusive , what is the greatest integer k for which 3 ^ k is a factor of p ?", + "Output Program": [ + "n0 = 1.0\nn1 = 35.0\nn2 = 3.0\nt0 = n2 * 4.0\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "what is the difference between the c . i . on rs . 6000 for 1 1 / 2 years at 4 % per annum compounded yearly and half - yearly ?", + "Output Program": [ + "n0 = 6000.0\nn1 = 1.0\nn2 = 1.0\nn3 = 2.0\nn4 = 4.0\nt0 = n3 / 100.0\nt1 = n4 / 100.0\nt2 = t0 + n1\nt3 = t1 + n1\nt4 = t2 * t2\nt5 = t2 * t3\nt6 = t2 * t4\nt7 = n0 * t5\nt8 = n0 * t6\nanswer = t8 - t7\nprint(answer)" + ], + "Output Answer": [ + "2.4479999999994106" + ], + "split": "train" + }, + { + "Input": "i chose a number and divide it by 9 . then i subtracted 100 from the result and got 10 . what was the number i chose ?", + "Output Program": [ + "n0 = 9.0\nn1 = 100.0\nn2 = 10.0\nt0 = n1 + n2\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "990" + ], + "split": "train" + }, + { + "Input": "find the value of 2.5 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ]", + "Output Program": [ + "n0 = 2.5\nn1 = 3.6\nn2 = 0.48\nn3 = 2.5\nn4 = 0.12\nn5 = 0.09\nn6 = 0.5\nt0 = n1 * n2\nt1 = n4 * n5\nt2 = n3 * t0\nt3 = n6 * t1\nt4 = t2 / t3\nanswer = n0 * t4\nprint(answer)" + ], + "Output Answer": [ + "2000.0000000000002" + ], + "split": "train" + }, + { + "Input": "on an order of 3 dozen boxes of a consumer product , a retailer receives an extra dozen free . this is equivalent to allowing him a discount of :", + "Output Program": [ + "n0 = 3.0\nt0 = n0 / 4.0\nt1 = t0 * 100.0\nanswer = 100.0 - t1\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "if bill can buy 3 pairs of jeans and 2 shirts for $ 69 or 2 pairs of jeans and 3 shirts for $ 61 , how much does one shirt cost ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 69.0\nn3 = 2.0\nn4 = 3.0\nn5 = 61.0\nt0 = n0 * n5\nt1 = n1 * n2\nt2 = n0 * n0\nt3 = n1 * n1\nt4 = t0 - t1\nt5 = t2 - t3\nanswer = t4 / t5\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "the cost of 10 kg of apples is equal to the cost of 24 kg of rice . the cost of 6 kg of flour equals the cost of 2 kg of rice . the cost of each kg of flour is rs . 20.50 . find the total cost of 4 kg of apples , 3 kg of rice and 5 kg of flour ?", + "Output Program": [ + "n0 = 10.0\nn1 = 24.0\nn2 = 6.0\nn3 = 2.0\nn4 = 20.5\nn5 = 4.0\nn6 = 3.0\nn7 = 5.0\nt0 = n2 * n4\nt1 = n4 * n7\nt2 = t0 / n3\nt3 = t2 * 3.0\nt4 = n1 * t2\nt5 = t3 + t1\nt6 = t4 / 10.0\nt7 = n5 * t6\nanswer = t5 + t7\nprint(answer)" + ], + "Output Answer": [ + "877.4" + ], + "split": "train" + }, + { + "Input": "the shopkeeper increased the price of a product by 25 % so that customer finds it difficult to purchase the required amount . but somehow the customer managed to purchase only 70 % of the required amount . what is the net difference in the expenditure on that product ?", + "Output Program": [ + "n0 = 25.0\nn1 = 70.0\nt0 = n0 + 100.0\nt1 = 100.0 * 100.0\nt2 = n1 * t0\nt3 = t1 - t2\nt4 = t3 * 100.0\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "12.5" + ], + "split": "train" + }, + { + "Input": "the difference between the squares of two consecutive odd integers is a square < 1000 whose root equals the combined sum of the digits of the two integers . what is the sum of the digits x of the larger integer ?", + "Output Program": [ + "import math\nn0 = 1000.0\nt0 = n0 / 10.0\nt1 = t0 + 1.0\nt2 = t1**min(2.0, 5)\nt3 = t1 - 2.0\nt4 = t3**min(2.0, 5)\nt5 = t2 - t4\nt6 = math.sqrt(max(0, t5))\nanswer = t6 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a teacher grades students \u2019 tests by subtracting twice the number of incorrect responses from the number of correct responses . if student a answers each of the 100 questions on her test and receives a score of 61 , how many questions did student a answer correctly ?", + "Output Program": [ + "n0 = 100.0\nn1 = 61.0\nt0 = n0 - n1\nt1 = t0 / 3.0\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "87" + ], + "split": "train" + }, + { + "Input": "a store purchased a pair of pants for $ 210 and was selling it at a price that equaled the purchase price of the pants plus a markup that was 25 percent of the selling price . after some time a store owner decided to decrease the selling price by 20 percent . what was the store ' s gross profit on this sale ?", + "Output Program": [ + "n0 = 210.0\nn1 = 25.0\nn2 = 20.0\nt0 = n0 * n2\nt1 = t0 / 100.0\nanswer = t1 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "if a 2 - b 2 = 5 and a * b = 2 , find a 4 + b 4 .", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 5.0\nn3 = 2.0\nn4 = 4.0\nn5 = 4.0\nt0 = n3**min(n0, 5)\nt1 = n2**min(n0, 5)\nt2 = t0 * n0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "if 1 + 2 + 3 + . . . + n = n ( n + 1 ) , then 3 ( 1 + 3 + 5 + . . . . + 79 ) = ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 3.0\nn3 = 1.0\nn4 = 3.0\nn5 = 1.0\nn6 = 3.0\nn7 = 5.0\nn8 = 79.0\nt0 = n8 + n0\nt1 = n8 - n0\nt2 = t1 / n1\nt3 = n8 * t0\nt4 = t2 + n0\nt5 = t3 / n1\nt6 = t4 * t2\nt7 = t5 - t6\nanswer = t7 * n2\nprint(answer)" + ], + "Output Answer": [ + "4800" + ], + "split": "train" + }, + { + "Input": "a certain car traveled twice as many miles from town a to town b as it did from town b to town c . from town a to town b , the car averaged 25 miles per gallon , and from town b to town c , the car averaged 30 miles per gallon . what is the average miles per gallon that the car achieved on its trip from town a through town b to town c ?", + "Output Program": [ + "n0 = 25.0\nn1 = 30.0\nt0 = n1 * 10.0\nt1 = t0 / 2.0\nt2 = t0 / n0\nt3 = t1 + t0\nt4 = t1 / n1\nt5 = t2 + t4\nanswer = t3 / t5\nprint(answer)" + ], + "Output Answer": [ + "26.470588235294116" + ], + "split": "train" + }, + { + "Input": "if w , x , y and z are distinct odd positive integers , then the maximum value of the expression ( w ^ 2 + x ^ 2 ) * ( y ^ 2 + z ^ 2 ) can be divisible by ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 2.0\nn3 = 2.0\nt0 = n0 + n0\nt1 = n0 * n0\nt2 = n0 * t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "john found that the average of 15 numbers is 40 . if 10 is added to each number then the mean of number is ?", + "Output Program": [ + "n0 = 15.0\nn1 = 40.0\nn2 = 10.0\n\nanswer = n1 + n2\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "if a ' s salary is 20 % less than b ' s salary , by how much percent is b ' s salary more than a ' s ?", + "Output Program": [ + "n0 = 20.0\nt0 = 100.0 - n0\nt1 = t0 / 100.0\nt2 = 100.0 - t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "the mean of 25 values was 190 . it was detected on rechecking that one value 165 was wrongly copied as 130 for the computation of the mean . find the correct mean .", + "Output Program": [ + "n0 = 25.0\nn1 = 190.0\nn2 = 165.0\nn3 = 130.0\nt0 = n0 * n1\nt1 = n2 - n3\nt2 = t0 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "191.4" + ], + "split": "train" + }, + { + "Input": "a man can swim in still water at 5 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ?", + "Output Program": [ + "n0 = 5.0\n\nanswer = n0 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "1.6666666666666667" + ], + "split": "train" + }, + { + "Input": "what is the total cost of 2 sandwiches at $ 1.49 each and 4 sodas at $ 0.87 each ?", + "Output Program": [ + "n0 = 2.0\nn1 = 1.49\nn2 = 4.0\nn3 = 0.87\nt0 = n0 * n1\nt1 = n2 * n3\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "6.46" + ], + "split": "train" + }, + { + "Input": "linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 450 , what were her original savings ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 450.0\nt0 = n0 / n1\nt1 = 1.0 - t0\nanswer = n2 / t1\nprint(answer)" + ], + "Output Answer": [ + "1800" + ], + "split": "train" + }, + { + "Input": "a man purchased 1 blankets @ rs . 100 each , 5 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ?", + "Output Program": [ + "n0 = 1.0\nn1 = 100.0\nn2 = 5.0\nn3 = 150.0\nn4 = 150.0\nt0 = n3 * 10.0\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "650" + ], + "split": "train" + }, + { + "Input": "rice weighing 29 / 4 pounds was divided equally and placed in 4 containers . how many ounces of rice were in each container ? ( note that 1 pound = 16 ounces )", + "Output Program": [ + "n0 = 29.0\nn1 = 4.0\nn2 = 4.0\nn3 = 1.0\nn4 = 16.0\nt0 = n0 / n1\nt1 = n4 * t0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "29" + ], + "split": "train" + }, + { + "Input": "for all positive integers m , [ m ] = 3 m when m is odd and [ m ] = ( 1 / 2 ) * m when m is even . what is [ 9 ] * [ 10 ] equivalent to ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 2.0\nn3 = 9.0\nn4 = 10.0\nt0 = n4 / n2\nt1 = n0 * n3\nt2 = t0 * t1\nanswer = t2 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "a cube with its sides numbered 1 through 6 is rolled twice , first landing on a and then landing on b . if any roll of the cube yields an equal chance of landing on any of the numbers 1 through 6 , what is the probability q that a + b is prime ?", + "Output Program": [ + "n0 = 1.0\nn1 = 6.0\nn2 = 1.0\nn3 = 6.0\nt0 = 12.0 + 3.0\nt1 = n0 / n1\nt2 = t1**min(2.0, 5)\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "0.41666666666666663" + ], + "split": "train" + }, + { + "Input": "the average weight of 9 persons increases by 1.5 kg . if a person weighing 65 kg is replaced by a new person , what could be the weight of the new person ?", + "Output Program": [ + "n0 = 9.0\nn1 = 1.5\nn2 = 65.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "78.5" + ], + "split": "train" + }, + { + "Input": "find the principle on a certain sum of money at 5 % per annum for 2 2 / 5 years if the amount being rs . 1344 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 2.0\nn3 = 5.0\nn4 = 1344.0\nt0 = n1 * n3\nt1 = n1 + t0\nt2 = t1 / n3\nt3 = n0 * t2\nt4 = t3 / 100.0\nt5 = t4 + 1.0\nanswer = n4 / t5\nprint(answer)" + ], + "Output Answer": [ + "1199.9999999999998" + ], + "split": "train" + }, + { + "Input": "how many 3 digit positive integers e exist that when divided by 7 leave a remainder of 5 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 5.0\nt0 = 10.0 + 4.0\nt1 = 10.0 * 100.0\nt2 = n1 * t0\nt3 = t1 - 1.0\nt4 = n2 + t2\nt5 = t3 - t4\nanswer = t5 / n1\nprint(answer)" + ], + "Output Answer": [ + "128" + ], + "split": "train" + }, + { + "Input": "3 x + y = 21 , and x + 3 y = 1 . find the value of 2 x + 2 y", + "Output Program": [ + "n0 = 3.0\nn1 = 21.0\nn2 = 3.0\nn3 = 1.0\nn4 = 2.0\nn5 = 2.0\nt0 = n1 + n3\nanswer = t0 / n5\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "thomas worked in the factory @ 4550 / - per week . owner told him to give the amount after one month . then how much amount will be paid to thomas ?", + "Output Program": [ + "n0 = 4550.0\nt0 = 10.0 * 100.0\nt1 = n0 * 2.0\nt2 = 100.0 * 4.0\nt3 = t0 * 10.0\nt4 = t3 + t1\nanswer = t4 + t2\nprint(answer)" + ], + "Output Answer": [ + "19500" + ], + "split": "train" + }, + { + "Input": "in a tree , 3 / 5 of the birds are parrots while the rest are toucans . if 1 / 3 of the parrots are female and 3 / 4 of the toucans are female , what fraction of the birds in the tree are male ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 1.0\nn3 = 3.0\nn4 = 3.0\nn5 = 4.0\nt0 = n0 / n1\nt1 = n2 / n0\nt2 = 2.0 / n1\nt3 = n0 / n5\nt4 = 1.0 - t1\nt5 = 1.0 - t3\nt6 = t0 * t4\nt7 = t2 * t5\nanswer = t6 + t7\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "at a supermarket , john spent 1 / 4 of his money on fresh fruits and vegetables , 1 / 3 on meat products , and 1 / 6 on bakery products . if he spent the remaining $ 6 on candy , how much did john spend at the supermarket ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 1.0\nn3 = 3.0\nn4 = 1.0\nn5 = 6.0\nn6 = 6.0\nt0 = n0 / n5\nt1 = n0 / n3\nt2 = n0 / n1\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n0 - t4\nanswer = n6 / t5\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "10 ^ 23 - 7 is divided by 6 , remainder is ?", + "Output Program": [ + "n0 = 10.0\nn1 = 23.0\nn2 = 7.0\nn3 = 6.0\nt0 = n1 - n0\nt1 = t0 - n3\nanswer = t1 - 4.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "when a student joe , weighing 45 kg , joins a group of students whose average weight is 30 kg , the average weight goes up by 1 kg . subsequently , if two students , excluding joe , leave the group the average weight comes back to 30 kg . what is the difference between the average weight of the two students who left and the weight of joe ?", + "Output Program": [ + "n0 = 45.0\nn1 = 30.0\nn2 = 1.0\nn3 = 30.0\nt0 = n1 + n2\nt1 = n0 - t0\nt2 = n1 * t1\nt3 = t1 - n2\nt4 = n0 + t2\nt5 = n1 * t3\nt6 = t4 - t5\nt7 = t6 / 2.0\nanswer = n0 - t7\nprint(answer)" + ], + "Output Answer": [ + "7.5" + ], + "split": "train" + }, + { + "Input": "if ( a + b ) = 14 , ( b + c ) = 9 and ( c + d ) = 3 , what is the value of ( a + d ) ?", + "Output Program": [ + "n0 = 14.0\nn1 = 9.0\nn2 = 3.0\nt0 = n0 + n2\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "the average weight of 8 persons increases by 4.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 4.5\nn2 = 65.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "101" + ], + "split": "train" + }, + { + "Input": "if the average ( arithmetic mean ) of a and b is 45 and the average of b and c is 60 , what is the value of c \u00e2 \u02c6 \u2019 a ?", + "Output Program": [ + "n0 = 45.0\nn1 = 60.0\nt0 = n1 * 2.0\nt1 = n0 * 2.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "a certain family has 3 sons : richard is 6 years older than david , and david is 8 years older than scott . if in 8 years , richard will be twice as old as scott , then how old was david 5 years ago ?", + "Output Program": [ + "n0 = 3.0\nn1 = 6.0\nn2 = 8.0\nn3 = 8.0\nn4 = 5.0\nt0 = n1 + n2\nanswer = t0 - n4\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "jill has 42 gallons of water stored in quart , half - gallon , and one gallon jars . she has equal numbers of each size jar holding the liquid . what is the total number of water filled jars ?", + "Output Program": [ + "n0 = 42.0\nt0 = 1.0 / 2.0\nt1 = t0 + 0.25\nt2 = t1 + 1.0\nt3 = n0 / t2\nanswer = t3 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "train" + }, + { + "Input": "of the 3 - digit integers greater than 700 , how many have distinct digits ?", + "Output Program": [ + "n0 = 3.0\nn1 = 700.0\nt0 = 10.0 - 1.0\nt1 = 10.0 - 2.0\nt2 = n0 * t0\nanswer = t2 * t1\nprint(answer)" + ], + "Output Answer": [ + "216" + ], + "split": "train" + }, + { + "Input": "if 2994 \u00e3 \u00b7 14.5 = 173 , then 29.94 \u00e3 \u00b7 1.45 = ?", + "Output Program": [ + "n0 = 2994.0\nn1 = 14.5\nn2 = 173.0\nn3 = 29.94\nn4 = 1.45\nt0 = n1 / n4\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "17.3" + ], + "split": "train" + }, + { + "Input": "if a * b * c = 130 , b * c * d = 65 , c * d * e = 500 and d * e * f = 250 the ( a * f ) / ( c * d ) = ?", + "Output Program": [ + "n0 = 130.0\nn1 = 65.0\nn2 = 500.0\nn3 = 250.0\nt0 = n0 * n3\nt1 = n1 * n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "the product of two numbers is 120 . the sum of their squares is 289 . the sum of the two numbers is :", + "Output Program": [ + "import math\nn0 = 120.0\nn1 = 289.0\nt0 = n0 * 4.0\nt1 = n0 * 2.0\nt2 = n1 - t1\nt3 = math.sqrt(max(0, t2))\nt4 = t3**min(2.0, 5)\nt5 = t0 + t4\nanswer = math.sqrt(max(0, t5))\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "the average of 6 no . ' s is 2.80 . the average of 2 of them is 2.4 , while the average of the other 2 is 2.3 . what is the average of the remaining 2 no ' s ?", + "Output Program": [ + "n0 = 6.0\nn1 = 2.8\nn2 = 2.0\nn3 = 2.4\nn4 = 2.0\nn5 = 2.3\nn6 = 2.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n2 * n5\nt3 = t1 + t2\nt4 = t0 - t3\nanswer = t4 / n2\nprint(answer)" + ], + "Output Answer": [ + "3.6999999999999993" + ], + "split": "train" + }, + { + "Input": "if grapes are 91 % water and raisins are 19 % water , then how many kilograms did a quantity of raisins , which currently weighs 9 kilograms , weigh when all the raisins were grapes ? ( assume that the only difference between their raisin - weight and their grape - weight is water that evaporated during their transformation . )", + "Output Program": [ + "n0 = 91.0\nn1 = 19.0\nn2 = 9.0\nt0 = 100.0 - n1\nt1 = 100.0 - n0\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = n2 * t2\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "81.00000000000001" + ], + "split": "train" + }, + { + "Input": "a bag contains an equal number of one rupee , 50 paise and 25 paise coins respectively . if the total value is 210 , how many coins of each type are there ?", + "Output Program": [ + "n0 = 50.0\nn1 = 25.0\nn2 = 210.0\nt0 = 1 / 4.0\nt1 = 1 / 2.0\nt2 = t0 + t1\nt3 = t2 + 1.0\nanswer = n2 / t3\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "find \u221a ? / 19 = 4 ?", + "Output Program": [ + "n0 = 19.0\nn1 = 4.0\nt0 = n0 * n1\nanswer = t0**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "5776" + ], + "split": "train" + }, + { + "Input": "an automobile parts supplier charges $ 25 per package of gaskets . when a customer orders more than 10 packages of gaskets , the supplier charges 4 / 5 the price for each package in excess of 10 . during a certain week , the supplier sold 50 packages of gaskets . if 20 percent of the gaskets went to company x , 15 percent to company y , and the rest to company z , what was the total amount , in dollars , that the parts supplier received in payment for the gaskets ?", + "Output Program": [ + "n0 = 25.0\nn1 = 10.0\nn2 = 4.0\nn3 = 5.0\nn4 = 10.0\nn5 = 50.0\nn6 = 20.0\nn7 = 15.0\nt0 = n2 / n3\nt1 = n6 / 100.0\nt2 = n0 * n1\nt3 = n0 * t0\nt4 = n5 * t1\nt5 = n0 * t4\nt6 = n5 - t4\nt7 = t5 + t5\nt8 = t6 - t4\nt9 = t8 - n1\nt10 = t3 * t9\nt11 = t10 + t2\nanswer = t11 + t7\nprint(answer)" + ], + "Output Answer": [ + "1150" + ], + "split": "train" + }, + { + "Input": "what is remainder of the division ( 1425 * 1427 * 1429 ) / 12 ?", + "Output Program": [ + "n0 = 1425.0\nn1 = 1427.0\nn2 = 1429.0\nn3 = 12.0\nt0 = n0 * n1\nt1 = n2 * t0\nt2 = t1 - 3.0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 67 kg . what is the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.5\nn2 = 67.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "87" + ], + "split": "train" + }, + { + "Input": "if a # b = ab \u2013 b + b ^ 2 , then 3 # 8 =", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 8.0\nt0 = n1 * n2\nt1 = n2**min(n0, 5)\nt2 = t0 - n2\nanswer = t1 + t2\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "a marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each . there can be no less than 8 musicians per row and no more than 30 musicians per row . how many different rectangular formations z are possible ?", + "Output Program": [ + "n0 = 240.0\nn1 = 8.0\nn2 = 30.0\n\nanswer = n0 / n2\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "the number of diagonals of a polygon of n sides is given by the formula f = n ( n - 3 ) / 2 . if a polygon has twice as many diagonals as sides , how many sides does it have ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\n\nanswer = n0 + n1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "given a two - digit number , the unit ' s digit exceeds its 10 ' s digit by 5 and the product of the given number and the sum of its digits is equal to 90 , which of the options is the number ?", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 5.0\nn2 = 90.0\nt0 = n0 + 1.0\nt1 = n1 * n1\nt2 = 4.0 * 60.0\nt3 = n0 * 2.0\nt4 = t2 + 3.0\nt5 = n1 * t0\nt6 = t0 * 2.0\nt7 = n0 + t5\nt8 = t6 * 2.0\nt9 = t1 - t4\nt10 = t7 * t7\nt11 = t6 * t9\nt12 = t11 * 4.0\nt13 = t10 - t12\nt14 = math.sqrt(max(0, t13))\nt15 = t14 - t7\nt16 = t15 / t8\nt17 = n1 + t16\nanswer = t17 + t3\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "train" + }, + { + "Input": "if \u00e2 \u20ac \u0153 * \u00e2 \u20ac \u009d is called \u00e2 \u20ac \u0153 + \u00e2 \u20ac \u009d , \u00e2 \u20ac \u0153 / \u00e2 \u20ac \u009d is called \u00e2 \u20ac \u0153 * \u00e2 \u20ac \u009d , \u00e2 \u20ac \u0153 - \u00e2 \u20ac \u009d is called \u00e2 \u20ac \u0153 / \u00e2 \u20ac \u009d , \u00e2 \u20ac \u0153 + \u00e2 \u20ac \u009d is called \u00e2 \u20ac \u0153 - \u00e2 \u20ac \u009d . 240 - 80 / 60 - 40 * 10 = ?", + "Output Program": [ + "n0 = 240.0\nn1 = 80.0\nn2 = 60.0\nn3 = 40.0\nn4 = 10.0\nt0 = n2 / n3\nt1 = n0 / n1\nt2 = t0 * t1\nanswer = n4 + t2\nprint(answer)" + ], + "Output Answer": [ + "14.5" + ], + "split": "train" + }, + { + "Input": "the least number which when increased by 3 each divisible by each one of 24 , 32 , 36 and 54 is :", + "Output Program": [ + "import scipy\nn0 = 3.0\nn1 = 24.0\nn2 = 32.0\nn3 = 36.0\nn4 = 54.0\nt0 = scipy.lcm(int(n1), int(n2))\nt1 = scipy.lcm(int(n3), int(t0))\nt2 = scipy.lcm(int(n4), int(t1))\nanswer = t2 - n0\nprint(answer)" + ], + "Output Answer": [ + "861" + ], + "split": "train" + }, + { + "Input": "in the xy - plane the point ( - 2 - 3 ) is the centre of a circle , the point ( - 2 , 2 ) lies inside the circle and the point ( 5 , - 3 ) lies outside the circle . if the radius r of the circle r is an integer then r =", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 2.0\nn3 = 2.0\nn4 = 5.0\nn5 = 3.0\nt0 = -n0\nt1 = n4 - t0\nt2 = n4 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "a , b and c play a cricket match . the ratio of the runs scored by them in the match is a : b = 1 : 3 and b : c = 1 : 5 . if the total runs scored by all of them are 95 , the runs scored by c are ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 5.0\nn4 = 95.0\nt0 = n0 / n1\nt1 = n3 / n0\nt2 = t0 + t1\nt3 = t2 + 1.0\nt4 = n4 / t3\nanswer = n3 * t4\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "dacid obtained 61 , 65 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?", + "Output Program": [ + "n0 = 61.0\nn1 = 65.0\nn2 = 82.0\nn3 = 67.0\nn4 = 85.0\nn5 = 100.0\nt0 = n0 + n1\nt1 = 10.0 / 2.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "train" + }, + { + "Input": "7500 + ( 1250 / 50 )", + "Output Program": [ + "n0 = 7500.0\nn1 = 1250.0\nn2 = 50.0\nt0 = n1 / n2\nanswer = n0 + t0\nprint(answer)" + ], + "Output Answer": [ + "7525" + ], + "split": "train" + }, + { + "Input": "if 7 / w + 7 / x = 7 / y and wx = y , then the average ( arithmetic mean ) of w and x is", + "Output Program": [ + "n0 = 7.0\nn1 = 7.0\nn2 = 7.0\nt0 = n0 + n0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "a box contains 9 slips that are each labeled with one number : 1 , 2 , 3 , 5 , 8 , 13 , 21 , and 55 . two of the slips are drawn at random from the box without replacement . what is the probability that the sum of the numbers on the two slips is equal to one of the numbers left in the box ?", + "Output Program": [ + "n0 = 9.0\nn1 = 1.0\nn2 = 2.0\nn3 = 3.0\nn4 = 5.0\nn5 = 8.0\nn6 = 13.0\nn7 = 21.0\nn8 = 55.0\nt0 = n3 * n4\nt1 = t0 + 10.0\nt2 = t1 + 3.0\nanswer = n4 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.17857142857142858" + ], + "split": "train" + }, + { + "Input": "if x = 1 + \u221a 2 , then what is the value of x 4 - 4 x 3 + 4 x 2 + 4 ?", + "Output Program": [ + "import math\nn0 = 1.0\nn1 = 2.0\nn2 = 4.0\nn3 = 4.0\nn4 = 3.0\nn5 = 4.0\nn6 = 2.0\nn7 = 4.0\nt0 = math.sqrt(max(0, n1))\nt1 = n0 + t0\nt2 = t1**min(2.0, 5)\nt3 = t1 - n1\nt4 = t3**min(2.0, 5)\nt5 = t2 * t4\nanswer = n2 + t5\nprint(answer)" + ], + "Output Answer": [ + "4.999999999999999" + ], + "split": "train" + }, + { + "Input": "if the average ( arithmetic mean ) of a and b is 45 and the average of b and c is 70 , what is the value of c \u2212 a ?", + "Output Program": [ + "n0 = 45.0\nn1 = 70.0\nt0 = n1 * 2.0\nt1 = n0 * 2.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "a certain class of students is being divided into teams . the class can either be divided into 10 teams with an equal number of players on each team or 24 teams with an equal number of players on each team . what is the lowest possible number of students in the class ?", + "Output Program": [ + "import scipy\nn0 = 10.0\nn1 = 24.0\n\nanswer = scipy.lcm(int(n0), int(n1))\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "there are 5 guys who have equal number of bullets . all of them shoot 4 bullets . the remaining bullets are equal to the total number of bullets remaining is equal to the bullets each had after division . what was the original number of bullets each one had ?", + "Output Program": [ + "n0 = 5.0\nn1 = 4.0\nt0 = n0 * n1\nt1 = n0 - 1.0\nt2 = t0 / t1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "a grocery shop has a sale of rs . 6735 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ?", + "Output Program": [ + "n0 = 6735.0\nn1 = 6927.0\nn2 = 6855.0\nn3 = 7230.0\nn4 = 6562.0\nn5 = 5.0\nn6 = 6500.0\nt0 = n5 + 1.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n6 * t0\nt4 = n3 + t2\nt5 = n4 + t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "4691" + ], + "split": "train" + }, + { + "Input": "1 / 4 of all the juniors and 2 / 3 of all the seniors are going on a trip . if there are 2 / 3 as many juniors as seniors , what fraction of the students are not going on the trip ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 2.0\nn3 = 3.0\nn4 = 2.0\nn5 = 3.0\nt0 = n2 / n3\nt1 = n0 / n1\nt2 = n1 * n3\nt3 = t0 * t2\nt4 = t2 + t3\nt5 = t1 * t3\nt6 = t3 + t5\nanswer = t6 / t4\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "a grocer has a sale of rs . 4000 , rs . 6524 , rs . 5689 , rs . 7230 and rs . 6000 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 7000 ?", + "Output Program": [ + "n0 = 4000.0\nn1 = 6524.0\nn2 = 5689.0\nn3 = 7230.0\nn4 = 6000.0\nn5 = 5.0\nn6 = 7000.0\nt0 = n5 + 1.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n6 * t0\nt4 = n3 + t2\nt5 = n4 + t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "12557" + ], + "split": "train" + }, + { + "Input": "at a contest with 2000 participants , 1 / 2 of the people are aged 16 to 18 . next year , the number of people aged 16 to 18 will increase by 1 / 4 . after this change , what percentage of the total 2000 people will the 16 - to 18 - year - olds represent ?", + "Output Program": [ + "n0 = 2000.0\nn1 = 1.0\nn2 = 2.0\nn3 = 16.0\nn4 = 18.0\nn5 = 16.0\nn6 = 18.0\nn7 = 1.0\nn8 = 4.0\nn9 = 2000.0\nn10 = 16.0\nn11 = 18.0\nt0 = n1 / n8\nt1 = n0 / 2.0\nt2 = t0 + 1.0\nt3 = t2 * t1\nt4 = t3 / n0\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "62.5" + ], + "split": "train" + }, + { + "Input": "the closest approximation of f ( 69.28 \u00d7 0.004 ) / 0.03 is", + "Output Program": [ + "n0 = 69.28\nn1 = 0.004\nn2 = 0.03\nt0 = n1 / n2\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "9.237333333333334" + ], + "split": "train" + }, + { + "Input": "find the largest number of 4 digits which is exactly divisible by 2718 , 1615", + "Output Program": [ + "import math\nimport scipy\nn0 = 4.0\nn1 = 2718.0\nn2 = 1615.0\nt0 = 10.0 * 1000.0\nt1 = n2 % 100.0\nt2 = n1 % 100.0\nt3 = n2 - t1\nt4 = n1 - t2\nt5 = t3 / 100.0\nt6 = t4 / 100.0\nt7 = scipy.lcm(int(t5), int(t6))\nt8 = scipy.lcm(int(t7), int(t1))\nt9 = scipy.lcm(int(t8), int(t2))\nt10 = t0 / t9\nt11 = math.floor(t10)\nanswer = t11 * t9\nprint(answer)" + ], + "Output Answer": [ + "8640" + ], + "split": "train" + }, + { + "Input": "a basketball team composed of 12 players scored 100 points in a particular contest . if none of the individual players scored fewer than 7 points , what is the greatest number of points w that an individual player might have scored ?", + "Output Program": [ + "n0 = 12.0\nn1 = 100.0\nn2 = 7.0\nt0 = n0 * n2\nt1 = n1 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "the average length of 6 strings is 80 cm . if the average length of one third of the strings is 70 cm , what is the average of the other strings ?", + "Output Program": [ + "n0 = 6.0\nn1 = 80.0\nn2 = 70.0\nt0 = n0 / 3.0\nt1 = n0 * n1\nt2 = n2 * t0\nt3 = n0 - t0\nt4 = t1 - t2\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "85" + ], + "split": "train" + }, + { + "Input": "a palindrome is a number that reads the same forward and backward , such as 242 . how many even 9 - digit numbers are palindromes ?", + "Output Program": [ + "import math\nn0 = 242.0\nn1 = 9.0\nt0 = n1 / 2.0\nt1 = math.floor(t0)\nt2 = 10.0**min(t1, 5)\nanswer = t2 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "40000" + ], + "split": "train" + }, + { + "Input": "at an upscale fast - food restaurant , shin can buy 3 burgers , 7 shakes , and one cola for $ 110 . at the same place it would cost $ 164.50 for 4 burgers , 10 shakes , and one cola . how much would it cost for a meal of one burger , one shake , and one cola ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 110.0\nn3 = 164.5\nn4 = 4.0\nn5 = 10.0\nt0 = n3 - n2\nt1 = n2 + t0\nt2 = t0 * 3.0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "sally has a gold credit card with a certain spending limit , and a platinum card with twice the spending limit of the gold card . currently , she has a balance on her gold card that is 1 / 3 of the spending limit on that card , and she has a balance on her platinum card that is 1 / 4 of the spending limit on that card . if sally transfers the entire balance on her gold card to her platinum card , what portion of her limit on the platinum card will remain unspent ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 4.0\nt0 = 1 / n3\nt1 = 1 / n1\nt2 = 1 / 2.0\nt3 = t1 * t2\nt4 = t0 + t3\nanswer = n0 - t4\nprint(answer)" + ], + "Output Answer": [ + "0.5833333333333334" + ], + "split": "train" + }, + { + "Input": "at a certain food stand , the price of each apple is 40 \u00a2 and the price of each orange is 60 \u00a2 . mary selects a total of 10 apples and oranges from the food stand , and the average ( arithmetic mean ) price of the 10 pieces of fruit is 52 \u00a2 . how many oranges must mary put back so that the average price of the pieces of fruit that she keeps is 44 \u00a2 ?", + "Output Program": [ + "n0 = 40.0\nn1 = 60.0\nn2 = 10.0\nn3 = 10.0\nn4 = 52.0\nn5 = 44.0\nt0 = n1 * n2\nt1 = n2 * n4\nt2 = n2 * n5\nt3 = n1 - n0\nt4 = n1 - n5\nt5 = t0 - t1\nt6 = t5 / t3\nt7 = n0 * t6\nt8 = n2 - t6\nt9 = n1 * t8\nt10 = t7 + t9\nt11 = t10 - t2\nanswer = t11 / t4\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "there were 35 students in a hostel . due to the admission of 7 new students the expenses of the mess were increased by rs . 42 per day while the average expenditure per head diminished by re 1 . what was the original expenditure of the mess ?", + "Output Program": [ + "n0 = 35.0\nn1 = 7.0\nn2 = 42.0\nn3 = 1.0\nt0 = n0 + n1\nt1 = n2 + t0\nt2 = t1 / n1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "420" + ], + "split": "train" + }, + { + "Input": "61 + 5 * 12 / ( 180 / 3 ) = ?", + "Output Program": [ + "n0 = 61.0\nn1 = 5.0\nn2 = 12.0\nn3 = 180.0\nn4 = 3.0\nt0 = n3 / n4\nt1 = n1 * n2\nt2 = t1 / t0\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "62" + ], + "split": "train" + }, + { + "Input": "a certain telescope increases the visual range at a particular location from 100 kilometers to 150 kilometers . by what percent is the visual range increased by using the telescope ?", + "Output Program": [ + "n0 = 100.0\nn1 = 150.0\nt0 = n1 - n0\nt1 = t0 / n0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "if 2994 \u00e3 \u00b7 14.5 = 175 , then 29.94 \u00e3 \u00b7 1.45 = ?", + "Output Program": [ + "n0 = 2994.0\nn1 = 14.5\nn2 = 175.0\nn3 = 29.94\nn4 = 1.45\nt0 = n1 / n4\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "17.5" + ], + "split": "train" + }, + { + "Input": "for a certain alarm system , each code is comprised of 5 digits , but no digit can be used more than twice . how many codes can be made ?", + "Output Program": [ + "import math\nn0 = 5.0\nt0 = math.factorial(min(15, int(10.0)))\nt1 = math.factorial(min(15, int(n0)))\nt2 = math.factorial(min(15, int(3.0)))\nt3 = math.factorial(min(15, int(2.0)))\nt4 = 10.0 - n0\nt5 = 10.0 - 1.0\nt6 = 10.0 - 2.0\nt7 = t1 / 2.0\nt8 = t1 / 4.0\nt9 = math.factorial(min(15, int(t4)))\nt10 = math.factorial(min(15, int(t5)))\nt11 = math.factorial(min(15, int(t6)))\nt12 = t5 - 3.0\nt13 = t0 / t9\nt14 = math.factorial(min(15, int(t12)))\nt15 = t11 * t3\nt16 = t0 / t15\nt17 = t2 * t14\nt18 = t10 / t17\nt19 = t16 * t6\nt20 = t18 * 10.0\nt21 = t8 * t19\nt22 = t7 * t20\nt23 = t13 + t22\nanswer = t23 + t21\nprint(answer)" + ], + "Output Answer": [ + "91440" + ], + "split": "train" + }, + { + "Input": "in the rectangular coordinate system , if the line x = 3 y + 5 passes through points ( m , n ) and ( m + 2 , n + p ) , what is the value of p ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 2.0\n\nanswer = n2 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "0.6666666666666666" + ], + "split": "train" + }, + { + "Input": "the average of 10 numbers was calculated as 20 . it is discovered later on that while calculating the average , one number , namely 86 , was incorrectly read as 26 . what is the correct average ?", + "Output Program": [ + "n0 = 10.0\nn1 = 20.0\nn2 = 86.0\nn3 = 26.0\nt0 = n0 * n1\nt1 = n2 - n3\nt2 = t0 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "when jessica withdrew $ 400 from her bank account , her account balance decreased by 2 / 5 . if she deposits an amount equal to 1 / 4 of the remaining balance , what will be the final balance in her bank account ?", + "Output Program": [ + "n0 = 400.0\nn1 = 2.0\nn2 = 5.0\nn3 = 1.0\nn4 = 4.0\nt0 = n3 / n4\nt1 = 3.0 / n2\nt2 = n3 + t0\nt3 = 1.0 - t1\nt4 = n0 / t3\nt5 = t4 - n0\nanswer = t2 * t5\nprint(answer)" + ], + "Output Answer": [ + "750" + ], + "split": "train" + }, + { + "Input": "the simple interest on a sum of money will be rs . 900 after 10 years . if the principal is trebled after 5 years what will be the total interest at the end of the tenth year ?", + "Output Program": [ + "n0 = 900.0\nn1 = 10.0\nn2 = 5.0\nt0 = n0 / n1\nt1 = n2 * t0\nt2 = t1 * 3.0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "1800" + ], + "split": "train" + }, + { + "Input": "what is the sum of all possible solutions to | x - 6 | ^ 2 + | x - 6 | = 20 ?", + "Output Program": [ + "n0 = 6.0\nn1 = 2.0\nn2 = 6.0\nn3 = 20.0\nt0 = n0 + 4.0\nt1 = n0 - 4.0\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "the number of boxes in a warehouse can be divided evenly into 5 equal shipments by boat or 24 equal shipments by truck . what is the smallest number of boxes that could be in the warehouse ?", + "Output Program": [ + "n0 = 5.0\nn1 = 24.0\nt0 = 2.0 * 2.0\nt1 = t0 * 2.0\nt2 = t1 * 3.0\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 30 paisa . if the share of y is rs . 45 , what is the total amount ?", + "Output Program": [ + "n0 = 45.0\nn1 = 30.0\nn2 = 45.0\nt0 = 100.0 / n0\nt1 = n1 / n0\nt2 = n2 * t0\nt3 = n2 * t1\nt4 = t2 + t3\nanswer = n2 + t4\nprint(answer)" + ], + "Output Answer": [ + "175" + ], + "split": "train" + }, + { + "Input": "a student chose a number , multiplied it by 3 , then subtracted 220 from the result and got 110 . what was the number he chose ?", + "Output Program": [ + "n0 = 3.0\nn1 = 220.0\nn2 = 110.0\nt0 = n1 + n2\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "110" + ], + "split": "train" + }, + { + "Input": "{ ( 476 + 424 ) 2 - 4 x 476 x 424 } = ?", + "Output Program": [ + "n0 = 476.0\nn1 = 424.0\nn2 = 2.0\nn3 = 4.0\nn4 = 476.0\nn5 = 424.0\nt0 = n0 + n1\nt1 = n0 * n3\nt2 = n1 * t1\nt3 = t0**min(n2, 5)\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "2704" + ], + "split": "train" + }, + { + "Input": "a certain telescope increases the visual range at a particular location from 90 kilometers to 150 kilometers . by what percent is the visual range increased by using the telescope ?", + "Output Program": [ + "n0 = 90.0\nn1 = 150.0\nt0 = n1 - n0\nt1 = t0 / n0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "66.66666666666666" + ], + "split": "train" + }, + { + "Input": "bill made a profit of 10 % by selling a product . if he had purchased that product for 10 % less and sold it at a profit of 30 % , he would have received $ 35 more . what was his original selling price ?", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 30.0\nn3 = 35.0\nt0 = n0 / 100.0\nt1 = n2 / 100.0\nt2 = t0 + 1.0\nt3 = t1 + 1.0\nt4 = 1.0 - t0\nt5 = t3 * t4\nt6 = t5 - t2\nt7 = n3 / t6\nanswer = t2 * t7\nprint(answer)" + ], + "Output Answer": [ + "549.9999999999995" + ], + "split": "train" + }, + { + "Input": "how many positive integers , from 2 to 100 , inclusive , are not divisible by odd integers greater than 1 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 100.0\nn2 = 1.0\nt0 = n0 * n0\nt1 = n0 * t0\nt2 = n0 * t1\nt3 = n0 * t2\nt4 = n0 * t3\nt5 = t4 - 4.0\nanswer = t5 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "find the sum the difference between the compound and s . i . on a certain sum of money for 2 years at 10 % per annum is rs . 20 of money ?", + "Output Program": [ + "n0 = 2.0\nn1 = 10.0\nn2 = 20.0\nt0 = n0 * n1\nt1 = n2 / t0\nt2 = t1 * 100.0\nanswer = t2 * t0\nprint(answer)" + ], + "Output Answer": [ + "2000" + ], + "split": "train" + }, + { + "Input": "find the least number must be added to 433124 so that remaining no . is divisible by 17 ?", + "Output Program": [ + "n0 = 433124.0\nn1 = 17.0\nt0 = n0 % n1\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "the average weight of 25 girls increases by 1 kg when a new girl comes in place of one of them weighing 55 kg . what might be the weight of the new girl ?", + "Output Program": [ + "n0 = 25.0\nn1 = 1.0\nn2 = 55.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "the average salary of the employees in a office is rs . 120 / month . the avg salary of officers is rs . 470 and of non officers is rs 110 . if the no . of officers is 15 , then find the no of nonofficers in the office .", + "Output Program": [ + "n0 = 120.0\nn1 = 470.0\nn2 = 110.0\nn3 = 15.0\nt0 = n1 * n3\nt1 = n0 * n3\nt2 = n0 - n2\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "525" + ], + "split": "train" + }, + { + "Input": "find the least number which when divided by 31 and 9 leaves a remainder of 3 in each case .", + "Output Program": [ + "import scipy\nn0 = 31.0\nn1 = 9.0\nn2 = 3.0\nt0 = scipy.lcm(int(n0), int(n1))\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "282" + ], + "split": "train" + }, + { + "Input": "in a college , 280 students study hindi , 254 students study sanskrit and 280 students study english . 97 students study hindi as well as physics , 138 students study sanskrit as well as english and 152 students study hindi as well as english . 73 students study all the 3 languages . how many total number of students are there in that college ?", + "Output Program": [ + "n0 = 280.0\nn1 = 254.0\nn2 = 280.0\nn3 = 97.0\nn4 = 138.0\nn5 = 152.0\nn6 = 73.0\nn7 = 3.0\nt0 = n0 + n1\nt1 = n0 + t0\nt2 = t1 - n3\nt3 = t2 - n4\nt4 = t3 - n5\nanswer = n6 + t4\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "train" + }, + { + "Input": "20 men shake hands with each other . maximum no of handshakes without cyclic handshakes .", + "Output Program": [ + "n0 = 20.0\nt0 = n0 / 2.0\nt1 = n0 - 1.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "190" + ], + "split": "train" + }, + { + "Input": "a certain company has records stored with a record storage firm in 15 - inch by 12 - inch by 10 - inch boxes . the boxes occupy 1.08 million cubic inches of space . if the company pays $ 0.2 per box per month for the record storage , what is the total amount that the company pays each month for record storage ?", + "Output Program": [ + "n0 = 15.0\nn1 = 12.0\nn2 = 10.0\nn3 = 1.08\nn4 = 0.2\nt0 = n0 * n1\nt1 = n2 * t0\nt2 = t1 / 100.0\nt3 = t2 / 100.0\nt4 = t3 / 100.0\nt5 = n3 / t4\nanswer = n4 * t5\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "two employees x and y are paid a total of rs . 528 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?", + "Output Program": [ + "n0 = 528.0\nn1 = 120.0\nt0 = 1.0 + 4.0\nt1 = t0 * 2.0\nt2 = t1 + 1.0\nt3 = n0 * t1\nt4 = t2 * 2.0\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "240" + ], + "split": "train" + }, + { + "Input": "sum of the squares of 3 no . ' s is 222 and the sum of their products taken two at a time is 131 . find the sum ?", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 222.0\nn2 = 131.0\nt0 = n2 * 2.0\nt1 = n1 + t0\nanswer = math.sqrt(max(0, t1))\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "a salesman ' s income consists of a commission and a base salary of $ 450 per week . over the past 5 weeks , his weekly income totals have been $ 406 , $ 413 , $ 420 , $ 436 and $ 395 . what must his average ( arithmetic mean ) commission be per week over the next two weeks so that his average weekly income is $ 500 over the 7 - week period ?", + "Output Program": [ + "n0 = 450.0\nn1 = 5.0\nn2 = 406.0\nn3 = 413.0\nn4 = 420.0\nn5 = 436.0\nn6 = 395.0\nn7 = 500.0\nn8 = 7.0\nt0 = n2 + n3\nt1 = n4 + n5\nt2 = n7 * n8\nt3 = t0 + t1\nt4 = n6 + t3\nt5 = t2 - t4\nt6 = t5 / 2.0\nanswer = t6 - n0\nprint(answer)" + ], + "Output Answer": [ + "265" + ], + "split": "train" + }, + { + "Input": "an art gallery has only paintings and sculptures . currently , 1 / 3 of the pieces of art are displayed , and 1 / 6 of the pieces on display are sculptures . if 1 / 3 of the pieces not on display are paintings , and 400 sculptures are not on display , how many pieces of art does the gallery have ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 6.0\nn4 = 1.0\nn5 = 3.0\nn6 = 400.0\nt0 = n0 / n1\nt1 = n0 - t0\nt2 = n6 / t1\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "899.9999999999998" + ], + "split": "train" + }, + { + "Input": "chris mixed 5 pounds of raisins with 4 pounds of nuts . if a pound of nuts costs 3 times as much as a pound of raisins , then the total cost of the raisins was what fraction of the total cost of the mixture ?", + "Output Program": [ + "n0 = 5.0\nn1 = 4.0\nn2 = 3.0\nt0 = n1 * n2\nt1 = n0 + t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.29411764705882354" + ], + "split": "train" + }, + { + "Input": "if an average hard drive had a capacity of 0.7 tb in 2000 , and average hard drive capacities double every 5 years , what will be the average hard drive capacity in 2050 ?", + "Output Program": [ + "n0 = 0.7\nn1 = 2000.0\nn2 = 5.0\nn3 = 2050.0\nt0 = n0 * 2.0\nt1 = t0 * 2.0\nt2 = t1 * 2.0\nt3 = t2 * 2.0\nt4 = t3 * 2.0\nt5 = t4 * 2.0\nt6 = t5 * 2.0\nt7 = t6 * 2.0\nt8 = t7 * 2.0\nt9 = t8 * 2.0\nt10 = n0 + t9\nanswer = t10 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "7175" + ], + "split": "train" + }, + { + "Input": "9 men went to a hotel . 8 of them spent rs . 3 each over their meals and the ninth spent rs . 2 more than the average expenditure of all the 9 . determine the total money spent by them ? a . rs . 29.25", + "Output Program": [ + "n0 = 9.0\nn1 = 8.0\nn2 = 3.0\nn3 = 2.0\nn4 = 9.0\nn5 = 29.25\nt0 = n0 * n3\nt1 = n1 * n2\nt2 = n0 - 1.0\nt3 = t0 + t1\nt4 = t3 / t2\nanswer = t4 + t1\nprint(answer)" + ], + "Output Answer": [ + "29.25" + ], + "split": "train" + }, + { + "Input": "find the average of all the numbers between 6 and 34 which are divisible by 5", + "Output Program": [ + "n0 = 6.0\nn1 = 34.0\nn2 = 5.0\nt0 = n0 + 4.0\nt1 = n1 - 4.0\nt2 = t0 + t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "when processing flower - nectar into honey bees ' extract , a considerable amount of water gets reduced . how much flower - nectar must be processed to yield 1 kg of honey , if nectar contains 50 % water , and the honey obtained from this nectar contains 25 % water ?", + "Output Program": [ + "n0 = 1.0\nn1 = 50.0\nn2 = 25.0\nt0 = n1 / 100.0\nt1 = 100.0 - n2\nt2 = t1 / 100.0\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "1.5" + ], + "split": "train" + }, + { + "Input": "95 white and black tiles will be used to form a 10 x 10 square pattern . if there must be at least one black tile in every row and at least one white tile in every column , what is the maximum difference between the number of black and white tiles that can be used ?", + "Output Program": [ + "n0 = 95.0\nn1 = 10.0\nn2 = 10.0\n\nanswer = n0 - n1\nprint(answer)" + ], + "Output Answer": [ + "85" + ], + "split": "train" + }, + { + "Input": "taequan is playing a dice game where he rolls two , fair , 6 - sided dice twice . if he gets the same roll on his second try as his first , he wins . if he rolled an 8 on his first try , what is the probability that he will win with his second roll ?", + "Output Program": [ + "n0 = 6.0\nn1 = 8.0\nt0 = n0 * n0\nt1 = n0 - 1.0\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.1388888888888889" + ], + "split": "train" + }, + { + "Input": "find the value of x : 3 x ^ 2 - 6 x + 3 = 0", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 6.0\nn3 = 3.0\nn4 = 0.0\nt0 = n2 / 3.0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "what is the smallest number which when increased by 3 is divisible by 27 , 35 , 25 , & 21 ?", + "Output Program": [ + "import scipy\nn0 = 3.0\nn1 = 27.0\nn2 = 35.0\nn3 = 25.0\nn4 = 21.0\nt0 = scipy.lcm(int(n1), int(n2))\nt1 = scipy.lcm(int(n3), int(n4))\nt2 = scipy.lcm(int(t0), int(t1))\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "4728" + ], + "split": "train" + }, + { + "Input": "the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 245 , what is the difference between the ages of patrick and monica ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 3.0\nn3 = 5.0\nn4 = 245.0\nt0 = n0 * n0\nt1 = n1 * n0\nt2 = n1 * n3\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n4 / t4\nt6 = t5 * t2\nt7 = t5 * t0\nanswer = t6 - t7\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "how many two - element subsets of < 1 , 23 , 45 , 67 > are there that do not contain the pair of elements 2 and 4 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 23.0\nn2 = 45.0\nn3 = 67.0\nn4 = 2.0\nn5 = 4.0\n\nanswer = n1 - 3.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "the average of 50 numbers id 50 . if two numbers , namely 45 and 55 are discarded , the average of the remaining numbers is :", + "Output Program": [ + "n0 = 50.0\nn1 = 50.0\nn2 = 45.0\nn3 = 55.0\nt0 = n2 + n3\nt1 = n0 * n1\nt2 = n0 - 2.0\nt3 = t1 - t0\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "tough and tricky questions : word problems . ak car company wants to manufacture a new car known as model x , and it is trying to determine how many cars it needs to sell in order to make an annual profit of $ 30 , 500000 . the annual fixed costs for model x total $ 50 , 200000 . in addition , each model x car has an average cost of $ 5000 per vehicle to manufacture . if the company forecasts it will sell 20000 model x cars this year , at what price must the company sell the car to achieve the desired annual profit ?", + "Output Program": [ + "n0 = 30.0\nn1 = 500000.0\nn2 = 50.0\nn3 = 200000.0\nn4 = 5000.0\nn5 = 20000.0\nt0 = 1000.0 * 1000.0\nt1 = n4 * n5\nt2 = n2 * t0\nt3 = n0 * t0\nt4 = n3 + t2\nt5 = n1 + t3\nt6 = t4 + t1\nt7 = t6 + t5\nanswer = t7 / n5\nprint(answer)" + ], + "Output Answer": [ + "9035" + ], + "split": "train" + }, + { + "Input": "according to the directions on a packet of smoothie mix , 1 3 - ounce packet of smoothie mix is to be combined with 15 ounces of water to make a smoothie . how many 3 - ounce packets of smoothie mix are required to prepare 150 12 - ounce smoothies ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 15.0\nn3 = 3.0\nn4 = 150.0\nn5 = 12.0\nt0 = n1 * 10.0\nanswer = n4 + t0\nprint(answer)" + ], + "Output Answer": [ + "180" + ], + "split": "train" + }, + { + "Input": "how many 3 - digit numbers are divisible by 6 in all ?", + "Output Program": [ + "n0 = 3.0\nn1 = 6.0\nt0 = 1000.0 / n1\nt1 = 100.0 / n1\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "train" + }, + { + "Input": "if 7 ^ k = 2 , then 7 ^ ( 4 k + 2 ) =", + "Output Program": [ + "n0 = 7.0\nn1 = 2.0\nn2 = 7.0\nn3 = 4.0\nn4 = 2.0\nt0 = n1**min(n3, 5)\nt1 = n0**min(n4, 5)\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "784" + ], + "split": "train" + }, + { + "Input": "little john had $ 5.10 . he spent $ 1.05 on sweets and gave to his two friends $ 1.00 each . how much money was left ?", + "Output Program": [ + "n0 = 5.1\nn1 = 1.05\nn2 = 1.0\nt0 = n2 + n2\nt1 = n1 + t0\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "2.05" + ], + "split": "train" + }, + { + "Input": "country x imported approximately $ 1.44 billion of goods in 1996 . if country x imported $ 488 million of goods in the first two months of 1997 and continued to import goods at the same rate for the rest of the year , by how much would country xs 1997 imports exceed those of 1996 ?", + "Output Program": [ + "n0 = 1.44\nn1 = 1996.0\nn2 = 488.0\nn3 = 1997.0\nn4 = 1997.0\nn5 = 1996.0\nt0 = 12.0 / 2.0\nt1 = n0 * 1000.0\nt2 = n2 * t0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "1488" + ], + "split": "train" + }, + { + "Input": "the average of the 5 numbers is 6.8 . if one of the numbers is multiplied by 3 , the average of the numbers increases to 9.2 . which of the 5 numbers is multiplied by 3 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 6.8\nn2 = 3.0\nn3 = 9.2\nn4 = 5.0\nn5 = 3.0\nt0 = n0 * n3\nt1 = n0 * n1\nt2 = t0 - t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "a , b , c subscribe rs . 50000 for a business . a subscribes rs . 4000 more than b and b rs . 5000 more than c . out of a total profit of rs . 30000 , b receives :", + "Output Program": [ + "n0 = 50000.0\nn1 = 4000.0\nn2 = 5000.0\nn3 = 30000.0\nt0 = n2 - n1\nt1 = n0 + t0\nt2 = t1 / 3.0\nt3 = t2 / n0\nanswer = n3 * t3\nprint(answer)" + ], + "Output Answer": [ + "10200" + ], + "split": "train" + }, + { + "Input": "there are 7 players in a bowling team with an average weight of 94 kg . if two new players join the team , one weighs 110 kg and the second weighs 60 kg , what will be the new average weight ?", + "Output Program": [ + "n0 = 7.0\nn1 = 94.0\nn2 = 110.0\nn3 = 60.0\nt0 = n2 + n3\nt1 = n0 + 2.0\nt2 = n0 * n1\nt3 = t0 + t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "92" + ], + "split": "train" + }, + { + "Input": "the average weight of 12 person ' s increases by 4 kg when a new person comes in place of one of them weighing 58 kg . what is the weight of the new person ?", + "Output Program": [ + "n0 = 12.0\nn1 = 4.0\nn2 = 58.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "106" + ], + "split": "train" + }, + { + "Input": "a certain telescope increases the visual range at a particular location from 60 kilometers to 150 kilometers . by what percent is the visual range increased by using the telescope ?", + "Output Program": [ + "n0 = 60.0\nn1 = 150.0\nt0 = n1 - n0\nt1 = t0 / n0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "train" + }, + { + "Input": "0.9 * 0.007 = \u00ad \u00ad \u00ad \u00ad \u00ad \u00ad \u00ad \u00ad \u00ad \u00ad _________", + "Output Program": [ + "n0 = 0.9\nn1 = 0.007\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "0.0063" + ], + "split": "train" + }, + { + "Input": "if ( - 3 ) ^ ( 2 x ) = 3 ^ ( 12 - x ) and x is an integer , what is the value of x ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 3.0\nn3 = 12.0\n\nanswer = n3 / n0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "in a division sum , the divisor is 10 times the quotient and 5 times the remainder . if the remainder is 46 , what is the dividend ?", + "Output Program": [ + "n0 = 10.0\nn1 = 5.0\nn2 = 46.0\nt0 = n1 * n2\nt1 = t0 / n0\nanswer = t1 * t0\nprint(answer)" + ], + "Output Answer": [ + "5290" + ], + "split": "train" + }, + { + "Input": "the sum of two numbers is 45 . their difference is 5 . the bigger number is", + "Output Program": [ + "n0 = 45.0\nn1 = 5.0\nt0 = n0 + n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "the average of 6 observations is 11 . a new observation is included and the new average is decreased by 1 . the seventh observation is ?", + "Output Program": [ + "n0 = 6.0\nn1 = 11.0\nn2 = 1.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n1 - n2\nt3 = t0 * t2\nanswer = t3 - t1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "a company wants to spend equal amounts of money for the purchase of two types of computer printers costing $ 350 and $ 200 per unit , respectively . what is the fewest number of computer printers that the company can purchase ?", + "Output Program": [ + "import scipy\nn0 = 350.0\nn1 = 200.0\nt0 = scipy.lcm(int(n0), int(n1))\nt1 = t0 / n0\nt2 = t0 / n1\nanswer = t1 + t2\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "a fair sided dice labeled 1 to 6 is tossed 2 times . what is the probability the sum of the 2 throws is 5 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 6.0\nn2 = 2.0\nn3 = 2.0\nn4 = 5.0\nt0 = n1**min(n2, 5)\nt1 = n4 - 1.0\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.1111111111111111" + ], + "split": "train" + }, + { + "Input": "in a race where 8 cars are running , the chance that car x will win is 1 / 2 , that y will win is 1 / 4 and that z will win is 1 / 3 . assuming that a dead heat is impossible , find the chance that one of them will win .", + "Output Program": [ + "n0 = 8.0\nn1 = 1.0\nn2 = 2.0\nn3 = 1.0\nn4 = 4.0\nn5 = 1.0\nn6 = 3.0\nt0 = n1 / n2\nt1 = n1 / n4\nt2 = n1 / n6\nt3 = t0 + t1\nanswer = t3 + t2\nprint(answer)" + ], + "Output Answer": [ + "1.0833333333333333" + ], + "split": "train" + }, + { + "Input": "the sum of the numbers is 264 . if the first number be twice the second and third number be one - third of the first , then the second number is :", + "Output Program": [ + "n0 = 264.0\nt0 = 1.0 + 10.0\nt1 = n0 * 3.0\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "train" + }, + { + "Input": "what is the remainder of w = 3 ^ 19 when divided by 10 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 19.0\nn2 = 10.0\nt0 = n1 % 4.0\nt1 = n0**min(t0, 5)\nanswer = t1 % n2\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 105 only . men \u00e2 \u20ac \u2122 s wages are ?", + "Output Program": [ + "n0 = 5.0\nn1 = 8.0\nn2 = 105.0\nt0 = n0 * 3.0\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "by how much does the larger root of the equation 2 b ^ 2 + 5 b = 12 exceed the smaller root ?", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 2.0\nn2 = 5.0\nn3 = 12.0\nt0 = n0 * n3\nt1 = n0 * n0\nt2 = n2**min(n0, 5)\nt3 = t0 * 4.0\nt4 = t3 + t2\nt5 = math.sqrt(max(0, t4))\nt6 = n2 + t5\nt7 = n2 - t5\nt8 = t6 / t1\nt9 = t7 / t1\nanswer = t8 - t9\nprint(answer)" + ], + "Output Answer": [ + "5.5" + ], + "split": "train" + }, + { + "Input": "product of two natural numbers is 17 . then , the sum of reciprocals of their squares is", + "Output Program": [ + "n0 = 17.0\nt0 = 1.0 / 1.0\nt1 = 1.0 / n0\nt2 = t0**min(2.0, 5)\nt3 = t1**min(2.0, 5)\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "1.0034602076124568" + ], + "split": "train" + }, + { + "Input": "a straight line in the xy - plane has a slope of 2 and a y - intercept of 2 . on this line , what is the x - coordinate of the point whose y - coordinate is 998 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 998.0\nt0 = n2 - n0\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "498" + ], + "split": "train" + }, + { + "Input": "of 70 players on a football team , 37 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?", + "Output Program": [ + "n0 = 70.0\nn1 = 37.0\nt0 = 1.0 / 3.0\nt1 = n0 - n1\nt2 = 1.0 - t0\nt3 = t2 * t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "59" + ], + "split": "train" + }, + { + "Input": "there are 200 female managers in a certain company . find the total number of female employees q in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers .", + "Output Program": [ + "n0 = 200.0\nn1 = 2.0\nn2 = 5.0\nn3 = 2.0\nn4 = 5.0\nt0 = n1 / n2\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "train" + }, + { + "Input": "if the sum of two numbers is 24 and the sum of their squares is 404 , then the product of the numbers is", + "Output Program": [ + "n0 = 24.0\nn1 = 404.0\nt0 = n0**min(2.0, 5)\nt1 = t0 - n1\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "86" + ], + "split": "train" + }, + { + "Input": "product of two natural numbers is 3 . then , the sum of reciprocals of their squares is", + "Output Program": [ + "n0 = 3.0\nt0 = 1.0 / 1.0\nt1 = 1.0 / n0\nt2 = t0**min(2.0, 5)\nt3 = t1**min(2.0, 5)\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "1.1111111111111112" + ], + "split": "train" + }, + { + "Input": "if the least common multiple of two prime numbers x and y is 10 , where x > y , then the value of 2 x + y is", + "Output Program": [ + "n0 = 10.0\nn1 = 2.0\nt0 = n0 / 2.0\nt1 = n1 * t0\nanswer = t1 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "if the number of white balls in a box are 6 times the black balls , which of the below is the total number of balls , if there are 8 black balls in the box ?", + "Output Program": [ + "n0 = 6.0\nn1 = 8.0\nt0 = n0 * n1\nanswer = n1 + t0\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "train" + }, + { + "Input": "how many of the positive divisors of 120 are also multiples of 4 not including 120 ?", + "Output Program": [ + "n0 = 120.0\nn1 = 4.0\nn2 = 120.0\nt0 = n0 / n1\nt1 = t0 / 2.0\nanswer = t1 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "the average of 6 observations is 12 . a new seventh observation is included and the new average is decreased by 1 . the seventh observation is :", + "Output Program": [ + "n0 = 6.0\nn1 = 12.0\nn2 = 1.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n1 - n2\nt3 = t0 * t2\nanswer = t3 - t1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "for a certain art exhibit , a museum sold admission tickets to a group of 30 people every 5 minutes from 9 : 00 in the morning to 5 : 55 in the afternoon , inclusive . the price of a regular admission ticket was $ 10 and the price of a student ticket was $ 5 . if on one day 3 times as many regular admission tickets were sold as student tickets , what was the total revenue from ticket sales that day ?", + "Output Program": [ + "n0 = 30.0\nn1 = 5.0\nn2 = 9.0\nn3 = 0.0\nn4 = 5.0\nn5 = 55.0\nn6 = 10.0\nn7 = 5.0\nn8 = 3.0\nt0 = 12.0 + n4\nt1 = n8 + 1.0\nt2 = t0 - n2\nt3 = t2 + 1.0\nt4 = t3 * 12.0\nt5 = n0 * t4\nt6 = t5 / t1\nt7 = n8 * t6\nt8 = n7 * t6\nt9 = n6 * t7\nanswer = t9 + t8\nprint(answer)" + ], + "Output Answer": [ + "28350" + ], + "split": "train" + }, + { + "Input": "2 cow \u2019 s and 8 goats are brought for rs . 1400 . if the average price of a goat be rs . 60 . what is the average price of a cow .", + "Output Program": [ + "n0 = 2.0\nn1 = 8.0\nn2 = 1400.0\nn3 = 60.0\nt0 = n1 * n3\nt1 = n2 - t0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "460" + ], + "split": "train" + }, + { + "Input": "1 = 6,2 = 36,3 = 363,4 = 364,5 = 365 , then 36 = ?", + "Output Program": [ + "n0 = 1.0\nn1 = 62.0\nn2 = 363.0\nn3 = 3634.0\nn4 = 3645.0\nn5 = 365.0\nn6 = 36.0\n\nanswer = 3.0 - n0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "two employees x and y are paid a total of rs . 600 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?", + "Output Program": [ + "n0 = 600.0\nn1 = 120.0\nt0 = 1.0 + 4.0\nt1 = t0 * 2.0\nt2 = t1 + 1.0\nt3 = n0 * t1\nt4 = t2 * 2.0\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "272.72727272727275" + ], + "split": "train" + }, + { + "Input": "mary ' s income is 40 percent more than tim ' s income , and tim ' s income is 40 percent less than juan ' s income . what percent of juan ' s income is mary ' s income ?", + "Output Program": [ + "n0 = 40.0\nn1 = 40.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = t0 + 1.0\nt3 = 1.0 - t1\nt4 = t2 * t3\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "84" + ], + "split": "train" + }, + { + "Input": "kim has 40 percent more money than sal and sal has 20 percent less money than phil . if sal and phil have a combined total of $ 1.80 , how much money does kim have ?", + "Output Program": [ + "n0 = 40.0\nn1 = 20.0\nn2 = 1.8\nt0 = n0 + 100.0\nt1 = 100.0 - n1\nt2 = t1 + 100.0\nt3 = t0 * t1\nt4 = n2 / t2\nt5 = t3 / 100.0\nanswer = t4 * t5\nprint(answer)" + ], + "Output Answer": [ + "1.12" + ], + "split": "train" + }, + { + "Input": "a gambler bought $ 3,000 worth of chips at a casino in denominations of $ 20 and $ 100 . that evening , the gambler lost 14 chips , and then cashed in the remainder . if the number of $ 20 chips lost was 2 more or 2 less than the number of $ 100 chips lost , what is the largest amount of money that the gambler could have received back ?", + "Output Program": [ + "n0 = 3000.0\nn1 = 20.0\nn2 = 100.0\nn3 = 14.0\nn4 = 20.0\nn5 = 2.0\nn6 = 2.0\nn7 = 100.0\nt0 = n3 + n5\nt1 = 1000.0 * 3.0\nt2 = t0 / n5\nt3 = n1 * t2\nt4 = t2 - n5\nt5 = n2 * t4\nt6 = t3 + t5\nanswer = t1 - t6\nprint(answer)" + ], + "Output Answer": [ + "2240" + ], + "split": "train" + }, + { + "Input": "if k ^ 3 is divisible by 336 , what is the least possible value of integer k ?", + "Output Program": [ + "n0 = 3.0\nn1 = 336.0\nt0 = n1 / 2.0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "84" + ], + "split": "train" + }, + { + "Input": "a box contains either blue or red flags . the total number of flags in the box is an even number . a group of children are asked to pick up two flags each . if all the flags are used up in the process such that 60 % of the children have blue flags , and 60 % have red flags , what percentage of children have flags of both the colors ?", + "Output Program": [ + "n0 = 60.0\nn1 = 60.0\nt0 = n0 + n1\nanswer = t0 - 100.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "half a number plus 6 is 11 . what is the number ?", + "Output Program": [ + "n0 = 6.0\nn1 = 11.0\nt0 = n1 - n0\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "n ^ ( n / 2 ) = 6 is true when n = 6 in the same way what is the value of n if n ^ ( n / 2 ) = 10 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 6.0\nn2 = 6.0\nn3 = 2.0\nn4 = 10.0\nt0 = n4**min(n0, 5)\nanswer = t0 / n4\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the average age of 11 boys is 50 , if the average age of first 6 boys is 49 and that of the last 6 is 52 . find the boy age ?", + "Output Program": [ + "n0 = 11.0\nn1 = 50.0\nn2 = 6.0\nn3 = 49.0\nn4 = 6.0\nn5 = 52.0\nt0 = n2 * n5\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 - t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "train" + }, + { + "Input": "a rope of which a calf is tied is increased from 9 m to 23 m , how much additional grassy ground shall it graze ?", + "Output Program": [ + "n0 = 9.0\nn1 = 23.0\nt0 = 3.0 + 4.0\nt1 = 10.0 * 2.0\nt2 = n1**min(2.0, 5)\nt3 = n0**min(2.0, 5)\nt4 = t1 + 2.0\nt5 = t2 - t3\nt6 = t4 / t0\nanswer = t6 * t5\nprint(answer)" + ], + "Output Answer": [ + "1408" + ], + "split": "train" + }, + { + "Input": "a new tower has just been built at the verbico military hospital ; the number of beds available for patients at the hospital is now 2 times the number available before the new tower was built . currently , 1 / 3 of the hospital ' s original beds , as well as 1 / 5 of the beds in the new tower , are occupied . for the purposes of renovating the hospital ' s original wing , all of the patients in the hospital ' s original beds must be transferred to beds in the new tower . if patients are neither admitted nor discharged during the transfer , what fraction of the beds in the new tower will be unoccupied once the transfer is complete ?", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 3.0\nn3 = 1.0\nn4 = 5.0\nt0 = n1 / n2\nt1 = n1 / n4\nt2 = n0 * n2\nt3 = n1 + t2\nt4 = t0 * t1\nanswer = t3 * t4\nprint(answer)" + ], + "Output Answer": [ + "0.4666666666666667" + ], + "split": "train" + }, + { + "Input": "the arithmetic mean and standard deviation of a certain normal distribution are 16.2 and 2.3 , respectively . what value is exactly 2 standard deviations less than the mean ?", + "Output Program": [ + "n0 = 16.2\nn1 = 2.3\nn2 = 2.0\nt0 = n1 * n2\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "11.6" + ], + "split": "train" + }, + { + "Input": "the simple interest on a sum of money will be rs . 600 after 10 years . if the principal is trebled after 5 years , what will be the total interest at the end of the tenth year ?", + "Output Program": [ + "n0 = 600.0\nn1 = 10.0\nn2 = 5.0\nt0 = n0 / n1\nt1 = n2 * t0\nt2 = t1 * 3.0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "1200" + ], + "split": "train" + }, + { + "Input": "we define that k @ j is the product of j number from k in increasing order for positive integers k , j . for example , 6 @ 4 = 6 * 7 * 8 * 9 . if a = 2020 and b = 2120 , what is the value w of the ratio a / b ?", + "Output Program": [ + "n0 = 6.0\nn1 = 4.0\nn2 = 6.0\nn3 = 7.0\nn4 = 8.0\nn5 = 9.0\nn6 = 2020.0\nn7 = 2120.0\nt0 = n6 / n6\nt1 = t0 + t0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "out of 3 consecutive odd numbers 8 times the first number is equal to addition of thrice the third number and adding 5 to twice the second . what is the first number ?", + "Output Program": [ + "n0 = 3.0\nn1 = 8.0\nn2 = 5.0\nt0 = n0 + 2.0\nt1 = 2.0 * 2.0\nt2 = n0 * 4.0\nt3 = t1 + t2\nt4 = n1 - t0\nt5 = n2 + t3\nanswer = t5 / t4\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "what is the smallest number which when increased by 3 is divisible by 9 , 35 , 25 and 21 ?", + "Output Program": [ + "import scipy\nn0 = 3.0\nn1 = 9.0\nn2 = 35.0\nn3 = 25.0\nn4 = 21.0\nt0 = scipy.lcm(int(n1), int(n2))\nt1 = scipy.lcm(int(n3), int(n4))\nt2 = scipy.lcm(int(t0), int(t1))\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "1578" + ], + "split": "train" + }, + { + "Input": "8 cups of milk are to be poured into a 4 - cup bottle and a 8 - cup bottle . if each bottle is to be filled to the same fraction of its capacity , how many cups of milk should be poured into the 8 - cup bottle ?", + "Output Program": [ + "n0 = 8.0\nn1 = 4.0\nn2 = 8.0\nn3 = 8.0\nt0 = n0 + n1\nt1 = n0 / t0\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "5.333333333333333" + ], + "split": "train" + }, + { + "Input": "there are some people in party , 1 / 3 rd left the party . then 2 / 5 th of the remaining left the party , then 2 / 3 rd of the remaining left the party . at last 6 were remaining . how many people were in total ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 2.0\nn3 = 5.0\nn4 = 2.0\nn5 = 3.0\nn6 = 6.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = n2 / n1\nt3 = 1.0 - t0\nt4 = 1.0 - t1\nt5 = 1.0 - t2\nt6 = t3 * t4\nt7 = t6 * t5\nanswer = n6 / t7\nprint(answer)" + ], + "Output Answer": [ + "44.99999999999999" + ], + "split": "train" + }, + { + "Input": "the average age of 15 students of a class is 15 years . out of these , the average age of 7 students is 14 years and that of the other 7 students is 16 years . the age of the 15 th student is", + "Output Program": [ + "n0 = 15.0\nn1 = 15.0\nn2 = 7.0\nn3 = 14.0\nn4 = 7.0\nn5 = 16.0\nn6 = 15.0\nt0 = n0 * n0\nt1 = n2 * n3\nt2 = n4 * n5\nt3 = t1 + t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "car a travels at 3 times the average speed of car b . car a started to travel at 12 : 00 o ' clock , car b started to travel at 16 : 00 o ' clock . what is the speed of car b ( in km / h ) if the total distance that both cars traveled until 18 : 00 was 1000 km ?", + "Output Program": [ + "n0 = 3.0\nn1 = 12.0\nn2 = 0.0\nn3 = 16.0\nn4 = 0.0\nn5 = 18.0\nn6 = 0.0\nn7 = 1000.0\nt0 = n5 - n1\nt1 = n5 - n3\nt2 = n0 * t0\nt3 = t2 + t1\nanswer = n7 / t3\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 931 . find the cost of each ice - cream cup ?", + "Output Program": [ + "n0 = 16.0\nn1 = 5.0\nn2 = 7.0\nn3 = 6.0\nn4 = 6.0\nn5 = 45.0\nn6 = 70.0\nn7 = 931.0\nt0 = n0 * n3\nt1 = n1 * n5\nt2 = n2 * n6\nt3 = n7 - t0\nt4 = t3 - t1\nt5 = t4 - t2\nanswer = t5 / n3\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "the average weight of 10 men is increased by 2 \u00bd kg when one of the men who weighs 68 kg is replaced by a new man . what is the weight of the new man ?", + "Output Program": [ + "n0 = 10.0\nn1 = 2.0\nn2 = 68.0\nt0 = 1.0 / n1\nt1 = n1 + t0\nt2 = n0 * t1\nanswer = n2 + t2\nprint(answer)" + ], + "Output Answer": [ + "93" + ], + "split": "train" + }, + { + "Input": "elena \u2019 s bread recipe calls for 3 ounces of butter for each 4 cups of flour used . she needs to make 6 times the original recipe . if 12 ounces of butter is used , then how many cups of flour are needed ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 6.0\nn3 = 12.0\n\nanswer = n1 * n2\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "a cricketer scored 136 runs which included 12 boundaries and 2 sixes . what percent of his total score did he make by running between the wickets .", + "Output Program": [ + "n0 = 136.0\nn1 = 12.0\nn2 = 2.0\nt0 = n1 * 4.0\nt1 = n2 * 3.0\nt2 = n2 * t1\nt3 = t0 + t2\nt4 = n0 - t3\nt5 = t4 / n0\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "55.88235294117647" + ], + "split": "train" + }, + { + "Input": "there are 6 people in the elevator . their average weight is 160 lbs . another person enters the elevator , and increases the average weight to 151 lbs . what is the weight of the 7 th person .", + "Output Program": [ + "n0 = 6.0\nn1 = 160.0\nn2 = 151.0\nn3 = 7.0\nt0 = n2 * n3\nt1 = n0 * n1\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "97" + ], + "split": "train" + }, + { + "Input": "what least fraction should be added to 1 / ( 2 \u00d7 3 ) + 1 / ( 3 \u00d7 4 ) + 1 / ( 4 \u00d7 5 ) + . . . . . . . + 1 / ( 21 \u00d7 22 ) so that the result is unity ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 3.0\nn3 = 1.0\nn4 = 3.0\nn5 = 4.0\nn6 = 1.0\nn7 = 4.0\nn8 = 5.0\nn9 = 1.0\nn10 = 21.0\nn11 = 22.0\nt0 = n1 + n2\nt1 = n1 * n2\nt2 = t0 + t1\nanswer = t1 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.5454545454545454" + ], + "split": "train" + }, + { + "Input": "how many 5 - digit numbers that do not contain the digits 4 or 7 are there ?", + "Output Program": [ + "n0 = 5.0\nn1 = 4.0\nn2 = 7.0\nt0 = 2.0 * 4.0\nt1 = n0 - 1.0\nt2 = t0**min(t1, 5)\nanswer = n2 * t2\nprint(answer)" + ], + "Output Answer": [ + "28672" + ], + "split": "train" + }, + { + "Input": "how many positive integers i less than 20 are either a multiple of 2 , an odd multiple of 9 , or the sum of a positive multiple of 2 and a positive multiple of 9 ?", + "Output Program": [ + "n0 = 20.0\nn1 = 2.0\nn2 = 9.0\nn3 = 2.0\nn4 = 9.0\nt0 = n2 + 1.0\nt1 = n1 + 3.0\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "the weights of 3 bags are in the ratio 4 : 5 : 6 . if the sum of the weights of the heaviest and the lightest bag is 45 kg more than the weight of the third bag , what is the weight of the lightest bag ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 5.0\nn3 = 6.0\nn4 = 45.0\nt0 = n1 + n3\nt1 = t0 - n2\nt2 = n4 / t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "a room is 6 meters 72 centimeters in length and 4 meters 32 centimeters in width . find the least number of square tiles of equal size required to cover the entire floor of the room .", + "Output Program": [ + "import scipy\nn0 = 6.0\nn1 = 72.0\nn2 = 4.0\nn3 = 32.0\nt0 = n0 * 100.0\nt1 = n2 * 100.0\nt2 = n1 + t0\nt3 = n3 + t1\nt4 = scipy.gcd(int(t2), int(t3))\nt5 = t2 * t3\nt6 = t4 * t4\nanswer = t5 / t6\nprint(answer)" + ], + "Output Answer": [ + "126" + ], + "split": "train" + }, + { + "Input": "if x is a positive integer with fewer than 3 digits , what is the probability q that x * ( x + 1 ) is a multiple of either 4 or 5 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 4.0\nn3 = 5.0\nt0 = 100.0 / n2\nt1 = 100.0 / n3\nt2 = 100.0 - 1.0\nt3 = t0 * 2.0\nt4 = t1 * 2.0\nt5 = t3 + t4\nt6 = t5 - n2\nanswer = t6 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.8686868686868687" + ], + "split": "train" + }, + { + "Input": "find the value of y from ( 12 ) ^ 3 x 6 ^ 4 \u00f7 432 = y ?", + "Output Program": [ + "n0 = 12.0\nn1 = 3.0\nn2 = 6.0\nn3 = 4.0\nn4 = 432.0\nt0 = n0**min(n1, 5)\nt1 = n2**min(n3, 5)\nt2 = t0 * t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "5184" + ], + "split": "train" + }, + { + "Input": "in a graduating class , 40 percent of the students are male . in this class , 60 percent of the male students and 40 percent of the female students are 25 years old or older . if one student in the class is randomly selected , approximately what is the probability that he or she will be less than 25 years old ?", + "Output Program": [ + "n0 = 40.0\nn1 = 60.0\nn2 = 40.0\nn3 = 25.0\nn4 = 25.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = n2 / 100.0\nt3 = t0 * t1\nt4 = 1.0 - t0\nt5 = t2 * t4\nt6 = t3 + t5\nanswer = 1.0 - t6\nprint(answer)" + ], + "Output Answer": [ + "0.52" + ], + "split": "train" + }, + { + "Input": "if n is a positive integer , what is the remainder when ( 7 ^ ( 4 n + 2 ) ) ( 6 ^ n ) is divided by 10 ?", + "Output Program": [ + "n0 = 7.0\nn1 = 4.0\nn2 = 2.0\nn3 = 6.0\nn4 = 10.0\nt0 = 3.0 * 3.0\nt1 = n3 * t0\nanswer = t1 % n4\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "a baker makes chocolate cookies and peanut cookies . his recipes allow him to make chocolate cookie in batches of 5 and peanut cookies in batches of 6 . if he makes exactly 94 cookies , what is the minimum number of chocolate chip cookies he makes ?", + "Output Program": [ + "n0 = 5.0\nn1 = 6.0\nn2 = 94.0\nt0 = n0 + n1\nt1 = n2 % t0\nt2 = n2 - t1\nt3 = t2 / t0\nanswer = n0 * t3\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "when y is divided by 264 , the remainder is 42 . what is the remainder when the same y is divided by 22 ?", + "Output Program": [ + "n0 = 264.0\nn1 = 42.0\nn2 = 22.0\n\nanswer = n1 % n2\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "9 people are planning to share equally the cost of a rental van . if one person withdraws from the arrangement and the others share equally the cost of the rental van , then the share of each of the remaining people will increase by . . . ?", + "Output Program": [ + "n0 = 9.0\nt0 = 1.0 / n0\nt1 = n0 - 1.0\nt2 = 1.0 / t1\nt3 = t2 - t0\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.12500000000000006" + ], + "split": "train" + }, + { + "Input": "a jogger running at 9 km / hr along side a railway track is 260 m ahead of the engine of a 120 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?", + "Output Program": [ + "n0 = 9.0\nn1 = 260.0\nn2 = 120.0\nn3 = 45.0\nt0 = n1 + n2\nt1 = 10.0 / 2.0\nt2 = n3 - n0\nt3 = t2 / 2.0\nt4 = t1 / t3\nt5 = t4 * t2\nanswer = t0 / t5\nprint(answer)" + ], + "Output Answer": [ + "38" + ], + "split": "train" + }, + { + "Input": "john has exactly 31 pens , and each pen is either bule , black , or red . if he has 5 more black pens than red pens , and twice as many blue pens as black pens , how many blue pens does john has ?", + "Output Program": [ + "n0 = 31.0\nn1 = 5.0\nt0 = n0 + n1\nt1 = t0 / 4.0\nanswer = t1 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "the average monthly salary of 20 employees in an organisation is rs . 1500 . if the manager ' s salary is added , then the average salary increases by rs . 500 . what is the manager ' s monthly salary ?", + "Output Program": [ + "n0 = 20.0\nn1 = 1500.0\nn2 = 500.0\nt0 = n1 + n2\nt1 = n0 + 1.0\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "12000" + ], + "split": "train" + }, + { + "Input": "the tax on a commodity is diminished by 20 % but its consumption is increased by 15 % . find the decrease percent in the revenue derived from it ?", + "Output Program": [ + "n0 = 20.0\nn1 = 15.0\nt0 = n1 + 100.0\nt1 = 100.0 - n0\nt2 = t0 * t1\nt3 = t2 / 100.0\nanswer = 100.0 - t3\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "in a school with 5 classes , each class has 2 students less than the previous class . how many students are there in the largest class if the total number of students at school is 140 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 140.0\nt0 = n1 + n1\nt1 = n1 + t0\nt2 = n1 + t1\nt3 = t1 + t1\nt4 = t3 + t2\nt5 = n2 - t4\nt6 = t5 / n0\nanswer = t2 + t6\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "excluding stoppages , the average speed of a bus is 60 km / hr and including stoppages , the average speed of the bus is 20 km / hr . for how many minutes does the bus stop per hour ?", + "Output Program": [ + "n0 = 60.0\nn1 = 20.0\nt0 = n1 / n0\nt1 = 1.0 * 60.0\nt2 = t0 * 60.0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "a , b , and c are integers and a < b < c . s is the set of all integers from a to b , inclusive . q is the set of all integers from b to c , inclusive . the median of set s is ( 3 / 4 ) * b . the median of set q is ( 8 / 8 ) * c . if r is the set of all integers from a to c , inclusive , what fraction of c is the median of set r ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 8.0\nn3 = 8.0\nt0 = n2 / n3\nt1 = n0 / n1\nt2 = t0 * 2.0\nt3 = t1 * 2.0\nt4 = t2 - 1.0\nt5 = t3 - 1.0\nt6 = 1.0 / t5\nt7 = t4 / t6\nt8 = t7 + 1.0\nanswer = t8 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "0.75" + ], + "split": "train" + }, + { + "Input": "what is the dividend . divisor 19 , the quotient is 9 and the remainder is 5 ?", + "Output Program": [ + "n0 = 19.0\nn1 = 9.0\nn2 = 5.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "176" + ], + "split": "train" + }, + { + "Input": "how many 4 - digit numbers are there such that all 3 digits are different and the first digit and last digit is not zero ?", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nt0 = n0 / 2.0\nt1 = 10.0 - 1.0\nt2 = t1**min(t0, 5)\nt3 = t1 - 1.0\nt4 = t3**min(t0, 5)\nanswer = t2 * t4\nprint(answer)" + ], + "Output Answer": [ + "5184" + ], + "split": "train" + }, + { + "Input": "32 = a + 2 b | a | > 2 if \u2018 a \u2019 and \u2018 b \u2019 are both integers , then what is the smallest possible values of \u2018 a \u2019 that can be used to solve the above equation .", + "Output Program": [ + "n0 = 32.0\nn1 = 2.0\nn2 = 2.0\n\nanswer = n1 * n1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "a salesman ' s income consists of a commission and a base salary of $ 350 per week . over the past 5 weeks , his weekly income totals have been $ 406 , $ 413 , $ 420 , $ 436 and $ 495 . what must his average ( arithmetic mean ) commission be per week over the next two weeks so that his average weekly income is $ 500 over the 7 - week period ?", + "Output Program": [ + "n0 = 350.0\nn1 = 5.0\nn2 = 406.0\nn3 = 413.0\nn4 = 420.0\nn5 = 436.0\nn6 = 495.0\nn7 = 500.0\nn8 = 7.0\nt0 = n2 + n3\nt1 = n4 + n5\nt2 = n7 * n8\nt3 = t0 + t1\nt4 = n6 + t3\nt5 = t2 - t4\nt6 = t5 / 2.0\nanswer = t6 - n0\nprint(answer)" + ], + "Output Answer": [ + "315" + ], + "split": "train" + }, + { + "Input": "the guests at a football banquet consumed a total of 411 pounds of food . if no individual guest consumed more than 2.5 pounds of food , what is the minimum number of guests that could have attended the banquet ?", + "Output Program": [ + "import math\nn0 = 411.0\nn1 = 2.5\nt0 = n0 / n1\nt1 = math.floor(t0)\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "165" + ], + "split": "train" + }, + { + "Input": "if n = 2 ^ 0.15 and n ^ b = 64 , b must equal", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 0.15\nn2 = 64.0\nt0 = math.log(max(1e-5, n2), 2)\nt1 = n0**min(n1, 5)\nt2 = math.log(max(1e-5, t1), 2)\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "39.99999999999998" + ], + "split": "train" + }, + { + "Input": "in an electric circuit , two resistors with resistances x and y are connected in parallel . if r is the combined resistance of these two resistors , then the reciprocal of r is equal to the sum of the reciprocals of x and y . what is r if x is 5 ohms and y is 7 ohms ?", + "Output Program": [ + "n0 = 5.0\nn1 = 7.0\nt0 = n0 + n1\nt1 = n0 * n1\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "2.9166666666666665" + ], + "split": "train" + }, + { + "Input": "a envelop weight 8.5 gm , if 850 of these envelop are sent with an advertisement mail . how much wieght ?", + "Output Program": [ + "n0 = 8.5\nn1 = 850.0\nt0 = n0 * n1\nanswer = t0 / 1000.0\nprint(answer)" + ], + "Output Answer": [ + "7.225" + ], + "split": "train" + }, + { + "Input": "a man is 28 years older than his son . in two years , his age will be twice the age of his son . what is the present age of his son ?", + "Output Program": [ + "n0 = 28.0\nt0 = 2.0 * 2.0\nt1 = 2.0 - 1.0\nt2 = t0 - 2.0\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "how many numbers from 10 to 100 are exactly divisible by 9 ?", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 100.0\nn2 = 9.0\nt0 = n1 / n2\nt1 = n0 / n2\nt2 = math.floor(t0)\nt3 = math.floor(t1)\nt4 = t3 + 1.0\nt5 = n2 * t2\nt6 = n2 * t4\nt7 = t5 - t6\nt8 = t7 / n2\nanswer = t8 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "what is the units digit of the expression 7 ^ 75 + 6 ?", + "Output Program": [ + "n0 = 7.0\nn1 = 75.0\nn2 = 6.0\nt0 = 3.0 + 4.0\nanswer = t0 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "a box contains either blue or red flags . the total number of flags in the box is an even number . a group of children are asked to pick up two flags each . if all the flags are used up in the process such that 60 % of the children have blue flags , and 65 % have red flags , what percentage of children have flags of both the colors ?", + "Output Program": [ + "n0 = 60.0\nn1 = 65.0\nt0 = n0 + n1\nanswer = t0 - 100.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "dacid obtained 96 , 95 , 82 , 87 and 92 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?", + "Output Program": [ + "n0 = 96.0\nn1 = 95.0\nn2 = 82.0\nn3 = 87.0\nn4 = 92.0\nn5 = 100.0\nt0 = n0 + n1\nt1 = 10.0 / 2.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "90.4" + ], + "split": "train" + }, + { + "Input": "of the 80 people in a room , 2 / 5 are women . if 1 / 2 of the people are married , what is the maximum number of women in the room who could be unmarried ?", + "Output Program": [ + "n0 = 80.0\nn1 = 2.0\nn2 = 5.0\nn3 = 1.0\nn4 = 2.0\nt0 = n1 / n2\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "in a group of ducks and cows , the total number of legs are 32 more than twice the no . of heads . find the total no . of buffaloes .", + "Output Program": [ + "n0 = 32.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "in 1 kg mixture of iron and manganese 20 % of manganese . how much iron should be added so that the proportion of manganese becomes 10 %", + "Output Program": [ + "n0 = 1.0\nn1 = 20.0\nn2 = 10.0\nt0 = n1 / 100.0\nt1 = n2 / 100.0\nt2 = t0 / t1\nanswer = t2 - n0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "if x \u00a4 y = ( x + y ) ^ 2 - ( x - y ) ^ 2 . then \u221a 3 \u00a4 \u221a 3 =", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 2.0\nn2 = 3.0\nn3 = 3.0\nt0 = math.sqrt(max(0, n2))\nt1 = t0 + t0\nanswer = t1**min(n0, 5)\nprint(answer)" + ], + "Output Answer": [ + "11.999999999999998" + ], + "split": "train" + }, + { + "Input": "hillary and eddy are climbing to the summit of mt . everest from a base camp 5,000 ft from the summit . when they depart for the summit at 06 : 00 , hillary climbs at a rate of 800 ft / hr with eddy lagging behind at a slower rate of 500 ft / hr . if hillary stops 1000 ft short of the summit and then descends at a rate of 1,000 ft / hr , at what time do hillary and eddy pass each other on her return trip ?", + "Output Program": [ + "n0 = 5000.0\nn1 = 6.0\nn2 = 0.0\nn3 = 800.0\nn4 = 500.0\nn5 = 1000.0\nn6 = 1000.0\nt0 = n0 - n5\nt1 = t0 / n3\nt2 = n1 + t1\nanswer = t2 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "how many kg of pure salt must be added to 100 kg of 10 % solution of salt and water to increase it to a 20 % solution ?", + "Output Program": [ + "n0 = 100.0\nn1 = 10.0\nn2 = 20.0\nt0 = n2 / n0\nt1 = n2 - n1\nt2 = 1.0 - t0\nanswer = t1 / t2\nprint(answer)" + ], + "Output Answer": [ + "12.5" + ], + "split": "train" + }, + { + "Input": "in a fuel station the service costs $ 2.30 per vehicle and every liter of fuel costs $ 0.70 . assuming that you fill up 4 mini - vans and 2 trucks , what will be the total cost , if a mini - van ' s tank is 65 liters and a truck ' s tank is 120 % bigger and they are all empty ?", + "Output Program": [ + "n0 = 2.3\nn1 = 0.7\nn2 = 4.0\nn3 = 2.0\nn4 = 65.0\nn5 = 120.0\nt0 = n2 + n3\nt1 = n4 * n5\nt2 = n2 * n4\nt3 = t1 / 100.0\nt4 = n1 * t2\nt5 = n0 * t0\nt6 = n4 + t3\nt7 = n3 * t6\nt8 = n1 * t7\nt9 = t8 + t4\nanswer = t9 + t5\nprint(answer)" + ], + "Output Answer": [ + "396" + ], + "split": "train" + }, + { + "Input": "find large number from below question the difference of two numbers is 1375 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder", + "Output Program": [ + "n0 = 1375.0\nn1 = 6.0\nn2 = 15.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nt2 = t0 / t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "1632" + ], + "split": "train" + }, + { + "Input": "find the value of 3.5 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ]", + "Output Program": [ + "n0 = 3.5\nn1 = 3.6\nn2 = 0.48\nn3 = 2.5\nn4 = 0.12\nn5 = 0.09\nn6 = 0.5\nt0 = n1 * n2\nt1 = n4 * n5\nt2 = n3 * t0\nt3 = n6 * t1\nt4 = t2 / t3\nanswer = n0 * t4\nprint(answer)" + ], + "Output Answer": [ + "2800.0000000000005" + ], + "split": "train" + }, + { + "Input": "dacid obtained 91 , 65 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?", + "Output Program": [ + "n0 = 91.0\nn1 = 65.0\nn2 = 82.0\nn3 = 67.0\nn4 = 85.0\nn5 = 100.0\nt0 = n0 + n1\nt1 = 10.0 / 2.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "78" + ], + "split": "train" + }, + { + "Input": "what sum of money put at c . i amounts in 2 years to rs . 8000 and in 3 years to rs . 9261 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 8000.0\nn2 = 3.0\nn3 = 9261.0\nt0 = n3 / n1\nt1 = t0 - 1.0\nt2 = t1 + 1.0\nt3 = t2**min(2.0, 5)\nanswer = n1 / t3\nprint(answer)" + ], + "Output Answer": [ + "5969.7231730930225" + ], + "split": "train" + }, + { + "Input": "calculate the value of y : 5 y ^ 2 - 8 y + 55 = 59", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 2.0\nn2 = 8.0\nn3 = 55.0\nn4 = 59.0\nt0 = n0 * n1\nt1 = n2**min(2.0, 5)\nt2 = n3 - n4\nt3 = n0 * t2\nt4 = t3 * 4.0\nt5 = t1 - t4\nt6 = math.sqrt(max(0, t5))\nt7 = n2 + t6\nanswer = t7 / t0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "the average ( arithmetic mean ) of all scores on a certain algebra test was 90 . if the average of the 8 male students \u2019 grades was 85 , and the average of the female students \u2019 grades was 92 , how many female students took the test ?", + "Output Program": [ + "n0 = 90.0\nn1 = 8.0\nn2 = 85.0\nn3 = 92.0\nt0 = n0 * n1\nt1 = n1 * n2\nt2 = n3 - n0\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "two trains of equal are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train passes the slower train in 72 sec . the length of each train is ?", + "Output Program": [ + "n0 = 46.0\nn1 = 36.0\nn2 = 72.0\nt0 = n0 - n1\nt1 = t0 * 1000.0\nt2 = t1 / 3600.0\nt3 = n2 * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "a student has to obtain 40 % of the total marks to pass . he got 150 marks and failed by 50 marks . the maximum marks are ?", + "Output Program": [ + "n0 = 40.0\nn1 = 150.0\nn2 = 50.0\nt0 = n1 + n2\nt1 = n0 / 100.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "train" + }, + { + "Input": "david has $ 1,800 at the beginning of his trip , after spending money , he still has exactly $ 800 less than he spent on the trip . how much money does john still have ?", + "Output Program": [ + "n0 = 1800.0\nn1 = 800.0\nt0 = n0 - n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "train" + }, + { + "Input": "kamal was 4 times as old as his son 8 years ago . after 8 years , kamal will be twice as old as his son . find out the present age of kamal .", + "Output Program": [ + "n0 = 4.0\nn1 = 8.0\nn2 = 8.0\nt0 = n0 * n0\nt1 = t0 / 2.0\nt2 = t1 * 4.0\nanswer = n1 + t2\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "find the least number of complete years in which a sum of money put out at 13 % compound interest will be more than double of itself ?", + "Output Program": [ + "import math\nn0 = 13.0\nt0 = n0 / 100.0\nt1 = math.log(max(1e-5, 2.0), 2)\nt2 = t0 + 1.0\nt3 = math.log(max(1e-5, t2), 2)\nt4 = t1 / t3\nt5 = t4 + 1.0\nanswer = math.floor(t5)\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "kiran has 85 currency notes in all , some of which were of rs . 100 denomination and the remaining of rs . 50 denomination . the total amount of all these currency notes was rs . 5000 . how much amount did she have in the denomination of rs . 50 ? a . b . c . none of these d . answer : option b explanation :", + "Output Program": [ + "n0 = 85.0\nn1 = 100.0\nn2 = 50.0\nn3 = 5000.0\nn4 = 50.0\nt0 = n0 * n2\nt1 = n3 - t0\nt2 = t1 / n2\nt3 = n0 - t2\nanswer = n2 * t3\nprint(answer)" + ], + "Output Answer": [ + "3500" + ], + "split": "train" + }, + { + "Input": "find the sum lend at c . i . at 5 p . c per annum will amount to rs . 500 in 2 years ?", + "Output Program": [ + "n0 = 5.0\nn1 = 500.0\nn2 = 2.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nt2 = t1**min(2.0, 5)\nanswer = n1 / t2\nprint(answer)" + ], + "Output Answer": [ + "453.51473922902494" + ], + "split": "train" + }, + { + "Input": "x varies inversely as square of y . given that y = 3 for x = 1 . the value of x for y = 4 will be equal to :", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 4.0\nt0 = n0**min(2.0, 5)\nt1 = n2**min(2.0, 5)\nt2 = n1 * t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.5625" + ], + "split": "train" + }, + { + "Input": "145 liters of a mixture of milk and water contains in the ratio 3 : 2 . how much water should now be added so that the ratio of milk and water becomes 3 : 4 ?", + "Output Program": [ + "n0 = 145.0\nn1 = 3.0\nn2 = 2.0\nn3 = 3.0\nn4 = 4.0\nt0 = n1 + n2\nt1 = n0 / t0\nanswer = n2 * t1\nprint(answer)" + ], + "Output Answer": [ + "58" + ], + "split": "train" + }, + { + "Input": "the overall age of x and y is 12 year greater than the overall age of y and z . z is how many decades younger that x ?", + "Output Program": [ + "n0 = 12.0\n\nanswer = n0 / 1.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "a certain telephone company company charges 3.10 cents for the first 1 / 5 of a minute plus 0.40 cents for each additional 1 / 5 of a minute . what would this company charge for a talk time of 8 minutes long ?", + "Output Program": [ + "n0 = 3.1\nn1 = 1.0\nn2 = 5.0\nn3 = 0.4\nn4 = 1.0\nn5 = 5.0\nn6 = 8.0\nt0 = n2 - n1\nt1 = n6 - n1\nt2 = n3 * t0\nt3 = n3 * t1\nt4 = n2 * t3\nt5 = t2 + t4\nanswer = n0 + t5\nprint(answer)" + ], + "Output Answer": [ + "18.700000000000003" + ], + "split": "train" + }, + { + "Input": "if the function q is defined by the formula q = 5 w / ( 4 vf ( z ^ 2 ) ) , by what factor will q be multiplied if w is quadrupled , f is doubled , and z is tripled ?", + "Output Program": [ + "n0 = 5.0\nn1 = 4.0\nn2 = 2.0\nt0 = 3.0**min(n2, 5)\nt1 = n2 * t0\nanswer = n1 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.2222222222222222" + ], + "split": "train" + }, + { + "Input": "5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 90 only . men \u2019 s wages are ?", + "Output Program": [ + "n0 = 5.0\nn1 = 8.0\nn2 = 90.0\nt0 = n0 * 3.0\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "what should be the least number to be added to the 4499 number to make it divisible by 9 ?", + "Output Program": [ + "n0 = 4499.0\nn1 = 9.0\nt0 = n0 % n1\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "we define that k @ j is the product of j number from k in increasing order for positive integers k , j . for example , 6 @ 4 = 6 * 7 * 8 * 9 . if a = 2020 and b = 2120 , what is the value e of the ratio a / b ?", + "Output Program": [ + "n0 = 6.0\nn1 = 4.0\nn2 = 6.0\nn3 = 7.0\nn4 = 8.0\nn5 = 9.0\nn6 = 2020.0\nn7 = 2120.0\nt0 = n6 / n6\nt1 = t0 + t0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "jane started baby - sitting when she was 20 years old . whenever she baby - sat for a child , that child was no more than half her age at the time . jane is currently 32 years old , and she stopped baby - sitting 10 years ago . what is the current age of the oldest person for whom jane could have baby - sat ?", + "Output Program": [ + "n0 = 20.0\nn1 = 32.0\nn2 = 10.0\nt0 = n0 / 2.0\nt1 = n1 - n0\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "if integer k is equal to the sum of all even multiples of 25 between 295 and 615 , what is the greatest prime factor of k ?", + "Output Program": [ + "import math\nn0 = 25.0\nn1 = 295.0\nn2 = 615.0\nt0 = n2 / n0\nt1 = n1 / n0\nt2 = math.floor(t0)\nt3 = math.floor(t1)\nt4 = n0 * t2\nt5 = n0 * t3\nt6 = t4 - t5\nt7 = t6 / n0\nt8 = t7 + 1.0\nanswer = t8 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "50 % of major airline companies equip their planes with wireless internet access . 70 % of major airlines offer passengers free on - board snacks . what is the greatest possible percentage of major airline companies that offer both wireless internet and free on - board snacks ?", + "Output Program": [ + "n0 = 50.0\nn1 = 70.0\n\nanswer = n0 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "a car travels uphill at 30 km / hr and downhill at 40 km / hr . it goes 100 km uphill and 50 km downhill . find the average speed of the car ?", + "Output Program": [ + "n0 = 30.0\nn1 = 40.0\nn2 = 100.0\nn3 = 50.0\nt0 = n2 + n3\nt1 = n2 / n0\nt2 = n3 / n1\nt3 = t1 + t2\nanswer = t0 / t3\nprint(answer)" + ], + "Output Answer": [ + "32.72727272727272" + ], + "split": "train" + }, + { + "Input": "the price of a bushel of corn is currently $ 3.20 , and the price of a peck of wheat is $ 7.80 . the price of corn is increasing at a constant rate of 5 x cents per day while the price of wheat is decreasing at a constant rate of x ( 2 ^ 1 / 2 ) - x cents per day . what is the approximate price when a bushel of corn costs the same amount as a peck of wheat ?", + "Output Program": [ + "import math\nn0 = 3.2\nn1 = 7.8\nn2 = 5.0\nn3 = 2.0\nn4 = 1.0\nn5 = 2.0\nt0 = math.sqrt(max(0, n3))\nt1 = n1 - n0\nt2 = t0 - n4\nt3 = n2 + t2\nt4 = t1 / t3\nt5 = n2 * t4\nanswer = n0 + t5\nprint(answer)" + ], + "Output Answer": [ + "7.448077718958487" + ], + "split": "train" + }, + { + "Input": "for what value of \u00e2 \u20ac \u0153 k \u00e2 \u20ac \u009d will the equation ( 2 kx 2 + 7 kx + 2 ) = 0 have equal roots ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 7.0\nn3 = 2.0\nn4 = 0.0\nt0 = n0 + n0\nt1 = n2**min(n0, 5)\nt2 = n0**min(t0, 5)\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.32653061224489793" + ], + "split": "train" + }, + { + "Input": "in how many ways can 5 different rings be worn in 4 particular fingers ? ( some fingers may get more than one ring and some may get no rings . ) can somebody explain ?", + "Output Program": [ + "n0 = 5.0\nn1 = 4.0\nt0 = 2.0 + 4.0\nt1 = n0 * n1\nt2 = t0 + 1.0\nt3 = t0 * t1\nt4 = t2 + 1.0\nt5 = t2 * t3\nanswer = t4 * t5\nprint(answer)" + ], + "Output Answer": [ + "6720" + ], + "split": "train" + }, + { + "Input": "a box contains 6 pairs of shoes ( 12 shoes in total ) . if two shoes are selected at random , what it is the probability that they are matching shoes ?", + "Output Program": [ + "n0 = 6.0\nn1 = 12.0\nt0 = n1 - 1.0\nanswer = 1.0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.09090909090909091" + ], + "split": "train" + }, + { + "Input": "a number x is 11 times another number y . the percentage that y is less than x is", + "Output Program": [ + "n0 = 11.0\nt0 = n0 - 1.0\nt1 = t0 / n0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "90.9090909090909" + ], + "split": "train" + }, + { + "Input": "ravi ' s 4 days average income is 1025.68 . but in a form he should write his average income as the greatest positive even integer less than or equal to his 4 days average income . what is the difference between his real average and form filling average ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 1025.68\nn2 = 4.0\nt0 = math.floor(n1)\nt1 = t0 - 1.0\nanswer = n1 - t1\nprint(answer)" + ], + "Output Answer": [ + "1.6800000000000637" + ], + "split": "train" + }, + { + "Input": "roy was suffering from severe headaches . he went to see his doctor and the doctor gave him 5 tablets asking him to take one tablet every 15 minutes . how much time will it take roy to consume all the 5 tablets ?", + "Output Program": [ + "n0 = 5.0\nn1 = 15.0\nn2 = 5.0\nt0 = n0 * n1\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "if one root of the equation 2 x ^ 2 + 3 x \u2013 k = 0 is 7 , what is the value of k ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 3.0\nn3 = 0.0\nn4 = 7.0\nt0 = n2 * n4\nt1 = n4**min(2.0, 5)\nt2 = n0 * t1\nanswer = t2 + t0\nprint(answer)" + ], + "Output Answer": [ + "119" + ], + "split": "train" + }, + { + "Input": "a certain clock marks every hour by striking a number of times equal to the hour , and the time required for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stroke and the end of the last stroke is 11 seconds . at 12 : 00 , how many seconds elapse between the beginning of the first stroke and the end of the last stroke ?", + "Output Program": [ + "n0 = 6.0\nn1 = 0.0\nn2 = 11.0\nn3 = 12.0\nn4 = 0.0\nt0 = 1.0 + 4.0\nt1 = n0 + t0\nt2 = n3 + t1\nt3 = n2 / t1\nanswer = t2 * t3\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "if a - b = 6 and a ^ 2 + b ^ 2 = 100 , find the value of ab", + "Output Program": [ + "import math\nn0 = 6.0\nn1 = 2.0\nn2 = 2.0\nn3 = 100.0\nt0 = math.sqrt(max(0, n3))\nt1 = t0 - n0\nt2 = t1 / n1\nt3 = n0 + t2\nt4 = t3 * t2\nanswer = n1 * t4\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "the average amount with a group of 7 numbers is rs . 20 . if the newly joined member has rs . 56 with him , what was the average amount with the group before his joining the group ?", + "Output Program": [ + "n0 = 7.0\nn1 = 20.0\nn2 = 56.0\nt0 = n0 * n1\nt1 = n0 - 1.0\nt2 = t0 - n2\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "in how many ways can a teacher write an answer key for a mini - quiz that contains 3 true - false questions followed by 2 multiples - choice questions with 4 answer choices each , if the correct answers to all true - false questions can not be the same ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 4.0\nt0 = 4.0 * 4.0\nt1 = n1 * n1\nt2 = t1 * 2.0\nt3 = t2 - n1\nanswer = t0 * t3\nprint(answer)" + ], + "Output Answer": [ + "96" + ], + "split": "train" + }, + { + "Input": "there are 3 departments having students 72 , 5824 . in an exam they have to be seated in rooms such that each room has equal number of students and each room has students of one type only ( no mixing of departments ) . find the minimum number of rooms required ?", + "Output Program": [ + "n0 = 3.0\nn1 = 72.0\nn2 = 5824.0\nt0 = n1 / 2.0\nt1 = t0 + 12.0\nt2 = t1 + 10.0\nt3 = t2 / 2.0\nanswer = t1 + t3\nprint(answer)" + ], + "Output Answer": [ + "77" + ], + "split": "train" + }, + { + "Input": "the price of a cycle is reduced by 25 per cent . the new price is reduced by a further 70 per cent . the two reductions together are equal to a single reduction of", + "Output Program": [ + "n0 = 25.0\nn1 = 70.0\nt0 = 100.0 - n1\nt1 = 100.0 - n0\nt2 = t0 / 100.0\nt3 = t2 * t1\nanswer = 100.0 - t3\nprint(answer)" + ], + "Output Answer": [ + "77.5" + ], + "split": "train" + }, + { + "Input": "what is the smallest number which when diminished by 8 , is divisible by 9 , 6 , 12 and 18 ?", + "Output Program": [ + "import scipy\nn0 = 8.0\nn1 = 9.0\nn2 = 6.0\nn3 = 12.0\nn4 = 18.0\nt0 = scipy.lcm(int(n1), int(n2))\nt1 = scipy.lcm(int(n3), int(n4))\nt2 = scipy.lcm(int(t0), int(t1))\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "44" + ], + "split": "train" + }, + { + "Input": "on a partly cloudy day , derek decides to walk back from work . when it is sunny , he walks at a speed of s miles / hr ( s is an integer ) and when it gets rain cloud , he increases his speed to ( s + 1 ) miles / hr . if his average speed for the entire distance is 2.8 miles / hr , what fraction of the total distance did he cover while the sun was shining on him ?", + "Output Program": [ + "import scipy\nn0 = 1.0\nn1 = 2.8\nt0 = scipy.lcm(int(2.0), int(3.0))\nt1 = t0 / n1\nanswer = t1 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "0.1428571428571428" + ], + "split": "train" + }, + { + "Input": "bob invested $ 2000 in fund a and $ 1000 in fund b . over the next two years , the money in fund a earned a total interest of 12 percent for the two years combined and the money in fund b earned 30 percent annual interest compounded annually . two years after bob made these investments . bob ' s investment in fund a was worth how much more than his investment in fund b ?", + "Output Program": [ + "n0 = 2000.0\nn1 = 1000.0\nn2 = 12.0\nn3 = 30.0\nt0 = n2 / 100.0\nt1 = n3 / 100.0\nt2 = t0 + 1.0\nt3 = t1 + 1.0\nt4 = n0 * t2\nt5 = t3**min(2.0, 5)\nt6 = n1 * t5\nanswer = t4 - t6\nprint(answer)" + ], + "Output Answer": [ + "549.9999999999998" + ], + "split": "train" + }, + { + "Input": "a salt manufacturing company produced a total of 2500 tonnes of salt in january of a particular year . starting from february its production increased by 100 tonnes every month over the previous months until the end of the year . find its ave 66 rage daily production for that year ?", + "Output Program": [ + "n0 = 2500.0\nn1 = 100.0\nn2 = 66.0\nt0 = 2.0 + 3.0\nt1 = n0 * 2.0\nt2 = n1 * 3.0\nt3 = 2.0 * 3.0\nt4 = 12.0 - 1.0\nt5 = n1 * t4\nt6 = t3 * 10.0\nt7 = t1 + t5\nt8 = t2 + t6\nt9 = t8 + t0\nt10 = t7 * 12.0\nt11 = t10 / 2.0\nanswer = t11 / t9\nprint(answer)" + ], + "Output Answer": [ + "100.27397260273973" + ], + "split": "train" + }, + { + "Input": "the proportion of copper and zinc in the brass is 13 : 7 . how much zinc will there be in 100 kg of brass ?", + "Output Program": [ + "n0 = 13.0\nn1 = 7.0\nn2 = 100.0\nt0 = n0 + n1\nt1 = n1 / t0\nanswer = n2 * t1\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "subtracting 2 % of a from a is equivalent to multiplying a by how much ?", + "Output Program": [ + "n0 = 2.0\nt0 = 100.0 - n0\nanswer = t0 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "0.98" + ], + "split": "train" + }, + { + "Input": "jerry bought a bottle of perfume for a gift for his wife . the perfume cost $ 92 before tax . if the total price including tax was $ 98.90 , find the tax rate", + "Output Program": [ + "n0 = 92.0\nn1 = 98.9\nt0 = n1 / n0\nt1 = t0 - 1.0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "7.499999999999996" + ], + "split": "train" + }, + { + "Input": "a 7 - digit number comprises of only 2 ' s and 3 ' s . how many of these are multiples of 12 ?", + "Output Program": [ + "import math\nn0 = 7.0\nn1 = 2.0\nn2 = 3.0\nn3 = 12.0\nt0 = n1 + n2\nt1 = math.factorial(min(15, int(n2)))\nt2 = math.factorial(min(15, int(n1)))\nt3 = math.factorial(min(15, int(t0)))\nt4 = t1 * t2\nt5 = t3 / t4\nanswer = t5 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "a big container is 30 % full with water . if 9 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container ?", + "Output Program": [ + "n0 = 30.0\nn1 = 9.0\nn2 = 3.0\nn3 = 4.0\nt0 = n2 / n3\nt1 = n0 / 100.0\nt2 = t0 - t1\nanswer = n1 / t2\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "a number is doubled and 15 is added . if resultant is trebled , it becomes 75 . what is that number", + "Output Program": [ + "n0 = 15.0\nn1 = 75.0\nt0 = n0 * 3.0\nt1 = 2.0 * 3.0\nt2 = n1 - t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "if 1 + 2 + 3 + . . . + n = n ( n + 1 ) , then 3 ( 1 + 3 + 5 + . . . . + 69 ) = ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 3.0\nn3 = 1.0\nn4 = 3.0\nn5 = 1.0\nn6 = 3.0\nn7 = 5.0\nn8 = 69.0\nt0 = n8 + 1.0\nt1 = n8 - 1.0\nt2 = t1 / 2.0\nt3 = n8 * t0\nt4 = t2 + 1.0\nt5 = t3 / 2.0\nt6 = t4 * t2\nt7 = t5 - t6\nanswer = t7 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "3675" + ], + "split": "train" + }, + { + "Input": "if the average ( arithmetic mean ) of 8 consecutive odd integers is 414 , then the least of these integers is", + "Output Program": [ + "n0 = 8.0\nn1 = 414.0\nt0 = n1 - n0\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "407" + ], + "split": "train" + }, + { + "Input": "a certain car uses one gallon of gasoline every 38 miles when it travels on highway , and one gallon of gasoline every 20 miles when it travels in the city . when a car travels 4 miles on highway and 4 additional miles in the city , it uses what percent more gasoline than if it travels 8 miles on the highway ?", + "Output Program": [ + "n0 = 38.0\nn1 = 20.0\nn2 = 4.0\nn3 = 4.0\nn4 = 8.0\nt0 = 1.0 / n1\nt1 = 1.0 / n0\nt2 = n2 * t0\nt3 = n2 * t1\nt4 = n4 * t1\nt5 = t2 + t3\nt6 = t5 - t4\nt7 = t6 / t4\nanswer = t7 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "45.000000000000014" + ], + "split": "train" + }, + { + "Input": "6 wires are by average 80 cm long each . if the average length of one third of the wires is 70 cm , what is the average of the other wires ?", + "Output Program": [ + "n0 = 6.0\nn1 = 80.0\nn2 = 70.0\nt0 = n0 * n1\nt1 = n2 * 2.0\nt2 = t0 - t1\nanswer = t2 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "85" + ], + "split": "train" + }, + { + "Input": "when 15 is divided by integer u , the remainder is 4 . for how many values of u is this be true ?", + "Output Program": [ + "n0 = 15.0\nn1 = 4.0\nt0 = n0 - n1\nt1 = n1 + t0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "if p # q denotes the least common multiple of p and q , then w = ( ( 12 # 16 ) # ( 18 # 24 ) ) = ?", + "Output Program": [ + "n0 = 12.0\nn1 = 16.0\nn2 = 18.0\nn3 = 24.0\nt0 = n2 * n3\nt1 = n0 * n1\nt2 = t0 - t1\nt3 = t2 / 2.0\nanswer = n3 + t3\nprint(answer)" + ], + "Output Answer": [ + "144" + ], + "split": "train" + }, + { + "Input": "a car travels from point a to point b . the average speed of the car is 60 km / hr and it travels the first half of the trip at a speed of 75 km / hr . what is the speed of the car in the second half of the trip ?", + "Output Program": [ + "n0 = 60.0\nn1 = 75.0\nt0 = n0 / 10.0\nt1 = n0 * n1\nt2 = n1 - n0\nt3 = n0 * t2\nt4 = t1 / t3\nt5 = n0 * t4\nanswer = t5 / t0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "for any number s , s * is defined as the greatest positive even integer less than or equal to s . what is the value of 5.2 \u2013 5.2 * ?", + "Output Program": [ + "n0 = 5.2\nn1 = 5.2\n\nanswer = n0 - 4.0\nprint(answer)" + ], + "Output Answer": [ + "1.2000000000000002" + ], + "split": "train" + }, + { + "Input": "the present ages of a , b & c are in the ratio of 5 : 7 : 8 . 7 years ago , the sum oftheir ages was 59 . what is the present age of eldest one ?", + "Output Program": [ + "n0 = 5.0\nn1 = 7.0\nn2 = 8.0\nn3 = 7.0\nn4 = 59.0\nt0 = n0 + n1\nt1 = n1 * 3.0\nt2 = n4 + t1\nt3 = n2 + t0\nt4 = t2 / t3\nanswer = n2 * t4\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "if the average ( arithmetic mean ) of 16 consecutive odd integers is 414 , then the least of these integers is", + "Output Program": [ + "n0 = 16.0\nn1 = 414.0\nt0 = n1 - n0\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "399" + ], + "split": "train" + }, + { + "Input": "real - estate salesman z is selling a house at a 30 percent discount from its retail price . real - estate salesman x vows to match this price , and then offers an additional 15 percent discount . real - estate salesman y decides to average the prices of salesmen z and x , then offer an additional 40 percent discount . salesman y ' s final price is what fraction of salesman x ' s final price ?", + "Output Program": [ + "n0 = 30.0\nn1 = 15.0\nn2 = 40.0\nt0 = 100.0 - n1\nt1 = 100.0 - n0\nt2 = 100.0 - n2\nt3 = t0 / 100.0\nt4 = t3 * t1\nt5 = t4 + t1\nt6 = t5 / 2.0\nt7 = t6 * t2\nt8 = t7 / 100.0\nt9 = t8 / t4\nanswer = t9 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "6.529411764705882" + ], + "split": "train" + }, + { + "Input": "the average weight of 30 boys sitting in a bus had some value . a new person added to them whose weight was 40 kg only . due to his arrival , the average weight of all the boys decreased by 2 kg . find the average weight of first 30 boys ?", + "Output Program": [ + "n0 = 30.0\nn1 = 40.0\nn2 = 2.0\nn3 = 30.0\nt0 = n0 + n0\nt1 = n1 + t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "102" + ], + "split": "train" + }, + { + "Input": "the original price of a suit is $ 200 . the price increased 25 % , and after this increase , the store published a 25 % off coupon for a one - day sale . given that the consumers who used the coupon on sale day were getting 25 % off the increased price , how much did these consumers pay for the suit ?", + "Output Program": [ + "n0 = 200.0\nn1 = 25.0\nn2 = 25.0\nn3 = 25.0\nt0 = n0 * n1\nt1 = t0 / 100.0\nt2 = n0 + t1\nt3 = n1 * t2\nt4 = t3 / 100.0\nanswer = t2 - t4\nprint(answer)" + ], + "Output Answer": [ + "187.5" + ], + "split": "train" + }, + { + "Input": "if x / 4 - x - 3 / 6 = 1 , then find the value of x .", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 6.0\nn3 = 1.0\nt0 = n1 / n2\nt1 = n3 + t0\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "bill made a profit of 10 % by selling a product . if he had purchased that product for 10 % less and sold it at a profit of 30 % , he would have received $ 42 more . what was his original selling price ?", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 30.0\nn3 = 42.0\nt0 = n0 / 100.0\nt1 = n2 / 100.0\nt2 = t0 + 1.0\nt3 = t1 + 1.0\nt4 = 1.0 - t0\nt5 = t3 * t4\nt6 = t5 - t2\nt7 = n3 / t6\nanswer = t2 * t7\nprint(answer)" + ], + "Output Answer": [ + "659.9999999999994" + ], + "split": "train" + }, + { + "Input": "3 numbers are in the ratio 4 : 5 : 6 and their average is 20 . the largest number is :", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 5.0\nn3 = 6.0\nn4 = 20.0\nt0 = n1 + n2\nt1 = n3 + t0\nt2 = t1 / n0\nt3 = n4 / t2\nanswer = n3 * t3\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "a father told his son ` ` i was as old as you are at present , at the time of your birth ' ' . if the father is 38 years old now , then what was the son ' s age 5 years ago in years ?", + "Output Program": [ + "n0 = 38.0\nn1 = 5.0\nt0 = n0 / 2.0\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "last year , for every 100 million vehicles that traveled on a certain highway , 96 vehicles were involved in accidents . if 3 billion vehicles traveled on the highway last year , how many of those vehicles were involved in accidents ? ( 1 billion = 1,000 , 000,000 )", + "Output Program": [ + "n0 = 100.0\nn1 = 96.0\nn2 = 3.0\nn3 = 1.0\nn4 = 1000.0\nn5 = 0.0\nt0 = n2 * 10.0\nanswer = n1 * t0\nprint(answer)" + ], + "Output Answer": [ + "2880" + ], + "split": "train" + }, + { + "Input": "if n = 2 ^ 0.25 and n ^ b = 16 , b must equal", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 0.25\nn2 = 16.0\nt0 = math.log(max(1e-5, n2), 2)\nt1 = n0**min(n1, 5)\nt2 = math.log(max(1e-5, t1), 2)\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "16.000000000000004" + ], + "split": "train" + }, + { + "Input": "a man distributed rs . 100 equally among his friends . if there had been 5 more friends , each would have received one rupee less . how many friends had he ?", + "Output Program": [ + "n0 = 100.0\nn1 = 5.0\nt0 = n0 / n1\nanswer = n1 + t0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "the average weight of a class of 24 students is 35 kg . if the weight of the teacher be included , the average rises by 400 g . the weight of the teacher is", + "Output Program": [ + "n0 = 24.0\nn1 = 35.0\nn2 = 400.0\nt0 = n0 + 1.0\nt1 = n2 / 1000.0\nt2 = n0 * n1\nt3 = n1 + t1\nt4 = t3 * t0\nanswer = t4 - t2\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "the average weight of a group of boys is 35 kg . after a boy of weight 40 kg joins the group , the average weight of the group goes up by 1 kg . find the number of boys in the group originally ?", + "Output Program": [ + "n0 = 35.0\nn1 = 40.0\nn2 = 1.0\nt0 = n0 + n2\nt1 = n1 - t0\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "if there are 200 questions in a 3 hr examination . among these questions are 20 type a problems , which requires twice as much as time be spent than the rest of the type b problems . how many minutes should be spent on type a problems ?", + "Output Program": [ + "n0 = 200.0\nn1 = 3.0\nn2 = 20.0\nt0 = n1 * 60.0\nt1 = n2 * 2.0\nt2 = n0 - n2\nt3 = t1 + t2\nt4 = t0 / t3\nt5 = t4 * 2.0\nanswer = n2 * t5\nprint(answer)" + ], + "Output Answer": [ + "32.72727272727273" + ], + "split": "train" + }, + { + "Input": "a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 36 percent of the distribution lies within one standard deviation d of the mean , what percent of the distribution is less than m + d ?", + "Output Program": [ + "n0 = 36.0\nt0 = 100.0 - n0\nt1 = t0 / 2.0\nanswer = 100.0 - t1\nprint(answer)" + ], + "Output Answer": [ + "68" + ], + "split": "train" + }, + { + "Input": "in a certain diving competition , 5 judges score each dive on a scale from 1 to 10 . the point value of the dive is obtained by dropping the highest score and the lowest score and multiplying the sum of the remaining scores by the degree of difficulty . if a dive with a degree of difficulty of 3.2 received scores of 7.5 , 8.8 , 9.0 , 6.0 , and 8.5 , what was the point value of the dive ?", + "Output Program": [ + "n0 = 5.0\nn1 = 1.0\nn2 = 10.0\nn3 = 3.2\nn4 = 7.5\nn5 = 8.8\nn6 = 9.0\nn7 = 6.0\nn8 = 8.5\nt0 = n4 + n5\nt1 = n8 + t0\nanswer = n3 * t1\nprint(answer)" + ], + "Output Answer": [ + "79.36000000000001" + ], + "split": "train" + }, + { + "Input": "what is the 100 th digit of ( 3 ! * 5 ! + 4 ! * 3 ! ) / 2 ?", + "Output Program": [ + "import math\nn0 = 100.0\nn1 = 3.0\nn2 = 5.0\nn3 = 4.0\nn4 = 3.0\nn5 = 2.0\nt0 = math.factorial(min(15, int(n1)))\nt1 = math.factorial(min(15, int(n2)))\nt2 = math.factorial(min(15, int(n3)))\nt3 = t0 * t1\nt4 = t2 * t0\nt5 = t3 + t4\nt6 = t5 / n5\nt7 = t6 / n0\nanswer = math.floor(t7)\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "if p and t are positive integers such that p > t > 1 , what is the remainder when 92 p \u00d7 5 p + t + 11 t \u00d7 6 pt is divided by 10 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 92.0\nn2 = 5.0\nn3 = 11.0\nn4 = 6.0\nn5 = 10.0\n\nanswer = n4 - n2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "there are 5 chess amateurs playing in villa ' s chess club tournament . if each chess amateur plays with exactly 4 other amateurs , what is the total number of chess games possible to be played in the tournament ?", + "Output Program": [ + "n0 = 5.0\nn1 = 4.0\nt0 = n0 * n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "in a urban village of india named ` ` owlna ' ' , 75 % people have refrigerator , 90 % people have television , 85 % people got computers and 75 % got air - conditionor . how many people ( minimum ) got all these luxury .", + "Output Program": [ + "n0 = 75.0\nn1 = 90.0\nn2 = 85.0\nn3 = 75.0\nt0 = 100.0 - n0\nt1 = 100.0 - n1\nt2 = 100.0 - n2\nt3 = 100.0 - n3\nt4 = t0 + t1\nt5 = t4 + t2\nt6 = t5 + t3\nanswer = 100.0 - t6\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "a bowl of nuts is prepared for a party . brand p mixed nuts are 20 % almonds and brand q ' s deluxe nuts are 25 % almonds . if a bowl contains a total of 67 ounces of nuts , representing a mixture of both brands , and 15 ounces of the mixture are almonds , how many ounces of brand q ' s deluxe mixed nuts are used ?", + "Output Program": [ + "n0 = 20.0\nn1 = 25.0\nn2 = 67.0\nn3 = 15.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = n2 * t0\nt3 = t1 - t0\nt4 = n3 - t2\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "how many odd 3 - digit integers smaller than 500 are there such that all their digits are different ?", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 500.0\nt0 = 10.0 - 1.0\nt1 = n0 - 1.0\nt2 = n1 - 100.0\nt3 = t2 / 100.0\nt4 = math.factorial(min(15, int(t0)))\nt5 = t0 - t1\nt6 = math.factorial(min(15, int(t5)))\nt7 = t4 / t6\nt8 = t7 * t3\nanswer = t8 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "144" + ], + "split": "train" + }, + { + "Input": "if the price of a tv is first decreased by 20 % and then increased by 50 % , then the net change in the price will be :", + "Output Program": [ + "n0 = 20.0\nn1 = 50.0\nt0 = n1 + 100.0\nt1 = 100.0 - n0\nt2 = t0 * t1\nt3 = t2 / 100.0\nanswer = t3 - 100.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "if x is equal to the sum of the integers from 10 to 20 , inclusive , and y is the number of even integers from 10 to 20 , inclusive , what is the value of x + y ?", + "Output Program": [ + "n0 = 10.0\nn1 = 20.0\nn2 = 10.0\nn3 = 20.0\nt0 = n0 + n1\nt1 = n1 - n0\nt2 = t1 + 1.0\nt3 = t1 / 2.0\nt4 = t0 / 2.0\nt5 = t3 + 1.0\nt6 = t2 * t4\nanswer = t5 + t6\nprint(answer)" + ], + "Output Answer": [ + "171" + ], + "split": "train" + }, + { + "Input": "find the least number which when divided by 33 and 8 leaves a remainder of 2 in each case .", + "Output Program": [ + "import scipy\nn0 = 33.0\nn1 = 8.0\nn2 = 2.0\nt0 = scipy.lcm(int(n0), int(n1))\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "266" + ], + "split": "train" + }, + { + "Input": "if greg buys 3 shirts , 4 trousers and 2 ties , the total cost is $ 90 . if greg buys 7 shirts , 2 trousers and 2 ties , the total cost is $ 50 . how much will it cost him to buy 3 trousers , 5 shirts and 2 ties ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 2.0\nn3 = 90.0\nn4 = 7.0\nn5 = 2.0\nn6 = 2.0\nn7 = 50.0\nn8 = 3.0\nn9 = 5.0\nn10 = 2.0\nt0 = n3 + n7\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "train" + }, + { + "Input": "a sum of money is sufficient to pay a ' s wages for 21 days and b ' s wages for 28 days . the same money is sufficient to pay the wages of both for ?", + "Output Program": [ + "n0 = 21.0\nn1 = 28.0\nt0 = 1.0 / n0\nt1 = 1.0 / n1\nt2 = t0 + t1\nanswer = 1.0 / t2\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "in a certain school , 20 % of students are below 8 years of age . the number of students above 8 years of age is 2 / 3 of the number of students of 8 years of age which is 24 . what is the total number of students in the school ?", + "Output Program": [ + "n0 = 20.0\nn1 = 8.0\nn2 = 8.0\nn3 = 2.0\nn4 = 3.0\nn5 = 8.0\nn6 = 24.0\nt0 = n3 / n4\nt1 = n0 / 100.0\nt2 = n6 * t0\nt3 = 1.0 - t1\nt4 = n6 + t2\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "if x + ( 1 / x ) = 5 , what is the value of r = x ^ 2 + ( 1 / x ) ^ 2 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 2.0\nn3 = 1.0\nn4 = 2.0\nt0 = n1**min(n2, 5)\nanswer = t0 - n2\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "the average of marks obtained by 120 boys was 39 . if the average of marks of passed boys was 39 and that of failed boys was 15 , the number of boys who passed the examination is ?", + "Output Program": [ + "n0 = 120.0\nn1 = 39.0\nn2 = 39.0\nn3 = 15.0\nt0 = n0 * n1\nt1 = n0 * n3\nt2 = n2 - n3\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 64000 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 8.0\nn2 = 64000.0\nt0 = n0 / n1\nt1 = n2 * t0\nt2 = n2 + t1\nt3 = t2 * t0\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "81000" + ], + "split": "train" + }, + { + "Input": "a company wants to spend equal amounts of money for the purchase of two types of computer printers costing $ 375 and $ 150 per unit , respectively . what is the fewest number of computer printers that the company can purchase ?", + "Output Program": [ + "import scipy\nn0 = 375.0\nn1 = 150.0\nt0 = scipy.lcm(int(n0), int(n1))\nt1 = t0 / n0\nt2 = t0 / n1\nanswer = t1 + t2\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "a grocer is storing soap boxes in cartons that measure 30 inches by 42 inches by 60 inches . if the measurement of each soap box is 7 inches by 6 inches by 5 inches , then what is the maximum number of soap boxes that can be placed in each carton ?", + "Output Program": [ + "n0 = 30.0\nn1 = 42.0\nn2 = 60.0\nn3 = 7.0\nn4 = 6.0\nn5 = 5.0\nt0 = n0 * n1\nt1 = n3 * n4\nt2 = n2 * t0\nt3 = n5 * t1\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "360" + ], + "split": "train" + }, + { + "Input": "if ( a - b - c + d = 13 ) and ( a + b - c - d = 5 ) , what is the value of ( b - d ) ^ 2 ?", + "Output Program": [ + "n0 = 13.0\nn1 = 5.0\nn2 = 2.0\nt0 = n0 + n1\nt1 = t0 / 2.0\nt2 = n1 - t1\nanswer = t2**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "find the value of 3 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ]", + "Output Program": [ + "n0 = 3.0\nn1 = 3.6\nn2 = 0.48\nn3 = 2.5\nn4 = 0.12\nn5 = 0.09\nn6 = 0.5\nt0 = n1 * n2\nt1 = n4 * n5\nt2 = n3 * t0\nt3 = n6 * t1\nt4 = t2 / t3\nanswer = n0 * t4\nprint(answer)" + ], + "Output Answer": [ + "2400.0000000000005" + ], + "split": "train" + }, + { + "Input": "jim is now twice as old as fred , who is 9 years older than sam . 6 years ago , jim was 5 times as old as sam . how old is jim now ?", + "Output Program": [ + "n0 = 9.0\nn1 = 6.0\nn2 = 5.0\nt0 = n0 * 2.0\nt1 = n1 * n2\nt2 = n0 - n1\nt3 = t1 - n1\nt4 = t0 + t3\nt5 = t4 / t2\nt6 = n0 + t5\nanswer = t6 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "46" + ], + "split": "train" + }, + { + "Input": "the price of a bushel of corn is currently $ 3.20 , and the price of a peck of wheat is $ 10.80 . the price of corn is increasing at a constant rate of 5 x cents per day while the price of wheat is decreasing at a constant rate of x ( 2 ^ 1 / 2 ) - x cents per day . what is the approximate price when a bushel of corn costs the same amount as a peck of wheat ?", + "Output Program": [ + "import math\nn0 = 3.2\nn1 = 10.8\nn2 = 5.0\nn3 = 2.0\nn4 = 1.0\nn5 = 2.0\nt0 = math.sqrt(max(0, 2.0))\nt1 = n1 - n0\nt2 = t0 - n4\nt3 = n2 + t2\nt4 = t1 / t3\nt5 = n2 * t4\nanswer = n0 + t5\nprint(answer)" + ], + "Output Answer": [ + "10.218563187844456" + ], + "split": "train" + }, + { + "Input": "on dividing 172 by a number , the quotient is 10 and the remainder is 2 . find the divisor .", + "Output Program": [ + "import math\nn0 = 172.0\nn1 = 10.0\nn2 = 2.0\nt0 = n0 / n1\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "a big container is 35 % full with water . if 48 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container in liters ?", + "Output Program": [ + "n0 = 35.0\nn1 = 48.0\nn2 = 3.0\nn3 = 4.0\nt0 = n2 / n3\nt1 = n0 / 100.0\nt2 = t0 - t1\nanswer = n1 / t2\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "in a box , there are 8 orange , 7 black and 6 white balls . if one ball is picked up randomly . what is the probability that it is neither orange nor white ?", + "Output Program": [ + "n0 = 8.0\nn1 = 7.0\nn2 = 6.0\nt0 = n0 + n1\nt1 = n2 + t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.38095238095238093" + ], + "split": "train" + }, + { + "Input": "suraj has a certain average of runs for 12 innings . in the 13 th innings he scores 96 runs thereby increasing his average by 5 runs . what is his average after the 13 th innings ?", + "Output Program": [ + "n0 = 12.0\nn1 = 13.0\nn2 = 96.0\nn3 = 5.0\nn4 = 13.0\nt0 = n0 * n3\nt1 = n1 - n0\nt2 = n2 - t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "total number of boys and girls in a school is 150 . if the number of boys is x , then girls become x % of the total number of students . the number of boys is", + "Output Program": [ + "n0 = 150.0\nt0 = n0 + 100.0\nt1 = n0 * 100.0\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "the average ( arithmetic mean ) of 20 , 40 , and 60 is 5 more than the average of 10 , 80 , and what number ?", + "Output Program": [ + "n0 = 20.0\nn1 = 40.0\nn2 = 60.0\nn3 = 5.0\nn4 = 10.0\nn5 = 80.0\nt0 = n0 + n1\nt1 = n3 * 3.0\nt2 = n2 + t0\nt3 = n4 + t1\nt4 = n5 + t3\nanswer = t2 - t4\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "if a = 105 and a ^ 3 = 21 * 49 * 45 * b , what is the value of b ?", + "Output Program": [ + "n0 = 105.0\nn1 = 3.0\nn2 = 21.0\nn3 = 49.0\nn4 = 45.0\nt0 = n2 * n3\nt1 = n0**min(n1, 5)\nt2 = n4 * t0\nanswer = t1 / t2\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "a number x is multiplied by 5 , and this product is then divided by 3 . if the positive square root of the result of these two operations equals x , what is the value of x if x \u2260 0 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nn2 = 0.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "1.6666666666666667" + ], + "split": "train" + }, + { + "Input": "if 9 gallons of gasoline are added to a tank that is already filled to 3 / 4 of its capacity , the tank is then filled to 9 / 10 of its capacity . how many gallons does the tank hold ?", + "Output Program": [ + "n0 = 9.0\nn1 = 3.0\nn2 = 4.0\nn3 = 9.0\nn4 = 10.0\nt0 = n3 / n4\nt1 = n1 / n2\nt2 = t0 - t1\nt3 = n0 / t2\nt4 = t3 * t1\nanswer = n0 + t4\nprint(answer)" + ], + "Output Answer": [ + "53.99999999999999" + ], + "split": "train" + }, + { + "Input": "what is the remainder when 121212 . . . . . . . ( 300 ) digits is divided by 99 .", + "Output Program": [ + "n0 = 121212.0\nn1 = 300.0\nn2 = 99.0\nt0 = 1.0 + 10.0\nt1 = n2 / t0\nanswer = t1 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "a batsman scored 1 runs in his 18 th innings and that makes his average 18 . find his average upto the 17 th innings ?", + "Output Program": [ + "n0 = 1.0\nn1 = 18.0\nn2 = 18.0\nn3 = 17.0\nt0 = n1 * n1\nt1 = t0 - n0\nanswer = t1 / n3\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "a student chose a number , multiplied it by 2 , then subtracted 148 from the result and got 110 . what was the number he chose ?", + "Output Program": [ + "n0 = 2.0\nn1 = 148.0\nn2 = 110.0\nt0 = n1 + n2\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "129" + ], + "split": "train" + }, + { + "Input": "in an election only two candidates contested 20 % of the voters did not vote and 120 votes were declared as invalid . the winner got 200 votes more than his opponent thus he secured 41 % votes of the total voters on the voter list . percentage votes of the defeated candidate out of the total votes casted is :", + "Output Program": [ + "n0 = 20.0\nn1 = 120.0\nn2 = 200.0\nn3 = 41.0\nt0 = n0 + 10.0\nt1 = n1 + n2\nt2 = n3 / 100.0\nt3 = t2 * 1000.0\nt4 = t1 * 10.0\nt5 = t0 + t3\nt6 = t5 + 1000.0\nt7 = t6 / t4\nanswer = t7 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "howmany 3 digit numbers are there tens digit place is more than hundreds digit place and units place less than hundreds digit place ?", + "Output Program": [ + "n0 = 3.0\nt0 = n0 * 10.0\nanswer = t0 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "average of 10 matches is 32 , how many runs one should should score to increase his average by 4 runs .", + "Output Program": [ + "n0 = 10.0\nn1 = 32.0\nn2 = 4.0\nt0 = n1 + n2\nt1 = n0 + 1.0\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "76" + ], + "split": "train" + }, + { + "Input": "what is the value of n if the sum of the consecutive odd intergers e from 1 to n equals 169 ?", + "Output Program": [ + "import math\nn0 = 1.0\nn1 = 169.0\nt0 = n0 * 2.0\nt1 = math.sqrt(max(0, n1))\nt2 = t1 * 2.0\nt3 = t2 - t0\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "a man purchased 3 blankets @ rs . 100 each , 2 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ?", + "Output Program": [ + "n0 = 3.0\nn1 = 100.0\nn2 = 2.0\nn3 = 150.0\nn4 = 150.0\nt0 = n3 * 10.0\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "900" + ], + "split": "train" + }, + { + "Input": "find the least number which when divided by 34 and 5 leaves a remainder of 4 in each case .", + "Output Program": [ + "import scipy\nn0 = 34.0\nn1 = 5.0\nn2 = 4.0\nt0 = scipy.lcm(int(n0), int(n1))\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "174" + ], + "split": "train" + }, + { + "Input": "a batsman makes a score of 87 runs in the 17 th inning and thus increases his avg by 3 . find his average after 17 th inning .", + "Output Program": [ + "n0 = 87.0\nn1 = 17.0\nn2 = 3.0\nn3 = 17.0\nt0 = n1 * n2\nt1 = n0 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "39" + ], + "split": "train" + }, + { + "Input": "if an average hard drive had a capacity of 0.1 tb in 2000 , and average hard drive capacities double every 5 years , what will be the average hard drive capacity in 2050 ?", + "Output Program": [ + "n0 = 0.1\nn1 = 2000.0\nn2 = 5.0\nn3 = 2050.0\nt0 = n0 * 2.0\nt1 = t0 * 2.0\nt2 = t1 * 2.0\nt3 = t2 * 2.0\nt4 = t3 * 2.0\nt5 = t4 * 2.0\nt6 = t5 * 2.0\nt7 = t6 * 2.0\nt8 = t7 * 2.0\nt9 = t8 * 2.0\nt10 = n0 + t9\nanswer = t10 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "1025" + ], + "split": "train" + }, + { + "Input": "( x + 3 ) is a factor in x ^ 2 - mx - 15 . what is the value of m ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 15.0\nt0 = n2 / n0\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "by approximately what percent is x greater than 4 / 7 if ( 1 / 7 ) ( x ) = 1 ?", + "Output Program": [ + "n0 = 4.0\nn1 = 7.0\nn2 = 1.0\nn3 = 7.0\nn4 = 1.0\nt0 = n0 / n1\nt1 = n1 - t0\nt2 = t1 / t0\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "1125.0000000000002" + ], + "split": "train" + }, + { + "Input": "if 4 a = 5 b and ab \u2260 0 , what is the ratio of a / 5 to b / 4 ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 0.0\nn3 = 5.0\nn4 = 4.0\nt0 = n0 * n1\nanswer = t0 / t0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "what number is that , to which if 1 , 5 , and 13 , be severally added , the first sum shall be to the second , as the second to the third ?", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 13.0\nt0 = n1 + n2\nt1 = n2 - n1\nt2 = n1 - n0\nt3 = n0 + t0\nt4 = n0 + t3\nt5 = t4 - t1\nanswer = t5 / t2\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "the price of a cycle is reduced by 25 per cent . the new price is reduced by a further 40 per cent . the two reductions together are equal to a single reduction of", + "Output Program": [ + "n0 = 25.0\nn1 = 40.0\nt0 = 100.0 - n1\nt1 = 100.0 - n0\nt2 = t0 / 100.0\nt3 = t2 * t1\nanswer = 100.0 - t3\nprint(answer)" + ], + "Output Answer": [ + "55" + ], + "split": "train" + }, + { + "Input": "what is the units digit of ( 147 ^ 25 ) ^ 50 ?", + "Output Program": [ + "n0 = 147.0\nn1 = 25.0\nn2 = 50.0\nt0 = 3.0 + 4.0\nanswer = t0 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "robin ' s average ( arithmetic mean ) test score on 9 tests is 82 . what must be robin ' s score on a 10 th test for his average score on the 10 tests to be 83 ?", + "Output Program": [ + "n0 = 9.0\nn1 = 82.0\nn2 = 10.0\nn3 = 10.0\nn4 = 83.0\nt0 = n2 * n4\nt1 = n0 * n1\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "92" + ], + "split": "train" + }, + { + "Input": "linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 220 , what were her original savings ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 220.0\nt0 = n0 / n1\nt1 = 1.0 - t0\nanswer = n2 / t1\nprint(answer)" + ], + "Output Answer": [ + "880" + ], + "split": "train" + }, + { + "Input": "if 10,000 microns = 1 decimeter , and 10,000 , 000,000 angstroms = 1 decimeter , how many angstroms equal 1 micron ?", + "Output Program": [ + "n0 = 10000.0\nn1 = 1.0\nn2 = 1000000000.0\nn3 = 1.0\nn4 = 1.0\n\nanswer = n1 / n1\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "a grand father has 3 grand children . age difference of two children among them is 3 . eldest child age is 3 times the youngest child \u2019 s age and the eldest child age is two year more than the sum of age of other two children . what is the age of the eldest child ?", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 3.0\nt0 = n0 * n0\nt1 = n0 + t0\nanswer = t1 + 3.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "the average of 50 numbers id 38 . if two numbers , namely 45 and 55 are discarded , the average of the remaining numbers is :", + "Output Program": [ + "n0 = 50.0\nn1 = 38.0\nn2 = 45.0\nn3 = 55.0\nt0 = n2 + n3\nt1 = n0 * n1\nt2 = n0 - 2.0\nt3 = t1 - t0\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "37.5" + ], + "split": "train" + }, + { + "Input": "which number need to add to 1782452 to get a number exactly divisible by 92 ?", + "Output Program": [ + "import math\nn0 = 1782452.0\nn1 = 92.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = t1 + 1.0\nt3 = t2 - t0\nanswer = n1 * t3\nprint(answer)" + ], + "Output Answer": [ + "48.00000000010186" + ], + "split": "train" + }, + { + "Input": "city x has a population 7 times as great as the population of city y , which has a population twice as great as the population of city z . what is the ratio of the population of city x to the population of city z ?", + "Output Program": [ + "n0 = 7.0\n\nanswer = n0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "225 , or 15 ^ 2 , is the first perfect square that begins with two 2 s . what is the sum of the digits of the next perfect square to begin with two 2 s ?", + "Output Program": [ + "n0 = 225.0\nn1 = 15.0\nn2 = 2.0\nn3 = 2.0\nn4 = 2.0\nt0 = n2 + n2\nt1 = 12.0 * 4.0\nt2 = 12.0 - 2.0\nt3 = t2 * t2\nt4 = t1 - 1.0\nt5 = t3 * t2\nt6 = t3 * 2.0\nt7 = t4**min(n2, 5)\nt8 = t5 * 2.0\nt9 = t8 + t6\nt10 = t7 - t9\nanswer = t0 + t10\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "if x > 0 , x / 50 + x / 25 is what percent of x ?", + "Output Program": [ + "n0 = 0.0\nn1 = 50.0\nn2 = 25.0\nt0 = 1.0 / n1\nt1 = 1.0 / n2\nt2 = t0 + t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "the price of commodity p increases by 40 paise every year , while the price of commodity q increases by 15 paise every year . if in 2001 , the price of commodity p was rs . 4.20 and that of q was rs . 6.30 , in which year commodity p will cost 40 paise more than the commodity q ?", + "Output Program": [ + "n0 = 40.0\nn1 = 15.0\nn2 = 2001.0\nn3 = 4.2\nn4 = 6.3\nn5 = 40.0\n\nanswer = n2 + 10.0\nprint(answer)" + ], + "Output Answer": [ + "2011" + ], + "split": "train" + }, + { + "Input": "if a \u00e3 \u2014 b = 2 a - 3 b + ab , then 1 \u00e3 \u2014 2 + 2 \u00e3 \u2014 1 is equal to :", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 1.0\nn3 = 2.0\nn4 = 2.0\nn5 = 1.0\nt0 = n0 * n2\nt1 = n0 * n1\nt2 = n0 * n0\nt3 = n1 * n2\nt4 = t0 - t1\nt5 = t2 - t3\nt6 = t0 + t4\nt7 = t0 + t5\nanswer = t6 + t7\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "the average marks of a class of 30 students is 40 and that of another class of 50 students is 60 . find the average marks of all the students ?", + "Output Program": [ + "n0 = 30.0\nn1 = 40.0\nn2 = 50.0\nn3 = 60.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "52.5" + ], + "split": "train" + }, + { + "Input": "a clock store sold a certain clock to a collector for 20 percent more than the store had originally paid for the clock . when the collector tried to resell the clock to the store , the store bought it back at 50 percent of what the collector had paid . the shop then sold the clock again at a profit of 80 percent on its buy - back price . if the difference between the clock ' s original cost to the shop and the clock ' s buy - back price was $ 100 , for how much did the shop sell the clock the second time ?", + "Output Program": [ + "n0 = 20.0\nn1 = 50.0\nn2 = 80.0\nn3 = 100.0\nt0 = n2 + n3\nt1 = n0 + n3\nt2 = t1 / 2.0\nt3 = t0 * t2\nt4 = t2 - n0\nt5 = t3 / n3\nt6 = n3 * t5\nanswer = t6 / t4\nprint(answer)" + ], + "Output Answer": [ + "270" + ], + "split": "train" + }, + { + "Input": "find the principle on a certain sum of money at 5 % per annum for 2 2 / 5 years if the amount being rs . 1680 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 2.0\nn3 = 5.0\nn4 = 1680.0\nt0 = n1 * n3\nt1 = n1 + t0\nt2 = t1 / n3\nt3 = n0 * t2\nt4 = t3 / 100.0\nt5 = t4 + 1.0\nanswer = n4 / t5\nprint(answer)" + ], + "Output Answer": [ + "1499.9999999999998" + ], + "split": "train" + }, + { + "Input": "a certain clock marks every hour by striking a number of times equal to the hour , and the time require for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stoke and the end of the last stroke is 22 seconds . at 9 : 00 , how many seconds elapse between the beginning of the first stroke and the end of the last stroke ?", + "Output Program": [ + "n0 = 6.0\nn1 = 0.0\nn2 = 22.0\nn3 = 9.0\nn4 = 0.0\nt0 = n3 - 1.0\nt1 = n0 - 1.0\nt2 = n3 + t0\nt3 = n0 + t1\nt4 = n2 / t3\nanswer = t2 * t4\nprint(answer)" + ], + "Output Answer": [ + "34" + ], + "split": "train" + }, + { + "Input": "the set s has 36 different subsets each of which contains exactly two elements . how many subsets of s could contain exactly 7 elements each ?", + "Output Program": [ + "import math\nn0 = 36.0\nn1 = 7.0\nt0 = math.factorial(min(15, int(n1)))\nt1 = n0 * 2.0\nt2 = t1 * 4.0\nt3 = t2 + 1.0\nt4 = math.sqrt(max(0, t3))\nt5 = t4 + 1.0\nt6 = t5 / 2.0\nt7 = math.factorial(min(15, int(t6)))\nt8 = t7 / t0\nanswer = t8 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "a 100 - litre mixture of milk and water contains 36 litres of milk . ' x ' litres of this mixture is removed and replaced with an equal quantum of water . if the process is repeated once , then the concentration of the milk stands reduced at 25 % . what is the value of x ?", + "Output Program": [ + "import math\nn0 = 100.0\nn1 = 36.0\nn2 = 25.0\nt0 = n2 / n1\nt1 = math.sqrt(max(0, t0))\nt2 = 1.0 - t1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "16.666666666666664" + ], + "split": "train" + }, + { + "Input": "x + ( 1 / x ) = 4 find x ^ 2 + ( 1 / x ^ 2 )", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 2.0\nn3 = 1.0\nn4 = 2.0\nt0 = n1**min(n2, 5)\nanswer = t0 - n2\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "for what value of k will the two equations 2 x + 4 = 4 ( x - 2 ) and - x + k = 2 x - 1 have the same solution ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 4.0\nn3 = 2.0\nn4 = 2.0\nn5 = 1.0\nt0 = n1 + 3.0\nanswer = t0 + 10.0\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "3 numbers are such that the second is as much lesser than thr third as the first is lesser than the second . if the product of the two smaller numbers is 85 and product of two larger number is 115 then find the middle number", + "Output Program": [ + "n0 = 3.0\nn1 = 85.0\nn2 = 115.0\nt0 = n1 + n2\nt1 = 10.0 * 2.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the average of marks obtained by 120 candidates was 35 . if the avg of marks of passed candidates was 39 & that of failed candidates was 39 and that of failed candidates was 15 , the no . of candidates who passed the examination is ?", + "Output Program": [ + "n0 = 120.0\nn1 = 35.0\nn2 = 39.0\nn3 = 39.0\nn4 = 15.0\nt0 = n0 * n1\nt1 = n0 * n4\nt2 = n2 - n4\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "a certain sum of money is divided among a , b and c so that for each rs . a has , b has 65 paisa and c 40 paisa . if c ' s share is rs . 32 , find the sum of money ?", + "Output Program": [ + "n0 = 65.0\nn1 = 40.0\nn2 = 32.0\nt0 = n0 + 100.0\nt1 = n2 / n1\nt2 = n1 + t0\nanswer = t2 * t1\nprint(answer)" + ], + "Output Answer": [ + "164" + ], + "split": "train" + }, + { + "Input": "if 3 / p = 4 & 3 / q = 18 then p - q = ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 3.0\nn3 = 18.0\nt0 = n0 / n1\nt1 = n0 / n3\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "0.5833333333333334" + ], + "split": "train" + }, + { + "Input": "the average of 11 results is 20 . the average of first 5 of them is 15 and that of last 5 is 22 . find the 6 th result ?", + "Output Program": [ + "n0 = 11.0\nn1 = 20.0\nn2 = 5.0\nn3 = 15.0\nn4 = 5.0\nn5 = 22.0\nn6 = 6.0\nt0 = n0 * n1\nt1 = n2 * n5\nt2 = n2 * n3\nt3 = t0 - t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "1 / 3 + 1 / 2 - 5 / 6 + 1 / 5 + 1 / 4 - 9 / 20 - 5 / 6 =", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 2.0\nn4 = 5.0\nn5 = 6.0\nn6 = 1.0\nn7 = 5.0\nn8 = 1.0\nn9 = 4.0\nn10 = 9.0\nn11 = 20.0\nn12 = 5.0\nn13 = 6.0\n\nanswer = n4 / n5\nprint(answer)" + ], + "Output Answer": [ + "0.8333333333333334" + ], + "split": "train" + }, + { + "Input": "the total of 334 of 20 paise and 25 paise make a sum of rs . 71 . the no of 20 paise coins is", + "Output Program": [ + "n0 = 334.0\nn1 = 20.0\nn2 = 25.0\nn3 = 71.0\nn4 = 20.0\nt0 = n0 * n2\nt1 = n3 * 100.0\nt2 = n2 - n1\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "250" + ], + "split": "train" + }, + { + "Input": "the guests at a football banquet consumed a total of 337 pounds of food . if no individual guest consumed more than 2 pounds of food , what is the minimum number of guests that could have attended the banquet ?", + "Output Program": [ + "import math\nn0 = 337.0\nn1 = 2.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "169" + ], + "split": "train" + }, + { + "Input": "what is the least number should be added to 929 , so the sum of the number is completely divisible by 30 ?", + "Output Program": [ + "import math\nn0 = 929.0\nn1 = 30.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = t1 + 1.0\nt3 = n1 * t2\nanswer = t3 - n0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "how many numbers from 29 to 119 are exactly divisible by 11 ?", + "Output Program": [ + "import math\nn0 = 29.0\nn1 = 119.0\nn2 = 11.0\nt0 = n1 / n2\nt1 = n0 / n2\nt2 = math.floor(t0)\nt3 = math.floor(t1)\nt4 = t3 + 1.0\nt5 = n2 * t2\nt6 = n2 * t4\nt7 = t5 - t6\nt8 = t7 / n2\nanswer = t8 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "two workers a and b are engaged to do a work . a working alone takes 8 hours more to complete the job than if both worked together . if b worked alone , he would need 4 1 / 2 hours more to complete the job than they both working together . what time would they take to do the work together ?", + "Output Program": [ + "import math\nn0 = 8.0\nn1 = 4.0\nn2 = 1.0\nn3 = 2.0\nt0 = n2 / n3\nt1 = n1 + t0\nt2 = n0 * t1\nanswer = math.sqrt(max(0, t2))\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "if 2 and 3 are positive integers , then 2 * 3 + 2 is", + "Output Program": [ + "n0 = 6.0\nn1 = 5.0\nn2 = 2.0\nn3 = 19.0\nt0 = n0 * n1\nt1 = n2 * t0\nt2 = t1 / n2\nanswer = t2 + 3.0\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "if f ( x ) = 1 / x and x is a natural number , what can not be the answer for f ( f ( x ) ) ?", + "Output Program": [ + "n0 = 1.0\nt0 = n0 * 1.0\nt1 = 2.0 * 4.0\nt2 = t1 - n0\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.14285714285714285" + ], + "split": "train" + }, + { + "Input": "if 28 less than 5 times a certain number is 232 . what is the number ?", + "Output Program": [ + "n0 = 28.0\nn1 = 5.0\nn2 = 232.0\nt0 = n0 * n1\nt1 = 10.0 * 4.0\nt2 = n2 + t0\nt3 = t2 - t0\nt4 = t3 - t0\nanswer = t4 - t1\nprint(answer)" + ], + "Output Answer": [ + "52" + ], + "split": "train" + }, + { + "Input": "a rope of which a calf is tied is increased from 10 m to 23 m , how much additional grassy ground shall it graze ?", + "Output Program": [ + "n0 = 10.0\nn1 = 23.0\nt0 = 3.0 + 4.0\nt1 = 10.0 * 2.0\nt2 = n1**min(2.0, 5)\nt3 = 10.0**min(2.0, 5)\nt4 = t1 + 2.0\nt5 = t2 - t3\nt6 = t4 / t0\nanswer = t6 * t5\nprint(answer)" + ], + "Output Answer": [ + "1348.2857142857142" + ], + "split": "train" + }, + { + "Input": "the tax on a commodity is diminished by 30 % but its consumption is increased by 10 % . find the decrease percent in the revenue derived from it ?", + "Output Program": [ + "n0 = 30.0\nn1 = 10.0\nt0 = n1 + 100.0\nt1 = 100.0 - n0\nt2 = t0 * t1\nt3 = t2 / 100.0\nanswer = 100.0 - t3\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "some consecutive natural numbers , starting with 1 , are written on the board . now , one of the numbers was erased and the average of the remaining numbers is 800 / 39 . find the number which was erased .", + "Output Program": [ + "n0 = 1.0\nn1 = 800.0\nn2 = 39.0\nt0 = n2 + 1.0\nt1 = t0 + 1.0\nt2 = t0 * t1\nt3 = t2 / 2.0\nanswer = t3 - n1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "what is the smallest number which when increased by 3 is divisible by 18 , 70 , 25 and 21 ?", + "Output Program": [ + "import scipy\nn0 = 3.0\nn1 = 18.0\nn2 = 70.0\nn3 = 25.0\nn4 = 21.0\nt0 = scipy.lcm(int(n1), int(n2))\nt1 = scipy.lcm(int(n3), int(n4))\nt2 = scipy.lcm(int(t0), int(t1))\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "3153" + ], + "split": "train" + }, + { + "Input": "in a survey of parents , exactly 7 / 8 of the mothers and 3 / 4 of the fathers held full - time jobs . if 60 percent of the parents surveyed were women , what percent of the parents did not hold full - time jobs ?", + "Output Program": [ + "n0 = 7.0\nn1 = 8.0\nn2 = 3.0\nn3 = 4.0\nn4 = 60.0\nt0 = n2 / n3\nt1 = n0 / n1\nt2 = 100.0 - n4\nt3 = t0 * t2\nt4 = n4 * t1\nt5 = t2 - t3\nt6 = n4 - t4\nanswer = t5 + t6\nprint(answer)" + ], + "Output Answer": [ + "17.5" + ], + "split": "train" + }, + { + "Input": "a certain sum becomes 4 times itself at simple interest in 8 years . in how many years does it become 10 times itself ?", + "Output Program": [ + "n0 = 4.0\nn1 = 8.0\nn2 = 10.0\nt0 = n2 - 1.0\nt1 = n0 - 1.0\nt2 = t0 / t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "product of two natural numbers is 5 . then , the sum of reciprocals of their squares is", + "Output Program": [ + "n0 = 5.0\nt0 = 1.0 / 1.0\nt1 = 1.0 / n0\nt2 = t0**min(2.0, 5)\nt3 = t1**min(2.0, 5)\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "1.04" + ], + "split": "train" + }, + { + "Input": "the average weight of 5 students decreases by 4 kg when one of them weighing 92 kg is replaced by a new student . the weight of the student is", + "Output Program": [ + "n0 = 5.0\nn1 = 4.0\nn2 = 92.0\nt0 = n0 * n1\nanswer = n2 - t0\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "train" + }, + { + "Input": "of the final grades received by the students in a certain math course , 1 / 5 are a ' s , 1 / 4 are b ' s , 1 / 2 are c ' s , and the remaining 25 grades are d ' s . what is the number of students in the course ?", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 1.0\nn3 = 4.0\nn4 = 1.0\nn5 = 2.0\nn6 = 25.0\nt0 = n0 / n1\nt1 = n0 / n3\nt2 = n0 / n5\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n0 - t4\nanswer = n6 / t5\nprint(answer)" + ], + "Output Answer": [ + "499.99999999999955" + ], + "split": "train" + }, + { + "Input": "if a * b * c = ( \u221a ( a + 2 ) ( b + 3 ) ) / ( c + 1 ) , find the value of 6 * 15 * 2 .", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 3.0\nn2 = 1.0\nn3 = 6.0\nn4 = 15.0\nn5 = 2.0\nt0 = n0 + n3\nt1 = n1 + n4\nt2 = n2 + n5\nt3 = t0 * t1\nt4 = math.sqrt(max(0, t3))\nanswer = t4 / t2\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "you collect pens . suppose you start out with 7 . mike gives you another 22 pens . since her father makes pens , cindy decides to double your pens . since you ' re nice , you give sharon 19 pens . how many pens do you have at the end ?", + "Output Program": [ + "n0 = 7.0\nn1 = 22.0\nn2 = 19.0\nt0 = n0 + n1\nt1 = t0 * 2.0\nanswer = t1 - n2\nprint(answer)" + ], + "Output Answer": [ + "39" + ], + "split": "train" + }, + { + "Input": "in august , a cricket team that played 120 matches won 30 % of the games it played . after a continuous winning streak , this team raised its average to 52 % . how many matches did the team win to attain this average ?", + "Output Program": [ + "n0 = 120.0\nn1 = 30.0\nn2 = 52.0\nt0 = n2 / 100.0\nt1 = n1 / 100.0\nt2 = n0 * t0\nt3 = n0 * t1\nt4 = 1.0 - t0\nt5 = t2 - t3\nanswer = t5 / t4\nprint(answer)" + ], + "Output Answer": [ + "55.000000000000014" + ], + "split": "train" + }, + { + "Input": "jim \u2019 s taxi service charges an initial fee of $ 2.05 at the beginning of a trip and an additional charge of $ 0.35 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?", + "Output Program": [ + "n0 = 2.05\nn1 = 0.35\nn2 = 2.0\nn3 = 5.0\nn4 = 3.6\nt0 = n2 / n3\nt1 = n4 / t0\nt2 = n1 * t1\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "5.199999999999999" + ], + "split": "train" + }, + { + "Input": "if a = 105 and a ^ 3 = 21 \u00d7 25 \u00d7 45 \u00d7 w , what is the value of w ?", + "Output Program": [ + "n0 = 105.0\nn1 = 3.0\nn2 = 21.0\nn3 = 25.0\nn4 = 45.0\nt0 = n2 * n3\nt1 = n0**min(n1, 5)\nt2 = n4 * t0\nanswer = t1 / t2\nprint(answer)" + ], + "Output Answer": [ + "49" + ], + "split": "train" + }, + { + "Input": "a certain car traveled twice as many miles from town a to town b as it did from town b to town c . from town a to town b , the car averaged 40 miles per gallon , and from town b to town c , the car averaged 50 miles per gallon . what is the average miles per gallon that the car achieved on its trip from town a through town b to town c ?", + "Output Program": [ + "n0 = 40.0\nn1 = 50.0\nt0 = n1 * 10.0\nt1 = t0 / 2.0\nt2 = t0 / n0\nt3 = t1 + t0\nt4 = t1 / n1\nt5 = t2 + t4\nanswer = t3 / t5\nprint(answer)" + ], + "Output Answer": [ + "42.857142857142854" + ], + "split": "train" + }, + { + "Input": "a car averages 45 mph for the first 4 hours of a trip and averages 75 mph for each additional hour . the average speed for the entire trip was 65 mph . how many hours long is the trip ?", + "Output Program": [ + "n0 = 45.0\nn1 = 4.0\nn2 = 75.0\nn3 = 65.0\nt0 = n3 * n1\nt1 = n0 * n1\nt2 = n2 - n3\nt3 = t0 - t1\nt4 = t3 / t2\nanswer = n1 + t4\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "the cricket team of 11 members is 25 yrs old & the wicket keeper is 3 yrs older . if the ages ofthese 2 are excluded , the average age of theremaining players is 1 year less than the average age of the whole team . what is the average age of the team ?", + "Output Program": [ + "n0 = 11.0\nn1 = 25.0\nn2 = 3.0\nn3 = 2.0\nn4 = 1.0\nt0 = n1 + 3.0\nt1 = n0 - n3\nt2 = n1 + t0\nt3 = n0 - t1\nt4 = t2 - t1\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "louie takes out a 3 - month loan of $ 2000 . the lender charges him 10 % interest per month compounded monthly . the terms of the loan state that louie must repay the loan in 3 equal monthly payments . to the nearest dollar , how much does louie have to pay each month ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2000.0\nn2 = 10.0\nn3 = 3.0\nt0 = 1.0 / 10.0\nt1 = t0 + 1.0\nt2 = n1 * t1\nt3 = t1 * t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "806.6666666666666" + ], + "split": "train" + }, + { + "Input": "if a certain toy store ' s revenue in november was 3 / 5 of its revenue in december and its revenue in january was 1 / 3 of its revenue in november , then the store ' s revenue in december was how many times the average ( arithmetic mean ) of its revenues in november and january ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 1.0\nn3 = 3.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = t0 * t1\nt3 = t0 + t2\nt4 = t3 / 2.0\nanswer = n2 / t4\nprint(answer)" + ], + "Output Answer": [ + "2.5" + ], + "split": "train" + }, + { + "Input": "the jogging track in a sports complex is 528 m in circumference . deepak and his wife start from the same point and walk in opposite directions at 4.5 km / hr and 3.75 km / hr respectively . they will meet for the first time in ?", + "Output Program": [ + "n0 = 528.0\nn1 = 4.5\nn2 = 3.75\nt0 = n1 + n2\nt1 = n0 / 1000.0\nt2 = t1 / t0\nanswer = t2 * 60.0\nprint(answer)" + ], + "Output Answer": [ + "3.84" + ], + "split": "train" + }, + { + "Input": "on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 420 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?", + "Output Program": [ + "n0 = 420.0\n\nanswer = n0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "840" + ], + "split": "train" + }, + { + "Input": "the average runs scored by a batsman in 20 matches is 40 . in the next 10 matches the batsman scored an average of 20 runs . find his average in all the 30 matches ?", + "Output Program": [ + "n0 = 20.0\nn1 = 40.0\nn2 = 10.0\nn3 = 20.0\nn4 = 30.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "33.333333333333336" + ], + "split": "train" + }, + { + "Input": "a certain number when divided by 39 leaves a remainder 17 , what is the remainder when the same number is divided by 13 ?", + "Output Program": [ + "n0 = 39.0\nn1 = 17.0\nn2 = 13.0\n\nanswer = n1 % n2\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "the total number of students in grades 1 and 2 is 30 more than the total number of students in grades 2 and 5 . how much lesser is the number of students in grade 5 as compared to grade 1 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 30.0\nn3 = 2.0\nn4 = 5.0\nn5 = 5.0\nn6 = 1.0\nt0 = n2 + n4\nt1 = n1 + t0\nt2 = n1 + t1\nt3 = n1 + t2\nt4 = t3 + 3.0\nt5 = t4 + 4.0\nt6 = t5 + 12.0\nanswer = t6 / n1\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "a football player scores 5 goals in his fifth match thus increasing his average goals score by 0.2 . the total number of goals in his 5 matches would be", + "Output Program": [ + "n0 = 5.0\nn1 = 0.2\nn2 = 5.0\nt0 = n0 * 4.0\nt1 = n2 * 4.0\nt2 = n1 * t1\nt3 = t0 - t2\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "the mean of 50 observations was 36 . it was found later that an observation 60 was wrongly taken as 23 . the corrected new mean is ?", + "Output Program": [ + "n0 = 50.0\nn1 = 36.0\nn2 = 60.0\nn3 = 23.0\nt0 = n0 * n1\nt1 = n0 - 2.0\nt2 = t1 - n3\nt3 = t0 + t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "36.5" + ], + "split": "train" + }, + { + "Input": "in a party every person shakes hands with every other person . if there were a total of 105 handshakes in the party then what is the number of persons present in the party ?", + "Output Program": [ + "import math\nn0 = 105.0\nt0 = n0 * 2.0\nt1 = t0 * 4.0\nt2 = t1 + 1.0\nt3 = math.sqrt(max(0, t2))\nt4 = t3 + 1.0\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "there are 7 players in a bowling team with an average weight of 76 kg . if two new players join the team , one weighs 110 kg and the second weighs 60 kg , what will be the new average weight ?", + "Output Program": [ + "n0 = 7.0\nn1 = 76.0\nn2 = 110.0\nn3 = 60.0\nt0 = n2 + n3\nt1 = n0 + 2.0\nt2 = n0 * n1\nt3 = t0 + t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "78" + ], + "split": "train" + }, + { + "Input": "in the hillside summer camp there are 50 children . 85 % of the children are boys and the rest are girls . the camp administrator decided to make the number of girls only 5 % of the total number of children in the camp . how many more boys must she bring to make that happen ?", + "Output Program": [ + "n0 = 50.0\nn1 = 85.0\nn2 = 5.0\nt0 = n2 / 100.0\nt1 = 100.0 - n2\nt2 = t1 / 100.0\nt3 = n0 * t0\nt4 = n0 * t2\nanswer = t4 + t3\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "the ratio 6 : 5 expressed as a percent equals", + "Output Program": [ + "n0 = 6.0\nn1 = 5.0\nt0 = n0 / n1\nanswer = t0 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "the unit digit in the product ( 624 * 708 * 913 * 463 ) is :", + "Output Program": [ + "n0 = 624.0\nn1 = 708.0\nn2 = 913.0\nn3 = 463.0\nt0 = 4.0 + 4.0\nt1 = n0 * n1\nt2 = n2 * t1\nt3 = n3 * t2\nt4 = t3 - t0\nanswer = t3 - t4\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "in the faculty of reverse - engineering , 226 second year students study numeric methods , 450 second year students study automatic control of airborne vehicles and 134 second year students study them both . how many students are there in the faculty if the second year students are approximately 80 % of the total ?", + "Output Program": [ + "n0 = 226.0\nn1 = 450.0\nn2 = 134.0\nn3 = 80.0\n\nanswer = n0 + n1\nprint(answer)" + ], + "Output Answer": [ + "676" + ], + "split": "train" + }, + { + "Input": "the difference between a two - digit number and the number obtained by interchanging the digit is 36 . what is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?", + "Output Program": [ + "n0 = 36.0\nn1 = 1.0\nn2 = 2.0\nt0 = n2 * 10.0\nt1 = n1 + t0\nt2 = t1 - 10.0\nt3 = t2 - n2\nt4 = n0 / t3\nt5 = n2 * t4\nt6 = t4 + t5\nt7 = t5 - t4\nanswer = t6 - t7\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a pharmaceutical company received $ 3 million in royalties on the first $ 20 million in sales of and then $ 9 million in royalties on the next $ 108 million in sales . by approximately what percentage did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 108 million in sales ?", + "Output Program": [ + "n0 = 3.0\nn1 = 20.0\nn2 = 9.0\nn3 = 108.0\nn4 = 20.0\nn5 = 108.0\nt0 = n0 / n1\nanswer = t0 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "dividing by 3 \u2044 9 and then multiplying by 5 \u2044 6 is the same as dividing by what number ?", + "Output Program": [ + "n0 = 3.0\nn1 = 9.0\nn2 = 5.0\nn3 = 6.0\nt0 = n1 / n0\nt1 = n2 / n3\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "2.5" + ], + "split": "train" + }, + { + "Input": "a basket of 1430 apples is divided equally among a group of apple lovers . if 45 people join the group , each apple lover would receive 9 apples less . how many s apples did each person get before 45 people joined the feast ?", + "Output Program": [ + "n0 = 1430.0\nn1 = 45.0\nn2 = 9.0\nn3 = 45.0\nt0 = 10.0 + 10.0\nt1 = t0 + 2.0\nt2 = n0 / t1\nt3 = n1 + t2\nt4 = n0 / t3\nanswer = n2 + t4\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "sobha ' s father was 38 years of age when she was born while her mother was 36 years old when her brother 4 years younger to her was born . what is the difference between the ages of her parents ?", + "Output Program": [ + "n0 = 38.0\nn1 = 36.0\nn2 = 4.0\nt0 = n0 + n2\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "if the average ( arithmetic mean ) of ( 2 a + 16 ) and ( 3 a - 8 ) is 74 , what is the value of a ?", + "Output Program": [ + "n0 = 2.0\nn1 = 16.0\nn2 = 3.0\nn3 = 8.0\nn4 = 74.0\nt0 = n0 + n2\nt1 = n0 * n4\nt2 = n1 - n3\nt3 = t1 - t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "find the number which is nearest to 457 and is exactly divisible by 11 .", + "Output Program": [ + "n0 = 457.0\nn1 = 11.0\nt0 = n0 % n1\nt1 = n1 - t0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "462" + ], + "split": "train" + }, + { + "Input": "12.1212 + 17.0005 - 9.1103 = ?", + "Output Program": [ + "n0 = 12.1212\nn1 = 17.0005\nn2 = 9.1103\nt0 = n0 + n1\nanswer = t0 - n2\nprint(answer)" + ], + "Output Answer": [ + "20.011399999999995" + ], + "split": "train" + }, + { + "Input": "a student chose a number , multiplied it by 2 , then subtracted 138 from the result and got 104 . what was the number he chose ?", + "Output Program": [ + "n0 = 2.0\nn1 = 138.0\nn2 = 104.0\nt0 = n1 + n2\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "121" + ], + "split": "train" + }, + { + "Input": "john want to buy a $ 100 trouser at the store , but he think it \u00e2 \u20ac \u2122 s too expensive . finally , it goes on sale for $ 75 . what is the percent decrease ?", + "Output Program": [ + "n0 = 100.0\nn1 = 75.0\n\nanswer = n0 - n1\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "what is the remainder when ( 55 ) ( 57 ) is divided by 8 ?", + "Output Program": [ + "n0 = 55.0\nn1 = 57.0\nn2 = 8.0\nt0 = n0 * n1\nanswer = t0 % n2\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "a dog is tied to a tree by a long nylon cord . if the dog runs from the due north side of the tree to the due south side of the tree with the cord extended to its full length at all items , and the dog ran approximately 30 feet , what was the approximate length of the nylon cord q , in feet ?", + "Output Program": [ + "n0 = 30.0\n\nanswer = n0 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "when positive integer x is divided by positive integer y , the remainder is 8 . if x / y = 76.4 , what is the value of y ?", + "Output Program": [ + "import math\nn0 = 8.0\nn1 = 76.4\nt0 = math.floor(n1)\nt1 = n1 - t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "19.999999999999716" + ], + "split": "train" + }, + { + "Input": "in a group of 120 people , 90 have an age of more 30 years , and the others have an age of less than 20 years . if a person is selected at random from this group , what is the probability the person ' s age is less than 20 ?", + "Output Program": [ + "n0 = 120.0\nn1 = 90.0\nn2 = 30.0\nn3 = 20.0\nn4 = 20.0\nt0 = n0 - n1\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.25" + ], + "split": "train" + }, + { + "Input": "solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 300 milliliters of solution x to create a solution that is 22 percent alcohol by volume ?", + "Output Program": [ + "n0 = 10.0\nn1 = 30.0\nn2 = 300.0\nn3 = 22.0\nt0 = n3 - n0\nt1 = n1 - n3\nt2 = t0 / t1\nanswer = n2 * t2\nprint(answer)" + ], + "Output Answer": [ + "450" + ], + "split": "train" + }, + { + "Input": "the average weight of a class is x pounds . when a new student weighing 90 pounds joins the class , the average decreases by 1 pound . in a few months the student \u2019 s weight increases to 110 pounds and the average weight of the class becomes x + 4 pounds . none of the other students \u2019 weights changed . what is the value of x ?", + "Output Program": [ + "n0 = 90.0\nn1 = 1.0\nn2 = 110.0\nn3 = 4.0\nt0 = n0 + n3\nt1 = n1 + n3\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "99" + ], + "split": "train" + }, + { + "Input": "what is the total number of positive integers that are less than 500 and that have no positive factor in common with 500 other than 1 ?", + "Output Program": [ + "n0 = 500.0\nn1 = 500.0\nn2 = 1.0\nt0 = n0 / 100.0\nt1 = n0 - 1.0\nt2 = n0 - 2.0\nt3 = n0 - 10.0\nt4 = t2 - 2.0\nt5 = n0 - t0\nt6 = t3 - 10.0\nt7 = t4 / 2.0\nt8 = t6 / 10.0\nt9 = t5 - t0\nt10 = t7 + 1.0\nt11 = n2 + t8\nt12 = t9 / t0\nt13 = t12 + 1.0\nt14 = t10 + t13\nt15 = t14 - t11\nanswer = t1 - t15\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "train" + }, + { + "Input": "in a simultaneous throw of pair of dice . find the probability of getting the total more than 7 .", + "Output Program": [ + "n0 = 7.0\nt0 = n0 + 4.0\nt1 = 2.0 + 4.0\nt2 = t0 + 4.0\nt3 = t1 * t1\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.4166666666666667" + ], + "split": "train" + }, + { + "Input": "krishan and nandan jointly started a business . krishan invested 6 times as nandan did and invested his money for double time as compared to nandan . nandan earned rs . 6000 . if the gain is proportional to the money invested and the time for which the money is invested then the total gain was ?", + "Output Program": [ + "n0 = 6.0\nn1 = 6000.0\nt0 = n0 * 2.0\nt1 = t0 + 1.0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "78000" + ], + "split": "train" + }, + { + "Input": "consider the word rotor . whichever way you read it , from left to right or from right to left , you get the same word . such a word is known as palindrome . find the maximum possible number of 5 - letter palindromes", + "Output Program": [ + "n0 = 5.0\nt0 = 10.0 + 10.0\nt1 = n0 - 2.0\nt2 = t0 + 3.0\nt3 = t2 + 3.0\nanswer = t3**min(t1, 5)\nprint(answer)" + ], + "Output Answer": [ + "17576" + ], + "split": "train" + }, + { + "Input": "find k if 64 \u00f7 k = 4 .", + "Output Program": [ + "n0 = 64.0\nn1 = 4.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "the mean of 50 observations is 200 . but later he found that there is decrements of 9 from each observations . what is the the updated mean is ?", + "Output Program": [ + "n0 = 50.0\nn1 = 200.0\nn2 = 9.0\n\nanswer = n1 - n2\nprint(answer)" + ], + "Output Answer": [ + "191" + ], + "split": "train" + }, + { + "Input": "a couple spent $ 184.80 in total while dining out and paid this amount using a credit card . the $ 184.80 figure included a 20 percent tip which was paid on top of the price which already included a sales tax of 10 percent on top of the price of the food . what was the actual price of the food before tax and tip ?", + "Output Program": [ + "n0 = 184.8\nn1 = 184.8\nn2 = 20.0\nn3 = 10.0\nt0 = n2 + 100.0\nt1 = n3 + 100.0\nt2 = n0 * 100.0\nt3 = t2 / t0\nt4 = t3 * 100.0\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "140" + ], + "split": "train" + }, + { + "Input": "the average weight of 8 person ' s increases by 4.2 kg when a new person comes in place of one of them weighing 65 kg . what is the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 4.2\nn2 = 65.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "98.6" + ], + "split": "train" + }, + { + "Input": "rates for having a manuscript typed at a certain typing service are $ 10 per page for the first time a page is typed and $ 5 per page each time a page is revised . if a certain manuscript has 100 pages , of which 30 were revised only once , 20 were revised twice , and the rest required no revisions , what was the total cost of having the manuscript typed ?", + "Output Program": [ + "n0 = 10.0\nn1 = 5.0\nn2 = 100.0\nn3 = 30.0\nn4 = 20.0\nt0 = n0 * n2\nt1 = n1 * n3\nt2 = n1 * n4\nt3 = t0 + t1\nt4 = t2 * 2.0\nanswer = t3 + t4\nprint(answer)" + ], + "Output Answer": [ + "1350" + ], + "split": "train" + }, + { + "Input": "if x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year , the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $ 74 . if $ 2,000 is the total amount invested , how much is invested at 8 percent ?", + "Output Program": [ + "n0 = 10.0\nn1 = 8.0\nn2 = 10.0\nn3 = 8.0\nn4 = 74.0\nn5 = 2000.0\nn6 = 8.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = n0 * 100.0\nt3 = n0 * n1\nt4 = t0 + t1\nt5 = t2 * 2.0\nt6 = t3 * 2.0\nt7 = n4 + t6\nt8 = t7 / t4\nanswer = t5 - t8\nprint(answer)" + ], + "Output Answer": [ + "700" + ], + "split": "train" + }, + { + "Input": "at the opening of a trading day at a certain stock exchange , the price per share of stock k was $ 28 . if the price per share of stock k was $ 29 at the closing of the day , what was the percent increase in the price per share of stock k for that day ?", + "Output Program": [ + "n0 = 28.0\nn1 = 29.0\nt0 = n1 / n0\nt1 = t0 - 1.0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "3.571428571428581" + ], + "split": "train" + }, + { + "Input": "bookman purchased 55 copies of a new book released recently , 10 of which are hardback and sold for $ 20 each , and rest are paperback and sold for $ 10 each . if 14 copies were sold and the total value of the remaining books was 360 , how many paperback copies were sold ?", + "Output Program": [ + "import scipy\nn0 = 55.0\nn1 = 10.0\nn2 = 20.0\nn3 = 10.0\nn4 = 14.0\nn5 = 360.0\nt0 = scipy.gcd(int(n0), int(n1))\nt1 = n1 * n2\nt2 = n0 - n1\nt3 = n1 * t2\nt4 = n2 * t0\nt5 = t3 + t1\nt6 = t5 - n5\nt7 = t6 - t4\nanswer = t7 / n1\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "in a company with 48 employees , some part - time and some full - time , exactly ( 1 / 3 ) of the part - time employees and ( 1 / 4 ) of the full - time employees take the subway to work . what is the greatest possible number r of employees who take the subway to work ?", + "Output Program": [ + "n0 = 48.0\nn1 = 1.0\nn2 = 3.0\nn3 = 1.0\nn4 = 4.0\nt0 = n0 * n2\nt1 = n2 * n4\nt2 = t0 / t1\nt3 = n0 - t1\nt4 = t3 / t2\nanswer = t2 + t4\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "the average earning of a mechanic for the first - 4 days of a week is rs . 18 and for the last 4 days is rs . 22 . if he earns rs . 13 on the fourth day , his average earning for the whole week is ?", + "Output Program": [ + "n0 = 4.0\nn1 = 18.0\nn2 = 4.0\nn3 = 22.0\nn4 = 13.0\nt0 = 3.0 + 4.0\nt1 = n0 * n1\nt2 = n0 * n3\nt3 = t1 + t2\nt4 = t3 - n4\nanswer = t4 / t0\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "what is the unit digit in the product ( 3 ^ 68 x 6 ^ 59 x 7 ^ 71 ) ?", + "Output Program": [ + "n0 = 3.0\nn1 = 68.0\nn2 = 6.0\nn3 = 59.0\nn4 = 7.0\nn5 = 71.0\nt0 = n0 * n2\nt1 = n0 * t0\nt2 = t1 - 4.0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "a man purchased 2 blankets @ rs . 100 each , 5 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ?", + "Output Program": [ + "n0 = 2.0\nn1 = 100.0\nn2 = 5.0\nn3 = 150.0\nn4 = 150.0\nt0 = n3 * 10.0\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "550" + ], + "split": "train" + }, + { + "Input": "zinc and copper are melted together in the ratio 9 : 11 . what is the weight of melted mixture , if 28.8 kg of zinc has been consumed in it ?", + "Output Program": [ + "n0 = 9.0\nn1 = 11.0\nn2 = 28.8\nt0 = n1 / n0\nt1 = n2 * t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "train" + }, + { + "Input": "the average weight of 5 person ' s increases by 5.5 kg when a new person comes in place of one of them weighing 68 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 5.0\nn1 = 5.5\nn2 = 68.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "95.5" + ], + "split": "train" + }, + { + "Input": "the average temperature for monday , tuesday , wednesday and thursday was 48 degrees and for tuesday , wednesday , thursday and friday was 46 degrees . if the temperature on monday was 44 degrees . find the temperature on friday ?", + "Output Program": [ + "n0 = 48.0\nn1 = 46.0\nn2 = 44.0\nt0 = n0 * 4.0\nt1 = n1 * 4.0\nt2 = t0 - t1\nanswer = n2 - t2\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "an ant walks an average of 1000 meters in 30 minutes . a beetle walks 10 % less distance at the same time on the average . assuming the beetle walks at her regular rate , what is its speed in km / h ?", + "Output Program": [ + "n0 = 1000.0\nn1 = 30.0\nn2 = 10.0\nt0 = n0 / 1000.0\nt1 = n1 / 60.0\nt2 = n2 / 100.0\nt3 = t0 / t1\nt4 = 1.0 - t2\nanswer = t3 * t4\nprint(answer)" + ], + "Output Answer": [ + "1.8" + ], + "split": "train" + }, + { + "Input": "an automobile parts supplier charges $ 20 per package of gaskets . when a customer orders more than 10 packages of gaskets , the supplier charges 4 / 5 the price for each package in excess of 10 . during a certain week , the supplier sold 60 packages of gaskets . if 20 percent of the gaskets went to company x , 15 percent to company y , and the rest to company z , what was the total amount , in dollars , that the parts supplier received in payment for the gaskets ?", + "Output Program": [ + "n0 = 20.0\nn1 = 10.0\nn2 = 4.0\nn3 = 5.0\nn4 = 10.0\nn5 = 60.0\nn6 = 20.0\nn7 = 15.0\nt0 = n2 / n3\nt1 = n6 / 100.0\nt2 = n0 * n1\nt3 = n0 * t0\nt4 = n5 * t1\nt5 = n0 * t4\nt6 = n5 - t4\nt7 = t5 + t5\nt8 = t6 - t4\nt9 = t8 - n1\nt10 = t3 * t9\nt11 = t10 + t2\nanswer = t11 + t7\nprint(answer)" + ], + "Output Answer": [ + "1096" + ], + "split": "train" + }, + { + "Input": "suraj has a certain average of runs for 8 innings . in the 9 th innings he scores 90 runs thereby increasing his average by 6 runs . what is his average after the 9 th innings ?", + "Output Program": [ + "n0 = 8.0\nn1 = 9.0\nn2 = 90.0\nn3 = 6.0\nn4 = 9.0\nt0 = n0 * n3\nt1 = n1 - n0\nt2 = n2 - t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "two heavily loaded sixteen - wheeler transport trucks are 940 kilometers apart , sitting at two rest stops on opposite sides of the same highway . driver a begins heading down the highway driving at an average speed of 90 kilometers per hour . exactly one hour later , driver b starts down the highway toward driver a , maintaining an average speed of 80 kilometers per hour . how many kilometers farther than driver b , will driver a have driven when they meet and pass each other on the highway ?", + "Output Program": [ + "n0 = 940.0\nn1 = 90.0\nn2 = 80.0\nt0 = n1 + n2\nt1 = n0 - n1\nt2 = n1 - n2\nt3 = t1 / t0\nt4 = t3 * t2\nanswer = n1 + t4\nprint(answer)" + ], + "Output Answer": [ + "140" + ], + "split": "train" + }, + { + "Input": "in an examination , 32 % of total students failed in hindi , 56 % failed in english and 12 % in both . the percentage of these who passed in both the subjects is :", + "Output Program": [ + "n0 = 32.0\nn1 = 56.0\nn2 = 12.0\nt0 = n0 + n1\nt1 = t0 - n2\nanswer = 100.0 - t1\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "a farmer has an apple orchard consisting of fuji and gala apple trees . due to high winds this year 10 % of his trees cross pollinated . the number of his trees that are pure fuji plus the cross - pollinated ones totals 221 , while 3 / 4 of all his trees are pure fuji . how many of his trees are pure gala ?", + "Output Program": [ + "n0 = 10.0\nn1 = 221.0\nn2 = 3.0\nn3 = 4.0\nt0 = n0 / 100.0\nt1 = n2 / n3\nt2 = t0 + t1\nt3 = n1 / t2\nanswer = t3 - n1\nprint(answer)" + ], + "Output Answer": [ + "39" + ], + "split": "train" + }, + { + "Input": "on a two - dimensional coordinate plane , the line q = x ^ 2 - x ^ 3 touches the x - axis in how many places ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nt0 = max(n0,n1)\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "the average ( arithmetic mean ) of the 5 positive integers k , m , r , s , and t is 10 , and k < m < r < s < t . if t is 20 , what is the greatest possible value of the median of the 5 integers ?", + "Output Program": [ + "n0 = 5.0\nn1 = 10.0\nn2 = 20.0\nn3 = 5.0\nt0 = n0 * n1\nt1 = t0 - n2\nt2 = t1 / 2.0\nanswer = t2 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "if a person walks at 15 km / hr instead of 10 km / hr , he would have walked 15 km more . the actual distance traveled by him is ?", + "Output Program": [ + "n0 = 15.0\nn1 = 10.0\nn2 = 15.0\nt0 = n0 - n1\nt1 = n2 / t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "the population of a bacteria culture doubles every 1 minutes . approximately how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria", + "Output Program": [ + "import math\nn0 = 1.0\nn1 = 1000.0\nn2 = 500000.0\nt0 = 1.0 + 4.0\nt1 = t0 * n1\nt2 = t1 * 100.0\nt3 = t2 / n1\nt4 = math.log(max(1e-5, t3), 2)\nanswer = n0 * t4\nprint(answer)" + ], + "Output Answer": [ + "8.965784284662087" + ], + "split": "train" + }, + { + "Input": "a , b and c have rs . 1000 between them , a and c together have rs . 700 and b and c rs . 600 . how much does c have ?", + "Output Program": [ + "n0 = 1000.0\nn1 = 700.0\nn2 = 600.0\nt0 = n1 + n2\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "if ( 1 / 2 ) ^ 18 ( 1 / 81 ) ^ k = 1 / 18 ^ 18 , then k =", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 18.0\nn3 = 1.0\nn4 = 81.0\nn5 = 1.0\nn6 = 18.0\nn7 = 18.0\nt0 = n1 * n2\nanswer = t0 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "a student finds the average of 9 positive integers . each integer contains two digits . by mistake , the boy interchanges the digits of one number say pq for qp . due to this , the average becomes 1 less than the previous one . what was the difference of the two digits p and q ?", + "Output Program": [ + "n0 = 9.0\nn1 = 1.0\nt0 = n1 / n0\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "a grocer has a sale of rs . 6435 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 7000 ?", + "Output Program": [ + "n0 = 6435.0\nn1 = 6927.0\nn2 = 6855.0\nn3 = 7230.0\nn4 = 6562.0\nn5 = 5.0\nn6 = 7000.0\nt0 = n5 + 1.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n6 * t0\nt4 = n3 + t2\nt5 = n4 + t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "7991" + ], + "split": "train" + }, + { + "Input": "during the first two weeks of january , the total rainfall in springdale was 30 inches . if the rainfall during the second week was 1.5 times the rainfall during the first week , what was the rainfall during the second week of january ?", + "Output Program": [ + "n0 = 30.0\nn1 = 1.5\nt0 = n1 + 1.0\nt1 = n1 / t0\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "what is the minimum value of | x - 4 | + | x + 2 | + | x - 5 | ?", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\nn2 = 5.0\n\nanswer = n1 + n2\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "the average weight of 8 persons increases by 4 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 4.0\nn2 = 65.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "97" + ], + "split": "train" + }, + { + "Input": "if p and q are positive integers each greater than 1 , and 17 ( p + 1 ) = 25 ( q + 1 ) , what is the least possible value of p + q ?", + "Output Program": [ + "n0 = 1.0\nn1 = 17.0\nn2 = 1.0\nn3 = 25.0\nn4 = 1.0\nt0 = n1 + n3\nanswer = t0 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "set s consists of integers { 12 , 34 } . if two numbers are chosen from set s at random , what is the probability that the sum of 2 numbers is more than 6 ?", + "Output Program": [ + "n0 = 12.0\nn1 = 34.0\nn2 = 2.0\nn3 = 6.0\n\nanswer = 1 / n3\nprint(answer)" + ], + "Output Answer": [ + "0.16666666666666666" + ], + "split": "train" + }, + { + "Input": "the average weight of 10 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 50 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 10.0\nn1 = 2.5\nn2 = 50.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "the average weight of 20 oarsmen in a boat is increased by 2 kg when one of the crew , who weight 40 kg is replaced by a new man . find the weight of the new man .", + "Output Program": [ + "n0 = 20.0\nn1 = 2.0\nn2 = 40.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "a gets 3 times as much money as b gets , b gets only rs . 25 more then what c gets . the 3 gets rs . 645 in all . find the share of b ?", + "Output Program": [ + "n0 = 3.0\nn1 = 25.0\nn2 = 3.0\nn3 = 645.0\nt0 = n1 + n3\nt1 = n0 + 1.0\nt2 = t1 + 1.0\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "134" + ], + "split": "train" + }, + { + "Input": "if ( a - b - c + d = 13 ) and ( a + b - c - d = 3 ) , what is the value of ( b - d ) ^ 2 ?", + "Output Program": [ + "n0 = 13.0\nn1 = 3.0\nn2 = 2.0\nt0 = n0 + n1\nt1 = t0 / n2\nt2 = n1 - t1\nanswer = t2**min(n2, 5)\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "if a ' s height is 20 % less than that of b , how much percent b ' s height is more than that of a ?", + "Output Program": [ + "n0 = 20.0\nt0 = 100.0 - n0\nt1 = n0 / t0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "a set of football matches is to be organized in a ` ` round - robin ' ' fashion , i . e . , every participating team plays a match against every other team once and only once . if 15 matches are totally played , how many teams participated ?", + "Output Program": [ + "n0 = 15.0\nt0 = n0 - 10.0\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "the average weight of 8 sailors in a boat is increased by 1 kg if one of them weighing 56 kg is replaced by a new sailor . the weight of the new sailor is ?", + "Output Program": [ + "n0 = 8.0\nn1 = 1.0\nn2 = 56.0\n\nanswer = n0 + n2\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "train" + }, + { + "Input": "there are some sweets in party , 1 / 3 rd eaten by kids . then 2 / 5 th of the remaining by men , then 2 / 3 rd of the remaining by women . at last 2 were remaining . how many sweets were in total ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 2.0\nn3 = 5.0\nn4 = 2.0\nn5 = 3.0\nn6 = 2.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = n2 / n1\nt3 = 1.0 - t0\nt4 = t1 * t3\nt5 = t3 - t4\nt6 = t2 * t5\nt7 = t5 - t6\nanswer = n2 / t7\nprint(answer)" + ], + "Output Answer": [ + "14.999999999999996" + ], + "split": "train" + }, + { + "Input": "a man has some hens and cows . if the number of heads be 60 and the number of feet equals 200 , then the number of hens will be :", + "Output Program": [ + "n0 = 60.0\nn1 = 200.0\nt0 = n0 * 4.0\nt1 = t0 - n1\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "of the total amount that jill spent on a shopping trip , excluding taxes , she spent 50 percent on clothing , 25 percent on food , and 25 percent on other items . if jill paid a 10 percent tax on the clothing , no tax on the food , and an 20 percent tax on all other items , then the total tax that she paid was what percent of the total amount that she spent , excluding taxes ?", + "Output Program": [ + "n0 = 50.0\nn1 = 25.0\nn2 = 25.0\nn3 = 10.0\nn4 = 20.0\nt0 = n3 / 100.0\nt1 = n4 / 100.0\nt2 = n0 * t0\nt3 = n2 * t1\nt4 = t2 + t3\nt5 = t4 / 100.0\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "if a 2 - b 2 = 11 and a * b = 5 , find a 4 + b 4 .", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 11.0\nn3 = 5.0\nn4 = 4.0\nn5 = 4.0\nt0 = n3**min(n0, 5)\nt1 = n2**min(n0, 5)\nt2 = t0 * n0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "171" + ], + "split": "train" + }, + { + "Input": "on july 1 of last year , total employees at company e was decreased by 10 percent . without any change in the salaries of the remaining employees , the average ( arithmetic mean ) employee salary was 10 percent more after the decrease in the number of employees than before the decrease . the total of the combined salaries of all the employees at company e after july 1 last year was what percent of that before july 1 last year ?", + "Output Program": [ + "n0 = 1.0\nn1 = 10.0\nn2 = 10.0\nn3 = 1.0\nn4 = 1.0\n\nanswer = n1 * n1\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "( 753 x 753 + 247 x 247 - 753 x 247 ) / ( 753 x 753 x 753 + 247 x 247 x 247 ) = ?", + "Output Program": [ + "n0 = 753.0\nn1 = 753.0\nn2 = 247.0\nn3 = 247.0\nn4 = 753.0\nn5 = 247.0\nn6 = 753.0\nn7 = 753.0\nn8 = 753.0\nn9 = 247.0\nn10 = 247.0\nn11 = 247.0\nt0 = n0 * n0\nt1 = n2 * n2\nt2 = n0 * n2\nt3 = t0 + t1\nt4 = n0 * t0\nt5 = n2 * t1\nt6 = t4 + t5\nt7 = t3 - t2\nanswer = t7 / t6\nprint(answer)" + ], + "Output Answer": [ + "0.001" + ], + "split": "train" + }, + { + "Input": "the tax on a commodity is diminished by 22 % but its consumption is increased by 9 % . find the decrease percent in the revenue derived from it ?", + "Output Program": [ + "n0 = 22.0\nn1 = 9.0\nt0 = n1 + 100.0\nt1 = 100.0 - n0\nt2 = t0 * t1\nt3 = t2 / 100.0\nanswer = 100.0 - t3\nprint(answer)" + ], + "Output Answer": [ + "14.980000000000004" + ], + "split": "train" + }, + { + "Input": "in a group of buffaloes and ducks , the number of legs are 24 more than twice the number of heads . what is the number of buffaloes in the group ?", + "Output Program": [ + "n0 = 24.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "what is the thousandths digit in the decimal equivalent of 57 / 5000 ?", + "Output Program": [ + "import math\nn0 = 57.0\nn1 = 5000.0\nt0 = n0 / n1\nt1 = t0 * 100.0\nanswer = math.floor(t1)\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg . what is the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.5\nn2 = 65.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "85" + ], + "split": "train" + }, + { + "Input": "in a party , there are rows arranged with 1220 and 30 chairs and there were 3 left in all the cases . when there were 11 rows . there were no chair left . if 30 chairs were added . then what will be the reminder ?", + "Output Program": [ + "n0 = 1220.0\nn1 = 30.0\nn2 = 3.0\nn3 = 11.0\nn4 = 30.0\n\nanswer = n3 - n2\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "for every integer n \u2265 3 , the function g ( n ) is defined as the product of all the odd integers from 1 to n , inclusive . what is the value of g ( 106 ) \u2013 g ( 103 ) ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 106.0\nn3 = 103.0\n\nanswer = n2 - n1\nprint(answer)" + ], + "Output Answer": [ + "105" + ], + "split": "train" + }, + { + "Input": "if x is 11 percent greater than 90 , then x =", + "Output Program": [ + "n0 = 11.0\nn1 = 90.0\nt0 = n0 / 100.0\nt1 = n1 * t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "99.9" + ], + "split": "train" + }, + { + "Input": "the total marks obtained by a student in mathematics and physics is 60 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together ?", + "Output Program": [ + "n0 = 60.0\nn1 = 20.0\nt0 = n0 + n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "if the product of the integers from 1 to n is divisible by 1029 , what is the least possible value of n ?", + "Output Program": [ + "n0 = 1.0\nn1 = 1029.0\nt0 = 3.0 + 4.0\nt1 = n1 / 3.0\nt2 = t1 / t0\nt3 = t2 / t0\nanswer = t3 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "average families of 4 pay $ 3000 for their health insurance deductibles annually . there will be a 2 / 3 increase in the deductibles for next year . how much more will the average family pay in deductibles next year ?", + "Output Program": [ + "n0 = 4.0\nn1 = 3000.0\nn2 = 2.0\nn3 = 3.0\nt0 = n1 * n2\nanswer = t0 / n3\nprint(answer)" + ], + "Output Answer": [ + "2000" + ], + "split": "train" + }, + { + "Input": "at the end of the month , a certain ocean desalination plant \u2019 s reservoir contained 6 million gallons of water . this amount is twice the normal level . if this amount represents 60 % of the reservoir \u2019 s total capacity , how many million gallons short of total capacity is the normal level ?", + "Output Program": [ + "n0 = 6.0\nn1 = 60.0\nt0 = n0 / 2.0\nt1 = n1 / 100.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "a sum of money lent out at s . i . amounts to a total of $ 600 after 2 years and to $ 850 after a further period of 5 years . what was the initial sum of money that was invested ?", + "Output Program": [ + "n0 = 600.0\nn1 = 2.0\nn2 = 850.0\nn3 = 5.0\nt0 = n1 / n3\nt1 = n2 - n0\nt2 = t0 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "train" + }, + { + "Input": "a certain board game is played by rolling a pair of fair 6 - sided dice and then moving one ' s piece forward the number of spaces indicated by the sum showing on the dice . a player is frozen if her opponent ' s piece comes to rest in the space already occupied by her piece . if player a is about to roll and is currently 8 spaces behind player b , what is the probability that player b will be frozen after player a rolls ?", + "Output Program": [ + "n0 = 6.0\nn1 = 8.0\nt0 = 1.0 + 4.0\nt1 = n0 * n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.1388888888888889" + ], + "split": "train" + }, + { + "Input": "we bought 85 hats at the store . blue hats cost $ 6 and green hats cost $ 7 . the total price was $ 548 . how many green hats did we buy ?", + "Output Program": [ + "n0 = 85.0\nn1 = 6.0\nn2 = 7.0\nn3 = 548.0\nt0 = n0 * n1\nanswer = n3 - t0\nprint(answer)" + ], + "Output Answer": [ + "38" + ], + "split": "train" + }, + { + "Input": "the age of somu is one - third his father ' s . 10 years back he was one - fifth of his father ' s age . what is his persent age ?", + "Output Program": [ + "n0 = 10.0\nt0 = 1.0 + 4.0\nt1 = n0 * t0\nt2 = t0 - 3.0\nt3 = t1 - n0\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 92.16 , the number of the member is the group is :", + "Output Program": [ + "import math\nn0 = 92.16\nt0 = n0 * 100.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "96" + ], + "split": "train" + }, + { + "Input": "if a person walks at 10 km / hr instead of 5 km / hr , he would have walked 20 km more . the actual distance traveled by him is ?", + "Output Program": [ + "n0 = 10.0\nn1 = 5.0\nn2 = 20.0\nt0 = n0 - n1\nt1 = n2 / t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "find the value of m 82519 x 9999 = m ?", + "Output Program": [ + "n0 = 82519.0\nn1 = 9999.0\nt0 = n1 - 4.0\nanswer = t0 * n0\nprint(answer)" + ], + "Output Answer": [ + "824777405" + ], + "split": "train" + }, + { + "Input": "if one root of the equation 2 x ^ 2 + 3 x \u2013 k = 0 is 4 , what is the value of k ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 3.0\nn3 = 0.0\nn4 = 4.0\nt0 = n2 * n4\nt1 = n4**min(n0, 5)\nt2 = n0 * t1\nanswer = t2 + t0\nprint(answer)" + ], + "Output Answer": [ + "44" + ], + "split": "train" + }, + { + "Input": "if a is an integer greater than 8 but less than 15 and b is an integer greater than 6 but less than 21 , what is the range of a / b ?", + "Output Program": [ + "n0 = 8.0\nn1 = 15.0\nn2 = 6.0\nn3 = 21.0\nt0 = n2 + 1.0\nt1 = n0 + 1.0\nt2 = n1 - 1.0\nt3 = n3 - 1.0\nt4 = t2 / t0\nt5 = t1 / t3\nanswer = t4 - t5\nprint(answer)" + ], + "Output Answer": [ + "1.55" + ], + "split": "train" + }, + { + "Input": "find large number from below question the difference of two numbers is 1500 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder", + "Output Program": [ + "n0 = 1500.0\nn1 = 6.0\nn2 = 15.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nt2 = t0 / t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "1782" + ], + "split": "train" + }, + { + "Input": "the ratio of number of boys and girls in a class is 3 : 2 . in the 1 st semester exam 20 % of boys and 25 % of girls get more than or equal to 90 % marks . what percentage of students get less than 90 % marks ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 1.0\nn3 = 20.0\nn4 = 25.0\nn5 = 90.0\nn6 = 90.0\nt0 = n0 + n1\nt1 = n3 / 100.0\nt2 = n4 / 100.0\nt3 = n2 - t1\nt4 = n2 - t2\nt5 = n0 * t3\nt6 = n1 * t4\nt7 = t5 + t6\nt8 = t7 / t0\nanswer = t8 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "78" + ], + "split": "train" + }, + { + "Input": "the average of 10 numbers is calculated as 23 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?", + "Output Program": [ + "n0 = 10.0\nn1 = 23.0\nn2 = 36.0\nn3 = 26.0\nt0 = n2 - n3\nt1 = t0 / n0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "he average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 60 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.5\nn2 = 60.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "a certain bus driver is paid a regular rate of $ 18 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 976 in total compensation , how many total hours did he work that week ?", + "Output Program": [ + "n0 = 18.0\nn1 = 40.0\nn2 = 40.0\nn3 = 75.0\nn4 = 976.0\nt0 = n3 + 100.0\nt1 = n0 * n1\nt2 = n0 * t0\nt3 = n4 - t1\nt4 = t2 / 100.0\nt5 = t3 / t4\nanswer = n1 + t5\nprint(answer)" + ], + "Output Answer": [ + "48.12698412698413" + ], + "split": "train" + }, + { + "Input": "how many positive integers less than 8,000 are there in which the sum of the digits equals 5 ?", + "Output Program": [ + "import math\nn0 = 8000.0\nn1 = 5.0\nt0 = n1 + 4.0\nt1 = math.factorial(min(15, int(n1)))\nt2 = 4.0 - 1.0\nt3 = math.factorial(min(15, int(t2)))\nt4 = t0 - 1.0\nt5 = math.factorial(min(15, int(t4)))\nt6 = t1 * t3\nanswer = t5 / t6\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "train" + }, + { + "Input": "c and d started a business by investing rs . 1000 / - and rs . 1500 / - respectively . find the d \u2019 s share out of a total profit of rs . 500 :", + "Output Program": [ + "n0 = 1000.0\nn1 = 1500.0\nn2 = 500.0\nt0 = n0 / n2\nt1 = n1 / n2\nt2 = t0 + t1\nanswer = n2 / t2\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "q and r are two - digit positive integers that have the same digits but in reverse order . if the positive difference between q and r is less than 70 , what is the greatest possible value of q minus r ?", + "Output Program": [ + "n0 = 70.0\nt0 = 10.0 - 1.0\nt1 = n0 % t0\nanswer = t1 * t0\nprint(answer)" + ], + "Output Answer": [ + "63" + ], + "split": "train" + }, + { + "Input": "at a certain paint store forest green is made by mixing 4 parts blue paint with 3 parts yellow paint . verdant green is made by mixing 4 parts yellow paint with 3 parts blue paint . how many liters of yellow paint must be added to 7 liters of forest green to change it to verdant green ?", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 4.0\nn3 = 3.0\nn4 = 7.0\nt0 = n0 / n1\nt1 = n0 * t0\nanswer = t1 - n1\nprint(answer)" + ], + "Output Answer": [ + "2.333333333333333" + ], + "split": "train" + }, + { + "Input": "seller selling an apple for rs . 16 , a seller loses 1 / 6 th of what it costs him . the cp of the apple is ?", + "Output Program": [ + "n0 = 16.0\nn1 = 1.0\nn2 = 6.0\n\nanswer = n0 + n1\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "what is the smallest number which when increased by 3 is divisible by 9 , 70 , 25 and 21 ?", + "Output Program": [ + "import scipy\nn0 = 3.0\nn1 = 9.0\nn2 = 70.0\nn3 = 25.0\nn4 = 21.0\nt0 = scipy.lcm(int(n1), int(n2))\nt1 = scipy.lcm(int(n3), int(n4))\nt2 = scipy.lcm(int(t0), int(t1))\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "3153" + ], + "split": "train" + }, + { + "Input": "an employee whose hourly wage was increased by 25 percent decided to reduce the number of hours worked per week so that the employee ' s total weekly income would remain unchanged . by what percent should the number of hours worked be reduced ?", + "Output Program": [ + "n0 = 25.0\nt0 = n0 + 100.0\nt1 = t0 / 100.0\nt2 = 100.0 / t1\nanswer = 100.0 - t2\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "there are 150 ' zeroes ' and 151 ' ones ' written on a black board . a step involves choosing 3 digits and replacing them with a single digit . if all the 3 digits are identical , they are replaced with the same digit . otherwise , the digit that appears twice replaces the 3 chosen digits . what is the minimum number of steps after which there will be no zero written on the blackboard ?", + "Output Program": [ + "n0 = 150.0\nn1 = 151.0\nn2 = 3.0\nn3 = 3.0\nn4 = 3.0\nt0 = n0 / 2.0\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "76" + ], + "split": "train" + }, + { + "Input": "the avg weight of a , b & c is 84 kg . if d joins the group , the avg weight of the group becomes 80 kg . if another man e who weights is 3 kg more than d replaces a , then the avgof b , c , d & e becomes 79 kg . what is the weight of a ?", + "Output Program": [ + "n0 = 84.0\nn1 = 80.0\nn2 = 3.0\nn3 = 79.0\nt0 = n1 * 4.0\nt1 = n3 * 4.0\nt2 = n0 * n2\nt3 = t0 - t2\nt4 = n2 + t3\nt5 = t1 - t4\nanswer = t0 - t5\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "if the price of a certain computer increased 30 percent from d dollars to 377 dollars , then 2 d =", + "Output Program": [ + "n0 = 30.0\nn1 = 377.0\nn2 = 2.0\nt0 = n0 + 100.0\nt1 = t0 / 100.0\nt2 = n1 / t1\nanswer = n2 * t2\nprint(answer)" + ], + "Output Answer": [ + "580" + ], + "split": "train" + }, + { + "Input": "find the unknown term 8 , 86 , x , - 4 , - 12", + "Output Program": [ + "n0 = 8.0\nn1 = 86.0\nn2 = 4.0\nn3 = 12.0\nt0 = n3 / n2\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a certain company retirement plan has arule of 70 provision that allows an employee to retire when the employee ' s age plus years of employment with the company total at least 70 . in what year could a female employee hired in 1988 on her 32 nd birthday first be eligible to retire under this provision ?", + "Output Program": [ + "n0 = 70.0\nn1 = 70.0\nn2 = 1988.0\nn3 = 32.0\nt0 = n0 - n3\nt1 = t0 / 2.0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "2007" + ], + "split": "train" + }, + { + "Input": "a certain protective additive increases from 45 days to 60 days the time between required maintenance checks on an industrial vehicle . by what percent is the time between maintenance checks increased by using the additive ?", + "Output Program": [ + "n0 = 45.0\nn1 = 60.0\nt0 = n1 - n0\nt1 = t0 / n0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "33.33333333333333" + ], + "split": "train" + }, + { + "Input": "a student got 74 % in math and 84 % in history . to get an overall average of 75 % , how much should the student get in the third subject ?", + "Output Program": [ + "n0 = 74.0\nn1 = 84.0\nn2 = 75.0\nt0 = n0 + n1\nt1 = n2 * 3.0\nanswer = t1 - t0\nprint(answer)" + ], + "Output Answer": [ + "67" + ], + "split": "train" + }, + { + "Input": "the captain of a cricket team of 11 members is 24 years old and the wicket keeper is 3 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ?", + "Output Program": [ + "n0 = 11.0\nn1 = 24.0\nn2 = 3.0\nt0 = n1 + n2\nt1 = n2 * n2\nt2 = n1 + t0\nt3 = t2 - t1\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "according to the formula f = 9 / 5 ( c ) + 32 , if the temperature in degrees farenheit ( f ) increases by 28 , by how much does the temperature in degrees celsius ( c ) increase ?", + "Output Program": [ + "n0 = 9.0\nn1 = 5.0\nn2 = 32.0\nn3 = 28.0\nt0 = n1 * n3\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "15.555555555555555" + ], + "split": "train" + }, + { + "Input": "cara took out a charge account at the general store and agreed to pay 5 % simple annual interest . if she charges $ 54 on her account in january , how much will she owe a year later , assuming she does not make any additional charges or payments ?", + "Output Program": [ + "n0 = 5.0\nn1 = 54.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "56.7" + ], + "split": "train" + }, + { + "Input": "one - tenth of the students at a nursery school are 4 years old or older . if 20 students have not yet reached their third birthday , and a total of 50 students are not between 3 years old and 4 years old , how many children are in the nursery school ?", + "Output Program": [ + "n0 = 4.0\nn1 = 20.0\nn2 = 50.0\nn3 = 3.0\nn4 = 4.0\nt0 = n2 - n1\nanswer = t0 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "if p / q = 3 / 4 then 3 p + 4 q = ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 3.0\nn3 = 4.0\nt0 = n1 / n0\nt1 = n0 * n0\nt2 = n0 * t0\nt3 = t2 * t2\nt4 = t3 + t1\nanswer = t4 / t2\nprint(answer)" + ], + "Output Answer": [ + "6.25" + ], + "split": "train" + }, + { + "Input": "2 men and 3 women are lined up in a row . what is the number of cases where they stand with each other in turn ? ( the number of cases in which men ( or women ) do not stand next to each other )", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 3.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(n1)))\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "( 0.82 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.82 ) ( power 2 ) + 0.082 + ( 0.1 ) ( power 2 ) is :", + "Output Program": [ + "n0 = 0.82\nn1 = 3.0\nn2 = 0.1\nn3 = 3.0\nn4 = 0.82\nn5 = 2.0\nn6 = 0.082\nn7 = 0.1\nn8 = 2.0\nt0 = n0**min(n1, 5)\nt1 = n2**min(n1, 5)\nt2 = n0**min(n5, 5)\nt3 = n2**min(n5, 5)\nt4 = n6 + t2\nt5 = t0 - t1\nt6 = t4 + t3\nanswer = t5 / t6\nprint(answer)" + ], + "Output Answer": [ + "0.72" + ], + "split": "train" + }, + { + "Input": "for every x , the action [ x ] is defined : [ x ] is the greatest integer less than or equal to x . what is the value of [ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 6.6 ?", + "Output Program": [ + "n0 = 6.5\nn1 = 2.0\nn2 = 3.0\nn3 = 2.0\nn4 = 7.2\nn5 = 8.4\nn6 = 6.6\nt0 = 4.0 / 10.0\nt1 = n1 * n4\nt2 = n5 - t0\nt3 = t1 + t2\nanswer = t3 - n6\nprint(answer)" + ], + "Output Answer": [ + "15.799999999999999" + ], + "split": "train" + }, + { + "Input": "at 1 : 00 pm , there were 10.0 grams of bacteria . the bacteria increased to x grams at 4 : 00 pm , and 25.6 grams at 7 : 00 pm . if the amount of bacteria present increased by the same fraction during each of the 3 - hour periods , how many grams of bacteria were present at 4 : 00 pm ?", + "Output Program": [ + "import math\nn0 = 1.0\nn1 = 0.0\nn2 = 10.0\nn3 = 4.0\nn4 = 0.0\nn5 = 25.6\nn6 = 7.0\nn7 = 0.0\nn8 = 3.0\nn9 = 4.0\nn10 = 0.0\nt0 = n5 / 10.0\nt1 = math.sqrt(max(0, t0))\nanswer = t1 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "the mean of 50 observations was 36 . it was found later that an observation 46 was wrongly taken as 23 . the corrected new mean is", + "Output Program": [ + "n0 = 50.0\nn1 = 36.0\nn2 = 46.0\nn3 = 23.0\nt0 = n0 * n1\nt1 = n0 - 2.0\nt2 = t1 - n3\nt3 = t0 + t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "36.5" + ], + "split": "train" + }, + { + "Input": "average weight of 15 boys in a class is 48 kgs . the average weight of the class of 25 students is 45 kgs . what is the average weight of the 15 girls in the class ?", + "Output Program": [ + "n0 = 15.0\nn1 = 48.0\nn2 = 25.0\nn3 = 45.0\nn4 = 15.0\nt0 = n2 * n3\nt1 = n0 * n1\nt2 = t0 - t1\nanswer = t2 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "40.5" + ], + "split": "train" + }, + { + "Input": "the sum of two numbers is 84 , and one of them is 12 more than the other . what are the two numbers ?", + "Output Program": [ + "n0 = 84.0\nn1 = 12.0\nt0 = n0 - n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "the sum of two numbers is 96 , and one of them is 12 more than the other . what are the two numbers ?", + "Output Program": [ + "n0 = 96.0\nn1 = 12.0\nt0 = n0 - n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "in a certain game , each player scores either 2 points or 5 points . if n players score 2 points and m players score 5 points , and the total number of points scored is 50 , what is the least possible positive difference q between n and m ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 2.0\nn3 = 5.0\nn4 = 50.0\n\nanswer = n1 - n0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "mary is expected to pay back a total sum of $ 819200 to her bank as mortgage . if she is expected to make a payment which is double of the previous months amount , how long will it take her to fully repay the loan if her initial payment was $ 400 .", + "Output Program": [ + "n0 = 819200.0\nn1 = 400.0\nt0 = n0 / 100.0\nt1 = t0 / 2.0\nt2 = t1 / 2.0\nt3 = t2 / 4.0\nt4 = t3 - 10.0\nt5 = t4 - 100.0\nt6 = t5 - 10.0\nt7 = t6 - 4.0\nt8 = t7 + 1.0\nanswer = n1 - t8\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "the average runs scored by a batsman in 20 matches is 40 . in the next 10 matches the batsman scored an average of 13 runs . find his average in all the 30 matches ?", + "Output Program": [ + "n0 = 20.0\nn1 = 40.0\nn2 = 10.0\nn3 = 13.0\nn4 = 30.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "31" + ], + "split": "train" + }, + { + "Input": "p , q and r have rs . 9000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?", + "Output Program": [ + "n0 = 9000.0\nt0 = 2.0 / 3.0\nt1 = t0 + 1.0\nt2 = n0 / t1\nanswer = t2 * t0\nprint(answer)" + ], + "Output Answer": [ + "3600.0000000000005" + ], + "split": "train" + }, + { + "Input": "if jake loses 8 pounds , he will weigh twice as much as his sister kendra . together they now weigh 293 pounds . what is jake \u2019 s present weight , in pounds ?", + "Output Program": [ + "n0 = 8.0\nn1 = 293.0\nt0 = n1 - n0\nt1 = t0 / 3.0\nt2 = t1 * 2.0\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "198" + ], + "split": "train" + }, + { + "Input": "two trains of equal are running on parallel lines in the same direction at 44 km / hr and 36 km / hr . the faster train passes the slower train in 36 sec . the length of each train is ?", + "Output Program": [ + "n0 = 44.0\nn1 = 36.0\nn2 = 36.0\nt0 = n0 - n1\nt1 = t0 * 1000.0\nt2 = t1 / 3600.0\nt3 = n2 * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "each of the 59 members in lourdes school class is required to sign up for a minimum of one and a maximum of 3 academic clubs . the 3 clubs to choose from are the poetry club , the history club , and the writing club . a total of 22 students sign up for the poetry club , 27 students for the history club , and 28 students for the writing club . if 6 students sign up for exactly two clubs , how many students sign up for all 3 clubs ?", + "Output Program": [ + "n0 = 59.0\nn1 = 3.0\nn2 = 3.0\nn3 = 22.0\nn4 = 27.0\nn5 = 28.0\nn6 = 6.0\nn7 = 3.0\nt0 = n3 + n4\nt1 = n5 + t0\nt2 = t1 - n0\nt3 = t2 - n6\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "average between two sets of numbers is closer to the set withmore no ' s ?", + "Output Program": [ + "t0 = 2.0 * 4.0\nanswer = t0 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "a student took 6 courses last year and received an average ( arithmetic mean ) grade of 100 points . the year before , the student took 5 courses and received an average grade of 70 points . to the nearest tenth of a point , what was the student \u2019 s average grade for the entire two - year period ?", + "Output Program": [ + "import math\nn0 = 6.0\nn1 = 100.0\nn2 = 5.0\nn3 = 70.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nt4 = t3 / t0\nanswer = math.floor(t4)\nprint(answer)" + ], + "Output Answer": [ + "86" + ], + "split": "train" + }, + { + "Input": "a certain mixture of nuts consists of 5 parts almonds to 1 parts walnuts , by weight . what is the number of pounds of almonds in 140 pounds of the mixture ?", + "Output Program": [ + "n0 = 5.0\nn1 = 1.0\nn2 = 140.0\nt0 = n0 + n1\nt1 = n0 * n2\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "116.66666666666667" + ], + "split": "train" + }, + { + "Input": "simplify : 0.4 * 0.5 + 0.3 * 0.2", + "Output Program": [ + "n0 = 0.4\nn1 = 0.5\nn2 = 0.3\nn3 = 0.2\nt0 = n0 * n1\nt1 = n2 * n3\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "0.26" + ], + "split": "train" + }, + { + "Input": "elena purchased brand x pens for $ 4.00 apiece and brand y for $ 2.80 apiece . if elena purchased a total of 12 of these pens for $ 40.00 , how many brand x pens did she purchase ?", + "Output Program": [ + "n0 = 4.0\nn1 = 2.8\nn2 = 12.0\nn3 = 40.0\nt0 = n0 * n2\nanswer = t0 - n3\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "if money is invested at r percent interest , compounded annually , the amount of investment will double in approximately 70 / r years . if pat ' s parents invested $ 10000 in a long term bond that pays 8 percent interest , compounded annually , what will be the approximate total amount of investment 18 years later , when pat is ready for college ?", + "Output Program": [ + "n0 = 70.0\nn1 = 10000.0\nn2 = 8.0\nn3 = 18.0\nt0 = n1 * 2.0\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "40000" + ], + "split": "train" + }, + { + "Input": "a man saves 20 % of his monthly salary . if an account of dearness of things he is to increase his monthly expenses by 20 % , he is only able to save rs . 240 per month . what is his monthly salary ?", + "Output Program": [ + "n0 = 20.0\nn1 = 20.0\nn2 = 240.0\nt0 = n1 / 100.0\nt1 = n2 * 100.0\nt2 = 100.0 - n0\nt3 = t0 * t2\nt4 = t3 + t2\nt5 = 100.0 - t4\nanswer = t1 / t5\nprint(answer)" + ], + "Output Answer": [ + "6000" + ], + "split": "train" + }, + { + "Input": "a case of 12 rolls of paper towels sells for $ 9 . the cost of one roll sold individually is $ 1 . what is the percent q of savings per roll for the 12 - roll package over the cost of 12 rolls purchased individually ?", + "Output Program": [ + "n0 = 12.0\nn1 = 9.0\nn2 = 1.0\nn3 = 12.0\nn4 = 12.0\nt0 = n1 / n0\nt1 = t0 * 100.0\nanswer = 100.0 - t1\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "arjun started a business with rs . 20000 and is joined afterwards by anoop with rs . 4000 . after how many months did anoop join if the profits at the end of the year are divided equally ?", + "Output Program": [ + "n0 = 20000.0\nn1 = 40.0\nn2 = 0.0\nt0 = 100.0 * 4.0\nt1 = 100.0 * 2.0\nt2 = n1 * 100.0\nt3 = t0 * 100.0\nt4 = t1 * 100.0\nt5 = t2 * 10.0\nt6 = t3 * 12.0\nt7 = t4 * 12.0\nt8 = t6 - t7\nanswer = t8 / t5\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "a class of 35 students has an average height of 180 cm . 7 students whose average height is 120 cm , left the class and 7 others whose average height is 140 cm , joined . calculate the new average height of the students of the class ( in cm ) is ?", + "Output Program": [ + "n0 = 35.0\nn1 = 180.0\nn2 = 7.0\nn3 = 120.0\nn4 = 7.0\nn5 = 140.0\nt0 = n0 * n1\nt1 = n2 * n5\nt2 = n2 * n3\nt3 = t1 - t2\nt4 = t0 + t3\nt5 = t4 / n0\nt6 = t5 + 12.0\nt7 = t6 + 4.0\nanswer = t7 + 4.0\nprint(answer)" + ], + "Output Answer": [ + "204" + ], + "split": "train" + }, + { + "Input": "at a certain food stand , the price of each apple is 40 \u00a2 and the price of each orange is 60 \u00a2 . mary selects a total of 10 apples and oranges from the food stand , and the average ( arithmetic mean ) price of the 10 pieces of fruit is 56 \u00a2 . how many oranges must mary put back so that the average price of the pieces of fruit that she keeps is 50 \u00a2 ?", + "Output Program": [ + "n0 = 40.0\nn1 = 60.0\nn2 = 10.0\nn3 = 10.0\nn4 = 56.0\nn5 = 50.0\nt0 = n1 * n2\nt1 = n2 * n4\nt2 = n2 * n5\nt3 = n1 - n0\nt4 = n1 - n5\nt5 = t0 - t1\nt6 = t5 / t3\nt7 = n0 * t6\nt8 = n2 - t6\nt9 = n1 * t8\nt10 = t7 + t9\nt11 = t10 - t2\nanswer = t11 / t4\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "think of a number , divide it by 5 and add 10 to it . the result is 21 . what is the number thought of ?", + "Output Program": [ + "n0 = 5.0\nn1 = 10.0\nn2 = 21.0\nt0 = n2 - n1\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "55" + ], + "split": "train" + }, + { + "Input": "the average of 6 numbers is 3.9 . the average of two of them is 3.4 , while the average of the other two is 3.85 . what is the average of the remaining two numbers ?", + "Output Program": [ + "n0 = 6.0\nn1 = 3.9\nn2 = 3.4\nn3 = 3.85\nt0 = n0 * n1\nt1 = n2 * 2.0\nt2 = n3 * 2.0\nt3 = t1 + t2\nt4 = t0 - t3\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "4.449999999999999" + ], + "split": "train" + }, + { + "Input": "the average weight of a , b and c is 45 kg . if the average weight of a and b be 41 kg and that of b and c be 43 kg , then the weight of b is :", + "Output Program": [ + "n0 = 45.0\nn1 = 41.0\nn2 = 43.0\nt0 = n1 * 2.0\nt1 = n2 * 2.0\nt2 = n0 * 3.0\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "if q = ( x \u2013 5 ) ^ 2 + ( x + 1 ) ^ 2 \u2013 6 , then y is least when x =", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 1.0\nn3 = 2.0\nn4 = 6.0\nt0 = n0 * n1\nt1 = n1 - t0\nt2 = t1 / n1\nt3 = t2 / n1\nanswer = -t3\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "what least number should be added to 1024 , so that the sum is completely divisible by 25 ?", + "Output Program": [ + "n0 = 1024.0\nn1 = 25.0\nt0 = n0 % n1\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "a student was asked to find the arithmetic mean of the numbers 3 , 117 , 915 , 138 , 1917 , 2114 and x . he found the mean to be 12 . what should be the remainder in the place of x ?", + "Output Program": [ + "n0 = 3.0\nn1 = 117.0\nn2 = 915.0\nn3 = 138.0\nn4 = 1917.0\nn5 = 2114.0\nn6 = 12.0\n\nanswer = 3.0 + 4.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "which of the numbers 1 , 2 , 3 , 4 , or 5 is nearest in value to the sum 2007 / 2999 + 8001 / 5998 + 2001 / 3999 = ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 3.0\nn3 = 4.0\nn4 = 5.0\nn5 = 2007.0\nn6 = 2999.0\nn7 = 8001.0\nn8 = 5998.0\nn9 = 2001.0\nn10 = 3999.0\nt0 = n5 / n6\nt1 = n7 / n8\nt2 = n4 / 10.0\nt3 = 10.0 * 100.0\nt4 = t0 + t1\nt5 = n6 + t3\nt6 = n9 / t5\nt7 = t4 + t6\nanswer = t7 + t2\nprint(answer)" + ], + "Output Answer": [ + "3.0035428163476343" + ], + "split": "train" + }, + { + "Input": "if jake loses 12 pounds , he will weigh twice as much as his sister . together they now weigh 156 pounds . what is jake \u2019 s present weight , in pounds ?", + "Output Program": [ + "n0 = 12.0\nn1 = 156.0\nt0 = n1 - n0\nt1 = t0 / 3.0\nt2 = t1 * 2.0\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "108" + ], + "split": "train" + }, + { + "Input": "the average age of a class of 19 students is 20 years . the average increased by 1 when the teacher ' s age also included . what is the age of the teacher ?", + "Output Program": [ + "n0 = 19.0\nn1 = 20.0\nn2 = 1.0\nt0 = n0 + n2\nt1 = n1 + n2\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "m and n are the x and y coordinates , respectively , of a point in the coordinate plane . if the points ( m , n ) and ( m + p , n + 4 ) both lie on the line defined by the equation x = ( y / 2 ) - ( 2 / 5 ) , what is the value of p ?", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\nn2 = 2.0\nn3 = 5.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "lilly has 10 fish and rosy has 14 fish . in total , how many fish do they have in all ?", + "Output Program": [ + "n0 = 10.0\nn1 = 14.0\n\nanswer = n0 + n1\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "a student scored an average of 55 marks in 3 subjects : physics , chemistry and mathematics . if the average marks in physics and mathematics is 90 and that in physics and chemistry is 70 , what are the marks in physics ?", + "Output Program": [ + "n0 = 55.0\nn1 = 3.0\nn2 = 90.0\nn3 = 70.0\nt0 = n2 * 2.0\nt1 = n3 * 2.0\nt2 = n0 * n1\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "155" + ], + "split": "train" + }, + { + "Input": "if x / y = 4 and y is not ' 0 ' what % of x is 2 x - y", + "Output Program": [ + "n0 = 4.0\nn1 = 0.0\nn2 = 2.0\nt0 = n0 + 1.0\nt1 = n2 + t0\nt2 = t0 * t0\nanswer = t1 * t2\nprint(answer)" + ], + "Output Answer": [ + "175" + ], + "split": "train" + }, + { + "Input": "find the principle on a certain sum of money at 11 % per annum for 2 2 / 5 years if the amount being rs . 1120 ?", + "Output Program": [ + "n0 = 11.0\nn1 = 2.0\nn2 = 2.0\nn3 = 5.0\nn4 = 1120.0\nt0 = n1 * n3\nt1 = n1 + t0\nt2 = t1 / n3\nt3 = n0 * t2\nt4 = t3 / 100.0\nt5 = t4 + 1.0\nanswer = n4 / t5\nprint(answer)" + ], + "Output Answer": [ + "886.0759493670886" + ], + "split": "train" + }, + { + "Input": "a number x is multiplied by 7 , and this product is then divided by 5 . if the positive square root of the result of these two operations equals x , what is the value of x if x \u2260 0 ?", + "Output Program": [ + "n0 = 7.0\nn1 = 5.0\nn2 = 0.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "1.4" + ], + "split": "train" + }, + { + "Input": "in 2 bags , there are to be put together 5 red and 12 white balls , neither bag being empty . how must the balls be divided so as to give a person who draws 1 ball from either bag -", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 12.0\nn3 = 1.0\nt0 = n1 + n2\nt1 = n0 * n0\nt2 = t0 - n3\nt3 = n1 / t2\nt4 = t1 / t2\nanswer = t3 + t4\nprint(answer)" + ], + "Output Answer": [ + "0.5625" + ], + "split": "train" + }, + { + "Input": "two trains of equal length are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train passes the slower train in 36 seconds . the length of each train is :", + "Output Program": [ + "n0 = 46.0\nn1 = 36.0\nn2 = 36.0\nt0 = n0 - n1\nt1 = t0 * 1000.0\nt2 = t1 / 3600.0\nt3 = n2 * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "the average of first 20 even numbers is ?", + "Output Program": [ + "n0 = 20.0\n\nanswer = n0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "the difference between the two numbers is 1 / 3 of the larger number . if the smaller one is 48 the larger one is", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 48.0\nt0 = n0 / n1\nt1 = 1.0 - t0\nanswer = n2 / t1\nprint(answer)" + ], + "Output Answer": [ + "71.99999999999999" + ], + "split": "train" + }, + { + "Input": "at an examination in which full marks were 500 . a got 10 % less than b , b got 25 % more than c and c got 20 % less than d . if a got 360 marks , what percentage of full marks was obtained by d ?", + "Output Program": [ + "n0 = 500.0\nn1 = 10.0\nn2 = 25.0\nn3 = 20.0\nn4 = 360.0\nt0 = n2 + 100.0\nt1 = 100.0 - n3\nt2 = 100.0 - n1\nt3 = t1 / 100.0\nt4 = t2 / 100.0\nt5 = t0 / 100.0\nt6 = t4 * t5\nt7 = t3 * t6\nt8 = n4 / t7\nt9 = t8 / n0\nanswer = t9 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "a local restaurant recently renovated its dining space , purchasing new tables and chairs to use in addition to the original tables and chairs . the new tables each seat 6 customers , while the original tables each seat 4 customers . altogether , the restaurant now has 40 tables and is capable of seating 212 customers . how many more new tables than original tables does the restaurant have ?", + "Output Program": [ + "n0 = 6.0\nn1 = 4.0\nn2 = 40.0\nn3 = 212.0\nt0 = n0 * n2\nt1 = n0 - n1\nt2 = t0 - n3\nt3 = t2 / t1\nt4 = n2 - t3\nanswer = t4 - t3\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "n and m are each 3 - digit integers . each of the numbers 2 , 3,4 , 6 , 7 , and 8 is a digit of either n or m . what is the smallest possible positive difference between n and m ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 34.0\nn3 = 6.0\nn4 = 7.0\nn5 = 8.0\nt0 = n1 - n5\nt1 = t0 * 10.0\nt2 = t1 + 100.0\nanswer = t2 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "39" + ], + "split": "train" + }, + { + "Input": "if the average ( arithmetic mean ) of ( 2 a + 16 ) and ( 3 a - 8 ) is 89 , what is the value of a ?", + "Output Program": [ + "n0 = 2.0\nn1 = 16.0\nn2 = 3.0\nn3 = 8.0\nn4 = 89.0\nt0 = n0 + n2\nt1 = n0 * n4\nt2 = n1 - n3\nt3 = t1 - t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "34" + ], + "split": "train" + }, + { + "Input": "if x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year , the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $ 92 . if $ 2000 is the total amount invested , how much is invested at 8 percent ?", + "Output Program": [ + "n0 = 10.0\nn1 = 8.0\nn2 = 10.0\nn3 = 8.0\nn4 = 92.0\nn5 = 2000.0\nn6 = 8.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = 10.0 * 100.0\nt3 = n0 * n1\nt4 = t0 + t1\nt5 = t2 * 2.0\nt6 = t3 * 2.0\nt7 = n4 + t6\nt8 = t7 / t4\nanswer = t5 - t8\nprint(answer)" + ], + "Output Answer": [ + "600" + ], + "split": "train" + }, + { + "Input": "for how many unique pairs of nonnegative integers { a , b } is the equation a ^ 2 - b ^ 2 = 25 true ?", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 2.0\nn2 = 25.0\nt0 = 1.0 + 4.0\nt1 = math.log(max(1e-5, n2), 2)\nt2 = math.log(max(1e-5, t0), 2)\nanswer = t1 / t2\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "set s contains exactly 10 numbers and has an average ( arithmetic mean ) of 6.2 . if one of the numbers in set s is increased by 8 , while all other numbers remain the same , what is the new average of set s ?", + "Output Program": [ + "n0 = 10.0\nn1 = 6.2\nn2 = 8.0\nt0 = n0 * n1\nt1 = n2 + t0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "in a certain egg - processing plant , every egg must be inspected , and is either accepted for processing or rejected . for every 96 eggs accepted for processing , 4 eggs are rejected . if , on a particular day , 12 additional eggs were accepted , but the overall number of eggs inspected remained the same , the ratio of those accepted to those rejected would be 99 to 1 . how many t eggs does the plant process per day ?", + "Output Program": [ + "n0 = 96.0\nn1 = 4.0\nn2 = 12.0\nn3 = 99.0\nn4 = 1.0\nt0 = n3 - n0\nt1 = n2 / t0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "train" + }, + { + "Input": "if a ( a - 4 ) = 12 and b ( b - 4 ) = 12 , where a \u2260 b , then a + b =", + "Output Program": [ + "n0 = 4.0\nn1 = 12.0\nn2 = 4.0\nn3 = 12.0\nt0 = n0 + n1\nt1 = n0 - n1\nt2 = t0 + t1\nt3 = t2 - 1.0\nt4 = t3 - 1.0\nt5 = t4 - 1.0\nanswer = t5 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "the price of commodity x increases by 45 cents every year , while the price of commodity y increases by 20 cents every year . in 2001 , the price of commodity x was $ 4.20 and the price of commodity y was $ 6.30 . in which year will the price of commodity x be 65 cents more than the price of commodity y ?", + "Output Program": [ + "n0 = 45.0\nn1 = 20.0\nn2 = 2001.0\nn3 = 4.2\nn4 = 6.3\nn5 = 65.0\nt0 = n5 / 100.0\nt1 = n0 / 100.0\nt2 = n4 - n3\nt3 = t0 + t2\nt4 = t1 - t2\nt5 = t3 / t4\nanswer = n2 + t5\nprint(answer)" + ], + "Output Answer": [ + "1999.3333333333333" + ], + "split": "train" + }, + { + "Input": "when a merchant imported a certain item , she paid a 7 percent import tax on the portion of the total value of the item in excess of $ 1,000 . if the amount of the import tax that the merchant paid was $ 112.70 , what was the total value of the item ?", + "Output Program": [ + "n0 = 7.0\nn1 = 1000.0\nn2 = 112.7\nt0 = n0 / 100.0\nt1 = n2 / t0\nanswer = t1 + n1\nprint(answer)" + ], + "Output Answer": [ + "2610" + ], + "split": "train" + }, + { + "Input": "what least number should be added to 1056 , so that the sum is completely divisible by 23", + "Output Program": [ + "n0 = 1056.0\nn1 = 23.0\nt0 = n0 % n1\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "the smallest number which when diminished by 6 , is divisible by 12 , 16 , 18 , 21 and 28 is", + "Output Program": [ + "n0 = 6.0\nn1 = 12.0\nn2 = 16.0\nn3 = 18.0\nn4 = 21.0\nn5 = 28.0\nt0 = 3.0 + 4.0\nt1 = 3.0**min(2.0, 5)\nt2 = 2.0**min(4.0, 5)\nt3 = t1 * t2\nt4 = t0 * t3\nanswer = t4 + n0\nprint(answer)" + ], + "Output Answer": [ + "1014" + ], + "split": "train" + }, + { + "Input": "instead of multiplying a number by 3 , the number is divided by 5 . what is the percentage of error obtained ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nt0 = n1 / n1\nt1 = n0 * n1\nt2 = t0 / t1\nt3 = t2 * 100.0\nanswer = 100.0 - t3\nprint(answer)" + ], + "Output Answer": [ + "93.33333333333333" + ], + "split": "train" + }, + { + "Input": "in an objective competitive exam , a correct answer score 4 marks and on a wrong answer 2 marks are negatively added . a student scores 420 marks from 150 question . how many answers were correct ?", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\nn2 = 420.0\nn3 = 150.0\nt0 = n0 + n1\nt1 = n3 * 2.0\nt2 = n2 + t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "in a division , divident is 690 , divisior is 36 and quotient is 19 . find the remainder .", + "Output Program": [ + "n0 = 690.0\nn1 = 36.0\nn2 = 19.0\n\nanswer = n0 % n1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "excluding stoppages , the average speed of a bus is 60 km / hr and including stoppages , the average speed of the bus is 30 km / hr . for how many minutes does the bus stop per hour ?", + "Output Program": [ + "n0 = 60.0\nn1 = 30.0\nt0 = n1 / n0\nt1 = 1.0 * 60.0\nt2 = t0 * 60.0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "a library has an average of 570 visitors on sundays and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :", + "Output Program": [ + "import math\nn0 = 570.0\nn1 = 240.0\nn2 = 30.0\nt0 = 3.0 + 4.0\nt1 = n2 / t0\nt2 = math.floor(t1)\nt3 = t2 + 1.0\nt4 = n0 * t3\nt5 = n2 - t3\nt6 = n1 * t5\nt7 = t4 + t6\nanswer = t7 / n2\nprint(answer)" + ], + "Output Answer": [ + "295" + ], + "split": "train" + }, + { + "Input": "one week , a certain truck rental lot had a total of 24 trucks , all of which were on the lot monday morning . if 50 % of the trucks that were rented out during the week were returned to the lot on or before saturday morning of that week , and if there were at least 12 trucks on the lot that saturday morning , what is the greatest number of different trucks that could have been rented out during the week ?", + "Output Program": [ + "n0 = 24.0\nn1 = 50.0\nn2 = 12.0\nt0 = n1 / 100.0\nt1 = n0 * t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "if the least common addition of two prime numbers x and y is 36 , where x < y , then the value of 4 x + y is", + "Output Program": [ + "n0 = 36.0\nn1 = 4.0\nt0 = 3.0 + 3.0\nt1 = n0 / n1\nt2 = n0 * 2.0\nt3 = t1 + t2\nanswer = t3 + t0\nprint(answer)" + ], + "Output Answer": [ + "87" + ], + "split": "train" + }, + { + "Input": "the average of 25 results is 24 . the average of first 12 of those is 14 and the average of last 12 is 17 . what is the 13 th result ?", + "Output Program": [ + "n0 = 25.0\nn1 = 24.0\nn2 = 12.0\nn3 = 14.0\nn4 = 12.0\nn5 = 17.0\nn6 = 13.0\nt0 = n0 * n1\nt1 = n2 * n5\nt2 = n2 * n3\nt3 = t0 - t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "228" + ], + "split": "train" + }, + { + "Input": "the average of 6 no . ' s is 3.95 . the average of 2 of them is 3.4 , while the average of theother 2 is 3.85 . what is the average of the remaining 2 no ' s ?", + "Output Program": [ + "n0 = 6.0\nn1 = 3.95\nn2 = 2.0\nn3 = 3.4\nn4 = 2.0\nn5 = 3.85\nn6 = 2.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n2 * n5\nt3 = t1 + t2\nt4 = t0 - t3\nanswer = t4 / n2\nprint(answer)" + ], + "Output Answer": [ + "4.600000000000001" + ], + "split": "train" + }, + { + "Input": "when a person aged 39 is added to a group of n people , the average age increases by 2 . when a person aged 15 is added instead , the average age decreases by 1 . what is the value of e ?", + "Output Program": [ + "n0 = 39.0\nn1 = 2.0\nn2 = 15.0\nn3 = 1.0\nt0 = n1 + n3\nt1 = n0 - n2\nt2 = t1 / t0\nanswer = t2 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "the present age of a father is 3 years more than 3 times the age of his son . 3 years hence , father as age will be 8 years more than twice the age of the son . find the present age of the father .", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 3.0\nn3 = 8.0\nt0 = n0 * n3\nanswer = n0 + t0\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "train" + }, + { + "Input": "15 - 2 + 4 \u00f7 1 / 2 \u00d7 8 = ?", + "Output Program": [ + "n0 = 15.0\nn1 = 2.0\nn2 = 4.0\nn3 = 1.0\nn4 = 2.0\nn5 = 8.0\nt0 = 1.0 / 2.0\nt1 = n0 - n1\nt2 = n2 / t0\nt3 = n5 * t2\nanswer = t3 + t1\nprint(answer)" + ], + "Output Answer": [ + "77" + ], + "split": "train" + }, + { + "Input": "when positive integer n is divided by 2 , the remainder is 1 . when n is divided by 7 , the remainder is 5 . what is the smallest positive integer p , such that ( n + p ) is a multiple of 10 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 7.0\nn3 = 5.0\nn4 = 10.0\nt0 = n3 % n2\nanswer = n4 - t0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "there were totally 100 men . 81 are married . 75 have t . v , 85 have radio , 70 have a . c . how many men have t . v , radio , a . c and also married ?", + "Output Program": [ + "n0 = 100.0\nn1 = 81.0\nn2 = 75.0\nn3 = 85.0\nn4 = 70.0\nt0 = n0 - n1\nt1 = n0 - n2\nt2 = n0 - n3\nt3 = n0 - n4\nt4 = t0 + t1\nt5 = t4 + t2\nt6 = t5 + t3\nanswer = n0 - t6\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "a vessel of capacity 2 litre has 20 % of alcohol and another vessel of capacity 6 litre had 40 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?", + "Output Program": [ + "n0 = 2.0\nn1 = 20.0\nn2 = 6.0\nn3 = 40.0\nn4 = 8.0\nn5 = 10.0\nt0 = n1 / 100.0\nt1 = n3 / 100.0\nt2 = n0 * t0\nt3 = n2 * t1\nt4 = t2 + t3\nt5 = t4 / n5\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "28.000000000000004" + ], + "split": "train" + }, + { + "Input": "find large number from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder ?", + "Output Program": [ + "n0 = 1365.0\nn1 = 6.0\nn2 = 15.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nt2 = t0 / t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "1620" + ], + "split": "train" + }, + { + "Input": "joan and karl each bought a sofa and the sum of their purchases was $ 600 . if twice of what joan paid was $ 90 more than what karl paid , what did joan pay for her sofa ?", + "Output Program": [ + "n0 = 600.0\nn1 = 90.0\nt0 = n0 + n1\nanswer = t0 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "230" + ], + "split": "train" + }, + { + "Input": "a satellite is composed of 24 modular units , each of which is equipped with a set of sensors , some of which have been upgraded . each unit contains the same number of non - upgraded sensors . if the number of non - upgraded sensors on one unit is 1 / 6 the total number of upgraded sensors on the entire satellite , what fraction of the sensors on the satellite have been upgraded ?", + "Output Program": [ + "n0 = 24.0\nn1 = 1.0\nn2 = 6.0\nt0 = n1 / n2\nt1 = n0 * t0\nt2 = n0 * t1\nt3 = n0 + t2\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.2" + ], + "split": "train" + }, + { + "Input": "the average salary of the employees in a office is rs . 120 / month . the avg salary of officers is rs . 450 and of non officers is rs 110 . if the no . of officers is 15 , then find the no of nonofficers in the office .", + "Output Program": [ + "n0 = 120.0\nn1 = 450.0\nn2 = 110.0\nn3 = 15.0\nt0 = n1 * n3\nt1 = n0 * n3\nt2 = n0 - n2\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "495" + ], + "split": "train" + }, + { + "Input": "there are 15 players in a chess group , and each player plays each of the others once . given that each game is played by two players , how many total games will be played ?", + "Output Program": [ + "n0 = 15.0\nt0 = n0 - 1.0\nt1 = n0 * t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "105" + ], + "split": "train" + }, + { + "Input": "two heavily loaded sixteen - wheeler transport trucks are 855 kilometers apart , sitting at two rest stops on opposite sides of the same highway . driver a begins heading down the highway driving at an average speed of 90 kilometers per hour . exactly one hour later , driver b starts down the highway toward driver a , maintaining an average speed of 80 kilometers per hour . how many kilometers farther than driver b , will driver a have driven when they meet and pass each other on the highway ?", + "Output Program": [ + "n0 = 855.0\nn1 = 90.0\nn2 = 80.0\nt0 = n1 + n2\nt1 = n0 - n1\nt2 = n1 - n2\nt3 = t1 / t0\nt4 = t3 * t2\nanswer = n1 + t4\nprint(answer)" + ], + "Output Answer": [ + "135" + ], + "split": "train" + }, + { + "Input": "a person spends 1 / 3 rd of the money with him on clothes , 1 / 5 th of the remaining on food and 1 / 4 th of the remaining on travel . now , he is left with rs 300 . how much did he have with him in the beginning ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 5.0\nn4 = 1.0\nn5 = 4.0\nn6 = 300.0\nt0 = n0 / n1\nt1 = n0 - t0\nt2 = t1 / n3\nt3 = t1 - t2\nt4 = t3 / n5\nt5 = t3 - t4\nanswer = n6 / t5\nprint(answer)" + ], + "Output Answer": [ + "749.9999999999999" + ], + "split": "train" + }, + { + "Input": "a student is ranked 16 th from right and 6 th from left . how many students are there in totality ?", + "Output Program": [ + "n0 = 16.0\nn1 = 6.0\nt0 = n0 + n1\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "the sum of the first 50 positive even integers is 2550 . what is the sum w of even integers from 102 to 200 inclusive ?", + "Output Program": [ + "n0 = 50.0\nn1 = 2550.0\nn2 = 102.0\nn3 = 200.0\nt0 = n2 + n3\nt1 = n3 - n2\nt2 = t1 / 2.0\nt3 = t0 / 2.0\nt4 = t2 + 1.0\nanswer = t4 * t3\nprint(answer)" + ], + "Output Answer": [ + "7550" + ], + "split": "train" + }, + { + "Input": "if a number x is 10 % less than another number y and y is 10 % more than 125 , then x is equal to", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 125.0\nt0 = n0 / 100.0\nt1 = 100.0 - n0\nt2 = t0 + 1.0\nt3 = t1 / 100.0\nt4 = n2 * t2\nanswer = t3 * t4\nprint(answer)" + ], + "Output Answer": [ + "123.75" + ], + "split": "train" + }, + { + "Input": "cost is expressed by the formula tb ^ 4 . if b is doubled , the new cost is what percent of the original cost ?", + "Output Program": [ + "n0 = 4.0\nt0 = 2.0**min(n0, 5)\nanswer = t0 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "1600" + ], + "split": "train" + }, + { + "Input": "3 people each took 5 tests . if the ranges of their scores in the 5 practice tests were 17 , 28 and 35 , 45 what is the minimum possible range in scores of the 3 test - takers ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 5.0\nn3 = 17.0\nn4 = 28.0\nn5 = 35.0\nn6 = 45.0\nn7 = 3.0\nt0 = n1 + n5\nanswer = n1 + t0\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "a sum of money is distributed among a , b , c , d in the proportion of 5 : 3 : 2 : 3 . if a gets $ 1000 more than b , what is the c ' s share ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nn2 = 2.0\nn3 = 3.0\nn4 = 1000.0\nt0 = n4 + n4\nt1 = 2.0 * t0\nt2 = t1 / 4.0\nt3 = n1 * t2\nanswer = t3 / n3\nprint(answer)" + ], + "Output Answer": [ + "1000" + ], + "split": "train" + }, + { + "Input": "the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 18000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is", + "Output Program": [ + "n0 = 8000.0\nn1 = 7.0\nn2 = 18000.0\nn3 = 6000.0\nt0 = n2 - n0\nt1 = n0 - n3\nt2 = n1 * t0\nt3 = t2 / t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "a sum of rs . 427 is to be divided among a , b and c in such a way that 3 times a \u2019 s share , 4 times b \u2019 s share and 7 times c \u2019 s share are all equal . the share of c is ?", + "Output Program": [ + "n0 = 427.0\nn1 = 3.0\nn2 = 4.0\nn3 = 7.0\nt0 = n3 / n1\nt1 = n3 / n2\nt2 = n3 / n3\nt3 = t0 + t1\nt4 = t3 + t2\nanswer = n0 / t4\nprint(answer)" + ], + "Output Answer": [ + "83.99999999999999" + ], + "split": "train" + }, + { + "Input": "if x and t are integers and 2 x \u2013 t = 11 , then 4 x + t can not be", + "Output Program": [ + "n0 = 2.0\nn1 = 11.0\nn2 = 4.0\nt0 = n1 + n2\nanswer = n0 + t0\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "find the value of 582964 x 99999 = m ?", + "Output Program": [ + "n0 = 582964.0\nn1 = 99999.0\nt0 = n1 - 4.0\nanswer = t0 * n0\nprint(answer)" + ], + "Output Answer": [ + "58293485180" + ], + "split": "train" + }, + { + "Input": "a big container is 30 % full with water . if 18 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container ?", + "Output Program": [ + "n0 = 30.0\nn1 = 18.0\nn2 = 3.0\nn3 = 4.0\nt0 = n2 / n3\nt1 = n0 / 100.0\nt2 = t0 - t1\nanswer = n1 / t2\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "the average age of 15 students of a class is 15 years . out of these , the average age of 7 students is 14 years and that of the other 7 students is 16 years , the age of the 15 th student is", + "Output Program": [ + "n0 = 15.0\nn1 = 15.0\nn2 = 7.0\nn3 = 14.0\nn4 = 7.0\nn5 = 16.0\nn6 = 15.0\nt0 = n0 * n0\nt1 = n2 * n3\nt2 = n4 * n5\nt3 = t1 + t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "( 258 % of 1265 ) \u00f7 6 = ?", + "Output Program": [ + "n0 = 258.0\nn1 = 1265.0\nn2 = 6.0\nt0 = n0 / 100.0\nt1 = n1 * t0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "543.95" + ], + "split": "train" + }, + { + "Input": "if ( 1 / 5 ) ^ n * ( 1 / 4 ) ^ 18 = 1 / ( 2 * ( 10 ) ^ 35 ) , then n =", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 1.0\nn3 = 4.0\nn4 = 18.0\nn5 = 1.0\nn6 = 2.0\nn7 = 10.0\nn8 = 35.0\nt0 = n8 - n7\nanswer = n7 + t0\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "let exp ( m , n ) = m to the power n . if exp ( 10 , m ) = n exp ( 22 ) where m and n are integers then n = ___ ?", + "Output Program": [ + "n0 = 10.0\nn1 = 22.0\nt0 = n0**min(2.0, 5)\nt1 = 2.0**min(2.0, 5)\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today ' s production of 90 units raises the average to 52 units per day , what is the value of n ?", + "Output Program": [ + "n0 = 50.0\nn1 = 90.0\nn2 = 52.0\nt0 = n1 - n0\nt1 = n2 - n0\nt2 = t0 / t1\nanswer = t2 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "when positive integer e is divided by 13 , the remainder is 2 . when n is divided by 8 , the remainder is 5 . how many such values are less than 180 ?", + "Output Program": [ + "n0 = 13.0\nn1 = 2.0\nn2 = 8.0\nn3 = 5.0\nn4 = 180.0\nt0 = n1 + n3\nt1 = n0 - n3\nanswer = t1 - t0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.48 per glass on the first day , what was the price per glass on the second day ?", + "Output Program": [ + "n0 = 0.48\nt0 = 1.0 + 1.0\nt1 = 1.0 + 2.0\nt2 = n0 * t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.32" + ], + "split": "train" + }, + { + "Input": "amit , sumit and pramit go to a seaside town to spend a vacation there and on the first day everybody decides to visit different tourist locations . after breakfast , each of them boards a different tourist vehicle from the nearest bus - depot . after 3 hours , sumit who had gone to a famous beach , calls on the mobile of pramit and claims that he has observed a shark in the waters . pramit learns from the local guide that at that time of the year , only 8 sea - creatures ( including a shark ) are observable and the probability of observing any creature is equal . however , amit and pramit later recall during their discussion that sumit has a reputation for not telling the truth 5 out of 6 times . what is the probability that sumit actually observed a shark in the waters ?", + "Output Program": [ + "n0 = 3.0\nn1 = 8.0\nn2 = 5.0\nn3 = 6.0\nt0 = n3 + 1.0\nt1 = 1.0 / n1\nt2 = 1.0 / n3\nt3 = n2 / n3\nt4 = t0 / n1\nt5 = t1 * t2\nt6 = t3 * t4\nt7 = t5 + t6\nanswer = t5 / t7\nprint(answer)" + ], + "Output Answer": [ + "0.027777777777777773" + ], + "split": "train" + }, + { + "Input": "there are 7 players in a bowling team with an average weight of 121 kg . if two new players join the team , one weighs 110 kg and the second weighs 60 kg , what will be the new average weight ?", + "Output Program": [ + "n0 = 7.0\nn1 = 121.0\nn2 = 110.0\nn3 = 60.0\nt0 = n2 + n3\nt1 = n0 + 2.0\nt2 = n0 * n1\nt3 = t0 + t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "113" + ], + "split": "train" + }, + { + "Input": "a student scored an average of 70 marks in 3 subjects : physics , chemistry and mathematics . if the average marks in physics and mathematics is 90 and that in physics and chemistry is 70 , what are the marks in physics ?", + "Output Program": [ + "n0 = 70.0\nn1 = 3.0\nn2 = 90.0\nn3 = 70.0\nt0 = n2 * 2.0\nt1 = n3 * 2.0\nt2 = n0 * n1\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "110" + ], + "split": "train" + }, + { + "Input": "the output of a factory is increased by 10 % to keep up with rising demand . to handle the holiday rush , this new output is increased by 30 % . by approximately what percent would the output of the factory now have to be decreased in order to restore the original output ?", + "Output Program": [ + "n0 = 10.0\nn1 = 30.0\nt0 = 10.0 + 100.0\nt1 = n1 + 100.0\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = t2 * t3\nt5 = t4 - 1.0\nt6 = t5 / t4\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "30.069930069930077" + ], + "split": "train" + }, + { + "Input": "what is the smallest integer k for which 64 ^ k > 4 ^ 19 ?", + "Output Program": [ + "import math\nn0 = 64.0\nn1 = 4.0\nn2 = 19.0\nt0 = n2 / 3.0\nt1 = math.floor(t0)\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "if 10 ! - 2 * ( 5 ! ) ^ 2 is divisible by 10 ^ n , what is the greatest value of n ?", + "Output Program": [ + "n0 = 10.0\nn1 = 2.0\nn2 = 5.0\nn3 = 2.0\nn4 = 10.0\n\nanswer = n2 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "in a 3 digit number , the 100 digit is 2 more than the tens digit and the units digit is 2 less than the tens digit . if the sum of the digits is 27 , find the number ?", + "Output Program": [ + "n0 = 3.0\nn1 = 100.0\nn2 = 2.0\nn3 = 2.0\nn4 = 27.0\nt0 = n4 / n0\nt1 = n2 + t0\nt2 = t0 * 10.0\nt3 = t0 - n2\nt4 = t1 * 100.0\nt5 = t4 + t2\nanswer = t5 + t3\nprint(answer)" + ], + "Output Answer": [ + "1197" + ], + "split": "train" + }, + { + "Input": "nina has exactly enough money to purchase 6 widgets . if the cost of each widget were reduced by $ 1 , then nina would have exactly enough money to purchase 8 widgets . how much money does nina have ?", + "Output Program": [ + "n0 = 6.0\nn1 = 1.0\nn2 = 8.0\nt0 = n1 * n2\nt1 = n2 - n0\nt2 = t0 / t1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "a , b and c rent a pasture . if a puts 10 oxen for 7 months , b puts 12 oxen for 5 months and c puts 15 oxen for 3 months for grazing and the rent of the pasture is rs . 210 , then how much amount should c pay as his share of rent ?", + "Output Program": [ + "n0 = 10.0\nn1 = 7.0\nn2 = 12.0\nn3 = 5.0\nn4 = 15.0\nn5 = 3.0\nn6 = 210.0\nt0 = n4 * n5\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nt4 = t3 + t0\nt5 = t0 / t4\nanswer = n6 * t5\nprint(answer)" + ], + "Output Answer": [ + "53.99999999999999" + ], + "split": "train" + }, + { + "Input": "two brothers ram and ravi appeared for an exam . the probability of selection of ram is 5 / 7 and that of ravi is 1 / 5 . find the probability that both of them are selected .", + "Output Program": [ + "n0 = 5.0\nn1 = 7.0\nn2 = 1.0\nn3 = 5.0\nt0 = n0 / n1\nt1 = n2 / n3\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "0.14285714285714288" + ], + "split": "train" + }, + { + "Input": "find the mean proportional between 49 & 64 ?", + "Output Program": [ + "n0 = 49.0\nn1 = 64.0\nt0 = n0 + n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "56.5" + ], + "split": "train" + }, + { + "Input": "50 % of a number is 10 less than 3 / 5 th of that number . what is the number ?", + "Output Program": [ + "n0 = 50.0\nn1 = 10.0\nn2 = 3.0\nn3 = 5.0\nt0 = 100.0 / n3\nt1 = n1 * n3\nt2 = t0 * t1\nt3 = n2 * t0\nt4 = t3 - n0\nanswer = t2 / t4\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "17 + 18 = 35 . how many such 2 consecutive numbers are there less than 200 when added gives a sum which is divisible by 5 ?", + "Output Program": [ + "n0 = 17.0\nn1 = 18.0\nn2 = 35.0\nn3 = 2.0\nn4 = 200.0\nn5 = 5.0\n\nanswer = n4 / n5\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "if a - b = 3 and a ^ 2 + b ^ 2 = 27 , find the value of ab .", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 2.0\nn2 = 2.0\nn3 = 27.0\nt0 = math.sqrt(max(0, n3))\nt1 = t0 - n0\nt2 = t1 / n1\nt3 = n0 + t2\nt4 = t3 * t2\nanswer = n1 * t4\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "in a division sum , the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 2 to the thrice of the remainder . the dividend is ?", + "Output Program": [ + "n0 = 6.0\nn1 = 5.0\nn2 = 2.0\nt0 = n0 * 3.0\nt1 = n2 + t0\nt2 = t1 / n1\nt3 = t1 * t2\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "86" + ], + "split": "train" + }, + { + "Input": "there are 50 employees in the office of abc company . of these , 22 have taken an accounting course , 14 have taken a course in finance and 15 have taken a marketing course . 10 of the employees have taken exactly two of the courses and 1 employee has taken all 3 of the courses . how many of the 50 employees have taken none of the courses ?", + "Output Program": [ + "n0 = 50.0\nn1 = 22.0\nn2 = 14.0\nn3 = 15.0\nn4 = 10.0\nn5 = 1.0\nn6 = 3.0\nn7 = 50.0\nt0 = n1 + n2\nt1 = n5 * 2.0\nt2 = n3 + t0\nt3 = t2 - n4\nt4 = t3 - t1\nanswer = n0 - t4\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "what is the sum of all possible 3 - digit numbers that can be constructed using the digits 1 , 2 , and 4 if each digit can be used only once in each number ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 2.0\nn3 = 4.0\nt0 = n2 + n3\nt1 = n1 + t0\nt2 = t1 * 100.0\nt3 = t1 * 10.0\nt4 = t2 + t3\nt5 = t4 + t1\nanswer = t5 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "1554" + ], + "split": "train" + }, + { + "Input": "a number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34 . such a least possible number x is", + "Output Program": [ + "n0 = 5.0\nn1 = 8.0\nn2 = 34.0\nt0 = n2 * 2.0\nt1 = n0 * n1\nt2 = n0 - 1.0\nt3 = t0 - t1\nt4 = t3 / t2\nanswer = t4 + t0\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "if 1 = x . 2 = 2 x 3 = 4 x . . . . what is 2 x * 6 x + 5 x / 4 x - 56 x", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 2.0\nn3 = 3.0\nn4 = 4.0\nn5 = 2.0\nn6 = 6.0\nn7 = 5.0\nn8 = 4.0\nn9 = 56.0\nt0 = n1 * n6\nt1 = n1 * t0\nt2 = t1 / 2.0\nanswer = t2 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the closest approximation of a ( 69.28 \u00d7 0.004 ) / 0.03 is", + "Output Program": [ + "n0 = 69.28\nn1 = 0.004\nn2 = 0.03\nt0 = n1 / n2\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "9.237333333333334" + ], + "split": "train" + }, + { + "Input": "mark and ann together were allocated n boxes of cookies to sell for a club project . mark sold 8 boxes less than n and ann sold 2 boxes less than n . if mark and ann have each sold at least one box of cookies , but together they have sold less than n boxes , what is the value of n ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.0\n\nanswer = n0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "the maximum number of students among them 890 pens and 630 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :", + "Output Program": [ + "import scipy\nn0 = 890.0\nn1 = 630.0\n\nanswer = scipy.gcd(int(n0), int(n1))\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "laura took out a charge account at the general store and agreed to pay 9 % simple annual interest . if she charges $ 35 on her account in january , how much will she owe a year later , assuming she does not make any additional charges or payments ?", + "Output Program": [ + "n0 = 9.0\nn1 = 35.0\nt0 = n0 / 100.0\nt1 = n1 * t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "38.15" + ], + "split": "train" + }, + { + "Input": "the sum of two numbers is 72 , and one of them is 12 more than the other . what are the two numbers ?", + "Output Program": [ + "n0 = 72.0\nn1 = 12.0\nt0 = n0 - n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "which digits should come in place of * and $ if the number 62684 * $ is divisible by both 8 and 5 ?", + "Output Program": [ + "import scipy\nn0 = 62684.0\nn1 = 8.0\nn2 = 5.0\nt0 = scipy.lcm(int(n1), int(n2))\nt1 = t0 * 2.0\nt2 = t1 / 10.0\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "an amount of money is to be divided between p , q and r in the ratio of 3 : 7 : 12 . if the difference between the shares of p and q is rs . 3200 , what will be the difference between q and r ' s share ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 12.0\nn3 = 3200.0\nt0 = n1 - n0\nt1 = n2 - n1\nt2 = n3 / t0\nanswer = t2 * t1\nprint(answer)" + ], + "Output Answer": [ + "4000" + ], + "split": "train" + }, + { + "Input": "if 5 - 5 / x = 4 + 4 / x , then x =", + "Output Program": [ + "n0 = 5.0\nn1 = 5.0\nn2 = 4.0\nn3 = 4.0\nt0 = n3 + n1\nt1 = n0 - n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "a gardener wants to plant trees in his garden in rows in such away that the number of trees in each row to be the same . if there are 24 rows the number of trees in each row is 42 if there are 12 more rows find the number of trees in each row ?", + "Output Program": [ + "n0 = 24.0\nn1 = 42.0\nn2 = 12.0\nt0 = n0 + n2\nt1 = n0 * n1\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "in a race where 16 cars are running , the chance that car x will win is 1 / 4 , that y will win is 1 / 12 and that z will win is 1 / 7 . assuming that a dead heat is impossible , find the chance that one of them will win .", + "Output Program": [ + "n0 = 16.0\nn1 = 1.0\nn2 = 4.0\nn3 = 1.0\nn4 = 12.0\nn5 = 1.0\nn6 = 7.0\nt0 = n1 / n2\nt1 = n1 / n4\nt2 = n1 / n6\nt3 = t0 + t1\nanswer = t3 + t2\nprint(answer)" + ], + "Output Answer": [ + "0.47619047619047616" + ], + "split": "train" + }, + { + "Input": "the cash realised on selling a 14 % stock is rs . 107.25 , brokerage being 1 / 4 % is ?", + "Output Program": [ + "n0 = 14.0\nn1 = 107.25\nn2 = 1.0\nn3 = 4.0\nt0 = n2 / n3\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "107" + ], + "split": "train" + }, + { + "Input": "set a contains all the even numbers between 10 and 50 inclusive . set b contains all the even numbers between 110 and 150 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ?", + "Output Program": [ + "n0 = 10.0\nn1 = 50.0\nn2 = 110.0\nn3 = 150.0\nt0 = n1 - n0\nt1 = n2 - n0\nt2 = t0 / 2.0\nt3 = t2 + 1.0\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "2100" + ], + "split": "train" + }, + { + "Input": "if x is an integer such that 5 < x < 21 , 7 < x < 18 , 13 > x > 2 , 12 > x > 9 , and x + 1 < 13 , then x is", + "Output Program": [ + "n0 = 5.0\nn1 = 21.0\nn2 = 7.0\nn3 = 18.0\nn4 = 13.0\nn5 = 2.0\nn6 = 12.0\nn7 = 9.0\nn8 = 1.0\nn9 = 13.0\nt0 = n4 - n8\nanswer = t0 - n8\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "at deluxe paint store , fuchsia paint is made by mixing 4 parts of red paint with 2 parts of blue paint . mauve paint is made by mixing 3 parts of red paint with 6 parts blue paint . how many liters of blue paint must be added to 24 liters of fuchsia to change it to mauve paint ?", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\nn2 = 3.0\nn3 = 6.0\nn4 = 24.0\nt0 = n0 + n1\nt1 = n0 / t0\nt2 = n2 / t0\nt3 = n3 / t0\nt4 = n4 * t1\nt5 = t4 / t2\nt6 = n4 - t4\nt7 = t5 * t3\nanswer = t7 - t6\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "h . c . f of 136 , 144 and a third number is 8 and their l . c . m is 2 ^ 4 * 3 ^ 2 * 17 * 7 . the third number is :", + "Output Program": [ + "n0 = 136.0\nn1 = 144.0\nn2 = 8.0\nn3 = 2.0\nn4 = 4.0\nn5 = 3.0\nn6 = 2.0\nn7 = 17.0\nn8 = 7.0\nt0 = n0 * n1\nt1 = n3**min(n4, 5)\nt2 = n5**min(n3, 5)\nt3 = t1 * t2\nt4 = n7 * t3\nt5 = n8 * t4\nt6 = n2 * t5\nt7 = t6 / t0\nt8 = n2 * t7\nanswer = t8 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "168" + ], + "split": "train" + }, + { + "Input": "if n = ( 33 ) ^ 43 + ( 43 ) ^ 32 what is the units digit of n ?", + "Output Program": [ + "n0 = 33.0\nn1 = 43.0\nn2 = 43.0\nn3 = 32.0\nt0 = 2.0 * 3.0\nt1 = n0 % 10.0\nt2 = n1 % 4.0\nt3 = n1 % 10.0\nt4 = t1**min(t2, 5)\nt5 = t3**min(4.0, 5)\nt6 = t4 + t5\nt7 = t6 % 100.0\nanswer = t7 - t0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "what is the smallest number which when diminished by 20 , is divisible 15 , 30 , 45 and 60 ?", + "Output Program": [ + "import scipy\nn0 = 20.0\nn1 = 15.0\nn2 = 30.0\nn3 = 45.0\nn4 = 60.0\nt0 = scipy.lcm(int(n1), int(n2))\nt1 = scipy.lcm(int(n3), int(n4))\nt2 = scipy.lcm(int(t0), int(t1))\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "train" + }, + { + "Input": "joe has a total of $ 200 in his two pockets . he takes one fourth of the money in his left pocket and puts it in his right pocket . he then takes $ 20 from his left pocket and puts it in his right pocket . if he now has an equal amount of money in each pocket , then how much money did he originally have in his left pocket ?", + "Output Program": [ + "n0 = 200.0\nn1 = 20.0\nt0 = n0 + n1\nt1 = 1.0 / 4.0\nt2 = n1 + t0\nt3 = 1.0 - t1\nt4 = t3 + t3\nanswer = t2 / t4\nprint(answer)" + ], + "Output Answer": [ + "160" + ], + "split": "train" + }, + { + "Input": "the price of a cycle is reduced by 25 per cent . the new price is reduced by a further 60 per cent . the two reductions together are equal to a single reduction of", + "Output Program": [ + "n0 = 25.0\nn1 = 60.0\nt0 = 100.0 - n1\nt1 = 100.0 - n0\nt2 = t0 / 100.0\nt3 = t2 * t1\nanswer = 100.0 - t3\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "train" + }, + { + "Input": "given a number , there is an algorithm described here to find it ' s sum and number of factors . for example , let us take the number 1225 ?", + "Output Program": [ + "n0 = 1225.0\nt0 = 3.0 + 4.0\nt1 = 2.0 + 3.0\nt2 = t0 + 1.0\nt3 = t1 + 1.0\nt4 = n0 / t1\nt5 = t1**min(2.0, 5)\nt6 = t3 + t5\nt7 = t4 / t1\nt8 = t2 + t7\nanswer = t8 * t6\nprint(answer)" + ], + "Output Answer": [ + "1767" + ], + "split": "train" + }, + { + "Input": "if p and q are prime numbers , how many divisors does the product p ^ 4 * q ^ 9 have ?", + "Output Program": [ + "n0 = 4.0\nn1 = 9.0\nt0 = n0 + 1.0\nt1 = n1 + 1.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "if a - b = 3 and a 2 + b 2 = 29 , find the value of ab ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 2.0\nn3 = 29.0\nt0 = n0**min(n1, 5)\nt1 = n3 - t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "if it is a 3 x 3 matrix , for which elements in first row are ( v , 50 , w ) , second row ( 196 , x , y ) and in third row are ( 269 , z , 123 ) . it is given that the sum of the numbers in each row , column , diagonal are same . then find the value of ( y + z ) .", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 50.0\nn3 = 196.0\nn4 = 269.0\nn5 = 123.0\nt0 = n4 + n5\nt1 = n3 + n4\nt2 = t0 - n2\nt3 = t1 - n2\nt4 = n4 + t2\nt5 = t2 + t3\nt6 = t4 - n5\nt7 = t5 - n5\nanswer = t6 + t7\nprint(answer)" + ], + "Output Answer": [ + "1122" + ], + "split": "train" + }, + { + "Input": "a bag contains an equal number of one rupee , 50 paise and 25 paise coins respectively . if the total value is 140 , how many coins of each type are there ?", + "Output Program": [ + "n0 = 50.0\nn1 = 25.0\nn2 = 140.0\nt0 = 1 / 4.0\nt1 = 1 / 2.0\nt2 = t0 + t1\nt3 = t2 + 1.0\nanswer = n2 / t3\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "a 80 gallon solution of salt and water is 10 % salt . how many gallons of water must be added to the solution in order to decrease the salt to 8 % of the volume ?", + "Output Program": [ + "n0 = 80.0\nn1 = 10.0\nn2 = 8.0\nt0 = n1 - n2\nt1 = n0 * t0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "the average height of 35 boys in a class was calculated as 184 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ?", + "Output Program": [ + "import math\nn0 = 35.0\nn1 = 184.0\nn2 = 166.0\nn3 = 106.0\nt0 = n0 * n1\nt1 = t0 - n2\nt2 = n3 + t1\nt3 = t2 / n0\nanswer = math.floor(t3)\nprint(answer)" + ], + "Output Answer": [ + "182" + ], + "split": "train" + }, + { + "Input": "jennifer had $ 90 to spend on herself . she spent 1 / 5 of the money on a sandwich , 1 / 6 for a ticket to a museum , and 1 / 2 of it on a book . how much money does jennifer have left over ?", + "Output Program": [ + "n0 = 90.0\nn1 = 1.0\nn2 = 5.0\nn3 = 1.0\nn4 = 6.0\nn5 = 1.0\nn6 = 2.0\nt0 = n1 / n2\nt1 = n1 / n4\nt2 = n1 / n6\nt3 = n0 * t0\nt4 = n0 * t1\nt5 = n0 * t2\nt6 = t3 + t4\nt7 = t6 + t5\nanswer = n0 - t7\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "in a group of ducks and cows , the total number of legs are 36 more than twice the no . of heads . find the total no . of buffaloes .", + "Output Program": [ + "n0 = 36.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "find large number from below question the difference of two numbers is 1335 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder", + "Output Program": [ + "n0 = 1335.0\nn1 = 6.0\nn2 = 15.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nt2 = t0 / t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "1584" + ], + "split": "train" + }, + { + "Input": "what is the product of all the possible values of x if x ^ 2 - 9 x + 20 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 9.0\nn2 = 20.0\n\nanswer = n2 / 1.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "in a group of ducks and cows , the total number of legs are 28 more than twice the number of heads . find the total number of cows .", + "Output Program": [ + "n0 = 28.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "a retailer bought a coat at wholesale and marked it up 90 % to its initial price of $ 76 . by how many more dollars does he need to increase the price to achieve a 100 % markup ?", + "Output Program": [ + "n0 = 90.0\nn1 = 76.0\nn2 = 100.0\nt0 = n0 / n2\nt1 = t0 + 1.0\nt2 = n1 / t1\nt3 = t2 * 2.0\nanswer = t3 - n1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "if bat = 58 hat = 52 cat = 57 then whats rat = ?", + "Output Program": [ + "n0 = 58.0\nn1 = 52.0\nn2 = 57.0\nt0 = n2 + 3.0\nt1 = 3.0 * 3.0\nt2 = t1 * 2.0\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "there are 5 chess amateurs playing in villa ' s chess club tournament . if each chess amateur plays with exactly 16 other amateurs , what is the total number of chess games possible to be played in the tournament ?", + "Output Program": [ + "n0 = 5.0\nn1 = 16.0\nt0 = n0 * n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "the average age of 15 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men . the average age of the two new men is", + "Output Program": [ + "n0 = 15.0\nn1 = 21.0\nn2 = 23.0\nt0 = n1 + n2\nt1 = n0 * 1.0\nt2 = t0 / 2.0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "37" + ], + "split": "train" + }, + { + "Input": "sum of the numbers from 1 to 29 is", + "Output Program": [ + "n0 = 1.0\nn1 = 29.0\nt0 = n0 + 2.0\nt1 = n0 + 10.0\nt2 = n0 + 12.0\nt3 = 12.0 + 2.0\nt4 = t0 + 4.0\nt5 = t0 + 2.0\nt6 = t0 + 12.0\nt7 = t4 + t5\nt8 = n0 + t5\nt9 = n0 + t6\nt10 = t7 + t8\nt11 = n0 + t8\nt12 = n0 + t9\nt13 = t10 + t11\nt14 = n0 + t11\nt15 = n0 + t12\nt16 = t13 + t14\nt17 = n0 + t14\nt18 = n0 + t15\nt19 = t16 + t17\nt20 = n0 + t18\nt21 = t19 + 10.0\nt22 = n0 + t20\nt23 = t21 + t1\nt24 = n0 + t22\nt25 = t23 + 12.0\nt26 = n0 + t24\nt27 = t25 + t2\nt28 = n0 + t26\nt29 = t27 + t3\nt30 = n0 + t28\nt31 = t29 + t6\nt32 = n0 + t30\nt33 = t31 + t9\nt34 = n0 + t32\nt35 = t33 + t12\nt36 = n0 + t34\nt37 = t35 + t15\nt38 = t37 + t18\nt39 = t38 + t20\nt40 = t39 + t22\nt41 = t40 + t24\nt42 = t41 + t26\nt43 = t42 + t28\nt44 = t43 + t30\nt45 = t44 + t32\nt46 = t45 + t34\nt47 = t46 + t36\nanswer = n1 + t47\nprint(answer)" + ], + "Output Answer": [ + "432" + ], + "split": "train" + }, + { + "Input": "20 percent of the programmers in a startup company weigh 200 pounds or more . 20 - 5 percent of the programmers that are under 200 pounds in that same company weigh 100 pounds or less . what percent of the programmers in the startup company weigh between 100 and 200 pounds ?", + "Output Program": [ + "n0 = 20.0\nn1 = 200.0\nn2 = 20.0\nn3 = 5.0\nn4 = 200.0\nn5 = 100.0\nn6 = 100.0\nn7 = 200.0\nt0 = n0 - n3\nt1 = n1 * t0\nt2 = t1 / n5\nanswer = t2 + t2\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "lisa and robert have taken the same number of photos on their school trip . lisa has taken 3 times as many photos as claire and robert has taken 12 more photos than claire . how many photos has claire taken ?", + "Output Program": [ + "n0 = 3.0\nn1 = 12.0\nt0 = n0 - 1.0\nanswer = n1 / t0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "a man has rs . 10350 in the form of rs . 50 notes and rs . 500 notes . the total number of notes are 72 . find the number of notes of rs . 50 denomination .", + "Output Program": [ + "n0 = 10350.0\nn1 = 50.0\nn2 = 500.0\nn3 = 72.0\nn4 = 50.0\nt0 = n2 * n3\nt1 = n2 - n1\nt2 = t0 - n0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "57" + ], + "split": "train" + }, + { + "Input": "a multiple choice test consists of 4 questions , and each question has 5 answer choices . in how many w ways can the test be completed if every question is unanswered ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\n\nanswer = n1**min(n0, 5)\nprint(answer)" + ], + "Output Answer": [ + "625" + ], + "split": "train" + }, + { + "Input": "rahim bought 40 books for rs . 600 from one shop and 20 books for rs . 240 from another . what is the average price he paid per book ?", + "Output Program": [ + "n0 = 40.0\nn1 = 600.0\nn2 = 20.0\nn3 = 240.0\nt0 = n1 + n3\nt1 = n0 + n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "the salary of a , b , c , d , e is rs . 9000 , rs . 5000 , rs . 11000 , rs . 7000 , rs . 9000 per month respectively , then the average salary of a , b , c , d , and e per month is", + "Output Program": [ + "n0 = 9000.0\nn1 = 5000.0\nn2 = 11000.0\nn3 = 7000.0\nn4 = 9000.0\nt0 = n0 + n1\nt1 = 1.0 + 4.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "8200" + ], + "split": "train" + }, + { + "Input": "a grocer has a sale of rs . 7435 , rs . 7920 , rs . 7855 , rs . 8230 and rs . 7560 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 7500 ?", + "Output Program": [ + "n0 = 7435.0\nn1 = 7920.0\nn2 = 7855.0\nn3 = 8230.0\nn4 = 7560.0\nn5 = 5.0\nn6 = 7500.0\nt0 = n5 + 1.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n6 * t0\nt4 = n3 + t2\nt5 = n4 + t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "6000" + ], + "split": "train" + }, + { + "Input": "david obtained 96 , 95 , 82 , 97 and 95 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology what are his average marks ?", + "Output Program": [ + "n0 = 96.0\nn1 = 95.0\nn2 = 82.0\nn3 = 97.0\nn4 = 95.0\nn5 = 100.0\nt0 = n0 + n1\nt1 = 2.0 + 3.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "93" + ], + "split": "train" + }, + { + "Input": "the average salary of a person for the months of january , february , march and april is rs . 8000 and that for the months february , march , april and may is rs . 8100 . if his salary for the month of may is rs . 6500 , find his salary for the month of january ?", + "Output Program": [ + "n0 = 8000.0\nn1 = 8100.0\nn2 = 6500.0\nt0 = n0 * 4.0\nt1 = n1 * 4.0\nt2 = t1 - n2\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "6100" + ], + "split": "train" + }, + { + "Input": "the denominator of a fraction is 1 less than twice the numerator . if the numerator and denominator are both increased by 1 , the fraction becomes 3 / 5 . find the fraction ?", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 3.0\nn3 = 5.0\nt0 = n2 * 2.0\nt1 = n3 * 2.0\nt2 = t0 - 1.0\nt3 = t1 - 1.0\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.5555555555555556" + ], + "split": "train" + }, + { + "Input": "set s consists of integers { 13 , 57 } . if two numbers are chosen from set s at random , what is the probability that the product of 2 numbers is more than 15 ?", + "Output Program": [ + "import math\nn0 = 13.0\nn1 = 57.0\nn2 = 2.0\nn3 = 15.0\nt0 = math.factorial(min(15, int(4.0)))\nt1 = t0 / n2\nt2 = t1 / n2\nanswer = 2.0 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.3333333333333333" + ], + "split": "train" + }, + { + "Input": "in a certain warehouse , 40 percent of the packages weigh less than 75 pounds , and a total of 48 packages weigh less than 25 pounds . if 80 percent of the packages weigh at least 25 pounds , how many of the packages weigh at least 25 pounds but less than 75 pounds ?", + "Output Program": [ + "n0 = 40.0\nn1 = 75.0\nn2 = 48.0\nn3 = 25.0\nn4 = 80.0\nn5 = 25.0\nn6 = 25.0\nn7 = 75.0\nt0 = 100.0 - n4\nt1 = n2 / t0\nt2 = t1 * 100.0\nt3 = n0 * t2\nt4 = t3 / 100.0\nanswer = t4 - n2\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "cost is expressed by the formula tb ^ 4 . if b is doubled , the new cost e is what percent of the original cost ?", + "Output Program": [ + "n0 = 4.0\nt0 = 2.0**min(n0, 5)\nanswer = t0 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "1600" + ], + "split": "train" + }, + { + "Input": "if 1 / 12 of the passengers on a ship are from north america , 1 / 4 are europeans , 1 / 9 are from africa , 1 / 6 are from asia and the remaining 42 people are citizens of other continents , then how many passengers are on board the ship ?", + "Output Program": [ + "n0 = 1.0\nn1 = 12.0\nn2 = 1.0\nn3 = 4.0\nn4 = 1.0\nn5 = 9.0\nn6 = 1.0\nn7 = 6.0\nn8 = 42.0\nt0 = n0 / n1\nt1 = n0 / n3\nt2 = n0 / n5\nt3 = n0 / n7\nt4 = t0 + t1\nt5 = t4 + t2\nt6 = t5 + t3\nt7 = n0 - t6\nanswer = n8 / t7\nprint(answer)" + ], + "Output Answer": [ + "107.99999999999999" + ], + "split": "train" + }, + { + "Input": "the ratio of the amount of the oil bill for the month of february to the amount of the oil bill for the month of january was 5 : 4 . if the oil bill for february had been $ 30 more , the corresponding ratio would have been 3 : 2 . how much was the oil bill for january ?", + "Output Program": [ + "n0 = 5.0\nn1 = 4.0\nn2 = 30.0\nn3 = 3.0\nn4 = 2.0\nt0 = n3 / n4\nt1 = n0 / n1\nt2 = t0 - t1\nanswer = n2 / t2\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "a certain company expects quarterly earnings of $ 0.80 per share of stock , half of which will be distributed as dividends to shareholders while the rest will be used for research and development . if earnings are greater than expected , shareholders will receive an additional $ 0.04 per share for each additional $ 0.10 of per share earnings . if quarterly earnings are $ 1.10 per share , what will be the dividend paid to a person who owns 600 shares of the company ' s stock ?", + "Output Program": [ + "n0 = 0.8\nn1 = 0.04\nn2 = 0.1\nn3 = 1.1\nn4 = 600.0\nt0 = n0 / 2.0\nt1 = n3 - n0\nt2 = t1 * 10.0\nt3 = n1 * t2\nt4 = t0 + t3\nanswer = n4 * t4\nprint(answer)" + ], + "Output Answer": [ + "312" + ], + "split": "train" + }, + { + "Input": "robert ate 13 chocolates , nickel ate 4 chocolates . how many more chocolates did robert ate than nickel ?", + "Output Program": [ + "n0 = 13.0\nn1 = 4.0\n\nanswer = n0 - n1\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "if a certain number is divided by 3 , the quotient , dividend , and divisor , added together , will amount to 63 . what is the number ?", + "Output Program": [ + "n0 = 3.0\nn1 = 63.0\nt0 = n0 + 1.0\nt1 = n1 - n0\nt2 = n0 * t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "a vendor sells 30 percent of the apples he had and throws away 20 percent of the remainder . the next day , the vendor sells 50 percent of the remaining apples and throws away the rest . in total , what percent of his apples does the vendor throw away ?", + "Output Program": [ + "n0 = 30.0\nn1 = 20.0\nn2 = 50.0\nt0 = n1 / 100.0\nt1 = 100.0 - n0\nt2 = t0 * t1\nt3 = t1 - t2\nt4 = t3 / 2.0\nanswer = t4 + t2\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "of 61 players on a cricket team , 37 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?", + "Output Program": [ + "n0 = 61.0\nn1 = 37.0\nt0 = 1.0 / 3.0\nt1 = n0 - n1\nt2 = 1.0 - t0\nt3 = t2 * t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "53" + ], + "split": "train" + }, + { + "Input": "a batsman in his 15 th innings makes a score of 85 , and thereby increases his average by 3 . what is his average after the 15 th innings ? he had never been \u2019 not out \u2019 .", + "Output Program": [ + "n0 = 15.0\nn1 = 85.0\nn2 = 3.0\nn3 = 15.0\nt0 = n0 * n2\nt1 = n1 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "43" + ], + "split": "train" + }, + { + "Input": "two - third of a positive number and 49 / 216 of its reciprocal are equal . the number is :", + "Output Program": [ + "import math\nn0 = 49.0\nn1 = 216.0\nt0 = n0 * 3.0\nt1 = n1 * 2.0\nt2 = t0 / t1\nanswer = math.sqrt(max(0, t2))\nprint(answer)" + ], + "Output Answer": [ + "0.5833333333333334" + ], + "split": "train" + }, + { + "Input": "average monthly income of a family of 4 earning members was rs . 782 . one of the earning members died and therefore , the average income came down to rs 650 . the income of the deceased was ?", + "Output Program": [ + "n0 = 4.0\nn1 = 782.0\nn2 = 650.0\nt0 = n0 * n1\nt1 = n0 - 1.0\nt2 = n2 * t1\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "1178" + ], + "split": "train" + }, + { + "Input": "what is remainder of the division ( 1125 * 1127 * 1129 ) / 12 ?", + "Output Program": [ + "n0 = 1125.0\nn1 = 1127.0\nn2 = 1129.0\nn3 = 12.0\nt0 = n0 * n1\nt1 = n2 * t0\nt2 = t1 - 3.0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 8000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is", + "Output Program": [ + "n0 = 8000.0\nn1 = 7.0\nn2 = 8000.0\nn3 = 6000.0\nt0 = n2 - n0\nt1 = n0 - n3\nt2 = n1 * t0\nt3 = t2 / t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "a library has an average of 140 visitors on sundays and 80 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :", + "Output Program": [ + "import math\nn0 = 140.0\nn1 = 80.0\nn2 = 30.0\nt0 = 3.0 + 4.0\nt1 = n2 / t0\nt2 = math.floor(t1)\nt3 = t2 + 1.0\nt4 = n0 * t3\nt5 = n2 - t3\nt6 = n1 * t5\nt7 = t4 + t6\nanswer = t7 / n2\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "a soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price . during the annual summer sale , everything in the store is an additional 20 percent off the original list price . if a replica jersey ' s list price is $ 80 , approximately what percent of the list price is the lowest possible sale price ?", + "Output Program": [ + "n0 = 30.0\nn1 = 50.0\nn2 = 20.0\nn3 = 80.0\n\nanswer = n3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "find the least number must be added to 228712 so that remaining no . is divisible by 9 ?", + "Output Program": [ + "n0 = 228712.0\nn1 = 9.0\nt0 = n0 % n1\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "if 4 gallons of gasoline are added to a tank that is already filled to 3 / 4 of its capacity , the tank is then filled to 9 / 10 of its capacity . how many gallons does the tank hold ?", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 4.0\nn3 = 9.0\nn4 = 10.0\nt0 = n3 / n4\nt1 = n1 / n2\nt2 = t0 - t1\nt3 = n0 / t2\nt4 = t3 * t1\nanswer = n0 + t4\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "a drink vendor has 50 liters of maaza , 144 liters of pepsi and 368 liters of sprite . he wants to pack them in cans , so that each can contains the same number of liters of a drink , and does n ' t want to mix any two drinks in a can . what is the least number of cans required ?", + "Output Program": [ + "import scipy\nn0 = 50.0\nn1 = 144.0\nn2 = 368.0\nt0 = scipy.gcd(int(n0), int(n1))\nt1 = scipy.gcd(int(n2), int(t0))\nt2 = n0 / t1\nt3 = n1 / t1\nt4 = n2 / t1\nt5 = t2 + t3\nanswer = t5 + t4\nprint(answer)" + ], + "Output Answer": [ + "281" + ], + "split": "train" + }, + { + "Input": "if the sum of 3 consecutive even numbers is 44 more than the average of these numbers , then the largest of these numbers is ?", + "Output Program": [ + "n0 = 3.0\nn1 = 44.0\nt0 = n1 - 4.0\nt1 = t0 / 2.0\nt2 = n0 + t1\nanswer = t2 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "a grocer has a sale of rs . 6435 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6600 ?", + "Output Program": [ + "n0 = 6435.0\nn1 = 6927.0\nn2 = 6855.0\nn3 = 7230.0\nn4 = 6562.0\nn5 = 5.0\nn6 = 6600.0\nt0 = n5 + 1.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n6 * t0\nt4 = n3 + t2\nt5 = n4 + t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "5591" + ], + "split": "train" + }, + { + "Input": "the maximum numbers of students among them 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is", + "Output Program": [ + "n0 = 1001.0\nn1 = 910.0\n\nanswer = n0 - n1\nprint(answer)" + ], + "Output Answer": [ + "91" + ], + "split": "train" + }, + { + "Input": "what least number must be subtracted from 427398 so that remaining no . is divisible by 13", + "Output Program": [ + "import math\nn0 = 427398.0\nn1 = 13.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "an old man distributed all the gold coins he had to his two sons into two different numbers such that the difference between the squares of the two numbers is 81 times the difference between the two numbers . how many coins did the old man have ?", + "Output Program": [ + "import math\nn0 = 81.0\n\nanswer = math.floor(n0)\nprint(answer)" + ], + "Output Answer": [ + "81" + ], + "split": "train" + }, + { + "Input": "how much is it cost $ 0.50 each tire for 8 tires ?", + "Output Program": [ + "n0 = 0.5\nn1 = 8.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "if x is less than y by 35 % then y exceed x by :", + "Output Program": [ + "n0 = 35.0\nt0 = 100.0 - n0\nt1 = 100.0 / t0\nt2 = t1 - 1.0\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "53.846153846153854" + ], + "split": "train" + }, + { + "Input": "the average weight of 29 students is 28 kg . by the admission of a new student , the average weight is reduced to 27.3 kg . the weight of the new student is", + "Output Program": [ + "n0 = 29.0\nn1 = 28.0\nn2 = 27.3\nt0 = n0 + 1.0\nt1 = n0 * n1\nt2 = n2 * t0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "a reduction of 40 % in the price of bananas would enable a man to obtain 64 more for rs . 40 . what is the reduced price / dozen ?", + "Output Program": [ + "n0 = 40.0\nn1 = 64.0\nn2 = 40.0\nt0 = n0 / 100.0\nt1 = n0 * t0\nt2 = t1 / n1\nanswer = t2 * 12.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "a certain company has records stored with a record storage firm in 15 - inch by 12 - inch by 10 - inch boxes . the boxes occupy 1.08 million cubic inches of space . if the company pays $ 0.4 per box per month for the record storage , what is the total amount that the company pays each month for record storage ?", + "Output Program": [ + "n0 = 15.0\nn1 = 12.0\nn2 = 10.0\nn3 = 1.08\nn4 = 0.4\nt0 = n0 * n1\nt1 = n2 * t0\nt2 = t1 / 100.0\nt3 = t2 / 100.0\nt4 = t3 / 100.0\nt5 = n3 / t4\nanswer = n4 * t5\nprint(answer)" + ], + "Output Answer": [ + "240" + ], + "split": "train" + }, + { + "Input": "a retailer bought a shirt at wholesale and marked it up 80 % to its initial price of $ 36 . by how many more dollars does he need to increase the price to achieve a 100 % markup ?", + "Output Program": [ + "n0 = 80.0\nn1 = 36.0\nn2 = 100.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nt2 = n1 / t1\nt3 = t2 * 2.0\nanswer = t3 - n1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "in the city of san durango , 60 people own cats , dogs , or rabbits . if 30 people owned cats , 40 owned dogs , 16 owned rabbits , and 12 owned exactly two of the 3 types of pet , how many people owned all 3 ?", + "Output Program": [ + "n0 = 60.0\nn1 = 30.0\nn2 = 40.0\nn3 = 16.0\nn4 = 12.0\nn5 = 3.0\nn6 = 3.0\nt0 = n1 + n2\nt1 = n3 + t0\nt2 = t1 - n4\nt3 = t2 - n0\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "in a house a hall is 20 m long , 15 m wide and 5 m high . its interior has to be covered with mat . what will be the total expenditure if it costs rs . 60 per square m ?", + "Output Program": [ + "n0 = 20.0\nn1 = 15.0\nn2 = 5.0\nn3 = 60.0\nt0 = n0 * n1\nt1 = n0 * n2\nt2 = n1 * n2\nt3 = t0 * 2.0\nt4 = t1 * 2.0\nt5 = t2 * 2.0\nt6 = n3 * t3\nt7 = n3 * t4\nt8 = n3 * t5\nt9 = t6 + t7\nanswer = t9 + t8\nprint(answer)" + ], + "Output Answer": [ + "57000" + ], + "split": "train" + }, + { + "Input": "the average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 66 kg . what is the correct weight ?", + "Output Program": [ + "n0 = 20.0\nn1 = 58.4\nn2 = 56.0\nn3 = 66.0\nt0 = n0 * n1\nt1 = n3 - n2\nt2 = t0 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "58.9" + ], + "split": "train" + }, + { + "Input": "what is the sum of the greatest common factor and the lowest common multiple of 36 and 56 ?", + "Output Program": [ + "n0 = 36.0\nn1 = 56.0\nt0 = n0 * n1\nanswer = t0 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "504" + ], + "split": "train" + }, + { + "Input": "vishal invested 10 % more than trishul . trishul invested 10 % less than raghu . if the total sum of their investments is rs . 7225 , how much amount did raghu invest ?", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 7225.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nt2 = 1.0 - t0\nt3 = t1 * t2\nt4 = t3 + t2\nt5 = t4 + 1.0\nanswer = n2 / t5\nprint(answer)" + ], + "Output Answer": [ + "2500" + ], + "split": "train" + }, + { + "Input": "in a box of 8 pencils , a total of 2 are defective . if a customer buys 3 pencils selected at random from the box , what is the probability that neither pencils will be defective ?", + "Output Program": [ + "import math\nn0 = 8.0\nn1 = 2.0\nn2 = 3.0\nt0 = math.factorial(min(15, int(n2)))\nt1 = math.factorial(min(15, int(n0)))\nt2 = n0 - n1\nt3 = n0 - n2\nt4 = math.factorial(min(15, int(t2)))\nt5 = math.factorial(min(15, int(t3)))\nt6 = t2 - n2\nt7 = math.factorial(min(15, int(t6)))\nt8 = t5 * t0\nt9 = t1 / t8\nt10 = t7 * t0\nt11 = t4 / t10\nanswer = t11 / t9\nprint(answer)" + ], + "Output Answer": [ + "0.35714285714285715" + ], + "split": "train" + }, + { + "Input": "a sum is divided between a and b in the ratio of 1 : 2 . a purchased a car from his part , which depreciates 14 2 / 7 % per annum and b deposited his amount in a bank , which pays him 20 % interest per annum compounded annually . by what percentage will the total sum of money increase after two years due to this investment pattern ( approximately ) .", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 14.0\nn3 = 2.0\nn4 = 7.0\nn5 = 20.0\nt0 = n5 + n5\nt1 = n4 + t0\nt2 = n0 + t1\nt3 = t2 / 100.0\nanswer = n5 + t3\nprint(answer)" + ], + "Output Answer": [ + "20.48" + ], + "split": "train" + }, + { + "Input": "the average age of a class of 15 students is 10 years . if the age of the teacher be included , then the average increased by 1 year . find the age of the teacher ?", + "Output Program": [ + "n0 = 15.0\nn1 = 10.0\nn2 = 1.0\nt0 = n0 + n2\nt1 = n1 + n2\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "there are some birds in cage , 1 / 3 rd fly away . then 2 / 5 th of the remaining left the cage , then 2 / 3 rd of the remaining left the cage . at last 8 were remaining . how many birds were in total ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 2.0\nn3 = 5.0\nn4 = 2.0\nn5 = 3.0\nn6 = 8.0\nt0 = n1 / n3\nt1 = n2 / n1\nt2 = n0 / n1\nt3 = t1 * t2\nt4 = t0 * t3\nanswer = n6 / t4\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "on dividing 199 by a number , the quotient is 11 and the remainder is 1 . find the divisor .", + "Output Program": [ + "import math\nn0 = 199.0\nn1 = 11.0\nn2 = 1.0\nt0 = n0 / n1\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "what is the nearest no . to 2304 which is divisible by 21 ?", + "Output Program": [ + "n0 = 2304.0\nn1 = 21.0\nt0 = n0 % n1\nanswer = n0 + t0\nprint(answer)" + ], + "Output Answer": [ + "2319" + ], + "split": "train" + }, + { + "Input": "if x and y are integers , what is the least positive number of 24 x + 20 y ?", + "Output Program": [ + "n0 = 24.0\nn1 = 20.0\n\nanswer = n0 - n1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "3 * 11 + 3 * 12 + 3 * 15 + 11 = ?", + "Output Program": [ + "n0 = 3.0\nn1 = 11.0\nn2 = 3.0\nn3 = 12.0\nn4 = 3.0\nn5 = 15.0\nn6 = 11.0\nt0 = n0 * n1\nt1 = n0 * n3\nt2 = n0 * n5\nt3 = t0 + t1\nt4 = t3 + t2\nanswer = n6 + t4\nprint(answer)" + ], + "Output Answer": [ + "125" + ], + "split": "train" + }, + { + "Input": "the age of the daughter is same as the digit in the mother ' s age , but in reverse order . in thirteen years mother will be twice as old as daughter will be then . what is the difference in their current age ?", + "Output Program": [ + "t0 = 1.0 + 12.0\nt1 = 10.0 - 1.0\nt2 = t1 + 10.0\nt3 = t0 + t2\nt4 = t3 / 4.0\nt5 = t4 / 2.0\nt6 = t5 + 10.0\nt7 = t5 * 10.0\nt8 = t7 + 1.0\nanswer = t8 - t6\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "train" + }, + { + "Input": "the average weight of 10 persons increases by 3.2 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 10.0\nn1 = 3.2\nn2 = 65.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "97" + ], + "split": "train" + }, + { + "Input": "the average of runs of a cricket player of 10 innings was 37 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?", + "Output Program": [ + "n0 = 10.0\nn1 = 37.0\nn2 = 4.0\nt0 = n0 + 1.0\nt1 = n1 + n2\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "81" + ], + "split": "train" + }, + { + "Input": "a company decreased the price of its main product by 75 % . subsequently , the number of units sold increased such that the total revenue remained unchanged . what was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product ?", + "Output Program": [ + "n0 = 75.0\n\nanswer = 100.0 / n0\nprint(answer)" + ], + "Output Answer": [ + "1.3333333333333333" + ], + "split": "train" + }, + { + "Input": "a ' s speed is 15 / 13 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that b beats a by 25 % of the length of the race ?", + "Output Program": [ + "n0 = 15.0\nn1 = 13.0\nn2 = 25.0\nt0 = n1 / n0\nt1 = 100.0 - n2\nt2 = t1 / 100.0\nt3 = t2 * t0\nt4 = 1.0 - t3\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "company c sells a line of 20 products with an average retail price of $ 1200 . if none of these products sells for less than $ 400 , and exactly 10 of the products sell for less than $ 1000 , what is the greatest possible selling price of the most expensive product ?", + "Output Program": [ + "n0 = 20.0\nn1 = 1200.0\nn2 = 400.0\nn3 = 10.0\nn4 = 1000.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n3 - 1.0\nt3 = n4 * t2\nt4 = t3 + t1\nanswer = t0 - t4\nprint(answer)" + ], + "Output Answer": [ + "11000" + ], + "split": "train" + }, + { + "Input": "in a box of 6 pencils , a total of 2 are defective . if a customer buys 3 pencils selected at random from the box , what is the probability that neither pencils will be defective ?", + "Output Program": [ + "import math\nn0 = 6.0\nn1 = 2.0\nn2 = 3.0\nt0 = math.factorial(min(15, int(n2)))\nt1 = math.factorial(min(15, int(n0)))\nt2 = n0 - n1\nt3 = n0 - n2\nt4 = math.factorial(min(15, int(t2)))\nt5 = math.factorial(min(15, int(t3)))\nt6 = t2 - n2\nt7 = math.factorial(min(15, int(t6)))\nt8 = t5 * t0\nt9 = t1 / t8\nt10 = t7 * t0\nt11 = t4 / t10\nanswer = t11 / t9\nprint(answer)" + ], + "Output Answer": [ + "0.2" + ], + "split": "train" + }, + { + "Input": "the sum of number of boys and girls in a school is 300 . if the number of boys is x , then the number of girls becomes x % of the total number of students . the number of boys is ?", + "Output Program": [ + "n0 = 300.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.82 per glass on the first day , what was the price per glass on the second day ?", + "Output Program": [ + "n0 = 0.82\nt0 = 1.0 + 1.0\nt1 = 1.0 + 2.0\nt2 = n0 * t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.5466666666666666" + ], + "split": "train" + }, + { + "Input": "every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 3200 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 8.0\nn2 = 3200.0\nt0 = n0 / n1\nt1 = n2 * t0\nt2 = n2 + t1\nt3 = t2 * t0\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "4050" + ], + "split": "train" + }, + { + "Input": "on a certain test , bill scored 20 more points than john , but half as many points as sue . if the sum of the scores of the 3 students was 160 points , how many points did bill receive ?", + "Output Program": [ + "n0 = 20.0\nn1 = 3.0\nn2 = 160.0\nt0 = n0 + n2\nt1 = 1.0 + 1.0\nt2 = t1 + 2.0\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "a library has an average of 630 visitors on sundays and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :", + "Output Program": [ + "import math\nn0 = 630.0\nn1 = 240.0\nn2 = 30.0\nt0 = 3.0 + 4.0\nt1 = n2 / t0\nt2 = math.floor(t1)\nt3 = t2 + 1.0\nt4 = n0 * t3\nt5 = n2 - t3\nt6 = n1 * t5\nt7 = t4 + t6\nanswer = t7 / n2\nprint(answer)" + ], + "Output Answer": [ + "305" + ], + "split": "train" + }, + { + "Input": "mary and mike enter into a partnership by investing $ 900 and $ 100 respectively . at the end of one year , they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business . if mary received $ 1600 more than mike did , what was the profit made by their business in that year ?", + "Output Program": [ + "n0 = 900.0\nn1 = 100.0\nn2 = 1600.0\nt0 = n0 / 1000.0\nt1 = n1 / 1000.0\nt2 = 1.0 / 3.0\nt3 = t0 - t1\nt4 = 1.0 - t2\nt5 = t3 * t4\nanswer = n2 / t5\nprint(answer)" + ], + "Output Answer": [ + "2999.9999999999995" + ], + "split": "train" + }, + { + "Input": "find the least number of complete years in which a sum of money put out at 15 % compound interest will be more than double of itself ?", + "Output Program": [ + "import math\nn0 = 15.0\nt0 = n0 / 100.0\nt1 = math.log(max(1e-5, 2.0), 2)\nt2 = t0 + 1.0\nt3 = math.log(max(1e-5, t2), 2)\nt4 = t1 / t3\nt5 = t4 + 1.0\nanswer = math.floor(t5)\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "jim \u00e2 \u20ac \u2122 s taxi service charges an initial fee of $ 2.25 at the beginning of a trip and an additional charge of $ 0.3 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?", + "Output Program": [ + "n0 = 2.25\nn1 = 0.3\nn2 = 2.0\nn3 = 5.0\nn4 = 3.6\nt0 = n2 / n3\nt1 = n4 / t0\nt2 = n1 * t1\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "4.949999999999999" + ], + "split": "train" + }, + { + "Input": "a & b started a partnership business . a ' s investment was thrice the investment of b and the period of his investment was two times the period of investments of b . if b received rs 3000 as profit , what is their total profit ?", + "Output Program": [ + "n0 = 3000.0\nt0 = 1.0 * 1.0\nt1 = 2.0 * 3.0\nt2 = t1 + t0\nt3 = t0 / t2\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "21000" + ], + "split": "train" + }, + { + "Input": "a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 64 percent of the distribution lies within one standard deviation d of the mean , what percent of the distribution is less than m + d ?", + "Output Program": [ + "n0 = 64.0\nt0 = 100.0 - n0\nt1 = t0 / 2.0\nanswer = 100.0 - t1\nprint(answer)" + ], + "Output Answer": [ + "82" + ], + "split": "train" + }, + { + "Input": "two trains of equal are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train passes the slower train in 27 sec . the length of each train is ?", + "Output Program": [ + "n0 = 46.0\nn1 = 36.0\nn2 = 27.0\nt0 = n0 - n1\nt1 = t0 * 1000.0\nt2 = t1 / 3600.0\nt3 = n2 * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "37.5" + ], + "split": "train" + }, + { + "Input": "sam \u2019 s car was fined when he gave joe and peter a ride , so they decided to help sam pay the fine . joe paid $ 7 more than 1 / 4 of the fine and peter paid $ 7 less than 1 / 3 of the fine , leaving pay $ 12 less than 1 / 2 the fine to complete the payment . what fraction of the fine did sam pay ?", + "Output Program": [ + "n0 = 7.0\nn1 = 1.0\nn2 = 4.0\nn3 = 7.0\nn4 = 1.0\nn5 = 3.0\nn6 = 12.0\nn7 = 1.0\nn8 = 2.0\nt0 = n1 / n2\nt1 = n1 / n5\nt2 = n1 / n8\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n6 * t4\nt6 = n6 + t5\nt7 = n8 * t6\nanswer = t7 + 10.0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "after spending rs . 5000 on rent , rs . 1500 on milk , rs . 4500 on groceries , rs . 2500 on childrens education rs . 2000 on petrol and rs . 5650 on miscellaneous expenses , mr . kishore saved 10 % of his monthly salary . how much did he save in rs . ?", + "Output Program": [ + "n0 = 5000.0\nn1 = 1500.0\nn2 = 4500.0\nn3 = 2500.0\nn4 = 2000.0\nn5 = 5650.0\nn6 = 10.0\nt0 = n0 + n1\nt1 = 100.0 - 10.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nt5 = n5 + t4\nt6 = t5 * 100.0\nt7 = t6 / t1\nanswer = t7 - t5\nprint(answer)" + ], + "Output Answer": [ + "2350" + ], + "split": "train" + }, + { + "Input": "a large box contains 15 small boxes and each small box contains 25 chocolate bars . how many chocolate bars are in the large box ?", + "Output Program": [ + "n0 = 15.0\nn1 = 25.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "375" + ], + "split": "train" + }, + { + "Input": "an assembly line produces 90 cogs per hour until an initial order of 60 cogs is completed . the speed of the assembly line is then immediately decreased so that it only produces 60 cogs per hour until another 60 cogs are produced . what is the overall average output , in cogs per hour , for the assembly line during this whole time ?", + "Output Program": [ + "n0 = 90.0\nn1 = 60.0\nn2 = 60.0\nn3 = 60.0\nt0 = n1 / n0\nt1 = n1 * 2.0\nt2 = t0 + 1.0\nanswer = t1 / t2\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "train" + }, + { + "Input": "ab + ba ___ 202 in the addition problem above , a and b represent digits in two different two - digit numbers . what is the sum of a and b ?", + "Output Program": [ + "import math\nn0 = 202.0\nt0 = 1.0 + 10.0\nt1 = n0 / t0\nt2 = t1 + 2.0\nanswer = math.floor(t2)\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "30 liters of a mixture is created by mixing liquid p and liquid q in the ratio 3 : 2 . how many liters of liquid q must be added to make the ratio 3 : 4 ?", + "Output Program": [ + "n0 = 30.0\nn1 = 3.0\nn2 = 2.0\nn3 = 3.0\nn4 = 4.0\nt0 = n3 + n4\nt1 = n1 + n2\nt2 = n0 * n1\nt3 = n0 * n2\nt4 = t2 / t1\nt5 = t3 / t1\nt6 = t0 * t4\nt7 = t6 / n3\nt8 = n4 * t7\nt9 = t8 / t0\nanswer = t9 - t5\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": ". for the fifa world cup , paul the octopus has been predicting the winner of each match with amazing success . it is rumored that in a match between 2 teams a and b , paul picks a with the same probability as a \u2019 s chances of winning . let \u2019 s assume such rumors to be true and that in a match between ghana and bolivia ; ghana the stronger team has a probability of 2 / 3 of winning the game . what is the probability that paul will correctly pick the winner of the ghana - bolivia game ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 3.0\nt0 = 2.0 + 3.0\nt1 = t0 * 10.0\nt2 = n2 + t1\nt3 = n2 + t2\nanswer = n2 + t3\nprint(answer)" + ], + "Output Answer": [ + "59" + ], + "split": "train" + }, + { + "Input": "john has 10 pairs of matched socks . if he loses 5 individual socks , what is the greatest number of pairs of matched socks he can have left ?", + "Output Program": [ + "n0 = 10.0\nn1 = 5.0\n\nanswer = n0 - 3.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "if { x } is the product of all even integers from 1 to x inclusive , what is the greatest prime factor of { 18 } + { 16 } ?", + "Output Program": [ + "n0 = 1.0\nn1 = 18.0\nn2 = 16.0\nt0 = n1 + n2\nt1 = n0 * 2.0\nt2 = t0 / 2.0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "a man is 27 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ?", + "Output Program": [ + "n0 = 27.0\nt0 = 2.0 * 2.0\nt1 = 2.0 - 1.0\nt2 = t0 - 2.0\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "[ ( 3.242 x 16 ) / 100 ] = ?", + "Output Program": [ + "n0 = 3.242\nn1 = 16.0\nn2 = 100.0\nt0 = n0 * n1\nt1 = t0 / n2\nanswer = t1 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "0.051871999999999995" + ], + "split": "train" + }, + { + "Input": "sabrina is contemplating a job switch . she is thinking of leaving her job paying $ 90000 per year to accept a sales job paying $ 45000 per year plus 15 percent commission for each sale made . if each of her sales is for $ 1500 , what is the least number of sales she must make per year if she is not to lose money because of the job change ?", + "Output Program": [ + "n0 = 90000.0\nn1 = 45000.0\nn2 = 15.0\nn3 = 1500.0\nt0 = n2 * n3\nt1 = n0 - n1\nt2 = t0 / 100.0\nanswer = t1 / t2\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "train" + }, + { + "Input": "a computer manufacturer produces a certain electronic component at a cost of $ 80 per component . shipping costs for delivering the components are $ 6 per unit . further , the manufacturer has costs of $ 16,500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 150 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?", + "Output Program": [ + "n0 = 80.0\nn1 = 6.0\nn2 = 16500.0\nn3 = 150.0\nt0 = n0 + n1\nt1 = 4.0 * 4.0\nt2 = n1 * 100.0\nt3 = t1 * 1000.0\nt4 = n3 * t0\nt5 = t3 + t2\nt6 = t5 + t4\nanswer = t6 / n3\nprint(answer)" + ], + "Output Answer": [ + "196.66666666666666" + ], + "split": "train" + }, + { + "Input": "the simple interest on a sum of money will be rs . 1000 after 10 years . if the principal is trebled after 5 years what will be the total interest at the end of the tenth year ?", + "Output Program": [ + "n0 = 1000.0\nn1 = 10.0\nn2 = 5.0\nt0 = n0 / n1\nt1 = n2 * t0\nt2 = t1 * 3.0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "2000" + ], + "split": "train" + }, + { + "Input": "an advertising agency finds that , of its 180 clients , 115 use television , 110 use radio and 130 use magazines . also , 85 use television and magazines , 75 use television and radio , 95 use radio and magazines . how many use all the 3 ?", + "Output Program": [ + "n0 = 180.0\nn1 = 115.0\nn2 = 110.0\nn3 = 130.0\nn4 = 85.0\nn5 = 75.0\nn6 = 95.0\nn7 = 3.0\nt0 = n1 + n2\nt1 = n4 + n5\nt2 = n3 + t0\nt3 = n6 + t1\nt4 = t2 - t3\nanswer = n0 - t4\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "in a certain brick wall , each row of bricks above the bottom row contains one less brick than the row just below it . if there are 5 rows in all and a total of 100 bricks in the wall , how many bricks does the bottom row contain ?", + "Output Program": [ + "n0 = 5.0\nn1 = 100.0\nt0 = n1 - 1.0\nt1 = t0 - 2.0\nt2 = t1 - 3.0\nt3 = t2 - 4.0\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "average age of 7 members of a family is 29 years . if present age of the youngest member is 5 year , find average age of the remaining members at the time of birth of the youngest member .", + "Output Program": [ + "n0 = 7.0\nn1 = 29.0\nn2 = 5.0\nt0 = n0 * n1\nt1 = n0 * n2\nt2 = n0 - 1.0\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "thabo owns exactly 200 books , and each book is either paperback fiction , paperback nonfiction , or hardcover nonfiction . if he owns 20 more paperback nonfiction books than hardcover nonfiction books , and twice as many paperback fiction books as paperback nonfiction books , how many hardcover books nonfiction books does thabo own ?", + "Output Program": [ + "n0 = 200.0\nn1 = 20.0\nt0 = n0 + n1\nt1 = t0 / 4.0\nanswer = t1 - n1\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "on rainy mornings , mo drinks exactly n cups of hot chocolate ( assume that n is an integer ) . on mornings that are not rainy , mo drinks exactly 4 cups of tea . last week mo drank a total of 26 cups of tea and hot chocolate together . if during that week mo drank 14 more tea cups than hot chocolate cups , then how many rainy days were there last week ?", + "Output Program": [ + "n0 = 4.0\nn1 = 26.0\nn2 = 14.0\nt0 = 3.0 + 4.0\nt1 = n1 + n2\nt2 = t1 / 2.0\nt3 = t2 / n0\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "pat , kate , and mark charged a total of 135 hours to a certain project . if pat charged twice as much time to the project as kate and 1 / 3 as much time as mark , how many more hours did mark charge to the project than kate ?", + "Output Program": [ + "n0 = 135.0\nn1 = 1.0\nn2 = 3.0\nt0 = n1 / n2\nt1 = n2 * 2.0\nt2 = n1 + t0\nt3 = n1 / t1\nt4 = t2 + t3\nt5 = n0 / t4\nt6 = t5 / t1\nanswer = t5 - t6\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "sum of the squares of 3 no . is 52 and the sum of their products taken two at a time is 72 . find the sum ?", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 52.0\nn2 = 72.0\nt0 = n2 * 2.0\nt1 = n1 + t0\nanswer = math.sqrt(max(0, t1))\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "what ratio must a shopkeeper mix peas and soybean of rs . 16 and rs . 25 / kg , as to obtain a mixture of rs . 19 ?", + "Output Program": [ + "n0 = 16.0\nn1 = 25.0\nn2 = 19.0\nt0 = n1 - n2\nt1 = n2 - n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "by how much does the larger root of the equation 2 a ^ 2 + 5 a = 12 exceed the smaller root ?", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 2.0\nn2 = 5.0\nn3 = 12.0\nt0 = n0 * n3\nt1 = n0 * 2.0\nt2 = n2**min(2.0, 5)\nt3 = t0 * 4.0\nt4 = t3 + t2\nt5 = math.sqrt(max(0, t4))\nt6 = n2 + t5\nt7 = n2 - t5\nt8 = t6 / t1\nt9 = t7 / t1\nanswer = t8 - t9\nprint(answer)" + ], + "Output Answer": [ + "5.5" + ], + "split": "train" + }, + { + "Input": "if x + 1 / x = 2 then find x 2 + 1 / x 2", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 2.0\nn3 = 1.0\nn4 = 2.0\n\nanswer = n1 / n0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "find large no . from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 5 as remainder", + "Output Program": [ + "n0 = 1365.0\nn1 = 6.0\nn2 = 5.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nt2 = t0 / t1\nt3 = n1 * t2\nanswer = n2 + t3\nprint(answer)" + ], + "Output Answer": [ + "1637" + ], + "split": "train" + }, + { + "Input": "mr . hanson has a pool of money from which to give out christmas bonuses to his 5 employees . he wants all his employees to have identical bonuses , but when he divides them out , he finds he has 2 dollars left over , as the payroll system will only accept whole dollar amounts . the next christmas , mr . hanson discovers the pool for the bonuses is 3 times the size . this time , how much money will be left over ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 3.0\nt0 = n0 - n2\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "calculate 469138 x 9999 = ?", + "Output Program": [ + "n0 = 469138.0\nn1 = 9999.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "4690910862" + ], + "split": "train" + }, + { + "Input": "if a = 105 and a ^ 3 = 21 \u00d7 25 \u00d7 45 \u00d7 e , what is the value of e ?", + "Output Program": [ + "n0 = 105.0\nn1 = 3.0\nn2 = 21.0\nn3 = 25.0\nn4 = 45.0\nt0 = n2 * n3\nt1 = n0**min(n1, 5)\nt2 = n4 * t0\nanswer = t1 / t2\nprint(answer)" + ], + "Output Answer": [ + "49" + ], + "split": "train" + }, + { + "Input": "a certain ball team has an equal number of right - and left - handed players . on a certain day , two - thirds of the players were absent from practice . of the players at practice that day , one - third were right handed . what is the ratio of the number of right - handed players who were not at practice that day to the number of left handed players who were not at practice ?", + "Output Program": [ + "t0 = 1.0 / 2.0\nt1 = 2.0 / 3.0\nt2 = 1.0 - t1\nt3 = t1 * t2\nt4 = t2 - t3\nt5 = t0 - t3\nt6 = t0 - t4\nanswer = t6 / t5\nprint(answer)" + ], + "Output Answer": [ + "1.3999999999999997" + ], + "split": "train" + }, + { + "Input": "how many numbers from 32 to 97 are exactly divisible by 9 ?", + "Output Program": [ + "import math\nn0 = 32.0\nn1 = 97.0\nn2 = 9.0\nt0 = n1 / n2\nt1 = n0 / n2\nt2 = math.floor(t0)\nt3 = math.floor(t1)\nt4 = t3 + 1.0\nt5 = n2 * t2\nt6 = n2 * t4\nt7 = t5 - t6\nt8 = t7 / n2\nanswer = t8 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "the distance from the x - axis to point p is half the distance from the y - axis to point p . if the coordinates of p are ( x , - 4 ) , how many units is p from the y - axis ?", + "Output Program": [ + "n0 = 4.0\n\nanswer = n0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a library has an average of 150 visitors on sundays and 120 on other days . the avearge number of visitors per day in a month of 30 days beginning with a sunday is ?", + "Output Program": [ + "import math\nn0 = 150.0\nn1 = 120.0\nn2 = 30.0\nt0 = 3.0 + 4.0\nt1 = n2 / t0\nt2 = math.floor(t1)\nt3 = t2 + 1.0\nt4 = n0 * t3\nt5 = n2 - t3\nt6 = n1 * t5\nt7 = t4 + t6\nanswer = t7 / n2\nprint(answer)" + ], + "Output Answer": [ + "125" + ], + "split": "train" + }, + { + "Input": "tickets numbered from 1 to 21 are mixed and then a ticket is selected randomly . what is the probability that the selected ticket bears a number which is a multiple of 3 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 21.0\nn2 = 3.0\nt0 = n1 / n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.3333333333333333" + ], + "split": "train" + }, + { + "Input": "a basket contains 5 apples , of which 1 is spoiled and the rest are good . if henry is to select 2 apples from the basket simultaneously and at random , what is the possibility that the 2 apples selected will include the spoiled apple ?", + "Output Program": [ + "import scipy\nn0 = 5.0\nn1 = 1.0\nn2 = 2.0\nn3 = 2.0\nt0 = scipy.special.comb(n0, n2)\nt1 = n0 - n1\nt2 = scipy.special.comb(t1, n1)\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.4" + ], + "split": "train" + }, + { + "Input": "the difference in compound interest earned on a deposit ( compounded annually ) in year 1 and year 2 is $ 40 . had the interest rate been 3 times its present value , the difference w would have been how much ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 40.0\nn3 = 3.0\nt0 = n2 * n3\nanswer = n3 * t0\nprint(answer)" + ], + "Output Answer": [ + "360" + ], + "split": "train" + }, + { + "Input": "3 machines operating independently , simultaneously , and at the same constant rate can fill a certain production order in 44 hours . if one additional machine were used under the same operating conditions , in how manyfewerhours of simultaneous operation could the production order be fulfilled ?", + "Output Program": [ + "n0 = 3.0\nn1 = 44.0\nt0 = n0 + 1.0\nt1 = n0 * n1\nt2 = t1 / t0\nanswer = n1 - t2\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "if n is an integer , f ( n ) = f ( n - 1 ) - n and f ( 4 ) = 14 . what is the value of f ( 6 ) ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 14.0\nn3 = 6.0\nt0 = n0 + n1\nt1 = n2 - t0\nanswer = t1 - n3\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "what is the smallest number which , when increased by 9 , is divisible by 8 , 11 , and 24 ?", + "Output Program": [ + "import scipy\nn0 = 9.0\nn1 = 8.0\nn2 = 11.0\nn3 = 24.0\nt0 = scipy.lcm(int(n2), int(n3))\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "255" + ], + "split": "train" + }, + { + "Input": "in a hostel there were 100 students . to accommodate 25 more students the average is decreased by rupees 10 . but total expenditure increased by rs . 500 . find the total expenditure of the hostel now ?", + "Output Program": [ + "n0 = 100.0\nn1 = 25.0\nn2 = 10.0\nn3 = 500.0\nt0 = n0 + n1\nt1 = n2 * t0\nt2 = n3 + t1\nt3 = t2 / n1\nt4 = t3 - n2\nanswer = t0 * t4\nprint(answer)" + ], + "Output Answer": [ + "7500" + ], + "split": "train" + }, + { + "Input": "pat , kate , and mark charged a total of 144 hours to a certain project . if pat charged twice as much time to the project as kate and 1 / 3 as much time as mark , how many more hours did mark charge to the project than kate ?", + "Output Program": [ + "n0 = 144.0\nn1 = 1.0\nn2 = 3.0\nt0 = n1 / n2\nt1 = n2 * 2.0\nt2 = n1 + t0\nt3 = n1 / t1\nt4 = t2 + t3\nt5 = n0 / t4\nt6 = t5 / t1\nanswer = t5 - t6\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "in the graduating class of a certain college , 48 percent of the students are male and 52 percent are female . in this class 50 percent of the male and 20 percent of the female students are 25 years old or older . if one student in the class is randomly selected , approximately what is the probability that he or she will be less than 25 years old ?", + "Output Program": [ + "n0 = 48.0\nn1 = 52.0\nn2 = 50.0\nn3 = 20.0\nn4 = 25.0\nn5 = 25.0\nt0 = n2 / 100.0\nt1 = 100.0 - n3\nt2 = t1 / 100.0\nt3 = t0 * t2\nanswer = 1.0 - t3\nprint(answer)" + ], + "Output Answer": [ + "0.6" + ], + "split": "train" + }, + { + "Input": "a grocer has a sale of rs . 5420 , rs . 5660 , rs . 6200 , rs . 6350 and rs . 6500 for 5 consecutive months . find the sale he should have in the sixth month , so that he gets an average sale of rs . 6200 ?", + "Output Program": [ + "n0 = 5420.0\nn1 = 5660.0\nn2 = 6200.0\nn3 = 6350.0\nn4 = 6500.0\nn5 = 5.0\nn6 = 6200.0\nt0 = n5 + 1.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n6 * t0\nt4 = n3 + t2\nt5 = n4 + t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "7070" + ], + "split": "train" + }, + { + "Input": "how many multiples of 4 are there between 16 and 112 , inclusive ?", + "Output Program": [ + "n0 = 4.0\nn1 = 16.0\nn2 = 112.0\nt0 = n2 - n1\nt1 = t0 / n0\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "jill has 35 gallons of water stored in quart , half - gallon , and one gallon jars . she has equal numbers of each size jar holding the liquid . what is the total number of water filled jars ?", + "Output Program": [ + "n0 = 35.0\nt0 = 1.0 / 2.0\nt1 = t0 + 0.25\nt2 = t1 + 1.0\nt3 = n0 / t2\nanswer = t3 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "in a theater , the first row has 14 seats and each row has 3 more seats than previous row . if the last row has 50 seats , what is the total number of seats in the theater ?", + "Output Program": [ + "n0 = 14.0\nn1 = 3.0\nn2 = 50.0\nt0 = n0 + n2\nt1 = n2 - n0\nt2 = n1 + t1\nt3 = t0 / 2.0\nt4 = t2 / n1\nanswer = t3 * t4\nprint(answer)" + ], + "Output Answer": [ + "416" + ], + "split": "train" + }, + { + "Input": "a student scored an average of 80 marks in 3 subjects : physics , chemistry and mathematics . if the average marks in physics and mathematics is 90 and that in physics and chemistry is 70 , what are the marks in physics ?", + "Output Program": [ + "n0 = 80.0\nn1 = 3.0\nn2 = 90.0\nn3 = 70.0\nt0 = n2 * 2.0\nt1 = n3 * 2.0\nt2 = n0 * n1\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "in an election , candidate douglas won 54 percent of the total vote in counties x and y . he won 62 percent of the vote in county x . if the ratio of people who voted in county x to county y is 2 : 1 , what percent of the vote did candidate douglas win in county y ?", + "Output Program": [ + "n0 = 54.0\nn1 = 62.0\nn2 = 2.0\nn3 = 1.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = n2 / 3.0\nt3 = n3 / 3.0\nt4 = t1 * t2\nt5 = t0 - t4\nt6 = t5 / t3\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "38.000000000000014" + ], + "split": "train" + }, + { + "Input": "harold and millicent are getting married and need to combine their already - full libraries . if harold , who has 1 / 2 as many books as millicent , brings 1 / 3 of his books to their new home , then millicent will have enough room to bring 1 / 2 of her books to their new home . what fraction of millicent ' s old library capacity is the new home ' s library capacity", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 1.0\nn3 = 3.0\nn4 = 1.0\nn5 = 2.0\nt0 = n0 / n3\nt1 = n0 / n1\nt2 = t0 * t1\nanswer = 1.0 - t2\nprint(answer)" + ], + "Output Answer": [ + "0.8333333333333334" + ], + "split": "train" + }, + { + "Input": "on dividing a number by 8 , we get 8 as quotient and 0 as remainder . on dividing the same number by 5 , what will be the remainder ?", + "Output Program": [ + "n0 = 8.0\nn1 = 8.0\nn2 = 0.0\nn3 = 5.0\nt0 = n0 * n1\nanswer = t0 % n3\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "let f ( x , y ) be defined as the remainder when ( x \u2013 y ) ! is divided by x . if x = 50 , what is the maximum value of y for which f ( x , y ) = 0 ?", + "Output Program": [ + "n0 = 50.0\nn1 = 0.0\nt0 = 1.0 + 4.0\nt1 = n0 / 2.0\nt2 = t1 / t0\nt3 = t2 * 2.0\nanswer = n0 - t3\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "in an ngo the daily average wages of 20 illiterate employees is decreased from rs . 25 to rs . 10 , thus the average salary of all the literate and illiterate employees is decreased rs . 10 per day . the no . of educated employees working in the ngo is ?", + "Output Program": [ + "n0 = 20.0\nn1 = 25.0\nn2 = 10.0\nn3 = 10.0\n\nanswer = n0 - n2\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "if a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20 , what is the probability r that this product will be a multiple of 45 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 20.0\nn2 = 45.0\nt0 = n1 + 4.0\nanswer = 1.0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.041666666666666664" + ], + "split": "train" + }, + { + "Input": "at the end of the day , february 14 th , a florist had 150 roses left in his shop , all of which were red , white or pink in color and either long or short - stemmed . a third of the roses were short - stemmed , 20 of which were white and 15 of which were pink . the percentage of pink roses that were short - stemmed equaled the percentage of red roses that were short - stemmed . if none of the long - stemmed roses were white , what percentage of the long - stemmed roses were red ?", + "Output Program": [ + "n0 = 14.0\nn1 = 150.0\nn2 = 20.0\nn3 = 15.0\nt0 = n1 / 3.0\nt1 = n1 - t0\nt2 = t0 - n2\nt3 = t2 - n3\nt4 = n3 + t3\nt5 = t1 * t3\nt6 = t5 / t4\nt7 = t6 / t1\nanswer = t7 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "carl bought 16 gumballs , lewis bought 12 gumballs , and carey bought x gumballs . the average ( arithmetic mean ) number of gumballs the 3 bought is between 19 and 25 , inclusive . what is the difference between the greatest number and the smallest number of gumballs carey could have bought ?", + "Output Program": [ + "n0 = 16.0\nn1 = 12.0\nn2 = 3.0\nn3 = 19.0\nn4 = 25.0\nt0 = n2 * n4\nt1 = n2 * n3\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "find the principle on a certain sum of money at 7 % per annum for 2 2 / 5 years if the amount being rs . 1120 ?", + "Output Program": [ + "n0 = 7.0\nn1 = 2.0\nn2 = 2.0\nn3 = 5.0\nn4 = 1120.0\nt0 = n1 * n3\nt1 = n1 + t0\nt2 = t1 / n3\nt3 = n0 * t2\nt4 = t3 / 100.0\nt5 = t4 + 1.0\nanswer = n4 / t5\nprint(answer)" + ], + "Output Answer": [ + "958.9041095890411" + ], + "split": "train" + }, + { + "Input": "how much is 80 % of 40 is greater than 2 / 5 of 25 ?", + "Output Program": [ + "n0 = 80.0\nn1 = 40.0\nn2 = 2.0\nn3 = 5.0\nn4 = 25.0\nt0 = n0 / 100.0\nt1 = n2 / n3\nt2 = n1 * t0\nt3 = n4 * t1\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "the average age of applicants for a new job is 30 , with a standard deviation of 7 . the hiring manager is only willing to accept applications whose age is within one standard deviation of the average age . what is the maximum number of different ages of the applicants ?", + "Output Program": [ + "n0 = 30.0\nn1 = 7.0\nt0 = n1 * 2.0\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "little john had $ 8.50 . he spent $ 1.25 on sweets and gave to his two friends $ 1.20 each . how much money was left ?", + "Output Program": [ + "n0 = 8.5\nn1 = 1.25\nn2 = 1.2\nt0 = n2 + n2\nt1 = n1 + t0\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "4.85" + ], + "split": "train" + }, + { + "Input": "a car averages 55 mph for the first 4 hours of a trip and averages 70 mph for each additional hour . the average speed for the entire trip was 60 mph . how many hours long is the trip ?", + "Output Program": [ + "n0 = 55.0\nn1 = 4.0\nn2 = 70.0\nn3 = 60.0\nt0 = n3 * n1\nt1 = n0 * n1\nt2 = n2 - n3\nt3 = t0 - t1\nt4 = t3 / t2\nanswer = n1 + t4\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "arnold and danny are two twin brothers that are celebrating their birthday . the product of their ages today is smaller by 11 from the product of their ages a year from today . what is their age today ?", + "Output Program": [ + "n0 = 11.0\nt0 = n0 - 1.0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "a man engaged a servant on the condition that he would pay him rs . 500 and a uniform after one year service . he served only for 9 months and received uniform and rs . 250 , find the price of the uniform ?", + "Output Program": [ + "n0 = 500.0\nn1 = 9.0\nn2 = 250.0\nt0 = n0 * n1\nt1 = 3.0 * 4.0\nt2 = n2 * t1\nt3 = t1 * 1.0\nt4 = t0 - t2\nt5 = t4 / t3\nanswer = t5 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "train" + }, + { + "Input": "a big container is 30 % full with water . if 27 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container ?", + "Output Program": [ + "n0 = 30.0\nn1 = 27.0\nn2 = 3.0\nn3 = 4.0\nt0 = n2 / n3\nt1 = n0 / 100.0\nt2 = t0 - t1\nanswer = n1 / t2\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "a box contains 9 slips that are each labeled with one number : 1 , 3 , 5 , 8 , 13 , 21 , 34 and 55 . two of the slips are drawn at random from the box without replacement . what is the probability that the sum of the numbers on the two slips is equal to one of the numbers left in the box ?", + "Output Program": [ + "n0 = 9.0\nn1 = 1.0\nn2 = 3.0\nn3 = 5.0\nn4 = 8.0\nn5 = 13.0\nn6 = 21.0\nn7 = 34.0\nn8 = 55.0\nt0 = n4 - n2\nt1 = n4 - n1\nt2 = n4 * t1\nt3 = t2 / 2.0\nanswer = t0 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.17857142857142858" + ], + "split": "train" + }, + { + "Input": "the operation is defined for all integers a and b by the equation ab = ( a - 1 ) ( b - 1 ) . if x 9 = 160 , what is the value of x ?", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 9.0\nn3 = 160.0\nt0 = n2 - n0\nt1 = n3 / t0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "the sum of the first 50 positive even integers is 2550 . what is the sum of the even integers from 302 to 400 inclusive ?", + "Output Program": [ + "n0 = 50.0\nn1 = 2550.0\nn2 = 302.0\nn3 = 400.0\nt0 = n2 + n3\nt1 = n3 - n2\nt2 = t1 / 2.0\nt3 = t0 / 2.0\nt4 = t2 + 1.0\nanswer = t4 * t3\nprint(answer)" + ], + "Output Answer": [ + "17550" + ], + "split": "train" + }, + { + "Input": "a man can row 3.3 km / hr in still water . it takes him twice as long to row upstream as to row downstream . what is the rate of the current ?", + "Output Program": [ + "n0 = 3.3\nt0 = n0 * 2.0\nt1 = t0 - n0\nanswer = t1 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "1.0999999999999999" + ], + "split": "train" + }, + { + "Input": "a , b and c rents a pasture for rs . 841 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should b pay ?", + "Output Program": [ + "n0 = 841.0\nn1 = 12.0\nn2 = 8.0\nn3 = 16.0\nn4 = 9.0\nn5 = 18.0\nn6 = 6.0\nt0 = n1 * n2\nt1 = n3 * n4\nt2 = n5 * n6\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n0 / t4\nanswer = t5 * t1\nprint(answer)" + ], + "Output Answer": [ + "348" + ], + "split": "train" + }, + { + "Input": "jacob is now 13 years younger than michael . if 9 years from now michael will be twice as old as jacob , how old will jacob be in 4 years ?", + "Output Program": [ + "n0 = 13.0\nn1 = 9.0\nn2 = 4.0\nt0 = n0 + n1\nt1 = n1 * 2.0\nt2 = t0 - t1\nanswer = n2 + t2\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 86.49 , the number of the member is the group is :", + "Output Program": [ + "import math\nn0 = 86.49\nt0 = n0 * 100.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "93" + ], + "split": "train" + }, + { + "Input": "the average of 65 numbers is 40 . if two numbers , 83 and 30 are discarded , then the average of the remaining numbers is nearly", + "Output Program": [ + "n0 = 65.0\nn1 = 40.0\nn2 = 83.0\nn3 = 30.0\nt0 = n2 + n3\nt1 = n0 * n1\nt2 = n0 - 2.0\nt3 = t1 - t0\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "39.476190476190474" + ], + "split": "train" + }, + { + "Input": "a + b + c + d = d + e + f + g = g + h + i = 17 given a = 4 . find value of g and h ?", + "Output Program": [ + "n0 = 17.0\nn1 = 4.0\nt0 = n0 * 3.0\nt1 = 3.0 * 3.0\nt2 = t1 + 1.0\nt3 = t2 / 2.0\nt4 = t3 * t1\nt5 = t0 - t4\nt6 = t5 - 1.0\nt7 = n1 + t6\nanswer = t7 + 10.0\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "when a merchant imported a certain item , she paid a 7 percent import tax on the portion of the total value of the item in excess of $ 1,000 . if the amount of the import tax that the merchant paid was $ 111.30 , what was the total value of the item ?", + "Output Program": [ + "n0 = 7.0\nn1 = 1000.0\nn2 = 111.3\nt0 = n0 / 100.0\nt1 = n2 / t0\nanswer = t1 + n1\nprint(answer)" + ], + "Output Answer": [ + "2590" + ], + "split": "train" + }, + { + "Input": "a 30 % alcohol mixture is added to a 50 % alcohol mixture to form a 10 litre mixture of 45 % alcohol . how much of the 30 % mixture was used ?", + "Output Program": [ + "n0 = 30.0\nn1 = 50.0\nn2 = 10.0\nn3 = 45.0\nn4 = 30.0\nt0 = n1 / 100.0\nt1 = n2 * t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "2.5" + ], + "split": "train" + }, + { + "Input": "if the charge of staying in a student youth hostel $ 18.00 / day for the first week , and $ 11.00 / day for each additional week , how much does it cost to stay for 23 days ?", + "Output Program": [ + "n0 = 18.0\nn1 = 11.0\nn2 = 23.0\nt0 = 3.0 + 4.0\nt1 = n0 * t0\nt2 = n2 - t0\nt3 = n1 * t2\nanswer = t1 + t3\nprint(answer)" + ], + "Output Answer": [ + "302" + ], + "split": "train" + }, + { + "Input": "find the smallest number of 6 digits which is exactly divisible by 111", + "Output Program": [ + "n0 = 6.0\nn1 = 111.0\nt0 = 100.0 * 100.0\nt1 = t0 * 10.0\nt2 = t1 - 100.0\nanswer = n1 + t2\nprint(answer)" + ], + "Output Answer": [ + "100011" + ], + "split": "train" + }, + { + "Input": "kareem is 3 times as old as his son . after 10 years , the sum of their ages will be 76 years . find their present ages .", + "Output Program": [ + "n0 = 3.0\nn1 = 10.0\nn2 = 76.0\nt0 = n0 + 1.0\nt1 = n1 * 2.0\nt2 = n2 - t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 200 milliliters of solution x to create a solution that is 25 percent alcohol by volume ?", + "Output Program": [ + "n0 = 10.0\nn1 = 30.0\nn2 = 200.0\nn3 = 25.0\nt0 = n3 - n0\nt1 = n1 - n3\nt2 = t0 / t1\nanswer = n2 * t2\nprint(answer)" + ], + "Output Answer": [ + "600" + ], + "split": "train" + }, + { + "Input": "the star running back on our football team got most of his total yardage running . the rest was catching passes . he caught passes for 60 yards . his total yardage was 150 yards . the running back for the other team got 200 yards . how many yards did the star running back on our football team get running ?", + "Output Program": [ + "n0 = 60.0\nn1 = 150.0\nn2 = 200.0\n\nanswer = n1 - n0\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "a straight line in the xy - plane has a slope of 4 and a y - intercept of 4 . on this line , what is the x - coordinate of the point whose y - coordinate is 800 ?", + "Output Program": [ + "n0 = 4.0\nn1 = 4.0\nn2 = 800.0\nt0 = n2 - n0\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "199" + ], + "split": "train" + }, + { + "Input": "if 4 ( p ' s capital ) = 6 ( q ' s capital ) = 10 ( r ' s capital ) , then out of the total profit of rs 4340 , r will receive", + "Output Program": [ + "n0 = 4.0\nn1 = 6.0\nn2 = 10.0\nn3 = 4340.0\nt0 = n0 + 1.0\nt1 = n2 + t0\nt2 = n2 + t1\nt3 = n1 + t2\nt4 = n1 / t3\nanswer = n3 * t4\nprint(answer)" + ], + "Output Answer": [ + "840" + ], + "split": "train" + }, + { + "Input": "for how many integer values of n will the value of the expression 4 n + 7 be an integer greater than 1 and less than 100 ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 7.0\nn2 = 1.0\nn3 = 100.0\nt0 = n3 - n1\nt1 = n2 - n1\nt2 = t0 / n0\nt3 = t1 / n0\nt4 = math.floor(t2)\nt5 = math.floor(t3)\nanswer = t4 - t5\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "if the arithmetic mean of p and q is 10 and the arithmetic mean of q and r is 25 , what is the value of r - p ?", + "Output Program": [ + "n0 = 10.0\nn1 = 25.0\nt0 = n1 * 2.0\nt1 = n0 * 2.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "10 percent of ram ' s monthly salary is equal to 8 percent of shyam ' s monthly salary . shyam ' s monthly salary is twice abhinav ' s monthly salary . if abhinav ' s annual salary is rs . 1.92 lakhs , find ram ' s monthly salary ?", + "Output Program": [ + "n0 = 10.0\nn1 = 8.0\nn2 = 1.92\nt0 = n2 / 12.0\nt1 = n1 * 100.0\nt2 = n0 * 100.0\nt3 = t0 * 2.0\nt4 = t1 * t3\nt5 = t4 / t2\nt6 = t5 * 100.0\nanswer = t6 * 1000.0\nprint(answer)" + ], + "Output Answer": [ + "25600" + ], + "split": "train" + }, + { + "Input": "when processing flower - nectar into honey bees ' extract , a considerable amount of water gets reduced . how much flower - nectar must be processed to yield 1 kg of honey , if nectar contains 50 % water , and the honey obtained from this nectar contains 15 % water ?", + "Output Program": [ + "n0 = 1.0\nn1 = 50.0\nn2 = 15.0\nt0 = n1 / 100.0\nt1 = 100.0 - n2\nt2 = t1 / 100.0\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "1.7" + ], + "split": "train" + }, + { + "Input": "the average ( arithmetic mean ) of 4 different positive integers is 16 . if the first of these integers in 3 times the second integer and the second integer is 2 less than the third integer , what is the least possible value of the fourth integer ?", + "Output Program": [ + "n0 = 4.0\nn1 = 16.0\nn2 = 3.0\nn3 = 2.0\nt0 = n2 + n3\nt1 = n0 * n1\nt2 = t0 * 12.0\nt3 = t1 - n3\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "if the operation \u20ac is defined for all x and y by the equation x \u20ac y = 2 * x * y , then 7 \u20ac ( 4 \u20ac 5 ) =", + "Output Program": [ + "n0 = 2.0\nn1 = 7.0\nn2 = 4.0\nn3 = 5.0\nt0 = n0 * n1\nt1 = n0 * n2\nt2 = n3 * t1\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "560" + ], + "split": "train" + }, + { + "Input": "( 9 ^ 5.6 x 9 ^ 10.3 ) \u00f7 9 ^ 2.56256 = 9 ^ ?", + "Output Program": [ + "n0 = 9.0\nn1 = 5.6\nn2 = 9.0\nn3 = 10.3\nn4 = 9.0\nn5 = 2.56256\nn6 = 9.0\nt0 = n1 + n3\nanswer = t0 - n5\nprint(answer)" + ], + "Output Answer": [ + "13.33744" + ], + "split": "train" + }, + { + "Input": "10 + 45", + "Output Program": [ + "n0 = 280.0\nn1 = 254.0\nn2 = 280.0\nn3 = 97.0\nn4 = 138.0\nn5 = 152.0\nn6 = 73.0\nn7 = 3.0\nt0 = n0 + n1\nt1 = n0 + t0\nt2 = t1 - n3\nt3 = t2 - n4\nt4 = t3 - n5\nanswer = n6 + t4\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "train" + }, + { + "Input": "equal amount of water were poured into two empty jars of different capacities , which made one jar 1 / 8 full and other jar 1 / 6 full . if the water in the jar with lesser capacity is then poured into the jar with greater capacity , what fraction of the larger jar will be filled with water ?", + "Output Program": [ + "n0 = 1.0\nn1 = 8.0\nn2 = 1.0\nn3 = 6.0\n\nanswer = 2.0 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.25" + ], + "split": "train" + }, + { + "Input": "a certain bus driver is paid a regular rate of $ 20 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 1000 in total compensation , how many total hours did he work that week ?", + "Output Program": [ + "n0 = 20.0\nn1 = 40.0\nn2 = 40.0\nn3 = 75.0\nn4 = 1000.0\nt0 = n3 + 100.0\nt1 = n0 * n1\nt2 = n0 * t0\nt3 = n4 - t1\nt4 = t2 / 100.0\nt5 = t3 / t4\nanswer = n1 + t5\nprint(answer)" + ], + "Output Answer": [ + "45.714285714285715" + ], + "split": "train" + }, + { + "Input": "what is the greatest integer m for which the number 20 ! / 10 ^ m is an integer ?", + "Output Program": [ + "import math\nn0 = 20.0\nn1 = 10.0\nt0 = n1 / 2.0\nt1 = n0 / t0\nanswer = math.floor(t1)\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "what least number must be subtracted from 9679 so that the remaining number is divisible by 15 ?", + "Output Program": [ + "import math\nn0 = 9679.0\nn1 = 15.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "the ages of two person differ by 20 years . if 8 years ago , the elder one be 5 times as old as the younger one , their present ages ( in years ) are respectively", + "Output Program": [ + "n0 = 20.0\nn1 = 8.0\nn2 = 5.0\nt0 = n1 * n2\nt1 = n0 - n1\nt2 = n2 - 1.0\nt3 = t0 + t1\nt4 = t3 / t2\nanswer = n0 + t4\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "a case of 12 rolls of paper towels sells for $ 9 . the cost of one roll sold individually is $ 1 . what is the percent of savings per roll for the 12 - roll package over the cost of 12 rolls purchased individually ?", + "Output Program": [ + "n0 = 12.0\nn1 = 9.0\nn2 = 1.0\nn3 = 12.0\nn4 = 12.0\nt0 = n1 / n0\nt1 = t0 * 100.0\nanswer = 100.0 - t1\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "what least number must be subtracted from 3830 so that the remaining number is divisible by 15 ?", + "Output Program": [ + "import math\nn0 = 3830.0\nn1 = 15.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "if 7 ^ ( x - y ) = 343 and 7 ^ ( x + y ) = 16807 , what is the value of x ?", + "Output Program": [ + "n0 = 7.0\nn1 = 343.0\nn2 = 7.0\nn3 = 16807.0\nt0 = n0 - 4.0\nt1 = n0 - 2.0\nt2 = t0 + t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "a man spends 2 / 5 of his salary on house rent , 3 / 10 of his salary on food and 1 / 8 of his salary on conveyance . if he has $ 1400 left with him , find his expenditure on food and conveyance .", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 3.0\nn3 = 10.0\nn4 = 1.0\nn5 = 8.0\nn6 = 1400.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = n4 / n5\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n4 - t4\nt6 = n6 / t5\nt7 = t6 * t1\nt8 = t6 * t2\nanswer = t7 + t8\nprint(answer)" + ], + "Output Answer": [ + "3399.999999999999" + ], + "split": "train" + }, + { + "Input": "how many of the integers between 25 and 45 are even ?", + "Output Program": [ + "n0 = 25.0\nn1 = 45.0\nt0 = n1 - n0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "bill made a profit of 10 % by selling a product . if he had purchased that product for 10 % less and sold it at a profit of 30 % , he would have received $ 28 more . what was his original selling price ?", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 30.0\nn3 = 28.0\nt0 = n0 / 100.0\nt1 = n2 / 100.0\nt2 = t0 + 1.0\nt3 = t1 + 1.0\nt4 = 1.0 - t0\nt5 = t3 * t4\nt6 = t5 - t2\nt7 = n3 / t6\nanswer = t2 * t7\nprint(answer)" + ], + "Output Answer": [ + "439.99999999999966" + ], + "split": "train" + }, + { + "Input": "sixty 5 percent of a number is 21 less than 4 fifth of that number . what is the number", + "Output Program": [ + "n0 = 5.0\nn1 = 21.0\nn2 = 4.0\nt0 = n1 * 100.0\nt1 = n0 * 3.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "140" + ], + "split": "train" + }, + { + "Input": "if n is an integer and 101 n ^ 2 is less than or equal to 8100 , what is the greatest possible value of n ?", + "Output Program": [ + "import math\nn0 = 101.0\nn1 = 2.0\nn2 = 8100.0\nt0 = n2 / n0\nt1 = math.sqrt(max(0, t0))\nanswer = math.floor(t1)\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "what does the hexa number e 78 in radix 7 .", + "Output Program": [ + "n0 = 78.0\nn1 = 7.0\nt0 = 10.0 + 3.0\nt1 = 1.0 + 4.0\nt2 = n0 * n1\nt3 = 10.0 * 100.0\nt4 = t0 * t3\nt5 = t2 + t4\nanswer = t5 - t1\nprint(answer)" + ], + "Output Answer": [ + "13541" + ], + "split": "train" + }, + { + "Input": "how much is 55 % of 40 is greater than 4 / 5 of 25 ?", + "Output Program": [ + "n0 = 55.0\nn1 = 40.0\nn2 = 4.0\nn3 = 5.0\nn4 = 25.0\nt0 = n0 / 100.0\nt1 = n2 / n3\nt2 = n1 * t0\nt3 = n4 * t1\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "find large number from below question the difference of two numbers is 1515 . on dividing the larger number by the smaller , we get 16 as quotient and the 15 as remainder", + "Output Program": [ + "n0 = 1515.0\nn1 = 16.0\nn2 = 15.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nt2 = t0 / t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "1600" + ], + "split": "train" + }, + { + "Input": "david spends $ 350 buying his favorite dolls . if he buys only small lemonhead dolls , which are $ 2 cheaper than the large lemonhead dolls , he could buy 20 more dolls than if he were to buy only large lemonhead dolls . how much does a large lemonhead doll cost ?", + "Output Program": [ + "n0 = 350.0\nn1 = 2.0\nn2 = 20.0\nt0 = n0 / 10.0\nt1 = n2 - n1\nt2 = t1 + 10.0\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "if money is invested at r percent interest , compounded annually , the amount of the investment will double in approximately 50 / r years . if luke ' s parents invested $ 12,500 in a long term bond that pays 12 percent interest compounded annually , what will be the approximate total amount of the investment 12 years later , when luke is ready for college ?", + "Output Program": [ + "n0 = 70.0\nn1 = 5000.0\nn2 = 8.0\nn3 = 18.0\nt0 = n1 * 2.0\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "20000" + ], + "split": "train" + }, + { + "Input": "arnold and danny are two twin brothers that are celebrating their birthday . the product of their ages today is smaller by 13 from the product of their ages a year from today . what is their age today ?", + "Output Program": [ + "n0 = 13.0\nt0 = n0 - 1.0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "what is the minimum possible range in scores of the 3 test - takers ? 3 people each took 5 tests . if the ranges of their scores in the 5 practice tests were 18 , 26 and 32 .", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 5.0\nn3 = 5.0\nn4 = 18.0\nn5 = 26.0\nn6 = 32.0\nt0 = n6 - n5\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "if k is a non - negative integer and 15 ^ k is a divisor of 759,325 then 3 ^ k - k ^ 3 =", + "Output Program": [ + "n0 = 15.0\nn1 = 759325.0\nn2 = 3.0\nn3 = 3.0\nt0 = 1.0 - 1.0\nt1 = n2**min(t0, 5)\nt2 = t0**min(n2, 5)\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "when tossed , a certain coin has equal probability of landing on either side . if the coin is tossed 3 times , what is the probability that it will land once on heads and twice tails ?", + "Output Program": [ + "n0 = 3.0\nt0 = 2.0**min(n0, 5)\nanswer = 1.0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.125" + ], + "split": "train" + }, + { + "Input": "the average of the marks of 10 students in a class is 80 . if the marks of each student are doubled , find the new average ?", + "Output Program": [ + "n0 = 10.0\nn1 = 80.0\n\nanswer = n1 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "160" + ], + "split": "train" + }, + { + "Input": "there were totally 100 men . 83 are married . 75 have t . v , 85 have radio , 70 have a . c . how many men have t . v , radio , a . c and also married ?", + "Output Program": [ + "n0 = 100.0\nn1 = 83.0\nn2 = 75.0\nn3 = 85.0\nn4 = 70.0\nt0 = n0 - n1\nt1 = n0 - n2\nt2 = n0 - n3\nt3 = n0 - n4\nt4 = t0 + t1\nt5 = t4 + t2\nt6 = t5 + t3\nanswer = n0 - t6\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "if an integer n is to be chosen at random from the integers 1 to 94 , inclusive , what is the probability that n ( n + 1 ) ( n + 2 ) will be divisible by 8 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 94.0\nn2 = 1.0\nn3 = 2.0\nn4 = 8.0\nt0 = n1 / n3\nt1 = n1 / n4\nt2 = t0 + t1\nanswer = t2 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.625" + ], + "split": "train" + }, + { + "Input": "what is x if x + 2 y = 10 and y = 1 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 10.0\nn2 = 1.0\nt0 = n0 * n2\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "what is the median of a set of consecutive integers if the sum of nth number from the beginning and nth number from the end is 50 ?", + "Output Program": [ + "n0 = 50.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "if a , b , c and d are positive integers less than 4 , and 4 ^ a + 3 ^ b + 2 ^ c + 1 ^ d = 78 then what is the value of b / c ?", + "Output Program": [ + "n0 = 4.0\nn1 = 4.0\nn2 = 3.0\nn3 = 2.0\nn4 = 1.0\nn5 = 78.0\n\nanswer = n3 / n3\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "on a school \u00e2 \u20ac \u2122 s annual day sweets were to be equally distributed amongst 112 children . but on that particular day , 32 children were absent . thus the remaining children got 6 extra sweets . how many sweets was each child originally supposed to get ?", + "Output Program": [ + "n0 = 112.0\nn1 = 32.0\nn2 = 6.0\nt0 = n0 - n1\nt1 = n2 * t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "if you wish to live to be 100 years old ( hypothetically ) , you must consume 500 calories less than your average daily allowance for your age . if you are in your 60 ' s , and your average daily allowance is 2000 calories per day , how many calories are you allowed in a week ?", + "Output Program": [ + "n0 = 100.0\nn1 = 500.0\nn2 = 60.0\nn3 = 2000.0\nt0 = 3.0 + 4.0\nt1 = n3 - n1\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "10500" + ], + "split": "train" + }, + { + "Input": "if an integer n is to be selected at random from 1 to 100 , inclusive , what is probability n ( n + 1 ) will be divisible by 16 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 100.0\nn2 = 1.0\nn3 = 16.0\n\nanswer = 2.0 / n3\nprint(answer)" + ], + "Output Answer": [ + "0.125" + ], + "split": "train" + }, + { + "Input": "a certain fraction is equivalent to 2 / 5 . if the numerator of the fraction is increased by 3 and the denominator is doubled , the new fraction is equivalent to 1 / 3 . what is the sum of the numerator and denominator of the original fraction ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 3.0\nn3 = 1.0\nn4 = 3.0\nt0 = n1 / n0\nt1 = n2 * t0\nt2 = n2 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "5.25" + ], + "split": "train" + }, + { + "Input": "it takes 30 days to fill a laboratory dish with bacteria . if the size of the bacteria doubles each day , how long did it take for the bacteria to fill 1 / 64 of the dish ?", + "Output Program": [ + "import math\nn0 = 30.0\nn1 = 1.0\nn2 = 64.0\nt0 = math.log(max(1e-5, n2), 2)\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "q - 2 : how many two digit numbers of distinct digits can be formed by using digits 1 , 2 , 3 , 4 , 5 , 6 and 7 such that the numbers are divisible by 3 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 2.0\nn3 = 3.0\nn4 = 4.0\nn5 = 5.0\nn6 = 6.0\nn7 = 7.0\nn8 = 3.0\nt0 = n0 + n1\nt1 = n0 + t0\nt2 = n3 + t1\nt3 = n4 + t2\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "a women purchased 3 towels @ rs . 100 each , 5 towels @ rs . 150 each and two towels at a certain rate which is now slipped off from his memory . but she remembers that the average price of the towels was rs . 150 . find the unknown rate of two towels ?", + "Output Program": [ + "n0 = 3.0\nn1 = 100.0\nn2 = 5.0\nn3 = 150.0\nn4 = 150.0\nt0 = n0 + n2\nt1 = n2 * n3\nt2 = n0 * n1\nt3 = t0 + 2.0\nt4 = n4 * t3\nt5 = t4 - t1\nanswer = t5 - t2\nprint(answer)" + ], + "Output Answer": [ + "450" + ], + "split": "train" + }, + { + "Input": "tough and tricky questions : distance / rate . on a reconnaissance mission , a state - of - the - art nuclear powered submarine traveled 300 miles to reposition itself in the proximity of an aircraft carrier . this journey would have taken 1 hour less if the submarine had traveled 10 miles per hour faster . what was the average speed , in miles per hour , for the actual journey ?", + "Output Program": [ + "import math\nn0 = 300.0\nn1 = 1.0\nn2 = 10.0\nt0 = n0 * n2\nt1 = n2**min(2.0, 5)\nt2 = t0 * 4.0\nt3 = t2 + t1\nt4 = math.sqrt(max(0, t3))\nt5 = t4 - n2\nanswer = t5 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "in a company with 48 employees , some part - time and some full - time , exactly ( 1 / 3 ) of the part - time employees and ( 1 / 4 ) of the full - time employees take the subway to work . what is the greatest possible number w of employees who take the subway to work ?", + "Output Program": [ + "n0 = 48.0\nn1 = 1.0\nn2 = 3.0\nn3 = 1.0\nn4 = 4.0\nt0 = n0 * n2\nt1 = n2 * n4\nt2 = t0 / t1\nt3 = n0 - t1\nt4 = t3 / t2\nanswer = t2 + t4\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "if sharon ' s weekly salary increased by 16 percent , she would earn $ 406 per week . if instead , her weekly salary were to increase by 10 percent , how much would she earn per week ?", + "Output Program": [ + "n0 = 16.0\nn1 = 406.0\nn2 = 10.0\nt0 = n0 / 100.0\nt1 = n2 / 100.0\nt2 = t0 + 1.0\nt3 = n1 / t2\nt4 = t1 * t3\nanswer = t3 + t4\nprint(answer)" + ], + "Output Answer": [ + "385" + ], + "split": "train" + }, + { + "Input": "what is the average of first 21 multiples of 6 ?", + "Output Program": [ + "n0 = 21.0\nn1 = 6.0\nt0 = n0 + 1.0\nt1 = n0 * t0\nt2 = t1 / 2.0\nt3 = t2 / n0\nanswer = n1 * t3\nprint(answer)" + ], + "Output Answer": [ + "66" + ], + "split": "train" + }, + { + "Input": "what is the sum of two consecutive even numbers , the difference of whose squares is 84 ?", + "Output Program": [ + "n0 = 84.0\nt0 = 2.0 * 2.0\nt1 = n0 - t0\nt2 = t1 / t0\nt3 = t2 + 2.0\nanswer = t3 + t2\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "if x > 0 , x / 5 + x / 25 is what percent of x ?", + "Output Program": [ + "n0 = 0.0\nn1 = 5.0\nn2 = 25.0\nt0 = 1.0 / n1\nt1 = 1.0 / n2\nt2 = t0 + t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "24.000000000000004" + ], + "split": "train" + }, + { + "Input": "if f ( f ( n ) ) + f ( n ) = 2 n + 3 , f ( 0 ) = 1 then f ( 2017 ) = ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 0.0\nn3 = 1.0\nn4 = 2017.0\n\nanswer = n3 + n4\nprint(answer)" + ], + "Output Answer": [ + "2018" + ], + "split": "train" + }, + { + "Input": "a solution is 90 % glycerin . if there are 4 gallons of the solution , how much water , in gallons must be addded to make a 75 % glycerin solution", + "Output Program": [ + "n0 = 90.0\nn1 = 4.0\nn2 = 75.0\nt0 = n0 / 100.0\nt1 = n2 / 100.0\nt2 = n1 * t0\nt3 = t2 / t1\nanswer = t3 - n1\nprint(answer)" + ], + "Output Answer": [ + "0.7999999999999998" + ], + "split": "train" + }, + { + "Input": "every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 65000 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 8.0\nn2 = 65000.0\nt0 = n0 / n1\nt1 = n2 * t0\nt2 = n2 + t1\nt3 = t2 * t0\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "82265.625" + ], + "split": "train" + }, + { + "Input": "the instructions state that cheryl needs 3 / 8 square yards of one type of material and 1 / 3 square yards of another type of material for a project . she buys exactly that amount . after finishing the project , however , she has 15 / 40 square yards left that she did not use . what is the total amount of square yards of material cheryl used ?", + "Output Program": [ + "n0 = 3.0\nn1 = 8.0\nn2 = 1.0\nn3 = 3.0\nn4 = 15.0\nn5 = 40.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = n4 / n5\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "0.33333333333333326" + ], + "split": "train" + }, + { + "Input": "at 6 ' o clock clock ticks 6 times . the time between first and last ticks was 30 sec . how much time it takes at 8 ' o clock .", + "Output Program": [ + "n0 = 6.0\nn1 = 6.0\nn2 = 30.0\nn3 = 8.0\nt0 = n0 - 1.0\nt1 = n3 - 1.0\nt2 = n2 / t0\nanswer = t2 * t1\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "9 fencers participate in a fencing championship . assuming all competitors have an equal chance of winning , how many possibilities are there with respect to how a first - place and second - place medal can be awarded ?", + "Output Program": [ + "import math\nn0 = 9.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = n0 - 2.0\nt2 = math.factorial(min(15, int(t1)))\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "train" + }, + { + "Input": "in a factory , an average of 70 tv ' s are produced per day for the fist 25 days of the months . a few workers fell ill for the next 5 days reducing the daily avg for the month to 68 sets / day . the average production per day for day last 5 days is ?", + "Output Program": [ + "n0 = 70.0\nn1 = 25.0\nn2 = 5.0\nn3 = 68.0\nn4 = 5.0\nt0 = n1 + n2\nt1 = n0 * n1\nt2 = n3 * t0\nt3 = t2 - t1\nanswer = t3 / n2\nprint(answer)" + ], + "Output Answer": [ + "58" + ], + "split": "train" + }, + { + "Input": "alex has 4 pens worth of { 22 , 25 , 30 , 40 } , what is the total mean and median of the worth of pens ?", + "Output Program": [ + "n0 = 4.0\nn1 = 22.0\nn2 = 25.0\nn3 = 30.0\nn4 = 40.0\nt0 = n1 + n2\nt1 = n2 + n3\nt2 = n3 + t0\nt3 = t1 / 2.0\nt4 = n4 + t2\nt5 = t4 / n0\nanswer = t5 - t3\nprint(answer)" + ], + "Output Answer": [ + "1.75" + ], + "split": "train" + }, + { + "Input": "if a father said to his elder son , ` ` i was as old as you are at the present at the time of your birth ' ' . if the father ' s age is 25 years now , what was the son ' s age 4 years back ?", + "Output Program": [ + "n0 = 25.0\nn1 = 4.0\nt0 = n0 / 2.0\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "8.5" + ], + "split": "train" + }, + { + "Input": "jim \u2019 s taxi service charges an initial fee of $ 2.25 at the beginning of a trip and an additional charge of $ 0.25 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?", + "Output Program": [ + "n0 = 2.25\nn1 = 0.25\nn2 = 2.0\nn3 = 5.0\nn4 = 3.6\nt0 = n2 / n3\nt1 = n4 / t0\nt2 = n1 * t1\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "4.5" + ], + "split": "train" + }, + { + "Input": "payal finished 2 / 3 of a book . she calculated that she finished 20 more pages than she has yet to read . how long is her book ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 20.0\nt0 = n0 / n1\nt1 = t0 / 2.0\nanswer = n2 / t1\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "there is a 1 km long wire placed on some number of poles which are in equal distance . if the number of poles is reduced by 1 then the distance of wire between each poles increases 1 ( 2 / 3 ) . how many poles are there initially .", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 1.0\nn3 = 2.0\nn4 = 3.0\nt0 = n0 + n0\nt1 = n3 / n4\nt2 = t0 * t1\nt3 = n4 * t2\nt4 = t3 * 12.0\nt5 = t4 / n3\nanswer = n3 + t5\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "if there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city , find the number of 4 wheelers parked there if the total number of wheels is 58 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 4.0\nn3 = 58.0\nt0 = n3 - n0\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "2 cow \u2019 s and 10 goats are brought for rs . 1500 . if the average price of a goat be rs . 70 . what is the average price of a cow .", + "Output Program": [ + "n0 = 2.0\nn1 = 10.0\nn2 = 1500.0\nn3 = 70.0\nt0 = n1 * n3\nt1 = n2 - t0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "train" + }, + { + "Input": "if x < y < z and y - x > 5 , where x is an even integer and y and z are odd integers , what is the least possible value f of z - x ?", + "Output Program": [ + "n0 = 5.0\nt0 = n0 + 2.0\nanswer = t0 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "in the set of positive integers from 1 to 60 , what is the sum of all the odd multiples of 5 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 60.0\nn2 = 5.0\nt0 = n2 * 3.0\nt1 = n1 * t0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "180" + ], + "split": "train" + }, + { + "Input": "if an integer w is to be chosen at random from the integers 1 to 96 , inclusive , what is the probability that w ( w + 1 ) ( w + 2 ) will be divisible by 8 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 96.0\nn2 = 1.0\nn3 = 2.0\nn4 = 8.0\nt0 = n1 / n4\nt1 = n1 / n3\nt2 = t0 + t1\nanswer = t2 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.625" + ], + "split": "train" + }, + { + "Input": "tickets numbered from 1 to 24 are mixed and then a ticket is selected randomly . what is the probability that the selected ticket bears a number which is a multiple of 3 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 24.0\nn2 = 3.0\nt0 = n1 / n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.3333333333333333" + ], + "split": "train" + }, + { + "Input": "a group of 55 adults and 70 children go for trekking . if there is meal for either 70 adults or 90 children and if 14 adults have their meal , find the total number of children that can be catered with the remaining food .", + "Output Program": [ + "n0 = 55.0\nn1 = 70.0\nn2 = 70.0\nn3 = 90.0\nn4 = 14.0\nt0 = n3 / n1\nt1 = n1 - n4\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "train" + }, + { + "Input": "robert ' s salary was decreased by 60 % and subsequently increased by 60 % . how much percentage does he lose ?", + "Output Program": [ + "n0 = 60.0\nn1 = 60.0\nt0 = n0 + 100.0\nt1 = 100.0 * 100.0\nt2 = 100.0 - n0\nt3 = t0 * t2\nt4 = t1 - t3\nt5 = t4 / t1\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "if x \u00a4 y = ( x + y ) ^ 2 - ( x - y ) ^ 2 . then \u221a 11 \u00a4 \u221a 11 =", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 2.0\nn2 = 11.0\nn3 = 11.0\nt0 = math.sqrt(max(0, n2))\nt1 = t0 + t0\nanswer = t1**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "44" + ], + "split": "train" + }, + { + "Input": "the average marks obtained by 120 candidates in a certain examination is 35 . find the total marks .", + "Output Program": [ + "n0 = 120.0\nn1 = 35.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "4200" + ], + "split": "train" + }, + { + "Input": "according to the directions on the can of frozen orange juice concentrate , 1 can of concentrate is to be mixed with 3 cans of water to make orange juice . how many 12 ounces cans of the concentrate are required to prepare 280 6 ounces servings of orange juice ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 12.0\nn3 = 280.0\nn4 = 6.0\nt0 = n3 * n4\nt1 = t0 / n2\nanswer = t1 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "a box contains either blue or red flags . the total number of flags in the box is an even number . a group of children are asked to pick up two flags each . if all the flags are used up in the process such that 60 % of the children have blue flags , and 45 % have red flags , what percentage of children have flags of both the colors ?", + "Output Program": [ + "n0 = 60.0\nn1 = 45.0\nt0 = n0 + n1\nanswer = t0 - 100.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "what is the average ( arithmetic mean ) of all multiples of 10 from 10 to 500 inclusive ?", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 500.0\nt0 = n0 + n2\nt1 = n2 - n0\nt2 = t1 / n0\nt3 = t2 + 1.0\nt4 = t0 * t3\nt5 = t4 / 2.0\nanswer = t5 / t3\nprint(answer)" + ], + "Output Answer": [ + "255" + ], + "split": "train" + }, + { + "Input": "find the sum the difference between the compound and s . i . on a certain sum of money for 2 years at 10 % per annum is rs . 15 of money ?", + "Output Program": [ + "n0 = 2.0\nn1 = 10.0\nn2 = 15.0\nt0 = n0 * n1\nt1 = n2 / t0\nt2 = t1 * 100.0\nanswer = t2 * t0\nprint(answer)" + ], + "Output Answer": [ + "1500" + ], + "split": "train" + }, + { + "Input": "one bottle is half - full of oil and another bottle with twice the capacity is one quarter full of oil . if water is added so that both the bottles are full and the contents of both are then poured into a third bottle that is empty and large enough to hold the contents of both , what fractions of the contents in the third bottle is oil ?", + "Output Program": [ + "t0 = 1.0 / 2.0\nt1 = 2.0 / 4.0\nt2 = t0 + t1\nt3 = 2.0 - t1\nt4 = 1.0 - t0\nt5 = t3 + t4\nt6 = t5 + t2\nanswer = t2 / t6\nprint(answer)" + ], + "Output Answer": [ + "0.3333333333333333" + ], + "split": "train" + }, + { + "Input": "a box contains 12 pairs of shoes ( 24 shoes in total ) . if two shoes are selected at random , what it is the probability that they are matching shoes ?", + "Output Program": [ + "n0 = 12.0\nn1 = 24.0\nt0 = n1 - 1.0\nanswer = 1.0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.043478260869565216" + ], + "split": "train" + }, + { + "Input": "if 2 ^ 5 , 3 ^ 3 , and 10 ^ 2 are all factors of the product of 936 and w where w is a positive integer , what is the smallest possible value of w ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 3.0\nn3 = 3.0\nn4 = 10.0\nn5 = 2.0\nn6 = 936.0\nt0 = n4 / n0\nt1 = n0**min(n0, 5)\nt2 = n2 * t1\nt3 = t0 * t2\nanswer = n0 * t3\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "in a school with 5 classes , each class has 2 students less then the previous class . how many students are there in the largest class if the total number of students at school is 95 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 95.0\nt0 = n1 + n1\nt1 = n1 + t0\nt2 = n1 + t1\nt3 = t1 + t1\nt4 = t3 + t2\nt5 = n2 - t4\nt6 = t5 / n0\nanswer = t2 + t6\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "if 6 < x < 10 < y < 17 , then what is the greatest possible positive integer difference of x and y ?", + "Output Program": [ + "n0 = 6.0\nn1 = 10.0\nn2 = 17.0\nt0 = n2 - n0\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "sandy bought 65 books for $ 1380 from one shop and 55 books for $ 900 from another shop . what is the average price that sandy paid per book ?", + "Output Program": [ + "n0 = 65.0\nn1 = 1380.0\nn2 = 55.0\nn3 = 900.0\nt0 = n1 + n3\nt1 = n0 + n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "in a factory , an average of 50 tv ' s are produced per day for the fist 25 days of the months . a few workers fell ill for the next 5 days reducing the daily avg for the month to 48 sets / day . the average production per day for day last 5 days is ?", + "Output Program": [ + "n0 = 50.0\nn1 = 25.0\nn2 = 5.0\nn3 = 48.0\nn4 = 5.0\nt0 = n1 + n2\nt1 = n0 * n1\nt2 = n3 * t0\nt3 = t2 - t1\nanswer = t3 / n2\nprint(answer)" + ], + "Output Answer": [ + "38" + ], + "split": "train" + }, + { + "Input": "pradeep has to obtain 40 % of the total marks to pass . he got 200 marks and failed by 20 marks . the maximum marks are", + "Output Program": [ + "n0 = 40.0\nn1 = 200.0\nn2 = 20.0\nt0 = n1 + n2\nt1 = n0 / 100.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "550" + ], + "split": "train" + }, + { + "Input": "a batsman makes a score of 56 runs in the 17 th inning and thus increases his averages by 3 . what is his average after 17 th inning ?", + "Output Program": [ + "n0 = 56.0\nn1 = 17.0\nn2 = 3.0\nn3 = 17.0\nt0 = n1 * n2\nt1 = n0 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "if 2 x + y = 6 and x + 2 y = 5 , then ( x + y ) / 3 =", + "Output Program": [ + "n0 = 2.0\nn1 = 6.0\nn2 = 2.0\nn3 = 5.0\nn4 = 3.0\nt0 = n0 * n1\nt1 = n0 * n0\nt2 = t0 - n3\nt3 = t1 - 1.0\nt4 = t2 / t3\nt5 = n0 * t4\nt6 = n1 - t5\nt7 = t4 + t6\nanswer = t7 / n4\nprint(answer)" + ], + "Output Answer": [ + "1.222222222222222" + ], + "split": "train" + }, + { + "Input": "if m and n are positive integers and m = 15 n - 1 , what is the remainder when m is divided by 5 ?", + "Output Program": [ + "n0 = 15.0\nn1 = 1.0\nn2 = 5.0\nt0 = n0 * 2.0\nt1 = n2 * n2\nt2 = t0 - n1\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "workers decided to raise rs . 3 lacs by equal contribution from each . had they contributed rs . 50 eachextra , the contribution would have been rs . 3.25 lacs . how many workers were they ?", + "Output Program": [ + "n0 = 3.0\nn1 = 50.0\nn2 = 3.25\nt0 = n2 - n0\nt1 = t0 * 1000.0\nt2 = t1 * 100.0\nanswer = t2 / n1\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "train" + }, + { + "Input": "in the xy - coordinate system , if ( m , n ) and ( m 1 2 , n 1 k ) are two points on the line with the equation x 5 2 y 1 5 , then k 5", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 1.0\nn3 = 5.0\nn4 = 2.0\nn5 = 1.0\nn6 = 5.0\nn7 = 5.0\nt0 = n0 / n1\nanswer = n1 * t0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "if 625 ^ ( - x ) + 25 ^ ( - 2 x ) + 5 ^ ( - 4 x ) = 11 , what is the value of x ?", + "Output Program": [ + "n0 = 625.0\nn1 = 25.0\nn2 = 2.0\nn3 = 5.0\nn4 = 4.0\nn5 = 11.0\n\nanswer = 1.0 / n4\nprint(answer)" + ], + "Output Answer": [ + "0.25" + ], + "split": "train" + }, + { + "Input": "find \u221a ? / 13 = 4 ?", + "Output Program": [ + "n0 = 13.0\nn1 = 4.0\nt0 = n0 * n1\nanswer = t0**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "2704" + ], + "split": "train" + }, + { + "Input": "how many odd prime numbers are there less than 125 ?", + "Output Program": [ + "n0 = 125.0\nt0 = n0 - 100.0\nanswer = t0 + 4.0\nprint(answer)" + ], + "Output Answer": [ + "29" + ], + "split": "train" + }, + { + "Input": "in an electric circuit , two resistors with resistances x and y are connected in parallel . if r is the combined resistance of these two resistors , then the reciprocal of r is equal to the sum of the reciprocals of x and y . what is r if x is 4 ohms and y is 6 ohms ?", + "Output Program": [ + "n0 = 4.0\nn1 = 6.0\nt0 = n0 + n1\nt1 = n0 * n1\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "2.4" + ], + "split": "train" + }, + { + "Input": "the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 40 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam .", + "Output Program": [ + "n0 = 80.0\nn1 = 5.0\nn2 = 40.0\nn3 = 90.0\nt0 = n1 * n3\nt1 = n1 * n2\nt2 = n3 - n0\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "when x is multiplied by 3 , the result is 16 more than the result of subtracting x from 36 . what is the value of x ?", + "Output Program": [ + "n0 = 3.0\nn1 = 16.0\nn2 = 36.0\nt0 = n1 + n2\nt1 = 1.0 + n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "5 ! / ( 5 - 3 ) ! = ?", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 5.0\nn2 = 3.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = n0 - n2\nt2 = math.factorial(min(15, int(t1)))\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "there are x persons and y chocolates . if each person is given 1 chocolate then 1 chocolate is left , if each person is given 2 chocolates then 1 person will be left . so how many persons and chocolates are there ? ?", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 2.0\nn3 = 1.0\nt0 = 12.0 * 3.0\nanswer = t0 - n2\nprint(answer)" + ], + "Output Answer": [ + "34" + ], + "split": "train" + }, + { + "Input": "a type of extra - large suv averages 12.2 miles per gallon ( mpg ) on the highway , but only 7.6 mpg in the city . what is the maximum distance , in miles , that this suv could be driven on 20 gallons of gasoline ?", + "Output Program": [ + "n0 = 12.2\nn1 = 7.6\nn2 = 20.0\n\nanswer = n0 * n2\nprint(answer)" + ], + "Output Answer": [ + "244" + ], + "split": "train" + }, + { + "Input": "united telephone charges a base rate of $ 9.00 for service , plus an additional charge of $ 0.25 per minute . atlantic call charges a base rate of $ 12.00 for service , plus an additional charge of $ 0.20 per minute . for what number of minutes would the bills for each telephone company be the same ?", + "Output Program": [ + "n0 = 9.0\nn1 = 0.25\nn2 = 12.0\nn3 = 0.2\nt0 = n2 - n0\nt1 = n1 - n3\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "60.000000000000014" + ], + "split": "train" + }, + { + "Input": "a scale 6 ft . 8 inches long is divided into 2 equal parts . find the length of each part .", + "Output Program": [ + "n0 = 6.0\nn1 = 8.0\nn2 = 2.0\nt0 = n0 * 12.0\nt1 = n1 + t0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "the tax on a commodity is diminished by 10 % and its consumption increases by 10 % . find the effects on revenue ?", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nt0 = n1 / 100.0\nt1 = n0 / 100.0\nt2 = t0 + 1.0\nt3 = 1.0 - t1\nt4 = t2 * t3\nt5 = t4 * 100.0\nanswer = 100.0 - t5\nprint(answer)" + ], + "Output Answer": [ + "0.9999999999999858" + ], + "split": "train" + }, + { + "Input": "if - 11 a and - 8 b are negative integers , then ( - 11 a ) * ( - 8 b ) + ab is", + "Output Program": [ + "n0 = 11.0\nn1 = 8.0\nn2 = 11.0\nn3 = 8.0\nt0 = n0 * n1\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "89" + ], + "split": "train" + }, + { + "Input": "what is the difference between the largest number and the least number written with the digits 5 , 3 , 1 , 4 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nn2 = 1.0\nn3 = 4.0\nt0 = n0 * 100.0\nt1 = n3 * 100.0\nt2 = n1 * 10.0\nt3 = n1 * 100.0\nt4 = n3 * 10.0\nt5 = t3 + 1000.0\nt6 = t0 * 10.0\nt7 = t6 + t1\nt8 = t5 + t4\nt9 = t7 + t2\nt10 = n0 + t8\nt11 = n2 + t9\nanswer = t11 - t10\nprint(answer)" + ], + "Output Answer": [ + "4086" + ], + "split": "train" + }, + { + "Input": "if ( a \u2013 b ) is 9 more than ( c + d ) and ( a + b ) is 3 less than ( c \u2013 d ) , then ( a \u2013 c ) is :", + "Output Program": [ + "n0 = 9.0\nn1 = 3.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "there are 408 boys and 240 girls in a school which are to be divided into equal sections of either boys or girls alone . find the total number of sections thus formed .", + "Output Program": [ + "n0 = 408.0\nn1 = 240.0\nt0 = n0 + n1\nt1 = 2.0 * 2.0\nt2 = t1 * 2.0\nt3 = t2 * 3.0\nanswer = t0 / t3\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "train" + }, + { + "Input": "if the function q is defined by the formula q = 5 w / ( 4 m ( z ^ 2 ) ) , by what factor will q be multiplied if w is quadrupled , m is doubled , and z is tripled ?", + "Output Program": [ + "n0 = 5.0\nn1 = 4.0\nn2 = 2.0\nt0 = 3.0**min(n2, 5)\nt1 = n2 * t0\nanswer = n1 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.2222222222222222" + ], + "split": "train" + }, + { + "Input": "carol spends 1 / 4 of her savings on a stereo and 2 / 3 less than she spent on the stereo for a television . what fraction of her savings did she spend on the stereo and television ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 2.0\nn3 = 3.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.25" + ], + "split": "train" + }, + { + "Input": "the ratio 5 : 4 expressed as a percent equals", + "Output Program": [ + "n0 = 5.0\nn1 = 4.0\nt0 = n0 / n1\nanswer = t0 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "125" + ], + "split": "train" + }, + { + "Input": "the average of runs of a cricket player of 20 innings was 32 . how many runs must he make in his next innings so as to increase his average of runs by 6 ?", + "Output Program": [ + "n0 = 20.0\nn1 = 32.0\nn2 = 6.0\nt0 = n0 + 1.0\nt1 = n1 + n2\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "158" + ], + "split": "train" + }, + { + "Input": "if x is the sum of first 100 positive even integers and y is the sum of first 100 positive odd integers , what is the value of x - y ? please try to explain your answers", + "Output Program": [ + "n0 = 100.0\nn1 = 100.0\n\nanswer = n0 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "the ratio of the amount of the oil bill for the month of february to the amount of the oil bill for the month of january was 3 : 2 . if the oil bill for february had been $ 30 more , the corresponding ratio would have been 5 : 3 . how much was the oil bill for january ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 30.0\nn3 = 5.0\nn4 = 3.0\nt0 = n3 / n4\nt1 = n0 / n1\nt2 = t0 - t1\nanswer = n2 / t2\nprint(answer)" + ], + "Output Answer": [ + "179.99999999999991" + ], + "split": "train" + }, + { + "Input": "a call center has two teams . each member of team a was able to process 1 / 5 calls as compared to each member of team b . if team a has 5 / 8 as many number of call center agents as team b , what fraction of the total calls was processed by team b ?", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 5.0\nn3 = 8.0\nt0 = n1 * n3\nt1 = n0 * n1\nt2 = t0 + t1\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.8888888888888888" + ], + "split": "train" + }, + { + "Input": "the jogging track in a sports complex is 1000 meters in circumference . deepak and his wife start from the same point and walk in opposite directions at 20 km / hr and 17 km / hr respectively . they will meet for the first time in ?", + "Output Program": [ + "n0 = 1000.0\nn1 = 20.0\nn2 = 17.0\n\nanswer = n1 + n2\nprint(answer)" + ], + "Output Answer": [ + "37" + ], + "split": "train" + }, + { + "Input": "if the sum of two numbers is 18 and the sum of their squares is 180 , then the product of the numbers is", + "Output Program": [ + "n0 = 18.0\nn1 = 180.0\nt0 = n0**min(2.0, 5)\nt1 = t0 - n1\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "train" + }, + { + "Input": "there are a total of 100 jars on the shelf . small jars hold 3 liters and large jars hold 5 liters . the jars can hold a total of 376 liters . how many small jars are on the shelf ?", + "Output Program": [ + "n0 = 100.0\nn1 = 3.0\nn2 = 5.0\nn3 = 376.0\nt0 = n0 * n1\nt1 = n3 - t0\nt2 = t1 / 2.0\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "62" + ], + "split": "train" + }, + { + "Input": "find large no . from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 10 as remainder", + "Output Program": [ + "n0 = 1365.0\nn1 = 6.0\nn2 = 10.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nt2 = t0 / t1\nt3 = n1 * t2\nanswer = n2 + t3\nprint(answer)" + ], + "Output Answer": [ + "1636" + ], + "split": "train" + }, + { + "Input": "a certain number when divided by 45 leaves a remainder 31 , what is the remainder if the same number be divided by 15 ?", + "Output Program": [ + "n0 = 45.0\nn1 = 31.0\nn2 = 15.0\n\nanswer = n1 % n2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "a person is saving money to purchase a car . he earns \u00e2 \u00a3 4000 per month and saves \u00e2 \u00a3 500 to buy the car . if he needs \u00e2 \u00a3 45000 to buy his dream car . how much money he will earn , before he saves enough money to buy the car ?", + "Output Program": [ + "n0 = 4000.0\nn1 = 500.0\nn2 = 45000.0\nt0 = n2 / n1\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "360000" + ], + "split": "train" + }, + { + "Input": "the rowing athletes in a rowing conference voted for coach of the year . each rower who voted chose exactly 3 coaches to vote for among the 36 coaches in the conference . if each of the 36 coaches received exactly 5 votes ( a 36 way tie ) , how many rowers voted for coach of the year ?", + "Output Program": [ + "n0 = 3.0\nn1 = 36.0\nn2 = 36.0\nn3 = 5.0\nn4 = 36.0\nt0 = n1 * n3\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "if grapes are 90 % water and raisins are 15 % water , then how many kilograms did a quantity of raisins , which currently weighs 12 kilograms , weigh when all the raisins were grapes ? ( assume that the only difference between their raisin - weight and their grape - weight is water that evaporated during their transformation . )", + "Output Program": [ + "n0 = 90.0\nn1 = 15.0\nn2 = 12.0\nt0 = 100.0 - n1\nt1 = 100.0 - n0\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = n2 * t2\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "101.99999999999999" + ], + "split": "train" + }, + { + "Input": "seller selling an apple for rs . 17 , a seller loses 1 / 6 th of what it costs him . the cp of the apple is ?", + "Output Program": [ + "n0 = 17.0\nn1 = 1.0\nn2 = 6.0\n\nanswer = n0 + n1\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "a bowler can take max . 3 wickets in a over . if he bowls 6 overs in an innings , how many maximum wickets can he take ?", + "Output Program": [ + "n0 = 3.0\nn1 = 6.0\nt0 = n0 * n1\nt1 = t0 - n1\nanswer = t1 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "( 5568 / 87 ) 1 / 3 + ( 72 x 2 ) 1 / 2 = ( ? ) 1 / 2 ?", + "Output Program": [ + "n0 = 5568.0\nn1 = 87.0\nn2 = 1.0\nn3 = 3.0\nn4 = 72.0\nn5 = 2.0\nn6 = 1.0\nn7 = 2.0\nn8 = 1.0\nn9 = 2.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = n2 / n5\nt3 = n4 * n5\nt4 = t0**min(t1, 5)\nt5 = t3**min(t2, 5)\nt6 = t4 + t5\nanswer = t6**min(n5, 5)\nprint(answer)" + ], + "Output Answer": [ + "256" + ], + "split": "train" + }, + { + "Input": "a batsman in his 12 th innings makes a score of 115 and thereby increases his average by 3 runs . what is his average after the 12 th innings if he had never been \u2018 not out \u2019 ?", + "Output Program": [ + "n0 = 12.0\nn1 = 115.0\nn2 = 3.0\nn3 = 12.0\nt0 = n0 * n2\nt1 = n1 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "82" + ], + "split": "train" + }, + { + "Input": "the ratio 3 : 5 expressed as a percent equals", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nt0 = n0 / n1\nanswer = t0 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "when positive integer n is divided by positive integer j , the remainder is 28 . if n / j = 142.07 , what is value of j ?", + "Output Program": [ + "n0 = 28.0\nn1 = 142.07\nt0 = 10.0 * 4.0\nt1 = t0 + 2.0\nt2 = t1 + 100.0\nt3 = n1 - t2\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "400.000000000039" + ], + "split": "train" + }, + { + "Input": "find the annual dividend received by nishita from 1200 preferred shares and 3000 common shares both of par value rs . 50 each if the dividend paid on preferred shares is 10 % and semi - annual dividend of 3 \u00bd % is declared on common shares .", + "Output Program": [ + "n0 = 1200.0\nn1 = 3000.0\nn2 = 50.0\nn3 = 10.0\nn4 = 3.0\nt0 = 1.0 / 2.0\nt1 = n0 * n2\nt2 = n1 * n2\nt3 = n4 + t0\nt4 = n3 * t1\nt5 = t4 / 100.0\nt6 = t3 * t2\nt7 = t6 / 100.0\nt8 = t5 + t7\nanswer = t8 + t7\nprint(answer)" + ], + "Output Answer": [ + "16500" + ], + "split": "train" + }, + { + "Input": "solve : 12.05 * 5.4 + 0.6", + "Output Program": [ + "n0 = 12.05\nn1 = 5.4\nn2 = 0.6\nt0 = n1 / n2\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "108.45000000000003" + ], + "split": "train" + }, + { + "Input": "list i : { y , 2 , 4 , 7 , 10 , 11 } list ii : { 3 , 3 , 4 , 6 , 7 , 10 } if the median q of list i is equal to the sum of the median of list ii and the mode of list ii , then y equals", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 7.0\nn3 = 10.0\nn4 = 11.0\nn5 = 3.0\nn6 = 3.0\nn7 = 4.0\nn8 = 6.0\nn9 = 7.0\nn10 = 10.0\n\nanswer = n5 + n8\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "if 45 - [ 28 - { 37 - ( 15 - * ) } ] = 58 , then * is equal to :", + "Output Program": [ + "n0 = 45.0\nn1 = 28.0\nn2 = 37.0\nn3 = 15.0\nn4 = 58.0\nt0 = n1 - n2\nt1 = n3 + t0\nt2 = n0 - t1\nanswer = n4 - t2\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "out of 40 applicants to a law school , 15 majored in political science , 20 had a grade point average higher than 3.0 , and 10 did not major in political science and had a gpa equal to or lower than 3.0 . how many r applicants majored in political science and had a gpa higher than 3.0 ?", + "Output Program": [ + "n0 = 40.0\nn1 = 15.0\nn2 = 20.0\nn3 = 3.0\nn4 = 10.0\nn5 = 3.0\nn6 = 3.0\nt0 = n1 + n4\nt1 = n0 - t0\nanswer = n2 - t1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "a grocer is storing soap boxes in cartons that measure 25 inches by 42 inches by 60 inches . if the measurement of each soap box is 7 inches by 12 inches by 5 inches , then what is the maximum number of soap boxes that can be placed in each carton ?", + "Output Program": [ + "n0 = 25.0\nn1 = 42.0\nn2 = 60.0\nn3 = 7.0\nn4 = 12.0\nn5 = 5.0\nt0 = n0 * n1\nt1 = n3 * n4\nt2 = n2 * t0\nt3 = n5 * t1\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "train" + }, + { + "Input": "if 25 % of x is 15 less than 15 % of 1600 , then x is ?", + "Output Program": [ + "n0 = 25.0\nn1 = 15.0\nn2 = 15.0\nn3 = 1600.0\nt0 = n2 / 100.0\nt1 = n0 / 100.0\nt2 = n3 * t0\nt3 = t2 - n1\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "900" + ], + "split": "train" + }, + { + "Input": "the milk level in a rectangular box measuring 50 feet by 25 feet is to be lowered by 6 inches . how many gallons of milk must be removed ? ( 1 cu ft = 7.5 gallons )", + "Output Program": [ + "n0 = 50.0\nn1 = 25.0\nn2 = 6.0\nn3 = 1.0\nn4 = 7.5\nt0 = n3 / 2.0\nt1 = n0 * n1\nt2 = t0 * t1\nanswer = n4 * t2\nprint(answer)" + ], + "Output Answer": [ + "4687.5" + ], + "split": "train" + }, + { + "Input": "in the new budget , the price of kerosene oil rose by 25 % . by how much percent must a person reduce his consumption so that his expenditure on it does not increase ?", + "Output Program": [ + "n0 = 25.0\nt0 = n0 - 4.0\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "if all of the telephone extensions in a certain company must be even numbers , and if each of the extensions uses all 4 of the digits 1 , 2 , 3 , and 8 , what is the greatest number of 4 - digit extensions that the company can have ?", + "Output Program": [ + "n0 = 4.0\nn1 = 1.0\nn2 = 2.0\nn3 = 3.0\nn4 = 8.0\nn5 = 4.0\n\nanswer = n0 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "there has been successive increases of 30 % and then 20 % in the price of gas from the previous month . by what percentage should a driver reduce gas consumption so that the expenditure does not change ?", + "Output Program": [ + "n0 = 30.0\nn1 = 20.0\nt0 = n0 + 100.0\nt1 = n1 * t0\nt2 = t1 / 100.0\nt3 = t0 + t2\nt4 = 100.0 / t3\nt5 = 1.0 - t4\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "35.89743589743589" + ], + "split": "train" + }, + { + "Input": "if m is an integer such that ( - 2 ) ^ 2 m = 2 ^ ( 24 - m ) then m = ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 2.0\nn3 = 24.0\nt0 = n0 + 1.0\nanswer = n3 / t0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a seller of used cars has 16 cars to sell and each of his clients selected 2 cars that he liked most . if each car was selected exactly thrice , how many clients visited the garage ?", + "Output Program": [ + "n0 = 16.0\nn1 = 2.0\nt0 = n0 / n1\nanswer = t0 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "the smallest fraction , which each of 6 / 7 , 5 / 14 , 10 / 21 will divide exactly is ?", + "Output Program": [ + "n0 = 6.0\nn1 = 7.0\nn2 = 5.0\nn3 = 14.0\nn4 = 10.0\nn5 = 21.0\nt0 = n0 * n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "4.285714285714286" + ], + "split": "train" + }, + { + "Input": "the ration of the father \u2019 s age to his son \u2019 s age is 7 : 3 . the product of their ages is 756 . the ratio of their ages after 6 years will be :", + "Output Program": [ + "import math\nn0 = 7.0\nn1 = 3.0\nn2 = 756.0\nn3 = 6.0\nt0 = n0 * n1\nt1 = n2 / t0\nt2 = math.sqrt(max(0, t1))\nt3 = n0 * t2\nt4 = n1 * t2\nt5 = n3 + t3\nt6 = n3 + t4\nanswer = t5 / t6\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "in the xy - coordinate system , what is the slope of the line that goes through the origin and is equidistant from the two points p = ( 4 , 6 ) and q = ( 6 , 2 ) ?", + "Output Program": [ + "n0 = 4.0\nn1 = 6.0\nn2 = 6.0\nn3 = 2.0\nt0 = n1 + n3\nt1 = n0 + n1\nt2 = t0 / 2.0\nt3 = t1 / 2.0\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.8" + ], + "split": "train" + }, + { + "Input": "if n divided by 11 has a remainder of 1 , what is the remainder when 5 times n is divided by 11 ?", + "Output Program": [ + "n0 = 11.0\nn1 = 1.0\nn2 = 5.0\nn3 = 11.0\n\nanswer = n1 * n2\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 47 , then how old is b ?", + "Output Program": [ + "n0 = 47.0\nt0 = 1.0 + 4.0\nt1 = n0 - 2.0\nt2 = t1 * 2.0\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "find the value of 658217 x 99999 = m ?", + "Output Program": [ + "n0 = 658217.0\nn1 = 99999.0\nt0 = n1 - 4.0\nanswer = t0 * n0\nprint(answer)" + ], + "Output Answer": [ + "65818408915" + ], + "split": "train" + }, + { + "Input": "a girl was asked to multiply a certain number by 43 . she multiplied it by 34 and got his answer less than the correct one by 1251 . find the number to be multiplied .", + "Output Program": [ + "n0 = 43.0\nn1 = 34.0\nn2 = 1251.0\nt0 = n0 - n1\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "139" + ], + "split": "train" + }, + { + "Input": "10 years ago , the age of peter was one - third the age of jacob at that time . the present age of jacob is 12 years more than the present age of peter . find the present age of peter ?", + "Output Program": [ + "n0 = 10.0\nn1 = 12.0\nt0 = n1 / 2.0\nanswer = n0 + t0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "at a supermarket , john spent 1 / 2 of his money on fresh fruits and vegetables , 1 / 3 on meat products , and 1 / 10 on bakery products . if he spent the remaining $ 8 on candy , how much did john spend at the supermarket ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 1.0\nn3 = 3.0\nn4 = 1.0\nn5 = 10.0\nn6 = 8.0\nt0 = n0 / n5\nt1 = n0 / n3\nt2 = n0 / n1\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n0 - t4\nanswer = n6 / t5\nprint(answer)" + ], + "Output Answer": [ + "120.00000000000003" + ], + "split": "train" + }, + { + "Input": "tough and tricky questions : exponents . if 5 ^ ( x + 1 ) * 4 ^ ( y - 1 ) = 25 ^ x * 64 ^ y , then x + y =", + "Output Program": [ + "import scipy\nn0 = 5.0\nn1 = 1.0\nn2 = 4.0\nn3 = 1.0\nn4 = 25.0\nn5 = 64.0\nt0 = scipy.gcd(int(n4), int(n5))\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "what is the remainder of e = 3 ^ 19 when divided by 10 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 19.0\nn2 = 10.0\nt0 = n1 % 4.0\nt1 = n0**min(t0, 5)\nanswer = t1 % 10.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "the average of 11 numbers is 9.9 . if the average of the first 6 numbers is 10.5 and that of the last 6 numbers is 11.4 , then the middle number is", + "Output Program": [ + "n0 = 11.0\nn1 = 9.9\nn2 = 6.0\nn3 = 10.5\nn4 = 6.0\nn5 = 11.4\nt0 = n2 * n3\nt1 = n2 * n5\nt2 = n0 * n1\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "22.5" + ], + "split": "train" + }, + { + "Input": "in how many ways can an answer key for a quiz be written if the quiz contains 3 true - false questions followed by 3 multiple - choice questions with 4 answer choices each , if the correct answers to all true - false questions can not be the same ?", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 4.0\nt0 = n2 * n2\nt1 = n1**min(n0, 5)\nt2 = t1 - n1\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "384" + ], + "split": "train" + }, + { + "Input": "if 2 ^ 5 , 3 ^ 3 , and 12 ^ 2 are all factors of the product of 936 and w where w is a positive integer , what is the smallest possible value of w ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 3.0\nn3 = 3.0\nn4 = 12.0\nn5 = 2.0\nn6 = 936.0\nt0 = n4 / n0\nt1 = n0**min(n0, 5)\nt2 = n2 * t1\nt3 = t0 * t2\nanswer = n0 * t3\nprint(answer)" + ], + "Output Answer": [ + "144" + ], + "split": "train" + }, + { + "Input": "when average age of 21 members are 0 , how many members greater than 0 ?", + "Output Program": [ + "n0 = 21.0\nn1 = 0.0\nn2 = 0.0\n\nanswer = n0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "how many times digit 6 is used while writing numbers from 80 to 1000 ?", + "Output Program": [ + "n0 = 6.0\nn1 = 80.0\nn2 = 1000.0\nt0 = 1.0 + 10.0\nt1 = n0 * 2.0\nt2 = n2 - n1\nt3 = t2 / 10.0\nt4 = t0 * t0\nt5 = t3 + t4\nanswer = t5 + t1\nprint(answer)" + ], + "Output Answer": [ + "225" + ], + "split": "train" + }, + { + "Input": "the average of 30 results is 20 and the average of other 20 results is 30 . what is the average of all the results ?", + "Output Program": [ + "n0 = 30.0\nn1 = 20.0\nn2 = 20.0\nn3 = 30.0\nt0 = n0 + n1\nt1 = n0 * n1\nt2 = t1 + t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "when an amount was distributed among 14 boys , each of them got $ 80 more than the amount received by each boy when the same amount is distributed equally among 18 boys . what was the amount ?", + "Output Program": [ + "n0 = 14.0\nn1 = 80.0\nn2 = 18.0\nt0 = 1.0 / n0\nt1 = 1.0 / n2\nt2 = t0 - t1\nanswer = n1 / t2\nprint(answer)" + ], + "Output Answer": [ + "5040" + ], + "split": "train" + }, + { + "Input": "2 ^ 35 ^ 26 ^ 1 find largest value ?", + "Output Program": [ + "n0 = 2.0\nn1 = 35.0\nn2 = 26.0\nn3 = 1.0\n\nanswer = n2 - n3\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "the sum of two numbers is 56 , and one of them is 12 more than the other . what are the two numbers ?", + "Output Program": [ + "n0 = 56.0\nn1 = 12.0\nt0 = n0 - n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "217 + 2.017 + 0.217 + 2.0017 = ?", + "Output Program": [ + "n0 = 217.0\nn1 = 2.017\nn2 = 0.217\nn3 = 2.0017\nt0 = n0 + n1\nt1 = n2 + t0\nanswer = n3 + t1\nprint(answer)" + ], + "Output Answer": [ + "221.2357" + ], + "split": "train" + }, + { + "Input": "dan ' s age after 18 years will be 8 times his age 3 years ago . what is the present age of dan ?", + "Output Program": [ + "n0 = 18.0\nn1 = 8.0\nn2 = 3.0\nt0 = n1 * n2\nt1 = n1 - 1.0\nt2 = n0 + t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "sum of the squares of 3 no . ' s is 99 and the sum of their products taken two at a time is 131 . find the sum ?", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 99.0\nn2 = 131.0\nt0 = n2 * 2.0\nt1 = n1 + t0\nanswer = math.sqrt(max(0, t1))\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "a box contains 7 purple , 5 blue and 11 yellow balls . what is the minimum number of tries required to get one blue and one yellow ball ?", + "Output Program": [ + "n0 = 7.0\nn1 = 5.0\nn2 = 11.0\nt0 = n0 + n2\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "3 men and 3 women are lined up in a row . what is the number of cases where they stand with each other in turn ? ( the number of cases in which men ( or women ) do not stand next to each other )", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 3.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(n1)))\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "sum of 42 odd numbers is ?", + "Output Program": [ + "n0 = 42.0\nt0 = n0 / 2.0\nt1 = n0 * 2.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "1764" + ], + "split": "train" + }, + { + "Input": "30 pens and 75 pencils were purchased for 510 . if the average price of a pencil was 2.00 , find the average price of a pen .", + "Output Program": [ + "n0 = 30.0\nn1 = 75.0\nn2 = 510.0\nn3 = 2.0\nt0 = n1 * n3\nt1 = n2 - t0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "the value of ( 0.137 + 0.098 ) \u00b2 - ( 0.137 - 0.098 ) \u00b2 / 0.137 \u00d7 0.098 is", + "Output Program": [ + "n0 = 0.137\nn1 = 0.098\nn2 = 0.137\nn3 = 0.098\nn4 = 0.137\nn5 = 0.098\nt0 = n0 + n1\nt1 = n0 * n1\nt2 = n0 - n1\nt3 = t0**min(2.0, 5)\nt4 = t2**min(2.0, 5)\nt5 = t3 - t4\nanswer = t5 / t1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "a grocer has a sale of rs . 6435 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6900 ?", + "Output Program": [ + "n0 = 6435.0\nn1 = 6927.0\nn2 = 6855.0\nn3 = 7230.0\nn4 = 6562.0\nn5 = 5.0\nn6 = 6900.0\nt0 = n5 + 1.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n6 * t0\nt4 = n3 + t2\nt5 = n4 + t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "7391" + ], + "split": "train" + }, + { + "Input": "a company purchased raw material worth 1 / 4 of it capital , 1 / 10 of the remaining is spent on machinery . how much fraction of the capital was left with the company after its expenditures on raw material and machinery ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 1.0\nn3 = 10.0\nt0 = 1.0 / n1\nt1 = n0 - t0\nt2 = t1 / n3\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "0.675" + ], + "split": "train" + }, + { + "Input": "if x = y = 2 z and xyz = 256 then what is the value of x ?", + "Output Program": [ + "n0 = 2.0\nn1 = 256.0\nt0 = 1.0 / 3.0\nt1 = n0 * n1\nanswer = t1**min(t0, 5)\nprint(answer)" + ], + "Output Answer": [ + "7.999999999999999" + ], + "split": "train" + }, + { + "Input": "if a \u00e3 \u2014 b = 2 a - 3 b + ab , then 4 \u00e3 \u2014 5 + 5 \u00e3 \u2014 4 is equal to :", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 4.0\nn3 = 5.0\nn4 = 5.0\nn5 = 4.0\nt0 = n0 * n2\nt1 = n0 * n1\nt2 = n3 * n3\nt3 = n1 * n2\nt4 = t0 - t1\nt5 = t2 - t3\nt6 = t0 + t4\nt7 = t0 + t5\nanswer = t6 + t7\nprint(answer)" + ], + "Output Answer": [ + "31" + ], + "split": "train" + }, + { + "Input": "what is the difference between the place values of two sevens in the numeral 54179759 ?", + "Output Program": [ + "n0 = 54179759.0\nt0 = 3.0 + 4.0\nt1 = t0 * 10.0\nt2 = t1 * 1000.0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "69930" + ], + "split": "train" + }, + { + "Input": "the manager at a health foods store mixes a unique superfruit juice cocktail that costs $ 1399.45 per litre to make . the cocktail includes mixed fruit juice and a \u00e7 ai berry juice , which cost $ 262.85 per litre and $ 3104.35 per litre , respectively . the manager has already opened 34 litres of the mixed fruit juice . how many litres of the a \u00e7 ai berry juice does he need to add ?", + "Output Program": [ + "n0 = 1399.45\nn1 = 262.85\nn2 = 3104.35\nn3 = 34.0\nt0 = n0 * n3\nt1 = n1 * n3\nt2 = n2 - n0\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "22.666666666666668" + ], + "split": "train" + }, + { + "Input": "the equation of line s is y = 4 / 3 * x - 100 . what is the smallest possible distance in the xy - plane from the point with coordinates ( 0 , 0 ) to any point on line s ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 3.0\nn2 = 100.0\nn3 = 0.0\nn4 = 0.0\nt0 = n2 * 3.0\nt1 = n0**min(2.0, 5)\nt2 = n1**min(2.0, 5)\nt3 = t1 + t2\nt4 = math.sqrt(max(0, t3))\nanswer = t0 / t4\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "jim \u00e2 \u20ac \u2122 s taxi service charges an initial fee of $ 2.0 at the beginning of a trip and an additional charge of $ 0.35 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?", + "Output Program": [ + "n0 = 2.0\nn1 = 0.35\nn2 = 2.0\nn3 = 5.0\nn4 = 3.6\nt0 = n2 / n3\nt1 = n4 / t0\nt2 = n1 * t1\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "5.15" + ], + "split": "train" + }, + { + "Input": "a two - digit number is such that the product of the digits is 8 . when 18 is added to the number , then the digits are reversed . the number is ?", + "Output Program": [ + "n0 = 8.0\nn1 = 18.0\nt0 = 10.0 - 1.0\nanswer = n1 / t0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "how many numbers from 10 to 47 are exactly divisible by 3 ?", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 47.0\nn2 = 3.0\nt0 = n1 / n2\nt1 = n0 / n2\nt2 = math.floor(t0)\nt3 = math.floor(t1)\nt4 = t3 + 1.0\nt5 = n2 * t2\nt6 = n2 * t4\nt7 = t5 - t6\nt8 = t7 / n2\nanswer = t8 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "a clothing store purchased a pair of pants for $ 81 and was selling it at a price that equaled the purchase price of the pants plus a markup that was 25 percent of the selling price . after some time a clothing store owner decided to decrease the selling price by 20 percent . what was the clothing store ' s gross profit on this sale ?", + "Output Program": [ + "n0 = 81.0\nn1 = 25.0\nn2 = 20.0\nt0 = n0 / 3.0\nt1 = 100.0 - n2\nt2 = n0 + t0\nt3 = t2 * t1\nt4 = t3 / 100.0\nanswer = t4 - n0\nprint(answer)" + ], + "Output Answer": [ + "5.400000000000006" + ], + "split": "train" + }, + { + "Input": "the wages earned by robin is 30 % more than that earned by erica . the wages earned by charles is 70 % more than that earned by erica . how much percent is the wages earned by charles more than that earned by robin ?", + "Output Program": [ + "n0 = 30.0\nn1 = 70.0\nt0 = n1 + 100.0\nt1 = n0 + 100.0\nt2 = t0 - t1\nt3 = t2 / t1\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "30.76923076923077" + ], + "split": "train" + }, + { + "Input": "two brothers ram and ravi appeared for an exam . the probability of selection of ram is 3 / 7 and that of ravi is 1 / 5 . find the probability that both of them are selected .", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 1.0\nn3 = 5.0\nt0 = n0 / n1\nt1 = n2 / n3\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "0.08571428571428572" + ], + "split": "train" + }, + { + "Input": "two trains start at same time from two stations and proceed towards each other at the rate of 20 km / hr and 25 km / hr respectively . when they meet , it is found that one train has traveled 60 km more than the other . what is the distance between the two stations ?", + "Output Program": [ + "n0 = 20.0\nn1 = 25.0\nn2 = 60.0\nt0 = n0 + n1\nt1 = n1 - n0\nt2 = n2 / t1\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "540" + ], + "split": "train" + }, + { + "Input": "the average of 7 consecutive numbers is 20 . the largest of these numbers is", + "Output Program": [ + "n0 = 7.0\nn1 = 20.0\nt0 = 1.0 + 2.0\nt1 = n0 * n1\nt2 = t0 + 1.0\nt3 = t2 + 1.0\nt4 = t3 + 1.0\nt5 = t4 + 1.0\nt6 = t5 + 1.0\nt7 = t6 + 1.0\nt8 = t7 + 1.0\nt9 = t8 + 1.0\nt10 = t8 + t9\nt11 = t1 - t10\nt12 = t11 / n0\nanswer = t4 + t12\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "if q and t are positive integers , qt + q + t can not be", + "Output Program": [ + "t0 = 1.0 + 2.0\nt1 = 1.0 * 2.0\nt2 = t0 + t1\nanswer = t2 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "total dinning bill for 9 people was $ 211.00 . if they add 15 % tip and divided the bill evenly , approximate . what was each persons find share", + "Output Program": [ + "n0 = 9.0\nn1 = 211.0\nn2 = 15.0\nt0 = n1 * n2\nt1 = t0 / 100.0\nt2 = n1 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "26.961111111111112" + ], + "split": "train" + }, + { + "Input": "a small company is planning to rent either computer a or computer b to print customer mailing lists . both computer a and computer b must be rented on an hourly basis . the rental fee is based only on the amount of time the computer is turned on . it will cost 40 percent more per hour to rent computer a than to rent computer b . computer b would , however , require 20 hours more than computer a to do the job . if either computer a , or computer b were rented the total cost to rent the computer would be $ 550.00 . what would be the approximate hourly charge to rent computer b ?", + "Output Program": [ + "n0 = 40.0\nn1 = 20.0\nn2 = 550.0\nt0 = 3.0 + 4.0\nt1 = n0 / 100.0\nt2 = n1 / 4.0\nt3 = t2 / 100.0\nt4 = t1 + t3\nt5 = t0 + t4\nanswer = t5 + t1\nprint(answer)" + ], + "Output Answer": [ + "7.8500000000000005" + ], + "split": "train" + }, + { + "Input": "if 4 / p = 8 & 4 / q = 18 then p - q = ?", + "Output Program": [ + "n0 = 4.0\nn1 = 8.0\nn2 = 4.0\nn3 = 18.0\nt0 = n0 / n1\nt1 = n0 / n3\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "0.2777777777777778" + ], + "split": "train" + }, + { + "Input": "a certain drink of type a is prepared by mixing 4 parts milk with 3 parts fruit juice . another drink of type b is prepared by mixing 4 parts of fruit juice and 3 parts of milk . how many liters of fruit juice must be added to 21 liters of drink a to convert it to drink b ?", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 4.0\nn3 = 3.0\nn4 = 21.0\nt0 = n0 + n1\nt1 = n0 / t0\nt2 = n1 / t0\nt3 = n4 * t1\nt4 = n4 * t2\nt5 = n0 * t3\nt6 = t5 / n1\nanswer = t6 - t4\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "the smallest 6 digit number exactly divisible by 111 is ?", + "Output Program": [ + "n0 = 6.0\nn1 = 111.0\nt0 = 100.0 * 1000.0\nt1 = t0 % n1\nt2 = n1 - t1\nanswer = t0 + t2\nprint(answer)" + ], + "Output Answer": [ + "100011" + ], + "split": "train" + }, + { + "Input": "having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.75 at the candy store . what is john \u2019 s weekly allowance ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 0.75\nt0 = n0 / n1\nt1 = 1.0 / 3.0\nt2 = 1.0 - t0\nt3 = t1 * t2\nt4 = t0 + t3\nt5 = 1.0 - t4\nanswer = n2 / t5\nprint(answer)" + ], + "Output Answer": [ + "2.8124999999999996" + ], + "split": "train" + }, + { + "Input": "david obtained 76 , 65 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?", + "Output Program": [ + "n0 = 76.0\nn1 = 65.0\nn2 = 82.0\nn3 = 67.0\nn4 = 85.0\nn5 = 100.0\nt0 = n0 + n1\nt1 = 2.0 + 3.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "dick and jane each saved $ 2,000 in 1989 . in 1990 dick saved 10 percent more than in 1989 , and together he and jane saved a total of $ 4,000 . approximately what percent less did jane save in 1990 than in 1989 ?", + "Output Program": [ + "n0 = 2000.0\nn1 = 1989.0\nn2 = 1990.0\nn3 = 10.0\nn4 = 1989.0\nn5 = 4000.0\nn6 = 1990.0\nn7 = 1989.0\nt0 = n3 / 100.0\nt1 = t0 + 1.0\nt2 = 2.0 - t1\nt3 = 1.0 - t2\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "10.000000000000009" + ], + "split": "train" + }, + { + "Input": "tough and tricky questions : exponents . if 7 ^ ( 3 x - 1 ) * 3 ^ ( 4 y - 3 ) = 49 ^ x * 27 ^ y , then x + y =", + "Output Program": [ + "n0 = 7.0\nn1 = 3.0\nn2 = 1.0\nn3 = 3.0\nn4 = 4.0\nn5 = 3.0\nn6 = 49.0\nn7 = 27.0\n\nanswer = n1 + n2\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "the average of runs of a cricket player of 10 innings was 18 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?", + "Output Program": [ + "n0 = 10.0\nn1 = 18.0\nn2 = 4.0\nt0 = n0 + 1.0\nt1 = n1 + n2\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "62" + ], + "split": "train" + }, + { + "Input": "if a = 105 and a ^ 3 = 21 * 25 * 15 * b , what is the value of b ?", + "Output Program": [ + "n0 = 105.0\nn1 = 3.0\nn2 = 21.0\nn3 = 25.0\nn4 = 15.0\nt0 = n2 * n3\nt1 = n0**min(n1, 5)\nt2 = n4 * t0\nanswer = t1 / t2\nprint(answer)" + ], + "Output Answer": [ + "147" + ], + "split": "train" + }, + { + "Input": "what is the range of all the roots of | x ^ 2 - 1 | = x ?", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 1.0\n\nanswer = math.sqrt(max(0, n1))\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "how many integers between 0 and 1000 do not contain the integer 1", + "Output Program": [ + "n0 = 0.0\nn1 = 1000.0\nn2 = 1.0\nt0 = 3.0 + 4.0\nt1 = 100.0 * 2.0\nt2 = t0 * 10.0\nt3 = t1 + t2\nt4 = t3 + 2.0\nanswer = n1 - t4\nprint(answer)" + ], + "Output Answer": [ + "728" + ], + "split": "train" + }, + { + "Input": "working simultaneously and independently at an identical constant rate , 4 machines of a certain type can produce a total of x units of product p in 6 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 3 x units of product p in 6 days ?", + "Output Program": [ + "n0 = 4.0\nn1 = 6.0\nn2 = 3.0\nn3 = 6.0\nt0 = n1 / n3\nt1 = n0 * n2\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "a batsman in his 12 th innings makes a score of 65 and thereby increases his average by 2 runs . what is his average after the 12 th innings if he had never been \u2018 not out \u2019 ?", + "Output Program": [ + "n0 = 12.0\nn1 = 65.0\nn2 = 2.0\nn3 = 12.0\nt0 = n0 * n2\nt1 = n1 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "43" + ], + "split": "train" + }, + { + "Input": "if the number is decreased by 5 and divided by 7 the result is 7 . what would be the result if 14 is subtracted and divided by 10 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 7.0\nn2 = 7.0\nn3 = 14.0\nn4 = 10.0\nt0 = n1 * n1\nt1 = n0 + t0\nt2 = t1 - n3\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "if w / x = 1 / 3 and w / y = 2 / 3 , then ( x + y ) / y =", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 2.0\nn3 = 3.0\nt0 = n2 / n0\nt1 = n3 / n1\nt2 = t0 / t1\nanswer = t2 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "farm tax is levied on the 60 % of the cultivated land . the tax department collected total $ 4000 through the farm tax from the village of mr . willam . mr . willam paid only $ 500 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :", + "Output Program": [ + "n0 = 60.0\nn1 = 4000.0\nn2 = 500.0\nt0 = n2 / n1\nt1 = t0 * 100.0\nt2 = t1 * 100.0\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "20.833333333333332" + ], + "split": "train" + }, + { + "Input": "the avg weight of a , b & c is 60 kg . if d joins the group , the avg weight of the group becomes 65 kg . if another man e who weights is 3 kg more than d replaces a , then the avgof b , c , d & e becomes 64 kg . what is the weight of a ?", + "Output Program": [ + "n0 = 60.0\nn1 = 65.0\nn2 = 3.0\nn3 = 64.0\nt0 = n1 * 4.0\nt1 = n3 * 4.0\nt2 = n0 * n2\nt3 = t0 - t2\nt4 = n2 + t3\nt5 = t1 - t4\nanswer = t0 - t5\nprint(answer)" + ], + "Output Answer": [ + "87" + ], + "split": "train" + }, + { + "Input": "a car travels uphill at 30 km / hr and downhill at 80 km / hr . it goes 100 km uphill and 50 km downhill . find the average speed of the car ?", + "Output Program": [ + "n0 = 30.0\nn1 = 80.0\nn2 = 100.0\nn3 = 50.0\nt0 = n2 + n3\nt1 = n2 / n0\nt2 = n3 / n1\nt3 = t1 + t2\nanswer = t0 / t3\nprint(answer)" + ], + "Output Answer": [ + "37.89473684210526" + ], + "split": "train" + }, + { + "Input": "if 15 machine can finish a job in 36 days , then how many more machines would be needed to finish the job in one - fourth less time ?", + "Output Program": [ + "n0 = 15.0\nn1 = 36.0\nt0 = 3.0 / 4.0\nt1 = n0 * n1\nt2 = n1 * t0\nt3 = t1 / t2\nanswer = t3 - n0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "if a randomly selected non - negative single digit integer is added to { 2 , 3 , 6 , 8 } . what is the probability that the median of the set will increase but the range still remains the same ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 6.0\nn3 = 8.0\n\nanswer = 4.0 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "0.4" + ], + "split": "train" + }, + { + "Input": "if a # b = ab \u2013 b + b ^ 2 , then 2 # 3 =", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 3.0\nt0 = n1 * n2\nt1 = n2**min(n0, 5)\nt2 = t0 - n2\nanswer = t1 + t2\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "andy solves problems 70 to 125 inclusive in a math exercise . how many problems does he solve ?", + "Output Program": [ + "n0 = 70.0\nn1 = 125.0\nt0 = n1 - n0\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "train" + }, + { + "Input": "if k is a non - negative integer and 21 ^ k is a divisor of 435,961 then 7 ^ k - k ^ 7 =", + "Output Program": [ + "n0 = 21.0\nn1 = 435961.0\nn2 = 7.0\nn3 = 7.0\nt0 = 1.0 - 1.0\nt1 = n2**min(t0, 5)\nt2 = t0**min(n2, 5)\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "the average weight of 10 person ' s increases by 4 kg when a new person comes in place of one of them weighing 70 kg . what is the weight of the new person ?", + "Output Program": [ + "n0 = 10.0\nn1 = 4.0\nn2 = 70.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "110" + ], + "split": "train" + }, + { + "Input": "the average of 4 consecutive odd numbers is 24 . find the largest number", + "Output Program": [ + "n0 = 4.0\nn1 = 24.0\nt0 = n0 * n1\nt1 = t0 / n0\nanswer = t1 + 3.0\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "train" + }, + { + "Input": "in 1996 , the property tax of a community is increased by 6 % over the 1995 tax . an additional surcharge of $ 200 is also added for a special project . if the petersons ' 1996 tax totals $ 2108 , find their property tax for the year 1995", + "Output Program": [ + "n0 = 1996.0\nn1 = 6.0\nn2 = 1995.0\nn3 = 200.0\nn4 = 1996.0\nn5 = 2108.0\nn6 = 1995.0\nt0 = n1 / 100.0\nt1 = n5 - n3\nt2 = t0 + 1.0\nanswer = t1 / t2\nprint(answer)" + ], + "Output Answer": [ + "1800" + ], + "split": "train" + }, + { + "Input": "in an election , candidate douglas won 64 percent of the total vote in counties x and y . he won 76 percent of the vote in county x . if the ratio of people who voted in county x to county y is 2 : 1 , what percent of the vote did candidate douglas win in county y ?", + "Output Program": [ + "n0 = 64.0\nn1 = 76.0\nn2 = 2.0\nn3 = 1.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = n2 / 3.0\nt3 = n3 / 3.0\nt4 = t1 * t2\nt5 = t0 - t4\nt6 = t5 / t3\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "40.00000000000002" + ], + "split": "train" + }, + { + "Input": "16 * 16 * 16 * 16 * 16 = 4 ^ ?", + "Output Program": [ + "n0 = 16.0\nn1 = 16.0\nn2 = 16.0\nn3 = 16.0\nn4 = 16.0\nn5 = 4.0\n\nanswer = max(n5,10.0)\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "when average age of 25 members are 0 , how many members greater than 0 ?", + "Output Program": [ + "n0 = 25.0\nn1 = 0.0\nn2 = 0.0\n\nanswer = n0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "2500 - ( 1002 / 20.04 ) = ?", + "Output Program": [ + "n0 = 2500.0\nn1 = 1002.0\nn2 = 20.04\nt0 = n1 / n2\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "2450" + ], + "split": "train" + }, + { + "Input": "solomon taken a loan rs . 15000 / - from co - operative society with an interest @ 11.5 % per month . at the same time he deposited rs . 10000 / - as fixed deposit with an interest @ 9.5 % per month . after one week sam asked the manager to calculate the interest to be paid . what is the interest amount for 7 days ?", + "Output Program": [ + "n0 = 15000.0\nn1 = 11.5\nn2 = 10000.0\nn3 = 9.5\nn4 = 7.0\nt0 = n0 * n1\nt1 = 10.0 * 3.0\nt2 = n2 * n3\nt3 = t0 / 100.0\nt4 = t2 / 100.0\nt5 = t3 / t1\nt6 = t4 / t1\nt7 = n4 * t5\nt8 = n4 * t6\nanswer = t7 - t8\nprint(answer)" + ], + "Output Answer": [ + "180.83333333333331" + ], + "split": "train" + }, + { + "Input": "a jogger running at 9 km / hr along side a railway track is 190 m ahead of the engine of a 120 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?", + "Output Program": [ + "n0 = 9.0\nn1 = 190.0\nn2 = 120.0\nn3 = 45.0\nt0 = n1 + n2\nt1 = 10.0 / 2.0\nt2 = n3 - n0\nt3 = t2 / 2.0\nt4 = t1 / t3\nt5 = t4 * t2\nanswer = t0 / t5\nprint(answer)" + ], + "Output Answer": [ + "31" + ], + "split": "train" + }, + { + "Input": "a business executive and his client are charging their dinner tab on the executive ' s expense account . the company will only allow them to spend a total of 75 $ for the meal . assuming that they will pay 7 % in sales tax for the meal and leave a 15 % tip , what is the most their food can cost ?", + "Output Program": [ + "n0 = 75.0\nn1 = 7.0\nn2 = 15.0\nt0 = n1 + n2\nt1 = t0 / 100.0\nt2 = t1 + 1.0\nanswer = n0 / t2\nprint(answer)" + ], + "Output Answer": [ + "61.47540983606557" + ], + "split": "train" + }, + { + "Input": "the average of 11 numbers is 50 . out of 11 numbers the average of first 6 no . is 58 , and last 6 numbers is 65 then find 6 th number ?", + "Output Program": [ + "n0 = 11.0\nn1 = 50.0\nn2 = 11.0\nn3 = 6.0\nn4 = 58.0\nn5 = 6.0\nn6 = 65.0\nn7 = 6.0\nt0 = n3 * n4\nt1 = n3 * n6\nt2 = n0 * n1\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "188" + ], + "split": "train" + }, + { + "Input": "a special municipal payroll tax charges not tax on a payroll less than $ 200000 and only 0.2 % on a company \u2019 s payroll above $ 200000 . if belfried industries paid $ 200 in this special municipal payroll tax , then they must have had a payroll of ?", + "Output Program": [ + "n0 = 200000.0\nn1 = 0.2\nn2 = 200000.0\nn3 = 200.0\nt0 = n1 / 100.0\nt1 = n3 / t0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "300000" + ], + "split": "train" + }, + { + "Input": "find large number from below question the difference of two numbers is 1200 . on dividing the larger number by the smaller , we get 5 as quotient and the 4 as remainder", + "Output Program": [ + "n0 = 1200.0\nn1 = 5.0\nn2 = 4.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nt2 = t0 / t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "1495" + ], + "split": "train" + }, + { + "Input": "in a recent election , james received 0.5 percent of the 2000 votes cast . to win the election , a candidate needed to receive more than 50 percent of the vote . how many additional votes would james have needed to win the election ?", + "Output Program": [ + "n0 = 0.5\nn1 = 2000.0\nn2 = 50.0\nt0 = n2 - n0\nt1 = t0 / 100.0\nt2 = n1 * t1\nanswer = t2 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "991" + ], + "split": "train" + }, + { + "Input": "if x / ( 11 p ) is an even prime number , where x is a positive integer and p is a prime number , what is the least value of x ?", + "Output Program": [ + "n0 = 11.0\nt0 = n0 * 2.0\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "44" + ], + "split": "train" + }, + { + "Input": "list i : { y , 2 , 4 , 7 , 10 , 11 } list ii : { 3 , 3 , 4 , 6 , 7 , 10 } if the median r of list i is equal to the sum of the median of list ii and the mode of list ii , then y equals", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 7.0\nn3 = 10.0\nn4 = 11.0\nn5 = 3.0\nn6 = 3.0\nn7 = 4.0\nn8 = 6.0\nn9 = 7.0\nn10 = 10.0\nt0 = n1 + n8\nt1 = t0 / n0\nt2 = n5 + t1\nt3 = n0 * t2\nanswer = t3 - n2\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "a computer manufacturer produces a certain electronic component at a cost of $ 80 per component . shipping costs for delivering the components are $ 4 per unit . further , the manufacturer has costs of $ 16,500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 150 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?", + "Output Program": [ + "n0 = 80.0\nn1 = 4.0\nn2 = 16500.0\nn3 = 150.0\nt0 = n0 + n1\nt1 = 4.0 * 4.0\nt2 = n1 * 100.0\nt3 = t1 * 1000.0\nt4 = n3 * t0\nt5 = t3 + t2\nt6 = t5 + t4\nanswer = t6 / n3\nprint(answer)" + ], + "Output Answer": [ + "193.33333333333334" + ], + "split": "train" + }, + { + "Input": "how many gallons of milk that is 10 percent butter - fat must be added to 8 gallons of milk that is 35 percent butterfat to obtain milk that is 20 percent butterfat ?", + "Output Program": [ + "n0 = 10.0\nn1 = 8.0\nn2 = 35.0\nn3 = 20.0\nt0 = n2 - n3\nt1 = n1 * t0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "a students was asked to find the arithmetic mean of the numbers 3 , 11 , 7 , 9 , 15 , 13 , 8 , 19 , 17 , 21 , 14 and x . he found the mean to be 12 . what should be the number in place of x ?", + "Output Program": [ + "n0 = 3.0\nn1 = 11.0\nn2 = 7.0\nn3 = 9.0\nn4 = 15.0\nn5 = 13.0\nn6 = 8.0\nn7 = 19.0\nn8 = 17.0\nn9 = 21.0\nn10 = 14.0\nn11 = 12.0\nt0 = n0 + n1\nt1 = n11 * n11\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nt5 = n5 + t4\nt6 = n6 + t5\nt7 = n7 + t6\nt8 = n8 + t7\nt9 = n9 + t8\nt10 = n10 + t9\nanswer = t1 - t10\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "the manager at a health foods store mixes a unique superfruit juice cocktail that costs $ 1399.45 per litre to make . the cocktail includes mixed fruit juice and a \u00e7 ai berry juice , which cost $ 262.85 per litre and $ 3104.35 per litre , respectively . the manager has already opened 36 litres of the mixed fruit juice . how many litres of the a \u00e7 ai berry juice does he need to add ?", + "Output Program": [ + "n0 = 1399.45\nn1 = 262.85\nn2 = 3104.35\nn3 = 36.0\nt0 = n0 * n3\nt1 = n1 * n3\nt2 = n2 - n0\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "24.000000000000007" + ], + "split": "train" + }, + { + "Input": "the cost to park a car in a certain parking garage is $ 15.00 for up to 2 hours of parking and $ 1.75 for each hour in excess of 2 hours . what is the average ( arithmetic mean ) cost per hour to park a car in the parking garage for 9 hours ?", + "Output Program": [ + "n0 = 15.0\nn1 = 2.0\nn2 = 1.75\nn3 = 2.0\nn4 = 9.0\nt0 = n4 - n1\nt1 = n2 * t0\nt2 = n0 + t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "3.0277777777777777" + ], + "split": "train" + }, + { + "Input": "the contents of a certain box consist of 14 apples and 12 oranges . how many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples ?", + "Output Program": [ + "n0 = 14.0\nn1 = 12.0\nn2 = 70.0\nt0 = n0 + n1\nt1 = n2 / 100.0\nt2 = n0 / t1\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "he total marks obtained by a student in physics , chemistry and mathematics is 110 more than the marks obtained by him in physics . what is the average mark obtained by him in chemistry and mathematics ?", + "Output Program": [ + "n0 = 110.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "55" + ], + "split": "train" + }, + { + "Input": "last year , for every 100 million vehicles that traveled on a certain highway , 80 vehicles were involved in accidents . if 4 billion vehicles traveled on the highway last year , how many of those vehicles were involved in accidents ? ( 1 billion = 1,000 , 000,000 )", + "Output Program": [ + "n0 = 100.0\nn1 = 80.0\nn2 = 4.0\nn3 = 1.0\nn4 = 1000.0\nn5 = 0.0\nt0 = n2 * 10.0\nanswer = n1 * t0\nprint(answer)" + ], + "Output Answer": [ + "3200" + ], + "split": "train" + }, + { + "Input": "on sunday , bill ran 4 more miles than he ran on saturday . julia did not run on saturday , but she ran twice the number of miles on sunday that bill ran on sunday . if bill and julia ran a total of 20 miles on saturday and sunday , how many miles did bill run on sunday ?", + "Output Program": [ + "n0 = 4.0\nn1 = 20.0\nt0 = n0 * 2.0\nt1 = n0 + t0\nt2 = n1 - t1\nt3 = t2 / n0\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "log root ( 8 ) / log 8 is equal to", + "Output Program": [ + "n0 = 8.0\nn1 = 8.0\nt0 = n0 / 4.0\nanswer = 1.0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "one - third less than 40 % of 180 is equal to :", + "Output Program": [ + "n0 = 40.0\nn1 = 180.0\nt0 = n0 / 100.0\nt1 = 1.0 / 3.0\nt2 = n1 * t0\nt3 = t1 * t2\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "when positive integer x is divided by 9 , the quotient is y and the remainder is 4 . when 2 x is divided by 7 , the quotient is 2 y and the remainder is 1 . what is the value of 5 y \u2013 x ?", + "Output Program": [ + "n0 = 9.0\nn1 = 4.0\nn2 = 2.0\nn3 = 7.0\nn4 = 2.0\nn5 = 1.0\nn6 = 5.0\nt0 = n1 * n2\nt1 = n3 * n4\nt2 = n0 * n2\nt3 = t0 - n5\nt4 = t1 - t2\nt5 = t3 / t4\nt6 = n6 * t5\nt7 = n0 * t5\nt8 = n1 + t7\nanswer = t6 - t8\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "a school has 4 maths 3 physics and 3 chemistry teachers each teacher can teach 2 subjects max what is he minimum number of teachers required", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 3.0\nn3 = 2.0\nt0 = n0 + n1\nt1 = n2 + t0\nanswer = t1 / n3\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "the tax on a commodity is diminished by 35 % but its consumption is increased by 15 % . find the decrease percent in the revenue derived from it ?", + "Output Program": [ + "n0 = 35.0\nn1 = 15.0\nt0 = n1 + 100.0\nt1 = 100.0 - n0\nt2 = t0 * t1\nt3 = t2 / 100.0\nanswer = 100.0 - t3\nprint(answer)" + ], + "Output Answer": [ + "25.25" + ], + "split": "train" + }, + { + "Input": "a university cafeteria offers 4 flavors of pizza - pepperoni , chicken , hawaiian and vegetarian . if a customer has an option ( but not the obligation ) to add extra cheese , mushrooms or both to any kind of pizza , how many different pizza varieties are available ?", + "Output Program": [ + "n0 = 4.0\n\nanswer = n0 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "the total age of a and b is 15 years more than the total age of b and c . c is how many year younger than a", + "Output Program": [ + "n0 = 15.0\n\nanswer = n0 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "306 \u00e3 \u00b7 ? \u00e3 \u2014 15 + 270 = 405", + "Output Program": [ + "n0 = 306.0\nn1 = 15.0\nn2 = 270.0\nn3 = 405.0\nt0 = n3 - n2\nt1 = n1 + t0\nt2 = t1 * 2.0\nt3 = t2 / 10.0\nt4 = t3 / 10.0\nt5 = t3 + t4\nanswer = t5 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "34" + ], + "split": "train" + }, + { + "Input": "what is the median of a set of consecutive integers if the sum of nth number from the beginning and nth number from the end is 120 ?", + "Output Program": [ + "n0 = 120.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "a student got twice as many sums wrong as he got right . if he attempted 48 sums in all , how many did he solve correctly ?", + "Output Program": [ + "n0 = 48.0\nt0 = 1.0 + 2.0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "reeya obtained 50 , 60 , 70 , 80 and 80 out of 100 in different subjects , what will be the average", + "Output Program": [ + "n0 = 50.0\nn1 = 60.0\nn2 = 70.0\nn3 = 80.0\nn4 = 80.0\nn5 = 100.0\nt0 = n0 + n1\nt1 = 1.0 + 4.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "68" + ], + "split": "train" + }, + { + "Input": "5 goats \u2019 s and 10 hens are brought for rs . 2500 . if the average price of a hen be rs . 50 . what is the average price of a goat .", + "Output Program": [ + "n0 = 5.0\nn1 = 10.0\nn2 = 2500.0\nn3 = 50.0\nt0 = n1 * n3\nt1 = n2 - t0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "train" + }, + { + "Input": "if m is a positive integer and m ^ 2 is divisible by 39 , then the largest positive integer that must divide m is ?", + "Output Program": [ + "n0 = 2.0\nn1 = 39.0\nt0 = n1 / 3.0\nt1 = t0 / 3.0\nanswer = t1 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "for any integer k greater than 1 , the symbol k * denotes the product of all integers between 1 and k , inclusive . if k * is a multiple of 315 what is the least possible value of k ?", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 315.0\nt0 = 1.0 + 4.0\nt1 = n2 / 3.0\nt2 = t1 / 3.0\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "find the value of a from ( 15 ) ^ 2 x 8 ^ 3 \u00e3 \u00b7 256 = a .", + "Output Program": [ + "n0 = 15.0\nn1 = 2.0\nn2 = 8.0\nn3 = 3.0\nn4 = 256.0\nt0 = n0**min(n1, 5)\nt1 = n2**min(n3, 5)\nt2 = t0 * t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "450" + ], + "split": "train" + }, + { + "Input": "the sum of two prime numbers is 85 . what is the product of these two prime numbers ?", + "Output Program": [ + "n0 = 85.0\nt0 = n0 - 2.0\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "166" + ], + "split": "train" + }, + { + "Input": "6 ! / ( 6 - 3 ) ! = ?", + "Output Program": [ + "import math\nn0 = 6.0\nn1 = 6.0\nn2 = 3.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = n0 - n2\nt2 = math.factorial(min(15, int(t1)))\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "if 22 percent of the students at a certain school went to a camping trip and took more than $ 100 , and 75 percent of the students who went to the camping trip did not take more than $ 100 , what percentage of the students at the school went to the camping trip ?", + "Output Program": [ + "n0 = 22.0\nn1 = 100.0\nn2 = 75.0\nn3 = 100.0\nt0 = n1 - n2\nt1 = t0 / n1\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "88" + ], + "split": "train" + }, + { + "Input": "if a : b : c = 3 : 4 : 7 , then the ratio ( a + b + c ) : c is equal to", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 7.0\nt0 = n0 + n1\nt1 = n2 + t0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a certain library assesses fines for overdue books as follows . on the first day that a book is overdue , the total fine is $ 0.05 . for each additional day that the book is overdue , the total fine is either increased by $ 0.30 or doubled , whichever results in the lesser amount . what is the total for a book on the fifth day it is overdue ?", + "Output Program": [ + "n0 = 0.05\nn1 = 0.3\nt0 = n0 * 2.0\nt1 = t0 * 2.0\nt2 = t1 * 2.0\nanswer = n1 + t2\nprint(answer)" + ], + "Output Answer": [ + "0.7" + ], + "split": "train" + }, + { + "Input": "linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 230 , what were her original savings ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 230.0\nt0 = n0 / n1\nt1 = 1.0 - t0\nanswer = n2 / t1\nprint(answer)" + ], + "Output Answer": [ + "920" + ], + "split": "train" + }, + { + "Input": "45 x ? = 10 % of 900", + "Output Program": [ + "n0 = 45.0\nn1 = 10.0\nn2 = 900.0\nt0 = n1 / 100.0\nt1 = n2 * t0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a circular road runs around a circular garden . if the sum of the circumferences of the inner and outer circles is 88 metres and the radius of the inner circle is one - third of the outer circle , then the width of the road is :", + "Output Program": [ + "n0 = 88.0\nt0 = n0 / 4.0\nt1 = t0 / 2.0\nanswer = t1 - 4.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "8 is 6 % of a , and 6 is 8 % of b . c equals b / a . what is the value of c ?", + "Output Program": [ + "n0 = 8.0\nn1 = 6.0\nn2 = 6.0\nn3 = 8.0\nt0 = n1 / n0\nt1 = n0 / n1\nt2 = t0 * 100.0\nt3 = t1 * 100.0\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.5625000000000001" + ], + "split": "train" + }, + { + "Input": "exactly 3 / 8 of the people in the room are under the age of 21 , and exactly 5 / 12 of the people in the room are over the age of 65 . if the total number of the people in the room is greater than 50 and less than 100 , how many people in the room are under the age of 21 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 8.0\nn2 = 21.0\nn3 = 5.0\nn4 = 12.0\nn5 = 65.0\nn6 = 50.0\nn7 = 100.0\nn8 = 21.0\nt0 = n1 * n4\nt1 = n0 * t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "we have boxes colored either red or blue . in each blue box there is a fixed number of blueberries . in each red box there is a fixed number of strawberries . if we dispose of one blue box for one additional red box , the total number of berries would increase by 10 , and the difference between the total number of strawberries and the total number of blueberries would increase by 50 . each blue box contains how many blueberries ?", + "Output Program": [ + "n0 = 10.0\nn1 = 50.0\nt0 = n1 - n0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "if x / y = 3 and ( 2 a - x ) / ( 3 b - y ) = 3 , then the value of a / b is ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 3.0\nn3 = 3.0\nt0 = 3.0 * 3.0\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "4.5" + ], + "split": "train" + }, + { + "Input": "if an average hard drive had a capacity of 0.3 tb in 2000 , and average hard drive capacities double every 5 years , what will be the average hard drive capacity in 2050 ?", + "Output Program": [ + "n0 = 0.3\nn1 = 2000.0\nn2 = 5.0\nn3 = 2050.0\nt0 = n0 * 2.0\nt1 = t0 * 2.0\nt2 = t1 * 2.0\nt3 = t2 * 2.0\nt4 = t3 * 2.0\nt5 = t4 * 2.0\nt6 = t5 * 2.0\nt7 = t6 * 2.0\nt8 = t7 * 2.0\nt9 = t8 * 2.0\nt10 = n0 + t9\nanswer = t10 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "3075" + ], + "split": "train" + }, + { + "Input": "if grapes are 93 % water and raisins are 16 % water , then how many kilograms did a quantity of raisins , which currently weighs 8 kilograms , weigh when all the raisins were grapes ? ( assume that the only difference between their raisin - weight and their grape - weight is water that evaporated during their transformation . )", + "Output Program": [ + "n0 = 93.0\nn1 = 16.0\nn2 = 8.0\nt0 = 100.0 - n1\nt1 = 100.0 - n0\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = n2 * t2\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "95.99999999999999" + ], + "split": "train" + }, + { + "Input": "in the rectangular coordinate system , what is the x - intercept of a line passing through ( 10 , 3 ) and ( \u2212 2 , \u2212 3 ) ?", + "Output Program": [ + "n0 = 10.0\nn1 = 3.0\nn2 = 2.0\nn3 = 3.0\nt0 = -n3\nt1 = -n2\nt2 = t0 - n1\nt3 = t1 - n0\nt4 = t2 / t3\nt5 = n0 * t4\nt6 = t5 - n1\nanswer = t6 / t4\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "the sum of the first 50 positive even integers is 2550 . what is the sum of the even integers from 402 to 500 inclusive ?", + "Output Program": [ + "n0 = 50.0\nn1 = 2550.0\nn2 = 402.0\nn3 = 500.0\nt0 = n2 + n3\nt1 = n3 - n2\nt2 = t1 / 2.0\nt3 = t0 / 2.0\nt4 = t2 + 1.0\nanswer = t4 * t3\nprint(answer)" + ], + "Output Answer": [ + "22550" + ], + "split": "train" + }, + { + "Input": "we run a business that rents out canoes and kayaks . a canoe rental costs $ 9 per day , and a kayak rental costs $ 12 dollars per day . one day , our business rents out 4 canoes for every 3 kayaks and receives a total of $ 432 in revenue . how many more canoes than kayaks were rented out ?", + "Output Program": [ + "n0 = 9.0\nn1 = 12.0\nn2 = 4.0\nn3 = 3.0\nn4 = 432.0\nt0 = n0 * n2\nt1 = n1 * n3\nt2 = n2 - n3\nt3 = t0 + t1\nt4 = n4 / t3\nanswer = t4 * t2\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "the average weight of 7 person ' s increases by 3.5 kg when a new person comes in place of one of them weighing 75 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 7.0\nn1 = 3.5\nn2 = 75.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "99.5" + ], + "split": "train" + }, + { + "Input": "what least number must be subtracted from 427398 so that remaining no . is divisible by 10", + "Output Program": [ + "import math\nn0 = 427398.0\nn1 = 10.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "the average age of applicants for a new job is 10 , with a standard deviation of 8 . the hiring manager is only willing to accept applicants whose age is within one standard deviation of the average age . assuming that all applicants ' ages are integers and that the endpoints of the range are included , what is the maximum number of different ages of the applicants ?", + "Output Program": [ + "n0 = 10.0\nn1 = 8.0\nt0 = n0 + n1\nt1 = n0 - n1\nt2 = t0 - t1\nanswer = t2 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "a certain clock marks every hour by striking a number of times equal to the hour , and the time required for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stroke and the end of the last stroke is 44 seconds . at 12 : 00 , how many seconds elapse between the beginning of the first stroke and the end of the last stroke ?", + "Output Program": [ + "n0 = 6.0\nn1 = 0.0\nn2 = 44.0\nn3 = 12.0\nn4 = 0.0\nt0 = 1.0 + 4.0\nt1 = n0 + t0\nt2 = n3 + t1\nt3 = n2 / t1\nanswer = t2 * t3\nprint(answer)" + ], + "Output Answer": [ + "92" + ], + "split": "train" + }, + { + "Input": "each week , harry is paid x dollars per hour for the first 21 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 41 hours if harry and james were paid the same amount last week , how many hours did harry work last week ?", + "Output Program": [ + "n0 = 21.0\nn1 = 1.5\nn2 = 40.0\nn3 = 2.0\nn4 = 41.0\nt0 = n2 + n3\nt1 = t0 - n0\nt2 = t1 / n1\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "if 2 x + y = 26 and x + 2 y = 10 , then ( x + y ) / 3 =", + "Output Program": [ + "n0 = 2.0\nn1 = 26.0\nn2 = 2.0\nn3 = 10.0\nn4 = 3.0\nt0 = n0 * n1\nt1 = n0 * n0\nt2 = t0 - n3\nt3 = t1 - 1.0\nt4 = t2 / t3\nt5 = n0 * t4\nt6 = n1 - t5\nt7 = t4 + t6\nanswer = t7 / n4\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 1015 . find the cost of each ice - cream cup ?", + "Output Program": [ + "n0 = 16.0\nn1 = 5.0\nn2 = 7.0\nn3 = 6.0\nn4 = 6.0\nn5 = 45.0\nn6 = 70.0\nn7 = 1015.0\nt0 = n0 * n3\nt1 = n1 * n5\nt2 = n2 * n6\nt3 = n7 - t0\nt4 = t3 - t1\nt5 = t4 - t2\nanswer = t5 / n3\nprint(answer)" + ], + "Output Answer": [ + "34" + ], + "split": "train" + }, + { + "Input": "a , b , c subscribe rs . 50000 for a business , a subscribes rs . 4000 more than b and b rs . 5000 more thanc . out of a total profit of rs . 35000 , a receives :", + "Output Program": [ + "n0 = 50000.0\nn1 = 4000.0\nn2 = 5000.0\nn3 = 35000.0\nt0 = n1 + n2\nt1 = n2 + t0\nt2 = n0 - t1\nt3 = t2 / 3.0\nt4 = t0 + t3\nt5 = t4 / n0\nanswer = n3 * t5\nprint(answer)" + ], + "Output Answer": [ + "14700" + ], + "split": "train" + }, + { + "Input": "linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 300 , what were her original savings ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 300.0\nt0 = n0 / n1\nt1 = 1.0 - t0\nanswer = n2 / t1\nprint(answer)" + ], + "Output Answer": [ + "1200" + ], + "split": "train" + }, + { + "Input": "8 people decided to split the restaurant bill evenly . if the bill was $ 214.18 dollars , how much money did they 1 cent is the smallest unit ?", + "Output Program": [ + "n0 = 8.0\nn1 = 214.18\nn2 = 1.0\nt0 = 3.0 / 100.0\nanswer = n1 + t0\nprint(answer)" + ], + "Output Answer": [ + "214.21" + ], + "split": "train" + }, + { + "Input": "in an examination , 25 % of total students failed in hindi , 50 % failed in english and 25 % in both . the percentage of these who passed in both the subjects is :", + "Output Program": [ + "n0 = 25.0\nn1 = 50.0\nn2 = 25.0\nt0 = n0 + n1\nt1 = t0 - n2\nanswer = 100.0 - t1\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "a & b started a partnership business . a ' s investment was thrice the investment of b and the period of his investment was two times the period of investments of b . if b received rs 4000 as profit , what is their total profit ?", + "Output Program": [ + "n0 = 4000.0\nt0 = 1.0 * 1.0\nt1 = 2.0 * 3.0\nt2 = t1 + t0\nt3 = t0 / t2\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "28000" + ], + "split": "train" + }, + { + "Input": "a canoe has two oars , left and right . each oar either works or breaks . the failure or non - failure of each oar is independent of the failure or non - failure of the other . you can still row the canoe with one oar . the probability that the left oar works is 3 / 5 . the probability that the right oar works is also 3 / 5 . what is the probability j that you can still row the canoe ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 3.0\nn3 = 5.0\nt0 = n0 / n1\nt1 = 2.0 / n1\nt2 = t0 * t1\nt3 = t0 * t0\nt4 = t2 + t2\nanswer = t4 + t3\nprint(answer)" + ], + "Output Answer": [ + "0.84" + ], + "split": "train" + }, + { + "Input": "what is the hcf of 2 / 3 , 4 / 9 and 6 / 18", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 4.0\nn3 = 9.0\nn4 = 6.0\nn5 = 18.0\n\nanswer = n0 / n5\nprint(answer)" + ], + "Output Answer": [ + "0.1111111111111111" + ], + "split": "train" + }, + { + "Input": "the mean proportional between 234 and 104 is", + "Output Program": [ + "import math\nn0 = 234.0\nn1 = 104.0\nt0 = n0 * n1\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "156" + ], + "split": "train" + }, + { + "Input": "a bus starts from city x . the number of women in the bus is half of the number of men . in city y , 16 men leave the bus and 8 women enter . now , number of men and women is equal . in the beginning , how many passengers entered the bus ?", + "Output Program": [ + "n0 = 16.0\nn1 = 8.0\nt0 = n0 + n1\nanswer = t0 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "train" + }, + { + "Input": "john works at a resort from the beginning of march to the end of september . during the month of august this past year , he made 6 times the average ( arithmetic mean ) of his monthly totals in tips for the other months . his total tips for august were what fraction of his total tips for all of the months he worked ?", + "Output Program": [ + "n0 = 6.0\nt0 = n0 * 2.0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "if 0.75 : x : : 3 : 8 , then x is equal to :", + "Output Program": [ + "n0 = 0.75\nn1 = 3.0\nn2 = 8.0\nt0 = n0 * n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 83200 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 8.0\nn2 = 83200.0\nt0 = n0 / n1\nt1 = n2 * t0\nt2 = n2 + t1\nt3 = t2 * t0\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "105300" + ], + "split": "train" + }, + { + "Input": "how many 3 digit even numbers do not use any digit more than once", + "Output Program": [ + "n0 = 3.0\nt0 = n0 * n0\nt1 = 2.0 * 4.0\nt2 = 1000.0 - 10.0\nt3 = t0 * 10.0\nt4 = t3 * t1\nt5 = t2 - t4\nanswer = t5 + 10.0\nprint(answer)" + ], + "Output Answer": [ + "280" + ], + "split": "train" + }, + { + "Input": "mother , her daughter and her grand child weighs 130 kg . daughter and her daughter ( child ) weighs 60 kg . child is 1 / 5 th of her grand mother . what is the age of the daughter ?", + "Output Program": [ + "n0 = 130.0\nn1 = 60.0\nn2 = 1.0\nn3 = 5.0\nt0 = n0 - n1\nt1 = t0 / n3\nanswer = n1 - t1\nprint(answer)" + ], + "Output Answer": [ + "46" + ], + "split": "train" + }, + { + "Input": "the value of ( 0.625 * 0.0729 * 28.9 ) / ( 0.0017 * 0.025 * 8.1 ) is", + "Output Program": [ + "n0 = 0.625\nn1 = 0.0729\nn2 = 28.9\nn3 = 0.0017\nn4 = 0.025\nn5 = 8.1\nt0 = n0 * n1\nt1 = n4 * n5\nt2 = n2 * t0\nt3 = n3 * t1\nt4 = t2 / t3\nanswer = t4 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "382.50000000000006" + ], + "split": "train" + }, + { + "Input": "in n is a positive integer less than 200 , and 14 n / 60 is an integer , then n has how many different positive prime factors ?", + "Output Program": [ + "n0 = 200.0\nn1 = 14.0\nn2 = 60.0\nt0 = 1.0 + 4.0\nt1 = n2 / 2.0\nt2 = t1 / 2.0\nt3 = t2 / 3.0\nt4 = t0 / t3\nanswer = t4 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "if the product of 4 integers is negative , at most how many of the integers can be negative ?", + "Output Program": [ + "n0 = 4.0\n\nanswer = n0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "the value of a scooter depreciates in such a way that its value of the end of each year is 3 / 4 of its value of the beginning of the same year . if the initial value of the scooter is rs . 40,000 , what is the value at the end of 3 years ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 40000.0\nn3 = 3.0\nt0 = n0 / n1\nt1 = 100.0 * 100.0\nt2 = n1 * t1\nt3 = t0**min(n3, 5)\nanswer = t2 * t3\nprint(answer)" + ], + "Output Answer": [ + "16875" + ], + "split": "train" + }, + { + "Input": "a 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2 . 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more . at the end of the two removal and replacement , what is the ratio r of milk and water in the resultant mixture ?", + "Output Program": [ + "n0 = 20.0\nn1 = 3.0\nn2 = 2.0\nn3 = 10.0\nt0 = n1 + n2\nt1 = n0 - n3\nt2 = n1 / t0\nt3 = n2 / t0\nt4 = t2 * t1\nt5 = t3 * t1\nt6 = n3 + t4\nt7 = t5 / n0\nt8 = t6 / n0\nt9 = t7 * t1\nt10 = t8 * t1\nt11 = n3 + t10\nanswer = t11 / t9\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "what is the smallest number which when diminished by 10 , is divisible 2 , 6 , 12 and 24 ?", + "Output Program": [ + "import scipy\nn0 = 10.0\nn1 = 2.0\nn2 = 6.0\nn3 = 12.0\nn4 = 24.0\nt0 = scipy.lcm(int(n1), int(n2))\nt1 = scipy.lcm(int(n3), int(n4))\nt2 = scipy.lcm(int(t0), int(t1))\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "34" + ], + "split": "train" + }, + { + "Input": "the cash realised on selling a 14 % stock is rs . 108.25 , brokerage being 1 / 4 % is ?", + "Output Program": [ + "n0 = 14.0\nn1 = 108.25\nn2 = 1.0\nn3 = 4.0\nt0 = n2 / n3\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "108" + ], + "split": "train" + }, + { + "Input": "3 boys are ages 4 , 6 and 7 respectively . 3 girls are ages 5 , 8 and 9 , respectively . if two of the boys and two of the girls are randomly selected and the sum of the selected children ' s ages is w , what is the difference between the probability that w is even and the probability that w is odd ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 6.0\nn3 = 7.0\nn4 = 3.0\nn5 = 5.0\nn6 = 8.0\nn7 = 9.0\nt0 = 1.0 / n0\nt1 = 2.0 / n0\nt2 = t0 * t0\nt3 = t1 * t1\nt4 = t0 * t1\nt5 = t2 + t3\nt6 = t4 + t4\nanswer = t5 - t6\nprint(answer)" + ], + "Output Answer": [ + "0.11111111111111116" + ], + "split": "train" + }, + { + "Input": "8 x 2.25 - 5 x 0.85 / 2.5 = ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.25\nn2 = 5.0\nn3 = 0.85\nn4 = 2.5\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = t0 - t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "5.5" + ], + "split": "train" + }, + { + "Input": "9773 + x = 13200 , then x is ?", + "Output Program": [ + "n0 = 9773.0\nn1 = 13200.0\n\nanswer = n1 - n0\nprint(answer)" + ], + "Output Answer": [ + "3427" + ], + "split": "train" + }, + { + "Input": "when 5 + 6 = 305 , 6 + 7 = 425 , 7 + 8 = 565 , then 8 + 9 = ?", + "Output Program": [ + "n0 = 5.0\nn1 = 6.0\nn2 = 305.0\nn3 = 6.0\nn4 = 7.0\nn5 = 425.0\nn6 = 7.0\nn7 = 8.0\nn8 = 565.0\nn9 = 8.0\nn10 = 9.0\nt0 = n7 * n10\nt1 = t0 * 10.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "725" + ], + "split": "train" + }, + { + "Input": "when the positive integer x is divided by 9 , the remainder is 5 . what is the remainder when 4 x is divided by 9 ?", + "Output Program": [ + "n0 = 9.0\nn1 = 5.0\nn2 = 4.0\nn3 = 9.0\nt0 = n1 * n2\nanswer = t0 % n0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "in a certain accounting class of 100 students , 70 % of the students took the final exam on the assigned day while the rest of the students took the exam on a make - up date . if the students on the assigned day had an average score of 60 % , and the students on the make - up date had an average score of 90 % , what was the average score for the entire class ?", + "Output Program": [ + "n0 = 100.0\nn1 = 70.0\nn2 = 60.0\nn3 = 90.0\nt0 = n1 * n2\nt1 = n0 - n1\nt2 = n3 * t1\nt3 = t0 + t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "69" + ], + "split": "train" + }, + { + "Input": "if 25 % of a class averages 80 % on a test , 50 % of the class averages 65 % on the test , and the remainder of the class averages 90 % on the test , what is the overall class average ?", + "Output Program": [ + "n0 = 25.0\nn1 = 80.0\nn2 = 50.0\nn3 = 65.0\nn4 = 90.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nt4 = 100.0 - t0\nt5 = n4 * t4\nt6 = t3 + t5\nanswer = t6 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "a dog is tied to a tree by a long nylon cord . if the dog runs from the due north side of the tree to the due south side of the tree with the cord extended to its full length at all items , and the dog ran approximately 30 feet , what was the approximate length of the nylon cord s , in feet ?", + "Output Program": [ + "n0 = 30.0\n\nanswer = n0 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "how many 4 digit numbers have no repeat digits , do not contain zero , and have a sum of digits d equal to 28 ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 28.0\nt0 = math.factorial(min(15, int(4.0)))\nt1 = n0 * t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "of the 645 speckled trout in a certain fishery that contains only speckled and rainbow trout , the number of males is 45 more than twice the number of females . if the ratio of female speckled trout to male rainbow trout is 4 : 3 and the ratio of male rainbow trout to all trout is 3 : 20 , how many female rainbow trout are there ?", + "Output Program": [ + "n0 = 645.0\nn1 = 45.0\nn2 = 4.0\nn3 = 3.0\nn4 = 3.0\nn5 = 20.0\nt0 = n0 - n1\nt1 = t0 / 3.0\nt2 = n3 * t1\nt3 = t2 / n2\nt4 = n5 * t3\nt5 = t4 / n3\nt6 = t5 - n0\nanswer = t6 - t3\nprint(answer)" + ], + "Output Answer": [ + "205" + ], + "split": "train" + }, + { + "Input": "which number should replace both the asterisks in ( * / 21 ) x ( * / 84 ) = 1 ?", + "Output Program": [ + "import math\nn0 = 21.0\nn1 = 84.0\nn2 = 1.0\nt0 = n0 * n1\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "mike took a taxi to the airport and paid $ 2.50 to start plus $ 0.25 per mile . annie took a different route to the airport and paid $ 2.50 plus $ 5.00 in bridge toll fees plus $ 0.25 per mile . if each was charged exactly the same amount , and annie ' s ride was 16 miles , how many miles was mike ' s ride ?", + "Output Program": [ + "n0 = 2.5\nn1 = 0.25\nn2 = 2.5\nn3 = 5.0\nn4 = 0.25\nn5 = 16.0\nt0 = n0 + n3\nt1 = n1 * n5\nt2 = t0 + t1\nt3 = t2 - n0\nanswer = t3 / n1\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "the milk level in a rectangular box measuring 62 feet by 25 feet is to be lowered by 6 inches . how many gallons of milk must be removed ? ( 1 cu ft = 7.5 gallons )", + "Output Program": [ + "n0 = 62.0\nn1 = 25.0\nn2 = 6.0\nn3 = 1.0\nn4 = 7.5\nt0 = n3 / 2.0\nt1 = n0 * n1\nt2 = t0 * t1\nanswer = n4 * t2\nprint(answer)" + ], + "Output Answer": [ + "5812.5" + ], + "split": "train" + }, + { + "Input": "if 20 % of ( x - y ) = 15 % of ( x + y ) , then what percent of x is y ?", + "Output Program": [ + "n0 = 20.0\nn1 = 15.0\nt0 = n0 + n1\nt1 = n0 - n1\nt2 = t1 / t0\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "14.285714285714285" + ], + "split": "train" + }, + { + "Input": "if a tap could fill entire tank in 18 hrs due to leakage , then in how much time tank can be emptied by leakage if tap can fill entire tank in 12 hrs without leakage ?", + "Output Program": [ + "n0 = 18.0\nn1 = 12.0\nt0 = 1.0 / n1\nt1 = 1.0 / n0\nt2 = t0 - t1\nanswer = 1 / t2\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "jill works as a waitress at the local diner where she earns an hourly wage of $ 4.00 per hour and a standard tip rate of 15 % of the cost of the orders she serves . if she worked 3 8 - hour shifts this week and averaged $ 40 in orders per hour , how much did jill earn this week ?", + "Output Program": [ + "n0 = 4.0\nn1 = 15.0\nn2 = 3.0\nn3 = 8.0\nn4 = 40.0\nt0 = n1 / 100.0\nt1 = n2 * n3\nt2 = n4 * t1\nt3 = n0 * t1\nt4 = t0 * t2\nanswer = t4 + t3\nprint(answer)" + ], + "Output Answer": [ + "240" + ], + "split": "train" + }, + { + "Input": "there are , in a certain league , 14 teams , and each team face another team for a total of 5 times . how many games are played in the season ?", + "Output Program": [ + "n0 = 14.0\nn1 = 5.0\nt0 = n0 / 2.0\nt1 = n0 - 1.0\nt2 = t1 * n1\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "455" + ], + "split": "train" + }, + { + "Input": "10 is added to a certain number , the sum is multiplied by 7 , the product is divided by 5 and 5 is subtracted from the quotient . the remainder left is half of 88 . what is the number ?", + "Output Program": [ + "n0 = 10.0\nn1 = 7.0\nn2 = 5.0\nn3 = 5.0\nn4 = 88.0\nt0 = n4 / 2.0\nt1 = n2 + t0\nt2 = n2 * t1\nt3 = t2 / n1\nanswer = t3 - n0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "the average of 25 results is 19 . the average of first 12 of those is 14 and the average of last 12 is 17 . what is the 13 th result ?", + "Output Program": [ + "n0 = 25.0\nn1 = 19.0\nn2 = 12.0\nn3 = 14.0\nn4 = 12.0\nn5 = 17.0\nn6 = 13.0\nt0 = n0 * n1\nt1 = n2 * n5\nt2 = n2 * n3\nt3 = t0 - t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "103" + ], + "split": "train" + }, + { + "Input": "mysoon collects glass ornaments . 10 more than 1 / 6 of the ornaments in her collection are handmade , and 1 / 2 of the handmade ornaments are antiques . if 1 / 3 of the ornaments in her collection are handmade antiques , how many ornaments are in her collection ?", + "Output Program": [ + "n0 = 10.0\nn1 = 1.0\nn2 = 6.0\nn3 = 1.0\nn4 = 2.0\nn5 = 1.0\nn6 = 3.0\nt0 = n6 / n2\nt1 = n0 * n6\nt2 = n4 - t0\nanswer = t1 / t2\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "a picnic attracts 240 persons . there are 40 more men than women , and 40 more adults than children . how many men are at this picnic ?", + "Output Program": [ + "n0 = 240.0\nn1 = 40.0\nn2 = 40.0\nt0 = n0 - n1\nt1 = t0 / 2.0\nt2 = n1 + t1\nt3 = t2 - n1\nt4 = t3 / 2.0\nanswer = n1 + t4\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "in a store , the total price for 20 shirts is $ 360 and the total price for 45 sweaters is $ 900 . by how much does the average ( arithmetic mean ) price of a sweater exceed that of a shirt in this store ?", + "Output Program": [ + "n0 = 20.0\nn1 = 360.0\nn2 = 45.0\nn3 = 900.0\nt0 = n3 / n2\nt1 = n1 / n0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.55 , a 20 - pack for $ 3.05 , and a 250 - pack for $ 22.95 . what is the greatest number of hot dogs you can buy at this store with $ 300 ?", + "Output Program": [ + "n0 = 8.0\nn1 = 1.55\nn2 = 20.0\nn3 = 3.05\nn4 = 250.0\nn5 = 22.95\nn6 = 300.0\nt0 = n6 / n5\nanswer = n4 * t0\nprint(answer)" + ], + "Output Answer": [ + "3267.97385620915" + ], + "split": "train" + }, + { + "Input": "maria bought 10 notebooks and 5 pens costing 2 dollars each . how much did maria pay ?", + "Output Program": [ + "n0 = 10.0\nn1 = 5.0\nn2 = 2.0\nt0 = n0 + n1\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "a jogger running at 9 km / hr along side a railway track is 280 m ahead of the engine of a 120 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?", + "Output Program": [ + "n0 = 9.0\nn1 = 280.0\nn2 = 120.0\nn3 = 45.0\nt0 = n1 + n2\nt1 = 10.0 / 2.0\nt2 = n3 - n0\nt3 = t2 / 2.0\nt4 = t1 / t3\nt5 = t4 * t2\nanswer = t0 / t5\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "in 10 years , a will be twice as old 5 as b was 10 years ago . if a is now 9 years older than b , the present age of b is", + "Output Program": [ + "n0 = 10.0\nn1 = 5.0\nn2 = 10.0\nn3 = 9.0\nt0 = n0 + n3\nt1 = n0 * 2.0\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "39" + ], + "split": "train" + }, + { + "Input": "how many integers between 400 and 1000 are there such that their unit digit is odd ?", + "Output Program": [ + "n0 = 400.0\nn1 = 1000.0\nt0 = n1 - n0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "how many 4 - digit numbers contain no . 2 ?", + "Output Program": [ + "n0 = 65.0\nn1 = 2.0\nn2 = 29.0\nn3 = 5.0\nt0 = n2 * n3\nt1 = n0 - n2\nt2 = t0 / t1\nt3 = n0 * t2\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "65" + ], + "split": "train" + }, + { + "Input": "a man owns 2 / 3 of market reserch beauro buzness , and sells 3 / 4 of his shares for 30000 rs , what is the value of buzness ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 3.0\nn3 = 4.0\nn4 = 30000.0\nt0 = n0 / n1\nt1 = n1 / n3\nt2 = t0 * t1\nanswer = n4 / t2\nprint(answer)" + ], + "Output Answer": [ + "60000" + ], + "split": "train" + }, + { + "Input": "at the opening of a trading day at a certain stock exchange , the price per share of stock k was $ 15 . if the price per share of stock k was $ 16 at the closing of the day , what was the percent increase in the price per share of stock k for that day ?", + "Output Program": [ + "n0 = 15.0\nn1 = 16.0\nt0 = n1 / n0\nt1 = t0 - 1.0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "6.666666666666665" + ], + "split": "train" + }, + { + "Input": "if a - b = 3 and a 2 + b 2 = 29 , then find the value of ab", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 2.0\nn3 = 29.0\nt0 = n0**min(n1, 5)\nt1 = n3 - t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "when greenville state university decided to move its fine arts collection to a new library , it had to package the collection in 20 - inch by 20 - inch by 15 - inch boxes . if the university pays $ 1.30 for every box , and if the university needs 3.06 million cubic inches to package the collection , what is the minimum amount the university must spend on boxes ?", + "Output Program": [ + "n0 = 20.0\nn1 = 20.0\nn2 = 15.0\nn3 = 1.3\nn4 = 3.06\nt0 = 1000.0 * 1000.0\nt1 = n0 * n0\nt2 = n4 * t0\nt3 = n2 * t1\nt4 = t2 / t3\nanswer = n3 * t4\nprint(answer)" + ], + "Output Answer": [ + "663" + ], + "split": "train" + }, + { + "Input": "if 0.6 : x : : 5 : 8 , then x is equal to :", + "Output Program": [ + "n0 = 0.6\nn1 = 5.0\nn2 = 8.0\nt0 = n0 * n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.96" + ], + "split": "train" + }, + { + "Input": "7 x + y = 19 , and x + 3 y = 1 . find the value of 2 x + y", + "Output Program": [ + "n0 = 7.0\nn1 = 19.0\nn2 = 3.0\nn3 = 1.0\nn4 = 2.0\nt0 = n0 * n2\nt1 = n0 - n1\nt2 = t0 - 1.0\nt3 = t1 / t2\nt4 = n2 * t3\nt5 = n3 - t4\nt6 = n4 * t5\nanswer = t3 + t6\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "each week , harry is paid x dollars per hour for the first 24 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 41 hours if harry and james were paid the same amount last week , how many hours did harry work last week ?", + "Output Program": [ + "n0 = 24.0\nn1 = 1.5\nn2 = 40.0\nn3 = 2.0\nn4 = 41.0\nt0 = n2 + n3\nt1 = t0 - n0\nt2 = t1 / n1\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "a box contains 10 tablets of medicine a and 16 tablets of medicine b . what is the least number of tablets that should be taken from the box to ensure that at least two tablets of each kind are among the extracted .", + "Output Program": [ + "n0 = 10.0\nn1 = 16.0\n\nanswer = n1 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "n a certain flower shop , which stocks 4 types of flowers , there are 1 / 3 as many violets as carnations , and 1 / 4 as many tulips as violets . if there are equal numbers of roses and tulips , what percent of the flowers in the shop are carnations ?", + "Output Program": [ + "n0 = 4.0\nn1 = 1.0\nn2 = 3.0\nn3 = 1.0\nn4 = 4.0\nt0 = n1 / n2\nt1 = t0 + t0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "66.66666666666666" + ], + "split": "train" + }, + { + "Input": "at a contest with 500 participants , 1 / 2 of the people are aged 28 to 32 . next year , the number of people aged 28 to 32 will increase by 1 / 8 . after this change , what percentage of the total 500 people will the 28 - to 32 - year - olds represent ?", + "Output Program": [ + "n0 = 500.0\nn1 = 1.0\nn2 = 2.0\nn3 = 28.0\nn4 = 32.0\nn5 = 28.0\nn6 = 32.0\nn7 = 1.0\nn8 = 8.0\nn9 = 500.0\nn10 = 28.0\nn11 = 32.0\nt0 = n1 / n8\nt1 = n0 / n2\nt2 = t0 + n1\nt3 = t2 * t1\nt4 = t3 / n0\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "56.25" + ], + "split": "train" + }, + { + "Input": "ashok secured average of 77 marks in 6 subjects . if the average of marks in 5 subjects is 74 , how many marks did he secure in the 6 th subject ?", + "Output Program": [ + "n0 = 77.0\nn1 = 6.0\nn2 = 5.0\nn3 = 74.0\nn4 = 6.0\nt0 = n0 * n1\nt1 = n2 * n3\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "92" + ], + "split": "train" + }, + { + "Input": "roses can be purchased individually for $ 7.30 , one dozen for $ 36 , or two dozen for $ 50 . what is the greatest number of roses that can be purchased for $ 680 ?", + "Output Program": [ + "import math\nn0 = 7.3\nn1 = 36.0\nn2 = 50.0\nn3 = 680.0\nt0 = n3 / n2\nt1 = 12.0 * 2.0\nt2 = math.floor(t0)\nt3 = n2 * t2\nt4 = t2 * t1\nt5 = n3 - t3\nt6 = t5 / n0\nt7 = math.floor(t6)\nanswer = t7 + t4\nprint(answer)" + ], + "Output Answer": [ + "316" + ], + "split": "train" + }, + { + "Input": "we bought 85 hats at the store . blue hats cost $ 6 and green hats cost $ 7 . the total price was $ 530 . how many green hats did we buy ?", + "Output Program": [ + "n0 = 85.0\nn1 = 6.0\nn2 = 7.0\nn3 = 530.0\nt0 = n0 * n1\nanswer = n3 - t0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "a volunteer organization is recruiting new members . in the fall they manage to increase their number by 5 % . by the spring however membership falls by 19 % . what is the total change in percentage from fall to spring ?", + "Output Program": [ + "n0 = 5.0\nn1 = 19.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = t0 + 1.0\nt3 = 1.0 - t1\nt4 = t2 * t3\nt5 = t4 * 100.0\nanswer = 100.0 - t5\nprint(answer)" + ], + "Output Answer": [ + "14.949999999999989" + ], + "split": "train" + }, + { + "Input": "what is the difference between local value & face value of 7 in the numeral 65793 ?", + "Output Program": [ + "n0 = 7.0\nn1 = 65793.0\nt0 = n0 * 100.0\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "693" + ], + "split": "train" + }, + { + "Input": "mike took a taxi to the airport and paid $ 2.50 to start plus $ 0.25 per mile . annie took a different route to the airport and paid $ 2.50 plus $ 5.00 in bridge toll fees plus $ 0.25 per mile . if each was charged exactly the same amount , and annie ' s ride was 14 miles , how many miles was mike ' s ride ?", + "Output Program": [ + "n0 = 2.5\nn1 = 0.25\nn2 = 2.5\nn3 = 5.0\nn4 = 0.25\nn5 = 14.0\nt0 = n0 + n3\nt1 = n1 * n5\nt2 = t0 + t1\nt3 = t2 - n0\nanswer = t3 / n1\nprint(answer)" + ], + "Output Answer": [ + "34" + ], + "split": "train" + }, + { + "Input": "when a certain tree was first planted , it was 4 feet tall , and the height of the tree increased by a constant amount each year for the next 6 years . at the end of the 6 th year , the tree was 1 / 7 taller than it was at the end of the 4 th year . by how many feet did the height of the tree increase each year ?", + "Output Program": [ + "n0 = 4.0\nn1 = 6.0\nn2 = 6.0\nn3 = 1.0\nn4 = 7.0\nn5 = 4.0\nt0 = n1 - n0\nt1 = n4 * t0\nt2 = t1 - n0\nanswer = n0 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.4" + ], + "split": "train" + }, + { + "Input": "a , b and c have rs . 500 between them , a and c together have rs . 200 and b and c rs . 350 . how much does c have ?", + "Output Program": [ + "n0 = 500.0\nn1 = 200.0\nn2 = 350.0\nt0 = n1 + n2\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "if a = 105 and a ^ 3 = 21 \u00d7 25 \u00d7 45 \u00d7 d , what is the value of d ?", + "Output Program": [ + "n0 = 105.0\nn1 = 3.0\nn2 = 21.0\nn3 = 25.0\nn4 = 45.0\nt0 = n2 * n3\nt1 = n0**min(n1, 5)\nt2 = n4 * t0\nanswer = t1 / t2\nprint(answer)" + ], + "Output Answer": [ + "49" + ], + "split": "train" + }, + { + "Input": "find a sum for 1 st 9 prime number ' s ?", + "Output Program": [ + "n0 = 1.0\nn1 = 9.0\nt0 = 2.0 + 3.0\nt1 = n1 + 2.0\nt2 = t0 + t0\nt3 = t0 + 2.0\nt4 = t1 + 2.0\nt5 = t2 + t3\nt6 = t4 + 4.0\nt7 = t5 + t1\nt8 = t6 + 2.0\nt9 = t7 + t4\nt10 = t8 + 4.0\nt11 = t9 + t6\nt12 = t11 + t8\nanswer = t12 + t10\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "a man is 25 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ?", + "Output Program": [ + "n0 = 25.0\nt0 = 2.0 * 2.0\nt1 = 2.0 - 1.0\nt2 = t0 - 2.0\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "calculate the sum of first 89 natural numbers .", + "Output Program": [ + "n0 = 89.0\nt0 = n0 + 1.0\nt1 = n0 / 2.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "4005" + ], + "split": "train" + }, + { + "Input": "a jogger running at 10 km / hr along side a railway track is 340 m ahead of the engine of a 120 m long train running at 46 km / hr in the same direction . in how much time will the train pass the jogger ?", + "Output Program": [ + "n0 = 10.0\nn1 = 340.0\nn2 = 120.0\nn3 = 46.0\nt0 = n1 + n2\nt1 = 10.0 / 2.0\nt2 = n3 - n0\nt3 = t2 / 2.0\nt4 = t1 / t3\nt5 = t4 * t2\nanswer = t0 / t5\nprint(answer)" + ], + "Output Answer": [ + "46" + ], + "split": "train" + }, + { + "Input": "today david , who is 40 years old , and his daughter , who is 12 years old , celebrate their birthdays . how many years will pass before david \u2019 s age is twice his daughter \u2019 s age ?", + "Output Program": [ + "n0 = 40.0\nn1 = 12.0\nt0 = n0 + n1\nt1 = t0 + 2.0\nt2 = t1 / 2.0\nt3 = t2 - n1\nanswer = t3 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "if ( 400 ) ( 7000 ) = ( 28000 ) ( 100 ^ x ) , what is the value of x ?", + "Output Program": [ + "n0 = 400.0\nn1 = 7000.0\nn2 = 28000.0\nn3 = 100.0\nt0 = n0 * n1\nt1 = t0 / n2\nanswer = t1 / n3\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.64 at the candy store . what is john \u2019 s weekly allowance ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 0.64\nt0 = n0 / n1\nt1 = 1.0 / n0\nt2 = 1.0 - t0\nt3 = t1 * t2\nt4 = t0 + t3\nt5 = 1.0 - t4\nanswer = n2 / t5\nprint(answer)" + ], + "Output Answer": [ + "2.3999999999999995" + ], + "split": "train" + }, + { + "Input": "the sum of the present age of henry and jill is 41 . what is their present ages if 7 years ago henry was twice the age of jill ?", + "Output Program": [ + "n0 = 41.0\nn1 = 7.0\nt0 = n0 + n1\nt1 = t0 / 3.0\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "if a person walks at 5 km / hr instead of 4 km / hr , he would have walked 6 km more . the actual distance traveled by him is ?", + "Output Program": [ + "n0 = 5.0\nn1 = 4.0\nn2 = 6.0\nt0 = n0 - n1\nt1 = n2 / t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "what is the difference between the largest number and the least number written with the digits 9 , 3 , 1 , 2 ?", + "Output Program": [ + "n0 = 9.0\nn1 = 3.0\nn2 = 1.0\nn3 = 2.0\nt0 = n0 * 100.0\nt1 = 4.0 * 100.0\nt2 = n1 * 10.0\nt3 = n1 * 100.0\nt4 = n3 * 10.0\nt5 = t3 + 1000.0\nt6 = t0 * 10.0\nt7 = t6 + t1\nt8 = t5 + t4\nt9 = t7 + t2\nt10 = n0 + t8\nt11 = n2 + t9\nanswer = t11 - t10\nprint(answer)" + ], + "Output Answer": [ + "8102" + ], + "split": "train" + }, + { + "Input": "the difference between a two - digit number and the number obtained by interchanging the positions of its digits is 45 . what is the difference between the two digits of that number ?", + "Output Program": [ + "n0 = 45.0\nt0 = 10.0 - 1.0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "the visitors of a modern art museum who watched a certain picasso painting were asked to fill in a short questionnaire indicating whether they had enjoyed looking at the picture and whether they felt they had understood it . according to the results of the survey , all 130 visitors who did not enjoy the painting also did not feel they had understood the painting , and the number of visitors who enjoyed the painting was equal to the number of visitors who felt they had understood the painting . if 3 / 4 of the visitors who answered the questionnaire both enjoyed the painting and felt they had understood the painting , then how many visitors answered the questionnaire ?", + "Output Program": [ + "n0 = 130.0\nn1 = 3.0\nn2 = 4.0\nt0 = n1 / n2\nt1 = 1.0 - t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "520" + ], + "split": "train" + }, + { + "Input": "if sharon ' s weekly salary increased by 16 percent , she would earn $ 348 per week . if instead , her weekly salary were to increase by 10 percent , how much would she earn per week ?", + "Output Program": [ + "n0 = 16.0\nn1 = 348.0\nn2 = 10.0\nt0 = n0 / 100.0\nt1 = n2 / 100.0\nt2 = t0 + 1.0\nt3 = n1 / t2\nt4 = t1 * t3\nanswer = t3 + t4\nprint(answer)" + ], + "Output Answer": [ + "330" + ], + "split": "train" + }, + { + "Input": "if the charge of staying in a student youth hostel $ 18.00 / day for the first week , and $ 14.00 / day for each additional week , how much does it cost to stay for 23 days ?", + "Output Program": [ + "n0 = 18.0\nn1 = 14.0\nn2 = 23.0\nt0 = 3.0 + 4.0\nt1 = n0 * t0\nt2 = n2 - t0\nt3 = n1 * t2\nanswer = t1 + t3\nprint(answer)" + ], + "Output Answer": [ + "350" + ], + "split": "train" + }, + { + "Input": "what is the unit digit in 4 ^ 100 ?", + "Output Program": [ + "n0 = 4.0\nn1 = 100.0\nt0 = n0**min(2.0, 5)\nanswer = t0 % 10.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "the price of 10 chairs is equal to that of 4 tables . the price of 15 chairs and 2 tables together is rs . 4000 . the total price of 12 chairs and 3 tables is :", + "Output Program": [ + "n0 = 10.0\nn1 = 4.0\nn2 = 15.0\nn3 = 2.0\nn4 = 4000.0\nn5 = 12.0\nn6 = 3.0\nt0 = n1 / n0\nt1 = n2 * t0\nt2 = n3 + t1\nt3 = n4 / t2\nt4 = n6 * t3\nt5 = t0 * t3\nt6 = n5 * t5\nanswer = t4 + t6\nprint(answer)" + ], + "Output Answer": [ + "3900" + ], + "split": "train" + }, + { + "Input": "if the remainder is 15 when the integer n is divided by 28 , what is the remainder when 2 n is divided by 14 ?", + "Output Program": [ + "n0 = 15.0\nn1 = 28.0\nn2 = 2.0\nn3 = 14.0\nt0 = n0 * n2\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "rice weighing 25 / 2 pounds was divided equally and placed in 4 containers . how many ounces of rice were in each container ? ( note that 1 pound = 16 ounces )", + "Output Program": [ + "n0 = 25.0\nn1 = 2.0\nn2 = 4.0\nn3 = 1.0\nn4 = 16.0\nt0 = n0 / n1\nt1 = n4 * t0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "two brother x and y appeared for an exam . the probability of selection of x is 1 / 7 and that of b is 2 / 9 . find the probability that both of them are selected .", + "Output Program": [ + "n0 = 1.0\nn1 = 7.0\nn2 = 2.0\nn3 = 9.0\nt0 = n0 / n1\nt1 = n2 / n3\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "0.031746031746031744" + ], + "split": "train" + }, + { + "Input": "3 models ( f , g , and h ) of cars are distributed among 3 showrooms . the number of cars in each showrooms must be equal and each model must be represented by at least one car in every showroom . there are 19 cars of model f , 17 cars of model g , and 15 cars of model h . what is the maximum number of cars of model f in any showroom ?", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 19.0\nn3 = 17.0\nn4 = 15.0\nt0 = n2 + n3\nt1 = n0 - 1.0\nt2 = n4 + t0\nt3 = t2 / n0\nanswer = t3 - t1\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "a group of 55 adults and 70 children go for trekking . if there is meal for either 70 adults or 90 children and if 7 adults have their meal , find the total number of children that can be catered with the remaining food .", + "Output Program": [ + "n0 = 55.0\nn1 = 70.0\nn2 = 70.0\nn3 = 90.0\nn4 = 7.0\nt0 = n3 / n1\nt1 = n1 - n4\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "81" + ], + "split": "train" + }, + { + "Input": "the average of 20 number is zero of them at the most , how many may be greater than zero ?", + "Output Program": [ + "n0 = 20.0\n\nanswer = n0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "find the principle on a certain sum of money at 5 % per annum for 2 2 / 5 years if the amount being rs . 1792 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 2.0\nn3 = 5.0\nn4 = 1792.0\nt0 = n1 * n3\nt1 = n1 + t0\nt2 = t1 / n3\nt3 = n0 * t2\nt4 = t3 / 100.0\nt5 = t4 + 1.0\nanswer = n4 / t5\nprint(answer)" + ], + "Output Answer": [ + "1599.9999999999998" + ], + "split": "train" + }, + { + "Input": "there are 200 female managers in a certain company . find the total number r of female employees in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers .", + "Output Program": [ + "n0 = 200.0\nn1 = 2.0\nn2 = 5.0\nn3 = 2.0\nn4 = 5.0\nt0 = n1 / n2\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "train" + }, + { + "Input": "what is the least number which when divided by 6 , 7 , 9 and 18 leaves remainder 4 in each care ?", + "Output Program": [ + "import scipy\nn0 = 6.0\nn1 = 7.0\nn2 = 9.0\nn3 = 18.0\nn4 = 4.0\nt0 = scipy.lcm(int(n0), int(n1))\nt1 = scipy.lcm(int(n2), int(n3))\nt2 = scipy.lcm(int(t0), int(t1))\nanswer = n4 + t2\nprint(answer)" + ], + "Output Answer": [ + "130" + ], + "split": "train" + }, + { + "Input": "a man has some hens and cows . if the number of heads be 44 and the number of feet equals 140 , then the number of hens will be :", + "Output Program": [ + "n0 = 44.0\nn1 = 140.0\nt0 = n0 * 4.0\nt1 = t0 - n1\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "in the x - y plane , there are 4 points ( 00 ) , ( 04 ) , ( 54 ) , and ( 50 ) . if these 4 points makes a rectangle , what is the probability that x + y < 4 ?", + "Output Program": [ + "n0 = 4.0\nn1 = 0.0\nn2 = 0.0\nn3 = 0.0\nn4 = 4.0\nn5 = 5.0\nn6 = 4.0\nn7 = 5.0\nn8 = 0.0\nn9 = 4.0\nn10 = 4.0\nt0 = 1.0 + 4.0\nt1 = n0 * n0\nt2 = t1 / 2.0\nt3 = n0 * t0\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.4" + ], + "split": "train" + }, + { + "Input": "in a mixture 60 litres , the ratio of milk and water 2 : 1 . if this ratio is to be 1 : 2 , then the quanity of water to be further added is", + "Output Program": [ + "n0 = 60.0\nn1 = 2.0\nn2 = 1.0\nn3 = 1.0\nn4 = 2.0\nt0 = n1 + n2\nt1 = n0 / t0\nt2 = n0 - t1\nt3 = n1 * t2\nanswer = t3 - t1\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "if an integer n is to be selected at random from 1 to 100 , inclusive , what is probability n ( n + 1 ) will be divisible by 8 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 100.0\nn2 = 1.0\nn3 = 8.0\n\nanswer = 2.0 / n3\nprint(answer)" + ], + "Output Answer": [ + "0.25" + ], + "split": "train" + }, + { + "Input": "if | x | = 9 x - 16 , then x = ?", + "Output Program": [ + "n0 = 9.0\nn1 = 16.0\nt0 = n0 - 1.0\nanswer = n1 / t0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "the average monthly salary of 24 employees in an organisation is rs . 2400 . if the manager ' s salary is added , then the average salary increases by rs . 100 . what is the manager ' s monthly salary ?", + "Output Program": [ + "n0 = 24.0\nn1 = 2400.0\nn2 = 100.0\nt0 = n1 + n2\nt1 = n0 + 1.0\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "4900" + ], + "split": "train" + }, + { + "Input": "a techno company has 14 machines of equal efficiency in its factory . the annual manufacturing costs are rs 42000 and establishment charges are rs 12000 . the annual output of the company is rs 70000 . the annual output and manufacturing costs are directly proportional to the number of machines . the shareholders get 12.5 profit , which is directly proportional to the annual output of the company . if 7.14 machines remain closed throughout the year , then the percentage decrease in the amount of profit of the shareholders would be :", + "Output Program": [ + "n0 = 14.0\nn1 = 42000.0\nn2 = 12000.0\nn3 = 70000.0\nn4 = 12.5\nn5 = 7.14\nt0 = n4 / 100.0\nt1 = n3 - n1\nt2 = n0 - 1.0\nt3 = t2 / n0\nt4 = t1 - n2\nt5 = t0 * t4\nt6 = t3 * t1\nt7 = t6 - n2\nt8 = t0 * t7\nt9 = t5 - t8\nt10 = t9 / t5\nanswer = t10 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "12.5" + ], + "split": "train" + }, + { + "Input": "a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 60 percent of the distribution lies within one standard deviation d of the mean , what percent of the distribution is less than m + d ?", + "Output Program": [ + "n0 = 60.0\nt0 = 100.0 - n0\nt1 = t0 / 2.0\nanswer = 100.0 - t1\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "8 kilograms of rice costing rs . 16 per kg is mixed with 4 kilograms of rice costing rs . 22 per kg . what is the average price of the mixture ?", + "Output Program": [ + "n0 = 8.0\nn1 = 16.0\nn2 = 4.0\nn3 = 22.0\nt0 = n0 + n2\nt1 = n2 * n3\nt2 = n0 * n1\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "9 ! / ( 9 - 3 ) ! = ?", + "Output Program": [ + "import math\nn0 = 9.0\nn1 = 9.0\nn2 = 3.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = n0 - n2\nt2 = math.factorial(min(15, int(t1)))\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "504" + ], + "split": "train" + }, + { + "Input": "if 213 \u00d7 16 = 3408 , then 1.6 \u00d7 21.3 is equal to :", + "Output Program": [ + "n0 = 213.0\nn1 = 16.0\nn2 = 3408.0\nn3 = 1.6\nn4 = 21.3\n\nanswer = n4 * n3\nprint(answer)" + ], + "Output Answer": [ + "34.080000000000005" + ], + "split": "train" + }, + { + "Input": "if x / ( 11 p ) is an odd prime number , where x is a positive integer and p is a prime number , what is the least value of x ?", + "Output Program": [ + "n0 = 11.0\nt0 = n0 * 3.0\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "66" + ], + "split": "train" + }, + { + "Input": "9 persons went to a hotel for taking their meals . 8 of them spent rs . 12 each on their meals and the ninth spent rs . 8 more than the average expenditure of all the 9 . what was the total money spent by them .", + "Output Program": [ + "n0 = 9.0\nn1 = 8.0\nn2 = 12.0\nn3 = 8.0\nn4 = 9.0\nt0 = n0 + n2\nt1 = n1 * n2\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "117" + ], + "split": "train" + }, + { + "Input": "the difference between a two - digit number and the number obtained by interchanging the positions of its digits is 36 . what is the difference between the two digits of that number ?", + "Output Program": [ + "n0 = 36.0\nt0 = 10.0 - 1.0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "if 6 pr = 360 and if 6 cr = 15 , find r ?", + "Output Program": [ + "n0 = 6.0\nn1 = 360.0\nn2 = 6.0\nn3 = 15.0\nt0 = n1 / n3\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "a pupil ' s marks were wrongly entered as 73 instead of 65 . due to the average marks for the class got increased by half . the number of pupils in the class is ?", + "Output Program": [ + "n0 = 73.0\nn1 = 65.0\nt0 = n0 - n1\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "in an examination , 25 % of total students failed in hindi , 35 % failed in english and 40 % in both . the percentage of these who passed in both the subjects is :", + "Output Program": [ + "n0 = 25.0\nn1 = 35.0\nn2 = 40.0\nt0 = n0 + n1\nt1 = t0 - n2\nanswer = 100.0 - t1\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "if ( 55 ^ 55 + 55 ) is divided by 56 , then the remainder is : ?", + "Output Program": [ + "n0 = 55.0\nn1 = 55.0\nn2 = 55.0\nn3 = 56.0\nt0 = n0 - n3\nanswer = n0 + t0\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "train" + }, + { + "Input": "g ( x ) is defined as the product of all even integers k such that 0 < k \u2264 x . for example , g ( 14 ) = 2 \u00d7 4 \u00d7 6 \u00d7 8 \u00d7 10 \u00d7 12 \u00d7 14 . if g ( a ) is divisible by 4 ^ 11 , what is the smallest possible value for a ?", + "Output Program": [ + "n0 = 0.0\nn1 = 14.0\nn2 = 2.0\nn3 = 4.0\nn4 = 6.0\nn5 = 8.0\nn6 = 10.0\nn7 = 12.0\nn8 = 14.0\nn9 = 4.0\nn10 = 11.0\n\nanswer = n2 * n7\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "the least common multiple of positive integer m and 3 - digit integer n is 690 . if n is not divisible by 3 and m is not divisible by 2 , what is the value of n ?", + "Output Program": [ + "n0 = 3.0\nn1 = 690.0\nn2 = 3.0\nn3 = 2.0\n\nanswer = n1 / n0\nprint(answer)" + ], + "Output Answer": [ + "230" + ], + "split": "train" + }, + { + "Input": "a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 percent of the distribution lies within one standard deviation d of the mean , what percent f of the distribution is less than m + d ?", + "Output Program": [ + "n0 = 68.0\nt0 = 100.0 - n0\nt1 = t0 / 2.0\nanswer = 100.0 - t1\nprint(answer)" + ], + "Output Answer": [ + "84" + ], + "split": "train" + }, + { + "Input": "a number is doubled and 5 is added . if the resultant is trebled , it becomes 111 . what is that number ?", + "Output Program": [ + "n0 = 5.0\nn1 = 111.0\nt0 = n0 * 3.0\nt1 = 2.0 * 3.0\nt2 = n1 - t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "find the difference between c . i and s . i on a sum of money rs . 2000 for 2 years . at 4 % p . a", + "Output Program": [ + "n0 = 2000.0\nn1 = 2.0\nn2 = 4.0\nt0 = n2 / 100.0\nt1 = t0 + 1.0\nt2 = n0 * t0\nt3 = n0 * t1\nt4 = n1 * t2\nt5 = t1 * t3\nt6 = t5 - n0\nanswer = t6 - t4\nprint(answer)" + ], + "Output Answer": [ + "3.200000000000273" + ], + "split": "train" + }, + { + "Input": "a positive number x is multiplied by 10 , and this product is then divided by 3 . if the positive square root of the result of these two operations equals x , what is the value of x ?", + "Output Program": [ + "n0 = 10.0\nn1 = 3.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "3.3333333333333335" + ], + "split": "train" + }, + { + "Input": "in a group of dogs and people , the number of legs was 28 more than twice the number of heads . how many dogs were there ? [ assume none of the people or dogs is missing a leg . ]", + "Output Program": [ + "n0 = 28.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "the average of runs of a cricket player of 20 innings was 32 . how many runs must he make in his next innings so as to increase his average of runs by 5 ?", + "Output Program": [ + "n0 = 20.0\nn1 = 32.0\nn2 = 5.0\nt0 = n0 + 1.0\nt1 = n1 + n2\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "137" + ], + "split": "train" + }, + { + "Input": "yearly subscription to professional magazines cost a company $ 840.00 . to make a 30 % cut in the magazine budget , how much less must be spent ?", + "Output Program": [ + "n0 = 840.0\nn1 = 30.0\nt0 = 100.0 - n1\nt1 = t0 / 100.0\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "588" + ], + "split": "train" + }, + { + "Input": "elena \u2019 s bread recipe calls for 3 ounces of butter for each 4 cups of flour used . she needs to make 7 times the original recipe . if 12 ounces of butter is used , then how many cups of flour are needed ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 7.0\nn3 = 12.0\n\nanswer = n1 * n2\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "in a can , there is a mixture of milk and water in the ratio 4 : 3 . if the can is filled with an additional 8 liters of milk , the can would be full and the ratio of milk and water would become 2 : 1 . find the capacity of the can ?", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 8.0\nn3 = 2.0\nn4 = 1.0\nt0 = n2 * n4\nt1 = n1 * n3\nt2 = n0 * n4\nt3 = t1 - t2\nt4 = t0 / t3\nt5 = n0 * t4\nt6 = n1 * t4\nt7 = n2 + t5\nanswer = t7 + t6\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "according to the directions on the can of frozen orange juice concentrate , 1 can of concentrate is to be mixed with 3 cans of water to make orange juice . how many 12 ounces cans of the concentrate are required to prepare 272 6 ounces servings of orange juice ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 12.0\nn3 = 272.0\nn4 = 6.0\nt0 = n3 * n4\nt1 = t0 / n2\nanswer = t1 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "34" + ], + "split": "train" + }, + { + "Input": "cereal a is 10 % sugar by weight , whereas healthier but less delicious cereal b is 2 % sugar by weight . to make a delicious and healthy mixture that is 6 % sugar , what should be the ratio of cereal a to cereal b , by weight ?", + "Output Program": [ + "n0 = 10.0\nn1 = 2.0\nn2 = 6.0\nt0 = n2 - n1\nt1 = n0 - n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "zachary is helping his younger brother , sterling , learn his multiplication tables . for every question that sterling answers correctly , zachary gives him 3 pieces of candy . for every question that sterling answers incorrectly , zachary takes away two pieces of candy . after 7 questions , if sterling had answered 2 more questions correctly , he would have earned 31 pieces of candy . how many of the 7 questions did zachary answer correctly ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 2.0\nn3 = 31.0\nn4 = 7.0\nt0 = n0 + n2\nt1 = n0 * n2\nt2 = n1 - n2\nt3 = n2 * t2\nt4 = t3 - t1\nt5 = n3 + t4\nanswer = t5 / t0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "find the least number which when divided by 35 and 11 leaves a remainder of 1 in each case .", + "Output Program": [ + "import scipy\nn0 = 35.0\nn1 = 11.0\nn2 = 1.0\nt0 = scipy.lcm(int(n0), int(n1))\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "386" + ], + "split": "train" + }, + { + "Input": "he total marks obtained by a student in physics , chemistry and mathematics is 150 more than the marks obtained by him in physics . what is the average mark obtained by him in chemistry and mathematics ?", + "Output Program": [ + "n0 = 150.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "carina has 85 ounces of coffee divided into 5 - and 10 - ounce packages . if she has 2 more 5 - ounce packages than 10 - ounce packages , how many 10 - ounce packages does she have ?", + "Output Program": [ + "n0 = 85.0\nn1 = 5.0\nn2 = 10.0\nn3 = 2.0\nn4 = 5.0\nn5 = 10.0\nn6 = 10.0\nt0 = n1 + n2\nt1 = n1 * n3\nt2 = n0 - t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "the sum of the numbers is 110 . if the first number be twice the second and third number be one - third of the first , then the second number is :", + "Output Program": [ + "n0 = 110.0\nt0 = 1.0 + 10.0\nt1 = n0 * 3.0\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "total dinning bill of 3 people was $ 139.00 and 10 % tip divided the bill evenly ? what is the bill amount each person shared .", + "Output Program": [ + "n0 = 3.0\nn1 = 139.0\nn2 = 10.0\nt0 = 1.0 / n2\nt1 = t0 + 1.0\nt2 = n1 * t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "50.96666666666667" + ], + "split": "train" + }, + { + "Input": "if the price of gasoline increases by 20 % and a driver intends to spend only 14 % more on gasoline , by how much percent should the driver reduce the quantity of gasoline that he buys ?", + "Output Program": [ + "n0 = 20.0\nn1 = 14.0\nt0 = n0 + 100.0\nt1 = n1 + 100.0\nt2 = t0 - t1\nt3 = t2 / t0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "the average of 7 consecutive numbers is 20 . the largest of these numbers is :", + "Output Program": [ + "n0 = 7.0\nn1 = 20.0\nt0 = 1.0 + 2.0\nt1 = n0 * n1\nt2 = t0 + 1.0\nt3 = t2 + 1.0\nt4 = t3 + 1.0\nt5 = t4 + 1.0\nt6 = t5 + 1.0\nt7 = t6 + 1.0\nt8 = t7 + 1.0\nt9 = t8 + 1.0\nt10 = t8 + t9\nt11 = t1 - t10\nt12 = t11 / n0\nanswer = t4 + t12\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "evaluate : 11 + sqrt ( - 4 + 6 \u00d7 4 \u00f7 3 )", + "Output Program": [ + "import math\nn0 = 11.0\nn1 = 4.0\nn2 = 6.0\nn3 = 4.0\nn4 = 3.0\nt0 = n1 * n2\nt1 = t0 / n4\nt2 = t1 - n1\nt3 = math.sqrt(max(0, t2))\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "total dinning bill for 7 people was $ 211.00 . if they add 15 % tip and divided the bill evenly , approximate . what was each persons find share", + "Output Program": [ + "n0 = 7.0\nn1 = 211.0\nn2 = 15.0\nt0 = n1 * n2\nt1 = t0 / 100.0\nt2 = n1 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "34.66428571428572" + ], + "split": "train" + }, + { + "Input": "every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 59000 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 8.0\nn2 = 59000.0\nt0 = n0 / n1\nt1 = n2 * t0\nt2 = n2 + t1\nt3 = t2 * t0\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "74671.875" + ], + "split": "train" + }, + { + "Input": "if the sum and difference of two numbers are 20 and 8 respectively , then the difference of their square is :", + "Output Program": [ + "n0 = 20.0\nn1 = 8.0\nt0 = n0 + n1\nt1 = t0 / 2.0\nt2 = t1**min(2.0, 5)\nt3 = n0 - t1\nt4 = t3**min(2.0, 5)\nanswer = t2 - t4\nprint(answer)" + ], + "Output Answer": [ + "160" + ], + "split": "train" + }, + { + "Input": "the average salary of all the workers in a workshop is rs . 9000 . the average salary of 6 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is ?", + "Output Program": [ + "n0 = 9000.0\nn1 = 6.0\nn2 = 12000.0\nn3 = 6000.0\nt0 = n2 - n0\nt1 = n0 - n3\nt2 = n1 * t0\nt3 = t2 / t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "the average of 50 numbers id 44 . if two numbers , namely 45 and 55 are discarded , the average of the remaining numbers is :", + "Output Program": [ + "n0 = 50.0\nn1 = 44.0\nn2 = 45.0\nn3 = 55.0\nt0 = n2 + n3\nt1 = n0 * n1\nt2 = n0 - 2.0\nt3 = t1 - t0\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "43.75" + ], + "split": "train" + }, + { + "Input": "6 persons in an organization including a and b were to be divided in two groups of 3 members each . the total number of groups containing both a and b is what fraction of the total number of groups which can be formed ?", + "Output Program": [ + "n0 = 6.0\nn1 = 3.0\nt0 = n0**min(2.0, 5)\nt1 = n0 - 1.0\nt2 = n0 * t1\nt3 = t1 - 1.0\nt4 = t2 * t3\nanswer = t0 / t4\nprint(answer)" + ], + "Output Answer": [ + "0.3" + ], + "split": "train" + }, + { + "Input": "the cost of a one - family home was $ 120,000 in 1980 . in 1988 , the price had increased to $ 192,000 . what was the percent increase in the cost of the home ?", + "Output Program": [ + "n0 = 120000.0\nn1 = 1980.0\nn2 = 1988.0\nn3 = 192000.0\nt0 = n3 / n0\nt1 = t0 - 1.0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "60.00000000000001" + ], + "split": "train" + }, + { + "Input": "a batsman in his 19 th inning makes a score of 100 and their by increasing his average by 2 . what is his average after the 19 th inning ?", + "Output Program": [ + "n0 = 19.0\nn1 = 100.0\nn2 = 2.0\nn3 = 19.0\nt0 = n0 * n2\nt1 = n1 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "train" + }, + { + "Input": "x and y are integers . a + b < 11 , and a > 6 . what is the smallest possible value of a - b ?", + "Output Program": [ + "n0 = 11.0\nn1 = 6.0\nt0 = n0 + n1\nt1 = t0 - 4.0\nt2 = t1 + 1.0\nt3 = t2 / 2.0\nanswer = t3 - 3.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "if x is the product of the positive integers from 1 to 8 , inclusive , and if i , k , m , and p are positive integers such that x = 2 ^ i * 3 ^ k * 5 ^ m * 7 ^ p , then i + k + m + p =", + "Output Program": [ + "n0 = 1.0\nn1 = 8.0\nn2 = 2.0\nn3 = 3.0\nn4 = 5.0\nn5 = 7.0\nt0 = n2 + n5\nt1 = n4 / n4\nt2 = n3 / n3\nt3 = t0 + t1\nanswer = t3 + t2\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "if n is the greatest number that will divide 1305 , 4665 and 6905 , leaving the same remainder in each case . what is the sum of the digits of n ?", + "Output Program": [ + "import math\nimport scipy\nn0 = 1305.0\nn1 = 4665.0\nn2 = 6905.0\nt0 = 10.0 * 100.0\nt1 = n1 - n0\nt2 = n2 - n1\nt3 = n2 - n0\nt4 = scipy.gcd(int(t1), int(t2))\nt5 = scipy.gcd(int(t4), int(t3))\nt6 = t5 / 10.0\nt7 = t6 / 10.0\nt8 = math.floor(t6)\nt9 = t7 / 10.0\nt10 = math.floor(t7)\nt11 = t8 * 10.0\nt12 = math.floor(t9)\nt13 = t10 * 100.0\nt14 = t4 - t11\nt15 = t12 * t0\nt16 = t4 - t13\nt17 = t16 / 10.0\nt18 = t4 - t15\nt19 = t18 / 100.0\nt20 = math.floor(t17)\nt21 = math.floor(t19)\nt22 = t12 + t21\nt23 = t22 + t20\nanswer = t23 + t14\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.90 at the candy store . what is john \u2019 s weekly allowance ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 0.9\nt0 = n0 / n1\nt1 = 1.0 / n0\nt2 = 1.0 - t0\nt3 = t1 * t2\nt4 = t0 + t3\nt5 = 1.0 - t4\nanswer = n2 / t5\nprint(answer)" + ], + "Output Answer": [ + "3.3749999999999996" + ], + "split": "train" + }, + { + "Input": "a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 % of the distribution lies one standard deviation f of the mean , what percent of the distribution is less than m + f ?", + "Output Program": [ + "n0 = 68.0\nt0 = 100.0 - n0\nt1 = t0 / 2.0\nanswer = 100.0 - t1\nprint(answer)" + ], + "Output Answer": [ + "84" + ], + "split": "train" + }, + { + "Input": "the result when a number subtracted from 100 is the same as the number added to 40 . what is the number ?", + "Output Program": [ + "n0 = 100.0\nn1 = 40.0\nt0 = n0 - n1\nt1 = t0 / 2.0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "train" + }, + { + "Input": "if a / b = 6 / 5 , then ( 5 a + 4 b ) / ( 5 a - 4 b ) = ?", + "Output Program": [ + "n0 = 6.0\nn1 = 5.0\nn2 = 5.0\nn3 = 4.0\nn4 = 5.0\nn5 = 4.0\nt0 = n0 * n1\nt1 = n1 * n3\nt2 = t0 + t1\nt3 = t0 - t1\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "running at their respective constant rate , machine x takes 2 days longer to produce w widgets than machines y . at these rates , if the two machines together produce 5 w / 4 widgets in 3 days , how many days would it take machine x alone to produce 1 w widgets .", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 4.0\nn3 = 3.0\nn4 = 1.0\nt0 = n0 * n4\nanswer = n3 * t0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "if the number 761 * 829 is completely divisible by 9 , then the smallest whole number in place of * will b", + "Output Program": [ + "n0 = 761.0\nn1 = 829.0\nn2 = 9.0\nt0 = 3.0 + 4.0\nt1 = 3.0 + 3.0\nt2 = 4.0 + 4.0\nt3 = t0 + t1\nt4 = t3 + 1.0\nt5 = t4 + t2\nt6 = t5 + 2.0\nt7 = n2 + t6\nt8 = t7 + 3.0\nanswer = t8 - t7\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "a \u201c palindromic integer \u201d is an integer that remains the same when its digits are reversed . so , for example , 43334 and 516615 are both examples of palindromic integers . how many 6 - digit palindromic integers are both even and greater than 600,000 ?", + "Output Program": [ + "n0 = 43334.0\nn1 = 516615.0\nn2 = 6.0\nn3 = 600000.0\nt0 = n2 - 4.0\nt1 = t0 * 10.0\nanswer = t1 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "train" + }, + { + "Input": "if p and q are prime numbers , how many divisors does the product p ^ 6 * q ^ 7 have ?", + "Output Program": [ + "n0 = 6.0\nn1 = 7.0\nt0 = n0 + 1.0\nt1 = n1 + 1.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "train" + }, + { + "Input": "if there is an equal probability of a child being born a boy or a girl , what is the probability that a couple who have 4 children have two children of the same sex and one of the opposite sex ?", + "Output Program": [ + "n0 = 4.0\n\nanswer = 2.0 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "when a certain number x is divided by 72 , the remainder is 19 . what is the remainder when x is divided by 8 ?", + "Output Program": [ + "n0 = 72.0\nn1 = 19.0\nn2 = 8.0\n\nanswer = n1 % n2\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "in a tournament prize of 1 st , 2 nd , and 3 rd is given in same interval . if total amount of prize rs 4800 and prize of 1 st is rs 2000 , find the interval ? ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 3.0\nn3 = 4800.0\nn4 = 1.0\nn5 = 2000.0\nt0 = n2 * n5\nt1 = t0 - n3\nanswer = t1 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "train" + }, + { + "Input": "a school has 9 english 7 history and 6 geography teachers each teacher can teach 2 subjects max what is he minimum number of teachers required", + "Output Program": [ + "n0 = 9.0\nn1 = 7.0\nn2 = 6.0\nn3 = 2.0\nt0 = n0 + n1\nt1 = n2 + t0\nanswer = t1 / n3\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "if in a certain code ` ` range ' ' is coded as 12345 and ` ` random ' ' is coded as 123678 . then the code for the word ` ` rand ' ' would be", + "Output Program": [ + "n0 = 12345.0\nn1 = 123678.0\nt0 = n1 % 100.0\nt1 = n1 - t0\nanswer = t1 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "1236" + ], + "split": "train" + }, + { + "Input": "the distance from the x - axis to point p is half the distance from the y - axis to point p . if the coordinates of p are ( x , - 9 ) , how many units is p from the y - axis ?", + "Output Program": [ + "n0 = 9.0\n\nanswer = n0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "if a ' s height is 45 % less than that of b , how much percent b ' s height is more than that of a ?", + "Output Program": [ + "n0 = 45.0\nt0 = 100.0 - n0\nt1 = n0 / t0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "81.81818181818183" + ], + "split": "train" + }, + { + "Input": "arnold and danny are two twin brothers that are celebrating their birthday . the product of their ages today is smaller by 9 from the product of their ages a year from today . what is their age today ?", + "Output Program": [ + "n0 = 9.0\nt0 = n0 - 1.0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "what least number should be subtracted from 997 so that the remainder when divided by 5 , 9 , and 11 will leave in each case the same remainder 3 ?", + "Output Program": [ + "n0 = 997.0\nn1 = 5.0\nn2 = 9.0\nn3 = 11.0\nn4 = 3.0\nt0 = n1 * n2\nt1 = n3 * t0\nt2 = t1 * 2.0\nt3 = n4 + t2\nanswer = n0 - t3\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "a garden center sells a certain grass seed in 5 - pound bags at $ 13.82 per bag , 10 - pound bags at $ 20.43 per bag , and 25 - pound bags $ 32.25 per bag . if a customer is to buy at least 65 pounds of the grass seed , but no more than 80 pounds , what is the least possible cost of the grass seed that the customer will buy ?", + "Output Program": [ + "n0 = 5.0\nn1 = 13.85\nn2 = 10.0\nn3 = 20.4\nn4 = 25.0\nn5 = 32.25\nn6 = 65.0\nn7 = 80.0\nt0 = n5 * 2.0\nt1 = n3 * 1.0\nt2 = n1 * 1.0\nt3 = t0 + t1\nanswer = t3 + t2\nprint(answer)" + ], + "Output Answer": [ + "98.75" + ], + "split": "train" + }, + { + "Input": "in a group of cows and chickens , the number of legs was 14 more than twice the number of heads . the number of cows was :", + "Output Program": [ + "n0 = 14.0\nt0 = 4.0 - 2.0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "what least number should be subtracted from 13604 such that the remainder is divisible by 87 ?", + "Output Program": [ + "n0 = 13604.0\nn1 = 87.0\n\nanswer = n0 % n1\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "2 : 5 = 4 / 3 : x . the value of x is ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 4.0\nn3 = 3.0\nt0 = n2 / n3\nt1 = n0 / n1\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "3.333333333333333" + ], + "split": "train" + }, + { + "Input": "the average of 17 numbers is 59 . average of the first 9 of them is 56 and that of the last 9 is 63 . find the 9 th number ?", + "Output Program": [ + "n0 = 17.0\nn1 = 59.0\nn2 = 9.0\nn3 = 56.0\nn4 = 9.0\nn5 = 63.0\nn6 = 9.0\nt0 = n5 * n6\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 - t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "68" + ], + "split": "train" + }, + { + "Input": "when positive integer x is divided by 10 , the quotient is y and the remainder is 3 . when 2 x is divided by 7 , the quotient is 3 y and the remainder is 1 . what is the value of 11 y \u2013 x ?", + "Output Program": [ + "n0 = 10.0\nn1 = 3.0\nn2 = 2.0\nn3 = 7.0\nn4 = 3.0\nn5 = 1.0\nn6 = 11.0\nt0 = n1 * n2\nt1 = n3 * n4\nt2 = n0 * n2\nt3 = t0 - n5\nt4 = t1 - t2\nt5 = t3 / t4\nt6 = n6 * t5\nt7 = n0 * t5\nt8 = n1 + t7\nanswer = t6 - t8\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "at an upscale fast - food restaurant , shin can buy 3 burgers , 7 shakes , and one cola for $ 120 . at the same place it would cost $ 160.50 for 4 burgers , 10 shakes , and one cola . how much would it cost for a meal of one burger , one shake , and one cola ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 120.0\nn3 = 160.5\nn4 = 4.0\nn5 = 10.0\nt0 = n3 - n2\nt1 = n2 + t0\nt2 = t0 * n0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "39" + ], + "split": "train" + }, + { + "Input": "two numbers are such that the square of one is 224 less than 8 times the square of the other . if the numbers be in the ratio of 3 : 4 , the numbers are", + "Output Program": [ + "import math\nimport scipy\nn0 = 224.0\nn1 = 8.0\nn2 = 3.0\nn3 = 4.0\nt0 = n2**min(2.0, 5)\nt1 = n3**min(2.0, 5)\nt2 = n0 * t0\nt3 = n1 * t0\nt4 = t3 - t1\nt5 = scipy.gcd(int(t2), int(t4))\nt6 = t2 / t5\nanswer = math.sqrt(max(0, t6))\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "if x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year , the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $ 83 . if $ 2,000 is the total amount invested , how much is invested at 8 percent ?", + "Output Program": [ + "n0 = 10.0\nn1 = 8.0\nn2 = 10.0\nn3 = 8.0\nn4 = 83.0\nn5 = 2000.0\nn6 = 8.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = n0 * 100.0\nt3 = n0 * n1\nt4 = t0 + t1\nt5 = t2 * 2.0\nt6 = t3 * 2.0\nt7 = n4 + t6\nt8 = t7 / t4\nanswer = t5 - t8\nprint(answer)" + ], + "Output Answer": [ + "650" + ], + "split": "train" + }, + { + "Input": "the ratio of expenditure and savings is 3 : 2 . if the income increases by 15 % and the savings increases by 6 % , then by how much percent should his expenditure increases ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 15.0\nn3 = 6.0\nt0 = n0 * n2\nt1 = n2 - n3\nt2 = n1 * t1\nt3 = t2 + t0\nanswer = t3 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "if an integer n is to be selected at random from 1 to 99 , inclusive , what is probability n ( n + 1 ) will be divisible by 3 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 99.0\nn2 = 1.0\nn3 = 3.0\n\nanswer = 2.0 / n3\nprint(answer)" + ], + "Output Answer": [ + "0.6666666666666666" + ], + "split": "train" + }, + { + "Input": "workers in a factory store products inside two different sized boxes . the bigger of the boxes can store 50 products while the smaller box can store 40 products . if a fresh batch of products numbering 212 in total were to be stored , what is the least number of products that will not be boxed ?", + "Output Program": [ + "n0 = 50.0\nn1 = 40.0\nn2 = 212.0\nt0 = n0 * 4.0\nanswer = n2 - t0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "in a hostel , the number of students decreased by 5 % and the price of food increased by 20 % over the previous year . if each student consumes the same amount of food then by how much should the consumption of food be cut short by every student , so that the total cost of the food remains the same as that of the previous year ?", + "Output Program": [ + "n0 = 5.0\nn1 = 20.0\nt0 = n1 + 100.0\nt1 = 100.0 * 100.0\nt2 = 100.0 - n0\nt3 = t0 * t2\nt4 = t1 / t3\nt5 = 1.0 - t4\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "12.28070175438597" + ], + "split": "train" + }, + { + "Input": "of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 130 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 3.0\nn3 = 4.0\nn4 = 3.0\nn5 = 5.0\nn6 = 130.0\nt0 = n1 / n5\nt1 = n1 / n3\nt2 = n0 / n1\nt3 = 1.0 - t0\nt4 = n6 / t3\nt5 = t4 / t1\nanswer = t5 / t2\nprint(answer)" + ], + "Output Answer": [ + "650" + ], + "split": "train" + }, + { + "Input": "for all real numbers v , an operation is defined by the equation v * = v - v / 3 . if ( v * ) * = 20 , then v =", + "Output Program": [ + "n0 = 3.0\nn1 = 20.0\nt0 = 1.0 / n0\nt1 = 1.0 - t0\nt2 = n1 / t1\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "44.99999999999999" + ], + "split": "train" + }, + { + "Input": "the difference of 2 digit no . & the no . obtained by interchanging the digits is 36 . what is the difference the sum and the number if the ratio between the digits of the number is 1 : 2 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 36.0\nn2 = 1.0\nn3 = 2.0\nt0 = n0 * 10.0\nt1 = t0 - 10.0\nt2 = t1 - 1.0\nt3 = n1 / t2\nt4 = n0 * t3\nt5 = t3 + t4\nt6 = t4 - t3\nanswer = t5 - t6\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "what is the sum of all 4 digit integers formed using the digits 2 , 3 , 4 and 5 ( repetition is allowed )", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\nn2 = 3.0\nn3 = 4.0\nn4 = 5.0\nt0 = n0 + n4\nt1 = 10.0 * 100.0\nt2 = n0**min(3.0, 5)\nt3 = t1 + 100.0\nt4 = n2 + t0\nt5 = t3 + 10.0\nt6 = n1 + t4\nt7 = t5 + 1.0\nt8 = t6 * t2\nanswer = t7 * t8\nprint(answer)" + ], + "Output Answer": [ + "995456" + ], + "split": "train" + }, + { + "Input": "the average age of an adult class is 40 years . 2 new students with an avg age of 32 years join the class . therefore decreasing the average by 4 year . find what was the original strength of class ?", + "Output Program": [ + "n0 = 40.0\nn1 = 2.0\nn2 = 32.0\nn3 = 4.0\nt0 = n1 * n2\nt1 = n0 - n3\nt2 = n1 * t1\nt3 = t2 - t0\nanswer = t3 / n3\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "the arithmetic mean and standard deviation of a certain normal distribution are 14.0 and 1.5 , respectively . what value is exactly 2 standard deviations less than the mean ?", + "Output Program": [ + "n0 = 14.0\nn1 = 1.5\nn2 = 2.0\nt0 = n1 * n2\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "if a * b denotes the greatest common divisor of a and b , then ( ( 16 * 20 ) * ( 18 * 24 ) ) = ?", + "Output Program": [ + "n0 = 16.0\nn1 = 20.0\nn2 = 18.0\nn3 = 24.0\nt0 = n2 / 3.0\nanswer = t0 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "in a class of 40 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 12 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?", + "Output Program": [ + "n0 = 40.0\nn1 = 2.0\nn2 = 12.0\nn3 = 1.0\nn4 = 12.0\nn5 = 2.0\nn6 = 3.0\nn7 = 2.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n1 * n4\nt3 = t1 + t2\nt4 = n4 + t1\nt5 = n1 + t4\nt6 = n0 - t5\nt7 = t6 - n3\nt8 = n6 * t7\nt9 = t3 + t8\nanswer = t0 - t9\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "the average score of a cricketer for 12 matches is 48 runs . if the average for first 8 matches is 40 , then average for last 4 matches is", + "Output Program": [ + "n0 = 12.0\nn1 = 48.0\nn2 = 8.0\nn3 = 40.0\nn4 = 4.0\nt0 = n0 + n1\nt1 = n3 / n2\nt2 = n4 - 3.0\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "train" + }, + { + "Input": "the average of 40 results is 30 and the average of other 30 results is 40 . what is the average of all the results ?", + "Output Program": [ + "n0 = 40.0\nn1 = 30.0\nn2 = 30.0\nn3 = 40.0\nt0 = n0 + n1\nt1 = n0 * n1\nt2 = t1 + t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "34.285714285714285" + ], + "split": "train" + }, + { + "Input": "in a box of 12 pens , a total of 4 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?", + "Output Program": [ + "n0 = 12.0\nn1 = 4.0\nn2 = 2.0\nt0 = n0 - n1\nt1 = n0 - 1.0\nt2 = t0 / n0\nt3 = t0 - 1.0\nt4 = t3 / t1\nanswer = t2 * t4\nprint(answer)" + ], + "Output Answer": [ + "0.4242424242424242" + ], + "split": "train" + }, + { + "Input": "the price of a certain painting increased by 30 % during the first year and decreased by 20 % during the second year . the price of the painting at the end of the 2 - year period was what percent of the original price ?", + "Output Program": [ + "n0 = 30.0\nn1 = 20.0\nn2 = 2.0\nt0 = n0 * n1\nt1 = n0 - n1\nt2 = t0 / 100.0\nt3 = t1 - t2\nanswer = t3 + 100.0\nprint(answer)" + ], + "Output Answer": [ + "104" + ], + "split": "train" + }, + { + "Input": "the divisor is 21 , the quotient is 14 and the remainder is 7 . what is the dividend ?", + "Output Program": [ + "n0 = 21.0\nn1 = 14.0\nn2 = 7.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "301" + ], + "split": "train" + }, + { + "Input": "at veridux corporation , there are 250 employees . of these , 90 are female , and the rest are males . there are a total of 40 managers , and the rest of the employees are associates . if there are a total of 160 male associates , how many female managers are there ?", + "Output Program": [ + "n0 = 250.0\nn1 = 90.0\nn2 = 40.0\nn3 = 160.0\n\nanswer = n2 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "think of a number , divide it by 5 and add 8 to it . the result is 61 . what is the number thought of ?", + "Output Program": [ + "n0 = 5.0\nn1 = 8.0\nn2 = 61.0\nt0 = n2 - n1\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "265" + ], + "split": "train" + }, + { + "Input": "which number should replace both the asterisks in ( * / 21 ) x ( * / 189 ) = 1 ?", + "Output Program": [ + "import math\nn0 = 21.0\nn1 = 189.0\nn2 = 1.0\nt0 = n0 * n1\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "63" + ], + "split": "train" + }, + { + "Input": "x = 13.165 y = 7.686 z = 11.545 the number a is obtained by first rounding the values of x , y , and z to the hundredths place and then adding the resulting values . the number b is obtained by first adding the values of x , y , and z and then rounding the sum to the hundredths place . what is the value of a \u2013 b ?", + "Output Program": [ + "import math\nn0 = 13.165\nn1 = 7.686\nn2 = 11.545\nt0 = n0 + n1\nt1 = n0 * 100.0\nt2 = n1 * 100.0\nt3 = n2 * 100.0\nt4 = n2 + t0\nt5 = math.floor(t1)\nt6 = math.floor(t2)\nt7 = math.floor(t3)\nt8 = t5 + t6\nt9 = t4 * 100.0\nt10 = t8 + t7\nt11 = math.floor(t9)\nt12 = t11 + 1.0\nt13 = t12 - t10\nanswer = t13 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "0.2" + ], + "split": "train" + }, + { + "Input": "a , b , c and d enter into partnership . a subscribes 1 / 3 of the capital b 1 / 4 , c 1 / 5 and d the rest . how much share did a get in a profit of rs . 2430 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 4.0\nn4 = 1.0\nn5 = 5.0\nn6 = 2430.0\nt0 = n0 / n1\nanswer = n6 * t0\nprint(answer)" + ], + "Output Answer": [ + "810" + ], + "split": "train" + }, + { + "Input": "dacid obtained 45 , 35 , 52 , 47 and 55 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?", + "Output Program": [ + "n0 = 45.0\nn1 = 35.0\nn2 = 52.0\nn3 = 47.0\nn4 = 55.0\nn5 = 100.0\nt0 = n0 + n1\nt1 = 10.0 / 2.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "46.8" + ], + "split": "train" + }, + { + "Input": "the product of a and b is equal to 10 more than twice the sum of a and b . if b = 9 , what is the value of b - a ?", + "Output Program": [ + "n0 = 10.0\nn1 = 9.0\nt0 = n1 * 2.0\nt1 = n1 - 2.0\nt2 = n0 + t0\nt3 = t2 / t1\nanswer = n1 - t3\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "if a 10 percent deposit that has been paid toward the purchase of a certain product is $ 150 , how much more remains to be paid ?", + "Output Program": [ + "n0 = 10.0\nn1 = 150.0\nt0 = 100.0 / n0\nt1 = n1 * t0\nanswer = t1 - n1\nprint(answer)" + ], + "Output Answer": [ + "1350" + ], + "split": "train" + }, + { + "Input": "an object thrown directly upward is at a height of h feet after t seconds , where h = - 15 ( t - 3 ) ^ 2 + 150 . at what height , in feet , is the object 2 seconds after it reaches its maximum height ?", + "Output Program": [ + "n0 = 15.0\nn1 = 3.0\nn2 = 2.0\nn3 = 150.0\nn4 = 2.0\nt0 = n1 + n2\nt1 = -n0\nt2 = t0 - n1\nt3 = t2**min(2.0, 5)\nt4 = t1 * t3\nanswer = n3 + t4\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "the average of 6 observations is 13 . a new observation is included and the new average is decreased by 1 . the seventh observation is ?", + "Output Program": [ + "n0 = 6.0\nn1 = 13.0\nn2 = 1.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n1 - n2\nt3 = t0 * t2\nanswer = t3 - t1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "a women in her conversation said ` ` if u reverse my own age , in figures represent my husbands age . he is of course senior to me and difference between our age is one 0 ne - eleventh of their sum . what is the woman ' s and her husbands age ?", + "Output Program": [ + "n0 = 0.0\nt0 = 1.0 + 4.0\nt1 = 1.0 * 1000.0\nt2 = t1 / 2.0\nt3 = t1 * 4.0\nt4 = t0 * 10.0\nt5 = t2 + t3\nanswer = t5 + t4\nprint(answer)" + ], + "Output Answer": [ + "4550" + ], + "split": "train" + }, + { + "Input": "a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 20.25 , the number of the member is the group is :", + "Output Program": [ + "import math\nn0 = 20.25\nt0 = n0 * 100.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "if the sum of two numbers is 24 and the sum of their squares is 400 , then the product of the numbers is", + "Output Program": [ + "n0 = 24.0\nn1 = 400.0\nt0 = n0**min(2.0, 5)\nt1 = t0 - n1\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "88" + ], + "split": "train" + }, + { + "Input": "the sum of 3 consecutive multiples of 3 is 117 . what is the largest number ?", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 117.0\nt0 = n2 / n0\nanswer = n0 + t0\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "company z has 50 employees . if the number of employees having birthdays on wednesday is more than the number of employees having birthdays on any other day of the week , each of which have same number of birth - days , what is the minimum number of employees having birthdays on wednesday .", + "Output Program": [ + "import math\nn0 = 50.0\nt0 = 3.0 + 4.0\nt1 = n0 / t0\nt2 = math.floor(t1)\nt3 = t2 + 1.0\nanswer = t3 + 4.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "the value of x . 320 \u00e3 \u00b7 2 \u00e3 \u00b7 3 = x", + "Output Program": [ + "n0 = 320.0\nn1 = 2.0\nn2 = 3.0\nt0 = 1.0 + 4.0\nt1 = n2 * 10.0\nt2 = t1 + 3.0\nt3 = t0 * 10.0\nt4 = t3 + 3.0\nt5 = t2 / 100.0\nanswer = t4 + t5\nprint(answer)" + ], + "Output Answer": [ + "53.33" + ], + "split": "train" + }, + { + "Input": "two employees x and y are paid a total of rs . 580 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?", + "Output Program": [ + "n0 = 580.0\nn1 = 120.0\nt0 = 1.0 + 4.0\nt1 = t0 * 2.0\nt2 = t1 + 1.0\nt3 = n0 * t1\nt4 = t2 * 2.0\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "263.6363636363636" + ], + "split": "train" + }, + { + "Input": "solve this 6 + 7 = 12 8 + 9 = 16 5 + 6 = 10 7 + 8 = 14 then , 3 + 3 = ? ?", + "Output Program": [ + "n0 = 6.0\nn1 = 7.0\nn2 = 12.0\nn3 = 8.0\nn4 = 9.0\nn5 = 16.0\nn6 = 5.0\nn7 = 6.0\nn8 = 10.0\nn9 = 7.0\nn10 = 8.0\nn11 = 14.0\nn12 = 3.0\nn13 = 3.0\nt0 = n2 - n0\nt1 = n1 - t0\nt2 = n12 - t1\nanswer = n12 + t2\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "if 3 / p = 8 & 3 / q = 18 then p - q = ?", + "Output Program": [ + "n0 = 3.0\nn1 = 8.0\nn2 = 3.0\nn3 = 18.0\nt0 = n0 / n1\nt1 = n0 / n3\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "0.20833333333333334" + ], + "split": "train" + }, + { + "Input": "the total cost of a vacation was divided among 4 people . if the total cost of the vacation had been divided equally among 5 people , the cost per person would have been $ 50 less . what was the total cost cost of the vacation ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 50.0\nt0 = n0 * n1\nt1 = n1 - n0\nt2 = n2 / t1\nanswer = t2 * t0\nprint(answer)" + ], + "Output Answer": [ + "1000" + ], + "split": "train" + }, + { + "Input": "34 , 45 , 56 , 67,78 , _ ?", + "Output Program": [ + "n0 = 2235.0\nn1 = 48.0\nn2 = 61.0\nn3 = 26.0\nn4 = 39.0\nn5 = 52.0\nn6 = 65.0\nt0 = n1 / 2.0\nanswer = t0 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "a man purchased 3 blankets @ rs . 100 each , 3 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ?", + "Output Program": [ + "n0 = 3.0\nn1 = 100.0\nn2 = 3.0\nn3 = 150.0\nn4 = 150.0\nt0 = n3 * 10.0\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "750" + ], + "split": "train" + }, + { + "Input": "an amount at compound interest sums to rs . 17640 / - in 2 years and to rs . 18522 / - in 3 years at the same rate of interest . find the rate percentage ?", + "Output Program": [ + "n0 = 17640.0\nn1 = 2.0\nn2 = 18522.0\nn3 = 3.0\nt0 = n2 - n0\nt1 = t0 / n0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "dan ' s age after 16 years will be 4 times his age 8 years ago . what is the present age of dan ?", + "Output Program": [ + "n0 = 16.0\nn1 = 4.0\nn2 = 8.0\nt0 = n1 * n2\nt1 = n1 - 1.0\nt2 = n0 + t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "5020 \u2212 ( 1004 \u00f7 20.08 ) = ?", + "Output Program": [ + "n0 = 5020.0\nn1 = 1004.0\nn2 = 20.08\nt0 = n1 / n2\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "4970" + ], + "split": "train" + }, + { + "Input": "it takes 60 identical printing machines 2 hours to print 300 cards . how much more time would it take 50 of these machines to print the same total ?", + "Output Program": [ + "n0 = 60.0\nn1 = 2.0\nn2 = 300.0\nn3 = 50.0\nt0 = n0 / n1\nt1 = n2 / n3\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "the maximum number of student amoung them 1802 pens and 1203 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :", + "Output Program": [ + "import scipy\nn0 = 1802.0\nn1 = 1203.0\n\nanswer = scipy.gcd(int(n0), int(n1))\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "if ( 10 ^ 4 * 3.456789 ) ^ 11 is written as a single term , how many digits would be to the right of the decimal place ?", + "Output Program": [ + "n0 = 10.0\nn1 = 4.0\nn2 = 3.456789\nn3 = 11.0\n\nanswer = n3 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "the average ( arithmetic mean ) of 16 students first quiz scores in a difficult english class is 62.5 . when one student dropped the class , the average of the remaining scores increased to 63.0 . what is the quiz score of the student who dropped the class ?", + "Output Program": [ + "n0 = 16.0\nn1 = 62.5\nn2 = 63.0\nt0 = n0 * n1\nt1 = n0 - 1.0\nt2 = n2 * t1\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "55" + ], + "split": "train" + }, + { + "Input": "one - fourth of the workers in palabras bookstore have read the latest book by j . saramago , and 5 / 8 of the workers have read the latest book by h . kureishi . the number of workers that have read neither book is one less than the number of the workers that have read the latest saramago book and have not read the latest kureishi book . if there are 40 workers in the palabras bookstore , how many of them have read both books ?", + "Output Program": [ + "n0 = 5.0\nn1 = 8.0\nn2 = 40.0\nt0 = n2 / 4.0\nt1 = n2 / n1\nt2 = t0 + t0\nt3 = n0 * t1\nt4 = t2 + t3\nt5 = t4 - n2\nt6 = t5 - 1.0\nanswer = t6 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "diana is painting statues . she has 7 / 8 of a gallon of paint remaining . each statue requires 1 / 16 gallon of paint . how many statues can she paint ?", + "Output Program": [ + "n0 = 7.0\nn1 = 8.0\nn2 = 1.0\nn3 = 16.0\nt0 = n0 / n1\nt1 = n2 / n3\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "when greenville state university decided to move its fine arts collection to a new library , it had to package the collection in 20 - inch by 20 - inch by 12 - inch boxes . if the university pays $ 0.40 for every box , and if the university needs 2.4 million cubic inches to package the collection , what is the minimum amount the university must spend on boxes ?", + "Output Program": [ + "n0 = 20.0\nn1 = 20.0\nn2 = 12.0\nn3 = 0.4\nn4 = 2.4\nt0 = 1000.0 * 1000.0\nt1 = n0 * n0\nt2 = n4 * t0\nt3 = n2 * t1\nt4 = t2 / t3\nanswer = n3 * t4\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "train" + }, + { + "Input": "in an electric circuit , two resistors with resistances x and y are connected in parallel . if r is the combined resistance of these two resistors , then the reciprocal of r is equal to the sum of the reciprocals of x and y . what is r if x is 3 ohms and y is 5 ohms ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nt0 = n0 + n1\nt1 = n0 * n1\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "1.875" + ], + "split": "train" + }, + { + "Input": "on dividing a number by 68 , we get 269 as quotient and 0 as remainder . on dividing the same number by 67 , what will be the remainder ?", + "Output Program": [ + "n0 = 68.0\nn1 = 269.0\nn2 = 0.0\nn3 = 67.0\nt0 = n0 * n1\nanswer = t0 % n3\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "what least number must be subtracted from 427398 so that remaining number is divisible by 15", + "Output Program": [ + "import math\nn0 = 427398.0\nn1 = 15.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "how many numbers from 10 to 46 are exactly divisible by 3 ?", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 46.0\nn2 = 3.0\nt0 = n1 / n2\nt1 = n0 / n2\nt2 = math.floor(t0)\nt3 = math.floor(t1)\nt4 = t3 + 1.0\nt5 = n2 * t2\nt6 = n2 * t4\nt7 = t5 - t6\nt8 = t7 / n2\nanswer = t8 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "the total number of digits used in numbering the pages of a book having 366 pages is", + "Output Program": [ + "n0 = 366.0\nt0 = n0 * 3.0\nt1 = 100.0 - 1.0\nt2 = 10.0 - 1.0\nt3 = t0 - t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "990" + ], + "split": "train" + }, + { + "Input": "if ( 1 / 5 ) ^ m * ( 1 / 4 ) ^ 2 = 1 / ( ( 10 ) ^ 4 ) , then m =", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 1.0\nn3 = 4.0\nn4 = 2.0\nn5 = 1.0\nn6 = 10.0\nn7 = 4.0\nt0 = n0 / n3\nt1 = n0 / n1\nt2 = n1 / n6\nt3 = n6 * t0\nt4 = n6 * t1\nt5 = t3 + t4\nanswer = t5 - t2\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "frank is 15 years younger then john . in 3 years john will be twice as old as frank . how old will frank be in 4 years ?", + "Output Program": [ + "n0 = 15.0\nn1 = 3.0\nn2 = 4.0\nt0 = n0 + n1\nt1 = n0 * 2.0\nt2 = t1 - t0\nanswer = n2 + t2\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "in a certain school , 20 % of students are below 8 years of age . the number of students above 8 years of age is 2 / 3 of the number of students of 8 years of age which is 72 . what is the total number of students in the school ?", + "Output Program": [ + "n0 = 20.0\nn1 = 8.0\nn2 = 8.0\nn3 = 2.0\nn4 = 3.0\nn5 = 8.0\nn6 = 72.0\nt0 = n3 / n4\nt1 = n0 / 100.0\nt2 = n6 * t0\nt3 = 1.0 - t1\nt4 = n6 + t2\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "train" + }, + { + "Input": "what number is obtained by adding the units digits of 734 ^ 99 and 347 ^ 83 ?", + "Output Program": [ + "n0 = 734.0\nn1 = 99.0\nn2 = 347.0\nn3 = 83.0\nt0 = 1.0 + 10.0\nt1 = n1 - n3\nt2 = n1 / t0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "the visitors of a modern art museum who watched a certain picasso painting were asked to fill in a short questionnaire indicating whether they had enjoyed looking at the picture and whether they felt they had understood it . according to the results of the survey , all 150 visitors who did not enjoy the painting also did not feel they had understood the painting , and the number of visitors who enjoyed the painting was equal to the number of visitors who felt they had understood the painting . if 3 / 4 of the visitors who answered the questionnaire both enjoyed the painting and felt they had understood the painting , then how many visitors answered the questionnaire ?", + "Output Program": [ + "n0 = 150.0\nn1 = 3.0\nn2 = 4.0\nt0 = n1 / n2\nt1 = 1.0 - t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "600" + ], + "split": "train" + }, + { + "Input": "what is the remainder when 123456789101112131415161718192021222324252627282930313233343536373839404142434481 is divided by 45 ?", + "Output Program": [ + "n0 = 1.2345678910111214e+80\nn1 = 45.0\nt0 = 10.0 - 1.0\nt1 = t0 * t0\nanswer = t1 % n1\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "in a race where 10 cars are running , the chance that car x will win is 1 / 7 , that y will win is 1 / 3 and that z will win is 1 / 5 . assuming that a dead heat is impossible , find the chance that one of them will win .", + "Output Program": [ + "n0 = 10.0\nn1 = 1.0\nn2 = 7.0\nn3 = 1.0\nn4 = 3.0\nn5 = 1.0\nn6 = 5.0\nt0 = n1 / n2\nt1 = n1 / n4\nt2 = n1 / n6\nt3 = t0 + t1\nanswer = t3 + t2\nprint(answer)" + ], + "Output Answer": [ + "0.6761904761904762" + ], + "split": "train" + }, + { + "Input": "a person decided to build a house in 100 days . he employed 100 men in the beginning and 100 more after 20 days and completed the construction in stipulated time . if he had not employed the additional men , how many days behind schedule would it have been finished ?", + "Output Program": [ + "n0 = 100.0\nn1 = 100.0\nn2 = 100.0\nn3 = 20.0\n\nanswer = n0 - n3\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "how much time does a train 100 metres long running at 72 km / hr take to pass a pole ?", + "Output Program": [ + "n0 = 100.0\nn1 = 72.0\nt0 = n0 / 1000.0\nt1 = t0 / n1\nanswer = t1 * 3600.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "in a division sum , the remainder is 0 . as student mistook the divisor by 12 instead of 21 and obtained 49 as quotient . what is the correct quotient ?", + "Output Program": [ + "n0 = 0.0\nn1 = 12.0\nn2 = 21.0\nn3 = 49.0\nt0 = n1 * n3\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.60 at the candy store . what is john \u2019 s weekly allowance ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 0.6\nt0 = n0 / n1\nt1 = 1.0 / n0\nt2 = 1.0 - t0\nt3 = t1 * t2\nt4 = t0 + t3\nt5 = 1.0 - t4\nanswer = n2 / t5\nprint(answer)" + ], + "Output Answer": [ + "2.2499999999999996" + ], + "split": "train" + }, + { + "Input": "a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 27 , the how old is b", + "Output Program": [ + "n0 = 27.0\nt0 = 1.0 + 4.0\nt1 = n0 - 2.0\nt2 = t1 * 2.0\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "what is the largest 4 digit number exactly divisible by 72 ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 72.0\nt0 = 10.0**min(n0, 5)\nt1 = t0 / n1\nt2 = math.floor(t1)\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "9936" + ], + "split": "train" + }, + { + "Input": "evaluate : 30 - | - x + 6 | for x = 10", + "Output Program": [ + "n0 = 30.0\nn1 = 6.0\nn2 = 10.0\nt0 = -n2\nt1 = n1 + t0\nt2 = -t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "benny goes to the market for buying some apples to be distributed between her 9 kids equally . she takes 360 dollars with her . the cost of each apple is 4 dollars . how many apples does she buy to share them equally between her eighteen kids ?", + "Output Program": [ + "n0 = 9.0\nn1 = 360.0\nn2 = 4.0\nt0 = n1 / n2\nt1 = n0 * 2.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "a charitable association sold an average of 66 raffle tickets per member . among the female members , the average was 70 raffle tickets . the male to female ratio of the association is 1 : 2 . what was the average number r of tickets sold by the male members of the association", + "Output Program": [ + "n0 = 66.0\nn1 = 70.0\nn2 = 1.0\nn3 = 2.0\nt0 = n2 + n3\nt1 = n1 * n3\nt2 = n0 * t0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "58" + ], + "split": "train" + }, + { + "Input": "if x is less than y by 50 % then y exceed x by :", + "Output Program": [ + "n0 = 50.0\nt0 = 100.0 - n0\nt1 = 100.0 / t0\nt2 = t1 - 1.0\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "in a division sum , the quotient is 20 , the divisor 66 and the remainder 55 , find the dividend ?", + "Output Program": [ + "n0 = 20.0\nn1 = 66.0\nn2 = 55.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "1375" + ], + "split": "train" + }, + { + "Input": "a and b are two partially filled buckets of water . if 6 liters are transferred from a to b , then a would contain one - third of the amount of water in b . alternatively , if 6 liters are transferred from b to a , b would contain one - half of the amount of water in a . bucket a contains how many liters of water ?", + "Output Program": [ + "n0 = 6.0\nn1 = 6.0\nt0 = n0 + 3.0\nt1 = n0 / 2.0\nt2 = 1.0 / 2.0\nt3 = t0 + 2.0\nt4 = t2 + 2.0\nt5 = t3 * t1\nanswer = t5 / t4\nprint(answer)" + ], + "Output Answer": [ + "13.2" + ], + "split": "train" + }, + { + "Input": "what is the total cost of 2 sandwiches at $ 2.49 each and 4 sodas at $ 1.87 each ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.49\nn2 = 4.0\nn3 = 1.87\nt0 = n0 * n1\nt1 = n2 * n3\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "12.46" + ], + "split": "train" + }, + { + "Input": "after a storm deposits 110 billion gallons of water into the city reservoir , the reservoir is 60 % full . if the original contents of the reservoir totaled 220 billion gallons , the reservoir was approximately what percentage full before the storm ?", + "Output Program": [ + "n0 = 110.0\nn1 = 60.0\nn2 = 220.0\nt0 = n0 + n2\nt1 = n1 / 100.0\nt2 = t0 / t1\nt3 = n2 / t2\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "how many numbers from 10 to 100000 are exactly divisible by 9 ?", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 100000.0\nn2 = 9.0\nt0 = n1 / n2\nt1 = n0 / n2\nt2 = math.floor(t0)\nt3 = math.floor(t1)\nt4 = t3 + 1.0\nt5 = n2 * t2\nt6 = n2 * t4\nt7 = t5 - t6\nt8 = t7 / n2\nanswer = t8 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "11110" + ], + "split": "train" + }, + { + "Input": "a company that ships boxes to a total of 12 distribution centers uses color coding to identify each center . if either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors , what is the minimum number of colors needed for the coding ? ( assume that the order of the colors in a pair does not matter . )", + "Output Program": [ + "import math\nn0 = 12.0\nt0 = n0 / 2.0\nt1 = math.factorial(min(15, int(3.0)))\nt2 = math.factorial(min(15, int(2.0)))\nt3 = t1 * t2\nt4 = t0 - 1.0\nt5 = math.factorial(min(15, int(t4)))\nt6 = t5 / t3\nanswer = t6 - t4\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "solve for x the equation log 9 ( x 3 ) = log 2 ( 8 )", + "Output Program": [ + "import math\nn0 = 9.0\nn1 = 3.0\nn2 = 2.0\nn3 = 8.0\nt0 = math.log(max(1e-5, n3), 2)\nt1 = math.log(max(1e-5, n0), 2)\nt2 = t0 * t1\nt3 = t2 / n1\nanswer = 2.0**min(t3, 5)\nprint(answer)" + ], + "Output Answer": [ + "9.000000000000002" + ], + "split": "train" + }, + { + "Input": "there are 6 more women than there are men on a local co - ed softball team . if there are a total of 16 players on the team , what is the ratio of men to women ?", + "Output Program": [ + "n0 = 6.0\nn1 = 16.0\nt0 = 1.0 + 1.0\nt1 = n1 - n0\nt2 = t1 / t0\nt3 = n0 + t2\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.45454545454545453" + ], + "split": "train" + }, + { + "Input": "a grocer has a sale of rs . 3435 , rs . 3927 , rs . 3855 , rs . 4230 and rs . 3562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 3500 ?", + "Output Program": [ + "n0 = 3435.0\nn1 = 3927.0\nn2 = 3855.0\nn3 = 4230.0\nn4 = 3562.0\nn5 = 5.0\nn6 = 3500.0\nt0 = n5 + 1.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n6 * t0\nt4 = n3 + t2\nt5 = n4 + t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "1991" + ], + "split": "train" + }, + { + "Input": "in a group of pigs and hens , the number of legs are 22 more than twice the number of heads . the number of pigs is", + "Output Program": [ + "n0 = 22.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "x + y = 19 , and x + 3 y = 1 . find the value of x + 2 y", + "Output Program": [ + "n0 = 19.0\nn1 = 3.0\nn2 = 1.0\nn3 = 2.0\nt0 = n3 + 4.0\nt1 = n3 * t0\nanswer = t1 - n3\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the average of 1 st 3 of 4 numbers is 6 and of the last 3 are 5 . if the sum of the first and the last number is 11 . what is the last numbers ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 4.0\nn3 = 6.0\nn4 = 3.0\nn5 = 5.0\nn6 = 11.0\nt0 = n1 * n3\nt1 = n6 - n3\nt2 = n1 + t1\nt3 = t0 - t2\nanswer = t3 - n3\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "a grocer has a sale of rs . 6400 , rs . 7000 , rs . 6800 , rs . 7200 and rs . 6500 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ?", + "Output Program": [ + "n0 = 6400.0\nn1 = 7000.0\nn2 = 6800.0\nn3 = 7200.0\nn4 = 6500.0\nn5 = 5.0\nn6 = 6500.0\nt0 = n5 + 1.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n6 * t0\nt4 = n3 + t2\nt5 = n4 + t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "5100" + ], + "split": "train" + }, + { + "Input": "elvin ' s monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for internet service . elvin ' s total telephone bill for january was $ 52 and elvin ' s total telephone bill for february was 76 $ . if elvin ' s charge for the calls he made in february was twice the charge for the calls he made in january , what is elvin ' s fixed monthly charge for internet service ?", + "Output Program": [ + "n0 = 52.0\nn1 = 76.0\nt0 = n0 * 2.0\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "how many 0 ' s are there in the binary form of 6 * 1024 + 4 * 64 + 2", + "Output Program": [ + "n0 = 0.0\nn1 = 6.0\nn2 = 1024.0\nn3 = 4.0\nn4 = 64.0\nn5 = 2.0\nt0 = n1 + n3\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "find out the c . i on rs . 8000 at 4 % p . a . compound half - yearly for 1 1 / 2 years", + "Output Program": [ + "n0 = 8000.0\nn1 = 4.0\nn2 = 1.0\nn3 = 1.0\nn4 = 2.0\nt0 = n1 / 100.0\nt1 = 3.0 / n4\nt2 = t0 + n2\nt3 = t2**min(t1, 5)\nt4 = n0 * t3\nanswer = t4 - n0\nprint(answer)" + ], + "Output Answer": [ + "484.76847061839544" + ], + "split": "train" + }, + { + "Input": "how many even number in the range between 10 to 120 inclusive are not divisible by 3", + "Output Program": [ + "n0 = 10.0\nn1 = 120.0\nn2 = 3.0\nt0 = n2 * 4.0\nt1 = n1 - n0\nt2 = n1 - 2.0\nt3 = t1 - 2.0\nt4 = t2 - t0\nt5 = t3 / 2.0\nt6 = t4 - n2\nt7 = t6 - n2\nt8 = t7 / n2\nt9 = t8 / 2.0\nanswer = t5 - t9\nprint(answer)" + ], + "Output Answer": [ + "37.33333333333333" + ], + "split": "train" + }, + { + "Input": "in the biology lab of ` ` jefferson ' ' high school there are 0.037 * 10 ^ 5 germs , equally divided among 74000 * 10 ^ ( - 3 ) petri dishes . how many germs live happily in a single dish ?", + "Output Program": [ + "n0 = 0.037\nn1 = 10.0\nn2 = 5.0\nn3 = 74000.0\nn4 = 10.0\nn5 = 3.0\nt0 = n3 / 1000.0\nt1 = 100.0 * 1000.0\nt2 = n0 * t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "if a certain number is divided by 2 , the quotient , dividend , and divisor , added together , will amount to 62 . what is the number ?", + "Output Program": [ + "n0 = 2.0\nn1 = 62.0\nt0 = n0 + 1.0\nt1 = n1 - n0\nt2 = n0 * t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "the average age of a group of n people is 14 years old . one more person aged 34 joins the group and the new average is 16 years old . what is the value of n ?", + "Output Program": [ + "n0 = 14.0\nn1 = 34.0\nn2 = 16.0\nt0 = n1 - n2\nt1 = n2 - n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "the number 0.650 is how much greater than 1 / 8 ?", + "Output Program": [ + "n0 = 0.65\nn1 = 1.0\nn2 = 8.0\nt0 = n1 / n2\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "0.525" + ], + "split": "train" + }, + { + "Input": "if x is an integer such that 0 < x < 7 , 0 < x < 15 , 5 > x > \u2013 1 , 3 > x > 0 , and x + 2 < 4 , then x is", + "Output Program": [ + "n0 = 0.0\nn1 = 7.0\nn2 = 0.0\nn3 = 15.0\nn4 = 5.0\nn5 = 1.0\nn6 = 3.0\nn7 = 0.0\nn8 = 2.0\nn9 = 4.0\nt0 = n4 - n8\nanswer = t0 - n8\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "a pineapple costs rs 7 each and a watermelon costs rs . 5 each . if i spend rs 38 on total what is the number of pineapple i purchased ?", + "Output Program": [ + "n0 = 7.0\nn1 = 5.0\nn2 = 38.0\nt0 = n0 * 4.0\nt1 = n2 - t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "in a division , a student took 87 as divisor instead of 36 . his answer was 24 . the correct answer is -", + "Output Program": [ + "n0 = 87.0\nn1 = 36.0\nn2 = 24.0\nt0 = n0 * n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "58" + ], + "split": "train" + }, + { + "Input": "if 1 is added to the denominator of fraction , the fraction becomes 1 / 2 . if 1 is added to the numerator , the fraction becomes 1 . the fraction is", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 2.0\nn3 = 1.0\nn4 = 1.0\nt0 = n0 + n0\nt1 = n0 + n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.6666666666666666" + ], + "split": "train" + }, + { + "Input": "find out the c . i on rs . 4000 at 4 % p . a . compound half - yearly for 1 1 / 2 years", + "Output Program": [ + "n0 = 4000.0\nn1 = 4.0\nn2 = 1.0\nn3 = 1.0\nn4 = 2.0\nt0 = n1 / 100.0\nt1 = 3.0 / n4\nt2 = t0 + n2\nt3 = t2**min(t1, 5)\nt4 = n0 * t3\nanswer = t4 - n0\nprint(answer)" + ], + "Output Answer": [ + "242.38423530919772" + ], + "split": "train" + }, + { + "Input": "if x + y = 10 , x - y = 18 , for integers of x and y , x = ?", + "Output Program": [ + "n0 = 10.0\nn1 = 18.0\nt0 = n0 + n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "find the least number must be subtracted from 964807 so that remaining no . is divisible by 8 ?", + "Output Program": [ + "import math\nn0 = 964807.0\nn1 = 8.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "a bus started its journey from mumbai and reached pune in 65 min with its average speed of 60 km / hr . if the average speed of the bus is increased by 5 km / hr , how much time will it take to cover the same distance ?", + "Output Program": [ + "n0 = 65.0\nn1 = 60.0\nn2 = 5.0\nt0 = n1 + n2\nt1 = n0 / n1\nt2 = n1 * t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "the mean of 50 observations is 200 . but later he found that there is decrements of 47 from each observations . what is the the updated mean is ?", + "Output Program": [ + "n0 = 50.0\nn1 = 200.0\nn2 = 47.0\n\nanswer = n1 - n2\nprint(answer)" + ], + "Output Answer": [ + "153" + ], + "split": "train" + }, + { + "Input": "how many 1 / 2 s are there in 37 1 / 2 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 37.0\nn3 = 1.0\nn4 = 2.0\nt0 = n0 / n4\nt1 = n0 / n1\nt2 = n2 + t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "a , b , c rent a pasture . if a puts 10 oxen for 7 months , b puts 12 oxen for 5 months and c puts 15 oxen for 3 months for grazing and the rent of the pasture is rs . 175 , then how much amount should c pay as his share of rent ?", + "Output Program": [ + "n0 = 10.0\nn1 = 7.0\nn2 = 12.0\nn3 = 5.0\nn4 = 15.0\nn5 = 3.0\nn6 = 175.0\n\nanswer = n4 * n5\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "in a box of 12 pens , a total of 6 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?", + "Output Program": [ + "n0 = 12.0\nn1 = 6.0\nn2 = 2.0\nt0 = n0 - n1\nt1 = n0 - 1.0\nt2 = t0 / n0\nt3 = t0 - 1.0\nt4 = t3 / t1\nanswer = t2 * t4\nprint(answer)" + ], + "Output Answer": [ + "0.22727272727272727" + ], + "split": "train" + }, + { + "Input": "if a randomly selected non - negative single digit integer is added to { 2 , 3 , 5 , 8 } . what is the probability that the median of the set will increase but the range still remains the same ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 5.0\nn3 = 8.0\n\nanswer = 4.0 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "0.4" + ], + "split": "train" + }, + { + "Input": "if x and y are numbers such that ( x + 4 ) ( y - 4 ) = 0 , what is the smallest possible value of x ^ 2 + y ^ 2", + "Output Program": [ + "n0 = 4.0\nn1 = 4.0\nn2 = 0.0\nn3 = 2.0\nn4 = 2.0\n\nanswer = n0**min(n3, 5)\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "if f ( f ( n ) ) + f ( n ) = 2 n + 3 , f ( 0 ) = 1 then f ( 2014 ) = ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 0.0\nn3 = 1.0\nn4 = 2014.0\n\nanswer = n3 + n4\nprint(answer)" + ], + "Output Answer": [ + "2015" + ], + "split": "train" + }, + { + "Input": "50 + 5 * 12 / ( 180 / 3 ) = ?", + "Output Program": [ + "n0 = 50.0\nn1 = 5.0\nn2 = 12.0\nn3 = 180.0\nn4 = 3.0\nt0 = n3 / n4\nt1 = n1 * n2\nt2 = t1 / t0\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "51" + ], + "split": "train" + }, + { + "Input": "mark bought a set of 6 flower pots of different sizes at a total cost of $ 7.80 . each pot cost 0.25 more than the next one below it in size . what was the cost , in dollars , of the largest pot ?", + "Output Program": [ + "n0 = 6.0\nn1 = 7.8\nn2 = 0.25\nt0 = n0 - 1.0\nt1 = n0 * t0\nt2 = n2 * t0\nt3 = t1 / 2.0\nt4 = n2 * t3\nt5 = n1 - t4\nt6 = t5 / n0\nanswer = t6 + t2\nprint(answer)" + ], + "Output Answer": [ + "1.9249999999999998" + ], + "split": "train" + }, + { + "Input": "in a survey of political preferences , 78 % of those asked were in favour of at least one of the proposals : i , ii and iii . 50 % of those asked favoured proposal i , 30 % favoured proposal ii , and 20 % favoured proposal iii . if 5 % of those asked favoured all 3 of the proposals , what x percentage of those asked favoured more than one of the 3 proposals .", + "Output Program": [ + "n0 = 78.0\nn1 = 50.0\nn2 = 30.0\nn3 = 20.0\nn4 = 5.0\nn5 = 3.0\nn6 = 3.0\nt0 = n1 + n2\nt1 = t0 - n4\nt2 = n3 + t1\nt3 = t2 - n4\nt4 = t3 - n0\nanswer = n4 + t4\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "elvin ' s monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for internet service . elvin ' s total telephone bill for january was $ 48 and elvin ' s total telephone bill for february was 90 $ . if elvin ' s charge for the calls he made in february was twice the charge for the calls he made in january , what is elvin ' s fixed monthly charge for internet service ?", + "Output Program": [ + "n0 = 48.0\nn1 = 90.0\nt0 = n0 * 2.0\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "find k if 56 / k = 4 .", + "Output Program": [ + "n0 = 56.0\nn1 = 4.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "jack spent 1 / 6 of his lifetime in adolescence . his facial hair started growing after 1 / 12 more of his life . he successfully married his girlfriend diana after 1 / 7 more of his life . their son was born after 5 years from then . the son lived just 1 / 2 of what jack lived . jack dies 4 years after his son died . how long did jack live ?", + "Output Program": [ + "n0 = 1.0\nn1 = 6.0\nn2 = 1.0\nn3 = 12.0\nn4 = 1.0\nn5 = 7.0\nn6 = 5.0\nn7 = 1.0\nn8 = 2.0\nn9 = 4.0\nt0 = n6 + n9\nt1 = n0 / n1\nt2 = n0 / n3\nt3 = n0 / n5\nt4 = n0 / n8\nt5 = t1 + t2\nt6 = t5 + t3\nt7 = t6 + t4\nt8 = 1.0 - t7\nanswer = t0 / t8\nprint(answer)" + ], + "Output Answer": [ + "83.99999999999996" + ], + "split": "train" + }, + { + "Input": "the total price of a basic computer and printer are $ 2,500 . if the same printer had been purchased with an enhanced computer whose price was $ 500 more than the price of the basic computer , then the price of the printer would have been 1 / 8 of that total . what was the price of the basic computer ?", + "Output Program": [ + "n0 = 2500.0\nn1 = 500.0\nn2 = 1.0\nn3 = 8.0\nt0 = 0.25 * 1000.0\nt1 = t0 * 10.0\nt2 = n1 + t1\nt3 = t2 / n3\nanswer = t1 - t3\nprint(answer)" + ], + "Output Answer": [ + "2125" + ], + "split": "train" + }, + { + "Input": "if x is equal to the sum of the integers from 10 to 30 , inclusive , and y is the number of even integers from 10 to 30 , inclusive , what is the value of x + y ?", + "Output Program": [ + "n0 = 10.0\nn1 = 30.0\nn2 = 10.0\nn3 = 30.0\nt0 = n0 + n1\nt1 = n1 - n0\nt2 = t1 + 1.0\nt3 = t1 / 2.0\nt4 = t0 / 2.0\nt5 = t3 + 1.0\nt6 = t2 * t4\nanswer = t5 + t6\nprint(answer)" + ], + "Output Answer": [ + "431" + ], + "split": "train" + }, + { + "Input": "the product of two numbers is 4107 . if the h . c . f . of these numbers is 37 , then the greater number is : explanation :", + "Output Program": [ + "n0 = 4107.0\nn1 = 37.0\nt0 = n1**min(2.0, 5)\nt1 = n0 / t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "111" + ], + "split": "train" + }, + { + "Input": "find large no . from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 35 as remainder", + "Output Program": [ + "n0 = 1365.0\nn1 = 6.0\nn2 = 35.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nt2 = t0 / t1\nt3 = n1 * t2\nanswer = n2 + t3\nprint(answer)" + ], + "Output Answer": [ + "1631" + ], + "split": "train" + }, + { + "Input": "n is a whole number which when divided by 4 gives 3 as remainder . what will be the remainder when 2 * n is divided by 4 ?", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 2.0\nn3 = 4.0\nt0 = n1 * n2\nanswer = t0 % n0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "if 6 ^ k = 4 , then 6 ^ ( 2 k + 3 ) =", + "Output Program": [ + "n0 = 6.0\nn1 = 4.0\nn2 = 6.0\nn3 = 2.0\nn4 = 3.0\nt0 = n1**min(n3, 5)\nt1 = n0**min(n4, 5)\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "3456" + ], + "split": "train" + }, + { + "Input": "approximately how many revolutions will be made by a car tire with a 13 - inch diameter if the car travels 1 \u2044 2 mile ?", + "Output Program": [ + "n0 = 13.0\nn1 = 1.0\nn2 = 2.0\nt0 = n1 / n2\nt1 = n2 * 3.0\nt2 = t1 / 10.0\nt3 = t1 * 10.0\nt4 = t2 + n1\nt5 = t3 + 3.0\nt6 = t4 / 10.0\nt7 = t5 * 10.0\nt8 = t6 + 4.0\nt9 = t7 + 3.0\nt10 = t8 / 10.0\nt11 = t9 * 10.0\nt12 = t10 + n1\nt13 = t11 + 3.0\nt14 = t13 + n2\nt15 = t12 / 10.0\nt16 = t15 + 3.0\nt17 = t14 * 10.0\nt18 = n0 * t16\nt19 = t18 / t17\nanswer = t0 / t19\nprint(answer)" + ], + "Output Answer": [ + "775.5724667489372" + ], + "split": "train" + }, + { + "Input": "a company that ships boxes to a total of 12 distribution centers uses color coding to identify each center . if either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors , what is the minimum number of colors needed for the coding ? ( assume that the order of the colors in a pair does not matter )", + "Output Program": [ + "import math\nn0 = 12.0\nt0 = n0 / 2.0\nt1 = math.factorial(min(15, int(3.0)))\nt2 = math.factorial(min(15, int(2.0)))\nt3 = t1 * t2\nt4 = t0 - 1.0\nt5 = math.factorial(min(15, int(t4)))\nt6 = t5 / t3\nanswer = t6 - t4\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "1 * 2 + 2 * 2 ^ 2 + 3 * 2 ^ 3 + 4 * 2 ^ 4 \u2026 \u2026 \u2026 \u2026 \u2026 \u2026 \u2026 \u2026 + 2012 * 2 ^ 2012", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 2.0\nn3 = 2.0\nn4 = 2.0\nn5 = 3.0\nn6 = 2.0\nn7 = 3.0\nn8 = 4.0\nn9 = 2.0\nn10 = 4.0\nn11 = 2012.0\nn12 = 2.0\nn13 = 2012.0\nt0 = n11 + 1.0\nt1 = n1 * t0\nanswer = n11 * t1\nprint(answer)" + ], + "Output Answer": [ + "8100312" + ], + "split": "train" + }, + { + "Input": "stock / number of shares v - - - - - - - - - - - - 68 w - - - - - - - - - - 112 x - - - - - - - - - - - - 56 y - - - - - - - - - - - - 94 z - - - - - - - - - - - - 45 the table shows the number of shares of each of the 5 stocks owned by mr sami . if mr . sami was to sell 20 shares of stock x and buy 23 shares of stock y , what would be the increase in the range of the numbers of shares of the 5 stocks owned by mr . sami ?", + "Output Program": [ + "n0 = 68.0\nn1 = 112.0\nn2 = 56.0\nn3 = 94.0\nn4 = 45.0\nn5 = 5.0\nn6 = 20.0\nn7 = 23.0\nn8 = 5.0\nt0 = n3 + n7\nt1 = n2 - n6\nt2 = n1 - n4\nt3 = t0 - t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "the mean of 50 observations was 32 . it was found later that an observation 48 was wrongly taken as 23 . the corrected new mean is", + "Output Program": [ + "n0 = 50.0\nn1 = 32.0\nn2 = 48.0\nn3 = 23.0\nt0 = n0 * n1\nt1 = n0 - 2.0\nt2 = t1 - n3\nt3 = t0 + t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "32.5" + ], + "split": "train" + }, + { + "Input": "0.009 / x = 0.05 . find the value of x", + "Output Program": [ + "n0 = 0.009\nn1 = 0.05\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.17999999999999997" + ], + "split": "train" + }, + { + "Input": "in a office work is distribute between p persons . if 1 / 6 members are absent then work increased for each person is ?", + "Output Program": [ + "n0 = 1.0\nn1 = 6.0\nt0 = n1 * 100.0\nt1 = n1 - n0\nt2 = t0 / t1\nanswer = t2 - 100.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "the total marks obtained by a student in mathematics and physics is 60 and his score in chemistry is 10 marks more than that in physics . find the average marks scored in mathamatics and chemistry together .", + "Output Program": [ + "n0 = 60.0\nn1 = 10.0\nt0 = n0 + n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "the sum of the non - prime numbers between 20 and 30 , non - inclusive , is", + "Output Program": [ + "n0 = 20.0\nn1 = 30.0\nt0 = n0 + 1.0\nt1 = t0 + 1.0\nt2 = t0 + t1\nt3 = t1 + 2.0\nt4 = t2 + t3\nt5 = t3 + 1.0\nt6 = t4 + t5\nt7 = t5 + 1.0\nt8 = t6 + t7\nt9 = t7 + 1.0\nt10 = t8 + t9\nt11 = t9 + 1.0\nanswer = t10 + t11\nprint(answer)" + ], + "Output Answer": [ + "173" + ], + "split": "train" + }, + { + "Input": "there are 60 supermarkets in the fgh chain . all of them are either in the us or canada . if there are 22 more fgh supermarkets in the us than in canada , how many fgh supermarkets are there in the us ?", + "Output Program": [ + "n0 = 60.0\nn1 = 22.0\nt0 = n0 + n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "41" + ], + "split": "train" + }, + { + "Input": "a salt manufacturing company produced a total of 1000 tonnes of salt in january of a particular year . starting from february its production increased by 100 tonnes every month over the previous months until the end of the year . find its ave 66 rage daily production for that year ?", + "Output Program": [ + "n0 = 1000.0\nn1 = 100.0\nn2 = 66.0\nt0 = 2.0 + 3.0\nt1 = n0 * 2.0\nt2 = 100.0 * 3.0\nt3 = 2.0 * 3.0\nt4 = 12.0 - 1.0\nt5 = n1 * t4\nt6 = t3 * 10.0\nt7 = t1 + t5\nt8 = t2 + t6\nt9 = t8 + t0\nt10 = t7 * 12.0\nt11 = t10 / 2.0\nanswer = t11 / t9\nprint(answer)" + ], + "Output Answer": [ + "50.95890410958904" + ], + "split": "train" + }, + { + "Input": "how much water should be added to 15 liters of a 20 % - solution of alcohol to reduce the concentration of alcohol in the solution by 75 % ?", + "Output Program": [ + "n0 = 15.0\nn1 = 20.0\nn2 = 75.0\nt0 = n2 / 100.0\nt1 = 100.0 * 2.0\nt2 = n1 * t0\nt3 = n1 - t2\nt4 = t1 / t3\nanswer = t4 - n0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "find two integers , neither of which ends in a zero , and whose product is exactly 1 , 00,000", + "Output Program": [ + "n0 = 1.0\nn1 = 0.0\nt0 = 100.0 * 100.0\nt1 = 12.0 * 3.0\nt2 = t0 * 100.0\nt3 = t1 - 4.0\nt4 = t2 / t3\nanswer = t2 / t4\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "in how many v ways can a 4 - letter password be chosen , using the letters a , b , c , d , e , and / or f , such that at least one letter is repeated within the password ?", + "Output Program": [ + "import math\nn0 = 4.0\nt0 = n0 + 2.0\nt1 = math.factorial(min(15, int(2.0)))\nt2 = math.factorial(min(15, int(n0)))\nt3 = math.factorial(min(15, int(t0)))\nt4 = t1 * t2\nt5 = t0**min(n0, 5)\nt6 = t3 / t4\nt7 = t6 * t2\nanswer = t5 - t7\nprint(answer)" + ], + "Output Answer": [ + "936" + ], + "split": "train" + }, + { + "Input": "the average expenditure of a labourer for 6 months was 85 and he fell into debt . in the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30 . his monthly income is", + "Output Program": [ + "n0 = 6.0\nn1 = 85.0\nn2 = 4.0\nn3 = 60.0\nn4 = 30.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nt4 = n4 + t3\nanswer = t4 / t0\nprint(answer)" + ], + "Output Answer": [ + "78" + ], + "split": "train" + }, + { + "Input": "in the xy - coordinate system , what is the slope of the line that goes through the point ( 4 , 4 ) and is equidistant from the two points p = ( 0 , 2 ) and q = ( 12 , 8 ) ?", + "Output Program": [ + "n0 = 4.0\nn1 = 4.0\nn2 = 0.0\nn3 = 2.0\nn4 = 12.0\nn5 = 8.0\nt0 = n2 + n3\nt1 = n0 + n2\nt2 = t0 / n3\nt3 = t1 / n3\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "train" + }, + { + "Input": "a sum of money is sufficient to pay b ' s wages for 12 days and c ' s wages for 24 days . the same money is sufficient to pay the wages of both for ?", + "Output Program": [ + "n0 = 12.0\nn1 = 24.0\nt0 = 1.0 / n1\nt1 = 1.0 / n0\nt2 = t0 + t1\nanswer = 1 / t2\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "jonathan , matthew and zac are picking strawberries from their yard . together they have picked a total of 550 strawberries . jonathan and matthew have picked 350 strawberries together . matthew and zac have picked 250 strawberries together . how many strawberries has zac picked by himself ?", + "Output Program": [ + "n0 = 550.0\nn1 = 350.0\nn2 = 250.0\nt0 = n1 + n2\nt1 = n0 - t0\nt2 = -t1\nanswer = t2 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "train" + }, + { + "Input": "the average age of students of a class is 15.8 years . the average age of boys in the class is 16.2 years and that of the girls is 15.4 years . the ration of the number of boys to the number of girls in the class is :", + "Output Program": [ + "n0 = 15.8\nn1 = 16.2\nn2 = 15.4\nt0 = n0 - n2\nt1 = n1 - n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "1.0000000000000044" + ], + "split": "train" + }, + { + "Input": "a number is doubled and 9 is added . if resultant is trebled , it becomes 75 . what is that number", + "Output Program": [ + "n0 = 9.0\nn1 = 75.0\nt0 = n0 * 3.0\nt1 = 2.0 * 3.0\nt2 = n1 - t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "( 112 x 5 ^ 4 ) = ?", + "Output Program": [ + "n0 = 112.0\nn1 = 5.0\nn2 = 4.0\nt0 = 1.0 + 4.0\nt1 = t0**min(4.0, 5)\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "70000" + ], + "split": "train" + }, + { + "Input": "x + ( 1 / x ) = 2 find x ^ 2 + ( 1 / x ^ 2 )", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 2.0\nn3 = 1.0\nn4 = 2.0\nt0 = n1**min(n2, 5)\nanswer = t0 - n2\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "in a box of 12 pens , a total of 3 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?", + "Output Program": [ + "n0 = 12.0\nn1 = 3.0\nn2 = 2.0\nt0 = n0 - n1\nt1 = n0 - 1.0\nt2 = t0 / n0\nt3 = t0 - 1.0\nt4 = t3 / t1\nanswer = t2 * t4\nprint(answer)" + ], + "Output Answer": [ + "0.5454545454545454" + ], + "split": "train" + }, + { + "Input": "alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 883 . find the cost of each ice - cream cup ?", + "Output Program": [ + "n0 = 16.0\nn1 = 5.0\nn2 = 7.0\nn3 = 6.0\nn4 = 6.0\nn5 = 45.0\nn6 = 70.0\nn7 = 883.0\nt0 = n0 * n3\nt1 = n1 * n5\nt2 = n2 * n6\nt3 = n7 - t0\nt4 = t3 - t1\nt5 = t4 - t2\nanswer = t5 / n3\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "drum x is 1 / 2 full of oil and drum y , which has twice the capacity of drum x , is 1 / 3 full of oil . if all of the oil in drum x is poured into drum y , then drum y will be filled to what capacity ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 1.0\nn3 = 3.0\nt0 = n0 / n3\nt1 = 12.0 / n1\nt2 = n0 / n1\nt3 = t0 * 12.0\nt4 = t1 * t2\nt5 = t3 + t4\nanswer = t5 / 12.0\nprint(answer)" + ], + "Output Answer": [ + "0.5833333333333334" + ], + "split": "train" + }, + { + "Input": "if 16 percent of the students at a certain school went to a camping trip and took more than $ 100 , and 75 percent of the students who went to the camping trip did not take more than $ 100 , what percentage of the students at the school went to the camping trip ?", + "Output Program": [ + "n0 = 16.0\nn1 = 100.0\nn2 = 75.0\nn3 = 100.0\nt0 = n1 - n2\nt1 = t0 / n1\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "train" + }, + { + "Input": "average of 10 matches is 32 , how many runs one should should score to increase his average by 6 runs .", + "Output Program": [ + "n0 = 10.0\nn1 = 32.0\nn2 = 6.0\nt0 = n1 + n2\nt1 = n0 + 1.0\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "98" + ], + "split": "train" + }, + { + "Input": "a multiple choice test consists of 4 questions , and each question has 5 answer choices . in how many r ways can the test be completed if every question is unanswered ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\n\nanswer = n1**min(n0, 5)\nprint(answer)" + ], + "Output Answer": [ + "625" + ], + "split": "dev" + }, + { + "Input": "the hcf and lcm of two numbers m and n are respectively 6 and 210 . if m + n = 72 , then 1 / m + 1 / n is equal to", + "Output Program": [ + "n0 = 6.0\nn1 = 210.0\nn2 = 72.0\nn3 = 1.0\nn4 = 1.0\nt0 = n0 * n1\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.05714285714285714" + ], + "split": "dev" + }, + { + "Input": "in a group of 160 people , 90 have an age of more 30 years , and the others have an age of less than 20 years . if a person is selected at random from this group , what is the probability the person ' s age is less than 20 ?", + "Output Program": [ + "n0 = 160.0\nn1 = 90.0\nn2 = 30.0\nn3 = 20.0\nn4 = 20.0\nt0 = n0 - n1\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.4375" + ], + "split": "dev" + }, + { + "Input": "an art gallery has only paintings and sculptures . currently , 1 / 3 of the pieces of art are displayed , and 1 / 6 of the pieces on display are sculptures . if 1 / 3 of the pieces not on display are paintings , and 800 sculptures are not on display , how many pieces of art does the gallery have ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 6.0\nn4 = 1.0\nn5 = 3.0\nn6 = 800.0\nt0 = n0 / n1\nt1 = n0 - t0\nt2 = n6 / t1\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "1799.9999999999995" + ], + "split": "dev" + }, + { + "Input": "set s contains exactly 10 numbers and has an average ( arithmetic mean ) of 6.2 . if one of the numbers in set s is increased by 7 , while all other numbers remain the same , what is the new average of set s ?", + "Output Program": [ + "n0 = 10.0\nn1 = 6.2\nn2 = 7.0\nt0 = n0 * n1\nt1 = n2 + t0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "6.9" + ], + "split": "dev" + }, + { + "Input": "if p ( a ) = 1 / 5 and p ( b ) = 2 / 5 , find p ( a n b ) if a and b are independent events .", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 2.0\nn3 = 5.0\nt0 = n0 / n1\nt1 = n2 / n3\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "0.08000000000000002" + ], + "split": "dev" + }, + { + "Input": "by the how much is two - fifth of 300 greater than 3 - fifths of 125 ?", + "Output Program": [ + "n0 = 300.0\nn1 = 3.0\nn2 = 125.0\nt0 = 2.0 + 3.0\nt1 = 2.0 / t0\nt2 = n1 / t0\nt3 = n0 * t1\nt4 = n2 * t2\nanswer = t3 - t4\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "dev" + }, + { + "Input": "a collection of books went on sale , and 2 / 3 of them were sold for $ 3.50 each . if none of the 40 remaining books were sold , what was the total amount received for the books that were sold ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 3.5\nn3 = 40.0\nt0 = n2 / n1\nt1 = 1.0 / n1\nt2 = n3 * t0\nt3 = t2 / t1\nanswer = n0 * t3\nprint(answer)" + ], + "Output Answer": [ + "280.00000000000006" + ], + "split": "dev" + }, + { + "Input": "if 2 a = 3 b and ab \u2260 0 , what is the ratio of a / 3 to b / 2 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 0.0\nn3 = 3.0\nn4 = 2.0\nt0 = n0 * n1\nanswer = t0 / t0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "dev" + }, + { + "Input": "each digit 1 through 5 is used exactly once to create a 5 - digit integer . if the 3 and the 4 can not be adjacent digits in the integer , how many 5 - digit integers are possible ?", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 5.0\nn3 = 3.0\nn4 = 4.0\nn5 = 5.0\nt0 = n1 * n4\nt1 = n3 * n4\nt2 = n3 * t0\nt3 = t1 * 2.0\nt4 = t2 * 2.0\nt5 = t3 * 2.0\nanswer = t4 - t5\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "dev" + }, + { + "Input": "at a recent small town election for mayor a total of 963 votes were cast for the 4 candidates , the winner exceding his opponents by 53 , 79 and 105 votes , respectively . how many votes were cast for each candidate ?", + "Output Program": [ + "n0 = 963.0\nn1 = 4.0\nn2 = 53.0\nn3 = 79.0\nn4 = 105.0\nt0 = n0 + n2\nt1 = n3 + n4\nt2 = t0 + t1\nt3 = t2 / 4.0\nanswer = t3 - n4\nprint(answer)" + ], + "Output Answer": [ + "195" + ], + "split": "dev" + }, + { + "Input": "the average weight of a , b and c is 45 kg . if the average weight of a and b be 40 kg and that of b and c be 47 kg , then the weight of b is :", + "Output Program": [ + "n0 = 45.0\nn1 = 40.0\nn2 = 47.0\nt0 = n1 * 2.0\nt1 = n2 * 2.0\nt2 = n0 * 3.0\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "39" + ], + "split": "dev" + }, + { + "Input": "the average of the marks of 30 students in a class is 45 . if the marks of each student are doubled , find the new average ?", + "Output Program": [ + "n0 = 30.0\nn1 = 45.0\n\nanswer = n1 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "dev" + }, + { + "Input": "mr . kramer , the losing candidate in a two - candidate election , received 942,568 votes , which was exactly 25 percent of all votes cast . approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast ?", + "Output Program": [ + "n0 = 942568.0\nn1 = 25.0\nn2 = 50.0\nt0 = n2 / 100.0\nt1 = n1 / 100.0\nt2 = t0 - t1\nt3 = 1.0 - t1\nt4 = t2 / t3\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "33.33333333333333" + ], + "split": "dev" + }, + { + "Input": "a certain company expects quarterly earnings of $ 0.80 per share of stock , half of which will be distributed as dividends to shareholders while the rest will be used for research and development . if earnings are greater than expected , shareholders will receive an additional $ 0.04 per share for each additional $ 0.10 of per share earnings . if quarterly earnings are $ 1.10 per share , what will be the dividend paid to a person who owns 100 shares of the company ' s stock ?", + "Output Program": [ + "n0 = 0.8\nn1 = 0.04\nn2 = 0.1\nn3 = 1.1\nn4 = 100.0\nt0 = n0 / 2.0\nt1 = n3 - n0\nt2 = t1 * 10.0\nt3 = n1 * t2\nt4 = t0 + t3\nanswer = n4 * t4\nprint(answer)" + ], + "Output Answer": [ + "52" + ], + "split": "dev" + }, + { + "Input": "roy is now 6 years older than julia and half of that amount older than kelly . if in 4 years , roy will be twice as old as julia , then in 4 years what would be roy \u2019 s age multiplied by kelly \u2019 s age ?", + "Output Program": [ + "n0 = 6.0\nn1 = 4.0\nn2 = 4.0\nt0 = n0 / 2.0\nt1 = n0 - n1\nt2 = n0 + t1\nt3 = n1 + t2\nt4 = t2 - t0\nt5 = n1 + t4\nanswer = t3 * t5\nprint(answer)" + ], + "Output Answer": [ + "108" + ], + "split": "dev" + }, + { + "Input": "the mean of 50 observations was 36 . it was found later an observation 48 was wrongly taken as 23 . the corrected new means is :", + "Output Program": [ + "n0 = 50.0\nn1 = 36.0\nn2 = 48.0\nn3 = 23.0\nt0 = n0 * n1\nt1 = n0 - 2.0\nt2 = t1 - n3\nt3 = t0 + t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "36.5" + ], + "split": "dev" + }, + { + "Input": "there are 750 male and female participants in a meeting . half the female participants and one - quarterof the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?", + "Output Program": [ + "n0 = 750.0\nt0 = n0 / 3.0\nt1 = t0 * 4.0\nt2 = t1 - n0\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "125" + ], + "split": "dev" + }, + { + "Input": "9 friends decided to divide the hotel bill evenly . if the bill was $ 124.15 dollars , how much money did they pay if 1 cent is the smallest unit ?", + "Output Program": [ + "n0 = 9.0\nn1 = 124.15\nn2 = 1.0\nt0 = 4.0 / 100.0\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "124.11" + ], + "split": "dev" + }, + { + "Input": "on sunday , bill ran 4 more miles than he ran on saturday . julia did not run on saturday , but she ran twice the number of miles on sunday that bill ran on sunday . if bill and julia ran a total of 36 miles on saturday and sunday , how many miles did bill run on sunday ?", + "Output Program": [ + "n0 = 4.0\nn1 = 36.0\nt0 = n0 * 2.0\nt1 = n0 + t0\nt2 = n1 - t1\nt3 = t2 / n0\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "dev" + }, + { + "Input": "the sum of first 45 natural numbers is ?", + "Output Program": [ + "n0 = 45.0\nt0 = n0 + 1.0\nt1 = n0 * t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "1035" + ], + "split": "dev" + }, + { + "Input": "in the storage room of a certain bakery , the ratio of sugar to flour is 5 to 5 , and the ratio of flour to baking soda is 10 to 1 . if there were 60 more pounds of baking soda in the room , the ratio of flour to baking soda would be 8 to 1 . how many pounds of sugar are stored in the room ?", + "Output Program": [ + "n0 = 5.0\nn1 = 5.0\nn2 = 10.0\nn3 = 1.0\nn4 = 60.0\nn5 = 8.0\nn6 = 1.0\nt0 = n0 / n1\nt1 = n4 * n5\nt2 = n2 - n5\nt3 = t1 / t2\nt4 = n2 * t3\nanswer = t0 * t4\nprint(answer)" + ], + "Output Answer": [ + "2400" + ], + "split": "dev" + }, + { + "Input": "the average weight of 8 person ' s increases by 3 kg when a new person comes in place of one of them weighing 70 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 3.0\nn2 = 70.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "94" + ], + "split": "dev" + }, + { + "Input": "a man can swim in still water at 4.5 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ?", + "Output Program": [ + "n0 = 4.5\n\nanswer = n0 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "1.5" + ], + "split": "dev" + }, + { + "Input": "ifaequals the sum of the even integers from 2 to 120 , inclusive , andbequals the sum of the odd integers from 1 to 119 , inclusive , what is the value of a - b ?", + "Output Program": [ + "n0 = 2.0\nn1 = 120.0\nn2 = 1.0\nn3 = 119.0\nt0 = n2 + n3\nt1 = n1 / n0\nt2 = n3 - n2\nt3 = n2 + t1\nt4 = t2 / n0\nt5 = t0 / n0\nt6 = n2 + t4\nt7 = t3 * t1\nt8 = t6 * t5\nanswer = t7 - t8\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "dev" + }, + { + "Input": "in may mrs lee ' s earnings were 50 percent of the lee family ' s total income . in june mrs lee earned 20 percent more than in may . if the rest of the family ' s income was the same both months , then , in june , mrs lee ' s earnings were approximately what percent of the lee family ' s total income ?", + "Output Program": [ + "n0 = 50.0\nn1 = 20.0\nt0 = n1 + 100.0\nt1 = t0 + 100.0\nt2 = t0 / t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "54.54545454545454" + ], + "split": "dev" + }, + { + "Input": "in a fuel station the service costs $ 2.10 per vehicle and every liter of fuel costs $ 0.60 . assuming that you fill up 3 mini - vans and 2 trucks , what will be the total cost , if a mini - van ' s tank is 65 liters and a truck ' s tank is 120 % bigger and they are all empty ?", + "Output Program": [ + "n0 = 2.1\nn1 = 0.6\nn2 = 3.0\nn3 = 2.0\nn4 = 65.0\nn5 = 120.0\nt0 = n2 + n3\nt1 = n4 * n5\nt2 = n2 * n4\nt3 = t1 / 100.0\nt4 = n1 * t2\nt5 = n0 * t0\nt6 = n4 + t3\nt7 = n3 * t6\nt8 = n1 * t7\nt9 = t8 + t4\nanswer = t9 + t5\nprint(answer)" + ], + "Output Answer": [ + "299.1" + ], + "split": "dev" + }, + { + "Input": "half a number plus 7 is 17 . what is the number ?", + "Output Program": [ + "n0 = 7.0\nn1 = 17.0\nt0 = n1 - n0\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "dev" + }, + { + "Input": "find the principle on a certain sum of money at 9 % per annum for 2 2 / 5 years if the amount being rs . 1120 ?", + "Output Program": [ + "n0 = 9.0\nn1 = 2.0\nn2 = 2.0\nn3 = 5.0\nn4 = 1120.0\nt0 = n1 * n3\nt1 = n1 + t0\nt2 = t1 / n3\nt3 = n0 * t2\nt4 = t3 / 100.0\nt5 = t4 + 1.0\nanswer = n4 / t5\nprint(answer)" + ], + "Output Answer": [ + "921.0526315789474" + ], + "split": "dev" + }, + { + "Input": "a man whose bowling average is 12.4 , takes 5 wickets for 26 runs and there by decreases his average by 0.4 . the number of wickets taken by him before his last match is ?", + "Output Program": [ + "import math\nn0 = 12.4\nn1 = 5.0\nn2 = 26.0\nn3 = 0.4\nt0 = math.floor(n0)\nt1 = n1 * t0\nt2 = n0 - t0\nt3 = t1 - n2\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "84.99999999999993" + ], + "split": "dev" + }, + { + "Input": "a 64 gallon solution of salt and water is 10 % salt . how many gallons of water must be added to the solution in order to decrease the salt to 8 % of the volume ?", + "Output Program": [ + "n0 = 64.0\nn1 = 10.0\nn2 = 8.0\nt0 = n1 - n2\nt1 = n0 * t0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "dev" + }, + { + "Input": "if a and b are the roots of the equation x 2 - 9 x + 9 = 0 , then the value of a 2 + b 2 is :", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 9.0\nn2 = 9.0\nn3 = 0.0\nn4 = 2.0\nn5 = 2.0\nt0 = n1 * 4.0\nt1 = n1**min(n0, 5)\nt2 = t1 - t0\nt3 = math.sqrt(max(0, t2))\nt4 = n1 + t3\nt5 = n1 - t3\nt6 = t5 / n0\nt7 = t4 / n0\nt8 = t6**min(n0, 5)\nt9 = t7**min(n0, 5)\nanswer = t8 + t9\nprint(answer)" + ], + "Output Answer": [ + "63" + ], + "split": "dev" + }, + { + "Input": "if k is an integer and 0.00010101 x 10 ^ k is greater than 100 , what is the least possible value of k ?", + "Output Program": [ + "import math\nn0 = 0.00010101\nn1 = 10.0\nn2 = 100.0\nt0 = n2 / n0\nt1 = math.log(max(1e-5, 10.0), 2)\nt2 = math.log(max(1e-5, t0), 2)\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "5.9956356288922485" + ], + "split": "dev" + }, + { + "Input": "how many numbers from 10 to 50 are exactly divisible by 3 .", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 50.0\nn2 = 3.0\nt0 = n1 / n2\nt1 = n0 / n2\nt2 = math.floor(t0)\nt3 = math.floor(t1)\nt4 = t3 + 1.0\nt5 = n2 * t2\nt6 = n2 * t4\nt7 = t5 - t6\nt8 = t7 / n2\nanswer = t8 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "dev" + }, + { + "Input": "10 % people of a village in sri lanka died by bombardment , 20 % of the remainder left the village on account of fear . if now the population is reduced to 3312 , how much was it in the beginning ?", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 20.0\nn2 = 3312.0\nt0 = 100.0 - n0\nt1 = 100.0 - n1\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = t2 * t3\nt5 = n2 / t4\nanswer = math.floor(t5)\nprint(answer)" + ], + "Output Answer": [ + "4599" + ], + "split": "dev" + }, + { + "Input": "if the price of 357 apples is rs . 1517.25 , what will be the approximate price of 49 dozens of such apples ?", + "Output Program": [ + "n0 = 357.0\nn1 = 1517.25\nn2 = 49.0\nt0 = n1 / n0\nt1 = n2 * 12.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "2499" + ], + "split": "dev" + }, + { + "Input": "what is the median of a set of consecutive integers if the sum of nth number from the beginning and nth number from the end is 110 ?", + "Output Program": [ + "n0 = 110.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "55" + ], + "split": "dev" + }, + { + "Input": "roses can be purchased individually for $ 6.30 , one dozen for $ 36 , or two dozen for $ 50 . what is the greatest number of roses that can be purchased for $ 680 ?", + "Output Program": [ + "import math\nn0 = 6.3\nn1 = 36.0\nn2 = 50.0\nn3 = 680.0\nt0 = n3 / n2\nt1 = 12.0 * 2.0\nt2 = math.floor(t0)\nt3 = n2 * t2\nt4 = t2 * t1\nt5 = n3 - t3\nt6 = t5 / n0\nt7 = math.floor(t6)\nanswer = t7 + t4\nprint(answer)" + ], + "Output Answer": [ + "316" + ], + "split": "dev" + }, + { + "Input": "the average mark of the students of a class in a particular exam is 80 . if 8 students whose average mark in that exam is 20 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam .", + "Output Program": [ + "n0 = 80.0\nn1 = 8.0\nn2 = 20.0\nn3 = 90.0\nt0 = n1 * n3\nt1 = n1 * n2\nt2 = n3 - n0\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "dev" + }, + { + "Input": "what is the smallest integer k for which 64 ^ k > 4 ^ 17 ?", + "Output Program": [ + "import math\nn0 = 64.0\nn1 = 4.0\nn2 = 17.0\nt0 = n2 / 3.0\nt1 = math.floor(t0)\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "dev" + }, + { + "Input": "the average weight of 29 students is 28 kg . by the admission of a new student , the average weight is reduced to 27.1 kg . the weight of the new student is", + "Output Program": [ + "n0 = 29.0\nn1 = 28.0\nn2 = 27.1\nt0 = n0 + 1.0\nt1 = n0 * n1\nt2 = n2 * t0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "dev" + }, + { + "Input": "what will be in unit ' s place digit of 3 to the power 34 .", + "Output Program": [ + "n0 = 3.0\nn1 = 34.0\n\nanswer = n0**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "dev" + }, + { + "Input": "an optometrist charges $ 150 per pair for soft contact lenses and $ 85 per pair for hard contact lenses . last week she sold 5 more pairs of soft lenses than hard lenses . if her total sales for pairs of contact lenses last week were $ 1,455 , what was the total number of pairs of contact lenses that she sold ?", + "Output Program": [ + "n0 = 150.0\nn1 = 85.0\nn2 = 5.0\nn3 = 1455.0\nt0 = n0 + n1\nt1 = 100.0 * 4.0\nt2 = n2 * 10.0\nt3 = n0 * n2\nt4 = t1 + t2\nt5 = n2 + t4\nt6 = t5 + 1000.0\nt7 = t6 - t3\nt8 = t7 / t0\nt9 = t8 * 2.0\nanswer = n2 + t9\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "dev" + }, + { + "Input": "a computer is programmed to multiply consecutive even integers 2 * 4 * 6 * 8 * \u2026 * n until the product is divisible by 1881 , what is the value of n ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 6.0\nn3 = 8.0\nn4 = 1881.0\nt0 = 1.0 + 10.0\nt1 = n4 / t0\nt2 = t1 / 3.0\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "114" + ], + "split": "dev" + }, + { + "Input": "in 10 years , a will be twice as old as b was 10 years ago . if a is now 9 years older than b , the present age of b is", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 9.0\nt0 = n0 * 2.0\nt1 = n0 + t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "39" + ], + "split": "dev" + }, + { + "Input": "given that p is a positive even integer with a positive units digit , if the units digit of p ^ 3 minus the units digit of p ^ 2 is equal to 0 , what is the units digit of p + 4 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 0.0\nn3 = 4.0\nt0 = n0 + n0\nanswer = n3 + t0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "dev" + }, + { + "Input": "the cash realised on selling a 14 % stock is rs . 105.25 , brokerage being 1 / 4 % is ?", + "Output Program": [ + "n0 = 14.0\nn1 = 105.25\nn2 = 1.0\nn3 = 4.0\nt0 = n2 / n3\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "105" + ], + "split": "dev" + }, + { + "Input": "there are 6 boxes numbered 1 , 2 , \u2026 , . 6 . each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered . the total number of ways in which this can be done is", + "Output Program": [ + "n0 = 6.0\nn1 = 1.0\nn2 = 2.0\nn3 = 6.0\nn4 = 1.0\nt0 = n0 + n1\nt1 = n0 * t0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "dev" + }, + { + "Input": "a , b , c and d enter into partnership . a subscribes 1 / 3 of the capital b 1 / 4 , c 1 / 5 and d the rest . how much share did a get in a profit of rs . 2490 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 4.0\nn4 = 1.0\nn5 = 5.0\nn6 = 2490.0\nt0 = n0 / n1\nanswer = n6 * t0\nprint(answer)" + ], + "Output Answer": [ + "830" + ], + "split": "dev" + }, + { + "Input": "the value of ( . 02 ) 2 + ( 0.52 ) 2 + ( 0.035 ) 2 / ( 0.002 ) 2 + ( 0.052 ) 2 + ( 0.0035 ) 2", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 0.52\nn3 = 2.0\nn4 = 0.035\nn5 = 2.0\nn6 = 0.002\nn7 = 2.0\nn8 = 0.052\nn9 = 2.0\nn10 = 0.0035\nn11 = 2.0\nt0 = n0 / 100.0\nt1 = n2**min(n0, 5)\nt2 = n4**min(n0, 5)\nt3 = n6**min(n0, 5)\nt4 = n8**min(n0, 5)\nt5 = n10**min(n0, 5)\nt6 = t3 + t4\nt7 = t0**min(n0, 5)\nt8 = t7 + t1\nt9 = t6 + t5\nt10 = t8 + t2\nanswer = t10 / t9\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "dev" + }, + { + "Input": "how much time does a train 160 metres long running at 72 km / hr take to pass a pole ?", + "Output Program": [ + "n0 = 160.0\nn1 = 72.0\nt0 = n0 / 1000.0\nt1 = t0 / n1\nanswer = t1 * 3600.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "dev" + }, + { + "Input": "find the smallest 4 - digit number which is a multiple of 112 .", + "Output Program": [ + "n0 = 4.0\nn1 = 112.0\nt0 = 10.0 - 1.0\nanswer = n1 * t0\nprint(answer)" + ], + "Output Answer": [ + "1008" + ], + "split": "dev" + }, + { + "Input": "the average age of 15 students of a class is 15 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years , the age of the 15 th student is", + "Output Program": [ + "n0 = 15.0\nn1 = 15.0\nn2 = 5.0\nn3 = 14.0\nn4 = 9.0\nn5 = 16.0\nn6 = 15.0\nt0 = n0 * n0\nt1 = n2 * n3\nt2 = n4 * n5\nt3 = t1 + t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "dev" + }, + { + "Input": "if x / 4 years ago roger was 21 years old and x / 4 years from now he will be 4 x years old , how old will he be 5 x years from now ?", + "Output Program": [ + "n0 = 4.0\nn1 = 21.0\nn2 = 4.0\nn3 = 4.0\nn4 = 5.0\nt0 = n0 * n4\nt1 = n1 - 1.0\nt2 = t1 / 2.0\nt3 = n0 * t0\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "dev" + }, + { + "Input": "if 45 - [ 28 - { 37 - ( 15 - * ) } ] = 54 , then * is equal to :", + "Output Program": [ + "n0 = 45.0\nn1 = 28.0\nn2 = 37.0\nn3 = 15.0\nn4 = 54.0\nt0 = n1 - n2\nt1 = n3 + t0\nt2 = n0 - t1\nanswer = n4 - t2\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "dev" + }, + { + "Input": "how many prime numbers are between 29 / 3 and 87 / 6 ?", + "Output Program": [ + "import math\nn0 = 29.0\nn1 = 3.0\nn2 = 87.0\nn3 = 6.0\n\nanswer = math.floor(2.0)\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "dev" + }, + { + "Input": "find the greatest number which leaves the same remainder when it divides 25 , 57 and 105 .", + "Output Program": [ + "n0 = 25.0\nn1 = 57.0\nn2 = 105.0\nt0 = n1 - n0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "dev" + }, + { + "Input": "find large no . from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder", + "Output Program": [ + "n0 = 1365.0\nn1 = 6.0\nn2 = 15.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nt2 = t0 / t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "1620" + ], + "split": "dev" + }, + { + "Input": "a furniture store owner decided to drop the price of her recliners by 20 % to spur business . by the end of the week she had sold 50 % more recliners . what is the percentage increase of the gross ?", + "Output Program": [ + "n0 = 20.0\nn1 = 50.0\nt0 = n1 / 100.0\nt1 = n0 / 100.0\nt2 = t0 + 1.0\nt3 = 1.0 - t1\nt4 = t2 * t3\nt5 = t4 * 100.0\nanswer = t5 - 100.0\nprint(answer)" + ], + "Output Answer": [ + "20.000000000000014" + ], + "split": "dev" + }, + { + "Input": "108 \u00e3 \u2014 108 + 92 \u00e3 \u2014 92 = ?", + "Output Program": [ + "n0 = 108.0\nn1 = 108.0\nn2 = 92.0\nn3 = 92.0\nt0 = n0**min(2.0, 5)\nt1 = n2**min(2.0, 5)\nt2 = t0 - n0\nt3 = t1 - n2\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "19928" + ], + "split": "dev" + }, + { + "Input": "1 - 1 - 1 - 1 - 1 - 1 do any operations between the numbers to make the sum as 37 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 1.0\nn3 = 1.0\nn4 = 1.0\nn5 = 1.0\nn6 = 37.0\nt0 = n0 + n0\nt1 = t0**min(t0, 5)\nt2 = n0 + t1\nt3 = t0**min(t1, 5)\nt4 = t0 * t3\nanswer = t2 + t4\nprint(answer)" + ], + "Output Answer": [ + "37" + ], + "split": "dev" + }, + { + "Input": "two trains of equal length are running on parallel lines in the same directions at 46 km / hr . and 36 km / hr . the faster trains pass the slower train in 18 seconds . the length of each train is :", + "Output Program": [ + "n0 = 46.0\nn1 = 36.0\nn2 = 18.0\nt0 = n0 - n1\nt1 = t0 * 1000.0\nt2 = t1 / 3600.0\nt3 = n2 * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "dev" + }, + { + "Input": "find the value of 2 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ]", + "Output Program": [ + "n0 = 2.0\nn1 = 3.6\nn2 = 0.48\nn3 = 2.5\nn4 = 0.12\nn5 = 0.09\nn6 = 0.5\nt0 = n1 * n2\nt1 = n4 * n5\nt2 = n3 * t0\nt3 = n6 * t1\nt4 = t2 / t3\nanswer = n0 * t4\nprint(answer)" + ], + "Output Answer": [ + "1600.0000000000002" + ], + "split": "dev" + }, + { + "Input": "jim \u2019 s taxi service charges an initial fee of $ 2.25 at the beginning of a trip and an additional charge of $ 0.35 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?", + "Output Program": [ + "n0 = 2.25\nn1 = 0.35\nn2 = 2.0\nn3 = 5.0\nn4 = 3.6\nt0 = n2 / n3\nt1 = n4 / t0\nt2 = n1 * t1\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "5.4" + ], + "split": "dev" + }, + { + "Input": "a prize of $ 1200 is to be distributed among 40 winners , each of whom must be awarded at least $ 40 . if 2 / 5 of the prize will be distributed to 3 / 5 of the winners , what is the greatest possible individual award ?", + "Output Program": [ + "n0 = 1200.0\nn1 = 40.0\nn2 = 40.0\nn3 = 2.0\nn4 = 5.0\nn5 = 3.0\nn6 = 5.0\nt0 = n0 * n3\nt1 = n1 * n5\nt2 = t0 / n4\nt3 = t1 / n4\nt4 = n0 - t2\nt5 = n1 - t3\nt6 = t5 - 1.0\nt7 = n1 * t6\nanswer = t4 - t7\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "dev" + }, + { + "Input": "of the goose eggs laid at a certain pond , 1 / 4 hatched and 4 / 5 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 120 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 4.0\nn3 = 5.0\nn4 = 3.0\nn5 = 5.0\nn6 = 120.0\nt0 = n4 / n5\nt1 = n1 / n3\nt2 = n0 / n1\nt3 = 1.0 - t0\nt4 = n6 / t3\nt5 = t4 / t1\nanswer = t5 / t2\nprint(answer)" + ], + "Output Answer": [ + "1500" + ], + "split": "dev" + }, + { + "Input": "2.08 can be expressed in terms of percentage as", + "Output Program": [ + "n0 = 2.08\n\nanswer = n0 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "208" + ], + "split": "dev" + }, + { + "Input": "a basketball team composed of 12 players scored 100 points in a particular contest . if none of the individual players scored fewer than 7 points , what is the greatest number of points e that an individual player might have scored ?", + "Output Program": [ + "n0 = 12.0\nn1 = 100.0\nn2 = 7.0\nt0 = n0 * n2\nt1 = n1 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "dev" + }, + { + "Input": "a certain company retirement plan has arule of 70 provision that allows an employee to retire when the employee ' s age plus years of employment with the company total at least 70 . in what year could a female employee hired in 1990 on her 32 nd birthday first be eligible to retire under this provision ?", + "Output Program": [ + "n0 = 70.0\nn1 = 70.0\nn2 = 1990.0\nn3 = 32.0\nt0 = n0 - n3\nt1 = t0 / 2.0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "2009" + ], + "split": "dev" + }, + { + "Input": "the average age of 17 persons in a office is 15 years . out of these , the average age of 5 of them is 14 years and that of the other 9 persons is 16 years . the age of the 15 th person is ?", + "Output Program": [ + "n0 = 17.0\nn1 = 15.0\nn2 = 5.0\nn3 = 14.0\nn4 = 9.0\nn5 = 16.0\nn6 = 15.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n4 * n5\nt3 = t0 - t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "41" + ], + "split": "dev" + }, + { + "Input": "5 % people of a village in sri lanka died by bombardment , 20 % of the remainder left the village on account of fear . if now the population is reduced to 3553 , how much was it in the beginning ?", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 20.0\nn2 = 3553.0\nt0 = 100.0 - n0\nt1 = 100.0 - n1\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = t2 * t3\nt5 = n2 / t4\nanswer = math.floor(t5)\nprint(answer)" + ], + "Output Answer": [ + "4675" + ], + "split": "dev" + }, + { + "Input": "every monday , marina eats one croissant and every tuesday she eats two croissants . on each subsequent day of the week , she eats a number of croissants equal to the sum of the croissants eaten on the two previous days , with the exception that if she eats more than 4 croissants on any particular day , the next day she will eat only one croissant . at the end of the week ( which runs from monday through sunday ) , the cycle resets , and marina goes back to eating one croissant on monday , two on tuesday , and so forth . if a particular month begins on a saturday , how many croissants will marina eat on the 30 th of that month ?", + "Output Program": [ + "n0 = 4.0\nn1 = 30.0\nt0 = 3.0 + 4.0\nt1 = t0 * 4.0\nt2 = n1 - t1\nanswer = t2 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "dev" + }, + { + "Input": "the average weight of 26 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg . find the average weights of all the boys in the class .", + "Output Program": [ + "n0 = 26.0\nn1 = 50.25\nn2 = 8.0\nn3 = 45.15\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "49.050000000000004" + ], + "split": "dev" + }, + { + "Input": "a one - foot stick is marked in 1 / 4 and 1 / 5 portion . how many total markings will there be , including the end points ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 1.0\nn3 = 5.0\n\nanswer = n1 + n3\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "dev" + }, + { + "Input": "find out the c . i on rs . 5000 at 4 % p . a . compound half - yearly for 1 1 / 2 years ?", + "Output Program": [ + "n0 = 5000.0\nn1 = 4.0\nn2 = 1.0\nn3 = 1.0\nn4 = 2.0\nt0 = n1 / 100.0\nt1 = 3.0 / n4\nt2 = t0 + n2\nt3 = t2**min(t1, 5)\nt4 = n0 * t3\nanswer = t4 - n0\nprint(answer)" + ], + "Output Answer": [ + "302.9802941364969" + ], + "split": "dev" + }, + { + "Input": "the average score of a cricketer in 2 matches is 30 and in other 3 matches is 40 . then find the average score in all the 5 matches ?", + "Output Program": [ + "n0 = 2.0\nn1 = 30.0\nn2 = 3.0\nn3 = 40.0\nn4 = 5.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = t0 + t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "dev" + }, + { + "Input": "60 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780 . the bigger part is :", + "Output Program": [ + "n0 = 60.0\nn1 = 10.0\nn2 = 22.0\nn3 = 780.0\nt0 = n0 * n1\nt1 = n2 - n1\nt2 = n3 - t0\nt3 = t2 / t1\nanswer = n0 - t3\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "dev" + }, + { + "Input": "there is one 4 - digit whole number n , such that the last 4 digits of n 2 are in fact the original number n", + "Output Program": [ + "n0 = 4.0\nn1 = 4.0\nn2 = 2.0\nt0 = 100.0 * 3.0\nt1 = 12.0 * 4.0\nt2 = 12.0 - 3.0\nt3 = t2 * 1000.0\nt4 = t1 - 10.0\nt5 = n2 * t4\nt6 = t0 + t5\nanswer = t6 + t3\nprint(answer)" + ], + "Output Answer": [ + "9376" + ], + "split": "dev" + }, + { + "Input": "if k is the greatest positive integer such that 3 ^ k is a divisor of 15 ! then k =", + "Output Program": [ + "n0 = 3.0\nn1 = 15.0\nt0 = n1 / n0\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "dev" + }, + { + "Input": "how many of the integers between 15 and 55 are even ?", + "Output Program": [ + "n0 = 15.0\nn1 = 55.0\nt0 = n1 - n0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "dev" + }, + { + "Input": "the grade point average of one third of the classroom is 45 ; the grade point average of the rest is 60 . what is the grade point average of the whole class ?", + "Output Program": [ + "n0 = 45.0\nn1 = 60.0\nt0 = n0 / 3.0\nt1 = n1 / 3.0\nt2 = t1 * 2.0\nanswer = t0 + t2\nprint(answer)" + ], + "Output Answer": [ + "55" + ], + "split": "dev" + }, + { + "Input": "marcella has 24 pairs of shoes . if she loses 9 individual shoes , what is the greatest number of matching pairs she could have left ?", + "Output Program": [ + "import math\nn0 = 24.0\nn1 = 9.0\nt0 = n1 / 2.0\nt1 = math.floor(t0)\nt2 = t1 + 1.0\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "dev" + }, + { + "Input": "he average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 70 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.5\nn2 = 70.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "dev" + }, + { + "Input": "if the function q is defined by the formula q = 5 w / ( 4 h ( z ^ 2 ) ) , by what factor will q be multiplied if w is quadrupled , h is doubled , and z is tripled ?", + "Output Program": [ + "n0 = 5.0\nn1 = 4.0\nn2 = 2.0\nt0 = 3.0**min(n2, 5)\nt1 = n2 * t0\nanswer = n1 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.2222222222222222" + ], + "split": "dev" + }, + { + "Input": "in a certain game , each player scores either 2 points or 5 points . if n players score 2 points and m players score 5 points , and the total number of points scored is 50 , what is the least possible positive difference w between n and m ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 2.0\nn3 = 5.0\nn4 = 50.0\n\nanswer = n1 - n0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "dev" + }, + { + "Input": "h is a positive integer and 225 and 216 are both divisors of h . if h = ( 2 ^ a ) * ( 3 ^ b ) * ( 5 ^ c ) , where a , b and c are positive integers , what is the least possible value of a + b + c ?", + "Output Program": [ + "n0 = 225.0\nn1 = 216.0\nn2 = 2.0\nn3 = 3.0\nn4 = 5.0\nt0 = n3 + n3\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "dev" + }, + { + "Input": "? x 12 = 173 x 240", + "Output Program": [ + "n0 = 12.0\nn1 = 173.0\nn2 = 240.0\nt0 = n1 * n2\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "3460" + ], + "split": "dev" + }, + { + "Input": "a man goes to shopkeeper and says that if u give me as much as i have , i will spend rs . 10 / - on ur shop . shopkeeper agrees and man moves to another shopkeeper ans asked same . at 3 rd shop after all the transaction , he was left with no money . find the initial amount with the man", + "Output Program": [ + "n0 = 10.0\nn1 = 3.0\nt0 = n0 / 2.0\nt1 = n0 + t0\nt2 = t1 / 2.0\nt3 = n0 + t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "8.75" + ], + "split": "dev" + }, + { + "Input": "what is the average of 4 tenths and 5 thousandths ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nt0 = n0 / 10.0\nt1 = 10.0 * 100.0\nt2 = n1 / t1\nt3 = t0 + t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "0.2025" + ], + "split": "dev" + }, + { + "Input": "the average weight of a , b and c is 43 kg . if the average weight of a and b be 48 kg and that of b and c be 42 kg , then the weight of b is :", + "Output Program": [ + "n0 = 43.0\nn1 = 48.0\nn2 = 42.0\nt0 = n1 * 2.0\nt1 = n2 * 2.0\nt2 = n0 * 3.0\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "51" + ], + "split": "dev" + }, + { + "Input": "the number 35 is equal to the sum of the cubes of two integers . what is the product of those integers ?", + "Output Program": [ + "import math\nn0 = 35.0\nt0 = n0 / 2.0\nt1 = 1.0 / 3.0\nt2 = t0**min(t1, 5)\nt3 = math.floor(t2)\nt4 = t3**min(3.0, 5)\nt5 = n0 - t4\nt6 = t5**min(t1, 5)\nanswer = t3 * t6\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "dev" + }, + { + "Input": "positive integer y is 50 percent of 25 percent of positive integer x , and y percent of x equals 100 . what is the value of y ?", + "Output Program": [ + "n0 = 50.0\nn1 = 25.0\nn2 = 100.0\nt0 = n0 / n2\nt1 = n1 / 100.0\nt2 = t0 * t1\nanswer = t2 * 1000.0\nprint(answer)" + ], + "Output Answer": [ + "125" + ], + "split": "dev" + }, + { + "Input": "in simple interest what sum amounts of rs . 1120 / - in 4 years and rs . 1200 / - in 5 years ?", + "Output Program": [ + "n0 = 1120.0\nn1 = 4.0\nn2 = 1200.0\nn3 = 5.0\nt0 = n2 - n0\nt1 = n1 * t0\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "800" + ], + "split": "dev" + }, + { + "Input": "set x consists of all two - digit primes and set y consists of all positive multiples of 4 less than 100 . if the two sets are combined into one , what will be the range of the new set ?", + "Output Program": [ + "n0 = 4.0\nn1 = 100.0\nt0 = n1 - 3.0\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "93" + ], + "split": "dev" + }, + { + "Input": "if x + y = 3 and x 2 y 3 + y 2 x 3 = 27 , what is the value of xy ?", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 2.0\nn2 = 3.0\nn3 = 2.0\nn4 = 3.0\nn5 = 27.0\nt0 = n5 / n0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "dev" + }, + { + "Input": "in one day , juan sends keith 8 times as many messages as he sends laurence , and laurence sends missy 4.5 times as many messages as he receives from juan . if missy received 18 messages from laurence , how many messages does keith receive from juan ?", + "Output Program": [ + "n0 = 8.0\nn1 = 4.5\nn2 = 18.0\nt0 = n2 / n1\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "dev" + }, + { + "Input": "when positive integer x is divided by positive integer y , the remainder is 9 . if x / y = 96.45 , what is the value of y ?", + "Output Program": [ + "import math\nn0 = 9.0\nn1 = 96.45\nt0 = math.floor(n1)\nt1 = n1 - t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "19.999999999999872" + ], + "split": "dev" + }, + { + "Input": "an employee \u2019 s annual salary was increased $ 5000 . if her new annual salary now equals $ 25000 what was the percent increase ?", + "Output Program": [ + "n0 = 5000.0\nn1 = 25000.0\nt0 = n1 - n0\nt1 = t0 / n1\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "dev" + }, + { + "Input": "the arithmetic mean and standard deviation of a certain normal distribution are 14.5 and 1.7 , respectively . what value is exactly 2 standard deviations less than the mean ?", + "Output Program": [ + "n0 = 14.5\nn1 = 1.7\nn2 = 2.0\nt0 = n1 * n2\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "11.1" + ], + "split": "dev" + }, + { + "Input": "what is the x - intercept of a line that passes through the point ( 3 , 4 ) and has a slope of 2 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 2.0\nt0 = n0 * n2\nt1 = t0 - n1\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "dev" + }, + { + "Input": "what least number should be subtracted from 13600 such that the remainder is divisible by 87 ?", + "Output Program": [ + "n0 = 13600.0\nn1 = 87.0\n\nanswer = n0 % n1\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "dev" + }, + { + "Input": "list k consists of 12 consecutive integers . if - 5 is the least integer in list k , what is the range of the positive integers in list k ?", + "Output Program": [ + "n0 = 12.0\nn1 = 5.0\nt0 = n0 - n1\nt1 = t0 - 1.0\nanswer = t1 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "dev" + }, + { + "Input": "a case contains c cartons . each carton contains b boxes , and each box contains 600 paper clips . how many paper clips are contained in 2 cases ?", + "Output Program": [ + "n0 = 600.0\nn1 = 2.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "1200" + ], + "split": "dev" + }, + { + "Input": "an army \u2019 s recruitment process included n rounds of selection tasks . for the first a rounds , the rejection percentage was 60 percent per round . for the next b rounds , the rejection percentage was 50 percent per round and for the remaining rounds , the selection percentage was 70 percent per round . if there were 10000 people who applied for the army and 350 were finally selected , what was the value of n ?", + "Output Program": [ + "n0 = 60.0\nn1 = 50.0\nn2 = 70.0\nn3 = 10000.0\nn4 = 350.0\nt0 = 1.0 + 4.0\nt1 = t0 + 2.0\nanswer = t1 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "dev" + }, + { + "Input": "evaluate : | 8 - 8 ( 3 - 12 ) | - | 5 - 11 | = ?", + "Output Program": [ + "n0 = 8.0\nn1 = 8.0\nn2 = 3.0\nn3 = 12.0\nn4 = 5.0\nn5 = 11.0\nt0 = n2 - n3\nt1 = n4 - n5\nt2 = n1 * t0\nt3 = -t1\nt4 = n0 - t2\nanswer = t4 - t3\nprint(answer)" + ], + "Output Answer": [ + "74" + ], + "split": "dev" + }, + { + "Input": "if a function f is defined by f ( x ) = - 1 / x for all non zero numbers x . if f ( a ) = - 1 / 3 and f ( ab ) = 1 / 6 then b = ?", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 3.0\nn3 = 1.0\nn4 = 6.0\n\nanswer = n4 / n2\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "dev" + }, + { + "Input": "the average of 11 10 prime numbers which are odd is ?", + "Output Program": [ + "n0 = 11.0\nn1 = 10.0\nt0 = n0 / 0.33\nt1 = t0 / 2.0\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "17.666666666666664" + ], + "split": "dev" + }, + { + "Input": "during the first two weeks of january , the total rainfall in springdale was 25 inches . if the rainfall during the second week was 1.5 times the rainfall during the first week , what was the rainfall during the second week of january ?", + "Output Program": [ + "n0 = 25.0\nn1 = 1.5\nt0 = n1 + 1.0\nt1 = n1 / t0\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "dev" + }, + { + "Input": "mary and mike enter into a partnership by investing $ 550 and $ 450 respectively . at the end of one year , they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business . if mary received $ 1000 more than mike did , what was the profit made by their business in that year ?", + "Output Program": [ + "n0 = 550.0\nn1 = 450.0\nn2 = 1000.0\nt0 = n0 / 1000.0\nt1 = n1 / 1000.0\nt2 = 1.0 / 3.0\nt3 = t0 - t1\nt4 = 1.0 - t2\nt5 = t3 * t4\nanswer = n2 / t5\nprint(answer)" + ], + "Output Answer": [ + "14999.999999999995" + ], + "split": "dev" + }, + { + "Input": "if the product of 10 integers is negative , at most how many of the integers can be negative ?", + "Output Program": [ + "n0 = 10.0\n\nanswer = n0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "dev" + }, + { + "Input": "in a division , a student took 63 as divisor instead of 36 . his answer was 24 . the correct answer is -", + "Output Program": [ + "n0 = 63.0\nn1 = 36.0\nn2 = 24.0\nt0 = n0 * n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "dev" + }, + { + "Input": "the sum of the numbers is 550 . if the first number be twice the second and third number be one - third of the first , then the second number is :", + "Output Program": [ + "n0 = 550.0\nt0 = 1.0 + 10.0\nt1 = n0 * 3.0\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "dev" + }, + { + "Input": "a certain kind of necklace is made from 9 green , 6 white , and 3 orange beads . what is the maximum number of these necklaces that can be made from 45 beads of each color ?", + "Output Program": [ + "n0 = 9.0\nn1 = 6.0\nn2 = 3.0\nn3 = 45.0\n\nanswer = n3 / n0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "dev" + }, + { + "Input": "the average of 45 results is 25 and the average of other 25 results is 45 . what is the average of all the results ?", + "Output Program": [ + "n0 = 45.0\nn1 = 25.0\nn2 = 25.0\nn3 = 45.0\nt0 = n0 + n1\nt1 = n0 * n1\nt2 = t1 + t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "32.142857142857146" + ], + "split": "dev" + }, + { + "Input": "10 friends meet for movie 20 for picnic and 5 for games 4 for movie & picnic 2 for movie & games , 0 for picnic & games , 2 for all , how many are students are there in all ?", + "Output Program": [ + "n0 = 10.0\nn1 = 20.0\nn2 = 5.0\nn3 = 4.0\nn4 = 2.0\nn5 = 0.0\nn6 = 2.0\nt0 = n0 + n1\nt1 = t0 - n3\nt2 = n2 + t1\nt3 = t2 - n4\nanswer = n4 + t3\nprint(answer)" + ], + "Output Answer": [ + "31" + ], + "split": "dev" + }, + { + "Input": "alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 961 . find the cost of each ice - cream cup ?", + "Output Program": [ + "n0 = 16.0\nn1 = 5.0\nn2 = 7.0\nn3 = 6.0\nn4 = 6.0\nn5 = 45.0\nn6 = 70.0\nn7 = 961.0\nt0 = n0 * n3\nt1 = n1 * n5\nt2 = n2 * n6\nt3 = n7 - t0\nt4 = t3 - t1\nt5 = t4 - t2\nanswer = t5 / n3\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "dev" + }, + { + "Input": "find large number from below question the difference of two numbers is 1311 . on dividing the larger number by the smaller , we get 11 as quotient and the 11 as remainder", + "Output Program": [ + "n0 = 1311.0\nn1 = 11.0\nn2 = 11.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nt2 = t0 / t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "1430" + ], + "split": "dev" + }, + { + "Input": "a bag contains an equal number of one rupee , 50 paise and 25 paise coins respectively . if the total value is 35 , how many coins of each type are there ?", + "Output Program": [ + "n0 = 50.0\nn1 = 25.0\nn2 = 35.0\nt0 = 1 / 4.0\nt1 = 1 / 2.0\nt2 = t0 + t1\nt3 = t2 + 1.0\nanswer = n2 / t3\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "dev" + }, + { + "Input": "how many positive even integers less than 100 contain digits 5 or 7 ?", + "Output Program": [ + "n0 = 100.0\nn1 = 5.0\nn2 = 7.0\n\nanswer = n1 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "dev" + }, + { + "Input": "the price of a certain painting increased by 25 % during the first year and decreased by 15 % during the second year . the price of the painting at the end of the 2 - year period was what percent of the original price ?", + "Output Program": [ + "n0 = 25.0\nn1 = 15.0\nn2 = 2.0\nt0 = n0 * n1\nt1 = n0 - n1\nt2 = t0 / 100.0\nt3 = t1 - t2\nanswer = t3 + 100.0\nprint(answer)" + ], + "Output Answer": [ + "106.25" + ], + "split": "dev" + }, + { + "Input": "rs . 1010 / - distributed among a , b and c such that on decreasing their shares by rs . 25 , rs . 10 and rs . 15 respectively , the balance money would be divided among them in the ratio 3 : 2 : 5 . then , c \u2019 s share is : ?", + "Output Program": [ + "n0 = 1010.0\nn1 = 25.0\nn2 = 10.0\nn3 = 15.0\nn4 = 3.0\nn5 = 2.0\nn6 = 5.0\nt0 = n1 + n2\nt1 = n4 + n5\nt2 = n3 + t0\nt3 = n6 + t1\nt4 = n0 - t2\nt5 = t4 / t3\nt6 = n6 * t5\nanswer = n3 + t6\nprint(answer)" + ], + "Output Answer": [ + "495" + ], + "split": "dev" + }, + { + "Input": "rs . 1210 were divided among 3 person p , q , r so that p : q = 5 : 4 and q : r = 9 : 10 . then r gets the amount ?", + "Output Program": [ + "n0 = 1210.0\nn1 = 3.0\nn2 = 5.0\nn3 = 4.0\nn4 = 9.0\nn5 = 10.0\nt0 = n2 / n3\nt1 = n5 / n4\nt2 = t0 + t1\nt3 = t2 + 1.0\nt4 = n0 / t3\nanswer = t4 * t1\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "dev" + }, + { + "Input": "a fruit drink is made of orange , watermelon , and grape juice , where 35 percent of the drink is orange juice and 35 percent is watermelon juice . if the drink is made with 45 ounces of grape juice , how many ounces is the drink total ?", + "Output Program": [ + "n0 = 35.0\nn1 = 35.0\nn2 = 45.0\nt0 = n0 + n1\nt1 = n0 * n2\nt2 = n1 * n2\nt3 = 100.0 - t0\nt4 = t1 / t3\nt5 = t2 / t3\nt6 = n2 + t4\nanswer = t6 + t5\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "dev" + }, + { + "Input": "for all real numbers v , an operation is defined by the equation v * = v - v / 3 . if ( v * ) * = 24 , then v =", + "Output Program": [ + "n0 = 3.0\nn1 = 24.0\nt0 = 1.0 / n0\nt1 = 1.0 - t0\nt2 = n1 / t1\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "53.999999999999986" + ], + "split": "dev" + }, + { + "Input": "if w / x = 2 / 3 and w / y = 6 / 15 , then ( x + y ) / y =", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 6.0\nn3 = 15.0\nt0 = n2 / n0\nt1 = n3 / n1\nt2 = t0 / t1\nanswer = t2 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "1.6" + ], + "split": "dev" + }, + { + "Input": "a \u201c palindromic integer \u201d is an integer that remains the same when its digits are reversed . so , for example , 43334 and 516615 are both examples of palindromic integers . how many 6 - digit palindromic integers are both even and greater than 500,000 ?", + "Output Program": [ + "n0 = 43334.0\nn1 = 516615.0\nn2 = 6.0\nn3 = 500000.0\nt0 = n2 - 4.0\nt1 = t0 * 10.0\nanswer = t1 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "dev" + }, + { + "Input": "the average price of an decoration piece increases over the years . if from 1990 to 1996 , the price of the decoration piece increased by 13 % and from 1996 to 2001 it increased by 20 % , what is the price of the decoration piece in 2001 if the price in 1990 was $ 11500 ?", + "Output Program": [ + "n0 = 1990.0\nn1 = 1996.0\nn2 = 13.0\nn3 = 1996.0\nn4 = 2001.0\nn5 = 20.0\nn6 = 2001.0\nn7 = 1990.0\nn8 = 11500.0\nt0 = n5 / 100.0\nt1 = n2 / 100.0\nt2 = t0 + 1.0\nt3 = t1 + 1.0\nt4 = n8 * t3\nanswer = t2 * t4\nprint(answer)" + ], + "Output Answer": [ + "15593.999999999996" + ], + "split": "dev" + }, + { + "Input": "the price of a bushel of corn is currently $ 3.20 , and the price of a peck of wheat is $ 8.80 . the price of corn is increasing at a constant rate of 5 x cents per day while the price of wheat is decreasing at a constant rate of x ( 2 ^ 1 / 2 ) - x cents per day . what is the approximate price when a bushel of corn costs the same amount as a peck of wheat ?", + "Output Program": [ + "import math\nn0 = 3.2\nn1 = 8.8\nn2 = 5.0\nn3 = 2.0\nn4 = 1.0\nn5 = 2.0\nt0 = math.sqrt(max(0, n3))\nt1 = n1 - n0\nt2 = t0 - n4\nt3 = n2 + t2\nt4 = t1 / t3\nt5 = n2 * t4\nanswer = n0 + t5\nprint(answer)" + ], + "Output Answer": [ + "8.371572875253811" + ], + "split": "dev" + }, + { + "Input": "when the price of a product was decreased by 20 % , the number sold increased by 60 % . what was the effect on the total revenue ?", + "Output Program": [ + "n0 = 20.0\nn1 = 60.0\nt0 = n1 / 100.0\nt1 = 100.0 - n0\nt2 = t0 + 1.0\nt3 = t1 / 100.0\nt4 = t2 * t3\nt5 = t4 - 1.0\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "28.000000000000025" + ], + "split": "dev" + }, + { + "Input": "in a rare coin collection , all coins are either pure gold or pure silver , and there is initially one gold coin for every 3 silver coins . with the addition of 15 more gold coins to the collection , the ratio of gold coins to silver coins is 1 to 2 . based on this information , how many total coins are there now in this collection ( after the acquisition ) ?", + "Output Program": [ + "n0 = 3.0\nn1 = 15.0\nn2 = 1.0\nn3 = 2.0\nt0 = n1 * n3\nt1 = n0 * t0\nt2 = t1 + t0\nanswer = n1 + t2\nprint(answer)" + ], + "Output Answer": [ + "135" + ], + "split": "dev" + }, + { + "Input": "a student has to obtain 35 % of the total marks to pass . he got 100 marks and failed by 40 marks . the maximum marks are ?", + "Output Program": [ + "n0 = 35.0\nn1 = 100.0\nn2 = 40.0\nt0 = n1 + n2\nt1 = n0 / 100.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "dev" + }, + { + "Input": "if a : b = 3 : 4 , b : c = 7 : 9 , c : d = 5 : 7 , find a : d ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 7.0\nn3 = 9.0\nn4 = 5.0\nn5 = 7.0\nt0 = n0 * n2\nt1 = n1 * n3\nt2 = n4 * t0\nt3 = n2 * t1\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.4166666666666667" + ], + "split": "dev" + }, + { + "Input": "the average age of an adult class is 40 years . 12 new students with an avg age of 32 years join the class . therefore decreasing the average by 4 year . find what was theoriginal strength of class ?", + "Output Program": [ + "n0 = 40.0\nn1 = 12.0\nn2 = 32.0\nn3 = 4.0\nt0 = n1 * n2\nt1 = n0 - n3\nt2 = n1 * t1\nt3 = t2 - t0\nanswer = t3 / n3\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "dev" + }, + { + "Input": "the total marks obtained by a student in mathematics and physics is 30 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together .", + "Output Program": [ + "n0 = 30.0\nn1 = 20.0\nt0 = n0 + n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "dev" + }, + { + "Input": "solve for x and check : 25 x = 675", + "Output Program": [ + "n0 = 25.0\nn1 = 675.0\nt0 = n1 / n0\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "675" + ], + "split": "dev" + }, + { + "Input": "given that x and y are events such that z ( x ) = 0.02 z ( y ) = 0.10 z ( xny ) = 0.10 z ( x | y ) = find z ( x | y ) and z ( x | y )", + "Output Program": [ + "n0 = 0.02\nn1 = 0.1\nn2 = 0.1\nt0 = n1 / n0\nanswer = 1 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.2" + ], + "split": "dev" + }, + { + "Input": "carrey rented a car for rs . 20 plus rs . 0.25 per kilometer driven . samuel rented a car for rs . 24 plus rs . 0.16 per kilometer driven . if each drove d km . and each was charged exactly the same amount for the rental , then d equals ?", + "Output Program": [ + "n0 = 20.0\nn1 = 0.25\nn2 = 24.0\nn3 = 0.16\nt0 = n2 - n0\nt1 = n1 - n3\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "44.44444444444444" + ], + "split": "dev" + }, + { + "Input": "the first doughnut is priced at $ 1 and then if you purchase additional doughnuts as dozens then the price is $ 6 / dozen . what is the total number of doughnuts purchased if you paid $ 24 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 6.0\nn2 = 24.0\nt0 = n2 / n1\nanswer = t0 * 12.0\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "dev" + }, + { + "Input": "in a certain supermarket , a triangular display of cans is arranged in 9 rows , numbered 1 through 9 from top to bottom . each successively numbered row contains 3 more cans than the row immediately above it . if there are fewer than 120 cans in the entire display , how many cans are in the seventh row ?", + "Output Program": [ + "import math\nn0 = 9.0\nn1 = 1.0\nn2 = 9.0\nn3 = 3.0\nn4 = 120.0\nt0 = n3 + n3\nt1 = n0 - n1\nt2 = n3 * t1\nt3 = n3 * t0\nt4 = t2 / 2.0\nt5 = n0 * t4\nt6 = n4 - t5\nt7 = t6 / n0\nt8 = math.floor(t7)\nanswer = t8 + t3\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "dev" + }, + { + "Input": "the average age of 10 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men . the average age of the two new men is", + "Output Program": [ + "n0 = 10.0\nn1 = 21.0\nn2 = 23.0\nt0 = n1 + n2\nt1 = n0 * 1.0\nt2 = t0 / 2.0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "dev" + }, + { + "Input": "the number of diagonals of a polygon of n sides is given by the formula q = n ( n - 3 ) / 2 . if a polygon has twice as many diagonals as sides , how many sides does it have ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\n\nanswer = n0 + n1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "dev" + }, + { + "Input": "the age of somu is one - third his father ' s . 8 years back he was one - fifth of his father ' s age . what is his persent age ?", + "Output Program": [ + "n0 = 8.0\nt0 = 1.0 + 4.0\nt1 = n0 * t0\nt2 = t0 - 3.0\nt3 = t1 - n0\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "dev" + }, + { + "Input": "exactly 3 / 7 of the people in the room are under the age of 21 , and exactly 5 / 9 of the people in the room are over the age of 65 . if the total number of the people in the room is greater than 50 and less than 100 , how many people in the room are under the age of 21 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 21.0\nn3 = 5.0\nn4 = 9.0\nn5 = 65.0\nn6 = 50.0\nn7 = 100.0\nn8 = 21.0\nt0 = n1 * n4\nt1 = n0 * t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "dev" + }, + { + "Input": "the product of two successive numbers is 7832 . which is the smaller of the two numbers ?", + "Output Program": [ + "import math\nn0 = 7832.0\n\nanswer = math.sqrt(max(0, n0))\nprint(answer)" + ], + "Output Answer": [ + "88.49858755935034" + ], + "split": "dev" + }, + { + "Input": "the value of 3.6 x 0.48 x 2.50 / 0.12 x 0.09 x 0.5 is", + "Output Program": [ + "n0 = 3.6\nn1 = 0.48\nn2 = 2.5\nn3 = 0.12\nn4 = 0.09\nn5 = 0.5\nt0 = n0 * n1\nt1 = n3 * n4\nt2 = n2 * t0\nt3 = n5 * t1\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "800.0000000000001" + ], + "split": "dev" + }, + { + "Input": "if 1 / 8 of a pencil is black 1 / 2 of the remaining is white and the remaining 7 / 2 is blue find the total length of the pencil ?", + "Output Program": [ + "n0 = 1.0\nn1 = 8.0\nn2 = 1.0\nn3 = 2.0\nn4 = 7.0\nn5 = 2.0\nt0 = n0 / n1\nt1 = n0 / n3\nt2 = n4 / n3\nt3 = t0 + t1\nt4 = t3 * t2\nt5 = 1.0 - t3\nt6 = t4 / t5\nanswer = t6 + t2\nprint(answer)" + ], + "Output Answer": [ + "9.333333333333332" + ], + "split": "dev" + }, + { + "Input": "the average temperature for monday , tuesday , wednesday and thursday was 48 degrees and for tuesday , wednesday , thursday and friday was 46 degrees . if the temperature on monday was 42 degrees . find the temperature on friday ?", + "Output Program": [ + "n0 = 48.0\nn1 = 46.0\nn2 = 42.0\nt0 = n0 * 4.0\nt1 = n1 * 4.0\nt2 = t0 - t1\nanswer = n2 - t2\nprint(answer)" + ], + "Output Answer": [ + "34" + ], + "split": "dev" + }, + { + "Input": "a certain taxi company charges $ 2.10 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ?", + "Output Program": [ + "n0 = 2.1\nn1 = 1.0\nn2 = 5.0\nn3 = 0.4\nn4 = 1.0\nn5 = 5.0\nn6 = 8.0\nt0 = n1 / n2\nt1 = n6 / t0\nt2 = t1 - n1\nt3 = n3 * t2\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "17.700000000000003" + ], + "split": "dev" + }, + { + "Input": "in x - y plane , there is a right triangle abc ( \u2220 b = 90 o ) . if the length of ac is 25 and the slope of line segment ac is 4 / 3 , what is the length of ab ?", + "Output Program": [ + "import math\nn0 = 90.0\nn1 = 25.0\nn2 = 4.0\nn3 = 3.0\nt0 = n2**min(2.0, 5)\nt1 = n3**min(2.0, 5)\nt2 = t0 + t1\nt3 = math.sqrt(max(0, t2))\nt4 = n1 / t3\nanswer = n2 * t4\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "dev" + }, + { + "Input": "a palindrome is a number that reads the same forward and backward , such as 343 . how many odd , 8 - digit numbers are palindromes ?", + "Output Program": [ + "n0 = 343.0\nn1 = 8.0\nt0 = n1 / 2.0\nt1 = 10.0**min(t0, 5)\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "5000" + ], + "split": "dev" + }, + { + "Input": "what is the difference between the local value of 1 and 2 in the number 2124 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 2124.0\nt0 = n0 * 100.0\nt1 = n1 * 10.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "dev" + }, + { + "Input": "in 10 years , a will be twice as old as b was 10 years ago . if a is now 7 years older than b the present age of b is", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 7.0\nt0 = n0 * 2.0\nt1 = n0 + t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "37" + ], + "split": "dev" + }, + { + "Input": "the operation is defined for all integers a and b by the equation ab = ( a - 1 ) ( b - 1 ) . if y 12 = 110 , what is the value of y ?", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 12.0\nn3 = 110.0\nt0 = n2 - n0\nt1 = n3 / t0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "dev" + }, + { + "Input": "the overall age of x and y is 19 year greater than the overall age of y and z . z is how many decades younger that x ?", + "Output Program": [ + "n0 = 19.0\n\nanswer = n0 / 1.0\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "dev" + }, + { + "Input": "for all real numbers v , an operation is defined by the equation v * = v - v / 3 . if ( v * ) * = 16 , then v =", + "Output Program": [ + "n0 = 3.0\nn1 = 16.0\nt0 = 1.0 / n0\nt1 = 1.0 - t0\nt2 = n1 / t1\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "35.99999999999999" + ], + "split": "dev" + }, + { + "Input": "country x imposes a two - tiered tax on imported cars : the first tier imposes a tax of 25 % of the car ' s price up to a certain price level . if the car ' s price is higher than the first tier ' s level , the tax on the portion of the price that exceeds this value is 15 % . if ron imported a $ 30000 imported car and ended up paying $ 5500 in taxes , what is the first tier ' s price level ?", + "Output Program": [ + "n0 = 25.0\nn1 = 15.0\nn2 = 30000.0\nn3 = 5500.0\nt0 = n1 / 100.0\nt1 = n0 / 100.0\nt2 = n2 * t0\nt3 = t1 - t0\nt4 = n3 - t2\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "10000" + ], + "split": "dev" + }, + { + "Input": "in the faculty of reverse - engineering , 230 second year students study numeric methods , 423 second year students study automatic control of airborne vehicles and 134 second year students study them both . how many students are there in the faculty if the second year students are approximately 80 % of the total ?", + "Output Program": [ + "n0 = 230.0\nn1 = 423.0\nn2 = 134.0\nn3 = 80.0\n\nanswer = n0 + n1\nprint(answer)" + ], + "Output Answer": [ + "653" + ], + "split": "dev" + }, + { + "Input": "the standard deviation of a normal distribution of data is 2 , and 3 standard deviations below the mean is greater than 48 . what is a possible value for the mean of the distribution ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 48.0\nt0 = n0 * n1\nt1 = n2 + t0\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "55" + ], + "split": "dev" + }, + { + "Input": "if the average of 5 positive integers is 60 and the difference between the largest and the smallest of these 5 numbers is 10 , what is the maximum value possible for the largest of these 5 integers ?", + "Output Program": [ + "n0 = 5.0\nn1 = 60.0\nn2 = 5.0\nn3 = 10.0\nn4 = 5.0\nt0 = n0 * n1\nt1 = t0 - n3\nt2 = t1 / n0\nanswer = n3 + t2\nprint(answer)" + ], + "Output Answer": [ + "68" + ], + "split": "dev" + }, + { + "Input": "sum of 53 odd numbers is ?", + "Output Program": [ + "n0 = 53.0\nt0 = n0 / 2.0\nt1 = n0 * 2.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "2809" + ], + "split": "dev" + }, + { + "Input": "find the value of 5 + 2 \u00e2 \u20ac \u00a2 ( 8 \u00e2 \u20ac \u201c 3 )", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 8.0\nn3 = 3.0\nt0 = n2 - n3\nt1 = n1 * t0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "dev" + }, + { + "Input": "what least number should be added to 1057 , so that the sum is completely divisible by 23", + "Output Program": [ + "n0 = 1057.0\nn1 = 23.0\nt0 = n0 % n1\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "dev" + }, + { + "Input": ". in digging a pond 20 m * 10 m * 5 m the volumes of the soil extracted will be ?", + "Output Program": [ + "n0 = 20.0\nn1 = 10.0\nn2 = 5.0\nt0 = n0 * n1\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "1000" + ], + "split": "dev" + }, + { + "Input": "when 1 / 20 % of 8,000 is subtracted from 1 / 10 of 8,000 , the difference is", + "Output Program": [ + "n0 = 1.0\nn1 = 20.0\nn2 = 8000.0\nn3 = 1.0\nn4 = 10.0\nn5 = 8000.0\nt0 = n2 / n4\nt1 = n1 * 100.0\nt2 = n2 / t1\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "796" + ], + "split": "dev" + }, + { + "Input": "dick and jane each saved $ 5,000 in 1989 . in 1990 dick saved 10 percent more than in 1989 , and together he and jane saved a total of $ 10,000 . approximately what percent less did jane save in 1990 than in 1989 ?", + "Output Program": [ + "n0 = 5000.0\nn1 = 1989.0\nn2 = 1990.0\nn3 = 10.0\nn4 = 1989.0\nn5 = 10000.0\nn6 = 1990.0\nn7 = 1989.0\nt0 = n3 / 100.0\nt1 = t0 + 1.0\nt2 = 2.0 - t1\nt3 = 1.0 - t2\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "10.000000000000009" + ], + "split": "dev" + }, + { + "Input": "robert ate 7 chocolates , nickel ate 5 chocolates . how many more chocolates did robert ate than nickel ?", + "Output Program": [ + "n0 = 7.0\nn1 = 5.0\n\nanswer = n0 - n1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "dev" + }, + { + "Input": "on dividing 109 by a number , the quotient is 9 and the remainder is 1 . find the divisor", + "Output Program": [ + "import math\nn0 = 109.0\nn1 = 9.0\nn2 = 1.0\nt0 = n0 / n1\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "dev" + }, + { + "Input": "having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 1.28 at the candy store . what is john \u2019 s weekly allowance ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 1.28\nt0 = n0 / n1\nt1 = 1.0 / n0\nt2 = 1.0 - t0\nt3 = t1 * t2\nt4 = t0 + t3\nt5 = 1.0 - t4\nanswer = n2 / t5\nprint(answer)" + ], + "Output Answer": [ + "4.799999999999999" + ], + "split": "dev" + }, + { + "Input": "if a person walks at 25 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance traveled by him is :", + "Output Program": [ + "n0 = 25.0\nn1 = 10.0\nn2 = 20.0\nt0 = n0 - n1\nt1 = n2 / t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "13.333333333333332" + ], + "split": "dev" + }, + { + "Input": "a big container is 30 % full with water . if 45 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container ?", + "Output Program": [ + "n0 = 30.0\nn1 = 45.0\nn2 = 3.0\nn3 = 4.0\nt0 = n2 / n3\nt1 = n0 / 100.0\nt2 = t0 - t1\nanswer = n1 / t2\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "dev" + }, + { + "Input": "a \u201c palindromic integer \u201d is an integer that remains the same when its digits are reversed . so , for example , 43334 and 516615 are both examples of palindromic integers . how many 6 - digit palindromic integers are both even and greater than 500000 ?", + "Output Program": [ + "n0 = 43334.0\nn1 = 516615.0\nn2 = 6.0\nn3 = 500000.0\nt0 = n2 - 4.0\nt1 = t0 * 10.0\nanswer = t1 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "dev" + }, + { + "Input": "the average of 7 numbers is 25 . if each number be multiplied by 5 . find the average of new set of numbers ?", + "Output Program": [ + "n0 = 7.0\nn1 = 25.0\nn2 = 5.0\n\nanswer = n1 * n2\nprint(answer)" + ], + "Output Answer": [ + "125" + ], + "split": "dev" + }, + { + "Input": "find the principle on a certain sum of money at 5 % per annum for 2 2 / 5 years if the amount being rs . 1008 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 2.0\nn3 = 5.0\nn4 = 1008.0\nt0 = n1 * n3\nt1 = n1 + t0\nt2 = t1 / n3\nt3 = n0 * t2\nt4 = t3 / 100.0\nt5 = t4 + 1.0\nanswer = n4 / t5\nprint(answer)" + ], + "Output Answer": [ + "899.9999999999999" + ], + "split": "dev" + }, + { + "Input": "at joes steakhouse the hourly wage for a chef is 20 % greater than that of a dishwasher , and the hourly wage of a dishwasher is half as much as the hourly wage of a manager . if a managers wage is $ 7.50 per hour , how much less than a manager does a chef earn each hour ?", + "Output Program": [ + "n0 = 20.0\nn1 = 7.5\nt0 = n0 + 100.0\nt1 = 1.0 / 2.0\nt2 = t0 / 100.0\nt3 = t2 * t1\nt4 = 1.0 - t3\nanswer = n1 * t4\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "dev" + }, + { + "Input": "there are 6 people in the elevator . their average weight is 152 lbs . another person enters the elevator , and increases the average weight to 151 lbs . what is the weight of the 7 th person .", + "Output Program": [ + "n0 = 6.0\nn1 = 152.0\nn2 = 151.0\nn3 = 7.0\nt0 = n2 * n3\nt1 = n0 * n1\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "145" + ], + "split": "dev" + }, + { + "Input": "how much is 70 % of 40 is greater than 4 / 5 of 25 ?", + "Output Program": [ + "n0 = 70.0\nn1 = 40.0\nn2 = 4.0\nn3 = 5.0\nn4 = 25.0\nt0 = n0 / 100.0\nt1 = n2 / n3\nt2 = n1 * t0\nt3 = n4 * t1\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "dev" + }, + { + "Input": "27 is a perfect cube . when x is added to the prime factor of 27 , the result is a prime number . what is x ?", + "Output Program": [ + "n0 = 27.0\nn1 = 27.0\nt0 = n0 - 3.0\nanswer = t0 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "dev" + }, + { + "Input": "the difference between two numbers is 2395 . when the larger number is divided by the smaller one , the quotient is 6 and the remainder is 15 . the smaller number is", + "Output Program": [ + "n0 = 2395.0\nn1 = 6.0\nn2 = 15.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "476" + ], + "split": "dev" + }, + { + "Input": "on dividing 22 by a number , the quotient is 7 and the remainder is 1 . find the divisor .", + "Output Program": [ + "import math\nn0 = 22.0\nn1 = 7.0\nn2 = 1.0\nt0 = n0 / n1\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "dev" + }, + { + "Input": "the smallest number which when diminished by 5 , is divisible by 12 , 16 , 18 , 21 and 28 is", + "Output Program": [ + "n0 = 5.0\nn1 = 12.0\nn2 = 16.0\nn3 = 18.0\nn4 = 21.0\nn5 = 28.0\nt0 = 3.0 + 4.0\nt1 = 3.0**min(2.0, 5)\nt2 = 2.0**min(4.0, 5)\nt3 = t1 * t2\nt4 = t0 * t3\nanswer = t4 + n0\nprint(answer)" + ], + "Output Answer": [ + "1013" + ], + "split": "dev" + }, + { + "Input": "the ratio between x and y is 7 / 5 ; x is multiplied by y and y is multiplied by x , what is the ratio between the new values of x and y ?", + "Output Program": [ + "n0 = 7.0\nn1 = 5.0\nt0 = n0 * n1\nanswer = t0 / t0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "dev" + }, + { + "Input": "when x is multiplied by 3 , the result is 14 more than the result of subtracting x from 26 . what is the value of x ?", + "Output Program": [ + "n0 = 3.0\nn1 = 14.0\nn2 = 26.0\nt0 = n1 + n2\nt1 = 1.0 + 3.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "dev" + }, + { + "Input": "in a house a hall is 20 m long , 15 m wide and 5 m high . its interior has to be covered with mat . what will be the total expenditure if it costs rs . 10 per square m ?", + "Output Program": [ + "n0 = 20.0\nn1 = 15.0\nn2 = 5.0\nn3 = 10.0\nt0 = n0 * n1\nt1 = n0 * n2\nt2 = n1 * n2\nt3 = t0 * 2.0\nt4 = t1 * 2.0\nt5 = t2 * 2.0\nt6 = n3 * t3\nt7 = n3 * t4\nt8 = n3 * t5\nt9 = t6 + t7\nanswer = t9 + t8\nprint(answer)" + ], + "Output Answer": [ + "9500" + ], + "split": "dev" + }, + { + "Input": "a library has an average of 540 visitors on sundays and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :", + "Output Program": [ + "import math\nn0 = 540.0\nn1 = 240.0\nn2 = 30.0\nt0 = 3.0 + 4.0\nt1 = n2 / t0\nt2 = math.floor(t1)\nt3 = t2 + 1.0\nt4 = n0 * t3\nt5 = n2 - t3\nt6 = n1 * t5\nt7 = t4 + t6\nanswer = t7 / n2\nprint(answer)" + ], + "Output Answer": [ + "290" + ], + "split": "dev" + }, + { + "Input": "the total age of a and b is 12 years more than the total age of b and c . c is how many year younger than a", + "Output Program": [ + "n0 = 12.0\n\nanswer = n0 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "dev" + }, + { + "Input": "if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer v that must divide n is ?", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 72.0\nt0 = n1 / n0\nt1 = math.sqrt(max(0, t0))\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "dev" + }, + { + "Input": "if 2 ^ 4 , 3 ^ 3 , and 13 ^ 3 are factors of the product of 1,452 and w , where w is a positive integer , what is the smallest possible value of w ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 3.0\nn3 = 3.0\nn4 = 13.0\nn5 = 3.0\nn6 = 1452.0\nt0 = n0**min(n0, 5)\nt1 = n2**min(n0, 5)\nt2 = t0 * t1\nanswer = n4 * t2\nprint(answer)" + ], + "Output Answer": [ + "468" + ], + "split": "dev" + }, + { + "Input": "a student has to obtain 33 % of the total marks to pass . he got 175 marks and failed by 56 marks . the maximum marks are ?", + "Output Program": [ + "n0 = 33.0\nn1 = 175.0\nn2 = 56.0\nt0 = n1 + n2\nt1 = n0 / 100.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "700" + ], + "split": "dev" + }, + { + "Input": "the maximum number of student amoung them 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :", + "Output Program": [ + "import scipy\nn0 = 1001.0\nn1 = 910.0\n\nanswer = scipy.gcd(int(n0), int(n1))\nprint(answer)" + ], + "Output Answer": [ + "91" + ], + "split": "dev" + }, + { + "Input": "a class of 20 students took a science test . 10 students had an average ( arithmetic mean ) score of 80 . the other students had an average score of 60 . what is the average score of the whole class ?", + "Output Program": [ + "n0 = 20.0\nn1 = 10.0\nn2 = 80.0\nn3 = 60.0\nt0 = n1 * n2\nt1 = n0 - n1\nt2 = n3 * t1\nt3 = t0 + t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "dev" + }, + { + "Input": "x varies inversely as square of y . given that y = 3 for x = 1 . the value of x for y = 9 will be equal to :", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 9.0\nt0 = n0**min(2.0, 5)\nt1 = n2**min(2.0, 5)\nt2 = n1 * t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.1111111111111111" + ], + "split": "dev" + }, + { + "Input": "find the mean proportional between 64 & 81 ?", + "Output Program": [ + "n0 = 64.0\nn1 = 81.0\nt0 = n0 + n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "72.5" + ], + "split": "dev" + }, + { + "Input": "if ( a + b ) = 12 , ( b + c ) = 9 and ( c + d ) = 3 , what is the value of ( a + d ) ?", + "Output Program": [ + "n0 = 12.0\nn1 = 9.0\nn2 = 3.0\nt0 = n0 + n2\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "dev" + }, + { + "Input": "in a store , the total price for 25 shirts is $ 400 and the total price for 75 sweaters is $ 1500 . by how much does the average ( arithmetic mean ) price of a sweater exceed that of a shirt in this store ?", + "Output Program": [ + "n0 = 25.0\nn1 = 400.0\nn2 = 75.0\nn3 = 1500.0\nt0 = n3 / n2\nt1 = n1 / n0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "dev" + }, + { + "Input": "find the average of the first 19 natural numbers ?", + "Output Program": [ + "n0 = 19.0\nt0 = n0 + 1.0\nt1 = t0 / 2.0\nt2 = n0 * t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "dev" + }, + { + "Input": "if the remainder is 11 when positive integer n is divided by 18 , what is the remainder when n is divided by 9 ?", + "Output Program": [ + "n0 = 11.0\nn1 = 18.0\nn2 = 9.0\n\nanswer = n1 / n2\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "dev" + }, + { + "Input": "if n = 16 \u00d7 10 ^ ( - p ) and \u2212 4 < p < 4 , how many different integer values of p will make n a perfect square ?", + "Output Program": [ + "n0 = 16.0\nn1 = 10.0\nn2 = 4.0\nn3 = 4.0\nt0 = n2 / 2.0\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "dev" + }, + { + "Input": "in 10 years , a will be twice as old as b was 10 years ago . if a is now 9 years older than b the present age of b is", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 9.0\nt0 = n0 * 2.0\nt1 = n0 + t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "39" + ], + "split": "dev" + }, + { + "Input": "a store reported total sales of $ 460 million for february of this year . if the total sales for the same month last year was $ 320 million , approximately what was the percent increase in sales ?", + "Output Program": [ + "n0 = 460.0\nn1 = 320.0\nt0 = n0 - n1\nt1 = t0 / n1\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "43.75" + ], + "split": "dev" + }, + { + "Input": "the ratio of a to b is 4 to 5 , where a and b are positive . if x equals a increased by 25 percent of a , and m equals b decreased by 40 percent of b , what is the value of m / x ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 25.0\nn3 = 40.0\nt0 = n2 + 100.0\nt1 = n1 / n0\nt2 = 100.0 - n3\nt3 = t2 / t0\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "0.6" + ], + "split": "dev" + }, + { + "Input": "in a certain country 1 / 5 of 8 = 4 . assuming the same proportion , what would be the value of 1 / 4 of 16 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 8.0\nn3 = 4.0\nn4 = 1.0\nn5 = 4.0\nn6 = 16.0\nt0 = n1 / n2\nanswer = n6 * t0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "dev" + }, + { + "Input": "calculate 24 x 99", + "Output Program": [ + "n0 = 24.0\nn1 = 99.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "2376" + ], + "split": "dev" + }, + { + "Input": "we bought a total of 90 books at the store . math books cost $ 4 and history books cost $ 5 . the total price was $ 390 . how many math books did we buy ?", + "Output Program": [ + "n0 = 90.0\nn1 = 4.0\nn2 = 5.0\nn3 = 390.0\nt0 = n0 * n1\nt1 = n3 - t0\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "dev" + }, + { + "Input": "a number when divided by 133 leaves 16 as a remainder . what will be the remainder if the number is divided by 50 ?", + "Output Program": [ + "n0 = 133.0\nn1 = 16.0\nn2 = 50.0\nt0 = n0 + n1\nanswer = t0 % n2\nprint(answer)" + ], + "Output Answer": [ + "49" + ], + "split": "dev" + }, + { + "Input": "if 1 / ( x + 1 ) + 1 / ( x - 1 ) = 1 / ( x - 1 ) , what is the value of x ?", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 1.0\nn3 = 1.0\nn4 = 1.0\nn5 = 1.0\nt0 = n0 + n0\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "dev" + }, + { + "Input": "evaluate 100 ^ 2 - 99 ^ 2 + 98 ^ 2 - 97 ^ 2 + 96 ^ 2 - 95 ^ 2 + . . . + 2 ^ 2 - 1 ^ 2 = ?", + "Output Program": [ + "n0 = 100.0\nn1 = 2.0\nn2 = 99.0\nn3 = 2.0\nn4 = 98.0\nn5 = 2.0\nn6 = 97.0\nn7 = 2.0\nn8 = 96.0\nn9 = 2.0\nn10 = 95.0\nn11 = 2.0\nn12 = 2.0\nn13 = 2.0\nn14 = 1.0\nn15 = 2.0\nt0 = n0 + 1.0\nt1 = n0 * t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "5050" + ], + "split": "dev" + }, + { + "Input": "the annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years r in which the population would be doubled assuming there is no emigration or immigration is", + "Output Program": [ + "n0 = 1000.0\nn1 = 39.4\nn2 = 19.4\nt0 = 10.0 * 3.0\nt1 = n1 - n2\nt2 = t1 / n0\nt3 = 100.0 - t0\nt4 = t2 * 100.0\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "dev" + }, + { + "Input": "the average ( arithmetic mean ) of 8 numbers is 43.1 . if the sum of half of these numbers is 158.4 , what is the average of the other half ?", + "Output Program": [ + "n0 = 8.0\nn1 = 43.1\nn2 = 158.4\nt0 = n0 / 2.0\nt1 = n0 * n1\nt2 = t1 - n2\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "46.6" + ], + "split": "dev" + }, + { + "Input": "a certain protective additive increases from 30 days to 45 days the time between required maintenance checks on an industrial vehicle . by what percent is the time between maintenance checks increased by using the additive ?", + "Output Program": [ + "n0 = 30.0\nn1 = 45.0\nt0 = n1 - n0\nt1 = t0 / n0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "dev" + }, + { + "Input": "in an examination , 300 students appeared . out of these students ; 30 % got first division , 54 % got second division and the remaining just passed . assuming that no student failed ; find the number of students who just passed .", + "Output Program": [ + "n0 = 300.0\nn1 = 30.0\nn2 = 54.0\nt0 = n1 + n2\nt1 = 100.0 - t0\nt2 = n0 * t1\nanswer = t2 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "dev" + }, + { + "Input": "5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 45 only . men \u00e2 \u20ac \u2122 s wages are ?", + "Output Program": [ + "n0 = 5.0\nn1 = 8.0\nn2 = 45.0\nt0 = n0 * 3.0\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "dev" + }, + { + "Input": "if x is 12 percent greater than 80 , then x =", + "Output Program": [ + "n0 = 12.0\nn1 = 80.0\nt0 = n0 / 100.0\nt1 = n1 * t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "89.6" + ], + "split": "dev" + }, + { + "Input": "the avg weight of a , b & c is 84 kg . if d joins the group , the avg weight of the group becomes 80 kg . if another man e who weights is 8 kg more than d replaces a , then the avgof b , c , d & e becomes 79 kg . what is the weight of a ?", + "Output Program": [ + "n0 = 84.0\nn1 = 80.0\nn2 = 8.0\nn3 = 79.0\nt0 = n1 * 4.0\nt1 = n3 * 4.0\nt2 = n0 * 3.0\nt3 = t0 - t2\nt4 = n2 + t3\nt5 = t1 - t4\nanswer = t0 - t5\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "dev" + }, + { + "Input": "at the end of year x , automobile installment credit accounted for 35 % of all outstanding consumer installment credit . at that time automobile finance companies extended $ 40 billion of credit , or 1 / 3 of the automobile installment credit . how many billion dollars of consumer installment credit was outstanding at that time ?", + "Output Program": [ + "n0 = 35.0\nn1 = 40.0\nn2 = 1.0\nn3 = 3.0\nt0 = n0 / 100.0\nt1 = n1 * n3\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "342.8571428571429" + ], + "split": "dev" + }, + { + "Input": "two kinds of vodka are mixed in the ratio 1 : 2 and 2 : 1 and they are sold fetching the profit 10 % and 40 % respectively . if the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4 / 3 and 5 / 3 times respectively , then the mixture will fetch the profit of", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 2.0\nn3 = 1.0\nn4 = 10.0\nn5 = 35.0\nn6 = 4.0\nn7 = 3.0\nn8 = 5.0\nn9 = 3.0\nt0 = n4 + n8\nt1 = n4 * n6\nt2 = t1 / n1\nanswer = t0 + t2\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "dev" + }, + { + "Input": "the total age of a and b is 16 years more than the total age of b and c . c is how many year younger than", + "Output Program": [ + "n0 = 16.0\n\nanswer = n0 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "dev" + }, + { + "Input": "find large number from below question the difference of two numbers is 1360 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder", + "Output Program": [ + "n0 = 1360.0\nn1 = 6.0\nn2 = 15.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nt2 = t0 / t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "1614" + ], + "split": "dev" + }, + { + "Input": "solve the equation 2 \u2013 x = 2 b \u2013 2 ax , where a and b are real parameters . find for which values of a the equation has for solution a natural number , if b = 7", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 2.0\nn3 = 7.0\nt0 = 1.0 + 1.0\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "dev" + }, + { + "Input": "in a caravan , in addition to 50 hens there are 45 goats and 8 camels with some keepers . if the total number of feet be 224 more than the number of heads , find the number of keepers .", + "Output Program": [ + "n0 = 50.0\nn1 = 45.0\nn2 = 8.0\nn3 = 224.0\nt0 = n0 + n1\nt1 = n0 * 2.0\nt2 = n1 * 4.0\nt3 = n2 * 4.0\nt4 = t1 + t2\nt5 = n2 + t0\nt6 = t4 + t3\nt7 = t6 - t5\nanswer = n3 - t7\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "dev" + }, + { + "Input": "in a village there are 150 men and 90 women in present time . if in next year population will be p = ( a ^ 2 + b ^ 2 ) ^ 1 / 2 , and in every year men are reduces 10 % . what is population of after 2 year .", + "Output Program": [ + "n0 = 150.0\nn1 = 90.0\nn2 = 2.0\nn3 = 2.0\nn4 = 1.0\nn5 = 2.0\nn6 = 10.0\nn7 = 2.0\nt0 = n4 / n6\nt1 = n4 / n2\nt2 = n0**min(2.0, 5)\nt3 = n1**min(2.0, 5)\nt4 = t2 + t3\nt5 = n4 - t0\nt6 = n0 * t5\nt7 = t4**min(t1, 5)\nt8 = t6**min(2.0, 5)\nt9 = t7 - t6\nt10 = t9**min(2.0, 5)\nt11 = t8 + t10\nanswer = t11**min(t1, 5)\nprint(answer)" + ], + "Output Answer": [ + "140.78099890167377" + ], + "split": "dev" + }, + { + "Input": "what is the value of n if the sum of the consecutive odd intergers r from 1 to n equals 169 ?", + "Output Program": [ + "import math\nn0 = 1.0\nn1 = 169.0\nt0 = n0 * 2.0\nt1 = math.sqrt(max(0, n1))\nt2 = t1 * 2.0\nt3 = t2 - t0\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "dev" + }, + { + "Input": "in a bag of small balls 1 / 4 are green , 1 / 8 are blue , 1 / 12 are yellow and the remaining 26 white . how many balls are blue ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 1.0\nn3 = 8.0\nn4 = 1.0\nn5 = 12.0\nn6 = 26.0\nt0 = n0 / n1\nt1 = n0 / n3\nt2 = n0 / n5\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = 1.0 - t4\nt6 = n6 / t5\nanswer = t6 * t1\nprint(answer)" + ], + "Output Answer": [ + "5.999999999999999" + ], + "split": "dev" + }, + { + "Input": "solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 300 milliliters of solution x to create a solution that is 15 percent alcohol by volume ?", + "Output Program": [ + "n0 = 10.0\nn1 = 30.0\nn2 = 300.0\nn3 = 15.0\nt0 = n3 - n0\nt1 = n1 - n3\nt2 = t0 / t1\nanswer = n2 * t2\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "dev" + }, + { + "Input": "which number need to add to 859622 to get a number divisible by 456 ?", + "Output Program": [ + "n0 = 859622.0\nn1 = 456.0\nt0 = n0 % n1\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "859560" + ], + "split": "dev" + }, + { + "Input": "let the number which when multiplied by 16 is increased by 375 .", + "Output Program": [ + "n0 = 16.0\nn1 = 375.0\nt0 = n0 - 1.0\nanswer = n1 / t0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "dev" + }, + { + "Input": "jill has 14 gallons of water stored in quart , half - gallon , and one gallon jars . she has equal numbers of each size jar holding the liquid . what is the total number of water filled jars ?", + "Output Program": [ + "n0 = 14.0\nt0 = 1.0 / 2.0\nt1 = t0 + 0.25\nt2 = t1 + 1.0\nt3 = n0 / t2\nanswer = t3 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "dev" + }, + { + "Input": "john has $ 1,600 at the beginning of his trip , after spending money , he still has exactly $ 600 less than he spent on the trip . how much money does john still have ?", + "Output Program": [ + "n0 = 1600.0\nn1 = 600.0\nt0 = n0 - n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "dev" + }, + { + "Input": "a , b and c started a business by investing rs . 800 / - , rs . 1000 / - and rs . 1200 / - respectively for two years . total profit is rs . 1000 / - . find the c ' s share ?", + "Output Program": [ + "n0 = 800.0\nn1 = 1000.0\nn2 = 1200.0\nn3 = 1000.0\nt0 = n0 + n1\nt1 = n2 + t0\nt2 = n1 / t1\nanswer = n2 * t2\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "dev" + }, + { + "Input": "the positive value of x that satisfies the equation ( 3 + 2 x ) ^ 5 = ( 1 + 3 x ) ^ 4 is between bunuel , can you please explain this one ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 5.0\nn3 = 1.0\nn4 = 3.0\nn5 = 4.0\nt0 = n3 / n1\nanswer = n3 + t0\nprint(answer)" + ], + "Output Answer": [ + "1.5" + ], + "split": "dev" + }, + { + "Input": "in a certain warehouse , 30 percent of the packages weigh less than 75 pounds , and a total of 48 packages weigh less than 25 pounds . if 80 percent of the packages weigh at least 25 pounds , how many of the packages weigh at least 25 pounds but less than 75 pounds ?", + "Output Program": [ + "n0 = 30.0\nn1 = 75.0\nn2 = 48.0\nn3 = 25.0\nn4 = 80.0\nn5 = 25.0\nn6 = 25.0\nn7 = 75.0\nt0 = 100.0 - n4\nt1 = n2 / t0\nt2 = t1 * 100.0\nt3 = n0 * t2\nt4 = t3 / 100.0\nanswer = t4 - n2\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "dev" + }, + { + "Input": "a student took 5 papers in an examination , where the full marks were the same for each paper . his marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10 . in all papers together , the candidate obtained 60 % of the total marks then , the number of papers in which he got more than 50 % marks is", + "Output Program": [ + "n0 = 5.0\nn1 = 6.0\nn2 = 7.0\nn3 = 8.0\nn4 = 9.0\nn5 = 10.0\nn6 = 60.0\nn7 = 50.0\n\nanswer = n0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "dev" + }, + { + "Input": "subtracting 5 % of a from a is equivalent to multiplying a by how much ?", + "Output Program": [ + "n0 = 5.0\nt0 = 100.0 - n0\nanswer = t0 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "0.95" + ], + "split": "dev" + }, + { + "Input": "jansi went out for shopping . she had in her handbag approximately rs . 15 / - in one rupee notes and 20 p . coins . when she returned she had as many one rupee notes as she originally had and as many 20 p . coins as she originally had one rupee notes . she actually came back with about one - third of what she had started out with . how much did she spend and exactly how much did she have with her when she started out ?", + "Output Program": [ + "import math\nn0 = 15.0\nn1 = 20.0\nn2 = 20.0\nt0 = 1.0 / 3.0\nt1 = 100.0 * 3.0\nt2 = n1 * 3.0\nt3 = t1 - n1\nt4 = 100.0 - t2\nt5 = t3 / t4\nt6 = n0 / t5\nt7 = math.floor(t6)\nt8 = n1 * t7\nt9 = t5 * t7\nt10 = t8 / 100.0\nt11 = t10 + t9\nt12 = t11 * t0\nanswer = t11 - t12\nprint(answer)" + ], + "Output Answer": [ + "9.600000000000001" + ], + "split": "dev" + }, + { + "Input": "in a party every person shakes hands with every other person . if there were a total of 120 handshakes in the party then what is the number of persons present in the party ?", + "Output Program": [ + "import math\nn0 = 120.0\nt0 = n0 * 2.0\nt1 = t0 * 4.0\nt2 = t1 + 1.0\nt3 = math.sqrt(max(0, t2))\nt4 = t3 + 1.0\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "dev" + }, + { + "Input": "when positive integer x is divided by positive integer y , the remainder is 6 . if x / y = 96.15 , what is the value of y ?", + "Output Program": [ + "import math\nn0 = 6.0\nn1 = 96.15\nt0 = math.floor(n1)\nt1 = n1 - t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "39.99999999999849" + ], + "split": "dev" + }, + { + "Input": "if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 276 games will be played during the tournament . find the number of participants .", + "Output Program": [ + "import math\nn0 = 276.0\nt0 = n0 * 2.0\nt1 = t0 * 4.0\nt2 = t1 + 1.0\nt3 = math.sqrt(max(0, t2))\nt4 = t3 + 1.0\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "dev" + }, + { + "Input": "3 friends had dinner at a restaurant . when the bill was received , akshitha paid 3 / 4 as much as veena paid and veena paid 1 / 2 as much as lasya paid . what fraction of the bill did veena pay ?", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 4.0\nn3 = 1.0\nn4 = 2.0\nt0 = n0 + n2\nt1 = n2 * n4\nt2 = t0 + t1\nanswer = n2 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.26666666666666666" + ], + "split": "dev" + }, + { + "Input": "a number x is 5 times another number y . the percentage that y is less than x is", + "Output Program": [ + "n0 = 5.0\nt0 = n0 - 1.0\nt1 = t0 / n0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "dev" + }, + { + "Input": "marketing executives for a certain chewing gum company projected a 40 percent increase in revenue this year over that of last year , but revenue this year actually decreased by 30 % . what percent of the projected revenue was the actual revenue ?", + "Output Program": [ + "n0 = 40.0\nn1 = 30.0\nt0 = n0 + 100.0\nt1 = 100.0 - n1\nt2 = t1 / t0\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "dev" + }, + { + "Input": "at a certain restaurant , the average ( arithmetic mean ) number of customers served for the past x days was 65 . if the restaurant serves 120 customers today , raising the average to 90 customers per day , what is the value of x ?", + "Output Program": [ + "n0 = 65.0\nn1 = 120.0\nn2 = 90.0\nt0 = n1 - n2\nt1 = n2 - n0\nt2 = n1 - 100.0\nt3 = t0 / t1\nt4 = t2 / 100.0\nanswer = t3 - t4\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "dev" + }, + { + "Input": "the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 148 , what is the difference between the ages of patrick and monica ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 3.0\nn3 = 5.0\nn4 = 148.0\nt0 = n0 * n0\nt1 = n1 * n0\nt2 = n1 * n3\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n4 / t4\nt6 = t5 * t2\nt7 = t5 * t0\nanswer = t6 - t7\nprint(answer)" + ], + "Output Answer": [ + "48.326530612244895" + ], + "split": "dev" + }, + { + "Input": "you collect baseball cards . suppose you start out with 15 . maria takes half of one more than the number of baseball cards you have . since you ' re nice , you give peter 1 baseball card . since his father makes baseball cards , paul decides to triple your baseball cards . how many baseball cards do you have at the end ?", + "Output Program": [ + "n0 = 15.0\nn1 = 1.0\nt0 = n0 - 4.0\nt1 = t0 - 4.0\nt2 = t1 - n1\nanswer = t2 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "dev" + }, + { + "Input": "xavier , yvonne , and zelda each try independently to solve a problem . if their individual probabilities for success are 1 / 4 , 2 / 3 and 5 / 8 , respectively , what is the probability that xavier and yvonne , but not zelda , will solve the problem ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 2.0\nn3 = 3.0\nn4 = 5.0\nn5 = 8.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = n4 / n5\nt3 = t0 * t1\nt4 = 1.0 - t2\nanswer = t3 * t4\nprint(answer)" + ], + "Output Answer": [ + "0.0625" + ], + "split": "dev" + }, + { + "Input": "in a certain lottery , the probability that a number between 1 and 15 , inclusive , is drawn is 1 / 3 . if the probability that a number 1 or larger is drawn is 2 / 3 , what is the probability that a number less than or equal to 15 is drawn ?", + "Output Program": [ + "n0 = 1.0\nn1 = 15.0\nn2 = 1.0\nn3 = 3.0\nn4 = 1.0\nn5 = 2.0\nn6 = 3.0\nn7 = 15.0\nt0 = n0 / n3\nt1 = n5 / n3\nt2 = n0 + t0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "0.6666666666666666" + ], + "split": "dev" + }, + { + "Input": "if x is less than y by 25 % then y exceed x by :", + "Output Program": [ + "n0 = 25.0\nt0 = 100.0 - n0\nt1 = 100.0 / t0\nt2 = t1 - 1.0\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "33.33333333333333" + ], + "split": "dev" + }, + { + "Input": "a pharmaceutical company received $ 8 million in royalties on the first $ 20 million in sales of the generic equivalent of one of its products and then $ 9 million in royalties on the next $ 108 million in sales . by approximately what percent did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 108 million in sales ?", + "Output Program": [ + "n0 = 8.0\nn1 = 20.0\nn2 = 9.0\nn3 = 108.0\nn4 = 20.0\nn5 = 108.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = t0 * 100.0\nt3 = t1 * 100.0\nt4 = t2 - t3\nt5 = t4 / t2\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "79.16666666666667" + ], + "split": "dev" + }, + { + "Input": "how many digits are required to number a book containing 240 pages ?", + "Output Program": [ + "n0 = 240.0\nt0 = 10.0 - 1.0\nt1 = n0 - 100.0\nt2 = t1 + 1.0\nt3 = t0 * 10.0\nt4 = t3 * 2.0\nt5 = t2 * 3.0\nt6 = t4 + t0\nanswer = t6 + t5\nprint(answer)" + ], + "Output Answer": [ + "612" + ], + "split": "dev" + }, + { + "Input": "out of 40 applicants to a law school , 15 majored in political science , 20 had a grade point average higher than 3.0 , and 10 did not major in political science and had a gpa equal to or lower than 3.0 . how many e applicants majored in political science and had a gpa higher than 3.0 ?", + "Output Program": [ + "n0 = 40.0\nn1 = 15.0\nn2 = 20.0\nn3 = 3.0\nn4 = 10.0\nn5 = 3.0\nn6 = 3.0\nt0 = n1 + n4\nt1 = n0 - t0\nanswer = n2 - t1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "dev" + }, + { + "Input": "in august , a cricket team that played 120 matches won 24 % of the games it played . after a continuous winning streak , this team raised its average to 52 % . how many matches did the team win to attain this average ?", + "Output Program": [ + "n0 = 120.0\nn1 = 24.0\nn2 = 52.0\nt0 = n2 / 100.0\nt1 = n1 / 100.0\nt2 = n0 * t0\nt3 = n0 * t1\nt4 = 1.0 - t0\nt5 = t2 - t3\nanswer = t5 / t4\nprint(answer)" + ], + "Output Answer": [ + "70.00000000000001" + ], + "split": "dev" + }, + { + "Input": "a ( 3 , w ^ 3 ) is the ( x , y ) coordinate of point located on the parabola y = x ^ 2 - 1 . what is the value of w ?", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 2.0\nn3 = 1.0\nt0 = n3 / n0\nt1 = n0**min(n2, 5)\nt2 = t1 - n3\nanswer = t2**min(t0, 5)\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "dev" + }, + { + "Input": "in x game of billiards , x can give y 20 points in 60 and he can give z 30 points in 60 . how many points can y give z in x game of 120 ?", + "Output Program": [ + "n0 = 20.0\nn1 = 60.0\nn2 = 30.0\nn3 = 60.0\nn4 = 120.0\nt0 = n1 - n0\nt1 = n1 - n2\nt2 = t0 * 3.0\nt3 = t1 * 3.0\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "dev" + }, + { + "Input": "in a factory , an average of 60 tv ' s are produced per day for the fist 25 days of the months . a few workers fell ill for the next 5 days reducing the daily avg for the month to 58 sets / day . the average production per day for day last 5 days is ?", + "Output Program": [ + "n0 = 60.0\nn1 = 25.0\nn2 = 5.0\nn3 = 58.0\nn4 = 5.0\nt0 = n1 + n2\nt1 = n0 * n1\nt2 = n3 * t0\nt3 = t2 - t1\nanswer = t3 / n2\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "dev" + }, + { + "Input": "a collection of books went on sale , and 2 / 3 of them were sold for $ 4.25 each . if none of the 30 remaining books were sold , what was the total amount received for the books that were sold ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 4.25\nn3 = 30.0\nt0 = n2 / n1\nt1 = 1.0 / n1\nt2 = n3 * t0\nt3 = t2 / t1\nanswer = n0 * t3\nprint(answer)" + ], + "Output Answer": [ + "255" + ], + "split": "dev" + }, + { + "Input": "in n is a positive integer less than 200 , and 14 n / 60 is an integer , then n has how many different positive prime factors s ?", + "Output Program": [ + "n0 = 200.0\nn1 = 14.0\nn2 = 60.0\nt0 = 1.0 + 4.0\nt1 = n2 / 2.0\nt2 = t1 / 2.0\nt3 = t2 / 3.0\nt4 = t0 / t3\nanswer = t4 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "dev" + }, + { + "Input": "the number obtained by interchanging the digits of a two - digit number is less than the original number by 36 . the sum of the digits of the number is 8 . what is the original number ?", + "Output Program": [ + "n0 = 36.0\nn1 = 8.0\nt0 = n1 + 10.0\nt1 = n0 / t0\nt2 = n1 - t1\nt3 = t2 * 10.0\nanswer = t1 + t3\nprint(answer)" + ], + "Output Answer": [ + "62" + ], + "split": "dev" + }, + { + "Input": "the population of 6 villages is 803 , 9001100 , 1023945 and 980 . what is the population of the seventh village if the average population of the 7 villages is 1000 ?", + "Output Program": [ + "n0 = 6.0\nn1 = 803.0\nn2 = 9001100.0\nn3 = 1023945.0\nn4 = 980.0\nn5 = 7.0\nn6 = 1000.0\nt0 = 10.0 + 10.0\nt1 = n5 * n6\nt2 = n0 * n4\nt3 = n5 * n5\nt4 = t2 - t3\nt5 = t4 - 100.0\nt6 = t0 + t5\nanswer = t1 - t6\nprint(answer)" + ], + "Output Answer": [ + "1249" + ], + "split": "dev" + }, + { + "Input": "if 625 ^ ( - x ) + 25 ^ ( - 2 x ) + 5 ^ ( - 4 x ) = 14 , what is the value of x ?", + "Output Program": [ + "n0 = 625.0\nn1 = 25.0\nn2 = 2.0\nn3 = 5.0\nn4 = 4.0\nn5 = 14.0\n\nanswer = 1.0 / n4\nprint(answer)" + ], + "Output Answer": [ + "0.25" + ], + "split": "dev" + }, + { + "Input": "if a , b , c , d , e and f are integers and ( ab + cdef ) < 0 , then what is the maximum number d of integers that can be negative ?", + "Output Program": [ + "n0 = 0.0\nt0 = 10.0 / 2.0\nanswer = n0 + t0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "dev" + }, + { + "Input": "if the price of a certain computer increased 30 percent from c dollars to 351 dollars , then 2 c =", + "Output Program": [ + "n0 = 30.0\nn1 = 351.0\nn2 = 2.0\nt0 = n0 + 100.0\nt1 = t0 / 100.0\nt2 = n1 / t1\nanswer = n2 * t2\nprint(answer)" + ], + "Output Answer": [ + "540" + ], + "split": "dev" + }, + { + "Input": "a computer manufacturer produces a certain electronic component at a cost of $ 80 per component . shipping costs for delivering the components are $ 5 per unit . further , the manufacturer has costs of $ 16500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 150 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?", + "Output Program": [ + "n0 = 80.0\nn1 = 5.0\nn2 = 16500.0\nn3 = 150.0\nt0 = n0 + n1\nt1 = 4.0 * 4.0\nt2 = n1 * 100.0\nt3 = t1 * 1000.0\nt4 = n3 * t0\nt5 = t3 + t2\nt6 = t5 + t4\nanswer = t6 / n3\nprint(answer)" + ], + "Output Answer": [ + "195" + ], + "split": "dev" + }, + { + "Input": "the average runs scored by a batsman in 30 matches is 50 . in the next 15 matches the batsman scored an average of 26 runs . find his average in all the 45 matches ?", + "Output Program": [ + "n0 = 30.0\nn1 = 50.0\nn2 = 15.0\nn3 = 26.0\nn4 = 45.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "dev" + }, + { + "Input": "what is the sum of the multiples of 4 between 63 and 151 inclusive ?", + "Output Program": [ + "n0 = 4.0\nn1 = 63.0\nn2 = 151.0\nt0 = n1 + 2.0\nt1 = n2 - 3.0\nt2 = t0 + t1\nt3 = t1 - t0\nt4 = t3 / n0\nt5 = t2 / 2.0\nt6 = t4 + 1.0\nanswer = t6 * t5\nprint(answer)" + ], + "Output Answer": [ + "2316.375" + ], + "split": "dev" + }, + { + "Input": "a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 46.24 , the number of the member is the group is :", + "Output Program": [ + "import math\nn0 = 46.24\nt0 = n0 * 100.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "68" + ], + "split": "dev" + }, + { + "Input": "arnold and danny are two twin brothers that are celebrating their birthday . the product of their ages today is smaller by 15 from the product of their ages a year from today . what is their age today ?", + "Output Program": [ + "n0 = 15.0\nt0 = n0 - 1.0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "dev" + }, + { + "Input": "when x is multiplied by 2 , the result is 19 more than the result of subtracting x from 26 . what is the value of x ?", + "Output Program": [ + "n0 = 2.0\nn1 = 19.0\nn2 = 26.0\nt0 = n1 + n2\nt1 = 1.0 + n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "dev" + }, + { + "Input": "the average of marks obtained by 120 boys was 38 . if the average of marks of passed boys was 39 and that of failed boys was 15 , the number of boys who passed the examination is ?", + "Output Program": [ + "n0 = 120.0\nn1 = 38.0\nn2 = 39.0\nn3 = 15.0\nt0 = n0 * n1\nt1 = n0 * n3\nt2 = n2 - n3\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "115" + ], + "split": "dev" + }, + { + "Input": "if x , y , and z are positive integers , and 2 x = 5 y = 8 z , then the least possible value of x + y + z is", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 8.0\nt0 = n0 * n1\nt1 = n2 * t0\nt2 = t1 / 2.0\nt3 = t2 / n0\nt4 = t2 / n1\nt5 = t2 / n2\nt6 = t3 + t4\nanswer = t6 + t5\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "dev" + }, + { + "Input": "5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 180 only . men \u00e2 \u20ac \u2122 s wages are ?", + "Output Program": [ + "n0 = 5.0\nn1 = 8.0\nn2 = 180.0\nt0 = n0 * 3.0\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "dev" + }, + { + "Input": "a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 72.25 , the number of the member is the group is :", + "Output Program": [ + "import math\nn0 = 72.25\nt0 = n0 * 100.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "85" + ], + "split": "dev" + }, + { + "Input": "if y > 0 , ( 2 y ) / 10 + ( 3 y ) / 10 is what percent of y ?", + "Output Program": [ + "n0 = 0.0\nn1 = 2.0\nn2 = 10.0\nn3 = 3.0\nn4 = 10.0\nt0 = n1 / n2\nt1 = n3 / n4\nt2 = t0 + t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "dev" + }, + { + "Input": "a man can swim in still water at 3 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ?", + "Output Program": [ + "n0 = 3.0\n\nanswer = n0 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "dev" + }, + { + "Input": "a number x is multiplied by 3 , and this product is then divided by 7 . if the positive square root of the result of these two operations equals x , what is the value of x if x \u2260 0 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 0.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.42857142857142855" + ], + "split": "dev" + }, + { + "Input": "joan took out a mortgage from hel local bank . each monthly mortgage payment she makes must be triple the amount of the previous month ' s payment . if her first payment is $ 100 , and the total amount she must pay back is $ 914800 , how many months will it take joan to pay back her mortgage ?", + "Output Program": [ + "import math\nn0 = 100.0\nn1 = 914800.0\nt0 = math.log(max(1e-5, 3.0), 2)\nt1 = n1 * 2.0\nt2 = t1 / n0\nt3 = t2 + 1.0\nt4 = math.log(max(1e-5, t3), 2)\nanswer = t4 / t0\nprint(answer)" + ], + "Output Answer": [ + "8.933535963686566" + ], + "split": "dev" + }, + { + "Input": "the grade point average of the entire class is 80 . if the average of one fourth of the class is 92 , what is the average of the rest of the class ?", + "Output Program": [ + "n0 = 80.0\nn1 = 92.0\nt0 = n0 * 4.0\nt1 = 4.0 - 1.0\nt2 = t0 - n1\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "76" + ], + "split": "dev" + }, + { + "Input": "( p / q - q / p ) = 21 / 10 . then find 4 p / q + 4 q / p ?", + "Output Program": [ + "n0 = 21.0\nn1 = 10.0\nn2 = 4.0\nn3 = 4.0\nt0 = n0 + n1\nt1 = n2 + 1.0\nt2 = n2 * n2\nt3 = t0 + t2\nt4 = t3 + 1.0\nt5 = t4 + 10.0\nanswer = t5 / t1\nprint(answer)" + ], + "Output Answer": [ + "11.6" + ], + "split": "dev" + }, + { + "Input": "a pupil ' s marks were wrongly entered as 85 instead of 45 . due to that the average marks for the class got increased by half . the number of pupils in the class is :", + "Output Program": [ + "n0 = 85.0\nn1 = 45.0\nt0 = n0 - n1\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "dev" + }, + { + "Input": "if the arithmetic mean of p and q is 10 and the arithmetic mean of q and r is 22 , what is the value of r - p ?", + "Output Program": [ + "n0 = 10.0\nn1 = 22.0\nt0 = n1 * 2.0\nt1 = n0 * 2.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "dev" + }, + { + "Input": "a man is 28 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ?", + "Output Program": [ + "n0 = 28.0\nt0 = 2.0 * 2.0\nt1 = 2.0 - 1.0\nt2 = t0 - 2.0\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "dev" + }, + { + "Input": "in an examination , 30 % of total students failed in hindi , 42 % failed in english and 28 % in both . the percentage of these who passed in both the subjects is :", + "Output Program": [ + "n0 = 30.0\nn1 = 42.0\nn2 = 28.0\nt0 = n0 + n1\nt1 = t0 - n2\nanswer = 100.0 - t1\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "dev" + }, + { + "Input": "on dividing 52 by a number , the quotient is 16 and the remainder is 4 . find the divisor ?", + "Output Program": [ + "import math\nn0 = 52.0\nn1 = 16.0\nn2 = 4.0\nt0 = n0 / n1\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "dev" + }, + { + "Input": "jim \u00e2 \u20ac \u2122 s taxi service charges an initial fee of $ 2.5 at the beginning of a trip and an additional charge of $ 0.35 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?", + "Output Program": [ + "n0 = 2.5\nn1 = 0.35\nn2 = 2.0\nn3 = 5.0\nn4 = 3.6\nt0 = n2 / n3\nt1 = n4 / t0\nt2 = n1 * t1\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "5.65" + ], + "split": "dev" + }, + { + "Input": "the average salary of the employees in a office is rs . 120 / month . the avg salary of officers is rs . 430 and of non officers is rs 110 . if the no . of officers is 15 , then find the no of nonofficers in the office .", + "Output Program": [ + "n0 = 120.0\nn1 = 430.0\nn2 = 110.0\nn3 = 15.0\nt0 = n1 * n3\nt1 = n0 * n3\nt2 = n0 - n2\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "465" + ], + "split": "dev" + }, + { + "Input": "dacid obtained 90 , 92 , 85 , 87 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?", + "Output Program": [ + "n0 = 90.0\nn1 = 92.0\nn2 = 85.0\nn3 = 87.0\nn4 = 85.0\nn5 = 100.0\nt0 = n0 + n1\nt1 = 10.0 / 2.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "87.8" + ], + "split": "dev" + }, + { + "Input": "the sum of ages of 5 children born at the intervals of 3 years each is 55 years . what is the age of the youngest child ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nn2 = 55.0\nt0 = n2 / n0\nt1 = t0 - n1\nanswer = t1 - n1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "dev" + }, + { + "Input": "workers decided to raise rs . 3 lacs by equal contribution from each . had they contributed rs . 50 eachextra , the contribution would have been rs . 3.75 lacs . how many workers were they ?", + "Output Program": [ + "n0 = 3.0\nn1 = 50.0\nn2 = 3.75\nt0 = n2 - n0\nt1 = t0 * 1000.0\nt2 = t1 * 100.0\nanswer = t2 / n1\nprint(answer)" + ], + "Output Answer": [ + "1500" + ], + "split": "dev" + }, + { + "Input": "what is the smallest integer that is multiple of 5 , 711", + "Output Program": [ + "n0 = 5.0\nn1 = 711.0\nt0 = 3.0 + 4.0\nt1 = 12.0 - 1.0\nt2 = t0 * t1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "385" + ], + "split": "dev" + }, + { + "Input": "the average waight of a , b , c is 45 kg . the avgwgt of a & b be 40 kg & that of b , c be 43 kg . find the wgt of b .", + "Output Program": [ + "n0 = 45.0\nn1 = 40.0\nn2 = 43.0\nt0 = n1 * 2.0\nt1 = n2 * 2.0\nt2 = n0 * 3.0\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "31" + ], + "split": "dev" + }, + { + "Input": "a father is now 3 times as old as his son . 8 years back , he was 4 times as old as his son . the age of the son ( in years ) is", + "Output Program": [ + "n0 = 3.0\nn1 = 8.0\nn2 = 4.0\nt0 = n1 * n2\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "dev" + }, + { + "Input": "in a house a hall is 20 m long , 15 m wide and 5 m high . its interior has to be covered with mat . what will be the total expenditure if it costs rs . 40 per square m ?", + "Output Program": [ + "n0 = 20.0\nn1 = 15.0\nn2 = 5.0\nn3 = 40.0\nt0 = n0 * n1\nt1 = n0 * n2\nt2 = n1 * n2\nt3 = t0 * 2.0\nt4 = t1 * 2.0\nt5 = t2 * 2.0\nt6 = n3 * t3\nt7 = n3 * t4\nt8 = n3 * t5\nt9 = t6 + t7\nanswer = t9 + t8\nprint(answer)" + ], + "Output Answer": [ + "38000" + ], + "split": "dev" + }, + { + "Input": "at a restaurant , glasses are stored in two different - sized boxes . one box contains 12 glasses , and the other contains 16 glasses . if the average number of glasses per box is 15 , and there are 16 more of the larger boxes , what is the total number of glasses e at the restaurant ? ( assume that all boxes are filled to capacity . )", + "Output Program": [ + "n0 = 12.0\nn1 = 16.0\nn2 = 15.0\nn3 = 16.0\nt0 = n1 * 2.0\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "480" + ], + "split": "dev" + }, + { + "Input": "a ship 77 km from the shore , springs a leak which admits to 9 / 4 tonnes of water in 11 / 2 minutes . 92 tonnes of water would sink it . but the pumps can throw out 12 tonnes of water per hour . find the average rate of sailing so that the ship may just reach the shore as it begins to sink .", + "Output Program": [ + "n0 = 77.0\nn1 = 9.0\nn2 = 4.0\nn3 = 11.0\nn4 = 2.0\nn5 = 92.0\nn6 = 12.0\nt0 = n1 / n2\nt1 = n3 / n4\nt2 = t1 / 60.0\nt3 = t0 / t2\nt4 = t3 - n6\nt5 = n5 / t4\nanswer = n0 / t5\nprint(answer)" + ], + "Output Answer": [ + "10.500000000000002" + ], + "split": "dev" + }, + { + "Input": "a library has an average of 600 visitors on sundays and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :", + "Output Program": [ + "import math\nn0 = 600.0\nn1 = 240.0\nn2 = 30.0\nt0 = 3.0 + 4.0\nt1 = n2 / t0\nt2 = math.floor(t1)\nt3 = t2 + 1.0\nt4 = n0 * t3\nt5 = n2 - t3\nt6 = n1 * t5\nt7 = t4 + t6\nanswer = t7 / n2\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "dev" + }, + { + "Input": "if a person walks at 20 km / hr instead of 10 km / hr , he would have walked 40 km more . the actual distance traveled by him is ?", + "Output Program": [ + "n0 = 20.0\nn1 = 10.0\nn2 = 40.0\nt0 = n0 - n1\nt1 = n2 / t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "dev" + }, + { + "Input": "there are 840 male and female participants in a meeting . half the female participants and one - quarterof the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?", + "Output Program": [ + "n0 = 840.0\nt0 = n0 / 3.0\nt1 = t0 * 4.0\nt2 = t1 - n0\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "140" + ], + "split": "dev" + }, + { + "Input": "the average temperature for monday , tuesday , wednesday and thursday was 48 degrees and for tuesday , wednesday , thursday and friday was 46 degrees . if the temperature on monday was 40 degrees . find the temperature on friday ?", + "Output Program": [ + "n0 = 48.0\nn1 = 46.0\nn2 = 40.0\nt0 = n0 * 4.0\nt1 = n1 * 4.0\nt2 = t0 - t1\nanswer = n2 - t2\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "dev" + }, + { + "Input": "find k if 64 / k = 4 .", + "Output Program": [ + "n0 = 64.0\nn1 = 4.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "dev" + }, + { + "Input": "if 1 + 3 = 10 ; 3 + 5 = 52 ; 5 + 7 = 174 then 7 + 11 = ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 10.0\nn3 = 3.0\nn4 = 5.0\nn5 = 52.0\nn6 = 5.0\nn7 = 7.0\nn8 = 174.0\nn9 = 7.0\nn10 = 11.0\nt0 = n9**min(n3, 5)\nt1 = n10**min(2.0, 5)\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "464" + ], + "split": "dev" + }, + { + "Input": "10 play kabadi , 30 play kho kho only , 5 play both gmaes . then how many in total ?", + "Output Program": [ + "n0 = 10.0\nn1 = 30.0\nn2 = 5.0\nt0 = n1 + n2\nt1 = n0 + t0\nanswer = t1 - n2\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "dev" + }, + { + "Input": "a student chose a number , multiplied it by 2 , then subtracted 138 from the result and got 110 . what was the number he chose ?", + "Output Program": [ + "n0 = 2.0\nn1 = 138.0\nn2 = 110.0\nt0 = n1 + n2\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "124" + ], + "split": "dev" + }, + { + "Input": "set s consists of integers { 8 , 11 , 12 , 14 , 15 } . if integer n is included in the set , the average ( arithmetic mean ) of set s will increase by 25 % . what is the value of integer n ?", + "Output Program": [ + "n0 = 8.0\nn1 = 11.0\nn2 = 12.0\nn3 = 14.0\nn4 = 15.0\nn5 = 25.0\nt0 = n2 + n3\nanswer = n3 + t0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "dev" + }, + { + "Input": "the average marks obtained by 50 candidates in a certain examination is 40 . find the total marks .", + "Output Program": [ + "n0 = 50.0\nn1 = 40.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "2000" + ], + "split": "dev" + }, + { + "Input": "3 ltr of water is added with 9 ltr of a solution containing 57 % of alcohol in the water . the % of alcohol in the new mixture is ?", + "Output Program": [ + "n0 = 3.0\nn1 = 9.0\nn2 = 57.0\nt0 = n0 + n1\nt1 = n2 / 100.0\nt2 = n1 * t1\nt3 = t2 / t0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "42.75" + ], + "split": "dev" + }, + { + "Input": "the batting average of a particular batsman is 60 runs in 46 innings . if the difference in his highest and lowest score is 140 runs and his average excluding these two innings is 58 runs , find his highest score .", + "Output Program": [ + "n0 = 60.0\nn1 = 46.0\nn2 = 140.0\nn3 = 58.0\nt0 = n0 * n1\nt1 = n1 - 2.0\nt2 = n3 * t1\nt3 = t0 - t2\nt4 = n2 + t3\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "174" + ], + "split": "dev" + }, + { + "Input": "if m ^ 2 - 8 m + 1 = 0 , then m ^ 3 + m ^ ( - 3 ) = ?", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 8.0\nn2 = 1.0\nn3 = 0.0\nn4 = 3.0\nn5 = 3.0\nt0 = 4.0 + 4.0\nt1 = 10.0 + 10.0\nt2 = 10.0 * 4.0\nt3 = t1 + t2\nt4 = math.sqrt(max(0, t3))\nt5 = t0 + t4\nt6 = t5 / n0\nanswer = t6**min(n4, 5)\nprint(answer)" + ], + "Output Answer": [ + "487.9979508110673" + ], + "split": "dev" + }, + { + "Input": "if 3 a \u2013 3 b \u2013 2 c = 32 and \u221a 3 a - \u221a ( 2 b + 2 c ) = 4 , what is the value of a + b + c ?", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 2.0\nn3 = 32.0\nn4 = 3.0\nn5 = 2.0\nn6 = 2.0\nn7 = 4.0\nt0 = n3 - n7\nt1 = t0 - n7\nt2 = t1 - 2.0\nt3 = t2 - 2.0\nt4 = t3 - 1.0\nt5 = t4 - n0\nt6 = t5 - 1.0\nt7 = n2 + t6\nt8 = t7 - n0\nanswer = t8 - 4.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "dev" + }, + { + "Input": "what is the dividend . divisor 15 , the quotient is 8 and the remainder is 5", + "Output Program": [ + "n0 = 15.0\nn1 = 8.0\nn2 = 5.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "125" + ], + "split": "dev" + }, + { + "Input": "on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 360 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?", + "Output Program": [ + "n0 = 360.0\n\nanswer = n0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "720" + ], + "split": "dev" + }, + { + "Input": "the cash realised on selling a 14 % stock is rs . 106.25 , brokerage being 1 / 4 % is ?", + "Output Program": [ + "n0 = 14.0\nn1 = 106.25\nn2 = 1.0\nn3 = 4.0\nt0 = n2 / n3\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "106" + ], + "split": "dev" + }, + { + "Input": "sowdharya had 90 currency notes in all , some of which are of rs 95 denomination and the remaining of rs 45 denomination . the total amount of all these currency notes was rs . 5000 . how much amount ( in rs ) did she have in the denomination of rs 45 ?", + "Output Program": [ + "n0 = 90.0\nn1 = 95.0\nn2 = 45.0\nn3 = 5000.0\nn4 = 45.0\nt0 = n0 * n2\nt1 = n1 - n2\nt2 = n3 - t0\nt3 = t2 / t1\nanswer = n0 - t3\nprint(answer)" + ], + "Output Answer": [ + "71" + ], + "split": "dev" + }, + { + "Input": "a salesman \u2019 s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1000 plus 2.5 % commission on all sales exceeding rs . 4,000 . if his remuneration as per new scheme was rs . 600 more than that by the previous schema , his sales were worth ?", + "Output Program": [ + "n0 = 5.0\nn1 = 1000.0\nn2 = 2.5\nn3 = 4000.0\nn4 = 600.0\nt0 = n0 / 100.0\nanswer = n4 / t0\nprint(answer)" + ], + "Output Answer": [ + "12000" + ], + "split": "dev" + }, + { + "Input": "village x has a population of 72000 , which is decreasing at the rate of 1200 per year . village y has a population of 42000 , which is increasing at the rate of 800 per year . in how many years will the population of the two villages be equal ?", + "Output Program": [ + "n0 = 72000.0\nn1 = 1200.0\nn2 = 42000.0\nn3 = 800.0\nt0 = n1 + n3\nt1 = n0 - n2\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "dev" + }, + { + "Input": "the average age of 15 students of a class is 15 years . out of these , the average age of 3 students is 14 years and that of the other 11 students is 16 years . the age of the 15 th student is", + "Output Program": [ + "n0 = 15.0\nn1 = 15.0\nn2 = 3.0\nn3 = 14.0\nn4 = 11.0\nn5 = 16.0\nn6 = 15.0\nt0 = n0 * n0\nt1 = n2 * n3\nt2 = n4 * n5\nt3 = t1 + t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "dev" + }, + { + "Input": "a number x is 6 times another number y . the percentage that y is less than x is", + "Output Program": [ + "n0 = 6.0\nt0 = n0 - 1.0\nt1 = t0 / n0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "83.33333333333334" + ], + "split": "dev" + }, + { + "Input": "a boy perform 5 times a reaction and his reading are 2 , 2.1 , 2 , 2.2 but unfortunately 5 th reading clearly not visible because a drop of chemical fall onto it . but luckily he have mean of all reading which is 2 . please help him in finding 5 th reading .", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 2.1\nn3 = 2.0\nn4 = 2.2\nn5 = 5.0\nn6 = 2.0\nn7 = 5.0\nt0 = n0 * n1\nt1 = t0 - n1\nt2 = t1 - n2\nt3 = t2 - n1\nanswer = t3 - n4\nprint(answer)" + ], + "Output Answer": [ + "1.7000000000000002" + ], + "split": "dev" + }, + { + "Input": "there are 8 teams in a certain league and each team plays each of the other teams exactly once . if each game is played by 2 teams , what is the total number of games played ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.0\nt0 = n0 - 1.0\nt1 = n0 * t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "dev" + }, + { + "Input": "in a certain archery competition , points were awarded as follows : the first place winner receives 11 points , the second place winner receives 7 points , the third place winner receives 5 points and the fourth place winner receives 2 points . no other points are awarded . john participated several times in the competition and finished first , second , third , or fourth each time . the product of all the points he received was 38500 . how many times did he participate in the competition ?", + "Output Program": [ + "import math\nn0 = 11.0\nn1 = 7.0\nn2 = 5.0\nn3 = 2.0\nn4 = 38500.0\nt0 = n0 * n1\nt1 = n2 * t0\nt2 = n3 * t1\nt3 = n4 / t2\nt4 = math.sqrt(max(0, t3))\nanswer = math.floor(t4)\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "dev" + }, + { + "Input": "if the sum of two numbers is 45 and the h . c . f and l . c . m of these numbers are 3 and 100 respectively , then the sum of the reciprocal of the numbers is equal to :", + "Output Program": [ + "n0 = 45.0\nn1 = 3.0\nn2 = 100.0\nt0 = n1 + n2\nt1 = n1 * n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.3433333333333333" + ], + "split": "dev" + }, + { + "Input": "mr . kramer , the losing candidate in a two - candidate election , received 942,568 votes , which was exactly 45 percent of all votes cast . approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast ?", + "Output Program": [ + "n0 = 942568.0\nn1 = 45.0\nn2 = 50.0\nt0 = n2 / 100.0\nt1 = n1 / 100.0\nt2 = t0 - t1\nt3 = 1.0 - t1\nt4 = t2 / t3\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "9.090909090909088" + ], + "split": "dev" + }, + { + "Input": "what is the least number should be added to 1056 , so the sum of the number is completely divisible by 29 ?", + "Output Program": [ + "import math\nn0 = 1056.0\nn1 = 29.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = t1 + 1.0\nt3 = n1 * t2\nanswer = t3 - n0\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "dev" + }, + { + "Input": "an optometrist charges $ 150 per pair for soft contact lenses and $ 85 per pair for hard contact lenses . last week she sold 5 more pairs of soft lenses than hard lenses . if her total sales for pairs of contact lenses last week were $ 1455 , what was the total number of pairs of contact lenses that she sold ?", + "Output Program": [ + "n0 = 150.0\nn1 = 85.0\nn2 = 5.0\nn3 = 1455.0\nt0 = n0 + n1\nt1 = 100.0 * 4.0\nt2 = n2 * 10.0\nt3 = n0 * n2\nt4 = t1 + t2\nt5 = n2 + t4\nt6 = t5 + 1000.0\nt7 = t6 - t3\nt8 = t7 / t0\nt9 = t8 * 2.0\nanswer = n2 + t9\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "dev" + }, + { + "Input": "if n is the product of all the integers from 5 to 20 , inclusive , what is the greatest integer k for which 2 ^ k is a factor of n ?", + "Output Program": [ + "n0 = 5.0\nn1 = 20.0\nn2 = 2.0\nt0 = 1.0 + 3.0\nt1 = t0 + 1.0\nt2 = n2 + t1\nt3 = t2 + 1.0\nt4 = t3 + 4.0\nt5 = t4 + 1.0\nanswer = n2 + t5\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "dev" + }, + { + "Input": "country c imposes a two - tiered tax on imported cars : the first tier imposes a tax of 12 % of the car ' s price up to a certain price level . if the car ' s price is higher than the first tier ' s level , the tax on the portion of the price that exceeds this value is 9 % . if ron imported a $ 18000 imported car and ended up paying $ 1950 in taxes , what is the first tier ' s price level ?", + "Output Program": [ + "n0 = 12.0\nn1 = 9.0\nn2 = 18000.0\nn3 = 1950.0\nt0 = n1 / 100.0\nt1 = n0 / 100.0\nt2 = 2.0 * 3.0\nt3 = t2 * 3.0\nt4 = t1 - t0\nt5 = t3 * 1000.0\nt6 = t0 * t5\nt7 = n3 - t6\nanswer = t7 / t4\nprint(answer)" + ], + "Output Answer": [ + "11000" + ], + "split": "dev" + }, + { + "Input": "the sum of 3 integers is 33 . the largest integer is 3 times the middle integer , and the smallest integer is 23 less than the largest integer . what is the product of the 3 integers ?", + "Output Program": [ + "n0 = 3.0\nn1 = 33.0\nn2 = 3.0\nn3 = 23.0\nn4 = 3.0\nt0 = n1 + n3\nt1 = 3.0 + 4.0\nt2 = n0 * t0\nt3 = t2 / t1\nt4 = t3 / n0\nt5 = t3 - n3\nt6 = t3 * t4\nanswer = t6 * t5\nprint(answer)" + ], + "Output Answer": [ + "192" + ], + "split": "dev" + }, + { + "Input": "joe \u2019 s average ( arithmetic mean ) test score across 4 equally weighted tests was 70 . he was allowed to drop his lowest score . after doing so , his average test score improved to 75 . what is the lowest test score that was dropped ?", + "Output Program": [ + "n0 = 4.0\nn1 = 70.0\nn2 = 75.0\nt0 = n0 * n1\nt1 = n2 * 3.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "55" + ], + "split": "dev" + }, + { + "Input": "the number of diagonals of a polygon of n sides is given by the formula v = n ( n - 3 ) / 2 . if a polygon has twice as many diagonals as sides , how many sides does it have ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\n\nanswer = n0 + n1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "dev" + }, + { + "Input": "andy solves problems 75 to 125 inclusive in a math exercise . how many problems does he solve ?", + "Output Program": [ + "n0 = 75.0\nn1 = 125.0\nt0 = n1 - n0\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "51" + ], + "split": "dev" + }, + { + "Input": "when 242 is divided by a certain divisor the remainder obtained is 15 . when 698 is divided by the same divisor the remainder obtained is 27 . however , when the sum of the two numbers 242 and 698 is divided by the divisor , the remainder obtained is 5 . what is the value of the divisor ?", + "Output Program": [ + "n0 = 242.0\nn1 = 15.0\nn2 = 698.0\nn3 = 27.0\nn4 = 242.0\nn5 = 698.0\nn6 = 5.0\nt0 = n1 + n3\nanswer = t0 - n6\nprint(answer)" + ], + "Output Answer": [ + "37" + ], + "split": "dev" + }, + { + "Input": "a bookseller has two display windows . she plans to display 3 new fiction books in the left window , and 3 new non - fiction books in the right window . assuming she can put the 4 fiction books in any order , and separately , the 3 non - fiction books in any order , how many total configurations will there be for the two display windows ?", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 4.0\nn3 = 3.0\nt0 = n0 * n2\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "dev" + }, + { + "Input": "sally has a gold credit card with a certain spending limit , and a platinum card with twice the spending limit of the gold card . currently , she has a balance on her gold card that is 1 / 3 of the spending limit on that card , and she has a balance on her platinum card that is 1 / 7 of the spending limit on that card . if sally transfers the entire balance on her gold card to her platinum card , what portion of her limit on the platinum card will remain unspent ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 7.0\nt0 = 1 / n3\nt1 = 1 / n1\nt2 = 1 / 2.0\nt3 = t1 * t2\nt4 = t0 + t3\nanswer = n0 - t4\nprint(answer)" + ], + "Output Answer": [ + "0.6904761904761905" + ], + "split": "dev" + }, + { + "Input": "of all the homes on gotham street , 1 / 3 are termite - ridden , and 4 / 7 of these are collapsing . what fraction of the homes are termite - ridden , but not collapsing ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 4.0\nn3 = 7.0\nt0 = n0 + 2.0\nt1 = n1 * n3\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.14285714285714285" + ], + "split": "dev" + }, + { + "Input": "what is the minimum value of | x - 4 | + | x + 5 | + | x - 5 | ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 5.0\n\nanswer = n1 + n2\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "dev" + }, + { + "Input": "a manufacturer produces a certain men ' s athletic shoe in integer sizes from 8 to 17 . for this particular shoe , each unit increase in size corresponds to a 1 / 4 - inch increase in the length of the shoe . if the largest size of this shoe is 10 % longer than the smallest size , how long , in inches , is the shoe in size 15 ?", + "Output Program": [ + "n0 = 8.0\nn1 = 17.0\nn2 = 1.0\nn3 = 4.0\nn4 = 10.0\nn5 = 15.0\nt0 = n2 / n3\nt1 = n4 / 100.0\nt2 = n1 - n0\nt3 = n5 - n0\nt4 = t0 * t2\nt5 = t0 * t3\nt6 = t4 / t1\nanswer = t6 + t5\nprint(answer)" + ], + "Output Answer": [ + "24.25" + ], + "split": "dev" + }, + { + "Input": "excluding stoppages , the average speed of a bus is 75 km / hr and including stoppages , the average speed of the bus is 40 km / hr . for how many minutes does the bus stop per hour ?", + "Output Program": [ + "n0 = 75.0\nn1 = 40.0\nt0 = n1 / n0\nt1 = 1.0 * 60.0\nt2 = t0 * 60.0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "dev" + }, + { + "Input": "if @ is a binary operation defined as the difference between an integer n and the product of n and 5 , then what is the largest positive integer n such that the outcome of the binary operation of n is less than 14 ?", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 14.0\nt0 = n0 - 1.0\nt1 = n1 / t0\nanswer = math.floor(t1)\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "dev" + }, + { + "Input": "if x ^ 2 \u2013 4 x = 5 , then one possible value of x \u2013 2 =", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 5.0\nn3 = 2.0\nt0 = 1.0**min(n0, 5)\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "dev" + }, + { + "Input": "how many digits are required to number a book containing 220 pages ?", + "Output Program": [ + "n0 = 220.0\nt0 = 10.0 - 1.0\nt1 = n0 - 100.0\nt2 = t1 + 1.0\nt3 = t0 * 10.0\nt4 = t3 * 2.0\nt5 = t2 * 3.0\nt6 = t4 + t0\nanswer = t6 + t5\nprint(answer)" + ], + "Output Answer": [ + "552" + ], + "split": "dev" + }, + { + "Input": "a case of 12 rolls of paper towels sells for $ 9 . the cost of one roll sold individually is $ 1 . what is the percent w of savings per roll for the 12 - roll package over the cost of 12 rolls purchased individually ?", + "Output Program": [ + "n0 = 12.0\nn1 = 9.0\nn2 = 1.0\nn3 = 12.0\nn4 = 12.0\nt0 = n1 / n0\nt1 = t0 * 100.0\nanswer = 100.0 - t1\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "dev" + }, + { + "Input": "last year department store x had a sales total for december that was 6 times the average ( arithmetic mean ) of the monthly sales totals for january through november . the sales total for december was what fraction of the sales total for the year ?", + "Output Program": [ + "n0 = 6.0\nt0 = 12.0 - 1.0\nt1 = n0 + t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.35294117647058826" + ], + "split": "dev" + }, + { + "Input": "what least no . must be subtracted from 101054 so that remaining no . is divisible by 10 ?", + "Output Program": [ + "import math\nn0 = 101054.0\nn1 = 10.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "dev" + }, + { + "Input": "machine \u2013 x produces 50 % of the total output and machine - y produces 75 % of the total output . an average of 9 units out of a 1000 goods manufactured by machine - x and two unit of 500 units produced by machine - x prove to be defective . what is the probability that a unit chosen at random from the total daily output of the factory is defective ?", + "Output Program": [ + "n0 = 50.0\nn1 = 75.0\nn2 = 9.0\nn3 = 1000.0\nn4 = 500.0\nt0 = n1 / 100.0\nt1 = n0 / 100.0\nt2 = n2 / t0\nt3 = n3 * t1\nt4 = n3 + t3\nt5 = t2 / 2.0\nt6 = n2 + t5\nt7 = n3 + t4\nanswer = t6 / t7\nprint(answer)" + ], + "Output Answer": [ + "0.006" + ], + "split": "dev" + }, + { + "Input": "two cycles are standing side - by - side . one cycle , which is 2.5 feets tall , casts a shadow that is 5 feets long . the other cycle is 2 feets tall . compute , in feets , the length of the shadow that the shorter cycle casts .", + "Output Program": [ + "n0 = 2.5\nn1 = 5.0\nn2 = 2.0\nt0 = n1 * n2\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "dev" + }, + { + "Input": "on a two - dimensional coordinate plane , the line a = x ^ 2 - x ^ 3 touches the x - axis in how many places ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nt0 = max(n0,n1)\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "dev" + }, + { + "Input": "3 positive integers a , b , and c are such that their average is 20 and a \u2264 b \u2264 c . if the median is ( a + 13 ) , what is the least possible value of c ?", + "Output Program": [ + "n0 = 3.0\nn1 = 20.0\nn2 = 13.0\nt0 = n2 + 1.0\nt1 = n0 * n1\nt2 = n2 + t0\nt3 = t1 - t2\nt4 = t3 / n0\nanswer = t0 + t4\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "dev" + }, + { + "Input": "if 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 22 , then n =", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 2.0\nn3 = 2.0\nn4 = 2.0\nn5 = 2.0\nn6 = 2.0\nn7 = 2.0\nn8 = 4.0\nn9 = 22.0\nt0 = n0 * n9\nt1 = t0 - n0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "dev" + }, + { + "Input": "a is the average ( arithmetic mean ) of the first 7 positive multiples of 5 and b is the median of the first 3 positive multiples of positive integer n . if the value of a ^ 2 \u2013 b ^ 2 is zero , what is the value of n ?", + "Output Program": [ + "n0 = 7.0\nn1 = 5.0\nn2 = 3.0\nn3 = 2.0\nn4 = 2.0\nt0 = n1 * 4.0\nanswer = t0 / n3\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "dev" + }, + { + "Input": "2 men and 4 women are lined up in a row . what is the number of cases where they stand with each other in turn ? ( the number of cases in which men ( or women ) do not stand next to each other )", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 4.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(n1)))\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "dev" + }, + { + "Input": "if ( 8000 ) ( 6000 ) = ( 480 ) ( 10 ^ y ) , what is the value of y ?", + "Output Program": [ + "import math\nn0 = 8000.0\nn1 = 6000.0\nn2 = 480.0\nn3 = 10.0\nt0 = math.log(max(1e-5, 10.0), 2)\nt1 = n0 * n1\nt2 = t1 / n2\nt3 = math.log(max(1e-5, t2), 2)\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "dev" + }, + { + "Input": "if ( 5 + k ) ( 5 - k ) = ( 5 ^ 2 ) - ( 2 ^ 3 ) , then what is the value of k ?", + "Output Program": [ + "n0 = 5.0\nn1 = 5.0\nn2 = 5.0\nn3 = 2.0\nn4 = 2.0\nn5 = 3.0\nt0 = n5 + 10.0\nt1 = n0 * n5\nanswer = t1 - t0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "dev" + }, + { + "Input": "a store reported total sales of $ 416 million for february of this year . if the total sales for the same month last year was $ 320 million , approximately what was the percent increase in sales ?", + "Output Program": [ + "n0 = 416.0\nn1 = 320.0\nt0 = n0 - n1\nt1 = t0 / n1\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "dev" + }, + { + "Input": "of the families in city x in 2000 , 30 percent owned a personal computer . the number of families in city x owning a computer in 2004 was 20 percent greater than it was in 1994 , and the total number of families in city x was 10 percent greater in 2004 than it was in 2000 . what percent of the families in city x owned a personal computer in 1998 ?", + "Output Program": [ + "n0 = 2000.0\nn1 = 30.0\nn2 = 2004.0\nn3 = 20.0\nn4 = 1994.0\nn5 = 10.0\nn6 = 2004.0\nn7 = 2000.0\nn8 = 1998.0\nt0 = n3 + 100.0\nt1 = n5 + 100.0\nt2 = n1 * t0\nt3 = t2 / 100.0\nt4 = t3 / t1\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "32.72727272727273" + ], + "split": "dev" + }, + { + "Input": "what is the smallest integer k for which 64 ^ k > 4 ^ 20 ?", + "Output Program": [ + "import math\nn0 = 64.0\nn1 = 4.0\nn2 = 20.0\nt0 = n2 / 3.0\nt1 = math.floor(t0)\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "dev" + }, + { + "Input": "if 2994 \u00e3 \u00b7 14.5 = 179 , then 29.94 \u00e3 \u00b7 1.45 = ?", + "Output Program": [ + "n0 = 2994.0\nn1 = 14.5\nn2 = 179.0\nn3 = 29.94\nn4 = 1.45\nt0 = n1 / n4\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "17.9" + ], + "split": "dev" + }, + { + "Input": "( \u221a 27 + \u221a 243 ) / \u221a 75 = ?", + "Output Program": [ + "import math\nn0 = 27.0\nn1 = 243.0\nn2 = 75.0\nt0 = math.sqrt(max(0, n0))\nt1 = math.sqrt(max(0, n1))\nt2 = math.sqrt(max(0, n2))\nt3 = t0 + t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "2.4" + ], + "split": "dev" + }, + { + "Input": "a set s = { x , - 8 , - 7 , - 6 , 6 , 8 , 9 , y } with elements arranged in increasing order . if the median and the mean of the set are the same , what is the value of | x | - | y | ?", + "Output Program": [ + "n0 = 8.0\nn1 = 7.0\nn2 = 6.0\nn3 = 6.0\nn4 = 8.0\nn5 = 9.0\nt0 = n0 + n5\nt1 = n2 + t0\nt2 = t1 - n2\nt3 = t2 - n1\nanswer = t3 - n0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "dev" + }, + { + "Input": "what is the sum of the digits of integer k , if k = ( 10 ^ 45 - 46 )", + "Output Program": [ + "n0 = 10.0\nn1 = 45.0\nn2 = 46.0\nt0 = n0 - 1.0\nt1 = n1 - 2.0\nt2 = t0 * t1\nanswer = t2 + n0\nprint(answer)" + ], + "Output Answer": [ + "397" + ], + "split": "dev" + }, + { + "Input": "if 5 a = 3125 , then the value of 5 ( a - 3 ) is :", + "Output Program": [ + "n0 = 5.0\nn1 = 3125.0\nn2 = 5.0\nn3 = 3.0\nt0 = n0 - n3\nanswer = n0**min(t0, 5)\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "dev" + }, + { + "Input": "what is the value of n if the sum of the consecutive odd intergers y from 1 to n equals 169 ?", + "Output Program": [ + "import math\nn0 = 1.0\nn1 = 169.0\nt0 = n0 * 2.0\nt1 = math.sqrt(max(0, n1))\nt2 = t1 * 2.0\nt3 = t2 - t0\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "dev" + }, + { + "Input": "if log 4 x + log 4 ( 1 / 6 ) = 1 / 2 then the value of x is ?", + "Output Program": [ + "n0 = 4.0\nn1 = 4.0\nn2 = 1.0\nn3 = 6.0\nn4 = 1.0\nn5 = 2.0\nt0 = n2 / n5\nt1 = n0**min(t0, 5)\nanswer = n3 * t1\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "dev" + }, + { + "Input": "marts income is 30 percent more than tims income and tims income is 40 percent less than juans income . what percentage of juans income is marts income", + "Output Program": [ + "n0 = 30.0\nn1 = 40.0\nt0 = n0 + 100.0\nt1 = 100.0 - n1\nt2 = 100.0 / t1\nt3 = t2 * 100.0\nt4 = t0 / t3\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "77.99999999999999" + ], + "split": "dev" + }, + { + "Input": "for any number z , z * is defined as the greatest positive even integer less than or equal to y . what is the value of 6.15 \u2013 6.15 * ?", + "Output Program": [ + "import math\nn0 = 6.15\nn1 = 6.15\nt0 = math.floor(n0)\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "0.15000000000000036" + ], + "split": "dev" + }, + { + "Input": "when positive integer x is divided by positive integer y , the remainder is 9 . if x / y = 96.15 , what is the value of y ?", + "Output Program": [ + "import math\nn0 = 9.0\nn1 = 96.15\nt0 = math.floor(n1)\nt1 = n1 - t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "59.999999999997726" + ], + "split": "dev" + }, + { + "Input": "during the first two weeks of january , the total rainfall in springdale was 20 inches . if the rainfall during the second week was 1.5 times the rainfall during the first week , what was the rainfall during the second week of january ?", + "Output Program": [ + "n0 = 20.0\nn1 = 1.5\nt0 = n1 + 1.0\nt1 = n1 / t0\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "dev" + }, + { + "Input": "if a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20 , what is the probability q that this product will be a multiple of 45 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 20.0\nn2 = 45.0\nt0 = n1 + 4.0\nanswer = 1.0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.041666666666666664" + ], + "split": "dev" + }, + { + "Input": "x and y are two towns . ganesh covers the distance from x to y at an average speed of 60 km / hr . however , he covers the distance from y to x at an average speed of 30 km / hr . his average speed during the whole journey in km / hr . is :", + "Output Program": [ + "n0 = 60.0\nn1 = 30.0\nt0 = n0 - 10.0\nt1 = t0 + 100.0\nt2 = t1 + t1\nt3 = t1 / n0\nt4 = t1 / n1\nt5 = t3 + t4\nanswer = t2 / t5\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "dev" + }, + { + "Input": "a drink vendor has 20 liters of maaza , 144 liters of pepsi and 368 liters of sprite . he wants to pack them in cans , so that each can contains the same number of liters of a drink , and does n ' t want to mix any two drinks in a can . what is the least number of cans required ?", + "Output Program": [ + "import scipy\nn0 = 20.0\nn1 = 144.0\nn2 = 368.0\nt0 = scipy.gcd(int(n0), int(n1))\nt1 = scipy.gcd(int(n2), int(t0))\nt2 = n0 / t1\nt3 = n1 / t1\nt4 = n2 / t1\nt5 = t2 + t3\nanswer = t5 + t4\nprint(answer)" + ], + "Output Answer": [ + "133" + ], + "split": "dev" + }, + { + "Input": "find the least number must be subtracted from 62575 so that remaining number is divisible by 99 .", + "Output Program": [ + "import math\nn0 = 62575.0\nn1 = 99.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "dev" + }, + { + "Input": "a man is 12 years older than his brother . in two years , his age will be twice the age of his brother . the present age of his brother is :", + "Output Program": [ + "n0 = 12.0\nt0 = n0 + 2.0\nt1 = 2.0 * 2.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "dev" + }, + { + "Input": "a certain mixture of nuts consists of 5 parts almonds to 2 parts walnuts , by weight . what is the number of pounds of almonds in 280 pounds of the mixture ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 280.0\nt0 = n0 + n1\nt1 = n0 * n2\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "dev" + }, + { + "Input": "how many 4 - digit numbers that do not contain the digits 2 , 3 , 4 , 5 , 6 , or 7 are there ?", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\nn2 = 3.0\nn3 = 4.0\nn4 = 5.0\nn5 = 6.0\nn6 = 7.0\nt0 = n0 * n2\nt1 = n0 * t0\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "192" + ], + "split": "dev" + }, + { + "Input": "the average weight of 6 person ' s increases by 1.8 kg when a new person comes in place of one of them weighing 69 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 6.0\nn1 = 1.8\nn2 = 69.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "79.8" + ], + "split": "dev" + }, + { + "Input": "a certain company retirement plan has arule of 70 provision that allows an employee to retire when the employee ' s age plus years of employment with the company total at least 70 . in what year could a female employee hired in 1986 on her 30 nd birthday first be eligible to retire under this provision ?", + "Output Program": [ + "n0 = 70.0\nn1 = 70.0\nn2 = 1986.0\nn3 = 30.0\nt0 = n0 - n3\nt1 = t0 / 2.0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "2006" + ], + "split": "dev" + }, + { + "Input": "to be considered for \u201c movie of the year , \u201d a film must appear in at least 1 / 4 of the top - 10 - movies lists submitted by the cinematic academy \u2019 s 785 members . what is the smallest number of top - 10 lists a film can appear on and still be considered for \u201c movie of the year \u201d ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 10.0\nn3 = 785.0\nn4 = 10.0\n\nanswer = n3 / n1\nprint(answer)" + ], + "Output Answer": [ + "196.25" + ], + "split": "dev" + }, + { + "Input": "the number 0.5 is how much greater than 1 / 3 ?", + "Output Program": [ + "n0 = 0.5\nn1 = 1.0\nn2 = 3.0\nt0 = n1 / n2\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "0.16666666666666669" + ], + "split": "dev" + }, + { + "Input": "there are 2 sections a and b in a class , consisting of 50 and 70 students respectively . if the average weight of section a is 50 kg and that of section b is 70 kg , find the average of the whole class ?", + "Output Program": [ + "n0 = 2.0\nn1 = 50.0\nn2 = 70.0\nn3 = 50.0\nn4 = 70.0\nt0 = n1 + n2\nt1 = n1 * n3\nt2 = n2 * n4\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "61.666666666666664" + ], + "split": "dev" + }, + { + "Input": "if x ^ 2 \u2013 3 x = 18 , then one possible value of x \u2013 4 =", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 18.0\nn3 = 4.0\nt0 = 1.0**min(n0, 5)\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "dev" + }, + { + "Input": "if 4 x + y = 8 and 3 x - 4 y = 5 , then what is the value of 7 x - 3 y ?", + "Output Program": [ + "n0 = 4.0\nn1 = 8.0\nn2 = 3.0\nn3 = 4.0\nn4 = 5.0\nn5 = 7.0\nn6 = 3.0\nt0 = n1 + n4\nanswer = t0 + 10.0\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "dev" + }, + { + "Input": "what number must be added to 6 , 16 and 8 to get an average of 13 ?", + "Output Program": [ + "n0 = 6.0\nn1 = 16.0\nn2 = 8.0\nn3 = 13.0\nt0 = n0 + n1\nt1 = n3 * 4.0\nt2 = n2 + t0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "dev" + }, + { + "Input": "the average age of 30 students in a class is 15 years . if the age of teacher is also included , the average becomes 16 years , find the age of the teacher .", + "Output Program": [ + "n0 = 30.0\nn1 = 15.0\nn2 = 16.0\nt0 = n0 * n1\nt1 = n2 + t0\nt2 = n0 + t1\nanswer = t2 - t0\nprint(answer)" + ], + "Output Answer": [ + "46" + ], + "split": "dev" + }, + { + "Input": "how many integers n are prime numbers in the range 200 < n < 220 ?", + "Output Program": [ + "n0 = 200.0\nn1 = 220.0\n\nanswer = n0 / n0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "dev" + }, + { + "Input": "10 % people of a village in sri lanka died by bombardment , 20 % of the remainder left the village on account of fear . if now the population is reduced to 4554 , how much was it in the beginning ?", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 20.0\nn2 = 4554.0\nt0 = 100.0 - n0\nt1 = 100.0 - n1\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = t2 * t3\nt5 = n2 / t4\nanswer = math.floor(t5)\nprint(answer)" + ], + "Output Answer": [ + "6324" + ], + "split": "dev" + }, + { + "Input": "cost is expressed by the formula tb ^ 4 . if b is doubled , the new cost w is what percent of the original cost ?", + "Output Program": [ + "n0 = 4.0\nt0 = 2.0**min(n0, 5)\nanswer = t0 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "1600" + ], + "split": "dev" + }, + { + "Input": "a cement mixture is composed of 3 elements . by weight , 1 / 2 of the mixture is sand , 1 / 5 of the mixture is water , and the remaining 15 pounds of the mixture is gravel . what is the weight of the entire mixture in pounds ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 2.0\nn3 = 1.0\nn4 = 5.0\nn5 = 15.0\nt0 = n1 / n2\nt1 = n3 / n4\nt2 = t0 + t1\nt3 = n1 - t2\nanswer = n5 / t3\nprint(answer)" + ], + "Output Answer": [ + "49.99999999999999" + ], + "split": "dev" + }, + { + "Input": "during the last 4 years , a large truck company purchased diesel at rates of $ 1.2 , $ 1.3 , $ 1.8 and $ 2.1 per gallon . what was the mean cost of diesel over the 4 - year period if the company spends the same amount of dollars on diesel each year ?", + "Output Program": [ + "n0 = 4.0\nn1 = 1.2\nn2 = 1.3\nn3 = 1.8\nn4 = 2.1\nn5 = 4.0\nt0 = n1 + n2\nt1 = n3 + n4\nt2 = n0 + n0\nt3 = t0 + t1\nt4 = t2 / 100.0\nt5 = t3 / n0\nanswer = t5 - t4\nprint(answer)" + ], + "Output Answer": [ + "1.52" + ], + "split": "dev" + }, + { + "Input": "after spending rs . 5000 on rent , rs . 1500 on milk , rs . 4500 on groceries , rs . 2500 on childrens education rs . 2000 on petrol and rs . 5200 on miscellaneous expenses , mr . kishore saved 10 % of his monthly salary . how much did he save in rs . ?", + "Output Program": [ + "n0 = 5000.0\nn1 = 1500.0\nn2 = 4500.0\nn3 = 2500.0\nn4 = 2000.0\nn5 = 5200.0\nn6 = 10.0\nt0 = n0 + n1\nt1 = 100.0 - n6\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nt5 = n5 + t4\nt6 = t5 * 100.0\nt7 = t6 / t1\nanswer = t7 - t5\nprint(answer)" + ], + "Output Answer": [ + "2300" + ], + "split": "dev" + }, + { + "Input": "shekar scored 76 , 65 , 82 , 47 and 85 marks in mathematics , science , social studies , english and biology respectively . what are his average marks ?", + "Output Program": [ + "n0 = 76.0\nn1 = 65.0\nn2 = 82.0\nn3 = 47.0\nn4 = 85.0\nt0 = n0 + n1\nt1 = 1.0 + 4.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "71" + ], + "split": "dev" + }, + { + "Input": "how many multiples of 4 are there between 12 and 104 , inclusive ?", + "Output Program": [ + "n0 = 4.0\nn1 = 12.0\nn2 = 104.0\nt0 = n2 - n1\nt1 = t0 / n0\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "dev" + }, + { + "Input": "how many kg of rice at rs . 6.60 per kg . be mixed with 56 kg of rice at rs . 9.60 per kg to get a mixture worth rs . 8.20 per kg", + "Output Program": [ + "n0 = 6.6\nn1 = 56.0\nn2 = 9.6\nn3 = 8.2\nt0 = n1 * n2\nt1 = n1 * n3\nt2 = n3 - n0\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "49.00000000000007" + ], + "split": "dev" + }, + { + "Input": "at joes steakhouse the hourly wage for a chef is 20 % greater than that of a dishwasher , and the hourly wage of a dishwasher is half as much as the hourly wage of a manager . if a managers wage is $ 6.50 per hour , how much less than a manager does a chef earn each hour ?", + "Output Program": [ + "n0 = 20.0\nn1 = 6.5\nt0 = n0 + 100.0\nt1 = 1.0 / 2.0\nt2 = t0 / 100.0\nt3 = t2 * t1\nt4 = 1.0 - t3\nanswer = n1 * t4\nprint(answer)" + ], + "Output Answer": [ + "2.6" + ], + "split": "dev" + }, + { + "Input": "the original price of a suit is $ 160 . the price increased 25 % , and after this increase , the store published a 25 % off coupon for a one - day sale . given that the consumers who used the coupon on sale day were getting 25 % off the increased price , how much did these consumers pay for the suit ?", + "Output Program": [ + "n0 = 160.0\nn1 = 25.0\nn2 = 25.0\nn3 = 25.0\nt0 = n0 * n1\nt1 = t0 / 100.0\nt2 = n0 + t1\nt3 = n1 * t2\nt4 = t3 / 100.0\nanswer = t2 - t4\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "dev" + }, + { + "Input": "the average of 11 numbers is 60 . out of 11 numbers the average of first 6 no . is 98 , and last 6 numbers is 65 then find 6 th number ?", + "Output Program": [ + "n0 = 11.0\nn1 = 60.0\nn2 = 11.0\nn3 = 6.0\nn4 = 98.0\nn5 = 6.0\nn6 = 65.0\nn7 = 6.0\nt0 = n3 * n4\nt1 = n3 * n6\nt2 = n0 * n1\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "318" + ], + "split": "dev" + }, + { + "Input": "what is the remainder if 7 ^ 12 is divided by 100 ?", + "Output Program": [ + "n0 = 7.0\nn1 = 12.0\nn2 = 100.0\nt0 = n2 / 2.0\nt1 = n0 * n0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "dev" + }, + { + "Input": "calculate the average of all the numbers between 10 and 86 which are divisible by 9 .", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 86.0\nn2 = 9.0\nt0 = n0 / n2\nt1 = n1 / n2\nt2 = math.floor(t0)\nt3 = math.floor(t1)\nt4 = t2 + 1.0\nt5 = t4 + t3\nt6 = t5 / 2.0\nanswer = n2 * t6\nprint(answer)" + ], + "Output Answer": [ + "49.5" + ], + "split": "dev" + }, + { + "Input": "the average of first 17 even numbers is ?", + "Output Program": [ + "n0 = 17.0\n\nanswer = n0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "dev" + }, + { + "Input": "if x * y = xy \u2013 2 ( x + y ) for all integers x and y , then 1 * ( \u2013 3 ) =", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 3.0\nt0 = -n2\nt1 = n1 + t0\nt2 = n1 * t0\nt3 = t1 * n0\nt4 = -t3\nanswer = t2 + t4\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "dev" + }, + { + "Input": "at a monthly meeting , 3 / 5 of the attendees were males and 7 / 8 of the male attendees arrived on time . if 4 / 5 of the female attendees arrived on time , what fraction of the attendees at the monthly meeting did not arrive on time ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 7.0\nn3 = 8.0\nn4 = 4.0\nn5 = 5.0\nt0 = n4 / n5\nt1 = n0 / n1\nt2 = n2 / n3\nt3 = 1.0 - t0\nt4 = 1.0 - t1\nt5 = 1.0 - t2\nt6 = t3 * t4\nt7 = t1 * t5\nanswer = t6 + t7\nprint(answer)" + ], + "Output Answer": [ + "0.15499999999999997" + ], + "split": "dev" + }, + { + "Input": "how many quarters are equal to 4 dollars ?", + "Output Program": [ + "n0 = 4.0\n\nanswer = n0 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "dev" + }, + { + "Input": "a fair 2 sided coin is flipped 4 times . what is the probability that tails will be the result at least twice , but not more than 4 times ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 4.0\nt0 = n0**min(n1, 5)\nt1 = 1 / t0\nt2 = t1 + t1\nt3 = n1 * t1\nt4 = t2 + t3\nanswer = 1.0 - t4\nprint(answer)" + ], + "Output Answer": [ + "0.625" + ], + "split": "dev" + }, + { + "Input": "in the forestside summer camp there are 50 children . 90 % of the children are boys and the rest are girls . the camp administrator decided to make the number of girls only 5 % of the total number of children in the camp . how many more boys must she bring to make that happen ?", + "Output Program": [ + "n0 = 50.0\nn1 = 90.0\nn2 = 5.0\nt0 = n1 / 100.0\nt1 = n2 / 100.0\nt2 = 1.0 - t0\nt3 = n0 * t2\nt4 = t3 / t1\nanswer = t4 - n0\nprint(answer)" + ], + "Output Answer": [ + "49.99999999999997" + ], + "split": "dev" + }, + { + "Input": "on dividing 109 by a number , the quotient is 9 and the remainder is 1 . find the divisor ?", + "Output Program": [ + "import math\nn0 = 109.0\nn1 = 9.0\nn2 = 1.0\nt0 = n0 / n1\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "dev" + }, + { + "Input": "if 0.75 : x : : 10 : 8 , then x is equal to :", + "Output Program": [ + "n0 = 0.75\nn1 = 10.0\nn2 = 8.0\nt0 = n0 * n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.6" + ], + "split": "dev" + }, + { + "Input": "there are 2 sections a and b in a class , consisting of 36 and 44 students respectively . if the average weight of section a is 40 kg and that of section b is 35 kg , find the average of the whole class ?", + "Output Program": [ + "n0 = 2.0\nn1 = 36.0\nn2 = 44.0\nn3 = 40.0\nn4 = 35.0\nt0 = n1 + n2\nt1 = n1 * n3\nt2 = n2 * n4\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "37.25" + ], + "split": "dev" + }, + { + "Input": "a box contains 100 pairs of shoes ( 200 shoes in total ) . if two shoes are selected at random , what it is the probability that they are matching shoes ?", + "Output Program": [ + "n0 = 100.0\nn1 = 200.0\nt0 = n1 - 1.0\nanswer = 1.0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.005025125628140704" + ], + "split": "dev" + }, + { + "Input": "the nasdaq index has decreased by 70 % since year 2000 . how much should the index increase in order to gain the same value as in year 2000 ?", + "Output Program": [ + "n0 = 70.0\nn1 = 2000.0\nn2 = 2000.0\nt0 = n0 / 100.0\nt1 = 1.0 - t0\nt2 = t0 / t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "233.33333333333331" + ], + "split": "dev" + }, + { + "Input": "the income tax in country x is 8 % of any income up to $ 5000 . for incomes over $ 5000 , an 8 % tax is imposed on the first $ 5000 , and a 10 % tax is imposed on the portion of the total income in excess of $ 5000 . if perry paid $ 950 in income tax last month , then what was perry ' s income ?", + "Output Program": [ + "n0 = 8.0\nn1 = 5000.0\nn2 = 5000.0\nn3 = 8.0\nn4 = 5000.0\nn5 = 10.0\nn6 = 5000.0\nn7 = 950.0\nt0 = n0 / 100.0\nt1 = n1 * t0\nt2 = n7 - t1\nt3 = n1 + t2\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "10550" + ], + "split": "dev" + }, + { + "Input": "if n = 2 ^ 0.15 and n ^ b = 8 , b must equal", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 0.15\nn2 = 8.0\nt0 = math.log(max(1e-5, n2), 2)\nt1 = n0**min(n1, 5)\nt2 = math.log(max(1e-5, t1), 2)\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "19.99999999999999" + ], + "split": "dev" + }, + { + "Input": "the value of a scooter depreciates in such a way that its value of the end of each year is 3 / 4 of its value of the beginning of the same year . if the initial value of the scooter is rs . 40000 , what is the value at the end of 2 years ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 40000.0\nn3 = 2.0\nt0 = n0 / n1\nt1 = 100.0 * 100.0\nt2 = n1 * t1\nt3 = t0**min(n3, 5)\nanswer = t2 * t3\nprint(answer)" + ], + "Output Answer": [ + "22500" + ], + "split": "dev" + }, + { + "Input": "5 years ago , paula was 3 times as old as karl . in 6 years , paula will be twice as old as karl . what is the sum of their ages now ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nn2 = 6.0\nt0 = n2 * 2.0\nt1 = n0 * n1\nt2 = n2 - t0\nt3 = t1 - n0\nt4 = -t2\nt5 = t4 + t3\nt6 = t5 * 3.0\nt7 = t6 - t3\nanswer = t5 + t7\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "dev" + }, + { + "Input": "a certain list consists of 21 different numbers . if n is in the list and n is 5 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction of the sum of the 21 numbers in the list ?", + "Output Program": [ + "n0 = 21.0\nn1 = 5.0\nn2 = 20.0\nn3 = 21.0\nt0 = n2 / 4.0\nt1 = 1.0 * 1.0\nt2 = n0 + t0\nt3 = t2 / 4.0\nt4 = t3 * 2.0\nt5 = t4 - n1\nt6 = t5 - 3.0\nanswer = t1 / t6\nprint(answer)" + ], + "Output Answer": [ + "0.2" + ], + "split": "dev" + }, + { + "Input": "a number exceeds by 40 from its 3 / 8 part . then the number is ?", + "Output Program": [ + "n0 = 40.0\nn1 = 3.0\nn2 = 8.0\nt0 = n0 * n2\nt1 = n2 - n1\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "dev" + }, + { + "Input": "in a government institute 20 nos . staffs are employed . in a festival season their boss give festival allowance to all . he says his accountant to calculate for 30 days @ 100 . also he says balance payment will give to driver and cleaning staff and to be adjust from petty cash . he had given rs . 65000 / - to the accountant . how much amount will taken from petty cash ?", + "Output Program": [ + "n0 = 20.0\nn1 = 30.0\nn2 = 100.0\nn3 = 65000.0\nt0 = n1 / 2.0\nt1 = n0 + t0\nt2 = n2 - t1\nanswer = n3 / t2\nprint(answer)" + ], + "Output Answer": [ + "1000" + ], + "split": "dev" + }, + { + "Input": "a type of extra - large suv averages 12.2 miles per gallon ( mpg ) on the highway , but only 7.6 mpg in the city . what is the maximum distance , in miles , that this suv could be driven on 25 gallons of gasoline ?", + "Output Program": [ + "n0 = 12.2\nn1 = 7.6\nn2 = 25.0\n\nanswer = n0 * n2\nprint(answer)" + ], + "Output Answer": [ + "305" + ], + "split": "dev" + }, + { + "Input": "5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 120 only . men \u00e2 \u20ac \u2122 s wages are ?", + "Output Program": [ + "n0 = 5.0\nn1 = 8.0\nn2 = 120.0\nt0 = n0 * 3.0\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "dev" + }, + { + "Input": "what is the 10 digit to the right of the decimal point , in the decimal expansion of ( 1 / 2 ) ^ 10 ?", + "Output Program": [ + "n0 = 10.0\nn1 = 1.0\nn2 = 2.0\nn3 = 10.0\nt0 = n2 * n2\nanswer = n1 + t0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "dev" + }, + { + "Input": "a man have 8 t - shirt and some pant . he can dress in 72 ways . then tell me the no . of pant that man have .", + "Output Program": [ + "n0 = 8.0\nn1 = 72.0\n\nanswer = n1 / n0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "dev" + }, + { + "Input": "on average , machine a will produce a completed item once every 4 minutes , and machine b will produce a completed item once every 5 minutes . the number of items machine a produces in a 24 - hour period is approximately what percent greater than the number of items machine b would produce in that same period ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 24.0\nt0 = 60.0 / n0\nt1 = 60.0 / n1\nt2 = n2 * t0\nt3 = n2 * t1\nt4 = t2 / t3\nt5 = t4 * 100.0\nanswer = t5 - 100.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "dev" + }, + { + "Input": "what is the divisor ? the dividend is 76 , the remainder is 8 , the quotient is 4", + "Output Program": [ + "n0 = 76.0\nn1 = 8.0\nn2 = 4.0\nt0 = n0 - n1\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "dev" + }, + { + "Input": "if 8 gallons of gasoline are added to a tank that is already filled to 3 / 4 of its capacity , the tank is then filled to 9 / 10 of its capacity . how many gallons does the tank hold ?", + "Output Program": [ + "n0 = 8.0\nn1 = 3.0\nn2 = 4.0\nn3 = 9.0\nn4 = 10.0\nt0 = n3 / n4\nt1 = n1 / n2\nt2 = t0 - t1\nt3 = n0 / t2\nt4 = t3 * t1\nanswer = n0 + t4\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "dev" + }, + { + "Input": "i chose a number and divide it by 2 . then i subtracted 100 from the result and got 4 . what was the number i chose ?", + "Output Program": [ + "n0 = 2.0\nn1 = 100.0\nn2 = 4.0\nt0 = n1 + n2\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "208" + ], + "split": "dev" + }, + { + "Input": "a certain protective additive increases from 50 days to 60 days the time between required maintenance checks on an industrial vehicle . by what percent is the time between maintenance checks increased by using the additive ?", + "Output Program": [ + "n0 = 50.0\nn1 = 60.0\nt0 = n1 - n0\nt1 = t0 / n0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "dev" + }, + { + "Input": "given that 268 * 74 = 19832 , find the values of 2.68 * 0.74 .", + "Output Program": [ + "n0 = 268.0\nn1 = 74.0\nn2 = 19832.0\nn3 = 2.68\nn4 = 0.74\n\nanswer = n3 * n4\nprint(answer)" + ], + "Output Answer": [ + "1.9832" + ], + "split": "dev" + }, + { + "Input": "if henry were to add 9 gallons of water to a tank that is already 3 / 4 full of water , the tank would be 7 / 8 full . how many gallons of water would the tank hold if it were full ?", + "Output Program": [ + "n0 = 9.0\nn1 = 3.0\nn2 = 4.0\nn3 = 7.0\nn4 = 8.0\nt0 = n3 / n4\nt1 = n1 / n2\nt2 = t0 - t1\nt3 = 1.0 / t2\nanswer = n0 * t3\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "dev" + }, + { + "Input": "a number is doubled and 5 is added . if the resultant is trebled , it becomes 129 . what is that number ?", + "Output Program": [ + "n0 = 5.0\nn1 = 129.0\nt0 = n0 * 3.0\nt1 = 2.0 * 3.0\nt2 = n1 - t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "dev" + }, + { + "Input": "s is a set of 50 consecutive multiples of 2 . if the smallest number in s is 56 , then the greatest number in s is", + "Output Program": [ + "n0 = 50.0\nn1 = 2.0\nn2 = 56.0\nt0 = n0 - 1.0\nt1 = n1 * t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "154" + ], + "split": "dev" + }, + { + "Input": "the total number of digit used in numbering the pages of a book having 366 pages , is :", + "Output Program": [ + "n0 = 366.0\nt0 = 10.0 - 1.0\nt1 = 100.0 - 1.0\nt2 = t0 * 10.0\nt3 = n0 - t1\nt4 = t2 * 2.0\nt5 = t3 * 3.0\nt6 = t4 + t0\nanswer = t6 + t5\nprint(answer)" + ], + "Output Answer": [ + "990" + ], + "split": "dev" + }, + { + "Input": "there are 5 boxes in a cargo . the weight of the 1 st box is 200 kg , the weight of the 2 nd box is 20 % higher than the third box , whose weight is 25 % higher than the 1 st box weight . the 4 th box which weighs 350 kg is 30 % lighter than the 5 th box . find the difference in average weight of the 4 heaviest boxes and the 4 lightest boxes .", + "Output Program": [ + "n0 = 5.0\nn1 = 1.0\nn2 = 200.0\nn3 = 2.0\nn4 = 20.0\nn5 = 25.0\nn6 = 1.0\nn7 = 4.0\nn8 = 350.0\nn9 = 30.0\nn10 = 5.0\nn11 = 4.0\nn12 = 4.0\nt0 = n8 - n5\nt1 = t0 - n5\nanswer = t1 / n7\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "dev" + }, + { + "Input": "in a maths test , students were asked to find 5 / 16 of a certain number . one of the students by mistake found 5 / 6 th of that number and his answer was 150 more than the correct answer . find the number .", + "Output Program": [ + "n0 = 5.0\nn1 = 16.0\nn2 = 5.0\nn3 = 6.0\nn4 = 150.0\nt0 = n1 * n4\nt1 = n0 * n1\nt2 = n0 * n3\nt3 = n3 * t0\nt4 = t1 - t2\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "288" + ], + "split": "dev" + }, + { + "Input": "bill downloads the movierevenge of the avengersto his computer in 2.5 hours , using a download manager that downloads from 3 sources marked a , b and c . each source provides download at a constant rate , but the rates of different sources are not necessarily identical . if the movie was downloaded from sources a and c alone , it would take 4 hours to complete the download . the next day , source b is available , but the other sources are inactive . how long will it take to download the trailer of the movie , a file that is 10 times smaller , from source b alone ?", + "Output Program": [ + "n0 = 2.5\nn1 = 3.0\nn2 = 4.0\nn3 = 10.0\nt0 = n1 * n2\nt1 = n2 * t0\nt2 = t1 - n2\nanswer = t2 - n2\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "dev" + }, + { + "Input": "the average ( arithmetic mean ) of the integers from 100 to 400 , inclusive , is how much greater than the average of the integers from 50 to 250 , inclusive ?", + "Output Program": [ + "n0 = 100.0\nn1 = 400.0\nn2 = 50.0\nn3 = 250.0\nt0 = n0 + n1\nt1 = n2 + n3\nt2 = t0 / 2.0\nt3 = t1 / 2.0\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "dev" + }, + { + "Input": "a tourist does not have to pay tax on the first $ 600 of goods he purchases in country b , but does have to pay a 11 percent tax on the portion of the total value that is in excess of $ 600 . what tax must be paid by a tourist if he buys goods with a total value of $ 1720 ?", + "Output Program": [ + "n0 = 600.0\nn1 = 11.0\nn2 = 600.0\nn3 = 1720.0\nt0 = n3 - n0\nt1 = n1 * t0\nanswer = t1 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "123.2" + ], + "split": "dev" + }, + { + "Input": "find the greatest number which on dividing 6215 and 7373 , leaves a reminder of 23 and 29 respectively", + "Output Program": [ + "import scipy\nn0 = 6215.0\nn1 = 7373.0\nn2 = 23.0\nn3 = 29.0\nt0 = n0 - n2\nt1 = n1 - n3\nanswer = scipy.gcd(int(t0), int(t1))\nprint(answer)" + ], + "Output Answer": [ + "144" + ], + "split": "dev" + }, + { + "Input": "the sum of ages of 5 children born at the intervals of 2 years each is 55 years . what is the age of the youngest child ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 55.0\nt0 = n2 / n0\nt1 = t0 - n1\nanswer = t1 - n1\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "dev" + }, + { + "Input": "3 / 5 * [ ( 2 / 3 + 3 / 8 ) / 2 ] - 1 / 16 =", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 2.0\nn3 = 3.0\nn4 = 3.0\nn5 = 8.0\nn6 = 2.0\nn7 = 1.0\nn8 = 16.0\nt0 = n0 / n1\nt1 = n2 / n0\nt2 = n0 / n5\nt3 = n7 / n8\nt4 = t1 + t2\nt5 = t4 / n2\nt6 = t0 * t5\nanswer = t6 - t3\nprint(answer)" + ], + "Output Answer": [ + "0.24999999999999994" + ], + "split": "dev" + }, + { + "Input": "a jogger running at 9 km / hr along side a railway track is 250 m ahead of the engine of a 120 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?", + "Output Program": [ + "n0 = 9.0\nn1 = 250.0\nn2 = 120.0\nn3 = 45.0\nt0 = n1 + n2\nt1 = 10.0 / 2.0\nt2 = n3 - n0\nt3 = t2 / 2.0\nt4 = t1 / t3\nt5 = t4 * t2\nanswer = t0 / t5\nprint(answer)" + ], + "Output Answer": [ + "37" + ], + "split": "dev" + }, + { + "Input": "of the 20,210 employees of the anvil factory , 2 / 7 are journeymen . if half of the journeymen were laid off , what percentage of the total remaining employees would be journeymen ?", + "Output Program": [ + "n0 = 20210.0\nn1 = 2.0\nn2 = 7.0\nt0 = n1 / n2\nt1 = t0 / n1\nt2 = 1.0 - t0\nt3 = t1 + t2\nt4 = t1 / t3\nt5 = t4 * 100.0\nanswer = t5 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "49.99999999999999" + ], + "split": "dev" + }, + { + "Input": "if jimmy drinks 8 ounces of water each time for 8 times a day . how much gallons of water he would have to prepare ahead to drink for 5 days ? ( 1 ounce = 0.0078125 gallon )", + "Output Program": [ + "n0 = 8.0\nn1 = 8.0\nn2 = 5.0\nn3 = 1.0\nn4 = 0.0078125\nt0 = n0 * n0\nt1 = n4 * t0\nanswer = n2 * t1\nprint(answer)" + ], + "Output Answer": [ + "2.5" + ], + "split": "dev" + }, + { + "Input": "the closest approximation of ( 69.28 \u00d7 0.004 ) / 0.03 is", + "Output Program": [ + "n0 = 69.28\nn1 = 0.004\nn2 = 0.03\nt0 = n1 / n2\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "9.237333333333334" + ], + "split": "dev" + }, + { + "Input": "as a treat for her two children , a mother runs to the freezer in which she has 3 cherry ice pops , 4 orange ice pops , and 4 lemon ice pops . she chooses two at random to bring outside to the children , but realizes as she runs out the door that she can not bring them different flavors without one being jealous of the other and getting even more upset . what is the probability that she has to return to the freezer to make sure that they each receive the same flavor ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 4.0\nt0 = n0 * 2.0\nt1 = n0 + t0\nt2 = t1 + t0\nt3 = n0 * t2\nt4 = t3 + 10.0\nt5 = t2 / t4\nanswer = 1.0 - t5\nprint(answer)" + ], + "Output Answer": [ + "0.7272727272727273" + ], + "split": "dev" + }, + { + "Input": "if x < y < z and y - x > 5 , where x is an even integer and y and z are odd integers , what is the least possible value a of z - x ?", + "Output Program": [ + "n0 = 5.0\nt0 = n0 + 2.0\nanswer = t0 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "dev" + }, + { + "Input": "for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today ' s production of 95 units raises the average to 55 units per day , what is the value of n ?", + "Output Program": [ + "n0 = 50.0\nn1 = 95.0\nn2 = 55.0\nt0 = n1 - n0\nt1 = n2 - n0\nt2 = t0 / t1\nanswer = t2 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "dev" + }, + { + "Input": "if the price of petrol increases by 40 , by how much must a user cut down his consumption so that his expenditure on petrol remains constant ?", + "Output Program": [ + "n0 = 40.0\nt0 = n0 + 100.0\nt1 = 100.0 / t0\nt2 = 1.0 - t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "28.57142857142857" + ], + "split": "dev" + }, + { + "Input": "the average of 6 no . ' s is 3.95 . the average of 2 of them is 3.8 , while the average of theother 2 is 3.85 . what is the average of the remaining 2 no ' s ?", + "Output Program": [ + "n0 = 6.0\nn1 = 3.95\nn2 = 2.0\nn3 = 3.8\nn4 = 2.0\nn5 = 3.85\nn6 = 2.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n2 * n5\nt3 = t1 + t2\nt4 = t0 - t3\nanswer = t4 / n2\nprint(answer)" + ], + "Output Answer": [ + "4.200000000000001" + ], + "split": "dev" + }, + { + "Input": "the average of 7 numbers is 24 . if each number be multiplied by 5 . find the average of new set of numbers ?", + "Output Program": [ + "n0 = 7.0\nn1 = 24.0\nn2 = 5.0\n\nanswer = n1 * n2\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "dev" + }, + { + "Input": "if rs . 544 be divided among a , b , c in such a way that a gets 2 / 3 of what b gets and b gets 1 / 4 of what c gets , then their shares are respectively ?", + "Output Program": [ + "n0 = 544.0\nn1 = 2.0\nn2 = 3.0\nn3 = 1.0\nn4 = 4.0\nt0 = n3 / n4\nt1 = n1 / n2\nt2 = t1 * t0\nt3 = t0 + t2\nt4 = t3 + n3\nanswer = n0 / t4\nprint(answer)" + ], + "Output Answer": [ + "384.00000000000006" + ], + "split": "dev" + }, + { + "Input": "m = { - 6 , - 5 , - 4 , - 3 , - 2 } t = { - 3 , - 2 , - 1 , 0 , 1 , 2 , 3 , 4 } if an integer is to be randomly selected from set m above and an integer is to be randomly selected from set t above , what is the probability that the product of the two integers will be negative ?", + "Output Program": [ + "n0 = 6.0\nn1 = 5.0\nn2 = 4.0\nn3 = 3.0\nn4 = 2.0\nn5 = 3.0\nn6 = 2.0\nn7 = 1.0\nn8 = 0.0\nn9 = 1.0\nn10 = 2.0\nn11 = 3.0\nn12 = 4.0\nt0 = n1 * n2\nt1 = n2 * n4\nt2 = n1 * t1\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "dev" + }, + { + "Input": "the average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 22 years . find the average age of the women ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.0\nn2 = 20.0\nn3 = 22.0\nt0 = n2 + n3\nt1 = n0 * n1\nt2 = t0 + t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "29" + ], + "split": "dev" + }, + { + "Input": "if 20 % of x is 15 less than 15 % of 1500 , then x is ?", + "Output Program": [ + "n0 = 20.0\nn1 = 15.0\nn2 = 15.0\nn3 = 1500.0\nt0 = n2 / 100.0\nt1 = n0 / 100.0\nt2 = n3 * t0\nt3 = t2 - n1\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "1050" + ], + "split": "dev" + }, + { + "Input": "if the average of 5 positive integers is 70 and the difference between the largest and the smallest of these 5 numbers is 10 , what is the maximum value possible for the largest of these 5 integers ?", + "Output Program": [ + "n0 = 5.0\nn1 = 70.0\nn2 = 5.0\nn3 = 10.0\nn4 = 5.0\nt0 = n0 * n1\nt1 = t0 - n3\nt2 = t1 / n0\nanswer = n3 + t2\nprint(answer)" + ], + "Output Answer": [ + "78" + ], + "split": "dev" + }, + { + "Input": "what number times ( 1 \u2044 6 ) ^ 2 will give the value of 6 ^ 3 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 6.0\nn2 = 2.0\nn3 = 6.0\nn4 = 3.0\nt0 = n1**min(n2, 5)\nt1 = n1**min(n4, 5)\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "7776" + ], + "split": "dev" + }, + { + "Input": "what is the least number that should be added to 1054 , so the sum of the number is divisible by 23 ?", + "Output Program": [ + "import math\nn0 = 1054.0\nn1 = 23.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = t1 + 1.0\nt3 = t2 - t0\nanswer = n1 * t3\nprint(answer)" + ], + "Output Answer": [ + "3.999999999999936" + ], + "split": "dev" + }, + { + "Input": "70 % of x is greater than 1 / 3 rd of x by 110 . what is x ?", + "Output Program": [ + "n0 = 70.0\nn1 = 1.0\nn2 = 3.0\nn3 = 110.0\nt0 = n0 / 100.0\nt1 = n1 / n2\nt2 = t0 - t1\nanswer = n3 / t2\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "dev" + }, + { + "Input": "in a competitive examination in state a , 6 % candidates got selected from the total appeared candidates . state b had an equal number of candidates appeared and 7 % candidates got selected with 80 more candidates got selected than a . what was the number of candidates appeared from each state ?", + "Output Program": [ + "n0 = 6.0\nn1 = 7.0\nn2 = 80.0\nt0 = n1 - n0\nt1 = t0 / 100.0\nanswer = n2 / t1\nprint(answer)" + ], + "Output Answer": [ + "8000" + ], + "split": "dev" + }, + { + "Input": "a farmer has an apple orchard consisting of fuji and gala apple trees . due to high winds this year 10 % of his trees cross pollinated . the number of his trees that are pure fuji plus the cross - pollinated ones totals 153 , while 3 / 4 of all his trees are pure fuji . how many of his trees are pure gala ?", + "Output Program": [ + "n0 = 10.0\nn1 = 153.0\nn2 = 3.0\nn3 = 4.0\nt0 = n0 / 100.0\nt1 = n2 / n3\nt2 = t0 + t1\nt3 = n1 / t2\nanswer = t3 - n1\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "dev" + }, + { + "Input": "a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 50 paisa . if the share of y is rs . 63 , what is the total amount ?", + "Output Program": [ + "n0 = 45.0\nn1 = 50.0\nn2 = 63.0\nt0 = 100.0 / n0\nt1 = n1 / n0\nt2 = n2 * t0\nt3 = n2 * t1\nt4 = t2 + t3\nanswer = n2 + t4\nprint(answer)" + ], + "Output Answer": [ + "273" + ], + "split": "dev" + }, + { + "Input": "find the value of 1 / ( 3 + 1 / ( 3 + 1 / ( 3 - 1 / 3 ) ) )", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 3.0\nn4 = 1.0\nn5 = 3.0\nn6 = 1.0\nn7 = 3.0\nt0 = n0 / n1\nt1 = n1 - t0\nt2 = n0 / t1\nt3 = n1 + t2\nt4 = n0 / t3\nt5 = n1 + t4\nanswer = n0 / t5\nprint(answer)" + ], + "Output Answer": [ + "0.30337078651685395" + ], + "split": "dev" + }, + { + "Input": "if a - b = 5 and a 2 + b 2 = 31 , find the value of ab .", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 2.0\nn3 = 31.0\nt0 = n0**min(n1, 5)\nt1 = n3 - t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "dev" + }, + { + "Input": "ray writes a two digit number . he sees that the number exceeds 4 times the sum of its digits by 3 . if the number is increased by 18 , the result is the same as the number formed by reversing the digits . find the number .", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 18.0\nt0 = n2 - n1\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "dev" + }, + { + "Input": "how many 3 - digit integers between 311 and 401 , exclusive , are divisible by 3 when the tens digit and the hundered digit are switched ?", + "Output Program": [ + "n0 = 3.0\nn1 = 311.0\nn2 = 401.0\nn3 = 3.0\nt0 = n2 - n1\nanswer = t0 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "dev" + }, + { + "Input": "a number x is mistakenly divided by 10 instead of being multiplied by 10 . what is the percentage error in the result ?", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nt0 = n0 * n0\nt1 = t0 - 1.0\nt2 = t1 / t0\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "99" + ], + "split": "dev" + }, + { + "Input": "if x > 3000 , then the value of ( 1.2 x ) / ( 0.5 x - 406 ) is closest to ?", + "Output Program": [ + "n0 = 3000.0\nn1 = 1.2\nn2 = 0.5\nn3 = 406.0\nt0 = 2.0 - n2\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "dev" + }, + { + "Input": "the smallest number which when diminished by 2 , is divisible by 12 , 16 , 18 , 21 and 28 is", + "Output Program": [ + "n0 = 2.0\nn1 = 12.0\nn2 = 16.0\nn3 = 18.0\nn4 = 21.0\nn5 = 28.0\nt0 = 3.0 + 4.0\nt1 = 3.0**min(n0, 5)\nt2 = n0**min(4.0, 5)\nt3 = t1 * t2\nt4 = t0 * t3\nanswer = t4 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "1010" + ], + "split": "dev" + }, + { + "Input": "two brother x and y appeared for an exam . the probability of selection of x is 1 / 3 and that of b is 2 / 7 . find the probability that both of them are selected .", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 2.0\nn3 = 7.0\nt0 = n0 / n1\nt1 = n2 / n3\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "0.09523809523809523" + ], + "split": "dev" + }, + { + "Input": "the events a and b are independent , the probability that event a occurs is greater than 0 , and the probability that event a occurs is twice the probability that event b occurs . the probability that at least one of events a and b occurs is 8 times the probability that both events a and b occur . what is the probability that event a occurs ?", + "Output Program": [ + "n0 = 0.0\nn1 = 8.0\nt0 = 1.0 + 2.0\nt1 = n1 * 2.0\nt2 = t1 + 2.0\nt3 = t0 / t2\nanswer = t3 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "0.3333333333333333" + ], + "split": "dev" + }, + { + "Input": "if - 2 and - 3 are negative integers , then - 2 * - 3 + 2 is", + "Output Program": [ + "n0 = 65.0\nn1 = 2.0\nn2 = 29.0\nn3 = 5.0\nt0 = n2 * n3\nt1 = n0 - n2\nt2 = t0 / t1\nt3 = n0 * t2\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "65" + ], + "split": "dev" + }, + { + "Input": "if a - b = 8 and a ^ 2 + b ^ 2 = 164 , find the value of ab", + "Output Program": [ + "import math\nn0 = 8.0\nn1 = 2.0\nn2 = 2.0\nn3 = 164.0\nt0 = math.sqrt(max(0, n3))\nt1 = t0 - n0\nt2 = t1 / n1\nt3 = n0 + t2\nt4 = t3 * t2\nanswer = n1 * t4\nprint(answer)" + ], + "Output Answer": [ + "49.99999999999999" + ], + "split": "dev" + }, + { + "Input": "a large box contains 20 small boxes and each small box contains 32 chocolate bars . how many chocolate bars are in the large box ?", + "Output Program": [ + "n0 = 20.0\nn1 = 32.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "640" + ], + "split": "dev" + }, + { + "Input": "in a mayoral election , candidate x received 1 / 2 more votes than candidate y , and candidate y received 2 / 5 fewer votes than z . if z received 25000 votes how many votes did candidate x received ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 2.0\nn3 = 5.0\nn4 = 25000.0\nt0 = n0 / n1\nt1 = n1 / n3\nt2 = 0.25 * 100.0\nt3 = n0 + t0\nt4 = t2 * 100.0\nt5 = 1.0 - t1\nt6 = t4 * 10.0\nt7 = t6 * t5\nanswer = t3 * t7\nprint(answer)" + ], + "Output Answer": [ + "22500" + ], + "split": "dev" + }, + { + "Input": "for a certain art exhibit , a museum sold admission tickets to a group of 30 people every 5 minutes from 9 : 00 in the morning to 4 : 55 in the afternoon , inclusive . the price of a regular admission ticket was $ 10 and the price of a student ticket was $ 6 . if on one day 3 times as many regular admission tickets were sold as student tickets , what was the total revenue from ticket sales that day ?", + "Output Program": [ + "n0 = 30.0\nn1 = 5.0\nn2 = 9.0\nn3 = 0.0\nn4 = 4.0\nn5 = 55.0\nn6 = 10.0\nn7 = 6.0\nn8 = 3.0\nt0 = 12.0 + 4.0\nt1 = n8 + 1.0\nt2 = t0 - n2\nt3 = t2 + 1.0\nt4 = t3 * 12.0\nt5 = n0 * t4\nt6 = t5 / t1\nt7 = n8 * t6\nt8 = n7 * t6\nt9 = n6 * t7\nanswer = t9 + t8\nprint(answer)" + ], + "Output Answer": [ + "25920" + ], + "split": "dev" + }, + { + "Input": "in a group of cows and chickens , the number of legs was 12 more than twice the number of heads . the number of cows was :", + "Output Program": [ + "n0 = 12.0\nt0 = 4.0 - 2.0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "dev" + }, + { + "Input": "if a - b = 3 and a ^ 2 + b ^ 2 = 29 , find the value of ab .", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 2.0\nn2 = 2.0\nn3 = 29.0\nt0 = math.sqrt(max(0, n3))\nt1 = t0 - n0\nt2 = t1 / n1\nt3 = n0 + t2\nt4 = t3 * t2\nanswer = n1 * t4\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "dev" + }, + { + "Input": "students at a school were on average 180 cm tall . the average female height was 170 cm , and the average male height was 182 cms . what was the ratio of men to women ?", + "Output Program": [ + "n0 = 180.0\nn1 = 170.0\nn2 = 182.0\nt0 = n0 - n1\nt1 = n2 - n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "dev" + }, + { + "Input": "jack has two dice , one has 6 equally probable sides , labeled 1 , 2 , 3 , 4 , 5 , 6 , and the other has 7 equally probable sides , labeled 1 , 2 , 3 , 4 , 5 , 6 , 7 . if jack rolls both dice what is the probability that both of the number ' s sum will be 13 ?", + "Output Program": [ + "n0 = 6.0\nn1 = 1.0\nn2 = 2.0\nn3 = 3.0\nn4 = 4.0\nn5 = 5.0\nn6 = 6.0\nn7 = 7.0\nn8 = 1.0\nn9 = 2.0\nn10 = 3.0\nn11 = 4.0\nn12 = 5.0\nn13 = 6.0\nn14 = 7.0\nn15 = 13.0\nt0 = 1.0 / n0\nt1 = n1 / n7\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "0.023809523809523808" + ], + "split": "dev" + }, + { + "Input": "if a = 105 and a ^ 3 = 21 * 25 * 315 * b , what is the value of b ?", + "Output Program": [ + "n0 = 105.0\nn1 = 3.0\nn2 = 21.0\nn3 = 25.0\nn4 = 315.0\nt0 = n2 * n3\nt1 = n0**min(n1, 5)\nt2 = n4 * t0\nanswer = t1 / t2\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "dev" + }, + { + "Input": "xavier , yvonne , and zelda each try independently to solve a problem . if their individual probabilities for success are 1 / 3 , 1 / 2 and 5 / 8 , respectively , what is the probability that xavier and yvonne , but not zelda , will solve the problem ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 2.0\nn4 = 5.0\nn5 = 8.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = n4 / n5\nt3 = t0 * t1\nt4 = n0 - t2\nanswer = t3 * t4\nprint(answer)" + ], + "Output Answer": [ + "0.0625" + ], + "split": "dev" + }, + { + "Input": "a tourist does not have to pay tax on the first $ 600 of goods he purchases in country b , but does have to pay a 7 percent tax on the portion of the total value that is in excess of $ 600 . what tax must be paid by a tourist if he buys goods with a total value of $ 1720 ?", + "Output Program": [ + "n0 = 600.0\nn1 = 7.0\nn2 = 600.0\nn3 = 1720.0\nt0 = n3 - n0\nt1 = n1 * t0\nanswer = t1 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "78.4" + ], + "split": "dev" + }, + { + "Input": "excepting \u2018 seldom \u2019 which means \u2013 rarely , infrequently and not often , is the antonym .", + "Output Program": [ + "n0 = 2235.0\nn1 = 48.0\nn2 = 61.0\nn3 = 26.0\nn4 = 39.0\nn5 = 52.0\nn6 = 65.0\nt0 = n1 / 2.0\nanswer = t0 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "dev" + }, + { + "Input": "the average height of 35 boys in a class was calculated as 181 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ?", + "Output Program": [ + "import math\nn0 = 35.0\nn1 = 181.0\nn2 = 166.0\nn3 = 106.0\nt0 = n0 * n1\nt1 = t0 - n2\nt2 = n3 + t1\nt3 = t2 / n0\nanswer = math.floor(t3)\nprint(answer)" + ], + "Output Answer": [ + "179" + ], + "split": "dev" + }, + { + "Input": "50 % of x is greater than 1 / 3 rd of x by 110 . what is x ?", + "Output Program": [ + "n0 = 50.0\nn1 = 1.0\nn2 = 3.0\nn3 = 110.0\nt0 = n0 / 100.0\nt1 = n1 / n2\nt2 = t0 - t1\nanswer = n3 / t2\nprint(answer)" + ], + "Output Answer": [ + "659.9999999999999" + ], + "split": "dev" + }, + { + "Input": "the average age of a , b and c is 26 years . if the average age of a and c is 29 years , what is the age of b in years ?", + "Output Program": [ + "n0 = 26.0\nn1 = 29.0\nt0 = n0 * 3.0\nt1 = n1 * 2.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "dev" + }, + { + "Input": "80 % of the population of a village is 64000 . the total population of the village is ?", + "Output Program": [ + "n0 = 80.0\nn1 = 64000.0\nt0 = 100.0 / n0\nanswer = n1 * t0\nprint(answer)" + ], + "Output Answer": [ + "80000" + ], + "split": "dev" + }, + { + "Input": "company c sells a line of 20 products with an average retail price of $ 1,200 . if none of these products sells for less than $ 400 , and exactly 10 of the products sell for less than $ 1,000 , what is the greatest possible selling price of the most expensive product ?", + "Output Program": [ + "n0 = 20.0\nn1 = 1200.0\nn2 = 400.0\nn3 = 10.0\nn4 = 1000.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n3 - 1.0\nt3 = n4 * t2\nt4 = t3 + t1\nanswer = t0 - t4\nprint(answer)" + ], + "Output Answer": [ + "11000" + ], + "split": "dev" + }, + { + "Input": "the total age of a and b is 12 year more than the total age of b and c . c is how many years younger than a ?", + "Output Program": [ + "n0 = 12.0\n\nanswer = n0 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "dev" + }, + { + "Input": "find the value of ( 100 + 20 / 90 ) \u00d7 90", + "Output Program": [ + "n0 = 100.0\nn1 = 20.0\nn2 = 90.0\nn3 = 90.0\nt0 = n1 / n2\nt1 = n0 + t0\nanswer = t1 * n2\nprint(answer)" + ], + "Output Answer": [ + "9020" + ], + "split": "dev" + }, + { + "Input": "a student chose a number , multiplied it by 2 , then subtracted 138 from the result and got 112 . what was the number he chose ?", + "Output Program": [ + "n0 = 2.0\nn1 = 138.0\nn2 = 112.0\nt0 = n1 + n2\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "125" + ], + "split": "dev" + }, + { + "Input": "find the value of ( 45 + 23 / 89 ) \u00d7 89", + "Output Program": [ + "n0 = 45.0\nn1 = 23.0\nn2 = 89.0\nn3 = 89.0\nt0 = n1 / n2\nt1 = n0 + t0\nanswer = t1 * n2\nprint(answer)" + ], + "Output Answer": [ + "4028" + ], + "split": "dev" + }, + { + "Input": "the average age of father and his two sons is 24 years . 5 years ago , the average age of the two sons was 15 years . if the difference between the ages of the two sons is 4 years , what is the present age of the father ?", + "Output Program": [ + "n0 = 24.0\nn1 = 5.0\nn2 = 15.0\nn3 = 4.0\nt0 = n0 * 3.0\nt1 = n2 * 2.0\nt2 = n1 * 2.0\nt3 = t1 + t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "dev" + }, + { + "Input": "a caterer ordered 225 ice - cream bars and 125 sundaes . if the total price was $ 200.00 and the price of each ice - cream bar was $ 0.60 , what was the price of each sundae ?", + "Output Program": [ + "n0 = 225.0\nn1 = 125.0\nn2 = 200.0\nn3 = 0.6\nt0 = n0 * n3\nt1 = n2 - t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.52" + ], + "split": "dev" + }, + { + "Input": "a no . when divided by the sum of 555 and 445 gives 2 times their difference as quotient & 50 as remainder . find the no . is ?", + "Output Program": [ + "n0 = 555.0\nn1 = 445.0\nn2 = 2.0\nn3 = 50.0\nt0 = n0 + n1\nt1 = n0 - n1\nt2 = n2 * t0\nt3 = t2 * t1\nanswer = n3 + t3\nprint(answer)" + ], + "Output Answer": [ + "220050" + ], + "split": "dev" + }, + { + "Input": "if p and q are prime numbers , how many divisors does the product p ^ 4 * q ^ 5 have ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nt0 = n0 + 1.0\nt1 = n1 + 1.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "dev" + }, + { + "Input": "the average ( arithmetic mean ) of all scores on a certain algebra test was 90 . if the average of the 8 male students \u2019 grades was 84 , and the average of the female students \u2019 grades was 92 , how many female students took the test ?", + "Output Program": [ + "n0 = 90.0\nn1 = 8.0\nn2 = 84.0\nn3 = 92.0\nt0 = n0 * n1\nt1 = n1 * n2\nt2 = n3 - n0\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "dev" + }, + { + "Input": "49 \u00e3 \u2014 49 = 7 ^ ?", + "Output Program": [ + "import math\nn0 = 49.0\nn1 = 49.0\nn2 = 7.0\nt0 = math.log(max(1e-5, n0), 2)\nt1 = math.log(max(1e-5, n2), 2)\nt2 = t0 + t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "dev" + }, + { + "Input": "a batsman in his 12 th inning makes a score of 60 and their by increasing his average by 4 . what is his average after the 12 th inning ?", + "Output Program": [ + "n0 = 12.0\nn1 = 60.0\nn2 = 4.0\nn3 = 12.0\nt0 = n0 * n2\nt1 = n1 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "dev" + }, + { + "Input": "find the ones digit of 73 ^ 351", + "Output Program": [ + "import math\nn0 = 73.0\nn1 = 351.0\nt0 = 3.0 + 4.0\nt1 = n1 / 4.0\nt2 = 10.0 * 2.0\nt3 = math.floor(t1)\nt4 = t0 * 10.0\nt5 = t3 * 4.0\nt6 = n0 - t4\nt7 = n1 - t5\nt8 = t6**min(t7, 5)\nanswer = t8 - t2\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "dev" + }, + { + "Input": "5 is added to a certain number , the sum is multiplied by 7 , the product is divided by 5 and 5 is subtracted from the quotient . the remainder left is half of 66 . what is the number ?", + "Output Program": [ + "n0 = 5.0\nn1 = 7.0\nn2 = 5.0\nn3 = 5.0\nn4 = 66.0\nt0 = n4 / 2.0\nt1 = n0 + t0\nt2 = n0 * t1\nt3 = t2 / n1\nanswer = t3 - n0\nprint(answer)" + ], + "Output Answer": [ + "22.142857142857142" + ], + "split": "dev" + }, + { + "Input": "a computer manufacturer produces a certain electronic component at a cost of $ 80 per component . shipping costs for delivering the components are $ 3 per unit . further , the manufacturer has costs of $ 16,500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 150 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?", + "Output Program": [ + "n0 = 80.0\nn1 = 3.0\nn2 = 16500.0\nn3 = 150.0\nt0 = n0 + n1\nt1 = 4.0 * 4.0\nt2 = n1 * 100.0\nt3 = t1 * 1000.0\nt4 = n3 * t0\nt5 = t3 + t2\nt6 = t5 + t4\nanswer = t6 / n3\nprint(answer)" + ], + "Output Answer": [ + "191.66666666666666" + ], + "split": "dev" + }, + { + "Input": "calculate the sum of first 60 natural numbers .", + "Output Program": [ + "n0 = 60.0\nt0 = n0 + 1.0\nt1 = n0 / 2.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "1830" + ], + "split": "dev" + }, + { + "Input": "buffalo gives 4 liter milk , cow gives ( 1 / 2 ) liter milk and goat gives 1 / 4 liter milk . you have to get 20 liter milk by 20 animals . what is the number of goats ?", + "Output Program": [ + "n0 = 4.0\nn1 = 1.0\nn2 = 2.0\nn3 = 1.0\nn4 = 4.0\nn5 = 20.0\nn6 = 20.0\n\nanswer = n0 - n2\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "dev" + }, + { + "Input": "a batsman makes a score of 85 runs in the 11 th inning and thus increases his average by 5 . find his average after 11 th inning .", + "Output Program": [ + "n0 = 85.0\nn1 = 11.0\nn2 = 5.0\nn3 = 11.0\nt0 = n1 * n2\nt1 = n0 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "dev" + }, + { + "Input": "every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 70400 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 8.0\nn2 = 70400.0\nt0 = n0 / n1\nt1 = n2 * t0\nt2 = n2 + t1\nt3 = t2 * t0\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "89100" + ], + "split": "dev" + }, + { + "Input": "if a - b = 3 and a ( power 2 ) + b ( power 2 ) = 29 , find the value of ab .", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 2.0\nn3 = 29.0\nt0 = n0**min(n1, 5)\nt1 = n3 - t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "dev" + }, + { + "Input": "a certain number when divided by 39 leaves a remainder 20 , what is the remainder when the same number is divided by 13 ?", + "Output Program": [ + "n0 = 39.0\nn1 = 20.0\nn2 = 13.0\n\nanswer = n1 % n2\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "dev" + }, + { + "Input": "if the sum of 5 consecutive even positive integers is a , then the sum of the next 5 even consecutive integers in terms of a is :", + "Output Program": [ + "n0 = 5.0\nn1 = 5.0\n\nanswer = n0 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "dev" + }, + { + "Input": "if one - third of one - fourth of a number is 18 , then 3 - tenth of that number is : a . 35", + "Output Program": [ + "n0 = 18.0\nn1 = 3.0\nn2 = 35.0\nt0 = 3.0 / 10.0\nt1 = n1 * 4.0\nt2 = n0 * t1\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "64.8" + ], + "split": "dev" + }, + { + "Input": "if a number n is chosen at random from the set of two - digit integers whose digits are both prime numbers , what is the probability e that n is divisible by 3 ?", + "Output Program": [ + "n0 = 3.0\nt0 = n0 + 2.0\nt1 = 4.0 * 4.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.3125" + ], + "split": "dev" + }, + { + "Input": "the greatest number that divides 690 and 875 leaving remainders 10 and 25 respectively is :", + "Output Program": [ + "import scipy\nn0 = 690.0\nn1 = 875.0\nn2 = 10.0\nn3 = 25.0\nt0 = scipy.gcd(int(n0), int(n1))\nt1 = n1 - n3\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "170" + ], + "split": "dev" + }, + { + "Input": "find the sum of all 3 digit natural numbers , which are divisible by 8 .", + "Output Program": [ + "n0 = 3.0\nn1 = 8.0\nt0 = 100.0 + 4.0\nt1 = 10.0 * 100.0\nt2 = t1 - n1\nt3 = t0 + t2\nt4 = t2 - t0\nt5 = t4 / n1\nt6 = t5 + 1.0\nt7 = t6 / 2.0\nanswer = t3 * t7\nprint(answer)" + ], + "Output Answer": [ + "61376" + ], + "split": "dev" + }, + { + "Input": "each of the products produced yesterday was checked by worker x or worker y . 0.5 % of the products checked by worker x are defective and 0.8 % of the products checked by worker y are defective . if the total defective rate of all the products checked by worker x and worker y is 0.65 % , what fraction of the products was checked by worker y ?", + "Output Program": [ + "n0 = 0.5\nn1 = 0.8\nn2 = 0.65\nt0 = n2 - n0\nt1 = n1 - n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "dev" + }, + { + "Input": "if the range q of the 6 numbers 4 , 314 , 710 and x is 12 , what is the difference between the greatest possible value of x and least possible value of x ?", + "Output Program": [ + "n0 = 6.0\nn1 = 4.0\nn2 = 314.0\nn3 = 710.0\nn4 = 12.0\nt0 = n1 + 3.0\nt1 = 12.0 + 2.0\nt2 = 3.0 + 4.0\nt3 = n0 + n1\nt4 = 1.0 + 10.0\nt5 = t0 + t1\nt6 = t5 + t2\nt7 = t6 + t3\nt8 = n4 + t7\nt9 = t8 - t4\nanswer = t9 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "dev" + }, + { + "Input": "total dinning bill of 9 people was $ 139.00 and 10 % tip divided the bill evenly ? what is the bill amount each person shared .", + "Output Program": [ + "n0 = 9.0\nn1 = 139.0\nn2 = 10.0\nt0 = 1.0 / n2\nt1 = t0 + 1.0\nt2 = n1 * t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "16.98888888888889" + ], + "split": "dev" + }, + { + "Input": "if 9 ^ y = 3 ^ 14 , what is y ?", + "Output Program": [ + "n0 = 9.0\nn1 = 3.0\nn2 = 14.0\n\nanswer = n2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "dev" + }, + { + "Input": "if the price of a certain computer increased 30 percent from b dollars to 351 dollars , then 2 b =", + "Output Program": [ + "n0 = 30.0\nn1 = 351.0\nn2 = 2.0\nt0 = n0 + 100.0\nt1 = t0 / 100.0\nt2 = n1 / t1\nanswer = n2 * t2\nprint(answer)" + ], + "Output Answer": [ + "540" + ], + "split": "dev" + }, + { + "Input": "vishal invested 10 % more than trishul . trishul invested 10 % less than raghu . if the total sum of their investments is rs . 5780 , how much amount did raghu invest ?", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 5780.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nt2 = 1.0 - t0\nt3 = t1 * t2\nt4 = t3 + t2\nt5 = t4 + 1.0\nanswer = n2 / t5\nprint(answer)" + ], + "Output Answer": [ + "2000" + ], + "split": "dev" + }, + { + "Input": "in a bus left side are 15 seats available , 3 few seats in right side because in rear exit door . each seat hold 3 people . in addition , there is a seat back can sit 12 people all together . how many people can sit in a bus ?", + "Output Program": [ + "n0 = 15.0\nn1 = 3.0\nn2 = 3.0\nn3 = 12.0\nt0 = n0 - n1\nt1 = n0 + t0\nt2 = n1 * t1\nanswer = n3 + t2\nprint(answer)" + ], + "Output Answer": [ + "93" + ], + "split": "dev" + }, + { + "Input": "if an average hard drive had a capacity of 0.4 tb in 2000 , and average hard drive capacities double every 5 years , what will be the average hard drive capacity in 2050 ?", + "Output Program": [ + "n0 = 0.4\nn1 = 2000.0\nn2 = 5.0\nn3 = 2050.0\nt0 = n0 * 2.0\nt1 = t0 * 2.0\nt2 = t1 * 2.0\nt3 = t2 * 2.0\nt4 = t3 * 2.0\nt5 = t4 * 2.0\nt6 = t5 * 2.0\nt7 = t6 * 2.0\nt8 = t7 * 2.0\nt9 = t8 * 2.0\nt10 = n0 + t9\nanswer = t10 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "4100" + ], + "split": "dev" + }, + { + "Input": "find the remainder when 6 ^ 50 is divided by 215", + "Output Program": [ + "n0 = 6.0\nn1 = 50.0\nn2 = 215.0\nt0 = n0**min(n1, 5)\nanswer = t0 % n2\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "dev" + }, + { + "Input": "the total marks obtained by a student in mathematics and physics is 50 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together .", + "Output Program": [ + "n0 = 50.0\nn1 = 20.0\nt0 = n0 + n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "dev" + }, + { + "Input": "rahul played weel in this season . his current batting averagge is 46 . if he score 78 runs in today match . his batting average will become 54 . how many matches had he played in this season .", + "Output Program": [ + "n0 = 46.0\nn1 = 78.0\nn2 = 54.0\nt0 = n1 - n2\nt1 = n2 - n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "dev" + }, + { + "Input": "tough and tricky questions : word problems . micheal , saren and donald decided to club together to buy a present . each of them gave equal amount of money . luckily saren negotiated a 20 % discount for the present so that each of them paid 4 dollars less . how much did they pay for a present ?", + "Output Program": [ + "n0 = 20.0\nn1 = 4.0\nt0 = n0 / 100.0\nt1 = n1 * 3.0\nt2 = t1 / t0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "dev" + }, + { + "Input": "a club wants to mix 25 pounds of candy worth $ 8.00 per pound with candy worth $ 5.00 per pound to reduce the cost of the mixture to $ 6.00 per pound . how many pounds of the $ 5.00 per pound candy should be used ?", + "Output Program": [ + "n0 = 25.0\nn1 = 8.0\nn2 = 5.0\nn3 = 6.0\nn4 = 5.0\nt0 = n0 * n1\nt1 = n0 * n3\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "dev" + }, + { + "Input": "pradeep has to obtain 20 % of the total marks to pass . he got 390 marks and failed by 25 marks . the maximum marks are", + "Output Program": [ + "n0 = 20.0\nn1 = 390.0\nn2 = 25.0\nt0 = n1 + n2\nt1 = n0 / 100.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "2075" + ], + "split": "dev" + }, + { + "Input": "a grocer has a sale of rs . 5420 , rs . 5660 , rs . 6200 , rs . 6350 and rs . 6500 for 5 consecutive months . find the sale he should have in the sixth month , so that he gets an average sale of rs . 6500 ?", + "Output Program": [ + "n0 = 5420.0\nn1 = 5660.0\nn2 = 6200.0\nn3 = 6350.0\nn4 = 6500.0\nn5 = 5.0\nn6 = 6500.0\nt0 = n5 + 1.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n6 * t0\nt4 = n3 + t2\nt5 = n4 + t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "8870" + ], + "split": "dev" + }, + { + "Input": "if 7 a = 8 b and ab \u2260 0 , what is the ratio of a / 8 to b / 7 ?", + "Output Program": [ + "n0 = 7.0\nn1 = 8.0\nn2 = 0.0\nn3 = 8.0\nn4 = 7.0\nt0 = n0 * n1\nanswer = t0 / t0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "dev" + }, + { + "Input": "3 candidates contested in an election and received 4136 , 7636 , 11628 votes respectively . what is the percentage of the total votes did the winning candidate get ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4136.0\nn2 = 7636.0\nn3 = 11628.0\nt0 = n1 + n2\nt1 = n3 + t0\nt2 = n3 / t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "49.69230769230769" + ], + "split": "dev" + }, + { + "Input": "in a hostel , the number of students decreased by 12 % and the price of food increased by 20 % over the previous year . if each student consumes the same amount of food then by how much should the consumption of food be cut short by every student , so that the total cost of the food remains the same as that of the previous year ?", + "Output Program": [ + "n0 = 12.0\nn1 = 20.0\nt0 = n1 + 100.0\nt1 = 100.0 * 100.0\nt2 = 100.0 - n0\nt3 = t0 * t2\nt4 = t1 / t3\nt5 = 1.0 - t4\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "5.303030303030298" + ], + "split": "dev" + }, + { + "Input": "the sum of number of boys and girls in a school is 1150 . if the number of boys is x , then the number of girls becomes x % of the total number of students . the number of boys is ?", + "Output Program": [ + "n0 = 1150.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "92" + ], + "split": "dev" + }, + { + "Input": "simplify : 3005 - 3000 + 10", + "Output Program": [ + "n0 = 3005.0\nn1 = 3000.0\nn2 = 10.0\nt0 = n1 / n2\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "2705" + ], + "split": "dev" + }, + { + "Input": "a sports retailer ordered white and yellow tennis balls in equal number but the dispatch clerk of the tennis ball company erred and dispatched 50 extra yellow balls and making ratio of white balls to yellow balls 8 / 15 . how many tennis balls did the retailer order originally .", + "Output Program": [ + "n0 = 50.0\nn1 = 8.0\nn2 = 15.0\nt0 = n0 * n1\nt1 = n2 - n1\nt2 = t0 / t1\nanswer = t2 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "114.28571428571429" + ], + "split": "dev" + }, + { + "Input": "the result when a number subtracted from 150 is the same as the number added to 68 . what is the number ?", + "Output Program": [ + "n0 = 150.0\nn1 = 68.0\nt0 = n0 - n1\nt1 = t0 / 2.0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "109" + ], + "split": "dev" + }, + { + "Input": "the sum of the even numbers between 1 and n is 85 * 86 , where n is an odd number , then n = ?", + "Output Program": [ + "n0 = 1.0\nn1 = 85.0\nn2 = 86.0\nt0 = n1 * 2.0\nanswer = t0 + n0\nprint(answer)" + ], + "Output Answer": [ + "171" + ], + "split": "dev" + }, + { + "Input": "total dinning bill of 6 people was $ 139.00 and 10 % tip divided the bill evenly ? what is the bill amount each person shared .", + "Output Program": [ + "n0 = 6.0\nn1 = 139.0\nn2 = 10.0\nt0 = 1.0 / n2\nt1 = t0 + 1.0\nt2 = n1 * t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "25.483333333333334" + ], + "split": "dev" + }, + { + "Input": "in a t . v . factory , an average of 63 tvs are produced per day for the fist 25 days of the months . a few workers fellill for the next 5 daysreducing the daily avg for the month to 58 sets / day . the average production per day for day last 5 days is ?", + "Output Program": [ + "n0 = 63.0\nn1 = 25.0\nn2 = 5.0\nn3 = 58.0\nn4 = 5.0\nt0 = n1 + n2\nt1 = n0 * n1\nt2 = n3 * t0\nt3 = t2 - t1\nanswer = t3 / n2\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "dev" + }, + { + "Input": "a part - time employee \u2019 s hourly wage was increased by 25 % . she decided to decrease the number of hours worked per week so that her total income did not change . by approximately what percent should the number of hours worked be decreased ?", + "Output Program": [ + "n0 = 25.0\nt0 = n0 + 100.0\nt1 = n0 / 100.0\nt2 = t0 / 100.0\nt3 = t1 / t2\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "dev" + }, + { + "Input": "which number can we add to 425897 to get a number exactly divisible by 456 ?", + "Output Program": [ + "n0 = 425897.0\nn1 = 456.0\nt0 = n0 % n1\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "dev" + }, + { + "Input": "how many numbers from 15 to 65 are exactly divisible by 5 ?", + "Output Program": [ + "import math\nn0 = 15.0\nn1 = 65.0\nn2 = 5.0\nt0 = n1 / n2\nt1 = n0 / n2\nt2 = math.floor(t0)\nt3 = math.floor(t1)\nt4 = t3 + 1.0\nt5 = n2 * t2\nt6 = n2 * t4\nt7 = t5 - t6\nt8 = t7 / n2\nanswer = t8 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "dev" + }, + { + "Input": "on thursday mabel handled 90 transactions . anthony handled 10 % more transactions than mabel , cal handled 2 / 3 rds of the transactions that anthony handled , and jade handled 15 more transactions than cal . how much transactions did jade handled ?", + "Output Program": [ + "n0 = 90.0\nn1 = 10.0\nn2 = 2.0\nn3 = 3.0\nn4 = 15.0\nt0 = n1 + 100.0\nt1 = n0 / 100.0\nt2 = t0 * t1\nt3 = n2 * t2\nt4 = t3 / 3.0\nanswer = n4 + t4\nprint(answer)" + ], + "Output Answer": [ + "81" + ], + "split": "dev" + }, + { + "Input": "at a restaurant , glasses are stored in two different - sized boxes . one box contains 12 glasses , and the other contains 16 glasses . if the average number of glasses per box is 15 , and there are 16 more of the larger boxes , what is the total number of glasses at the restaurant ? ( assume that all boxes are filled to capacity . )", + "Output Program": [ + "n0 = 12.0\nn1 = 16.0\nn2 = 15.0\nn3 = 16.0\nt0 = n1 * 2.0\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "480" + ], + "split": "dev" + }, + { + "Input": "two employees x and y are paid a total of rs . 700 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?", + "Output Program": [ + "n0 = 700.0\nn1 = 120.0\nt0 = 1.0 + 4.0\nt1 = t0 * 2.0\nt2 = t1 + 1.0\nt3 = n0 * t1\nt4 = t2 * 2.0\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "318.1818181818182" + ], + "split": "dev" + }, + { + "Input": "mr . depak has $ 449774 in his bank account . what is the least amount of money ( in whole number of dollars ) that he must add to his account if he wants to split this money evenly among her 6 best friends ? options :", + "Output Program": [ + "n0 = 449774.0\nn1 = 6.0\nt0 = n0 + 1.0\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "dev" + }, + { + "Input": "the ages of two person differ by 12 years . if 5 years ago , the elder one be 5 times as old as the younger one , their present ages ( in years ) are respectively", + "Output Program": [ + "n0 = 12.0\nn1 = 5.0\nn2 = 5.0\nt0 = n1 * n2\nt1 = n0 - n1\nt2 = n2 - 1.0\nt3 = t0 + t1\nt4 = t3 / t2\nanswer = n0 + t4\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "dev" + }, + { + "Input": "a cab driver 5 days income was $ 300 , $ 150 , $ 750 , $ 200 , $ 600 . then his average income is ?", + "Output Program": [ + "n0 = 5.0\nn1 = 300.0\nn2 = 150.0\nn3 = 750.0\nn4 = 200.0\nn5 = 600.0\nt0 = n1 + n2\nt1 = n3 + t0\nt2 = n4 + t1\nt3 = n5 + t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "dev" + }, + { + "Input": "a trained covered x km at 90 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 3 x km .", + "Output Program": [ + "n0 = 90.0\nn1 = 2.0\nn2 = 20.0\nn3 = 3.0\nt0 = n0 / n0\nt1 = n0 * 3.0\nt2 = n0 * 2.0\nt3 = t2 / n2\nt4 = t0 + t3\nanswer = t1 / t4\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "dev" + }, + { + "Input": "a theater charges $ 12 for seats in the orchestra and $ 8 for seats in the balcony . on a certain night , a total of 340 tickets were sold for a total cost of $ 3,320 . how many more tickets were sold that night for seats in the balcony than for seats in the orchestra ?", + "Output Program": [ + "n0 = 12.0\nn1 = 8.0\nn2 = 340.0\nn3 = 3320.0\nt0 = n0 * n2\nt1 = 1000.0 * 3.0\nt2 = 100.0 * 3.0\nt3 = 10.0 * 2.0\nt4 = n0 - n1\nt5 = t1 + t2\nt6 = t5 + t3\nt7 = t0 - t6\nt8 = t7 / t4\nt9 = n2 - t8\nanswer = t8 - t9\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "dev" + }, + { + "Input": "there are 8 stores in town that had a total of 22 visitors on a particular day . however , only 12 people went shopping that day ; some people visited more than one store . if 8 people visited exactly two stores each , and everyone visited at least one store , what is the largest number of stores anyone could have visited ?", + "Output Program": [ + "n0 = 8.0\nn1 = 22.0\nn2 = 12.0\nn3 = 8.0\nt0 = n0 * 2.0\nt1 = n2 - n0\nt2 = n1 - t0\nt3 = t1 - 1.0\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "dev" + }, + { + "Input": "4 men and 3 women are lined up in a row . what is the number of cases where they stand with each other in turn ? ( the number of cases in which men ( or women ) do not stand next to each other )", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 3.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(n1)))\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "144" + ], + "split": "dev" + }, + { + "Input": "a box contains 9 apples , 8 of which are red . an apple is drawn from the box and its color is noted before it is eaten . this is done a total of n times , and the probability that a red apple is drawn each time is less than 0.5 . what is the smallest possible value of n ?", + "Output Program": [ + "n0 = 9.0\nn1 = 8.0\nn2 = 0.5\nt0 = n2 * n1\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "dev" + }, + { + "Input": "the sum of the even numbers between 1 and n is 89 * 90 , where n is an odd number , then n = ?", + "Output Program": [ + "n0 = 1.0\nn1 = 89.0\nn2 = 90.0\nt0 = n1 * 2.0\nanswer = t0 + n0\nprint(answer)" + ], + "Output Answer": [ + "179" + ], + "split": "dev" + }, + { + "Input": "the average weight of 8 persons increases by 5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 5.0\nn2 = 65.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "105" + ], + "split": "dev" + }, + { + "Input": "if 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 28 , then n =", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 2.0\nn3 = 2.0\nn4 = 2.0\nn5 = 2.0\nn6 = 2.0\nn7 = 2.0\nn8 = 4.0\nn9 = 28.0\nt0 = n0 * n9\nt1 = t0 - n0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "dev" + }, + { + "Input": "a welder received an order to make a 1 million liter cube - shaped tank . if he has only 4 x 2 meter sheets of metal that can be cut , how many metal sheets will be required for this order y ? ( 1 cubic meter = 1000 liters )", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 2.0\nn3 = 1.0\nn4 = 1000.0\nt0 = n0 / 3.0\nt1 = n1 * n2\nt2 = n4**min(t0, 5)\nt3 = t2 * t2\nt4 = t3 * 12.0\nt5 = t4 / 2.0\nanswer = t5 / t1\nprint(answer)" + ], + "Output Answer": [ + "74.99999999999997" + ], + "split": "dev" + }, + { + "Input": "if a / b = 4 / 3 , then ( 3 a + 2 b ) / ( 3 a - 2 b ) = ?", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 3.0\nn3 = 2.0\nn4 = 3.0\nn5 = 2.0\nt0 = n0 * n1\nt1 = n1 * n3\nt2 = t0 + t1\nt3 = t0 - t1\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "dev" + }, + { + "Input": "a man spend 1 / 5 of his salary on food , 1 / 10 of his salary on house rent and 3 / 5 salary on clothes . he still has $ 15000 left with him . find salary . .", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 1.0\nn3 = 10.0\nn4 = 3.0\nn5 = 5.0\nn6 = 15000.0\nt0 = n0 / n1\nt1 = n0 / n3\nt2 = n4 / n1\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = 1.0 - t4\nanswer = n6 / t5\nprint(answer)" + ], + "Output Answer": [ + "150000.00000000003" + ], + "split": "dev" + }, + { + "Input": "car dealership x , the total profit from sales increased by 30 percent over the previous years , while the number of cars sold decreased by 30 percent over the previous years . approximately what was the average percent increase in profit per car over the previous year .", + "Output Program": [ + "n0 = 30.0\nn1 = 30.0\nt0 = n0 + 100.0\nt1 = 100.0 / 10.0\nt2 = 10.0 - 3.0\nt3 = t0 / t2\nt4 = t3 - t1\nt5 = t4 / t1\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "85.71428571428574" + ], + "split": "dev" + }, + { + "Input": "the price of a bushel of corn is currently $ 3.20 , and the price of a peck of wheat is $ 6.80 . the price of corn is increasing at a constant rate of 5 x cents per day while the price of wheat is decreasing at a constant rate of x ( 2 ^ 1 / 2 ) - x cents per day . what is the approximate price when a bushel of corn costs the same amount as a peck of wheat ?", + "Output Program": [ + "import math\nn0 = 3.2\nn1 = 6.8\nn2 = 5.0\nn3 = 2.0\nn4 = 1.0\nn5 = 2.0\nt0 = math.sqrt(max(0, n3))\nt1 = n1 - n0\nt2 = t0 - n4\nt3 = n2 + t2\nt4 = t1 / t3\nt5 = n2 * t4\nanswer = n0 + t5\nprint(answer)" + ], + "Output Answer": [ + "6.524582562663163" + ], + "split": "dev" + }, + { + "Input": "2001 + 1015", + "Output Program": [ + "n0 = 280.0\nn1 = 254.0\nn2 = 280.0\nn3 = 97.0\nn4 = 138.0\nn5 = 152.0\nn6 = 73.0\nn7 = 3.0\nt0 = n0 + n1\nt1 = n0 + t0\nt2 = t1 - n3\nt3 = t2 - n4\nt4 = t3 - n5\nanswer = n6 + t4\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "dev" + }, + { + "Input": "in 10 years , a will be twice as old as b was 10 years ago . if a is now 5 years older than b the present age of b is", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 5.0\nt0 = n0 * 2.0\nt1 = n0 + t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "dev" + }, + { + "Input": "the total number of digits used in numbering the pages of a book having 369 pages is", + "Output Program": [ + "n0 = 369.0\nt0 = n0 * 3.0\nt1 = 100.0 - 1.0\nt2 = 10.0 - 1.0\nt3 = t0 - t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "999" + ], + "split": "dev" + }, + { + "Input": "the average height of 35 boys in a class was calculated as 182 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ?", + "Output Program": [ + "import math\nn0 = 35.0\nn1 = 182.0\nn2 = 166.0\nn3 = 106.0\nt0 = n0 * n1\nt1 = t0 - n2\nt2 = n3 + t1\nt3 = t2 / n0\nanswer = math.floor(t3)\nprint(answer)" + ], + "Output Answer": [ + "180" + ], + "split": "dev" + }, + { + "Input": "rs 378 is divided among the 3 children such that 12 times of anusha is equal to 8 times of babu which is equal to 6 times of esha . how much the rupee anusha get ?", + "Output Program": [ + "n0 = 378.0\nn1 = 3.0\nn2 = 12.0\nn3 = 8.0\nn4 = 6.0\nt0 = n2 / n3\nt1 = n2 / n4\nt2 = t0 + 1.0\nt3 = t2 + t1\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "84" + ], + "split": "dev" + }, + { + "Input": "the price of 10 chairs is equal to that of 4 tables . the price of 15 chairs and 2 tables together is rs . 4000 . the total price of 12 chairs and 3 tables is ?", + "Output Program": [ + "n0 = 10.0\nn1 = 4.0\nn2 = 15.0\nn3 = 2.0\nn4 = 4000.0\nn5 = 12.0\nn6 = 3.0\nt0 = n1 / n0\nt1 = n2 * t0\nt2 = n3 + t1\nt3 = n4 / t2\nt4 = n6 * t3\nt5 = t0 * t3\nt6 = n5 * t5\nanswer = t4 + t6\nprint(answer)" + ], + "Output Answer": [ + "3900" + ], + "split": "dev" + }, + { + "Input": "the average age of 15 students of a class is 15 years . out of these , the average age of 6 students is 14 years and that of the other 8 students is 16 years . the age of the 15 th student is", + "Output Program": [ + "n0 = 15.0\nn1 = 15.0\nn2 = 6.0\nn3 = 14.0\nn4 = 8.0\nn5 = 16.0\nn6 = 15.0\nt0 = n0 * n0\nt1 = n2 * n3\nt2 = n4 * n5\nt3 = t1 + t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "dev" + }, + { + "Input": "in an organisation there are 1000 employees out of which 250 earn below 10 k $ and 500 earn between 10 k $ and 50 k $ . what is the total percentage of employees who earn less than 50 k $ ?", + "Output Program": [ + "n0 = 1000.0\nn1 = 250.0\nn2 = 10.0\nn3 = 500.0\nn4 = 10.0\nn5 = 50.0\nn6 = 50.0\nt0 = n0 - n1\nt1 = t0 / n0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "dev" + }, + { + "Input": "how many quarters are equal to 6 dollars ?", + "Output Program": [ + "n0 = 6.0\n\nanswer = n0 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "dev" + }, + { + "Input": "the price of 2 sarees and 4 shirts is rs . 1600 . with the same money one can buy 1 saree and 6 shirts . if one wants to buy 12 shirts , how much shall he have to pay ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 1600.0\nn3 = 1.0\nn4 = 6.0\nn5 = 12.0\nt0 = n4 - n1\nt1 = n0 - n3\nt2 = t0 / t1\nt3 = n0 * t2\nt4 = n1 + t3\nt5 = n2 / t4\nanswer = n5 * t5\nprint(answer)" + ], + "Output Answer": [ + "2400" + ], + "split": "dev" + }, + { + "Input": "in a company with 48 employees , some part - time and some full - time , exactly ( 1 / 3 ) of the part - time employees and ( 1 / 4 ) of the full - time employees take the subway to work . what is the greatest possible number y of employees who take the subway to work ?", + "Output Program": [ + "n0 = 48.0\nn1 = 1.0\nn2 = 3.0\nn3 = 1.0\nn4 = 4.0\nt0 = n0 * n2\nt1 = n2 * n4\nt2 = t0 / t1\nt3 = n0 - t1\nt4 = t3 / t2\nanswer = t2 + t4\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "dev" + }, + { + "Input": "a garden center sells a certain grass seed in 5 - pound bags at $ 13.80 per bag , 10 - pound bags at $ 20.43 per bag , and 25 - pound bags $ 32.25 per bag . if a customer is to buy at least 65 pounds of the grass seed , but no more than 80 pounds , what is the least possible cost of the grass seed that the customer will buy ?", + "Output Program": [ + "n0 = 5.0\nn1 = 13.8\nn2 = 10.0\nn3 = 20.43\nn4 = 25.0\nn5 = 32.25\nn6 = 65.0\nn7 = 80.0\nt0 = n5 * 2.0\nt1 = n3 * 1.0\nt2 = n1 * 1.0\nt3 = t0 + t1\nanswer = t3 + t2\nprint(answer)" + ], + "Output Answer": [ + "98.73" + ], + "split": "dev" + }, + { + "Input": "a student appeared in the mock cat . the test paper contained 3 sections namely qa , di and va . the percentage marks in all va was equal to the average of percentage marks in all the 3 sections . coincidentally , if we reverse the digit of the percentage marks of qa we get the percentage marks of di . the percentage marks in va scored by student could be :", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nt0 = n0 * n0\nt1 = t0 + 2.0\nt2 = t1 + t1\nt3 = t2 + t1\nt4 = t3 + t1\nt5 = t4 + t1\nanswer = t5 + t1\nprint(answer)" + ], + "Output Answer": [ + "66" + ], + "split": "dev" + }, + { + "Input": "two trains of equal are running on parallel lines in the same direction at 45 km / hr and 36 km / hr . the faster train passes the slower train in 36 sec . the length of each train is ?", + "Output Program": [ + "n0 = 45.0\nn1 = 36.0\nn2 = 36.0\nt0 = n0 - n1\nt1 = t0 * 1000.0\nt2 = t1 / 3600.0\nt3 = n2 * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "dev" + }, + { + "Input": "how many unique positive odd integers less than 100 are equal to the product of a positive multiple of 5 and an odd number ?", + "Output Program": [ + "n0 = 100.0\nn1 = 5.0\nt0 = n0 / n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "dev" + }, + { + "Input": "1345 - ( 1002 / 20.04 ) = ?", + "Output Program": [ + "n0 = 1345.0\nn1 = 1002.0\nn2 = 20.04\nt0 = n1 / n2\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "1295" + ], + "split": "dev" + }, + { + "Input": "the guests at a football banquet consumed a total of 325 pounds of food . if no individual guest consumed more than 2 pounds of food , what is the minimum number of guests that could have attended the banquet ?", + "Output Program": [ + "import math\nn0 = 325.0\nn1 = 2.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "163" + ], + "split": "dev" + }, + { + "Input": "how many 3 - digit numbers abc , in which a , b , and c are each digits , satisfy the equation 2 b = a + c ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nt0 = n0 * 12.0\nt1 = n1 * 4.0\nt2 = t0 + t1\nanswer = t2 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "dev" + }, + { + "Input": "in cliff \u2019 s impressive rock collection , there are half as many igneous rocks as sedimentary rocks . of the igneous rocks , 2 / 3 are shiny and the rest are matte , while 1 / 5 of the sedimentary rocks are shiny . if there are 40 shiny igneous rocks , how many total rocks does cliff have ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 1.0\nn3 = 5.0\nn4 = 40.0\nt0 = n0 * n1\nt1 = n4 * t0\nt2 = t1 / n0\nt3 = n1 * t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "180" + ], + "split": "dev" + }, + { + "Input": "3 sets of 40 , 50 and 60 students appeared for an examination and the pass percentage was 100 , 90 and 80 respectively . the pass percentage of the whole set is", + "Output Program": [ + "n0 = 3.0\nn1 = 40.0\nn2 = 50.0\nn3 = 60.0\nn4 = 100.0\nn5 = 90.0\nn6 = 80.0\nt0 = n1 + n2\nt1 = n5 / 100.0\nt2 = n6 / 100.0\nt3 = n3 + t0\nt4 = n2 * t1\nt5 = n3 * t2\nt6 = n1 + t4\nt7 = t6 + t5\nt8 = t7 / t3\nanswer = t8 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "88.66666666666667" + ], + "split": "dev" + }, + { + "Input": "list r contains 5 numbers that have an average value of 60 . if the median of the numbers in the list is equal to the mean and the largest number is equal to 20 more than two times the smallest number , what is the smallest possible value in the list ?", + "Output Program": [ + "n0 = 5.0\nn1 = 60.0\nn2 = 20.0\nt0 = n0 * n1\nt1 = t0 - n1\nt2 = t1 - n1\nt3 = t2 - n2\nt4 = t3 - n2\nanswer = t4 / n0\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "dev" + }, + { + "Input": "if a - b = 6 and a 2 + b 2 = 50 , find the value of ab .", + "Output Program": [ + "n0 = 6.0\nn1 = 2.0\nn2 = 2.0\nn3 = 50.0\nt0 = n0**min(n1, 5)\nt1 = n3 - t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "dev" + }, + { + "Input": "the price of 3 pants and 6 t - shirts is rs . 750 . with the same money one can buy 1 pant and 12 t - shirts . if one wants to buy 8 t - shirts , how much shall she have to pay ?", + "Output Program": [ + "n0 = 3.0\nn1 = 6.0\nn2 = 750.0\nn3 = 1.0\nn4 = 12.0\nn5 = 8.0\nt0 = n4 - n1\nt1 = n0 - n3\nt2 = t0 / t1\nt3 = n0 * t2\nt4 = n1 + t3\nt5 = n2 / t4\nanswer = n5 * t5\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "dev" + }, + { + "Input": "a certain debt will be paid in 65 installments from january 1 to december 31 of a certain year . each of the first 20 payments is to be $ 410 ; each of the remaining payments is to be $ 65 more than each of the first 20 payments . what is the average ( arithmetic mean ) payment that will be made on the debt for the year ?", + "Output Program": [ + "n0 = 65.0\nn1 = 1.0\nn2 = 31.0\nn3 = 20.0\nn4 = 410.0\nn5 = 65.0\nn6 = 20.0\nt0 = n4 + n5\nt1 = n3 * n4\nt2 = n0 - n3\nt3 = t0 * t2\nt4 = t1 + t3\nanswer = t4 / n0\nprint(answer)" + ], + "Output Answer": [ + "455" + ], + "split": "dev" + }, + { + "Input": "in 7 given numbers , the average of first 4 numbers is 4 and that of last 4 numbers is also 4 . if the average of these 7 numbers is 3 , the fourth number is ?", + "Output Program": [ + "n0 = 7.0\nn1 = 4.0\nn2 = 4.0\nn3 = 4.0\nn4 = 4.0\nn5 = 7.0\nn6 = 3.0\nt0 = n1 * n1\nt1 = n0 * n6\nt2 = t0 + t0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "dev" + }, + { + "Input": "at the beginning of a year , the owner of a jewel shop raised the price of all the jewels in his shop by x % and lowered them by x % . the price of one jewel after this up and down cycle reduced by rs . 100 . the owner carried out the same procedure after a month . after this second up - down cycle , the price of that jewel was rs . 2304 . find the original price of that jewel ( in rs . )", + "Output Program": [ + "n0 = 100.0\nn1 = 2304.0\nt0 = n0 * 2.0\nanswer = n1 + t0\nprint(answer)" + ], + "Output Answer": [ + "2504" + ], + "split": "dev" + }, + { + "Input": "in goshawk - eurasian nature reserve 30 percent of the birds are hawks , and 40 percent of the non - hawks are paddyfield - warblers . if there are 25 percent as many kingfishers as paddyfield - warblers in the reserve , then what percent of the birds in the nature reserve are not hawks , paddyfield - warblers , or kingfishers ?", + "Output Program": [ + "n0 = 30.0\nn1 = 40.0\nn2 = 25.0\nt0 = n2 + n2\nt1 = t0 / 2.0\nanswer = t1 + 10.0\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "dev" + }, + { + "Input": "a dog is tied to a tree by a long nylon cord . if the dog runs from the due north side of the tree to the due south side of the tree with the cord extended to its full length at all items , and the dog ran approximately 30 feet , what was the approximate length of the nylon cord , in feet ?", + "Output Program": [ + "n0 = 30.0\n\nanswer = n0 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "dev" + }, + { + "Input": "the sum of two numbers is 66 . how much should be added to the sum for it to be exactly divisible by 9 leaving 0 as the reminder ?", + "Output Program": [ + "n0 = 66.0\nn1 = 9.0\nn2 = 0.0\nt0 = 100.0 - n1\nt1 = t0 - n1\nt2 = t1 - 10.0\nanswer = t2 - n0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "dev" + }, + { + "Input": "what is next no . 11 23 47 83 131 191 263 347 443 551 ? ? ?", + "Output Program": [ + "n0 = 11.0\nn1 = 23.0\nn2 = 47.0\nn3 = 83.0\nn4 = 131.0\nn5 = 191.0\nn6 = 263.0\nn7 = 347.0\nn8 = 443.0\nn9 = 551.0\nt0 = 2.0 * 60.0\nanswer = n9 + t0\nprint(answer)" + ], + "Output Answer": [ + "671" + ], + "split": "dev" + }, + { + "Input": "zinc and copper are melted together in the ratio 9 : 11 . what is the weight of melted mixture , if 31.5 kg of zinc has been consumed in it ?", + "Output Program": [ + "n0 = 9.0\nn1 = 11.0\nn2 = 31.5\nt0 = n1 / n0\nt1 = n2 * t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "dev" + }, + { + "Input": "a man is 20 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is", + "Output Program": [ + "n0 = 20.0\nt0 = 2.0 * 2.0\nt1 = 2.0 - 1.0\nt2 = t0 - 2.0\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "dev" + }, + { + "Input": "an order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth . what be the cost of a carpet whose length and breadth are 40 % more and 25 % more respectively than the first carpet . given that the ratio of carpet is rs . 45 per sq m ?", + "Output Program": [ + "n0 = 6.0\nn1 = 1.44\nn2 = 40.0\nn3 = 25.0\nn4 = 45.0\nt0 = n2 + 100.0\nt1 = n3 + 100.0\nt2 = n0 * n1\nt3 = t0 / 100.0\nt4 = t1 / 100.0\nt5 = t3 * t2\nt6 = n0 * t4\nt7 = t5 * t6\nanswer = n4 * t7\nprint(answer)" + ], + "Output Answer": [ + "4082.4" + ], + "split": "dev" + }, + { + "Input": "jack , jill , and sandy each have one try to make a basket from half court . if their individual probabilities of making the basket are 1 / 6 , 1 / 7 , and 1 / 8 respectively , what is the probability that jill and sandy will make a basket but jack will miss ?", + "Output Program": [ + "n0 = 1.0\nn1 = 6.0\nn2 = 1.0\nn3 = 7.0\nn4 = 1.0\nn5 = 8.0\nt0 = n0 / n3\nt1 = n0 / n5\nt2 = n0 / n1\nt3 = t0 * t1\nt4 = 1.0 - t2\nanswer = t3 * t4\nprint(answer)" + ], + "Output Answer": [ + "0.01488095238095238" + ], + "split": "dev" + }, + { + "Input": "if abc = ab ^ 3 = 180 where a , b and c are positive integers , what is the value of ` c \u2019 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 180.0\nt0 = n1 / n1\nanswer = t0**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "dev" + }, + { + "Input": "the average of first 12 even numbers is ?", + "Output Program": [ + "n0 = 12.0\n\nanswer = n0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "dev" + }, + { + "Input": "in a company with 48 employees , some part - time and some full - time , exactly ( 1 / 3 ) of the part - time employees and ( 1 / 4 ) of the full - time employees take the subway to work . what is the greatest possible number h of employees who take the subway to work ?", + "Output Program": [ + "n0 = 48.0\nn1 = 1.0\nn2 = 3.0\nn3 = 1.0\nn4 = 4.0\nt0 = n0 * n2\nt1 = n2 * n4\nt2 = t0 / t1\nt3 = n0 - t1\nt4 = t3 / t2\nanswer = t2 + t4\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "dev" + }, + { + "Input": "a batsman in his 12 th innings makes a score of 60 and thereby increases his average by 2 runs . what is his average after the 12 th innings if he had never been \u2018 not out \u2019 ?", + "Output Program": [ + "n0 = 12.0\nn1 = 60.0\nn2 = 2.0\nn3 = 12.0\nt0 = n0 * n2\nt1 = n1 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "38" + ], + "split": "dev" + }, + { + "Input": "a mixture of 150 liters of wine and water contains 15 % water . how much more water should be added so that water becomes 25 % of the new mixture ?", + "Output Program": [ + "n0 = 150.0\nn1 = 15.0\nn2 = 25.0\nt0 = n2 / 100.0\nt1 = n1 / 100.0\nt2 = n0 * t0\nt3 = n0 * t1\nt4 = 1.0 - t0\nt5 = t2 - t3\nanswer = t5 / t4\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "dev" + }, + { + "Input": "the circulation for magazine p in 1961 was 4 times the average ( arithmetic mean ) yearly circulation for magazine p for the years 1962 - 1970 . what is the ratio of the circulation in 1961 to the total circulation during 1961 - 1970 for magazine p ?", + "Output Program": [ + "n0 = 1961.0\nn1 = 4.0\nn2 = 1962.0\nn3 = 1970.0\nn4 = 1961.0\nn5 = 1961.0\nn6 = 1970.0\nt0 = n3 - n2\nt1 = t0 + 1.0\nt2 = n1 + t1\nt3 = t2 + 1.0\nanswer = n1 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.2857142857142857" + ], + "split": "dev" + }, + { + "Input": "mary , peter , and lucy were picking chestnuts . mary picked twice as much chestnuts than peter . lucy picked 2 kg more than peter . together the 3 of them picked 26 kg of chestnuts . how many kilograms did mary pick ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 26.0\nt0 = n0 + n0\nt1 = n2 - n0\nt2 = t1 / t0\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "dev" + }, + { + "Input": "a number when divided by 779 gives a remainder 47 . by dividing the same number by 19 , what would be the remainder ?", + "Output Program": [ + "n0 = 779.0\nn1 = 47.0\nn2 = 19.0\nt0 = n2 * 2.0\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "dev" + }, + { + "Input": "in a group of cows and hens , the number of legs are 8 more than twice the number of heads . the number of cows is :", + "Output Program": [ + "n0 = 8.0\n\nanswer = n0 - 4.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "dev" + }, + { + "Input": "reeya obtained 55 , 67 , 76 , 82 and 85 out of 100 in different subjects , what will be the average", + "Output Program": [ + "n0 = 55.0\nn1 = 67.0\nn2 = 76.0\nn3 = 82.0\nn4 = 85.0\nn5 = 100.0\nt0 = n0 + n1\nt1 = 1.0 + 4.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "73" + ], + "split": "dev" + }, + { + "Input": "1370 , x , 1070 , - 180 , - 6430", + "Output Program": [ + "n0 = 1370.0\nn1 = 1070.0\nn2 = 180.0\nn3 = 6430.0\nt0 = 10.0 * 2.0\nt1 = n0 - n2\nt2 = t0 + t1\nanswer = t2 + 100.0\nprint(answer)" + ], + "Output Answer": [ + "1310" + ], + "split": "dev" + }, + { + "Input": "the average of runs of a cricket player of 10 innings was 33 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?", + "Output Program": [ + "n0 = 10.0\nn1 = 33.0\nn2 = 4.0\nt0 = n0 + 1.0\nt1 = n1 + n2\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "77" + ], + "split": "dev" + }, + { + "Input": "the average score of a cricketer in 2 matches is 60 and in other 3 matches is 50 . then find the average score in all the 5 matches ?", + "Output Program": [ + "n0 = 2.0\nn1 = 60.0\nn2 = 3.0\nn3 = 50.0\nn4 = 5.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = t0 + t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "dev" + }, + { + "Input": "what is the remainder when ( 63 ) ( 65 ) is divided by 8 ?", + "Output Program": [ + "n0 = 63.0\nn1 = 65.0\nn2 = 8.0\nt0 = n0 * n1\nanswer = t0 % n2\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "dev" + }, + { + "Input": "a , b and c are partners in a business . their capitals are respectively , rs . 5000 , rs . 6000 and rs . 4000 . a gets 30 % of the total profit for managing the business . the remaining profit is divided among 3 in the ratio of their capitals . in the end of the year , the profit of a is rs . 200 more than the sum of the profits of b and c . find the total profit ?", + "Output Program": [ + "n0 = 5000.0\nn1 = 6000.0\nn2 = 4000.0\nn3 = 30.0\nn4 = 3.0\nn5 = 200.0\nt0 = n0 + n1\nt1 = 10.0 * 100.0\nt2 = n2 + t0\nt3 = t2 / t1\nanswer = n5 * t3\nprint(answer)" + ], + "Output Answer": [ + "3000" + ], + "split": "dev" + }, + { + "Input": "$ 100 is divided amongst a , b and c so that a may get 1 / 4 as much as b and c together , b may get 3 / 5 as much as a and c together , then the share of a is", + "Output Program": [ + "n0 = 100.0\nn1 = 1.0\nn2 = 4.0\nn3 = 3.0\nn4 = 5.0\nt0 = n1 / n2\nt1 = t0 + 1.0\nt2 = n0 / t1\nanswer = t2 * t0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "dev" + }, + { + "Input": "how many positive even integers less than 100 contain digits 5 or 9 ?", + "Output Program": [ + "n0 = 100.0\nn1 = 5.0\nn2 = 9.0\n\nanswer = n1 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "dev" + }, + { + "Input": "farm tax is levied on the 45 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . willam . mr . willam paid only $ 480 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :", + "Output Program": [ + "n0 = 45.0\nn1 = 3840.0\nn2 = 480.0\nt0 = n2 / n1\nt1 = t0 * 100.0\nt2 = t1 * 100.0\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "27.77777777777778" + ], + "split": "dev" + }, + { + "Input": "a local elementary school has 1049 students and 9 teachers , how many students would have to be added to the school to make sure each teacher has the same amount of students in their classroom ?", + "Output Program": [ + "import math\nn0 = 1049.0\nn1 = 9.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = n1 * t1\nt3 = n0 - t2\nanswer = n1 - t3\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "dev" + }, + { + "Input": "the average marks of 30 students in a class is 100 . but a student mark is wrongly noted as 70 instead of 10 then find the correct average marks ?", + "Output Program": [ + "n0 = 30.0\nn1 = 100.0\nn2 = 70.0\nn3 = 10.0\nt0 = n0 * n1\nt1 = t0 - n2\nt2 = n3 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "98" + ], + "split": "dev" + }, + { + "Input": "sandy gets 3 marks for each correct sum and loses 2 marks for each incorrect sum . sandy attempts 30 sums and obtains 50 marks . how many sums did sandy get correct ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 30.0\nn3 = 50.0\nt0 = n0 + n1\nt1 = n1 * n2\nt2 = n3 + t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "dev" + }, + { + "Input": "if m is a positive integer and m ^ 2 is divisible by 24 , then the largest positive integer that must divide m is ?", + "Output Program": [ + "n0 = 2.0\nn1 = 24.0\nt0 = n1 / 3.0\nt1 = t0 / 3.0\nanswer = t1 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "dev" + }, + { + "Input": "average monthly income of a family of 4 earning members was rs . 840 . one of the earning members died and therefore , the average income came down to rs 650 . the income of the deceased was ?", + "Output Program": [ + "n0 = 4.0\nn1 = 840.0\nn2 = 650.0\nt0 = n0 * n1\nt1 = n0 - 1.0\nt2 = n2 * t1\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "1410" + ], + "split": "dev" + }, + { + "Input": "x and y are two towns . ganesh covers the distance from x to y at an average speed of 43 km / hr . however , he covers the distance from y to x at an average speed of 34 km / hr . his average speed during the whole journey in km / hr . is :", + "Output Program": [ + "n0 = 43.0\nn1 = 34.0\nt0 = n0 - 10.0\nt1 = t0 + 100.0\nt2 = t1 + t1\nt3 = t1 / n0\nt4 = t1 / n1\nt5 = t3 + t4\nanswer = t2 / t5\nprint(answer)" + ], + "Output Answer": [ + "37.97402597402597" + ], + "split": "dev" + }, + { + "Input": "visitors to show were charged rs . 15 each on the first day . rs . 7.50 on the second day , rs . 2.50 on the third day and total attendance on the 3 days were in ratio 2 : 5 : 13 respectively . the average charge per person for the whole show is ?", + "Output Program": [ + "n0 = 15.0\nn1 = 7.5\nn2 = 2.5\nn3 = 3.0\nn4 = 2.0\nn5 = 5.0\nn6 = 13.0\nt0 = n5 + n6\nt1 = n0 * n4\nt2 = n1 * n5\nt3 = n2 * n6\nt4 = t1 + t2\nt5 = n4 + t0\nt6 = t4 + t3\nanswer = t6 / t5\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "dev" + }, + { + "Input": "for each color copy , print shop x charges $ 1.20 and print shop y charges $ 1.70 . how much greater is the charge for 40 color copies at print shop y than at print shop x ?", + "Output Program": [ + "n0 = 1.2\nn1 = 1.7\nn2 = 40.0\nt0 = n1 * n2\nt1 = n0 * n2\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "dev" + }, + { + "Input": "a number x is 12 times another number y . the percentage that y is less than x is", + "Output Program": [ + "n0 = 12.0\nt0 = n0 - 1.0\nt1 = t0 / n0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "91.66666666666666" + ], + "split": "dev" + }, + { + "Input": "the average age of a family of 5 members is 20 years . if the age of the youngest member be 10 years then what was the average age of the family at the time of the birth of the youngest member ?", + "Output Program": [ + "n0 = 5.0\nn1 = 20.0\nn2 = 10.0\nt0 = n0 * n1\nt1 = t0 - n2\nt2 = t1 / 4.0\nanswer = t2 - n2\nprint(answer)" + ], + "Output Answer": [ + "12.5" + ], + "split": "dev" + }, + { + "Input": "how many unique positive odd integers less than 90 are equal to the product of a positive multiple of 5 and an odd number ?", + "Output Program": [ + "n0 = 90.0\nn1 = 5.0\nt0 = n0 / n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "dev" + }, + { + "Input": "if # is an operation which results in adding the digits of integer until a single digit is left , what is the probability that a number picked up in first 90 positive integers will have the result of # as an odd digit ? ( example 99 = 9 + 9 = 18 = 1 + 8 = 9 , so # = 9 )", + "Output Program": [ + "n0 = 90.0\nn1 = 99.0\nn2 = 9.0\nn3 = 9.0\nn4 = 18.0\nn5 = 1.0\nn6 = 8.0\nn7 = 9.0\nn8 = 9.0\nt0 = n2 + n5\nt1 = t0 / 2.0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "0.5555555555555556" + ], + "split": "dev" + }, + { + "Input": "operation # is defined as : a # b = 4 a ^ 2 + 4 b ^ 2 + 8 ab for all non - negative integers . what is the value of ( a + b ) + 6 , when a # b = 100 ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 2.0\nn2 = 4.0\nn3 = 2.0\nn4 = 8.0\nn5 = 6.0\nn6 = 100.0\nt0 = n6 / n0\nt1 = math.sqrt(max(0, t0))\nanswer = n5 + t1\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "dev" + }, + { + "Input": "the sum of all the digits of the integers from 18 to 21 inclusive is 24 ( 1 + 8 + 1 + 9 + 2 + 0 + 2 + 1 = 24 ) . what is the sum t of all the digits of the integers from 0 to 99 inclusive ?", + "Output Program": [ + "n0 = 18.0\nn1 = 21.0\nn2 = 24.0\nn3 = 1.0\nn4 = 8.0\nn5 = 1.0\nn6 = 9.0\nn7 = 2.0\nn8 = 0.0\nn9 = 2.0\nn10 = 1.0\nn11 = 24.0\nn12 = 0.0\nn13 = 99.0\nt0 = n6 + n3\nt1 = 10.0 * n7\nt2 = n6 * t0\nt3 = t2 / n7\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "900" + ], + "split": "dev" + }, + { + "Input": "in \u03b4 pqs above , if pq = 2 and ps = 3 , then", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\n\nanswer = n1 / n0\nprint(answer)" + ], + "Output Answer": [ + "1.5" + ], + "split": "dev" + }, + { + "Input": "if a \u00e3 \u2014 b = 2 a - 3 b + ab , then 3 \u00e3 \u2014 2 + 2 \u00e3 \u2014 3 is equal to :", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 3.0\nn3 = 2.0\nn4 = 2.0\nn5 = 3.0\nt0 = n0 * n2\nt1 = n0 * n1\nt2 = n0 * n0\nt3 = n1 * n2\nt4 = t0 - t1\nt5 = t2 - t3\nt6 = t0 + t4\nt7 = t0 + t5\nanswer = t6 + t7\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "dev" + }, + { + "Input": "bill made a profit of 10 % by selling a product . if he had purchased that product for 10 % less and sold it at a profit of 30 % , he would have received $ 63 more . what was his original selling price ?", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 30.0\nn3 = 63.0\nt0 = n0 / 100.0\nt1 = n2 / 100.0\nt2 = t0 + 1.0\nt3 = t1 + 1.0\nt4 = 1.0 - t0\nt5 = t3 * t4\nt6 = t5 - t2\nt7 = n3 / t6\nanswer = t2 * t7\nprint(answer)" + ], + "Output Answer": [ + "989.9999999999992" + ], + "split": "dev" + }, + { + "Input": "{ - 10 , - 6 , - 5 , - 4 , - 2.5 , - 1 , 0 , 2.5 , 4 , 6 , 7 , 10 } a number is to be selected at random from the set above . what is the probability that the number selected will be a solution of the equation ( x + 5 ) ( x + 10 ) ( 2 x - 5 ) = 0 ?", + "Output Program": [ + "n0 = 10.0\nn1 = 6.0\nn2 = 5.0\nn3 = 4.0\nn4 = 2.5\nn5 = 1.0\nn6 = 0.0\nn7 = 2.5\nn8 = 4.0\nn9 = 6.0\nn10 = 7.0\nn11 = 10.0\nn12 = 5.0\nn13 = 10.0\nn14 = 2.0\nn15 = 5.0\nn16 = 0.0\nt0 = n5 + n14\nt1 = n0 + n14\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.25" + ], + "split": "dev" + }, + { + "Input": "the average of 10 numbers is calculated as 18 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?", + "Output Program": [ + "n0 = 10.0\nn1 = 18.0\nn2 = 36.0\nn3 = 26.0\nt0 = n2 - n3\nt1 = t0 / n0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "dev" + }, + { + "Input": "the sum of the squares of the first 15 positive integers ( 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + . . . + 15 ^ 2 ) is equal to 1240 . what is the sum of the squares of the second 15 positive integers ( 16 ^ 2 + 17 ^ 2 + 18 ^ 2 + . . . + 30 ^ 2 ) ?", + "Output Program": [ + "n0 = 15.0\nn1 = 1.0\nn2 = 2.0\nn3 = 2.0\nn4 = 2.0\nn5 = 3.0\nn6 = 2.0\nn7 = 15.0\nn8 = 2.0\nn9 = 1240.0\nn10 = 15.0\nn11 = 16.0\nn12 = 2.0\nn13 = 17.0\nn14 = 2.0\nn15 = 18.0\nn16 = 2.0\nn17 = 30.0\nn18 = 2.0\nt0 = n17 + n1\nt1 = n5 + n5\nt2 = n17 * n2\nt3 = t2 + n1\nt4 = n17 * t0\nt5 = t3 * t4\nt6 = t5 / t1\nanswer = t6 - n9\nprint(answer)" + ], + "Output Answer": [ + "8215" + ], + "split": "dev" + }, + { + "Input": "there are 2 sections a and b in a class , consisting of 50 and 50 students respectively . if the average weight of section a is 60 kg and that of section b is 80 kg , find the average of the whole class ?", + "Output Program": [ + "n0 = 2.0\nn1 = 50.0\nn2 = 50.0\nn3 = 60.0\nn4 = 80.0\nt0 = n1 + n2\nt1 = n1 * n3\nt2 = n2 * n4\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "dev" + }, + { + "Input": "in a school with 632 students , the average age of the boys is 12 years and that of the girls is 11 years . if the average age of the school is 11 years 9 months , then the number of girls in the school is", + "Output Program": [ + "n0 = 632.0\nn1 = 12.0\nn2 = 11.0\nn3 = 11.0\nn4 = 9.0\nt0 = n4 / n1\nt1 = n0 * n1\nt2 = n2 + t0\nt3 = n0 * t2\nanswer = t1 - t3\nprint(answer)" + ], + "Output Answer": [ + "158" + ], + "split": "dev" + }, + { + "Input": "the average height of 35 boys in a class was calculated as 183 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ?", + "Output Program": [ + "import math\nn0 = 35.0\nn1 = 183.0\nn2 = 166.0\nn3 = 106.0\nt0 = n0 * n1\nt1 = t0 - n2\nt2 = n3 + t1\nt3 = t2 / n0\nanswer = math.floor(t3)\nprint(answer)" + ], + "Output Answer": [ + "181" + ], + "split": "dev" + }, + { + "Input": "each of the products produced yesterday was checked by worker x or worker y . 0.5 % of the products checked by worker x are defective and 0.8 % of the products checked by worker y are defective . if the total defective rate of all the products checked by worker x and worker y is 0.55 % , what fraction of the products was checked by worker y ?", + "Output Program": [ + "n0 = 0.5\nn1 = 0.8\nn2 = 0.55\nt0 = n2 - n0\nt1 = n1 - n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.1666666666666668" + ], + "split": "dev" + }, + { + "Input": "9 years ago i was 5 times as old as my eldest son . today i am 3 times his age . how old am i now ?", + "Output Program": [ + "n0 = 9.0\nn1 = 5.0\nn2 = 3.0\nt0 = n0 * n1\nanswer = n0 + t0\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "dev" + }, + { + "Input": "a caterer ordered 125 ice - cream bars and 125 sundaes . if the total price was $ 225.00 and the price of each ice - cream bar was $ 0.60 , what was the price of each sundae ?", + "Output Program": [ + "n0 = 125.0\nn1 = 125.0\nn2 = 225.0\nn3 = 0.6\nt0 = n0 * n3\nt1 = n2 - t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "1.2" + ], + "split": "dev" + }, + { + "Input": "the least number which should be added to 1789 so that the sum is exactly divisible by 5 , 6 , 4 and 3 is ?", + "Output Program": [ + "n0 = 1789.0\nn1 = 5.0\nn2 = 6.0\nn3 = 4.0\nn4 = 3.0\nt0 = n1 * n3\nt1 = 10.0 * 3.0\nt2 = n4 * t0\nt3 = t1 - 1.0\nt4 = n0 / t2\nt5 = t4 - t3\nt6 = t2 * t5\nanswer = t2 - t6\nprint(answer)" + ], + "Output Answer": [ + "11.000000000000014" + ], + "split": "dev" + }, + { + "Input": "i chose a number and divide it by 8 . then i subtracted 160 from the result and got 12 . what was the number i chose ?", + "Output Program": [ + "n0 = 8.0\nn1 = 160.0\nn2 = 12.0\nt0 = n1 + n2\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "1376" + ], + "split": "dev" + }, + { + "Input": "a certain number of horses and an equal number of men are going somewhere . half of the owners are on their horses ' back while the remaining ones are walking along leading their horses . if the number of legs walking on the ground is 40 , how many horses are there ?", + "Output Program": [ + "n0 = 40.0\nt0 = 2.0 / 2.0\nt1 = t0 + 4.0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "dev" + }, + { + "Input": "there are 4 chess amateurs playing in villa ' s chess club tournament . if each chess amateur plays with exactly 4 other amateurs , what is the total number of chess games possible to be played in the tournament ?", + "Output Program": [ + "n0 = 4.0\nn1 = 4.0\nt0 = n0 * n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "dev" + }, + { + "Input": "let the number which when multiplied by 15 is increased by 280 .", + "Output Program": [ + "n0 = 15.0\nn1 = 280.0\nt0 = n0 - 1.0\nanswer = n1 / t0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "dev" + }, + { + "Input": "in a school with 5 classes , each class has 2 students less than the previous class . how many students are there in the largest class if the total number of students at school is 105 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 105.0\nt0 = n1 + n1\nt1 = n1 + t0\nt2 = n1 + t1\nt3 = t1 + t1\nt4 = t3 + t2\nt5 = n2 - t4\nt6 = t5 / n0\nanswer = t2 + t6\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "dev" + }, + { + "Input": "the toll t , in dollars , for a truck using a certain bridge is given by the formula t = 0.50 + 0.50 ( x \u2212 2 ) , where x is the number of axles on the truck . what is the toll for an 18 - wheel truck that has 2 wheels on its front axle and 4 wheels on each of its other axles ?", + "Output Program": [ + "n0 = 0.5\nn1 = 0.5\nn2 = 2.0\nn3 = 18.0\nn4 = 2.0\nn5 = 4.0\nt0 = n3 - n2\nt1 = t0 / n5\nt2 = t1 + 1.0\nt3 = t2 - n2\nt4 = n1 * t3\nanswer = n0 + t4\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "dev" + }, + { + "Input": "in a group of 100 people , 90 have an age of more 30 years , and the others have an age of less than 20 years . if a person is selected at random from this group , what is the probability the person ' s age is less than 20 ?", + "Output Program": [ + "n0 = 100.0\nn1 = 90.0\nn2 = 30.0\nn3 = 20.0\nn4 = 20.0\nt0 = n0 - n1\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.1" + ], + "split": "dev" + }, + { + "Input": "how much is 80 % of 45 is greater than 4 / 5 of 25 ?", + "Output Program": [ + "n0 = 80.0\nn1 = 45.0\nn2 = 4.0\nn3 = 5.0\nn4 = 25.0\nt0 = n0 / 100.0\nt1 = n2 / n3\nt2 = n1 * t0\nt3 = n4 * t1\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "dev" + }, + { + "Input": "if p ( a ) = 5 / 7 and p ( b ) = 2 / 5 , find p ( a n b ) if a and b are independent events .", + "Output Program": [ + "n0 = 5.0\nn1 = 7.0\nn2 = 2.0\nn3 = 5.0\nt0 = n0 / n1\nt1 = n2 / n3\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "0.28571428571428575" + ], + "split": "dev" + }, + { + "Input": "in digging a pond 20 m * 10 m * 5 m the volumes of the soil extracted will be ?", + "Output Program": [ + "n0 = 20.0\nn1 = 10.0\nn2 = 5.0\nt0 = n0 * n1\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "1000" + ], + "split": "dev" + }, + { + "Input": "if the average ( arithmetic mean ) of a and b is 110 , and the average of b and c is 170 , what is the value of a \u2212 c ?", + "Output Program": [ + "n0 = 110.0\nn1 = 170.0\nt0 = n1 * 2.0\nt1 = n0 * 2.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "dev" + }, + { + "Input": "line m lies in the xy - plane . the y - intercept of line m is - 2 , and line m passes through the midpoint of the line segment whose endpoints are ( 2 , 8 ) and ( 144 ) . what is the slope of line m ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 8.0\nn3 = 144.0\nt0 = n3 % 10.0\nt1 = n2 + t0\nt2 = n3 - t0\nt3 = t1 / 2.0\nt4 = t2 / 10.0\nt5 = n0 + t4\nt6 = t5 / 2.0\nt7 = t6 - n0\nanswer = t3 / t7\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "dev" + }, + { + "Input": "the average weight of a , b and c is 60 kg . if the average weight of a and b be 70 kg and that of b and c be 50 kg , then the weight of b is :", + "Output Program": [ + "n0 = 60.0\nn1 = 70.0\nn2 = 50.0\nt0 = n1 * 2.0\nt1 = n2 * 2.0\nt2 = n0 * 3.0\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "dev" + }, + { + "Input": "after spending rs . 5000 on rent , rs . 1500 on milk , rs . 4500 on groceries , rs . 2500 on childrens education rs . 2000 on petrol and rs . 2500 on miscellaneous expenses , mr . kishore saved 10 % of his monthly salary . how much did he save in rs . ?", + "Output Program": [ + "n0 = 5000.0\nn1 = 1500.0\nn2 = 4500.0\nn3 = 2500.0\nn4 = 2000.0\nn5 = 2500.0\nn6 = 10.0\nt0 = n0 + n1\nt1 = 100.0 - n6\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nt5 = n5 + t4\nt6 = t5 * 100.0\nt7 = t6 / t1\nanswer = t7 - t5\nprint(answer)" + ], + "Output Answer": [ + "2000" + ], + "split": "dev" + }, + { + "Input": "find the product of the local value and absolute value of 4 in 564823", + "Output Program": [ + "n0 = 4.0\nn1 = 564823.0\nt0 = n0 * 1000.0\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "16000" + ], + "split": "dev" + }, + { + "Input": "robert ' s salary was decreased by 70 % and subsequently increased by 70 % . how much percentage does he lose ?", + "Output Program": [ + "n0 = 70.0\nn1 = 70.0\nt0 = n0 + 100.0\nt1 = 100.0 * 100.0\nt2 = 100.0 - n0\nt3 = t0 * t2\nt4 = t1 - t3\nt5 = t4 / t1\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "49" + ], + "split": "dev" + }, + { + "Input": "the difference between the value of a number increased by 12.5 % and the value of the original number decreased by 25 % is 30 . what is the original number e ?", + "Output Program": [ + "n0 = 12.5\nn1 = 25.0\nn2 = 30.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = t0 + 1.0\nt3 = 1.0 - t1\nt4 = t2 - t3\nanswer = n2 / t4\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "dev" + }, + { + "Input": "what is the remainder when you divide 2 ^ 200 - 3 by 7 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 200.0\nn2 = 3.0\nn3 = 7.0\nt0 = n0 * n1\nanswer = t0 % n2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "dev" + }, + { + "Input": "the total marks obtained by a student in mathematics and physics is 32 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together .", + "Output Program": [ + "n0 = 32.0\nn1 = 20.0\nt0 = n0 + n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "dev" + }, + { + "Input": "in the rectangular coordinate system , if the line x = 4 y + 5 passes through points ( m , n ) and ( m + 2 , n + p ) , what is the value of p ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 2.0\n\nanswer = n2 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "dev" + }, + { + "Input": "the average weight of 4 students decreases by 8 kg when one of them weighing 96 kg is replaced by a new student . the weight of the student is", + "Output Program": [ + "n0 = 4.0\nn1 = 8.0\nn2 = 96.0\nt0 = n0 * n1\nanswer = n2 - t0\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "dev" + }, + { + "Input": "an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 16 - meter platform and caught it after it had traveled 45 meters . how many times did the ball bounce ?", + "Output Program": [ + "n0 = 16.0\nn1 = 45.0\nt0 = n0 / 2.0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "dev" + }, + { + "Input": "average between 2 sets of numbers is closer to the set with more no ' s ?", + "Output Program": [ + "t0 = 2.0 * 4.0\nanswer = t0 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "dev" + }, + { + "Input": "elvin ' s monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for internet service . elvin ' s total telephone bill for january was $ 46 and elvin ' s total telephone bill for february was 76 $ . if elvin ' s charge for the calls he made in february was twice the charge for the calls he made in january , what is elvin ' s fixed monthly charge for internet service ?", + "Output Program": [ + "n0 = 46.0\nn1 = 76.0\nt0 = n0 * 2.0\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "dev" + }, + { + "Input": "a batsman in his 17 th innings makes a score of 85 and their by increasing his average by 3 . what is his average after the 17 thinnings ?", + "Output Program": [ + "n0 = 17.0\nn1 = 85.0\nn2 = 3.0\nn3 = 17.0\nt0 = n0 * n2\nt1 = n1 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "37" + ], + "split": "dev" + }, + { + "Input": "the average ( arithmetic mean ) of 4 different integers is 76 . if the largest integer is 90 , what is the least possible value of the smallest integer ?", + "Output Program": [ + "n0 = 4.0\nn1 = 76.0\nn2 = 90.0\nt0 = n0 * n1\nt1 = n2 - 1.0\nt2 = n2 - 2.0\nt3 = t0 - n2\nt4 = t3 - t1\nanswer = t4 - t2\nprint(answer)" + ], + "Output Answer": [ + "37" + ], + "split": "dev" + }, + { + "Input": "the average salary of all the workers in a workshop is $ 8000 . the average salary of 7 technicians is $ 12000 and the average salary of the rest is $ 6000 . the total number of workers in the shop is ?", + "Output Program": [ + "n0 = 8000.0\nn1 = 7.0\nn2 = 12000.0\nn3 = 6000.0\nt0 = n1 * n2\nt1 = n1 * n3\nt2 = n0 - n3\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "dev" + }, + { + "Input": "if john makes a contribution to a charity fund at school , the average contribution size will increase by 50 % reaching $ 75 per person . if there were 3 other contributions made before john ' s , what is the size of his donation ?", + "Output Program": [ + "n0 = 50.0\nn1 = 75.0\nn2 = 3.0\nt0 = n2 + 1.0\nt1 = n1 * t0\nt2 = n0 * t0\nt3 = t1 - t2\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "dev" + }, + { + "Input": "seller selling an apple for rs . 18 , a seller loses 1 / 6 th of what it costs him . the cp of the apple is ?", + "Output Program": [ + "n0 = 18.0\nn1 = 1.0\nn2 = 6.0\n\nanswer = n0 + n1\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "dev" + }, + { + "Input": "if n is a positive integer and the product of all the integers from 1 to n , inclusive , is a multiple of 8 , what is the least possible value of n ?", + "Output Program": [ + "n0 = 1.0\nn1 = 8.0\n\nanswer = n1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "dev" + }, + { + "Input": "a man saves 20 % of his monthly salary . if an account of dearness of things he is to increase his monthly expenses by 20 % , he is only able to save rs . 250 per month . what is his monthly salary ?", + "Output Program": [ + "n0 = 20.0\nn1 = 20.0\nn2 = 250.0\nt0 = n1 / 100.0\nt1 = n2 * 100.0\nt2 = 100.0 - n0\nt3 = t0 * t2\nt4 = t3 + t2\nt5 = 100.0 - t4\nanswer = t1 / t5\nprint(answer)" + ], + "Output Answer": [ + "6250" + ], + "split": "dev" + }, + { + "Input": "if 15 students in a class average 75 % on an exam and 10 students average 90 % on the same exam , what is the average in percent for all 25 students ?", + "Output Program": [ + "n0 = 15.0\nn1 = 75.0\nn2 = 10.0\nn3 = 90.0\nn4 = 25.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = t0 + t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "81" + ], + "split": "dev" + }, + { + "Input": "for each of her sales , a saleswoman receives a commission equal to 20 percent of the first $ 500 of the total amount of the sale , plus 50 percent of the total amount in excess of $ 500 . if the total amount of one of her sales was $ 800 , the saleswoman \u2019 s commission was approximately what percent of the total amount of the sale ?", + "Output Program": [ + "n0 = 20.0\nn1 = 500.0\nn2 = 50.0\nn3 = 500.0\nn4 = 800.0\nt0 = n0 / 100.0\nt1 = n2 / 100.0\nt2 = n4 - n1\nt3 = n1 * t0\nt4 = t1 * t2\nt5 = t3 + t4\nt6 = t5 / n4\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "31.25" + ], + "split": "dev" + }, + { + "Input": "tourist purchased a total of 30 travelers checks in $ 50 and $ 100 denominations . the total worth of the travelers checks is $ 1800 . how many checks of $ 50 denominations can he spend so that average amount ( arithmetic mean ) of the remaining travelers checks is $ 100 ?", + "Output Program": [ + "n0 = 30.0\nn1 = 50.0\nn2 = 100.0\nn3 = 1800.0\nn4 = 50.0\nn5 = 100.0\nt0 = n0 * n5\nt1 = n5 - n1\nt2 = t0 - n3\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "dev" + }, + { + "Input": "average of 5 consecutive even numbers is 35 . find the greatest number in these 5 numbers ?", + "Output Program": [ + "n0 = 5.0\nn1 = 35.0\nn2 = 5.0\nt0 = 2.0 + 2.0\nt1 = n0 * n1\nt2 = t0 + 2.0\nt3 = t2 + 2.0\nt4 = t2 + t2\nt5 = t3 + t4\nt6 = t5 + t1\nanswer = t6 / n0\nprint(answer)" + ], + "Output Answer": [ + "39" + ], + "split": "dev" + }, + { + "Input": "john found that the average of 15 no . ' s is 40 . if 10 is added to each number then the mean of number is ?", + "Output Program": [ + "n0 = 15.0\nn1 = 40.0\nn2 = 10.0\n\nanswer = n1 + n2\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "dev" + }, + { + "Input": "a car salesman earns a base salary of $ 1000 per month plus a commission of $ 200 for each car he sells . if the car salesman earned $ 2000 in march , how many cars does he need to sell in april in order to double his march earnings ?", + "Output Program": [ + "n0 = 1000.0\nn1 = 200.0\nn2 = 2000.0\nt0 = n2 * 2.0\nt1 = t0 - n0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "dev" + }, + { + "Input": "barbata invests $ 2200 in the national bank at 5 % . how much additional money must she invest at 8 % so that the total annual income will be equal to 6 % of her entire investment ?", + "Output Program": [ + "n0 = 2200.0\nn1 = 5.0\nn2 = 8.0\nn3 = 6.0\nt0 = n3 / 100.0\nt1 = n1 / 100.0\nt2 = n2 / 100.0\nt3 = n0 * t0\nt4 = n0 * t1\nt5 = t2 - t0\nt6 = t3 - t4\nanswer = t6 / t5\nprint(answer)" + ], + "Output Answer": [ + "1099.9999999999998" + ], + "split": "dev" + }, + { + "Input": "24 lbs of coffee p and 25 lbs of coffee v are mixed to make coffee x and y . the ratio of p to v in coffee x is 4 to 1 , in y is 1 to 5 . how much of p is contained in the mixture x ?", + "Output Program": [ + "n0 = 24.0\nn1 = 25.0\nn2 = 4.0\nn3 = 1.0\nn4 = 1.0\nn5 = 5.0\nt0 = n0 * n5\nt1 = n0 - n5\nt2 = t0 - n1\nt3 = t2 / t1\nanswer = n2 * t3\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "dev" + }, + { + "Input": "the average of 10 numbers is 0 . in those 10 , at the least , how many may be greater than or equal to zero ?", + "Output Program": [ + "n0 = 10.0\nn1 = 0.0\nn2 = 10.0\n\nanswer = n1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "dev" + }, + { + "Input": "if x + y = 260 , x - y = 200 , for integers of x and y , y = ?", + "Output Program": [ + "n0 = 260.0\nn1 = 200.0\nt0 = n0 + n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "230" + ], + "split": "dev" + }, + { + "Input": "suraj has a certain average of runs for 16 innings . in the 17 th innings he scores 92 runs thereby increasing his average by 4 runs . what is his average after the 17 th innings ?", + "Output Program": [ + "n0 = 16.0\nn1 = 17.0\nn2 = 92.0\nn3 = 4.0\nn4 = 17.0\nt0 = n0 * n3\nt1 = n1 - n0\nt2 = n2 - t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "dev" + }, + { + "Input": "a man has some hens and cows . if the number of heads be 48 and the number of feet equals 136 , then the number of hens will be", + "Output Program": [ + "n0 = 48.0\nn1 = 136.0\nt0 = n0 * 4.0\nt1 = t0 - n1\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "dev" + }, + { + "Input": "the average of 25 results is 20 . the average of first 12 of those is 14 and the average of last 12 is 17 . what is the 13 th result ?", + "Output Program": [ + "n0 = 25.0\nn1 = 20.0\nn2 = 12.0\nn3 = 14.0\nn4 = 12.0\nn5 = 17.0\nn6 = 13.0\nt0 = n0 * n1\nt1 = n2 * n5\nt2 = n2 * n3\nt3 = t0 - t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "128" + ], + "split": "dev" + }, + { + "Input": "in an examination , 300 students appeared . out of these students ; 26 % got first division , 54 % got second division and the remaining just passed . assuming that no student failed ; find the number of students who just passed .", + "Output Program": [ + "n0 = 300.0\nn1 = 26.0\nn2 = 54.0\nt0 = n1 + n2\nt1 = 100.0 - t0\nt2 = n0 * t1\nanswer = t2 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "dev" + }, + { + "Input": "equal amount of water were poured into two empty jars of different capacities , which made one jar 1 / 3 full and other jar 1 / 2 full . if the water in the jar with lesser capacity is then poured into the jar with greater capacity , what fraction of the larger jar will be filled with water ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 2.0\n\nanswer = 2.0 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.6666666666666666" + ], + "split": "dev" + }, + { + "Input": "mary ' s income is 60 percent more than tim ' s income , and tim ' s income is 60 percent less than juan ' s income . what percent of juan ' s income is mary ' s income ?", + "Output Program": [ + "n0 = 60.0\nn1 = 60.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = t0 + 1.0\nt3 = 1.0 - t1\nt4 = t2 * t3\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "64.00000000000001" + ], + "split": "dev" + }, + { + "Input": "12 . what is the dividend . divisor 17 , the quotient is 9 and the remainder is 7 .", + "Output Program": [ + "n0 = 12.0\nn1 = 17.0\nn2 = 9.0\nn3 = 7.0\nt0 = n1 * n2\nanswer = n3 + t0\nprint(answer)" + ], + "Output Answer": [ + "160" + ], + "split": "dev" + }, + { + "Input": "if 1 / ( x + 4 ) + 1 / ( x - 4 ) = 1 / ( x - 4 ) , what is the value of x ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 1.0\nn3 = 4.0\nn4 = 1.0\nn5 = 4.0\nt0 = n1 + n0\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "dev" + }, + { + "Input": "the average of 9 observations was 8 , that of the 1 st of 5 being 10 and that of the last 5 being 8 . what was the 5 th observation ?", + "Output Program": [ + "n0 = 9.0\nn1 = 8.0\nn2 = 1.0\nn3 = 5.0\nn4 = 10.0\nn5 = 5.0\nn6 = 8.0\nn7 = 5.0\nt0 = n3 * n4\nt1 = n1 * n3\nt2 = n0 * n1\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "dev" + }, + { + "Input": "sophia finished 2 / 3 of a book . she calculated that she finished 30 more pages than she has yet to read . how long is her book ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 30.0\nt0 = n0 / n1\nt1 = 1.0 - t0\nanswer = n2 / t1\nprint(answer)" + ], + "Output Answer": [ + "89.99999999999999" + ], + "split": "dev" + }, + { + "Input": "which expression is the greatest ?", + "Output Program": [ + "t0 = 3.0 * 3.0\nt1 = 3600.0 - 4.0\nt2 = 3600.0 - t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.9986095661846496" + ], + "split": "dev" + }, + { + "Input": "if there are 200 questions in a 3 hr examination . among these questions are 100 type a problems , which requires twice as much as time be spent than the rest of the type b problems . how many minutes should be spent on type a problems ?", + "Output Program": [ + "n0 = 200.0\nn1 = 3.0\nn2 = 100.0\nt0 = n1 * 60.0\nt1 = n2 * 2.0\nt2 = n0 - n2\nt3 = t1 + t2\nt4 = t0 / t3\nt5 = t4 * 2.0\nanswer = n2 * t5\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "dev" + }, + { + "Input": "a card board of size 34 * 14 has to be attached to a wooden box and a total of 35 pins are to be used on the each side of the card box . find the total number of pins used .", + "Output Program": [ + "n0 = 34.0\nn1 = 14.0\nn2 = 35.0\nt0 = 1.0 + 4.0\nt1 = 10.0 - 1.0\nt2 = t0 * t1\nt3 = t2 - 10.0\nanswer = t3 + 100.0\nprint(answer)" + ], + "Output Answer": [ + "135" + ], + "split": "dev" + }, + { + "Input": "evaluate combination 98 c 96 = 98 ! / ( 96 ) ! ( 2 ) !", + "Output Program": [ + "n0 = 98.0\nn1 = 96.0\nn2 = 98.0\nn3 = 96.0\nn4 = 2.0\nt0 = n0 - 1.0\nt1 = n0 * t0\nanswer = t1 / n4\nprint(answer)" + ], + "Output Answer": [ + "4753" + ], + "split": "dev" + }, + { + "Input": "a ranch has both horses and ponies . exactly 3 / 10 of the ponies have horseshoes , and exactly 5 / 8 of the ponies with horseshoes are from iceland . if there are 4 more horses than ponies , what is the minimum possible combined number of horses and ponies on the ranch ?", + "Output Program": [ + "import scipy\nn0 = 3.0\nn1 = 10.0\nn2 = 5.0\nn3 = 8.0\nn4 = 4.0\nt0 = n1 / n2\nt1 = n3 * t0\nt2 = scipy.lcm(int(n1), int(t1))\nt3 = n4 + t2\nanswer = t3 + t2\nprint(answer)" + ], + "Output Answer": [ + "164" + ], + "split": "dev" + }, + { + "Input": "there are 5 chess amateurs playing in villa ' s chess club tournament . if each chess amateur plays with exactly 8 other amateurs , what is the total number of chess games possible to be played in the tournament ?", + "Output Program": [ + "n0 = 5.0\nn1 = 8.0\nt0 = n0 * n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "dev" + }, + { + "Input": "if a store owner increases a product \u2019 s price by 20 percent and then increases this price by another 15 percent , what percent of the original price is the total price increase ?", + "Output Program": [ + "n0 = 20.0\nn1 = 15.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = t0 * 100.0\nt3 = t2 + 100.0\nt4 = t3 * t1\nanswer = t4 + t2\nprint(answer)" + ], + "Output Answer": [ + "38" + ], + "split": "dev" + }, + { + "Input": "if 5 students are made to sit in a row , then 6 do n ' t have seats . if 12 students are made to sit in a row , then 3 rows are empty . how many students have to sit a row such that each row has equal number of students and all students are seated ?", + "Output Program": [ + "n0 = 5.0\nn1 = 6.0\nn2 = 12.0\nn3 = 3.0\nt0 = n2 * n3\nt1 = n2 - n0\nt2 = n1 + t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "dev" + }, + { + "Input": "a pupil ' s marks were wrongly entered as 85 instead of 33 . due to that the average marks for the class got increased by half . the number of pupils in the class is :", + "Output Program": [ + "n0 = 85.0\nn1 = 33.0\nt0 = n0 - n1\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "104" + ], + "split": "dev" + }, + { + "Input": "a student has to obtain 33 % of the total marks to pass . he got 125 marks and failed by 40 marks . the maximum marks are ?", + "Output Program": [ + "n0 = 33.0\nn1 = 125.0\nn2 = 40.0\nt0 = n1 + n2\nt1 = n0 / 100.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "dev" + }, + { + "Input": "the telephone company wants to add an area code composed of 2 letters to every phone number . in order to do so , the company chose a special sign language containing 524 different signs . if the company used 522 of the signs fully and two remained unused , how many additional area codes can be created if the company uses all 524 signs ?", + "Output Program": [ + "n0 = 2.0\nn1 = 524.0\nn2 = 522.0\nn3 = 524.0\nt0 = n1 - n2\nt1 = n2 * t0\nanswer = t1 * t0\nprint(answer)" + ], + "Output Answer": [ + "2088" + ], + "split": "dev" + }, + { + "Input": "a case contains c cartons . each carton contains b boxes , and each box contains 200 paper clips . how many paper clips are contained in 2 cases ?", + "Output Program": [ + "n0 = 200.0\nn1 = 2.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "dev" + }, + { + "Input": "what is the value of x ^ 2 yz \u2212 xyz ^ 2 , if x = \u2212 2 , y = 1 , and z = 1 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 2.0\nn3 = 1.0\nn4 = 1.0\nt0 = -n0\nt1 = n3 * t0\nt2 = t0 - n3\nt3 = n3 * t1\nanswer = t3 * t2\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "dev" + }, + { + "Input": "2.205 divided by 0.3 gives", + "Output Program": [ + "n0 = 2.205\nn1 = 0.3\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "7.3500000000000005" + ], + "split": "dev" + }, + { + "Input": "having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.88 at the candy store . what is john \u2019 s weekly allowance ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 0.88\nt0 = n0 / n1\nt1 = 1.0 / n0\nt2 = 1.0 - t0\nt3 = t1 * t2\nt4 = t0 + t3\nt5 = 1.0 - t4\nanswer = n2 / t5\nprint(answer)" + ], + "Output Answer": [ + "3.2999999999999994" + ], + "split": "dev" + }, + { + "Input": "exactly 3 / 7 of the people in the room are under the age of 21 , and exactly 5 / 10 of the people in the room are over the age of 65 . if the total number of the people in the room is greater than 50 and less than 100 , how many people in the room are under the age of 21 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 21.0\nn3 = 5.0\nn4 = 10.0\nn5 = 65.0\nn6 = 50.0\nn7 = 100.0\nn8 = 21.0\nt0 = n1 * n4\nt1 = n0 * t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "dev" + }, + { + "Input": "a 5 - digit number is formed by the digits 2 , 45 , 68 ( each digit used exactly once ) . what is the probability that the number formed is divisible by 4 ?", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 2.0\nn2 = 45.0\nn3 = 68.0\nn4 = 4.0\nt0 = math.factorial(min(15, int(n4)))\nt1 = math.factorial(min(15, int(n0)))\nt2 = n1 * t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.4" + ], + "split": "dev" + }, + { + "Input": "if x is 20 percent more than y and y is 60 percent less than z , then x is what percent of z ?", + "Output Program": [ + "n0 = 20.0\nn1 = 60.0\nt0 = n0 / 100.0\nt1 = 100.0 - n1\nt2 = t0 + 1.0\nanswer = t2 * t1\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "dev" + }, + { + "Input": "the area of one square is x ^ 2 + 4 x + 4 and the area of another square is 4 x ^ 2 \u2212 12 x + 9 . if the sum of the perimeters of both squares is 32 , what is the value of x ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 4.0\nn3 = 4.0\nn4 = 2.0\nn5 = 12.0\nn6 = 9.0\nn7 = 32.0\nt0 = n5 / n0\nt1 = t0 * n3\nt2 = t1 - n1\nt3 = n7 - t2\nanswer = t3 / n1\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "dev" + }, + { + "Input": "keats library purchases a number of new books , all in the category of biography , and the library does not acquire any other books . with the addition of the new biographies , the biography collection of the library amounts to 30 % of the total number of books in the library . if prior to the purchase , only 20 % of the books in keats library were biographies , by what percent has the number of biographies in the library increased ?", + "Output Program": [ + "n0 = 30.0\nn1 = 20.0\nt0 = n0 * 100.0\nt1 = n1 * 100.0\nt2 = 100.0 - n0\nt3 = t0 - t1\nt4 = t3 / t2\nt5 = t4 / n1\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "71.42857142857143" + ], + "split": "dev" + }, + { + "Input": "if the average ( arithmetic mean ) of the 4 numbers 3 , 16 , 33 , and ( n + 1 ) is 20 , then n =", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 16.0\nn3 = 33.0\nn4 = 1.0\nn5 = 20.0\nt0 = n1 + n2\nt1 = n0 * n5\nt2 = n3 + t0\nt3 = n4 + t2\nanswer = t1 - t3\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "dev" + }, + { + "Input": "the mean of 50 observations is 200 . but later he found that there is decrements of 6 from each observations . what is the the updated mean is ?", + "Output Program": [ + "n0 = 50.0\nn1 = 200.0\nn2 = 6.0\n\nanswer = n1 - n2\nprint(answer)" + ], + "Output Answer": [ + "194" + ], + "split": "dev" + }, + { + "Input": "find the constant k so that : - x 2 - ( k + 10 ) x - 8 = - ( x - 2 ) ( x - 4 )", + "Output Program": [ + "n0 = 2.0\nn1 = 10.0\nn2 = 8.0\nn3 = 2.0\nn4 = 4.0\nt0 = n0 + n4\nanswer = n1 + t0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "dev" + }, + { + "Input": "102 \u00e3 \u2014 102 + 98 \u00e3 \u2014 98 = ?", + "Output Program": [ + "n0 = 102.0\nn1 = 102.0\nn2 = 98.0\nn3 = 98.0\nt0 = n0**min(2.0, 5)\nt1 = n2**min(2.0, 5)\nt2 = t0 - n0\nt3 = t1 - n2\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "19808" + ], + "split": "dev" + }, + { + "Input": "30 pens and 75 pencils were purchased for 750 . if the average price of a pencil was 2.00 , find the average price of a pen .", + "Output Program": [ + "n0 = 30.0\nn1 = 75.0\nn2 = 750.0\nn3 = 2.0\nt0 = n1 * n3\nt1 = n2 - t0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "dev" + }, + { + "Input": "the visitors of a modern art museum who watched a certain picasso painting were asked to fill in a short questionnaire indicating whether they had enjoyed looking at the picture and whether they felt they had understood it . according to the results of the survey , all 110 visitors who did not enjoy the painting also did not feel they had understood the painting , and the number of visitors who enjoyed the painting was equal to the number of visitors who felt they had understood the painting . if 3 / 4 of the visitors who answered the questionnaire both enjoyed the painting and felt they had understood the painting , then how many visitors answered the questionnaire ?", + "Output Program": [ + "n0 = 110.0\nn1 = 3.0\nn2 = 4.0\nt0 = n1 / n2\nt1 = 1.0 - t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "440" + ], + "split": "dev" + }, + { + "Input": "exactly 3 sides of a certain 10 - sided die are red . what is the probability that kumar rolls the die 3 times and the die lands with a red side up for the first time on the third roll ?", + "Output Program": [ + "n0 = 3.0\nn1 = 10.0\nn2 = 3.0\nt0 = n0 / n1\nt1 = n1 - n0\nt2 = t1 / n1\nt3 = t2**min(2.0, 5)\nanswer = t0 * t3\nprint(answer)" + ], + "Output Answer": [ + "0.14699999999999996" + ], + "split": "dev" + }, + { + "Input": "the average runs scored by a batsman in 25 matches is 45 . in the next 7 matches the batsman scored an average of 15 runs . find his average in all the 32 matches ?", + "Output Program": [ + "n0 = 25.0\nn1 = 45.0\nn2 = 7.0\nn3 = 15.0\nn4 = 32.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "38.4375" + ], + "split": "dev" + }, + { + "Input": "a student has to obtain 50 % of the total marks to pass . he got 200 marks and failed by 20 marks . the maximum marks are ?", + "Output Program": [ + "n0 = 50.0\nn1 = 200.0\nn2 = 20.0\nt0 = n1 + n2\nt1 = n0 / 100.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "440" + ], + "split": "dev" + }, + { + "Input": "the tax on a commodity is diminished by 20 % but its consumption is increased by 10 % . find the decrease percent in the revenue derived from it ?", + "Output Program": [ + "n0 = 20.0\nn1 = 10.0\nt0 = n1 + 100.0\nt1 = 100.0 - n0\nt2 = t0 * t1\nt3 = t2 / 100.0\nanswer = 100.0 - t3\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "dev" + }, + { + "Input": "a small pool filled only with water will require an additional 300 gallons of water in order to be filled to 80 % of its capacity . if pumping in these additional 300 gallons of water will increase the amount of water in the pool by 25 % , what is the total capacity of the pool in gallons ?", + "Output Program": [ + "n0 = 300.0\nn1 = 80.0\nn2 = 300.0\nn3 = 25.0\nt0 = n1 / 100.0\nt1 = n0 * 100.0\nt2 = t1 / n3\nt3 = n0 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "1875" + ], + "split": "dev" + }, + { + "Input": "if 2 ^ 5 , 3 ^ 3 , and 14 ^ 2 are all factors of the product of 936 and w where w is a positive integer , what is the smallest possible value of w ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 3.0\nn3 = 3.0\nn4 = 14.0\nn5 = 2.0\nn6 = 936.0\nt0 = n4 / n0\nt1 = n0**min(n0, 5)\nt2 = n2 * t1\nt3 = t0 * t2\nanswer = n0 * t3\nprint(answer)" + ], + "Output Answer": [ + "168" + ], + "split": "dev" + }, + { + "Input": "a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 1032 in total compensation , how many total hours did he work that week ?", + "Output Program": [ + "n0 = 16.0\nn1 = 40.0\nn2 = 40.0\nn3 = 75.0\nn4 = 1032.0\nt0 = n3 + 100.0\nt1 = n0 * n1\nt2 = n0 * t0\nt3 = n4 - t1\nt4 = t2 / 100.0\nt5 = t3 / t4\nanswer = n1 + t5\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "dev" + }, + { + "Input": "p , q and r have rs . 7000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?", + "Output Program": [ + "n0 = 7000.0\nt0 = 2.0 / 3.0\nt1 = t0 + 1.0\nt2 = n0 / t1\nanswer = t2 * t0\nprint(answer)" + ], + "Output Answer": [ + "2800" + ], + "split": "dev" + }, + { + "Input": "the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 75 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.5\nn2 = 75.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "95" + ], + "split": "dev" + }, + { + "Input": "when a merchant imported a certain item , she paid a 7 percent import tax on the portion of the total value of the item in excess of $ 1,000 . if the amount of the import tax that the merchant paid was $ 109.20 , what was the total value of the item ?", + "Output Program": [ + "n0 = 7.0\nn1 = 1000.0\nn2 = 109.2\nt0 = n0 / 100.0\nt1 = n2 / t0\nanswer = t1 + n1\nprint(answer)" + ], + "Output Answer": [ + "2560" + ], + "split": "dev" + }, + { + "Input": "at the end of the day , february 14 th , a florist had 120 roses left in his shop , all of which were red , white or pink in color and either long or short - stemmed . a third of the roses were short - stemmed , 20 of which were white and 10 of which were pink . the percentage of pink roses that were short - stemmed equaled the percentage of red roses that were short - stemmed . if none of the long - stemmed roses were white , what percentage of the long - stemmed roses were red ?", + "Output Program": [ + "n0 = 14.0\nn1 = 120.0\nn2 = 20.0\nn3 = 10.0\nt0 = n1 / 3.0\nt1 = n1 - t0\nt2 = t0 - n2\nt3 = t2 - n3\nt4 = n3 + t3\nt5 = t1 * t3\nt6 = t5 / t4\nt7 = t6 / t1\nanswer = t7 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "dev" + }, + { + "Input": "the difference between a two - digit number and the number obtained by interchanging the positions of its digits is 27 . what is the difference between the two digits of that number ?", + "Output Program": [ + "n0 = 27.0\nt0 = 10.0 - 1.0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "dev" + }, + { + "Input": "set # 1 = { a , b , c , d , e , f } set # 2 = { k , l , m , n , o , p } there are these two sets of letters , and you are going to pick exactly one letter from each set . what is the probability of picking at least one vowel ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nt0 = 2.0 + 4.0\nt1 = 2.0 + 3.0\nt2 = 4.0 / t0\nt3 = t1 / t0\nt4 = t2 * t3\nanswer = n0 - t4\nprint(answer)" + ], + "Output Answer": [ + "0.4444444444444444" + ], + "split": "dev" + }, + { + "Input": "if a no . when divided by 44 , gives 432 as quotient and 0 as remainder . what will be the remainder when dividing thesame no . by 31", + "Output Program": [ + "n0 = 44.0\nn1 = 432.0\nn2 = 0.0\nn3 = 31.0\nt0 = n0 * n1\nanswer = t0 % n3\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "dev" + }, + { + "Input": "the age of somu is one - third his father ' s . 7 years back he was one - fifth of his father ' s age . what is his persent age ?", + "Output Program": [ + "n0 = 7.0\nt0 = 1.0 + 4.0\nt1 = n0 * t0\nt2 = t0 - 3.0\nt3 = t1 - n0\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "dev" + }, + { + "Input": "in a class , there are 18 boys who are over 160 cm tall . if these constitute 3 - fourths of the boys and the total number of boys is two - thirds of the total number of students in the class , what is the number of girls in the class ?", + "Output Program": [ + "n0 = 18.0\nn1 = 160.0\nn2 = 3.0\nt0 = n2 / 4.0\nt1 = 2.0 / n2\nt2 = n0 / t0\nt3 = t2 / t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "dev" + }, + { + "Input": "find value of x : 121 \u00d7 54 = x", + "Output Program": [ + "n0 = 121.0\nn1 = 54.0\nt0 = n0 + n0\nt1 = n0 * n0\nt2 = t1 / 2.0\nt3 = t0 + t2\nanswer = t3 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "75625" + ], + "split": "dev" + }, + { + "Input": "if 2 ^ 5 , 3 ^ 3 , and 13 ^ 2 are all factors of the product of 936 and w where w is a positive integer , what is the smallest possible value of w ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 3.0\nn3 = 3.0\nn4 = 13.0\nn5 = 2.0\nn6 = 936.0\nt0 = n4 / n0\nt1 = n0**min(n0, 5)\nt2 = n2 * t1\nt3 = t0 * t2\nanswer = n0 * t3\nprint(answer)" + ], + "Output Answer": [ + "156" + ], + "split": "dev" + }, + { + "Input": "i chose a number and divide it by 12 . then i subtracted 240 from the result and got 8 . what was the number i chose ?", + "Output Program": [ + "n0 = 12.0\nn1 = 240.0\nn2 = 8.0\nt0 = n1 + n2\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "2976" + ], + "split": "dev" + }, + { + "Input": "on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.30 per glass on the first day , what was the price per glass on the second day ?", + "Output Program": [ + "n0 = 0.3\nt0 = 1.0 + 1.0\nt1 = 1.0 + 2.0\nt2 = n0 * t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.19999999999999998" + ], + "split": "dev" + }, + { + "Input": "if 3 / w + 3 / x = 3 / y and wx = y , then the average ( arithmetic mean ) of w and x is", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 3.0\nt0 = n0 + n0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "dev" + }, + { + "Input": "- - - - - - - - - - - - - - - - yes - - - - - - - - - no - - - - unsure subject m - - - - 500 - - - - - - - - 200 - - - - - 100 subject r - - - - 400 - - - - - - - - 100 - - - - - 300 a total of 800 students were asked whether they found two subjects , m and r , interesting . each answer was either yes or no or unsure , and the numbers of students who gave these answers are listed in the table above . if 140 students answered yes only for subject m , how many of the students did not answer yes for either subject ?", + "Output Program": [ + "n0 = 500.0\nn1 = 200.0\nn2 = 100.0\nn3 = 400.0\nn4 = 100.0\nn5 = 300.0\nn6 = 800.0\nn7 = 140.0\nt0 = n0 - n7\nt1 = n7 + t0\nt2 = n3 - t0\nt3 = t1 + t2\nanswer = n6 - t3\nprint(answer)" + ], + "Output Answer": [ + "260" + ], + "split": "dev" + }, + { + "Input": "a number when divided b the sum of 555 and 445 gives two times their difference as quotient and 30 as the remainder . the number is :", + "Output Program": [ + "n0 = 555.0\nn1 = 445.0\nn2 = 30.0\nt0 = n0 - n1\nt1 = t0 * 2.0\nt2 = t1 * 100.0\nanswer = n2 + t2\nprint(answer)" + ], + "Output Answer": [ + "22030" + ], + "split": "dev" + }, + { + "Input": "if x ^ 2 + 9 / x ^ 2 = 10 , what is the value of x - 3 / x", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 9.0\nn2 = 2.0\nn3 = 10.0\nn4 = 3.0\nt0 = 2.0 * 3.0\nt1 = n3 - t0\nanswer = math.sqrt(max(0, t1))\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "dev" + }, + { + "Input": "if { x } is the product of all even integers from 1 to x inclusive , what is the greatest prime factor of { 12 } + { 10 } ?", + "Output Program": [ + "n0 = 1.0\nn1 = 12.0\nn2 = 10.0\nt0 = n1 + n2\nt1 = n0 * 2.0\nt2 = t0 / 2.0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "dev" + }, + { + "Input": "a women purchased 3 towels @ rs . 100 each , 5 towels @ rs . 150 each and two towels at a certain rate which is now slipped off from his memory . but she remembers that the average price of the towels was rs . 165 . find the unknown rate of two towels ?", + "Output Program": [ + "n0 = 3.0\nn1 = 100.0\nn2 = 5.0\nn3 = 150.0\nn4 = 165.0\nt0 = n0 + n2\nt1 = n2 * n3\nt2 = n0 * n1\nt3 = t0 + 2.0\nt4 = n4 * t3\nt5 = t4 - t1\nanswer = t5 - t2\nprint(answer)" + ], + "Output Answer": [ + "600" + ], + "split": "dev" + }, + { + "Input": "every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 57600 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 8.0\nn2 = 57600.0\nt0 = n0 / n1\nt1 = n2 * t0\nt2 = n2 + t1\nt3 = t2 * t0\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "72900" + ], + "split": "dev" + }, + { + "Input": "find the 10 th term of an arithmetic progression whose first term is 8 and the common difference is 2 .", + "Output Program": [ + "n0 = 10.0\nn1 = 8.0\nn2 = 2.0\nt0 = n0 - 1.0\nt1 = n2 * t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "dev" + }, + { + "Input": "if ( 10 x + 2 ) / 4 - ( 3 x - 6 ) / 18 = ( 2 x + 4 ) / 3 , then what is the value of x ?", + "Output Program": [ + "import scipy\nn0 = 10.0\nn1 = 2.0\nn2 = 4.0\nn3 = 3.0\nn4 = 6.0\nn5 = 18.0\nn6 = 2.0\nn7 = 4.0\nn8 = 3.0\nt0 = scipy.lcm(int(n2), int(n5))\nt1 = scipy.lcm(int(n3), int(t0))\nt2 = t1 / n3\nt3 = t1 / n2\nt4 = t1 / n5\nt5 = n2 * t2\nt6 = n1 * t3\nt7 = n4 * t4\nt8 = n0 * t3\nt9 = n3 * t4\nt10 = n1 * t2\nt11 = t5 - t6\nt12 = t8 - t9\nt13 = t11 - t7\nt14 = t12 - t10\nanswer = t13 / t14\nprint(answer)" + ], + "Output Answer": [ + "0.3" + ], + "split": "dev" + }, + { + "Input": "oil cans x and y are right circular cylinders and the height and radius of y are each 4 times those of x . if the oil in can x filled to capacity sells for $ 2 , how much does the oil in y sell for if y is only half filled ?", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\nt0 = n0**min(n1, 5)\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "dev" + }, + { + "Input": "how many distinct integer values of n satisfy the inequality | | n - 3 | + 4 | \u2264 15 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 15.0\nt0 = 3.0 * 4.0\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "dev" + }, + { + "Input": "a telephone company needs to create a set of 3 - digit area codes . the company is entitled to use only digits 2 , 4 and 3 , which can be repeated . if the product of the digits in the area code must be even , how many different codes can be created ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 4.0\nn3 = 3.0\nt0 = n0**min(n0, 5)\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "dev" + }, + { + "Input": "if p # q denotes the least common multiple of p and q , then e = ( ( 12 # 16 ) # ( 18 # 24 ) ) = ?", + "Output Program": [ + "n0 = 12.0\nn1 = 16.0\nn2 = 18.0\nn3 = 24.0\nt0 = n2 * n3\nt1 = n0 * n1\nt2 = t0 - t1\nt3 = t2 / 2.0\nanswer = n3 + t3\nprint(answer)" + ], + "Output Answer": [ + "144" + ], + "split": "dev" + }, + { + "Input": "if m is an integer such that ( - 2 ) ^ 2 m = 2 ^ ( 6 - m ) then m = ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 2.0\nn3 = 6.0\nt0 = n0 + 1.0\nanswer = n3 / t0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "dev" + }, + { + "Input": "if rs . 10 be allowed as true discount on a bill of rs . 110 due at the end of a certain time , then the discount allowed on the same sum due at the end of double the time is :", + "Output Program": [ + "n0 = 10.0\nn1 = 110.0\nt0 = n0 + n1\nt1 = t0 - 100.0\nt2 = t1 / t0\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "18.333333333333332" + ], + "split": "dev" + }, + { + "Input": "a shopkeeper gave an additional 20 per cent concession on the reduced price after giving 30 per cent standard concession on an article . if arun bought that article for 1120 , what was the original price ?", + "Output Program": [ + "n0 = 20.0\nn1 = 30.0\nn2 = 1120.0\nt0 = n2 * 100.0\nt1 = 100.0 - n0\nt2 = 100.0 - n1\nt3 = t0 * 100.0\nt4 = t3 / t1\nanswer = t4 / t2\nprint(answer)" + ], + "Output Answer": [ + "2000" + ], + "split": "dev" + }, + { + "Input": "if x , y , and z are positive integers and 3 x = 4 y = 7 z , then the least possible value of x - y + z is", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 7.0\nt0 = n0 * n1\nt1 = n2 * t0\nt2 = t1 / n2\nt3 = t1 / n0\nt4 = t1 / n1\nt5 = t3 - t4\nanswer = t2 + t5\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "dev" + }, + { + "Input": "if log 10 5 + log 10 ( 5 x + 1 ) = log 10 ( x + 5 ) + 1 , then x is equal to :", + "Output Program": [ + "n0 = 10.0\nn1 = 5.0\nn2 = 10.0\nn3 = 5.0\nn4 = 1.0\nn5 = 10.0\nn6 = 5.0\nn7 = 1.0\nt0 = n0 - n4\nt1 = n1 - 2.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "dev" + }, + { + "Input": "the difference between the heights of two trees is 20 cm . 10 years ago , the taller one was thrice as taller as the shorter one . the present height of the taller tree is", + "Output Program": [ + "n0 = 20.0\nn1 = 10.0\nt0 = n0 + n1\nanswer = n1 * t0\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "dev" + }, + { + "Input": "in an examination , 35 % of total students failed in hindi , 45 % failed in english and 20 % in both . the percentage of these who passed in both the subjects is :", + "Output Program": [ + "n0 = 35.0\nn1 = 45.0\nn2 = 20.0\nt0 = n0 + n1\nt1 = t0 - n2\nanswer = 100.0 - t1\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "dev" + }, + { + "Input": "8 people went to a restaurant for dinner . 7 of them spent $ 10 each on their meals and the eighth spent $ 7 more than the average expenditure of all 8 people . what was the total amount of money that the 8 people spent ?", + "Output Program": [ + "n0 = 8.0\nn1 = 7.0\nn2 = 10.0\nn3 = 7.0\nn4 = 8.0\nn5 = 8.0\nt0 = n1 * n2\nt1 = n0 - 1.0\nt2 = n1 + t0\nt3 = t2 / t1\nt4 = n1 + t3\nanswer = t4 + t0\nprint(answer)" + ], + "Output Answer": [ + "88" + ], + "split": "dev" + }, + { + "Input": "a grocer is storing soap boxes in cartons that measure 25 inches by 42 inches by 60 inches . if the measurement of each soap box is 7 inches by 6 inches by 10 inches , then what is the maximum number of soap boxes that can be placed in each carton ?", + "Output Program": [ + "n0 = 25.0\nn1 = 42.0\nn2 = 60.0\nn3 = 7.0\nn4 = 6.0\nn5 = 10.0\nt0 = n0 * n1\nt1 = n3 * n4\nt2 = n2 * t0\nt3 = n5 * t1\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "dev" + }, + { + "Input": "in a university the average age in an arts class is 21 and average age in technical class is 18 . what is the age average of university if there are 8 arts classes and 5 technical classes ?", + "Output Program": [ + "n0 = 21.0\nn1 = 18.0\nn2 = 8.0\nn3 = 5.0\nt0 = n2 + n3\nt1 = n0 * n2\nt2 = n1 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "19.846153846153847" + ], + "split": "dev" + }, + { + "Input": "every disk in a bag is either blue , yellow or green . the ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8 . if the total number of disks in the bag is 144 , how many more green disks than blue disks are in the bag ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 8.0\nn3 = 144.0\nt0 = n0 + n1\nt1 = n2 - n0\nt2 = n2 + t0\nt3 = n3 / t2\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "dev" + }, + { + "Input": "if the sum of two numbers is 22 and the sum of their squares is 404 , then the product of the numbers is", + "Output Program": [ + "n0 = 22.0\nn1 = 404.0\nt0 = n0**min(2.0, 5)\nt1 = t0 - n1\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "dev" + }, + { + "Input": "there are 200 female managers in a certain company . find the total number w of female employees in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers .", + "Output Program": [ + "n0 = 200.0\nn1 = 2.0\nn2 = 5.0\nn3 = 2.0\nn4 = 5.0\nt0 = n1 / n2\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "dev" + }, + { + "Input": "the sum of two numbers is 77 . 5 times one number is equal to 6 times the other . the bigger of the two numbers is", + "Output Program": [ + "n0 = 77.0\nn1 = 5.0\nn2 = 6.0\nt0 = n2 / n1\nt1 = t0 + 1.0\nt2 = n0 / t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "dev" + }, + { + "Input": "3 people took gmat practice tests in which the minimum and maximum possible scores are 200 and 800 , respectively . they each took a test 3 times , and no one scored below 400 or over 700 . if the individual ranges of the 3 people ' s scores in those 3 practice tests were 40 , 70 and 100 , what is the difference between the maximum and minimum possible ranges of all their scores put together .", + "Output Program": [ + "n0 = 3.0\nn1 = 200.0\nn2 = 800.0\nn3 = 3.0\nn4 = 400.0\nn5 = 700.0\nn6 = 3.0\nn7 = 3.0\nn8 = 40.0\nn9 = 70.0\nn10 = 100.0\nt0 = n5 - n4\nanswer = t0 - n10\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "dev" + }, + { + "Input": "if p / q = 3 / 11 , then 2 p + q = ?", + "Output Program": [ + "n0 = 3.0\nn1 = 11.0\nn2 = 2.0\nt0 = n0 * n2\nanswer = n1 + t0\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "dev" + }, + { + "Input": "what is the probability of rolling a total of 5 with a single roll of two fair 6 - sided dice , each with the distinct numbers 1 through 6 on each side ?", + "Output Program": [ + "n0 = 5.0\nn1 = 6.0\nn2 = 1.0\nn3 = 6.0\nt0 = n1 * n1\nanswer = 4.0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.1111111111111111" + ], + "split": "dev" + }, + { + "Input": "the population of a city is 415600 . it increased by 25 % in the first year and decreased by 30 % in the second year . what is the population of the city at the end of second year ?", + "Output Program": [ + "n0 = 415600.0\nn1 = 25.0\nn2 = 30.0\nt0 = n1 + 100.0\nt1 = 100.0 - n2\nt2 = t1 / 100.0\nt3 = t0 / 100.0\nt4 = n0 * t3\nanswer = t2 * t4\nprint(answer)" + ], + "Output Answer": [ + "363650" + ], + "split": "dev" + }, + { + "Input": "a fruit juice company earns $ 150 per 100 gallons of apple juice sold , $ 170 per 100 gallons of guava juice sold , $ 130 per 100 gallons of grape juice sold , $ 100 per 100 gallons of orange juice . if the company manages to sell 230 gallons of apple , 210 gallons of guava , 310 gallons of grape , 270 gallons of orange on a particular day . what is the average earning of the company per 100 gallon of the juice sold ?", + "Output Program": [ + "n0 = 150.0\nn1 = 100.0\nn2 = 170.0\nn3 = 100.0\nn4 = 130.0\nn5 = 100.0\nn6 = 100.0\nn7 = 100.0\nn8 = 230.0\nn9 = 210.0\nn10 = 310.0\nn11 = 270.0\nn12 = 100.0\nt0 = n4 + 4.0\nt1 = 4.0 + 4.0\nt2 = t1 / 10.0\nanswer = t0 + t2\nprint(answer)" + ], + "Output Answer": [ + "134.8" + ], + "split": "dev" + }, + { + "Input": "if a mixture is 1 \u2044 7 alcohol by volume and 2 \u2044 7 water by volume , what is the ratio of the volume of alcohol to the volume of water in this mixture ?", + "Output Program": [ + "n0 = 1.0\nn1 = 7.0\nn2 = 2.0\nn3 = 7.0\nt0 = n0 / n1\nt1 = n2 / n1\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "dev" + }, + { + "Input": "the average of 10 numbers is 7 . if each number is multiplied by 12 , then the average of new set of numbers is", + "Output Program": [ + "n0 = 10.0\nn1 = 7.0\nn2 = 12.0\n\nanswer = n1 * n2\nprint(answer)" + ], + "Output Answer": [ + "84" + ], + "split": "dev" + }, + { + "Input": "if 5 x = 3 y and xy \u2260 0 , what is the ratio of 1 / 5 * x to 1 / 6 * y ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nn2 = 0.0\nn3 = 1.0\nn4 = 5.0\nn5 = 1.0\nn6 = 6.0\nt0 = n3 / n4\nt1 = n3 / n6\nt2 = n1 / n0\nt3 = t0 / t1\nanswer = t3 * t2\nprint(answer)" + ], + "Output Answer": [ + "0.7200000000000001" + ], + "split": "dev" + }, + { + "Input": "for every integer n \u2265 3 , the function g ( n ) is defined as the product of all the odd integers from 1 to n , inclusive . what is the value of g ( 101 ) \u2013 g ( 99 ) ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 101.0\nn3 = 99.0\n\nanswer = n2 - n1\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "dev" + }, + { + "Input": "two trains of equal length are running on parallel lines in the same directions at 46 km / hr . and 36 km / hr . the faster trains pass the slower train in 72 seconds . the length of each train is :", + "Output Program": [ + "n0 = 46.0\nn1 = 36.0\nn2 = 72.0\nt0 = n0 - n1\nt1 = t0 * 1000.0\nt2 = t1 / 3600.0\nt3 = n2 * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "dev" + }, + { + "Input": "sophia finished 2323 of a book . she calculated that she finished 90 more pages than she has yet to read . how long is her book ?", + "Output Program": [ + "n0 = 2323.0\nn1 = 90.0\nt0 = 2.0 / 3.0\nt1 = 1.0 - t0\nt2 = t0 - t1\nanswer = n1 / t2\nprint(answer)" + ], + "Output Answer": [ + "270.00000000000006" + ], + "split": "dev" + }, + { + "Input": "how many zeroes are there at the end of the number n , if n = 70 ! + 140 ! ?", + "Output Program": [ + "n0 = 70.0\nn1 = 140.0\nt0 = 1.0 + 4.0\nt1 = n0 / t0\nanswer = t1 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "dev" + }, + { + "Input": "if 15 percent of the students at a certain school went to a camping trip and took more than $ 100 , and 75 percent of the students who went to the camping trip did not take more than $ 100 , what percentage of the students at the school went to the camping trip ?", + "Output Program": [ + "n0 = 15.0\nn1 = 100.0\nn2 = 75.0\nn3 = 100.0\nt0 = n1 - n2\nt1 = t0 / n1\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "dev" + }, + { + "Input": "an object thrown directly upward is at a height of h feet after t seconds , where h = - 14 ( t - 3 ) ^ 2 + 150 . at what height , in feet , is the object 2 seconds after it reaches its maximum height ?", + "Output Program": [ + "n0 = 14.0\nn1 = 3.0\nn2 = 2.0\nn3 = 150.0\nn4 = 2.0\nt0 = n1 + n2\nt1 = -n0\nt2 = t0 - n1\nt3 = t2**min(n2, 5)\nt4 = t1 * t3\nanswer = n3 + t4\nprint(answer)" + ], + "Output Answer": [ + "94" + ], + "split": "dev" + }, + { + "Input": "of the families in city x in 1994 , 35 percent owned a personal computer . the number of families in city x owning a computer in 1998 was 20 percent greater than it was in 1994 , and the total number of families in city x was 4 percent greater in 1998 than it was in 1994 . what percent of the families in city x owned a personal computer in 1998 ?", + "Output Program": [ + "n0 = 1994.0\nn1 = 35.0\nn2 = 1998.0\nn3 = 20.0\nn4 = 1994.0\nn5 = 4.0\nn6 = 1998.0\nn7 = 1994.0\nn8 = 1998.0\nt0 = n3 + 100.0\nt1 = n5 + 100.0\nt2 = n1 * t0\nt3 = t2 / 100.0\nt4 = t3 / t1\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "40.38461538461539" + ], + "split": "dev" + }, + { + "Input": "two brothers ram and ravi appeared for an exam . the probability of selection of ram is 4 / 7 and that of ravi is 1 / 5 . find the probability that both of them are selected .", + "Output Program": [ + "n0 = 4.0\nn1 = 7.0\nn2 = 1.0\nn3 = 5.0\nt0 = n0 / n1\nt1 = n2 / n3\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "0.11428571428571428" + ], + "split": "dev" + }, + { + "Input": "3 / 4 of a number is 19 less than the original number . the number is ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 19.0\n\nanswer = n1 * n2\nprint(answer)" + ], + "Output Answer": [ + "76" + ], + "split": "dev" + }, + { + "Input": "the average runs scored by a batsman in 20 matches is 40 . in the next 10 matches the batsman scored an average of 30 runs . find his average in all the 30 matches ?", + "Output Program": [ + "n0 = 20.0\nn1 = 40.0\nn2 = 10.0\nn3 = 30.0\nn4 = 30.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "36.666666666666664" + ], + "split": "dev" + }, + { + "Input": "anne bought doughnuts for a class breakfast party . she bought 6 chocolate doughnuts , 8 coconut doughnuts , and 8 jam - filled doughnuts . how many doughnuts did anne buy in all ?", + "Output Program": [ + "n0 = 6.0\nn1 = 8.0\nn2 = 8.0\nt0 = n0 + n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "dev" + }, + { + "Input": "90 % of the population of a village is 36000 . the total population of the village is ?", + "Output Program": [ + "n0 = 90.0\nn1 = 36000.0\nt0 = 100.0 / n0\nanswer = n1 * t0\nprint(answer)" + ], + "Output Answer": [ + "40000" + ], + "split": "dev" + }, + { + "Input": "if there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city , find the number of 4 wheelers parked there if the total number of wheels is 66 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 4.0\nn3 = 66.0\nt0 = n3 - n0\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "dev" + }, + { + "Input": "the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 60 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam .", + "Output Program": [ + "n0 = 80.0\nn1 = 5.0\nn2 = 60.0\nn3 = 90.0\nt0 = n1 * n3\nt1 = n1 * n2\nt2 = n3 - n0\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "dev" + }, + { + "Input": "find the value of 72515 x 9999 = m ?", + "Output Program": [ + "n0 = 72515.0\nn1 = 9999.0\nt0 = n1 - 4.0\nanswer = t0 * n0\nprint(answer)" + ], + "Output Answer": [ + "724787425" + ], + "split": "dev" + }, + { + "Input": "sandy bought 65 books for $ 1080 from one shop and 55 books for $ 840 from another shop . what is the average price that sandy paid per book ?", + "Output Program": [ + "n0 = 65.0\nn1 = 1080.0\nn2 = 55.0\nn3 = 840.0\nt0 = n1 + n3\nt1 = n0 + n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "dev" + }, + { + "Input": "the average height of 20 students in a class was calculated as 175 cm . it has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 136 cm . what was the actual average height of the students in the class ?", + "Output Program": [ + "n0 = 20.0\nn1 = 175.0\nn2 = 151.0\nn3 = 136.0\nt0 = n0 * n1\nt1 = n2 - n3\nt2 = t0 - t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "174.25" + ], + "split": "dev" + }, + { + "Input": "working simultaneously and independently at an identical constant rate , 5 machines of a certain type can produce a total of x units of product p in 4 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 2 x units of product p in 2 days ?", + "Output Program": [ + "n0 = 5.0\nn1 = 4.0\nn2 = 2.0\nn3 = 2.0\nt0 = n1 / n3\nt1 = n0 * n2\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "dev" + }, + { + "Input": "a seller of used cars has 12 cars to sell and each of his clients selected 4 cars that he liked most . if each car was selected exactly thrice , how many clients visited the garage ?", + "Output Program": [ + "n0 = 12.0\nn1 = 4.0\nt0 = n0 / n1\nanswer = t0 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "dev" + }, + { + "Input": "set a contains all the even numbers between 2 and 50 inclusive . set b contains all the even numbers between 62 and 110 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ?", + "Output Program": [ + "n0 = 2.0\nn1 = 50.0\nn2 = 62.0\nn3 = 110.0\nt0 = n1 - n0\nt1 = n2 - n0\nt2 = t0 / 2.0\nt3 = t2 + 1.0\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "1500" + ], + "split": "dev" + }, + { + "Input": "a certain sum of money is divided among a , b and c so that for each rs . a has , b has 65 paisa and c 40 paisa . if c ' s share is rs . 56 , find the sum of money ?", + "Output Program": [ + "n0 = 65.0\nn1 = 40.0\nn2 = 56.0\nt0 = n0 + 100.0\nt1 = n2 / n1\nt2 = n1 + t0\nanswer = t2 * t1\nprint(answer)" + ], + "Output Answer": [ + "287" + ], + "split": "dev" + }, + { + "Input": "john purchased 1375 large bottles at $ 1.75 per bottle and 690 small bottles at $ 1.35 per bottle . what was the approximate average price paid per bottle ?", + "Output Program": [ + "n0 = 1375.0\nn1 = 1.75\nn2 = 690.0\nn3 = 1.35\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "1.6163438256658595" + ], + "split": "dev" + }, + { + "Input": "a rope of which a calf is tied is increased from 12 m to 23 m , how much additional grassy ground shall it graze ?", + "Output Program": [ + "n0 = 12.0\nn1 = 23.0\nt0 = 3.0 + 4.0\nt1 = 10.0 * 2.0\nt2 = n1**min(2.0, 5)\nt3 = n0**min(2.0, 5)\nt4 = t1 + 2.0\nt5 = t2 - t3\nt6 = t4 / t0\nanswer = t6 * t5\nprint(answer)" + ], + "Output Answer": [ + "1210" + ], + "split": "dev" + }, + { + "Input": "the average marks of a class of 12 students is 40 and that of another class of 28 students is 60 . find the average marks of all the students ?", + "Output Program": [ + "n0 = 12.0\nn1 = 40.0\nn2 = 28.0\nn3 = 60.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "dev" + }, + { + "Input": "if 10 gallons of grape juice are added to 40 gallons of a mixture , which contains 20 percent grape juice then what percent of the resulting mixture is grape juice ?", + "Output Program": [ + "n0 = 10.0\nn1 = 40.0\nn2 = 20.0\nt0 = n0 + n1\nt1 = n2 / 100.0\nt2 = n1 * t1\nt3 = n0 + t2\nt4 = t3 / t0\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "dev" + }, + { + "Input": "as a treat for her two crying children , a mother runs to the freezer in which she has 4 cherry ice pops , 3 orange ice pops , and 4 lemon - lime ice pops . if she chooses two at random to bring outside to the children , but realizes as she runs out the door that she can not bring them different flavors without one invariably being jealous of the other and getting even more upset , what is the probability that she has to return to the freezer to make sure that they each receive the same flavor ?", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 4.0\nt0 = n0 - n1\nt1 = 100.0 - t0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.010101010101010102" + ], + "split": "dev" + }, + { + "Input": "a group of 7 teenagers recently visited the japanese restaurant . the total bill for the meal , including 20 % gratuity , came to $ 840 . on average , how much did the meal of each individual cost before gratuity ?", + "Output Program": [ + "n0 = 7.0\nn1 = 20.0\nn2 = 840.0\nt0 = n2 / n1\nt1 = t0 - n1\nt2 = t1 - 10.0\nanswer = t2 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "dev" + }, + { + "Input": "a 415 m long train is running at 63 km / hr . in how much time will it cross a tunnel 285 m long ?", + "Output Program": [ + "n0 = 415.0\nn1 = 63.0\nn2 = 285.0\nt0 = n0 + n2\nt1 = n1 * 0.2778\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "39.99680025597952" + ], + "split": "dev" + }, + { + "Input": "let s is a set of all natural numbers less than 120 such that hcf of any element in s and 120 is 1 . find the sum of all elements in s ?", + "Output Program": [ + "n0 = 120.0\nn1 = 120.0\nn2 = 1.0\nt0 = n2 + 4.0\nt1 = 2.0 * 4.0\nt2 = t0 * 100.0\nt3 = t1 * 10.0\nt4 = t2 + 1000.0\nt5 = t3 + 4.0\nanswer = t4 + t5\nprint(answer)" + ], + "Output Answer": [ + "1584" + ], + "split": "dev" + }, + { + "Input": "4 balls of different colors are to be placed in 3 different boxes such that any box contains at least 1 ball . what is the maximum number of different ways in which this can be done ?", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 1.0\nt0 = n0 * n1\nt1 = n1 * 2.0\nt2 = t0 * 2.0\nt3 = t1 * t1\nt4 = t2 * t1\nanswer = t4 + t3\nprint(answer)" + ], + "Output Answer": [ + "180" + ], + "split": "dev" + }, + { + "Input": "the average height of 35 boys in a class was calculated as 185 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ?", + "Output Program": [ + "import math\nn0 = 35.0\nn1 = 185.0\nn2 = 166.0\nn3 = 106.0\nt0 = n0 * n1\nt1 = t0 - n2\nt2 = n3 + t1\nt3 = t2 / n0\nanswer = math.floor(t3)\nprint(answer)" + ], + "Output Answer": [ + "183" + ], + "split": "dev" + }, + { + "Input": "whats the reminder when 65,985 , 241,545 , 898,754 , 582,556 , 898,522 , 454,889 is divided by 16", + "Output Program": [ + "n0 = 65985.0\nn1 = 241545.0\nn2 = 898754.0\nn3 = 582556.0\nn4 = 898522.0\nn5 = 454889.0\nn6 = 16.0\nt0 = 2.0 + 3.0\nt1 = 2.0 * 4.0\nt2 = 10.0 - 1.0\nt3 = t0 + 12.0\nt4 = t2 * 100.0\nt5 = t0 * 100.0\nt6 = t5 * 10.0\nt7 = t3 * t0\nt8 = t4 + t6\nt9 = t8 + t7\nt10 = t9 % n6\nanswer = t1 + t10\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "dev" + }, + { + "Input": "if 4 ( p ' s capital ) = 6 ( q ' s capital ) = 10 ( r ' s capital ) , then out of the total profit of rs 4650 , r will receive", + "Output Program": [ + "n0 = 4.0\nn1 = 6.0\nn2 = 10.0\nn3 = 4650.0\nt0 = n0 + 1.0\nt1 = n2 + t0\nt2 = n2 + t1\nt3 = n1 + t2\nt4 = n1 / t3\nanswer = n3 * t4\nprint(answer)" + ], + "Output Answer": [ + "900" + ], + "split": "dev" + }, + { + "Input": "the average age of 15 students of a class is 15 years . out of these , the average age of 8 students is 14 years and that of the other 6 students is 16 years , the age of the 15 th student is", + "Output Program": [ + "n0 = 15.0\nn1 = 15.0\nn2 = 8.0\nn3 = 14.0\nn4 = 6.0\nn5 = 16.0\nn6 = 15.0\nt0 = n0 * n0\nt1 = n2 * n3\nt2 = n4 * n5\nt3 = t1 + t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "dev" + }, + { + "Input": "a committee is reviewing a total of 40 x black - and - white films and 10 y color films for a festival . if the committee selects y / x % of the black - and - white films and all of the color films , what fraction of the selected films are in color ?", + "Output Program": [ + "n0 = 40.0\nn1 = 10.0\nt0 = n0 / 100.0\nt1 = n1 + t0\nanswer = n1 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.9615384615384615" + ], + "split": "dev" + }, + { + "Input": "the total age of a and b is 14 years more than the total age of b and c . c is how many years younger than a ?", + "Output Program": [ + "n0 = 14.0\n\nanswer = n0 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "dev" + }, + { + "Input": "in a party every person shakes hands with every other person . if there were a total of 171 handshakes in the party then what is the number of persons present in the party ?", + "Output Program": [ + "import math\nn0 = 171.0\nt0 = n0 * 2.0\nt1 = t0 * 4.0\nt2 = t1 + 1.0\nt3 = math.sqrt(max(0, t2))\nt4 = t3 + 1.0\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "dev" + }, + { + "Input": "a man performs 3 / 5 of the total journey by rail , 17 / 20 by bus and the remaining 6.5 km on foot . his total journey is", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 17.0\nn3 = 20.0\nn4 = 6.5\n\nanswer = n3 * n4\nprint(answer)" + ], + "Output Answer": [ + "130" + ], + "split": "dev" + }, + { + "Input": "a straight line in the xy - plane has a slope of 2 and a y - intercept of 2 . on this line , what is the x - coordinate of the point whose y - coordinate is 540 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 540.0\nt0 = n2 - n0\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "269" + ], + "split": "dev" + }, + { + "Input": "in a class of 25 students in an examination in maths 3 students scored 95 marks each , 3 get zero each and the average of the rest was 45 . what is the average of the whole class ?", + "Output Program": [ + "n0 = 25.0\nn1 = 3.0\nn2 = 95.0\nn3 = 3.0\nn4 = 45.0\nt0 = n1 + n3\nt1 = n1 * n2\nt2 = n0 - t0\nt3 = n4 * t2\nt4 = t3 + t1\nanswer = t4 / n0\nprint(answer)" + ], + "Output Answer": [ + "45.6" + ], + "split": "dev" + }, + { + "Input": "for a certain art exhibit , a museum sold admission tickets to a group of 50 people every 5 minutes from 9 : 00 in the morning to 5 : 55 in the afternoon , inclusive . the price of a regular admission ticket was $ 10 and the price of a student ticket was $ 6 . if on one day 3 times as many regular admission tickets were sold as student tickets , what was the total revenue from ticket sales that day ?", + "Output Program": [ + "n0 = 50.0\nn1 = 5.0\nn2 = 9.0\nn3 = 0.0\nn4 = 5.0\nn5 = 55.0\nn6 = 10.0\nn7 = 6.0\nn8 = 3.0\nt0 = 12.0 + n4\nt1 = n8 + 1.0\nt2 = t0 - n2\nt3 = t2 + 1.0\nt4 = t3 * 12.0\nt5 = n0 * t4\nt6 = t5 / t1\nt7 = n8 * t6\nt8 = n7 * t6\nt9 = n6 * t7\nanswer = t9 + t8\nprint(answer)" + ], + "Output Answer": [ + "48600" + ], + "split": "dev" + }, + { + "Input": "sum of 3 numbers 264 , if the first number be twice then second and third number be one third of the first , then the second number is", + "Output Program": [ + "n0 = 3.0\nn1 = 264.0\nt0 = 1.0 + 2.0\nt1 = 2.0 / 3.0\nt2 = t0 + t1\nanswer = n1 / t2\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "dev" + }, + { + "Input": "find the least number must be subtracted from 105829 so that remaining no . is divisible by 21 ?", + "Output Program": [ + "import math\nn0 = 105829.0\nn1 = 21.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "dev" + }, + { + "Input": "the average age of 50 students in a class is 14 years . if the age of teacher is also included , the average becomes 15 years , find the age of the teacher .", + "Output Program": [ + "n0 = 50.0\nn1 = 14.0\nn2 = 15.0\nt0 = n0 * n1\nt1 = n2 + t0\nt2 = n0 + t1\nanswer = t2 - t0\nprint(answer)" + ], + "Output Answer": [ + "65" + ], + "split": "dev" + }, + { + "Input": "the total cost of a vacation was divided among 3 people . if the total cost of the vacation had been divided equally among 4 people , the cost per person would have been $ 60 less . what was the total cost cost of the vacation ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 60.0\nt0 = n0 * n1\nt1 = n1 - n0\nt2 = n2 / t1\nanswer = t2 * t0\nprint(answer)" + ], + "Output Answer": [ + "720" + ], + "split": "dev" + }, + { + "Input": "if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer w that must divide n is ?", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 72.0\nt0 = n1 / n0\nt1 = math.sqrt(max(0, t0))\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "dev" + }, + { + "Input": "evaluate : 10111 - 10 * 2 * 5 = ?", + "Output Program": [ + "n0 = 10111.0\nn1 = 10.0\nn2 = 2.0\nn3 = 5.0\nt0 = n1 * n2\nt1 = n3 * t0\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "10011" + ], + "split": "dev" + }, + { + "Input": "a jar of 364 marbles is divided equally among a group of marble - players today . if 2 people joined the group in the future , each person would receive 1 marble less . how many people are there in the group today ?", + "Output Program": [ + "import math\nn0 = 364.0\nn1 = 2.0\nn2 = 1.0\nt0 = n0 * n1\nt1 = n1**min(n1, 5)\nt2 = t0 * 4.0\nt3 = t2 + t1\nt4 = math.sqrt(max(0, t3))\nt5 = t4 - n1\nanswer = t5 / n1\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "dev" + }, + { + "Input": "if 1 / 5 th of a number decreased by 5 is 5 , then the number is", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 5.0\nn3 = 5.0\nt0 = n1 + n1\nt1 = n0 / n1\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "dev" + }, + { + "Input": "if ( x + 3 ) ^ 2 / ( 2 x + 15 ) = 3 , then the difference between the two possible values of x is :", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 2.0\nn2 = 2.0\nn3 = 15.0\nn4 = 3.0\nt0 = n0 * n3\nt1 = n0 * 3.0\nt2 = t0 - t1\nt3 = math.sqrt(max(0, t2))\nanswer = t3 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "dev" + }, + { + "Input": "a placed 3 sheets with two carbons to get two extra copies of the original . then he decided to get more carbon copies and folded the paper in such a way that the upper half of the sheets were on top of the lower half . then he typed . how many carbon copies did he get ?", + "Output Program": [ + "n0 = 3.0\n\nanswer = n0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "dev" + }, + { + "Input": "the average age of applicants for a new job is 30 , with a standard deviation of 8 . the hiring manager is only willing to accept applicants whose age is within one standard deviation of the average age . assuming that all applicants ' ages are integers and that the endpoints of the range are included , what is the maximum number of different ages of the applicants ?", + "Output Program": [ + "n0 = 30.0\nn1 = 8.0\nt0 = n0 + n1\nt1 = n0 - n1\nt2 = t0 - t1\nanswer = t2 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "dev" + }, + { + "Input": "the cost of 8 dozen pencil and 2 dozen note book is 520 rupee . if cost of 3 pencil and 4 note book is 60 rupee , then sum of the cost of 1 pencil and 1 note book will be ( in rupee )", + "Output Program": [ + "n0 = 8.0\nn1 = 2.0\nn2 = 520.0\nn3 = 3.0\nn4 = 4.0\nn5 = 60.0\nn6 = 1.0\nn7 = 1.0\nt0 = 3.0 + 3.0\nt1 = n0 * 12.0\nt2 = n5 * t0\nt3 = n3 * t0\nt4 = n2 - t2\nt5 = t1 - t3\nt6 = t4 / t5\nt7 = n3 * t6\nt8 = n5 - t7\nt9 = t8 / n4\nanswer = t6 + t9\nprint(answer)" + ], + "Output Answer": [ + "15.512820512820513" + ], + "split": "dev" + }, + { + "Input": "8 years ago , p was half of q ' s age . if the ratio of their present ages is 3 : 4 what will be the total of their present ages ?", + "Output Program": [ + "n0 = 8.0\nn1 = 3.0\nn2 = 4.0\nt0 = n1 + n2\nt1 = n0 / 2.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "dev" + }, + { + "Input": "the average of 6 no . ' s is 4.60 . the average of 2 of them is 3.4 , while the average of the other 2 is 3.8 . what is the average of the remaining 2 no ' s ?", + "Output Program": [ + "n0 = 6.0\nn1 = 4.6\nn2 = 2.0\nn3 = 3.4\nn4 = 2.0\nn5 = 3.8\nn6 = 2.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n2 * n5\nt3 = t1 + t2\nt4 = t0 - t3\nanswer = t4 / n2\nprint(answer)" + ], + "Output Answer": [ + "6.6" + ], + "split": "dev" + }, + { + "Input": "what least number must be subtracted from 13294 so that the remainder is exactly divisible by 97 ?", + "Output Program": [ + "import math\nn0 = 13294.0\nn1 = 97.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "dev" + }, + { + "Input": "the average speed of a car is 1 4 / 5 times the avg speed of a bike . a tractor covers 575 km in 23 hrs . how much distance will the car cover in 4 hrs if the speed of the bike is twice speed of the tractor ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 5.0\nn3 = 575.0\nn4 = 23.0\nn5 = 4.0\nt0 = n1 / n2\nt1 = n3 / n4\nt2 = n0 + t0\nt3 = t1 * 2.0\nt4 = t2 * t3\nanswer = n5 * t4\nprint(answer)" + ], + "Output Answer": [ + "360" + ], + "split": "dev" + }, + { + "Input": "the difference between a number and its 3 - fourth is 100 . what is 25 % of that number ?", + "Output Program": [ + "n0 = 3.0\nn1 = 100.0\nn2 = 25.0\nt0 = n0 / 4.0\nt1 = n2 / n1\nt2 = 1.0 - t0\nt3 = n1 / t2\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "dev" + }, + { + "Input": "i chose a number and divide it by 4 . then i subtracted 175 from the result and got 10 . what was the number i chose ?", + "Output Program": [ + "n0 = 4.0\nn1 = 175.0\nn2 = 10.0\nt0 = n1 + n2\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "740" + ], + "split": "dev" + }, + { + "Input": "how many 3 digit numbers n are divisible by 78 or 91 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 78.0\nn2 = 91.0\nt0 = n0 * 2.0\nt1 = n2 - n1\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "dev" + }, + { + "Input": "if x is 50 percent greater than 88 , then x =", + "Output Program": [ + "n0 = 50.0\nn1 = 88.0\nt0 = n0 / 100.0\nt1 = n1 * t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "132" + ], + "split": "dev" + }, + { + "Input": "if x represents the product of the first 15 positive integers , then x is not a multiple of :", + "Output Program": [ + "n0 = 15.0\nt0 = n0 + 4.0\nanswer = t0 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "57" + ], + "split": "dev" + }, + { + "Input": "the sum of all the digits of the integers from 18 to 21 inclusive is 24 ( 1 + 8 + 1 + 9 + 2 + 0 + 2 + 1 = 24 ) . what is the sum e of all the digits of the integers from 0 to 99 inclusive ?", + "Output Program": [ + "n0 = 18.0\nn1 = 21.0\nn2 = 24.0\nn3 = 1.0\nn4 = 8.0\nn5 = 1.0\nn6 = 9.0\nn7 = 2.0\nn8 = 0.0\nn9 = 2.0\nn10 = 1.0\nn11 = 24.0\nn12 = 0.0\nn13 = 99.0\nt0 = n6 + 1.0\nt1 = 10.0 * 2.0\nt2 = n6 * t0\nt3 = t2 / 2.0\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "900" + ], + "split": "dev" + }, + { + "Input": "subtracting 3 % of a from a is equivalent to multiplying a by how much ?", + "Output Program": [ + "n0 = 3.0\nt0 = 100.0 - n0\nanswer = t0 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "0.97" + ], + "split": "dev" + }, + { + "Input": "when a certain number x is divided by 61 , the remainder is 24 . what is the remainder when x is divided by 5 ?", + "Output Program": [ + "n0 = 61.0\nn1 = 24.0\nn2 = 5.0\n\nanswer = n1 % n2\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "dev" + }, + { + "Input": "approximately how many revolutions will be made by a car tire with a 10 - inch diameter if the car travels 1 \u2044 2 mile ?", + "Output Program": [ + "n0 = 10.0\nn1 = 1.0\nn2 = 2.0\nt0 = n1 / n2\nt1 = n2 * 3.0\nt2 = t1 / 10.0\nt3 = t1 * 10.0\nt4 = t2 + n1\nt5 = t3 + 3.0\nt6 = t4 / 10.0\nt7 = t5 * 10.0\nt8 = t6 + 4.0\nt9 = t7 + 3.0\nt10 = t8 / 10.0\nt11 = t9 * 10.0\nt12 = t10 + n1\nt13 = t11 + 3.0\nt14 = t13 + n2\nt15 = t12 / 10.0\nt16 = t15 + 3.0\nt17 = t14 * 10.0\nt18 = n0 * t16\nt19 = t18 / t17\nanswer = t0 / t19\nprint(answer)" + ], + "Output Answer": [ + "1008.2442067736184" + ], + "split": "dev" + }, + { + "Input": "robert ' s salary was increased by 50 % and subsequently decreased by 10 % . how much percentage does he gain ?", + "Output Program": [ + "n0 = 50.0\nn1 = 10.0\nt0 = n0 + 100.0\nt1 = n1 * 2.0\nt2 = 100.0 - 10.0\nt3 = t0 / 100.0\nt4 = t2 / 100.0\nt5 = t3 * t4\nt6 = t5 * 100.0\nt7 = t6 - 100.0\nanswer = t7 - t1\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "dev" + }, + { + "Input": "a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 29.16 , the number of the member is the group is :", + "Output Program": [ + "import math\nn0 = 29.16\nt0 = n0 * 100.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "dev" + }, + { + "Input": "the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 66 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.5\nn2 = 66.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "86" + ], + "split": "dev" + }, + { + "Input": "what is the sum between the place values of two 3 ' s in the numeral 63130", + "Output Program": [ + "n0 = 3.0\nn1 = 63130.0\nt0 = n0 * 10.0\nt1 = n0 * 1000.0\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "3030" + ], + "split": "dev" + }, + { + "Input": "the average weight of 20 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg . find the average weights of all the boys in the class .", + "Output Program": [ + "n0 = 20.0\nn1 = 50.25\nn2 = 8.0\nn3 = 45.15\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "48.792857142857144" + ], + "split": "dev" + }, + { + "Input": "what is the difference between the c . i . on rs . 9000 for 1 1 / 2 years at 4 % per annum compounded yearly and half - yearly ?", + "Output Program": [ + "n0 = 9000.0\nn1 = 1.0\nn2 = 1.0\nn3 = 2.0\nn4 = 4.0\nt0 = n3 / 100.0\nt1 = n4 / 100.0\nt2 = t0 + 1.0\nt3 = t1 + 1.0\nt4 = t2 * t2\nt5 = t2 * t3\nt6 = t2 * t4\nt7 = n0 * t5\nt8 = n0 * t6\nanswer = t8 - t7\nprint(answer)" + ], + "Output Answer": [ + "3.67200000000048" + ], + "split": "dev" + }, + { + "Input": "a couple spent $ 198 in total while dining out and paid this amount using a credit card . the $ 198 figure included a 20 percent tip which was paid on top of the price which already included a sales tax of 10 percent on top of the price of the food . what was the actual price of the food before tax and tip ?", + "Output Program": [ + "n0 = 198.0\nn1 = 198.0\nn2 = 20.0\nn3 = 10.0\nt0 = n2 + 100.0\nt1 = n3 + 100.0\nt2 = n0 * 100.0\nt3 = t2 / t0\nt4 = t3 * 100.0\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "dev" + }, + { + "Input": "in an election , candidate douglas won 58 percent of the total vote in counties x and y . he won 64 percent of the vote in county x . if the ratio of people who voted in county x to county y is 2 : 1 , what percent of the vote did candidate douglas win in county y ?", + "Output Program": [ + "n0 = 58.0\nn1 = 64.0\nn2 = 2.0\nn3 = 1.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = n2 / 3.0\nt3 = n3 / 3.0\nt4 = t1 * t2\nt5 = t0 - t4\nt6 = t5 / t3\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "46" + ], + "split": "dev" + }, + { + "Input": "if x is an integer and 2.134 \u00d7 10 ^ x is less than 21,000 , what is the greatest possible value for x ?", + "Output Program": [ + "import math\nn0 = 2.134\nn1 = 10.0\nn2 = 21000.0\nt0 = n2 / n0\nt1 = math.log(max(1e-5, n1), 2)\nt2 = math.log(max(1e-5, t0), 2)\nt3 = t2 / t1\nanswer = math.floor(t3)\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "dev" + }, + { + "Input": "the average weight of a group of persons increased from 48 kg to 51 kg , when two persons weighing 78 kg and 93 kg join the group . find the initial number of members in the group ?", + "Output Program": [ + "n0 = 48.0\nn1 = 51.0\nn2 = 78.0\nn3 = 93.0\nt0 = n2 + n3\nt1 = n1 * 2.0\nt2 = n1 - n0\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "dev" + }, + { + "Input": "dhoni bought 5 toys with the average cost of $ 10 . if david also buys the sixth toy with the price of $ 16 , what is the average ( arithmetic mean ) price of those 6 toys ?", + "Output Program": [ + "n0 = 5.0\nn1 = 10.0\nn2 = 16.0\nn3 = 6.0\nt0 = n1 + 12.0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "dev" + }, + { + "Input": "gold is 10 times as heavy as water and copper is 6 times as heavy as water . in what ratio should these be mixed to get an alloy 8 times as heavy as water ?", + "Output Program": [ + "n0 = 10.0\nn1 = 6.0\nn2 = 8.0\nt0 = n2 - n1\nt1 = n0 - n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "dev" + }, + { + "Input": "a waitress ' s income consists of her salary and tips . during one week , her tips were 3 / 4 of her salary . what fraction of her income for the week came from tips ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nt0 = n0 + n1\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.42857142857142855" + ], + "split": "dev" + }, + { + "Input": "the average age of 20 students of a class is 20 years . out of these , the average age of 9 students is 11 years and that of the other 10 students is 24 years . the age of the 20 th student is ?", + "Output Program": [ + "n0 = 20.0\nn1 = 20.0\nn2 = 9.0\nn3 = 11.0\nn4 = 10.0\nn5 = 24.0\nn6 = 20.0\nt0 = n0 * n0\nt1 = n2 * n3\nt2 = n4 * n5\nt3 = t1 + t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "61" + ], + "split": "dev" + }, + { + "Input": "a man engaged a servant on the condition that he would pay him rs . 500 and a uniform after one year service . he served only for 9 months and received uniform and rs . 300 , find the price of the uniform ?", + "Output Program": [ + "n0 = 500.0\nn1 = 9.0\nn2 = 300.0\nt0 = n0 * n1\nt1 = 3.0 * 4.0\nt2 = n2 * t1\nt3 = t1 * 1.0\nt4 = t0 - t2\nt5 = t4 / t3\nanswer = t5 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "dev" + }, + { + "Input": "in an examination , 300 students appeared . out of these students ; 29 % got first division , 54 % got second division and the remaining just passed . assuming that no student failed ; find the number of students who just passed .", + "Output Program": [ + "n0 = 300.0\nn1 = 29.0\nn2 = 54.0\nt0 = n1 + n2\nt1 = 100.0 - t0\nt2 = n0 * t1\nanswer = t2 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "51" + ], + "split": "dev" + }, + { + "Input": "if x + y = 20 , x - y = 36 , for integers of x and y , x = ?", + "Output Program": [ + "n0 = 20.0\nn1 = 36.0\nt0 = n0 + n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "dev" + }, + { + "Input": "what is the tens digit of 6 ^ 19 ?", + "Output Program": [ + "import math\nn0 = 6.0\nn1 = 19.0\nt0 = 1.0 + 4.0\nt1 = n1 % t0\nt2 = n0**min(t1, 5)\nt3 = t2 % 100.0\nt4 = t3 / 10.0\nanswer = math.floor(t4)\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "dev" + }, + { + "Input": "cost of 2 bats and 3 balls is rs . 1300 . the cost of 3 bats and 2 balls is rs . 1200 . the cost of each balls is more than that of each bat by ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 1300.0\nn3 = 3.0\nn4 = 2.0\nn5 = 1200.0\n\nanswer = n2 - n5\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "dev" + }, + { + "Input": "m = { - 6 , - 5 , - 4 , - 3 , - 2 } t = { - 2 , - 1 , 1 , 2 , 3 } if an integer is to be randomly selected from set m above and an integer is to be randomly selected from set t above , what is the probability that the product of the two integers will be negative ?", + "Output Program": [ + "n0 = 6.0\nn1 = 5.0\nn2 = 4.0\nn3 = 3.0\nn4 = 2.0\nn5 = 2.0\nn6 = 1.0\nn7 = 1.0\nn8 = 2.0\nn9 = 3.0\n\nanswer = n3 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.6" + ], + "split": "dev" + }, + { + "Input": "what is the total cost of 2 sandwiches at $ 2.45 each and 4 sodas at $ 0.87 each ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.45\nn2 = 4.0\nn3 = 0.87\nt0 = n0 * n1\nt1 = n2 * n3\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "8.38" + ], + "split": "dev" + }, + { + "Input": "priya and her father differ in their ages by 31 years . after 8 years . if the sum of their ages will be 69 , their present ages are", + "Output Program": [ + "n0 = 31.0\nn1 = 8.0\nn2 = 69.0\nt0 = n2 - n1\nt1 = t0 - n1\nt2 = n0 + t1\nt3 = t2 / 2.0\nanswer = t3 - n0\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "dev" + }, + { + "Input": "when positive integer k is divided by 5 , the remainder is 2 . when k is divided by 6 , the remainder is 5 . if k is less than 38 , what is the remainder when k is divided by 7 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 6.0\nn3 = 5.0\nn4 = 38.0\nn5 = 7.0\nt0 = n0 + 12.0\nanswer = t0 % n5\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "dev" + }, + { + "Input": "if an organization were to sell n tickets for a theater production , the total revenue from ticket sales would be 20 percent greater than the total costs of the production . if the organization actually sold all but 5 percent of the n tickets , the total revenue from ticket sales was what percent greater than the total costs of the production ?", + "Output Program": [ + "n0 = 20.0\nn1 = 5.0\nt0 = 12.0 + 4.0\nanswer = t0 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "dev" + }, + { + "Input": "the average of 5 consecutive odd numbers is 55 . what is the difference between the highest and lowest numbers ?", + "Output Program": [ + "n0 = 5.0\nn1 = 55.0\nt0 = n0 - 1.0\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "dev" + }, + { + "Input": "in a class of 25 students in an examination in maths 3 students scored 95 marks each , 5 get zero each and the average of the rest was 45 . what is the average of the whole class ?", + "Output Program": [ + "n0 = 25.0\nn1 = 3.0\nn2 = 95.0\nn3 = 5.0\nn4 = 45.0\nt0 = n1 + n3\nt1 = n1 * n2\nt2 = n0 - t0\nt3 = n4 * t2\nt4 = t3 + t1\nanswer = t4 / n0\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "dev" + }, + { + "Input": "a school has 4 section of chemistry in class x having 40 , 35 , 45 and 42 students . the mean marks obtained in chemistry test are 50 , 60 , 55 and 45 respectively for the 4 sections . determine the overall average of marks per student .", + "Output Program": [ + "n0 = 4.0\nn1 = 40.0\nn2 = 35.0\nn3 = 45.0\nn4 = 42.0\nn5 = 50.0\nn6 = 60.0\nn7 = 55.0\nn8 = 45.0\nn9 = 4.0\nt0 = n1 + n2\nt1 = n1 * n5\nt2 = n2 * n6\nt3 = n3 * n7\nt4 = n3 * n4\nt5 = t1 + t2\nt6 = n3 + t0\nt7 = t5 + t3\nt8 = n4 + t6\nt9 = t7 + t4\nanswer = t9 / t8\nprint(answer)" + ], + "Output Answer": [ + "52.25308641975309" + ], + "split": "dev" + }, + { + "Input": "a grocer has a sale of rs . 3435 , rs . 3920 , rs . 3855 , rs . 4230 and rs . 3560 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 3500 ?", + "Output Program": [ + "n0 = 3435.0\nn1 = 3920.0\nn2 = 3855.0\nn3 = 4230.0\nn4 = 3560.0\nn5 = 5.0\nn6 = 3500.0\nt0 = n5 + 1.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n6 * t0\nt4 = n3 + t2\nt5 = n4 + t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "2000" + ], + "split": "dev" + }, + { + "Input": "how many numbers from 45 to 110 are exactly divisible by 12 ?", + "Output Program": [ + "import math\nn0 = 45.0\nn1 = 110.0\nn2 = 12.0\nt0 = n1 / n2\nt1 = n0 / n2\nt2 = math.floor(t0)\nt3 = math.floor(t1)\nt4 = t3 + 1.0\nt5 = n2 * t2\nt6 = n2 * t4\nt7 = t5 - t6\nt8 = t7 / n2\nanswer = t8 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "dev" + }, + { + "Input": "a man has rs . 10350 in the form of rs . 50 notes and rs . 500 notes . the total number of notes are 108 . find the number of notes of rs . 50 denomination .", + "Output Program": [ + "n0 = 10350.0\nn1 = 50.0\nn2 = 500.0\nn3 = 108.0\nn4 = 50.0\nt0 = n2 * n3\nt1 = n2 - n1\nt2 = t0 - n0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "97" + ], + "split": "dev" + }, + { + "Input": "after a storm deposits 120 billion gallons of water into the city reservoir , the reservoir is 85 % full . if the original contents of the reservoir totaled 220 billion gallons , the reservoir was approximately what percentage full before the storm ?", + "Output Program": [ + "n0 = 120.0\nn1 = 85.0\nn2 = 220.0\nt0 = n0 + n2\nt1 = n1 / 100.0\nt2 = t0 / t1\nt3 = n2 / t2\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "55.00000000000001" + ], + "split": "dev" + }, + { + "Input": "find the value of 72517 x 9999 = m ?", + "Output Program": [ + "n0 = 72517.0\nn1 = 9999.0\nt0 = n1 - 4.0\nanswer = t0 * n0\nprint(answer)" + ], + "Output Answer": [ + "724807415" + ], + "split": "dev" + }, + { + "Input": "10 % people of a village in sri lanka died by bombardment , 15 % of the remainder left the village on account of fear . if now the population is reduced to 2907 , how much was it in the beginning ?", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 15.0\nn2 = 2907.0\nt0 = 100.0 - n0\nt1 = 100.0 - n1\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = t2 * t3\nt5 = n2 / t4\nanswer = math.floor(t5)\nprint(answer)" + ], + "Output Answer": [ + "3800" + ], + "split": "dev" + }, + { + "Input": "average of 5 numbers is 20 , and the sum of 3 of the numbers is 48 , what is the average of the other 2 numbers ?", + "Output Program": [ + "n0 = 5.0\nn1 = 20.0\nn2 = 3.0\nn3 = 48.0\nn4 = 2.0\nt0 = n0 * n1\nt1 = t0 - n3\nanswer = t1 / n4\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "dev" + }, + { + "Input": "the population of a city increases by 4 % per year but due to migration it decrease by 1 % per years . what will be the percentage increase in population in 3 years ?", + "Output Program": [ + "n0 = 4.0\nn1 = 1.0\nn2 = 3.0\nt0 = n0 - n1\nt1 = t0 + 100.0\nt2 = t1 * t0\nt3 = t2 / 100.0\nt4 = t3 + t0\nt5 = t4 + 100.0\nt6 = t5 * t0\nt7 = t6 / 100.0\nanswer = t4 + t7\nprint(answer)" + ], + "Output Answer": [ + "9.2727" + ], + "split": "dev" + }, + { + "Input": "the average height of 35 boys in a class was calculated as 185 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ) . ?", + "Output Program": [ + "import math\nn0 = 35.0\nn1 = 185.0\nn2 = 166.0\nn3 = 106.0\nt0 = n0 * n1\nt1 = t0 - n2\nt2 = n3 + t1\nt3 = t2 / n0\nanswer = math.floor(t3)\nprint(answer)" + ], + "Output Answer": [ + "183" + ], + "split": "dev" + }, + { + "Input": "the cost to park a car in a certain parking garage is $ 10.00 for up to 2 hours of parking and $ 1.75 for each hour in excess of 2 hours . what is the average ( arithmetic mean ) cost per hour to park a car in the parking garage for 9 hours ?", + "Output Program": [ + "n0 = 10.0\nn1 = 2.0\nn2 = 1.75\nn3 = 2.0\nn4 = 9.0\nt0 = n4 - n1\nt1 = n2 * t0\nt2 = n0 + t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "2.4722222222222223" + ], + "split": "dev" + }, + { + "Input": "the least number which when divided by 5 , 6 , 7 and 8 leaves a remainder 3 , but when divided by 9 leaves no remainder , is :", + "Output Program": [ + "import scipy\nn0 = 5.0\nn1 = 6.0\nn2 = 7.0\nn3 = 8.0\nn4 = 3.0\nn5 = 9.0\nt0 = scipy.lcm(int(n0), int(n1))\nt1 = scipy.lcm(int(n2), int(t0))\nt2 = scipy.lcm(int(n3), int(t1))\nanswer = t2 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "1680" + ], + "split": "dev" + }, + { + "Input": "1 men takes 37 $ to eat a pizza in restaurant such that it have discount multiple of 4 if u eat more pizza . discount increase by multiple of 4 every pizza u eat . for 1 pizza 0 % off . for 2 pizza % off for 3 pizza 8 % off . pizza without discount is 10 $ . how much that man eats the pizza .", + "Output Program": [ + "n0 = 1.0\nn1 = 37.0\nn2 = 4.0\nn3 = 4.0\nn4 = 1.0\nn5 = 0.0\nn6 = 2.0\nn7 = 3.0\nn8 = 8.0\nn9 = 10.0\nt0 = n2 * n9\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "dev" + }, + { + "Input": "if there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city , find the number of 4 wheelers parked there if the total number of wheels is 46 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 4.0\nn3 = 46.0\nt0 = n3 - n0\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "dev" + }, + { + "Input": "the average of temperatures at noontime from monday to friday is 60 ; the lowest one is 40 , what is the possible maximum range of the temperatures ?", + "Output Program": [ + "n0 = 60.0\nn1 = 40.0\nt0 = 2.0 + 3.0\nt1 = n1 * 4.0\nt2 = n0 * t0\nt3 = t2 - t1\nanswer = t3 - n1\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "dev" + }, + { + "Input": "a number is doubled and 9 is added . if resultant is trebled , it becomes 63 . what is that number", + "Output Program": [ + "n0 = 9.0\nn1 = 63.0\nt0 = n0 * 3.0\nt1 = 2.0 * 3.0\nt2 = n1 - t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "dev" + }, + { + "Input": "a waiter ' s salary consists of his salary and tips . during one week his tips were 7 / 4 of his salary . what fraction of his income came from tips ?", + "Output Program": [ + "n0 = 7.0\nn1 = 4.0\nt0 = n0 / n1\nt1 = t0 + 1.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.6363636363636364" + ], + "split": "dev" + }, + { + "Input": "the total age of a and b is 15 years more than the total age of b and c . c is how many year younger than", + "Output Program": [ + "n0 = 15.0\n\nanswer = n0 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "dev" + }, + { + "Input": "what is remainder of the division ( 1625 * 1627 * 1629 ) / 12 ?", + "Output Program": [ + "n0 = 1625.0\nn1 = 1627.0\nn2 = 1629.0\nn3 = 12.0\nt0 = n0 * n1\nt1 = n2 * t0\nt2 = t1 - 3.0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "dev" + }, + { + "Input": "if henry were to add 8 gallons of water to a tank that is already 3 / 4 full of water , the tank would be 7 / 8 full . how many gallons of water would the tank hold if it were full ?", + "Output Program": [ + "n0 = 8.0\nn1 = 3.0\nn2 = 4.0\nn3 = 7.0\nn4 = 8.0\nt0 = n3 / n4\nt1 = n1 / n2\nt2 = t0 - t1\nt3 = 1.0 / t2\nanswer = n0 * t3\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "dev" + }, + { + "Input": "if x gets 25 % more than y and y gets 20 % more than z , the share of z out of rs . 1110 will be :", + "Output Program": [ + "n0 = 25.0\nn1 = 20.0\nn2 = 1110.0\nt0 = n1 / 100.0\nt1 = n0 / 100.0\nt2 = t0 + 1.0\nt3 = t1 + 1.0\nt4 = t3 * t2\nt5 = t2 + t4\nt6 = t5 + 1.0\nanswer = n2 / t6\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "dev" + }, + { + "Input": "a 50 ml after - shave lotion at 30 % alcohol is mixed with 30 ml of pure water . what is the percentage of alcohol in the new solution ?", + "Output Program": [ + "n0 = 50.0\nn1 = 30.0\nn2 = 30.0\nt0 = n0 + n1\nt1 = n0 * n1\nt2 = t1 / 100.0\nt3 = t2 / t0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "18.75" + ], + "split": "dev" + }, + { + "Input": "a \u2019 s speed is 17 / 14 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?", + "Output Program": [ + "n0 = 17.0\nn1 = 14.0\nt0 = n0 - n1\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.17647058823529413" + ], + "split": "dev" + }, + { + "Input": "the total of 336 of 20 paise and 25 paise make a sum of rs . 71 . the no of 20 paise coins is", + "Output Program": [ + "n0 = 336.0\nn1 = 20.0\nn2 = 25.0\nn3 = 71.0\nn4 = 20.0\nt0 = n0 * n2\nt1 = n3 * 100.0\nt2 = n2 - n1\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "260" + ], + "split": "dev" + }, + { + "Input": "the number of the members of a club is more than 50 and less than 80 . when 4 people sit at a table , other people exactly divided to 8 - people groups ( 8 people sit at a table ) or 7 - people groups ( 7 people sit at a table ) . if the members are divided to 9 - people groups , how many people will be left ?", + "Output Program": [ + "import scipy\nn0 = 50.0\nn1 = 80.0\nn2 = 4.0\nn3 = 8.0\nn4 = 8.0\nn5 = 7.0\nn6 = 7.0\nn7 = 9.0\nt0 = scipy.lcm(int(n3), int(n5))\nt1 = n2 + t0\nanswer = t1 % n7\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "dev" + }, + { + "Input": "5 men are equal to as many women as are equal to 8 boys . all of them earn $ 90 only . men \u2019 s wages are ?", + "Output Program": [ + "n0 = 5.0\nn1 = 8.0\nn2 = 90.0\nt0 = n0 * 3.0\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "dev" + }, + { + "Input": "two trains of equal are running on parallel lines in the same direction at 48 km / hr and 36 km / hr . the faster train passes the slower train in 36 sec . the length of each train is ?", + "Output Program": [ + "n0 = 48.0\nn1 = 36.0\nn2 = 36.0\nt0 = n0 - n1\nt1 = t0 * 1000.0\nt2 = t1 / 3600.0\nt3 = n2 * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "dev" + }, + { + "Input": "a teacher grades students \u2019 tests by subtracting twice the number of incorrect responses from the number of correct responses . if student a answers each of the 100 questions on her test and receives a score of 76 , how many questions did student a answer correctly ?", + "Output Program": [ + "n0 = 100.0\nn1 = 76.0\nt0 = n0 - n1\nt1 = t0 / 3.0\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "92" + ], + "split": "dev" + }, + { + "Input": "p , q and r have $ 4000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?", + "Output Program": [ + "n0 = 4000.0\nt0 = 2.0 * 2.0\nt1 = 1.0 * 3.0\nt2 = t0 / 3.0\nt3 = n0 * t0\nt4 = t2 * 3.0\nt5 = t4 + t1\nt6 = t5 + t1\nanswer = t3 / t6\nprint(answer)" + ], + "Output Answer": [ + "1600" + ], + "split": "dev" + }, + { + "Input": "if x ^ 2 + ( 1 / x ^ 2 ) = 6 , x ^ 4 + ( 1 / x ^ 4 ) = ?", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 2.0\nn3 = 6.0\nn4 = 4.0\nn5 = 1.0\nn6 = 4.0\nt0 = n3**min(n0, 5)\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "34" + ], + "split": "dev" + }, + { + "Input": "( 935421 x 625 ) = ?", + "Output Program": [ + "n0 = 935421.0\nn1 = 625.0\nt0 = 1.0 + 4.0\nt1 = t0**min(4.0, 5)\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "584638125" + ], + "split": "dev" + }, + { + "Input": "how many integers v are prime numbers in the range 200 < v < 220 ?", + "Output Program": [ + "n0 = 200.0\nn1 = 220.0\nt0 = n1 - n0\nt1 = t0 - 12.0\nt2 = t1 / 4.0\nanswer = t2 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "dev" + }, + { + "Input": "if the average of 20 digits is 500 and the average of 14 of them is 390 , calculate the average of the remaining 6 numbers ?", + "Output Program": [ + "n0 = 20.0\nn1 = 500.0\nn2 = 14.0\nn3 = 390.0\nn4 = 6.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = t0 - t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "756.6666666666666" + ], + "split": "dev" + }, + { + "Input": "if p / q = 4 / 5 , then the value of 25 / 7 + { ( 2 q - p ) / ( 2 q + p ) } is ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 25.0\nn3 = 7.0\nn4 = 2.0\nn5 = 2.0\nt0 = n2 / n3\nt1 = n0 / n1\nt2 = n4 + t1\nt3 = n4 - t1\nt4 = t3 / t2\nanswer = t0 + t4\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "dev" + }, + { + "Input": "the milk level in a rectangular box measuring 58 feet by 25 feet is to be lowered by 6 inches . how many gallons of milk must be removed ? ( 1 cu ft = 7.5 gallons )", + "Output Program": [ + "n0 = 58.0\nn1 = 25.0\nn2 = 6.0\nn3 = 1.0\nn4 = 7.5\nt0 = n3 / 2.0\nt1 = n0 * n1\nt2 = t0 * t1\nanswer = n4 * t2\nprint(answer)" + ], + "Output Answer": [ + "5437.5" + ], + "split": "dev" + }, + { + "Input": "after replacing an old member by a new member , it was found that the average age of 5 members of a club is the same as it was 3 years ago . what is the difference between the ages of the replaced and the new member ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "dev" + }, + { + "Input": "zinc and copper are melted together in the ratio 9 : 11 . what is the weight of melted mixture , if 26.1 kg of zinc has been consumed in it ?", + "Output Program": [ + "n0 = 9.0\nn1 = 11.0\nn2 = 26.1\nt0 = n1 / n0\nt1 = n2 * t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "58.00000000000001" + ], + "split": "dev" + }, + { + "Input": "a person x started at 3 hours earlier at 40 km / h from a place p , then another person y followed him at 60 km / h . started his journey at 3 o ' clock , afternoon . what is the diference in time when x was 30 km ahead of y and when y was 30 km ahead of x ?", + "Output Program": [ + "n0 = 3.0\nn1 = 40.0\nn2 = 60.0\nn3 = 3.0\nn4 = 30.0\nn5 = 30.0\nt0 = n1 / 2.0\nt1 = n0 * n1\nt2 = n4 + t1\nt3 = t1 - n4\nt4 = t2 / t0\nt5 = t3 / t0\nanswer = t4 - t5\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "dev" + }, + { + "Input": "there are 5 fictions and 6 non - fictions . how many cases are there such that 2 fictions and 2 non - fictions are selected from them ?", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 6.0\nn2 = 2.0\nn3 = 2.0\nt0 = math.factorial(min(15, int(2.0)))\nt1 = n0 * 4.0\nt2 = n0 * n1\nt3 = t1 * t2\nt4 = t0**min(2.0, 5)\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "dev" + }, + { + "Input": "the age of somu is one - third his father ' s . 6 years back he was one - fifth of his father ' s age . what is his persent age ?", + "Output Program": [ + "n0 = 6.0\nt0 = 1.0 + 4.0\nt1 = n0 * t0\nt2 = t0 - 3.0\nt3 = t1 - n0\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "dev" + }, + { + "Input": "12 . what is the dividend . divisor 17 , the quotient is 9 and the remainder is 10 .", + "Output Program": [ + "n0 = 12.0\nn1 = 17.0\nn2 = 9.0\nn3 = 10.0\nt0 = n1 * n2\nanswer = n3 + t0\nprint(answer)" + ], + "Output Answer": [ + "163" + ], + "split": "dev" + }, + { + "Input": "how many quarters are equal to 7 dollars ?", + "Output Program": [ + "n0 = 7.0\n\nanswer = n0 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "dev" + }, + { + "Input": "the difference between the value of a number increased by 25 % and the value of the original number decreased by 30 % is 22 . what is the original number ?", + "Output Program": [ + "n0 = 25.0\nn1 = 30.0\nn2 = 22.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = t0 + 1.0\nt3 = 1.0 - t1\nt4 = t2 - t3\nanswer = n2 / t4\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "dev" + }, + { + "Input": "if a - b = 3 and a ^ 2 + b ^ 2 = 33 , find the value of ab .", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 2.0\nn2 = 2.0\nn3 = 33.0\nt0 = math.sqrt(max(0, n3))\nt1 = t0 - n0\nt2 = t1 / n1\nt3 = n0 + t2\nt4 = t3 * t2\nanswer = n1 * t4\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "dev" + }, + { + "Input": "1 : 3 = 1 2 / 3 : x . the value of x is ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 2.0\nn4 = 3.0\nt0 = n3 / n1\nt1 = n0 / n1\nt2 = n0 + t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "dev" + }, + { + "Input": "the average earning of amechanic for the first 4 days of a week is rs . 25 and for the last 4 days is rs . 22 . if heearns rs . 20 on the fourth day , his average earning forthe whole week is ?", + "Output Program": [ + "n0 = 4.0\nn1 = 25.0\nn2 = 4.0\nn3 = 22.0\nn4 = 20.0\nt0 = 3.0 + 4.0\nt1 = n0 * n1\nt2 = n0 * n3\nt3 = t1 + t2\nt4 = t3 - n4\nanswer = t4 / t0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "dev" + }, + { + "Input": "find ( 7 x + 2 y ) / ( x - 2 y ) if x / 2 y = 3 / 2 ?", + "Output Program": [ + "n0 = 7.0\nn1 = 2.0\nn2 = 2.0\nn3 = 2.0\nn4 = 3.0\nn5 = 2.0\nt0 = n4 / n2\nt1 = n2 * t0\nt2 = n0 * t1\nt3 = t1 - n2\nt4 = n1 + t2\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "dev" + }, + { + "Input": "the population of a town increased from 1 , 75,000 to 2 , 97,500 in a decade . the average percent increase of population per year is", + "Output Program": [ + "n0 = 1.0\nn1 = 75000.0\nn2 = 2.0\nn3 = 97500.0\nt0 = 100.0 * 1000.0\nt1 = n1 + t0\nt2 = n2 * t0\nt3 = n3 + t2\nt4 = t3 - t1\nt5 = t4 / 10.0\nt6 = t5 / t1\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "7.000000000000001" + ], + "split": "dev" + }, + { + "Input": "in an exam , gibi scored 59 percent , jigi scored 55 percent , mike scored 99 percent and lizzy 67 percent . the maximum score awarded in the exam is 700 . find the average mark scored by all the 4 students ?", + "Output Program": [ + "n0 = 59.0\nn1 = 55.0\nn2 = 99.0\nn3 = 67.0\nn4 = 700.0\nn5 = 4.0\nt0 = n0 + n1\nt1 = n2 + n3\nt2 = t0 + t1\nt3 = n4 * t2\nt4 = t3 / 100.0\nanswer = t4 / n5\nprint(answer)" + ], + "Output Answer": [ + "490" + ], + "split": "dev" + }, + { + "Input": "in how many no . between 10 and 50 exactly two of the digits is 5 ?", + "Output Program": [ + "n0 = 10.0\nn1 = 50.0\nn2 = 5.0\nt0 = n1 / n0\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "dev" + }, + { + "Input": "3.20 can be expressed in terms of percentage as", + "Output Program": [ + "n0 = 3.2\n\nanswer = n0 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "320" + ], + "split": "dev" + }, + { + "Input": "a person was asked to subtract 25 % of a number from the original but he subtracted 25 from the number . his answer was 25 more than correct one . what was the original number ?", + "Output Program": [ + "n0 = 25.0\nn1 = 25.0\nn2 = 25.0\nt0 = n0 + n0\nt1 = n0 / 100.0\nt2 = 1.0 - t1\nt3 = 1.0 - t2\nanswer = t0 / t3\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "dev" + }, + { + "Input": "carolyn bought 17 gumballs , lew bought 12 gumballs , and carey bought x gumballs . the average ( arithmetic mean ) number of gumballs the 3 bought is between 19 and 25 , inclusive . what is the difference between the greatest number and the smallest number of gumballs carey could have bought ?", + "Output Program": [ + "n0 = 17.0\nn1 = 12.0\nn2 = 3.0\nn3 = 19.0\nn4 = 25.0\nt0 = n0 + n1\nt1 = n2 * n4\nt2 = n2 * n3\nt3 = t1 - t0\nt4 = t2 - t0\nanswer = t3 - t4\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "dev" + }, + { + "Input": "if a mixture is 2 \u2044 7 alcohol by volume and 3 \u2044 7 water by volume , what is the ratio of the volume of alcohol to the volume of water in this mixture ?", + "Output Program": [ + "n0 = 2.0\nn1 = 7.0\nn2 = 3.0\nn3 = 7.0\nt0 = n0 / n1\nt1 = n2 / n1\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.6666666666666666" + ], + "split": "dev" + }, + { + "Input": "20 percent of country y ' s yearly exports come from fruit exports . one - sixth of all fruit exports from country y are orange exports . if country y generates $ 4.25 million from its orange exports , how much money does it generate from its yearly total of exports ?", + "Output Program": [ + "n0 = 20.0\nn1 = 4.25\nt0 = 2.0 * 3.0\nt1 = 1.0 / t0\nt2 = n1 / t1\nt3 = t2 * 100.0\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "127.5" + ], + "split": "dev" + }, + { + "Input": "what is the value of n if the sum of the consecutive odd intergers w from 1 to n equals 169 ?", + "Output Program": [ + "import math\nn0 = 1.0\nn1 = 169.0\nt0 = n0 * 2.0\nt1 = math.sqrt(max(0, n1))\nt2 = t1 * 2.0\nt3 = t2 - t0\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "dev" + }, + { + "Input": "evaluate : 7899665 - 12 * 3 * 2 = ?", + "Output Program": [ + "n0 = 7899665.0\nn1 = 12.0\nn2 = 3.0\nn3 = 2.0\nt0 = n1 * n2\nt1 = n3 * t0\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "7899593" + ], + "split": "dev" + }, + { + "Input": "if 9 / ( 1 + 4 / x ) = 1 , then x =", + "Output Program": [ + "n0 = 9.0\nn1 = 1.0\nn2 = 4.0\nn3 = 1.0\nt0 = n0 - n1\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "dev" + }, + { + "Input": "an automobile parts supplier charges $ 25 per package of gaskets . when a customer orders more than 10 packages of gaskets , the supplier charges 4 / 5 the price for each package in excess of 10 . during a certain week , the supplier sold 60 packages of gaskets . if 15 percent of the gaskets went to company x , 15 percent to company y , and the rest to company z , what was the total amount , in dollars , that the parts supplier received in payment for the gaskets ?", + "Output Program": [ + "n0 = 25.0\nn1 = 10.0\nn2 = 4.0\nn3 = 5.0\nn4 = 10.0\nn5 = 60.0\nn6 = 15.0\nn7 = 15.0\nt0 = n2 / n3\nt1 = n6 / 100.0\nt2 = n0 * n1\nt3 = n0 * t0\nt4 = n5 * t1\nt5 = n0 * t4\nt6 = n5 - t4\nt7 = t5 + t5\nt8 = t6 - t4\nt9 = t8 - n1\nt10 = t3 * t9\nt11 = t10 + t2\nanswer = t11 + t7\nprint(answer)" + ], + "Output Answer": [ + "1340" + ], + "split": "dev" + }, + { + "Input": "the average of the marks of 25 students in a class is 70 . if the marks of each student are doubled , find the new average ?", + "Output Program": [ + "n0 = 25.0\nn1 = 70.0\n\nanswer = n1 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "140" + ], + "split": "dev" + }, + { + "Input": "for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today ' s production of 110 units raises the average to 55 units per day , what is the value of n ?", + "Output Program": [ + "n0 = 50.0\nn1 = 110.0\nn2 = 55.0\nt0 = n1 - n0\nt1 = n2 - n0\nt2 = t0 / t1\nanswer = t2 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "dev" + }, + { + "Input": "the population of locusts in a certain swarm doubles every two hours . if 4 hours ago there were 1,000 locusts in the swarm , in approximately how many hours will the swarm population exceed 128,000 locusts ?", + "Output Program": [ + "n0 = 4.0\nn1 = 1000.0\nn2 = 128000.0\nt0 = 10.0 / 2.0\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "dev" + }, + { + "Input": "mixture contains alcohol and water in the ratio 4 : 3 . if 5 liters of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture .", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 5.0\nn3 = 4.0\nn4 = 5.0\nt0 = n0 * n4\nt1 = n0 * n2\nt2 = n0 * n1\nt3 = t1 - t2\nt4 = t0 / t3\nanswer = n0 * t4\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "dev" + }, + { + "Input": "a grocer has a sale of rs . 5435 , rs . 5927 , rs . 5855 , rs . 6230 and rs . 5562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 5500 ?", + "Output Program": [ + "n0 = 5435.0\nn1 = 5927.0\nn2 = 5855.0\nn3 = 6230.0\nn4 = 5562.0\nn5 = 5.0\nn6 = 5500.0\nt0 = n5 + 1.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n6 * t0\nt4 = n3 + t2\nt5 = n4 + t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "3991" + ], + "split": "dev" + }, + { + "Input": "find the result of equation of the ellipse whose foci are at ( 0 , - 5 ) and ( 0 , 5 ) and the length of its major axis is 14 .", + "Output Program": [ + "n0 = 0.0\nn1 = 5.0\nn2 = 0.0\nn3 = 5.0\nn4 = 14.0\nt0 = n1 + n1\nt1 = t0 + 4.0\nanswer = t1 / n4\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "dev" + }, + { + "Input": "if 12 machine can finish a job in 40 days , then how many more machines would be needed to finish the job in one - fourth less time ?", + "Output Program": [ + "n0 = 12.0\nn1 = 40.0\nt0 = 3.0 / 4.0\nt1 = n0 * n1\nt2 = n1 * t0\nt3 = t1 / t2\nanswer = t3 - n0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "dev" + }, + { + "Input": "following an increase in prices , the price of a candy box was 20 pounds and the price of a can of soda was 6 pounds . if the price of a candy box was raised by 25 % , and the price of a can of soda was raised by 50 % . what was the price of a box of candy plus a can of soda before prices were raised ?", + "Output Program": [ + "n0 = 20.0\nn1 = 6.0\nn2 = 25.0\nn3 = 50.0\nt0 = n2 + 100.0\nt1 = n3 + 100.0\nt2 = n0 * 100.0\nt3 = n1 * 100.0\nt4 = t2 / t0\nt5 = t3 / t1\nanswer = t4 + t5\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "dev" + }, + { + "Input": "in a photography exhibition , some photographs were taken by octavia the photographer , and some photographs were framed by jack the framer . jack had framed 24 photographs taken by octavia , and 12 photographs taken by other photographers . if 36 of the photographs in the exhibition were taken by octavia , how many photographs were either framed by jack or taken by octavia ?", + "Output Program": [ + "n0 = 24.0\nn1 = 12.0\nn2 = 36.0\nt0 = n0 + n1\nt1 = n2 - n0\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "dev" + }, + { + "Input": "what is value of ( p + q ) / ( p - q ) if p / q = 7 ?", + "Output Program": [ + "n0 = 7.0\nt0 = n0 + 1.0\nt1 = n0 - 1.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "1.3333333333333333" + ], + "split": "dev" + }, + { + "Input": "a windmill is taking advantage of strong air currents in order to produce electrical energy . on a typical day the wind speed is around 20 mph and in that speed the windmill produces 400 kw / h ( kilowatts per hour ) . on a stormy day a windmill produces 20 % more energy . how much kw / h can 3 windmills produce in two hours on a stormy day ?", + "Output Program": [ + "n0 = 20.0\nn1 = 400.0\nn2 = 20.0\nn3 = 3.0\nt0 = n0 * n1\nt1 = t0 / 100.0\nt2 = n1 + t1\nt3 = n3 * t2\nanswer = t3 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "2880" + ], + "split": "dev" + }, + { + "Input": "if x and j are integers and 2 x \u2013 j = 11 , then 4 x + j can not be", + "Output Program": [ + "n0 = 2.0\nn1 = 11.0\nn2 = 4.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n1 - t0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "dev" + }, + { + "Input": "joe \u2019 s average ( arithmetic mean ) test score across 4 equally weighted tests was 45 . he was allowed to drop his lowest score . after doing so , his average test score improved to 50 . what is the lowest test score that was dropped ?", + "Output Program": [ + "n0 = 4.0\nn1 = 45.0\nn2 = 50.0\nt0 = n0 * n1\nt1 = n2 * 3.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "dev" + }, + { + "Input": "if y > 0 , ( 4 y ) / 20 + ( 3 y ) / 10 is what percent of y ?", + "Output Program": [ + "n0 = 0.0\nn1 = 4.0\nn2 = 20.0\nn3 = 3.0\nn4 = 10.0\nt0 = n1 / n2\nt1 = n3 / n4\nt2 = t0 + t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "dev" + }, + { + "Input": "in the number 10,0 ab , a and b represent the tens and units digits , respectively . if 11,0 ab is divisible by 55 , what is the greatest possible value of b \u00d7 a ?", + "Output Program": [ + "n0 = 100.0\nn1 = 110.0\nn2 = 55.0\nt0 = n1 / 10.0\nt1 = n2 / t0\nt2 = t1 - 2.0\nanswer = t1 * t2\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "dev" + }, + { + "Input": "si on a certain sum of money for 3 yrs at 8 percent / annum is 1 / 2 the ci on rs . 4000 for 2 yrs at 10 percent / annum . the sum placed on si is ?", + "Output Program": [ + "n0 = 3.0\nn1 = 8.0\nn2 = 1.0\nn3 = 2.0\nn4 = 4000.0\nn5 = 2.0\nn6 = 10.0\nt0 = n6 / 100.0\nt1 = n0 * n1\nt2 = n2 + t0\nt3 = t2**min(2.0, 5)\nt4 = n4 * t3\nt5 = t4 - n4\nt6 = t5 / 2.0\nt7 = t6 * 100.0\nanswer = t7 / t1\nprint(answer)" + ], + "Output Answer": [ + "1750.0000000000018" + ], + "split": "dev" + }, + { + "Input": "what is the sum of the first 23 natural numbers ( starting from 1 ) ?", + "Output Program": [ + "n0 = 23.0\nn1 = 1.0\nt0 = n0 / 2.0\nt1 = n0 - n1\nt2 = t1 + 2.0\nanswer = t2 * t0\nprint(answer)" + ], + "Output Answer": [ + "276" + ], + "split": "dev" + }, + { + "Input": "out of 3 consecutive odd numbers 11 times the first number is equal to addition of thrice the third number and adding 16 to 4 times the second . what is the first number ?", + "Output Program": [ + "n0 = 3.0\nn1 = 11.0\nn2 = 16.0\nn3 = 4.0\nt0 = n1 - n3\nanswer = n2 - t0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "dev" + }, + { + "Input": "according to the formula f = 9 / 5 ( c ) + 32 , if the temperature in degrees farenheit ( f ) increases by 26 , by how much does the temperature in degrees celsius ( c ) increase ?", + "Output Program": [ + "n0 = 9.0\nn1 = 5.0\nn2 = 32.0\nn3 = 26.0\nt0 = n1 * n3\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "14.444444444444445" + ], + "split": "dev" + }, + { + "Input": "the captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average of the team ?", + "Output Program": [ + "n0 = 11.0\nn1 = 26.0\nn2 = 3.0\nt0 = n1 + n2\nt1 = n2 * n2\nt2 = n1 + t0\nt3 = t2 - t1\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "dev" + }, + { + "Input": "a person spends 1 / 3 rd of the money with him on clothes , 1 / 5 th of the remaining on food and 1 / 4 th of the remaining on travel . now , he is left with rs 200 . how much did he have with him in the beginning ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 5.0\nn4 = 1.0\nn5 = 4.0\nn6 = 200.0\nt0 = n0 / n1\nt1 = n0 - t0\nt2 = t1 / n3\nt3 = t1 - t2\nt4 = t3 / n5\nt5 = t3 - t4\nanswer = n6 / t5\nprint(answer)" + ], + "Output Answer": [ + "499.9999999999999" + ], + "split": "dev" + }, + { + "Input": "the shopkeeper increased the price of a product by 25 % so that customer finds it difficult to purchase the required amount . but somehow the customer managed to purchase only 76 % of the required amount . what is the net difference in the expenditure on that product ?", + "Output Program": [ + "n0 = 25.0\nn1 = 76.0\nt0 = n0 + 100.0\nt1 = 100.0 * 100.0\nt2 = n1 * t0\nt3 = t1 - t2\nt4 = t3 * 100.0\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "dev" + }, + { + "Input": "if a number n is chosen at random from the set of two - digit integers whose digits are both prime numbers , what is the probability r that n is divisible by 3 ?", + "Output Program": [ + "n0 = 3.0\nt0 = n0 + 2.0\nt1 = 4.0 * 4.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.3125" + ], + "split": "dev" + }, + { + "Input": "0 - - - : - | - - - : - - | - : - - : - | - - : - - - | - : - - - - 1 on the number line above , the segment from 0 to 1 has been divided into fifths , as indicated by the large tick marks , and also into sevenths , as indicated by the small tick marks . what is the least possible distance x between any two of the tick marks ?", + "Output Program": [ + "n0 = 0.0\nn1 = 1.0\nn2 = 0.0\nn3 = 1.0\nt0 = 2.0 + 3.0\nt1 = 3.0 + 4.0\nt2 = t0 * t1\nanswer = n1 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.02857142857142857" + ], + "split": "dev" + }, + { + "Input": "each of the products produced yesterday was checked by worker x or worker y . 0.5 % of the products checked by worker x are defective and 0.8 % of the products checked by worker y are defective . if the total defective rate of all the products checked by worker x and worker y is 0.74 % , what fraction of the products was checked by worker y ?", + "Output Program": [ + "n0 = 0.5\nn1 = 0.8\nn2 = 0.74\nt0 = n2 - n0\nt1 = n1 - n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.7999999999999998" + ], + "split": "dev" + }, + { + "Input": "a sports equipment store sold ping pong rackets for a total of $ 637 . if the average ( arithmetic mean ) price of a pair of rackets is $ 9.8 , how many pairs were sold ?", + "Output Program": [ + "n0 = 637.0\nn1 = 9.8\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "65" + ], + "split": "dev" + }, + { + "Input": "if - 3 x + 4 y = 28 and 3 x - 2 y = 8 , what is the product of x and y ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 28.0\nn3 = 3.0\nn4 = 2.0\nn5 = 8.0\nt0 = n2 + n5\nt1 = t0 / n4\nt2 = n4 * t1\nt3 = n5 + t2\nt4 = t3 / n0\nanswer = t4 * t1\nprint(answer)" + ], + "Output Answer": [ + "264" + ], + "split": "dev" + }, + { + "Input": "if y > 0 , ( 9 y ) / 20 + ( 3 y ) / 10 is what percent of y ?", + "Output Program": [ + "n0 = 0.0\nn1 = 9.0\nn2 = 20.0\nn3 = 3.0\nn4 = 10.0\nt0 = n1 / n2\nt1 = n3 / n4\nt2 = t0 + t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "dev" + }, + { + "Input": "all the students of class are told to sit in circle shape . here the boy at the 5 th position is exactly opposite to 20 th boy . total number of boys in the class ?", + "Output Program": [ + "n0 = 5.0\nn1 = 20.0\nt0 = n1 - n0\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "dev" + }, + { + "Input": "an equal number of desks and bookcases are to be placed along a library wall that is 15 meters long . each desk is 2 meters long , and each bookshelf is 1.5 meters long . if the maximum possible number of desks and bookcases are to be placed along the wall , then the space along the wall that is left over will be how many meters f long ?", + "Output Program": [ + "n0 = 15.0\nn1 = 2.0\nn2 = 1.5\nt0 = n1 * 4.0\nt1 = n2 * 4.0\nt2 = t0 + t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "dev" + }, + { + "Input": "for every even positive integer m , f ( m ) represents the product of all even integers from 2 to m , inclusive . for example , f ( 12 ) = 2 x 4 x 6 x 8 x 10 x 12 . what is the greatest prime factor of f ( 24 ) ?", + "Output Program": [ + "n0 = 2.0\nn1 = 12.0\nn2 = 2.0\nn3 = 4.0\nn4 = 6.0\nn5 = 8.0\nn6 = 10.0\nn7 = 12.0\nn8 = 24.0\nt0 = n8 / n0\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "dev" + }, + { + "Input": "in a group of ducks and cows , the total number of legs are 40 more than twice the number of heads . find the total number of cows .", + "Output Program": [ + "n0 = 40.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "dev" + }, + { + "Input": "a student chose a number , multiplied it by 2 , then subtracted 138 from the result and got 102 . what was the number he chose ?", + "Output Program": [ + "n0 = 2.0\nn1 = 138.0\nn2 = 102.0\nt0 = n1 + n2\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "dev" + }, + { + "Input": "the product of two successive numbers is 4160 . which is the smaller of the two numbers ?", + "Output Program": [ + "import math\nn0 = 4160.0\n\nanswer = math.sqrt(max(0, n0))\nprint(answer)" + ], + "Output Answer": [ + "64.4980619863884" + ], + "split": "dev" + }, + { + "Input": "soymilk are sold in packages of two or 3 only . if hannah bought 17 soymilk exactly , what could be the number of large packs hannah bought ?", + "Output Program": [ + "n0 = 3.0\nn1 = 17.0\nt0 = 2.0 * 4.0\nt1 = n1 - t0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "dev" + }, + { + "Input": "if 4 / ( 1 + 3 / x ) = 1 , then x =", + "Output Program": [ + "n0 = 4.0\nn1 = 1.0\nn2 = 3.0\nn3 = 1.0\nt0 = n0 - n1\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "dev" + }, + { + "Input": "there are , in a certain league , 20 teams , and each team face another team for a total of 10 times . how many games are played in the season ?", + "Output Program": [ + "n0 = 20.0\nn1 = 10.0\nt0 = n0 / 2.0\nt1 = n0 - 1.0\nt2 = t1 * n1\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "1900" + ], + "split": "dev" + }, + { + "Input": "if integer k is equal to the sum of all even multiples of 15 between 390 and 615 , what is the greatest prime factor of k ?", + "Output Program": [ + "import math\nn0 = 15.0\nn1 = 390.0\nn2 = 615.0\nt0 = n2 / n0\nt1 = n1 / n0\nt2 = math.floor(t0)\nt3 = math.floor(t1)\nt4 = n0 * t2\nt5 = n0 * t3\nt6 = t4 - t5\nt7 = t6 / n0\nt8 = t7 + 1.0\nanswer = t8 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "dev" + }, + { + "Input": "a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 30 paisa . if the share of y is rs . 54 , what is the total amount ?", + "Output Program": [ + "n0 = 45.0\nn1 = 30.0\nn2 = 54.0\nt0 = 100.0 / n0\nt1 = n1 / n0\nt2 = n2 * t0\nt3 = n2 * t1\nt4 = t2 + t3\nanswer = n2 + t4\nprint(answer)" + ], + "Output Answer": [ + "210" + ], + "split": "dev" + }, + { + "Input": "the expenditure of a businessman increase consistently by 10 % per year . if his present expenditure is rs . 20000 then what will his expenditure be after 2 years ?", + "Output Program": [ + "n0 = 10.0\nn1 = 20000.0\nn2 = 2.0\nt0 = n0 + 100.0\nt1 = t0 / 100.0\nt2 = t1**min(n2, 5)\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "24200.000000000004" + ], + "split": "dev" + }, + { + "Input": "farm tax is levied on the 25 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . william . mr . william paid only $ 480 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :", + "Output Program": [ + "n0 = 25.0\nn1 = 3840.0\nn2 = 480.0\nt0 = n2 / n1\nt1 = t0 * 100.0\nt2 = t1 * 100.0\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "dev" + }, + { + "Input": "a textile manufacturing firm employees 100 looms . it makes fabrics for a branded company . the aggregate sales value of the output of the 100 looms is rs 5 , 00,000 and the monthly manufacturing expenses is rs 1 , 50,000 . assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms . monthly establishment charges are rs 75000 . if one loom breaks down and remains idle for one month , the decrease in profit is :", + "Output Program": [ + "n0 = 100.0\nn1 = 100.0\nn2 = 5.0\nn3 = 0.0\nn4 = 1.0\nn5 = 50000.0\nn6 = 75000.0\nt0 = n2 * 1000.0\nt1 = n6 * 2.0\nt2 = n0 - n4\nt3 = n6 + t1\nt4 = t2 / n0\nt5 = t0 * 100.0\nt6 = t4 * t5\nt7 = t4 * t1\nt8 = t5 - t3\nt9 = t6 - t7\nt10 = t9 - n6\nanswer = t8 - t10\nprint(answer)" + ], + "Output Answer": [ + "3500" + ], + "split": "dev" + }, + { + "Input": "when positive integer x is divided by 11 , the quotient is y and the remainder is 4 . when 2 x is divided by 8 , the quotient is 3 y and the remainder is 1 . what is the value of 13 y \u2013 x ?", + "Output Program": [ + "n0 = 11.0\nn1 = 4.0\nn2 = 2.0\nn3 = 8.0\nn4 = 3.0\nn5 = 1.0\nn6 = 13.0\nt0 = n1 * n2\nt1 = n3 * n4\nt2 = n0 * n2\nt3 = t0 - n5\nt4 = t1 - t2\nt5 = t3 / t4\nt6 = n6 * t5\nt7 = n0 * t5\nt8 = n1 + t7\nanswer = t6 - t8\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "dev" + }, + { + "Input": "a jar of 180 marbles is divided equally among a group of marble - players today . if 2 people joined the group in the future , each person would receive 1 marble less . how many people are there in the group today ?", + "Output Program": [ + "import math\nn0 = 180.0\nn1 = 2.0\nn2 = 1.0\nt0 = n0 * n1\nt1 = n1**min(n1, 5)\nt2 = t0 * 4.0\nt3 = t2 + t1\nt4 = math.sqrt(max(0, t3))\nt5 = t4 - n1\nanswer = t5 / n1\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "dev" + }, + { + "Input": "a cricketer whose bowling average is 12.4 runs per wicket takes 5 wickets for 26 runs and there by decreases his average by 0.4 . the number age of the family now is :", + "Output Program": [ + "n0 = 12.4\nn1 = 5.0\nn2 = 26.0\nn3 = 0.4\nt0 = n0 - n3\nt1 = n1 * t0\nt2 = t1 - n2\nanswer = t2 / n3\nprint(answer)" + ], + "Output Answer": [ + "85" + ], + "split": "dev" + }, + { + "Input": "the average of first 5 multiples of 5 is", + "Output Program": [ + "n0 = 5.0\nn1 = 5.0\nt0 = n0 * 2.0\nt1 = n0 * 3.0\nt2 = n0 * 4.0\nt3 = n0 * n0\nt4 = n0 + t0\nt5 = t4 + t1\nt6 = t5 + t2\nt7 = t6 + t3\nanswer = t7 / n0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "dev" + }, + { + "Input": "of the 180 people at a party , 70 were women , and 30 women tried the appetizer . if 50 people did not try the appetizer , what is the total number of men who tried the appetizer ?", + "Output Program": [ + "n0 = 180.0\nn1 = 70.0\nn2 = 30.0\nn3 = 50.0\nt0 = n0 - n3\nanswer = t0 - n2\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "dev" + }, + { + "Input": "we run a business that rents out canoes and kayaks . a canoe rental costs $ 15 per day , and a kayak rental costs $ 18 dollars per day . one day , our business rents out 3 canoes for every 2 kayaks and receives a total of $ 405 in revenue . how many more canoes than kayaks were rented out ?", + "Output Program": [ + "n0 = 15.0\nn1 = 18.0\nn2 = 3.0\nn3 = 2.0\nn4 = 405.0\nt0 = n0 * n2\nt1 = n1 * n3\nt2 = n2 - n3\nt3 = t0 + t1\nt4 = n4 / t3\nanswer = t4 * t2\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "dev" + }, + { + "Input": "in a company the manager wants to give some gifts to all of the workers . in each block there are about 100 workers are there . the total amount for giving the gifts for all the workers is $ 4000 . the worth of the gift is $ 4 . how many blocks are there in the company ?", + "Output Program": [ + "n0 = 100.0\nn1 = 4000.0\nn2 = 4.0\nt0 = n1 / n2\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "dev" + }, + { + "Input": "the sum of first n consecutive odd integers is n ^ 2 . what is the sum of all odd integers between 15 and 41 inclusive .", + "Output Program": [ + "n0 = 2.0\nn1 = 15.0\nn2 = 41.0\nt0 = n2 + 1.0\nt1 = n1 - n0\nt2 = t1 + 1.0\nt3 = t0 / n0\nt4 = t2 / n0\nt5 = t3**min(n0, 5)\nt6 = t4**min(n0, 5)\nanswer = t5 - t6\nprint(answer)" + ], + "Output Answer": [ + "392" + ], + "split": "dev" + }, + { + "Input": "what is the dividend . divisor 17 , the quotient is 8 and the remainder is 5", + "Output Program": [ + "n0 = 17.0\nn1 = 8.0\nn2 = 5.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "141" + ], + "split": "dev" + }, + { + "Input": "4 friends are pooling their money for pizza . emma has 8 dollars . daya has 25 % more money than emma , jeff has 2 / 5 of the money daya has , and brenda has 4 more dollars than jeff . how much money does brenda have ?", + "Output Program": [ + "n0 = 4.0\nn1 = 8.0\nn2 = 25.0\nn3 = 2.0\nn4 = 5.0\nn5 = 4.0\nt0 = n2 + 100.0\nt1 = t0 / 100.0\nt2 = n1 * t1\nt3 = n3 * t2\nt4 = t3 / n4\nanswer = n0 + t4\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "dev" + }, + { + "Input": "mike took a taxi to the airport and paid $ 2.50 to start plus $ 0.25 per mile . annie took a different route to the airport and paid $ 2.50 plus $ 5.00 in bridge toll fees plus $ 0.25 per mile . if each was charged exactly the same amount , and annie ' s ride was 26 miles , how many miles was mike ' s ride ?", + "Output Program": [ + "n0 = 2.5\nn1 = 0.25\nn2 = 2.5\nn3 = 5.0\nn4 = 0.25\nn5 = 26.0\nt0 = n0 + n3\nt1 = n1 * n5\nt2 = t0 + t1\nt3 = t2 - n0\nanswer = t3 / n1\nprint(answer)" + ], + "Output Answer": [ + "46" + ], + "split": "dev" + }, + { + "Input": "the average weight of 6 person ' s increases by 4.5 kg when a new person comes in place of one of them weighing 75 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 6.0\nn1 = 4.5\nn2 = 75.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "102" + ], + "split": "dev" + }, + { + "Input": "a , b , c , d , e are the 5 electronic shops in the naza market , which have 20 , 30 , 60 , 80 and 50 t . v . sets with them respectively , then the average number of t . v . sets in each shop is", + "Output Program": [ + "n0 = 5.0\nn1 = 20.0\nn2 = 30.0\nn3 = 60.0\nn4 = 80.0\nn5 = 50.0\nt0 = n3 + n4\nt1 = n1 + n2\nt2 = n5 + t1\nt3 = t0 + t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "dev" + }, + { + "Input": "a no . when divided by 281 gives a remainder 160 , what remainder will be obtainedby dividingthe same no . 21 ?", + "Output Program": [ + "n0 = 281.0\nn1 = 160.0\nn2 = 21.0\nt0 = n0 + n1\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "dev" + }, + { + "Input": "the sum of even numbers between 1 and 31 is", + "Output Program": [ + "import math\nn0 = 1.0\nn1 = 31.0\nt0 = n0 + n1\nt1 = n1 / 2.0\nt2 = math.floor(t1)\nt3 = t2 / 2.0\nanswer = t0 * t3\nprint(answer)" + ], + "Output Answer": [ + "240" + ], + "split": "dev" + }, + { + "Input": "if the average ( arithmetic mean ) of a and b is 45 and the average of b and c is 50 , what is the value of c \u00e2 \u02c6 \u2019 a ?", + "Output Program": [ + "n0 = 45.0\nn1 = 50.0\nt0 = n1 * 2.0\nt1 = n0 * 2.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "dev" + }, + { + "Input": "the average age of an adult class is 40 years . 12 new students with an avg age of 32 years join the class . therefore decreasing theaverage by 4 year . find what was theoriginal strength of class ?", + "Output Program": [ + "n0 = 40.0\nn1 = 12.0\nn2 = 32.0\nn3 = 4.0\nt0 = n1 * n2\nt1 = n0 - n3\nt2 = n1 * t1\nt3 = t2 - t0\nanswer = t3 / n3\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "dev" + }, + { + "Input": "if n is an integer and 101 n ^ 2 is less than or equal to 6400 , what is the greatest possible value of n ?", + "Output Program": [ + "import math\nn0 = 101.0\nn1 = 2.0\nn2 = 6400.0\nt0 = n2 / n0\nt1 = math.sqrt(max(0, t0))\nanswer = math.floor(t1)\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "dev" + }, + { + "Input": "a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets rs . 500 more than d , what is a ' s share ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 4.0\nn3 = 3.0\nn4 = 500.0\nt0 = n0 + n1\nt1 = n2 + t0\nt2 = n3 + t1\nt3 = n2 / t2\nt4 = n3 / t2\nt5 = n0 / t2\nt6 = t3 - t4\nt7 = n4 / t6\nanswer = t7 * t5\nprint(answer)" + ], + "Output Answer": [ + "2500" + ], + "split": "dev" + }, + { + "Input": "the cash realised on selling a 14 % stock is rs . 109.25 , brokerage being 1 / 4 % is ?", + "Output Program": [ + "n0 = 14.0\nn1 = 109.25\nn2 = 1.0\nn3 = 4.0\nt0 = n2 / n3\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "109" + ], + "split": "dev" + }, + { + "Input": "if p and q are positive integers each greater than 1 , and 17 ( p + 1 ) = 21 ( q + 1 ) , what is the least possible value of p + q ?", + "Output Program": [ + "n0 = 1.0\nn1 = 17.0\nn2 = 1.0\nn3 = 21.0\nn4 = 1.0\nt0 = n1 + n3\nanswer = t0 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "dev" + }, + { + "Input": "the ratio of a to b is 4 to 5 , where a and b are positive . if x equals a increased by 25 percent of a , and m equals b decreased by 60 percent of b , what is the value of m / x ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 25.0\nn3 = 60.0\nt0 = n2 + 100.0\nt1 = n1 / n0\nt2 = 100.0 - n3\nt3 = t2 / t0\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "0.4" + ], + "split": "dev" + }, + { + "Input": "when 2 / 9 of the votes on a certain resolution have been counted , 3 / 4 of those counted are in favor of the resolution . what fraction q of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution ?", + "Output Program": [ + "n0 = 2.0\nn1 = 9.0\nn2 = 3.0\nn3 = 4.0\nn4 = 2.0\nn5 = 1.0\nt0 = n0 + n5\nt1 = n0 / n1\nt2 = n2 / n3\nt3 = n1 - n0\nt4 = n0 / t0\nt5 = t3 / n1\nt6 = t1 * t2\nt7 = t1 - t6\nt8 = t4 - t7\nanswer = t8 / t5\nprint(answer)" + ], + "Output Answer": [ + "0.7857142857142856" + ], + "split": "dev" + }, + { + "Input": "if x 2 + kx - 3 , is divisible by ( x - 1 ) , what is the value of k", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 1.0\nt0 = n2**min(n0, 5)\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "dev" + }, + { + "Input": "if ( x - 10 ) ( y - 5 ) ( z - 2 ) = 1000 then what is the least value of x + y + z ? if x , y , z are all integer no .", + "Output Program": [ + "n0 = 10.0\nn1 = 5.0\nn2 = 2.0\nn3 = 1000.0\nt0 = n0 * n1\nt1 = t0 / n1\nanswer = t1 - 3.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "dev" + }, + { + "Input": "at an upscale fast - food restaurant , shin can buy 3 burgers , 7 shakes , and one cola for $ 120 . at the same place it would cost $ 164.50 for 4 burgers , 10 shakes , and one cola . how much would it cost for a meal of one burger , one shake , and one cola ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 120.0\nn3 = 164.5\nn4 = 4.0\nn5 = 10.0\nt0 = n3 - n2\nt1 = n2 + t0\nt2 = t0 * n0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "31" + ], + "split": "dev" + }, + { + "Input": "65 % of x = 20 % of 682.50 . find the value of x ?", + "Output Program": [ + "n0 = 65.0\nn1 = 20.0\nn2 = 682.5\nt0 = n2 / 100.0\nt1 = n1 * t0\nt2 = t1 * 100.0\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "210" + ], + "split": "dev" + }, + { + "Input": "evaluate : | 5 - 8 ( 3 - 12 ) | - | 5 - 11 | = ?", + "Output Program": [ + "n0 = 5.0\nn1 = 8.0\nn2 = 3.0\nn3 = 12.0\nn4 = 5.0\nn5 = 11.0\nt0 = n2 - n3\nt1 = n4 - n5\nt2 = n1 * t0\nt3 = -t1\nt4 = n0 - t2\nanswer = t4 - t3\nprint(answer)" + ], + "Output Answer": [ + "71" + ], + "split": "dev" + }, + { + "Input": "if x < y < z and y - x > 11 , where x is an even integer and y and z are odd integers , what is the least possible value of z - x ?", + "Output Program": [ + "n0 = 11.0\nt0 = n0 + 2.0\nanswer = t0 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "dev" + }, + { + "Input": "find k if 24 / k = 4 .", + "Output Program": [ + "n0 = 24.0\nn1 = 4.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "dev" + }, + { + "Input": "a merchandise feedback online portal accords \u2018 ratings \u2019 to a product by recording the percentage of customers who have reported their views as either \u2018 satisfied \u2019 or \u2018 unsatisfied \u2019 only . the portal rounds off the exact percentage value calculated to the closest integral value . if the percentage of unsatisfied customers as recorded by the portal is 57 % , what is the least possible number of people that could have reported their views as \u2018 satisfied \u2019 ?", + "Output Program": [ + "n0 = 57.0\nt0 = 3.0 + 4.0\nanswer = t0 - 4.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "dev" + }, + { + "Input": "in a certain school , 20 % of students are below 8 years of age . the number of students above 8 years of age is 2 / 3 of the number of students of 8 years of age which is 48 . what is the total number of students in the school ?", + "Output Program": [ + "n0 = 20.0\nn1 = 8.0\nn2 = 8.0\nn3 = 2.0\nn4 = 3.0\nn5 = 8.0\nn6 = 48.0\nt0 = n3 / n4\nt1 = n0 / 100.0\nt2 = n6 * t0\nt3 = 1.0 - t1\nt4 = n6 + t2\nanswer = t4 / t3\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "dev" + }, + { + "Input": "there are 4 people of different heights standing in order of increasing height . the difference is 2 inches between the first person and the second person , and also between the second person and the third person . the difference between the third person and the fourth person is 6 inches and the average height is 78 . how tall is the fourth person ?", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\nn2 = 6.0\nn3 = 78.0\nt0 = n0 + n2\nt1 = n0 * n3\nt2 = n2 + t0\nt3 = t1 - t2\nt4 = t3 / n0\nanswer = t0 + t4\nprint(answer)" + ], + "Output Answer": [ + "84" + ], + "split": "dev" + }, + { + "Input": "if a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20 , what is the probability w that this product will be a multiple of 45 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 20.0\nn2 = 45.0\nt0 = n1 + 4.0\nanswer = 1.0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.041666666666666664" + ], + "split": "dev" + }, + { + "Input": "during a pizza buffet where a eats more times 1.8 than b , and b eats 8 times less than c . find the leat number of times all the 3 has to eat", + "Output Program": [ + "n0 = 1.8\nn1 = 8.0\nn2 = 3.0\nt0 = n0 * 10.0\nt1 = t0 / n2\nt2 = t1 * t1\nanswer = t2 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "360" + ], + "split": "dev" + }, + { + "Input": "ashok secured average of 72 marks in 6 subjects . if the average of marks in 5 subjects is 74 , how many marks did he secure in the 6 th subject ?", + "Output Program": [ + "n0 = 72.0\nn1 = 6.0\nn2 = 5.0\nn3 = 74.0\nn4 = 6.0\nt0 = n0 * n1\nt1 = n2 * n3\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "62" + ], + "split": "dev" + }, + { + "Input": "of the 130 employees at company x , 80 are full - time , and 100 have worked at company x for at least a year . there are 20 employees at company x who aren \u2019 t full - time and haven \u2019 t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ?", + "Output Program": [ + "n0 = 130.0\nn1 = 80.0\nn2 = 100.0\nn3 = 20.0\nt0 = n0 - n1\nanswer = t0 - n3\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "dev" + }, + { + "Input": "a pharmaceutical company received $ 4 million in royalties on the first $ 20 million in sales of the generic equivalent of one of its products and then $ 9 million in royalties on the next $ 108 million in sales . by approximately what percent did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 108 million in sales ?", + "Output Program": [ + "n0 = 4.0\nn1 = 20.0\nn2 = 9.0\nn3 = 108.0\nn4 = 20.0\nn5 = 108.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = t0 * 100.0\nt3 = t1 * 100.0\nt4 = t2 - t3\nt5 = t4 / t2\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "58.333333333333336" + ], + "split": "dev" + }, + { + "Input": "a father said to his son , ` ` i was as old as you are at the present at the time of your birth ' ' . if the father ' s age is 52 years now , the son ' s age 5 years back was :", + "Output Program": [ + "n0 = 52.0\nn1 = 5.0\nt0 = n0 / 2.0\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "dev" + }, + { + "Input": "at a certain fruit stand , the price of each apple is 40 cents and the price of each orange is 60 cents . mary selects a total of 20 apples and oranges from the fruit stand , and the average ( arithmetic mean ) price of the 20 pieces of fruit is 56 cents . how many oranges must mary put back so that the average price of the pieces of fruit that she keeps is 52 cents ?", + "Output Program": [ + "n0 = 40.0\nn1 = 60.0\nn2 = 20.0\nn3 = 20.0\nn4 = 56.0\nn5 = 52.0\nt0 = n2 * n4\nt1 = n2 * n5\nt2 = n1 - n5\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "dev" + }, + { + "Input": "there are 20 cm , 21 cm , 22 cm , 23 cm , 24 cm , 25 cm rods of quantities 23 , 64 , 32 respectively . find average of this data .", + "Output Program": [ + "n0 = 20.0\nn1 = 21.0\nn2 = 22.0\nn3 = 23.0\nn4 = 24.0\nn5 = 25.0\nn6 = 23.0\nn7 = 64.0\nn8 = 32.0\nt0 = n3 + n7\nt1 = n0 * n3\nt2 = n1 * n3\nt3 = n2 * n7\nt4 = n3 * n7\nt5 = n4 * n8\nt6 = n5 * n8\nt7 = t1 + t2\nt8 = n8 + t0\nt9 = t7 + t3\nt10 = t8 * 2.0\nt11 = t9 + t4\nt12 = t11 + t5\nt13 = t12 + t6\nanswer = t13 / t10\nprint(answer)" + ], + "Output Answer": [ + "22.65126050420168" + ], + "split": "dev" + }, + { + "Input": "if n is a positive integer and n ^ 2 is divisible by 18 , then what is the largest positive integer that must divide n ?", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 18.0\nt0 = n1 / n0\nt1 = math.sqrt(max(0, t0))\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "dev" + }, + { + "Input": "an employee \u2019 s annual salary was increased $ 25000 . if her new annual salary now equals $ 90000 , what was the percent increase ?", + "Output Program": [ + "n0 = 25000.0\nn1 = 90000.0\nt0 = 0.25 * 100.0\nt1 = 100.0 - 10.0\nt2 = t1 * 1000.0\nt3 = t0 * 1000.0\nt4 = t2 - t3\nt5 = t2 / t4\nt6 = t5 - 1.0\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "38.46153846153846" + ], + "split": "dev" + }, + { + "Input": "a school has 11 maths 8 physics and 5 chemistry teachers each teacher can teach 3 subjects max what is he minimum number of teachers required", + "Output Program": [ + "n0 = 11.0\nn1 = 8.0\nn2 = 5.0\nn3 = 3.0\nt0 = n0 + n1\nt1 = n2 + t0\nanswer = t1 / n3\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "dev" + }, + { + "Input": "| - 2 | ( | - 25 | - | 5 | ) = ? ? source : preparation material mba center", + "Output Program": [ + "n0 = 2.0\nn1 = 25.0\nn2 = 5.0\nt0 = n1 - n2\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "dev" + }, + { + "Input": "at a certain fruit stand , the price of each apple is 40 cents and the price of each orange is 60 cents . mary selects a total of 30 apples and oranges from the fruit stand , and the average ( arithmetic mean ) price of the 30 pieces of fruit is 56 cents . how many oranges must mary put back so that the average price of the pieces of fruit that she keeps is 52 cents ?", + "Output Program": [ + "n0 = 40.0\nn1 = 60.0\nn2 = 30.0\nn3 = 30.0\nn4 = 56.0\nn5 = 52.0\nt0 = n2 * n4\nt1 = n2 * n5\nt2 = n1 - n5\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "dev" + }, + { + "Input": "assume that f ( 1 ) = 0 and f ( m + n ) = f ( m ) + f ( n ) + 4 ( 9 mn - 1 ) . for all natural numbers ( integers > 0 ) m and n . what is the value of f ( 17 ) ?", + "Output Program": [ + "n0 = 1.0\nn1 = 0.0\nn2 = 4.0\nn3 = 9.0\nn4 = 1.0\nn5 = 0.0\nn6 = 17.0\nt0 = 1.0 + 4.0\nt1 = 2.0 * 4.0\nt2 = n2 * 10.0\nt3 = n6 * 4.0\nt4 = t2 + 3.0\nt5 = n3 + t3\nt6 = n2 * t1\nt7 = t0 * 100.0\nt8 = t6 + t6\nt9 = t6 + 3.0\nt10 = t4 + 100.0\nt11 = t5 - 2.0\nt12 = t7 + t11\nt13 = n2 * t9\nt14 = n2 * t10\nt15 = t8 + t13\nt16 = t12 * 4.0\nt17 = t15 + t15\nt18 = t17 + t14\nt19 = t18 + t18\nt20 = t19 + t16\nanswer = t20 + t14\nprint(answer)" + ], + "Output Answer": [ + "4832" + ], + "split": "dev" + }, + { + "Input": "if ( 2 ^ 16 ) ( 25 ^ s ) = 5 ( 10 ^ m ) what is the value of m ?", + "Output Program": [ + "n0 = 2.0\nn1 = 16.0\nn2 = 25.0\nn3 = 5.0\nn4 = 10.0\nt0 = n4 / n3\nanswer = t0**min(4.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "dev" + }, + { + "Input": "90 + 5 * 12 / ( 180 / 3 ) = ?", + "Output Program": [ + "n0 = 90.0\nn1 = 5.0\nn2 = 12.0\nn3 = 180.0\nn4 = 3.0\nt0 = n3 / n4\nt1 = n1 * n2\nt2 = t1 / t0\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "91" + ], + "split": "dev" + }, + { + "Input": "a welder received an order to make a 1 million liter cube - shaped tank . if he has only 2 x 3 meter sheets of metal that can be cut , how many metal sheets will be required for this order ? ( 1 cubic meter = 1000 liters )", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 3.0\nn3 = 1.0\nn4 = 1000.0\nt0 = n1 * n2\nt1 = t0 * 100.0\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "dev" + }, + { + "Input": "when x is multiplied by 3 , the result is 10 more than the result of subtracting x from 26 . what is the value of x ?", + "Output Program": [ + "n0 = 3.0\nn1 = 10.0\nn2 = 26.0\nt0 = n1 + n2\nt1 = 1.0 + n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "dev" + }, + { + "Input": "1,000 ^ 2 + 1,001 ^ 2 + 1,002 ^ 2 + 1,003 ^ 2 + 1,004 ^ 2 =", + "Output Program": [ + "n0 = 1000.0\nn1 = 2.0\nn2 = 1001.0\nn3 = 2.0\nn4 = 1002.0\nn5 = 2.0\nn6 = 1003.0\nn7 = 2.0\nn8 = 1004.0\nn9 = 2.0\n\nanswer = n1 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "dev" + }, + { + "Input": "in a room filled with 6 people , all 6 people have exactly 1 sibling in the room . if two individuals are selected from the room at random , what is the probability that those two individuals are not siblings ?", + "Output Program": [ + "n0 = 6.0\nn1 = 6.0\nn2 = 1.0\nt0 = n0 - 1.0\nt1 = n0 * t0\nt2 = t0 - 1.0\nt3 = n0 * t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.8" + ], + "split": "dev" + }, + { + "Input": "find the least number of complete years in which a sum of money put out at 50 % compound interest will be more than double of itself ?", + "Output Program": [ + "import math\nn0 = 50.0\nt0 = n0 / 100.0\nt1 = math.log(max(1e-5, 2.0), 2)\nt2 = t0 + 1.0\nt3 = math.log(max(1e-5, t2), 2)\nt4 = t1 / t3\nt5 = t4 + 1.0\nanswer = math.floor(t5)\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "dev" + }, + { + "Input": "excluding stoppages , the average speed of a bus is 60 km / hr and including stoppages , the average speed of the bus is 40 km / hr . for how many minutes does the bus stop per hour ?", + "Output Program": [ + "n0 = 60.0\nn1 = 40.0\nt0 = n1 / n0\nt1 = 1.0 * 60.0\nt2 = t0 * 60.0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "dev" + }, + { + "Input": "the average of runs of a cricket player of 20 innings was 32 . how many runs must he make in his next innings so as to increase his average of runs by 8 ?", + "Output Program": [ + "n0 = 20.0\nn1 = 32.0\nn2 = 8.0\nt0 = n0 + 1.0\nt1 = n1 + n2\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "dev" + }, + { + "Input": "a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 17 , the how old is b ? a . 7 b . 8 c . 9 d . 10 explanation :", + "Output Program": [ + "n0 = 17.0\nn1 = 7.0\nn2 = 8.0\nn3 = 9.0\nn4 = 10.0\nt0 = 1.0 + 4.0\nt1 = n0 - 2.0\nt2 = t1 / t0\nanswer = t2 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "dev" + }, + { + "Input": "the average of 50 numbers id 20 . if two numbers , namely 45 and 55 are discarded , the average of the remaining numbers is :", + "Output Program": [ + "n0 = 50.0\nn1 = 20.0\nn2 = 45.0\nn3 = 55.0\nt0 = n2 + n3\nt1 = n0 * n1\nt2 = n0 - 2.0\nt3 = t1 - t0\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "18.75" + ], + "split": "dev" + }, + { + "Input": "find remainder if ( 67 ^ 67 + 67 ) is divided by 68", + "Output Program": [ + "n0 = 67.0\nn1 = 67.0\nn2 = 67.0\nn3 = 68.0\n\nanswer = n0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "66" + ], + "split": "dev" + }, + { + "Input": "a man can swim in still water at 12 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ?", + "Output Program": [ + "n0 = 12.0\n\nanswer = n0 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "dev" + }, + { + "Input": "a certain meter records voltage between 0 and 10 volts inclusive . if the average value of 3 recordings on the meter was 4 volts , what was the smallest possible recording in volts ?", + "Output Program": [ + "n0 = 0.0\nn1 = 10.0\nn2 = 3.0\nn3 = 4.0\nt0 = n2 * n3\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "dev" + }, + { + "Input": "5 drainage pipes , each draining water from a pool at the same constant rate , together can drain a certain pool in 12 days . how many additional pipes q , each draining water at the same constant rate , will be needed to drain the pool in 4 days ?", + "Output Program": [ + "n0 = 5.0\nn1 = 12.0\nn2 = 4.0\nt0 = n0 * n1\nt1 = t0 / n2\nanswer = t1 - n0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "dev" + }, + { + "Input": "the average weight of 4 person ' s increases by 8.5 kg when a new person comes in place of one of them weighing 95 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 4.0\nn1 = 8.5\nn2 = 95.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "129" + ], + "split": "dev" + }, + { + "Input": "a club wants to mix 10 pounds of candy worth $ 8.00 per pound with candy worth $ 5.00 per pound to reduce the cost of the mixture to $ 6.00 per pound . how many pounds of the $ 5.00 per pound candy should be used ?", + "Output Program": [ + "n0 = 10.0\nn1 = 8.0\nn2 = 5.0\nn3 = 6.0\nn4 = 5.0\nt0 = n0 * n1\nt1 = n0 * n3\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "dev" + }, + { + "Input": "1 = 62 = 363 = 3634 = 3645 = 365 , then 36 = ?", + "Output Program": [ + "n0 = 1.0\nn1 = 62.0\nn2 = 363.0\nn3 = 3634.0\nn4 = 3645.0\nn5 = 365.0\nn6 = 36.0\n\nanswer = 3.0 - n0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "dev" + }, + { + "Input": "find large number from below question the difference of two numbers is 1000 . on dividing the larger number by the smaller , we get 10 as quotient and the 10 as remainder", + "Output Program": [ + "n0 = 1000.0\nn1 = 10.0\nn2 = 10.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nt2 = t0 / t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "1100" + ], + "split": "dev" + }, + { + "Input": "the average height of 30 girls out of a class of 40 is 160 cm . and that of the remaining girls is 156 cm . the average height of the whole class is :", + "Output Program": [ + "n0 = 30.0\nn1 = 40.0\nn2 = 160.0\nn3 = 156.0\nt0 = n0 * n2\nt1 = n3 * 10.0\nt2 = t0 + t1\nanswer = t2 / n1\nprint(answer)" + ], + "Output Answer": [ + "159" + ], + "split": "dev" + }, + { + "Input": "a man owns 1 / 3 of market reserch beauro buzness , and sells 3 / 5 of his shares for 15000 rs , what is the value of buzness ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 3.0\nn3 = 5.0\nn4 = 15000.0\nt0 = n0 / n1\nt1 = n1 / n3\nt2 = t0 * t1\nanswer = n4 / t2\nprint(answer)" + ], + "Output Answer": [ + "75000" + ], + "split": "dev" + }, + { + "Input": "jaylen was planning to save all summer for a pair of jordan 12 s . they cost $ 250 . jaylen figured that he could cut grass to help with the cost of the sneakers . how many yards would jaylen have to cut if he charges $ 2.15 per yard ?", + "Output Program": [ + "n0 = 8.0\nt0 = n0 - 1.0\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "dev" + }, + { + "Input": "at the end of the month , a certain ocean desalination plant \u2019 s reservoir contained 30 million gallons of water . this amount is twice the normal level . if this amount represents 75 % of the reservoir \u2019 s total capacity , how many million gallons short of total capacity is the normal level ?", + "Output Program": [ + "n0 = 30.0\nn1 = 75.0\nt0 = n0 / 2.0\nt1 = n1 / 100.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "dev" + }, + { + "Input": "matt gets a $ 1000 commission on a big sale . this commission alone raises his average commission by $ 150 . if matt ' s new average commission is $ 250 , how many sales has matt made ?", + "Output Program": [ + "n0 = 1000.0\nn1 = 150.0\nn2 = 250.0\nt0 = 1000.0 - 100.0\nt1 = n2 - n1\nt2 = n2 - t1\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "dev" + }, + { + "Input": "average between two sets of numbers is closer to the set withmore numbers ?", + "Output Program": [ + "t0 = 2.0 * 4.0\nanswer = t0 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "dev" + }, + { + "Input": "crazy eddie has a key chain factory . eddie managed to decrease the cost of manufacturing his key chains while keeping the same selling price , and thus increased the profit from the sale of each key chain from 50 % of the selling price to 50 % of the selling price . if the manufacturing cost is now $ 50 , what was it before the decrease ?", + "Output Program": [ + "n0 = 50.0\nn1 = 50.0\nn2 = 50.0\nt0 = n1 / 100.0\nt1 = n0 / 100.0\nt2 = n1 / t0\nt3 = t2 * t1\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "dev" + }, + { + "Input": "what is the tens digit of 6 ^ 22 ?", + "Output Program": [ + "import math\nn0 = 6.0\nn1 = 22.0\nt0 = 1.0 + 4.0\nt1 = n1 % t0\nt2 = n0**min(t1, 5)\nt3 = t2 % 100.0\nt4 = t3 / 10.0\nanswer = math.floor(t4)\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "dev" + }, + { + "Input": "a certain sum of money is divided among a , b and c such that a gets one - third of what b and c together get and b gets two - seventh of what a and c together get . if the amount received by a is $ 15 more than that received by b , find the total amount shared by a , b and c .", + "Output Program": [ + "n0 = 15.0\nt0 = n0 * 3.0\nt1 = n0 * 2.0\nt2 = t0 * 2.0\nt3 = t2 + t1\nt4 = n0 + t3\nt5 = t3 + t4\nt6 = t4 * 3.0\nt7 = t6 - t3\nanswer = t5 + t7\nprint(answer)" + ], + "Output Answer": [ + "540" + ], + "split": "dev" + }, + { + "Input": "williams works at a resort from the beginning of march to the end of september . during the month of august this past year , he made 8 times the average ( arithmetic mean ) of his monthly totals in tips for the other months . his total tips for august were what fraction of his total tips for all of the months he worked ?", + "Output Program": [ + "n0 = 8.0\nt0 = 3.0 + 4.0\nt1 = t0 - 1.0\nt2 = n0 + t1\nanswer = n0 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.5714285714285714" + ], + "split": "dev" + }, + { + "Input": "a ' s speed is 20 / 13 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that b beats a by 80 % of the length of the race ?", + "Output Program": [ + "n0 = 20.0\nn1 = 13.0\nn2 = 80.0\nt0 = n1 / n0\nt1 = 100.0 - n2\nt2 = t1 / 100.0\nt3 = t2 * t0\nt4 = 1.0 - t3\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "87" + ], + "split": "dev" + }, + { + "Input": "marginal cost is the cost of increasing the quantity produced ( or purchased ) by one unit . if the fixed cost for n products is $ 12,000 and the marginal cost is $ 200 , and the total cost is $ 16,000 , what is the value of n ?", + "Output Program": [ + "n0 = 12000.0\nn1 = 200.0\nn2 = 16000.0\nt0 = n2 - n0\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "dev" + }, + { + "Input": "the average salary of all the workers in a workshop is rs . 8000 . the average salary of 8 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is :", + "Output Program": [ + "n0 = 8000.0\nn1 = 8.0\nn2 = 12000.0\nn3 = 6000.0\nt0 = n2 - n0\nt1 = n0 - n3\nt2 = n1 * t0\nt3 = t2 / t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "dev" + }, + { + "Input": "what is the sum of all 3 digit numbers that leave a remainder of ' 2 ' when divided by 7 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 7.0\nt0 = n0 * n0\nt1 = 1000.0 - n0\nt2 = t0 * 10.0\nt3 = t2 + t0\nt4 = n0 + t3\nt5 = t4 + t1\nt6 = t1 - t4\nt7 = t6 / n2\nt8 = t7 + 1.0\nt9 = t8 / n1\nanswer = t5 * t9\nprint(answer)" + ], + "Output Answer": [ + "70807" + ], + "split": "dev" + }, + { + "Input": "a box contains 10 tablets of medicine a and 10 tablets of medicine b . what is the least number of tablets that should be taken from the box to ensure that at least two tablets of each kind are among the extracted .", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\n\nanswer = n1 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "dev" + }, + { + "Input": "what least number must be subtracted from 42739 so that remaining no . is divisible by 15", + "Output Program": [ + "import math\nn0 = 42739.0\nn1 = 15.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "dev" + }, + { + "Input": "for each color copy , print shop x charges $ 1.25 and print shop y charges $ 2.75 . how much greater is the charge for 40 color copies at print shop y than at print shop x ?", + "Output Program": [ + "n0 = 1.25\nn1 = 2.75\nn2 = 40.0\nt0 = n1 * n2\nt1 = n0 * n2\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "dev" + }, + { + "Input": "25 * 25 * 25 * 25 * 25 = 5 ^ ?", + "Output Program": [ + "n0 = 25.0\nn1 = 25.0\nn2 = 25.0\nn3 = 25.0\nn4 = 25.0\nn5 = 5.0\n\nanswer = max(n5,10.0)\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "dev" + }, + { + "Input": "subtract . simplify your answer and write it as a proper fraction or as a whole or mixed number . 4 / 5 - 1 / 5 =", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 1.0\nn3 = 5.0\nt0 = n0 - n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.6" + ], + "split": "dev" + }, + { + "Input": "q and r are two - digit positive integers that have the same digits but in reverse order . if the positive difference between q and r is less than 30 , what is the greatest possible value of q minus r ?", + "Output Program": [ + "n0 = 30.0\nt0 = 10.0 - 1.0\nt1 = n0 % t0\nanswer = t1 * t0\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "dev" + }, + { + "Input": "if equation | x / 5 | + | y / 5 | = 2 encloses a certain region on the coordinate plane , what is the area of this region ?", + "Output Program": [ + "n0 = 5.0\nn1 = 5.0\nn2 = 2.0\nt0 = n2 * n0\nt1 = t0**min(n2, 5)\nanswer = t1 + t1\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "dev" + }, + { + "Input": "the price of a certain painting increased by 30 % during the first year and decreased by 15 % during the second year . the price of the painting at the end of the 2 - year period was what percent of the original price ?", + "Output Program": [ + "n0 = 30.0\nn1 = 15.0\nn2 = 2.0\nt0 = n0 * n1\nt1 = n0 - n1\nt2 = t0 / 100.0\nt3 = t1 - t2\nanswer = t3 + 100.0\nprint(answer)" + ], + "Output Answer": [ + "110.5" + ], + "split": "dev" + }, + { + "Input": "a student was asked to find 4 / 5 of a number . but the student divided the number by 4 / 5 , thus the student got 27 more than the correct answer . find the number .", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 4.0\nn3 = 5.0\nn4 = 27.0\nt0 = n0 / n1\nt1 = n4 * t0\nt2 = t0 * t0\nt3 = t0 * t1\nt4 = 1.0 - t2\nt5 = t3 / t4\nanswer = t5 / t0\nprint(answer)" + ], + "Output Answer": [ + "60.00000000000002" + ], + "split": "dev" + }, + { + "Input": "the units digit of ( 35 ) ^ ( 7 ) + ( 93 ) ^ ( 45 ) is :", + "Output Program": [ + "n0 = 35.0\nn1 = 7.0\nn2 = 93.0\nn3 = 45.0\nt0 = n3 % 4.0\nt1 = n0 % 10.0\nt2 = n2 * t0\nt3 = t2 % 10.0\nanswer = t3 + t1\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "dev" + }, + { + "Input": "crazy eddie has a key chain factory . eddie managed to decrease the cost of manufacturing his key chains while keeping the same selling price , and thus increased the profit from the sale of each key chain from 20 % of the selling price to 50 % of the selling price . if the manufacturing cost is now $ 50 , what was it before the decrease ?", + "Output Program": [ + "n0 = 20.0\nn1 = 50.0\nn2 = 50.0\nt0 = n1 / 100.0\nt1 = n0 / 100.0\nt2 = n1 / t0\nt3 = t2 * t1\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "dev" + }, + { + "Input": "find the value o f 72519 x 9999 = m ?", + "Output Program": [ + "n0 = 72519.0\nn1 = 9999.0\nt0 = n1 - 4.0\nanswer = t0 * n0\nprint(answer)" + ], + "Output Answer": [ + "724827405" + ], + "split": "dev" + }, + { + "Input": "the annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years x in which the population would be doubled assuming there is no emigration or immigration is", + "Output Program": [ + "n0 = 1000.0\nn1 = 39.4\nn2 = 19.4\nt0 = 10.0 * 3.0\nt1 = n1 - n2\nt2 = t1 / n0\nt3 = 100.0 - t0\nt4 = t2 * 100.0\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "dev" + }, + { + "Input": "when the positive integer y is divided by 9 , the remainder is 5 . what is the remainder when 3 y is divided by 9 ?", + "Output Program": [ + "n0 = 9.0\nn1 = 5.0\nn2 = 3.0\nn3 = 9.0\nt0 = n0 + n1\nt1 = n2 * t0\nanswer = t1 % n0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "dev" + }, + { + "Input": "let s be the set of all positive integers that , when divided by 8 , have a remainder of 5 . what is the 70 th number in this set ?", + "Output Program": [ + "n0 = 8.0\nn1 = 5.0\nn2 = 70.0\nt0 = n2 - 1.0\nt1 = n0 * t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "557" + ], + "split": "dev" + }, + { + "Input": "find the maximum value of the function f ( x ) = x \u2212 5 if x is a number between - 5 and 13 .", + "Output Program": [ + "n0 = 5.0\nn1 = 5.0\nn2 = 13.0\n\nanswer = n2 - n0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "dev" + }, + { + "Input": "the average of 5 quantities is 12 . the average of 3 of them is 4 . what is the average of remaining 2 numbers ?", + "Output Program": [ + "n0 = 5.0\nn1 = 12.0\nn2 = 3.0\nn3 = 4.0\nn4 = 2.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = t0 - t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "dev" + }, + { + "Input": "a trained covered x km at 30 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 3 x km .", + "Output Program": [ + "n0 = 30.0\nn1 = 2.0\nn2 = 20.0\nn3 = 3.0\nt0 = n0 / n0\nt1 = n0 * n3\nt2 = n0 * n1\nt3 = t2 / n2\nt4 = t0 + t3\nanswer = t1 / t4\nprint(answer)" + ], + "Output Answer": [ + "22.5" + ], + "split": "dev" + }, + { + "Input": "gopi gives rs . 90 plus one turban as salary to his servant for one year . the servant leaves after 9 months and receives rs . 60 and the turban . find the price of the turban .", + "Output Program": [ + "n0 = 90.0\nn1 = 9.0\nn2 = 60.0\nt0 = n0 - n2\nt1 = 12.0 - n1\nt2 = t0 / t1\nt3 = t2 * 12.0\nanswer = t3 - n0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "dev" + }, + { + "Input": "p has $ 32 more than what q and r together would have had if both b and c had 1 / 6 of what p has . how much does p have ?", + "Output Program": [ + "n0 = 32.0\nn1 = 1.0\nn2 = 6.0\nt0 = n1 / n2\nt1 = t0 * 2.0\nt2 = n1 - t1\nanswer = n0 / t2\nprint(answer)" + ], + "Output Answer": [ + "47.99999999999999" + ], + "split": "dev" + }, + { + "Input": "a salt manufacturing company produced a total of 2000 tonnes of salt in january of a particular year . starting from february its production increased by 100 tonnes every month over the previous months until the end of the year . find its ave 66 rage daily production for that year ?", + "Output Program": [ + "n0 = 2000.0\nn1 = 100.0\nn2 = 66.0\nt0 = 2.0 + 3.0\nt1 = n0 * 2.0\nt2 = n1 * 3.0\nt3 = 2.0 * 3.0\nt4 = 12.0 - 1.0\nt5 = n1 * t4\nt6 = t3 * 10.0\nt7 = t1 + t5\nt8 = t2 + t6\nt9 = t8 + t0\nt10 = t7 * 12.0\nt11 = t10 / 2.0\nanswer = t11 / t9\nprint(answer)" + ], + "Output Answer": [ + "83.83561643835617" + ], + "split": "dev" + }, + { + "Input": "the average age of a group of n people is 14 years old . one more person aged 32 joins the group and the new average is 16 years old . what is the value of n ?", + "Output Program": [ + "n0 = 14.0\nn1 = 32.0\nn2 = 16.0\nt0 = n1 - n2\nt1 = n2 - n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "dev" + }, + { + "Input": "rewrite ( 10 ^ 38 ) \u2013 85 as a base 10 integer , what is the sum of the digits in that integer ?", + "Output Program": [ + "n0 = 10.0\nn1 = 38.0\nn2 = 85.0\nn3 = 10.0\nt0 = 2.0 + 3.0\nt1 = n1 - 2.0\nt2 = 10.0 - 1.0\nt3 = t1 * t2\nt4 = t3 + 1.0\nanswer = t4 + t0\nprint(answer)" + ], + "Output Answer": [ + "330" + ], + "split": "dev" + }, + { + "Input": "he average of 10 numbers is 23 . if each number is increased by 4 , what will the new average be ?", + "Output Program": [ + "n0 = 10.0\nn1 = 23.0\nn2 = 4.0\n\nanswer = n1 + n2\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "dev" + }, + { + "Input": "first column specifies the no of days prior to departure information . second column specifies the percentage discount offered . 0 - 6 days = = > 0 % 7 - 13 days = = > 10 % 14 - 29 days = = > 25 % 30 days or more = = > 40 % the table above shows the discount structure for advanced purchase of tickets at a particular airline . a passenger bought a ticket at this airline for $ 1050 . the ticket agent informed her that , had she purchased the ticket one day later , she would have paid $ 210 more . how many days before her departure did she purchase her ticket .", + "Output Program": [ + "n0 = 0.0\nn1 = 6.0\nn2 = 0.0\nn3 = 7.0\nn4 = 13.0\nn5 = 10.0\nn6 = 14.0\nn7 = 29.0\nn8 = 25.0\nn9 = 30.0\nn10 = 40.0\nn11 = 1050.0\nn12 = 210.0\nt0 = n3 * 4.0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "dev" + }, + { + "Input": "a no . when divided by 158 gives a remainder 50 , what remainder will be obtainedby dividingthe same no . 16 ?", + "Output Program": [ + "n0 = 158.0\nn1 = 50.0\nn2 = 16.0\nt0 = n0 + n1\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "dev" + }, + { + "Input": "sum of the squares of 3 no . ' s is 62 and the sum of their products taken two at a time is 131 . find the sum ?", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 62.0\nn2 = 131.0\nt0 = n2 * 2.0\nt1 = n1 + t0\nanswer = math.sqrt(max(0, t1))\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "dev" + }, + { + "Input": "how many multiples of 4 are there between 12 and 92 , inclusive ?", + "Output Program": [ + "n0 = 4.0\nn1 = 12.0\nn2 = 92.0\nt0 = n2 - n1\nt1 = t0 / n0\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "dev" + }, + { + "Input": "a metered rikshaw charges rs 13.50 for the first 1 km and 2.50 per 1 / 3 km there after . what would the charge if this rikshaw is hired for 13 kms ? in approx ? ?", + "Output Program": [ + "n0 = 13.5\nn1 = 1.0\nn2 = 2.5\nn3 = 1.0\nn4 = 3.0\nn5 = 13.0\nt0 = n1 / n4\nt1 = n5 - n1\nt2 = t1 / t0\nt3 = n2 * t2\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "103.5" + ], + "split": "dev" + }, + { + "Input": "a man opens a shop . he buys water bottles for 50 cents each , fruit for 25 cents each , and snacks for a dollar each . he wants to start a bundle of selling a bottle a water , 3 snacks and 2 fruits for d dollars . every 5 th bundle sold will be sold for 2 dollars and a complimentary snack at the owner ' s expense . what should he charge at least to not lose any money ?", + "Output Program": [ + "n0 = 50.0\nn1 = 25.0\nn2 = 3.0\nn3 = 2.0\nn4 = 5.0\nn5 = 2.0\nt0 = n4 / 10.0\nt1 = 1.0 / 10.0\nt2 = n2 * 1.0\nt3 = n3 * t0\nt4 = t2 + t3\nt5 = t4 + t0\nanswer = t5 + t1\nprint(answer)" + ], + "Output Answer": [ + "4.6" + ], + "split": "dev" + }, + { + "Input": "a box contains 11 apples , 10 of which are red . an apple is drawn from the box and its color is noted before it is eaten . this is done a total of n times , and the probability that a red apple is drawn each time is less than 0.5 . what is the smallest possible value of n ?", + "Output Program": [ + "n0 = 11.0\nn1 = 10.0\nn2 = 0.5\nt0 = n2 * 10.0\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "dev" + }, + { + "Input": "if the price of a certain computer increased 30 percent from x dollars to 351 dollars , then 2 x =", + "Output Program": [ + "n0 = 30.0\nn1 = 351.0\nn2 = 2.0\nt0 = n0 + 100.0\nt1 = t0 / 100.0\nt2 = n1 / t1\nanswer = n2 * t2\nprint(answer)" + ], + "Output Answer": [ + "540" + ], + "split": "dev" + }, + { + "Input": "in the mundane goblet competition , 6 teams compete in a \u201c round robin \u201d format : that is , each team plays every other team exactly once . a team gets 3 points for a win , 1 point for a tie ( a draw ) , and 0 points for a loss . what is the difference between the maximum total points and the minimum total points that can be gained by all teams ( added together ) in the mundane goblet competition ?", + "Output Program": [ + "n0 = 6.0\nn1 = 3.0\nn2 = 1.0\nn3 = 0.0\nt0 = n0 * 2.0\nanswer = t0 + 3.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "dev" + }, + { + "Input": "diana is painting statues . she has 3 / 6 of a gallon of paint remaining . each statue requires 1 / 6 gallon of paint . how many statues can she paint ?", + "Output Program": [ + "n0 = 3.0\nn1 = 6.0\nn2 = 1.0\nn3 = 6.0\nt0 = n0 / n1\nt1 = n2 / n3\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "dev" + }, + { + "Input": "the average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg . find the average weights of all the boys in the class .", + "Output Program": [ + "n0 = 16.0\nn1 = 50.25\nn2 = 8.0\nn3 = 45.15\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "48.550000000000004" + ], + "split": "dev" + }, + { + "Input": "how much water should be added to 13 liters of a 20 % - solution of alcohol to reduce the concentration of alcohol in the solution by 75 % ?", + "Output Program": [ + "n0 = 13.0\nn1 = 20.0\nn2 = 75.0\nt0 = n2 / 100.0\nt1 = 100.0 * 2.0\nt2 = n1 * t0\nt3 = n1 - t2\nt4 = t1 / t3\nanswer = t4 - n0\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "dev" + }, + { + "Input": "a student got twice as many sums wrong as he got right . if he attempted 36 sums in all , how many did he solve correctly ?", + "Output Program": [ + "n0 = 36.0\nt0 = 1.0 + 2.0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "dev" + }, + { + "Input": "20.036 divided by 0.04 gives :", + "Output Program": [ + "n0 = 20.036\nn1 = 0.04\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "500.90000000000003" + ], + "split": "dev" + }, + { + "Input": "a grocer has a sale of rs . 6435 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6800 ?", + "Output Program": [ + "n0 = 6435.0\nn1 = 6927.0\nn2 = 6855.0\nn3 = 7230.0\nn4 = 6562.0\nn5 = 5.0\nn6 = 6800.0\nt0 = n5 + 1.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n6 * t0\nt4 = n3 + t2\nt5 = n4 + t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "6791" + ], + "split": "dev" + }, + { + "Input": "when 17 is divided by positive integer x , the remainder is 1 . for how many values of x is this true ?", + "Output Program": [ + "import math\nn0 = 17.0\nn1 = 1.0\nt0 = n0 - n1\nanswer = math.log(max(1e-5, t0), 2)\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "dev" + }, + { + "Input": "what least number should be subtracted from 1398 so that the remainder when divided by 7 , 9 , and 11 will leave in each case the same remainder 5 ?", + "Output Program": [ + "n0 = 1398.0\nn1 = 7.0\nn2 = 9.0\nn3 = 11.0\nn4 = 5.0\nt0 = n1 * n2\nt1 = n3 * t0\nt2 = t1 * 2.0\nt3 = n4 + t2\nanswer = n0 - t3\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "dev" + }, + { + "Input": "a girl was asked to multiply a certain number by 43 . she multiplied it by 34 and got his answer less than the correct one by 1233 . find the number to be multiplied .", + "Output Program": [ + "n0 = 43.0\nn1 = 34.0\nn2 = 1233.0\nt0 = n0 - n1\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "137" + ], + "split": "dev" + }, + { + "Input": "( 69842 x 69842 - 30158 x 30158 ) / ( 69842 - 30158 ) = ?", + "Output Program": [ + "n0 = 69842.0\nn1 = 69842.0\nn2 = 30158.0\nn3 = 30158.0\nn4 = 69842.0\nn5 = 30158.0\nt0 = n0 * n0\nt1 = n2 * n2\nt2 = n0 - n2\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "100000" + ], + "split": "dev" + }, + { + "Input": "2 pipes can separately fill a tank in 20 hrs and 30 hrs respectively . both the pipes are opened to fillthe tank , a leak develops in the tank through which one - third of water supplied by both the pipes goes out . what is the total time taken to fill the tank ?", + "Output Program": [ + "n0 = 2.0\nn1 = 20.0\nn2 = 30.0\nt0 = 1.0 / 3.0\nt1 = 1 / n1\nt2 = 1 / n2\nt3 = t0 + 1.0\nt4 = t1 + t2\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "15.999999999999998" + ], + "split": "dev" + }, + { + "Input": "an assembly line produces 15 cogs per hour until an initial order of 60 cogs is completed . the speed of the assembly line is then immediately increased so that it can produce 60 cogs per hour until another 60 cogs are produced . what is the overall average output , in cogs per hour , for the assembly line during this whole time ?", + "Output Program": [ + "n0 = 15.0\nn1 = 60.0\nn2 = 60.0\nn3 = 60.0\nt0 = n1 / n0\nt1 = n1 * 2.0\nt2 = t0 + 1.0\nanswer = t1 / t2\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "dev" + }, + { + "Input": "little john had $ 7.10 . he spent $ 1.05 on sweets and gave to his two friends $ 1.00 each . how much money was left ?", + "Output Program": [ + "n0 = 7.1\nn1 = 1.05\nn2 = 1.0\nt0 = n2 + n2\nt1 = n1 + t0\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "4.05" + ], + "split": "dev" + }, + { + "Input": "in a class of 32 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 10 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?", + "Output Program": [ + "n0 = 32.0\nn1 = 2.0\nn2 = 12.0\nn3 = 1.0\nn4 = 10.0\nn5 = 2.0\nn6 = 3.0\nn7 = 2.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n1 * n4\nt3 = t1 + t2\nt4 = n4 + t1\nt5 = n1 + t4\nt6 = n0 - t5\nt7 = t6 - n3\nt8 = n6 * t7\nt9 = t3 + t8\nanswer = t0 - t9\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "dev" + }, + { + "Input": "the average of 10 numbers is calculated as 21 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?", + "Output Program": [ + "n0 = 10.0\nn1 = 21.0\nn2 = 36.0\nn3 = 26.0\nt0 = n2 - n3\nt1 = t0 / n0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "dev" + }, + { + "Input": "in a family gathering , there is a basket in which there are oranges , bananas and apples . half of the people in the family eat oranges , half of the other half eat bananas and the rest eat apples . if the number of people who eat oranges are 10 less than the total number of people , find the number of people in the gathering .", + "Output Program": [ + "n0 = 10.0\n\nanswer = n0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "dev" + }, + { + "Input": "excluding stoppages , the average speed of a bus is 60 km / hr and including stoppages , the average speed of the bus is 15 km / hr . for how many minutes does the bus stop per hour ?", + "Output Program": [ + "n0 = 60.0\nn1 = 15.0\nt0 = n1 / n0\nt1 = 1.0 * 60.0\nt2 = t0 * 60.0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "dev" + }, + { + "Input": "( ( ( 13 ! ) ^ 16 ) - ( ( 13 ! ) ^ 8 ) ) / ( ( ( 13 ! ) ^ 8 ) + ( ( 13 ! ) ^ 4 ) ) = a then what is the units digit for a / ( ( 13 ! ) ^ 4 ) =", + "Output Program": [ + "n0 = 13.0\nn1 = 16.0\nn2 = 13.0\nn3 = 8.0\nn4 = 13.0\nn5 = 8.0\nn6 = 13.0\nn7 = 4.0\nn8 = 13.0\nn9 = 4.0\nt0 = n0 - 3.0\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "dev" + }, + { + "Input": "vishal invested 10 % more than trishul . trishul invested 10 % less than raghu . if the total sum of their investments is rs . 6358 , how much amount did raghu invest ?", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 6358.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nt2 = 1.0 - t0\nt3 = t1 * t2\nt4 = t3 + t2\nt5 = t4 + 1.0\nanswer = n2 / t5\nprint(answer)" + ], + "Output Answer": [ + "2200" + ], + "split": "dev" + }, + { + "Input": "in n is a positive integer less than 200 , and 14 n / 60 is an integer , then n has how many different positive prime factors a ?", + "Output Program": [ + "n0 = 200.0\nn1 = 14.0\nn2 = 60.0\nt0 = 1.0 + 4.0\nt1 = n2 / 2.0\nt2 = t1 / 2.0\nt3 = t2 / 3.0\nt4 = t0 / t3\nanswer = t4 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "dev" + }, + { + "Input": "the payment per hour for a daily - wages employee is increased by 33.33 and the working time is reduced by 33.33 % . what is the percentage change in the employee ' s income ?", + "Output Program": [ + "n0 = 33.33\nn1 = 33.33\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nt2 = 1.0 - t0\nanswer = t1 * t2\nprint(answer)" + ], + "Output Answer": [ + "0.88891111" + ], + "split": "dev" + }, + { + "Input": "there are 38 students in a certain geometry class . if two thirds of the students are boys and 3 fourths of the boys are under 6 feet tall , how many boys in the class are under 6 feet tall ?", + "Output Program": [ + "n0 = 38.0\nn1 = 3.0\nn2 = 6.0\nn3 = 6.0\nt0 = n0 * 2.0\nt1 = n1 * 4.0\nt2 = n1 * t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "dev" + }, + { + "Input": "a boat crossed a lake from north to east at the speed of 7 km / h , entered a river and covered twice as much distance going upstream at 6 km / h . it then turned around and stopped at the south shore of the lake . if it averaged 3.8 km / h that day , what was its approximate downstream speed ?", + "Output Program": [ + "n0 = 7.0\nn1 = 6.0\nn2 = 3.8\nt0 = n0 - n1\nanswer = n0 + t0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "dev" + }, + { + "Input": "there are 28 balls which are red , blue or green . if 12 balls are green and the sum of red balls and green balls is less than 24 , at most how many red balls are there ?", + "Output Program": [ + "n0 = 28.0\nn1 = 12.0\nn2 = 24.0\n\nanswer = n1 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "dev" + }, + { + "Input": "what is 3 / 4 of 4 / 5 of 2 / 3 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 4.0\nn3 = 5.0\nn4 = 2.0\nn5 = 3.0\nt0 = n0 / n1\nt1 = n1 / n3\nt2 = n4 / n0\nt3 = t1 * t2\nanswer = t0 * t3\nprint(answer)" + ], + "Output Answer": [ + "0.4" + ], + "split": "dev" + }, + { + "Input": "if the numerator of a fraction is increased by 20 % and its denominator is diminished by 25 % value of the fraction is 2 / 15 . find the original fraction ?", + "Output Program": [ + "n0 = 20.0\nn1 = 25.0\nn2 = 2.0\nn3 = 15.0\nt0 = n0 + 100.0\nt1 = n2 / n3\nt2 = 100.0 - n1\nt3 = t0 / 100.0\nt4 = t2 / 100.0\nt5 = t3 / t4\nanswer = t1 / t5\nprint(answer)" + ], + "Output Answer": [ + "0.08333333333333334" + ], + "split": "dev" + }, + { + "Input": "when w is divided by 13 , the reminder is 0 . if w is 3 more than it value and when divided by 11 its remainder is 0 . what is the value of w ?", + "Output Program": [ + "n0 = 13.0\nn1 = 0.0\nn2 = 3.0\nn3 = 11.0\nn4 = 0.0\n\nanswer = n0 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "52" + ], + "split": "dev" + }, + { + "Input": "a high school has 400 students 1 / 2 attend the airthmetic club , 5 / 8 attend the biology club and 3 / 4 attend the chemistry club . 1 / 8 attend all 3 clubs . if every student attends at least one club how many students attend exactly 2 clubs .", + "Output Program": [ + "n0 = 400.0\nn1 = 1.0\nn2 = 2.0\nn3 = 5.0\nn4 = 8.0\nn5 = 3.0\nn6 = 4.0\nn7 = 1.0\nn8 = 8.0\nn9 = 3.0\nn10 = 2.0\nt0 = n1 / n2\nt1 = n3 / n4\nt2 = n5 / n6\nt3 = n1 / n4\nt4 = n0 * t0\nt5 = n0 * t1\nt6 = n0 * t2\nt7 = n0 * t3\nt8 = t4 + t5\nt9 = n2 * t7\nt10 = t8 + t6\nt11 = t10 - t9\nanswer = t11 - n0\nprint(answer)" + ], + "Output Answer": [ + "250" + ], + "split": "dev" + }, + { + "Input": "a is two years older than b who is twice as old as c . if the total of the ages of a , b nd c be 27 , then how old is b ?", + "Output Program": [ + "n0 = 27.0\nt0 = 1.0 + 4.0\nt1 = n0 - 2.0\nt2 = t1 * 2.0\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "dev" + }, + { + "Input": "2 ^ 46655 mod 9 = ?", + "Output Program": [ + "n0 = 2.0\nn1 = 46655.0\nn2 = 9.0\nt0 = 2.0 + 3.0\nt1 = n0**min(t0, 5)\nanswer = t1 % n2\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "dev" + }, + { + "Input": "a computer manufacturer produces a certain electronic component at a cost of $ 80 per component . shipping costs for delivering the components are $ 2 per unit . further , the manufacturer has costs of $ 16,200 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 150 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?", + "Output Program": [ + "n0 = 80.0\nn1 = 2.0\nn2 = 16200.0\nn3 = 150.0\nt0 = n0 + n1\nt1 = 4.0 * 4.0\nt2 = n1 * 100.0\nt3 = t1 * 1000.0\nt4 = n3 * t0\nt5 = t3 + t2\nt6 = t5 + t4\nanswer = t6 / n3\nprint(answer)" + ], + "Output Answer": [ + "190" + ], + "split": "dev" + }, + { + "Input": "in a box of 9 pens , a total of 3 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?", + "Output Program": [ + "n0 = 9.0\nn1 = 3.0\nn2 = 2.0\nt0 = n0 - n1\nt1 = n0 - 1.0\nt2 = t0 / n0\nt3 = t0 - 1.0\nt4 = t3 / t1\nanswer = t2 * t4\nprint(answer)" + ], + "Output Answer": [ + "0.41666666666666663" + ], + "split": "dev" + }, + { + "Input": "find a two digit number , given that the sum of the digits is 9 and the difference of the digits is 3 . ?", + "Output Program": [ + "n0 = 9.0\nn1 = 3.0\nt0 = 3.0 + 4.0\nt1 = 3.0 * 3.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "63" + ], + "split": "dev" + }, + { + "Input": "if x is an integer and 2.13 \u00d7 10 ^ x is less than 2100 , what is the greatest possible value for x ?", + "Output Program": [ + "import math\nn0 = 2.13\nn1 = 10.0\nn2 = 2100.0\nt0 = n2 / n0\nt1 = math.log(max(1e-5, n1), 2)\nt2 = math.log(max(1e-5, t0), 2)\nt3 = t2 / t1\nanswer = math.floor(t3)\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "dev" + }, + { + "Input": "300 first - time customers of a fashion store were surveyed for their shopping experience right after leaving the store . 60 % of the customers in the survey had purchased clothes for less than $ 100 . 40 % of the customers in the survey reported they were overall satisfied with their purchase . 45 % of the customers that had purchased clothes for less than $ 100 reported they were overall satisfied with their purchase . what percent of the customers surveyed purchased clothes for at least $ 100 and reported that they were not overall satisfied with their purchase ?", + "Output Program": [ + "n0 = 300.0\nn1 = 60.0\nn2 = 100.0\nn3 = 40.0\nn4 = 45.0\nn5 = 100.0\nn6 = 100.0\nt0 = n3 / n2\nt1 = n4 / n2\nt2 = n1 / n2\nt3 = n0 * t0\nt4 = n0 * t2\nt5 = t1 * t4\nt6 = t3 - t5\nt7 = t6 / n0\nanswer = t7 * n2\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "dev" + }, + { + "Input": "the monthly rent of a shop of dimension 18 feet \u00d7 22 feet is rs . 2244 . what is the annual rent per square foot of the shop ? ( a ) rs . 5 ( 2 / 3 )", + "Output Program": [ + "n0 = 18.0\nn1 = 22.0\nn2 = 2244.0\nn3 = 5.0\nn4 = 2.0\nn5 = 3.0\nt0 = 10.0 + 2.0\nt1 = n0 * n1 # area of rectangle\nt2 = n2 / t1\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "68" + ], + "split": "dev" + }, + { + "Input": "if the radius of a cylinder is made 3 times and height is doubled , what is the new volume of the cylinder divided by the old one ?", + "Output Program": [ + "n0 = 3.0\nt0 = n0 * 4.0\nt1 = 2.0 * 3.0\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "dev" + }, + { + "Input": "the average marks of a class of 35 students is 40 and that of another class of 45 students is 60 . find the average marks of all the students ?", + "Output Program": [ + "n0 = 35.0\nn1 = 40.0\nn2 = 45.0\nn3 = 60.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "51.25" + ], + "split": "dev" + }, + { + "Input": "if m is a positive integer and m ^ 2 is divisible by 33 , then the largest positive integer that must divide m is ?", + "Output Program": [ + "n0 = 2.0\nn1 = 33.0\nt0 = n1 / 3.0\nt1 = t0 / 3.0\nanswer = t1 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "dev" + }, + { + "Input": "from a total of 5 boys and 6 girls , how many 4 - person committees can be selected if the committee must have exactly 2 boys and 2 girls ?", + "Output Program": [ + "n0 = 5.0\nn1 = 6.0\nn2 = 4.0\nn3 = 2.0\nn4 = 2.0\nt0 = n0 * 3.0\nt1 = n0 * n3\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "dev" + }, + { + "Input": "the simple interest on a sum of money will be rs . 1400 after 10 years . if the principal is trebled after 5 years what will be the total interest at the end of the tenth year ?", + "Output Program": [ + "n0 = 1400.0\nn1 = 10.0\nn2 = 5.0\nt0 = n0 / n1\nt1 = n2 * t0\nt2 = t1 * 3.0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "2800" + ], + "split": "dev" + }, + { + "Input": "45 % of x is greater than 1 / 3 rd of x by 110 . what is x ?", + "Output Program": [ + "n0 = 45.0\nn1 = 1.0\nn2 = 3.0\nn3 = 110.0\nt0 = n0 / 100.0\nt1 = n1 / n2\nt2 = t0 - t1\nanswer = n3 / t2\nprint(answer)" + ], + "Output Answer": [ + "942.8571428571427" + ], + "split": "dev" + }, + { + "Input": "a / ( b / c ) in the expression above , a , b , and c are different numbers and each is one of the numbers 2 , 3 , or 6 . what is the largest possible value of the expression ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 6.0\nt0 = n0 / n2\nanswer = n1 / t0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "dev" + }, + { + "Input": "a batsman makes a score of 87 runs in the 17 th inning and thus increases his average by 3 . find his average after 17 th inning .", + "Output Program": [ + "n0 = 87.0\nn1 = 17.0\nn2 = 3.0\nn3 = 17.0\nt0 = n1 * n2\nt1 = n0 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "39" + ], + "split": "dev" + }, + { + "Input": "if y is a positive number and 1 / 2 the square root of x is the cube root of y , then y =", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nt0 = n1**min(3.0, 5)\nanswer = t0 * t0\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "dev" + }, + { + "Input": "the sum of the ages of 4 children born at the intervals of 1 years each is 12 years . what is the age of the youngest child ?", + "Output Program": [ + "n0 = 4.0\nn1 = 1.0\nn2 = 12.0\nt0 = n0 / 2.0\nt1 = n0 - 1.0\nt2 = n2 / t0\nt3 = n1 * t1\nt4 = t2 - t3\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "1.5" + ], + "split": "dev" + }, + { + "Input": "what is the decimal equivalent of ( 1 / 2 ) ^ 2 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 2.0\nt0 = n0 / n1\nanswer = t0**min(n2, 5)\nprint(answer)" + ], + "Output Answer": [ + "0.25" + ], + "split": "dev" + }, + { + "Input": "when x is even , [ x ] = x / 2 + 1 , when x is odd [ x ] = 2 x + 1 then [ 6 ] * [ 3 ] = ?", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 2.0\nn3 = 1.0\nn4 = 6.0\nn5 = 3.0\nt0 = n4 / n0\nt1 = n0 * n5\nt2 = t0 + 1.0\nt3 = t1 + 1.0\nanswer = t2 * t3\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "dev" + }, + { + "Input": "if a 2 - b 2 = 10 and a * b = 5 , find a 4 + b 4 .", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 10.0\nn3 = 5.0\nn4 = 4.0\nn5 = 4.0\nt0 = n3**min(2.0, 5)\nt1 = n2**min(2.0, 5)\nt2 = t0 * 2.0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "dev" + }, + { + "Input": "in an office , totally there are 2800 employees and 25 % of the total employees are males . 30 % of the males in the office are at - least 50 years old . find the number of males aged below 50 years ?", + "Output Program": [ + "n0 = 2800.0\nn1 = 25.0\nn2 = 30.0\nn3 = 50.0\nn4 = 50.0\nt0 = n0 * n1\nt1 = 100.0 - n2\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nanswer = t2 * t3\nprint(answer)" + ], + "Output Answer": [ + "489.99999999999994" + ], + "split": "dev" + }, + { + "Input": "when 3 is added to half of one - third of one - fifth of a number , the result is one - fifteenth of the number . find the number ?", + "Output Program": [ + "n0 = 3.0\nt0 = 2.0 + 3.0\nt1 = t0 * 3.0\nt2 = 1.0 / t1\nt3 = t2 / 2.0\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "dev" + }, + { + "Input": "a certain psychologist charges $ 20 more for the first hour of therapy than for each additional hour . if the total charge to a patient who receives 5 hours of therapy is $ 300 , what is the total charge to a patient who receives only 3 hours of therapy ?", + "Output Program": [ + "n0 = 20.0\nn1 = 5.0\nn2 = 300.0\nn3 = 3.0\nt0 = n2 - n0\nt1 = t0 / n1\nt2 = n3 * t1\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "188" + ], + "split": "dev" + }, + { + "Input": "( \u221a 112 + \u221a 567 ) / \u221a 175 = ?", + "Output Program": [ + "import math\nn0 = 112.0\nn1 = 567.0\nn2 = 175.0\nt0 = math.sqrt(max(0, n0))\nt1 = math.sqrt(max(0, n1))\nt2 = math.sqrt(max(0, n2))\nt3 = t0 + t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "2.6" + ], + "split": "dev" + }, + { + "Input": "every disk in a bag is either blue , yellow or green . the ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8 . if the total number of disks in the bag is 126 , how many more green disks than blue disks are in the bag ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 8.0\nn3 = 126.0\nt0 = n0 + n1\nt1 = n2 - n0\nt2 = n2 + t0\nt3 = n3 / t2\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "dev" + }, + { + "Input": "ben left a job paying $ 75000 per year to accept a sales job paying $ 45000 per year plus 15 percent commission . if each of his sales is for $ 750 , what is the least number of sales he must make per year if he is not to lose money because of the change ?", + "Output Program": [ + "n0 = 75000.0\nn1 = 45000.0\nn2 = 15.0\nn3 = 750.0\nt0 = n2 / 100.0\nt1 = n0 - n1\nt2 = t1 / t0\nanswer = t2 / n3\nprint(answer)" + ], + "Output Answer": [ + "266.6666666666667" + ], + "split": "dev" + }, + { + "Input": "find large number from below question the difference of two numbers is 1355 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder", + "Output Program": [ + "n0 = 1355.0\nn1 = 6.0\nn2 = 15.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nt2 = t0 / t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "1608" + ], + "split": "dev" + }, + { + "Input": "if x + y = 290 , x - y = 200 , for integers of x and y , y = ?", + "Output Program": [ + "n0 = 290.0\nn1 = 200.0\nt0 = n0 + n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "245" + ], + "split": "dev" + }, + { + "Input": "the mean of 50 observations is 200 . but later he found that there is decrements of 34 from each observations . what is the the updated mean is ?", + "Output Program": [ + "n0 = 50.0\nn1 = 200.0\nn2 = 34.0\n\nanswer = n1 - n2\nprint(answer)" + ], + "Output Answer": [ + "166" + ], + "split": "dev" + }, + { + "Input": "the sum of first 45 natural numbers is", + "Output Program": [ + "n0 = 45.0\nt0 = n0 + 1.0\nt1 = n0 * t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "1035" + ], + "split": "dev" + }, + { + "Input": "what is the dividend . divisor 13 , the quotient is 17 and the remainder is 1", + "Output Program": [ + "n0 = 13.0\nn1 = 17.0\nn2 = 1.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "222" + ], + "split": "dev" + }, + { + "Input": "a man performs 3 / 5 of the total journey by rail , 17 / 20 by bus and the remaining 6.5 km on foot . his total journey is :", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 17.0\nn3 = 20.0\nn4 = 6.5\n\nanswer = n3 * n4\nprint(answer)" + ], + "Output Answer": [ + "130" + ], + "split": "dev" + }, + { + "Input": "there are 300 female managers in a certain company . find the total number of female employees in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers .", + "Output Program": [ + "n0 = 300.0\nn1 = 2.0\nn2 = 5.0\nn3 = 2.0\nn4 = 5.0\nt0 = n1 / n2\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "750" + ], + "split": "dev" + }, + { + "Input": "anne bought doughnuts for a class breakfast party . she bought 9 chocolate doughnuts , 7 coconut doughnuts , and 9 jam - filled doughnuts . how many doughnuts did anne buy in all ?", + "Output Program": [ + "n0 = 9.0\nn1 = 7.0\nn2 = 9.0\nt0 = n0 + n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "dev" + }, + { + "Input": "for the symbol , m \u201d n = n ^ 2 \u2212 m for all values of m and n . what is the value of 6 \u201d 3 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 6.0\nn2 = 3.0\nt0 = n2**min(n0, 5)\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "dev" + }, + { + "Input": "two - third of a positive number and 144 / 216 of its reciprocal are equal . the number is :", + "Output Program": [ + "import math\nn0 = 144.0\nn1 = 216.0\nt0 = n0 * 3.0\nt1 = n1 * 2.0\nt2 = t0 / t1\nanswer = math.sqrt(max(0, t2))\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "dev" + }, + { + "Input": "after 6 games , team b had an average of 70 points per game . if it got only 47 points in game 7 , how many more points does it need to score to get its total above 500 ?", + "Output Program": [ + "n0 = 6.0\nn1 = 70.0\nn2 = 47.0\nn3 = 7.0\nn4 = 500.0\nt0 = n0 * n1\nt1 = n2 + t0\nanswer = n4 - t1\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "dev" + }, + { + "Input": "if a ' s height is 40 % less than that of b , how much percent b ' s height is more than that of a ?", + "Output Program": [ + "n0 = 40.0\nt0 = 100.0 - n0\nt1 = n0 / t0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "66.66666666666666" + ], + "split": "dev" + }, + { + "Input": "how many prime numbers are between 25 / 3 and 84 / 6 ?", + "Output Program": [ + "import math\nn0 = 25.0\nn1 = 3.0\nn2 = 84.0\nn3 = 6.0\n\nanswer = math.floor(2.0)\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "dev" + }, + { + "Input": "a company wants to spend equal amounts of money for the purchase of two types of computer printers costing $ 400 and $ 350 per unit , respectively . what is the fewest number of computer printers that the company can purchase ?", + "Output Program": [ + "import scipy\nn0 = 400.0\nn1 = 350.0\nt0 = scipy.lcm(int(n0), int(n1))\nt1 = t0 / n0\nt2 = t0 / n1\nanswer = t1 + t2\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "dev" + }, + { + "Input": "in a room filled with 6 people , all 6 people have exactly 2 siblings in the room . if two individuals are selected from the room at random , what is the probability that those two individuals are not siblings ?", + "Output Program": [ + "n0 = 6.0\nn1 = 6.0\nn2 = 2.0\nt0 = n0 - 1.0\nt1 = n0 * t0\nt2 = t0 - n2\nt3 = n0 * t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.6" + ], + "split": "dev" + }, + { + "Input": "if a / b = 1 / 3 , b / c = 2 , c / d = 1 / 2 , d / e = 3 and e / f = 1 / 10 , then what is the value of abc / def ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 2.0\nn3 = 1.0\nn4 = 2.0\nn5 = 3.0\nn6 = 1.0\nn7 = 10.0\nt0 = n1 * n1\nt1 = n1 * n7\nt2 = n2 * t1\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.15" + ], + "split": "dev" + }, + { + "Input": "if a = 105 and a ^ 3 = 21 \u00d7 25 \u00d7 45 \u00d7 z , what is the value of z ?", + "Output Program": [ + "n0 = 105.0\nn1 = 3.0\nn2 = 21.0\nn3 = 25.0\nn4 = 45.0\nt0 = n2 * n3\nt1 = n0**min(n1, 5)\nt2 = n4 * t0\nanswer = t1 / t2\nprint(answer)" + ], + "Output Answer": [ + "49" + ], + "split": "dev" + }, + { + "Input": "which number should replace both the asterisks in ( * / 20 ) x ( * / 80 ) = 1 ?", + "Output Program": [ + "import math\nn0 = 20.0\nn1 = 80.0\nn2 = 1.0\nt0 = n0 * n1\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "dev" + }, + { + "Input": "a couple spent $ 211.20 in total while dining out and paid this amount using a credit card . the $ 211.20 figure included a 20 percent tip which was paid on top of the price which already included a sales tax of 10 percent on top of the price of the food . what was the actual price of the food before tax and tip ?", + "Output Program": [ + "n0 = 211.2\nn1 = 211.2\nn2 = 20.0\nn3 = 10.0\nt0 = n2 + 100.0\nt1 = n3 + 100.0\nt2 = n0 * 100.0\nt3 = t2 / t0\nt4 = t3 * 100.0\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "160" + ], + "split": "dev" + }, + { + "Input": "at a school , 3 - fifths of the male students and two - thirds of the female students speak a foreign language . if the number of males is equal to the number of females , what fraction of the students speak a foreign language ?", + "Output Program": [ + "n0 = 3.0\nt0 = 2.0 + 3.0\nt1 = 100.0 / 2.0\nt2 = 2.0 / 3.0\nt3 = n0 / t0\nt4 = t2 * t1\nt5 = t3 * t1\nt6 = t5 + t4\nanswer = t6 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "0.6333333333333333" + ], + "split": "dev" + }, + { + "Input": "the captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . find out the average age of the team .", + "Output Program": [ + "n0 = 11.0\nn1 = 26.0\nn2 = 3.0\nt0 = n1 + n2\nt1 = n2 * n2\nt2 = n1 + t0\nt3 = t2 - t1\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "dev" + }, + { + "Input": "a box contains 7 pairs of shoes ( 14 shoes in total ) . if two shoes are selected at random , what it is the probability that they are matching shoes ?", + "Output Program": [ + "n0 = 7.0\nn1 = 14.0\nt0 = n1 - 1.0\nanswer = 1.0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.07692307692307693" + ], + "split": "dev" + }, + { + "Input": "when positive integer x is divided by positive integer y , the remainder is 3 . if x / y = 96.12 , what is the value of y ?", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 96.12\nt0 = math.floor(n1)\nt1 = n1 - t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "24.99999999999905" + ], + "split": "dev" + }, + { + "Input": "if john makes a contribution to a charity fund at school , the average contribution size will increase by 50 % reaching $ 75 per person . if there were 1 other contributions made before john ' s , what is the size of his donation ?", + "Output Program": [ + "n0 = 50.0\nn1 = 75.0\nn2 = 1.0\nt0 = n2 + 1.0\nt1 = n1 * t0\nt2 = n0 * t0\nt3 = t1 - t2\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "dev" + }, + { + "Input": "if sharon ' s weekly salary increased by 16 percent , she would earn $ 348 per week . if instead , her weekly salary were to increase by 15 percent , how much would she earn per week ?", + "Output Program": [ + "n0 = 16.0\nn1 = 348.0\nn2 = 15.0\nt0 = n0 / 100.0\nt1 = n2 / 100.0\nt2 = t0 + 1.0\nt3 = n1 / t2\nt4 = t1 * t3\nanswer = t3 + t4\nprint(answer)" + ], + "Output Answer": [ + "345" + ], + "split": "dev" + }, + { + "Input": "the average monthly salary of 8 workers and one supervisor in a factory was 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . whenthesupervisor , whosesalarywas 430 . when the supervisor , whose salary was 870 per month , retired , a new person was appointed and then the average salary of 9 people was $ $ 440 per month . the salary of the new supervisor is :", + "Output Program": [ + "n0 = 8.0\nn1 = 430.0\nn2 = 430.0\nn3 = 430.0\nn4 = 430.0\nn5 = 870.0\nn6 = 9.0\nn7 = 440.0\nt0 = n6 * n7\nt1 = n1 * n6\nt2 = t1 - n5\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "960" + ], + "split": "dev" + }, + { + "Input": "if ( m - 8 ) is a factor of m ^ 2 - hm - 24 , then h =", + "Output Program": [ + "n0 = 8.0\nn1 = 2.0\nn2 = 24.0\nt0 = n2 / n0\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "dev" + }, + { + "Input": "a bowl contains equal numbers of red , orange , green , blue , and yellow candies . kaz eats all of the green candies and half of the orange ones . next , he eats half of the remaining pieces of each color . finally , he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 20 % of the original number . what percent of the red candies remain ?", + "Output Program": [ + "n0 = 20.0\nt0 = 2.0 + 3.0\nt1 = 100.0 / t0\nt2 = t1 / 2.0\nt3 = t2 / 2.0\nt4 = t2 + t3\nt5 = n0 - t4\nt6 = t5 / 2.0\nt7 = t6 / t1\nanswer = t7 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "12.5" + ], + "split": "dev" + }, + { + "Input": "the average of 2 , 76 and x is 5 . find the value of x ?", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 76.0\nn2 = 5.0\nt0 = n1 / 10.0\nt1 = n2 * 4.0\nt2 = n1 % 10.0\nt3 = math.floor(t0)\nt4 = t3 + t2\nt5 = n0 + t4\nanswer = t1 - t5\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "dev" + }, + { + "Input": "if y > 0 , ( 6 y ) / 20 + ( 3 y ) / 10 is what percent of y ?", + "Output Program": [ + "n0 = 0.0\nn1 = 6.0\nn2 = 20.0\nn3 = 3.0\nn4 = 10.0\nt0 = n1 / n2\nt1 = n3 / n4\nt2 = t0 + t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "dev" + }, + { + "Input": "if the number is divided by 3 , it reduced by 36 . the number is", + "Output Program": [ + "n0 = 3.0\nn1 = 36.0\nt0 = n0 * n1\nt1 = n0 - 1.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "dev" + }, + { + "Input": "if w / x = 1 / 3 and w / y = 3 / 4 , then ( x + y ) / y =", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 3.0\nn3 = 4.0\nt0 = n2 / n0\nt1 = n3 / n1\nt2 = t0 / t1\nanswer = t2 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "3.25" + ], + "split": "dev" + }, + { + "Input": "a man is 20 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ?", + "Output Program": [ + "n0 = 20.0\nt0 = 2.0 * 2.0\nt1 = 2.0 - 1.0\nt2 = t0 - 2.0\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "dev" + }, + { + "Input": "rice weighing 35 / 2 pounds was divided equally and placed in 4 containers . how many ounces of rice were in each container ? ( note that 1 pound = 16 ounces )", + "Output Program": [ + "n0 = 35.0\nn1 = 2.0\nn2 = 4.0\nn3 = 1.0\nn4 = 16.0\nt0 = n0 / n1\nt1 = n4 * t0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "dev" + }, + { + "Input": "ashok secured average of 74 marks in 6 subjects . if the average of marks in 5 subjects is 74 , how many marks did he secure in the 6 th subject ?", + "Output Program": [ + "n0 = 74.0\nn1 = 6.0\nn2 = 5.0\nn3 = 74.0\nn4 = 6.0\nt0 = n0 * n1\nt1 = n2 * n3\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "74" + ], + "split": "dev" + }, + { + "Input": "if 4 ( p ' s capital ) = 6 ( q ' s capital ) = 10 ( r ' s capital ) , then out of the total profit of rs 4030 , r will receive", + "Output Program": [ + "n0 = 4.0\nn1 = 6.0\nn2 = 10.0\nn3 = 4030.0\nt0 = n0 + 1.0\nt1 = n2 + t0\nt2 = n2 + t1\nt3 = n1 + t2\nt4 = n1 / t3\nanswer = n3 * t4\nprint(answer)" + ], + "Output Answer": [ + "780" + ], + "split": "dev" + }, + { + "Input": "mark and ann together were allocated n boxes of cookies to sell for a club project . mark sold 11 boxes less than n and ann sold 2 boxes less than n . if mark and ann have each sold at least one box of cookies , but together they have sold less than n boxes , what is the value of n ?", + "Output Program": [ + "n0 = 11.0\nn1 = 2.0\n\nanswer = n0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "dev" + }, + { + "Input": "in a forest 10 rabbits were caught , tagged with electronic markers , then released . a month later , 10 rabbits were captured in the same forest . of these 10 rabbits , it was found that 2 had been tagged with the electronic markers . if the percentage of tagged rabbits in the second sample approximates the percentage of tagged rabbits in the forest , and if no rabbits had either left or entered the forest over the preceding month , what is the approximate number of rabbits in the forest ?", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 10.0\nn3 = 2.0\nt0 = n0 + n0\nt1 = n3 / n0\nt2 = n0 + t0\nt3 = t1 * 100.0\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "dev" + }, + { + "Input": "tough and tricky questions : remainders . 1 ^ 1 + 2 ^ 2 + 3 ^ 3 + . . . + 7 ^ 7 is divided by 7 . what is the remainder ?", + "Output Program": [ + "import math\nn0 = 1.0\nn1 = 1.0\nn2 = 2.0\nn3 = 2.0\nn4 = 3.0\nn5 = 3.0\nn6 = 7.0\nn7 = 7.0\nn8 = 7.0\nt0 = n0 + 4.0\nt1 = 2.0 + 4.0\nt2 = 1.0 + 4.0\nt3 = n6 + t0\nt4 = t3 + t1\nt5 = t4 + t2\nt6 = t5 + t1\nt7 = t6 + 3.0\nt8 = t7 / n6\nt9 = math.floor(t8)\nt10 = n6 * t9\nanswer = t7 - t10\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "dev" + }, + { + "Input": "average marks of a , b , c is 48 . when d joins average becomes 47 . e has 3 more marks than d . average marks of b , c , d , e is 48 . what is the marks of a ?", + "Output Program": [ + "n0 = 48.0\nn1 = 47.0\nn2 = 3.0\nn3 = 48.0\nt0 = n0 * 3.0\nt1 = n0 * 4.0\nt2 = n1 * 4.0\nt3 = t2 - t0\nt4 = n2 + t3\nt5 = t4 + t3\nt6 = t1 - t5\nanswer = t0 - t6\nprint(answer)" + ], + "Output Answer": [ + "43" + ], + "split": "dev" + }, + { + "Input": "a random 10 - letter code is to be formed using the letters a , b , c , d , e , f , g , h , i and i ( only the \u201c i \u201d will be used twice ) . what is the probability that a code that has the two i \u2019 s adjacent to one another will be formed ?", + "Output Program": [ + "import math\nn0 = 10.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = n0 - 2.0\nt2 = n0 - 1.0\nt3 = math.factorial(min(15, int(t1)))\nt4 = t0 / t3\nt5 = t3 * t2\nt6 = t4 / 2.0\nt7 = t6 * t3\nanswer = t5 / t7\nprint(answer)" + ], + "Output Answer": [ + "0.2" + ], + "split": "dev" + }, + { + "Input": "at the end of the day , february 14 th , a florist had 90 roses left in his shop , all of which were red , white or pink in color and either long or short - stemmed . a third of the roses were short - stemmed , 15 of which were white and 10 of which were pink . the percentage of pink roses that were short - stemmed equaled the percentage of red roses that were short - stemmed . if none of the long - stemmed roses were white , what percentage of the long - stemmed roses were red ?", + "Output Program": [ + "n0 = 14.0\nn1 = 90.0\nn2 = 15.0\nn3 = 10.0\nt0 = n1 / 3.0\nt1 = n1 - t0\nt2 = t0 - n2\nt3 = t2 - n3\nt4 = n3 + t3\nt5 = t1 * t3\nt6 = t5 / t4\nt7 = t6 / t1\nanswer = t7 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "33.33333333333333" + ], + "split": "dev" + }, + { + "Input": "if the integer n has exactly 4 positive divisors , including 1 and n , how many positive divisors does n ^ 3 have ?", + "Output Program": [ + "n0 = 4.0\nn1 = 1.0\nn2 = 3.0\nt0 = n0 - 2.0\nanswer = n0**min(t0, 5)\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "dev" + }, + { + "Input": "company c sells a line of 25 products with an average retail price of $ 1,200 . if none of these products sells for less than $ 400 , and exactly 10 of the products sell for less than $ 1,000 , what is the greatest possible selling price of the most expensive product ?", + "Output Program": [ + "n0 = 25.0\nn1 = 1200.0\nn2 = 400.0\nn3 = 10.0\nn4 = 1000.0\nt0 = 100.0 * 12.0\nt1 = n2 * n3\nt2 = n0 - n3\nt3 = n0 * t0\nt4 = t2 - 1.0\nt5 = t4 * n4\nt6 = t1 + t5\nanswer = t3 - t6\nprint(answer)" + ], + "Output Answer": [ + "12000" + ], + "split": "dev" + }, + { + "Input": "a man purchased earphone on friday . but he forgot how much it cost . the data he have are mean expenditure of all 7 days is 500 . expenditure on mon , tue , wed , thurs , sat , sun are 450600 , 400500 , 550300 . on friday he purchased 3 things one earphone , one pen and one notebook . pen cost 30 and notebook cost 50 . then what is cost of earphone ?", + "Output Program": [ + "n0 = 7.0\nn1 = 500.0\nn2 = 450600.0\nn3 = 400500.0\nn4 = 550300.0\nn5 = 3.0\nn6 = 30.0\nn7 = 50.0\nt0 = n1 + 100.0\nt1 = n1 + n7\nt2 = n0 * n1\nt3 = n1 - n7\nt4 = n1 - 100.0\nt5 = t0 + t3\nt6 = t4 - 100.0\nt7 = t5 + t4\nt8 = n1 + t7\nt9 = t8 + t1\nt10 = t9 + t6\nt11 = t2 - t10\nt12 = t11 - n6\nanswer = t12 - n7\nprint(answer)" + ], + "Output Answer": [ + "620" + ], + "split": "dev" + }, + { + "Input": "how many prime numbers are between 51 / 13 and 89 / 9 ?", + "Output Program": [ + "import math\nn0 = 51.0\nn1 = 13.0\nn2 = 89.0\nn3 = 9.0\n\nanswer = math.floor(2.0)\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "dev" + }, + { + "Input": "what least no . must be subtracted from 5026 so that remaining no . is divisible by 5 ?", + "Output Program": [ + "import math\nn0 = 5026.0\nn1 = 5.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "dev" + }, + { + "Input": "when 2 / 9 of the votes on a certain resolution have been counted , 3 / 4 of those counted are in favor of the resolution . what fraction x of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution ?", + "Output Program": [ + "n0 = 2.0\nn1 = 9.0\nn2 = 3.0\nn3 = 4.0\nn4 = 2.0\nn5 = 1.0\nt0 = n0 + n5\nt1 = n0 / n1\nt2 = n2 / n3\nt3 = n1 - n0\nt4 = n0 / t0\nt5 = t3 / n1\nt6 = t1 * t2\nt7 = t1 - t6\nt8 = t4 - t7\nanswer = t8 / t5\nprint(answer)" + ], + "Output Answer": [ + "0.7857142857142856" + ], + "split": "dev" + }, + { + "Input": "f ( x ) is a function such that f ( 2 x + 1 ) = 2 f ( x ) + 1 for all real numbers x and f ( 0 ) = 2 . find the value of f ( 3 ) .", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 2.0\nn3 = 1.0\nn4 = 0.0\nn5 = 2.0\nn6 = 3.0\nt0 = n0 * n6\nt1 = n0 * t0\nanswer = t1 - n1\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "dev" + }, + { + "Input": "a pupil ' s marks were wrongly entered as 83 instead of 63 . due to that the average marks for the class got increased by half . the number of pupils in the class is :", + "Output Program": [ + "n0 = 83.0\nn1 = 63.0\nt0 = n0 - n1\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "dev" + }, + { + "Input": "there are 20 players on a rugby team . if the average weight of the players is 180 pounds , what will be the new average height if a 210 pound player will join the team ?", + "Output Program": [ + "n0 = 20.0\nn1 = 180.0\nn2 = 210.0\nt0 = n0 + 1.0\nt1 = n0 * n1\nt2 = n2 + t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "181.42857142857142" + ], + "split": "dev" + }, + { + "Input": "if in a 20 over cricket match , there were no wide balls , no wides , no extras and no overthrows . what is the maximum number of runs that a batsman can score in an ideal case scenario ?", + "Output Program": [ + "n0 = 20.0\nt0 = n0 * 10.0\nt1 = n0 + t0\nt2 = t1 + 1.0\nanswer = t2 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "663" + ], + "split": "dev" + }, + { + "Input": "if the average of 5 positive integers is 50 and the difference between the largest and the smallest of these 5 numbers is 10 , what is the maximum value possible for the largest of these 5 integers ?", + "Output Program": [ + "n0 = 5.0\nn1 = 50.0\nn2 = 5.0\nn3 = 10.0\nn4 = 5.0\nt0 = n0 * n1\nt1 = t0 - n3\nt2 = t1 / n0\nanswer = n3 + t2\nprint(answer)" + ], + "Output Answer": [ + "58" + ], + "split": "dev" + }, + { + "Input": "what is the smallest number which , when increased by 7 , is divisible by 8 , 11 , and 24 ?", + "Output Program": [ + "import scipy\nn0 = 7.0\nn1 = 8.0\nn2 = 11.0\nn3 = 24.0\nt0 = scipy.lcm(int(n2), int(n3))\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "257" + ], + "split": "dev" + }, + { + "Input": "the grade point average of one third of the classroom is 15 ; the grade point average of the rest is 18 . what is the grade point average of the whole class ?", + "Output Program": [ + "n0 = 15.0\nn1 = 18.0\nt0 = n0 / 3.0\nt1 = n1 / 3.0\nt2 = t1 * 2.0\nanswer = t0 + t2\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "dev" + }, + { + "Input": "the contents of a certain box consist of 24 oranges and 30 kiwis . how many kiwis must be added to the box so that exactly 30 % of the pieces of fruit in the box will be oranges ?", + "Output Program": [ + "n0 = 24.0\nn1 = 30.0\nn2 = 30.0\nt0 = n0 + n1\nt1 = n1 / 100.0\nt2 = t0 * t1\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "26.000000000000004" + ], + "split": "dev" + }, + { + "Input": "a box contain the number of balls which is as much greater than 44 is less than 70 . the number of balls is ?", + "Output Program": [ + "n0 = 44.0\nn1 = 70.0\nt0 = n0 + n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "57" + ], + "split": "dev" + }, + { + "Input": "robert ' s salary was decreased by 20 % and subsequently increased by 20 % . how much percentage does he lose ?", + "Output Program": [ + "n0 = 20.0\nn1 = 20.0\nt0 = n0 + 100.0\nt1 = 100.0 * 100.0\nt2 = 100.0 - n0\nt3 = t0 * t2\nt4 = t1 - t3\nt5 = t4 / t1\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "dev" + }, + { + "Input": "12 . what is the dividend . divisor 17 , the quotient is 9 and the remainder is 6 .", + "Output Program": [ + "n0 = 12.0\nn1 = 17.0\nn2 = 9.0\nn3 = 6.0\nt0 = n1 * n2\nanswer = n3 + t0\nprint(answer)" + ], + "Output Answer": [ + "159" + ], + "split": "dev" + }, + { + "Input": "a , b , c and d enter into partnership . a subscribes 1 / 3 of the capital b 1 / 4 , c 1 / 5 and d the rest . how much share did a get in a profit of rs . 2400 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 4.0\nn4 = 1.0\nn5 = 5.0\nn6 = 2400.0\nt0 = n0 / n1\nanswer = n6 * t0\nprint(answer)" + ], + "Output Answer": [ + "800" + ], + "split": "dev" + }, + { + "Input": "a grocer has a sale of rs . 5420 , rs . 5660 , rs . 6200 , rs . 6350 and rs . 6500 for 5 consecutive months . find the sale he should have in the sixth month , so that he gets an average sale of rs . 6400 ?", + "Output Program": [ + "n0 = 5420.0\nn1 = 5660.0\nn2 = 6200.0\nn3 = 6350.0\nn4 = 6500.0\nn5 = 5.0\nn6 = 6400.0\nt0 = n5 + 1.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n6 * t0\nt4 = n3 + t2\nt5 = n4 + t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "8270" + ], + "split": "dev" + }, + { + "Input": "the sum of first n consecutive odd integers is n ^ 2 . what is the sum of all odd integers between 9 and 39 inclusive .", + "Output Program": [ + "n0 = 2.0\nn1 = 9.0\nn2 = 39.0\nt0 = n2 + 1.0\nt1 = n1 - n0\nt2 = t1 + 1.0\nt3 = t0 / n0\nt4 = t2 / n0\nt5 = t3**min(n0, 5)\nt6 = t4**min(n0, 5)\nanswer = t5 - t6\nprint(answer)" + ], + "Output Answer": [ + "384" + ], + "split": "dev" + }, + { + "Input": "if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 153 games will be played during the tournament . find the number of participants .", + "Output Program": [ + "import math\nn0 = 153.0\nt0 = n0 * 2.0\nt1 = t0 * 4.0\nt2 = t1 + 1.0\nt3 = math.sqrt(max(0, t2))\nt4 = t3 + 1.0\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "dev" + }, + { + "Input": "the sum of the present ages of a father and his son is 42 years . 6 years ago , father ' s age was 4 times the age of the son . after 6 years , son ' s age will be :", + "Output Program": [ + "n0 = 42.0\nn1 = 6.0\nn2 = 4.0\nn3 = 6.0\nt0 = n2 + 1.0\nt1 = n1 * n2\nt2 = t1 - n1\nt3 = n0 + t2\nt4 = t3 / t0\nanswer = n1 + t4\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "dev" + }, + { + "Input": "the average of 6 no . ' s is 3.95 . the average of 2 of them is 4.2 , while the average of theother 2 is 3.85 . what is the average of the remaining 2 no ' s ?", + "Output Program": [ + "n0 = 6.0\nn1 = 3.95\nn2 = 2.0\nn3 = 4.2\nn4 = 2.0\nn5 = 3.85\nn6 = 2.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n2 * n5\nt3 = t1 + t2\nt4 = t0 - t3\nanswer = t4 / n2\nprint(answer)" + ], + "Output Answer": [ + "3.8000000000000007" + ], + "split": "dev" + }, + { + "Input": "what is the decimal equivalent of ( 1 / 4 ) ^ 2 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 2.0\nt0 = n0 / n1\nanswer = t0**min(n2, 5)\nprint(answer)" + ], + "Output Answer": [ + "0.0625" + ], + "split": "dev" + }, + { + "Input": "if 5 + 7 / x = 6 - 5 / x , then x =", + "Output Program": [ + "n0 = 5.0\nn1 = 7.0\nn2 = 6.0\nn3 = 5.0\nt0 = n0 + n1\nt1 = n2 - n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "dev" + }, + { + "Input": "the population of a bacteria culture doubles every 2 minutes . approximately how many minutes will it take for the population to grow from 1000 to 1000000 bacteria", + "Output Program": [ + "n0 = 2.0\nn1 = 1000.0\nn2 = 1000000.0\nt0 = n2 / n1\nt1 = t0 / 100.0\nanswer = t1 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "dev" + }, + { + "Input": "if a person walks at 20 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance traveled by him is :", + "Output Program": [ + "n0 = 20.0\nn1 = 10.0\nn2 = 20.0\nt0 = n0 - n1\nt1 = n2 / t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "dev" + }, + { + "Input": "on dividing 190 by a number , the quotient is 9 and the remainder is 1 . find the divisor ?", + "Output Program": [ + "import math\nn0 = 190.0\nn1 = 9.0\nn2 = 1.0\nt0 = n0 / n1\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "dev" + }, + { + "Input": "a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 98.01 , the number of the member is the group is :", + "Output Program": [ + "import math\nn0 = 98.01\nt0 = n0 * 100.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "99" + ], + "split": "dev" + }, + { + "Input": "if n is an integer and 101 n ^ 2 is less than or equal to 10000 , what is the greatest possible value of n ?", + "Output Program": [ + "import math\nn0 = 101.0\nn1 = 2.0\nn2 = 10000.0\nt0 = n2 / n0\nt1 = math.sqrt(max(0, t0))\nanswer = math.floor(t1)\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "test" + }, + { + "Input": "there are 1000 buildings in a street . a sign - maker is contracted to number the houses from 1 to 1000 . how many zeroes will he need ?", + "Output Program": [ + "n0 = 1000.0\nn1 = 1.0\nn2 = 1000.0\nt0 = n0 / 10.0\nt1 = 10.0 - n1\nt2 = t1 * 10.0\nt3 = t0 + t2\nanswer = t3 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "192" + ], + "split": "test" + }, + { + "Input": "bookman purchased 55 copies of a new book released recently , 10 of which are hardback and sold for $ 20 each , and rest are paperback and sold for $ 10 each . if 14 copies were sold and the total value of the remaining books was 460 , how many paperback copies were sold ?", + "Output Program": [ + "import scipy\nn0 = 55.0\nn1 = 10.0\nn2 = 20.0\nn3 = 10.0\nn4 = 14.0\nn5 = 460.0\nt0 = scipy.gcd(int(n0), int(n1))\nt1 = n1 * n2\nt2 = n0 - n1\nt3 = n1 * t2\nt4 = n2 * t0\nt5 = t3 + t1\nt6 = t5 - n5\nt7 = t6 - t4\nanswer = t7 / n1\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "test" + }, + { + "Input": "diana is painting statues . she has 1 / 2 of a gallon of paint remaining . each statue requires 1 / 16 gallon of paint . how many statues can she paint ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 1.0\nn3 = 16.0\nt0 = n0 / n1\nt1 = n2 / n3\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "test" + }, + { + "Input": "if the price of gasoline increases by 25 % and a driver intends to spend only 20 % more on gasoline , by how much percent should the driver reduce the quantity of gasoline that he buys ?", + "Output Program": [ + "n0 = 25.0\nn1 = 20.0\nt0 = n0 + 100.0\nt1 = n1 + 100.0\nt2 = t0 - t1\nt3 = t2 / t0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "test" + }, + { + "Input": "an art gallery has only paintings and sculptures . currently , 1 / 3 of the pieces of art are displayed , and 1 / 6 of the pieces on display are sculptures . if 1 / 3 of the pieces not on display are paintings , and 1000 sculptures are not on display , how many pieces of art does the gallery have ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 1.0\nn3 = 6.0\nn4 = 1.0\nn5 = 3.0\nn6 = 1000.0\nt0 = n0 / n1\nt1 = 1.0 - t0\nt2 = n6 / t1\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "2249.9999999999995" + ], + "split": "test" + }, + { + "Input": "a corporation double its annual bonus to 100 of its employees . what percent of the employees \u2019 new bonus is the increase ?", + "Output Program": [ + "n0 = 100.0\nt0 = 2.0 - 1.0\nt1 = t0 / 2.0\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "test" + }, + { + "Input": "what is the unit digit in the product ( 3 ^ 65 x 6 ^ 59 x 7 ^ 71 ) ?", + "Output Program": [ + "n0 = 3.0\nn1 = 65.0\nn2 = 6.0\nn3 = 59.0\nn4 = 7.0\nn5 = 71.0\nt0 = n0 * n2\nt1 = n0 * t0\nt2 = t1 - 4.0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "test" + }, + { + "Input": "the maximum number of students among them 1345 pens and 775 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :", + "Output Program": [ + "import scipy\nn0 = 1345.0\nn1 = 775.0\n\nanswer = scipy.gcd(int(n0), int(n1))\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "test" + }, + { + "Input": "two - third of a positive number and 16 / 216 of its reciprocal are equal . find the positive number .", + "Output Program": [ + "import math\nn0 = 16.0\nn1 = 216.0\nt0 = n0 * 3.0\nt1 = n1 * 2.0\nt2 = t0 / t1\nanswer = math.sqrt(max(0, t2))\nprint(answer)" + ], + "Output Answer": [ + "0.3333333333333333" + ], + "split": "test" + }, + { + "Input": "find large number from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder", + "Output Program": [ + "n0 = 1365.0\nn1 = 6.0\nn2 = 15.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nt2 = t0 / t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "1620" + ], + "split": "test" + }, + { + "Input": "in a recent election , james received 0.5 percent of the 2,000 votes cast . to win the election , a candidate needed to receive more than 50 percent of the vote . how many additional votes would james have needed to win the election ?", + "Output Program": [ + "n0 = 0.5\nn1 = 2000.0\nn2 = 50.0\nt0 = n2 - n0\nt1 = t0 / 100.0\nt2 = n1 * t1\nanswer = t2 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "991" + ], + "split": "test" + }, + { + "Input": "what least number must be subtracted from 3832 so that the remaining number is divisible by 5 ?", + "Output Program": [ + "import math\nn0 = 3832.0\nn1 = 5.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "test" + }, + { + "Input": "a profit of rs . 900 is divided between x and y in the ratio of 1 / 2 : 1 / 3 . what is the difference between their profit shares ?", + "Output Program": [ + "n0 = 900.0\nn1 = 1.0\nn2 = 2.0\nn3 = 1.0\nn4 = 3.0\nt0 = n1 / n2\nt1 = n1 / n4\nt2 = t0 + t1\nt3 = n0 / t2\nt4 = t3 / n2\nt5 = t3 / n4\nanswer = t4 - t5\nprint(answer)" + ], + "Output Answer": [ + "180" + ], + "split": "test" + }, + { + "Input": "a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 27 , the how old is b ?", + "Output Program": [ + "n0 = 27.0\nt0 = 1.0 + 4.0\nt1 = n0 - 2.0\nt2 = t1 * 2.0\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "test" + }, + { + "Input": "calculate the share of y , if rs . 2880 is divided among x , y and z in the ratio 3 : 5 : 8 ?", + "Output Program": [ + "n0 = 2880.0\nn1 = 3.0\nn2 = 5.0\nn3 = 8.0\nt0 = n1 + n2\nt1 = n3 + t0\nt2 = n0 / t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "540" + ], + "split": "test" + }, + { + "Input": "3 years ago , paula was 3 times as old as karl . in 9 years , paula will be twice as old as karl . what is the sum of their ages now ?", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 9.0\nt0 = n2 * 2.0\nt1 = n0 * n1\nt2 = n2 - t0\nt3 = t1 - n0\nt4 = -t2\nt5 = t4 + t3\nt6 = t5 * n1\nt7 = t6 - t3\nanswer = t5 + t7\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "test" + }, + { + "Input": "the digital sum of a number is the sum of its digits . for how many of the positive integers 24 - 140 inclusive is the digital sum a multiple of 7 ?", + "Output Program": [ + "n0 = 24.0\nn1 = 140.0\nn2 = 7.0\nt0 = n0 - n2\nanswer = t0 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "test" + }, + { + "Input": "the average weight of 18 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg . find the average weights of all the boys in the class .", + "Output Program": [ + "n0 = 18.0\nn1 = 50.25\nn2 = 8.0\nn3 = 45.15\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "48.68076923076923" + ], + "split": "test" + }, + { + "Input": "what is the probability for a family with 3 children to have a girl and two boys ( assuming the probability of having a boy or a girl is equal ) ?", + "Output Program": [ + "n0 = 3.0\nt0 = 1.0 / 2.0\nt1 = t0**min(n0, 5)\nt2 = t1 * 2.0\nt3 = 1.0 - t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "0.375" + ], + "split": "test" + }, + { + "Input": "a manufacturer produces a certain men ' s athletic shoe in integer sizes from 8 to 17 . for this particular shoe , each unit increase in size corresponds to a 1 / 5 - inch increase in the length of the shoe . if the largest size of this shoe is 30 % longer than the smallest size , how long , in inches , is the shoe in size 15 ?", + "Output Program": [ + "n0 = 8.0\nn1 = 17.0\nn2 = 1.0\nn3 = 5.0\nn4 = 30.0\nn5 = 15.0\nt0 = n2 / n3\nt1 = n4 / 100.0\nt2 = n1 - n0\nt3 = n5 - n0\nt4 = t0 * t2\nt5 = t0 * t3\nt6 = t4 / t1\nanswer = t6 + t5\nprint(answer)" + ], + "Output Answer": [ + "7.4" + ], + "split": "test" + }, + { + "Input": "the average weight of 20 persons sitting in a boat had some value . a new person added to them whose weight was 46 kg only . due to his arrival , the average weight of all the persons decreased by 5 kg . find the average weight of first 20 persons ?", + "Output Program": [ + "n0 = 20.0\nn1 = 46.0\nn2 = 5.0\nn3 = 20.0\nt0 = n0 + 1.0\nt1 = n2 * t0\nanswer = t1 - n1\nprint(answer)" + ], + "Output Answer": [ + "59" + ], + "split": "test" + }, + { + "Input": "half a number plus 7 is 11 . what is the number ?", + "Output Program": [ + "n0 = 7.0\nn1 = 11.0\nt0 = n1 - n0\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "test" + }, + { + "Input": "of the total amount that jill spent on a shopping trip , excluding taxes , she spent 25 percent on clothing , 25 percent on food , and 50 percent on other items . if jill paid a 10 percent tax on the clothing , no tax on the food , and an 2 percent tax on all other items , then the total tax that she paid was what percent of the total amount that she spent , excluding taxes ?", + "Output Program": [ + "n0 = 25.0\nn1 = 25.0\nn2 = 50.0\nn3 = 10.0\nn4 = 2.0\nt0 = n3 / 100.0\nt1 = n4 / 100.0\nt2 = n0 * t0\nt3 = n2 * t1\nt4 = t2 + t3\nt5 = t4 / 100.0\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "3.5000000000000004" + ], + "split": "test" + }, + { + "Input": "how many 1 / 6 s are there in 37 1 / 2 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 6.0\nn2 = 37.0\nn3 = 1.0\nn4 = 2.0\nt0 = n0 / n4\nt1 = n0 / n1\nt2 = n2 + t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "225" + ], + "split": "test" + }, + { + "Input": "if sharon ' s weekly salary increased by 15 percent , she would earn $ 460 per week . if instead , her weekly salary were to increase by 10 percent , how much would she earn per week ?", + "Output Program": [ + "n0 = 15.0\nn1 = 460.0\nn2 = 10.0\nt0 = n0 / 100.0\nt1 = n2 / 100.0\nt2 = t0 + 1.0\nt3 = n1 / t2\nt4 = t1 * t3\nanswer = t3 + t4\nprint(answer)" + ], + "Output Answer": [ + "440.00000000000006" + ], + "split": "test" + }, + { + "Input": "the difference of 2 digit number & the number obtained by interchanging the digits is 36 . what is the difference the sum and the number if the ratio between the digits of the number is 1 : 2 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 36.0\nn2 = 1.0\nn3 = 2.0\nt0 = n0 * 10.0\nt1 = t0 - 10.0\nt2 = t1 - 1.0\nt3 = n1 / t2\nt4 = n0 * t3\nt5 = t3 + t4\nt6 = t4 - t3\nanswer = t5 - t6\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "test" + }, + { + "Input": "if the average ( arithmetic mean ) of a and b is 100 , and the average of b and c is 160 , what is the value of a \u2212 c ?", + "Output Program": [ + "n0 = 100.0\nn1 = 160.0\nt0 = n1 * 2.0\nt1 = n0 * 2.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "test" + }, + { + "Input": "if n = 2 ^ 0.20 and n ^ b = 16 , b must equal", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 0.2\nn2 = 16.0\nt0 = math.log(max(1e-5, n2), 2)\nt1 = n0**min(n1, 5)\nt2 = math.log(max(1e-5, t1), 2)\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "19.99999999999999" + ], + "split": "test" + }, + { + "Input": "find the average of all the number between 6 and 34 which are divisible by 5 .", + "Output Program": [ + "n0 = 6.0\nn1 = 34.0\nn2 = 5.0\nt0 = n0 + 4.0\nt1 = n1 - 4.0\nt2 = t0 + t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "test" + }, + { + "Input": "oil cans x and y are right circular cylinders and the height and radius of y are each 5 times those of x . if the oil in can x filled to capacity sells for $ 1 , how much does the oil in y sell for if y is only 1 / 5 th filled ?", + "Output Program": [ + "n0 = 5.0\nn1 = 1.0\nn2 = 1.0\nn3 = 5.0\nt0 = n0**min(n1, 5)\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "test" + }, + { + "Input": "cindy has her eye on a sundress but thinks it is too expensive . it goes on sale for 15 % less than the original price . before cindy can buy the dress , however , the store raises the new price by 25 % . if the dress cost $ 51 after it went on sale for 15 % off , what is the difference between the original price and the final price ?", + "Output Program": [ + "n0 = 15.0\nn1 = 25.0\nn2 = 51.0\nn3 = 15.0\nt0 = n1 + 100.0\nt1 = 100.0 - n0\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = n2 / t3\nt5 = n2 * t2\nanswer = t5 - t4\nprint(answer)" + ], + "Output Answer": [ + "3.75" + ], + "split": "test" + }, + { + "Input": "a grocer has a sale of rs . 4435 , rs . 4927 , rs . 4855 , rs . 5230 and rs . 4562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 4500 ?", + "Output Program": [ + "n0 = 4435.0\nn1 = 4927.0\nn2 = 4855.0\nn3 = 5230.0\nn4 = 4562.0\nn5 = 5.0\nn6 = 4500.0\nt0 = n5 + 1.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n6 * t0\nt4 = n3 + t2\nt5 = n4 + t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "2991" + ], + "split": "test" + }, + { + "Input": "what is the sum of all 3 digit integers formed using the digits 34 and 5 ( repetition is allowed )", + "Output Program": [ + "n0 = 3.0\nn1 = 34.0\nn2 = 5.0\nt0 = 10.0 + 100.0\nt1 = n0 + n2\nt2 = 3.0**min(2.0, 5)\nt3 = t0 + 1.0\nt4 = t1 + 4.0\nt5 = t3 * t4\nanswer = t5 * t2\nprint(answer)" + ], + "Output Answer": [ + "11988" + ], + "split": "test" + }, + { + "Input": "there are 6 people in the elevator . their average weight is 150 lbs . another person enters the elevator , and increases the average weight to 151 lbs . what is the weight of the 7 th person .", + "Output Program": [ + "n0 = 6.0\nn1 = 150.0\nn2 = 151.0\nn3 = 7.0\nt0 = n2 * n3\nt1 = n0 * n1\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "157" + ], + "split": "test" + }, + { + "Input": "average of money that group of 4 friends pay for rent each month is $ 800 . after one persons rent is increased by 20 % the new mean is $ 860 . what was original rent of friend whose rent is increased ?", + "Output Program": [ + "n0 = 4.0\nn1 = 800.0\nn2 = 20.0\nn3 = 860.0\nt0 = n2 / 100.0\nt1 = n3 - n1\nt2 = n0 * t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "1200" + ], + "split": "test" + }, + { + "Input": "the average ( arithmetic mean ) of 4 positive integers is 50 . if the average of 2 of these integers is 40 , what is the greatest possible value that one of the other 2 integers can have ?", + "Output Program": [ + "n0 = 4.0\nn1 = 50.0\nn2 = 2.0\nn3 = 40.0\nn4 = 2.0\nt0 = n0 * n1\nt1 = n2 * n3\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "test" + }, + { + "Input": "the average salary of the employees in a office is rs . 120 / month . the avg salary of officers is rs . 460 and of non officers is rs 110 . if the no . of officers is 15 , then find the no of nonofficers in the office .", + "Output Program": [ + "n0 = 120.0\nn1 = 460.0\nn2 = 110.0\nn3 = 15.0\nt0 = n1 * n3\nt1 = n0 * n3\nt2 = n0 - n2\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "510" + ], + "split": "test" + }, + { + "Input": "a cricketer whose bowling average is 12.4 runs per wicket takes 5 wickets for 26 runs and there by decreases his average by 0.4 . the number age of the family now is ?", + "Output Program": [ + "n0 = 12.4\nn1 = 5.0\nn2 = 26.0\nn3 = 0.4\nt0 = n0 - n3\nt1 = n1 * t0\nt2 = t1 - n2\nanswer = t2 / n3\nprint(answer)" + ], + "Output Answer": [ + "85" + ], + "split": "test" + }, + { + "Input": "out of 40 applicants to a law school , 15 majored in political science , 20 had a grade point average higher than 3.0 , and 10 did not major in political science and had a gpa equal to or lower than 3.0 . how many t applicants majored in political science and had a gpa higher than 3.0 ?", + "Output Program": [ + "n0 = 40.0\nn1 = 15.0\nn2 = 20.0\nn3 = 3.0\nn4 = 10.0\nn5 = 3.0\nn6 = 3.0\nt0 = n1 + n4\nt1 = n0 - t0\nanswer = n2 - t1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "test" + }, + { + "Input": "if 5 a = 6 b and ab \u2260 0 , what is the ratio of a / 6 to b / 5 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 6.0\nn2 = 0.0\nn3 = 6.0\nn4 = 5.0\nt0 = n0 * n1\nanswer = t0 / t0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "test" + }, + { + "Input": "a container contains 1000 liters of milk , from this container 10 liters of milk was taken out and replaced by water . this process was repeated further 2 times . how much milk is now contained by the container ?", + "Output Program": [ + "n0 = 1000.0\nn1 = 10.0\nn2 = 2.0\nt0 = n0 - n1\nt1 = t0 - n1\nanswer = t1 - n1\nprint(answer)" + ], + "Output Answer": [ + "970" + ], + "split": "test" + }, + { + "Input": "a and b enterd into a partnership investing rs . 16000 and rs . 12000 respectively . after 3 months , a withdrew rs . 5000 while b invested rs . 5000 more . after 3 more months . c joins the business with a capital of rs . 21000 . the share of b exceeds that of c , out of a total profit of rs . 26400 after one year by", + "Output Program": [ + "n0 = 16000.0\nn1 = 12000.0\nn2 = 3.0\nn3 = 5000.0\nn4 = 5000.0\nn5 = 3.0\nn6 = 21000.0\nn7 = 26400.0\nt0 = n1 + n3\nt1 = n1 * n2\nt2 = n0 * n2\nt3 = 12.0 - n2\nt4 = n0 - n3\nt5 = t0 * t3\nt6 = t4 * t3\nt7 = t3 - n2\nt8 = t1 + t5\nt9 = t2 + t6\nt10 = n6 * t7\nt11 = t9 + t8\nt12 = t11 + t10\nt13 = t8 / t12\nt14 = t10 / t12\nt15 = n7 * t13\nt16 = n7 * t14\nanswer = t15 - t16\nprint(answer)" + ], + "Output Answer": [ + "3600.000000000001" + ], + "split": "test" + }, + { + "Input": "dan ' s age after 16 years will be 6 times his age 4 years ago . what is the present age of dan ?", + "Output Program": [ + "n0 = 16.0\nn1 = 6.0\nn2 = 4.0\nt0 = n1 * n2\nt1 = n1 - 1.0\nt2 = n0 + t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "test" + }, + { + "Input": "if ( 18 ^ a ) * 9 ^ ( 3 a \u2013 1 ) = ( 2 ^ 3 ) ( 3 ^ b ) and a and b are positive integers , what is the value of a ?", + "Output Program": [ + "n0 = 18.0\nn1 = 9.0\nn2 = 3.0\nn3 = 1.0\nn4 = 2.0\nn5 = 3.0\nn6 = 3.0\n\nanswer = n2 * n3\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "test" + }, + { + "Input": "average between two sets of numbers is closer to the set with morenumbers ?", + "Output Program": [ + "t0 = 2.0 * 4.0\nanswer = t0 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "test" + }, + { + "Input": "the average of runs of a cricket player of 10 innings was 34 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?", + "Output Program": [ + "n0 = 10.0\nn1 = 34.0\nn2 = 4.0\nt0 = n0 + 1.0\nt1 = n1 + n2\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "78" + ], + "split": "test" + }, + { + "Input": "a , b and c play a cricket match . the ratio of the runs scored by them in the match is a : b = 2 : 3 and b : c = 2 : 5 . if the total runs scored by all of them are 75 , the runs scored by b are ? a . 15 b . 18", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 2.0\nn3 = 5.0\nn4 = 75.0\nn5 = 15.0\nn6 = 18.0\nt0 = n0 / n3\nt1 = n0 / n1\nt2 = t1 * t0\nt3 = t0 + t2\nt4 = t3 + 1.0\nt5 = n4 / t4\nanswer = t5 * t0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "test" + }, + { + "Input": "the average ( arithmetic mean ) of 20 , 40 , and 60 is 6 more than the average of 10 , 70 , and what number ?", + "Output Program": [ + "n0 = 20.0\nn1 = 40.0\nn2 = 60.0\nn3 = 6.0\nn4 = 10.0\nn5 = 70.0\nt0 = n0 + n1\nt1 = n3 * 3.0\nt2 = n2 + t0\nt3 = n4 + t1\nt4 = n5 + t3\nanswer = t2 - t4\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "test" + }, + { + "Input": "the average height of 20 students in a class was calculated as 175 cm . it has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 131 cm . what was the actual average height of the students in the class ?", + "Output Program": [ + "n0 = 20.0\nn1 = 175.0\nn2 = 151.0\nn3 = 131.0\nt0 = n0 * n1\nt1 = n2 - n3\nt2 = t0 - t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "174" + ], + "split": "test" + }, + { + "Input": "mr yadav spends 60 % of his monthly salary on consumable items and 50 % of the remaining on clothes and transport . he saves the remaining amount . if his savings at the end of the year were 24000 , how much amount per month would he have spent on clothes and transport ?", + "Output Program": [ + "n0 = 60.0\nn1 = 50.0\nn2 = 24000.0\nt0 = 3.0 * 4.0\nt1 = 100.0 - n0\nt2 = n1 * t1\nt3 = t2 / 100.0\nt4 = t3 / 100.0\nt5 = n2 / t4\nt6 = t5 / t0\nanswer = t6 * t4\nprint(answer)" + ], + "Output Answer": [ + "2000" + ], + "split": "test" + }, + { + "Input": "10 camels cost as much as 24 horses , 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants . if the cost of 10 elephants is rs . 170000 , find the cost of a camel ?", + "Output Program": [ + "n0 = 10.0\nn1 = 24.0\nn2 = 16.0\nn3 = 4.0\nn4 = 6.0\nn5 = 4.0\nn6 = 10.0\nn7 = 170000.0\nt0 = n1 * n3\nt1 = n0 * n2\nt2 = n3 * t0\nt3 = n4 * t1\nt4 = n7 * t2\nt5 = n0 * t3\nanswer = t4 / t5\nprint(answer)" + ], + "Output Answer": [ + "6800" + ], + "split": "test" + }, + { + "Input": "when the positive integer k is divided by the positive integer n , the remainder is 11 . if k / n = 81.1 , what is the value of n ?", + "Output Program": [ + "n0 = 11.0\nn1 = 81.1\nt0 = 2.0 / 10.0\nt1 = n1 * 10.0\nt2 = n0 / t0\nt3 = t1 - 2.0\nt4 = t3 / 10.0\nt5 = t4 * t2\nt6 = n0 + t5\nanswer = t6 / t2\nprint(answer)" + ], + "Output Answer": [ + "81.1" + ], + "split": "test" + }, + { + "Input": "if a person walks at 10 km / hr instead of 8 km / hr , he would have walked 14 km more . the actual distance traveled by him is ?", + "Output Program": [ + "n0 = 10.0\nn1 = 8.0\nn2 = 14.0\nt0 = n0 - n1\nt1 = n2 / t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "test" + }, + { + "Input": "3 people candidates contested an election and they received 1136 , 7636 and 11628 votes respectively . what is the percentage of the total votes did the winning candidate get ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1136.0\nn2 = 7636.0\nn3 = 11628.0\nt0 = n1 + n2\nt1 = n3 + t0\nt2 = n3 / t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "56.99999999999999" + ], + "split": "test" + }, + { + "Input": "a and b started a business jointly a ' s investment was thrice the investment of b and the period of his investment was two times the period of investment of b . if b received rs . 4000 as profit , then their total profit is", + "Output Program": [ + "n0 = 4000.0\nt0 = 2.0 * 3.0\nt1 = t0 + 1.0\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "28000" + ], + "split": "test" + }, + { + "Input": "excluding stoppages , the average speed of a bus is 100 km / hr and including stoppages , the average speed of the bus is 40 km / hr . for how many minutes does the bus stop per hour ?", + "Output Program": [ + "n0 = 100.0\nn1 = 40.0\nt0 = n1 / n0\nt1 = 1.0 * 60.0\nt2 = t0 * 60.0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "test" + }, + { + "Input": "the general hospital is comprised of , 3 / 5 pediatricians , 1 / 4 surgeons , and the rest are gp doctors . if 1 / 4 of the surgeons are heart surgeons , and the hospital doubles the number of gp doctors , what proportion of the hospital are now heart surgeons ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 1.0\nn3 = 4.0\nn4 = 1.0\nn5 = 4.0\nt0 = n2 + n2\nt1 = n1 * n3\nt2 = n3 + t1\nt3 = n0 - t0\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.041666666666666664" + ], + "split": "test" + }, + { + "Input": "a corporation 5 times its annual bonus to 10 of its employees . what percent of the employees \u2019 new bonus is the increase ?", + "Output Program": [ + "n0 = 5.0\nn1 = 10.0\nt0 = n0 - 1.0\nt1 = t0 / n0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "test" + }, + { + "Input": "the sum of ages of 5 children born at the intervals of 3 years each is 50 years . what is the age of the youngest child ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nn2 = 50.0\nt0 = n2 / n0\nt1 = t0 - n1\nanswer = t1 - n1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "test" + }, + { + "Input": "yearly subscription to professional magazines cost a company $ 940.00 . to make a 25 % cut in the magazine budget , how much less must be spent ?", + "Output Program": [ + "n0 = 940.0\nn1 = 25.0\nt0 = 100.0 - n1\nt1 = t0 / 100.0\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "705" + ], + "split": "test" + }, + { + "Input": "the mean of 50 observations was 40 . it was found later that an observation 48 was wrongly taken as 23 . the corrected new mean is", + "Output Program": [ + "n0 = 50.0\nn1 = 40.0\nn2 = 48.0\nn3 = 23.0\nt0 = n0 * n1\nt1 = n0 - 2.0\nt2 = t1 - n3\nt3 = t0 + t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "40.5" + ], + "split": "test" + }, + { + "Input": "a certain tests consists 8 sections with 25 questions , numbered from 1 to 25 , in each section . if a student answered all of the even - numbered questions correctly and 3 / 4 of the odd - numbered questions correctly , what was the total number of questions he answered correctly ? a . 150 b . 172 c . 174 d . 175 e . 176", + "Output Program": [ + "n0 = 8.0\nn1 = 25.0\nn2 = 1.0\nn3 = 25.0\nn4 = 3.0\nn5 = 4.0\nn6 = 150.0\nn7 = 172.0\nn8 = 174.0\nn9 = 175.0\nn10 = 176.0\nt0 = n4 / n5\nt1 = n0 * n1\nt2 = t1 / 2.0\nt3 = t2 * t0\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "175" + ], + "split": "test" + }, + { + "Input": "when greenville state university decided to move its fine arts collection to a new library , it had to package the collection in 20 - inch by 20 - inch by 15 - inch boxes . if the university pays $ 0.60 for every box , and if the university needs 3.06 million cubic inches to package the collection , what is the minimum amount the university must spend on boxes ?", + "Output Program": [ + "n0 = 20.0\nn1 = 20.0\nn2 = 15.0\nn3 = 0.6\nn4 = 3.06\nt0 = 1000.0 * 1000.0\nt1 = n0 * n0\nt2 = n4 * t0\nt3 = n2 * t1\nt4 = t2 / t3\nanswer = n3 * t4\nprint(answer)" + ], + "Output Answer": [ + "306" + ], + "split": "test" + }, + { + "Input": "the sum of ages of 5 children born at the intervals of 3 years each is 80 years . what is the age of the youngest child ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nn2 = 80.0\nt0 = n2 / n0\nt1 = t0 - n1\nanswer = t1 - n1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "test" + }, + { + "Input": "a no . when divided by the sum of 555 and 445 gives 2 times their difference as quotient & 10 as remainder . find the no . is ?", + "Output Program": [ + "n0 = 555.0\nn1 = 445.0\nn2 = 2.0\nn3 = 10.0\nt0 = n0 + n1\nt1 = n0 - n1\nt2 = n2 * t0\nt3 = t2 * t1\nanswer = n3 + t3\nprint(answer)" + ], + "Output Answer": [ + "220010" + ], + "split": "test" + }, + { + "Input": "john has $ 1600 at the beginning of his trip , after spending money , he still has exactly $ 600 less than he spent on the trip . how much money does john still have ?", + "Output Program": [ + "n0 = 1600.0\nn1 = 600.0\nt0 = n0 - n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "test" + }, + { + "Input": "students at a school were on average 180 cm tall . the average female height was 170 cm , and the average male height was 181 cms . what was the ratio of men to women ?", + "Output Program": [ + "n0 = 180.0\nn1 = 170.0\nn2 = 181.0\nt0 = n0 - n1\nt1 = n2 - n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "test" + }, + { + "Input": "if 50 % of ( x - y ) = 30 % of ( x + y ) then what percent of x is y ?", + "Output Program": [ + "n0 = 50.0\nn1 = 30.0\nt0 = n0 + n1\nt1 = n0 - n1\nt2 = t1 / t0\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "test" + }, + { + "Input": "a no . when divided by the sum of 555 and 445 gives 2 times their difference as quotient & 60 as remainder . find the no . is ?", + "Output Program": [ + "n0 = 555.0\nn1 = 445.0\nn2 = 2.0\nn3 = 60.0\nt0 = n0 + n1\nt1 = n0 - n1\nt2 = n2 * t0\nt3 = t2 * t1\nanswer = n3 + t3\nprint(answer)" + ], + "Output Answer": [ + "220060" + ], + "split": "test" + }, + { + "Input": "if an integer n is to be selected at random from 1 to 100 , inclusive , what is probability n ( n + 1 ) will be divisible by 32 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 100.0\nn2 = 1.0\nn3 = 32.0\n\nanswer = 2.0 / n3\nprint(answer)" + ], + "Output Answer": [ + "0.0625" + ], + "split": "test" + }, + { + "Input": "today jim is twice as old as fred , and sam is 4 years younger than fred . 4 years ago jim was 8 times as old as sam . how old is jim now ?", + "Output Program": [ + "n0 = 4.0\nn1 = 4.0\nn2 = 8.0\nt0 = n2 * n2\nt1 = n2 - 2.0\nt2 = t0 - n0\nt3 = t2 / t1\nanswer = t3 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "test" + }, + { + "Input": "a store sells 2 kinds of jelly beans mixes ( a and b ) both made up of red and yellow beans . if b contains 20 % more red beans than a but 10 % fewer yellow beans . and jar a contains twice as many red beans as yellow by what percent is the number of beans in jar b larger than the number in jar a", + "Output Program": [ + "n0 = 2.0\nn1 = 20.0\nn2 = 10.0\nt0 = n1 + 100.0\nt1 = 100.0 - n2\nt2 = t0 + t1\nt3 = t2 / 100.0\nt4 = t3 - 2.0\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "10.000000000000009" + ], + "split": "test" + }, + { + "Input": "when 242 is divided by a certain divisor the remainder obtained is 12 . when 698 is divided by the same divisor the remainder obtained is 16 . however , when the sum of the two numbers 242 and 698 is divided by the divisor , the remainder obtained is 10 . what is the value of the divisor ?", + "Output Program": [ + "n0 = 242.0\nn1 = 12.0\nn2 = 698.0\nn3 = 16.0\nn4 = 242.0\nn5 = 698.0\nn6 = 10.0\nt0 = n1 + n3\nanswer = t0 - n6\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "test" + }, + { + "Input": "a and b start a business jointly . a invests rs 16000 for 8 month and b remains in the business for 4 months . out of total profit , b claims 2 / 7 of the profit . how much money was contributed by b ?", + "Output Program": [ + "n0 = 16000.0\nn1 = 8.0\nn2 = 4.0\nn3 = 2.0\nn4 = 7.0\nt0 = n2 + 1.0\nt1 = n1 / n2\nt2 = n0 * n1\nt3 = t1 * t2\nt4 = n2 * t0\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "12800" + ], + "split": "test" + }, + { + "Input": "two employees x and y are paid a total of rs . 440 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?", + "Output Program": [ + "n0 = 440.0\nn1 = 120.0\nt0 = 1.0 + 4.0\nt1 = t0 * 2.0\nt2 = t1 + 1.0\nt3 = n0 * t1\nt4 = t2 * 2.0\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "test" + }, + { + "Input": "how many gallons of milk that is 10 percent butter - fat must be added to 8 gallons of milk that is 25 percent butterfat to obtain milk that is 20 percent butterfat ?", + "Output Program": [ + "n0 = 10.0\nn1 = 8.0\nn2 = 25.0\nn3 = 20.0\nt0 = n2 - n3\nt1 = n1 * t0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "test" + }, + { + "Input": "a envelop weight 8.5 gm , if 820 of these envelop are sent with an advertisement mail . how much wieght ?", + "Output Program": [ + "n0 = 8.5\nn1 = 820.0\nt0 = n0 * n1\nanswer = t0 / 1000.0\nprint(answer)" + ], + "Output Answer": [ + "6.97" + ], + "split": "test" + }, + { + "Input": "there are 16 bees in the hive , then 6 more fly . how many bees are there in all ?", + "Output Program": [ + "n0 = 16.0\nn1 = 6.0\n\nanswer = n0 + n1\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "test" + }, + { + "Input": "find the constant k so that : - x 2 - ( k + 8 ) x - 8 = - ( x - 2 ) ( x - 4 )", + "Output Program": [ + "n0 = 2.0\nn1 = 8.0\nn2 = 8.0\nn3 = 2.0\nn4 = 4.0\nt0 = n0 + n4\nanswer = n1 + t0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "test" + }, + { + "Input": "two ants , arthur and amy , have discovered a picnic and are bringing crumbs back to the anthill . amy makes twice as many trips and carries one and a half times as many crumbs per trip as arthur . if arthur carries a total of b crumbs to the anthill , how many crumbs will amy bring to the anthill , in terms of b ?", + "Output Program": [ + "t0 = 1.0 / 2.0\nt1 = t0 + 1.0\nanswer = t1 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "test" + }, + { + "Input": "a certain number of badges were distributed among a class of students . the student who got 1 / 6 th of the total number of badges actually got 5 times the average number of badges the others got ! how many students were there in the class ?", + "Output Program": [ + "n0 = 1.0\nn1 = 6.0\nn2 = 5.0\nt0 = n1 * n2\nt1 = t0 - n2\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "test" + }, + { + "Input": "tough and tricky questions : work / rate problems . a group of 4 junior lawyers require 7 hours to complete a legal research assignment . how many hours would it take a group of 3 legal assistants to complete the same research assignment assuming that a legal assistant works at two - thirds the rate of a junior lawyer ? source : chili hot gmat", + "Output Program": [ + "n0 = 4.0\nn1 = 7.0\nn2 = 3.0\nt0 = 2.0 / 3.0\nt1 = n2 * t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "test" + }, + { + "Input": "if x and y are numbers such that ( x + 6 ) ( y - 6 ) = 0 , what is the smallest possible value of x ^ 2 + y ^ 2", + "Output Program": [ + "n0 = 6.0\nn1 = 6.0\nn2 = 0.0\nn3 = 2.0\nn4 = 2.0\n\nanswer = n0**min(n3, 5)\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "test" + }, + { + "Input": "the difference of a larger number and a smaller number is 6 . the sum of the larger number and twice the smaller is 15 . what is the larger number ?", + "Output Program": [ + "n0 = 6.0\nn1 = 15.0\nt0 = 1.0 + 2.0\nt1 = n0 * 2.0\nt2 = n1 + t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "test" + }, + { + "Input": "a vessel of capacity 2 litre has 16 % of alcohol and another vessel of capacity 6 litre had 40 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?", + "Output Program": [ + "n0 = 2.0\nn1 = 16.0\nn2 = 6.0\nn3 = 40.0\nn4 = 8.0\nn5 = 10.0\nt0 = n1 / 100.0\nt1 = n3 / 100.0\nt2 = n0 * t0\nt3 = n2 * t1\nt4 = t2 + t3\nt5 = t4 / n5\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "27.200000000000003" + ], + "split": "test" + }, + { + "Input": "there are 3 prizes to be distributed among 10 students . if no students gets more than one prize , then this can be done in ?", + "Output Program": [ + "n0 = 3.0\nn1 = 10.0\nt0 = n0 * n1\nt1 = n1 - 1.0\nt2 = n1 * t1\nanswer = t0 + t2\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "test" + }, + { + "Input": "a student got 72 % in math and 82 % in history . to get an overall average of 75 % , how much should the student get in the third subject ?", + "Output Program": [ + "n0 = 72.0\nn1 = 82.0\nn2 = 75.0\nt0 = n0 + n1\nt1 = n2 * 3.0\nanswer = t1 - t0\nprint(answer)" + ], + "Output Answer": [ + "71" + ], + "split": "test" + }, + { + "Input": "a person travels from p to q a speed of 60 km / hr and returns by increasing his speed by 20 % . what is his average speed for both the trips ?", + "Output Program": [ + "n0 = 60.0\nn1 = 20.0\nt0 = n1 / 100.0\nt1 = t0 + 1.0\nt2 = n0 * t1\nt3 = n0 + t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "66" + ], + "split": "test" + }, + { + "Input": "a student was asked to find 4 / 5 of a number . but the student divided the number by 4 / 5 , thus the student got 9 more than the correct answer . find the number .", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 4.0\nn3 = 5.0\nn4 = 9.0\nt0 = n0 / n1\nt1 = n4 * t0\nt2 = t0 * t0\nt3 = t0 * t1\nt4 = 1.0 - t2\nt5 = t3 / t4\nanswer = t5 / t0\nprint(answer)" + ], + "Output Answer": [ + "20.000000000000007" + ], + "split": "test" + }, + { + "Input": "if jake loses 8 pounds , he will weigh twice as much as his sister kendra . together they now weigh 284 pounds . what is jake \u2019 s present weight , in pounds ?", + "Output Program": [ + "n0 = 8.0\nn1 = 284.0\nt0 = n1 - n0\nt1 = t0 / 3.0\nt2 = t1 * 2.0\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "192" + ], + "split": "test" + }, + { + "Input": "a man is 30 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is", + "Output Program": [ + "n0 = 30.0\nt0 = 2.0 * 2.0\nt1 = 2.0 - 1.0\nt2 = t0 - 2.0\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "test" + }, + { + "Input": "n = 1 ! + 2 ! + 3 ! . . . . . + 10 ! . what is the last digit of n ^ n ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 3.0\nn3 = 10.0\nt0 = n3 - n2\nanswer = t0**min(1.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "test" + }, + { + "Input": "set s contains exactly 10 numbers and has an average ( arithmetic mean ) of 6.2 . if one of the numbers in set s is increased by 3 , while all other numbers remain the same , what is the new average of set s ?", + "Output Program": [ + "n0 = 10.0\nn1 = 6.2\nn2 = 3.0\nt0 = n0 * n1\nt1 = n2 + t0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "6.5" + ], + "split": "test" + }, + { + "Input": "what is the area inscribed by the lines y = 2 , x = 2 , y = 10 - x on an xy - coordinate plane ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 10.0\nt0 = 0.25 * 2.0\nt1 = n2 - n0\nt2 = t1 - n0\nt3 = t0 * t2\nanswer = t3 * t2\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "test" + }, + { + "Input": "if n is a positive integer , what is the remainder when ( 4 ^ ( 4 n + 3 ) ) ( 6 ^ n ) is divided by 10 ?", + "Output Program": [ + "n0 = 4.0\nn1 = 4.0\nn2 = 3.0\nn3 = 6.0\nn4 = 10.0\nt0 = 3.0 * 3.0\nt1 = n3 * t0\nanswer = t1 % n4\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "test" + }, + { + "Input": "when tossed , a certain coin has equal probability of landing on either side . if the coin is tossed 4 times , what is the probability that it will land twice on heads and twice tails ?", + "Output Program": [ + "n0 = 4.0\nt0 = 2.0**min(n0, 5)\nanswer = 1.0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.0625" + ], + "split": "test" + }, + { + "Input": "mary ' s income is 60 percent more than tim ' s income , and tim ' s income is 50 percent less than juan ' s income . what percent of juan ' s income is mary ' s income ?", + "Output Program": [ + "n0 = 60.0\nn1 = 50.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = t0 + 1.0\nt3 = 1.0 - t1\nt4 = t2 * t3\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "test" + }, + { + "Input": "the circumferences of the fore and hind - wheels of a carriage are 2 2 / 5 and 3 3 / 7 meters respectively . a chalk mark is put on the point of contact of each wheel with the ground at any given moment . how far will the carriage have travelled so that their chalk marks may be again on the ground at the same time ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 5.0\nn3 = 3.0\nn4 = 3.0\nn5 = 7.0\nt0 = n3 * n5\nanswer = n3 + t0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "test" + }, + { + "Input": "a 100 - litre mixture of milk and water contains 30.25 litres of milk . ' x ' litres of this mixture is removed and replaced with an equal quantum of water . if the process is repeated once , then the concentration of the milk stands reduced at 25 % . what is the value of x ?", + "Output Program": [ + "import math\nn0 = 100.0\nn1 = 30.25\nn2 = 25.0\nt0 = n2 / n1\nt1 = math.sqrt(max(0, t0))\nt2 = 1.0 - t1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "9.090909090909093" + ], + "split": "test" + }, + { + "Input": "m and n are the x and y coordinates , respectively , of a point in the coordinate plane . if the points ( m , n ) and ( m + p , n + 12 ) both lie on the line defined by the equation x = ( y / 4 ) - ( 2 / 5 ) , what is the value of p ?", + "Output Program": [ + "n0 = 12.0\nn1 = 4.0\nn2 = 2.0\nn3 = 5.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "test" + }, + { + "Input": "the equation of line a is y = 4 / 3 * x - 100 . what is the smallest possible distance in the xy - plane from the point with coordinates ( 0 , 0 ) to any point on line a ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 3.0\nn2 = 100.0\nn3 = 0.0\nn4 = 0.0\nt0 = n1 * n2\nt1 = n0**min(2.0, 5)\nt2 = n1**min(2.0, 5)\nt3 = t1 + t2\nt4 = math.sqrt(max(0, t3))\nanswer = t0 / t4\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "test" + }, + { + "Input": "the average age of applicants for a new job is 31 , with a standard deviation of 6 . the hiring manager is only willing to accept applications whose age is within one standard deviation of the average age . what is the maximum number of different ages of the applicants ?", + "Output Program": [ + "n0 = 31.0\nn1 = 6.0\nt0 = n1 * 2.0\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "test" + }, + { + "Input": "in the faculty of reverse - engineering , 226 second year students study numeric methods , 423 second year students study automatic control of airborne vehicles and 134 second year students study them both . how many students are there in the faculty if the second year students are approximately 80 % of the total ?", + "Output Program": [ + "n0 = 226.0\nn1 = 423.0\nn2 = 134.0\nn3 = 80.0\n\nanswer = n0 + n1\nprint(answer)" + ], + "Output Answer": [ + "649" + ], + "split": "test" + }, + { + "Input": "the average of 5 quantities is 9 . the average of 3 of them is 4 . what is the average of remaining 2 numbers ?", + "Output Program": [ + "n0 = 5.0\nn1 = 9.0\nn2 = 3.0\nn3 = 4.0\nn4 = 2.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = t0 - t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "16.5" + ], + "split": "test" + }, + { + "Input": "the average height of 30 students in a class was calculated as 177 cm . it has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 106 cm . what was the actual average height of the students in the class ?", + "Output Program": [ + "n0 = 30.0\nn1 = 177.0\nn2 = 151.0\nn3 = 106.0\nt0 = n0 * n1\nt1 = n2 - n3\nt2 = t0 - t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "175.5" + ], + "split": "test" + }, + { + "Input": "the average temperature for monday , tuesday and wednsday is 36.3 degrees c . the average temperature for tuesday , wednesday and thursday is 36.7 degrees c . if monday \u2019 s temperature recorded as 39 degrees c , find the thursday \u2019 s temperature ?", + "Output Program": [ + "n0 = 36.3\nn1 = 36.7\nn2 = 39.0\nt0 = n1 * 3.0\nt1 = n0 * 3.0\nt2 = t1 - n2\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "40.20000000000002" + ], + "split": "test" + }, + { + "Input": "a palindrome is a number that reads the same forward and backward , such as 343 . how many odd , 6 - digit numbers are palindromes ?", + "Output Program": [ + "n0 = 343.0\nn1 = 6.0\nt0 = n1 / 2.0\nt1 = 10.0**min(t0, 5)\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "test" + }, + { + "Input": "p , q and r have $ 6000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?", + "Output Program": [ + "n0 = 6000.0\nt0 = 2.0 * 2.0\nt1 = 1.0 * 3.0\nt2 = t0 / 3.0\nt3 = n0 * t0\nt4 = t2 * 3.0\nt5 = t4 + t1\nt6 = t5 + t1\nanswer = t3 / t6\nprint(answer)" + ], + "Output Answer": [ + "2400" + ], + "split": "test" + }, + { + "Input": "light glows for every 15 seconds . how many max . times did it glow between 1 : 57 : 58 and 3 : 20 : 47 am .", + "Output Program": [ + "n0 = 15.0\nn1 = 1.0\nn2 = 57.0\nn3 = 58.0\nn4 = 3.0\nn5 = 20.0\nn6 = 47.0\nt0 = n6 + 2.0\nt1 = 2.0 + 60.0\nt2 = n5 + t1\nt3 = t2 * 60.0\nt4 = t0 + t3\nanswer = t4 / n0\nprint(answer)" + ], + "Output Answer": [ + "331.26666666666665" + ], + "split": "test" + }, + { + "Input": "a sum of money lent out at s . i . amounts to rs . 820 after 2 years and to rs . 1020 after a further period of 5 years . the sum is ?", + "Output Program": [ + "n0 = 820.0\nn1 = 2.0\nn2 = 1020.0\nn3 = 5.0\nt0 = n2 - n0\nt1 = t0 / n3\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "740" + ], + "split": "test" + }, + { + "Input": "a business executive and his client are charging their dinner tab on the executive ' s expense account . the company will only allow them to spend a total of 60 $ for the meal . assuming that they will pay 7 % in sales tax for the meal and leave a 15 % tip , what is the most their food can cost ?", + "Output Program": [ + "n0 = 60.0\nn1 = 7.0\nn2 = 15.0\nt0 = n1 + n2\nt1 = t0 / 100.0\nt2 = t1 + 1.0\nanswer = n0 / t2\nprint(answer)" + ], + "Output Answer": [ + "49.18032786885246" + ], + "split": "test" + }, + { + "Input": "for 2 consecutive yrs , my incomes are in the ratio of 4 : 7 and expenses in the ratio of 3 : 5 . if my income in the 2 nd yr is rs . 42000 & my expenses in the first yr in rs . 21000 , my total savings for the two - year is", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 7.0\nn3 = 3.0\nn4 = 5.0\nn5 = 2.0\nn6 = 42000.0\nn7 = 21000.0\nt0 = n4 * n7\nt1 = n1 * n6\nt2 = t0 / n3\nt3 = t1 / n2\nt4 = n6 - t2\nt5 = t3 - n7\nanswer = t4 + t5\nprint(answer)" + ], + "Output Answer": [ + "10000" + ], + "split": "test" + }, + { + "Input": "the captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ?", + "Output Program": [ + "n0 = 11.0\nn1 = 26.0\nn2 = 3.0\nt0 = n1 + n2\nt1 = n2 * n2\nt2 = n1 + t0\nt3 = t2 - t1\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "test" + }, + { + "Input": "- 24 * 29 + 1240 = ?", + "Output Program": [ + "n0 = 24.0\nn1 = 29.0\nn2 = 1240.0\nt0 = -n0\nt1 = n1 * t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "544" + ], + "split": "test" + }, + { + "Input": "if a randomly selected non - negative single digit integer is added to { 2 , 3 , 4 , 7 } . what is the probability that the median of the set will increase but the range still remains the same ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 4.0\nn3 = 7.0\n\nanswer = 4.0 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "0.4" + ], + "split": "test" + }, + { + "Input": "a student chose a number , multiplied it by 6 , then subtracted 250 from the result and got 122 . what was the number he chose ?", + "Output Program": [ + "n0 = 6.0\nn1 = 250.0\nn2 = 122.0\nt0 = n1 + n2\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "62" + ], + "split": "test" + }, + { + "Input": "in an election contested by two parties , party d secured 12 % of the total votes more than party r . if party r got 132000 votes , by how many votes did it lose the election ?", + "Output Program": [ + "n0 = 12.0\nn1 = 132000.0\nt0 = 100.0 - n0\nt1 = t0 / 2.0\nt2 = n1 / t1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "36000" + ], + "split": "test" + }, + { + "Input": "a multiple choice test consists of 4 questions , and each question has 5 answer choices . in how many e ways can the test be completed if every question is unanswered ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\n\nanswer = n1**min(n0, 5)\nprint(answer)" + ], + "Output Answer": [ + "625" + ], + "split": "test" + }, + { + "Input": "two employees x and y are paid a total of rs . 660 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?", + "Output Program": [ + "n0 = 660.0\nn1 = 120.0\nt0 = 1.0 + 4.0\nt1 = t0 * 2.0\nt2 = t1 + 1.0\nt3 = n0 * t1\nt4 = t2 * 2.0\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "test" + }, + { + "Input": "the value of x + x ( xx ) when x = 7", + "Output Program": [ + "n0 = 7.0\nt0 = n0 * n0\nt1 = n0 * t0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "350" + ], + "split": "test" + }, + { + "Input": "in a class of 40 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 11 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?", + "Output Program": [ + "n0 = 40.0\nn1 = 2.0\nn2 = 12.0\nn3 = 1.0\nn4 = 11.0\nn5 = 2.0\nn6 = 3.0\nn7 = 2.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n1 * n4\nt3 = t1 + t2\nt4 = n4 + t1\nt5 = n1 + t4\nt6 = n0 - t5\nt7 = t6 - n3\nt8 = n6 * t7\nt9 = t3 + t8\nanswer = t0 - t9\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "test" + }, + { + "Input": "if ( t - 8 ) is a factor of t ^ 2 - kt - 45 , then k =", + "Output Program": [ + "n0 = 8.0\nn1 = 2.0\nn2 = 45.0\n\nanswer = n1 + 10.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "test" + }, + { + "Input": "set a contains all the even numbers between 12 and 50 inclusive . set b contains all the even numbers between 112 and 150 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ?", + "Output Program": [ + "n0 = 12.0\nn1 = 50.0\nn2 = 112.0\nn3 = 150.0\nt0 = n1 - n0\nt1 = n2 - n0\nt2 = t0 / 2.0\nt3 = t2 + 1.0\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "2000" + ], + "split": "test" + }, + { + "Input": "if x / y = 5 / 3 , then ( x + y ) / ( x - y ) = ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\nt0 = n0 + n1\nt1 = n0 - n1\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "test" + }, + { + "Input": "a number , when 35 is subtracted from it , reduces to its 80 percent . what is 4 - fifth of that number ?", + "Output Program": [ + "n0 = 35.0\nn1 = 80.0\nn2 = 4.0\nt0 = 1.0 + 4.0\nt1 = n2 / t0\nt2 = n0 * t0\nanswer = t1 * t2\nprint(answer)" + ], + "Output Answer": [ + "140" + ], + "split": "test" + }, + { + "Input": "a library has an average of 425 visitors on sundays and 325 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :", + "Output Program": [ + "import math\nn0 = 425.0\nn1 = 325.0\nn2 = 30.0\nt0 = 3.0 + 4.0\nt1 = n2 / t0\nt2 = math.floor(t1)\nt3 = t2 + 1.0\nt4 = n0 * t3\nt5 = n2 - t3\nt6 = n1 * t5\nt7 = t4 + t6\nanswer = t7 / n2\nprint(answer)" + ], + "Output Answer": [ + "341.6666666666667" + ], + "split": "test" + }, + { + "Input": "a certain list consists of 21 different numbers . if n is in the list and n is 4 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction q of the sum of the 21 numbers in the list ?", + "Output Program": [ + "n0 = 21.0\nn1 = 4.0\nn2 = 20.0\nn3 = 21.0\nt0 = n2 / n1\nt1 = 1.0 * 1.0\nt2 = n0 + t0\nt3 = t2 / n1\nt4 = t3 * 2.0\nt5 = t4 - n1\nt6 = t5 - 3.0\nanswer = t1 / t6\nprint(answer)" + ], + "Output Answer": [ + "0.16666666666666666" + ], + "split": "test" + }, + { + "Input": "a father said his son , ` ` i was as old as you are at present at the time of your birth . ` ` if the father age is 48 now , the son age 5 years back was", + "Output Program": [ + "n0 = 48.0\nn1 = 5.0\nt0 = n0 / 2.0\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "test" + }, + { + "Input": "if | x - 20 | = 40 what is the sum of all the values of x .", + "Output Program": [ + "n0 = 20.0\nn1 = 40.0\nt0 = n0 + n1\nt1 = n1 - n0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "test" + }, + { + "Input": "mathew is planning a vacation trip to london next year from today for 5 days , he has calculated he would need about $ 3000 for expenses , including a round - trip plane ticket from l . a to london . he nets around $ 1500 monthly in gross income , after all bills are paid , he is left with about $ 350 each month free for whatever he desires . how much money would mathew need to evenly save from his $ 350 to have $ 3000 in his bank within 12 months ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3000.0\nn2 = 1500.0\nn3 = 350.0\nn4 = 350.0\nn5 = 3000.0\nn6 = 12.0\n\nanswer = n1 / n6\nprint(answer)" + ], + "Output Answer": [ + "250" + ], + "split": "test" + }, + { + "Input": "if jake loses 8 pounds , he will weigh twice as much as his sister kendra . together they now weigh 281 pounds . what is jake \u2019 s present weight , in pounds ?", + "Output Program": [ + "n0 = 8.0\nn1 = 281.0\nt0 = n1 - n0\nt1 = t0 / 3.0\nt2 = t1 * 2.0\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "190" + ], + "split": "test" + }, + { + "Input": "2 cow \u2019 s and 5 goats are brought for rs . 1050 . if the average price of a goat be rs . 90 . what is the average price of a cow .", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 1050.0\nn3 = 90.0\nt0 = n1 * n3\nt1 = n2 - t0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "test" + }, + { + "Input": "how many 3 digit positive integers with distinct digits are there , which are not multiples of 10 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 10.0\nt0 = n0 * n0\nt1 = t0 - 1.0\nt2 = t0 * t1\nanswer = t2 * t1\nprint(answer)" + ], + "Output Answer": [ + "576" + ], + "split": "test" + }, + { + "Input": "3 pounds of 05 grass seed contain 1 percent herbicide . a different type of grass seed , 20 , which contains 20 percent herbicide , will be mixed with 3 pounds of 05 grass seed . how much grass seed of type 20 should be added to the 3 pounds of 05 grass seed so that the mixture contains 15 percent herbicide ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 1.0\nn3 = 20.0\nn4 = 20.0\nn5 = 3.0\nn6 = 5.0\nn7 = 20.0\nn8 = 3.0\nn9 = 5.0\nn10 = 15.0\nt0 = n0 * n10\nt1 = n3 - n10\nt2 = t0 - n0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "8.4" + ], + "split": "test" + }, + { + "Input": "if f ( f ( n ) ) + f ( n ) = 2 n + 3 and f ( 0 ) = 1 , what is the value of f ( 2012 ) ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 0.0\nn3 = 1.0\nn4 = 2012.0\n\nanswer = n3 + n4\nprint(answer)" + ], + "Output Answer": [ + "2013" + ], + "split": "test" + }, + { + "Input": "a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 51.84 , the number of the member is the group is :", + "Output Program": [ + "import math\nn0 = 51.84\nt0 = n0 * 100.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "test" + }, + { + "Input": "how many 3 digit number formed by using 23 , 45 , 67 once such that number is divisible by 15 .", + "Output Program": [ + "n0 = 3.0\nn1 = 23.0\nn2 = 45.0\nn3 = 67.0\nn4 = 15.0\nt0 = n2 / n0\nt1 = t0 / n0\nanswer = t1 + 3.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "test" + }, + { + "Input": "how many 3 digit positive integers t exist that when divided by 7 leave a remainder of 5 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 5.0\nt0 = 10.0 + 4.0\nt1 = 10.0 * 100.0\nt2 = n1 * t0\nt3 = t1 - 1.0\nt4 = n2 + t2\nt5 = t3 - t4\nanswer = t5 / n1\nprint(answer)" + ], + "Output Answer": [ + "128" + ], + "split": "test" + }, + { + "Input": "the average of 10 numbers is calculated as 16 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?", + "Output Program": [ + "n0 = 10.0\nn1 = 16.0\nn2 = 36.0\nn3 = 26.0\nt0 = n2 - n3\nt1 = t0 / n0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "test" + }, + { + "Input": "the operation is defined for all integers a and b by the equation ab = ( a - 1 ) ( b - 1 ) . if x 20 = 190 , what is the value of x ?", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 20.0\nn3 = 190.0\nt0 = n2 - n0\nt1 = n3 / t0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "test" + }, + { + "Input": "if the arithmetic mean of seventy 5 numbers is calculated , it is 35 . if each number is increased by 5 , then mean of new number is ?", + "Output Program": [ + "n0 = 5.0\nn1 = 35.0\nn2 = 5.0\n\nanswer = n0 + n1\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "test" + }, + { + "Input": "8873 + x = 13200 , then x is ?", + "Output Program": [ + "n0 = 8873.0\nn1 = 13200.0\n\nanswer = n1 - n0\nprint(answer)" + ], + "Output Answer": [ + "4327" + ], + "split": "test" + }, + { + "Input": "a box contains 8 pairs of shoes ( 16 shoes in total ) . if two shoes are selected at random , what it is the probability that they are matching shoes ?", + "Output Program": [ + "n0 = 8.0\nn1 = 16.0\nt0 = n1 - 1.0\nanswer = 1.0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.06666666666666667" + ], + "split": "test" + }, + { + "Input": "in an exam 80 % of the boys and 40 % of the girls passed . the number of girls who passed is 120 , which is 2 / 3 rd of the number of boys who failed . what is the total number of students who appeared for the exam ?", + "Output Program": [ + "n0 = 80.0\nn1 = 40.0\nn2 = 120.0\nn3 = 2.0\nn4 = 3.0\nt0 = n3 / n4\nt1 = n1 / 100.0\nt2 = 100.0 - n0\nt3 = t2 / 100.0\nt4 = n2 / t1\nt5 = t3 * t0\nt6 = n2 / t5\nanswer = t6 + t4\nprint(answer)" + ], + "Output Answer": [ + "1200" + ], + "split": "test" + }, + { + "Input": "a \u2019 s speed is 25 / 18 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?", + "Output Program": [ + "n0 = 25.0\nn1 = 18.0\nt0 = n0 - n1\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.28" + ], + "split": "test" + }, + { + "Input": "the total of 324 of 20 paise and 25 paise make a sum of rs . 71 . the no of 20 paise coins is", + "Output Program": [ + "n0 = 324.0\nn1 = 20.0\nn2 = 25.0\nn3 = 71.0\nn4 = 20.0\nt0 = n0 * n2\nt1 = n3 * 100.0\nt2 = n2 - n1\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "test" + }, + { + "Input": "if 20 liters of chemical x are added to 80 liters of a mixture that is 15 % chemical x and 85 % chemical y , then what percentage of the resulting mixture is chemical x ?", + "Output Program": [ + "n0 = 20.0\nn1 = 80.0\nn2 = 15.0\nn3 = 85.0\nt0 = n2 / 100.0\nt1 = n1 * t0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "test" + }, + { + "Input": "a set consists of 12 numbers , all are even or multiple of 5 . if 4 numbers are even and 10 numbers are multiple of 5 , how many numbers is multiple of 10 ?", + "Output Program": [ + "n0 = 12.0\nn1 = 5.0\nn2 = 4.0\nn3 = 10.0\nn4 = 5.0\nn5 = 10.0\n\nanswer = n0 - n3\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "test" + }, + { + "Input": "two employees x and y are paid a total of rs . 506 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?", + "Output Program": [ + "n0 = 506.0\nn1 = 120.0\nt0 = 1.0 + 4.0\nt1 = t0 * 2.0\nt2 = t1 + 1.0\nt3 = n0 * t1\nt4 = t2 * 2.0\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "230" + ], + "split": "test" + }, + { + "Input": "the average age of 15 students of a class is 15 years . out of these , the average age of 4 students is 14 years and that of the other 10 students is 16 years . the age of the 15 th student is", + "Output Program": [ + "n0 = 15.0\nn1 = 15.0\nn2 = 4.0\nn3 = 14.0\nn4 = 10.0\nn5 = 16.0\nn6 = 15.0\nt0 = n0 * n0\nt1 = n2 * n3\nt2 = n4 * n5\nt3 = t1 + t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "test" + }, + { + "Input": "a certain sum of money is divided among a , b and c so that for each rs . a has , b has 65 paisa and c 40 paisa . if c ' s share is rs . 40 , find the sum of money ?", + "Output Program": [ + "n0 = 65.0\nn1 = 40.0\nn2 = 40.0\nt0 = n0 + 100.0\nt1 = n2 / n1\nt2 = n1 + t0\nanswer = t2 * t1\nprint(answer)" + ], + "Output Answer": [ + "205" + ], + "split": "test" + }, + { + "Input": "two trains leave the train station at the same time . one train , on the blue line , heads east - while the other , on the red line , heads west . if the train on the blue line averages 40 km / hr and the other train averages 40 km / hr - how long will it take for the trains to be 100 km apart ?", + "Output Program": [ + "n0 = 40.0\nn1 = 40.0\nn2 = 100.0\nt0 = n2 / 2.0\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "1.25" + ], + "split": "test" + }, + { + "Input": "given that 100.48 = x , 100.70 = y and xz = y 2 , then the value of z is close to :", + "Output Program": [ + "n0 = 100.48\nn1 = 100.7\nn2 = 2.0\nt0 = n1 - 100.0\nt1 = n0 - 100.0\nt2 = t0 * 2.0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "2.9166666666666545" + ], + "split": "test" + }, + { + "Input": "how many digits are required to number a book containing 250 pages ?", + "Output Program": [ + "n0 = 250.0\nt0 = 10.0 - 1.0\nt1 = n0 - 100.0\nt2 = t1 + 1.0\nt3 = t0 * 10.0\nt4 = t3 * 2.0\nt5 = t2 * 3.0\nt6 = t4 + t0\nanswer = t6 + t5\nprint(answer)" + ], + "Output Answer": [ + "642" + ], + "split": "test" + }, + { + "Input": "at scratch and dents rent - a - car , it costs $ 34.95 a day plus $ 0.23 per mile to rent a car . at rent - a - lemon , the charge is $ 25.00 a day plus $ 1.31 per mile . if you need to rent a car for 3 days , how many miles ( to nearest tenth ) must you drive for a car from both agencies to cost the same amount ?", + "Output Program": [ + "n0 = 34.95\nn1 = 0.23\nn2 = 25.0\nn3 = 1.31\nn4 = 3.0\nt0 = n0 * n4\nt1 = n2 * n4\nt2 = n3 - n1\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "27.638888888888896" + ], + "split": "test" + }, + { + "Input": "if p is a prime number greater than 3 , find the remainder when p ^ 2 + 16 is divided by 12 .", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 16.0\nn3 = 12.0\nt0 = 1.0 + 4.0\nt1 = n0 * n3\nt2 = t0**min(2.0, 5)\nt3 = n2 + t2\nanswer = t3 - t1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "test" + }, + { + "Input": "if x is 20 percent greater than 55 , then x =", + "Output Program": [ + "n0 = 20.0\nn1 = 55.0\nt0 = n0 / 100.0\nt1 = n1 * t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "66" + ], + "split": "test" + }, + { + "Input": "find the value of 72519 x 9999 = y ?", + "Output Program": [ + "n0 = 72519.0\nn1 = 9999.0\nt0 = n1 - 4.0\nanswer = t0 * n0\nprint(answer)" + ], + "Output Answer": [ + "724827405" + ], + "split": "test" + }, + { + "Input": "average of 15 results is 43 . if the average of first 7 results is 41 and average of last 7 results is 45 then find the eighth result ?", + "Output Program": [ + "n0 = 15.0\nn1 = 43.0\nn2 = 7.0\nn3 = 41.0\nn4 = 7.0\nn5 = 45.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n2 * n5\nt3 = t1 + t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "43" + ], + "split": "test" + }, + { + "Input": "a student chose a number , multiplied it by 3 , then subtracted 138 from the result and got 102 . what was the number he chose ?", + "Output Program": [ + "n0 = 3.0\nn1 = 138.0\nn2 = 102.0\nt0 = n1 + n2\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "test" + }, + { + "Input": "what is the sum of all possible solutions to | x - 3 | ^ 2 + | x - 3 | = 20 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 3.0\nn3 = 20.0\nt0 = n0 + 4.0\nt1 = n0 - 4.0\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "test" + }, + { + "Input": "5 years ago , the average age of a and b was 15 years . average age of a , b and c today is 20 years . how old will c be after 14 years ?", + "Output Program": [ + "n0 = 5.0\nn1 = 15.0\nn2 = 20.0\nn3 = 14.0\nt0 = n2 * 3.0\nt1 = n1 * 2.0\nt2 = n0 + t1\nt3 = n0 + t2\nt4 = t0 - t3\nanswer = n3 + t4\nprint(answer)" + ], + "Output Answer": [ + "34" + ], + "split": "test" + }, + { + "Input": "the function f ( p ) represents the number of ways that prime numbers can be uniquely summed to form a certain number p such that p = a + b + c + d \u2026 where those summed variables are each prime and a \u2264 b \u2264 c \u2264 d . . . for instance f ( 8 ) = 3 and the unique ways are 2 + 2 + 2 + 2 and 2 + 3 + 3 and 3 + 5 . what is f ( 12 ) ?", + "Output Program": [ + "n0 = 8.0\nn1 = 3.0\nn2 = 2.0\nn3 = 2.0\nn4 = 2.0\nn5 = 2.0\nn6 = 2.0\nn7 = 3.0\nn8 = 3.0\nn9 = 3.0\nn10 = 5.0\nn11 = 12.0\nt0 = n11 / 4.0\nanswer = t0 + 4.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "test" + }, + { + "Input": "a student chose a number , multiplied it by 5 , then subtracted 275 from the result and got 135 . what was the number he chose ?", + "Output Program": [ + "n0 = 5.0\nn1 = 275.0\nn2 = 135.0\nt0 = n1 + n2\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "82" + ], + "split": "test" + }, + { + "Input": "in a can , there is a mixture of milk and water in the ratio 3 : 2 . if the can is filled with an additional 6 liters of milk , the can would be full and the ratio of milk and water would become 2 : 1 . find the capacity of the can ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 6.0\nn3 = 2.0\nn4 = 1.0\nt0 = n2 * n4\nt1 = n1 * n3\nt2 = n0 * n4\nt3 = t1 - t2\nt4 = t0 / t3\nt5 = n0 * t4\nt6 = n1 * t4\nt7 = n2 + t5\nanswer = t7 + t6\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "test" + }, + { + "Input": "what is the remainder if 7 ^ 16 is divided by 100 ?", + "Output Program": [ + "n0 = 7.0\nn1 = 16.0\nn2 = 100.0\nt0 = n2 / 2.0\nt1 = n0 * n0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "test" + }, + { + "Input": "a large box contains 17 small boxes and each small box contains 25 chocolate bars . how many chocolate bars are in the large box ?", + "Output Program": [ + "n0 = 17.0\nn1 = 25.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "425" + ], + "split": "test" + }, + { + "Input": "what is the product of all the possible values of x if x ^ 2 + 5 x + 6 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 6.0\n\nanswer = n2 / 1.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "test" + }, + { + "Input": "jim \u2019 s taxi service charges an initial fee of $ 2.45 at the beginning of a trip and an additional charge of $ 0.35 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?", + "Output Program": [ + "n0 = 2.45\nn1 = 0.35\nn2 = 2.0\nn3 = 5.0\nn4 = 3.6\nt0 = n2 / n3\nt1 = n4 / t0\nt2 = n1 * t1\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "5.6" + ], + "split": "test" + }, + { + "Input": "a bowl contains equal numbers of red , orange , green , blue , and yellow candies . kaz eats all of the green candies and half of the orange ones . next , he eats half of the remaining pieces of each color . finally , he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 24 % of the original number . what percent of the red candies remain ?", + "Output Program": [ + "n0 = 24.0\nt0 = 2.0 + 3.0\nt1 = 100.0 / t0\nt2 = t1 / 2.0\nt3 = t2 / 2.0\nt4 = t2 + t3\nt5 = n0 - t4\nt6 = t5 / 2.0\nt7 = t6 / t1\nanswer = t7 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "22.5" + ], + "split": "test" + }, + { + "Input": "a man has $ 480 in the denominations of one - dollar , 5 - dollar notes and 10 - dollar . the number of dollars of each denomination is equal . what is the total number of dollar that he has ?", + "Output Program": [ + "n0 = 480.0\nn1 = 5.0\nn2 = 10.0\nt0 = n0 * n2\nt1 = t0 / 60.0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "test" + }, + { + "Input": "find how many positive integers less than 10000 are there such thatthe sum of the digits of the no . is divisible by 3 ?", + "Output Program": [ + "import math\nn0 = 10000.0\nn1 = 3.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "3334" + ], + "split": "test" + }, + { + "Input": "a bowl contains equal numbers of red , orange , green , blue , and yellow candies . kaz eats all of the green candies and half of the orange ones . next , he eats half of the remaining pieces of each color . finally , he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 25 % of the original number . what percent of the red candies remain ?", + "Output Program": [ + "n0 = 25.0\nt0 = 2.0 + 3.0\nt1 = 100.0 / t0\nt2 = t1 / 2.0\nt3 = t2 / 2.0\nt4 = t2 + t3\nt5 = n0 - t4\nt6 = t5 / 2.0\nt7 = t6 / t1\nanswer = t7 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "test" + }, + { + "Input": "if - 4 and - 8 are negative integers , then - 4 * - 8 + 2 is", + "Output Program": [ + "n0 = 11.0\nn1 = 8.0\nn2 = 11.0\nn3 = 8.0\nt0 = n0 * n1\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "89" + ], + "split": "test" + }, + { + "Input": "the maximum number of students among them 1234 pens and 874 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :", + "Output Program": [ + "import scipy\nn0 = 1234.0\nn1 = 874.0\n\nanswer = scipy.gcd(int(n0), int(n1))\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "test" + }, + { + "Input": "if the average ( arithmetic mean ) of a and b is 120 , and the average of b and c is 150 , what is the value of a \u2212 c ?", + "Output Program": [ + "n0 = 120.0\nn1 = 150.0\nt0 = n1 * 2.0\nt1 = n0 * 2.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "test" + }, + { + "Input": "a vessel of capacity 2 litre has 25 % of alcohol and another vessel of capacity 6 litre had 30 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?", + "Output Program": [ + "n0 = 2.0\nn1 = 25.0\nn2 = 6.0\nn3 = 30.0\nn4 = 8.0\nn5 = 10.0\nt0 = n1 / 100.0\nt1 = n3 / 100.0\nt2 = n0 * t0\nt3 = n2 * t1\nt4 = t2 + t3\nt5 = t4 / n5\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "test" + }, + { + "Input": "solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 150 milliliters of solution x to create a solution that is 25 percent alcohol by volume ?", + "Output Program": [ + "n0 = 10.0\nn1 = 30.0\nn2 = 150.0\nn3 = 25.0\nt0 = n3 - n0\nt1 = n1 - n3\nt2 = t0 / t1\nanswer = n2 * t2\nprint(answer)" + ], + "Output Answer": [ + "450" + ], + "split": "test" + }, + { + "Input": "the average ( arithmetic mean ) of 16 students first quiz scores in a difficult english class is 62.5 . when one student dropped the class , the average of the remaining scores increased to 65.0 . what is the quiz score of the student who dropped the class ?", + "Output Program": [ + "n0 = 16.0\nn1 = 62.5\nn2 = 65.0\nt0 = n0 * n1\nt1 = n0 - 1.0\nt2 = n2 * t1\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "test" + }, + { + "Input": "when positive integer x is divided by positive integer y , the remainder is 8 . if x / y = 96.12 , what is the value of y ?", + "Output Program": [ + "import math\nn0 = 8.0\nn1 = 96.12\nt0 = math.floor(n1)\nt1 = n1 - t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "66.66666666666414" + ], + "split": "test" + }, + { + "Input": "calculate 469200 x 9999 = ?", + "Output Program": [ + "n0 = 469200.0\nn1 = 9999.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "4691530800" + ], + "split": "test" + }, + { + "Input": "a is two years older than b who is twice as old as c . if the total ages of a , b and c be 27 . what is the age of b ?", + "Output Program": [ + "n0 = 27.0\nt0 = 1.0 + 4.0\nt1 = n0 - 2.0\nt2 = t1 * 2.0\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "test" + }, + { + "Input": "a certain debt will be paid in 52 installments from january 1 to december 31 of a certain year . each of the first 22 payments is to be $ 410 ; each of the remaining payments is to be $ 65 more than each of the first 22 payments . what is the average ( arithmetic mean ) payment that will be made on the debt for the year ?", + "Output Program": [ + "n0 = 52.0\nn1 = 1.0\nn2 = 31.0\nn3 = 22.0\nn4 = 410.0\nn5 = 65.0\nn6 = 22.0\nt0 = n4 + n5\nt1 = n3 * n4\nt2 = n0 - n3\nt3 = t0 * t2\nt4 = t1 + t3\nanswer = t4 / n0\nprint(answer)" + ], + "Output Answer": [ + "447.5" + ], + "split": "test" + }, + { + "Input": "a number when divided by a certain divisor left remainder 241 , when twice the number was divided by the same divisor , the remainder was 102 . find the divisor ?", + "Output Program": [ + "n0 = 241.0\nn1 = 102.0\nt0 = n0 * 2.0\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "380" + ], + "split": "test" + }, + { + "Input": "s is a positive integer and multiple of 2 ; p = 4 ^ s , what is the remainder when p is divided by 10 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 10.0\nt0 = n1**min(n0, 5)\nanswer = t0 % n2\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "test" + }, + { + "Input": "if the sum of two numbers is 22 and the sum of their squares is 386 , then the product of the numbers is", + "Output Program": [ + "n0 = 22.0\nn1 = 386.0\nt0 = n0**min(2.0, 5)\nt1 = t0 - n1\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "49" + ], + "split": "test" + }, + { + "Input": "if m is an integer such that ( - 2 ) ^ 2 m = 2 ^ ( 15 - m ) then m = ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 2.0\nn3 = 15.0\nt0 = n0 + 1.0\nanswer = n3 / t0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "test" + }, + { + "Input": "$ 378 is divided among a , b , and c so that a receives half as much as b , and b receives half as much as c . how much money is c ' s share ?", + "Output Program": [ + "n0 = 378.0\nt0 = 1.0 / 2.0\nt1 = t0 + 1.0\nt2 = t1 + 2.0\nt3 = n0 / t2\nanswer = t3 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "216" + ], + "split": "test" + }, + { + "Input": "a customer bought a product at the shop . however , the shopkeeper increased the price of the product by 20 % so that the customer could not buy the required amount of the product . the customer managed to buy only 80 % of the required amount . what is the difference in the amount of money that the customer paid for the second purchase compared to the first purchase ?", + "Output Program": [ + "n0 = 20.0\nn1 = 80.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = t0 + 1.0\nt3 = t2 * t1\nt4 = 1.0 - t3\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "4.0000000000000036" + ], + "split": "test" + }, + { + "Input": "there is a lot of speculation that the economy of a country depends on how fast people spend their money in addition to how much they save . auggie was very curious to test this theory . auggie spent all of his money in 5 stores . in each store , he spent rs . 4 more than one - half of what he had when he went in . how many rupees did auggie have when he entered the first store ?", + "Output Program": [ + "n0 = 5.0\nn1 = 4.0\nt0 = n1 * 2.0\nt1 = n1 + t0\nt2 = t1 * 2.0\nt3 = n1 + t2\nt4 = t3 * 2.0\nt5 = n1 + t4\nt6 = t5 * 2.0\nt7 = n1 + t6\nanswer = t7 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "248" + ], + "split": "test" + }, + { + "Input": "3 people are planning to share equally the cost of a rental car . if one person withdraws from the arrangement and the others share equally the entire cost of the car , then the share of each of the remaining persons increased by :", + "Output Program": [ + "n0 = 3.0\nt0 = 1.0 / 2.0\nt1 = 1.0 / n0\nt2 = t0 - t1\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.5000000000000001" + ], + "split": "test" + }, + { + "Input": "how many 1 / 8 s are there in 37 1 / 2 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 8.0\nn2 = 37.0\nn3 = 1.0\nn4 = 2.0\nt0 = n0 / n4\nt1 = n0 / n1\nt2 = n2 + t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "test" + }, + { + "Input": "the average runs of a cricket player of 10 innings was 20 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?", + "Output Program": [ + "n0 = 10.0\nn1 = 20.0\nn2 = 4.0\nt0 = n0 + 1.0\nt1 = n1 + n2\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "test" + }, + { + "Input": "the sum of the even numbers between 1 and k is 79 * 80 , where k is an odd number , then k =", + "Output Program": [ + "n0 = 1.0\nn1 = 79.0\nn2 = 80.0\nt0 = n1 * 2.0\nanswer = t0 + n0\nprint(answer)" + ], + "Output Answer": [ + "159" + ], + "split": "test" + }, + { + "Input": "ele , the circus elephant , is currently 3 times older than lyn , the circus lion . in 15 years from now , lyn the circus lion will be exactly half as old as ele , the circus elephant . how old is ele today ?", + "Output Program": [ + "n0 = 3.0\nn1 = 15.0\nt0 = n1 * 2.0\nt1 = t0 - n1\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "test" + }, + { + "Input": "a man is 30 years older than his son . in two years , his age will be twice the age of his son . the present age of this son is", + "Output Program": [ + "n0 = 30.0\nt0 = 2.0 * 2.0\nt1 = 2.0 - 1.0\nt2 = t0 - 2.0\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "test" + }, + { + "Input": "a pupil ' s marks were wrongly entered as 83 instead of 53 . due to the average marks for the class got increased by half . the number of pupils in the class is ?", + "Output Program": [ + "n0 = 83.0\nn1 = 53.0\nt0 = n0 - n1\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "test" + }, + { + "Input": "a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 948 in total compensation , how many total hours did he work that week ?", + "Output Program": [ + "n0 = 16.0\nn1 = 40.0\nn2 = 40.0\nn3 = 75.0\nn4 = 948.0\nt0 = n3 + 100.0\nt1 = n0 * n1\nt2 = n0 * t0\nt3 = n4 - t1\nt4 = t2 / 100.0\nt5 = t3 / t4\nanswer = n1 + t5\nprint(answer)" + ], + "Output Answer": [ + "51" + ], + "split": "test" + }, + { + "Input": "a salesman commission is 5 % on all sales upto $ 10000 and 4 % on all sales exceeding this . he remits $ 31100 to his parent company after deducting his commission . find the total sales ?", + "Output Program": [ + "n0 = 5.0\nn1 = 10000.0\nn2 = 4.0\nn3 = 31100.0\nt0 = n2 / 100.0\nt1 = n0 * n1\nt2 = n1 * n2\nt3 = t1 / 100.0\nt4 = t2 / 100.0\nt5 = 1.0 - t0\nt6 = t3 - t4\nt7 = n3 + t6\nanswer = t7 / t5\nprint(answer)" + ], + "Output Answer": [ + "32500" + ], + "split": "test" + }, + { + "Input": "for any positive number x , the function [ x ] denotes the greatest integer less than or equal to x . for example , [ 1 ] = 1 , [ 1.367 ] = 1 and [ 1.999 ] = 1 . if k is a positive integer such that k ^ 2 is divisible by 45 and 80 , what is the units digit of k ^ 3 / 4000 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 1.367\nn3 = 1.0\nn4 = 1.999\nn5 = 1.0\nn6 = 2.0\nn7 = 45.0\nn8 = 80.0\nn9 = 3.0\nn10 = 4000.0\nt0 = n6 * n9\nt1 = t0 * t0\nt2 = t1 * t0\nanswer = t2 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "test" + }, + { + "Input": "paul ' s income is 40 % less than rex ' s income , quentin ' s income is 20 % less than paul ' s income , and sam ' s income is 40 % less than paul ' s income . if rex gave 40 % of his income to sam and 60 % of his income to quentin , quentin ' s new income would be what fraction of sam ' s new income ?", + "Output Program": [ + "n0 = 40.0\nn1 = 20.0\nn2 = 40.0\nn3 = 40.0\nn4 = 60.0\nt0 = n0 + n1\nt1 = n4 * 100.0\nt2 = n0 * 100.0\nt3 = 100.0 - n1\nt4 = n4 * t3\nt5 = n4 * t0\nt6 = t1 + t4\nt7 = t2 + t5\nanswer = t6 / t7\nprint(answer)" + ], + "Output Answer": [ + "1.4210526315789473" + ], + "split": "test" + }, + { + "Input": "if p / q = 3 / 7 , then 2 p + q = ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 2.0\nt0 = n0 * n2\nanswer = n1 + t0\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "test" + }, + { + "Input": "in a box of 9 pens , a total of 2 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?", + "Output Program": [ + "n0 = 9.0\nn1 = 2.0\nn2 = 2.0\nt0 = n0 - n1\nt1 = n0 - 1.0\nt2 = t0 / n0\nt3 = t0 - 1.0\nt4 = t3 / t1\nanswer = t2 * t4\nprint(answer)" + ], + "Output Answer": [ + "0.5833333333333334" + ], + "split": "test" + }, + { + "Input": "last year the price range ( per kg ) for 100 varieties of apples in wholesale market was $ 100 . if the prices of each of the 100 varieties increased by 10 percent this year over what it was last year , what is the range of the wholesale prices of the 1000 varieties of apples this year ?", + "Output Program": [ + "n0 = 100.0\nn1 = 100.0\nn2 = 100.0\nn3 = 10.0\nn4 = 1000.0\nt0 = n3 + 100.0\nt1 = t0 / 100.0\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "110.00000000000001" + ], + "split": "test" + }, + { + "Input": "in an election between two candidates a and b , the number of valid votes received by a exceeds those received by b by 15 % of the total number of votes polled . if 20 % of the votes polled were invalid and a total of 4720 votes were polled , then how many valid votes did b get ?", + "Output Program": [ + "n0 = 15.0\nn1 = 20.0\nn2 = 4720.0\nt0 = n1 / 100.0\nt1 = n0 * n2\nt2 = t1 / 100.0\nt3 = 1.0 - t0\nt4 = n2 * t3\nt5 = t4 - t2\nanswer = t5 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "1534" + ], + "split": "test" + }, + { + "Input": "the average age of 6 men increases by 2 years when two women are included in place of two men of ages 20 and 24 years . find the average age of the women ?", + "Output Program": [ + "n0 = 6.0\nn1 = 2.0\nn2 = 20.0\nn3 = 24.0\nt0 = n2 + n3\nt1 = n0 * n1\nt2 = t0 + t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "test" + }, + { + "Input": "operation # is defined as : a # b = 4 a ^ 2 + 4 b ^ 2 + 8 ab for all non - negative integers . what is the value of ( a + b ) + 4 , when a # b = 100 ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 2.0\nn2 = 4.0\nn3 = 2.0\nn4 = 8.0\nn5 = 4.0\nn6 = 100.0\nt0 = n6 / n0\nt1 = math.sqrt(max(0, t0))\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "test" + }, + { + "Input": "each of 3 investments has a 20 % of becoming worthless within a year of purchase , independently of what happens to the other two investments . if simone invests an equal sum k in each of these 3 investments on january 1 , the approximate chance that by the end of the year , she loses no more than 1 / 3 of her original investment is", + "Output Program": [ + "n0 = 3.0\nn1 = 20.0\nn2 = 3.0\nn3 = 1.0\nn4 = 1.0\nn5 = 3.0\nt0 = n1 / 100.0\nt1 = t0**min(n0, 5)\nt2 = 1.0 - t0\nt3 = t0 * t2\nt4 = t0 * t3\nt5 = n0 * t4\nt6 = t5 + t1\nt7 = -t6\nt8 = n3 + t7\nanswer = t8 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "89.6" + ], + "split": "test" + }, + { + "Input": "a ferry can transport 50 tons of vehicles . automobiles range in weight from 1,600 to 3,200 pounds . what is the greatest number of automobiles that can be loaded onto the ferry ?", + "Output Program": [ + "n0 = 50.0\nn1 = 1600.0\nn2 = 3200.0\nt0 = 1000.0 * 2.0\nt1 = n1 / t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "62.5" + ], + "split": "test" + }, + { + "Input": "a bank pays interest to its customers on the last day of the year . the interest paid to a customer is calculated as 10 % of the average monthly balance maintained by the customer . john is a customer at the bank . on the last day , when the interest was accumulated into his account , his bank balance doubled to $ 5080 . what is the average monthly balance maintained by john in his account during the year ?", + "Output Program": [ + "n0 = 10.0\nn1 = 5080.0\nt0 = n0 / 2.0\nanswer = n1 * t0\nprint(answer)" + ], + "Output Answer": [ + "25400" + ], + "split": "test" + }, + { + "Input": "reeya obtained 40 , 60 , 70 , 80 and 80 out of 100 in different subjects , what will be the average", + "Output Program": [ + "n0 = 40.0\nn1 = 60.0\nn2 = 70.0\nn3 = 80.0\nn4 = 80.0\nn5 = 100.0\nt0 = n0 + n1\nt1 = 1.0 + 4.0\nt2 = n2 + t0\nt3 = n3 + t2\nt4 = n4 + t3\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "66" + ], + "split": "test" + }, + { + "Input": "when positive integer k is divided by 5 , the remainder is 2 . when k is divided by 6 , the remainder is 5 . if k is less than 24 , what is the remainder when k is divided by 7 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 6.0\nn3 = 5.0\nn4 = 24.0\nn5 = 7.0\nt0 = n0 + 12.0\nanswer = t0 % n5\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "test" + }, + { + "Input": "is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 32 , then how old is b ?", + "Output Program": [ + "n0 = 32.0\nt0 = 1.0 + 4.0\nt1 = n0 - 2.0\nt2 = t1 * 2.0\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "test" + }, + { + "Input": "mary ' s income is 60 % more than tim ' s income and tim ' s income is 60 % less than juan ' s income . what % of juan ' s income is mary ' s income .", + "Output Program": [ + "n0 = 60.0\nn1 = 60.0\nt0 = n0 / 100.0\nt1 = 100.0 - n1\nt2 = t0 * t1\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "test" + }, + { + "Input": "the average expenditure of a labourer for 6 months was 95 and he fell into debt . in the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30 . his monthly income i", + "Output Program": [ + "n0 = 6.0\nn1 = 95.0\nn2 = 4.0\nn3 = 60.0\nn4 = 30.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nt4 = n4 + t3\nanswer = t4 / t0\nprint(answer)" + ], + "Output Answer": [ + "84" + ], + "split": "test" + }, + { + "Input": "a driver just filled the car ' s gas tank with 18 liters of gasohol , a mixture consisting of 5 % ethanol and 95 % gasoline . if the car runs best on a mixture consisting of 10 % ethanol and 90 % gasoline , how many liters of ethanol must be added into the gas tank for the car to achieve optimum performance ?", + "Output Program": [ + "n0 = 18.0\nn1 = 5.0\nn2 = 95.0\nn3 = 10.0\nn4 = 90.0\nt0 = n0 * n1\nt1 = 100.0 - n3\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "test" + }, + { + "Input": "in the new budget the price of wheat rose by 8 % . by how much percent must a person reduce his consumption so that his expenditure on it does not increase ?", + "Output Program": [ + "n0 = 8.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nt2 = t0 / t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "7.4074074074074066" + ], + "split": "test" + }, + { + "Input": "a , b and c started a business with a total investment of rs . 72000 . a invests rs . 6000 more than b and b invests rs . 3000 less than c . if the total profit at the end of a year is rs . 8640 , find a ' s share .", + "Output Program": [ + "n0 = 72000.0\nn1 = 6000.0\nn2 = 3000.0\nn3 = 8640.0\nt0 = n1 + n2\nt1 = n0 - t0\nt2 = t1 / 3.0\nt3 = n1 + t2\nt4 = t3 / n0\nanswer = n3 * t4\nprint(answer)" + ], + "Output Answer": [ + "3240" + ], + "split": "test" + }, + { + "Input": "a certain list consists of 21 different numbers . if n is in the list and n is 4 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction e of the sum of the 21 numbers in the list ?", + "Output Program": [ + "n0 = 21.0\nn1 = 4.0\nn2 = 20.0\nn3 = 21.0\nt0 = n2 / n1\nt1 = 1.0 * 1.0\nt2 = n0 + t0\nt3 = t2 / n1\nt4 = t3 * 2.0\nt5 = t4 - n1\nt6 = t5 - 3.0\nanswer = t1 / t6\nprint(answer)" + ], + "Output Answer": [ + "0.16666666666666666" + ], + "split": "test" + }, + { + "Input": "if 0.20 : x : : 4 : 2 , then x is equal to", + "Output Program": [ + "n0 = 0.2\nn1 = 4.0\nn2 = 2.0\nt0 = n0 * n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.1" + ], + "split": "test" + }, + { + "Input": "s is a set of 85 consecutive multiples of 5 . if the smallest number in s is 90 , then the greatest number in s is", + "Output Program": [ + "n0 = 85.0\nn1 = 5.0\nn2 = 90.0\nt0 = n0 - 1.0\nt1 = n1 * t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "510" + ], + "split": "test" + }, + { + "Input": "find the value of ( 70 + 28 / 100 ) \u00d7 100", + "Output Program": [ + "n0 = 70.0\nn1 = 28.0\nn2 = 100.0\nn3 = 100.0\nt0 = n1 / n2\nt1 = n0 + t0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "7028" + ], + "split": "test" + }, + { + "Input": "if 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 20 , then n =", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 2.0\nn3 = 2.0\nn4 = 2.0\nn5 = 2.0\nn6 = 2.0\nn7 = 2.0\nn8 = 4.0\nn9 = 20.0\nt0 = n0 * n9\nt1 = t0 - n0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "test" + }, + { + "Input": "in a division sum , the remainder is 8 and the divisor is 6 times the quotient and is obtained by adding 3 to the thrice of the remainder . the dividend is :", + "Output Program": [ + "n0 = 8.0\nn1 = 6.0\nn2 = 3.0\nt0 = n0 * 3.0\nt1 = n2 + t0\nt2 = t1 / n1\nt3 = t1 * t2\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "129.5" + ], + "split": "test" + }, + { + "Input": "10 stickers numbered 1 to 10 are placed in a bowl , mixed up thoroughly and then one sticker is drawn randomly . if it is known that the number on the drawn sticker is more than 3 , what is the probability that it is an even number ?", + "Output Program": [ + "n0 = 10.0\nn1 = 1.0\nn2 = 10.0\nn3 = 3.0\nt0 = 4.0 / n0\nt1 = n0 - n3\nt2 = n0 / t1\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "0.5714285714285715" + ], + "split": "test" + }, + { + "Input": "for a certain exam , a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean . what was the mean score w for the exam ?", + "Output Program": [ + "n0 = 58.0\nn1 = 2.0\nn2 = 98.0\nn3 = 3.0\nt0 = n1 + n3\nt1 = n0 * n3\nt2 = n1 * n2\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "74" + ], + "split": "test" + }, + { + "Input": "in a factory , an average of 50 tv ' s are produced per day for the fist 25 days of the months . a few workers fell ill for the next 5 days reducing the daily avg for the month to 43 sets / day . the average production per day for day last 5 days is ?", + "Output Program": [ + "n0 = 50.0\nn1 = 25.0\nn2 = 5.0\nn3 = 43.0\nn4 = 5.0\nt0 = n1 + n2\nt1 = n0 * n1\nt2 = n3 * t0\nt3 = t2 - t1\nanswer = t3 / n2\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "test" + }, + { + "Input": "find the principle on a certain sum of money at 5 % per annum for 2 2 / 5 years if the amount being rs . 1904 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 2.0\nn3 = 5.0\nn4 = 1904.0\nt0 = n1 * n3\nt1 = n1 + t0\nt2 = t1 / n3\nt3 = n0 * t2\nt4 = t3 / 100.0\nt5 = t4 + 1.0\nanswer = n4 / t5\nprint(answer)" + ], + "Output Answer": [ + "1699.9999999999998" + ], + "split": "test" + }, + { + "Input": "the overall age of x and y is 11 year greater than the overall age of y and z . z is how many decades younger that x ?", + "Output Program": [ + "n0 = 11.0\n\nanswer = n0 / 1.0\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "test" + }, + { + "Input": "the mean of 50 observations was 36 . it was found later that an observation 47 was wrongly taken as 23 . the corrected new mean is", + "Output Program": [ + "n0 = 50.0\nn1 = 36.0\nn2 = 47.0\nn3 = 23.0\nt0 = n0 * n1\nt1 = n0 - 2.0\nt2 = t1 - n3\nt3 = t0 + t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "36.5" + ], + "split": "test" + }, + { + "Input": "a group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 7 with 3 students left over . what is the sum of the two smallest possible values of n ?", + "Output Program": [ + "n0 = 4.0\nn1 = 1.0\nn2 = 7.0\nn3 = 3.0\nt0 = n2 * 2.0\nt1 = 2.0 * 3.0\nt2 = n3 + t0\nt3 = n2 * t1\nt4 = n3 + t3\nanswer = t2 + t4\nprint(answer)" + ], + "Output Answer": [ + "62" + ], + "split": "test" + }, + { + "Input": "the batting average of a particular batsman is 60 runs in 46 innings . if the difference in his highest and lowest score is 170 runs and his average excluding these two innings is 58 runs , find his highest score .", + "Output Program": [ + "n0 = 60.0\nn1 = 46.0\nn2 = 170.0\nn3 = 58.0\nt0 = n0 * n1\nt1 = n1 - 2.0\nt2 = n3 * t1\nt3 = t0 - t2\nt4 = n2 + t3\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "189" + ], + "split": "test" + }, + { + "Input": "find the value of ( 950 + 220 / 900 ) \u00d7 900", + "Output Program": [ + "n0 = 950.0\nn1 = 220.0\nn2 = 900.0\nn3 = 900.0\nt0 = n1 / n2\nt1 = n0 + t0\nanswer = t1 * n2\nprint(answer)" + ], + "Output Answer": [ + "855220" + ], + "split": "test" + }, + { + "Input": "__ 2 a x __ b ____ cc in the multiplication problem above , a , b , and c represent distinct digits . if the sum of a and b is equal to 4.6 , what is the value of c ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.6\nt0 = 1.0 + 4.0\nt1 = n1 - n0\nt2 = t1 * 10.0\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "5.199999999999999" + ], + "split": "test" + }, + { + "Input": "country c imposes a two - tiered tax on imported cars : the first tier imposes a tax of 12 % of the car ' s price up to a certain price level . if the car ' s price is higher than the first tier ' s level , the tax on the portion of the price that exceeds this value is 9 % . if ron imported a $ 18,000 imported car and ended up paying $ 1950 in taxes , what is the first tier ' s price level ?", + "Output Program": [ + "n0 = 12.0\nn1 = 9.0\nn2 = 18000.0\nn3 = 1950.0\nt0 = n1 / 100.0\nt1 = n0 / 100.0\nt2 = 2.0 * 3.0\nt3 = t2 * 3.0\nt4 = t1 - t0\nt5 = t3 * 1000.0\nt6 = t0 * t5\nt7 = n3 - t6\nanswer = t7 / t4\nprint(answer)" + ], + "Output Answer": [ + "11000" + ], + "split": "test" + }, + { + "Input": "mary sold boxes of butter cookies . ann sold 5 times as much as she did . 18 boxes of cookies were sold that day , how many boxes did mary sell ?", + "Output Program": [ + "n0 = 5.0\nn1 = 18.0\nt0 = n0 + 1.0\nanswer = n1 / t0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "test" + }, + { + "Input": "a batsman in his 9 th inning makes a score of 75 and their by increasing his average by 7 . what is his average after the 9 th inning ?", + "Output Program": [ + "n0 = 9.0\nn1 = 75.0\nn2 = 7.0\nn3 = 9.0\nt0 = n0 * n2\nt1 = n1 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "test" + }, + { + "Input": "a man engaged a servant on the condition that he would pay him rs . 1000 and a uniform after one year service . he served only for 9 months and received uniform and rs . 550 , find the price of the uniform ?", + "Output Program": [ + "n0 = 1000.0\nn1 = 9.0\nn2 = 550.0\nt0 = n0 * n1\nt1 = 3.0 * 4.0\nt2 = n2 * t1\nt3 = t1 * 1.0\nt4 = t0 - t2\nt5 = t4 / t3\nanswer = t5 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "800" + ], + "split": "test" + }, + { + "Input": "i chose a number and divide it by 4 . then i subtracted 18 from the result and got 7 . what was the number i chose ?", + "Output Program": [ + "n0 = 4.0\nn1 = 18.0\nn2 = 7.0\nt0 = n1 + n2\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "test" + }, + { + "Input": "the original price of a suit is $ 100 . the price increased 20 % , and after this increase , the store published a 20 % off coupon for a one - day sale . given that the consumers who used the coupon on sale day were getting 20 % off the increased price , how much did these consumers pay for the suit ?", + "Output Program": [ + "n0 = 100.0\nn1 = 20.0\nn2 = 20.0\nn3 = 20.0\nt0 = n0 * n1\nt1 = t0 / 100.0\nt2 = n0 + t1\nt3 = n1 * t2\nt4 = t3 / 100.0\nanswer = t2 - t4\nprint(answer)" + ], + "Output Answer": [ + "96" + ], + "split": "test" + }, + { + "Input": "the average runs scored by a batsman in 20 matches is 40 . in the next 30 matches the batsman scored an average of 20 runs . find his average in all the 50 matches ?", + "Output Program": [ + "n0 = 20.0\nn1 = 40.0\nn2 = 30.0\nn3 = 20.0\nn4 = 50.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "test" + }, + { + "Input": "for a group of n people , k of whom are of the same sex , the ( n - k ) / n expression yields an index for a certain phenomenon in group dynamics for members of that sex . for a group that consists of 20 people , 8 of whom are females , by how much does the index for the females exceed the index for the males in the group ?", + "Output Program": [ + "n0 = 20.0\nn1 = 8.0\nt0 = n1 / n0\nt1 = n0 - n1\nt2 = t1 / n0\nanswer = t2 - t0\nprint(answer)" + ], + "Output Answer": [ + "0.19999999999999996" + ], + "split": "test" + }, + { + "Input": "chocolate bars are sold in packages of 4 or 9 only . if mark bought 97 chocolate bars exactly , what could be the number of large packs mark bought ?", + "Output Program": [ + "n0 = 4.0\nn1 = 9.0\nn2 = 97.0\nt0 = n0 * n0\nt1 = n2 - t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "test" + }, + { + "Input": "find the least number must be subtracted from 531742 so that remaining no . is divisible by 3 ?", + "Output Program": [ + "import math\nn0 = 531742.0\nn1 = 3.0\nt0 = n0 / n1\nt1 = math.floor(t0)\nt2 = n1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "test" + }, + { + "Input": "a man sells an article at 10 % gain . had be sold at for rs . 60 / - more he could have gained 20 % what is cost price of article", + "Output Program": [ + "n0 = 10.0\nn1 = 60.0\nn2 = 20.0\nt0 = n2 - n0\nt1 = n1 / t0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "600" + ], + "split": "test" + }, + { + "Input": "if x \u00a4 y = ( x + y ) ^ 2 - ( x - y ) ^ 2 . then \u221a 7 \u00a4 \u221a 7 =", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 2.0\nn2 = 7.0\nn3 = 7.0\nt0 = math.sqrt(max(0, n2))\nt1 = t0 + t0\nanswer = t1**min(n0, 5)\nprint(answer)" + ], + "Output Answer": [ + "28.000000000000004" + ], + "split": "test" + }, + { + "Input": "the average of 10 consecutive integers is 15 . then , 9 is deducted from the first consecutive number , 8 is deducted from the second , 7 is deducted form the third , and so on until the last number which remains unchanged . what is the new average ?", + "Output Program": [ + "n0 = 10.0\nn1 = 15.0\nn2 = 9.0\nn3 = 8.0\nn4 = 7.0\nt0 = 1.0 + 4.0\nt1 = n0 * n1\nt2 = n2 * t0\nt3 = t1 - t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "10.5" + ], + "split": "test" + }, + { + "Input": "the product of x and y is a constant . if the value of x is increased by 60 % , by what percentage must the value of y be decreased ?", + "Output Program": [ + "n0 = 60.0\nt0 = n0 + 100.0\nt1 = 100.0 / t0\nt2 = 1.0 - t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "37.5" + ], + "split": "test" + }, + { + "Input": "linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 400 , what were her original savings ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 400.0\nt0 = n0 / n1\nt1 = 1.0 - t0\nanswer = n2 / t1\nprint(answer)" + ], + "Output Answer": [ + "1600" + ], + "split": "test" + }, + { + "Input": "the cost of producing x tools by a company is given by c ( x ) = 600 x + 5500 ( in $ ) a ) what is the cost of 100 tools ?", + "Output Program": [ + "n0 = 600.0\nn1 = 5500.0\nn2 = 100.0\nt0 = n0 * n2\nanswer = n1 + t0\nprint(answer)" + ], + "Output Answer": [ + "65500" + ], + "split": "test" + }, + { + "Input": "a , b and c have rs . 400 between them , a and c together have rs . 200 and b and c rs . 350 . how much does c have ?", + "Output Program": [ + "n0 = 400.0\nn1 = 200.0\nn2 = 350.0\nt0 = n1 + n2\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "test" + }, + { + "Input": "( 0.0066 ) ( 3.6 ) / ( 0.04 ) ( 0.1 ) ( 0.006 ) =", + "Output Program": [ + "n0 = 0.0066\nn1 = 3.6\nn2 = 0.04\nn3 = 0.1\nn4 = 0.006\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n4 * t1\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "990" + ], + "split": "test" + }, + { + "Input": "if the sales tax reduced from 3 1 / 2 % to 3 1 / 3 % , then what difference does it make to a person who purchases an article with market price of rs . 9600 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 2.0\nn3 = 3.0\nn4 = 1.0\nn5 = 3.0\nn6 = 9600.0\nt0 = n1 / n2\nt1 = n1 / n0\nt2 = n0 + t0\nt3 = n0 + t1\nt4 = t2 - t3\nt5 = n6 * t4\nanswer = t5 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "15.999999999999986" + ], + "split": "test" + }, + { + "Input": "if x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year , the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $ 38 . if $ 2,000 is the total amount invested , how much is invested at 8 percent ?", + "Output Program": [ + "n0 = 10.0\nn1 = 8.0\nn2 = 10.0\nn3 = 8.0\nn4 = 38.0\nn5 = 2000.0\nn6 = 8.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = n0 * 100.0\nt3 = n0 * n1\nt4 = t0 + t1\nt5 = t2 * 2.0\nt6 = t3 * 2.0\nt7 = n4 + t6\nt8 = t7 / t4\nanswer = t5 - t8\nprint(answer)" + ], + "Output Answer": [ + "900" + ], + "split": "test" + }, + { + "Input": "a batsman scores 26 runs and increases his average from 14 to 15 . find the runs to be made if he wants top increasing the average to 19 in the same match ?", + "Output Program": [ + "n0 = 26.0\nn1 = 14.0\nn2 = 15.0\nn3 = 19.0\nt0 = n0 - n2\nt1 = t0 + 1.0\nt2 = n1 * t0\nt3 = n3 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "74" + ], + "split": "test" + }, + { + "Input": "a total of 520 players participated in a single tennis knock out tournament . what is the total number of matches played in the tournament ? ( knockout means if a player loses , he is out of the tournament ) . no match ends in a tie .", + "Output Program": [ + "n0 = 520.0\nt0 = n0 / 2.0\nt1 = t0 / 2.0\nt2 = t0 + t1\nt3 = t1 / 2.0\nt4 = t2 + t3\nt5 = t3 / 2.0\nt6 = t4 + t5\nt7 = t5 / 2.0\nt8 = t6 + t7\nt9 = t7 / 2.0\nt10 = t8 + t9\nt11 = t9 / 2.0\nt12 = t10 + t11\nt13 = t11 / 2.0\nt14 = t12 + t13\nt15 = t13 / 2.0\nanswer = t14 + t15\nprint(answer)" + ], + "Output Answer": [ + "518.984375" + ], + "split": "test" + }, + { + "Input": "solving a linear equation with several occurrences of the variable , solve for w . simplify answer as much as possible . ( 7 w + 6 ) / 6 + ( 9 w + 8 ) / 2 = 22", + "Output Program": [ + "n0 = 7.0\nn1 = 6.0\nn2 = 6.0\nn3 = 9.0\nn4 = 8.0\nn5 = 2.0\nn6 = 22.0\nt0 = n1 * n5\nt1 = n1 * n4\nt2 = n1 * n3\nt3 = n0 * 2.0\nt4 = t1 + t0\nt5 = t2 + t3\nt6 = n6 * t0\nt7 = t6 - t4\nanswer = t7 / t5\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "test" + }, + { + "Input": "if ( 6 ) ( x ^ 2 ) has 3 different prime factors , at most how many different prime factors does x have ?", + "Output Program": [ + "n0 = 6.0\nn1 = 2.0\nn2 = 3.0\n\nanswer = n2 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "test" + }, + { + "Input": "a person saved $ 10 in buying an item on sale . if he spent $ 200 for the item , approximately how much percent he saved in the transaction ?", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 200.0\nt0 = n0 + n1\nt1 = n0 / t0\nt2 = t1 * 100.0\nt3 = math.floor(t2)\nanswer = t3 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "test" + }, + { + "Input": "an astronomer noted that a grouping of red giant stars had an average solar mass of 8 m each , and a grouping of white dwarf stars had an average solar mass of 1.5 m each . if the astronomer calculated the total solar mass of both groupings to be 49 m , what total number of red giant stars and white dwarf stars did the astronomer note ?", + "Output Program": [ + "n0 = 8.0\nn1 = 1.5\nn2 = 49.0\nt0 = 2.0 + 4.0\nt1 = n1 * t0\nt2 = n2 - t1\nt3 = t2 / n0\nanswer = t0 + t3\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "test" + }, + { + "Input": "village a \u2019 s population is 300 greater than village b ' s population . if village b \u2019 s population were reduced by 600 people , then village a \u2019 s population would be 4 times as large as village b ' s population . what is village b ' s current population ?", + "Output Program": [ + "n0 = 300.0\nn1 = 600.0\nn2 = 4.0\nt0 = n1 * n2\nt1 = n2 - 1.0\nt2 = n0 + t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "900" + ], + "split": "test" + }, + { + "Input": "the average monthly salary of 10 employees in an organisation is rs . 1600 . if the manager ' s salary is added , then the average salary increases by rs . 100 . what is the manager ' s monthly salary ?", + "Output Program": [ + "n0 = 10.0\nn1 = 1600.0\nn2 = 100.0\nt0 = n1 + n2\nt1 = n0 + 1.0\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "2700" + ], + "split": "test" + }, + { + "Input": "if an integer n is to be chosen at random from the integers 1 to 96 , inclusive , what is the probability that n ( n + 1 ) ( n + 2 ) will be divisible by 6 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 96.0\nn2 = 1.0\nn3 = 2.0\nn4 = 6.0\nt0 = n1 / n3\nt1 = n1 / n4\nt2 = t0 + t1\nanswer = t2 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.6666666666666666" + ], + "split": "test" + }, + { + "Input": "how many integers from 0 to 50 inclusive have a remainder of 3 when divided by 5 ?", + "Output Program": [ + "n0 = 0.0\nn1 = 50.0\nn2 = 3.0\nn3 = 5.0\n\nanswer = 100.0 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "test" + }, + { + "Input": "6 students wrote science exam . their average marks are 70 . 5 students got 65 , 75 , 55 , 72 and 69 marks respectively . therefore what is the marks of the sixth student ?", + "Output Program": [ + "n0 = 6.0\nn1 = 70.0\nn2 = 5.0\nn3 = 65.0\nn4 = 75.0\nn5 = 55.0\nn6 = 72.0\nn7 = 69.0\nt0 = n3 + n4\nt1 = n0 * n1\nt2 = n5 + t0\nt3 = n6 + t2\nt4 = n7 + t3\nanswer = t1 - t4\nprint(answer)" + ], + "Output Answer": [ + "84" + ], + "split": "test" + }, + { + "Input": "the sum of 7 th and 23 rd term of a . p . is equal to the sum of 8 th , 15 th and 13 th term . find the term which is 0", + "Output Program": [ + "n0 = 7.0\nn1 = 23.0\nn2 = 8.0\nn3 = 15.0\nn4 = 13.0\nn5 = 0.0\nt0 = n2 + n3\nt1 = n0 + n1\nt2 = n4 + t0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "test" + }, + { + "Input": "when 200 is divided by positive integer x , the remainder is 3 . what is the remainder when 297 is divided by x ?", + "Output Program": [ + "n0 = 200.0\nn1 = 3.0\nn2 = 297.0\nt0 = n2 - 100.0\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "test" + }, + { + "Input": "in a party every person shakes hands with every other person . if there were a total of 190 handshakes in the party then what is the number of persons present in the party ?", + "Output Program": [ + "import math\nn0 = 190.0\nt0 = n0 * 2.0\nt1 = t0 * 4.0\nt2 = t1 + 1.0\nt3 = math.sqrt(max(0, t2))\nt4 = t3 + 1.0\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "test" + }, + { + "Input": "what is remainder of the division ( 1525 * 1527 * 1529 ) / 12 ?", + "Output Program": [ + "n0 = 1525.0\nn1 = 1527.0\nn2 = 1529.0\nn3 = 12.0\nt0 = n0 * n1\nt1 = n2 * t0\nt2 = t1 - 3.0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "test" + }, + { + "Input": "a pharmaceutical company received $ 5 million in royalties on the first $ 20 million in sales of the generic equivalent of one of its products and then $ 9 million in royalties on the next $ 108 million in sales . by approximately what percent did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 108 million in sales ?", + "Output Program": [ + "n0 = 5.0\nn1 = 20.0\nn2 = 9.0\nn3 = 108.0\nn4 = 20.0\nn5 = 108.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = t0 * 100.0\nt3 = t1 * 100.0\nt4 = t2 - t3\nt5 = t4 / t2\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "66.66666666666667" + ], + "split": "test" + }, + { + "Input": "if the average of w , b , c , 14 and 15 is 12 . what is the average value of w , b , c and 29", + "Output Program": [ + "n0 = 14.0\nn1 = 15.0\nn2 = 12.0\nn3 = 29.0\nt0 = 1.0 + 4.0\nt1 = n2 * t0\nt2 = t1 - n1\nt3 = t2 - n0\nt4 = n3 + t3\nanswer = t4 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "test" + }, + { + "Input": "after 6 games , team b had an average of 65 points per game . if it got only 47 points in game 7 , how many more points does it need to score to get its total above 500 ?", + "Output Program": [ + "n0 = 6.0\nn1 = 65.0\nn2 = 47.0\nn3 = 7.0\nn4 = 500.0\nt0 = n0 * n1\nt1 = n2 + t0\nanswer = n4 - t1\nprint(answer)" + ], + "Output Answer": [ + "63" + ], + "split": "test" + }, + { + "Input": "on thursday mabel handled 90 transactions . anthony handled 10 % more transactions than mabel , cal handled 2 / 3 rds of the transactions that anthony handled , and jade handled 16 more transactions than cal . how much transactions did jade handled ?", + "Output Program": [ + "n0 = 90.0\nn1 = 10.0\nn2 = 2.0\nn3 = 3.0\nn4 = 16.0\nt0 = n1 + 100.0\nt1 = n0 / 100.0\nt2 = t0 * t1\nt3 = n2 * t2\nt4 = t3 / n3\nanswer = n4 + t4\nprint(answer)" + ], + "Output Answer": [ + "82" + ], + "split": "test" + }, + { + "Input": "list a consists of 12 consecutive integers . if - 4 is the least integer in list a , what is the range of positive integers in list a ?", + "Output Program": [ + "n0 = 12.0\nn1 = 4.0\nt0 = n1 + 1.0\nt1 = n0 - t0\nanswer = t1 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "test" + }, + { + "Input": "if an integer n is to be chosen at random from the integers 1 to 96 , inclusive , what is the probability that n ( n + 1 ) ( n + 2 ) will be divisible by 4 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 96.0\nn2 = 1.0\nn3 = 2.0\nn4 = 4.0\nt0 = n1 / n3\nt1 = n1 / n4\nt2 = t0 + t1\nanswer = t2 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.75" + ], + "split": "test" + }, + { + "Input": "when y is divided by 288 , the remainder is 44 . what is the remainder when the same y is divided by 24 ?", + "Output Program": [ + "n0 = 288.0\nn1 = 44.0\nn2 = 24.0\n\nanswer = n1 % n2\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "test" + }, + { + "Input": "a box contains 10 tablets of medicine a and 17 tablets of medicine b . what is the least number of tablets that should be taken from the box to ensure that at least two tablets of each kind are among the extracted .", + "Output Program": [ + "n0 = 10.0\nn1 = 17.0\n\nanswer = n1 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "test" + }, + { + "Input": "the milk level in a rectangular box measuring 60 feet by 25 feet is to be lowered by 6 inches . how many gallons of milk must be removed ? ( 1 cu ft = 7.5 gallons )", + "Output Program": [ + "n0 = 60.0\nn1 = 25.0\nn2 = 6.0\nn3 = 1.0\nn4 = 7.5\nt0 = n3 / 2.0\nt1 = n0 * n1\nt2 = t0 * t1\nanswer = n4 * t2\nprint(answer)" + ], + "Output Answer": [ + "5625" + ], + "split": "test" + }, + { + "Input": "country x taxes each of its citizens an amount equal to 13 percent of the first $ 40,000 of income , plus 20 percent of all income in excess of $ 40,000 . if a citizen of country x is taxed a total of $ 8,000 , what is her income ?", + "Output Program": [ + "n0 = 13.0\nn1 = 40000.0\nn2 = 20.0\nn3 = 40000.0\nn4 = 8000.0\nt0 = n0 / 100.0\nt1 = n2 / 100.0\nt2 = 2.0 * 4.0\nt3 = 10.0 * 4.0\nt4 = t2 * 1000.0\nt5 = t3 * 1000.0\nt6 = t0 * t5\nt7 = t4 - t6\nt8 = t7 / t1\nanswer = t8 + t5\nprint(answer)" + ], + "Output Answer": [ + "54000" + ], + "split": "test" + }, + { + "Input": "the average marks of 20 students in a class is 100 . but a student mark is wrongly noted as 50 instead of 10 then find the correct average marks ?", + "Output Program": [ + "n0 = 20.0\nn1 = 100.0\nn2 = 50.0\nn3 = 10.0\nt0 = n0 * n1\nt1 = t0 - n2\nt2 = n3 + t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "98" + ], + "split": "test" + }, + { + "Input": "a parking garage rents parking spaces for $ 10 per week or $ 20 per month . how much does a person save in a year by renting by the month rather than by the week ?", + "Output Program": [ + "n0 = 10.0\nn1 = 20.0\nt0 = 2.0 + 3.0\nt1 = n1 * 12.0\nt2 = t0 * n0\nt3 = t2 + 2.0\nt4 = n0 * t3\nanswer = t4 - t1\nprint(answer)" + ], + "Output Answer": [ + "280" + ], + "split": "test" + }, + { + "Input": "jill has 21 gallons of water stored in quart , half - gallon , and one gallon jars . she has equal numbers of each size jar holding the liquid . what is the total number of water filled jars ?", + "Output Program": [ + "n0 = 21.0\nt0 = 1.0 / 2.0\nt1 = t0 + 0.25\nt2 = t1 + 1.0\nt3 = n0 / t2\nanswer = t3 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "test" + }, + { + "Input": "if 8 a = 9 b and ab \u2260 0 , what is the ratio of a / 9 to b / 8 ?", + "Output Program": [ + "n0 = 8.0\nn1 = 9.0\nn2 = 0.0\nn3 = 9.0\nn4 = 8.0\nt0 = n0 * n1\nanswer = t0 / t0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "test" + }, + { + "Input": "in a theater , the first row has 17 seats and each row has 3 more seats than previous row . if the last row has 44 seats , what is the total number of seats in the theater ?", + "Output Program": [ + "n0 = 17.0\nn1 = 3.0\nn2 = 44.0\nt0 = n0 + n2\nt1 = n2 - n0\nt2 = n1 + t1\nt3 = t0 / 2.0\nt4 = t2 / n1\nanswer = t3 * t4\nprint(answer)" + ], + "Output Answer": [ + "305" + ], + "split": "test" + }, + { + "Input": "running at their respective constant rate , machine x takes 2 days longer to produce w widgets than machines y . at these rates , if the two machines together produce 5 w / 4 widgets in 3 days , how many days would it take machine x alone to produce 6 w widgets .", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 4.0\nn3 = 3.0\nn4 = 6.0\nt0 = n0 * n4\nanswer = n3 * t0\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "test" + }, + { + "Input": "the number of timeshare condos available at sunset beach is 2 / 5 the number of timeshare condos available at playa del mar . if the total number of timeshare condos available at the two beaches combined is 350 , what is the difference between the number of condos available at sunset beach and the number of condos available at playa del mar ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 350.0\nt0 = n0 * n2\nt1 = n0 * n1\nt2 = t0 / n1\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "test" + }, + { + "Input": "the fuel indicator in a car shows 1 / 5 th of the fuel tank as full . when 22 more liters of fuel are poured in to the tank , the indicator rests at the 3 / 4 of the full mark . find the capacity of the tank .", + "Output Program": [ + "n0 = 1.0\nn1 = 5.0\nn2 = 22.0\nn3 = 3.0\nn4 = 4.0\nt0 = n3 / n4\nt1 = n0 / n1\nt2 = t0 - t1\nanswer = n2 / t2\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "test" + }, + { + "Input": "find large no . from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 30 as remainder", + "Output Program": [ + "n0 = 1365.0\nn1 = 6.0\nn2 = 30.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nt2 = t0 / t1\nt3 = n1 * t2\nanswer = n2 + t3\nprint(answer)" + ], + "Output Answer": [ + "1632" + ], + "split": "test" + }, + { + "Input": "how many prime numbers are between 28 / 3 and 86 / 6 ?", + "Output Program": [ + "import math\nn0 = 28.0\nn1 = 3.0\nn2 = 86.0\nn3 = 6.0\n\nanswer = math.floor(2.0)\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "test" + }, + { + "Input": "if john makes a contribution to a charity fund at school , the average contribution size will increase by 50 % reaching $ 75 per person . if there were 4 other contributions made before john ' s , what is the size of his donation ?", + "Output Program": [ + "n0 = 50.0\nn1 = 75.0\nn2 = 4.0\nt0 = n2 + 1.0\nt1 = n1 * t0\nt2 = n0 * t0\nt3 = t1 - t2\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "175" + ], + "split": "test" + }, + { + "Input": "if 0.5 : x : : 5 : 8 , then x is equal to :", + "Output Program": [ + "n0 = 0.5\nn1 = 5.0\nn2 = 8.0\nt0 = n0 * n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.8" + ], + "split": "test" + }, + { + "Input": "the average weight of 8 people increases by 2.5 kg when a new person comes in place of one of them weighing 75 kg . what is the weight of the new person ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.5\nn2 = 75.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "95" + ], + "split": "test" + }, + { + "Input": "bottle r contains 250 capsules and costs $ 5.25 . bottle t contains 130 capsules and costs $ 2.99 . what is the difference between the cost per capsule for bottle r and the cost per capsule for bottle t ?", + "Output Program": [ + "n0 = 250.0\nn1 = 5.25\nn2 = 130.0\nn3 = 2.99\nt0 = n3 / n2\nt1 = n1 / n0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "0.0020000000000000018" + ], + "split": "test" + }, + { + "Input": "a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 66 percent of the distribution lies within one standard deviation d of the mean , what percent of the distribution is less than m + d ?", + "Output Program": [ + "n0 = 66.0\nt0 = 100.0 - n0\nt1 = t0 / 2.0\nanswer = 100.0 - t1\nprint(answer)" + ], + "Output Answer": [ + "83" + ], + "split": "test" + }, + { + "Input": "the unit digit in the product 4556 * 3432 * 4581 * 2784 is ?", + "Output Program": [ + "n0 = 4556.0\nn1 = 3432.0\nn2 = 4581.0\nn3 = 2784.0\nt0 = 4.0 + 4.0\nt1 = n0 * n1\nt2 = n2 * t1\nt3 = n3 * t2\nt4 = t3 - t0\nanswer = t3 - t4\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "test" + }, + { + "Input": "to be considered for \u201c movie of the year , \u201d a film must appear in at least 1 / 4 of the top - 10 - movies lists submitted by the cinematic academy \u2019 s 760 members . what is the smallest number of top - 10 lists a film can appear on and still be considered for \u201c movie of the year \u201d ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 10.0\nn3 = 760.0\nn4 = 10.0\n\nanswer = n3 / n1\nprint(answer)" + ], + "Output Answer": [ + "190" + ], + "split": "test" + }, + { + "Input": "each child has 4 crayons and 14 apples . if there are 9 children , how many crayons are there in total ?", + "Output Program": [ + "n0 = 4.0\nn1 = 14.0\nn2 = 9.0\n\nanswer = n0 * n2\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "test" + }, + { + "Input": "find the value of m 12519 x 9999 = m ?", + "Output Program": [ + "n0 = 12519.0\nn1 = 9999.0\nt0 = n1 - 4.0\nanswer = t0 * n0\nprint(answer)" + ], + "Output Answer": [ + "125127405" + ], + "split": "test" + }, + { + "Input": "find the value of ( 875 233 / 899 ) \u00d7 899", + "Output Program": [ + "n0 = 875.0\nn1 = 233.0\nn2 = 899.0\nn3 = 899.0\nt0 = n1 / n2\nt1 = n0 + t0\nanswer = t1 * n2\nprint(answer)" + ], + "Output Answer": [ + "786858" + ], + "split": "test" + }, + { + "Input": "rates for having a manuscript typed at a certain typing service are $ 5 per page for the first time a page is typed and $ 2 per page each time a page is revised . if a certain manuscript has 100 pages , of which 40 were revised only once , 10 were revised twice , and the rest required no revisions , what was the total cost of having the manuscript typed ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 100.0\nn3 = 40.0\nn4 = 10.0\nt0 = n0 * n2\nt1 = n1 * n3\nt2 = n1 * n4\nt3 = t0 + t1\nt4 = t2 * 2.0\nanswer = t3 + t4\nprint(answer)" + ], + "Output Answer": [ + "620" + ], + "split": "test" + }, + { + "Input": "a department of 10 people - 6 men and 4 women - needs to send a team of 5 to a conference . if they want to make sure that there are no more than 3 members of the team from any one gender , how many distinct groups are possible to send ?", + "Output Program": [ + "n0 = 10.0\nn1 = 6.0\nn2 = 4.0\nn3 = 5.0\nn4 = 3.0\nt0 = n1 * n3\nt1 = n2 * t0\nt2 = t1 + t0\nanswer = t2 + t0\nprint(answer)" + ], + "Output Answer": [ + "180" + ], + "split": "test" + }, + { + "Input": "jean drew a gumball at random from a jar of pink and blue gumballs . since the gumball she selected was blue and she wanted a pink one , she replaced it and drew another . the second gumball also happened to be blue and she replaced it as well . if the probability of her drawing the two blue gumballs was 25 / 36 , what is the probability that the next one she draws will be pink ?", + "Output Program": [ + "import math\nn0 = 25.0\nn1 = 36.0\nt0 = n0 / n1\nt1 = math.sqrt(max(0, t0))\nanswer = 1.0 - t1\nprint(answer)" + ], + "Output Answer": [ + "0.16666666666666663" + ], + "split": "test" + }, + { + "Input": "if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 253 games will be played during the tournament . what is the number of participants ?", + "Output Program": [ + "import math\nn0 = 253.0\nt0 = n0 * 2.0\nt1 = t0 * 4.0\nt2 = t1 + 1.0\nt3 = math.sqrt(max(0, t2))\nt4 = t3 + 1.0\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "test" + }, + { + "Input": "p has $ 63 more than what q and r together would have had if both b and c had 1 / 9 of what p has . how much does p have ?", + "Output Program": [ + "n0 = 63.0\nn1 = 1.0\nn2 = 9.0\nt0 = n1 / n2\nt1 = t0 * 2.0\nt2 = 1.0 - t1\nanswer = n0 / t2\nprint(answer)" + ], + "Output Answer": [ + "81" + ], + "split": "test" + }, + { + "Input": "a jogger running at 9 km / hr along side a railway track is 240 m ahead of the engine of a 140 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?", + "Output Program": [ + "n0 = 9.0\nn1 = 240.0\nn2 = 140.0\nn3 = 45.0\nt0 = n1 + n2\nt1 = 10.0 / 2.0\nt2 = n3 - n0\nt3 = t2 / 2.0\nt4 = t1 / t3\nt5 = t4 * t2\nanswer = t0 / t5\nprint(answer)" + ], + "Output Answer": [ + "38" + ], + "split": "test" + }, + { + "Input": "if the price of a certain computer increased 30 percent from a dollars to 351 dollars , then 2 a =", + "Output Program": [ + "n0 = 30.0\nn1 = 351.0\nn2 = 2.0\nt0 = n0 + 100.0\nt1 = t0 / 100.0\nt2 = n1 / t1\nanswer = n2 * t2\nprint(answer)" + ], + "Output Answer": [ + "540" + ], + "split": "test" + }, + { + "Input": "how many 5 - digit numbers are there , if the two leftmost digits are even , the other digits are odd and the digit 2 can not appear more than once in the number .", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nt0 = 3.0 + 4.0\nt1 = 3.0 * 4.0\nt2 = n0**min(3.0, 5)\nt3 = t0 + t1\nanswer = t3 * t2\nprint(answer)" + ], + "Output Answer": [ + "2375" + ], + "split": "test" + }, + { + "Input": "alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 1081 . find the cost of each ice - cream cup ?", + "Output Program": [ + "n0 = 16.0\nn1 = 5.0\nn2 = 7.0\nn3 = 6.0\nn4 = 6.0\nn5 = 45.0\nn6 = 70.0\nn7 = 1081.0\nt0 = n0 * n3\nt1 = n1 * n5\nt2 = n2 * n6\nt3 = n7 - t0\nt4 = t3 - t1\nt5 = t4 - t2\nanswer = t5 / n3\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "test" + }, + { + "Input": "the ages of two person , differ by 20 years . if 5 years ag , the elder one be 5 times as old as the younger one their present ages ( in years ) are respectively", + "Output Program": [ + "n0 = 20.0\nn1 = 5.0\nn2 = 5.0\n\nanswer = n0 + 10.0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "test" + }, + { + "Input": "the price of stock increased by 8 % last year and decreased by 6 % this year . what is the net percentage change in the price of the stock ?", + "Output Program": [ + "n0 = 8.0\nn1 = 6.0\nt0 = n0 + 100.0\nt1 = 100.0 - n1\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = t2 * t3\nt5 = t4 * 100.0\nanswer = t5 - 100.0\nprint(answer)" + ], + "Output Answer": [ + "1.5200000000000102" + ], + "split": "test" + }, + { + "Input": "boys and girls in a class are writing letters . there are twice as many girls as boys in the class , and each girl writes 3 more letters than each boy . if boys write 24 of the 90 total letters written by the class , how many letters does each boy write ?", + "Output Program": [ + "n0 = 3.0\nn1 = 24.0\nn2 = 90.0\nt0 = n0 * n1\nt1 = n0 * 2.0\nt2 = n2 - t0\nt3 = t2 / t1\nanswer = n1 / t3\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "test" + }, + { + "Input": "if 9 ! / 3 ^ x is an integer , what is the greatest possible value of x ?", + "Output Program": [ + "n0 = 9.0\nn1 = 3.0\nt0 = n0 / n1\nt1 = n1 / t0\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "test" + }, + { + "Input": "the average of 13 result is 60 . average of the first 7 of them is 57 and that of the last 7 is 61 . find the 8 th result ?", + "Output Program": [ + "n0 = 13.0\nn1 = 60.0\nn2 = 7.0\nn3 = 57.0\nn4 = 7.0\nn5 = 61.0\nn6 = 8.0\nt0 = n2 * n3\nt1 = n2 * n5\nt2 = n0 * n1\nt3 = t0 + t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "46" + ], + "split": "test" + }, + { + "Input": "if x / ( 9 p ) is an even prime number , where x is a positive integer and p is a prime number , what is the least value of x ?", + "Output Program": [ + "n0 = 11.0\nt0 = n0 * 2.0\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "44" + ], + "split": "test" + }, + { + "Input": "5 % people of a village in sri lanka died by bombardment , 15 % of the remainder left the village on account of fear . if now the population is reduced to 3443 , how much was it in the beginning ?", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 15.0\nn2 = 3443.0\nt0 = 100.0 - n0\nt1 = 100.0 - n1\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = t2 * t3\nt5 = n2 / t4\nanswer = math.floor(t5)\nprint(answer)" + ], + "Output Answer": [ + "4263" + ], + "split": "test" + }, + { + "Input": "if henry were to add 6 gallons of water to a tank that is already 3 / 4 full of water , the tank would be 7 / 8 full . how many gallons of water would the tank hold if it were full ?", + "Output Program": [ + "n0 = 6.0\nn1 = 3.0\nn2 = 4.0\nn3 = 7.0\nn4 = 8.0\nt0 = n3 / n4\nt1 = n1 / n2\nt2 = t0 - t1\nt3 = 1.0 / t2\nanswer = n0 * t3\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "test" + }, + { + "Input": "in arun ' s opinion , his weight is greater than 63 kg but leas than 72 kg . his brother does not agree with arun and he thinks that arun ' s weight is greater than 60 kg but less than 70 kg . his mother ' s view is that his weight can not be greater than 66 kg . if all of them are correct in their estimation , what is the average of diferent probable weights of arun ?", + "Output Program": [ + "n0 = 63.0\nn1 = 72.0\nn2 = 60.0\nn3 = 70.0\nn4 = 66.0\nt0 = n0 + 1.0\nt1 = n4 + t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "65" + ], + "split": "test" + }, + { + "Input": "the cost of 10 kg of mangos is equal to the cost of 24 kg of rice . the cost of 6 kg of flour equals the cost of 2 kg of rice . the cost of each kg of flour is $ 25 . find the total cost of 4 kg of mangos , 3 kg of rice and 5 kg of flour ?", + "Output Program": [ + "n0 = 10.0\nn1 = 24.0\nn2 = 6.0\nn3 = 2.0\nn4 = 25.0\nn5 = 4.0\nn6 = 3.0\nn7 = 5.0\nt0 = n1 / n0\nt1 = n2 * n4\nt2 = n4 * n7\nt3 = t1 / n3\nt4 = t0 * t3\nt5 = n6 * t3\nt6 = n5 * t4\nt7 = t6 + t5\nanswer = t7 + t2\nprint(answer)" + ], + "Output Answer": [ + "1070" + ], + "split": "test" + }, + { + "Input": "a student got twice as many sums wrong as he got right . if he attempted 27 sums in all , how many did he solve correctly ?", + "Output Program": [ + "n0 = 27.0\nt0 = 1.0 + 2.0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "test" + }, + { + "Input": "the compound interest on a sum for 2 years is rs . 832 and the simple interest on the same sum for the same period is rs . 800 . the difference between the compound and simple interest for 3 years will be", + "Output Program": [ + "n0 = 2.0\nn1 = 832.0\nn2 = 800.0\nn3 = 3.0\nt0 = n2 / n0\nt1 = n1 - n2\nt2 = t1 / t0\nt3 = n1 * t2\nanswer = t3 + t1\nprint(answer)" + ], + "Output Answer": [ + "98.56" + ], + "split": "test" + }, + { + "Input": "the sum q of prime numbers that are greater than 60 but less than 70 is", + "Output Program": [ + "n0 = 60.0\nn1 = 70.0\nt0 = n0 + 1.0\nt1 = n1 - 3.0\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "128" + ], + "split": "test" + }, + { + "Input": "the probability that a man will be alive for 10 more yrs is 1 / 2 & the probability that his wife will alive for 10 more yrs is 1 / 3 . the probability that none of them will be alive for 10 more yrs , is", + "Output Program": [ + "n0 = 10.0\nn1 = 1.0\nn2 = 2.0\nn3 = 10.0\nn4 = 1.0\nn5 = 3.0\nn6 = 10.0\nt0 = n1 / n2\nt1 = n1 / n5\nt2 = n1 - t0\nt3 = n1 - t1\nanswer = t2 * t3\nprint(answer)" + ], + "Output Answer": [ + "0.33333333333333337" + ], + "split": "test" + }, + { + "Input": "a special municipal payroll tax charges not tax on a payroll less than $ 200,000 and only 0.2 % on a company \u2019 s payroll above $ 200,000 . if belfried industries paid $ 200 in this special municipal payroll tax , then they must have had a payroll of ?", + "Output Program": [ + "n0 = 200000.0\nn1 = 0.2\nn2 = 200000.0\nn3 = 200.0\nt0 = n1 / 100.0\nt1 = n3 / t0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "300000" + ], + "split": "test" + }, + { + "Input": "if 25 ^ 5 \u00d7 5 ^ ( - 1 ) = ( 125 ) ^ x , then what is the value of x ?", + "Output Program": [ + "n0 = 25.0\nn1 = 5.0\nn2 = 5.0\nn3 = 1.0\nn4 = 125.0\nt0 = n1 * 2.0\nt1 = t0 - n3\nanswer = t1 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "test" + }, + { + "Input": "in kaya ' s teacher ' s desk there are 24 pink highlighters , 28 yellow highlighters , and 25 blue highlighters . how many highlighters are there in all ?", + "Output Program": [ + "n0 = 24.0\nn1 = 28.0\nn2 = 25.0\nt0 = n0 + n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "77" + ], + "split": "test" + }, + { + "Input": "the denominator of a fraction is 6 greater than the numerator . if the numerator and the denominator are increased by 1 , the resulting fraction is equal to 4 \u00e2 \u0081 \u201e 5 . what is the value of the original fraction ?", + "Output Program": [ + "n0 = 6.0\nn1 = 1.0\nn2 = 4.0\nn3 = 5.0\nt0 = n0 + n1\nt1 = n3 - n2\nt2 = n2 * t0\nt3 = t2 - n3\nt4 = t3 / t1\nt5 = n0 + t4\nanswer = t4 / t5\nprint(answer)" + ], + "Output Answer": [ + "0.7931034482758621" + ], + "split": "test" + }, + { + "Input": "consider the sets tn = { n , n + 1 , n + 2 , n + 3 , n + 4 ) , where n = 1 , 2 , 3 , \u2026 , 96 . how many of these sets contain 6 or any integral multiple thereof ( i . e . , any one of the numbers 6 , 12 , 18 , \u2026 ) ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 3.0\nn3 = 4.0\nn4 = 1.0\nn5 = 2.0\nn6 = 3.0\nn7 = 96.0\nn8 = 6.0\nn9 = 6.0\nn10 = 12.0\nn11 = 18.0\nt0 = 2.0 + 3.0\nt1 = t0 / n8\nanswer = n7 * t1\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "test" + }, + { + "Input": "20 people went to a hotel for combine dinner party 12 of them spent rs . 70 each on their dinner and rest spent 4 more than the average expenditure of all the 20 . what was the total money spent by them .", + "Output Program": [ + "n0 = 20.0\nn1 = 12.0\nn2 = 70.0\nn3 = 4.0\nn4 = 20.0\nt0 = n1 * n2\nt1 = n0 - n1\nt2 = n3 * t1\nt3 = n0 - t1\nt4 = t0 + t2\nt5 = t4 / t3\nanswer = n0 * t5\nprint(answer)" + ], + "Output Answer": [ + "1453.3333333333335" + ], + "split": "test" + }, + { + "Input": "50 % of the population of a village is 23040 . the total population of the village is ?", + "Output Program": [ + "n0 = 50.0\nn1 = 23040.0\nt0 = 100.0 / n0\nanswer = n1 * t0\nprint(answer)" + ], + "Output Answer": [ + "46080" + ], + "split": "test" + }, + { + "Input": "if a # b = ab \u2013 b + b ^ 2 , then 3 # 4 =", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 4.0\nt0 = n1 * n2\nt1 = n2**min(n0, 5)\nt2 = t0 - n2\nanswer = t1 + t2\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "test" + }, + { + "Input": "is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 42 , then how old is b ?", + "Output Program": [ + "n0 = 42.0\nt0 = 2.0 + 3.0\nt1 = n0 - 2.0\nt2 = t1 / t0\nanswer = t2 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "test" + }, + { + "Input": "last year the range of the annual bonus of the 100 employees at company x was $ 20000 . if the annual bonus of each of the 100 employees this year is 10 percent greater than it was last year , what is the range of the annual bonus of the 100 employees this year ?", + "Output Program": [ + "n0 = 100.0\nn1 = 20000.0\nn2 = 100.0\nn3 = 10.0\nn4 = 100.0\nt0 = n3 / 100.0\nt1 = t0 + 1.0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "22000" + ], + "split": "test" + }, + { + "Input": "a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 1004 in total compensation , how many total hours did he work that week ?", + "Output Program": [ + "n0 = 16.0\nn1 = 40.0\nn2 = 40.0\nn3 = 75.0\nn4 = 1004.0\nt0 = n3 + 100.0\nt1 = n0 * n1\nt2 = n0 * t0\nt3 = n4 - t1\nt4 = t2 / 100.0\nt5 = t3 / t4\nanswer = n1 + t5\nprint(answer)" + ], + "Output Answer": [ + "53" + ], + "split": "test" + }, + { + "Input": "the contents of a certain box consist of 14 apples and 25 oranges . how many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples ?", + "Output Program": [ + "n0 = 14.0\nn1 = 25.0\nn2 = 70.0\nt0 = n0 + n1\nt1 = n2 / 100.0\nt2 = n0 / t1\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "test" + }, + { + "Input": "how many prime numbers are between 13 / 3 and 83 / 6 ?", + "Output Program": [ + "import math\nn0 = 13.0\nn1 = 3.0\nn2 = 83.0\nn3 = 6.0\n\nanswer = math.floor(2.0)\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "test" + }, + { + "Input": "in a division sum , the quotient is 18 , the divisor 43 and the remainder 12 , find the dividend ?", + "Output Program": [ + "n0 = 18.0\nn1 = 43.0\nn2 = 12.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "786" + ], + "split": "test" + }, + { + "Input": "niall ' s income is 60 % less than rex ' s income , and sam ' s income is 25 % less than niall ' s income . if rex gave 60 % of his income to sam and 40 % of his income to niall , niall ' s new income would be what fraction of sam ' s new income ?", + "Output Program": [ + "n0 = 60.0\nn1 = 25.0\nn2 = 60.0\nn3 = 40.0\nt0 = n3 + n3\nt1 = t0 + 10.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.8888888888888888" + ], + "split": "test" + }, + { + "Input": "if 2 a = 4 b = 10 , then 40 ab =", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 10.0\nn3 = 40.0\nt0 = n2 / n0\nt1 = n2 / n1\nt2 = t0 * t1\nanswer = n3 * t2\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "test" + }, + { + "Input": "rahim bought 52 books for rs . 1200 from one shop and 32 books for rs . 480 from another . what is the average price he paid per book ?", + "Output Program": [ + "n0 = 52.0\nn1 = 1200.0\nn2 = 32.0\nn3 = 480.0\nt0 = n1 + n3\nt1 = n0 + n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "test" + }, + { + "Input": "if 2 ^ 5 , 4 ^ 3 , and 13 ^ 2 are all factors of the product of 936 and w where w is a positive integer , what is the smallest possible value of w ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 4.0\nn3 = 3.0\nn4 = 13.0\nn5 = 2.0\nn6 = 936.0\nt0 = n4 / n0\nt1 = n0**min(n0, 5)\nt2 = n2 * t1\nt3 = t0 * t2\nanswer = n0 * t3\nprint(answer)" + ], + "Output Answer": [ + "208" + ], + "split": "test" + }, + { + "Input": "if 3 < x < 6 < y < 11 , then what is the greatest possible positive integer difference of x and y ?", + "Output Program": [ + "n0 = 3.0\nn1 = 6.0\nn2 = 11.0\nt0 = n2 - n0\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "test" + }, + { + "Input": "chris age after 20 years will be 5 times his age 5 years back . what is the present age of chris ?", + "Output Program": [ + "n0 = 20.0\nn1 = 5.0\nn2 = 5.0\nt0 = n1 * n1\nt1 = n1 - 1.0\nt2 = n0 + t0\nt3 = t2 / t1\nt4 = t3 - n1\nanswer = t3 - t4\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "test" + }, + { + "Input": "the average of 7 numbers is 23 . if each number be multiplied by 5 . find the average of new set of numbers ?", + "Output Program": [ + "n0 = 7.0\nn1 = 23.0\nn2 = 5.0\n\nanswer = n1 * n2\nprint(answer)" + ], + "Output Answer": [ + "115" + ], + "split": "test" + }, + { + "Input": "if taxi fares were $ 3.00 for the first 1 / 5 mile and $ 0.20 for each 1 / 5 mile there after , then the taxi fare for a 4 - mile ride was", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 5.0\nn3 = 0.2\nn4 = 1.0\nn5 = 5.0\nn6 = 4.0\nt0 = n1 / n2\nt1 = n6 / t0\nt2 = t1 - n1\nt3 = n3 * t2\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "6.800000000000001" + ], + "split": "test" + }, + { + "Input": "the total age of a and b is 18 years more than the total age of b and c . c is how many year younger than", + "Output Program": [ + "n0 = 18.0\n\nanswer = n0 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "test" + }, + { + "Input": "the greatest number which on dividing 1657 and 2037 leaves remainders 9 and 5 respectively , is :", + "Output Program": [ + "import scipy\nn0 = 1657.0\nn1 = 2037.0\nn2 = 9.0\nn3 = 5.0\nt0 = n1 - n3\nt1 = n0 - n2\nanswer = scipy.gcd(int(t0), int(t1))\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "test" + }, + { + "Input": "barbata invests $ 2400 in the national bank at 5 % . how much additional money must she invest at 8 % so that the total annual income will be equal to 6 % of her entire investment ?", + "Output Program": [ + "n0 = 2400.0\nn1 = 5.0\nn2 = 8.0\nn3 = 6.0\nt0 = n3 / 100.0\nt1 = n1 / 100.0\nt2 = n2 / 100.0\nt3 = n0 * t0\nt4 = n0 * t1\nt5 = t2 - t0\nt6 = t3 - t4\nanswer = t6 / t5\nprint(answer)" + ], + "Output Answer": [ + "1199.9999999999998" + ], + "split": "test" + }, + { + "Input": "difference between a two - digit number and the number obtained by interchanging the two digits is 36 , what is the difference between two numbers", + "Output Program": [ + "n0 = 36.0\nt0 = 10.0 - 1.0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "test" + }, + { + "Input": "the average score of a cricketer in 6 matches is 27 and in other 4 matches is 32 . then find the average score in all the 10 matches ?", + "Output Program": [ + "n0 = 6.0\nn1 = 27.0\nn2 = 4.0\nn3 = 32.0\nn4 = 10.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = t0 + t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "29" + ], + "split": "test" + }, + { + "Input": "a farmer has an apple orchard consisting of fuji and gala apple trees . due to high winds this year 10 % of his trees cross pollinated . the number of his trees that are pure fuji plus the cross - pollinated ones totals 136 , while 3 / 4 of all his trees are pure fuji . how many of his trees are pure gala ?", + "Output Program": [ + "n0 = 10.0\nn1 = 136.0\nn2 = 3.0\nn3 = 4.0\nt0 = n0 / 100.0\nt1 = n2 / n3\nt2 = t0 + t1\nt3 = n1 / t2\nanswer = t3 - n1\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "test" + }, + { + "Input": "at a monthly meeting , 1 / 3 of the attendees were males and 4 / 5 of the male attendees arrived on time . if 5 / 6 of the female attendees arrived on time , what fraction of the attendees at the monthly meeting did not arrive on time ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 4.0\nn3 = 5.0\nn4 = 5.0\nn5 = 6.0\nt0 = n4 / n5\nt1 = n0 / n1\nt2 = n2 / n3\nt3 = 1.0 - t0\nt4 = 1.0 - t1\nt5 = 1.0 - t2\nt6 = t3 * t4\nt7 = t1 * t5\nanswer = t6 + t7\nprint(answer)" + ], + "Output Answer": [ + "0.17777777777777776" + ], + "split": "test" + }, + { + "Input": "a company wants to spend equal amounts of money for the purchase of two types of computer printers costing $ 300 and $ 200 per unit , respectively . what is the fewest number of computer printers that the company can purchase ?", + "Output Program": [ + "import scipy\nn0 = 300.0\nn1 = 200.0\nt0 = scipy.lcm(int(n0), int(n1))\nt1 = t0 / n0\nt2 = t0 / n1\nanswer = t1 + t2\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "test" + }, + { + "Input": "if p is a prime number greater than 3 , find the remainder when p ^ 2 + 14 is divided by 12 .", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 14.0\nn3 = 12.0\nt0 = 1.0 + 4.0\nt1 = n0 * n3\nt2 = t0**min(n1, 5)\nt3 = n2 + t2\nanswer = t3 - t1\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "test" + }, + { + "Input": "5 + 5", + "Output Program": [ + "n0 = 8.0\nt0 = n0 - 1.0\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "test" + }, + { + "Input": "a man has some hens and cows . if the number of heads be 42 and the number of feet equals 124 , then the number of hens will be", + "Output Program": [ + "n0 = 42.0\nn1 = 124.0\nt0 = n0 * 4.0\nt1 = t0 - n1\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "test" + }, + { + "Input": "find large number from below question the difference of two numbers is 1385 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder", + "Output Program": [ + "n0 = 1385.0\nn1 = 6.0\nn2 = 15.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nt2 = t0 / t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "1644" + ], + "split": "test" + }, + { + "Input": "the price of a certain product increased by the same percent from 1960 to 1970 as from 1970 to 1980 . if its price of $ 1.20 in 1970 was 150 percent of its price in 1960 , what was its price in 1980 ?", + "Output Program": [ + "n0 = 1960.0\nn1 = 1970.0\nn2 = 1970.0\nn3 = 1980.0\nn4 = 1.2\nn5 = 1970.0\nn6 = 150.0\nn7 = 1960.0\nn8 = 1980.0\nt0 = n6 / 100.0\nanswer = n4 * t0\nprint(answer)" + ], + "Output Answer": [ + "1.7999999999999998" + ], + "split": "test" + }, + { + "Input": "a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 37 , the how old is b ?", + "Output Program": [ + "n0 = 37.0\nt0 = 1.0 + 4.0\nt1 = n0 - 2.0\nt2 = t1 * 2.0\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "test" + }, + { + "Input": "if c and t are positive integers , ct + c + t can not be", + "Output Program": [ + "\nanswer = 2.0 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "test" + }, + { + "Input": "a trained covered x km at 40 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 7 x km .", + "Output Program": [ + "n0 = 40.0\nn1 = 2.0\nn2 = 20.0\nn3 = 7.0\nt0 = n0 / n0\nt1 = n0 * n3\nt2 = n0 * n1\nt3 = t2 / n2\nt4 = t0 + t3\nanswer = t1 / t4\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "test" + }, + { + "Input": "if the average of 6 digits is 16 and the average of 4 of them is 10 , calculate the average of the remaining 2 numbers ?", + "Output Program": [ + "n0 = 6.0\nn1 = 16.0\nn2 = 4.0\nn3 = 10.0\nn4 = 2.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = t0 - t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "test" + }, + { + "Input": "a team of 8 persons joins in a shooting competition . the best marksman scored 85 points . if he had scored 92 points , the average score for the team would have been 84 . the number of points , the team scored was :", + "Output Program": [ + "n0 = 8.0\nn1 = 85.0\nn2 = 92.0\nn3 = 84.0\nt0 = n0 * n3\nt1 = n1 + t0\nanswer = t1 - n2\nprint(answer)" + ], + "Output Answer": [ + "665" + ], + "split": "test" + }, + { + "Input": "find large number from below question the difference of two numbers is 1380 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder", + "Output Program": [ + "n0 = 1380.0\nn1 = 6.0\nn2 = 15.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nt2 = t0 / t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "1638" + ], + "split": "test" + }, + { + "Input": "tough and tricky questions : word problems . operation # is defined as : a # b = 4 a ^ 2 + 4 b ^ 2 + 8 ab for all non - negative integers . what is the value of ( a + b ) + 8 , when a # b = 100 ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 2.0\nn2 = 4.0\nn3 = 2.0\nn4 = 8.0\nn5 = 8.0\nn6 = 100.0\nt0 = n6 / n0\nt1 = math.sqrt(max(0, t0))\nanswer = n4 + t1\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "test" + }, + { + "Input": "according to the directions on the can of frozen orange juice concentrate , 1 can of concentrate is to be mixed with 3 cans of water to make orange juice . how many 12 ounces cans of the concentrate are required to prepare 240 6 ounces servings of orange juice ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 12.0\nn3 = 240.0\nn4 = 6.0\nt0 = n3 * n4\nt1 = t0 / n2\nanswer = t1 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "test" + }, + { + "Input": "mr yadav spends 60 % of his monthly salary on consumable items and 50 % of the remaining on clothes and transport . he saves the remaining amount . if his savings at the end of the year were 38400 , how much amount per month would he have spent on clothes and transport ?", + "Output Program": [ + "n0 = 60.0\nn1 = 50.0\nn2 = 38400.0\nt0 = 3.0 * 4.0\nt1 = 100.0 - n0\nt2 = n1 * t1\nt3 = t2 / 100.0\nt4 = t3 / 100.0\nt5 = n2 / t4\nt6 = t5 / t0\nanswer = t6 * t4\nprint(answer)" + ], + "Output Answer": [ + "3200" + ], + "split": "test" + }, + { + "Input": "if 4 ( p ' s capital ) = 6 ( q ' s capital ) = 10 ( r ' s capital ) , then out of the total profit of rs 3410 , r will receive", + "Output Program": [ + "n0 = 4.0\nn1 = 6.0\nn2 = 10.0\nn3 = 3410.0\nt0 = n0 + 1.0\nt1 = n2 + t0\nt2 = n2 + t1\nt3 = n1 + t2\nt4 = n1 / t3\nanswer = n3 * t4\nprint(answer)" + ], + "Output Answer": [ + "660" + ], + "split": "test" + }, + { + "Input": "running at their respective constant rates , machine x takes 2 days longer to produce w widgets than machine y . at these rates , if the two machines together produce 5 / 4 w widgets in 3 days , how many days would it take machine x alone to produce 1 w widgets ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 4.0\nn3 = 3.0\nn4 = 1.0\nt0 = n2 * n3\nt1 = n0 * t0\nt2 = t1 - t0\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "test" + }, + { + "Input": "a bag contains an equal number of one rupee , 50 paise and 25 paise coins respectively . if the total value is 175 , how many coins of each type are there ?", + "Output Program": [ + "n0 = 50.0\nn1 = 25.0\nn2 = 175.0\nt0 = 1 / 4.0\nt1 = 1 / 2.0\nt2 = t0 + t1\nt3 = t2 + 1.0\nanswer = n2 / t3\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "test" + }, + { + "Input": "little john had $ 16.10 . he spent $ 3.25 on sweets and gave to his two friends $ 2.20 each . how much money was left ?", + "Output Program": [ + "n0 = 16.1\nn1 = 3.25\nn2 = 2.2\nt0 = n2 + n2\nt1 = n1 + t0\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "8.450000000000001" + ], + "split": "test" + }, + { + "Input": "a person has 100 $ in 10 $ and 5 $ bill . if the 5 $ bill quantity is twice that of 10 $ bill . what is quantity of 10 $ .", + "Output Program": [ + "n0 = 100.0\nn1 = 10.0\nn2 = 5.0\nn3 = 5.0\nn4 = 10.0\nn5 = 10.0\nt0 = n0 / n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "test" + }, + { + "Input": "for a group of n people , k of whom are of the same sex , the ( n - k ) / n expression yields an index for a certain phenomenon in group dynamics for members of that sex . for a group that consists of 20 people , 5 of whom are females , by how much does the index for the females exceed the index for the males in the group ?", + "Output Program": [ + "n0 = 20.0\nn1 = 5.0\nt0 = n1 / n0\nt1 = n0 - n1\nt2 = t1 / n0\nanswer = t2 - t0\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "test" + }, + { + "Input": "of the families in city x in 1998 , 30 percent owned a personal computer . the number of families in city x owning a computer in 2002 was 20 percent greater than it was in 1998 , and the total number of families in city x was 8 percent greater in 2002 than it was in 1998 . what percent of the families in city x owned a personal computer in 2002 ?", + "Output Program": [ + "n0 = 1998.0\nn1 = 30.0\nn2 = 2002.0\nn3 = 20.0\nn4 = 1998.0\nn5 = 8.0\nn6 = 2002.0\nn7 = 1998.0\nn8 = 2002.0\nt0 = n3 + 100.0\nt1 = n5 + 100.0\nt2 = n1 * t0\nt3 = t2 / 100.0\nt4 = t3 / t1\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "33.33333333333333" + ], + "split": "test" + }, + { + "Input": "if y > 0 , ( 2 y ) / 20 + ( 3 y ) / 10 is what percent of y ?", + "Output Program": [ + "n0 = 0.0\nn1 = 2.0\nn2 = 20.0\nn3 = 3.0\nn4 = 10.0\nt0 = n1 / n2\nt1 = n3 / n4\nt2 = t0 + t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "test" + }, + { + "Input": "the mean of 50 observations was 36 . it was found later that an observation 58 was wrongly taken as 43 . the corrected new mean is ?", + "Output Program": [ + "n0 = 50.0\nn1 = 36.0\nn2 = 58.0\nn3 = 43.0\nt0 = n0 * n1\nt1 = n0 - 2.0\nt2 = t1 - n3\nt3 = t0 + t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "36.1" + ], + "split": "test" + }, + { + "Input": "3 - twentieths of the members of a social club are retirees who are also bridge players , 5 - twentieths of the members are retirees , and one - half of the members are bridge players . if 120 of the members are neither retirees nor bridge players , what is the total number of members in the social club ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 120.0\nt0 = n1 * 4.0\nt1 = n2 - t0\nanswer = t1 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "test" + }, + { + "Input": "the total marks obtained by a student in mathematics and physics is 80 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together .", + "Output Program": [ + "n0 = 80.0\nn1 = 20.0\nt0 = n0 + n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "test" + }, + { + "Input": "the price of commodity x increases by 30 cents every year , while the price of commodity y increases by 20 cents every year . if in 2001 , the price of commodity x was $ 4.20 and the price of commodity y was $ 4.40 , in which year will commodity x cost 80 cents more than the commodity y ?", + "Output Program": [ + "n0 = 30.0\nn1 = 20.0\nn2 = 2001.0\nn3 = 4.2\nn4 = 4.4\nn5 = 80.0\nt0 = n5 / 100.0\nt1 = n0 / 100.0\nt2 = n4 - n3\nt3 = t0 + t2\nt4 = t1 - t2\nt5 = t3 / t4\nanswer = n2 + t5\nprint(answer)" + ], + "Output Answer": [ + "2011" + ], + "split": "test" + }, + { + "Input": "the average ( arithmetic mean ) of 20 , 40 , and 60 is 5 more than the average of 10 , 70 , and what number ?", + "Output Program": [ + "n0 = 20.0\nn1 = 40.0\nn2 = 60.0\nn3 = 5.0\nn4 = 10.0\nn5 = 70.0\nt0 = n0 + n1\nt1 = n3 * 3.0\nt2 = n2 + t0\nt3 = n4 + t1\nt4 = n5 + t3\nanswer = t2 - t4\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "test" + }, + { + "Input": "a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 percent of the distribution lies within one standard deviation d of the mean , what percent e of the distribution is less than m + d ?", + "Output Program": [ + "n0 = 68.0\nt0 = 100.0 - n0\nt1 = t0 / 2.0\nanswer = 100.0 - t1\nprint(answer)" + ], + "Output Answer": [ + "84" + ], + "split": "test" + }, + { + "Input": "village p \u2019 s population is 1150 greater than village q ' s population . if village q \u2019 s population were reduced by 200 people , then village p \u2019 s population would be 4 times as large as village q ' s population . what is village q ' s current population ?", + "Output Program": [ + "n0 = 1150.0\nn1 = 200.0\nn2 = 4.0\nt0 = n1 * n2\nt1 = n0 + t0\nanswer = t1 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "650" + ], + "split": "test" + }, + { + "Input": "ramesh has solved 108 questions in an examination . if he got only \u2018 0 \u2019 marks , then how many questions were wrong when one mark is given for each one correct answer and 1 / 3 mark is subtracted on each wrong answer .", + "Output Program": [ + "n0 = 108.0\nn1 = 0.0\nn2 = 1.0\nn3 = 3.0\nt0 = n2 / n3\nt1 = t0 + 1.0\nt2 = n0 * t0\nt3 = t2 / t1\nanswer = n0 - t3\nprint(answer)" + ], + "Output Answer": [ + "81" + ], + "split": "test" + }, + { + "Input": "the simple interest in 14 months on a certain sum at the rate of 6 per cent per annum is 250 more than the interest on the same sum at the rate of 8 per cent in 8 months . how much amount was borrowed ?", + "Output Program": [ + "n0 = 14.0\nn1 = 6.0\nn2 = 250.0\nn3 = 8.0\nn4 = 8.0\nt0 = n0 / 12.0\nt1 = n1 / 100.0\nt2 = n3 / 12.0\nt3 = n3 / 100.0\nt4 = t0 * t1\nt5 = t2 * t3\nt6 = t4 - t5\nanswer = n2 / t6\nprint(answer)" + ], + "Output Answer": [ + "14999.99999999999" + ], + "split": "test" + }, + { + "Input": "a fruit - salad mixture consists of apples , peaches , and grapes in the ratio 9 : 6 : 5 , respectively , by weight . if 40 pounds of the mixture is prepared , the mixture includes how many more pounds of apples than grapes ?", + "Output Program": [ + "n0 = 9.0\nn1 = 6.0\nn2 = 5.0\nn3 = 40.0\nt0 = n0 * 2.0\nt1 = n2 * 2.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "test" + }, + { + "Input": "find the average of all the numbers between 6 and 34 which are divisible by 5 .", + "Output Program": [ + "n0 = 6.0\nn1 = 34.0\nn2 = 5.0\nt0 = n0 + 4.0\nt1 = n1 - 4.0\nt2 = t0 + t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "test" + }, + { + "Input": "in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 8 eggs . if the cost of each pound of rice is $ 0.24 , then how many cents does a liter of kerosene cost ? [ one dollar has 100 cents . ]", + "Output Program": [ + "n0 = 8.0\nn1 = 0.24\nn2 = 100.0\nt0 = 1.0 / 2.0\nt1 = n1 * n2\nt2 = n0 / t0\nt3 = t2 / 12.0\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "test" + }, + { + "Input": "a student has to obtain 30 % of the total marks to pass . he got 150 marks and failed by 30 marks . the maximum marks are ?", + "Output Program": [ + "n0 = 30.0\nn1 = 150.0\nn2 = 30.0\nt0 = n1 + n2\nt1 = n0 / 100.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "600" + ], + "split": "test" + }, + { + "Input": "we bought 85 hats at the store . blue hats cost $ 6 and green hats cost $ 7 . the total price was $ 560 . how many green hats did we buy ?", + "Output Program": [ + "n0 = 85.0\nn1 = 6.0\nn2 = 7.0\nn3 = 560.0\nt0 = n0 * n1\nanswer = n3 - t0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "test" + }, + { + "Input": "rakesh ' s mathematics test had 75 problems , 10 arithmetic , 30 algebra , 35 geometry problems . although he answered 70 % of arithmetic , 40 % of arithmetic and 60 % of geometry problems correctly , still he got less than 60 % problems right . how many more questions he would have to answer more to get passed ?", + "Output Program": [ + "n0 = 75.0\nn1 = 10.0\nn2 = 30.0\nn3 = 35.0\nn4 = 70.0\nn5 = 40.0\nn6 = 60.0\nn7 = 60.0\nt0 = n0 * n6\nt1 = n1 * n4\nt2 = n2 * n5\nt3 = n3 * n6\nt4 = t0 / 100.0\nt5 = t1 / 100.0\nt6 = t2 / 100.0\nt7 = t3 / 100.0\nt8 = t5 + t6\nt9 = t8 + t7\nanswer = t4 - t9\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "test" + }, + { + "Input": "a number x is multiplied by 7 , and this product is then divided by 3 . if the positive square root of the result of these two operations equals x , what is the value of x if x \u2260 0 ?", + "Output Program": [ + "n0 = 7.0\nn1 = 3.0\nn2 = 0.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "2.3333333333333335" + ], + "split": "test" + }, + { + "Input": "one day , connie plays a game with a fair 6 - sided die . connie rolls the die until she rolls a 6 , at which point the game ends . if she rolls a 6 on her first turn , connie wins 6 dollars . for each subsequent turn , connie wins 1 6 of the amount she would have won the previous turn . what is connie ' s expected earnings from the game ?", + "Output Program": [ + "n0 = 6.0\nn1 = 6.0\nn2 = 6.0\nn3 = 6.0\nn4 = 1.0\nn5 = 6.0\nt0 = n0 - n4\nt1 = t0 / n0\nt2 = t1 / n0\nt3 = 1.0 - t2\nanswer = 1.0 / t3\nprint(answer)" + ], + "Output Answer": [ + "1.161290322580645" + ], + "split": "test" + }, + { + "Input": "in a group of ducks and cows , the total number of legs are 26 more than twice the no . of heads . find the total no . of buffaloes .", + "Output Program": [ + "n0 = 26.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "test" + }, + { + "Input": "given a + b = 1 , find the value of 2 a + 2 b . two solutions are presented below . only one is correct , even though both yield the correct answer .", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 2.0\nt0 = n0 + n1\nt1 = n1 + t0\nanswer = t1 - t0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "test" + }, + { + "Input": "what is the sum of all possible 3 - digit numbers that can be constructed using the digits 2 , 3 , and 5 if each digit can be used only once in each number ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 3.0\nn3 = 5.0\nt0 = n2 + n3\nt1 = n1 + t0\nt2 = t1 * 100.0\nt3 = t1 * 10.0\nt4 = t2 + t3\nt5 = t4 + t1\nanswer = t5 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "2220" + ], + "split": "test" + }, + { + "Input": "the averge score of a cricketer for 10 matches is 45 runs . if the average for the first 6 matches is 48 . then find the average for the last 4 matches ?", + "Output Program": [ + "n0 = 10.0\nn1 = 45.0\nn2 = 6.0\nn3 = 48.0\nn4 = 4.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = t0 - t1\nanswer = t2 / n4\nprint(answer)" + ], + "Output Answer": [ + "40.5" + ], + "split": "test" + }, + { + "Input": "which is the least number that must be subtracted from 1856 so that the remainder when divided by 7 , 12 , 10 is 4 ?", + "Output Program": [ + "import scipy\nn0 = 1856.0\nn1 = 7.0\nn2 = 12.0\nn3 = 10.0\nn4 = 4.0\nt0 = scipy.lcm(int(n1), int(n2))\nt1 = scipy.lcm(int(n3), int(t0))\nt2 = scipy.gcd(int(n0), int(t1))\nt3 = t2 * t1\nt4 = n4 + t3\nanswer = n0 - t4\nprint(answer)" + ], + "Output Answer": [ + "172" + ], + "split": "test" + }, + { + "Input": "a farm has chickens , cows and sheep . there are 6 times the number of chickens and cows than sheep . if there are more cows than chickens or sheep , and together , cows and chickens have a total of 100 feet and heads , how many sheep live at the farm ?", + "Output Program": [ + "n0 = 6.0\nn1 = 100.0\n\nanswer = n0 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "test" + }, + { + "Input": "in a group of ducks and cows , the total number of legs are 28 more than twice the no . of heads . find the total no . of buffaloes .", + "Output Program": [ + "n0 = 28.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "test" + }, + { + "Input": "a man has some hens and cows . if the number of heads be 50 and the number of feet equals 160 , then the number of hens will be :", + "Output Program": [ + "n0 = 50.0\nn1 = 160.0\nt0 = n0 * 4.0\nt1 = t0 - n1\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "test" + }, + { + "Input": "how many even multiples of 65 are there between 649 and 1301 ?", + "Output Program": [ + "n0 = 65.0\nn1 = 649.0\nn2 = 1301.0\nt0 = n0 * 2.0\nt1 = n2 - n1\nt2 = t1 / t0\nanswer = t2 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "6.015384615384615" + ], + "split": "test" + }, + { + "Input": "if ( 2 to the x ) - ( 2 to the ( x - 2 ) ) = 3 ( 2 to the 5 ) , what is the value of x ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 2.0\nn3 = 3.0\nn4 = 2.0\nn5 = 5.0\n\nanswer = n0 + n5\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "test" + }, + { + "Input": "in an examination , the percentage of students qualified to the students appeared from school ' p ' is 70 % . in school ' q ' , the number of students appeared is 30 % more than the students appeared from school ' p ' and the number of students qualified from school ' q ' is 50 % more than the students qualified from school ' p ' . what is the % of students qualified to the number of students appeared from school ' q ' ?", + "Output Program": [ + "n0 = 70.0\nn1 = 30.0\nn2 = 50.0\nt0 = n2 + 100.0\nt1 = n1 + 100.0\nt2 = n0 / 100.0\nt3 = t0 / 100.0\nt4 = t1 / 100.0\nt5 = t3 * t2\nt6 = t5 / t4\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "80.76923076923075" + ], + "split": "test" + }, + { + "Input": "there are 4 people of different heights standing in order of increasing height . the difference is 2 inches between the first person and the second person , and also between the second person and the third person . the difference between the third person and the fourth person is 6 inches and the average height is 75 . how tall is the fourth person ?", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\nn2 = 6.0\nn3 = 75.0\nt0 = n0 + n2\nt1 = n0 * n3\nt2 = n2 + t0\nt3 = t1 - t2\nt4 = t3 / n0\nanswer = t0 + t4\nprint(answer)" + ], + "Output Answer": [ + "81" + ], + "split": "test" + }, + { + "Input": "if there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city , find the number of 4 wheelers parked there if the total number of wheels is 82 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 4.0\nn3 = 82.0\nt0 = n3 - n0\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "test" + }, + { + "Input": "if 50 % of x is 25 less than 25 % of 2500 , then x is ?", + "Output Program": [ + "n0 = 50.0\nn1 = 25.0\nn2 = 25.0\nn3 = 2500.0\nt0 = n2 / 100.0\nt1 = n0 / 100.0\nt2 = n3 * t0\nt3 = t2 - n1\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "1200" + ], + "split": "test" + }, + { + "Input": "in an examination , 30 % of total students failed in hindi , 35 % failed in english and 35 % in both . the percentage of these who passed in both the subjects is :", + "Output Program": [ + "n0 = 30.0\nn1 = 35.0\nn2 = 35.0\nt0 = n0 + n1\nt1 = t0 - n2\nanswer = 100.0 - t1\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "test" + }, + { + "Input": "the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is ?", + "Output Program": [ + "n0 = 8000.0\nn1 = 7.0\nn2 = 12000.0\nn3 = 6000.0\nt0 = n2 - n0\nt1 = n0 - n3\nt2 = n1 * t0\nt3 = t2 / t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "test" + }, + { + "Input": "a student chose a number , multiplied it by 2 , then subtracted 138 from the result and got 108 . what was the number he chose ?", + "Output Program": [ + "n0 = 2.0\nn1 = 138.0\nn2 = 108.0\nt0 = n1 + n2\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "123" + ], + "split": "test" + }, + { + "Input": "in a group of ducks and cows , the total number of legs are 8 more than twice the no . of heads . find the total no . of buffaloes .", + "Output Program": [ + "n0 = 8.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "test" + }, + { + "Input": "if log 8 x + log 8 1 / 6 = 1 / 3 , then the value of x is :", + "Output Program": [ + "n0 = 8.0\nn1 = 8.0\nn2 = 1.0\nn3 = 6.0\nn4 = 1.0\nn5 = 3.0\nt0 = n2 / n5\nt1 = n0**min(t0, 5)\nanswer = n3 * t1\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "test" + }, + { + "Input": "if the sum of two numbers is 12 and the sum of their squares is 124 , then the product of the numbers is", + "Output Program": [ + "n0 = 12.0\nn1 = 124.0\nt0 = n0**min(2.0, 5)\nt1 = t0 - n1\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "test" + }, + { + "Input": "50 men shake hands with each other . maximum no of handshakes without cyclic handshakes .", + "Output Program": [ + "n0 = 50.0\nt0 = n0 / 2.0\nt1 = n0 - 1.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "1225" + ], + "split": "test" + }, + { + "Input": "if p ( a ) = 3 / 5 and p ( b ) = 2 / 5 , find p ( a n b ) if a and b are independent events .", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 2.0\nn3 = 5.0\nt0 = n0 / n1\nt1 = n2 / n3\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "0.24" + ], + "split": "test" + }, + { + "Input": "if x < y < z and y - x > 5 , where x is an even integer and y and z are odd integers , what is the least possible value q of z - x ?", + "Output Program": [ + "n0 = 5.0\nt0 = n0 + 2.0\nanswer = t0 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "test" + }, + { + "Input": "the ratio of a to b is 4 to 5 , where a and b are positive . if x equals a increased by 75 percent of a , and m equals b decreased by 60 percent of b , what is the value of m / x ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 75.0\nn3 = 60.0\nt0 = n2 + 100.0\nt1 = n1 / n0\nt2 = 100.0 - n3\nt3 = t2 / t0\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "0.2857142857142857" + ], + "split": "test" + }, + { + "Input": "in a certain apartment building , there are one - bedroom and two - bedroom apartments . the rental prices of the apartment depend on a number of factors , but on average , two - bedroom apartments have higher rental prices than do one - bedroom apartments . let m be the average rental price for all apartments in the building . if m is $ 700 higher than the average rental price for all one - bedroom apartments , and if the average rental price for all two - bedroom apartments is $ 2,100 higher that m , then what percentage of apartments in the building are two - bedroom apartments ?", + "Output Program": [ + "n0 = 700.0\nn1 = 2100.0\nt0 = n0 * 100.0\nt1 = 1000.0 * 2.0\nt2 = t1 + 100.0\nt3 = n0 + t2\nanswer = t0 / t3\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "test" + }, + { + "Input": "in 10 years , a will be twice as old 5 as b was 10 years ago . if a is now 5 years older than b , the present age of b is", + "Output Program": [ + "n0 = 10.0\nn1 = 5.0\nn2 = 10.0\nn3 = 5.0\nt0 = n0 + n3\nt1 = n0 * 2.0\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "test" + }, + { + "Input": "if 2 + 7 = 57 ; 3 + 6 = 63 ; 5 + 9 = 206 then 5 + 8 = ?", + "Output Program": [ + "n0 = 2.0\nn1 = 7.0\nn2 = 57.0\nn3 = 3.0\nn4 = 6.0\nn5 = 63.0\nn6 = 5.0\nn7 = 9.0\nn8 = 206.0\nn9 = 5.0\nn10 = 8.0\nt0 = n9**min(n3, 5)\nt1 = n10**min(n0, 5)\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "189" + ], + "split": "test" + }, + { + "Input": "if a 2 - b 2 = 9 and a * b = 4 , find a 4 + b 4 .", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 9.0\nn3 = 4.0\nn4 = 4.0\nn5 = 4.0\nt0 = n3**min(n0, 5)\nt1 = n2**min(n0, 5)\nt2 = t0 * n0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "113" + ], + "split": "test" + }, + { + "Input": "a number is doubled and 9 is added . if the resultant is trebled , it becomes 81 . what is that number ?", + "Output Program": [ + "n0 = 9.0\nn1 = 81.0\nt0 = n0 * 3.0\nt1 = 2.0 * 3.0\nt2 = n1 - t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "test" + }, + { + "Input": "in a renowned city , the average birth rate is 9 people every two seconds and the death rate is 3 people every two seconds . estimate the size of the population net increase that occurs in one day .", + "Output Program": [ + "n0 = 9.0\nn1 = 3.0\nt0 = n0 - n1\nt1 = t0 * 3600.0\nanswer = t1 * 12.0\nprint(answer)" + ], + "Output Answer": [ + "259200" + ], + "split": "test" + }, + { + "Input": "in a certain game , a large container is filled with red , yellow , green , and blue beads worth , respectively , 7 , 5 , 3 , and 2 points each . a number of beads are then removed from the container . if the product of the point values of the removed beads is 30 , 870000 , how many red beads were removed ?", + "Output Program": [ + "n0 = 7.0\nn1 = 5.0\nn2 = 3.0\nn3 = 2.0\nn4 = 30.0\nn5 = 870000.0\nt0 = n2 * 1.0\nanswer = t0 / 1.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "test" + }, + { + "Input": "# 88 a necklace is made by stringing q no individual beads together in the repeating pattern red bead , green bead , white bead , blue bead , and yellow bead . if the necklace design begins with a red bead and ends with a white bead , then q could equal", + "Output Program": [ + "n0 = 88.0\nt0 = 2.0 + 3.0\nt1 = n0 / n0\nt2 = t1 + 2.0\nt3 = t2 + t0\nt4 = t3 + t0\nt5 = t4 + t0\nt6 = t5 + t0\nanswer = t6 + t0\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "test" + }, + { + "Input": "( 0.15 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.15 ) ( power 2 ) + 0.015 + ( 0.1 ) ( power 2 ) is :", + "Output Program": [ + "n0 = 0.15\nn1 = 3.0\nn2 = 0.1\nn3 = 3.0\nn4 = 0.15\nn5 = 2.0\nn6 = 0.015\nn7 = 0.1\nn8 = 2.0\nt0 = n0**min(n1, 5)\nt1 = n2**min(n1, 5)\nt2 = n0**min(n5, 5)\nt3 = n2**min(n5, 5)\nt4 = n6 + t2\nt5 = t0 - t1\nt6 = t4 + t3\nanswer = t5 / t6\nprint(answer)" + ], + "Output Answer": [ + "0.04999999999999999" + ], + "split": "test" + }, + { + "Input": "a retailer sells 7 shirts . the first 2 he sells for $ 38 and $ 42 . if the retailer wishes to sell the 7 shirts for an overall average price of over $ 50 , what must be the minimum average price of the remaining 5 shirts ?", + "Output Program": [ + "n0 = 7.0\nn1 = 2.0\nn2 = 38.0\nn3 = 42.0\nn4 = 7.0\nn5 = 50.0\nn6 = 5.0\nt0 = n2 + n3\nt1 = n0 * n5\nt2 = n0 - n1\nt3 = t1 - t0\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "test" + }, + { + "Input": "if a 10 percent deposit that has been paid toward the purchase of a certain product is $ 160 , how much more remains to be paid ?", + "Output Program": [ + "n0 = 10.0\nn1 = 160.0\nt0 = 100.0 / n0\nt1 = n1 * t0\nanswer = t1 - n1\nprint(answer)" + ], + "Output Answer": [ + "1440" + ], + "split": "test" + }, + { + "Input": "you need to pick any number from ' 1 , 3 , 5 , 7 , 9 , 11 , 13 and 15 ' to make below equation true . ( ) + ( ) + ( ) = 30 can you solve it ?", + "Output Program": [ + "import math\nn0 = 1.0\nn1 = 3.0\nn2 = 5.0\nn3 = 7.0\nn4 = 9.0\nn5 = 11.0\nn6 = 13.0\nn7 = 15.0\nn8 = 30.0\nt0 = math.factorial(min(15, int(n1)))\nt1 = n5 + t0\nanswer = n6 + t1\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "test" + }, + { + "Input": "the sum of the fourth and twelfth term of an arithmetic progression is 20 . what is the sum of the first 16 terms of the arithmetic progression ?", + "Output Program": [ + "n0 = 20.0\nn1 = 16.0\nt0 = n0 * n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "160" + ], + "split": "test" + }, + { + "Input": "on dividing 73 by a number , the quotient is 9 and the remainder is 1 . find the divisor ?", + "Output Program": [ + "import math\nn0 = 73.0\nn1 = 9.0\nn2 = 1.0\nt0 = n0 / n1\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "test" + }, + { + "Input": "shruti purchased several number of 3 articles p , q and r in the proportion 3 : 2 : 3 . if the unit costs of the articles p , q and r are 200 , rs . 90 and rs . 60 respectively , how many articles of q must have been purchased in the total purchases of rs . 4800 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 2.0\nn3 = 3.0\nn4 = 200.0\nn5 = 90.0\nn6 = 60.0\nn7 = 4800.0\nt0 = n0 * n4\nt1 = n2 * n5\nt2 = n0 * n6\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n7 / t4\nanswer = n2 * t5\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "test" + }, + { + "Input": "the least number which when increased by 5 each divisible by each one of 24 , 32 , 36 and 54 is :", + "Output Program": [ + "import scipy\nn0 = 5.0\nn1 = 24.0\nn2 = 32.0\nn3 = 36.0\nn4 = 54.0\nt0 = scipy.lcm(int(n1), int(n2))\nt1 = scipy.lcm(int(n3), int(t0))\nt2 = scipy.lcm(int(n4), int(t1))\nanswer = t2 - n0\nprint(answer)" + ], + "Output Answer": [ + "859" + ], + "split": "test" + }, + { + "Input": "when jessica withdrew $ 200 from her bank account , her account balance decreased by 2 / 5 . if she deposits an amount equal to 1 / 3 of the remaining balance , what will be the final balance in her bank account ?", + "Output Program": [ + "n0 = 200.0\nn1 = 2.0\nn2 = 5.0\nn3 = 1.0\nn4 = 3.0\nt0 = n3 / n4\nt1 = 3.0 / n2\nt2 = n3 + t0\nt3 = n3 - t1\nt4 = n0 / t3\nt5 = t4 - n0\nanswer = t2 * t5\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "test" + }, + { + "Input": "what least number should be added to 1536 , so that the sum is completely divisible by 21 ?", + "Output Program": [ + "n0 = 1536.0\nn1 = 21.0\nt0 = n0 % n1\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "test" + }, + { + "Input": "when n is divided by 19 , the remainder is 7 . find thee difference between previous remainder and the remainder when 18 n is divided by 9 ?", + "Output Program": [ + "n0 = 19.0\nn1 = 7.0\nn2 = 18.0\nn3 = 9.0\nt0 = n2 % n3\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "test" + }, + { + "Input": "the jogging track in a sports complex is 1000 meters in circumference . deepak and his wife start from the same point and walk in opposite directions at 20 km / hr and 15 km / hr respectively . they will meet for the first time in ?", + "Output Program": [ + "n0 = 1000.0\nn1 = 20.0\nn2 = 15.0\n\nanswer = n1 + n2\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "test" + }, + { + "Input": "the average weight of a class of 24 students is 35 kg . if the weight of the teacher be included , the average rises by 400 g . the weight of the teacher is :", + "Output Program": [ + "n0 = 24.0\nn1 = 35.0\nn2 = 400.0\nt0 = n0 + 1.0\nt1 = n2 / 1000.0\nt2 = n0 * n1\nt3 = n1 + t1\nt4 = t3 * t0\nanswer = t4 - t2\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "test" + }, + { + "Input": "the contents of a certain box consist of 14 apples and 24 oranges . how many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples ?", + "Output Program": [ + "n0 = 14.0\nn1 = 24.0\nn2 = 70.0\nt0 = n0 + n1\nt1 = n2 / 100.0\nt2 = n0 / t1\nanswer = t0 - t2\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "test" + }, + { + "Input": "mary ' s income is 60 percent more than tim ' s income , and tim ' s income is 40 percent less than juan ' s income . what percent of juan ' s income is mary ' s income ?", + "Output Program": [ + "n0 = 60.0\nn1 = 40.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = t0 + 1.0\nt3 = 1.0 - t1\nt4 = t2 * t3\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "96" + ], + "split": "test" + }, + { + "Input": "a straight line in the xy - plane has a slope of 2 and a y - intercept of 2 . on this line , what is the x - coordinate of the point whose y - coordinate is 550 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 550.0\nt0 = n2 - n0\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "274" + ], + "split": "test" + }, + { + "Input": "if xy = 4 , x / y = 16 , for positive numbers x and y , y = ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 16.0\nt0 = n0 / n1\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "0.5" + ], + "split": "test" + }, + { + "Input": "the average ( arithmetic mean ) of all scores on a certain algebra test was 90 . if the average of the 8 male students \u2019 grades was 86 , and the average of the female students \u2019 grades was 92 , how many female students took the test ?", + "Output Program": [ + "n0 = 90.0\nn1 = 8.0\nn2 = 86.0\nn3 = 92.0\nt0 = n0 * n1\nt1 = n1 * n2\nt2 = n3 - n0\nt3 = t0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "test" + }, + { + "Input": "laura took out a charge account at the general store and agreed to pay 8 % simple annual interest . if she charges $ 35 on her account in january , how much will she owe a year later , assuming she does not make any additional charges or payments ?", + "Output Program": [ + "n0 = 8.0\nn1 = 35.0\nt0 = n0 / 100.0\nt1 = n1 * t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "37.8" + ], + "split": "test" + }, + { + "Input": "a man purchased 3 blankets @ rs . 100 each , 4 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ?", + "Output Program": [ + "n0 = 3.0\nn1 = 100.0\nn2 = 4.0\nn3 = 150.0\nn4 = 150.0\nt0 = n3 * 10.0\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "600" + ], + "split": "test" + }, + { + "Input": "rates for having a manuscript typed at a certain typing service are $ 6 per page for the first time a page is typed and $ 4 per page each time a page is revised . if a certain manuscript has 100 pages , of which 40 were revised only once , 10 were revised twice , and the rest required no revisions , what was the total cost of having the manuscript typed ?", + "Output Program": [ + "n0 = 6.0\nn1 = 4.0\nn2 = 100.0\nn3 = 40.0\nn4 = 10.0\nt0 = n0 * n2\nt1 = n1 * n3\nt2 = n1 * n4\nt3 = t0 + t1\nt4 = t2 * 2.0\nanswer = t3 + t4\nprint(answer)" + ], + "Output Answer": [ + "840" + ], + "split": "test" + }, + { + "Input": "a group of 55 adults and 70 children go for trekking . if there is meal for either 70 adults or 90 children and if 28 adults have their meal , find the total number of children that can be catered with the remaining food .", + "Output Program": [ + "n0 = 55.0\nn1 = 70.0\nn2 = 70.0\nn3 = 90.0\nn4 = 28.0\nt0 = n3 / n1\nt1 = n1 - n4\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "54.00000000000001" + ], + "split": "test" + }, + { + "Input": "if x / y = 7 / 4 , then ( x + y ) / ( x - y ) = ?", + "Output Program": [ + "n0 = 7.0\nn1 = 4.0\nt0 = n0 + n1\nt1 = n0 - n1\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "3.6666666666666665" + ], + "split": "test" + }, + { + "Input": "if taxi fares were $ 1.00 for the first 1 / 5 mile and $ 0.50 for each 1 / 5 mile there after , then the taxi fare for a 3 - mile ride was", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 5.0\nn3 = 0.5\nn4 = 1.0\nn5 = 5.0\nn6 = 3.0\nt0 = n1 / n2\nt1 = n6 / t0\nt2 = t1 - n1\nt3 = n3 * t2\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "test" + }, + { + "Input": "of the families in city x in 1956 , 25 percent owned a personal computer . the number of families in city x owning a computer in 1960 was 15 percent greater than it was in 1956 , and the total number of families in city x was 5 percent greater in 1956 than it was in 1960 . what percent of the families in city x owned a personal computer in 1960 ?", + "Output Program": [ + "n0 = 1956.0\nn1 = 25.0\nn2 = 1960.0\nn3 = 15.0\nn4 = 1956.0\nn5 = 5.0\nn6 = 1956.0\nn7 = 1960.0\nn8 = 1960.0\nt0 = n3 + 100.0\nt1 = n5 + 100.0\nt2 = n1 * t0\nt3 = t2 / 100.0\nt4 = t3 / t1\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "27.380952380952383" + ], + "split": "test" + }, + { + "Input": "a certain sum of money is divided among a , b and c so that for each rs . a has , b has 65 paisa and c 40 paisa . if c ' s share is rs . 24 , find the sum of money ?", + "Output Program": [ + "n0 = 65.0\nn1 = 40.0\nn2 = 24.0\nt0 = n0 + 100.0\nt1 = n2 / n1\nt2 = n1 + t0\nanswer = t2 * t1\nprint(answer)" + ], + "Output Answer": [ + "123" + ], + "split": "test" + }, + { + "Input": "tough and tricky questions : combinations . 8 contestants representing 4 different countries advance to the finals of a fencing championship . assuming all competitors have an equal chance of winning , how many possibilities are there with respect to how a first - place and second - place medal can be awarded ?", + "Output Program": [ + "n0 = 8.0\nn1 = 4.0\nt0 = n1 - 1.0\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "test" + }, + { + "Input": "if ' x ' is a positive integer exactly divisible by 6 or 15 but not divisible by 12 . what could possibly be the value of ' x ' ?", + "Output Program": [ + "n0 = 6.0\nn1 = 15.0\nn2 = 12.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "test" + }, + { + "Input": "monica planned her birthday party . she prepared 5 muffins for each of her guests and kept aside two additional muffins in case someone will want extra . after the party , it turned out that one of the guests did n ' t come but every one of the guests that did come ate 6 muffins and 6 muffins remained . how many guests did monica plan on ?", + "Output Program": [ + "n0 = 5.0\nn1 = 6.0\nn2 = 6.0\nt0 = n1 + n1\nt1 = t0 - 2.0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "test" + }, + { + "Input": "a \u2019 s speed is 20 / 13 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?", + "Output Program": [ + "n0 = 20.0\nn1 = 13.0\nt0 = n0 - n1\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.35" + ], + "split": "test" + }, + { + "Input": "what is the largest number of 4 digits which is divisible by 15 , 25 , 40 and 75 ?", + "Output Program": [ + "import scipy\nn0 = 4.0\nn1 = 15.0\nn2 = 25.0\nn3 = 40.0\nn4 = 75.0\nt0 = scipy.lcm(int(n1), int(n2))\nt1 = 100.0 * 100.0\nt2 = scipy.lcm(int(n3), int(t0))\nt3 = t1 - 1.0\nt4 = scipy.lcm(int(n4), int(t2))\nt5 = t3 % t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "9600" + ], + "split": "test" + }, + { + "Input": "how many odd 3 - digit integers greater than 800 are there such that all their digits are different ?", + "Output Program": [ + "n0 = 3.0\nn1 = 800.0\nt0 = 2.0 + 3.0\nt1 = n0 + t0\nt2 = t0 * 1.0\nt3 = t1 * 4.0\nt4 = t1 * t2\nanswer = t3 + t4\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "test" + }, + { + "Input": "how much is 80 % of 40 is greater than 4 / 5 of 30 ?", + "Output Program": [ + "n0 = 80.0\nn1 = 40.0\nn2 = 4.0\nn3 = 5.0\nn4 = 30.0\nt0 = n0 / 100.0\nt1 = n2 / n3\nt2 = n1 * t0\nt3 = n4 * t1\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "test" + }, + { + "Input": "how many unique positive odd integers less than 60 are equal to the product of a positive multiple of 5 and an odd number ?", + "Output Program": [ + "n0 = 60.0\nn1 = 5.0\nt0 = n0 / n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "test" + }, + { + "Input": "a certain quantity is measured on two different scales , the t - scale and the s - scale , that are related linearly . measurements on the t - scale of 6 and 24 correspond to measurements on the s - scale of 30 and 60 , respectively . what measurement on the t - scale corresponds to a measurement of 100 on the s - scale ?", + "Output Program": [ + "n0 = 6.0\nn1 = 24.0\nn2 = 30.0\nn3 = 60.0\nn4 = 100.0\nt0 = n4 - n3\nt1 = n3 - n2\nt2 = n1 - n0\nt3 = t0 / t1\nt4 = t3 * t2\nanswer = n1 + t4\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "test" + }, + { + "Input": "the sum of two numbers is 184 . if one - third of the one exceeds one - seventh of the other by 8 , find the smaller number .", + "Output Program": [ + "n0 = 184.0\nn1 = 8.0\nt0 = 3.0 + 4.0\nt1 = n0 * 3.0\nt2 = t0 + 3.0\nt3 = t0 * 3.0\nt4 = n1 * t3\nt5 = t1 + t4\nanswer = t5 / t2\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "test" + }, + { + "Input": "the sum of the first 50 positive even integers is 2550 . what is the sum q of even integers from 102 to 200 inclusive ?", + "Output Program": [ + "n0 = 50.0\nn1 = 2550.0\nn2 = 102.0\nn3 = 200.0\nt0 = n2 + n3\nt1 = n3 - n2\nt2 = t1 / 2.0\nt3 = t0 / 2.0\nt4 = t2 + 1.0\nanswer = t4 * t3\nprint(answer)" + ], + "Output Answer": [ + "7550" + ], + "split": "test" + }, + { + "Input": "rs . 385 were divided among x , y , z in such a way that x had rs . 20 more than y and z had rs 15 more than x . how much was y \u2019 s share ?", + "Output Program": [ + "n0 = 385.0\nn1 = 20.0\nn2 = 15.0\nt0 = n1 + n1\nt1 = n2 + t0\nt2 = n0 - t1\nt3 = t2 / 3.0\nt4 = n1 + t3\nanswer = n2 + t4\nprint(answer)" + ], + "Output Answer": [ + "145" + ], + "split": "test" + }, + { + "Input": "when n divided by 3 , the remainder is 2 . when n divided by 4 , the remainder is 1 what is the the remainder when divided by 16", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 2.0\nn2 = 4.0\nn3 = 1.0\nn4 = 16.0\nt0 = 12.0 + 3.0\nt1 = 2.0 + 4.0\nt2 = t0 + t1\nt3 = t2 / n4\nanswer = math.floor(t3)\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "test" + }, + { + "Input": "mr . x , a mathematician , defines a number as ' connected with 6 if it is divisible by 6 or if the sum of its digits is 6 , or if 6 is one of the digits of the number . other numbers are all ' not connected with 6 ' . as per this definition , the number of integers from 1 to 60 ( both inclusive ) which are not connected with 6 is", + "Output Program": [ + "n0 = 6.0\nn1 = 6.0\nn2 = 6.0\nn3 = 6.0\nn4 = 6.0\nn5 = 1.0\nn6 = 60.0\nn7 = 6.0\nt0 = 10.0 + 3.0\nt1 = t0 + 4.0\nanswer = n6 - t1\nprint(answer)" + ], + "Output Answer": [ + "43" + ], + "split": "test" + }, + { + "Input": "a camera lens filter kit containing 5 filters sells for $ 67.50 . if the filters are purchased individually , 2 of them are priced at $ 7.45 each , 2 at $ 10.05 each , 1 at $ 14.50 . the amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually ?", + "Output Program": [ + "n0 = 5.0\nn1 = 67.5\nn2 = 2.0\nn3 = 7.45\nn4 = 2.0\nn5 = 10.05\nn6 = 1.0\nn7 = 14.5\nn8 = 5.0\nt0 = n2 * n3\nt1 = n2 * n5\nt2 = t0 + t1\nt3 = n7 + t2\nt4 = n1 - t3\nt5 = t4 * 100.0\nanswer = t5 / n1\nprint(answer)" + ], + "Output Answer": [ + "26.666666666666668" + ], + "split": "test" + }, + { + "Input": "if n is the product of integers from 1 to 20 inclusive what is the greatest integer k for which 2 ^ k is a factor of n ? .", + "Output Program": [ + "import math\nn0 = 1.0\nn1 = 20.0\nn2 = 2.0\nt0 = n1 / n2\nt1 = n2**min(2.0, 5)\nt2 = n2**min(3.0, 5)\nt3 = n1 / t1\nt4 = n1 / t2\nt5 = t1**min(n2, 5)\nt6 = t0 + t3\nt7 = n1 / t5\nt8 = math.floor(t4)\nt9 = math.floor(t7)\nt10 = t6 + t9\nanswer = t10 + t8\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "test" + }, + { + "Input": "a man performs 1 / 2 of the total journey by rail , 1 / 4 by bus and the remaining 4 km on foot . his total journey is", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 1.0\nn3 = 4.0\nn4 = 4.0\n\nanswer = n3 * n4\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "test" + }, + { + "Input": "one - third less than 25 % of 180 is equal to :", + "Output Program": [ + "n0 = 25.0\nn1 = 180.0\nt0 = n0 / 100.0\nt1 = 1.0 / 3.0\nt2 = n1 * t0\nt3 = t1 * t2\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "test" + }, + { + "Input": "in arun \u2019 s opinion , his weight is greater than 65 kg but less than 72 kg . his brother doest not agree with arun and he thinks that arun \u2019 s weight is greater than 60 kg but less than 70 kg . his mother \u2019 s view is that his weight can not be greater than 68 kg . if all are them are correct in their estimation , what is the average of different probable weights of arun ?", + "Output Program": [ + "n0 = 65.0\nn1 = 72.0\nn2 = 60.0\nn3 = 70.0\nn4 = 68.0\nt0 = n4 - 1.0\nt1 = t0 - 1.0\nt2 = t0 + t1\nt3 = n4 + t2\nanswer = t3 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "67" + ], + "split": "test" + }, + { + "Input": "in a weight - lifting competition , the total weight of joe ' s two lifts was 450 pounds . if twice the weight of his first lift was 300 pounds more than the weight of his second lift , what was the weight , in pounds , of his first lift ?", + "Output Program": [ + "n0 = 450.0\nn1 = 300.0\nt0 = n0 + n1\nanswer = t0 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "250" + ], + "split": "test" + }, + { + "Input": "ramu rides his bike at an average speed of 45 km / hr and reaches his desitination in 4 hours . somu covers the same distance in 6 hours . if ramu covered his journey at an average speed which was 9 km / hr less and somu covered his journey at an average speed which was 10 km / hr more , then the difference in their times taken to reach the destination would be ( in minutes ) .", + "Output Program": [ + "n0 = 45.0\nn1 = 4.0\nn2 = 6.0\nn3 = 9.0\nn4 = 10.0\nt0 = n0 * n1\nt1 = n0 - n3\nt2 = t0 / t1\nt3 = t0 / n2\nt4 = n4 + t3\nt5 = t0 / t4\nt6 = t2 - t5\nanswer = t6 * 60.0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "test" + }, + { + "Input": "elena purchased brand x pens for $ 5.00 apiece and brand y for $ 2.80 apiece . if elena purchased a total of 12 of these pens for $ 42.00 , how many brand x pens did she purchase ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.8\nn2 = 12.0\nn3 = 42.0\nt0 = 4.0 * n2\nanswer = t0 - n3\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "test" + }, + { + "Input": "a certain drink of type a is prepared by mixing 4 parts milk with 3 parts fruit juice . another drink of type b is prepared by mixing 4 parts of fruit juice and 3 parts of milk . how many liters of fruit juice must be added to 84 liters of drink a to convert it to drink b ?", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 4.0\nn3 = 3.0\nn4 = 84.0\nt0 = n0 + n1\nt1 = n0 / t0\nt2 = n1 / t0\nt3 = n4 * t1\nt4 = n4 * t2\nt5 = n0 * t3\nt6 = t5 / n1\nanswer = t6 - t4\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "test" + }, + { + "Input": "in a certain game , each player scores either 2 points or 5 points . if n players score 2 points and m players score 5 points , and the total number of points scored is 50 , what is the least possible positive r difference between n and m ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 2.0\nn3 = 5.0\nn4 = 50.0\n\nanswer = n1 - n0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "test" + }, + { + "Input": "in a school with 620 students , the average age of the boys is 12 years and that of the girls is 11 years . if the average age of the school is 11 years 9 months , then the number of girls in the school is", + "Output Program": [ + "n0 = 620.0\nn1 = 12.0\nn2 = 11.0\nn3 = 11.0\nn4 = 9.0\nt0 = n4 / n1\nt1 = n0 * n1\nt2 = n2 + t0\nt3 = n0 * t2\nanswer = t1 - t3\nprint(answer)" + ], + "Output Answer": [ + "155" + ], + "split": "test" + }, + { + "Input": "the jogging track in a sports complex is 1000 meters in circumference . deepak and his wife start from the same point and walk in opposite directions at 20 km / hr and 14 km / hr respectively . they will meet for the first time in ?", + "Output Program": [ + "n0 = 1000.0\nn1 = 20.0\nn2 = 14.0\n\nanswer = n1 + n2\nprint(answer)" + ], + "Output Answer": [ + "34" + ], + "split": "test" + }, + { + "Input": "if x is a number such that x ^ 2 + 2 x - 24 = 0 and x ^ 2 - 5 x + 4 = 0 , then x =", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 24.0\nn3 = 0.0\nn4 = 2.0\nn5 = 5.0\nn6 = 4.0\nn7 = 0.0\nt0 = n2 + n6\nt1 = n0 + n5\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "test" + }, + { + "Input": "a library has an average of 510 visitors on sunday and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is", + "Output Program": [ + "n0 = 510.0\nn1 = 240.0\nn2 = 30.0\nt0 = 1.0 + 4.0\nt1 = n0 * t0\nt2 = t0 * t0\nt3 = n1 * t2\nt4 = t1 + t3\nanswer = t4 / n2\nprint(answer)" + ], + "Output Answer": [ + "285" + ], + "split": "test" + }, + { + "Input": "what is the median of a set of consecutive integers if the sum of nth number from the beginning and nth number from the end is 150 ?", + "Output Program": [ + "n0 = 150.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "test" + }, + { + "Input": "a certain car uses one gallon of gasoline every 32 miles when it travels on highway , and one gallon of gasoline every 20 miles when it travels in the city . when a car travels 4 miles on highway and 4 additional miles in the city , it uses what percent more gasoline than if it travels 8 miles on the highway ?", + "Output Program": [ + "n0 = 32.0\nn1 = 20.0\nn2 = 4.0\nn3 = 4.0\nn4 = 8.0\nt0 = 1.0 / n1\nt1 = 1.0 / n0\nt2 = n2 * t0\nt3 = n2 * t1\nt4 = n4 * t1\nt5 = t2 + t3\nt6 = t5 - t4\nt7 = t6 / t4\nanswer = t7 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "30.000000000000004" + ], + "split": "test" + }, + { + "Input": "find the least number of complete years in which a sum of money put out at 25 % compound interest will be more than double of itself ?", + "Output Program": [ + "import math\nn0 = 25.0\nt0 = n0 / 100.0\nt1 = math.log(max(1e-5, 2.0), 2)\nt2 = t0 + 1.0\nt3 = math.log(max(1e-5, t2), 2)\nt4 = t1 / t3\nt5 = t4 + 1.0\nanswer = math.floor(t5)\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "test" + }, + { + "Input": "7 m - 20 = 2 m , then m + 7 is equal to ?", + "Output Program": [ + "n0 = 7.0\nn1 = 20.0\nn2 = 2.0\nn3 = 7.0\nt0 = n0 - n2\nt1 = n1 / t0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "test" + }, + { + "Input": "the smallest value of n , for which 2 n + 1 is not a prime number is", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\n\nanswer = n0 + n0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "test" + }, + { + "Input": "two 100 multiples of 7 are chosen at random , and 300 multiples of 8 are chosen at random . approximately what percentage of the 500 selected numbers are odd ?", + "Output Program": [ + "n0 = 100.0\nn1 = 7.0\nn2 = 300.0\nn3 = 8.0\nn4 = 500.0\nt0 = n0 / n4\nanswer = t0 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "test" + }, + { + "Input": "j is 25 % less than p and 20 % less than t . t is x % less than p . what is the value of x ?", + "Output Program": [ + "n0 = 25.0\nn1 = 20.0\nt0 = n0 * n0\nanswer = t0 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "6.25" + ], + "split": "test" + }, + { + "Input": "in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 8 eggs . if the cost of each pound of rice is $ 0.33 , then how many q cents does a liter of kerosene cost ? [ one dollar has 100 cents . ]", + "Output Program": [ + "n0 = 8.0\nn1 = 0.33\nn2 = 100.0\nt0 = 1.0 / 2.0\nt1 = n1 * n2\nt2 = n0 / t0\nt3 = t2 / 12.0\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "44" + ], + "split": "test" + }, + { + "Input": "sum of the squares of 3 no . is 276 and the sum of their products taken two at a time is 150 . find the sum ?", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 276.0\nn2 = 150.0\nt0 = n2 * 2.0\nt1 = n1 + t0\nanswer = math.sqrt(max(0, t1))\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "test" + }, + { + "Input": "in a survey of parents , exactly 7 / 8 of the mothers and 3 / 4 of the fathers held full - time jobs . if 40 percent of the parents surveyed were women , what percent of the parents did not hold full - time jobs ?", + "Output Program": [ + "n0 = 7.0\nn1 = 8.0\nn2 = 3.0\nn3 = 4.0\nn4 = 40.0\nt0 = n2 / n3\nt1 = n0 / n1\nt2 = 100.0 - n4\nt3 = t0 * t2\nt4 = n4 * t1\nt5 = t2 - t3\nt6 = n4 - t4\nanswer = t5 + t6\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "test" + }, + { + "Input": "a grocer has a sale of rs . 6435 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ?", + "Output Program": [ + "n0 = 6435.0\nn1 = 6927.0\nn2 = 6855.0\nn3 = 7230.0\nn4 = 6562.0\nn5 = 5.0\nn6 = 6500.0\nt0 = n5 + 1.0\nt1 = n0 + n1\nt2 = n2 + t1\nt3 = n6 * t0\nt4 = n3 + t2\nt5 = n4 + t4\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "4991" + ], + "split": "test" + }, + { + "Input": "the average monthly salary of 25 employees in an organisation is rs . 2500 . if the manager ' s salary is added , then the average salary increases by rs . 200 . what is the manager ' s monthly salary ?", + "Output Program": [ + "n0 = 25.0\nn1 = 2500.0\nn2 = 200.0\nt0 = n1 + n2\nt1 = n0 + 1.0\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "7700" + ], + "split": "test" + }, + { + "Input": "in a party every person shakes hands with every other person . if there are 105 hands shakes , find the number of person in the party .", + "Output Program": [ + "import math\nn0 = 105.0\nt0 = n0 * 2.0\nt1 = t0 * 4.0\nt2 = t1 + 1.0\nt3 = math.sqrt(max(0, t2))\nt4 = t3 + 1.0\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "test" + }, + { + "Input": "if x \u00a4 y = ( x + y ) ^ 2 - ( x - y ) ^ 2 . then \u221a 2 \u00a4 \u221a 2 =", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 2.0\nn2 = 2.0\nn3 = 2.0\nt0 = math.sqrt(max(0, n2))\nt1 = t0 + t0\nanswer = t1**min(n0, 5)\nprint(answer)" + ], + "Output Answer": [ + "8.000000000000002" + ], + "split": "test" + }, + { + "Input": "find \u221a ? / 20 = 4 ?", + "Output Program": [ + "n0 = 20.0\nn1 = 4.0\nt0 = n0 * n1\nanswer = t0**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "6400" + ], + "split": "test" + }, + { + "Input": "a box contains 14 pairs of shoes ( 28 shoes in total ) . if two shoes are selected at random , what it is the probability that they are matching shoes ?", + "Output Program": [ + "n0 = 14.0\nn1 = 28.0\nt0 = n1 - 1.0\nanswer = 1.0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.037037037037037035" + ], + "split": "test" + }, + { + "Input": "3 years ago , the average age of a , b and c was 27 years and that of b and c 5 years ago was 20 years . a \u2019 s present age is :", + "Output Program": [ + "n0 = 3.0\nn1 = 27.0\nn2 = 5.0\nn3 = 20.0\nt0 = n0 * n1\nt1 = n0 * n0\nt2 = n3 * 2.0\nt3 = n2 * 2.0\nt4 = t0 + t1\nt5 = t2 + t3\nanswer = t4 - t5\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "test" + }, + { + "Input": "the average of 5 consecutive even numbers a , b , c , d and e is 20 . what percent of e is d ?", + "Output Program": [ + "n0 = 5.0\nn1 = 20.0\nt0 = 2.0 * 2.0\nt1 = 2.0 * 3.0\nt2 = 2.0 * 4.0\nt3 = t0 + 2.0\nt4 = t3 + t1\nt5 = t4 + t2\nt6 = t5 / n0\nt7 = n1 - t6\nt8 = t7 + 2.0\nt9 = t8 + 2.0\nt10 = t9 + 2.0\nt11 = t10 + 2.0\nt12 = t10 / t11\nanswer = t12 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "91.66666666666666" + ], + "split": "test" + }, + { + "Input": "if m is a positive integer and m ^ 2 is divisible by 36 , then the largest positive integer that must divide m is ?", + "Output Program": [ + "n0 = 2.0\nn1 = 36.0\nt0 = n1 / 3.0\nt1 = t0 / 3.0\nanswer = t1 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "test" + }, + { + "Input": "on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.60 per glass on the first day , what was the price per f glass on the second day ?", + "Output Program": [ + "n0 = 0.6\nt0 = 1.0 + 1.0\nt1 = 1.0 + 2.0\nt2 = n0 * t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.39999999999999997" + ], + "split": "test" + }, + { + "Input": "in the seaside summer camp there are 50 children . 90 % of the children are boys and the rest are girls . the camp administrator decided to make the number of girls only 5 % of the total number of children in the camp . how many more boys must she bring to make that happen ?", + "Output Program": [ + "n0 = 50.0\nn1 = 90.0\nn2 = 5.0\nt0 = n0 * n1\nt1 = t0 / 100.0\nt2 = n0 - t1\nt3 = t2 * 100.0\nt4 = t3 / n2\nanswer = t4 - n0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "test" + }, + { + "Input": "the average price of 3 items of furniture is rs . 15000 . if their prices are in the ratio 2 : 4 : 8 , the price of the cheapest item is ?", + "Output Program": [ + "n0 = 3.0\nn1 = 15000.0\nn2 = 2.0\nn3 = 4.0\nn4 = 8.0\nt0 = n0 * n1\nanswer = t0 / n4\nprint(answer)" + ], + "Output Answer": [ + "5625" + ], + "split": "test" + }, + { + "Input": "when 1 is added to half of one - third of one - fifth of a number , the result is one - fifteenth of the number . find the number ?", + "Output Program": [ + "n0 = 1.0\nt0 = 2.0 + 3.0\nt1 = t0 * 3.0\nt2 = 1.0 / t1\nt3 = t2 / 2.0\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "test" + }, + { + "Input": "if a person walks at 14 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance traveled by him is ?", + "Output Program": [ + "n0 = 14.0\nn1 = 10.0\nn2 = 20.0\nt0 = n0 - n1\nt1 = n2 / t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "test" + }, + { + "Input": "sum of 36 odd numbers is ?", + "Output Program": [ + "n0 = 36.0\nt0 = n0 / 2.0\nt1 = n0 * 2.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "1296" + ], + "split": "test" + }, + { + "Input": "15 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ?", + "Output Program": [ + "n0 = 15.0\nt0 = n0 - 1.0\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "210" + ], + "split": "test" + }, + { + "Input": "1 / 0.05 is equal to", + "Output Program": [ + "n0 = 1.0\nn1 = 0.05\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "test" + }, + { + "Input": "the average salary of all the workers in a workshop is rs . 8000 . the average salary of 9 technicians is rs . 18000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is :", + "Output Program": [ + "n0 = 8000.0\nn1 = 9.0\nn2 = 18000.0\nn3 = 6000.0\nt0 = n2 - n0\nt1 = n0 - n3\nt2 = n1 * t0\nt3 = t2 / t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "test" + }, + { + "Input": "find the sum the difference between the compound and s . i . on a certain sum of money for 2 years at 10 % per annum is rs . 10 of money ?", + "Output Program": [ + "n0 = 2.0\nn1 = 10.0\nn2 = 10.0\nt0 = n0 * n1\nt1 = n2 / t0\nt2 = t1 * 100.0\nanswer = t2 * t0\nprint(answer)" + ], + "Output Answer": [ + "1000" + ], + "split": "test" + }, + { + "Input": "a room is 7 meters 68 centimeters in length and 4 meters 32 centimeters in width . find the least number of square tiles of equal size required to cover the entire floor of the room .", + "Output Program": [ + "import scipy\nn0 = 7.0\nn1 = 68.0\nn2 = 4.0\nn3 = 32.0\nt0 = n0 * 100.0\nt1 = n2 * 100.0\nt2 = n1 + t0\nt3 = n3 + t1\nt4 = scipy.gcd(int(t2), int(t3))\nt5 = t2 * t3\nt6 = t4 * t4\nanswer = t5 / t6\nprint(answer)" + ], + "Output Answer": [ + "144" + ], + "split": "test" + }, + { + "Input": "1 \u00f7 [ 1 + 1 \u00f7 { 1 + 1 \u00f7 ( 1 \u00f7 1 ) } ] = ?", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 1.0\nn3 = 1.0\nn4 = 1.0\nn5 = 1.0\nn6 = 1.0\nt0 = n0 / n0\nt1 = n0 + t0\nt2 = n0 / t1\nt3 = n0 + t2\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.6666666666666666" + ], + "split": "test" + }, + { + "Input": "a line that passes through ( \u2013 1 , \u2013 4 ) and ( 2 , k ) has a slope = k . what is the value of k ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 2.0\n\nanswer = n1 / n2\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "test" + }, + { + "Input": "p , q and r have $ 8000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?", + "Output Program": [ + "n0 = 8000.0\nt0 = 2.0 * 2.0\nt1 = 1.0 * 3.0\nt2 = t0 / 3.0\nt3 = n0 * t0\nt4 = t2 * 3.0\nt5 = t4 + t1\nt6 = t5 + t1\nanswer = t3 / t6\nprint(answer)" + ], + "Output Answer": [ + "3200" + ], + "split": "test" + }, + { + "Input": "of the 3,600 employees of company x , 16 / 25 are clerical . if the clerical staff were to be reduced by 1 / 4 , what percent of the total number of the remaining employees would then be clerical ?", + "Output Program": [ + "n0 = 3600.0\nn1 = 16.0\nn2 = 25.0\nn3 = 1.0\nn4 = 4.0\nt0 = n1 / n2\nt1 = n3 / n4\nt2 = n3 - t1\nt3 = n3 - t0\nt4 = t0 * t2\nt5 = t4 + t3\nt6 = t4 / t5\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "57.14285714285714" + ], + "split": "test" + }, + { + "Input": "the difference between two numbers is 1365 . when the larger number is divided by the smaller one , the quotient is 6 and the remainder is 15 . the smaller number is", + "Output Program": [ + "n0 = 1365.0\nn1 = 6.0\nn2 = 15.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "270" + ], + "split": "test" + }, + { + "Input": "the sum of present age of abe and the age before 7 years is 33 . find the present age of abe . what will be his age after 7 years ?", + "Output Program": [ + "n0 = 7.0\nn1 = 33.0\nn2 = 7.0\nt0 = n0 + n1\nt1 = t0 / 2.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "test" + }, + { + "Input": "when a person aged 39 is added to a group of n people , the average age increases by 2 . when a person aged 15 is added instead , the average age decreases by 1 . what is the value of t ?", + "Output Program": [ + "n0 = 39.0\nn1 = 2.0\nn2 = 15.0\nn3 = 1.0\nt0 = n1 + n3\nt1 = n0 - n2\nt2 = t1 / t0\nanswer = t2 - n3\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "test" + }, + { + "Input": "the average earning of a person for the first 4 days of a week is rs 18 and for the last 4 days is rs 22 . if he earns rs 20 on the fourth day , his average earning for the whole week is ?", + "Output Program": [ + "n0 = 4.0\nn1 = 18.0\nn2 = 4.0\nn3 = 22.0\nn4 = 20.0\nt0 = 3.0 + 4.0\nt1 = n0 * n1\nt2 = n0 * n3\nt3 = t1 + t2\nt4 = t3 - n4\nanswer = t4 / t0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "test" + }, + { + "Input": "in plutarch enterprises , 70 % of the employees are marketers , 10 % are engineers , and the rest are managers . marketers make an average salary of $ 50000 a year , and engineers make an average of $ 80000 . what is the average salary for managers if the average for all employees is also $ 80000 ?", + "Output Program": [ + "n0 = 70.0\nn1 = 10.0\nn2 = 50000.0\nn3 = 80000.0\nn4 = 80000.0\nt0 = n0 + n1\nt1 = 10.0 / 2.0\nt2 = t0 * 1000.0\nt3 = t1 * 10.0\nt4 = t2 * 100.0\nt5 = t2 * 10.0\nt6 = t3 * 1000.0\nt7 = n0 * t6\nt8 = t4 - t5\nt9 = t8 - t7\nanswer = t9 / n1\nprint(answer)" + ], + "Output Answer": [ + "370000" + ], + "split": "test" + }, + { + "Input": "john purchased 1370 large bottles at $ 1.99 per bottle and 690 small bottles at $ 1.50 per bottle . what was the approximate average price paid per bottle ?", + "Output Program": [ + "n0 = 1370.0\nn1 = 1.99\nn2 = 690.0\nn3 = 1.5\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n2 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "1.825873786407767" + ], + "split": "test" + }, + { + "Input": "2034 - ( 1002 / 20.04 ) = ?", + "Output Program": [ + "n0 = 2034.0\nn1 = 1002.0\nn2 = 20.04\nt0 = n1 / n2\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "1984" + ], + "split": "test" + }, + { + "Input": "compute all real solutions to 16 x + 4 x + 1 - 96 = 0", + "Output Program": [ + "n0 = 16.0\nn1 = 4.0\nn2 = 1.0\nn3 = 96.0\nn4 = 0.0\nt0 = n1 - n2\nt1 = t0 - n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "1.5" + ], + "split": "test" + }, + { + "Input": "virginia , adrienne , and dennis have taught history for a combined total of 87 years . if virginia has taught for 9 more years than adrienne and for 9 fewer years than dennis , for how many years has dennis taught ?", + "Output Program": [ + "n0 = 87.0\nn1 = 9.0\nn2 = 9.0\nt0 = n1 + n2\nt1 = n1 + t0\nt2 = n0 - t1\nt3 = t2 / 3.0\nanswer = t0 + t3\nprint(answer)" + ], + "Output Answer": [ + "38" + ], + "split": "test" + }, + { + "Input": "a certain number of two digits is 3 times the sum of its digits and if 45 be added to it , the degits are reversed . the number is .", + "Output Program": [ + "n0 = 3.0\nn1 = 45.0\nt0 = n1 - 10.0\nt1 = 10.0 - n0\nt2 = t1 - 2.0\nt3 = t0 / t2\nt4 = t3 - t2\nt5 = t4 * 10.0\nanswer = t3 + t5\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "test" + }, + { + "Input": "an angry arjun carried some arrows for fighting with bheeshm . with half the arrows , he cut down the arrows thrown by bheeshm on him and with 6 other arrows he killed the chariot driver of bheeshm . with one arrow each he knocked down respectively the chariot , the flag and the bow of bheeshm . finally , with one more than 4 times the square root of arrows he laid bheeshm unconscious on an arrow bed . find the total number of arrows arjun had .", + "Output Program": [ + "n0 = 6.0\nn1 = 4.0\nt0 = n0 + n1\nanswer = t0**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "test" + }, + { + "Input": "in the above number , a and b represent the tens and units digits , respectively . if the above number is divisible by 15 , what is the greatest possible value of b x a ?", + "Output Program": [ + "n0 = 15.0\nt0 = 3.0 + 4.0\nt1 = 2.0 + 3.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "test" + }, + { + "Input": "let s be the set of all positive integers that , when divided by 8 , have a remainder of 5 . what is the 79 th number in this set ?", + "Output Program": [ + "n0 = 8.0\nn1 = 5.0\nn2 = 79.0\nt0 = n2 - 1.0\nt1 = n0 * t0\nanswer = n1 + t1\nprint(answer)" + ], + "Output Answer": [ + "629" + ], + "split": "test" + }, + { + "Input": "the average of 30 numbers is 25 . if each number is multiplied by 5 , find the new average ?", + "Output Program": [ + "n0 = 30.0\nn1 = 25.0\nn2 = 5.0\n\nanswer = n1 * n2\nprint(answer)" + ], + "Output Answer": [ + "125" + ], + "split": "test" + }, + { + "Input": "\u221a ( 21 ) ^ 2", + "Output Program": [ + "import math\nn0 = 21.0\nn1 = 2.0\nt0 = n0**min(n1, 5)\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "test" + }, + { + "Input": "a certain animal in the zoo has consumed 39 pounds of food in 6 days . if it continues to eat at the same rate , in how many more days will its total consumption be 117 pounds ?", + "Output Program": [ + "n0 = 39.0\nn1 = 6.0\nn2 = 117.0\nt0 = n0 / n1\nt1 = n2 / t0\nanswer = t1 - n1\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "test" + }, + { + "Input": "in a class of 42 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 10 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?", + "Output Program": [ + "n0 = 42.0\nn1 = 2.0\nn2 = 12.0\nn3 = 1.0\nn4 = 10.0\nn5 = 2.0\nn6 = 3.0\nn7 = 2.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n1 * n4\nt3 = t1 + t2\nt4 = n4 + t1\nt5 = n1 + t4\nt6 = n0 - t5\nt7 = t6 - n3\nt8 = n6 * t7\nt9 = t3 + t8\nanswer = t0 - t9\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "test" + }, + { + "Input": "a set of consecutive positive integers beginning with 1 is written on the blackboard . a student came along and erased one number . the average of the remaining numbers is 35 * 7 / 17 . what was the number erased ?", + "Output Program": [ + "import math\nn0 = 1.0\nn1 = 35.0\nn2 = 7.0\nn3 = 17.0\nt0 = n2 / n3\nt1 = n1 + t0\nt2 = t1 * 2.0\nt3 = math.floor(t2)\nt4 = t3 / 2.0\nt5 = t3 - 1.0\nt6 = t4 * t5\nt7 = t5 - n0\nt8 = t1 * t7\nanswer = t6 - t8\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "test" + }, + { + "Input": "find the number which is nearest to 3105 and is exactly divisible by 21 ?", + "Output Program": [ + "n0 = 3105.0\nn1 = 21.0\nt0 = n0 % n1\nt1 = n1 - t0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "3108" + ], + "split": "test" + }, + { + "Input": "if a ( a - 8 ) = 9 and b ( b - 8 ) = 9 , where a \u2260 b , then a + b =", + "Output Program": [ + "n0 = 8.0\nn1 = 9.0\nn2 = 8.0\nn3 = 9.0\nt0 = 4.0 + n1\nt1 = n0 - n1\nt2 = t0 + t1\nt3 = t2 - 1.0\nt4 = t3 - 1.0\nt5 = t4 - 1.0\nanswer = t5 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "test" + }, + { + "Input": "during the first two weeks of june , the total rainfall in springdale was 40 inches . if the rainfall during the second week was 1.5 times the rainfall during the first week , what was the rainfall in inches during the second week of june ?", + "Output Program": [ + "n0 = 40.0\nn1 = 1.5\nt0 = n1 + 1.0\nt1 = n0 / t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "test" + }, + { + "Input": "15 lts are taken of from a container full of liquid a and replaced with liquid b . again 15 more lts of the mixture is taken and replaced with liquid b . after this process , if the container contains liquid a and b in the ratio 9 : 16 , what is the capacity of the container h ?", + "Output Program": [ + "import math\nn0 = 15.0\nn1 = 15.0\nn2 = 9.0\nn3 = 16.0\nt0 = n2 + n3\nt1 = n2 / t0\nt2 = math.sqrt(max(0, t1))\nt3 = 1.0 - t2\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "37.5" + ], + "split": "test" + }, + { + "Input": "if 0.45 : x : : 4 : 2 , then x is equal to", + "Output Program": [ + "n0 = 0.45\nn1 = 4.0\nn2 = 2.0\nt0 = n0 * n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.225" + ], + "split": "test" + }, + { + "Input": "if 0.75 : x : : 5 : 12 , then x is equal to :", + "Output Program": [ + "n0 = 0.75\nn1 = 5.0\nn2 = 12.0\nt0 = n0 * n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "1.8" + ], + "split": "test" + }, + { + "Input": "two employees x and y are paid a total of rs . 650 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?", + "Output Program": [ + "n0 = 650.0\nn1 = 120.0\nt0 = 1.0 + 4.0\nt1 = t0 * 2.0\nt2 = t1 + 1.0\nt3 = n0 * t1\nt4 = t2 * 2.0\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "295.45454545454544" + ], + "split": "test" + }, + { + "Input": "the average speed of a car is 1 3 / 5 times the avg speed of a bike . a tractor covers 575 km in 23 hrs . how much distance will the car cover in 4 hrs if the speed of the bike is twice speed of the tractor ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 5.0\nn3 = 575.0\nn4 = 23.0\nn5 = 4.0\nt0 = n1 / n2\nt1 = n3 / n4\nt2 = n0 + t0\nt3 = t1 * 2.0\nt4 = t2 * t3\nanswer = n5 * t4\nprint(answer)" + ], + "Output Answer": [ + "320" + ], + "split": "test" + }, + { + "Input": "which number need to add to 859622 to get a number exactly divisible by 456 ?", + "Output Program": [ + "n0 = 859622.0\nn1 = 456.0\nt0 = n0 % n1\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "859560" + ], + "split": "test" + }, + { + "Input": "x and y are both integers . if x / y = 59.40 , then what is the sum of all the possible two digit remainders of x / y ?", + "Output Program": [ + "n0 = 59.4\nt0 = 2.0 + 3.0\nt1 = 3.0 / 2.0\nt2 = n0 * t0\nt3 = t1 * 100.0\nt4 = t2 + 3.0\nanswer = t4 + t3\nprint(answer)" + ], + "Output Answer": [ + "450" + ], + "split": "test" + }, + { + "Input": "when a certain number x is divided by 54 , the remainder is 22 . what is the remainder when x is divided by 18 ?", + "Output Program": [ + "n0 = 54.0\nn1 = 22.0\nn2 = 18.0\n\nanswer = n1 % n2\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "test" + }, + { + "Input": "marketing executives for a certain chewing gum company projected a 20 percent increase in revenue this year over that of last year , but revenue this year actually decreased by 35 % . what percent of the projected revenue was the actual revenue ?", + "Output Program": [ + "n0 = 20.0\nn1 = 35.0\nt0 = n0 + 100.0\nt1 = 100.0 - n1\nt2 = t1 / t0\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "54.166666666666664" + ], + "split": "test" + }, + { + "Input": "the average age of 18 students of a class is 18 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years , the age of the 18 th student is", + "Output Program": [ + "n0 = 18.0\nn1 = 18.0\nn2 = 5.0\nn3 = 14.0\nn4 = 9.0\nn5 = 16.0\nn6 = 18.0\nt0 = n0 * n0\nt1 = n2 * n3\nt2 = n4 * n5\nt3 = t1 + t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "110" + ], + "split": "test" + }, + { + "Input": "on dividing 123 by a number , the quotient is 7 and the remainder is 4 . find the divisor .", + "Output Program": [ + "import math\nn0 = 123.0\nn1 = 7.0\nn2 = 4.0\nt0 = n0 / n1\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "test" + }, + { + "Input": "a certain country is divided into 6 provinces . each province consists entirely of progressives and traditionalists . if each province contains the same number of traditionalists and the number of traditionalists in any given province is 1 / 18 the total number of progressives in the entire country , what fraction of the country is traditionalist ?", + "Output Program": [ + "n0 = 6.0\nn1 = 1.0\nn2 = 18.0\nt0 = n0 / n2\nt1 = n1 + t0\nt2 = t0 / t1\nanswer = n1 - t2\nprint(answer)" + ], + "Output Answer": [ + "0.75" + ], + "split": "test" + }, + { + "Input": "a sum of rs . 66000 is divided into 3 parts such that the simple interests accrued on them for 6 , two and 11 years respectively may be equal . find the amount deposited for 11 years .", + "Output Program": [ + "n0 = 66000.0\nn1 = 3.0\nn2 = 6.0\nn3 = 11.0\nn4 = 11.0\nt0 = n2 * 10.0\nanswer = t0 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "6000" + ], + "split": "test" + }, + { + "Input": "in smithtown , the ratio of right - handed people to left - handed people is 3 to 1 and the ratio of men to women is 3 to 2 . if the number of right - handed men is maximized , then what percent z of all the people in smithtown are left - handed women ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 3.0\nn3 = 2.0\nt0 = n0 + n1\nt1 = n0 + n3\nt2 = t0 / t1\nt3 = n3 * t2\nt4 = n0 * t2\nt5 = n0 - t4\nt6 = t3 - t5\nt7 = t6 / t0\nanswer = t7 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "25.00000000000001" + ], + "split": "test" + }, + { + "Input": "the average age of 20 men in the class is 15.6 years . 5 new men join and the new average becomes 14.56 years . what was the average age of 5 new men ?", + "Output Program": [ + "n0 = 20.0\nn1 = 15.6\nn2 = 5.0\nn3 = 14.56\nn4 = 5.0\nt0 = n0 + n2\nt1 = n0 * n1\nt2 = n3 * t0\nt3 = t2 - t1\nanswer = t3 / n2\nprint(answer)" + ], + "Output Answer": [ + "10.4" + ], + "split": "test" + }, + { + "Input": "the average age of 15 students of a class is 15 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years . tee age of the 15 th student is ?", + "Output Program": [ + "n0 = 15.0\nn1 = 15.0\nn2 = 5.0\nn3 = 14.0\nn4 = 9.0\nn5 = 16.0\nn6 = 15.0\nt0 = n0 * n0\nt1 = n2 * n3\nt2 = n4 * n5\nt3 = t1 + t2\nanswer = t0 - t3\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "test" + }, + { + "Input": "when a merchant imported a certain item , she paid a 7 percent import tax on the portion of the total value of the item in excess of $ 1000 . if the amount of the import tax that the merchant paid was $ 109.90 , what was the total value of the item ?", + "Output Program": [ + "n0 = 7.0\nn1 = 1000.0\nn2 = 109.9\nt0 = n0 / 100.0\nt1 = n2 / t0\nanswer = t1 + 1000.0\nprint(answer)" + ], + "Output Answer": [ + "2570" + ], + "split": "test" + }, + { + "Input": "when positive integer n is divided by 3 , the remainder is 1 . when n is divided by 5 , the remainder is 4 . what is the smallest positive integer p , such that ( n + p ) is a multiple of 11 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 5.0\nn3 = 4.0\nn4 = 11.0\nt0 = n3 % n2\nanswer = n4 - t0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "test" + }, + { + "Input": "if 40 % of ( x - y ) = 20 % of ( x + y ) , then what percent of x is y ?", + "Output Program": [ + "n0 = 40.0\nn1 = 20.0\nt0 = n0 + n1\nt1 = n0 - n1\nt2 = t1 / t0\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "33.33333333333333" + ], + "split": "test" + }, + { + "Input": "if 3 < x < 6 < y < 9 , then what is the greatest possible positive integer difference of x and y ?", + "Output Program": [ + "n0 = 3.0\nn1 = 6.0\nn2 = 9.0\nt0 = n2 - n0\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "test" + }, + { + "Input": "for a certain art exhibit , a museum sold admission tickets to a group of 30 people every 6 minutes from 9 : 00 in the morning to 6 : 00 in the afternoon , inclusive . the price of a regular admission ticket was $ 10 and the price of a student ticket was $ 6 . if on one day 2 times as many regular admission tickets were sold as student tickets , what was the total revenue from ticket sales that day ?", + "Output Program": [ + "n0 = 30.0\nn1 = 6.0\nn2 = 9.0\nn3 = 0.0\nn4 = 6.0\nn5 = 0.0\nn6 = 10.0\nn7 = 6.0\nn8 = 2.0\nt0 = 12.0 + n4\nt1 = 3.0 + 1.0\nt2 = t0 - n2\nt3 = t2 + 1.0\nt4 = t3 * 12.0\nt5 = n0 * t4\nt6 = t5 / t1\nt7 = n8 * t6\nt8 = n7 * t6\nt9 = n6 * t7\nanswer = t9 + t8\nprint(answer)" + ], + "Output Answer": [ + "23400" + ], + "split": "test" + }, + { + "Input": "company t produces two kinds of stereos : basic and deluxe . of the stereos produced by company t last month , 2 / 3 were basic and the rest were deluxe . if it takes 7 / 5 as many hours to produce a deluxe stereo as it does to produce a basic stereo , then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 7.0\nn3 = 5.0\nt0 = n2 / n3\nt1 = n0 * n3\nt2 = n3 * t0\nt3 = t1 * 1.0\nt4 = t3 + t2\nanswer = t2 / t4\nprint(answer)" + ], + "Output Answer": [ + "0.4117647058823529" + ], + "split": "test" + }, + { + "Input": "pat , kate , and mark charged a total of 126 hours to a certain project . if pat charged twice as much time to the project as kate and 1 / 3 as much time as mark , how many more hours did mark charge to the project than kate ?", + "Output Program": [ + "n0 = 126.0\nn1 = 1.0\nn2 = 3.0\nt0 = n1 / n2\nt1 = n2 * 2.0\nt2 = n1 + t0\nt3 = n1 / t1\nt4 = t2 + t3\nt5 = n0 / t4\nt6 = t5 / t1\nanswer = t5 - t6\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "test" + }, + { + "Input": "on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 380 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?", + "Output Program": [ + "n0 = 380.0\n\nanswer = n0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "760" + ], + "split": "test" + }, + { + "Input": "andy solves problems 74 to 135 inclusive in a math exercise . how many problems does he solve ?", + "Output Program": [ + "n0 = 74.0\nn1 = 135.0\nt0 = n1 - n0\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "62" + ], + "split": "test" + }, + { + "Input": "what is the sum of the multiples of 4 between 38 and 127 inclusive ?", + "Output Program": [ + "n0 = 4.0\nn1 = 38.0\nn2 = 127.0\nt0 = n1 + 2.0\nt1 = n2 - 3.0\nt2 = t0 + t1\nt3 = t1 - t0\nt4 = t3 / n0\nt5 = t2 / 2.0\nt6 = t4 + 1.0\nanswer = t6 * t5\nprint(answer)" + ], + "Output Answer": [ + "1804" + ], + "split": "test" + }, + { + "Input": "there are 50 boys in a class . their average weight is 45 kg . when one boy leaves the class , the average reduces by 100 g . find the weight of the boy who left the class .", + "Output Program": [ + "n0 = 50.0\nn1 = 45.0\nn2 = 100.0\nt0 = n0 - 1.0\nt1 = n2 * t0\nt2 = t1 / 1000.0\nanswer = n1 + t2\nprint(answer)" + ], + "Output Answer": [ + "49.9" + ], + "split": "test" + }, + { + "Input": "if w / x = 1 / 3 and w / y = 4 / 15 , then ( x + y ) / y =", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 4.0\nn3 = 15.0\nt0 = n2 / n0\nt1 = n3 / n1\nt2 = t0 / t1\nanswer = t2 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "1.8" + ], + "split": "test" + }, + { + "Input": "a university cafeteria offers 6 flavors of pizza - pork , gobi - manjurian , pepperoni , chicken , hawaiian and vegetarian . if a customer has an option ( but not the obligation ) to add extra cheese , mushrooms or both to any kind of pizza , how many different pizza varieties are available ?", + "Output Program": [ + "n0 = 6.0\n\nanswer = n0 * n0\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "test" + }, + { + "Input": "in a mixture of 45 litres the ratio of milk to water is 4 : 1 . additional 12 litres of water is added to the mixture . find the ratio of milk to water in the resulting mixture .", + "Output Program": [ + "n0 = 45.0\nn1 = 4.0\nn2 = 1.0\nn3 = 12.0\nt0 = n1 + n2\nt1 = n0 / t0\nt2 = n3 + t1\nt3 = n0 - t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "1.7142857142857142" + ], + "split": "test" + }, + { + "Input": "what is the greater of the two numbers whose product is 2496 , given that the sum of the two numbers exceeds their difference by 64 ?", + "Output Program": [ + "n0 = 2496.0\nn1 = 64.0\nt0 = 2.0**min(4.0, 5)\nt1 = t0 * 2.0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "78" + ], + "split": "test" + }, + { + "Input": "of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 125 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 3.0\nn3 = 4.0\nn4 = 3.0\nn5 = 5.0\nn6 = 125.0\nt0 = n1 / n5\nt1 = n1 / n3\nt2 = 2.0 / 3.0\nt3 = 1.0 - t0\nt4 = n6 / t3\nt5 = t4 / t1\nanswer = t5 / t2\nprint(answer)" + ], + "Output Answer": [ + "625.0000000000001" + ], + "split": "test" + }, + { + "Input": "the average salary per month of 55 employees in a company is rs 8500 . if the managers salary is added , the average salary increases to rs 8800 , what is the salary of the manager ?", + "Output Program": [ + "n0 = 55.0\nn1 = 8500.0\nn2 = 8800.0\nt0 = n0 + 1.0\nt1 = n0 * n1\nt2 = n2 * t0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "25300" + ], + "split": "test" + }, + { + "Input": "in a simultaneous throw of pair of dice . find the probability of getting the total more than 7", + "Output Program": [ + "n0 = 7.0\nt0 = n0 + 4.0\nt1 = 2.0 + 4.0\nt2 = t0 + 4.0\nt3 = t1 * t1\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.4166666666666667" + ], + "split": "test" + }, + { + "Input": "how many boxes do we need if we have to carry 250 apples into boxes that each hold 25 apples ?", + "Output Program": [ + "n0 = 250.0\nn1 = 25.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "test" + }, + { + "Input": "the mean of 50 observations was 36 . it was found later that an observation 48 was wrongly taken as 23 . the corrected new mean is :", + "Output Program": [ + "n0 = 50.0\nn1 = 36.0\nn2 = 48.0\nn3 = 23.0\nt0 = n0 * n1\nt1 = n0 - 2.0\nt2 = t1 - n3\nt3 = t0 + t2\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "36.5" + ], + "split": "test" + }, + { + "Input": "simplify : 0.3 * 0.3 + 0.3 * 0.3", + "Output Program": [ + "n0 = 0.3\nn1 = 0.3\nn2 = 0.3\nn3 = 0.3\nt0 = n0 * n1\nt1 = n2 * n3\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "0.18" + ], + "split": "test" + }, + { + "Input": "{ - 10 , - 6 , - 5 , - 4 , - 2.5 , - 1 , 0 , 2.5 , 4 , 6 , 7 , 10 } a number is to be selected at random from the set above . what is the probability that the number will be a solution to the equation ( x - 4 ) ( x + 9 ) ( 2 x + 5 ) = 0 ?", + "Output Program": [ + "n0 = 10.0\nn1 = 6.0\nn2 = 5.0\nn3 = 4.0\nn4 = 2.5\nn5 = 1.0\nn6 = 0.0\nn7 = 2.5\nn8 = 4.0\nn9 = 6.0\nn10 = 7.0\nn11 = 10.0\nn12 = 4.0\nn13 = 9.0\nn14 = 2.0\nn15 = 5.0\nn16 = 0.0\nt0 = n1 * n14\nanswer = n5 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.08333333333333333" + ], + "split": "test" + }, + { + "Input": "the maximum number of students among them 848 pens and 630 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils ?", + "Output Program": [ + "import scipy\nn0 = 848.0\nn1 = 630.0\n\nanswer = scipy.gcd(int(n0), int(n1))\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "test" + }, + { + "Input": "the captain of a cricket team of 11 members is 29 years old and the wicket keeper is 3 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ?", + "Output Program": [ + "n0 = 11.0\nn1 = 29.0\nn2 = 3.0\nt0 = n1 + n2\nt1 = n2 * n2\nt2 = n1 + t0\nt3 = t2 - t1\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "test" + }, + { + "Input": "the average monthly salary of 20 employees in an organisation is rs . 1400 . if the manager ' s salary is added , then the average salary increases by rs . 100 . what is the manager ' s monthly salary ?", + "Output Program": [ + "n0 = 20.0\nn1 = 1400.0\nn2 = 100.0\nt0 = n1 + n2\nt1 = n0 + 1.0\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "3500" + ], + "split": "test" + }, + { + "Input": "exactly 3 / 7 of the people in the room are under the age of 21 , and exactly 5 / 12 of the people in the room are over the age of 65 . if the total number of the people in the room is greater than 50 and less than 100 , how many people in the room are under the age of 21 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 21.0\nn3 = 5.0\nn4 = 12.0\nn5 = 65.0\nn6 = 50.0\nn7 = 100.0\nn8 = 21.0\nt0 = n1 * n4\nt1 = n0 * t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "test" + }, + { + "Input": "if the average of r , b , c , 14 and 15 is 12 . what is the average value of r , b , c and 29", + "Output Program": [ + "n0 = 14.0\nn1 = 15.0\nn2 = 12.0\nn3 = 29.0\nt0 = 1.0 + 4.0\nt1 = n0 + n1\nt2 = n2 * t0\nt3 = t2 - t1\nt4 = n3 + t3\nanswer = t4 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "test" + }, + { + "Input": "x varies inversely as square of y . given that y = 3 for x = 1 . the value of x for y = 5 will be equal to :", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 5.0\nt0 = n0**min(2.0, 5)\nt1 = n2**min(2.0, 5)\nt2 = n1 * t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.36" + ], + "split": "test" + }, + { + "Input": "a positive number x is multiplied by 5 , and this product is then divided by 3 . if the positive square root of the result of these two operations equals x , what is the value of x ?", + "Output Program": [ + "n0 = 5.0\nn1 = 3.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "1.6666666666666667" + ], + "split": "test" + }, + { + "Input": "the price of commodity x increases by 40 paise every year , while the price of commodity y increases by 15 paise every year . if in 2001 , the price of commodity x was rs . 4.20 and that of y was rs . 6.30 , in which year commodity x will cost 40 paise more than the commodity y ?", + "Output Program": [ + "n0 = 40.0\nn1 = 15.0\nn2 = 2001.0\nn3 = 4.2\nn4 = 6.3\nn5 = 40.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = n4 - n3\nt3 = t0 + t2\nt4 = t0 - t1\nt5 = t3 / t4\nanswer = n2 + t5\nprint(answer)" + ], + "Output Answer": [ + "2011" + ], + "split": "test" + }, + { + "Input": "if n is an integer , f ( n ) = f ( n - 1 ) - n and f ( 4 ) = 13 . what is the value of f ( 6 ) ?", + "Output Program": [ + "n0 = 1.0\nn1 = 4.0\nn2 = 13.0\nn3 = 6.0\nt0 = n0 + n1\nt1 = n2 - t0\nanswer = t1 - n3\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "test" + }, + { + "Input": "if the average ( arithmetic mean ) of a and b is 45 and the average of b and c is 85 , what is the value of c \u00e2 \u02c6 \u2019 a ?", + "Output Program": [ + "n0 = 45.0\nn1 = 85.0\nt0 = n1 * 2.0\nt1 = n0 * 2.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "test" + }, + { + "Input": "a envelop weight 9.2 gm , if 800 of these envelop are sent with an advertisement mail . how much wieght ?", + "Output Program": [ + "n0 = 9.2\nn1 = 800.0\nt0 = n0 * n1\nanswer = t0 / 1000.0\nprint(answer)" + ], + "Output Answer": [ + "7.359999999999999" + ], + "split": "test" + }, + { + "Input": "what least number should be added to 1022 , so that the sum is completely divisible by 25 ?", + "Output Program": [ + "n0 = 1022.0\nn1 = 25.0\nt0 = n0 % n1\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "test" + }, + { + "Input": "63 + 5 * 12 / ( 180 / 3 ) = ?", + "Output Program": [ + "n0 = 63.0\nn1 = 5.0\nn2 = 12.0\nn3 = 180.0\nn4 = 3.0\nt0 = n3 / n4\nt1 = n1 * n2\nt2 = t1 / t0\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "test" + }, + { + "Input": "a certain scholarship committee awarded scholarships in the amounts of $ 1250 , $ 2500 and $ 4000 . the committee awarded twice as many $ 2500 scholarships as $ 4000 and it awarded 3 times as many $ 1250 scholarships as $ 2500 scholarships . if the total of $ 75000 was awarded in $ 1250 scholarships , how many $ 4000 scholarships were awarded ?", + "Output Program": [ + "n0 = 1250.0\nn1 = 2500.0\nn2 = 4000.0\nn3 = 2500.0\nn4 = 4000.0\nn5 = 3.0\nn6 = 1250.0\nn7 = 2500.0\nn8 = 75000.0\nn9 = 1250.0\nn10 = 4000.0\nt0 = n8 / n0\nt1 = n5 * 2.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "test" + }, + { + "Input": "in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 6 eggs . if the cost of each pound of rice is $ 0.33 , then how many cents does a liter of kerosene cost ? [ one dollar has 100 cents . ]", + "Output Program": [ + "n0 = 6.0\nn1 = 0.33\nn2 = 100.0\nt0 = 1.0 / 2.0\nt1 = n1 * n2\nt2 = n0 / t0\nt3 = t2 / 12.0\nanswer = t3 * t1\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "test" + }, + { + "Input": "a pupil ' s marks were wrongly entered as 73 instead of 40 . due to the average marks for the class got increased by half . the number of pupils in the class is ?", + "Output Program": [ + "n0 = 73.0\nn1 = 40.0\nt0 = n0 - n1\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "66" + ], + "split": "test" + }, + { + "Input": "if an integer n is to be chosen at random from the integers 1 to 96 , inclusive , what is the probability that n ( n + 1 ) ( n + 2 ) will be divisible by 8 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 96.0\nn2 = 1.0\nn3 = 2.0\nn4 = 8.0\nt0 = n1 / n3\nt1 = n1 / n4\nt2 = t0 + t1\nanswer = t2 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.625" + ], + "split": "test" + }, + { + "Input": "if n divided by 8 has a remainder of 1 , what is the remainder when 3 times n is divided by 8 ?", + "Output Program": [ + "n0 = 8.0\nn1 = 1.0\nn2 = 3.0\nn3 = 8.0\n\nanswer = n1 * n2\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "test" + }, + { + "Input": "if y is 90 % greater than x , than x is what % less than y ?", + "Output Program": [ + "n0 = 90.0\nt0 = n0 + 100.0\nt1 = n0 / t0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "47.368421052631575" + ], + "split": "test" + }, + { + "Input": "the average weight of 10 persons increases by 4.2 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 10.0\nn1 = 4.2\nn2 = 65.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "107" + ], + "split": "test" + }, + { + "Input": "a certain class of students is being divided into teams . the class can either be divided into 8 teams with an equal number of players on each team or 24 teams with an equal number of players on each team . what is the lowest possible number of students in the class ?", + "Output Program": [ + "import scipy\nn0 = 8.0\nn1 = 24.0\n\nanswer = scipy.lcm(int(n0), int(n1))\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "test" + }, + { + "Input": "a caterer ordered 125 ice - cream bars and 125 sundaes . if the total price was $ 275.00 and the price of each ice - cream bar was $ 0.60 , what was the price of each sundae ?", + "Output Program": [ + "n0 = 125.0\nn1 = 125.0\nn2 = 275.0\nn3 = 0.6\nt0 = n0 * n3\nt1 = n2 - t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "1.6" + ], + "split": "test" + }, + { + "Input": "a batsman makes a score of 50 runs in the 6 th inning and thus increases his average by 2 . find his average after 6 th inning .", + "Output Program": [ + "n0 = 50.0\nn1 = 6.0\nn2 = 2.0\nn3 = 6.0\nt0 = n1 * n2\nt1 = n0 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "test" + }, + { + "Input": "a high school has 360 students 1 / 2 attend the arithmetic club , 5 / 8 attend the biology club and 3 / 4 attend the chemistry club . 3 / 8 attend all 3 clubs . if every student attends at least one club how many students attend exactly 2 clubs .", + "Output Program": [ + "n0 = 360.0\nn1 = 1.0\nn2 = 2.0\nn3 = 5.0\nn4 = 8.0\nn5 = 3.0\nn6 = 4.0\nn7 = 3.0\nn8 = 8.0\nn9 = 3.0\nn10 = 2.0\nt0 = n0 * n1\nt1 = n0 * n3\nt2 = n0 * n5\nt3 = t0 / n2\nt4 = t1 / n4\nt5 = t2 / n6\nt6 = t2 / n4\nt7 = t3 + t4\nt8 = n2 * t6\nt9 = t7 + t5\nt10 = t9 - t8\nanswer = t10 - n0\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "test" + }, + { + "Input": "what is x if x + 5 y = 24 and y = 2 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 24.0\nn2 = 2.0\nt0 = n0 * n2\nanswer = n1 - t0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "test" + }, + { + "Input": "the wages earned by robin is 20 % more than that earned by erica . the wages earned by charles is 60 % more than that earned by erica . how much percent is the wages earned by charles more than that earned by robin ?", + "Output Program": [ + "n0 = 20.0\nn1 = 60.0\nt0 = n1 + 100.0\nt1 = n0 + 100.0\nt2 = t0 - t1\nt3 = t2 / t1\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "33.33333333333333" + ], + "split": "test" + }, + { + "Input": "there are two numbers . if 10 % of the first number is added to the second number , then the second number increases to its 6 - fifth . what is the ratio of the first number to the second number ?", + "Output Program": [ + "n0 = 10.0\nn1 = 6.0\nt0 = n0 / 2.0\nt1 = 1.0 / n0\nt2 = 1.0 / t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "test" + }, + { + "Input": "each child has 2 pencils and 13 skittles . if there are 6 children , how many pencils are there in total ?", + "Output Program": [ + "n0 = 2.0\nn1 = 13.0\nn2 = 6.0\n\nanswer = n0 * n2\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "test" + }, + { + "Input": "the sum of the first 50 positive even integers is 2550 . what is the sum of the even integers from 502 to 600 inclusive ?", + "Output Program": [ + "n0 = 50.0\nn1 = 2550.0\nn2 = 502.0\nn3 = 600.0\nt0 = n2 + n3\nt1 = n3 - n2\nt2 = t1 / 2.0\nt3 = t0 / 2.0\nt4 = t2 + 1.0\nanswer = t4 * t3\nprint(answer)" + ], + "Output Answer": [ + "27550" + ], + "split": "test" + }, + { + "Input": "when x is multiplied by 3 , the result is 18 more than the result of subtracting x from 70 . what is the value of x ?", + "Output Program": [ + "n0 = 3.0\nn1 = 18.0\nn2 = 70.0\nt0 = n1 + n2\nt1 = 1.0 + n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "test" + }, + { + "Input": "there has been successive increases of 20 % and then 10 % in the price of gas from the previous month . by what percentage should a driver reduce gas consumption so that the expenditure does not change ?", + "Output Program": [ + "n0 = 20.0\nn1 = 10.0\nt0 = n0 + 100.0\nt1 = n1 * t0\nt2 = t1 / 100.0\nt3 = t0 + t2\nt4 = 100.0 / t3\nt5 = 1.0 - t4\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "24.242424242424242" + ], + "split": "test" + }, + { + "Input": "a satellite is composed of 30 modular units , each of which is equipped with a set of sensors , some of which have been upgraded . each unit contains the same number of non - upgraded sensors . if the number of non - upgraded sensors on one unit is 1 / 6 the total number of upgraded sensors on the entire satellite , what fraction of the sensors on the satellite have been upgraded ?", + "Output Program": [ + "n0 = 30.0\nn1 = 1.0\nn2 = 6.0\nt0 = n1 / n2\nt1 = n0 * t0\nt2 = n0 * t1\nt3 = n0 + t2\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.16666666666666666" + ], + "split": "test" + }, + { + "Input": "a certain class of students is being divided into teams . the class can either be divided into 16 teams with an equal number of players on each team or 24 teams with an equal number of players on each team . what is the lowest possible number of students in the class ?", + "Output Program": [ + "import scipy\nn0 = 16.0\nn1 = 24.0\n\nanswer = scipy.lcm(int(n0), int(n1))\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "test" + }, + { + "Input": "a salesman ' s income consists of a commission and a base salary of $ 350 per week . over the past 5 weeks , his weekly income totals have been $ 556 , $ 413 , $ 420 , $ 436 and $ 395 . what must his average ( arithmetic mean ) commission be per week over the next two weeks so that his average weekly income is $ 500 over the 7 - week period ?", + "Output Program": [ + "n0 = 350.0\nn1 = 5.0\nn2 = 556.0\nn3 = 413.0\nn4 = 420.0\nn5 = 436.0\nn6 = 395.0\nn7 = 500.0\nn8 = 7.0\nt0 = n2 + n3\nt1 = n4 + n5\nt2 = n7 * n8\nt3 = t0 + t1\nt4 = n6 + t3\nt5 = t2 - t4\nt6 = t5 / 2.0\nanswer = t6 - n0\nprint(answer)" + ], + "Output Answer": [ + "290" + ], + "split": "test" + }, + { + "Input": "a man can row 4.8 km / hr in still water . it takes him twice as long to row upstream as to row downstream . what is the rate of the current ?", + "Output Program": [ + "n0 = 4.8\nt0 = n0 * 2.0\nt1 = t0 - n0\nanswer = t1 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "1.5999999999999999" + ], + "split": "test" + }, + { + "Input": "125 liters of a mixture of milk and water contains in the ratio 3 : 2 . how much water should now be added so that the ratio of milk and water becomes 3 : 4 ?", + "Output Program": [ + "n0 = 125.0\nn1 = 3.0\nn2 = 2.0\nn3 = 3.0\nn4 = 4.0\nt0 = n1 + n2\nt1 = n0 / t0\nanswer = n2 * t1\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "test" + }, + { + "Input": "a pupil ' s marks were wrongly entered as 35 instead of 23 . due to that the average marks for the class got increased by half . the number of pupils in the class is :", + "Output Program": [ + "n0 = 35.0\nn1 = 23.0\nt0 = n0 - n1\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "test" + }, + { + "Input": "q is as much younger than r as he is older than t . if the sum of the ages of r and t is 50 years , what is definitely the difference between r and q ' s age ?", + "Output Program": [ + "n0 = 50.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "test" + }, + { + "Input": "if x and y are integers , what is the least positive number of 24 x + 21 y ?", + "Output Program": [ + "n0 = 24.0\nn1 = 21.0\n\nanswer = n0 - n1\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "test" + }, + { + "Input": "the average of runs of a cricket player of 20 innings was 32 . how many runs must he make in his next innings so as to increase his average of runs by 3 ?", + "Output Program": [ + "n0 = 20.0\nn1 = 32.0\nn2 = 3.0\nt0 = n0 + 1.0\nt1 = n1 + n2\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "95" + ], + "split": "test" + }, + { + "Input": "joan took out a mortgage from hel local bank . each monthly mortgage payment she makes must be triple the amount of the previous month ' s payment . if her first payment is $ 100 , and the total amount she must pay back is $ 36400 , how many months will it take joan to pay back her mortgage ?", + "Output Program": [ + "import math\nn0 = 100.0\nn1 = 36400.0\nt0 = math.log(max(1e-5, 3.0), 2)\nt1 = n1 * 2.0\nt2 = t1 / n0\nt3 = t2 + 1.0\nt4 = math.log(max(1e-5, t3), 2)\nanswer = t4 / t0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "test" + }, + { + "Input": "a big container is 35 % full with water . if 16 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container in liters ?", + "Output Program": [ + "n0 = 35.0\nn1 = 16.0\nn2 = 3.0\nn3 = 4.0\nt0 = n2 / n3\nt1 = n0 / 100.0\nt2 = t0 - t1\nanswer = n1 / t2\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "test" + }, + { + "Input": "in objective test a correct ans score 4 marks and on a wrong ans 2 marks are - - - . a student score 480 marks from 150 question . how many ans were correct ?", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\nn2 = 480.0\nn3 = 150.0\nt0 = n0 + n1\nt1 = n1 * n3\nt2 = n2 + t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "130" + ], + "split": "test" + }, + { + "Input": "a number when divided by a certain divisor left remainder 251 , when twice the number was divided by the same divisor , the remainder was 112 . find the divisor ?", + "Output Program": [ + "n0 = 251.0\nn1 = 112.0\nt0 = n0 * 2.0\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "390" + ], + "split": "test" + }, + { + "Input": "excluding stoppages , the average speed of a bus is 120 km / hr and including stoppages , the average speed of the bus is 40 km / hr . for how many minutes does the bus stop per hour ?", + "Output Program": [ + "n0 = 120.0\nn1 = 40.0\nt0 = n1 / n0\nt1 = 1.0 * 60.0\nt2 = t0 * 60.0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "test" + }, + { + "Input": "the average of 6 no . ' s is 3.95 . the average of 2 of them is 4 , while the average of theother 2 is 3.85 . what is the average of the remaining 2 no ' s ?", + "Output Program": [ + "n0 = 6.0\nn1 = 3.95\nn2 = 2.0\nn3 = 4.0\nn4 = 2.0\nn5 = 3.85\nn6 = 2.0\nt0 = n0 * n1\nt1 = n2 * n3\nt2 = n2 * n5\nt3 = t1 + t2\nt4 = t0 - t3\nanswer = t4 / n2\nprint(answer)" + ], + "Output Answer": [ + "4.000000000000002" + ], + "split": "test" + }, + { + "Input": "the population of a town increased from 50000 to 80000 in a decade . the average percent increase of population per year is :", + "Output Program": [ + "n0 = 50000.0\nn1 = 80000.0\nt0 = n1 - n0\nt1 = t0 / n0\nt2 = t1 * 100.0\nanswer = t2 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "test" + }, + { + "Input": "carina has 130 ounces of coffee divided into 5 - and 10 - ounce packages . if she has 2 more 5 - ounce packages than 10 - ounce packages , how many 10 - ounce packages does she have ?", + "Output Program": [ + "n0 = 130.0\nn1 = 5.0\nn2 = 10.0\nn3 = 2.0\nn4 = 5.0\nn5 = 10.0\nn6 = 10.0\nt0 = n1 + n2\nt1 = n1 * n3\nt2 = n0 - t1\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "test" + }, + { + "Input": "if x = 1 / q and y = ( 2 / q ) - 6 , then for what value of q , x is equal to y ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 6.0\nt0 = n1 - n0\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "0.16666666666666666" + ], + "split": "test" + }, + { + "Input": "a certain telescope increases the visual range at a particular location from 70 kilometers to 150 kilometers . by what percent is the visual range increased by using the telescope ?", + "Output Program": [ + "n0 = 70.0\nn1 = 150.0\nt0 = n1 - n0\nt1 = t0 / n0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "114.28571428571428" + ], + "split": "test" + }, + { + "Input": "after 6 games , team b had an average of 75 points per game . if it got only 47 points in game 7 , how many more points does it need to score to get its total above 500 ?", + "Output Program": [ + "n0 = 6.0\nn1 = 75.0\nn2 = 47.0\nn3 = 7.0\nn4 = 500.0\nt0 = n0 * n1\nt1 = n2 + t0\nanswer = n4 - t1\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "test" + }, + { + "Input": "p has $ 21 more than what q and r together would have had if both b and c had 1 / 5 of what p has . how much does p have ?", + "Output Program": [ + "n0 = 21.0\nn1 = 1.0\nn2 = 5.0\nt0 = n1 / n2\nt1 = t0 * 2.0\nt2 = n1 - t1\nanswer = n0 / t2\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "test" + }, + { + "Input": "a large box contains 18 small boxes and each small box contains 25 chocolate bars . how many chocolate bars are in the large box ?", + "Output Program": [ + "n0 = 18.0\nn1 = 25.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "450" + ], + "split": "test" + }, + { + "Input": "find the number which is nearest to 3105 and is exactly divisible by 21 .", + "Output Program": [ + "n0 = 3105.0\nn1 = 21.0\nt0 = n0 % n1\nt1 = n1 - t0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "3108" + ], + "split": "test" + }, + { + "Input": "5.40 can be expressed in terms of percentage as", + "Output Program": [ + "n0 = 5.4\n\nanswer = n0 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "540" + ], + "split": "test" + }, + { + "Input": "a number is mistakenly divided by 5 instead of being multiplied by 5 . find the percentage change in the result due t this mistake .", + "Output Program": [ + "n0 = 5.0\nn1 = 5.0\nt0 = n0 * n0\nt1 = 100.0 / t0\nt2 = t0 - 1.0\nanswer = t1 * t2\nprint(answer)" + ], + "Output Answer": [ + "96" + ], + "split": "test" + }, + { + "Input": "determine the value of 3 * 27 / 31 + 81 / 93", + "Output Program": [ + "n0 = 3.0\nn1 = 27.0\nn2 = 31.0\nn3 = 81.0\nn4 = 93.0\nt0 = n0 * n1\nt1 = n4 - n3\nt2 = n3 + t0\nt3 = t2 - t1\nt4 = t3 + 1.0\nanswer = t4 / n2\nprint(answer)" + ], + "Output Answer": [ + "4.870967741935484" + ], + "split": "test" + }, + { + "Input": "in goshawk - eurasian nature reserve 30 percent of the birds are hawks , and 40 percent of the non - hawks are paddyfield - warblers . if there are 25 percent as many kingfishers as paddyfield - warblers in the reserve , then what percent of the birds e in the nature reserve are not hawks , paddyfield - warblers , or kingfishers ?", + "Output Program": [ + "n0 = 30.0\nn1 = 40.0\nn2 = 25.0\nt0 = n2 + n2\nt1 = t0 / 2.0\nanswer = t1 + 10.0\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "test" + }, + { + "Input": "what is the smallest integer t greater than 1 that leaves a remainder of 1 when divided by any of the integers 6 , 8 , and 10 ?", + "Output Program": [ + "import scipy\nn0 = 1.0\nn1 = 1.0\nn2 = 6.0\nn3 = 8.0\nn4 = 10.0\nt0 = scipy.lcm(int(n2), int(n3))\nt1 = scipy.lcm(int(n4), int(t0))\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "121" + ], + "split": "test" + }, + { + "Input": "the smallest number when increased by ` ` 1 ` ` is exactly divisible by 2 , 8 , 24 , 36 is :", + "Output Program": [ + "import scipy\nn0 = 1.0\nn1 = 2.0\nn2 = 8.0\nn3 = 24.0\nn4 = 36.0\nt0 = scipy.lcm(int(n3), int(n4))\nanswer = t0 - n0\nprint(answer)" + ], + "Output Answer": [ + "71" + ], + "split": "test" + }, + { + "Input": "the maximum number of students among them 1200 pens and 820 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils ?", + "Output Program": [ + "import scipy\nn0 = 1200.0\nn1 = 820.0\n\nanswer = scipy.gcd(int(n0), int(n1))\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "test" + }, + { + "Input": "a soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price . during the annual summer sale , everything in the store is an additional 20 percent off the original list price . if a replica jersey ' s list price is $ 80 , approximately what w percent of the list price is the lowest possible sale price ?", + "Output Program": [ + "n0 = 30.0\nn1 = 50.0\nn2 = 20.0\nn3 = 80.0\n\nanswer = n3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "test" + }, + { + "Input": "an amount at compound interest sums to rs . 17640 / - in 2 years and to rs . 20286 / - in 3 years at the same rate of interest . find the rate percentage ?", + "Output Program": [ + "n0 = 17640.0\nn1 = 2.0\nn2 = 20286.0\nn3 = 3.0\nt0 = n2 - n0\nt1 = t0 / n0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "test" + }, + { + "Input": "5 years ago , the average age of a , b , c and d was 45 years . with e joining them now , the average of all the 5 is 50 years . the age of e is ?", + "Output Program": [ + "n0 = 5.0\nn1 = 45.0\nn2 = 5.0\nn3 = 50.0\nt0 = n0 * n3\nt1 = 2.0 * 2.0\nt2 = n0 * 4.0\nt3 = n1 * t1\nt4 = t3 + t2\nanswer = t0 - t4\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "test" + }, + { + "Input": "sandy bought 65 books for $ 1180 from one shop and 55 books for $ 860 from another shop . what is the average price that sandy paid per book ?", + "Output Program": [ + "n0 = 65.0\nn1 = 1180.0\nn2 = 55.0\nn3 = 860.0\nt0 = n1 + n3\nt1 = n0 + n2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "test" + }, + { + "Input": "( 3 x + 2 ) ( 2 x - 1 ) = ax ^ 2 + kx + n . what is the value of a - n + k ?", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 2.0\nn3 = 1.0\nn4 = 2.0\nt0 = n0 * n1\nt1 = n1 * n3\nt2 = n1 * n1\nt3 = n0 * n3\nt4 = t0 + t1\nt5 = t2 - t3\nanswer = t4 + t5\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "test" + }, + { + "Input": "what is the average ( arithmetic mean ) of 10 , 2030 , 4050 , 6070 , 8090 ?", + "Output Program": [ + "n0 = 10.0\nn1 = 2030.0\nn2 = 4050.0\nn3 = 6070.0\nn4 = 8090.0\nt0 = n0 + n1\nt1 = 1.0 + 4.0\nt2 = 10.0 * 100.0\nt3 = n2 + t0\nt4 = t2 * 4.0\nt5 = n3 + t3\nt6 = n4 + t5\nt7 = t6 / t1\nanswer = t7 - t4\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "test" + }, + { + "Input": "for a group of n people , k of whom are of the same sex , the ( n - k ) / n expression yields an index for a certain phenomenon in group dynamics for members of that sex . for a group that consists of 20 people , 6 of whom are females , by how much does the index for the females exceed the index for the males in the group ?", + "Output Program": [ + "n0 = 20.0\nn1 = 6.0\nt0 = n1 / n0\nt1 = n0 - n1\nt2 = t1 / n0\nanswer = t2 - t0\nprint(answer)" + ], + "Output Answer": [ + "0.39999999999999997" + ], + "split": "test" + }, + { + "Input": "the difference of 2 digit number & the number obtained by interchanging the digits is 36 . what is the sum and the number if the ratio between the digits of the number is 1 : 2 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 36.0\nn2 = 1.0\nn3 = 2.0\nt0 = n0 * n2\nt1 = 10.0 - n2\nt2 = t0 * t1\nt3 = t2 - t1\nt4 = n1 / t3\nanswer = t4 * n0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "test" + }, + { + "Input": "a man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses . next year his income increases by 40 % but his savings increase by 100 % . if his total expenditure in 2 years is double his expenditure in 1 st year , what % age of his income in the first year did he save ?", + "Output Program": [ + "n0 = 40.0\nn1 = 100.0\nn2 = 2.0\nn3 = 1.0\nt0 = n0 + n1\nt1 = n1 * n2\nt2 = n1 + t0\nt3 = t2 - t1\nt4 = t3 / 100.0\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "test" + }, + { + "Input": "find large number from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 10 as remainder", + "Output Program": [ + "n0 = 1365.0\nn1 = 6.0\nn2 = 10.0\nt0 = n0 - n2\nt1 = n1 - 1.0\nt2 = t0 / t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "1626" + ], + "split": "test" + }, + { + "Input": "for all positive integers m and v , the expression m \u03b8 v represents the remainder when m is divided by v . what is the value of ( ( 90 \u03b8 33 ) \u03b8 17 ) - ( 97 \u03b8 ( 33 \u03b8 17 ) ) ?", + "Output Program": [ + "n0 = 90.0\nn1 = 33.0\nn2 = 17.0\nn3 = 97.0\nn4 = 33.0\nn5 = 17.0\nt0 = n0 % n1\nt1 = n1 % n2\nt2 = t0 % n2\nt3 = n3 % t1\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "test" + }, + { + "Input": "if 1,000 microns = 1 decimeter , and 1,000 , 000,000 angstroms = 1 decimeter , how many angstroms equal 1 micron ?", + "Output Program": [ + "n0 = 1000.0\nn1 = 1.0\nn2 = 1000.0\nn3 = 0.0\nn4 = 1.0\nn5 = 1.0\nt0 = 100.0 * 100.0\nt1 = n1 / t0\nanswer = t1 * t0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "test" + }, + { + "Input": "if the sales tax reduced from 3 1 / 2 % to 3 1 / 3 % , then what difference does it make to a person who purchases an article with market price of $ 8400 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 2.0\nn3 = 3.0\nn4 = 1.0\nn5 = 3.0\nn6 = 8400.0\nt0 = n1 / n2\nt1 = n1 / n0\nt2 = n0 + t0\nt3 = n0 + t1\nt4 = t2 - t3\nt5 = n6 * t4\nanswer = t5 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "13.99999999999999" + ], + "split": "test" + }, + { + "Input": "cost is expressed by the formula tb ^ 4 . if b is doubled , the new cost q is what percent of the original cost ?", + "Output Program": [ + "n0 = 4.0\nt0 = 2.0**min(n0, 5)\nanswer = t0 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "1600" + ], + "split": "test" + }, + { + "Input": "albert is 2 times mary \u2019 s age and 4 times as old as betty . mary is 12 years younger than albert . how old is betty ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 12.0\nt0 = n0 * n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "test" + }, + { + "Input": "marts income is 50 percent more than tims income and tims income is 40 percent less than juans income . what percentage of juans income is marts income", + "Output Program": [ + "n0 = 50.0\nn1 = 40.0\nt0 = n0 + 100.0\nt1 = 100.0 - n1\nt2 = 100.0 / t1\nt3 = t2 * 100.0\nt4 = t0 / t3\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "89.99999999999999" + ], + "split": "test" + }, + { + "Input": "what least number should be subtracted from 13601 such that the remainder is divisible by 87 ?", + "Output Program": [ + "n0 = 13601.0\nn1 = 87.0\n\nanswer = n0 % n1\nprint(answer)" + ], + "Output Answer": [ + "29" + ], + "split": "test" + }, + { + "Input": "3251 + 587 + 369 - ? = 3007", + "Output Program": [ + "n0 = 3251.0\nn1 = 587.0\nn2 = 369.0\nn3 = 3007.0\nt0 = n0 + n1\nt1 = n2 + t0\nanswer = t1 - n3\nprint(answer)" + ], + "Output Answer": [ + "1200" + ], + "split": "test" + }, + { + "Input": "rs . 1775 is divided amongst a , b , c so that 5 times a ' s share , 3 times b ' s share and 7 times c ' s share are all equal . find c ' s share ?", + "Output Program": [ + "n0 = 1775.0\nn1 = 5.0\nn2 = 3.0\nn3 = 7.0\nt0 = n3 / n1\nt1 = n3 / n2\nt2 = t0 + t1\nt3 = t2 + 1.0\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "375" + ], + "split": "test" + }, + { + "Input": "n ^ ( n / 2 ) = 2 is true when n = 2 in the same way what is the value of n if n ^ ( n / 2 ) = 4 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 2.0\nn3 = 2.0\nn4 = 4.0\nt0 = n4**min(n0, 5)\nanswer = t0 / n4\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "test" + }, + { + "Input": "if a - b = 3 and a ( power 2 ) + b ( power 2 ) = 23 , find the value of ab .", + "Output Program": [ + "n0 = 3.0\nn1 = 2.0\nn2 = 2.0\nn3 = 23.0\nt0 = n0**min(n1, 5)\nt1 = n3 - t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "test" + }, + { + "Input": "find a sum for first 8 prime numbers ?", + "Output Program": [ + "n0 = 8.0\nt0 = 2.0 + 3.0\nt1 = t0 + 2.0\nt2 = t1 + 4.0\nt3 = n0 + t2\nt4 = t2 + 2.0\nt5 = t4 + 4.0\nt6 = t5 + t4\nt7 = t6 + t2\nt8 = t7 + t1\nt9 = t8 + t0\nt10 = t9 + 3.0\nt11 = t10 + 2.0\nanswer = t3 + t11\nprint(answer)" + ], + "Output Answer": [ + "77" + ], + "split": "test" + }, + { + "Input": "a jogger running at 9 km / hr along side a railway track is 290 m ahead of the engine of a 120 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?", + "Output Program": [ + "n0 = 9.0\nn1 = 290.0\nn2 = 120.0\nn3 = 45.0\nt0 = n1 + n2\nt1 = 10.0 / 2.0\nt2 = n3 - n0\nt3 = t2 / 2.0\nt4 = t1 / t3\nt5 = t4 * t2\nanswer = t0 / t5\nprint(answer)" + ], + "Output Answer": [ + "41" + ], + "split": "test" + }, + { + "Input": "working simultaneously and independently at an identical constant rate , 20 machines of a certain type can produce a total of x units of product p in 4 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 3 x units of product p in 8 days ?", + "Output Program": [ + "n0 = 20.0\nn1 = 4.0\nn2 = 3.0\nn3 = 8.0\nt0 = n1 / n3\nt1 = n0 * n2\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "test" + }, + { + "Input": "the sum of first n consecutive odd integers is n ^ 2 . what is the sum of all odd integers between 13 and 31 inclusive .", + "Output Program": [ + "n0 = 2.0\nn1 = 13.0\nn2 = 31.0\nt0 = n2 + 1.0\nt1 = n1 - n0\nt2 = t1 + 1.0\nt3 = t0 / n0\nt4 = t2 / n0\nt5 = t3**min(2.0, 5)\nt6 = t4**min(n0, 5)\nanswer = t5 - t6\nprint(answer)" + ], + "Output Answer": [ + "220" + ], + "split": "test" + }, + { + "Input": "if a mixture is 5 \u2044 9 alcohol by volume and 4 \u2044 9 water by volume , what is the ratio of the volume of alcohol to the volume of water in this mixture ?", + "Output Program": [ + "n0 = 5.0\nn1 = 9.0\nn2 = 4.0\nn3 = 9.0\nt0 = n0 / n1\nt1 = n2 / n1\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "1.2500000000000002" + ], + "split": "test" + }, + { + "Input": "s = { 12 , 35 , 69 } t = { 45 , 67 , 13 } what is the probability that x chosen from s and y chosen from t will result x * y = even", + "Output Program": [ + "n0 = 12.0\nn1 = 35.0\nn2 = 69.0\nn3 = 45.0\nn4 = 67.0\nn5 = 13.0\nt0 = n0 / 4.0\nt1 = t0 + 2.0\nt2 = t0 * t0\nanswer = t1 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.5555555555555556" + ], + "split": "test" + }, + { + "Input": "a certain roller coaster has 3 cars , and a passenger is equally likely to ride in any 1 of the 3 cars each time that passenger rides the roller coaster . if a certain passenger is to ride the roller coaster 3 times , what is the probability that the passenger will ride in each of the 3 cars ?", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 1.0\nn2 = 3.0\nn3 = 3.0\nn4 = 3.0\nt0 = n1 / n0\nt1 = math.factorial(min(15, int(n0)))\nt2 = t0**min(n0, 5)\nanswer = t1 * t2\nprint(answer)" + ], + "Output Answer": [ + "0.22222222222222215" + ], + "split": "test" + }, + { + "Input": "a tank holds x gallons of a saltwater solution that is 20 % salt by volume . one fourth of the water is evaporated , leaving all of the salt . when 20 gallons of water and 40 gallons of salt are added , the resulting mixture is 33 1 / 3 % salt by volume . what is the value of x ?", + "Output Program": [ + "n0 = 20.0\nn1 = 20.0\nn2 = 40.0\nn3 = 33.0\nn4 = 1.0\nn5 = 3.0\nt0 = n0 / 100.0\nt1 = n4 / 4.0\nt2 = n2 * 2.0\nt3 = t0 * 2.0\nt4 = t2 - n1\nt5 = n4 - t0\nt6 = t1 * t5\nt7 = t5 - t6\nt8 = t7 - t3\nanswer = t4 / t8\nprint(answer)" + ], + "Output Answer": [ + "299.9999999999999" + ], + "split": "test" + }, + { + "Input": "if 20 liters of chemical x are added to 80 liters of a mixture that is 25 % chemical x and 75 % chemical y , then what percentage of the resulting mixture is chemical x ?", + "Output Program": [ + "n0 = 20.0\nn1 = 80.0\nn2 = 25.0\nn3 = 75.0\nt0 = n2 / 100.0\nt1 = n1 * t0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "test" + }, + { + "Input": "an amount at compound interest sums to rs . 17640 / - in 2 years and to rs . 19404 / - in 3 years at the same rate of interest . find the rate percentage ?", + "Output Program": [ + "n0 = 17640.0\nn1 = 2.0\nn2 = 19404.0\nn3 = 3.0\nt0 = n2 - n0\nt1 = t0 / n0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "test" + }, + { + "Input": "a man is 22 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is :", + "Output Program": [ + "n0 = 22.0\nt0 = 2.0 * 2.0\nt1 = 2.0 - 1.0\nt2 = t0 - 2.0\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "test" + }, + { + "Input": "if y > 0 , ( 10 y ) / 20 + ( 3 y ) / 10 is what percent of y ?", + "Output Program": [ + "n0 = 0.0\nn1 = 10.0\nn2 = 20.0\nn3 = 3.0\nn4 = 10.0\nt0 = n1 / n2\nt1 = n3 / n4\nt2 = t0 + t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "test" + }, + { + "Input": "let the number which when multiplied by 11 is increased by 300 .", + "Output Program": [ + "n0 = 11.0\nn1 = 300.0\nt0 = n0 - 1.0\nanswer = n1 / t0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "test" + }, + { + "Input": "in a division , a student took 78 as divisor instead of 36 . his answer was 24 . the correct answer is -", + "Output Program": [ + "n0 = 78.0\nn1 = 36.0\nn2 = 24.0\nt0 = n0 * n2\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "52" + ], + "split": "test" + }, + { + "Input": "in what proportion must rice at rs 3.10 per kg be mixed with rice at rs 3.75 per kg , so that the mixture be worth rs 3.25 a kg ?", + "Output Program": [ + "n0 = 3.1\nn1 = 3.75\nn2 = 3.25\nt0 = n1 - n2\nt1 = n2 - n0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "3.3333333333333353" + ], + "split": "test" + }, + { + "Input": "a batsman had a certain average of runs for 16 innings . in the 17 th innings , he made a score of 87 runs thereby increasing his average by 3 . what is his average after 17 innings ?", + "Output Program": [ + "n0 = 16.0\nn1 = 17.0\nn2 = 87.0\nn3 = 3.0\nn4 = 17.0\nt0 = n1 * n3\nt1 = n2 - t0\nanswer = n3 + t1\nprint(answer)" + ], + "Output Answer": [ + "39" + ], + "split": "test" + }, + { + "Input": "if a > x > y > z on the number line , y is halfway between x and z , and x is halfway between w and z , then ( y - x ) / ( y - a ) =", + "Output Program": [ + "t0 = 2.0 + 2.0\nt1 = t0 - 1.0\nanswer = 1.0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.3333333333333333" + ], + "split": "test" + }, + { + "Input": "3 friends james , david and charlie divide $ 1230 amongs them in such a way that if $ 5 , $ 10 and $ 15 are removed from the sums that james , david and charlie received respectively , then the share of the sums that they got will be in the ratio of 9 : 10 : 11 . how much did charlie receive ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1230.0\nn2 = 5.0\nn3 = 10.0\nn4 = 15.0\nn5 = 9.0\nn6 = 10.0\nn7 = 11.0\nt0 = n2 + n3\nt1 = n3 + n5\nt2 = n4 + t0\nt3 = n7 + t1\nt4 = n1 - t2\nt5 = t4 / t3\nt6 = n7 * t5\nt7 = n4 + t6\nt8 = t7 + t5\nt9 = t8 + t5\nt10 = t9 + t5\nanswer = t10 + t5\nprint(answer)" + ], + "Output Answer": [ + "615" + ], + "split": "test" + }, + { + "Input": "the price of commodity x increases by 45 cents every year , while the price of commodity y increases by 20 cents every year . in 2001 , the price of commodity x was $ 5.20 and the price of commodity y was $ 7.30 . in which year will the price of commodity x be 10 cents less than the price of commodity y ?", + "Output Program": [ + "n0 = 45.0\nn1 = 20.0\nn2 = 2001.0\nn3 = 5.2\nn4 = 7.3\nn5 = 10.0\nt0 = n5 / 100.0\nt1 = n0 / 100.0\nt2 = n4 - n3\nt3 = t0 + t2\nt4 = t1 - t2\nt5 = t3 / t4\nanswer = n2 + t5\nprint(answer)" + ], + "Output Answer": [ + "1999.6666666666667" + ], + "split": "test" + }, + { + "Input": "if a wholesaler distributes items to several outlets ( a , b , c and d ) in the ratio of 1 / 12 : 1 / 13 : 1 / 15 : 1 / 2 , then find the total number of items the wholesaler distributes ?", + "Output Program": [ + "n0 = 1.0\nn1 = 12.0\nn2 = 1.0\nn3 = 13.0\nn4 = 1.0\nn5 = 15.0\nn6 = 1.0\nn7 = 2.0\nt0 = 3.0 + 4.0\nt1 = 100.0 * 4.0\nt2 = n5 * 4.0\nt3 = t1 + 100.0\nt4 = t0 + t2\nanswer = t3 + t4\nprint(answer)" + ], + "Output Answer": [ + "567" + ], + "split": "test" + }, + { + "Input": "the average weight of 4 person ' s increases by 1.5 kg when a new person comes in place of one of them weighing 95 kg . what might be the weight of the new person ?", + "Output Program": [ + "n0 = 4.0\nn1 = 1.5\nn2 = 95.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "101" + ], + "split": "test" + }, + { + "Input": "subtracting 30 from a number , the remainder is one fourth of the number . find the number ?", + "Output Program": [ + "n0 = 30.0\nt0 = 1.0 / 4.0\nt1 = 1.0 - t0\nanswer = n0 / t1\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "test" + }, + { + "Input": "anne bought doughnuts for a class breakfast party . she bought 12 chocolate doughnuts , 6 coconut doughnuts , and 8 jam - filled doughnuts . how many doughnuts did anne buy in all ?", + "Output Program": [ + "n0 = 12.0\nn1 = 6.0\nn2 = 8.0\nt0 = n0 + n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "test" + }, + { + "Input": "if the number is divided by 3 , it reduced by 34 . the number is", + "Output Program": [ + "n0 = 3.0\nn1 = 34.0\nt0 = n0 * n1\nt1 = n0 - 1.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "51" + ], + "split": "test" + }, + { + "Input": "if a train runs at 40 kmph , it reach its destination late by 11 minutes but if it runs at 50 kmph it is late by 5 minutes only . the correct time for a train to complete its journey is ? let the correct time to complete the journey be x min distance covered in ( x + 11 ) min . at 40 kmph distance covered in ( x + 5 ) min . at 50 kmph ( x + 11 ) / 60 * 40 = ( x + 5 ) / 60 * 50 x = 19 min", + "Output Program": [ + "n0 = 40.0\nn1 = 11.0\nn2 = 50.0\nn3 = 5.0\nn4 = 11.0\nn5 = 40.0\nn6 = 5.0\nn7 = 50.0\nn8 = 11.0\nn9 = 60.0\nn10 = 40.0\nn11 = 5.0\nn12 = 60.0\nn13 = 50.0\nn14 = 19.0\nt0 = n0 * n9\nt1 = n2 * n9\nt2 = n1 * t0\nt3 = n3 * t1\nt4 = t1 - t0\nt5 = t2 - t3\nanswer = t5 / t4\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "test" + }, + { + "Input": "if an integer e is to be chosen at random from the integers 1 to 96 , inclusive , what is the probability that e ( e + 1 ) ( e + 2 ) will be divisible by 8 ?", + "Output Program": [ + "n0 = 1.0\nn1 = 96.0\nn2 = 1.0\nn3 = 2.0\nn4 = 8.0\nt0 = n1 / n4\nt1 = t0 / n4\nt2 = n3 * t1\nt3 = n3 + t2\nanswer = t3 / n4\nprint(answer)" + ], + "Output Answer": [ + "0.625" + ], + "split": "test" + }, + { + "Input": "if ( 2 to the x ) - ( 2 to the ( x - 2 ) ) = 3 ( 2 to the 9 ) , what is the value of x ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nn2 = 2.0\nn3 = 3.0\nn4 = 2.0\nn5 = 9.0\n\nanswer = n0 + n5\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "test" + }, + { + "Input": "if the average of 5 positive integers is 65 and the difference between the largest and the smallest of these 5 numbers is 10 , what is the maximum value possible for the largest of these 5 integers ?", + "Output Program": [ + "n0 = 5.0\nn1 = 65.0\nn2 = 5.0\nn3 = 10.0\nn4 = 5.0\nt0 = n0 * n1\nt1 = t0 - n3\nt2 = t1 / n0\nanswer = n3 + t2\nprint(answer)" + ], + "Output Answer": [ + "73" + ], + "split": "test" + }, + { + "Input": "a sum of money is distributed among a , b , c , d in the proportion of 1 : 3 : 4 : 2 . if c gets $ 500 more than d , what is the b ' s share ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 4.0\nn3 = 2.0\nn4 = 500.0\nt0 = n4 + n4\nt1 = n3 * t0\nt2 = t1 / n2\nt3 = n1 * t2\nanswer = t3 / n3\nprint(answer)" + ], + "Output Answer": [ + "750" + ], + "split": "test" + }, + { + "Input": "the number 341 is equal to the sum of the cubes of two integers . what is the product of those integers ?", + "Output Program": [ + "import math\nn0 = 341.0\nt0 = n0 / 2.0\nt1 = 1.0 / 3.0\nt2 = t0**min(t1, 5)\nt3 = math.floor(t2)\nt4 = t3**min(3.0, 5)\nt5 = n0 - t4\nt6 = t5**min(t1, 5)\nanswer = t3 * t6\nprint(answer)" + ], + "Output Answer": [ + "29.999999999999996" + ], + "split": "test" + }, + { + "Input": "45 x ? = 25 % of 900", + "Output Program": [ + "n0 = 45.0\nn1 = 25.0\nn2 = 900.0\nt0 = n1 / 100.0\nt1 = n2 * t0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "test" + }, + { + "Input": "| x + 3 | \u2013 | 4 - x | = | 7 + x | how many solutions will this equation have ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 7.0\nt0 = n0 + n1\nt1 = t0 * 2.0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "test" + }, + { + "Input": "a man covers a certain distance q in a train . if the train moved 4 km / hr faster , it would take 30 min less . if it moved 2 km / hr slower , it would take 20 mins more . find the distance ?", + "Output Program": [ + "n0 = 4.0\nn1 = 30.0\nn2 = 2.0\nn3 = 20.0\nt0 = n0 * n2\nt1 = t0 - n0\nt2 = t1 / 2.0\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "test" + }, + { + "Input": "x varies inversely as square of y . given that y = 3 for x = 1 . the value of x for y = 7 will be equal to :", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 7.0\nt0 = n0**min(2.0, 5)\nt1 = n2**min(2.0, 5)\nt2 = n1 * t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.1836734693877551" + ], + "split": "test" + }, + { + "Input": "each machine of type a has 3 steel parts and 3 chrome parts . each machine of type b has 6 steel parts and 5 chrome parts . if a certain group of type a and type b machines has a total of 60 steel parts and 44 chrome parts , how many machines are in the group", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 6.0\nn3 = 5.0\nn4 = 60.0\nn5 = 44.0\nt0 = n2 + n3\nt1 = n0 + n1\nt2 = n5 / t0\nt3 = n4 / t1\nanswer = t2 + t3\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "test" + }, + { + "Input": "a clothing store purchased a pair of pants for $ 90 and was selling it at a price that equaled the purchase price of the pants plus a markup that was 25 percent of the selling price . after some time a clothing store owner decided to decrease the selling price by 20 percent . what was the clothing store ' s gross profit on this sale ?", + "Output Program": [ + "n0 = 90.0\nn1 = 25.0\nn2 = 20.0\nt0 = n0 / 3.0\nt1 = 100.0 - n2\nt2 = n0 + t0\nt3 = t2 * t1\nt4 = t3 / 100.0\nanswer = t4 - n0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "test" + }, + { + "Input": "the annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years q in which the population would be doubled assuming there is no emigration or immigration is", + "Output Program": [ + "n0 = 1000.0\nn1 = 39.4\nn2 = 19.4\nt0 = 10.0 * 3.0\nt1 = n1 - n2\nt2 = t1 / n0\nt3 = 100.0 - t0\nt4 = t2 * 100.0\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "test" + }, + { + "Input": "how many unique positive odd integers less than 70 are equal to the product of a positive multiple of 5 and an odd number ?", + "Output Program": [ + "n0 = 70.0\nn1 = 5.0\nt0 = n0 / n1\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "test" + }, + { + "Input": "find the value of 201834 x 99999 = m ?", + "Output Program": [ + "n0 = 201834.0\nn1 = 99999.0\nt0 = n1 - 4.0\nanswer = t0 * n0\nprint(answer)" + ], + "Output Answer": [ + "20182390830" + ], + "split": "test" + }, + { + "Input": "if a 5 percent deposit that has been paid toward the purchase of a certain product is $ 70 , how much more remains to be paid ?", + "Output Program": [ + "n0 = 5.0\nn1 = 70.0\nt0 = 100.0 / n0\nt1 = n1 * t0\nanswer = t1 - n1\nprint(answer)" + ], + "Output Answer": [ + "1330" + ], + "split": "test" + }, + { + "Input": "there are 6 people in the elevator . their average weight is 170 lbs . another person enters the elevator , and increases the average weight to 151 lbs . what is the weight of the 7 th person .", + "Output Program": [ + "n0 = 6.0\nn1 = 170.0\nn2 = 151.0\nn3 = 7.0\nt0 = n2 * n3\nt1 = n0 * n1\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "37" + ], + "split": "test" + }, + { + "Input": "the mean of 50 observations is 100 . but later he found that there is decrements of 13 from each observations . what is the the updated mean is ?", + "Output Program": [ + "n0 = 50.0\nn1 = 100.0\nn2 = 13.0\n\nanswer = n1 - n2\nprint(answer)" + ], + "Output Answer": [ + "87" + ], + "split": "test" + }, + { + "Input": "if x and y are integers such that x ^ 2 = y and xy = 27 , then x \u2013 y = ?", + "Output Program": [ + "n0 = 2.0\nn1 = 27.0\nt0 = 1.0 / 3.0\nt1 = n1**min(t0, 5)\nt2 = t1**min(2.0, 5)\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "test" + }, + { + "Input": "a pupil ' s marks were wrongly entered as 83 instead of 63 . due to the average marks for the class got increased by half . the number of pupils in the class is ?", + "Output Program": [ + "n0 = 83.0\nn1 = 63.0\nt0 = n0 - n1\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "test" + }, + { + "Input": "3 / 4 of 1 / 2 of 2 / 5 of 5080 = ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 1.0\nn3 = 2.0\nn4 = 2.0\nn5 = 5.0\nn6 = 5080.0\nt0 = n3 / n5\nt1 = n0 / n1\nt2 = n2 / n3\nt3 = t1 * t2\nt4 = t0 * t3\nanswer = n6 * t4\nprint(answer)" + ], + "Output Answer": [ + "762.0000000000001" + ], + "split": "test" + }, + { + "Input": "8 people decided to split the restaurant bill evenly . if the bill was $ 214.15 dollars , how much money did they 1 cent is the smallest unit ?", + "Output Program": [ + "n0 = 8.0\nn1 = 214.15\nn2 = 1.0\nt0 = 3.0 / 100.0\nanswer = n1 + t0\nprint(answer)" + ], + "Output Answer": [ + "214.18" + ], + "split": "test" + }, + { + "Input": "a soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price . during the annual summer sale , everything in the store is an additional 20 percent off the original list price . if a replica jersey ' s list price is $ 80 , approximately what y percent of the list price is the lowest possible sale price ?", + "Output Program": [ + "n0 = 30.0\nn1 = 50.0\nn2 = 20.0\nn3 = 80.0\n\nanswer = n3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "test" + }, + { + "Input": "each year for 4 years , a farmer increased the number of trees in a certain orchard by 1 / 4 of the number of trees in the orchard of the preceding year . if all of the trees thrived and there were 12500 trees in the orchard at the end of 4 year period , how many trees were in the orchard at the beginning of the 4 year period .", + "Output Program": [ + "n0 = 4.0\nn1 = 1.0\nn2 = 4.0\nn3 = 12500.0\nn4 = 4.0\nn5 = 4.0\nt0 = n1 / n0\nt1 = n1 + t0\nt2 = t1**min(n0, 5)\nanswer = n3 / t2\nprint(answer)" + ], + "Output Answer": [ + "5120" + ], + "split": "test" + }, + { + "Input": "in the youth summer village there are 200 people , 100 of them are not working , 75 of them have families and 125 of them like to sing in the shower . what is the largest possible number of people in the village , which are working , that do n ' t have families and that are singing in the shower ?", + "Output Program": [ + "n0 = 200.0\nn1 = 100.0\nn2 = 75.0\nn3 = 125.0\nt0 = n1 + n2\nt1 = n3 + t0\nanswer = t1 - n0\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "test" + }, + { + "Input": "of 70 players on a football team , 43 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?", + "Output Program": [ + "n0 = 70.0\nn1 = 43.0\nt0 = 1.0 / 3.0\nt1 = n0 - n1\nt2 = 1.0 - t0\nt3 = t2 * t1\nanswer = n1 + t3\nprint(answer)" + ], + "Output Answer": [ + "61" + ], + "split": "test" + }, + { + "Input": "the bus fare for two persons for travelling between agra and aligarh id 4 - thirds the train fare between the same places for one person . the total fare paid by 6 persons travelling by bus and 8 persons travelling by train between the two places is rs . 1512 . find the train fare between the two places for one person ?", + "Output Program": [ + "n0 = 4.0\nn1 = 6.0\nn2 = 8.0\nn3 = 1512.0\nt0 = n1 / 2.0\nt1 = n0 / 3.0\nt2 = t0 * t1\nt3 = n2 + t2\nanswer = n3 / t3\nprint(answer)" + ], + "Output Answer": [ + "126" + ], + "split": "test" + }, + { + "Input": "evaluate : | 6 - 8 ( 3 - 12 ) | - | 5 - 11 | = ?", + "Output Program": [ + "n0 = 6.0\nn1 = 8.0\nn2 = 3.0\nn3 = 12.0\nn4 = 5.0\nn5 = 11.0\nt0 = n2 - n3\nt1 = n4 - n5\nt2 = n1 * t0\nt3 = -t1\nt4 = n0 - t2\nanswer = t4 - t3\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "test" + }, + { + "Input": "on increasing the number of lines in a page by 100 , they become 240 . what is the % of increase in the no . of lines in the page ?", + "Output Program": [ + "n0 = 100.0\nn1 = 240.0\nt0 = n1 - n0\nt1 = n1 / t0\nt2 = t1 * 100.0\nanswer = t2 - 100.0\nprint(answer)" + ], + "Output Answer": [ + "71.42857142857142" + ], + "split": "test" + }, + { + "Input": "find the sum 3 / 10 + 5 / 100 + 8 / 1000 in decimal form ?", + "Output Program": [ + "n0 = 3.0\nn1 = 10.0\nn2 = 5.0\nn3 = 100.0\nn4 = 8.0\nn5 = 1000.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = n4 / n5\nt3 = t0 + t1\nanswer = t3 + t2\nprint(answer)" + ], + "Output Answer": [ + "0.358" + ], + "split": "test" + }, + { + "Input": "3 distinct single digit no a , b , c are in g . p . if abs ( x ) for real x is the absolute value of x ( x if x is positive or zero , and x if x is negative ) , then the no . of different possible values of abs ( a + b - c ) is", + "Output Program": [ + "n0 = 3.0\n\nanswer = n0 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "test" + }, + { + "Input": "sum of 19 odd numbers is ?", + "Output Program": [ + "n0 = 19.0\nt0 = n0 / 2.0\nt1 = n0 * 2.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "361" + ], + "split": "test" + }, + { + "Input": "a certain car traveled twice as many miles from town a to town b as it did from town b to town c . from town a to town b , the car averaged 10 miles per gallon , and from town b to town c , the car averaged 12 miles per gallon . what is the average miles per gallon that the car achieved on its trip from town a through town b to town c ?", + "Output Program": [ + "n0 = 10.0\nn1 = 12.0\nt0 = n1 * 10.0\nt1 = t0 / 2.0\nt2 = t0 / n0\nt3 = t1 + t0\nt4 = t1 / n1\nt5 = t2 + t4\nanswer = t3 / t5\nprint(answer)" + ], + "Output Answer": [ + "10.588235294117647" + ], + "split": "test" + }, + { + "Input": "on sunday , bill ran 4 more miles than he ran on saturday . julia did not run on saturday , but she ran twice the number of miles on sunday that bill ran on sunday . if bill and julia ran a total of 16 miles on saturday and sunday , how many miles did bill run on sunday ?", + "Output Program": [ + "n0 = 4.0\nn1 = 16.0\nt0 = n0 * 2.0\nt1 = n0 + t0\nt2 = n1 - t1\nt3 = t2 / n0\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "test" + }, + { + "Input": "if x < y < z and y - x > 7 , where x is an even integer and y and z are odd integers , what is the least possible value of z - x ?", + "Output Program": [ + "n0 = 7.0\nt0 = n0 + 2.0\nanswer = t0 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "test" + }, + { + "Input": "a hollow iron pipe is 21 cm long and its external diameter is 8 cm . if the thickness of the pipe is 1 cm and iron weighs 8 g / cm ^ 3 , then the weight of the pipe is :", + "Output Program": [ + "import math\nn0 = 21.0\nn1 = 8.0\nn2 = 1.0\nn3 = 8.0\nn4 = 3.0\nt0 = n1 / 2.0\nt1 = t0 - n2\nt2 = math.pi * t0**2 * n0\nt3 = math.pi * t1**2 * n0\nt4 = t2 - t3\nt5 = n1 * t4\nanswer = t5 / 1000.0\nprint(answer)" + ], + "Output Answer": [ + "3.694512960621597" + ], + "split": "test" + }, + { + "Input": "the average weight of 7 persons increases by 1.5 kg . if a person weighing 65 kg is replaced by a new person , what could be the weight of the new person ?", + "Output Program": [ + "n0 = 7.0\nn1 = 1.5\nn2 = 65.0\nt0 = n0 * n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "75.5" + ], + "split": "test" + }, + { + "Input": "he total marks obtained by a student in physics , chemistry and mathematics is 170 more than the marks obtained by him in physics . what is the average mark obtained by him in chemistry and mathematics ?", + "Output Program": [ + "n0 = 170.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "85" + ], + "split": "test" + }, + { + "Input": "25 onions on a scale weigh 5.12 kg . when 3 onions are removed from the scale , the average weight of the 22 onions is 200 grams . what is the average weight ( in grams ) of the 3 onions which were removed ?", + "Output Program": [ + "n0 = 25.0\nn1 = 5.12\nn2 = 3.0\nn3 = 22.0\nn4 = 200.0\nn5 = 3.0\nt0 = n1 * 1000.0\nt1 = n3 * n4\nt2 = t0 - t1\nanswer = t2 / n2\nprint(answer)" + ], + "Output Answer": [ + "240" + ], + "split": "test" + }, + { + "Input": "a profit of rs . 600 is divided between x and y in the ratio of 1 / 2 : 1 / 3 . what is the difference between their profit shares ?", + "Output Program": [ + "n0 = 600.0\nn1 = 1.0\nn2 = 2.0\nn3 = 1.0\nn4 = 3.0\nt0 = n1 / n2\nt1 = n1 / n4\nt2 = t0 + t1\nt3 = n0 / t2\nt4 = t3 / n2\nt5 = t3 / n4\nanswer = t4 - t5\nprint(answer)" + ], + "Output Answer": [ + "120.00000000000003" + ], + "split": "test" + }, + { + "Input": "3 candidates contested an election and received 1000 , 2000 and 4000 votes respectively . what percentage of the total votes did the winning candidate got ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1000.0\nn2 = 2000.0\nn3 = 4000.0\nt0 = n1 + n2\nt1 = n3 + t0\nt2 = n3 / t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "57.14285714285714" + ], + "split": "test" + }, + { + "Input": "an old man distributed all the gold coins he had to his two sons into two different numbers such that the difference between the squares of the two numbers is 64 times the difference between the two numbers . how many coins did the old man have ?", + "Output Program": [ + "import math\nn0 = 64.0\n\nanswer = math.floor(n0)\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "test" + }, + { + "Input": "12.036 divided by 0.04 gives :", + "Output Program": [ + "n0 = 12.036\nn1 = 0.04\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "300.9" + ], + "split": "test" + }, + { + "Input": "if 20 liters of chemical x are added to 80 liters of a mixture that is 5 % chemical x and 95 % chemical y , then what percentage of the resulting mixture is chemical x ?", + "Output Program": [ + "n0 = 20.0\nn1 = 80.0\nn2 = 5.0\nn3 = 95.0\nt0 = n2 / 100.0\nt1 = n1 * t0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "test" + }, + { + "Input": "for a certain exam , a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean . what was the mean score r for the exam ?", + "Output Program": [ + "n0 = 58.0\nn1 = 2.0\nn2 = 98.0\nn3 = 3.0\nt0 = n1 + n3\nt1 = n0 * n3\nt2 = n1 * n2\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "74" + ], + "split": "test" + }, + { + "Input": "in one year , the population , of a village increased by 10 % and in the next year , it decreased by 10 % . if at the end of 2 nd year , the population was 7920 , what was it in the beginning ?", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 2.0\nn3 = 7920.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nt2 = 1.0 - t0\nt3 = n3 / t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "7999.999999999999" + ], + "split": "test" + }, + { + "Input": "if 4 ( p ' s capital ) = 6 ( q ' s capital ) = 10 ( r ' s capital ) , then out of the total profit of rs 3720 , r will receive", + "Output Program": [ + "n0 = 4.0\nn1 = 6.0\nn2 = 10.0\nn3 = 3720.0\nt0 = n0 + 1.0\nt1 = n2 + t0\nt2 = n2 + t1\nt3 = n1 + t2\nt4 = n1 / t3\nanswer = n3 * t4\nprint(answer)" + ], + "Output Answer": [ + "720" + ], + "split": "test" + }, + { + "Input": "the batting average of a particular batsman is 60 runs in 46 innings . if the difference in his highest and lowest score is 160 runs and his average excluding these two innings is 58 runs , find his highest score .", + "Output Program": [ + "n0 = 60.0\nn1 = 46.0\nn2 = 160.0\nn3 = 58.0\nt0 = n0 * n1\nt1 = n1 - 2.0\nt2 = n3 * t1\nt3 = t0 - t2\nt4 = n2 + t3\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "184" + ], + "split": "test" + }, + { + "Input": "the total age of a and b is 14 years more than the total age of b and c . c is how many year younger than a", + "Output Program": [ + "n0 = 14.0\n\nanswer = n0 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "test" + }, + { + "Input": "if n is a positive integer and n ^ 2 is divisible by 200 , then what is the largest positive integer that must divide n ?", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 200.0\nt0 = n1 / n0\nt1 = math.sqrt(max(0, t0))\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "test" + }, + { + "Input": "find the smallest number of 6 digits exactly divisible by 25 , 3545 and 15 .", + "Output Program": [ + "n0 = 6.0\nn1 = 25.0\nn2 = 3545.0\nn3 = 15.0\nt0 = 100.0**min(2.0, 5)\nanswer = t0 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "100000" + ], + "split": "test" + }, + { + "Input": "in a certain apartment building , there are one - bedroom and two - bedroom apartments . the rental prices of the apartment depend on a number of factors , but on average , two - bedroom apartments have higher rental prices than do one - bedroom apartments . let m be the average rental price for all apartments in the building . if m is $ 700 higher than the average rental price for all one - bedroom apartments , and if the average rental price for all two - bedroom apartments is $ 2100 higher that m , then what percentage of apartments in the building are two - bedroom apartments ?", + "Output Program": [ + "n0 = 700.0\nn1 = 2100.0\nt0 = n0 * 100.0\nt1 = 1000.0 * 2.0\nt2 = t1 + 100.0\nt3 = n0 + t2\nanswer = t0 / t3\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "test" + }, + { + "Input": "a batsman makes a score of 76 runs in the 17 th inning and thus increases his average by 3 . find his average after 17 th inning .", + "Output Program": [ + "n0 = 76.0\nn1 = 17.0\nn2 = 3.0\nn3 = 17.0\nt0 = n1 * n2\nt1 = n0 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "test" + }, + { + "Input": "find the remainder of the division ( 2 ^ 14 ) / 7 .", + "Output Program": [ + "n0 = 2.0\nn1 = 14.0\nn2 = 7.0\nt0 = n0**min(n1, 5)\nanswer = t0 % n2\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "test" + }, + { + "Input": "barbata invests $ 2600 in the national bank at 5 % . how much additional money must she invest at 8 % so that the total annual income will be equal to 6 % of her entire investment ?", + "Output Program": [ + "n0 = 2600.0\nn1 = 5.0\nn2 = 8.0\nn3 = 6.0\nt0 = n3 / 100.0\nt1 = n1 / 100.0\nt2 = n2 / 100.0\nt3 = n0 * t0\nt4 = n0 * t1\nt5 = t2 - t0\nt6 = t3 - t4\nanswer = t6 / t5\nprint(answer)" + ], + "Output Answer": [ + "1299.9999999999998" + ], + "split": "test" + }, + { + "Input": "at a restaurant , glasses are stored in two different - sized boxes . one box contains 12 glasses , and the other contains 16 glasses . if the average number of glasses per box is 15 , and there are 16 more of the larger boxes , what is the total number of glasses w at the restaurant ? ( assume that all boxes are filled to capacity . )", + "Output Program": [ + "n0 = 12.0\nn1 = 16.0\nn2 = 15.0\nn3 = 16.0\nt0 = n1 * 2.0\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "480" + ], + "split": "test" + }, + { + "Input": "if x is equal to the sum of the integers from 40 to 50 , inclusive , and y is the number of even integers from 40 to 50 , inclusive , what is the value of x + y ?", + "Output Program": [ + "n0 = 40.0\nn1 = 50.0\nn2 = 40.0\nn3 = 50.0\nt0 = n0 + n1\nt1 = n1 - n0\nt2 = t1 + 1.0\nt3 = t1 / 2.0\nt4 = t0 / 2.0\nt5 = t3 + 1.0\nt6 = t2 * t4\nanswer = t5 + t6\nprint(answer)" + ], + "Output Answer": [ + "501" + ], + "split": "test" + }, + { + "Input": "mother , her daughter and her grand child weighs 140 kg . daughter and her daughter ( child ) weighs 60 kg . child is 1 / 5 th of her grand mother . what is the age of the daughter ?", + "Output Program": [ + "n0 = 140.0\nn1 = 60.0\nn2 = 1.0\nn3 = 5.0\nt0 = n0 - n1\nt1 = t0 / n3\nanswer = n1 - t1\nprint(answer)" + ], + "Output Answer": [ + "44" + ], + "split": "test" + }, + { + "Input": "a mixture of sand and cement contains , 3 parts of sand and 5 parts of cement . how much of the mixture must be substituted with sand to make the mixture half sand and half cement ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nt0 = n0 + n1\nt1 = n0 / n1\nt2 = t1 + 1.0\nanswer = t2 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.2" + ], + "split": "test" + }, + { + "Input": "a mixture contains milk and water in the ratio 5 : 2 . on adding 10 liters of water , the ratio of milk to water becomes 5 : 3 . the quantity of milk in the original mixture is ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 10.0\nn3 = 5.0\nn4 = 3.0\nt0 = n4 + n1\nt1 = n3 / n4\nt2 = n0 / t0\nt3 = n1 / t0\nt4 = n2 * t1\nt5 = t3 * t1\nt6 = t2 - t5\nanswer = t4 / t6\nprint(answer)" + ], + "Output Answer": [ + "50.000000000000014" + ], + "split": "test" + }, + { + "Input": "students of 3 different classes appeared in common examination . pass average of 10 students of first class was 45 % , pass average of 15 students of second class was 60 % and pass average of 25 students of third class was 80 % then what will be the pass average of all students of 3 classes ?", + "Output Program": [ + "n0 = 3.0\nn1 = 10.0\nn2 = 45.0\nn3 = 15.0\nn4 = 60.0\nn5 = 25.0\nn6 = 80.0\nn7 = 3.0\nt0 = n1 + n3\nt1 = n1 * n2\nt2 = n3 * n4\nt3 = n5 * n6\nt4 = n5 + t0\nt5 = t1 / 100.0\nt6 = t2 / 100.0\nt7 = t3 / 100.0\nt8 = t5 + t6\nt9 = t8 + t7\nt10 = t9 * 100.0\nanswer = t10 / t4\nprint(answer)" + ], + "Output Answer": [ + "67" + ], + "split": "test" + }, + { + "Input": "34.94 + 240.016 + 23.98 = ?", + "Output Program": [ + "n0 = 34.94\nn1 = 240.016\nn2 = 23.98\nt0 = n0 + n1\nanswer = n2 + t0\nprint(answer)" + ], + "Output Answer": [ + "298.93600000000004" + ], + "split": "test" + }, + { + "Input": "meera purchased two 3 items from a shop . total price for 3 items is rs . 2000 / - she have given rs . 3000 / - what is the balance amount meera got ?", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 2000.0\nn3 = 3000.0\n\nanswer = n3 - n2\nprint(answer)" + ], + "Output Answer": [ + "1000" + ], + "split": "test" + }, + { + "Input": "what is the smallest integer e greater than 1 that leaves a remainder of 1 when divided by any of the integers 6 , 8 , and 10 ?", + "Output Program": [ + "import scipy\nn0 = 1.0\nn1 = 1.0\nn2 = 6.0\nn3 = 8.0\nn4 = 10.0\nt0 = scipy.lcm(int(n2), int(n3))\nt1 = scipy.lcm(int(n4), int(t0))\nanswer = t1 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "121" + ], + "split": "test" + }, + { + "Input": "if ( a - b - c + d = 18 ) and ( a + b - c - d = 4 ) , what is the value of ( b - d ) ^ 2 ?", + "Output Program": [ + "n0 = 18.0\nn1 = 4.0\nn2 = 2.0\nt0 = n0 + n1\nt1 = t0 / n2\nt2 = n1 - t1\nanswer = t2**min(n2, 5)\nprint(answer)" + ], + "Output Answer": [ + "49" + ], + "split": "test" + }, + { + "Input": "john purchased some shirts and trousers for $ 800 . he paid $ 400 less for the shirts than he did for the trousers . if he bought 5 shirts and the cost of a shirt is $ 20 less than that of a trouser , how many trousers did he buy ?", + "Output Program": [ + "n0 = 800.0\nn1 = 400.0\nn2 = 5.0\nn3 = 20.0\nt0 = n3 + n3\nt1 = n3 + t0\nt2 = n2 * t0\nt3 = n0 - t2\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "test" + }, + { + "Input": "the average age of a class of 24 students is 23 years . the average increased by 1 when the teacher ' s age also included . what is the age of the teacher ?", + "Output Program": [ + "n0 = 24.0\nn1 = 23.0\nn2 = 1.0\nt0 = n0 + n2\nt1 = n1 + n2\nt2 = n0 * n1\nt3 = t0 * t1\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "test" + }, + { + "Input": "on dividing 21 by a number , the quotient is 10 and the remainder is 1 . find the divisor .", + "Output Program": [ + "import math\nn0 = 21.0\nn1 = 10.0\nn2 = 1.0\nt0 = n0 / n1\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "test" + }, + { + "Input": "the original price of a suit is $ 200 . the price increased 20 % , and after this increase , the store published a 20 % off coupon for a one - day sale . given that the consumers who used the coupon on sale day were getting 20 % off the increased price , how much did these consumers pay for the suit ?", + "Output Program": [ + "n0 = 200.0\nn1 = 20.0\nn2 = 20.0\nn3 = 20.0\nt0 = n0 * n1\nt1 = t0 / 100.0\nt2 = n0 + t1\nt3 = n1 * t2\nt4 = t3 / 100.0\nanswer = t2 - t4\nprint(answer)" + ], + "Output Answer": [ + "192" + ], + "split": "test" + }, + { + "Input": "in a basketball game , dhoni scored 30 points more than dravid , but only half as many points as shewag . if the 3 players scored a combined total of 150 points , how many points did dhoni score ?", + "Output Program": [ + "n0 = 30.0\nn1 = 3.0\nn2 = 150.0\nt0 = n0 + n2\nt1 = 1.0 + 2.0\nt2 = t1 + 1.0\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "test" + }, + { + "Input": "on a partly cloudy day , milton decides to walk back from work . when it is sunny , he walks at a speed of s miles / hr ( s is an integer ) and when it gets cloudy , he increases his speed to ( s + 1 ) miles / hr . if his average speed for the entire distance is 2.8 miles / hr , what fraction of the total distance did he cover while the sun was shining on him ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.8\nt0 = n1 + n1\nt1 = n1 + t0\nt2 = t1 + t0\nt3 = t2 / 2.0\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "0.14285714285714288" + ], + "split": "test" + }, + { + "Input": "a number when divided by a certain divisor left remainder 245 , when twice the number was divided by the same divisor , the remainder was 112 . find the divisor ?", + "Output Program": [ + "n0 = 245.0\nn1 = 112.0\nt0 = n0 * 2.0\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "378" + ], + "split": "test" + }, + { + "Input": "85 white and black tiles will be used to form a 10 x 10 square pattern . if there must be at least one black tile in every row and at least one white tile in every column , what is the maximum difference between the number of black and white tiles that can be used ?", + "Output Program": [ + "n0 = 85.0\nn1 = 10.0\nn2 = 10.0\n\nanswer = n0 - n1\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "test" + }, + { + "Input": "a certain list consists of 21 different numbers . if n is in the list and n is 4 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction t of the sum of the 21 numbers in the list ?", + "Output Program": [ + "n0 = 21.0\nn1 = 4.0\nn2 = 20.0\nn3 = 21.0\nt0 = n2 / n1\nt1 = 1.0 * 1.0\nt2 = n0 + t0\nt3 = t2 / n1\nt4 = t3 * 2.0\nt5 = t4 - n1\nt6 = t5 - 3.0\nanswer = t1 / t6\nprint(answer)" + ], + "Output Answer": [ + "0.16666666666666666" + ], + "split": "test" + }, + { + "Input": "find the least number of complete years in which a sum of money put out at 45 % compound interest will be more than double of itself ?", + "Output Program": [ + "import math\nn0 = 45.0\nt0 = n0 / 100.0\nt1 = math.log(max(1e-5, 2.0), 2)\nt2 = t0 + 1.0\nt3 = math.log(max(1e-5, t2), 2)\nt4 = t1 / t3\nt5 = t4 + 1.0\nanswer = math.floor(t5)\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "test" + }, + { + "Input": "the avg weight of a , b & c is 55 kg . if d joins the group , the avg weight of the group becomes 60 kg . if another man e who weights is 3 kg more than d replaces a , then the avgof b , c , d & e becomes 58 kg . what is the weight of a ?", + "Output Program": [ + "n0 = 55.0\nn1 = 60.0\nn2 = 3.0\nn3 = 58.0\nt0 = n1 * 4.0\nt1 = n3 * 4.0\nt2 = n0 * n2\nt3 = t0 - t2\nt4 = n2 + t3\nt5 = t1 - t4\nanswer = t0 - t5\nprint(answer)" + ], + "Output Answer": [ + "86" + ], + "split": "test" + }, + { + "Input": "a certain drink of type a is prepared by mixing 4 parts milk with 3 parts fruit juice . another drink of type b is prepared by mixing 4 parts of fruit juice and 3 parts of milk . how many liters of fruit juice must be added to 105 liters of drink a to convert it to drink b ?", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 4.0\nn3 = 3.0\nn4 = 105.0\nt0 = n0 + n1\nt1 = n0 / t0\nt2 = n1 / t0\nt3 = n4 * t1\nt4 = n4 * t2\nt5 = n0 * t3\nt6 = t5 / n1\nanswer = t6 - t4\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "test" + }, + { + "Input": "the product of x and y is a constant . if the value of x is increased by 40 % , by what percentage must the value of y be decreased ?", + "Output Program": [ + "n0 = 40.0\nt0 = n0 + 100.0\nt1 = 100.0 / t0\nt2 = 1.0 - t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "28.57142857142857" + ], + "split": "test" + }, + { + "Input": "if a and b are the roots of the equation x 2 - 6 x + 6 = 0 , then the value of a 2 + b 2 is :", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 6.0\nn2 = 6.0\nn3 = 0.0\nn4 = 2.0\nn5 = 2.0\nt0 = n1 * 4.0\nt1 = n1**min(n0, 5)\nt2 = t1 - t0\nt3 = math.sqrt(max(0, t2))\nt4 = n1 + t3\nt5 = n1 - t3\nt6 = t5 / n0\nt7 = t4 / n0\nt8 = t6**min(n0, 5)\nt9 = t7**min(n0, 5)\nanswer = t8 + t9\nprint(answer)" + ], + "Output Answer": [ + "23.999999999999993" + ], + "split": "test" + }, + { + "Input": "6 persons in an organization including x and y were to be divided in two groups of 3 members each . the total number of groups containing both x and y is what fraction of the total number of groups which can be formed ?", + "Output Program": [ + "import math\nn0 = 6.0\nn1 = 3.0\nt0 = math.factorial(min(15, int(n1)))\nt1 = n0 - 1.0\nt2 = t1 * 4.0\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.3" + ], + "split": "test" + }, + { + "Input": "having scored 94 runs in the 19 th inning , a cricketer increases his average score by 4 . what will be his average score after 19 innings ?", + "Output Program": [ + "n0 = 94.0\nn1 = 19.0\nn2 = 4.0\nn3 = 19.0\nt0 = n1 * n2\nt1 = n0 - t0\nanswer = n2 + t1\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "test" + }, + { + "Input": "mike took a taxi to the airport and paid $ 2.50 to start plus $ 0.25 per mile . annie took a different route to the airport and paid $ 2.50 plus $ 5.00 in bridge toll fees plus $ 0.25 per mile . if each was charged exactly the same amount , and annie ' s ride was 18 miles , how many miles was mike ' s ride ?", + "Output Program": [ + "n0 = 2.5\nn1 = 0.25\nn2 = 2.5\nn3 = 5.0\nn4 = 0.25\nn5 = 18.0\nt0 = n0 + n3\nt1 = n1 * n5\nt2 = t0 + t1\nt3 = t2 - n0\nanswer = t3 / n1\nprint(answer)" + ], + "Output Answer": [ + "38" + ], + "split": "test" + }, + { + "Input": "in a box of 11 pens , a total of 3 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?", + "Output Program": [ + "n0 = 11.0\nn1 = 3.0\nn2 = 2.0\nt0 = n0 - n1\nt1 = n0 - 1.0\nt2 = t0 / n0\nt3 = t0 - 1.0\nt4 = t3 / t1\nanswer = t2 * t4\nprint(answer)" + ], + "Output Answer": [ + "0.509090909090909" + ], + "split": "test" + }, + { + "Input": "a father said his son , ` ` i was as old as you are at present at the time of your birth . ` ` if the father age is 40 now , the son age 5 years back was", + "Output Program": [ + "n0 = 40.0\nn1 = 5.0\nt0 = n0 / 2.0\nanswer = t0 - n1\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "test" + }, + { + "Input": "mark bought a set of 6 flower pots of different sizes at a total cost of $ 8.00 . each pot cost 0.25 more than the next one below it in size . what was the cost , in dollars , of the largest pot ?", + "Output Program": [ + "n0 = 6.0\nn1 = 8.0\nn2 = 0.25\nt0 = n0 - 1.0\nt1 = n0 * t0\nt2 = n2 * t0\nt3 = t1 / 2.0\nt4 = n2 * t3\nt5 = n1 - t4\nt6 = t5 / n0\nanswer = t6 + t2\nprint(answer)" + ], + "Output Answer": [ + "1.9583333333333335" + ], + "split": "test" + }, + { + "Input": "32.32 / 2000 is equal to :", + "Output Program": [ + "n0 = 32.32\nn1 = 2000.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.01616" + ], + "split": "test" + }, + { + "Input": "george went to a fruit market with certain amount of money . with this money he can buy either 50 oranges or 40 mangoes . he retains 5 % of the money for taxi fare and buys 25 mangoes . how many oranges can he buy ?", + "Output Program": [ + "n0 = 50.0\nn1 = 40.0\nn2 = 5.0\nn3 = 25.0\nt0 = n2 / 100.0\nt1 = n3 / n0\nt2 = 1.0 - t0\nt3 = t2 - t1\nanswer = n0 * t3\nprint(answer)" + ], + "Output Answer": [ + "22.499999999999996" + ], + "split": "test" + }, + { + "Input": "in an examination , there were 2,000 candidates , out of which 900 candidates were girls and rest were boys . if 36 % of the boys and 32 % of the girls passed , then the total percentage of failed candidates is ?", + "Output Program": [ + "n0 = 2000.0\nn1 = 900.0\nn2 = 36.0\nn3 = 32.0\nt0 = n2 / 100.0\nt1 = n3 / 100.0\nt2 = 10.0 * 100.0\nt3 = t2 * 2.0\nt4 = n1 * t1\nt5 = t3 - n1\nt6 = t0 * t5\nt7 = t3 - t6\nt8 = t7 - t4\nt9 = t8 / t3\nanswer = t9 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "65.8" + ], + "split": "test" + }, + { + "Input": "anne earned $ 3 an hour baby - sitting , and $ 4 an hour working in the garden . last week she did baby - sitting for 5 hours and garden work for 3 hours . how much more money does she need to buy a game that costs $ 35 ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 5.0\nn3 = 3.0\nn4 = 35.0\nt0 = n0 * n2\nt1 = n0 * n1\nt2 = t0 + t1\nanswer = n4 - t2\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "test" + }, + { + "Input": "if the average ( arithmetic mean ) of a and b is 45 and the average of b and c is 80 , what is the value of c \u00e2 \u02c6 \u2019 a ?", + "Output Program": [ + "n0 = 45.0\nn1 = 80.0\nt0 = n1 * 2.0\nt1 = n0 * 2.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "test" + }, + { + "Input": "a envelop weight 8.2 gm , if 800 of these envelop are sent with an advertisement mail . how much wieght ?", + "Output Program": [ + "n0 = 8.2\nn1 = 800.0\nt0 = n0 * n1\nanswer = t0 / 1000.0\nprint(answer)" + ], + "Output Answer": [ + "6.559999999999999" + ], + "split": "test" + }, + { + "Input": "two employees x and y are paid a total of rs . 750 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?", + "Output Program": [ + "n0 = 750.0\nn1 = 120.0\nt0 = 1.0 + 4.0\nt1 = t0 * 2.0\nt2 = t1 + 1.0\nt3 = n0 * t1\nt4 = t2 * 2.0\nanswer = t3 / t4\nprint(answer)" + ], + "Output Answer": [ + "340.90909090909093" + ], + "split": "test" + }, + { + "Input": "if n is a prime number greater than 5 , what is the remainder when n ^ 2 is divided by 12 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 12.0\nt0 = n0 + 2.0\nt1 = n2 * 4.0\nt2 = t0**min(n1, 5)\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "test" + }, + { + "Input": "set j consists of 5 consecutive even numbers . if the smallest term in the set is - 2 , what is the range of the positive integers in set j ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nt0 = -n1\nt1 = n0 - 1.0\nt2 = n1 * t1\nt3 = t2 + t0\nanswer = t3 - n1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "test" + }, + { + "Input": "a student chose a number , multiplied it by 2 , then subtracted 180 from the result and got 104 . what was the number he chose ?", + "Output Program": [ + "n0 = 2.0\nn1 = 180.0\nn2 = 104.0\nt0 = n1 + n2\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "142" + ], + "split": "test" + }, + { + "Input": "in a certain warehouse , 50 percent of the packages weigh less than 75 pounds , and a total of 48 packages weigh less than 25 pounds . if 80 percent of the packages weigh at least 25 pounds , how many of the packages weigh at least 25 pounds but less than 75 pounds ?", + "Output Program": [ + "n0 = 50.0\nn1 = 75.0\nn2 = 48.0\nn3 = 25.0\nn4 = 80.0\nn5 = 25.0\nn6 = 25.0\nn7 = 75.0\nt0 = 100.0 - n4\nt1 = n2 / t0\nt2 = t1 * 100.0\nt3 = n0 * t2\nt4 = t3 / 100.0\nanswer = t4 - n2\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "test" + }, + { + "Input": "how many of the integers between 20 and 80 are even ?", + "Output Program": [ + "n0 = 20.0\nn1 = 80.0\nt0 = n1 - n0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "test" + }, + { + "Input": "if a and b are positive integers , and a = 5 b + 20 , the greatest common divisor of a and b can not be", + "Output Program": [ + "n0 = 5.0\nn1 = 20.0\nt0 = n1 / n0\nanswer = t0 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "test" + }, + { + "Input": "there are 690 male and female participants in a meeting . half the female participants and one - quarter of the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?", + "Output Program": [ + "n0 = 690.0\nt0 = n0 / 3.0\nt1 = t0 * 4.0\nt2 = t1 - n0\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "115" + ], + "split": "test" + }, + { + "Input": "4 shepherds were watching over the flocks and they were commenting on how many sheep they each had . if ram had 3 more sheep than he would have one less than rahul . wheras akar has the same number as the other 3 shepherds put togeher . if john had 3 less sheep he would have exactly trile the number of ram . if they were evenly distributed if they would each have 11 seep how many sheep did ram have ?", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 3.0\nn3 = 3.0\nn4 = 11.0\nt0 = n0 + n1\nt1 = n0 + 1.0\nt2 = n4 * 2.0\nt3 = t2 - t0\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "test" + } + ], + "Metadata": [ + { + "Answer": 269.99999999999994, + "Options": "a ) 229 , b ) 270 , c ) 877 , d ) 266 , e ) 281", + "Correct": "b", + "Explanation": "let xx be the total number of pages in the book , then she finished 23 \u22c5 x 23 \u22c5 x pages . then she has x \u2212 23 \u22c5 x = 13 \u22c5 xx \u2212 23 \u22c5 x = 13 \u22c5 x pages left . 23 \u22c5 x \u2212 13 \u22c5 x = 9023 \u22c5 x \u2212 13 \u22c5 x = 90 13 \u22c5 x = 9013 \u22c5 x = 90 x = 270 x = 270 so the book is 270 pages long . answer : b" + }, + { + "Answer": 80.00000000000003, + "Options": "a ) 60 , b ) 70 , c ) 80 , d ) 90 , e ) 100", + "Correct": "c", + "Explanation": "\"let the number be x . ( 5 / 4 ) * x = ( 4 / 5 ) * x + 36 25 x = 16 x + 720 9 x = 720 x = 80 the answer is c .\"" + }, + { + "Answer": 30.000000000000004, + "Options": "a ) 30 % . , b ) 71 % . , c ) 49 % . , d ) 29 % . , e ) 51 % .", + "Correct": "a", + "Explanation": "\"30 % of 2 litres = 0.6 litres 40 % of 6 litres = 2.4 litres therefore , total quantity of alcohol is 3.0 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 30 % answer : a\"" + }, + { + "Answer": 220, + "Options": "a ) 238 , b ) 277 , c ) 220 , d ) 200 , e ) 288", + "Correct": "c", + "Explanation": "\"explanation : let the number of 20 paise coins be x . then the no of 25 paise coins = ( 324 - x ) . 0.20 * ( x ) + 0.25 ( 324 - x ) = 70 = > x = 220 . . answer : c ) 220\"" + }, + { + "Answer": 1.625, + "Options": "a ) $ 1.62 , b ) $ 1.85 , c ) $ 2.00 , d ) $ 2.15 , e ) $ 2.30", + "Correct": "a", + "Explanation": "\"this question can be solved with a handful of different algebra approaches ( as has been shown in the various posts ) . since the question asks for the price of the largest pot , and the answers are prices , we can test the answers . we ' re told that there are 6 pots and that each pot costs 25 cents more than the next . the total price of the pots is $ 8.25 . we ' re asked for the price of the largest ( most expensive ) pot . since the total price is $ 8.25 ( a 10 - cent increment ) and the the difference in sequential prices of the pots is 10 cents , the largest pot probably has a price that is a 10 - cent increment . from the answer choices , i would then test answer a first if . . . . the largest pot = $ 1.625 1.125 1.225 1.325 1.425 1.525 1.625 total = $ 8.25 so this must be the answer . a\"" + }, + { + "Answer": 43, + "Options": "a ) 10 % , b ) 40 % , c ) 43 % , d ) 64 % , e ) 140 %", + "Correct": "c", + "Explanation": "let the sped be 100 an increase of 30 % the speed now is 130 a further increase of 10 % on 130 = 13 total increase = 43 on 100 = 43 % c" + }, + { + "Answer": 32, + "Options": "a ) 30 , b ) 31 , c ) 32 , d ) 35 , e ) 37", + "Correct": "c", + "Explanation": "answer the required greatest number is the hcf of 263 - 7 , 935 - 7 , 1383 - 7 i . e . 256 , 928 and 1376 hcf = 32 correct option : c" + }, + { + "Answer": 22, + "Options": "a ) 18 , b ) 22 , c ) 20 , d ) 30 , e ) 28", + "Correct": "b", + "Explanation": "\"solution average = ( ( 8 + 12 + 16 + 20 + 24 + 28 + 32 + 36 ) / 8 ) = 186 / 7 = 22 answer b\"" + }, + { + "Answer": 28, + "Options": "a ) 22 , b ) 24 , c ) 26 , d ) 20 , e ) 28", + "Correct": "e", + "Explanation": "\"explanation : let number of hens = h and number of cows = c number of heads = 50 = > h + c = 48 - - - ( equation 1 ) number of feet = 144 = > 2 h + 4 c = 144 = > h + 2 c = 72 - - - ( equation 2 ) ( equation 2 ) - ( equation 1 ) gives 2 c - c = 72 - 50 = > c = 22 substituting the value of c in equation 1 , we get h + 22 = 50 = > h = 50 - 22 = 28 i . e . , number of hens = 28 answer : e\"" + }, + { + "Answer": 2, + "Options": "a ) 3 / 7 , b ) 34 , c ) 1 , d ) 2 , e ) 3", + "Correct": "d", + "Explanation": "answer given exp . = 11 / 7 + { ( 2 q - p ) / ( 2 q + p ) } dividing numerator as well as denominator by q , exp = 11 / 7 + { 2 - p / q ) / ( 2 + p / q ) } = 11 / 7 + { ( 2 - 4 / 5 ) / ( 2 + 4 / 5 ) } = 11 / 7 + 6 / 14 = 11 / 7 + 3 / 7 = 14 / 7 = 2 correct option : d" + }, + { + "Answer": 40, + "Options": "a ) 32 , b ) 36 , c ) 40 , d ) 44 , e ) 48", + "Correct": "c", + "Explanation": "14 liters is 35 % of the capacity c . 14 = 0.35 c c = 14 / 0.35 = 40 liters . the answer is c ." + }, + { + "Answer": 375, + "Options": "a ) $ 200 , b ) $ 375 , c ) $ 400 , d ) $ 500 , e ) $ 600", + "Correct": "b", + "Explanation": "c for cost . p price per person . c = 3 * p c = 5 * p - 250 substituting the value of p from the first equation onto the second we get p = 125 . plugging in the value of p in the first equation , we get c = 375 . which leads us to answer choice b" + }, + { + "Answer": 35, + "Options": "a ) 35 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 80 %", + "Correct": "a", + "Explanation": "\"can be reduced to y / 20 + 3 y / 10 = 7 y / 20 = 35 % a\"" + }, + { + "Answer": 17, + "Options": "a ) 2 , b ) 5 , c ) 11 , d ) 17 , e ) 23", + "Correct": "d", + "Explanation": "\"f ( 36 ) = 2 * 4 * 6 * 8 * 10 * 12 * 14 * 16 * 18 * 20 * 22 * 24 * 26 * 28 * 30 * 32 * 34 * 36 the greatest prime factor in this list is 17 . the answer is d .\"" + }, + { + "Answer": 71, + "Options": "a ) 9 , b ) 71 , c ) 85 , d ) 92 , e ) 90", + "Correct": "b", + "Explanation": "\"age of the 15 th student = 19 * 15 - ( 14 * 5 + 16 * 9 ) = 285 - 214 = 71 years answer is b\"" + }, + { + "Answer": 1.5811388300841898, + "Options": "a ) 1.3 , b ) 1.58 , c ) 2.03 , d ) 2.15 , e ) 3.15", + "Correct": "b", + "Explanation": "explanation : \u221a ( 5 / 2 ) = \u221a ( 5 \u00d7 2 / 2 \u00d7 2 ) = \u221a ( 10 ) / 2 = 3.16 / 2 = 1.58 answer : b" + }, + { + "Answer": 115, + "Options": "a ) $ 115.8 , b ) $ 248.75 , c ) $ 200 , d ) $ 171.6 , e ) $ 190", + "Correct": "a", + "Explanation": "$ 9.65 * 12 = $ 115.8 . answer is a ." + }, + { + "Answer": 375, + "Options": "a ) 375 , b ) 475 , c ) 500 , d ) 670 , e ) 700", + "Correct": "a", + "Explanation": "\"required number = ( 75 / 2 ) / ( 1 / 10 ) = ( 75 / 2 x 10 / 1 ) = 375 . answer : a\"" + }, + { + "Answer": 0.3571428571428571, + "Options": "a ) 2 / 10 , b ) 3 / 11 , c ) 4 / 13 , d ) 5 / 14 , e ) 6 / 17", + "Correct": "d", + "Explanation": "\"p ( neither pen is defective ) = 5 / 8 * 4 / 7 = 5 / 14 the answer is d .\"" + }, + { + "Answer": 3.9956356288922485, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "c", + "Explanation": "\"0.0010101 * 10 ^ k > 10 we need to move the decimal point to the right 4 places to get 10.101 this is equivalent to multiplying by 10 ^ 4 . the answer is c .\"" + }, + { + "Answer": 81, + "Options": "a ) 3 , b ) 9 , c ) 81 , d ) 27 , e ) 243", + "Correct": "c", + "Explanation": "3 ^ ab = 3 ^ 3 therefore ab = 3 either a = 1 or 3 or b = 3 or 1 therefore 3 ^ a * 3 ^ b = 3 ^ ( a + b ) = 3 ^ 4 = 81 c" + }, + { + "Answer": 56, + "Options": "a ) a ) 56 , b ) b ) 35 , c ) c ) 39 , d ) d ) 40 , e ) e ) 45", + "Correct": "a", + "Explanation": "\"x \u2013 3 / 8 x = 35 x = 56 answer : a\"" + }, + { + "Answer": 0.9, + "Options": "a ) 1.12 , b ) 1.16 , c ) 1.2 , d ) 0.9 , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : ( x * 5 ) = ( 0.75 * 6 ) x = 4.5 / 5 = 0.9 answer : d\"" + }, + { + "Answer": 32550, + "Options": "a ) 24,550 , b ) 28,550 , c ) 32,550 , d ) 36,550 , e ) 40,550", + "Correct": "c", + "Explanation": "\"2 + 4 + 6 + 8 + . . . + 100 = 2550 602 + 604 + . . . + 700 = 50 ( 600 ) + ( 2 + 4 + . . . + 100 ) = 30,000 + 2550 = 32,550 the answer is c .\"" + }, + { + "Answer": 35, + "Options": "a ) 31 , b ) 35 , c ) 88 , d ) 13 , e ) 12", + "Correct": "b", + "Explanation": "\"total score of the batsman in 10 matches = 400 . total score of the batsman in the next 10 matches = 300 . total score of the batsman in the 20 matches = 700 . average score of the batsman = 700 / 20 = 35 . answer : b\"" + }, + { + "Answer": 290, + "Options": "a ) 400 , b ) 360 , c ) 300 , d ) 290 , e ) 200", + "Correct": "d", + "Explanation": "answer is d . total giraffes = 300 = 3 * other animals ( x ) or x = 10 . so , difference in giraffes and x = 300 - 10 = 290 ." + }, + { + "Answer": 0.4375, + "Options": "a ) 3 / 8 , b ) 7 / 16 , c ) 1 / 2 , d ) 5 / 8 , e ) 7 / 8", + "Correct": "b", + "Explanation": "let capapcity of a = x sand = x / 4 capacity of b = x / 2 sand = 3 x / 16 a total = x / 4 + 3 x / 16 = 7 x / 16 answer : b" + }, + { + "Answer": 4, + "Options": "a ) 4 , b ) 0 , c ) 1 , d ) 2 , e ) 24", + "Correct": "a", + "Explanation": "since f ( n ) = f ( n - 1 ) - n then : f ( 6 ) = f ( 5 ) - 6 and f ( 5 ) = f ( 4 ) - 5 . as given that f ( 4 ) = 15 then f ( 5 ) = 15 - 5 = 10 - - > substitute the value of f ( 5 ) back into the first equation : f ( 6 ) = f ( 5 ) - 6 = 10 - 6 = 4 . answer : a . questions on funtions to practice :" + }, + { + "Answer": 48, + "Options": "a ) 53 , b ) 52 , c ) 51 , d ) 50 , e ) 48", + "Correct": "e", + "Explanation": "\"125 - 78 + 1 = 48 ' e ' is the answer\"" + }, + { + "Answer": 0.375, + "Options": "a ) 5 / 8 , b ) 3 / 4 , c ) 3 / 8 , d ) 7 / 4 , e ) 5 / 6", + "Correct": "c", + "Explanation": "\"at least twice , but not more than 3 timesmeans exactly 2 times , 3 times the probability of getting exactly k results out of n flips is nck / 2 ^ n 3 c 2 / 2 ^ 3 = 3 / 8 option : c\"" + }, + { + "Answer": 0.19999999999999996, + "Options": "a ) 1 / 5 , b ) 1 / 4 , c ) 7 / 20 , d ) 3 / 5 , e ) it can not be determined from the given information .", + "Correct": "a", + "Explanation": "plug in simple numbers . take 100 couples for example . 3 / 5 of 100 couples have more than one child = 60 couples . 2 / 5 of 100 couples have more than 3 kids = 40 couples . this implies that 40 couples are a subset of 60 couples and the complement of 60 couples within those 100 couples , which equals 20 couples have either one or no kids at all . we need to find couples that have 2 or 3 kids , so essentially , it is 60 - 40 = 20 . fraction will be 20 / 100 = 1 / 5 . option a" + }, + { + "Answer": 17, + "Options": "a ) 3 , b ) 6 , c ) 17 , d ) 23 , e ) 24", + "Correct": "c", + "Explanation": "\"2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 18 = > 4 x 2 ^ 2 n = 4 ^ 24 = 2 ^ 36 = > 2 ^ 2 x 2 ^ 2 n = 2 ^ 36 = > 2 ^ ( 2 n + 2 ) = 2 ^ 36 = > 2 n + 2 = 36 = > n = 17 so . answer will be c .\"" + }, + { + "Answer": 65, + "Options": "a ) 45 , b ) 65 , c ) 55 , d ) 75 , e ) 85", + "Correct": "b", + "Explanation": "\"assume total distance = 100 miles time taken for 35 miles = 35 / 35 = 1 hour time taken for the rest of the 65 miles = 65 / v hours . average speed = 50 therefore the total time needed = 2 hours . 2 = 1 + 65 / v hence v = 65 mph answer : b\"" + }, + { + "Answer": 2, + "Options": "a ) 1 / 2 , b ) 2 / 3 , c ) 1 , d ) 3 / 2 , e ) 2", + "Correct": "e", + "Explanation": "x be the weight of a hammer and y be the weight of a wrench . ( 2 x + 2 y ) = 1 / 3 * ( 8 x + 5 y ) 3 ( 2 x + 2 y ) = ( 8 x + 5 y ) 6 x + 6 y = 8 x + 5 y y = 2 x ans - e" + }, + { + "Answer": 42.857142857142854, + "Options": "a ) 42.85 , b ) 44 , c ) 48 , d ) 38 , e ) 40", + "Correct": "a", + "Explanation": "\"1 ) cost of repairing = 10.5 ( for one year ) , therefore for 2 years it would be $ 21 . 2 ) cost of new pair which will last for 2 years is $ 30.00 percentage change formula = ( final value - initial value ) / ( initial value ) * 100 . in this case the final value would be the price of new shoe initial value would be the cost of repairing the old shoe . i . e ( 30 - 21 ) / ( 21 ) * 100 = 42.85 % . ans is a\"" + }, + { + "Answer": 2.4690000000000003, + "Options": "a ) 2.91 , b ) 2.911 , c ) 2.469 , d ) 2.586 , e ) 2.499", + "Correct": "c", + "Explanation": "2.12 + . 004 + . 345 0 = 0 - 2.12 - 0.004 - 0.345 0 = - 2.469 answer : c" + }, + { + "Answer": 99, + "Options": "a ) 90 , b ) 99 , c ) 97 , d ) 95 , e ) 65", + "Correct": "b", + "Explanation": "\"30 * 33 / 2 = 5 / 2 * 2 * x = > x = 99 answer b\"" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9", + "Correct": "a", + "Explanation": "\"let x be the amount of liquid q to be added . ( 2 / 5 ) * 20 + x = ( 3 / 7 ) * ( 20 + x ) 280 + 35 x = 300 + 15 x 20 x = 20 x = 1 the answer is a .\"" + }, + { + "Answer": 68, + "Options": "a ) 70 , b ) 66 , c ) 68 , d ) 69 , e ) 72", + "Correct": "c", + "Explanation": "solution : member in group * age increased = difference of replacement or , 8 * 1 = new comer - man going out or , new comer = 8 + 60 ; or , new comer = 68 years . answer : option c" + }, + { + "Answer": 0.25, + "Options": "a ) 1 / 4 , b ) 1 / 8 , c ) 3 / 8 , d ) 3 / 16 , e ) 5 / 16", + "Correct": "a", + "Explanation": "one case is rainy - rainy - rainy - not rainy . the probability of this case is ( 1 / 2 ) ^ 4 = 1 / 16 the number of possible cases is 4 c 3 = 4 . p ( exactly 3 rainy days ) = 4 * 1 / 16 = 1 / 4 the answer is a ." + }, + { + "Answer": 64800, + "Options": "a ) 81000 , b ) 81028 , c ) 27772 , d ) 29889 , e ) 64800", + "Correct": "e", + "Explanation": "51200 * 9 / 8 * 9 / 8 = 64800 . answer : e" + }, + { + "Answer": 6.6, + "Options": "a ) 6.6 , b ) 6.7 , c ) 6.8 , d ) 6.85 , e ) 6.9", + "Correct": "a", + "Explanation": "\"old set s - total is avg * no of elements = 6.2 * 10 = 62 if one number is increased by 4 then total increased to 62 + 4 = 66 new avg - 66 / 10 = 6.6 . hence answer is a .\"" + }, + { + "Answer": 50, + "Options": "a ) 33 , b ) 11 , c ) 38 , d ) 50 , e ) 12", + "Correct": "d", + "Explanation": "\"assume that the person would have covered x km if travelled at 10 km / hr \u21d2 speed = distancetime = x 10 . . . . . ( equation 1 ) give that the person would have covered ( x + 20 ) km if travelled at 14 km / hr \u21d2 speed = distancetime = ( x + 20 ) 14 . . . . . ( equation 2 ) from equations 1 and 2 , x 10 = ( x + 20 ) 1414 x = 10 x + 2004 x = 200 x = 2004 = 50 answer : d\"" + }, + { + "Answer": 0.29411764705882354, + "Options": "a ) 2 / 11 , b ) 3 / 14 , c ) 5 / 17 , d ) 7 / 20 , e ) 11 / 30", + "Correct": "c", + "Explanation": "\"let x be the fraction of her take - home pay that the worker saved . let p be the monthly pay . 12 xp = 5 ( 1 - x ) p 12 xp = 5 p - 5 xp 17 xp = 5 p x = 5 / 17 the answer is c .\"" + }, + { + "Answer": 300, + "Options": "a ) 164 , b ) 297 , c ) 300 , d ) 345 , e ) 482", + "Correct": "c", + "Explanation": "\"many approaches are possible . for example : consider numbers from 0 to 999 written as follows : 1 . 000 2 . 001 3 . 002 4 . 003 . . . . . . . . . 1000 . 999 we have 1000 numbers . we used 3 digits per number , hence used total of 3 * 1000 = 3000 digits . now , why should any digit have preferences over another ? we used each of 10 digits equal # of times , thus we used each digit ( including 8 ) 3000 / 10 = 300 times . answer : c .\"" + }, + { + "Answer": 15, + "Options": "a ) a ) 12 , b ) b ) 15 , c ) c ) 16 , d ) d ) 17 , e ) e ) 18", + "Correct": "b", + "Explanation": "\"d = ( d - r ) / q = ( 136 - 1 ) / 9 = 135 / 9 = 15 b )\"" + }, + { + "Answer": 18, + "Options": "a ) 8 , b ) 12 , c ) 18 , d ) 14 , e ) 16", + "Correct": "c", + "Explanation": "\"amount of salt = 7.2 assume x gallons of water are added . 7.2 / 72 + x = 8 / 100 720 = 8 x + 576 8 x = 144 x = 18 correct option : c\"" + }, + { + "Answer": 1200, + "Options": "a ) 8981 , b ) 3799 , c ) 1200 , d ) 2693 , e ) 1732", + "Correct": "c", + "Explanation": "\"p - - - 10 - - - - 600 p - - - 5 - - - - - 300 3 p - - - 5 - - - - - 900 - - - - - - = > 1200 answer : c\"" + }, + { + "Answer": 1, + "Options": "a ) 3 , b ) 1 , c ) 6 , d ) 8 , e ) 9", + "Correct": "b", + "Explanation": "\"explanation : on dividing 427751 by 10 we get the remainder 1 , so 1 should be subtracted option b\"" + }, + { + "Answer": 905, + "Options": "a ) rs . 692.80 , b ) rs . 905 , c ) rs . 990 , d ) rs . 1385 , e ) none", + "Correct": "b", + "Explanation": "\"answer income of the deceased = total income of 4 members - total income of remaining 3 members . = 735 x 3 - 650 x 2 rs . = 905 rs . correct option : b\"" + }, + { + "Answer": 0.9677419354838709, + "Options": "a ) 1 / 130 , b ) 1 / 5 , c ) 3 / 13 , d ) 10 / 13 , e ) 30 / 31", + "Correct": "e", + "Explanation": "\"it ' s y / xpercentnot y / x . if x = 20 and y = 10 . then : 20 x = 400 black - and - white films ; 6 y = 60 color films . y / x % = 10 / 20 % = 0.5 % of the black - and - white films , so 2 black - and - white films and all 60 color films , thus total of 62 films were selected . color films thus compose x = 60 / 62 = 30 / 31 of the selected films . answer : e .\"" + }, + { + "Answer": 19, + "Options": "a ) a ) 12 , b ) b ) 6 , c ) c ) 10 , d ) d ) 16 , e ) e ) 19", + "Correct": "e", + "Explanation": "it seems that the accepted answer is wrong , according to wolframalpha . the answer should be 31 , which is n ' t even listed as a selectable answer . e" + }, + { + "Answer": 26, + "Options": "a ) 26 , b ) 29 , c ) 19 , d ) 30 , e ) 40", + "Correct": "a", + "Explanation": "\"at 6 ' o clock , there would be 6 strikes . first strike , then a short interval , the second strike , then a short interval and so on till the 6 th strike . so there would be in all 5 intervals between 6 strikes . similarly , between 7 strikes , there would be 6 intervals . according to the question , the time spent in the strike and the interval is same . at 6 ' o clock , the 6 strikes and the 5 intervals together take 22 sec so each strike and each interval takes 2 secs . at 7 ' o clock , the 7 strikes and 6 intervals will take 2 * ( 7 + 6 ) = 26 secs a\"" + }, + { + "Answer": 2007, + "Options": "a ) 2007 , b ) 2008 , c ) 2009 , d ) 2010 , e ) 2011", + "Correct": "a", + "Explanation": "\"the cost of commodity x increases by 10 cents per year relative to commodity y . the price of x must gain 20 + 40 = 60 cents on commodity y , which will take 6 years . the answer is a .\"" + }, + { + "Answer": 25, + "Options": "a ) 25.5 , b ) 2.5 , c ) 25 , d ) . 25 , e ) none of these", + "Correct": "c", + "Explanation": "\"explanation : 1 / 0.04 = ( 1 * 100 ) / 4 = 100 / 4 = 25 option c\"" + }, + { + "Answer": 0.625, + "Options": "a ) 1 / 4 , b ) 3 / 8 , c ) 1 / 2 , d ) 29 / 46 , e ) 3 / 4", + "Correct": "d", + "Explanation": "\"n ( n + 1 ) ( n + 2 ) will be divisible by 8 when n is a multiple of 2 or when ( n + 1 ) is a multiple of 8 . thus when n is even , this whole expression will be divisible by 8 . from 1 to 96 , there are 46 even integers . now when ( n + 1 ) is multiple by 8 , we have 12 such values for ( n + 1 ) probability that n ( n + 1 ) ( n + 2 ) will be divisible by 8 = ( 46 + 12 ) / 92 = 58 / 96 = 29 / 46 ans is d\"" + }, + { + "Answer": 250, + "Options": "a ) a ) 250 , b ) b ) 249 , c ) c ) 248 , d ) d ) 247 , e ) e ) 246", + "Correct": "a", + "Explanation": "\"a + b + c = 300 a + c = 200 b + c = 350 - - - - - - - - - - - - - - a + b + 2 c = 550 a + b + c = 300 - - - - - - - - - - - - - - - - c = 250 answer : a\"" + }, + { + "Answer": 100.00000000000003, + "Options": "a ) 200 minutes , b ) 100 minutes , c ) 120 minutes , d ) 140 minutes , e ) 160 minutes", + "Correct": "b", + "Explanation": "\"lets take number of minutesx . given that , 7 + 0.25 x = 12 + 0.2 x - > 0.05 x = 2 - > x = 100 minutes ans b\"" + }, + { + "Answer": 24, + "Options": "a ) 6 , b ) 12 , c ) 14 , d ) 24 , e ) 28", + "Correct": "d", + "Explanation": "\"equate the fat : 0.1 x + 0.5 * 8 = 0.2 ( x + 8 ) - - > x = 24 . answer : d .\"" + }, + { + "Answer": 11, + "Options": "a ) 11 , b ) 10 , c ) 12 , d ) 14 , e ) 16", + "Correct": "a", + "Explanation": "\"let ' s say age of richard is ` ` r ' ' age of david is ` ` d ' ' age of scott is ` ` s ' ' now richard is 6 years older than david , i . e . r = d + 6 david is 8 years older than scott i . e . d = s + 8 if in 8 years , richard will be twice as old as scott i . e . r + 8 = 2 x ( s + 8 ) i . e . r + 8 = 2 s + 16 i . e . r = 2 s + 8 but r = d + 6 = ( s + 8 ) + 6 = s + 14 therefore , 2 s + 8 = s + 14 i . e . s = 6 i . e . r = 20 i . e . d = 14 now , how old was david 3 years ago ? i . e . d - 4 = 14 - 3 = 11 years answer : a\"" + }, + { + "Answer": 50, + "Options": "a ) 50 % , b ) 44.4 % , c ) 22.2 % , d ) 33.3 % , e ) 25 %", + "Correct": "a", + "Explanation": "\"60 % of ( x - y ) = 20 % of ( x + y ) 60 / 100 ( x - y ) = 20 / 100 ( x + y ) 4 x = 8 y required percentage = y / x * 100 = 4 y / 8 y * 100 = 50 % answer is a\"" + }, + { + "Answer": 33.666666666666664, + "Options": "a ) 28 , b ) 31 , c ) 34 , d ) 37 , e ) 40", + "Correct": "c", + "Explanation": "\"the first number is 22 = 16 + 6 ( 1 ) . we can continue adding 6 to make a list : 22 , 28 , 34 , . . . the last number is 220 = 16 + 6 ( 34 ) there are 34 numbers in the list . the answer is c .\"" + }, + { + "Answer": 399.99999999999966, + "Options": "a ) 80 , b ) 110 , c ) 160 , d ) 200 , e ) 400", + "Correct": "e", + "Explanation": "\"we start by creating a variable for the total number of students in the math course . we can say : t = total number of students in the math course next , we can use variable t in an equation that we translate from the given information . we are given that , of the final grades received by the students in a certain math course , 1 / 5 are a ' s , 1 / 4 are b ' s , 1 / 2 are c ' s , and the remaining 20 grades are d ' s . since this represents all the grades in the class , it represents all the students in the class . thus we know : # a \u2019 s + # b \u2019 s + # c \u2019 s + # d \u2019 s = total number of students in the class 1 / 5 ( t ) + \u00bc ( t ) + \u00bd ( t ) + 20 = t we can multiply the entire equation by 20 to cancel out the denominators of the fractions and we have : 4 t + 5 t + 10 t + 400 = 20 t 19 t + 400 = 20 t 400 = t there are a total of 400 students in the math class . answer is e .\"" + }, + { + "Answer": 16, + "Options": "a ) 12 , b ) 13 , c ) 16.6 , d ) 16 , e ) 23", + "Correct": "d", + "Explanation": "the range of a set of data is the difference between the highest and lowest values in the set in this set , highest number = 83 lowest number = 67 range = highest - lowest = 83 - 67 = 16 option d" + }, + { + "Answer": 355, + "Options": "a ) w = 350 , b ) w = 353 , c ) w = 354 , d ) 356 , e ) 357", + "Correct": "b", + "Explanation": "\"focus on the points where the number of digits in squares change : 1 , 2 , 3 - single digit squares . first 2 digit number is 10 . 4 , 5 , . . . 9 - two digit squares . to get 9 , the last number with two digit square , think that first 3 digit number is 100 which is 10 ^ 2 . so 9 ^ 2 must be the last 2 digit square . 10 , 11 , 12 , . . . 31 - three digit squares . to get 31 , think of 1000 - the first 4 digit number . it is not a perfect square but 900 is 30 ^ 2 . 32 ^ 2 = 2 ^ 10 = 1024 , the first 4 digit square . 32 - 99 - four digit squares . to get 99 , think of 10,000 - the first 5 digit number which is 100 ^ 2 . so number of digits in s ( 99 ) = 3 * 1 + 6 * 2 + 22 * 3 + 68 * 4 = 3 + 12 + 66 + 272 = 353 . b\"" + }, + { + "Answer": 10, + "Options": "a ) 16 , b ) 12 , c ) 10 , d ) 20 , e ) 10", + "Correct": "c", + "Explanation": "\"( a + b ) - ( b - c ) = 10 a - c = 10 answer is c\"" + }, + { + "Answer": 96, + "Options": "a ) 12 , b ) 42 , c ) 64 , d ) 96 , e ) 84", + "Correct": "d", + "Explanation": "\"explanation : average after 9 innings = 32 required number of runs = ( 32 * 9 ) \u2013 ( 24 * 8 ) = 288 \u2013 192 = 96 answer d\"" + }, + { + "Answer": 253, + "Options": "a ) 251 , b ) 253 , c ) 255 , d ) 257 , e ) 260", + "Correct": "b", + "Explanation": "\"let the middle digit be x . then , 2 x = 10 or x = 5 . so , the number is either 253 or 352 . since the number increases on reversing the digits , so the hundred ' s digits is smaller than the unit ' s digit . hence , required number = 253 . option b\"" + }, + { + "Answer": 340.8, + "Options": "a ) 0.3408 , b ) 3.408 , c ) 34.08 , d ) 340.8 , e ) none of these", + "Correct": "d", + "Explanation": "solution 1.6 \u00d7 21.3 = ( 16 / 10 x 213 ) = ( 16 x 213 / 10 ) = 3408 / 10 = 340.8 . answer d" + }, + { + "Answer": 7, + "Options": "a ) 5 , b ) 7 , c ) 15 , d ) 12 , e ) 13", + "Correct": "b", + "Explanation": "median is the middle number of a sorted distribution . in case of even number of items , median will be the average of middle two values . the question asks fora new number that will cause the median of new set at 10 . mentionable that given set is already sorted and number of items of new set will be 5 + 1 = 6 . to get median 10 , the sum of 3 th 4 th term should be 20 i . e . 3 + 7 . so to keep the median 10 , the new item should be > = 7 answer is b" + }, + { + "Answer": 7, + "Options": "a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 12", + "Correct": "c", + "Explanation": "\"sol . let the numbers be x . then , x - 4 = 21 / x \u21d4 x 2 - 4 x - 21 = 0 \u21d4 ( x - 7 ) ( x + 3 ) = 0 \u21d4 x = 7 . answer c\"" + }, + { + "Answer": 0.4, + "Options": "a ) 1 / 4 , b ) 1 / 3 , c ) 2 / 5 , d ) 4 / 9 , e ) 1 / 2", + "Correct": "c", + "Explanation": "for the product of 2 numbers to be positive either both of them must be positive or both of them must be negative : p ( positive , positive ) = 2 / 5 * 2 / 4 = 4 / 20 ; p ( negative , negative ) = 2 / 5 * 2 / 4 = 4 / 20 . p = 4 / 20 + 4 / 20 = 8 / 20 = 2 / 5 . answer : c ." + }, + { + "Answer": 2, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 7", + "Correct": "c", + "Explanation": "\"mean = ( x + x + 2 + x + 4 + x + 7 + x + 17 ) / 5 = ( 5 x + 30 ) / 5 = x + 6 median = x + 4 thus mean - median = x + 6 - ( x + 4 ) = 2 answer = c\"" + }, + { + "Answer": 4.545454545454546, + "Options": "a ) 4.54 % , b ) 9.09 % , c ) 10 % , d ) 11 % , e ) 12.25 %", + "Correct": "a", + "Explanation": "no ; the choices will be approximated only when gmat question explicitly mentions that ; here the answer is very close 4.54 , not 5 . jar y has 10 % more marbles than x y = 1.1 x if k marbles are taken out of y . the remaining marbles in jar y = 1.1 x - k if k marbles are added to x . the new marbles ' count in jar x = x + k and we know they are equal ; x + k = 1.1 x - k 2 k = 0.1 x k = 0.05 x the marbles taken out of y = 0.05 x question is : 0.05 x is what percent of marbles that was originally there in y i . e . 1.1 x 0.05 x 1.1 x \u2217 1000.05 x 1.1 x \u2217 100 0.05 x 1.1 x \u2217 1000.05 x 1.1 x \u2217 100 5011 = 4.54 \u00af \u2248 4.545011 = 4.54 \u00af \u2248 4.54 answer : a" + }, + { + "Answer": 62.5, + "Options": "a ) 45 % , b ) 62.5 % , c ) 35 % , d ) 32.5 % , e ) 30 %", + "Correct": "b", + "Explanation": "\"price = p initially price reduced by 25 % which means new price is 3 / 4 p now on this new price further 50 percent is reduced which means the new price is merely 50 percent of 3 / 4 p = = > ( 3 / 4 ) x ( 1 / 2 ) p = 3 / 8 p is the new price after both deduction which is 37.5 percent of the original value p . this implies this entire series of deduction is worth having discounted 62.5 % of p . so answer is b = 62.5 %\"" + }, + { + "Answer": 5, + "Options": "a ) 12 , b ) 7 , c ) 5 , d ) 15 , e ) 6", + "Correct": "c", + "Explanation": "125 / 25 = 5 the answer is c ." + }, + { + "Answer": 1360, + "Options": "a ) 980 , b ) 1150 , c ) 1360 , d ) 1540 , e ) 1720", + "Correct": "c", + "Explanation": "\"the number of ways to choose two teams is 17 c 2 = 17 * 16 / 2 = 136 the total number of games in the season is 10 * 136 = 1360 . the answer is c .\"" + }, + { + "Answer": 180.00000000000003, + "Options": "a ) 165 , b ) 170 , c ) 175 , d ) 180 , e ) 185", + "Correct": "d", + "Explanation": "27 * 200 = 5400 . the other 3 carrots weigh a total of 540 grams . the average weight is 540 / 3 = 180 grams . the answer is d ." + }, + { + "Answer": 675, + "Options": "a ) 540 km , b ) 675 km , c ) 276 km , d ) 178 km , e ) 176 km", + "Correct": "b", + "Explanation": "\"explanation : let us assume that trains meet after ' x ' hours distance = speed * time distance traveled by two trains = 20 x km and 25 x km resp . as one train travels 75 km more than the other , 25 x \u00e2 \u20ac \u201c 20 x = 75 5 x = 75 x = 15 hours as the two trains are moving towards each other , relative speed = 20 + 25 = 45 km / hr therefore , total distance = 45 * 15 = 675 km . answer : b\"" + }, + { + "Answer": 3, + "Options": "a ) x / 2 , b ) x , c ) 3 x / 2 , d ) 2 x , e ) 3 x", + "Correct": "e", + "Explanation": "\"lets do it by picking up numbers . let arthur carry 2 crumbs per trip , this means amy carries 3 crumbs per trip . also let arthur make 2 trips and so amy makes 4 trips . thus total crumbs carried by arthur ( c ) = 2 x 2 = 4 , total crumbs carried by amy = 3 x 4 = 12 . 12 is 3 times 4 , so e\"" + }, + { + "Answer": 58, + "Options": "a ) 55 , b ) 56 , c ) 57 , d ) 58 , e ) 59", + "Correct": "d", + "Explanation": "\"20 x + 47 = 21 ( x \u2013 5 ) x = 58 answer : d\"" + }, + { + "Answer": 3.263999999999214, + "Options": "a ) s . 3.26 , b ) s . 2.08 , c ) s . 2.02 , d ) s . 2.83 , e ) s . 2.42", + "Correct": "a", + "Explanation": "\"c . i . when interest is compounded yearly = [ 8000 * ( 1 + 4 / 100 ) * ( 1 + ( 1 / 2 * 4 ) / 100 ] = 8000 * 26 / 25 * 51 / 50 = rs . 8486.4 c . i . when interest is compounded half - yearly = [ 8000 * ( 1 + 2 / 100 ) 2 ] = ( 8000 * 51 / 50 * 51 / 50 * 51 / 50 ) = rs . 8489.66 difference = ( 8489.66 - 8486.4 = rs . 3.26 . answer : a\"" + }, + { + "Answer": 153.75280898876406, + "Options": "a ) 743 , b ) 154 , c ) 852 , d ) 741 , e ) 785", + "Correct": "b", + "Explanation": "divisor * quotient + remainder = dividend divisor = ( dividend ) - ( remainder ) / quotient ( 13698 - 14 ) / 89 = 154 answer ( b )" + }, + { + "Answer": 14, + "Options": "a ) 14 , b ) 17 , c ) 11 , d ) 19 , e ) 99", + "Correct": "a", + "Explanation": "\"let the son ' s present age be x years . then , ( 38 - x ) = x x = 19 . son ' s age 5 years back = ( 19 - 5 ) = 14 years answer : a\"" + }, + { + "Answer": 1000, + "Options": "a ) 250 , b ) 500 , c ) 750 , d ) 1000 , e ) 1500", + "Correct": "d", + "Explanation": "\"this is best solved using overlapping sets or a venn diagram . we know that a = 2 b , and that 500 people purchased both a and b . further , those purchasing both was double those purchasing b only . this gives us 250 people purchasing b only . with the 500 that pruchased both , we have a total of 750 that purchased b and this is 1 / 2 of those that purchased a . so , 1500 purchased a . less the 500 that purchased both , x = 1000 purchased a only . ( this is much simpler to solve using the venn diagram ) . correct answer is d . 1000\"" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9", + "Correct": "b", + "Explanation": "we have equation 2 n + 5 m = 50 we have factor 2 in first number and we have factor 5 in second number . lcm ( 2 , 5 ) = 10 so we can try some numbers and we should start from 5 because it will be less list than for 2 2 * 5 = 10 and n should be equal 20 4 * 5 = 20 and n should be equal 15 6 * 5 = 30 and n should be equal 10 8 * 5 = 40 and n should be equal 5 10 * 5 = 50 and n should be equal 0 third variant give us the mininal difference n - m = 10 - 6 = 4 and there is some mistake in my way of thinking because we do n ' t have such answer ) if we change the task and will seek for difference between m and n than minimal result e will be 8 - 5 = 3 and answer b" + }, + { + "Answer": 125, + "Options": "a ) 25 , b ) 75 , c ) 125 , d ) 225 , e ) 625", + "Correct": "c", + "Explanation": "there are 5 choices for each of the first three digits . the number of possible palindromes is 5 ^ 3 = 125 . the answer is c ." + }, + { + "Answer": 75, + "Options": "a ) 20 , b ) 25 , c ) 55 , d ) 75 , e ) 80", + "Correct": "d", + "Explanation": "\"the arithmetic mean of 4 equally weighted tests was 90 . so what we can assume is that we have 4 test scores , each 90 . he dropped his lowest score and the avg went to 95 . this means that the lowest score was not 90 and other three scores had given the lowest score 5 each to make it up to 90 too . when the lowest score was removed , the other 3 scores got their 5 back . so the lowest score was 3 * 5 = 15 less than 90 . so the lowest score = 90 - 15 = 75 answer ( d )\"" + }, + { + "Answer": 17, + "Options": "a ) 87 , b ) 12 , c ) 30 , d ) 28 , e ) 17", + "Correct": "e", + "Explanation": "\"10 + 12 + 6 * 2 = 34 / 2 = 17 answer : e\"" + }, + { + "Answer": 596.9499999999998, + "Options": "a ) 407.09 , b ) 479.75 , c ) 523.93 , d ) 596.95 , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : let 3639 + 11.95 \u2013 x = 3054 then , x = ( 3639 + 11.95 ) \u2013 3054 = 3650.95 \u2013 3054 = 596.95 answer : d\"" + }, + { + "Answer": 0.19999999999999996, + "Options": "a ) $ 4 , b ) $ 0.2 , c ) $ 1 , d ) $ 3 , e ) $ 1.65", + "Correct": "b", + "Explanation": "lets assume price of coffee in june = 100 x price of milk powder in june = 100 x price of coffee in july = 400 x ( because of 300 % increase in price ) price of milk powder in july = 20 x ( because of 80 % decrease in price ) price of 1.5 pound of coffee 1.5 pound of milk powder in july will be = 600 x + 30 x = 630 x as per question 630 x = 6.30 $ x = 0.01 s so the price of milk powder in july = 20 x = 20 x 0.01 = 0.2 $ / pound answer b" + }, + { + "Answer": 72, + "Options": "a ) 6 , b ) 36 , c ) 48 , d ) 60 , e ) 72", + "Correct": "e", + "Explanation": "prime factorization of 18 = 2 * 3 ^ 2 prime factorization of 24 = 2 ^ 3 * 3 lcm of the given numbers = 2 ^ 3 * 3 ^ 2 = 72 answer e" + }, + { + "Answer": 18, + "Options": "a ) 15 days , b ) 18 days , c ) 21 days , d ) 24 days , e ) 27 days", + "Correct": "b", + "Explanation": "2 oxen = 3 buffaloes = 4 cows also : 15 buffaloes + 8 oxen + 24 cows = 10 oxen + 8 oxen + 12 oxen = 30 oxen there is enough fodder for 1 oxen for 30 * 48 days . 60 cows + 30 buffaloes = 30 oxen + 20 oxen = 50 oxen the new total is equal to 80 oxen instead of 30 oxen . 30 * 48 / 80 oxen = 18 days the answer is b ." + }, + { + "Answer": 5, + "Options": "a ) 5 % , b ) 7 % , c ) 3 % , d ) 9 % , e ) 15 %", + "Correct": "a", + "Explanation": "a 10 % 100 - [ ( 100 - 65 ) + ( 100 - 95 ) + ( 100 - 75 ) + ( 100 - 70 ) ] = 100 - ( 30 + 25 + 35 + 5 ) = 100 - 95" + }, + { + "Answer": 24, + "Options": "a ) 28 , b ) 27 , c ) 26 , d ) 22 , e ) 24", + "Correct": "e", + "Explanation": "\"explanation : let the average score of the first 18 innings be n 18 n + 96 = 19 ( n + 4 ) = > n = 20 so , average score after 19 th innings = x + 4 = 24 . answer : e\"" + }, + { + "Answer": 6, + "Options": "a ) 4 , b ) 3 , c ) 2 , d ) 0 , e ) 6", + "Correct": "e", + "Explanation": "1019 \u00e3 \u00b7 25 = 40 with remainder = 19 19 + 6 = 25 . hence 6 should be added to 1019 so that the sum will be divisible by 25 answer : option e" + }, + { + "Answer": 121, + "Options": "a ) 121 , b ) 168 , c ) 189 , d ) 190 , e ) 200", + "Correct": "a", + "Explanation": "solution average of 7 people after the last one enters = 151 . \u00e2 \u02c6 \u00b4 required weight = ( 7 x 151 ) - ( 6 x 156 ) = 1057 - 936 = 121 . answer a" + }, + { + "Answer": 30, + "Options": "a ) 30 , b ) 12 , c ) 18 , d ) 22 , e ) 08", + "Correct": "a", + "Explanation": "2 * 15 = 30 . answer is a ." + }, + { + "Answer": 18, + "Options": "a ) 3 , b ) 5 , c ) 18 , d ) 6 , e ) 8", + "Correct": "c", + "Explanation": "x can be written as 62 k + 7 or x = 7 , 69,131 , etc . x + 11 = 62 k + 7 + 11 = 62 k + 18 or x + 11 = 18 , 80,142 etc . when divided by 31 , we will get the remainder 18 . c" + }, + { + "Answer": 16, + "Options": "a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16", + "Correct": "e", + "Explanation": "so the question just means that we have to find all the multiples w of 7 between 1 to 100 so there are 14 multiples of 7 ( 7 - 98 ) but 49 and 98 contain two 7 ' s as factors so we have to add 14 + 2 = 16 e" + }, + { + "Answer": 400, + "Options": "a ) a ) 400 , b ) b ) 450 , c ) c ) 500 , d ) d ) 550 , e ) e ) 600", + "Correct": "a", + "Explanation": "\"10 * 145 = 1450 3 * 100 + 5 * 150 = 1050 1450 \u2013 1050 = 400 a\"" + }, + { + "Answer": 12, + "Options": "a ) 10 , b ) 20 , c ) 40 , d ) 60 , e ) 12", + "Correct": "e", + "Explanation": "method 2 : each person is one participant of 4 games . so there are in all 4 * 6 = 24 instances of one participant games . but each game has 2 participants so total number of games = 24 / 2 = 12 e" + }, + { + "Answer": 192, + "Options": "a ) 192 , b ) 280 , c ) 384 , d ) 400 , e ) 500", + "Correct": "a", + "Explanation": "\"explanation : let the number be x . 5 * x / 6 = 5 * x / 16 + 100 25 * x / 48 = 100 x = 192 answer a\"" + }, + { + "Answer": 0.5555555555555556, + "Options": "a ) 10 / 16 , b ) 6 / 16 , c ) 4 / 16 , d ) 6 / 10 , e ) 5 / 9", + "Correct": "e", + "Explanation": "\"w = m + 4 w + m = 14 m + 4 + m = 14 2 m = 10 m = 5 w = 9 ratio : 5 : 9 ans : e\"" + }, + { + "Answer": 370.8333333333333, + "Options": "a ) 349 , b ) 541.75 , c ) 224.37 , d ) 370.833 , e ) none of these", + "Correct": "d", + "Explanation": "explanation : given exp . 8900 * 1 / 6 * 1 / 4 = 370.833 answer : d" + }, + { + "Answer": 9.09090909090909, + "Options": "a ) 9.09 % , b ) 10 % , c ) 12 1 / 2 % , d ) 15 % , e ) 16 2 / 3 %", + "Correct": "a", + "Explanation": "mp = 0.1 cp sp = cp + 0.1 cp = 1.1 cp hence mp = 0.1 / 1.1 sp = 1 / 1 sp . hence mp is 9.09 % of sp answer a" + }, + { + "Answer": 7272.727272727273, + "Options": "a ) rs . 6500 , b ) rs . 7500 , c ) rs . 7200 , d ) rs . 7273 , e ) rs . 6300", + "Correct": "d", + "Explanation": "\"income = rs . 100 expenditure = rs . 90 savings = rs . 10 present expenditure 90 + 90 * ( 5 / 100 ) = rs . 94.5 present savings = 100 \u2013 94.5 = rs . 5.50 if savings is rs . 5.50 , salary = rs . 100 if savings is rs . 400 , salary = 100 / 5.5 * 400 = 7273 answer : d\"" + }, + { + "Answer": 26, + "Options": "a ) 23 kg , b ) 24 kg , c ) 25 kg , d ) 26 kg , e ) 27 kg", + "Correct": "d", + "Explanation": "let the weight of d , e and f are a , b and c respectively . average weight of d , e and f = 42 a + b + c = 42 \u00d7 3 = 126 - - - equation ( 1 ) average weight of d and e = 35 a + b = 35 \u00d7 2 = 70 - - - equation ( 2 ) average weight of e and f = 41 b + c = 41 \u00d7 2 = 82 - - - equation ( 3 ) equation ( 2 ) + equation ( 3 ) - equation ( 1 ) = > a + b + b + c - ( a + b + c ) = 70 + 82 - 126 = > b = 152 - 126 = 26 weight of b = 26 kg answer : d" + }, + { + "Answer": 52, + "Options": "a ) 52 , b ) 37 , c ) 39 , d ) 43 , e ) 42", + "Correct": "a", + "Explanation": "\"average score before 20 th innings = 90 - 2 \u00d7 20 = 50 average score after 20 th innings = > 50 + 2 = 52 answer : a\"" + }, + { + "Answer": 355, + "Options": "a ) 350 , b ) 353 , c ) 354 , d ) 356 , e ) 357", + "Correct": "b", + "Explanation": "\"focus on the points where the number of digits in squares change : 1 , 2 , 3 - single digit squares . first 2 digit number is 10 . 4 , 5 , . . . 9 - two digit squares . to get 9 , the last number with two digit square , think that first 3 digit number is 100 which is 10 ^ 2 . so 9 ^ 2 must be the last 2 digit square . 10 , 11 , 12 , . . . 31 - three digit squares . to get 31 , think of 1000 - the first 4 digit number . it is not a perfect square but 900 is 30 ^ 2 . 32 ^ 2 = 2 ^ 10 = 1024 , the first 4 digit square . 32 - 99 - four digit squares . to get 99 , think of 10,000 - the first 5 digit number which is 100 ^ 2 . so number of digits in s ( 99 ) = 3 * 1 + 6 * 2 + 22 * 3 + 68 * 4 = 3 + 12 + 66 + 272 = 353 ; answer : b\"" + }, + { + "Answer": 58.00000000000001, + "Options": "a ) 56 , b ) 45 , c ) 58.2 , d ) 58 , e ) 46", + "Correct": "d", + "Explanation": "explanation : for 9 kg a , mixture = ( 9 + 11 ) kg . for 26.1 kg a , mixture = ( ( 20 / 9 ) x 26.1 ) kg = 58 kg . answer : d" + }, + { + "Answer": 18, + "Options": "a ) 11 , b ) 12 , c ) 18 , d ) 14 , e ) 15", + "Correct": "c", + "Explanation": "\"- x 2 - ( k + 12 ) x - 8 = - ( x - 2 ) ( x - 4 ) : given - x 2 - ( k + 12 ) x - 8 = - x 2 + 6 x - 8 - ( k + 12 ) = 6 : two polynomials are equal if their corresponding coefficients are equal . k = - 18 : solve the above for k correct answer c\"" + }, + { + "Answer": 81.5, + "Options": "a ) 81.8 , b ) 81.1 , c ) 81.2 , d ) 81.5 , e ) 81.9", + "Correct": "d", + "Explanation": "let the number of students in classes a , b and c be p , q and r respectively . then , total score of a = 83 p , total score of b = 76 q , total score of c = 85 r . also given that , ( 83 p + 76 q ) / ( p + q ) = 79 = > 4 p = 3 q . ( 76 q + 85 r ) / ( q + r ) = 81 = > 4 r = 5 q , = > q = 4 p / 3 and r = 5 p / 3 therefore , average score of a , b , c = ( 83 p + 76 q + 85 r ) / ( p + q + r ) = 978 / 12 = 81.5 answer : d" + }, + { + "Answer": 23, + "Options": "a ) 23 , b ) 20 , c ) 15 , d ) 26 , e ) 28", + "Correct": "a", + "Explanation": "\"nos a and b ab = 120 and a 2 + b 2 = 289 ( a + b ) 2 = 529 a + b = root ( 529 ) = 23 answer a\"" + }, + { + "Answer": 7, + "Options": "a ) 2.25 , b ) 7 , c ) 4.25 , d ) 5.25 , e ) 6.25", + "Correct": "b", + "Explanation": "\"squaring on both sides ( x + 1 / x ) ^ 2 = 3 ^ 2 x ^ 2 + 1 / x ^ 2 = 9 - 2 x ^ 2 + 1 / x ^ 2 = 7 answer : b\"" + }, + { + "Answer": 465, + "Options": "a ) 443 , b ) 450 , c ) 465 , d ) 468 , e ) 475", + "Correct": "c", + "Explanation": "\"total number of installments = 52 payment per installment for the first 8 installments = 410 payment per installment for the remaining 32 installments = 410 + 65 = 475 average = ( 8 * 410 + 44 * 475 ) / 52 = 465 answer c\"" + }, + { + "Answer": 200, + "Options": "a ) 300 , b ) 120 , c ) 150 , d ) 170 , e ) 200", + "Correct": "e", + "Explanation": "\"n th term of a . p . is given by a + ( n - 1 ) d 4 th term = a + 3 d 12 th term = a + 11 d given a + 3 d + a + 11 d = 20 - - > 2 a + 14 d = 20 - - > a + 7 d = 10 sum of n term of a . p = n / 2 [ 2 a + ( n - 1 ) d ] subsitiuing n = 20 . . . we get 20 / 2 [ 2 a + 14 d ] = 20 [ a + 7 d ] = 20 * 10 = 200 . . . answer is e . . .\"" + }, + { + "Answer": 60, + "Options": "a ) $ 20 , b ) $ 40 , c ) $ 50 , d ) $ 80 , e ) $ 60", + "Correct": "e", + "Explanation": "\"deargoodyear 2013 , i ' m happy to help . this is a relatively straightforward problem , not very challenging . btw , crazy eddiewas the actually name of an electronics chain on the east coast of the usa back in the 1970 s . manufacturing now is $ 50 . they now are making a 50 % profit , so the selling price must be $ 100 . they had this same selling price , $ 100 , before they made the change , and had a profit of 40 % , so the manufacturing must have been $ 60 . answer = ( e ) .\"" + }, + { + "Answer": 12, + "Options": "a ) 7 , b ) 9 , c ) 11 , d ) 12 , e ) 13", + "Correct": "d", + "Explanation": "\"sum of the deviations of the numbers in the set from the mean is always zero 1 , 2 , 4 , 5 , 6 , 9 , 9 , 10 , 12 mean is 7 so the list is - 6 - 5 - 3 - 2 - 1 + 2 + 2 + 3 + 5 . . . this shud total to zero but this is - 5 , hence we need a number that is 5 more than the mean to get a + 5 and make it zero hence the answer is 7 + 5 = 12 d\"" + }, + { + "Answer": 40, + "Options": "a ) 89 , b ) 20 , c ) 40 , d ) 88 , e ) 34", + "Correct": "c", + "Explanation": "\"speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 200 + 200 = 360 m . time taken = 400 / 10 = 40 sec . answer : option c\"" + }, + { + "Answer": 1380, + "Options": "a ) 1360.47 , b ) 1355.8 , c ) 1380 , d ) 1350 , e ) 1333", + "Correct": "c", + "Explanation": "add 1200 , 1300 , 1400 , 1510 , 1520 , 1530 , and 1200 grouping numbers together may quicken the addition sum = 9660 9660 / 7 = 1380 c" + }, + { + "Answer": 5, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 1", + "Correct": "d", + "Explanation": "here we can assume that one subject is of 100 marks so total there are 5 subjects = > 100 * 5 = 500 . now according to the question he secured 60 % of those which is 60 % of 500 = 300 marks in total . the ratio between the marks is given as 5 : 6 : 7 : 8 : 9 , so now we can distribute 300 marks according to the ratio . total ratio = 35 for 6 : ( 300 / 35 ) * 6 = 51.4 similarly , we will get for others as 60 , 68.57 , 77.14 hence , there are 5 subject where he secured more that 50 % . the answer is 5 . d" + }, + { + "Answer": 23.999999999999996, + "Options": "a ) 0 , b ) 5 , c ) 10 , d ) 24 , e ) 20", + "Correct": "d", + "Explanation": "\"x = \u221a 6 and y also = \u221a 6 applying the function ( \u221a 6 + \u221a 6 ) ^ 2 - ( \u221a 6 - \u221a 6 ) ^ 2 = ( 2 \u221a 6 ) ^ 2 - 0 = 4 x 6 = 24 . note : alternative approach is the entire function is represented as x ^ 2 - y ^ 2 = ( x + y ) ( x - y ) which can be simplified as ( x + y + x - y ) ( x + y - ( x - y ) ) = ( 2 x ) ( 2 y ) = 4 xy . substituting x = \u221a 6 and y = \u221a 6 you get the answer 24 . answer d\"" + }, + { + "Answer": 331.2, + "Options": "a ) 400 km , b ) 500 km , c ) 331.2 km , d ) 550 km , e ) 600 km", + "Correct": "c", + "Explanation": "\"sol . average speed of a tractor = 23 km / h the speed of a bus in an hour = 23 \u00d7 2 = 46 km the speed of a car in an hour = 9 / 5 * 46 = 82.8 km so , the distance covered by car in 4 h is 82.8 \u00d7 4 = 331.2 km ans . ( c )\"" + }, + { + "Answer": 17, + "Options": "a ) 18 , b ) 19 , c ) 17 , d ) 15 , e ) 16", + "Correct": "c", + "Explanation": "editing my solution : number of switches = 56 number of switches turned on by x : 3 , 6 , . . . 54 = 18 number of switches turned on by y : 5 , 10 , . . . . 55 = 11 few switches are turned on by x and later turned off by y : lcm ( 35 ) = 15 x = 15 , 30 , . . . . 90 = 6 . subtract the above 6 switches from both x and y as they are turned off . number of switches that are turned on = ( 18 - 6 ) + ( 11 - 6 ) = 17 answer : c" + }, + { + "Answer": 6993, + "Options": "a ) 0 , b ) 7896 , c ) 6993 , d ) 903 , e ) 803", + "Correct": "c", + "Explanation": "( local value ) - ( face value ) = ( 7000 - 7 ) = 6993 . answer : c" + }, + { + "Answer": 51.193820224719104, + "Options": "a ) 53.2 , b ) 52.2 , c ) 51.2 , d ) 8.2 , e ) 54.2", + "Correct": "c", + "Explanation": "given exp . = ( 15 ) ^ 2 x 9 ^ 2 \u00e3 \u00b7 356 = b = 225 x 81 \u00e3 \u00b7 356 = 51.2 c" + }, + { + "Answer": 0.56, + "Options": "a ) 0.52 , b ) 0.42 , c ) 0.48 , d ) 0.64 , e ) 0.56", + "Correct": "e", + "Explanation": "\"given exp . = 0.2 * 0.4 + ( 0.6 * 0.8 ) = 0.08 + 0.48 = 0.56 answer is e .\"" + }, + { + "Answer": 37.5, + "Options": "a ) a : 45 , b ) b : 25 , c ) c : 37.5 , d ) d : 36 , e ) e : 42", + "Correct": "c", + "Explanation": "\"if you have a 37.5 liter capacity , you start with 37.5 l of a and 0 l of b . 1 st replacement after the first replacement you have 37.5 - 15 = 22.5 l of a and 15 l of b . the key is figuring out how many liters of a and b , respectively , are contained in the next 15 liters of mixture to be removed . the current ratio of a to total mixture is 22.5 / 37.5 ; expressed as a fraction this becomes ( 45 / 2 ) / ( 75 / 2 ) , or 45 / 2 * 2 / 75 . canceling the 2 s and factoring out a 5 leaves the ratio as 9 / 15 . note , no need to reduce further as we ' re trying to figure out the amount of a and b in 15 l of solution . 9 / 15 of a means there must be 6 / 15 of b . multiply each respective ratio by 15 to get 9 l of a and 6 l of b in the next 15 l removal . final replacement the next 15 l removal means 9 liters of a and 6 liters of b are removed and replaced with 15 liters of b . 22.5 - 9 = 13.5 liters of a . 15 liters of b - 6 liters + 15 more liters = 24 liters of b . test to the see if the final ratio = 9 / 16 ; 13.5 / 24 = ( 27 / 2 ) * ( 1 / 24 ) = 9 / 16 . choice c is correct .\"" + }, + { + "Answer": 9, + "Options": "a ) 17 : 3 , b ) 9 : 1 , c ) 3 : 17 , d ) 5 : 3 , e ) 11 : 2", + "Correct": "b", + "Explanation": "\"he 20 litre mixture contains milk and water in the ratio of 3 : 2 . therefore , there will be 12 litres of milk in the mixture and 8 litres of water in the mixture . step 1 . when 10 litres of the mixture is removed , 6 litres of milk is removed and 4 litres of water is removed . therefore , there will be 6 litres of milk and 4 litres of water left in the container . it is then replaced with pure milk of 10 litres . now the container will have 16 litres of milk and 4 litres of water . step 2 . when 10 litres of the new mixture is removed , 8 litres of milk and 2 litres of water is removed . the container will have 8 litres of milk and 2 litres of water in it . now 10 litres of pure milk is added . therefore , the container will have 18 litres of milk and 2 litres of water in it at the end of the second step . therefore , the ratio of milk and water is 18 : 2 or 9 : 1 . shortcut . we are essentially replacing water in the mixture with pure milk . let w _ o be the amount of water in the mixture originally = 8 litres . let w _ r be the amount of water in the mixture after the replacements have taken place . then , { w _ r } / { w _ o } = ( 1 - r / m ) ^ n where r is the amount of the mixture replaced by milk in each of the steps , m is the total volume of the mixture and n is the number of times the cycle is repeated . hence , { w _ r } / { w _ o } \u00a0 = ( 1 / 2 ) ^ 2 \u00a0 = 1 / 4 therefore e , w _ r \u00a0 = { w _ o } / 4 = 8 / 4 \u00a0 = 2 litres . b\"" + }, + { + "Answer": 255, + "Options": "a ) $ 255 , b ) $ 275 , c ) $ 510 , d ) $ 1,250 , e ) $ 2,550", + "Correct": "a", + "Explanation": "\"total no . of boxes = 3060000 / ( 20 \u00d7 20 \u00d7 15 ) = 510 total cost = 510 \u00d7 $ 0.5 = $ 255 answer a\"" + }, + { + "Answer": 36.5, + "Options": "a ) 36.02 , b ) 36.14 , c ) 36.12 , d ) 36.11 , e ) 36.8", + "Correct": "b", + "Explanation": "explanation : correct sum = ( 36 * 50 + 30 - 23 ) = 1825 . correct mean = = 1807 / 50 = 36.14 answer : b ) 36.14" + }, + { + "Answer": 5800, + "Options": "a ) 2348 , b ) 7250 , c ) 2767 , d ) 1998 , e ) 5800", + "Correct": "e", + "Explanation": "explanation : a b c investment 3 x 4 x 5 x rate of return 6 y % 5 y % 4 y % return \\ inline \\ frac { 18 xy } { 100 } \\ inline \\ frac { 20 xy } { 100 } \\ inline \\ frac { 20 xy } { 100 } total = ( 18 + 20 + 20 ) = \\ inline \\ frac { 58 xy } { 100 } b ' s earnings - a ' s earnings = \\ inline \\ frac { 2 xy } { 100 } = 200 total earning = \\ inline \\ frac { 58 xy } { 100 } = 5800 answer : e ) rs . 5800" + }, + { + "Answer": 15, + "Options": "a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 15", + "Correct": "e", + "Explanation": "\"sum of 14 even numbers = 14 * 15 = 210 average = 210 / 14 = 15 answer : e\"" + }, + { + "Answer": 9, + "Options": "a ) 12 , b ) 9 , c ) 3 , d ) 7.5 , e ) 2.5", + "Correct": "b", + "Explanation": "we have 2 equations 1 . 4 ( 3 x + 4 y ) = 48 - - > 3 x + 4 y = 12 - - > 9 x + 12 y = 36 2 . kx + 12 y = 30 substract 1 - 2 , we get ( 9 - k ) x = 6 i . e . x = 6 / ( 9 - k ) then , by looking at options , we get some value of x except for b . when we put k = 9 , x becomes 6 / 0 and hence answer is b" + }, + { + "Answer": 1986, + "Options": "a ) 1986 , b ) 1985 , c ) 1987 , d ) 1988 , e ) 1989", + "Correct": "a", + "Explanation": "sum of year = 1 + 9 + 8 + 0 = ( 18 ) 1 + 8 = 9 1 + 9 + 8 + 2 = ( 20 ) 2 + 0 = 2 1 + 9 + 8 + 4 = ( 13 ) 1 + 3 = 4 now 9 + 2 + 4 = ( 15 ) 1 + 5 = 6 nd option a 1 + 9 + 8 + 6 = 24 ( 2 + 4 ) = 6 answer : a" + }, + { + "Answer": 75, + "Options": "a ) 75 kg , b ) 85 kg , c ) 95 kg , d ) 65 kg , e ) 55 kg", + "Correct": "a", + "Explanation": "\"the total weight increase = ( 8 x 2.5 ) kg = 20 kg weight of new person = ( 55 + 20 ) kg = 75 kg the answer is a .\"" + }, + { + "Answer": 28, + "Options": "a ) 16 , b ) 22 , c ) 28 , d ) 34 , e ) 40", + "Correct": "c", + "Explanation": "l . c . m . of 5 , 6 , 4 and 3 = 60 . when dividing 5432 by 60 , the remainder is 32 . the number to be added = 60 - 32 = 28 . the answer is c ." + }, + { + "Answer": 2, + "Options": "a ) 3 , b ) 7.5 , c ) 2.25 , d ) 2 , e ) 4", + "Correct": "d", + "Explanation": "\"m = 6 s = x ds = 6 + x us = 6 - x 6 + x = ( 6 - x ) 2 6 + x = 12 - 2 x 3 x = 6 x = 2 answer : d\"" + }, + { + "Answer": 0.09375, + "Options": "a ) 0 , b ) 1 / 9 , c ) 2 / 9 , d ) 3 / 32 , e ) 1", + "Correct": "d", + "Explanation": "\"if he is to ride 4 times and since he can choose any of the 4 cars each time , total number of ways is = 4 * 4 * 4 * 4 = 256 now the number of ways if he is to choose a different car each time is = 4 * 3 * 2 * 1 = 24 so the probability is = 24 / 256 = 6 / 64 = 3 / 32 = 3 / 32 answer : d\"" + }, + { + "Answer": 17, + "Options": "a ) 17 , b ) 35 , c ) 20 , d ) 32 , e ) 21", + "Correct": "a", + "Explanation": "\"age of b = age of ( a + b + c ) \u00e2 \u20ac \u201c age of ( a + c ) = 25 \u00e3 \u2014 3 \u00e2 \u20ac \u201c 29 \u00e3 \u2014 2 = 75 \u00e2 \u20ac \u201c 58 = 17 years a\"" + }, + { + "Answer": 99.075, + "Options": "a ) 125.8 , b ) 102.8 , c ) 99.375 , d ) 100.52 , e ) 122", + "Correct": "c", + "Explanation": "\"explanation : correct sum = ( 100 * 40 + 50 - 75 ) = 3975 . correct mean = = 3975 / 40 = 99.375 answer : c\"" + }, + { + "Answer": 20.5, + "Options": "a ) 16 , b ) 20.5 , c ) 17.5 , d ) 20 , e ) 4.5", + "Correct": "b", + "Explanation": "total entrance fee is ( 2 * $ 5 ) + ( 1.20 * 5 ) = $ 16 total rides fee is ( 0.50 * 3 ) * 3 = $ 4.50 total money spent is $ 20.50 answer is b" + }, + { + "Answer": 5, + "Options": "a ) 3 : 2 , b ) 2 : 1 , c ) 4 : 3 , d ) 4 : 1 , e ) 5 : 1", + "Correct": "e", + "Explanation": "( 5 / 9 ) * p + ( 2 / 9 ) * q = ( 4 / 9 ) * p + ( 7 / 9 ) * q p = 5 q p / q = 5 / 1 the answer is e ." + }, + { + "Answer": 260, + "Options": "a ) $ 260 , b ) $ 96 , c ) $ 26 , d ) $ 120 , e ) $ 240", + "Correct": "a", + "Explanation": "\"eps actual > eps expected . each gets and additional . 12 per share . thus . 52 * 500 - - > $ 260 answer is a\"" + }, + { + "Answer": 5, + "Options": "a ) 3 , b ) 1 , c ) 4 , d ) 2 , e ) 5", + "Correct": "e", + "Explanation": "let ' s test out some values of p and q that satisfy the given information . s leaves are remainder of 2 when divided by 6 so , s could equal 8 t leaves are remainder of 3 when divided by 6 so , t could equal 3 what is the remainder when s \u2013 t is divided by 6 ? so , s - t = 8 - 3 = 5 , and when we divide 5 by 6 , we get 0 with remainder 5 answer : e" + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) 9 , c ) 10 , d ) 16 , e ) 17", + "Correct": "a", + "Explanation": "\"let the ages of children be x , ( x + 2 ) , ( x + 4 ) , ( x + 6 ) and ( x + 8 ) years . then , x + ( x + 2 ) + ( x + 4 ) + ( x + 6 ) + ( x + 8 ) = 40 5 x = 20 x = 4 . x + 8 = 4 + 8 = 12 answer : a\"" + }, + { + "Answer": 1620, + "Options": "a ) 1234 , b ) 1456 , c ) 1256 , d ) 1456 , e ) 1635", + "Correct": "e", + "Explanation": "\"let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 15 5 x = 1350 x = 270 large number = 270 + 1365 = 1635 e\"" + }, + { + "Answer": 120, + "Options": "a ) 80 , b ) 100 , c ) 105 , d ) 120 , e ) 110", + "Correct": "d", + "Explanation": "\"4 th term + 12 th term = 16 i . e . , ( a + 3 d ) + ( a + 11 d ) = 16 now , sum of first 15 terms = ( 15 / 2 ) * [ 2 a + ( 15 - 1 ) d ] = ( 15 / 2 ) * [ 2 a + 14 d ] = ( 15 / 2 ) * 16 - - - - - - - - - - - - - - - from ( 1 ) = 120 answer : d\"" + }, + { + "Answer": 0.75, + "Options": "a ) 5 / 2 , b ) 3 / 2 , c ) 3 / 4 , d ) 2 / 5 , e ) 0", + "Correct": "c", + "Explanation": "\"we are given x = 1 \u2013 2 t and y = 2 t \u2013 2 , and we need to determine the value for t when x = y . we should notice that both x and y are already in terms of t . thus , we can substitute 1 \u2013 2 t for x and 2 t \u2013 2 for y in the equation x = y . this gives us : 1 \u2013 2 t = 2 t \u2013 2 3 = 4 t 3 / 4 = t the answer is c .\"" + }, + { + "Answer": 6, + "Options": "a ) 5 , b ) 8 , c ) 4 , d ) 6 , e ) 3", + "Correct": "d", + "Explanation": "\"2 ab = ( a ( power 2 ) + b ( power 2 ) - ( a - b ) ( power 2 ) = 21 - 9 = 12 ab = 6 . answer is d .\"" + }, + { + "Answer": 204, + "Options": "a ) 238 , b ) 204 , c ) 678 , d ) 169 , e ) 161", + "Correct": "b", + "Explanation": "ans : the total number of squares in a n x n chess board is equal to ` ` the sum of first n natural number squares ' ' i . e . , n ( n + 1 ) ( 2 n + 1 ) 6 n ( n + 1 ) ( 2 n + 1 ) 6 so substituting 8 in the above formula we get 204 answer : b" + }, + { + "Answer": 2, + "Options": "a ) a ) 4 , b ) b ) 3 , c ) c ) 2 , d ) d ) 5 , e ) e ) 6", + "Correct": "c", + "Explanation": "\"explanation : 686 = 36 x 19 + r 686 = 684 + r r = 686 - 684 = 2 answer : option c\"" + }, + { + "Answer": 53.513513513513516, + "Options": "a ) 52.2 , b ) 59.5 , c ) 52.8 , d ) 53.5 , e ) 52.1", + "Correct": "d", + "Explanation": "\"sum of the marks for the class of 24 students = 24 * 40 = 960 sum of the marks for the class of 50 students = 50 * 60 = 3000 sum of the marks for the class of 74 students = 960 + 3000 = 3960 average marks of all the students = 3960 / 74 = 53.5 answer : d\"" + }, + { + "Answer": 150, + "Options": "a ) rs . 300 , b ) rs . 200 , c ) rs . 240 , d ) rs . 150 , e ) none of these", + "Correct": "d", + "Explanation": "\"z share = z , y = 1.2 z x = 1.25 \u00e3 \u2014 1.2 z , x + y + z = 555 ( 1.25 \u00e3 \u2014 1.2 + 1.2 + 1 ) z = 55 3.7 z = 555 , z = 150 answer : . d\"" + }, + { + "Answer": 11915, + "Options": "a ) s . 49180 , b ) s . 49910 , c ) s . 11915 , d ) s 6997 , e ) s . 5000", + "Correct": "c", + "Explanation": "total sale for 5 months = rs . ( 2500 + 6500 + 9855 + 7230 + 7000 ) = rs . 33085 . required sale = rs . [ ( 7500 x 6 ) - 33085 ] = rs . ( 45000 - 33085 ) = rs . 11915 . c" + }, + { + "Answer": 3.75, + "Options": "a ) 15 / 4 , b ) 13 / 2 , c ) 9 / 7 , d ) 1 / 5 , e ) 7 / 6", + "Correct": "a", + "Explanation": "\"the way to approach this problem is 6 < a < 17 and 3 < b < 29 minimum possible value of a is 7 and maximum is 16 minimum possible value of b is 4 and maximum is 28 range = max a / min b - min a / max b ( highest - lowest ) 16 / 4 - 7 / 28 = 15 / 4 hence a\"" + }, + { + "Answer": 800, + "Options": "a ) 650 , b ) 700 , c ) 750 , d ) 800 , e ) 850", + "Correct": "d", + "Explanation": "x + y = 1200 so y = 1200 - x x = 3 y - 400 x = 3 ( 1200 - x ) - 400 4 x = 3200 x = 800 the answer is d ." + }, + { + "Answer": 36, + "Options": "a ) 500 % , b ) 250 % , c ) 500 / 3 % , d ) 36 % , e ) 60 %", + "Correct": "d", + "Explanation": "z = 100 ; y = 30 so x = 36 x as % of z = 36 / 100 * 100 = > 36 % answer will be ( d )" + }, + { + "Answer": 100, + "Options": "a ) 321 , b ) 65 , c ) 120 , d ) 100 , e ) 80", + "Correct": "d", + "Explanation": "1 million distinct 3 digit initials are needed . let the number of required alphabets in the language be \u2018 n \u2019 . therefore , using \u2018 n \u2019 alphabets we can form n * n * n = n 3 distinct 3 digit initials . note distinct initials is different from initials where the digits are different . for instance , aaa and bbb are acceptable combinations in the case of distinct initials while they are not permitted when the digits of the initials need to be different . this n 3 different initials = 1 million i . e . n 3 = 106 ( 1 million = 106 ) = > n 3 = ( 102 ) 3 = > n = 102 = 100 hence , the language needs to have a minimum of 100 alphabets to achieve the objective . ans : d" + }, + { + "Answer": 14, + "Options": "a ) 8 , b ) 12 , c ) 13 , d ) 14 , e ) 16", + "Correct": "d", + "Explanation": "\"amount of salt = 5.6 assume x gallons of water are added . 5.6 / 56 + x = 8 / 100 560 = 8 x + 448 8 x = 112 x = 14 correct option : d\"" + }, + { + "Answer": 3480, + "Options": "a ) 2348 , b ) 3480 , c ) 2767 , d ) 1998 , e ) 2771", + "Correct": "b", + "Explanation": "\"explanation : a b c investment 3 x 4 x 5 x rate of return 6 y % 5 y % 4 y % return \\ inline \\ frac { 18 xy } { 100 } \\ inline \\ frac { 20 xy } { 100 } \\ inline \\ frac { 20 xy } { 100 } total = ( 18 + 20 + 20 ) = \\ inline \\ frac { 58 xy } { 100 } b ' s earnings - a ' s earnings = \\ inline \\ frac { 2 xy } { 100 } = 120 total earning = \\ inline \\ frac { 58 xy } { 100 } = 3480 answer : b ) rs . 3480\"" + }, + { + "Answer": 64.7, + "Options": "a ) 35.67 % , b ) 64.75 % , c ) 68.57 % , d ) 69.57 % , e ) none of these", + "Correct": "b", + "Explanation": "\"girls = 900 , boys = 1100 passed = ( 38 % of 1100 ) + ( 32 % of 900 ) = 418 + 288 = 706 failed = 2000 - 706 = 1294 failed % = [ ( 1294 / 2000 ) x 100 ] % = 64.7 % . answer : b\"" + }, + { + "Answer": 59.99999999999997, + "Options": "a ) $ 60 , b ) $ 80 , c ) $ 100 , d ) $ 120 , e ) $ 140", + "Correct": "a", + "Explanation": "\"3 : 2 = 9 : 6 and 5 : 3 = 10 : 6 . an increase in $ 10 increases the ratio by 1 : 6 . therefore , january ' s bill was 6 ( $ 10 ) = $ 60 . the answer is a .\"" + }, + { + "Answer": 305, + "Options": "a ) 190 , b ) 195 , c ) 305 , d ) 205 , e ) 210", + "Correct": "c", + "Explanation": "\"this question can be solved with the average formula and ' bunching . ' we ' re asked for the average of all of the multiples of 10 from 10 to 600 , inclusive . to start , we can figure out the total number of terms rather easily : 1 ( 10 ) = 10 2 ( 10 ) = 20 . . . 60 ( 10 ) = 600 so we know that there are 60 total numbers . we can now figure out the sum of those numbers with ' bunching ' : 10 + 600 = 610 20 + 590 = 610 30 + 580 = 610 etc . since there are 60 total terms , this pattern will create 30 ' pairs ' of 610 . thus , since the average = ( sum of terms ) / ( number of terms ) , we have . . . ( 30 ) ( 610 ) / ( 60 ) = 305 final answer : c\"" + }, + { + "Answer": 20.0133422281521, + "Options": "a ) 15 % , b ) 20 % , c ) 25 % , d ) 60 % , e ) 80 %", + "Correct": "b", + "Explanation": "\"listed selling price of chair = 74.95 $ discounted selling price of chair = 59.95 $ discount = 74.95 - 59.95 = 15 $ % decrease in price of chair = ( 15 / 74.95 ) * 100 % = 20 % approx answer b\"" + }, + { + "Answer": 420.00000000000006, + "Options": "a ) s . 420 , b ) s . 360 , c ) s . 389 , d ) s . 368 , e ) s . 323", + "Correct": "a", + "Explanation": "\"( a = 2 / 3 b and b = 1 / 4 c ) = a / b = 2 / 3 and b / c = 1 / 4 a : b = 2 : 3 and b : c = 1 : 4 = 3 : 12 a : b : c = 2 : 3 : 12 a ; s share = 595 * 2 / 17 = rs . 70 b ' s share = 595 * 3 / 17 = rs . 105 c ' s share = 595 * 12 / 17 = rs . 420 . answer : a\"" + }, + { + "Answer": 33.33333333333333, + "Options": "a ) 9 % , b ) 15 % , c ) 25 % , d ) 33 % , e ) 50 %", + "Correct": "d", + "Explanation": "let ' s plug in somenicenumbers and see what ' s needed . let ' s say the employee used to make $ 1 / hour and worked 100 hours / week so , the total weekly income was $ 100 / week after the 50 % wage increase , the employee makes $ 1.50 / hour we want the employee ' s income to remain at $ 100 / week . so , we want ( $ 1.50 / hour ) ( new # of hours ) = $ 100 divide both sides by 1.50 to get : new # of hours = 100 / 1.50 \u2248 67 hours so , the number of hours decreases from 100 hours to ( approximately ) 67 hours . this represents a 33 % decrease ( approximately ) . answer : d" + }, + { + "Answer": 117, + "Options": "a ) 107 , b ) 117 , c ) 127 , d ) 137 , e ) 147", + "Correct": "b", + "Explanation": "\"let us calculate both the length and width of the room in centimeters . length = 6 meters and 24 centimeters = 624 cm width = 4 meters and 32 centimeters = 432 cm as we want the least number of square tiles required , it means the length of each square tile should be as large as possible . further , the length of each square tile should be a factor of both the length and width of the room . hence , the length of each square tile will be equal to the hcf of the length and width of the room = hcf of 624 and 432 = 48 thus , the number of square tiles required = ( 624 x 432 ) / ( 48 x 48 ) = 13 x 9 = 117 answer : b\"" + }, + { + "Answer": 37, + "Options": "a ) 20 , b ) 37 , c ) 42 , d ) 53 , e ) 64", + "Correct": "b", + "Explanation": "\"x + ( x - 14 ) = 60 - - > x = 37 . answer : b .\"" + }, + { + "Answer": 23, + "Options": "a ) 18 , b ) 21 , c ) 23 , d ) 25 , e ) 27", + "Correct": "c", + "Explanation": "\"let the average age of the whole team be x years . 11 x - ( 26 + 29 ) = 9 ( x - 1 ) = > 11 x - 9 x = 46 = > 2 x = 46 = > x = 23 . so , average age of the team is 23 years . c\"" + }, + { + "Answer": 24, + "Options": "a ) 24 , b ) 36 , c ) 48 , d ) 60 , e ) 72", + "Correct": "a", + "Explanation": "\"let total no of students in the class be n so , we are told that n is divisible by both 12 24 so , lets find the least common multiple of 12 24 , ie 24 so our answer is ( a ) 24\"" + }, + { + "Answer": 220, + "Options": "a ) $ 220 , b ) $ 340 , c ) $ 150 , d ) $ 100 , e ) $ 120", + "Correct": "a", + "Explanation": "step 1 : find the cost of the children ' s tickets . 6 \u00d7 $ 10 = $ 60 step 2 : find the cost of the adults ' tickets . 10 \u00d7 $ 16 = $ 160 step 3 : find the total cost . $ 60 + $ 160 = $ 220 the zoo tickets will cost $ 220 . answer is a ." + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 12 , c ) 15 , d ) 20 , e ) 24", + "Correct": "a", + "Explanation": "\"you could set - up a quick table and brute force the answer . a 6 * 50 300 1800 - 300 1500 24 62.50 b 16 * 50 600 1800 - 600 1200 18 66.67 c 15 * 50 750 1800 - 750 1050 15 70.00 d 20 * 50 1000 1800 - 1000 800 10 80.00 e 24 * 50 1200 1800 - 1200 600 6 100.00 answer is a\"" + }, + { + "Answer": 2.4000000000000004, + "Options": "a ) 7 / 4 , b ) 10 / 3 , c ) 12 / 5 , d ) 15 / 7 , e ) 18 / 11", + "Correct": "c", + "Explanation": "\"the time it takes printer x is 16 hours . the combined rate of y and z is 1 / 10 + 1 / 20 = 3 / 20 the time it takes y and z is 20 / 3 the ratio of times is 16 / ( 20 / 3 ) = 3 * 16 / 20 = 12 / 5 the answer is c .\"" + }, + { + "Answer": 71, + "Options": "a ) 59 kg , b ) 62 kg , c ) 74 kg , d ) 85 kg , e ) 71 kg", + "Correct": "e", + "Explanation": "\"total weight increased = 1.8 * 10 = 18 kg weight of the new man = 53 + 18 = 71 kg answer is e\"" + }, + { + "Answer": 390, + "Options": "a ) 350 , b ) 370 , c ) 390 , d ) 430 , e ) none", + "Correct": "c", + "Explanation": "\"explanation : assumed mean = rs . 350 total excess than assumed mean = 4 \u00d7 ( rs . 420 - rs . 350 ) = rs . 280 therefore , increase in average expenditure = rs . 280 / 7 = rs . 40 therefore , average expenditure for 7 days = rs . 350 + rs . 40 = rs . 390 correct option : c\"" + }, + { + "Answer": 840, + "Options": "a ) 720 , b ) 750 , c ) 820 , d ) 840 , e ) 860", + "Correct": "d", + "Explanation": "\"25 % of x = x / 4 ; 15 % of 1500 = 15 / 100 * 1500 = 225 given that , x / 4 = 225 - 15 = > x / 4 = 210 = > x = 840 . answer : d\"" + }, + { + "Answer": 45, + "Options": "a ) 25 % , b ) 35 % , c ) 45 % , d ) 55 % , e ) 65 %", + "Correct": "c", + "Explanation": "\"to maximize the percentage of companies offering both , let ' s assume that all 45 % of companies which offer wireless internet also offer snacks . the answer is c .\"" + }, + { + "Answer": 4, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "d", + "Explanation": "to get a 5 , you need one high and three lows ( you could have had 2 highs and one low , but the constraint is that you must have three low cards ) hlll = 4 ! 3 ! = 4 4 ! is the number of ways you can arrange these four spaces . divide by 3 ! because you you repeat three low cards ans : d" + }, + { + "Answer": 38, + "Options": "a ) 35 , b ) 37 , c ) 38 , d ) 41 , e ) 42", + "Correct": "c", + "Explanation": "\"explanation : let b ' s age = x years . then , as age = ( x + 8 ) years . ( x + 8 + 10 ) = 2 ( x \u2014 10 ) hence x = 38 . present age of b = 38 years answer : option c\"" + }, + { + "Answer": 44.99999999999999, + "Options": "a ) 38 , b ) 40 , c ) 42 , d ) 45 , e ) 50", + "Correct": "d", + "Explanation": "the time to produce the first 60 cogs is 60 / 36 = 5 / 3 hours . the time to produce the next 60 cogs is 60 / 60 = 1 hour . the average output is 120 cogs / ( 8 / 3 ) hours = 45 cogs per hour . the answer is d ." + }, + { + "Answer": 4, + "Options": "a ) 4 , b ) 7 , c ) 8 , d ) 5 , e ) 3", + "Correct": "a", + "Explanation": "\"explanation : let the number be x . then , ( x - 5 ) / 7 = 7 = > x - 5 = 49 x = 54 . : ( x - 2 ) / 13 = ( 54 - 2 ) / 13 = 4 answer : option a\"" + }, + { + "Answer": 360, + "Options": "a ) 360 , b ) 227 , c ) 268 , d ) 198 , e ) 176", + "Correct": "a", + "Explanation": "\"12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 12 / 29 * 870 = 360 answer : a\"" + }, + { + "Answer": 1400, + "Options": "a ) 800 , b ) 1400 , c ) 1000 , d ) 1100 , e ) 1200", + "Correct": "b", + "Explanation": "\"0.2 x = 4 ( 870 - 800 ) 0.2 x = 280 x = 1400 answer b\"" + }, + { + "Answer": 13.333333333333332, + "Options": "a ) 3 / 80 , b ) 3 / 5 , c ) 4 , d ) 5 / 3 , e ) 40 / 3", + "Correct": "e", + "Explanation": "\"30 / 100 = 3 / 10 n = 2 ^ 3 / 10 n ^ b = 2 ^ 4 ( 2 ^ 3 / 10 ) ^ b = 2 ^ 4 b = 40 / 3 answer : e\"" + }, + { + "Answer": 33, + "Options": "a ) 25 , b ) 35 , c ) 23 , d ) 22 , e ) 33", + "Correct": "e", + "Explanation": "\"let the number of students who wrote the exam be x . total marks of students = 90 x . total marks of ( x - 3 ) students = 80 ( x - 3 ) 90 x - ( 3 * 40 ) = 95 ( x - 3 ) 165 = 5 x = > x = 33 answer : e\"" + }, + { + "Answer": 15, + "Options": "a ) 10 , b ) 12 , c ) 18 , d ) 20 , e ) 15", + "Correct": "e", + "Explanation": "\"each employee will get a gift worth of = $ 2 total employees = 6000 / 2 = 3000 total blocks = 3000 / 200 = 15 correct option is e\"" + }, + { + "Answer": 10, + "Options": "a ) 10 , b ) 19 , c ) 20 , d ) 21 , e ) 22", + "Correct": "a", + "Explanation": "\"from right 6 , from left 5 total = 6 + 5 - 1 = 10 answer : a\"" + }, + { + "Answer": 165, + "Options": "a ) 98 , b ) 165 , c ) 180 , d ) 253 , e ) none of these", + "Correct": "b", + "Explanation": "solution : dividing each side by 15 , we obtain ( 15 x / 15 ) = ( 165 / 15 ) therefore : x = 11 check : 15 x = 165 ( 15 * 11 ) = 165 165 = 165 answer : b" + }, + { + "Answer": 1, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "b", + "Explanation": "taking the prices of products in ascending order ( already arranged ) $ 50 , $ 50 , $ 97 , $ 97 , $ 97 , $ 120 , $ 125 , $ 155 , $ 199 , $ 199 , $ 239 we see that median value is the 6 th value as there in total 11 values given arithmetic mean = total / number of entries = 1428 / 11 = 129.8181 we are asked to find how many unit sales on that day were greater than the mean sale price but less than the median sale price as we can clearly see that there is one value between $ 120 and $ 129.81 , answer is 1 unit correct answer - b" + }, + { + "Answer": 15, + "Options": "a ) 8 , b ) 12 , c ) 15 , d ) 17 , e ) 18", + "Correct": "c", + "Explanation": "\"let original strength = y then , 40 y + 15 x 32 = ( y + 15 ) x 36 \u00e2 \u2021 \u2019 40 y + 480 = 36 y + 540 \u00e2 \u2021 \u2019 4 y = 60 \u00e2 \u02c6 \u00b4 y = 15 c\"" + }, + { + "Answer": 3.3222591362126246, + "Options": "a ) 100 / 6 , b ) 289 / 4 , c ) 128 / 7 , d ) 456 / 6 , e ) 1000 / 301", + "Correct": "e", + "Explanation": "explanation : log 2 10 = 1 / log 102 = 1 / 0.3010 = 10000 / 3010 = 1000 / 301 answer e" + }, + { + "Answer": 32, + "Options": "a ) 64 and 15,625 , b ) 32 and 3,125 , c ) 64 and 15,620 , d ) 64 and 15,635 , e ) 64 and 16,625", + "Correct": "b", + "Explanation": "1 , 00,000 = 10 ^ 5 = 10 x 10 x 10 x 10 x 10 = ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) = ( 2 ^ 5 ) x ( 5 ^ 5 ) = 32 x 3125 so the numbers are 32 and 3,125 answer : b" + }, + { + "Answer": 80, + "Options": "a ) 20 % , b ) 30 % , c ) 40 % , d ) 70 % , e ) 80 %", + "Correct": "e", + "Explanation": "\"the is always the difference between our starting and ending points . in this case , it \u2019 s 100 \u2013 20 = 80 . the \u201c original \u201d is our starting point ; in this case , it \u2019 s 100 . ( 80 / 100 ) * 100 = ( 0.8 ) * 100 = 80 % . e\"" + }, + { + "Answer": 40, + "Options": "a ) 20 , b ) 25 , c ) 30 , d ) 40 , e ) 50", + "Correct": "d", + "Explanation": "\"let the list price be 2 x for min sale price , the first discount given should be 50 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 40 and 0.8 x = 32 so lowest sale price is 32 , which is q = 40 % of 80 hence , d is the answer\"" + }, + { + "Answer": 1, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "b", + "Explanation": "easier to start with numbers that are of the form 17 p + 1 - - - > 18 , 35,52 , 69,86 . out of these , there is only one ( 69 ) is also of the form 4 q + 1 . thus 1 is the answer . b is the correct answer ." + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 17", + "Correct": "a", + "Explanation": "8 k 8 k 88 - - - - - - - - 16 y 6 trial and error or just plug - in method might be the shortest way to solve this problem . though you can narrow down the possible values of k to just two : 7 and 8 - - > 8 * * + 7 * * = 16 * * or 8 * * + 8 * * = 16 * * ( k can not be less than 7 or 9 , as the result wo n ' t be 16 * * ) . after that it ' s easy to get that k = 7 and y = 6 . answer : a ." + }, + { + "Answer": 120, + "Options": "a ) 70 , b ) 120 , c ) 100 , d ) 90 , e ) 110", + "Correct": "b", + "Explanation": "let the total number of boys and girls at the beginning of the year be 3 x and 4 x respectively . now 10 boys and 20 girls are transferred to another school . thus no . of boys and girls students left in the school x are 3 x - 10 and 4 x - 20 respectively . the ratio of these boys and girls students = 4 / 5 thus we have ( 3 x - 10 ) / ( 4 x - 20 ) = 4 / 5 15 x - 50 = 16 x - 80 x = 30 thus total no . of boys at the beginning of the year = 4 ( 30 ) = 120 answer is option b" + }, + { + "Answer": 972, + "Options": "a ) 972 , b ) 990 , c ) 1098 , d ) 1305 , e ) 1405", + "Correct": "a", + "Explanation": "\"total number of digits = ( no . of digits in 1 - digit page nos . + no . of digits in 2 - digit page nos . + no . of digits in 3 - digit page nos . ) = ( 1 x 9 + 2 x 90 + 3 x 261 ) = ( 9 + 180 + 783 ) = 972 . answer : a\"" + }, + { + "Answer": 877.4, + "Options": "a ) 347.4 , b ) 987.4 , c ) 877.4 , d ) 637.4 , e ) 667.4", + "Correct": "c", + "Explanation": "\"c $ 877.40 let the costs of each kg of mangos and each kg of rice be $ a and $ r respectively . 10 a = 24 r and 6 * 20.50 = 2 r a = 12 / 5 r and r = 61.5 a = 147.6 required total cost = 4 * 147.6 + 3 * 61.5 + 5 * 20.5 = 590.4 + 184.5 + 102.5 = $ 877.40\"" + }, + { + "Answer": 0.4, + "Options": "a ) 1 / 9 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 2 / 5", + "Correct": "e", + "Explanation": "\"n ( n + 1 ) to be divisible by 3 either n or n + 1 must be a multiples of 3 . in each following group of numbers : { 1 , 2 , 3 , 4 , 5 } , { 6 , 7 , 8 , 9 , 10 } , . . . , { 96 , 97 , 98 , 99,100 } there is exactly 1 numbers out of 5 satisfying the above condition . for example in { 1 , 2 , 3 , 4 , 5 } n can be : 4 or 5 . thus , the overall probability is 2 / 5 . answer : d .\"" + }, + { + "Answer": 25, + "Options": "a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 25", + "Correct": "e", + "Explanation": "\"check two extreme cases : jane = 18 , child = 9 , years ago = 34 - 18 = 16 - - > child ' s age now = 9 + 16 = 25 ; jane = 22 , child = 11 , years ago = 34 - 22 = 12 - - > child ' s age now = 11 + 12 = 23 . answer : e .\"" + }, + { + "Answer": 5, + "Options": "a ) 2.8 % , b ) 3.6 % , c ) 4.4 % , d ) 5 % , e ) 6.0 %", + "Correct": "d", + "Explanation": "let amount spent by jill = 100 clothing = 50 , food = 20 , others = 30 tax on clothing = 2 tax on others = 3 percentage = 5 / 100 = 5 % answer : d" + }, + { + "Answer": 9, + "Options": "a ) 9 , b ) 8 , c ) 7 , d ) 10 , e ) 11", + "Correct": "a", + "Explanation": "let p equal the number of each sized jar then 16 p + 28 p + 40 p = 252 84 p = 252 p = 3 therefore , the total number of jars of peanut butter jeff has = 3 p = 9 answer : a" + }, + { + "Answer": 5, + "Options": "a ) 2.3 , b ) 2.6 , c ) 3.6 , d ) 4.5 , e ) 5", + "Correct": "e", + "Explanation": "\"sum of the remaining two numbers = ( 2.5 * 6 ) - [ ( 1.1 * 2 ) + ( 1.4 * 2 ) ] = 15 - ( 2.2 + 2.8 ) = 15 - 5 = 10 required average = ( 10 / 2 ) = 5 answer : e\"" + }, + { + "Answer": 0.6666666666666667, + "Options": "a ) 1 / 4 , b ) 1 / 2 , c ) 2 / 3 , d ) 1 , e ) 5 / 4", + "Correct": "c", + "Explanation": "min value of a / b will be when b is highest and a is lowest - - - > a = 10 and b = 30 so , a / b = 1 / 3 max value of a / b will be when b is lowest and a is highest - - - > a = 20 and b = 20 so , a / b = 1 range is 1 - ( 1 / 3 ) = 2 / 3 . answer should be c" + }, + { + "Answer": 72, + "Options": "a ) 95 , b ) 90 , c ) 85 , d ) 78 , e ) 72", + "Correct": "e", + "Explanation": "\"let x be the number of students in the school . 0.18 x students went to the trip and took more than 100 $ . they compose ( 100 - 75 ) = 25 % of all students who went to the trip . therefore the toal of 0.18 x / 0.25 = 0.72 x students went to the camping which is 72 % . the answer is e\"" + }, + { + "Answer": 195, + "Options": "a ) $ 28 , b ) $ 82 , c ) $ 110 , d ) $ 138 , e ) $ 195", + "Correct": "e", + "Explanation": "by the question , the equation would be 150 p - 85 * 150 - 16500 = 0 p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component . solving the equation , we get p = $ 195 . answer e for me ." + }, + { + "Answer": 42, + "Options": "a ) 10 , b ) 12 , c ) 42 , d ) 20 , e ) 22", + "Correct": "c", + "Explanation": "\"let original strength = y then , 50 y + 12 x 32 = ( y + 12 ) x 46 \u00e2 \u2021 \u2019 50 y + 384 = 46 y + 552 \u00e2 \u2021 \u2019 4 y = 168 \u00e2 \u02c6 \u00b4 y = 42 c\"" + }, + { + "Answer": 750, + "Options": "a ) $ 300 , b ) $ 400 , c ) $ 450 , d ) $ 625 , e ) $ 750", + "Correct": "e", + "Explanation": "if anne had $ 150 less , katherine would have three times more than anne . make this statement into an equation and simplify : 3 ( a \u2013 150 ) = k 3 a \u2013 450 = k and if katherine had twice as much , she would have three times more than anne : 2 k = 3 a substitute 3 a \u2013 450 for k into the last equation and solve for a 2 ( 3 a \u2013 450 ) = 3 a 6 a \u2013 900 = 3 a \u2013 900 = \u2013 3 a 300 = a now substitute 300 for a into the same equation and solve for k : 2 k = 3 ( 300 ) 2 k = 900 k = 450 thus , together anne and katherine have 300 + 450 = 750 correct answer e ) $ 750" + }, + { + "Answer": 0.15625, + "Options": "a ) 5 / 32 , b ) 5 / 27 , c ) 1 / 27 , d ) 1 / 32 , e ) 27 / 32", + "Correct": "a", + "Explanation": "\"we have the ratio of a \u2019 s speed and b \u2019 s speed . this means , we know how much distance a covers compared with b in the same time . this is what the beginning of the race will look like : ( start ) a _________ b ______________________________ if a covers 32 meters , b covers 27 meters in that time . so if the race is 32 meters long , when a reaches the finish line , b would be 5 meters behind him . if we want the race to end in a dead heat , we want b to be at the finish line too at the same time . this means b should get a head start of 5 meters so that he doesn \u2019 t need to cover that . in that case , the time required by a ( to cover 32 meters ) would be the same as the time required by b ( to cover 27 meters ) to reach the finish line . so b should get a head start of 5 / 32 th of the race . answer ( a )\"" + }, + { + "Answer": 44, + "Options": "a ) 42 , b ) 43 , c ) 44 , d ) 45 , e ) 46", + "Correct": "c", + "Explanation": "\"let \u2018 x \u2019 be the average score after 12 th innings \u21d2 12 x = 11 \u00d7 ( x \u2013 1 ) + 55 \u2234 x = 44 answer c\"" + }, + { + "Answer": 2520, + "Options": "a ) 1209 , b ) 1324 , c ) 1245 , d ) 1300 , e ) 2535", + "Correct": "e", + "Explanation": "\"let the smaller number be x . then larger number = ( x + 2415 ) . x + 2415 = 21 x + 15 20 x = 2400 x = 120 large number = 120 + 2415 = 2535 answer : e\"" + }, + { + "Answer": 90, + "Options": "a ) a ) 36 , b ) b ) 90 , c ) c ) 40 , d ) d ) 42 , e ) e ) 44", + "Correct": "b", + "Explanation": "\"let b be the number of blue hats and let g be the number of green hats . b + g = 85 . b = 85 - g . 6 b + 7 g = 600 . 6 ( 85 - g ) + 7 g = 600 . 510 - 6 g + 7 g = 600 . g = 600 - 510 = 90 . the answer is b .\"" + }, + { + "Answer": 2499, + "Options": "a ) rs . 2500 , b ) rs . 2300 , c ) rs . 2200 , d ) rs . 1400 , e ) none of these", + "Correct": "a", + "Explanation": "\"let the required price be x more apples , more price ( direct proportion ) hence we can write as apples 357 : ( 49 \u00d7 12 ) } : : 1517.25 : x \u21d2 357 x = ( 49 \u00d7 12 ) \u00d7 1517.25 \u21d2 x = ( 49 \u00d7 12 \u00d7 1517.25 ) / 357 = ( 7 \u00d7 12 \u00d7 1517.25 ) / 51 = ( 7 \u00d7 4 \u00d7 1517.25 ) / 17 = 7 \u00d7 4 \u00d7 89.25 \u2248 2500 . answer a\"" + }, + { + "Answer": 200, + "Options": "a ) 82 m , b ) 150 m , c ) 172 m , d ) 200 m , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : the relative speed of train is 46 - 36 = 10 km / hr = ( 10 x 5 ) / 18 = 25 / 9 m / s 10 \u00d7 518 = 259 m / s in 144 secs the total distance traveled is 144 x 25 / 9 = 400 m . therefore the length of each train is = 400 / 2 = 200 m . answer d\"" + }, + { + "Answer": 90, + "Options": "a ) $ 80 , b ) $ 90 , c ) $ 100 , d ) $ 110 , e ) $ 120", + "Correct": "b", + "Explanation": "\"the difference in the two prices is $ 2.75 - $ 1.25 = $ 1.50 for each color copy . each color copy will cost an extra $ 1.50 at print shop y . 60 * $ 1.50 = $ 90 the answer is b .\"" + }, + { + "Answer": 33.333333333333336, + "Options": "a ) 50 km , b ) 56 km , c ) 60 km , d ) 70 km , e ) 33.3 km", + "Correct": "e", + "Explanation": "\"let the actual distance travelled be x km . x / 10 = ( x + 20 ) / 16 16 x = 10 x + 200 6 x = 200 x = 33.3 km . answer : e\"" + }, + { + "Answer": 32, + "Options": "a ) 28 , b ) 32 , c ) 36 , d ) 40 , e ) 44", + "Correct": "b", + "Explanation": "\"the point of intersection is ( - 8 , - 8 ) . the triangle has a base of length 8 and a height of 8 . area = ( 1 / 2 ) * base * height = ( 1 / 2 ) * 8 * 8 = 32 the answer is b .\"" + }, + { + "Answer": 177.77777777777783, + "Options": "a ) $ 200 , b ) $ 177.78 , c ) $ 100 , d ) $ 277.78 , e ) $ 377.78", + "Correct": "b", + "Explanation": "\"let us suppose there are 100 people . 40 % of them donated $ 16000 ( 400 * 40 ) $ 16000 is 60 % of total amount . so total amount = 16000 * 100 / 60 remaining amount is 40 % of total amount . 40 % of total amount = 16000 * ( 100 / 60 ) * ( 40 / 100 ) = 32000 / 3 this amount has to be divided by 60 ( remaining people are 60 ) so per head amount is 32000 / 3 / 60 = 32000 / 180 = 1600 / 9 = $ 177.78 ; answer : b\"" + }, + { + "Answer": 78, + "Options": "a ) 78 , b ) 65 , c ) 58 , d ) 62 , e ) 48", + "Correct": "a", + "Explanation": "\"6 th number = sum of 1 st 6 no . s + sum of last 6 no . s - sum of 11 no . s answer = 6 * 58 + 6 * 65 - 11 * 60 = 78 answer is a\"" + }, + { + "Answer": 3.5999999999999996, + "Options": "a ) $ 3.15 , b ) $ 4.45 , c ) $ 3.60 , d ) $ 5.05 , e ) $ 5.40", + "Correct": "c", + "Explanation": "\"let the fixed charge of jim \u2019 s taxi service = 2.25 $ and charge per 2 / 5 mile ( . 4 mile ) = . 15 $ total charge for a trip of 3.6 miles = 2.25 + ( 3.6 / . 4 ) * . 15 = 2.25 + 9 * . 15 = 3.6 $ answer c\"" + }, + { + "Answer": 30, + "Options": "a ) 22 , b ) 30 , c ) 99 , d ) 38 , e ) 27", + "Correct": "b", + "Explanation": "\"total age increased = ( 8 * 2 ) years = 16 years . sum of ages of two new men = ( 21 + 23 + 16 ) years = 60 years average age of two new men = ( 60 / 2 ) years = 30 years . answer : b\"" + }, + { + "Answer": 0.6666666666666666, + "Options": "a ) 1 / 9 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6", + "Correct": "d", + "Explanation": "n ( n + 2 ) to be divisible by 3 either n or n + 2 must be a multiples of 3 . in each following group of numbers : { 1 , 2 , 3 } , { 4 , 5 , 6 } , { 7 , 8 , 9 } , . . . , { 97 , 98 , 99 } there are exactly 2 numbers out of 3 satisfying the above condition . for example in { 1 , 2 , 3 } n can be : 1 , or 3 . thus , the overall probability is 2 / 3 . answer : d ." + }, + { + "Answer": 27, + "Options": "a ) 26 , b ) 22 , c ) 25 , d ) 27 , e ) 29", + "Correct": "d", + "Explanation": "\"( 4 ) ^ 11 x ( 7 ) ^ 3 x ( 11 ) ^ 2 = ( 2 x 2 ) ^ 11 x ( 7 ) ^ 3 x ( 11 ) ^ 2 = 2 ^ 11 x 2 ^ 11 x 7 ^ 3 x 11 ^ 2 = 2 ^ 22 x 7 ^ 3 x 11 ^ 2 total number of prime factors = ( 22 + 3 + 2 ) = 27 . answer is d .\"" + }, + { + "Answer": 0.30000000000000004, + "Options": "a ) 0.05 , b ) 0.0625 , c ) 0.2 , d ) 0.3 , e ) 0.6", + "Correct": "d", + "Explanation": "\"index for females = ( 20 - 7 ) / 20 = 13 / 20 = 0.65 index for males = ( 20 - 13 / 20 = 7 / 20 = 0.35 index for females exceeds males by 0.65 - 0.35 = 0.3 answer : d\"" + }, + { + "Answer": 15, + "Options": "a ) a ) 10 , b ) b ) 12 , c ) c ) 15 , d ) d ) 20 , e ) e ) 25", + "Correct": "c", + "Explanation": "the difference between the highest and lowest salaries is $ 100000 . so there are at least 2 people - say one with salary 0 and the other with 100 k . no salary will be outside this range . median = 50 k more than lowest . so median is right in the center of lowest and highest since lowest and highest differ by 100 k . in our example , median = 50 k . since there are more than 2 people , there would probably be a person at 50 k . mean = 20 k more than median so in our example , mean salary = 70 k on the number line , 0 . . . . . . . . 50 k ( median ) . . . . . . . . 100 k mean = 70 k so there must be people more toward 100 k to bring the mean up to 70 k . since we want to add minimum people , we will add people at 100 k to quickly make up the right side deficit . 0 and 50 k are ( 70 k + 20 k ) = 90 k away from 70 k . 100 k is 30 k away from 70 k . to bring the mean to 70 k , we will add two people at 100 k each to get : 0 . . . . 50 k . . . . . 100 k , 100 k , 100 k but when we add more people to the right of 70 k , the median will shift to the right . we need to keep the median at 50 k . so every time we add people to the right of 70 k , we need to add people at 50 k too to balance the median . 50 k is 20 k less than 70 k while 100 k is 30 k more than 70 k . to keep the mean same , we need to add 2 people at 100 k for every 3 people we add at 50 k . so if we add 3 people at 50 k and 2 people at 100 k , we get : 0 , . . . 50 k , 50 k , 50 k , 50 k , . . . 100 k , 100 k , 100 k , 100 k , 100 k the median is not at 50 k yet . add another 3 people at 50 k and another 2 at 100 k to get 0 , 50 k , 50 k , 50 k , 50 k , 50 k , 50 k , 50 k , 100 k , 100 k , 100 k , 100 k , 100 k , 100 k , 100 k now the median is 50 k and mean is 70 k . total number of people is 15 . answer ( c )" + }, + { + "Answer": 71.11111111111111, + "Options": "a ) 71.11 , b ) 71.12 , c ) 71.1 , d ) 71.17 , e ) 71.13", + "Correct": "a", + "Explanation": "\"car travels first 160 km at 64 km / hr time taken to travel first 160 km = distancespeed = 16064 car travels next 160 km at 80 km / hr time taken to travel next 160 km = distancespeed = 16080 total distance traveled = 160 + 160 = 2 \u00d7 160 total time taken = 16064 + 16080 average speed = total distance traveledtotal time taken = 2 \u00d7 16016064 + 16080 = 2164 + 180 = 2 \u00d7 64 \u00d7 8080 + 64 = 2 \u00d7 64 \u00d7 80144 = 2 \u00d7 8 \u00d7 8018 = 6409 = 71.11 km / hr answer : a\"" + }, + { + "Answer": 340, + "Options": "a ) $ 200 , b ) $ 220 , c ) $ 280 , d ) $ 300 , e ) $ 340", + "Correct": "e", + "Explanation": "\"total value of the prize = $ 800 number of people = 20 2 / 5 of 800 ( = $ 320 ) should be distributed among 3 / 5 of 20 ( = 12 people ) with each getting $ 20 each . remaining money = 800 - 320 = $ 480 . now in order to ' maximize ' 1 prize , we need to minimise the others and we have been given that each should get $ 20 . thus , minimising the remaining 7 people ( = 20 - 12 - 1 . ' - 1 ' to exclude 1 that needs to be maximised ) = 7 * 20 = 140 . thus the maximum award can be = 480 - 140 = $ 340 , hence e is the correct answer .\"" + }, + { + "Answer": 4, + "Options": "a ) 2 , b ) 4 , c ) 3 , d ) 1 , e ) 0", + "Correct": "b", + "Explanation": "let the numbers be x and y . then , x + y = 42 and xy = 437 x - y = sqrt [ ( x + y ) 2 - 4 xy ] = sqrt [ ( 42 ) 2 - 4 x 437 ] = sqrt [ 1764 \u2013 1748 ] = sqrt [ 16 ] = 4 . required difference = 4 . answer is b ." + }, + { + "Answer": 310, + "Options": "a ) 300 , b ) 310 , c ) 320 , d ) 330 , e ) 340", + "Correct": "b", + "Explanation": "for breakfast , cara ate 240 / 6 = 40 grams . for lunch , cara ate 240 / 8 = 30 grams . for dinner , cara ate 240 grams . the total is 40 + 30 + 240 = 310 grams . the answer is b ." + }, + { + "Answer": 2, + "Options": "a ) 10 , b ) 5 , c ) 2 , d ) 3 , e ) 1", + "Correct": "c", + "Explanation": "rule of subtraction : p ( a ) = 1 - p ( a ' ) rule of multiplication : p ( a \u2229 b ) = p ( a ) p ( b ) the probability that the quarterback throws a completed pass at least once in 2 throws is 1 - ( 7 / 10 ) ^ 2 = 1 - 49 / 100 = 51 / 100 > 50 % answer : c" + }, + { + "Answer": 700, + "Options": "a ) 225 , b ) 275 , c ) 325 , d ) 350 , e ) 700", + "Correct": "e", + "Explanation": "this problem is a general word translation . we first define variables and then set up equations . we can define the following variables : f = the weight of the first lift s = the weight of the second lift we are given that the total weight of joe ' s two lifts was 1800 pounds . we sum the two variables to obtain : f + s = 1800 we are also given that twice the weight of his first lift was 300 pounds more than the weight of his second lift . we express this as : 2 f = 300 + s 2 f \u2013 300 = s we can now plug in ( 2 f \u2013 300 ) for s into the first equation , so we have : f + 2 f \u2013 300 = 1800 3 f = 2100 f = 700 answer is e ." + }, + { + "Answer": 7, + "Options": "a ) a ) 4 , b ) b ) 3 , c ) c ) 2 , d ) d ) 5 , e ) e ) 7", + "Correct": "e", + "Explanation": "\"explanation : 729 = 38 x 19 + r 729 = 722 + r r = 729 - 722 = 7 answer : option e\"" + }, + { + "Answer": 14, + "Options": "a ) a ) 23 , b ) b ) 21 , c ) c ) 52 , d ) d ) 56 , e ) e ) 14", + "Correct": "e", + "Explanation": "\"let the total number of workers be x . then , 9000 x = ( 12000 * 7 ) + 6000 ( x - 7 ) = > 3000 x = 42000 = x = 14 . answer : e\"" + }, + { + "Answer": 78, + "Options": "a ) a ) 70 , b ) b ) 76 , c ) c ) 78 , d ) d ) 80 , e ) e ) 88", + "Correct": "c", + "Explanation": "explanation : average after 11 innings should be 38 so , required score = ( 11 * 38 ) - ( 10 * 34 ) = 418 - 340 = 78 answer : option c" + }, + { + "Answer": 4, + "Options": "a ) 4 , b ) 3 , c ) 2 , d ) 0 , e ) 5", + "Correct": "a", + "Explanation": "\"1021 \u00e3 \u00b7 25 = 40 with remainder = 21 21 + 4 = 25 . hence 4 should be added to 1021 so that the sum will be divisible by 25 answer : option a\"" + }, + { + "Answer": 272, + "Options": "a ) 154 , b ) 184 , c ) 240 , d ) 272 , e ) 306", + "Correct": "d", + "Explanation": "\"2 * 17 c 2 = 2 * 136 = 272 the answer is d .\"" + }, + { + "Answer": 12, + "Options": "a ) 16 , b ) 14 , c ) 12 , d ) 18 , e ) 21", + "Correct": "c", + "Explanation": "( x ^ n + 1 ) will be divisible by ( x + 1 ) only when n is odd ; ( 13 ^ 13 + 1 ) will be divisible by ( 13 + 1 ) ; ( 13 ^ 13 + 1 ) + 12 when divided by 14 will give 12 as remainder . correct option : c" + }, + { + "Answer": 175, + "Options": "a ) 76 , b ) 101 , c ) 126 , d ) 151 , e ) 176", + "Correct": "e", + "Explanation": "we ' re asked to find the least number that gives us a remainder of 1 when divided by 25 and gives us a remainder of 1 when divided by 7 . you might notice , rather quickly , that all of the answers gives us a remainder when divided by 25 . . . 76 = 75 + 1 101 = 100 + 1 126 = 125 + 1 151 = 150 + 1 176 = 175 + 1 so the real question is ` ` which of these 5 is the least number that has a remainder of 1 when divided by 7 ? ' ' from here , you can just do the ` ` brute force ' ' math : a : 76 / 7 = 10 r 6 not a match b : 101 / 7 = 14 r 3 not a match c : 126 / 7 = 18 r 0 not a match d : 151 / 7 = 21 r 4 not a match none of these numbers ` ` fits ' ' the description , so the answer must be e . e : 176 / 7 = 25 r 1 ; answer : e" + }, + { + "Answer": 56, + "Options": "a ) 56 hours , b ) 28 hours , c ) 55 hours , d ) 66 hours , e ) 47 hours", + "Correct": "a", + "Explanation": "1 / a + 1 / b + 1 / c = 1 / 16 ( given ) also given that a = 2 b and b = 2 c = > 1 / 2 b + 1 / b + 2 / b = 1 / 16 = > ( 1 + 2 + 4 ) / 2 b = 1 / 16 = > 2 b / 7 = 16 = > b = 56 hours . answer : a" + }, + { + "Answer": 11.76470588235294, + "Options": "a ) 25 % , b ) 22.2 % , c ) 20 % , d ) 12.5 % , e ) 11.7 %", + "Correct": "e", + "Explanation": "\"welcome , just post the question and the choices let ' s see , the way i did it was 1 / 6 are clerical out of 3600 so 600 are clerical 600 reduced by 1 / 3 is 600 * 1 / 3 so it reduced 200 people , so there is 400 clerical people left but since 200 people left , it also reduced from the total of 3600 so there are 3400 people total since 400 clerical left / 3400 people total you get ( a ) 11.7 % answer : e\"" + }, + { + "Answer": 5, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "c", + "Explanation": "solution least number of 6 digital is 100000 . l . c . m . of 4 , 610 and 15 = 60 . on dividing 100000 by 60 , the remainder obtained is 40 . so , least number of 6 digits divisible by 4 , 610 and 15 = 100000 + ( 60 - 40 ) = 100020 . so , n = ( 100020 + 2 ) = 100022 . sum of digits in n = ( 1 + 2 + 2 ) = 5 . answer c" + }, + { + "Answer": 63, + "Options": "a ) 35 , b ) 42 , c ) 45 , d ) 49 , e ) 63", + "Correct": "e", + "Explanation": "\"first step will be to break down all the numbers into their prime factors . 105 = 3 * 5 * 7 21 = 7 * 3 25 = 5 * 5 35 = 7 * 5 so , ( 105 ) ^ 3 = 3 * 7 * 5 * 5 * 7 * 5 * b therefore ( 3 * 5 * 7 ) ^ 3 = 3 * 5 ^ 3 * 7 ^ 2 * b therefore , b = 3 ^ 3 * 5 ^ 3 * 7 ^ 3 / 3 * 5 ^ 3 * 7 ^ 2 b = 3 ^ 2 * 7 = 9 * 7 = 63 correct answer e .\"" + }, + { + "Answer": 80, + "Options": "a ) 80 . , b ) 75 , c ) 70 , d ) 65 . , e ) 54 .", + "Correct": "a", + "Explanation": "\"driving at 60 km / h for 20 minutes , distance covered = 60 * 1 / 3 = 20 km driving at 90 km / h for 40 minutes , distance covered = 90 * 2 / 3 = 60 km average speed = total distance / total time = 80 / 1 = 80 km / h answer : a\"" + }, + { + "Answer": 0.5, + "Options": "a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 5 , e ) 5 / 6", + "Correct": "a", + "Explanation": "multiply all terms of the given equation by ( a - 3 ) ( a + 2 ) , simplify and solve ( a - 3 ) ( a + 2 ) [ - 3 / ( a - 3 ) ] = ( a - 3 ) ( a + 2 ) [ 3 / ( a + 2 ) ] - 3 ( a + 2 ) = 3 ( a - 3 ) a = 1 / 2 correct answer a" + }, + { + "Answer": 164.6315789473684, + "Options": "a ) a ) 426 , b ) b ) 526 , c ) c ) 207 , d ) d ) 165 , e ) e ) 297", + "Correct": "d", + "Explanation": "given ratio = 1 / 2 : 2 / 3 : 3 / 4 = 6 : 4 : 9 1 st part = 782 * 4 / 19 = rs . 165 answer : d" + }, + { + "Answer": 17, + "Options": "a ) 12 , b ) 29 , c ) 27 , d ) 17 , e ) 99", + "Correct": "d", + "Explanation": "\"explanation : let the number be x . therefore , 3 ( 2 x + 5 ) = 117 6 x + 15 = 117 6 x = 102 x = 17 answer : d\"" + }, + { + "Answer": 4, + "Options": "a ) a ) 4 , b ) b ) 3 , c ) c ) 2 , d ) d ) 5 , e ) e ) 6", + "Correct": "a", + "Explanation": "\"explanation : 760 = 36 x 21 + r 760 = 756 + r r = 760 - 756 = 4 answer : option a\"" + }, + { + "Answer": 28.57142857142857, + "Options": "a ) 27.5 litres , b ) 26.67 litres , c ) 27.67 litres , d ) 28.57 litres , e ) 26 litres", + "Correct": "d", + "Explanation": "\"working formula . . . initial concentration * initial volume = final concentration * final volume . let x is the part removed from 100 lts . 49 % ( 1 - x / 100 ) ^ 2 = 25 % * 100 % ( 1 - x / 100 ) ^ 2 = 25 / 49 - - - - - - > ( 1 - x / 100 ) ^ 2 = ( 5 / 7 ) ^ 2 100 - x = 500 / 7 x = 28.57 . . . ans d\"" + }, + { + "Answer": 4095, + "Options": "a ) 4096 , b ) 4055 , c ) 4092 , d ) 4085 , e ) 4095", + "Correct": "e", + "Explanation": "whenever the rate of reduction is ' half of the total and half of it ' , the answer is always ( 2 ^ n ) - 1 , where ' n ' is the number of times the process is repeated . here , the process is repeated 12 times . so answer is ( 2 ^ 12 ) - 1 = 4095 answer e" + }, + { + "Answer": 12, + "Options": "a ) 8 , b ) 12 , c ) 12 , d ) 14 , e ) 16", + "Correct": "b", + "Explanation": "let ' s say age of richard is ` ` r ' ' age of david is ` ` d ' ' age of scott is ` ` s ' ' now richard is 6 years older than david , i . e . r = d + 6 david is 8 years older than scott i . e . d = s + 8 if in 8 years , richard will be twice as old as scott i . e . r + 8 = 2 x ( s + 8 ) i . e . r + 8 = 2 s + 16 i . e . r = 2 s + 8 but r = d + 6 = ( s + 8 ) + 6 = s + 14 therefore , 2 s + 8 = s + 14 i . e . s = 6 i . e . r = 20 i . e . d = 14 now , how old was david 2 years ago ? i . e . d - 2 = 14 - 2 = 12 years answer : b" + }, + { + "Answer": 69, + "Options": "a ) 35 , b ) 37 , c ) 42 , d ) 50 , e ) 69", + "Correct": "e", + "Explanation": "the number of liters in each can = hcf of 40 , 144 and 368 = 8 liters . number of cans of maaza = 40 / 8 = 5 number of cans of pepsi = 144 / 8 = 18 number of cans of sprite = 368 / 8 = 46 the total number of cans required = 5 + 18 + 46 = 69 cans . answer : e" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 6 , e ) 12", + "Correct": "c", + "Explanation": "then the wordings of question are misleading . moreover , it ' d also be a bad way to convey x = 4 n , if it really wanted to convey so . from other questions that i have seen , proper wordings could be : if x is three times as large as n or simply , if x is three times n . c" + }, + { + "Answer": 8, + "Options": "a ) 10 , b ) 7 , c ) 6 , d ) 5 , e ) 8", + "Correct": "e", + "Explanation": "\"lcm of 15 = 15 1 / 3 marking are ( table of 5 ) 0 . . . . . . 5 . . . . . . 10 . . . . . 15 ( total = 4 ) 1 / 5 marking are ( table of 3 ) 0 . . . . . . . 3 . . . . . . 6 . . . . . . 9 . . . . . . . . 12 . . . . . . 15 ( total = 6 ) overlapping markings are 0 . . . . . . . . 15 ( total = 2 ) total markings = 4 + 6 - 2 = 8 answer = e\"" + }, + { + "Answer": 66, + "Options": "a ) 86.5 kg , b ) 66.5 kg , c ) 46.5 kg , d ) 65.5 kg , e ) 16.5 kg", + "Correct": "d", + "Explanation": "\"let arun ' s weight be x kg . according to arun , 64 < x < 72 . according to arun ' s brother , 60 < x < 70 . according to arun ' s mother , x < 67 . the values satisfying all the above conditions are 65 and 66 . required average = ( 65 + 66 ) / 2 = 65.5 kg answer : d\"" + }, + { + "Answer": 110, + "Options": "a ) 18 , b ) 36 , c ) 72 , d ) 110 , e ) 108", + "Correct": "d", + "Explanation": "\"let kate charge for x hours , then pat charged for 2 x and mat - for 6 x . so , 2 x + 6 x + x = 198 - total hours charged for , x = 22 . mat charged 6 x - x or 5 x for more hours than kate , or for 110 hours . d is correct\"" + }, + { + "Answer": 69760, + "Options": "a ) 39760 , b ) 49760 , c ) 59760 , d ) 69760 , e ) 70000", + "Correct": "d", + "Explanation": "zip codes with 5 digits ( all five digits can be repeated ) : 10 ^ 5 = 100,000 zip codes with no digit being repeated : 10 * 9 * 8 * 7 * 6 = 30,240 zip codes with at least one digit being repeated : 100,000 - 30,240 = 69,760 = 69760 ans : d" + }, + { + "Answer": 24, + "Options": "a ) 22 , b ) 24 , c ) 28 , d ) 32 , e ) 44", + "Correct": "b", + "Explanation": "\"g ( e ) = 4 ^ 11 = 2 ^ 22 . so we have to find a product with atleast 22 2 ' s in it . in option 1 22 the total no of 2 ' s = [ 22 / 2 ] + [ 22 / 4 ] + [ 22 / 8 ] + [ 22 / 16 ] = 11 + 5 + 2 + 1 = 19 in option 2 24 the total no of 2 ' s = [ 24 / 2 ] + [ 24 / 4 ] + [ 24 / 8 ] + [ 24 / 16 ] = 12 + 6 + 3 + 1 = 22 . hence b\"" + }, + { + "Answer": 95, + "Options": "a ) 95 , b ) 64 , c ) 1012 , d ) 9 , e ) 0", + "Correct": "a", + "Explanation": "the multiplication ( e . g . 7 ^ 8 ) and division ( e . g . 6 / 2 ) is done first and then the sum ( e . g . 3 + 12 ) and subtraction ( e . g . 56 - 3 ) , and the answer is 95 , option a ." + }, + { + "Answer": 59, + "Options": "a ) $ 24 , b ) $ 27 , c ) $ 59 , d ) $ 75 , e ) $ 35", + "Correct": "c", + "Explanation": "step 1 : find the cost of the loaves of bread . 3 \u00d7 $ 3 = $ 9 step 2 : find the cost of the orange juice . 3 \u00d7 $ 6 = $ 18 step 3 : find the total cost of the groceries . $ 9 + $ 18 = $ 27 step 4 : find the amount of money left . $ 86 \u2013 $ 27 = $ 59 erik has $ 59 left . answer is c ." + }, + { + "Answer": 24.75, + "Options": "a ) 22 % , b ) 23 % , c ) 24.5 % , d ) 24.75 % , e ) 30 %", + "Correct": "d", + "Explanation": "\"we have a 3 litre solution containing 33 % of alcohol in the water . = > quantity of alcohol in the solution = 3 \u00e3 \u2014 33 / 100 now 1 litre of water is added to the solution . = > total quantity of the new solution = 3 + 1 = 4 percentage of alcohol in the new solution = 3 \u00e3 \u2014 33 / 100 4 \u00e3 \u2014 100 = 3 \u00e3 \u2014 331004 \u00e3 \u2014 100 = 3 \u00e3 \u2014 8.25 / 100 = 24.75 % d\"" + }, + { + "Answer": 0.25, + "Options": "a ) 1 / 17 , b ) 3 / 17 , c ) 1 / 10 , d ) 5 / 20 , e ) 3 / 10", + "Correct": "d", + "Explanation": "\"we have the ratio of a \u2019 s speed and b \u2019 s speed . this means , we know how much distance a covers compared with b in the same time . this is what the beginning of the race will look like : ( start ) a _________ b ______________________________ if a covers 20 meters , b covers 15 meters in that time . so if the race is 20 meters long , when a reaches the finish line , b would be 5 meters behind him . if we want the race to end in a dead heat , we want b to be at the finish line too at the same time . this means b should get a head start of 5 meters so that he doesn \u2019 t need to cover that . in that case , the time required by a ( to cover 20 meters ) would be the same as the time required by b ( to cover 15 meters ) to reach the finish line . so b should get a head start of 5 / 20 th of the race . answer ( d )\"" + }, + { + "Answer": 163, + "Options": "a ) 163 , b ) 171 , c ) 177 , d ) 185 , e ) 193", + "Correct": "a", + "Explanation": "\"let n - 1 = 2 a . 2 + 4 + . . . + 2 a = 2 * ( 1 + 2 + . . . + a ) = 2 * ( a ) ( a + 1 ) / 2 = ( a ) ( a + 1 ) = 81 * 82 then a = 81 and n = 163 . the answer is a .\"" + }, + { + "Answer": 4.8, + "Options": "a ) $ 4.50 , b ) $ 6.00 , c ) $ 4.00 , d ) $ 5.50 , e ) $ 4.80", + "Correct": "e", + "Explanation": "4 baskets - > total cost = 4 * avg cost = 4 * 4 = 16 fifth basket cost = 8 total cost for 5 baskets = 16 + 8 = 24 am = 24 / 5 = 4.80 answer : e" + }, + { + "Answer": 4, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "e", + "Explanation": "n = 5 x + 3 , for some integer x n ^ 2 = ( 5 x + 3 ) ^ 2 = 5 y + 9 , for some integer y when we divide this by 5 , the remainder is 4 . the answer is e ." + }, + { + "Answer": 1, + "Options": "a ) 0 , b ) 1 , c ) 35 , d ) 120 , e ) 245", + "Correct": "b", + "Explanation": "\"8 + 2 + 3 + 4 + 3 + 5 = 25 , so this number is not divisible by 3 and thus not divisible by 15 . therefore , k = 0 5 ^ k - k ^ 5 = 1 - 0 = 1 the answer is b .\"" + }, + { + "Answer": 5, + "Options": "a ) 0 . , b ) 1 . , c ) 2 . , d ) 4 . , e ) 5 .", + "Correct": "e", + "Explanation": "\"the number of members is 5 k + 3 = 6 j + 3 the only number in this range which satisfies this is 33 . 33 / 7 = 4 ( 7 ) + 5 the answer is e .\"" + }, + { + "Answer": 160, + "Options": "a ) 160 , b ) 163 , c ) 164 , d ) 165 , e ) 166", + "Correct": "a", + "Explanation": "explanation : let the number = x , then , x - ( 3 / 5 ) x = 64 , = > ( 2 / 5 ) x = 64 = > 2 x = 64 * 5 , = > x = 160 answer : option a" + }, + { + "Answer": 156, + "Options": "a ) 12 , b ) 39 , c ) 54 , d ) 64 , e ) 156", + "Correct": "e", + "Explanation": "required mean proportion is = ( root of 234 ) ( root of 104 ) = root of ( 13 * 9 * 2 * 13 * 18 ) = ( 13 * 3 * 4 ) = 156 answer : e" + }, + { + "Answer": 38.58974358974359, + "Options": "a ) 34 , b ) 43 , c ) 40 , d ) 38.6 , e ) 29", + "Correct": "d", + "Explanation": "\"solution : average speed = 2 xy / x + y = 2 * 43 * 35 / 43 + 35 = 38.6 answer : d\"" + }, + { + "Answer": 0.047619047619047616, + "Options": "a ) 1 / 35 , b ) 3 / 35 , c ) 1 / 21 , d ) 2 / 35 , e ) none", + "Correct": "c", + "Explanation": "\"answer we have , m x n = 6 x 210 = 1260 \u00e2 \u02c6 \u00b4 1 / m + 1 / n = ( m + n ) / mn = 60 / 1260 = 1 / 21 correct option : c\"" + }, + { + "Answer": 60, + "Options": "a ) 53 % , b ) 58 % , c ) 60 % , d ) 64 % , e ) 75 %", + "Correct": "c", + "Explanation": "\"last year revenue = 100 ( assume ) ; this year revenue = 75 ; projected revenue = 125 . actual / projected * 100 = 75 / 125 * 100 = 60 % . answer : c .\"" + }, + { + "Answer": 2.666666666666667, + "Options": "a ) 4 / 3 , b ) 5 / 3 , c ) 7 / 3 , d ) 8 / 3 , e ) 10 / 3", + "Correct": "d", + "Explanation": "an alternate to the alligation method is the more direct / algebraic method : let x be the amount of petrol to be added . new total amount of water = 4 + x total amount of diesel = 4 new total = 4 + 4 + x = 8 + x final ratio required ( for petrol ) = 5 / ( 5 + 3 ) = 5 / 8 thus , ( 4 + x ) / ( 8 + x ) = 5 / 8 - - > solving for x you get x = 8 / 3 . d is thus the correct answer ." + }, + { + "Answer": 4, + "Options": "a ) 10 , b ) 15 , c ) 6 , d ) 4 , e ) 5", + "Correct": "d", + "Explanation": "x ^ 2 + y ^ 2 should make you think of these formulas : ( x + y ) ( x + y ) = x ^ 2 + y ^ 2 + 2 xy we already know ( x + y ) = - 4 and x * y = 6 ( x + y ) ( x + y ) = ( - 4 ) ( - 4 ) = x ^ 2 + y ^ 2 + 2 * ( 6 ) x ^ 2 + y ^ 2 = 16 - 12 = 4 answer : d" + }, + { + "Answer": 3000, + "Options": "a ) 1266 , b ) 3000 , c ) 2866 , d ) 2999 , e ) 2678", + "Correct": "b", + "Explanation": "\"4 - - - 2000 5 - - - ? = > 3000 answer : b :\"" + }, + { + "Answer": 15.759999999999991, + "Options": "a ) 16.16 % , b ) 15.76 % , c ) 14.14 % , d ) 13.13 % , e ) 12.12 %", + "Correct": "b", + "Explanation": "\"( 100 % + 4 % ) * ( 100 % - 19 % ) = 1.04 * . 81 = 0.8424 . 1 - 0.8424 = 15.76 % lost = - 15.76 % the answer is b the organization has lost 15.76 % of its total volunteers from fall to spring .\"" + }, + { + "Answer": 2.507936507936508, + "Options": "a ) 195 / 63 , b ) 2.5 , c ) 155 / 63 , d ) 125 / 63 , e ) 185 / 63", + "Correct": "b", + "Explanation": "\"( \u221a 1.21 ) / ( \u221a 0.81 ) + ( \u221a 0.81 ) / ( \u221a 0.49 ) 11 / 9 + 9 / 7 = > 2.50 answer is b\"" + }, + { + "Answer": 80.00000000000001, + "Options": "a ) 40 , b ) 52 , c ) 68 , d ) 80 , e ) 98", + "Correct": "d", + "Explanation": "\"let the no of matches played more = x so , ( 120 + x ) * 52 / 100 = 24 + x by solving we get x = 80 answer : d\"" + }, + { + "Answer": 68.2, + "Options": "a ) 67 , b ) 68 , c ) 87 , d ) 26 , e ) 75", + "Correct": "b", + "Explanation": "\"average = ( 72 + 45 + 72 + 77 + 75 ) / 5 = 341 / 5 = 68 . answer : b\"" + }, + { + "Answer": 1, + "Options": "a ) 9 , b ) 1 , c ) 2 , d ) 18 , e ) 19", + "Correct": "b", + "Explanation": "\"2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 18 - 16 = 2 ab = 1 . answer : b\"" + }, + { + "Answer": 40, + "Options": "a ) 19 , b ) 29 , c ) 40 , d ) 49 , e ) 59", + "Correct": "c", + "Explanation": "\"let the average after 17 th inning = x then average after 16 th inning = ( x - 3 ) therefore 16 ( x - 3 ) + 88 = 17 x therefore x = 40 answer : c\"" + }, + { + "Answer": 90, + "Options": "a ) 90 % , b ) 30 % , c ) 40 % , d ) 70 % , e ) 80 %", + "Correct": "a", + "Explanation": "\"the is always the difference between our starting and ending points . in this case , it \u2019 s 100 \u2013 10 = 90 . the \u201c original \u201d is our starting point ; in this case , it \u2019 s 100 . ( 90 / 100 ) * 100 = ( 0.9 ) * 100 = 90 % . a\"" + }, + { + "Answer": 1200, + "Options": "a ) 1300 , b ) 1100 , c ) 1000 , d ) 1200 , e ) 800", + "Correct": "d", + "Explanation": "\"let the price of a pant and a t - shirt be rs . x and rs . y respectively . then , 3 x + 6 y = 2250 . . . . ( i ) and x + 12 y = 2250 . . . . ( ii ) divide equation ( i ) by 3 , we get the below equation . = x + 2 y = 750 . - - - ( iii ) now subtract ( iii ) from ( ii ) x + 12 y = 2250 ( - ) x + 2 y = 750 - - - - - - - - - - - - - - - - 10 y = 1500 - - - - - - - - - - - - - - - - y = 150 cost of 8 t - shirts = 8 * 150 = 1200 answer : d\"" + }, + { + "Answer": 210, + "Options": "a ) 100 , b ) 210 , c ) 300 , d ) 400 , e ) 500", + "Correct": "b", + "Explanation": "\"since 190 students answered yes only for subject m , then the remaining 310 students who answered yes for subject m , also answered yes for subject r . so , 310 students answered yes for both subjects . if 310 students answered yes for both subjects , then 400 - 310 = 90 students answered yes only for subject r . so , we have that : 200 students answered yes only for subject m ; 90 students answered yes only for subject r ; 300 students answered yes for both subjects ; therefore 800 - ( 200 + 90 + 300 ) = 210 students did not answer yes for either subject . answer : b .\"" + }, + { + "Answer": 1, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "b", + "Explanation": "when we solve any of these equations : 28 + 3 ( z = 4 ) or 56 + 3 ( z = 8 ) we end up with numbers to which we have to subtract 1 to end up with a number that is exactly divisible by 2 . this is why we know that every result we get is going to have 1 as a remainder . hence answer is b ." + }, + { + "Answer": 11, + "Options": "a ) 16 , b ) 12 , c ) 11 , d ) 20 , e ) 10", + "Correct": "c", + "Explanation": "\"( a + b ) - ( b - c ) = 11 a - c = 11 answer is c\"" + }, + { + "Answer": 0.23255813953488372, + "Options": "a ) 0.23255 , b ) 0.14544 , c ) 0.25632 , d ) 0.35466 , e ) 0.63435", + "Correct": "a", + "Explanation": "total land of sukhiya = \\ inline \\ frac { 480 x } { 0.6 } = 800 x \\ therefore cultivated land of village = 344000 x \\ therefore required percentage = \\ inline \\ frac { 800 x } { 344000 } \\ times 100 = 0.23255 a" + }, + { + "Answer": 0.2, + "Options": "a ) 0.15 , b ) 0.20 , c ) 0.25 , d ) 0.30 , e ) 0.33", + "Correct": "b", + "Explanation": "the total number of pairs s , b possible is 4 * 5 = 20 . out of these 20 pairs only 4 sum up to 9 : ( 2 , 7 ) ; ( 3 , 6 ) , ( 4 , 5 ) and ( 5 , 4 ) . the probability thus is 4 / 20 = 0.2 . answer : b ." + }, + { + "Answer": 2.9166666666666545, + "Options": "a ) 1.2 , b ) 1.45 , c ) 2.2 , d ) 2.9 , e ) none", + "Correct": "d", + "Explanation": "sol . xz = y \u00b2 \u21d4 ( 10 0.48 ) z ( 100.70 ) 2 ( 10 0.48 z ) = 10 ( 2 \u00d7 0.70 ) = 101.40 \u21d4 0.48 z = 1.40 \u21d4 z = 140 / 48 = 35 / 12 = 2.9 ( approx ) . answer d" + }, + { + "Answer": 21.428571428571427, + "Options": "a ) 20 , b ) 18 , c ) 21.4 , d ) 16 , e ) 10", + "Correct": "c", + "Explanation": "\"step 1 ) took lcm of 20 and 25 . . came as 100 . step 2 ) 100 distance between b to c . . . do 100 / 25 hence 4 gallons used step 3 ) twice distance . . hence 100 * 2 = 200 . . . do as above . . 200 / 20 = 10 gallons used step 4 ) total gallons . . 4 + 10 = 14 gallons step ) total miles = 100 + 200 = 300 miles hence . . average of whole journey = 300 / 14 which comes to 21.4 answer : c\"" + }, + { + "Answer": 23, + "Options": "a ) 20 , b ) 24 , c ) 26 , d ) 23 , e ) 30", + "Correct": "d", + "Explanation": "\"( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 267 + 2 * 131 a + b + c = \u221a 529 = 23 d\"" + }, + { + "Answer": 26, + "Options": "a ) 30 , b ) 26 , c ) 28 , d ) 29 , e ) 45", + "Correct": "b", + "Explanation": "\"explanation : if teacher ' s age is 15 years , there is no change in the average . but teacher has contributed 1 year to all the students along with maintaining his age at 16 . age of teacher = average age of all + total increase in age = 16 + ( 1 x 10 ) = 26 years answer : b\"" + }, + { + "Answer": 3500, + "Options": "a ) 2984 , b ) 2983 , c ) 3500 , d ) 2981 , e ) none of these", + "Correct": "c", + "Explanation": "\"3550 - 50 = 3500 answer : c\"" + }, + { + "Answer": 3, + "Options": "a ) z / 2 , b ) z , c ) 3 z / 2 , d ) 2 z , e ) 3 z", + "Correct": "e", + "Explanation": "\"lets do it by picking up numbers . let arthur carry 2 crumbs per trip , this means amy carries 3 crumbs per trip . also let arthur make 2 trips and so amy makes 4 trips . thus total crumbs carried by arthur ( z ) = 2 x 2 = 4 , total crumbs carried by amy = 3 x 4 = 12 . 12 is 3 times 4 , so e\"" + }, + { + "Answer": 0.42857142857142855, + "Options": "a ) 3 / 7 , b ) 5 / 4 , c ) 5 / 8 , d ) 5 / 9 , e ) 6 / 9", + "Correct": "a", + "Explanation": "\"income = salary ( s ) + tips = s + s * 3 / 4 = s * 7 / 4 tips = s * 3 / 4 fraction of his income came from tips = ( s * 3 / 4 ) / ( s * 7 / 4 ) = 3 / 7 answer : a\"" + }, + { + "Answer": 5, + "Options": "a ) a ) 2 , b ) b ) 3 , c ) c ) 5 , d ) d ) 5 , e ) e ) 6", + "Correct": "c", + "Explanation": "on dividing 509 by 9 , we get remainder = 5 therefore , required number to be subtracted = 5 answer : c" + }, + { + "Answer": 8, + "Options": "a ) 12 , b ) 10 , c ) 9 , d ) 8 , e ) 11", + "Correct": "d", + "Explanation": "the bottom row has x bricks x + x - 1 + x - 2 + x - 3 + x - 4 = 50 5 x - 10 = 50 5 x = 40 x = 8 answer : d" + }, + { + "Answer": 1.75, + "Options": "a ) $ 1.75 , b ) $ 1.85 , c ) $ 2.00 , d ) $ 2.15 , e ) $ 2.30", + "Correct": "a", + "Explanation": "\"this question can be solved with a handful of different algebra approaches ( as has been shown in the various posts ) . since the question asks for the price of the largest pot , and the answers are prices , we can test the answers . we ' re told that there are 6 pots and that each pot costs 25 cents more than the next . the total price of the pots is $ 8.25 . we ' re asked for the price of the largest ( most expensive ) pot . since the total price is $ 8.25 ( a 15 - cent increment ) and the the difference in sequential prices of the pots is 15 cents , the largest pot probably has a price that is a 15 - cent increment . from the answer choices , i would then test answer a first if . . . . the largest pot = $ 1.75 1 1.15 1.3 1.45 1.6 1.75 total = $ 8.25 so this must be the answer . a\"" + }, + { + "Answer": 5, + "Options": "a ) 1 , b ) 2 , c ) 4 , d ) 5 , e ) 7", + "Correct": "d", + "Explanation": "\"d = ( d - r ) / q = ( 23 - 3 ) / 4 = 20 / 4 = 5 d\"" + }, + { + "Answer": 54, + "Options": "a ) 54 , b ) 72 , c ) 96 , d ) 144 , e ) 432", + "Correct": "a", + "Explanation": "plaudia can choose any two of four different candles and any 8 of 9 different flowers for a centerpiece arrangement . 2 candles from 4 candles : 4 c 2 : 6 8 flowers from 9 flowers : 9 c 8 : 9 so total grouping 9 * 6 = 54 . answer is a ." + }, + { + "Answer": 32, + "Options": "a ) 12 % , b ) 26 % , c ) 29 % , d ) 32 % , e ) 60 %", + "Correct": "d", + "Explanation": "\"in the first plot 30 % of 300 seeds germinated , so 0.3 x 300 = 90 seeds germinated . in the second plot , 35 % of 200 seeds germinated , so 0.35 x 200 = 70 seeds germinated . since 90 + 70 = 260 seeds germinated out of a total of 300 + 200 = 500 seeds , the percent of seeds that germinated is ( 160 / 500 ) x 100 % , or 32 % . answer : d .\"" + }, + { + "Answer": 37, + "Options": "a ) 28 , b ) 27 , c ) 12 , d ) 37 , e ) 01", + "Correct": "d", + "Explanation": "\"explanation : 16 x + 85 = 17 ( x + 3 ) x = 34 + 3 = 37 answer : d\"" + }, + { + "Answer": 3600, + "Options": "a ) 2400 , b ) 3600 , c ) 3998 , d ) 2539 , e ) 1930", + "Correct": "b", + "Explanation": "\"b 3600 let the amount with r be $ r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 9000 - r ) = > 3 r = 18000 - 2 r = > 5 r = 18000 = > r = 3600 .\"" + }, + { + "Answer": 16, + "Options": "a ) 16 , b ) 9 , c ) 8 , d ) 11 , e ) 10", + "Correct": "a", + "Explanation": "\"explanation : let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 42 \u21d2 5 x = 40 \u21d2 x = 8 . hence , b ' s age = 2 x = 16 years . answer : a\"" + }, + { + "Answer": 11, + "Options": "a ) 11 , b ) 15 , c ) 20 , d ) 38 , e ) 56", + "Correct": "a", + "Explanation": "product of three numbers = 210 210 = 2 * 3 * 5 * 7 = 5 * 6 * 7 . so , the three numbers are 5 , 6 and 7 . and sum of smallest of these two = 5 + 6 = 11 . answer : option a" + }, + { + "Answer": 80, + "Options": "a ) 38 , b ) 27 , c ) 99 , d ) 17 , e ) 80", + "Correct": "e", + "Explanation": "\"explanation : number of subjects = 6 average of marks in 6 subjects = 75 therefore total marks in 6 subjects = 75 * 6 = 450 now , no . of subjects = 5 total marks in 5 subjects = 74 * 5 = 370 therefore marks in 6 th subject = 450 \u2013 370 = 80 answer : e\"" + }, + { + "Answer": 80, + "Options": "a ) 50 , b ) 40 , c ) 60 , d ) 80 , e ) 70", + "Correct": "d", + "Explanation": "\"we have x + x % of 400 = 400 x + x / 100 * 400 = 400 5 * x = 400 x = 80 answer is d\"" + }, + { + "Answer": 31.000000000000007, + "Options": "a ) 27 % , b ) 29 % , c ) 31 % , d ) 33 % , e ) 35 %", + "Correct": "c", + "Explanation": "\"let x be the amount of money paid for the first purchase . the second time , the customer paid 0.6 ( 1.15 x ) = 0.69 x . the difference is 31 % . the answer is c .\"" + }, + { + "Answer": 0.16666666666666666, + "Options": "a ) 1 / 2 , b ) 2 , c ) 1 / 3 , d ) 3 , e ) 1 / 6", + "Correct": "e", + "Explanation": "\"very easy question . 2 variables and 2 easy equations . xy = 1 - - - > x = 1 / y - ( i ) x / y = 36 - - - > replacing ( i ) here - - - > 1 / ( y ^ 2 ) = 36 - - - > y ^ 2 = 1 / 36 - - - > y = 1 / 6 or - 1 / 6 the question states that x and y are positive integers . therefore , y = 1 / 6 is the answer . answer e .\"" + }, + { + "Answer": 28, + "Options": "a ) 14 m , b ) 24 m , c ) 28 m , d ) 40 m , e ) none of the above", + "Correct": "c", + "Explanation": "distance travel in 1 round = 88000 / 1000 m = 88 m perimeter = 88 m , 2 \u03c0 r = 882 r = [ 88 * 7 / 22 ] = 28 m hence , diameter = 28 m answer c" + }, + { + "Answer": 3, + "Options": "a ) 2 , b ) 3 , c ) 5 , d ) 7 , e ) 8", + "Correct": "b", + "Explanation": "\"on dividing 427398 by 15 we get the remainder 3 , so 3 should be subtracted b\"" + }, + { + "Answer": 79, + "Options": "a ) 77 % , b ) 78 % , c ) 79 % , d ) 80 % , e ) 81 %", + "Correct": "c", + "Explanation": "\"( 15 * 73 + 10 * 88 ) / 25 = 79 % the answer is c .\"" + }, + { + "Answer": 17, + "Options": "a ) 4 % increase , b ) 17 % increase , c ) 10 % decrease , d ) 6 % increase , e ) none of these", + "Correct": "b", + "Explanation": "\"explanation : solution : let the original price be rs . 100 . new final price = 130 % of ( 10 % of 100 ) = rs . 130 / 100 * 90 / 100 * 100 = rs . 117 . . ' . increase = 17 % answer : b\"" + }, + { + "Answer": 13780, + "Options": "a ) 15360 , b ) 13780 , c ) 15060 , d ) 14930 , e ) 16075", + "Correct": "b", + "Explanation": "\"6000 + 10000 - ( 0.12 * 6000 + 0.15 * 10000 ) = 13780 . answer : b .\"" + }, + { + "Answer": 0.375, + "Options": "a ) 1 / 140 , b ) 1 / 180 , c ) 3 / 12 , d ) 3 / 8 , e ) 57 / 120", + "Correct": "d", + "Explanation": "\"required probability = p ( x ) + p ( y ) + p ( z ) ( all the events are mutually exclusive ) . = 1 / 8 + 1 / 12 + 1 / 6 = 3 / 8 answer : d\"" + }, + { + "Answer": 98, + "Options": "a ) a ) 78 , b ) b ) 82 , c ) c ) 98 , d ) d ) 91 , e ) e ) 85", + "Correct": "c", + "Explanation": "\"correct avg marks = 100 + ( 10 - 60 ) / 25 avg = 100 - 2 = 98 answer is c\"" + }, + { + "Answer": 2345, + "Options": "a ) 2345 , b ) 4500 , c ) 5000 , d ) 6000 , e ) 7000", + "Correct": "a", + "Explanation": "2000 + 300 + 40 + 5 = 2345 answer a" + }, + { + "Answer": 43, + "Options": "a ) 36 , b ) 42 , c ) 44 , d ) 43 , e ) none", + "Correct": "d", + "Explanation": "\"17 ( p + 1 ) = 29 ( q + 1 ) - - > ( p + 1 ) / ( q + 1 ) = 28 / 17 - - > the least positive value of p + 1 is 28 , so the least value of p is 27 and the least positive value of q + 1 is 17 , so the least value of q is 16 - - > the least value of p + q is 27 + 16 = 43 . answer : d\"" + }, + { + "Answer": 3, + "Options": "a ) 3 , b ) 5 , c ) 5.6 , d ) 5.7 , e ) 6.5", + "Correct": "a", + "Explanation": "if $ x $ is the number , x / 4 * 12 = 9 = > 3 x = 9 = > x = 3 a" + }, + { + "Answer": 1000, + "Options": "a ) 600 , b ) 700 , c ) 800 , d ) 900 , e ) 1000", + "Correct": "e", + "Explanation": "\"let x be the number of eggs that were laid . ( 3 / 5 ) ( 4 / 5 ) ( 1 / 4 ) x = 120 ( 12 / 100 ) x = 120 x = 1000 the answer is e .\"" + }, + { + "Answer": 19, + "Options": "a ) 21 , b ) 29 , c ) 19 , d ) 14 , e ) 10", + "Correct": "c", + "Explanation": "explanation : sum of 10 even numbers = 18 * 19 = 342 average = 342 / 18 = 19 answer : option c" + }, + { + "Answer": 8, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", + "Correct": "b", + "Explanation": "\"p is a positiveeveninteger with apositive units digit - - > the units digit of p can be 2 , 4 , 6 , or 8 - - > in order the units digit of p ^ 3 - p ^ 2 to be 0 , the units digit of p ^ 3 and p ^ 2 must be the same . thus the units digit of p can be 0 , 1 , 5 or 6 . intersection of values is 6 , thus the units digit of p + 2 is 6 + 2 = 8 . answer : b .\"" + }, + { + "Answer": 12, + "Options": "a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16", + "Correct": "c", + "Explanation": "\"let dan ' s present age be x . x + 18 = 5 ( x - 6 ) 4 x = 48 x = 12 the answer is c .\"" + }, + { + "Answer": 45, + "Options": "a ) 40.9 % , b ) 41.9 % , c ) 42.9 % , d ) 43.9 % , e ) 44.9 %", + "Correct": "e", + "Explanation": "\"let v be the total volume of the new solution . then a volume of v / 2 was added from each solution a and b . the amount of alcohol added to the new solution was : ( 4 / 9 ) ( v / 2 ) + ( 5 / 11 ) ( v / 2 ) = 2 v / 9 + 5 v / 22 = 89 v / 198 . the concentration of alcohol is 89 / 198 = 44.9 % the answer is e .\"" + }, + { + "Answer": 82, + "Options": "a ) 85 , b ) 94 , c ) 82 , d ) 72 , e ) none", + "Correct": "c", + "Explanation": "description : = > x + y = 10 , x - y = 6 adding these 2 x = 16 = > x = 8 , y = 2 . thus the number is 82 answer c" + }, + { + "Answer": 365, + "Options": "a ) $ 350 , b ) $ 400 , c ) $ 365 , d ) $ 385 , e ) $ 375", + "Correct": "c", + "Explanation": "official solution : ( c ) first , we need to add up the wages over the past 5 weeks : $ 406 + $ 413 + $ 420 + $ 436 + $ 395 = $ 2070 . to average $ 400 over 7 weeks , the salesman would need to earn : $ 400 \u00d7 7 = $ 2800 . subtract $ 2070 from $ 2800 to determine how much he would need to earn , in total , over the next 2 weeks to average $ 400 for the 7 weeks : $ 2800 \u2013 $ 2070 = $ 730 . dividing $ 730 by 2 will give us the amount he needs to earn on average over the next 2 weeks : $ 730 / 2 = $ 365 . the correct answer is choice ( c ) ." + }, + { + "Answer": 573, + "Options": "a ) 573 , b ) 608 , c ) 613 , d ) 616 , e ) 621", + "Correct": "a", + "Explanation": "the set s = { 5 , 13 , 21 , 29 , . . . . . . . . . . . . . . . . . . . . . } 1 st number = 8 * 0 + 5 = 5 2 nd number = 8 * 1 + 5 = 13 3 rd number = 8 * 2 + 5 = 21 72 th number = 8 * ( 72 - 1 ) + 5 = 573 answer = a" + }, + { + "Answer": 8, + "Options": "a ) 4 , b ) 6 , c ) 8 , d ) 12 , e ) 16", + "Correct": "c", + "Explanation": "the question is asking how many factors 190 has . 190 = 2 * 5 * 19 the number of factors is 2 ^ 3 = 8 the answer is c ." + }, + { + "Answer": 150, + "Options": "a ) 150 , b ) 500 / 3 , c ) 400 , d ) 480 , e ) 600", + "Correct": "a", + "Explanation": "\"we know that x is 10 % , y is 30 % and w . avg = 25 % . what does this mean with respect to w . avg technique ? w . avg is 1 portion away from y and 3 portion away from x so for every 1 portion of x we will have to add 3 portions of y . if x = 50 then y = 150 answer : a\"" + }, + { + "Answer": 15, + "Options": "a ) 14 , b ) 20 , c ) 22 , d ) 24 , e ) 15", + "Correct": "e", + "Explanation": "for a total of 51000 chips ( adding s 1 , s 2 , s 3 , s 4 ) total number of defective chips is 17 ( ( adding defective chips of s 1 , s 2 , s 3 , s 4 ) so ratio is 12 / 48000 or 1 every 4000 chips . keeping this ratio constant for 60000 chips number of defective chips will be ( 1 / 4000 ) * 60000 = 15 e" + }, + { + "Answer": 753.0000000000001, + "Options": "a ) 392 , b ) 229 , c ) 753 , d ) 493 , e ) 540", + "Correct": "c", + "Explanation": "\"c 753 ? = 5020 * ( 2 / 5 ) * ( 1 / 2 ) * ( 3 / 4 ) = 753\"" + }, + { + "Answer": 360, + "Options": "a ) 120 , b ) 240 , c ) 360 , d ) 480 , e ) 720", + "Correct": "c", + "Explanation": "c ) 360 short way : there are 6 c ! ways to do the six tasks . half will have wheels before axles and half will have axles before wheels . so we want t = 6 c ! / 2 - > 720 / 2 = 360" + }, + { + "Answer": 48.75, + "Options": "a ) 52.5 , b ) 52.9 , c ) 52.1 , d ) 48.75 , e ) 42.5", + "Correct": "d", + "Explanation": "\"sum of the marks for the class of 30 students = 30 * 30 = 900 sum of the marks for the class of 50 students = 50 * 60 = 3000 sum of the marks for the class of 80 students = 900 + 3000 = 3900 average marks of all the students = 3900 / 80 = 48.75 answer : d\"" + }, + { + "Answer": 1.7034146341463414, + "Options": "a ) $ 1.63 , b ) $ 1.64 , c ) $ 1.68 , d ) $ 1.70 , e ) $ 1.76", + "Correct": "d", + "Explanation": "\"( 1300 * 1.89 + 750 * 1.38 ) / ( 1300 + 750 ) = ~ 1.70 option ( d )\"" + }, + { + "Answer": 75, + "Options": "a ) 50 , b ) 100 , c ) 490 , d ) 500 , e ) 75", + "Correct": "e", + "Explanation": "\"average price for a pair of rackets = $ 9.8 total cost = $ 9.8 * x = $ 735 x = 75 pairs were sold . answer : e\"" + }, + { + "Answer": 185, + "Options": "a ) 150 , b ) 185 , c ) 190 , d ) 210 , e ) 220", + "Correct": "b", + "Explanation": "\"185 answer is b\"" + }, + { + "Answer": 22, + "Options": "a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24", + "Correct": "c", + "Explanation": "\"10 * 18 - 26 + 66 = 220 220 / 10 = 22 the answer is c .\"" + }, + { + "Answer": 50, + "Options": "a ) 22 , b ) 65 , c ) 12 , d ) 36 , e ) 50", + "Correct": "e", + "Explanation": "5 * 10 = 50 . answer is e ." + }, + { + "Answer": 3, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 3", + "Correct": "e", + "Explanation": "prime factorization of given numbers 10 = 2 * 5 25 = 5 ^ 2 35 = 5 * 7 lcm of the given numbers = 2 * 5 ^ 2 * 7 = 50 * 7 = 350 therefore , number of integers = 1050 / 350 = 3 answer : option e" + }, + { + "Answer": 30, + "Options": "a ) 25 , b ) 30 , c ) 28 , d ) 36 , e ) 42", + "Correct": "b", + "Explanation": "\"( ( 2 a + 16 ) + ( 3 a - 8 ) ) / 2 = ( 5 a + 8 ) / 2 = 79 a = 30 the answer is b .\"" + }, + { + "Answer": 7, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9", + "Correct": "c", + "Explanation": "\"let x be the number of canoes . then 2 x / 3 is the number of kayaks . 12 x + ( 2 x / 3 ) * 18 = 504 12 x + 12 x = 504 24 x = 504 x = 21 ( canoes ) 2 x / 3 = 14 ( kayaks ) there were 21 - 14 = 7 more canoes rented out . the answer is c .\"" + }, + { + "Answer": 116, + "Options": "a ) 96 , b ) 106 , c ) 122 , d ) 116 , e ) 122", + "Correct": "d", + "Explanation": "\"average = total runs / no . of innings = 32 so , total = average x no . of innings = 32 * 20 = 640 now increase in avg = 4 runs . so , new avg = 32 + 4 = 36 runs total runs = new avg x new no . of innings = 36 * 21 = 756 runs made in the 11 th inning = 756 - 640 = 116 answer : d\"" + }, + { + "Answer": 0.41666666666666663, + "Options": "a ) 0 , b ) 1 / 12 , c ) 5 / 12 , d ) 7 / 18 , e ) 4 / 9", + "Correct": "c", + "Explanation": "total # of outcomes is 6 * 6 = 36 ; favorable outcomes : a - b - - > prime 1 - 1 - - > 2 ; 1 - 2 - - > 3 ; 2 - 1 - - > 3 ; 1 - 4 - - > 5 ; 4 - 1 - - > 5 ; 2 - 3 - - > 5 ; 3 - 2 - - > 5 ; 1 - 6 - - > 7 ; 6 - 1 - - > 7 ; 2 - 5 - - > 7 ; 5 - 2 - - > 7 ; 3 - 4 - - > 7 ; 4 - 3 - - > 7 ; 6 - 5 - - > 11 ; 5 - 6 - - > 11 . total of 15 favorable outcomes r = 15 / 36 . answer : c ." + }, + { + "Answer": 70, + "Options": "a ) 29 , b ) 38 , c ) 39 , d ) 70 , e ) 75", + "Correct": "d", + "Explanation": "\"average = ( 51 + 65 + 82 + 67 + 85 ) / 5 = 70 answer : d\"" + }, + { + "Answer": 1.125, + "Options": "a ) 9 / 8 , b ) 4 / 1 , c ) 2 / 3 , d ) 3 / 4 , e ) 3 / 2", + "Correct": "a", + "Explanation": "\"given that milk / water = 4 x / x and 4 x + x = 45 - - > x = 9 . thus milk = 4 x = 36 liters and water = x = 9 liters . new ratio = 36 / ( 9 + 23 ) = 36 / 32 = 9 / 8 . answer : a .\"" + }, + { + "Answer": 75, + "Options": "a ) 75 , b ) 66 , c ) 55 , d ) 44 , e ) 12", + "Correct": "a", + "Explanation": "let the marks obtained by the student in physics , chemistry and mathematics be p , c and m respectively . p + c + m = 150 + p c + m = 150 average mark obtained by the student in chemistry and mathematics = ( c + m ) / 2 = 150 / 2 = 75 . answer : a" + }, + { + "Answer": 58.333333333333336, + "Options": "a ) 53.33 % , b ) 50 % , c ) 58.33 % , d ) 55.33 % , e ) 68 %", + "Correct": "c", + "Explanation": "\"i just wanted to mention a couple of things here : * this is a pure ratio question ; the number 3000 is completely irrelevant , and you can ignore it if you like . when we increase something by 1 / 6 , we are multiplying it by 1 + 1 / 6 = 7 / 6 , so the answer here must be ( 1 / 2 ) * ( 7 / 6 ) = 7 / 12 = 58.33 % . answer : c\"" + }, + { + "Answer": 56, + "Options": "a ) 25 , b ) 40 , c ) 64 , d ) 80 , e ) 56", + "Correct": "e", + "Explanation": "\"7 / 8 x - 3 / 4 x = 7 galls 1 / 8 * x = 7 gallons x = 56 gallons answer e\"" + }, + { + "Answer": 48.550000000000004, + "Options": "a ) 47.55 kgs , b ) 48 kgs , c ) 48.55 kgs , d ) 49.25 kgs , e ) none of these", + "Correct": "c", + "Explanation": "\"solution required average = ( 50.25 x 16 + 45.15 x 8 / 16 + 8 ) = ( 804 + 361.20 / 24 ) = 1165.20 / 24 = 48.55 answer c\"" + }, + { + "Answer": 224, + "Options": "a ) 150 , b ) 164 , c ) 259 , d ) 311 , e ) 224", + "Correct": "e", + "Explanation": "required number of ways = 4 c 1 * 8 c 5 = 224 answer is e" + }, + { + "Answer": 0.5625, + "Options": "a ) 1 / 4 , b ) 3 / 8 , c ) 1 / 2 , d ) 9 / 16 , e ) 3 / 4", + "Correct": "d", + "Explanation": "\"i get 5 / 8 as well 1 to 96 inclusive means we have 48 odd and 48 even integers e o e / 16 = integer , therefore we have 48 / 96 numbers divisible by 8 o e o / 16 = not integer we can not forget multiples of 16 from 1 to 96 we have 6 numbers that are multiple of 16 therefore , 48 / 96 + 6 / 96 = 54 / 96 = 9 / 16 answer : d\"" + }, + { + "Answer": 16, + "Options": "a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 16", + "Correct": "e", + "Explanation": "\"while this question can be solved with a rather straight - forward algebra approach ( as the other posters have noted ) , it can also be solved by testing the answers . one of those numbers must be the total number of goals . . . from a tactical standpoint , it ' s best to test either answer b or answer d , so if the answer is not correct , then you would have a gauge for whether you should gohigherorlowerwith your next test . here , i ' ll start with answer e = 16 goals if . . . . total goals = 16 goals 5 th game = 4 goals 1 st 4 games = 12 goals avg . for 1 st 4 games = 12 / 4 = 3 goal / game avg . for all 5 games = 6 / 5 = 3.2 goals / game this is an exact match for what we ' re told in the prompt , so answer e must be the answer .\"" + }, + { + "Answer": 59, + "Options": "a ) 58 , b ) 59 , c ) 60 , d ) 61 , e ) 62", + "Correct": "b", + "Explanation": "remainder of 1 when divided by 2 : ( 2 - 1 = 1 ) remainder of 2 when divided by 3 : ( 3 - 2 = 1 ) remainder of 3 when divided by 4 : ( 4 - 3 = 1 ) remainder of 9 when divided by 10 : ( 2 - 1 = 1 ) so n + 1 should be divisible by 23 , 410 ( where n is desired number ) l . c . m . of 23 , 410 = 60 ( = n + 1 ) n = 59 answer : b" + }, + { + "Answer": 12, + "Options": "a ) $ 10 , b ) $ 12 , c ) $ 13.20 , d ) $ 15 , e ) $ 16.80", + "Correct": "b", + "Explanation": "\"let the price of one shirt be ss and of jeans be j : 3 j + 2 s = 69 2 j + 3 s = 66 subtracting the second from the first gives : j \u2212 s = 3 or j = s + 3 plug j in either of the equations and solve for s , which is $ 12 answer : b .\"" + }, + { + "Answer": 1, + "Options": "a ) 123 , b ) 1 , c ) 235 , d ) 305 , e ) 505", + "Correct": "b", + "Explanation": "\"explanation : required number = h . c . f . of ( 1657 - 10 ) and ( 2037 - 7 ) = h . c . f . of 1647 and 2030 = 1 . answer : b\"" + }, + { + "Answer": 5, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "e", + "Explanation": "\"@ ( n ) = 5 n - n we need to find the largest positive integer such that 5 n - n < 21 . then 4 n < 21 and n < 5.25 . the largest possible integer is n = 5 . the answer is e .\"" + }, + { + "Answer": 92, + "Options": "a ) 92 , b ) 42 , c ) 64 , d ) 76 , e ) 84", + "Correct": "a", + "Explanation": "explanation : average after 14 innings = 27 required number of runs = ( 27 * 14 ) \u2013 ( 22 * 13 ) = 378 \u2013 286 = 92 answer a" + }, + { + "Answer": 0.225, + "Options": "a ) 1 / 60 , b ) 2 / 50 , c ) 9 / 40 , d ) 3 / 40 , e ) 4 / 50", + "Correct": "c", + "Explanation": "the probability of success of at least two students will involve the following possibilities . the first two students are successful , the last two students are successful , the first and third students are successful and all the three students are successful . therefore , the required probability = 1 / 2 x 1 / 4 x 4 / 5 + 1 / 4 x 1 / 5 x 1 / 2 + 1 / 2 x 1 / 5 x 3 / 4 + 1 / 2 x 1 / 4 x 1 / 5 = 9 / 40 answer : c" + }, + { + "Answer": 0.75, + "Options": "a ) 27 / 4 , b ) 27 / 8 , c ) 3 / 4 , d ) 3 / 8 , e ) 1 / 4", + "Correct": "c", + "Explanation": "\"say a = 3 . then : a / b = 1 / 3 - - > b = 9 ; b / c = 2 - - > c = 9 / 2 ; c / d = 1 / 2 - - > d = 9 ; d / e = 3 - - > e = 3 ; e / f = 1 / 2 - - > f = 6 . abc / def = ( 3 * 9 * 9 / 2 ) / ( 9 * 3 * 6 ) = 3 / 4 . answer : c .\"" + }, + { + "Answer": 36, + "Options": "a ) 28 , b ) 30 , c ) 33 , d ) 36 , e ) 28", + "Correct": "d", + "Explanation": "\"the average of 7 consecutive numbers will be the 4 th number which is given to be = 33 5 th number = 34 , 6 th number = 35 , 7 th number = 36 answer : d .\"" + }, + { + "Answer": 0.7142857142857143, + "Options": "a ) 25 / 9 , b ) 9 / 5 , c ) 5 / 7 , d ) 3 / 5 , e ) 9 / 25", + "Correct": "c", + "Explanation": "\"sqrt ( 5 x / 7 ) to be perfect square x has to 5 / 7 ans : c\"" + }, + { + "Answer": 33, + "Options": "a ) 33 , b ) 36 , c ) 37 , d ) 38 , e ) 39", + "Correct": "a", + "Explanation": "42 x = 15 x + 1.5 x ( h - 15 ) = = > 42 = 15 + 1.5 ( h - 15 ) = = > h - 15 = 27 / 1.5 = 18 = = > h = 33 answer is a" + }, + { + "Answer": 25, + "Options": "a ) 28 , b ) 24 , c ) 23 , d ) 22 , e ) 25", + "Correct": "e", + "Explanation": "initial charge / transaction ratio = 1 / 5 = 3 / 15 revised charge / transaction ratio = . 75 / 3 = 3.75 / 15 answer : e" + }, + { + "Answer": 1, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5", + "Correct": "b", + "Explanation": "note that x 5 + 2 x 3 + 8 x 2 + 16 = ( x 3 + 8 ) ( x 2 + 2 ) = ( x + 2 ) ( x 2 - 2 x + 4 ) ( x 2 + 2 ) . since the quadratic equations x 2 - 2 x + 4 = 0 and x 2 + 2 = 0 have no real solutions , the original equation has just one real solution , x = - 2 . correct answer b" + }, + { + "Answer": 18, + "Options": "a ) 23 years , b ) 22 years , c ) 21 years , d ) 20 years , e ) 18 years", + "Correct": "e", + "Explanation": "\"let present age of the son = x years then , present age the man = ( x + 20 ) years given that , in 2 years , man ' s age will be twice the age of his son \u00e2 \u2021 \u2019 ( x + 20 ) + 2 = 2 ( x + 2 ) \u00e2 \u2021 \u2019 x = 18 answer : e\"" + }, + { + "Answer": 7, + "Options": "a ) 22 , b ) 11 , c ) 9 , d ) 6 , e ) 7", + "Correct": "e", + "Explanation": "\"( 18 ^ a ) * 9 ^ ( 3 a \u2013 1 ) = ( 2 ^ 7 ) ( 3 ^ b ) = 2 ^ a . 9 ^ a . 9 ^ ( 3 a \u2013 1 ) = ( 2 ^ 7 ) ( 3 ^ b ) just compare powers of 2 from both sides answer = 7 = e\"" + }, + { + "Answer": 105, + "Options": "a ) 75 kg , b ) 85 kg , c ) 95 kg , d ) 65 kg , e ) 105 kg", + "Correct": "e", + "Explanation": "\"the total weight increase = ( 8 x 2.5 ) kg = 20 kg weight of new person = ( 85 + 20 ) kg = 105 kg the answer is e .\"" + }, + { + "Answer": 258, + "Options": "a ) a ) 78 , b ) b ) 65 , c ) c ) 258 , d ) d ) 62 , e ) e ) 48", + "Correct": "c", + "Explanation": "\"7 th number = sum of 1 st 6 no . s + sum of last 6 no . s - sum of 11 no . s answer = 6 * 68 + 6 * 75 - 10 * 60 = 258 answer is c\"" + }, + { + "Answer": 58.666666666666664, + "Options": "a ) 74 , b ) 76 , c ) 78 , d ) 58.67 , e ) 82.2", + "Correct": "d", + "Explanation": "\"mean - 5 sd = 42 mean + 2.5 sd = 67 by solving above equations we get , sd ( absolute value ) = 3.33 mean = 58.67 ans . d\"" + }, + { + "Answer": 37.5, + "Options": "a ) a : 45 , b ) b : 25 , c ) c : 37.5 , d ) d : 36 , e ) e : 42", + "Correct": "c", + "Explanation": "\"if you have a 37.5 liter capacity , you start with 37.5 l of a and 0 l of b . 1 st replacement after the first replacement you have 37.5 - 15 = 22.5 l of a and 15 l of b . the key is figuring out how many liters of a and b , respectively , are contained in the next 15 liters of mixture to be removed . the current ratio of a to total mixture is 22.5 / 37.5 ; expressed as a fraction this becomes ( 45 / 2 ) / ( 75 / 2 ) , or 45 / 2 * 2 / 75 . canceling the 2 s and factoring out a 5 leaves the ratio as 9 / 15 . note , no need to reduce further as we ' re trying to figure out the amount of a and b in 15 l of solution . 9 / 15 of a means there must be 6 / 15 of b . multiply each respective ratio by 15 to get 9 l of a and 6 l of b in the next 15 l removal . final replacement the next 15 l removal means 9 liters of a and 6 liters of b are removed and replaced with 15 liters of b . 22.5 - 9 = 13.5 liters of a . 15 liters of b - 6 liters + 15 more liters = 24 liters of b . test to the see if the final ratio = 9 / 16 ; 13.5 / 24 = ( 27 / 2 ) * ( 1 / 24 ) = 9 / 16 . choice c is correct .\"" + }, + { + "Answer": 15, + "Options": "a ) 2 , b ) 15 , c ) 7 , d ) 10 , e ) 9", + "Correct": "b", + "Explanation": "explanation : identify the parts , set up equation , and solve . number of games initially won by the team : 50 % * 40 = 20 additional games won by the team leaving a 20 % average . ( let x represent the unknown number of additional games won . ) therefore , the total number of games played is 40 + x , and the total number of games won is 20 + x . this gives the equation as : 20 % * ( 40 + x ) = 20 + x solve : let ' s get rid of the percent sign 20 / 100 * ( 40 + x ) = 20 + x 1 / 5 * ( 40 + x ) = 20 + x get rid of the fraction : 5 [ 1 / 5 * ( 40 + x ) ] = 5 ( 20 + x ) 1 * ( 40 + x ) = 100 + 5 x 40 + x = 100 + 5 x ( 40 - 100 ) + x = ( 100 - 100 ) + 5 x - 60 + x = 5 x - 60 + ( x - x ) + 5 x - x - 60 = 4 x 15 = x answer : b" + }, + { + "Answer": 25, + "Options": "a ) 8 % , b ) - 25 % , c ) 11 % , d ) 12.5 % , e ) 14.8 %", + "Correct": "b", + "Explanation": "\"typical dosage per 15 pound of the body weight = 2 c . c typical dosage per 120 pound of the body weight = 2 * ( 120 / 15 ) = 2 * 8 = 16 c . c dosage prescribed by doctor for 120 pound patient = 12 c . c % prescribed dosage greater than the typical dosage = ( 12 - 16 / 16 ) * 100 % = ( - 4 / 16 ) * 100 % = - 25 % answer b\"" + }, + { + "Answer": 2, + "Options": "a ) 2 , b ) 6 , c ) 5 , d ) 3 , e ) 4", + "Correct": "a", + "Explanation": "since the average increased by 29.7 and there were a total of 10 numbers , it means the incorrect number was 198 greater than the correct number . say , the correct number was abc ( where a , b and c are the digits of the 3 digit number ) then the incorrect number was cba . 100 c + 10 b + a - ( 100 a + 10 b + c ) = 198 99 c - 99 a = 99 ( c - a ) = 198 198 = 99 * 2 = 99 ( c - a ) so c - a = 2 answer ( a )" + }, + { + "Answer": 10, + "Options": "a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16", + "Correct": "b", + "Explanation": "\"let ' s say age of richard is ` ` r ' ' age of david is ` ` d ' ' age of scott is ` ` s ' ' now richard is 6 years older than david , i . e . r = d + 6 david is 8 years older than scott i . e . d = s + 8 if in 8 years , richard will be twice as old as scott i . e . r + 8 = 2 x ( s + 8 ) i . e . r + 8 = 2 s + 16 i . e . r = 2 s + 8 but r = d + 6 = ( s + 8 ) + 6 = s + 14 therefore , 2 s + 8 = s + 14 i . e . s = 6 i . e . r = 20 i . e . d = 14 now , how old was david 4 years ago ? i . e . d - 4 = 14 - 4 = 10 years answer : b\"" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "a", + "Explanation": "explanation : since group b contains 23 questions , the marks associated with this group are 46 . now , check for option ( 1 ) , if group ( c ) has one question , the marks associated with this group will be 3 . thus total marks will be 49 . total number of questions = 100 , group ( a ) will have 76 questions , the corresponding weightage being 76 marks . answer : a" + }, + { + "Answer": 14, + "Options": "a ) 11 . , b ) 12 . , c ) 13 . , d ) 14 . , e ) 14.5", + "Correct": "d", + "Explanation": "\"price of candy before price increase = 10 / 1.25 = 8 price of soda before price increase = 9 / 1.5 = 6 total price = 8 + 6 = 14 d is the answer\"" + }, + { + "Answer": 35, + "Options": "a ) 20 , b ) 35 , c ) 48 , d ) 50 , e ) 59", + "Correct": "b", + "Explanation": "\"production during these 5 days = total production in a month - production in first 25 days . = 30 x 60 - 25 x 65 = 175 \u2234 average for last 5 days = 175 / 5 = 35 aswer : b\"" + }, + { + "Answer": 80, + "Options": "a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90", + "Correct": "d", + "Explanation": "kk is 3 - digit integer . any 3 digit integer can be expressed as 100 a + 10 b + c 100 a + 10 b + c . now , we are told that ( 100 a + 10 b + c ) + 99 = 100 c + 10 b + a ( 100 a + 10 b + c ) + 99 = 100 c + 10 b + a - - > 99 c \u2212 99 a = 9999 c \u2212 99 a = 99 - - > c \u2212 a = 1 c \u2212 a = 1 - - > there are 8 pairs of cc and aa possible such that their difference to be 1 : ( 9,8 ) , ( 8,7 ) , . . . , and ( 2,1 ) ( note that aa can not be 0 as kk is 3 - digit integer and its hundreds digit , aa , is more than or equal to 1 ) . also , bb , tens digit of kk , could tale 10 values ( 0 , 1 , . . . , 9 ) so there are total of 8 * 10 = 80 such numbers possible . example : 102 - 201 ; 112 - 211 ; 122 - 221 ; . . . 899 - 998 . answer : d ." + }, + { + "Answer": 5, + "Options": "a ) 9 , b ) 8 , c ) 7 , d ) 6 , e ) 5", + "Correct": "e", + "Explanation": "\"0 . [ u ] 225 [ / u = 0.225225225 . . . . . every 3 rd digit is 5 and every multiple of 3 will be the digit 5 . since 81 is multiple of 3 , the 81 st digit is 5 . answer e\"" + }, + { + "Answer": 0.08333333333333334, + "Options": "a ) 1 / 12 , b ) 1 / 8 , c ) 1 / 6 , d ) 1 / 4 , e ) 1 / 2", + "Correct": "a", + "Explanation": "x * ( 120 / 100 ) - - - - - - - - - - - - - - - - = 2 / 15 y * ( 75 / 100 ) x / y = 1 / 12 answer : a" + }, + { + "Answer": 24, + "Options": "a ) 24 , b ) 34 , c ) 35 , d ) 36 , e ) 39", + "Correct": "a", + "Explanation": "4 ! / ( 4 - 3 ) ! = 4 ! / 1 ! = 4 * 3 * 2 = 24 . hence , the correct answer is a ." + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 22", + "Correct": "a", + "Explanation": "explanation : let number of zookeepers be x . then , total number of feet = 2 x 30 + 4 x 22 + 4 x 8 + 2 x = 2 x + 180 . total number of heads = 30 + 22 + 8 + x = 60 + x . therefore ( 2 x + 180 ) - 132 = ( 60 + x ) + or x = 12 . answer : a" + }, + { + "Answer": 7, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "e", + "Explanation": "since no flowers are to be left out , then the number of bouquets must be a factor of both 21 and 91 . for example , we can not have 2 bouquets since we can not divide 91 red tulips into 2 bouquets without one tulip left over . only answer choice which is a factor of 91 is e ( 7 ) . answer : e ." + }, + { + "Answer": 1, + "Options": "a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 1", + "Correct": "e", + "Explanation": "if we divide 1049 by 25 remainder is 24 25 - 24 = 1 answer : e" + }, + { + "Answer": 84, + "Options": "a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %", + "Correct": "d", + "Explanation": "\"d the prompt says that 68 % of the population lies between m - d and m + d . thus , 32 % of the population is less than m - d or greater than m + d . since the population is symmetric , half of this 32 % is less than m - d and half is greater than m + d . thus , w = ( 68 + 16 ) % or ( 100 - 16 ) % of the population is less than m + d .\"" + }, + { + "Answer": 24.666666666666668, + "Options": "a ) 17 litres , b ) 24.67 litres , c ) 11 litres , d ) 24.07 litres , e ) 38.67 litres", + "Correct": "b", + "Explanation": "\"262.85 ( 37 ) + 3 , 104.35 x = 1 , 399.45 ( 37 + x ) solve the equation . 262.85 ( 37 ) + 3 , 104.35 x = 1 , 399.45 ( 37 + x ) 9725.45 + 3 , 104.35 x = 51779.65 + 1 , 399.45 x 9725.45 + 1 , 704.9 x = 51779.65 1 , 704.9 x = 42054.2 x \u2248 24.67 answer is b .\"" + }, + { + "Answer": 0.93, + "Options": "a ) 0.93 , b ) 9.4 , c ) 0.094 , d ) 94 , e ) none", + "Correct": "a", + "Explanation": "\"answer let a - 7 % of a = ab . \u21d2 ( 93 x a ) / 100 = ab \u2234 b = 0.93 correct option : a\"" + }, + { + "Answer": 78, + "Options": "a ) 66 , b ) 70 , c ) 74 , d ) 78 , e ) 82", + "Correct": "d", + "Explanation": "let the present age of sandy be 7 x years and that of molly be 2 x years . ( 7 x + 16 ) / ( 2 x + 16 ) = 5 / 2 4 x = 48 x = 12 six years ago , sandy ' s age was 7 ( 12 ) - 6 = 78 the answer is d ." + }, + { + "Answer": 27, + "Options": "a ) 20 , b ) 27 , c ) 28 , d ) 30 , e ) none of these", + "Correct": "b", + "Explanation": "solution : required average = ( total sum of multiple of 9 ) / 5 = ( 9 + 18 + 27 + 36 + 45 ) / 5 = 27 note that , average of 9 and 45 is also 27 . and average of 18 and 36 is also 27 . answer : option b" + }, + { + "Answer": 150, + "Options": "a ) 190 , b ) 160 , c ) 120 , d ) 151 , e ) 150", + "Correct": "e", + "Explanation": "\"5 + 7 + 11 = 23 690 / 23 = 30 so y ' s share = 5 * 30 = 150 answer : e\"" + }, + { + "Answer": 9, + "Options": "a ) a ) 4 , b ) b ) 7 , c ) c ) 9 , d ) d ) 5 , e ) e ) 2", + "Correct": "c", + "Explanation": "12 - 3 = 9 . answer is c" + }, + { + "Answer": 25, + "Options": "a ) 15 , b ) 20 , c ) 23 , d ) 24 , e ) 25", + "Correct": "e", + "Explanation": "the average falls between the 5 th and 6 th integers , integer 5 = 20 , integer 6 = 21 . counting up to the tenth integer we get 25 . answer : e" + }, + { + "Answer": 23, + "Options": "a ) 19 , b ) 21 , c ) 23 , d ) 25 , e ) 27", + "Correct": "c", + "Explanation": "\"let x be the correct sums and ( 30 - x ) be the incorrect sums . 3 x - 2 ( 30 - x ) = 55 5 x = 115 x = 23 the answer is c .\"" + }, + { + "Answer": 5, + "Options": "a ) - 4 , b ) - 2 , c ) 5 , d ) 13 , e ) 22", + "Correct": "c", + "Explanation": "\"the equation that can be formed is : 3 x - 4 = 16 - x or , 4 x = 20 or , x = 5 . answer : c\"" + }, + { + "Answer": 80, + "Options": "a ) 72 , b ) 80 , c ) 120 , d ) 150 , e ) 100", + "Correct": "b", + "Explanation": "\"explanation : let the number of students be x . then , number of students above 8 years of age = ( 100 - 25 ) % of x = 75 % of x . 75 % of x = 36 + 2 / 3 of 36 75 / 100 x = 60 x = 80 . answer : option b\"" + }, + { + "Answer": 36, + "Options": "a ) 36 , b ) 45 , c ) 52 , d ) 44 , e ) 39", + "Correct": "a", + "Explanation": "difference between the place value and face value of 4 = 40 - 4 = 36 answer is a" + }, + { + "Answer": 34.5, + "Options": "a ) 33 , b ) 77 , c ) 48 , d ) 99 , e ) 34.5", + "Correct": "e", + "Explanation": "\"speed on return trip = 130 % of 30 = 39 km / hr . average speed of trip = 30 + 39 / 2 = 69 / 2 = 34.5 km / hr answer : e\"" + }, + { + "Answer": 69, + "Options": "a ) 69 , b ) 72 , c ) 75 , d ) 78 , e ) 80", + "Correct": "a", + "Explanation": "\"income of 6 months = ( 6 \u00d7 70 ) \u2013 debt = 420 \u2013 debt income of the man for next 4 months = 4 \u00d7 60 + debt + 30 = 270 + debt \u2234 income of 10 months = 690 average monthly income = 690 \u00f7 10 = 69 answer a\"" + }, + { + "Answer": 30, + "Options": "a ) 30 , b ) 120 , c ) 130 , d ) 140 , e ) 150", + "Correct": "a", + "Explanation": "\"solution : let xx be the number he chose , then 8 \u22c5 x \u2212 138 = 102 8 x = 240 x = 30 answer a\"" + }, + { + "Answer": 36, + "Options": "a ) 37 , b ) 36 , c ) 22 , d ) 90 , e ) 28", + "Correct": "b", + "Explanation": "let number of notes of each denomination be x . then , x + 5 x + 10 x = 192 16 x = 192 x = 12 . hence , total number of notes = 3 x = 36 . answer : b" + }, + { + "Answer": 16, + "Options": "a ) 6 , b ) 12 , c ) 14 , d ) 16 , e ) 28", + "Correct": "d", + "Explanation": "\"equate the fat : 0.1 x + 0.4 * 8 = 0.2 ( x + 8 ) - - > x = 16 . answer : d .\"" + }, + { + "Answer": 630, + "Options": "a ) 630 km , b ) 540 km , c ) 276 km , d ) 178 km , e ) 176 km", + "Correct": "a", + "Explanation": "\"explanation : let us assume that trains meet after ' x ' hours distance = speed * time distance traveled by two trains = 20 x km and 25 x km resp . as one train travels 70 km more than the other , 25 x \u00e2 \u20ac \u201c 20 x = 70 5 x = 70 x = 14 hours as the two trains are moving towards each other , relative speed = 20 + 25 = 45 km / hr therefore , total distance = 45 * 14 = 630 km . answer : a\"" + }, + { + "Answer": 21, + "Options": "a ) 21 , b ) 32 , c ) 30 , d ) 41 , e ) 37", + "Correct": "a", + "Explanation": "\"10 + 12 + 10 * 2 = 42 / 2 = 21 answer : a\"" + }, + { + "Answer": 8400, + "Options": "a ) 8400 , b ) 14703 , c ) 37798 , d ) 13777 , e ) 14778", + "Correct": "a", + "Explanation": "explanation : let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 < = > 3 x = 36000 < = > x = 12000 . a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . c ' s share = rs . ( 35000 * 12 / 50 ) = rs . 8,400 . answer : a )" + }, + { + "Answer": 42.000000000000014, + "Options": "a ) 36 , b ) 42 , c ) 45 , d ) 48 , e ) 51", + "Correct": "b", + "Explanation": "\"let r be the original speed and let t be the original time . since the distance remains the same ( we ' re just changing the rate and time ) , any increase in rate or time is met with a decrease in the other term . decreasing the time by 1 / 3 would give us : d = ( r ) ( t ) = ( 2 t / 3 ) ( x * r ) x = 3 / 2 since ( 2 t / 3 ) ( 3 r / 2 ) = ( r ) ( t ) = d 3 r / 2 = r + 21 r / 2 = 21 r = 42 the answer is b .\"" + }, + { + "Answer": 5, + "Options": "a ) 1 , b ) 4 , c ) 5 , d ) 0 , e ) 3", + "Correct": "c", + "Explanation": "let the number be x . then , 7 x - 15 = 2 x + 10 = > 5 x = 25 = > x = 5 . hence , the required number is 5 . answer is c ." + }, + { + "Answer": 3000, + "Options": "a ) 2000 , b ) 2500 , c ) 3000 , d ) 3500 , e ) 4000", + "Correct": "c", + "Explanation": "let monthly income of a = x monthly income of b = y monthly income of c = z x + y = 2 \u00d7 4050 . . . . ( equation 1 ) y + z = 2 \u00d7 5250 . . . . ( equation 2 ) z + x = 2 \u00d7 4200 . . . . ( equation 3 ) ( equation 1 ) + ( equation 3 ) - ( equation 2 ) = > x + y + x + z - ( y + z ) = ( 2 \u00d7 4050 ) + ( 2 \u00d7 4200 ) - ( 2 \u00d7 5250 ) = > 2 x = 2 ( 4050 + 4200 - 5250 ) = > x = 3000 i . e . , monthly income of a = 3000 answer : c" + }, + { + "Answer": 69, + "Options": "a ) 18 , b ) 29 , c ) 37 , d ) 44 , e ) 69", + "Correct": "e", + "Explanation": "option bc can be ruled out as they themselves are prime numbers 18 = 2 * 9 = 3 * 6 > > ignore 44 = 2 * 22 = 4 * 11 > > ignore 69 = 3 * 23 > > answer answer = e" + }, + { + "Answer": 0.5, + "Options": "a ) 1 / 2 , b ) 1 / 3 , c ) 2 / 3 , d ) 1 / 4 , e ) 1 / 5", + "Correct": "a", + "Explanation": "\"r - > a / b = 20 * 21 * \u2026 \u2026 * 39 / 21 * 22 * \u2026 . * 39 * 40 = 20 / 40 = 1 / 2 . therefore , the answer is a .\"" + }, + { + "Answer": 224, + "Options": "a ) s . 130 , b ) s . 140 , c ) s . 150 , d ) s . 224 , e ) s . 280", + "Correct": "d", + "Explanation": "\"let the amount paid to a per week = x and the amount paid to b per week = y then x + y = 560 but x = 150 % of y = 150 y / 100 = 15 y / 10 \u2234 15 y / 10 + y = 560 \u21d2 y [ 15 / 10 + 1 ] = 560 \u21d2 25 y / 10 = 560 \u21d2 25 y = 5600 \u21d2 y = 5600 / 25 = rs . 224 d )\"" + }, + { + "Answer": 140, + "Options": "a ) 360 , b ) 420 , c ) 510 , d ) 320 , e ) 140", + "Correct": "e", + "Explanation": "\"lcm = 2 * 2 * 5 * 7 = 140 . answer is e\"" + }, + { + "Answer": 3029, + "Options": "a ) 2984 , b ) 3029 , c ) 2982 , d ) 2981 , e ) none of these", + "Correct": "b", + "Explanation": "\"3034 - 5 = 3029 answer : b\"" + }, + { + "Answer": 196, + "Options": "a ) 180 , b ) 184 , c ) 188 , d ) 192 , e ) 196", + "Correct": "e", + "Explanation": "\"j + k = 290 and so k = 290 - j j - 8 = 2 k j - 8 = 2 ( 290 - j ) 3 j = 588 j = 196 the answer is e .\"" + }, + { + "Answer": 1300, + "Options": "a ) 1300 , b ) 1992 , c ) 9921 , d ) 2798 , e ) 2789", + "Correct": "a", + "Explanation": "\"p = 13 ( 100 / 10 ) 2 = > p = 1300 answer : a\"" + }, + { + "Answer": 75, + "Options": "a ) 65 , b ) 69 , c ) 72 , d ) 75 , e ) none", + "Correct": "d", + "Explanation": "\"sol . average = 76 + 65 + 82 + 67 + 85 / 5 ) = ( 375 / 5 ) = 75 . answer d\"" + }, + { + "Answer": 6, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 6", + "Correct": "e", + "Explanation": "make sure to follow posting guidelines ( link in my signatures ) . title of the thread must mention the first few words of the question itself . as for the question , the most straightforward way is to list out the factors ( this is fine for this question as 180 is a relatively small number ) . number of factors of 180 ( = 2 ^ 2 * 3 ^ 2 * 5 ) = 18 . so listing the factors gives us : 1 , 180 2 , 90 3 , 60 4 , 45 5 , 36 6 , 30 9 , 20 10 , 18 12 , 15 as the question asks us about the factors of the form 4 k + 2 - - - > eliminate all odd factors . you are now left with 24 , 610 , 1218 , 2030 , 3660 , 90180 for the form 4 k + 2 , the first few values are 2 , 6 , 10 , 14 , 18 , 22 , 26 , 30 . . . already giving you 5 factors ( = 2 , 610 , 1830 ) . you can stop here and mark 6 ( 6 th one = 90 ) as the correct answer as 5 is not given . for checking any particular factor whether they conform to the form 4 k + 2 - - - > do the following 4 k + 2 = 36 - - - > 4 k = 34 - - > this will not give you an integer value for k - - - > reject . proceed with others until you find all the values asked . e is thus the correct answer ." + }, + { + "Answer": 0.8461538461538461, + "Options": "a ) 7 / 13 , b ) 4 / 5 , c ) 9 / 13 , d ) 11 / 13 , e ) 7 / 10", + "Correct": "d", + "Explanation": "lets pick smart numbers . total number of students : 20 woodwind ( 1 / 2 ) : 10 brass ( 2 / 5 ) : 8 percussion ( 1 / 10 ) : 2 after leaving school woodwind : 5 brass : 6 percussion : 2 new total number of students : 13 woodwind and brass : 11 answer 11 / 13 or d" + }, + { + "Answer": 4, + "Options": "a ) 3 , b ) 2 , c ) 1 , d ) 0 , e ) 4", + "Correct": "e", + "Explanation": "\"| 16 - 5 | - | 5 - 12 | = | 11 | - | - 7 | = 11 - 7 = 4 correct answer e\"" + }, + { + "Answer": 5, + "Options": "a ) 4 % , b ) 6 % , c ) 5 % , d ) 50 % , e ) none of these", + "Correct": "c", + "Explanation": "explanation : increase in the population in 10 years = 2 , 62500 - 1 , 75000 = 87500 % ncrease in the population in 10 years = ( 87500 / 175000 ) \u00d7 100 = 8750 / 175 = 50 % average % increase of population per year = 50 % / 10 = 5 % answer : option c" + }, + { + "Answer": 641, + "Options": "a ) 601 , b ) 611 , c ) 621 , d ) 631 , e ) 641", + "Correct": "e", + "Explanation": "\"x = 20 + 21 + . . . + 40 = 21 ( 30 ) = 630 y = 11 x + y = 641 the answer is e .\"" + }, + { + "Answer": 20, + "Options": "a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 21", + "Correct": "d", + "Explanation": "\"x + ( x + 2 ) + ( x + 7 ) + ( x + 11 ) = 100 4 x + 20 = 100 4 x = 80 x = 20 the answer is d .\"" + }, + { + "Answer": 8, + "Options": "a ) 40 , b ) 44 , c ) 48 , d ) 8 , e ) 56", + "Correct": "d", + "Explanation": "\"let the capacity of the can be t litres . quantity of milk in the mixture before adding milk = 1 / 6 ( t - 2 ) after adding milk , quantity of milk in the mixture = 3 / 8 t . 3 t / 8 - 2 = 1 / 6 = ( t - 2 ) 10 t = 96 - 16 = > t = 8 answer : d\"" + }, + { + "Answer": 72, + "Options": "a ) 22 , b ) 65 , c ) 72 , d ) 78 , e ) 90", + "Correct": "c", + "Explanation": "6 * 12 = 72 . answer is c" + }, + { + "Answer": 163, + "Options": "a ) 162 , b ) 163 , c ) 164 , d ) 165 , e ) 166", + "Correct": "b", + "Explanation": "f ( 1 ) = 1 f ( 2 ) = f ( 1 + 1 ) = 1 + 1 + 8 - 2 = 8 f ( 3 ) = f ( 2 + 1 ) = 8 + 1 + ( 8 * 2 * 1 ) - 2 = 23 f ( 6 ) = f ( 3 + 3 ) = 23 + 23 + ( 8 * 3 * 3 ) - 2 = 116 f ( 7 ) = f ( 6 + 1 ) = 116 + 1 + ( 8 * 6 * 1 ) - 2 = 163 thus ans is 163 answer : b" + }, + { + "Answer": 47, + "Options": "a ) 17 , b ) 25 , c ) 35 , d ) 42 , e ) 47", + "Correct": "e", + "Explanation": "to maximize c , we should minimize ( d - 12 ) ^ 2 . ( d - 12 ) ^ 2 is a square of a number , thus its smallest possible value is 0 ( for d = 12 ) . in this case we ' d have 5 c + 0 = 235 - - > c = 47 . answer : e ." + }, + { + "Answer": 4, + "Options": "a ) 2 , b ) 4 , c ) 8 , d ) 16 , e ) 32", + "Correct": "b", + "Explanation": "\"4 \u00f8 2 = 2 ^ 4 / 2 ^ 2 = 4 4 \u00f8 2 = 2 ^ 4 / 2 ^ 2 = 4 the answer is b .\"" + }, + { + "Answer": 24, + "Options": "a ) 24 , b ) 30 , c ) 35 , d ) 40 , e ) 45", + "Correct": "a", + "Explanation": "\"lots of ways to tackle this . 20 % of 180 = 36 1 / 3 of 36 = 12 so , 1 / 3 , less than 36 is equal to 36 - 12 = 24 answer : a\"" + }, + { + "Answer": 54.54545454545454, + "Options": "a ) 46.2 % , b ) 54.54 % , c ) 63 % , d ) 70 % , e ) none of these", + "Correct": "b", + "Explanation": "\"explanation : number of runs made by running = 132 - ( 12 x 4 + 2 x 6 ) = 132 - ( 60 ) = 72 now , we need to calculate 72 is what percent of 132 . = > 72 / 132 * 100 = 54.54 % answer : b\"" + }, + { + "Answer": 4, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "d", + "Explanation": "72 = 8 * 9 divisibility 0 f 8 last 3 place should be divisible by 8 lly divisibility of 9 sum of digit should be divisible by 9 840 divisible by 8 nd 36 divisible by 9 answer : d" + }, + { + "Answer": 50, + "Options": "a ) 20 , b ) 25 , c ) 50 , d ) 45 , e ) 75", + "Correct": "c", + "Explanation": "\"average = 40 , sum of temperatures = 40 * 5 = 200 as the min temperature is 30 , max would be 200 - 4 * 30 = 80 - - > the range = 80 ( max ) - 30 ( min ) = 50 answer : c\"" + }, + { + "Answer": 1626, + "Options": "a ) 1245 , b ) 1345 , c ) 1455 , d ) 1577 , e ) 1641", + "Correct": "e", + "Explanation": "\"let the smaller number be x . then larger number = ( x + 1370 ) . x + 1370 = 6 x + 15 5 x = 1355 x = 271 large number = 271 + 1370 = 1641 e\"" + }, + { + "Answer": 5800, + "Options": "a ) rs . 5800 , b ) rs . 3618 , c ) rs . 3600 , d ) rs . 3619 , e ) rs . 3610", + "Correct": "a", + "Explanation": "\"manager ' s monthly salary = rs . ( 2200 * 19 - 2000 * 18 ) = rs . 5800 answer : a\"" + }, + { + "Answer": 1, + "Options": "a ) 2 , b ) 5 , c ) 1 , d ) 6 , e ) 7", + "Correct": "c", + "Explanation": "the sum of the digits of the number is divisible by 3 , then the number is divisible by 3 . 2 + 3 + x + 5 + 7 = 17 + x least value of x may be 1 therefore 17 + 1 = 18 is divisible by 3 . c" + }, + { + "Answer": 275, + "Options": "a ) 198 , b ) 275 , c ) 299 , d ) 402 , e ) 205", + "Correct": "b", + "Explanation": "\"last term = first term + ( total no . of terms - 1 ) consecutive difference s is a set of 45 consecutive multiples of 5 . if the smallest number in s is 55 , then the greatest number in s is first term = 55 ; total terms = 45 ; difference = 5 55 + ( 44 ) 5 = 275 ans b\"" + }, + { + "Answer": 70.00000000000001, + "Options": "a ) 40 , b ) 45 , c ) 38 , d ) 50 , e ) 70", + "Correct": "e", + "Explanation": "let , father \u00e2 \u20ac \u2122 s current age is a years . then , man \u00e2 \u20ac \u2122 s current age = [ ( 2 / 5 ) a ] years . therefore , [ ( 2 / 5 ) a + 14 ] = ( 1 / 2 ) ( a + 14 ) 2 ( 2 a + 70 ) = 5 ( a + 14 ) a = 70 e" + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 7 , c ) 8 , d ) 9 , e ) 10", + "Correct": "a", + "Explanation": "\"say there are ' a ' associate professors . so we have 2 a pencils and a charts . say there are ' b ' assistant professors . so we have b pencils and 2 b charts . total pencils are 10 so 2 a + b = 10 total charts are 11 so a + 2 b = 5 add both : 3 a + 3 b = 15 so a + b = 5 total number of people = 5 a\"" + }, + { + "Answer": 7, + "Options": "a ) seven 7 , b ) 8 , c ) 9 , d ) 15 , e ) 17", + "Correct": "a", + "Explanation": "\"2 ) the average of the new group of numbers is 35 7 / 17 . the denominator of that fraction tells us that the total number of terms in the new list must be a multiple of 17 : 17 , 34 , 51 , 68 , 85 , etc . 3 ) since we ' re removing 1 number from a list of consecutive positive integers , we could quickly limit down the possible number of terms in the original list : if new = 17 , old = 18 , but the numbers from 1 to 18 would not have an average in the mid - 30 s ( it would be much smaller ) . eliminate this option . if new = 34 , old = 35 , but we run into the same problem . the average wo n ' t match here either . eliminate this option . if new = 51 , old = 52 , same problem here . eliminate this option . if new = 68 , old = 69 . . . . here we have a group of numbers that might just be what we ' re looking for . in theold group , the average is themiddle term = 35 , which is really close to the new average once we remove a number . now , we just have to figure out which of the 5 answers was removed ( and that changed the new average to 35 7 / 17 ) . there are a couple of ways to do this math , but i ' m going to use the answers to save myself some steps : sum of 1 to 69 , inclusive = 69 ( 35 ) = 2415 remove answer b . . . . 2415 - 8 = 2407 new average = 2407 / 68 = 35 27 / 68 now , we can compare 27 / 68 to 7 / 17 27 / 68 and 28 / 68 this is really close , but is not the answer . eliminate b . the answer is either a or c . since 28 / 68 is a bigger fraction than 27 / 68 , we need the sum ( of the 68 integers ) to be bigger . . . which means we need to remove a smaller number . final answer : a\"" + }, + { + "Answer": 8.5, + "Options": "a ) 6 , b ) 8.5 , c ) 11.5 , d ) 12 , e ) 12.5", + "Correct": "b", + "Explanation": "\"mean = 10.5 two standard deviations is 1 + 1 = 2 there could be two calues for this . mean + two standard deviations = 12.5 mean - two standard deviations = 8.5 answer choice has 8.5 and so b is the answer .\"" + }, + { + "Answer": 0.034, + "Options": "a ) 0.034 , b ) 0.024 , c ) 0.352 , d ) 0.063 , e ) 0.026", + "Correct": "a", + "Explanation": "error = ( 81.5 \u2013 81.472 ) km = 0.028 . required percentage = [ ( 0.028 / 81.472 ) * 100 ] % = 0.034 % . answer a ." + }, + { + "Answer": 0.5, + "Options": "a ) 10 / 16 , b ) 6 / 16 , c ) 5 / 10 , d ) 6 / 10 , e ) 4 / 10", + "Correct": "c", + "Explanation": "w = m + 5 w + m = 15 m + 5 + m = 15 2 m = 10 m = 5 w = 10 ratio : 5 : 10 ans : c" + }, + { + "Answer": 11000, + "Options": "a ) $ 4000 , b ) $ 5000 , c ) $ 9000 , d ) $ 11000 , e ) $ 13000", + "Correct": "d", + "Explanation": "break down the question in to steps : step # 1 : incentives received by 5 salesmen - - > abcde step # 2 : mean and median of the incentives is $ 7000 : via number properties - - > total incentives = 7000 * 5 = 35000 ab 7000 de step # 3 : only mode among the observations is $ 12000 : mode is the value that appears most often in a set of data . therefore 12000 must occur more then once and since 12000 is larger than the mean ( 7000 ) the most it can occur is twice in our list . if we place the numbers in ascending order we haveab 70001200012000 step # 4 : what is the difference z between the highest and the lowest incentive : - the total paid has to equal mean * # of numbers = 7000 * 5 = 35 000 . - the three values we have so far ( 12000 12000 and 7000 ) equal 31000 . - therefore the first two numbers ( ab ) must equal 4000 - there is only one mode which is 12000 , therefore 4000 must be equal to a set of two numbers that are not the and a < b if a = 1000 b = 3000 - - > difference between the highest and the lowest incentive = 12000 - 1000 = 11000 no other options for a or b to fit the criteria final list : 1000300070001200012000 answer d" + }, + { + "Answer": 350, + "Options": "a ) 0.35 % , b ) 3.5 % , c ) 35 % , d ) 350 % , e ) 0.0035 %", + "Correct": "d", + "Explanation": "\"answer : option d 3.5 = 35 / 10 = ( 35 / 10 * 100 ) = 350 %\"" + }, + { + "Answer": 17, + "Options": "a ) 16 , b ) 17 , c ) 19 , d ) 22 , e ) 26", + "Correct": "b", + "Explanation": "the total sum of the numbers should be increased by 10 . then the average will increase by 10 / 10 = 1 . the correct average is 17 . the answer is b ." + }, + { + "Answer": 285, + "Options": "a ) 285 , b ) 227 , c ) 271 , d ) 187 , e ) 199", + "Correct": "a", + "Explanation": "\"since the month begins with a sunday , so there will be five sundays in the month , required average = ( 510 * 5 + 240 * 25 ) / 30 = 8550 / 30 = 285 . answer : a\"" + }, + { + "Answer": 37.45, + "Options": "a ) $ 2.10 , b ) $ 37.10 , c ) $ 37.45 , d ) $ 38.10 , e ) $ 38.80", + "Correct": "c", + "Explanation": "\"principal that is amount taken by laura at year beginning = 35 $ rate of interest = 7 % interest = ( 7 / 100 ) * 35 = 2.45 $ total amount that laura owes a year later = 35 + 2.45 = 37.45 $ answer c\"" + }, + { + "Answer": 113, + "Options": "a ) 119 , b ) 117 , c ) 116 , d ) 113 , e ) 115", + "Correct": "d", + "Explanation": "\"explanation : total of the 10 digits - 10 * 80 = 800 total of the 6 digits - 6 * 58 = 348 total of the remaining 4 digits - 800 - 348 = 452 average of the remaining 4 numbers = 452 / 4 = 113 answer : d\"" + }, + { + "Answer": 22680, + "Options": "a ) $ 20960 , b ) $ 21920 , c ) $ 22680 , d ) $ 28500 , e ) $ 29160", + "Correct": "c", + "Explanation": "\"from 9 : 00 in the morning to 5 : 55 in the afternoon , inclusive there are 9 * 12 = 108 five - minute intervals , thus total of 108 * 30 tickets were sold . say x student and 3 x regular tickets were sold , then x + 3 x = 108 * 30 - - > x = 27 * 30 and 3 x = 3 * ( 27 * 30 ) = 27 * 90 . therefore , the total revenue from ticket sales that day was 27 * 30 * 4 + 27 * 90 * 8 = $ 22,680 . answer : c .\"" + }, + { + "Answer": 1.5, + "Options": "a ) $ 1.50 , b ) $ 2.50 , c ) $ 4.10 , d ) $ 4.70 , e ) $ 8.20", + "Correct": "a", + "Explanation": "\"let x be the cost of a bus ride . x + ( x + 685 ) = 985 2 x = 300 x = $ 1.50 the answer is a .\"" + }, + { + "Answer": 8, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 4 , e ) 3", + "Correct": "c", + "Explanation": "\"since 32 / k = 4 and 32 / 8 = 4 , then k = 8 correct answer c\"" + }, + { + "Answer": 42, + "Options": "a ) 21 , b ) 35 , c ) 39 , d ) 42 , e ) 65", + "Correct": "d", + "Explanation": "\"the total number of the people in the room must be a multiple of both 7 and 14 ( in order 3 / 7 and 5 / 14 of the number to be an integer ) , thus the total number of the people must be a multiple of lcm of 7 and 14 , which is 98 . since , the total number of the people in the room is greater than 50 and less than 100 , then there are 98 people in the room . therefore there are 3 / 7 * 98 = 42 people in the room under the age of 21 . answer : d .\"" + }, + { + "Answer": 18, + "Options": "a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20", + "Correct": "d", + "Explanation": "\"let the number of ducks be d and number of cows be c then , total number of legs = 2 d + 4 c = 2 ( d + 2 c ) total number of heads = c + d given that total number of legs are 36 more than twice the number of heads = > 2 ( d + 2 c ) = 36 + 2 ( c + d ) = > d + 2 c = 18 + c + d = > 2 c = 18 + c = > c = 18 i . e . , total number of cows = 18 answer is d .\"" + }, + { + "Answer": 12, + "Options": "a ) 16 , b ) 12 , c ) 15 , d ) 20 , e ) 10", + "Correct": "b", + "Explanation": "\"( a + b ) - ( b - c ) = 12 a - c = 12 answer is b\"" + }, + { + "Answer": 4100, + "Options": "a ) s . 4100 , b ) s . 4270 , c ) s . 4500 , d ) s . 4550 , e ) s . 2500", + "Correct": "a", + "Explanation": "\"sum of the salaries of the person for the months of january , february , march and april = 4 * 8000 = 32000 - - - - ( 1 ) sum of the salaries of the person for the months of february , march , april and may = 4 * 8600 = 34400 - - - - ( 2 ) ( 2 ) - ( 1 ) i . e . may - jan = 2400 salary of may is rs . 6500 salary of january = rs . 4100 answer : a\"" + }, + { + "Answer": 16, + "Options": "a ) s . 17 , b ) s . 18 , c ) s . 16 , d ) s . 11 , e ) s . 10", + "Correct": "c", + "Explanation": "\"average price per book = ( 1500 + 340 ) / ( 55 + 60 ) = 1840 / 115 = rs . 16 answer : c\"" + }, + { + "Answer": 18, + "Options": "a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22", + "Correct": "a", + "Explanation": "\"10 * 16 - 26 + 46 = 180 180 / 10 = 18 the answer is a .\"" + }, + { + "Answer": 1, + "Options": "a ) 0.5 , b ) 1 , c ) 1.5 , d ) 2 , e ) 3", + "Correct": "b", + "Explanation": "let x be the number of desks and bookcases that are placed along the library wall . 2 x + 1.5 x < 15 3.5 x < 15 since x is a non negative integer , the largest number x can be is 4 . when x is 4 , the desks and bookcases take up 3.5 * 4 = 14 m , leaving 1 m of empty space . thus , i believe the answer is b ) 1" + }, + { + "Answer": 16, + "Options": "a ) - 29 , b ) - 19 , c ) 16 , d ) 29 , e ) 39", + "Correct": "c", + "Explanation": "45 - [ 28 - { 37 - ( 15 - * ) } ] = 55 = > 45 - [ 28 - { 37 - 15 + * } ] = 55 45 - [ 28 - 37 + 15 - * ] = 55 = > 45 [ 43 - 37 - * ] = 55 45 - [ 6 - * ] = 55 = > 45 - 6 + * = 55 39 + * = 55 = > * = 55 - 39 = 16 answer : c" + }, + { + "Answer": 7, + "Options": "a ) 0 , b ) 1 , c ) 5 , d ) 7 , e ) 9", + "Correct": "d", + "Explanation": "\"i looked for patterns : ^ 2 - units digit 9 ^ 3 - units digit 7 ^ 4 - units digit 1 ^ 5 - units digit 3 hence , we can see that when raised to a power which is multiple of 4 , the units digit is 1 , and when to an even power not multiple of 4 , the units digit is 9 and we can then see : ^ 16 - units digit 1 , or ^ 18 - units digit 9 and ^ 19 - units digit 7 therefore , q = when divided by 10 , the remainder must be 7 . d\"" + }, + { + "Answer": 49.25925925925926, + "Options": "a ) a ) 47 , b ) b ) 45.6 , c ) c ) 44 , d ) d ) 48 , e ) e ) 49.3", + "Correct": "e", + "Explanation": "explanation : total marks obtained by a class of 25 students = 5 * 95 + 3 * 0 + 19 * 45 = 1330 average marks of whole class = 1330 / 27 = 49.3 answer : option e" + }, + { + "Answer": 24, + "Options": "a ) 10 hours , b ) 12 hours , c ) 14 hours , d ) 24 hours , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : speed of the boat = 6 km / hr speed downstream = ( 6 + 2 ) = 8 km / hr speed upstream = ( 6 - 2 ) = 4 km / hr distance travelled downstream = distance travelled upstream = 64 km total time taken = time taken downstream + time taken upstream = ( 64 / 8 ) + ( 64 / 4 ) = = 24 hr . answer : option d\"" + }, + { + "Answer": 5, + "Options": "a ) 3 , b ) 5 , c ) 6 , d ) 11 , e ) 16", + "Correct": "b", + "Explanation": "\"( m - 8 ) ( m - a ) = m ^ 2 - pm - 24 a = - 3 p = 8 + a = 5 = b\"" + }, + { + "Answer": 8, + "Options": "a ) $ 9 , b ) $ 8 , c ) $ 4 , d ) $ 6 , e ) $ 5", + "Correct": "b", + "Explanation": "\"my lunch = l , my friends lunch = l + 1 ( l ) + ( l + 1 ) = 15 l + l + 1 - 1 = 15 - 1 2 l = 14 l = 7 my friends lunch l + 1 = 7 + 1 = $ 8 , the answer is b\"" + }, + { + "Answer": 24, + "Options": "a ) 4 , b ) 24 , c ) 40 , d ) 16 , e ) 20", + "Correct": "b", + "Explanation": "write the prime factorization . 600 = ( 2 ^ 3 ) ( 3 ^ 1 ) ( 5 ^ 2 ) the number of divisors ( including 1 and the number itself ) is the product of one plus the exponents . ( 3 + 1 ) ( 1 + 1 ) ( 2 + 1 ) = 24 answer : b" + }, + { + "Answer": 0.5833333333333333, + "Options": "a ) 1 / 6 , b ) 1 / 3 , c ) 7 / 12 , d ) 2 / 3 , e ) 5 / 6", + "Correct": "c", + "Explanation": "so not a vowel in set - 1 : 1 / 2 and not a vowel in ser - 2 : 5 / 6 now , 1 / 2 \u2217 5 / 6 = 5 / 12 this is for not a vowel . then for at least one vowel will be = 1 \u2212 5 / 12 = 7 / 12 answer will be c ." + }, + { + "Answer": 1200, + "Options": "a ) 3387 , b ) 1000 , c ) 1200 , d ) 2787 , e ) 1121", + "Correct": "c", + "Explanation": "\"20 * 12 * 5 = 1200 answer : c\"" + }, + { + "Answer": 7, + "Options": "a ) 7 , b ) 16 , c ) 10 , d ) 11 , e ) can not be determined", + "Correct": "a", + "Explanation": "following approach will take you only couple of sec . \\ ( 7 ^ { 100 } = ( 7 ^ { 50 } ) ^ 2 \\ ) the sum of digits ( digital root ) of a perfect square can only be 1 , 4 , 7 or 9 . for example \\ ( 7 ^ 2 = 49 \\ ) = > dr = 4 + 9 = 13 = > 1 + 3 = 4 and etc . checking available options . answer a ." + }, + { + "Answer": 0.7857142857142856, + "Options": "a ) 11 / 14 , b ) 13 / 18 , c ) 4 / 7 , d ) 3 / 7 , e ) 3 / 14", + "Correct": "a", + "Explanation": "\"if we use variable for total votes there will be too many fractions to manipulate with , so pick some smart # : let set total # of votes is 18 . 2 / 9 of the votes on a certain resolution have been counted - - > 4 counted and 18 - 4 = 14 votes left to be counted ; 3 / 4 of those counted are in favor of the resolution - - > 3 in favor and 1 against ; ratio of those who voted against to those who voted for to be 2 to 1 there should be total of 18 * 2 / 3 = 12 people who voted against , so in the remaining 14 votes there should be 12 - 1 = 11 people who voted against . thus w = 11 / 14 of the remaining votes must be against . answer : a .\"" + }, + { + "Answer": 17, + "Options": "a ) 12 , b ) 27 , c ) 21 , d ) 17 , e ) 11", + "Correct": "d", + "Explanation": "\"( a + b ) - ( b + c ) = 17 a - c = 17 . c is younger than a by 17 years . answer : d\"" + }, + { + "Answer": 80, + "Options": "a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 80", + "Correct": "e", + "Explanation": "start small and check for any pattern : 10 ^ 2 - 47 = 53 - > number of digits = power of 10 ; number of 9 s = ( power of 10 ) - 2 ; 53 is the last 2 digits 10 ^ 3 - 47 = 953 - > number of digits = power of 10 ; number of 9 s = ( power of 10 ) - 2 ; 53 is the last 2 digits . . . extrapolate 10 ^ 10 - 47 - > number of digits = 10 ; number of 9 s = 8 ; 53 will be the last 2 digits sum , a = 9 * 8 + 5 + 3 = 80 . answer ( e ) ." + }, + { + "Answer": 42, + "Options": "a ) 24 , b ) 17 , c ) 28 , d ) 42 , e ) it can not be determined from the information given .", + "Correct": "d", + "Explanation": "a = ( 1 , 2,3 , 4,5 , 6,7 ) , sum of this = 28 b = ( 7 , 8,9 , 10,11 , 12,13 ) , sum of this = 70 the differenct between 70 - 28 = 42 hence , 42 is the answer i . e . d" + }, + { + "Answer": 162, + "Options": "a ) 150 , b ) 162 , c ) 154 , d ) 158 , e ) 144", + "Correct": "b", + "Explanation": "\"d = d * q + r d = 17 * 9 + 9 d = 153 + 9 d = 162 answer b\"" + }, + { + "Answer": 56, + "Options": "a ) a ) 23 , b ) b ) 21 , c ) c ) 52 , d ) d ) 56 , e ) e ) 12", + "Correct": "d", + "Explanation": "\"let the total number of workers be x . then , 6750 x = ( 12000 * 7 ) + 6000 ( x - 7 ) = > 750 x = 42000 = x = 56 . answer : d\"" + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) 14 , c ) 15 , d ) 16 , e ) 17", + "Correct": "a", + "Explanation": "d = ( d - r ) / q = ( 109 - 1 ) / 9 = 108 / 9 = 18 a" + }, + { + "Answer": 395.4, + "Options": "a ) $ 382.10 , b ) $ 395.40 , c ) $ 404.30 , d ) $ 416.80 , e ) $ 426.50", + "Correct": "b", + "Explanation": "\"the service cost of 4 vans and 2 trucks is 6 * 2.20 $ 13.20 the fuel in 4 vans is 4 * 65 = 260 liters the fuel in 2 trucks is 2 * 65 * 2.2 = 286 liters the total fuel ( vans + trucks ) = 546 liters the total fuel cost is 546 * 0.7 = $ 382.20 the total cost is $ 382.20 + $ 13.20 = $ 395.40 the answer is b .\"" + }, + { + "Answer": 78, + "Options": "a ) 66 , b ) 70 , c ) 74 , d ) 78 , e ) 82", + "Correct": "d", + "Explanation": "\"n = 4 k + 1 = 7 j + 4 let ' s start at 1 = 4 ( 0 ) + 1 and keep adding 4 until we find a number in the form 7 j + 4 . 1 , 5 , 9 , 13 , 17 , 21 , 25 = 7 ( 3 ) + 4 the next such number is 25 + 4 * 7 = 53 . 25 + 53 = 78 the answer is d .\"" + }, + { + "Answer": 360, + "Options": "a ) 120 , b ) 240 , c ) 360 , d ) 480 , e ) 720", + "Correct": "c", + "Explanation": "c ) 360 short way : there are 6 c ! ways to do the six tasks . half will have wheels before axles and half will have axles before wheels . so we want y = 6 c ! / 2 - > 720 / 2 = 360" + }, + { + "Answer": 0.2222222222222222, + "Options": "a ) 1 / 9 , b ) 2 / 9 , c ) 4 / 9 , d ) 3 / 9 , e ) 2 / 27", + "Correct": "b", + "Explanation": "we just need to find the factor thats all , e - > quadrupled - > 4 e x - > doubled - > 2 x z - > tripled - > 3 z hence , z ^ 2 = 9 z ^ 2 e is in numerator , and x * z in denominator . hence , additional factor being introduced = 4 / 2 * 9 = 4 / 18 = 2 / 9 = b" + }, + { + "Answer": 60, + "Options": "a ) 40 , b ) 60 , c ) 80 , d ) 90 , e ) 100", + "Correct": "b", + "Explanation": "let x = total feed required for the planned period n = number of chicken t = total time of the planned feed x = nt 1 ) x = ( n - 15 ) * ( t + 4 ) 2 ) x = ( n + 20 ) * ( t - 3 ) equating 1 & 2 ( n - 15 ) * ( t + 4 ) = ( n + 20 ) * ( t - 3 ) 7 n = 35 t n = 5 t x = n * n / 5 substituting this value in 1 n * n / 5 = ( n - 15 ) * ( n / 5 + 4 ) 5 n = 300 n = 60 b" + }, + { + "Answer": 42, + "Options": "a ) 18 , b ) 24 , c ) 30 , d ) 36 , e ) 42", + "Correct": "e", + "Explanation": "\"987654 / 456 = 2165 with a remainder of 414 . we need to add 456 - 414 = 42 the answer is e .\"" + }, + { + "Answer": 211, + "Options": "a ) 187 , b ) 193 , c ) 199 , d ) 205 , e ) 211", + "Correct": "e", + "Explanation": "let n - 1 = 2 a . 2 + 4 + . . . + 2 a = 2 * ( 1 + 2 + . . . + a ) = 2 * ( a ) ( a + 1 ) / 2 = ( a ) ( a + 1 ) = 105 * 106 then a = 105 and n = 211 . the answer is e ." + }, + { + "Answer": 20, + "Options": "a ) 387 , b ) 39 , c ) 37 , d ) 20 , e ) 28", + "Correct": "d", + "Explanation": "hint : see problem 20 and solve by yourself . answer : a ) 120 hectares ; b ) 7 days ; c ) 8 days . answer : d" + }, + { + "Answer": 4000, + "Options": "a ) 4050 , b ) 3500 , c ) 4000 , d ) 4500 , e ) 5000", + "Correct": "c", + "Explanation": "let p , q and r represent their respective monthly incomes . then , we have : p + q = ( 5050 x 2 ) = 10100 . . . . ( i ) q + r = ( 6250 x 2 ) = 12500 . . . . ( ii ) p + r = ( 5200 x 2 ) = 10400 . . . . ( iii ) adding ( i ) , ( ii ) and ( iii ) , we get : 2 ( p + q + r ) = 33000 or p + q + r = 16500 . . . . ( iv ) subtracting ( ii ) from ( iv ) , we get p = 4000 . p ' s monthly income = rs . 4000 . answer : c" + }, + { + "Answer": 11.5, + "Options": "a ) 8 , b ) 12 , c ) 16 , d ) 24 , e ) 46 / 4", + "Correct": "e", + "Explanation": "\"i ' m going to focus on denominator only . . ( 2 ^ 23 ) . ( ( 3 ^ 4 ) ^ k = 18 ^ 23 ( 2 ^ 23 ) . ( ( 3 ^ 4 k ) = ( 2 . 3 ^ 2 ) ^ 23 ( 2 ^ 23 ) . ( ( 3 ^ 4 k ) = ( 2 ^ 23 ) . ( 3 ^ 2 ) ^ 23 hence 4 k = 46 k = 46 / 4 answer e i hope it ' s quite clear\"" + }, + { + "Answer": 208, + "Options": "a ) $ 208 , b ) $ 96 , c ) $ 104 , d ) $ 120 , e ) $ 240", + "Correct": "a", + "Explanation": "\"eps actual > eps expected . each gets and additional . 12 per share . thus . 52 * 400 - - > $ 208 answer is a\"" + }, + { + "Answer": 7, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9", + "Correct": "c", + "Explanation": "840 = 2 * 2 * 2 * 3 * 5 * 7 , so n must be at least 7 . the answer is c ." + }, + { + "Answer": 4691110842, + "Options": "a ) 4586970843 , b ) 4686970743 , c ) 4691100843 , d ) 4586870843 , e ) 4691110842", + "Correct": "e", + "Explanation": "\"answer 469158 x 9999 = 469157 x ( 10000 - 1 ) = 4691580000 - 469158 = 4691110842 . option : e\"" + }, + { + "Answer": 28, + "Options": "a ) 22 , b ) 23 , c ) 24 , d ) 26 , e ) 28", + "Correct": "e", + "Explanation": "\"let hens be x and cows be y now , feet : x * 2 + y * 4 = 136 heads : x * 1 + y * 1 = 48 implies , 2 x + 4 y = 136 and x + y = 48 solving these two equations , we get x = 28 and y = 20 therefore , hens are 28 . answer : e\"" + }, + { + "Answer": 86, + "Options": "a ) 86 , b ) 88 , c ) 92 , d ) 94 , e ) 96", + "Correct": "a", + "Explanation": "\"divisor = ( 6 * 3 ) + 2 = 20 5 * quotient = 20 quotient = 4 . dividend = ( divisor * quotient ) + remainder dividend = ( 20 * 4 ) + 6 = 86 . a\"" + }, + { + "Answer": 20, + "Options": "a ) 21 years , b ) 22 years , c ) 20 years , d ) 24 years , e ) 26 years", + "Correct": "c", + "Explanation": "\"explanation : let ' s son age is x , then father age is x + 22 . = > 2 ( x + 2 ) = ( x + 22 + 2 ) = > 2 x + 4 = x + 24 = > x = 20 years option c\"" + }, + { + "Answer": 24, + "Options": "a ) 0.20 , b ) 0.24 , c ) 20 , d ) 24 , e ) 55", + "Correct": "d", + "Explanation": "\"a dozen eggs cost as much as a pound of rice - - > 12 eggs = 1 pound of rice = 24 cents ; a half - liter of kerosene costs as much as 6 eggs - - > 6 eggs = 1 / 2 liters of kerosene . how many cents does a liter of kerosene cost - - > 1 liter of kerosene = 12 eggs = 12 / 12 * 24 = 24 cents . answer : d .\"" + }, + { + "Answer": 0.43333333333333335, + "Options": "a ) 1 / 17 , b ) 13 / 30 , c ) 17 / 30 , d ) 11 / 30 , e ) 11 / 13", + "Correct": "b", + "Explanation": "\"we have the ratio of a \u2019 s speed and b \u2019 s speed . this means , we know how much distance a covers compared with b in the same time . this is what the beginning of the race will look like : ( start ) a _________ b ______________________________ if a covers 30 meters , b covers 17 meters in that time . so if the race is 30 meters long , when a reaches the finish line , b would be 13 meters behind him . if we want the race to end in a dead heat , we want b to be at the finish line too at the same time . this means b should get a head start of 13 meters so that he doesn \u2019 t need to cover that . in that case , the time required by a ( to cover 30 meters ) would be the same as the time required by b ( to cover 17 meters ) to reach the finish line . so b should get a head start of 13 / 30 th of the race . answer ( b )\"" + }, + { + "Answer": 941.6, + "Options": "a ) 347.6 , b ) 987.6 , c ) 941.6 , d ) 637.6 , e ) 667.6", + "Correct": "c", + "Explanation": "\"let the costs of each kg of mangos and each kg of rice be $ a and $ r respectively . 10 a = 24 r and 6 * 22 = 2 r a = 12 / 5 r and r = 66 a = 158.4 required total cost = 4 * 158.4 + 3 * 66 + 5 * 22 = 633.6 + 198 + 110 = $ 941.60 c\"" + }, + { + "Answer": 36, + "Options": "a ) 6 , b ) 36 , c ) 19 , d ) 27 , e ) none of these", + "Correct": "b", + "Explanation": "27 ( 2 ) < 765 < 28 ( 2 ) \u2234 required no . of chairs to be excluded = 765 \u2013 729 = 36 answer b" + }, + { + "Answer": 15, + "Options": "a ) 11 , b ) 12 , c ) 14 , d ) 15 , e ) 18", + "Correct": "d", + "Explanation": "\"let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 30 = > 2 x = 30 = > x = 15 d\"" + }, + { + "Answer": 130, + "Options": "a ) 75 , b ) 100 , c ) 125 , d ) 130 , e ) 225", + "Correct": "d", + "Explanation": "\"female = x male = 780 - x x / 2 + 780 - x / 4 = 1 / 3 * ( 780 ) = 260 x = 260 x / 2 = 130 is supposed to be the answer m is missing something correct option d\"" + }, + { + "Answer": 32, + "Options": "a ) 16 , b ) 19 , c ) 15 , d ) 32 , e ) 40", + "Correct": "d", + "Explanation": "\"let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . ( x + 34 ) + 2 = 2 ( x + 2 ) x + 36 = 2 x + 4 = > x = 32 . answer : d\"" + }, + { + "Answer": 37, + "Options": "a ) 28 sec , b ) 16 sec , c ) 37 sec , d ) 18 sec , e ) 17 sec", + "Correct": "c", + "Explanation": "\"speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 240 + 120 = 370 m . time taken = 370 / 10 = 37 sec . answer : c\"" + }, + { + "Answer": 12, + "Options": "a ) 6 , b ) 12 , c ) 24 , d ) 36 , e ) 48", + "Correct": "b", + "Explanation": "\"q : if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer m that must divide n is : a 6 , b 12 , c 24 , d 36 , e 48 n ^ 2 is divisible by 72 , but it must also be greater than 72 . if n is an integer , then n ^ 2 must be a perfect square . the factorization of 72 is ( 8 ) ( 9 ) , so if it is multiplied by 2 , it will be ( 2 ) ( 8 ) ( 9 ) = ( 16 ) ( 9 ) = 144 , a perfect square . so n ^ 2 must be at least 144 or a multiple of 144 , which means that n must be 12 or a multiple of 12 . b\"" + }, + { + "Answer": 4, + "Options": "a ) 13 , b ) 12 , c ) 9 , d ) 8 , e ) 4", + "Correct": "e", + "Explanation": "\"there are total 72 workers . one - fourth of the workers in palabras bookstore have read the latest book by j . saramago , so 18 have read saramago . 5 / 8 of the workers have read the latest book by h . kureishi . so ( 5 / 8 ) * 72 = 45 have read kureishi the number of workers that have read neither book is one less than the number of the workers that have read the latest saramago book and have not read the latest kureishi book if b workers have read both books , 18 - b have read saramago but not kureishi . so , ( 18 - b - 1 ) have read neither . total = n ( a ) + n ( b ) - both + neither 72 = 18 + 45 - b + ( 18 - b - 1 ) b = 4 answer ( e )\"" + }, + { + "Answer": 4000.000000000002, + "Options": "a ) rs . 4000 , b ) rs . 4500 , c ) rs . 5500 , d ) rs . 6000 , e ) rs . 6500", + "Correct": "a", + "Explanation": "let investment in 12 % stock be rs . x . then , investment in 15 % stock = rs . ( 12000 - x ) . 12 / 120 * x + 15 / 125 * ( 12000 - x ) = 1360 x / 10 + 3 / 25 ( 12000 - x ) = 1360 5 x + 72000 - 6 x = 1360 x 50 x = 4000 . answer = a" + }, + { + "Answer": 0.037500000000000006, + "Options": "a ) 11 / 8 , b ) 3 / 80 , c ) 9 / 64 , d ) 5 / 64 , e ) 3 / 64", + "Correct": "b", + "Explanation": "\"p ( xavier will solve ) = 1 / 5 p ( yvonne will solve ) = 1 / 2 p ( zelda will not solve ) = 1 - 5 / 8 = 3 / 8 . now , we need to multiply all this ps to find an answer : p = ( 1 / 5 ) * ( 1 / 2 ) * ( 3 / 8 ) = 3 / 80 . ans . b .\"" + }, + { + "Answer": 5.700000000000003, + "Options": "a ) 2 % , b ) 8.7 % , c ) 5.7 % , d ) 6.7 % , e ) 1 %", + "Correct": "c", + "Explanation": "\"100 * 100 = 10000 82 * 115 = 9430 - - - - - - - - - - - 10000 - - - - - - - - - - - 570 100 - - - - - - - - - - - ? = > 5.7 % decrease answer : c\"" + }, + { + "Answer": 82, + "Options": "a ) 92 , b ) 80 , c ) 72 , d ) 82 , e ) 28", + "Correct": "d", + "Explanation": "mabel handled 90 transaction , anthony 10 % more transaction the mabel . anthony = 90 + 90 * 10 % , = 90 + 90 * 0.10 , = 90 + 9 , = 99 , cal handled 2 / 3 rds than anthony handled , cal = 2 / 3 * 99 = 66 , jade handled 16 more than cal . jade = 66 + 16 = 82 , jade handled = 82 tranasactions . correct answer : ( d )" + }, + { + "Answer": 23.999999999999996, + "Options": "a ) 24 , b ) 26 , c ) 28 , d ) 30 , e ) 36", + "Correct": "a", + "Explanation": "\"let the total weight be x . sand content = ( 1 / 3 ) x water content = ( 1 / 4 ) x gravel = x - ( 1 / 3 ) x - ( 1 / 4 ) x = ( 5 / 12 ) x = 10 x = 24 then answer will be a = 24\"" + }, + { + "Answer": 117, + "Options": "a ) 117 , b ) 180 , c ) 150 , d ) 200 , e ) 250", + "Correct": "a", + "Explanation": "exp . let the total expenditure be x , then the average = x / 9 , 8 * 12 + [ x / 9 + 8 ] = x or [ x - x / 9 ] = 104 . 8 x / 9 = 104 , x = 104 * 9 / 8 = 117 . answer : a" + }, + { + "Answer": 18, + "Options": "a ) 15 days , b ) 18 days , c ) 21 days , d ) 24 days , e ) 27 days", + "Correct": "b", + "Explanation": "\"2 oxen = 3 buffaloes = 4 cows also : 15 buffaloes + 8 oxen + 24 cows = 10 oxen + 8 oxen + 12 oxen = 30 oxen there is enough fodder for 1 oxen for 30 * 36 days . 40 cows + 15 buffaloes = 20 oxen + 10 oxen = 30 oxen the new total is equal to 60 oxen instead of 30 oxen . 30 * 36 / 60 oxen = 18 days the answer is b .\"" + }, + { + "Answer": 9, + "Options": "a ) 8 , b ) 10 , c ) 12 , d ) 9 , e ) 6", + "Correct": "d", + "Explanation": "gcd of ( b - 2 ) ! , ( b + 1 ) ! , and ( b + 4 ) ! is 5040 . find x . best way to find n is substitute each of the answer and find out the correct one . only option d gave the correct answer . option d : 9 and find gcd or 7 ! , 10 ! and 13 ! . 7 ! itself is 5040 and 7 ! which is contained in the other two factorials . this satisfies the condition , hence answer is 9 . answer is d ." + }, + { + "Answer": 0.1388888888888889, + "Options": "a ) 5 / 46 , b ) 7 / 36 , c ) 1 / 36 , d ) 5 / 36 , e ) 5 / 37", + "Correct": "d", + "Explanation": "a / d = ( 1 / 4 ) * ( 13 / 9 ) * ( 5 / 13 ) = > 5 / 36 answer : d" + }, + { + "Answer": 9, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 12", + "Correct": "c", + "Explanation": "\"27 ^ z > 3 ^ 24 converting into the same bases : 27 ^ z > 27 ^ 8 therefore for the equation to hold true , z > 8 or z = 9 option c\"" + }, + { + "Answer": 43, + "Options": "a ) 48 , b ) 41 , c ) 46 , d ) 43 , e ) 96", + "Correct": "d", + "Explanation": "let a and b be the two numbers ( a + b ) ^ 2 = a ^ 2 + 2 ab + b ^ 2 given ( a + b ) = 21 a ^ 2 + b ^ 2 = 527 so , 21 ^ 2 = 527 + 2 ab 2 ab = 527 - 441 2 ab = 86 ab = 43 ans d" + }, + { + "Answer": 55, + "Options": "a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 55", + "Correct": "e", + "Explanation": "\"i think we can use double - matrix method and solve using only one variable . our goal is to find the number of hardcover nonfiction books . let that number be x . we are given that all 140 books are either paperback fiction , paperback nonfiction , or hardcover nonfiction . this implies that number of hardcover fiction books is 0 . double - matrix : p = paperback ; h = hardcover ; f = fiction ; nf = nonfiction p h total f 2 x + 40 0 nf x + 20 x total 3 x + 60 x 280 3 x + 60 + x = 280 x = 55 answer ( e . )\"" + }, + { + "Answer": 15, + "Options": "a ) 0 , b ) 5 , c ) 10 , d ) 15 , e ) 25", + "Correct": "d", + "Explanation": "you should notice that 55 * 2 = 110 so 11,000 is divisible by 55 : 55 * 200 = 11,000 ( or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55 ) - - > b * a = 0 * 0 = 0 . next number divisible by 55 is 11,000 + 55 = 11,055 : b * a = 5 * 5 = 15 ( next number wo n ' t have 110 as the first 3 digits so we have only two options 0 and 25 ) . answer : e . ! please post ps questions in the ps subforum : gmat - problem - solving - ps - 140 / please post ds questions in the ds subforum : gmat - data - sufficiency - ds - 141 / no posting of ps / ds questions is allowed in the mainmath forum . d" + }, + { + "Answer": 16, + "Options": "a ) 14 kg , b ) 15 kg , c ) 18 kg , d ) 19 kg , e ) 16 kg", + "Correct": "e", + "Explanation": "explanation let a , b , c represent their respective weights . then , we have : a + b + c = ( 30 x 3 ) = 90 \u00e2 \u20ac \u00a6 . ( i ) a + b = ( 25 x 2 ) = 50 \u00e2 \u20ac \u00a6 . ( ii ) b + c = ( 28 x 2 ) = 56 \u00e2 \u20ac \u00a6 . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 106 \u00e2 \u20ac \u00a6 . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 16 . b \u00e2 \u20ac \u2122 s weight = 16 kg . answer e" + }, + { + "Answer": 60.00000000000001, + "Options": "a ) 60 % , b ) 50 % , c ) 55 % , d ) 40 % , e ) 33.3 %", + "Correct": "a", + "Explanation": "increase = 192000 - 120000 = 72000 % increase = 72000 * 100 / 120000 = 60 % answer : option a" + }, + { + "Answer": 29, + "Options": "a ) 25 liters , b ) 29 liters , c ) 30 liters , d ) 32 liters , e ) 35 liters", + "Correct": "b", + "Explanation": "\"let x ltr water to be added 2 ltr alcohol to be represented as ( 20 ( 1 - 3 / 4 ( new soln . = 11 + x ) ) ) 2 = 5 % * ( 11 + x ) - - - - - - - - > x = 29 ans b\"" + }, + { + "Answer": 5200, + "Options": "a ) s . 9800 , b ) s . 3800 , c ) s . 9800 , d ) s . 5200 , e ) s . 6880", + "Correct": "d", + "Explanation": "\"cost of the camel = p 10 camels = 24 horses 16 horses = 4 oxen 6 oxen = 4 elephants 10 elephants = rs . 130000 p = rs . [ ( 24 * 4 * 4 * 130000 ) / ( 10 * 16 * 6 * 10 ) ] p = rs . ( 49920000 / 9600 ) = > p = rs . 5200 answer : d\"" + }, + { + "Answer": 1950, + "Options": "a ) rs 1950 , b ) rs 2000 , c ) rs 745 , d ) rs 765 , e ) none", + "Correct": "a", + "Explanation": "required amount = 42900 / 22 = rs 1950 answer a" + }, + { + "Answer": 15, + "Options": "a ) 5 % , b ) 10 % , c ) 15 % , d ) 20 % , e ) 25 %", + "Correct": "c", + "Explanation": "\"say currently both a dozen eggs and 10 pounds of oranges cost $ 100 ( they are at the same price ) . so , to buy a dozen eggs and 10 pounds of oranges we need $ 100 . after the increase , the price of a dozen eggs will be $ 109 and the price of 10 pounds of oranges will be $ 106 . so after the increase , to buy a dozen eggs and 10 pounds of oranges we ' ll need $ 215 . increase = 15 % . answer : c .\"" + }, + { + "Answer": 18, + "Options": "a ) 10 hours , b ) 12 hours , c ) 14 hours , d ) 18 hours , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : speed of the boat = 6 km / hr speed downstream = ( 6 + 2 ) = 8 km / hr speed upstream = ( 6 - 2 ) = 4 km / hr distance traveled downstream = distance traveled upstream = 48 km total time taken = time taken downstream + time taken upstream = ( 48 / 8 ) + ( 48 / 4 ) = 18 hr . answer : option d\"" + }, + { + "Answer": 25.00000000000001, + "Options": "a ) 50 % , b ) 40 % , c ) 25 % , d ) 20 % , e ) 10 %", + "Correct": "c", + "Explanation": "\"looking at the ratio we can take total number of people = 20 . . ans 5 / 20 or 25 % c\"" + }, + { + "Answer": 42, + "Options": "a ) 41 , b ) 42 , c ) 43 , d ) 44 , e ) 45", + "Correct": "b", + "Explanation": "solution : all except 42 were crushed means that all the ants except 42 were crushed beneath the man ' s foot . hence , 42 ants are alive now answer b" + }, + { + "Answer": 6, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "e", + "Explanation": "\"if the average price is 54 , then mary has 7 oranges and 3 apples ( a ratio of 7 : 3 ) . for the average price to be 45 , the ratio should be 1 : 3 . mary must put back 6 oranges . the answer is e .\"" + }, + { + "Answer": 360, + "Options": "a ) 60 , b ) 116 , c ) 210 , d ) 263 , e ) 360", + "Correct": "e", + "Explanation": "since < x > = 2 x + ( 2 x - 1 ) + ( 2 x - 2 ) + . . . . . . 2 + 1 = 1 + 2 + . . + ( 2 x - 2 ) + ( 2 x - 1 ) + 2 x then < x > is basically the sum of all integers from 1 to 2 x , inclusive . hence < 2 > is the sum of all integers from 1 to 2 * 2 = 4 and < 4 > is the sum of all integers from 1 to 2 * 4 = 8 - > < 4 > = 36 and < 2 > = 10 - - > < 3 > * < 2 > = 21 * 10 = 360 answer : e" + }, + { + "Answer": 500.00000000000006, + "Options": "a ) 300 , b ) 600 , c ) 800 , d ) 500 , e ) 900", + "Correct": "d", + "Explanation": "\"explanation : let their maximum marks be x . then , 35 % of x = 150 + 25 = > 35 / 100 x = 175 x = ( 17500 / 35 ) x = 500 . answer : d\"" + }, + { + "Answer": 400, + "Options": "a ) rs . 300 , b ) rs . 400 , c ) rs . 480 , d ) rs . 490 , e ) rs . 500", + "Correct": "b", + "Explanation": "\"p : q = 5 : 4 , q : r = 9 : 10 = ( 9 x 4 / 9 ) : ( 10 x 4 / 9 ) = 4 : 40 / 9 . so , p : q : r = 5 : 4 : 40 / 9 = 45 : 36 : 40 sum of ratio terms is = ( 45 + 36 + 40 ) = 121 . r share of amount is rs ( 1210 x 40 / 121 ) = rs . 400 . b\"" + }, + { + "Answer": 20, + "Options": "a ) 19 , b ) 20 , c ) 25 , d ) 30 , e ) 64", + "Correct": "b", + "Explanation": "by formula , ( a + b + c ) ^ 2 = a ^ 2 + b ^ 2 + c ^ 2 + 2 ( ab + bc + ca ) , since , a ^ 2 + b ^ 2 + c ^ 2 = 390 and ab + bc + ca = 5 , ( a + b + c ) ^ 2 = 390 + 2 ( 5 ) = 400 = 20 ^ 2 therefore : a + b + c = 20 answer : b" + }, + { + "Answer": 26, + "Options": "a ) 22 , b ) 24 , c ) 26 , d ) 20 , e ) 18", + "Correct": "c", + "Explanation": "let number of hens = h number of cows = c number of heads = 48 \u21d2 h + c = 48 \u22ef ( 1 ) number of feet = 140 \u21d2 2 h + 4 c = 140 \u21d2 h + 2 c = 70 \u22ef ( 2 ) ( 2 ) \u2212 ( 1 ) gives 2 c \u2212 c = 70 \u2212 48 \u21d2 c = 22 substituting the value of c in ( 1 ) , we get h + 22 = 48 \u21d2 h = 48 \u2212 22 = 26 h + 22 = 48 \u21d2 h = 48 \u2212 22 = 26 i . e . , number of hens = 26 answer : c" + }, + { + "Answer": 120.25, + "Options": "a ) 120.25 , b ) 120.35 , c ) 106.5 , d ) 156 , e ) 240", + "Correct": "a", + "Explanation": "\"explanation : cash realised = rs . ( 120.50 - 0.25 ) = rs . 120.25 . answer : a\"" + }, + { + "Answer": 32, + "Options": "a ) 16 , b ) 18 , c ) 32 , d ) 19 , e ) 12", + "Correct": "c", + "Explanation": "\"total time taken = x / 40 + 2 x / 20 hours = 5 x / 40 = x / 8 hours average speed = 4 x / ( x / 8 ) = 32 kmph answer : c\"" + }, + { + "Answer": 217.68707482993196, + "Options": "a ) 217 , b ) 287 , c ) 400 , d ) 288 , e ) 171", + "Correct": "a", + "Explanation": "\"explanation : 240 = p ( 21 / 20 ) 2 p = 217 answer : a\"" + }, + { + "Answer": 1600, + "Options": "a ) 800 , b ) 900 , c ) 1600 , d ) 1100 , e ) 1200", + "Correct": "c", + "Explanation": "0.2 x = 4 ( 880 - 800 ) 0.2 x = 320 x = 1600 answer c" + }, + { + "Answer": 6.5, + "Options": "a ) 5.5 kg , b ) 11 kg , c ) 30 kg , d ) 6.5 kg , e ) 71 kg", + "Correct": "d", + "Explanation": "\"after two persons leave the group the average remains the same . that means the weight of the two persons = 43 + 30 = 73 so , the average the two persons = 36.5 that gives the answer 43 - 36.5 = 6.5 answer d\"" + }, + { + "Answer": 78.08, + "Options": "a ) 78.08 , b ) 73.6 , c ) 75.2 , d ) 76.8 , e ) 81.6", + "Correct": "a", + "Explanation": "\"degree of difficulty of dive = 3.2 scores are 6.0 , 7.5 , 8.0 , 8.5 and 9.0 we can drop 6.0 and 9.0 sum of the remaining scores = ( 7.5 + 8.3 + 8.6 ) = 24 point of value of the dive = 24.4 * 3.2 = 78.08 answer a\"" + }, + { + "Answer": 40, + "Options": "a ) 38 , b ) 40 , c ) 78 , d ) 88 , e ) 125", + "Correct": "b", + "Explanation": "xyz is a 3 digit integer divisible by 5 . so z can take only 0 or 5 . we are also given that x = 2 y this means x + y ( 2 y + y ) must be a multiple of 3 xy 5 or xy 0 case 1 x + y + 0 = 11 x + y = 11 this ca n ' t be the case because 11 is not a multiple of 3 case 2 x + y + 5 = 11 x + y = 6 solving we get , x = 4 y = 2 so the 3 digit number is 425 thus the product of the digits will be = 4 x 2 x 5 = 40 answer b" + }, + { + "Answer": 0.041666666666666664, + "Options": "a ) 1 / 32 , b ) 1 / 28 , c ) 1 / 24 , d ) 1 / 16 , e ) 1 / 14", + "Correct": "c", + "Explanation": "\"there are 3 single digit multiple of 3 , that is , 3 , 6,9 . there are 8 prime nos less than 20 - 2,3 , 5,7 , 11,13 , 17,19 total outcome - 8 * 3 = 24 favourable outcome = 1 ( 9 * 5 ) hence required probability t = 1 / 24 . answer c .\"" + }, + { + "Answer": 100000, + "Options": "a ) 100 , b ) 10 , c ) 10000 , d ) 100000 , e ) 1000000", + "Correct": "d", + "Explanation": "\"10 ^ ( 655 ) \u00e3 \u00b7 10 ^ ( 651 ) = 10 ^ ( 655 - 651 ) = 10 ^ 5 = 100000 answer : d\"" + }, + { + "Answer": 70, + "Options": "a ) a ) 10 , b ) b ) 25 , c ) c ) 40 , d ) d ) 55 , e ) e ) 70", + "Correct": "e", + "Explanation": "\"total score of 16 students is 16 * 62.50 = 1000 total score of 15 students is 15 * 62 = 930 so , the score of the person who left is 70 ( 1000 - 930 ) answer will be ( e )\"" + }, + { + "Answer": 5.000000000000043, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "e", + "Explanation": "( 1076 / 23 ) gives a remainder 18 so we need to add 5 . the answer is e ." + }, + { + "Answer": 0.10666666666666667, + "Options": "a ) 1 / 40 , b ) 8 / 75 , c ) 75 / 4 , d ) 75 / 8 , e ) 75 / 6", + "Correct": "b", + "Explanation": "( 1 / a ) + ( 1 / b ) = ( a + b ) / ab = 40 / 375 = 8 / 75 answer : b" + }, + { + "Answer": 20, + "Options": "a ) 1 , b ) 8 , c ) 12 , d ) 20 , e ) 7", + "Correct": "d", + "Explanation": "\"5 * 4 = 20 quarters answer : d\"" + }, + { + "Answer": 2, + "Options": "a ) 3 , b ) 2 , c ) 1 , d ) 4 , e ) 5", + "Correct": "b", + "Explanation": "rule of subtraction : p ( a ) = 1 - p ( a ' ) rule of multiplication : p ( a \u2229 b ) = p ( a ) p ( b ) the probability that the pitcher throws a strike at least once in 2 guesses is 1 - ( 3 / 5 ) ^ 2 = 1 - 9 / 25 = 16 / 25 > 50 % . answer : b" + }, + { + "Answer": 58.333333333333336, + "Options": "a ) 45 , b ) 58.33 % , c ) 600 / 11 , d ) 55 , e ) 35", + "Correct": "b", + "Explanation": "\"explanation : number of runs made by running , = > 120 \u2212 ( 5 \u00d7 4 + 5 \u00d7 6 ) . = > 120 \u2212 ( 50 ) . = > 70 . hence , the required percentage is : - = > 70 / 120 * 100 = > 58.33 % answer : b\"" + }, + { + "Answer": 400, + "Options": "a ) 100 , b ) 300 , c ) 400 , d ) 3,000 , e ) 4,000", + "Correct": "c", + "Explanation": "\"straight pluggin in for me . as usual , i started with c and got the answer . lets ' back calculate and see what we get let us consider eggs processed each day to be 400 so initial ratio of eggs processed and rejected is 96 : 4 or 24 : 1 so out of 400 eggs , there will be 384 eggs processed and 16 rejected . now if the no . of eggs inspected remain and 12 more eggs get accepted that means there r = 384 + 12 = 396 eggs accepted and 4 rejected . . . and the ratio will be 99 : 1 bingo . . . this is what the questions says . . . . its always a good idea to start with c .\"" + }, + { + "Answer": 2, + "Options": "a ) 1 , b ) 2 , c ) 17 / 5 , d ) 18 / 5 , e ) 4", + "Correct": "b", + "Explanation": "\"2 * ( x + 2 y = 5 ) equals 2 x + 4 y = 10 2 x + 4 y = 10 - 2 x + y = 7 = 3 y = 3 therefore y = 1 plug and solve . . . 2 x + 1 = 7 2 x = 6 x = 3 ( 2 * 3 * 1 ) / 3 = 6 / 3 = 2 b\"" + }, + { + "Answer": 29.160000000000004, + "Options": "a ) 26.34 litres , b ) 27.36 litres , c ) 28 litres , d ) 29.16 litres , e ) 30 litres", + "Correct": "d", + "Explanation": "\"amount of milk left after 3 operations = [ 40 ( 1 - 4 / 40 ) ^ 3 ] litres = 40 x 9 / 10 x 9 / 10 x 9 / 10 = 29.16 litres answer : d\"" + }, + { + "Answer": 10, + "Options": "a ) 3 , b ) 9 , c ) 10 , d ) 12 , e ) 14", + "Correct": "c", + "Explanation": "\"when we look at the two equations , we can relize some similarity , so lets work on it . . 3 a \u2013 2 b \u2013 2 c = 32 can be written as \u221a 3 a ^ 2 - \u221a ( 2 b + 2 c ) ^ 2 = 32 { \u221a 3 a - \u221a ( 2 b + 2 c ) } { \u221a 3 a + \u221a ( 2 b + 2 c ) } = 32 . . or 4 * \u221a 3 a + \u221a ( 2 b + 2 c ) = 32 . . or \u221a 3 a + \u221a ( 2 b + 2 c ) = 8 . . now lets work on these two equations 1 ) \u221a 3 a - \u221a ( 2 b + 2 c ) = 4 . . 2 ) \u221a 3 a + \u221a ( 2 b + 2 c ) = 8 . . a ) add the two eq . . \u221a 3 a + \u221a ( 2 b + 2 c ) + \u221a 3 a - \u221a ( 2 b + 2 c ) = 12 . . 2 \u221a 3 a = 12 . . or \u221a 3 a = 6 . . 3 a = 36 . . a = 12 . b ) subtract 1 from 2 . . \u221a 3 a + \u221a ( 2 b + 2 c ) - \u221a 3 a + \u221a ( 2 b + 2 c ) = 4 . . 2 \u221a ( 2 b + 2 c ) = 4 . . \u221a ( 2 b + 2 c ) = 2 . . 2 b + 2 c = 4 . . or b + c = 2 . . from a and b a + b + c = 12 + 2 = 14 . . c\"" + }, + { + "Answer": 200, + "Options": "a ) a ) 200 , b ) b ) 190 , c ) c ) 180 , d ) d ) 170 , e ) e ) 160", + "Correct": "a", + "Explanation": "\"a + b + c = 350 a + c = 200 b + c = 350 - - - - - - - - - - - - - - a + b + 2 c = 550 a + b + c = 350 - - - - - - - - - - - - - - - - c = 200 answer : a\"" + }, + { + "Answer": 600, + "Options": "a ) $ 900 , b ) $ 300 , c ) $ 600 , d ) $ 700 , e ) $ 800", + "Correct": "c", + "Explanation": "\"if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 2 / 4 = 1 / 2 on a tv but the tv cost her $ 300 . so 1 / 2 of her savings is $ 300 . so her original savings are 2 times $ 300 = $ 600 correct answer c\"" + }, + { + "Answer": 8, + "Options": "a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8", + "Correct": "e", + "Explanation": "m ^ 2 + n ^ 2 = 10 and m , n are integers means that 10 is the sum of two perfect squares . 10 is the sum of only one pair of perfect squares 1 and 9 . so , there can be 8 such points , 4 in each quadrant : ( 1 , 3 ) ; ( 1 , - 3 ) ; ( - 1 , 3 ) ; ( - 1 , - 3 ) ; ( 3 , 1 ) ; ( 3 , - 1 ) ; ( - 3 , 1 ) ; ( - 3 , - 1 ) . answer : e ." + }, + { + "Answer": 14090, + "Options": "a ) 14090 , b ) 16010 , c ) 15060 , d ) 14930 , e ) 16075", + "Correct": "a", + "Explanation": "5000 + 12000 - ( 0.15 * 5000 + 0.18 * 12000 ) = 14090 . answer : a ." + }, + { + "Answer": 199.99999999999997, + "Options": "a ) 100 , b ) 160 , c ) 120 , d ) 200 , e ) none of these", + "Correct": "d", + "Explanation": "let the number = x . 4 \u2044 5 \u00d7 3 \u2044 8 x = 24 or x = 24 \u00d7 2 \u00d7 5 / 3 = 80 \u2234 250 per cent of the number = 250 \u2044 100 \u00d7 80 = 200 answer d" + }, + { + "Answer": 8665, + "Options": "a ) 8163 , b ) 8633 , c ) 8663 , d ) 8636 , e ) none of these", + "Correct": "b", + "Explanation": "\"explanation : formula = \u221a a \u00d7 b a = 7921 and b = 9409 \u221a 7921 \u00d7 9409 = 89 \u00d7 97 = 8633 answer : option b\"" + }, + { + "Answer": 32, + "Options": "a ) 30 , b ) 31 , c ) 32 , d ) 33 , e ) 34", + "Correct": "c", + "Explanation": "total price of 5 packet milk = 5 * 20 = 100 total price of 3 packet milk = 3 * 12 = 36 total price of 2 packet returned milk = 100 - 36 = 64 average price of 2 packet milk = 64 / 2 = 32 correct option answer : c" + }, + { + "Answer": 7, + "Options": "a ) 7 , b ) 20 , c ) 28 , d ) 14 , e ) 19", + "Correct": "a", + "Explanation": "\"number of statues = all the paint \u00f7 amount used per statue = 7 / 8 \u00f7 1 / 8 = 7 / 8 * 8 / 1 = 7 / 1 = 7 answer is a .\"" + }, + { + "Answer": 9.037837837837836, + "Options": "a ) 8.58 , b ) 8.76 , c ) 9.04 , d ) 9.12 , e ) 9.25", + "Correct": "c", + "Explanation": "\"distance = 19 km time = 8 / 11 + 11 / 8 = ( 64 + 121 ) / 88 = 185 / 88 hours average speed = ( 19 * 88 ) / 185 = 9.04 km / h the answer is c .\"" + }, + { + "Answer": 6, + "Options": "a ) 5 , b ) 6 , c ) 9 , d ) 11 , e ) 12", + "Correct": "b", + "Explanation": "\"option ' b ' 13 / 10 = 1 and 76 / 10 = 7 = = > 7 - 1 = 6 numbers\"" + }, + { + "Answer": 70, + "Options": "a ) 46 , b ) 42 , c ) 56 , d ) 70 , e ) 58", + "Correct": "d", + "Explanation": "i ' m going in on this one . so let ' s say that we have the following so we know that l 1 = 60 and that c and l 1 = 0.15 x , we should set up a double set matrix btw but anyways , i ' m just explaining the point with this problem . now we are told that 0.15 x = 30 , therefore the grand total is 200 . now we know that l 2 is 200 - 60 = 140 . we also learn that c and no c are equally represented thus 100 each . therefore no c and no l 2 will be 100 - 30 = 70 . thus d is the correct answer choice" + }, + { + "Answer": 9000, + "Options": "a ) 9000 , b ) 24000 , c ) 26682 , d ) 29973 , e ) 12312", + "Correct": "a", + "Explanation": "\"x * ( 90 / 100 ) = 8100 x = 90 * 100 x = 9000 answer : a\"" + }, + { + "Answer": 174, + "Options": "a ) $ 120 , b ) $ 135 , c ) $ 150 , d ) $ 174 , e ) $ 192", + "Correct": "d", + "Explanation": "let the charge for first hour = x + 40 then charge for each additional hour = x x + 40 + 4 x = 375 = > 5 x = 335 = > x = 67 total charge for patient for 3 hours of therapy = x + 40 + x = 2 x + 40 = 174 $ answer d" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 5 , c ) 6 , d ) 7 , e ) 9", + "Correct": "a", + "Explanation": "explanation : clearly 4864 is divisible by 4 so 9 p 2 must be divisible by 3 . so ( 9 + p + 2 ) must be divisible by 3 . so p = 1 . answer : a ) 1" + }, + { + "Answer": 24, + "Options": "a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25", + "Correct": "d", + "Explanation": "\"the multiples of 4 are from 4 * 5 up to 4 * 28 . 28 - 5 + 1 = 24 . the answer is d .\"" + }, + { + "Answer": 0.3200000000000003, + "Options": "a ) 1.5 , b ) 0.5 , c ) 0.32 , d ) 0.25 , e ) 6.32", + "Correct": "c", + "Explanation": "since z * is defined as the greatest positive even integer less than or equal to z , then 6.32 * = 6 ( the greatest positive even integer less than or equal to 6.32 is 6 ) . hence , 6.32 \u2013 6.32 * = 6.32 - 6 = 0.32 answer : c ." + }, + { + "Answer": 18, + "Options": "a ) 12 , b ) 27 , c ) 21 , d ) 18 , e ) 11", + "Correct": "d", + "Explanation": "( a + b ) - ( b + c ) = 18 a - c = 18 . c is younger than a by 18 years . answer : d" + }, + { + "Answer": 6, + "Options": "a ) 1 , b ) 2 , c ) 4 , d ) 6 , e ) 8", + "Correct": "d", + "Explanation": "x = 7 q + 5 4 x = 7 * 4 q + 20 4 x = 7 * 4 q + 7 * 2 + 6 4 x = 7 ( 4 q + 2 ) + 6 4 x = 7 k + 6 ( k = 4 q + 2 ) answer d" + }, + { + "Answer": 82, + "Options": "a ) 75 kg , b ) 82 kg , c ) 86 kg , d ) data inadequate , e ) none of these", + "Correct": "b", + "Explanation": "\"total weight increased = ( 4 x 3 ) kg = 12 kg . weight of new person = ( 70 + 12 ) kg = 82 kg . answer : option b\"" + }, + { + "Answer": 30, + "Options": "a ) 20 , b ) 35 , c ) 30 , d ) 40 , e ) 42", + "Correct": "c", + "Explanation": "let the boys are x , then girls are 7 x , total = x + 7 x = 8 x so it should be multiple of 8 , 30 is not a multiple of 8 . c" + }, + { + "Answer": 50, + "Options": "a ) 20 % , b ) 30 % , c ) 50 % , d ) 70 % , e ) 80 %", + "Correct": "c", + "Explanation": "\"the is always the difference between our starting and ending points . in this case , it \u2019 s 100 \u2013 50 = 50 . the \u201c original \u201d is our starting point ; in this case , it \u2019 s 100 . ( 50 / 100 ) * 100 = ( 0.5 ) * 100 = 50 % . c\"" + }, + { + "Answer": 10, + "Options": "a ) 2 , b ) 3 , c ) 6 , d ) 10 , e ) 11", + "Correct": "d", + "Explanation": "\"the lcm of 9 , 11 , and 13 is 1,287 . the next multiple is 2 * 1,287 = 2,574 . 2,574 + { remainder } = 2,574 + 6 = 2,580 , which is 10 less than 2,590 . answer : d .\"" + }, + { + "Answer": 21.875, + "Options": "a ) 22 % , b ) 24 % , c ) 25 % , d ) 27 % , e ) 28 %", + "Correct": "a", + "Explanation": "\"total sales = 800 comission = ( 20 / 100 ) * 500 + ( 25 / 100 ) * 300 = 100 + 75 = 175 % comission = ( 175 / 800 ) * 100 = 21.8 ~ 22 % answer is a\"" + }, + { + "Answer": 50, + "Options": "a ) 100 , b ) 75 , c ) 25 , d ) 50 , e ) 125", + "Correct": "d", + "Explanation": "\"total = 100 not working = 50 having family = 25 like to sing in shower = 75 working = 100 - 50 = 50 not having family = 100 - 25 = 75 like to sing in shower = 75 largest possible number is the lowest possible among the above thus 50 d\"" + }, + { + "Answer": 84, + "Options": "a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %", + "Correct": "d", + "Explanation": "\"d the prompt says that 68 % of the population lies between m - d and m + d . thus , 32 % of the population is less than m - d or greater than m + d . since the population is symmetric , half of this 32 % is less than m - d and half is greater than m + d . thus , j = ( 68 + 16 ) % or ( 100 - 16 ) % of the population is less than m + d . d\"" + }, + { + "Answer": 52, + "Options": "a ) 24 , b ) 52 , c ) 96 , d ) 144 , e ) 648", + "Correct": "b", + "Explanation": "possible scenarios are : 1 . gold / silver / bronze / no medal ( no ties ) - 4 ! = 24 ; 2 . gold / gold / silver / no medal - 4 ! / 2 ! = 12 ; 3 . gold / silver / silver / no medal - 4 ! / 2 ! = 12 ; 4 . gold / gold / gold / no medal - 4 ! / 3 ! = 4 . total z : 24 + 12 + 12 + 4 = 52 answer : b ." + }, + { + "Answer": 50, + "Options": "a ) 50 , b ) 45 . , c ) 40 . , d ) 30 . , e ) 25 .", + "Correct": "a", + "Explanation": "\"given there are 50 students , 90 % of 50 = 45 boys and remaining 5 girls . now here 90 % are boys and 10 % are girls . now question is asking about how many boys do we need to add , to make the girls percentage to 5 or 5 % . . if we add 50 to existing 45 then the count will be 95 and the girls number will be 5 as it . now boys are 95 % and girls are 5 % . ( out of 100 students = 95 boys + 5 girls ) . answer : option a is correct .\"" + }, + { + "Answer": 27, + "Options": "a ) 26 , b ) 27 , c ) 46 , d ) 57 , e ) none", + "Correct": "b", + "Explanation": "sol . let the numbers be 3 x , 3 x + 3 and 3 x + 6 . then , 3 x + ( 3 x + 3 ) + ( 3 x + 6 ) = 72 \u21d4 9 x = 63 \u21d4 x = 7 . \u2234 largest number = 3 x + 6 = 27 . answer b" + }, + { + "Answer": 84, + "Options": "a ) 20 cs , b ) cs / 2 , c ) 84 cs , d ) ( 2 cs ) / 12 , e ) ( 24 c ) / s", + "Correct": "c", + "Explanation": "ans : c solution : simple multiplication s students , c classes , 7 books / month = 84 books a year total number of books = 84 cs" + }, + { + "Answer": 18, + "Options": "a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22", + "Correct": "a", + "Explanation": "christopher age = x george age , y = x + 8 - - - - - - - - - - > ( 1 ) ford age , z = x - 2 - - - - - - - - - - - - > ( 2 ) sum of their ages , x + y + z = 60 - - - - > ( 3 ) substitute z and y values in equation ( 3 ) therefore , x + ( x + 8 ) + ( x - 2 ) = 60 = > 3 x + 8 - 2 = 60 = > 3 x = 60 - 6 = > 3 x = 54 = > x = 54 / 3 x = 18 answer : a" + }, + { + "Answer": 10, + "Options": "a ) 1 , b ) 10 , c ) 100 , d ) 1000 , e ) 10000", + "Correct": "b", + "Explanation": "\"10 ^ ( 65 ) \u00e3 \u00b7 10 ^ ( 64 ) = 10 ^ ( 65 - 64 ) = 10 ^ 1 = 10 answer : b\"" + }, + { + "Answer": 72, + "Options": "a ) 69 , b ) 70 , c ) 71 , d ) 72 , e ) 75", + "Correct": "d", + "Explanation": "sum of the marks for the 11 students = 11 * 36 = 396 . the marks of each student are doubled , the sum also will be doubled . the new sum = 396 * 2 = 792 . so , the new average = 792 / 11 = 72 . answer : d" + }, + { + "Answer": 504, + "Options": "a ) a ) 220 , b ) b ) 490 , c ) c ) 380 , d ) d ) 450 , e ) e ) 504", + "Correct": "e", + "Explanation": "\"the only thing you have to do is a simple multiply we have : 18 * 28 = 504 correct answer is : e ) 504\"" + }, + { + "Answer": 65, + "Options": "a ) 65 , b ) 79 , c ) 68 , d ) 87 , e ) 90", + "Correct": "a", + "Explanation": "\"we just enter this root into the equation in order to recieve an equation to find the answer ! 2 * 5 ^ 2 + 3 * 5 - k = 0 k = 50 + 15 = 65 the answer is a\"" + }, + { + "Answer": 9.237333333333334, + "Options": "a ) 0.092 , b ) 0.92 , c ) 9.2 , d ) 92 , e ) 920", + "Correct": "c", + "Explanation": "\"q = ( 69.28 \u00d7 0.004 ) / 0.03 1 . 0.004 = 4 \u00d7 10 ^ ( - 3 ) 2 . 0.03 = 3 \u00d7 10 ^ ( - 2 ) 3 . ( a \u00d7 b ) / c = a \u00d7 ( b / c ) 4 . 0.004 / 0.03 = 4 \u00d7 10 ^ ( - 3 ) / ( 3 \u00d7 10 ^ ( - 2 ) ) = 4 \u00d7 10 ^ ( - 3 - ( - 2 ) ) / 3 = 4 \u00d7 10 ^ ( - 1 ) / 3 = ( 4 / 3 ) \u00d7 10 ^ ( - 1 ) = 1.333 \u00d7 10 ^ ( - 1 ) therefore , ( 69.28 \u00d7 0.004 ) / 0.03 = 69.28 \u00d7 ( 0.004 / 0.03 ) = 69.28 \u00d7 1.33 \u00d7 10 ^ ( - 1 ) = 69.28 \u00d7 1.33 / 10 = 6.928 * 1.33 now , 7 \u00d7 2 = 14 7 \u00d7 1 = 7 or better : 6.9 \u00d7 1 = 6.9 6.9 \u00d7 2 = 13.8 hence , 6.9 < 6.928 \u00d7 1.33 < 13.8 9.2 is the only answer that satisfies this condition . c\"" + }, + { + "Answer": 120, + "Options": "a ) 120 , b ) 160 , c ) 132 , d ) 130 , e ) none of these", + "Correct": "a", + "Explanation": "\"number of male employees = 800 * 25 / 100 = 200 required number of male employees who are less than 50 years old = 200 * ( 100 - 40 ) % = 200 * 60 / 100 = 120 . answer : a\"" + }, + { + "Answer": 18, + "Options": "a ) 3 , b ) 18 , c ) 6 , d ) 16 , e ) 5", + "Correct": "b", + "Explanation": "\"x can be written as 82 k + 5 or x = 5 , 87,169 , etc . x + 13 = 82 k + 5 + 13 = 82 k + 18 or x + 13 = 18,100 , 182 etc . when divided by 41 , we will get the remainder 18 . b\"" + }, + { + "Answer": 309.297052154195, + "Options": "a ) 221 , b ) 309 , c ) 400 , d ) 288 , e ) 171", + "Correct": "b", + "Explanation": "\"explanation : 341 = p ( 21 / 20 ) 2 p = 309.29 answer : b\"" + }, + { + "Answer": 20, + "Options": "a ) 20 , b ) 36 , c ) 48 , d ) 50 , e ) 59", + "Correct": "a", + "Explanation": "\"production during these 5 days = total production in a month - production in first 25 days . = 30 x 45 - 25 x 50 = 100 \u2234 average for last 5 days = 100 / 5 = 20 a\"" + }, + { + "Answer": 0.2999999999999999, + "Options": "a ) 0.68 , b ) 0.6 , c ) 0.8 , d ) 0.3 , e ) none of them", + "Correct": "d", + "Explanation": "\"given expression = ( 1.2 ) ( power 3 ) - ( 0.9 ) ( power 3 ) / ( 1.2 ) ( power 2 ) + ( 1.2 x 0.9 ) + ( 0.9 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 1.2 - 0.9 ) = 0.3 answer is d\"" + }, + { + "Answer": 800, + "Options": "a ) $ 500 , b ) $ 600 , c ) $ 700 , d ) $ 800 , e ) $ 900", + "Correct": "d", + "Explanation": "\"if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 200 . so 1 / 4 of her savings is $ 200 . so her original savings are 4 times $ 200 = $ 800 correct answer d\"" + }, + { + "Answer": 480, + "Options": "a ) 96 , b ) 240 , c ) q = 256 , d ) q = 384 , e ) q = 480", + "Correct": "e", + "Explanation": "\"most test takers would recognize the system of equations in this prompt and just do algebra to get to the solution ( and that ' s fine ) . the wording of the prompt and the ' spread ' of the answer choices actually provide an interesting ' brute force ' shortcut that you can take advantage of to eliminate the 4 wrong answers . . . . we ' re told that there are 2 types of boxes : those that hold 12 glasses and those that hold 16 glasses . since the average number of boxes is 15 , we know that there must be at least some of each . we ' re also told that that there are 16 more of the larger boxes . this means , at the minimum , we have . . . 1 small box and 17 large boxes = 1 ( 12 ) + 17 ( 16 ) = 12 + 272 = 284 glasses at the minimum since the question asks for the total number of glasses , we can now eliminate answers a , b and c . . . . the difference in the number of boxes must be 16 though , so we could have . . . . 2 small boxes and 18 large boxes 3 small boxes and 19 large boxes etc . with every additional small box + large box that we add , we add 12 + 16 = 28 more glasses . thus , we can justadd 28 suntil we hit the correct answer . . . . 284 + 28 = 312 312 + 28 = 340 340 + 28 = 368 368 + 28 = 396 at this point , we ' ve ' gone past ' answer d , so the correct answer must be answer e . . . . . but here ' s the proof . . . . 396 + 28 = 424 424 + 28 = 452 452 + 28 = 480 final answer : e\"" + }, + { + "Answer": 84, + "Options": "a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %", + "Correct": "d", + "Explanation": "\"16 % ________________________________________________ m + h 34 % ________________________________________________ m 34 % ________________________________________________ m - h 16 % since 68 % lies one standard deviation from mean m , = > 50 % of 68 % lies on either side as it is symmetric about m . thus 16 % lie below m - h and 16 % lie above m + h now below m + h = 16 + 34 + 34 = 84 % hence d\"" + }, + { + "Answer": 1349, + "Options": "a ) 2674 , b ) 1349 , c ) 3343 , d ) 3678 , e ) 3679", + "Correct": "b", + "Explanation": "let four digits is a , b , c & d . . . so by given b is 3 a c is 4 a d is 9 a so ans is 1349 answer : b" + }, + { + "Answer": 150, + "Options": "a ) 127 , b ) 150 , c ) 177 , d ) 167 , e ) 122", + "Correct": "b", + "Explanation": "a + b + c = 590 5 a = 6 b = 8 c = x a : b : c = 1 / 5 : 1 / 6 : 1 / 8 = 24 : 20 : 15 15 / 59 * 590 = rs . 150 answer : b" + }, + { + "Answer": 360, + "Options": "a ) 40 / 3 , b ) 40 , c ) 120 , d ) 360 , e ) 420", + "Correct": "d", + "Explanation": "case 1 : deposit = $ x ; rate of increase = r . interest yearned in 1 year = xr . deposit in 1 year = x + xr . interest yearned in 2 year = ( x + xr ) r . the difference c = ( x + xr ) r - xr = xr ^ 2 = 40 . case 2 : deposit = $ x ; rate of increase = 3 r . interest yearned in 1 year = x ( 3 r ) . deposit in 1 year = x + 3 xr . interest yearned in 2 year = ( x + 3 xr ) 3 r . the difference = ( x + 3 xr ) 3 r - 3 xr = 9 xr ^ 2 . since from case 1 we know that xr ^ 2 = 40 , then 9 xr ^ 2 = 9 * 40 = 360 . answer : d ." + }, + { + "Answer": 9, + "Options": "a ) 9 , 10 , b ) 10 , 11 , c ) 11 , 12 , d ) 12 , 13 , e ) none of these", + "Correct": "a", + "Explanation": "let the two consecutive positive integers be x and x + 1 x 2 + ( x + 1 ) 2 - x ( x + 1 ) = 91 x 2 + x - 90 = 0 ( x + 10 ) ( x - 9 ) = 0 = > x = - 10 or 9 . as x is positive x = 9 hence the two consecutive positive integers are 9 and 10 . answer : a" + }, + { + "Answer": 0.25, + "Options": "a ) 27 / 4 , b ) 27 / 8 , c ) 3 / 4 , d ) 3 / 8 , e ) 1 / 4", + "Correct": "e", + "Explanation": "\"say a = 2 . then : a / b = 1 / 3 - - > b = 6 ; b / c = 2 - - > c = 3 ; c / d = 1 / 2 - - > d = 6 ; d / e = 3 - - > e = 2 ; e / f = 1 / 6 - - > f = 12 . abc / def = ( 2 * 6 * 3 ) / ( 6 * 2 * 12 ) = 1 / 4 . answer : e .\"" + }, + { + "Answer": 384, + "Options": "a ) 384 , b ) 76 , c ) 26 , d ) 28 , e ) 11", + "Correct": "a", + "Explanation": "\"explanation : let the number be x . 5 * x / 6 = 5 * x / 16 + 200 25 * x / 48 = 200 x = 384 answer : a\"" + }, + { + "Answer": 10, + "Options": "a ) 50 , b ) 100 , c ) 75 , d ) 25 , e ) 10", + "Correct": "e", + "Explanation": "50 % of x = x / 2 ; 5 % of 500 = 5 / 100 * 500 = 25 given that , x / 2 = 25 - 20 = > x / 2 = 5 = > x = 10 . answer : e" + }, + { + "Answer": 9996, + "Options": "a ) 9800 , b ) 9898 , c ) 9702 , d ) 9604 , e ) 9996", + "Correct": "e", + "Explanation": "largest 4 digit number is 9999 after doing 9999 \u00f7 98 we get remainder 3 hence largest 4 digit number exactly divisible by 98 = 9999 - 3 = 9996 e" + }, + { + "Answer": 156, + "Options": "a ) 120 , b ) 156 , c ) 108 , d ) 105 , e ) 86", + "Correct": "b", + "Explanation": "let the present ages of the father and son be 2 x and x years respectively . then , ( 2 x - 26 ) = 3 ( x - 26 ) x = 52 . required sum = ( 2 x + x ) = 3 x = 156 years . answer is b" + }, + { + "Answer": 0.25, + "Options": "a ) 3 , b ) 6 , c ) 1 / 4 , d ) 1 / 3 , e ) 9", + "Correct": "c", + "Explanation": "\"explanation : solution : given x = k / y ^ 2 , where k is constant . now , y = 3 and x = 1 gives k = 9 . . ' . x = 9 / y ^ 2 = > x = 9 / 6 ^ 2 = 1 / 4 answer : c\"" + }, + { + "Answer": 18, + "Options": "a ) 22 , b ) 65 , c ) 18 , d ) 36 , e ) 10", + "Correct": "c", + "Explanation": "3 * 6 = 18 . answer is c ." + }, + { + "Answer": 25, + "Options": "a ) 16 , b ) 25 , c ) 19 , d ) 26 , e ) 17", + "Correct": "b", + "Explanation": "a let the number be p , then the square will be p ^ 2 according to question : 2 p = ( p / 5 ) + 9 = > 10 p = p + 45 = > p = 5 p ^ 2 = 5 ^ 2 = 25 . answer : b" + }, + { + "Answer": 78, + "Options": "a ) 115 , b ) 116 , c ) 117 , d ) 78 , e ) 119", + "Correct": "d", + "Explanation": "\"x : y : z = 100 : 45 : 50 20 : 9 : 10 9 - - - 18 39 - - - ? = > 78 answer : d\"" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9", + "Correct": "b", + "Explanation": "\"we have equation 2 n + 5 m = 50 we have factor 2 in first number and we have factor 5 in second number . lcm ( 2 , 5 ) = 10 so we can try some numbers and we should start from 5 because it will be less list than for 2 2 * 5 = 10 and n should be equal 20 4 * 5 = 20 and n should be equal 15 6 * 5 = 30 and n should be equal 10 8 * 5 = 40 and n should be equal 5 10 * 5 = 50 and n should be equal 0 third variant give us the mininal difference n - m = 10 - 6 = 4 and there is some mistake in my way of thinking because we do n ' t have such answer ) if we change the task and will seek for difference between m and n than minimal result t will be 8 - 5 = 3 and answer b\"" + }, + { + "Answer": 212, + "Options": "a ) 207 , b ) 209 , c ) 211 , d ) 212 , e ) 213", + "Correct": "d", + "Explanation": "sum of the deviations of the numbers in the set from the mean is always zero 201 , 202 , 204 , 205 , 206 , 209 , 209 , 210 , 212 mean is 207 so the list is - 6 - 5 - 3 - 2 - 1 + 2 + 2 + 3 + 5 . . . this shud total to zero but this is - 5 , hence we need a number that is 5 more than the mean to get a + 5 and make it zero hence the answer is 207 + 5 = 212 d" + }, + { + "Answer": 10, + "Options": "a ) 5 , b ) 7 , c ) 10 , d ) 12 , e ) 14", + "Correct": "c", + "Explanation": "\"let the number of cows be x and their legs be 4 x . let the number of chicken be y and their legs be 2 x . total number of legs = 4 x + 2 y . total number of heads = x + y . the number of legs was 20 more than twice the number of heads . therefore , 2 \u00d7 ( x + y ) + 20 = 4 x + 2 y . or , 2 x + 2 y + 20 = 4 x + 2 y . or , 2 x + 20 = 4 x [ subtracting 2 y from both sides ] . or , 20 = 4 x \u2013 2 x [ subtracting 2 x from both sides ] . or , 20 = 2 x . or , x = 10 [ dividing by 2 on both sides ] . therefore , the number of cows = 10 . correct answer : c ) 10\"" + }, + { + "Answer": 21, + "Options": "a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24", + "Correct": "b", + "Explanation": "39 x = 25 + 12 + 15 + 19 + ( x \u2013 4 ) 44 39 x = 71 + 44 x - 176 5 x = 105 x = 21 answer : b" + }, + { + "Answer": 480, + "Options": "a ) a . 480 , b ) b . 300 , c ) c . 600 , d ) d . 410 , e ) e . 240", + "Correct": "a", + "Explanation": "\"volume per box : 15 x 12 x 10 = 1,800 total volume : 1 , 080,000 number of boxes : total volume / volume per box = 1 , 080,000 / 1,800 = 600 price per month : number of boxes * price per box = 600 * 0.8 = 480 answer : a\"" + }, + { + "Answer": 150, + "Options": "a ) 82 m , b ) 50 m , c ) 72 m , d ) 150 m , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : the relative speed of train is 46 - 36 = 10 km / hr = ( 10 x 5 ) / 18 = 25 / 9 m / s 10 \u00d7 518 = 259 m / s in 108 secs the total distance traveled is 108 x 25 / 9 = 300 m . therefore the length of each train is = 300 / 2 = 150 m . answer d\"" + }, + { + "Answer": 95, + "Options": "a ) 56 , b ) 65 , c ) 75 , d ) 89 , e ) 95", + "Correct": "e", + "Explanation": "a + b + c = 3 * 80 = 240 a + b + c + d = 4 * 82 = 328 - - - - ( i ) so , d = 88 & e = 88 + 3 = 91 b + c + d + e = 81 * 4 = 324 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 328 \u2013 324 = 4 a = e + 4 = 91 + 4 = 95 answer : e" + }, + { + "Answer": 78, + "Options": "a ) 78 % , b ) 250 % , c ) 500 / 3 % , d ) 125 % , e ) 60 %", + "Correct": "a", + "Explanation": "\"z = 100 ; y = 60 so x = 78 x as % of z = 78 / 100 * 100 = > 78 % answer will be ( a )\"" + }, + { + "Answer": 64.99999999999999, + "Options": "a ) 40 % , b ) 50 % , c ) 65 % , d ) 70 % , e ) 80 %", + "Correct": "c", + "Explanation": "\"can be reduced to 7 y / 20 + 6 y / 20 = 13 y / 20 = 65 % answer c\"" + }, + { + "Answer": 35.00007699999992, + "Options": "a ) 51 , b ) 87 , c ) 35 , d ) 75 , e ) 68", + "Correct": "c", + "Explanation": "sum of all the 15 numbers = 15 * 75 = 1,125 sum of the first 8 of them = 8 * 68 = 544 sum of the last 8 of them = 8 * 77 = 616 so , the 8 th number = 544 + 616 - 1,125 = 35 . answer : c" + }, + { + "Answer": 4038, + "Options": "a ) 4038 , b ) 8076 , c ) 9691.2 , d ) 4845.6 , e ) none of these", + "Correct": "a", + "Explanation": "\u2235 amount , he have spent in 1 month on clothes transport = amount spent on saving per month \u2235 amount , spent on clothes and transport = 48456 \u2044 12 = 4038 answer a" + }, + { + "Answer": 50, + "Options": "a ) 46 , b ) 47 , c ) 48 , d ) 49 , e ) 50", + "Correct": "e", + "Explanation": "\"mother + daughter + child = 110 kg daughter + child = 60 kg mother = 110 - 60 = 50 kg child = 1 / 5 th of mother = ( 1 / 5 ) * 50 = 10 kg so now daughter = 110 - ( mother + child ) = 110 - ( 50 + 10 ) = 50 kg answer : e\"" + }, + { + "Answer": 6, + "Options": "a ) 5.5 kg , b ) 6 kg , c ) 30 kg , d ) 36.5 kg , e ) 71 kg", + "Correct": "b", + "Explanation": "after two persons leave the group the average remains the same . that means the weight of the two persons = 42 + 30 = 72 so , the average the two persons = 36 that gives the answer 42 - 36 = 6 answer b" + }, + { + "Answer": 20, + "Options": "a ) 10 , b ) 12 , c ) 16 , d ) 22 , e ) 20", + "Correct": "e", + "Explanation": "sol . let the numbers be x and ( 44 - x ) . then , 5 x = 6 ( 44 - x ) \u21d4 11 x = 264 \u21d4 x = 24 . so , the numbers are 24 and 20 . answer e" + }, + { + "Answer": 50, + "Options": "a ) 20 , b ) 25 , c ) 40 , d ) 50 , e ) 75", + "Correct": "d", + "Explanation": "\"there are 5 days so the sum of temperature can be 50 * 5 = 250 lowest is 40 . to find the maximum range we can say the temperature was the lowest for 4 of the 5 days so 4 * 40 = 160 . on the fifth day it is 250 - 160 = 90 range is therefore 90 - 40 = 50 answer d\"" + }, + { + "Answer": 140, + "Options": "a ) 166 , b ) 140 , c ) 178 , d ) 177 , e ) 169", + "Correct": "b", + "Explanation": "\"x : y : z = 100 : 45 : 30 20 : 9 : 6 9 - - - 36 35 - - - ? = > 140 answer : b\"" + }, + { + "Answer": 33, + "Options": "a ) 33 , b ) 47 , c ) 50 , d ) 53 , e ) 62", + "Correct": "a", + "Explanation": "\"if you list the amount eaten each hour , you ' ll get an equally spaced list , increasing by 3 each hour . in any equally spaced list , the median equals the mean . here , the mean is 270 / 9 = 30 , so the median is also 30 , and that is the amount eaten in the 5 th hour . we need to add 3 to find the total eaten in the next hour , so the answer is 33 . option a\"" + }, + { + "Answer": 60, + "Options": "a ) 70 % , b ) 60 % , c ) 30 % , d ) 75 % , e ) none of above", + "Correct": "b", + "Explanation": "\"explanation : actually it means 15 is what percent of 25 , which can be calculated as , ( 15 / 25 ) * 100 = 15 * 4 = 60 answer : option b\"" + }, + { + "Answer": 20, + "Options": "a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20", + "Correct": "e", + "Explanation": "let the total money be $ x x ' s 1 day work = $ x / 36 y ' s 1 day work = $ x / 45 x + y 1 day work = $ x / 20 money is sufficient to pay the wages of both for 20 days answer is e" + }, + { + "Answer": 32, + "Options": "a ) 32 , b ) 36 , c ) 37 , d ) 38 , e ) 39", + "Correct": "a", + "Explanation": "\"42 x = 12 x + 1.5 x ( h - 12 ) = = > 42 = 12 + 1.5 ( h - 12 ) = = > h - 12 = 30 / 1.5 = 20 = = > h = 32 answer is a\"" + }, + { + "Answer": 60, + "Options": "a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60", + "Correct": "e", + "Explanation": "quantity of milk = ( 60 x 2 / 3 ) litres = 40 litres . quantity of water in it = ( 60 - 40 ) litres = 20 litres . new ratio = 1 : 2 let quantity of water to be added further be x litres . then , milk : water = ( 40 / ( 20 + x ) ) now , ( 40 / ( 20 + x ) ) = 1 / 2 = 20 + x = 80 = x = 60 . therefore , quantity of water to be added = 60 litres . answer is e ." + }, + { + "Answer": 11.5, + "Options": "a ) 10.5 , b ) 11 , c ) 11.5 , d ) 12 , e ) 12.5", + "Correct": "c", + "Explanation": "the total subtracted is ( 9 + 8 + . . . + 1 ) = ( 9 * 10 ) / 2 = 45 on average , each number will be reduced by 45 / 10 = 4.5 therefore , the overall average will be reduced by 4.5 the answer is c ." + }, + { + "Answer": 330, + "Options": "a ) 805 , b ) 740 , c ) 670 , d ) 530 , e ) 330", + "Correct": "e", + "Explanation": "( 2 * 61.5 ) + 47 + x > 500 123 + 47 + x > 500 170 + x > 500 = > x > 330 option e" + }, + { + "Answer": 0.14999999999999994, + "Options": "a ) 1 / 60 , b ) 1 / 15 , c ) 3 / 20 , d ) 3 / 5 , e ) 3 / 4", + "Correct": "c", + "Explanation": "if initially he had x hats . x / 4 were brown . sold x * 2 / 3 hats . left with x / 3 hats . sold ( x / 4 ) * ( ( 4 / 5 ) = x / 5 brown hats and left with x / 4 - x / 5 = x / 20 brown hats . fraction of brown hats in total remaining hats = ( x / 20 ) / ( x / 3 ) = 3 / 20 hats answer : c" + }, + { + "Answer": 3025, + "Options": "a ) 3025 , b ) 4200 , c ) 3060 , d ) 3210 , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : here , the given statement is like ( a + b ) 2 - 4 ab where a = 481 and b = 426 ( a + b ) 2 - 4 ab = ( a 2 + 2 ab + b 2 ) - 4 ab = a 2 - 2 ab + b 2 = ( a - b ) 2 hence { ( 481 + 426 ) 2 - 4 x 481 x 426 } = ( 481 - 426 ) 2 = 552 = 3025 . answer : option a\"" + }, + { + "Answer": 20, + "Options": "a ) 20 , b ) 24 , c ) 26 , d ) 28 , e ) 30", + "Correct": "a", + "Explanation": "( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 138 + 2 * 131 a + b + c = \u221a 400 = 20 a" + }, + { + "Answer": 6, + "Options": "a ) 4 , b ) 6 , c ) 8 , d ) 5 , e ) 3", + "Correct": "b", + "Explanation": "explanation : let the number be x . then , ( x - 5 ) / 7 = 7 = > x - 5 = 49 x = 54 . : ( x - 6 ) / 8 = ( 54 - 6 ) / 8 = 6 answer : option b" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 2 , c ) 4 , d ) 3 , e ) 5", + "Correct": "d", + "Explanation": "\"i solved the second degree equation and found it like this : x ^ 2 - mx - 40 = 0 ( x - 8 ) ( x + 5 ) = 0 x = 8 or x = - 5 substituting both values for x in the equation we find : x ^ 2 - mx - 40 = > ( - 5 ) ^ 2 - m ( - 5 ) = 40 = > 25 + 5 m = 40 = > 5 m = 40 - 25 = 15 = > m = 3 and with 8 , using a similar process we end up with : ( 8 ) ^ 2 - m ( 8 ) = 40 - 8 m = 40 - 64 = - 24 m = 3 ao , ans d\"" + }, + { + "Answer": 80, + "Options": "a ) 70 , b ) 75 , c ) 80 , d ) 85 , e ) 90", + "Correct": "c", + "Explanation": "b : c : d = 100 : 150 : 100 20 : 30 : 10 30 - - - 40 60 - - - ? = > 80 answer : c" + }, + { + "Answer": 74.0909090909091, + "Options": "a ) 74.1 , b ) 56.3 , c ) 67.8 , d ) 79.7 , e ) 19.4", + "Correct": "a", + "Explanation": "\"sum of the marks for the class of 58 students = 58 * 67 = 3886 sum of the marks for the class of 52 students = 52 * 82 = 4264 sum of the marks for the class of 110 students = 3886 + 4262 = 8150 average marks of all the students = 4200 / 80 = 74.1 answer : a\"" + }, + { + "Answer": 5, + "Options": "a ) 10 , b ) 99 , c ) 5 , d ) 22 , e ) 29", + "Correct": "c", + "Explanation": "\"let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 28 x = 4 ( 3 x + 5 ) 16 x = 20 x = 1.25 quantity of alcohol = ( 4 x 1.25 ) litres = 5 litres . answer : c\"" + }, + { + "Answer": 0.30337078651685395, + "Options": "a ) 13 / 89 , b ) 15 / 87 , c ) 27 / 89 , d ) 27 / 87 , e ) 89 / 27", + "Correct": "c", + "Explanation": "\"1 / [ 3 + ( 1 / ( 3 + 1 / ( 3 - 1 / 3 ) ) ) ] = > 1 / [ 3 + 1 / ( 3 + 1 / ( 8 / 3 ) ) ] = > 1 / [ 3 + 1 / ( 3 + 3 / 8 ) ] = > 1 / [ 3 + 8 / 27 ] = > 1 / ( 89 / 27 ) = > 27 / 89 c )\"" + }, + { + "Answer": 495, + "Options": "a ) $ 455 , b ) $ 495 , c ) $ 525 , d ) $ 550 , e ) $ 585", + "Correct": "b", + "Explanation": "\"90 % remains to be paid so the remaining amount is 9 * 55 = $ 495 . the answer is b .\"" + }, + { + "Answer": 40, + "Options": "a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 39", + "Correct": "b", + "Explanation": "b 40 let daughter \u2019 s age = a and mother \u2019 s age = b given : 2 a + b = 70 and , a + 2 b = 95 solving b , we will get b = 40 ." + }, + { + "Answer": 360, + "Options": "a ) 120 , b ) 240 , c ) 360 , d ) 480 , e ) 720", + "Correct": "c", + "Explanation": "c ) 360 short way : there are 6 c ! ways to do the six tasks . half will have wheels before axles and half will have axles before wheels . so we want r = 6 c ! / 2 - > 720 / 2 = 360" + }, + { + "Answer": 136, + "Options": "a ) 136 , b ) 192 , c ) 198 , d ) 122 , e ) 142", + "Correct": "a", + "Explanation": "required number = ( lcm of 4 , 6,8 , and 10 ) + 16 = 120 + 16 = 136 option a" + }, + { + "Answer": 85, + "Options": "a ) 85 , b ) 87 , c ) 89 , d ) 91 , e ) 93", + "Correct": "a", + "Explanation": "\"let x be the height of the first person . then the heights are x , x + 2 , x + 4 , and x + 10 . 4 x + 16 = 4 ( 79 ) = 316 x = 75 and the fourth person has a height of 75 + 10 = 85 inches the answer is a .\"" + }, + { + "Answer": 25, + "Options": "a ) 25 , b ) 30 , c ) 35 , d ) 15 , e ) 10", + "Correct": "a", + "Explanation": "i simply looked at the 3 different possible scores for each individual test : 15 , 30,25 we have to find the minimum range : 30 - 15 = 15 30 - 25 = 5 25 - 15 = 10 the find the minimum range , you have to make the set of the 5 scores as small as possible . which means that 4 of the 5 scores of each individual person is zero . 5 * 5 = 25 . answer : a" + }, + { + "Answer": 3000, + "Options": "a ) 7000 , b ) 6000 , c ) 5000 , d ) 4000 , e ) 3000", + "Correct": "e", + "Explanation": "total rebecca = x + 15000 ; total = x + 15000 + 18000 x + 15000 / x + 33000 = 50 / 100 therefore x = 3000 e" + }, + { + "Answer": 143, + "Options": "a ) 125 , b ) 126 , c ) 130 , d ) 143 , e ) 151", + "Correct": "d", + "Explanation": "\"3 * 13 + 3 * 14 + 3 * 17 + 11 = 39 + 42 + 51 + 11 = 143 the answer is d .\"" + }, + { + "Answer": 0.875, + "Options": "a ) 5 / 6 , b ) 3 / 4 , c ) 7 / 8 , d ) 1 / 8 , e ) 1 / 2", + "Correct": "c", + "Explanation": "if mrs . susna ' s class has 24 students , the number of students receiving as , bs , or cs , are 6 , 12 , and 3 respectively . that means 21 / 24 of her students are receiving passing grades or 7 / 8 . ( answer : c )" + }, + { + "Answer": 1035, + "Options": "a ) 1035 , b ) 1040 , c ) 1042 , d ) 1045 , e ) 1050", + "Correct": "a", + "Explanation": "\"let sn = ( 1 + 2 + 3 + . . . + 45 ) . this is an a . p . in which a = 1 , d = 1 , n = 45 . sn = n [ 2 a + ( n - 1 ) d ] = 45 x [ 2 x 1 + ( 45 - 1 ) x 1 ] = 45 x 46 = ( 45 x 23 ) 2 2 2 = 45 x ( 20 + 3 ) = 45 x 20 + 45 x 3 = 900 + 135 = 1035 . shorcut method : sn = n ( n + 1 ) = 45 ( 45 + 1 ) = 1035 . 2 2 a\"" + }, + { + "Answer": 2000, + "Options": "a ) 1500 , b ) 1600 , c ) 1750 , d ) 1900 , e ) 2000", + "Correct": "e", + "Explanation": "let the price of basic computer be c and the price of the printer be p : c + p = $ 2,500 . the price of the enhanced computer will be c + 500 and total price for that computer and the printer will be 2,500 + 500 = $ 3,000 . now , we are told that the price of the printer is 1 / 6 of that new total price : p = 1 / 6 * $ 3,000 = $ 500 . plug this value in the first equation : c + 500 = $ 2,500 - - > c = $ 2000 answer : e ." + }, + { + "Answer": 25, + "Options": "a ) 10 % , b ) 20 % , c ) 25 % , d ) 50 % , e ) 75 %", + "Correct": "c", + "Explanation": "let say company a has x employes and b has y employees . now they merge and total no of employees = x + y employees . per the question company a ' s workforce consists of 10 percent managers and 90 percent software engineers . company b ' s workforce consists of 30 percent managers , 10 percent software engineers , and 60 percent support staff . we translate it into equation as follows : . 1 x + . 3 y = . 25 ( x + y ) = > x + 3 y = 2.5 ( x + y ) = > . 5 y = 1.5 x = > y = 3 x . now we know total employee = x + y . we need to find % age of x in total ( x + y ) ie x / ( x + y ) x 100 % = > x / ( 3 x + x ) [ substitute y = 3 x ] = > x / 4 x x 100 % = > . 25 x 100 % = > 25 % . answer : c" + }, + { + "Answer": 91, + "Options": "a ) 91 , b ) 98 , c ) 105 , d ) 112 , e ) 119", + "Correct": "a", + "Explanation": "\"14 c 2 = 91 the answer is a .\"" + }, + { + "Answer": 6, + "Options": "a ) 3.5 , b ) 6 , c ) 8 , d ) 7 , e ) 4", + "Correct": "b", + "Explanation": "\"let the number be x . then , 3 ( 2 x + 9 ) = 63 2 x = 12 = > x = 6 answer : b\"" + }, + { + "Answer": 420, + "Options": "a ) $ 500 , b ) $ 650 , c ) $ 420 , d ) $ 375 , e ) $ 625", + "Correct": "c", + "Explanation": "\"avg = sum of observations / number of observations avg income = ( 300 + 150 + 750 + 400 + 500 ) / 5 = 420 answer is c\"" + }, + { + "Answer": 163, + "Options": "a ) 154 , b ) 124 , c ) 153 , d ) 163 , e ) 183", + "Correct": "d", + "Explanation": "divisor = ( dividend - remainder ) / quotient = ( 12401 - 13 ) / 76 = 12388 / 76 = 163 divisor = 163 answer d" + }, + { + "Answer": 78, + "Options": "a ) 78 % , b ) 79 % , c ) 80 % , d ) 81 % , e ) 82 %", + "Correct": "a", + "Explanation": "( 15 * 70 + 10 * 90 ) / 25 = 78 % the answer is a ." + }, + { + "Answer": 12, + "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12", + "Correct": "e", + "Explanation": "\"total marks of male = m total marks of female = f number of males = 8 number of females = f given : ( m + f ) / ( 8 + f ) = 90 - - - - - - - - - - - - - 1 also given , m / 8 = 87 thus m = 696 - - - - - - - - - 2 also , f / f = 92 thus f = 92 f - - - - - - - - - 3 put 2 and 3 in 1 : we get ( 696 + 92 f ) / ( 8 + f ) = 90 solving this we get f = 12 answer : e\"" + }, + { + "Answer": 45, + "Options": "a ) 41 , b ) 44 , c ) 45 , d ) 47 , e ) 50", + "Correct": "c", + "Explanation": "\"the rate of 30 machines is rate = job / time = x / 3 units per day - - > the rate of 1 machine 1 / 30 * ( x / 3 ) = x / 90 units per day ; now , again as { time } * { combined rate } = { job done } then 10 * ( m * x / 90 ) = 5 x - - > m = 45 . answer : c .\"" + }, + { + "Answer": 435, + "Options": "a ) 190 , b ) 200 , c ) 210 , d ) 220 , e ) 435", + "Correct": "e", + "Explanation": "\"or , if there are n persons then no . of shakehands = nc 2 = 30 c 2 = 435 answer : e\"" + }, + { + "Answer": 2, + "Options": "a ) 4 , b ) 7 , c ) 8 , d ) 2 , e ) 3", + "Correct": "d", + "Explanation": "\"explanation : let the number be x . then , ( x - 5 ) / 7 = 7 = > x - 5 = 49 x = 54 . : ( x - 34 ) / 10 = ( 54 - 34 ) / 10 = 2 answer : option d\"" + }, + { + "Answer": 21, + "Options": "a ) 20 , b ) 21 , c ) 26 , d ) 28 , e ) 30", + "Correct": "b", + "Explanation": "\"( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 179 + 2 * 131 a + b + c = \u221a 441 = 21 b\"" + }, + { + "Answer": 15, + "Options": "a ) 15 , b ) 18 , c ) 21 , d ) 23 , e ) 25", + "Correct": "a", + "Explanation": "let x be pair of shoes and y be pair of boots . 22 x + 16 y = 460 . . . eq 1 8 x + 32 y = 560 . . . . eq 2 . now multiply eq 1 by 2 and sub eq 2 . 44 x = 920 8 x = 560 . 36 x = 360 = > x = 10 . sub x in eq 2 . . . . we get 80 + 32 y = 560 . . . then we get 32 y = 480 then y = 25 differenece between x and y is 15 answer : a" + }, + { + "Answer": 10, + "Options": "a ) 11 years , b ) 10 years , c ) 18 years , d ) 189 years , e ) 28 years", + "Correct": "b", + "Explanation": "\"let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 27 5 x = 25 = > x = 5 hence , b ' s age = 2 x = 10 years . answer : b\"" + }, + { + "Answer": 562.5, + "Options": "a ) 300 , b ) 400 , c ) 562.5 , d ) 600 , e ) none of these", + "Correct": "c", + "Explanation": "as per question stem 2 / 5 m ( portion of men employees who are managers ) + 225 ( portion of female employees who are managers ) = 2 / 5 t ( portion of total number of employees who are managers ) , thus we get that 2 / 5 m + 225 = 2 / 5 t , or 2 / 5 ( t - m ) = 225 , from here we get that t - m = 562.5 , that would be total number of female employees and the answer ( c )" + }, + { + "Answer": 6, + "Options": "a ) 7.67 % , b ) 6 % , c ) 0.54 % , d ) 9.54 % , e ) 8.54 %", + "Correct": "b", + "Explanation": "before increase total cost = 4 + 3 + 2 = 9 , after increasing the cost = 9.54 so increase of . 54 over 9 , equal to 6 % answer : b" + }, + { + "Answer": 0.125, + "Options": "a ) 1 / 6 , b ) 1 / 8 , c ) 1 / 10 , d ) 1 / 12 , e ) 1 / 15", + "Correct": "b", + "Explanation": "explanation : 377 \u00f7 13 \u00f7 29 \u00d7 1 / 4 \u00f7 2 = ? = > ? = ( 337 / ( 13 \u00d7 29 \u00d7 4 \u00d7 2 ) ) = 1 / 8 answer : option b" + }, + { + "Answer": 66.6, + "Options": "a ) 75 , b ) 27.6 , c ) 66.6 , d ) 16.5 , e ) 11", + "Correct": "c", + "Explanation": "\"explanation : average = ( 70 + 60 + 78 + 60 + 65 ) / 5 = 333 / 5 = 66.6 . answer : c\"" + }, + { + "Answer": 90, + "Options": "a ) 18 , b ) 100 , c ) 90 , d ) 45 , e ) 120", + "Correct": "c", + "Explanation": "explanation : let first number be x . so , 2 nd no . = 2 x & 3 rd no . = 8 x . so , x + 2 x + 8 x = 165 \u00d7 3 = 495 11 x = 495 / 11 x = 495 / 11 hence , first number is x = 45 so , second number is = 2 x 45 = 90 answer : c" + }, + { + "Answer": 8, + "Options": "a ) 4 , b ) 8 , c ) 11 , d ) 12 , e ) 15", + "Correct": "b", + "Explanation": "\"the question basically asks how many positive odd integers less than 80 are odd multiples of 5 so we have 5,15 , 25,35 , 45,55 , 65,75 = 8 b\"" + }, + { + "Answer": 41, + "Options": "a ) 89 , b ) 20 , c ) 36 , d ) 41 , e ) 34", + "Correct": "d", + "Explanation": "\"speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 200 + 210 = 410 m . time taken = 410 / 10 = 41 sec . answer : option d\"" + }, + { + "Answer": 25, + "Options": "a ) 40 , b ) 25 , c ) 30 , d ) 50 , e ) 35", + "Correct": "b", + "Explanation": "\"answer let the number be x . then , x - 20 = 30 - x \u00e2 \u2021 \u2019 2 x = 30 + 20 = 50 \u00e2 \u2021 \u2019 2 x = 50 \u00e2 \u02c6 \u00b4 x = 25 correct option : b\"" + }, + { + "Answer": 100, + "Options": "a ) $ 160 , b ) $ 96 , c ) $ 90 , d ) $ 80 , e ) $ 100", + "Correct": "e", + "Explanation": "3 investors and 3 clients - so total 6 people the bill $ 720 includes 20 % gratuity . . . so the actual cost of dinner was $ 600 now , the cost per person will be $ 600 / 6 which is $ 100 option e" + }, + { + "Answer": 40, + "Options": "a ) 33 , b ) 21 , c ) 38 , d ) 40 , e ) 92", + "Correct": "d", + "Explanation": "explanation : average score = 37 grace mark 3 is given to 35 student then its average will be 3 . hence new average = 37 + 3 = 40 answer : d" + }, + { + "Answer": 0.2727272727272727, + "Options": "a ) 1 / 7 , b ) 1 / 5 , c ) 1 / 4 , d ) 1 / 3 , e ) 3 / 11", + "Correct": "e", + "Explanation": "1 lbs of raisin = $ 1 3 lbs of raisin = $ 3 1 lbs of nuts = $ 2 4 lbs of nuts = $ 8 total value of mixture = 8 + 3 = 11 fraction of the value of raisin = 3 / 11 ans : e" + }, + { + "Answer": 94, + "Options": "a ) 78 , b ) 80 , c ) 87 , d ) 91 , e ) 94", + "Correct": "e", + "Explanation": "explanations 1 ) the average of the first 16 students is 77 . this means , the sum of these 16 scores is sum = ( average ) * ( number of scores ) = 77 * 16 = 1232 once taqeesha takes her test , the average of all 17 scores is 78 . this means , the sum of these 17 scores is : sum = ( average ) * ( number of scores ) = 78 * 17 = 1326 once we had the sum of the 16 scores , all we had to do was add taqeesha \u2019 s score to that total to get the sum of all 17 . therefore , the difference in these two sums is taqeesha \u2019 s score . 1326 \u2013 1232 = 94 . answer : e ." + }, + { + "Answer": 2970, + "Options": "a ) 2652 , b ) 2578 , c ) 2970 , d ) 3354 , e ) 4234", + "Correct": "c", + "Explanation": "c 2970 here d = a + 3 a + a + 3 = 109 2 a = 106 a = 53 so , numbers are 53 , 54 , 55 and 56 \u2234 b \u00d7 c = 54 \u00d7 55 = 2970" + }, + { + "Answer": 0.19999999999999996, + "Options": "a ) 1 / 15 , b ) 4 / 5 , c ) 4 / 15 , d ) 1 / 5 , e ) 2 / 5", + "Correct": "d", + "Explanation": "tot students = x 1 st year student = x / 2 - - - - > non majaor = 4 / 5 ( x / 2 ) - - - - - > maj = 1 / 5 ( x / 2 ) 2 nd year student = x / 2 - - - - > maj = 4 ( 1 / 5 ( x / 2 ) ) = 2 / 5 ( x ) - - - > non major = x / 2 - 2 / 5 ( x ) = 1 / 5 ( x ) hence 1 / 5 d" + }, + { + "Answer": 5, + "Options": "a ) 4 , b ) 3 , c ) 5 , d ) 2 , e ) 1", + "Correct": "c", + "Explanation": "let ' s test out some values of m and n that satisfy the given information . a leaves are remainder of 2 when divided by 6 so , a could equal 8 b leaves are remainder of 3 when divided by 6 so , b could equal 3 what is the remainder when a \u2013 b is divided by 6 ? so , a - b = 8 - 3 = 5 , and when we divide 5 by 6 , we get 0 with remainder 5 answer : c" + }, + { + "Answer": 13, + "Options": "a ) 15 , b ) 25 , c ) 35 , d ) 13 , e ) 55", + "Correct": "d", + "Explanation": "\"a 1 = 120 / 3 = 40 a 2 = a 1 - 9 = 31 sum of second list = 31 * 3 = 93 therefore the number = 93 - 80 = 13 answer : d\"" + }, + { + "Answer": 15, + "Options": "a ) 9 . , b ) 12 . , c ) 15 . , d ) 16 , e ) 18 .", + "Correct": "c", + "Explanation": "\"expand this to get : ( 2 x + y ) ( 2 z + w ) = 4 xz + 2 xw + 2 yz + yw = 4 xz + yw + 2 xw + 2 yz [ i rearranged the terms ] = 3 + 2 xw + 2 yz [ replaced 4 xz + yw with 3 ] = 3 + 2 ( xw + yz ) factored out a 2 = 3 + 2 ( 6 ) = 3 + 12 = 15 answer : c\"" + }, + { + "Answer": 152, + "Options": "a ) 125 , b ) 126 , c ) 130 , d ) 148 , e ) 152", + "Correct": "e", + "Explanation": "\"3 * 14 + 3 * 15 + 3 * 18 + 11 = 42 + 45 + 54 + 11 = 152 the answer is e .\"" + }, + { + "Answer": 545, + "Options": "a ) 545 , b ) 525 , c ) 535 , d ) 625 , e ) 105", + "Correct": "a", + "Explanation": "\"explanation : = 550 \u2212 ( 104 / 208 x 10 ) = 550 \u2212 5 = 545 option a\"" + }, + { + "Answer": 0.25, + "Options": "a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 5 , d ) 1 / 6 , e ) 1 / 7", + "Correct": "b", + "Explanation": "\"let x be the fraction of her take - home pay that the worker saved . let p be the monthly pay . 12 xp = 4 ( 1 - x ) p 12 xp = 4 p - 4 xp 16 xp = 4 p x = 1 / 4 the answer is b .\"" + }, + { + "Answer": 0.39999999999999997, + "Options": "a ) 0.1 , b ) 0.4 , c ) 0.82 , d ) 0.8 , e ) none", + "Correct": "b", + "Explanation": "\"sol . ( x \u00d7 6 ) = ( 0.60 \u00d7 4 ) \u21d2 x = 2.4 / 6 = 0.40 . answer b\"" + }, + { + "Answer": 460, + "Options": "a ) $ 420 , b ) $ 440 , c ) $ 450 , d ) $ 460 , e ) $ 480", + "Correct": "d", + "Explanation": "the average revenue was $ 400 per day over a 10 - day period - - > total revenue over 10 - day period is 10 * $ 400 = $ 4000 ; the average daily revenue was $ 360 for the first 6 days - - > total revenue for the first 6 days is 6 * $ 360 = 2160 ; total revenue for the last 4 days is $ 4000 - 2160 = $ 1840 ; average daily revenue for the last 4 days is $ 1840 / 4 = $ 460 . answer : d ." + }, + { + "Answer": 402.1148036253776, + "Options": "a ) 333 , b ) 383 , c ) 402 , d ) 433 , e ) 483", + "Correct": "c", + "Explanation": "let the monthly payment be xx . after the 1 st month there will be 1000 \u2217 1.1 \u2212 x dollars left to repay ; after the 2 nd month there will be ( 1000 \u2217 1.1 \u2212 x ) \u2217 1.1 \u2212 x = 1210 \u2212 2.1 x dollars left to repay ; after the 3 rd month there should be 0 dollars left to repay : ( 1210 \u2212 2.1 x ) \u2217 1.1 \u2212 x = 0 - - > 1331 = 3.31 x - - > x \u2248 402 x \u2248 402 answer : c ." + }, + { + "Answer": 6, + "Options": "a ) $ 6 , b ) $ 5 , c ) $ 5.5 , d ) $ 6.5 , e ) $ 7", + "Correct": "a", + "Explanation": "4 pillowss - > total cost = 4 * avg cost = 4 * 5 = 20 fifth pillow cost = 10 total cost for 5 pillows = 20 + 10 = 30 am = 30 / 5 = 6 hence a" + }, + { + "Answer": 26, + "Options": "a ) 12 % , b ) 26 % , c ) 29 % , d ) 30 % , e ) 60 %", + "Correct": "b", + "Explanation": "\"in the first plot 20 % of 300 seeds germinated , so 0.20 x 300 = 60 seeds germinated . in the second plot , 35 % of 200 seeds germinated , so 0.35 x 200 = 70 seeds germinated . since 60 + 70 = 130 seeds germinated out of a total of 300 + 200 = 500 seeds , the percent of seeds that germinated is ( 130 / 500 ) x 100 % , or 26 % . answer : b .\"" + }, + { + "Answer": 4, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "d", + "Explanation": "p = 125 * 243 * 16 / 405 p = 5 ^ 3 * 3 * 9 ^ 2 * 4 ^ 2 / ( 5 * 9 ^ 2 ) p = 5 ^ 2 * 3 * 4 ^ 2 p = 20 ^ 2 * 3 = 1200 answer d" + }, + { + "Answer": 25, + "Options": "a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 25", + "Correct": "e", + "Explanation": "\"check two extreme cases : jane = 18 , child = 9 , years ago = 34 - 18 = 16 - - > child ' s age now = 9 + 16 = 25 ; jane = 24 , child = 12 , years ago = 34 - 24 = 10 - - > child ' s age now = 12 + 10 = 22 . answer : e .\"" + }, + { + "Answer": 77.76, + "Options": "a ) 68.8 , b ) 73.6 , c ) 75.2 , d ) 76.8 , e ) 77.76", + "Correct": "e", + "Explanation": "\"degree of difficulty of dive = 3.2 scores are 6.0 , 7.5 , 8.0 , 8.8 and 9.0 we can drop 6.0 and 9.0 sum of the remaining scores = ( 7.5 + 8 + 8.8 ) = 24.3 point of value of the dive = 24 * 3.2 = 77.76 answer e\"" + }, + { + "Answer": 216, + "Options": "a ) 122 , b ) 210 , c ) 216 , d ) 217 , e ) 220", + "Correct": "c", + "Explanation": "first step : we should determine which 5 digits from given 6 , would form the 5 digit number divisible by 3 . we have six digits : 0,1 , 2,3 , 4,5 . their sum = 15 . for a number to be divisible by 3 the sum of the digits must be divisible by 3 . as the sum of the six given numbers is 15 ( divisible by 3 ) only 5 digits good to form our 5 digit number would be 15 - 0 = ( 1 , 2,3 , 4,5 ) and 15 - 3 = ( 0 , 1,2 , 4,5 ) . meaning that no other 5 from given six will total the number divisible by 3 . second step : we have two set of numbers : 1 , 2,3 , 4,5 and 0 , 1,2 , 4,5 . how many 5 digit numbers can be formed using this two sets : 1 , 2,3 , 4,5 - - > 5 ! as any combination of these digits would give us 5 digit number divisible by 3 . 5 ! = 120 . 0 , 1,2 , 4,5 - - > here we can not use 0 as the first digit , otherwise number wo n ' t be any more 5 digit and become 4 digit . so , total combinations 5 ! , minus combinations with 0 as the first digit ( combination of 4 ) 4 ! - - > 5 ! - 4 ! = 96 120 + 96 = 216 answer : c ." + }, + { + "Answer": 146.66666666666666, + "Options": "a ) $ 146.6 , b ) $ 120 , c ) $ 180 , d ) $ 220 , e ) $ 260", + "Correct": "a", + "Explanation": "lets assume al have amount a in his bank account and eliot ' s bank account got e amount . we can form an equation from the first condition . a - e = 1 / 12 * ( a + e ) = = > 11 a = 13 e - - - - - - - - - - - - ( 1 ) second condition gives two different amounts , al ' s amount = 1.1 a and eliot ' s amount = 1.2 e 1.1 a = 22 + 1.15 e = = > 11 a = 220 + 11.5 e - - - - - - - ( 2 ) substituting ( 1 ) in ( 2 ) : 13 e = 220 + 11.5 e = = > 1.5 e = 220 or e = 440 / 3 = 146.6 a" + }, + { + "Answer": 7, + "Options": "a ) 3 % , b ) 8 % , c ) 7 % , d ) 10 % , e ) 15 %", + "Correct": "c", + "Explanation": "\"c 7 % 100 - [ ( 100 - 80 ) + ( 100 - 82 ) + ( 100 - 70 ) + ( 100 - 75 ) ] = 100 - ( 20 + 18 + 30 + 25 ) = 100 - 93\"" + }, + { + "Answer": 5, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "d", + "Explanation": "\"minimuum should be 1 maximum should be 4 : 1 out of a or b to make the multiplication negative 3 out of c , d , e or f to make the multiplication negative . negative + negative < 0 answer : c maximum will be 5 . . you dont require both the multiplicatin to be negative for entire equation to be negative . . . any one a or b can be negative to make ab negative and it can still be more ( away from 0 ) than the multiplication of 4 other - ve numbers . . . actually by writing minimum required as 1 out of 6 , you are actually meaning 5 out of 6 also possible as you will see w = 5 or 1 will give you same equation . . ans d\"" + }, + { + "Answer": 24, + "Options": "a ) 24 , b ) 66 , c ) 88 , d ) 27 , e ) 91", + "Correct": "a", + "Explanation": "explanation : number of boys in the row = ( 6 + 10 + 8 ) = 24 answer : a ) 24" + }, + { + "Answer": 8, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 4 , e ) 3", + "Correct": "c", + "Explanation": "\"since 64 / k = 8 and 64 / 8 = 8 , then k = 8 correct answer c\"" + }, + { + "Answer": 60, + "Options": "a ) 30 , b ) 60 , c ) 120 , d ) 240 , e ) 480", + "Correct": "b", + "Explanation": "\"the least number of trees that are required = lcm ( 4 , 5 , 6 ) = 60 . answer : b\"" + }, + { + "Answer": 10, + "Options": "a ) 18 , b ) 8 , c ) 12 , d ) 10 , e ) none of these", + "Correct": "d", + "Explanation": "\"90 - 40 = 50 40 - 20 = 20 90 - 20 = 70 the h . c . f of 20 , 50 and 70 is 10 . answer : d\"" + }, + { + "Answer": 5991, + "Options": "a ) rs . 1991 , b ) rs . 2991 , c ) rs . 3991 , d ) rs . 4991 , e ) rs . 5991", + "Correct": "e", + "Explanation": "\"explanation : total sale for 5 months = rs . ( 7435 + 7927 + 7855 + 8230 + 7562 ) = rs . 39009 . required sale = rs . [ ( 7500 x 6 ) \u00e2 \u20ac \u201c 39009 ] = rs . ( 45000 \u00e2 \u20ac \u201c 39009 ) = rs . 5991 . answer e\"" + }, + { + "Answer": 74.99999999999716, + "Options": "a ) 96 , b ) 87 , c ) 75 , d ) 25 , e ) 12", + "Correct": "c", + "Explanation": "\"by the definition of a remainder , the remainder here is equal to 9 / y . the remainder in decimal form is given as . 12 therefore , 9 / y = . 12 solve for y and get 75 . c\"" + }, + { + "Answer": 76, + "Options": "a ) 57 , b ) 76 , c ) 77 , d ) 87 , e ) 97", + "Correct": "b", + "Explanation": "\"money collected = ( 57.76 x 100 ) paise = 5776 paise numbers of members = 5776 squareroot = 76 answer b\"" + }, + { + "Answer": 17, + "Options": "a ) 15 , b ) 17 , c ) 11 , d ) 18 , e ) 13", + "Correct": "b", + "Explanation": "\"let the population of two villages be equal after p years then , 76000 - 1200 p = 42000 + 800 p 2000 p = 34000 p = 17 answer is b .\"" + }, + { + "Answer": 89, + "Options": "a ) a ) 70 , b ) b ) 76 , c ) c ) 78 , d ) d ) 89 , e ) e ) 88", + "Correct": "d", + "Explanation": "\"explanation : average after 11 innings should be 39 so , required score = ( 11 * 39 ) - ( 10 * 34 ) = 429 - 340 = 89 answer : option d\"" + }, + { + "Answer": 11.99999999999999, + "Options": "a ) 10 % , b ) 12 % , c ) 14 % , d ) 16 % , e ) 18 %", + "Correct": "b", + "Explanation": "\"let x be the amount of money paid for the first purchase . the second time , the customer paid 0.8 ( 1.1 x ) = 0.88 x . the difference is 12 % . the answer is b .\"" + }, + { + "Answer": 18, + "Options": "a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22", + "Correct": "a", + "Explanation": "explanation : let first number be x . so , 2 nd no . = 4 x & 3 rd no . = 8 x . so , x + 4 x + 8 x = 78 \u00d7 3 = 234 . 13 x = 234 x = 234 / 13 hence , smallest number x = 18 . answer : a" + }, + { + "Answer": 6, + "Options": "a ) 3 hours . , b ) 4 hours . , c ) 4 hours and 20 minutes . , d ) 5 hours and 50 minutes , e ) 6 hours .", + "Correct": "e", + "Explanation": "s 1 = 2 s 2 since , speed is inversely proportional to time we have , s 1 / s 2 = 2 / 1 = t 2 / t 1 therefore , the time taken for one trip = 60 + 120 = 180 minutes total = 180 * 2 = 360 minutes = 6 hours answer : e" + }, + { + "Answer": 26, + "Options": "a ) 43 , b ) 26 , c ) 33 , d ) 21 , e ) 28", + "Correct": "b", + "Explanation": "\"b 26 let the number of hens be x and the number of cows be y . then , x + y = 48 . . . . ( i ) and 2 x + 4 y = 140 x + 2 y = 70 . . . . ( ii ) solving ( i ) and ( ii ) we get : x = 26 , y = 22 . the required answer = 26 .\"" + }, + { + "Answer": 4, + "Options": "a ) 3.5 , b ) 6 , c ) 8 , d ) 7 , e ) 4", + "Correct": "e", + "Explanation": "\"let the number be x . then , 3 ( 2 x + 9 ) = 51 2 x = 8 = > x = 4 answer : e\"" + }, + { + "Answer": 9032, + "Options": "a ) 2387 , b ) 2888 , c ) 9000 , d ) 2837 , e ) 2271", + "Correct": "c", + "Explanation": "\"explanation : 9000 + 16 2 / 3 % of ? = 10500 = > 9000 + 50 / 3 % of ? = 10500 50 / ( 3 * 100 ) of ? = 1500 = > ? = 1500 * 6 ? = 9000 answer : c\"" + }, + { + "Answer": 0.36, + "Options": "a ) 3 / 10 , b ) 6 / 17 , c ) 9 / 25 , d ) 10 / 33 , e ) 12 / 35", + "Correct": "c", + "Explanation": "\"6 a / 100 = 10 a = 500 / 3 b / 10 = 6 b = 60 c = b / a = 60 * 3 / 500 = 9 / 25 the answer is c .\"" + }, + { + "Answer": 859560, + "Options": "a ) 546577 , b ) 674645 , c ) 566578 , d ) 465766 , e ) 859622", + "Correct": "e", + "Explanation": "dividend = quotient * divisor + reminder 859622 / 456 gives quotient = 1885 and reminder = 62 . so , the next number divisible by 456 is 456 places infront of 456 * 1885 which means 456 \u2013 62 = 394 should be added to 859622 . e" + }, + { + "Answer": 121, + "Options": "a ) 31 , b ) 35 , c ) 50 , d ) 99 , e ) 121", + "Correct": "e", + "Explanation": "\"2 ^ 10 = 1.024 * 10 ^ 3 = > 2 ^ 100 = ( 1.024 ) ^ 10 * 10 ^ 120 therefore 121 digits would be my best guess e\"" + }, + { + "Answer": 0.9090909090909091, + "Options": "a ) 20 / 11 , b ) 16 / 11 , c ) 17 / 11 , d ) 10 / 11 , e ) 19 / 11", + "Correct": "d", + "Explanation": "\"say x = y = 10 . in this case we would have : 40 x = 200 black - and - white films ; 4 y = 40 color films . y / x % = 10 / 10 % = 1 % of the black - and - white films , so 4 black - and - white films and all 40 color films , thus total of 44 films were selected . color films thus compose 40 / 44 = 10 / 11 of the selected films . answer : d\"" + }, + { + "Answer": 0.4, + "Options": "a ) 6 / 25 , b ) 5 / 16 , c ) 4 / 9 , d ) 3 / 7 , e ) 2 / 5", + "Correct": "e", + "Explanation": "let x be the fraction of her take - home pay that the worker saved . let p be the monthly pay . 12 xp = 8 ( 1 - x ) p 12 xp = 8 p - 8 xp 20 xp = 8 p x = 2 / 5 the answer is e ." + }, + { + "Answer": 1271, + "Options": "a ) 1211 , b ) 1231 , c ) 1251 , d ) 1271 , e ) 1291", + "Correct": "d", + "Explanation": "\"x = 50 + 51 + . . . + 70 = 21 ( 60 ) = 1260 y = 11 x + y = 1271 the answer is d .\"" + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 10 , c ) 11 , d ) 12 , e ) 14", + "Correct": "a", + "Explanation": "\"explanation : let the number be x . then , 12 x = x 2 + 36 = > x 2 - 12 x + 36 = 0 = > ( x - 6 ) ( x - 6 ) = 0 = > x = 6 answer : a\"" + }, + { + "Answer": 400, + "Options": "a ) 200 , b ) 250 , c ) 300 , d ) 350 , e ) 400", + "Correct": "e", + "Explanation": "x = rs . 5000 / - y = rs . 15000 / - x share 1 part & y share 3 parts total 4 parts - - - - - > rs . 1600 / - - - - - > 1 part - - - - - - - > rs . 400 / - x share = 1 part - - - - - > rs . 400 / - e" + }, + { + "Answer": 6, + "Options": "a ) 8 rs . , b ) 7 rs . , c ) 6 rs . , d ) 4 rs . , e ) 5 rs .", + "Correct": "c", + "Explanation": "5 m = xw = 7 b 5 m + xw + 7 b - - - - - 90 rs . 5 m + 5 m + 5 m - - - - - 90 rs . 15 m - - - - - - 90 rs . = > 1 m = 6 rs . answer : c" + }, + { + "Answer": 2, + "Options": "a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 2 , d ) 2 , e ) 4 / 7", + "Correct": "d", + "Explanation": "\"p ( b | a ) = p ( a \u00e2 \u02c6 \u00aa b ) / p ( a ) p ( b | a ) = ( 16 / 15 ) / ( 8 / 15 ) = 2 . d\"" + }, + { + "Answer": 50, + "Options": "a ) 4 % , b ) 18 % , c ) 36 % , d ) 40 % , e ) 50 %", + "Correct": "e", + "Explanation": "given w = 0.6 x , x = 0.6 y , z = 0.54 y , substituting , w = 2 / 3 z - - - - > z = 1.5 w and thus z is 50 % greater than w . e is the correct answer ." + }, + { + "Answer": 2, + "Options": "a ) 2 . , b ) 4 . , c ) 5 . , d ) 7 . , e ) 9 .", + "Correct": "a", + "Explanation": "\"ad = ( a + 1 ) ( d + 1 ) - 5 0 = a + d - 4 a + d = 4 a = d ( as they are twin brothers ) a = d = 2 a is the answer\"" + }, + { + "Answer": 8, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", + "Correct": "b", + "Explanation": "a : m = 4 : 7 let the ages of a & m be x & 22 - x x / 22 - x = 4 / 7 x = 8 a = 8 yrs answer : b" + }, + { + "Answer": 540, + "Options": "a ) 540 , b ) 570 , c ) 619 , d ) 649 , e ) 700", + "Correct": "a", + "Explanation": "\"before price increase price = y after 30 % price increase price = y + ( 30 / 100 ) * y = 1.3 y = 351 ( given ) i . e . y = 351 / 1.3 = $ 270 i . e . 2 y = 2 * 270 = 540 answer : option a\"" + }, + { + "Answer": 6, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "d", + "Explanation": "\"let x be the wholesale price . then 1.6 x = 24 and x = 24 / 1.6 = 15 . to achieve a 100 % markup , the price needs to be $ 30 . the retailer needs to increase the price by $ 6 more . the answer is d .\"" + }, + { + "Answer": 8, + "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12", + "Correct": "a", + "Explanation": "we have ( 1023 ^ 3923 ) + ( 3081 ^ 3921 ) ( 3923 / 4 ) = 4 n + 3 ( 3921 / 4 ) = 4 n + 1 where n can be any integer now through cyclicity we can obtain or you can learn the chart from arun sharma number ending in 4 n + 1 4 n + 2 4 n + 3 4 n 1 1 1 1 1 2 2 4 8 6 3 3 9 7 1 in this way 7 + 1 = 8 is the unit ' s place digit answer : a" + }, + { + "Answer": 70, + "Options": "a ) 30 km , b ) 40 km , c ) 70 km , d ) 80 km , e ) 90 km", + "Correct": "c", + "Explanation": "let the total journey be x km . x / 35 - x / 40 = 15 / 60 solving for x , we get x = 70 therefore , total journey = 70 km . answer : c" + }, + { + "Answer": 1717, + "Options": "a ) 12 , b ) 1 , c ) 1728 , d ) 1717 , e ) 4", + "Correct": "d", + "Explanation": "12 ^ ( 190 ) can be written as . ( ( 12 ^ 3 ) ^ 63 ) * 12 . 12 ^ 3 when divided by 1729 gives a remainder q - 1 . so in the numerator we have - 12 . now acccording to remainder theorm the answer will be 1729 - 12 = 1717 . d" + }, + { + "Answer": 465.1162790697675, + "Options": "a ) 450 , b ) 465.12 , c ) 475 , d ) 500.15 , e ) 200", + "Correct": "b", + "Explanation": "system of equations a = ( 43 / 100 ) c ( 1 / 4 ) a = 50 - - > a = 200 substitution 200 = ( 43 / 100 ) c c = ( 100 / 43 ) 200 calculate 200 / 43 * 100 - the the correct answer is 465.12 . the correct answer is b ." + }, + { + "Answer": 4, + "Options": "a ) 1 , b ) 4 , c ) 5 , d ) 7 , e ) 9", + "Correct": "b", + "Explanation": "we are not concerned what 21 / 22 means . . we have to look at the decimal . . 0.9544 means 0.95454545 . . . . so leaving first digit to the right of decimal , all odd numbered digits are 4 and all even numbered are 5 . . here 57 is odd , so ans is 4 answer is b" + }, + { + "Answer": 13.285714285714286, + "Options": "a ) 13.3 , b ) 10.8 , c ) 10.7 , d ) 11.4 , e ) 12.5", + "Correct": "a", + "Explanation": "9 / 8 * 7 + 5 - 10 this expression becomes 9 - 8 / 7 * 5 + 10 after exchanging the symbols then the values for it would be 9 - 1.142 * 5 + 10 = 13.290 ( app ) = 13.3 answer : a" + }, + { + "Answer": 1792, + "Options": "a ) 1692 , b ) 1792 , c ) 1795 , d ) 1892 , e ) 1992", + "Correct": "b", + "Explanation": "the number is 1792 . let the number be represented as 1000 x + 100 y + 10 z + t acc to ques , xyzt = 126 x + y + z + t = 10 x + z = 19 so , number in thousands and tens place are 1 and 9 respectively . the remaining factor is 14 which is 7 * 2 so the number is 1792 . answer : b" + }, + { + "Answer": 48.00000000000001, + "Options": "a ) 25 , b ) 36 , c ) 10 , d ) 48 , e ) 45", + "Correct": "d", + "Explanation": "let x be that amount so accordind to question , eqn will be like : ( ( ( x - x / 3 ) + 10 ) - ( ( ( x - x / 3 ) + 10 ) / 3 ) ) + 20 = x = > ( ( 2 x / 3 + 10 ) - ( ( 2 x / 3 + 10 ) / 3 ) ) + 20 = x = > 3 x - 4 x / 3 = 80 = > x = 48 answer : d" + }, + { + "Answer": 28.999999999999996, + "Options": "a ) 12 % , b ) 26 % , c ) 29 % , d ) 30 % , e ) 60 %", + "Correct": "c", + "Explanation": "in the first plot 25 % of 300 seeds germinated , so 0.25 x 300 = 75 seeds germinated . in the second plot , 35 % of 200 seeds germinated , so 0.35 x 200 = 70 seeds germinated . since 75 + 70 = 145 seeds germinated out of a total of 300 + 200 = 500 seeds , the percent of seeds that germinated is ( 145 / 500 ) x 100 % , or 29 % . answer : c ." + }, + { + "Answer": 7, + "Options": "a ) 5 , b ) 7 , c ) 13 , d ) 14 , e ) 16", + "Correct": "b", + "Explanation": "explanation : ( n - 1 ) ! is always divisible by n unless and untill n is a prime number e . g . ( 5 - 1 ) ! = 4 ! which is not divisible by 5 bcuz 5 is a prime number therefore , find all prime numbers in the range of 12 to 40 i . e 13 , 17 , 19 , 23 , 29 , 31 and 37 hence , the number of positive integers n is 7 . answer : b" + }, + { + "Answer": 1620, + "Options": "a ) 1236 , b ) 1356 , c ) 1470 , d ) 1556 , e ) 1635", + "Correct": "e", + "Explanation": "\"let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 15 5 x = 1350 x = 270 large number = 270 + 1365 = 1635 e\"" + }, + { + "Answer": 24, + "Options": "a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24", + "Correct": "e", + "Explanation": "let the student ' s present age be x years . then , man ' s present age = ( x + 26 ) years . ( x + 26 ) + 2 = 2 ( x + 2 ) x + 28 = 2 x + 4 x = 24 . answer : e" + }, + { + "Answer": 0.2, + "Options": "a ) 0.15 , b ) 0.20 , c ) 0.25 , d ) 0.30 , e ) 0.33", + "Correct": "b", + "Explanation": "rearrange the first set : a = { 54 , 32 } b = { 45 , 67 , 8 } as you can see numbers in each column ( the numbers of the same color ) give the sum of 9 . so there are 4 such pares possible , total # of pairs is 4 * 5 = 20 . t = favorable / total = 4 / 20 = 0.2 . answer : b . or : we can select any number from set a ( 4 / 4 = 1 ) but in this case we must select its matching pair from set b ( the number of the same color ) and since there are only one matching pair of this particular number in b then the probability of this is 1 / 5 . so , overall : t = 1 * 1 / 5 . answer : b ." + }, + { + "Answer": 35.86313713864835, + "Options": "a ) 10 , b ) 12 , c ) 14 , d ) 36 , e ) 18", + "Correct": "d", + "Explanation": "\"this one ' s easy . 1000 * 2 ^ t = 500,000 2 ^ t = 500 now gauging , since 2 ^ 8 = 256 , then 2 ^ 9 = 512 so t = 9 but be careful , ' t ' is in time intervals of 4 minutes so answer is 9 * 4 = 36 minutes answer ( d )\"" + }, + { + "Answer": 42, + "Options": "a ) 32 , b ) 36 , c ) 38 , d ) 42 , e ) 48", + "Correct": "d", + "Explanation": "let oj be the bottles of orange juice and let aj be the bottles of apple juice . ( oj ) + aj = 70 . aj = 70 - ( oj ) . 70 ( oj ) + 60 aj = 4620 . 70 ( oj ) + 60 ( 70 - oj ) = 4620 . 10 ( oj ) + 4200 = 4620 . oj = 42 . the answer is d ." + }, + { + "Answer": 11, + "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12", + "Correct": "d", + "Explanation": "total number of hours practiced mon through fri : 5 * 2 = 10 total number of hours that will be practiced in a 7 day week considering 3 hours a day average : 7 * 3 = 21 thus 21 - 10 = 11 hours still need to be practiced ( on sat and sun combined ) d" + }, + { + "Answer": 200, + "Options": "a ) \u2212 220 , b ) \u2212 200 , c ) 100 , d ) 135 , e ) it can not be determined from the information given", + "Correct": "b", + "Explanation": "\"a + b = 160 b + c = 360 a - c = - 200 . imo option b .\"" + }, + { + "Answer": 24, + "Options": "a ) 24 , b ) 35 , c ) 39 , d ) 60 , e ) 65", + "Correct": "a", + "Explanation": "\"the total number of the people in the room must be a multiple of both 7 and 8 ( in order 3 / 7 and 5 / 8 of the number to be an integer ) , thus the total number of the people must be a multiple of lcm of 7 and 8 , which is 56 . since , the total number of the people in the room is greater than 50 and less than 100 , then there are 56 people in the room . therefore there are 3 / 7 * 56 = 24 people in the room under the age of 21 . answer : a .\"" + }, + { + "Answer": 20, + "Options": "a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24", + "Correct": "a", + "Explanation": "let x be the amount of pears that she sold . then she poached 0.5 x . then she canned 1.2 * 0.5 x = 0.6 x . the total amount of pears is x + 0.5 x + 0.6 x = 2.1 x the fraction of pears that she sold is 1 / 2.1 = 10 / 21 . the number of pears she sold is ( 10 / 21 ) * 42 = 20 . the answer is a ." + }, + { + "Answer": 1, + "Options": "a ) 0 , b ) 1 , c ) 45 , d ) 130 , e ) 520", + "Correct": "b", + "Explanation": "9 + 2 + 9 + 2 + 6 + 0 = 28 , so this number is not divisible by 3 and thus not divisible by 30 . therefore , k = 0 3 ^ k - k ^ 3 = 1 - 0 = 1 the answer is b ." + }, + { + "Answer": 8.3, + "Options": "a ) $ 8.30 , b ) $ 20.75 , c ) $ 22.50 , d ) $ 42.75 , e ) $ 45.00", + "Correct": "a", + "Explanation": "let number of apple , orange , strawberry and grape candies be a , o , s and g respectively . a = 2 o s = 2 g a = 2 s a = 4 g a + o + s + g = 90 = > a + a / 2 + a / 2 + a / 4 = 90 = > 9 a / 4 = 90 = > a = 40 o = 20 s = 20 g = 10 cost of each candy = . 1 $ mininum amount of money required to guarantee that you would buy at least three of each type of candy we can buy 40 apple candies , 20 orange candies , 20 strawberry candies and 3 grape candies to ensure atleast 3 of each type of candies . total = 83 candies amount required = 83 * . 1 = 8.30 $ answer a" + }, + { + "Answer": 72, + "Options": "a ) 22 , b ) 33 , c ) 44 , d ) 66 , e ) 72", + "Correct": "e", + "Explanation": "\"x / ( 12 p ) = odd prime number x = odd prime number * 11 p least value of x = lowest odd prime number * 11 * lowest value of p = 3 * 12 * 2 = 72 answer e\"" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 4 , c ) 6 , d ) 7 , e ) 13", + "Correct": "a", + "Explanation": "\"2 ( 3 x - 5 ) - 16 = 3 ( x - 6 ) - 5 3 x = 3 x = 1 the answer is a .\"" + }, + { + "Answer": 47, + "Options": "a ) 42 , b ) 43 , c ) 44 , d ) 45 , e ) 47", + "Correct": "e", + "Explanation": "let \u2018 x \u2019 be the average score after 12 th innings \u21d2 12 x = 11 \u00d7 ( x \u2013 3 ) + 80 \u2234 x = 47 answer e" + }, + { + "Answer": 64.00000000000001, + "Options": "a ) 64 % , b ) 65 % , c ) 66 % , d ) 67 % , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : let the number be x , then , 5 / 3 \u2212 3 / 5 = 16 / 15 x error % = ( 16 / 15 x \u2217 3 / 5 \u2217 100 ) option a\"" + }, + { + "Answer": 6, + "Options": "a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "e", + "Explanation": "3 ^ 2 y = 3 ^ 12 2 y = 12 , therefore y = 6 e" + }, + { + "Answer": 5, + "Options": "a ) 4 , b ) 7 , c ) 8 , d ) 5 , e ) 3", + "Correct": "d", + "Explanation": "\"explanation : let the number be x . then , ( x - 5 ) / 7 = 7 = > x - 5 = 49 x = 54 . : ( x - 4 ) / 10 = ( 54 - 4 ) / 10 = 5 answer : option d\"" + }, + { + "Answer": 23, + "Options": "a ) 23 , b ) 11 , c ) 12 , d ) 14 , e ) 15", + "Correct": "a", + "Explanation": "\"- > x ^ 4 + ( 1 / x ^ 4 ) = ( x ^ 2 ) ^ 2 + ( 1 / x ^ 2 ) ^ 2 = ( x ^ 2 + 1 / x ^ 2 ) ^ 2 - 2 x ^ 2 ( 1 / x ^ 2 ) = 5 ^ 2 - 2 = 23 . thus , the answer is a .\"" + }, + { + "Answer": 64, + "Options": "a ) 86.5 kg , b ) 63.5 kg , c ) 46.5 kg , d ) 26.5 kg , e ) 16.5 kg", + "Correct": "b", + "Explanation": "\"let arun ' s weight be x kg . according to arun , 62 < x < 72 . according to arun ' s brother , 60 < x < 70 . according to arun ' s mother , x < 65 . the values satisfying all the above conditions are 63 and 64 . required average = ( 63 + 64 ) / 2 = 63.5 kg answer : b\"" + }, + { + "Answer": 45, + "Options": "a ) 45 , b ) 43 , c ) 40 , d ) 38 , e ) 29", + "Correct": "a", + "Explanation": "solution : average speed = 2 xy / x + y = 2 * 60 * 36 / 60 + 36 = 45 answer : a" + }, + { + "Answer": 1520, + "Options": "a ) rs . 3500 , b ) rs . 1520 , c ) rs . 4996 , d ) rs . 4000 , e ) rs . 900", + "Correct": "b", + "Explanation": "total sale for 5 months = rs . ( 2500 + 4000 + 3540 ) = rs . 10040 . required sale = rs . [ ( 2890 x 4 ) - 10040 ] = rs . ( 11560 - 10040 ) = rs . 1520 . b )" + }, + { + "Answer": 0.66, + "Options": "a ) 0.66 , b ) 0.68 , c ) 0.96 , d ) 0.69 , e ) 0.76", + "Correct": "a", + "Explanation": "\"given expression = ( 0.76 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.76 ) ( power 2 ) + ( 0.76 x 0.1 ) + ( 0.1 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 0.76 - 0.1 ) = 0.66 answer is a .\"" + }, + { + "Answer": 16, + "Options": "a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17", + "Correct": "d", + "Explanation": "the twenty - first century runs from the year 2001 to 2100 inclusive , so with the exception of the year 2100 , for which the digital sum is three anyway , the first two digits of all the other years are fixed as 20 . hence for the sum of all the digits to be square the sum of the last two digits number be two less than a perfect square . as the maximum sum of the last two digits is 18 , the greatest sum will be 20 . therefore we can obtain digital sums of 4 , 9 , or 16 , with the last two digits adding to 2 , 7 , or 14 respectively . 4 : 2002 , 2011 , 2020 9 : 2007 , 2016 , 2025 , 2034 , 2043 , 2052 , 2061 , 2070 16 : 2059 , 2068 , 2077 , 2086 , 2095 that is , there are sixteen years during the twenty - first century for which the digital sum is square . answer : d" + }, + { + "Answer": 5, + "Options": "a ) - 1 , b ) 0 , c ) 3 , d ) 4 , e ) 5", + "Correct": "e", + "Explanation": "\"0 . [ u ] 125 [ / u = 0.525525525 . . . . . every 3 rd digit is 5 and every multiple of 3 will be the digit 5 . since 81 is multiple of 3 , the 81 st digit is 5 . answer e\"" + }, + { + "Answer": 48.975, + "Options": "a ) 48.975 , b ) 42.255 , c ) 50 , d ) 51.255 , e ) 52.253", + "Correct": "a", + "Explanation": "\"explanation : average weight of 24 boys = 50.25 total weight of 24 boys = 50.25 \u00d7 24 average weight of remaining 8 boys = 45.15 total weight of remaining 8 boys = 45.15 \u00d7 8 total weight of all boys in the class = ( 50.25 \u00d7 24 ) + ( 45.15 \u00d7 8 ) total boys = 24 + 8 = 32 average weight of all the boys = ( 50.25 \u00d7 24 ) + ( 45.15 \u00d7 8 ) / 32 = 48.975 answer : option a\"" + }, + { + "Answer": 20, + "Options": "a ) 40 , b ) 80 , c ) 20 , d ) 24 , e ) 36", + "Correct": "c", + "Explanation": "40 and 80 are both divisible by 4 and 5 but also by 8 . so they are not the right answer . 24 and 36 are both clearly not divisible by 5 ( not correct ) 20 is both divisible by 4 and 5 but not by 8 . answer : ( c )" + }, + { + "Answer": 30000, + "Options": "a ) 3277 , b ) 2977 , c ) 30000 , d ) 6077 , e ) 17112", + "Correct": "c", + "Explanation": "\"explanation : 40,000 * ( 3 / 4 ) ^ 1 answer : c\"" + }, + { + "Answer": 384, + "Options": "a ) 54 , b ) 76 , c ) 152 , d ) 384 , e ) none of these", + "Correct": "d", + "Explanation": "solution required number = product of first three multiplies of 3 = ( 4 \u00e3 \u2014 8 \u00e3 \u2014 12 ) = 384 . answer d" + }, + { + "Answer": 22, + "Options": "a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24", + "Correct": "c", + "Explanation": "\"the average of 14 , 32 , and 53 is 33 . the average of 21 , 47 and x is 30 . then 21 + 47 + x = 90 . x = 22 . the answer is c .\"" + }, + { + "Answer": 12, + "Options": "a ) 6 , b ) 12 , c ) 24 , d ) 48 , e ) none", + "Correct": "b", + "Explanation": "sol . \u221a 2 n = 64 \u21d4 ( 2 n ) 1 / 2 \u21d4 2 n / 2 = 26 \u21d4 n / 2 = 6 \u21d4 n = 12 . answer b" + }, + { + "Answer": 31500, + "Options": "a ) 28000 , b ) 30000 , c ) 31500 , d ) 34000 , e ) none of these", + "Correct": "c", + "Explanation": "\"explanation : suppose b ' s investment = x . then a ' s investment = 3 x suppose bs period of investment = y , then a ' s period of investment = 2 y a : b = 3 x * 2 y : xy = 6 : 1 total profit * 1 / 7 = 4500 = > total profit = 4500 * 7 = 31500 . answer : option c\"" + }, + { + "Answer": 9, + "Options": "a ) 10 % , b ) 9 % , c ) 25 % , d ) 30 % , e ) 50 %", + "Correct": "b", + "Explanation": "\"let original salary be $ 100 salary after decreasing 30 % = 100 - 100 x 30 / 100 = $ 70 salary after increasing 30 % on $ 70 = 70 + 70 x 30 / 100 = $ 91 percentage of loss = 100 - 91 = 9 % answer : b\"" + }, + { + "Answer": 20, + "Options": "a ) 20 , b ) 12 , c ) 15 , d ) 16 , e ) 10", + "Correct": "a", + "Explanation": "\"( a + b ) - ( b - c ) = 20 a - c = 20 answer is a\"" + }, + { + "Answer": 100, + "Options": "a ) 100 kgs , b ) 88.5 kgs , c ) 86.5 kgs , d ) 67.5 kgs , e ) 88.2 kgs", + "Correct": "a", + "Explanation": "\"average weight = [ ( a + b + c + ( a + b ) + ( b + c ) + ( c + a ) + ( a + b + c ) ] / 7 = 4 ( a + b + c ) / 7 = 4 x 175 / 7 = 100 kgs answer : a\"" + }, + { + "Answer": 5.485, + "Options": "a ) 2.91 , b ) 5.911 , c ) 5.485 , d ) 5.986 , e ) 2.999", + "Correct": "c", + "Explanation": "\"4.75 + . 303 + . 432 = 0 0 = 0 - 4.75 - 0.303 - 0.432 0 = - 5.485 answer : c\"" + }, + { + "Answer": 93.33333333333333, + "Options": "a ) 93 , b ) 225 , c ) 288 , d ) 324 , e ) 336", + "Correct": "a", + "Explanation": "1 / 4 x + 70 = x that means 70 = 3 / 4 x x = ( 70 * 4 ) / 3 = 280 / 3 = 93 a is the answer ." + }, + { + "Answer": 800, + "Options": "a ) 500 , b ) 600 , c ) 800 , d ) 900 , e ) 1200", + "Correct": "c", + "Explanation": "let total number of boys be x and total number of girls be y . y = 400 = > x = 600 and ^ = i 50 = > y = 200 now , x + y = 800 c" + }, + { + "Answer": 2050, + "Options": "a ) 256 , b ) 5122 , c ) 768 , d ) 2048 , e ) 1536", + "Correct": "d", + "Explanation": "\"0.2 * 2 ^ 10 = 0.2 * 1024 = 204.8 the answer is d .\"" + }, + { + "Answer": 21, + "Options": "a ) 21 , b ) 22 , c ) 23 , d ) 25 , e ) 28", + "Correct": "a", + "Explanation": "\"let the average age of the whole team be x years . 11 x - ( 24 + 27 ) = 9 ( x - 1 ) = > 11 x - 9 x = 42 = > 2 x = 42 = > x = 21 . so , average age of the team is 21 years . a\"" + }, + { + "Answer": 0.0003999999999999976, + "Options": "a ) 0.0005 , b ) 0.0004 , c ) 0.0006 , d ) 0.0002 , e ) 0.0001", + "Correct": "b", + "Explanation": "0.0320 + 0.0004 = 0.0324 ( 0.18 ) ^ 2 answer : b" + }, + { + "Answer": 40, + "Options": "a ) 50 , b ) 40 , c ) 267 , d ) 29 , e ) 27", + "Correct": "b", + "Explanation": "\"a + b + c = 500 a + c = 200 b + c = 340 - - - - - - - - - - - - - - a + b + 2 c = 540 a + b + c = 500 - - - - - - - - - - - - - - - - c = 40 answer : b\"" + }, + { + "Answer": 12, + "Options": "a ) 3 , b ) 9 , c ) 12 , d ) 19 , e ) 25", + "Correct": "c", + "Explanation": "these functions questions might look intimidating , but they just test your knowledge about how well you can substitute values [ [ x ] ] = x ^ 2 + 2 x + 4 [ [ 2 ] ] = 2 ^ 2 + 2 * 2 + 4 = 12 . option c" + }, + { + "Answer": 78468.75, + "Options": "a ) 81000 , b ) 78468.75 , c ) 81008 , d ) 81066 , e ) 81022", + "Correct": "b", + "Explanation": "\"62000 * 9 / 8 * 9 / 8 = 78468.75 answer : b\"" + }, + { + "Answer": 36, + "Options": "a ) 36 , b ) 302 , c ) 272 , d ) 292 , e ) 271", + "Correct": "a", + "Explanation": "explanation : let total students be 100 . hence , marks of 20 students is 0 as they were absent . 30 students scored 20 marks ( as they failed by 20 marks ) 10 students scored 40 marks ( just passed ) 40 students scored 65 marks ( average of 65 ) therefore , average score of the class is : ( 0 + 600 + 400 + 2600 ) / 100 = 3600 / 100 = 36 answer : a" + }, + { + "Answer": 285, + "Options": "a ) 150 , b ) 225 , c ) 285 , d ) 315 , e ) 374", + "Correct": "c", + "Explanation": "\"since the month begin with sunday , so there will be five sundays in the month required average = ( 510 * 5 + 240 * 25 ) / 30 = 8550 / 30 = 285 answer is c\"" + }, + { + "Answer": 60, + "Options": "a ) 75 , b ) 65 , c ) 85 , d ) 95 , e ) 60", + "Correct": "e", + "Explanation": "\"total increase in weight = 8 \u00d7 2.5 = 20 if x is the weight of the new person , total increase in weight = x \u2212 40 = > 20 = x - 40 = > x = 20 + 40 = 60 answer is e .\"" + }, + { + "Answer": 250, + "Options": "a ) 2378 , b ) 2697 , c ) 250 , d ) 5000 , e ) 6971", + "Correct": "c", + "Explanation": "explanation : we have , p = 2 q & s = 4 r further q = r & p + q + r + s = 1,000 thus we get , 2 q + q + q + 4 q = 1,000 8 q = 1,000 or q = rs . 125 thus , r = rs . 125 , p = 250 & s = rs . 500 hence , the required difference = ( s \u2013 p ) = ( 500 \u2013 250 ) = rs . 250 answer : c" + }, + { + "Answer": 48, + "Options": "a ) 22 , b ) 897 , c ) 268 , d ) 20 , e ) 48", + "Correct": "e", + "Explanation": "a + 10 = 2 ( b - 10 ) . . . . . . . . ( 1 ) a = b + 9 . . . . . . . . . ( 2 ) from equations . 1 & 2 we get b = 39 a will be 39 + 9 = 48 years old . answer : e" + }, + { + "Answer": 400, + "Options": "a ) rs 429 , b ) rs 412 , c ) rs 400 , d ) rs 129 , e ) rs 122", + "Correct": "c", + "Explanation": "\"let c = x . then b = x / 2 and a = x / 4 a : b : c = 1 : 2 : 4 . c ' s share rs . [ ( 4 / 7 ) * 700 ) = 400 answer : c\"" + }, + { + "Answer": 24, + "Options": "a ) a ) 32 , b ) b ) 24 , c ) c ) 39 , d ) d ) 40 , e ) e ) 45", + "Correct": "b", + "Explanation": "x \u2013 3 / 8 x = 15 x = 24 answer : b" + }, + { + "Answer": 752, + "Options": "a ) 654 , b ) 752 , c ) 656 , d ) 657 , e ) 658", + "Correct": "b", + "Explanation": "\"total cost 940 940 * 20 / 100 = 188 so the cut in amount is 188 the less amount to be spend is 940 - 188 = 752 answer : b\"" + }, + { + "Answer": 500, + "Options": "a ) 600 , b ) 500 , c ) 400 , d ) 300 , e ) none of these", + "Correct": "b", + "Explanation": "explanation : given that the student got 125 marks and still he failed by 40 marks = > the minimum pass mark = 125 + 40 = 165 given that minimum pass mark = 33 % of the total mark = > total mark \u00d7 ( 33 / 100 ) = 165 = > total mark = 16500 / 33 = 500 answer : option b" + }, + { + "Answer": 12.5, + "Options": "a ) 25.5 , b ) 2.5 , c ) 12.5 , d ) . 25 , e ) none of these", + "Correct": "c", + "Explanation": "\"explanation : 1 / 0.08 = ( 1 * 100 ) / 8 = 100 / 8 = 12.5 option c\"" + }, + { + "Answer": 5, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "d", + "Explanation": "when a certain number x is divided by 52 , the remainder is 19 . what is the remainder when x is divided by 7 ? putting a value say x = 19 we get remainder as 19 when divided by 52 . when 19 divided by 7 we get 5 as remainder . d is the answer ." + }, + { + "Answer": 1, + "Options": "a ) \u2013 1 , b ) 0 , c ) 1 , d ) 2 , e ) 3", + "Correct": "c", + "Explanation": "660660 = 2 ^ 2 x 3 ^ 1 x 5 ^ 1 x 11 ^ 1 w < x < y < z = 2 < 3 < 5 < 11 so , can can say - w = 2 x = 3 y = 5 z = 11 hence a = 2 , b = c = d = 1 ( a + b ) \u2013 ( c + d ) will be ( 2 + 1 ) \u2013 ( 1 + 1 ) = 1 answer will be ( c )" + }, + { + "Answer": 5, + "Options": "a ) 3 , b ) 2 , c ) 1 , d ) 5 , e ) 4", + "Correct": "d", + "Explanation": "| 14 - 5 | - | 8 - 12 | = | 9 | - | - 4 | = 9 - 4 = 5 correct answer d" + }, + { + "Answer": 15, + "Options": "a ) 11 , b ) 15 , c ) 77 , d ) 33 , e ) 88", + "Correct": "b", + "Explanation": "\"add the numbers of highlighters . 3 + 7 + 5 = 15 . answer is b .\"" + }, + { + "Answer": 900, + "Options": "a ) 450 , b ) 810 , c ) 900 , d ) 1000 , e ) 1100", + "Correct": "c", + "Explanation": "\"we want the sum of the digits from 0 to 99 , so i approximated : 0 - 9 - > 45 - > ( 9 + 0 ) * 10 / 2 40 - 49 - > 85 ( 13 + 4 ) * 10 / 2 90 - 99 - > 135 ( 18 + 9 ) * 10 / 2 we can see at a glance that theweightgoes up as the numbers go up ( meaning the difference between 85 and 45 is 40 , while 135 - 85 is 50 , this means that the second part of this sequence carries more weight for our result ) , so we know that the final answer has to be more than 850 ( 85 * 10 ) but close to it , and that ' s just w = 900 : the answer is c .\"" + }, + { + "Answer": 30, + "Options": "a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 45", + "Correct": "d", + "Explanation": "let joe scored point = x then tim scored = x + 20 ken scored = 2 * ( x + 20 ) = 2 x + 40 as given , x + x + 20 + 2 x + 40 = 100 points 4 x + 60 = 100 x = 100 - 60 / 4 = 10 so tim scored = x + 20 i . e ) 10 + 20 = 30 answer : d" + }, + { + "Answer": 25.4, + "Options": "a ) $ 2.40 , b ) $ 25.20 , c ) $ 25.40 , d ) $ 25.60 , e ) $ 25.50", + "Correct": "c", + "Explanation": "\"in 8 miles , initial 1 / 5 mile charge is $ 2 rest of the distance = 8 - ( 1 / 5 ) = 39 / 5 rest of the distance charge = 39 ( 0.6 ) = $ 23.4 ( as the charge is 0.6 for every 1 / 5 mile ) = > total charge for 4 miles = 2 + 23.4 = 25.4 answer is c\"" + }, + { + "Answer": 57600, + "Options": "a ) 57600 , b ) 44000 , c ) 34936 , d ) 25640 , e ) none", + "Correct": "a", + "Explanation": "\"answer \u2235 40 % of p = 23040 \u2234 p = ( 23040 x 100 ) / 40 = 57600 correct option : a\"" + }, + { + "Answer": 11, + "Options": "a ) 8 , b ) 12 , c ) 16 , d ) 24 , e ) 11", + "Correct": "e", + "Explanation": "i ' m going to focus on denominator only . . ( 2 ^ 22 ) . ( ( 3 ^ 4 ) ^ k = 18 ^ 22 ( 2 ^ 22 ) . ( ( 3 ^ 4 k ) = ( 2 . 3 ^ 2 ) ^ 22 ( 2 ^ 22 ) . ( ( 3 ^ 4 k ) = ( 2 ^ 24 ) . ( 3 ^ 2 ) ^ 22 hence 4 k = 44 k = 11 answer e i hope it ' s quite clear" + }, + { + "Answer": 1.0082644628099173, + "Options": "a ) 290 / 289 , b ) 122 / 121 , c ) 290 / 90 , d ) 290 / 19 , e ) none of these", + "Correct": "b", + "Explanation": "\"explanation : if the numbers are a , b , then ab = 17 , as 17 is a prime number , so a = 1 , b = 17 . 1 / a 2 + 1 / b 2 = 1 / 1 ( 2 ) + 1 / 11 ( 2 ) = 122 / 121 option b\"" + }, + { + "Answer": 21, + "Options": "a ) 18 , b ) 21 , c ) 24 , d ) 27 , e ) 28", + "Correct": "b", + "Explanation": "let x be the correct sums and ( 30 - x ) be the incorrect sums . 3 x - 2 ( 30 - x ) = 45 5 x = 105 x = 21 the answer is b ." + }, + { + "Answer": 31, + "Options": "a ) 18 , b ) 19 , c ) 20 , d ) 31 , e ) 22", + "Correct": "d", + "Explanation": "\"from right 21 , from left 11 total = 21 + 11 - 1 = 31 answer : d\"" + }, + { + "Answer": 66660, + "Options": "a ) 66660 , b ) 66760 , c ) 66860 , d ) 66960 , e ) 67660", + "Correct": "a", + "Explanation": "total no . formed = 4 ! = 4 * 3 * 2 * 1 = 24 each digit will be used at each positions , 6 times sum of digits at unit place = 6 * 1 + 6 * 2 + 6 * 3 + 6 * 4 = 6 * ( 1 + 2 + 3 + 4 ) = 60 this sum will be same for hundred , tens & unit places sum of all 4 digit numbers formed using digits 12 , 34 = 1000 * 60 + 100 * 60 + 10 * 60 + 60 = 60 * ( 1000 + 100 + 10 + 1 ) = 60 * 1111 = 66660 answer : a" + }, + { + "Answer": 960, + "Options": "a ) $ 900 , b ) $ 800 , c ) $ 960 , d ) $ 700 , e ) $ 1500", + "Correct": "c", + "Explanation": "\"if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 240 . so 1 / 4 of her savings is $ 240 . so her original savings are 4 times $ 240 = $ 960 correct answer c\"" + }, + { + "Answer": 2.7916666666666665, + "Options": "a ) $ 1.40 , b ) $ 1.58 , c ) $ 2.00 , d ) $ 2.64 , e ) $ 2.79", + "Correct": "e", + "Explanation": "3 * 2.25 + 4 * 1.50 + 4 * 1 = 6.75 + 6 + 4 = 16.75 . this is the sale for 6 tickets avg sale per ticket : 16.75 / 6 = $ 2 . 79 answer : e" + }, + { + "Answer": 108, + "Options": "a ) 120 , b ) 76 , c ) 108 , d ) 105 , e ) 86", + "Correct": "c", + "Explanation": "let the present ages of the father and son be 2 x and x years respectively . then , ( 2 x - 18 ) = 3 ( x - 18 ) x = 36 . required sum = ( 2 x + x ) = 3 x = 108 years . answer is c" + }, + { + "Answer": 0.375, + "Options": "a ) 0.125 , b ) 0.25 , c ) 0.375 , d ) 0.5 , e ) 0.666", + "Correct": "c", + "Explanation": "\"p = ncm * p ^ m * q ^ ( n - m ) n - the total number of trials . m - the number of trials with heads . n - m - the number of trials with tails . p - probability of heads . q - probability of tails . p = 3 c 2 * ( 1 / 2 ) ^ 2 * ( 1 / 2 ) ^ 1 = 3 / 8 = 0.375 answer : c\"" + }, + { + "Answer": 60, + "Options": "a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80", + "Correct": "c", + "Explanation": "\"total people at party = 160 women = 70 so men 160 - 70 = 90 no . of pple who tried appetizer = 160 - 50 ( given info ) = 110 no of women who tried appetizer = 50 so remaining ppl ( men ) who tried the appetizer = 110 - 50 = 60 correct option c\"" + }, + { + "Answer": 36, + "Options": "a ) 30 % , b ) 33 % , c ) 36 % , d ) 39 % , e ) 42 %", + "Correct": "c", + "Explanation": "\"the amount of chemical x in the solution is 20 + 0.2 ( 80 ) = 36 liters . 36 liters / 100 liters = 36 % the answer is c .\"" + }, + { + "Answer": 90, + "Options": "a ) 55 , b ) 65 , c ) 75 , d ) 85 , e ) 90", + "Correct": "e", + "Explanation": "let the marks obtained by the student in physics , chemistry and mathematics be p , c and m respectively . p + c + m = 180 + p c + m = 180 average mark obtained by the student in chemistry and mathematics = ( c + m ) / 2 = 180 / 2 = 90 . answer : e" + }, + { + "Answer": 25, + "Options": "a ) 28 , b ) 18 , c ) 27 , d ) 25 , e ) 21", + "Correct": "d", + "Explanation": "\"average price per book = ( 581 + 594 ) / ( 27 + 20 ) = 1175 / 47 = rs . 25 answer : d\"" + }, + { + "Answer": 1012, + "Options": "a ) 1008 , b ) 1012 , c ) 1022 , d ) 1032 , e ) 1043", + "Correct": "b", + "Explanation": "\"required number = ( l . c . m of 12 , 16 , 18 , 21,28 ) + 4 = 1008 + 4 = 1012 answer : b\"" + }, + { + "Answer": 251, + "Options": "a ) 200 , b ) 251 , c ) 250 , d ) 262 , e ) 254", + "Correct": "b", + "Explanation": "\"diver = ( 8 * 3 ) + 3 = 27 3 * quotient = 27 quotient = 9 dividend = ( divisor * quotient ) + remainder dividend = ( 27 * 9 ) + 8 = 251 b\"" + }, + { + "Answer": 378, + "Options": "a ) 358 , b ) 348 , c ) 368 , d ) 388 , e ) 378", + "Correct": "e", + "Explanation": "x = - 5 and y = 8 x - y = - 5 - 8 = - 13 x * y = - 5 * 8 = - 40 now we apply it in the equation 2 ( x - y ) ^ 2 - xy = 2 ( - 13 ) ^ 2 - ( - 40 ) = = > 2 * 169 + 40 = 338 + 40 = 378 answer : e" + }, + { + "Answer": 0.75, + "Options": "a ) 1 / 2 , b ) 1 , c ) 3 / 4 , d ) 2 , e ) 5 / 2", + "Correct": "c", + "Explanation": "b = 4 k + 1 . . . ( 1 ) b + 1 = ak + 1 . . . ( 2 ) 5 = ak + 1 . . . ( 3 ) taking ( 2 ) and ( 3 ) 5 = b + 1 b = 4 taking ( 1 ) 4 = 4 k + 1 k = 3 / 4 answer : c" + }, + { + "Answer": 500, + "Options": "a ) $ 200 , b ) $ 400 , c ) $ 500 , d ) $ 800 , e ) $ 1,200", + "Correct": "c", + "Explanation": "\"suppose total money spent = x not spend ( money he still has ) = x - 500 x + x - 500 = 1500 x = 1000 money not spend = 1000 - 500 = 500 answer : c\"" + }, + { + "Answer": 40.000000000000014, + "Options": "a ) 30 , b ) 35 , c ) 40 , d ) 45 , e ) 50", + "Correct": "c", + "Explanation": "\"let the number be x . ( 5 / 4 ) * x = ( 4 / 5 ) * x + 18 25 x = 16 x + 360 9 x = 360 x = 40 the answer is c .\"" + }, + { + "Answer": 13, + "Options": "a ) 12 , b ) 13 , c ) 10 , d ) 18 , e ) 13", + "Correct": "b", + "Explanation": "\"2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 35 - 9 = 26 ab = 13 . answer is b .\"" + }, + { + "Answer": 640, + "Options": "a ) 600 , b ) 640 , c ) 500 , d ) 520 , e ) 720", + "Correct": "b", + "Explanation": "\"let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 320 ) = 2 + 2 ( extra ) = > 2 x - 640 = x = > x = 640 . answer : b\"" + }, + { + "Answer": 5865863355, + "Options": "a ) 5865863355 , b ) 5665863355 , c ) 4865863355 , d ) 4665863355 , e ) none of these", + "Correct": "a", + "Explanation": "explanation : although it is a simple question , but the trick is to save time in solving this . rather than multiplying it we can do as follows : 586645 * ( 10000 - 1 ) = 5866450000 - 586645 = 5865863355 option a" + }, + { + "Answer": 23.076923076923073, + "Options": "a ) 25 % , b ) 23 % , c ) 16.67 % , d ) 33.33 % , e ) none of these", + "Correct": "b", + "Explanation": "\"explanation : let us assume before increase the petrol will be rs . 100 . after increase it will be rs ( 100 + 30 ) i . e 130 . now , his consumption should be reduced to : - = ( 130 \u2212 100 ) / 130 \u2217 100 . hence , the consumption should be reduced to 23 % . answer : b\"" + }, + { + "Answer": 230, + "Options": "a ) 115 , b ) 230 , c ) 460 , d ) 575 , e ) 690", + "Correct": "b", + "Explanation": "the lcm of n and e is 690 = 2 * 3 * 5 * 23 . e is not divisible by 2 , thus 2 goes to n n is not divisible by 3 , thus 3 goes to e . from above : n must be divisible by 2 and not divisible by 3 : n = 2 * . . . in order n to be a 3 - digit number it must take all other primes too : n = 2 * 5 * 23 = 230 . answer : b ." + }, + { + "Answer": 20, + "Options": "a ) 8 , b ) 20 , c ) 10 , d ) 11 , e ) 12", + "Correct": "b", + "Explanation": "\"let x be the number . always replace ` ` is ' ' with an equal sign ( 1 / 2 ) x + 5 = 15 ( 1 / 2 ) x = 15 - 5 ( 1 / 2 ) x = 10 x = 20 correct answer is b\"" + }, + { + "Answer": 25, + "Options": "a ) 50 % , b ) 125 % , c ) 25 % , d ) none of above , e ) 30 %", + "Correct": "c", + "Explanation": "\"explanation : actually it means 5 is what percent of 20 , which can be calculated as , ( 5 / 20 ) * 100 = 5 * 5 = 25 option c\"" + }, + { + "Answer": 20, + "Options": "a ) $ 4 , b ) $ 14 , c ) $ 5 , d ) $ 15 , e ) $ 20", + "Correct": "e", + "Explanation": "\"1 / 5 x $ 150 = $ 30 for sandwich 1 / 6 x $ 150 = $ 25 for museum 1 / 2 x $ 150 = $ 75 for book $ 30 + $ 25 + $ 75 = $ 130 spent $ 150 - $ 130 = $ 20 left over correct answer e\"" + }, + { + "Answer": 23, + "Options": "a ) 28 , b ) 27 , c ) 23 , d ) 22 , e ) 24", + "Correct": "c", + "Explanation": "\"explanation : let the average score of the first 18 innings be n 18 n + 95 = 19 ( n + 4 ) = > n = 19 so , average score after 19 th innings = x + 4 = 23 . answer : c\"" + }, + { + "Answer": 10, + "Options": "a ) 20 , b ) 18 , c ) 11 , d ) 10 , e ) 5", + "Correct": "d", + "Explanation": "add these two equations 6 x + 4 y = 20 divide by 2 ( to get 3 x + 2 y ) answer will be d . 10" + }, + { + "Answer": 1.2, + "Options": "a ) 1.12 , b ) 1.2 , c ) 1.25 , d ) 1.3 , e ) none", + "Correct": "b", + "Explanation": "\"( x * 5 ) = ( 0.75 * 8 ) x = 6 / 5 x = 1.20 answer = b\"" + }, + { + "Answer": 42.857142857142854, + "Options": "a ) 2.5 % , b ) 10 % , c ) 5 % , d ) 15 % , e ) 43 %", + "Correct": "e", + "Explanation": "\"50 % of ( x - y ) = 20 % of ( x + y ) ( 50 / 100 ) ( x - y ) = ( 20 / 100 ) ( x + y ) 5 ( x - y ) = 2 ( x + y ) 3 x = 7 y x = 7 / 3 y therefore required percentage = ( ( y / x ) x 100 ) % = ( ( y / ( 7 / 3 ) y ) x 100 ) = 43 % answer is e .\"" + }, + { + "Answer": 11, + "Options": "a ) 11 , b ) 12 , c ) 15 , d ) 18 , e ) 16", + "Correct": "a", + "Explanation": "25 + 10 n = 125 n = 10 total time = n + 1 hrs = 10 + 1 hrs = 11 hrs answer : a" + }, + { + "Answer": 61.80339887498949, + "Options": "a ) 62 % , b ) 73 % , c ) 41 % , d ) 71 % , e ) none of these", + "Correct": "a", + "Explanation": "explanation : according to the question : - = > b / a = a / ( a + b ) . as b is a percent of a , let us assume b = ax . then , equation ( 1 ) can be re - written as = > x = 11 + x . = > x ( 1 + x ) = 1 . = > x 2 + x + 1 = 0 . = > x = \u2212 1 \u00b1 5 / \u221a 2 thus , x = \u2212 1 + 5 / \u221a 2 = > 0.62 . = > 62 % . answer : a" + }, + { + "Answer": 780, + "Options": "a ) 237 , b ) 780 , c ) 197 , d ) 287 , e ) 720", + "Correct": "b", + "Explanation": "\"explanation : let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 390 ) = 2 + 2 ( extra ) = > 2 x - 780 = x = > x = 780 . answer : b\"" + }, + { + "Answer": 35, + "Options": "a ) 25 % , b ) 35 % , c ) 45 % , d ) 70 % , e ) 80 %", + "Correct": "b", + "Explanation": "\"1 . we are given the following percentages : 30 ( 70 ) , 40 ( 60 ) , 25 ( 75 ) . there are two threads from here . first starts at 30 % and finishes there . second one starts at 70 , then 40 , and then 25 . we need a value that is divisible by 7 , 2 , and 5 at least once . lets pick a number now , say 700 . so say if non hawks are 700 ( this is 70 % of the total , so total = 1000 ) , then paddy warbs are 2 / 5 x 700 = 1400 / 5 = 280 . kingfishers , therefore , are 280 / 4 = 70 . lets add them up . 300 hawks + 280 peddy warbs + 70 kingsifhers = 650 . so all others are 1000 - 650 = 350 or 35 % of total birds . the main job here to to identify the smart number to start the question with . this can be time consuming , but once identified , this question can be solved fairly quickly . 2 . another method : if x is total - - > non hawks = 0.7 x - - > warbs = 0.4 ( 0.7 x ) - - > kfs = 0.25 ( 0.4 ( 0.7 x ) ) . our job is to find out b : ( 0.3 x + 0.28 x + 0.07 x ) / x . or 0.65 x / x = 0.65 . we need to find 1 - 0.65 = 0.35 or 35 % . b\"" + }, + { + "Answer": 12, + "Options": "a ) 22 , b ) 18 , c ) 12 , d ) 88 , e ) 66", + "Correct": "c", + "Explanation": "\"initial average age of the 10 persons be p . age of the new person q . sum of the ages of the initial 10 persons = 10 p new average = ( p - 3 ) 10 ( p - 3 ) = 10 p - 42 + q = > q = 12 answer : c\"" + }, + { + "Answer": 160, + "Options": "a ) 160 , b ) 161 , c ) 162 , d ) 163 , e ) 164", + "Correct": "a", + "Explanation": "\"to minimize one quantity maximize other . 159 * 2 ( max possible amount of food a guest could consume ) = 318 pounds , so there must be more than 159 guests , next integer is 160 . answer : a .\"" + }, + { + "Answer": 98.56, + "Options": "a ) 98.5 , b ) 08.56 , c ) 98.56 , d ) 98.86 , e ) 98.46", + "Correct": "c", + "Explanation": "explanation : difference in c . i and s . i in 2 years = rs . 32 s . i for 1 year = rs . 400 s . i for rs . 400 for one year = rs . 32 rate = [ 100 * 32 ) / ( 400 * 1 ) % = 8 % difference between in c . i and s . i for 3 rd year = s . i on rs . 832 = rs . ( 832 * 8 * 1 ) / 100 = rs . 66.56 answer : c ) rs . 98.56" + }, + { + "Answer": 22, + "Options": "a ) 16 , b ) 12 , c ) 18 , d ) 22 , e ) 08", + "Correct": "d", + "Explanation": "2 * 11 = 22 . answer is d ." + }, + { + "Answer": 61376, + "Options": "a ) 61376 , b ) 54411 , c ) 612314 , d ) 64170 , e ) 64171", + "Correct": "a", + "Explanation": "\"the three digit natural numbers divisible by 8 are 104 , 112 , 120 , \u2026 . 992 . let sndenote their sum . that is , sn = 104 112 120 128 , 992 g + + + + + . now , the sequence 104 , 112 , 120 , g , 992 forms an a . p . a = 104 , d = 8 , l = 992 n = l - a / d n = 112 s 112 = n / 2 ( a + l ) = 61376 answer a 61376\"" + }, + { + "Answer": 5000, + "Options": "a ) 13000 , b ) 7000 , c ) 10000 , d ) 5000 , e ) none of these", + "Correct": "d", + "Explanation": "explanation : profit = 5 , 00,000 \u00e2 \u02c6 \u2019 ( 1 , 50,000 + 75,000 ) = rs . 2 , 75,000 . since , such loom contributes equally to sales and manufacturing expenses . but the monthly charges are fixed at rs 75,000 . if one loan breaks down sales and expenses will decrease . new profit : - = > 500000 \u00e3 \u2014 ( 69 / 70 ) \u00e2 \u02c6 \u2019 150000 \u00e3 \u2014 ( 69 / 70 ) \u00e2 \u02c6 \u2019 75000 . = > rs 2 , 70,000 . decrease in profit = > 2 , 75,000 \u00e2 \u02c6 \u2019 2 , 70,000 = > rs . 5,000 . answer : d" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 9 , e ) 27", + "Correct": "a", + "Explanation": "since f ( abc ) = 3 * f ( def ) , i would assume that f = c - 1 from the function above . the answer should be ( a )" + }, + { + "Answer": 220070, + "Options": "a ) 145646 , b ) 236578 , c ) 645353 , d ) 456546 , e ) 220070", + "Correct": "e", + "Explanation": "\"( 555 + 445 ) * 2 * 110 + 70 = 220000 + 70 = 220070 e\"" + }, + { + "Answer": 1260, + "Options": "a ) $ 880 , b ) $ 990 , c ) $ 1,000 , d ) $ 1,100 , e ) $ 1,260", + "Correct": "e", + "Explanation": "\"10 / 100 p = 140 > > p = 140 * 100 / 10 = 1400 1400 - 140 = 1260 answer : e\"" + }, + { + "Answer": 8, + "Options": "a ) - $ 56 , b ) - $ 6 , c ) $ 0 , d ) $ 6 , e ) $ 8", + "Correct": "e", + "Explanation": "a professional janitor can clean a certain high school in ( 4 + 4 ) or 8 hours so ( applying rule # 1 ) , the janitor can clean 1 / 8 of the school in one hour a student sentenced to detention can clean that same high school in 20 hours so ( applying rule # 1 ) , the student can clean 1 / 20 of the school in one hour so , combined , the student and janitor can clean ( 1 / 8 + 1 / 20 ) of the school in one hour 1 / 8 + 1 / 20 = 5 / 40 + 2 / 40 = 7 / 40 so , in one hour they can clean 7 / 40 of the school . applying rule # 2 , it will takethem 40 / 7 hoursto clean the entire school . the janitor earns $ 21 / hour and the student earns $ 7 / hour , so their combined rate is $ 28 / hour . theircombined wages = ( pay rate ) ( time ) = ( $ 28 / hour ) ( 40 / 7 hours ) = $ 160 working alone , the janitor takes 8 hours and earns $ 21 / hour so , working alone , the janitor ' s earnings = ( pay rate ) ( time ) = ( $ 21 / hour ) ( 8 hours ) = $ 168 $ 168 - $ 160 = $ 8 , so the answer is e" + }, + { + "Answer": 856, + "Options": "a ) 427 , b ) 859 , c ) 869 , d ) 856 , e ) none of these", + "Correct": "d", + "Explanation": "\"solution required number = ( l . c . m . of 24 , 32 , 36 , 54 ) - 8 = 864 - 8 = 856 . answer d\"" + }, + { + "Answer": 6, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "d", + "Explanation": "\"the number of members is 7 k + 4 = 6 j + 4 the only number in this range which satisfies this is 46 . 46 / 8 = 5 ( 8 ) + 6 the answer is d .\"" + }, + { + "Answer": 20, + "Options": "a ) 11 , b ) 17 , c ) 13 , d ) 20 , e ) none of these", + "Correct": "d", + "Explanation": "\"let that divisor be x since remainder is 11 or 18 it means divisor is greater than 18 . now 242 - 11 = 231 = kx ( k is an integer and 234 is divisble by x ) similarly 698 - 18 = 680 = lx ( l is an integer and 689 is divisible by x ) adding both 698 and 242 = ( 231 + 680 ) + 11 + 18 = x ( k + l ) + 29 when we divide this number by x then remainder will be equal to remainder of ( 29 divided by x ) = 9 hence x = 29 - 9 = 20 hence d\"" + }, + { + "Answer": 0.1, + "Options": "a ) $ 4 , b ) $ 0.1 , c ) $ 1 , d ) $ 3 , e ) $ 1.65", + "Correct": "b", + "Explanation": "\"lets assume price of coffee in june = 100 x price of green tea in june = 100 x price of coffee in july = 200 x ( because of 100 % increase in price ) price of green tea in july = 10 x ( because of 90 % decrease in price ) price of 1.5 pound of coffee 1.5 pound of green tea in july will be = 300 x + 15 x = 315 x as per question 315 x = 3.15 $ x = 0.01 s so the price of green tea in july = 10 x = 10 x 0.01 = 0.1 $ / pound answer b\"" + }, + { + "Answer": 25, + "Options": "a ) 9 % , b ) 11 % , c ) 15 % , d ) 25 % , e ) 90 %", + "Correct": "d", + "Explanation": "\"cost of 12 paper towels individually = 1 * 12 = 12 cost of a set of 12 paper towels = 9 cost of one roll = 9 / 12 = 3 / 4 = 0.75 savings per roll = 1 - . 75 = 0.25 % of savings is e = . 25 / 1 * 100 = 25 % d is the answer .\"" + }, + { + "Answer": 9, + "Options": "a ) 12 , b ) 9 , c ) 3 , d ) 7.5 , e ) 2.5", + "Correct": "b", + "Explanation": "\"we have 2 equations 1 . 3 ( 3 x + 4 y ) = 36 - - > 3 x + 4 y = 12 - - > 9 x + 12 y = 36 2 . kx + 12 y = 30 substract 1 - 2 , we get ( 9 - k ) x = 6 i . e . x = 6 / ( 9 - k ) then , by looking at options , we get some value of x except for b . when we put k = 9 , x becomes 6 / 0 and hence answer is b\"" + }, + { + "Answer": 2, + "Options": "a ) 5 , b ) 3 , c ) 4 , d ) 2 , e ) 6", + "Correct": "d", + "Explanation": "\"t = the number of cups of tea c = the number of cups of hot chocolate t + c = 36 t - c = 14 - > t = 25 . c = 11 . mo drinks 5 cups of tea a day then number of days that are not rainy = 25 / 5 = 5 so number of rainy days = 7 - 5 = 2 d is the answer .\"" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "c", + "Explanation": "\"let x be the wholesale price . then 1.8 x = 27 and x = 27 / 1.8 = 15 . to achieve a 100 % markup , the price needs to be $ 30 . the retailer needs to increase the price by $ 3 more . the answer is c .\"" + }, + { + "Answer": 54, + "Options": "a ) 71 , b ) 44 , c ) 54 , d ) 16 , e ) 18", + "Correct": "c", + "Explanation": "explanation : required sum = ( 66 - 3 x 4 ) years = ( 66 - 12 ) years = 54 years . answer : c" + }, + { + "Answer": 0.6, + "Options": "a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 5", + "Correct": "e", + "Explanation": "\"let p be the number of progressives in the country as a whole . in each province , the number of traditionalists is p / 12 the total number of traditionalists is 8 p / 12 = 2 p / 3 . the total population is p + 2 p / 3 = 5 p / 3 p / ( 5 p / 3 ) = 3 / 5 the answer is e .\"" + }, + { + "Answer": 6, + "Options": "a ) rs . 6 , b ) rs . 6.5 , c ) rs . 8 , d ) rs . 5 , e ) rs . 2", + "Correct": "a", + "Explanation": "\"answer : option a 5 m = xw = 8 b 5 m + xw + 8 b - - - - - 90 rs . 5 m + 5 m + 5 m - - - - - 90 rs . 15 m - - - - - - 90 rs . = > 1 m = 6 rs .\"" + }, + { + "Answer": 4, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) none , e ) 6", + "Correct": "b", + "Explanation": "\"solution ( 2 \u00d7 1 + 1 ) = 3 . ( 2 \u00d7 2 + 1 ) = 5 . ( 2 \u00d7 3 + 1 ) = 7 . ( 2 \u00d7 4 + 1 ) = 9 . which is not prime , n = 4 . answer b\"" + }, + { + "Answer": 3999.248141349427, + "Options": "a ) 4000 , b ) 8877 , c ) 2877 , d ) 2678 , e ) 1011", + "Correct": "a", + "Explanation": "\"7000 - - - - 2261 100 - - - - ? = > 32.3 % x * 1323 / 100 * 1323 / 100 = 7000 x * 1.75 = 7000 x = 7000 / 1.75 = > 3999.25 answer : a\"" + }, + { + "Answer": 265, + "Options": "a ) $ 245 , b ) $ 255 , c ) $ 265 , d ) $ 275 , e ) $ 285", + "Correct": "c", + "Explanation": "\"1.2 n + n = 583 2.2 n = 583 n = 265 the answer is c .\"" + }, + { + "Answer": 4, + "Options": "a ) 2 , b ) 4 , c ) 6 , d ) 14 , e ) 16", + "Correct": "b", + "Explanation": "\"we know dividend = divisor * quotient + remainder = = = > 217 = divisor * 54 + 1 = = = = = > 216 / 54 = divisor = = = > divisor = 4 ans - b\"" + }, + { + "Answer": 7, + "Options": "a ) 1 , b ) 5 , c ) 7 , d ) 9 , e ) 13", + "Correct": "c", + "Explanation": "on dividing 1387 by 15 we get the remainder 7 , so 7 should be subtracted . the answer is c ." + }, + { + "Answer": 4, + "Options": "a ) 1 , b ) 2 , c ) 4 , d ) 7 , e ) 9", + "Correct": "c", + "Explanation": "2 / 9 = 0.22222 . . . . = = > 99 th digit is 2 3 / 11 = 0.27272727 . . . . = = > every odd digit is 2 . so , 99 th digit will be 2 . 2 + 2 = 4 answer : c" + }, + { + "Answer": 50, + "Options": "a ) 17 , b ) 25 , c ) 27 , d ) 35 , e ) 50", + "Correct": "e", + "Explanation": "let the present ages of aman , bren , and charlie be 5 x , 8 x and 7 x respectively . 5 x - 8 + 8 x - 8 + 7 x - 8 = 76 x = 5 present age of bren = 8 * 5 = 40 bren ' s age 10 years hence = 40 + 10 = 50 answer = e" + }, + { + "Answer": 0.5384615384615384, + "Options": "a ) 1 / 2 , b ) 7 / 13 , c ) 4 / 13 , d ) 8 / 29 , e ) 6 / 33", + "Correct": "b", + "Explanation": "now ultimately the speed of every machine is given with respect to mach o . so lets assume the speed of o , say 12 hrs to make x units ( assuming 6 because we can see we will need to divide by 3 and 4 mach o makes x units in 12 hrs so , mach n = 2 / 7 of o = 2 / 7 * 12 = 24 / 7 hrs to make x units and mach m = 3 / 4 of n = 3 / 4 * 24 / 7 = 1 / 6 hrs to make x units no they are running simultaneously . lets see how much each mach makes in 1 hr mach o = x / 12 units mach n = 7 / 24 units mach m = x / 6 units in 1 hr , together they make - x / 12 + 7 / 24 + x / 6 = 13 / 24 so what ratio of this has mach n made ? ( 7 / 24 ) / ( 13 / 24 ) = 7 / 13 ans : b = 7 / 13" + }, + { + "Answer": 16, + "Options": "a ) 21 years , b ) 22 years , c ) 23 years , d ) 12 years , e ) 16 years", + "Correct": "e", + "Explanation": "\"explanation : let ' s son age is x , then father age is x + 18 . = > 2 ( x + 2 ) = ( x + 18 + 2 ) = > 2 x + 4 = x + 20 = > x = 16 years option e\"" + }, + { + "Answer": 989.9999999999999, + "Options": "a ) 950 , b ) 940 , c ) 980 , d ) 960 , e ) 990", + "Correct": "e", + "Explanation": "\"( 0.0088 ) ( 4.5 ) / ( 0.05 ) ( 0.1 ) ( 0.008 ) = 0.0088 * 450 / 5 * ( 0.1 ) ( 0.008 ) = 0.088 * 90 / 1 * 0.008 = 88 * 90 / 8 = 11 * 90 = 990 answer : e\"" + }, + { + "Answer": 32, + "Options": "a ) 32 , b ) 43 , c ) 44 , d ) 45 , e ) 46", + "Correct": "a", + "Explanation": "\"let \u2018 x \u2019 be the average score after 12 th innings \u21d2 12 x = 11 \u00d7 ( x \u2013 3 ) + 65 \u2234 x = 32 answer a\"" + }, + { + "Answer": 14, + "Options": "a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 17", + "Correct": "c", + "Explanation": "\"explanation : let the number be x . then , 15 x = x + 196 = \u203a 14 x = 196 = \u203a x = 14 . answer : option c\"" + }, + { + "Answer": 300, + "Options": "a ) 250 / 3 , b ) 500 / 3 , c ) 300 , d ) 480 , e ) 600", + "Correct": "c", + "Explanation": "\"we know that x is 10 % , y is 30 % and w . avg = 25 % . what does this mean with respect to w . avg technique ? w . avg is 1 portion away from y and 3 portion away from x so for every 1 portion of x we will have to add 3 portions of y . if x = 100 then y = 300 answer : c\"" + }, + { + "Answer": 40.92, + "Options": "a ) $ 7.15 , b ) $ 8.87 , c ) $ 28.96 , d ) $ 35.57 , e ) $ 40.92", + "Correct": "e", + "Explanation": "operating system overhead for 1 run = 1.07 $ mounting of data tape = 5.35 $ cost per 1 millisecond of computer time = . 023 $ total cost of 1 run of a program that requires 1.5 seconds of computer time = 1.07 + ( . 023 * 1500 ) + 5.35 = 1.07 + 34.5 + 5.35 = 40.92 $ answer e" + }, + { + "Answer": 4, + "Options": "a ) 2 , b ) 4 , c ) 0 , d ) 10 , e ) 3", + "Correct": "b", + "Explanation": "4 x + y = 34 2 x - y = 20 6 x = 54 x = 9 y = - 2 y ^ 2 = 4 answer is b" + }, + { + "Answer": 1.875, + "Options": "a ) 15 / 8 , b ) 14 / 3 , c ) 41 / 7 , d ) 3 / 18 , e ) 18 / 4", + "Correct": "a", + "Explanation": "say a = 2 . then : a / b = 5 / 2 - - > b = 2 / 5 ; b / c = 1 / 2 - - > c = 4 / 5 ; c / d = 1 - - > d = 4 / 5 ; d / e = 3 / 2 - - > e = 8 / 15 ; e / f = 4 / 3 - - > f = 2 / 5 . abc / def = ( 1 * 2 / 5 * 4 / 5 ) / ( 4 / 5 * 8 / 15 * 2 / 5 ) = 15 / 8 . answer : a ." + }, + { + "Answer": 102, + "Options": "a ) 102 % , b ) 105 % , c ) 120 % , d ) 135 % , e ) 140 %", + "Correct": "a", + "Explanation": "\"assume that price is 100 price at the end of yr 1 : 100 + 20 = 120 price at the end of year 2 = 120 - 120 * 0.15 = 120 * 0.85 = 102 hence required answer = ( 102 / 100 ) * 100 % = 102 % answer is a .\"" + }, + { + "Answer": 1, + "Options": "a ) 30 , b ) 18 , c ) 10 , d ) 9 , e ) 1", + "Correct": "e", + "Explanation": "\"( average production for n days ) * n = ( total production for n days ) - - > 50 n = ( total production for n days ) ; ( total production for n days ) + 60 = ( average production for n + 1 days ) * ( n + 1 ) - - > 50 n + 60 = 55 * ( n + 1 ) - - > n = 1 . answer : e .\"" + }, + { + "Answer": 33, + "Options": "a ) 24 , b ) 77 , c ) 297 , d ) 267 , e ) 29", + "Correct": "a", + "Explanation": "answer : a" + }, + { + "Answer": 4, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9", + "Correct": "a", + "Explanation": "solution n = h . c . f . of ( 4665 - 1305 ) , ( 6905 - 4665 ) and ( 6905 - 1305 ) = h . c . f . of 3360 , 2240 and 5600 = 1120 . sum of digits in n = ( 1 + 1 + 2 + 0 ) = 4 . answer a" + }, + { + "Answer": 4900, + "Options": "a ) 4500 , b ) 4600 , c ) 4300 , d ) 4900 , e ) 5000", + "Correct": "d", + "Explanation": "sum of first n even numbers = n ( n + 1 ) = 4970 sum of first n odd numbers = n ^ 2 = 70 * 70 = 4900 ( here n = 70 ) answer : d" + }, + { + "Answer": 32, + "Options": "a ) 31 , b ) 32 , c ) 33 , d ) 34 , e ) 35", + "Correct": "b", + "Explanation": "total age of the grandparents = 64 \u00e3 \u2014 2 = 128 total age of the parents = 39 \u00e3 \u2014 2 = 78 total age of the grandchildren = 6 \u00e3 \u2014 3 = 18 average age of the family = ( 128 + 78 + 18 ) / 7 = 224 / 7 = 32 years the answer is b ." + }, + { + "Answer": 3, + "Options": "a ) 5 , b ) 7 , c ) 9 , d ) 3 , e ) 12", + "Correct": "d", + "Explanation": "\"49 / 11 = 4 and 79 / 11 = 7 = = > 7 - 4 = 3 numbers answer : d\"" + }, + { + "Answer": 4.8, + "Options": "a ) 2.9 min , b ) 3.9 min , c ) 4.2 min , d ) 4.8 min , e ) 5.6 min", + "Correct": "d", + "Explanation": "clearly , the two will meet when they are 640 m apart . to be ( 4.2 + 3.8 ) = 8.0 km apart , they take 1 hour . that is 60 min . to be 640 m apart , they take ( 640 / 8000 * 60 ) min = 4.8 min . answer : d" + }, + { + "Answer": 13, + "Options": "a ) 15 , b ) 19 , c ) 11 , d ) 18 , e ) 13", + "Correct": "e", + "Explanation": "let the population of two villages be equal after p years then , 68000 - 1200 p = 42000 + 800 p 2000 p = 26000 p = 13 answer is e ." + }, + { + "Answer": 2, + "Options": "a ) 10 , b ) 2 , c ) 12 , d ) 14 , e ) 15", + "Correct": "b", + "Explanation": "- > x ^ 4 + ( 1 / x ^ 4 ) = ( x ^ 2 ) ^ 2 + ( 1 / x ^ 2 ) ^ 2 = ( x ^ 2 + 1 / x ^ 2 ) ^ 2 - 2 x ^ 2 ( 1 / x ^ 2 ) = 2 ^ 2 - 2 = 2 . thus , the answer is b ." + }, + { + "Answer": 9, + "Options": "a ) 10 , b ) 9 , c ) 8 , d ) 5 , e ) 12", + "Correct": "b", + "Explanation": "the lattice points that are in the square , that lie on the x and y axes , are ( 0 , 0 ) , ( 0 , 1 ) , ( 1 , 0 ) , ( 0 , - 1 ) , and ( - 1 , 0 ) . the lattice points in the square and not on the x and y axes are ( 1 , 1 ) , ( - 1 , 1 ) , ( 1 , - 1 ) , and ( - 1 , - 1 ) . there are a total of 9 lattice points in the square . answer : b" + }, + { + "Answer": 89.99999999999999, + "Options": "a ) 124 % , b ) 120 % , c ) 96 % , d ) 90 % , e ) 64 %", + "Correct": "d", + "Explanation": "\"juan ' s income = 100 ( assume ) ; tim ' s income = 60 ( 40 percent less than juan ' s income ) ; mary ' s income = 90 ( 50 percent more than tim ' s income ) . thus , mary ' s income ( 90 ) is 90 % of juan ' s income ( 100 ) . answer : d .\"" + }, + { + "Answer": 138, + "Options": "a ) 130 , b ) 132 , c ) 134 , d ) 136 , e ) 138", + "Correct": "e", + "Explanation": "\"let the required number be x . then , 43 x \u2013 34 x = 1242 or 9 x = 1242 or x = 138 . required number = 138 . answer : e\"" + }, + { + "Answer": 302.9802941364969, + "Options": "a ) 306.09 , b ) 306.07 , c ) 306.04 , d ) 306.03 , e ) 306.01", + "Correct": "c", + "Explanation": "\"a = 5000 ( 51 / 50 ) 3 = 5306.04 5000 - - - - - - - - - - - 306.04 answer : c\"" + }, + { + "Answer": 26, + "Options": "a ) 25 liters , b ) 27 liters , c ) 26 liters , d ) 32 liters , e ) 35 liters", + "Correct": "c", + "Explanation": "\"let x ltr water to be added 2 ltr alcohol to be represented as ( 20 ( 1 - 3 / 4 ( new soln . = 14 + x ) ) ) 2 = 5 % * ( 14 + x ) - - - - - - - - > x = 26 ans c\"" + }, + { + "Answer": 30, + "Options": "a ) 15 , b ) 25 , c ) 30 , d ) 45 , e ) 55", + "Correct": "c", + "Explanation": "\"let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 92 ( x - 5 ) 80 x - ( 5 * 20 ) = 92 ( x - 5 ) 360 = 12 x = > x = 30 answer : c\"" + }, + { + "Answer": 46, + "Options": "a ) 46 kg , b ) 48 kg , c ) 70 kg , d ) 72 kg , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : let the weight of student be x kg . given , difference in average weight = 5 kg = > ( 86 - x ) / 8 = 5 = > x = 46 answer : a\"" + }, + { + "Answer": 28800, + "Options": "a ) 28800 , b ) 24000 , c ) 24936 , d ) 25640 , e ) none", + "Correct": "a", + "Explanation": "\"answer \u2235 80 % of p = 23040 \u2234 p = ( 23040 x 100 ) / 80 = 28800 correct option : a\"" + }, + { + "Answer": 200, + "Options": "a ) 100 , b ) 150 , c ) 200 , d ) 250 , e ) 300", + "Correct": "c", + "Explanation": "\"18 % is 8 % - points higher than 10 % but 12 % - points lower than 30 % . thus there should be 3 parts of solution x for 2 parts of solution y . we should add 200 ml of solution y . the answer is c .\"" + }, + { + "Answer": 1, + "Options": "a ) 4 , b ) can not be determined , c ) 2 , d ) 6 , e ) 1", + "Correct": "e", + "Explanation": "take square of any prime number remainder will be 1 ans e" + }, + { + "Answer": 0.23255813953488372, + "Options": "a ) 0.23255 , b ) 0.14544 , c ) 0.25632 , d ) 0.35466 , e ) 0.63435", + "Correct": "a", + "Explanation": "total land of sukhiya = \\ inline \\ frac { 480 x } { 0.6 } = 800 x \\ therefore cultivated land of village = 344000 x \\ therefore required percentage = \\ inline \\ frac { 800 x } { 344000 } \\ times 100 = 0.23255 a" + }, + { + "Answer": 2, + "Options": "a ) 2 , b ) 33 , c ) 38 , d ) 35 , e ) 14", + "Correct": "a", + "Explanation": "formula : ( constant ) / ( lcm of two nos ) = 100 / ( 5 * 10 ) = 2 answer : a" + }, + { + "Answer": 170, + "Options": "a ) 200 , b ) 230 , c ) 140 , d ) 170 , e ) none of these", + "Correct": "d", + "Explanation": "explanation : f ( 2 x + 3 ) = ( x - 3 ) ( x + 4 ) put x = 13 f ( 2 * 13 + 3 ) = ( 13 - 3 ) * ( 13 + 4 ) = 10 * 17 f ( 29 ) = 170 answer : d" + }, + { + "Answer": 7, + "Options": "a ) 5 , b ) 7 , c ) 9 , d ) 10 , e ) 12", + "Correct": "b", + "Explanation": "in aptitude tests , we get questions on divisibility by 11 . a number is divisible by 11 , when the difference between the sum of digits at even places and at odd places is 0 or multiple of 11 the given number is n 183 . ( sum of digits at even places ) \u2013 ( sum of digits at odd places ) = 0 ( 8 + n ) - ( 3 + 1 ) = 0 ( 8 + n ) - 4 = 0 here the value of n must be 7 b" + }, + { + "Answer": 25.00000000000001, + "Options": "a ) 50 % , b ) 40 % , c ) 25 % , d ) 20 % , e ) 10 %", + "Correct": "c", + "Explanation": "\"looking at the ratio we can take total number of people = 20 . . ans 5 / 20 or 25 % c\"" + }, + { + "Answer": 27, + "Options": "a ) 12 , b ) 15 , c ) 18 , d ) 24 , e ) 27", + "Correct": "e", + "Explanation": "xyzyx x can be 1 , 2 , or 3 , thus 3 options . y can be 1 , 2 , or 3 , thus 3 options . z can be 1 , 2 , or 3 , thus 3 options . total 3 ^ 3 = 27 . answer : e ." + }, + { + "Answer": 17.647058823529413, + "Options": "a ) 50.5 % , b ) 44.4 % , c ) 22.2 % , d ) 17.6 % , e ) 25 %", + "Correct": "d", + "Explanation": "\"20 % of ( x - y ) = 14 % of ( x + y ) 20 / 100 ( x - y ) = 14 / 100 ( x + y ) 6 x = 34 y required percentage = y / x * 100 = 6 y / 34 y * 100 = 17.64 % answer is d\"" + }, + { + "Answer": 360.00000000000006, + "Options": "a ) rs . 260 , b ) rs . 360 , c ) rs . 350 , d ) rs . 364 , e ) rs . 362", + "Correct": "b", + "Explanation": "\"( a = 2 / 3 b and b = 1 / 4 c ) = a / b = 2 / 3 and b / c = 1 / 4 a : b = 2 : 3 and b : c = 1 : 4 = 3 : 12 a : b : c = 2 : 3 : 12 a ; s share = 510 * 2 / 17 = rs . 60 b ' s share = 510 * 3 / 17 = rs . 90 c ' s share = 510 * 12 / 17 = rs . 360 . answer : b\"" + }, + { + "Answer": 140, + "Options": "a ) a ) 140 , b ) b ) 134 , c ) c ) 148 , d ) d ) 158 , e ) e ) 160", + "Correct": "a", + "Explanation": "\"d = d * q + r d = 15 * 9 + 5 d = 135 + 5 d = 140 answer a\"" + }, + { + "Answer": 25, + "Options": "a ) 25 % , b ) 50 % , c ) 62.5 % , d ) 72.5 % , e ) 75 %", + "Correct": "a", + "Explanation": "( a ) 25 % , to be divisible by 8 the number needs to have 3 2 s in it . only a multiple of 4 can provide that . number of numbers divisible by 4 = 96 / 4 = 24 . so p ( 8 ) = 24 / 96 = 25 % ." + }, + { + "Answer": 66, + "Options": "a ) 39 , b ) 50 , c ) 66 , d ) 57 , e ) 60", + "Correct": "c", + "Explanation": "g + h = 90 . . . 1 ; g / 4 + h / 3 = 25 . . . . 2 or 3 g + 4 h = 25 * 12 = 300 g = 90 - h or 3 ( 90 - h ) + 4 h = 300 h = 300 - 270 = 30 then g = 96 - 30 = 66 c" + }, + { + "Answer": 11, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 11", + "Correct": "e", + "Explanation": "\"the product of 12 integers is negative thus an odd number of integers need to be negative to have a negative product we are asked at most how many are required . so , the highest odd integer before 6 , i . e . 11 correct option : e\"" + }, + { + "Answer": 190, + "Options": "a ) 10 , b ) 30 , c ) 190 , d ) 60 , e ) 90", + "Correct": "c", + "Explanation": "\"20 players are there . two players play one game with one another . so 20 c 2 = 20 * 19 / 2 = 190 so option c is correct\"" + }, + { + "Answer": 50, + "Options": "a ) 50 km , b ) 56 km , c ) 70 km , d ) 80 km , e ) 46 km", + "Correct": "a", + "Explanation": "\"let the actual distance travelled be x km . then , x / 10 = ( x + 20 ) / 14 14 x = 10 x + 200 4 x = 200 x = 50 km . answer : a\"" + }, + { + "Answer": 1225, + "Options": "a ) 1000 , b ) 3000 , c ) 1225 , d ) 6000 , e ) 9000", + "Correct": "c", + "Explanation": "\"50 players are there . two players play one game with one another . so 50 c 2 = 50 * 49 / 2 = 1225 so option c is correct\"" + }, + { + "Answer": 5, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "d", + "Explanation": "\"minimuum should be 1 maximum should be 4 : 1 out of a or b to make the multiplication negative 3 out of c , d , e or f to make the multiplication negative . negative + negative < 0 answer : c maximum will be 5 . . you dont require both the multiplicatin to be negative for entire equation to be negative . . . any one a or b can be negative to make ab negative and it can still be more ( away from 0 ) than the multiplication of 4 other - ve numbers . . . actually by writing minimum required as 1 out of 6 , you are actually meaning 5 out of 6 also possible as you will see e = 5 or 1 will give you same equation . . ans d\"" + }, + { + "Answer": 57.87755102040816, + "Options": "a ) 54 , b ) 51 , c ) 58 , d ) 55 , e ) 52", + "Correct": "c", + "Explanation": "\"for 40 hrs = 40 * 14 = 560 excess = 998 - 560 = 438 for extra hours = . 75 ( 14 ) = 10.5 + 14 = 24.5 number of extra hrs = 438 / 24.5 = 17.8 = 18 approx . total hrs = 40 + 18 = 58 answer c\"" + }, + { + "Answer": 442.5, + "Options": "a ) 442.5 , b ) 450 , c ) 465 , d ) 468 , e ) 475", + "Correct": "a", + "Explanation": "\"total number of installments = 40 payment per installment for the first 20 installments = 410 payment per installment for the remaining 20 installments = 410 + 65 = 475 average = ( 20 * 410 + 20 * 475 ) / 40 = 442.50 answer a\"" + }, + { + "Answer": 13000, + "Options": "a ) 150000 , b ) 16000 , c ) 15000 , d ) 190000 , e ) 13000", + "Correct": "e", + "Explanation": "\"if value of business = x total sell ( 2 x / 3 ) ( 3 / 4 ) = 6500 - > x = 13000 answer : e\"" + }, + { + "Answer": 100, + "Options": "a ) 90 % , b ) 99 % , c ) 100 % , d ) 101 % , e ) 110 %", + "Correct": "b", + "Explanation": "the total number of employees = n the average salary = x total salary to all emplyoees = xn after the total number of employees = n - 0.1 n = 0.9 n the average salary = x + 10 % of x = 1.1 x total salary to all emplyoees = 0.9 n ( 1.1 x ) total salary after as a % of total salary before r = [ 0.9 n ( 1.1 x ) ] / xn = 0.99 or 99 % . b" + }, + { + "Answer": 80, + "Options": "a ) 98.5 kgs , b ) 80 kgs , c ) 76.5 kgs , d ) 67.5 kgs , e ) 58.2 kgs", + "Correct": "b", + "Explanation": "\"average weight = [ ( a + b + c + ( a + b ) + ( b + c ) + ( c + a ) + ( a + b + c ) ] / 7 = 4 ( a + b + c ) / 7 = 4 x 140 / 7 = 80 kgs answer : b\"" + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) - 12 , c ) 1 / 12 , d ) - 1 / 12 , e ) 3", + "Correct": "a", + "Explanation": "( 27 / 4 ) x - 18 = 3 x + 27 = > 27 x - 72 = 12 x + 108 = > 15 x = 180 = > x = 12 answer : a" + }, + { + "Answer": 248, + "Options": "a ) 179 , b ) 208 , c ) 210 , d ) 223 , e ) 248", + "Correct": "e", + "Explanation": "explanation : total runs scored by the batsman = 63 * 46 = 2898 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2898 \u2013 2552 = 346 runs . let the highest score be x , hence the lowest score = x \u2013 150 x + ( x - 150 ) = 346 2 x = 496 x = 248 runs answer e" + }, + { + "Answer": 302, + "Options": "a ) 285 , b ) 305 , c ) 315 , d ) 350 , e ) 245", + "Correct": "b", + "Explanation": "\"2 + 3 = > 2 \u00e3 \u2014 3 = 6 = > 6 \u00e3 \u2014 10 + 5 = 65 3 + 4 = > 3 \u00e3 \u2014 4 = 12 = > 12 \u00e3 \u2014 10 + 5 = 125 4 + 5 = > 4 \u00e3 \u2014 5 = 20 = > 20 \u00e3 \u2014 10 + 5 = 205 then 5 + 6 = > 5 \u00e3 \u2014 6 = 30 = > 30 \u00e3 \u2014 10 + 5 = 305 answer : b\"" + }, + { + "Answer": 306, + "Options": "a ) 6 , b ) 106 , c ) 206 , d ) 306 , e ) 406", + "Correct": "d", + "Explanation": "\"( 7 ' ) ' = ( 3 * 7 - 3 ) ' = 18 ' = 18 * 18 - 18 = 306 answer d\"" + }, + { + "Answer": 1200, + "Options": "a ) s . 1200 , b ) s . 5400 , c ) s . 5400 , d ) s . 4999 , e ) s . 5000", + "Correct": "a", + "Explanation": "\"total sale for 5 months = rs . ( 5400 + 9000 + 6300 + 7200 + 4500 ) = rs . 32400 . required sale = rs . [ ( 5600 x 6 ) - 32400 ] = rs . ( 33600 - 32400 ) = rs . 1200 . option a\"" + }, + { + "Answer": 20, + "Options": "a ) 20 , b ) 50 , c ) 60 , d ) 80 , e ) 100", + "Correct": "a", + "Explanation": "total cost for n products = fixed cost for n products + n * marginal cost - - > $ 16,000 = $ 12,000 + n * $ 200 - - > n = 20 . answer : a ." + }, + { + "Answer": 224, + "Options": "a ) $ 212 , b ) $ 216 , c ) $ 220 , d ) $ 224 , e ) $ 228", + "Correct": "d", + "Explanation": "\"let the shares for a , b , and c be x , 2 x , and 4 x respectively . 7 x = 392 x = 56 4 x = 224 the answer is d .\"" + }, + { + "Answer": 4.9, + "Options": "a ) 0.5 , b ) 4.63 , c ) 4.9 , d ) 7.7 , e ) 49.1", + "Correct": "c", + "Explanation": "if we read the q , we can easily home on to the answer , , the numerator is clearly between 40 and 50 . . denomiator is close to 10 . . so d = ( 0.889 \u00d7 55 ) / 9.97 is between 4 and 5 . . it may tempt us to solve it since ther are two values between 4 and 5 . . but the catch is innearest tenth 4.63 can be called nearest to hundreth and no tenth , so can be eliminated . . 4.9 is our answer . . . c" + }, + { + "Answer": 261, + "Options": "a ) 259 , b ) 261 , c ) 263 , d ) 265 , e ) 267", + "Correct": "b", + "Explanation": "the least number which when divided by different divisors leaving the same remainder in each case = lcm ( different divisors ) + remainder left in each case . hence the required least number = lcm ( 37 , 7 ) + 2 = 261 . answer : b" + }, + { + "Answer": 28.00000000000003, + "Options": "a ) 10 % , b ) 15 % , c ) 20 % , d ) 28 % , e ) 50 %", + "Correct": "d", + "Explanation": "\"say a recliner is actually worth $ 100 if she sells 100 recliners then she earns $ 10000 after the discount of 20 % , she will earn $ 80 per recliner and she sells 60 % more ie . , 160 recliners hence her sales tields 160 * 80 = $ 12800 increase in sales = 12800 - 10000 = $ 2800 so % increase = 2800 * 100 / 10000 = 28 % d is the answer\"" + }, + { + "Answer": 35, + "Options": "a ) 30 , b ) 35 , c ) 38 , d ) 40 , e ) 45", + "Correct": "b", + "Explanation": "\"10 play kabadi = > n ( a ) = 10 , 5 play both gmaes . = > n ( anb ) = 5 25 play kho kho only , = > n ( b ) = n ( b only ) + n ( anb ) = 25 + 5 = 30 total = > n ( aub ) = n ( a ) + n ( b ) - n ( anb ) = 10 + 30 - 5 = 35 answer : b\"" + }, + { + "Answer": 3, + "Options": "a ) 5 , b ) 2 , c ) 7 , d ) 9 , e ) 3", + "Correct": "e", + "Explanation": "\"number = 5 * 5 + 0 = 25 11 ) 25 ( 2 22 - - - - - - - - 3 required number = 0 . answer : e\"" + }, + { + "Answer": 0.3333333333333333, + "Options": "a ) 3 , b ) 2 , c ) 1 / 2 , d ) 1 / 3 , e ) there is n ' t enough data to answer the question .", + "Correct": "d", + "Explanation": "answer is d : 1 / 3 u - v = ( u + v ) / 2 solving for v / u = 1 / 3 d" + }, + { + "Answer": 0.3333333333333333, + "Options": "a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6", + "Correct": "b", + "Explanation": "\"x = 6 y + 5 , and thus y = x / 6 - 5 / 6 the slope is 1 / 6 . the slope of a line through points ( m , n ) and ( m + 2 , n + p ) is ( n + p - n ) / ( m + 2 - m ) = p / 2 p / 2 = 1 / 6 and thus p = 1 / 3 the answer is b .\"" + }, + { + "Answer": 209, + "Options": "a ) 2.09 % , b ) 20.9 % , c ) 209 % , d ) 0.209 % , e ) none of these", + "Correct": "c", + "Explanation": "\"explanation : while calculation in terms of percentage we need to multiply by 100 , so 2.09 * 100 = 209 answer : option c\"" + }, + { + "Answer": 49.5, + "Options": "a ) 5.5 , b ) 11 , c ) 47.5 , d ) 66 , e ) 49.5", + "Correct": "e", + "Explanation": "total price of six cans = 6 * 36.5 = 219 total price of 4 cans = 4 * 30 = 120 total rice of two cans = 219 - 120 = 99 average price of two cans = 99 / 2 = 49.5 c another way to do it is this : assume that the four leftover cans were of 30 c each . the avg was 36.5 c initially because the two cans were 36.5 c each and were providing another 6.5 c of cost to other 4 cans . so cost of the two cans = 2 * 36.5 + 4 * 6.5 = 99 avg cost of the two cans = 99 / 2 = 49.5 c answer ( e )" + }, + { + "Answer": 2, + "Options": "a ) 12 , b ) 17 , c ) 18 , d ) 77 , e ) 2", + "Correct": "e", + "Explanation": "answer : 2 option : e" + }, + { + "Answer": 22, + "Options": "a ) 23 years , b ) 22 years , c ) 21 years , d ) 20 years , e ) 30 years", + "Correct": "b", + "Explanation": "\"let present age of the son = x years then present age the man = ( x + 24 ) years given that in 2 years man ' s age will be twice the age of his son x = 22 answer b\"" + }, + { + "Answer": 60, + "Options": "a ) 50 . , b ) 45 . , c ) 40 . , d ) 60 . , e ) 25 .", + "Correct": "d", + "Explanation": "\"given there are 60 students , 90 % of 60 = 54 boys and remaining 6 girls . now here 90 % are boys and 10 % are girls . now question is asking about how many boys do we need to add , to make the girls percentage to 5 or 5 % . . if we add 60 to existing 54 then the count will be 114 and the girls number will be 6 as it . now boys are 95 % and girls are 5 % . ( out of 120 students = 114 boys + 6 girls ) . imo option d is correct .\"" + }, + { + "Answer": 38, + "Options": "a ) 42 , b ) 35 , c ) 40 , d ) 33 , e ) 38", + "Correct": "e", + "Explanation": "\"the bottom row has x bricks x + x - 1 + x - 2 + x - 3 + x - 4 = 200 5 x - 10 = 200 5 x = 190 x = 38 answer : e\"" + }, + { + "Answer": 3, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "a", + "Explanation": "\"cant think of a straight approach but here is how i solved it : k is divided by 5 and remainder is 2 . this means k = 5 n + 2 ( n is an integer ) so the possible values of k = { 2 , 7 , 12 , 17 , 22 , 27 , 32 , 37 } ( less than 41 ) secondly , if k is divided by 6 , the remainder is 5 = > k = 6 m + 5 so the possible value set for k = { 5 , 11 , 17 , 23 , 29,35 } ( less than 41 ) 17 is the only common number in both the sets . hence k = 17 answer : a\"" + }, + { + "Answer": 3200.0000000000005, + "Options": "a ) 800 , b ) 3200 , c ) 900 , d ) 1600 , e ) none", + "Correct": "b", + "Explanation": "\"answer 4 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ] = 4 x [ ( 36 x 48 x 250 ) / ( 12 x 9 x 5 ) ] = 4 x 4 x 4 x 50 = 3200 correct option : b\"" + }, + { + "Answer": 9, + "Options": "a ) 4 , b ) 9 , c ) 6 , d ) 8 , e ) 10", + "Correct": "b", + "Explanation": "\"fastly i reduce 60 % till it gets closer to our required 2000 candidates step ( 1 ) 40000 accepted . step ( 2 ) another 40 % of 40000 = 16000 accepted . here it is quiet observable that if we further deduct candidate by 60 % it would change our probablity of easy going 2000 candidate . so i would get to second stage of recruitment where 50 % is accepted step ( 3 ) 50 % of 16000 = 8000 step ( 4 ) 50 % of 8000 = 4000 step ( 5 ) 50 % of 4000 = 2000 step ( 6 ) 50 % of 2000 = 1000 step ( 7 ) 50 % of 1000 = 500 step ( 8 ) 50 % of 500 = 250 step ( 9 ) 70 % of 350 = 175 ( our target ) total 9 steps required . ans b\"" + }, + { + "Answer": 4, + "Options": "a ) 5 , b ) 6 , c ) 3 , d ) 4 , e ) 7", + "Correct": "d", + "Explanation": "a , b , c may be ( 1 , 2,4 ) & ( 4 , 2,1 ) ( 1 , 3,9 ) & ( 9 , 3,1 ) ( 2 , 4,8 ) & ( 8 , 4,2 ) ( 4 , 6,9 ) & ( 9 , 6,4 ) find abs ( a + b + c ) for these 8 gps 7,13 , 15,19 so , we get 4 different values answer : d" + }, + { + "Answer": 0.5555555555555555, + "Options": "a ) 15 / 2 , b ) 9 / 4 , c ) 5 / 9 , d ) 7 / 5 , e ) 9 / 7", + "Correct": "c", + "Explanation": "blue tin or red tin : 2 / 3 ( n ) red tin : ( 1 / 3 ) n blue tin : ( 1 / 4 ) n what the last statment meant , is it wants this fraction : ( # of cookies in green tin ) / ( # of cookies in red and green tin ) # of cookies in green tin = 2 n / 3 - n / 4 = 8 n - 3 n / 12 = 5 n / 12 # of cookies in red and green tin = n / 3 + 5 n / 12 = 9 n / 12 fraction w = 5 n / 12 * 12 / 9 n = 5 / 9 ( c )" + }, + { + "Answer": 40, + "Options": "a ) 30 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 70 %", + "Correct": "b", + "Explanation": "\"to maximize the percentage of companies offering both , let ' s assume that all 40 % of companies which offer wireless internet also offer snacks . the answer is b .\"" + }, + { + "Answer": 22.5043, + "Options": "a ) 9 % , b ) 9.27 % , c ) 22.50 % , d ) 12 % , e ) none of these", + "Correct": "c", + "Explanation": "\"actual increase in population = 7 % let , earlier population = 100 then the population after 3 years = 100 ( 1 + 7 / 100 ) ^ 3 = 122.5043 \u2234 required percentage = 22.50 % answer : c\"" + }, + { + "Answer": 400, + "Options": "a ) 16 , b ) 80 , c ) 160 , d ) 180 , e ) 400", + "Correct": "e", + "Explanation": "\"prime digits 2 , 3,5 and 7 . three digit numbers _ _ _ 1 st place can be filled in 4 ways 2 nd place can be filled in 10 ways 3 rd place can be filled in 10 ways total = 4 * 10 * 10 = 400 ans : e\"" + }, + { + "Answer": 18.25, + "Options": "a ) \u2013 108 , b ) \u2013 44 , c ) 10 , d ) 16 , e ) 18.25", + "Correct": "e", + "Explanation": "# p = 2 p - 20 - - - > # ( # p ) = 2 ( 2 p - 20 ) - 20 = 4 p - 60 and thus # ( 4 p - 60 ) = 2 ( 4 p - 60 ) - 20 = 8 p - 140 = 6 - - - > 8 p = 146 - - - > p = 18.25 , e is the correct answer ." + }, + { + "Answer": 25, + "Options": "a ) 20 kg , b ) 25 kg , c ) 30 kg , d ) 35 kg , e ) none of these", + "Correct": "b", + "Explanation": "since , expenditure = price \u00d7 consumption \u2234 110 % of 30 = 132 \u2044 100 \u00d7 new consumption \u21d2 110 \u2044 100 \u00d7 30 = 132 \u2044 100 \u00d7 new consumption \u21d2 new consumption = 25 kg answer b" + }, + { + "Answer": 173, + "Options": "a ) 145 , b ) 38 , c ) 173 , d ) 156 , e ) 189", + "Correct": "c", + "Explanation": "n th term of a . p = a + ( n - 1 ) * d = 5 + ( 25 - 1 ) * 7 , = 5 + 168 = 173 . answer : c" + }, + { + "Answer": 0.62, + "Options": "a ) 0.56 , b ) 0.62 , c ) 0.68 , d ) 0.74 , e ) 0.8", + "Correct": "b", + "Explanation": "let x be the total number of students . the number students who are younger than 25 is 0.5 * 0.4 x + 0.7 * 0.6 x = 0.62 x the answer is b ." + }, + { + "Answer": 8, + "Options": "a ) 1 , b ) 5 , c ) 7 , d ) 8 , e ) 11", + "Correct": "d", + "Explanation": "let me define terms : in g ( a ) = r a is argument , r is result , g ( ) is function , in g ( g ( g ( g ( g ( a ) ) ) ) ) , g 1 is inner most , g 5 is outermost for identification . from definition of function g , we can deduce that : if result is even then two possibilities for argument = 1 even 1 odd if result is odd then one possibility for argument = 1 even since final result = 19 = odd possibilities : g 1 : 1 even g 2 : 1 * ( even , odd ) = 1 even 1 odd g 3 : 1 * ( even , odd ) + 1 even = 2 even 1 odd g 4 : 2 * ( even , odd ) + 1 even = 3 even 2 odd g 5 : 3 * ( even , odd ) + 2 even = 5 even 3 odd = total 8 ans d it is !" + }, + { + "Answer": 25, + "Options": "a ) 7 , b ) 33 , c ) 12 , d ) 17 , e ) 25", + "Correct": "e", + "Explanation": "16 + 9 = 25 . answer is e ." + }, + { + "Answer": 21, + "Options": "a ) 10 , b ) 12 , c ) 21 , d ) 18 , e ) 20", + "Correct": "c", + "Explanation": "\"sp = 20 loss = cp 21 loss = cp \u2212 sp = cp \u2212 20 \u21d2 cp 21 = cp \u2212 20 \u21d2 20 cp 21 = 20 \u21d2 cp 21 = 1 \u21d2 cp = 21 c\"" + }, + { + "Answer": 27.599999999999998, + "Options": "a ) $ 22 , b ) $ 27.6 , c ) $ 30 , d ) $ 36 , e ) $ 40", + "Correct": "b", + "Explanation": "\"b its is . let price = x ( x - 1.15 ) 8 = 6 x x = 4.6 hence total money = 6 * 4.6 = 27.6\"" + }, + { + "Answer": 1, + "Options": "a ) $ 3 , b ) $ 2 , c ) $ 9 , d ) $ 1 , e ) $ 4", + "Correct": "d", + "Explanation": "zoey and her 5 friends is 6 people in all . $ 7 , 348340 must be divisible by 6 if she wants to split it evenly . the money is divisible by 6 if it ' s divisible by 2 and 3 . 7 + 3 + 4 + 8 + 3 + 4 + 0 = 29 . 2 and 3 cant go into 29 . adding 1 dollar makes it 30 . 2 and 3 can go into 30 so 6 can also . the answer is d ." + }, + { + "Answer": 2, + "Options": "a ) 2 , b ) 6278 , c ) 277 , d ) 281 , e ) 22", + "Correct": "a", + "Explanation": "we use pencil to write on a paper but here pencil is coded as mirror . so , the answer is mirror . answer : a" + }, + { + "Answer": 25, + "Options": "a ) 20 % , b ) 30 % , c ) 25 % , d ) 15 % , e ) 50 %", + "Correct": "c", + "Explanation": "\"50 % of ( x - y ) = 30 % of ( x + y ) 50 / 100 ( x - y ) = 30 / 100 ( x + y ) x = 4 y required percentage = y / x * 100 = y / 4 y * 100 = 25 % answer is c\"" + }, + { + "Answer": 9, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9", + "Correct": "e", + "Explanation": "fastly i reduce 60 % till it gets closer to our required 2000 candidates step ( 1 ) 40000 accepted . step ( 2 ) another 40 % of 40000 = 16000 accepted . here it is quiet observable that if we further deduct candidate by 60 % it would change our probablity of easy going 2000 candidate . so i would get to second stage of recruitment where 50 % is accepted step ( 3 ) 50 % of 16000 = 8000 step ( 4 ) 50 % of 8000 = 4000 step ( 5 ) 50 % of 4000 = 2000 step ( 6 ) 50 % of 2000 = 1000 step ( 7 ) 50 % of 1000 = 500 step ( 8 ) 70 % of 500 = 350 step ( 9 ) 70 % of 350 = 245 ( our target ) total 9 steps required . ans e" + }, + { + "Answer": 66, + "Options": "a ) 50 , b ) 52 , c ) 65 , d ) 42 , e ) 66", + "Correct": "e", + "Explanation": "sixth result = 58 * 6 + 63 * 6 - 60 * 11 = 66 answer is e" + }, + { + "Answer": 12, + "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12", + "Correct": "e", + "Explanation": "\"8 + 4 = 12 correct answer is e ) 12\"" + }, + { + "Answer": 270, + "Options": "a ) 250 , b ) 270 , c ) 310 , d ) 330 , e ) 350", + "Correct": "b", + "Explanation": "a : b : c = 1 : 3 : 12 total parts = 16 b ' s share is = 3 parts 16 - - - - - > 1440 1 - - - - - > 90 3 - - - - - > 270 ( b ' s share is 270 ) b )" + }, + { + "Answer": 3, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "d", + "Explanation": "t = 12 a + 3 = 18 b + 3 2 a = 3 b - - > min ( a , b ) = ( 3,2 ) so minimum number of toys - - > 12 * 3 + 3 = 39 when toys are grouped into 7 , 4 will remain ungrouped so in order to make another group of 7 toys - - > 7 - 4 = 3 toys at least to be added . answer : d" + }, + { + "Answer": 33, + "Options": "a ) 65 degrees , b ) 73 degrees , c ) 37 degrees , d ) 34 degrees , e ) 33 degrees", + "Correct": "e", + "Explanation": "\"m + tu + w + th = 4 * 48 = 192 tu + w + th + f = 4 * 46 = 184 m = 41 tu + w + th = 192 - 41 = 151 f = 184 \u2013 151 = 33 answer : e\"" + }, + { + "Answer": 2, + "Options": "a ) 1.8 , b ) 2.2 , c ) 2 , d ) 1.9 , e ) 2.4", + "Correct": "c", + "Explanation": "say x dozen eggs were sold in may . then 2 x / 3 dozen eggs were sold in april and 2 * 2 x / 3 = 4 x / 3 dozen eggs were sold in may . total x + 2 x / 3 + 4 x / 3 = 3 x dozen eggs were sold in three months . total sales : 2 x / 3 * 1.2 + x * 1.2 + 4 x / 3 * 3.00 = $ 6.00 x . the average price per dozen 6.00 x / 3 x = $ 2.00 c" + }, + { + "Answer": 60, + "Options": "a ) 30 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 70 %", + "Correct": "d", + "Explanation": "first find out ( ratio of royalties to sales ) : 2 : 10 first 0.2 8 : 100 second 0.08 decrease = 0.2 - 0.08 = 0.12 percent = ( 0.12 / 0.20 ) = 60 % . answer : d" + }, + { + "Answer": 78, + "Options": "a ) 78 kg , b ) 60 kg , c ) 64 kg , d ) 70 kg , e ) none", + "Correct": "a", + "Explanation": "\"sol . for 9 kg zinc , mixture melted = ( 9 + 11 ) kg . for 35.1 kg zinc , mixture , melted = [ 20 / 9 x 35.1 ] kg = 78 kg . answer a\"" + }, + { + "Answer": 525, + "Options": "a ) 360 , b ) 420 , c ) 510 , d ) 525 , e ) 280", + "Correct": "d", + "Explanation": "\"lcm = 3 * 5 * 5 * 7 = 525 . answer is d\"" + }, + { + "Answer": 42, + "Options": "a ) 41 , b ) 42 , c ) 43 , d ) 44 , e ) 45", + "Correct": "b", + "Explanation": "she gave 1 penny more than the half in the purse i . e ( x / 2 + 1 ) now she is left with : : ( x - ( x / 2 + 1 ) ) = ( x - 2 ) / 2 now to the beggar : : she gave 2 pennies more than the half in the purse i . e ( x - 2 ) / 4 + 2 and she is left with : : ( ( x - 2 ) / 2 ) - ( ( x - 2 ) / 4 + 2 ) = ( x - 10 ) / 4 now at last sh gave 3 pennies more then the half she was left with i . e ( ( x - 10 ) / 8 + 3 ) = a so she is left with ( x - 10 ) / 4 - a = ( x - 34 ) / 8 now acc . to quest ( x - 34 ) / 8 = 1 hence x = 42 answer : b" + }, + { + "Answer": 26, + "Options": "a ) 15 , b ) 26 , c ) 37 , d ) 42 , e ) 60", + "Correct": "b", + "Explanation": "\"take lcm of 2,5 and 6 = 30 now 2 x = 30 = > x = 15 5 y = 30 = > y = 6 6 z = 30 = > z = 5 15 + 6 + 5 = 26 . option b .\"" + }, + { + "Answer": 72000, + "Options": "a ) 81000 , b ) 85000 , c ) 75000 , d ) 72000 , e ) 77000", + "Correct": "d", + "Explanation": "let savings in national savings certificate = x and savings in public provident fund = ( 180000 - x ) 1 / 3 x = 1 / 2 ( 180000 \u2212 x ) \u21d2 2 x = 3 ( 180000 \u2212 x ) \u21d2 2 x = 540000 \u2212 3 x \u21d2 5 x = 540000 \u21d2 x = 540000 / 5 = 108000 savings in public provident fund = ( 180000 - 108000 ) = 72000 answer is d ." + }, + { + "Answer": 25, + "Options": "a ) 25 , b ) 32 , c ) 35 , d ) 30 , e ) 45", + "Correct": "a", + "Explanation": "\"explanation : hcf ( 408 , 192 ) = 24 the number of boys or girls that can be placed in a section = 24 . thus the total number of sections is given by 408 / 24 + 192 / 24 = 17 + 8 = 25 answer : a\"" + }, + { + "Answer": 26.66666666666667, + "Options": "a ) 9 , b ) 12 , c ) 15 , d ) 16 , e ) 26.6", + "Correct": "e", + "Explanation": "\"in 40 liters , red = 5 / 8 * 40 = 25 and blue = 15 so , 25 / ( 15 + x ) = 3 / 5 or , x = 26.6 ( answer e )\"" + }, + { + "Answer": 40, + "Options": "a ) a ) 25 , b ) b ) 34 , c ) c ) 50 , d ) d ) 40 , e ) e ) 100", + "Correct": "d", + "Explanation": "its d . total juice rquired = 320 * 6 = 1920 ounce 12 ounce concentate makes = 12 * 4 = 48 ounce juice total cans required = 1920 / 48 = 40 . answer d" + }, + { + "Answer": 24, + "Options": "a ) 6 , b ) 12 , c ) 24 , d ) 120 , e ) none", + "Correct": "c", + "Explanation": "sol . required number = 1 \u00d7 2 \u00d7 3 \u00d7 4 = 24 . answer c" + }, + { + "Answer": 3927, + "Options": "a ) 3327 , b ) 3237 , c ) 3927 , d ) 2337 , e ) none of these", + "Correct": "c", + "Explanation": "\"answer x = 13800 - 9873 = 3927 option : c\"" + }, + { + "Answer": 300, + "Options": "a ) 210 , b ) 252 , c ) 280 , d ) 300 , e ) 420", + "Correct": "d", + "Explanation": "maximum number of soap boxes that can be placed in each carton = volume of each carton / volume of each box = ( 25 * 42 * 60 ) / ( 7 * 6 * 5 ) = 300 answer : d" + }, + { + "Answer": 260, + "Options": "a ) s . 250 , b ) s . 280 , c ) s . 290 , d ) s . 260 , e ) s . 300", + "Correct": "d", + "Explanation": "\"let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 572 but x = 120 % of y = 120 y / 100 = 12 y / 10 \u2234 12 y / 10 + y = 572 \u21d2 y [ 12 / 10 + 1 ] = 572 \u21d2 22 y / 10 = 572 \u21d2 22 y = 5720 \u21d2 y = 5720 / 22 = 520 / 2 = rs . 260 d\"" + }, + { + "Answer": 2, + "Options": "a ) 2 , b ) 5 , c ) 7 , d ) 24 , e ) 35", + "Correct": "a", + "Explanation": "\"given : ab = 2 ( a + b ) + 11 and b = 7 hence 7 a = 2 a + 14 + 11 5 a = 25 , a = 5 ( a potential trap . do not get excited here . we need to find b - a , not a ) b - a = 7 - 5 = 2 correct option : a\"" + }, + { + "Answer": 8, + "Options": "a ) 6 , b ) 5 , c ) 2 , d ) 8 , e ) 2", + "Correct": "d", + "Explanation": "\"9 m = xw = 7 b 9 m + xw + 7 b - - - - - 216 rs . 9 m + 9 m + 9 m - - - - - 216 rs . 27 m - - - - - - 216 rs . = > 1 m = 8 rs . answer : d\"" + }, + { + "Answer": 24, + "Options": "a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36", + "Correct": "b", + "Explanation": "\"2 oxen = 3 buffaloes = 4 cows also : 15 buffaloes + 8 oxen + 24 cows = 10 oxen + 8 oxen + 12 oxen = 30 oxen there is enough fodder for 1 oxen for 30 * 48 days . 40 cows + 15 buffaloes = 20 oxen + 10 oxen = 30 oxen the new total is equal to 60 oxen instead of 30 oxen . 30 * 48 / 60 oxen = 24 days the answer is b .\"" + }, + { + "Answer": 5, + "Options": "a ) 4 , b ) 5 , c ) 7 , d ) 6 , e ) 8", + "Correct": "b", + "Explanation": "\"on dividing 378461 by 13 we get the remainder 5 , so 5 should be subtracted b\"" + }, + { + "Answer": 21.73913043478261, + "Options": "a ) 20.8 , b ) 21.46 , c ) 21.74 , d ) 22.3 , e ) 21.4", + "Correct": "c", + "Explanation": "\"1 ) cost of repairing = 11.5 ( for one year ) , therefore for 2 years it would be $ 23 . 2 ) cost of new pair which will last for 2 years is $ 28 . percentage change formula = ( final value - initial value ) / ( initial value ) * 100 . in this case the final value would be the price of new shoeinitial value would be the cost of repairing the old shoe . i . e ( 28 - 23 ) / ( 23 ) * 100 = 21.74 % . ans is c\"" + }, + { + "Answer": 324, + "Options": "a ) rs . 424 , b ) rs . 524 , c ) rs . 324 , d ) rs . 350 , e ) rs . 354", + "Correct": "c", + "Explanation": "\"soln : - ( 330 / 110 ) 108 = 324 in this case long division does not take much time . ( 330 / 110 ) 108 = 324 answer : c\"" + }, + { + "Answer": 60, + "Options": "a ) 60 , b ) 40 , c ) 44 , d ) 48 , e ) 52", + "Correct": "a", + "Explanation": "\"for 40 hrs = 40 * 16 = 640 excess = 1200 - 640 = 560 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 560 / 28 = 20 total hrs = 40 + 20 = 60 answer a 60\"" + }, + { + "Answer": 29, + "Options": "a ) 11 , b ) 21 , c ) 22 , d ) 29 , e ) 32", + "Correct": "d", + "Explanation": "my attempt : 5 ^ ( 29 ) * 4 ^ ( 15 ) = 2 * 10 ^ p 5 ^ ( 29 ) * 2 ^ ( 30 ) = 2 * ( 2 * 5 ) ^ p 5 ^ ( 29 ) * 2 ^ ( 30 ) = 2 * 2 ^ ( p ) * 5 ^ ( p ) 5 ^ ( 29 ) * 2 ^ ( 30 ) = 2 ^ ( p + 1 ) * 5 ^ ( p ) = > ( p + 1 ) = 30 = > p = 29 answer : 29 ( d )" + }, + { + "Answer": 64, + "Options": "a ) 29 , b ) 45 , c ) 81 , d ) 64 , e ) 18", + "Correct": "d", + "Explanation": "\"2 ^ k = 4 2 ^ 2 k = 4 ^ 2 2 ^ 2 k = 16 2 ^ ( 2 k + 2 ) = 2 ^ 2 k * 2 ^ 2 = 16 * 4 = 64 answer : d\"" + }, + { + "Answer": 52.82051282051282, + "Options": "a ) 52.2 , b ) 59.5 , c ) 52.8 , d ) 52.5 , e ) 52.1", + "Correct": "c", + "Explanation": "\"sum of the marks for the class of 28 students = 28 * 40 = 1120 sum of the marks for the class of 50 students = 50 * 60 = 3000 sum of the marks for the class of 78 students = 1120 + 3000 = 4120 average marks of all the students = 4120 / 78 = 52.8 answer : c\"" + }, + { + "Answer": 512, + "Options": "a ) 256 , b ) 512 , c ) 432 , d ) 352 , e ) 640", + "Correct": "b", + "Explanation": "let total number of children be x . then , x * ( 1 / 8 ) x = ( x / 2 ) x 16 x = 64 . number of notebooks = ( 1 / 8 ) x ^ 2 = ( 1 / 8 ) x 64 x 64 = 512 . answer is b ." + }, + { + "Answer": 127, + "Options": "a ) 125 , b ) 127 , c ) 129 , d ) 131 , e ) 150", + "Correct": "b", + "Explanation": "explanation : in this type of question , its obvious we need to calculate the hcf , trick is hcf of ( 1661 - 10 ) and ( 2045 - 13 ) = hcf ( 1651 , 2032 ) = 127 option b" + }, + { + "Answer": 31, + "Options": "a ) 31 , b ) 40 , c ) 22 , d ) 27 , e ) 25", + "Correct": "a", + "Explanation": "the n th term = a + ( n - 1 ) * d 62 = 2 + ( n - 1 ) * 2 , 62 \u2013 2 = ( n - 1 ) * 2 , n = 60 / 2 + 1 = 31 . answer : a" + }, + { + "Answer": 4, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "b", + "Explanation": "since the integers are consecutive , we can write each as the previous integer + 1 . for example , b = a + 1 , and c = b + 1 . we can also reverse this : a + 1 = b , and b + 1 = c . since ab = d + 1 , we can also write this ab = e . since a + b = e - 1 , then a + b = ab - 1 . find the pair of consecutive integers whose sum is one less than its product . these numbers are 2 and 3 ( sum : 5 ; product : 6 ) . now that we know how the series starts , we can find the value of c . if the first two numbers are 2 and 3 , the third number is 4 ( option b ) ." + }, + { + "Answer": 8, + "Options": "a ) 13 , b ) 8 , c ) 11 , d ) 12 , e ) 14", + "Correct": "b", + "Explanation": "explanation : let the number be x . then , 15 x = x 2 + 56 = > x 2 - 15 x + 56 = 0 = > ( x - 7 ) ( x - 8 ) = 0 = > x = 7 or 8 answer : option b" + }, + { + "Answer": 1.3333333333333333, + "Options": "a ) 3 / 4 , b ) 1 , c ) 4 / 3 , d ) 2 , e ) 7 / 2", + "Correct": "c", + "Explanation": "\"this is a considerably more difficult one , which will involve some algebra . let \u2019 s say that the \u201c first \u201d point is ( \u2013 1 , \u2013 4 ) and the \u201c second , \u201d ( 3 , k ) . the rise = k + 4 , which involves a variable . the run = 3 \u2013 ( \u2013 1 ) = 4 . there the slope is ( k + 4 ) / 4 , and we can set this equal to k and solve for k . { { k + 4 } / 4 } = k k + 4 = 4 k 4 = 3 k k = 4 / 3 answer = c\"" + }, + { + "Answer": 720, + "Options": "a ) a . 720 , b ) b . 256 , c ) c . 1 , d ) d . 12 , e ) e . 36", + "Correct": "a", + "Explanation": "if i have to paint 6 sides with 6 different colour . . . first face can have 6 c 1 options , 2 nd would have 5 c 1 , and subsequent ones would have 4 c 1 , 3 c 1 , 2 c 1 and 1 options respectively . total options = 6 c 1 x 5 c 1 x 4 c 1 x 3 c 1 x 2 c 1 x 1 = 720 distinct ways correct answer - a" + }, + { + "Answer": 3, + "Options": "a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 8", + "Correct": "b", + "Explanation": "i like to put the numbers in prime factors so it is easier and faster to visualize . 14 * n / 60 if we write the factors of 14 - - > 2 , 7 , and the factors of 60 - - > 2 , 2 , 3 , 5 , we have ( 2 * 7 * n ) / ( 2 ^ 2 * 3 * 5 ) simplifying 7 * n / ( 2 * 3 * 5 ) the only way the equation above has an integer value is if n has at least the factors 2 , 3 and 5 , so we can simplify again and we have the number 7 . the number could be 2 * 3 * 5 , or 2 * 3 * 5 * 2 , or 2 * 3 * 5 * . . . . . however to be less than 200 we can not add any prime number . 2 * 3 * 5 = 120 if we added the next prime factor 7 , we would have r = 2 * 3 * 5 * 7 = 840 thus , answer b" + }, + { + "Answer": 55, + "Options": "a ) 75 , b ) 65 , c ) 55 , d ) 95 , e ) 80", + "Correct": "c", + "Explanation": "\"total increase in weight = 8 \u00d7 2.5 = 20 if x is the weight of the new person , total increase in weight = x \u2212 35 = > 20 = x - 35 = > x = 20 + 35 = 55 answer is c .\"" + }, + { + "Answer": 6, + "Options": "a ) - 4.5 . , b ) - 2 . , c ) - 1.7 . , d ) 3 . , e ) 6 .", + "Correct": "e", + "Explanation": "x + y = 2 x + 2 z y = x + 2 z - - - - - - - - - - 1 x - 2 y = 4 z x - 4 z = 2 y - - - - - - - - - 2 subtracting equation 1 from equation 2 - 6 z = y y / z = - 6 e is the answer" + }, + { + "Answer": 132, + "Options": "a ) 190 , b ) 132 , c ) 210 , d ) 220 , e ) 225", + "Correct": "b", + "Explanation": "\"though 2 * ( 12 c 2 ) is the correct approcah to do this , but for people like me who find perm , comb n prob a nightmare , an easy approach can be used . the first guy has to play 2 matches with the rest of 11 , so he ' ll play 22 matches . similarly , second guy has to play with the rest of 10 as his 2 games with the first guy are already played . so he plays 20 matches . this continues like this and the total matches are 22 + 20 + 18 . . . + 2 22 + 20 + . . . + 2 = 2 ( 11 + 10 + . . . + 1 ) = 2 ( ( 11 * 12 ) / 2 ) = 11 * 12 = 132 . answer : b\"" + }, + { + "Answer": 32, + "Options": "a ) 42 , b ) 32 , c ) 48 , d ) 28 , e ) 38", + "Correct": "b", + "Explanation": "\"x / 48 = 24 . x = 24 * 48 . so correct answer would be , ( 24 * 48 ) / 36 = 32 . answer : b\"" + }, + { + "Answer": 320, + "Options": "a ) 600 , b ) 320 , c ) 500 , d ) 520 , e ) 720", + "Correct": "b", + "Explanation": "\"let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 160 ) = 2 + 2 ( extra ) = > 2 x - 320 = x = > x = 320 . answer : b\"" + }, + { + "Answer": 240.00000000000006, + "Options": "a ) 160 , b ) 180 , c ) 200 , d ) 240 , e ) none", + "Correct": "d", + "Explanation": "\"answer let the number be n . then , ( n / 5 ) + 6 = ( n / 4 ) - 6 \u00e2 \u2021 \u2019 ( n / 4 ) - ( n / 5 ) = 12 \u00e2 \u2021 \u2019 ( 5 n - 4 n ) / 20 = 12 \u00e2 \u02c6 \u00b4 n = 240 option : d\"" + }, + { + "Answer": 4, + "Options": "a ) 4 , b ) 7 , c ) 9 , d ) 5 , e ) 2", + "Correct": "a", + "Explanation": "7 - 3 = 4 . answer is a" + }, + { + "Answer": 262, + "Options": "a ) 251 , b ) 261 , c ) 262 , d ) 269 , e ) 278", + "Correct": "c", + "Explanation": "\"there are 31 digits in 10 ^ 30 when we subtract 54 from it , there will be 30 digits left . 10 ^ 30 can be written as 9999999 . . . . ( 30 times ) + 1 so , 10 ^ 30 - 54 = 9999999 . . . . ( 30 times ) + 1 - 54 = 9999999 . . . . ( 30 times ) - 53 consider the last 2 digits , 99 - 53 = 46 the last 2 digits will be 46 . and our number would be 99999 . . . . . . 99946 with 2 less 9 s after subtraction . number of 9 s left are 28 and the last two digits are 46 the sum of the digits will be ( 28 * 9 ) + 4 + 6 = 262 answer : - c\"" + }, + { + "Answer": 40, + "Options": "a ) 40 , b ) 50 , c ) 62 , d ) 45 , e ) 56", + "Correct": "a", + "Explanation": "\"let the average after 11 th inning = x then , average after 10 th inning = x - 5 10 ( x - 5 ) + 90 = 11 x x = 90 - 50 = 40 answer is a\"" + }, + { + "Answer": 28, + "Options": "a ) 28 years , b ) 19 years , c ) 29 years , d ) 10 years , e ) 12 years", + "Correct": "a", + "Explanation": "\"let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 72 5 x = 70 = > x = 14 hence , b ' s age = 2 x = 28 years . answer : a\"" + }, + { + "Answer": 14.999999999999991, + "Options": "a ) 3 % , b ) 5 % , c ) 10 % , d ) 15 % , e ) 18 %", + "Correct": "d", + "Explanation": "1990 dick saved = $ 1150 jane saved = $ 850 ( jane saved $ 150 less than she did the prior year ) jane saved approximately $ 150 / 1000 $ ( 15 % ) less in 1990 answer : d" + }, + { + "Answer": 0.8600000000000001, + "Options": "a ) $ 0.60 , b ) $ 0.70 , c ) $ 0.86 , d ) $ 0.90 , e ) $ 1.00", + "Correct": "c", + "Explanation": "\"1 st day fine - 0.07 2 nd day fine - 0.07 * 2 = 0.14 ( as doubling gives lower value ) 3 rd day fine - 0.14 * 2 = 0.28 ( as doubling gives lower value ) 4 rd day fine - 0.28 * 2 = 0.56 ( as doubling gives lower value ) 5 th day fine - 0.56 + 0.3 = 0.86 ( as doubling gives higher value we add 0.3 this time ) answer : c .\"" + }, + { + "Answer": 6, + "Options": "a ) 5 , b ) 6 , c ) 9 , d ) 11 , e ) 12", + "Correct": "b", + "Explanation": "\"19 / 11 = 1 and 79 / 11 = 7 = = > 7 - 1 = 6 numbers answer : b\"" + }, + { + "Answer": 80, + "Options": "a ) 12 , b ) 28 , c ) 160 , d ) 180 , e ) 80", + "Correct": "e", + "Explanation": "\"let the numbers be x and y . then , x + y = 10 and x - y = 8 x 2 - y 2 = ( x + y ) ( x - y ) = 10 * 8 = 80 . answer : e\"" + }, + { + "Answer": 300, + "Options": "a ) 300 , b ) 380 , c ) 180 , d ) 415 , e ) 264", + "Correct": "a", + "Explanation": "\"many approaches are possible . for example : consider numbers from 0 to 999 written as follows : 1 . 000 2 . 001 3 . 002 4 . 003 . . . . . . . . . 1000 . 999 we have 1000 numbers . we used 3 digits per number , hence used total of 3 * 1000 = 3000 digits . now , why should any digit have preferences over another ? we used each of 10 digits equal # of times , thus we used each digit ( including 5 ) 3000 / 10 = 300 times . answer : a .\"" + }, + { + "Answer": 400, + "Options": "a ) $ 420 , b ) $ 410 , c ) $ 400 , d ) $ 390 , e ) $ 380", + "Correct": "c", + "Explanation": "\"avg = sum of observations / number of observations avg income = ( 200 + 150 + 750 + 400 + 500 ) / 5 = 400 answer is c\"" + }, + { + "Answer": 0.15625, + "Options": "a ) 27 / 32 , b ) 1 / 2 , c ) 5 / 32 , d ) 5 / 27 , e ) . 2 / 3", + "Correct": "c", + "Explanation": "simly 50 / 320 = 5 / 32 answer will be ( c )" + }, + { + "Answer": 84, + "Options": "a ) 80 , b ) 81 , c ) 82 , d ) 83 , e ) 84", + "Correct": "e", + "Explanation": "\"solution : mabel handled 90 transactions anthony handled 10 % more transactions than mabel anthony = 90 + 90 \u00d7 10 % = 90 + 90 \u00d7 0.10 = 90 + 9 = 99 cal handled 2 / 3 rds of the transactions than anthony handled cal = 2 / 3 \u00d7 99 = 66 jade handled 18 more transactions than cal . jade = 66 + 18 = 84 jade handled = 84 transactions . answer : e\"" + }, + { + "Answer": 36, + "Options": "a ) 35 , b ) 45 , c ) 25 , d ) 36 , e ) 55", + "Correct": "d", + "Explanation": "\"a : b : c = 10 \u00d7 7 : 12 \u00d7 5 : 15 \u00d7 3 = 2 \u00d7 7 : 12 \u00d7 1 : 3 \u00d7 3 = 14 : 12 : 9 amount that c should pay = 140 \u00d7 9 / 35 = 4 \u00d7 9 = 36 answer is d\"" + }, + { + "Answer": 1.484, + "Options": "a ) 0.1484 , b ) 14.84 , c ) 1.484 , d ) 2.762 , e ) none", + "Correct": "c", + "Explanation": "\"answer required difference = ( 12 x 24.2 ) / 100 - ( 10 x 14.2 ) / 100 = 2.904 - 1.42 = 1.484 . correct option : c\"" + }, + { + "Answer": 4.56, + "Options": "a ) 4.56 min , b ) 5.28 min , c ) 5.08 min , d ) 9.28 min , e ) 5.988 min", + "Correct": "a", + "Explanation": "\"clearly , the two will meet when they are 627 m apart . to be ( 4.5 + 3.75 ) = 8.25 km apart , they take 1 hour . to be 627 m apart , they take ( 100 / 825 * 627 / 1000 ) hrs = ( 627 / 8250 * 60 ) min = 4.56 min . answer : a\"" + }, + { + "Answer": 156, + "Options": "a ) 115 , b ) 116 , c ) 117 , d ) 118 , e ) 156", + "Correct": "e", + "Explanation": "\"x : y : z = 100 : 45 : 50 20 : 9 : 10 9 - - - 36 39 - - - ? = > 156 answer : e\"" + }, + { + "Answer": 2008, + "Options": "a ) 2008 , b ) 2004 , c ) 2005 , d ) 2006 , e ) 2007", + "Correct": "a", + "Explanation": "\"she must gain at least 70 points , now she has 32 and every year gives her two more points : one for age and one for additional year of employment , so 32 + 2 * ( # of years ) = 70 - - > ( # of years ) = 19 - - > 1989 + 19 = 2008 . answer : a .\"" + }, + { + "Answer": 7, + "Options": "a ) 5 , b ) 7 , c ) 6 , d ) 4 , e ) 3", + "Correct": "b", + "Explanation": "\"lets say 5 and 10 ounce packages be x and y respectively . given that , 5 x + 10 y = 115 and x = y + 2 . what is the value of y . substituting the x in first equation , 5 y + 10 + 10 y = 85 - > y = 105 / 15 . = 7 b\"" + }, + { + "Answer": 50, + "Options": "a ) - 29 , b ) 50 , c ) - 30 , d ) 30 , e ) 60", + "Correct": "b", + "Explanation": "\"from - 49 to - 1 - - > 49 nos . zero - - > 1 number from + 1 to + 49 - - > 49 nos . when we add up nos . from - 49 to + 49 sum will be zero . total 99 nos will be added . 100 th number will be 50 . sum of these 100 nos . = 50 . b is the answer .\"" + }, + { + "Answer": 32, + "Options": "a ) 25 , b ) 30 , c ) 28 , d ) 32 , e ) 42", + "Correct": "d", + "Explanation": "\"( ( 2 a + 16 ) + ( 3 a - 8 ) ) / 2 = ( 5 a + 8 ) / 2 = 84 a = 32 the answer is d .\"" + }, + { + "Answer": 190, + "Options": "a ) 12 , b ) 28 , c ) 160 , d ) 180 , e ) 190", + "Correct": "e", + "Explanation": "let the numbers be x and y . then , x + y = 10 and x - y = 19 x 2 - y 2 = ( x + y ) ( x - y ) = 10 * 19 = 190 . answer : e" + }, + { + "Answer": 56, + "Options": "a ) 95 , b ) 90 , c ) 85 , d ) 80 , e ) 56", + "Correct": "e", + "Explanation": "let x be the number of students in the school . 0.14 x students went to the trip and took more than 100 $ . they compose ( 100 - 75 ) = 25 % of all students who went to the trip . therefore the toal of 0.14 x / 0.25 = 0.56 x students went to the camping which is 56 % . the answer is e" + }, + { + "Answer": 43.99999999999999, + "Options": "a ) 31 % . , b ) 44 % . , c ) 49 % . , d ) 29 % . , e ) 51 % .", + "Correct": "b", + "Explanation": "\"40 % of 2 litres = 0.8 litres 60 % of 6 litres = 3.6 litres therefore , total quantity of alcohol is 4.4 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 44 % b\"" + }, + { + "Answer": 130, + "Options": "a ) 100 , b ) 130 , c ) 150 , d ) 180 , e ) 199", + "Correct": "b", + "Explanation": "\"65 % of x = 20 % of 422.50 then , 65 / 100 * x = 20 / 100 * 4225 / 10 x = 845 / 10 * 100 / 65 = 130 answer is b\"" + }, + { + "Answer": 50, + "Options": "a ) 20 % , b ) 305 , c ) 50 % , d ) 55 % , e ) 60 %", + "Correct": "c", + "Explanation": "explanation : number of pages increased = 80 now , the number of pages of book = 240 number of pages of the books before increase = 240 \u2013 80 = 160 % increase in the number of pages in the book = 80 160 x 100 % = 50 % c" + }, + { + "Answer": 50, + "Options": "a ) 40 % , b ) 50 % , c ) 55 % , d ) 65 % , e ) 70 %", + "Correct": "b", + "Explanation": "number of runs made by running = 110 - ( 3 x 4 + 8 x 6 ) = 120 - ( 60 ) = 60 now , we need to calculate 60 is what percent of 120 . = > 60 / 120 * 100 = 50 % b" + }, + { + "Answer": 3, + "Options": "a ) 3 , b ) 10 , c ) 9 , d ) 8 , e ) 7", + "Correct": "a", + "Explanation": "a u b u c = a + b + c - ab - bc - ac + abc 86 = 28 + 23 + 44 - ab - bc - ac + 3 = > ab + bc + ac = 12 exactly two classes = ab + bc + ac - 3 abc = 12 - 3 * 3 = 3 hence a" + }, + { + "Answer": 12, + "Options": "a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15", + "Correct": "b", + "Explanation": "\"100 - ( 100 - 82 ) - ( 100 - 75 ) - ( 100 - 85 ) - ( 100 - 70 ) = 100 - 18 - 25 - 15 - 30 = 100 - 88 = 12 answer : b\"" + }, + { + "Answer": 1170, + "Options": "a ) rs . 692.80 , b ) rs . 820 , c ) rs . 1170 , d ) rs . 1385 , e ) none", + "Correct": "c", + "Explanation": "\"answer income of the deceased = total income of 4 members - total income of remaining 3 members . = 735 x 4 - 590 x 3 rs . = 1170 rs . correct option : c\"" + }, + { + "Answer": 1.694915254237288, + "Options": "a ) 1.5 hours , b ) 1.27 hours , c ) 1.73 hours , d ) 2 hours , e ) 1.69 hours", + "Correct": "e", + "Explanation": "the cars travel ( 145 + 150 = 295 ) miles in one hour . 500 miles / 295 miles / hour = 1.69 hours answer is e" + }, + { + "Answer": 15, + "Options": "a ) 20 , b ) 15 , c ) 25 , d ) 30 , e ) 35", + "Correct": "b", + "Explanation": "explanation : average = ( 7 + 14 + 21 + 28 + 35 ) / 7 = 105 / 7 = 15 option b" + }, + { + "Answer": 100, + "Options": "a ) 150 , b ) 110 , c ) 100 , d ) 200 , e ) 50", + "Correct": "c", + "Explanation": "eq of line = y = mx + c m = 4 x = 50 y = 50 * 4 + c , substitute y by 300 as given in question . 300 = 200 + c , c = 100 correct option is c" + }, + { + "Answer": 20, + "Options": "a ) 20 % , b ) 25 % , c ) 55 % , d ) 65 % , e ) none of above", + "Correct": "a", + "Explanation": "explanation : actually it means 4 is what percent of 20 , which can be calculated as , ( 4 / 20 ) * 100 = 4 * 5 = 20 answer : option a" + }, + { + "Answer": 2.3333333333333335, + "Options": "a ) 0 , b ) 2 , c ) 2.5 , d ) 7 / 3 , e ) 10", + "Correct": "d", + "Explanation": "\"spotting the pattern of equations both are in form of ( x + c ) ^ 2 so a 1 = ( x + 4 ) ^ 2 a 2 = ( 2 x - 3 ) ^ 2 l 1 = x + 5 l 2 = 2 x - 3 p 1 = 4 ( x + 4 ) p 2 = 4 ( 2 x - 3 ) p 1 + p 2 = 32 4 ( x + 4 ) + 4 ( 2 x - 3 ) = 32 . . . . . . . . . . . . . . > x = 7 / 3 answer : d\"" + }, + { + "Answer": 900, + "Options": "a ) 700 , b ) 900 , c ) 705 , d ) none of these , e ) 506", + "Correct": "b", + "Explanation": "\"explanation : 45 / . 05 = 4500 / 5 = 900 option b\"" + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 305 , c ) 365 , d ) 405 , e ) 495", + "Correct": "a", + "Explanation": "510 , 512 , 514 , 516 , and 518 , so total 5 . hence option a ." + }, + { + "Answer": 110, + "Options": "a ) 27 , b ) 36 , c ) 29 , d ) 10 , e ) 110", + "Correct": "e", + "Explanation": "\"let the price of turban be x . thus , for one year the salary = ( 90 + x ) for 9 months he should earn 3434 ( 90 + x ) . now he gets one turban and rs . 40 . thus , 3434 ( 90 + x ) = 40 + x or 270 + 3 x = 160 + 4 x or x = 110 answer : e\"" + }, + { + "Answer": 136, + "Options": "a ) 112 , b ) 144 , c ) 136 , d ) 132 , e ) 118", + "Correct": "c", + "Explanation": "the 8 rows form an arithmetic progression with first term 10 and last 24 . avg is 17 . so 17 * 8 = 136 answer is c ." + }, + { + "Answer": 1600, + "Options": "a ) 2000 , b ) 2573 , c ) 1600 , d ) 2950 , e ) none of these", + "Correct": "c", + "Explanation": "\"solution : dividing each side by - 200 , we obtain ( - 200 x / - 200 ) = ( 1600 / - 200 ) therefore : x = - 8 check : - 200 x = 1600 ( - 200 * - 8 ) = 1600 1600 = 1600 answer : c\"" + }, + { + "Answer": 360, + "Options": "a ) 400 , b ) 360 , c ) 270 , d ) 180 , e ) 90", + "Correct": "b", + "Explanation": "total birds = 450 = 5 * other animals ( x ) or x = 90 . so , difference in birds and x = 450 - 90 = 360 . answer is b ." + }, + { + "Answer": 8, + "Options": "a ) 2 , b ) 4 , c ) 8 , d ) 12 , e ) 16", + "Correct": "c", + "Explanation": "\"16 ^ y = 4 ^ 2 y = 4 ^ 16 2 y = 16 y = 8 the answer is c .\"" + }, + { + "Answer": 285, + "Options": "a ) 285 , b ) 337 , c ) 878 , d ) 227 , e ) 291", + "Correct": "a", + "Explanation": "\"explanation : since the month begins with a sunday , so there will be five sundays in the month , required average = ( 510 * 5 + 240 * 25 ) / 30 = 8550 / 30 = 285 . answer : a\"" + }, + { + "Answer": 70, + "Options": "a ) 75 kg , b ) 50 kg , c ) 70 kg , d ) 80 kg , e ) 60 kg", + "Correct": "c", + "Explanation": "\"explanation : total increase in weight = 8 \u00e3 \u2014 2.5 = 20 if x is the weight of the new person , total increase in weight = x \u00e2 \u02c6 \u2019 50 = > 20 = x - 50 = > x = 20 + 50 = 70 answer : option c\"" + }, + { + "Answer": 16, + "Options": "a ) 12.4 , b ) 14 , c ) 16 , d ) 18.6 , e ) none of these", + "Correct": "c", + "Explanation": "explanation : sum of numbers = ( 10 \u00d7 \u00d7 15 - 26 + 36 ) = 160 correct average = 160 / 10 = 16 correct option : c" + }, + { + "Answer": 3, + "Options": "a ) s , b ) 3 s , c ) 4 s , d ) - 3 s , e ) - 4 s", + "Correct": "b", + "Explanation": "squaring on both the sides gives z ^ 2 = 6 zs - 9 s ^ 2 = z ^ 2 - 6 zs + 9 s ^ 2 = z ( z - 3 s ) - 3 s ( z - 3 s ) = ( z - 3 s ) ( z - 3 s ) = z = 3 s answer = b" + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16", + "Correct": "a", + "Explanation": "look at the below representation of the problem : steel chrome total a 2 3 40 > > no . of type a machines = 40 / 5 = 8 b 3 5 32 > > no . of type b machines = 32 / 8 = 4 so the answer is 12 i . e a . hope its clear ." + }, + { + "Answer": 20, + "Options": "a ) 32 , b ) 20 , c ) 28 , d ) 11 , e ) 18", + "Correct": "b", + "Explanation": "\"average = ( 10 + 15 + 20 + 25 + 30 ) / 5 = 100 / 5 = 20 . answer : b\"" + }, + { + "Answer": 0.5, + "Options": "a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6", + "Correct": "c", + "Explanation": "so not a vowel in set - 1 : 3 / 5 and not a vowel in ser - 2 : 5 / 6 now , 3 / 5 \u2217 5 / 6 = 12 this is for not a vowel . then for at least one vowel will be = 1 \u2212 1 / 2 = 1 / 2 answer will be c ." + }, + { + "Answer": 21, + "Options": "a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22", + "Correct": "d", + "Explanation": "\"from right 17 , from left 5 total = 17 + 5 - 1 = 21 answer : d\"" + }, + { + "Answer": 9, + "Options": "a ) 12 , b ) 9 , c ) 18 , d ) 77 , e ) 26", + "Correct": "b", + "Explanation": "\"answer : 9 option : b\"" + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 12 , c ) 16 , d ) 20 , e ) 22", + "Correct": "a", + "Explanation": "\"let original strength = y then , 40 y + 12 x 34 = ( y + 12 ) x 36 \u00e2 \u2021 \u2019 40 y + 408 = 36 y + 432 \u00e2 \u2021 \u2019 4 y = 48 \u00e2 \u02c6 \u00b4 y = 6 a\"" + }, + { + "Answer": 15, + "Options": "a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15", + "Correct": "e", + "Explanation": "\"100 - ( 100 - 85 ) - ( 100 - 75 ) - ( 100 - 85 ) - ( 100 - 70 ) = 100 - 15 - 25 - 15 - 30 = 100 - 85 = 15 answer : e\"" + }, + { + "Answer": 43, + "Options": "a ) 23 , b ) 32 , c ) 35 , d ) 43 , e ) 44", + "Correct": "d", + "Explanation": "\"let number of years taught by virginia = v number of years taught by adrienne = a number of years taught by dennis = d v + a + d = 96 v = a + 9 = > a = v - 9 v = d - 9 = > a = ( d - 9 ) - 9 = d - 18 d - 9 + d - 18 + d = 102 = > 3 d = 102 + 27 = 129 = > d = 43 answer d\"" + }, + { + "Answer": 24, + "Options": "a ) 22 , b ) 24 , c ) 28 , d ) 32 , e ) 44", + "Correct": "b", + "Explanation": "\"g ( r ) = 4 ^ 11 = 2 ^ 22 . so we have to find a product with atleast 22 2 ' s in it . in option 1 22 the total no of 2 ' s = [ 22 / 2 ] + [ 22 / 4 ] + [ 22 / 8 ] + [ 22 / 16 ] = 11 + 5 + 2 + 1 = 19 in option 2 24 the total no of 2 ' s = [ 24 / 2 ] + [ 24 / 4 ] + [ 24 / 8 ] + [ 24 / 16 ] = 12 + 6 + 3 + 1 = 22 . hence b\"" + }, + { + "Answer": 119.99999999999997, + "Options": "a ) 110 , b ) 115 , c ) 120 , d ) 125 , e ) 130", + "Correct": "c", + "Explanation": "1 / 12 + 1 / 8 + 1 / 3 + 1 / 6 = ( 2 + 3 + 8 + 4 ) / 24 = 17 / 24 let x be the number of passengers on the ship . 35 = ( 7 / 24 ) x x = 120 the answer is c ." + }, + { + "Answer": 2240, + "Options": "a ) $ 2,040 , b ) $ 2,120 , c ) $ 2,240 , d ) $ 1,920 , e ) $ 1,400", + "Correct": "c", + "Explanation": "\"in order to maximize the amount of money that the gambler kept , we should maximize # of $ 20 chips lost and minimize # of $ 100 chips lost , which means that # of $ 20 chips lost must be 2 more than # of $ 100 chips lost . so , if # of $ 20 chips lost is x then # of $ 100 chips lost should be x - 2 . now , given that total # of chips lost is 13 : x + x - 3 = 13 - - > x = 8 : 8 $ 20 chips were lost and 8 - 2 = 6 $ 100 chips were lost . total worth of chips lost is 8 * 20 + 6 * 100 = $ 760 , so the gambler kept $ 3,000 - $ 760 = $ 2,240 . answer : c .\"" + }, + { + "Answer": 32, + "Options": "a ) 30 , 10 , b ) 32 , 12 , c ) 29 , 9 , d ) 50 , 30 , e ) 20,10", + "Correct": "b", + "Explanation": "\"let their ages be x and ( x + 20 ) years . then , 5 ( x - 7 ) = ( x + 20 - 7 ) = > 4 x = 48 = > x = 12 their present ages are 32 years and 12 year . answer : b\"" + }, + { + "Answer": 69, + "Options": "a ) 65 , b ) 69 , c ) 75 , d ) 85 , e ) 90", + "Correct": "b", + "Explanation": "\"explanation : average = ( 76 + 65 + 82 + 67 + 55 ) / 5 = 375 / 5 = 69 hence average = 69 answer : b\"" + }, + { + "Answer": 68, + "Options": "a ) 69 minutes , b ) 68 minutes , c ) 58 minutes , d ) 48 minutes , e ) 67 minutes", + "Correct": "b", + "Explanation": "let the width of the smaller rectangle is 4 units then , the length of the smaller rectangle is 6 units ( that is 50 % more than the width ) now the perimeter of the rectangle is 2 ( 6 + 4 ) = 20 units so , 20 units is covered in 20 units , implies covers one unit in one minute so now coming to the larger rectangle the width = 16 units , length = 18 units , perimeter = 2 ( 16 + 18 ) 68 units thus , to cover the larger field , 68 minutes required to cover the rectangle . answer : b" + }, + { + "Answer": 6.8, + "Options": "a ) $ 6.80 , b ) $ 8.40 , c ) $ 7.70 , d ) $ 4.70 , e ) $ 3.90", + "Correct": "a", + "Explanation": "linda spent 1.20 ? 3 = $ 3.60 on notebooks the total amount of money that linda spent is equal to 3.60 + 1.50 + 1.70 = $ 6.80 correct answer a" + }, + { + "Answer": 30, + "Options": "a ) 5 % , b ) 7 % , c ) 9 % , d ) 11 % , e ) 30 %", + "Correct": "e", + "Explanation": "\"explanation : the difference of two successive amounts must be the simple interest in 1 year on the lower amount of money . s . i = 22932 / - - 17640 / - = rs . 5292 / - rate of interest = ( 5292 / 22932 ) \u00d7 ( 100 / 1 ) = > 30 % answer : option e\"" + }, + { + "Answer": 15, + "Options": "a ) 10 , b ) 15 , c ) 8 , d ) 12 , e ) 20", + "Correct": "b", + "Explanation": "\"4 n + 7 > 1 4 n > - 6 n > - ( 3 / 2 ) n > - 1.5 ( n = - 1 , 0 , 1 , 2 3 . . . . . . . . upto infinity ) from second constraint 4 n + 7 < 60 4 n < 53 n < 13 . 25 n = ( - infinity , . . . . . . . - 3 , - 2 , - 1 , 0 , 1 , 2 , . . . . . . . . . upto 13 ) combining the two - 1.5 < n < 13.25 n = 1 to 13 ( 48 integers ) and n = - 1 and 0 so 15 integers . b\"" + }, + { + "Answer": 0.2, + "Options": "a ) 0.15 , b ) 0.20 , c ) 0.25 , d ) 0.30 , e ) 0.33", + "Correct": "b", + "Explanation": "the total number of pairs r , b possible is 4 * 5 = 20 . out of these 20 pairs only 4 sum up to 9 : ( 2 , 7 ) ; ( 3 , 6 ) , ( 4 , 5 ) and ( 5 , 4 ) . the probability thus is 4 / 20 = 0.2 . answer : b ." + }, + { + "Answer": 25.01563477173233, + "Options": "a ) 15 % , b ) 20 % , c ) 25 % , d ) 60 % , e ) 80 %", + "Correct": "c", + "Explanation": "\"listed selling price of chair = 79.95 $ discounted selling price of chair = 59.95 $ discount = 79.95 - 59.95 = 20 $ % decrease in price of chair = ( 20 / 79.95 ) * 100 % = 25 % approx answer c\"" + }, + { + "Answer": 15, + "Options": "a ) 6 , b ) 9 , c ) 10 , d ) 12 , e ) 15", + "Correct": "e", + "Explanation": "this is an inverse proportional problem . . . . . . 5 pipes in 16 days ; so for 4 days , it will be = 16 x 5 / 4 = 20 so , 20 - 5 = 15 answer e" + }, + { + "Answer": 105, + "Options": "a ) a ) 31 , b ) b ) 41 , c ) c ) 106 , d ) d ) 61 , e ) e ) 71", + "Correct": "c", + "Explanation": "lcm = 105 = > 105 + 1 = 106 answer : c" + }, + { + "Answer": 127, + "Options": "a ) 121 , b ) 124 , c ) 127 , d ) 122 , e ) 129", + "Correct": "c", + "Explanation": "\"required number = h . c . f . of ( 1657 - 6 ) and ( 2037 - 5 ) = h . c . f . of 1651 and 2032 _______ 1651 ) 2032 ( 1 1651 1651 _______ 381 ) 1651 ( 4 1524 _________ 127 ) 381 ( 3 381 0 required number = 127 . answer is c .\"" + }, + { + "Answer": 1478, + "Options": "a ) 1478 , b ) 1578 , c ) 1678 , d ) 1778 , e ) 1798", + "Correct": "a", + "Explanation": "the dollar deposits are in an a . p . 1,2 , 3,4 . . . 52 with common difference 1 sum of the terms is n ( n + 1 ) / 2 i . e 52 * ( 52 + 1 ) / 2 = 52 * 53 / 2 = 1378 total deposit therefore with chiu - lihas is 100 + 1378 = 1478 $" + }, + { + "Answer": 250, + "Options": "a ) 250 , b ) 84 , c ) 40 , d ) 28 , e ) 20", + "Correct": "a", + "Explanation": "almonds : walnuts = 5 : 2 total mixture has 7 parts in a 350 pound mixture , almonds are 5 / 7 ( total mixture ) = 5 / 7 * 350 = 250 pounds answer ( a )" + }, + { + "Answer": 0.25, + "Options": "a ) 1 / 4 , b ) - 1 , c ) 5 / 4 , d ) 3 / 2 , e ) 3 / 4", + "Correct": "a", + "Explanation": "x = - 5 / 4 and y = - 3 / 2 = = > - 2 ( - 5 / 4 ) - ( 3 / 2 ) ^ 2 = 10 / 4 - 9 / 4 = 1 / 4 ans : a" + }, + { + "Answer": 0.9986095661846496, + "Options": "a ) 3252 / 3257 , b ) 3456 / 3461 , c ) 3591 / 3596 , d ) 3641 / 3656 , e ) 3453 / 3458", + "Correct": "d", + "Explanation": "\"options can be re - written as ( x - 5 ) x = > 1 - ( 5 / x ) a ) 1 - ( 5 / 3257 ) b ) 1 - ( 5 / 3461 ) c ) 1 - ( 5 / 3596 ) d ) 1 - ( 5 / 3656 ) e ) 1 - ( 5 / 3458 ) to get the largest among these second half should be the least and so denominator to be largest . hence ' d ' .\"" + }, + { + "Answer": 86, + "Options": "a ) 87 , b ) 89 , c ) 86 , d ) 93 , e ) 95", + "Correct": "c", + "Explanation": "\"total score on 3 tests = 78 * 3 = 234 jerry wants the average to be = 80 hence total score on 4 tests should be = 80 * 4 = 320 score required on the fourth test = 320 - 234 = 86 option c\"" + }, + { + "Answer": 25, + "Options": "a ) 20 , b ) 25 , c ) 30 , d ) 35 , e ) 40", + "Correct": "b", + "Explanation": "let the present age of rohan be x years then , given : x + 15 = 4 ( x - 15 ) x = 25 answer : b" + }, + { + "Answer": 2, + "Options": "a ) 8 , b ) 10 , c ) 2 , d ) 14 , e ) 16", + "Correct": "c", + "Explanation": "subhas ' s 1 hr copy page = 50 / 10 = 5 page ( subhas + prakash ) ' s 1 hr copy page = 300 / 40 = 7.5 page from above prakash ' s 1 hr copy page = 2.5 page so time taken in 30 page ' s copy = ( 5 / 2.5 ) = 2 hrs answer : c" + }, + { + "Answer": 9.420289855072461, + "Options": "a ) 19 % , b ) 15 % , c ) 25 % , d ) 40 % , e ) 9.4 %", + "Correct": "e", + "Explanation": "\"cost of food ( c ) = food consumed per student ( f ) * number of students ( n ) * price of food ( p ) originally , c = fnp when number of students decrease by 8 % , and the price of food increases by 20 % , c = f ( new ) * ( 0.92 n ) * ( 1.2 p ) = > f ( new ) = f / ( 0.92 * 1.2 ) = > f ( new ) = 0.906 f therefore the new cost of food must be 90.6 % of the old cost , or the cost of food must decrease by 9.4 % answer : e\"" + }, + { + "Answer": 450, + "Options": "a ) 250 , b ) 440 , c ) 510 , d ) 575 , e ) 449", + "Correct": "e", + "Explanation": "\"2 multiples are 102 , 104,106 , - - - - - - - - - , 994 , 996,998 it should be mentioned whether 1 and 89 are inclusive . the answer is ( 998 - 102 ) / 2 + 1 = 449 answer is e\"" + }, + { + "Answer": 197, + "Options": "a ) 128 , b ) 197 , c ) 127 , d ) 182 , e ) 091", + "Correct": "b", + "Explanation": "\"explanation : let ' n ' is the smallest number which divided by 13 and 16 leaves respective remainders of 2 and 5 . required number = ( lcm of 13 and 16 ) - ( common difference of divisors and remainders ) = ( 208 ) - ( 11 ) = 197 . answer : b\"" + }, + { + "Answer": 16, + "Options": "a ) 12 , b ) 27 , c ) 18 , d ) 16 , e ) 81", + "Correct": "d", + "Explanation": "\"( 80 / 100 ) * 40 \u00e2 \u20ac \u201c ( 4 / 5 ) * 20 32 - 16 = 16 answer : d\"" + }, + { + "Answer": 23.076923076923073, + "Options": "a ) 15 % , b ) 20 % , c ) 23 % , d ) 30 % , e ) none", + "Correct": "c", + "Explanation": "\"sol . let the original consumption = 100 kg and new consumption = x kg . so , 100 x 10 = x \u00d7 13 = x = 77 kg . \u2234 reduction in consumption = 23 % . answer c\"" + }, + { + "Answer": 2, + "Options": "a ) 3 / 10 , b ) 2 , c ) 1 / 2 , d ) 2 / 3 , e ) 6 / 5", + "Correct": "b", + "Explanation": "\"say , the tree grows by x feet every year . then , 4 + 6 x = ( 1 + 1 / 3 ) ( 4 + 4 x ) or , x = 2 answer b\"" + }, + { + "Answer": 9, + "Options": "a ) 17 : 3 , b ) 9 : 1 , c ) 3 : 17 , d ) 5 : 3 , e ) 11 : 2", + "Correct": "b", + "Explanation": "\"he 20 litre mixture contains milk and water in the ratio of 3 : 2 . therefore , there will be 12 litres of milk in the mixture and 8 litres of water in the mixture . step 1 . when 10 litres of the mixture is removed , 6 litres of milk is removed and 4 litres of water is removed . therefore , there will be 6 litres of milk and 4 litres of water left in the container . it is then replaced with pure milk of 10 litres . now the container will have 16 litres of milk and 4 litres of water . step 2 . when 10 litres of the new mixture is removed , 8 litres of milk and 2 litres of water is removed . the container will have 8 litres of milk and 2 litres of water in it . now 10 litres of pure milk is added . therefore , the container will have 18 litres of milk and 2 litres of water in it at the end of the second step . therefore , the ratio of milk and water is 18 : 2 or 9 : 1 . shortcut . we are essentially replacing water in the mixture with pure milk . let w _ o be the amount of water in the mixture originally = 8 litres . let w _ r be the amount of water in the mixture after the replacements have taken place . then , { w _ r } / { w _ o } = ( 1 - r / m ) ^ n where r is the amount of the mixture replaced by milk in each of the steps , m is the total volume of the mixture and n is the number of times the cycle is repeated . hence , { w _ r } / { w _ o } \u00a0 = ( 1 / 2 ) ^ 2 \u00a0 = 1 / 4 therefore w , w _ r \u00a0 = { w _ o } / 4 = 8 / 4 \u00a0 = 2 litres . b\"" + }, + { + "Answer": 87.37864077669903, + "Options": "a ) 68.99 % , b ) 66.55 % , c ) 91.23 % , d ) 77.77 % , e ) 87.37 %", + "Correct": "e", + "Explanation": "\"say a 100 families existed in 1994 then the number of families owning a computer in 1994 - 60 number of families owning computer in 1998 = 60 * 150 / 100 = 90 number of families in 1998 = 103 the percentage = 90 / 103 * 100 = 87.37 % . answer : e\"" + }, + { + "Answer": 2.650793650793651, + "Options": "a ) 2.65 , b ) 145 / 63 , c ) 155 / 63 , d ) 125 / 63 , e ) 185 / 63", + "Correct": "a", + "Explanation": "( \u221a 1.21 ) / ( \u221a 0.81 ) + ( \u221a 1.00 ) / ( \u221a 0.49 ) 11 / 9 + 10 / 7 = > 2.65 answer is a" + }, + { + "Answer": 402.11480362537765, + "Options": "a ) 333 , b ) 383 , c ) 402 , d ) 433 , e ) 483", + "Correct": "c", + "Explanation": "after 1 st month : ( 1000 ) ( 1.1 ) - x = 1100 - x after 2 nd month : ( 1100 - x ) ( 1.1 ) - x = 1210 - 2.21 x after 3 rd month : ( 1210 - 2.21 x ) ( 1.1 ) - x = 1331 - 3.31 x now , the amount after the last payment in 3 rd month must bring the total to 0 . hence : 1331 - 3.31 x = 0 x = 1331 / 3.31 = 402.11 the answer is c" + }, + { + "Answer": 8, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 6 , e ) 5", + "Correct": "b", + "Explanation": "2520 = 2 ^ 3 * 3 ^ 2 * 5 * 7 here , 7 is the highest prime , so find the no . of 7 ' s in 50 ! only no . of 7 ' s in 50 ! = [ 50 / 7 ] + [ 50 / 7 ^ 2 ] = 7 + 1 = 8 answer : b" + }, + { + "Answer": 48, + "Options": "a ) a ) 32 , b ) b ) 35 , c ) c ) 39 , d ) d ) 40 , e ) e ) 48", + "Correct": "e", + "Explanation": "\"x \u2013 3 / 8 x = 30 x = 48 answer : e\"" + }, + { + "Answer": 83, + "Options": "a ) 80 kg , b ) 83 kg , c ) 70 kg , d ) 75 kg , e ) 85 kg", + "Correct": "b", + "Explanation": "since the average has increased by 2.5 kg , the weight of the man who stepped in must be equal to 58 + 10 x 2.5 58 + 25 = 83 kg ans : ' b '" + }, + { + "Answer": 4, + "Options": "a ) 4 , b ) 2 , c ) 0 , d ) \u2212 2 , e ) \u2212 4", + "Correct": "a", + "Explanation": "\"slope = rise / run = 10 / 20 = 1 / 2 the equation of the line is y = ( 1 / 2 ) x + b 3 = ( 1 / 2 ) ( 10 ) + b b = - 2 the equation of the line is y = ( 1 / 2 ) x - 2 to find the x - intercept , let y = 0 : 0 = ( 1 / 2 ) x - 2 x = 4 the answer is a .\"" + }, + { + "Answer": 250, + "Options": "a ) $ 250 , b ) $ 275 , c ) $ 510 , d ) $ 1,250 , e ) $ 2,550", + "Correct": "a", + "Explanation": "\"the volume of each box is 20 * 20 * 12 = 4800 cubic inches . number of boxes = 2 , 400,000 / 4800 = 500 boxes total cost = 500 \u00d7 $ 0.5 = $ 250 the answer is a .\"" + }, + { + "Answer": 36, + "Options": "a ) 19 , b ) 29 , c ) 36 , d ) 49 , e ) 59", + "Correct": "c", + "Explanation": "\"let the average after 17 th inning = x then average after 16 th inning = ( x - 3 ) therefore 16 ( x - 3 ) + 84 = 17 x therefore x = 36 answer : c\"" + }, + { + "Answer": 41, + "Options": "a ) 41 , b ) 910 , c ) 1001 , d ) 1911 , e ) none", + "Correct": "a", + "Explanation": "\"olution required number of students . = h . c . f of 451 and 410 . \u00e2 \u20ac \u00b9 = \u00e2 \u20ac \u00ba 41 . answer a\"" + }, + { + "Answer": 4, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "d", + "Explanation": "\"@ ( n ) = 5 n - n we need to find the largest positive integer such that 5 n - n < 18 . then 4 n < 18 and n < 4.5 the largest possible integer is n = 4 . the answer is d .\"" + }, + { + "Answer": 1999.5151515151515, + "Options": "a ) 2006 , b ) 2007 , c ) 2008 , d ) 2009 , e ) 2010", + "Correct": "c", + "Explanation": "\"the price of commodity x increases 25 cents each year relative to commodity y . the price difference is $ 2.10 and commodity x needs to be 35 cents less than commodity y . $ 1.75 / 25 cents = 7 years the answer is 2001 + 7 years = 2008 . the answer is c .\"" + }, + { + "Answer": 14, + "Options": "a ) 5 , b ) 14 , c ) 10 , d ) 20 , e ) 30", + "Correct": "b", + "Explanation": "what is the greatest positive integer x such that 3 ^ x is a factor of 9 ^ 7 ? 9 ^ 7 = ( 3 ^ 2 ) ^ 7 = 3 ^ 14 b . 14" + }, + { + "Answer": 21, + "Options": "a ) 11 , b ) 21 , c ) 31 , d ) 61 , e ) 51", + "Correct": "b", + "Explanation": "\"look at the below representation of the problem : steel chrome total a 3 2 50 > > no . of type a machines = 50 / 5 = 10 b 2 4 66 > > no . of type b machines = 66 / 6 = 11 so the answer is 21 i . e b . hope its clear .\"" + }, + { + "Answer": 64, + "Options": "a ) 42 , b ) 43 , c ) 44 , d ) 64 , e ) 46", + "Correct": "d", + "Explanation": "\"let \u2018 x \u2019 be the average score after 12 th innings \u21d2 12 x = 11 \u00d7 ( x \u2013 1 ) + 75 \u2234 x = 64 answer d\"" + }, + { + "Answer": 8.000000000000007, + "Options": "a ) 6.66 % , b ) 8 % , c ) 10 % , d ) 12 % , e ) 12.5 %", + "Correct": "b", + "Explanation": "\"let price of original price of gasoline = 10 $ and let original consumption of gasoline = 10 amount spend on gasoline originally = 10 * 10 = 100 $ the price of gasoline increases by 25 % and ron intends to spend only 15 % more on gasoline increased price of gasoline = 12.5 $ now ron intends to spend on gasoline = 1.15 * 100 = 115 $ consumption of gasoline needs to be = 115 / 12.5 = 1150 / 125 = 46 / 5 = 9.2 reduction in consumption of gasoline = 10 - 9.2 = . 8 % reduction in consumption of gasoline = . 8 / 10 * 100 % = 8 % answer b\"" + }, + { + "Answer": 0.016833333333333332, + "Options": "a ) 1.012526333 , b ) 0.012625333 , c ) 0.125263333 , d ) 0.126253333 , e ) 0.016833333", + "Correct": "e", + "Explanation": "\"25.25 / 2000 = 2525 / 200000 = 0.016833333 answer : e\"" + }, + { + "Answer": 156, + "Options": "a ) 131 , b ) 135 , c ) 156 , d ) 177 , e ) 188", + "Correct": "c", + "Explanation": "\"lets say j is the weight of jack and s is the wt of his sister . if he loses 20 pounds , he s twice as heavy as his sister . j - 20 = 2 * s also , together they weight 224 pounds j + s = 224 solvong the 2 equation , we get j = 156 pounds ! c\"" + }, + { + "Answer": 73, + "Options": "a ) 40 , b ) 50 , c ) 73 , d ) 70 , e ) 80", + "Correct": "c", + "Explanation": "\"according to order of operations , inner brackets first . hence | 7 - 8 ( 3 - 12 ) | - | 5 - 11 | = | 7 - 8 * ( - 9 ) | - | 5 - 11 | according to order of operations , multiplication within absolute value signs ( which may be considered as brackets when it comes to order of operations ) next . hence = | 7 + 72 | - | 5 - 11 | = | 79 | - | - 6 | = 79 - 6 = 73 correct answer c ) 73\"" + }, + { + "Answer": 50, + "Options": "a ) 0 , b ) - 100 , c ) - 50 , d ) 50 , e ) 100", + "Correct": "d", + "Explanation": "there will be two cases x - 25 = 50 and x - 25 = - 50 solve for x = > x = 50 + 25 = > x = 75 or x = - 50 + 25 = > x = - 25 the sum of both values will be 75 + - 25 = 50 answer is d" + }, + { + "Answer": 117, + "Options": "a ) 1 , b ) 117 , c ) 116 , d ) equal to their h . c . f , e ) can not be calculated", + "Correct": "b", + "Explanation": "\"h . c . f of co - prime numbers is 1 . so , l . c . m = 117 / 1 = 117 . answer : b\"" + }, + { + "Answer": 48, + "Options": "a ) 9 , b ) 11 , c ) 24 , d ) 48 , e ) 54", + "Correct": "d", + "Explanation": "terry can pick one lunch salad bar . . . . we can choose lettuce 2 c 1 , tomatoes - 3 c 1 and olives - 4 c 1 . . . two types of soups , if he picks one then 2 c 1 ways . terry decided to have the combo : soup + salad . . . hmmm . . . using the above information , we get ( 2 c 1 * 2 c 1 * 3 c 1 * 4 c 1 ) = 48 . . ans option d is correct answer . ." + }, + { + "Answer": 30, + "Options": "a ) 72 , b ) 43 , c ) 91 , d ) 40 , e ) 30", + "Correct": "e", + "Explanation": "\"( x ^ n + 1 ) will be divisible by ( x + 1 ) only when n is odd ; ( 31 ^ 31 + 1 ) will be divisible by ( 31 + 1 ) ; ( 31 ^ 31 + 1 ) + 30 when divided by will give 30 as remainder . correct option : e\"" + }, + { + "Answer": 3786, + "Options": "a ) 400 , b ) 5550 , c ) 6922 , d ) 3786 , e ) 5553", + "Correct": "d", + "Explanation": "use following formulae for such problems : sum of evenly spaced integers = ( # of integers ) * ( mean of integers ) # of integers = [ ( last - first ) / 2 ] + 1 mean of integers = ( last + first ) / 2 in above problem : # of integers = [ ( 111 - 1 ) / 2 ] + 1 = 56 and [ ( 50 - 2 ) / 2 ] + 1 = 25 mean of integers = ( 111 + 1 ) / 2 = 56 and ( 50 + 2 ) / 2 = 26 sum of integers = ( 56 * 56 ) = 3136 and ( 25 * 26 ) = 650 thus their sum ( m + t ) = 3786 answer : d" + }, + { + "Answer": 3086, + "Options": "a ) 3066 , b ) 3586 , c ) 3086 , d ) 3968 , e ) 3286", + "Correct": "c", + "Explanation": "\"explanation : 36 * 85 + 26 = 3086 answer : c\"" + }, + { + "Answer": 72.22222222222221, + "Options": "a ) 8 % , b ) 15 % , c ) 45 % , d ) 52 % , e ) 72 %", + "Correct": "e", + "Explanation": "\"solution : this is a percent decrease problem . we will use the formula : percent change = ( new \u2013 old ) / old x 100 to calculate the final answer . we first set up the ratios of royalties to sales . the first ratio will be for the first 20 million in sales , and the second ratio will be for the next 108 million in sales . because all of the sales are in millions , we do not have to express all the trailing zeros in our ratios . first 20 million royalties / sales = 6 / 20 = 3 / 10 next 108 million royalties / sales = 9 / 108 = 1 / 12 because each ratio is not an easy number to use , we can simplify each one by multiplying each by the lcm of the two denominators , which is 60 . keep in mind that we are able to do this only because our answer choices are expressed in percents . first 20 million royalties / sales = ( 6 / 20 ) x 60 = 18 next 108 million royalties / sales = 9 / 108 = ( 1 / 12 ) x 60 = 5 we can plug 18 and 5 into our percent change formula : ( new \u2013 old ) / old x 100 [ ( 5 \u2013 18 ) / 18 ] x 100 - 650 / 9 x 100 at this point we can stop and consider the answer choices . since we know that 650 / 9 is just a bit less than \u00bd , we know that - 650 / 9 x 100 is about a 72 % decrease . answer e .\"" + }, + { + "Answer": 898.8, + "Options": "a ) 347.8 , b ) 987.8 , c ) 877.8 , d ) 898.8 , e ) 667.4", + "Correct": "d", + "Explanation": "\"let the costs of each kg of mangos and each kg of rice be $ a and $ r respectively . 10 a = 24 r and 6 * 21 = 2 r a = 12 / 5 r and r = 63 a = 151.2 required total cost = 4 * 151.2 + 3 * 63 + 5 * 21 = 604.8 + 189 + 105 = $ 898.80 d\"" + }, + { + "Answer": 1040, + "Options": "a ) 540 , b ) 1040 , c ) 2040 , d ) 1030 , e ) 15,30", + "Correct": "b", + "Explanation": "if f is age of father and s is age of son f = 4 s f + 20 = 2 * ( s + 20 ) 4 s + 20 = 2 s + 40 2 s = 20 s = 10 f = 40 answer : b" + }, + { + "Answer": 54, + "Options": "a ) 24 , b ) 30 , c ) 48 , d ) 54 , e ) 72", + "Correct": "d", + "Explanation": "210 is the answer when 2 , 3 , 5 and 7 are multiplied . 210 can also be arrive using 56 and 7 and 1 , 5 , 6 and 7 . so sum of arrangements of 2357 , 567 and 1567 . this translates to 4 ! + 3 ! + 4 ! , this equals to 24 + 6 + 24 = 54 , d is the answer ." + }, + { + "Answer": 1.0119999999999998, + "Options": "a ) 1.004 , b ) 1.006 , c ) 1.008 , d ) 1.012 , e ) 1.016", + "Correct": "d", + "Explanation": "as compared to 1 , 0.003 is a very small quantity . thus , we can write ( 1 + 0.003 ) ^ 4 is nearly equal to ( 1 + 4 * 0.003 ) = 1.012 . as the question asks for approximation to three decimal places , the further terms will anyways not come into picture . d ." + }, + { + "Answer": 900, + "Options": "a ) $ 900 , b ) $ 800 , c ) $ 850 , d ) $ 950 , e ) $ 920", + "Correct": "a", + "Explanation": "answer = a the total cost of the trip ( $ 13500.00 ) divided by 15 equals $ 900.00 ." + }, + { + "Answer": 199, + "Options": "a ) 179 , b ) 367 , c ) 269 , d ) 177 , e ) 199", + "Correct": "e", + "Explanation": "\"explanation : total runs scored by the batsman = 60 * 46 = 2760 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2760 \u00e2 \u20ac \u201c 2552 = 208 runs . let the highest score be x , hence the lowest score = x \u00e2 \u20ac \u201c 190 x + ( x - 190 ) = 208 2 x = 398 x = 199 runs answer : e\"" + }, + { + "Answer": 59.99999999999999, + "Options": "a ) 45 , b ) 49 , c ) 52 , d ) 60 , e ) 74", + "Correct": "d", + "Explanation": "let number of boys = x then number of girls = ( 100 - x ) 3.60 x + 2.40 ( 100 - x ) = 312 \u00a1 \u00ea 1.2 x = 312 - 240 = 72 \u00a1 \u00ea x = 60 answer : d" + }, + { + "Answer": 60, + "Options": "a ) 25 , b ) 60 , c ) 90 , d ) 140 , e ) it can not be determined from the information given .", + "Correct": "b", + "Explanation": "- ( a + b = 60 ) b + c = 120 c - a = 60 b . 60" + }, + { + "Answer": 100, + "Options": "a ) 25 % , b ) 50 % , c ) 75 % , d ) 100 % , e ) 200 %", + "Correct": "d", + "Explanation": "mean of f is ( - 4 - 1 + 0 + 6 + 9 ) / 5 = 2 ; in order the increase to be minimal we should replace two smallest elements of f , which are - 4 and - 1 , with two smallest primes , which are 2 and 3 . hence our new set will be { 2 , 3 , 0 , 6 , 9 } - - > new mean is ( 2 + 3 + 0 + 6 + 9 ) / 5 = 4 . percent increase = ( 4 - 2 ) / 2 * 100 = 100 % . answer : d ." + }, + { + "Answer": 0.5, + "Options": "a ) 3 / 10 , b ) 2 / 5 , c ) 1 / 2 , d ) 2 / 3 , e ) 6 / 5", + "Correct": "c", + "Explanation": "\"say , the tree grows by x feet every year . then , 4 + 6 x = ( 1 + 1 / 6 ) ( 4 + 4 x ) or , x = 1 / 2 answer c\"" + }, + { + "Answer": 0.6923076923076923, + "Options": "a ) 9 / 13 , b ) 1 / 6 , c ) 1 / 3 , d ) 4 / 9 , e ) 5 / 9", + "Correct": "a", + "Explanation": "her tips were 9 / 4 of her salary . let ' s say her salary = $ 4 this mean her tips = ( 9 / 4 ) ( $ 4 ) = $ 9 so , her total income = $ 4 + $ 9 = $ 13 what fraction of her income for the week came from tips $ 9 $ 13 = 9 / 13 = a" + }, + { + "Answer": 624877405, + "Options": "a ) 724533811 , b ) 625127481 , c ) 545463251 , d ) 725117481 , e ) 677899932", + "Correct": "b", + "Explanation": "\"62519 x 9999 = 62519 x ( 10000 - 1 ) = 62519 x 10000 - 62519 x 1 = 625190000 - 62519 = 625127481 b\"" + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) 32 , c ) 22 , d ) 15 , e ) 20", + "Correct": "a", + "Explanation": "number of pieces = italian sausage \u00f7 2 / 3 of an inch = 8 \u00f7 2 / 3 = 8 / 1 \u00f7 2 / 3 = 8 / 1 * 3 / 2 = 24 / 2 = 12 . answer is a ." + }, + { + "Answer": 166, + "Options": "a ) a ) 145 , b ) b ) 148 , c ) c ) 150 , d ) d ) 153 , e ) e ) 166", + "Correct": "e", + "Explanation": "\"d = d * q + r d = 20 * 8 + 6 d = 160 + 6 d = 166 answer : e\"" + }, + { + "Answer": 1.9832, + "Options": "a ) 1.9732 , b ) 1.0025 , c ) 1.5693 , d ) 1.0266 , e ) none", + "Correct": "a", + "Explanation": "\"solution sum of decimals places = ( 2 + 2 ) = 4 . therefore , = 2.68 \u00d7 . 74 = 1.9732 answer a\"" + }, + { + "Answer": 1099.999999999999, + "Options": "a ) $ 770 , b ) $ 660 , c ) $ 700 , d ) $ 1100 , e ) $ 840", + "Correct": "d", + "Explanation": "\"let the original purchase price be x so original selling price at 10 % profit = 1.1 x if product is purchased at 10 % less of original = 0.9 x profit of 30 % on this price = 1.3 ( 0.9 x ) he would have received $ 70 more in second scenario = > 1.3 ( 0.9 x ) - 1.1 x = 70 = > 0.07 x = 70 = > x = $ 1000 original purchase price = $ 1000 hence , original selling price ( at 10 % of profit ) = 1.1 ( 1000 ) = $ 1100 option d\"" + }, + { + "Answer": 1, + "Options": "a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1", + "Correct": "e", + "Explanation": "3 / 5 of the 50 pizzas cooked on saturday = 30 pizzas 3 / 5 of the remaining pizzas on sunday = 12 pizzas we ' re left with ( 50 - 30 - 12 ) = 8 pizzas for the remaining 3 days . the prompt tells us that each day has fewer pizzas than the day before it , so we ca n ' t have duplicate numbers . m t w 5 2 1 = 8 w = 1 e" + }, + { + "Answer": 80, + "Options": "a ) 60 , b ) 80 , c ) 40 , d ) 120 , e ) 160", + "Correct": "b", + "Explanation": "\"explanatory answer let the original number be x . let a be the value obtained when x is increased by 12.5 % . therefore , a = x + 12.5 % of x let b be the value obtained when x is decreased by 25 % . therefore , b = x - 25 % of x the question states that a - b = 30 i . e . , x + 12.5 % of x - ( x - 25 % of x ) = 30 x + 12.5 % of x - x + 25 % of x = 30 37.5 % of x = 30 x = 30 / 37.5 * 100 = 80 the correct choice is ( b )\"" + }, + { + "Answer": 40, + "Options": "a ) a ) 40 % , b ) b ) 10 % , c ) c ) . 4 % , d ) d ) 50 % , e ) e ) 12 %", + "Correct": "a", + "Explanation": "ratio of boys to total attendance ( 2 / 7 ) ratio of girls to total attendance ( 5 / 7 ) percentage increase is ( difference / initial quantity ) * 100 ( 2 / 7 ) / ( 5 / 7 ) * 100 = 40 % correct answer is a" + }, + { + "Answer": 35, + "Options": "a ) 20 , b ) 21 , c ) 35 , d ) 23 , e ) 24", + "Correct": "c", + "Explanation": "\"solution let the toatl number of workers be x . then 8000 x = ( 16000 x 7 ) + 6000 ( x - 7 ) x = 35 . answer c\"" + }, + { + "Answer": 0.5833333333333333, + "Options": "a ) 7 / 12 , b ) 1 / 6 , c ) 1 / 8 , d ) 5 / 17 , e ) 12 / 7", + "Correct": "a", + "Explanation": "to sum 1 / 3 and 1 / 4 multiply both sides by 12 12 * n = 12 * 1 / 3 + 12 * 1 / 4 12 * n = 4 + 3 n = 7 / 12 ans : a" + }, + { + "Answer": 6.0181818181818185, + "Options": "a ) 5 , b ) 6 , c ) 9 , d ) 10 , e ) 11", + "Correct": "b", + "Explanation": "\"550 = 10 * 55 1100 = 20 * 55 the even multiples are 55 multiplied by 10 , 12 , 14 , 16 , 18 , and 20 for a total of 6 . the answer is b .\"" + }, + { + "Answer": 0.012625, + "Options": "a ) 1.012526 , b ) 0.012625 , c ) 0.12526 , d ) 0.12625 , e ) 0.12725", + "Correct": "b", + "Explanation": "\"25.25 / 2000 = 2525 / 200000 = 0.012625 answer : b\"" + }, + { + "Answer": 182, + "Options": "a ) $ 182 , b ) $ 191 , c ) $ 200 , d ) $ 209 , e ) $ 219", + "Correct": "a", + "Explanation": "\"given the foregoing discussion , it may be obvious now the trap - mistake answer is ( c ) . even if you can \u2019 t remember the correct thing to do , at the very least , learn to spot the trap ! the multiplier for a 30 % increases is 1 + 0.30 = 1.3 , and the multiplier for a 30 % decrease is 1 \u2013 0.30 = 0.70 , so the combined change is 1.3 * 0.7 = 0.91 , 91 % percent of the original , or a 9 % decreases . now , multiply $ 200 * 0.91 = $ 182 . answer = ( a ) .\"" + }, + { + "Answer": 4, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "d", + "Explanation": "\"xy = 4 as x + y = 2 x 2 y 3 + y 2 x 3 = 32 x 2 y 2 ( y + x ) = 32 substituting x + y x 2 y 2 = 16 xy = 4 answer : d\"" + }, + { + "Answer": 11.999999999999986, + "Options": "a ) 10 , b ) 12 , c ) 37 , d ) 29 , e ) 22", + "Correct": "b", + "Explanation": "explanation : let the original price be rs . 100 . decreased by 20 % = 80 then increased 10 % on rs 80 = 80 + 8 = 88 net change in price = 100 - 88 = 12 answer : b" + }, + { + "Answer": 1584, + "Options": "a ) 4038 , b ) 8076 , c ) 9691.2 , d ) 1584 , e ) 1625", + "Correct": "d", + "Explanation": "\"\u2235 amount , he have spent in 1 month on clothes transport = amount spent on saving per month \u2235 amount , spent on clothes and transport = 19008 \u2044 12 = 1584 answer d\"" + }, + { + "Answer": 4, + "Options": "a ) 4 , b ) 10 , c ) 12 , d ) 14 , e ) 15", + "Correct": "a", + "Explanation": "\"explanation : = > 3 ( 2 x + 9 ) = 51 = > 2 x + 9 = 17 = > x = 4 answer : option a\"" + }, + { + "Answer": 2197, + "Options": "a ) 2107 , b ) 2197 , c ) 2187 , d ) 2177 , e ) 2167", + "Correct": "b", + "Explanation": "explanation : expenditure = 1000 x 1.3 x 1.3 x 1.3 = 2197 answer : option b" + }, + { + "Answer": 1.5, + "Options": "a ) 1 / 2 , b ) 1 , c ) 2 , d ) 3 / 2 , e ) 4", + "Correct": "d", + "Explanation": "since ( m , n ) and ( m + 2 , n + k ) are two points on the line with the equation x = 2 y + 5 they should satisfy m = 2 n + 5 and m + 3 = 2 * ( n + k ) + 5 . by 1 st equation we have m - 2 n = 5 and by 2 nd equation m - 2 n = 2 k + 2 - - - > 5 = 2 k + 2 - - - > k = 3 / 2 . the answer is , therefore , ( d ) ." + }, + { + "Answer": 384, + "Options": "a ) 384 , b ) 350 , c ) 400 , d ) 200 , e ) 250", + "Correct": "a", + "Explanation": "the product of 4 consecutive numbers is always divisible by 4 ! . since , we have 4 even numbers , we have an additional 2 available with each number . now , using both the facts , we can say that the product of 4 consecutive even numbers is always divisible by , 2 ^ 4 * 4 ! 16 * 24 = 384 answer a" + }, + { + "Answer": 6250, + "Options": "a ) 1250 , b ) 6250 , c ) 600 , d ) 7500 , e ) 375", + "Correct": "b", + "Explanation": "\"max no . of crates = 5 . max weight = 1250 kg max . weight carried = 5 * 1250 = 6250 kg = b\"" + }, + { + "Answer": 64, + "Options": "a ) 27 , b ) 64 , c ) 45 , d ) 72 , e ) 18", + "Correct": "b", + "Explanation": "\"ages of p and mi = 3 x : 5 x ages of mi and mo = 3 x : 5 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 25 x sum = 49 x = 196 x = 4 difference if ages of pa and mo = 25 x - 9 x = 16 x = 16 * 4 = 64 answer b\"" + }, + { + "Answer": 355, + "Options": "a ) y = 350 , b ) y = 353 , c ) y = 354 , d ) y = 356 , e ) y = 357", + "Correct": "b", + "Explanation": "\"focus on the points where the number of digits in squares change : 1 , 2 , 3 - single digit squares . first 2 digit number is 10 . 4 , 5 , . . . 9 - two digit squares . to get 9 , the last number with two digit square , think that first 3 digit number is 100 which is 10 ^ 2 . so 9 ^ 2 must be the last 2 digit square . 10 , 11 , 12 , . . . 31 - three digit squares . to get 31 , think of 1000 - the first 4 digit number . it is not a perfect square but 900 is 30 ^ 2 . 32 ^ 2 = 2 ^ 10 = 1024 , the first 4 digit square . 32 - 99 - four digit squares . to get 99 , think of 10,000 - the first 5 digit number which is 100 ^ 2 . so number of digits in s ( 99 ) = 3 * 1 + 6 * 2 + 22 * 3 + 68 * 4 = 3 + 12 + 66 + 272 = 353 . b\"" + }, + { + "Answer": 9, + "Options": "a ) 9 miles , b ) 10 miles , c ) 11 miles , d ) 12 miles , e ) 13 miles", + "Correct": "a", + "Explanation": "the girls ran 34 + 20 = 54 laps . 54 x 1 / 6 = 54 / 6 , which reduces to 9 . the girls ran 9 miles correct answer a" + }, + { + "Answer": 1, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "b", + "Explanation": "50 ! / 2520 ^ n 2520 - > 2 ^ 3 * 3 ^ 2 * 5 ^ 1 * 7 ^ 1 here 7 is the largest prime factor . . . so in order to find the minimum value of ` ` n ' ' , it is enough to find the minimum power of ` ` 7 ' ' . . . nd for maximum value of ` ` n ' ' , find max power of 7 . . . for max . value of n , find 50 / 7 ^ 1 + 50 / 7 ^ 2 = 7 + 1 = 8 [ quotient only ] max . value of n which is perfectly divisible by 2520 ^ n is ( 8 ) min . value is 1 max value : 8 min value : 1 answer : b" + }, + { + "Answer": 15, + "Options": "a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15", + "Correct": "e", + "Explanation": "given , fog + fog + fog + fog = 1464 4 ( fog ) = 1464 = > fog = 366 face value of f is : 3 face value of o is : 6 face value of g is : 6 so f + o + g = 3 + 6 + 6 = 15 answer : e" + }, + { + "Answer": 0.33333333333333337, + "Options": "a ) 1 / 4 , b ) 1 / 3 , c ) 3 / 4 , d ) 1 , e ) 5 / 4", + "Correct": "b", + "Explanation": "\"min value of a / b will be when b is highest and a is lowest - - - > a = 40 and b = 60 so , a / b = 2 / 3 max value of a / b will be when b is lowest and a is highest - - - > a = 50 and b = 50 so , a / b = 1 range is 1 - ( 2 / 3 ) = 1 / 3 . answer should be b .\"" + }, + { + "Answer": 165, + "Options": "a ) 99 , b ) 18 , c ) 165 , d ) 10 , e ) 15", + "Correct": "c", + "Explanation": "50 * 33 / 2 = 5 / 2 * 2 * x = > x = 165 answer : c" + }, + { + "Answer": 672, + "Options": "a ) 784 , b ) 672 , c ) 492 , d ) 372 , e ) 300", + "Correct": "b", + "Explanation": "\"9 pages from 1 to 9 will require 9 digits . 90 pages from 10 to 99 will require 90 * 2 = 180 digits . 260 - ( 90 + 9 ) = 161 pages will require 161 * 3 = 483 digits . the total number of digits is 9 + 180 + 483 = 672 . the answer is b .\"" + }, + { + "Answer": 20, + "Options": "a ) 25 , b ) 30 , c ) 20 , d ) 45 , e ) 90", + "Correct": "c", + "Explanation": "\"number of pens = 1340 number of pencils = 1280 required number of students = h . c . f . of 1340 and 1280 = 20 answer is c\"" + }, + { + "Answer": 2, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "c", + "Explanation": "\"n = 18 k + 10 2 n = 2 ( 18 k + 10 ) = 4 k * 9 + 20 = 4 k * 9 + 2 * 9 + 2 = 9 j + 2 the answer is c .\"" + }, + { + "Answer": 135, + "Options": "a ) 65 , b ) 66 , c ) 67 , d ) 131 , e ) 134", + "Correct": "e", + "Explanation": "\"the answer to the question is indeed e . the problem with above solutions is that they do not consider words like aa , bb , . . . the number of 1 letter words ( x ) that can be made from 67 letters is 67 ; the number of 2 letter words ( xx ) that can be made from 67 letters is 67 * 67 , since each x can take 67 values . total : 67 + 67 * 67 . similarly : the number of 1 letter words ( x ) that can be made from 66 letters is 66 ; the number of 2 letter words ( xx ) that can be made from 66 letters is 66 * 66 , since each x can take 66 values . total : 66 + 66 * 66 . the difference is ( 67 + 67 * 67 ) - ( 66 + 66 * 66 ) = 134 . answer : e .\"" + }, + { + "Answer": 200, + "Options": "a ) $ 100 , b ) $ 150 , c ) $ 125 , d ) $ 200 , e ) $ 250", + "Correct": "d", + "Explanation": "\"a : ( b + c ) = 2 : 3 a ' s share = 500 * 2 / 5 = $ 200 answer is d\"" + }, + { + "Answer": 1859, + "Options": "a ) 1859 , b ) 2999 , c ) 2834 , d ) 2777 , e ) 2991", + "Correct": "a", + "Explanation": "\"let the total number of votes polled in the election be 100 k . number of valid votes = 100 k - 20 % ( 100 k ) = 80 k let the number of votes polled in favour of a and b be a and b respectively . a - b = 15 % ( 100 k ) = > a = b + 15 k = > a + b = b + 15 k + b now , 2 b + 15 k = 80 k and hence b = 32.5 k it is given that 100 k = 5720 32.5 k = 32.5 k / 100 k * 85720 = 1859 the number of valid votes polled in favour of b is 1859 . answer : a\"" + }, + { + "Answer": 50, + "Options": "a ) 30 , b ) 20 , c ) 15 , d ) 44 , e ) 50", + "Correct": "e", + "Explanation": "given expression = ( 18 - 3.0 ) / 0.3 = 15 / 0.3 = 150 / 3 = 50 answer is e ." + }, + { + "Answer": 90, + "Options": "a ) 72 , b ) 90 , c ) 124 , d ) 132 , e ) 140", + "Correct": "b", + "Explanation": "\"we see that h will be a maximum h = 150 when t - 2 = 0 , that is when t = 2 . at t = 4 , h = - 15 ( 4 - 2 ) ^ 2 + 150 = - 15 ( 4 ) + 150 = 90 the answer is b .\"" + }, + { + "Answer": 56.25, + "Options": "a ) 56.25 , b ) 60 , c ) 52.5 , d ) 5.25 , e ) none of these", + "Correct": "a", + "Explanation": "a + 10 d = 5.25 , a + 6 d = 3.25 , 4 d = 2 , d = \u00bd a + 5 = 5.25 , a = 0.25 = \u00bc , s 15 = 15 / 2 ( 2 * \u00bc + 14 * \u00bd ) = 15 / 2 ( 1 / 2 + 14 / 2 ) = 15 / 2 * 15 / 2 = 225 / 4 = 56.25 answer : a" + }, + { + "Answer": 58.75, + "Options": "a ) 52.5 , b ) 52.9 , c ) 52.1 , d ) 58.75 , e ) 42.5", + "Correct": "d", + "Explanation": "\"sum of the marks for the class of 30 students = 30 * 40 = 1200 sum of the marks for the class of 50 students = 50 * 70 = 3500 sum of the marks for the class of 80 students = 1200 + 3500 = 4700 average marks of all the students = 4700 / 80 = 58.75 answer : d\"" + }, + { + "Answer": 710, + "Options": "a ) $ 430 , b ) $ 620 , c ) $ 650 , d ) $ 680 , e ) $ 710", + "Correct": "e", + "Explanation": "\"for 100 - 30 - 20 = 50 pages only cost is 5 $ per page for the first time page is typed - 50 * 5 = 250 $ ; for 30 pages the cost is : first time 5 $ + 3 $ of the first revision - 30 * ( 5 + 3 ) = 240 $ ; for 20 pages the cost is : first time 5 $ + 3 $ of the first revision + 3 $ of the second revision - 20 ( 5 + 3 + 3 ) = 220 $ ; total : 250 + 240 + 220 = 710 $ . answer : e .\"" + }, + { + "Answer": 12.000000000000002, + "Options": "a ) $ 10 , b ) $ 24 , c ) $ 26 , d ) $ 12 , e ) $ 36", + "Correct": "d", + "Explanation": "josh + doug + brad = 68 ; josh = 2 brad , josh = 3 / 4 doug josh + 1 / 2 josh + 4 / 3 josh = 68 ( substituted the given values ) josh = 24 . 24 = 3 / 4 doug = > doug = 32 josh + doug + brad = 68 24 + 32 + brad = 68 brad = 12 answer is d ." + }, + { + "Answer": 1, + "Options": "a ) 3 , b ) 2 , c ) 1 , d ) 0 , e ) 4", + "Correct": "c", + "Explanation": "\"6 ^ 23 = 6 ^ ( 4 * 5 + 3 ) = 6 ^ ( 20 ) * 6 ^ 3 last 3 digits = 216 216 / 5 remainder = 1 answer : c\"" + }, + { + "Answer": 97.49871794028884, + "Options": "a ) 78 , b ) 68 , c ) 88 , d ) 97 , e ) 37", + "Correct": "d", + "Explanation": "\"d 97 from the given alternatives , 97 \u00d7 98 = 9506 \u2234 smaller number = 97\"" + }, + { + "Answer": 0.8, + "Options": "a ) 4 / 5 , b ) 5 / 4 , c ) 3 / 5 , d ) 2 / 5 , e ) 3 / 4", + "Correct": "a", + "Explanation": "\"let the required fraction be x . then 1 / x - x = 9 / 20 ( 1 - x ^ 2 ) / x = 9 / 20 = = > 20 - 20 x ^ 2 = 9 x 20 x ^ 2 + 9 x - 20 = 0 20 x ^ 2 + 25 x - 16 x - 20 = 0 5 x ( 4 x + 5 ) - 4 ( 4 x + 5 ) = 0 ( 4 x + 5 ) ( 5 x - 4 ) = 0 x = 4 / 5 ( neglecting - ve value ) answer a ) 4 / 5\"" + }, + { + "Answer": 18, + "Options": "a ) 14 years , b ) 18 years , c ) 20 years , d ) 22 years , e ) 16 years", + "Correct": "b", + "Explanation": "\"let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . ( x + 20 ) + 2 = 2 ( x + 2 ) x + 22 = 2 x + 4 x = 18 . answer : b\"" + }, + { + "Answer": 80, + "Options": "a ) 80 , b ) 90 , c ) 100 , d ) 110 , e ) 120", + "Correct": "a", + "Explanation": "\"20 liters is 25 % of the capacity c . 20 = 0.25 c c = 80 liters . the answer is a .\"" + }, + { + "Answer": 7, + "Options": "a ) 12 , b ) 8 , c ) 28 , d ) 7 , e ) 27", + "Correct": "d", + "Explanation": "let total number of mice = m number of white mice = 2 / 3 m = 14 m = 21 number of brown mice = 1 / 3 m = 1 / 3 * 21 = > brown mice = 7 answer d" + }, + { + "Answer": 865, + "Options": "a ) 545 , b ) 685 , c ) 865 , d ) 495 , e ) 534", + "Correct": "c", + "Explanation": "\"let y x 48 = 173 x 240 then y = ( 173 x 240 ) / 48 = 173 x 5 = 865 . answer : c\"" + }, + { + "Answer": 4.4, + "Options": "a ) 2.8 % , b ) 4.4 % , c ) 4.6 % , d ) 5.2 % , e ) 6.0 %", + "Correct": "b", + "Explanation": "assume she has $ 200 to spend . tax clothing = 50 % = $ 100 = $ 4.00 food = 20 % = $ 40 = $ 0.00 items = 30 % = $ 60 = $ 4.80 total tax = $ 8.80 % of total amount = 8.8 / 200 * 100 = 4.4 % b )" + }, + { + "Answer": 0.0046296296296296285, + "Options": "a ) 41 / 50 , b ) 1 / 216 , c ) 1 / 221 , d ) 1 / 84 , e ) 1 / 42", + "Correct": "b", + "Explanation": "to guarantee that john will get some monetary payoff he must score the maximum score of 6 + 6 + 6 = 18 , because if he gets even one less than that so 17 , someone can get 18 and john will get nothing . p ( 18 ) = 1 / 6 ^ 3 = 1 / 216 . answer : b ." + }, + { + "Answer": 5, + "Options": "a ) 10 , b ) 5 , c ) 16 , d ) 18 , e ) 21", + "Correct": "b", + "Explanation": "24 = 1 * 2 * 3 * 4 so w = 1 , x = 2 , y = 3 , z = 4 w + z = 1 + 4 = 5 answer - b" + }, + { + "Answer": 94, + "Options": "a ) 30 , b ) 44 , c ) 36 , d ) 56 , e ) 94", + "Correct": "e", + "Explanation": "\"explanation : lcm of 5 , 6 , 9 and 18 is 90 required number = 90 + 4 = 94 answer : option e\"" + }, + { + "Answer": 37, + "Options": "a ) 31 % . , b ) 71 % . , c ) 49 % . , d ) 29 % . , e ) 37 % .", + "Correct": "e", + "Explanation": "\"35 % of 2 litres = 0.7 litres 50 % of 6 litres = 3 litres therefore , total quantity of alcohol is 3.7 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 37 % e\"" + }, + { + "Answer": 8, + "Options": "a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 9", + "Correct": "d", + "Explanation": "8 , x , 6,2 , - 4 , - 12 i guess each differ in d range of 2 8 - 8 = 0 8 - 6 = 2 6 - 2 = 4 2 - 6 = - 4 - 4 - 8 = - 12 answer : d" + }, + { + "Answer": 6000, + "Options": "a ) 60 , b ) 600 , c ) 6000 , d ) 60000 , e ) 6", + "Correct": "c", + "Explanation": "( face value of 7 ) x ( local value of 8 ) = 7 x 8000 = 56000 local value of 6 in 56000 = 6000 c" + }, + { + "Answer": 6, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 6", + "Correct": "e", + "Explanation": "unit digit in 12 ^ 100 = unit digit in [ ( 12 ^ 4 ) ^ 25 ] but unit digit in 12 ^ 4 = 6 unit digit 12 ^ 100 = 6 answer is e" + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 3 , c ) 2 , d ) 1 , e ) 0", + "Correct": "a", + "Explanation": "\"4 \u201d 3 = 9 - 4 = 5 answer : a\"" + }, + { + "Answer": 8, + "Options": "a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 8", + "Correct": "e", + "Explanation": "\"p \u00e3 \u00b7 44 = 432 = > p = 432 * 44 = 19008 p / 38 = 19008 / 38 = 500 , remainder = 8 e\"" + }, + { + "Answer": 6.999999999999995, + "Options": "a ) 7 , b ) 25 , c ) 35 , d ) 45 , e ) 75", + "Correct": "a", + "Explanation": "\"out of 300 - 180 purchased for less than 100 $ 120 for more out of 300 - 120 responded as satisfied and 180 responded disatisfied out of 180 ( purchased less than 100 $ ) - 55 % = 99 responded as satisfied , so remaining satisfied are 120 - 99 = 21 so 21 is what percentage of 300 - 7 % so the answer should be a\"" + }, + { + "Answer": 52, + "Options": "a ) 78 , b ) 26 , c ) 52 , d ) 54 , e ) 56", + "Correct": "c", + "Explanation": "\"explanation : 36 + 32 + 9 * 4 = 104 / 2 = 52 answer : c\"" + }, + { + "Answer": 29, + "Options": "a ) 2 , b ) 4 , c ) 8 , d ) 29 , e ) 32", + "Correct": "d", + "Explanation": "\"lets assign variables to all the areas in venn diagram of three . three different units are dog , cat , snake = total = 59 only dog = d = 15 only cat = c = 10 only snake = s exactly dog and cat = 5 exactly dog and snake = x exactly cat and snake = y all three = 3 so 59 = 15 + 10 + 5 + 3 + x + y + s we need to know total snakes = x + y + s + 3 = 29 answer : d\"" + }, + { + "Answer": 1050, + "Options": "a ) $ 1050 , b ) $ 2500 , c ) $ 3000 , d ) $ 3400 , e ) $ 8000", + "Correct": "a", + "Explanation": "let the shares of a , b , c , d are 2 x , 3 x , 4 x , 6 x 6 x - 4 x = 700 x = 350 b ' s share = 3 x = $ 1050 answer is a" + }, + { + "Answer": 27, + "Options": "a ) 23 , b ) 20 , c ) 27 , d ) 5 , e ) 2", + "Correct": "c", + "Explanation": "\"soln : { 26 } + { 24 } = 26 * { 24 } + { 24 } = 27 * { 24 } answer : c\"" + }, + { + "Answer": 6.400000000001455, + "Options": "a ) 0.16 , b ) 0.64 , c ) 80.08 , d ) 64 , e ) 6.4", + "Correct": "e", + "Explanation": "required product = 80 x 0.08 = 6.4 answer is e" + }, + { + "Answer": 22.5, + "Options": "a ) 22.5 % , b ) 21.5 % , c ) 20.5 % , d ) 12.5 % , e ) 10.5 %", + "Correct": "a", + "Explanation": "total honda brand red cars = 90 / 100 * 5000 = 4500 total red cars = 60 / 100 * 9000 = 5400 no . of non - honda cars = 9000 - 5000 = 4000 no . of non - honda red cars = 5400 - 4500 = 900 % of non - honda red cars = 900 / 4000 * 100 = 22.5 % answer : a" + }, + { + "Answer": 50, + "Options": "a ) 42.0 , b ) 48.0 , c ) 50.0 , d ) 52.2 , e ) 54.0", + "Correct": "c", + "Explanation": "explanation : in such a case the middle number ( d ) is the average \u2234 d = 9 and a = 6 and g = 12 required percentage = 6 / 12 x 100 = 50.0 answer : option c" + }, + { + "Answer": 1.6, + "Options": "a ) 16 , b ) 1.6 , c ) 0.16 , d ) 0.016 , e ) none of these", + "Correct": "b", + "Explanation": "explanation : ( 204 / 12.75 ) = 16 \u21d2 ( 20.4 ) / ( 1.275 ) = 16 ( \u2235 divided numerator and denominator by 10 ) \u21d2 2.04 / 1.275 = 1.6 ( \u2235 divided lhs and rhs by 10 ) answer : option b" + }, + { + "Answer": 5, + "Options": "a ) 7 , b ) 5 , c ) 9 , d ) 10 , e ) 11", + "Correct": "b", + "Explanation": "\"101 * n ^ 2 < = 3600 n ^ 2 < = 3600 / 101 which will be less than 81 since 3600 / 100 = 36 which is the square of 9 next closest value of n where n ^ 2 < = 36 is 5 ans b\"" + }, + { + "Answer": 155, + "Options": "a ) 150 , b ) 153 , c ) 154 , d ) 155 , e ) 156", + "Correct": "d", + "Explanation": "\"explanation : let the number = x , then , x - ( 3 / 5 ) x = 62 , = > ( 2 / 5 ) x = 62 = > 2 x = 62 * 5 , = > x = 155 answer : option d\"" + }, + { + "Answer": 75, + "Options": "a ) 82 m , b ) 50 m , c ) 75 m , d ) 80 m , e ) none of these", + "Correct": "c", + "Explanation": "\"explanation : the relative speed of train is 46 - 36 = 10 km / hr = ( 10 x 5 ) / 18 = 25 / 9 m / s 10 \u00d7 518 = 259 m / s in 54 secs the total distance traveled is 54 x 25 / 9 = 150 m . therefore the length of each train is = 150 / 2 = 75 m . answer c\"" + }, + { + "Answer": 47, + "Options": "a ) 10 , b ) 11 , c ) 12 , d ) 14 , e ) 47", + "Correct": "e", + "Explanation": "\"- > x ^ 4 + ( 1 / x ^ 4 ) = ( x ^ 2 ) ^ 2 + ( 1 / x ^ 2 ) ^ 2 = ( x ^ 2 + 1 / x ^ 2 ) ^ 2 - 2 x ^ 2 ( 1 / x ^ 2 ) = 7 ^ 2 - 2 = 47 . thus , the answer is e .\"" + }, + { + "Answer": 55, + "Options": "a ) 54 , b ) 55 , c ) 59 , d ) 71 , e ) 92", + "Correct": "b", + "Explanation": "\"total = 64 thrower = 37 rest = 64 - 37 = 27 left handed = 27 / 3 = 9 right handed = 18 if all thrower are right handed then total right handed is 37 + 18 = 55 so b . 55 is the right answer\"" + }, + { + "Answer": 53, + "Options": "a ) 50 , b ) 53 , c ) 49 , d ) 48 , e ) 44", + "Correct": "b", + "Explanation": "\"sum of 5 integer ( a , b , c , d , e ) = 5 * 45 = 225 e - a = 10 i . e . e = a + 10 for e to be maximum remaining 4 must be as small as possible since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers i . e . a + a + a + a + ( a + 10 ) = 225 i . e . 5 a = 215 i . e . a = 43 i . e . largest e = 43 + 10 = 53 answer : option b\"" + }, + { + "Answer": 120, + "Options": "a ) 360 , b ) 420 , c ) 120 , d ) 320 , e ) 280", + "Correct": "c", + "Explanation": "\"lcm = 2 * 2 * 2 * 3 * 5 = 120 . answer is c\"" + }, + { + "Answer": 2, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 6 , e ) 2", + "Correct": "e", + "Explanation": "\"explanation : 39 + 15 = 54 / 13 = 2 ( remainder ) answer : e\"" + }, + { + "Answer": 0.5, + "Options": "a ) 2 / 5 , b ) 1 / 2 , c ) 11 / 16 , d ) 5 / 7 , e ) 3 / 4", + "Correct": "b", + "Explanation": "\"the answer isc : 11 / 16 . the key to this problem is remembering that the median for a consecutive set of numbers is equivalent to its mean . for example , the mean and median of a set consisting of x , x + 1 , x + 2 , . . . , y will always be ( x + y ) / 2 . for set s , consisting of numbers ( a , a + 1 , . . . , b ) , the median is given to be 3 / 4 * b : ( a + b ) / 2 = ( 3 / 4 ) * b a = b / 2 for set q , consisting of numbers ( b , b + 1 , . . . , c ) , the median is given to be 4 / 8 * c : ( b + c ) / 2 = ( 4 / 8 ) * c b = 0 for set r , consisting of numbers ( a , a + 1 , . . . c ) , the median needs to be found : a = b / 2 = ( 0 ) / 2 = 0 median = ( a + c ) / 2 = ( 0 + c ) / 2 = c / 2 = ( 1 / 2 ) * c ( answer b )\"" + }, + { + "Answer": 56, + "Options": "a ) 56 , b ) 80 , c ) 20 , d ) 25 , e ) 26", + "Correct": "a", + "Explanation": "\"let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 . x / 2 = ( 73 - 45 ) = > x / 2 = 28 = > x = 56 . answer : a\"" + }, + { + "Answer": 5.200000000000003, + "Options": "a ) 5.2 , b ) 2.6 , c ) 3.6 , d ) 4.5 , e ) 4.6", + "Correct": "a", + "Explanation": "\"sum of the remaining two numbers = ( 5.40 * 6 ) - [ ( 5.2 * 2 ) + ( 5.8 * 2 ) ] = 32.40 - ( 10.4 + 11.6 ) = 32.40 - 22.0 = 10.40 . required average = ( 10.4 / 2 ) = 5.2 answer : a\"" + }, + { + "Answer": 8, + "Options": "a ) 10 , b ) 12 , c ) 8 , d ) 12 , e ) 14", + "Correct": "c", + "Explanation": "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 16 = > 2 x = 16 = > x = 8 c" + }, + { + "Answer": 88.57142857142857, + "Options": "a ) 98.5 kgs , b ) 88.5 kgs , c ) 86.5 kgs , d ) 67.5 kgs , e ) 88.2 kgs", + "Correct": "b", + "Explanation": "\"average weight = [ ( a + b + c + ( a + b ) + ( b + c ) + ( c + a ) + ( a + b + c ) ] / 7 = 4 ( a + b + c ) / 7 = 4 x 155 / 7 = 88.5 kgs answer : b\"" + }, + { + "Answer": 20, + "Options": "a ) 16 , b ) 18 , c ) 20 , d ) 22 , e ) 24", + "Correct": "c", + "Explanation": "\"since there are only 18 integers , another approach is the just list all 18 . we get : - 12 , - 10 , - 8 , - 6 , - 4 , - 2 , 0,2 , 4 , 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20 , 22 range of positive integers = 22 - 2 = 20 answer : c\"" + }, + { + "Answer": 3, + "Options": "a ) $ 2.00 , b ) $ 2.25 , c ) $ 2.50 , d ) $ 2.75 , e ) $ 3.00", + "Correct": "e", + "Explanation": "\"let x be the value of the weekly allowance . ( 2 / 3 ) ( 3 / 5 ) x = 120 cents ( 2 / 5 ) x = 120 x = $ 3.00 the answer is e .\"" + }, + { + "Answer": 14, + "Options": "a ) 9 , b ) 12 , c ) 14 , d ) 16 , e ) 18", + "Correct": "c", + "Explanation": "\"in 16 liters , red = 5 / 8 * 16 = 10 and blue = 6 so , 10 / ( 6 + x ) = 3 / 6 or , x = 14 ( answer c )\"" + }, + { + "Answer": 5, + "Options": "a ) 1 , b ) 5 , c ) 7 , d ) 8 , e ) 2", + "Correct": "b", + "Explanation": "explanation : \\ inline \\ fn _ jvn [ ( 100 \\ times 35 ) + ( 200 \\ times 5 ) ] men can finish the work in 1 day \\ inline \\ fn _ jvn \\ therefore 4500 men can finish the work in 1 day . 100 men can finish it in \\ inline \\ fn _ jvn \\ frac { 4500 } { 100 } = 45 days . this is 5 days behind schedule answer : b" + }, + { + "Answer": 188, + "Options": "a ) 131 , b ) 135 , c ) 139 , d ) 147 , e ) 188", + "Correct": "e", + "Explanation": "\"consider sister weight now as x jakes weight ( 2 times + 8 ) = 2 x + 8 ( 2 x + 8 ) + ( x ) = 278 x = 90 jake ' s weight is . . . . 188 correct answer is e\"" + }, + { + "Answer": 72, + "Options": "a ) 2134 , b ) 2234 , c ) 2540 , d ) 2560 , e ) 72", + "Correct": "e", + "Explanation": "\"72 e\"" + }, + { + "Answer": 0.125, + "Options": "a ) 1 / 12 , b ) 1 / 9 , c ) 1 / 8 , d ) 1 1 / 9 , e ) 2 1 / 9", + "Correct": "c", + "Explanation": "total bought = 2 / 9 + 1 / 8 left part 4 / 18 - - - > 2 / 9 so used part 2 / 9 + 1 / 8 - 2 / 9 = 1 / 8 answer : c" + }, + { + "Answer": 75, + "Options": "a ) 62 , b ) 66 , c ) 18 , d ) 75 , e ) 12", + "Correct": "d", + "Explanation": "\"explanation : age of the 17 th student = [ 17 * 17 - ( 14 * 5 + 16 * 9 ) ] = ( 289 - 214 ) = 75 years . answer : d\"" + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 19 , c ) 29 , d ) 30 , e ) 33", + "Correct": "a", + "Explanation": "\"total of integers = 68 * 4 = 272 lowest of the least possible integer is when the middle 2 intergers are at the maximum or equal to the highest possible integer . but all integers are distinct . so if the largest integer is 90 , then the middle 2 will be 88 and 89 lowest of least possible integer = 272 - ( 90 + 89 + 88 ) = 272 - 267 = 5 answer : a\"" + }, + { + "Answer": 0.6666666666666667, + "Options": "a ) 1 / 12 , b ) 1 / 9 , c ) 2 / 3 , d ) 1 1 / 9 , e ) 2 1 / 9", + "Correct": "c", + "Explanation": "\"total bought = 4 / 9 + 2 / 3 left part 8 / 18 - - - > 4 / 9 so used part 4 / 9 + 2 / 3 - 4 / 9 = 2 / 3 answer : c\"" + }, + { + "Answer": 99, + "Options": "a ) $ 72 , b ) $ 85 , c ) $ 99 , d ) $ 101 , e ) $ 202", + "Correct": "c", + "Explanation": "solution - total money distributed is $ 198 . in order to maximize median , one person has to accept $ 0 and remaining two people share $ 99 each . hence median is $ 99 . ans c" + }, + { + "Answer": 0.6833333333333333, + "Options": "a ) 52 / 45 , b ) 23 / 47 , c ) 60 / 41 , d ) 51 / 42 , e ) 41 / 60", + "Correct": "e", + "Explanation": "\"the way to approach this problem is 2 < a < 11 and 11 < b < 21 minimum possible value of a is 3 and maximum is 10 minimum possible value of b is 12 and maximum is 20 range = max a / min b - min a / max b ( highest - lowest ) 10 / 12 - 3 / 20 = 41 / 60 hence e\"" + }, + { + "Answer": 357000, + "Options": "a ) 280000 , b ) 300000 , c ) 355000 , d ) 356000 , e ) 357000", + "Correct": "e", + "Explanation": "total number of invalid votes = 15 % of 560000 = 15 / 100 \u00d7 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 \u2013 84000 = 476000 percentage of votes polled in favour of candidate x = 75 % therefore , the number of valid votes polled in favour of candidate x = 75 % of 476000 = 75 / 100 \u00d7 476000 = 35700000 / 100 = 357000 e )" + }, + { + "Answer": 220020, + "Options": "a ) 122456 , b ) 220020 , c ) 220022 , d ) 235467 , e ) 220026", + "Correct": "b", + "Explanation": "\"( 555 + 445 ) * 2 * 110 + 20 = 220000 + 20 = 220020 b\"" + }, + { + "Answer": 600, + "Options": "a ) 300 bc , b ) 300 b / c , c ) 600 bc , d ) 600 b / c , e ) 600 / bc", + "Correct": "c", + "Explanation": "\"2 cases * c cartons / case * b boxes / carton * 300 clips / box = 600 bc paper clips the answer is c .\"" + }, + { + "Answer": 5, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 5", + "Correct": "e", + "Explanation": "\"mean = ( x + x + 2 + x + 4 + x + 7 + x + 32 ) / 5 = ( 5 x + 45 ) / 5 = x + 9 median = x + 4 thus mean - median = x + 9 - ( x + 4 ) = 5 answer = e\"" + }, + { + "Answer": 36.000000000000014, + "Options": "a ) 36 , b ) 40 , c ) 44 , d ) 48 , e ) 52", + "Correct": "a", + "Explanation": "\"let r be the original speed and let t be the original time . since the distance remains the same ( we ' re just changing the rate and time ) , any increase in rate or time is met with a decrease in the other term . decreasing the time by 1 / 3 would give us : d = ( r ) ( t ) = ( 2 t / 3 ) ( x * r ) x = 3 / 2 since ( 2 t / 3 ) ( 3 r / 2 ) = ( r ) ( t ) = d 3 r / 2 = r + 18 r / 2 = 18 r = 36 the answer is a .\"" + }, + { + "Answer": 7, + "Options": "a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 12", + "Correct": "b", + "Explanation": "\"9 / 11 = 0 and 79 / 11 = 7 = = > 7 - 0 = 7 numbers answer : b\"" + }, + { + "Answer": 5, + "Options": "a ) a ) 4 , b ) b ) 1 , c ) c ) 2 , d ) d ) 3 , e ) e ) 5", + "Correct": "e", + "Explanation": "\"explanation : ( 1053 / 23 ) gives remainder 18 18 + 5 = 23 , so we need to add 5 answer : option e\"" + }, + { + "Answer": 80, + "Options": "a ) 76 kg , b ) 80 kg , c ) 85 kg , d ) data inadequate , e ) none of these", + "Correct": "b", + "Explanation": "\"explanation : total weight increased = ( 6 x 2.5 ) kg = 15 kg . weight of new person = ( 65 + 15 ) kg = 80 kg . answer : b\"" + }, + { + "Answer": 2.0000000000000004, + "Options": "a ) 1 / 2 , b ) 2 / 3 , c ) 2 / 1 , d ) 3 / 2 , e ) 4 / 3", + "Correct": "c", + "Explanation": "\"( 1 / 2 ) g = ( 1 / 6 ) ( b + g ) 6 g = 2 b + 2 g 4 g = 2 b b / g = 2 / 1 . the answer is c .\"" + }, + { + "Answer": 81.81818181818181, + "Options": "a ) 33.33 % , b ) 25 % , c ) 81.81 % , d ) 66.66 % , e ) none of these", + "Correct": "c", + "Explanation": "\"using formula ( x / ( 100 - x ) * 100 ) where x is percentage decrease ( here it is 25 % ) = > 45 / ( 100 - 45 ) * 100 = 81.81 % answer : c\"" + }, + { + "Answer": 1, + "Options": "a ) 1 hr , b ) 2 hr , c ) 6 hr , d ) 8 hr , e ) 7 hr", + "Correct": "a", + "Explanation": "let the duration of the flight be x hours . then , 600 / x - 600 / ( x + 1 / 2 ) = 200 x ( 2 x + 1 ) = 3 2 x 2 + x - 3 = 0 ( 2 x + 3 ) ( x - 1 ) = 0 x = 1 hr . answer : a" + }, + { + "Answer": 320, + "Options": "a ) 198 , b ) 297 , c ) 320 , d ) 402 , e ) 405", + "Correct": "c", + "Explanation": "last term = first term + ( total no . of terms - 1 ) consecutive difference s is a set of 64 consecutive multiples of 4 . if the smallest number in s is 68 , then the greatest number in s is first term = 68 ; total terms = 64 ; difference = 4 68 + ( 63 ) 4 = 320 ans c" + }, + { + "Answer": 0.3611111111111111, + "Options": "a ) 3 / 8 , b ) 13 / 36 , c ) 17 / 36 , d ) 19 / 36 , e ) 23 / 36", + "Correct": "b", + "Explanation": "if you calculate 3 ^ s for 1 st roll , all 6 results will be 9 , 81 , 6561 , 729 , 9 , 81 . this result is the same for 2 nd roll . 9 , 81 , 6561 , 729 , 9 , 81 . about distance : if the first result is 9 and the second is also 9 , the distance is 9 - 9 = 0 which is smaller than 9 . if the first result is 9 and the second is 81 , the distance is 81 - 9 = 72 which is also smaller than b which has the value of 81 . if the first result is 81 and the second is 9 , the distance will be greater than b . distance 81 - 9 = 72 > 9 . on the first roll , the probability of getting result 9 is 2 / 6 . in this case no other alternative values for second roll which would make the distance greater than b . so probability is 0 . so next estimations are : probability of getting 81 on the first roll ( 2 / 6 ) * probability of getting 9 on the second roll ( 2 / 6 ) = 1 / 9 probability of getting 729 on the first roll ( 1 / 6 ) * probability of getting 9 , 81 on the second roll ( 4 / 6 ) = 1 / 9 probability of getting 6561 on the first roll ( 1 / 6 ) * probability of getting 9 , 81 , 729 on the first roll ( 5 / 6 ) = 5 / 36 all together : 1 / 9 + 1 / 9 + 5 / 36 = 13 / 36 = b" + }, + { + "Answer": 0.7142857142857143, + "Options": "a ) 4 / 9 , b ) 5 / 4 , c ) 5 / 8 , d ) 5 / 7 , e ) 6 / 9", + "Correct": "d", + "Explanation": "income = salary ( s ) + tips = s + s * 5 / 2 = s * 7 / 2 tips = s * 7 / 2 fraction of his income came from tips = ( s * 5 / 2 ) / ( s * 7 / 2 ) = 5 / 7 answer : d" + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) 5 , c ) 6 , d ) 16 , e ) 18", + "Correct": "a", + "Explanation": "\"x can be written as 82 k + 5 or x = 5 , 87,169 , etc . when k = 0 , 1,2 etc x + 7 = 82 k + 5 + 7 = 82 k + 12 or x + 7 = 12,94 , 176 etc . k = 0 , 1,2 when divided by 41 , we will get the remainder 12 . a\"" + }, + { + "Answer": 6.25, + "Options": "a ) $ 0.00 , b ) $ 1.00 , c ) $ 3.40 , d ) $ 5.00 , e ) $ 6.25", + "Correct": "e", + "Explanation": "\"0.85 * { original price } = $ 85 - - > { original price } = $ 100 . { final price } = $ 85 * 1.25 = $ 106.25 . the difference = $ 106.25 - $ 100 = $ 6.25 . answer : e .\"" + }, + { + "Answer": 0.9677419354838709, + "Options": "a ) 1 / 130 , b ) 1 / 5 , c ) 3 / 13 , d ) 10 / 13 , e ) 30 / 31", + "Correct": "e", + "Explanation": "it ' s y / xpercentnot y / x . if x = 20 and y = 10 . then : 20 x = 400 black - and - white films ; 6 y = 60 color films . y / x % = 10 / 20 % = 0.5 % of the black - and - white films , so 2 black - and - white films and all 60 color films , thus total of 62 films were selected . color films thus compose q = 60 / 62 = 30 / 31 of the selected films . answer : e ." + }, + { + "Answer": 855, + "Options": "a ) 171 , b ) 855 , c ) 870 , d ) 788 , e ) 684", + "Correct": "b", + "Explanation": "\"system of equations a = ( 20 / 100 ) c ( 1 / 3 ) a = 57 - - > a = 171 substitution 171 = ( 20100 ) c c = ( 100 / 20 ) 171 - calculate 171 / 20 * 100 the correct answer b . the answer is 855 .\"" + }, + { + "Answer": 9, + "Options": "a ) 6 , b ) 9 , c ) 12 , d ) 15 , e ) 18", + "Correct": "b", + "Explanation": "\"2 oxen = 3 buffaloes = 4 cows also : 15 buffaloes + 8 oxen + 24 cows = 10 oxen + 8 oxen + 12 oxen = 30 oxen there is enough fodder for 1 oxen for 30 * 24 days . 60 cows + 30 buffaloes = 30 oxen + 20 oxen = 50 oxen the new total is equal to 80 oxen instead of 30 oxen . 30 * 24 / 80 oxen = 9 days the answer is b .\"" + }, + { + "Answer": 24, + "Options": "a ) 6 , b ) 9 , c ) 24 , d ) 30 , e ) 35", + "Correct": "c", + "Explanation": "explanation : volume of block = ( 6 x 9 x 12 ) cm 3 = 648 cm 3 side of largest cube = h . c . f of 6 , 912 = 3 cm volume of the cube = ( 3 x 3 x 3 ) = 27 cm 3 number of cubes = ( 648 / 27 ) = 24 answer : c" + }, + { + "Answer": 12, + "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12", + "Correct": "e", + "Explanation": "\"the total number of books the students borrowed is 25 * 2 = 50 . the students who borrowed zero , one , or two books borrowed 12 * 1 + 4 * 2 = 20 books . the 7 students who borrowed at least three books borrowed 50 - 20 = 30 books . if 6 of these students borrowed exactly 3 books , then the maximum that one student could have borrowed is 30 - 18 = 12 books . the answer is e .\"" + }, + { + "Answer": 27.99999999999998, + "Options": "a ) 16 , b ) 28 , c ) 32 , d ) 44 , e ) 48", + "Correct": "b", + "Explanation": "\"lets say x ounces of p is mixed with q . = > 68 - x ounces of q is present in the mixture ( as the total = 68 ounces ) given total almond weight = 15 ounces ( 20 x / 100 ) + ( 25 / 100 ) ( 68 - x ) = 15 = > x = 40 = > 68 - 40 = 28 ounces of q is present in the mixture . answer is b .\"" + }, + { + "Answer": 241, + "Options": "a ) 124 , b ) 241 , c ) 394 , d ) 421 , e ) 842", + "Correct": "b", + "Explanation": "ratio of a : b : c = 2 : 4 : 1 two possible greatest single digit values for b are 8 and 4 if b is 8 , then x = 482 if b is 4 , then x = 241 difference = 482 - 241 = 241 b is the answer" + }, + { + "Answer": 140, + "Options": "a ) 100 , b ) 120 , c ) 140 , d ) 130 , e ) 115", + "Correct": "c", + "Explanation": "let the number be x then , 4 x / 5 - ( 65 % of x ) = 21 4 x / 5 - 65 x / 100 = 21 x = 140 answer is c" + }, + { + "Answer": 28, + "Options": "a ) 24 , b ) 26 , c ) 28 , d ) 30 , e ) 32", + "Correct": "c", + "Explanation": "\"let x be the original number of apples . on day one , the vendor throws away ( 0.4 ) ( 0.4 ) x = 0.16 x . the remaining apples are ( 0.6 ) ( 0.4 ) x = 0.24 x . on day two , the vendor throws away ( 0.5 ) ( 0.24 ) x = 0.12 x . the vendor throws away a total of 0.16 x + 0.12 x = 0.28 x . the vendor throws away 28 percent of the apples . the answer is c .\"" + }, + { + "Answer": 11.999999999999996, + "Options": "a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14", + "Correct": "d", + "Explanation": "\"let x be the original number of pears . on day one , the vendor throws away ( 0.5 ) ( 0.2 ) x = 0.1 x . the remaining pears are ( 0.5 ) ( 0.2 ) x = 0.1 x . on day two , the vendor throws away ( 0.2 ) ( 0.1 ) x = 0.02 x . the vendor throws away a total of 0.1 x + 0.02 x = 0.12 x . the vendor throws away 12 percent of the pears . the answer is d .\"" + }, + { + "Answer": 93, + "Options": "a ) 75 kg , b ) 65 kg , c ) 55 kg , d ) 85 kg , e ) 93 kg", + "Correct": "e", + "Explanation": "\"total weight increased = ( 8 x 3.5 ) kg = 28 kg . weight of new person = ( 65 + 28 ) kg = 93 kg . answer : e\"" + }, + { + "Answer": 18.400000000000002, + "Options": "a ) 15.6 , b ) 16.0 , c ) 18.4 , d ) 18.7 , e ) 19.1", + "Correct": "c", + "Explanation": "\"a certain taxi company charges $ 2.80 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ? a . 15.60 b . 16.00 c . 17.50 d . 18.70 e . 19.10 1 / 5 miles = 0.2 miles . the cost of 8 miles long ride would be $ 2.80 for the first 0.2 miles plus ( 8 - 0.2 ) / 0.2 * 0.4 = $ 2.8 + $ 15.6 = $ 18.4 . answer : c .\"" + }, + { + "Answer": 36, + "Options": "a ) 90 , b ) 82 , c ) 80 , d ) 45 , e ) 36", + "Correct": "e", + "Explanation": "let the three digit number be represented as x y z . there are 3 cases : case i . [ x = y ] z is not equal to xy : xxzoryyz x can be either 7 , 8 or 9 , so digit at x can be chosen in 3 ways after x is chosen , y can be chosen in 1 way after xy are chosen , z can be chosen in 9 ways thus , possible no of digits = ( 3 ways ) * ( 1 way ) * ( 9 ways ) = 27 . . . . ( 1 ) [ example numbers : 774,779 , 882,993 etc ] case ii . [ x = z ] y is not equal to xz : xyxorzyz x can be either 7 , 8 or 9 , so digit at x can be chosen in 3 ways after x is chosen , z can be chosen in 1 way after xz are chosen , z can be chosen in 9 ways thus , possible no of digits = ( 3 ways ) * ( 9 ways ) * ( 1 way ) = 27 . . . . ( 2 ) [ example numbers : 747,797 , 828,939 etc ] case iii . [ y = z ] x is not equal to yz : xyyorxzz x can be either 7 , 8 or 9 , so digit at x can be chosen in 3 ways after x is chosen , y can be chosen in 9 ways after y is chosen , z can have 1 way thus , possible no of digits = ( 3 ways ) * ( 1 way ) * ( 9 ways ) = 27 . . . . ( 3 ) [ example numbers : 744,799 , 822,933 etc ] therefore , total numbers of possible digits [ sum of case ( 1 ) , ( 2 ) ( 3 ) above ] = 27 + 27 + 27 - 1 = 80 one digit is subtracted from total number of possible digits to eliminate one possibility of xyz = 700 to satisfy the condition that digit > 200 . answer : ( e )" + }, + { + "Answer": 25, + "Options": "a ) 18 % , b ) 72 % , c ) 25 % , d ) 12 % , e ) 52 %", + "Correct": "c", + "Explanation": "\"100 * 100 = 10000 60 * 125 = 7500 10000 - - - - - - - 2500 100 - - - - - - - ? = 25 % answer : c\"" + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 10 , c ) 15 , d ) 25 , e ) 35", + "Correct": "a", + "Explanation": "total applicants = 40 political science = 15 and non political science = 40 - 15 = 25 gpa > 3.0 = 20 and gpa < = 3.0 = 20 10 non political science students had gpa < = 3.0 - - > 15 non political science students had gpa > 3.0 gpa > 3.0 in political science = total - ( gpa > 3.0 in non political science ) q = 20 - 15 = 5 answer : a" + }, + { + "Answer": 8185, + "Options": "a ) 2480 , b ) 3490 , c ) 6785 , d ) 8245 , e ) 9255", + "Correct": "d", + "Explanation": "\"you ' ll never need a formula for the sums of squares on the actual gmat . you do n ' t need to use that formula here , though it ' s not all that straightforward to solve without one . two different approaches : 16 ^ 2 + 17 ^ 2 + 18 ^ 2 + . . . + 30 ^ 2 = ( 15 + 1 ) ^ 2 + ( 15 + 2 ) ^ 2 + ( 15 + 3 ) ^ 2 + . . . + ( 15 + 15 ) ^ 2 now we can expand each square ; they are all in the ( x + y ) ^ 2 = x ^ 2 + 2 xy + y ^ 2 pattern . = ( 15 ^ 2 + 2 * 15 + 1 ^ 2 ) + ( 15 ^ 2 + 4 * 15 + 2 ^ 2 ) + ( 15 ^ 2 + 6 * 15 + 3 ^ 2 ) + . . . + ( 15 ^ 2 + 30 * 15 + 15 ^ 2 ) now we have fifteen 15 ^ 2 terms , so adding these gives 15 * 15 ^ 2 = 15 ^ 3 = 3375 . we also have the entire sum 1 ^ 2 + 2 ^ 2 + . . . + 15 ^ 2 , which we know is equal to 1240 . finally adding the middle terms , we have : 2 * 15 + 4 * 15 + 6 * 15 + . . . + 30 * 15 = 15 ( 2 + 4 + 6 + . . . . + 30 ) = 15 * 2 * ( 1 + 2 + 3 + . . . + 15 ) = 15 * 2 * 8 * 15 = 3600 so the sum must be 3375 + 1240 + 3600 = 8215 alternatively , we can use a different factoring pattern . we want to find the value of 30 ^ 2 + 29 ^ 2 + . . . + 17 ^ 2 + 16 ^ 2 . well if we subtract 15 ^ 2 + 14 ^ 2 + . . . . + 2 ^ 2 + 1 ^ 2 from this , the answer will be 1240 less than what we want to find . so if we can find the value of 30 ^ 2 + 29 ^ 2 + . . . + 17 ^ 2 + 16 ^ 2 - ( 15 ^ 2 + 14 ^ 2 + . . . . + 2 ^ 2 + 1 ^ 2 ) then we can add 1240 to get the answer . now grouping the terms above to get differences of squares , we have = ( 30 ^ 2 - 15 ^ 2 ) + ( 29 ^ 2 - 14 ^ 2 ) + . . . + ( 16 ^ 2 - 1 ^ 2 ) and factoring each of these using x ^ 2 - y ^ 2 = ( x + y ) ( x - y ) , we have = 45 * 15 + 43 * 15 + 41 * 15 + . . . + 17 * 15 = 15 ( 45 + 43 + 41 + . . . + 17 ) in brackets we have an equally spaced sum with fifteen terms , which we can evaluate using the familiar formula . so the above equals 15 * 15 * 62 / 2 = 6975 and adding back the 1270 , we get the answer of 8245 . ( ans d )\"" + }, + { + "Answer": 180, + "Options": "a ) 100 % , b ) 160 % , c ) 180 % , d ) 200 % , e ) 220 %", + "Correct": "c", + "Explanation": "say vartan ' s wages last week were $ 100 , so he spent 0.15 * 100 = $ 15 on recreation ; this week ' s wages is 0.9 * 100 = $ 90 , so he spends 0.3 * 90 = $ 27 on recreation ; 27 / 15 = 1.8 , hence the amount he spends on recreation this week is 180 % of the amount he spent on recreation last week : 15 * 1.8 = 27 . answer : c ." + }, + { + "Answer": 12, + "Options": "a ) 23 , b ) 27 , c ) 12 , d ) 43 , e ) 37", + "Correct": "c", + "Explanation": "explanation : from the options itself , we can see that option c old = 30 young = 18 30 + 18 = 48 by reducing this years only by one before 6 years old = 24 ( half of young ) young = 12 ( twice of old ) answer : c" + }, + { + "Answer": 88.23529411764707, + "Options": "a ) 60 % , b ) 72 % , c ) 88 % , d ) 95 % , e ) 110 %", + "Correct": "c", + "Explanation": "let x be the number of new biographies added to the library . let b be the original number of biographies , so the original number of books was 5 b . 0.32 ( 5 b + x ) = b + x 0.6 b = 0.68 x x = 0.88 b the answer is c ." + }, + { + "Answer": 40, + "Options": "a ) 46 , b ) 49 , c ) 40 , d ) 38 , e ) 35", + "Correct": "c", + "Explanation": "total marks obtained by a class of 20 students = 2 * 100 + 3 * 0 + 15 * 40 = 200 + 600 = 800 : average marks of whole class = 800 / 20 = 40 answer is c ." + }, + { + "Answer": 10, + "Options": "a ) 22 kg , b ) 21.6 kg , c ) 22.4 kg , d ) 10 kg , e ) none of these", + "Correct": "d", + "Explanation": "\"exp . the total weight of 29 students = 29 * 28 the total weight of 30 students = 30 * 27.4 weight of the new student = ( 30 * 27.4 \u2013 29 * 28 ) = 822 - 812 = 10 answer : d\"" + }, + { + "Answer": 3, + "Options": "a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 9", + "Correct": "a", + "Explanation": "let the number be x . then , x + 17 = 60 x x 2 + 17 x - 60 = 0 ( x + 20 ) ( x - 3 ) = 0 x = 3 option a" + }, + { + "Answer": 12.5, + "Options": "a ) 10.5 , b ) 11 , c ) 11.5 , d ) 12 , e ) 12.5", + "Correct": "e", + "Explanation": "\"mean = 17.5 two standard deviations is 2.5 + 2.5 = 5.0 there could be two calues for this . mean + two standard deviations = 22.5 mean - two standard deviations = 12.5 answer choice has 12.5 and so e is the answer .\"" + }, + { + "Answer": 0.3076923076923077, + "Options": "a ) 0.31 , b ) 0.55 , c ) 0.65 , d ) 0.75 , e ) 0.85", + "Correct": "a", + "Explanation": "\"number of people whose age is less than 20 is given by 130 - 90 = 40 probability p that a person selected at random from the group is less than 20 is given by 40 / 130 = 0.31 correct answer a\"" + }, + { + "Answer": 68.8, + "Options": "a ) 69 , b ) 75 , c ) 82 , d ) 91 , e ) 56", + "Correct": "a", + "Explanation": "mean = ( 17 + 27 + 31 + 53 + 62 ) / 5 = 38 median = 31 sum = 38 + 31 = 69 option a" + }, + { + "Answer": 48, + "Options": "a ) 44 % , b ) 48 % , c ) 52 % , d ) 42 % , e ) 46 %", + "Correct": "b", + "Explanation": "\"first calculate the distance , b has covered with his speed in the time , in which a reached 60 % of the race . then add the remaining distance as head start for b to win the race . its best to apply ratios concept here . since a ' s speed is 15 / 13 of b , therefore , b ' s speed is 13 / 15 of a distance covered by b = speed x time = ( 13 / 15 ) x ( 0.6 ) = 0.52 % ( which means b would have covered 0.52 of the race length during the time in which a has covered 0.6 of the race length . therefore to win , b needs a headstart of ( 1 - 0.52 = ) 0.48 of the race length . so the answer is b\"" + }, + { + "Answer": 12.5, + "Options": "a ) 1.4 % , b ) 5.9 % , c ) 11.1 % , d ) 12.5 % , e ) 23.6 %", + "Correct": "d", + "Explanation": "\"opening = 8 closing = 9 rise in price = 1 so , percent increase = 18 \u2217 10018 \u2217 100 = > 12.50 % thus answer will be ( d )\"" + }, + { + "Answer": 52, + "Options": "a ) 52 , b ) 47 , c ) 48 , d ) 49 , e ) 50", + "Correct": "a", + "Explanation": "\"the standard deviation ( { sd } ) = 2 ; 3 standard deviations below the mean is greater than 45 : { mean } - 3 * { sd } > 45 ; { mean } - 6 > 45 ; { mean } > 51 . answer : a .\"" + }, + { + "Answer": 9938, + "Options": "a ) 30002 , b ) 70002 , c ) 50002 , d ) 90002 , e ) 10002", + "Correct": "e", + "Explanation": "\"according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 10010 - 12 * 3 * 2 = 10010 - 8 = 10002 correct answer e\"" + }, + { + "Answer": 1596, + "Options": "a ) 1235 , b ) 1345 , c ) 1678 , d ) 1767 , e ) 1611", + "Correct": "e", + "Explanation": "let the smaller number be x . then larger number = ( x + 1345 ) . x + 1345 = 6 x + 15 5 x = 1330 x = 266 large number = 266 + 1345 = 1611 e" + }, + { + "Answer": 18, + "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 18", + "Correct": "e", + "Explanation": "\"10 + 8 = 18 correct answer is e ) 18\"" + }, + { + "Answer": 76, + "Options": "a ) 2 , b ) 4 , c ) 70 , d ) 76 , e ) none", + "Correct": "d", + "Explanation": "\"sol . average after 11 innings = 36 . therefore required numbert of runs = ( 36 \u00d7 11 ) \u2013 ( 32 \u00d7 10 ) = 396 - 320 = 76 . answer d\"" + }, + { + "Answer": 4000, + "Options": "a ) rs . 3000 , b ) rs . 4000 , c ) rs . 5000 , d ) rs . 6000 , e ) rs . 7000", + "Correct": "b", + "Explanation": "\"let p , q and r represent their respective monthly incomes . then , we have : p + q = ( 5050 x 2 ) = 10100 . . . . ( i ) q + r = ( 6250 x 2 ) = 12500 . . . . ( ii ) p + r = ( 5200 x 2 ) = 10400 . . . . ( iii ) adding ( i ) , ( ii ) and ( iii ) , we get : 2 ( p + q + r ) = 33000 or p + q + r = 16500 . . . . ( iv ) subtracting ( ii ) from ( iv ) , we get p = 4000 . p ' s monthly income = rs . 4000 . b )\"" + }, + { + "Answer": 28, + "Options": "a ) 9 , b ) 12 , c ) 18 , d ) 28 , e ) 363", + "Correct": "d", + "Explanation": "\", p ^ 2 , p ^ 3 and q , q ^ 1 , q ^ 2 . . . . q ^ 6 together essentially there are 18 different combinations you can make ( 3 x 6 ) also you have to include the different combinations the p and q exponents can be a divisor . there are 3 different p exponents and 6 different q exponents : p , p ^ 2 , p ^ 3 , q , q ^ 2 , q ^ 3 . . . q ^ 6 also add 1 since ` ` 1 ' ' can also be a divisor . 18 + 3 + 6 + 1 = 28 , answer : d\"" + }, + { + "Answer": 172800, + "Options": "a ) 32,300 , b ) 172,800 , c ) 468,830 , d ) 338,200 , e ) 259,200", + "Correct": "b", + "Explanation": "\"every 2 seconds , 4 persons are added ( 6 - 2 ) . every second 2 persons are added . in a day 24 hrs = 24 * 60 minutes = 24 * 60 * 60 = 86400 seconds . 86400 * 2 = 172800 option b is the answer .\"" + }, + { + "Answer": 15.700000000000001, + "Options": "a ) 12.6 . , b ) 15.8 . , c ) 14.4 . , d ) 16.2 . , e ) 16.4 .", + "Correct": "b", + "Explanation": "\"[ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.3 ] - 6.6 = 6 * 0 + 2 * 7.2 + 8 - 6.6 = 0 + 14.4 + 1.4 15.8 answer b\"" + }, + { + "Answer": 0.25, + "Options": "a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6", + "Correct": "c", + "Explanation": "\"x = 8 y + 5 , and thus y = x / 8 - 5 / 8 the slope is 1 / 8 . the slope of a line through points ( m , n ) and ( m + 2 , n + p ) is ( n + p - n ) / ( m + 2 - m ) = p / 2 p / 2 = 1 / 8 and thus p = 1 / 4 the answer is c .\"" + }, + { + "Answer": 9, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9", + "Correct": "e", + "Explanation": "\"sol . let the ten \u2019 s digit be x and unit \u2019 s digit be y , then , ( 10 x + y ) - ( 10 y + x ) = 81 \u21d4 9 ( x - y ) = 81 \u21d4 x - y = 9 answer e\"" + }, + { + "Answer": 57.22222222222222, + "Options": "a ) 52.6 , b ) 52.4 , c ) 52.1 , d ) 57 , e ) 52.9", + "Correct": "d", + "Explanation": "\"sum of the marks for the class of 35 students = 35 * 45 = 1575 sum of the marks for the class of 55 students = 55 * 65 = 3575 sum of the marks for the class of 90 students = 1575 + 3575 = 5150 average marks of all the students = 5150 / 90 = 57 . answer : d\"" + }, + { + "Answer": 60, + "Options": "a ) $ 60 , b ) $ 55 , c ) $ 42 , d ) $ 31 , e ) $ 100", + "Correct": "a", + "Explanation": "\"3 / 10 a = 1 / 5 b a = 1 / 5 * 10 / 3 b a = 2 / 3 b a / b = 2 / 3 a : b = 2 : 3 b ' s share = 100 * 3 / 5 = $ 60 answer is a\"" + }, + { + "Answer": 40, + "Options": "a ) 23 , b ) 32 , c ) 40 , d ) 41 , e ) 44", + "Correct": "c", + "Explanation": "\"let number of years taught by virginia = v number of years taught by adrienne = a number of years taught by dennis = d v + a + d = 96 v = a + 9 = > a = v - 9 v = d - 9 = > a = ( d - 9 ) - 9 = d - 18 d - 9 + d - 18 + d = 93 = > 3 d = 93 + 27 = 120 = > d = 40 answer c\"" + }, + { + "Answer": 0.9999999999999898, + "Options": "a ) 5 % , b ) 4 % , c ) 3 % , d ) 2 % , e ) 1 %", + "Correct": "e", + "Explanation": "\"let x be the amount of money paid for the first purchase . the second time , the customer paid 0.9 ( 1.1 x ) = 0.99 x . the difference is 1 % . the answer is e .\"" + }, + { + "Answer": 0.04, + "Options": "a ) 0.02 , b ) 0.2 , c ) 0.04 , d ) 0.4 , e ) 4", + "Correct": "c", + "Explanation": "\"solution given expression = ( 11.98 ) 2 + ( 0.02 ) 2 + 11.98 \u00d7 x . for the given express to be a perfect square , we must have 11.98 \u00d7 x = 2 \u00d7 11.98 \u00d7 0.02 or x = 0.04 . answer c\"" + }, + { + "Answer": 178, + "Options": "a ) 178.89 cm , b ) 178.29 cm , c ) 178.79 cm , d ) 177.89 cm , e ) 178.69 cm", + "Correct": "b", + "Explanation": "calculated average height of 35 boys = 180 cm . wrong total height of 35 boys = 180 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 180 * 35 cm - 166 cm + 106 cm = 180 * 35 cm - 166 cm + 106 cm / 35 = 180 cm - 60 / 35 cm = 180 cm - 1.71 cm = 178.29 cm . answer : b" + }, + { + "Answer": 1.5, + "Options": "a ) 3 / 2 , b ) 5 / 2 , c ) 7 / 2 , d ) 9 / 2 , e ) 11 / 2", + "Correct": "a", + "Explanation": "2 / 2 + 1 / 2 = 1 + 1 / 2 = 3 / 2 answer : a" + }, + { + "Answer": 20, + "Options": "a ) 15 % , b ) 18 % , c ) 20 % , d ) 25 % , e ) 26 %", + "Correct": "c", + "Explanation": "\"1 st year income = i 1 st year savings = s 1 st year expense = e 1 2 nd year income = 1.2 i 2 nd year savings = 2 s ( 100 % increase ) 2 nd year expense = e 2 e 1 + e 2 = 2 e 1 e 2 = e 1 that means expenses are same during both years . with increase of 20 % income the savings increased by 100 % . or s = . 2 i or s = 20 % of income c is the answer\"" + }, + { + "Answer": 4, + "Options": "a ) 6 , b ) 7 , c ) 4 , d ) 5 , e ) 8", + "Correct": "c", + "Explanation": "product of 95 and . 02554 is 2.4263 . therefore number of digits to right of decimal point is 4 answer is c ." + }, + { + "Answer": 89, + "Options": "a ) 67 , b ) 26 , c ) 89 , d ) 26 , e ) 75", + "Correct": "c", + "Explanation": "\"average = ( 86 + 85 + 92 + 87 + 95 ) / 5 = 445 / 5 = 89 . answer : c\"" + }, + { + "Answer": 50, + "Options": "a ) 50 , b ) 54 , c ) 55 , d ) 56 , e ) 60", + "Correct": "a", + "Explanation": "\"let x be the original weight . the weight of the grape pulp was 0.08 x . since the grape pulp is 80 % of the raisins , 0.08 x = 0.8 ( 5 ) . then x = 50 kg . the answer is a .\"" + }, + { + "Answer": 90, + "Options": "a ) 55 , b ) 90 , c ) 73 , d ) 82 , e ) 91", + "Correct": "b", + "Explanation": "\"let the number of correct responses be x then the number of incorrect responses = 100 - x according to question x - 2 ( 100 - x ) = 70 ( subtracting twice of incorrect from correct ) 3 x = 270 x = 90 answer : b\"" + }, + { + "Answer": 153, + "Options": "a ) 190 , b ) 153 , c ) 210 , d ) 220 , e ) 230", + "Correct": "b", + "Explanation": "\"1 st person will shake hand with 17 people 2 nd person will shake hand with 16 people 3 rd person will shake hand with 15 people . . . . . . total no . of handshakes = 17 + . . . + 3 + 2 + 1 = 17 * ( 17 + 1 ) / 2 = 153 or , if there are n persons then no . of shakehands = nc 2 = 18 c 2 = 153 answer : b\"" + }, + { + "Answer": 346, + "Options": "a ) 545 , b ) 685 , c ) 865 , d ) 495 , e ) 346", + "Correct": "e", + "Explanation": "let y x 120 = 173 x 240 then y = ( 173 x 240 ) / 120 = 346 . answer : e" + }, + { + "Answer": 16, + "Options": "a ) 27 % , b ) 21 % , c ) 19 % , d ) 18 % , e ) 16 %", + "Correct": "e", + "Explanation": "\"let the total number of parents = 100 number of women = 40 number of men = 60 number of mothers who held full time jobs = 3 / 4 * 40 = 30 number of fathers who held full time jobs = 9 / 10 * 60 = 54 total number of parents who held full time jobs = 84 total number of parents who did not hold jobs = 100 - 84 = 16 alternatively , percentage of women = 40 % percentage of women who did not hold full time jobs = ( 1 - 3 / 4 ) * 100 % = 25 % of all mothers did not have full time jobs 25 % of 40 % - - > 10 % of the total parents percentage of men = 60 % percentage of men who held full time jobs = ( 1 - 9 / 10 ) * 100 % = 10 % of all fathers did not have full time jobs 10 % of 60 % - - > 6 % of the total parents therefore , percentage of parents who did not hold full time jobs = 10 + 6 = 16 % answer e - 16 %\"" + }, + { + "Answer": 1200.0000000000002, + "Options": "a ) 220 , b ) 230 , c ) 1200 , d ) 560 , e ) 590", + "Correct": "c", + "Explanation": "\"n * 50 = ( 360000 - 300000 ) = 60000 n = 60000 / 50 = 1200 c\"" + }, + { + "Answer": 0.375, + "Options": "a ) 0.375 , b ) 0.25 , c ) 0.325 , d ) 0.5 , e ) 0.666", + "Correct": "a", + "Explanation": "\"total number of ways in which h or t can appear in 3 tosses of coin is = 2 * 2 * 2 = 8 ways for 2 t and 1 th thus probability is = p ( htt ) + p ( tth ) + p ( tht ) = 1 / 8 + 1 / 8 + 1 / 8 = 3 / 8 = . 375 answer : a\"" + }, + { + "Answer": 145, + "Options": "a ) a ) 51 , b ) b ) 58 , c ) c ) 145 , d ) d ) 190 , e ) e ) 210", + "Correct": "c", + "Explanation": "\"a very helpful rule to know in arithmetic is the rule that in evenly spaced sets , average = median . because the average will equal the median in these sets , then we quickly know that the median of this set of consecutive odd integer numbers is 154 . there are 10 numbers in the set , and in a set with an even number of terms the median is just the average of the two most median terms ( here the 5 th and 6 th numbers in the set ) . this means that numbers 5 and 6 in this set are 153 and 155 . because we know that number 5 is 153 , we know that the smallest number is 4 odd numbers below this , which means that it is 4 * 2 = 8 below this ( every odd number is every other number ) . therefore 153 - 8 = 145 , answer choice c\"" + }, + { + "Answer": 89.6, + "Options": "a ) 90 % , b ) 80 % , c ) 70 % , d ) 60 % , e ) 40 %", + "Correct": "a", + "Explanation": "the problem asks for the approximate chance that no more than 1 / 3 of the original investment is lost . we can apply the \u201c 1 \u2013 x \u201d technique : what \u2019 s the chance that more than 1 / 3 of the original investment is lost ? there are two outcomes we have to separately measure : ( a ) all 3 investments become worthless . ( b ) 2 of the 3 investments become worthless , while 1 doesn \u2019 t . outcome ( a ) : the probability is ( 0.2 ) ( 0.2 ) ( 0.2 ) = 0.008 , or a little less than 1 % . outcome ( b ) : call the investments x , y , and z . the probability that x retains value , while y and z become worthless , is ( 0.8 ) ( 0.2 ) ( 0.2 ) = 0.032 . now , we have to do the same thing for the specific scenarios in which y retains value ( while x and z don \u2019 t ) and in which z retains value ( while x and y don \u2019 t ) . each of those scenarios results in the same math : 0.032 . thus , we can simply multiply 0.032 by 3 to get 0.096 , or a little less than 10 % . the sum of these two probabilities is 0.008 + 0.096 = 0.104 , or a little more than 10 % . finally , subtracting from 100 % and rounding , we find that the probability we were looking for is approximately 90 % . the correct answer is a . this problem illustrates the power of diversification in financial investments . all else being equal , it \u2019 s less risky to hold a third of your money in three uncorrelated ( independent ) but otherwise equivalent investments than to put all your eggs in one of the baskets . that said , be wary of historical correlations ! housing price changes in different us cities were not so correlated \u2014 and then they became highly correlated during the recent housing crisis ( they all fell together ) , fatally undermining spreadsheet models that assumed that these price changes were independent ." + }, + { + "Answer": 150000, + "Options": "a ) 150000 , b ) 160000 , c ) 170000 , d ) 190000 , e ) 250000", + "Correct": "a", + "Explanation": "\"if value of business = x total sell ( 2 x / 3 ) ( 3 / 4 ) = 75000 - > x = 150000 answer : a\"" + }, + { + "Answer": 15, + "Options": "a ) 15 , b ) 20 , c ) 22 , d ) 12 , e ) 8", + "Correct": "a", + "Explanation": "a joey sold 15 ice creams that day . the fourth kid bought a single ice cream . therefore , we have the following equation : total - ( total / 2 + 1 / 2 ) = 1 solving it , we get the total as 3 . let ' s work this method till we reach the first kid . the first kid bought 15 / 2 + 1 / 2 = 8 ( leaving 7 ) the second kid bought 7 / 2 + 1 / 2 = 4 ( leaving 3 ) the third kid bought 3 / 2 + 1 / 2 = 2 ( leaving 1 ) the fourth kid bought 1 / 2 + 1 / 2 = 1 adding all of them together , we get 8 + 4 + 2 + 1 = 15 ." + }, + { + "Answer": 480, + "Options": "a ) $ 200 , b ) $ 300 , c ) $ 480 , d ) $ 500 , e ) $ 600", + "Correct": "c", + "Explanation": "\"c for cost . p price per person . c = 3 * p c = 4 * p - 160 substituting the value of p from the first equation onto the second we get p = 160 . plugging in the value of p in the first equation , we get c = 480 . which leads us to answer choice c\"" + }, + { + "Answer": 107.14285714285714, + "Options": "a ) 107 , b ) 84 , c ) 40 , d ) 28 , e ) 20", + "Correct": "a", + "Explanation": "\"almonds : walnuts = 5 : 2 total mixture has 7 parts in a 150 pound mixture , almonds are 5 / 7 ( total mixture ) = 5 / 7 * 150 = 107 pounds answer ( a )\"" + }, + { + "Answer": 5, + "Options": "a ) 4 and 1 , b ) 1 and 5 , c ) 5 and 1 , d ) 3 and 5 , e ) 5 and 3", + "Correct": "c", + "Explanation": "\"line k passes through the origin and has slope 1 / 5 means that its equation is y = 1 / 5 * x . thus : ( x , 1 ) = ( 5 , 1 ) and ( 5 , y ) = ( 5,1 ) - - > x = 5 and y = 1 answer : c\"" + }, + { + "Answer": 5015, + "Options": "a ) 15 , b ) 20 , c ) 5015 , d ) 25 , e ) 35", + "Correct": "c", + "Explanation": "\"explanation : = 5020 \u2212 ( 502 / 1004 \u00d7 10 ) = 5020 \u2212 5 = 5015 option c\"" + }, + { + "Answer": 50, + "Options": "a ) 48 , b ) 50 , c ) 54 , d ) 66 , e ) 86", + "Correct": "b", + "Explanation": "\"the total sum of the numbers should be increased by 40 . then the average will increase by 40 / 10 = 4 . the correct average is 50 . the answer is b .\"" + }, + { + "Answer": 25, + "Options": "a ) 12.5 % , b ) 20 % , c ) 25 % , d ) 50 % , e ) 100 %", + "Correct": "c", + "Explanation": "\"correct answer : c solution : c . we can set up equations for income before and after the wage reduction . initially , the employee earns w wage and works h hours per week . after the reduction , the employee earns . 8 w wage and works x hours . by setting these equations equal to each other , we can determine the increase in hours worked : wh = . 8 wx ( divide both sides by . 8 w ) 1.25 h = x we know that the new number of hours worked w will be 25 % greater than the original number . the answer is c .\"" + }, + { + "Answer": 8, + "Options": "a ) $ 7.2 , b ) $ 7.5 , c ) $ 8 , d ) $ 9 , e ) $ 10", + "Correct": "c", + "Explanation": "a and b is not an integer . so we start with c if large doll costs $ 8 , then he can buy 320 / 8 = 40 large dolls and 320 / 4 = 80 small dolls . difference is 40 , which is we wanted . answer c ." + }, + { + "Answer": 200, + "Options": "a ) s . 200 , b ) s . 100 , c ) s . 300 , d ) s . 50 , e ) s . 90", + "Correct": "a", + "Explanation": "\"a profit of rs . 1000 is divided between x and y in the ratio of 1 / 2 : 1 / 3 or 3 : 2 . so profits are 600 and 400 . difference in profit share = 600 - 400 = 200 answer : a\"" + }, + { + "Answer": 0.41666666666666674, + "Options": "a ) 1 / 6 , b ) 1 / 4 , c ) 2 / 7 , d ) 1 / 3 , e ) 5 / 12", + "Correct": "e", + "Explanation": "\"total marbles in the box = 120 white marbles = 120 / 4 = 30 green marbles = 120 / 3 = 40 w + g = 70 red + blue = 50 p ( red or blue ) = 50 / 120 = 5 / 12 answer : e\"" + }, + { + "Answer": 31, + "Options": "a ) 44 , b ) 56 , c ) 16 , d ) 32 , e ) 31", + "Correct": "e", + "Explanation": "\"by formula , ( a + b + c ) ^ 2 = a ^ 2 + b ^ 2 + c ^ 2 + 2 ( ab + bc + ca ) , since , a ^ 2 + b ^ 2 + c ^ 2 = 941 and ab + bc + ca = 10 , ( a + b + c ) ^ 2 = 941 + 2 ( 10 ) = 961 = 31 ^ 2 therefore : a + b + c = 31 answer : e\"" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9", + "Correct": "a", + "Explanation": "\"the tens digit of 6 in integer power starting from 2 ( 6 ^ 1 has no tens digit ) repeats in a pattern of 5 : { 3 , 1 , 9 , 7 , 5 } : the tens digit of 6 ^ 2 = 36 is 3 . the tens digit of 6 ^ 3 = 216 is 1 . the tens digit of 6 ^ 4 = . . . 96 is 9 . the tens digit of 6 ^ 5 = . . . 76 is 7 . the tens digit of 6 ^ 6 = . . . 56 is 5 . the tens digit of 6 ^ 7 = . . . 36 is 3 again . etc . . . 18 has the form 5 n + 3 , so the tens digit of 6 ^ 18 is 1 . the answer is a .\"" + }, + { + "Answer": 15.5, + "Options": "a ) 14 , b ) 14.5 , c ) 15 , d ) 15.5 , e ) 16", + "Correct": "d", + "Explanation": "\"the total subtracted is ( 9 + 8 + . . . + 1 ) = ( 9 * 10 ) / 2 = 45 on average , each number will be reduced by 45 / 10 = 4.5 therefore , the overall average will be reduced by 4.5 the answer is d .\"" + }, + { + "Answer": 90, + "Options": "a ) 40 , b ) 80 , c ) 70 , d ) 60 , e ) 90", + "Correct": "e", + "Explanation": "\"200 men do the rest of the work in 100 - 10 = 90 days 100 men can do the rest of the work in 90 * 200 / 100 = 180 days required number of days = 180 - 90 = 90 days answer is e\"" + }, + { + "Answer": 30, + "Options": "a ) 30 kg , b ) 37 kg , c ) 42 kg , d ) 55.12 kg , e ) 29.78 kg", + "Correct": "a", + "Explanation": "\"total weight of 36 + 44 students = 36 * 30 + 24 * 30 = 1800 average weight of the class is = 1800 / 60 = 30 kg answer is a\"" + }, + { + "Answer": 1.75, + "Options": "a ) $ 1.75 , b ) $ 2.50 , c ) $ 4.10 , d ) $ 4.70 , e ) $ 8.20", + "Correct": "a", + "Explanation": "\"let x be the cost of a bus ride . x + ( x + 635 ) = 985 2 x = 350 x = $ 1.75 the answer is a .\"" + }, + { + "Answer": 261, + "Options": "a ) 135 , b ) 261 , c ) 422 , d ) 430 , e ) 438", + "Correct": "b", + "Explanation": "\"the number of liters in each can = hcf of 10 , 144 and 368 = 2 liters . number of cans of maaza = 10 / 2 = 5 number of cans of pepsi = 144 / 2 = 72 number of cans of sprite = 368 / 2 = 184 the total number of cans required = 5 + 72 + 184 = 261 cans . answer : b\"" + }, + { + "Answer": 5, + "Options": "a ) 55 , b ) 5 , c ) 10 , d ) 45 , e ) 4", + "Correct": "b", + "Explanation": "let the numbers be a and b and hcf is x , then , a + b = 45 and ab = x * 120 = 120 x required sum = 1 / a + 1 / b = ( a + b ) / ab = 45 / 120 x = 11 / 120 . x = 5 . answer : b" + }, + { + "Answer": 27.27272727272727, + "Options": "a ) 23 % , b ) 27 % , c ) 31 % , d ) 35 % , e ) 39 %", + "Correct": "b", + "Explanation": "\"let p be the original price per unit of gas . let x be the original gas consumption . let y be the reduced gas consumption . y * 1.1 * 1.25 * p = x * p y = x / ( 1.1 * 1.25 ) which is about 0.73 x which is a decrease of about 27 % . the answer is b .\"" + }, + { + "Answer": 68.75, + "Options": "a ) 44 % , b ) 40 % , c ) 68.75 % , d ) 56.25 % , e ) 36 %", + "Correct": "c", + "Explanation": "\"the dealer uses weight which is 20 % less than the real weight . or ( 1 - 1 / 5 ) or 4 / 5 of real weight . it means that he is selling $ 4 worth of product for $ 5 . the dealer then further added 35 % impurities to the product . it means that he is selling $ 5 worth of product for $ 6.75 . so his profit is $ 6.75 - $ 4 = $ 2 and his profit percent is ( 2.75 / 4 ) * 100 = 68.75 % answer : - c\"" + }, + { + "Answer": 48, + "Options": "a ) $ 22 , b ) $ 24 , c ) $ 30 , d ) $ 36 , e ) $ 48", + "Correct": "e", + "Explanation": "e its is . let price = x ( x - 2 ) 8 = 6 x x = 8 hence total money = 6 * 8 = 48" + }, + { + "Answer": 99.99999999999991, + "Options": "a ) 80 , b ) 110 , c ) 160 , d ) 100 , e ) 400", + "Correct": "d", + "Explanation": "\"we start by creating a variable for the total number of students in the math course . we can say : t = total number of students in the math course next , we can use variable t in an equation that we translate from the given information . we are given that , of the final grades received by the students in a certain math course , 1 / 5 are a ' s , 1 / 4 are b ' s , 1 / 2 are c ' s , and the remaining 5 grades are d ' s . since this represents all the grades in the class , it represents all the students in the class . thus we know : # a \u2019 s + # b \u2019 s + # c \u2019 s + # d \u2019 s = total number of students in the class 1 / 5 ( t ) + \u00bc ( t ) + \u00bd ( t ) + 5 = t we can multiply the entire equation by 20 to cancel out the denominators of the fractions and we have : 4 t + 5 t + 10 t + 100 = 20 t 19 t + 100 = 20 t 100 = t there are a total of 100 students in the math class . answer is d .\"" + }, + { + "Answer": 4.333333333333333, + "Options": "a ) 0 , b ) 4.3 , c ) 2.5 , d ) 4.67 , e ) 10", + "Correct": "b", + "Explanation": "spotting the pattern of equations both are in form of ( x + c ) ^ 2 so a 1 = ( x + 6 ) ^ 2 a 2 = ( 2 x - 3 ) ^ 2 l 1 = x + 6 l 2 = 2 x - 3 p 1 = 4 ( x + 6 ) p 2 = 4 ( 2 x - 3 ) p 1 + p 2 = 64 4 ( x + 6 ) + 4 ( 2 x - 3 ) = 64 . . . . . . . . . . . . . . > x = 4.3 answer : b" + }, + { + "Answer": 408.00000000000006, + "Options": "a ) s . 300 , b ) s . 408 , c ) s . 389 , d ) s . 368 , e ) s . 323", + "Correct": "b", + "Explanation": "\"( a = 2 / 3 b and b = 1 / 4 c ) = a / b = 2 / 3 and b / c = 1 / 4 a : b = 2 : 3 and b : c = 1 : 4 = 3 : 12 a : b : c = 2 : 3 : 12 a ; s share = 578 * 2 / 17 = rs . 68 b ' s share = 578 * 3 / 17 = rs . 102 c ' s share = 578 * 12 / 17 = rs . 408 . answer : b\"" + }, + { + "Answer": 22, + "Options": "a ) 22 kg , b ) 21.6 kg , c ) 22.4 kg , d ) 21 kg , e ) 23 kg", + "Correct": "a", + "Explanation": "\"the total weight of 29 students = 29 * 28 the total weight of 30 students = 30 * 27.8 weight of the new student = ( 30 * 27.8 \u2013 29 * 28 ) = 834 - 812 = 22 answer : a\"" + }, + { + "Answer": 0.4, + "Options": "a ) 0.4 , b ) 0.5 , c ) 0.65 , d ) 0.75 , e ) 0.85", + "Correct": "a", + "Explanation": "\"number of people whose age is less than 20 is given by 150 - 90 = 60 probability p that a person selected at random from the group is less than 20 is given by 60 / 150 = 0.4 correct answer a\"" + }, + { + "Answer": 12550, + "Options": "a ) 5,150 , b ) 7,550 , c ) 10,150 , d ) 12,550 , e ) 20,150", + "Correct": "d", + "Explanation": "\"2 + 4 + 6 + 8 + . . . + 100 = 2550 202 + 204 + . . . + 300 = 50 ( 200 ) + ( 2 + 4 + . . . + 100 ) = 10,000 + 2550 = 12,550 the answer is d .\"" + }, + { + "Answer": 89, + "Options": "a ) 60 kg , b ) 70 kg , c ) 80 kg , d ) 89 kg , e ) 95 kg", + "Correct": "d", + "Explanation": "\"total weight increased = ( 8 x 3 ) kg = 24 kg . weight of new person = ( 65 + 24 ) kg = 89 kg . d )\"" + }, + { + "Answer": 43.75, + "Options": "a ) 46.85 % , b ) 43.75 % , c ) 50 % , d ) 56.25 % , e ) 36 %", + "Correct": "b", + "Explanation": "the dealer uses weight which is 20 % less than the real weight . or ( 1 - 1 / 5 ) or 4 / 5 of real weight . it means that he is selling $ 4 worth of product for $ 5 . the dealer then further added 20 % impurities to the product . it means that he is selling $ 5 worth of product for $ 5.75 . so his profit is $ 5.75 - $ 4 = $ 1.75 and his profit percent is ( 1.75 / 4 ) * 100 = 43.75 % answer : - b" + }, + { + "Answer": 4.166666666666667, + "Options": "a ) 3.56 , b ) 4.16 , c ) 4.86 , d ) 5.1 , e ) 5.2", + "Correct": "b", + "Explanation": "the cost of one orange = 5 / 12 = 0.416 the cost of ten oranges = 0.416 x 10 = $ 4.16 answer : b" + }, + { + "Answer": 117, + "Options": "a ) 108 , b ) 111 , c ) 114 , d ) 117 , e ) 120", + "Correct": "d", + "Explanation": "` ` rat ' ' = ( 18 + 1 + 20 ) * 3 = 117 . the answer is d ." + }, + { + "Answer": 9, + "Options": "a ) 3 , b ) 14 , c ) 9 , d ) 21 , e ) none of these", + "Correct": "c", + "Explanation": "\"explanation \u221a ( 9 ) ^ 2 = ? or , ? = 9 answer c\"" + }, + { + "Answer": 32, + "Options": "a ) 36 , b ) 34 , c ) 38 , d ) 32 , e ) 31", + "Correct": "d", + "Explanation": "explanation : let us consider , ribbon is denoted by r clips is denoted by c soaps is denoted by s now according to the question , = > 3 r + 7 c + s = 120 - - - - - - - - ( 1 ) = > 4 r + 10 c + s = 164 - - - - - - - - ( 2 ) ( 1 ) - ( 2 ) = > ( 3 r - 4 r ) + ( 7 c - 10 c ) + ( s - s ) = 120 - 164 = > - r - 3 c = - 44 multily the equation by - 1 , it becomes = > r + 3 c = 44 - - - - - - - ( 3 ) now perform this operation 2 * ( 1 ) - ( 2 ) = > 2 r + 4 c + s = 76 - - - - - - - ( 4 ) finaly ( 4 ) - ( 3 ) = > r + c + s = 32 hence , the cost of 1 ribbon , 1 clip and 1 saop would be 32 rs . answer : d" + }, + { + "Answer": 5, + "Options": "a ) 3 , b ) 5 , c ) 6 , d ) 11 , e ) 16", + "Correct": "b", + "Explanation": "\"( m - 8 ) ( m - a ) = m ^ 2 - km - 24 a = - 3 k = 8 + a = 5 = b\"" + }, + { + "Answer": 30, + "Options": "a ) 5 % , b ) 10 % , c ) 15 % , d ) 20 % , e ) 30 %", + "Correct": "e", + "Explanation": "solution : let the total number of flags be 100 ( even number ) let the total number of ' blue ' flags alone be ' a ' let the total number of ' red ' flags alone be ' b ' let the total number of ' both ' flags be ' c ' we have given , total number of blue flags = 60 % = 60 = a + c total number of red flags = 70 % = 70 = b + c total number of flags = a + b + c = 100 ( since all the flags have been utilized ) so , substituting for c in the third equation , we have , 60 - c + c + 70 - c = 100 c = 30 option e ." + }, + { + "Answer": 35, + "Options": "a ) 35 , b ) 90 , c ) 11 , d ) 10 , e ) 9", + "Correct": "a", + "Explanation": "\"number start between 25 to 95 is 70 numbers half of them is even . . which is 35 answer : a\"" + }, + { + "Answer": 18, + "Options": "a ) 15 , b ) 19 , c ) 11 , d ) 18 , e ) 13", + "Correct": "d", + "Explanation": "\"let the population of two villages be equal after p years then , 78000 - 1200 p = 42000 + 800 p 2000 p = 36000 p = 18 answer is d .\"" + }, + { + "Answer": 2, + "Options": "a ) 4 , b ) 3 , c ) 2 , d ) 1 , e ) 0", + "Correct": "c", + "Explanation": "explanation : let n \u00f7 4 = p , remainder = 3 = > n = 4 p + 3 2 n = 2 ( 4 p + 3 ) = 8 p + 6 = 8 p + 4 + 2 = 4 ( 2 p + 1 ) + 2 hence , if 2 n is divided by 4 , we will get 2 as remainder . answer : c" + }, + { + "Answer": 4579, + "Options": "a ) 4079 , b ) 4579 , c ) 5579 , d ) 5679 , e ) 5779", + "Correct": "b", + "Explanation": "\"total sale for 5 months = rs . ( 5124 + 5366 + 5808 + 5399 + 6124 ) = rs . 27821 . required sale = rs . [ ( 5400 x 6 ) - 27821 ] = rs . ( 32400 - 27821 ) = rs . 4579 . answer : b\"" + }, + { + "Answer": 0.03125, + "Options": "a ) 1 / 32 , b ) 7 / 8 , c ) 9 / 64 , d ) 5 / 64 , e ) 3 / 64", + "Correct": "a", + "Explanation": "\"p ( xavier will solve ) = 1 / 4 p ( yvonne will solve ) = 1 / 2 p ( zelda will not solve ) = 1 - 5 / 8 = 3 / 8 . now , we need to multiply all this ps to find an answer : p = ( 1 / 4 ) * ( 1 / 3 ) * ( 3 / 8 ) = 1 / 32 . ans . a .\"" + }, + { + "Answer": 942.8571428571429, + "Options": "a ) 540 , b ) 128 , c ) 100 , d ) 942 , e ) 942.86", + "Correct": "e", + "Explanation": "\"\u03c0 ( 202 \u2013 102 ) = 942.86 answer : e\"" + }, + { + "Answer": 7, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "e", + "Explanation": "\"let x = 5.1 and y = 12.1 greatest possible difference = 12.1 - 5.1 = 7 answer e\"" + }, + { + "Answer": 154, + "Options": "a ) 100 , b ) 120 , c ) 190 , d ) 160 , e ) 154", + "Correct": "e", + "Explanation": "x + y = x [ y + ( x - 1 ) ] = x ^ 2 + xy - x 12 + 6 = 12 [ 6 + ( 12 - 1 ) ] = 792 10 + 2 = 10 [ 2 + ( 10 - 1 ) ] = 110 1 + 9 = 1 [ 9 + ( 1 - 1 ) ] = 9 2 + 7 = 2 [ 7 + ( 2 - 1 ) ] = 16 11 + 4 = 11 [ 4 + ( 11 - 1 ) ] = 154 answer : e" + }, + { + "Answer": 0.4375, + "Options": "a ) 1 / 2 , b ) 3 / 8 , c ) 5 / 16 , d ) 1 / 4 , e ) 7 / 16", + "Correct": "e", + "Explanation": "start by deciding on a number of students to represent the number of students in the senior class . for this example i will choose 300 students . that would make the number of students in the junior class 100 . then we can find out how many students are taking japanese in each grade and add them together . ( 1 / 3 ) * 300 = 100 and ( 3 / 4 ) * 100 = 75 . 100 + 75 = 175 . there are a total of 400 students in the junior class and senior class combined ( 100 + 300 = 300 ) , and there are 175 total students in japanese , so 175 students in japanese / 400 total students equals 7 / 16 of the students in both classes that study japanese . answer : e" + }, + { + "Answer": 857, + "Options": "a ) 857 , b ) 859 , c ) 869 , d ) 4320 , e ) none of these", + "Correct": "a", + "Explanation": "\"solution required number = ( l . c . m . of 24 , 32 , 36 , 54 ) - 7 = 864 - 7 = 857 . answer a\"" + }, + { + "Answer": 57.14285714285714, + "Options": "a ) 33 % , b ) 40 % , c ) 55 % , d ) 57.14 % , e ) 66.14 %", + "Correct": "d", + "Explanation": "\"i just wanted to mention a couple of things here : * this is a pure ratio question ; the number 3,500 is completely irrelevant , and you can ignore it if you like . when we increase something by 1 / 7 , we are multiplying it by 1 + 1 / 7 = 8 / 7 , so the answer here must be ( 1 / 2 ) * ( 8 / 7 ) = 4 / 7 = 57.14 % . answer : d\"" + }, + { + "Answer": 23, + "Options": "a ) and 27 , b ) and 24 , c ) and 23 , d ) and 29 , e ) of these", + "Correct": "c", + "Explanation": "\"let the age of jill 11 years ago be x , age of henry be 2 x x + 11 + 2 x + 11 = 40 x = 6 present ages will be 17 and 23 answer : c\"" + }, + { + "Answer": 10, + "Options": "a ) $ 9 , b ) $ 3 , c ) $ 4 , d ) $ 6 , e ) $ 10", + "Correct": "e", + "Explanation": "\"my lunch = l , my friends lunch = l + 5 ( l ) + ( l + 5 ) = 15 l + l + 5 - 5 = 15 - 5 2 l = 10 l = 5 my friends lunch l + 5 = 5 + 5 = $ 10 , the answer is e\"" + }, + { + "Answer": 4, + "Options": "a ) 4 , b ) 15 , c ) 18 , d ) 21 , e ) 24", + "Correct": "a", + "Explanation": "the list should be wmwmw . hence , from women 2 ! and men 2 ! , we get ( 2 ! ) ( 2 ! ) = 4 . therefore , the correct answer is a ." + }, + { + "Answer": 231, + "Options": "a ) 99 , b ) 18 , c ) 16 , d ) 10 , e ) 231", + "Correct": "e", + "Explanation": "\"70 * 33 / 2 = 5 / 2 * 2 * x = > x = 231 answer : e\"" + }, + { + "Answer": 3.622, + "Options": "a ) 3.622 , b ) 3.911 , c ) 4.938 , d ) 2.986 , e ) 2.999", + "Correct": "a", + "Explanation": "\"3.15 + . 014 + . 458 = 0 0 = 0 - 3.15 - 0.014 - 0.458 0 = - 3.622 answer : a\"" + }, + { + "Answer": 33.33333333333333, + "Options": "a ) 33 % , b ) 10 % , c ) 5 % , d ) 15 % , e ) 25 %", + "Correct": "a", + "Explanation": "\"60 % of ( x - y ) = 30 % of ( x + y ) ( 60 / 100 ) ( x - y ) = ( 30 / 100 ) ( x + y ) 6 ( x - y ) = 3 ( x + y ) 3 x = 9 y x = 3 y therefore required percentage = ( ( y / x ) x 100 ) % = ( ( y / 3 y ) x 100 ) = 33 % answer is a .\"" + }, + { + "Answer": 625, + "Options": "a ) 24 , b ) 120 , c ) 625 , d ) 720 , e ) 1024", + "Correct": "c", + "Explanation": "5 choices for each of the 4 questions , thus total q of 5 * 5 * 5 * 5 = 5 ^ 4 = 625 ways to answer all of them . answer : c ." + }, + { + "Answer": 0.2857142857142857, + "Options": "a ) 2 / 7 , b ) 1 / 2 , c ) 3 / 4 , d ) 1 , e ) 5 / 4", + "Correct": "a", + "Explanation": "\"min value of a / b will be when b is highest and a is lowest - - - > a = 50 and b = 70 so , a / b = 5 / 7 max value of a / b will be when b is lowest and a is highest - - - > a = 60 and b = 60 so , a / b = 1 range is 1 - ( 5 / 7 ) = 2 / 7 . answer should be a .\"" + }, + { + "Answer": 10, + "Options": "a ) 10 , 5 , b ) 8 , 7 , c ) 9 , 6 , d ) 11 , 4 , e ) 12 , 3", + "Correct": "a", + "Explanation": "x + y = 15 - - - ( i ) x - y = 5 - - - - - ( ii ) by adding ( i ) and ( ii ) - - - - - - - - - - - - 2 x = 20 = = > x = 20 / 2 = 10 by replacing the value of x in ( i ) we get 10 + y = 15 = = > y = 15 - 10 = 5 . so , x = 10 , y = 5 answer a ) 10 , 5" + }, + { + "Answer": 36, + "Options": "a ) 23 % , b ) 36 % , c ) 30 % , d ) 34 % , e ) 42 %", + "Correct": "b", + "Explanation": "\"b 10 % 100 - [ ( 100 - 90 ) + ( 100 - 86 ) + ( 100 - 80 ) + ( 100 - 80 ) ] = 100 - ( 10 + 14 + 20 + 20 ) = 100 - 64\"" + }, + { + "Answer": 40, + "Options": "a ) 39 % , b ) 40 % , c ) 41 % , d ) 42 % , e ) 43 %", + "Correct": "b", + "Explanation": "let v be the total volume of the new solution . then a volume of v / 2 was added from each solution a and b . the amount of alcohol added to the new solution was : ( 1 / 5 ) ( v / 2 ) + ( 3 / 5 ) ( v / 2 ) = v / 10 + 3 v / 10 = 4 v / 10 = 2 v / 5 . the concentration of alcohol is 2 / 5 = 40 % the answer is b ." + }, + { + "Answer": 40, + "Options": "a ) 33 , b ) 40 , c ) 99 , d ) 28 , e ) 72", + "Correct": "b", + "Explanation": "\"explanation : let the original price of the cycle be 100 . after the first reduction the price will be 75 . this new price is then reduced by 20 % = 0.8 x 75 = 60 60 represents a reduction of 40 percent on the original . answer : b ) 40 %\"" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9", + "Correct": "a", + "Explanation": "1 / 7 = 014285 . . . ( a repeating pattern one digit long ) a" + }, + { + "Answer": 2, + "Options": "a ) 2 times , b ) 2.5 times , c ) 3 times , d ) 3.8 times , e ) 4 times", + "Correct": "a", + "Explanation": "ronit ' s present age be x years . then , father ' s present age = ( x + 3 x ) years = 4 x years therefore ( 4 x + 8 ) = 5 / 2 ( x + 8 ) 8 x + 16 = 5 x + 40 3 x = 24 , x = 8 , ratio = ( 4 x + 16 ) / ( x + 16 ) = 48 / 24 = 2 , correct answer ( a )" + }, + { + "Answer": 9600, + "Options": "a ) 9800 , b ) 9600 , c ) 9400 , d ) 9500 , e ) 9200", + "Correct": "b", + "Explanation": "greatest number of four digits = 9999 lcm of 15 , 25 , 40 and 75 = 600 9999 \u00f7 600 = 16 , remainder = 399 hence , greatest number of four digits which is divisible by 15 , 25 , 40 and 75 = 9999 - 399 = 9600 answer : b" + }, + { + "Answer": 7, + "Options": "a ) 8 , b ) 9 , c ) 7 , d ) 6 , e ) 5", + "Correct": "c", + "Explanation": "\"lcm of 12 = 12 1 / 3 marking are ( table of 4 ) 0 . . . . . . 4 . . . . . . 8 . . . . . 12 ( total = 4 ) 1 / 4 marking are ( table of 3 ) 0 . . . . . . . 3 . . . . . . 6 . . . . . . 9 . . . . . . . . 12 ( total = 5 ) overlapping markings are 0 . . . . . . . . 12 ( total = 2 ) total markings = 4 + 5 - 2 = 7 answer = c\"" + }, + { + "Answer": 2, + "Options": "a ) 24 , b ) 12 , c ) 6 , d ) 4 , e ) 2", + "Correct": "e", + "Explanation": "\"the greatest common divisor of 20 and 16 is 4 . hence 20 * 16 = 4 ( note that * here denotes the function not multiplication ) . the greatest common divisor of 18 and 24 is 6 . hence 18 * 24 = 6 . hence ( ( 20 * 16 ) * ( 18 * 24 ) ) = 4 * 6 . the greatest common divisor of 4 and 6 is 2 . answer ; e .\"" + }, + { + "Answer": 8, + "Options": "a ) 1 , b ) 8 , c ) 12 , d ) 9 , e ) 7", + "Correct": "b", + "Explanation": "b . 8 quarters" + }, + { + "Answer": 85, + "Options": "a ) 75 , b ) 276 , c ) 87 , d ) 85 , e ) 11", + "Correct": "d", + "Explanation": "\"explanation : average = ( 86 + 85 + 82 + 87 + 85 ) / 5 = 425 / 5 = 85 . answer : d\"" + }, + { + "Answer": 40.98360655737705, + "Options": "a ) 39.55 $ , b ) 40.63 $ , c ) 41.63 $ , d ) 42.15 $ , e ) 43.15 $", + "Correct": "b", + "Explanation": "\"let x be the amount the most their food can cost . x + 0.07 x + 0 . 15 x = 50 solving for x , x = 40.98 $ , this is the maximum amount that can be used for food . hence 40.63 $ is the maximum value less than 40.98 $ hence option b\"" + }, + { + "Answer": 29, + "Options": "a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29", + "Correct": "e", + "Explanation": "\"present age = x before 7 yrs , y = x - 7 after 7 yrs , z = x + 7 by the qn , x + ( x - 7 ) = 37 2 x - 7 = 37 2 x = 37 + 7 x = 44 / 2 x = 22 z = x + 7 = 22 + 7 = 29 answer : e\"" + }, + { + "Answer": 4403, + "Options": "a ) 4423 , b ) 4403 , c ) 4413 , d ) 2403 , e ) 4375", + "Correct": "b", + "Explanation": "\"= ( 55 + 113 / 78 ) \u00d7 78 = ( 4290 + 113 ) / 78 \u00d7 78 = 4403 / 78 \u00d7 78 = 4403 answer is b .\"" + }, + { + "Answer": 11, + "Options": "a ) 14 years , b ) 12 years , c ) 56 years , d ) 66 years , e ) 11 years", + "Correct": "e", + "Explanation": "\"given that a + b = 11 + b + c = > a \u00e2 \u20ac \u201c c = 11 + b \u00e2 \u20ac \u201c b = 11 = > c is younger than a by 11 years answer : e\"" + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) 6 , c ) 14 , d ) 16 , e ) 10", + "Correct": "a", + "Explanation": "n ^ ( n / 2 ) = 12 apply log n / 2 logn = log 12 nlogn = 2 log 12 = log 12 ^ 2 = log 144 logn = log 144 now apply antilog n = 144 / n now n = 12 answer : a" + }, + { + "Answer": 35, + "Options": "a ) 35 , b ) 42 , c ) 44 , d ) 46 , e ) none", + "Correct": "a", + "Explanation": "\"17 ( p + 1 ) = 29 ( q + 1 ) - - > ( p + 1 ) / ( q + 1 ) = 20 / 17 - - > the least positive value of p + 1 is 20 , so the least value of p is 19 and the least positive value of q + 1 is 17 , so the least value of q is 16 - - > the least value of p + q is 19 + 16 = 35 . answer : a\"" + }, + { + "Answer": 16, + "Options": "a ) 16 , b ) 18 , c ) 36 , d ) 19 , e ) 32", + "Correct": "a", + "Explanation": "\"number of pens = 1008 number of pencils = 928 required number of students = h . c . f . of 1008 and 928 = 16 answer is a\"" + }, + { + "Answer": 22, + "Options": "a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 26", + "Correct": "c", + "Explanation": "10 + 12 = 22 the answer is c ." + }, + { + "Answer": 37.5, + "Options": "a ) a : 45 , b ) b : 25 , c ) c : 37.5 , d ) d : 36 , e ) e : 42", + "Correct": "c", + "Explanation": "\"if you have a 37.5 liter capacity , you start with 37.5 l of a and 0 l of b . 1 st replacement after the first replacement you have 37.5 - 15 = 22.5 l of a and 15 l of b . the key is figuring out how many liters of a and b , respectively , are contained in the next 15 liters of mixture to be removed . the current ratio of a to total mixture is 22.5 / 37.5 ; expressed as a fraction this becomes ( 45 / 2 ) / ( 75 / 2 ) , or 45 / 2 * 2 / 75 . canceling the 2 s and factoring out a 5 leaves the ratio as 9 / 15 . note , no need to reduce further as we ' re trying to figure out the amount of a and b in 15 l of solution . 9 / 15 of a means there must be 6 / 15 of b . multiply each respective ratio by 15 to get 9 l of a and 6 l of b in the next 15 l removal . final replacement the next 15 l removal means 9 liters of a and 6 liters of b are removed and replaced with 15 liters of b . 22.5 - 9 = 13.5 liters of a . 15 liters of b - 6 liters + 15 more liters = 24 liters of b . test to the see if the final ratio = 9 / 16 ; 13.5 / 24 = ( 27 / 2 ) * ( 1 / 24 ) = 9 / 16 . choice c is correct .\"" + }, + { + "Answer": 7, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 11 , e ) 12", + "Correct": "c", + "Explanation": "\"answer = c = 7 if least = - 3 , then largest = 8 range = 8 - 1 = 7\"" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 0 , c ) 5 , d ) 6 , e ) 7", + "Correct": "a", + "Explanation": "explanation : given , ( ab ) 2 = ccb . [ only 1 , 5 and 6 on squaring will result with same digits in units place . ] taking a = 2 , b = 1 , = > ( 21 ) ^ 2 = 441 > 300 . hence , the required value of b = 1 answer : a" + }, + { + "Answer": 97.95918367346938, + "Options": "a ) 97.959 % , b ) 98.959 % , c ) 99.959 % , d ) 96.959 % , e ) 95.959 %", + "Correct": "a", + "Explanation": "\"let the number be x the right number is 7 x the wrong number is x / 7 error is ( 7 x - x / 7 ) = 48 x / 7 percentage of error is ( ( 48 x / 7 ) / 7 x ) * 100 = 97.959 % answer : a\"" + }, + { + "Answer": 69, + "Options": "a ) 68 , b ) 69 , c ) 70 , d ) 71 , e ) 72", + "Correct": "b", + "Explanation": "case 1 - 1000 - 1099 - there are 56 distinct digits case 2 - 1200 - 1209 - there are 7 distinct digits case 3 - 1230 - 1239 ( excluding 1239 ) - there are 6 distinct digits hence , 56 + 7 + 6 = 69 answer : b" + }, + { + "Answer": 43, + "Options": "a ) 38 , b ) 43 , c ) 50 , d ) 53 , e ) 62", + "Correct": "b", + "Explanation": "\"if you list the amount eaten each hour , you ' ll get an equally spaced list , increasing by 3 each hour . in any equally spaced list , the median equals the mean . here , the mean is 360 / 9 = 40 , so the median is also 40 , and that is the amount eaten in the 5 th hour . we need to add 3 to find the total eaten in the next hour , so the answer is 43 . option b\"" + }, + { + "Answer": 36.5, + "Options": "a ) 36.0 , b ) 36.5 , c ) 36.24 , d ) 36.12 , e ) 36.22", + "Correct": "e", + "Explanation": "\"explanation : correct sum = ( 36 * 50 + 434 - 23 ) = 1825 . correct mean = = 1811 / 50 = 36.5 answer : e ) 36.22\"" + }, + { + "Answer": 93, + "Options": "a ) - 14 , b ) 14 , c ) 33 , d ) 83 , e ) 93", + "Correct": "e", + "Explanation": "answer : e" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "a", + "Explanation": "given there are 20 apples . if 1 extra apple is added , then it becomes 21 which can be divided equally that is 7 apples to each baby . option a is correct ." + }, + { + "Answer": 0.125, + "Options": "a ) 1 / 9 , b ) 1 / 8 , c ) 1 / 7 , d ) 7 / 8 , e ) 8 / 7", + "Correct": "b", + "Explanation": "when there are eight people , the share of each person is 1 / 8 th the total cost answer : b" + }, + { + "Answer": 11, + "Options": "a ) 11 , b ) 22 , c ) 77 , d ) 33 , e ) 88", + "Correct": "a", + "Explanation": "\"add the numbers of highlighters . 4 + 2 + 5 = 11 . answer is a .\"" + }, + { + "Answer": 90, + "Options": "a ) 75 kg , b ) 50 kg , c ) 85 kg , d ) 90 kg , e ) 60 kg", + "Correct": "d", + "Explanation": "\"explanation : total increase in weight = 10 \u00e3 \u2014 2.5 = 25 if x is the weight of the new person , total increase in weight = x \u00e2 \u02c6 \u2019 65 = > 25 = x - 65 = > x = 25 + 65 = 90 answer : option d\"" + }, + { + "Answer": 8515, + "Options": "a ) 8545 , b ) 8770 , c ) 8515 , d ) 7999 , e ) 7989", + "Correct": "c", + "Explanation": "\"x * ( 90 / 100 ) * ( 85 / 100 ) = 6514 x = 8515 answer : c\"" + }, + { + "Answer": 13.043478260869565, + "Options": "a ) 13 % , b ) 15 % , c ) 25 % , d ) 50 % , e ) 100 %", + "Correct": "a", + "Explanation": "\"let ' s plug in somenicenumbers and see what ' s needed . let ' s say the employee used to make $ 1 / hour and worked 100 hours / week so , the total weekly income was $ 100 / week after the 15 % wage increase , the employee makes $ 1.15 / hour we want the employee ' s income to remain at $ 100 / week . so , we want ( $ 1.15 / hour ) ( new # of hours ) = $ 100 divide both sides by 1.15 to get : new # of hours = 100 / 1.15 \u2248 87 hours so , the number of hours decreases from 100 hours to ( approximately ) 87 hours . this represents a 13 % decrease ( approximately ) . answer : a\"" + }, + { + "Answer": 37.5, + "Options": "a ) 29.3 % , b ) 33.4 % , c ) 37.5 % , d ) 41.6 % , e ) 45.7 %", + "Correct": "c", + "Explanation": "\"y = 1.6 x x = y / 1.6 = 10 y / 16 = 5 y / 8 x is 3 / 8 less which is 37.5 % less than y . the answer is c .\"" + }, + { + "Answer": 51.49757275833493, + "Options": "a ) 51 , b ) 68 , c ) 57 , d ) 55 , e ) 37", + "Correct": "a", + "Explanation": "\"a 51 from the given alternatives , 51 \u00d7 52 = 2652 \u2234 smaller number = 51\"" + }, + { + "Answer": 1, + "Options": "a ) 0 , b ) 1 , c ) 45 , d ) 130 , e ) 520", + "Correct": "b", + "Explanation": "9 + 2 + 9 + 2 + 6 + 0 = 28 , so this number is not divisible by 3 and thus not divisible by 30 . therefore , k = 0 3 ^ k - k ^ 3 = 1 - 0 = 1 the answer is b ." + }, + { + "Answer": 99, + "Options": "a ) 95 kg . , b ) 99 kg . , c ) 89 kg . , d ) 90 kg . , e ) 92 kg .", + "Correct": "b", + "Explanation": "\"the new average will be = ( 103 * 7 + 110 + 60 ) / 9 = 99 kgs b is the answer\"" + }, + { + "Answer": 55, + "Options": "a ) 48 , b ) 51 , c ) 47 , d ) 49 , e ) 55", + "Correct": "e", + "Explanation": "sum of all the 21 numbers = 21 * 44 = 924 sum of the first 11 of them = 11 * 48 = 528 sum of the last 11 of them = 11 * 41 = 451 so , the 11 th number = 528 + 451 - 924 = 55 . answer : e" + }, + { + "Answer": 11, + "Options": "a ) - 4 , b ) - 2 , c ) 11 , d ) 13 , e ) 22", + "Correct": "c", + "Explanation": "\"the equation that can be formed is : 3 x - 18 = 26 - x or , 4 x = 44 or , x = 11 . c answer .\"" + }, + { + "Answer": 50, + "Options": "a ) 50 , b ) 75 , c ) 69 , d ) 79 , e ) 82", + "Correct": "a", + "Explanation": "\"number of pens = 100 number of pencils = 50 required number of students = h . c . f . of 100 and 50 = 50 answer is a\"" + }, + { + "Answer": 5, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "e", + "Explanation": "product of reciprocal roots = 1 product of roots of quadratic eqn ax ^ 2 + bx + c = 0 is c / a . hence k / 5 = 1 k = 5 answer : e" + }, + { + "Answer": 350, + "Options": "a ) s . 150 , b ) s . 200 , c ) s . 250 , d ) s . 350 , e ) s . 400", + "Correct": "d", + "Explanation": "\"let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 770 but x = 120 % of y = 120 y / 100 = 12 y / 10 \u00e2 \u02c6 \u00b4 12 y / 10 + y = 770 \u00e2 \u2021 \u2019 y [ 12 / 10 + 1 ] = 770 \u00e2 \u2021 \u2019 22 y / 10 = 770 \u00e2 \u2021 \u2019 22 y = 7700 \u00e2 \u2021 \u2019 y = 700 / 22 = 700 / 2 = rs . 350 d )\"" + }, + { + "Answer": 8, + "Options": "a ) 2 . , b ) 4 . , c ) 5 . , d ) 7 . , e ) 8 .", + "Correct": "e", + "Explanation": "\"ad = ( a + 1 ) ( d + 1 ) - 17 0 = a + d - 16 a + d = 16 a = d ( as they are twin brothers ) a = d = 8 e is the answer\"" + }, + { + "Answer": 37.5, + "Options": "a ) 22.5 % , b ) 31.5 % , c ) 37.5 % , d ) 42.5 % , e ) 46.5 %", + "Correct": "c", + "Explanation": "\"let x be the original number of each color so there are a total of 5 x candies . kaz eats all of the green candies and half of the orange ones . there are 0 green candies and 0.5 x orange candies remaining . he eats half of the remaining pieces of each color . there are 0.25 x orange candies , and 0.5 x each of red , yellow , and blue candies . he eats red and yellow candies in equal proportions . orange + blue + red + yellow = 0.75 x + red + yellow = 1.5 x red + yellow = 0.75 x red = 0.375 x , since red = yellow . the answer is c .\"" + }, + { + "Answer": 65, + "Options": "a ) 55 , b ) 65 , c ) 75 , d ) 85 , e ) 95", + "Correct": "b", + "Explanation": "\"let the marks obtained by the student in physics , chemistry and mathematics be p , c and m respectively . p + c + m = 130 + p c + m = 130 average mark obtained by the student in chemistry and mathematics = ( c + m ) / 2 = 130 / 2 = 65 . answer : b\"" + }, + { + "Answer": 120, + "Options": "a ) 22 , b ) 120 , c ) 388 , d ) 377 , e ) 272", + "Correct": "b", + "Explanation": "explanation : commission up to 10000 = \\ inline 10000 \\ times \\ frac { 9 } { 100 } = 900 again after 10000 , commission : bonus 9 : 3 \\ inline \\ rightarrow 3 x : x \\ therefore bonus = \\ inline ( 1380 - 900 ) \\ times \\ frac { 1 } { 4 } = rs . 120 answer : b ) rs . 120" + }, + { + "Answer": 32, + "Options": "a ) 20 , b ) 32 , c ) 100 , d ) 200 , e ) 400", + "Correct": "b", + "Explanation": "the equation can be reduced to intercept form as | x / 4 | + | y / 4 | = 1 , so these are lines in four quadrants with x and y intercept as 14 , so it is a rhombus with diagonals of 8 each and hence area = 1 / 2 * d 1 * d 2 = 1 / 2 * 8 * 8 = 32 . answer b ." + }, + { + "Answer": 8, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8", + "Correct": "e", + "Explanation": "\"64 ^ k > 4 ^ 22 4 ^ ( 3 k ) > 4 ^ 22 3 k > 22 k = 8 the answer is e .\"" + }, + { + "Answer": 0.675, + "Options": "a ) \u00bd , b ) 27 / 40 , c ) 1 / 50 , d ) 1 / 500 , e ) 2 / 500", + "Correct": "b", + "Explanation": "let x be the difference then . 8 - 1 / 8 = x 8 / 10 - 1 / 8 = x x = 27 / 40 ans b" + }, + { + "Answer": 24, + "Options": "a ) 24 , b ) 26 , c ) 28 , d ) 30 , e ) none", + "Correct": "a", + "Explanation": "let the ten ' s digit be x . then , unit ' s digit = x + 2 . number = 10 x + ( x + 2 ) = 11 x + 2 . sum of digits = x + ( x + 2 ) = 2 x + 2 . ( 11 x + 2 ) ( 2 x + 2 ) = 144 22 x 2 + 26 x - 140 = 0 11 x 2 + 13 x - 70 = 0 ( x - 2 ) ( 11 x + 35 ) = 0 x = 2 . hence , required number = 11 x + 2 = 24 . option a" + }, + { + "Answer": 276, + "Options": "a ) 276 , b ) 295 , c ) 230 , d ) 225 , e ) 245", + "Correct": "a", + "Explanation": "\"required number = ( lcm of 8 , 12 , 22 and 24 ) + 12 = 264 + 12 = 276 answer : option a\"" + }, + { + "Answer": 8, + "Options": "a ) 9 , b ) 8 , c ) 7 , d ) 6 , e ) 5", + "Correct": "b", + "Explanation": "explanation : this is only possible only when the hundreds digit has the least value and tens and units has the highest value . so we could get the highest possible sum but possible lowest number . so by this logic this number could only be 199 . so the difference is 8 . note : remember a number given as abc i . e abc = ax 100 + bx 10 + c . so 123 = 1 x 100 + 2 x 10 + 3 . answer : b" + }, + { + "Answer": 86, + "Options": "a ) 84.71 kmph . , b ) 85.74 kmph . , c ) 83.71 kmph . , d ) 85.71 kmph . , e ) 84.71 kmph .", + "Correct": "d", + "Explanation": "given speed = 60 kmph . it means niharika covered 60 km in 60 min ( 1 hour ) . so , in 30 min he will cover 30 km . 30 % time reduced = 30 - 30 % of 30 = 21 min . thus , niharika needs to cover 30 km in 21 min ( 0.35 hour ) . speed * time = distance . speed * 0.35 = 30 speed = 85.71 kmph . answer : option d" + }, + { + "Answer": 37, + "Options": "a ) 37 % . , b ) 71 % . , c ) 49 % . , d ) 29 % . , e ) 51 % .", + "Correct": "a", + "Explanation": "\"20 % of 2 litres = 0.4 litres 55 % of 6 litres = 3.3 litres therefore , total quantity of alcohol is 3.7 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 37 % a\"" + }, + { + "Answer": 930, + "Options": "a ) 732 , b ) 990 , c ) 1098 , d ) 930 , e ) 1405", + "Correct": "d", + "Explanation": "\"total number of digits = ( no . of digits in 1 - digit page nos . + no . of digits in 2 - digit page nos . + no . of digits in 3 - digit page nos . ) = ( 1 x 9 + 2 x 90 + 3 x 247 ) = ( 9 + 180 + 741 ) = 930 . answer : d\"" + }, + { + "Answer": 3.4000000000000004, + "Options": "a ) $ 1.40 , b ) $ 2.40 , c ) $ 3.40 , d ) $ 4.40 , e ) $ 5.40", + "Correct": "c", + "Explanation": "\"manager wages per hour = $ 8.50 dishwasher wages per hour = half of manager ' s wages . = 1 / 2 ( $ 8.50 ) = = > $ 4.25 chef wages per hour = 20 % greater than dishwasher wages - - > 20 % of $ 4.25 = ( 20 * ( $ 4.25 ) ) / 100 - - > ( $ 85 ) / 100 - - > $ 0.85 therefore , chef wages per hour = $ 4.25 + $ 0.85 = = > $ 5.10 difference of wages between manager and chef = $ 8.50 - $ 5.10 = = > $ 3.40 answer : c\"" + }, + { + "Answer": 19802, + "Options": "a ) 10002 , b ) 20004 , c ) 20002 , d ) 20102 , e ) 20202", + "Correct": "c", + "Explanation": "\"explanation : ( a + b ) 2 + ( a \u00e2 \u02c6 \u2019 b ) 2 = 2 ( a 2 + b 2 ) ( reference : basic algebraic formulas ) 1012 + 992 = ( 100 + 1 ) 2 + ( 100 \u00e2 \u02c6 \u2019 1 ) 2 = 2 ( 1002 + 12 ) = 2 ( 10000 + 1 ) = 20002 . answer : option c\"" + }, + { + "Answer": 1000, + "Options": "a ) 500 bc , b ) 500 b / c , c ) 1000 bc , d ) 1000 b / c , e ) 1000 / bc", + "Correct": "c", + "Explanation": "\"2 cases * c cartons / case * b boxes / carton * 500 clips / box = 1000 bc paper clips the answer is c .\"" + }, + { + "Answer": 2300, + "Options": "a ) 2300 , b ) 2887 , c ) 2000 , d ) 1129 , e ) 1192", + "Correct": "a", + "Explanation": "\"let money invested by raghu = rs . x money invested by trishul = 9 / 10 x = 0.9 x money invested by vishal = 9 / 10 x * 110 / 100 = 0.99 x also , x + 0.9 x + 0.99 x = 6647 = x = 6647 / 2.89 = 2300 therefore , amount invested by raghu is rs . 2300 . answer : a\"" + }, + { + "Answer": 300, + "Options": "a ) 225 , b ) 275 , c ) 300 , d ) 350 , e ) 400", + "Correct": "c", + "Explanation": "\"this problem is a general word translation . we first define variables and then set up equations . we can define the following variables : f = the weight of the first lift s = the weight of the second lift we are given that the total weight of joe ' s two lifts was 600 pounds . we sum the two variables to obtain : f + s = 600 we are also given that twice the weight of his first lift was 300 pounds more than the weight of his second lift . we express this as : 2 f = 300 + s 2 f \u2013 300 = s we can now plug in ( 2 f \u2013 300 ) for s into the first equation , so we have : f + 2 f \u2013 300 = 600 3 f = 900 f = 300 answer is c\"" + }, + { + "Answer": 10, + "Options": "a ) 25 , b ) 20 , c ) 15 , d ) 10 , e ) 5", + "Correct": "d", + "Explanation": "\"let age of c = x . then , age of b = 2 x age of a = 2 + 2 x total age of a , b and c = 27 \u21d2 ( 2 + 2 x ) + 2 x + x = 27 \u21d2 5 x = 25 \u21d2 x = 255 = 5 b ' s age = 2 x = 2 \u00d7 5 = 10 answer is d .\"" + }, + { + "Answer": 95, + "Options": "a ) 86 , b ) 16 , c ) 76 , d ) 95 , e ) 26", + "Correct": "d", + "Explanation": "\"given m + p + c = 75 * 3 = 225 - - - ( 1 ) m + p = 90 * 2 = 180 - - - ( 2 ) p + c = 70 * 2 = 140 - - - ( 3 ) where m , p and c are marks obtained by the student in mathematics , physics and chemistry . p = ( 2 ) + ( 3 ) - ( 1 ) = 180 + 140 - 225 = 95 answer : d\"" + }, + { + "Answer": 2.6666666666666665, + "Options": "a ) 9 / 4 , b ) 3 / 2 , c ) 8 / 3 , d ) 2 / 3 , e ) 1 / 2", + "Correct": "c", + "Explanation": "\"sq rt ( 8 x / 3 ) = x = > 8 x / 3 = x ^ 2 = > x = 8 / 3 ans - c\"" + }, + { + "Answer": 268.1818181818182, + "Options": "a ) s . 268 , b ) s . 288 , c ) s . 298 , d ) s . 300 , e ) s . 388", + "Correct": "a", + "Explanation": "\"let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 590 but x = 120 % of y = 120 y / 100 = 12 y / 10 \u2234 12 y / 10 + y = 590 \u21d2 y [ 12 / 10 + 1 ] = 590 \u21d2 22 y / 10 = 590 \u21d2 22 y = 5900 \u21d2 y = 5900 / 22 = 500 / 2 = rs . 268 a )\"" + }, + { + "Answer": 2, + "Options": "a ) 2 : 6 , b ) 2 : 1 , c ) 7 : 1 , d ) 2 : 8 , e ) 2 : 2", + "Correct": "b", + "Explanation": "10 % of x = 20 % of y 10 x / 100 = 20 y / 100 = > x / 10 = y / 5 x / y = 10 / 5 = 2 / 1 x : y = 2 : 1 . answer : b" + }, + { + "Answer": 18, + "Options": "a ) 18 , b ) 20 , c ) 26 , d ) 28 , e ) 30", + "Correct": "a", + "Explanation": "\"solution let the number be x . then , 12 x - x = 198 \u2039 = \u203a 11 x = 198 x \u2039 = \u203a 18 . answer a\"" + }, + { + "Answer": 9, + "Options": "a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 9", + "Correct": "e", + "Explanation": "if a number is divisible by 9 , the sum of its digits must be a multiple of 9 . here , 2 + 7 + 4 + 5 + 2 = 20 , the next multiple of 9 is 27 . 7 must be added to 27452 to make it divisible by 9 e" + }, + { + "Answer": 60, + "Options": "a ) 12 , b ) 30 , c ) 60 , d ) 90 , e ) 120", + "Correct": "c", + "Explanation": "240 can be written as ( 2 ^ 4 ) * 3 * 5 . for a ^ 3 to be divisible by 240 it should contain atleast 2 ^ 4 and 3 and 5 in its factors . we can leave out option a because 12 doesnt have 5 as one of its factor . now if we check for option b , 30 can be written as 2 * 3 * 5 , hence 30 ^ 3 will have 3 as the maximum power of 2 , so we can leave out this option too . option c is the right answer if we follow the same method as we followed for other two previous options . 60 = ( 2 ^ 2 ) * 3 * 5 ; 60 ^ 3 = ( 2 ^ 6 ) * ( 3 ^ 3 ) * ( 5 ^ 3 ) . so it shows that 60 ^ 3 is divisible by 240 and hence the answer . answer : c" + }, + { + "Answer": 50, + "Options": "a ) 50 , b ) 25 , c ) 40 , d ) 45 , e ) 75", + "Correct": "a", + "Explanation": "\"average = 60 , sum of temperatures = 60 * 5 = 300 as the min temperature is 50 , max would be 300 - 4 * 50 = 100 - - > the range = 100 ( max ) - 50 ( min ) = 50 answer : a\"" + }, + { + "Answer": 76, + "Options": "a ) 96 , b ) 76 , c ) 56 , d ) 36 , e ) 16", + "Correct": "b", + "Explanation": "\"( ( 301 * 402 * 503 * 604 * 646 ) * ( 547 * 448 * 349 ) ) ^ 2 if you observe above digits , last digit are : 1,2 , 3,4 , 6,7 , 8,9 ; 5 is missing ; so i have rearranged them so that multiplication will be easy for me as initial 4 digits have last two digits as 01 , 02,03 , 04,46 and final three as 47 * 48 * 49 . solving for only last two digits and multiplying them we get : ( ( 06 * 04 * 46 ) ( 56 * 49 ) ) ^ 2 = ( 44 * 44 ) ^ 2 = 36 ^ 2 = 76 hence answer is b\"" + }, + { + "Answer": 6, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 11 , e ) 12", + "Correct": "b", + "Explanation": "since - 4 is the least integer in list f , then 7 is the largest integer in that list . thus the range of the positive integers in the list is 7 - 1 = 6 . answer : b ." + }, + { + "Answer": 30, + "Options": "a ) 16 , b ) 19 , c ) 15 , d ) 22 , e ) 30", + "Correct": "e", + "Explanation": "\"let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . ( x + 32 ) + 2 = 2 ( x + 2 ) x + 34 = 2 x + 4 = > x = 30 . answer : e\"" + }, + { + "Answer": 16, + "Options": "a ) 12 % , b ) 14 % , c ) 16 % , d ) 20 % , e ) 22 %", + "Correct": "c", + "Explanation": "\"explanation : 100 * 100 = 10000 80 * 105 = 8400 10000 - - - - - - - 1600 100 - - - - - - - ? = 16 % c )\"" + }, + { + "Answer": 30, + "Options": "a ) 25 , b ) 30 , c ) 35 , d ) 40 , e ) 45", + "Correct": "b", + "Explanation": "let x be the number of blueberries in each blue box . then there are x + 20 strawberries in each red box . x + ( x + 20 ) = 80 x = 30 the answer is b ." + }, + { + "Answer": 25.00000000000001, + "Options": "a ) 50 % , b ) 40 % , c ) 25 % , d ) 20 % , e ) 10 %", + "Correct": "c", + "Explanation": "\"looking at the ratio we can take total number of people = 20 . . ans 5 / 20 or 25 % c\"" + }, + { + "Answer": 22, + "Options": "a ) 21 years , b ) 22 years , c ) 23 years , d ) 24 years , e ) 26 years", + "Correct": "b", + "Explanation": "\"explanation : let ' s son age is x , then father age is x + 24 . = > 2 ( x + 2 ) = ( x + 24 + 2 ) = > 2 x + 4 = x + 26 = > x = 22 years option b\"" + }, + { + "Answer": 8, + "Options": "a ) 19 , b ) 12 , c ) 11 , d ) 10 , e ) 8", + "Correct": "e", + "Explanation": "\"out of the 14 integers : 7 are odd and 7 are even . if we need to make sure that the product of all the integers withdrawn is even then we need to make sure that we have at least one even number . in the worst case : 1 . we will end up picking odd numbers one by one , so we will pick all 7 odd numbers first 2 . 8 th number will be the first even number so we need to withdraw at least 8 numbers to make sure that we get one even number and the product of all the integers picked is even . so , answer will be 8 . ( e )\"" + }, + { + "Answer": 120, + "Options": "a ) 600 , b ) 700 , c ) 120 , d ) 900 , e ) none", + "Correct": "c", + "Explanation": "\"solution : let xx be the number i chose , then x / 6 \u00e2 \u02c6 \u2019 15 = 5 x / 6 = 20 x = 120 answer c\"" + }, + { + "Answer": 4, + "Options": "a ) 4 , b ) 6 , c ) 7 , d ) 8 , e ) 9", + "Correct": "a", + "Explanation": "\"division of total diatance travelled will be 16 + 16 + 8 + 4 + 0.5 ans : 4\"" + }, + { + "Answer": 59, + "Options": "a ) 54 , b ) 55 , c ) 59 , d ) 71 , e ) 92", + "Correct": "c", + "Explanation": "\"total = 90 thrower = 37 rest = 90 - 37 = 33 left handed = 33 / 3 = 11 right handed = 22 if all thrower are right handed then total right handed is 37 + 22 = 59 so c . 59 is the right answer\"" + }, + { + "Answer": 0.5, + "Options": "a ) 1 / 9 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6", + "Correct": "c", + "Explanation": "\"n ( n + 1 ) to be divisible by 4 either n or n + 1 must be a multiples of 4 . in each following group of numbers : { 1 , 2 , 3 , 4 } , { 5 , 6 , 7 , 8 } , . . . , { 97 , 98 , 99 , 100 } there are exactly 2 numbers out of 3 satisfying the above condition . for example in { 1 , 2 , 3 , 4 } n can be : 3 , or 4 . thus , the overall probability is 2 / 4 = 1 / 2 . answer : c .\"" + }, + { + "Answer": 23, + "Options": "a ) 23 , b ) 25 , c ) 27 , d ) 31 , e ) 35", + "Correct": "a", + "Explanation": "let the numbers be x and y . then , xy = 120 and x 2 + y 2 = 289 . ( x + y ) 2 = x 2 + y 2 + 2 xy = 289 + ( 2 x 120 ) = 529 x + y = 529 = 23 . option a" + }, + { + "Answer": 292.5, + "Options": "a ) rs . 292.50 , b ) rs . 297.50 , c ) rs . 298 , d ) rs . 298.50 , e ) none of these", + "Correct": "a", + "Explanation": "explanation : let the average expenditure be rs . x then , 9 x = [ 8 \u00d7 30 + ( x + 20 ) ] \u21d4 9 x = x + 260 \u21d4 x = 32.50 total money spent = 9 x = rs . ( 9 x 32.5 o ) = rs 292 . 50 answer : a" + }, + { + "Answer": 2, + "Options": "a ) 1 , b ) 1.5 , c ) 2 , d ) 2.5 , e ) 3", + "Correct": "c", + "Explanation": "\"let x be the number of liters of ethanol added to the gas tank . 0.05 ( 36 ) + x = 0.1 ( 36 + x ) 0.9 x = 3.6 - 1.8 = 1.8 x = 2 liters the answer is c .\"" + }, + { + "Answer": 18, + "Options": "a ) 17 , b ) 18 , c ) 22 , d ) 26 , e ) 36", + "Correct": "b", + "Explanation": "\"the total sum of the numbers should be increased by 20 . then the average will increase by 20 / 10 = 2 . the correct average is 18 . the answer is b .\"" + }, + { + "Answer": 20, + "Options": "a ) 23 % , b ) 17 % , c ) 11 % , d ) 10 % , e ) 20 %", + "Correct": "e", + "Explanation": "\"e 10 % 100 - [ ( 100 - 85 ) + ( 100 - 90 ) + ( 100 - 75 ) + ( 100 - 70 ) ] = 100 - ( 30 + 25 + 10 + 15 ) = 100 - 80\"" + }, + { + "Answer": 25, + "Options": "a ) 23 % , b ) 24 % , c ) 25 % , d ) 26 % , e ) 27 %", + "Correct": "c", + "Explanation": "expensive item = $ 100 ; cheap item = $ 80 ; we must increase $ 80 to $ 100 , so by $ 20 , which is 25 % increase : ( 100 - 80 ) / 80 = 1 / 4 = 0.25 answer : c ." + }, + { + "Answer": 29, + "Options": "a ) 18 , b ) 29 , c ) 39 , d ) 49 , e ) 59", + "Correct": "b", + "Explanation": "\"let x be added to each term of the ratio 4 : 15 . new ratio becomes ( 4 + x ) / ( 15 + x ) , which is given to be equal to 3 : 4 . this means , ( 4 + x ) / ( 15 + x ) = 3 / 4 solving we get , x = 29 . ans b\"" + }, + { + "Answer": 7, + "Options": "a ) 2 , b ) 3 , c ) 5 , d ) 7 , e ) 11", + "Correct": "d", + "Explanation": "( 11 ! \u00d7 10 ! \u2009 + 10 ! \u00d7 9 ! ) / 111 in numerator take out 10 ! * 9 ! as common term 10 ! \u2217 9 ! ( 11 \u00d7 10 \u2009 + 1 ) / 111 10 ! \u2217 9 ! \u2217 111 / 111 10 ! \u2217 9 ! 10 ! has 7 as the greatest prime factor , so ans is 7 answer : d" + }, + { + "Answer": 55, + "Options": "a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60", + "Correct": "d", + "Explanation": "\"11 c 2 = 55 the answer is d .\"" + }, + { + "Answer": 20, + "Options": "a ) 19 , b ) 20 , c ) 21 , d ) 22 , e ) 23", + "Correct": "b", + "Explanation": "10 * 17 - 26 + 56 = 200 200 / 10 = 20 the answer is b ." + }, + { + "Answer": 8, + "Options": "a ) 1 , b ) 8 , c ) 5 , d ) 6 , e ) 7", + "Correct": "b", + "Explanation": "\"let seventh observation = x . then , according to the question we have = > ( 90 + x ) / 7 = 14 = > x = 8 hence , the seventh observation is 8 answer : b\"" + }, + { + "Answer": 780, + "Options": "a ) 872 , b ) 738 , c ) 837 , d ) 780 , e ) 83", + "Correct": "d", + "Explanation": "\"25 % of x = x / 4 ; 15 % of 1500 = 15 / 100 * 1500 = 225 given that , x / 4 = 225 - 30 = > x / 4 = 195 = > x = 780 . answer : d\"" + }, + { + "Answer": 11, + "Options": "a ) 8 , b ) 9 , c ) 11 , d ) 15 , e ) 18", + "Correct": "c", + "Explanation": "\"a = 2 m = m + 22 m = 22 a = 44 a = 4 b , and so b = 11 the answer is c .\"" + }, + { + "Answer": 0.13333333333333333, + "Options": "a ) 2 / 69 , b ) 2 / 20 , c ) 2 / 18 , d ) 2 / 29 , e ) 2 / 15", + "Correct": "e", + "Explanation": "\"explanation : let a be the event that x is selected and b is the event that y is selected . p ( a ) = 1 / 5 , p ( b ) = 2 / 3 . let c be the event that both are selected . p ( c ) = p ( a ) \u00e3 \u2014 p ( b ) as a and b are independent events : = ( 1 / 5 ) \u00e3 \u2014 ( 2 / 3 ) = 2 / 15 answer : e ) 2 / 15\"" + }, + { + "Answer": 3682, + "Options": "a ) 3,551 , b ) 3,668 , c ) 3,733 , d ) 3,822 , e ) 3,957", + "Correct": "b", + "Explanation": "\"first factor each of 25 , 49 , 15 , and 21 into primes : 25 = 5 * 5 ; 49 = 7 * 7 ; 15 = 3 * 5 ; 21 = 3 * 7 the smallest number divisible by each of the numbers is 3 * 5 * 5 * 7 * 7 = 3,675 3,675 - 7 = 3,668 thus 3,668 + 7 is the smallest number divisible by 25 , 49 , 15 , and 21 b\"" + }, + { + "Answer": 50, + "Options": "a ) 1.4 % , b ) 50 % , c ) 11.1 % , d ) 12.5 % , e ) 23.6 %", + "Correct": "b", + "Explanation": "opening = 10 closing = 15 rise in price = 5 so , percent increase = 5 / 10 * 100 = 50 % answer : b" + }, + { + "Answer": 3.408, + "Options": "a ) 0.3408 , b ) 3.408 , c ) 34.08 , d ) 340.8 , e ) none of these", + "Correct": "b", + "Explanation": "\"solution 1.6 \u00d7 2.13 = ( 16 / 10 x 213 / 100 ) = ( 16 x 213 / 1000 ) = 3408 / 100 = 3.408 . answer b\"" + }, + { + "Answer": 13, + "Options": "a ) 13 , b ) 12 , c ) 11 , d ) 15 , e ) 16", + "Correct": "a", + "Explanation": "in a room of n people , the number of possible handshakes is c ( n , 2 ) or n ( n - 1 ) / 2 so n ( n - 1 ) / 2 = 78 or n ( n - 1 ) = 156 or n = 13 answer is ( a )" + }, + { + "Answer": 40, + "Options": "a ) 20 , b ) 40 , c ) 60 , d ) 80 , e ) 90", + "Correct": "b", + "Explanation": "explanation : given , 50 % of x equals the sum of y and 20 . = > ( 50 / 100 ) \u00d7 x = y + 20 . = > x / 2 = y + 20 . = > x = 2 y + 40 . = > x \u2013 2 y = 40 . answer : b" + }, + { + "Answer": 19, + "Options": "a ) 12.5 % , b ) 17.5 % , c ) 19 % , d ) 21 % , e ) none of these", + "Correct": "c", + "Explanation": "let the weights of ram and shyam be 4 x and 5 x . now , according to question , 4 x \u00d7 110 / 100 + shyam ? snewwt 4 x \u00d7 110100 + shyam ? s new wt = 82.8 . . . . . . . . ( i ) and 4 x + 5 x = 9 x + 115 / 100 = 82.8 . . . . . . . . ( ii ) from ( ii ) , x = 8 putting in ( i ) , we get shyam \u2019 s new wt = ( 82.8 \u2013 35.2 ) = 47.6 % increase in shyam \u2019 s wt = ( 47.6 \u2212 40 / 40 \u00d7 100 ) = 19 answer c" + }, + { + "Answer": 2399.9999999999995, + "Options": "a ) 1200 , b ) 3000 , c ) 2400 , d ) 3600 , e ) 2450", + "Correct": "c", + "Explanation": "\"let the additional invested amount for 8 % interest be x ; equation will be ; 2400 + 0.04 * 2400 + x + 0.08 x = 2400 + x + 0.06 ( 2400 + x ) 0.04 * 2400 + 0.08 x = 0.06 x + 0.06 * 2400 0.02 x = 2400 ( 0.06 - 0.04 ) x = 2400 * 0.02 / 0.02 = 2400 ans : c\"" + }, + { + "Answer": 4, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "d", + "Explanation": "\"2 m = 12 - m 3 m = 12 m = 4 the answer is d .\"" + }, + { + "Answer": 9, + "Options": "a ) $ 9 , b ) $ 15 , c ) $ 18 , d ) $ 21 , e ) $ 27", + "Correct": "a", + "Explanation": "\"let q ' s hourly wage be x , then p ' s hourly wage is 1.5 x let t be the number of hours that q needs , then p needs t - 10 hours to do the job . since they both are paid an equal total amount of $ 540 : x * t = 1.5 x * ( t - 10 ) t = 30 hours and q ' s hourly wage is 540 / 30 = $ 18 p ' s hourly wage is 540 / ( t - 10 ) = $ 27 which is $ 9 per hour more . the answer is a .\"" + }, + { + "Answer": 100, + "Options": "a ) 160 , b ) 120 , c ) 100 , d ) 150 , e ) 170", + "Correct": "c", + "Explanation": "\"sum of the marks for the 12 students = 12 * 50 = 600 . the marks of each student are doubled , the sum also will be doubled . the new sum = 600 * 2 = 1200 . so , the new average = 1200 / 12 = 100 . answer : c\"" + }, + { + "Answer": 0.09166666666666666, + "Options": "a ) 11 / 122 , b ) 11 / 120 , c ) 11 / 121 , d ) 11 / 140 , e ) 11 / 111", + "Correct": "b", + "Explanation": "explanation : let the numbers be a and b . then , a + b = 55 and ab = 5 x 120 = 600 . the required sum answer : b ) 11 / 120" + }, + { + "Answer": 5700, + "Options": "a ) 2177 , b ) 2876 , c ) 4500 , d ) 5700 , e ) 6711", + "Correct": "d", + "Explanation": "\"sum of the salaries of the person for the months of january , february , march and april = 4 * 8000 = 32000 - - - - ( 1 ) sum of the salaries of the person for the months of february , march , april and may = 4 * 8200 = 32800 - - - - ( 2 ) ( 2 ) - ( 1 ) i . e . may - jan = 800 salary of may is rs . 6500 salary of january = rs . 5700 . answer : d\"" + }, + { + "Answer": 21, + "Options": "a ) 11 years , b ) 17 years , c ) 21 years , d ) 14 years , e ) 12 years", + "Correct": "c", + "Explanation": "\"age of the 15 th student = [ 15 * 15 - ( 12 * 5 + 16 * 9 ) ] = ( 225 - 204 ) = 21 years . answer : c\"" + }, + { + "Answer": 8, + "Options": "a ) a ) 8 , b ) b ) 25 , c ) c ) 40 , d ) d ) 55 , e ) e ) 70", + "Correct": "a", + "Explanation": "\"total score of 16 students is 16 * 60.50 = 968 total score of 15 students is 15 * 64 = 960 so , the score of the person who left is 8 ( 968 - 960 ) answer will be ( a\"" + }, + { + "Answer": 56000, + "Options": "a ) 38000 , b ) 47000 , c ) 48000 , d ) 51000 , e ) 56000", + "Correct": "e", + "Explanation": "median of the car is 52000 therefore 52000 is the middle number . assuming y > = x , x will have to be the median value i . e . 52000 . therefore the remaining value would have to be between 52000 and 57000 inclusive . the only answer choice that fits is w = 56000 . e" + }, + { + "Answer": 4, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "e", + "Explanation": "\"on dividing 568219 by 5 we get the remainder 4 , so 4 should be subtracted e\"" + }, + { + "Answer": 7, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 4 , e ) 5", + "Correct": "a", + "Explanation": "from the given information , ( 272738 - 13 , 232342 - 17 ) are exactly divisible by that two digit number . we have to find the hcf of the given numbers 272725 , 232325 . hcf = 25 . so sum of the digits = 7 . answer : a" + }, + { + "Answer": 63, + "Options": "a ) a ) 51 , b ) b ) 63 , c ) c ) 45 , d ) d ) 40 , e ) e ) 36", + "Correct": "b", + "Explanation": "\"explanation : let the number be x . then , x - ( x / 3 ) = 42 = > 2 x / 3 = 42 = > x = 63 answer : option b\"" + }, + { + "Answer": 21, + "Options": "a ) 20 , b ) 21 , c ) 23 , d ) 25 , e ) 26", + "Correct": "b", + "Explanation": "\"y = 288 * a + 45 = ( 24 * 12 ) * a + 24 + 21 the answer is b .\"" + }, + { + "Answer": 82516.58333333333, + "Options": "a ) 82,650 , b ) 64,850 , c ) 64,749 , d ) 49,700 , e ) 56,720", + "Correct": "a", + "Explanation": "\"find the number , upon sum of 3 digits of a number gives a reminder 2 when it is divided by 6 seeing the options after dividing an finding the reminder of 2 my answer was a\"" + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10", + "Correct": "a", + "Explanation": "every such number must be divisible by l . c . m of 4 , 5,6 i . e , 60 . such numbers are 240,300 , 360,420 , 480,540 . clearly , there are 6 such numbers answer : a" + }, + { + "Answer": 38, + "Options": "a ) 36 , b ) 37 , c ) 38 , d ) 39 , e ) 40", + "Correct": "c", + "Explanation": "\"m / nm > 5 x / 24 x m = 8 8 / nm > 5 x / 24 x 8 / nm - 5 x / 24 x > 0 ( 192 x - 5 x * nm ) / ( 24 x * nm ) > 0 192 x - 5 x * nm > 0 5 x * nm < 192 x nm < 192 x / 5 x nm < 38.4 maximum number of non managers = 38 answer : c\"" + }, + { + "Answer": 21.428571428571427, + "Options": "a ) 31.56 , b ) 25.65 , c ) 21.43 , d ) 28.36 , e ) 27.96", + "Correct": "c", + "Explanation": "total score of the batsman in 15 matches = 450 . total score of the batsman in the next 20 matches = 300 . total score of the batsman in the 35 matches = 750 . average score of the batsman = 750 / 35 = 21.43 . answer : c" + }, + { + "Answer": 5, + "Options": "a ) 3 , b ) 7 , c ) 15 , d ) 5 , e ) 25", + "Correct": "d", + "Explanation": "jacob = x years , mike = x + 12 years 11 years from now , 2 ( x + 11 ) = x + 23 2 x + 22 = x + 23 x = 1 x + 4 = 5 years answer d" + }, + { + "Answer": 40, + "Options": "a ) 20 , b ) 25 , c ) 30 , d ) 40 , e ) 50", + "Correct": "d", + "Explanation": "\"let the list price be 2 x for min sale price , the first discount given should be 50 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 40 and 0.8 x = 32 so lowest sale price is 32 , which e is 40 % of 80 hence , d is the answer\"" + }, + { + "Answer": 0.15789473684210525, + "Options": "a ) 1 / 7 , b ) 1 / 5 , c ) 1 / 4 , d ) 1 / 3 , e ) 3 / 19", + "Correct": "e", + "Explanation": "\"1 lbs of raisin = $ 1 3 lbs of raisin = $ 3 1 lbs of nuts = $ 4 4 lbs of nuts = $ 16 total value of mixture = 16 + 3 = 19 fraction of the value of raisin = 3 / 19 ans : e\"" + }, + { + "Answer": 9, + "Options": "a ) 16.2 , b ) 4 , c ) 5 , d ) 9 , e ) 11", + "Correct": "d", + "Explanation": "\"answer let 45 x a = ( 25 x 900 ) / 100 \u2234 a = ( 45 x 9 ) / 45 = 9 correct option : d\"" + }, + { + "Answer": 60, + "Options": "a ) 48 , b ) 60 , c ) 84 , d ) 96 , e ) 69", + "Correct": "b", + "Explanation": "arun age x . ( x - 6 ) / 18 = y y is gokul age which is 3 x = 60 answer : b" + }, + { + "Answer": 75625, + "Options": "a ) 68225 , b ) 75625 , c ) 76569 , d ) 45854 , e ) 45858", + "Correct": "b", + "Explanation": "explanation : this question can be solved by 2 approaches : = > direct multiplication = > numerical operations direct multiplication is quite time consuming and involves a lot of calculations . an easier approach is based on numerical operations . = > 121 x ( 10 / 2 ) 4 = 121 x 10000 / 16 = 75625 answer : b" + }, + { + "Answer": 0.08333333333333333, + "Options": "a ) 1 / 12 , b ) 1 / 6 , c ) 1 / 4 , d ) 1 / 3 , e ) 1 / 2", + "Correct": "a", + "Explanation": "x = - 4 prob = 1 / 12 answer - a" + }, + { + "Answer": 40.3, + "Options": "a ) 40.2 , b ) 40.4 , c ) 40.6 , d ) 40.8 , e ) 40.1", + "Correct": "e", + "Explanation": "\"sum of 10 numbers = 402 corrected sum of 10 numbers = 402 \u2013 13 + 31 \u2013 19 = 401 hence , new average = 401 \u2044 10 = 40.1 answer e\"" + }, + { + "Answer": 0.4444444444444445, + "Options": "a ) 5 / 27 , b ) 2 / 9 , c ) 1 / 3 , d ) 4 / 9 , e ) 2 / 3", + "Correct": "d", + "Explanation": "\"probability of not burning out during the first 6 months 1 - 1 / 3 = 2 / 3 probability of not burning out during the next 6 months 2 / 3 / 2 = 1 / 3 , hence probability of burning out 1 - 1 / 3 = 2 / 3 . probability of burning out during the period from 6 months to 1 year = probability of not burning out in first 6 months * probability of burning out in next 6 months = 2 / 3 * 2 / 3 = 4 / 9 answer : d .\"" + }, + { + "Answer": 5922, + "Options": "a ) 4902 , b ) 4922 , c ) 5922 , d ) 5924 , e ) 5928", + "Correct": "c", + "Explanation": "\"total sale for 5 months = rs . ( 5921 + 5468 + 5568 + 6088 + 6433 ) = rs . 29478 . required sale = rs . [ ( 5900 x 6 ) - 29478 ] = rs . ( 35400 - 29478 ) = rs . 5922 . answer : c\"" + }, + { + "Answer": 2625, + "Options": "a ) $ 2225 , b ) $ 2782 , c ) $ 1625 , d ) $ 2629 , e ) $ 2625", + "Correct": "e", + "Explanation": "explanation : let ' s start with what the total price of the refrigerator would be . if 25 % is equal to $ 875 then 100 % equals $ x . we just have to multiply $ 875 by 4 to get total amount = $ 3500 . out of this amount we then need to deduct the amount already paid which was $ 875 so we have $ 3500 - $ 875 = $ 2625 answer : option e" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "a", + "Explanation": "\"when a certain number x is divided by 63 , the remainder is 25 . what is the remainder when x is divided by 8 ? putting a value say x = 255 we get remainder as 25 when divided by 63 . when 25 divided by 8 we get 1 as remainder . a is the answer .\"" + }, + { + "Answer": 501.99999999999994, + "Options": "a ) 5.02 % , b ) 50.2 % , c ) 209 % , d ) 502 % , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : while calculation in terms of percentage we need to multiply by 100 , so 5.02 * 100 = 502 answer : option d\"" + }, + { + "Answer": 36.5, + "Options": "a ) 36.6 , b ) 36.1 , c ) 36.5 , d ) 36.2 , e ) 36.9", + "Correct": "c", + "Explanation": "\"correct sum = ( 36 * 50 + 48 - 23 ) = 1825 . correct mean = 1825 / 50 = 36.5 answer : c\"" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "c", + "Explanation": "\"substitute y by 10 in x + 3 y = 33 x + 3 ( 10 ) = 33 x + 30 = 33 if we substitute x by 3 in x + 30 = 33 , we have 3 + 30 = 33 . hence x = 3 correct answer c\"" + }, + { + "Answer": 97, + "Options": "a ) 97 , b ) 89 , c ) 90 , d ) 93 , e ) 95", + "Correct": "a", + "Explanation": "\"total score on 3 tests = 85 * 3 = 255 jerry wants the average to be = 88 hence total score on 4 tests should be = 88 * 4 = 352 score required on the fourth test = 352 - 255 = 97 option a\"" + }, + { + "Answer": 4, + "Options": "a ) 9 , b ) 8 , c ) 7 , d ) 6 , e ) 4", + "Correct": "e", + "Explanation": "let the age of the youngest child = x then , the ages of 5 children can be written as x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 50 \u21d2 5 x + 30 = 50 \u21d2 5 x = 20 \u21d2 x = 205 = 4 answer is e ." + }, + { + "Answer": 48, + "Options": "a ) 40 kmph , b ) 45 kmph , c ) 48 kmph , d ) 50 kmph , e ) 55 kmph", + "Correct": "c", + "Explanation": "\"total time taken = x / 40 + 2 x / 20 hours = 5 x / 40 = x / 8 hours average speed = 6 x / ( x / 8 ) = 48 kmph answer : c\"" + }, + { + "Answer": 4, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "e", + "Explanation": "n = 5 x + 3 , for some integer x ( n - 1 ) ^ 2 = ( 5 x + 2 ) ^ 2 = 5 y + 4 , for some integer y when we divide this by 5 , the remainder is 4 . the answer is e ." + }, + { + "Answer": 450, + "Options": "a ) 350 , b ) 450 , c ) 500 , d ) 650 , e ) 700", + "Correct": "b", + "Explanation": "\"required number = ( 75 / 2 ) / ( 1 / 12 ) = ( 75 / 2 x 12 / 1 ) = 450 . answer : b\"" + }, + { + "Answer": 2002.684, + "Options": "a ) 2008 , b ) 2009 , c ) 2010 , d ) 2011 , e ) none of these", + "Correct": "d", + "Explanation": "explanation : let the commodity p costs 40 paise more than the commodity q after n years price of the commodity p in 2001 = rs . 4.20 since the price of the commodity p increases by rs 0.40 every year , price of the commodity p after n years from 2001 = rs . 4.20 + ( n \u00d7 . 40 ) price of the commodity q in 2001 = rs . 6.30 since the price of the commodity q increases by rs 0.15 every year , price of the commodity q after n years from 2001 = rs . 6.30 + ( n \u00d7 . 15 ) since the commodity p costs rs . 0.40 more that the commodity q after n years from 2001 , 4.20 + ( n \u00d7 . 40 ) = 6.30 + ( n \u00d7 . 15 ) + 0.40 = > ( 40 n - . 15 n ) = 6.30 - 4.20 + 0.40 = 2.5 = > . 25 n = 2.5 \u21d2 n = 2.5 / . 25 = 250 / 25 = 101.15 \u00af = > commodity p costs rs . 0.40 more that the commodity q after 10 years from 2001 . i . e . , in 2011 . answer : option d" + }, + { + "Answer": 616, + "Options": "a ) 661 , b ) 600 , c ) 620 , d ) 616 , e ) none of these", + "Correct": "d", + "Explanation": "\"number of male employees = 2200 * 40 / 100 = 880 required number of male employees who are less than 50 years old = 880 * ( 100 - 30 ) % = 880 * 75 / 100 = 616 . answer : d\"" + }, + { + "Answer": 4, + "Options": "a ) 4 , b ) 5 , c ) 9 , d ) 8 , e ) 10", + "Correct": "a", + "Explanation": "\"the age of children x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 50 5 x = 20 , x = 4 . correct answer ( a )\"" + }, + { + "Answer": 1, + "Options": "a ) 13 , b ) 3 , c ) 15 , d ) 1 , e ) 2", + "Correct": "d", + "Explanation": "explanation : required number = ( 87 - 54 ) , ( 172 - 87 ) , ( 172 - 54 ) = h . c . f of 33,85 and 118 is 1 answer : option d" + }, + { + "Answer": 0.7222222222222222, + "Options": "a ) 11 / 30 , b ) 29 / 60 , c ) 17 / 30 , d ) 13 / 18 , e ) 11 / 15", + "Correct": "d", + "Explanation": "\"let s assume the platinum card spending limit = x gold card spending limit will be = x / 2 balance on gold card is = x / 2 * 1 / 3 = x / 6 platinum card unspent limit is = x - 1 / 9 x = 8 / 9 x so if gold card balance is transferred then the rest unspent will be 8 / 9 x - x / 6 = 13 / 18 x so the ans is d\"" + }, + { + "Answer": 45, + "Options": "a ) a ) 45 , b ) b ) 34 , c ) c ) 50 , d ) d ) 67 , e ) e ) 100", + "Correct": "a", + "Explanation": "\"its a . total juice rquired = 360 * 6 = 2160 ounce 12 ounce concentate makes = 12 * 4 = 48 ounce juice total cans required = 2160 / 48 = 45 . answer a\"" + }, + { + "Answer": 125, + "Options": "a ) 86 , b ) 165 , c ) 76 , d ) 125 , e ) 26", + "Correct": "d", + "Explanation": "\"given m + p + c = 65 * 3 = 195 - - - ( 1 ) m + p = 90 * 2 = 180 - - - ( 2 ) p + c = 70 * 2 = 140 - - - ( 3 ) where m , p and c are marks obtained by the student in mathematics , physics and chemistry . p = ( 2 ) + ( 3 ) - ( 1 ) = 180 + 140 - 195 = 125 answer : d\"" + }, + { + "Answer": 250, + "Options": "a ) 150 , b ) 200 , c ) 250 , d ) 245 , e ) 225", + "Correct": "c", + "Explanation": "looking at the numbers it looks like ( 1 x 5 ) ^ 5 ( 2 x 5 ) ^ 10 . . . ( 10 x 5 ) ^ 50 1 . determine the limiting factor . is it 2 or is it 5 ? we know that all the numbers are multiple of 5 but not of 2 . thus , the limiting factor in this case is 2 . let ' s drop all the 5 . then , we count factors of 2 of even multiples . 2 ^ 10 = 10 4 ^ 20 = 20 + 20 6 ^ 30 = 30 8 ^ 40 = 40 + 40 + 40 10 ^ 50 = 50 250 answer : c" + }, + { + "Answer": 0.1428571428571428, + "Options": "a ) 1 / 4 , b ) 4 / 5 , c ) 1 / 5 , d ) 1 / 6 , e ) 1 / 7", + "Correct": "e", + "Explanation": "if s is an integer and we know that the average speed is 2.8 , s must be = 2 . that meanss + 1 = 3 . this implies that the ratio of time for s = 2 is 1 / 4 of the total time . the formula for distance / rate is d = rt . . . so the distance travelled when s = 2 is 2 t . the distance travelled for s + 1 = 3 is 3 * 4 t or 12 t . therefore , total distance covered while the sun was shining over him is t = 2 / 14 = 1 / 7 . answer : e" + }, + { + "Answer": 170000.00000000003, + "Options": "a ) $ 10700 , b ) $ 17000 , c ) $ 180000 , d ) $ 1700 , e ) $ 170000", + "Correct": "e", + "Explanation": "\"[ 1 / ( x 1 / y 1 + x 2 / y 2 + x 3 / y 3 ) ] * total amount = balance amount [ 1 - ( 1 / 5 + 1 / 10 + 3 / 5 ) } * total salary = $ 17000 , = [ 1 - 9 / 10 ] * total salary = $ 17000 , total salary = $ 17000 * 10 = $ 180000 , correct answer ( e )\"" + }, + { + "Answer": 129, + "Options": "a ) $ 144 , b ) $ 130 , c ) $ 80 , d ) $ 110 , e ) $ 129", + "Correct": "e", + "Explanation": "step 1 : find the cost of the ice cream . 19 \u00d7 $ 7 = $ 133 step 2 : find the cost of the yoghurt . 4 \u00d7 $ 1 = $ 4 step 3 : find how much more the ice cream cost than the yoghurt . $ 133 \u2013 $ 4 = $ 129 tara spent $ 129 more on ice cream . answer is e ." + }, + { + "Answer": 36, + "Options": "a ) 41 , b ) 42 , c ) 36 , d ) 44 , e ) 45", + "Correct": "c", + "Explanation": "\"n ( n - 1 ) / 2 = 9 * 8 / 2 = 36 answer : c\"" + }, + { + "Answer": 300, + "Options": "a ) 210 , b ) 252 , c ) 280 , d ) 320 , e ) 300", + "Correct": "e", + "Explanation": "\"however the process of dividing the volume of box by the volume of a soap seems flawed but it does work in this case due to the numbers dimensions of the box = 25 * 48 * 60 dimensions of the soap = 5 * 6 * 8 we get = 5 x 6 x 10 = 300 so the question is why this particular arrangement , in order to maximize number of soaps we need to minimize the space wasted and this is the only config where we dont waste any space so we can expect the maximum number the answer is ( e )\"" + }, + { + "Answer": 500.00000000000006, + "Options": "a ) $ 550 , b ) $ 600 , c ) $ 500 , d ) $ 400 , e ) $ 450", + "Correct": "c", + "Explanation": "\"if 50 books constitute 1 / 3 rd of the total , then 2 / 3 rd of the total = 100 books amount received for sold books = 100 * 5 = $ 500 answer : c\"" + }, + { + "Answer": 5, + "Options": "a ) 6 rs , b ) 7 rs , c ) 8 rs , d ) 5 rs , e ) 1 rs", + "Correct": "d", + "Explanation": "\"5 m = xw = 8 b 5 m + xw + 8 b - - - - - 75 rs . 5 m + 5 m + 5 m - - - - - 75 rs . 15 m - - - - - - 75 rs . = > 1 m = 5 rs . answer : d\"" + }, + { + "Answer": 4, + "Options": "a ) $ 5 , b ) $ 10 , c ) $ 14 , d ) $ 4 , e ) $ 28", + "Correct": "d", + "Explanation": "bill = fixed charge + charge of calls made in jan , bill = fixed charge ( let , y ) + charge of calls made in jan ( let , x ) = $ 40 in feb , bill = fixed charge ( let , y ) + charge of calls made in feb ( then , 2 x ) = $ 76 i . e . x + y = 40 and 2 x + y = 76 take the difference if two equations i . e . ( 2 x + y ) - ( x + y ) = 76 - 40 i . e . x = 36 i . e . fixed monthly charge , y = 4 answer : option d" + }, + { + "Answer": 14, + "Options": "a ) 22 , b ) 11 , c ) 25 , d ) 14 , e ) 16", + "Correct": "d", + "Explanation": "solution : sum of ages of 4 members 5 years ago = 94 = > sum of present ages of 4 members = 94 + 4 * 5 = 114 difference in the sum of the ages = difference in the ages of daughter and daughter - in - law difference in the sum of the ages = 114 - 100 = 14 = > difference in the ages of daughter and daughter - in - law = 14 answer d" + }, + { + "Answer": 30, + "Options": "a ) a ) 7 , b ) b ) 5 , c ) c ) 4 , d ) d ) 18 , e ) e ) 30", + "Correct": "e", + "Explanation": "\"explanation : = > 40 \u00d7 ? + ( 12 + 8 ) \u00d7 3 / 5 = 1212 = > 40 \u00d7 ? = 1212 - ( 12 + 8 ) \u00d7 3 / 5 = > 40 \u00d7 ? = 1212 - 20 \u00d7 3 / 5 = > 40 \u00d7 ? = 1212 - 20 \u00d7 3 / 5 = 1200 = > ? = 1200 / 40 = 30 answer : option e\"" + }, + { + "Answer": 2, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "c", + "Explanation": "\"f ( x ) + 3 f ( 8 - x ) = f ( 2 ) + 3 f ( 6 ) = 2 : x = 2 above f ( 6 ) + 3 f ( 2 ) = 6 : x = 6 above f ( 6 ) = 6 - 3 f ( 2 ) : solve equation c for f ( 6 ) f ( 2 ) + 3 ( 6 - 3 f ( 2 ) ) = 2 : substitute f ( 2 ) = 2 : solve above equation correct answer c\"" + }, + { + "Answer": 91, + "Options": "a ) 55 , b ) 60 , c ) 73 , d ) 82 , e ) 91", + "Correct": "e", + "Explanation": "\"a score of 73 brings to mind that it is an odd number even though you are subtracting an even number ( twice the incorrect responses ) out of the correct responses score . so the correct responses score must be an odd number too ( odd - even = odd ) . since the overall score is 73 , the number of correct responses must be more than 73 since the student answered all questions . only 91 satisfies both these conditions . answer ( e )\"" + }, + { + "Answer": 72.5, + "Options": "a ) 76 kg , b ) 77 kg , c ) 72.5 kg , d ) data inadequate , e ) none of these", + "Correct": "c", + "Explanation": "\"total weight increases = 5 \u00d7 1.5 = 7.5 kg so the weight of new person = 65 + 7.5 = 72.5 kg answer c\"" + }, + { + "Answer": 100, + "Options": "a ) 90 % , b ) 99 % , c ) 100 % , d ) 101 % , e ) 110 %", + "Correct": "b", + "Explanation": "\"the total number of employees = n the average salary = x total salary to all emplyoees = xn after the total number of employees = n - 0.1 n = 0.9 n the average salary = x + 10 % of x = 1.1 x total salary to all emplyoees = 0.9 n ( 1.1 x ) total salary after as a % of total salary before e = [ 0.9 n ( 1.1 x ) ] / xn = 0.99 or 99 % = b\"" + }, + { + "Answer": 2, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "b", + "Explanation": "for calculating the unit place of these type of question ( exponent ) as the power of 2 repeats after 4 , so we will divide the exponent by 4 e . g , 2 ^ 1 = 2 and 2 ^ ( 4 + 1 ) = 32 , both have same unit place 369 / 4 gives the remainder as 1 so we can write 322 ^ 369 = 2 ^ 1 = 2 so , the unit place will be 2 answer : b" + }, + { + "Answer": 561, + "Options": "a ) 550 , b ) 551 , c ) 560 , d ) 561 , e ) 572", + "Correct": "d", + "Explanation": "this is a perfect example of why you should not use formulas without understanding them properly . if you understand them , you will not make a mistake and will save time . the formula quoted by the original poster : n ( n + 1 ) is absolutely fine . but one needs to understand that n is the number of even terms starting from the first even term . ( i discuss why this is so here : sum of even numbers from 40 to 60 using this formula will be : 30 * 31 - 19 * 20 = 10 ( 3 * 31 - 19 * 2 ) = 550 since number of terms is 11 , required sum is 561 but , i would not use this formula for this question and would do it the way many of you have done : average = 50 ( it is the middle number ) , number of terms = 11 ( no formula again . any 10 consecutive integers have 5 even and 5 odd numbers . 41 to 60 will have 10 even integers and 40 is the 11 th one ) sum = 50 * 11 + 11 = 561 answer is d" + }, + { + "Answer": 7900, + "Options": "a ) 7000 , b ) 7900 , c ) 6000 , d ) 5000 , e ) 4000", + "Correct": "b", + "Explanation": "\"state a and state b had an equal number of candidates appeared . in state a , 6 % candidates got selected from the total appeared candidates in state b , 7 % candidates got selected from the total appeared candidates but in state b , 79 more candidates got selected than state a from these , it is clear that 1 % of the total appeared candidates in state b = 79 = > total appeared candidates in state b = 79 x 100 = 7900 = > total appeared candidates in state a = total appeared candidates in state b = 7900\"" + }, + { + "Answer": 190.00000000000006, + "Options": "a ) 160 , b ) 170 , c ) 180 , d ) 190 , e ) 200", + "Correct": "d", + "Explanation": "\"16 * 180 = 2880 . the other 4 carrots weigh a total of 760 grams . the average weight is 760 / 4 = 190 grams . the answer is d .\"" + }, + { + "Answer": 0.6666666666666666, + "Options": "a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 3 , e ) none of these", + "Correct": "b", + "Explanation": "\"explanation : a \u00e2 \u02c6 \u2014 b \u00e2 \u02c6 \u2014 c / b \u00e2 \u02c6 \u2014 c \u00e2 \u02c6 \u2014 d = 130 / 65 = > a / d = 2 d \u00e2 \u02c6 \u2014 e \u00e2 \u02c6 \u2014 f / c \u00e2 \u02c6 \u2014 d \u00e2 \u02c6 \u2014 e = 250 / 750 = > f / c = 1 / 3 a / d * f / c = 2 * 1 / 3 = 2 / 3 answer : b\"" + }, + { + "Answer": 1.6666666666666665, + "Options": "a ) 1 / 3 , b ) 2 / 3 , c ) 4 / 3 , d ) 5 / 3 , e ) 7 / 3", + "Correct": "d", + "Explanation": "\"( 2 / 3 ) g = ( 1 / 4 ) ( b + g ) 8 g = 3 b + 3 g 5 g = 3 b b / g = 5 / 3 . the answer is d .\"" + }, + { + "Answer": 10, + "Options": "a ) 123 , b ) 127 , c ) 235 , d ) 305 , e ) 10", + "Correct": "e", + "Explanation": "explanation : required number = h . c . f . of ( 1442 - 12 ) and ( 1816 - 6 ) = h . c . f . of 1430 and 1810 = 10 . answer : e" + }, + { + "Answer": 3.5, + "Options": "a ) 3 , b ) 3.5 , c ) 4 , d ) 4.5 , e ) 5", + "Correct": "b", + "Explanation": "\"222 - 198 = 24 pounds lost in 3 months 24 / 3 = 8 , so joe is losing weight at a rate of 8 pounds per month . . . . in approximately how many months will he weigh 170 pounds ? a simple approach is to just list the weights . now : 198 lbs in 1 month : 190 lbs in 2 months : 182 lbs in 3 months : 174 lbs in 4 months : 166 lbs since 170 pounds is halfway between 174 and 166 , the correct answer must be 3.5 months . answer : b\"" + }, + { + "Answer": 5, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "d", + "Explanation": "\"2 ( 2 x - 3 ) - 11 = 2 ( x - 2 ) - 3 2 x = 10 x = 5 the answer is d .\"" + }, + { + "Answer": 1200, + "Options": "a ) 1200 , b ) 1723 , c ) 1129 , d ) 2613 , e ) 1372", + "Correct": "a", + "Explanation": "\"a b has 62.5 % or ( 5 / 8 ) of the milk in a . therefore , let the quantity of milk in container a ( initially ) be 8 k . quantity of milk in b = 8 k - 5 k = 3 k . quantity of milk in container c = 8 k - 3 k = 5 k container : a b c quantity of milk : 8 k 3 k 5 k it is given that if 150 liters was transferred from container c to container b , then both the containers would have equal quantities of milk . 5 k - 150 = 3 k + 150 = > 2 k = 300 = > k = 150 the initial quantity of milk in a = 8 k = 8 * 150 = 1200 liters .\"" + }, + { + "Answer": 15, + "Options": "a ) 14 , b ) 20 , c ) 15 , d ) 28 , e ) 30", + "Correct": "c", + "Explanation": "\"solution let the number be x . then , 13 x - x = 180 \u2039 = \u203a 12 x = 180 x \u2039 = \u203a 15 . answer c\"" + }, + { + "Answer": 1000, + "Options": "a ) 1 , b ) 100 , c ) 10000 , d ) 100000 , e ) 1000", + "Correct": "e", + "Explanation": "\"10 ^ ( 655 ) \u00e3 \u00b7 10 ^ ( 652 ) = 10 ^ ( 655 - 652 ) = 10 ^ 3 = 1000 answer : e\"" + }, + { + "Answer": 32, + "Options": "a ) 32 min , b ) 40 min , c ) 35 min , d ) 25 min , e ) 20 min", + "Correct": "a", + "Explanation": "\"clearly , the two will meet when they are 1000 m apart to be 20 + 12 = 32 km apart , they take 1 hour to be 1000 m apart , they take 32 * 1000 / 1000 = 32 min . answer is a\"" + }, + { + "Answer": 0.4285714285714286, + "Options": "a ) 1 / 49 , b ) 4 / 7 , c ) 3 / 7 , d ) 16 / 49 , e ) 40 / 49", + "Correct": "c", + "Explanation": "\"the probability of drawing a pink gumball both times is the same . the probability that she drew two blue gumballs = 16 / 49 = ( 4 / 7 ) * ( 4 / 7 ) therefore probability that the next one she draws is pink = 3 / 7 option ( c )\"" + }, + { + "Answer": 110, + "Options": "a ) 110 , b ) 70.4 , c ) 86 , d ) 105.6 , e ) 108", + "Correct": "a", + "Explanation": "\"x = 88 * 1.25 = 110 so the answer is a .\"" + }, + { + "Answer": 5, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "e", + "Explanation": "\"if the average price is 54 , then mary has 7 oranges and 3 apples ( a ratio of 7 : 3 ) . for the average price to be 48 , the ratio should be 2 : 3 . mary must put back 5 oranges . the answer is e .\"" + }, + { + "Answer": 500, + "Options": "a ) $ 200 , b ) $ 500 , c ) $ 600 , d ) $ 800 , e ) $ 1,200", + "Correct": "b", + "Explanation": "suppose total money spent = x not spend ( money he still has ) = x - 800 x + x - 800 = 1800 x = 1300 money not spend = 1300 - 800 = 500 answer : b" + }, + { + "Answer": 216, + "Options": "a ) 122 , b ) 210 , c ) 216 , d ) 217 , e ) 225", + "Correct": "c", + "Explanation": "we should determine which 5 digits from given 6 , would form the 5 digit number divisible by 3 . we have six digits : 0 , 1 , 2 , 3 , 4 , 5 . their sum = 15 . for a number to be divisible by 3 the sum of the digits must be divisible by 3 . as the sum of the six given numbers is 15 ( divisible by 3 ) only 5 digits good to form our 5 digit number would be 15 - 0 = { 1 , 2 , 3 , 4 , 5 } and 15 - 3 = { 0 , 1 , 2 , 4 , 5 } . meaning that no other 5 from given six will total the number divisible by 3 . second step : we have two set of numbers : 1 , 2 , 3 , 4 , 5 and 0 , 1 , 2 , 4 , 5 . how many 5 digit numbers can be formed using these two sets : 1 , 2 , 3 , 4 , 5 - - > 5 ! as any combination of these digits would give us 5 digit number divisible by 3 . 5 ! = 120 . 0 , 1 , 2 , 4 , 5 - - > here we can not use 0 as the first digit , otherwise number wo n ' t be any more 5 digit and become 4 digit . so , desired # would be total combinations 5 ! , minus combinations with 0 as the first digit ( combination of 4 ) 4 ! - - > 5 ! - 4 ! = 4 ! ( 5 - 1 ) = 4 ! * 4 = 96 120 + 96 = 216 = e answer : c ." + }, + { + "Answer": 29.999999999999996, + "Options": "a ) $ 20 , b ) $ 30 , c ) $ 50 , d ) $ 90 , e ) $ 110", + "Correct": "b", + "Explanation": "\"let ' s let t = total number of dollars spent at the supermarket . with this variable we can set up an equation and determine t . we are given that john spent 1 / 5 of his money on fresh fruits and vegetables , or ( 1 / 5 ) t , 1 / 3 on meat products , or ( 1 / 3 ) t , and 1 / 10 on bakery products , or ( 1 / 10 ) t . we are also given that he spent the remaining $ 11 on candy . since we know where all his money was allocated , we can sum these values together and set the sum to t . so we have : ( 1 / 5 ) t + ( 1 / 3 ) t + ( 1 / 10 ) t + 11 = t to get rid of the fractions we can multiply the entire equation by 30 , and we obtain : 6 t + 10 t + 3 t + 330 = 30 t 19 t + 330 = 30 t 330 = 11 t t = 30 john spent $ 90 at the supermarket . answer : b\"" + }, + { + "Answer": 35, + "Options": "a ) 18 % , b ) 20 % , c ) 21 % , d ) 33 % , e ) can not be determined", + "Correct": "d", + "Explanation": "answer : d ." + }, + { + "Answer": 700, + "Options": "a ) 600 , b ) 650 , c ) 700 , d ) 750 , e ) none of these", + "Correct": "c", + "Explanation": "as per question stem 2 / 5 m ( portion of men employees who are managers ) + 280 ( portion of female employees who are managers ) = 2 / 5 t ( portion of total number of employees who are managers ) , thus we get that 2 / 5 m + 280 = 2 / 5 t , or 2 / 5 ( t - m ) = 280 , from here we get that t - m = 700 , that would be total number of female employees and the answer ( c )" + }, + { + "Answer": 3000, + "Options": "a ) 3050 , b ) 3000 , c ) 4000 , d ) 4050 , e ) 3100", + "Correct": "b", + "Explanation": "\"explanation : let p , q and r represent their respective monthly incomes . then , we have : p + q = ( 2050 x 2 ) = 4100 . . . . ( i ) q + r = ( 5250 x 2 ) = 10500 . . . . ( ii ) p + r = ( 6200 x 2 ) = 12400 . . . . ( iii ) adding ( i ) , ( ii ) and ( iii ) , we get : 2 ( p + q + r ) = 27000 or p + q + r = 13500 . . . . ( iv ) subtracting ( ii ) from ( iv ) , we get p = 3000 . p ' s monthly income = rs . 3000 . answer : b\"" + }, + { + "Answer": 0.2, + "Options": "a ) 77 / 2 , b ) 1 / 7 , c ) 78 / 85 , d ) 1 / 5 , e ) 47 / 85", + "Correct": "d", + "Explanation": "\"let us say probability of a occuring is a . let us say probability of b occuring is b . a = 2 b probability ( either a or b or both ) = 14 times probability ( a and b ) a * ( 1 - b ) + b * ( 1 - a ) + ab = 14 * ab substituting a = 2 b in the second equation : 2 b * ( 1 - b ) + b * ( 1 - 2 b ) + 2 b * b = 14 * 2 b * b 3 b - 2 b ^ 2 = 28 b ^ 2 3 b = 30 b ^ 2 b = 3 / 30 = 1 / 10 so , a = 2 b = 1 / 5 the correct answer is d .\"" + }, + { + "Answer": 8, + "Options": "a ) 8 , b ) 3 , c ) 7 , d ) 9 , e ) 10", + "Correct": "a", + "Explanation": "a b + g = 8 for b in range ( 199 ) : for g in range ( 199 ) : sum 1 = 2 * b * g + 42 sum 2 = ( b + g ) * ( b + g + 1 ) if ( sum 1 = = sum 2 ) : print ( b , g , sum 1 ) ( b , g ) = ( 35 ) = > b + g = 8" + }, + { + "Answer": 17, + "Options": "a ) 17 , b ) 77 , c ) 66 , d ) 55 , e ) 31", + "Correct": "a", + "Explanation": "s : e = 1 : 3 e : m = 1 : 4 - - - - - - - - - - - - s : e : m = 1 : 4 : 12 1 / 17 * 170 = 17 answer : a" + }, + { + "Answer": 1, + "Options": "a ) 7 , b ) 1 , c ) 9 , d ) 10 , e ) 11", + "Correct": "b", + "Explanation": "\"7 ^ 8 can be written as ( 7 ^ 4 ) ^ 2 if we divide 7 ^ 4 by 100 the reminder is 1 so , ( 7 ^ 4 ) ^ 2 by 100 , the reminder is 1 ^ 2 = 1 answer : b\"" + }, + { + "Answer": 190, + "Options": "a ) 100 , b ) 190 , c ) 150 , d ) 180 , e ) 199", + "Correct": "b", + "Explanation": "\"65 % of x = 20 % of 615.50 then , 65 / 100 * x = 20 / 100 * 6175 / 10 x = 190 answer is b\"" + }, + { + "Answer": 11, + "Options": "a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 12", + "Correct": "d", + "Explanation": "\"option ' d ' 12 / 6 = 2 and 82 / 6 = 13 = = > 13 - 2 = 11 numbers\"" + }, + { + "Answer": 48, + "Options": "a ) 20 , b ) 36 , c ) 48 , d ) 60 , e ) 84", + "Correct": "c", + "Explanation": "question says they are both related linearly so they the relationships can be represented by standard linear definition y = mx + b . let s scale = y . and r scale = x . 30 = 6 m + b eqn 1 60 = 24 m + b eqn 2 eqn 2 - eqn 1 = > 30 = 18 m = > m = 5 / 3 solving for b using either equation gives us b = 20 linear relationship is represented by y = ( 5 / 3 ) x + 20 solve for 100 : 100 = 5 / 3 x + 20 80 = 5 / 3 x x = 48 ans = c" + }, + { + "Answer": 18, + "Options": "a ) 16 , b ) 18 , c ) 20 , d ) 13 , e ) 14", + "Correct": "b", + "Explanation": "explanation : clearly 11 mornings and 12 afternoons = 23 half days = > since 13 days raining means 13 half days . = > so 23 - 13 = 10 halfdays ( not effecetd by rain ) = > so 10 halfdays = 5 fulldays hence , total no . of days = 13 + 5 = 18 days answer : b" + }, + { + "Answer": 2800, + "Options": "a ) 13000 , b ) 7000 , c ) 10000 , d ) 2800 , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : profit = 5 , 00,000 \u00e2 \u02c6 \u2019 ( 1 , 50,000 + 75,000 ) = rs . 2 , 75,000 . since , such loom contributes equally to sales and manufacturing expenses . but the monthly charges are fixed at rs 75,000 . if one loan breaks down sales and expenses will decrease . new profit : - = > 500000 \u00e3 \u2014 ( 124 / 125 ) \u00e2 \u02c6 \u2019 150000 \u00e3 \u2014 ( 124 / 125 ) \u00e2 \u02c6 \u2019 75000 . = > rs 2 , 72,200 . decrease in profit = > 2 , 75,000 \u00e2 \u02c6 \u2019 2 , 72,200 = > rs . 2,800 . answer : d\"" + }, + { + "Answer": 0.00390625, + "Options": "a ) 0.0039 , b ) 0.0625 , c ) 0.16 , d ) 0.25 , e ) 0.5", + "Correct": "a", + "Explanation": "\"( 1 / 4 ) ^ 4 = 1 / 256 = 0.0039 answer : a\"" + }, + { + "Answer": 0.5, + "Options": "a ) 2 / 10 , b ) 5 / 10 , c ) 10 / 5 , d ) 7 / 6 , e ) 6 / 7", + "Correct": "b", + "Explanation": "( ( a + b ) / c ) / 2 = ( a + b ) / 2 c the expression will have the least value when numerator ( a + b ) is the smallest . = ( 2 + 3 ) / 2 * 5 = 5 / 10 answer b" + }, + { + "Answer": 25, + "Options": "a ) 33 , b ) 28 , c ) 27 , d ) 24 , e ) 25", + "Correct": "e", + "Explanation": "it is given that a quartile is the middle number of all numbers less than median . . so lets arrange the number in ascending order - 42 , 24 , 30 , 22 , 26 , 27 , 33 and 35 22 , 24 , 26 , 27 , 30 , 33 , 35 , 42 , . . . numbers less than median are 22 , 24 , 26 , 27 . . the median of these numbers = center of 24 and 26 = 25 e" + }, + { + "Answer": 7, + "Options": "a ) 7 , b ) 9 , c ) 8 , d ) 5 , e ) 4", + "Correct": "a", + "Explanation": "x + y = 25 xy = 144 ( x - y ) 2 = ( x + y ) 2 \u00e2 \u20ac \u201c 4 xy ( x - y ) 2 = 625 \u00e2 \u20ac \u201c 576 = > ( x \u00e2 \u20ac \u201c y ) = 7 answer : a" + }, + { + "Answer": 20, + "Options": "a ) 10 % , b ) 15 % , c ) 20 % , d ) 40 % , e ) none", + "Correct": "c", + "Explanation": "sol . let sum = x . then , s . i . = 3 x \u2234 rate = [ 100 * s . i . / p * t ] = [ 100 * 3 x / x * 15 ] % = 20 % . answer c" + }, + { + "Answer": 0.39999999999999997, + "Options": "a ) $ 015 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45", + "Correct": "d", + "Explanation": "\"on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.6 = 3 * x - - > x = $ 0.4 . answer : d .\"" + }, + { + "Answer": 314.19, + "Options": "a ) $ 314.16 , b ) $ 314.17 , c ) $ 314.18 , d ) $ 314.19 , e ) $ 314.20", + "Correct": "d", + "Explanation": "this is equivalent to finding the first number that is divisible by 9 that occurs after 31416 . in order to divide the sum in 9 parts , the amount must be divisible by 9 divisibility rule of 9 : the sum of the digits must be divisible by 9 sum of digits of 31416 = 15 and 18 is divisible by 9 . hence , we need to add 3 to this number for it to be divisible by 9 correct option : d" + }, + { + "Answer": 40, + "Options": "a ) 60 , b ) 40 , c ) 100 , d ) 28 , e ) 50", + "Correct": "b", + "Explanation": "follow reverse process 48 + 12 = 60 \u2013 10 = 50 \u00f7 5 = 10 \u00d7 \u00d7 4 = 40 option b" + }, + { + "Answer": 18, + "Options": "a ) 6 , b ) 42 , c ) 24 , d ) 18 , e ) 95", + "Correct": "d", + "Explanation": "a / b + b / a = ( a 2 + b 2 ) / ab = ( a 2 + b 2 + a + b ) / ab = [ ( a + b ) 2 - 2 ab ] / ab a + b = - 10 / 1 = - 10 ab = 5 / 1 = 5 hence a / b + b / a = [ ( - 10 ) 2 - 2 ( 5 ) ] / 5 = 90 / 5 = 18 . d )" + }, + { + "Answer": 198.75, + "Options": "a ) 191 , b ) 199 , c ) 193 , d ) 212 , e ) 213", + "Correct": "b", + "Explanation": "total movies submitted are 795 . as per question we need to take 1 / 4 of 795 to be considered for top 10 movies = 198.75 approximate the value we 199 . imo option b is the correct answer . . ." + }, + { + "Answer": 3, + "Options": "a ) 1.7 , b ) 1.9 , c ) 3 , d ) 1.5 , e ) 1.2", + "Correct": "c", + "Explanation": "\"m = 9 s = x ds = 9 + x us = 9 - x 9 + x = ( 9 - x ) 2 9 + x = 18 - 2 x 3 x = 9 x = 3 answer : c\"" + }, + { + "Answer": 12, + "Options": "a ) 3 , b ) 6 , c ) 9 , d ) 10.5 , e ) 12", + "Correct": "e", + "Explanation": "\"the x - axis is 6 units from the point p . thus the y - axis is 12 units from the point p . the answer is e .\"" + }, + { + "Answer": 15120, + "Options": "a ) 15120 , b ) 14500 , c ) 14900 , d ) 14300 , e ) 14000", + "Correct": "a", + "Explanation": "total amount invested = 50000 assume that investment of c = x . then investment of b = 5000 + x , investment of a = 4000 + 5000 + x = 9000 + x x + 5000 + x + 9000 + x = 50000 \u21d2 3 x + 14000 = 50000 \u21d2 3 x = 50000 \u2013 14000 = 36000 \u21d2 x = 36000 / 3 = 12000 investment of c = x = 12000 investment of b = 5000 + x = 17000 investment of a = 9000 + x = 21000 ratio of the investment of a , b and c = 21000 : 17000 : 12000 = 21 : 17 : 12 share of a = total profit \u00d7 21 / 50 = 36000 \u00d7 21 / 50 = 15,120 answer is a ." + }, + { + "Answer": 0.6666666666666666, + "Options": "a ) 1 / 9 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6", + "Correct": "d", + "Explanation": "\"n ( n + 1 ) to be divisible by 2 either n or n + 1 must be a multiples of 2 . in each following group of numbers : { 1 , 2 , 3 } , { 4 , 5 , 6 } , { 7 , 8 , 9 } , . . . , { 97 , 98 , 99 } there are exactly 2 numbers out of 3 satisfying the above condition . for example in { 1 , 2 , 3 } n can be : 2 , or 3 . thus , the overall probability is 2 / 3 . answer : d .\"" + }, + { + "Answer": 20, + "Options": "a ) 20 , b ) 24 , c ) 26 , d ) 28 , e ) 30", + "Correct": "a", + "Explanation": "\"women = 1 / 4 * 80 = 20 married = 3 / 4 * 80 = 60 unmarried = 20 max ( un - married women ) = 20 answer a\"" + }, + { + "Answer": 398.2, + "Options": "a ) 395 , b ) 275 , c ) 355 , d ) 415 , e ) 398.2", + "Correct": "e", + "Explanation": "\"the mean of numbers 12 , x , 42 , 78 and 104 is 62 : 12 + x + 42 + 78 + 104 = 62 * 5 - - > x = 74 ; so , the mean of 128 , 255 , 511 , 1023 and x is ( 128 + 255 + 511 + 1023 + 74 ) / 5 = 398.2 . answer : e .\"" + }, + { + "Answer": 7.5, + "Options": "a ) 7.5 , b ) 6 , c ) 5.5 , d ) 6.5 , e ) 5", + "Correct": "a", + "Explanation": "let the present ages of ramesh and mahesh be 2 x and 5 x years respectively . ( 2 x + 10 ) / ( 5 x + 10 ) = 10 / 15 6 x + 30 = 10 x + 20 = > x = 2.5 difference in their ages will be the same at all times . this difference = difference of their present ages = > 5 x - 2 x = 3 x = > 7.5 years answer : a" + }, + { + "Answer": 2100, + "Options": "a ) 2200 , b ) 2000 , c ) 2100 , d ) 2300 , e ) none", + "Correct": "c", + "Explanation": "solution : actual salary is 2000 rupees 5 % of 2000 = 2000 * 5 / 100 = 100 so 100 rupees increased = 2000 + 100 = 2100 he will get salary of 2100 answer c" + }, + { + "Answer": 66, + "Options": "a ) 64 % , b ) 66 % , c ) 68 % , d ) 70 % , e ) 72 %", + "Correct": "b", + "Explanation": "70 % of the class scored 60 % and 30 % of the class scored 80 % . the difference between 60 % and 80 % is 20 % . the average will be 60 % + 0.3 ( 20 % ) = 66 % . the answer is b ." + }, + { + "Answer": 720, + "Options": "a ) 6 , b ) 32 , c ) 120 , d ) 720 , e ) 820", + "Correct": "d", + "Explanation": "solution since 32 p 6 = k 32 c 6 \u21d2 32 ! / ( 32 - 6 ) ! = k 32 ! / ( 32 - 6 ) ! \u21d2 k = 6 ! = 720 . answer d" + }, + { + "Answer": 8, + "Options": "a ) 0 , b ) 2 , c ) 4 , d ) 8 , e ) more than 8", + "Correct": "d", + "Explanation": "i think its 8 | | | q - 5 | - 10 | - 5 | = 2 let | q - 5 | = a which makes above | | a - 10 | - 5 | = 2 let | a - 10 | = b which makes | b - 5 | = 2 now for the above b can take 3 , 7 for every b = 3 a can have 13 , 7 and for b = 7 a can have 17 and 3 so ' a ' has four solutions 13 , 7 , 17 and 3 for a = 13 ; q has 18 or - 8 thus has 2 for every combination hence 4 x 2 = 8 answer d" + }, + { + "Answer": 3.1875, + "Options": "a ) $ 1.40 , b ) $ 2.40 , c ) $ 3.40 , d ) $ 3.19 , e ) $ 5.40", + "Correct": "d", + "Explanation": "\"manager wages per hour = $ 8.50 dishwasher wages per hour = half of manager ' s wages . = 1 / 2 ( $ 8.50 ) = = > $ 4.25 chef wages per hour = 25 % greater than dishwasher wages - - > 25 % of $ 4.25 = ( 25 * ( $ 4.25 ) ) / 100 - - > ( $ 106.25 ) / 100 - - > $ 1.06 therefore , chef wages per hour = $ 4.25 + $ 1.06 = = > $ 5.31 difference of wages between manager and chef = $ 8.50 - $ 5.31 = = > $ 3.19 answer : d\"" + }, + { + "Answer": 39, + "Options": "a ) 39 yr , b ) 42 yr , c ) 45 yr , d ) 32 yr , e ) 50 yr", + "Correct": "a", + "Explanation": "\"let b ' s present age = x years then a ' s present age = x + 9 years x + 9 + 10 = 2 ( x - 10 ) x + 19 = 2 x - 20 x = 39 years answer is a\"" + }, + { + "Answer": 114.85, + "Options": "a ) $ 220.85 , b ) $ 214.85 , c ) $ 114.85 , d ) $ 314.85 , e ) $ 104.85", + "Correct": "c", + "Explanation": "krish spent and gave to his two friends a total of 35.25 + 25.20 + 25.20 = $ 85.65 money left 200.50 - 85.65 = $ 114.85 correct answer is c ) $ 114.85" + }, + { + "Answer": 65, + "Options": "a ) 18 , b ) 36 , c ) 72 , d ) 90 , e ) 65", + "Correct": "e", + "Explanation": "\"65 all u do is do 2 : 1 : 6 = > 2 x + x + 6 x = 117 = > x = 13 26 : 13 : 78 78 - 13 = 65 answer e\"" + }, + { + "Answer": 51.95187165775401, + "Options": "a ) 50.25 , b ) 52.25 , c ) 51.95 , d ) 53.25 , e ) none of the above", + "Correct": "c", + "Explanation": "required average marks = 65 \u00e3 \u2014 50 + 35 \u00e3 \u2014 60 + 45 \u00e3 \u2014 55 + 42 \u00e3 \u2014 45 / 65 + 35 + 45 + 42 = 3250 + 2100 + 2475 + 1890 / 187 = 9715 \u00e2 \u0081 \u201e 187 = 51.95 answer c" + }, + { + "Answer": 22, + "Options": "a ) 20 . , b ) 21 , c ) 22 , d ) 23 , e ) 24", + "Correct": "c", + "Explanation": "if 1430 is divisible by anyone of the answer choices . a . 1430 / 20 = 143 / 2 b 1430 / 21 = 1430 / 21 c 1430 / 22 = 65 if 1430 apple was divided among 65 people , each would have received 22 . after addition of 45 people the answer should be 13 . 1430 / 110 = 13 . c is the answer ." + }, + { + "Answer": 30, + "Options": "a ) 4 , b ) 6 , c ) 8 , d ) 30 , e ) 12", + "Correct": "d", + "Explanation": "\"i am getting 12 . e . hope havent done any calculation errors . . approach . . let y = no . of days taken by y to do w widgets . then x will take y + 2 days . 1 / ( y + 2 ) + 1 / y = 5 / 12 ( 5 / 12 is because ( 5 / 4 ) w widgets are done in 3 days . so , x widgets will be done in 12 / 5 days or 5 / 12 th of a widget in a day ) solving , we have y = 4 = > x takes 6 days to doing x widgets . so , he will take 30 days to doing 5 w widgets . answer : d\"" + }, + { + "Answer": 280, + "Options": "a ) s . 250 , b ) s . 280 , c ) s . 290 , d ) s . 299 , e ) s . 300", + "Correct": "b", + "Explanation": "\"let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 616 but x = 120 % of y = 120 y / 100 = 12 y / 10 \u2234 12 y / 10 + y = 616 \u21d2 y [ 12 / 10 + 1 ] = 616 \u21d2 22 y / 10 = 616 \u21d2 22 y = 6160 \u21d2 y = 6160 / 22 = 560 / 2 = rs . 280 b\"" + }, + { + "Answer": 9, + "Options": "a ) 3 , b ) 7 , c ) 9 , d ) 21 , e ) 25", + "Correct": "c", + "Explanation": "\"jacob = x years , michael = x + 14 years 9 years from now , 2 ( x + 9 ) = x + 23 2 x + 18 = x + 23 x = 5 x + 4 = 9 years answer c\"" + }, + { + "Answer": 12, + "Options": "a ) 10 , b ) 11 , c ) 12 , d ) 15 , e ) 17", + "Correct": "c", + "Explanation": "\"let possible value of x is 126 least possible value of x / 19 is 126 / 19 = > 6 quotient with remainder 12 thus answer is ( c ) 12\"" + }, + { + "Answer": 20, + "Options": "a ) 12 , b ) 29 , c ) 20 , d ) 15 , e ) 99", + "Correct": "c", + "Explanation": "\"explanation : let the number be x . therefore , 3 ( 2 x + 5 ) = 135 6 x + 15 = 135 6 x = 120 x = 20 answer : c\"" + }, + { + "Answer": 6, + "Options": "a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10", + "Correct": "c", + "Explanation": "\"the average of 10 , 30 , and 50 is 30 . the average of 20 , 40 and x is 22 . then 20 + 40 + x = 66 . x = 6 . the answer is c .\"" + }, + { + "Answer": 780, + "Options": "a ) 780 , b ) 891 , c ) 812 , d ) 847 , e ) 890", + "Correct": "a", + "Explanation": "\"solution we know that ( 1 + 2 + 3 + . . . . . + 39 ) = n ( n + 1 ) / 2 therefore ( 1 + 2 + 3 + . . . . + 39 ) = ( 39 \u00d7 40 / 2 ) = 780 . answer a\"" + }, + { + "Answer": 60, + "Options": "a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80", + "Correct": "c", + "Explanation": "\"total people at party = 150 women = 70 so men 150 - 70 = 80 no . of pple who tried appetizer = 150 - 50 ( given info ) = 100 no of women who tried appetizer = 40 so remaining ppl ( men ) who tried the appetizer = 100 - 40 = 60 correct option c\"" + }, + { + "Answer": 13.333333333333334, + "Options": "a ) 11.33 kmph , b ) 12.33 kmph , c ) 13.33 kmph , d ) 14.33 kmph , e ) 23.33 kmph", + "Correct": "c", + "Explanation": "\"total time taken = x / 40 + 4 x / 20 hours = 9 x / 40 hours average speed = 3 x / ( 9 x / 40 ) = 13.33 kmph answer : c\"" + }, + { + "Answer": 0.5, + "Options": "a ) 1 / 4 , b ) 3 / 8 , c ) 1 / 2 , d ) 5 / 8 , e ) 3 / 4", + "Correct": "c", + "Explanation": "the sum of the three numbers on the balls selected from the box to be odd one should select either three odd numbered balls ( odd + odd + odd = odd ) or two even numbered balls and one odd numbered ball ( even + even + odd = odd ) ; p ( ooo ) = ( 1 / 2 ) ^ 3 ; p ( eeo ) = 3 * ( 1 / 2 ) ^ 2 * 1 / 2 = 3 / 8 ( you should multiply by 3 as the scenario of two even numbered balls and one odd numbered ball can occur in 3 different ways : eeo , eoe , or oee ) ; so finally p = 1 / 8 + 3 / 8 = 1 / 2 . answer : c ." + }, + { + "Answer": 900, + "Options": "a ) 300 , b ) 600 , c ) 900 , d ) 800 , e ) 500", + "Correct": "c", + "Explanation": "\"let p ' s capital be p , q ' s capital be q , and r ' s capital be r then 4 p = 6 q = 10 r 2 p = 3 q = 5 r \u22ef ( a ) from ( a ) , q = 2 p / 3 \u22ef ( 1 ) r = 2 p / 5 \u22ef ( 2 ) p : q : r = p : 2 p / 3 : 2 p / 5 = 15 : 10 : 6 r ' s share = 4650 \u00d7 6 / 31 = 150 \u00d7 6 = 900 answer is c .\"" + }, + { + "Answer": 357, + "Options": "a ) $ 255 , b ) $ 357 , c ) $ 510 , d ) $ 1,250 , e ) $ 2,550", + "Correct": "b", + "Explanation": "\"total no . of boxes = 3060000 / ( 20 \u00d7 20 \u00d7 15 ) = 510 total cost = 510 \u00d7 $ 0.7 = $ 357 answer b\"" + }, + { + "Answer": 7, + "Options": "a ) 5 , b ) 7 , c ) 8 , d ) 10 , e ) 11", + "Correct": "b", + "Explanation": "\"y = 7 is the correct answer . good solution buneul . b\"" + }, + { + "Answer": 70, + "Options": "a ) 70 , b ) 86.5 , c ) 80 , d ) 88.5 , e ) 75", + "Correct": "a", + "Explanation": "\"total increase in weight = 5 \u00d7 4 = 20 if x is the weight of the new person , total increase in weight = x \u2212 50 = > 20 = x - 50 = > x = 20 + 50 = 70 answer : a\"" + }, + { + "Answer": 17, + "Options": "a ) 9 years , b ) 11 years , c ) 17 years , d ) 21 years , e ) 25 years", + "Correct": "c", + "Explanation": "\"solution age of the 15 th student = [ 15 x 15 - ( 14 x 8 + 16 x 6 ) ] = ( 225 - 208 ) = 17 years . answer c\"" + }, + { + "Answer": 130, + "Options": "a ) 55 , b ) 65 , c ) 100 , d ) 109 , e ) 129", + "Correct": "e", + "Explanation": "\"a + b + c + d = 200 a + b = 70 c + d = 130 greatest possible = 129 ( just less than 1 ) answer = e\"" + }, + { + "Answer": 16.000000000000004, + "Options": "a ) 16 % , b ) 18 % , c ) 20 % , d ) 22 % , e ) 24 %", + "Correct": "a", + "Explanation": "let x be the amount of money paid for the first purchase . the second time , the customer paid 0.7 ( 1.2 x ) = 0.84 x . the difference is 16 % . the answer is a ." + }, + { + "Answer": 5, + "Options": "a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8", + "Correct": "b", + "Explanation": "c = n ( n - 3 ) c = 2 * n 2 n = n ( n - 3 ) = > 2 = n - 3 = > n = 5 answer b" + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) 81 , c ) 77 , d ) 66 , e ) 73", + "Correct": "a", + "Explanation": "\"( a + b ) - ( b + c ) = 12 a - c = 12 answer : a\"" + }, + { + "Answer": 0.5, + "Options": "a ) 1 / 3 , b ) 2 / 5 , c ) 3 / 7 , d ) 1 / 2 , e ) 4 / 7", + "Correct": "d", + "Explanation": "the time from beginning of march to the end of september is 7 months . if x is the average monthly tip for all months other than august then his august month tip will be 6 * x his total tip for the 7 months = 6 * ( average tip for the months other than august ) + 6 x = 12 x august tips as a fraction of total tips = 6 x / 12 x = 1 / 2 . so d" + }, + { + "Answer": 8, + "Options": "a ) 0 , b ) 2 , c ) 4 , d ) 8 , e ) more than 8", + "Correct": "d", + "Explanation": "i think its 8 | | | n - 5 | - 10 | - 5 | = 2 let | n - 5 | = a which makes above | | a - 10 | - 5 | = 2 let | a - 10 | = b which makes | b - 5 | = 2 now for the above b can take 3 , 7 for every b = 3 a can have 13 , 7 and for b = 7 a can have 17 and 3 so ' a ' has four solutions 13 , 7 , 17 and 3 for a = 13 ; x has 18 or - 8 thus has 2 for every combination hence 4 x 2 = 8 answer d" + }, + { + "Answer": 54.32380952380952, + "Options": "a ) 56 , b ) 51 , c ) 59 , d ) 54 , e ) 52", + "Correct": "d", + "Explanation": "\"for 40 hrs = 40 * 15 = 600 excess = 976 - 600 = 376 for extra hours = . 75 ( 15 ) = 11.25 + 15 = 26.25 number of extra hrs = 376 / 26.25 = 14.3 = 14 approx . total hrs = 40 + 14 = 54 answer d\"" + }, + { + "Answer": 2, + "Options": "a ) 12 , b ) 17 , c ) 2 , d ) 77 , e ) 26", + "Correct": "c", + "Explanation": "\"answer : 2 option : c\"" + }, + { + "Answer": 4399, + "Options": "a ) a ) 3800 , b ) b ) 4200 , c ) c ) 4400 , d ) d ) 4500 , e ) e ) 4600", + "Correct": "c", + "Explanation": "\"x * ( 90 / 100 ) * ( 80 / 100 ) = 3168 x = 4400 answer : c\"" + }, + { + "Answer": 1770, + "Options": "a ) 190 , b ) 200 , c ) 210 , d ) 1770 , e ) 230", + "Correct": "d", + "Explanation": "\"1 st person will shake hand with 59 people 2 nd person will shake hand with 58 people 3 rd person will shake hand with 57 people . . . . . . total no . of handshakes = 59 + 58 + 57 + . . . + 3 + 2 + 1 = 19 * ( 19 + 1 ) / 2 = 1770 or , if there are n persons then no . of shakehands = nc 2 = 60 c 2 = 1770 answer : d\"" + }, + { + "Answer": 1.631999999999607, + "Options": "a ) s . 2.04 , b ) s . 2.08 , c ) s . 1.63 , d ) s . 2.83 , e ) s . 2.42", + "Correct": "c", + "Explanation": "\"c . i . when interest is compounded yearly = [ 4000 * ( 1 + 4 / 100 ) * ( 1 + ( 1 / 2 * 4 ) / 100 ] = 4000 * 26 / 25 * 51 / 50 = rs . 4243.2 c . i . when interest is compounded half - yearly = [ 4000 * ( 1 + 2 / 100 ) 2 ] = ( 4000 * 51 / 50 * 51 / 50 * 51 / 50 ) = rs . 4244.83 difference = ( 4244.83 - 4243.2 ) = rs . 1.63 . answer : c\"" + }, + { + "Answer": 0.6595061728395062, + "Options": "a ) 0.0066 % , b ) 0.066 % , c ) 0.66 % , d ) 6.6 % , e ) 66 %", + "Correct": "c", + "Explanation": "since 1 billion is 1000 million soc changing all quantities to million finland forest area = 53.42 million hect . worlds ' s forest area = 8.076 billion hect . % = 53.42 * 100 / 8.076 * 1000 = 0.66 % answer c" + }, + { + "Answer": 13, + "Options": "a ) 16 , b ) 12 , c ) 15 , d ) 20 , e ) 13", + "Correct": "e", + "Explanation": "\"( a + b ) - ( b - c ) = 13 a - c = 13 answer is e\"" + }, + { + "Answer": 44, + "Options": "a ) 30 , b ) 80 , c ) 44 , d ) 25 , e ) 26", + "Correct": "c", + "Explanation": "\"let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 . x / 2 = ( 67 - 45 ) = > x / 2 = 22 = > x = 44 . answer : c\"" + }, + { + "Answer": 843, + "Options": "a ) 837 , b ) 947 , c ) 1027 , d ) 1155 , e ) 1231", + "Correct": "a", + "Explanation": "\"factor each of the numbers 8 , 15 , 35 , and 40 into primes : 12 = 2 * 2 * 3 ; 15 = 3 * 5 ; 35 = 5 * 7 ; 40 = 2 * 2 * 2 * 5 the smallest number divisible by all of them is thus 2 * 2 * 2 * 3 * 5 * 7 = 840 837 + 3 = 840 a\"" + }, + { + "Answer": 7, + "Options": "a ) 5 , b ) 7 , c ) 8 , d ) 10 , e ) 11", + "Correct": "b", + "Explanation": "\"r = 7 is the correct answer . good solution buneul . b\"" + }, + { + "Answer": 3.333333333333333, + "Options": "a ) 1 / 4 , b ) 1 / 2 , c ) 10 / 3 , d ) 2 , e ) 4", + "Correct": "c", + "Explanation": "\"n = 2 d / 5 j = n / 2 = d / 5 the average of november and january is ( n + j ) / 2 = 3 d / 5 / 2 = 3 d / 10 d is 10 / 3 times the average of november and january . the answer is c .\"" + }, + { + "Answer": 25, + "Options": "a ) 23 , b ) 24 , c ) 25 , d ) 26 , e ) 27", + "Correct": "c", + "Explanation": "average age of people = 30 so have total age = 210 before 7 years we have to deduct each person age by seven years 210 - 35 = 161 so average age would be 175 / 7 = 25 answer : c" + }, + { + "Answer": 1000, + "Options": "a ) $ 900 , b ) $ 300 , c ) $ 600 , d ) $ 1000 , e ) $ 800", + "Correct": "d", + "Explanation": "\"if linda spent 3 / 5 of her savings on furnitute , the rest 5 / 5 - 3 / 5 = 2 / 5 on a tv but the tv cost her $ 400 . so 2 / 5 of her savings is $ 400 . so her original savings are 5 / 2 times $ 400 = $ 2000 / 2 = $ 1000 correct answer d\"" + }, + { + "Answer": 782, + "Options": "a ) s . 440 , b ) s . 500 , c ) s . 540 , d ) s . 782 , e ) s . 840", + "Correct": "d", + "Explanation": "\"s . i for 5 years = ( 1020 - 850 ) = rs . 170 . s . i . for 2 years = 170 / 5 * 2 = rs . 68 . principal = ( 850 - 68 ) = rs . 782 . answer : d\"" + }, + { + "Answer": 176.22471910112358, + "Options": "a ) 743 , b ) 154 , c ) 852 , d ) 176 , e ) 785", + "Correct": "d", + "Explanation": "\"divisor * quotient + remainder = dividend divisor = ( dividend ) - ( remainder ) / quotient ( 15698 - 14 ) / 89 = 176 answer ( d )\"" + }, + { + "Answer": 1.9832, + "Options": "a ) 1.9832 , b ) 1.0025 , c ) 1.5693 , d ) 1.0266 , e ) none", + "Correct": "a", + "Explanation": "solution sum of decimals places = ( 2 + 2 ) = 4 . therefore , = 2.68 \u00d7 . 74 = 1.9832 answer a" + }, + { + "Answer": 1550, + "Options": "a ) 1750 , b ) 2789 , c ) 2500 , d ) 1550 , e ) 2000", + "Correct": "d", + "Explanation": "total production of salt by the company in that year = 1000 + 1100 + 1200 + . . . . + 2100 = 18600 . average monthly production of salt for that year = 18600 / 12 = 1550 . answer : d" + }, + { + "Answer": 59, + "Options": "a ) 58 , b ) 59 , c ) 68 , d ) 69 , e ) 78", + "Correct": "b", + "Explanation": "\"10 x + 69 = 11 ( x + 1 ) x = 58 + 1 = 59 answer : b\"" + }, + { + "Answer": 9, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 12", + "Correct": "c", + "Explanation": "\"27 ^ b > 3 ^ 24 converting into the same bases : 27 ^ b > 27 ^ 8 therefore for the equation to hold true , b > 8 or b = 9 option c\"" + }, + { + "Answer": 8, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8", + "Correct": "e", + "Explanation": "\"9 ^ y = 3 ^ 2 y = 3 ^ 16 2 y = 16 y = 8 the answer is e .\"" + }, + { + "Answer": 21, + "Options": "a ) 6 , b ) 9 , c ) 16 , d ) 4 , e ) 21", + "Correct": "e", + "Explanation": "3 x + 5 x + 7 x = 45 x = 3 7 x = 21 answer : e" + }, + { + "Answer": 137, + "Options": "a ) 120 kg , b ) 130 kg , c ) 137 kg , d ) 190 kg , e ) none", + "Correct": "c", + "Explanation": "\"solution total weight increased = ( 10 x 7.2 ) kg = 72 kg . weight of new person = ( 65 + 72 ) kg = 137 kg . answer c\"" + }, + { + "Answer": 195, + "Options": "a ) 115 , b ) 116 , c ) 195 , d ) 118 , e ) 119", + "Correct": "c", + "Explanation": "\"x : y : z = 100 : 45 : 50 20 : 9 : 10 9 - - - 45 39 - - - ? = > 195 answer : c\"" + }, + { + "Answer": 20, + "Options": "a ) 20 , b ) 15 , c ) 25 , d ) 13 , e ) 42", + "Correct": "a", + "Explanation": "\"x + y = 4 x - y = 36 2 x = 40 x = 20 answer is a\"" + }, + { + "Answer": 48, + "Options": "a ) 36 , b ) 40 , c ) 44 , d ) 48 , e ) 52", + "Correct": "d", + "Explanation": "\"for 40 hrs = 40 * 16 = 640 excess = 864 - 640 = 224 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 224 / 28 = 56 / 7 = 8 total hrs = 40 + 8 = 48 answer d 48\"" + }, + { + "Answer": 50, + "Options": "a ) 50 , b ) 100 , c ) 150 , d ) 200 , e ) 250", + "Correct": "a", + "Explanation": "\"14 % is 4 % - points higher than 10 % but 16 % - points lower than 30 % . thus there should be 4 parts of solution x for 1 part of solution y . we should add 50 ml of solution y . the answer is a .\"" + }, + { + "Answer": 1.2, + "Options": "a ) 0.75 , b ) 1.2 , c ) 1.8 , d ) 2.4 , e ) 4.25", + "Correct": "b", + "Explanation": "\"say the cost price of 80 pencils was $ 80 ( $ 1 per pencil ) and the selling price of 1 pencil was p . selling at a loss : 80 - 80 p = 16 p - - > p = 5 / 6 . ( cost price ) / ( selling price ) = 1 / ( 5 / 6 ) = 6 / 5 = 1.2 . answer : b .\"" + }, + { + "Answer": 20, + "Options": "a ) 20 % decrease , b ) 10 % increase , c ) 10 % decrease , d ) 15 % increase , e ) 25 % decrease", + "Correct": "a", + "Explanation": "\"let the original price be $ 100 new final price = 160 % of ( 50 % of $ 100 ) = 160 / 100 * 50 / 100 * 100 = $ 80 decrease is 20 % answer is a\"" + }, + { + "Answer": 4, + "Options": "a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10", + "Correct": "b", + "Explanation": "1 . divide both sides by 7 : 2 . simplify both sides : x - 1 = 3 3 . add 1 to both sides : x - 1 + 1 = 3 + 1 4 . simplify both sides : x = 4 b" + }, + { + "Answer": 105, + "Options": "a ) 388 , b ) 105 , c ) 288 , d ) 266 , e ) 281", + "Correct": "b", + "Explanation": "x : y : z = 100 : 45 : 30 20 : 9 : 6 9 - - - 27 35 - - - ? = > 105 answer : b" + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 8 , c ) 10 , d ) 12 , e ) 15", + "Correct": "a", + "Explanation": "\"a = 2 m = m + 10 m = 10 a = 20 a = 4 b , and so b = 5 the answer is a .\"" + }, + { + "Answer": 57.5, + "Options": "a ) 56.5 rupees , b ) 58.5 rupees , c ) 57.5 rupees , d ) 59.5 rupees , e ) 55.5 rupees", + "Correct": "c", + "Explanation": "the total days worked = 1 + 0.333 + 0.667 + 0.125 + 0.75 = 2.875 days amount for 2.875 days is ( 2.875 * 20 ) 57.5 rupees answer : c" + }, + { + "Answer": 5, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "d", + "Explanation": "solution let the number be x . = then , 7 x - 15 = 2 x + 10 = 5 x = 25 \u2039 = \u203a x = 5 . hence the required number is 5 . answer d" + }, + { + "Answer": 3.75, + "Options": "a ) $ 2.75 , b ) $ 3.25 , c ) $ 3.75 , d ) $ 4.25 , e ) $ 4.75", + "Correct": "c", + "Explanation": "\"let x be the value of the weekly allowance . ( 2 / 3 ) ( 2 / 5 ) x = 100 cents ( 4 / 15 ) x = 100 x = $ 3.75 the answer is c .\"" + }, + { + "Answer": 4, + "Options": "a ) 1 / 2 , b ) 2 , c ) 5 / 2 , d ) 4 , e ) 5", + "Correct": "d", + "Explanation": "if e < 2 , then 2 - e = 5 / 2 ; e = - 1 / 2 if e > 2 , then e - 2 = 5 / 2 ; e = 9 / 2 9 / 2 - 1 / 2 = 8 / 2 = 4 = d" + }, + { + "Answer": 113, + "Options": "a ) 131 , b ) 135 , c ) 113 , d ) 147 , e ) 188", + "Correct": "c", + "Explanation": "\"j = jake \u2019 s current weight , in pounds s = sister \u2019 s current weight , in pounds we are told that \u201c if jake loses 8 pounds , he will weigh twice as much as his sister . we put this into an equation : j \u2013 33 = 2 s j = 2 s + 33 ( equation 1 ) next , we are told that \u201c together they now weigh 153 pounds . \u201d we can also put this into an equation . j + s = 153 ( equation 2 ) to solve this equation , we can substitute 2 s + 8 from equation 1 for the variable j in equation 2 : 2 s + 33 = 153 - s 3 s = 120 s = 40 j + 40 = 153 j = 113 answer : c\"" + }, + { + "Answer": 246, + "Options": "a ) 288 , b ) 262 , c ) 246 , d ) 205 , e ) 267", + "Correct": "c", + "Explanation": "\"a : b : c = 100 : 65 : 40 = 20 : 13 : 8 8 - - - - 48 41 - - - - ? = > rs . 246 answer : c\"" + }, + { + "Answer": 18, + "Options": "a ) rs . 17 , b ) rs . 18 , c ) rs . 12 , d ) rs . 11 , e ) rs . 10", + "Correct": "b", + "Explanation": "\"average price per book = ( 1150 + 920 ) / ( 65 + 50 ) = 2070 / 115 = rs . 18 answer : b\"" + }, + { + "Answer": 300, + "Options": "a ) 300 , b ) 350 , c ) 400 , d ) 425 , e ) 275", + "Correct": "a", + "Explanation": "explanation : average price of a hen = rs . 30 total price of 10 hens = 10 * 30 = rs . 300 but total price of 3 pigs and 10 hens = rs . 1200 total price of 3 pigs is = 1200 - 300 = 900 average price of a pig = 900 / 3 = rs . 300 answer : a" + }, + { + "Answer": 3900, + "Options": "a ) 4038 , b ) 8076 , c ) 9691.2 , d ) 4845.6 , e ) 3900", + "Correct": "e", + "Explanation": "\"\u2235 amount , he have spent in 1 month on clothes transport = amount spent on saving per month \u2235 amount , spent on clothes and transport = 46800 \u2044 12 = 3900 answer e\"" + }, + { + "Answer": 9, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10", + "Correct": "d", + "Explanation": "\"x < y < z to find the least possible value for z - x ; we need to find the values for z and x that can be closest to each other . if x is some even number , then what could be minimum possible odd z . if x is some even number y - x > 5 ; y > x + 5 ; minimum value for y = x + 5 + 2 = x + 7 [ note : x + 5 is as even + odd = odd and nearest odd greater than x + 5 is x + 5 + 2 ] minimum value for z = y + 2 = x + 7 + 2 = x + 9 [ note : z = y + 2 because both z and y are odd . difference between two odd numbers is 2 ] s = z - x = x + 9 - x = 9 ans : d\"" + }, + { + "Answer": 0.08, + "Options": "a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 10 , d ) 2 / 25 , e ) 1 / 20", + "Correct": "d", + "Explanation": "5 % is 5 / 100 = 1 / 20 10 % is 10 / 100 = 1 / 10 the increase must be greater than 1 / 20 and less than 1 / 10 . 1 / 4 , 1 / 5 , and 1 / 10 are not less than 1 / 10 . 1 / 20 is not greater than 1 / 20 . the only option left is 2 / 25 , which is in the specified range . answer : d" + }, + { + "Answer": 76, + "Options": "a ) 79 , b ) 99 , c ) 88 , d ) 88 , e ) 76", + "Correct": "e", + "Explanation": "\"average = ( 73 + 69 + 92 + 64 + 82 ) / 5 = 380 / 5 = 76 answer : e\"" + }, + { + "Answer": 19, + "Options": "a ) 19 , b ) 88 , c ) 267 , d ) 26 , e ) 28", + "Correct": "a", + "Explanation": "explanation : let the first part be x . 8 x + 3 ( 36 \u2013 x ) = 203 8 x + 108 \u2013 3 x = 203 5 x + 108 = 203 5 x = 95 x = 19 answer : a" + }, + { + "Answer": 192, + "Options": "a ) 160 , b ) 168 , c ) 176 , d ) 184 , e ) 192", + "Correct": "e", + "Explanation": "\"r = j + 8 = k + 4 r + 2 = 2 ( j + 2 ) ( j + 8 ) + 2 = 2 j + 4 j = 6 r = 14 k = 10 in 2 years ( r + 2 ) ( k + 2 ) = 16 * 12 = 192 the answer is e .\"" + }, + { + "Answer": 11.5, + "Options": "a ) 10.5 , b ) 11 , c ) 11.5 , d ) 12 , e ) 12.5", + "Correct": "c", + "Explanation": "\"the value which isexactlytwo sd less than the mean is : mean - 2 * sd = 14.5 - 2 * 1.5 = 11.5 . answer : c .\"" + }, + { + "Answer": 25, + "Options": "a ) 20 years , b ) 22 years , c ) 24 years , d ) 25 years , e ) 27 years", + "Correct": "d", + "Explanation": "\"age of the 15 th student = [ 15 * 15 - ( 14 * 4 + 16 * 9 ) ] = ( 225 - 200 ) = 25 years . answer : d\"" + }, + { + "Answer": 49.6, + "Options": "a ) a ) 47 , b ) b ) 45.6 , c ) c ) 44 , d ) d ) 48 , e ) e ) 49.6", + "Correct": "e", + "Explanation": "\"explanation : total marks obtained by a class of 25 students = 5 * 95 + 3 * 0 + 17 * 45 = 1240 average marks of whole class = 1240 / 25 = 49.6 answer : option e\"" + }, + { + "Answer": 15.96, + "Options": "a ) 12 , b ) 13 , c ) 16 , d ) 15 , e ) 11", + "Correct": "c", + "Explanation": "\"multiples of 25 = 25 , 50,75 , - - - - - 400 number of multiples of 25 = > 25 * 16 = 400 answer is c\"" + }, + { + "Answer": 13, + "Options": "a ) 0 , b ) 2 , c ) 12 , d ) 13 , e ) 15", + "Correct": "d", + "Explanation": "the range w of a set is the difference between the largest and smallest elements of a set . without x , the difference between the largest and smallest elements of a set is 14 - 3 = 11 < 12 , which means that in order 12 to be the range of the set x must be either the smallest element so that 14 - x = 12 - - - > x = 2 or x must the largest element so that x - 3 = 12 - - > x = 15 . the the difference between the greatest possible value of x and least possible value of x is 15 - 2 = 13 . answer : d ." + }, + { + "Answer": 5, + "Options": "a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3", + "Correct": "c", + "Explanation": "\"x is an integer and 2.134 \u00d7 10 x is less than 220,000 , what is the greatest possible value for x ? for 2.134 \u00d7 10 x is less than 220,000 to remain true , the greatest number is 213,400 , which makes x = 5 c . 5\"" + }, + { + "Answer": 4691100843, + "Options": "a ) 4586970843 , b ) 4686970743 , c ) 4691100843 , d ) 4586870843 , e ) none", + "Correct": "c", + "Explanation": "\"answer 469157 x 9999 = 469157 x ( 10000 - 1 ) = 4691570000 - 469157 = 4691100843 . option : c\"" + }, + { + "Answer": 4320, + "Options": "a ) 516 , b ) 3096 , c ) 6192 , d ) 628 , e ) 4320", + "Correct": "e", + "Explanation": "number of mangoes = 12 dozens = 12 \u00d7 10 = 120 \u2234 number of mangoes in 36 boxes = 36 \u00d7 120 = 4320 answer e" + }, + { + "Answer": 100, + "Options": "a ) 196 , b ) 94 , c ) 90 , d ) 100 , e ) 120", + "Correct": "d", + "Explanation": "two numbers must be 16 and 17 16 + 17 = 33 required number is 17 six times of this number = 6 * 17 = 102 two less than 102 = 102 - 2 = 100 answer : d" + }, + { + "Answer": 9, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 12", + "Correct": "c", + "Explanation": "\"27 ^ x > 3 ^ 24 converting into the same bases : 27 ^ x > 27 ^ 8 therefore for the equation to hold true , x > 8 or x = 9 option c\"" + }, + { + "Answer": 0.5599999999999999, + "Options": "a ) 0.56 , b ) 0.62 , c ) 0.5 , d ) 0.48 , e ) 0.52", + "Correct": "a", + "Explanation": "0.56 option ' a '" + }, + { + "Answer": 806006795, + "Options": "a ) 807518799 , b ) 806436469 , c ) 807538799 , d ) 806329359 , e ) 817431046", + "Correct": "d", + "Explanation": "\"80641 x 9999 = 80641 x ( 10000 - 1 ) = 80641 x 10000 - 80641 x 1 = 806410000 - 80641 = 806329359 d\"" + }, + { + "Answer": 47.95000000000027, + "Options": "a ) 47.095 , b ) 47.752 , c ) 47.932 , d ) 47.95 , e ) none", + "Correct": "d", + "Explanation": "explanation let 3889 + 12.952 \u2013 x = 3854.002 . then x = ( 3889 + 12.952 ) \u2013 3854.002 = 3901.952 \u2013 3854.002 = 47.95 . answer d" + }, + { + "Answer": 38, + "Options": "a ) 35.29 kg , b ) 37.25 kg , c ) 42 kg , d ) 38 kg , e ) 29.78 kg", + "Correct": "d", + "Explanation": "\"total weight of 36 + 44 students = 24 * 40 + 16 * 35 = 1520 average weight of the class is = 1520 / 40 = 38 kg answer is d\"" + }, + { + "Answer": 5.999999999999999, + "Options": "a ) 6 , b ) 5 , c ) 4 , d ) 3 , e ) 2", + "Correct": "a", + "Explanation": "add the left terms and right terms of the two equation to obtain a new equation x + 5 x + 4 y + 6 y = 5 + 7 group and simplify 6 x + 10 y = 12 divide all terms of the above equation by 2 to obtain a new equation 3 x + 5 y = 6 correct answer a" + }, + { + "Answer": 19.000000000000004, + "Options": "a ) 19 , b ) 25 , c ) 35 , d ) 45 , e ) 75", + "Correct": "a", + "Explanation": "out of 300 - 180 purchased for less than 100 $ 120 for more out of 300 - 120 responded as satisfied and 180 responded disatisfied out of 180 ( purchased less than 100 $ ) - 35 % = 63 responded as satisfied , so remaining satisfied are 120 - 63 = 57 so 57 is what percentage of 300 - 19 % so the answer should be a" + }, + { + "Answer": 128, + "Options": "a ) 176 kg , b ) 80 kg , c ) 185 kg , d ) 90 kg , e ) 128 kg", + "Correct": "e", + "Explanation": "\"solution total weight increased = ( 10 x 6.3 ) kg = 63 kg . weight of new person = ( 65 + 63 ) kg = 128 kg . answer e\"" + }, + { + "Answer": 58, + "Options": "a ) 50 , b ) 56 , c ) 58 , d ) 62 , e ) 66", + "Correct": "c", + "Explanation": "\"given that , total average t sold is 66 , male / female = 1 / 2 and female average is 70 . average of male members isx . ( 70 * f + x * m ) / ( m + f ) = 66 - > solving this equation after substituting 2 m = f , x = 58 . ans c .\"" + }, + { + "Answer": 2, + "Options": "a ) 6 , b ) 1 , c ) 4 , d ) 3 , e ) 2", + "Correct": "e", + "Explanation": "a number is divisible by 3 if the sum of the digits is divisible by 3 . . here , 6 + 2 + 5 + 5 + 7 + 3 = 28 , the next multiple of 3 is 30 . 2 must be added to 625574 to make it divisible by 3 e" + }, + { + "Answer": 11, + "Options": "a ) 9 , b ) 8 , c ) 5 , d ) 11 , e ) 15", + "Correct": "d", + "Explanation": "\"on dividing 2000 by 17 , we get 11 as remainder . required number to be subtracted = 11 answer d\"" + }, + { + "Answer": 35, + "Options": "a ) $ 21 , b ) $ 35 , c ) $ 31 , d ) $ 41 , e ) it can not be determined", + "Correct": "b", + "Explanation": "\"let ' s suppose that the price of a burger is bb , of a shake - ss and that of a cola is cc . we can then construct these equations : 3 b + 7 s + c = 120 4 b + 10 s + c = 162.5 subtracting the first equation from the second gives us b + 3 s = 42.5 now if we subtract the new equation two times from first or 3 times from second we will get b + s + c = 35 . in any case , there is no necessity to know each item ' s price , just the sum . answer : b\"" + }, + { + "Answer": 11, + "Options": "a ) - 11 , b ) \u2013 12 , c ) 11 , d ) 12 , e ) 10", + "Correct": "c", + "Explanation": "solution : ( 4 + 3 ) + ( 8 - 3 - 1 ) = 7 + ( 8 - 3 - 1 ) = 7 + 8 - 3 - 1 = 15 - 1 = 11 answer : ( c )" + }, + { + "Answer": 90000, + "Options": "a ) 100 , b ) 610 , c ) 729 , d ) 900 , e ) 90000", + "Correct": "e", + "Explanation": "take the task of building palindromes and break it intostages . stage 1 : select the 9 th digit we can choose 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 1 in 9 ways stage 2 : select the 8 th , 7 th , 6 th , 5 th digit we can choose 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 2 in 10 ways important : at this point , the remaining digits are alreadylocked in . stage 3 : select the 4 th , 3 rd , 2 nd , 1 st digit so , we can complete this stage in 1 way . by thefundamental counting principle ( fcp ) , we can complete all 5 stages ( and thus build a 9 - digit palindrome ) in ( 9 ) ( 10 ) ( 10 ) ( 10 ) ( 10 ) ( 1 ) ( 1 ) ( 1 ) ( 1 ) ways ( = 90000 ways ) answer : e" + }, + { + "Answer": 610, + "Options": "a ) 600 , b ) 610 , c ) 500 , d ) 520 , e ) 720", + "Correct": "b", + "Explanation": "\"let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 305 ) = 2 + 2 ( extra ) = > 2 x - 610 = x = > x = 610 . answer : b\"" + }, + { + "Answer": 20, + "Options": "a ) 25 , b ) 30 , c ) 10 , d ) 15 , e ) 20", + "Correct": "e", + "Explanation": "the ratio of shadow to height is constant , so if x is the length of the shadow , then 20 / 10 = 40 / x and x = 20 . correct answer e" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 0 , c ) - 1 , d ) 2 , e ) 4", + "Correct": "a", + "Explanation": "\"since f ( n ) = f ( n - 1 ) - n then : f ( 6 ) = f ( 5 ) - 6 and f ( 5 ) = f ( 4 ) - 5 . as given that f ( 4 ) = 12 then f ( 5 ) = 12 - 5 = 7 - - > substitute the value of f ( 5 ) back into the first equation : f ( 6 ) = f ( 5 ) - 6 = 7 - 6 = 1 . answer : a . questions on funtions to practice :\"" + }, + { + "Answer": 318, + "Options": "a ) $ 318 , b ) $ 289 , c ) $ 282 , d ) $ 274 , e ) $ 286", + "Correct": "a", + "Explanation": "total number of days of stay = 23 charge of staying in first week = 18 * 7 = 126 $ charge of staying for additional days = ( 23 - 7 ) * 12 = 16 * 12 = 192 $ total charge = 126 + 192 = 318 $ answer a" + }, + { + "Answer": 2.25, + "Options": "a ) 4.5 , b ) 5 , c ) 2.25 , d ) 5.7 , e ) 6.5", + "Correct": "c", + "Explanation": "\"if $ x $ is the number , x / 3 * 12 = 9 = > 4 x = 9 = > x = 2.25 c\"" + }, + { + "Answer": 25.999999999999996, + "Options": "a ) 24 , b ) 26 , c ) 25 , d ) 27 , e ) 28", + "Correct": "b", + "Explanation": "for amy ' s deal to be better , the cost has to be less or equal to lucia ' s assuming ' n ' is the number of pounds of kale , the equation is 20 x + ( n - 20 ) ( 0.8 x ) < = 14 x + ( n - 14 ) ( 0.9 x ) resolve it : = = > 20 x + 0.8 nx - 16 x < = 14 x + 0.9 nx - 12.6 x = = > 2.6 x < = 0.1 nx = = > 26 x < = nx = = > x ( n - 26 ) > = 0 as x can not be 0 , = = > n - 26 > = 0 = = > n > = 26 so the minimum value is 26 ' b ' would be the correct answer" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "c", + "Explanation": "\"( 1 ) x = 11 y + 4 ( 2 ) 2 x = 18 y + 1 let ' s subtract equation ( 1 ) from equation ( 2 ) . 7 y - 3 = x 7 y - x = 3 the answer is c .\"" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "c", + "Explanation": "140800 = 1 * 5 ^ 2 * 8 ^ 3 * 11 the factors of 8 must come from the purple point value , so there are 3 purple chips . the answer is c ." + }, + { + "Answer": 699.9999999999999, + "Options": "a ) 400 , b ) 500 , c ) 700 , d ) none of these , e ) 506", + "Correct": "c", + "Explanation": "\"explanation : 49 / . 07 = 4900 / 7 = 700 option c\"" + }, + { + "Answer": 10000, + "Options": "a ) 10 , b ) 100 , c ) 1000 , d ) 10000 , e ) none of these", + "Correct": "d", + "Explanation": "explanation : = ( 103 ) 7 / ( 10 ) 17 = ( 10 ) 21 / ( 10 ) 17 = 10 ( 4 ) = 10000 option d" + }, + { + "Answer": 13.333333333333334, + "Options": "a ) 11 liters , b ) 11.2 liters , c ) 12.5 liters , d ) 13.78 liters , e ) 13.33 liters", + "Correct": "e", + "Explanation": "\"number of liters of water in 200 liters of the mixture = 20 % of 120 = 20 / 100 * 200 = 40 liters . p liters of water added to the mixture to make water 25 % of the new mixture . total amount of water becomes ( 40 + p ) and total volume of mixture is ( 200 + p ) . ( 40 + p ) = 25 / 100 * ( 200 + p ) 160 + 4 p = 200 + p p = 13.33 liters . answer : e\"" + }, + { + "Answer": 3.4, + "Options": "a ) 3.4 , b ) 4.5 , c ) 6.2 , d ) 5.7 , e ) 6.9", + "Correct": "a", + "Explanation": "let the numbers be a , b , c , d , e , f so , total of these 5 numbers must be 25 or , a + b + c + d + e = 25 so , 12 must be subtracted from the total sum i . e a + b + c + d + e - 8 or , 25 - 8 = 17 hence average of the 5 numbers now is 17 / 5 = > 3.4 so , answer will be a" + }, + { + "Answer": 1840, + "Options": "a ) 1840 , b ) 1700 , c ) 2350 , d ) 2500 , e ) 8000", + "Correct": "a", + "Explanation": "\"16 pounds and 4 ounces = 16 * 16 + 4 = 260 ounces . 13 tons = 13 * 2300 pound = 13 * 2300 * 16 ounces . hence the answer is ( 13 * 2300 * 16 ) / 260 = 1840 . answer : a .\"" + }, + { + "Answer": 24.265, + "Options": "a ) $ 30.14 , b ) 45.14 , c ) 34.66 , d ) 32.29 , e ) 24.26", + "Correct": "e", + "Explanation": "211 * 15 = 3165 / 100 = 31.65 211 + 31.65 = 242.65 242.65 / 10 = 24.26 answer : e" + }, + { + "Answer": 660, + "Options": "a ) 237 , b ) 287 , c ) 197 , d ) 660 , e ) 720", + "Correct": "d", + "Explanation": "\"explanation : let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 330 ) = 2 + 2 ( extra ) = > 2 x - 660 = x = > x = 660 . answer : d\"" + }, + { + "Answer": 18, + "Options": "a ) 4 , b ) 18 , c ) 15 , d ) 20 , e ) 24", + "Correct": "b", + "Explanation": "you could set - up a quick table and brute force the answer . a 4 * 50 200 1800 - 200 1600 26 61.54 b 18 * 50 600 1800 - 900 0900 12 75.00 c 15 * 50 750 1800 - 750 1050 15 70.00 d 20 * 50 1000 1800 - 1000 800 10 80.00 e 24 * 50 1200 1800 - 1200 600 6 100.00 answer is b" + }, + { + "Answer": 3, + "Options": "a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3", + "Correct": "e", + "Explanation": "\"if x = 4 2.134 \u00d7 10 ^ 4 = 21340 > 21000 so , x = 3 answer : e\"" + }, + { + "Answer": 25.116279069767444, + "Options": "a ) 72 min , b ) 25.11628 min , c ) 70 min , d ) 74.11682 min , e ) 76 min", + "Correct": "b", + "Explanation": "\"x = time for type b prolems 2 x = time for type a problem total time = 3 hrs = 180 min 185 x + 15 * 2 x = 180 x = 180 / 215 x = 0.837209 time taken for type a problem = 15 * 2 * 0.837209 = 25.11628 min answer : b\"" + }, + { + "Answer": 20, + "Options": "a ) 25 % , b ) 22.2 % , c ) 20 % , d ) 12.5 % , e ) 11.1 %", + "Correct": "c", + "Explanation": "\"let ' s see , the way i did it was 1 / 3 are clerical out of 3600 so 1200 are clerical 1200 reduced by 1 / 2 is 1200 * 1 / 2 so it reduced 600 people , so there is 600 clerical people left but since 600 people left , it also reduced from the total of 3600 so there are 3000 people total since 600 clerical left / 3000 people total you get ( c ) 20 %\"" + }, + { + "Answer": 7, + "Options": "a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 7", + "Correct": "e", + "Explanation": "j = 3 s after 9 years j + 9 = 2 ( s + 9 ) j = 2 s + 9 2 s + 9 = 3 s s = 9 two years ago s = 9 - 2 = 7 e is the answer" + }, + { + "Answer": 49, + "Options": "a ) 7 , b ) 14 , c ) 49 , d ) 21 , e ) none of these", + "Correct": "c", + "Explanation": "\"explanation \u221a ( 49 ) 2 = ? or , ? = 49 answer c\"" + }, + { + "Answer": 5.333333333333333, + "Options": "a ) 2 / 3 , b ) 7 / 3 , c ) 5 / 2 , d ) 8 / 3 , e ) 16 / 3", + "Correct": "e", + "Explanation": "let x be the # of cups going into the 8 cup bottle . so . . . . x / 8 = ( ( 8 - x ) / 4 ) 64 - 8 x = 4 x 64 = 12 x x = 16 / 3 . answer : e" + }, + { + "Answer": 17, + "Options": "a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17", + "Correct": "e", + "Explanation": "\"14 n + 32 = 15 ( n + 1 ) n = 17 the answer is e .\"" + }, + { + "Answer": 130, + "Options": "a ) a ) 110 , b ) b ) 122 , c ) c ) 120 , d ) d ) 125 , e ) e ) 130", + "Correct": "e", + "Explanation": "\"explanation : average of new numbers = 26 * 5 = 130 answer : option e\"" + }, + { + "Answer": 22, + "Options": "a ) 22 , b ) 48 , c ) 45 , d ) 72 , e ) 18", + "Correct": "a", + "Explanation": "\"ages of p and mi = 3 x : 5 x ages of mi and mo = 3 x : 4 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 20 x sum = 44 x = 88 x = 2 difference if ages of pa and mo = 20 x - 9 x = 11 x = 11 * 2 = 22 answer a\"" + }, + { + "Answer": 0.12499999999999997, + "Options": "a ) 1 / 4 , b ) 3 / 8 , c ) 9 / 16 , d ) 1 / 8 , e ) 16 / 9", + "Correct": "d", + "Explanation": "3 / 7 * 7 / 8 * 1 / 3 = 1 / 8 answer : d" + }, + { + "Answer": 8200, + "Options": "a ) 8400 , b ) 8200 , c ) 6000 , d ) 5000 , e ) 4000", + "Correct": "b", + "Explanation": "\"state a and state b had an equal number of candidates appeared . in state a , 6 % candidates got selected from the total appeared candidates in state b , 7 % candidates got selected from the total appeared candidates but in state b , 82 more candidates got selected than state a from these , it is clear that 1 % of the total appeared candidates in state b = 82 = > total appeared candidates in state b = 82 x 100 = 8200 = > total appeared candidates in state a = total appeared candidates in state b = 8200\"" + }, + { + "Answer": 34, + "Options": "a ) 28 sec , b ) 16 sec , c ) 34 sec , d ) 18 sec , e ) 17 sec", + "Correct": "c", + "Explanation": "\"speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 240 + 100 = 340 m . time taken = 340 / 10 = 34 sec . answer : c\"" + }, + { + "Answer": 2834, + "Options": "a ) 1888 , b ) 2999 , c ) 2834 , d ) 2777 , e ) 2991", + "Correct": "c", + "Explanation": "\"let the total number of votes polled in the election be 100 k . number of valid votes = 100 k - 20 % ( 100 k ) = 80 k let the number of votes polled in favour of a and b be a and b respectively . a - b = 15 % ( 100 k ) = > a = b + 15 k = > a + b = b + 15 k + b now , 2 b + 15 k = 80 k and hence b = 32.5 k it is given that 100 k = 8720 32.5 k = 32.5 k / 100 k * 8720 = 2834 the number of valid votes polled in favour of b is 2834 . answer : c\"" + }, + { + "Answer": 470, + "Options": "a ) 0.47 , b ) 47 , c ) 470 , d ) 4700 , e ) none", + "Correct": "c", + "Explanation": "\"solution given expression = 4.7 \u00d7 ( 13.26 + 9.43 + 77.31 ) = 4.7 \u00d7 100 = 470 . answer c\"" + }, + { + "Answer": 815, + "Options": "a ) s . 800 , b ) s . 810 , c ) s . 815 , d ) s . 900 , e ) s . 920", + "Correct": "c", + "Explanation": "\"2445 * 1 / 3 = 815 option c\"" + }, + { + "Answer": 21.11111111111111, + "Options": "a ) 120 / 9 , b ) 140 / 9 , c ) 150 / 9 , d ) 190 / 9 , e ) 170 / 9", + "Correct": "d", + "Explanation": "let the total number of workers be y . so sum of salary for all workers = sum of salary of 10 technician + sum of salary for other y - 10 workers . 10 x 1200 + 820 ( y - 10 ) = 1000 y \u21d2 12000 + 820 y - 8200 = 1000 y \u21d2 180 y = 3800 \u2234 y = 190 / 9 so total number of workers = 190 / 9 d" + }, + { + "Answer": 40, + "Options": "a ) 91 , b ) 40 , c ) 80 , d ) 90 , e ) none of these", + "Correct": "b", + "Explanation": "\"solution required number of student = h . c . f of 1080 and 920 = 40 . answer b\"" + }, + { + "Answer": 6, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9", + "Correct": "b", + "Explanation": "as , 4 ^ 3 / 3 = 64 / 3 remainder = 1 and also 4 / 3 = 1 and 5 ^ 3 / 3 remainder = 2 and also 5 / 3 = 2 so it does not matter on the power value so the answer will be 76 / 7 remainder = 6 answer : b" + }, + { + "Answer": 380, + "Options": "a ) 380 , b ) 470 , c ) 560 , d ) 650 , e ) 740", + "Correct": "a", + "Explanation": "\"2 * 20 c 2 = 2 * 190 = 380 the answer is a .\"" + }, + { + "Answer": 1999.6764705882354, + "Options": "a ) 2010 , b ) 2011 , c ) 2012 , d ) 2013 , e ) 2014", + "Correct": "a", + "Explanation": "\"the price of commodity x increases 25 cents each year relative to commodity y . the price difference is $ 2.10 and commodity x needs to be 15 cents more than commodity y . $ 2.25 / 25 cents = 9 years the answer is 2001 + 9 years = 2010 . the answer is a .\"" + }, + { + "Answer": 60, + "Options": "a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60", + "Correct": "e", + "Explanation": "from the question stem we know that we need a mixture of 100 pounds of peanuts and cashews . if we represent peanuts as x and cashews as y , we get x + y = 100 . since the wholesaler wants to sell the mixture of 100 pounds @ $ 2.50 , we can write this as : $ 2.5 * ( x + y ) = $ 1.5 x + $ 4 y from the equation x + y = 100 , we can rewrite y as y = 100 - x and substitute this into our equation to get : $ 2.5 * ( x + 100 - x ) = $ 1.5 x + $ 4 ( 100 - x ) if you solve for x , you will get x = 60 , and therefore y = 40 . so the wholesaler must use 40 pounds of cashews . you can substitute into the original equation to see that : $ 250 = $ 1.5 ( 60 ) + $ 4 ( 40 ) answer is e" + }, + { + "Answer": 8300, + "Options": "a ) 7000 , b ) 8300 , c ) 6000 , d ) 5000 , e ) 4000", + "Correct": "b", + "Explanation": "\"state a and state b had an equal number of candidates appeared . in state a , 6 % candidates got selected from the total appeared candidates in state b , 7 % candidates got selected from the total appeared candidates but in state b , 83 more candidates got selected than state a from these , it is clear that 1 % of the total appeared candidates in state b = 83 = > total appeared candidates in state b = 83 x 100 = 8300 = > total appeared candidates in state a = total appeared candidates in state b = 8300\"" + }, + { + "Answer": 16, + "Options": "a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16", + "Correct": "e", + "Explanation": "\"we know that : x > 1 , y > 1 , and x + 3 y < 902 , and it is given that length means no of factors . for any value of x and y , the max no of factors can be obtained only if factor is smallest no all factors are equal . hence , lets start with smallest no 2 . 2 ^ 1 = 2 2 ^ 2 = 4 2 ^ 3 = 8 2 ^ 4 = 16 2 ^ 5 = 32 2 ^ 6 = 64 2 ^ 7 = 128 2 ^ 8 = 256 2 ^ 9 = 512 2 ^ 10 = 1024 ( it exceeds 1000 , so , x ca n ' t be 2 ^ 10 ) so , max value that x can take is 2 ^ 9 , for which has length of integer is 9 . now , since x = 512 , x + 3 y < 902 so , 3 y < 390 = = > y < 130 so , y can take any value which is less than 130 . and to get the maximum no of factors of smallest integer , we can say y = 2 ^ 7 for 2 ^ 7 has length of integer is 7 . so , combined together : 9 + 7 = 16 . e\"" + }, + { + "Answer": 19, + "Options": "a ) 19 , b ) 21 , c ) 23 , d ) 25 , e ) 27", + "Correct": "a", + "Explanation": "a = b + 10 so b = a - 10 . a + 6 = 2 ( b + 6 ) . a + 6 = 2 ( a - 10 + 6 ) . a + 6 = 2 a - 8 . a = 14 . in 5 years , alice will be 19 years old . the answer is a ." + }, + { + "Answer": 30, + "Options": "a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50", + "Correct": "c", + "Explanation": "\"i think we can use double - matrix method and solve using only one variable . our goal is to find the number of hardcover nonfiction books . let that number be x . we are given that all 140 books are either paperback fiction , paperback nonfiction , or hardcover nonfiction . this implies that number of hardcover fiction books is 0 . double - matrix : p = paperback ; h = hardcover ; f = fiction ; nf = nonfiction p h total f 2 x + 40 0 nf x + 20 x total 3 x + 60 x 180 3 x + 60 + x = 180 x = 30 answer ( c . )\"" + }, + { + "Answer": 6, + "Options": "a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8", + "Correct": "c", + "Explanation": "total subjects = 7 + 6 + 5 = 18 max subjects by 1 teacher = 3 so , min of teachers required = 18 / 3 = 6 answer : c" + }, + { + "Answer": 48, + "Options": "a ) 0.33 , b ) 0.44 , c ) 0.48 , d ) 44 , e ) 48", + "Correct": "e", + "Explanation": "\"a dozen eggs cost as much as a pound of rice - - > 12 eggs = 1 pound of rice = 36 cents ; a half - liter of kerosene costs as much as 8 eggs - - > 8 eggs = 1 / 2 liters of kerosene . how many cents does a liter of kerosene cost - - > 1 liter of kerosene = 16 eggs = 16 / 12 * 36 = 48 cents . answer : e .\"" + }, + { + "Answer": 0.3333333333333333, + "Options": "a ) 1 / 2 , b ) 2 / 3 , c ) 1 / 4 , d ) 1 / 3 , e ) 3 / 4", + "Correct": "d", + "Explanation": "\"start by deciding on a number of students to represent the number of students in the senior class . for this example i will choose 200 students . that would make the number of students in the junior class 100 . then we can find out how many students are taking japanese in each grade and add them together . ( 3 / 8 ) * 200 = 75 and ( 1 / 4 ) * 100 = 25 . 75 + 25 = 100 . there are a total of 300 students in the junior class and senior class combined ( 100 + 200 = 300 ) , and there are 100 total students in japanese , so 100 students in japanese / 300 total students equals 1 / 3 of the students in both classes that study japanese . answer : d\"" + }, + { + "Answer": 151, + "Options": "a ) 150 , b ) 151 , c ) 250 , d ) 350 , e ) none", + "Correct": "b", + "Explanation": "\"sol . let the number of grils be x . then , number of boys = ( 600 - x ) . then , ( 11 3 / 4 \u00d7 604 ) \u21d4 11 x + 12 ( 604 - x ) \u21d4 x = 7248 - 7097 \u21d4 151 . answer b\"" + }, + { + "Answer": 56.25, + "Options": "a ) 44 % , b ) 40 % , c ) 50 % , d ) 56.25 % , e ) 36.25 %", + "Correct": "d", + "Explanation": "\"the dealer uses weight which is 20 % less than the real weight . or ( 1 - 1 / 5 ) or 4 / 5 of real weight . it means that he is selling $ 4 worth of product for $ 5 . the dealer then further added 25 % impurities to the product . it means that he is selling $ 5 worth of product for $ 6.25 . so his profit is $ 6.25 - $ 4 = $ 2.25 and his profit percent is ( 2.25 / 4 ) * 100 = 56.25 % answer : - d\"" + }, + { + "Answer": 95, + "Options": "a ) 85 yrs , b ) 95 yrs , c ) 93 yrs , d ) 82 yrs , e ) 90 yrs", + "Correct": "b", + "Explanation": "\"let b ' s present age = x years then a ' s present age = x + 5 years x + 5 + 30 = 2 ( x - 30 ) x + 35 = 2 x - 60 x = 95 years answer is b\"" + }, + { + "Answer": 23, + "Options": "a ) 21 , b ) 20 , c ) 23 , d ) 27 , e ) 31", + "Correct": "c", + "Explanation": "we know dividend = divisor * quotient + remainder = = = > 997 = divisor * 43 + 8 = = = = = > 989 / 43 = divisor = = = > divisor = 23 ans - c" + }, + { + "Answer": 54, + "Options": "a ) 52 , b ) 54 , c ) 55 , d ) 56 , e ) 58", + "Correct": "b", + "Explanation": "\"a two - digit integer ` ` ab ' ' can be expressed algebraically as 10 a + b . q - r = ( 10 a + b ) - ( 10 b + a ) = 9 ( a - b ) < 60 . the greatest multiple of 9 which is less than 60 is 54 . the answer is b .\"" + }, + { + "Answer": 630, + "Options": "a ) rs 450 , b ) rs 920 , c ) rs 550 , d ) rs . 630 , e ) none of these", + "Correct": "d", + "Explanation": "explanation : let the original average expenditure be rs . x then , 42 ( x - 1 ) - 35 x = 84 ? 7 x = 126 ? x = 18 therefore original expenditure = rs . ( 35 18 ) = rs . 630 . answer : d" + }, + { + "Answer": 150, + "Options": "a ) 12 , b ) 150 , c ) 160 , d ) 180 , e ) 18", + "Correct": "b", + "Explanation": "\"let the numbers be x and y . then , x + y = 15 and x - y = 10 x 2 - y 2 = ( x + y ) ( x - y ) = 15 * 10 = 150 . answer : b\"" + }, + { + "Answer": 11, + "Options": "a ) 11 , b ) 12 , c ) 13 , d ) 15 , e ) 16", + "Correct": "a", + "Explanation": "\"let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 22 = > 2 x = 22 = > x = 11 a\"" + }, + { + "Answer": 4, + "Options": "a ) 1 , b ) 2 , c ) 4 , d ) 6 , e ) 7", + "Correct": "c", + "Explanation": "d = ( d - r ) / q = ( 23 - 3 ) / 5 = 20 / 5 = 4 c" + }, + { + "Answer": 560, + "Options": "a ) 88 , b ) 560 , c ) 99 , d ) 550 , e ) 540", + "Correct": "b", + "Explanation": "= ( 1 x 2 ) ^ 2 + ( 2 x 2 ) ^ 2 , + ( 2 x 3 ) ^ 3 + . . . . . . ( 2 x 7 ) ^ 2 = 2 ^ 2 x ( 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + . . . . . . . + 7 ^ 2 ) formula is = 1 / 6 n ( n + 1 ) ( 2 n + 1 ) = ( 4 x 1 / 6 x 7 x 8 x 15 ) = ( 4 x 140 ) = 560 answer is b" + }, + { + "Answer": 0.4, + "Options": "a ) 0.2 , b ) 0.3 , c ) 0.4 , d ) 0.5 , e ) none of these", + "Correct": "c", + "Explanation": "solution : we calculate f ( 0 ) , f ( x - 2 ) , f ( 2 x + 1 ) , namely f ( 0 ) = 0 + 4 = 4 ; f ( x - 2 ) = x - 2 + 4 = x + 2 ; f ( 2 x + 1 ) = 2 x + 1 + 4 = 2 x + 5 the equation gets this look [ 3 ( x + 2 ) ] / 4 + 4 = 2 x + 5 < = > 3 ( x + 2 ) + 16 = 4 ( 2 x + 5 ) < = > 3 x + 6 + 16 = 8 x + 20 < = > 22 - 20 = 8 x - 3 x < = > 2 = 5 x < = > x = 0.4 answer c" + }, + { + "Answer": 999944, + "Options": "a ) 998765 , b ) 998907 , c ) 999944 , d ) 999954 , e ) 999990", + "Correct": "c", + "Explanation": "largest 6 digit number is 999999 after doing 999999 \u00f7 88 we get remainder 55 hence largest 6 digit number exactly divisible by 88 = 999999 - 55 = 999944 c" + }, + { + "Answer": 52, + "Options": "a ) 40 , b ) 44 , c ) 52 , d ) 88 , e ) 90", + "Correct": "c", + "Explanation": "\"sol . let the numbers be x and y . then , ( x + y ) = 18 and x 2 + y 2 = 220 . now , 2 xy = ( x + y ) 2 - ( x 2 + y 2 ) = ( 18 ) 2 - 220 = 324 - 220 = 104 xy = 52 . answer c\"" + }, + { + "Answer": 56, + "Options": "a ) 31 , b ) 51 , c ) 56 , d ) 62 , e ) 93", + "Correct": "c", + "Explanation": "basically , the question asks how many 4 digit numbers ( including those in the form 0 xxx , 00 xx , and 000 x ) have digits which add up to 5 . think about the question this way : we know that there is a total of 5 to be spread among the 4 digits , we just have to determine the number of ways it can be spread . let x represent a sum of 1 , and | represent a separator between two digits . as a result , we will have 5 x ' s ( digits add up to the 5 ) , and 3 | ' s ( 3 digit separators ) . so , for example : xx | x | x | x = 2111 | | xxx | xx = 0032 etc . there are 8 c 3 ways to determine where to place the separators . hence , the answer is 8 c 3 = 56 . answer : c" + }, + { + "Answer": 2, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 2", + "Correct": "e", + "Explanation": "\"assume x is quotient here , n = 10 x + 7 - - - - - - - - - - ( 1 ) and n = 5 x + ? we can also write equation ( 1 ) as : n = ( 10 x + 5 ) + 2 . ie 5 ( 2 x + 1 ) + 1 ie the first term is perfectly divisible by 5 . so , the remainder left is 2 so , answer ( e ) is right choice .\"" + }, + { + "Answer": 5, + "Options": "a ) 8 , b ) 7.5 , c ) 6.5 , d ) 5 , e ) 6", + "Correct": "d", + "Explanation": "\"solution : let x be added to each term . according to question , ( 7 + x ) / ( 11 + x ) = 3 / 4 ; or , 33 + 3 x = 28 + 4 x ; or , x = 5 . answer : option d\"" + }, + { + "Answer": 495, + "Options": "a ) $ 495 , b ) $ 510 , c ) $ 480 , d ) $ 375 , e ) $ 360", + "Correct": "a", + "Explanation": "explanatory answer let the sums of money received by a , b and c be x , y and z respectively . then x - 10 : y - 20 : z - 15 is 11 a : 18 a : 24 a when $ 10 , $ 20 and $ 15 are removed , we are removing a total of $ 45 from $ 1105 . therefore , 11 a + 18 a + 24 a = 1105 - 45 = 1060 i . e . , 53 a = 1060 or a = 20 . we know that z - 15 = 24 a = 24 * 20 = 480 therefore , z = 480 + 15 = $ 495 correct choice is ( a )" + }, + { + "Answer": 42, + "Options": "a ) 46 , b ) 47 , c ) 42 , d ) 49 , e ) 50", + "Correct": "c", + "Explanation": "\"mother + daughter + child = 150 kg daughter + child = 60 kg mother = 150 - 60 = 90 kg child = 1 / 5 th of mother = ( 1 / 5 ) * 90 = 18 kg so now daughter = 120 - ( mother + child ) = 150 - ( 90 + 18 ) = 42 kg answer : c\"" + }, + { + "Answer": 400, + "Options": "a ) 225 , b ) 275 , c ) 325 , d ) 350 , e ) 400", + "Correct": "e", + "Explanation": "\"this problem is a general word translation . we first define variables and then set up equations . we can define the following variables : f = the weight of the first lift s = the weight of the second lift we are given that the total weight of joe ' s two lifts was 900 pounds . we sum the two variables to obtain : f + s = 900 we are also given that twice the weight of his first lift was 300 pounds more than the weight of his second lift . we express this as : 2 f = 300 + s 2 f \u2013 300 = s we can now plug in ( 2 f \u2013 300 ) for s into the first equation , so we have : f + 2 f \u2013 300 = 900 3 f = 1,200 f = 400 answer is e .\"" + }, + { + "Answer": 20, + "Options": "a ) 50.5 % , b ) 44.4 % , c ) 22.2 % , d ) 33.3 % , e ) 20 %", + "Correct": "e", + "Explanation": "\"30 % of ( x - y ) = 20 % of ( x + y ) 30 / 100 ( x - y ) = 20 / 100 ( x + y ) x = 5 y required percentage = y / x * 100 = y / 5 y * 100 = 20 % answer is e\"" + }, + { + "Answer": 4, + "Options": "a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3", + "Correct": "d", + "Explanation": "\"21340 * 10 ^ - 4 * 10 ^ x < 210,000 , x = 4 because the next zero on the right side will make 21,340 > 210,000 answer d ,\"" + }, + { + "Answer": 43200, + "Options": "a ) 43,100 , b ) 43,200 , c ) 43,300 , d ) 43,400 , e ) 43,450", + "Correct": "b", + "Explanation": "\"this question can be modified so that the birth rate is given every m seconds and the death rate is given every n seconds . for this particular question : increase in the population every 2 seconds = 4 - 3 = 1 people . total 2 second interval in a day = 24 * 60 * 60 / 2 = 43,200 population increase = 43,200 * 1 = 43,200 . hence b .\"" + }, + { + "Answer": 63, + "Options": "a ) 63 , b ) 37 , c ) 54 , d ) 99 , e ) 01", + "Correct": "a", + "Explanation": "\"the number of students with first division = 25 % of 300 = 25 / 100 \u00d7 300 = 8400 / 100 = 75 and , the number of students with second division = 54 % of 300 = 54 / 100 \u00d7 300 = 16200 / 100 = 162 therefore , the number of students who just passed = 300 \u2013 ( 75 + 162 ) = 63 answer : a\"" + }, + { + "Answer": 220025, + "Options": "a ) 145646 , b ) 236578 , c ) 645353 , d ) 456546 , e ) 220025", + "Correct": "e", + "Explanation": "\"( 555 + 445 ) * 2 * 110 + 25 = 220000 + 25 = 220025 e\"" + }, + { + "Answer": 11, + "Options": "a ) 11 , b ) 17 , c ) 11 , d ) 19 , e ) 99", + "Correct": "a", + "Explanation": "let the son ' s present age be x years . then , ( 32 - x ) = x x = 16 . son ' s age 5 years back = ( 16 - 5 ) = 11 years answer : a" + }, + { + "Answer": 32, + "Options": "a ) 0 , b ) 12 , c ) 32 , d ) 20 , e ) 25", + "Correct": "c", + "Explanation": "\"12 * 56 = 672 672 % 21 = 32 answer : c\"" + }, + { + "Answer": 63.00000000000001, + "Options": "a ) 33 , b ) 54 , c ) 63 , d ) 17 , e ) 01", + "Correct": "c", + "Explanation": "\"explanation : as there is meal for 70 adults and 21 have their meal , the meal left can be catered to 49 adults . now , 70 adults = 90 children 7 adults = 9 children therefore , 49 adults = 63 children hence , the meal can be catered to 63 children . answer : c\"" + }, + { + "Answer": 12, + "Options": "a ) s . 17 , b ) s . 18 , c ) s . 12 , d ) s . 11 , e ) s . 10", + "Correct": "c", + "Explanation": "\"average price per book = ( 520 + 248 ) / ( 42 + 22 ) = 768 / 64 = rs . 12 answer : c\"" + }, + { + "Answer": 1011, + "Options": "a ) 1008 , b ) 1011 , c ) 1022 , d ) 1032 , e ) 1043", + "Correct": "b", + "Explanation": "\"required number = ( l . c . m of 12 , 16 , 18 , 21,28 ) + 3 = 1008 + 3 = 1011 answer : b\"" + }, + { + "Answer": 1.000000000000006, + "Options": "a ) 7 : 3 , b ) 2 : 3 , c ) 9 : 3 , d ) 6 : 3 , e ) 1 : 1", + "Correct": "e", + "Explanation": "\"explanation : let the ratio be k : 1 . then , k * 16.4 + 1 * 15.2 = ( k + 1 ) * 15.8 < = > ( 16.4 - 15.8 ) k = ( 15.8 - 15.2 ) < = > k = 0.6 / 0.6 = 1 / 1 . required ratio = 1 / 1 : 1 = 1 : 1 . answer : e\"" + }, + { + "Answer": 119.99999999999994, + "Options": "a ) $ 100 , b ) $ 120 , c ) $ 140 , d ) $ 160 , e ) $ 180", + "Correct": "b", + "Explanation": "\"3 : 2 = 9 : 6 and 5 : 3 = 10 : 6 . an increase in $ 20 increases the ratio by 1 : 6 . therefore , january ' s bill was 6 ( $ 20 ) = $ 120 . the answer is b .\"" + }, + { + "Answer": 0.4, + "Options": "a ) 7 / 30 , b ) 7 / 21 , c ) 2 / 5 , d ) 12 / 29 , e ) 4 / 7", + "Correct": "c", + "Explanation": "soda water = 12 / 21 natural lemon juice = 7 / 21 the quantities of sugar and papaya puree are equal . total units are 21 of which 12 + 7 = 19 are used up by above two . remaining is 2 which is equally divided between sugar and papaya puree : sugar = 1 / 21 papaya puree = 1 / 21 thus ratio of soda : lemon : sugar : puree = 12 : 7 : 1 : 1 now , lemon is doubled , puree is three times and remaining are the same . resultant ratio is = 12 : 14 : 1 : 3 ratio of soda water in the resultant mixture = 12 / ( 12 + 14 + 1 + 3 ) = 12 / 30 = 2 / 5 answer : c" + }, + { + "Answer": 1170, + "Options": "a ) 1040 , b ) 1170 , c ) 1150 , d ) 4160 , e ) none of these", + "Correct": "b", + "Explanation": "\"number of male employees = 5200 * 45 / 100 = 2340 required number of male employees who are less than 50 years old = 4160 * ( 100 - 50 ) % = 2340 * 50 / 100 = 1170 . answer : b\"" + }, + { + "Answer": 33, + "Options": "a ) a ) 32 , b ) b ) 38 , c ) c ) 30 , d ) d ) 31 , e ) e ) 33", + "Correct": "e", + "Explanation": "division rule for 3 - sum of all digits is multiple of 3 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78 81 84 87 90 93 96 99 ans - e" + }, + { + "Answer": 23, + "Options": "a ) q = 21 , b ) q = 22 , c ) q = 23 , d ) 24 , e ) 27", + "Correct": "c", + "Explanation": "squaring on both sides , x ^ 2 + ( 1 / x ) ^ 2 + 2 ( x ) ( 1 / x ) = 5 ^ 2 x ^ 2 + ( 1 / x ) ^ 2 = 23 answer : c" + }, + { + "Answer": 468, + "Options": "a ) 198 , b ) 288 , c ) 363 , d ) 396 , e ) 468", + "Correct": "e", + "Explanation": "i will go with e ( pending elements to match is 2 ^ 2 * 3 ^ 2 * 13 ^ 1 = 468" + }, + { + "Answer": 400, + "Options": "a ) 100 , b ) 300 , c ) 400 , d ) 3,000 , e ) 4,000", + "Correct": "c", + "Explanation": "\"straight pluggin in for me . as usual , i started with c and got the answer . lets ' back calculate and see what we get let us consider eggs processed each day to be 400 so initial ratio of eggs processed and rejected is 96 : 4 or 24 : 1 so out of 400 eggs , there will be 384 eggs processed and 16 rejected . now if the no . of eggs inspected remain and 12 more eggs get accepted that means there w = 384 + 12 = 396 eggs accepted and 4 rejected . . . and the ratio will be 99 : 1 bingo . . . this is what the questions says . . . . its always a good idea to start with c .\"" + }, + { + "Answer": 0.1111111111111111, + "Options": "a ) 2 / 3 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 6 , e ) 1 / 9", + "Correct": "e", + "Explanation": "let the probability of heads be x and the probability of tails be 1 - x . so , we are given that p ( one tails and one heads ) = 2 * x * ( 1 - x ) = 1 / 2 . p ( two heads and two tails ) = 4 ! / ( 2 ! 2 ! ) * x ^ 2 * ( 1 - x ) ^ 2 = 6 * ( x * ( 1 - x ) ) ^ 2 . we are multiplying by 4 ! / ( 2 ! 2 ! ) because hhtt scenario can occur in several ways : hhtt , htht , thht , . . . ( permutation of 4 letters hhtt where 2 t ' s and 2 h ' s are the same ) . since from 2 * x * ( 1 - x ) = 1 / 2 it follows that x * ( 1 - x ) = 1 / 4 , then 4 * ( x * ( 1 - x ) ) ^ 2 = 4 * ( 1 / 6 ) ^ 2 = 1 / 9 . answer : e ." + }, + { + "Answer": 259.09090909090907, + "Options": "a ) s . 259 , b ) s . 289 , c ) s . 299 , d ) s . 300 , e ) s . 389", + "Correct": "a", + "Explanation": "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 570 but x = 120 % of y = 120 y / 100 = 12 y / 10 \u2234 12 y / 10 + y = 570 \u21d2 y [ 12 / 10 + 1 ] = 570 \u21d2 22 y / 10 = 570 \u21d2 22 y = 5700 \u21d2 y = 5700 / 22 = rs . 259 a )" + }, + { + "Answer": 4.200000000000001, + "Options": "a ) 4.5 , b ) 4.2 , c ) 4.7 , d ) 4.8 , e ) none of these", + "Correct": "b", + "Explanation": "solution : sum of the remaining two numbers = ( 3.95 \u00d7 6 ) - [ ( 3.8 \u00d7 2 ) + ( 3.85 \u00d7 2 ) ] = 23.70 - ( 7.6 + 7.7 ) = 23.70 - 15.3 = 8.4 . \u2234 required average = 8.4 / 2 = 4.2 answer b" + }, + { + "Answer": 23, + "Options": "a ) 7 , b ) 13 , c ) 16 , d ) 21 , e ) 23", + "Correct": "e", + "Explanation": "general rule for such kind of problems : to maximize one quantity , minimize the others ; to minimize one quantity , maximize the others . thus to maximize the number of points of one particular player minimize the number of points of all other 11 players . minimum number of points for a player is 7 , so the minimum number of points of 11 players is 7 * 11 = 77 . therefore , the maximum number of points q for 12 th player is 100 - 77 = 23 . answer : e ." + }, + { + "Answer": 12, + "Options": "a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 14", + "Correct": "d", + "Explanation": "let the number of each size of jar = w then 1 / 4 w + 1 / 2 w + w = 7 1 3 / 4 w = 7 w = 4 the total number of jars = 3 w = 12 answer : d" + }, + { + "Answer": 14, + "Options": "a ) 8 , b ) 14 , c ) 16 , d ) 17 , e ) 18", + "Correct": "b", + "Explanation": "let the ages of children be x , ( x + 2 ) , ( x + 4 ) , ( x + 6 ) and ( x + 8 ) years . then , x + ( x + 2 ) + ( x + 4 ) + ( x + 6 ) + ( x + 8 ) = 50 5 x = 30 x = 6 x + 8 = 6 + 8 = 14 answer : b" + }, + { + "Answer": 10, + "Options": "a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50", + "Correct": "a", + "Explanation": "\"m + h = 80 h = 80 - m 4 m + 5 h = 390 4 m + 5 * ( 80 - m ) = 390 m = 10 the answer is a .\"" + }, + { + "Answer": 93.5, + "Options": "a ) 102 % , b ) 105 % , c ) 95 % , d ) 93.5 % , e ) 90 %", + "Correct": "d", + "Explanation": "\"easiest thing to do : assume that price is 100 price at the end of yr 1 : 100 + 10 = 110 price at the end of year 2 = 110 - 110 * 0.15 = 110 * 0.85 = 93.5 hence required answer = ( 93.5 / 100 ) * 100 % = 93.5 % answer is d .\"" + }, + { + "Answer": 85, + "Options": "a ) 79 , b ) 99 , c ) 88 , d ) 85 , e ) 75", + "Correct": "d", + "Explanation": "\"average = ( 86 + 89 + 82 + 87 + 81 ) / 5 = 425 / 5 = 85 . answer : d\"" + }, + { + "Answer": 8, + "Options": "a ) 3 , b ) 6 , c ) 8 , d ) 12 , e ) 18", + "Correct": "c", + "Explanation": "can you explain your method . i solved it differently xyz , where z must be 5 . therefore 1 variation of digit in z . y can be any of the 4 possible choices . x can be any of the 3 possible choices . 4 + 3 + 1 = 8 c" + }, + { + "Answer": 20, + "Options": "a ) 16 , b ) 18 , c ) 14 , d ) 20 , e ) 22", + "Correct": "d", + "Explanation": "explanation : sum of 1 st 10 natural numbers ( 1 \u2013 10 ) = 1 + 2 + \u2026 10 = 55 . sum of next 10 natural numbers ( 11 \u2013 20 ) = 10 + 11 + 12 + \u2026 20 = 100 + 55 = 155 . sum of next 10 natural numbers ( 31 \u2013 40 ) = 255 . sum of numbers from 31 \u2013 40 = 355 and so on and on . so , we have here 55 + 155 + 255 = 465 . if we add 355 to 465 , it will be way more than 575 . so , we can add one by one . 465 + 31 + 32 + 33 = 561 . 465 + 31 + 32 + 33 + 34 = 595 . thus , the sum should be 595 instead of 575 , and the missing number is 20 . answer : d" + }, + { + "Answer": 6, + "Options": "a ) $ 6.5 , b ) $ 6 , c ) $ 7 , d ) $ 8 , e ) $ 9", + "Correct": "b", + "Explanation": "a is not an integer . so we start with b . if large doll costs $ 6 , then he can buy 300 / 6 = 50 large dolls and 300 / 4 = 75 small dolls . difference is 25 , which is we wanted . answer b ." + }, + { + "Answer": 939.5973154362416, + "Options": "a ) 939.6 , b ) 928.8 , c ) 927.78 , d ) 926.82 , e ) 902.1", + "Correct": "a", + "Explanation": "\"1120 = p [ 1 + ( 8 * 12 / 5 ) / 100 ] p = 939.60 answer : a\"" + }, + { + "Answer": 30, + "Options": "a ) 22 , b ) 21 , c ) 88 , d ) 30 , e ) 29", + "Correct": "d", + "Explanation": "\"explanation : lot the total number of workers be v then , 8 ooov = ( 12000 * 10 ) + 6000 ( v - 10 ) < = > 2000 v = 60000 < = > v = 30 answer : d ) 30\"" + }, + { + "Answer": 4, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "e", + "Explanation": "only the unit ' s digit of the product will decide the remainder when divided by 5 . hence , 2 * 2 * 1 = will give units digit as 4 so , whatever be the number , if it ends in 4 , the remainder after dividing with 5 will be 4 . optione" + }, + { + "Answer": 20, + "Options": "a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30", + "Correct": "c", + "Explanation": "let pauls age be ' a ' and peters be ' e ' e + a = 35 ( given ) e = 35 - a - - - - - - eq 1 when peter was as old as paul that is when peter ' s age was ' a ' pauls age was a - ( e - a ) = 2 a - e now peters age is e = 2 ( 2 a - e ) e = 4 a - 2 e 3 e = 4 a 3 ( 35 - a ) = 4 a 105 - 3 a = 4 a a = 15 hence e = 20 answer : c" + }, + { + "Answer": 4543, + "Options": "a ) 2988 , b ) 4543 , c ) 4400 , d ) 2871 , e ) 881", + "Correct": "b", + "Explanation": "\"x * ( 92 / 100 ) * ( 85 / 100 ) = 3553 x = 4543 answer : b\"" + }, + { + "Answer": 8, + "Options": "a ) 0 , b ) 2 , c ) 3 , d ) 8 , e ) 16", + "Correct": "d", + "Explanation": "answer d i opted to put the random value option . i used 0 , 4 , - 4 and the the extreme of 60 and - 60 . . i was able to solve it in 1 : 09 d" + }, + { + "Answer": 37.05882352941177, + "Options": "a ) 32 kmph , b ) 33 kmph , c ) 34 kmph , d ) 35 kmph , e ) 37 kmph", + "Correct": "e", + "Explanation": "avg speed = total distance / total time . total distance traveled = 100 + 50 = 150 km ; time taken for uphill journey = 100 / 30 = 10 / 3 ; time taken for down hill journey = 50 / 60 = 5 / 7 ; avg speed = 150 / ( 10 / 3 + 5 / 7 ) = 37 kmph answer : e" + }, + { + "Answer": 54, + "Options": "a ) 54 , b ) 72 , c ) 96 , d ) 144 , e ) 432", + "Correct": "a", + "Explanation": "vlaudia can choose any two of four different candles and any 8 of 9 different flowers for a centerpiece arrangement . 2 candles from 4 candles : 4 c 2 : 6 8 flowers from 9 flowers : 9 c 8 : 9 so total grouping 9 * 6 = 54 . answer is a ." + }, + { + "Answer": 105, + "Options": "a ) 105 , b ) 110 , c ) 115 , d ) 120 , e ) 125", + "Correct": "a", + "Explanation": "\"15 c 2 = 105 the answer is a .\"" + }, + { + "Answer": 85, + "Options": "a ) 80 , b ) 138 , c ) 100 , d ) 129 , e ) 85", + "Correct": "e", + "Explanation": "\"average price per book = ( 6500 + 2000 ) / ( 65 + 35 ) = 8500 / 100 = rs . 85 answer : e\"" + }, + { + "Answer": 800, + "Options": "a ) s . 800 , b ) s . 85 , c ) s . 90 , d ) s . 100 , e ) s . 120", + "Correct": "a", + "Explanation": "\"9 / 12 = 3 / 4 * 800 = 600 400 - - - - - - - - - - - - - 200 1 / 4 - - - - - - - - 200 1 - - - - - - - - - ? = > rs . 800 answer : a\"" + }, + { + "Answer": 198.33333333333334, + "Options": "a ) $ 28 , b ) $ 82 , c ) $ 110 , d ) $ 138 , e ) $ 197", + "Correct": "e", + "Explanation": "\"by the question , the equation would be 150 p - 87 * 150 - 16500 = 0 p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component . solving the equation , we get p = $ 197 . answer e for me .\"" + }, + { + "Answer": 0.39166666666666666, + "Options": "a ) 1 / 140 , b ) 1 / 180 , c ) 27 / 410 , d ) 47 / 120 , e ) 57 / 120", + "Correct": "d", + "Explanation": "\"required probability = p ( x ) + p ( y ) + p ( z ) ( all the events are mutually exclusive ) . = 1 / 6 + 1 / 10 + 1 / 8 = 47 / 120 answer : d\"" + }, + { + "Answer": 112, + "Options": "a ) 112 % , b ) b . 100 % , c ) 96 % , d ) 80 % , e ) 64 %", + "Correct": "a", + "Explanation": "\"even i got 96 % j = 100 t = 100 * 0.7 = 70 m = 70 * 1.6 = 112 if mary ' s income is x percent of j m = j * x / 100 x = m * 100 / j = 112 * 100 / 100 = 112 ans : a\"" + }, + { + "Answer": 26, + "Options": "a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 30", + "Correct": "d", + "Explanation": "we have 3 places ( - - - ) to fill & we can use only digits 2 , 4 , 5 first place can be filled in 3 ways 2 nd place can be filled in 3 ways because we can repeat the digits 3 rd place can be filled in 3 ways because we can repeat the digits total no of codes = 3 x 3 x 3 = 27 but one combination ( 555 ) will not be even so total no of even codes = 27 - 1 = 26 answer d" + }, + { + "Answer": 859560, + "Options": "a ) 345652 , b ) 547678 , c ) 356789 , d ) 778990 , e ) 859622", + "Correct": "e", + "Explanation": "\"dividend = quotient * divisor + reminder 859622 / 456 gives quotient = 1885 and reminder = 62 . so , the next number divisible by 456 is 456 places infront of 456 * 1885 which means 456 \u2013 62 = 394 should be added to 859622 . e\"" + }, + { + "Answer": 25, + "Options": "a ) 12.5 % , b ) 20 % , c ) 25 % , d ) 50 % , e ) 100 %", + "Correct": "c", + "Explanation": "\"correct answer : c solution : c . we can set up equations for income before and after the wage reduction . initially , the employee earns w wage and works h hours per week . after the reduction , the employee earns . 8 w wage and works x hours . by setting these equations equal to each other , we can determine the increase in hours worked : wh = . 8 wx ( divide both sides by . 8 w ) 1.25 h = x we know that the new number of hours worked e will be 25 % greater than the original number . the answer is c .\"" + }, + { + "Answer": 9, + "Options": "a ) 9 , b ) 11 , c ) 15 , d ) 5 , e ) 20", + "Correct": "a", + "Explanation": "221 + 43 = 264 / 17 = 9 answer a" + }, + { + "Answer": 88, + "Options": "a ) 52 , b ) 49 , c ) 95 , d ) 88 , e ) 66", + "Correct": "d", + "Explanation": "\"right side = 15 seat left side = 15 - 3 ( 3 few seat in right side ) = 12 seat total = 15 + 12 = 27 people can seat in 27 seat = 27 * 3 = 81 people can seat in last seat = 7 total people can seat = 81 + 7 = 88 answer : d\"" + }, + { + "Answer": 0.14285714285714285, + "Options": "a ) 1 / 7 , b ) 1 / 6 , c ) 1 / 5 , d ) 1 / 4 , e ) 1 / 3", + "Correct": "a", + "Explanation": "\"let x be the fraction of her take - home pay that the worker saved . let p be the monthly pay . 12 xp = 2 ( 1 - x ) p 12 xp = 2 p - 2 xp 14 xp = 2 p x = 1 / 7 the answer is a .\"" + }, + { + "Answer": 400, + "Options": "a ) $ 340 , b ) $ 360 , c ) $ 380 , d ) $ 400 , e ) $ 420", + "Correct": "d", + "Explanation": "\"s . i for 5 years = $ 820 - $ 520 = $ 300 the s . i . is $ 60 / year s . i . for 2 years = $ 120 principal = $ 520 - $ 120 = $ 400 the answer is d .\"" + }, + { + "Answer": 55, + "Options": "a ) a ) 70 , b ) b ) 77 , c ) c ) 55 , d ) d ) 81 , e ) e ) 82", + "Correct": "c", + "Explanation": "required average = 7 ( 1 + 2 + . . . . + 21 ) / 21 ( 5 / 21 ) x ( ( 21 x 22 ) / 2 ) ( because sum of first 21 natural numbers ) = 55 c" + }, + { + "Answer": 3, + "Options": "a ) 5 , b ) 46 , c ) 52 , d ) 12 , e ) 3", + "Correct": "e", + "Explanation": "here , e and f are events p ( e | f ) = p ( enf ) / p ( f ) = 75 / 25 = 3 p ( f | e ) = p ( enf ) / p ( e ) = 75 / 75 = 1 . e )" + }, + { + "Answer": 60, + "Options": "a ) 50 , b ) 60 , c ) 40 , d ) 18 , e ) 22", + "Correct": "b", + "Explanation": "given ratio = 5 : 7 : 4 : 8 , sum of ratio = 24 : . the smallest part = ( 360 * 4 / 24 ) = 60 answer : b" + }, + { + "Answer": 25, + "Options": "a ) 25 inches , b ) 77 inches , c ) 66 inches , d ) 97 inches , e ) 66 inches", + "Correct": "a", + "Explanation": "\"explanation : total length of scale in inches = ( 10 * 12 ) + 5 = 125 inches length of each of the 5 parts = 125 / 5 = 25 inches answer : a\"" + }, + { + "Answer": 470, + "Options": "a ) 0.47 , b ) 47 , c ) 470 , d ) 4700 , e ) none of these", + "Correct": "c", + "Explanation": "solution given expression = 4.7 \u00d7 ( 13.26 + 9.43 + 77.31 ) = 4.7 \u00d7 100 = 470 . answer c" + }, + { + "Answer": 0.425, + "Options": "a ) 1.0 , b ) 0.5 , c ) 0.75 , d ) 0.425 , e ) 0.3", + "Correct": "d", + "Explanation": "\"the ant walks an average of 500 meters in 60 minutes 500 meters in 1 hours the beetle walks 15 % less distance = 500 - 75 = 425 meters in 60 minutes 0.425 km in 1 hours speed = 0.425 * 1 = 0.425 km / h i guess option d should be 0.425\"" + }, + { + "Answer": 149.99999999999994, + "Options": "a ) 37.5 , b ) 75 , c ) 100 , d ) 150 , e ) 175", + "Correct": "d", + "Explanation": "\"original mixture has 20 % salt and 80 % water . total = x out of which salt = 0.2 x and water = 0.8 x now , 1 / 4 water evaporates and all salt remains . so what remains is 0.2 x salt and 0.6 x water . now 20 gallons salt is added and 10 gallons of water is added . so salt now becomes - > ( 0.2 x + 20 ) and water - - > ( 0.6 x + 10 ) amount of salt is 33.33 % of total . so amount of water is 66.66 % . so salt is half of the volume of water . so ( 0.2 x + 20 ) = ( 0.6 x + 10 ) / 2 , solving , x = 150 . answer : d\"" + }, + { + "Answer": 325, + "Options": "a ) 156 , b ) 162 , c ) 325 , d ) 324 , e ) 326", + "Correct": "c", + "Explanation": "\"buy as many $ 50 deals as possible . we can by 650 / 50 = 13 two dozen roses , thus total of 13 * 24 = 312 roses . we are left with 680 - 650 = $ 30 . we can buy 30 / 2.3 = ~ 13 roses for that amount . total = 312 + 13 = 325 . answer : c .\"" + }, + { + "Answer": 131, + "Options": "a ) 65 , b ) 66 , c ) 67 , d ) 131 , e ) 130", + "Correct": "e", + "Explanation": "the answer to the question is indeed e . the problem with above solutions is that they do not consider words like aa , bb , . . . the number of 1 letter words ( x ) that can be made from 65 letters is 65 ; the number of 2 letter words ( xx ) that can be made from 65 letters is 65 * 65 , since each x can take 65 values . total : 65 + 65 * 65 . similarly : the number of 1 letter words ( x ) that can be made from 64 letters is 64 ; the number of 2 letter words ( xx ) that can be made from 64 letters is 64 * 64 , since each x can take 64 values . total : 64 + 64 * 64 . the difference is ( 65 + 65 * 65 ) - ( 64 + 64 * 64 ) = 130 . answer : e ." + }, + { + "Answer": 210, + "Options": "a ) 330 , b ) 300 , c ) 252 , d ) 225 , e ) 210", + "Correct": "e", + "Explanation": "baker ram is storing cake boxes in cartons the dimensions of the carton are 25 x 42 x 60 and those of each cake box are 8 x 7 x 5 . to maximize number of boxes try and fit maximum into the base of the box . if you take the base as 25 x 42 and fit 5 x 6 boxes of 5 x 7 , then the total number of boxes is 5 x 6 x integer ( 60 / 8 ) = 5 x 6 x 7 = 210 . alternatively you could try taking the base as 60 x 42 and fit 12 x 6 boxes of 5 x 7 , then the total number of boxes is 12 x 6 x integer ( 25 / 8 ) = 12 x 6 x 3 = 216 . but since that is not an answer option , i go with ( e ) 210 ." + }, + { + "Answer": 13, + "Options": "a ) 7 % , b ) 10 % , c ) 13 % , d ) 16 % , e ) 19 %", + "Correct": "c", + "Explanation": "the percent of alcohol in the solution is ( 0.05 ( 40 ) + 4.5 ) / 50 = 6.5 / 50 = 13 % the answer is c ." + }, + { + "Answer": 72, + "Options": "a ) 72 , b ) 23 , c ) 29 , d ) 26 , e ) 13", + "Correct": "a", + "Explanation": "\"sum of the marks for the 12 students = 12 * 36 = 432 . the marks of each student are doubled , the sum also will be doubled . the new sum = 432 * 2 = 864 . so , the new average = 864 / 12 = 72 . answer : a\"" + }, + { + "Answer": 9, + "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12", + "Correct": "b", + "Explanation": "since 19,683 is an odd number , it is not a multiple of 4 . this means that y must equal zero . since x - y = 9 and y = 0 , then x = 9 . the answer is b ." + }, + { + "Answer": 14, + "Options": "a ) 6 rs , b ) 2 rs , c ) 4 rs , d ) 9 rs , e ) 14 rs", + "Correct": "e", + "Explanation": "\"5 m = xw = 8 b 5 m + xw + 8 b - - - - - 210 rs . 5 m + 5 m + 5 m - - - - - 210 rs . 15 m - - - - - - 210 rs . = > 1 m = 14 rs . answer : e\"" + }, + { + "Answer": 50, + "Options": "a ) 40 , b ) 80 , c ) 50 , d ) 60 , e ) 50", + "Correct": "c", + "Explanation": "200 men do the rest of the work in 100 - 50 = 50 days 100 men can do the rest of the work in 50 * 200 / 100 = 100 days required number of days = 100 - 50 = 50 days answer is c" + }, + { + "Answer": 32, + "Options": "a ) 20 , b ) 23 , c ) 25 , d ) 32 , e ) 42", + "Correct": "d", + "Explanation": "\"x + y = 24 x - y = 40 2 x = 64 x = 32 answer is d\"" + }, + { + "Answer": 30, + "Options": "a ) 30 , b ) 35 , c ) 40 , d ) 45 , e ) 50", + "Correct": "a", + "Explanation": "222 = 2 * 2 + 2 = 6 333 = 3 * 3 + 3 = 12 444 = 4 * 4 + 4 = 20 555 = 5 * 5 + 5 = 30 answer : a" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 8 , c ) 6 , d ) 4 , e ) 3", + "Correct": "e", + "Explanation": "find f - 1 ( x ) and then find f - 1 ( - 3 ) y = 5 - 2 x , given x = 5 - 2 y , interchange x and y 2 y = 5 - x , y = log 2 ( 5 - x ) , solve for y f - 1 ( x ) = log 2 ( 5 - x ) , inverse function f - 1 ( - 3 ) = log 2 ( 5 + 3 ) = log 2 ( 23 ) = 3 correct answer e" + }, + { + "Answer": 158, + "Options": "a ) $ 150 , b ) $ 152 , c ) $ 154 , d ) $ 156 , e ) $ 158", + "Correct": "e", + "Explanation": "j + k = 400 so k = 400 - j 2 j = k + 74 2 j = ( 400 - j ) + 74 3 j = 474 j = 158 the answer is e ." + }, + { + "Answer": 40, + "Options": "a ) $ 40 , b ) $ 160 , c ) $ 220 , d ) $ 240 , e ) $ 260", + "Correct": "a", + "Explanation": "\"10 $ per week ! an year has 52 weeks . annual charges per year = 52 * 10 = 520 $ 30 $ per month ! an year has 12 months . annual charges per year = 12 * 40 = 480 $ 520 - 480 = 40 ans a\"" + }, + { + "Answer": 30, + "Options": "a ) 30 , b ) 35 , c ) 38 , d ) 40 , e ) 45", + "Correct": "a", + "Explanation": "\"10 play kabadi = > n ( a ) = 10 , 5 play both gmaes . = > n ( anb ) = 5 20 play kho kho only , = > n ( b ) = n ( b only ) + n ( anb ) = 20 + 5 = 25 total = > n ( aub ) = n ( a ) + n ( b ) - n ( anb ) = 10 + 25 - 5 = 30 answer : a\"" + }, + { + "Answer": 21, + "Options": "a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22", + "Correct": "d", + "Explanation": "\"let n be the number of participants . the number of games is nc 2 = n * ( n - 1 ) / 2 = 210 n * ( n - 1 ) = 420 = 21 * 20 ( trial and error ) the answer is d .\"" + }, + { + "Answer": 6, + "Options": "a ) \u2212 48 , b ) \u2212 2 , c ) 6 , d ) 9 , e ) 48", + "Correct": "c", + "Explanation": "\"i . e . if a = - 1 then b = 7 or if a = 7 then b = - 1 but in each case a + b = - 1 + 7 = 6 answer : option c\"" + }, + { + "Answer": 50, + "Options": "a ) 46 , b ) 48 , c ) 50 , d ) 52 , e ) 54", + "Correct": "c", + "Explanation": "\"sum of all the 13 numbers = 13 * 60 = 780 sum of the first 6 of them = 6 * 57 = 342 sum of the last 8 of them = 8 * 61 = 488 so , the 8 th number = 342 + 488 - 780 = 50 . answer : c\"" + }, + { + "Answer": 8, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", + "Correct": "b", + "Explanation": "\"let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 22 5 x = 20 = > x = 4 hence , b ' s age = 2 x = 8 years . answer : b\"" + }, + { + "Answer": 347.7, + "Options": "a ) $ 341.50 , b ) $ 344.60 , c ) $ 347.70 , d ) $ 350.80 , e ) $ 353.90", + "Correct": "c", + "Explanation": "\"the service cost of 3 vans and 2 trucks is 5 * 2.20 $ 11.00 the fuel in 3 vans is 3 * 65 = 195 liters the fuel in 2 trucks is 2 * 65 * 2.2 = 286 liters the total fuel ( vans + trucks ) = 481 liters the total fuel cost is 481 * 0.7 = $ 336.70 the total cost is $ 336.70 + $ 11.00 = $ 347.70 the answer is c .\"" + }, + { + "Answer": 70, + "Options": "a ) 20 % , b ) 30 % , c ) 40 % , d ) 70 % , e ) 80 %", + "Correct": "d", + "Explanation": "\"the is always the difference between our starting and ending points . in this case , it \u2019 s 100 \u2013 30 = 70 . the \u201c original \u201d is our starting point ; in this case , it \u2019 s 100 . ( 70 / 100 ) * 100 = ( 0.7 ) * 100 = 70 % . d\"" + }, + { + "Answer": 4, + "Options": "a ) 5 , b ) 3 , c ) 2 , d ) 4 , e ) 0", + "Correct": "d", + "Explanation": "\"5 \u201d 3 = 9 - 5 = 4 answer : d\"" + }, + { + "Answer": 30, + "Options": "a ) 31 , b ) 32 , c ) 35 , d ) 30 , e ) 45", + "Correct": "d", + "Explanation": "\"explanation : hcf ( 408 , 312 ) = 24 the number of boys or girls that can be placed in a section = 24 . thus the total number of sections is given by 408 / 24 + 312 / 24 = 17 + 13 = 30 answer : d\"" + }, + { + "Answer": 70, + "Options": "a ) 35 yrs , b ) 40 yrs , c ) 50 yrs , d ) 60 yrs , e ) 70 yrs", + "Correct": "e", + "Explanation": "\"let b ' s present age = x years then a ' s present age = x + 10 years x + 10 + 20 = 2 ( x - 20 ) x + 30 = 2 x - 40 x = 70 years answer is e\"" + }, + { + "Answer": 945, + "Options": "a ) $ 945 , b ) $ 965 , c ) $ 1025 , d ) $ 1050 , e ) $ 1105", + "Correct": "a", + "Explanation": "\"90 % remains to be paid so the remaining amount is 9 * 105 = $ 945 . the answer is a .\"" + }, + { + "Answer": 500, + "Options": "a ) 100 , b ) 200 , c ) 500 , d ) 1000 , e ) 5000", + "Correct": "c", + "Explanation": "5.4 * 10 ^ 6 / 10800 = = > 54 * 10 ^ 3 / 108 = = > 54000 / 108 = 500 answer : c" + }, + { + "Answer": 25, + "Options": "a ) 12.5 % , b ) 20 % , c ) 25 % , d ) 50 % , e ) 100 %", + "Correct": "c", + "Explanation": "\"correct answer : c solution : c . we can set up equations for income before and after the wage reduction . initially , the employee earns w wage and works h hours per week . after the reduction , the employee earns . 8 w wage and works x hours . by setting these equations equal to each other , we can determine the increase in hours worked : wh = . 8 wx ( divide both sides by . 8 w ) 1.25 h = x we know that the new number of hours worked r will be 25 % greater than the original number . the answer is c .\"" + }, + { + "Answer": 4891, + "Options": "a ) 4857 , b ) 4184 , c ) 4012 , d ) 4891 , e ) 5291", + "Correct": "d", + "Explanation": "\"let the sale in the sixth month = x then ( 6535 + 6927 + 6855 + 7230 + 6562 + x ) / 6 = 6500 = > 6535 + 6927 + 6855 + 7230 + 6562 + x = 6 \u00d7 6500 = > 34109 + x = 39000 = > x = 39000 \u2212 34109 = 4891 answer : d\"" + }, + { + "Answer": 300, + "Options": "a ) 110 , b ) 111 , c ) 271 , d ) 300 , e ) 304", + "Correct": "d", + "Explanation": "another approach : in the range 0 - 100 : 7 as units digit - 10 times ( 7 , 17 , 27 , . . . , 97 ) ; 7 as tens digit - 10 time ( 71 , 72 , 73 , . . . , 79 ) ; so in first one hundred numbers 7 is written 10 + 10 = 20 times . in 10 hundreds 7 as units or tens digit will be written 10 * 20 = 200 times . plus 100 times when 7 is written as hundreds digit ( 700 , 701 , 702 , . . . , 799 ) . total 200 + 100 = 300 . answer : d ." + }, + { + "Answer": 4700, + "Options": "a ) 2177 , b ) 2876 , c ) 4700 , d ) 2981 , e ) 2711", + "Correct": "c", + "Explanation": "\"sum of the salaries of the person for the months of january , february , march and april = 4 * 8000 = 32000 - - - - ( 1 ) sum of the salaries of the person for the months of february , march , april and may = 4 * 8450 = 33800 - - - - ( 2 ) ( 2 ) - ( 1 ) i . e . may - jan = 1800 salary of may is rs . 6500 salary of january = rs . 4700 . answer : c\"" + }, + { + "Answer": 100.00000000000003, + "Options": "a ) 60 , b ) 80 , c ) 100 , d ) 120 , e ) 140", + "Correct": "c", + "Explanation": "\"let the number be x . ( 5 / 4 ) * x = ( 4 / 5 ) * x + 45 25 x = 16 x + 900 9 x = 900 x = 100 the answer is c .\"" + }, + { + "Answer": 128, + "Options": "a ) 125 , b ) 126 , c ) 127 , d ) 128 , e ) 129", + "Correct": "d", + "Explanation": "2 ^ 3 + 7 ^ 2 = 57 3 ^ 3 + 6 ^ 2 = 63 5 ^ 3 + 9 ^ 2 = 206 and 4 ^ 3 + 8 ^ 2 = 128 answer : d" + }, + { + "Answer": 12, + "Options": "a ) 6 , b ) 12 , c ) 24 , d ) 36 , e ) 48", + "Correct": "b", + "Explanation": "\"q : if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer q that must divide n is : a 6 , b 12 , c 24 , d 36 , e 48 n ^ 2 is divisible by 72 , but it must also be greater than 72 . if n is an integer , then n ^ 2 must be a perfect square . the factorization of 72 is ( 8 ) ( 9 ) , so if it is multiplied by 2 , it will be ( 2 ) ( 8 ) ( 9 ) = ( 16 ) ( 9 ) = 144 , a perfect square . so n ^ 2 must be at least 144 or a multiple of 144 , which means that n must be 12 or a multiple of 12 . b\"" + }, + { + "Answer": 4.000000000000002, + "Options": "a ) . 25 , b ) . 235 , c ) 4 , d ) 3 , e ) 2", + "Correct": "c", + "Explanation": "\"( 2.502 + 0.064 ) 2 - ( 2.502 - 0.064 ) 2 / 2.502 * 0.064 = ( a + b ) 2 - ( a - b ) / ab = 4 ab / ab = 4 answer : c\"" + }, + { + "Answer": 20, + "Options": "a ) 50 , b ) 78 , c ) 267 , d ) 20 , e ) 27", + "Correct": "d", + "Explanation": "a + b + c = 500 a + c = 200 b + c = 320 - - - - - - - - - - - - - - a + b + 2 c = 520 a + b + c = 500 - - - - - - - - - - - - - - - - c = 20 answer : d" + }, + { + "Answer": 0.6666666666666667, + "Options": "a ) 2 / 3 , b ) 29 / 60 , c ) 17 / 30 , d ) 19 / 30 , e ) 11 / 15", + "Correct": "a", + "Explanation": "\"let s assume the platinum card spending limit = x gold card spending limit will be = x / 2 balance on gold card is = x / 2 * 1 / 3 = x / 6 platinum card unspent limit is = x - 1 / 6 x = 5 / 6 x so if gold card balance is transferred then the rest unspent will be 5 / 6 x - x / 6 = 2 / 3 x so the ans is a\"" + }, + { + "Answer": 33, + "Options": "a ) 31 kg , b ) 32 kg , c ) 33 kg , d ) 34 kg , e ) none of these", + "Correct": "c", + "Explanation": "\"explanation : let a , b , c represent their respective weights . then , we have : a + b + c = ( 45 x 3 ) = 135 \u2026 . ( i ) a + b = ( 40 x 2 ) = 80 \u2026 . ( ii ) b + c = ( 44 x 2 ) = 88 \u2026 . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 168 \u2026 . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 33 . b \u2019 s weight = 33 kg . answer : c\"" + }, + { + "Answer": 13, + "Options": "a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17", + "Correct": "a", + "Explanation": "1000 + 200 x = 3600 x = 13 cars . the answer is a ." + }, + { + "Answer": 0.13636363636363635, + "Options": "a ) 1 / 22 , b ) 1 / 19 , c ) 3 / 19 , d ) 2 / 19 , e ) 3 / 22", + "Correct": "e", + "Explanation": "\"we have the ratio of a \u2019 s speed and b \u2019 s speed . this means , we know how much distance a covers compared with b in the same time . this is what the beginning of the race will look like : ( start ) a _________ b ______________________________ if a covers 22 meters , b covers 19 meters in that time . so if the race is 22 meters long , when a reaches the finish line , b would be 3 meters behind him . if we want the race to end in a dead heat , we want b to be at the finish line too at the same time . this means b should get a head start of 3 meters so that he doesn \u2019 t need to cover that . in that case , the time required by a ( to cover 22 meters ) would be the same as the time required by b ( to cover 19 meters ) to reach the finish line . so b should get a head start of 3 / 22 th of the race . answer ( e )\"" + }, + { + "Answer": 94, + "Options": "a ) 94 kg , b ) 95 kg , c ) 96 kg , d ) 97 kg , e ) 98 kg", + "Correct": "a", + "Explanation": "total weight increased = 8 x 3 kg = 24 kg . weight of new person = 70 + 24 kg = 94 kg answer : a" + }, + { + "Answer": 95, + "Options": "a ) 92 , b ) 95 , c ) 98 , d ) 101 , e ) 104", + "Correct": "b", + "Explanation": "\"k - 32 = 9 t / 5 k = 9 t / 5 + 32 k = 9 ( 35 ) / 5 + 32 = 95 the answer is b .\"" + }, + { + "Answer": 10, + "Options": "a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18", + "Correct": "a", + "Explanation": "\"legs 10 * 4 = 40 now half on their horses so remaining on the walk so 5 men 5 men has 10 legs so , 10 + 40 = 50 legs walking answer : a\"" + }, + { + "Answer": 1994, + "Options": "a ) 1992 , b ) 1993 , c ) 1994 , d ) 1995 , e ) 1996", + "Correct": "e", + "Explanation": "let the no of years it takes is x . 540 + 30 x = 780 - 10 x - - > 40 x = 240 and x = 6 . thus , it happens in 1996 . e ." + }, + { + "Answer": 19, + "Options": "a ) 19 , b ) 20 , c ) 21 , d ) 22 , e ) 23", + "Correct": "a", + "Explanation": "3 numbers containing 3 - - - > 3 , 1323 , . . . = 10 numbers - - - - > 30 , 3132 . . . = 10 numbers total = 20 - 1 = 19 answer : a" + }, + { + "Answer": 4, + "Options": "a ) 24 , b ) 12 , c ) 8 , d ) 2 , e ) 4", + "Correct": "e", + "Explanation": "\"in this question however , because we are told that exactly 64 frisbees have been sold and revenue was exactly $ 204 , there is only one possible solution for the number of $ 3 and $ 4 frisbees sold . to solve , we have 2 equations and 2 unknowns let x = number of $ 3 frisbees sold let y = number of $ 4 frisbees sold x + y = 64 3 x + 4 y = 196 x = 64 - y 3 ( 64 - y ) + 4 y = 196 192 - 3 y + 4 y = 196 y = 4 answer : e\"" + }, + { + "Answer": 1.5, + "Options": "a ) 2 , b ) 3 / 2 , c ) 4 , d ) 5 , e ) can not be determined from the information given .", + "Correct": "b", + "Explanation": "the average of three integers a , b , and c is exactly twice the median - - > ( a + b + c ) / 3 = 1 b / 2 - - > since a = 0 , then ( 0 + b + c ) / 3 = 1 b / 2 - - > c = 3 b / 2 - - > c / b = 3 / 2 . answer : b ." + }, + { + "Answer": 72, + "Options": "a ) 48 , b ) 54 , c ) 60 , d ) 66 , e ) 72", + "Correct": "e", + "Explanation": "\"we see that h will be a maximum h = 120 when t - 3 = 0 , that is when t = 3 . at t = 5 , h = - 12 * ( 5 - 3 ) ^ 2 + 120 = - 12 ( 4 ) + 120 = 72 the answer is e .\"" + }, + { + "Answer": 10, + "Options": "a ) 46 , b ) 10 , c ) 56 , d ) - 46 , e ) 28", + "Correct": "b", + "Explanation": "\"there will be two cases x - 5 = 23 and x - 5 = - 23 solve for x = > x = 23 + 5 = > x = 28 or x = - 23 + 5 = > x = - 18 the sum of both values will be 28 + - 18 = 10 answer is b\"" + }, + { + "Answer": 1936, + "Options": "a ) 76 , b ) 1936 , c ) 1304 , d ) 1296 , e ) none", + "Correct": "b", + "Explanation": "answer let \u221a n / 11 = 4 then \u221a n = 11 x 4 = 44 \u2234 n = 44 x 44 = 1936 . correct option : b" + }, + { + "Answer": 0.39999999999999997, + "Options": "a ) $ 015 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45", + "Correct": "d", + "Explanation": "\"on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.6 = 3 * x - - > x = $ 0.4 . answer : d .\"" + }, + { + "Answer": 24, + "Options": "a ) 22 , b ) 24 , c ) 26 , d ) 20 , e ) 28", + "Correct": "b", + "Explanation": "\"explanation : let number of hens = h and number of cows = c number of heads = 44 = > h + c = 44 - - - ( equation 1 ) number of feet = 128 = > 2 h + 4 c = 128 = > h + 2 c = 64 - - - ( equation 2 ) ( equation 2 ) - ( equation 1 ) gives 2 c - c = 64 - 44 = > c = 20 substituting the value of c in equation 1 , we get h + 22 = 44 = > h = 44 - 20 = 24 i . e . , number of hens = 24 answer : b\"" + }, + { + "Answer": 90, + "Options": "a ) 70 , b ) 80 , c ) 90 , d ) 100 , e ) 110", + "Correct": "c", + "Explanation": "( 4 * 85 + x ) / 5 = 86 x = ( 5 * 86 ) - ( 4 * 85 ) x = 430 - 340 total score required 430 - 340 = 90 correct answer is c" + }, + { + "Answer": 0.76, + "Options": "a ) 0.86 , b ) 0.68 , c ) 0.96 , d ) 0.69 , e ) 0.76", + "Correct": "e", + "Explanation": "given expression = ( 0.86 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.86 ) ( power 2 ) + ( 0.86 x 0.1 ) + ( 0.1 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 0.86 - 0.1 ) = 0.76 answer is e" + }, + { + "Answer": 250, + "Options": "a ) 100 , b ) 250 , c ) 300 , d ) 400 , e ) 500", + "Correct": "b", + "Explanation": "\"since 150 students answered yes only for subject m , then the remaining 350 students who answered yes for subject m , also answered yes for subject r . so , 350 students answered yes for both subjects . if 350 students answered yes for both subjects , then 400 - 350 = 50 students answered yes only for subject r . so , we have that : 200 students answered yes only for subject m ; 50 students answered yes only for subject r ; 300 students answered yes for both subjects ; therefore 800 - ( 200 + 50 + 300 ) = 250 students did not answer yes for either subject . answer : b .\"" + }, + { + "Answer": 2, + "Options": "a ) 3 , b ) 2 , c ) 4 , d ) 1 , e ) 0", + "Correct": "b", + "Explanation": "since 653 xy is divisible by 5 as well as 2 . so y = 0 now 653 x 0 must be divisible by 8 so 3 x 0 must be 8 this happens when x = 2 hence , x + y = 2 + 0 = 2 answer b 2" + }, + { + "Answer": 30, + "Options": "a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50", + "Correct": "c", + "Explanation": "\"450 = 2 * 3 ^ 2 * 5 ^ 2 if 450 divides n ^ 2 , then n must be divisible by 2 * 3 * 5 = 30 the answer is c .\"" + }, + { + "Answer": 720, + "Options": "a ) 1250 , b ) 625 , c ) 600 , d ) 7500 , e ) 720", + "Correct": "e", + "Explanation": "\"max no . of crates = 6 . max weight = 120 kg max . weight carried = 6 * 120 = 720 kg = e\"" + }, + { + "Answer": 65, + "Options": "a ) 75 kg , b ) 65 kg , c ) 85 kg , d ) 80 kg , e ) 60 kg", + "Correct": "b", + "Explanation": "\"explanation : total increase in weight = 8 \u00e3 \u2014 2.5 = 20 if x is the weight of the new person , total increase in weight = x \u00e2 \u02c6 \u2019 45 = > 20 = x - 45 = > x = 20 + 45 = 65 answer : option b\"" + }, + { + "Answer": 20, + "Options": "a ) 12 , b ) 16 , c ) 20 , d ) 32 , e ) 48", + "Correct": "c", + "Explanation": "\"3.456789 ^ 10 has 6 * 10 = 60 decimal places . 10 ^ 40 moves the decimal place to the right 40 places . ( 10 ^ 4 * 3.456789 ) ^ 10 has 60 - 40 = 20 digits after the decimal point . the answer is c .\"" + }, + { + "Answer": 21, + "Options": "a ) 7 , b ) 14 , c ) 21 , d ) 28 , e ) 35", + "Correct": "c", + "Explanation": "\"in 63 liters of drink a , there are 36 liters of milk and 27 liters of juice . with 36 liters of milk , we need a total of 48 liters of juice to make drink b . we need to add 21 liters of juice . the answer is c .\"" + }, + { + "Answer": 4, + "Options": "a ) 3 , b ) 3.5 , c ) 4 , d ) 4.5 , e ) 5", + "Correct": "c", + "Explanation": "222 - 198 = 24 pounds lost in 12 months 24 / 12 = 2 , so joe is losing weight at a rate of 2 pounds per month . . . . in approximately how many months will he weigh 190 pounds ? a simple approach is to just list the weights . now : 198 lbs in 1 month : 196 lbs in 2 months : 194 lbs in 3 months : 192 lbs in 4 months : 190 lbs answer : c" + }, + { + "Answer": 24, + "Options": "a ) $ 5 , b ) $ 10 , c ) $ 14 , d ) $ 24 , e ) $ 28", + "Correct": "d", + "Explanation": "\"bill = fixed charge + charge of calls made in jan , bill = fixed charge ( let , y ) + charge of calls made in jan ( let , x ) = $ 50 in feb , bill = fixed charge ( let , y ) + charge of calls made in feb ( then , 2 x ) = $ 76 i . e . x + y = 50 and 2 x + y = 76 take the difference if two equations i . e . ( 2 x + y ) - ( x + y ) = 76 - 50 i . e . x = 26 i . e . fixed monthly charge , y = 26 answer : d\"" + }, + { + "Answer": 12000, + "Options": "a ) 12028 , b ) 12000 , c ) 12019 , d ) 12197 , e ) 18000", + "Correct": "c", + "Explanation": "[ 1300 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 600 x = 18000 answer : c" + }, + { + "Answer": 5.25, + "Options": "a ) $ 1.50 , b ) $ 2.50 , c ) $ 5.25 , d ) $ 4.50 , e ) $ 5.50", + "Correct": "c", + "Explanation": "the jelly is extra information . 14.00 \u00e2 \u20ac \u201c 3 x 2.25 \u00e2 \u20ac \u201c 2.00 = 14.00 \u00e2 \u20ac \u201c 6.75 \u00e2 \u20ac \u201c 2.00 = 5.25 . you have $ 5.25 left . correct answer c" + }, + { + "Answer": 1.2, + "Options": "a ) 1.9 , b ) 1.7 , c ) 1.2 , d ) 1.5 , e ) 1.1", + "Correct": "c", + "Explanation": "\"speed of boat in still water ( b ) = 3.6 km / hr . speed of boat with stream ( down stream ) , d = b + u speed of boat against stream ( up stream ) , u = b \u2013 u it is given upstream time is twice to that of down stream . \u21d2 downstream speed is twice to that of upstream . so b + u = 2 ( b \u2013 u ) \u21d2 u = b / 3 = 1.2 km / hr . answer : c\"" + }, + { + "Answer": 20.000000000000004, + "Options": "a ) 2 minutes , b ) 10 minutes , c ) 20 minutes , d ) 40 minutes , e ) 60 minutes", + "Correct": "c", + "Explanation": "\"lets take number of minutesx . given that , 11 + 0.25 x = 12 + 0.2 x - > 0.05 x = 2 - > x = 20 minutes ans c\"" + }, + { + "Answer": 1683, + "Options": "a ) 1677 , b ) 1683 , c ) 2523 , d ) 3363 , e ) none of these", + "Correct": "b", + "Explanation": "solution l . c . m . of 5 , 6 , 7 , 8 = 840 . so , required number is of the form 840 k + 3 . least value of k for which ( 840 k + 3 ) is divisible by 9 is k = 2 . so , required number = ( 840 \u00d7 2 + 3 ) = 1683 . answer b" + }, + { + "Answer": 240, + "Options": "a ) 90 , b ) 110 , c ) 120 , d ) 130 , e ) 240", + "Correct": "e", + "Explanation": "\"orchestra seats - a balcony seats - b a + b = 380 and 12 a + 8 b = 3320 solving equations simultaneously ( multiply equation 1 with 8 and subtract from second equation ) 4 a = 3320 - 8 * 380 = 3320 - 3040 = 280 i . e . a = 70 and b = 380 - 70 = 310 more seats in balcony than orchestra = b - a = 310 - 70 = 240 answer : option e\"" + }, + { + "Answer": 2.727272727272727, + "Options": "a ) 7 / 30 , b ) 11 / 30 , c ) 11 / 15 , d ) 30 / 11 , e ) 15 / 11", + "Correct": "d", + "Explanation": "1 / r = 1 / x + 1 / y 1 / r = 1 / 5 + 1 / 6 = 11 / 30 r = 30 / 11 the answer is d ." + }, + { + "Answer": 2500, + "Options": "a ) 2500 , b ) 2000 , c ) 1600 , d ) 4545 , e ) 6565", + "Correct": "a", + "Explanation": "detailed solution let the number of appearing students be 100 . pass only in 0 topic \u2013 10 1 \u2013 16 ( 20 % of 80 ) 2 \u2013 20 ( 25 % of 80 ) 3 \u2013 20 % ( 100 \u2013 ( 16 + 20 + 24 + 20 ) ) 4 \u2013 24 % 5 \u2013 20 % therefore , 20 % of x = 500 = ) x = 2500 correct answer : a" + }, + { + "Answer": 20, + "Options": "a ) 10 , b ) 30 , c ) 50 , d ) 20 , e ) 30", + "Correct": "d", + "Explanation": "\"explanation : milk : water = 3 : 2 after adding 10 liters of water milk : water = 2 : 3 olny water patrs increase when mixture of water milk : wate = 3 : 2 = 2 * ( 3 : 2 ) = 6 : 4 after adding 10 liters of water milk : water = 2 : 3 = 3 * ( 2 : 3 ) = 6 : 9 milk parts always same short cut method : milk : water = 6 : 4 after adding 10 liters of water milk : water = 6 : 9 milk is same but water increse 10 liters then the water ratio is increse 5 parts 5 part - - - - - > 10 liters the quantity of milk in the original mixture is = 6 : 4 = 6 + 4 = 10 10 parts - - - - - > 20 liters ( answer is = 20 ) short cut method - 2 : for only milk problems milk : water 6 : 4 6 : 9 milk ratio same but water ratio 5 parts incress per 10 liters 5 part of ratio - - - - - - - > 10 liters 10 part of ratio - - - - - - > 20 liters answer : option d\"" + }, + { + "Answer": 37, + "Options": "a ) 35 , b ) 37 , c ) 42 , d ) 30 , e ) 38", + "Correct": "b", + "Explanation": "\"the number of liters in each can = hcf of 80 , 144 and 368 = 16 liters . number of cans of maaza = 80 / 16 = 5 number of cans of pepsi = 144 / 16 = 9 number of cans of sprite = 368 / 16 = 23 the total number of cans required = 5 + 9 + 23 = 37 cans . answer : b\"" + }, + { + "Answer": 528.0642570281125, + "Options": "a ) 505 , b ) 515 , c ) 525 , d ) 538 , e ) 567", + "Correct": "c", + "Explanation": "\"explanation : ? = ( 112 x 2348 / 100 ) \u00f7 5 = 2630 / 5 = 526 = 525 answer : option c\"" + }, + { + "Answer": 400, + "Options": "a ) 387 , b ) 400 , c ) 776 , d ) 268 , e ) 181", + "Correct": "b", + "Explanation": "\"441 = p ( 21 / 20 ) 2 p = 400 answer : b\"" + }, + { + "Answer": 0.4, + "Options": "a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 2 / 5", + "Correct": "e", + "Explanation": "\"for n ( n + 1 ) to be a multiple of 5 , either n or n + 1 has to be a multiple of 5 . thus n must be of the form 5 k or 5 k - 1 . the probability is 2 / 5 . the answer is e .\"" + }, + { + "Answer": 5095, + "Options": "a ) 5200 , b ) 5150 , c ) 5250 , d ) 6150 , e ) 5095", + "Correct": "e", + "Explanation": "explanation : = 5100 \u2212 ( 102 / 204 \u00d7 10 ) = 5100 \u2212 5 = 5095 option e" + }, + { + "Answer": 31, + "Options": "a ) 27 , b ) 29 , c ) 28 , d ) 30 , e ) 31", + "Correct": "e", + "Explanation": "\"13603 \u00f7 87 = 156 , remainder = 31 hence 31 is the least number which can be subtracted from 13603 such that the remainder is divisible by 87 answer is e\"" + }, + { + "Answer": 1600, + "Options": "a ) rs . 1000 , b ) rs . 1200 , c ) rs . 1400 , d ) rs . 1600 , e ) rs . 2500", + "Correct": "d", + "Explanation": "explanation : total simple interest received , i = rs . 1600 principal , p = 7000 period , n = 5 years rate of interest , r = ? simple interest , i = p n r 100 i = pnr 100 \u21d2 1600 = 7000 \u00d7 5 \u00d7 r 100 \u21d2 r = 1600 \u00d7 100 7000 \u00d7 5 = 160 35 = 32 7 % \u21d2 1600 = 7000 \u00d7 5 \u00d7 r 100 \u21d2 r = 1600 \u00d7 1007000 \u00d7 5 = 16035 = 327 % by rule of alligation , rate of interest % from part 1 rate of interest % from part 2 6 4 net rate of interest % 32 7 327 32 7 \u2212 4 = 4 7 327 \u2212 4 = 47 6 \u2212 32 7 = 10 7 6 \u2212 327 = 107 = > part 1 : part 2 = 4 7 : 10 7 = 4 : 10 = 2 : 5 = 47 : 107 = 4 : 10 = 2 : 5 given that total amount is rs . 7000 . therefore , the amount lent at 6 % per annum ( part 1 amount ) = 7000 \u00d7 2 7 = rs . 2000 d )" + }, + { + "Answer": 860, + "Options": "a ) $ 860 , b ) $ 850 , c ) $ 840 , d ) $ 830 , e ) $ 820", + "Correct": "a", + "Explanation": "\"50 pages typed 1 x 35 pages typed 2 x ( original + one revision ) 15 pages typed 3 x ( original + two revisions ) 50 ( 6 ) + 35 ( 6 + 4 ) + 15 ( 6 + 4 + 4 ) = 300 + 350 + 210 = 860 answer - a\"" + }, + { + "Answer": 0.15789473684210525, + "Options": "a ) 12 / 112 , b ) 6 / 81 , c ) 11 / 61 , d ) 12 / 33 , e ) 3 / 19", + "Correct": "e", + "Explanation": "\"let us say probability of a occuring is a . let us say probability of b occuring is b . a = 2 b probability ( either a or b or both ) = 8 times probability ( a and b ) a * ( 1 - b ) + b * ( 1 - a ) + ab = 18 * ab substituting a = 2 b in the second equation : 2 b * ( 1 - b ) + b * ( 1 - 2 b ) + 2 b * b = 18 * 2 b * b 3 b - 2 b ^ 2 = 36 b ^ 2 3 b = 38 b ^ 2 b = 3 / 38 so , a = 2 b = 6 / 38 = 3 / 19 the correct answer is e .\"" + }, + { + "Answer": 8, + "Options": "a ) 12 , b ) 16 , c ) 8 , d ) 24 , e ) 26", + "Correct": "c", + "Explanation": "explanation : suppose the boy got x sums right and 2 x sums wrong . then , x + 2 x = 24 3 x = 24 x = 8 . answer : c" + }, + { + "Answer": 38, + "Options": "a ) 35 kg , b ) 37 kg , c ) 42 kg , d ) 38 kg , e ) 29.78 kg", + "Correct": "d", + "Explanation": "\"total weight of 36 + 44 students = 30 * 40 + 20 * 35 = 1900 average weight of the class is = 1900 / 50 = 38 kg answer is d\"" + }, + { + "Answer": 9.237333333333334, + "Options": "a ) 0.092 , b ) 0.92 , c ) 9.2 , d ) 92 , e ) 920", + "Correct": "c", + "Explanation": "\"d ( 69.28 \u00d7 0.004 ) / 0.03 1 . 0.004 = 4 \u00d7 10 ^ ( - 3 ) 2 . 0.03 = 3 \u00d7 10 ^ ( - 2 ) 3 . ( a \u00d7 b ) / c = a \u00d7 ( b / c ) 4 . 0.004 / 0.03 = 4 \u00d7 10 ^ ( - 3 ) / ( 3 \u00d7 10 ^ ( - 2 ) ) = 4 \u00d7 10 ^ ( - 3 - ( - 2 ) ) / 3 = 4 \u00d7 10 ^ ( - 1 ) / 3 = ( 4 / 3 ) \u00d7 10 ^ ( - 1 ) = 1.333 \u00d7 10 ^ ( - 1 ) therefore , ( 69.28 \u00d7 0.004 ) / 0.03 = 69.28 \u00d7 ( 0.004 / 0.03 ) = 69.28 \u00d7 1.33 \u00d7 10 ^ ( - 1 ) = 69.28 \u00d7 1.33 / 10 = 6.928 * 1.33 now , 7 \u00d7 2 = 14 7 \u00d7 1 = 7 or better : 6.9 \u00d7 1 = 6.9 6.9 \u00d7 2 = 13.8 hence , 6.9 < 6.928 \u00d7 1.33 < 13.8 9.2 is the only answer that satisfies this condition . c\"" + }, + { + "Answer": 25, + "Options": "a ) 10 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 50 %", + "Correct": "c", + "Explanation": "\"let original salary be $ 100 new final salary = 150 % of ( 50 % of $ 100 ) = ( 150 / 100 ) * ( 50 / 100 ) * 100 = $ 75 decrease = 25 % correct option is c\"" + }, + { + "Answer": 40, + "Options": "a ) 35 , b ) 15 , c ) 40 , d ) 52 , e ) 14", + "Correct": "c", + "Explanation": "c let the sum of nine member ( total ) = x and the age of old one = z so its average 4 yrs before = ( x + z ) / 10 . after 4 yrs let z be replaced by y . so now avg = ( x + 4 * 10 + y ) / 10 now ( x + z ) / 10 = ( x + 40 + y ) / 10 so after solving it found z = y + 40 . so old person is 40 yrs older than young one ." + }, + { + "Answer": 900, + "Options": "a ) 800 , b ) 900 , c ) 1000 , d ) 1100 , e ) 1200", + "Correct": "b", + "Explanation": "\"0.75 * 600 = 0.5 * x x = 7.5 / 5 * 600 = 900\"" + }, + { + "Answer": 400, + "Options": "a ) 400 , b ) 400 , c ) 445 , d ) 465 , e ) none of the above", + "Correct": "b", + "Explanation": "let the original average expenditure be ` x . then , 42 ( x \u2013 1 ) \u2013 35 x = 42 \u21d4 7 x = 84 \u21d2 x = 12 . \u2234 original expenditure = ( 35 \u00d7 12 ) = 420 . answer b" + }, + { + "Answer": 35.91, + "Options": "a ) $ 22 , b ) $ 23.94 , c ) $ 36 , d ) $ 25.20 , e ) $ 30", + "Correct": "c", + "Explanation": "soln : - 945 / 25 = x + 0.05 x 945 / 25 = 1.05 x x = 36 answer : c" + }, + { + "Answer": 60.5, + "Options": "a ) 55.5 , b ) 61.5 , c ) 53.5 , d ) 78.5 , e ) 60.5", + "Correct": "e", + "Explanation": "\"( 11 + 22 + . . . + 110 ) / 10 = 11 ( 1 + 2 + . . . + 10 ) / 10 = 11 ( 10 ) ( 11 ) / ( 10 * 2 ) = 121 / 2 = 60.5 option e\"" + }, + { + "Answer": 77, + "Options": "a ) 45 , b ) 65 , c ) 77 , d ) 89 , e ) 90", + "Correct": "c", + "Explanation": "\"a + b + c = 3 * 84 = 252 a + b + c + d = 4 * 80 = 320 - - - - ( i ) so , d = 68 & e = 68 + 5 = 73 b + c + d + e = 79 * 4 = 316 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 320 \u2013 316 = 4 a = e + 4 = 73 + 4 = 77 c\"" + }, + { + "Answer": 24, + "Options": "a ) 20 , b ) 24 , c ) 36 , d ) 48 , e ) 96", + "Correct": "b", + "Explanation": "we are given that golds gym class can be divided into 8 teams or 12 teams , with an equal number of players on each team . translating this into two mathematical expressions we can say , where g is the total number of students in the gym class , that : g / 8 = integer and g / 12 = integer this means that g is a multiple of both 8 and 12 . we are asked to determine the lowest number of students in the class , or the lowest value for variable \u201c g \u201d . because we know that g is a multiple of 8 and of 12 , we need to find the least common multiple of 8 and 12 . although there are technical ways for determining the least common multiple , the easiest method is to analyze the multiples of 8 and 12 until we find one in common . starting with 8 , we have : 8 , 16 , 24 , 32 for 12 , we have : 12 , 24 for the multiples of 12 , we stopped at 24 , because we see that 24 is also a multiple of 8 . thus , 24 is the least common multiple of 8 and 12 , and therefore we know that the lowest possible number of students in the gym class is 24 . answer b ." + }, + { + "Answer": 1399.9999999999998, + "Options": "a ) 1000 , b ) 2777 , c ) 2889 , d ) 1400 , e ) 2771", + "Correct": "d", + "Explanation": "\"1568 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 1400 . answer : d\"" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 2 , c ) - 1 , d ) - 3 , e ) - 4", + "Correct": "c", + "Explanation": "\"c - 1 19 x + 19 y + 17 = - 19 x + 19 y - 21 38 x = - 38 = > x = - 1\"" + }, + { + "Answer": 720, + "Options": "a ) 720 , b ) 830 , c ) 940 , d ) 1050 , e ) 1160", + "Correct": "a", + "Explanation": "6 ! = 720 the answer is a ." + }, + { + "Answer": 0.05, + "Options": "a ) 1 / 19 , b ) 3 / 19 , c ) 1 / 10 , d ) 1 / 20 , e ) 3 / 10", + "Correct": "d", + "Explanation": "\"let d be the full distance . let x be the fraction of the distance that b runs . let v be the speed at which b runs . the time should be the same for both runners . time = d / ( 20 v / 19 ) = xd / v ( 19 / 20 ) * d / v = x * d / v x = 19 / 20 b should have a head start of 1 / 20 of the full distance . the answer is d .\"" + }, + { + "Answer": 1, + "Options": "a ) 5 , b ) 3 , c ) 1 , d ) 7 , e ) 9", + "Correct": "c", + "Explanation": "solution : 1 as stated 1 = 6 = > 6 = 1 answer c" + }, + { + "Answer": 6000, + "Options": "a ) 2000 , b ) 4000 , c ) 5000 , d ) 6000 , e ) none", + "Correct": "d", + "Explanation": "sol . let c = x . then , b = 4 x and 2 a = 3 * 4 x = 12 x or a = 6 x . \u2234 a : b : c = 6 x : 4 x : x = 6 : 4 : 1 . so , b \u2019 s capital = rs . [ 16500 * 4 / 11 ] = rs . 6000 . answer d" + }, + { + "Answer": 60, + "Options": "a ) 62 kg , b ) 60 kg , c ) 70 kg , d ) 72 kg , e ) none of these", + "Correct": "b", + "Explanation": "\"explanation : let the weight of student be x kg . given , difference in average weight = 6 kg = > ( 120 - x ) / 10 = 6 = > x = 60 answer : b\"" + }, + { + "Answer": 36, + "Options": "a ) 35 , b ) 36 , c ) 37 , d ) 38 , e ) 39", + "Correct": "b", + "Explanation": "\"james worked for 41 hours hence he earned 40 * x + 1 * 2 x = 42 x dollars ; we know that harry also earned the same 42 x dollars , out of which he earned 30 x dollars for thefirst 30 hoursplus 12 x additional dollars . since for each additional hour he gets 2 x dollars then he worked for 12 x / 2 x = 6 additional hours , so harry worked for total of 30 + 6 = 36 hours . answer : b .\"" + }, + { + "Answer": 30, + "Options": "a ) 20 , b ) 30 , c ) 60 , d ) 70 , e ) 10", + "Correct": "b", + "Explanation": "b 30 let the three numbers be x , y and z . sum of the numbers is 98 . x + y + z = 98 \u2026 \u2026 \u2026 \u2026 \u2026 \u2026 ( i ) the ratio of the first to the second is 2 / 3 . x / y = 2 / 3 . x = 2 / 3 \u00d7 y . x = 2 y / 3 . the ratio of the second to the third is 5 / 8 . y / z = 5 / 8 . z / y = 8 / 5 . z = 8 / 5 \u00d7 y . z = 8 y / 5 . put the value of x = 2 y / 3 and z = 8 y / 5 in ( i ) . 2 y / 3 + y + 8 y / 5 = 98 49 y / 15 = 98 . 49 y = 98 \u00d7 15 . 49 y = 1470 . y = 1470 / 49 . y = 30 . therefore , the second number is 30 ." + }, + { + "Answer": 6, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 6", + "Correct": "e", + "Explanation": "\"( 55 ) ( 57 ) = ( 56 - 1 ) ( 56 + 1 ) = 56 ^ 2 - 1 which is 1 less than a multiple of 7 . then the remainder will be 6 . the answer is e .\"" + }, + { + "Answer": 0.55, + "Options": "a ) 2 / 3 , b ) 3 / 5 , c ) 7 / 10 , d ) 9 / 20 , e ) 11 / 20", + "Correct": "e", + "Explanation": "\"p ( red or blue ) = 1 - p ( white ) - p ( green ) = 20 / 20 - 5 / 20 - 4 / 20 = 11 / 20 the answer is e .\"" + }, + { + "Answer": 7, + "Options": "a ) $ 9 , b ) $ 3 , c ) $ 7 , d ) $ 6 , e ) $ 5", + "Correct": "c", + "Explanation": "\"my lunch = l , my friends lunch = l + 1 ( l ) + ( l + 3 ) = 11 l + l + 3 - 3 = 11 - 3 2 l = 8 l = 4 my friends lunch l + 3 = 4 + 3 = $ 7 , the answer is c\"" + }, + { + "Answer": 9, + "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 7", + "Correct": "b", + "Explanation": "there can be multiple possible rates of apple , banana and orange to satisfy given conditions , but cost of 1 apple , 1 banana , 1 orange will be rs 9 . 1 x + 3 y + 5 z = 21 . . . . . . . . ( 1 ) 7 x + 5 y + 3 z = 51 . . . . . . . . ( 2 ) adding ( 1 ) and ( 2 ) , we get 8 x + 8 y + 8 z = 72 8 * ( x + y + z ) = 72 x + y + z = 9 answer : b" + }, + { + "Answer": 49, + "Options": "a ) 35 , b ) 42 , c ) 45 , d ) 49 , e ) 54", + "Correct": "d", + "Explanation": "\"a = 105 = 3 * 5 * 7 a ^ 3 = 21 \u00d7 25 \u00d7 45 \u00d7 q = > a ^ 3 = ( 7 * 3 ) x ( 5 * 5 ) x ( 3 ^ 2 * 5 ) x q = > a ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x q = > ( 3 * 5 * 7 ) ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x q q = 7 ^ 2 = 49 answer d\"" + }, + { + "Answer": 21, + "Options": "a ) 1 , b ) 19 , c ) 21 , d ) 30 , e ) 33", + "Correct": "c", + "Explanation": "total of integers = 72 * 4 = 288 lowest of the least possible integer is when the middle 2 intergers are at the maximum or equal to the highest possible integer . but all integers are distinct . so if the largest integer is 90 , then the middle 2 will be 88 and 89 lowest of least possible integer = 288 - ( 90 + 89 + 88 ) = 288 - 267 = 21 answer : c" + }, + { + "Answer": 80.25, + "Options": "a ) $ 79.25 , b ) $ 79.50 , c ) $ 79.75 , d ) $ 80.00 , e ) $ 80.25", + "Correct": "e", + "Explanation": "1.07 * $ 75 = $ 80.25 the answer is e ." + }, + { + "Answer": 8, + "Options": "a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12", + "Correct": "c", + "Explanation": "\"while this question can be solved with a rather straight - forward algebra approach ( as the other posters have noted ) , it can also be solved by testing the answers . one of those numbers must be the total number of goals . . . from a tactical standpoint , it ' s best to test either answer b or answer d , so if the answer is not correct , then you would have a gauge for whether you should gohigherorlowerwith your next test . here , i ' ll start with answer c = 8 goals if . . . . total goals = 8 goals 5 th game = 2 goals 1 st 4 games = 6 goals avg . for 1 st 4 games = 6 / 4 = 1.5 goal / game avg . for all 5 games = 8 / 5 = 1.6 goals / game this is an exact match for what we ' re told in the prompt , so answer c must be the answer .\"" + }, + { + "Answer": 851, + "Options": "a ) 810 , b ) 811 , c ) 830 , d ) 850 , e ) 851", + "Correct": "e", + "Explanation": "since the integers from 30 - 50 are consecutive we can use the ` ` median x # of terms formula ' ' to determine x . there are 21 terms and the median is 40 . this gives a total of 21 x 40 = 840 . there are 11 even integers from 30 - 50 = y . therefore , x + y = 851 . answer : e" + }, + { + "Answer": 40, + "Options": "a ) 32 , b ) 34 , c ) 36 , d ) 38 , e ) 40", + "Correct": "e", + "Explanation": "women = 2 / 5 * 100 = 40 married = 1 / 4 * 100 = 25 unmarried = 75 max ( un - married women ) = 40 answer e" + }, + { + "Answer": 4.166666666666666, + "Options": "a ) 5 / 2 , b ) 10 / 3 , c ) 15 / 4 , d ) 25 / 3 , e ) 25 / 6", + "Correct": "e", + "Explanation": "\"n = 2 d / 5 j = n / 5 = 2 d / 25 the average of november and january is ( n + j ) / 2 = 12 d / 25 / 2 = 6 d / 25 d is 25 / 6 times the average of november and january . the answer is e .\"" + }, + { + "Answer": 360.00000000000006, + "Options": "a ) rs . 300 , b ) rs . 360 , c ) rs . 389 , d ) rs . 368 , e ) rs . 323", + "Correct": "b", + "Explanation": "\"( a = 2 / 3 b and b = 1 / 4 c ) = a / b = 2 / 3 and b / c = 1 / 4 a : b = 2 : 3 and b : c = 1 : 4 = 3 : 12 a : b : c = 2 : 3 : 12 a ; s share = 510 * 2 / 17 = rs . 60 b ' s share = 510 * 3 / 17 = rs . 90 c ' s share = 510 * 12 / 17 = rs . 360 . answer : b\"" + }, + { + "Answer": 144, + "Options": "a ) 216 , b ) 180 , c ) 144 , d ) 108 , e ) 72", + "Correct": "c", + "Explanation": "\"there are several ways to find the least common multiple of two numbers . in this case , the most efficient method is to use the greatest common factor : ( a * b ) / ( gcf ab ) = lcm ab the greatest common factor of 12 and 16 is 4 . so , 12 # 16 = 12 * 16 / 4 = 48 . the greatest common factor of 18 and 24 is 6 . so , 18 # 24 = 18 * 24 / 6 = 72 finally , the greatest common factor of 48 and 72 is 24 . so , p = ( ( 12 # 16 ) # ( 18 # 24 ) ) = 48 # 72 = ( 48 * 72 ) / 24 = 2 * 72 = 144 the correct answer is c .\"" + }, + { + "Answer": 6, + "Options": "a ) 22 , b ) 11 , c ) 9 , d ) 6 , e ) 3", + "Correct": "d", + "Explanation": "\"( 18 ^ a ) * 9 ^ ( 3 a \u2013 1 ) = ( 2 ^ 6 ) ( 3 ^ b ) = 2 ^ a . 9 ^ a . 9 ^ ( 3 a \u2013 1 ) = ( 2 ^ 6 ) ( 3 ^ b ) just compare powers of 2 from both sides answer = 6 = d\"" + }, + { + "Answer": 388.88888888888886, + "Options": "a ) 270 % , b ) 310 % , c ) 350 % , d ) 390 % , e ) 430 %", + "Correct": "d", + "Explanation": "\"let x be the number of new biographies added to the library . let b be the original number of biographies , so the original number of books was 5 b . 0.55 ( 5 b + x ) = b + x 1.75 b = 0.45 x x = 3.9 b the answer is d .\"" + }, + { + "Answer": 600, + "Options": "a ) 225 , b ) 275 , c ) 325 , d ) 350 , e ) 600", + "Correct": "e", + "Explanation": "\"this problem is a general word translation . we first define variables and then set up equations . we can define the following variables : f = the weight of the first lift s = the weight of the second lift we are given that the total weight of joe ' s two lifts was 1500 pounds . we sum the two variables to obtain : f + s = 1500 we are also given that twice the weight of his first lift was 300 pounds more than the weight of his second lift . we express this as : 2 f = 300 + s 2 f \u2013 300 = s we can now plug in ( 2 f \u2013 300 ) for s into the first equation , so we have : f + 2 f \u2013 300 = 1500 3 f = 1,800 f = 600 answer is e .\"" + }, + { + "Answer": 109, + "Options": "a ) 123 , b ) 109 , c ) 100 , d ) 156 , e ) 240", + "Correct": "b", + "Explanation": "\"explanation : cash realised = rs . ( 109.25 - 0.25 ) = rs . 109 . answer : b\"" + }, + { + "Answer": 38, + "Options": "a ) 28 , b ) 29 , c ) 34 , d ) 38 , e ) 36", + "Correct": "d", + "Explanation": "possible values of a and b can be 54 ; 45 and 120 ; 201 maximum possible value for a - b is 20 - 1 = 19 minimum possible value for a - b is 1 - 20 = - 19 19 - ( - 19 ) = 38 ans is d" + }, + { + "Answer": 1299.9999999999998, + "Options": "a ) 1000 , b ) 2217 , c ) 2889 , d ) 2777 , e ) 1300", + "Correct": "e", + "Explanation": "\"1456 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 1300 answer : e\"" + }, + { + "Answer": 1349, + "Options": "a ) 1123 , b ) 1234 , c ) 1349 , d ) 1455 , e ) 1567", + "Correct": "c", + "Explanation": "first digit is 1 / 3 second digit = > the numbers can be 1 & 3 , 2 & 6 , 3 & 9 . first + second = third = > we can eliminate 3 & 9 since 3 + 9 = 12 . last is 3 times the second = > we can eliminate option 2 & 6 since 3 * 6 = 18 . hence the number is 1349 c" + }, + { + "Answer": 101.33333333333333, + "Options": "a ) 101 , b ) 225 , c ) 304 , d ) 324 , e ) 336", + "Correct": "a", + "Explanation": "\"1 / 4 x + 76 = x that means 76 = 3 / 4 x x = ( 76 * 4 ) / 3 = 304 / 3 = 101 a is the answer\"" + }, + { + "Answer": 8, + "Options": "a ) 9 % decrease , b ) 8 % decrease , c ) 6 % decrease , d ) 1 % decrease , e ) 2 % decrease", + "Correct": "b", + "Explanation": "\"100 * 100 = 10000 80 * 115 = 9200 - - - - - - - - - - - 10000 - - - - - - - - - - - 800 100 - - - - - - - - - - - ? = > 8 % decrease answer : b\"" + }, + { + "Answer": 25600, + "Options": "a ) 32256 , b ) 24000 , c ) 24936 , d ) 25600 , e ) none", + "Correct": "d", + "Explanation": "\"answer \u2235 90 % of p = 23040 \u2234 p = ( 23040 x 100 ) / 90 = 25600 correct option : d\"" + }, + { + "Answer": 134.4, + "Options": "a ) $ 54.00 , b ) $ 64.80 , c ) $ 90.00 , d ) $ 100.80 , e ) $ 134.40", + "Correct": "e", + "Explanation": "\"correct answer : e the tourist must pay tax on $ 1720 - $ 600 = $ 1120 . thus , the amount of tax he has to pay is 0.12 ( $ 1120 ) = $ 134.40 . the correct answer is e .\"" + }, + { + "Answer": 30, + "Options": "a ) 21 , b ) 30 , c ) 11 , d ) 10 , e ) 9", + "Correct": "b", + "Explanation": "\"number start between 45 to 105 is 60 numbers half of them is even . . which is 30 answer : b\"" + }, + { + "Answer": 470, + "Options": "a ) 654 , b ) 655 , c ) 656 , d ) 657 , e ) 470", + "Correct": "e", + "Explanation": "\"total cost 940 940 * 50 / 100 = 470 so the cut in amount is 470 the less amount to be spend is 940 - 470 = 470 answer : e\"" + }, + { + "Answer": 32.24999999999998, + "Options": "a ) 32.25 % , b ) 23.34 % , c ) 36 % , d ) 39 % , e ) 29 %", + "Correct": "a", + "Explanation": "new price is 1.15 * 1.15 * old price = 1.3225 * old price increase in price = 0.3225 * old price % increase = 100 * 0.3225 * old price / old price = 32.25 % answer : a" + }, + { + "Answer": 756.0000000000001, + "Options": "a ) 392 , b ) 229 , c ) 756 , d ) 493 , e ) 540", + "Correct": "c", + "Explanation": "c 756 ? = 5040 * ( 2 / 5 ) * ( 1 / 2 ) * ( 3 / 4 ) = 756" + }, + { + "Answer": 40, + "Options": "a ) 40.2 , b ) 40.4 , c ) 40.6 , d ) 40.8 , e ) none of the above", + "Correct": "b", + "Explanation": "\"sum of 10 numbers = 402 corrected sum of 10 numbers = 402 \u2013 13 + 31 \u2013 16 = 404 hence , new average = 404 \u2044 10 = 40.4 answer b\"" + }, + { + "Answer": 12, + "Options": "a ) a ) 23 , b ) b ) 21 , c ) c ) 52 , d ) d ) 56 , e ) e ) 12", + "Correct": "e", + "Explanation": "let the total number of workers be x . then , 9500 x = ( 12000 * 7 ) + 6000 ( x - 7 ) = > 3500 x = 42000 = x = 12 . answer : e" + }, + { + "Answer": 16.666666666666668, + "Options": "a ) 25.5 , b ) 16.7 , c ) 25 , d ) . 25 , e ) none of these", + "Correct": "b", + "Explanation": "\"explanation : 1 / 0.06 = ( 1 * 100 ) / 6 = 100 / 6 = 16.7 option b\"" + }, + { + "Answer": 2, + "Options": "a ) 4 , b ) 2 , c ) 6 , d ) 7 , e ) 8", + "Correct": "b", + "Explanation": "a + b + c = 18 b + c + d = 9 a + d = 13 a \u2013 d = 9 a + d = 13 2 d = 4 d = 2 answer : b" + }, + { + "Answer": 32, + "Options": "a ) 16 , b ) 24 , c ) 32 , d ) 48 , e ) 54", + "Correct": "c", + "Explanation": "after 8 girls left remaining 8 girls now boys 16 are twice as many as remaining girls . initially boys = 16 and girls = 16 . answer : c" + }, + { + "Answer": 5, + "Options": "a ) 4.5 , b ) 5 , c ) 5.6 , d ) 5.7 , e ) 6.5", + "Correct": "b", + "Explanation": "\"if $ x $ is the number , x / 6 * 12 = 10 = > 2 x = 10 = > x = 5 b\"" + }, + { + "Answer": 0.2857142857142857, + "Options": "a ) 4 / 7 , b ) 5 / 7 , c ) 3 / 7 , d ) 2 / 7 , e ) 1 / 7", + "Correct": "d", + "Explanation": "there are 9 years from 1972 - 1980 , inclusive . let ' s say the average circulation every year between 1972 - 1980 inclusive is x . so the total circulation is 9 x from 1972 - 1980 , inclusive . in 1971 , the circulation is 4 x . so total circulation for 1971 - 1980 is 4 x + 9 x = 13 x . ratio of circulation in 1971 to total circulation during 1971 - 1980 is 4 x to 14 x or 4 / 14 = 2 / 7 answer : d" + }, + { + "Answer": 53.1578947368421, + "Options": "a ) 52.2 , b ) 59.5 , c ) 52.8 , d ) 52.5 , e ) 53.1", + "Correct": "e", + "Explanation": "sum of the marks for the class of 26 students = 26 * 40 = 1040 sum of the marks for the class of 50 students = 50 * 60 = 3000 sum of the marks for the class of 76 students = 1040 + 3000 = 4040 average marks of all the students = 4040 / 76 = 53.15 answer : e" + }, + { + "Answer": 10, + "Options": "a ) 19 , b ) 12 , c ) 11 , d ) 10 , e ) 3", + "Correct": "d", + "Explanation": "out of the 18 integers : 9 are odd and 9 are even . if we need to make sure that the product of all the integers withdrawn is even then we need to make sure that we have at least one even number . in the worst case : 1 . we will end up picking odd numbers one by one , so we will pick all 9 odd numbers first 2 . 10 th number will be the first even number so we need to withdraw at least 10 numbers to make sure that we get one even number and the product of all the integers picked is even . so , answer will be 10 . ( d )" + }, + { + "Answer": 0.25, + "Options": "a ) - 1 , b ) - 1 / 2 , c ) - 1 / 4 , d ) 1 / 4 , e ) 1 / 2", + "Correct": "d", + "Explanation": "because f is periodic , we know that f ( - 3 / 2 ) = f ( 1 / 2 ) = ( 1 / 2 ) 2 = 1 = 4 . because f is odd , we know that f ( 1 ) = - f ( / 1 ) , but because f is periodic , f ( 1 ) = f ( - 1 ) . therefore , f ( 1 ) = 0 and the answer is 1 = 4 . correct answer d" + }, + { + "Answer": 77.4193548387097, + "Options": "a ) 71.11 , b ) 71.12 , c ) 71.1 , d ) 71.17 , e ) 77.42", + "Correct": "e", + "Explanation": "car travels first 160 km at 75 km / hr time taken to travel first 160 km = distancespeed = 160 / 75 car travels next 160 km at 80 km / hr time taken to travel next 160 km = distancespeed = 160 / 80 total distance traveled = 160 + 160 = 2 \u00d7 160 total time taken = 160 / 75 + 160 / 80 average speed = total distance traveled / total time taken = 320 / ( 160 / 75 + 160 / 80 ) = 77.42 km / hr answer : e" + }, + { + "Answer": 41.17647058823529, + "Options": "a ) 18.7 , b ) 25.5 , c ) 33.3 , d ) 41.2 , e ) 54.4", + "Correct": "d", + "Explanation": "y = 1.7 x x = y / 1.7 = 10 y / 17 x is 7 / 17 less which is about 41.2 % less than y . the answer is d ." + }, + { + "Answer": 5.5, + "Options": "a ) $ 3.15 , b ) $ 4.45 , c ) $ 4.80 , d ) $ 5.50 , e ) $ 5.40", + "Correct": "d", + "Explanation": "\"let the fixed charge of jim \u00e2 \u20ac \u2122 s taxi service = 2.35 $ and charge per 2 / 5 mile ( . 4 mile ) = . 35 $ total charge for a trip of 3.6 miles = 2.35 + ( 3.6 / . 4 ) * . 35 = 2.35 + 9 * . 35 = 5.5 $ answer d\"" + }, + { + "Answer": 400000, + "Options": "a ) $ 180,000 , b ) $ 400,000 , c ) $ 220,000 , d ) $ 402,000 , e ) $ 2 , 200,000", + "Correct": "b", + "Explanation": "\"answer : b , ( with different approach ) : the 400 paid is 0.2 % of the additional amount above 200,000 . let it be x now 0.2 % of x = 400 therefore x = 200,000 total = 200,000 + x = 400,000\"" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 0 , c ) 3 , d ) 2 , e ) 4", + "Correct": "c", + "Explanation": "\"remainder will be number / 100 here as the divisor is two digit number = 12 . hence checking for the last two digits = 5 * 7 * 9 = 15 thus remainder = 3 . answer : c\"" + }, + { + "Answer": 8, + "Options": "a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16", + "Correct": "a", + "Explanation": "answer : a 2 , 16 , 4 , 14 , 6 , 12 , 8 ? there are two alternate sequences : + 2 and - 2 ." + }, + { + "Answer": 26, + "Options": "a ) 14 , b ) 17 , c ) 11 , d ) 19 , e ) 26", + "Correct": "e", + "Explanation": "\"let the son ' s present age be x years . then , ( 62 - x ) = x x = 31 . son ' s age 5 years back = ( 31 - 5 ) = 26 years answer : e\"" + }, + { + "Answer": 30, + "Options": "a ) 20 , b ) 18 , c ) 19 , d ) 15 , e ) 30", + "Correct": "e", + "Explanation": "\"explanation : numbers divisible by 6 are 12 , 18,24 , 30,36 , 42,48 , average = ( 12 + 18 + 24 + 30 + 36 + 42 + 48 , ) / 7 = 210 / 7 = 30 answer : e\"" + }, + { + "Answer": 1260, + "Options": "a ) $ 1360 , b ) $ 1250 , c ) $ 1260 , d ) $ 1270 , e ) $ 1280", + "Correct": "c", + "Explanation": "\"a = 1 / 3 ( b + c ) = > c = 3 a - b - - - ( 1 ) b = 2 / 7 ( a + c ) = > c = 3.5 b - a - - ( b ) a - b = $ 35 a = 35 + b ( 1 ) = = = > c = 105 + 3 b - b = 2 b + 105 = = > 2 b - c = - 105 - - - ( 3 ) ( 2 ) = = = > c = 3.5 b - b - 35 = 2.5 b - 35 = = > 2.5 b - c = 35 - - - ( 4 ) from ( 4 ) and ( 3 ) 0.5 b = 140 b = $ 280 a = $ 315 c = 945 - 280 = $ 665 total amount = 315 + 280 + 665 = $ 1260 answer : c\"" + }, + { + "Answer": 960, + "Options": "a ) 600 , b ) 700 , c ) 800 , d ) 960 , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : let p ' s capital = p , q ' s capital = q and r ' s capital = r then 4 p = 6 q = 10 r = > 2 p = 3 q = 5 r = > q = 2 p / 3 r = 2 p / 5 p : q : r = p : 2 p / 3 : 2 p / 5 = 15 : 10 : 6 r ' s share = 4960 * ( 6 / 31 ) = 160 * 6 = 960 . answer : option d\"" + }, + { + "Answer": 6, + "Options": "a ) 5 , b ) 6 , c ) 1 , d ) 2 , e ) 3", + "Correct": "b", + "Explanation": "detailed solution to begin with , the question should read ` ` find the 44 th digit ' ' . any number of the form abcabc is a multiple of 1001 . 1001 is 7 * 11 * 13 . so , any number of the form abcabc is a multiple of 13 . so , a number comprising 42 2 ' s would be a multiple of 13 , so would a number comprising 36 2 ' s . so , in effect , we are left with a two digit number 2 a , where a is the 44 th digit . 26 is a multiple of 13 , so the 44 th digit should be 6 . correct answer b" + }, + { + "Answer": 75, + "Options": "a ) 70 kg , b ) 72 kg , c ) 75 kg , d ) 80 kg , e ) none of these", + "Correct": "c", + "Explanation": "explanation : a + b + c = ( 84 x 3 ) = 252 kg , a + b + c + d = ( 80 x 4 ) = 320 kg . d = ( 320 - 252 ) = 68 , e = ( 68 + 3 ) = 7 l . b + c + d + e = ( 79 x 4 ) = 316 . ( a + b + c + d ) - ( b + c + d + e ) = ( 320 - 316 ) kg = 4 kg . a - e = 4 = a = ( 4 + e ) = 75 kg answer : c" + }, + { + "Answer": 25, + "Options": "a ) 13.28 % , b ) 14.28 % , c ) 15.28 % , d ) 16.28 % , e ) 25 %", + "Correct": "e", + "Explanation": "\"let total % of work is 100 % total person = p 1 / 5 person are absent of total person . so absent person is 1 / 5 p ie p / 5 . left person is , p - p / 5 = 4 p / 5 . p person do the work 100 % 1 person do the work 100 * p % 4 p / 5 person do the work ( 100 * p * 5 ) / 4 p % = 125 % work increased for each person is = ( 125 - 100 ) % = 25 % answer : e\"" + }, + { + "Answer": 2120, + "Options": "a ) $ 2,040 , b ) $ 2,120 , c ) $ 1,960 , d ) $ 1,920 , e ) $ 1,400", + "Correct": "b", + "Explanation": "in order to maximize the amount of money that the gambler kept , we should maximize # of $ 20 chips lost and minimize # of $ 100 chips lost , which means that # of $ 20 chips lost must be 2 more than # of $ 100 chips lost . so , if # of $ 20 chips lost is x then # of $ 100 chips lost should be x - 2 . now , given that total # of chips lost is 16 : x + x - 2 = 16 - - > x = 9 : 9 $ 20 chips were lost and 9 - 2 = 7 $ 100 chips were lost . total worth of chips lost is 9 * 20 + 7 * 100 = $ 880 , so the gambler kept $ 3,000 - $ 880 = $ 2,120 . answer : b ." + }, + { + "Answer": 2, + "Options": "a ) 2 , b ) 2 and 4 , c ) 2 , 4 and 8 , d ) 2 , 4 and 9 , e ) none of these", + "Correct": "a", + "Explanation": "explanation : the sum of the first 100 natural numbers = ( 100 x 101 ) / 2 = ( 50 x 101 ) as 101 is an odd number and 50 is divisible by 2 , so the sum is always divisible by 2 . answer : option a" + }, + { + "Answer": 8123.076923076918, + "Options": "a ) 8223 , b ) 8123 , c ) 8323 , d ) 8423 , e ) 8523", + "Correct": "b", + "Explanation": "let total salary be x a / q = > x = ( x / 3 ) + ( x / 4 ) + ( x / 5 ) + 1760 = > x - 47 x / 60 = 1760 = > 13 x / 60 = 1760 = > x = 1760 * 60 / 13 = > x = 8123 ( approax ) answer : b" + }, + { + "Answer": 9984, + "Options": "a ) 4676 , b ) 4678 , c ) 9984 , d ) 9504 , e ) 9936", + "Correct": "c", + "Explanation": "largest 4 digit number = 9999 9999 \u00f7 48 = 208 , remainder = 15 hence largest 4 digit number exactly divisible by 48 = 9999 - 15 = 9984 answer : c" + }, + { + "Answer": 48, + "Options": "a ) 360 liters , b ) 256 , c ) 48 , d ) 525 , e ) 425", + "Correct": "c", + "Explanation": "4 x = 3 ( x + 4 ) , where x may be number of times 4 l bucket is used . 4 x = 3 ( x + 4 ) - - > 1 . x = 12 , substitute x to lhs or rhs of 1 , which gets you the capacity , and it is 48 . answer : c" + }, + { + "Answer": 307, + "Options": "a ) 306 , b ) 307 , c ) 308 , d ) 309 , e ) 310", + "Correct": "b", + "Explanation": "power is 443 = > 443 / 4 rem = 3 so , 443 ^ 3 = 86938307 last 3 digit = 307 answer : b" + }, + { + "Answer": 258, + "Options": "a ) a ) 258 , b ) b ) 65 , c ) c ) 58 , d ) d ) 62 , e ) e ) 48", + "Correct": "a", + "Explanation": "\"6 th number = sum of 1 st 6 no . s + sum of last 6 no . s - sum of 11 no . s answer = 6 * 78 + 6 * 75 - 11 * 60 = 258 answer is a\"" + }, + { + "Answer": 80, + "Options": "a ) 124 % , b ) b ) 120 % , c ) c ) 96 % , d ) d ) 80 % , e ) e ) 64 %", + "Correct": "d", + "Explanation": "\"m = ( 160 / 100 ) t t = ( 50 / 100 ) j = > m = ( 80 / 100 ) j answer d .\"" + }, + { + "Answer": 62, + "Options": "a ) 12 liters , b ) 62 liters , c ) 41 liters , d ) 50 liters , e ) 34 liters", + "Correct": "b", + "Explanation": "milk = 3 / 5 * 155 = 93 liters water = 62 liters 93 : ( 62 + p ) = 3 : 4 186 + 3 p = 372 = > p = 62 62 liters of water are to be added for the ratio become 3 : 4 . answer : b" + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 4 , c ) 5 , d ) 2 , e ) 3", + "Correct": "a", + "Explanation": "a number is divisible by 8 if the number formed by the last three digits is divisible by 8 . here , 821562 = 562 , the next multiple of 9 is 568 . 6 must be added to 821562 to make it divisible by 8 a" + }, + { + "Answer": 9, + "Options": "a ) 0 , b ) 5 , c ) 7 , d ) 1 , e ) 9", + "Correct": "e", + "Explanation": "\"unit digit in 3 ^ 58 = unit digit in [ ( 3 ^ 4 ) ^ 14 ] * 3 ^ 2 = 1 * 9 = 9 answer is e\"" + }, + { + "Answer": 90, + "Options": "a ) 25 , b ) 50 , c ) 90 , d ) 140 , e ) it can not be determined from the information given .", + "Correct": "c", + "Explanation": "\"- ( a + b = 70 ) b + c = 160 c - a = 90 c . 90\"" + }, + { + "Answer": 10, + "Options": "a ) 50 , b ) 70 , c ) 10 , d ) 105 , e ) 140", + "Correct": "c", + "Explanation": "rented = 4 / 7 * 490 = 280 . rented two - bedroom = 6 / 7 * 280 = 240 ; rented one - bedroom = 1 / 7 * 280 = 40 ( or 280 - 240 = 40 ) . rented one - bedroom units are 1 / 5 of all one - bedroom : 1 / 6 * { all one bedroom } = 40 - - > { all one - bedroom } = 240 . { all two - bedroom } = 490 - 240 = 250 . two - bedroom not rented = 250 - 240 = 10 . answer : c ." + }, + { + "Answer": 52, + "Options": "a ) 51 , b ) 52 , c ) 59 , d ) 55 , e ) 56", + "Correct": "b", + "Explanation": "\"for 40 hrs = 40 * 16 = 640 excess = 976 - 640 = 336 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 336 / 28 = 12 total hrs = 40 + 12 = 52 answer b\"" + }, + { + "Answer": 85, + "Options": "a ) 75 kg , b ) 55 kg , c ) 45 kg , d ) 85 kg , e ) 25 kg", + "Correct": "d", + "Explanation": "explanation : total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 65 + 20 ) kg = 85 kg . answer : d" + }, + { + "Answer": 2014, + "Options": "a ) 2014 , b ) 2088 , c ) 270 , d ) 1881 , e ) 1781", + "Correct": "a", + "Explanation": "\"f ( f ( 0 ) ) + f ( 0 ) = 2 ( 0 ) + 3 \u21d2 \u21d2 f ( 1 ) = 3 - 1 = 2 , f ( 1 ) = 2 f ( f ( 1 ) ) + f ( 1 ) = 2 ( 1 ) + 3 \u21d2 \u21d2 f ( 2 ) = 5 - 2 = 3 , f ( 2 ) = 3 f ( f ( 2 ) ) + f ( 2 ) = 2 ( 2 ) + 3 \u21d2 \u21d2 f ( 3 ) = 7 - 3 = 4 , f ( 3 ) = 4 . . . . . . . . . . . . . . f ( 2013 ) = 2014 ans : a\"" + }, + { + "Answer": 599.9999999999994, + "Options": "a ) 80 , b ) 110 , c ) 160 , d ) 600 , e ) 400", + "Correct": "d", + "Explanation": "\"we start by creating a variable for the total number of students in the math course . we can say : t = total number of students in the math course next , we can use variable t in an equation that we translate from the given information . we are given that , of the final grades received by the students in a certain math course , 1 / 5 are a ' s , 1 / 4 are b ' s , 1 / 2 are c ' s , and the remaining 30 grades are d ' s . since this represents all the grades in the class , it represents all the students in the class . thus we know : # a \u2019 s + # b \u2019 s + # c \u2019 s + # d \u2019 s = total number of students in the class 1 / 5 ( t ) + \u00bc ( t ) + \u00bd ( t ) + 30 = t we can multiply the entire equation by 20 to cancel out the denominators of the fractions and we have : 4 t + 5 t + 10 t + 600 = 20 t 19 t + 600 = 20 t 600 = t there are a total of 600 students in the math class . answer is d .\"" + }, + { + "Answer": 8600, + "Options": "a ) rs . 7000 , b ) rs . 8000 , c ) rs . 8600 , d ) rs . 9000 , e ) none", + "Correct": "c", + "Explanation": "answer average salary = 8000 + 5000 + 14000 + 7000 + 9000 / 5 = rs . 8600 correct option : c" + }, + { + "Answer": 0.8571428571428571, + "Options": "a ) a ) 1.12 , b ) b ) 1.2 , c ) c ) 0.95 , d ) d ) 0.85 , e ) e ) 0.9", + "Correct": "d", + "Explanation": "\"( x * 7 ) = ( 0.75 * 8 ) x = 6 / 7 x = 0.85 answer = d\"" + }, + { + "Answer": 25, + "Options": "a ) 25 % , b ) 22.2 % , c ) 20 % , d ) 12.5 % , e ) 11.1 %", + "Correct": "a", + "Explanation": "\"let ' s see , the way i did it was 1 / 3 are clerical out of 3600 so 1200 are clerical 1200 reduced by 1 / 3 is 1200 * 1 / 3 so it reduced 400 people , so there is 800 clerical people left but since 400 people left , it also reduced from the total of 3600 so there are 3200 people total since 800 clerical left / 3200 people total you get ( a ) 25 %\"" + }, + { + "Answer": 120, + "Options": "a ) 18 , b ) 36 , c ) 120 , d ) 90 , e ) 108", + "Correct": "c", + "Explanation": "\"let kate charge for x hours , then pat charged for 2 x and mat - for 6 x . so , 2 x + 6 x + x = 216 - total hours charged for , x = 24 . mat charged 6 x - x or 5 x for more hours than kate , or for 120 hours . c is correct\"" + }, + { + "Answer": 17, + "Options": "a ) 13 % , b ) 14 % , c ) 15 % , d ) 16 % , e ) 17 %", + "Correct": "e", + "Explanation": "\"the percent of alcohol in the solution is ( 0.05 ( 40 ) + 6.5 ) / 50 = 8.5 / 50 = 17 % the answer is e .\"" + }, + { + "Answer": 40, + "Options": "a ) rs 30 , b ) rs 40 , c ) rs 70 , d ) rs 210 , e ) rs 310", + "Correct": "b", + "Explanation": "explanation : let a = punith , b = michael , c = suresh . a : b = 3 : 4 and b : c = 7 / 2 : 3 = ( 8 / 7 ) * ( 7 / 2 ) * ( 8 / 7 ) * 3 = 4 : ( 24 / 7 ) a : b : c = 3 : 4 : 24 / 7 = 21 : 28 : 24 . bs share = rs . [ 730 * ( 28 / 73 ) ] = rs . 280 . cs share = rs . [ 730 * ( 24 / 73 ) ] = rs . 240 . difference of their shares = 40 answer : b" + }, + { + "Answer": 0.34999999999999964, + "Options": "a ) 0.35 , b ) 0.5 , c ) 6.25 , d ) 0.25 , e ) 6.0", + "Correct": "a", + "Explanation": "\"since z * is defined as the greatest positive even integer less than or equal to z , then 6.35 * = 6 ( the greatest positive even integer less than or equal to 6.35 is 6 ) . hence , 6.35 \u2013 6.35 * = 6.35 - 6 = 0.35 answer : a .\"" + }, + { + "Answer": 161, + "Options": "a ) 161 , b ) 152 , c ) 154 , d ) 158 , e ) 144", + "Correct": "a", + "Explanation": "\"d = d * q + r d = 17 * 9 + 8 d = 153 + 8 d = 161 answer a\"" + }, + { + "Answer": 2442, + "Options": "a ) 2442 , b ) 2552 , c ) 2662 , d ) 2772 , e ) 2882", + "Correct": "a", + "Explanation": "\"there are 6 possible arrangements of the three numbers . then each number will be in the hundreds , tens , and ones place two times each . the sum is 2 ( 222 ) + 2 ( 444 ) + 2 ( 555 ) = 2442 the answer is a .\"" + }, + { + "Answer": 35, + "Options": "a ) 30 , b ) 35 , c ) 25 , d ) 28 , e ) 32", + "Correct": "b", + "Explanation": "let their ages be x years and ( x + 20 ) years then , ( x + 20 ) - 15 = 2 ( x - 15 ) x + 5 = 2 x - 30 x = 35 answer is b" + }, + { + "Answer": 1050, + "Options": "a ) 105 , b ) 168 , c ) 342 , d ) 660 , e ) 1050", + "Correct": "e", + "Explanation": "\"given : 0.7 * 600 = 0.4 x - - > 420 = 4 / 10 * x - - > x = 1,050 . answer : e .\"" + }, + { + "Answer": 225, + "Options": "a ) $ 225 , b ) $ 150 , c ) $ 200 , d ) $ 250 , e ) $ 450", + "Correct": "a", + "Explanation": "\"cavg = average contribution before john cavg * 1.5 = 75 , therefore the average cont is $ 50 before john . if he needs to increase the average contribution by $ 25 , he must put in $ 25 for each of the 6 people . so $ 150 . but , he also has to put in the average for himself ( the seventh person ) , so add $ 75 . so $ 225 is your answer . answer a\"" + }, + { + "Answer": 51, + "Options": "a ) a ) 99 , b ) b ) 84 , c ) c ) 51 , d ) d ) 65 , e ) e ) 57", + "Correct": "c", + "Explanation": "a ) 99 = 9 * 11 b ) 84 = 4 * 7 * 3 c ) 51 = 17 * 3 d ) 65 = 5 * 13 e ) 57 = 19 * 3 since 17 is not there in first 15 positive numbers it is the only possibility c" + }, + { + "Answer": 100, + "Options": "a ) 90 kg , b ) 100 kg , c ) 95 kg , d ) 85 kg , e ) 92 kg", + "Correct": "b", + "Explanation": "\"total weight increased = 10 x 5 kg = 50 kg . weight of new person = 50 + 50 kg = 100 kg answer : b\"" + }, + { + "Answer": 11, + "Options": "a ) a ) 11 , b ) b ) 14 , c ) c ) 16 , d ) d ) 18 , e ) e ) 22", + "Correct": "a", + "Explanation": "\"d = ( d - r ) / q = ( 144 - 1 ) / 13 = 143 / 13 = 11 a )\"" + }, + { + "Answer": 25, + "Options": "a ) 24 , b ) 26 , c ) 30 , d ) 25 , e ) 40", + "Correct": "d", + "Explanation": "\"let the number of coins one son got be x and the number of coins another got be y . total = x + y . x ^ 2 - y ^ 2 = 25 ( x - y ) - - > x + y = 25 . answer : d .\"" + }, + { + "Answer": 50, + "Options": "a ) 20 , b ) 50 , c ) 30 , d ) 40 , e ) 10", + "Correct": "b", + "Explanation": "solution the answer will be 50 since , ( 125 \u00d7 122 ) will give 50 as the last two digits . answer b" + }, + { + "Answer": 44.82892142331043, + "Options": "a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 45", + "Correct": "e", + "Explanation": "\"this one ' s easy . 1000 * 2 ^ t = 500,000 2 ^ t = 500 now gauging , since 2 ^ 8 = 256 , then 2 ^ 9 = 512 so t = 9 but be careful , ' t ' is in time intervals of 5 minutes so answer is 9 * 5 = 45 minutes answer ( e )\"" + }, + { + "Answer": 12, + "Options": "a ) 8 , b ) 12 , c ) 14 , d ) 16 , e ) 18", + "Correct": "b", + "Explanation": "\"since there are only 10 integers , another approach is the just list all 10 . we get : - 4 , - 2 , 0,2 , 4 , 6 , 8 , 10 , 12 , 14 range of positive integers = 14 - 2 = 12 answer : b\"" + }, + { + "Answer": 3, + "Options": "a ) 3 / 7 , b ) 34 , c ) 1 , d ) 2 , e ) 3", + "Correct": "e", + "Explanation": "\"answer given exp . = 18 / 7 + { ( 2 q - p ) / ( 2 q + p ) } dividing numerator as well as denominator by q , exp = 18 / 7 + { 2 - p / q ) / ( 2 + p / q ) } = 18 / 7 + { ( 2 - 4 / 5 ) / ( 2 + 4 / 5 ) } = 18 / 7 + 6 / 14 = 18 / 7 + 3 / 7 = 21 / 7 = 3 correct option : e\"" + }, + { + "Answer": 2, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "b", + "Explanation": "\"26 / 3 = 8 . xxx 85 / 6 = 14 . xxx so we need to find prime numbers between 8 ( exclusive ) - 13 ( inclusive ) there are 2 prime numbers 1113 hence answer will be ( b ) 2 b\"" + }, + { + "Answer": 87, + "Options": "a ) a ) 70 , b ) b ) 76 , c ) c ) 78 , d ) d ) 80 , e ) e ) 87", + "Correct": "e", + "Explanation": "\"explanation : average after 11 innings should be 37 so , required score = ( 11 * 37 ) - ( 10 * 32 ) = 407 - 320 = 87 answer : option e\"" + }, + { + "Answer": 6, + "Options": "a ) 8 , b ) 9 , c ) 6 , d ) 11 , e ) 12", + "Correct": "c", + "Explanation": "\"2 + 4 = 6 correct answer is c ) 6\"" + }, + { + "Answer": 75.00000000000001, + "Options": "a ) 40 , b ) 52 , c ) 68 , d ) 75 , e ) 98", + "Correct": "d", + "Explanation": "\"let the no of matches played more = x so , ( 120 + x ) * 52 / 100 = 26.4 + x by solving we get x = 75 answer : d\"" + }, + { + "Answer": 24, + "Options": "a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24", + "Correct": "e", + "Explanation": "\"check two extreme cases : jane = 16 , child = 8 , years ago = 32 - 16 = 16 - - > child ' s age now = 8 + 16 = 24 ; jane = 22 , child = 11 , years ago = 32 - 22 = 10 - - > child ' s age now = 11 + 10 = 21 . answer : e .\"" + }, + { + "Answer": 15, + "Options": "a ) 15 , b ) 30 , c ) 25 , d ) 10 , e ) 15", + "Correct": "a", + "Explanation": "explanation : combined efficiency of all the three boats = 60 passenger / trip now , consider option ( a ) 15 trips and 150 passengers means efficiency of b 1 = 10 p / t which means in carrying 50 passengers b 1 must has taken 5 trips . so the rest trips equal to 5 ( 10 - 5 = 5 ) in which b 2 and b 3 together carried remaining 250 ( 300 - 50 = 250 ) passengers . therefore the efficiency of b 2 and b 3 = 250 / 5 = 50 p / t since , the combined efficiency of b 1 , b 2 and b 3 is 60 . which is same as given in the first statement hence option ( a ) is correct answer : a" + }, + { + "Answer": 34, + "Options": "a ) 22 , b ) 30 , c ) 34 , d ) 38 , e ) 27", + "Correct": "c", + "Explanation": "\"total age increased = ( 12 * 2 ) years = 24 years . sum of ages of two new men = ( 21 + 23 + 24 ) years = 68 years average age of two new men = ( 68 / 2 ) years = 34 years . answer : c\"" + }, + { + "Answer": 19, + "Options": "a ) 17 , b ) 19 , c ) 25 , d ) 31 , e ) 46", + "Correct": "b", + "Explanation": "\"the total sum of the numbers should be increased by 30 . then the average will increase by 30 / 10 = 3 . the correct average is 19 . the answer is b .\"" + }, + { + "Answer": 6.900000000000002, + "Options": "a ) 2.3 , b ) 2.6 , c ) 6.9 , d ) 4.5 , e ) 4.6", + "Correct": "c", + "Explanation": "\"sum of the remaining two numbers = ( 6.4 * 6 ) - [ ( 6.2 * 2 ) + ( 6.1 * 2 ) ] = 38.40 - ( 12.4 + 12.2 ) = 38.40 - 24.6 = 13.80 required average = ( 13.8 / 2 ) = 6.9 answer : c\"" + }, + { + "Answer": 4, + "Options": "a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "b", + "Explanation": "\"total subjects = 6 + 5 + 5 = 16 max subjects by 1 teacher = 4 so , min of teachers required = 16 / 4 = 4 answer : b\"" + }, + { + "Answer": 104, + "Options": "a ) 104 , b ) 106 , c ) 102 , d ) 192 , e ) 122", + "Correct": "a", + "Explanation": "\"cash realised = rs . ( 104.25 - 0.25 ) = rs . 104 . answer : a\"" + }, + { + "Answer": 23, + "Options": "a ) a ) 7 , b ) b ) 27 , c ) c ) 23 , d ) d ) 19 , e ) e ) 21", + "Correct": "c", + "Explanation": "15 + 8 = 23 . answer is c ." + }, + { + "Answer": 765.3846153846154, + "Options": "a ) $ 752 , b ) $ 755 , c ) $ 765 , d ) $ 773 , e ) $ 775", + "Correct": "c", + "Explanation": "= ( 750 * 6 + 770 * 20 ) / 26 = 765 answer is c . posted from my mobile device" + }, + { + "Answer": 0.5454545454545454, + "Options": "a ) 6 / 11 , b ) 8 / 13 , c ) 11 / 16 , d ) 12 / 17 , e ) 14 / 19", + "Correct": "a", + "Explanation": "let the numerator be x . then the denominator is x + 5 . x + 1 / x + 6 = 7 / 12 . 12 x + 12 = 7 x + 42 . 5 x = 30 . x = 6 . the original fraction is 6 / 11 . the answer is a ." + }, + { + "Answer": 120, + "Options": "a ) 108 , b ) 119 , c ) 120 , d ) 135 , e ) 143", + "Correct": "c", + "Explanation": "\"let the 2 positive numbers x and y x + y = 22 - - 1 x ^ 2 - y ^ 2 = 44 = > ( x + y ) ( x - y ) = 44 - - 2 using equation 1 in 2 , we get = > x - y = 2 - - 3 solving equation 1 and 3 , we get x = 12 y = 10 product = 12 * 10 = 120 answer c\"" + }, + { + "Answer": 0.7333333333333333, + "Options": "a ) 1 / 9 , b ) 1 / 6 , c ) 1 / 3 , d ) 4 / 9 , e ) 11 / 15", + "Correct": "e", + "Explanation": "\"her tips were 11 / 4 of her salary . let ' s say her salary = $ 4 this mean her tips = ( 11 / 4 ) ( $ 4 ) = $ 11 so , her total income = $ 4 + $ 11 = $ 15 what fraction of her income for the week came from tips $ 11 / $ 15 = 11 / 15 = e\"" + }, + { + "Answer": 1999.1818181818182, + "Options": "a ) 2010 , b ) 2011 , c ) 2012 , d ) 2013 , e ) 2014", + "Correct": "d", + "Explanation": "\"the price of commodity x increases 25 cents each year relative to commodity y . the price difference is $ 2.10 and commodity x needs to be 90 cents more than commodity y . $ 3.00 / 25 cents = 12 years the answer is 2001 + 12 years = 2013 . the answer is d .\"" + }, + { + "Answer": 45, + "Options": "a ) 18 , b ) 19 , c ) 45 , d ) 21 , e ) 22", + "Correct": "c", + "Explanation": "explanation : let first number be x . so , 2 nd no . = 2 x & 3 rd no . = 8 x . so , x + 2 x + 8 x = 165 \u00d7 3 = 495 11 x = 495 / 11 x = 495 / 11 hence , smallest number x = 45 answer : c" + }, + { + "Answer": 4200, + "Options": "a ) rs . 4000 , b ) rs . 4500 , c ) rs . 4300 , d ) rs . 4200 , e ) none of these", + "Correct": "d", + "Explanation": "explanation : let c . p . of a mixer be rs . x and that of a t . v . be rs . y . then , 2 x + y = 7000 and 2 y + x = 9800 . multiplying 2 nd equatien by 2 and subtracting first from it , we get 3 y = 19600 - 7000 = 12600 or y = 4200 c . p . of a t . v . = rs . 4200 answer : d" + }, + { + "Answer": 76.16000000000001, + "Options": "a ) 68.8 , b ) 73.6 , c ) 75.2 , d ) 76.16 , e ) 81.6", + "Correct": "d", + "Explanation": "degree of difficulty of dive = 3.2 scores are 6.0 , 7.5 , 8.0 , 8.5 and 9.0 we can drop 6.0 and 9.0 sum of the remaining scores = ( 7.5 + 7.8 + 8.5 ) = 23.8 point of value of the dive = 23.8 * 3.2 = 76.16 answer d" + }, + { + "Answer": 15, + "Options": "a ) 11 , b ) 15 , c ) 13 , d ) 14 , e ) can not be determined", + "Correct": "b", + "Explanation": "explanation : let the number be ' n ' 15 \u00d7 n = 150 \u21d2 n = 10 correct option : b" + }, + { + "Answer": 74, + "Options": "a ) 74 , b ) 76 , c ) 78 , d ) 80 , e ) 82", + "Correct": "a", + "Explanation": "a score of 58 was 2 standard deviations below the mean - - > 58 = mean - 2 d a score of 98 was 3 standard deviations above the mean - - > 98 = mean + 3 d solving above for mean q = 74 . answer : a ." + }, + { + "Answer": 54, + "Options": "a ) 46 , b ) 54 , c ) 48 , d ) 49 , e ) 50", + "Correct": "b", + "Explanation": "the standard deviation ( { sd } ) = 2 ; 3 standard deviations below the mean is greater than 47 : { mean } - 3 * { sd } > 47 ; { mean } - 6 > 47 ; { mean } > 53 . answer : b ." + }, + { + "Answer": 125, + "Options": "a ) 125 , b ) 189 , c ) 297 , d ) 267 , e ) 298", + "Correct": "a", + "Explanation": "\"sum of the 35 numbers = 35 * 25 = 875 if each number is multiplied by 5 , the sum also gets multiplied by 5 and the average also gets multiplied by 5 . thus , the new average = 25 * 5 = 125 . answer : a\"" + }, + { + "Answer": 20, + "Options": "a ) 20 , b ) 27 , c ) 25 , d ) 99 , e ) 21", + "Correct": "a", + "Explanation": "\"let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 80 x - ( 5 * 50 ) = 90 ( x - 5 ) 200 = 10 x = > x = 20 . answer : a\"" + }, + { + "Answer": 1600, + "Options": "a ) rs . 3000 , b ) rs . 1600 , c ) rs . 2400 , d ) rs . 4000 , e ) none of these", + "Correct": "b", + "Explanation": "\"let the amount with r be rs . r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 4000 - r ) = > 3 r = 8000 - 2 r = > 5 r = 8000 = > r = 1600 . answer : b\"" + }, + { + "Answer": 10, + "Options": "a ) 2 , b ) 5 , c ) 10 , d ) 12 , e ) 15", + "Correct": "c", + "Explanation": "the q talks of total capacity , normal level , present level , shortage etc . . so it is all about not going wrong in these terms 14 mg = 70 % of total . . total = 14 / . 7 = 20 mg . . normal level = 1 / 2 of 20 = 10 mg . . shortage of normal level = 20 - 10 = 10 mg . . c" + }, + { + "Answer": 6, + "Options": "a ) 20 , b ) - 6 , c ) 30 , d ) 32 , e ) 48", + "Correct": "b", + "Explanation": "\"1 * 1 * 3 - ( 1 * 1 * 9 ) = 3 - 9 = - 6 ans : b\"" + }, + { + "Answer": 33.33333333333333, + "Options": "a ) 1.4 % , b ) 5.9 % , c ) 11.1 % , d ) 12.5 % , e ) 33.33 %", + "Correct": "e", + "Explanation": "\"opening = 6 closing = 8 rise in price = 2 so , percent increase = 2 / 6 * 100 = 33.33 % answer : e\"" + }, + { + "Answer": 100, + "Options": "a ) 377 , b ) 197 , c ) 187 , d ) 100 , e ) 822", + "Correct": "d", + "Explanation": "\"explanation : 9 / 12 = 3 / 4 * 900 = 675 650 - - - - - - - - - - - - - 25 1 / 4 - - - - - - - - 25 1 - - - - - - - - - ? = > rs . 100 answer : d\"" + }, + { + "Answer": 50, + "Options": "a ) 13.28 % , b ) 14 % , c ) 15 % , d ) 16 % , e ) 50 %", + "Correct": "e", + "Explanation": "\"let total % of work is 100 % total person = p 1 / 3 person are absent of total person . so absent person is 1 / 3 p ie p / 3 . left person is , p - p / 3 = 2 p / 3 . p person do the work 100 % 1 person do the work 100 * p % 2 p / 3 person do the work ( 100 * p * 3 ) / 2 p % = 150 % work increased for each person is = ( 150 - 100 ) % = 50 % answer : e\"" + }, + { + "Answer": 4900, + "Options": "a ) s . 4580 , b ) s . 4570 , c ) s . 4500 , d ) s . 4550 , e ) s . 4900", + "Correct": "e", + "Explanation": "\"sum of the salaries of the person for the months of january , february , march and april = 4 * 8000 = 32000 - - - - ( 1 ) sum of the salaries of the person for the months of february , march , april and may = 4 * 8400 = 33600 - - - - ( 2 ) ( 2 ) - ( 1 ) i . e . may - jan = 1600 salary of may is rs . 6500 salary of january = rs . 4900 answer : e\"" + }, + { + "Answer": 7, + "Options": "a ) 5 , b ) 7 , c ) 8 , d ) 10 , e ) 11", + "Correct": "b", + "Explanation": "\"w = 7 is the correct answer . good solution buneul . b\"" + }, + { + "Answer": 89, + "Options": "a ) 23 , b ) 25 , c ) 89 , d ) 30 , e ) 32", + "Correct": "c", + "Explanation": "explanation : = 80 \u00e2 \u02c6 \u2019 [ 5 \u00e2 \u02c6 \u2019 ( 6 + 2 ( 7 \u00e2 \u02c6 \u2019 8 + 5 ) ) ] ( please check due to overline , sign has been changed ) = 80 \u00e2 \u02c6 \u2019 [ 5 \u00e2 \u02c6 \u2019 ( 6 + 2 \u00e3 \u2014 4 ) ) ] = 80 \u00e2 \u02c6 \u2019 [ \u00e2 \u02c6 \u2019 9 ] = 80 + 9 = 89 option c" + }, + { + "Answer": 1, + "Options": "a ) - 1 , b ) 77 , c ) 8 , d ) 3 , e ) 2", + "Correct": "a", + "Explanation": "\"19 x + 19 y + 17 = - 19 x + 19 y - 21 38 x = - 38 = > x = - 1 answer : a\"" + }, + { + "Answer": 36, + "Options": "a ) 22 , b ) 36 , c ) 55 , d ) 77 , e ) 88", + "Correct": "b", + "Explanation": "\"let f = pure fuji , g = pure gala and c - cross pollinated . c = 10 % of x where x is total trees . c = . 1 x also 3 x / 4 = f and c + f = 204 = > . 1 x + 3 / 4 x = 204 = > x = 240 240 - 204 = pure gala = 36 . answer b\"" + }, + { + "Answer": 11.999999999999998, + "Options": "a ) 8 , b ) 12 , c ) 21 , d ) 27 , e ) 39", + "Correct": "b", + "Explanation": "\"3 ^ 3 + 4 ^ 3 = 91 therefore number is 3 * 4 = 12 b\"" + }, + { + "Answer": 64.00000000000001, + "Options": "a ) 54 , b ) 48 , c ) 65 , d ) 25 , e ) 64", + "Correct": "e", + "Explanation": "let the number be x . then , error = 5 / 3 x - 3 / 5 x = 16 / 15 x . error % = ( 16 x / 15 * 3 / 5 x * 100 ) % = 64 % answer e ) 64 %" + }, + { + "Answer": 32, + "Options": "a ) 32 , b ) 34 , c ) 35 , d ) 36 , e ) 37", + "Correct": "a", + "Explanation": "x ^ 0.8 = 16 x = ( 2 ^ 4 ) ^ ( 10 / 8 ) x = 2 ^ 5 x = 32 answer : a" + }, + { + "Answer": 1200, + "Options": "a ) 1200 , b ) 1992 , c ) 9921 , d ) 2798 , e ) 2789", + "Correct": "a", + "Explanation": "\"p = 12 ( 100 / 10 ) 2 = > p = 1200 answer : a\"" + }, + { + "Answer": 24.99999999999998, + "Options": "a ) 23 , b ) 24 , c ) 25 , d ) 26 , e ) 27", + "Correct": "c", + "Explanation": "\"12.4 * x + 26 = ( 3 + x ) 12 solve equation x = 25 answer : c\"" + }, + { + "Answer": 11, + "Options": "a ) 8 % , b ) 11 % , c ) 14 % , d ) 17 % , e ) 20 %", + "Correct": "b", + "Explanation": "\"the percent of alcohol in the solution is ( 0.05 ( 40 ) + 3.5 ) / 50 = 5.5 / 50 = 11 % the answer is b .\"" + }, + { + "Answer": 7550, + "Options": "a ) 5100 , b ) 7550 , c ) 10100 , d ) 15500 , e ) 20100", + "Correct": "b", + "Explanation": "\"my solution is : first 50 even integers : 2 4 6 8 < . . . > integers from 102 to 200 102 104 106 108 < . . . > we notice that each integer from the second set is 100 more than the respective integer in the first set . since we have 50 even integers from 102 to 200 , then : e = 2550 + ( 100 * 50 ) = 7550 . b\"" + }, + { + "Answer": 47.32142857142857, + "Options": "a ) a ) 47.3 , b ) b ) 45.6 , c ) c ) 44 , d ) d ) 48 , e ) e ) 49", + "Correct": "a", + "Explanation": "\"explanation : total marks obtained by a class of 25 students = 4 * 95 + 3 * 0 + 21 * 45 = 1325 average marks of whole class = 1325 / 28 = 47.3 answer : option a\"" + }, + { + "Answer": 10, + "Options": "a ) 27 , b ) 36 , c ) 29 , d ) 10 , e ) 11", + "Correct": "d", + "Explanation": "\"let the price of turban be x . thus , for one year the salary = ( 90 + x ) for 9 months he should earn 3434 ( 90 + x ) . now he gets one turban and rs . 65 . thus , 3434 ( 90 + x ) = 65 + x or 270 + 3 x = 260 + 4 x or x = 10 answer : d\"" + }, + { + "Answer": 60.526315789473685, + "Options": "a ) 46.2 % , b ) 54.54 % , c ) 60.52 % , d ) 70 % , e ) none of these", + "Correct": "c", + "Explanation": "\"explanation : number of runs made by running = 152 - ( 12 x 4 + 2 x 6 ) = 152 - ( 60 ) = 92 now , we need to calculate 92 is what percent of 152 . = > 92 / 152 * 100 = 60.52 % answer : c\"" + }, + { + "Answer": 49.99999999999996, + "Options": "a ) 25 , b ) 35 , c ) 50 , d ) 20 , e ) 15", + "Correct": "c", + "Explanation": "let the original income = $ 100 . then , expenditure = $ 75 and savings = $ 25 new income = $ 120 , new expenditure = $ ( ( 110 / 100 ) * 75 ) = rs . 165 / 2 new savings = $ ( 120 - ( 165 / 2 ) ) = $ 75 / 2 increase in savings = $ ( ( 75 / 2 ) - 25 ) = $ 25 / 2 increase % = ( ( 25 / 2 ) * ( 1 / 25 ) * 100 ) % = 50 % . answer c ) 50 ." + }, + { + "Answer": 4.5, + "Options": "a ) 4.5 hr , b ) 4.8 hr , c ) 4.9 hr , d ) 5.5 hr , e ) 6.5 hr", + "Correct": "a", + "Explanation": "for a 1 hour talk he took total of 9 hr time 1 hr = 9 hr ( 2 + 7 ) 30 min = 1 / 2 hr = ? so 9 * 1 / 2 div by 1 4.5 hr answer : a" + }, + { + "Answer": 7550, + "Options": "a ) 5100 , b ) 7550 , c ) 10100 , d ) 15500 , e ) 20100", + "Correct": "b", + "Explanation": "\"my solution is : first 50 even integers : 2 4 6 8 < . . . > integers from 102 to 200 102 104 106 108 < . . . > we notice that each integer from the second set is 100 more than the respective integer in the first set . since we have 50 even integers from 102 to 200 , then : t = 2550 + ( 100 * 50 ) = 7550 . b\"" + }, + { + "Answer": 42.857142857142854, + "Options": "a ) 30.6 % , b ) 34.4 % , c ) 38.7 % , d ) 42.9 % , e ) 46.5 %", + "Correct": "d", + "Explanation": "\"y = 1.75 x x = y / 1.75 = 100 y / 175 = 4 y / 7 x is 3 / 7 less which is about 42.9 % less than y . the answer is d .\"" + }, + { + "Answer": 6, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "d", + "Explanation": "suppose anoop joined after 3 months . then , 20000 * 12 = 40000 * ( 12 \u2013 x ) = > = > x = 6 . answer : d" + }, + { + "Answer": 91, + "Options": "a ) 87 , b ) 91 , c ) 95 , d ) 99 , e ) 103", + "Correct": "b", + "Explanation": "\"14 c 2 = 91 the answer is b .\"" + }, + { + "Answer": 180, + "Options": "a ) 130 , b ) 140 , c ) 150 , d ) 170 , e ) 180", + "Correct": "e", + "Explanation": "\"let the amount paid to a per week = x and the amount paid to b per week = y then x + y = 450 but x = 150 % of y = 150 y / 100 = 15 y / 10 \u2234 15 y / 10 + y = 450 \u21d2 y [ 15 / 10 + 1 ] = 450 \u21d2 25 y / 10 = 450 \u21d2 25 y = 4500 \u21d2 y = 4500 / 25 = rs . 180 e\"" + }, + { + "Answer": 36, + "Options": "a ) 3.6 sec , b ) 18 sec , c ) 36 sec , d ) 72 sec , e ) none", + "Correct": "c", + "Explanation": "\"speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 240 + 120 = 360 m . time taken = 360 / 10 = 36 sec answer : c\"" + }, + { + "Answer": 0.6666666666666666, + "Options": "a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6", + "Correct": "d", + "Explanation": "in general , the remainder divided by integer n is the same as the remainder that up to tens of n is divided by 8 . thus , in order for 46 , x , y 12 to be divided by 8 , y 12 should be divided by 8 . amongst 3 , 5,8 , 3 and 5 can be divided by 8 . therefore , w = two out of three can be divided and the answer is d ." + }, + { + "Answer": 51, + "Options": "a ) 48 , b ) 51 , c ) 60 , d ) 71 , e ) 96", + "Correct": "b", + "Explanation": "\"the total sum of the numbers should be increased by 50 . then the average will increase by 50 / 10 = 5 . the correct average is 51 . the answer is b .\"" + }, + { + "Answer": 60, + "Options": "a ) 50 , b ) 45 , c ) 60 , d ) 55 , e ) 53", + "Correct": "c", + "Explanation": "\"as half the circle shape consist of 40 - 10 = 30 boys , so total number of boys in full circle = 2 * 30 = 60 answer : c\"" + }, + { + "Answer": 19.5, + "Options": "a ) 17.25 % , b ) 19 , c ) 19.5 % , d ) 21.5 % , e ) 22 %", + "Correct": "c", + "Explanation": "we have a 15 litre solution containing 26 % alcohol in water . = > quantity of alcohol in the solution = 15 \u00e3 \u2014 26 / 100 now 5 litre of water is added to the solution . = > total quantity of the new solution = 15 + 5 = 20 percentage of alcohol in the new solution = 15 \u00e3 \u2014 26 / 100 20 \u00e3 \u2014 100 = 15 \u00e3 \u2014 26 / 10020 \u00e3 \u2014 100 = 15 \u00e3 \u2014 1.3 / 100 = 19.5 % c" + }, + { + "Answer": 41, + "Options": "a ) 41 , b ) 36 , c ) 39 , d ) 21 , e ) 11", + "Correct": "a", + "Explanation": "add the numbers of doughnuts . 15 + 12 + 14 = 41 . answer is a ." + }, + { + "Answer": 12, + "Options": "a ) 11 . , b ) 12 , c ) 13 , d ) 14 , e ) 14.5", + "Correct": "b", + "Explanation": "\"let the candy and soda before the increase be c and s respectively so increased price of can = c ( 1 + 25 / 100 ) = 10 - - - - - - - - - - - > c = 8 increase price of soda : s ( 1 + 1 / 2 ) = 6 - - - - - - - - - - - > s = 4 hence total = 8 + 4 = 12 . . hence answer : b\"" + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) 13 , c ) 16.6 , d ) 17 , e ) 23", + "Correct": "a", + "Explanation": "answer of set d is 12 = a" + }, + { + "Answer": 3500, + "Options": "a ) 2788 , b ) 3500 , c ) 7282 , d ) 2782 , e ) 2729", + "Correct": "b", + "Explanation": "\"4 - - - 2800 5 - - - ? = > 3500 answer : b\"" + }, + { + "Answer": 12.5, + "Options": "a ) 10 % , b ) 15 % , c ) 17.5 % , d ) 25 % , e ) 12.5 %", + "Correct": "e", + "Explanation": "\"consider base price - $ 100 25 % increase = 1.25 * 100 = $ 125 then a 10 % decrease on new price = 0.9 * 125 = $ 112.5 so final price of radio - $ 112.5 therefore a 12.5 % increase correct option - e\"" + }, + { + "Answer": 29, + "Options": "a ) 29 , b ) 10 , c ) 20 , d ) 40 , e ) 45", + "Correct": "a", + "Explanation": "\"solution - lets say , single hamburgersxand double hamburgersy given that , x + y = 50 and 1 x + 1.5 y = 64.50 . by solving the equations y = 29 . ans a .\"" + }, + { + "Answer": 349, + "Options": "a ) 7 , b ) 141 , c ) 29 , d ) 349 , e ) 359", + "Correct": "d", + "Explanation": "the actual question has bar on decimal part . hence the number is 2.5252525252 . . . . . . so let x = 2.525252 . . then 100 x = 252.525252 100 x - x = 250 x = 250 / 99 so ans = num + den = 349 answer : d" + }, + { + "Answer": 560.0000000000001, + "Options": "a ) rs . 540 , b ) rs . 580 , c ) rs . 560 , d ) rs . 620 , e ) rs . 650", + "Correct": "c", + "Explanation": "\"soln : - ( 575 / 115 ) 112 = 560 in this case long division does not take much time . ( 23 / 5 ) = 4.6 4.6 * 112 = rs . 560 answer : c\"" + }, + { + "Answer": 672, + "Options": "a ) 672 , b ) 682 , c ) 328 , d ) 964 , e ) 285", + "Correct": "a", + "Explanation": "the given numbers are 8,12 , 32,14 thus the l . c . m is 2 * 2 * 2 * 1 * 3 * 4 * 7 = 672 the answer is a" + }, + { + "Answer": 20, + "Options": "a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22", + "Correct": "c", + "Explanation": "from right 13 , from left 8 total = 13 + 8 - 1 = 20 answer : c" + }, + { + "Answer": 8, + "Options": "a ) 6 , b ) 8 , c ) 14 , d ) 16 , e ) 28", + "Correct": "b", + "Explanation": "\"equate the fat : 0.1 x + 0.30 * 8 = 0.2 ( x + 8 ) - - > x = 8 . answer : b .\"" + }, + { + "Answer": 100, + "Options": "a ) 25 % , b ) 33 1 / 3 % , c ) 100 % , d ) 66 2 / 3 % , e ) 75 %", + "Correct": "c", + "Explanation": "\"general formula for percent increase or decrease , ( percent change ) : percent = change / original \u2217 100 so , the time between maintenance checks increased by ( 60 \u2212 30 ) / 30 \u2217 100 = 100 answer : c\"" + }, + { + "Answer": 500, + "Options": "a ) $ 460 , b ) $ 480 , c ) $ 500 , d ) $ 520 , e ) $ 540", + "Correct": "c", + "Explanation": "\"avg = sum of observations / number of observations avg income = ( 600 + 250 + 450 + 400 + 800 ) / 5 = 500 answer is c\"" + }, + { + "Answer": 80, + "Options": "a ) 50 m , b ) 72 m , c ) 80 m , d ) 82 m , e ) 84 m", + "Correct": "c", + "Explanation": "\"let the length of each train be x m . then , distance covered = 2 x m . relative speed = 52 - 36 = 16 km / hr . = 16 * 5 / 18 = 40 / 9 m / sec . 2 x / 36 = 40 / 9 = > x = 80 . answer : c\"" + }, + { + "Answer": 36, + "Options": "a ) 21 , b ) 20 , c ) 25 , d ) 36 , e ) 45", + "Correct": "d", + "Explanation": "\"let number is x . when 10 added to it , = ( x + 10 ) 2 multiplied to sum , = 2 * ( x + 10 ) now , = [ { 2 * ( x + 10 ) } / 2 ] and , = [ { 2 * ( x + 10 ) } / 2 ] - 2 according to question , [ { 2 * ( x + 10 ) } / 2 ] - 2 = half of 88 [ ( 2 x + 20 ) / 2 ) = 44 + 2 x + 10 = 46 x + 10 = 46 x = 46 - 10 x = 36 so , required number is : 36 . answer : d\"" + }, + { + "Answer": 450, + "Options": "a ) 300 , b ) 375 , c ) 450 , d ) 500 , e ) 575", + "Correct": "c", + "Explanation": "\"as per the question 200 = 2 a / 5 thus - a which is the total amount = 500 the amount thus left = 300 she then deposited 1 / 2 of 300 = 150 total amount in her account = 450 answer c\"" + }, + { + "Answer": 4, + "Options": "a ) 1 , b ) 2 , c ) 5 , d ) 4 , e ) 8", + "Correct": "d", + "Explanation": "\"( 1100 / 23 ) gives remainder 19 19 + 4 = 23 , so we need to add 4 answer : d\"" + }, + { + "Answer": 0.32000000000000006, + "Options": "a ) 8 / 25 , b ) 1 / 25 , c ) 2 / 25 , d ) 3 / 14 , e ) 25 / 8", + "Correct": "a", + "Explanation": "\"p ( a n b ) = p ( a ) . p ( b ) p ( a n b ) = 4 / 5 . 2 / 5 p ( a n b ) = 8 / 25 . a\"" + }, + { + "Answer": 48, + "Options": "a ) 14 , b ) 24 , c ) 28 , d ) 48 , e ) 96", + "Correct": "d", + "Explanation": "first , look for all 4 digits without repeat that add up to 28 . to avoid repetition , start with the highest numbers first . start from the largest number possible 9874 . then the next largest number possible is 9865 . after this , you ' ll realize no other solution . clearly the solution needs to start with a 9 ( cuz otherwise 8765 is the largest possible , but only equals 26 ) . with a 9 , you also need an 8 ( cuz otherwise 9765 is the largest possible , but only equals 27 ) . with 98 __ only 74 and 65 work . so you have two solutions . each can be rearranged in 4 ! = 24 ways . so f = 24 + 24 = 48 . d" + }, + { + "Answer": 76, + "Options": "a ) 29 , b ) 38 , c ) 76 , d ) 37 , e ) 75", + "Correct": "c", + "Explanation": "\"average = ( 81 + 65 + 82 + 67 + 85 ) / 5 = 76 . answer : c\"" + }, + { + "Answer": 29, + "Options": "a ) 29 , b ) 1 , c ) 10 , d ) 30 , e ) 8", + "Correct": "a", + "Explanation": "average of 30 numbers = 0 . sum of 30 numbers ( 0 x 30 ) = 0 . it is quite possible that 29 of these numbers may be positive and if their sum is a the 30 th number is ( - a ) . answer : option a" + }, + { + "Answer": 9, + "Options": "a ) 1 , b ) 2 , c ) 5 , d ) 9 , e ) 11", + "Correct": "d", + "Explanation": "\"on dividing the given number by 342 , let k be the quotient and 47 as remainder . then , number \u2013 342 k + 47 = ( 19 x 18 k + 19 x 2 + 9 ) = 19 ( 18 k + 2 ) + 9 . \uf05c the given number when divided by 19 , gives ( 18 k + 2 ) as quotient and 9 as remainder . answer d\"" + }, + { + "Answer": 36, + "Options": "a ) 6 , b ) 14 , c ) 36 , d ) 21 , e ) none of these", + "Correct": "c", + "Explanation": "explanation \u221a ( 36 ) ^ 2 = ? or , ? = 36 answer c" + }, + { + "Answer": 70, + "Options": "a ) 55 , b ) 70 , c ) 75 , d ) 85 , e ) 95", + "Correct": "b", + "Explanation": "\"let the marks obtained by the student in physics , chemistry and mathematics be p , c and m respectively . p + c + m = 140 + p c + m = 140 average mark obtained by the student in chemistry and mathematics = ( c + m ) / 2 = 140 / 2 = 70 . answer : b\"" + }, + { + "Answer": 7, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", + "Correct": "a", + "Explanation": "\"p is a positive even integer with a positive units digit - - > the units digit of p can be 2 , 4 , 6 , or 8 - - > only in order the units digit of p ^ 3 - p ^ 2 to be 0 , the units digit of p ^ 3 and p ^ 2 must be the same . i . e 0 , 1,5 or 6 intersection of values is 6 , thus the units digit of p + 1 is 6 + 1 = 9 . answer : a .\"" + }, + { + "Answer": 0.6, + "Options": "a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 5", + "Correct": "e", + "Explanation": "let p be the number of progressives in the country as a whole . in each province , the number of traditionalists is p / 9 the total number of traditionalists is 6 p / 9 = 2 p / 3 . the total population is p + 2 p / 3 = 5 p / 3 p / ( 5 p / 3 ) = 3 / 5 the answer is e ." + }, + { + "Answer": 2016, + "Options": "a ) 2016 , b ) 2088 , c ) 270 , d ) 1881 , e ) 1781", + "Correct": "a", + "Explanation": "\"f ( f ( 0 ) ) + f ( 0 ) = 2 ( 0 ) + 3 \u21d2 \u21d2 f ( 1 ) = 3 - 1 = 2 , f ( 1 ) = 2 f ( f ( 1 ) ) + f ( 1 ) = 2 ( 1 ) + 3 \u21d2 \u21d2 f ( 2 ) = 5 - 2 = 3 , f ( 2 ) = 3 f ( f ( 2 ) ) + f ( 2 ) = 2 ( 2 ) + 3 \u21d2 \u21d2 f ( 3 ) = 7 - 3 = 4 , f ( 3 ) = 4 . . . . . . . . . . . . . . f ( 2015 ) = 2016 ans : a\"" + }, + { + "Answer": 0.125, + "Options": "a ) 1 / 9 , b ) 1 / 8 , c ) 1 / 11 , d ) 1 / 13 , e ) 2 / 5", + "Correct": "b", + "Explanation": "p ( not a and not b ) = 1 - ( p ( a ) + p ( b ) - p ( ab ) ) which you might find somewhere in your text . substituting in our probabilities we get : p ( not a and not b ) = 1 - ( 3 / 4 + 1 / 2 - 3 / 8 ) p ( not a and not b ) = 1 - ( 7 / 8 ) p ( not a and not b ) = 1 / 8 . b" + }, + { + "Answer": 1776, + "Options": "a ) 1443 , b ) 1554 , c ) 1665 , d ) 1776 , e ) 1887", + "Correct": "d", + "Explanation": "\"there are 6 possible arrangements of the three numbers . then each number will be in the hundreds , tens , and ones place two times each . the sum is 2 ( 111 ) + 2 ( 333 ) + 2 ( 444 ) = 1776 the answer is d .\"" + }, + { + "Answer": 1, + "Options": "a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2", + "Correct": "d", + "Explanation": "d 1 - 14 x + 14 z + 18 = - 14 x + 14 z - 10 - 28 x + 28 = 0 - 28 x = - 28 = > x = 1" + }, + { + "Answer": 239.99999999999994, + "Options": "a ) 240 , b ) 250 , c ) 280 , d ) 300 , e ) 320", + "Correct": "a", + "Explanation": "\"1 / 3 + 1 / 8 + 1 / 5 + 1 / 6 = ( 40 + 15 + 24 + 20 ) / 120 = 99 / 120 let x be the number of passengers on the ship . 42 = ( 21 / 120 ) x = 7 x / 40 x = 240 the answer is a .\"" + }, + { + "Answer": 22500, + "Options": "a ) 18000 , b ) 22500 , c ) 24000 , d ) 26000 , e ) 32000", + "Correct": "b", + "Explanation": "z = 25 - - > y received 2 / 5 fewer votes than z - - > y = z - 2 / 5 * z = 15 ; x received 1 / 2 more votes than y - - > x = y + 1 / 2 * y = 22,5 . answer : b ." + }, + { + "Answer": 100, + "Options": "a ) 90 % , b ) 99 % , c ) 100 % , d ) 101 % , e ) 110 %", + "Correct": "b", + "Explanation": "\"the total number of employees = n the average salary = x total salary to all emplyoees = xn after the total number of employees = n - 0.1 n = 0.9 n the average salary = x + 10 % of x = 1.1 x total salary to all emplyoees = 0.9 n ( 1.1 x ) total salary after as a % of total salary before t = [ 0.9 n ( 1.1 x ) ] / xn = 0.99 or 99 % . b\"" + }, + { + "Answer": 0.3, + "Options": "a ) 2 / 3 , b ) 2 / 5 , c ) 3 / 5 , d ) 3 / 10 , e ) 7 / 20", + "Correct": "d", + "Explanation": "1 / 2 of the small beaker is 1 / 10 of the large beaker . 1 / 10 + 1 / 5 = 3 / 10 the answer is d ." + }, + { + "Answer": 22, + "Options": "a ) 22 , b ) 25 , c ) 26 , d ) 28 , e ) 29", + "Correct": "a", + "Explanation": "( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 222 + 2 * 131 a + b + c = \u221a 484 = 22 a" + }, + { + "Answer": 1750, + "Options": "a ) 1500 , b ) 1600 , c ) 1750 , d ) 1900 , e ) 2000", + "Correct": "c", + "Explanation": "\"let the price of basic computer be c and the price of the printer be p : c + p = $ 2,500 . the price of the enhanced computer will be c + 500 and total price for that computer and the printer will be 2,500 + 500 = $ 3,000 . now , we are told that the price of the printer is 1 / 4 of that new total price : p = 1 / 4 * $ 3,000 = $ 750 . plug this value in the first equation : c + 750 = $ 2,500 - - > c = $ 1,750 answer : c .\"" + }, + { + "Answer": 9, + "Options": "a ) 16 , b ) 14 , c ) 18 , d ) 6 , e ) 9", + "Correct": "e", + "Explanation": "n ^ ( n / 2 ) = 9 apply log n / 2 logn = log 9 nlogn = 2 log 9 = log 9 ^ 2 = log 81 logn = log 81 now apply antilog n = 81 / n now n = 9 . answer : e" + }, + { + "Answer": 42, + "Options": "a ) 39 , b ) 40 , c ) 41 , d ) 42 , e ) 43", + "Correct": "d", + "Explanation": "( 58 seconds + 26 seconds ) / 2 = 42 seconds correct option is : d" + }, + { + "Answer": 0.5625, + "Options": "a ) 3 / 8 , b ) 1 / 2 , c ) 9 / 16 , d ) 5 / 7 , e ) 3 / 4", + "Correct": "c", + "Explanation": "the answer isc : 11 / 16 . the key to this problem is remembering that the median for a consecutive set of numbers is equivalent to its mean . for example , the mean and median of a set consisting of x , x + 1 , x + 2 , . . . , y will always be ( x + y ) / 2 . for set s , consisting of numbers ( a , a + 1 , . . . , b ) , the median is given to be 3 / 4 * b : ( a + b ) / 2 = ( 3 / 4 ) * b a = b / 2 for set q , consisting of numbers ( b , b + 1 , . . . , c ) , the median is given to be 5 / 8 * c : ( b + c ) / 2 = ( 5 / 8 ) * c b = ( 1 / 4 ) * c for set r , consisting of numbers ( a , a + 1 , . . . c ) , the median needs to be found : a = b / 2 = ( 1 / 4 * c ) / 2 = ( 1 / 8 ) * c median = ( a + c ) / 2 = ( 1 / 8 * c + c ) / 2 = ( 9 / 8 ) * c / 2 = ( 9 / 16 ) * c ( answer c )" + }, + { + "Answer": 180.66666666666666, + "Options": "a ) 151 , b ) 149 , c ) 152 , d ) 148 , e ) 180.67", + "Correct": "e", + "Explanation": "\"corrected mean = 180 \u00d7 30 \u2212 135 + 155 / 30 = 5400 \u2212 135 + 155 / 30 = 5420 / 30 = 180.67 answer e\"" + }, + { + "Answer": 360, + "Options": "a ) 120 , b ) 240 , c ) 360 , d ) 720 , e ) 1440", + "Correct": "c", + "Explanation": "x - x - x - x - x - - > there are 3 even digits from 1 to 7 , inclusive thus options for the first and the last x ' s are : 3 - x - x - x - 2 . other x ' s can take following values : 3 - 5 - 4 - 3 - 2 - - > 3 * 5 * 4 * 3 * 2 = 360 . answer : c ." + }, + { + "Answer": 46, + "Options": "a ) 42 . , b ) 46 . , c ) 50 . , d ) 54 . , e ) 58 .", + "Correct": "b", + "Explanation": "\"n = 4 k + 1 = 7 j + 2 let ' s start at 1 = 4 ( 0 ) + 1 and keep adding 4 until we find a number in the form 7 j + 2 . 1 , 5 , 9 = 7 ( 1 ) + 2 the next such number is 9 + 4 * 7 = 37 . 9 + 37 = 46 the answer is b .\"" + }, + { + "Answer": 4, + "Options": "a ) 4 , b ) 2 , c ) 0 , d ) \u2212 2 , e ) \u2212 4", + "Correct": "a", + "Explanation": "first , solve for the slope , m : m = ( y 2 - y 1 ) / ( x 2 - x 1 ) = ( - 5 - 3 ) / ( - 6 - 10 ) = - 8 / - 16 or 1 / 2 then you can re - write the equation as y = ( 1 / 2 ) x + b and plug in one of the points to find b , the y intercept . using point ( 10 , 3 ) : 3 = ( 1 / 2 ) ( 10 ) + b , which can be simplified to 3 = 5 + b . solve for b and you get b = - 2 . the equation now reads : y = ( 1 / 2 ) x - 2 . to find the x intercept , plug in 0 for y : 0 = ( 1 / 2 ) x - 2 , which simplifies to 2 = ( 1 / 2 ) x . from this , we can see that the x intercept = 4 . answer is a ." + }, + { + "Answer": 2, + "Options": "a ) 5 : 2 , b ) 4 : 3 , c ) 3 : 2 , d ) 2 : 1 , e ) 4 : 1", + "Correct": "d", + "Explanation": "\"( 5 / 8 ) * p + ( 1 / 4 ) * q = ( 3 / 8 ) * p + ( 3 / 4 ) * q 2 p = 4 q p / q = 2 / 1 the answer is d .\"" + }, + { + "Answer": 84, + "Options": "a ) 33 , b ) 77 , c ) 48 , d ) 84 , e ) 21", + "Correct": "d", + "Explanation": "\"speed on return trip = 110 % of 80 = 88 km / hr . average speed of trip = 80 + 88 / 2 = 168 / 2 = 84 km / hr answer : d\"" + }, + { + "Answer": 5, + "Options": "a ) 3 , b ) 5 , c ) 8 , d ) 13 , e ) 15", + "Correct": "b", + "Explanation": "\"total # of students = 38 avg # of books per student = 2 total # of books = 38 * 2 = 76 # of student borrowed at least 3 books = 38 - 2 - 12 - 10 = 14 # of books borrowed by above 14 students = 76 - ( 12 * 1 ) + ( 10 * 2 ) = 44 considering that 13 out of above 14 students borrowed only 3 books , # of books borrowed = 13 * 3 = 39 so maximum # of books borrowed by any single student = 44 - 39 = 5 option b\"" + }, + { + "Answer": 300, + "Options": "a ) 420 , b ) 260 , c ) 200 , d ) 300 , e ) 400", + "Correct": "d", + "Explanation": "explanation : ( 5 ) 1.25 \u00d7 ( 12 ) 0.25 \u00d7 ( 60 ) 0.75 = ( 5 ) 1.25 \u00d7 ( 12 ) 0.25 \u00d7 ( 12 \u00d7 5 ) 0.75 = ( 5 ) 1.25 \u00d7 ( 12 ) 0.25 \u00d7 ( 12 ) 0.75 \u00d7 ( 5 ) 0.75 = ( 5 ) ( 1.25 + 0.75 ) \u00d7 ( 12 ) ( 0.25 + 0.75 ) = ( 5 ) 2 \u00d7 ( 12 ) 1 = 25 \u00d7 12 = 300 answer : option d" + }, + { + "Answer": 97.14285714285714, + "Options": "a ) 97.1 kgs , b ) 88.5 kgs , c ) 86.5 kgs , d ) 67.5 kgs , e ) 88.2 kgs", + "Correct": "a", + "Explanation": "\"average weight = [ ( a + b + c + ( a + b ) + ( b + c ) + ( c + a ) + ( a + b + c ) ] / 7 = 4 ( a + b + c ) / 7 = 4 x 170 / 7 = 97.1 kgs answer : a\"" + }, + { + "Answer": 1400, + "Options": "a ) 3387 , b ) 1000 , c ) 2866 , d ) 2787 , e ) 1400", + "Correct": "e", + "Explanation": "\"28 * 10 * 5 = 1400 answer : e\"" + }, + { + "Answer": 271.07142857142856, + "Options": "a ) a ) 125 , b ) b ) 175 , c ) c ) 271 , d ) d ) 375 , e ) e ) 524", + "Correct": "c", + "Explanation": "\"explanation : ? = ( 150 x 1265 / 100 ) \u00f7 7 = 189750 / 700 = 271 answer : option c\"" + }, + { + "Answer": 0.95, + "Options": "a ) 23 / 34 , b ) 57 / 60 , c ) 51 / 67 , d ) 19 / 71 , e ) 75 / 64", + "Correct": "b", + "Explanation": "\"the way to approach this problem is 2 < a < 7 and 4 < b < 13 minimum possible value of a is 3 and maximum is 6 minimum possible value of b is 5 and maximum is 12 range = max a / min b - min a / max b ( highest - lowest ) 6 / 5 - 3 / 12 = 57 / 60 hence b\"" + }, + { + "Answer": 6, + "Options": "a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 8", + "Correct": "d", + "Explanation": "answer = d = 6 number . . . . . . . . . . . . . . . . factors . . . . . . . . . . . . . . . . . . . . . . . . product 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 2 , 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 2 , 3 , 6 . . . . . . . . . . . . . . . . . . . . . . . . . 36 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 2 , 4 , 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 3 , 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 2 , 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 2 , 3 , 4 , 6 , 12 . . . . . . . . . . . . . . . . . 12 * 12 * 12 number which we are looking for = 12 answer = d" + }, + { + "Answer": 4, + "Options": "a ) 30 , b ) 18 , c ) 10 , d ) 9 , e ) 4", + "Correct": "e", + "Explanation": "\"( average production for n days ) * n = ( total production for n days ) - - > 50 n = ( total production for n days ) ; ( total production for n days ) + 90 = ( average production for n + 1 days ) * ( n + 1 ) - - > 50 n + 90 = 58 * ( n + 1 ) - - > n = 4 . or as 40 extra units increased the average for n + 1 days by 8 units per day then 40 / ( n + 1 ) = 8 - - > n = 4 . answer : e .\"" + }, + { + "Answer": 21.333333333333332, + "Options": "a ) 17 litres , b ) 21.3 litres , c ) 11 litres , d ) 07 litres , e ) 38 litres", + "Correct": "b", + "Explanation": "\"262.85 ( 32 ) + 3 , 104.35 x = 1 , 399.45 ( 32 + x ) solve the equation . 262.85 ( 32 ) + 3 , 104.35 x = 1 , 399.45 ( 32 + x ) 8 , 411.2 + 3 , 104.35 x = 44 , 782.4 + 1 , 399.45 x 8 , 411.2 + 1 , 704.9 x = 44 , 782.4 1 , 704.9 x = 36 , 371.2 x \u2248 21.3 answer is b .\"" + }, + { + "Answer": 21, + "Options": "a ) 20 , b ) 11 , c ) 21 , d ) 41 , e ) none of these", + "Correct": "c", + "Explanation": "x ^ + y ^ 2 + z ^ 2 = 241 xy + yz + zx = 100 as we know . . ( x + y + z ) ^ 2 = x ^ 2 + y ^ 2 + z ^ 2 + 2 ( xy + yz + zx ) so ( x + y + z ) ^ 2 = 241 + ( 2 * 100 ) ( x + y + z ) ^ 2 = 441 so x + y + z = 21 answer : c" + }, + { + "Answer": 2.2, + "Options": "a ) 4 / 5 , b ) 6 / 5 , c ) 7 / 5 , d ) 11 / 5 , e ) 9 / 5", + "Correct": "d", + "Explanation": "\"w / x = 1 / 6 = > x = 6 w and w / y = 1 / 5 = > y = 5 w ( x + y ) / y = ( 6 w + 5 w ) / 5 w = 11 w / 5 w = 11 / 5 correct option : d\"" + }, + { + "Answer": 13, + "Options": "a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14", + "Correct": "d", + "Explanation": "let x be the amount of liquid q to be added . ( 3 / 7 ) * 35 + x = ( 7 / 12 ) * ( 35 + x ) 1260 + 84 x = 1715 + 49 x 35 x = 455 x = 13 the answer is d ." + }, + { + "Answer": 76, + "Options": "a ) 74 , b ) 76 , c ) 78 , d ) 80 , e ) 82", + "Correct": "b", + "Explanation": "\"mean - 2 sd = 60 mean + 3 sd = 100 by solving above we get , sd ( absolute value ) = 8 mean = 76 ans . b\"" + }, + { + "Answer": 29, + "Options": "a ) and 27 , b ) and 24 , c ) and 22 , d ) and 29 , e ) of these", + "Correct": "d", + "Explanation": "\"let the age of jill 9 years ago be x , age of henry be 2 x x + 9 + 2 x + 9 = 48 x = 10 present ages will be 19 and 29 answer : d\"" + }, + { + "Answer": 12, + "Options": "a ) 8 , b ) 12 , c ) 15 , d ) 16 , e ) 19", + "Correct": "b", + "Explanation": "let original strength = y then , 40 y + 12 x 32 = ( y + 12 ) x 36 \u21d2 40 y + 384 = 36 y + 432 \u21d2 4 y = 48 \u2234 y = 12 b" + }, + { + "Answer": 839.9999999999998, + "Options": "a ) 8.4 , b ) 840 , c ) 84.0 , d ) 0.84 , e ) 0.084", + "Correct": "b", + "Explanation": "( 0.0048 ) ( 3.5 ) / ( 0.05 ) ( 0.1 ) ( 0.004 ) = 0.0048 * 350 / 5 ( 0.1 ) ( 0.004 ) = 0.048 * 70 / 1 ( 0.004 ) = 48 * 70 / 4 = 12 * 70 = 840 answer : b" + }, + { + "Answer": 37, + "Options": "a ) 47 , b ) 37 , c ) 39 , d ) 43 , e ) 42", + "Correct": "b", + "Explanation": "average score before 17 th innings = 85 - 3 \u00d7 17 = 34 average score after 17 th innings = > 34 + 3 = 37 answer : b" + }, + { + "Answer": 5.5, + "Options": "a ) 5.5 % , b ) 3.6 % , c ) 4.4 % , d ) 5.2 % , e ) 6.0 %", + "Correct": "a", + "Explanation": "\"let amount spent by jill = 100 clothing = 50 , food = 20 , others = 30 tax on clothing = 2.5 tax on others = 3 percentage = 5.5 / 100 = 5.5 % answer : a\"" + }, + { + "Answer": 120, + "Options": "a ) 8 , b ) 64 , c ) 120 , d ) 102 , e ) 144", + "Correct": "c", + "Explanation": "if 80 % of the packages weigh at least 25 pounds this means that 20 % of the packages weigh less than 25 pounds let t = total number of packages so , 20 % of t = # of packages that weigh less than 25 pounds 48 packages weigh less than 25 pounds great . so , 20 % of t = 48 rewrite to get : 0.2 t = 48 solve : t = 240 70 % of the packages weigh less than 75 pounds so , 70 % oft = number of packages that weigh less than 75 pounds 70 % of 240 = 168 , so 168 packages weigh less than 75 pounds of those 168 packages that weigh less than 75 pounds , 48 packages weigh less than 25 pounds . so , the number of packages that weight between 25 and 75 pounds = 168 - 48 = 120 = c" + }, + { + "Answer": 3775, + "Options": "a ) 2525 , b ) 2975 , c ) 3225 , d ) 3775 , e ) 3885", + "Correct": "d", + "Explanation": "\"( 51 + 52 + 53 + \u2026 \u2026 \u2026 + 100 ) = ( 1 + 2 + 3 + \u2026 \u2026 . + 100 ) - ( 1 + 2 + 3 + 4 + \u2026 \u2026 + 50 ) = ( 100 * 101 ) / 2 - ( 50 * 51 ) / 2 = ( 5050 - 1275 ) = 3775 . answer : d\"" + }, + { + "Answer": 30.5, + "Options": "a ) 35.2 , b ) 36.1 , c ) 30.5 , d ) 39.1 , e ) none", + "Correct": "c", + "Explanation": "\"sol . therefore correct sum = ( 30 \u00d7 50 + 48 \u2013 23 ) = 1525 . therefore correct mean = 1525 / 50 = 30.5 . answer c\"" + }, + { + "Answer": 68, + "Options": "a ) 60 kg , b ) 75 kg , c ) 68 kg , d ) 85 kg , e ) 90 kg", + "Correct": "c", + "Explanation": "\"total weight increased = ( 6 x 3.5 ) kg = 21 kg . weight of new person = ( 47 + 21 ) kg = 68 kg option c\"" + }, + { + "Answer": 160, + "Options": "a ) s . 260 , b ) s . 160 , c ) s . 360 , d ) s . 50 , e ) s . 90", + "Correct": "b", + "Explanation": "\"a profit of rs . 800 is divided between x and y in the ratio of 1 / 2 : 1 / 3 or 3 : 2 . so profits are 480 and 320 . difference in profit share = 480 - 320 = 160 answer : b\"" + }, + { + "Answer": 6, + "Options": "a ) 10 , b ) 6 , c ) 4 , d ) 0 , e ) it can not be determined", + "Correct": "b", + "Explanation": "it is essential to recognize that the remainder when an integer is divided by 10 is simply the units digit of that integer . to help see this , consider the following examples : 4 / 10 is 0 with a remainder of 4 14 / 10 is 1 with a remainder of 4 5 / 10 is 0 with a remainder of 5 105 / 10 is 10 with a remainder of 5 it is also essential to remember that the a is a positive integer and multiple of 2 . any integer that is a multiple of 2 is an even number . so , a must be a positive even integer . with these two observations , the question can be simplified to : what is the units digit of 4 raised to an even positive integer ? the units digit of 4 raised to an integer follows a specific repeating pattern : 4 ^ 1 = 4 4 ^ 2 = 16 4 ^ 3 = 64 4 ^ 4 = 256 4 ^ ( odd number ) - - > units digit of 4 4 ^ ( even number ) - - > units digit of 6 there is a clear pattern regarding the units digit . 4 raised to any odd integer has a units digit of 4 while 4 raised to any even integer has a units digit of 6 . since a must be an even integer , the units digit of p = 4 ^ a will always be 6 . consequently , the remainder when p = 4 ^ a is divided by 10 will always be 6 . in case this is too theoretical , consider the following examples : a = 2 - - > p = 4 ^ a = 16 - - > p / 10 = 1 with a remainder of 6 a = 4 - - > p = 4 ^ a = 256 - - > p / 10 = 25 with a remainder of 6 a = 6 - - > p = 4 ^ a = 4096 - - > p / 10 = 409 with a remainder of 6 a = 8 - - > p = 4 ^ a = 65536 - - > p / 10 = 6553 with a remainder of 6 answer : b ." + }, + { + "Answer": 1.0204081632653061, + "Options": "a ) 50 / 49 , b ) 1 / 289 , c ) 290 / 90 , d ) 290 / 19 , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : if the numbers are a , b , then ab = 7 , as 17 is a prime number , so a = 1 , b = 7 . 1 / a 2 + 1 / b 2 = 1 / 1 ( 2 ) + 1 / 7 ( 2 ) = 50 / 49 option a\"" + }, + { + "Answer": 26, + "Options": "a ) 20 , b ) 22 , c ) 26 , d ) 24 , e ) 30", + "Correct": "c", + "Explanation": "\"total # of codes possible is 3 * 3 * 3 = 27 . oit of those 27 codes only the product of 333 and will be odd , the remaining 26 will have either 2 or 4 in them , which ensures that their product will be even . therefore the number of codes where the product of the digits is even = ( total ) - ( restriction ) = 27 - 1 = 26 . answer : c\"" + }, + { + "Answer": 40, + "Options": "a ) 39 , b ) 40 , c ) 41 , d ) 42 , e ) 43", + "Correct": "b", + "Explanation": "\"solution start with 5 pens . mike gives you 20 pens : 5 + 20 = 25 pens . cindy doubles the number of pens you have : 25 \u00e3 \u2014 2 = 50 pens . sharon takes 10 pens from you : 50 - 10 = 40 pens . so you have 40 at the end . correct answer : b\"" + }, + { + "Answer": 4, + "Options": "a ) 2.8 % , b ) 3.6 % , c ) 4 % , d ) 5.2 % , e ) 6.0 %", + "Correct": "c", + "Explanation": "\"let amount spent by jill = 100 clothing = 40 , food = 30 , others = 30 tax on clothing = 1.6 tax on others = 2.4 percentage = 4 / 100 = 4 % answer : c\"" + }, + { + "Answer": 48, + "Options": "a ) 48 , b ) 120 , c ) 130 , d ) 140 , e ) 150", + "Correct": "a", + "Explanation": "\"solution : let xx be the number he chose , then 5 \u22c5 x \u2212 138 = 102 5 x = 240 x = 48 answer a\"" + }, + { + "Answer": 0.7083333333333334, + "Options": "a ) 11 / 30 , b ) 29 / 60 , c ) 17 / 24 , d ) 19 / 30 , e ) 11 / 15", + "Correct": "c", + "Explanation": "let s assume the platinum card spending limit = x gold card spending limit will be = x / 2 balance on gold card is = x / 2 * 1 / 3 = x / 6 platinum card unspent limit is = x - 1 / 8 x = 7 / 8 x so if gold card balance is transferred then the rest unspent will be 7 / 8 x - x / 6 = 17 / 24 x so the ans is c" + }, + { + "Answer": 15, + "Options": "a ) 23 , b ) 20 , c ) 15 , d ) 5 , e ) 2", + "Correct": "c", + "Explanation": "\"soln : { 14 } + { 12 } = 14 * { 12 } + { 12 } = 15 * { 12 } answer : c\"" + }, + { + "Answer": 23, + "Options": "a ) w = 21 , b ) w = 22 , c ) w = 23 , d ) w = 24 , e ) 27", + "Correct": "c", + "Explanation": "\"squaring on both sides , x ^ 2 + ( 1 / x ) ^ 2 + 2 ( x ) ( 1 / x ) = 5 ^ 2 x ^ 2 + ( 1 / x ) ^ 2 = 23 answer : c\"" + }, + { + "Answer": 540, + "Options": "a ) 540 , b ) 570 , c ) 619 , d ) 649 , e ) 700", + "Correct": "a", + "Explanation": "\"before price increase price = d after 30 % price increase price = d + ( 30 / 100 ) * d = 1.3 d = 351 ( given ) i . e . d = 351 / 1.3 = $ 270 i . e . 2 d = 2 * 270 = 540 answer : option a\"" + }, + { + "Answer": 9, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 21 , e ) 14", + "Correct": "c", + "Explanation": "\"sol . on dividing the given number by 342 , let k be the quotient and 47 as remainder . then , number \u2013 342 k + 47 = ( 19 x 18 k + 19 x 2 + 9 ) = 19 ( 18 k + 2 ) + 9 . the given number when divided by 19 , gives ( 18 k + 2 ) as quotient and 9 as remainder . option c\"" + }, + { + "Answer": 4.25, + "Options": "a ) 29 / 16 , b ) 19 / 16 , c ) 15 / 16 , d ) 17 / 4 , e ) 0", + "Correct": "d", + "Explanation": "1 / 2 + [ ( 2 / 3 * 3 / 8 ) + 4 ] - 8 / 16 = 1 / 2 + [ ( 1 / 4 ) + 4 ] - 8 / 16 = 1 / 2 + [ 17 / 4 ] - 9 / 16 = 8 / 16 + 68 / 16 - 8 / 16 = 68 / 16 = 17 / 4 d" + }, + { + "Answer": 16.666666666666664, + "Options": "a ) 12.00 % , b ) 16.67 % , c ) 18.33 % , d ) 20.00 % , e ) 21.50 %", + "Correct": "b", + "Explanation": "suppose when v = 5 x 10 x 20 = 1000 cm , the price is $ 1200 per cm price = $ 1.2 the price is $ 1200 if v = 6 x 10 x 20 = 1000 cm . per cm price = $ 1.0 so the price is decreased by $ 0.2 so the % price decreased by $ 0.2 / 1.20 = 16.67 % answer : b" + }, + { + "Answer": 1.4000000000000001, + "Options": "a ) 1.9 , b ) 1.7 , c ) 1.4 , d ) 1.5 , e ) 1.1", + "Correct": "c", + "Explanation": "\"speed of boat in still water ( b ) = 4.2 km / hr . speed of boat with stream ( down stream ) , d = b + u speed of boat against stream ( up stream ) , u = b \u2013 u it is given upstream time is twice to that of down stream . \u21d2 downstream speed is twice to that of upstream . so b + u = 2 ( b \u2013 u ) \u21d2 u = b / 3 = 1.4 km / hr . answer : c\"" + }, + { + "Answer": 16, + "Options": "a ) 15 , b ) 18 , c ) 16 , d ) 22 , e ) none", + "Correct": "c", + "Explanation": "\"sol . average = ( 12 + 14 + 16 + 18 + 20 / 5 ) = 80 / 5 = 16 . answer c\"" + }, + { + "Answer": 0.23076923076923078, + "Options": "a ) 21 / 26 , b ) 25 / 26 , c ) 11 / 26 , d ) 6 / 26 , e ) 22 / 33", + "Correct": "d", + "Explanation": "\"let us say probability of a occuring is a . let us say probability of b occuring is b . a = 2 b probability ( either a or b or both ) = 12 times probability ( a and b ) a * ( 1 - b ) + b * ( 1 - a ) + ab = 12 * ab substituting a = 2 b in the second equation : 2 b * ( 1 - b ) + b * ( 1 - 2 b ) + 2 b * b = 12 * 2 b * b 3 b - 2 b ^ 2 = 24 b ^ 2 3 b = 26 b ^ 2 b = 3 / 26 = 3 / 26 so , a = 2 b = 6 / 26 the correct answer is d .\"" + }, + { + "Answer": 6.8, + "Options": "a ) 6.6 kg , b ) 6.8 kg , c ) 6.7 kg , d ) 6.9 kg , e ) 7.8 kg", + "Correct": "b", + "Explanation": "\"800 * 8.5 6800.0 gm 6.8 kg answer : b\"" + }, + { + "Answer": 50, + "Options": "a ) 40 % , b ) 50 % , c ) 65 % , d ) 68 % , e ) 70 %", + "Correct": "b", + "Explanation": "\"number of runs made by running = 110 - ( 3 x 4 + 8 x 6 ) = 120 - ( 60 ) = 60 now , we need to calculate 60 is what percent of 120 . = > 60 / 120 * 100 = 50 % b\"" + }, + { + "Answer": 0.75, + "Options": "a ) 44 / 7 , b ) 9 / 8 , c ) 25 / 8 , d ) 3 / 4 , e ) 7 / 8", + "Correct": "d", + "Explanation": "\"let us say probability of a occuring is a . let us say probability of b occuring is b . a = 2 b probability ( either a or b or both ) = 3 times probability ( a and b ) a * ( 1 - b ) + b * ( 1 - a ) + ab = 3 * ab substituting a = 2 b in the second equation : 2 b * ( 1 - b ) + b * ( 1 - 2 b ) + 2 b * b = 3 * 2 b * b 3 b - 2 b ^ 2 = 6 b ^ 2 3 b = 8 b ^ 2 b = 3 / 8 = 3 / 8 so , a = 2 b = 3 / 4 the correct answer is d .\"" + }, + { + "Answer": 110, + "Options": "a ) 40 , b ) 50 , c ) 60 , d ) 110 , e ) 80", + "Correct": "d", + "Explanation": "l + m = m + n - 60 / n = 2 l + 10 60 = m + n - l - m 60 = n - l 60 = 2 l + 10 - l 50 = l 2 ( 50 ) + 10 = 110 d" + }, + { + "Answer": 17, + "Options": "a ) 22 , b ) 38 , c ) 11 , d ) 17 , e ) 91", + "Correct": "d", + "Explanation": "explanation : total age of the 10 students = 10 \u00d7 14 = 140 total age of 15 students including the newly joined 5 students = 15 \u00d7 15 = 225 total age of the new students = 225 \u2212 140 = 85 average age = 85 / 5 = 17 years answer : d" + }, + { + "Answer": 73, + "Options": "a ) 65 , b ) 69 , c ) 75 , d ) 85 , e ) 73", + "Correct": "e", + "Explanation": "\"explanation : average = ( 76 + 65 + 82 + 67 + 75 ) / 5 = 365 / 5 = 73 hence average = 73 answer : e\"" + }, + { + "Answer": 127, + "Options": "a ) 127 , b ) 100 , c ) 129 , d ) 160 , e ) 200", + "Correct": "a", + "Explanation": "\"solution : let x be the number he chose , then 2 * x * 152 = 102 2 x = 254 x = 127 correct answer a\"" + }, + { + "Answer": 1.3333333333333335, + "Options": "a ) 1 , b ) 1 / 2 , c ) 5 / 6 , d ) 2 / 3 , e ) 4 / 3", + "Correct": "e", + "Explanation": "\"range of a / b = max ( a / b ) - min ( a / b ) to get max ( a / b ) = > max ( a ) / min ( b ) = 25 / 15 to get min ( a / b ) = > min ( a ) / max ( b ) = 10 / 30 range = 25 / 15 - 10 / 30 = 4 / 3\"" + }, + { + "Answer": 99.9999999999962, + "Options": "a ) 84 , b ) 98 , c ) 51 , d ) 65 , e ) 100", + "Correct": "e", + "Explanation": "\"when positive integer x is divided by positive integer y , the remainder is 12 - - > x = qy + 12 ; x / y = 75.12 - - > x = 75 y + 0.12 y ( so q above equals to 75 ) ; 0.12 y = 12 - - > y = 100 . answer : e .\"" + }, + { + "Answer": 3.5833333333333335, + "Options": "a ) $ 3.58 , b ) $ 1.67 , c ) $ 2.25 , d ) $ 2.37 , e ) $ 2.50", + "Correct": "a", + "Explanation": "\"total cost of parking for 9 hours = 20 $ for the first 2 hours and then 1.75 for ( 9 - 2 ) hours = 20 + 7 * 1.75 = 32.25 thus the average parking price = 32.25 / 9 = 3.58 $ a is the correct answer .\"" + }, + { + "Answer": 200, + "Options": "a ) 12 , b ) 28 , c ) 160 , d ) 200 , e ) 18", + "Correct": "d", + "Explanation": "\"let the numbers be x and y . then , x + y = 20 and x - y = 8 x 2 - y 2 = ( x + y ) ( x - y ) = 20 * 10 = 200 . answer : d\"" + }, + { + "Answer": 20, + "Options": "a ) 10 , b ) 40 , c ) 20 , d ) 30 , e ) 25", + "Correct": "c", + "Explanation": "\"let the number of students who wrote the exam be x . total marks of students = 90 x . total marks of ( x - 2 ) students = 95 ( x - 2 ) 90 x - ( 2 * 45 ) = 95 ( x - 2 ) 100 = 5 x = > x = 20 answer : c\"" + }, + { + "Answer": 7250, + "Options": "a ) 2348 , b ) 7250 , c ) 2767 , d ) 1998 , e ) 2771", + "Correct": "b", + "Explanation": "\"explanation : a b c investment 3 x 4 x 5 x rate of return 6 y % 5 y % 4 y % return \\ inline \\ frac { 18 xy } { 100 } \\ inline \\ frac { 20 xy } { 100 } \\ inline \\ frac { 20 xy } { 100 } total = ( 18 + 20 + 20 ) = \\ inline \\ frac { 58 xy } { 100 } b ' s earnings - a ' s earnings = \\ inline \\ frac { 2 xy } { 100 } = 250 total earning = \\ inline \\ frac { 58 xy } { 100 } = 7250 answer : b ) rs . 7250\"" + }, + { + "Answer": 0.6666666666666666, + "Options": "a ) 2 / 3 , b ) - 1 , c ) 0 , d ) - 2 / 3 , e ) 2", + "Correct": "a", + "Explanation": "\"a = 3 , b = - 5 , c = 2 x 1,2 = ( 5 \u00e2 \u00b1 \u00e2 \u02c6 \u0161 ( ( - 5 ) ^ 2 - 4 \u00e3 \u2014 3 \u00e3 \u2014 2 ) ) / ( 2 \u00e3 \u2014 3 ) = ( 5 \u00e2 \u00b1 \u00e2 \u02c6 \u0161 ( 25 - 24 ) ) / 6 = ( 5 \u00e2 \u00b1 1 ) / 6 x 1 = ( 5 + 1 ) / 6 = 6 / 6 = 1 x 2 = ( 5 - 1 ) / 6 = 4 / 6 = 2 / 3 a\"" + }, + { + "Answer": 8, + "Options": "a ) 4 , b ) 8 , c ) 2 , d ) 6 , e ) 10", + "Correct": "b", + "Explanation": "n ^ ( n / 2 ) = 8 apply log n / 2 logn = log 8 nlogn = 2 log 8 = log 8 ^ 2 = log 64 logn = log 64 now apply antilog n = 64 / n now n = 8 . answer : b" + }, + { + "Answer": 12.000000000000002, + "Options": "a ) 3 / 80 , b ) 3 / 5 , c ) 12 , d ) 5 / 3 , e ) 80 / 3", + "Correct": "c", + "Explanation": "\"25 / 100 = 1 / 4 n = 2 ^ 1 / 4 n ^ b = 2 ^ 3 ( 2 ^ 1 / 4 ) ^ b = 2 ^ 3 b = 12 answer : c\"" + }, + { + "Answer": 0.04863, + "Options": "a ) 0.045388 , b ) 4.5388 , c ) 453.88 , d ) 473.88 , e ) 0.04863", + "Correct": "e", + "Explanation": "\"answer multiplying 3.242 x 15 = 4.863 now divide 4.863 by 100 so , 4.863 \u00f7 100 = 0.04863 \u2234 shift the decimal two places to the left as 100 correct option : e\"" + }, + { + "Answer": 29, + "Options": "a ) 26 , b ) 22 , c ) 25 , d ) 27 , e ) 29", + "Correct": "e", + "Explanation": "\"( 4 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 2 = ( 2 x 2 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 2 = 2 ^ 11 x 2 ^ 11 x 7 ^ 5 x 11 ^ 2 = 2 ^ 22 x 7 ^ 5 x 11 ^ 2 total number of prime factors = ( 22 + 5 + 2 ) = 29 . answer is e .\"" + }, + { + "Answer": 1296, + "Options": "a ) 1296 , b ) 4 , c ) 8 , d ) 16 , e ) 32", + "Correct": "a", + "Explanation": "\"( x + y ) ^ 2 - ( x - y ) ^ 2 ( x + y + x - y ) ( x + y - x + y ) ( 2 x ) ( 2 y ) 4 xy 4 6 ^ 4 = 1296 answer a\"" + }, + { + "Answer": 25, + "Options": "a ) 5 , b ) 14 , c ) 25 , d ) 21 , e ) none of these", + "Correct": "c", + "Explanation": "\"explanation \u221a ( 25 ) ^ 2 = ? or , ? = 25 answer c\"" + }, + { + "Answer": 10, + "Options": "a ) - 9 , b ) 9 , c ) - 10 , d ) 10 , e ) 20", + "Correct": "d", + "Explanation": "\"from - 9 to - 1 - - > 9 nos . zero - - > 1 number from + 1 to + 9 - - > 9 nos . when we add up nos . from - 9 to + 9 sum will be zero . total 19 nos will be added . 20 th number will be 10 . sum of these 20 nos . = 10 . d is the answer .\"" + }, + { + "Answer": 18180, + "Options": "a ) 15360 , b ) 16010 , c ) 18180 , d ) 14930 , e ) 16075", + "Correct": "c", + "Explanation": "\"6000 + 15000 - ( 0.12 * 6000 + 0.14 * 15000 ) = 18180 . answer : c .\"" + }, + { + "Answer": 0.4666666666666667, + "Options": "a ) 1 / 12 , b ) 7 / 15 , c ) 2 / 13 , d ) 2 / 15 , e ) 1 / 17", + "Correct": "b", + "Explanation": "\"first , there are 8 c 3 ways you can select 3 good pencils from 4 good ones . second , there are 10 c 3 ways you select 3 pencils from 6 ones in the box . then , the probability that neither pen will be defective is : 8 c 3 / 10 c 3 = 56 / 120 = 7 / 15 answer is b\"" + }, + { + "Answer": 500, + "Options": "a ) 300 , b ) 400 , c ) 500 , d ) 600 , e ) 700", + "Correct": "c", + "Explanation": "explanation : n * 50 = ( 325000 - 300000 ) = 25000 n = 25000 / 50 = 500 option c" + }, + { + "Answer": 100, + "Options": "a ) a ) 100 , b ) b ) 122 , c ) c ) 120 , d ) d ) 125 , e ) e ) 145", + "Correct": "a", + "Explanation": "\"explanation : average of new numbers = 20 * 5 = 100 answer : option a\"" + }, + { + "Answer": 18395, + "Options": "a ) 18695 , b ) 18325 , c ) 18365 , d ) 18395 , e ) 18485", + "Correct": "d", + "Explanation": "according to the stem we should use the digits 0 through 9 to construct 2 four - digit integers , so that their sum is as big as possible . to maximize the sum , maximize the thousands digits of a and c , so make them 9 and 8 . next , maximize hundreds digits . make them 7 and 6 . next maximize 10 ' s digit place by 5 and 4 use the remaining digits ( 3 , and 2 ) for units digits . so , a would be 9753 , and c would be 8642 . 9753 + 8642 = 18395 answer : d ." + }, + { + "Answer": 5, + "Options": "a ) 8 , b ) 5 , c ) 7 , d ) 6 , e ) 9", + "Correct": "b", + "Explanation": "63 / 29 , thereforerequired number is : 5 , correct answer ( b )" + }, + { + "Answer": 0.5, + "Options": "a ) 1 / 2 , b ) 2 , c ) 1 / 3 , d ) 3 , e ) 1 / 6", + "Correct": "a", + "Explanation": "very easy question . 2 variables and 2 easy equations . xy = 9 - - - > x = 9 / y - ( i ) x / y = 36 - - - > replacing ( i ) here - - - > 9 / ( y ^ 2 ) = 36 - - - > y ^ 2 = 9 / 36 = 1 / 4 - - - > y = 1 / 2 or - 1 / 2 the question states that x and y are positive integers . therefore , y = 1 / 2 is the answer . answer a ." + }, + { + "Answer": 10000, + "Options": "a ) 10000 , b ) 8000 , c ) 1988 , d ) 1277 , e ) 2081", + "Correct": "a", + "Explanation": "x * 120 / 100 * 80 / 100 = 9600 x * 0.96 = 9600 x = 9600 / 0.96 = > 10000 answer : a" + }, + { + "Answer": 500, + "Options": "a ) 475 , b ) 600 , c ) 550 , d ) 500 , e ) 525", + "Correct": "d", + "Explanation": "x * ( 90 / 100 ) = 450 x = 5 * 100 x = 500 answer : d" + }, + { + "Answer": 35, + "Options": "a ) 54 , b ) 25 , c ) 45 , d ) 35 , e ) 52", + "Correct": "d", + "Explanation": "\"d 35\"" + }, + { + "Answer": 10, + "Options": "a ) 4 . , b ) 6 . , c ) 7 . , d ) 8 . , e ) 10", + "Correct": "e", + "Explanation": "otal teams = 18 bad teams = ( 2 / 3 ) * 18 = 12 rich teams = 9 so maximum value that the both rich and bad can take will be 9 . so e = 10 can not be that value . answer : e" + }, + { + "Answer": 300, + "Options": "a ) 238 , b ) 277 , c ) 278 , d ) 200 , e ) 300", + "Correct": "e", + "Explanation": "explanation : let the number of 20 paise coins be x . then the no of 25 paise coins = ( 344 - x ) . 0.20 * ( x ) + 0.25 ( 344 - x ) = 71 = > x = 300 . . answer : e ) 300" + }, + { + "Answer": 1.5, + "Options": "a ) 8 , b ) 5 , c ) 11 , d ) 3 , e ) 1.5", + "Correct": "e", + "Explanation": "\"6 * 15 * 3 = ( \u221a ( 6 + 2 ) ( 15 + 3 ) ) / ( 7 + 1 ) = ( \u221a 8 * 18 ) / 8 = ( \u221a 144 ) / 8 = 12 / 8 = 1.5 answer is e\"" + }, + { + "Answer": 10, + "Options": "a ) 10 a , b ) 12 a , c ) 14 a , d ) 16 a , e ) 18 a", + "Correct": "a", + "Explanation": "total movies = 100 . comedies = 64 . action + drama = 36 . since there were 5 times as many dramas as action movies , then action + 5 * action = 36 - - > action = a = 6 . comedies = 60 = 10 a . a" + }, + { + "Answer": 281, + "Options": "a ) 388 , b ) 282 , c ) 378 , d ) 292 , e ) 281", + "Correct": "e", + "Explanation": "explanation : since the difference between the divisors and the respective remainders is not constant , back substitution is the convenient method . none of the given numbers is satisfying the condition . answer : e" + }, + { + "Answer": 49, + "Options": "a ) $ 45 , b ) $ 47 , c ) $ 49 , d ) $ 51 , e ) $ 53", + "Correct": "c", + "Explanation": "\"p = ( 2 / 7 ) * p + 35 ( 5 / 7 ) * p = 35 p = 49 the answer is c .\"" + }, + { + "Answer": 124, + "Options": "a ) 124 , b ) 297 , c ) 394 , d ) 421 , e ) 842", + "Correct": "a", + "Explanation": "ratio of a : b : c = 1 : 2 : 4 two possible greatest single digit values for c are 8 and 4 if c is 8 , then x = 248 if c is 4 , then x = 124 difference = 248 - 124 = 124 a is the answer" + }, + { + "Answer": 32, + "Options": "a ) 34 , b ) 32 , c ) 17 , d ) 27 , e ) 28", + "Correct": "b", + "Explanation": "explanation : 35 - [ 23 - { 19 - ( 15 - x ) } ] = 12 \u00d7 2 \u00d7 2 = 48 = > 35 - 23 + ( 19 - 15 + x ) = 48 = > 12 + 4 + x = 48 = > x = 48 - ( 4 + 12 ) = 32 answer : option b" + }, + { + "Answer": 9, + "Options": "a ) 9 , b ) 0 , c ) 1 , d ) 2 , e ) 4", + "Correct": "a", + "Explanation": "\"since f ( n ) = f ( n - 1 ) - n then : f ( 6 ) = f ( 5 ) - 6 and f ( 5 ) = f ( 4 ) - 5 . as given that f ( 4 ) = 20 then f ( 5 ) = 20 - 5 = 15 - - > substitute the value of f ( 5 ) back into the first equation : f ( 6 ) = f ( 5 ) - 6 = 15 - 6 = 9 . answer : a . questions on funtions to practice :\"" + }, + { + "Answer": 12960, + "Options": "a ) 11260 , b ) 11860 , c ) 12360 , d ) 12960 , e ) 13560", + "Correct": "d", + "Explanation": "15 = 3 * 5 32 = 2 ^ 5 45 = 3 ^ 2 * 5 54 = 2 * 3 ^ 3 lcm = 2 ^ 5 * 3 ^ 3 * 5 = 4320 the smallest five - digit number that is a multiple of 4320 is 3 * 4320 = 12,960 the answer is d ." + }, + { + "Answer": 15, + "Options": "a ) 15 , b ) 88 , c ) 77 , d ) 20 , e ) 99", + "Correct": "a", + "Explanation": "\"in 1 hr , the bus covers 60 km without stoppages and 45 km with stoppages . stoppage time = time take to travel ( 60 - 45 ) km i . e 15 km at 60 km / hr . stoppage time = 15 / 60 hrs = 15 min . answer : a\"" + }, + { + "Answer": 0.6, + "Options": "a ) 10 / 16 , b ) 9 / 15 , c ) 4 / 16 , d ) 6 / 10 , e ) 4 / 10", + "Correct": "b", + "Explanation": "\"w = m + 6 w + m = 24 m + 6 + m = 24 2 m = 18 m = 9 w = 15 ratio : 9 : 15 ans : b\"" + }, + { + "Answer": 1, + "Options": "a ) 2 , b ) 2.2 , c ) 1 , d ) 4 , e ) 5", + "Correct": "c", + "Explanation": "i solved the second degree equation and found it like this : x ^ 2 - mx - 42 = 0 ( x - 7 ) ( x + 6 ) = 0 x = 7 or x = - 6 substituting both values for x in the equation we find : x ^ 2 - mx - 42 = > ( - 6 ) ^ 2 - m ( - 6 ) = 42 = > 36 + 6 m = 42 = > 6 m = 42 - 36 = 6 = > m = 1 and with 7 , using a similar process we end up with : ( 7 ) ^ 2 - m ( 7 ) = 42 - 7 m = 42 - 49 = - 7 m = - 1 ao , ans c" + }, + { + "Answer": 1080, + "Options": "a ) $ 880 , b ) $ 990 , c ) $ 1,000 , d ) $ 1,100 , e ) $ 1,080", + "Correct": "e", + "Explanation": "\"10 / 100 p = 120 > > p = 120 * 100 / 10 = 1200 1200 - 120 = 1080 answer : e\"" + }, + { + "Answer": 3, + "Options": "a ) a ) 4 , b ) b ) 1 , c ) c ) 2 , d ) d ) 3 , e ) e ) 5", + "Correct": "d", + "Explanation": "\"explanation : ( 1056 / 24 ) gives remainder 21 21 + 3 = 24 , so we need to add 3 . answer : option d\"" + }, + { + "Answer": 60, + "Options": "a ) 24 , b ) 54 , c ) 60 , d ) 84 , e ) 94", + "Correct": "c", + "Explanation": "total permutations possible = 18 + 16 + 14 + 12 = 60 answer : c" + }, + { + "Answer": 1.2, + "Options": "a ) 2 / 1 , b ) 4 / 1 , c ) 6 / 5 , d ) 3 / 4 , e ) 3 / 2", + "Correct": "c", + "Explanation": "\"given that milk / water = 4 x / x and 4 x + x = 45 - - > x = 9 . thus milk = 4 x = 36 liters and water = x = 9 liters . new ratio = 36 / ( 9 + 21 ) = 36 / 30 = 6 / 5 . answer : c .\"" + }, + { + "Answer": 7, + "Options": "a ) 8 , b ) 5 , c ) 7 , d ) 4 , e ) 6", + "Correct": "c", + "Explanation": "let the cost of 1 book = x , let the cost of 1 magazine = y 2 x + 2 y = 26 x = ( 26 - 2 y ) / 2 x = 13 - y again , ( 13 - y ) + 3 y = 27 13 + 2 y = 27 2 y = 14 y = 7 answer : c" + }, + { + "Answer": 64, + "Options": "a ) 45 % , b ) 56 % , c ) 64 % , d ) 75 % , e ) 80 %", + "Correct": "c", + "Explanation": "last year attendance = 100 ( assume ) ; projected attendance = 125 ; actual attendance = 80 . the actual attendance therefore was ( actual ) / ( project ) = 80 / 125 * 100 = 64 $ of the projected attendance . answer : c ." + }, + { + "Answer": 235, + "Options": "a ) 200 , b ) 235 , c ) 50 , d ) 115 , e ) 150", + "Correct": "b", + "Explanation": "\"x + y = 270 x - y = 200 2 x = 70 x = 35 y = 235 answer is b\"" + }, + { + "Answer": 48.89, + "Options": "a ) 48.89 , b ) 42.25 , c ) 50 , d ) 51.25 , e ) 52.25", + "Correct": "a", + "Explanation": "explanation : average weight of 22 boys = 50.25 total weight of 22 boys = 50.25 \u00d7 22 average weight of remaining 8 boys = 45.15 total weight of remaining 8 boys = 45.15 \u00d7 8 total weight of all boys in the class = ( 50.25 \u00d7 16 ) + ( 45.15 \u00d7 8 ) total boys = 22 + 8 = 30 average weight of all the boys = ( ( 50.25 \u00d7 22 ) + ( 45.15 \u00d7 8 ) ) / 30 = 48.89 answer : option a" + }, + { + "Answer": 24, + "Options": "a ) 24 , b ) 12 , c ) 8 , d ) 4 , e ) 2", + "Correct": "a", + "Explanation": "\"in this question however , because we are told that exactly 64 frisbees have been sold and revenue was exactly $ 204 , there is only one possible solution for the number of $ 3 and $ 4 frisbees sold . to solve , we have 2 equations and 2 unknowns let x = number of $ 3 frisbees sold let y = number of $ 4 frisbees sold x + y = 60 3 x + 4 y = 204 x = 60 - y 3 ( 60 - y ) + 4 y = 204 180 - 3 y + 4 y = 204 y = 24 answer : a\"" + }, + { + "Answer": 1.4444444444444444, + "Options": "a ) 0.75 , b ) 0.8 , c ) 1 , d ) 1.2 , e ) 1.44", + "Correct": "e", + "Explanation": "\"say the cost price of 90 pencils was $ 90 ( $ 1 per pencil ) and the selling price of 1 pencil was p . selling at a loss : 90 - 90 p = 40 p - - > p = 9 / 13 . ( cost price ) / ( selling price ) = 1 / ( 9 / 13 ) = 13 / 9 = 1.44 . answer : e .\"" + }, + { + "Answer": 36, + "Options": "a ) 4 . , b ) 8 . , c ) 12 . , d ) 16 . , e ) 36 .", + "Correct": "e", + "Explanation": "\"eq 1 : a - b - c + d = 18 eq 2 : a + b - c - d = 6 ( 1 ) subtract eq 1 from eq 2 a - b - c + d = 18 - a + b - c - d = 6 - - - - - - - - - - - - - - - - - - - - - - - - - 2 b + 2 d = 12 ( 2 ) simplify - b + d = 6 b - d = - 6 ( b - d ) ^ 2 = ( - 6 ) ^ 2 = 36 my answer : e\"" + }, + { + "Answer": 19.999999999999996, + "Options": "a ) 15 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) none", + "Correct": "b", + "Explanation": "\"sol . let the original consumption = 100 kg and new consumption = x kg . so , 100 x 6 = x \u00d7 7.50 = x = 80 kg . \u2234 reduction in consumption = 20 % . answer b\"" + }, + { + "Answer": 7, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8", + "Correct": "d", + "Explanation": "\"the number of members is 7 k + 5 = 8 j + 5 the only number in this range which satisfies this is 61 . 61 / 9 = 6 ( 9 ) + 7 the answer is d .\"" + }, + { + "Answer": 64.42376521116678, + "Options": "a ) 63 , b ) 64.28 , c ) 65 , d ) 66 , e ) 68", + "Correct": "b", + "Explanation": "given : - violets - c / 3 carnations - c tulip - c / 9 rose - c / 9 total flowers in terms of c = c / 3 + c + c / 9 + c / 9 = 14 c / 9 percentage of carnations = c / 14 c / 9 * 100 = 64.28 % answer b" + }, + { + "Answer": 0.05714285714285714, + "Options": "a ) 2 / 35 , b ) 2 / 30 , c ) 2 / 63 , d ) 2 / 29 , e ) 2 / 10", + "Correct": "a", + "Explanation": "\"explanation : let a be the event that x is selected and b is the event that y is selected . p ( a ) = 1 / 5 , p ( b ) = 2 / 7 . let c be the event that both are selected . p ( c ) = p ( a ) \u00e3 \u2014 p ( b ) as a and b are independent events : = ( 1 / 5 ) \u00e3 \u2014 ( 2 / 7 ) = 2 / 35 answer : a ) 2 / 35\"" + }, + { + "Answer": 86, + "Options": "a ) 87 , b ) 86 , c ) 28 , d ) 76 , e ) 80", + "Correct": "b", + "Explanation": "\"average after 11 innings = 46 required number of runs = ( 46 * 11 ) - ( 42 * 10 ) = 506 - 420 = 86 . answer : b\"" + }, + { + "Answer": 19, + "Options": "a ) 27 % , b ) 21 % , c ) 19 % , d ) 18 % , e ) 16 %", + "Correct": "c", + "Explanation": "\"fathers without full - time jobs are 1 / 4 * 3 / 5 = 3 / 20 of all the parents surveyed . mothers without full - time jobs are 1 / 10 * 2 / 5 = 2 / 50 of all the parents surveyed . the percent of parents without full - time jobs is 3 / 20 + 2 / 50 = 19 / 100 = 19 % the answer is c .\"" + }, + { + "Answer": 32, + "Options": "a ) $ 8 , b ) $ 9 , c ) $ 27 , d ) $ 32 , e ) $ 36", + "Correct": "d", + "Explanation": "josh + doug + brad = 68 ; josh = 2 brad , josh = 3 / 4 doug josh + 1 / 2 josh + 4 / 3 josh = 68 ( substituted the given values ) josh = 24 . 24 = 3 / 4 doug = > doug = 32 answer is d ." + }, + { + "Answer": 14, + "Options": "a ) 12 , b ) 14 , c ) 13 , d ) 15 , e ) 16", + "Correct": "b", + "Explanation": "\"let p = 5 , q = 4 then 2 * 5 + 4 = 14 so 2 p + q = 14 . answer : b\"" + }, + { + "Answer": 0.058823529411764705, + "Options": "a ) 1 / 190 , b ) 1 / 17 , c ) 1 / 19 , d ) 1 / 10 , e ) 1 / 9", + "Correct": "b", + "Explanation": "\"the problem with your solution is that we do n ' t choose 1 shoe from 18 , but rather choose the needed one after we just took one and need the second to be the pair of it . so , the probability would simply be : 1 / 1 * 1 / 17 ( as after taking one at random there are 17 shoes left and only one is the pair of the first one ) = 1 / 17 answer : b .\"" + }, + { + "Answer": 8, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) x = 8", + "Correct": "e", + "Explanation": "the combinations could be { ( 1,240 ) , ( 2,120 ) , ( 3,80 ) , ( 4,60 ) , ( 5,48 ) , ( 6,40 ) , ( 8,30 ) , ( 10,24 ) , ( 12,20 ) , ) 15,16 ) , ( 16,15 ) , ( 20,12 ) , ( 24,10 ) , ( 30,8 ) , ( 40,6 ) , ( 48,5 ) , ( 60,4 ) , ( 80,3 ) , ( 120,2 ) , ( 240,1 ) } of these we are told 8 < = t < = 30 so we can remove these pairs , and we are left only with . { ( 8,30 , ( 10,24 ) , ( 12,20 ) , ( 15,16 ) , ( 16,15 ) , ( 20,12 ) , ( 24,10 ) , ( 30,8 ) } hence 8 . e" + }, + { + "Answer": 1221, + "Options": "a ) 888 , b ) 333 , c ) 555 , d ) 1221 , e ) 889", + "Correct": "d", + "Explanation": "given exp . = ( a 3 + b 3 ) = ( a + b ) = ( 666 + 555 ) = 1221 ( a 2 - ab + b 2 ) answer d" + }, + { + "Answer": 95.99999999999636, + "Options": "a ) 96 , b ) 75 , c ) 48 , d ) 25 , e ) 12", + "Correct": "a", + "Explanation": "\"when positive integer x is divided by positive integer y , the remainder is 11.52 - - > x = qy + 11.52 ; x / y = 96.12 - - > x = 96 y + 0.12 y ( so q above equals to 96 ) ; 0.12 y = 11.52 - - > y = 96 . answer : a .\"" + }, + { + "Answer": 0.03408, + "Options": "a ) 0.3408 , b ) 3.408 , c ) 34.08 , d ) 340.8 , e ) 0.03408", + "Correct": "e", + "Explanation": "\"solution 0.016 \u00d7 2.13 = ( 16 / 1000 x 213 / 100 ) = ( 16 / 1000 x 213 / 100 ) = 3408 / 100000 = 0.03408 . answer e\"" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9", + "Correct": "a", + "Explanation": "integer is divisible by 9 - sum of digits is divisible by 9 answer : a" + }, + { + "Answer": 131, + "Options": "a ) a ) 130 , b ) b ) 131 , c ) c ) 148 , d ) d ) 158 , e ) e ) 160", + "Correct": "b", + "Explanation": "\"d = d * q + r d = 14 * 9 + 5 d = 126 + 5 d = 131 answer b\"" + }, + { + "Answer": 1, + "Options": "a ) 1.0 , b ) 1.5 , c ) 2.0 , d ) 2.5 , e ) 3.0", + "Correct": "a", + "Explanation": "this is a good question to understand the difference between mean and median . mean : average of all the numbers . ( sum of all the elements divided by the number of elements ) median : arrange the elements of the set in increasing order . if the number of terms is odd , the middle term is the median . if the number of terms is even , the average of middle two terms is the median coming to this question , mean = ( 1 + 7 + 18 + 20 + 29 + 33 ) / 6 = 18 median = ( 18 + 20 ) / 2 = 19 difference = 1 option a" + }, + { + "Answer": 1680, + "Options": "a ) 1680 , b ) 1700 , c ) 2350 , d ) 2500 , e ) 8000", + "Correct": "a", + "Explanation": "\"16 pounds and 4 ounces = 16 * 16 + 4 = 260 ounces . 13 tons = 13 * 2100 pound = 13 * 2100 * 16 ounces . hence the answer is ( 13 * 2100 * 16 ) / 260 = 1680 . answer : a .\"" + }, + { + "Answer": 360, + "Options": "a ) 120 , b ) 180 , c ) 240 , d ) 360 , e ) 480", + "Correct": "d", + "Explanation": "sice the distance covered by both the wheels should be same so let x be the no . of revolutions by the back wheel so 240 * 2 * pie * 30 = x * 2 * pie * 20 so x = 360 . answer : d" + }, + { + "Answer": 20, + "Options": "a ) 5 , b ) 9 , c ) 12 , d ) 20 , e ) 30", + "Correct": "d", + "Explanation": "in order x ! to be divisible by 1,000 , it should have at least 3 trailing zeros . a trailing 0 in factorial of a number is produced by 2 and 5 in it : 2 * 5 = 10 . so , we need 10 to be in x ! at least in power of 3 . 5 ! = 120 has 1 trailing zeros . 10 ! will have 2 trailing zeros . 15 ! will have 3 trailing zeros . 20 ! will have 5 trailing zeros . answer : d ." + }, + { + "Answer": 22, + "Options": "a ) - 4 , b ) - 2 , c ) 11 , d ) 13 , e ) 22", + "Correct": "e", + "Explanation": "\"the equation that can be formed is : 3 x - 26 = 62 - x or , 4 x = 88 or , x = 22 . answer : e\"" + }, + { + "Answer": 979.0209790209791, + "Options": "a ) 979 , b ) 1288 , c ) 2778 , d ) 2682 , e ) 1021", + "Correct": "a", + "Explanation": "\"1120 = p [ 1 + ( 6 * 12 / 5 ) / 100 ] p = 979 answer : a\"" + }, + { + "Answer": 288, + "Options": "a ) $ 288 , b ) $ 135 , c ) $ 90 , d ) $ 60 , e ) $ 54", + "Correct": "a", + "Explanation": "\"since 2 / 3 of the books in the collection were sold , 1 / 3 were not sold . the 36 unsold books represent 1 / 3 of the total number of books in the collection , and 2 / 3 of the total number of books equals 2 ( 36 ) or 72 . the total proceeds of the sale was 72 ( $ 4 ) or $ 288 . the best answer is therefore a . answer : a .\"" + }, + { + "Answer": 75, + "Options": "a ) 25 % , b ) 35 % , c ) 75 % , d ) 45 % , e ) 55 %", + "Correct": "c", + "Explanation": "a b ab a xor b ( ab ) + ( a xor b ) ( ab ) ( a xor b ) 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 1 1 0 1 1 1 0 1 0 so , we are getting 3 wrong answers out of 4 probability of error is 3 / 4 = 75 % answer : c" + }, + { + "Answer": 40, + "Options": "a ) 14 % , b ) 25 % , c ) 28 % , d ) 34 % , e ) 40 %", + "Correct": "e", + "Explanation": "\"official solution : if we start with 40 gallons of a mixture that is 10 % grape juice , then we have : 40 \u00d7 0.10 = 4 gallons of grape juice . 40 \u00d7 0.90 = 36 gallons of other components . if we add 20 gallons of grape juice , we will end up with 24 gallons of grape juice and 36 gallons of other components , and we will have a total of 60 gallons of the mixture . so 24 / 60 of the new mixture is grape juice . now we convert this to a percent : percent grape juice = 40 / 100 = 40 % . the correct answer is choice ( e )\"" + }, + { + "Answer": 16, + "Options": "a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16", + "Correct": "e", + "Explanation": "x = the number of red balls y = the number of blue balls z = the number of white balls from the first sentence we have equation # 1 : x + y + z = 100 . . . the box has 12 more blue balls than white balls . . . equation # 2 : y = 12 + z . . . thrice as many red balls as blue balls . . . equation # 3 : x = 2 y solve equation # 2 for z : z = y - 12 now , we can replace both x and z with y in equation # 1 2 y + y + ( y - 12 ) = 100 4 y - 12 = 100 4 y = 112 y = 28 there are 28 blue balls . this is 15 more than the number of white balls , so z = 16 . that ' s the answer . just as a check , x = 56 , and 56 + 28 + 16 = 100 . answer = 16 , ( e )" + }, + { + "Answer": 11, + "Options": "a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15", + "Correct": "a", + "Explanation": "\"explanation : given that a + b = 11 + b + c = > a ? c = 11 + b ? b = 11 = > c is younger than a by 11 years answer : option a\"" + }, + { + "Answer": 5.8, + "Options": "a ) 29 / 5 , b ) 28 / 3 , c ) 27 / 6 , d ) 25 / 4 , e ) 29 / 6", + "Correct": "a", + "Explanation": "( 6 ! - 4 ! ) / 5 ! ( 4 ! * 5 * 6 - 4 ! ) / 5 ! 4 ! ( 5 * 6 - 1 ) / 4 ! * 5 29 / 5 answer a" + }, + { + "Answer": 15, + "Options": "a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16", + "Correct": "d", + "Explanation": "let the total money be $ x p ' s 1 day work = $ x / 24 q ' s 1 day work = $ x / 40 p + q 1 day work = $ x / 15 money is sufficient to pay the wages of both for 15 days answer is d" + }, + { + "Answer": 7, + "Options": "a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 7", + "Correct": "e", + "Explanation": "\"let ' s say age of richard is ` ` r ' ' age of david is ` ` d ' ' age of scott is ` ` s ' ' now richard is 6 years older than david , i . e . r = d + 6 david is 8 years older than scott i . e . d = s + 8 if in 8 years , richard will be twice as old as scott i . e . r + 8 = 2 x ( s + 8 ) i . e . r + 8 = 2 s + 16 i . e . r = 2 s + 8 but r = d + 6 = ( s + 8 ) + 6 = s + 14 therefore , 2 s + 8 = s + 14 i . e . s = 6 i . e . r = 20 i . e . d = 14 now , how old was david 7 years ago ? i . e . d - 7 = 14 - 7 = 7 years answer : e\"" + }, + { + "Answer": 8400, + "Options": "a ) 7000 , b ) 8400 , c ) 6000 , d ) 5000 , e ) 4000", + "Correct": "b", + "Explanation": "\"state a and state b had an equal number of candidates appeared . in state a , 6 % candidates got selected from the total appeared candidates in state b , 7 % candidates got selected from the total appeared candidates but in state b , 84 more candidates got selected than state a from these , it is clear that 1 % of the total appeared candidates in state b = 84 = > total appeared candidates in state b = 84 x 100 = 8400 = > total appeared candidates in state a = total appeared candidates in state b = 8400\"" + }, + { + "Answer": 12, + "Options": "a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13", + "Correct": "d", + "Explanation": "96 + 44 d = 48 ( d + 1 ) . 4 d = 48 . d = 12 . the answer is d ." + }, + { + "Answer": 201, + "Options": "a ) $ 150 , b ) $ 248.75 , c ) $ 200 , d ) $ 201.3 , e ) $ 190", + "Correct": "d", + "Explanation": "$ 9.15 * 22 = $ 201.3 . answer is d ." + }, + { + "Answer": 84, + "Options": "a ) 66 , 78 , b ) 70 , 82 , c ) 94 , 106 , d ) 84 , 96 , e ) none of these", + "Correct": "d", + "Explanation": "explanation : out of the given numbers , the two with h . c . f . 12 and difference 12 are 84 and 96 . answer is d" + }, + { + "Answer": 15, + "Options": "a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 19", + "Correct": "c", + "Explanation": "\"p \u00e3 \u00b7 44 = 432 = > p = 432 * 44 = 19008 p / 39 = 19008 / 39 = 487 , remainder = 15 c\"" + }, + { + "Answer": 0.25, + "Options": "a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 6 , d ) 1 / 8 , e ) 1 / 24", + "Correct": "a", + "Explanation": "\"let x be the number of upgraded sensors on the satellite . the number of non - upgraded sensors per unit is x / 8 . the number of non - upgraded sensors on the whole satellite is 24 ( x / 8 ) = 3 x . the fraction of sensors which have been upgraded is x / ( x + 3 x ) = x / 4 x = 1 / 4 the answer is a .\"" + }, + { + "Answer": 8, + "Options": "a ) 2 , b ) 4 , c ) 8 , d ) 16 , e ) 32", + "Correct": "c", + "Explanation": "\"4 \u00f8 2 = 2 ^ 4 / 2 ^ 2 = 4 4 \u00f8 1 = 2 ^ 4 / 2 = 8 the answer is c .\"" + }, + { + "Answer": 12, + "Options": "a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14", + "Correct": "c", + "Explanation": "\"since 531,441 is an odd number , it is not a multiple of 4 . this means that y must equal zero . since x - y = 12 and y = 0 , then x = 12 . the answer is c .\"" + }, + { + "Answer": 5, + "Options": "a ) 7 , b ) 5 , c ) 6 , d ) 4 , e ) 3", + "Correct": "b", + "Explanation": "if vijay gives ' x ' marbles to ajay then vijay and ajay would have v - x and a + x marbles . v - x = a + x - - - ( 1 ) if ajay gives 2 x marbles to vijay then ajay and vijay would have a - 2 x and v + 2 x marbles . v + 2 x - ( a - 2 x ) = 30 = > v - a + 4 x = 30 - - - ( 2 ) from ( 1 ) we have v - a = 2 x substituting v - a = 2 x in ( 2 ) 6 x = 30 = > x = 5 . answer : b" + }, + { + "Answer": 15, + "Options": "a ) 15 , b ) 25 , c ) 40 , d ) 45 , e ) 75", + "Correct": "a", + "Explanation": "\"there are 5 days so the sum of temperature can be 45 * 5 = 225 lowest is 42 . to find the maximum range we can say the temperature was the lowest for 4 of the 5 days so 4 * 42 = 168 . on the fifth day it is 225 - 168 = 57 range is therefore 57 - 42 = 15 answer a\"" + }, + { + "Answer": 8, + "Options": "a ) 9 , b ) 10 , c ) 11 , d ) 8 , e ) 12", + "Correct": "d", + "Explanation": "\"now : rosy = x , david = x + 12 in 4 years rosy = x + 4 , david = x + 12 + 4 or 2 ( x + 4 ) x + 16 = 2 x + 8 x = 8 rosy is 8 years old answer : d\"" + }, + { + "Answer": 160, + "Options": "a ) 1200 , b ) 160 , c ) 360 , d ) 240 , e ) none of these", + "Correct": "b", + "Explanation": "explanation : let the original no . of students be x . according to situation , 48 x + 120 * 32 = ( x + 120 ) 36 \u21d2 x = 40 so , required no . of students after joining the new students = x + 120 = 160 . answer : b" + }, + { + "Answer": 6, + "Options": "a ) 15 , b ) 6 , c ) 1 , d ) 5 , e ) 12", + "Correct": "b", + "Explanation": "we ' re given the equation 9 - 4 / x = 7 + 8 / x . we ' re asked for the value of x . the common - denominator of these 4 numbers is x , so we have to multiple 2 of the numbers to give them that denominator . . . 9 x - 4 x / x = 7 x + 8 x / x we can then eliminate that denominator , which gives us . . . . 9 x - 4 = 7 x + 8 12 = 2 x both 2 x and 12 have a common denominator of 2 , so we divide both sides by 2 for our final answer . . . 6 = x b" + }, + { + "Answer": 118.74999999999997, + "Options": "a ) 118.75 % , b ) 128.75 % , c ) 116.75 % , d ) 117.75 % , e ) 114.75 %", + "Correct": "a", + "Explanation": "say david ' s wages last week were $ 100 , so he spent 0.40 * 100 = $ 40 on recreation ; this week ' s wages is 0.95 * 100 = $ 95 , so he spends 0.5 * 95 = $ 47.5 on recreation ; 47.5 / 40 = 1.1875 , hence the amount he spends on recreation this week is 118.75 % of the amount he spent on recreation last week : 40 * 1.1875 = 47.5 answer : a" + }, + { + "Answer": 96, + "Options": "a ) 86 , b ) 92 , c ) 84 , d ) 102 , e ) 96", + "Correct": "e", + "Explanation": "the equations raised . a + b = c b = 3 a a = 12 then b = 36 and c = 48 a + b + c = 96 answer : e" + }, + { + "Answer": 4350, + "Options": "a ) 2348 , b ) 7250 , c ) 4350 , d ) 1998 , e ) 2771", + "Correct": "c", + "Explanation": "\"explanation : a b c investment 3 x 4 x 5 x rate of return 6 y % 5 y % 4 y % return \\ inline \\ frac { 18 xy } { 100 } \\ inline \\ frac { 20 xy } { 100 } \\ inline \\ frac { 20 xy } { 100 } total = ( 18 + 20 + 20 ) = \\ inline \\ frac { 58 xy } { 100 } b ' s earnings - a ' s earnings = \\ inline \\ frac { 2 xy } { 100 } = 150 total earning = \\ inline \\ frac { 58 xy } { 100 } = 4350 answer : c ) rs . 4350\"" + }, + { + "Answer": 14, + "Options": "a ) 14 , b ) 21 , c ) 88 , d ) 37 , e ) 29", + "Correct": "a", + "Explanation": "\"explanation : lot the total number of workers be v then , 10000 v = ( 12000 * 7 ) + 8000 ( v - 7 ) < = > 2000 v = 28000 < = > v = 14 answer : a ) 14\"" + }, + { + "Answer": 149.58904109589042, + "Options": "a ) 140 , b ) 149 , c ) 156 , d ) 195 , e ) 100", + "Correct": "b", + "Explanation": "\"total production of salt by the company in that year = 4000 + 4100 + 4200 + . . . . + 5100 = 54600 . average monthly production of salt for that year = 54600 / 365 \u00e2 \u2030 \u02c6 149 answer : b\"" + }, + { + "Answer": 48, + "Options": "a ) 48 , b ) 37 , c ) 39 , d ) 43 , e ) 42", + "Correct": "a", + "Explanation": "\"average score before 17 th innings = 80 - 2 \u00d7 17 = 46 average score after 17 th innings = > 46 + 2 = 48 answer : a\"" + }, + { + "Answer": 4, + "Options": "a ) 1 , b ) 7 . , c ) 4 , d ) 3 , e ) 9", + "Correct": "c", + "Explanation": "a number ending in a 0 is divisible by 2 . a number ending in 2 zeroes is divisible by 4 . a number ending in 3 zeroes is divisible by 8 . given the obscene number , you should immediately be convinced that you will need to focus on a very small part of it . 445876 , 985420 , 215546 , 656452 = 445876 , 985420 , 215546 , 656000 + 452 the first number is divisible by 8 . you just have to find the remainder when you divide 452 by 8 . that will be the remainder when you divide the original number by 8 . 452 / 8 gives remainder 4 . answer ( c )" + }, + { + "Answer": 26, + "Options": "a ) 26 - 38 , b ) 50 - 34 , c ) 60 - 24 , d ) 42 - 42 , e ) 21 - 63", + "Correct": "a", + "Explanation": "\"in this problem , we are asked to find two numbers . therefore , we must let x be one of them . let x , then , be the first number . we are told that the other number is 12 more , x + 12 . the problem states that their sum is 64 : word problem = 64 the line over x + 12 is a grouping symbol called a vinculum . it saves us writing parentheses . we have : 2 x = 64 \u00e2 \u02c6 \u2019 12 = 52 . x = 52 / 2 = 26 . this is the first number . therefore the other number is x + 12 = 26 + 12 = 38 . the sum of 26 + 38 is 64 . a\"" + }, + { + "Answer": 22, + "Options": "a ) 14 years , b ) 18 years , c ) 20 years , d ) 22 years , e ) none", + "Correct": "d", + "Explanation": "\"solution let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . then \u2039 = \u203a ( x + 24 ) + 2 = 2 ( x + 2 ) \u2039 = \u203a x + 26 = 2 x + 4 x = 22 . answer d\"" + }, + { + "Answer": 658, + "Options": "a ) 654 , b ) 655 , c ) 656 , d ) 657 , e ) 658", + "Correct": "e", + "Explanation": "\"total cost 940 940 * 30 / 100 = 282 so the cut in amount is 282 the less amount to be spend is 940 - 282 = 658 answer : e\"" + }, + { + "Answer": 2, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "b", + "Explanation": "suppose 4 barrels are b 1 , b 2 , b 3 , b 4 in ascending capacity . ( b 1 + b 2 + b 3 + b 4 ) / 4 = 8 b 1 + b 2 + b 3 + b 4 = 32 median is 10 . . . . . . . as the no . of terms are even i . e 4 , median = ( b 2 + b 3 ) / 2 = = > b 2 + b 3 = 20 now we have b 1 + b 4 = 32 - 20 = 12 only the following possible cases can be there : 19 , 1111 110 , 1011 210 , 1010 max value of smallest barrel e = 2 = b" + }, + { + "Answer": 24, + "Options": "a ) 24 , b ) 26 , c ) 42 , d ) 46 , e ) 48", + "Correct": "a", + "Explanation": "let the ten ' s digit be x . then , unit ' s digit = x + 2 . number = 10 x + ( x + 2 ) = 11 x + 2 sum of digits = x + ( x + 2 ) = 2 x + 2 ( 11 x + 2 ) ( 2 x + 2 ) = 144 2 x 2 + 26 x - 140 = 0 ( x - 2 ) ( 11 x + 35 ) = 0 x = 2 hence , required number = 11 x + 2 = 24 . answer : a" + }, + { + "Answer": 75, + "Options": "a ) 65 , b ) 69 , c ) 75 , d ) 85 , e ) 90", + "Correct": "c", + "Explanation": "\"explanation : average = ( 76 + 65 + 82 + 67 + 85 ) / 5 = 375 / 5 = 75 hence average = 75 answer : c\"" + }, + { + "Answer": 363.6363636363636, + "Options": "a ) s . 200.63 , b ) s . 250.63 , c ) s . 290.63 , d ) s . 300.63 , e ) s . 363.63", + "Correct": "e", + "Explanation": "\"let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 800 but x = 120 % of y = 120 y / 100 = 12 y / 10 \u2234 12 y / 10 + y = 800 \u21d2 y [ 12 / 10 + 1 ] = 800 \u21d2 22 y / 10 = 800 \u21d2 22 y = 8000 \u21d2 y = 8000 / 22 = rs . 363.63 e )\"" + }, + { + "Answer": 28, + "Options": "a ) 1 , b ) 4 , c ) 9 , d ) 13 , e ) 28", + "Correct": "e", + "Explanation": "solving through algebra route : 5 b + 7 f = x amount if we multiply this equation with 4 we get : 20 b + 28 f = 4 x therefore , we got 20 ounces of butter and 4 x amount of quantity when we use 28 ounces of floor . ans : e" + }, + { + "Answer": 266.6666666666667, + "Options": "a ) 40 , b ) 200 , c ) 266 , d ) 267 , e ) 600", + "Correct": "d", + "Explanation": "in order not to lose money because of the change tom ' s total commission must beat least $ 75000 - $ 45000 = $ 30000 , so total sales must beat least $ 30000 / 0.15 = $ 200000 . which means that he must makeat least $ 200000 / 750 = 800 / 3 = 266.6 sales , so 267 sales . answer : d ." + }, + { + "Answer": 83, + "Options": "a ) 45 , b ) 62 , c ) 75 , d ) 83 , e ) 90", + "Correct": "d", + "Explanation": "when it comes to averages , we know thataverage value = ( sum of n values ) / n we can rewrite this into a useful formula : sum of n values = ( average value ) ( n ) the average of five integers is 63 so , the sum of all 5 integers = ( 63 ) ( 6 ) = 378 the average of three of the integers is 65 so , the sum of the 3 integers = ( 65 ) ( 3 ) = 195 so , the sum of the 2 remaining integers = 378 - 195 = 183 if the sum of the 2 remaining integers = 183 , and we want to minimize one value , we must maximize the other value . 100 is the maximum value so let 1 integer = 100 , which means the other must equal 83 answer : d" + }, + { + "Answer": 1, + "Options": "a ) 3 hours , b ) 2.4 hours , c ) 1.4 hours , d ) 1 hour , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : let the duration of the flight be x hours . then 600 / x \u2212 600 / x + 1 / 2 = 200 600 / x \u2212 1200 / 2 x + 1 = 200 x ( 2 x + 1 ) = 3 2 x 2 + x \u2212 3 = 0 = > ( 2 x + 3 ) ( x \u2212 1 ) = 0 neglecting the negative value for x we get x = 1 option d\"" + }, + { + "Answer": 281, + "Options": "a ) 171 , b ) 281 , c ) 361 , d ) 461 , e ) 561", + "Correct": "b", + "Explanation": "\"sum s = n / 2 { 2 a + ( n - 1 ) d } = 11 / 2 { 2 * 20 + ( 11 - 1 ) * 1 } = 11 * 25 = 275 = x number of even number = ( 30 - 20 ) / 2 + 1 = 6 = y x + y = 275 + 6 = 281 b\"" + }, + { + "Answer": 3989, + "Options": "a ) $ 3556.25 , b ) $ 3988.89 , c ) $ 3836.56 , d ) $ 3745.56 , e ) $ 3428.56", + "Correct": "b", + "Explanation": "number of managers is 9 their average salary is $ 1300 number of associates is 18 their average salary is $ 12,000 total salary of managers is 9 * 1300 = $ 11700 total salary of associates is 18 * 12,000 = $ 96,000 total salary for the departmental store is 96,000 + 11700 = 107700 average salary for the departmental store is 107700 / 9 + 18 = 3988.89 answer is b" + }, + { + "Answer": 36, + "Options": "a ) 10 % , b ) 15 % , c ) 20 % , d ) 36 % , e ) 50 %", + "Correct": "d", + "Explanation": "say a recliner is actually worth $ 100 if she sells 100 recliners then she earns $ 10000 after the discount of 20 % , she will earn $ 80 per recliner and she sells 70 % more ie . , 170 recliners hence her sales tields 170 * 80 = $ 13600 increase in sales = 13600 - 10000 = $ 3600 so % increase = 3600 * 100 / 10000 = 36 % d is the answer" + }, + { + "Answer": 0.75, + "Options": "a ) 1 / 5 , b ) 1 / 3 , c ) 2 / 5 , d ) 3 / 4 , e ) 3 / 5", + "Correct": "d", + "Explanation": "we do n ' t need to get into calculations for solving this question . we can use the concept of weighted averages . we know that if the average speed for the entire journey was 40 mph , then he drove at 50 mph for a longer duration of time . 10 30 10 - - 40 - - - - - - 50 this shows that you can divide the entire journey into 4 equal parts . thus , 3 / 4 part he drove at 50 mph and 1 / 4 part he drove at 10 mph . answer : d" + }, + { + "Answer": 65.00000000000001, + "Options": "a ) 40 , b ) 52 , c ) 65 , d ) 80 , e ) 98", + "Correct": "c", + "Explanation": "\"let the no of matches played more = x so , ( 120 + x ) * 52 / 100 = 31.2 + x by solving we get x = 65 answer : c\"" + }, + { + "Answer": 26.999999999999996, + "Options": "a ) 35 , b ) 27 , c ) 25 , d ) 15 , e ) 55", + "Correct": "b", + "Explanation": "\"a : b : c = 10 \u00d7 7 : 12 \u00d7 5 : 15 \u00d7 3 = 2 \u00d7 7 : 12 \u00d7 1 : 3 \u00d7 3 = 14 : 12 : 9 amount that c should pay = 105 \u00d7 9 / 35 = 3 \u00d7 9 = 27 answer is b .\"" + }, + { + "Answer": 5, + "Options": "a ) 3 , b ) 2 , c ) 8 , d ) 6 , e ) 5", + "Correct": "e", + "Explanation": "amount of milk = 20 \u00d7 3 / 4 = 15 litre and water = 5 litre let x litre milk to be added then 15 + x / 5 = 4 / 1 = 15 + x = 20 , x = 5 answer e" + }, + { + "Answer": 18.1, + "Options": "a ) 15.6 , b ) 18.1 , c ) 17.5 , d ) 18.7 , e ) 19.1", + "Correct": "b", + "Explanation": "a certain taxi company charges $ 2.50 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ? a . 15.60 b . 16.00 c . 17.50 d . 18.70 e . 19.10 1 / 5 miles = 0.2 miles . the cost of 8 miles long ride would be $ 2.50 for the first 0.2 miles plus ( 8 - 0.2 ) / 0.2 * 0.4 = $ 2.50 + $ 15.6 = $ 18.1 . answer : b ." + }, + { + "Answer": 2.3333333333333335, + "Options": "a ) 7 / 3 , b ) 3 / 2 , c ) 4 / 3 , d ) 2 / 3 , e ) 1 / 2", + "Correct": "a", + "Explanation": "\"sq rt ( 7 x / 3 ) = x = > 7 x / 3 = x ^ 2 = > x = 7 / 3 ans - a\"" + }, + { + "Answer": 42, + "Options": "a ) 23 , b ) 19 , c ) 42 , d ) 20 , e ) 21", + "Correct": "c", + "Explanation": "\"let the total number of workers be x . then , 8000 x = ( 18000 * 7 ) + 6000 ( x - 7 ) = 2000 x = 84000 = x = 42 . answer : c\"" + }, + { + "Answer": 28.000000000000007, + "Options": "a ) 28 % , b ) 25 % , c ) 18.5 % , d ) 16 % , e ) none of these", + "Correct": "a", + "Explanation": "solution : charge per call in february = 350 / 150 = 7 / 3 = 2.33 charge per call in march = [ 350 + ( 50 * 1.4 ) ] / 250 = 420 / 250 = 42 / 25 = 1.68 % cheaper call rate in march = [ ( 2.33 - 1.68 ) / 2.33 ] * 100 = 28 % . answer : option a" + }, + { + "Answer": 134, + "Options": "a ) 122 , b ) 126 , c ) 134 , d ) 148 , e ) 151", + "Correct": "c", + "Explanation": "3 * 12 + 3 * 13 + 3 * 16 + 11 = 36 + 39 + 48 + 11 = 134 the answer is c ." + }, + { + "Answer": 24, + "Options": "a ) 7 , b ) 33 , c ) 12 , d ) 24 , e ) 25", + "Correct": "d", + "Explanation": "16 + 8 = 24 . answer is d ." + }, + { + "Answer": 33.33333333333333, + "Options": "a ) 33.33 , b ) 27.33 , c ) 28.38 , d ) 29.37 , e ) 28.31", + "Correct": "a", + "Explanation": "answer : 33.33" + }, + { + "Answer": 70, + "Options": "a ) 27 , b ) 36 , c ) 29 , d ) 10 , e ) 70", + "Correct": "e", + "Explanation": "\"let the price of turban be x . thus , for one year the salary = ( 90 + x ) for 9 months he should earn 3434 ( 90 + x ) . now he gets one turban and rs . 50 . thus , 3434 ( 90 + x ) = 50 + x or 270 + 3 x = 200 + 4 x or x = 70 answer : e\"" + }, + { + "Answer": 16, + "Options": "a ) 11 . , b ) 12 . , c ) 16 . , d ) 14 . , e ) 14.5", + "Correct": "c", + "Explanation": "\"price of candy before price increase = 10 / 1.25 = 8 price of soda before price increase = 12 / 1.5 = 8 total price = 8 + 8 = 16 c is the answer\"" + }, + { + "Answer": 151, + "Options": "a ) 151 , b ) 149 , c ) 152 , d ) 148 , e ) none of the above", + "Correct": "a", + "Explanation": "\"corrected mean = 150 \u00d7 30 \u2212 135 + 165 / 30 = 4500 \u2212 135 + 165 / 30 = 4530 / 30 = 151 answer a\"" + }, + { + "Answer": 2125, + "Options": "a ) 2025 , b ) 2125 , c ) 2225 , d ) 2325 , e ) 2425", + "Correct": "b", + "Explanation": "explanation : total expenditure for the first 3 months = 3 \u00e3 \u2014 1700 = 5100 total expenditure for 4 months = 4 \u00e3 \u2014 1550 = 6200 total expenditure for 5 months = 5 \u00e3 \u2014 1800 = 9000 total expenditure and saving ( which is income for one year ) = 5100 + 6200 + 9000 + 5200 = rs . 25500 so , average monthly income = 25500 / 12 = rs . 2125 answer b" + }, + { + "Answer": 2.3333333333333353, + "Options": "a ) 3 / 5 , b ) 3 / 2 , c ) 5 / 3 , d ) 5 / 7 , e ) 7 / 3", + "Correct": "e", + "Explanation": "\"c . p of 1 kg of cheaper rice = rs 3.10 c . p of 1 kg of expensive rice = rs 3.60 the mixture be worth for 1 kg = rs 3.25 by the alligation rule : quantity of cheaper rice / quantity of expensive rice = ( 3.6 - 3.25 ) / ( 3.25 - 3.10 ) = ( 0.35 ) / ( 0.15 ) = 7 / 3 e\"" + }, + { + "Answer": 50, + "Options": "a ) 50 % , b ) 52 % , c ) 56 % , d ) 70 % , e ) 74 %", + "Correct": "a", + "Explanation": "\"say a 100 families existed in 1994 then the number of families owning a computer in 1994 - 40 number of families owning computer in 1998 = 40 * 130 / 100 = 52 number of families in 1998 = 104 the percentage = 52 / 104 * 100 = 50 % . answer : a\"" + }, + { + "Answer": 42, + "Options": "a ) 15 , b ) 30 , c ) 35 , d ) 42 , e ) 45", + "Correct": "d", + "Explanation": "lots of ways to tackle this . 35 % of 180 = 63 1 / 3 of 63 = 21 so , 1 / 3 less than 63 is equal to 63 - 21 = 42 answer : d" + }, + { + "Answer": 1080, + "Options": "a ) $ 214 million , b ) $ 1120 million , c ) $ 1144 million , d ) $ 1240 million , e ) $ 1080 million", + "Correct": "e", + "Explanation": "\"convert units to millions as answer is in millions 1996 imports = $ 1.44 bill = $ 1440 mill i . e . 1440 / 12 = $ 120 mill / month 1997 imports = $ 420 mill / 2 month i . e . $ 210 mill / month difference / month = 210 - 120 = 90 difference / year = $ 90 mill * 12 = $ 1080 mill answer : e\"" + }, + { + "Answer": 150, + "Options": "a ) 150 , b ) 84 , c ) 40 , d ) 28 , e ) 20", + "Correct": "a", + "Explanation": "\"almonds : walnuts = 5 : 2 total mixture has 7 parts in a 210 pound mixture , almonds are 5 / 7 ( total mixture ) = 5 / 7 * 210 = 150 pounds answer ( a )\"" + }, + { + "Answer": 2400, + "Options": "a ) 8981 , b ) 3799 , c ) 1200 , d ) 2400 , e ) 1732", + "Correct": "d", + "Explanation": "\"p - - - 10 - - - - 1200 p - - - 5 - - - - - 600 3 p - - - 5 - - - - - 1800 - - - - - - = > 2400 answer : d\"" + }, + { + "Answer": 160.00000000000003, + "Options": "a ) 160 , b ) 180 , c ) 200 , d ) 220 , e ) none", + "Correct": "a", + "Explanation": "\"answer let the number be n . then , ( n / 5 ) + 4 = ( n / 4 ) - 4 \u00e2 \u2021 \u2019 ( n / 4 ) - ( n / 5 ) = 8 \u00e2 \u2021 \u2019 ( 5 n - 4 n ) / 20 = 8 \u00e2 \u02c6 \u00b4 n = 160 option : a\"" + }, + { + "Answer": 52, + "Options": "a ) 40 , b ) 41 , c ) 52 , d ) 62 , e ) 73", + "Correct": "c", + "Explanation": "\"total age of all students = 25 \u00e3 \u2014 26 total age of all students + age of the teacher = 26 \u00e3 \u2014 27 age of the teacher = 27 \u00e3 \u2014 26 \u00e2 \u02c6 \u2019 25 \u00e3 \u2014 26 = 26 ( 27 \u00e2 \u02c6 \u2019 25 ) = 26 \u00e3 \u2014 2 = 52 answer is c .\"" + }, + { + "Answer": 268.2, + "Options": "a ) 240 , b ) 270 , c ) 295 , d ) 360 , e ) 340", + "Correct": "b", + "Explanation": "\"let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 15 5 x = 1350 x = 270 smaller number = 270 answer : b\"" + }, + { + "Answer": 0.5, + "Options": "a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 3 / 5 , e ) 4 / 5", + "Correct": "a", + "Explanation": "( 96 g + 90 b ) / ( g + b ) = 94 96 g + 90 b = 94 ( g + b ) 2 g = 4 b b / g = 1 / 2 the answer is a ." + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 3 , c ) 6 , d ) 9 , e ) 12", + "Correct": "b", + "Explanation": "9 - 3 1 / 3 + 3 = 9 - 3 \u00f7 1 / 3 + 3 = 9 - ( 3 x 3 ) + 3 = 9 - 9 + 3 = 3 correct answer : b" + }, + { + "Answer": 7, + "Options": "a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 9", + "Correct": "d", + "Explanation": "the units digit of 73 ^ 355 will be the same as the units digit of 3 ^ 355 . 3 ^ 1 = 3 - - > the units digit is 3 ; 3 ^ 2 = 9 - - > the units digit is 9 ; 3 ^ 3 = 27 - - > the units digit is 7 ; 3 ^ 4 = 81 - - > the units digit is 1 ; 3 ^ 5 = 243 - - > the units digit is 3 again ; . . . so , as you can see the units digit repeats in blocks of 4 : { 3 , 9 , 7 , 1 } , { 3 , 9 , 7 , 1 } , . . . now , since 355 = 352 + 3 = ( multiple of 4 ) + 2 , then the units digit of 3 ^ 355 will be the third number in the pattern thus 7 . answer : d ." + }, + { + "Answer": 300, + "Options": "a ) 732 % , b ) 560 % , c ) 641 % , d ) 370 % , e ) 300 %", + "Correct": "e", + "Explanation": "\"what percent is x greater than 1 / 2 if ( 1 / 2 ) ( x ) = 1 ? = > x = 2 % change = [ ( 2 - 1 / 2 ) / ( 1 / 2 ) ] * 100 = ( 4 - 1 ) * 100 = 300 % approx ans , e\"" + }, + { + "Answer": 91, + "Options": "a ) 84 , b ) 89 , c ) 90 , d ) 92 , e ) 91", + "Correct": "e", + "Explanation": "\"set x = { 11 , 13 , 17 , . . . . . . . . . . . . . , 83 , 89 , 97 } set y = { 6 , 12 , 18 , . . . . . . . . . . . . . . . , 84 , 90 , 96 } combining two sets , say set z set z = { 6 , 11 , 12 , 13 , 17 , 18 , . . . . . . . . . . . . . . . . . . . , 83 , 84 , 89 , 90 , 96,97 } range = max value - min value range ( z ) = 97 - 6 = 91 oa e is the answer .\"" + }, + { + "Answer": 60, + "Options": "a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70", + "Correct": "d", + "Explanation": "\"let number of pounds of 5 $ candy to be used be w 6 = ( 30 * 8 + 5 * w ) / ( 30 + w ) = > 180 + 6 w = 240 + 5 w = > w = 60 answer d\"" + }, + { + "Answer": 70, + "Options": "a ) 50 , b ) 80 , c ) 70 , d ) 60 , e ) 71", + "Correct": "c", + "Explanation": "explanation : average = ( 66 + 75 + 52 + 68 + 89 ) / 5 = 70 . answer : c ) 70" + }, + { + "Answer": 4375, + "Options": "a ) 13000 , b ) 7000 , c ) 10000 , d ) 4375 , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : profit = 5 , 00,000 \u00e2 \u02c6 \u2019 ( 1 , 50,000 + 75,000 ) = rs . 2 , 75,000 . since , such loom contributes equally to sales and manufacturing expenses . but the monthly charges are fixed at rs 75,000 . if one loan breaks down sales and expenses will decrease . new profit : - = > 500000 \u00e3 \u2014 ( 79 / 80 ) \u00e2 \u02c6 \u2019 150000 \u00e3 \u2014 ( 79 / 80 ) \u00e2 \u02c6 \u2019 75000 . = > rs 2 , 70,625 . decrease in profit = > 2 , 75,000 \u00e2 \u02c6 \u2019 2 , 70,625 = > rs . 4,375 answer : d\"" + }, + { + "Answer": 900, + "Options": "a ) 280 , b ) 400 , c ) 540 , d ) 900 , e ) 840", + "Correct": "d", + "Explanation": "\"of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month : 2 / 3 * 3 / 4 = 1 / 2 survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year : ( 1 - 3 / 5 ) * 1 / 2 = 1 / 5 survived the first year . 180 geese survived the first year : 1 / 5 * ( total ) = 180 - - > ( total ) = 900 . answer : d .\"" + }, + { + "Answer": 2, + "Options": "a ) 2 l , b ) 3 l , c ) 2.5 l , d ) 4 l , e ) 5 l", + "Correct": "a", + "Explanation": "total mixture = 20 ltr water contain = 10 % of 20 ltr = > 2 ltr water it means 18 ltr is acid in that mixture we have to make 20 % water so . . 20 % of 20 = 4 ltr water must be there in the new mixture we have already 2 ltr water so we have to add 2 ltr more answer : a" + }, + { + "Answer": 87.5, + "Options": "a ) 30 % , b ) 33 1 / 2 % , c ) 40 % , d ) 60 % , e ) 87.5 %", + "Correct": "e", + "Explanation": "\"original visual range = 80 km new visual range = 150 km percent increase in the visual range by using the telescope = ( 150 - 80 ) / 80 * 100 % = 7 / 8 * 100 % = 87.5 % answer e\"" + }, + { + "Answer": 10.000000000000014, + "Options": "a ) 10 , b ) 388 , c ) 37 , d ) 29 , e ) 22", + "Correct": "a", + "Explanation": "\"explanation : let the original price be rs . 100 . new final price = 120 % of ( 75 % of rs . 100 ) = rs . ( 120 / 100 * 75 / 100 * 100 ) = rs . 90 . decrease = 10 % answer : a ) 10\"" + }, + { + "Answer": 55, + "Options": "a ) 18 , b ) 28 , c ) 48 , d ) 38 , e ) 55", + "Correct": "e", + "Explanation": "\"let x = the number sought . then x / 11 + x + 11 = 71 and x = 55 . e\"" + }, + { + "Answer": 0.0020000000000000018, + "Options": "a ) 1 / 100 , b ) 1 / 1500 , c ) 1 / 2 , d ) 1 / 500 , e ) 1 / 600", + "Correct": "d", + "Explanation": "\"explanation : 0.127 expressed as a fraction = 127 / 1000 1 / 8 can also be expressed as ( 1 x 125 ) / ( 8 x 125 ) = 125 / 1000 the difference is 2 / 1000 , which is 1 / 500 answer is d\"" + }, + { + "Answer": 2, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "b", + "Explanation": "two . n = 7 * p , and both 7 and p are prime . so the answer is b ." + }, + { + "Answer": 96.1, + "Options": "a ) 89 % , b ) 97.1 % , c ) 96.1 % , d ) 86.1 % , e ) none of these", + "Correct": "c", + "Explanation": "solution : non - defective products , { [ ( 25 * 0.98 ) + ( 35 * 0.96 ) + ( 40 * 0.95 ) ] / 100 } * 100 = 96.1 % . answer : option c" + }, + { + "Answer": 14, + "Options": "a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17", + "Correct": "b", + "Explanation": "\"the total number of books the students borrowed is 20 * 2 = 40 . the students who borrowed zero , one , or two books borrowed 9 * 1 + 4 * 2 = 17 books . the 4 students who borrowed at least three books borrowed 40 - 17 = 23 books . if 3 of these students borrowed exactly 3 books , then the maximum that one student could have borrowed is 23 - 9 = 14 books . the answer is b .\"" + }, + { + "Answer": 0.1428571428571428, + "Options": "a ) 1 / 4 , b ) 4 / 5 , c ) 1 / 5 , d ) 1 / 6 , e ) 1 / 7", + "Correct": "e", + "Explanation": "if s is an integer and we know that the average speed is 2.8 , s must be = 2 . that meanss + 1 = 3 . this implies that the ratio of time for s = 2 is 1 / 4 of the total time . the formula for distance / rate is d = rt . . . so the distance travelled when s = 2 is 2 t . the distance travelled for s + 1 = 3 is 3 * 4 t or 12 t . therefore , total distance covered while the sun was shining over him is r = 2 / 14 = 1 / 7 . answer : e" + }, + { + "Answer": 31, + "Options": "a ) 24 kg , b ) 62 kg , c ) 34 kg , d ) 31 kg , e ) 37 kg", + "Correct": "d", + "Explanation": "\"let a , b , c represent their respective weights . then , we have : a + b + c = ( 45 * 3 ) = 135 - - - ( i ) a + b = ( 40 * 2 ) = 80 - - - ( ii ) b + c = ( 43 * 2 ) = 86 - - - ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 166 - - - ( iv ) subtracting ( i ) from ( iv ) , we get : b = 31 b ' s weight = 31 kg . answer : d\"" + }, + { + "Answer": 99.99999999999997, + "Options": "a ) 50 , b ) 100 , c ) 120 , d ) 140 , e ) 180", + "Correct": "b", + "Explanation": "60 % * x + 80 % * ( 400 - x ) = 65 % * 400 ans = 100 answer : b" + }, + { + "Answer": 84, + "Options": "a ) a ) 84 , b ) b ) 104 , c ) c ) 110 , d ) d ) 72 , e ) of these", + "Correct": "a", + "Explanation": "\"let the greater and the smaller number be g and s respectively . gs = 2560 g + s exceeds g - s by 64 i . e . , g + s - ( g - s ) = 64 i . e . , 2 s = 64 = > s = 32 . g = 2688 / s = 84 . answer : a\"" + }, + { + "Answer": 70, + "Options": "a ) 70 , b ) 50 , c ) 40 , d ) 270 , e ) 170", + "Correct": "a", + "Explanation": "\"7 / 10 * 100 = 70 answer : a\"" + }, + { + "Answer": 549.7025036818851, + "Options": "a ) 249.7 , b ) 529.7 , c ) 549.7 , d ) 594.7 , e ) 119.7", + "Correct": "c", + "Explanation": "given exp . = ( 8 ) ^ 3 x 9 ^ 3 \u00e3 \u00b7 679 = c = 512 x 729 \u00e3 \u00b7 679 = 549.7 c" + }, + { + "Answer": 12, + "Options": "a ) 20 , b ) 12 , c ) 16 , d ) 14 , e ) 18", + "Correct": "b", + "Explanation": "explanation : the sum of the roots of the quadratic equation ax 2 + ax + c = 0 are ( - b / a ) and the product of the roots are ( c / a ) . thus , in the equation x 2 - ax + 20 = 0 , where a = 1 , b = - a and c = 20 . we get , product of the roots = 20 sum of the roots = - ( - 12 ) / 1 = 12 answer : b" + }, + { + "Answer": 59, + "Options": "a ) $ 55.10 , b ) $ 59.20 , c ) $ 59.40 , d ) $ 59.00 , e ) $ 55.00", + "Correct": "d", + "Explanation": "\"in 10 miles , initial 1 / 5 mile charge is $ 10 rest of the distance = 10 - ( 1 / 5 ) = 49 / 5 rest of the distance charge = 49 ( 1.00 ) = $ 49.00 ( as the charge is 1.00 for every 1 / 5 mile ) = > total charge for 4 miles = 10 + 49.00 = 59.00 answer is d\"" + }, + { + "Answer": 20, + "Options": "a ) 24 , b ) 26 , c ) 20 , d ) 22 , e ) 18", + "Correct": "c", + "Explanation": "\"4 n + 7 > 1 4 n > - 6 n > - ( 3 / 2 ) n > - 1.5 ( n = - 1 , 0 , 1 , 2 3 . . . . . . . . upto infinity ) from second constraint 4 n + 7 < 80 4 n < 73 n < 18 . 25 n = ( - infinity , . . . . . . . - 3 , - 2 , - 1 , 0 , 1 , 2 , . . . . . . . . . upto 18 ) combining the two - 1.5 < n < 18.25 n = 1 to 18 ( 18 integers ) and n = - 1 and 0 so 20 integers . c is the answer\"" + }, + { + "Answer": 0.2857142857142857, + "Options": "a ) 1 / 2 , b ) 1 / 5 , c ) 2 / 3 , d ) 2 / 7 , e ) 1 / 7", + "Correct": "d", + "Explanation": "\"first , there are 5 c 3 ways you can select 3 good pencils from 4 good ones . second , there are 7 c 3 ways you select 3 pencils from 6 ones in the box . then , the probability that neither pen will be defective is : 5 c 3 / 7 c 3 = 10 / 35 = 2 / 7 answer is d\"" + }, + { + "Answer": 100, + "Options": "a ) 60 , b ) 70 , c ) 80 , d ) 90 , e ) 100", + "Correct": "e", + "Explanation": "if a takes 1 step in one second , then b takes 3 steps in one second . if a takes t 1 seconds to take 50 steps , then b takes 150 steps in t 1 seconds . for b , to take 150 steps he requires t 1 seconds , then to take 75 steps he requires t 1 / 2 seconds . now use relative velocity l - v * t 1 = 50 ( for first person ) l - v * t 1 / 2 = 75 ( for second person ) s ( escalator w . r . t ground ) - s ( person w . r . t escalator ) = s 1 ( person w . r . t ground ) s , s , s 1 are the steps now put the v * t 1 from 1 into the second equation and u get l - ( l - 50 ) / 2 = 75 l + 50 = 150 l = 100 answer : e" + }, + { + "Answer": 10, + "Options": "a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14", + "Correct": "a", + "Explanation": "\"since 59,049 is an odd number , it is not a multiple of 4 . this means that y must equal zero . since x - y = 10 and y = 0 , then x = 10 . the answer is a .\"" + }, + { + "Answer": 12, + "Options": "a ) a ) 23 , b ) b ) 13 , c ) c ) 19 , d ) d ) 12 , e ) e ) 10", + "Correct": "d", + "Explanation": "let x equal the number and then change the words into an equation and solve for x : 4 x \u2013 3 = 9 ( x \u2013 7 ) 4 x \u2013 3 = 9 x \u2013 63 60 = 5 x 12 = x correct answer d ) 12" + }, + { + "Answer": 8100, + "Options": "a ) 8100 , b ) 3388 , c ) 7767 , d ) 2009 , e ) 22888", + "Correct": "a", + "Explanation": "\"6400 * 9 / 8 * 9 / 8 = 8100 answer : a\"" + }, + { + "Answer": 2699.9999999999995, + "Options": "a ) 360 , b ) 2700 , c ) 540 , d ) 640 , e ) 720", + "Correct": "b", + "Explanation": "\"too many words and redundant info there . ( i ) 1 / 3 of the pieces of art are displayed , hence 2 / 3 of the pieces of art are not displayed . ( ii ) 1 / 6 of the pieces on display are sculptures , hence 5 / 6 of the pieces on display are paintings . ( iii ) 1 / 3 of the pieces not on display are paintings , hence 2 / 3 of the pieces not on display are sculptures . 1200 sculptures are not on display , so according to ( iii ) 2 / 3 * { not on display } = 1200 - - > { not on display } = 1800 . according to ( i ) 2 / 3 * { total } = 1800 - - > { total } = 2700 . answer : b .\"" + }, + { + "Answer": 7.3, + "Options": "a ) $ 1.56 , b ) $ 2.40 , c ) $ 3.80 , d ) $ 4.20 , e ) $ 7.30", + "Correct": "e", + "Explanation": "\"in 3 miles , initial 1 / 5 mile charge is $ 1 rest of the distance = 3 - ( 1 / 5 ) = 14 / 5 rest of the distance charge = 14 ( 0.45 ) = $ 6.3 ( as the charge is 0.45 for every 1 / 5 mile ) = > total charge for 3 miles = 1 + 6.3 = 7.3 answer is e .\"" + }, + { + "Answer": 5040, + "Options": "a ) 4581 , b ) 5040 , c ) 3682 , d ) 1231 , e ) 1563", + "Correct": "b", + "Explanation": "the even numbers between 14 and 21 are 1416 , 1820 . find the lcm of these numbers lcm = 2 ^ 4 * 7 * 3 ^ 2 * 5 the answer is b )" + }, + { + "Answer": 13, + "Options": "a ) 3 , b ) 7 , c ) 15 , d ) 21 , e ) 13", + "Correct": "e", + "Explanation": "\"jacob = x years , mike = x + 12 years 3 years from now , 2 ( x + 3 ) = x + 15 2 x + 6 = x + 15 x = 9 x + 4 = 13 years answer e\"" + }, + { + "Answer": 288, + "Options": "a ) 288 , b ) 364 , c ) 410 , d ) 424 , e ) 450", + "Correct": "a", + "Explanation": "\"we ' re dealing with a sequence of consecutive odd integers : 13 to 35 , inclusive . we ' re asked for the sum of this group . 1 ) start with the sum of the smallest and the biggest : 13 + 35 = 48 2 ) now look at the ' next smallest ' and the ' next biggest ' : 15 + 33 = 48 now we have proof that there is no middle term . we have 6 bunches of 48 . 6 ( 48 ) = 288 a\"" + }, + { + "Answer": 4, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "d", + "Explanation": "f ( 3 ) / g ( 3 ) = product ( 1 to 3 ^ 2 ) / 1.2 ^ 2.3 ^ 2 = 1 . 2.3 . 4.5 . 6.7 . 8.9 / 1 . 4.9 = 1 . 2.3 . ( 2 ^ 2 ) . 5 . ( 2.3 ) . 7 . ( 2 ^ 3 ) . 9 / 1 . ( 2 ^ 2 ) . 9 = 1 . ( 2 ^ 7 ) . 3.5 . 7.9 / 1 . ( 2 ^ 2 ) . 9 loof for 2 ^ 7 / 2 ^ 2 = 2 ^ 5 - - - - exponent 4 answer : d" + }, + { + "Answer": 50, + "Options": "a ) 48 , b ) 49 , c ) 50 , d ) 51 , e ) 52", + "Correct": "c", + "Explanation": "from first constraint 4 n + 7 > 1 4 n > - 6 n > - ( 3 / 2 ) n > - 1.5 ( n = - 1 , 0 , 1 , 2 3 . . . . . . . . upto infinity ) from second constraint 4 n + 7 < 200 4 n < 193 n < 48 . 25 n = ( - infinity , . . . . . . . - 3 , - 2 , - 1 , 0 , 1 , 2 , . . . . . . . . . upto 48 ) combining the two - 1.5 < n < 48.25 n = 1 to 48 ( 48 integers ) and n = - 1 and 0 so 50 integers . c is the answer" + }, + { + "Answer": 1857.1428571428573, + "Options": "a ) 1000 , b ) 1250 , c ) 1300 , d ) 1600 , e ) 1857.14", + "Correct": "e", + "Explanation": "\"300 gallons of water increases capacity by 30 % that means 30 % is 300 gallons , so 100 % would be = 300 * 100 / 30 = 1000 gallons now 1000 + 300 gallons is 70 % capacity of tank . so 100 % capacity would be = 1300 * 100 / 70 = 1857.14 e is the answer\"" + }, + { + "Answer": 28000, + "Options": "a ) $ 28000 , b ) $ 15000 , c ) $ 12000 , d ) $ 10000 , e ) $ 9000", + "Correct": "a", + "Explanation": "\"since investment doubles in 70 / r years then for r = 8 it ' ll double in 70 / 8 = ~ 9 years ( we are not asked about the exact amount so such an approximation will do ) . thus in 18 years investment will double twice and become ( $ 7,000 * 2 ) * 2 = $ 28,000 ( after 9 years investment will become $ 7,000 * 2 = $ 14,000 and in another 9 years it ' ll become $ 14,000 * 2 = $ 28,000 ) . answer : a .\"" + }, + { + "Answer": 8, + "Options": "a ) 8 , b ) 7 , c ) 10 , d ) 12 , e ) 14", + "Correct": "a", + "Explanation": "\"let the number of cows be x and their legs be 4 x . let the number of chicken be y and their legs be 2 x . total number of legs = 4 x + 2 y . total number of heads = x + y . the number of legs was 16 more than twice the number of heads . therefore , 2 \u00d7 ( x + y ) + 16 = 4 x + 2 y . or , 2 x + 2 y + 16 = 4 x + 2 y . or , 2 x + 16 = 4 x [ subtracting 2 y from both sides ] . or , 16 = 4 x \u2013 2 x [ subtracting 2 x from both sides ] . or , 16 = 2 x . or , x = 8 [ dividing by 2 on both sides ] . therefore , the number of cows = 7 . correct answer : a ) 8\"" + }, + { + "Answer": 3, + "Options": "a ) 2 / 1 , b ) 4 / 1 , c ) 2 / 3 , d ) 3 / 4 , e ) 3 / 1", + "Correct": "e", + "Explanation": "\"given that milk / water = 4 x / x and 4 x + x = 45 - - > x = 9 . thus milk = 4 x = 36 liters and water = x = 9 liters . new ratio = 36 / ( 9 + 3 ) = 36 / 12 = 3 / 1 . answer : e .\"" + }, + { + "Answer": 15.000000000000007, + "Options": "a ) 10 litres , b ) 12 litres , c ) 15 litres , d ) 18 litres , e ) 21 litres", + "Correct": "c", + "Explanation": "c . p . of 1 litre of milk = rs . 20 \u00d7 2 / 3 = rs . 40 / 3 . c . p . of 1 litre of water = rs 0 . mean price = rs . 32 / 3 . by the rule of alligation , we have : c . p of 1 litre c . p of 1 litre of water of milk ( 0 ) ( rs . 40 / 3 ) \\ / mean price ( rs . 32 / 3 ) / \\ 40 / 3 \u2212 32 / 3 32 / ( 3 \u2212 0 ) 8 / 3 32 / 3 the ratio of water and milk = 8 / 3 : 32 / 3 . = 8 : 32 = 1 : 4 . thus , quantity of water to be added to 60 litres of milk : = ( 1 / 4 ) \u00d7 60 litres . = 15 litres . answer : c" + }, + { + "Answer": 50, + "Options": "a ) $ 50 , b ) $ 64 , c ) $ 75 , d ) $ 96 , e ) can not be determined", + "Correct": "a", + "Explanation": "\"solution : 3 x + 4 y + 2 z = 40 7 x + 2 y + 2 z = 60 adding both the equations = 10 x + 6 y + 4 z = 100 5 x + 3 y + 2 z = 50 ans a\"" + }, + { + "Answer": 120, + "Options": "a ) 120 cm , b ) 150 cm , c ) 160 cm , d ) 190 cm , e ) of these", + "Correct": "a", + "Explanation": "let the heights of the three boys be 4 k , 5 k and 6 k respectively . 4 k + 6 k = 5 k + 150 = > 5 k = 150 = > k = 30 therefore the height of the lightest boy = 4 k = 4 ( 30 ) = 120 cm . answer : a" + }, + { + "Answer": 0.2962962962962963, + "Options": "a ) 1 / 5 , b ) 1 / 3 , c ) 8 / 27 , d ) 1 / 27 , e ) 7 / 8", + "Correct": "c", + "Explanation": "no zonk ! : 1 st box = no zonk ! = 2 / 3 2 nd box = no zonk ! = 2 / 3 3 rd box = no zonk ! = 2 / 3 ( 2 / 3 ) ( 2 / 3 ) ( 2 / 3 ) = 8 / 27 8 / 27 is the probability of no zonk ! , so . . . answer : c" + }, + { + "Answer": 40, + "Options": "a ) 33 kg , b ) 31 kg , c ) 32 kg , d ) 40 kg , e ) 37 kg", + "Correct": "d", + "Explanation": "\"let a , b , c represent their respective weights . then , we have : a + b + c = ( 42 x 3 ) = 126 . . . . ( i ) a + b = ( 40 x 2 ) = 80 . . . . ( ii ) b + c = ( 43 x 2 ) = 86 . . . . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 166 . . . . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 40 . b ' s weight = 40 kg . d\"" + }, + { + "Answer": 1.4814814814814814, + "Options": "a ) 31 \u2044 5 , b ) 16 \u2044 5 , c ) 20 \u2044 9 , d ) 40 / 27 , e ) 5 \u2044 16", + "Correct": "d", + "Explanation": "say x / 3 / 8 * 5 / 9 = x * 8 / 3 * 5 / 9 = x * 40 / 27 d" + }, + { + "Answer": 8, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9", + "Correct": "d", + "Explanation": "( 10 x + y ) = ( 10 y + x ) + 9 = > 9 x - 9 y = 9 = > x - y = 1 and only 8 numbers satisfy this condition and the numbers are 21,32 , 43,54 , 65,76 , 87,98 answer : d" + }, + { + "Answer": 76.6, + "Options": "a ) 76.6 , b ) 75 , c ) 80 , d ) 85 , e ) 90", + "Correct": "a", + "Explanation": "explanation : ( 65 + 67 + 76 + 80 + 95 / 5 ) = 76.6 option a" + }, + { + "Answer": 2.5499999999999994, + "Options": "a ) 2.215 . , b ) 2.55 , c ) 2.775 . , d ) 3.2 . , e ) 3.5 .", + "Correct": "b", + "Explanation": "\"the ant walks an average of 600 meters in 12 minutes 600 meters in 1 / 5 hours the beetle walks 15 % less distance = 600 - 90 = 510 meters in 12 minutes 0.510 km in 12 / 60 = 1 / 5 hours speed = 0.510 * 5 = 2.55 km / h correct answer b = 2.55\"" + }, + { + "Answer": 4300, + "Options": "a ) $ 4100 , b ) $ 4300 , c ) $ 4500 , d ) $ 4700 , e ) $ 4900", + "Correct": "b", + "Explanation": "each month , the project should spend $ 42,000 / 12 = $ 3500 . in 8 months , the project should spend 8 * $ 3500 = $ 28,000 . the project is under budget by $ 28,000 - $ 23,700 = $ 4300 . the answer is b ." + }, + { + "Answer": 8, + "Options": "a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10", + "Correct": "d", + "Explanation": "\"if a ^ 2 - b ^ 2 = 0 , then let ' s assume that a = b . a must equal the 4 th positive multiple of 4 , thus a = 16 , which also equals b . b is the second positive multiple of n , thus n = 16 / 2 = 8 . the answer is d .\"" + }, + { + "Answer": 139, + "Options": "a ) 136 , b ) 137 , c ) 138 , d ) 139 , e ) 140", + "Correct": "d", + "Explanation": "\"d = d * q + r d = 19 * 7 + 6 d = 133 + 6 d = 139\"" + }, + { + "Answer": 42.857142857142854, + "Options": "a ) 50.5 % , b ) 42.8 % , c ) 22.2 % , d ) 33.3 % , e ) 25 %", + "Correct": "b", + "Explanation": "\"50 % of ( x - y ) = 20 % of ( x + y ) 50 / 100 ( x - y ) = 20 / 100 ( x + y ) 3 x = 7 y required percentage = y / x * 100 = 3 y / 7 y * 100 = 42.85 % answer is b\"" + }, + { + "Answer": 66, + "Options": "a ) 66 liters , b ) 32 liters , c ) 41 liters , d ) 50 liters , e ) 34 liters", + "Correct": "a", + "Explanation": "\"milk = 3 / 5 * 165 = 99 liters water = 66 liters 99 : ( 66 + p ) = 3 : 4 198 + 3 p = 396 = > p = 66 66 liters of water are to be added for the ratio become 3 : 4 . answer : a\"" + }, + { + "Answer": 800, + "Options": "a ) 800 , b ) 900 , c ) 1000 , d ) 1100 , e ) 1200", + "Correct": "a", + "Explanation": "\"0.25 x = 4 ( 850 - 800 ) 0.25 x = 200 x = 800 answer a\"" + }, + { + "Answer": 0.3181818181818182, + "Options": "a ) 5 / 22 , b ) 4 / 22 , c ) 3 / 22 , d ) 9 / 22 , e ) 7 / 22", + "Correct": "e", + "Explanation": "# of basic stereos was 3 / 4 of total and # of deluxe stereos was 1 / 4 of total , let ' s assume total = 16 , then basic = 12 and deluxe = 4 . now , if time needed to produce one deluxe stereo is 1 unit than time needed to produce one basic stereo would be 7 / 5 units . total time for basic would be 12 * 1 = 12 and total time for deluxe would be 4 * 7 / 5 = 28 / 5 - - > total time for both of them would be 12 + 28 / 5 = 88 / 5 - - > deluxe / total = 28 / 5 / 88 / 5 = 28 / 88 = 7 / 22 e" + }, + { + "Answer": 1656, + "Options": "a ) 1235 , b ) 1345 , c ) 1678 , d ) 1767 , e ) 1671", + "Correct": "e", + "Explanation": "\"let the smaller number be x . then larger number = ( x + 1395 ) . x + 1395 = 6 x + 15 5 x = 1380 x = 276 large number = 276 + 1395 = 1671 e\"" + }, + { + "Answer": 25, + "Options": "a ) 20 , b ) 25 , c ) 40 , d ) 45 , e ) 75", + "Correct": "b", + "Explanation": "\"average = 50 , sum of temperatures = 50 * 5 = 250 as the min temperature is 45 , max would be 250 - 4 * 45 = 70 - - > the range = 70 ( max ) - 45 ( min ) = 25 answer : b .\"" + }, + { + "Answer": 900, + "Options": "a ) s . 440 , b ) s . 850 , c ) s . 450 , d ) s . 900 , e ) s . 950", + "Correct": "d", + "Explanation": "\"total sale for 5 months = rs . ( 800 + 900 + 1000 + 700 + 800 ) = rs . 4200 required sale = rs . [ ( 850 x 6 ) - 4200 ] = rs . ( 5100 - 4200 ) = rs . 900 . option d\"" + }, + { + "Answer": 230, + "Options": "a ) 115 , b ) 230 , c ) 460 , d ) 575 , e ) 690", + "Correct": "b", + "Explanation": "the lcm of n and d is 690 = 2 * 3 * 5 * 23 . d is not divisible by 2 , thus 2 goes to n n is not divisible by 3 , thus 3 goes to d . from above : n must be divisible by 2 and not divisible by 3 : n = 2 * . . . in order n to be a 3 - digit number it must take all other primes too : n = 2 * 5 * 23 = 230 . answer : b ." + }, + { + "Answer": 172800, + "Options": "a ) 172,700 , b ) 172,800 , c ) 172,900 , d ) 173,000 , e ) 173,100", + "Correct": "b", + "Explanation": "\"this question can be modified so that the birth rate is given every m seconds and the death rate is given every n seconds . for this particular question : increase in the population every 2 seconds = 7 - 3 = 4 people . total 2 second interval in a day = 24 * 60 * 60 / 2 = 43,200 population increase = 43,200 * 4 = 172,800 . hence b .\"" + }, + { + "Answer": 75, + "Options": "a ) 50 , b ) 26 , c ) 75 , d ) 28 , e ) 21", + "Correct": "c", + "Explanation": "\"let the length of each train be x m . then , distance covered = 2 x m . relative speed = 46 - 36 = 10 km / hr . = 10 * 5 / 18 = 25 / 9 m / sec . 2 x / 54 = 25 / 9 = > x = 75 . answer : c\"" + }, + { + "Answer": 10, + "Options": "a ) 10 , b ) 6 , c ) 8 , d ) none of these , e ) can not be determined", + "Correct": "a", + "Explanation": "\"solution let the number be x . then , 3 ( 2 x + 8 ) \u2039 = \u203a 84 \u2039 = \u203a 2 x + 8 = 28 \u2039 = \u203a 2 x = 20 x = 10 . answer a\"" + }, + { + "Answer": 6, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "e", + "Explanation": "\"10 * 5 + 36 \u2013 26 = 60 / 10 = 6 answer : e\"" + }, + { + "Answer": 28, + "Options": "a ) 9 , b ) 14 , c ) 21 , d ) 28 , e ) 42", + "Correct": "d", + "Explanation": "3.456789 ^ 14 has 6 * 14 = 84 decimal places . 10 ^ 56 moves the decimal place to the right 56 places . ( 10 ^ 4 * 3.456789 ) ^ 14 has 84 - 56 = 28 digits after the decimal point . the answer is d ." + }, + { + "Answer": 24.999999999999993, + "Options": "a ) 5 % , b ) 10 % , c ) 20 % , d ) 25 % , e ) 50 %", + "Correct": "d", + "Explanation": "let j , f , m be the values of the stock in jan , feb and march . thus , per the question , j = 0.9 f = 1.2 m - - - - > m = 0.75 f thus the % decrease from f to m = ( f - m ) / ( f ) * 100 = ( f - 0.75 f ) / f * 100 = 0.25 * 100 = 25 % , d is the correct answer ." + }, + { + "Answer": 1.3333333333333333, + "Options": "a ) 9 / 4 , b ) 3 / 2 , c ) 4 / 3 , d ) 2 / 3 , e ) 1 / 2", + "Correct": "c", + "Explanation": "sq rt ( 4 x / 3 ) = x = > 4 x / 3 = x ^ 2 = > x = 4 / 3 ans - c" + }, + { + "Answer": 925, + "Options": "a ) 1925 , b ) 600 , c ) 925 , d ) 1325 , e ) 900", + "Correct": "c", + "Explanation": "\"explanation : let their maximum marks be x . then , 20 % of x = 160 + 25 = > 20 / 100 x = 185 x = ( 18500 / 20 ) x = 925 . answer : c\"" + }, + { + "Answer": 2.0399999999999636, + "Options": "a ) rs . 2.04 , b ) rs . 2.09 , c ) rs . 2.06 , d ) rs . 2.22 , e ) rs . 2.08", + "Correct": "a", + "Explanation": "\"c . i . when interest is compounded yearly = [ 5000 * ( 1 + 4 / 100 ) * ( 1 + ( 1 / 2 * 4 ) / 100 ] = 5000 * 26 / 25 * 51 / 50 = rs . 5304 c . i . when interest is compounded half - yearly = [ 5000 * ( 1 + 2 / 100 ) 2 ] = ( 5000 * 51 / 50 * 51 / 50 * 51 / 50 ) = rs . 5306.04 difference = ( 5306.04 - 5304 ) = rs . 2.04 . answer : a\"" + }, + { + "Answer": 220, + "Options": "a ) 156 , b ) 220 , c ) 130 , d ) 240 , e ) none", + "Correct": "b", + "Explanation": "\"explanation : average amount paid by 5 persons = rs . 100 increase in average due to rs . 120 paid extra by the 6 th men = rs . 100 / 5 = rs . 20 therefore , average expenditure of 6 friends = rs . 100 + rs . 20 = rs . 120 therefore , amount paid by the 6 th men = rs . 120 + rs . 100 = rs . 220 correct option : b\"" + }, + { + "Answer": 1530, + "Options": "a ) 1370 , b ) 1530 , c ) 1790 , d ) 1950 , e ) 2110", + "Correct": "b", + "Explanation": "\"the number of ways to choose two teams is 18 c 2 = 18 * 17 / 2 = 153 the total number of games in the season is 10 * 153 = 1530 . the answer is b .\"" + }, + { + "Answer": 0.005, + "Options": "a ) 0.5 , b ) 0.05 , c ) 0.005 , d ) 0.0005 , e ) 5", + "Correct": "c", + "Explanation": "as 1 / 2 = 0.5 and its percent value will be 0.5 / 100 = 0.005 answer : c" + }, + { + "Answer": 0.8, + "Options": "a ) 2 / 5 , b ) 3 / 4 , c ) 4 / 5 , d ) 5 / 4 , e ) 3 / 2", + "Correct": "c", + "Explanation": "\"x equals a increased by 25 percent of a = > x = a + 25 % a = 1.25 a m equals b decreased by 20 percent of b = > m = b - 20 % b = 0.8 b m / x = 0.8 b / 1.25 a putting the value of b / a = 5 / 4 we get m / x = 4 / 5 answer : c\"" + }, + { + "Answer": 12.087912087912088, + "Options": "a ) 8 % , b ) 9 % , c ) 10 % , d ) 11 % , e ) 12 %", + "Correct": "e", + "Explanation": "\"actual price = 20 + 2.75 = $ 22.75 saving = 2.75 / 22.75 * 100 = 12 % approximately answer is e\"" + }, + { + "Answer": 30.5, + "Options": "a ) 30.5 , b ) 26 , c ) 30 , d ) 18 , e ) 11", + "Correct": "a", + "Explanation": "\"explanation : 18 + 22 + 7 * 3 = 61 / 2 = 30.5 answer : a\"" + }, + { + "Answer": 599.9999999999999, + "Options": "a ) 120 , b ) 600 , c ) 1000 , d ) 360 , e ) 240", + "Correct": "b", + "Explanation": "\"let the additional invested amount for 10 % interest be x ; equation will be ; 2400 + 0.05 * 2400 + x + 0.10 x = 2400 + x + 0.06 ( 2400 + x ) 0.05 * 2400 + 0.10 x = 0.06 x + 0.06 * 2400 0.04 x = 2400 ( 0.06 - 0.05 ) x = 2400 * 0.01 / 0.04 = 600 ans : b\"" + }, + { + "Answer": 75, + "Options": "a ) 88 % , b ) 75 % , c ) 67 % , d ) 63 % , e ) 50 %", + "Correct": "b", + "Explanation": "the only way to have an odd product is if both integers are odd . p ( odd product ) = 1 / 2 * 1 / 2 = 1 / 4 p ( even product ) = 1 - 1 / 4 = 3 / 4 = 75 % the answer is b ." + }, + { + "Answer": 48, + "Options": "a ) 3 , b ) 6 , c ) 48 , d ) 12 , e ) 14", + "Correct": "c", + "Explanation": "let the number of each size of jar = wthen 1 / 4 w + 1 / 2 w + w = 28 1 3 / 4 w = 28 w = 16 the total number of jars = 3 w = 48 answer : c" + }, + { + "Answer": 115, + "Options": "a ) 110 , b ) 111 , c ) 115 , d ) 123 , e ) none", + "Correct": "c", + "Explanation": "explanation : average amount paid by 10 persons = rs . 60 increase in average due to rs . 50 paid extra by the 11 th men = rs . 50 / 10 = rs . 5 therefore , average expenditure of 11 friends = rs . 60 + rs . 5 = rs . 65 therefore , amount paid by the 11 th men = rs . 65 + rs . 50 = rs . 115 correct option : c" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "a", + "Explanation": "\"( 7 ^ 700 ) mod 100 = [ 7 ^ ( 2 * 350 ) ] mod 100 = [ 49 ^ 350 ] mod 100 = [ ( 50 - 1 ) ^ 350 ] mod 100 = [ { 350 c 349 } * 50 * ( - 1 ) ^ 349 + 350 c 350 * ( - 1 ) ^ 350 ] mod 100 = [ - 350 * 50 + 1 ] mod 100 = 1 mod 100 so , evidently , the remainder will be 1 . answer : a\"" + }, + { + "Answer": 79, + "Options": "a ) 74 , b ) 75 , c ) 76 , d ) 77 , e ) 79", + "Correct": "e", + "Explanation": "ratio is 4 : 6 : 5 , numbers are 4 x , 6 x , 5 x total scores of each class is ( 65 * 4 x + 6 x * 90 + 77 * 5 x ) = 260 x + 540 x + 385 x = 1185 x total number of students = 15 x average = 1185 x / 15 x = 79 e is the answer" + }, + { + "Answer": 30, + "Options": "a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50", + "Correct": "c", + "Explanation": "let present age of the elder person = x and present age of the younger person = x \u2212 16 ( x \u2212 6 ) = 3 ( x \u2212 16 \u2212 6 ) x \u2212 6 = 3 x \u2212 66 2 x = 60 x = 60 / 2 = 30 answer : option c" + }, + { + "Answer": 2, + "Options": "a ) 2 / 1 , b ) 4 / 1 , c ) 2 / 3 , d ) 3 / 4 , e ) 3 / 2", + "Correct": "a", + "Explanation": "\"given that milk / water = 4 x / x and 4 x + x = 45 - - > x = 9 . thus milk = 4 x = 36 liters and water = x = 9 liters . new ratio = 36 / ( 9 + 9 ) = 36 / 18 = 2 / 1 . answer : a .\"" + }, + { + "Answer": 10, + "Options": "a ) - 1 , b ) 6 , c ) 7 , d ) 10 , e ) 14", + "Correct": "d", + "Explanation": "\"denote | x - 5 | as y : y ^ 2 + y = 20 - - > y = - 5 or y = 4 . discard the first solution since y = | x - 5 | , so it ' s an absolute value and thus can not be negative . y = | x - 5 | = 4 - - > x = 9 or x = - 1 . the sum = 10 answer : d .\"" + }, + { + "Answer": 1585, + "Options": "a ) 1590 , b ) 1600 , c ) 1950 , d ) 1630 , e ) 1760", + "Correct": "a", + "Explanation": "explanation : let the number that anil wanted to multiply be ' y ' . he was expected to find the value of 35 y . instead , he found the value of 53 y . the difference between the value that he got ( 53 y ) and what he was expected to get ( 35 y ) is 540 . = > 53 y - 35 y = 540 = > ( 53 - 35 ) * y = 540 = > y = 30 therefore , the correct product = 53 * 30 = 1590 answer : a" + }, + { + "Answer": 50, + "Options": "a ) 51 , b ) 20 , c ) 40 , d ) 50 , e ) 55", + "Correct": "d", + "Explanation": "\"x / 10 students are > 4 yrs 20 students are < 3 yrs x / 10 + 20 = 25 x / 10 = 5 x = 50 answer : d\"" + }, + { + "Answer": 18, + "Options": "a ) 11 , b ) 15 , c ) 12 , d ) 17 , e ) 18", + "Correct": "e", + "Explanation": "\"e 18 ( x + y ) \u00e2 \u20ac \u201c ( y + z ) = 18 x \u00e2 \u20ac \u201c z = 18\"" + }, + { + "Answer": 10.819672131147541, + "Options": "a ) 10.2 kmph , b ) 10.4 kmph , c ) 10.8 kmph , d ) 11.8 kmph , e ) none", + "Correct": "c", + "Explanation": "sol . total distance travelled = ( 10 + 12 ) km / hr = 22 km / hr . total time taken = [ 10 / 12 + 12 / 10 ] hrs = 61 / 30 hrs \u2234 average speed = [ 22 * 30 / 61 ] km / hr = 10.8 km / hr . answer c" + }, + { + "Answer": 4, + "Options": "a ) 8 / 2 , b ) 2 / 4 , c ) 1 / 8 , d ) 2 / 4 , e ) 4 / 6", + "Correct": "a", + "Explanation": "( a / 2 ) / ( b / c ) = ( a * c ) / 2 b the expression will have the largest value when numerator ( a * c ) is the largest . = ( 2 * 4 ) / 2 * 1 = 8 / 2 answer a" + }, + { + "Answer": 0.75, + "Options": "a ) 1 / 2 , b ) 3 / 5 , c ) 5 / 7 , d ) 9 / 11 , e ) 3 / 4", + "Correct": "e", + "Explanation": "\"let the original fraction be x / y then , 115 % of x / 92 % of y = 15 / 16 115 x / 92 y = 15 / 16 x / y = 3 / 4 answer is e\"" + }, + { + "Answer": 74.99999999999997, + "Options": "a ) 37.5 , b ) 75 , c ) 100 , d ) 150 , e ) 175", + "Correct": "b", + "Explanation": "\"nope , 150 . i can only get it by following pr ' s backsolving explanation . i hate that . original mixture has 20 % salt and 80 % water . total = x out of which salt = 0.2 x and water = 0.8 x now , 1 / 4 water evaporates and all salt remains . so what remains is 0.2 x salt and 0.6 x water . now 10 gallons salt is added and 5 gallons of water is added . so salt now becomes - > ( 0.2 x + 10 ) and water - - > ( 0.6 x + 5 ) amount of salt is 33.33 % of total . so amount of water is 66.66 % . so salt is half of the volume of water . so ( 0.2 x + 10 ) = ( 0.6 x + 5 ) / 2 = 0.4 x + 20 = 0.6 x + 5 = > 0.2 x = 15 solving , x = 75 answer : b\"" + }, + { + "Answer": 23.840000000000003, + "Options": "a ) 20 % , b ) 18 % , c ) 15 % , d ) 12 % , e ) 24 %", + "Correct": "e", + "Explanation": "\"100 * 100 = 10000 68 * 112 = 7616 10000 - - - - - - - 2384 100 - - - - - - - ? = 24 % answer : e\"" + }, + { + "Answer": 13, + "Options": "a ) - 4 , b ) - 2 , c ) 11 , d ) 13 , e ) 22", + "Correct": "d", + "Explanation": "\"the equation that can be formed is : 3 x - 26 = 26 - x or , 4 x = 52 or , x = 13 . d answer .\"" + }, + { + "Answer": 288, + "Options": "a ) 180 , b ) 130 , c ) 140 , d ) 160 , e ) 288", + "Correct": "e", + "Explanation": "\"white : yellow = x : ( x + 90 ) = 8 : 13 - - > 13 x = 8 x + 720 - - > x = 144 . the total # of balls originally x + x = 144 + 144 = 288 . answer : e .\"" + }, + { + "Answer": 1683, + "Options": "a ) 1683 , b ) 1684 , c ) 1685 , d ) 1582 , e ) 1584", + "Correct": "a", + "Explanation": "explanation : l . c . m . of 5,6 , 7,8 = 840 . required number is of the form 840 k + 3 least value of k for which ( 840 k + 3 ) is divisible by 9 is k = 2 . required number = ( 840 x 2 + 3 ) = 1683 answer is a" + }, + { + "Answer": 0.03125, + "Options": "a ) 1 / 32 , b ) 7 / 8 , c ) 9 / 64 , d ) 5 / 64 , e ) 3 / 64", + "Correct": "a", + "Explanation": "\"p ( xavier will solve ) = 1 / 6 p ( yvonne will solve ) = 1 / 2 p ( zelda will not solve ) = 1 - 5 / 8 = 3 / 8 . now , we need to multiply all this ps to find an answer : p = ( 1 / 6 ) * ( 1 / 2 ) * ( 3 / 8 ) = 1 / 32 . ans . a .\"" + }, + { + "Answer": 60, + "Options": "a ) 58 kg , b ) 60 kg , c ) 64 kg , d ) 70 kg , e ) none", + "Correct": "b", + "Explanation": "\"sol . for 9 kg zinc , mixture melted = ( 9 + 11 ) kg . for 27 kg zinc , mixture , melted = [ 20 / 9 x 27 ] kg = 60 kg . answer b\"" + }, + { + "Answer": 7, + "Options": "a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 11", + "Correct": "c", + "Explanation": "\"3 < x < 10 , 6 < x < 18 , - 2 < x < 9 0 < x < 8 x < 8 from above : 6 < x < 8 - - > x = 7 . answer : c .\"" + }, + { + "Answer": 211, + "Options": "a ) 2 , b ) 11 , c ) 13 , d ) 17 , e ) 211", + "Correct": "e", + "Explanation": "p ( 12 ) + 11 = 2 \u2217 3 \u2217 5 \u2217 7 \u2217 11 + 11 = 11 ( 2 \u2217 3 \u2217 5 \u2217 7 + 1 ) = 11 \u2217 211 . both 11 and 211 are primes : 11 is the smallest prime of p ( 12 ) + 11 and 211 is the second smallest prime of p ( 12 ) + 11 . answer : e ." + }, + { + "Answer": 13, + "Options": "a ) 1 , b ) 19 , c ) 29 , d ) 13 , e ) 33", + "Correct": "d", + "Explanation": "\"total of integers = 70 * 4 = 280 lowest of the least possible integer is when the middle 2 intergers are at the maximum or equal to the highest possible integer . but all integers are distinct . so if the largest integer is 90 , then the middle 2 will be 88 and 89 lowest of least possible integer = 280 - ( 90 + 89 + 88 ) = 280 - 267 = 13 answer : d\"" + }, + { + "Answer": 32500, + "Options": "a ) 32500 , b ) 2500 , c ) 22500 , d ) 30000 , e ) 40000", + "Correct": "a", + "Explanation": "let his total sales be rs . x . now ( total sales ) \u2013 ( commission ) = rs . 31100 x - [ ( 5 % of 10000 + 4 % of ( x - 10000 ) ] = 31100 x - [ ( ( 5 / 100 ) * 10000 + ( 4 / 100 ) * ( x - 10000 ) ] = 31100 \uf0f3 x - 500 - ( ( x - 10000 ) / 25 ) = 31100 \uf0f3 x - ( x / 25 ) = 31200 \uf0f3 24 x / 25 = 31200 \uf0f3 x = [ ( 31200 * 25 ) / 24 ) = 32500 . total sales = rs . 32500 answer a" + }, + { + "Answer": 672.1628045157456, + "Options": "a ) 669 , b ) 660 , c ) 360 , d ) 720 , e ) 1,440", + "Correct": "a", + "Explanation": "diameter of car tire = 15 inches radius of car tire = 7.5 inches = 7.5 * 2.54 cm = 19.05 cm circumference of the car tire = 2 * pi * 19.05 = 2 * 3.14 * 19.05 = 119.63 cm distance traveled by car = . 5 mile = . 5 * 1.6 km = . 8 km = 800 m = 8 * 10 ^ 4 cm number of revolutions = distance traveled / circumference of tire = 8 * 10 ^ 4 / 119.63 = 668.73 since the answer choices are far apart we should use estimation in this question . ideally , in the gmat the conversion between units would be provided . answer a" + }, + { + "Answer": 240, + "Options": "a ) 190 , b ) 200 , c ) 210 , d ) 220 , e ) 240", + "Correct": "e", + "Explanation": "2 * 16 c 2 = 2 * 120 = 240 the answer is e ." + }, + { + "Answer": 32, + "Options": "a ) 44 , b ) 41 , c ) 38 , d ) 35 , e ) 32", + "Correct": "e", + "Explanation": "\"let n = total students in class total points for 1 / 3 class = 30 n / 3 = 10 n total points for 2 / 3 class = 33 * 2 n / 3 = 22 n total points for whole class = 10 n + 22 n = 32 n 32 n total class points / n total students = 32 grade point average for total class answer : e\"" + }, + { + "Answer": 252, + "Options": "a ) 237 , b ) 278 , c ) 278 , d ) 252 , e ) 271", + "Correct": "d", + "Explanation": "explanation : since there are 5 cups of each kind , prepared with milk or tea leaves added first , are identical hence , total number of different people ways of presenting the cups to the expert is 10 ! / ( 5 ! x 5 ! ) = 252 answer : d ) 252" + }, + { + "Answer": 400, + "Options": "a ) 200 , b ) 300 , c ) 400 , d ) 500 , e ) 600", + "Correct": "c", + "Explanation": "let the numbers be x and y . then , xy = 9375 and x = 15 . y xy = 9375 ( x / y ) 15 y 2 = 625 . y = 25 . x = 15 y = ( 15 x 25 ) = 375 . sum of the numbers = x + y = 375 + 25 = 400 . c" + }, + { + "Answer": 0.4500000000000002, + "Options": "a ) 0.45 , b ) 0.5 , c ) 6.45 , d ) 0.25 , e ) 6.0", + "Correct": "a", + "Explanation": "\"since z * is defined as the greatest positive even integer less than or equal to z , then 6.45 * = 6 ( the greatest positive even integer less than or equal to 6.45 is 6 ) . hence , 6.45 \u2013 6.45 * = 6.45 - 6 = 0.45 answer : a .\"" + }, + { + "Answer": 31, + "Options": "a ) 31 , b ) 22 , c ) 25 , d ) 27 , e ) 29", + "Correct": "a", + "Explanation": "\"( 4 ) ^ 11 x ( 7 ) ^ 7 x ( 11 ) ^ 2 = ( 2 x 2 ) ^ 11 x ( 7 ) ^ 7 x ( 11 ) ^ 2 = 2 ^ 11 x 2 ^ 11 x 7 ^ 7 x 11 ^ 2 = 2 ^ 22 x 7 ^ 7 x 11 ^ 2 total number of prime factors = ( 22 + 7 + 2 ) = 31 . answer is a .\"" + }, + { + "Answer": 2, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "b", + "Explanation": "\"let number of apples = a number of oranges = b a + b = 10 - - - 1 . 48 = ( . 4 a + . 6 b ) / 10 = > 48 = 4 a + 6 b - - - - 2 solving 1 and 2 , we get a = 6 b = 4 let the number of oranges put back = c 45 * ( 10 - c ) = 40 * 6 + 60 ( 4 - c ) = > c = 2 answer b\"" + }, + { + "Answer": 18540, + "Options": "a ) 15360 , b ) 16010 , c ) 15060 , d ) 14930 , e ) 18540", + "Correct": "e", + "Explanation": "\"6000 + 15000 - ( 0.11 * 6000 + 0.12 * 15000 ) = 18540 . answer : e .\"" + }, + { + "Answer": 375, + "Options": "a ) $ 374 , b ) $ 382 , c ) $ 385 , d ) $ 392 , e ) $ 375", + "Correct": "e", + "Explanation": "\"( 348 / 116 ) 125 = 375 in this case long division does not take much time . ( 348 / 116 ) = 3 3 * 125 = 375 ( 300 + 75 ) answer e\"" + }, + { + "Answer": 3161, + "Options": "a ) 2988 , b ) 2776 , c ) 4400 , d ) 2871 , e ) 3162", + "Correct": "e", + "Explanation": "\"x * ( 95 / 100 ) * ( 85 / 100 ) = 2553 x = 3162 answer : e\"" + }, + { + "Answer": 2509, + "Options": "a ) 1888 , b ) 2999 , c ) 2834 , d ) 2509 , e ) 2991", + "Correct": "d", + "Explanation": "let the total number of votes polled in the election be 100 k . number of valid votes = 100 k - 20 % ( 100 k ) = 80 k let the number of votes polled in favour of a and b be a and b respectively . a - b = 15 % ( 100 k ) = > a = b + 15 k = > a + b = b + 15 k + b now , 2 b + 15 k = 80 k and hence b = 32.5 k it is given that 100 k = 7720 32.5 k = 32.5 k / 100 k * 7720 = 2509 the number of valid votes polled in favour of b is 2834 . answer : d" + }, + { + "Answer": 8, + "Options": "a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14", + "Correct": "b", + "Explanation": "\"l = r l = 3 c r = c + 16 3 c = c + 16 c = 8 the answer is b .\"" + }, + { + "Answer": 8, + "Options": "a ) 0 , b ) 1 , c ) 8 , d ) 3 , e ) 4", + "Correct": "c", + "Explanation": "\"unit digit in the given product = unit digit in 8 * 6 * 2 * 3 = 8 answer is c\"" + }, + { + "Answer": 54, + "Options": "a ) 15 % , b ) 20 % , c ) 25 % , d ) 54 % , e ) 75 %", + "Correct": "d", + "Explanation": "initially 72 % and 28 % split 80 % is further divided as 25 % and 75 % q is asking about that 75 % let total be ' 100 ' then that 75 % is ( 3 / 4 ) \u2217 72 so , the required % is [ ( 3 / 4 ) \u2217 72 / 100 ] \u2217 100 = 54 % answer : d" + }, + { + "Answer": 9, + "Options": "a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9", + "Correct": "e", + "Explanation": "\"7 ^ 1 = 7 7 ^ 2 = 49 7 ^ 3 = 343 7 ^ 4 = 1 ( last digit ) 7 ^ 5 = 7 ( last digit ) and the cycle repeats after every 4 powers therefore , last digit of 7 ^ 6 = 9 answer e\"" + }, + { + "Answer": 1688, + "Options": "a ) 246 , b ) 248 , c ) 1692 , d ) 15,128 , e ) 30,256", + "Correct": "c", + "Explanation": "\"# of 2 - letter codes possible from 424 different signs = 424 * 424 . # of 2 - letter codes possible from 422 different signs = 422 * 422 . the difference = 424 ^ 2 - 422 ^ 2 = ( 424 - 422 ) ( 424 + 422 ) = 1692 . answer : c .\"" + }, + { + "Answer": 8, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9", + "Correct": "d", + "Explanation": "\"let bill run x on saturday , so he will run x + 4 on sunday . . julia will run 2 * ( x + 4 ) on sunday . . totai = x + x + 4 + 2 x + 8 = 28 . . 4 x + 12 = 28 . . x = 4 . . ans = x + 4 = 4 + 4 = 8 aswer d\"" + }, + { + "Answer": 10, + "Options": "a ) 5 , b ) 8 , c ) 10 , d ) 13 , e ) 17", + "Correct": "c", + "Explanation": "\"official solution : ( b ) we know that a # b = 100 and a # b = 4 a \u00b2 + 4 b \u00b2 + 8 ab . so 4 a \u00b2 + 4 b \u00b2 + 8 ab = 100 we can see that 4 a \u00b2 + 4 b \u00b2 + 8 ab is a well - known formula for ( 2 a + 2 b ) \u00b2 . therefore ( 2 a + 2 b ) \u00b2 = 100 . ( 2 a + 2 b ) is non - negative number , since both a and b are non - negative numbers . so we can conclude that 2 ( a + b ) = 10 . ( a + b ) + 5 = 10 / 2 + 5 = 10 . the correct answer is c .\"" + }, + { + "Answer": 69, + "Options": "a ) 65 % , b ) 67 % , c ) 69 % , d ) 71 % , e ) 73 %", + "Correct": "c", + "Explanation": "\"72 + 84 + x = 3 * 75 x = 69 the answer is c .\"" + }, + { + "Answer": 164300.5, + "Options": "a ) 897 , b ) 164850 , c ) 164749 , d ) 149700 , e ) 156720", + "Correct": "b", + "Explanation": "the series is = > 101 + . . . 998 number of terms = > 300 sum = > 300 / 2 * [ 101 + 998 ] hence sum r = > 164850 i . e . option b" + }, + { + "Answer": 45, + "Options": "a ) 60 , b ) 70 , c ) 80 , d ) 100 , e ) 45", + "Correct": "e", + "Explanation": "let x be the number of 25 ounce cans . therefore ( x + 30 ) is the number of 15 ounce cans . total volume is same , therefore 25 x = 15 ( x + 30 ) 10 x = 450 x = 45 ans - e" + }, + { + "Answer": 3.40000000000002, + "Options": "a ) 2 % , b ) 3.8 % , c ) 3.4 % , d ) 3.6 % , e ) 1 %", + "Correct": "c", + "Explanation": "100 * 100 = 10000 84 * 115 = 9660 - - - - - - - - - - - 10000 - - - - - - - - - - - 340 100 - - - - - - - - - - - ? = > 3.4 % decrease answer : c" + }, + { + "Answer": 30, + "Options": "a ) 90 , b ) 60 , c ) 30 , d ) 1911 , e ) none of these", + "Correct": "c", + "Explanation": "\"solution required number of student = h . c . f of 2010 and 1050 = 30 . answer c\"" + }, + { + "Answer": 55.223880597014926, + "Options": "a ) 55.22 % , b ) 54.54 % , c ) 63 % , d ) 70 % , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : number of runs made by running = 134 - ( 12 x 4 + 2 x 6 ) = 134 - ( 60 ) = 74 now , we need to calculate 72 is what percent of 134 . = > 74 / 134 * 100 = 55.22 % answer : a\"" + }, + { + "Answer": 1038, + "Options": "a ) 545 , b ) 685 , c ) 1038 , d ) 495 , e ) 534", + "Correct": "c", + "Explanation": "\"let y x 40 = 173 x 240 then y = ( 173 x 240 ) / 40 = 1038 answer : c\"" + }, + { + "Answer": 5700, + "Options": "a ) $ 5700 , b ) $ 5500 , c ) $ 5800 , d ) $ 5200 , e ) $ 5880", + "Correct": "a", + "Explanation": "explanation : let ' s start with what the total price of the car would be . if 5 % is equal to $ 300 then 100 % equals $ x . we just have to multiply $ 300 by 20 to get total amount = $ 6000 . out of this amount we then need to deduct the amount already paid which was $ 300 so we have $ 6000 - $ 300 = $ 5700 answer : option a" + }, + { + "Answer": 4, + "Options": "a ) 23 , b ) 28 , c ) 4 , d ) 1 , e ) 25", + "Correct": "c", + "Explanation": "if the remainder is same in each case and remainder is not given , hcf of the differences of the numbers is the required greatest number 6905 - 1305 = 5600 6905 - 4665 = 2240 4665 - 1305 = 3360 hence , the greatest number which divides 1305 , 4665 and 6905 and gives the same remainder , n = hcf of 5600 , 2240 , 3360 = 1120 sum of digits in n = sum of digits in 1120 = 1 + 1 + 2 + 0 = 4 answer is c" + }, + { + "Answer": 21, + "Options": "a ) 10 , b ) 16 , c ) 21 , d ) 24 , e ) 27", + "Correct": "c", + "Explanation": "should be 21 . mid intended to type a seven - digit number there are two possibilities for placing 2 3 s . case 1 : two 3 s were missed consecutively . i . e . he typed 33 and it came blank on screen . - 5 - 2 - 1 - 1 - 5 - in this arrangement we can fit 33 in 6 ways . ( six dashes , each dash represent one possible place for placing 33 ) case 2 : two 3 s are not together , i . e . they have one or more digits between them . - 5 - 2 - 1 - 1 - 5 - , in this arrangement if we place first 3 at first dash i . e . 35 - 2 - 1 - 1 - 5 - then the other 3 can fit into 5 places . if we place first 3 at second dash i . e . - 532 - 1 - 1 - 5 - then the other 3 can fit into 4 places . if we place first 3 at third dash i . e . - 5 - 231 - 1 - 5 - then the other 3 can fit into 3 places . if we place first 3 at fourth dash i . e . - 5 - 2 - 131 - 5 - then the other 3 can fit into 2 places . if we place first 3 at fifth dash i . e . - 5 - 2 - 1 - 135 - then the other 3 can fit into 1 place . so total 15 ways . case 2 + case 1 = 6 + 15 = 21 ways answer c" + }, + { + "Answer": 0.041666666666666664, + "Options": "a ) 719 / 720 , b ) 1 / 24 , c ) 2 / 233 , d ) 3 / 543 , e ) 1 / 720", + "Correct": "b", + "Explanation": "4 ties and 4 shirts . . . red tie can take any of 4 shirts . . orange can take any of the remaining 3 shirts yellow any of remaining 2 . . and so on till last indigo chooses the 1 remaining . . total ways = 4 * 3 * 2 * 1 = 24 out of this 720 , only 1 way will have same colour tie and shirt . . prob = 1 / 720 b" + }, + { + "Answer": 29400, + "Options": "a ) 14700 , b ) 24703 , c ) 29400 , d ) 33777 , e ) 34778", + "Correct": "c", + "Explanation": "explanation : let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 < = > 3 x = 36000 < = > x = 12000 . a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . a ' s share = rs . ( 70000 * 21 / 50 ) = rs . 29,400 . answer : c )" + }, + { + "Answer": 0.84, + "Options": "a ) 9 / 25 , b ) 10 / 25 , c ) 6 / 10 , d ) 2 / 3 , e ) 21 / 25", + "Correct": "e", + "Explanation": "\"simply look at the question from the other side . what is the probability that you can \u2019 t row the canoe ? this would be 2 / 5 x 2 / 5 = 4 / 25 . using the idea that the probability q of something happening is 1 \u2013 the probability that it doesn \u2019 t happen , you can use the following equation to reach the right answer : 1 \u2013 4 / 25 = 21 / 25 . answer choice e .\"" + }, + { + "Answer": 19.999999999999996, + "Options": "a ) 10 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) none", + "Correct": "b", + "Explanation": "\"solution let the original consumption = 100 kg and new consumption = x kg . so , 100 x 6 = x \u00d7 7.50 x = 80 kg . reduction in consumption = 20 % . answer b\"" + }, + { + "Answer": 42, + "Options": "a ) 36 , b ) 42 , c ) 44 , d ) 46 , e ) none", + "Correct": "b", + "Explanation": "17 ( p + 1 ) = 29 ( q + 1 ) - - > ( p + 1 ) / ( q + 1 ) = 29 / 17 - - > the least positive value of p + 1 is 29 , so the least value of p is 28 and the least positive value of q + 1 is 15 , so the least value of q is 14 - - > the least value of p + q is 28 + 14 = 42 . answer : b ." + }, + { + "Answer": 13, + "Options": "a ) 13 , b ) 15 , c ) 16 , d ) 17 , e ) 18", + "Correct": "a", + "Explanation": "\"12 , 15 , 18 , 21 , 24 , 27 , 30 , 33 , 36 , 39 , 42 , 45,48 . 13 numbers . 10 / 3 = 3 and 50 / 3 = 16 = = > 16 - 3 = 13 . therefore 13 digits a )\"" + }, + { + "Answer": 3, + "Options": "a ) 3 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "a", + "Explanation": "assume x is quotient here , n = 18 x + 3 - - - - - - - - - - ( 1 ) and n = 6 x + ? we can also write first term as n = ( 18 x + 6 ) = 6 ( 3 x + 1 ) + 3 ie 6 ( 3 x + 1 ) + 3 ie the first term is perfectly divisible by 6 . so , the remainder left is 3 . so , answer ( a ) is right choice ." + }, + { + "Answer": 31.25, + "Options": "a ) 31.25 % , b ) 25 % , c ) 12.5 % , d ) 0.2083 % , e ) none", + "Correct": "a", + "Explanation": "\"only trick n this question is to ignore 40 % information as farm tax is levied uniformly in the village and that includes mr william ' s land . what percentage of tax mr william paid ? this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 480 / 3840 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 40 ) = 31.25 % and the answer is not there in the options . the correct answer is ( a ) .\"" + }, + { + "Answer": 100, + "Options": "a ) 30 , b ) 60 , c ) 80 , d ) 100 , e ) none of these", + "Correct": "d", + "Explanation": "solution given expression = ( 7.5 \u00d7 7.5 + 2 \u00d7 7.5 \u00d7 2.5 + 2.5 \u00d7 2.5 ) = ( a 2 + 2 ab + b 2 ) = ( a + b ) 2 = ( 7.5 + 2.5 ) 2 = 102 = 100 . answer d" + }, + { + "Answer": 90, + "Options": "a ) 90 , b ) 110 , c ) 120 , d ) 130 , e ) 220", + "Correct": "a", + "Explanation": "\"orchestra seats - a balcony seats - b a + b = 350 and 12 a + 8 b = 3320 solving equations simultaneously ( multiply equation 1 with 8 and subtract from second equation ) 4 a = 3320 - 8 * 350 = 3320 - 2800 = 520 i . e . a = 130 and b = 350 - 130 = 220 more seats in balcony than orchestra = b - a = 220 - 130 = 90 answer : option a\"" + }, + { + "Answer": 10, + "Options": "a ) 10 , b ) 12 , c ) 13 , d ) 15 , e ) 18", + "Correct": "a", + "Explanation": "\"2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 29 - 9 = 20 ab = 10 . answer : a\"" + }, + { + "Answer": 32, + "Options": "a ) 16 , b ) 12 , c ) 18 , d ) 22 , e ) 32", + "Correct": "e", + "Explanation": "4 * 8 = 32 . answer is e ." + }, + { + "Answer": 33, + "Options": "a ) 9 , b ) 10 , c ) 8 , d ) 9.5 , e ) none of these", + "Correct": "a", + "Explanation": "answer : a" + }, + { + "Answer": 1.4999999999999998, + "Options": "a ) $ 1.50 , b ) $ 2.00 , c ) $ 2.50 , d ) $ 3.00 , e ) $ 3.50", + "Correct": "a", + "Explanation": "\"x = 3 x / 5 + 1 / 3 * 2 x / 5 + 40 4 x / 15 = 40 x = 150 = $ 1.50 the answer is a .\"" + }, + { + "Answer": 68, + "Options": "a ) 35.67 % , b ) 64.75 % , c ) 68.00 % , d ) 69.57 % , e ) none of these", + "Correct": "c", + "Explanation": "\"girls = 900 , boys = 1100 passed = ( 32 % of 1100 ) + ( 32 % of 900 ) = 352 + 288 = 640 failed = 2000 - 640 = 1360 failed % = [ ( 1360 / 2000 ) x 100 ] % = 68 % . answer : c\"" + }, + { + "Answer": 26, + "Options": "a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 29", + "Correct": "c", + "Explanation": "\"x / 2 y = 3 / 2 = > x = 6 y / 2 = 3 y = > ( 7 x + 5 y ) / ( x - 2 y ) = ( ( 7 * ( 3 y ) ) + 5 y ) / ( 3 y - 2 y ) = > 26 y / y = 26 answer : c\"" + }, + { + "Answer": 57, + "Options": "a ) 55 , b ) 56 , c ) 57 , d ) 58 , e ) 59", + "Correct": "c", + "Explanation": "explanation : let the average weight of the 59 students be a . so the total weight of the 59 of them will be 59 * a . the questions states that when the weight of this student who left is added , the total weight of the class = 59 a + 45 when this student is also included , the average weight decreases by 0.2 kgs 59 a + 45 / 60 = a \u2212 0.2 = > 59 a + 45 = 60 a - 12 = > 45 + 12 = 60 a - 59 a = > a = 57 answer : option c" + }, + { + "Answer": 3, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8", + "Correct": "b", + "Explanation": "first of all , see thisgmat blog postand check the related lesson linked below for some background on function notation . we can plug anything in for x and get a result . you can find f ( 1 ) , for example , by plugging in 1 where x is , and you would get 12 - 1 / 2 = 11.5 . or we could find f ( 2 ) , which would be 12 - 4 / 2 = 10 . so the notation f ( 2 k ) means that we are going to plug a 2 k in for x everywhere in the formula for f ( x ) . that would be : f ( 2 k ) = 12 - ( 2 k ) ^ 2 / 2 = 12 - 2 k ^ 2 . remember that we have to square both the 2 and the k , to get 4 k 2 . now , this expression , the output , we will set equal to 2 k . 12 - 2 k ^ 2 = 2 k - - > k = - 4 or k = 3 . all the answers are positive , so we choose k = 3 . answer = b" + }, + { + "Answer": 1710, + "Options": "a ) 1710 , b ) 1920 , c ) 2440 , d ) 2860 , e ) 3260", + "Correct": "a", + "Explanation": "\"the number of ways to choose two teams is 19 c 2 = 19 * 18 / 2 = 171 the total number of games in the season is 10 * 171 = 1710 . the answer is a .\"" + }, + { + "Answer": 30, + "Options": "a ) 30 seconds , b ) 20 seconds , c ) 40 seconds , d ) 10 seconds , e ) none", + "Correct": "a", + "Explanation": "7.2 km = 7200 m . 1 h = 3600 s . the speed will be 7200 m / 3600 s = 2 m / s . the necessary time to climb will be 20 seconds . when descending , if the speed is two times greater , the necessary time will be two times smaller , so 10 seconds . the total necessary time is 20 s + 10 s = 30 seconds . answer a" + }, + { + "Answer": 44, + "Options": "a ) 25 , b ) 56 , c ) 45 , d ) 36 , e ) 44", + "Correct": "e", + "Explanation": "let the son ' s present age be x years father ' s present age = ( 4 x + 4 ) 4 x + 4 + 4 = 2 ( x + 4 ) + 10 4 x + 8 = 2 x + 18 x = 5 father ' s present age = 4 x + 4 = 4 * 10 + 4 = 44 years answer is e" + }, + { + "Answer": 36, + "Options": "a ) 35 , b ) 36 , c ) 37 , d ) 38 , e ) 39", + "Correct": "b", + "Explanation": "\"8 / 7 * 32 = 36.6 the answer is b .\"" + }, + { + "Answer": 15, + "Options": "a ) 9 , b ) 16 , c ) 15 , d ) 25 1 / 3 , e ) 28 1 / 2", + "Correct": "c", + "Explanation": "3 / 4 pint is required to make 3 / 4 + 2 / 3 = 17 / 12 pint of perfect pink so 17 / 12 pint requires 3 / 4 pint of red . . 1 pint will require 3 / 4 * 12 / 17 = 9 / 17 . . 30 pints will require 9 / 17 * 30 = 15 pints . . c" + }, + { + "Answer": 2304, + "Options": "a ) 2304 , b ) 2305 , c ) 2309 , d ) 2310 , e ) 2311", + "Correct": "a", + "Explanation": "\"trees increase by 1 / 4 the number of trees in preceding year . hence , correct answer must be divisible by 4 . based on divisibility rules , if last 2 digits are divisible by 4 then the number is divisible by 4 . thus , we can eliminate b , c , d , e the answer to be a again , trees increase by 1 / 4 the number of trees in preceding year . hence , the number of trees increase by 5 / 4 times the number of trees the preceding year . if x = initial number of trees = 2304 year 1 = 5 / 4 x year 2 = ( 5 / 4 ) ( 5 / 4 ) x year 3 = ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) x year 4 = ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) x only for answer d : ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) 2304 = 5625 hence , correct answer = a\"" + }, + { + "Answer": 9944, + "Options": "a ) 9900 , b ) 9999 , c ) 9988 , d ) 9944 , e ) 9966", + "Correct": "d", + "Explanation": "\"explanation : largest 4 digit number is 9999 after doing 9999 \u00f7 88 we get remainder 55 hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944 answer : option d\"" + }, + { + "Answer": 20, + "Options": "a ) 25 % , b ) 20 % , c ) 50 % , d ) 66 2 / 3 % , e ) 75 %", + "Correct": "b", + "Explanation": "\"general formula for percent increase or decrease , ( percent change ) : percent = change / original \u2217 100 so , the time between maintenance checks increased by 30 \u2212 25 / 25 \u2217 100 = 20 answer : b .\"" + }, + { + "Answer": 8, + "Options": "a ) 24 , b ) 18 , c ) 16 , d ) 12 , e ) 8", + "Correct": "e", + "Explanation": "\"4 machines do x units in 6 days we have x / 6 = > rate of the 4 machines we know that we need to have 2 x units in 4 days therefore , we need to get to 2 x / 4 rate of the machines . rate of one machine is x / 6 * 1 / 4 = x / 24 . now , we need to know how many machines need to work simultaneously , to get 2 x done in 6 days . 2 x / 6 work needs to be done by machines that work at x / 24 rate . let ' s assign a constant y for the number of machines : ( x / 24 ) * y = 2 x / 6 y = 2 x / 6 * 24 / x cancel 6 with 24 , and x with x and get - > 8 . answer choice e\"" + }, + { + "Answer": 1.002770083102493, + "Options": "a ) 290 / 289 , b ) 1 / 289 , c ) 290 / 90 , d ) 362 / 361 , e ) none of these", + "Correct": "d", + "Explanation": "explanation : if the numbers are a , b , then ab = 19 , as 17 is a prime number , so a = 1 , b = 19 . 1 / a 2 + 1 / b 2 = 1 / 1 ( 2 ) + 1 / 19 ( 2 ) = 362 / 361 option d" + }, + { + "Answer": 22, + "Options": "a ) 20 . , b ) 21 . , c ) 22 . , d ) 23 . , e ) 24 .", + "Correct": "c", + "Explanation": "\"before solving it algebraically , let us prime factorize 1430 = 2 * 5 * 11 * 13 . since number of apples per person * total persons u = 1430 , the answer should be a factor of 1430 . only c is . and that ' s your answer . c\"" + }, + { + "Answer": 6303, + "Options": "a ) 5037 , b ) 5447 , c ) 5867 , d ) 6297 , e ) 6617", + "Correct": "d", + "Explanation": "\"when increased by 3 , the number must include at least 2 ^ 2 * 3 ^ 2 * 5 ^ 2 * 7 = 6300 the answer is d .\"" + }, + { + "Answer": 343, + "Options": "a ) 343 , b ) 199 , c ) 121 , d ) 69 , e ) 249", + "Correct": "a", + "Explanation": "a ( a ( a ( 0 ) ) ) = a ( a ( 1 ) ) = a ( 3 ) = ( 6 + 1 ) ^ 3 = 343 . thus , the answer is a ." + }, + { + "Answer": 24, + "Options": "a ) 21 , b ) 22 , c ) 23 , d ) 25 , e ) 24", + "Correct": "e", + "Explanation": "\"let the average age of the whole team be x years . 11 x - ( 27 + 30 ) = 9 ( x - 1 ) = > 11 x - 9 x = 48 = > 2 x = 48 = > x = 24 . so , average age of the team is 24 years . e\"" + }, + { + "Answer": 7, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10", + "Correct": "b", + "Explanation": "\"to get 40 points as end of season we need another 28 points or more from remaining 15 matches : option a = 6 * 3 + 9 * 1 = 27 option b = 7 * 3 + 8 * 1 = 29 hence option b - 7\"" + }, + { + "Answer": 3, + "Options": "a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3", + "Correct": "e", + "Explanation": "\"if x = 4 3.134 \u00d7 10 ^ 4 = 31340 > 31000 so , x = 3 answer : e\"" + }, + { + "Answer": 15, + "Options": "a ) 10 hours , b ) 12 hours , c ) 14 hours , d ) 15 hours , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : speed of the boat = 6 km / hr speed downstream = ( 6 + 2 ) = 8 km / hr speed upstream = ( 6 - 2 ) = 4 km / hr distance travelled downstream = distance travelled upstream = 40 km total time taken = time taken downstream + time taken upstream = ( 40 / 8 ) + ( 40 / 4 ) = 15 d\"" + }, + { + "Answer": 50, + "Options": "a ) 1 , b ) 50 , c ) 19 , d ) 20 , e ) 21", + "Correct": "b", + "Explanation": "\"this is a solution from beatthegmat : even numbers : ( 100 - 2 ) / 2 + 1 = 50 even integers . ( 100 + 2 ) / 2 = 51 is the average of the even set . sum = avg * ( # of elements ) = 51 * 50 = 2550 = a odd numbers : ( 99 - 1 ) / 2 + 1 = 50 odd integers . ( 99 + 1 ) / 2 = 50 is the average of the odd set . sum = avg * ( # of elements ) = 50 * 50 = 2500 = b a - b = 2550 - 2500 = 50 . ( b )\"" + }, + { + "Answer": 22, + "Options": "a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22", + "Correct": "e", + "Explanation": "let the one digit numbers x , y , z sum of all possible two digit numbers = ( 10 x + y ) + ( 10 x + z ) + ( 10 y + x ) + ( 10 y + z ) + ( 10 z + x ) + ( 10 z + y ) = 22 ( x + y + z ) therefore sum of all possible two digit numbers when divided by sum of one digit numbers gives 22 . answer e" + }, + { + "Answer": 1100, + "Options": "a ) $ 1010 , b ) $ 1100 , c ) $ 1110 , d ) $ 1101 , e ) $ 1200", + "Correct": "b", + "Explanation": "answer = b the total cost of the trip ( $ 12100.00 ) divided by 11 equals $ 1100.00 ." + }, + { + "Answer": 40, + "Options": "a ) 20 , b ) 25 , c ) 30 , d ) 40 , e ) 50", + "Correct": "d", + "Explanation": "let the list price be 2 x for min sale price , the first discount given should be 50 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 40 and 0.8 x = 32 so lowest sale price is 32 , which r is 40 % of 80 hence , d is the answer" + }, + { + "Answer": 14, + "Options": "a ) 7 , b ) 9 , c ) 12 , d ) 14 , e ) 18", + "Correct": "d", + "Explanation": "in 42 liters of drink a , there are 24 liters of milk and 18 liters of juice . with 24 liters of milk , we need a total of 32 liters of juice to make drink b . we need to add 14 liters of juice . the answer is d ." + }, + { + "Answer": 0.0156, + "Options": "a ) a . 0.156 , b ) b . 0.01506 , c ) c . 0.0156 , d ) d . 0.0001566 , e ) e . 0.00001566", + "Correct": "c", + "Explanation": "let total production be 10000 units . . . . a produces 4000 units and 36 units are defective b produces 6000 units and 120 units are defective so , out of total 10,000 units 156 units are defective . . . so the required probability = 156 / 10000 = > 0.0156 answer will be ( c )" + }, + { + "Answer": 4, + "Options": "a ) 3 : 2 , b ) 1 : 2 , c ) 4 : 1 , d ) 5 : 2 , e ) 4 : 3", + "Correct": "c", + "Explanation": "\"g = 10 w c = 5 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 10 w + 5 wx = x + 1 * 9 w 10 + 5 x = 9 ( x + 1 ) x = 1 / 4 ratio of gold with copper = 1 : 1 / 4 = 4 : 1 answer is c\"" + }, + { + "Answer": 0.6666666666666667, + "Options": "a ) 2 / 3 , b ) 1 / 4 , c ) 7 / 9 , d ) 1 / 5 , e ) 8 / 11", + "Correct": "a", + "Explanation": "lets pick smart numbers . total number of students : 12 p . e . ( 1 / 2 ) : 6 theatre ( 1 / 3 ) : 4 music ( 1 / 6 ) : 2 after leaving school p . e . : 4 theatre : 3 music : 2 new total number of students : 9 p . e . and music : 6 answer 2 / 3 or a" + }, + { + "Answer": 575, + "Options": "a ) rs . 575 , b ) rs . 600 , c ) rs . 625 , d ) rs . 485 , e ) rs . 590", + "Correct": "a", + "Explanation": "\"soln : - ( 600 / 120 ) 115 = 575 in this case long division does not take much time . ( 5 / 1 ) 115 = rs . 575 answer : a\"" + }, + { + "Answer": 1.375, + "Options": "a ) 0.75 , b ) 0.8 , c ) 1.375 , d ) 1.4 , e ) 1.85", + "Correct": "c", + "Explanation": "say the cost price of 80 pencils was $ 80 ( $ 1 per pencil ) and the selling price of 1 pencil was p . selling at a loss : 80 - 80 p = 30 p - - > p = 8 / 11 . ( cost price ) / ( selling price ) = 1 / ( 8 / 11 ) = 11 / 8 = 1.375 . answer : c ." + }, + { + "Answer": 59, + "Options": "a ) 46 , b ) 59 , c ) 63 , d ) 75 , e ) 88", + "Correct": "b", + "Explanation": "sum of all the 9 numbers = 9 * 104 = 936 sum of the first 5 of them = 5 * 99 = 495 sum of the last 5 of them = 5 * 100 = 500 so , the 5 th number = 495 + 500 - 936 = 59 . answer : b" + }, + { + "Answer": 101, + "Options": "a ) 123 , b ) 106 , c ) 100 , d ) 101 , e ) 240", + "Correct": "d", + "Explanation": "\"explanation : cash realised = rs . ( 101.25 - 0.25 ) = rs . 101 . answer : d\"" + }, + { + "Answer": 16.666666666666668, + "Options": "a ) 15 % , b ) 25 % , c ) 0.125 % , d ) 0.2083 % , e ) 16.667 %", + "Correct": "e", + "Explanation": "\"this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 480 / 3840 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 75 ) = 16.667 % the correct answer is ( e ) .\"" + }, + { + "Answer": 8, + "Options": "a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14", + "Correct": "b", + "Explanation": "substitute y by 2 in 2 x - y = 14 2 x - 2 = 14 2 x = 16 if we substitute x by 8 , we have 2 ( 8 ) = 16 . hence x = 8 correct answer b" + }, + { + "Answer": 26, + "Options": "a ) 18 , b ) 82 , c ) 26 , d ) 27 , e ) 29", + "Correct": "c", + "Explanation": "\"let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 x / 2 = ( 83 - 70 ) = > x / 2 = 13 = > x = 26 . answer : c\"" + }, + { + "Answer": 38.5, + "Options": "a ) 36.9 , b ) 38.5 , c ) 18.5 , d ) 32.5 , e ) 28.5", + "Correct": "b", + "Explanation": "\"explanation : numbers divisible by 7 are 21,28 , 35,42 , 49,56 , average = ( 21 + 28 + 35 + 42 + 49 + 56 , ) / 6 = 231 / 6 = 38.5 answer : b\"" + }, + { + "Answer": 25, + "Options": "a ) 22 , b ) 99 , c ) 25 , d ) 66 , e ) 887", + "Correct": "c", + "Explanation": "\"total time taken = x / 50 + 2 x / 20 hours = 6 x / 50 = 3 x / 25 hours average speed = 3 x / ( 3 x / 25 ) = 25 kmph answer : c\"" + }, + { + "Answer": 143, + "Options": "a ) 135 , b ) 137 , c ) 143 , d ) 310 , e ) 380", + "Correct": "c", + "Explanation": "\"the number of liters in each can = hcf of 60 , 144 and 368 = 4 liters . number of cans of maaza = 60 / 4 = 15 number of cans of pepsi = 144 / 4 = 36 number of cans of sprite = 368 / 4 = 92 the total number of cans required = 15 + 36 + 92 = 143 cans . answer : c\"" + }, + { + "Answer": 33.333333333333336, + "Options": "a ) $ 28.50 , b ) $ 30.50 , c ) $ 33.33 , d ) $ 40.50 , e ) $ 50.00", + "Correct": "c", + "Explanation": "first 2 shirts are sold for $ 30 and $ 20 = $ 50 . to get average price of $ 30 , total sale should be 5 * $ 30 = $ 150 so remaining 3 shirts to be sold for $ 150 - $ 50 = $ 100 answer should be 100 / 3 = $ 33.33 that is c" + }, + { + "Answer": 30, + "Options": "a ) 30 , b ) 33 , c ) 55 , d ) 77 , e ) 88", + "Correct": "a", + "Explanation": "\"let f = pure fuji , g = pure gala and c - cross pollinated . c = 10 % of x where x is total trees . c = . 1 x also 3 x / 4 = f and c + f = 170 = > . 1 x + 3 / 4 x = 170 = > x = 200 200 - 170 = pure gala = 30 . answer a\"" + }, + { + "Answer": 44, + "Options": "a ) 44 years , b ) 18 years , c ) 20 years , d ) 22 years , e ) 16 years", + "Correct": "a", + "Explanation": "\"let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . ( x + 46 ) + 2 = 2 ( x + 2 ) x + 48 = 2 x + 4 x = 44 . answer : a\"" + }, + { + "Answer": 15, + "Options": "a ) 15 , b ) 66 , c ) 25 , d ) 88 , e ) 17", + "Correct": "a", + "Explanation": "explanation : to maximize the value of vx - yz , we make yz negative and vx as maximum as possible using given value . vx \u2212 yz = ( \u2212 3 ) 2 \u2212 ( \u2212 3 \u00d7 2 ) vx \u2212 yz = ( \u2212 3 ) 2 \u2212 ( \u2212 3 \u00d7 2 ) = 15 answer : a" + }, + { + "Answer": 43.2, + "Options": "a ) 34 , b ) 43.2 , c ) 40 , d ) 38 , e ) 29", + "Correct": "b", + "Explanation": "\"solution : average speed = 2 xy / x + y = 2 * 54 * 36 / 54 + 36 = 43.2 answer : b\"" + }, + { + "Answer": 1, + "Options": "a ) 6 , b ) 1 , c ) 0 , d ) 8 , e ) 7", + "Correct": "b", + "Explanation": "\"every prime number greater than 3 can be written 6 n + 1 or 6 n - 1 . if p = 6 n + 1 , then p ^ 2 + 13 = 36 n ^ 2 + 12 n + 1 + 12 = 36 n ^ 2 + 12 n + 12 + 1 if p = 6 n - 1 , then p ^ 2 + 13 = 36 n ^ 2 - 12 n + 1 + 12 = 36 n ^ 2 - 12 n + 12 + 1 when divided by 12 , it must leave a remainder of 1 . the answer is b .\"" + }, + { + "Answer": 1.036111111111111, + "Options": "a ) 18.6 , b ) 9.3 , c ) 6.2 , d ) 3.1 , e ) 1.03", + "Correct": "e", + "Explanation": "\"number of passengers using kennedy airport = 37 / 3 = ~ 12.43 passengers using miami airport = 12.43 / 4 = ~ 3.1 passengers using logan airport = 3.1 / 3 = ~ 1.03 so e\"" + }, + { + "Answer": 4, + "Options": "a ) \u2212 48 , b ) \u2212 4 , c ) 4 , d ) 9 , e ) 48", + "Correct": "c", + "Explanation": "\"i . e . if a = - 1 then b = 5 or if a = 5 then b = - 1 but in each case a + b = - 1 + 5 = 4 answer : option c\"" + }, + { + "Answer": 0.25, + "Options": "a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4", + "Correct": "a", + "Explanation": "assume 100 persons in a company person knows c + + = 4 / 10 = 100 * 4 / 100 = 20 persons person knows java = 2 / 4 = 100 * 2 / 4 = 50 persons neither = 2 / 8 = 100 * 2 / 8 = 25 persons according to our assumption 100 person = 20 + 50 + 25 = 95 person covered ( 5 remaining ) so , total possibility = 20 person ( c + + ) + 5 ( remaining ) = 25 persons which is 25 / 100 = 1 / 4 answer : a" + }, + { + "Answer": 23, + "Options": "a ) 87 , b ) 98 , c ) 30 , d ) 28 , e ) 23", + "Correct": "e", + "Explanation": "\"20 + 10 + 8 * 2 = 46 / 2 = 23 answer : e\"" + }, + { + "Answer": 0.30000000000000004, + "Options": "a ) \u00bd , b ) 3 / 10 , c ) 1 / 50 , d ) 1 / 500 , e ) 2 / 500", + "Correct": "b", + "Explanation": "\"let x be the difference then . 8 - 1 / 2 = x 8 / 10 - 1 / 2 = x x = 3 / 10 ans b\"" + }, + { + "Answer": 5, + "Options": "a ) $ 0.00 , b ) $ 1.00 , c ) $ 3.40 , d ) $ 5.00 , e ) $ 6.80", + "Correct": "d", + "Explanation": "0.85 * { original price } = $ 68 - - > { original price } = $ 80 . { final price } = $ 68 * 1.25 = $ 85 . the difference = $ 85 - $ 85 = $ 5 . answer : d ." + }, + { + "Answer": 0.4, + "Options": "a ) $ 4 , b ) $ 0.4 , c ) $ 1 , d ) $ 3 , e ) $ 1.65", + "Correct": "b", + "Explanation": "\"lets assume price of coffee in june = 100 x price of tea in june = 100 x price of coffee in july = 300 x ( because of 200 % increase in price ) price of tea in july = 40 x ( because of 60 % decrease in price ) price of 1.5 pound of coffee 1.5 pound of tea in july will be = 450 x + 60 x = 510 x as per question 510 x = 5.10 $ x = 0.01 s so the price of tea in july = 40 x = 40 x 0.01 = 0.4 $ / pound answer b\"" + }, + { + "Answer": 0.2999999999999998, + "Options": "a ) 1.5 , b ) 0.5 , c ) 6.25 , d ) 0.25 , e ) 0.3", + "Correct": "e", + "Explanation": "\"since z * is defined as the greatest positive even integer less than or equal to z , then 6.30 * = 6 ( the greatest positive even integer less than or equal to 6.30 is 6 ) . hence , 6.30 \u2013 6.30 * = 6.30 - 6 = 0.30 answer : e .\"" + }, + { + "Answer": 163, + "Options": "a ) 160 , b ) 161 , c ) 162 , d ) 163 , e ) 164", + "Correct": "d", + "Explanation": "\"to minimize one quantity maximize other . 162 * 2.5 ( max possible amount of food a guest could consume ) = 405 pounds , so there must be more than 162 guests , next integer is 163 . answer : d .\"" + }, + { + "Answer": 1, + "Options": "a ) 0.5 , b ) 1 , c ) 1.5 , d ) 2 , e ) 3", + "Correct": "b", + "Explanation": "\"let x be the number of desks and bookcases that are placed along the library wall . 2 x + 1.5 x < 15 3.5 x < 15 since x is a non negative integer , the largest number x can be is 4 . when x is 4 , the desks and bookcases take up 3.5 * 4 = 14 m , leaving 1 m of empty space . thus , i believe the answer is b ) 1\"" + }, + { + "Answer": 1.6666666666666667, + "Options": "a ) 1 , b ) 4 / 3 , c ) 17 / 5 , d ) 18 / 5 , e ) 5 / 3", + "Correct": "e", + "Explanation": "\"we have two equations : 2 x + y = 7 x + 2 y = 8 notice that something nice happens when we add them . we get : 3 x + 3 y = 15 divide both sides by 3 to get : x + y = 5 so , ( x + y ) / 3 = 5 / 3 answer : e\"" + }, + { + "Answer": 13.88888888888889, + "Options": "a ) 15 % , b ) 25 % , c ) 0.125 % , d ) 13.88 % , e ) none", + "Correct": "d", + "Explanation": "\"this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 480 / 3840 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 90 ) = 13.88 % the correct answer is ( d ) .\"" + }, + { + "Answer": 4500, + "Options": "a ) 2177 , b ) 2876 , c ) 4500 , d ) 2981 , e ) 2711", + "Correct": "c", + "Explanation": "\"sum of the salaries of the person for the months of january , february , march and april = 4 * 8000 = 32000 - - - - ( 1 ) sum of the salaries of the person for the months of february , march , april and may = 4 * 8500 = 34000 - - - - ( 2 ) ( 2 ) - ( 1 ) i . e . may - jan = 2000 salary of may is rs . 6500 salary of january = rs . 4500 . answer : c\"" + }, + { + "Answer": 250, + "Options": "a ) 200 , b ) 250 , c ) 50 , d ) 115 , e ) 150", + "Correct": "b", + "Explanation": "\"x + y = 300 x - y = 200 2 x = 100 x = 50 y = 250 answer is b\"" + }, + { + "Answer": 32, + "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 21 , e ) 32", + "Correct": "e", + "Explanation": "\"total marks of male = m total marks of female = f number of males = 8 number of females = f given : ( m + f ) / ( 8 + f ) = 90 - - - - - - - - - - - - - 1 also given , m / 8 = 82 thus m = 656 - - - - - - - - - 2 also , f / f = 92 thus f = 92 f - - - - - - - - - 3 put 2 and 3 in 1 : we get ( 656 + 92 f ) / ( 8 + f ) = 90 solving this we get f = 32 ans : e\"" + }, + { + "Answer": 20, + "Options": "a ) 30 , b ) 31 , c ) 45 , d ) 90 , e ) 20", + "Correct": "e", + "Explanation": "1 sd from the mean is adding and subtrating the amount if standard deviation from the mean one time . 2 sd from the mean is adding and subtracting twice . 1 sd from the mean ranges from 70 to 50 , where 70 is within sd above the mean and 50 within 1 sd below the mean 2 sd = 10 twice = 20 from the the mean , which is 80 to 40 , where 80 is within 2 sd above the mean and 20 is within 2 sd below the mean . answer = e" + }, + { + "Answer": 0.03840000000000001, + "Options": "a ) 0 , b ) 24 / 625 , c ) 2 / 9 , d ) 1 / 3 , e ) 1", + "Correct": "b", + "Explanation": "\"if he is to ride 5 times and since he can choose any of the 5 cars each time , total number of ways is = 5 * 5 * 5 * 5 * 5 = 3125 now the number of ways if he is to choose a different car each time is = 5 * 4 * 3 * 2 * 1 = 120 so the probability is = 120 / 3125 = 24 / 625 answer : b\"" + }, + { + "Answer": 4, + "Options": "a ) 2 , b ) 4 , c ) 7 , d ) 8 , e ) 9", + "Correct": "b", + "Explanation": "\"explanation : 35 + 25 = 60 / 15 = 4 ( remainder ) b\"" + }, + { + "Answer": 25, + "Options": "a ) 22 , b ) 26 , c ) 25 , d ) 28 , e ) 12", + "Correct": "c", + "Explanation": "\"let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 80 x - ( 5 * 40 ) = 90 ( x - 5 ) 250 = 10 x = > x = 25 answer : c\"" + }, + { + "Answer": 14, + "Options": "a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16", + "Correct": "c", + "Explanation": "\"according to order of operations , inner brackets first where 5 x 3 \u00e3 \u00b7 3 is first calculated since it has a multiplication and a division . 5 \u00e3 \u2014 3 \u00e3 \u00b7 3 = 15 \u00e3 \u00b7 3 = 5 hence 13 + sqrt ( - 4 + 5 \u00e3 \u2014 3 \u00e3 \u00b7 3 ) = 13 + sqrt ( - 4 + 5 ) = 13 + sqrt ( 1 ) = 13 + 1 = 14 correct answer c ) 14\"" + }, + { + "Answer": 20, + "Options": "a ) 70 % , b ) 90 % , c ) 60 % , d ) 50 % , e ) 20 %", + "Correct": "e", + "Explanation": "\"given ratio = 1 / 6 : 1 / 5 = 5 : 6 let first number be 5 x and the second number be 9 x . the second number is more than first number by 1 x . required percentage = x / 5 x * 100 = 20 % . answer : e\"" + }, + { + "Answer": 9984, + "Options": "a ) 4676 , b ) 4678 , c ) 8888 , d ) 9504 , e ) 9984", + "Correct": "e", + "Explanation": "\"largest 4 digit number = 9999 9999 \u00f7 24 = 416 , remainder = 15 hence largest 4 digit number exactly divisible by 24 = 9999 - 15 = 9984 answer : e\"" + }, + { + "Answer": 77, + "Options": "a ) 67 kg , b ) 77 kg , c ) 87 kg , d ) 97 kg , e ) none of these", + "Correct": "b", + "Explanation": "\"explanation : let the average weight of 8 persons be \u2018 x \u2019 years and the age of the new person be \u2018 y \u2019 years so , ( 8 x \u2013 65 + y ) / 8 = x + 1.5 so , y = 77 kgs 65 + 8 x 1.5 = 77 kgs answer b\"" + }, + { + "Answer": 7, + "Options": "a ) 1 , b ) 2 , c ) 4 , d ) 5 , e ) 7", + "Correct": "e", + "Explanation": "\"( 71 ) ( 73 ) = ( 72 - 1 ) ( 72 + 1 ) = 72 ^ 2 - 1 which is 1 less than a multiple of 8 . then the remainder will be 7 . the answer is e .\"" + }, + { + "Answer": 7, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 7", + "Correct": "e", + "Explanation": "\"the product of 8 integers is negative thus an odd number of integers need to be negative to have a negative product we are asked at most how many are required . so , the highest odd integer before 6 , i . e . 7 correct option : e\"" + }, + { + "Answer": 36.45, + "Options": "a ) 36.45 minutes , b ) 36.47 minutes , c ) 36.41 minutes , d ) 36.42 minutes , e ) 36.65 minutes", + "Correct": "a", + "Explanation": "explanation : maximum number of trials required = 9 * 9 * 9 = 729 . since for each combination trial , 3 seconds are required to open the briefcase is given as 3 * 729 = 2187 seconds = 36.45 minutes . answer : a" + }, + { + "Answer": 1.5, + "Options": "a ) 1.2 , b ) 1.5 , c ) 1.8 , d ) 2.1 , e ) 2.4", + "Correct": "b", + "Explanation": "let x be the number of liters of ethanol added to the gas tank . 0.05 ( 27 ) + x = 0.1 ( 27 + x ) 0.9 x = 2.7 - 1.35 = 1.35 x = 1.5 liters the answer is b ." + }, + { + "Answer": 32000, + "Options": "a ) $ 20000 , b ) $ 15000 , c ) $ 32000 , d ) $ 10000 , e ) $ 9000", + "Correct": "c", + "Explanation": "\"since investment doubles in 70 / r years then for r = 4 it ' ll double in 70 / 4 = ~ 18 years ( we are not asked about the exact amount so such an approximation will do ) . thus in 36 years investment will double twice and become ( $ 8,000 * 2 ) * 2 = $ 32,000 ( after 18 years investment will become $ 8,000 * 2 = $ 16,000 and in another 18 years it ' ll become $ 16,000 * 2 = $ 32,000 ) . answer : c .\"" + }, + { + "Answer": 24, + "Options": "a ) 0 , b ) 12 , c ) 13 , d ) 20 , e ) 24", + "Correct": "e", + "Explanation": "\"12 * 42 = 504 504 % 21 = 24 answer : e\"" + }, + { + "Answer": 112, + "Options": "a ) 112 , b ) 111 , c ) 212 , d ) 115 , e ) 113", + "Correct": "a", + "Explanation": "required numbers are = ( 11 + 13 + 17 + 19 + 23 + 29 ) = 112 note : 1 is not a prime number answer a" + }, + { + "Answer": 193.75, + "Options": "a ) 191 , b ) 194 , c ) 193 , d ) 212 , e ) 213", + "Correct": "b", + "Explanation": "\"total movies submitted are 775 . as per question we need to take 1 / 4 of 775 to be considered for top 10 movies = 193.75 approximate the value we 194 . imo option b is the correct answer . . .\"" + }, + { + "Answer": 84, + "Options": "a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %", + "Correct": "d", + "Explanation": "\"16 % ________________________________________________ a + d 34 % ________________________________________________ a 34 % ________________________________________________ a - d 16 % since 68 % lies one standard deviation from mean a , = > 50 % of 68 % lies on either side as it is symmetric about a . thus 16 % lie below a - d and 16 % lie above a + d now below a + d = 16 + 34 + 34 = 84 % hence d\"" + }, + { + "Answer": 0.1875, + "Options": "a ) 27 / 4 , b ) 27 / 8 , c ) 3 / 4 , d ) 3 / 16 , e ) 1 / 4", + "Correct": "d", + "Explanation": "\"say a = 2 . then : a / b = 1 / 3 - - > b = 6 ; b / c = 2 - - > c = 3 ; c / d = 1 / 2 - - > d = 6 ; d / e = 3 - - > e = 2 ; e / f = 1 / 8 - - > f = 16 . abc / def = ( 2 * 6 * 3 ) / ( 6 * 2 * 16 ) = 3 / 16 . answer : d .\"" + }, + { + "Answer": 8, + "Options": "a ) 7 % , b ) 8 % , c ) 9 % , d ) 10 % , e ) 11 %", + "Correct": "b", + "Explanation": "\"cost of kit = $ 87.50 if filters are purchased individually - $ 16.45 * 2 + $ 14.05 * 2 + $ 19.50 = $ 80.50 amount saved = $ 87.50 - $ 80.50 = $ 7 required % age = ( $ 7 / $ 87.50 ) * 100 = 8 % so , the correct answer is b .\"" + }, + { + "Answer": 149, + "Options": "a ) a ) 130 , b ) b ) 134 , c ) c ) 149 , d ) d ) 158 , e ) e ) 160", + "Correct": "c", + "Explanation": "\"d = d * q + r d = 16 * 9 + 5 d = 144 + 5 d = 149 answer c\"" + }, + { + "Answer": 50, + "Options": "a ) 18 , b ) 28 , c ) 48 , d ) 38 , e ) 50", + "Correct": "e", + "Explanation": "\"let x = the number sought . then x / 5 + x + 5 = 65 . x = 50 . e\"" + }, + { + "Answer": 221, + "Options": "a ) 209 , b ) 212 , c ) 215 , d ) 218 , e ) 221", + "Correct": "e", + "Explanation": "\"k - 32 = 9 t / 5 k = 9 t / 5 + 32 k = 9 ( 105 ) / 5 + 32 = 221 the answer is e .\"" + }, + { + "Answer": 40.8, + "Options": "a ) 47 , b ) 46 , c ) 41 , d ) 48 , e ) 45", + "Correct": "c", + "Explanation": "\"the question actually asks the highest power of 10 which divides 300 ! ( for a number to be an integer - without any remainder all the trailing zeroe ' s must be divided by the denominator ) 10 = 2 x 5 170 factorial will have 41 as - 170 / 5 = 34 34 / 5 = 6 6 / 5 = 1 so answer will be ( c ) 41\"" + }, + { + "Answer": 0.25, + "Options": "a ) 1 / 7 , b ) 1 / 5 , c ) 1 / 4 , d ) 1 / 3 , e ) 3 / 7", + "Correct": "c", + "Explanation": "\"1 lbs of raisin = $ 1 3 lbs of raisin = $ 3 1 lbs of nuts = $ 3 3 lbs of nuts = $ 9 total value of mixture = 9 + 3 = 12 fraction of the value of raisin = 3 / 12 = 1 / 4 ans : c\"" + }, + { + "Answer": 190, + "Options": "a ) 90 , b ) 190 , c ) 120 , d ) 130 , e ) 220", + "Correct": "b", + "Explanation": "orchestra seats - a balcony seats - b a + b = 370 and 12 a + 8 b = 3320 solving equations simultaneously ( multiply equation 1 with 8 and subtract from second equation ) 4 a = 3320 - 8 * 370 = 3320 - 2960 = 360 i . e . a = 90 and b = 370 - 90 = 280 more seats in balcony than orchestra = b - a = 280 - 90 = 190 answer : option b" + }, + { + "Answer": 40.975, + "Options": "a ) 42 - 45 , b ) 41 - 43 , c ) 39 - 41 , d ) 37 - 39 , e ) 36 - 37", + "Correct": "b", + "Explanation": "\"10 % ( 37.25 ) = 3.725 15 % ( 37.25 ) = 5.5875 total amount could have been 37.25 + 3.725 and 37.25 + 5.5875 = > could have been between 40.975 and 42.8375 = > approximately between 41 and 43 answer is b .\"" + }, + { + "Answer": 0.3333333333333333, + "Options": "a ) 3 / 8 , b ) 3 / 4 , c ) 1 / 3 , d ) 4 / 5 , e ) 1 / 2", + "Correct": "c", + "Explanation": "start by deciding on a number of students to represent the number of students in the senior class . for this example i will choose 200 students . that would make the number of students in the junior class 100 . then we can find out how many students are taking japanese in each grade and add them together . ( 1 / 8 ) * 200 = 25 and ( 3 / 4 ) * 100 = 75 . 25 + 75 = 100 . there are a total of 300 students in the junior class and senior class combined ( 100 + 200 = 300 ) , and there are 100 total students in japanese , so 100 students in japanese / 300 total students equals 1 / 3 of the students in both classes that study japanese . answer : c" + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 9 , c ) 12 , d ) 18 , e ) 24", + "Correct": "a", + "Explanation": "given that c = 5 a = 2 b . . and a = c - 12 = 5 a - 12 - - > 4 a = 12 - - > a = 3 substituting the values a = 3 , c = 15 and b = 6 . . ans a = 6 . ." + }, + { + "Answer": 0.6222222222222222, + "Options": "a ) 7 / 12 , b ) 11 / 20 , c ) 17 / 30 , d ) 28 / 45 , e ) 51 / 90", + "Correct": "d", + "Explanation": "\"# defective pens = 2 # good pens = 8 probability of the 1 st pen being good = 8 / 10 probability of the 2 nd pen being good = 7 / 9 total probability = 8 / 10 * 7 / 9 = 28 / 45 the answer is d .\"" + }, + { + "Answer": 225, + "Options": "a ) 250 , b ) 275 , c ) 260 , d ) 225 , e ) 230", + "Correct": "d", + "Explanation": "4 th term + 12 th term = 30 i . e . , ( a + 3 d ) + ( a + 11 d ) = 30 now , sum of first 15 terms = ( 15 / 2 ) * [ 2 a + ( 15 - 1 ) d ] = ( 15 / 2 ) * [ 2 a + 14 d ] = ( 15 / 2 ) * 30 - - - - - - - - - - - - - - - from ( 1 ) = 225 answer : d" + }, + { + "Answer": 25, + "Options": "a ) 0 , b ) 4 , c ) 9 , d ) 25 , e ) 16", + "Correct": "d", + "Explanation": "\"from ( x + 5 ) ( y - 5 ) = 0 it follows that either x = - 5 or y = 5 . thus either x ^ 2 = 25 or y ^ 2 = 25 . now , if x ^ 2 = 8125 , then the least value of y ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 25 + 0 = 25 . similarly if y ^ 2 = 25 , then the least value of x ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 0 + 25 = 25 . answer : d .\"" + }, + { + "Answer": 2912, + "Options": "a ) 2924 , b ) 2916 , c ) 2614 , d ) 2912 , e ) 2215", + "Correct": "d", + "Explanation": "\"= ( 19 + 43 / 151 ) \u00d7 151 = ( 2869 + 43 ) / 151 \u00d7 151 = 2912 / 151 \u00d7 151 = 2912 answer is d .\"" + }, + { + "Answer": 300, + "Options": "a ) a ) 300 , b ) b ) 290 , c ) c ) 280 , d ) d ) 270 , e ) e ) 66", + "Correct": "a", + "Explanation": "\"a + b + c = 250 a + c = 200 b + c = 350 - - - - - - - - - - - - - - a + b + 2 c = 550 a + b + c = 250 - - - - - - - - - - - - - - - - c = 300 answer : a\"" + }, + { + "Answer": 118, + "Options": "a ) 22 , b ) 38 , c ) 62 , d ) 122 , e ) 118", + "Correct": "e", + "Explanation": "\"factorise 1947 . . 3 * 11 * 59 . . so n has to be a multiple of largest prime number , 61 . . so n = 2 * 59 = 118 . . ans : e\"" + }, + { + "Answer": 1061, + "Options": "a ) 1021 , b ) 1041 , c ) 1061 , d ) 1081 , e ) 1101", + "Correct": "c", + "Explanation": "\"x = 40 + 41 + . . . + 60 = 21 ( 50 ) = 1050 y = 11 x + y = 1061 the answer is c .\"" + }, + { + "Answer": 37, + "Options": "a ) 17 kg , b ) 20 kg , c ) 26 kg , d ) 31 kg , e ) 37 kg", + "Correct": "e", + "Explanation": "\"let d sum of a , b , c is 3 * 45 = 135 and sum of a and b s 2 * 40 = 80 sum of b and c is 2 * 46 = 92 hence 80 + 92 - 144 = 37 ans = 37 answer : e\"" + }, + { + "Answer": 19, + "Options": "a ) 19 , b ) 2 , c ) 5 , d ) 6 , e ) 8", + "Correct": "a", + "Explanation": "\"( 1156 / 25 ) gives remainder 6 6 + 19 = 25 , so we need to add 19 answer : a\"" + }, + { + "Answer": 17, + "Options": "a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18", + "Correct": "d", + "Explanation": "x + ( x + 4 ) + ( x + 5 ) + ( x + 7 ) = 84 4 x + 16 = 84 4 x = 68 x = 17 the answer is d ." + }, + { + "Answer": 30, + "Options": "a ) 30 , b ) 32 , c ) 40 , d ) 36 , e ) 38", + "Correct": "a", + "Explanation": "explanation : sum of all the numbers = 25 * 8 = 200 sum of first two numbers = 40 sum of next three numbers ( i . e . , 3 rd , 4 th and 5 th ) = 78 so , sum of first five numbers = 118 and sum of 6 th , 7 th and 8 th number = 82 assuming sixth number to be x , we get 7 th number = x + 4 and 8 th number = x + 6 . so , x + ( x + 4 ) + ( x + 6 ) = 82 = > x = 24 . hence , last number ( 8 th number ) = 30 . answer : a" + }, + { + "Answer": 9, + "Options": "a ) 5 , b ) 9 , c ) 4 , d ) 10 , e ) 3", + "Correct": "b", + "Explanation": "\"2 ab = ( a ( power 2 ) + b ( power 2 ) - ( a - b ) ( power 2 ) = 27 - 9 = 18 ab = 9 . answer is b .\"" + }, + { + "Answer": 35, + "Options": "a ) 30 % , b ) 37 % , c ) 65 % , d ) 35 % , e ) 45 %", + "Correct": "d", + "Explanation": "explanation : solution : let original salary = rs . 100 . new final salary = 130 % of ( 50 % of rs . 100 ) = rs . ( 130 / 100 * 50 / 100 * 100 ) = rs . 65 . . ' . decrease = 35 % answer : d" + }, + { + "Answer": 28, + "Options": "a ) 24 , b ) 25 , c ) 28 , d ) 30 , e ) 32", + "Correct": "c", + "Explanation": "let a = 2 k , b = 3 k , and c = 4 k . a + b + c = 2 k + 3 k + 4 k = 9 k since the average is 42 : 9 k / 3 = 42 3 k = 42 k = 14 then a = 28 . the answer is c ." + }, + { + "Answer": 166, + "Options": "a ) a ) 166 , b ) b ) 148 , c ) c ) 150 , d ) d ) 153 , e ) e ) 158", + "Correct": "a", + "Explanation": "\"d = d * q + r d = 18 * 9 + 4 d = 166 answer : a\"" + }, + { + "Answer": 0.02775, + "Options": "a ) 0.004 , b ) 0.02775 , c ) 2.775 , d ) 3.6036 , e ) 36.036", + "Correct": "b", + "Explanation": "approximate . 1 / . 03 = 100 / 3 = 33 1 / . 37 = 100 / 37 = 3 denominator becomes 33 + 3 = 36 1 / 36 = . 02 something answer ( b )" + }, + { + "Answer": 342.00000000007276, + "Options": "a ) 345 , b ) 342 , c ) 343 , d ) 342 , e ) 341", + "Correct": "b", + "Explanation": "\"956734 / 412 = 2322 and reminder = 70 . 412 - 70 = 342 so , the next number divisible by 412 is 342 places in front of 956734 which means 342 + 956734 = 957076 342 should be added to 956734 b\"" + }, + { + "Answer": 8, + "Options": "a ) 9 , b ) 8 , c ) 0 , d ) 2 , e ) 1", + "Correct": "b", + "Explanation": "\"explanation : given , number is divisible by 8 only if ' a 24 ' is divisible by 8 . . : highest value of a is ' 8 ' . answer : option b\"" + }, + { + "Answer": 40, + "Options": "a ) 0 , b ) 12 , c ) 13 , d ) 40 , e ) 25", + "Correct": "d", + "Explanation": "\"12 * 70 = 840 840 % 21 = 40 answer : d\"" + }, + { + "Answer": 15, + "Options": "a ) 12 , b ) 15 , c ) 17 , d ) 19 , e ) 21", + "Correct": "b", + "Explanation": "\"the worst case scenario will be if we remove all 13 tablets of medicine b first . the next 2 tablets we remove have to be of medicine a , so to guarantee that at least two tablets of each kind will be taken we should remove minimum of 13 + 2 = 15 tablets . answer : b .\"" + }, + { + "Answer": 1620, + "Options": "a ) 1245 , b ) 1430 , c ) 1540 , d ) 1600 , e ) 1635", + "Correct": "e", + "Explanation": "\"let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 15 5 x = 1350 x = 270 large number = 270 + 1365 = 1635 e\"" + }, + { + "Answer": 56, + "Options": "a ) 56 , b ) 59 , c ) 63 , d ) 71 , e ) 92", + "Correct": "a", + "Explanation": "\"total = 70 thrower = 28 rest = 70 - 28 = 42 left handed = 42 / 3 = 14 right handed = 28 if all thrower are right handed then total right handed is 28 + 28 = 56 so a . 56 is the right answer\"" + }, + { + "Answer": 33.333333333333336, + "Options": "a ) 13.3 , b ) 38.3 , c ) 35.3 , d ) 31.3 , e ) 33.3", + "Correct": "e", + "Explanation": "\"explanation : total of the 8 digits - 8 * 20 = 160 total of the 5 digits - 5 * 12 = 60 total of the remaining 3 digits - 160 - 60 = 100 average of the remaining 3 numbers = 100 / 3 = 33.3 answer : e\"" + }, + { + "Answer": 450, + "Options": "a ) 278 , b ) 277 , c ) 278 , d ) 450 , e ) 272", + "Correct": "d", + "Explanation": "\"10 * 150 = 1500 3 * 100 + 5 * 150 = 1050 1500 \u2013 1050 = 450 answer : d\"" + }, + { + "Answer": 35, + "Options": "a ) 25 % , b ) 35 % , c ) 45 % , d ) 70 % , e ) 80 %", + "Correct": "b", + "Explanation": "\"1 . we are given the following percentages : 30 ( 70 ) , 40 ( 60 ) , 25 ( 75 ) . there are two threads from here . first starts at 30 % and finishes there . second one starts at 70 , then 40 , and then 25 . we need a value that is divisible by 7 , 2 , and 5 at least once . lets pick a number now , say 700 . so say if non hawks are 700 ( this is 70 % of the total , so total = 1000 ) , then paddy warbs are 2 / 5 x 700 = 1400 / 5 = 280 . kingfishers , therefore , are 280 / 4 = 70 . lets add them up . 300 hawks + 280 peddy warbs + 70 kingsifhers = 650 . so all others are 1000 - 650 = 350 or 35 % of total birds . the main job here to to identify the smart number to start the question with . this can be time consuming , but once identified , this question can be solved fairly quickly . 2 . another method : if x is total - - > non hawks = 0.7 x - - > warbs = 0.4 ( 0.7 x ) - - > kfs = 0.25 ( 0.4 ( 0.7 x ) ) . our job is to find out x : ( 0.3 x + 0.28 x + 0.07 x ) / x . or 0.65 x / x = 0.65 . we need to find 1 - 0.65 = 0.35 or 35 % . b\"" + }, + { + "Answer": 50000, + "Options": "a ) $ 40,000 , b ) $ 50,000 , c ) $ 64,000 , d ) $ 66,667 , e ) $ 80,000", + "Correct": "b", + "Explanation": "equation is correct , so math must be a problem . 0.15 * 40,000 + 0.2 * ( x - 40,000 ) = 8,000 - - > 6,000 + 0.2 x - 8,000 = 8,000 - - > 0.2 x = 10,000 - - > x = 50,000 . answer : b ." + }, + { + "Answer": 673, + "Options": "a ) 515 . , b ) 545 . , c ) 618 . , d ) 674 . , e ) 666 .", + "Correct": "d", + "Explanation": "\"answer is d : 674 solution : total number of students studying both are 423 + 250 - 134 = 539 ( subtracting the 134 since they were included in the both the other numbers already ) . so 80 % of total is 539 , so 100 % is approx . 674 .\"" + }, + { + "Answer": 3900, + "Options": "a ) rs . 3800 , b ) rs . 3900 , c ) rs . 4000 , d ) rs . 4200 , e ) rs . 4400", + "Correct": "b", + "Explanation": "\"let the cost of a chair and that of a table be rs . x and rs . y respectively . then , 10 x = 4 y or y = 5 x . 2 15 x + 2 y = 4000 15 x + 2 x 5 x = 4000 2 20 x = 4000 x = 200 . so , y = 5 x 200 = 500 . 2 hence , the cost of 12 chairs and 3 tables = 12 x + 3 y = rs . ( 2400 + 1500 ) = rs . 3900 . b\"" + }, + { + "Answer": 95, + "Options": "a ) 94 % , b ) 92 % , c ) 95 % , d ) 93 % , e ) 97 %", + "Correct": "c", + "Explanation": "let the number be x the right number is 2 x the wrong number is x / 10 error is ( 2 x - x / 10 ) = 19 x / 10 percentage of error is ( ( 19 x / 10 ) / 2 x ) * 100 = 95 % answer : c" + }, + { + "Answer": 9, + "Options": "a ) 30 , b ) 18 , c ) 10 , d ) 9 , e ) 7", + "Correct": "d", + "Explanation": "\"( average production for n days ) * n = ( total production for n days ) - - > 50 n = ( total production for n days ) ; ( total production for n days ) + 90 = ( average production for n + 1 days ) * ( n + 1 ) - - > 50 n + 90 = 54 * ( n + 1 ) - - > n = 9 . or as 40 extra units increased the average for n + 1 days by 4 units per day then 40 / ( n + 1 ) = 4 - - > n = 9 . answer d .\"" + }, + { + "Answer": 1992, + "Options": "a ) 1998 , b ) 2001 , c ) 2002 , d ) 2003 , e ) none of these", + "Correct": "c", + "Explanation": "we go on counting the odd days from 1991 onward still the sum is divisible by 7 . the number of such days are 14 upto the year 2001 . so , the calender for 1991 will be repeated in the year 2002 . answer c" + }, + { + "Answer": 27, + "Options": "a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 29", + "Correct": "d", + "Explanation": "\"x / 2 y = 3 / 2 = > x = 6 y / 2 = 3 y = > ( 7 x + 6 y ) / ( x - 2 y ) = ( ( 7 * ( 3 y ) ) + 6 y ) / ( 3 y - 2 y ) = > 27 y / y = 27 answer : d\"" + }, + { + "Answer": 8, + "Options": "a ) 9 , b ) 7 , c ) 3 , d ) 8 , e ) 12", + "Correct": "d", + "Explanation": "explanatory answer any quadratic equation will have real and distinct roots if the discriminant d > 0 the discriminant ' d ' of a quadratic equation ax 2 + bx + c = 0 is given by b 2 - 4 ac in this question , the value of d = 62 - 4 * 1 * k if d > 0 , then 36 > 4 k or k < 9 . therefore , the highest integral value that k can take is 8 . correct choice is ( d )" + }, + { + "Answer": 720, + "Options": "a ) $ 320 , b ) $ 420 , c ) $ 720 , d ) $ 220 , e ) $ 200", + "Correct": "c", + "Explanation": "\"a = 1 / 3 ( b + c ) = > c = 3 a - b - - - ( 1 ) b = 2 / 7 ( a + c ) = > c = 3.5 b - a - - ( b ) a - b = $ 20 a = 20 + b ( 1 ) = = = > c = 60 + 3 b - b = 2 b + 60 = = > 2 b - c = - 60 - - - ( 3 ) ( 2 ) = = = > c = 3.5 b - b - 20 = 2.5 b - 20 = = > 2.5 b - c = 20 - - - ( 4 ) from ( 4 ) and ( 3 ) 0.5 b = 80 b = $ 160 a = $ 180 c = 540 - 160 = $ 380 total amount = 180 + 160 + 380 = $ 720 answer : c\"" + }, + { + "Answer": 79, + "Options": "a ) 76 , b ) 79 , c ) 85 , d ) 87 , e ) 89", + "Correct": "b", + "Explanation": "\"explanation : average = total runs / no . of innings = 35 so , total = average x no . of innings = 35 x 10 = 350 . now increase in avg = 4 runs . so , new avg = 35 + 4 = 39 runs total runs = new avg x new no . of innings = 39 x 11 = 429 runs made in the 11 th inning = 429 - 350 = 79 answer : b\"" + }, + { + "Answer": 16, + "Options": "a ) a ) 12 , b ) b ) 14 , c ) c ) 16 , d ) d ) 18 , e ) e ) 22", + "Correct": "c", + "Explanation": "\"d = ( d - r ) / q = ( 161 - 1 ) / 10 = 160 / 10 = 16 c )\"" + }, + { + "Answer": 13.700000000000017, + "Options": "a ) 9 , b ) 9.2 , c ) 10 , d ) 13.7 , e ) 12", + "Correct": "d", + "Explanation": "explanation : 1 to 11 = 11 * 10.7 = 117.7 1 to 6 = 6 * 10.5 = 63 6 to 11 = 6 * 11.4 = 68.4 63 + 68.4 = 131.4 \u2013 117.7 = 13.7 6 th number = 13.7 d )" + }, + { + "Answer": 2999.9999999999995, + "Options": "a ) 3000 , b ) 4000 , c ) 5000 , d ) 6900 , e ) 6677", + "Correct": "a", + "Explanation": "say the profit was $ x . tom share = x / 6 ( half of the third ) + ( x - x / 3 ) * 0.7 jerry share = x / 6 ( half of the third ) + ( x - x / 3 ) * 0.3 thus ( x - x / 3 ) * 0.7 - ( x - x / 3 ) * 0.3 = 800 - - > x = 3000 . answer is a" + }, + { + "Answer": 0.3504, + "Options": "a ) 0.3504 , b ) 0.4209 , c ) 0.4889 , d ) 0.6412 , e ) 0.4612", + "Correct": "a", + "Explanation": "given exp . = 0.72 * 0.43 + ( 0.12 * 0.34 ) = 0.3096 + 0.0408 = 0.3504 answer is a" + }, + { + "Answer": 8164.378472940381, + "Options": "a ) 8164 , b ) 8877 , c ) 2877 , d ) 2678 , e ) 1011", + "Correct": "a", + "Explanation": "\"8880 - - - - 381 100 - - - - ? = > 4.29 % x * 104.29 / 100 * 104.29 / 100 = 8880 x * 1.0876 = 8880 x = 8880 / 1.0876 = > 8164.38 answer : a\"" + }, + { + "Answer": 22, + "Options": "a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25", + "Correct": "b", + "Explanation": "n ( aubuc ) = 6 + 15 + 6 - 2 - 2 - 2 + 1 = 22 answer : b" + }, + { + "Answer": 69, + "Options": "a ) 67 , b ) 68 , c ) 69 , d ) 70 , e ) 71", + "Correct": "c", + "Explanation": "x - 18 = 3 [ 86 - x ] x = 69 answer : c" + }, + { + "Answer": 31, + "Options": "a ) 12 % , b ) 26 % , c ) 29 % , d ) 31 % , e ) 60 %", + "Correct": "d", + "Explanation": "\"in the first plot 25 % of 300 seeds germinated , so 0.25 x 300 = 75 seeds germinated . in the second plot , 40 % of 200 seeds germinated , so 0.4 x 200 = 80 seeds germinated . since 75 + 80 = 155 seeds germinated out of a total of 300 + 200 = 500 seeds , the percent of seeds that germinated is ( 155 / 500 ) x 100 % , or 31 % . answer : d .\"" + }, + { + "Answer": 50.00000000000002, + "Options": "a ) 25 % , b ) 30 % , c ) 50 % , d ) 75 % , e ) 80 %", + "Correct": "c", + "Explanation": "given voters in ratio 2 : 1 let x has 200 votersy has 100 voters for x 66 % voted means 74 * 200 = 148 votes combined for xy has 300 voters and voted 66 % so total votes = 198 balance votes = 198 - 148 = 50 as y has 100 voters so 50 votes means 50 % of votes required ans c" + }, + { + "Answer": 4250, + "Options": "a ) rs . 4250 , b ) rs . 4228 , c ) rs . 4128 , d ) rs . 4988 , e ) rs . 4192", + "Correct": "a", + "Explanation": "amithab ' s total expenditure for jan - june = 4200 x 6 = 25200 expenditure for feb - june = 25200 - 1200 = 24000 expenditure for the months of feb - july = 24000 + 1500 = 25500 the average expenditure = { 25500 } / { 6 } = 4250 answer : a" + }, + { + "Answer": 60, + "Options": "a ) 60 years , b ) 33 , c ) 77 , d ) 66 , e ) 101", + "Correct": "a", + "Explanation": "explanation : let neha ' s present age be ' x ' years . her age 12 years ago = ( x \u2013 12 ) years therefore , her mother ' s age 12 years ago = 4 ( x \u2013 12 ) her mother ' s present age = 4 x \u2013 48 + 12 = 4 x \u2013 36 neha ' s age after 12 years = x + 12 her mother ' s age after 12 years = 4 x \u2013 36 + 12 = 4 x \u2013 24 4 x \u2013 24 = 2 ( x + 12 ) 4 x \u2013 2 x = 24 + 24 x = 24 therefore , neha ' s present age = 24 her mother ' s present age = 4 x \u2013 36 = 4 ( 24 ) \u2013 36 = 60 years answer : a" + }, + { + "Answer": 64.00000000000001, + "Options": "a ) 22 , b ) 64 , c ) 365 , d ) 29 , e ) 36", + "Correct": "b", + "Explanation": "\"let the number be x . then , ideally he should have multiplied by x by 5 / 3 . hence correct result was . by mistake he multiplied x by 3 / 5 . hence the result with error = then , error = error % = = 64 % answer : b\"" + }, + { + "Answer": 497, + "Options": "a ) 288 , b ) 497 , c ) 168 , d ) 127 , e ) 664", + "Correct": "b", + "Explanation": "explanation : 6 * 84 = 504 - 7 = 497 answer : b" + }, + { + "Answer": 600, + "Options": "a ) 600 , b ) 620 , c ) 650 , d ) 700 , e ) 720", + "Correct": "a", + "Explanation": "\"0.6 * 500 = 0.5 * x x = 6 / 5 * 500 = 600\"" + }, + { + "Answer": 0.8, + "Options": "a ) 5 / 2 , b ) 3 / 2 , c ) 4 / 5 , d ) 2 / 5 , e ) 0", + "Correct": "c", + "Explanation": "\"we are given x = 1 \u2013 3 t and y = 2 t \u2013 3 , and we need to determine the value for t when x = y . we should notice that both x and y are already in terms of t . thus , we can substitute 1 \u2013 3 t for x and 2 t \u2013 3 for y in the equation x = y . this gives us : 1 \u2013 3 t = 2 t \u2013 3 4 = 5 t 4 / 5 = t the answer is c .\"" + }, + { + "Answer": 30, + "Options": "a ) 18 , b ) 92 , c ) 27 , d ) 26 , e ) 30", + "Correct": "e", + "Explanation": "\"explanation : let the present age of person be x years . then , 3 ( x + 5 ) - 3 ( x - 5 ) = x < = > ( 3 x + 15 ) - ( 3 x - 15 ) = x < = > x = 30 . . answer : e\"" + }, + { + "Answer": 40.66, + "Options": "a ) 40 , b ) 36.5 , c ) 46.5 , d ) 20.5 , e ) 40.6", + "Correct": "e", + "Explanation": "\"explanation : correct sum = ( 40 * 50 + 45 - 15 ) = 2030 correct mean = = 2030 / 50 = 40.6 answer : e\"" + }, + { + "Answer": 41, + "Options": "a ) 5 , b ) 10 , c ) 20 , d ) 41 , e ) 45", + "Correct": "d", + "Explanation": "\"solution - lets say , single hamburgersxand double hamburgersy given that , x + y = 50 and 1 x + 1.5 y = 70.50 . by solving the equations y = 41 . ans d .\"" + }, + { + "Answer": 11, + "Options": "a ) $ 9 , b ) $ 3 , c ) $ 4 , d ) $ 6 , e ) $ 11", + "Correct": "e", + "Explanation": "my lunch = l , my friends lunch = l + 3 ( l ) + ( l + 3 ) = 19 l + l + 3 - 3 = 19 - 3 2 l = 16 l = 8 my friends lunch l + 3 = 8 + 3 = $ 11 , the answer is e" + }, + { + "Answer": 25, + "Options": "a ) 22 , b ) 30 , c ) 25 , d ) 38 , e ) 27", + "Correct": "c", + "Explanation": "\"total age increased = ( 3 * 2 ) years = 6 years . sum of ages of two new men = ( 21 + 23 + 6 ) years = 50 years average age of two new men = ( 50 / 2 ) years = 25 years . answer : c\"" + }, + { + "Answer": 4500, + "Options": "a ) 2500 , b ) 4500 , c ) 3500 , d ) 4000 , e ) 1300", + "Correct": "b", + "Explanation": "\"to solve we will set up a proportion . we know that \u201c 100 million vehicles is to 75 accidents as 6 billion vehicles is to x accidents \u201d . to express everything in terms of \u201c millions \u201d , we can use 6,000 million rather than 6 billion . creating a proportion we have : 100 / 75 = 6,000 / x cross multiplying gives us : 100 x = 6,000 * 75 x = 60 * 75 = 4500 answer : b\"" + }, + { + "Answer": 3, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "a", + "Explanation": "\"1 < x < 9 , 2 < x < 15 , - 1 < x < 7 0 < x < 4 x + 1 < 5 from above : 2 < x < 4 - - > x = 3 . answer : a .\"" + }, + { + "Answer": 100, + "Options": "a ) 50 , b ) 90 , c ) 100 , d ) 120 , e ) 140", + "Correct": "c", + "Explanation": "\"let the number of candidate who passed = y then , 39 y + 15 ( 120 - y ) = 120 x 35 \u21d2 24 y = 4200 - 1800 \u2234 y = 2400 / 24 = 100 c\"" + }, + { + "Answer": 44, + "Options": "a ) 0.33 , b ) 0.44 , c ) 0.55 , d ) 44 , e ) 55", + "Correct": "d", + "Explanation": "\"main thing to remember is answer is asked in cents , however when we calculate , it comes up as 0.44 $ just multiply by 100 , answer f = 44 . d\"" + }, + { + "Answer": 49.99999999999996, + "Options": "a ) 30 % , b ) 35 % , c ) 40 % , d ) 45 % , e ) 50 %", + "Correct": "e", + "Explanation": "\"let the original income = rs . 100 . then , expenditure = rs . 75 and savings = rs . 25 new income = rs . 120 , new expenditure = rs . ( ( 110 / 100 ) * 75 ) = rs . 165 / 2 new savings = rs . ( 120 - ( 165 / 2 ) ) = rs . 75 / 2 increase in savings = rs . ( ( 75 / 2 ) - 25 ) = rs . 25 / 2 increase % = ( ( 25 / 2 ) * ( 1 / 25 ) * 100 ) % = 50 % . answer e 50 %\"" + }, + { + "Answer": 12, + "Options": "a ) 12 kg , b ) 10 kg , c ) 20 kg , d ) 72 kg , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : let the weight of student be x kg . given , difference in average weight = 12 kg = > ( 72 - x ) / 5 = 12 = > x = 12 answer : a\"" + }, + { + "Answer": 3024, + "Options": "a ) 3002 , b ) 3013 , c ) 3024 , d ) 3036 , e ) none of these", + "Correct": "b", + "Explanation": "solution here ( 18 - 7 ) = 11 , ( 21 - 10 ) = 11 and ( 24 - 13 ) = 11 . l . c . m . of 1821 and 24 is 504 . let required number be 504 k - 11 . least value of k for which ( 504 k - 11 ) is divisible 23 is k = 6 . so , required number = 504 \u00d7 6 - 11 = 3024 - 11 = 3013 . answer b" + }, + { + "Answer": 0.16666666666666666, + "Options": "a ) 1 / 12 , b ) 1 / 6 , c ) 1 / 4 , d ) 1 / 3 , e ) 1 / 2", + "Correct": "b", + "Explanation": "roots of the equation ( x - 5 ) ( x + 10 ) ( 2 x - 5 ) = 0 are x = 5 , x = - 10 and x = 5 / 2 = 2.5 . so , two solutions present in our set of 12 distinct numbers , therefore p = 2 / 12 = 1 / 6 . answer : b ." + }, + { + "Answer": 1.2, + "Options": "a ) 1.2 kg , b ) 1.5 kg , c ) 1.7 kg , d ) 1.9 kg , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : flower - nectar contains 50 % of non - water part . in honey this non - water part constitutes 60 % ( 100 - 40 ) . therefore 0.5 x amount of flower - nectar = 0.60 x amount of honey = 0.60 x 1 kg therefore amount of flower - nectar needed = ( 0.60 / 0.51 ) kg = 1.2 kgs answer : a\"" + }, + { + "Answer": 0.4, + "Options": "a ) 2 / 3 , b ) 2 / 5 , c ) 3 / 4 , d ) 3 / 7 , e ) 5 / 8", + "Correct": "b", + "Explanation": "the line y = - x + 4 intersects the rectangle and these three points of intersection ( 0,0 ) , ( 0,4 ) and ( 4,0 ) form a triangle . the points below the line y = - x + 4 satisfy x + y < 4 . the area of this triangle is ( 1 / 2 ) ( 4 ) ( 4 ) = 8 the area of the rectangle is 20 . p ( x + y < 4 ) = 8 / 20 = 2 / 5 the answer is b ." + }, + { + "Answer": 0.5, + "Options": "a ) 1 / 2 , b ) 1 / 3 , c ) 2 / 3 , d ) 1 / 4 , e ) 1 / 5", + "Correct": "a", + "Explanation": "q - > a / b = 20 * 21 * \u2026 \u2026 * 39 / 21 * 22 * \u2026 . * 39 * 40 = 20 / 40 = 1 / 2 . therefore , the answer is a ." + }, + { + "Answer": 9, + "Options": "a ) 6 , b ) 12 , c ) 15 , d ) 9 , e ) 7", + "Correct": "d", + "Explanation": "number be = 2 x , 3 x , 4 x , ( 2 x ) 2 + ( 4 x ) 2 = 180 20 x = 180 \u21d2 x = 9 \u21d2 x = 3 , midline number = 3 \u00d7 3 = 9 answer : d" + }, + { + "Answer": 82, + "Options": "a ) 67 , b ) 74 , c ) 82 , d ) 98 , e ) 34", + "Correct": "c", + "Explanation": "1941 ^ 3846 unit digit = 1 ^ 4 = 1 10 th digit = 4 * 6 = 24 = 2 means last two digit = 41 and 1972 ^ 4181 unit digit = 1 10 th digit = 7 * 2 = 14 mean last two digit = 41 hence , 41 + 41 = 82" + }, + { + "Answer": 1248, + "Options": "a ) 1248 , b ) 1723 , c ) 1129 , d ) 2613 , e ) 1372", + "Correct": "a", + "Explanation": "\"a b has 62.5 % or ( 5 / 8 ) of the milk in a . therefore , let the quantity of milk in container a ( initially ) be 8 k . quantity of milk in b = 8 k - 5 k = 3 k . quantity of milk in container c = 8 k - 3 k = 5 k container : a b c quantity of milk : 8 k 3 k 5 k it is given that if 156 liters was transferred from container c to container b , then both the containers would have equal quantities of milk . 5 k - 156 = 3 k + 156 = > 2 k = 312 = > k = 156 the initial quantity of milk in a = 8 k = 8 * 156 = 1248 liters .\"" + }, + { + "Answer": 57, + "Options": "a ) 54 , b ) 55 , c ) 57 , d ) 71 , e ) 92", + "Correct": "c", + "Explanation": "\"total = 67 thrower = 37 rest = 67 - 37 = 30 left handed = 30 / 3 = 10 right handed = 20 if all thrower are right handed then total right handed is 30 + 20 = 57 so c . 57 is the right answer\"" + }, + { + "Answer": 4791, + "Options": "a ) 4857 , b ) 4184 , c ) 4012 , d ) 4791 , e ) 5291", + "Correct": "d", + "Explanation": "let the sale in the sixth month = x then ( 6635 + 6927 + 6855 + 7230 + 6562 + x ) / 6 = 6500 = > 6635 + 6927 + 6855 + 7230 + 6562 + x = 6 \u00d7 6500 = > 34209 + x = 39000 = > x = 39000 \u2212 34209 = 4791 answer : d" + }, + { + "Answer": 3, + "Options": "a ) 2 , b ) 6 , c ) 5 , d ) 4 , e ) 3", + "Correct": "e", + "Explanation": "\"e 3\"" + }, + { + "Answer": 87.5, + "Options": "a ) 12.5 % , b ) 87.5 % , c ) 80 % , d ) 11 % , e ) 1 %", + "Correct": "b", + "Explanation": "\"say y = 1 and x = 8 . then y = 1 is less than x = 8 by ( 8 - 1 ) / 8 * 100 = 7 / 8 * 100 = 87.5 % . answer : b .\"" + }, + { + "Answer": 4250, + "Options": "a ) rs . 4250 , b ) rs . 4288 , c ) rs . 4227 , d ) rs . 4218 , e ) rs . 4219", + "Correct": "a", + "Explanation": "\"explanation : amithab ' s total expenditure for jan - june = 4200 x 6 = 25200 expenditure for feb - june = 25200 - 1200 = 24000 expenditure for the months of feb - july = 24000 + 1500 = 25500 the average expenditure = { 25500 } { 6 } = 4250 answer : a\"" + }, + { + "Answer": 2, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "c", + "Explanation": "in my view the answer should be c f / 5 has remainder = 3 - > f = 5 x q + 3 y / 5 has a remainder = 4 - > y = 5 x q + 3 combining both ( ( 5 x q 1 + 3 ) + ( 5 x q 2 + 3 ) ) / 5 = 5 ( q 1 + q 2 ) / 5 + 7 / 5 = q 1 + q 2 + 7 / 5 7 / 5 = 1 + 2 / 5 = > remainder 2 answer c" + }, + { + "Answer": 21, + "Options": "a ) 21 , b ) 20 , c ) 22 , d ) 25 , e ) 40", + "Correct": "a", + "Explanation": "\"let the total number of workers be x . then , 8000 x = ( 12000 * 7 ) + 6000 ( x - 7 ) = 2000 x = 42000 = x = 21 . answer a\"" + }, + { + "Answer": 33, + "Options": "a ) 33 , b ) 34 , c ) 35 , d ) 36 , e ) 37", + "Correct": "a", + "Explanation": "sol . let the son \u2019 s present age be x years . then , father \u2019 s present age = ( 3 x + 3 ) years . therefore ( 3 x + 3 + 3 ) = 2 ( x + 3 ) + 10 \u2039 = \u203a 3 x + 6 = 2 x + 16 \u2039 = \u203a x = 10 hence , father \u2019 s present age = ( 3 x + 3 ) = ( 3 x 10 + 3 ) years = 33 years . answer a" + }, + { + "Answer": 13, + "Options": "a ) a ) 11 , b ) b ) 12 , c ) c ) 13 , d ) d ) 14 , e ) e ) 15", + "Correct": "c", + "Explanation": "\"explanation : given that a + b = 13 + b + c = > a \u2013 c = 13 + b \u2013 b = 13 = > c is younger than a by 13 years answer : option c\"" + }, + { + "Answer": 44.99999999999999, + "Options": "a ) 40 , b ) 45 , c ) 49 , d ) 51 , e ) 43", + "Correct": "b", + "Explanation": "\"a : b : c = 10 \u00d7 7 : 12 \u00d7 5 : 15 \u00d7 3 = 2 \u00d7 7 : 12 \u00d7 1 : 3 \u00d7 3 = 14 : 12 : 9 amount that c should pay = 175 \u00d7 ( 9 / 35 ) = 5 \u00d7 9 = 45 answer is b .\"" + }, + { + "Answer": 24000, + "Options": "a ) 26799 , b ) 24000 , c ) 26682 , d ) 29973 , e ) 12312", + "Correct": "b", + "Explanation": "\"x * ( 96 / 100 ) = 23040 x = 240 * 100 x = 24000 answer : b\"" + }, + { + "Answer": 3300, + "Options": "a ) 3600 , b ) 3890 , c ) 3300 , d ) 2789 , e ) 2891", + "Correct": "c", + "Explanation": "\"explanation : manager ' s monthly salary rs . ( 1300 * 21 - 1200 * 20 ) = rs . 3300 . answer : c\"" + }, + { + "Answer": 29, + "Options": "a ) 31 , b ) 32 , c ) 35 , d ) 30 , e ) 29", + "Correct": "e", + "Explanation": "explanation : hcf ( 408 , 288 ) = 24 the number of boys or girls that can be placed in a section = 24 . thus the total number of sections is given by 408 / 24 + 288 / 24 = 17 + 12 = 29 answer : e" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9", + "Correct": "b", + "Explanation": "\"p \u00e3 \u00b7 44 = 432 = > p = 432 * 44 = 19008 p / 35 = 19008 / 35 = 543 , remainder = 3 b\"" + }, + { + "Answer": 74.66666666666667, + "Options": "a ) 71.11 , b ) 71.12 , c ) 71.1 , d ) 74.66 , e ) 71.13", + "Correct": "d", + "Explanation": "\"car travels first 160 km at 70 km / hr time taken to travel first 160 km = distancespeed = 160 / 70 car travels next 160 km at 80 km / hr time taken to travel next 160 km = distancespeed = 160 / 80 total distance traveled = 160 + 160 = 2 \u00d7 160 total time taken = 160 / 70 + 160 / 80 average speed = total distance traveled / total time taken = 320 / ( 160 / 70 + 160 / 80 ) = 74.66 km / hr answer : d\"" + }, + { + "Answer": 75, + "Options": "a ) 20 , b ) 25 , c ) 55 , d ) 75 , e ) 80", + "Correct": "d", + "Explanation": "\"the arithmetic mean of 4 equally weighted tests was 90 . so what we can assume is that we have 4 test scores , each 90 . he dropped his lowest score and the avg went to 95 . this means that the lowest score was not 90 and other three scores had given the lowest score 5 each to make it up to 90 too . when the lowest score was removed , the other 3 scores got their 5 back . so the lowest score was 3 * 5 = 15 less than 90 . so the lowest score = 90 - 15 = 75 answer ( d )\"" + }, + { + "Answer": 55, + "Options": "a ) 55 , b ) 45 , c ) 65 , d ) 78 , e ) 64", + "Correct": "a", + "Explanation": "\"( x + x 1 + . . . x 14 ) / 15 = 40 55 option a\"" + }, + { + "Answer": 68, + "Options": "a ) 68 , b ) 72 , c ) 78 , d ) 88 , e ) 312", + "Correct": "a", + "Explanation": "average score for first 4 rounds = 78 average score after 5 rounds = 76 score scott needs on his 5 th round to drop average score by 2 points = 78 - ( 2 * 5 ) = 68 answer a alternatively , sum of scores of first 4 rounds = 78 * 4 = 312 sum of scores after 5 rounds = 76 * 5 = 380 score scott needs on his 5 th round to drop average score by 2 points = 380 - 312 = 68 answer a" + }, + { + "Answer": 100, + "Options": "a ) 70 , b ) 90 , c ) 120 , d ) 100 , e ) 140", + "Correct": "d", + "Explanation": "\"a + b + c = 600 a + c = 250 b + c = 450 - - - - - - - - - - - - - - a + b + 2 c = 700 a + b + c = 600 - - - - - - - - - - - - - - - - c = 100 answer : d\"" + }, + { + "Answer": 1, + "Options": "a ) 0.5 , b ) 1 , c ) 1.5 , d ) 2 , e ) 3", + "Correct": "b", + "Explanation": "\"let x be the number of desks and bookcases that are placed along the library wall . 2 x + 1.5 x < 15 3.5 x < 15 since x is a non negative integer , the largest number x can be is 4 . when x is 4 , the desks and bookcases take up 3.5 * 4 = 14 m = k , leaving 1 m of empty space . thus , i believe the answer is b ) 1\"" + }, + { + "Answer": 20, + "Options": "a ) a ) 6.7 , b ) b ) 1.3 , c ) c ) 9.6 , d ) d ) 20 , e ) e ) 7.9", + "Correct": "d", + "Explanation": "\"amount salt in 100 kg solution = 10 * 100 / 100 = 10 kg let x kg of pure salt be added then ( 10 + x ) / ( 100 + x ) = 25 / 100 40 + 4 x = 100 + x 3 x = 60 x = 20 answer is d\"" + }, + { + "Answer": 43, + "Options": "a ) 43.0 , b ) 45.5 , c ) 46.0 , d ) 49.0 , e ) 50.0", + "Correct": "a", + "Explanation": "in arun ' s company 60 % of the employees earn less than $ 50,000 a year , 50 and 51 employee will be each 43 k . hence median = ( 43 k + 43 k ) / 2" + }, + { + "Answer": 7, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "e", + "Explanation": "the number of members is 7 k + 5 = 6 j + 5 the only number in this range which satisfies this is 47 . 47 / 8 = 5 ( 8 ) + 7 the answer is e ." + }, + { + "Answer": 40, + "Options": "a ) 50.0 % , b ) 40.0 % , c ) 30.0 % , d ) 20.0 % , e ) 10.0 %", + "Correct": "b", + "Explanation": "opening : lemons / oranges = 50 / 60 = 100 / 120 closing : lemons / oranges = 20 / 40 = 60 / 120 aside : it ' s useful to write both ratios with the same denominator . this allows us to ignore the denominator and focus solely on the numerators . so , our ratio went from 100 / 120 to 60 / 120 ignoring the denominators , we went from 100 to 60 the percent change = 100 ( difference in values ) / ( original value ) = ( 100 ) ( 100 - 60 ) / 100 = ( 100 ) ( 40 ) / 100 ) = 40 answer : b" + }, + { + "Answer": 0.8686868686868687, + "Options": "a ) 4 / 99 , b ) 2 / 25 , c ) 8 / 99 , d ) 49 / 100 , e ) 86 / 99", + "Correct": "e", + "Explanation": "\"interesting question ! also one that we should be able to answer very quickly be keeping an eye on our best friends , the answer choices . we know that x belongs to the set { 1 , 2 , 3 , . . . , 99 } . we want to know the probability z that x ( x + 1 ) is a multiple of either 4 or 5 . when will this happen ? if either x or ( x + 1 ) is a multiple of 4 or 5 . since 4 * 5 is 20 , let ' s look at the first 20 numbers to get a rough idea of how often this happens . out of the numbers from 1 to 20 : 4 , 5 , 6 , 8 , 9 , 10 , 11 , 12 , 13 , 15 , 16 , 17 , 20 so , 14 out of the first 20 numbers match our criteria . since : probability = ( # of desired outcomes ) / ( total # of possibilities ) , we guesstimate the answer to be 14 / 20 . since ( e ) is the only answer greater than 1 / 2 , we go with ( e ) .\"" + }, + { + "Answer": 108, + "Options": "a ) 123 , b ) 106 , c ) 108 , d ) 156 , e ) 240", + "Correct": "c", + "Explanation": "\"explanation : cash realised = rs . ( 108.25 - 0.25 ) = rs . 108 . answer : c\"" + }, + { + "Answer": 28.57142857142857, + "Options": "a ) 24.4 % , b ) 28.6 % , c ) 32.3 % , d ) 36.5 % , e ) 40.9 %", + "Correct": "b", + "Explanation": "\"y = 1.4 x x = y / 1.4 = 10 y / 14 = 5 y / 7 x is 2 / 7 less which is 28.6 % less than y . the answer is b .\"" + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 6 , c ) 4 , d ) 7 , e ) 8", + "Correct": "a", + "Explanation": "sa ' s + co + ca + cats = 16 . sa ' s + 1 + 1 + cats = 16 or sa ' s + cats = 14 . sa ' s ( 2 ) + 2 + 1 + cats * 4 = 41 sa ' s * 2 + cats * 4 = 38 or sa ' s + cats * 2 = 19 or 14 - cats + cat * 2 = 19 then cats = 5 a" + }, + { + "Answer": 0.02857142857142857, + "Options": "a ) 1 / 35 , b ) 2 / 3 , c ) 7 / 35 , d ) 5 / 7 , e ) 7 / 5", + "Correct": "a", + "Explanation": "\"let a be the event that ram is selected and b is the event that ravi is selected . p ( a ) = 1 / 7 p ( b ) = 1 / 5 let c be the event that both are selected . p ( c ) = p ( a ) x p ( b ) as a and b are independent events : = 1 / 7 x 1 / 5 = 1 / 35 answer : a\"" + }, + { + "Answer": 14, + "Options": "a ) 11 , b ) 14 , c ) 18 , d ) 23 , e ) none of these", + "Correct": "b", + "Explanation": "\"let that divisor be x since remainder is 6 or 13 it means divisor is greater than 13 . now 242 - 6 = 236 = kx ( k is an integer and 234 is divisble by x ) similarly 698 - 13 = 685 = lx ( l is an integer and 689 is divisible by x ) adding both 698 and 242 = ( 236 + 685 ) + 6 + 13 = x ( k + l ) + 19 when we divide this number by x then remainder will be equal to remainder of ( 19 divided by x ) = 5 hence x = 19 - 5 = 14 hence b\"" + }, + { + "Answer": 21, + "Options": "a ) 10 hours , b ) 12 hours , c ) 14 hours , d ) 21 hours , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : speed of the boat = 6 km / hr speed downstream = ( 6 + 2 ) = 8 km / hr speed upstream = ( 6 - 2 ) = 4 km / hr distance travelled downstream = distance travelled upstream = 56 km total time taken = time taken downstream + time taken upstream = ( 56 / 8 ) + ( 56 / 4 ) = 21 hr . answer : option d\"" + }, + { + "Answer": 2.999999999999993, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "c", + "Explanation": "\"( 1055 / 23 ) gives a remainder 20 so we need to add 3 . the answer is c .\"" + }, + { + "Answer": 75, + "Options": "a ) 45 , b ) 60 , c ) 75 , d ) 90 , e ) 95", + "Correct": "c", + "Explanation": "let number of notes of each denomination be x . then x + 5 x + 10 x = 400 16 x = 400 x = 25 . hence , total number of notes = 3 x = 75 answer : option c" + }, + { + "Answer": 750.0000000000001, + "Options": "a ) 392 , b ) 229 , c ) 753 , d ) 750 , e ) 540", + "Correct": "d", + "Explanation": "\"d 750 ? = 5000 * ( 2 / 5 ) * ( 1 / 2 ) * ( 3 / 4 ) = 750\"" + }, + { + "Answer": 50, + "Options": "a ) 0 , b ) 25 , c ) 50 , d ) 75 , e ) 100", + "Correct": "c", + "Explanation": "\"75 percent are not first - year associates - - > this means 75 percent associates are either two or more than two years already , we know % of second - year associates = 25 % so , % of associates there for more than two years = 75 % - 25 % = 50 % . . = > ( c ) . . is it correct ?\"" + }, + { + "Answer": 12, + "Options": "a ) 9 , b ) 11 , c ) 13 , d ) 12 , e ) 17", + "Correct": "d", + "Explanation": "\"( 2 to the power x ) - ( 2 to the power ( x - 2 ) ) = 3 ( 2 to the power 10 ) 2 ^ x - 2 ^ ( x - 2 ) = 3 . 2 ^ 10 hence x = 12 . answer is d\"" + }, + { + "Answer": 4, + "Options": "a ) 7 , b ) 6 , c ) 3 , d ) 5 , e ) 4", + "Correct": "e", + "Explanation": "\"answer dividing numerator as well as denominator by b , we get given exp . = ( 4 a + 3 b ) / ( 4 a - 3 b ) = ( 4 a / b + 3 ) / ( 4 a / b - 3 ) since a / b = 5 / 4 this implies that = [ ( 4 * 5 ) / 4 + 3 ] / [ ( 4 * 5 ) / 4 - 3 ) ] = ( 5 + 3 ) / ( 5 - 3 ) = 4 option : e\"" + }, + { + "Answer": 64, + "Options": "a ) 60 , b ) 61 , c ) 62 , d ) 63 , e ) 64", + "Correct": "e", + "Explanation": "\"64 players answer : e\"" + }, + { + "Answer": 2013, + "Options": "a ) 2013 , b ) 2088 , c ) 270 , d ) 1881 , e ) 1781", + "Correct": "a", + "Explanation": "\"f ( f ( 0 ) ) + f ( 0 ) = 2 ( 0 ) + 3 \u21d2 \u21d2 f ( 1 ) = 3 - 1 = 2 , f ( 1 ) = 2 f ( f ( 1 ) ) + f ( 1 ) = 2 ( 1 ) + 3 \u21d2 \u21d2 f ( 2 ) = 5 - 2 = 3 , f ( 2 ) = 3 f ( f ( 2 ) ) + f ( 2 ) = 2 ( 2 ) + 3 \u21d2 \u21d2 f ( 3 ) = 7 - 3 = 4 , f ( 3 ) = 4 . . . . . . . . . . . . . . f ( 2012 ) = 2013 ans : a\"" + }, + { + "Answer": 0.9992159937279498, + "Options": "a ) a ) 3 , b ) b ) 2 , c ) c ) 6 , d ) d ) 9 , e ) e ) 1 / 5", + "Correct": "e", + "Explanation": "\"102 x = 25 ( 10 x ) 2 = 52 10 x = 5 1 / 10 x = 1 / 5 10 - x = 1 / 5 answer : e\"" + }, + { + "Answer": 25, + "Options": "a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29", + "Correct": "a", + "Explanation": "\"the bacteria doubles each day , so after 29 days , the dish was half full . after 28 days , the dish was one quarter full . after 27 days , the dish was one eighth full . after 26 days , the dish was one sixteenth full . after 25 days , the dish was 1 / 32 full . the answer is a .\"" + }, + { + "Answer": 20, + "Options": "a ) s . 17 , b ) s . 18 , c ) s . 12 , d ) s . 11 , e ) s . 20", + "Correct": "e", + "Explanation": "\"average price per book = ( 1500 + 340 ) / ( 32 + 60 ) = 1840 / 92 = rs . 20 answer : e\"" + }, + { + "Answer": 20, + "Options": "a ) $ 38 , b ) $ 18 , c ) $ 99 , d ) $ 27 , e ) $ 20", + "Correct": "e", + "Explanation": "\"average price per book = ( 1480 + 920 ) / ( 65 + 55 ) = 2400 / 120 = $ 20 the answer is e .\"" + }, + { + "Answer": 1708249, + "Options": "a ) 1601249 , b ) 1607249 , c ) 1701249 , d ) 1708249 , e ) none", + "Correct": "d", + "Explanation": "\"answer 1307 x 1307 = ( 1307 ) 2 = ( 1300 + 7 ) 2 = ( 1300 ) 2 + ( 7 ) 2 + 2 x 1300 x 7 = 1690000 + 49 + 18200 = 1708249 option : d\"" + }, + { + "Answer": 0.06349206349206349, + "Options": "a ) 1 / 35 , b ) 3 / 35 , c ) 5 / 37 , d ) 4 / 63 , e ) none", + "Correct": "d", + "Explanation": "\"answer we have , m x n = 6 x 210 = 1260 \u00e2 \u02c6 \u00b4 1 / m + 1 / n = ( m + n ) / mn = 80 / 1260 = 4 / 63 correct option : d\"" + }, + { + "Answer": 1, + "Options": "a ) 64 / 27 , b ) 9 / 16 , c ) 1 , d ) 6 / 8 , e ) 8 / 6", + "Correct": "c", + "Explanation": "\"a nice fast approach is the first find a pair of numbers that satisfy the given equation : 3 a = 4 b here ' s one pair : a = 4 and b = 3 what is the ratio of a / 9 to b / 8 ? in other words , what is the value of ( a / 4 ) / ( b / 3 ) ? plug in values to get : ( a / 4 ) / ( b / 3 ) = ( 4 / 4 ) / ( 3 / 3 ) = 1 / 1 = 1 c\"" + }, + { + "Answer": 36629, + "Options": "a ) x = 53186760 , b ) x = 26593379 , c ) x = 73260 , d ) x = 36629 , e ) x = 6666", + "Correct": "d", + "Explanation": "33 = 3 * 11 44 = 2 * 2 * 11 55 = 5 * 11 666 = 2 * 3 * 3 * 37 so 2 x + 2 = 2 * 2 * 3 * 3 * 5 * 11 * 37 = 73260 , and x = ( 73260 - 2 ) / 2 = 36629 , which is option d ." + }, + { + "Answer": 45, + "Options": "a ) 10 , b ) 20 , c ) 45 , d ) 60 , e ) 120", + "Correct": "c", + "Explanation": "\"each person is one participant of 6 games . so there are in all 6 * 15 = 90 instances of one participant games . but each game has 2 participants so total number of games = 90 / 2 = 45 c\"" + }, + { + "Answer": 0.578125, + "Options": "a ) 37 / 64 , b ) 8 / 27 , c ) 2 / 3 , d ) 19 / 27 , e ) 65 / 81", + "Correct": "a", + "Explanation": "at the end of each day we will have 3 / 4 alive . so after 3 days we will have ( 3 / 4 ) ^ 3 people alive . therefore , fraction of dead people will be 1 - ( 3 / 4 ) ^ 3 = 37 / 64 . the correct answer is a ." + }, + { + "Answer": 17.999999999999986, + "Options": "a ) 11 , b ) 13 , c ) 14 , d ) 18 , e ) 10", + "Correct": "d", + "Explanation": "\"required difference = [ 3 \u00bd % of rs . 10800 ] \u2013 [ 3 1 / 3 % of rs . 10800 ] = [ ( 7 / 20 - ( 10 / 3 ) ] % of rs . 10800 = 1 / 6 % of rs . 10800 = rs . [ ( 1 / 6 ) 8 ( 1 / 100 ) * 10800 ] = rs . 18 . answer is d .\"" + }, + { + "Answer": 125, + "Options": "a ) 120 , b ) 123 , c ) 124 , d ) 125 , e ) 359", + "Correct": "d", + "Explanation": "\"explanation : let the number = x , then , x - ( 3 / 5 ) x = 50 , = > ( 2 / 5 ) x = 50 = > 2 x = 50 * 5 , = > x = 125 option d\"" + }, + { + "Answer": 6, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) none of the above", + "Correct": "d", + "Explanation": "\"( x + 3 ) \u00d7 60 + x \u00d7 120 + ( x \u2212 3 ) \u00d7 180 / ( x + 3 ) + x + ( x \u2212 3 ) = 100 \u21d2 360 x \u2212 360 / 3 x = 100 \u21d2 60 x = 360 \u21d2 x = 6 answer d\"" + }, + { + "Answer": 9, + "Options": "a ) 30 , b ) 4 , c ) 9 , d ) 8 , e ) none", + "Correct": "c", + "Explanation": "sol . there are four prime numbers between 4 and 15 . they are 5 , 7 , 11 , 13 \u00e2 \u02c6 \u00b4 required average = [ 5 + 7 + 11 + 13 / 4 ] = 36 / 4 = 9 answer c" + }, + { + "Answer": 7945.70154338681, + "Options": "a ) 7945 , b ) 8877 , c ) 2877 , d ) 2678 , e ) 1011", + "Correct": "a", + "Explanation": "\"8800 - - - - 461 100 - - - - ? = > 5.238 % x * 105.238 / 100 * 105.238 / 100 = 8800 x * 1.1075 = 8800 x = 8800 / 1.1075 = > 7945.70 answer : a\"" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 5 , c ) 3 , d ) 6 , e ) 7", + "Correct": "c", + "Explanation": "c ) 3" + }, + { + "Answer": 32, + "Options": "a ) 32 , b ) 40 , c ) 64 , d ) 80 , e ) 96", + "Correct": "a", + "Explanation": "\"7 / 8 x - 3 / 4 x = 4 galls 1 / 8 * x = 4 gallons x = 32 gallons answer a\"" + }, + { + "Answer": 47.673469387755105, + "Options": "a ) 27 , b ) 48 , c ) 45 , d ) 72 , e ) 18", + "Correct": "b", + "Explanation": "\"ages of p and mi = 3 x + 5 x ages of mi and mo = 3 x : 5 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 25 x sum = 47 x = 146 x = 3 difference if ages of pa and mo = 25 x - 9 x = 16 x = 16 * 3 = 48 answer b\"" + }, + { + "Answer": 2.125, + "Options": "a ) $ 1.75 , b ) $ 1.85 , c ) $ 2.00 , d ) $ 2.12 , e ) $ 2.30", + "Correct": "d", + "Explanation": "\"this question can be solved with a handful of different algebra approaches ( as has been shown in the various posts ) . since the question asks for the price of the largest pot , and the answers are prices , we can test the answers . we ' re told that there are 6 pots and that each pot costs 30 cents more than the next . the total price of the pots is $ 8.25 . we ' re asked for the price of the largest ( most expensive ) pot . since the total price is $ 8.25 ( a 30 - cent increment ) and the the difference in sequential prices of the pots is 30 cents , the largest pot probably has a price that is a 30 - cent increment . from the answer choices , i would then test answer d if . . . . the largest pot = $ 2.125 the other 5 pots are . . . . 0.625 0.925 1.225 1.525 1.825 2.125 total = $ 8.25 so this must be the answer . d\"" + }, + { + "Answer": 26, + "Options": "a ) 22 , b ) 99 , c ) 26 , d ) 66 , e ) 887", + "Correct": "c", + "Explanation": "\"total time taken = x / 65 + 2 x / 20 hours = 3 x / 26 hours average speed = 3 x / ( 3 x / 26 ) = 26 kmph answer : c\"" + }, + { + "Answer": 0.2, + "Options": "a ) 0 , b ) 1 / 12 , c ) 1 , d ) 1 / 5 , e ) 1 / 3", + "Correct": "d", + "Explanation": "since ( x \u2013 y ) + ( y \u2013 z ) + ( z \u2013 x ) = 0 , so ( x \u2013 y ) \u00b3 + ( y \u2013 z ) \u00b3 + ( z \u2013 x ) \u00b3 = 3 ( x \u2013 y ) ( y \u2013 z ) ( z \u2013 x ) . ( 3 ( x \u2013 y ) ( y \u2013 z ) ( z \u2013 x ) ) / ( 15 ( x \u2013 y ) ( y \u2013 z ) ( z \u2013 x ) ) = 1 / 5 . answer : d" + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10", + "Correct": "a", + "Explanation": "the number of trailing zeros in the decimal representation of n ! , the factorial of a non - negative integer n , can be determined with this formula : n 5 + n 52 + n 53 + . . . + n 5 k , where k must be chosen such that 5 k \u2264 n x = 1 * 2 * 3 . . . . * 50 = 50 ! no . of trailing zeros in 50 ! = 50 / 5 + 50 / 5 ^ 2 = 10 + 2 = 12 100 ^ k = 10 ^ 2 k \u2192 k = 12 / 2 = 6 a" + }, + { + "Answer": 3149.999999999999, + "Options": "a ) 360 , b ) 3150 , c ) 540 , d ) 640 , e ) 720", + "Correct": "b", + "Explanation": "\"too many words and redundant info there . ( i ) 1 / 3 of the pieces of art are displayed , hence 2 / 3 of the pieces of art are not displayed . ( ii ) 1 / 6 of the pieces on display are sculptures , hence 5 / 6 of the pieces on display are paintings . ( iii ) 1 / 3 of the pieces not on display are paintings , hence 2 / 3 of the pieces not on display are sculptures . 1400 sculptures are not on display , so according to ( iii ) 2 / 3 * { not on display } = 1400 - - > { not on display } = 2100 . according to ( i ) 2 / 3 * { total } = 2100 - - > { total } = 3150 . answer : b .\"" + }, + { + "Answer": 64, + "Options": "a ) 55 , b ) 56 , c ) 64 , d ) 65 , e ) 66", + "Correct": "c", + "Explanation": "\"let n = total students in class total points for 1 / 3 class = 60 n / 3 = 20 n total points for 2 / 3 class = 66 * 2 n / 3 = 44 n total points for whole class = 20 n + 44 n = 64 n 64 n total class points / n total students = 64 grade point average for total class answer : c\"" + }, + { + "Answer": 33, + "Options": "a ) 0.33 , b ) 33 , c ) 0.033 , d ) 0.0033 , e ) 3.3 e - 05", + "Correct": "b", + "Explanation": "99 * 0.33 = 32.67 approx . 33 answer : b" + }, + { + "Answer": 7, + "Options": "a ) a ) 7 , b ) b ) 9 , c ) c ) 11 , d ) d ) 13 , e ) e ) 15", + "Correct": "a", + "Explanation": "explanation : x + y = 10 2 x \u2013 3 y = 5 x = 7 y = 3 a )" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 20 , c ) 30 , d ) 40 , e ) 50", + "Correct": "a", + "Explanation": "it ' s simple can be solved by elimination of answer choices . option b and c are too large , not possible . even de are large to have correct choice . ans : a" + }, + { + "Answer": 438.53333333333336, + "Options": "a ) a ) 125 , b ) b ) 439 , c ) c ) 225 , d ) d ) 375 , e ) e ) 524", + "Correct": "b", + "Explanation": "\"explanation : ? = ( 208 x 1265 / 100 ) \u00f7 6 = 263120 / 600 = 439 answer : option b\"" + }, + { + "Answer": 22, + "Options": "a ) 25 , b ) 22 , c ) 30 , d ) 35 , e ) 42", + "Correct": "b", + "Explanation": "\"average in 5 matches = ( 2 * 40 + 3 * 10 ) / 2 + 3 = 80 + 30 / 5 = 110 / 5 = 22 answer is b\"" + }, + { + "Answer": 69.00000000008731, + "Options": "a ) 69 , b ) 62 , c ) 61 , d ) 63 , e ) 64", + "Correct": "a", + "Explanation": "8679921 / 330 = 26302 and reminder = 261 . 330 - 261 = 69 so , the next number divisible by 339 is 69 places in front of 8679921 which means 69 + 8679921 = 8679990 69 should be added to 8679921 a" + }, + { + "Answer": 4.8, + "Options": "a ) 4 % , b ) 8 % , c ) 4.2 % , d ) 4.8 % , e ) 5 %", + "Correct": "d", + "Explanation": "\"let ' s say there is a total of 100 students at this college . 60 percent of the total number of students are freshmen . # of freshmen = 60 % of 100 = 60 40 percent of the fresh - men are enrolled in the school of liberal arts . . . number of liberal arts freshmen = 40 % of 60 = 24 . . . and , of these , 20 percent are psychology majors . . . number of liberal arts freshmen who are psychology majors = 20 % of 24 = 4.8 what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts ? 4.8 / 100 = 4.8 % answer : d\"" + }, + { + "Answer": 6, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8", + "Correct": "c", + "Explanation": "\"64 ^ k > 4 ^ 16 4 ^ ( 3 k ) > 4 ^ 16 3 k > 16 k = 6 the answer is c .\"" + }, + { + "Answer": 122, + "Options": "a ) 116 , b ) 119 , c ) 122 , d ) 125 , e ) 128", + "Correct": "c", + "Explanation": "\"k - 32 = 9 t / 5 k = 9 t / 5 + 32 k = 9 ( 50 ) / 5 + 32 = 122 the answer is c .\"" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 7", + "Correct": "c", + "Explanation": "q = p 1 + p 2 + p 3 + p 4 + p 5 + p 6 + p 7 = even ( and all primes are distinct ) if the least prime is 2 then we have sum of q = even . ans . c . 3" + }, + { + "Answer": 18, + "Options": "a ) 22 , b ) 20 , c ) 19 , d ) 18 , e ) 17", + "Correct": "d", + "Explanation": "whenever you are asked to find the number of digits , try to bring the number in multiples of 10 . this way , we can wasily calculate the umber of 0 ' s through the powers of 10 50 ^ 8 \u00d7 8 ^ 3 \u00d7 11 ^ 2 x 10 ^ 4 = ( 5 ^ 2 * 2 ) ^ 8 * 2 ^ 9 * 11 ^ 2 * 10 ^ 4 = 5 ^ 16 * 2 ^ 17 * 11 ^ 2 * 10 ^ 4 = 2 * 11 ^ 2 * 10 ^ 16 * 10 ^ 4 = 242 * 10 ^ 16 x 10 ^ 4 hence we would have 16 trailing 0 ' s and the three digits from 242 total digits = 3 + 20 = 23 correct option : d" + }, + { + "Answer": 3, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "b", + "Explanation": "\"if x , y , and z are consecutive numbers and x > y > z , then y = z + 1 and x = z + 2 . 2 x + 3 y + 3 z = 5 y + 11 2 z + 4 + 3 z + 3 + 3 z = 5 z + 5 + 11 3 z = 9 z = 3 the answer is b .\"" + }, + { + "Answer": 0.032420000000000004, + "Options": "a ) 0.045388 , b ) 4.5388 , c ) 0.03242 , d ) 473.88 , e ) none of these", + "Correct": "c", + "Explanation": "\"answer multiplying 3.242 x 10 = 3.242 now divide 3.242 by 100 so , 3.242 \u00f7 100 = 0.03242 \u2234 shift the decimal two places to the left as 100 correct option : c\"" + }, + { + "Answer": 8, + "Options": "a ) 5 , b ) 6 , c ) 8 , d ) 7 , e ) 9", + "Correct": "c", + "Explanation": "explanation : let the number be x . then , x + 8 = 128 x ( 1 / x ) = > x < sup > 2 < / sup > + 8 x - 128 = 0 = > ( x + 16 ) ( x - 8 ) = 0 = > x = 8 answer : option c" + }, + { + "Answer": 7, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", + "Correct": "a", + "Explanation": "\"a simple and elegant solution . as addition of 39 , shifts mean by 2 , and addition of 15 , shifts mean by 1 to the other side , we have the mean lying between 3915 , and in a ratio of 2 : 1 39 - 15 = 24 24 divide by 3 is 8 . meaning mean of the n terms is 15 + 8 = 39 - 16 = 23 now , from first statement , when a person aged 39 is added to a group of n people , the average age increases by 2 . r * 23 + 39 = 25 * ( r + 1 ) r = 7 ans . ( a )\"" + }, + { + "Answer": 27, + "Options": "a ) 10 , b ) 18 , c ) 13 , d ) 21 , e ) 27", + "Correct": "e", + "Explanation": "working backward , 108 divided by 4 is 27 . this number fits the rules of three and nine , where the digits add up to a sum divisible by nine . answer is e ." + }, + { + "Answer": 33, + "Options": "a ) 480 , b ) 239 , c ) 270 , d ) 282 , e ) 112", + "Correct": "a", + "Explanation": "answer : a" + }, + { + "Answer": 13, + "Options": "a ) 13 , b ) 25 , c ) 26 , d ) 27 , e ) 29", + "Correct": "a", + "Explanation": "\"x / 2 y = 3 / 2 = > x = 10 y / 2 = 5 y = > ( 7 x + 4 y ) / ( x - 2 y ) = ( ( 7 * ( 5 y ) ) + 4 y ) / ( 5 y - 2 y ) = > 39 y / 3 y = 13 answer : a\"" + }, + { + "Answer": 2485, + "Options": "a ) 1200 , b ) 1340 , c ) 1234 , d ) 1203 , e ) 2485", + "Correct": "e", + "Explanation": "( 11 ^ 2 + 12 ^ 2 + 13 ^ 2 + . . . + 20 ^ 2 ) = ( 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + . . . + 20 ^ 2 ) - ( 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + . . . + 10 ^ 2 ) 6 = 20 x 21 x 41 - 10 x 11 x 21 6 6 = ( 2870 - 385 ) = 2485 e" + }, + { + "Answer": 60, + "Options": "a ) 20 liters , b ) 30 liters , c ) 50 liters , d ) 60 liters , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : quantity of milk = 60 * ( 2 / 3 ) = 40 liters quantity of water = 60 - 40 = 20 liters as per question we need to add water to get quantity 2 : 1 = > 40 / ( 20 + x ) = 1 / 2 = > 20 + x = 80 = > x = 60 liters option d\"" + }, + { + "Answer": 18.08695652173913, + "Options": "a ) rs . 18.28 , b ) rs . 20 , c ) rs . 18.08 , d ) rs . 28.08 , e ) rs . 38.08", + "Correct": "c", + "Explanation": "average price per book = ( 1160 + 920 ) / ( 65 + 50 ) = 2080 / 115 = rs . 18.08 answer : c" + }, + { + "Answer": 246.94736842105266, + "Options": "a ) a ) 426 , b ) b ) 526 , c ) c ) 247 , d ) d ) 204 , e ) e ) 297", + "Correct": "c", + "Explanation": "given ratio = 1 / 2 : 2 / 3 : 3 / 4 = 6 : 4 : 9 1 st part = 782 * 6 / 19 = rs . 247 answer : c" + }, + { + "Answer": 20, + "Options": "a ) 5 , b ) 8 , c ) 15 , d ) 18 , e ) 20", + "Correct": "e", + "Explanation": "the average number of books per student was 2 means that total of 2 * 30 = 60 books were borrowed ; 5 + 12 + 8 = 25 students borrowed total of 5 * 0 + 12 * 1 + 8 * 2 = 28 books ; so 60 - 28 = 32 books are left to distribute among 30 - 25 = 5 students , these 5 arethe rest who borrowed at least 3 books ; tomaximizethe number of books one student from above 5 could have borrowed we shouldminimizethe number of books other 4 students from 5 could have borrowed . minimum these 4 students could have borrowed is 3 books per student , so total number of books they could have borrowed is 4 * 3 = 12 books . so the 5 th student could have borrowed is 32 - 12 = 20 books . answer : e ." + }, + { + "Answer": 700, + "Options": "a ) 200 , b ) 350 , c ) 700 , d ) 900 , e ) 1,400", + "Correct": "c", + "Explanation": "\"5 / 100 ( 400 ) = 2 / 10 ( x ) x = 700 . . answer : c\"" + }, + { + "Answer": 90, + "Options": "a ) 90 , b ) 98 , c ) 35 , d ) 99 , e ) 80", + "Correct": "a", + "Explanation": "\"though 2 * ( 10 c 2 ) is the correct approcah to do this , but for people like me who find perm , comb n prob a nightmare , an easy approach can be used . the first guy has to play 2 matches with the rest of 9 , so he ' ll play 18 matches . similarly , second guy has to play with the rest of 8 as his 2 games with the first guy are already played . so he plays 16 matches . this continues like this and the total matches are 18 + 16 + 14 . . . + 2 18 + 16 + . . . + 2 = 2 ( 9 + 8 + . . . + 1 ) = 2 ( ( 9 * 10 ) / 2 ) = 9 * 10 = 90 . answer : a\"" + }, + { + "Answer": 40.00000000000001, + "Options": "a ) 15 % , b ) 20 % , c ) 22.5 % , d ) 25 % , e ) 40 %", + "Correct": "e", + "Explanation": "\"4 miles on the highway = 4 / 36 gallons ; 4 miles in the city = 4 / 20 gallons ; total = 4 / 36 + 4 / 20 = 14 / 45 gallons . 8 miles on the highway = 8 / 30 gallons . the % change = ( 14 / 45 - 8 / 36 ) / ( 8 / 36 ) = 0.40 . answer : e .\"" + }, + { + "Answer": 8, + "Options": "a ) $ 5 , b ) $ 8 , c ) $ 11 , d ) $ 14 , e ) $ 17", + "Correct": "b", + "Explanation": "\"let q ' s hourly wage be x , then p ' s hourly wage is 1.5 x let t be the number of hours that q needs , then p needs t - 10 hours to do the job . since they both are paid an equal total amount of $ 480 : x * t = 1.5 x * ( t - 10 ) t = 30 hours and q ' s hourly wage is 480 / 30 = $ 16 p ' s hourly wage is 480 / ( t - 10 ) = $ 24 which is $ 8 per hour more . the answer is b .\"" + }, + { + "Answer": 4, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "b", + "Explanation": "3 < x < 6 < y < 8 ; 3 < x y < 8 3 + y < x + 8 y - x < 5 . positive integer difference is 4 ( for example y = 7.5 and x = 3.5 ) answer : b ." + }, + { + "Answer": 1.5, + "Options": "a ) $ 1.20 , b ) $ 1.50 , c ) $ 1.80 , d ) $ 2.00 , e ) $ 2.50", + "Correct": "b", + "Explanation": "\"let x be the value of the weekly allowance . ( 2 / 3 ) ( 2 / 5 ) x = 40 cents ( 4 / 15 ) x = 40 x = $ 1.50 the answer is b .\"" + }, + { + "Answer": 10, + "Options": "a ) 22 , b ) 67 , c ) 10 , d ) 12 , e ) 66", + "Correct": "c", + "Explanation": "\"( 75 / 100 ) * 40 \u2013 ( 4 / 5 ) * 25 = 10 answer : c\"" + }, + { + "Answer": 15, + "Options": "a ) 12 , b ) 29 , c ) 27 , d ) 15 , e ) 99", + "Correct": "d", + "Explanation": "\"explanation : let the number be x . therefore , 3 ( 2 x + 5 ) = 105 6 x + 15 = 105 6 x = 90 x = 15 answer : d\"" + }, + { + "Answer": 45, + "Options": "a ) 30 , b ) 35 , c ) 38 , d ) 40 , e ) 45", + "Correct": "e", + "Explanation": "\"10 play kabadi = > n ( a ) = 10 , 5 play both gmaes . = > n ( anb ) = 5 35 play kho kho only , = > n ( b ) = n ( b only ) + n ( anb ) = 35 + 5 = 40 total = > n ( aub ) = n ( a ) + n ( b ) - n ( anb ) = 10 + 40 - 5 = 45 answer : e\"" + }, + { + "Answer": 27, + "Options": "a ) 26 , b ) 27 , c ) 28 , d ) 29 , e ) 30", + "Correct": "b", + "Explanation": "8 / 7 * 24 = 27.4 the answer is b ." + }, + { + "Answer": 240, + "Options": "a ) 250 , b ) 260 , c ) 500 , d ) 280 , e ) 240", + "Correct": "e", + "Explanation": "tray one as t 1 and tray two as t 2 . t 2 = t 1 - 20 cups as equation a . t 1 + t 2 = 500 cups in total as equation b . substitute equation a into equation b , resulting in t 1 + ( t 1 - 20 ) = 500 transpose like terms , 2 * t 1 = 500 + 20 ( 2 * t 1 ) / 2 = 520 / 2 t 1 = 260 , thus t 2 is t 1 less 20 cups , which is 240 cups . answer is e ." + }, + { + "Answer": 251, + "Options": "a ) 250 , b ) 150 , c ) 500 , d ) 100 , e ) 200", + "Correct": "a", + "Explanation": "500 numbers between - 500 and 1000 out of which half would be even , half odd . number of even unit digit number = 250 . correct option is a" + }, + { + "Answer": 50, + "Options": "a ) 40 % , b ) 45 % , c ) 50 % , d ) 60 % , e ) 70 %", + "Correct": "c", + "Explanation": "\"1 st year income = i 1 st year savings = s 1 st year expense = e 1 2 nd year income = 1.5 i 2 nd year savings = 2 s ( 100 % increase ) 2 nd year expense = e 2 e 1 + e 2 = 2 e 1 e 2 = e 1 that means expenses are same during both years . with increase of 50 % income the savings increased by 100 % . or s = . 5 i or s = 50 % of income c is the answer\"" + }, + { + "Answer": 84.61538461538461, + "Options": "a ) 20 % , b ) 305 , c ) 50 % , d ) 55 % , e ) 84.6 %", + "Correct": "e", + "Explanation": "\"explanation : number of pages increased = 110 now , the number of pages of book = 240 number of pages of the books before increase = 240 \u2013 110 = 130 % increase in the number of pages in the book = 110 / 130 x 100 % = 84.6 % e\"" + }, + { + "Answer": 33, + "Options": "a ) 33 , b ) 32 , c ) 31 , d ) 30 , e ) 29", + "Correct": "a", + "Explanation": "yes there is a different way of arriving at that answer . . . . u can also use airthmetic progression to get the answer since the first term to be divisble by 3 is 102 . . take that as a . . the starting no and since 198 is the last digit to be divisible by 3 take that as n . . . since the difference is 3 take that as d no u have to find what term is 198 take that as nth term the formula for that is n = a + ( n - 1 ) * d 198 = 102 + ( n - 1 ) * 3 from this u get n = 33" + }, + { + "Answer": 30, + "Options": "a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60", + "Correct": "b", + "Explanation": "\"let number of pounds of 5 $ candy to be used be w 6 = ( 15 * 8 + 5 * w ) / ( 15 + w ) = > 90 + 6 w = 120 + 5 w = > w = 30 answer b\"" + }, + { + "Answer": 340, + "Options": "a ) 820 , b ) 340 , c ) 420 , d ) 209 , e ) none of these", + "Correct": "b", + "Explanation": "300 + 5 \u00d7 8 = ? or , ? = 300 + 40 = 340 answer b" + }, + { + "Answer": 24, + "Options": "a ) 18 kmph , b ) 17 kmph , c ) 24 kmph , d ) 19 kmph , e ) 12 kmph", + "Correct": "c", + "Explanation": "\"total time taken = x / 40 + 2 x / 20 hours = 5 x / 40 = x / 8 hours average speed = 3 x / ( x / 8 ) = 24 kmph answer : c\"" + }, + { + "Answer": 81, + "Options": "a ) 81 , b ) 65 , c ) 75 , d ) 89 , e ) 90", + "Correct": "a", + "Explanation": "\"a + b + c = 3 * 70 = 210 a + b + c + d = 4 * 70 = 280 - - - - ( i ) so , d = 70 & e = 70 + 3 = 73 b + c + d + e = 68 * 4 = 272 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 280 \u2013 272 = 8 a = e + 8 = 73 + 8 = 81 answer : a\"" + }, + { + "Answer": 40, + "Options": "a ) 25.5 , b ) 2.5 , c ) 40 , d ) . 25 , e ) none of these", + "Correct": "c", + "Explanation": "\"explanation : 1 / 0.025 = ( 1 * 1000 ) / 25 = 1000 / 25 = 40 option c\"" + }, + { + "Answer": 70, + "Options": "a ) 49 , b ) 55 , c ) 69 , d ) 70 , e ) 82", + "Correct": "d", + "Explanation": "\"according to order of operations , inner brackets first . hence | 4 - 8 ( 3 - 12 ) | - | 5 - 11 | = | 4 - 8 * ( - 9 ) | - | 5 - 11 | according to order of operations , multiplication within absolute value signs ( which may be considered as brackets when it comes to order of operations ) next . hence = | 4 + 72 | - | 5 - 11 | = | 76 | - | - 6 | = 76 - 6 = 70 correct answer d ) 70\"" + }, + { + "Answer": 11028, + "Options": "a ) 11028 , b ) 14172 , c ) 14284 , d ) 14015 , e ) 14397", + "Correct": "a", + "Explanation": "use following formulae for such problems : sum of evenly spaced integers = ( # of integers ) * ( mean of integers ) # of integers = [ ( last - first ) / 2 ] + 1 mean of integers = ( last + first ) / 2 in above problem : # of integers = [ ( 224 - 2 ) / 2 ] + 1 = 112 and [ ( 80 - 8 ) / 2 ] + 1 = 37 mean of integers = ( 224 + 2 ) / 2 = 113 and ( 80 + 8 ) / 2 = 44 sum of integers = ( 112 * 113 ) = 12656 and ( 37 * 44 ) = 1628 thus their difference ( i - k ) = 12656 - 1628 = 11028 answer : a" + }, + { + "Answer": 660, + "Options": "a ) 660 , b ) 738 , c ) 837 , d ) 840 , e ) 83", + "Correct": "a", + "Explanation": "\"25 % of x = x / 4 ; 12 % of 1500 = 12 / 100 * 1500 = 180 given that , x / 4 = 180 - 15 = > x / 4 = 165 = > x = 660 . answer : a\"" + }, + { + "Answer": 13, + "Options": "a ) 3 , b ) 33 , c ) 43 , d ) 23 , e ) 13", + "Correct": "e", + "Explanation": "according to order of operations , inner brackets first where 6 \u00d7 4 \u00f7 3 is first calculated since it has a multiplication and a division . 6 \u00d7 4 \u00f7 3 = 24 \u00f7 3 = 8 hence 11 + sqrt ( - 4 + 6 \u00d7 4 \u00f7 3 ) = 11 + sqrt ( - 4 + 8 ) = 11 + sqrt ( 4 ) = 11 + 2 = 13 correct answer is e ) 13" + }, + { + "Answer": 2401, + "Options": "a ) 2398 , b ) 2399 , c ) 2400 , d ) 2401 , e ) 2402", + "Correct": "d", + "Explanation": "sum of 1 st n odd no . s = 1 + 3 + 5 + 7 + . . . = n ^ 2 so , sum of 1 st 49 odd numbers = 49 ^ 2 = 2401 answer : d" + }, + { + "Answer": 16.666666666666664, + "Options": "a ) 16.66 % , b ) 33.33 % , c ) 44.44 % , d ) 55.55 % , e ) 19.92 %", + "Correct": "a", + "Explanation": "\"x * y = constt . let x = y = 100 in beginning i . e . x * y = 100 * 100 = 10000 x ( 100 ) - - - becomes - - - > 1.2 x ( 120 ) i . e . 120 * new ' y ' = 10000 i . e . new ' y ' = 10000 / 120 = 83.33 i . e . y decreases from 100 to 83.33 i . e . decrease of 16.66 % answer : option a\"" + }, + { + "Answer": 7, + "Options": "a ) a ) 7 , b ) b ) 6 , c ) c ) 9 , d ) d ) 11 , e ) e ) none of the above", + "Correct": "a", + "Explanation": "sol . total packages 490 each truck carries 70 packages = 490 / 70 = 7 answer : a" + }, + { + "Answer": 7, + "Options": "a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 7", + "Correct": "e", + "Explanation": "\"let seventh observation = x . then , according to the question we have = > ( 84 + x ) / 7 = 13 = > x = 7 . hence , the seventh observation is 7 . answer : e\"" + }, + { + "Answer": 4520, + "Options": "a ) 2520 , b ) 3520 , c ) 4520 , d ) 1520 , e ) 1750", + "Correct": "c", + "Explanation": "\"( 4500 + 20 ) / 90 * 90 = 4520 answer : c\"" + }, + { + "Answer": 360, + "Options": "a ) $ 374 , b ) $ 382 , c ) $ 385 , d ) $ 360 , e ) $ 399", + "Correct": "d", + "Explanation": "\"( 348 / 116 ) 120 = 360 in this case long division does not take much time . ( 348 / 116 ) = 3 3 * 120 = 360 ( 300 + 60 ) answer d\"" + }, + { + "Answer": 4, + "Options": "a ) 12 , b ) 17 , c ) 18 , d ) 4 , e ) 26", + "Correct": "d", + "Explanation": "\"answer : 4 option : d\"" + }, + { + "Answer": 40, + "Options": "a ) 125 , b ) 70 , c ) 40 , d ) 25 , e ) none of these", + "Correct": "c", + "Explanation": "let x be the first number and y be the second number . 1 \u2044 5 x = 5 \u2044 8 y \\ x \u2044 y = 25 \u2044 8 . . . . . . ( i ) x + 35 = 4 y or , 25 \u2044 8 y + 35 = 4 y \\ y = 40 answee c" + }, + { + "Answer": 33, + "Options": "a ) 27 , b ) 48 , c ) 45 , d ) 72 , e ) 33", + "Correct": "e", + "Explanation": "ages of p and mi = 3 x : 5 x ages of mi and mo = 3 x : 4 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 20 x sum = 44 x = 132 x = 3 difference if ages of pa and mo = 20 x - 9 x = 11 x = 11 * 3 = 33 answer e" + }, + { + "Answer": 110, + "Options": "a ) 38 , b ) 27 , c ) 99 , d ) 110 , e ) 80", + "Correct": "d", + "Explanation": "\"explanation : number of subjects = 6 average of marks in 6 subjects = 80 therefore total marks in 6 subjects = 80 * 6 = 480 now , no . of subjects = 5 total marks in 5 subjects = 74 * 5 = 370 therefore marks in 6 th subject = 480 \u2013 370 = 110 answer : d\"" + }, + { + "Answer": 253, + "Options": "a ) 145 , b ) 253 , c ) 370 , d ) 352 , e ) 300", + "Correct": "b", + "Explanation": "explanation : let the middle digit be x . then , 2 x = 10 or x = 5 . so , the number is either 253 or 352 . since the number increases on reversing the digits , so the hundred ' s digit is smaller than the unit ' s digit . hence , required number = 253 . answer is b" + }, + { + "Answer": 20, + "Options": "a ) 25 % , b ) 22.2 % , c ) 20 % , d ) 12.5 % , e ) 11.1 %", + "Correct": "c", + "Explanation": "\"let ' s see , the way i did it was 1 / 4 are clerical out of 3600 so 900 are clerical 900 reduced by 1 / 4 is 900 * 1 / 4 so it reduced 225 people , so there is 675 clerical people left but since 225 people left , it also reduced from the total of 3600 so there are 3375 people total since 675 clerical left / 3375 people total you get ( c ) 20 %\"" + }, + { + "Answer": 66, + "Options": "a ) 55 , b ) 66 , c ) 77 , d ) 88 , e ) 99", + "Correct": "b", + "Explanation": "\"12 c 2 = 66 the answer is b .\"" + }, + { + "Answer": 17, + "Options": "a ) 14 , b ) 16 , c ) 17 , d ) 20 , e ) 26", + "Correct": "c", + "Explanation": "since 11 y = even therefore y has to beevensince 11 is a odd integer ( even * odd = even ) similarly , y is the product of all integers in set x but all integers in set x are odd except the unknown a and since x contains only prime numbers , a has to equal to 2 . . . ( 2 is the only even prime number and the product of all prime numbers in set x has to be even , even * odd = even ) since you know value of a you can calculate the range = largest integer in the set minus smallest integer in the set = 19 - 2 = 17 answer is c" + }, + { + "Answer": 42.857142857142854, + "Options": "a ) 43 % , b ) 42.85 % , c ) 45.25 % , d ) 46.23 % , e ) 41.66 %", + "Correct": "b", + "Explanation": "\"say a 100 families existed in 1992 then the number of families owning a computer in 1992 - 30 number of families owning computer in 1999 = 30 * 150 / 100 = 45 number of families in 1999 = 105 the percentage = 45 / 105 * 100 = 42.85 % . answer : b\"" + }, + { + "Answer": 50, + "Options": "a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 100", + "Correct": "b", + "Explanation": "\"a + b + c = 400 a + c = 300 b + c = 150 - - - - - - - - - - - - - - a + b + 2 c = 450 a + b + c = 400 - - - - - - - - - - - - - - - - c = 50 answer : b\"" + }, + { + "Answer": 16, + "Options": "a ) 1 : 8 , b ) 1 : 4 , c ) 2 : 1 , d ) 4 : 1 , e ) 16 : 1", + "Correct": "e", + "Explanation": "\"x = 8 y , y = 2 * z x : y , y : z 8 : 1 , 2 : 1 16 : 2 , 2 : 1 so , x : z = 16 : 1 ( e )\"" + }, + { + "Answer": 1600, + "Options": "a ) 3387 , b ) 1600 , c ) 2866 , d ) 2787 , e ) 1121", + "Correct": "b", + "Explanation": "\"20 * 10 * 8 = 1600 answer : b\"" + }, + { + "Answer": 89, + "Options": "a ) 52 , b ) 49 , c ) 95 , d ) 88 , e ) 89", + "Correct": "e", + "Explanation": "\"right side = 15 seat left side = 15 - 3 ( 3 few seat in right side ) = 12 seat total = 15 + 12 = 27 people can seat in 27 seat = 27 * 3 = 81 people can seat in last seat = 8 total people can seat = 81 + 8 = 89 answer : e\"" + }, + { + "Answer": 0.06666666666666667, + "Options": "a ) 15 / 56 , b ) 3 / 28 , c ) 1 / 28 , d ) 1 / 15 , e ) 1 / 168", + "Correct": "d", + "Explanation": "since , two of the choices are prefixed , we are free to choose 1 from the rest of the 8 avilable . so 8 c 1 is the numerator . total no of ways we can choose 3 from 10 is 10 c 3 , which is the denominator . so , the probability : 8 c 1 / 10 c 3 = 1 / 15 ans is d ." + }, + { + "Answer": 83, + "Options": "a ) 80 , b ) 81 , c ) 82 , d ) 83 , e ) 84", + "Correct": "d", + "Explanation": "\"solution : mabel handled 90 transactions anthony handled 10 % more transactions than mabel anthony = 90 + 90 \u00d7 10 % = 90 + 90 \u00d7 0.10 = 90 + 9 = 99 cal handled 2 / 3 rds of the transactions than anthony handled cal = 2 / 3 \u00d7 99 = 66 jade handled 16 more transactions than cal . jade = 66 + 17 = 83 jade handled = 83 transactions . answer : d\"" + }, + { + "Answer": 90, + "Options": "a ) 50 , b ) 40 , c ) 60 , d ) 90 , e ) 70", + "Correct": "d", + "Explanation": "we have x + x % of 900 = 900 x + x / 100 * 900 = 900 10 * x = 900 x = 90 answer is d" + }, + { + "Answer": 3, + "Options": "a ) 3 , b ) 9 , c ) 11 , d ) 12 , e ) 15", + "Correct": "a", + "Explanation": "explanation : x / 2 \u2013 x / 4 = 3 = > x = 12 1 + 2 = 3 a" + }, + { + "Answer": 155, + "Options": "a ) 168 , b ) 100 , c ) 155 , d ) 160 , e ) 200", + "Correct": "c", + "Explanation": "\"solution : let x be the number he chose , then 2 * x * 200 = 110 2 x = 310 x = 155 correct answer c\"" + }, + { + "Answer": 81, + "Options": "a ) 70 , b ) 72 , c ) 75 , d ) 78 , e ) 81", + "Correct": "e", + "Explanation": "income of 6 months = ( 6 \u00d7 90 ) \u2013 debt = 540 \u2013 debt income of the man for next 4 months = 4 \u00d7 60 + debt + 30 = 270 + debt \u2234 income of 10 months = 810 average monthly income = 810 \u00f7 10 = 81 answer e" + }, + { + "Answer": 2.879628878919216, + "Options": "a ) 195 / 63 , b ) 2.879 , c ) 155 / 63 , d ) 125 / 63 , e ) 185 / 63", + "Correct": "b", + "Explanation": "\"( \u221a 1.1 ) / ( \u221a 0.81 ) + ( \u221a 1.44 ) / ( \u221a 0.49 ) = > 2.879 answer is b\"" + }, + { + "Answer": 9, + "Options": "a ) 8 , b ) 9 , c ) 14 , d ) 17 , e ) 20", + "Correct": "b", + "Explanation": "but you can not take xy + 3 to mean xy = - 3 . . only if xy + 3 = 0 , it will mean xy = - 3 . . rest your solution is perfect and you will get your correct answer as 15 - 2 * 3 = 9 . . answer b" + }, + { + "Answer": 1, + "Options": "a ) 1.0 , b ) 1.5 , c ) 2.0 , d ) 2.5 , e ) 3.0", + "Correct": "a", + "Explanation": "this is a good question to understand the difference between mean and median . mean : average of all the numbers . ( sum of all the elements divided by the number of elements ) median : arrange the elements of the set in increasing order . if the number of terms is odd , the middle term is the median . if the number of terms is even , the average of middle two terms is the median coming to this question , mean = ( 1 + 7 + 18 + 20 + 29 + 33 ) / 6 = 18 median = ( 18 + 20 ) / 2 = 19 difference = 1 option a" + }, + { + "Answer": 0.1111111111111111, + "Options": "a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 0 , d ) 1 / 9 , e ) 1 / 5", + "Correct": "d", + "Explanation": "\"given x = k / y 2 , where k is a constant . now , y = 2 and x = 1 gives k = 4 . x = 4 / y 2 = > x = 4 / 62 , when y = 6 = > x = 4 / 36 = 1 / 9 . answer : d\"" + }, + { + "Answer": 4900, + "Options": "a ) 6660 , b ) 3600 , c ) 2400 , d ) 4900 , e ) 5400", + "Correct": "d", + "Explanation": "by using the formula , t [ n ( n - 1 ) / 2 ] , where t = no . of games between two teams and n = total no . of teams , we get : 4900 option d ." + }, + { + "Answer": 4, + "Options": "a ) 3 , b ) 0 , c ) 5 , d ) 4 , e ) 2", + "Correct": "d", + "Explanation": "\"given expression = ( 8 - 2.8 ) / 1.3 = 5.2 / 1.3 = 52 / 1.3 = 4 . answer is d .\"" + }, + { + "Answer": 0.4, + "Options": "a ) 3 / 5 , b ) 2 / 5 , c ) 4 / 5 , d ) 1 / 5 , e ) 6 / 5", + "Correct": "b", + "Explanation": "first notice the number of months for which he worked - march to sept i . e . 7 months avg of monthly totals in tips for months other than august = x tips in august = 4 x total tips for all months = 6 * x + 4 x = 10 x tips for august / total tips for all months = 4 x / 10 x = 2 / 5 answer : b" + }, + { + "Answer": 25.971200000000003, + "Options": "a ) 9 % , b ) 9.27 % , c ) 25.97 % , d ) 12 % , e ) none of these", + "Correct": "c", + "Explanation": "\"actual increase in population = 8 % let , earlier population = 100 then the population after 3 years = 100 ( 1 + 8 / 100 ) ^ 3 = 125.97 \u2234 required percentage = 25.97 % answer : c\"" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9", + "Correct": "a", + "Explanation": "18,888 / 11 = 1717 with a remainder of 1 . we need to subtract the remainder to get a multiple of 11 . the answer is a ." + }, + { + "Answer": 632, + "Options": "a ) 632 , b ) 731 , c ) 533 , d ) 434 , e ) none of the above", + "Correct": "a", + "Explanation": "that numbers are x , 6 x - 4 so sum = x + 6 x - 4 = 38 7 x = 42 = = > x = 6 another no is 32 answer is 6 , 32 answer : a" + }, + { + "Answer": 9001, + "Options": "a ) 1 , b ) 9000 , c ) 9001 , d ) 90001 , e ) none", + "Correct": "c", + "Explanation": "solution required remainder = ( 10000 - 999 ) = 9001 answer c" + }, + { + "Answer": 40, + "Options": "a ) - 29 , b ) 39 , c ) - 30 , d ) 40 , e ) 60", + "Correct": "d", + "Explanation": "\"from - 39 to - 1 - - > 39 nos . zero - - > 1 number from + 1 to + 39 - - > 39 nos . when we add up nos . from - 39 to + 39 sum will be zero . total 79 nos will be added . 80 th number will be 40 . sum of these 80 nos . = 40 . d is the answer .\"" + }, + { + "Answer": 24, + "Options": "a ) 22 , b ) 24 , c ) 26 , d ) 20 , e ) 28", + "Correct": "b", + "Explanation": "\"explanation : let number of hens = h and number of cows = c number of heads = 46 = > h + c = 46 - - - ( equation 1 ) number of feet = 136 = > 2 h + 4 c = 136 = > h + 2 c = 68 - - - ( equation 2 ) ( equation 2 ) - ( equation 1 ) gives 2 c - c = 68 - 46 = > c = 22 substituting the value of c in equation 1 , we get h + 22 = 46 = > h = 46 - 22 = 24 i . e . , number of hens = 24 answer : b\"" + }, + { + "Answer": 210, + "Options": "a ) 187 , b ) 211 , c ) 207 , d ) 219 , e ) 227", + "Correct": "b", + "Explanation": "\"let ' n ' is the smallest number which divided by 13 and 17 leaves respective remainders of 3 and 7 . required number = ( lcm of 13 and 17 ) - ( common difference of divisors and remainders ) = ( 221 ) - ( 10 ) = 211 . answer : b\"" + }, + { + "Answer": 17, + "Options": "a ) 11 , b ) 12 , c ) 17 , d ) 14 , e ) 15", + "Correct": "c", + "Explanation": "\"- x 2 - ( k + 11 ) x - 8 = - ( x - 2 ) ( x - 4 ) : given - x 2 - ( k + 11 ) x - 8 = - x 2 + 6 x - 8 - ( k + 11 ) = 6 : two polynomials are equal if their corresponding coefficients are equal . k = - 17 : solve the above for k correct answer c\"" + }, + { + "Answer": 480, + "Options": "a ) 96 , b ) 240 , c ) r = 256 , d ) r = 384 , e ) r = 480", + "Correct": "e", + "Explanation": "most test takers would recognize thesystemof equations in this prompt and just do algebra to get to the solution ( and that ' s fine ) . the wording of the prompt and the ' spread ' of the answer choices actually provide an interesting ' brute force ' shortcut that you can take advantage of to eliminate the 4 wrong answers . . . . we ' re told that there are 2 types of boxes : those that hold 12 glasses and those that hold 16 glasses . since the average number of boxes is 15 , we know that there must be at least some of each . we ' re also told that that there are 16 more of the larger boxes . this means , at the minimum , we have . . . 1 small box and 17 large boxes = 1 ( 12 ) + 17 ( 16 ) = 12 + 272 = 284 glasses at the minimum since the question asks for the total number of glasses , we can now eliminate answers a , b and c . . . . the difference in the number of boxes must be 16 though , so we could have . . . . 2 small boxes and 18 large boxes 3 small boxes and 19 large boxes etc . with every additional small box + large box that we add , we add 12 + 16 = 28 more glasses . thus , we can justadd 28 suntil we hit the correct answer . . . . 284 + 28 = 312 312 + 28 = 340 340 + 28 = 368 368 + 28 = 396 at this point , we ' ve ' gone past ' answer d , so the correct answer must be answer e . . . . . but here ' s the proof . . . . 396 + 28 = 424 424 + 28 = 452 452 + 28 = 480 final answer : e" + }, + { + "Answer": 33.333333333333314, + "Options": "a ) 33.3 % , b ) 305 , c ) 50 % , d ) 55 % , e ) 60 %", + "Correct": "a", + "Explanation": "\"explanation : number of pages increased = 60 now , the number of pages of book = 240 number of pages of the books before increase = 240 \u2013 60 = 180 % increase in the number of pages in the book = 60 / 180 x 100 % = 33.3 % a\"" + }, + { + "Answer": 35, + "Options": "a ) 18 % , b ) 20 % , c ) 21 % , d ) 35 % , e ) can not be determined", + "Correct": "d", + "Explanation": "answer : d ." + }, + { + "Answer": 1500, + "Options": "a ) 1400 , b ) 1500 , c ) 1505 , d ) none of these , e ) 1506", + "Correct": "b", + "Explanation": "\"explanation : 75 / . 05 = 7500 / 5 = 1500 option b\"" + }, + { + "Answer": 12.121212121212121, + "Options": "a ) 8 % , b ) 9 % , c ) 10 % , d ) 11 % , e ) 12 %", + "Correct": "e", + "Explanation": "\"actual price = 29 + 4 = $ 33 saving = 4 / 33 * 100 = 12 % approximately answer is e\"" + }, + { + "Answer": 16, + "Options": "a ) 22 , b ) 24 , c ) 16 , d ) 18 , e ) 20", + "Correct": "c", + "Explanation": "a ^ 2 + b ^ 2 should make you think of these formulas : ( a + b ) ( a + b ) = a ^ 2 + b ^ 2 + 2 ab we already know ( a + b ) = - 6 and a * b = 10 ( a + b ) ( a + b ) = ( - 6 ) ( - 6 ) = a ^ 2 + b ^ 2 + 2 * ( 10 ) a ^ 2 + b ^ 2 = 36 - 20 = 16 answer : c" + }, + { + "Answer": 300, + "Options": "a ) a ) 220 , b ) b ) 490 , c ) c ) 380 , d ) d ) 300 , e ) e ) 690", + "Correct": "d", + "Explanation": "\"the only thing you have to do is a simple multiply we have : 15 * 20 = 300 correct answer is : d ) 300\"" + }, + { + "Answer": 48, + "Options": "a ) 2 , b ) 8 , c ) 15 , d ) 21 , e ) 48", + "Correct": "e", + "Explanation": "\"solution - simply substitute 3 and 6 in equation in the place of a and b respectively . 3 # 6 = 3 * 6 - 6 + 6 ^ 2 = 18 - 6 + 36 = 48 . ans e\"" + }, + { + "Answer": 10, + "Options": "a ) rs 10 , b ) rs 9 , c ) rs 0 , d ) rs 55 , e ) rs 8", + "Correct": "a", + "Explanation": "let the value of turban = rs x for 1 year = 90 + x for 9 months ( i , e 3 / 4 year ) = 65 + x i , e 1 : ( 90 + x ) : : 3 / 4 : ( 65 + x ) i , e ( 90 + x ) / ( 65 + x ) = 1 / ( 3 / 4 ) 270 + 3 x = 260 + 4 x thus x = 10 answer : a" + }, + { + "Answer": 88.8, + "Options": "a ) 86.25 , b ) 84 , c ) 85 , d ) 88.8 , e ) 80", + "Correct": "d", + "Explanation": "\"mean - 7 sd = 86 mean + 3 sd = 90 by solving above equations we get , sd ( absolute value ) = 0.4 mean = 88.8 ans . d\"" + }, + { + "Answer": 48, + "Options": "a ) 42 , b ) 32 , c ) 48 , d ) 28 , e ) 38", + "Correct": "c", + "Explanation": "\"x / 72 = 24 . x = 24 * 72 . so correct answer would be , ( 24 * 72 ) / 36 = 48 . answer : c\"" + }, + { + "Answer": 16, + "Options": "a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18", + "Correct": "c", + "Explanation": "5 c 2 = 10 the number of test subjects is 10 + 6 = 16 the answer is c ." + }, + { + "Answer": 252.94117647058826, + "Options": "a ) 100 % , b ) 16 2 / 3 % , c ) 200 % , d ) 253 % , e ) 183 1 / 3 %", + "Correct": "d", + "Explanation": "assume 100 enrollments present in 1990 85 / 3 % of 1990 = enrollments on 1980 enrollments on 1980 = 28.33 % change = ( enrollment in 1990 - enrollment in 1980 ) * 100 / ( enrollment in 1980 ) = ( 100 - 28.33 ) * 100 / 28.333 = 7166.67 / 28.333 = 253 % ans - d" + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 8 , c ) 11 , d ) 12 , e ) 14", + "Correct": "a", + "Explanation": "\"l = r l = 3 c r = c + 10 3 c = c + 10 c = 5 the answer is a .\"" + }, + { + "Answer": 6.022222222222222, + "Options": "a ) 5 , b ) 6 , c ) 9 , d ) 10 , e ) 11", + "Correct": "b", + "Explanation": "450 = 10 * 45 900 = 20 * 45 the even multiples are 45 multiplied by 10 , 12 , 14 , 16 , 18 , and 20 for a total of 6 . the answer is b ." + }, + { + "Answer": 342, + "Options": "a ) 286 , b ) 342 , c ) 422 , d ) 540 , e ) 618", + "Correct": "b", + "Explanation": "\"2 * 19 c 2 = 2 * 171 = 342 the answer is b .\"" + }, + { + "Answer": 260, + "Options": "a ) 260 , b ) 150 , c ) 817 , d ) 716 , e ) 616", + "Correct": "a", + "Explanation": "a + b + c = 585 4 a = 6 b = 3 c = x a : b : c = 1 / 4 : 1 / 6 : 1 / 3 = 3 : 2 : 4 4 / 9 * 585 = rs . 260 answer : a" + }, + { + "Answer": 38, + "Options": "a ) 37 , b ) 38 , c ) 39 , d ) 40 , e ) 41", + "Correct": "b", + "Explanation": "\"let present age of a be a and b be b a + 10 = 2 * ( b - 10 ) = > 2 b - a = 30 . . . . . . ( i ) a = b + 8 = > 2 b - b - 8 = 30 b = 38 so the present age of b is 38 years answer : b\"" + }, + { + "Answer": 1600, + "Options": "a ) t = 200 , b ) t = 600 , c ) t = 800 , d ) t = 1600 , e ) t = 50", + "Correct": "d", + "Explanation": "\"original cost c 1 = t 1 * b 1 ^ 4 new cost c 2 = t 2 * b 2 ^ 4 . . . . only b is doubled so t 2 = t 1 and b 2 = 2 b 1 c 2 = t 2 * ( 2 b 1 ) ^ 4 = 16 ( t 1 * b 1 ^ 4 ) = 16 c 1 16 times c 1 = > 1600 % of c 1 ans d = 1600\"" + }, + { + "Answer": 400, + "Options": "a ) 100 , b ) 300 , c ) 400 , d ) 3000 , e ) 4000", + "Correct": "c", + "Explanation": "straight pluggin in for me . as usual , i started with c and got the answer . lets ' back calculate and see what we get let us consider eggs processed each day to be 400 so initial ratio of eggs processed and rejected is 96 : 4 or 24 : 1 so out of 400 eggs , there will be 384 eggs processed and 16 rejected . now if the no . of eggs inspected remain and 12 more eggs get accepted that means there q = 384 + 12 = 396 eggs accepted and 4 rejected . . . and the ratio will be 99 : 1 bingo . . . this is what the questions says . . . . its always a good idea to start with c ." + }, + { + "Answer": 42, + "Options": "a ) 39,30 , b ) 41,32 , c ) 42,33 , d ) 43,34 , e ) 35,36", + "Correct": "c", + "Explanation": "let their marks be ( x + 9 ) and x . then x + 9 = 56 / 100 ( x + 9 + x ) 3 x = 99 x = 33 their marks 42 and 33 answer c" + }, + { + "Answer": 11, + "Options": "a ) 4 , b ) 7 , c ) 8 , d ) 11 , e ) 12", + "Correct": "d", + "Explanation": "\"here the idea is to go expressing each factor from one to eight , decomposed into its primes : 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 = 1 * 2 * 3 * ( 2 * 2 ) * 5 + ( 2 * 3 ) * 7 * ( 2 * 2 * 2 ) = 2 ^ 7 * 3 ^ 2 * 5 ^ 1 * 7 ^ 1 then i = 7 k = 2 m = 1 p = 1 i + k + m + p = 11 correct answer d\"" + }, + { + "Answer": 15, + "Options": "a ) a ) 16 , b ) b ) 15 , c ) c ) 19 , d ) d ) 22 , e ) e ) 24", + "Correct": "b", + "Explanation": "\"explanation : 10 * 14 + 36 \u2013 26 = 150 = > 150 / 10 = 15 b )\"" + }, + { + "Answer": 14, + "Options": "a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15", + "Correct": "d", + "Explanation": "\"sum of 8 quantities = total no of quantities x average of them = 6 x 8 = 48 sum of 4 quantities = 4 x 5 = 20 sum of 4 quantities + sum of 2 quantities = sum of 6 quantities 20 + sum of 2 quantities = 48 sum of 2 quantities = 28 average of 2 quantities = sum of 2 quantities / 2 = 28 / 2 = 14 answer : d\"" + }, + { + "Answer": 77, + "Options": "a ) 15 , b ) 21 , c ) 17 , d ) 57 , e ) 77", + "Correct": "e", + "Explanation": "total money = rs . 10350 . let 50 rupees note was x . then 500 rupees note = 90 - x now , 50 * x + 500 * ( 90 - x ) = 10350 50 x + 45000 - 500 x = 10350 - 450 x = - 34650 x = 77 . no . of 50 rupees note = 77 . answer : option e" + }, + { + "Answer": 12, + "Options": "a ) 10 , b ) 12 , c ) 16 , d ) 20 , e ) 22", + "Correct": "b", + "Explanation": "\"let original strength = y then , 40 y + 12 x 32 = ( y + 12 ) x 36 \u21d2 40 y + 384 = 36 y + 432 \u21d2 4 y = 48 \u2234 y = 12 b\"" + }, + { + "Answer": 10, + "Options": "a ) 2.5 , b ) 5 , c ) 7.5 , d ) 10 , e ) 12", + "Correct": "d", + "Explanation": "\"the x - axis is 5 units from the point p . thus the y - axis is 10 units from the point p . the answer is d .\"" + }, + { + "Answer": 53, + "Options": "a ) 47 , b ) 53 , c ) 56 , d ) 61 , e ) 64", + "Correct": "b", + "Explanation": "\"let m be the number of math books and let h be the number of history books . m + h = 90 . h = 90 - m . 4 m + 5 h = 397 . 4 m + 5 ( 90 - m ) = 397 . - m + 450 = 397 . m = 450 - 397 = 53 . the answer is b .\"" + }, + { + "Answer": 232, + "Options": "a ) s . 130 , b ) s . 140 , c ) s . 150 , d ) s . 232 , e ) s . 280", + "Correct": "d", + "Explanation": "\"let the amount paid to a per week = x and the amount paid to b per week = y then x + y = 580 but x = 150 % of y = 150 y / 100 = 15 y / 10 \u2234 15 y / 10 + y = 580 \u21d2 y [ 15 / 10 + 1 ] = 580 \u21d2 25 y / 10 = 580 \u21d2 25 y = 5800 \u21d2 y = 5800 / 25 = rs . 232 d )\"" + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10", + "Correct": "a", + "Explanation": "\"say there are ' a ' associate professors . so we have 2 a pencils and a charts . say there are ' b ' assistant professors . so we have b pencils and 2 b charts . total pencils are 10 so 2 a + b = 7 total charts are 11 so a + 2 b = 11 add both : 3 a + 3 b = 18 so a + b = 6 total number of people = 6 a\"" + }, + { + "Answer": 80, + "Options": "a ) 60 , b ) 80 , c ) 40 , d ) 120 , e ) 160", + "Correct": "b", + "Explanation": "\"( 1 + 1 / 8 ) x - ( 1 - 1 / 4 ) x = 30 ( 9 / 8 ) x - ( 3 / 4 ) x = 30 x = 80 = r answer : b\"" + }, + { + "Answer": 180, + "Options": "a ) 180.27 cm , b ) 180.29 cm , c ) 978.29 cm , d ) 178.89 cm , e ) 176.29 cm", + "Correct": "b", + "Explanation": "\"calculated average height of 35 boys = 182 cm . wrong total height of 35 boys = 182 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 182 cm - ( 166 cm - 106 cm ) / 35 = 182 cm - 60 / 35 cm = 182 cm - 1.71 cm = 180.29 cm . answer : b\"" + }, + { + "Answer": 118, + "Options": "a ) 111.7 , b ) 118.7 , c ) 113.7 , d ) 218.7 , e ) 418.7", + "Correct": "b", + "Explanation": "here , a : b : c : d = 1 / 4 : 1 / 6 : 1 / 10 : 1 / 9 1 ) l . c . m of 4 : 6 : 10 : 9 is 180 2 ) find the number of pens each friend received - - - - - - - - - ( to find no . of pens each friend has , multiply the ratio with the l . c . m . calculated ) a = ( 1 / 4 ) x 180 = 45 b = ( 1 / 6 ) x 180 = 30 c = ( 1 / 10 ) x 180 = 18 d = ( 1 / 7 ) x 180 = 25.7 3 ) total number of toys = ( 45 x + 30 x + 18 x + 25.7 x ) = 118.7 x minimum number of pens ( x ) = 1 therefore , total number of pens = 118.7 pens . correct option : b" + }, + { + "Answer": 153, + "Options": "a ) 107 , b ) 153 , c ) 178 , d ) 198 , e ) 165", + "Correct": "b", + "Explanation": "\"let us calculate both the length and width of the room in centimeters . length = 8 meters and 16 centimeters = 816 cm width = 4 meters and 32 centimeters = 432 cm as we want the least number of square tiles required , it means the length of each square tile should be as large as possible . further , the length of each square tile should be a factor of both the length and width of the room . hence , the length of each square tile will be equal to the hcf of the length and width of the room = hcf of 816 and 432 = 48 thus , the number of square tiles required = ( 816 x 432 ) / ( 48 x 48 ) = 17 x 9 = 153 answer : b\"" + }, + { + "Answer": 75000, + "Options": "a ) 70000 , b ) 73000 , c ) 75000 , d ) 77000 , e ) 79000", + "Correct": "c", + "Explanation": "sp * ( 110 / 100 ) = 82500 sp = 750 * 100 = > sp = 75000 answer : c" + }, + { + "Answer": 72, + "Options": "a ) 35 , b ) 45 , c ) 25 , d ) 72 , e ) 55", + "Correct": "d", + "Explanation": "a : b : c = 10 \u00d7 7 : 12 \u00d7 5 : 15 \u00d7 3 = 2 \u00d7 7 : 12 \u00d7 1 : 3 \u00d7 3 = 14 : 12 : 9 amount that c should pay = 280 \u00d7 9 / 35 = 8 \u00d7 9 = 72 answer is d" + }, + { + "Answer": 207, + "Options": "a ) 85 , b ) 74 , c ) 67 , d ) 53 , e ) 207", + "Correct": "e", + "Explanation": "\"( 4 * 61.5 ) + 47 + x > 500 246 + 47 + x > 500 293 + x > 500 = > x > 207 option e\"" + }, + { + "Answer": 5.279999999999999, + "Options": "a ) 5.29 min , b ) 5.28 min , c ) 5.08 min , d ) 9.28 min , e ) 5.988 min", + "Correct": "b", + "Explanation": "\"clearly , the two will meet when they are 726 m apart . to be ( 4.5 + 3.75 ) = 8.25 km apart , they take 1 hour . to be 726 m apart , they take ( 100 / 825 * 726 / 1000 ) hrs = ( 242 / 2750 * 60 ) min = 5.28 min . answer : b\"" + }, + { + "Answer": 805, + "Options": "a ) s . 800 , b ) s . 810 , c ) s . 805 , d ) s . 900 , e ) s . 920", + "Correct": "c", + "Explanation": "2415 * 1 / 3 = 805 option c" + }, + { + "Answer": 400, + "Options": "a ) 300 , b ) 250 , c ) 280 , d ) 320 , e ) 400", + "Correct": "e", + "Explanation": "\"let the maximum marks be x then , 45 % of x = 150 + 30 45 x / 100 = 180 45 x = 180 * 100 = 18000 x = 400 answer is e\"" + }, + { + "Answer": 222, + "Options": "a ) 104 , b ) 60 , c ) 52 , d ) 50 , e ) 222", + "Correct": "e", + "Explanation": "f ( x ) = 2 x ^ 2 + y f ( 2 ) = 30 = > 2 * ( 2 ) ^ 2 + y = 30 = > 8 + y = 30 = > y = 22 f ( 10 ) = 2 * ( 10 ) ^ 2 + 22 = 222 answer e" + }, + { + "Answer": 0.125, + "Options": "a ) 1 / 16 , b ) 1 / 3 , c ) 1 / 6 , d ) 1 / 2 , e ) 1 / 8", + "Correct": "e", + "Explanation": "\"must be once on twice and once on tails 1 / 2 * 1 / 2 * 1 / 2 = 1 / 8 answer : e\"" + }, + { + "Answer": 25, + "Options": "a ) 25 , b ) 20 , c ) 18 , d ) 16 , e ) 14", + "Correct": "a", + "Explanation": "explanation : [ ( 5 / 2 \u00f7 1 / 2 \u00d7 5 / 2 ) ] / [ ( 5 / 2 \u00d7 1 / 2 \u00f7 5 / 2 ) ] = [ 5 / 2 \u00d7 2 / 1 \u00d7 5 / 2 ] / [ 5 / 2 \u00d7 1 / 2 \u00d7 2 / 5 ] = 25 / 2 / 1 / 2 = 25 / 2 x 2 / 1 = 25 answer : option a" + }, + { + "Answer": 9637, + "Options": "a ) 9263 , b ) 9244 , c ) 9636 , d ) 9623 , e ) 9637", + "Correct": "e", + "Explanation": "\"= ( 85 + 32 / 113 ) \u00d7 113 = ( 9605 + 32 ) / 113 \u00d7 113 = 9637 / 113 \u00d7 113 = 9637 answer is e .\"" + }, + { + "Answer": 49, + "Options": "a ) 23 , b ) 49 , c ) 22 , d ) 20 , e ) 21", + "Correct": "b", + "Explanation": "\"let the total number of workers be x . then , 8000 x = ( 20000 * 7 ) + 6000 ( x - 7 ) = 2000 x = 98000 = x = 49 . answer : b\"" + }, + { + "Answer": 14, + "Options": "a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18", + "Correct": "a", + "Explanation": "there are 10 % of water in 70 l - - > there are 7 l of waters ; after x liters of water is added amount of water becomes ( 7 + x ) liters , which on the other hand is 1 / 4 th ( 25 % ) of new ( 70 + x ) liters of mixture : 7 + x = 1 / 4 * ( 70 + x ) - - > 28 + 4 x = 70 + x - - > x = 14 answer : a" + }, + { + "Answer": 0.9986095661846496, + "Options": "a ) 1977452 / 1977455 , b ) 1982466 / 1982469 , c ) 1982487 / 1982490 , d ) 1982456 / 1982459 , e ) 1982465 / 1982468", + "Correct": "c", + "Explanation": "\"the difference between each numerator / denominator pair is three . the largest expression ( which in this case will also be the closest to one ) is the expression where ' 3 ' is the smallest fraction of the numerator ( or the denominator ) . the largest numerator is 1982487 , or c , and this will give an expression with a value closest to one . we can also demonstrate that this approach works with some simple logic . taking numerator / denominator pairs that differ by three . . . 1 / 4 = 0.25 2 / 5 = 0.4 3 / 6 = 0.5 . . . 27 / 30 = 0.9 . . . 1982487 / 1982490 = 0.999998486 . . . answer : c\"" + }, + { + "Answer": 31, + "Options": "a ) 2 , b ) 3 , c ) 5 , d ) 7 , e ) 31", + "Correct": "e", + "Explanation": "i ' m happy to help with this . we know 4 = 2 ^ 2 , so 4 ^ 17 = ( 2 ^ 2 ) ^ 17 = 2 ^ ( 2 * 17 ) = 2 ^ 34 that takes advantage of a law of exponents that says ( a ^ n ) ^ m = a ^ ( n * m ) so , 4 ^ 17 - 2 ^ 29 = 2 ^ 34 - 2 ^ 29 = 2 ^ ( 29 + 5 ) - 2 ^ 29 = ( 2 ^ 29 ) * ( 2 * 6 ) - 2 ^ 29 = ( 2 ^ 6 - 1 ) * ( 2 ^ 29 ) = ( 32 - 1 ) * ( 2 ^ 29 ) = 31 * ( 2 ^ 29 ) the prime factors of 31 are 31 , so the largest prime factor is 31 , answer choice d . here ' s a blog you may find helpful . http : / / magoosh . com / gmat / 2012 / gmat - math - factors / does all that make sense ? please let me know if you have any further questions . mike wow . i am floored by how great of an explanation you provided . posts like that make me really think that doing thousands of practice problems with good explanations beats out reading books on math every day of the week . e" + }, + { + "Answer": 120, + "Options": "a ) 344 , b ) 251 , c ) 411 , d ) 212 , e ) 120", + "Correct": "e", + "Explanation": "let x be the number he chose , then 2 \u22c5 x \u2212 138 = 102 2 x = 240 x = 120 correct answer is e ) 120" + }, + { + "Answer": 14, + "Options": "a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14", + "Correct": "e", + "Explanation": "\"l = r l = 3 c r = c + 28 3 c = c + 28 c = 14 the answer is e .\"" + }, + { + "Answer": 3, + "Options": "a ) 2 , b ) 3 , c ) 7 , d ) 9 , e ) 10", + "Correct": "b", + "Explanation": "\"let possible value of x is 80 least possible value of x / 11 is 80 / 11 = > 7 quotient with remainder 3 thus answer is ( b ) 3\"" + }, + { + "Answer": 15, + "Options": "a ) 9 % , b ) 11 % , c ) 13 % , d ) 15 % , e ) 17 %", + "Correct": "d", + "Explanation": "\"the percent of alcohol in the solution is ( 0.05 ( 40 ) + 5.5 ) / 50 = 7.5 / 50 = 15 % the answer is d .\"" + }, + { + "Answer": 48000, + "Options": "a ) 15,000 , b ) 25,000 , c ) 40,000 , d ) 48,000 , e ) 60,000", + "Correct": "d", + "Explanation": "let a be the first candidate and b be the second one . given x + 16000 = 5 ( x - 16000 ) = > x = 24000 2 x = 48000 imo option d ." + }, + { + "Answer": 9975, + "Options": "a ) 4676 , b ) 4678 , c ) 9975 , d ) 9504 , e ) 9936", + "Correct": "c", + "Explanation": "\"largest 4 digit number = 9999 9999 \u00f7 35 = 285 , remainder = 24 hence largest 4 digit number exactly divisible by 88 = 9999 - 24 = 9975 answer : c\"" + }, + { + "Answer": 75, + "Options": "a ) 15 , b ) 125 , c ) 25 , d ) 75 , e ) 50", + "Correct": "d", + "Explanation": "so , according to a mean of a set of even numbers from 0 to 100 = ( 0 + 100 ) / 2 = 50 and mean of a set of even numbers from 0 to 50 = ( 0 + 50 ) / 2 = 25 sum = 50 + 25 = 75 answer : d ." + }, + { + "Answer": 200, + "Options": "a ) $ 150 , b ) $ 200 , c ) $ 320 , d ) $ 650 , e ) $ 810", + "Correct": "b", + "Explanation": "\"the volume of each box is 20 * 20 * 12 = 4800 cubic inches . number of boxes = 1 , 920,000 / 4800 = 400 boxes total cost = 400 \u00d7 $ 0.5 = $ 200 the answer is b .\"" + }, + { + "Answer": 0.36363636363636365, + "Options": "a ) 2 / 9 , b ) 1 / 3 , c ) 2 / 5 , d ) 4 / 11 , e ) 7 / 9", + "Correct": "d", + "Explanation": "\"mode : the mode of any set is the term which has the highest frequency ( occurrence ) highest frequent term in the set is 5 ( with frequency 4 ) hence mode = 5 four terms ( 1 , 2 , 3 , 4 ) out of a total of 11 terms are less than mode of the set . fraction of set that are less than mode of set = 4 / 11 answer : option d\"" + }, + { + "Answer": 15580, + "Options": "a ) 15360 , b ) 15720 , c ) 15060 , d ) 14930 , e ) 16075", + "Correct": "b", + "Explanation": "\"6000 + 14000 - ( 0.2 * 6000 + 0.22 * 14000 ) = 15720 . answer : b .\"" + }, + { + "Answer": 45, + "Options": "a ) 33 , b ) 36 , c ) 39 , d ) 42 , e ) 45", + "Correct": "e", + "Explanation": "\"10 c 2 = 45 the answer is e .\"" + }, + { + "Answer": 0.16666666666666666, + "Options": "a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6", + "Correct": "e", + "Explanation": "there are total 4 c 2 = 64 c 2 = 6 ways to choose 2 equations out of 4 at random . we want the product of 2 equations in format x 2 \u2212 ( by ) 2 x 2 \u2212 ( by ) 2 , where b is a constant coefficient of term y 2 y 2 . also note equation does not contain any xyxy term . there are only 2 equations , ( x + y ) & ( x - y ) which gives the product x 2 \u2212 y 2 x 2 \u2212 y 2 . product of all other equations will contain term xyxy so answer = 1 / 6 ans : e" + }, + { + "Answer": 1575, + "Options": "a ) 1235 , b ) 1346 , c ) 1590 , d ) 1635 , e ) 1489", + "Correct": "c", + "Explanation": "\"let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 7 x + 15 6 x = 1350 x = 225 large number = 225 + 1365 = 1590 c\"" + }, + { + "Answer": 7, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", + "Correct": "a", + "Explanation": "\"a simple and elegant solution . as addition of 39 , shifts mean by 2 , and addition of 15 , shifts mean by 1 to the other side , we have the mean lying between 3915 , and in a ratio of 2 : 1 39 - 15 = 24 24 divide by 3 is 8 . meaning mean of the n terms is 15 + 8 = 39 - 16 = 23 now , from first statement , when a person aged 39 is added to a group of n people , the average age increases by 2 . q * 23 + 39 = 25 * ( q + 1 ) q = 7 ans . ( a )\"" + }, + { + "Answer": 198, + "Options": "a ) 99 , b ) 18 , c ) 16 , d ) 198 , e ) 15", + "Correct": "d", + "Explanation": "\"60 * 33 / 2 = 5 / 2 * 2 * x = > x = 198 answer : d\"" + }, + { + "Answer": 4200, + "Options": "a ) a ) 3800 , b ) b ) 4200 , c ) c ) 4400 , d ) d ) 4500 , e ) e ) 4600", + "Correct": "b", + "Explanation": "\"x * ( 90 / 100 ) * ( 85 / 100 ) = 3213 x = 4200 answer : b\"" + }, + { + "Answer": 30, + "Options": "a ) 89 , b ) 20 , c ) 36 , d ) 88 , e ) 30", + "Correct": "e", + "Explanation": "\"speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 180 + 120 = 300 m . time taken = 300 / 10 = 30 sec . answer : option e\"" + }, + { + "Answer": 0.25, + "Options": "a ) 2.25 , b ) 3.25 , c ) 4.25 , d ) 5.25 , e ) 0.25", + "Correct": "e", + "Explanation": "\"squaring on both sides ( x + 1 / x ) ^ 2 = 1.5 ^ 2 x ^ 2 + 1 / x ^ 2 = 2.25 - 2 x ^ 2 + 1 / x ^ 2 = 0.25 answer : e\"" + }, + { + "Answer": 12, + "Options": "a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 15", + "Correct": "c", + "Explanation": "\"given that , a + b = 12 + b + c \u21d2 a - c = 12 therefore , c is younger than a by 12 years answer is c .\"" + }, + { + "Answer": 61.875, + "Options": "a ) 125 , b ) 95 , c ) 80 , d ) 61.8 , e ) 50", + "Correct": "d", + "Explanation": "answer : b the temperature of coffee 10 minutes after it was poured ( 120 f ) will help in solving the constant \u201c a \u201d . 120 = 120 ( 2 ^ 10 a ) + 60 2 ^ - 1 = 2 ^ 10 a a = - 1 / 10 the temperature of coffee 60 minutes after it was poured is : f = 120 ( 2 ^ - 60 / 10 ) + 60 f = 120 * 1 / 64 + 60 f = 15 / 8 + 60 f = 495 / 8 = 61.8 d" + }, + { + "Answer": 85, + "Options": "a ) 76 , b ) 76.5 , c ) 85 , d ) 80 , e ) none of these", + "Correct": "c", + "Explanation": "\"explanation : total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 65 + 20 ) kg = 85 kg . answer : c\"" + }, + { + "Answer": 21, + "Options": "a ) 15 liters , b ) 21 liters , c ) 12 liters , d ) 18 liters , e ) 25 liters", + "Correct": "b", + "Explanation": "1 st ratio = 7 : 5 2 nd ratio = 7 : 9 difference of cross products ratio = 7 * 9 - 7 * 5 = 28 common factor of the 1 st ratio = ( quantity replaced / sum of terms in 1 st ratio ) + ( quantity replaced * term a in 2 nd ratio / difference ) = ( 9 / 7 + 5 ) + ( 9 * 7 / 28 ) = 3 quantity of a = 7 * 3 = 21 liters answer is b" + }, + { + "Answer": 2.6944444444444446, + "Options": "a ) $ 1.09 , b ) $ 2.69 , c ) $ 2.25 , d ) $ 2.37 , e ) $ 2.50", + "Correct": "b", + "Explanation": "\"total cost of parking for 9 hours = 12 $ for the first 2 hours and then 1.75 for ( 9 - 2 ) hours = 12 + 7 * 1.75 = 24.25 thus the average parking price = 24.25 / 9 = 2.69 $ b is the correct answer .\"" + }, + { + "Answer": 550, + "Options": "a ) 420 , b ) 550 , c ) 490 , d ) 450 , e ) 457", + "Correct": "b", + "Explanation": "\"10 * 160 = 1600 3 * 100 + 5 * 150 = 1050 1600 \u2013 1050 = 550 answer : b\"" + }, + { + "Answer": 50, + "Options": "a ) 25 , b ) 30 , c ) 50 , d ) 75 , e ) 40", + "Correct": "c", + "Explanation": "\"assume the length of each train = x total distance covered for overtaking the slower train = x + x = 2 x relative speed = 46 - 36 = 10 km / hr = ( 10 \u00d7 10 ) / 36 = 100 / 36 m / s time = 36 seconds 2 x / ( 100 / 36 ) = 36 = > ( 2 x \u00d7 36 ) / 100 = 36 = > x = 50 meter answer is c .\"" + }, + { + "Answer": 57.692307692307686, + "Options": "a ) 53 % , b ) 57.7 % , c ) 62.5 % , d ) 64 % , e ) 75 %", + "Correct": "b", + "Explanation": "\"last year revenue = 100 ( assume ) ; this year revenue = 75 ; projected revenue = 130 . actual / projected * 100 = 75 / 130 * 100 = 57.7 % . answer : b .\"" + }, + { + "Answer": 2982, + "Options": "a ) 3345 , b ) 1250 , c ) 1540 , d ) 2997 , e ) 1635", + "Correct": "d", + "Explanation": "\"let the smaller number be x . then larger number = ( x + 1365 ) . x + 2500 = 6 x + 15 5 x = 2485 x = 497 large number = 497 + 1365 = 2997 d\"" + }, + { + "Answer": 36, + "Options": "a ) 24 , b ) 30 , c ) 36 , d ) 42 , e ) 48", + "Correct": "c", + "Explanation": "\"let ( y / 18 ) x ( y / 72 ) = 1 y ^ 2 = 18 x 72 = 18 x 18 x 4 y = ( 18 x 2 ) = 36 the answer is c .\"" + }, + { + "Answer": 0.21428571428571427, + "Options": "a ) 1 / 4 , b ) 4 / 15 , c ) 3 / 14 , d ) 4 / 11 , e ) 4 / 5", + "Correct": "c", + "Explanation": "let avg for 11 mos . = 10 therefore , dec = 30 year total = 11 * 10 + 30 = 140 answer = 30 / 140 = 3 / 14 = c" + }, + { + "Answer": 10, + "Options": "a ) 10 , b ) 12 , c ) 15 , d ) 18 , e ) 19", + "Correct": "a", + "Explanation": "\"2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 29 - 9 = 20 = > ab = 10 . answer : a\"" + }, + { + "Answer": 25, + "Options": "a ) 15 % , b ) 25 % , c ) 0.125 % , d ) 0.2083 % , e ) none", + "Correct": "b", + "Explanation": "only trick n this question is to ignore 50 % information as farm tax is levied uniformly in the village and that includes mr william ' s land . what percentage of tax mr william paid ? this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 480 / 3840 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 50 ) = 25 % and the answer is not there in the options . the correct answer is ( b ) ." + }, + { + "Answer": 1120, + "Options": "a ) 336 , b ) 784 , c ) 1120 , d ) 1804 , e ) 1936", + "Correct": "c", + "Explanation": "number is divisible by 4 if the last two digits form a number divisible by 4 . therefore last two digits can be : 00 ; 04 ; 08 ; 12 16 ; . . . 96 . basically multiples of 4 in the range 0 - 96 , inclusive . multiples of 4 in a range 0 - 96 , inclusive are last multiple in the range \u2212 first multiple in the range 4 + 1 = 25 last multiple in the range \u2212 first multiple in the range 4 + 1 = 25 but 3 numbers out of these 25 are not formed with distinct digits : 00 , 44 , and 88 . hence the numbers we are looking for can have only 22 endings . if there is 0 in the ending ( 04 , 08 , 20 , 40 , 60 , 80 - total 6 such numbers ) , then the first and second digit can take 8 and 7 choices each = 56 choices total . as there are 6 numbers with 0 in ending , hence total 6 * 56 = 336 . if there is no 0 in the ending ( total 22 - 6 with zero = 16 such numbers ) , then the first digit can take 7 choices ( 10 - 2 digits in the ending and zero , so total 3 digits = 7 , as 4 - digit number can not start with zero ) and the second digit can take 7 choices too ( 10 digits - 3 digits we ' ve already used ) = 7 * 7 = 49 choices total . as there are 16 numbers without zero in ending , hence total 16 * 49 = 784 . total : 336 + 784 = 1120 answer : c ." + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 4 , c ) 3 , d ) 6 , e ) 7", + "Correct": "a", + "Explanation": "required subsets are = { 6,7 } , { 6,8 } , { 6,9 } , { 7,8 } , { 7,9 } = 5 answer : a" + }, + { + "Answer": 39, + "Options": "a ) 2 , b ) 4 , c ) 8 , d ) 39 , e ) 32", + "Correct": "d", + "Explanation": "\"lets assign variables to all the areas in venn diagram of three . three different units are dog , cat , snake = total = 69 only dog = d = 15 only cat = c = 10 only snake = s exactly dog and cat = 5 exactly dog and snake = x exactly cat and snake = y all three = 3 so 69 = 15 + 10 + 5 + 3 + x + y + s we need to know total snakes = x + y + s + 3 = 39 answer : d\"" + }, + { + "Answer": 38.46153846153846, + "Options": "a ) 15 % , b ) 162 \u2044 3 % , c ) 20 % , d ) 38.46 % , e ) 24 %", + "Correct": "d", + "Explanation": "new annual salary = $ 90,000 salary increase = $ 25,000 . original salary = $ 90,000 - $ 25,000 . = $ 75,000 % increase = ( $ 25,000 / $ 65,000 ) * 100 = 38.46 % hence d ." + }, + { + "Answer": 8, + "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12", + "Correct": "a", + "Explanation": "\"let the time for which car averages 60 mph = t 65 * ( t + 4 ) = 70 * 4 + 60 t = > 5 t = 20 = > t = 4 total duration of the trip = 4 + 4 = 8 answer a\"" + }, + { + "Answer": 23, + "Options": "a ) 23 , b ) 20 , c ) 12 , d ) 128 , e ) 171", + "Correct": "a", + "Explanation": "\"let the numbers be x and y . then , xy = 120 and x 2 + y 2 = 289 . ( x + y ) 2 = x 2 + y 2 + 2 xy = 289 + ( 2 x 120 ) = 529 x + y = 529 = 23 . answer a\"" + }, + { + "Answer": 13.88888888888889, + "Options": "a ) 9 , b ) 13.88 , c ) 47 , d ) 48 3 / 5 , e ) 59", + "Correct": "b", + "Explanation": "\"you can plug in values . c = 5 / 9 * ( f - 32 ) f = 32 - - > c = 0 ; f = 32 + 25 = 57 - - > c = 5 / 9 * 25 = 13.88 . increase = 13.88 degrees . answer : b .\"" + }, + { + "Answer": 71, + "Options": "a ) 71 , b ) 69 , c ) 72 , d ) 75 , e ) none", + "Correct": "a", + "Explanation": "\"sol . average = 76 + 60 + 72 + 65 + 82 / 5 ) = ( 355 / 5 ) = 71 . answer a\"" + }, + { + "Answer": 4, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8", + "Correct": "a", + "Explanation": "we can use ( n + 1 ) ^ 2 greater than ( n + 7 ) which gives n > 2 , - 3 . . . . . . . . now there are four integers - 2 . - 1 , 01 in between - 3 and 2 . so answer is 4 . answer : a" + }, + { + "Answer": 19.1125, + "Options": "a ) 11.84 , b ) 12.84 , c ) 23.84 , d ) 19.11 , e ) 10.12", + "Correct": "d", + "Explanation": "\"dinner bill of 8 person = 139 + 10 % tip so , 10 % of 139 = ( 139 * 10 ) / 100 = 13.9 so , the actual total amount = 139 + 13.9 = $ 152.9 so per head bill = 152.9 / 8 = $ 19.11 answer : d\"" + }, + { + "Answer": 759.0000000000001, + "Options": "a ) 392 , b ) 759 , c ) 753 , d ) 493 , e ) 540", + "Correct": "b", + "Explanation": "\"b 759 ? = 5060 * ( 2 / 5 ) * ( 1 / 2 ) * ( 3 / 4 ) = 759\"" + }, + { + "Answer": 40.2, + "Options": "a ) 40.2 , b ) 40.4 , c ) 40.6 , d ) 40.8 , e ) none of the above", + "Correct": "a", + "Explanation": "sum of 10 numbers = 402 corrected sum of 10 numbers = 402 \u2013 13 + 31 \u2013 18 = 402 hence , new average = 402 \u2044 10 = 40.2 answer a" + }, + { + "Answer": 120.00000000000001, + "Options": "a ) $ 100 , b ) $ 150 , c ) $ 125 , d ) $ 120 , e ) $ 250", + "Correct": "d", + "Explanation": "\"a : ( b + c ) = 2 : 3 a ' s share = 300 * 2 / 5 = $ 120 answer is d\"" + }, + { + "Answer": 32, + "Options": "a ) 3 , b ) 16 , c ) 28 , d ) 32 , e ) 56", + "Correct": "d", + "Explanation": "ways to select 3 people from 8 people ( 4 twins x 2 ) = 8 c 3 = 56 ways to select 1 twin + 1 people = 4 c 1 * 6 c 1 = 24 ways to select a group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen x = 56 - 24 = 32 ans : d" + }, + { + "Answer": 4, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "d", + "Explanation": "this is equivalent to : - 2 x * 4 y * 5 z = 16000 y = z ( given ) 2 x * 4 y * 5 y = 16000 2 x * y ^ 2 = 16000 / 20 2 x * y ^ 2 = 800 now from options given we will figure out which number will divide 800 and gives us a perfect square : - which gives us x = 4 as 2 * 4 * y ^ 2 = 800 y ^ 2 = 100 y = 10 number of yellow chips = 4 hence d" + }, + { + "Answer": 8, + "Options": "a ) 5 , b ) 8 , c ) 4 , d ) 10 , e ) 3", + "Correct": "b", + "Explanation": "2 ab = ( a ( power 2 ) + b ( power 2 ) - ( a - b ) ( power 2 ) = 25 - 9 = 16 ab = 8 . answer is b ." + }, + { + "Answer": 106, + "Options": "a ) 123 , b ) 106 , c ) 100 , d ) 156 , e ) 240", + "Correct": "b", + "Explanation": "explanation : cash realised = rs . ( 106.25 - 0.25 ) = rs . 106 . answer : b" + }, + { + "Answer": 25, + "Options": "a ) 22 , b ) 25 , c ) 28 , d ) 31 , e ) 34", + "Correct": "b", + "Explanation": "\"25 / 4 \u00f7 4 = 25 / 16 pounds in each container 25 / 16 pounds * 16 ounces / pound = 25 ounces in each container the answer is b .\"" + }, + { + "Answer": 349, + "Options": "a ) 349 , b ) 300 , c ) 500 , d ) 450 , e ) 250", + "Correct": "a", + "Explanation": "x = 13 p + 11 and x = 17 q + 9 13 p + 11 = 17 q + 9 17 q - 13 p = 2 q = 2 + 13 p / 17 least value of p which q = 2 + 13 p / 17 = > 26 x = ( 13 * 26 + 11 ) = 349 answer a" + }, + { + "Answer": 11, + "Options": "a ) 4 , b ) 6 , c ) 8 , d ) 11 , e ) 12", + "Correct": "d", + "Explanation": "while this question can be solved with a rather straight - forward algebra approach ( as the other posters have noted ) , it can also be solved by testing the answers . one of those numbers must be the total number of goals . . . from a tactical standpoint , it ' s best to test either answer b or answer d , so if the answer is not correct , then you would have a gauge for whether you should go higher or lower with your next test . here , i ' ll start with answer d = 11 goals if . . . . total goals = 11 goals 5 th game = 3 goals 1 st 4 games = 8 goals avg . for 4 games = 8 / 4 = 2 goals / game avg . for all 5 games = 6 / 5 = 2.2 goals / game 2.2 * 5 = 11 so answer d" + }, + { + "Answer": 4.9956356288922485, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "c", + "Explanation": "\"0.00010101 * 10 ^ k > 10 we need to move the decimal point to the right 5 places to get 10.101 this is equivalent to multiplying by 10 ^ 5 . the answer is c .\"" + }, + { + "Answer": 8, + "Options": "a ) 3 , b ) 5 , c ) 6 , d ) 8 , e ) 9", + "Correct": "d", + "Explanation": "\"explanation : on dividing 42398 by 15 we get the remainder 8 , so 8 should be subtracted option d\"" + }, + { + "Answer": 22, + "Options": "a ) 14 years , b ) 18 years , c ) 20 years , d ) 22 years , e ) 17 years", + "Correct": "d", + "Explanation": "\"let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . ( x + 24 ) + 2 = 2 ( x + 2 ) x + 26 = 2 x + 4 x = 22 . answer d\"" + }, + { + "Answer": 100, + "Options": "a ) 18 , b ) 36 , c ) 72 , d ) 90 , e ) 100", + "Correct": "e", + "Explanation": "let kate charge for x hours , then pat charged for 2 x and mat - for 6 x . so , 2 x + 6 x + x = 180 - total hours charged for , x = 20 . mat charged 6 x - x or 5 x for more hours than kate , or for 100 hours . e is correct" + }, + { + "Answer": 2, + "Options": "a ) m = 2 , b ) m = 5 , c ) m = 8 , d ) 10 , e ) 11", + "Correct": "a", + "Explanation": "really hard . but let ' s start with few concepts : 1 . square of an odd integer will be odd . 2 . difference of odd and odd will be even . 3 . any odd integer can be expressed as difference of two squares . 4 . an even integer can be expressed as difference of two squares only if that even integer is a multiple of 4 . assume two odd integers to be ( 2 x - 1 ) and ( 2 x + 1 ) . difference of their squares = ( 2 x + 1 ) ^ 2 - ( 2 x - 1 ) ^ 2 = 4 x ^ 2 + 1 + 4 x - ( 4 x ^ 2 + 1 - 4 x ) = 4 x ^ 2 + 1 + 4 x - 4 x ^ 2 - 1 + 4 x = 8 x now root of 8 x needs to be an integer such that it is equal to the sum of the digits of the two odd integers . 8 = 2 ^ 3 , so x needs to be such that itcompletesa perfect square . if we find x , we can find the value of 2 x + 1 ( larger integer ) and then sum of its digits . let ' s check the options , starting with c . for sum to be 8 , few possibilities are : 17 , 35 , 53 , 71 if we take 17 , the pair is 15 and 17 , meaning x = 8 . 8 x = 64 root of 64 = 4 but 4 is not equal to 1 + 5 + 1 + 7 . reject . if we take 35 , the pair is 33 and 35 , meaning x = 17 . 8 x = 8 * 17 reject since perfect square is not possible . if we take 53 , the pair is 51 and 53 , meaning x = 26 . 8 x = 8 * 26 reject since perfect square is not possible . if we take 71 , the pair is 69 and 71 , meaning x = 35 . 8 x = 8 * 35 reject since perfect square is not possible . i tried each option and the possibilities and then got lost . then , it occurred to me that i was only checking 2 - digit integers . what about 3 - digits ? starting with option a , only 2 - digit odd integer whose sum is 2 is 101 . if we take 101 , the pair is 99 and 101 , meaning x = 50 . 8 x = 8 * 50 = 400 root of 400 = 20 which is indeed equal to 9 + 9 + 1 + 1 . answer ( a ) ." + }, + { + "Answer": 7, + "Options": "a ) 3 , b ) 2 , c ) 9 , d ) 7 , e ) 1", + "Correct": "d", + "Explanation": "f ( x ) = 2 x + 3 g ( x ) = ( x - 3 ) / 2 gof ( x ) = 2 x + 3 \u2212 32 = x 2 x + 3 \u2212 32 = x gogof ( x ) = x \u2212 32 x \u2212 32 fogogof ( x ) = 2 ( x \u2212 32 ) + 32 ( x \u2212 32 ) + 3 = 2 x \u2212 6 + 622 x \u2212 6 + 62 = x fofogogof ( x ) = 2 x + 3 this means , when we apply two times g ( x ) and two time f ( x ) on f ( x ) we get f ( x ) . this pattern continues , hence the answer is option ( d ) ." + }, + { + "Answer": 3108, + "Options": "a ) 1208 , b ) 3108 , c ) 241 , d ) 217 , e ) 3147", + "Correct": "b", + "Explanation": "\"on dividing 3105 by 21 , we get 18 as remainder . \uf05c number to be added to 3105 = ( 21 - 18 ) - 3 . hence , required number = 3105 + 3 = 3108 . answer b 3108\"" + }, + { + "Answer": 30, + "Options": "a ) 21 , b ) 24 , c ) 27 , d ) 30 , e ) 33", + "Correct": "d", + "Explanation": "p = 3 q so q = p / 3 p + 11 = 2 ( q + 11 ) = 2 ( p / 3 + 11 ) p / 3 = 11 p = 33 three years ago , p was 30 . the answer is d ." + }, + { + "Answer": 6, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "d", + "Explanation": "\"the class borrowed a total of 40 * 2 = 80 books . the 27 students who borrowed 0 , 1 , or 2 books borrowed a total of 12 + 13 * 2 = 38 . to maximize the number of books borrowed by 1 student , let ' s assume that 12 students borrowed 3 books and 1 student borrowed the rest . 80 - 38 - 3 * 12 = 6 the maximum number of books borrowed by any student is 6 . the answer is d .\"" + }, + { + "Answer": 1, + "Options": "a ) 0 , b ) 1 , c ) 4 , d ) 5 , e ) 6", + "Correct": "b", + "Explanation": "\"t = the number of cups of tea c = the number of cups of hot chocolate t + c = 26 t - c = 10 - > t = 18 . c = 8 . mo drinks 3 cups of tea a day then number of days that are not rainy = 18 / 3 = 6 so number of rainy days = 7 - 6 = 1 b is the answer .\"" + }, + { + "Answer": 36.5, + "Options": "a ) 36.7 , b ) 36.4 , c ) 36.5 , d ) 36.9 , e ) 36.3", + "Correct": "b", + "Explanation": "\"correct sum = ( 36 * 50 + 45 - 23 ) = 1822 . correct mean = 1822 / 50 = 36.4 answer : b\"" + }, + { + "Answer": 50000, + "Options": "a ) rs . 500000 , b ) rs . 50000 , c ) rs . 5000 , d ) rs . 15000 , e ) rs . 6000", + "Correct": "b", + "Explanation": "let x amount he has then 20 % of 25 % of 30 % of x = 750 so x = 50000 answer : b" + }, + { + "Answer": 44, + "Options": "a ) 0.33 , b ) 0.44 , c ) 0.55 , d ) 44 , e ) 55", + "Correct": "d", + "Explanation": "\"main thing to remember is answer is asked in cents , however when we calculate , it comes up as 0.44 $ just multiply by 100 , answer r = 44 . d\"" + }, + { + "Answer": 98.2, + "Options": "a ) 79 , b ) 99 , c ) 88 , d ) 88 , e ) 98", + "Correct": "e", + "Explanation": "\"average = ( 96 + 98 + 99 + 100 + 98 ) / 5 = 491 / 5 = 98 . answer : e\"" + }, + { + "Answer": 0.1, + "Options": "a ) 7 / 16 , b ) 7 / 15 , c ) 10 / 21 , d ) 17 / 35 , e ) 1 / 10", + "Correct": "e", + "Explanation": "\"let the total # of cups be 10 . # of small cups sold 3 / 5 * 10 = 6 ; # of large cups sold 10 - 6 = 4 ; let the price of small cup be $ 6 , then the price of larges cup would be 1 / 6 * 6 = $ 1 ; revenue from small cups : 6 * $ 6 = $ 36 ; revenue from large cups cups : 4 * $ 1 = $ 4 ; fraction of total revenue from large cups : 4 / ( 36 + 4 ) = 1 / 10 . answer : e .\"" + }, + { + "Answer": 0.13333333333333341, + "Options": "a ) 2 / 15 , b ) 3 / 5 , c ) 1 / 6 , d ) 1 / 7 , e ) none of these", + "Correct": "a", + "Explanation": "explanation : 2 / 3 = . 66 , 3 / 4 = . 75 , 4 / 5 = . 8 and 5 / 7 = . 71 so biggest is 4 / 5 and smallest is 2 / 3 their difference is 4 / 5 - 2 / 3 = 2 / 15 option a" + }, + { + "Answer": 0.3125, + "Options": "a ) 1 / 4 , b ) 4 / 15 , c ) 1 / 3 , d ) 5 / 16 , e ) 4 / 5", + "Correct": "d", + "Explanation": "\"let avg for 11 mos . = 10 therefore , dec = 50 year total = 11 * 10 + 50 = 160 answer = 50 / 160 = 5 / 16 = d\"" + }, + { + "Answer": 0.3333333333333333, + "Options": "a ) 3 , b ) 6 , c ) 1 / 3 , d ) 1 / 2 , e ) 1 / 6", + "Correct": "c", + "Explanation": "\"if line l divides the rectangle into two identical quadrilaterals , then it must pass through the center ( 3 , 1 ) . the slope of a line passing through ( 0,0 ) and ( 3 , 1 ) is 1 / 3 . the answer is c .\"" + }, + { + "Answer": 720, + "Options": "a ) $ 640 , b ) $ 680 , c ) $ 720 , d ) $ 760 , e ) $ 800", + "Correct": "c", + "Explanation": "\"90 % remains to be paid so the remaining amount is 9 * 80 = $ 720 . the answer is c .\"" + }, + { + "Answer": 5, + "Options": "a ) 6 , b ) 5 , c ) 4 , d ) 3 , e ) 2", + "Correct": "b", + "Explanation": "an easy way to solve this question will be just to mark the points on the coordinate plane . you ' ll see that the distance between the center ( 2 , 1 ) and the point inside the circle ( - 2 , 1 ) is 4 units ( both points are on y = 1 line so the distance will simply be 2 - ( - 2 ) = 4 ) so the radius must be more than 4 units . the distance between the center ( 2,1 ) and the point outside the circle ( 2 , - 5 ) is 6 units ( both points are on x = 2 line so the distance will simply be 1 - ( - 5 ) = 6 ) so the radius must be less than 6 units , which implies 4 < r < 6 , thus as r is an integer then r = 5 . answer : b ." + }, + { + "Answer": 5, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "c", + "Explanation": "\"16 / 4 = 4 16 / 16 = 1 4 + 1 = 5 k = 5 answer : c\"" + }, + { + "Answer": 80, + "Options": "a ) 60 , b ) 80 , c ) 40 , d ) 120 , e ) 160", + "Correct": "b", + "Explanation": "\"( 1 + 1 / 8 ) x - ( 1 - 1 / 4 ) x = 30 ( 9 / 8 ) x - ( 3 / 4 ) x = 30 x = 80 = t answer : b\"" + }, + { + "Answer": 70, + "Options": "a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80", + "Correct": "d", + "Explanation": "\"according to order of operations , inner brackets first . hence | 4 - 8 ( 3 - 12 ) | - | 5 - 11 | = | 4 - 8 * ( - 9 ) | - | 5 - 11 | according to order of operations , multiplication within absolute value signs ( which may be considered as brackets when it comes to order of operations ) next . hence = | 4 + 72 | - | 5 - 11 | = | 76 | - | - 6 | = 76 - 6 = 70 correct answer d ) 70\"" + }, + { + "Answer": 354.2, + "Options": "a ) a ) 354 , b ) b ) 175 , c ) c ) 225 , d ) d ) 375 , e ) e ) 524", + "Correct": "a", + "Explanation": "\"explanation : ? = ( 168 x 1265 / 100 ) \u00f7 6 = 212520 / 600 = 354 answer : option a\"" + }, + { + "Answer": 1050, + "Options": "a ) 650 , b ) 750 , c ) 850 , d ) 950 , e ) 1050", + "Correct": "e", + "Explanation": "\"the number of ways to choose two teams is 15 c 2 = 15 * 14 / 2 = 105 the total number of games in the season is 10 * 105 = 1050 . the answer is e .\"" + }, + { + "Answer": 3, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "b", + "Explanation": "explanation : treat 3 : 12 as 3 / 12 and x : 16 as x / 16 , treat : : as = so we get 3 / 12 = x / 16 = > 12 x = 48 = > x = 4 option b" + }, + { + "Answer": 270, + "Options": "a ) 30 , b ) 45 , c ) 270 , d ) 90 , e ) 135", + "Correct": "c", + "Explanation": "\"we can start with the known quantity and then go on to find the others . shiny igneous ricks are 30 . these are ( 1 / 3 ) of total igneous rocks . ( 1 / 3 ) * total igneous rocks = 30 total igneous rocks = 30 * ( 3 ) = 90 total sedimentary rocks = 2 * total igneous rocks = 2 * 90 = 180 total number of rocks = 90 + 180 = 270 answer ( c )\"" + }, + { + "Answer": 30, + "Options": "a ) 22 , b ) 23 , c ) 24 , d ) 30 , e ) 28", + "Correct": "d", + "Explanation": "\"let hens be x and cows be y now , feet : x * 2 + y * 4 = 140 heads : x * 1 + y * 1 = 50 implies , 2 x + 4 y = 140 and x + y = 50 solving these two equations , we get x = 30 and y = 20 therefore , hens are 26 . answer : d\"" + }, + { + "Answer": 19, + "Options": "a ) 12 , b ) 14 , c ) 13 , d ) 15 , e ) 19", + "Correct": "e", + "Explanation": "\"let p = 6 , q = 7 then 2 * 6 + 7 = 19 so 2 p + q = 19 . answer : e\"" + }, + { + "Answer": 2999.9999999999995, + "Options": "a ) $ 3000 , b ) $ 3500 , c ) $ 4000 , d ) $ 4200 , e ) $ 4500", + "Correct": "a", + "Explanation": "\"explanatory answer let the profit made during the year be $ 3 x therefore , $ x would have been shared equally and the remaining $ 2 x would have been shared in the ratio 8 : 2 . i . e . , 80 % of 2 x would go to mary and 20 % of 2 x would go to mike . hence , mary would get ( 80 - 20 ) % of 2 x more than mike or 60 % of 2 x = $ 1200 i . e . , ( 60 / 100 ) * 2 x = 1200 or 2 x = 2000 . hence , the profit made by the company during the year $ 3 x = $ 3000 . answer : a\"" + }, + { + "Answer": 2000, + "Options": "a ) 3000 , b ) 2000 , c ) 4000 , d ) 2500 , e ) 3500", + "Correct": "b", + "Explanation": "explanatory answer this question is a word problem in linear equations . the problem is solved by framing two linear equations from the information given in the question and solving them . let ' s ' be the number of small slices and ' b ' the number of large slices sold on that night . therefore , s + b = 5000 . . . eqn ( 1 ) each small slice was sold for rs . 150 . therefore , ' s ' small slices would have fetched rs . 150 s . each large slice was sold for rs . 250 . therefore , ' b ' large slices would have fetched rs . 250 b . total value of sale = 150 s + 250 b = 10 , 50000 ( note the left hand side is in rupees and hence we have to convert right hand also to rupees from lakhs of rupees ) or 150 s + 250 b = 10 , 50000 . . . eqn ( 2 ) multiplying equation ( 1 ) by 150 , we get 150 s + 150 b = 7 , 50000 . . . eqn ( 3 ) subtracting eqn ( 3 ) from eqn ( 2 ) , we get 100 b = 300000 or b = 3000 we know that s + b = 5000 so , s = 5000 - b = 5000 - 3000 = 2000 . 2000 small slices were sold . answer b" + }, + { + "Answer": 236.61904761904762, + "Options": "a ) 380 times , b ) 236 times , c ) 382 times , d ) 392 times , e ) 482 times", + "Correct": "b", + "Explanation": "\"time difference is 1 hr , 22 min , 49 sec = 4969 sec . so , light glows floor ( 4969 / 21 ) = 236 times . answer : b\"" + }, + { + "Answer": 33, + "Options": "a ) 42 , b ) 38 , c ) 28 , d ) 29 , e ) 11", + "Correct": "a", + "Explanation": "answer : a" + }, + { + "Answer": 0.08333333333333331, + "Options": "a ) 0 , b ) 1 / 36 , c ) 1 / 12 , d ) 1 / 6 , e ) 1 / 4", + "Correct": "c", + "Explanation": "say canister c has a capacity of 6 liters . it ' s half full , thus there can be poured 3 liters of water . canister b is 12 liters and there are 4 liters of water . we can pour 3 liters from d to c and 1 liter will still be left in d , which is 1 / 12 of its total capacity . answer : c ." + }, + { + "Answer": 3700, + "Options": "a ) 3700 , b ) 3890 , c ) 88798 , d ) 2789 , e ) 2891", + "Correct": "a", + "Explanation": "\"explanation : manager ' s monthly salary rs . ( 1700 * 21 - 1600 * 20 ) = rs . 3700 . answer : a ) 3700\"" + }, + { + "Answer": 190000.00000000003, + "Options": "a ) $ 10900 , b ) $ 19000 , c ) $ 190000 , d ) $ 1900 , e ) none", + "Correct": "c", + "Explanation": "\"[ 1 / ( x 1 / y 1 + x 2 / y 2 + x 3 / y 3 ) ] * total amount = balance amount [ 1 - ( 1 / 5 + 1 / 10 + 3 / 5 ) } * total salary = $ 19000 , = [ 1 - 9 / 10 ] * total salary = $ 19000 , total salary = $ 19000 * 10 = $ 190000 , correct answer ( c )\"" + }, + { + "Answer": 69.1, + "Options": "a ) 35.67 % , b ) 64.75 % , c ) 68.57 % , d ) 69.10 % , e ) none of these", + "Correct": "d", + "Explanation": "\"girls = 900 , boys = 1100 passed = ( 30 % of 1100 ) + ( 32 % of 900 ) = 330 + 288 = 618 failed = 2000 - 618 = 1382 failed % = [ ( 1382 / 2000 ) x 100 ] % = 69.1 % . answer : d\"" + }, + { + "Answer": 1.888888888888889, + "Options": "a ) 1 , b ) 4 / 3 , c ) 17 / 9 , d ) 18 / 5 , e ) 4", + "Correct": "c", + "Explanation": "\"we have two equations : 2 x + y = 7 x + 2 y = 10 notice that something nice happens when we add them . we get : 3 x + 3 y = 17 divide both sides by 3 to get : x + y = 17 / 3 so , ( x + y ) / 3 = 17 / 9 answer : c\"" + }, + { + "Answer": 18.75, + "Options": "a ) 22.5 , b ) 20.0 , c ) 18.75 , d ) 12.5 , e ) 10.0", + "Correct": "c", + "Explanation": "r . p . = $ 25.00 sale % = 25 s . p . = r . p . * ( 1 - ( sale % / 100 ) ) = 25 * ( 1 - ( 25 / 100 ) ) = 18.75 answer : c" + }, + { + "Answer": 227.27272727272728, + "Options": "a ) s . 227 , b ) s . 287 , c ) s . 297 , d ) s . 300 , e ) s . 380", + "Correct": "a", + "Explanation": "\"let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 500 but x = 120 % of y = 120 y / 100 = 12 y / 10 \u2234 12 y / 10 + y = 500 \u21d2 y [ 12 / 10 + 1 ] = 500 \u21d2 22 y / 10 = 500 \u21d2 22 y = 5000 \u21d2 y = 5000 / 22 = rs . 227.77 a )\"" + }, + { + "Answer": 19, + "Options": "a ) 11 , b ) 10 , c ) 18 , d ) 19 , e ) 21", + "Correct": "d", + "Explanation": "\"explanation : numbers divisible by 2 are 12,14 , 16,18 , 20,22 , 24,26 , average = ( 12 + 14 + 16 + 18 + 20 + 22 + 24 + 26 , ) / 8 = 152 / 8 = 19 answer : d\"" + }, + { + "Answer": 84, + "Options": "a ) 22 , b ) 84 , c ) 28 , d ) 76 , e ) 21", + "Correct": "b", + "Explanation": "\"explanation : the least number of trees that are required = lcm ( 7 , 6,4 ) = 84 . answer : b\"" + }, + { + "Answer": 23, + "Options": "a ) 23 , b ) 20 , c ) 11 , d ) 5 , e ) 2", + "Correct": "a", + "Explanation": "\"soln : { 22 } + { 20 } = 22 * { 20 } + { 20 } = 23 * { 20 } answer : a\"" + }, + { + "Answer": 400, + "Options": "a ) rs . 300 , b ) rs . 200 , c ) rs . 240 , d ) rs . 400 , e ) none of these", + "Correct": "d", + "Explanation": "\"z share = z , y = 1.2 z x = 1.25 \u00e3 \u2014 1.2 z , x + y + z = 1480 ( 1.25 \u00e3 \u2014 1.2 + 1.2 + 1 ) z = 1480 3.7 z = 1480 , z = 400 answer : . d\"" + }, + { + "Answer": 6, + "Options": "a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8", + "Correct": "d", + "Explanation": "\"on dividing 724946 by 10 we get the remainder 6 , so 6 should be subtracted d\"" + }, + { + "Answer": 84, + "Options": "a ) 500 % , b ) 250 % , c ) 500 / 3 % , d ) 84 % , e ) 60 %", + "Correct": "d", + "Explanation": "\"z = 100 ; y = 70 so x = 84 x as % of z = 84 / 100 * 100 = > 84 % answer will be ( d )\"" + }, + { + "Answer": 12, + "Options": "a ) 4 liters , b ) 8 liters , c ) 10 liters , d ) 12 liters , e ) 12.5 liters", + "Correct": "d", + "Explanation": "\"number of liters of water in 180 liters of the mixture = 20 % of 120 = 20 / 100 * 180 = 36 liters . p liters of water added to the mixture to make water 25 % of the new mixture . total amount of water becomes ( 36 + p ) and total volume of mixture is ( 180 + p ) . ( 36 + p ) = 25 / 100 * ( 180 + p ) 96 + 4 p = 180 + p p = 12 liters . answer : d\"" + }, + { + "Answer": 7070, + "Options": "a ) 21 , b ) 7000.0707 , c ) 7777 , d ) 7014 , e ) 7000.0077", + "Correct": "b", + "Explanation": "\"required sum = 7000 + 0.0700 + 0.0007 = 7000.0707 answer is b\"" + }, + { + "Answer": 18, + "Options": "a ) a ) 23 , b ) b ) 21 , c ) c ) 18 , d ) d ) 56 , e ) e ) 12", + "Correct": "c", + "Explanation": "\"let the total number of workers be x . then , 8000 x = ( 12000 * 6 ) + 6000 ( x - 6 ) = > 2000 x = 36000 = x = 18 . answer : c\"" + }, + { + "Answer": 0.4666666666666667, + "Options": "a ) 3 / 5 , b ) 4 / 15 , c ) 7 / 15 , d ) 8 / 15 , e ) 17 / 30", + "Correct": "c", + "Explanation": "the fraction of birds that are male robins is ( 2 / 3 ) ( 2 / 5 ) = 4 / 15 . the fraction of birds that are male bluejays is ( 1 / 3 ) ( 3 / 5 ) = 1 / 5 . the total fraction of male birds is 4 / 15 + 1 / 5 = 7 / 15 . the answer is c ." + }, + { + "Answer": 1400, + "Options": "a ) 2261 , b ) 2888 , c ) 1400 , d ) 2699 , e ) 2771", + "Correct": "c", + "Explanation": "\"p - - - 10 - - - - 700 p - - - 5 - - - - - 350 3 p - - - 5 - - - - - 1050 - - - - - - = > 1400 answer : c\"" + }, + { + "Answer": 999.9999999999998, + "Options": "a ) 1200 , b ) 3000 , c ) 1000 , d ) 3600 , e ) 2400", + "Correct": "c", + "Explanation": "\"let the additional invested amount for 8 % interest be x ; equation will be ; 2000 + 0.05 * 2000 + x + 0.08 x = 2000 + x + 0.06 ( 2000 + x ) 0.05 * 2000 + 0.08 x = 0.06 x + 0.06 * 2000 0.02 x = 2000 ( 0.06 - 0.05 ) x = 2000 * 0.01 / 0.02 = 1000 ans : ` ` c ' '\"" + }, + { + "Answer": 34, + "Options": "a ) 17 , b ) 18 , c ) 34 , d ) 35 , e ) 36", + "Correct": "c", + "Explanation": "( ( 1 ^ ( m + 1 ) ) / ( 5 ^ ( m + 1 ) ) ) ( ( 1 ^ 18 ) / ( 4 ^ 18 ) ) = 1 / ( 2 ( 10 ) ^ 35 ) ( ( 1 / 5 ) ^ ( m + 1 ) ) * ( ( 1 / 2 ) ^ 36 ) = 1 / ( 2 * ( 2 * 5 ) ^ 35 ) ) 2 ^ 36 will cancel out , since 1 can be written as 1 ^ 35 , so ( 1 / 5 ) ^ ( m + 1 ) = ( 1 / 5 ) ^ 35 ( ( 1 / 5 ) ^ ( m + 1 ) ) * ( ( 1 / 2 ) ^ 36 ) = 1 / [ ( 2 ^ 36 ) * ( 5 ^ 35 ) ] so , m = 34 answer c" + }, + { + "Answer": 122, + "Options": "a ) 123 , b ) 267 , c ) 277 , d ) 122 , e ) 120", + "Correct": "d", + "Explanation": "\"let xx be the number he chose , then 2 \u00e2 \u2039 \u2026 x \u00e2 \u02c6 \u2019 138 = 106 x = 122 answer : d\"" + }, + { + "Answer": 58, + "Options": "a ) 50 , b ) 56 , c ) 58 , d ) 62 , e ) 66", + "Correct": "c", + "Explanation": "\"given that , total average q sold is 66 , male / female = 1 / 2 and female average is 70 . average of male members isx . ( 70 * f + x * m ) / ( m + f ) = 66 - > solving this equation after substituting 2 m = f , x = 58 . ans c .\"" + }, + { + "Answer": 4000, + "Options": "a ) 196 , b ) 1996 , c ) 2996 , d ) 3996 , e ) 6000", + "Correct": "d", + "Explanation": "explanation : place value = local value face value = absolute value the place value of 4 in 564823 is 4 x 1000 = 4000 the face value of 4 in 564823 is nothing but 4 . = > 4000 - 4 = 3996 answer : option d" + }, + { + "Answer": 5.999999999999999, + "Options": "a ) 6 , b ) 6.6 , c ) 60 , d ) 100 , e ) 110", + "Correct": "a", + "Explanation": "i think the correct answer is a . machine x produces at a speed of x sp / hour and b at a speed of b sp / hour . so , 660 / x = ( 660 / b ) + 10 and x = 1,1 x - - - > 1,1 * 660 = 660 + 11 x - - - > a = 6 , so answer a is correct" + }, + { + "Answer": 30, + "Options": "a ) 11 , b ) 66 , c ) 28 , d ) 30 , e ) 99", + "Correct": "d", + "Explanation": "\"let ' s take the present age of the elder person = x and the present age of the younger person = x \u2013 16 ( x \u2013 6 ) = 3 ( x - 16 - 6 ) = > x \u2013 6 = 3 x \u2013 66 = > 2 x = 60 = > x = 60 / 2 = 30 answer : d\"" + }, + { + "Answer": 19, + "Options": "a ) 19 , b ) 14 , c ) 8 , d ) 9.5 , e ) none of these", + "Correct": "a", + "Explanation": "answer : a ( 5 x 10 - 3 x 4 ) / 2 = 19" + }, + { + "Answer": 12, + "Options": "a ) 40 , b ) 44 , c ) 12 , d ) 88 , e ) 48", + "Correct": "c", + "Explanation": "\"according to the given conditions x + y = 22 and x ^ 2 + y ^ 2 = 460 now ( x + y ) ^ 2 = x ^ 2 + y ^ 2 + 2 xy so 22 ^ 2 = 460 + 2 xy so xy = 24 / 2 = 12 answer : c\"" + }, + { + "Answer": 25, + "Options": "a ) 47 , b ) 25 , c ) 37 , d ) 33 , e ) 29", + "Correct": "b", + "Explanation": "# of terms = ( n - 1 / 2 ) + 1 { ( last term - first term ) / 2 + 1 | sum = ( 1 + n ) / 2 * # of terms = ( n + 1 ) ^ 2 / 4 = 169 n + 1 = 13 * 2 n + 1 = 26 n = 25 . answer : b" + }, + { + "Answer": 35, + "Options": "a ) a ) 41 , b ) b ) 38 , c ) c ) 35 , d ) d ) 29 , e ) e ) 28", + "Correct": "c", + "Explanation": "the answer shud be 38 . ( 50 - 3 - 4 - 5 = 38 ) yes , if you go the 50 - 3 way , then it will be 38 . if instead you go the 50 - 4 way ( which they have suggested ) , the answer will be 35 . as i said , there is ambiguity here . answer is c" + }, + { + "Answer": 7, + "Options": "a ) 13 , b ) 10 , c ) 9 , d ) 8 , e ) 7", + "Correct": "e", + "Explanation": "a u b u c = a + b + c - ab - bc - ac + abc 68 = 21 + 26 + 34 - ab - bc - ac + 3 = > ab + bc + ac = 16 exactly two classes = ab + bc + ac - 3 abc = 16 - 3 * 3 = 7 hence e" + }, + { + "Answer": 82.26086956521739, + "Options": "a ) 83 , b ) 56 , c ) 34 , d ) 12 , e ) 26", + "Correct": "a", + "Explanation": "lets say the family income is 100 in may , lee earned 80 family income is 20 in june , lee earned 20 % more than may , so it is ( 80 + 20 * 80 / 100 = 96 ) family income is same 20 in june lee ' s income percent is 96 * 100 / 116 ~ 83 ans is a" + }, + { + "Answer": 2, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "b", + "Explanation": "29 / 4 = 7 . xxx 87 / 5 = 17 . xxx so we need to find prime numbers between 7 ( exclusive ) - 16 ( inclusive ) there are 2 prime numbers 1113 hence answer will be ( b ) 2 b" + }, + { + "Answer": 19520, + "Options": "a ) $ 12436 , b ) $ 13344 , c ) $ 71234 , d ) $ 15736 , e ) $ 19403", + "Correct": "e", + "Explanation": "1 st - 40,000 . 2 nd - 0.8 * 40,000 = 32,000 3 rd - 0.8 * 32,000 = 25,600 4 th - 0.8 * 25,600 = ~ 20,480 range = 40,000 - 20,480 = 19520 answer : e ." + }, + { + "Answer": 11, + "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12", + "Correct": "d", + "Explanation": "three years ago : a : b : c = 1 : 2 : 3 let a = 1 x , b = 2 x , and c = 3 x . today : ( x + 3 ) + ( 2 x + 3 ) + ( 3 x + 3 ) = 57 x = 8 so the present age of a is x + 3 = 11 the answer is d ." + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "c", + "Explanation": "\"1,1 , 2,1 , 2,3 , 1,2 , 3,4 , 1,2 , __ ? looking at the series 1 12 123 1234 12 ( 3 ) 45 so the answer is 3 . answer : c\"" + }, + { + "Answer": 18, + "Options": "a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19", + "Correct": "d", + "Explanation": "\"explanation : let the number of persons be n \u00e2 \u02c6 \u00b4 total handshakes = nc 2 = 153 n ( n - 1 ) / 2 = 153 \u00e2 \u02c6 \u00b4 n = 18 answer : option d\"" + }, + { + "Answer": 0.5, + "Options": "a ) 1 / 2 , b ) 1 , c ) 2 , d ) 5 / 2 , e ) 4", + "Correct": "a", + "Explanation": "\"since ( m , n ) and ( m + 2 , n + k ) are two points on the line with the equation x = 2 y + 5 they should satisfy m = 2 n + 5 and m + 1 = 2 * ( n + k ) + 5 . by 1 st equation we have m - 2 n = 5 and by 2 nd equation m - 2 n = 2 k + 4 - - - > 5 = 2 k + 4 - - - > k = 1 / 2 . the answer is , therefore , ( a ) .\"" + }, + { + "Answer": 14, + "Options": "a ) 6 , b ) 12 , c ) 14 , d ) 18 , e ) 20", + "Correct": "c", + "Explanation": "\"solution required numbers is divisible by 72 as well as by 112 , if it is divisible by their lcm , which is 1008 . now , 1008 when divided by 72 , gives quotient = 14 . required number = 14 . answer c\"" + }, + { + "Answer": 145, + "Options": "a ) 140 , b ) 143 , c ) 144 , d ) 145 , e ) 146", + "Correct": "d", + "Explanation": "\"explanation : let the number = x , then , x - ( 3 / 5 ) x = 58 , = > ( 2 / 5 ) x = 58 = > 2 x = 58 * 5 , = > x = 145 answer : option d\"" + }, + { + "Answer": 24.16, + "Options": "a ) 25 , b ) 13 , c ) 17 , d ) 24 , e ) 19", + "Correct": "d", + "Explanation": "\"3 + 2 . ( 8 - 3 ) = 3 + 2 ( 5 ) , = 3 + 2 * 5 , = 3 + 10 , = 13 , correct answer : ( d )\"" + }, + { + "Answer": 360, + "Options": "a ) 300 , b ) 360 , c ) 400 , d ) 500 , e ) 575", + "Correct": "b", + "Explanation": "\"as per the question 200 = 2 a / 5 thus - a which is the total amount = 500 the amount thus left = 300 she then deposited 1 / 5 of 300 = 60 total amount in her account = 360 answer b\"" + }, + { + "Answer": 41, + "Options": "a ) 39 , b ) 40 , c ) 41 , d ) 42 , e ) 43", + "Correct": "c", + "Explanation": "\"9 / 7 * 32 = 41.1 the answer is c .\"" + }, + { + "Answer": 18.51851851851852, + "Options": "a ) 17.69 , b ) 14.85 , c ) 21.3 , d ) 16.5 , e ) 18.51", + "Correct": "e", + "Explanation": "\"1 ) cost of repairing = 13.5 ( for one year ) , therefore for 2 years it would be $ 27 . 2 ) cost of new pair which will last for 2 years is $ 32 . percentage change formula = ( final value - initial value ) / ( initial value ) * 100 . in this case the final value would be the price of new shoe initial value would be the cost of repairing the old shoe . i . e ( 32 - 27 ) / ( 27 ) * 100 = 18.51 % . ans is e\"" + }, + { + "Answer": 7, + "Options": "a ) - 14 , b ) 14 , c ) - 7 , d ) 7 , e ) 0", + "Correct": "d", + "Explanation": "explanation : x = y < = > 55 + 2 q = 4 q + 41 < = > 2 q = 14 < = > q = 7 . answer : d" + }, + { + "Answer": 225, + "Options": "a ) 200 km , b ) 212 km , c ) 224 km , d ) 230 km , e ) 256 km", + "Correct": "c", + "Explanation": "distance = speed x time let time taken to travel the first half = x hr then time taken to travel the second half = ( 10 - x ) hr distance covered in the the first half = 21 x distance covered in the the second half = 24 ( 10 - x ) but distance covered in the the first half = distance covered in the the second half = > 21 x = 24 ( 10 - x ) = > 21 x = 240 - 24 x = > 45 x = 240 = > 9 x = 48 = > 3 x = 16 \u21d2 x = 163 hence distance covered in the the first half = 21 x = 21 \u00d7 163 = 7 \u00d7 16 = 112 kmtotal distance = 2 \u00d7 112 = 224 km c" + }, + { + "Answer": 0.25, + "Options": "a ) 0 , b ) 1 / 4 , c ) 2 / 5 , d ) 1 / 2 , e ) 3 / 5", + "Correct": "b", + "Explanation": "we will have a negative product only if 1 or 2 are selected from set t . p ( negative product ) = 2 / 8 = 1 / 4 the answer is b ." + }, + { + "Answer": 2, + "Options": "a ) 1 , b ) 2 , c ) 0 , d ) 6 , e ) 7", + "Correct": "b", + "Explanation": "( 5 ! * 5 ! + 5 ! * 3 ! ) / 5 = 5 ! ( 5 ! + 3 ! ) / 5 = 120 ( 120 + 6 ) / 5 = 3024 units digit of the above product will be equal to 2 answer b" + }, + { + "Answer": 14, + "Options": "a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14", + "Correct": "e", + "Explanation": "\"since average price of a pencil = 2 \u2234 price of 75 pencils = 150 \u2234 price of 30 pens = ( 570 \u2013 150 ) = 360 \u2234 average price of a pen = 420 \u2044 60 = 14 answer e\"" + }, + { + "Answer": 30, + "Options": "a ) 30 m , b ) 72 m , c ) 80 m , d ) 82 m , e ) 84 m", + "Correct": "a", + "Explanation": "\"let the length of each train be x m . then , distance covered = 2 x m . relative speed = 42 - 36 = 6 km / hr . = 6 * 5 / 18 = 5 / 3 m / sec . 2 x / 36 = 5 / 3 = > x = 30 . answer : a\"" + }, + { + "Answer": 35, + "Options": "a ) 22 , b ) 21 , c ) 35 , d ) 37 , e ) 29", + "Correct": "c", + "Explanation": "\"explanation : lot the total number of workers be v then , 8 ooov = ( 16000 * 7 ) + 6000 ( v - 7 ) < = > 2000 v = 70000 < = > v = 35 answer : c ) 35\"" + }, + { + "Answer": 1, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "b", + "Explanation": "the equation that can be formed w is 13 x + 2 = 8 y + 5 . . 13 x - 3 = 8 y . . . as we can see x can take only odd values as the rhs will always be even . . also x can take values till 13 as 13 * 14 > 180 . . now we have to substitue x as 1 , 35 , 79 , 1113 . . . once we find 7 fitting in , any other value need not be checked as every 4 th value will give us answer so next value will be 15 . . ans 1 . . b" + }, + { + "Answer": 0.07272727272727272, + "Options": "a ) 1 / 11 , b ) 2 / 11 , c ) 2 / 33 , d ) 4 / 55 , e ) 5 / 66", + "Correct": "d", + "Explanation": "the average of the numbers is 6 the total number of ways to choose 2 cards from 11 cards is 11 c 2 = 55 . the ways to choose 2 cards with a sum less than the average are : { 1,2 } , { 1,3 } , { 1,4 } , { 2,3 } the probability is 4 / 55 the answer is d ." + }, + { + "Answer": 17, + "Options": "a ) 16 , b ) 18 , c ) 22 , d ) 17 , e ) 20", + "Correct": "d", + "Explanation": "\"by formula , ( a + b + c ) ^ 2 = a ^ 2 + b ^ 2 + c ^ 2 + 2 ( ab + bc + ca ) , since , a ^ 2 + b ^ 2 + c ^ 2 = 281 and ab + bc + ca = 4 , ( a + b + c ) ^ 2 = 281 + 2 ( 4 ) = 289 = 17 ^ 2 therefore : a + b + c = 17 answer : d\"" + }, + { + "Answer": 840, + "Options": "a ) 840 , b ) 600 , c ) 800 , d ) 1000 , e ) 900", + "Correct": "a", + "Explanation": "\"explanation : let their maximum marks be x . then , 25 % of x = 185 + 25 = > 25 / 100 x = 210 x = ( 210100 / 25 ) x = 840 . answer : a\"" + }, + { + "Answer": 29.25, + "Options": "a ) 29 , b ) 29.25 , c ) 31 , d ) 31.23 , e ) 32", + "Correct": "b", + "Explanation": "average of 9 = x 9 x = 8 * 3 + x * 2 x = 3.25 total = 9 * 3.25 = 29.25 b" + }, + { + "Answer": 200, + "Options": "a ) 200 m , b ) 300 m , c ) 270 m , d ) 160 m , e ) 150 m", + "Correct": "a", + "Explanation": "explanation : ratio of the speeds of a and b = 5 : 1 = 5 : 3 thus , in race of 5 m , a gains 2 m over b . 2 m are gained by a in a race of 5 m . 80 m will be gained by a in race of 5 / 2 x 80 m = 200 m winning post is 200 m away from the starting point . answer is a" + }, + { + "Answer": 16, + "Options": "a ) 15 % , b ) 16 % , c ) 0.125 % , d ) 0.2083 % , e ) none", + "Correct": "b", + "Explanation": "\"this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 480 / 5000 ) x 100 = 9.6 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 9.6 % x ( 100 / 60 ) = 16 % the correct answer is ( b ) .\"" + }, + { + "Answer": 500, + "Options": "a ) $ 450 , b ) $ 500 , c ) $ 600 , d ) $ 650 , e ) $ 750", + "Correct": "b", + "Explanation": "the average monthly salary of a factory worker is : $ 30000 / 15 = $ 2000 . the average monthly salary of an office worker is : $ 75000 / 30 = $ 2500 . the difference in average salary is : $ 2500 - $ 2000 = $ 500 . the answer is b ." + }, + { + "Answer": 10, + "Options": "a ) 20 , b ) 15 , c ) 10 , d ) 12 , e ) 25", + "Correct": "c", + "Explanation": "\"let the number of students who wrote the exam be x . total marks of students = 70 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 70 x - ( 5 * 50 ) = 90 ( x - 5 ) 200 = 20 x = > x = 10 answer : c\"" + }, + { + "Answer": 31, + "Options": "a ) 65 degrees , b ) 73 degrees , c ) 31 degrees , d ) 34 degrees , e ) 74 degrees", + "Correct": "c", + "Explanation": "\"m + tu + w + th = 4 * 48 = 192 tu + w + th + f = 4 * 46 = 184 m = 39 tu + w + th = 192 - 39 = 153 f = 184 \u2013 153 = 31 answer : c\"" + }, + { + "Answer": 14, + "Options": "a ) 21 years , b ) 14 years , c ) 16 years , d ) 18 years , e ) 26 years", + "Correct": "b", + "Explanation": "\"explanation : let ' s son age is x , then father age is x + 16 . = > 2 ( x + 2 ) = ( x + 16 + 2 ) = > 2 x + 4 = x + 18 = > x = 14 years option b\"" + }, + { + "Answer": 130, + "Options": "a ) 110 , b ) 120 , c ) 130 , d ) 140 , e ) 150", + "Correct": "c", + "Explanation": "1 ^ 3 + 3 - 2 = 2 , 2 ^ 3 + 3 - 1 = 10 , 3 ^ 3 + 3 - 0 = 30 , 4 ^ 3 + 3 + 1 = 68 , 5 ^ 3 + 3 + 2 = 130 answer : c" + }, + { + "Answer": 540, + "Options": "a ) 160 , b ) 165 , c ) 180 , d ) 190 , e ) 540", + "Correct": "e", + "Explanation": "answer : option ' e ' 600 - 60 = 540" + }, + { + "Answer": 100, + "Options": "a ) rs . 300 , b ) rs . 200 , c ) rs . 100 , d ) rs . 350 , e ) none of these", + "Correct": "c", + "Explanation": "z share = z , y = 1.2 z x = 1.25 \u00e3 \u2014 1.2 z , x + y + z = 740 ( 1.25 \u00e3 \u2014 1.2 + 1.2 + 1 ) z = 37 3.7 z = 370 , z = 100 answer : . c" + }, + { + "Answer": 14, + "Options": "a ) 14 , b ) 19 , c ) 11 , d ) 18 , e ) 13", + "Correct": "a", + "Explanation": "\"let the population of two villages be equal after p years then , 70000 - 1200 p = 42000 + 800 p 2000 p = 28000 p = 14 answer is a .\"" + }, + { + "Answer": 1730, + "Options": "a ) 545 , b ) 685 , c ) 865 , d ) 1730 , e ) 534", + "Correct": "d", + "Explanation": "\"let y x 24 = 173 x 240 then y = ( 173 x 240 ) / 24 = 173 x 10 = 1730 answer : d\"" + }, + { + "Answer": 54.44444444444444, + "Options": "a ) 45 % , b ) 48 % , c ) 54 % , d ) 58 % , e ) 65 %", + "Correct": "c", + "Explanation": "\"when the storm deposited 115 billion gallons , volume of water in the reservoir = 245 + 115 = 360 billion gallons if this is only 80 % of the capacity of the reservoir , the total capacity of the reservoir = 360 / 0.8 = 450 billion gallons therefore percentage of reservoir that was full before the storm = ( 245 / 450 ) * 100 = 54.4 % option c\"" + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 18 , c ) 10 , d ) 99 , e ) 38", + "Correct": "a", + "Explanation": "let x = the youngest child . each of the other four children will then be x + 2 , x + 4 , x + 6 , x + 8 . we know that the sum of their ages is 50 . so , x + ( x + 2 ) + ( x + 4 ) + ( x + 6 ) + ( x + 8 ) = 50 therefore the youngest child is 6 years old answer : a" + }, + { + "Answer": 0.1428571428571428, + "Options": "a ) 1 / 7 , b ) 4 / 7 , c ) 3 / 7 , d ) 16 / 49 , e ) 40 / 49", + "Correct": "a", + "Explanation": "\"the probability of drawing a pink gumball both times is the same . the probability that she drew two blue gumballs = 36 / 49 = ( 6 / 7 ) * ( 6 / 7 ) therefore probability that the next one she draws is pink = 1 / 7 option ( a )\"" + }, + { + "Answer": 740, + "Options": "a ) 237 , b ) 287 , c ) 197 , d ) 740 , e ) 720", + "Correct": "d", + "Explanation": "explanation : let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 370 ) = 2 + 2 ( extra ) = > 2 x - 740 = x = > x = 740 . answer : d" + }, + { + "Answer": 13, + "Options": "a ) 9 , b ) 11 , c ) 13 , d ) 15 , e ) 17", + "Correct": "c", + "Explanation": "\"( 2 to the power x ) - ( 2 to the power ( x - 2 ) ) = 3 ( 2 to the power 11 ) 2 ^ x - 2 ^ ( x - 2 ) = 3 . 2 ^ 11 hence x = 13 . answer is c\"" + }, + { + "Answer": 0.2, + "Options": "a ) 5 , b ) 4 , c ) 1 / 2 , d ) 1 / 5 , e ) 1 / 8", + "Correct": "d", + "Explanation": "if line l divides the rectangle into two identical quadrilaterals , then it must pass through the center ( 5 , 1 ) . the slope of a line passing through ( 0,0 ) and ( 5 , 1 ) is 1 / 5 . the answer is d ." + }, + { + "Answer": 77.7, + "Options": "a ) 77.7 , b ) 91.0 , c ) 88.0 , d ) 70.9 , e ) 71.2", + "Correct": "a", + "Explanation": "\"11 % of 70 = ( 70 * 0.11 ) = 7.7 11 % greater than 70 = 70 + 7.7 = 77.7 answer is clearly a .\"" + }, + { + "Answer": 0.28, + "Options": "a ) 0.28 , b ) 0.26 , c ) 1 , d ) 0 , e ) 2", + "Correct": "a", + "Explanation": "explanation : 12.86 \u00d7 12.86 + 12.86 \u00d7 p + 0.14 \u00d7 0.14 = ( 12.86 ) 2 + 12.86 \u00d7 p + ( 0.14 ) 2 this can be written as ( 12.86 + 0.14 ) 2 = 132 , if 12.86 \u00d7 p = 2 \u00d7 12.86 \u00d7 0.14 i . e . , if p = 2 \u00d7 0.14 = 0.28 hence , p = 0.28 . answer : option a" + }, + { + "Answer": 40, + "Options": "a ) 36 , b ) 40 , c ) 99 , d ) 13 , e ) 12", + "Correct": "b", + "Explanation": "\"let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 . x / 2 = ( 83 - 63 ) = > x / 2 = 20 = > x = 40 . answer : b\"" + }, + { + "Answer": 12.519999999999982, + "Options": "a ) 16.16 % , b ) 15.15 % , c ) 14.14 % , d ) 13.33 % , e ) 12.52 %", + "Correct": "e", + "Explanation": "( 100 % + 8 % ) * ( 100 % - 19 % ) = 1.08 * . 81 = 0.8748 1 - 0.8748 = 12.52 % lost = - 12.52 % the answer is e the organization has lost 12.52 % of its total volunteers from fall to spring ." + }, + { + "Answer": 500, + "Options": "a ) 8 , b ) 13 , c ) 28 , d ) 6 , e ) 2", + "Correct": "b", + "Explanation": "b" + }, + { + "Answer": 120, + "Options": "a ) $ 115 , b ) $ 120 , c ) $ 125 , d ) $ 130 , e ) $ 135", + "Correct": "b", + "Explanation": "\"let the price of the meal be x . after a 10 % sales tax addition , the price is 1.1 * x after a 20 % tip on this amount , the total is 1.2 * 1.1 * x = 1.32 x 1.32 x = 158.40 x = 120 the correct answer is b .\"" + }, + { + "Answer": 1, + "Options": "a ) 1 / 2 , b ) 1 , c ) 2 , d ) 5 / 2 , e ) 4", + "Correct": "b", + "Explanation": "\"since ( m , n ) and ( m + 2 , n + k ) are two points on the line with the equation x = 2 y + 5 they should satisfy m = 2 n + 3 and m + 2 = 2 * ( n + k ) + 3 . by 1 st equation we have m - 2 n = 3 and by 2 nd equation m - 2 n = 2 k + 1 - - - > 3 = 2 k + 1 - - - > k = 1 . the answer is , therefore , ( b ) .\"" + }, + { + "Answer": 24.999999999999645, + "Options": "a ) 96 , b ) 75 , c ) 48 , d ) 25 , e ) 12", + "Correct": "d", + "Explanation": "\"guys , one more simple funda . 5 / 2 = 2.5 now . 5 x 2 = 1 is the remainder 25 / 4 = 6.25 now . 25 x 4 = 1 is the remainder 32 / 5 = 6.4 now . 4 x 5 = 2 is the remainder given x / y = 96.2 and remainder is 5 so . 2 x y = 5 hence y = 25 ans d\"" + }, + { + "Answer": 64, + "Options": "a ) a ) 90 , b ) b ) 32 , c ) c ) 64 , d ) d ) 70 , e ) of these", + "Correct": "c", + "Explanation": "\"let the greater and the smaller number be g and s respectively . gs = 2048 g + s exceeds g - s by 64 i . e . , g + s - ( g - s ) = 64 i . e . , 2 s = 64 = > s = 32 . g = 2048 / s = 64 . answer : c\"" + }, + { + "Answer": 75, + "Options": "a ) 74 , b ) m = 75 , c ) m = 175 , d ) m = 680 , e ) 690", + "Correct": "b", + "Explanation": "\"i solved this question by plugging in numbers from the answer choices . a . ) 74 starting with answer choice a , i immediately eliminated it because 74 is not even divisible by 5 . b . ) 75 i divide 75 / 5 and get 15 as an answer . i divide 75 / 34 and get a remainder of 7 . 15 - 7 = 8 so i know the correct answer isb\"" + }, + { + "Answer": 4, + "Options": "a ) 2 pm , b ) 9 pm , c ) 3 pm , d ) 4 pm , e ) 6 pm", + "Correct": "d", + "Explanation": "\"a day has 24 hrs . assume x hours have passed . remaining time is ( 24 - x ) 24 \u2212 x = 1 / 2 x \u21d2 x = 16 time is 4 pm answer : d\"" + }, + { + "Answer": 345600, + "Options": "a ) 32,300 , b ) 172,800 , c ) 345,600 , d ) 338,200 , e ) 259,200", + "Correct": "c", + "Explanation": "\"every 2 seconds , 8 persons are added ( 10 - 2 ) . every second 4 persons are added . in a day 24 hrs = 24 * 60 minutes = 24 * 60 * 60 = 86400 seconds . 86400 * 4 = 345600 option c\"" + }, + { + "Answer": 280, + "Options": "a ) $ 270 , b ) $ 280 , c ) $ 290 , d ) $ 300 , e ) $ 310", + "Correct": "b", + "Explanation": "\"1.2 n + n = 616 2.2 n = 616 n = 280 the answer is b .\"" + }, + { + "Answer": 25, + "Options": "a ) 25 % , b ) 28 % , c ) 33 % , d ) 40 % , e ) 50 %", + "Correct": "a", + "Explanation": "average score in first test be x so derby score = 0.5 x ( first test ) derby score = 1.5 ( 0.5 x ) ( second test ) = . 75 x so less than x by . 25 answer a 25 %" + }, + { + "Answer": 280, + "Options": "a ) $ 100 , b ) $ 150 , c ) $ 125 , d ) $ 280 , e ) $ 250", + "Correct": "d", + "Explanation": "a : ( b + c ) = 2 : 3 a ' s share = 700 * 2 / 5 = $ 280 answer is d" + }, + { + "Answer": 11, + "Options": "a ) 11 , b ) 14 , c ) 15 , d ) 18 , e ) 30", + "Correct": "a", + "Explanation": "within one standard deviation of the average age means 31 + / - 7 26 - - 31 - - 36 number of dif . ages - 26 27 28 29 30 31 32 33 34 35 36 total = 11 a" + }, + { + "Answer": 380, + "Options": "a ) $ 360 , b ) $ 380 , c ) $ 430 , d ) $ 290 , e ) $ 520", + "Correct": "b", + "Explanation": "official solution : ( b ) first , we need to add up the wages over the past 7 weeks : $ 406 + $ 413 + $ 420 + $ 436 + $ 395 + $ 410 + $ 360 = $ 2840 . to average $ 400 over 9 weeks , the salesman would need to earn : $ 400 \u00d7 9 = $ 3600 . subtract $ 2840 from $ 3600 to determine how much he would need to earn , in total , over the next 2 weeks to average $ 400 for the 9 weeks : $ 3600 \u2013 $ 2840 = $ 760 . dividing $ 760 by 2 will give us the amount he needs to earn on average over the next 2 weeks : $ 760 / 2 = $ 380 . the correct answer is choice ( b ) ." + }, + { + "Answer": 93, + "Options": "a ) 55 , b ) 60 , c ) 93 , d ) 82 , e ) 91", + "Correct": "c", + "Explanation": "\"let the number of correct responses be x then the number of incorrect responses = 100 - x according to question x - 2 ( 100 - x ) = 79 ( subtracting twice of incorrect from correct ) 3 x = 279 x = 93 answer : c\"" + }, + { + "Answer": 20, + "Options": "a ) 28 , b ) 20 , c ) 27 , d ) 29 , e ) 21", + "Correct": "b", + "Explanation": "\"average price per book = ( 1000 + 800 ) / ( 50 + 40 ) = 1800 / 90 = rs . 20 answer : b\"" + }, + { + "Answer": 19, + "Options": "a ) 8 , b ) 14 , c ) 15 , d ) 18 , e ) 19", + "Correct": "e", + "Explanation": "\"within one standard deviation of the average age means 31 + / - 7 24 - - 31 - - 38 number of dif . ages - 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 total = 19 e\"" + }, + { + "Answer": 2083.33, + "Options": "a ) $ 2100 , b ) $ 2222 , c ) $ 2320 , d ) $ 2083.33 , e ) $ 2183.33", + "Correct": "d", + "Explanation": "there is a property to solve such questions withcommon selling priceandcommon % gain and loss . such cases always result in a loss and . . . total % loss = ( common gain % or loss % / 10 ) ^ 2 hence here loss % = ( 20 / 10 ) ^ 2 = 4 % which means he recovered only 96 % of his investment which amount to a total revenue = 25000 + 25000 = 50000 i . e . 96 % of cost = 40000 therefore , 4 % of cost ( loss ) = $ 2083.33 answer : d" + }, + { + "Answer": 99.99, + "Options": "a ) 99.999 , b ) 100.2 , c ) 134 , d ) 99.99 , e ) 99.9", + "Correct": "d", + "Explanation": "required difference = 100 - 0.01 = 99.99 answer is d" + }, + { + "Answer": 23, + "Options": "a ) e = 21 , b ) e = 22 , c ) e = 23 , d ) 24 , e ) 27", + "Correct": "c", + "Explanation": "\"squaring on both sides , x ^ 2 + ( 1 / x ) ^ 2 + 2 ( x ) ( 1 / x ) = 5 ^ 2 x ^ 2 + ( 1 / x ) ^ 2 = 23 answer : c\"" + }, + { + "Answer": 0.25, + "Options": "a ) 1 / 32 , b ) 1 / 4 , c ) 1 , d ) 4 , e ) 5", + "Correct": "b", + "Explanation": "\"explanation : given , = > 4 a / 100 = 8 . = > a = 8 \u00d7 ( 100 / 4 ) = 200 . - - - - - - - - - ( i ) and , = > ( 8 / 100 ) \u00d7 b = 4 . = > b = 50 . - - - - - - - - - ( ii ) now , c = b / a ( from ( i ) and ( ii ) ) = > 50 / 200 . = > 1 / 4 . answer : b\"" + }, + { + "Answer": 50, + "Options": "a ) 50 kg , b ) 60 kg , c ) 61 kg , d ) 62 kg , e ) 91 kg", + "Correct": "a", + "Explanation": "let a = avg . wt . of additional 30 friends original total weight = ( 30 friends ) ( 30 kg avge ) = 900 kg ( 900 + 30 a ) / ( 30 + 30 ) = 40 kg avge a = 50 kg answer - a" + }, + { + "Answer": 30, + "Options": "a ) 10 , 40 , b ) 20 , 30 , c ) 35 , 15 , d ) 30 , 20 , e ) 15 , 35", + "Correct": "d", + "Explanation": "explanation : x + y = 50 2 x \u00e3 \u00a2 \u00e2 \u201a \u00ac \u00e2 \u20ac \u0153 2 y = 20 x = 30 y = 20 answer : d" + }, + { + "Answer": 34.99999999999999, + "Options": "a ) 35 , b ) 24 , c ) 17 , d ) 6 , e ) 5", + "Correct": "a", + "Explanation": "sol . ( b ) the sum of roots = a + b = 7 product of roots = ab = 8 now , a 2 + b 2 = ( a + b ) 2 - 2 ab = 49 - 14 = 35 answer a" + }, + { + "Answer": 16, + "Options": "a ) 12 , b ) 13 , c ) 14 , d ) 16 , e ) 19", + "Correct": "d", + "Explanation": "\"look at the below representation of the problem : steel chrome total a 4 2 30 > > no . of type a machines = 30 / 6 = 5 b 2 1 33 > > no . of type b machines = 33 / 3 = 11 so the answer is 16 i . e d . hope its clear .\"" + }, + { + "Answer": 125, + "Options": "a ) 75 , b ) 100 , c ) 125 , d ) 175 , e ) 225", + "Correct": "c", + "Explanation": "\"female = x male = 750 - x x / 2 + 750 - x / 4 = 1 / 3 * ( 750 ) = 250 x = 250 x / 2 = 125 is supposed to be the answer answer : c\"" + }, + { + "Answer": 180, + "Options": "a ) 188 , b ) 180 , c ) 156 , d ) 840 , e ) 121", + "Correct": "b", + "Explanation": "\"25 % of x = x / 4 ; 10 % of 500 = 10 / 100 * 500 = 50 given that , x / 4 = 50 - 5 = > x / 4 = 45 = > x = 180 . answer : b\"" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 10 , c ) 9 , d ) 0 , e ) 8", + "Correct": "a", + "Explanation": "explanation : e = ( x - 1 ) ( x - 6 ) ( x - 3 ) ( x - 4 ) + 10 e = ( x 2 - 7 x + 6 ) ( x 2 - 7 x + 12 ) + 10 let x 2 - 7 x + 6 = y e = y 2 + 6 y + 10 e = ( y + 3 ) 2 + 1 minimum value = 1 , when y = - 3 answer : a" + }, + { + "Answer": 32, + "Options": "a ) 76 sec , b ) 67 sec , c ) 98 sec , d ) 36 sec , e ) 32 sec", + "Correct": "e", + "Explanation": "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 200 + 120 = 320 m . time taken = 320 / 10 = 32 sec . answer : e" + }, + { + "Answer": 43, + "Options": "a ) 35 , b ) 30 , c ) 43 , d ) 60 , e ) 65", + "Correct": "c", + "Explanation": "\"a = 6 x , b = 6 z therefore ( 6 x . 10 + 6 z ) - ( 10 x + z ) = ( 6 - 1 ) ( 10 x + z ) = 5 . ( 10 x + z ) number should be divisible by 5 c\"" + }, + { + "Answer": 196, + "Options": "a ) 131 , b ) 135 , c ) 169 , d ) 196 , e ) 212", + "Correct": "d", + "Explanation": "\"lets say j is the weight of jack and s is the wt of his sister . if he loses 8 pounds , he s twice as heavy as his sister . j - 8 = 2 * s also , together they weight 290 pounds j + s = 290 solvong the 2 equation , we get j = 196 pounds ! d\"" + }, + { + "Answer": 4, + "Options": "a ) 123 , b ) 127 , c ) 235 , d ) 4 , e ) 505", + "Correct": "d", + "Explanation": "\"explanation : required number = h . c . f . of ( 1642 - 6 ) and ( 1856 - 4 ) = h . c . f . of 1636 and 1852 = 4 . answer : d\"" + }, + { + "Answer": 22, + "Options": "a ) 22 , b ) 20 , c ) 19 , d ) 16 , e ) 15", + "Correct": "a", + "Explanation": "\"marcella has 27 pairs of shoes and loses 9 shoes . to minimize the loss of identical pairs of shoes we want marcella to lose as many identical pairs as possible . this would yield 4 identical pairs and 1 additional shoe ( destroying 5 pairs of shoes ) . the 27 pairs of shoes minus the 5 ' destroyed ' pairs yields 22 pairs that still fulfill the requirements . answer : a\"" + }, + { + "Answer": 20, + "Options": "a ) 5 , b ) 4 , c ) 20 , d ) 25 , e ) 30", + "Correct": "c", + "Explanation": "since each desired number is divisible by 5 , so we must have 5 at the unit place . so , there is 1 way of doing it . the tens place can now be filled by any of the remaining 5 digits ( 2 , 3 , 6 , 7 , 9 ) . so , there are 5 ways of filling the tens place . the hundreds place can now be filled by any of the remaining 4 digits . so , there are 4 ways of filling it . required number of numbers = ( 1 x 5 x 4 ) = 20 . answer c" + }, + { + "Answer": 17, + "Options": "a ) 8 , b ) 16 , c ) 17 , d ) 18 , e ) 34", + "Correct": "c", + "Explanation": "\"minimum age = average - 1 standard deviation = 20 - 8 = 12 maximum age = average + 1 standard deviation = 20 + 8 = 28 maximum number of different ages of the applicants = 28 - 12 + 1 = 17 answer c\"" + }, + { + "Answer": 2800, + "Options": "a ) 2800 , b ) 2403 , c ) 3998 , d ) 2539 , e ) 1930", + "Correct": "a", + "Explanation": "a 2800 let the amount with r be $ r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 7000 - r ) = > 3 r = 14000 - 2 r = > 5 r = 14000 = > r = 2800 ." + }, + { + "Answer": 114.4, + "Options": "a ) 68 , b ) 70.4 , c ) 86 , d ) 114.4 , e ) 108", + "Correct": "d", + "Explanation": "\"x = 88 * 1.3 = 114.4 so the answer is d .\"" + }, + { + "Answer": 4, + "Options": "a ) - 5 , b ) - 4 , c ) 4 , d ) 3 , e ) 2", + "Correct": "c", + "Explanation": "1 . subtract 1 from both sides : x + 1 - 1 = 5 - 1 2 . simplify both sides : x = 4 c" + }, + { + "Answer": 10, + "Options": "a ) 4 , b ) 3 , c ) 2 , d ) 10 , e ) 5", + "Correct": "d", + "Explanation": "\"1015 \u00e3 \u00b7 25 = 40 with remainder = 15 15 + 10 = 25 . hence 10 should be added to 1015 so that the sum will be divisible by 25 answer : option d\"" + }, + { + "Answer": 240, + "Options": "a ) 240 , b ) 789 , c ) 520 , d ) 879 , e ) 456", + "Correct": "a", + "Explanation": "explanation : let sn = ( 2 + 4 + 6 + . . . + 30 ) . this is an a . p . in which a = 2 , d = 2 and l = 30 let the number of terms be n . then a + ( n - 1 ) d = 30 = > 2 + ( n - 1 ) x 2 = 30 n = 15 . sn = n / 2 ( a + l ) = 15 / 2 x ( 2 + 30 ) = ( 15 x 16 ) = 240 . answer : a" + }, + { + "Answer": 53, + "Options": "a ) 38 , b ) 47 , c ) 50 , d ) 53 , e ) 62", + "Correct": "d", + "Explanation": "\"suppose food eaten in first hour : x the ap is : x , x + 3 , x + 6 , . . . . [ number of terms ' n ' = 9 ] therefore , 9 / 2 [ 2 x + ( 9 - 1 ) * 3 ] = 450 . solving for x , x = 38 . now , 6 th term will be : x + ( 6 - 1 ) * d = 38 + 5 * 3 = 53 . hence d ! !\"" + }, + { + "Answer": 75, + "Options": "a ) 56 kg , b ) 90 kg , c ) 75 kg , d ) data inadequate , e ) none of these", + "Correct": "c", + "Explanation": "\"c 75 kg total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 55 + 20 ) kg = 75 kg .\"" + }, + { + "Answer": 1.4, + "Options": "a ) 1.2 kg , b ) 1.5 kg , c ) 1.4 kg , d ) 1.9 kg , e ) none of these", + "Correct": "c", + "Explanation": "\"explanation : flower - nectar contains 50 % of non - water part . in honey this non - water part constitutes 70 % ( 100 - 30 ) . therefore 0.5 x amount of flower - nectar = 0.70 x amount of honey = 0.70 x 1 kg therefore amount of flower - nectar needed = ( 0.70 / 0.51 ) kg = 1.4 kgs answer : c\"" + }, + { + "Answer": 15, + "Options": "a ) 11 , b ) 12 , c ) 15 , d ) 14 , e ) 19", + "Correct": "c", + "Explanation": "- x 2 - ( k + 9 ) x - 8 = - ( x - 2 ) ( x - 4 ) : given - x 2 - ( k + 9 ) x - 8 = - x 2 + 6 x - 8 - ( k + 9 ) = 6 : two polynomials are equal if their corresponding coefficients are equal . k = - 15 : solve the above for k correct answer c" + }, + { + "Answer": 40, + "Options": "a ) a ) 36 , b ) b ) 40 , c ) c ) 41 , d ) d ) 42 , e ) e ) 44", + "Correct": "b", + "Explanation": "\"let b be the number of blue hats and let g be the number of green hats . b + g = 85 . b = 85 - g . 6 b + 7 g = 550 . 6 ( 85 - g ) + 7 g = 550 . 510 - 6 g + 7 g = 550 . g = 550 - 510 = 40 . the answer is b .\"" + }, + { + "Answer": 24.000000000000004, + "Options": "a ) 24 , b ) 42 , c ) 36 , d ) 48 , e ) 50", + "Correct": "a", + "Explanation": "number is 24 as 1 / 4 th of 24 = 6 1 / 5 th of 25 ( 24 + 1 ) = 5 6 = 5 + 1 answer : a" + }, + { + "Answer": 29.000000000000004, + "Options": "a ) 31 % . , b ) 71 % . , c ) 49 % . , d ) 29 % . , e ) 51 % .", + "Correct": "d", + "Explanation": "25 % of 2 litres = 0.5 litres 40 % of 6 litres = 2.4 litres therefore , total quantity of alcohol is 2.9 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 29 % answer : d" + }, + { + "Answer": 325027405, + "Options": "a ) 724533811 , b ) 353654655 , c ) 545463251 , d ) 725117481 , e ) 325157481", + "Correct": "e", + "Explanation": "\"32519 x 9999 = 32519 x ( 10000 - 1 ) = 32519 x 10000 - 32519 x 1 = 325190000 - 32519 = 325157481 e\"" + }, + { + "Answer": 42000, + "Options": "a ) 28000 , b ) 30000 , c ) 42000 , d ) 34000 , e ) none of these", + "Correct": "c", + "Explanation": "explanation : suppose b ' s investment = x . then a ' s investment = 3 x suppose bs period of investment = y , then a ' s period of investment = 2 y a : b = 3 x * 2 y : xy = 6 : 1 total profit * 1 / 7 = 6000 = > total profit = 6000 * 7 = 42000 . answer : option c" + }, + { + "Answer": 21.5, + "Options": "a ) 21.5 , b ) 10.6 , c ) 8 , d ) 9.5 , e ) none of these", + "Correct": "a", + "Explanation": "\"answer : a ( 5 x 11 - 3 x 4 ) / 2 = 21.5\"" + }, + { + "Answer": 20, + "Options": "a ) 10 , b ) 20 , c ) 15 , d ) 26 , e ) 18", + "Correct": "b", + "Explanation": "4 x + y + z = 80 - - - - - - - - - - 1 ) 2 x - y - z = 40 - - - - - - - - - - - - - 2 ) 3 x + y - z = 20 - - - - - - - - - - - - 3 ) from 1 ) and 2 ) 6 x = 120 x = 20 answer is b" + }, + { + "Answer": 26, + "Options": "a ) 26 , b ) 43 , c ) 44 , d ) 45 , e ) 46", + "Correct": "a", + "Explanation": "\"let \u2018 x \u2019 be the average score after 12 th innings \u21d2 12 x = 11 \u00d7 ( x \u2013 2 ) + 48 \u2234 x = 26 answer a\"" + }, + { + "Answer": 85, + "Options": "a ) 76 kg , b ) 76.5 kg , c ) 85 kg , d ) 90 kg , e ) none", + "Correct": "c", + "Explanation": "\"sol . total weight increased = ( 8 \u00d7 2.5 ) kg = 20 kg . weight of new person = ( 65 + 20 ) kg = 85 kg . answer c\"" + }, + { + "Answer": 0.625, + "Options": "a ) 3 / 8 , b ) 1 / 2 , c ) 11 / 16 , d ) 5 / 8 , e ) 3 / 4", + "Correct": "d", + "Explanation": "\"the answer isc : 11 / 16 . the key to this problem is remembering that the median for a consecutive set of numbers is equivalent to its mean . for example , the mean and median of a set consisting of x , x + 1 , x + 2 , . . . , y will always be ( x + y ) / 2 . for set s , consisting of numbers ( a , a + 1 , . . . , b ) , the median is given to be 3 / 4 * b : ( a + b ) / 2 = ( 3 / 4 ) * b a = b / 2 for set q , consisting of numbers ( b , b + 1 , . . . , c ) , the median is given to be 6 / 8 * c : ( b + c ) / 2 = ( 6 / 8 ) * c b = ( 1 / 2 ) * c for set r , consisting of numbers ( a , a + 1 , . . . c ) , the median needs to be found : a = b / 2 = ( 1 / 2 * c ) / 2 = ( 1 / 4 ) * c median = ( a + c ) / 2 = ( 1 / 4 * c + c ) / 2 = ( 5 / 4 ) * c / 2 = ( 5 / 8 ) * c ( answer d )\"" + }, + { + "Answer": 3, + "Options": "a ) 3 , b ) 4 , c ) 6 , d ) 7 , e ) 8", + "Correct": "a", + "Explanation": "let the number be x . then , x + 17 = 60 x x 2 + 17 x - 60 = 0 ( x + 20 ) ( x - 3 ) = 0 x = 3 a" + }, + { + "Answer": 14, + "Options": "a ) 14 , b ) 25 , c ) 35 , d ) 45 , e ) 55", + "Correct": "a", + "Explanation": "\"let the number of students who wrote the exam be x . total marks of students = 75 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 65 x - ( 5 * 20 ) = 90 ( x - 5 ) 350 = 25 x = > x = 14 answer : a\"" + }, + { + "Answer": 11.03448275862069, + "Options": "a ) 10.03 % , b ) 11.03 % , c ) 12.03 % , d ) 13.03 % , e ) 11 %", + "Correct": "b", + "Explanation": "cost of kit = $ 72.50 if filters are purchased individually - $ 12.45 * 2 + $ 14.05 * 2 + $ 11.50 = $ 64.50 amount saved = $ 72.50 - $ 64.50 = $ 8 required % age = ( $ 8 / $ 72.50 ) * 100 = 11.03 % so , the correct answer is b ." + }, + { + "Answer": 0.5714285714285714, + "Options": "a ) 4 / 7 , b ) 1 / 3 , c ) 5 / 3 , d ) 12 / 7 , e ) 17 / 20", + "Correct": "a", + "Explanation": "let total number of juniors = j total number of seniors = s ( 1 / 2 ) j = ( 2 / 3 ) s = > s = 3 / 4 j total number of students = j + s = ( 7 / 4 ) j fraction of the students in the room are juniors = j / ( j + s ) = j / [ ( 7 / 4 ) j ] = 4 / 7 answer a" + }, + { + "Answer": 44402, + "Options": "a ) 14439 , b ) 44398 , c ) 44400 , d ) 44402 , e ) 15005", + "Correct": "b", + "Explanation": "\"lcm = 44400 44400 - 2 = 44398 answer : b\"" + }, + { + "Answer": 8, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8", + "Correct": "e", + "Explanation": "lcm of the given numbers = 175 therefore , number of integers = 1400 / 175 = 8 answer is option e" + }, + { + "Answer": 44, + "Options": "a ) 36 , b ) 39 , c ) 42 , d ) 44 , e ) none of the above", + "Correct": "d", + "Explanation": "\"let the average after 17 th inning = x . then , average after 16 th inning = ( x \u2013 3 ) . \u2234 16 ( x \u2013 3 ) + 92 = 17 x or x = ( 92 \u2013 48 ) = 44 . answer d\"" + }, + { + "Answer": 1565, + "Options": "a ) 1595 , b ) 1569 , c ) 1265 , d ) 1555 , e ) 1565", + "Correct": "e", + "Explanation": "\"explanation : 65 * 24 + 5 = 1565 answer : e\"" + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10", + "Correct": "a", + "Explanation": "\"say there are ' a ' associate professors . so we have 2 a pencils and a charts . say there are ' b ' assistant professors . so we have b pencils and 2 b charts . total pencils are 10 so 2 a + b = 10 total charts are 11 so a + 2 b = 8 add both : 3 a + 3 b = 18 so a + b = 6 total number of people = 6 a\"" + }, + { + "Answer": 5.85, + "Options": "a ) $ 3.15 , b ) $ 4.45 , c ) $ 4.80 , d ) $ 5.05 , e ) $ 5.85", + "Correct": "e", + "Explanation": "\"let the fixed charge of jim \u00e2 \u20ac \u2122 s taxi service = 2.25 $ and charge per 2 / 5 mile ( . 4 mile ) = . 4 $ total charge for a trip of 3.6 miles = 2.25 + ( 3.6 / . 4 ) * . 4 = 2.25 + 9 * . 4 = 5.85 $ answer e\"" + }, + { + "Answer": 44, + "Options": "a ) 0.33 , b ) 0.44 , c ) 0.55 , d ) 44 , e ) 55", + "Correct": "d", + "Explanation": "\"main thing to remember is answer is asked in cents , however when we calculate , it comes up as 0.44 $ just multiply by 100 , answer w = 44 . d\"" + }, + { + "Answer": 6332, + "Options": "a ) 2233 , b ) 2222 , c ) 2211 , d ) 6382 , e ) 23,17", + "Correct": "d", + "Explanation": "option 2 take n = 10 a + b . given that , ( 10 a + b ) + 18 = k 2 = ( a + b ) 2 given number = k 2 - 18 = ( 10 a + b ) that means , when we add 18 to the given number it should be a perfect square . so k 2 takes the following values . 1 , 4 , 9 , 16 , 25 , 36 , 49 , 64 , 81 , 100 , 121 , . . . . 1 to 16 are ruled out as if we subtract 18 from them , the resulting number is a single digit number . now 25 - 18 = 7 36 - 18 = 18 49 - 18 = 31 64 - 18 = 46 81 - 18 = 63 100 - 18 = 82 121 - 18 = 103 now 63 , 82 satisfies . answer : d" + }, + { + "Answer": 2229, + "Options": "a ) 2339 , b ) 2229 , c ) 4429 , d ) 5529 , e ) 2669", + "Correct": "b", + "Explanation": "b 2229 ? = [ ( 26.3 * 12 * 20 ) / 3 ] + 125 ? = 2104 + 125 = 2229" + }, + { + "Answer": 16, + "Options": "a ) $ 1.00 , b ) $ 16 , c ) $ 5.00 , d ) $ 6.00 , e ) $ 20.00", + "Correct": "b", + "Explanation": "\"b for me 14 people with 1 $ each - > maximum = 16\"" + }, + { + "Answer": 8, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9", + "Correct": "d", + "Explanation": "\"sol . let the ten \u2019 s digit be x and unit \u2019 s digit be y , then , ( 10 x + y ) - ( 10 y + x ) = 72 \u21d4 9 ( x - y ) = 72 \u21d4 x - y = 8 answer d\"" + }, + { + "Answer": 0.0625, + "Options": "a ) 1 / 8 , b ) 1 / 16 , c ) 1 / 15 , d ) 1 / 32 , e ) 1 / 31", + "Correct": "b", + "Explanation": "\"let x be the fraction of the distance that b runs . let v be the speed at which b runs . the time should be the same for both runners . time = d / ( 16 v / 15 ) = xd / v ( 15 / 16 ) * d / v = x * d / v x = 15 / 16 b should have a head start of 1 / 16 of the full distance . the answer is b .\"" + }, + { + "Answer": 1780, + "Options": "a ) a ) 1780 , b ) b ) 1250 , c ) c ) 10780 , d ) d ) 10500 , e ) e ) 8600", + "Correct": "a", + "Explanation": "total fees = rs . 25000 / - advance fees = 8280 / - balance fees = 25000 - 8280 = 16720 paid amount = 18500 / - incentive amount = 18500 - 16720 = 1780 / - answer is a" + }, + { + "Answer": 0.5714285714285714, + "Options": "a ) 1 / 49 , b ) 4 / 7 , c ) 3 / 7 , d ) 16 / 49 , e ) 40 / 49", + "Correct": "b", + "Explanation": "the probability of drawing a pink gumball both times is the same . the probability that she drew two blue gumballs = 9 / 49 = ( 3 / 7 ) * ( 3 / 7 ) therefore probability that the next one she draws is pink = 4 / 7 option ( b )" + }, + { + "Answer": 1000, + "Options": "a ) 5000 , b ) 4000 , c ) 1000 , d ) 6000 , e ) 8000", + "Correct": "c", + "Explanation": "\"total sale for 5 months = rs . ( 2435 + 2920 + 2855 + 3230 + 2560 ) = rs . 14000 . required sale = rs . [ ( 2500 x 6 ) - 14000 ] = rs . ( 15000 - 14000 ) = rs . 1000 answer : option c\"" + }, + { + "Answer": 8054.545267355626, + "Options": "a ) 8054 , b ) 8877 , c ) 2877 , d ) 2678 , e ) 1011", + "Correct": "a", + "Explanation": "\"8840 - - - - 421 100 - - - - ? = > 4.76 % x * 104.76 / 100 * 104.76 / 100 = 8840 x * 1.0975 = 8840 x = 8840 / 1.0975 = > 8054.54 answer : a\"" + }, + { + "Answer": 1.2909944487358056, + "Options": "a ) 1.29 , b ) 1.39 , c ) 1.49 , d ) 1.59 , e ) 1.69", + "Correct": "a", + "Explanation": "= > root 5 / root 3 = ( root 5 / root 3 ) * ( root 3 / root 3 ) = root 15 / root 9 = 3.87 / 3 = 1.29 answer : a" + }, + { + "Answer": 2, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "a", + "Explanation": "t = the number of cups of tea c = the number of cups of hot chocolate t + c = 20 t - c = 10 - > t = 15 . c = 5 . mo drinks 3 cups of tea a day then number of days that are not rainy = 15 / 3 = 5 so number of rainy days = 7 - 5 = 2 a is the answer ." + }, + { + "Answer": 5191, + "Options": "a ) 4857 , b ) 4184 , c ) 4012 , d ) 5191 , e ) 5291", + "Correct": "d", + "Explanation": "\"let the sale in the sixth month = x then ( 6235 + 6927 + 6855 + 7230 + 6562 + x ) / 6 = 6500 = > 6235 + 6927 + 6855 + 7230 + 6562 + x = 6 \u00d7 6500 = > 33809 + x = 39000 = > x = 39000 \u2212 33809 = 5191 answer : d\"" + }, + { + "Answer": 15, + "Options": "a ) 18 , b ) 56 , c ) 12 , d ) 15 , e ) 14", + "Correct": "d", + "Explanation": "initial average age of the 10 persons be p . age of the new person q . sum of the ages of the initial 10 persons = 10 p new average = ( p - 3 ) 10 ( p - 3 ) = 10 p - 45 + q = > q = 15 answer : d" + }, + { + "Answer": 0.39999999999999997, + "Options": "a ) $ 0.15 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45", + "Correct": "d", + "Explanation": "\"we are given that orangeade is made on day 1 with an equal amount of water and orange juice . we can set this information up into a ratio using a variable multiplier : w : oj = x : x thus , orangeade quantity = amount of water + amount of oj = x + x = 2 x we are next given that orangeade on day 2 was made by mixing the same amount of orange juice with twice the amount of water . we can set this information up into a ratio using a variable multiplier : w : oj = 2 x : x thus , orangeade quantity = amount of water + amount of oj = 2 x + x = 3 x we also know that all orangeade made was sold and that the revenue on both days was the same . we can therefore set up the following equation : day 1 revenue = day 2 revenue that is , ( quantity sold day 1 ) ( price per glass day 1 ) = ( quantity sold day 2 ) ( price per glass day 2 ) let a be the amount of orangeade a glass can hold , then quantity sold day 1 = the number of glasses of orangeade sold on day 1 = 2 x / a similarly , quantity sold day 2 = the number of glasses of orangeade sold on day 2 = 3 x / a we also know that the price per glass on day 1 = $ 0.6 but we don \u2019 t know the price per glass on day 2 , so let \u2019 s label it as variable p . we now have : ( 2 x / a ) ( 0.6 ) = ( 3 x / a ) ( p ) multiplying both sides by a , we have : ( 2 x ) ( 0.6 ) = ( 3 x ) ( p ) 1.2 x = 3 xp 1.2 = 3 p p = 0.4 thus , each glass of orangeade was sold for $ 0.40 on day 2 . answer d .\"" + }, + { + "Answer": 6, + "Options": "a ) 8 , b ) 7 , c ) 4 , d ) 5 , e ) 6", + "Correct": "e", + "Explanation": "last 3 digit can not divisible by 8 so , reject option a 1254 is not divisible by 7 last number is not 0 or 5 , so neglect 4 is not divide 1254 divisibility rule of 6 is a number divisible both by 3 and 2 . 1254 attains both divisible . so the number is divisible by 6 option e" + }, + { + "Answer": 4, + "Options": "a ) 1 , b ) 3 , c ) 4 , d ) 6 , e ) 8", + "Correct": "c", + "Explanation": "explanation : 35 + 25 = 60 / 15 = 4 ( remainder ) c" + }, + { + "Answer": 800, + "Options": "a ) $ 280 , b ) $ 800 , c ) $ 892 , d ) $ 1,108 , e ) $ 1,200", + "Correct": "b", + "Explanation": "\"( a ) $ 280 ( b ) $ 800 ( c ) $ 892 ( d ) $ 1,108 ( e ) $ 1,200 y = 2000 - x . 1 x - . 08 ( 2000 - x ) = 56 . - 160 + . 18 x = 56 x = 1200 and y = 800 answer : b\"" + }, + { + "Answer": 34, + "Options": "a ) 24 , b ) 30 , c ) 32 , d ) 34 , e ) 36", + "Correct": "d", + "Explanation": "\"solution let the two parts be ( 54 - x ) and x . then , 10 ( 54 - x ) + 22 x = 780 = 12 x = 240 \u2039 = \u203a x = 20 . therefore bigger part = ( 54 - x ) = 34 . answer d\"" + }, + { + "Answer": 49, + "Options": "a ) 50 , b ) 52 , c ) 49 , d ) 32 , e ) 35", + "Correct": "c", + "Explanation": "total age of students = > 32 \u00d7 16 = 512 yrs total age inclusive staff = 33 \u00d7 ( 16 + 1 ) = 561 = > staff ' s age 561 - 512 = 49 yrs answer c" + }, + { + "Answer": 250, + "Options": "a ) a ) 250 , b ) b ) 350 , c ) c ) 450 , d ) d ) 470 , e ) e ) 500", + "Correct": "a", + "Explanation": "\"explanation : 10 * 150 = 1500 5 * 100 + 5 * 150 = 1250 1500 \u2013 1250 = 250 a\"" + }, + { + "Answer": 30, + "Options": "a ) 30 , b ) 18 , c ) 16 , d ) 12 , e ) 8", + "Correct": "a", + "Explanation": "5 machines do x units in 8 days we have x / 8 = > rate of the 5 machines we know that we need to have 3 x units in 4 days therefore , we need to get to 3 x / 4 rate of the machines . rate of one machine is x / 8 * 1 / 5 = x / 40 . now , we need to know how many machines need to work simultaneously , to get 3 x done in 4 days . 3 x / 4 work needs to be done by machines that work at x / 40 rate . let ' s assign a constant y for the number of machines : ( x / 40 ) * y = 3 x / 4 y = 3 x / 4 * 40 / x cancel 4 with 40 , and x with x and get - > 30 . answer choice a" + }, + { + "Answer": 33, + "Options": "a ) 30 % , b ) 33 % , c ) 35 % , d ) 40 % , e ) 45 %", + "Correct": "b", + "Explanation": "we have a 11 litre solution containing 42 % of alcohol in the water . = > quantity of alcohol in the solution = 11 \u00d7 42 100 = 11 \u00d7 42100 now 3 litre of water is added to the solution . = > total quantity of the new solution = 11 + 3 = 14 percentage of alcohol in the new solution = 11 \u00d7 42 100 14 \u00d7 100 = 11 \u00d7 4210014 \u00d7 100 = 11 \u00d7 3 100 = 33 % b )" + }, + { + "Answer": 600, + "Options": "a ) 1250 , b ) 625 , c ) 600 , d ) 7500 , e ) 375", + "Correct": "c", + "Explanation": "max no . of crates = 5 . max weight = 120 kg max . weight carried = 5 * 120 = 600 kg = c" + }, + { + "Answer": 27.666666666666668, + "Options": "a ) 10 , b ) 20 , c ) 30 , d ) 27.7 , e ) 50", + "Correct": "d", + "Explanation": "23 + 29 + 31 = 83 / 3 = 27.7 answer : d" + }, + { + "Answer": 8, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8", + "Correct": "e", + "Explanation": "\"24 x + 16 y = 8 ( 3 x + 2 y ) which will be a minimum positive number when 3 x + 2 y = 1 . 3 ( 1 ) + 2 ( - 1 ) = 1 then 8 ( 3 x + 2 y ) can have a minimum positive value of 8 . the answer is e .\"" + }, + { + "Answer": 2006, + "Options": "a ) 2003 , b ) 2004 , c ) 2005 , d ) 2006 , e ) 2007", + "Correct": "d", + "Explanation": "\"she must gain at least 70 points , now she has 32 and every year gives her two more points : one for age and one for additional year of employment , so 32 + 2 * ( # of years ) = 70 - - > ( # of years ) = 19 - - > 1987 + 19 = 2006 . answer : d .\"" + }, + { + "Answer": 45, + "Options": "a ) 41 , b ) 42 , c ) 43 , d ) 44 , e ) 45", + "Correct": "e", + "Explanation": "n ( n - 1 ) / 2 = 10 * 9 / 2 = 45 answer : e" + }, + { + "Answer": 10, + "Options": "a ) 10 , b ) 12 , c ) 13 , d ) 14 , e ) 15", + "Correct": "a", + "Explanation": "( 6 x \u2013 5 y + 3 z ) - ( 5 x \u2013 6 y + 2 z ) = 22 - 12 or , x + y + z = 10 option a is the ans" + }, + { + "Answer": 43.18181818181819, + "Options": "a ) 20 % , b ) 24 % , c ) 30 % , d ) 43 % , e ) 79 %", + "Correct": "d", + "Explanation": "\"take it as original output = 100 . to meet demand increase by 10 % , then output = 110 . to meet holiday demand , new output increase by 60 % then output equals 176 to restore new holidy demand output to original 100 . final - initial / final * 100 = 76 / 176 * 100 = 8 / 33 * 100 = 43 % approxiamately . option d is correct .\"" + }, + { + "Answer": 1250, + "Options": "a ) 800 , b ) 900 , c ) 1000 , d ) 1100 , e ) 1250", + "Correct": "e", + "Explanation": "\"0.16 x = 4 ( 850 - 800 ) 0.16 x = 200 x = 1250 answer e\"" + }, + { + "Answer": 54, + "Options": "a ) 27 , b ) 36 , c ) 54 , d ) 72 , e ) 90", + "Correct": "c", + "Explanation": "let ( y / 18 ) x ( y / 162 ) = 1 y ^ 2 = 18 x 162 = 18 x 18 x 9 y = ( 18 x 3 ) = 54 the answer is c ." + }, + { + "Answer": 22, + "Options": "a ) 22 , b ) 36 , c ) 39 , d ) 21 , e ) 11", + "Correct": "a", + "Explanation": "\"add the numbers of doughnuts . 5 + 6 + 11 = 22 . answer is a .\"" + }, + { + "Answer": 50, + "Options": "a ) 27 , b ) 36 , c ) 29 , d ) 50 , e ) 11", + "Correct": "d", + "Explanation": "let the price of turban be x . thus , for one year the salary = ( 90 + x ) for 9 months he should earn 3434 ( 90 + x ) . now he gets one turban and rs . 55 . thus , 3434 ( 90 + x ) = 55 + x or 270 + 3 x = 220 + 4 x or x = 50 answer : d" + }, + { + "Answer": 37.5, + "Options": "a ) 38.5 , b ) 37.5 , c ) 37.0 , d ) 36.5 , e ) none of these", + "Correct": "b", + "Explanation": "average of the remaining set of numbers [ 50 x 38 - ( 45 + 55 ) ] / ( 50 - 2 ) = ( 1900 - 100 ) / 48 = 37.5 answer : b" + }, + { + "Answer": 16.666666666666664, + "Options": "a ) 16.7 % , b ) 20 % , c ) 24.67 % , d ) 33.33 % , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : let us assume before increase the petrol will be rs . 100 . after increase it will be rs ( 100 + 20 ) i . e 120 . now , his consumption should be reduced to : - = ( 120 \u2212 100 ) / 120 \u2217 100 . hence , the consumption should be reduced to 16.7 % . answer : a\"" + }, + { + "Answer": 2, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 25 , e ) 20 , 870,080", + "Correct": "a", + "Explanation": "we need to know the number of widgets ( which weigh 5 pounds each ) . the number of times that 5 divides the number is related to the number of times that 10 divides the number . when we divide 104 , 350,400 by 100 , we get 104 , 350,400 = 1 , 043,504 * 5 ^ 2 * 2 ^ 2 . 1 , 043,504 is not divisible by 5 , thus there are 2 widgets . the answer is a ." + }, + { + "Answer": 52, + "Options": "a ) $ 36 , b ) $ 44 , c ) $ 52 , d ) $ 60 , e ) $ 68", + "Correct": "c", + "Explanation": "started to test answer c if he had 52 , then he spent 13 at hardware store now he was left with 39 $ he spent 9 dollars on cleaning , thus he remained with 30 $ he then spent 1 / 2 of 30 , or 15 , and was left with 15 . hence , the only option that can be right is c ." + }, + { + "Answer": 4, + "Options": "a ) $ 1 , b ) $ 2 , c ) $ 3 , d ) $ 4 , e ) $ 6", + "Correct": "d", + "Explanation": "to find the least amount that must be added to the account to split the money evenly among 9 of its vendors , the total divisible by 9 simply add the individual digits of the total = 3 + 2 + 9 + 8 + 6 + 4 = 32 if you add 4 , the number is divisible by 9 ( 32 + 4 ) correct option : d" + }, + { + "Answer": 17, + "Options": "a ) 11 , b ) 12 , c ) 14 , d ) 17 , e ) 18", + "Correct": "d", + "Explanation": "\"let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 34 = > 2 x = 34 = > x = 17 d\"" + }, + { + "Answer": 36, + "Options": "a ) 0 , b ) 36 , c ) 13 , d ) 20 , e ) 25", + "Correct": "b", + "Explanation": "\"12 * 63 = 756 756 % 21 = 36 answer : b\"" + }, + { + "Answer": 0.8, + "Options": "a ) 4 / 0 , b ) 4 / 1 , c ) 4 / 5 , d ) 4 / 2 , e ) 4 / 3", + "Correct": "c", + "Explanation": "\"explanation : let the required fraction be x . then , ( 1 / x ) - x = 9 / 20 1 - x ^ ( 2 ) / x = 9 / 20 = > 20 - 20 * x ^ ( 2 ) = 9 * x . 20 * x ^ ( 2 ) + 9 * x - 20 = 0 . = > ( 4 * x + 5 ) ( 5 * x - 4 ) = 0 . = > x = 4 / 5 . answer : c ) 4 / 5\"" + }, + { + "Answer": 3000, + "Options": "a ) 1500 , b ) 2000 , c ) 2500 , d ) 2800 , e ) 3000", + "Correct": "e", + "Explanation": "\"let the shares of a , b , c and d be rs . 5 x , rs . 3 x , rs . 5 x and rs . 4 x respectively . then , 5 x - 4 x = 1000 x = 1000 . b ' s share = rs . 3 x = rs . ( 3 x 1000 ) = rs . 3000 . answer : e\"" + }, + { + "Answer": 70, + "Options": "a ) 50 , b ) 100 , c ) 70 , d ) 500 , e ) 980", + "Correct": "c", + "Explanation": "average price for a pair of rackets = $ 9.8 total cost = $ 9.8 * x = $ 686 x = 70 pairs were sold . answer : c" + }, + { + "Answer": 93, + "Options": "a ) kg , b ) 70 kg , c ) 80 kg , d ) 90 kg , e ) 93 kg", + "Correct": "e", + "Explanation": "\"total weight increased = ( 8 x 3.5 ) kg = 28 kg . weight of new person = ( 65 + 28 ) kg = 93 kg . e )\"" + }, + { + "Answer": 0.6, + "Options": "a ) 1 / 25 , b ) 1 / 6 , c ) 3 / 5 , d ) 5 , e ) 6", + "Correct": "c", + "Explanation": "( 1 / x + 1 / y ) = 15 canbe solved as { ( x + y ) / xy } = 5 . substituting for 1 / xy = 5 , we get x + y = 15 / 5 = = > ( x + y ) / 5 = 15 / ( 5 * 5 ) = 3 / 5 . c" + }, + { + "Answer": 7, + "Options": "a ) 0 , b ) 2 , c ) 5 , d ) 7 , e ) 9", + "Correct": "d", + "Explanation": "if a door is closed at the start , it requires an odd number of people to operate to be open at the end . only the perfect squares have an odd number of factors . the doors which are open at the end are : 1 , 4 , 9 , 16 , 25 , 36 , 49 for a total of 7 doors . the answer is d ." + }, + { + "Answer": 0.7272727272727273, + "Options": "a ) 3 / 2 , b ) 3 / 4 , c ) 8 / 11 , d ) 1 / 2 , e ) 1 / 5", + "Correct": "c", + "Explanation": "\"let team b has 8 agents , so team a has 5 agents let each agent of team b picked up 5 calls , so total calls by team b = 40 so , each agent in team a picked up 3 calls , so total calls for team a = 15 fraction for team b = 40 / ( 40 + 15 ) = 8 / 11 = answer = c\"" + }, + { + "Answer": 5.249999999999986, + "Options": "a ) $ 5.625 , b ) $ 1.00 , c ) $ 3.40 , d ) $ 5.25 , e ) $ 6.80", + "Correct": "d", + "Explanation": "\"0.85 * { original price } = $ 71.4 - - > { original price } = $ 84 . { final price } = $ 71.4 * 1.25 = $ 89.25 . the difference = $ 89.25 - $ 84 = $ 5.25 answer : d .\"" + }, + { + "Answer": 35, + "Options": "a ) 17 , b ) 18 , c ) 34 , d ) 35 , e ) 36", + "Correct": "d", + "Explanation": "we need to arrive at a common base . - - > ( 5 ) ^ ( - e ) * 2 ^ ( - 36 ) = 2 ^ ( - 36 ) * 5 ^ ( - 35 ) 5 ^ ( - e ) = 5 ^ ( - 35 ) - e = - 35 e = 35 = d" + }, + { + "Answer": 4, + "Options": "a ) 3 , b ) 2 , c ) 1 , d ) 0 , e ) 4", + "Correct": "e", + "Explanation": "\"| 13 - 3 | - | 4 - 10 | = | 10 | - | - 6 | = 10 - 6 = 4 correct answer e\"" + }, + { + "Answer": 2291.6666666666665, + "Options": "a ) $ 2291.7 , b ) $ 1546.8 , c ) $ 2546.5 , d ) $ 1879.3 , e ) $ 3125.3", + "Correct": "a", + "Explanation": "mean of the salaries = ( $ 1000 + $ 2500 + $ 3100 + $ 3650 + $ 1500 + $ 2000 ) / 6 = 13750 / 6 = $ 2291.7 answer is a" + }, + { + "Answer": 49.99999999999996, + "Options": "a ) 96 , b ) 75 , c ) 50 , d ) 25 , e ) 12", + "Correct": "c", + "Explanation": "\"guys , one more simple funda . 5 / 2 = 2.5 now . 5 x 2 = 1 is the remainder 25 / 4 = 6.25 now . 25 x 4 = 1 is the remainder 32 / 5 = 6.4 now . 4 x 5 = 2 is the remainder given x / y = 6.12 and remainder is 6 so . 12 x y = 6 hence y = 50 ans c\"" + }, + { + "Answer": 20, + "Options": "a ) 40 sec , b ) 50 sec , c ) 60 sec , d ) 20 sec , e ) 25 sec", + "Correct": "d", + "Explanation": "total initial bogies is 12 + 12 = 2412 + 12 = 24 additional bogies = 16 \u00e2 \u02c6 \u2019 12 = 4 24 bogies is 12 + 12 = 24 additional bogies = 16 - 12 = 4 24 bogies take 2 min 2 * 60 / 24 * 4 = 20 sec answer d" + }, + { + "Answer": 37, + "Options": "a ) rs . 23 , b ) rs . 37 , c ) rs . 45 , d ) rs . 67 , e ) rs . 77", + "Correct": "b", + "Explanation": "as the win leads to multiplying the amount by 1.5 and loss leads to multiplying the amount by 0.5 , we will multiply initial amount by 1.5 thrice and by 0.5 thrice ( in any order ) . the overall resultant will remain same . so final amount with the person will be ( in all cases ) : = 64 ( 1.5 ) ( 1.5 ) ( 1.5 ) ( 0.5 ) ( 0.5 ) ( 0.5 ) = = 64 ( 1.5 ) ( 1.5 ) ( 1.5 ) ( 0.5 ) ( 0.5 ) ( 0.5 ) = rs 2727 hence the final result is : 64 \u2212 27 = 3764 \u2212 27 = 37 : a loss of rs . 37 b" + }, + { + "Answer": 0.84, + "Options": "a ) 9 / 25 , b ) 10 / 25 , c ) 6 / 10 , d ) 2 / 3 , e ) 21 / 25", + "Correct": "e", + "Explanation": "\"simply look at the question from the other side . what is the probability that you can \u2019 t row the canoe ? this would be 2 / 5 x 2 / 5 = 4 / 25 . using the idea that the probability of something happening is 1 \u2013 the probability that it doesn \u2019 t happen , you can use the following equation to reach the right answer y : 1 \u2013 4 / 25 = 21 / 25 . answer choice e .\"" + }, + { + "Answer": 93, + "Options": "a ) 63 , b ) 93 , c ) 139 , d ) 147 , e ) 188", + "Correct": "b", + "Explanation": "\"lets say j is the weight of jack and s is the wt of his sister . if he loses 15 pounds , he s twice as heavy as his sister . j - 15 = 2 * s also , together they weight 132 pounds j + s = 132 solvong the 2 equation , we get j = 93 pounds ! b\"" + }, + { + "Answer": 0.04000000000000001, + "Options": "a ) 0.0016 , b ) 0.04 , c ) 0.16 , d ) 0.25 , e ) 0.5", + "Correct": "b", + "Explanation": "\"( 1 / 5 ) \u00b2 = ( 1 / 5 ) ( 1 / 5 ) = 1 / 25 approach # 1 : use long division to divide 25 into 1 to get 1 / 25 = 0.04 b\"" + }, + { + "Answer": 20, + "Options": "a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 26", + "Correct": "b", + "Explanation": "let the total number of workers be y . so sum of salary for all workers = sum of salary of 5 technician + sum of salary for other y - 5 workers . 5 x 900 + 700 ( y - 5 ) = 750 y \u21d2 4500 + 700 y - 3500 = 750 y \u21d2 50 y = 1000 \u2234 y = 20 so total number of workers = 20 b" + }, + { + "Answer": 50, + "Options": "a ) 37 , b ) 26 , c ) 30 , d ) 50 , e ) 11", + "Correct": "d", + "Explanation": "\"explanation : 18 + 22 + 10 * 6 = 100 / 2 = 50 answer : d\"" + }, + { + "Answer": 24, + "Options": "a ) 28 , b ) 12 , c ) 24 , d ) 16 , e ) 19", + "Correct": "c", + "Explanation": "\"let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 48 = > 2 x = 48 = > x = 24 c\"" + }, + { + "Answer": 0.6666666666666666, + "Options": "a ) 5 / 12 , b ) 12 / 5 , c ) 25 / 144 , d ) 2 / 3 , e ) 146 / 25", + "Correct": "d", + "Explanation": "\"let the number be x . then , 2 / 3 x = 64 / 216 * 1 / x x 2 = 64 / 216 * 3 / 2 = 64 / 144 = 4 / 9 x = 2 / 3 answer : d\"" + }, + { + "Answer": 60.00000000000021, + "Options": "a ) 120 , b ) 60 , c ) 30 , d ) 24 , e ) 12", + "Correct": "b", + "Explanation": "n = decimal part of 24.2 * remainder i . e . ( 12 ) hence 0.2 * n = 12 n = 60 . b" + }, + { + "Answer": 4, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 7", + "Correct": "c", + "Explanation": "solution let the number be x . = then , 2 x + 20 = 8 x \u2013 4 = 6 x = 24 \u2039 = \u203a x = 4 . answer c" + }, + { + "Answer": 10.25, + "Options": "a ) 2.25 , b ) 3.25 , c ) 10.25 , d ) 5.25 , e ) 6.25", + "Correct": "c", + "Explanation": "squaring on both sides ( x + 1 / x ) ^ 2 = 3.5 ^ 2 x ^ 2 + 1 / x ^ 2 = 12.25 - 2 x ^ 2 + 1 / x ^ 2 = 10.25 answer : c" + }, + { + "Answer": 8262, + "Options": "a ) 6084 , b ) 3788 , c ) 2077 , d ) 8262 , e ) 1812", + "Correct": "d", + "Explanation": "\"explanation : 1259 9521 - - - - - - - - - - - - 8262 answer : d\"" + }, + { + "Answer": 51.901041666666664, + "Options": "a ) 50.9 , b ) 52.9 , c ) 51.9 , d ) 53.25 , e ) none of the above", + "Correct": "c", + "Explanation": "\"required average marks = 70 \u00e3 \u2014 50 + 35 \u00e3 \u2014 60 + 45 \u00e3 \u2014 55 + 42 \u00e3 \u2014 45 / 70 + 35 + 45 + 42 = 3500 + 2100 + 2475 + 1890 / 192 = 9965 \u00e2 \u0081 \u201e 192 = 51.90 answer c\"" + }, + { + "Answer": 4, + "Options": "a ) 2 , b ) 5 , c ) 12 , d ) 8 , e ) 4", + "Correct": "e", + "Explanation": "\"( 40 / 100 ) * 60 \u00e2 \u20ac \u201c ( 4 / 5 ) * 25 24 - 20 = 4 answer : e\"" + }, + { + "Answer": 12000, + "Options": "a ) 16060 , b ) 14000 , c ) 18000 , d ) 12000 , e ) none of these", + "Correct": "d", + "Explanation": "we have , si = p \u00d7 r \u00d7 t / 100 \u2234 11400 = p \u00d7 6 \u00d7 2 / 100 + p \u00d7 9 \u00d7 3 / 100 + p \u00d7 14 \u00d7 4 / 100 or , 12 p + 27 p + 56 p = 11400 \u00d7 100 or , 95 p = 11400 \u00d7 100 \u2234 p = 12000 answer d" + }, + { + "Answer": 27, + "Options": "a ) 23 , b ) 24 , c ) 25 , d ) 26 , e ) 27", + "Correct": "e", + "Explanation": "present age of boy x and previous age of boy y so present age of dad : 8 y and previous age is x so the gap between duration must be same so 8 y - x = x - y - - > x = 9 y / 2 and x + 8 y = 75 ( given ) - - > 9 y / 2 + y = 75 so y = 6 and and x = 27 therefore fathers age is 8 y = 8 * 6 = 48 and child ' s age = x = 27 answer : e" + }, + { + "Answer": 26, + "Options": "a ) 9 , b ) 14 , c ) 17 , d ) 23 , e ) 26", + "Correct": "e", + "Explanation": "my take is option d ( 23 ) i followed a simple approach ( explained below ) : test 1 : ada ' s score = paul ' s score + 10 test 2 : ada ' s score = paul ' s score + 4 avg . of paul ' s score = 4 points higher than avg . of ada ' s score this implies that : sum of paul ' s score [ 3 tests ] = 12 points higher than sum of ada ' s score [ 3 tests ] ( 12 points higher since 3 points were given in terms of average of 3 scores ) so , paul needs to score 23 points higher than ada in test 3 , since paul needs to compensate for the lower score in test 1 and test 2 ( 26 = 10 + 4 + 12 ) e" + }, + { + "Answer": 15, + "Options": "a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16", + "Correct": "d", + "Explanation": "\"let part time emp = x let full time emp = y then , 48 = x + y . . . . . . . . . ( 1 ) ( 1 / 3 ) x + ( 1 / 4 ) y = no . of ppl taking the subway 4 x + 3 y / 12 = no . of ppl taking the subway using 1 x / 12 + 3 * 48 / 12 = no . of ppl taking the subway so , the minimum value of x has to be 12 . hence to maximize the no . put 36 for x 36 / 12 + 12 / 4 = 15 answer : d\"" + }, + { + "Answer": 47, + "Options": "a ) 44 , b ) 45 , c ) 46 , d ) 47 , e ) 48", + "Correct": "d", + "Explanation": "\"9 / 7 * 37 = 47.6 the answer is d .\"" + }, + { + "Answer": 45, + "Options": "a ) 20 , b ) 45 , c ) 55 , d ) 65 , e ) 80", + "Correct": "b", + "Explanation": "\"the arithmetic mean of 4 equally weighted tests was 60 . so what we can assume is that we have 4 test scores , each 60 . he dropped his lowest score and the avg went to 65 . this means that the lowest score was not 60 and other three scores had given the lowest score 5 each to make it up to 60 too . when the lowest score was removed , the other 3 scores got their 5 back . so the lowest score was 3 * 5 = 15 less than 60 . so the lowest score = 60 - 15 = 45 answer ( b )\"" + }, + { + "Answer": 22, + "Options": "a ) 11 , b ) 22 , c ) 77 , d ) 33 , e ) 88", + "Correct": "b", + "Explanation": "add the numbers of highlighters . 9 + 8 + 5 = 22 . answer is b ." + }, + { + "Answer": 186, + "Options": "a ) 186 , b ) 120 , c ) 152 , d ) 220 , e ) 220", + "Correct": "a", + "Explanation": "\"explanation : age of the 20 th student = [ 20 * 20 - ( 14 * 5 + 16 * 9 ) ] = ( 400 - 214 ) = 186 years . answer : a\"" + }, + { + "Answer": 3.7, + "Options": "a ) $ 4.70 , b ) $ 4.80 , c ) $ 3.85 , d ) $ 3.80 , e ) $ 3.70", + "Correct": "e", + "Explanation": "roshini spent and gave to his two friends a total of x + 3.40 + 3.40 = $ 3.65 money spent for sweet = 10.50 - 6.80 = $ 3.70 correct answer is e ) $ 3.70" + }, + { + "Answer": 60, + "Options": "a ) 40 , b ) 50 , c ) 60 , d ) 45 , e ) 56", + "Correct": "c", + "Explanation": "\"let the average after 11 th inning = x then , average after 10 th inning = x - 5 10 ( x - 5 ) + 110 = 11 x x = 110 - 50 = 60 answer is c\"" + }, + { + "Answer": 16, + "Options": "a ) 16,8 , b ) 10,2 , c ) 17,6 , d ) 14,10 , e ) 12,4", + "Correct": "a", + "Explanation": "\"let numbers be x and y . equation ( i ) : x - y = 8 equation ( ii ) : ( x + y ) / 4 = 6 solve system of equations : x = 16 , y = 8 a is the correct answer .\"" + }, + { + "Answer": 5, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "e", + "Explanation": "\"x is the buy price . x + 80 % x = 1,8 x is the sale price = 45 so x , the buy price becomes 45 / 1,8 = 25 % 100 mark up means x + 100 % x = 2 x so 50 . 50 - 45 = 5 answer : e\"" + }, + { + "Answer": 1.25, + "Options": "a ) $ 0.50 , b ) $ 1.00 , c ) $ 1.25 , d ) $ 1.50 , e ) $ 1.75", + "Correct": "c", + "Explanation": "oa is definitely wrong . the answer should be c ." + }, + { + "Answer": 60, + "Options": "a ) 50 , b ) 45 , c ) 55 , d ) 60 , e ) 65", + "Correct": "d", + "Explanation": "\"assume total distance = 100 miles time taken for 40 miles = 40 / 40 = 1 hour time taken for the rest of the 60 miles = 60 / v hours . average speed = 50 therefore the total time needed = 2 hours . 2 = 1 + 60 / v hence v = 60 mph answer : d\"" + }, + { + "Answer": 31, + "Options": "a ) 28 , b ) 30 , c ) 32 , d ) 34 , e ) 31", + "Correct": "e", + "Explanation": "\"let the weight of a , b and c are a , b and c respectively . average weight of a , b and c = 45 a + b + c = 45 \u00d7 3 = 135 - - - equation ( 1 ) average weight of a and b = 40 a + b = 40 \u00d7 2 = 80 - - - equation ( 2 ) average weight of b and c = 43 b + c = 43 \u00d7 2 = 86 - - - equation ( 3 ) equation ( 2 ) + equation ( 3 ) - equation ( 1 ) = > a + b + b + c - ( a + b + c ) = 80 + 86 - 135 = > b = 80 + 86 - 135 = 166 - 135 = 31 weight of b = 31 kg answer is e .\"" + }, + { + "Answer": 5, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "c", + "Explanation": "\"4 < x < 6 < y < 10 ; 4 < x y < 10 4 + y < x + 10 y - x < 6 . positive integer difference is 5 ( for example y = 9.5 and x = 4.5 ) answer : c .\"" + }, + { + "Answer": 21, + "Options": "a ) 21 , b ) 30 , c ) 45 , d ) 60 , e ) 90", + "Correct": "a", + "Explanation": "\"7 players are there . two players play one game with one another . so 7 c 2 = 7 * 6 / 2 = 21 so option a is correct\"" + }, + { + "Answer": 56.75, + "Options": "a ) 55.8 , b ) 51.8 , c ) 53.8 , d ) 56.8 , e ) 52.8", + "Correct": "d", + "Explanation": "sum of the marks for the class of 39 students = 39 * 45 = 1755 sum of the marks for the class of 35 students = 35 * 70 = 2450 sum of the marks for the class of 74 students = 1755 + 2450 = 4205 average marks of all the students = 4205 / 74 = 56.8 answer : d" + }, + { + "Answer": 57, + "Options": "a ) 33 , b ) 57 , c ) 54 , d ) 99 , e ) 01", + "Correct": "b", + "Explanation": "\"the number of students with first division = 27 % of 300 = 27 / 100 \u00d7 300 = 8100 / 100 = 81 and , the number of students with second division = 54 % of 300 = 54 / 100 \u00d7 300 = 16200 / 100 = 162 therefore , the number of students who just passed = 300 \u2013 ( 81 + 162 ) = 57 answer : b\"" + }, + { + "Answer": 8, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", + "Correct": "b", + "Explanation": "start from 1 : 1368 , start from 2 : 2358 , start from 3 : 378 , start from 4 : 48 , start from 5 : 528 , start from 6 : 678 , start from 7 : 78 , why start from 8 ? ? ? , start from 9 : 918 . so flights can start from all 8 other cities . answer : b" + }, + { + "Answer": 671.2018140589569, + "Options": "a ) 221 , b ) 287 , c ) 400 , d ) 288 , e ) 671", + "Correct": "e", + "Explanation": "\"explanation : 740 = p ( 21 / 20 ) 2 p = 671 answer : e\"" + }, + { + "Answer": 9, + "Options": "a ) 4.5 , b ) 5 , c ) 5.6 , d ) 5.7 , e ) 9", + "Correct": "e", + "Explanation": "\"if $ x $ is the number , x / 6 * 12 = 18 = > 2 x = 18 = > x = 9 e\"" + }, + { + "Answer": 100, + "Options": "a ) 10 , b ) 25 , c ) 50 , d ) 75 , e ) 100", + "Correct": "e", + "Explanation": "\"surprisingly no one answered this easy one . property of a set of consecutive integerz . mean = median = ( first element + last element ) / 2 = ( second element + last but one element ) / 2 = ( third element + third last element ) / 2 etc . etc . so mean = median = 200 / 2 = 100 answer is e\"" + }, + { + "Answer": 300, + "Options": "a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500", + "Correct": "c", + "Explanation": "\"since 2 + 3 = 5 & 7 + 8 = 15 any combination with these no be will give u desirable result . . . so total no in 100 will be 20 & that ' s why in 1000 , it will be 20 x 15 = 300 . answer : c\"" + }, + { + "Answer": 43.99999999999999, + "Options": "a ) 40 m 2 , b ) 44 m 2 , c ) 48 m 2 , d ) 36 m 2 , e ) none of these", + "Correct": "b", + "Explanation": "\"required area covered in 5 revolutions = 5 \u00d7 2 \u03c0 rh = 5 \u00d7 2 \u00d7 22 \u2044 7 \u00d7 0.7 \u00d7 2 = 44 m 2 answer b\"" + }, + { + "Answer": 132, + "Options": "a ) 127 , b ) 128 , c ) 130 , d ) 131 , e ) 132", + "Correct": "e", + "Explanation": "\"e = d * q + r e = 16 * 8 + 4 e = 128 + 4 e = 132\"" + }, + { + "Answer": 2, + "Options": "a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) none of the above", + "Correct": "a", + "Explanation": "\"( x + 1 ) \u00d7 60 + x \u00d7 120 + ( x \u2212 1 ) \u00d7 180 / ( x + 1 ) + x + ( x \u2212 1 ) = 100 \u21d2 360 x \u2212 120 / 3 x = 100 \u21d2 60 x = 120 \u21d2 x = 2 answer a\"" + }, + { + "Answer": 4, + "Options": "a ) 2 , b ) 4 , c ) 7 , d ) 8 , e ) 9", + "Correct": "b", + "Explanation": "explanation : 35 + 25 = 60 / 15 = 4 ( remainder ) b" + }, + { + "Answer": 2, + "Options": "a ) 0 , b ) 3 , c ) 5 , d ) 8 , e ) 2", + "Correct": "e", + "Explanation": "let x be the number and y be the quotient . then , x = 357 x y + 36 = ( 17 x 21 x y ) + ( 17 x 2 ) + 2 = 17 x ( 21 y + 2 ) + 2 ) required remainder = 2 . answer : option e" + }, + { + "Answer": 3, + "Options": "a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3", + "Correct": "e", + "Explanation": "lets say 5 and 10 ounce packages be x and y respectively . given that , 5 x + 10 y = 55 and x = y + 2 . what is the value of y . substituting the x in first equation , 5 y + 10 + 10 y = 55 - > y = 45 / 15 . = 3 e" + }, + { + "Answer": 7, + "Options": "a ) 3 , b ) 4 , c ) 7 , d ) 8 , e ) 9", + "Correct": "c", + "Explanation": "let number of packs of four = f let number of packs of seven = s 4 f + 7 s = 69 now , we need to test for values of s . since sum 69 is odd and 4 f will always be even , e ca n ' t be even . now , we can test for values e = 3 , 7 and 9 4 * 5 + 7 * 7 = 20 + 49 = 69 answer c" + }, + { + "Answer": 29, + "Options": "a ) 30 , 10 , b ) 25 , 5 , c ) 29 , 9 , d ) 50 , 30 , e ) 20,10", + "Correct": "c", + "Explanation": "\"let their ages be x and ( x + 20 ) years . then , 5 ( x - 4 ) = ( x + 20 - 4 ) = > 4 x = 36 = > x = 9 their present ages are 29 years and 9 year . answer : c\"" + }, + { + "Answer": 125, + "Options": "a ) 80 , b ) 100 , c ) 120 , d ) 125 , e ) 135", + "Correct": "d", + "Explanation": "so last digit can be filled in 5 ways - 1 , 3,5 , 7,9 there are 5 possibilities . the answer is 5 \u2217 5 \u2217 5 = 125 the correct answer is d" + }, + { + "Answer": 6, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "d", + "Explanation": "\"let , average commission = x no . of items sold = y total commission = xy new commission = xy + 1300 new average = ( xy + 1300 ) / ( y + 1 ) = 150 + x i . e . ( xy + 1300 ) = ( y + 1 ) * ( 150 + x ) i . e . ( xy + 1300 ) = ( xy + x + 150 y + 150 ) i . e . ( 1150 ) = ( x + 150 y ) new commission = 400 = 150 + x i . e . x = 250 i . e . y = 6 new sales = y + 1 = 7 answer : option d\"" + }, + { + "Answer": 20, + "Options": "a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22", + "Correct": "c", + "Explanation": "\"13 th from right means = x + 12 8 th from left means = 7 + x total = 12 + 7 + 1 = 20 answer : c\"" + }, + { + "Answer": 13, + "Options": "a ) 14 , 7 , b ) 10 , 5 , c ) 13 , 8 , d ) 12 , 8 , e ) 8 , 12", + "Correct": "c", + "Explanation": "explanation : let the present ages of a and b be ' a ' and ' b ' respectively . 3 ( a + 7 ) = 4 ( ( b + 7 ) - - - ( 1 ) = > 3 a - 4 b = 7 - - - - - - - ( 1 ) a - b = 5 - - - - - - - ( 2 ) solving ( 1 ) and ( 2 ) we get b = 8 substituting b = 8 in second equation , we get a = 13 . answer : c = > 2 a = 32 = > a = 16 . answer : c" + }, + { + "Answer": 10, + "Options": "a ) a ) 10 , b ) b ) 8 , c ) c ) 6 , d ) d ) 4 , e ) e ) 2", + "Correct": "a", + "Explanation": "\"x = 20 - 2 y x = 20 - 10 . x = 10 answer : a\"" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 4 / 3 , c ) 17 / 5 , d ) 18 / 5 , e ) 4", + "Correct": "a", + "Explanation": "\"we have two equations : 2 x + y = 4 x + 2 y = 5 notice that something nice happens when we add them . we get : 3 x + 3 y = 9 divide both sides by 3 to get : x + y = 3 so , ( x + y ) / 3 = 3 / 3 = 1 answer : a\"" + }, + { + "Answer": 858, + "Options": "a ) 858 , b ) 859 , c ) 869 , d ) 4320 , e ) none of these", + "Correct": "a", + "Explanation": "\"solution required number = ( l . c . m . of 24 , 32 , 36 , 54 ) - 5 = 864 - 6 = 858 . answer a\"" + }, + { + "Answer": 90.5, + "Options": "a ) a ) 59 , b ) b ) 61 , c ) c ) 63 , d ) d ) 65 , e ) e ) 90", + "Correct": "e", + "Explanation": "\"formula = \u221a a \u00d7 b a = 81 and b = 100 \u221a 81 \u00d7 100 = 9 \u00d7 10 = 90 e\"" + }, + { + "Answer": 1234490, + "Options": "a ) 32435453 , b ) 1234554 , c ) 76768786 , d ) 97979797 , e ) 75868656", + "Correct": "b", + "Explanation": "\"according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 1234562 - 12 * 3 * 2 = 1234562 - 8 = 1234554 correct answer b\"" + }, + { + "Answer": 1, + "Options": "a ) 0 , b ) 1 , c ) 36 , d ) 120 , e ) 524", + "Correct": "b", + "Explanation": "\"8 + 5 + 6 + 7 + 3 + 6 = 35 , so this number is not divisible by 3 and thus not divisible by 12 . therefore , k = 0 3 ^ k - k ^ 3 = 1 - 0 = 1 the answer is b .\"" + }, + { + "Answer": 10, + "Options": "a ) 91 , b ) 10 , c ) 1001 , d ) 1911 , e ) none of these", + "Correct": "b", + "Explanation": "\"explanation : required number of students = h . c . f of 1230 and 920 = 10 . answer : b\"" + }, + { + "Answer": 47.80600000000004, + "Options": "a ) a ) 47.095 , b ) b ) 47.752 , c ) c ) 47.806 , d ) d ) 47.95 , e ) of the above", + "Correct": "c", + "Explanation": "let 3889 + 12.808 - x = 3854.002 . then x = ( 3889 + 12.808 ) - 3854.002 = 3901.808 - 3854.002 = 47.806 . answer = c" + }, + { + "Answer": 11.999999999999998, + "Options": "a ) 12 days , b ) 15 days , c ) 20 days , d ) 18 days , e ) 22 days", + "Correct": "a", + "Explanation": "\"let the total money be $ x a ' s 1 day work = $ x / 20 b ' s 1 day work = $ x / 30 a + b 1 day work = $ x / 12 money is sufficient to pay the wages of both for 12 days answer is a\"" + }, + { + "Answer": 42, + "Options": "a ) 32 , b ) 42 , c ) 83 , d ) 71 , e ) 92", + "Correct": "b", + "Explanation": "\"( x ^ n + 1 ) will be divisible by ( x + 1 ) only when n is odd ; ( 43 ^ 43 + 1 ) will be divisible by ( 43 + 1 ) ; ( 43 ^ 43 + 1 ) + 42 when divided by 44 will give 42 as remainder . correct option : b\"" + }, + { + "Answer": 290, + "Options": "a ) 238 , b ) 290 , c ) 278 , d ) 200 , e ) 288", + "Correct": "b", + "Explanation": "\"explanation : let the number of 20 paise coins be x . then the no of 25 paise coins = ( 342 - x ) . 0.20 * ( x ) + 0.25 ( 342 - x ) = 71 = > x = 290 . . answer : b ) 290\"" + }, + { + "Answer": 10, + "Options": "a ) 10 , b ) 12 , c ) 13 , d ) 15 , e ) 16", + "Correct": "a", + "Explanation": "\"let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 20 = > 2 x = 20 = > x = 10 a\"" + }, + { + "Answer": 27, + "Options": "a ) 27 kg , b ) 20 kg , c ) 26 kg , d ) 31 kg , e ) 35 kg", + "Correct": "a", + "Explanation": "\"let d sum of a , b , c is 3 * 45 = 135 and sum of a and b s 2 * 40 = 80 sum of b and c is 2 * 41 = 82 hence 80 + 82 - 135 = 27 ans = 27 answer : a\"" + }, + { + "Answer": 17, + "Options": "a ) 17 , b ) 18 , c ) 16 , d ) 19 , e ) 14", + "Correct": "a", + "Explanation": "let ' s use trial and error to find the two numbers . 20 * 18 = 360 ( too high ) 19 * 17 = 323 the answer is a ." + }, + { + "Answer": 2984, + "Options": "a ) 1964 , b ) 1984 , c ) 2964 , d ) 2984 , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : = 3034 \u2212 ( 1002 / 2004 \u00d7 100 ) = 3034 \u2212 50 = 2984 option d\"" + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 6 , c ) 8 , d ) 7 , e ) 4", + "Correct": "a", + "Explanation": "\"let the number be x . then , 3 ( 2 x + 9 ) = 57 2 x = 10 = > x = 5 answer : a\"" + }, + { + "Answer": 10, + "Options": "a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13", + "Correct": "b", + "Explanation": "\"if n = 10 mark sold 1 box and ann sold 8 boxes total 9 < 10 answer : b\"" + }, + { + "Answer": 54, + "Options": "a ) 12 liters , b ) 32 liters , c ) 41 liters , d ) 54 liters , e ) 34 liters", + "Correct": "d", + "Explanation": "\"milk = 3 / 5 * 135 = 81 liters water = 54 liters 81 : ( 54 + p ) = 3 : 4 162 + 3 p = 324 = > p = 54 54 liters of water are to be added for the ratio become 3 : 4 . answer : d\"" + }, + { + "Answer": 35, + "Options": "a ) 66 , b ) 35 , c ) 42 , d ) 27 , e ) 11", + "Correct": "b", + "Explanation": "x / 7 = y / 9 = > x : y = 7 : 9 7 / 16 * 90 = 35 answer : b" + }, + { + "Answer": 152400, + "Options": "a ) rs 108000 , b ) rs 144000 , c ) rs 132000 , d ) rs 152400 , e ) none of these", + "Correct": "d", + "Explanation": "explanation : raj ' s salary as on 1 jan 1991 is rs 400 per month . his increment in his month salary is rs 40 per annum his total salary from 1 jan 1991 to 31 st dec 2000 i . e . in ten years = > 12 [ 2 ( 400 ) + ( 10 \u2212 1 ) 40 ] \u00d7 10 / 2 . = > rs 69600 . ramu ' s salary as on jan 1 st 1991 is rs 550 and his half yearly increment in his month salary is rs 20 . his total salary from 1 jan 1991 to dec 31 , 2000 = > 6 [ 2 ( 500 ) + ( 20 \u2212 1 ) 20 ] \u00d7 20 / 2 . = > rs 82000 . total salary of raj and ramu in the ten year period : = > rs . 69600 + rs . 82800 . = > rs 1 , 52400 . answer : d" + }, + { + "Answer": 24, + "Options": "a ) 25 % , b ) 20 % , c ) 22 % , d ) 21 % , e ) 24 %", + "Correct": "e", + "Explanation": "let ' s say there is a total of 100 students at this college . 80 percent of the total number of students are freshmen . # of freshmen = 80 % of 100 = 80 60 percent of the fresh - men are enrolled in the school of liberal arts . . . number of liberal arts freshmen = 60 % of 80 = 48 . . . and , of these , 50 percent are psychology majors . . . number of liberal arts freshmen who are psychology majors = 50 % of 48 = 24 what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts ? 24 / 100 = 24 % answer : e" + }, + { + "Answer": 662, + "Options": "a ) $ 412 , b ) $ 526 , c ) $ 585 , d ) $ 605 , e ) $ 662", + "Correct": "e", + "Explanation": "craig receives a commission of $ 50 on each appliance plus a 10 % commission on total sales , thus his commission was 6 * 50 + 0.1 * 3620 = 662 . answer : e ." + }, + { + "Answer": 3, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "b", + "Explanation": "2 ^ 3 x = 2 ^ 9 3 x = 9 , therefore x = 3 answer b" + }, + { + "Answer": 848, + "Options": "a ) 600 , b ) 700 , c ) 800 , d ) 900 , e ) 848", + "Correct": "e", + "Explanation": "\"solution : let x be the number i chose , then x / 8 \u00e2 \u02c6 \u2019 100 = 6 x / 8 = 106 x = 848 answer e\"" + }, + { + "Answer": 155.28125, + "Options": "a ) 180 times , b ) 381 times , c ) 155 times , d ) 392 times , e ) 150 times", + "Correct": "c", + "Explanation": "\"time difference is 1 hr , 22 min , 49 sec = 4969 sec . so , light glows floor ( 4969 / 32 ) = 15582 times . answer : c\"" + }, + { + "Answer": 71, + "Options": "a ) 71 , b ) 910 , c ) 1001 , d ) 1911 , e ) none", + "Correct": "a", + "Explanation": "\"olution required number of students . = h . c . f of 781 and 710 . \u00e2 \u20ac \u00b9 = \u00e2 \u20ac \u00ba 71 . answer a\"" + }, + { + "Answer": 66, + "Options": "a ) 58 , b ) 59 , c ) 62 , d ) 66 , e ) 74", + "Correct": "d", + "Explanation": "explanation : a + b = 60 , a = 2 b 2 b + b = 60 = > b = 20 then a = 40 . 3 years , their ages will be 43 and 23 . sum of their ages = 43 + 23 = 66 . d )" + }, + { + "Answer": 0.05714285714285714, + "Options": "a ) 2 / 35 , b ) 2 / 3 , c ) 7 / 35 , d ) 5 / 7 , e ) 7 / 5", + "Correct": "a", + "Explanation": "\"let a be the event that ram is selected and b is the event that ravi is selected . p ( a ) = 2 / 7 p ( b ) = 1 / 5 let c be the event that both are selected . p ( c ) = p ( a ) x p ( b ) as a and b are independent events : = 2 / 7 x 1 / 5 = 2 / 35 answer : a\"" + }, + { + "Answer": 1, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "b", + "Explanation": "2 ^ ( 4 x + 4 ) = 2 ^ ( 12 x - 4 ) 4 x + 4 = 12 x \u2212 4 x = 1 answer b" + }, + { + "Answer": 75, + "Options": "a ) 39 , b ) 40 , c ) 41 , d ) 75 , e ) 43", + "Correct": "d", + "Explanation": "\"solution start with 25 pens . mike gives you 22 pens : 25 + 22 = 47 pens . cindy doubles the number of pens you have : 47 \u00e3 \u2014 2 = 94 pens . sharon takes 19 pens from you : 94 - 19 = 75 pens . so you have 75 at the end . correct answer : d\"" + }, + { + "Answer": 180.75, + "Options": "a ) 504 , b ) 532 , c ) 210 , d ) 180 , e ) 280", + "Correct": "d", + "Explanation": "lcm of 7 , 8 and 9 is 504 , thus 523 fbc must be divisible by 504 . 523 fbc = 523000 + fbc 523000 divided by 504 gives a remainder of 352 . hence , 352 + fbc = k * 504 . k = 1 fbc = 152 - - > f * b * c = 10 k = 2 fbc = 656 - - > f * b * c = 180 as fbc is three digit number k can not be more than 2 . two answers ? well only one is listed in answer choices , so d . answer : d ." + }, + { + "Answer": 5, + "Options": "a ) $ 2.50 , b ) $ 3.00 , c ) $ 3.50 , d ) $ 4.00 , e ) $ 5.00", + "Correct": "e", + "Explanation": "\"number of wheels in truck = 18 number of wheels on its front axle = 2 number of wheels remaining = 16 number of axles remaining axles = 16 / 2 = 8 total number of axles = 9 t = 1.50 + 0.50 ( 9 \u2212 2 ) = 1.50 + . 5 * 7 = 1.5 + 1.5 = 5 $ answer e\"" + }, + { + "Answer": 0.1428571428571428, + "Options": "a ) 1 / 4 , b ) 4 / 5 , c ) 1 / 5 , d ) 1 / 6 , e ) 1 / 7", + "Correct": "e", + "Explanation": "if s is an integer and we know that the average speed is 2.8 , s must be = 2 . that meanss + 1 = 3 . this implies that the ratio of time for s = 2 is 1 / 4 of the total time . the formula for distance / rate is d = rt . . . so the distance travelled when s = 2 is 2 t . the distance travelled for s + 1 = 3 is 3 * 4 t or 12 t . therefore , total distance covered while the sun was shining over him is w = 2 / 14 = 1 / 7 . answer : e" + }, + { + "Answer": 170, + "Options": "a ) 300 , b ) 120 , c ) 150 , d ) 170 , e ) 270", + "Correct": "d", + "Explanation": "\"n th term of a . p . is given by a + ( n - 1 ) d 4 th term = a + 3 d 12 th term = a + 11 d given a + 3 d + a + 11 d = 20 - - > 2 a + 14 d = 20 - - > a + 7 d = 10 sum of n term of a . p = n / 2 [ 2 a + ( n - 1 ) d ] subsitiuing n = 17 . . . we get 17 / 2 [ 2 a + 14 d ] = 17 [ a + 7 d ] = 17 * 10 = 170 . . . answer is d . . .\"" + }, + { + "Answer": 440, + "Options": "a ) $ 400 , b ) $ 420 , c ) $ 440 , d ) $ 460 , e ) $ 480", + "Correct": "c", + "Explanation": "\"avg = sum of observations / number of observations avg income = ( 400 + 250 + 650 + 400 + 500 ) / 5 = 440 answer is c\"" + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10", + "Correct": "a", + "Explanation": "every such number must be divisible by l . c . m of 4 , 5,6 i . e , 60 . such numbers are 240,300 , 360,420 , 480,540 . clearly , there are 6 such numbers answer : a" + }, + { + "Answer": 74, + "Options": "a ) 65 , b ) 69 , c ) 74 , d ) 75 , e ) none", + "Correct": "c", + "Explanation": "\"sol . average = 76 + 60 + 82 + 67 + 85 / 5 ) = ( 375 / 5 ) = 74 . answer c\"" + }, + { + "Answer": 37, + "Options": "a ) 37 , b ) 35 , c ) 25 , d ) 20 , e ) 42", + "Correct": "a", + "Explanation": "\"x + y = 14 x - y = 60 2 x = 74 x = 37 answer is a\"" + }, + { + "Answer": 3.0000000000000004, + "Options": "a ) 2 \u221a 2 , b ) 2 \u221a 3 , c ) 3 \u221a 2 , d ) 3 \u221a 3 , e ) 3", + "Correct": "e", + "Explanation": "\"( \u221a 27 + \u221a 243 ) / \u221a 48 = ( 3 \u221a 3 + 9 \u221a 3 ) / 4 \u221a 3 = 12 \u221a 3 / 4 \u221a 3 = 3 . hence , the correct answer is e .\"" + }, + { + "Answer": 189.00000000000068, + "Options": "a ) 6 , b ) 21 , c ) 27 , d ) 189 , e ) 192", + "Correct": "d", + "Explanation": "another approach is to use two variables . let m = present number of males let f = present number of females the ratio of male to female employees is 7 : 8 so , m / f = 7 / 8 cross multiply to get 7 f = 8 m if 3 more men were hired , this ratio would increase to 8 : 9 so , ( m + 3 ) / f = 8 / 9 cross multiply to get 9 ( m + 3 ) = 8 f expand : 9 m + 27 = 8 f we now have a system of two equations and two variables : 7 f = 8 m 9 m + 27 = 8 f solve to get : m = 189 and f = 216 answer : d" + }, + { + "Answer": 50, + "Options": "a ) 18 , b ) 15 , c ) 33 , d ) 39 , e ) 50", + "Correct": "e", + "Explanation": "current age of the guy = a years . then , 5 ( a + 5 ) \u2013 5 ( a \u2013 5 ) = a ( 5 a + 25 ) \u2013 ( 5 a \u2013 25 ) = a a = 50 e" + }, + { + "Answer": 75, + "Options": "a ) 33 , b ) 75 , c ) 48 , d ) 99 , e ) 21", + "Correct": "b", + "Explanation": "speed on return trip = 150 % of 60 = 90 km / hr . average speed of trip = 60 + 90 / 2 = 150 / 2 = 75 km / hr answer : b" + }, + { + "Answer": 14, + "Options": "a ) 22 , b ) 14 , c ) 88 , d ) 12 , e ) 66", + "Correct": "b", + "Explanation": "\"( 85 / 100 ) * 40 \u2013 ( 4 / 5 ) * 25 = 14 answer : b\"" + }, + { + "Answer": 347.2, + "Options": "a ) $ 338.50 , b ) $ 341.40 , c ) $ 344.30 , d ) $ 347.20 , e ) $ 350.10", + "Correct": "d", + "Explanation": "the service cost of 3 vans and 2 trucks is 5 * 2.10 $ 10.50 the fuel in 3 vans is 3 * 65 = 195 liters the fuel in 2 trucks is 2 * 65 * 2.2 = 286 liters the total fuel ( vans + trucks ) = 481 liters the total fuel cost is 481 * 0.7 = $ 336.70 the total cost is $ 336.70 + $ 10.50 = $ 347.20 the answer is d ." + }, + { + "Answer": 18, + "Options": "a ) 11 . , b ) 12 . , c ) 13 . , d ) 18 . , e ) 14.5", + "Correct": "d", + "Explanation": "price of candy before price increase = 10 / 1.25 = 8 price of soda before price increase = 15 / 1.5 = 10 total price = 8 + 10 = 18 d is the answer" + }, + { + "Answer": 224, + "Options": "a ) 120 , b ) 190 , c ) 224 , d ) 298 , e ) 256", + "Correct": "c", + "Explanation": "\"there are 2 ^ 4 = 16 possibilities for the true - false answers . however we need to remove two cases for tttt and ffff . there are 4 * 4 = 16 possibilities for the multiple choice questions . the total number of possibilities is 14 * 16 = 224 . the answer is c .\"" + }, + { + "Answer": 45, + "Options": "a ) 43 , b ) 44 , c ) 45 , d ) 47 , e ) 48", + "Correct": "c", + "Explanation": "explanation : if teacher ' s age is 14 years , there is no change in the average . but teacher has contributed 1 year to all the students along with maintaining his age at 15 . age of teacher = average age of all + total increase in age = 15 + ( 1 x 30 ) = 45 years answer : c" + }, + { + "Answer": 89, + "Options": "a ) 75 kg , b ) 65 kg , c ) 55 kg , d ) 89 kg , e ) 25 kg", + "Correct": "d", + "Explanation": "total weight increased = ( 8 x 3 ) kg = 24 kg . weight of new person = ( 65 + 24 ) kg = 89 kg . answer : d" + }, + { + "Answer": 25, + "Options": "a ) 65 , b ) 55 , c ) 45 , d ) 35 , e ) 25", + "Correct": "e", + "Explanation": "am i missing something here ? ? ? it seems straightforward . . . . . . the obvious maximum that have all 3 is 55 , because you are limited by the smallest number . the minimum is simply the sum of the max of each people who dont have the product , so : 100 - 90 = 10 do n ' t have cell 100 - 85 = 15 do n ' t have dvd and 100 - 55 = 45 do n ' t have mp 3 so a total of 10 + 15 + 45 = 70 combined who might not have some combination of the 3 products . so subtract that from 100 , to give you the minimum of the people who could have all 3 and you get 100 - 70 = 30 . 55 - 30 = 25 e" + }, + { + "Answer": 30, + "Options": "a ) 40 , b ) 26 , c ) 27 , d ) 28 , e ) 30", + "Correct": "e", + "Explanation": "\"let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 40 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 40 + 20 ) / 2 = 30 . answer : e\"" + }, + { + "Answer": 3600, + "Options": "a ) 3600 , b ) 2988 , c ) 2789 , d ) 2887 , e ) 1297", + "Correct": "a", + "Explanation": "\"manager ' s monthly salary rs . ( 1600 * 21 - 1500 * 20 ) = rs . 3600 . answer : a\"" + }, + { + "Answer": 0.5714285714285714, + "Options": "a ) 3 / 2 , b ) 3 / 4 , c ) 4 / 7 , d ) 1 / 2 , e ) 1 / 5", + "Correct": "c", + "Explanation": "\"let team b has 8 agents , so team a has 5 agents let each agent of team b picked up 5 calls , so total calls by team b = 40 so , each agent in team a picked up 6 calls , so total calls for team a = 30 fraction for team b = 40 / ( 40 + 30 ) = 4 / 7 = answer = c\"" + }, + { + "Answer": 2, + "Options": "a ) a ) 4 , b ) b ) 3 , c ) c ) 5 , d ) d ) 2 , e ) e ) 8", + "Correct": "d", + "Explanation": "explanation : = > 300 \u00d7 ? + ( 12 + 4 ) \u00d7 1 / 8 = 602 = > 300 \u00d7 ? = 602 - ( 12 + 4 ) \u00d7 1 / 8 = > 300 \u00d7 ? = 602 - 2 = 600 = > ? = 600 / 300 = 2 answer : option d" + }, + { + "Answer": 17, + "Options": "a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 22", + "Correct": "a", + "Explanation": "we need to find the median which is the third value when the numbers are in increasing order . since k < m < r < s < t , the median would be r . the average of the positive integers is 16 which means that in effect , all numbers are equal to 16 . if the largest number is 42 , it is 26 more than 16 . we need r to be maximum so k and m should be as small as possible to get the average of 16 . since all the numbers are positive integers , k and m can not be less than 1 and 2 respectively . 1 is 15 less than 16 and 2 is 14 less than 16 which means k and m combined are 29 less than the average . 42 is already 26 more than 16 and hence we only have 29 - 26 = 3 extra to distribute between r and s . since s must be greater than r , r can be 16 + 1 = 17 and s can be 16 + 2 = 18 . so r is 17 . answer ( a )" + }, + { + "Answer": 9, + "Options": "a ) $ 1.00 , b ) $ 1.25 , c ) $ 5.00 , d ) $ 9.00 , e ) $ 20.00", + "Correct": "d", + "Explanation": "d for me 11 people with 1 $ each - > maximum = 9" + }, + { + "Answer": 72, + "Options": "a ) a ) 51 , b ) b ) 50 , c ) c ) 45 , d ) d ) 72 , e ) e ) 36", + "Correct": "d", + "Explanation": "\"explanation : let the number be x . then , x - ( x / 3 ) = 48 = > 2 x / 3 = 48 = > x = 72 answer : option d\"" + }, + { + "Answer": 25, + "Options": "a ) 3 , b ) 6 , c ) 12 , d ) 23 , e ) 25", + "Correct": "e", + "Explanation": "\"2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 26 = > 4 x 2 ^ 2 n = 4 ^ 26 = 2 ^ 52 = > 2 ^ 2 x 2 ^ 2 n = 2 ^ 52 = > 2 ^ ( 2 n + 2 ) = 2 ^ 52 = > 2 n + 2 = 52 = > n = 25 so . answer will be e\"" + }, + { + "Answer": 4.5, + "Options": "a ) a ) 4.5 , b ) b ) 12 , c ) c ) 15 , d ) d ) 18 , e ) e ) 20", + "Correct": "a", + "Explanation": "\"explanation : 2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 34 - 25 = 9 ab = 4.5 . answer : a\"" + }, + { + "Answer": 0.125, + "Options": "a ) 64 , b ) 1 / 8 , c ) 1 , d ) 8 , e ) 1 / 64", + "Correct": "b", + "Explanation": "say r = 2 = > a 1 = 64 when r = 1 ; v 2 = 8 v 2 = 1 / 8 * v 1 . answer : b" + }, + { + "Answer": 50, + "Options": "a ) 40 , b ) 50 , c ) 28 , d ) 38 , e ) 48", + "Correct": "b", + "Explanation": "\"as half the circle shape consist of 33 - 8 = 25 boys , so total number of boys in full circle = 2 * 25 = 50 answer : b\"" + }, + { + "Answer": 20, + "Options": "a ) 1 , b ) 10 , c ) 19 , d ) 20 , e ) 21", + "Correct": "d", + "Explanation": "this is a solution from beatthegmat : even numbers : ( 40 - 2 ) / 2 + 1 = 20 even integers . ( 40 + 2 ) / 2 = 21 is the average of the even set . sum = avg * ( # of elements ) = 21 * 20 = 420 = a odd numbers : ( 39 - 1 ) / 2 + 1 = 20 odd integers . ( 39 + 1 ) / 2 = 20 is the average of the odd set . sum = avg * ( # of elements ) = 20 * 20 = 400 = b a - b = 420 - 400 = 20 . answer : d" + }, + { + "Answer": 7, + "Options": "a ) 5 , b ) 7 , c ) 8 , d ) 10 , e ) 11", + "Correct": "b", + "Explanation": "\"t = 7 is the correct answer . good solution buneul . b\"" + }, + { + "Answer": 34, + "Options": "a ) 26 , b ) 30 , c ) 34 , d ) 38 , e ) 42", + "Correct": "c", + "Explanation": "\"the average of the numbers in set s is 10 . if we increase the mean by 40 % , the new mean is 14 . thus , on average , 5 numbers increase by 4 . therefore n = 14 + 20 = 34 the answer is c .\"" + }, + { + "Answer": 136, + "Options": "a ) 130 , b ) 132 , c ) 134 , d ) 136 , e ) 138", + "Correct": "d", + "Explanation": "\"let the required number be x . then , 43 x \u2013 34 x = 1224 or 9 x = 1224 or x = 136 . required number = 136 . answer : d\"" + }, + { + "Answer": 3683.333333333334, + "Options": "a ) $ 1116.3 , b ) $ 3583.3 , c ) $ 3283.3 , d ) $ 3683.3 , e ) $ 2683.3", + "Correct": "d", + "Explanation": "explanation : let ' s start with what the total price of the washing machine would be . if 15 % is equal to $ 650 then 100 % equals $ x . we just have to multiply $ 650 by 6.67 to get total amount = $ 4333.3 . out of this amount we then need to deduct the amount already paid which was $ 650 so we have $ 4333.3 - $ 650 = $ 3683.3 answer : option d" + }, + { + "Answer": 2000, + "Options": "a ) 600 , b ) 1200 , c ) 1500 , d ) 1600 , e ) 2000", + "Correct": "e", + "Explanation": "\"sugar : flour = 5 : 6 = 25 : 30 ; flour : soda = 10 : 1 = 30 : 3 ; thus we have that sugar : flour : soda = 25 x : 30 x : 3 x . also given that 30 x / ( 3 x + 60 ) = 8 / 1 - - > x = 80 - - > sugar = 25 x = 2,000 . answer : e .\"" + }, + { + "Answer": 1024, + "Options": "a ) 4 , b ) 16 , c ) 64 , d ) 256 , e ) 1024", + "Correct": "e", + "Explanation": "\"x * ( 1 / 4 ) ^ 2 = 4 ^ 3 x = 4 ^ 2 * 4 ^ 3 = 4 ^ 5 = 1024 the answer is e .\"" + }, + { + "Answer": 251, + "Options": "a ) 151 , b ) 149 , c ) 152 , d ) 251 , e ) none of the above", + "Correct": "d", + "Explanation": "\"corrected mean = 250 \u00d7 30 \u2212 135 + 165 / 30 = 7500 \u2212 135 + 165 / 30 = 7530 / 30 = 251 answer d\"" + }, + { + "Answer": 9.8019801980198, + "Options": "a ) 9.3 , b ) 9.6 , c ) 9.8 , d ) 10.1 , e ) 10.3", + "Correct": "c", + "Explanation": "\"distance = 20 km time = 9 / 11 + 11 / 9 = ( 81 + 121 ) / 99 = 202 / 99 hours average speed = ( 20 * 99 ) / 202 = 9.8 km / h the answer is c .\"" + }, + { + "Answer": 228, + "Options": "a ) 200 , b ) 228 , c ) 182 , d ) 102 , e ) 128", + "Correct": "b", + "Explanation": "\"a 2 - b 2 = 10 : given a 4 + b 4 - 2 a 2 b 2 = 102 : square both sides and expand . a * b = 8 : given a 2 b 2 = 82 : square both sides . a 4 + b 4 - 2 ( 64 ) = 100 : substitute a 4 + b 4 = 228 correct answer b\"" + }, + { + "Answer": 51, + "Options": "a ) 51 , b ) 55 , c ) 59 , d ) 71 , e ) 92", + "Correct": "a", + "Explanation": "total = 58 thrower = 37 rest = 58 - 37 = 21 left handed = 21 / 3 = 7 right handed = 14 if all thrower are right handed then total right handed is 37 + 14 = 51 so a . 51 is the right answer" + }, + { + "Answer": 110, + "Options": "a ) 75 , b ) 110 , c ) 125 , d ) 175 , e ) 225", + "Correct": "b", + "Explanation": "\"female = x male = 660 - x x / 2 + 660 - x / 4 = 1 / 3 * ( 660 ) = 220 x = 220 x / 2 = 110 is supposed to be the answer m is missing something correct option b\"" + }, + { + "Answer": 4.5, + "Options": "a ) 4 , b ) 2 , c ) 9 / 2 , d ) - 9 / 2 , e ) - 8 / 2", + "Correct": "c", + "Explanation": "work within the parenthesis first so solve ( 3 @ 2 ) first ( 3 @ 2 ) = ( 3 ^ 2 ) / 2 = 9 / 2 so 9 / 2 is the answer . . . . this question is merely testing order of operations remember pemdas answer : c" + }, + { + "Answer": 3, + "Options": "a ) 8 , b ) 5 , c ) 11 , d ) 3 , e ) 4", + "Correct": "d", + "Explanation": "\"6 * 15 * 3 = ( \u221a ( 6 + 2 ) ( 15 + 3 ) ) / ( 3 + 1 ) = ( \u221a 8 * 18 ) / 4 = ( \u221a 144 ) / 4 = 12 / 4 = 3 . answer is d .\"" + }, + { + "Answer": 40, + "Options": "a ) 1 , b ) 10 , c ) 19 , d ) 40 , e ) 21", + "Correct": "d", + "Explanation": "\"this is a solution from beatthegmat : even numbers : ( 80 - 2 ) / 2 + 1 = 40 even integers . ( 80 + 2 ) / 2 = 41 is the average of the even set . sum = avg * ( # of elements ) = 41 * 40 = 1640 = a odd numbers : ( 79 - 1 ) / 2 + 1 = 40 odd integers . ( 79 + 1 ) / 2 = 40 is the average of the odd set . sum = avg * ( # of elements ) = 40 * 40 = 1600 = b a - b = 1640 - 1600 = 40 . answer : d\"" + }, + { + "Answer": 6150, + "Options": "a ) 256 , b ) 512 , c ) 768 , d ) 6144 , e ) 1536", + "Correct": "d", + "Explanation": "\"0.6 * 2 ^ 10 = 0.6 * 1024 = 614.4 the answer is d .\"" + }, + { + "Answer": 18, + "Options": "a ) 18 , b ) 16 , c ) 34 , d ) 25 , e ) 12", + "Correct": "a", + "Explanation": "father ' s age = 10 x + y so son ' s age = 10 y + x . . after 5 years , 10 x + y + 5 = 2 * ( 10 y + x + 5 ) . . . . so 5 + 19 y = 8 x . . . check for odd values of y , y = 1 satisfies the eqn with x = 3 . . . so ages are 31 and 13 and ans as found correctly by u is a . . 18" + }, + { + "Answer": 4000, + "Options": "a ) 2000 , b ) 3000 , c ) 4000 , d ) 5000 , e ) 6200", + "Correct": "c", + "Explanation": "\"explanation : let monthly income of a = a monthly income of b = b monthly income of c = c a + b = 2 \u00d7 5050 . . . . ( equation 1 ) b + c = 2 \u00d7 6250 . . . . ( equation 2 ) a + c = 2 \u00d7 5200 . . . . ( equation 3 ) ( equation 1 ) + ( equation 3 ) - ( equation 2 ) = > a + b + a + c - ( b + c ) = ( 2 \u00d7 5050 ) + ( 2 \u00d7 5200 ) - ( 2 \u00d7 6250 ) = > 2 a = 2 ( 5050 + 5200 - 6250 ) = > a = 4000 i . e . , monthly income of a = 4000 answer is c\"" + }, + { + "Answer": 23, + "Options": "a ) 20 , b ) 21 , c ) 23 , d ) 25 , e ) 26", + "Correct": "c", + "Explanation": "\"let the average age of the whole team be x years . 11 x - ( 25 + 30 ) = 9 ( x - 1 ) 11 x - 9 x = 46 2 x = 46 x = 23 . the average age of the team is 23 years . the answer is c .\"" + }, + { + "Answer": 6, + "Options": "a ) 10 , b ) 19 , c ) 20 , d ) 9 , e ) 12", + "Correct": "d", + "Explanation": "d" + }, + { + "Answer": 70, + "Options": "a ) 40 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 80 %", + "Correct": "d", + "Explanation": "can be reduced to 2 y / 5 + 3 y / 10 = 2 y / 5 = 70 % d" + }, + { + "Answer": 44.44444444444444, + "Options": "a ) 45 % , b ) 55 % , c ) 35 % , d ) 40 % , e ) 44.44 %", + "Correct": "e", + "Explanation": "\"x * y = constt . let x = y = 100 in beginning i . e . x * y = 100 * 100 = 10000 x ( 100 ) - - - becomes - - - > 1.8 x ( 180 ) i . e . 180 * new ' y ' = 10000 i . e . new ' y ' = 10000 / 180 = 55.55 i . e . y decreases from 100 to 55.55 i . e . decrease of 44.44 % answer : option e\"" + }, + { + "Answer": 9, + "Options": "a ) 11 , b ) 12 , c ) 9 , d ) 14 , e ) 15", + "Correct": "c", + "Explanation": "\"explanation : age of the 15 th student = [ 15 * 15 - ( 14 * 5 + 16 * 9 ) ] = 9 years . answer : c\"" + }, + { + "Answer": 80, + "Options": "a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80", + "Correct": "e", + "Explanation": "\"let number of pounds of 5 $ candy to be used be w 6 = ( 20 * 10 + 5 * w ) / ( 20 + w ) = > 120 + 6 w = 200 + 5 w = > w = 80 answer e\"" + }, + { + "Answer": 18, + "Options": "a ) 16 , b ) 12 , c ) 15 , d ) 18 , e ) 10", + "Correct": "d", + "Explanation": "\"( a + b ) - ( b - c ) = 18 a - c = 18 answer is d\"" + }, + { + "Answer": 16, + "Options": "a ) $ 14 , b ) $ 2 , c ) $ 10 , d ) $ 16 , e ) $ 18", + "Correct": "d", + "Explanation": "sale price ( sp ) = 240 + markup ( mp ) - - > mp = sp - 240 and given mp = sp / 4 ( 25 % is 1 / 4 th ) so sp / 4 = sp - 240 3 sp / 4 = 240 sp = 320 now a discount of 20 % is given so new sp is . 8 * 320 = 256 profit = 256 - 240 = 16 answer is d" + }, + { + "Answer": 96, + "Options": "a ) 92 , b ) 96 , c ) 100 , d ) 104 , e ) 108", + "Correct": "b", + "Explanation": "\"1 / 4 + 1 / 8 + 1 / 12 + 1 / 6 = ( 6 + 3 + 2 + 4 ) / 24 = 15 / 24 let x be the number of passengers on the ship . 36 = ( 9 / 24 ) x = 3 x / 8 x = 96 the answer is b .\"" + }, + { + "Answer": 125, + "Options": "a ) $ 125 , b ) $ 135 , c ) $ 145 , d ) $ 155 , e ) $ 165", + "Correct": "a", + "Explanation": "let p be jack ' s original paycheck value . the value after taxes t is given by t = p - 20 % p let s be the amount put into savings , given by s = t - 80 % t for s = $ 20 , solve for p $ 20 = ( p - 20 % p ) - 80 % ( p - 20 % p ) p = $ 125 correct answer a" + }, + { + "Answer": 0.84, + "Options": "a ) 9 / 25 , b ) 10 / 25 , c ) 6 / 10 , d ) 2 / 3 , e ) 21 / 25", + "Correct": "e", + "Explanation": "\"simply look at the question from the other side . what is the probability that you can \u2019 t row the canoe ? this would be 2 / 5 x 2 / 5 = 4 / 25 . using the idea that the probability of something happening is 1 \u2013 the probability that it doesn \u2019 t happen , you can use the following equation to reach the right answer w : 1 \u2013 4 / 25 = 21 / 25 . answer choice e .\"" + }, + { + "Answer": 468, + "Options": "a ) 518 , b ) 452 , c ) 468 , d ) 502 , e ) 396", + "Correct": "c", + "Explanation": "solution 96 pages were unread so on second week have 5 / 9 so unread pages = 1 - 5 / 9 = 4 / 9 96 * 9 / 4 = 216 then , on first week unread pages were 216 total pages = 216 * 13 / 6 = 468 so answer is c" + }, + { + "Answer": 0.0012000000000000001, + "Options": "a ) 0.012 , b ) 0.12 , c ) 0.0012 , d ) 0.00012 , e ) none of them", + "Correct": "c", + "Explanation": "204 / 17 = 12 . dividend contains 4 places of decimal . 0.2040 / 17 = 0.0012 . answer is c ." + }, + { + "Answer": 77, + "Options": "a ) 57 , b ) 67 , c ) 77 , d ) 87 , e ) 97", + "Correct": "c", + "Explanation": "\"money collected = ( 59.29 x 100 ) paise = 5929 paise . number of members = 5929 = 77 . answer : c\"" + }, + { + "Answer": 1, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 6", + "Correct": "b", + "Explanation": "a = 3 , b = - 6 , c = 3 x 1,2 = ( 6 \u00b1 \u221a ( ( - 6 ) 2 - 4 \u00d7 3 \u00d7 3 ) ) / ( 2 \u00d7 3 ) = ( 6 \u00b1 \u221a ( 36 - 36 ) ) / 6 = ( 6 \u00b1 0 ) / 6 x 1 = x 2 = 1 b" + }, + { + "Answer": 20, + "Options": "a ) 6 , b ) 12 , c ) 14 , d ) 16 , e ) 20", + "Correct": "e", + "Explanation": "equate the fat : 0.1 x + 0.45 * 8 = 0.2 ( x + 8 ) - - > x = 20 . answer : e ." + }, + { + "Answer": 306, + "Options": "a ) 230 , b ) 274 , c ) 306 , d ) 354 , e ) 424", + "Correct": "c", + "Explanation": "\"2 * 18 c 2 = 2 * 153 = 306 the answer is c .\"" + }, + { + "Answer": 1.2000000000000002, + "Options": "a ) 1.2 , b ) 1.5 , c ) 1.8 , d ) 2.1 , e ) 2.4", + "Correct": "a", + "Explanation": "let x be the amount of pure alcohol required . 0.4 ( 6 ) + x = 0.5 ( x + 6 ) 0.5 x = 3 - 2.4 x = 1.2 liters the answer is a ." + }, + { + "Answer": 8, + "Options": "a ) 0 , b ) 1 , c ) 3 , d ) 4 , e ) 8", + "Correct": "e", + "Explanation": "i tried plugging in numbers x = 9 q + 5 x = 14 7 x = 98 7 x / 9 = 9 * 10 + 8 remainder is 8 answer is e ." + }, + { + "Answer": 3, + "Options": "a ) 5 , b ) 3 , c ) 6 , d ) 7 , e ) 10", + "Correct": "b", + "Explanation": "\"cant think of a straight approach but here is how i solved it : k is divided by 5 and remainder is 2 . this means k = 5 n + 2 ( n is an integer ) so the possible values of k = { 2 , 7 , 12 , 17 , 22 , 27 , 32 , 37 } ( less than 42 ) secondly , if k is divided by 6 , the remainder is 5 = > k = 6 m + 5 so the possible value set for k = { 5 , 11 , 17 , 23 , 29 , 35,41 } ( less than 42 ) 17 is the only common number in both the sets . hence k = 17 answer : b\"" + }, + { + "Answer": 40, + "Options": "a ) 40 , b ) 120 , c ) 130 , d ) 140 , e ) 150", + "Correct": "a", + "Explanation": "\"solution : let xx be the number he chose , then 6 \u22c5 x \u2212 138 = 102 6 x = 240 x = 40 answer a\"" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "c", + "Explanation": "\"explanation : total age of 4 members , 10 years ago = ( 24 x 4 ) years = 96 years . total age of 4 members now = [ 96 + ( 10 x 4 ) ] years = 136 years . total age of 6 members now = ( 24 x 6 ) years = 144 years . sum of the ages of 2 children = ( 144 - 136 ) years = 8 years . let the age of the younger child be x years . then , age of the elder child = ( x + 2 ) years . so , x + ( x + 2 ) = 8 \u21d4 x = 3 age of younger child = 3 years . answer : c\"" + }, + { + "Answer": 510, + "Options": "a ) 233 , b ) 600 , c ) 510 , d ) 771 , e ) 191", + "Correct": "c", + "Explanation": "\"explanation : total salary of 8 workers and supervisor together = 9 \u00e3 \u2014 430 = 3870 now total salary of 8 workers = 3870 \u00e2 \u02c6 \u2019 870 = 3000 total salary of 9 workers including the new supervisor = 9 \u00e3 \u2014 390 = 3510 salary of the new supervisor = 3510 \u00e2 \u02c6 \u2019 3000 = 510 answer : c\"" + }, + { + "Answer": 0.11764705882352941, + "Options": "a ) 1 / 16 , b ) 2 / 15 , c ) 2 / 17 , d ) 1 / 8 , e ) 1 / 7", + "Correct": "c", + "Explanation": "\"let x be the fraction of the distance that b runs . let v be the speed at which b runs . the time should be the same for both runners . time = d / ( 17 v / 15 ) = xd / v ( 15 / 17 ) * d / v = x * d / v x = 15 / 17 b should have a head start of 2 / 17 of the full distance . the answer is c .\"" + }, + { + "Answer": 6075, + "Options": "a ) 6150 , b ) 6200 , c ) 6050 , d ) 6075 , e ) 5075", + "Correct": "d", + "Explanation": "\"explanation : to solve this use the formula of ap , sn = ( n / 2 ) ( a + l ) . . . . . . . . . . . . . . . . ( 1 ) to find n , use = > tn = a + ( n - 1 ) d = > 89 = 1 + ( n - 1 ) 2 = > n = 45 use value of n in ( 1 ) then , sn = ( 45 / 2 ) ( 1 + 89 ) = 2025 ans : - 3 ( sn ) = 6075 answer : d\"" + }, + { + "Answer": 84, + "Options": "a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %", + "Correct": "d", + "Explanation": "\"d the prompt says that 68 % of the population lies between m - d and m + d . thus , 32 % of the population is less than m - d or greater than m + d . since the population is symmetric , half of this 32 % is less than m - d and half is greater than m + d . thus , q = ( 68 + 16 ) % or ( 100 - 16 ) % of the population is less than m + d .\"" + }, + { + "Answer": 6, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "d", + "Explanation": "the last digit of 11 n \u2212 1 is 0 , so 5 always divides 11 n \u2212 1 . also , checking the remainders when the powers of 11 are divided by 3 and 7 we get that 3 divides 11 n \u2212 1 exactly when n is even , and 7 divides 11 n \u2212 1 exactly when 3 divides n . correct answer d" + }, + { + "Answer": 59, + "Options": "a ) 2 , b ) 4 , c ) 8 , d ) 59 , e ) 32", + "Correct": "d", + "Explanation": "\"lets assign variables to all the areas in venn diagram of three . three different units are dog , cat , snake = total = 89 only dog = d = 15 only cat = c = 10 only snake = s exactly dog and cat = 5 exactly dog and snake = x exactly cat and snake = y all three = 3 so 89 = 15 + 10 + 5 + 3 + x + y + s we need to know total snakes = x + y + s + 3 = 59 answer : d\"" + }, + { + "Answer": 225, + "Options": "a ) $ 155 , b ) $ 225 , c ) $ 510 , d ) $ 850 , e ) $ 1250", + "Correct": "b", + "Explanation": "\"the volume of each box is 20 * 20 * 12 = 4800 cubic inches . number of boxes = 2 , 160,000 / 4800 = 450 boxes total cost = 450 \u00d7 $ 0.5 = $ 225 the answer is b .\"" + }, + { + "Answer": 45, + "Options": "a ) 90 , b ) 45 , c ) 110 , d ) 40 , e ) 50", + "Correct": "b", + "Explanation": "\"explanation : milk : water = 6 : 3 6 x : 3 x + 10 = 6 : 5 5 [ 6 x ] = 6 [ 3 x + 10 ] 30 x = 18 x + 60 30 x - 18 x = 60 12 x = 60 x = 5 the quantity of milk in the original mixture is = 6 : 3 = 6 + 3 = 9 9 x = 45 short cut method - 2 : for only milk problems milk : water 6 : 3 6 : 5 milk ratio same but water ratio 2 part incress per 10 liters 2 part of ratio - - - - - - - > 10 liters 9 part of ratio - - - - - - - > 45 liters answer : option b\"" + }, + { + "Answer": 0.7142857142857143, + "Options": "a ) 1 / 2 , b ) 3 / 5 , c ) 4 / 7 , d ) 5 / 7 , e ) 7 / 9", + "Correct": "d", + "Explanation": "\"let the original fraction be x / y then , 120 % of x / 90 % of y = 20 / 21 120 x / 90 y = 20 / 21 x / y = 5 / 7 answer is d\"" + }, + { + "Answer": 0.2, + "Options": "a ) 1 / 5 , b ) 3 / 4 , c ) 4 / 5 , d ) 5 / 4 , e ) 3 / 2", + "Correct": "a", + "Explanation": "\"a / b = 4 / 5 m / x = ( 1 / 5 ) * 5 / ( 5 / 4 ) * 4 = 1 / 5 the answer is a .\"" + }, + { + "Answer": 20000, + "Options": "a ) rs . 22,000 , b ) rs . 21,000 , c ) rs . 20,000 , d ) rs . 23,000 , e ) rs . 24,000", + "Correct": "c", + "Explanation": "\"income = rs . 100 expenditure = rs . 90 savings = rs . 10 present expenditure 90 + 90 * ( 10 / 100 ) = rs . 99 present savings = 100 \u2013 99 = rs . 1 if savings is rs . 1 , salary = rs . 100 if savings is rs . 200 , salary = 100 / 1 * 200 = 20000 answer : c\"" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "a", + "Explanation": "since bianca and callie are both within 1 jelly bean of each other and aaron has 5 , dante must provide 3 of his 9 jelly beans so each child has no more than 1 fewer jelly bean than any other child . dante + aaron = 9 + 5 = 14 / 2 = 7 9 - 8 = 1 so dante must provide 3 jelly beans to aaron . answer ( a )" + }, + { + "Answer": 0.7857142857142856, + "Options": "a ) 11 / 14 , b ) 13 / 18 , c ) 4 / 7 , d ) 3 / 7 , e ) 3 / 14", + "Correct": "a", + "Explanation": "\"if we use variable for total votes there will be too many fractions to manipulate with , so pick some smart # : let set total # of votes is 18 . 2 / 9 of the votes on a certain resolution have been counted - - > 4 counted and 18 - 4 = 14 votes left to be counted ; 3 / 4 of those counted are in favor of the resolution - - > 3 in favor and 1 against ; ratio of those who voted against to those who voted for to be 2 to 1 there should be total of 18 * 2 / 3 = 12 people who voted against , so in the remaining 14 votes there should be 12 - 1 = 11 people who voted against . thus f = 11 / 14 of the remaining votes must be against . answer : a .\"" + }, + { + "Answer": 796, + "Options": "a ) 50 , b ) 200 , c ) 380 , d ) 798 , e ) 400", + "Correct": "d", + "Explanation": "1 / 20 % of 8000 = 4 1 / 10 of 8000 = 800 800 - 2 = 798 ans : d" + }, + { + "Answer": 25, + "Options": "a ) 33 , b ) 28 , c ) 27 , d ) 25 , e ) 23", + "Correct": "d", + "Explanation": "\"it is given that a quartile is the middle number of all numbers less than median . . so lets arrange the number in ascending order - 42 , 24 , 30 , 28 , 26 , 19 , 33 and 35 19 , 24 , 26 , 28 , 30 , 33 , 35 , 42 . . . numbers less than median are 19 , 24 , 26 , 28 . . the median of these numbers = center of 24 and 26 = 25 d\"" + }, + { + "Answer": 128, + "Options": "a ) 128 , b ) 142 , c ) 143 , d ) 141 , e ) 129", + "Correct": "e", + "Explanation": "\"minimum three digit number is 100 and maximum three digit number is 999 . the first three digit number that leaves remainder 5 when divided by 7 is 103 . 14 * 7 = 98 + 5 = 103 the second three digit number that leaves remainder 5 when divided by 7 is 110 . 15 * 7 = 105 + 5 = 110 the third three digit number that leaves remainder 5 when divided by 7 is 117 and so on the last three digit number that leaves remainder 5 when divided by 7 is 999 142 * 7 = 994 + 5 = 999 therefore , we identify the sequence 103 , 110,117 . . . . . 999 use the formula of last term last term = first term + ( n - 1 ) * common difference you will get the answer 129 that is definitely e .\"" + }, + { + "Answer": 500, + "Options": "a ) 500 , b ) 1000 , c ) 1200 , d ) 1300 , e ) 1500", + "Correct": "a", + "Explanation": "let the price of a chudi and a top be rs . x and rs . y respectively . then , 3 x + 6 y = 1500 . . . . ( i ) and x + 12 y = 1500 . . . . ( ii ) divide equation ( i ) by 3 , we get the below equation . = x + 2 y = 500 . - - - ( iii ) now subtract ( iii ) from ( ii ) x + 12 y = 1500 ( - ) x + 2 y = 500 - - - - - - - - - - - - - - - - 10 y = 1000 - - - - - - - - - - - - - - - - cost of 5 tops = 5 * 100 = 500 answer : a" + }, + { + "Answer": 3, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "b", + "Explanation": "\"when a certain number x is divided by 63 , the remainder is 27 . what is the remainder when x is divided by 8 ? putting a value say x = 27 we get remainder as 27 when divided by 63 . when 27 divided by 8 we get 3 as remainder . b is the answer .\"" + }, + { + "Answer": 11, + "Options": "a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14", + "Correct": "b", + "Explanation": "\"d = ( d - r ) / q = ( 100 - 1 ) / 9 = 99 / 9 = 11 b )\"" + }, + { + "Answer": 66, + "Options": "a ) 1 , b ) 63 , c ) 66 , d ) 67 , e ) none of these", + "Correct": "c", + "Explanation": "\"( x ^ n + 1 ) will be divisible by ( x + 1 ) only when n is odd ; ( 67 ^ 67 + 1 ) will be divisible by ( 67 + 1 ) ; ( 67 ^ 67 + 1 ) + 66 when divided by 68 will give 66 as remainder . correct option : c\"" + }, + { + "Answer": 4, + "Options": "a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10", + "Correct": "b", + "Explanation": "use the initial letter of each name as a variable : r = k + 2 b = m \u2212 6 m = r + 2 k = 2 + bk = = r \u2212 2 b = k \u2212 2 = ( r \u2212 2 ) \u2212 2 = r \u2212 4 m = r + 2 r + b + m + k = 20 r + r \u2212 4 + r + 2 + r \u2212 2 = 20 r = 6 k = r \u2212 2 = 6 \u2212 2 = 4 answer : b" + }, + { + "Answer": 0.36363636363636365, + "Options": "a ) 2 / 9 , b ) 1 / 3 , c ) 4 / 11 , d ) 2 / 3 , e ) 7 / 9", + "Correct": "c", + "Explanation": "mode : the mode of any set is the term which has the highest frequency ( occurrence ) highest frequent term in the set is 5 ( with frequency 4 ) hence mode = 5 two terms ( 3 , 3 , 4 , 4 ) out of a total of 11 terms are less than mode of the set . fraction of set that are less than mode of set = 4 / 11 answer : option c" + }, + { + "Answer": 23.17142857142857, + "Options": "a ) 31.23 , b ) 25.12 , c ) 36.25 , d ) 23.17 , e ) 27.66", + "Correct": "d", + "Explanation": "total score of the batsman in 22 matches = 616 . total score of the batsman in the next 13 matches = 195 . total score of the batsman in the 35 matches = 811 . average score of the batsman = 811 / 35 = 23.17 . answer : d" + }, + { + "Answer": 90, + "Options": "a ) 48 , b ) 54 , c ) 72 , d ) 84 , e ) 90", + "Correct": "e", + "Explanation": "\"let the second number be x . then , first number = 2 x and third number = 2 x / 3 . 2 x + x + 2 x / 3 = 330 11 x / 3 = 330 x = 90 answer : e\"" + }, + { + "Answer": 750, + "Options": "a ) 1250 , b ) 625 , c ) 600 , d ) 750 , e ) 375", + "Correct": "d", + "Explanation": "\"max no . of crates = 5 . max weight = 150 kg max . weight carried = 5 * 150 = 750 kg = d\"" + }, + { + "Answer": 8, + "Options": "a ) 17 years , b ) 19 years , c ) 29 years , d ) 8 years , e ) 12 years", + "Correct": "d", + "Explanation": "\"let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 22 5 x = 20 = > x = 4 hence , b ' s age = 2 x = 8 years . answer : d\"" + }, + { + "Answer": 20, + "Options": "a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30", + "Correct": "c", + "Explanation": "as half the circle shape consist of 16 - 6 = 10 boys , so total number of boys in full circle = 2 * 10 = 20 answer : c" + }, + { + "Answer": 1892.8571428571427, + "Options": "a ) rs . 1000.15 , b ) rs . 1100.95 , c ) rs . 1892.85 , d ) rs . 1050.85 , e ) rs . 1200.25", + "Correct": "c", + "Explanation": "\"2120 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 1892.85 answer : c\"" + }, + { + "Answer": 8, + "Options": "a ) 8 , b ) 12 , c ) 15 , d ) 17 , e ) 18", + "Correct": "a", + "Explanation": "\"let original strength = y then , 40 y + 8 x 32 = ( y + 8 ) x 36 \u00e2 \u2021 \u2019 40 y + 256 = 36 y + 288 \u00e2 \u2021 \u2019 4 y = 32 \u00e2 \u02c6 \u00b4 y = 8 a\"" + }, + { + "Answer": 2, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "b", + "Explanation": "\"that is 1056 / 23 = 45 remainder = 21 = > 21 + 2 = 23 hence 2 should be added to 1056 so that the sum will be divisible by 23 answer is option b\"" + }, + { + "Answer": 480, + "Options": "a ) 96 , b ) 240 , c ) t = 256 , d ) t = 384 , e ) t = 480", + "Correct": "e", + "Explanation": "\"most test takers would recognize the system of equations in this prompt and just do algebra to get to the solution ( and that ' s fine ) . the wording of the prompt and the ' spread ' of the answer choices actually provide an interesting ' brute force ' shortcut that you can take advantage of to eliminate the 4 wrong answers . . . . we ' re told that there are 2 types of boxes : those that hold 12 glasses and those that hold 16 glasses . since the average number of boxes is 15 , we know that there must be at least some of each . we ' re also told that that there are 16 more of the larger boxes . this means , at the minimum , we have . . . 1 small box and 17 large boxes = 1 ( 12 ) + 17 ( 16 ) = 12 + 272 = 284 glasses at the minimum since the question asks for the total number of glasses , we can now eliminate answers a , b and c . . . . the difference in the number of boxes must be 16 though , so we could have . . . . 2 small boxes and 18 large boxes 3 small boxes and 19 large boxes etc . with every additional small box + large box that we add , we add 12 + 16 = 28 more glasses . thus , we can justadd 28 suntil we hit the correct answer . . . . 284 + 28 = 312 312 + 28 = 340 340 + 28 = 368 368 + 28 = 396 at this point , we ' ve ' gone past ' answer d , so the correct answer must be answer e . . . . . but here ' s the proof . . . . 396 + 28 = 424 424 + 28 = 452 452 + 28 = 480 final answer : e\"" + }, + { + "Answer": 792, + "Options": "a ) 694 , b ) 792 , c ) 698 , d ) 784 , e ) 789", + "Correct": "b", + "Explanation": "explanation : number of digits in 1 digit numbers = 1 to 9 = 9 number of digits in 2 digit numbers = 10 to 99 = 90 ( 2 ) = 180 number of digits in 3 digit numbers = 100 to 300 = 201 ( 3 ) = 603 total = 792 answer : option b" + }, + { + "Answer": 1399.9999999999998, + "Options": "a ) 1200 , b ) 3000 , c ) 1000 , d ) 1400 , e ) 2400", + "Correct": "d", + "Explanation": "\"let the additional invested amount for 8 % interest be x ; equation will be ; 2800 + 0.05 * 2800 + x + 0.08 x = 2800 + x + 0.06 ( 2800 + x ) 0.05 * 2800 + 0.08 x = 0.06 x + 0.06 * 2800 0.02 x = 2800 ( 0.06 - 0.05 ) x = 2800 * 0.01 / 0.02 = 1400 ans : ` ` d ' '\"" + }, + { + "Answer": 48, + "Options": "a ) 46 , b ) 47 , c ) 48 , d ) 49 , e ) 50", + "Correct": "c", + "Explanation": "\"mother + daughter + child = 120 kg daughter + child = 60 kg mother = 120 - 60 = 60 kg child = 1 / 5 th of mother = ( 1 / 5 ) * 60 = 12 kg so now daughter = 120 - ( mother + child ) = 120 - ( 60 + 12 ) = 48 kg answer : c\"" + }, + { + "Answer": 1.4999999999999998, + "Options": "a ) 1 / 2 , b ) 3 / 2 , c ) 1 / 3 , d ) 2 / 3 , e ) 4 / 3", + "Correct": "b", + "Explanation": "\"( 1 / 2 ) g = ( 1 / 5 ) ( b + g ) 5 g = 2 b + 2 g 3 g = 2 b b / g = 3 / 2 . the answer is b .\"" + }, + { + "Answer": 4, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "d", + "Explanation": "\"substitute y by 3 in x + 2 y = 10 x + 2 ( 3 ) = 10 x + 6 = 10 if we substitute x by 4 in x + 6 = 10 , we have 4 + 6 = 10 . hence x = 4 correct answer d\"" + }, + { + "Answer": 800, + "Options": "a ) 800 , b ) 1000 , c ) 1200 , d ) 1400 , e ) 1600", + "Correct": "a", + "Explanation": "\"10 a * 6 b = 20 * 20 = 400 60 ab = 400 i . e . 120 ab = 800 answer : option a\"" + }, + { + "Answer": 448.0000000000291, + "Options": "a ) 418 , b ) 148 , c ) 448 , d ) 248 , e ) 348", + "Correct": "c", + "Explanation": "\"7844213 / 549 = 14288 and reminder = 101 . 549 - 101 = 448 so , the next number divisible by 549 is 448 places in front of 7844213 which means 448 + 7844213 = 7844661 448 should be added to 7844213 c\"" + }, + { + "Answer": 24, + "Options": "a ) 20 inches , b ) 77 inches , c ) 24 inches , d ) 97 inches , e ) 66 inches", + "Correct": "c", + "Explanation": "\"explanation : total length of scale in inches = ( 7 * 12 ) + 12 = 96 inches length of each of the 4 parts = 96 / 4 = 24 inches answer : c\"" + }, + { + "Answer": 20, + "Options": "a ) 18 , b ) 20 , c ) 12 , d ) 8 , e ) 4", + "Correct": "b", + "Explanation": "\"n - not rented trucks ; r - rented trucks n + r = 20 n + r / 2 = 10 r = 20 b\"" + }, + { + "Answer": 36.02, + "Options": "a ) 36.7 , b ) 36.1 , c ) 36.5 , d ) 36.02 , e ) 36.3", + "Correct": "d", + "Explanation": "\"correct sum = ( 36 * 50 + 48 - 47 ) = 1801 . correct mean = 1801 / 50 = 36.02 answer : d\"" + }, + { + "Answer": 12, + "Options": "a ) 11.0 , b ) 12.0 , c ) 13.0 , d ) 14.0 , e ) 15.0", + "Correct": "b", + "Explanation": "solution : h stopped 1000 ft before reaching the final point , time taken to reach 4000 ft = 4000 / 800 = 5 hrs . this means she reached there at 11 : 00 . speed difference between them is 800 - 500 = 300 ft / hr so by the time h stops they have 1500 ft of distance so now here we use relative speed formula they both are travelling toward each other with speed of 1000 and 500 total 1500 ft / hr and distance bwn them is 1500 ft so time taken to meet = 1 hr from 11 : 00 means 12 : 00 is the answer . b" + }, + { + "Answer": 80, + "Options": "a ) $ 80 , b ) $ 50 , c ) $ 25 , d ) $ 200 , e ) $ 50", + "Correct": "a", + "Explanation": "\"a : ( b + c ) = 2 : 3 a ' s share = 200 * 2 / 5 = $ 80 answer is a\"" + }, + { + "Answer": 174.99999999999986, + "Options": "a ) 173 , b ) 174 , c ) 175 , d ) 176 , e ) 177", + "Correct": "c", + "Explanation": "\"12.4 * x + 26 = ( 8 + x ) 12 solve equation x = 175 answer : c\"" + }, + { + "Answer": 9, + "Options": "a ) 0 , b ) 9 , c ) 19 , d ) 29 , e ) 18", + "Correct": "b", + "Explanation": "number = 342 k + 47 = 19 * 18 k + 19 * 2 + 9 = 19 ( 18 k + 2 ) + 9 . the given number when divided by 19 gives 18 k + 2 as quotient and 9 as remainder . answer b 9" + }, + { + "Answer": 29, + "Options": "a ) 26 , b ) 27 , c ) 28 , d ) 29 , e ) 30", + "Correct": "d", + "Explanation": "\"the average of 24 , 35 , and 58 is 39 . the average of 19 , 51 and x is 33 . then 19 + 51 + x = 99 . x = 29 . the answer is d .\"" + }, + { + "Answer": 96, + "Options": "a ) 98 % , b ) 97 % , c ) 96 % , d ) 99 % , e ) 95 %", + "Correct": "c", + "Explanation": "\"let the number be x the right number is 5 x the wrong number is x / 5 error is ( 5 x - x / 5 ) = 24 x / 5 percentage of error is ( ( 24 x / 5 ) / 5 x ) * 100 = 96 % answer : c\"" + }, + { + "Answer": 84.70588235294117, + "Options": "a ) 71.11 , b ) 84.7 , c ) 71.1 , d ) 71.17 , e ) 71.13", + "Correct": "b", + "Explanation": "\"car travels first 160 km at 90 km / hr time taken to travel first 160 km = distancespeed = 160 / 90 car travels next 160 km at 80 km / hr time taken to travel next 160 km = distancespeed = 160 / 80 total distance traveled = 160 + 160 = 2 \u00d7 160 total time taken = 160 / 90 + 160 / 80 average speed = total distance traveled / total time taken = 320 / ( 160 / 90 + 160 / 80 ) = 84.7 km / hr answer : b\"" + }, + { + "Answer": 60000, + "Options": "a ) $ 40,000 , b ) $ 56,000 , c ) $ 60,000 , d ) $ 66,667 , e ) $ 80,000", + "Correct": "c", + "Explanation": "\"equation is correct , so math must be a problem . 0.10 * 40,000 + 0.2 * ( x - 40,000 ) = 8,000 - - > 4,000 + 0.2 x - 8,000 = 8,000 - - > 0.2 x = 12,000 - - > x = 60,000 . answer : c .\"" + }, + { + "Answer": 88, + "Options": "a ) 80 , b ) 82 , c ) 84 , d ) 86 , e ) 88", + "Correct": "e", + "Explanation": "e . 88 peter must score at least an 80 for sure . if he scores an 8 , then he will need to score 2 pots for each of the 4 other tests tomake upthe difference . they each were at 78 ( at least the average is , but this is a small point and does n ' t matter to the answer ) . so 4 tests that were each 2 points short of the 80 average that is desired means the next test must be 8 points higher than the desired average , so 80 + 8 = 88 ." + }, + { + "Answer": 256.2, + "Options": "a ) 190 , b ) 284.6 , c ) 300 , d ) 256 , e ) 312", + "Correct": "d", + "Explanation": "\"so 12.2 * 21 = 256 . . imo option d is correct answer . .\"" + }, + { + "Answer": 44, + "Options": "a ) 45 , b ) 38 , c ) 44 , d ) 40 , e ) 46", + "Correct": "c", + "Explanation": "\"n th term of a . p = a + ( n - 1 ) * d = 2 + ( 15 - 1 ) * 3 , = 2 + 42 = 44 . answer : c\"" + }, + { + "Answer": 3500, + "Options": "a ) 1900 , b ) 3500 , c ) 4000 , d ) 4200 , e ) 4450", + "Correct": "b", + "Explanation": "\"let the number of 50 \u2013 rupee notes be x . then , the number of 100 - rupee notes = ( 85 \u2013 x ) 50 x + 100 ( 85 \u2013 x ) = 5000 = x + 2 ( 85 \u2013 x ) = 100 = x = 70 so , required amount = rs . ( 50 x 70 ) = rs . 3500 answer : option b\"" + }, + { + "Answer": 96, + "Options": "a ) 24 , b ) 52 , c ) 96 , d ) 144 , e ) 648", + "Correct": "c", + "Explanation": "gold can be awarded in 4 ways , then silver can be awarded in 3 ways and bronze in 2 ways . therefore the total number of ways are : 4 * 3 * 2 = 24 ways of awarding the medals and the same number of ways of forming the circle . this is when there is no tie . and if there is tie , for example all three receive the gold or the silver or the bronze , then there are 4 more cases . which implies 24 * 4 = 96 . ans : c" + }, + { + "Answer": 1.9607843137254943, + "Options": "a ) 19 % , b ) 15 % , c ) 25 % , d ) 40 % , e ) 1.96 %", + "Correct": "e", + "Explanation": "\"cost of food ( c ) = food consumed per student ( f ) * number of students ( n ) * price of food ( p ) originally , c = fnp when number of students decrease by 15 % , and the price of food increases by 20 % , c = f ( new ) * ( 0.85 n ) * ( 1.2 p ) = > f ( new ) = f / ( 0.85 * 1.2 ) = > f ( new ) = 0.9804 f therefore the new cost of food must be 98.04 % of the old cost , or the cost of food must decrease by 1.96 % ( option e )\"" + }, + { + "Answer": 8, + "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 13 , e ) 15", + "Correct": "a", + "Explanation": "answer required average = ( ( 7 - 1 ) + ( 8 - 1 ) + ( 10 - 1 ) + ( 13 - 1 ) + ( 6 - 1 ) + ( 10 - 1 ) ) / 6 = ( 7 + 8 + 10 + 13 + 6 + 10 ) / 6 - ( 6 x 1 ) / 6 = 9 - 1 = 8 correct option : a" + }, + { + "Answer": 27, + "Options": "a ) 10 hours , b ) 12 hours , c ) 14 hours , d ) 27 hours , e ) none of these", + "Correct": "d", + "Explanation": "explanation : speed of the boat = 6 km / hr speed downstream = ( 6 + 2 ) = 8 km / hr speed upstream = ( 6 - 2 ) = 4 km / hr distance travelled downstream = distance travelled upstream = 72 km total time taken = time taken downstream + time taken upstream = ( 72 / 8 ) + ( 72 / 4 ) = 27 hr . answer : option d" + }, + { + "Answer": 2, + "Options": "a ) 6 , b ) 8 , c ) 10 , d ) 11 , e ) 2", + "Correct": "e", + "Explanation": "2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 29 - 25 = 4 ab = 2 . answer : e" + }, + { + "Answer": 34.25, + "Options": "a ) 33.5 , b ) 33.5 , c ) 34.25 , d ) 35 , e ) none of these", + "Correct": "c", + "Explanation": "solution required average = ( 38.9 x 10 ) - ( 42 x 6 ) / 4 = 137 / 4 = 34.25 answer c" + }, + { + "Answer": 49, + "Options": "a ) 49 , b ) 55 , c ) 59 , d ) 71 , e ) 92", + "Correct": "a", + "Explanation": "\"total = 55 thrower = 37 rest = 55 - 37 = 18 left handed = 18 / 3 = 6 right handed = 12 if all thrower are right handed then total right handed is 37 + 12 = 49 so a . 49 is the right answer\"" + }, + { + "Answer": 8, + "Options": "a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10", + "Correct": "d", + "Explanation": "factor the left side of the equation : t ^ 2 \u00e2 \u20ac \u201c 12 t + 20 = 0 ( t \u00e2 \u20ac \u201c 2 ) ( t \u00e2 \u20ac \u201c 10 ) = 0 t = 2 , t = 10 thus , a = 10 and b = 2 . so a \u00e2 \u20ac \u201c b = 10 \u00e2 \u20ac \u201c 2 = 8 . the answer is d ." + }, + { + "Answer": 29, + "Options": "a ) 1 , b ) 19 , c ) 29 , d ) 30 , e ) 33", + "Correct": "c", + "Explanation": "\"total of integers = 74 * 4 = 296 lowest of the least possible integer is when the middle 2 intergers are at the maximum or equal to the highest possible integer . but all integers are distinct . so if the largest integer is 90 , then the middle 2 will be 88 and 89 lowest of least possible integer = 296 - ( 90 + 89 + 88 ) = 296 - 267 = 29 answer : c\"" + }, + { + "Answer": 6500.000000000001, + "Options": "a ) 6500 , b ) 3550 , c ) 4250 , d ) 2250 , e ) 3250", + "Correct": "a", + "Explanation": "ratio of shares of a , b , c , d = ( 24 x 3 ) : ( 10 x 5 ) : ( 35 x 4 ) : ( 21 x 3 ) = 72 : 50 : 140 : 63 . let total rent be rs . x . then , a \u2019 s share = rs . ( 72 x ) / 325 ( 72 x ) / 325 = 1440 = x = ( 1440 x 325 ) / 72 = 6500 hence , total rent of the field is rs . 6500 . answer is a ." + }, + { + "Answer": 25, + "Options": "a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25", + "Correct": "e", + "Explanation": "\"the multiples of 4 are from 4 * 3 up to 4 * 27 . 27 - 3 + 1 = 25 . the answer is e .\"" + }, + { + "Answer": 24.999999999999996, + "Options": "a ) 10 , b ) 12 , c ) 25 , d ) 18 , e ) 19", + "Correct": "c", + "Explanation": "\"2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 150 - 100 = 50 = > ab = 25 answer : c\"" + }, + { + "Answer": 27.122641509433965, + "Options": "a ) 27.12 % , b ) 23.12 % , c ) 25.55 % , d ) 31.22 % , e ) 56.22 %", + "Correct": "a", + "Explanation": "\"say a 100 families existed in 1994 then the number of families owning a computer in 1994 - 25 number of families owning computer in 1998 = 25 * 115 / 100 = 28.75 number of families in 1998 = 106 the percentage = 28.75 / 106 * 100 = 27.12 % . answer : a\"" + }, + { + "Answer": 50, + "Options": "a ) 50 , b ) 40 , c ) 60 , d ) 100 , e ) 70", + "Correct": "a", + "Explanation": "\"we have x + x % of 100 = 100 x + x / 100 * 100 = 100 2 * x = 100 x = 50 answer is a\"" + }, + { + "Answer": 0.5000000000000001, + "Options": "a ) 1 / 2 , b ) 1 / 3 , c ) 2 / 3 , d ) 1 / 4 , e ) 3 / 4", + "Correct": "a", + "Explanation": "\"( 1 / 2 ) g = ( 1 / 3 ) ( b + g ) 3 g = 2 b + 2 g g = 2 b b / g = 1 / 2 . the answer is a .\"" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "c", + "Explanation": "assuming i have understood the symbols used correctly answer is c - 3 a 7 = 2 s 6 + 4 = 316 a 6 = 312 / 2 = 156 = 2 a 5 + 4 a 5 = 152 / 2 = 76 = q 4 q 4 = 4 q 3 + 8 = 76 q 3 = 68 / 4 = 17 q 3 = 4 q 2 + 8 = 17 q 2 = 9 / 4 = 2.25 q 2 = 4 q 1 + 8 q 1 will not be integer = c" + }, + { + "Answer": 586, + "Options": "a ) $ 570 , b ) $ 586 , c ) $ 630 , d ) $ 686 , e ) $ 715", + "Correct": "b", + "Explanation": "official solution : ( b ) first , we need to add up the wages over the past 5 weeks : $ 406 + $ 413 + $ 420 + $ 436 + $ 395 = $ 2070 . to average $ 500 over 10 weeks , the salesman would need to earn : $ 500 \u00d7 10 = $ 5000 . subtract $ 2070 from $ 5000 to determine how much he would need to earn , in total , over the next 5 weeks to average $ 500 for the 10 weeks : $ 5000 \u2013 $ 2070 = $ 2930 . dividing $ 2930 by 5 will give us the amount he needs to earn on average over the next 5 weeks : $ 2930 / 5 = $ 586 . the correct answer is choice ( b ) ." + }, + { + "Answer": 6, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 6 , e ) 4", + "Correct": "d", + "Explanation": "explanation : 39 + 19 = 58 / 13 = 6 ( remainder ) answer : d" + }, + { + "Answer": 10, + "Options": "a ) 4 % , b ) 5 % , c ) 6 % , d ) 8 % , e ) 10 %", + "Correct": "e", + "Explanation": "\"let x be the amount of gasoline the driver buys originally . let y be the new amount of gasoline the driver should buy . let p be the original price per liter . ( 1.2 * p ) y = 1.08 ( p * x ) y = ( 1.08 / 1.2 ) x = 0.9 x which is a reduction of 10 % . the answer is e .\"" + }, + { + "Answer": 70, + "Options": "a ) 70 kg , b ) 80 kg , c ) 85 kg , d ) 90 kg , e ) 95 kg", + "Correct": "a", + "Explanation": "\"total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 50 + 20 ) kg = 70 kg . a )\"" + }, + { + "Answer": 83.99999999999999, + "Options": "a ) 82 , b ) 83 , c ) 84 , d ) 85 , e ) 86", + "Correct": "c", + "Explanation": "\"a + b + c = 427 3 a = 4 b = 7 c = > ( 7 c / 3 ) + ( 7 c / 4 ) + c = 427 = > c = 84 answer : c\"" + }, + { + "Answer": 84, + "Options": "a ) 83 % , b ) 83 1 \u2044 2 % , c ) 84 % , d ) 85 % , e ) 86 2 \u2044 3 %", + "Correct": "c", + "Explanation": "the average percentage = ( 15 x 80 % + 10 x 90 % ) / 25 = ( 15 x 80 % + 10 x 80 % + 10 x 10 % ) / 25 . . . . . . ( as 90 % = 10 % + 80 % ) = ( 25 x 80 % + 10 x 10 % ) / 25 = 80 % + 10 x 10 % / 25 = 80 % + 4 % = 84 % answer : c" + }, + { + "Answer": 0.7619047619047619, + "Options": "a ) 5 / 21 , b ) 3 / 7 , c ) 4 / 7 , d ) 5 / 7 , e ) 16 / 21", + "Correct": "e", + "Explanation": "\"# of selections of 2 out of 7 - c 27 = 21 c 72 = 21 ; # of selections of 2 people which are not siblings - c 12 \u2217 c 12 c 21 \u2217 c 21 ( one from first pair of siblings * one from second pair of siblings ) + c 12 \u2217 c 13 c 21 \u2217 c 31 ( one from first pair of siblings * one from triple ) + c 1 ^ _ 2 * c ^ 1 _ 3 ( one from second pair of siblings * one from triple ) = 4 + 6 + 6 = 16 = 4 + 6 + 6 = 16 . p = 16 / 21 answer : e\"" + }, + { + "Answer": 82, + "Options": "a ) 58 , b ) 66 , c ) 74 , d ) 82 , e ) 90", + "Correct": "d", + "Explanation": "897326 / 456 = 1967 with a remainder of 374 . we need to add 456 - 374 = 82 the answer is d ." + }, + { + "Answer": 2160, + "Options": "a ) 2160 , b ) 2350 , c ) 2000 , d ) 2300 , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : total exp = 5000 + 1500 + 4500 + 2500 + 2000 + 3940 = 19440 exp in % = 100 - 10 = 90 % , 19440 = 90 % saving = 10 % = 19440 x 10 / 90 = rs . 2160 answer : a\"" + }, + { + "Answer": 51, + "Options": "a ) 46 , b ) 47 , c ) 48 , d ) 49 , e ) 51", + "Correct": "e", + "Explanation": "\"the standard deviation ( { sd } ) = 2 ; 3 standard deviations below the mean is greater than 44 : { mean } - 3 * { sd } > 44 ; { mean } - 6 > 44 ; { mean } > 50 . answer : e .\"" + }, + { + "Answer": 0.3125, + "Options": "a ) 7 / 16 , b ) 5 / 16 , c ) 3 / 16 , d ) 7 / 8 , e ) 5 / 8", + "Correct": "b", + "Explanation": "the total number of x and y pairs is 4 * 4 = 16 . there are five pairs such that x / y is an integer . the probability that x / y is an integer is 5 / 16 . the answer is b ." + }, + { + "Answer": 12, + "Options": "a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16", + "Correct": "c", + "Explanation": "the daily production was raised by 5 units for n days , which has a weighting of 5 n . 5 n = 115 - 55 = 60 n = 12 the answer is c ." + }, + { + "Answer": 58.85, + "Options": "a ) 67.4 kg , b ) 57.75 kg , c ) 58.85 kg , d ) 49.4 kg , e ) none of these", + "Correct": "c", + "Explanation": "\"actual total weight is ( 20 \u00e3 \u2014 58.4 - 56 + 65 ) = 1177 kgs actual average weight is 1177 / 20 = 58.85 kgs answer is c\"" + }, + { + "Answer": 7, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "e", + "Explanation": "\"p ( choosing a red apple 7 times in a row ) = 12 / 13 * 11 / 12 * 10 / 11 * 9 / 10 * 8 / 9 * 7 / 8 * 6 / 7 = 6 / 13 < 0.5 the answer is e .\"" + }, + { + "Answer": 24, + "Options": "a ) 15 , b ) 16 , c ) 19 , d ) 24 , e ) 36", + "Correct": "d", + "Explanation": "step 1 : find out the number of products you get . 5 distinct numbers in set a and 4 distinct in set b so number of products = 5 * 4 = 20 step 2 : remove the products that appear more than once . notice that 5 , 7 , 11 and 13 are primes and none of their multiples are in either set . so ignore them . we just need to focus on 2 and 3 of set a and 2 , 4 and 6 of set b . 2 , 3 2 , 4 , 6 the only product repeated when you take a number from each set is 12 . ( 3 * 4 and 2 * 6 ) rest all are distinct . answer = 20 - 1 = 24 note here that the second step will involve manual calculation since it will depend on the specific numbers you have in the two sets . d" + }, + { + "Answer": 1925, + "Options": "a ) 770 , b ) 870 , c ) 1825 , d ) 1925 , e ) 925", + "Correct": "d", + "Explanation": "let no be : x 1 / 7 x - 1 / 11 x = 100 4 x / 77 = 100 x = 7700 / 4 = 1925 answer : d" + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10", + "Correct": "a", + "Explanation": "we start by calculating the median of the numbers of list i : 3 , 4 , 8 , 19 . we see that the numbers in the list are in order already and , since we have an even number of numbers , the median is the average of the two middle numbers . median = ( 4 + 8 ) / 2 median = 12 / 2 median = 6 the median of list i is 6 . looking at list ii : x , 3 , 4 , 8 , 19 , we see that we have an odd number of terms . thus , when the list is ordered from least to greatest the median must be the middle term . since the medians of the two lists must be equal , we know that the median of list ii must be 6 and therefore x is 6 . the answer is a ." + }, + { + "Answer": 0.6666666666666666, + "Options": "a ) 8 / 12 , b ) 6 / 16 , c ) 4 / 16 , d ) 6 / 10 , e ) 4 / 10", + "Correct": "a", + "Explanation": "\"w = m + 4 w + m = 20 m + 4 + m = 20 2 m = 16 m = 8 w = 12 ratio : 8 : 12 ans : a\"" + }, + { + "Answer": 30, + "Options": "a ) 19 , b ) 20 , c ) 30 , d ) 33 , e ) 34", + "Correct": "c", + "Explanation": "\"though 2 * ( 6 c 2 ) is the correct approcah to do this , but for people like me who find perm , comb n prob a nightmare , an easy approach can be used . the first guy has to play 2 matches with the rest of 5 , so he ' ll play 10 matches . similarly , second guy has to play with the rest of 4 as his 2 games with the first guy are already played . so he plays 8 matches . this continues like this and the total matches are 10 + 8 + 6 . . . + 2 10 + 8 + . . . + 2 = 2 ( 5 + 4 + . . . + 1 ) = 2 ( ( 5 * 6 ) / 2 ) = 5 * 6 = 30 . answer : c\"" + }, + { + "Answer": 11, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 11 , e ) can not be determined from the information given .", + "Correct": "d", + "Explanation": "the average of three integers a , b , and c is exactly twice the median - - > ( a + b + c ) / 3 = 4 b - - > since a = 0 , then ( 0 + b + c ) / 3 = 4 b - - > c = 11 b - - > c / b = 11 . answer : d ." + }, + { + "Answer": 2.4, + "Options": "a ) 1.8 , b ) 2.1 , c ) 2.4 , d ) 2.7 , e ) 3.0", + "Correct": "c", + "Explanation": "\"let x be the amount of pure alcohol required . 0.3 ( 6 ) + x = 0.5 ( x + 6 ) 0.5 x = 3 - 1.8 x = 2.4 liters the answer is c .\"" + }, + { + "Answer": 45, + "Options": "a ) 45 , b ) 50 , c ) 55 , d ) 100 , e ) 60", + "Correct": "a", + "Explanation": "0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 are in your mobile phone . therefore 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45 answer is a" + }, + { + "Answer": 4.08, + "Options": "a ) 5.29 min , b ) 5.28 min , c ) 4.08 min , d ) 9.28 min , e ) 5.988 min", + "Correct": "c", + "Explanation": "clearly , the two will meet when they are 561 m apart . to be ( 4.5 + 3.75 ) = 8.25 km apart , they take 1 hour . to be 561 m apart , they take ( 100 / 825 * 561 / 1000 ) hrs = ( 561 / 8250 * 60 ) min = 4.08 min . answer : c" + }, + { + "Answer": 25, + "Options": "a ) 25 % , b ) 33 1 / 3 % , c ) 50 % , d ) 66 2 / 3 % , e ) 75 %", + "Correct": "a", + "Explanation": "\"general formula for percent increase or decrease , ( percent change ) : percent = change / original \u2217 100 so , the time between maintenance checks increased by 25 \u2212 20 / 20 \u2217 100 = 25 answer : a .\"" + }, + { + "Answer": 264, + "Options": "a ) 160 , b ) 264 , c ) 360 , d ) 354 , e ) 400", + "Correct": "b", + "Explanation": "75 x / 100 - x / 3 = 110 5 x / 12 = 110 x = 264 answer : b" + }, + { + "Answer": 2, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "a", + "Explanation": "\"8 people visited 2 stores each for 16 visits . to maximize the number of stores that one person visited , let ' s assume that 3 people visited 1 store each . the number of remaining visits is 21 - 16 - 3 = 2 , which is the maximum that one person could have visited . the answer is a .\"" + }, + { + "Answer": 23, + "Options": "a ) 23 , b ) 24 , c ) 25 , d ) 26 , e ) 27", + "Correct": "a", + "Explanation": "\"average age of people = 30 so have total age = 210 before 7 years we have to deduct each person age by seven years 210 - 49 = 161 so average age would be 161 / 7 = 23 answer : a\"" + }, + { + "Answer": 399.29999999999967, + "Options": "a ) $ 357.67 , b ) $ 375.85 , c ) $ 387.40 , d ) $ 399.30 , e ) $ 433.33", + "Correct": "d", + "Explanation": "l = 993 r = 0.1 c = 1.1 ^ 3 = 1.331 insert all of these in the formula and we get p = 993 * 1.331 * 0.1 / 0.331 in order to resolve above without a calc , we need to find the approx value of 0.1331 / 0.331 ~ 0.4 ~ ~ 993 * 0.4 ~ 397 answer d" + }, + { + "Answer": 12.5, + "Options": "a ) 7.5 , b ) 10 , c ) 12.5 , d ) 15 , e ) 17.5", + "Correct": "c", + "Explanation": "\"the point of intersection is ( - 5 , - 5 ) . the triangle has a base of length 5 and a height of 5 . area = ( 1 / 2 ) * base * height = ( 1 / 2 ) * 5 * 5 = 12.5 the answer is c .\"" + }, + { + "Answer": 35, + "Options": "a ) 30 mph , b ) 32 mph , c ) 35 mph , d ) 37 mph , e ) 38 mph", + "Correct": "c", + "Explanation": "the time to complete the first 30 miles was ( 30 miles / 60 mph ) = ( 1 / 2 ) hours . the time to complete the whole trip was ( 100 miles / 40 mph ) = ( 5 / 2 ) hours . the time to complete the last 70 miles was ( 5 / 2 ) - ( 1 / 2 ) = ( 2 ) hours . the average speed in the last 70 miles was ( 70 miles / 2 hours ) = 35 mph . the answer is c ." + }, + { + "Answer": 63.6, + "Options": "a ) $ 62.40 , b ) $ 62.80 , c ) $ 63.20 , d ) $ 63.60 , e ) $ 64.00", + "Correct": "d", + "Explanation": "\"1.06 * $ 60 = $ 63.60 the answer is d .\"" + }, + { + "Answer": 335, + "Options": "a ) 312 , b ) 335 , c ) 347 , d ) 361 , e ) 383", + "Correct": "b", + "Explanation": "\"722425 / 456 = 1584 with a remainder of 121 . we need to add 456 - 121 = 335 the answer is b .\"" + }, + { + "Answer": 750, + "Options": "a ) $ 550 , b ) $ 650 , c ) $ 750 , d ) $ 850 , e ) $ 950", + "Correct": "c", + "Explanation": "\"0.1 x = 0.08 ( 2000 - x ) + 65 0.18 x = 225 x = 1250 then the amount invested at 8 % is $ 2000 - $ 1250 = $ 750 the answer is c .\"" + }, + { + "Answer": 128, + "Options": "a ) 128 , b ) 142 , c ) 143 , d ) 141 , e ) 129", + "Correct": "e", + "Explanation": "minimum three digit number is 100 and maximum three digit number is 999 . the first three digit number that leaves remainder 5 when divided by 7 is 103 . 14 * 7 = 98 + 5 = 103 the second three digit number that leaves remainder 5 when divided by 7 is 110 . 15 * 7 = 105 + 5 = 110 the third three digit number that leaves remainder 5 when divided by 7 is 117 and so on the last three digit number that leaves remainder 5 when divided by 7 is 999 142 * 7 = 994 + 5 = 999 therefore , we identify the sequence 103 , 110,117 . . . . . 999 use the formula of last term last term = first term + ( n - 1 ) * common difference you will get the answer 129 that is definitely e ." + }, + { + "Answer": 0.17500000000000002, + "Options": "a ) 3 / 140 , b ) 1 / 28 , c ) 3 / 56 , d ) 3 / 35 , e ) 7 / 40", + "Correct": "e", + "Explanation": "p = p ( a wins , b wins , c loses ) + p ( a wins , b loses , c wins ) + p ( a loses , b wins , c wins ) = 1 / 5 * 3 / 8 * 5 / 7 + 1 / 5 * 5 / 8 * 2 / 7 + 4 / 5 * 3 / 8 * 2 / 7 = 7 / 40 . answer : e ." + }, + { + "Answer": 16, + "Options": "a ) 5 , b ) 6 , c ) 15 , d ) 16 , e ) 18", + "Correct": "d", + "Explanation": "basically the length of an integer is the sum of the powers of its prime factors . for example the length of 24 is 4 because 24 = 2 ^ 3 * 3 ^ 1 - - > 3 + 1 = 4 . given : x + 3 y < 1,000 . now , to maximize the length of x or y ( to maximize the sum of the powers of their primes ) we should minimize their prime bases . minimum prime base is 2 : so if x = 2 ^ 9 = 512 then its length is 9 - - > 512 + 3 y < 1,000 - - > y < 162.7 - - > maximum length of y can be 7 as 2 ^ 7 = 128 - - > 9 + 7 = 16 . answer : d ." + }, + { + "Answer": 500, + "Options": "a ) 280 , b ) 400 , c ) 540 , d ) 500 , e ) 840", + "Correct": "d", + "Explanation": "\"of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month : 2 / 3 * 3 / 4 = 1 / 2 survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year : ( 1 - 3 / 5 ) * 1 / 2 = 1 / 5 survived the first year . 100 geese survived the first year : 1 / 5 * ( total ) = 100 - - > ( total ) = 500 . answer : d .\"" + }, + { + "Answer": 12, + "Options": "a ) 10 minutes , b ) 12 minutes , c ) 18 minutes , d ) 19 minutes , e ) 16 minutes", + "Correct": "b", + "Explanation": "b 12 minutes explanation : yes , surely they can all make it out of the cave . first , father and mother will go . time taken = 2 minutes . father comes back . time taken = 2 + 1 = 3 minutes . both children go . time taken = 3 + 5 = 8 minutes . mother comes back . time taken = 8 + 2 = 10 minutes . mother and father go . time taken = 10 + 2 = 12 minutes . thus in 12 minutes , all of them will be out of the cave through the tunnel ." + }, + { + "Answer": 0.12, + "Options": "a ) 72 / 100 , b ) 3 / 25 , c ) 4 / 5 , d ) 1 / 6 , e ) 1 / 9", + "Correct": "b", + "Explanation": "explanation : let , the number of the ball picked first = a , second = b and third = c and these three numbers a , b and c are distinct . three distinct ball can be picked in ( 10 \u00d7 9 \u00d7 8 ) ways . the order of a , b and c can be as follows : - ( i ) a > b > c . ( ii ) a > c > b . ( iii ) b > c > a . ( iv ) b > a > c . ( v ) c > a > b . ( vi ) c > b > a . they will occur equal number of times . so , the number of ways in which ( a > b > c ) are : - = > 1 / 6 x 10 x 9 x 8 . = > 120 . hence , the required probability is : - = > 120 / ( 10 x 10 x 10 ) . = > 3 / 25 . answer : b" + }, + { + "Answer": 1200, + "Options": "a ) 750 , b ) 900 , c ) 1050 , d ) 1200 , e ) 1350", + "Correct": "d", + "Explanation": "the number of ways to choose two teams is 16 c 2 = 16 * 15 / 2 = 120 the total number of games in the season is 10 * 120 = 1200 . the answer is d ." + }, + { + "Answer": 87.5, + "Options": "a ) 30 % , b ) 70 % , c ) 80 % , d ) 87.5 % , e ) none", + "Correct": "d", + "Explanation": "solution let number of students appeared from school a = 100 . then , number of students qualified from school a = 70 . number of students appeared from school b = 120 . number of students qualified from school b = [ 150 / 100 x 70 ] = 105 . required percentage = [ 105 / 120 x 100 ] % = 87.5 % answer d" + }, + { + "Answer": 17, + "Options": "a ) - 29 , b ) - 19 , c ) 17 , d ) 29 , e ) 39", + "Correct": "c", + "Explanation": "\"45 - [ 28 - { 37 - ( 15 - * ) } ] = 56 = > 45 - [ 28 - { 37 - 15 + * } ] = 56 45 - [ 28 - 37 + 15 - * ] = 56 = > 45 [ 43 - 37 - * ] = 56 45 - [ 6 - * ] = 56 = > 45 - 6 + * = 56 39 + * = 56 = > * = 56 - 39 = 17 answer : c\"" + }, + { + "Answer": 16.666666666666668, + "Options": "a ) 16.5 , b ) 14.33 , c ) 12.5 , d ) 15.8 , e ) 16.66", + "Correct": "e", + "Explanation": "80 * 100 / 480 = 16.66 % answer e" + }, + { + "Answer": 211, + "Options": "a ) 97 , b ) 151 , c ) 209 , d ) 211 , e ) 219", + "Correct": "d", + "Explanation": "what is the largest possible sum of these three numbers that we can form ? maximize the first digit : 76 + 73 + 71 = 220 = even , so not a prime . let ' s try next largest sum , switch digits in 76 and we ' ll get : 67 + 73 + 71 = 211 = prime . answer : d ." + }, + { + "Answer": 352, + "Options": "a ) 351 , b ) 360 , c ) 363 , d ) 369 , e ) 378", + "Correct": "a", + "Explanation": "\"there are 41 digits in 10 ^ 4 when we subtract 46 from it , there will be 40 digits left . 10 ^ 4 can be written as 9999999 . . . . ( 40 times ) + 1 so , 10 ^ 40 - 46 = 9999999 . . . . ( 40 times ) + 1 - 46 = 9999999 . . . . ( 40 times ) - 45 consider the last 2 digits , 99 - 45 = 54 the last 2 digits will be 54 . and our number would be 99999 . . . . . . 99954 with 2 less 9 s after subtraction . number of 9 s left are 38 and the last two digits are 54 the sum of the digits will be ( 38 * 9 ) + 5 + 4 = 351 answer : - a\"" + }, + { + "Answer": 645, + "Options": "a ) 605 , b ) 608 , c ) 613 , d ) 616 , e ) 645", + "Correct": "e", + "Explanation": "\"the set s = { 5 , 13 , 21 , 29 , . . . . . . . . . . . . . . . . . . . . . } 1 st number = 8 * 0 + 5 = 5 2 nd number = 8 * 1 + 5 = 13 3 rd number = 8 * 2 + 5 = 21 81 th number = 8 * ( 81 - 1 ) + 5 = 645 answer = e\"" + }, + { + "Answer": 13, + "Options": "a ) 6 , b ) 7 , c ) 13 , d ) 9 , e ) 12", + "Correct": "c", + "Explanation": "say the number of people having birthdays on wednesday is x and the number of people having birthdays on each of the other 6 days is y . then x + 6 y = 61 . now , plug options for x . only c and e give an integer value for y . but only for c x > y as needed . answer : c ." + }, + { + "Answer": 500, + "Options": "a ) a ) 400 , b ) b ) 450 , c ) c ) 500 , d ) d ) 550 , e ) e ) 600", + "Correct": "c", + "Explanation": "10 * 155 = 1550 3 * 100 + 5 * 150 = 1050 1550 \u2013 1050 = 500 c" + }, + { + "Answer": 79, + "Options": "a ) 25 , b ) 35 , c ) 75 , d ) 80 , e ) 79", + "Correct": "e", + "Explanation": "\"a + b + c = 3 * 84 = 252 a + b + c + d = 4 * 80 = 320 - - - - ( i ) so , d = 68 & e = 68 + 7 = 75 b + c + d + e = 79 * 4 = 316 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 320 \u00e2 \u20ac \u201c 316 = 4 a = e + 4 = 75 + 4 = 79 e\"" + }, + { + "Answer": 8, + "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12", + "Correct": "a", + "Explanation": "\"4 + 4 = 8 correct answer is a ) 8\"" + }, + { + "Answer": 57.5, + "Options": "a ) 55.65 , b ) 57.5 , c ) 62.5 , d ) 45.25 , e ) 50", + "Correct": "b", + "Explanation": "correct avg marks = 60 + ( 15 - 90 ) / 30 avg = 60 - 2.5 = 57.5 answer is b" + }, + { + "Answer": 32, + "Options": "a ) 28 , b ) 32 , c ) 36 , d ) 40 , e ) 44", + "Correct": "b", + "Explanation": "m + h = 80 h = 80 - m 4 m + 5 h = 368 4 m + 5 * ( 80 - m ) = 368 m = 32 the answer is b ." + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "a", + "Explanation": "xy = 1 as x + y = 25 x 2 y 3 + y 2 x 3 = 25 x 2 y 2 ( y + x ) = 25 substituting x + y x 2 y 2 = 1 xy = 1 answer : a" + }, + { + "Answer": 0.16000000000000003, + "Options": "a ) 7 / 25 , b ) 4 / 25 , c ) 8 / 25 , d ) 2 / 13 , e ) 3 / 17", + "Correct": "b", + "Explanation": "\"p ( a n b ) = p ( a ) . p ( b ) p ( a n b ) = 2 / 5 . 2 / 5 p ( a n b ) = 4 / 25 . b\"" + }, + { + "Answer": 36.5, + "Options": "a ) 35.24 , b ) 36.14 , c ) 36.24 , d ) 36.44 , e ) none", + "Correct": "d", + "Explanation": "\"solution correct sum = ( 36 x 50 + 45 - 23 ) = 1822 . \u00e2 \u02c6 \u00b4 correct mean = 1822 / 50 = 36.44 . answer d\"" + }, + { + "Answer": 7, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8", + "Correct": "d", + "Explanation": "\"sa ' s + co + ca + cats = 15 . sa ' s + 1 + 1 + cats = 15 or sa ' s + cats = 13 . sa ' s ( 2 ) + 2 + 1 + cats * 4 = 43 sa ' s * 2 + cats * 4 = 40 or sa ' s + cats * 2 = 20 or 13 - cats + cat * 2 = 20 then cats = 7 d\"" + }, + { + "Answer": 9, + "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12", + "Correct": "b", + "Explanation": "15 n + 35 = 17 ( n + 1 ) 2 n = 18 n = 9 the answer is b ." + }, + { + "Answer": 2, + "Options": "a ) a ) 10 , b ) b ) 8 , c ) c ) 6 , d ) d ) 4 , e ) e ) 2", + "Correct": "e", + "Explanation": "\"x = 10 - 2 y x = 10 - 8 . x = 2 answer : e\"" + }, + { + "Answer": 54, + "Options": "a ) 47 , b ) 54 , c ) 56 , d ) 61 , e ) 64", + "Correct": "b", + "Explanation": "\"m + h = 90 h = 90 - m 4 m + 5 h = 396 4 m + 5 * ( 90 - m ) = 396 m = 54 the answer is b .\"" + }, + { + "Answer": 31.000000000000004, + "Options": "a ) 30 , b ) 45 , c ) 50 , d ) 31 , e ) 21", + "Correct": "d", + "Explanation": "\"given expression = ( 43.2 - 6 ) / 1.2 = 37.2 / 1.2 = 31 answer is d .\"" + }, + { + "Answer": 363600, + "Options": "a ) 45,000 , b ) 360,000 , c ) 364,500 , d ) 363,600 , e ) 396,900", + "Correct": "d", + "Explanation": "say x was the # of hardback copies sold from the time the first paperback copy was sold . then the total # of paperback copies sold was 9 x ; hence the total # of copies sold was ( hardback ) + ( paperback ) = ( 36 + x ) + ( 9 x ) = 440 - - > x = 40.4 . so , the total # of paperback copies sold was 9 x = 9 * 40.4 = 363.6 or 363,600 . answer : d ." + }, + { + "Answer": 12, + "Options": "a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 19", + "Correct": "b", + "Explanation": "\"let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 24 = > 2 x = 24 = > x = 12 b\"" + }, + { + "Answer": 0.8666666666666667, + "Options": "a ) 10 / 15 , b ) 11 / 15 , c ) 12 / 15 , d ) 13 / 15 , e ) 14 / 15", + "Correct": "d", + "Explanation": "the probability of a student possessing a ball point pen in exam is 3 / 5 . the probability of a student not possessing a ball point pen in exam is 2 / 5 & possessing an ink pen is 2 / 3 . & not possessing an ink pen is 1 / 3 . his probability of possessing none of them = 2 / 5 * 1 / 3 = 2 / 15 his probability of possessing one of them = 1 - 2 / 15 = 13 / 15 answer : d" + }, + { + "Answer": 16, + "Options": "a ) 14 , b ) 26 , c ) 16 , d ) 36 , e ) 46", + "Correct": "c", + "Explanation": "explanation : = 248 + 64 \u2212 \u2212 \u221a \u2212 \u2212 \u2212 \u2212 \u2212 \u2212 \u2212 \u2212 \u2212 \u221a = 248 + 8 \u2212 \u2212 \u2212 \u2212 \u2212 \u2212 \u221a = 256 \u2212 \u2212 \u2212 \u221a = 16 answer : c" + }, + { + "Answer": 290, + "Options": "a ) s . 250 , b ) s . 280 , c ) s . 290 , d ) s . 299 , e ) s . 300", + "Correct": "c", + "Explanation": "\"let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 638 but x = 120 % of y = 120 y / 100 = 12 y / 10 \u2234 12 y / 10 + y = 638 \u21d2 y [ 12 / 10 + 1 ] = 638 \u21d2 22 y / 10 = 638 \u21d2 22 y = 6380 \u21d2 y = 6380 / 22 = 580 / 2 = rs . 290 c\"" + }, + { + "Answer": 16, + "Options": "a ) 14 , b ) 12 , c ) 10 , d ) 16 , e ) 18", + "Correct": "d", + "Explanation": "\"we know that : x > 1 , y > 1 , and x + 3 y < 1000 , and it is given that length means no of factors . for any value of x and y , the max no of factors can be obtained only if factor is smallest noall factors are equal . hence , lets start with smallest no 2 . 2 ^ 1 = 2 2 ^ 2 = 4 2 ^ 3 = 8 2 ^ 4 = 16 2 ^ 5 = 32 2 ^ 6 = 64 2 ^ 7 = 128 2 ^ 8 = 256 2 ^ 9 = 512 2 ^ 10 = 1024 ( it exceeds 920 , so , x ca n ' t be 2 ^ 10 ) so , max value that x can take is 2 ^ 9 , for which has length of integer is 9 . now , since x = 512 , x + 3 y < 920 so , 3 y < 408 = = > y < 136 so , y can take any value which is less than 136 . and to get the maximum no of factors of smallest integer , we can say y = 2 ^ 7 for 2 ^ 7 has length of integer is 7 . so , combined together : 9 + 7 = 16 . d\"" + }, + { + "Answer": 100, + "Options": "a ) 80 , b ) 90 , c ) 100 , d ) 120 , e ) 130", + "Correct": "c", + "Explanation": "let the number of candidate who passed = y then , 39 y + 15 ( 120 - y ) = 120 x 35 \u21d2 24 y = 4200 - 1800 \u2234 y = 2400 / 24 = 100 c" + }, + { + "Answer": 299.99999999999983, + "Options": "a ) 300 , b ) 230 , c ) 500 , d ) 560 , e ) 590", + "Correct": "a", + "Explanation": "\"n * 50 = ( 315000 - 300000 ) = 15000 n = 15000 / 50 = 300 a\"" + }, + { + "Answer": 106, + "Options": "a ) 115 kg . , b ) 110 kg . , c ) 106 kg . , d ) 105 kg . , e ) 100 kg .", + "Correct": "c", + "Explanation": "\"the new average will be = ( 112 * 7 + 110 + 60 ) / 9 = 106 kgs c is the answer\"" + }, + { + "Answer": 13, + "Options": "a ) a ) 14 , b ) b ) 13 , c ) c ) 16 , d ) d ) 8 , e ) e ) 6", + "Correct": "b", + "Explanation": "\"explanation : let the number of ducks be d and number of cows be c then , total number of legs = 2 d + 4 c = 2 ( d + 2 c ) total number of heads = c + d given that total number of legs are 26 more than twice the number of heads = > 2 ( d + 2 c ) = 26 + 2 ( c + d ) = > d + 2 c = 13 + c + d = > 2 c = 13 + c = > c = 13 i . e . , total number of cows = 13 answer : b\"" + }, + { + "Answer": 1500, + "Options": "a ) 1500 , b ) 1600 , c ) 1750 , d ) 1900 , e ) 2000", + "Correct": "a", + "Explanation": "\"let the price of basic computer be c and the price of the printer be p : c + p = $ 2,500 . the price of the enhanced computer will be c + 500 and total price for that computer and the printer will be 2,500 + 500 = $ 3,000 . now , we are told that the price of the printer is 1 / 3 of that new total price : p = 1 / 3 * $ 3,000 = $ 1000 plug this value in the first equation : c + 1000 = $ 2,500 - - > c = $ 1,500 . answer : a .\"" + }, + { + "Answer": 20, + "Options": "a ) 3 , b ) 6 , c ) 14 , d ) 17 , e ) 20", + "Correct": "e", + "Explanation": "\"the objective here is that 70 % of the fruit in the box should be apples . now , there are 14 apples at start and there is no talk of removing any apples , so number of apples should remain 14 and they should constitute 70 % of total fruit , so total fruit = 14 / 0.7 = 20 so we should have 20 - 14 = 6 oranges . right now , there are 26 oranges , so to get to 6 oranges , we should remove 26 - 6 = 20 oranges . answer e\"" + }, + { + "Answer": 248.45, + "Options": "a ) 380 times , b ) 381 times , c ) 382 times , d ) 248 times , e ) 482 times", + "Correct": "d", + "Explanation": "\"time difference is 1 hr , 22 min , 49 sec = 4969 sec . so , light glows floor ( 4969 / 20 ) = 248 times . answer : d\"" + }, + { + "Answer": 34, + "Options": "a ) 34 , b ) 36 , c ) 37 , d ) 38 , e ) 39", + "Correct": "a", + "Explanation": "\"42 x = 18 x + 1.5 x ( h - 18 ) = = > 42 = 18 + 1.5 ( h - 18 ) = = > h - 18 = 24 / 1.5 = 16 = = > h = 34 answer is a\"" + }, + { + "Answer": 12, + "Options": "a ) 1 , b ) - 1 , c ) 3 , d ) 12 , e ) 13", + "Correct": "d", + "Explanation": "if x < 0 and y < 0 , then we ' ll have x - x + y = 7 and x - y - y = 6 . from the first equation y = 7 , so we can discard this case since y is not less than 0 . if x > = 0 and y < 0 , then we ' ll have x + x + y = 7 and x - y - y = 6 . solving gives x = 4 > 0 and y = - 1 < 0 - - > x + y = 3 . since in ps questions only one answer choice can be correct , then the answer is c ( so , we can stop here and not even consider other two cases ) . answer : c . adding both eqn we get 2 x + ixi + iyi = 13 now considering x < 0 and y > 0 2 x - x + y = 13 we get x + y = 12 hence answer should be d" + }, + { + "Answer": 103, + "Options": "a ) 87 , b ) 95 , c ) 102 , d ) 103 , e ) 115", + "Correct": "d", + "Explanation": "form 1 pm to 5 pm . excluding the actual hour chime we have 20 ( 1 pm ) + 20 ( 2 pm ) + 20 ( 3 pm ) + 20 ( 4 pm ) + 8 ( 5 pm ) = 88 now the hour chimes are 1 + 2 + 3 + 4 + 5 = 15 total = 88 + 15 = 103 answer d ." + }, + { + "Answer": 13, + "Options": "a ) 13 , b ) 24 , c ) c is elder than a , d ) data inadequate , e ) none", + "Correct": "a", + "Explanation": "\"solution [ ( a + b ) - ( b + c ) ] = 13 \u00e2 \u20ac \u00b9 = \u00e2 \u20ac \u00ba a - c = 13 . answer a\"" + }, + { + "Answer": 5, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "d", + "Explanation": "\"product of even number of - ve numbers is positive so it cant be 6 . answer : d\"" + }, + { + "Answer": 10.5, + "Options": "a ) 2.625 cm , b ) 3 cm , c ) 10.5 cm , d ) 15 cm , e ) none of these", + "Correct": "c", + "Explanation": "total rainfall = 3 x 7 = 21 cm hence , rainfall received on tuesday = 21 / 2 ( as it rained as much on tuesday as on all the others days of the week combined ) = 10.5 cm . answer : c" + }, + { + "Answer": 12, + "Options": "a ) 14 , b ) 12 , c ) 1200 , d ) 1.2 , e ) 14.11", + "Correct": "b", + "Explanation": "3 * 10 ^ 2 = 300 4 * 10 ^ - 2 = 0.04 ( 3 * 10 ^ 2 ) * ( 4 * 10 ^ - 2 ) = 300 * 0.04 = 12.00 the answer is option b" + }, + { + "Answer": 35, + "Options": "a ) 20 , b ) k = 25 , c ) 30 , d ) k = 35 , e ) 40", + "Correct": "d", + "Explanation": "\"suppose the population of the country in current year is 1000 . so annual increase is 1000 + 39.4 - 19.4 = 1020 hence every year there is an increase of 2 % . 2000 = 1000 ( 1 + ( 2 / 100 ) ) ^ n n = 35 answer is d .\"" + }, + { + "Answer": 40, + "Options": "a ) 32 , b ) 50 , c ) 40 , d ) 20 , e ) 10", + "Correct": "c", + "Explanation": "\"let there be x pupils in the class . total increase in marks = x x 1 / 2 = x / 2 x / 2 = ( 83 - 63 ) x / 2 = 20 x = 40 . answer : c\"" + }, + { + "Answer": 201.79999999999998, + "Options": "a ) 10.09 , b ) 1.06 , c ) 10.06 , d ) 201.8 , e ) 100.9", + "Correct": "d", + "Explanation": "\"= 4.036 / 0.02 = 403.6 / 2 = 201.8 answer is d .\"" + }, + { + "Answer": 4, + "Options": "a ) 4 , b ) 2 , c ) 0 , d ) \u2212 2 , e ) \u2212 4", + "Correct": "a", + "Explanation": "\"slope = rise / run = 9 / 18 = 1 / 2 the equation of the line is y = ( 1 / 2 ) x + b 3 = ( 1 / 2 ) ( 10 ) + b b = - 2 the equation of the line is y = ( 1 / 2 ) x - 2 to find the x - intercept , let y = 0 : 0 = ( 1 / 2 ) x - 2 x = 4 the answer is a .\"" + }, + { + "Answer": 2300, + "Options": "a ) 2300 , b ) 2550 , c ) 5050 , d ) 6275 , e ) 11325", + "Correct": "a", + "Explanation": "\"set a contains 6 , 8 , . . . 50 set b contains 102 , 104 , 106 . . . 150 number of terms in each set = 23 difference between corresponding terms in set a and b = 100 difference between sum of set b and set a = 100 * 23 = 2300 answer a\"" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 0 , c ) - 1 , d ) - 2 , e ) - 4", + "Correct": "a", + "Explanation": "\"( 1 ) x = 11 y + 4 ( 2 ) 2 x = 24 y + 3 let ' s subtract equation ( 1 ) from equation ( 2 ) . 13 y - 1 = x 13 y - x = 1 the answer is a .\"" + }, + { + "Answer": 2.999999999999999, + "Options": "a ) 9 , b ) 6 , c ) 4 , d ) 3 , e ) none of these", + "Correct": "d", + "Explanation": "3 x \u2013 5 y = 5 . . . ( i ) and xx + y = 57 xx + y = 57 \u21d2 7 x = 5 x + 5 y \u21d2 2 x = 5 y . . . ( ii ) from ( i ) and ( ii ) , x = 5 and y = 2 \u2234 x \u2013 y = 3 answer d" + }, + { + "Answer": 95, + "Options": "a ) 75 kg , b ) 95 kg , c ) 45 kg , d ) 85 kg , e ) 25 kg", + "Correct": "b", + "Explanation": "\"explanation : total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 75 + 20 ) kg = 95 kg . answer : b\"" + }, + { + "Answer": 98.75, + "Options": "a ) $ 94.03 , b ) $ 96.75 , c ) $ 98.75 , d ) $ 102.07 , e ) $ 105.3", + "Correct": "c", + "Explanation": "\"there can be 2 cases 1 ) 25 + 25 + 10 + 5 = $ 98.75 or 2 ) 25 + 25 + 25 = $ 96.75 c\"" + }, + { + "Answer": 13.99999999999999, + "Options": "a ) rs . 12 , b ) rs . 16 , c ) rs . 14 , d ) rs . 10 , e ) rs . 18", + "Correct": "c", + "Explanation": "\"required difference = [ 3 \u00bd % of rs . 8400 ] \u2013 [ 3 1 / 3 % of rs . 8400 ] = [ ( 7 / 20 - ( 10 / 3 ) ] % of rs . 8400 = 1 / 6 % of rs . 8400 = rs . [ ( 1 / 6 ) 8 ( 1 / 100 ) * 8400 ] = rs . 14 . answer is c .\"" + }, + { + "Answer": 29, + "Options": "a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 29", + "Correct": "e", + "Explanation": "x / 2 y = 3 / 2 = > x = 6 y / 2 = 3 y = > ( 7 x + 8 y ) / ( x - 2 y ) = ( ( 7 * ( 3 y ) ) + 8 y ) / ( 3 y - 2 y ) = > 29 y / y = 29 answer : e" + }, + { + "Answer": 6, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 11 , e ) 12", + "Correct": "b", + "Explanation": "since - 4 is the least integer in list d , then 7 is the largest integer in that list . thus the range of the positive integers in the list is 7 - 1 = 6 . answer : b ." + }, + { + "Answer": 135.5, + "Options": "a ) 72 kg , b ) 77.5 kg , c ) 135.5 kg , d ) data inadequate , e ) none of these", + "Correct": "c", + "Explanation": "\"total weight increased = ( 9 x 5.5 ) kg = 49.5 kg . weight of new person = ( 86 + 49.5 ) kg = 135.5 kg . answer : option c\"" + }, + { + "Answer": 96, + "Options": "a ) 96 , b ) 280 , c ) 384 , d ) 400 , e ) 500", + "Correct": "a", + "Explanation": "\"explanation : let the number be x . 5 * x / 6 = 5 * x / 16 + 50 25 * x / 48 = 50 x = 96 answer a\"" + }, + { + "Answer": 90, + "Options": "a ) 45 , b ) 38 , c ) 44 , d ) 90 , e ) 96", + "Correct": "d", + "Explanation": "\"n th term of a . p = a + ( n - 1 ) * d = 2 + ( 12 - 1 ) * 8 , = 2 + 88 = 90 . answer : d\"" + }, + { + "Answer": 120.00000000000003, + "Options": "a ) 20 minutes , b ) 110 minutes , c ) 120 minutes , d ) 140 minutes , e ) 160 minutes", + "Correct": "c", + "Explanation": "\"lets take number of minutesx . given that , 6 + 0.25 x = 12 + 0.2 x - > 0.05 x = 2 - > x = 120 minutes ans c\"" + }, + { + "Answer": 14, + "Options": "a ) 3 , b ) 6 , c ) 14 , d ) 17 , e ) 20", + "Correct": "c", + "Explanation": "the objective here is that 70 % of the fruit in the box should be apples . now , there are 14 apples at start and there is no talk of removing any apples , so number of apples should remain 14 and they should constitute 70 % of total fruit , so total fruit = 14 / 0.7 = 20 so we should have 20 - 14 = 6 oranges . right now , there are 20 oranges , so to get to 6 oranges , we should remove 20 - 6 = 14 oranges . answer c" + }, + { + "Answer": 1166.6666666666667, + "Options": "a ) $ 1166 , b ) $ 1168 , c ) $ 1166.6 , d ) $ 1167 , e ) none of the above", + "Correct": "d", + "Explanation": "to keep the amount exact when dividing for 3 , we have to work backwards through division . dividing 3500 by 3 will give us 1166.66 then by subtracting . 66 , we get 1166 , and we multiply it by 3 to get 3498 . to get enough for the down payment , we add 3 to 3498 . dividing the result by 3 gives us our answer . correct option : d" + }, + { + "Answer": 187.46067415730337, + "Options": "a ) 743 , b ) 154 , c ) 187 , d ) 741 , e ) 785", + "Correct": "c", + "Explanation": "\"divisor * quotient + remainder = dividend divisor = ( dividend ) - ( remainder ) / quotient ( 16698 - 14 ) / 89 = 187 answer ( c )\"" + }, + { + "Answer": 5040, + "Options": "a ) 5000 , b ) 5030 , c ) 5010 , d ) 5040 , e ) 5020", + "Correct": "d", + "Explanation": "let the total amount be rs . x the , x / 14 - x / 18 = 80 < = > 2 x / 126 = 80 < = > x / 63 = 63 x 80 = 5040 . hence the total amount is 5040 answer is d ." + }, + { + "Answer": 16, + "Options": "a ) 18 , b ) 16 , c ) 19 , d ) 21 , e ) 15", + "Correct": "b", + "Explanation": "( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 156 + 2 * 50 a + b + c = \u00e2 \u02c6 \u0161 256 = 16 answer b" + }, + { + "Answer": 21.701388888888893, + "Options": "a ) 15.502 % , b ) 25.7014 % , c ) 12.502 % , d ) 21.7014 % , e ) none", + "Correct": "d", + "Explanation": "\"only trick n this question is to ignore 60 % information as farm tax is levied uniformly in the village and that includes mr william ' s land . what percentage of tax mr william paid ? this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 500 / 3840 ) x 100 = 13.02083 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 13.02083 % x ( 100 / 60 ) = 21.7014 % and the answer is not there in the options . the correct answer is ( d ) .\"" + }, + { + "Answer": 35, + "Options": "a ) 19 , b ) 29 , c ) 35 , d ) 49 , e ) 59", + "Correct": "c", + "Explanation": "\"let the average after 17 th inning = x then average after 16 th inning = ( x - 3 ) therefore 16 ( x - 3 ) + 83 = 17 x therefore x = 35 answer : c\"" + }, + { + "Answer": 10, + "Options": "a ) 10 , b ) - 2 , c ) 11 , d ) 13 , e ) 22", + "Correct": "a", + "Explanation": "\"the equation that can be formed is : 3 x - 20 = 20 - x or , 4 x = 40 or , x = 10 . answer : a\"" + }, + { + "Answer": 2.911, + "Options": "a ) 2.91 , b ) 2.911 , c ) 2.938 , d ) 2.986 , e ) 2.999", + "Correct": "b", + "Explanation": "\"2.75 + . 003 + . 158 = 0 0 = 0 - 2.75 - 0.003 - 0.158 0 = - 2.911 answer : b\"" + }, + { + "Answer": 42, + "Options": "a ) 22 , b ) 33 , c ) 55 , d ) 42 , e ) 88", + "Correct": "d", + "Explanation": "\"let f = pure fuji , g = pure gala and c - cross pollinated . c = 10 % of x where x is total trees . c = . 1 x also 3 x / 4 = f and c + f = 238 = > . 1 x + 3 / 4 x = 238 = > x = 280 280 - 238 = pure gala = 42 . answer d\"" + }, + { + "Answer": 3, + "Options": "a ) 6 , b ) 4 , c ) 3 , d ) 5 , e ) 2", + "Correct": "c", + "Explanation": "\"the least number to be added to the numbers to make them divisible by 9 is equal to the difference of the least multiple of 9 greater than the sum of the digits and sum of the digits . sum of digits = 15 . nearest multiple of 9 greater than sum of digits = 18 . hence 3 has to be added . answer : c\"" + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 17", + "Correct": "a", + "Explanation": "8 k 8 k 88 - - - - - - - - 16 t 6 trial and error or just plug - in method might be the shortest way to solve this problem . though you can narrow down the possible values of k to just two : 7 and 8 - - > 8 * * + 7 * * = 16 * * or 8 * * + 8 * * = 16 * * ( k can not be less than 7 or 9 , as the result wo n ' t be 16 * * ) . after that it ' s easy to get that k = 7 and t = 6 . answer : a ." + }, + { + "Answer": 12656.25, + "Options": "a ) 3277 , b ) 2977 , c ) 12656 , d ) 6077 , e ) 17112", + "Correct": "c", + "Explanation": "\"explanation : 40,000 * ( 3 / 4 ) ^ 4 answer : c\"" + }, + { + "Answer": 800, + "Options": "a ) 800 , b ) 3799 , c ) 1200 , d ) 2693 , e ) 1732", + "Correct": "a", + "Explanation": "\"p - - - 10 - - - - 400 p - - - 5 - - - - - 200 3 p - - - 5 - - - - - 600 - - - - - - = > 800 answer : a\"" + }, + { + "Answer": 459, + "Options": "a ) $ 255 , b ) $ 275 , c ) $ 459 , d ) $ 1,250 , e ) $ 2,550", + "Correct": "c", + "Explanation": "\"total no . of boxes = 3060000 / ( 20 \u00d7 20 \u00d7 15 ) = 510 total cost = 510 \u00d7 $ 0.9 = $ 459 answer c\"" + }, + { + "Answer": 1, + "Options": "a ) 0.2 , b ) 1.2 , c ) 1.8 , d ) 2.2 , e ) 1.0", + "Correct": "e", + "Explanation": "\"since y * is defined as the greatest positive even integer less than or equal to y , then 5.0 * = 4 ( the greatest positive even integer less than or equal to 5.0 is 4 ) . hence , 5.0 \u2013 5.0 * = 5.0 - 4 = 1.0 answer : e .\"" + }, + { + "Answer": 313, + "Options": "a ) a ) 160 , b ) b ) 289 , c ) c ) 250 , d ) d ) 313 , e ) e ) 525", + "Correct": "d", + "Explanation": "\"a very helpful rule to know in arithmetic is the rule that in evenly spaced sets , average = median . because the average will equal the median in these sets , then we quickly know that the median of this set of consecutive odd integer numbers is 414 . there are 102 numbers in the set , and in a set with an even number of terms the median is just the average of the two most median terms ( here the 51 st and 52 nd numbers in the set ) . this means that numbers 51 and 52 in this set are 413 and 415 . because we know that number 51 is 413 , we know that the smallest number is 50 odd numbers below this , which means that it is 50 * 2 = 100 below this ( every odd number is every other number ) . therefore 413 - 100 = 313 , answer choice d\"" + }, + { + "Answer": 50, + "Options": "a ) 30 , b ) 35 , c ) 38 , d ) 40 , e ) 50", + "Correct": "e", + "Explanation": "\"10 play kabadi = > n ( a ) = 10 , 5 play both gmaes . = > n ( anb ) = 5 40 play kho kho only , = > n ( b ) = n ( b only ) + n ( anb ) = 40 + 5 = 45 total = > n ( aub ) = n ( a ) + n ( b ) - n ( anb ) = 10 + 45 - 5 = 50 answer : e\"" + }, + { + "Answer": 82, + "Options": "a ) 80 , b ) 81 , c ) 82 , d ) 83 , e ) 84", + "Correct": "c", + "Explanation": "1 + 2 = 10 . . . . . ( 1 + 2 ) ^ 2 + 1 = 10 2 + 3 = 26 . . . . . . . ( 2 + 3 ) ^ 2 + 1 = 26 3 + 4 = 50 then . . . ( 3 + 4 ) ^ 2 + 1 = 50 4 + 5 = 82 . . . . . . . . ( 4 + 5 ) ^ 2 + 1 = 82 answer : c" + }, + { + "Answer": 0.2222222222222222, + "Options": "a ) 2 / 9 , b ) 1 / 3 , c ) 2 / 5 , d ) 2 / 3 , e ) 7 / 9", + "Correct": "a", + "Explanation": "highest frequent term in the set is 5 ( with frequency 4 ) hence mode = 5 two terms ( 3 , 4 ) out of a total of 9 terms are less than mode of the set . fraction of set that are less than mode of set = 2 / 9 answer : option a" + }, + { + "Answer": 37.66666666666667, + "Options": "a ) 33.0 , b ) 37.66 , c ) 32.1 , d ) 31.23 , e ) 19", + "Correct": "b", + "Explanation": "explanation : let the two parts be ( 56 - x ) and x . then , 10 ( 56 - x ) + 22 x = 780 = > 12 x = 220 = > x = 20 . bigger part = ( 56 - x ) = 37.66 . answer : b ) 37.66" + }, + { + "Answer": 2, + "Options": "a ) 2 , b ) 4 , c ) 8 , d ) 6 , e ) 1", + "Correct": "a", + "Explanation": "the integer should be divisible by : 1 and 2 . the least common multiple of these integers is lcm = 1 * 2 = 2 answer : a" + }, + { + "Answer": 512, + "Options": "a ) 513 , b ) 512 , c ) 517 , d ) 519 , e ) 521", + "Correct": "b", + "Explanation": "trees increase by 1 / 4 the number of trees in preceding year . hence , correct answer must be divisible by 4 . based on divisibility rules , if last 2 digits are divisible by 4 then the number is divisible by 4 . thus , we can eliminate a , c , d , e the answer to be b again , trees increase by 1 / 4 the number of trees in preceding year . hence , the number of trees increase by 5 / 4 times the number of trees the preceding year . if x = initial number of trees = 512 year 1 = 5 / 4 x year 2 = ( 5 / 4 ) ( 5 / 4 ) x year 3 = ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) x year 4 = ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) x only for answer d : ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) 512 = 1250 hence , correct answer = b" + }, + { + "Answer": 12, + "Options": "a ) 16.2 , b ) 12 , c ) 5 , d ) 500 , e ) none", + "Correct": "b", + "Explanation": "\"answer let 45 x a = ( 60 x 900 ) / 100 \u2234 a = ( 60 x 9 ) / 45 = 12 correct option : b\"" + }, + { + "Answer": 6.8, + "Options": "a ) 6.6 , b ) 6.7 , c ) 6.8 , d ) 6.85 , e ) 6.9", + "Correct": "c", + "Explanation": "\"old set s - total is avg * no of elements = 6.2 * 10 = 62 if one number is increased by 6 then total increased to 62 + 6 = 68 new avg - 68 / 10 = 6.8 . hence answer is c .\"" + }, + { + "Answer": 675999, + "Options": "a ) 456780 , b ) 678918 , c ) 997479 , d ) 997916 , e ) 997920", + "Correct": "b", + "Explanation": "when you divide a positive integer by 10 , the remainder will just be the units digit . we know the remainder is 8 when we divide by 10 , so b is the only possible answer ." + }, + { + "Answer": 120, + "Options": "a ) 96 , b ) 106 , c ) 122 , d ) 116 , e ) 120", + "Correct": "e", + "Explanation": "\"average = total runs / no . of innings = 36 so , total = average x no . of innings = 36 * 20 = 720 now increase in avg = 4 runs . so , new avg = 36 + 4 = 40 runs total runs = new avg x new no . of innings = 40 * 21 = 840 runs made in the 11 th inning = 840 - 720 = 120 answer : e\"" + }, + { + "Answer": 3, + "Options": "a ) 2 , b ) 3 , c ) 7 , d ) 24 , e ) 35", + "Correct": "b", + "Explanation": "\"ab = 14 + 2 ( a + b ) 8 a = 14 + 2 a + 16 6 a = 30 a = 5 b - a = 8 - 5 = 3 b is the answer\"" + }, + { + "Answer": 719, + "Options": "a ) 724 , b ) 721 , c ) 720 , d ) 719 , e ) 700", + "Correct": "d", + "Explanation": "lcm = 720 720 - 1 = 719 answer : d" + }, + { + "Answer": 3.599999999999999, + "Options": "a ) $ 3.00 , b ) $ 3.20 , c ) $ 3.40 , d ) $ 3.60 , e ) $ 3.80", + "Correct": "d", + "Explanation": "\"x = 3 x / 5 + 1 / 3 * 2 x / 5 + 96 4 x / 15 = 96 x = $ 3.60 = $ 3.60 the answer is d .\"" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "a", + "Explanation": "\"substitute y by 3 in x + 3 y = 10 x + 3 ( 3 ) = 10 x + 9 = 10 if we substitute x by 1 in x + 9 = 10 , we have 1 + 9 = 10 . hence x = 1 correct answer a\"" + }, + { + "Answer": 8000, + "Options": "a ) 8000 , b ) 10000 , c ) 12000 , d ) 9000 , e ) none of these", + "Correct": "a", + "Explanation": "let the principal = p then p \u00d7 8 \u00d7 4 / 100 + p \u00d7 10 \u00d7 6 / 100 + p \u00d7 12 \u00d7 5 / 100 = 12160 \u21d2 152 p = 12160 \u00d7 100 or 12160 \u00d7 100 / 152 = 8000 answer a" + }, + { + "Answer": 9944, + "Options": "a ) 9999 , b ) 9944 , c ) 9988 , d ) 9900 , e ) 9991", + "Correct": "b", + "Explanation": "\"largest 4 digit number = 9999 9999 \u00f7 88 = 113 , remainder = 55 hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944 answer is b\"" + }, + { + "Answer": 72, + "Options": "a ) 56 , b ) 60 , c ) 64 , d ) 68 , e ) 72", + "Correct": "e", + "Explanation": "let x be the original number of pears . on day one , the vendor throws away ( 0.5 ) ( 0.8 ) x = 0.4 x . the remaining pears are ( 0.5 ) ( 0.8 ) x = 0.4 x . on day two , the vendor throws away ( 0.8 ) ( 0.4 ) x = 0.32 x . the vendor throws away a total of 0.4 x + 0.32 x = 0.72 x . the vendor throws away 72 percent of the pears . the answer is e ." + }, + { + "Answer": 20, + "Options": "a ) 20 % , b ) 30 % , c ) 40 % , d ) 50 % , e ) 60 %", + "Correct": "a", + "Explanation": "\"the is always the difference between our starting and ending points . in this case , it \u00e2 \u20ac \u2122 s 100 \u00e2 \u20ac \u201c 80 = 20 . the \u00e2 \u20ac \u0153 original \u00e2 \u20ac \u009d is our starting point ; in this case , it \u00e2 \u20ac \u2122 s 100 . ( 20 / 100 ) * 100 = ( 0.2 ) * 100 = 20 % . a\"" + }, + { + "Answer": 8, + "Options": "a ) 2 , b ) 4 , c ) 5 , d ) 8 , e ) 9", + "Correct": "d", + "Explanation": "\"explanation : let the number be v . then , 3 ( 2 x + 9 ) = 75 . 2 x + 9 = 25 = > 2 x = 16 = > x = 8 answer : d ) 8\"" + }, + { + "Answer": 38, + "Options": "a ) 18 , b ) 22 , c ) 28 , d ) 32 , e ) 38", + "Correct": "e", + "Explanation": "total children = 190 . let each student gets x chocolates if all were present . so , total chocolates = 190 x . 70 students were absent . so , no of extra chocolates distributed among 120 students , = 14 * 70 = 980 . now , total chocolates = 190 x 120 * ( x + 14 ) = 190 120 x + 1680 = 190 x 70 x = 1680 x = 24 . total no of chocolates = 24 * 190 = 4560 . no of chocolates each student gets on that day = 4560 / 120 = 38 . answer : option e" + }, + { + "Answer": 44, + "Options": "a ) 33 , b ) 36 , c ) 44 , d ) 63 , e ) 66", + "Correct": "c", + "Explanation": "from the given equations , a = 4 x , b = 4 z ( 10 a + b ) - ( 10 x + z ) = 40 x + 4 z - 10 x - z = 30 x + 3 z = 3 ( 10 x + z ) therefore the resultant should be divisible by 3 which is n ' t possible only in the case of c . hence c is the answer" + }, + { + "Answer": 2, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "c", + "Explanation": "apparently it ' s z = x ^ 2 - x ^ 3 instead of z = x ^ 2 - z ^ 3 . in this case : the x - intercept is the value ( s ) of x for z = 0 . 0 = x ^ 2 - x ^ 3 ; 0 = x ^ 2 ( 1 - x ) ; x = 0 or x = 1 . answer : c ." + }, + { + "Answer": 724777430, + "Options": "a ) 725067486 , b ) 436567874 , c ) 653658791 , d ) 725117481 , e ) 357889964", + "Correct": "a", + "Explanation": "\"72514 x 9999 = 72514 x ( 10000 - 1 ) = 72514 x 10000 - 72514 x 1 = 725140000 - 72514 = 725067486 a\"" + }, + { + "Answer": 24, + "Options": "a ) - 12 , b ) - 22 , c ) 24 , d ) 36 , e ) 42", + "Correct": "c", + "Explanation": "\"there will be two cases x - 12 = 100 or x - 12 = - 100 = > x = 112 or x = - 88 sum of both the values will be - 88 + 112 = 24 answer is c\"" + }, + { + "Answer": 20, + "Options": "a ) \u2013 7 , b ) 7 , c ) 20 , d ) 12 , e ) 14", + "Correct": "c", + "Explanation": "x ^ 2 - 8 x + 17 = | x - 5 | rhs can be - ve or + ve x ^ 2 - 9 x + 22 = 0 x ^ 2 - 7 x + 12 = 0 x = 11,4 , 3,2 we test all 3 values in original equation , all ok . thus , sum = 11 + 4 + 3 + 2 = 20 ans ( c )" + }, + { + "Answer": 120, + "Options": "a ) 120 % , b ) 0.120 % , c ) 1.20 % , d ) 0.209 % , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : while calculation in terms of percentage we need to multiply by 100 , so 1.20 * 100 = 120 answer : option a\"" + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20", + "Correct": "a", + "Explanation": "\"let the number of ducks be d and number of cows be c then , total number of legs = 2 d + 4 c = 2 ( d + 2 c ) total number of heads = c + d given that total number of legs are 24 more than twice the number of heads = > 2 ( d + 2 c ) = 24 + 2 ( c + d ) = > d + 2 c = 12 + c + d = > 2 c = 12 + c = > c = 12 i . e . , total number of cows = 12 answer is a .\"" + }, + { + "Answer": 35, + "Options": "a ) 31 kg , b ) 32 kg , c ) 33 kg , d ) 35 kg , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : let a , b , c represent their respective weights . then , we have : a + b + c = ( 45 x 3 ) = 135 \u2026 . ( i ) a + b = ( 40 x 2 ) = 80 \u2026 . ( ii ) b + c = ( 45 x 2 ) = 90 \u2026 . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 170 \u2026 . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 35 . b \u2019 s weight = 35 kg . answer : d\"" + }, + { + "Answer": 0.5555555555555556, + "Options": "a ) 4 / 9 , b ) 5 / 4 , c ) 5 / 8 , d ) 5 / 9 , e ) 6 / 9", + "Correct": "d", + "Explanation": "\"income = salary ( s ) + tips = s + s * 5 / 4 = s * 9 / 4 tips = s * 5 / 4 fraction of his income came from tips = ( s * 5 / 4 ) / ( s * 9 / 4 ) = 5 / 9 answer : d\"" + }, + { + "Answer": 528, + "Options": "a ) 273 , b ) 528 , c ) 539 , d ) 538 , e ) 723", + "Correct": "b", + "Explanation": "\"assume x soldiers join the fort . 1200 soldiers have provision for 1200 ( days for which provisions last them ) ( rate of consumption of each soldier ) = 1200 ( 30 ) ( 3 ) kg also provisions available for ( 1200 + x ) soldiers is ( 1200 + x ) ( 25 ) ( 2.5 ) kg as the same provisions are available = > 1200 ( 30 ) ( 3 ) = ( 1200 + x ) ( 25 ) ( 2.5 ) x = [ 1200 ( 30 ) ( 3 ) ] / [ ( 25 ) ( 2.5 ) ] - 1200 x = 528 answer : option b\"" + }, + { + "Answer": 8100, + "Options": "a ) 7000 , b ) 8100 , c ) 6000 , d ) 5000 , e ) 4000", + "Correct": "b", + "Explanation": "state a and state b had an equal number of candidates appeared . in state a , 6 % candidates got selected from the total appeared candidates in state b , 7 % candidates got selected from the total appeared candidates but in state b , 81 more candidates got selected than state a from these , it is clear that 1 % of the total appeared candidates in state b = 81 = > total appeared candidates in state b = 81 x 100 = 8100 = > total appeared candidates in state a = total appeared candidates in state b = 8100" + }, + { + "Answer": 50.000000000000014, + "Options": "a ) 40 , b ) 45 , c ) 38 , d ) 50 , e ) 39", + "Correct": "d", + "Explanation": "\"let , father \u00e2 \u20ac \u2122 s current age is a years . then , man \u00e2 \u20ac \u2122 s current age = [ ( 2 / 5 ) a ] years . therefore , [ ( 2 / 5 ) a + 10 ] = ( 1 / 2 ) ( a + 10 ) 2 ( 2 a + 50 ) = 5 ( a + 10 ) a = 50 d\"" + }, + { + "Answer": 85, + "Options": "a ) 64 , b ) 72 , c ) 80 , d ) 85 , e ) none of the above", + "Correct": "d", + "Explanation": "\"let the number of wickets taken till the last match be x . then , 12.4 x + 26 / x + 5 = 12 \u21d2 12.4 x + 26 = 12 x + 60 \u21d2 0.4 x = 34 \u21d2 x = 34 \u2044 0.4 = 340 \u2044 4 = 85 . answer d\"" + }, + { + "Answer": 90, + "Options": "a ) 52 , b ) 49 , c ) 95 , d ) 90 , e ) 66", + "Correct": "d", + "Explanation": "\"right side = 15 seat left side = 15 - 3 ( 3 few seat in right side ) = 12 seat total = 15 + 12 = 27 people can seat in 27 seat = 27 * 3 = 81 people can seat in last seat = 9 total people can seat = 81 + 9 = 90 answer : d\"" + }, + { + "Answer": 50, + "Options": "a ) 20 , b ) 25 , c ) 50 , d ) 45 , e ) 75", + "Correct": "c", + "Explanation": "average = 25 , sum of temperatures = 25 * 5 = 125 as the min temperature is 15 , max would be 125 - 4 * 15 = 65 - - > the range = 65 ( max ) - 15 ( min ) = 50 answer : c" + }, + { + "Answer": 5091, + "Options": "a ) 4857 , b ) 4184 , c ) 4012 , d ) 5091 , e ) 5291", + "Correct": "d", + "Explanation": "\"let the sale in the sixth month = x then ( 6335 + 6927 + 6855 + 7230 + 6562 + x ) / 6 = 6500 = > 6335 + 6927 + 6855 + 7230 + 6562 + x = 6 \u00d7 6500 = > 33909 + x = 39000 = > x = 39000 \u2212 33909 = 5091 answer : d\"" + }, + { + "Answer": 22, + "Options": "a ) 0.22 , b ) 0.44 , c ) 0.55 , d ) 22 , e ) 55", + "Correct": "d", + "Explanation": "a dozen eggs cost as much as a pound of rice - - > 12 eggs = 1 pound of rice = 33 cents ; a half - liter of kerosene costs as much as 8 eggs - - > 4 eggs = 1 / 2 liters of kerosene . how many cents does a liter of kerosene cost - - > 1 liter of kerosene = 8 eggs = 8 / 12 * 33 = 22 cents . answer : d ." + }, + { + "Answer": 28, + "Options": "a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 28", + "Correct": "e", + "Explanation": "\"solution let the toatl number of workers be x . then 8000 x = ( 14000 x 7 ) + 6000 ( x - 7 ) x = 28 . answer e\"" + }, + { + "Answer": 56, + "Options": "a ) 1 , b ) 4 , c ) 9 , d ) 13 , e ) 56", + "Correct": "e", + "Explanation": "\"solving through algebra route : 8 b + 14 f = x amount if we multiply this equation with 4 we get : 32 b + 56 f = 4 x therefore , we got 32 ounces of butter and 4 x amount of quantity when we use 56 ounces of floor . ans : e\"" + }, + { + "Answer": 25, + "Options": "a ) 30 , b ) 25 , c ) 15 , d ) 10 , e ) 5", + "Correct": "b", + "Explanation": "five kilograms of oranges contained 95 % of water . if the next day the concentration of water decreased by 5 % , what was the new weight of the oranges , in kilograms ? ( a ) 30 ( b ) 25 ( c ) 15 ( d ) 10 ( e ) 5 if b is the answer , then the question means that the concentration of water the newt day became 90 % . out of 5 kilograms 95 % , or 4.75 kilograms was water and 0.25 kilograms was non - water . the next day , after some water evaporated , oranges became 90 % water and 10 % of non - water , so the next day 0.25 kilograms of non - water composed 10 % of oranges , which means that the new weight of the oranges was x * 0.10 = 0.25 - - > x = 25 kilograms . answer : b ." + }, + { + "Answer": 151.25, + "Options": "a ) 151 , b ) 149 , c ) 151.25 , d ) 148 , e ) none of the above", + "Correct": "c", + "Explanation": "corrected mean = 150 \u00d7 20 \u2212 135 + 160 / 20 = 3000 \u2212 135 + 160 / 20 = 3025 / 20 = 151.25 answer c" + }, + { + "Answer": 17760, + "Options": "a ) 17760 , b ) 18540 , c ) 16320 , d ) 14640 , e ) 15640", + "Correct": "a", + "Explanation": "iman = 45 and 1 women = 60 then 1 / 9 man = 1 / 9 * 45 = 5 and 1 / 12 of women = 1 / 12 * 60 = 5 total people 3552 = 3552 * 5 = 17760 answer : a" + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 1 , c ) 2 , d ) 4 , e ) 7", + "Correct": "a", + "Explanation": "\"mean = ( x + x + 2 + x + 4 + x + 7 + x + 37 ) / 5 = ( 5 x + 50 ) / 5 = x + 10 median = x + 4 thus mean - median = x + 10 - ( x + 4 ) = 6 answer = a\"" + }, + { + "Answer": 105, + "Options": "a ) 106.25 , b ) 105.5 , c ) 105.75 , d ) 106 , e ) 105.0", + "Correct": "e", + "Explanation": "rate of flow of water in second hour = 36 gallons per hour rate of flow of water in first hour = 36 / ( 3 / 2 ) = 24 gallons per hour rate of flow of water in third hour = ( 125 / 100 ) * 36 = ( 5 / 4 ) * 36 = 45 gallons per hour number of gallons of water that flowed through the pipe during the entire 3 hours = 24 + 36 + 45 = 105 gallons answer e" + }, + { + "Answer": 499849, + "Options": "a ) 588338 , b ) 499449 , c ) 399826 , d ) 788392 , e ) 622975", + "Correct": "b", + "Explanation": "b the required number is 499449 . the maximum sum of a number under 5 lakh will be of the number 499999 i . e . 49 . thus the required number must be close to 499999 . the root of 499999 ~ 707.106 by calculating the square of 707 , we get 499849 which is the answer ." + }, + { + "Answer": 0.4642857142857143, + "Options": "a ) 3 / 7 , b ) 11 / 14 , c ) 13 / 28 , d ) 19 / 28 , e ) 29 / 42", + "Correct": "c", + "Explanation": "p ( red or blue ) = 1 - p ( white ) - p ( green ) = 28 / 28 - 7 / 28 - 8 / 28 = 13 / 28 the answer is c ." + }, + { + "Answer": 96, + "Options": "a ) 20 % , b ) 40 % , c ) 64 % , d ) 80 % , e ) 96 %", + "Correct": "e", + "Explanation": "a real world problem \u2014 - yum ! \u2014 - but again , the specifics of the shape don \u2019 t matter . diameter increases 40 % , so k = 1.4 in this case . \u201c amount of pizza \u201d just means the area of the circle , so k ^ 2 = ( 1.4 ) ^ 2 = 1.96 , which is the multiplier for a 96 % increase . that \u2019 s the percent increase in area . answer = e" + }, + { + "Answer": 57, + "Options": "a ) 55 , b ) 56 , c ) 57 , d ) 58 , e ) 59", + "Correct": "c", + "Explanation": "20 x + 48 = 21 ( x \u2013 5 ) x = 57 answer : c" + }, + { + "Answer": 20, + "Options": "a ) rs 10 , b ) rs 20 , c ) rs 24 , d ) rs 28 , e ) none of these", + "Correct": "b", + "Explanation": "explanation : let c = x . then a = ( x \ufffd 20 ) and b = ( x \ufffd 40 ) . x + x - 20 + x - 40 = 120 or x = 60 . a : b : c = 40 : 20 : 60 = 2 : 1 : 3 . b ' s share = rs . 120 * ( 1 / 6 ) = rs . 20 answer : b" + }, + { + "Answer": 516, + "Options": "a ) s . 440 , b ) s . 500 , c ) s . 540 , d ) s . 740 , e ) s . 516", + "Correct": "e", + "Explanation": "\"s . i for 5 years = ( 1020 - 660 ) = rs . 360 . s . i . for 2 years = 360 / 5 * 2 = rs . 144 . principal = ( 660 - 144 ) = rs . 516 . answer : e\"" + }, + { + "Answer": 35.714285714285715, + "Options": "a ) 35.7 % , b ) 25 % , c ) 32 % , d ) 30.8 % , e ) 60 %", + "Correct": "a", + "Explanation": "\"from the first plot 0.30 * 500 = 150 ; from the second plot 0.50 * 200 = 100 ; total percent = ( 150 + 100 ) / ( 500 + 200 ) = 0.357 . answer : a .\"" + }, + { + "Answer": 19, + "Options": "a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 21", + "Correct": "c", + "Explanation": "solution prime numbers less than 70 are = 12 . 2,3 , 5,7 , 11,13 , 17,19 , 23,29 , 31,37 , 41,43 , 47,53 , 59,61 , and 67 their number is 19 . answer c" + }, + { + "Answer": 0.09999999999999998, + "Options": "a ) 1 / 5 , b ) 1 / 10 , c ) 7 / 20 , d ) 3 / 5 , e ) it can not be determined from the given information .", + "Correct": "b", + "Explanation": "\"plug in simple numbers . take 100 couples for example . 3 / 5 of 100 couples have more than one child = 60 couples . 1 / 2 of 100 couples have more than 3 kids = 50 couples . this implies that 50 couples are a subset of 60 couples and the complement of 60 couples within those 100 couples , which equals 40 couples have either one or no kids at all . we need to find couples that have 2 or 3 kids , so essentially , it is 60 - 50 = 10 . fraction will be 10 / 100 = 1 / 10 . option b\"" + }, + { + "Answer": 0.8024691358024691, + "Options": "a ) 23 / 24 , b ) 31 / 36 , c ) 55 / 64 , d ) 65 / 81 , e ) 75 / 121", + "Correct": "d", + "Explanation": "p ( no even digits ) = 2 / 3 * 2 / 3 * 2 / 3 * 2 / 3 = 16 / 81 p ( at least one even digit ) = 1 - 16 / 81 = 65 / 81 the answer is d ." + }, + { + "Answer": 7, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9", + "Correct": "c", + "Explanation": "\"the greatest number that exactly divides 35 , 91 and 840 is the hcf of the three numbers . so , calculating hcf we get the answer 7 . answer : c\"" + }, + { + "Answer": 5.5, + "Options": "a ) 4.5 , b ) 5 , c ) 5.5 , d ) 5.8 , e ) 6", + "Correct": "c", + "Explanation": "\"if $ x $ is the number , x / 6 * 12 = 11 = > 2 x = 11 = > x = 5.5 c\"" + }, + { + "Answer": 72, + "Options": "a ) 80 , b ) 54 , c ) 54 , d ) 72 , e ) 12", + "Correct": "d", + "Explanation": "given 3 x + 4 y = 60 - - - eq 1 6 x - 4 y = 12 - - eq 2 sum both eqns we get 9 x = 72 = > x = 8 sum 6 x in eq 2 = > 48 - 4 y = 12 . = > y = 9 now xy = 8 * 9 = 72 option d is correct answer ." + }, + { + "Answer": 18, + "Options": "a ) 8 , b ) 10 , c ) 12 , d ) 18 , e ) 16", + "Correct": "d", + "Explanation": "\"ifno caris selected more than once then the number of clients = 18 / 3 = 6 but since every car is being selected three times so no . of clients must be thrice as well = 6 * 3 = 18 answer : option d\"" + }, + { + "Answer": 950, + "Options": "a ) $ 550 , b ) $ 650 , c ) $ 750 , d ) $ 850 , e ) $ 950", + "Correct": "e", + "Explanation": "\"95 % remains to be paid so the remaining amount is 19 * 50 = $ 950 . the answer is e .\"" + }, + { + "Answer": 200, + "Options": "a ) 200 , b ) 250 , c ) 300 , d ) 350 , e ) 400", + "Correct": "a", + "Explanation": "\"a + b + c = 700 a + c = 300 b + c = 600 - - - - - - - - - - - - - - a + b + 2 c = 900 a + b + c = 700 - - - - - - - - - - - - - - - - c = 200 answer : a\"" + }, + { + "Answer": 504, + "Options": "a ) 360 , b ) 504 , c ) 510 , d ) 320 , e ) 280", + "Correct": "b", + "Explanation": "\"lcm = 2 * 2 * 2 * 3 * 3 * 7 = 504 . answer is b\"" + }, + { + "Answer": 2, + "Options": "a ) 5 , b ) 3 , c ) 1 , d ) 4 , e ) 2", + "Correct": "e", + "Explanation": "green is 7 / 10 gold is 4 / 5 which can also be written as 8 / 10 white is 1 / 2 which can also be written as 5 / 10 7 / 10 + 8 / 10 + 5 / 10 = 2 answer is e ) 2" + }, + { + "Answer": 500, + "Options": "a ) rs . 500 , b ) rs . 600 , c ) rs . 700 , d ) rs . 1500 , e ) rs . 2500", + "Correct": "a", + "Explanation": "\"sum of the salaries of the person for the months of january , february , march and april = 4 * 8000 = 32000 - - - - ( 1 ) sum of the salaries of the person for the months of february , march , april and may = 4 * 9500 = 38000 - - - - ( 2 ) ( 2 ) - ( 1 ) i . e . may - jan = 6000 salary of may is rs . 6500 salary of january = rs . 500 answer : a\"" + }, + { + "Answer": 69.99999999999999, + "Options": "a ) 75 % , b ) 72 % , c ) 70 % , d ) 73 % , e ) 74 %", + "Correct": "c", + "Explanation": "\"say david ' s wages last week were $ 100 , so he spent 0.20 * 100 = $ 20 on recreation ; this week ' s wages is 0.70 * 100 = $ 70 , so he spends 0.2 * 70 = $ 14 on recreation ; 14 / 20 = 0.70 , hence the amount he spends on recreation this week is 70 % of the amount he spent on recreation last week : 20 * 0.7 = 14 answer : c\"" + }, + { + "Answer": 30, + "Options": "a ) 24 , b ) 26 , c ) 28 , d ) 30 , e ) 32", + "Correct": "d", + "Explanation": "let c be the capacity of the can . ( 4 / 7 ) * ( c - 10 ) + 10 = ( 5 / 7 ) * c 4 c - 40 + 70 = 5 c c = 30 the answer is d ." + }, + { + "Answer": 0.42857142857142855, + "Options": "a ) 1 / 5 , b ) 2 / 3 , c ) 3 / 7 , d ) 3 / 5 , e ) 4 / 5", + "Correct": "c", + "Explanation": "let x be the amount of fuel high octane = x / 5 regular = 4 x / 5 price of regular = y price of high octante = 3 y cost of high octane in the fuel = 3 y * x / 5 total cost = 3 y * x / 5 + 4 x / 5 * y % = cost of high octante / total cost = 3 / 7 answer is c" + }, + { + "Answer": 14.4, + "Options": "a ) 10.2 , b ) 12.1 , c ) 8.1 , d ) 15.6 , e ) 14.4", + "Correct": "e", + "Explanation": "\"x is 20 % greater than 12 means x is 1.2 times 12 ( in other words 12 + 20 / 100 * 12 = 1.2 * 12 ) therefore , x = 1.2 * 12 = 14.4 answer : e\"" + }, + { + "Answer": 70, + "Options": "a ) 66 % , b ) 67 % , c ) 68 % , d ) 69 % , e ) 70 %", + "Correct": "e", + "Explanation": "\"74 + 81 + x = 3 * 75 x = 70 the answer is e .\"" + }, + { + "Answer": 36, + "Options": "a ) 50 min , b ) 40 min , c ) 35 min , d ) 25 min , e ) 36 min", + "Correct": "e", + "Explanation": "\"clearly , the two will meet when they are 1000 m apart to be 20 + 16 = 36 km apart , they take 1 hour to be 1000 m apart , they take 36 * 1000 / 1000 = 36 min . answer is e\"" + }, + { + "Answer": 0.13333333333333333, + "Options": "a ) 2 / 69 , b ) 2 / 15 , c ) 2 / 63 , d ) 2 / 29 , e ) 2 / 10", + "Correct": "b", + "Explanation": "\"explanation : let a be the event that x is selected and b is the event that y is selected . p ( a ) = 1 / 3 , p ( b ) = 2 / 5 . let c be the event that both are selected . p ( c ) = p ( a ) \u00e3 \u2014 p ( b ) as a and b are independent events : = ( 1 / 3 ) \u00e3 \u2014 ( 2 / 5 ) = 2 / 15 answer : b ) 2 / 15\"" + }, + { + "Answer": 20, + "Options": "a ) 20 % , b ) 30 % , c ) 40 % , d ) 70 % , e ) 90 %", + "Correct": "a", + "Explanation": "to maximize the percentage of companies offering both , let ' s assume that all 20 % of companies which offer wireless internet also offer snacks . the answer is a ." + }, + { + "Answer": 75.6, + "Options": "a ) a ) 87 , b ) b ) 99 , c ) c ) 68 , d ) d ) 82 , e ) e ) 76", + "Correct": "e", + "Explanation": "\"average = ( 74 + 65 + 82 + 67 + 90 ) / 5 = 380 / 5 = 76 . answer : e\"" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "a", + "Explanation": "\"the product of 2 integers is negative thus an odd number of integers need to be negative to have a negative product we are asked at most how many are required . so , the highest odd integer before 6 , i . e . 1 correct option : a\"" + }, + { + "Answer": 4, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 4 , e ) 3", + "Correct": "d", + "Explanation": "\"since 16 / k = 4 and 16 / 4 = 4 , then k = 4 correct answer d\"" + }, + { + "Answer": 1600, + "Options": "a ) 8981 , b ) 3799 , c ) 1200 , d ) 1600 , e ) 1732", + "Correct": "d", + "Explanation": "\"p - - - 10 - - - - 800 p - - - 5 - - - - - 400 3 p - - - 5 - - - - - 1200 - - - - - - = > 1600 answer : d\"" + }, + { + "Answer": 138, + "Options": "a ) a . 138 , b ) b . 50 , c ) c . 48 , d ) d . 46 , e ) e . 44", + "Correct": "a", + "Explanation": "\"at 6 : 00 it ' ll chime 6 times . if we assume that the time taken to chime is x , then time between chimes is also x . so you have 6 chimes , which is 6 x and 5 time intervals between chimes . this means that 11 x = 66 seconds . thus x = 6 seconds . by a similar logic , at 12 : 00 , there are 12 chimes and 11 intervals so the total time is ( 12 + 11 ) x = 23 x = 138 seconds . answer a\"" + }, + { + "Answer": 23.076923076923077, + "Options": "a ) 10 % , b ) 12 % , c ) 15 % , d ) 17 % , e ) 23 %", + "Correct": "e", + "Explanation": "\"lets assume that candidate got 35 % votes and total votes is 100 . candidate won = 35 remaining = 65 to get 50 % , candidate requires 15 votes from 100 which is 15 % and 15 votes from 65 . 15 / 65 = 23.07 which is approx 23 % . hence the answer is e\"" + }, + { + "Answer": 17, + "Options": "a ) 16.2 , b ) 16.4 , c ) 16.6 , d ) 16.8 , e ) 17.0", + "Correct": "e", + "Explanation": "\"let x be the factor by which the bacteria increases every three hours . at 4 : 00 pm , the amount of bacteria was 10 x and at 7 : 00 pm it was 10 x ^ 2 . 10 x ^ 2 = 28.9 x ^ 2 = 2.89 x = 1.7 at 4 : 00 pm , the amount of bacteria was 10 ( 1.7 ) = 17 grams . the answer is e .\"" + }, + { + "Answer": 4, + "Options": "a ) 4 , b ) 10 , c ) 9 , d ) 6 , e ) 5", + "Correct": "a", + "Explanation": "\"53 x + 78 = 58 ( x + 1 ) = > 5 x = 20 = > x = 4 answer : a\"" + }, + { + "Answer": 13, + "Options": "a ) 10.6 kg , b ) 10.8 kg , c ) 11 kg , d ) 13 kg , e ) none", + "Correct": "d", + "Explanation": "\"answer weight of new student = total weight of all 20 students - total weight of initial 19 students = ( 20 x 14.9 - 19 x 15 ) kg = 13 kg . correct option : d\"" + }, + { + "Answer": 8, + "Options": "a ) 4 , b ) 8 , c ) 16 , d ) 12 , e ) 14", + "Correct": "b", + "Explanation": "\"since the number is greater than the number obtained on reversing the digits , so the ten ' s digit is greater than the unit ' s digit . let ten ' s and unit ' s digits be 2 x and x respectively . then , ( 10 x 2 x + x ) - ( 10 x + 2 x ) = 36 9 x = 36 x = 4 . required difference = ( 2 x + x ) - ( 2 x - x ) = 2 x = 8 . answer : b\"" + }, + { + "Answer": 30, + "Options": "a ) 15 min , b ) 18 min , c ) 16 min , d ) 20 min , e ) 30 min", + "Correct": "e", + "Explanation": "\"in 1 hr , the bus covers 80 km without stoppages and 40 km with stoppages . stoppage time = time take to travel ( 80 - 40 ) km i . e 40 km at 80 km / hr . stoppage time = 40 / 80 hrs = 30 min answer : e\"" + }, + { + "Answer": 100011, + "Options": "a ) 100011 , b ) 111111 , c ) 101111 , d ) 201111 , e ) 211111", + "Correct": "a", + "Explanation": "smallest number of 6 digits is 100000 . on dividing 100000 by 111 , we get 100 as remainder . number to be added = ( 111 - 100 ) - 11 . hence , required number = 100011 option a" + }, + { + "Answer": 127, + "Options": "a ) 123 , b ) 127 , c ) 235 , d ) 305 , e ) 505", + "Correct": "b", + "Explanation": "\"explanation : required number = h . c . f . of ( 1657 - 6 ) and ( 2037 - 5 ) = h . c . f . of 1651 and 2032 = 127 . answer : b\"" + }, + { + "Answer": 54, + "Options": "a ) 33 , b ) 37 , c ) 54 , d ) 99 , e ) 01", + "Correct": "c", + "Explanation": "\"the number of students with first division = 28 % of 300 = 28 / 100 \u00d7 300 = 8400 / 100 = 84 and , the number of students with second division = 54 % of 300 = 54 / 100 \u00d7 300 = 16200 / 100 = 162 therefore , the number of students who just passed = 300 \u2013 ( 84 + 162 ) = 54 answer : c\"" + }, + { + "Answer": 14, + "Options": "a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14", + "Correct": "e", + "Explanation": "\"sum of 13 even numbers = 13 * 14 = 110 average = 182 / 13 = 14 answer : e\"" + }, + { + "Answer": 370000, + "Options": "a ) $ 80,000 , b ) $ 130,000 , c ) $ 240,000 , d ) $ 370,000 , e ) $ 320,000", + "Correct": "d", + "Explanation": "for sake of ease , let ' s say there are 10 employees : 7 marketers , 1 engineers , and 2 manager . average company salary * number of employees = total company salary > > > $ 80,000 * 10 = $ 800,000 subtract the combined salaries for the marketers ( 7 * $ 50,000 ) and the engineers ( $ 80,000 ) > > > $ 800,000 - $ 350,000 - $ 80,000 = $ 370,000 . the correct answer is d ." + }, + { + "Answer": 0.5, + "Options": "a ) 7 / 17 , b ) 14 / 31 , c ) 7 / 15 , d ) 17 / 35 , e ) 1 / 2", + "Correct": "e", + "Explanation": "the easiest way for me is to plug in numbers . let the number of basic stereos produced be 40 , and number of delux stereos produced be 20 . total of 60 stereos . if it takes an hour to produce a basic stereo then it will take 1.6 hours to produce a deluxe stereo . 40 basic stereos = 40 hours . 20 delux stereos = 32 hours . total hours = 72 then the fraction would be 32 / 72 = 4 / 9 . therefore answer e" + }, + { + "Answer": 26, + "Options": "a ) 26 , b ) 27 , c ) 30 , d ) 35 , e ) 42", + "Correct": "a", + "Explanation": "\"average in 5 matches = ( 2 * 20 + 3 * 30 ) / 2 + 3 = 40 + 90 / 5 = 130 / 5 = 26 answer is a\"" + }, + { + "Answer": 8, + "Options": "a ) 8 , b ) 10 , c ) 9 , d ) 6 , e ) 5", + "Correct": "a", + "Explanation": "\"51 x + 78 = 54 ( x + 1 ) = > 3 x = 24 = > x = 8 answer : a\"" + }, + { + "Answer": 674.9999999999999, + "Options": "a ) 75 , b ) 125 , c ) 675 , d ) 1100 , e ) 1250", + "Correct": "c", + "Explanation": "\"7 a * 2 b = 15 * 15 = 225 14 ab = 225 i . e . 42 ab = 675 answer : option c\"" + }, + { + "Answer": 1.05, + "Options": "a ) 1.05 , b ) 1.16 , c ) 1.2 , d ) 1.3 , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : ( x * 5 ) = ( 0.75 * 7 ) x = 5.25 / 5 = 1.05 answer : a\"" + }, + { + "Answer": 66, + "Options": "a ) 66 , b ) 67 , c ) 68 , d ) 69 , e ) 70", + "Correct": "a", + "Explanation": "the worst case senario will be first take 40 red then take 22 green then take 1 + 1 red + green then take 2 orange . so total 40 + 22 + 2 + 2 = 66 answer : a" + }, + { + "Answer": 56, + "Options": "a ) 55 , b ) 56 , c ) 57 , d ) 58 , e ) 59", + "Correct": "b", + "Explanation": "\"20 x + 49 = 21 ( x \u2013 5 ) x = 56 answer : b\"" + }, + { + "Answer": 10, + "Options": "a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18", + "Correct": "a", + "Explanation": "\"15 n + 37 = 17 ( n + 1 ) 2 n = 20 n = 10 the answer is a .\"" + }, + { + "Answer": 19, + "Options": "a ) 19 , b ) 18 , c ) 16 , d ) 11 , e ) 17", + "Correct": "a", + "Explanation": "\"sum of 18 even numbers = 18 * 19 = 342 average = 342 / 18 = 19 answer : a\"" + }, + { + "Answer": 98, + "Options": "a ) 98 , b ) 100 , c ) 0 , d ) 99 , e ) 97", + "Correct": "a", + "Explanation": "g ( 99 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 g ( 97 ) = 1 * 3 * 5 * 7 * 9 * . . . * 97 g ( 99 ) - g ( 97 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 - 1 * 3 * 5 * 7 * 9 * . . . * 97 = 1 * 3 * 5 * 7 * 9 * . . . * 97 * ( 99 - 1 ) = 1 * 3 * 5 * 7 * 9 * . . . * 97 * 98 hence : a ." + }, + { + "Answer": 190, + "Options": "a ) 90 , b ) 190 , c ) 120 , d ) 130 , e ) 220", + "Correct": "b", + "Explanation": "orchestra seats - a balcony seats - b a + b = 370 and 12 a + 8 b = 3320 solving equations simultaneously ( multiply equation 1 with 8 and subtract from second equation ) 4 a = 3320 - 8 * 370 = 3320 - 2960 = 360 i . e . a = 90 and b = 370 - 90 = 280 more seats in balcony than orchestra = b - a = 280 - 90 = 190 answer : option b" + }, + { + "Answer": 21, + "Options": "a ) $ 10 , b ) $ 12 , c ) $ 13.20 , d ) $ 21 , e ) $ 16.80", + "Correct": "d", + "Explanation": "\"3 j + 2 s = 69 2 j + 3 s = 81 - - - - - - - - - - - - - - - - 5 j + 5 s = 150 - - - - ( divide by 5 ) - - - > j + s = 30 3 j + 2 s = j + 2 ( j + s ) = j + 60 = 69 - - - > j = 9 3 * 9 + 2 s = 69 27 + 2 s = 69 2 s = 42 s = 21 answer : d\"" + }, + { + "Answer": 14, + "Options": "a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20", + "Correct": "b", + "Explanation": "the number of zeroes at the end of 60 ! will be less than the number of zeroes at the end of 120 ! hence it is sufficient to calculate the number of zeroes at the end of 60 ! the number of zeroes = [ 60 / 5 ] + [ 60 / 25 ] + [ 60 / 125 ] = 12 + 2 + 0 = 14 the answer is b ." + }, + { + "Answer": 22, + "Options": "a ) a ) 12 , b ) b ) 14 , c ) c ) 16 , d ) d ) 18 , e ) e ) 22", + "Correct": "e", + "Explanation": "\"d = ( d - r ) / q = ( 265 - 1 ) / 12 = 264 / 12 = 22 e )\"" + }, + { + "Answer": 0.5, + "Options": "a ) 1 / 4 , b ) 1 / 8 , c ) 1 / 7 , d ) 1 / 2 , e ) 3", + "Correct": "d", + "Explanation": "one way to look at it : the number from set a can be anything . the number selected from set b will determine whether the sum is odd or even . for example , if a 4 is selected from set a , we need a 0 from set b to get an even sum . if a 5 is selected from set a , we need a 1 from set b to get an even sum . and so on . so , p ( sum is even ) = p ( select any number from set aandselect the number from set b that makes the sum even ) = p ( select any number from set a ) xp ( select the number from set b that makes the sum even ) = 1 x 1 / 2 = 1 / 2 = d" + }, + { + "Answer": 5750, + "Options": "a ) 5000 , b ) 5750 , c ) 2878 , d ) 2990 , e ) 2771", + "Correct": "b", + "Explanation": "\"income = rs . 100 expenditure = rs . 80 savings = rs . 20 present expenditure 80 * ( 20 / 100 ) = rs . 96 present savings = 100 \u00e2 \u20ac \u201c 96 = rs . 4 100 - - - - - - 4 ? - - - - - - - - - 230 = > 5750 answer : b\"" + }, + { + "Answer": 54, + "Options": "a ) 54 , b ) 45 , c ) 65 , d ) 78 , e ) 64", + "Correct": "a", + "Explanation": "( x + x 1 + . . . x 14 ) / 15 = 40 54 option a" + }, + { + "Answer": 180, + "Options": "a ) 32 , b ) 180 , c ) 60 , d ) 27 , e ) 11", + "Correct": "b", + "Explanation": "\"explanation : let the number be 26 + 1 / 2 [ 1 / 3 ( a / 5 ) ] = a / 15 = > 6 = a / 30 = > a = 180 answer : b\"" + }, + { + "Answer": 933.4285714285714, + "Options": "a ) 933.4 , b ) 1219 , c ) 1210 , d ) 1212 , e ) 1312", + "Correct": "a", + "Explanation": "\"\u03c0 ( 212 \u2013 122 ) = 933.4 answer : a\"" + }, + { + "Answer": 160, + "Options": "a ) 160 , b ) 200 , c ) 250 , d ) 350 , e ) none", + "Correct": "a", + "Explanation": "sol . let the number of grils be x . then , number of boys = ( 640 - x ) . then , ( 11 3 / 4 \u00d7 640 ) \u21d4 11 x + 12 ( 640 - x ) \u21d4 x = 7680 - 7520 \u21d4 160 . answer a" + }, + { + "Answer": 18, + "Options": "a ) 10 , b ) 11 , c ) 18 , d ) 13 , e ) 14", + "Correct": "c", + "Explanation": "\"since average price of a pencil = 2 \u2234 price of 75 pencils = 150 \u2234 price of 30 pens = ( 690 \u2013 150 ) = 540 \u2234 average price of a pen = 540 \u2044 60 = 18 answer c\"" + }, + { + "Answer": 16, + "Options": "a ) 4 % increase , b ) 10 % increase , c ) 10 % decrease , d ) 16 % increase , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : solution : let the original price be rs . 100 . new final price = 145 % of ( 80 % of 100 ) = rs . 145 / 100 * 80 / 100 * 100 = rs . 116 . . ' . increase = 16 % answer : d\"" + }, + { + "Answer": 11, + "Options": "a ) 13 , b ) 11 , c ) 16 , d ) 17 , e ) 18", + "Correct": "b", + "Explanation": "\"12 , 15 , 18 , 21 , 24 , 27 , 30 , 33 , 36 , 39 , 42 . 11 numbers . 10 / 3 = 3 and 43 / 3 = 14 = = > 14 - 3 = 11 . therefore 11 digits b )\"" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 25 , c ) 35 , d ) 45 , e ) 75", + "Correct": "a", + "Explanation": "\"out of 300 - 180 purchased for less than 100 $ 120 for more out of 300 - 120 responded as satisfied and 180 responded disatisfied out of 180 ( purchased less than 100 $ ) - 65 % = 117 responded as satisfied , so remaining satisfied are 120 - 117 = 3 so 3 is what percentage of 300 - 1 % so the answer should be a\"" + }, + { + "Answer": 560, + "Options": "a ) 540 , b ) 570 , c ) 619 , d ) 649 , e ) 560", + "Correct": "e", + "Explanation": "before price increase price = d after 30 % price increase price = d + ( 30 / 100 ) * d = 1.3 d = 364 ( given ) i . e . d = 364 / 1.3 = $ 280 i . e . 2 d = 2 * 280 = 560 answer : option e" + }, + { + "Answer": 724817410, + "Options": "a ) 456578972 , b ) 436567874 , c ) 653658791 , d ) 725117481 , e ) 725107482", + "Correct": "e", + "Explanation": "\"72518 x 9999 = 72518 x ( 10000 - 1 ) = 72518 x 10000 - 72518 x 1 = 725180000 - 72518 = 725107482 e\"" + }, + { + "Answer": 800, + "Options": "a ) 50 , b ) 100 , c ) 625 , d ) 800 , e ) 1250", + "Correct": "d", + "Explanation": "\"6 a * 7 b = 20 * 20 = 400 42 ab = 400 i . e . 84 ab = 800 answer : option d\"" + }, + { + "Answer": 180, + "Options": "a ) 12.5 % , b ) 40 % , c ) 180 % , d ) 125 % , e ) none", + "Correct": "c", + "Explanation": "\"solution 9 : 5 = 9 / 5 = ( 9 / 5 x 100 ) % . = 180 % . answer c\"" + }, + { + "Answer": 367, + "Options": "a ) 370 , b ) 365 , c ) 380 , d ) 367 , e ) 460", + "Correct": "d", + "Explanation": "\"easy solution : n = dq 1 + 241 2 n = 2 dq 1 + 482 - ( 1 ) 2 n = dq 2 + 115 - ( 2 ) as ( 1 ) = ( 2 ) = 2 n d * ( q 2 - 2 q 1 ) = 367 d * some integer = 367 checking all options only ( d ) syncs with it . answer d\"" + }, + { + "Answer": 5, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "e", + "Explanation": "e ) 5" + }, + { + "Answer": 50, + "Options": "a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 50", + "Correct": "e", + "Explanation": "forget conventional ways of solving math questions . in ps , ivy approach is the easiest and quickest way to find the answer . the sum of the squares of the first 4 positive integers = 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + 4 ^ 2 + 5 ^ 2 + 6 ^ 2 = 91 the sum of the prime numbers between the first square ( = 1 ) and fourth square ( = 16 ) = 2 + 3 + 5 + 7 + 11 + 13 = 41 . so the difference between 41 and 91 is 50 . so the answer is ( e ) ." + }, + { + "Answer": 5, + "Options": "a ) 3.9 , b ) 5 , c ) 5.3 , d ) 1.5 , e ) 5.2", + "Correct": "b", + "Explanation": "\"m = 15 s = x ds = 15 + x us = 15 - x 15 + x = ( 15 - x ) 2 15 + x = 30 - 2 x 3 x = 15 x = 5 answer : b\"" + }, + { + "Answer": 88, + "Options": "a ) 76 , b ) 86 , c ) 90 , d ) 88 , e ) 78", + "Correct": "d", + "Explanation": "r + w = 134 two red toys are removed from the lot and now there are twice red ones as white ones r - 2 = 2 w sub 1 st one we get 134 - w - 2 = 2 w 132 = 3 w w = 44 r = 88 actually red will be 90 now 88 answer : d" + }, + { + "Answer": 50, + "Options": "a ) 20 % , b ) 25 % , c ) 30 % , d ) 50 % , e ) 55 %", + "Correct": "d", + "Explanation": "change in ratio of royalties to sales = 2 / 12 - 4 / 48 = 1 / 12 % decrease = ( 1 / 12 ) / ( 2 / 12 ) * 100 = 50 % ( approx ) answer : d )" + }, + { + "Answer": 35, + "Options": "a ) 65 degrees , b ) 73 degrees , c ) 37 degrees , d ) 35 degrees , e ) 74 degrees", + "Correct": "d", + "Explanation": "m + tu + w + th = 4 * 48 = 192 tu + w + th + f = 4 * 46 = 184 m = 43 tu + w + th = 192 - 43 = 149 f = 184 \u2013 149 = 35 answer : d" + }, + { + "Answer": 4, + "Options": "a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10", + "Correct": "b", + "Explanation": "mother ' s age when albert ' s brother was born = 46 years father ' s age when albert ' s brother was born = 48 + 2 = 50 years required difference = 50 - 46 = 4 years answer is b" + }, + { + "Answer": 80, + "Options": "a ) 80 , b ) 81 , c ) 82 , d ) 83 , e ) 84", + "Correct": "a", + "Explanation": "\"solution : mabel handled 90 transactions anthony handled 10 % more transactions than mabel anthony = 90 + 90 \u00d7 10 % = 90 + 90 \u00d7 0.10 = 90 + 9 = 99 cal handled 2 / 3 rds of the transactions than anthony handled cal = 2 / 3 \u00d7 99 = 66 jade handled 14 more transactions than cal . jade = 66 + 14 = 80 jade handled = 80 transactions . answer : a\"" + }, + { + "Answer": 0.39999999999999997, + "Options": "a ) $ 015 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45", + "Correct": "d", + "Explanation": "\"on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.6 = 3 * x - - > x = $ 0.4 . answer : d .\"" + }, + { + "Answer": 67, + "Options": "a ) 60 % , b ) 65 % , c ) 67 % , d ) 70 % , e ) 75 %", + "Correct": "c", + "Explanation": "\"70 % of the class scored 55 % and 30 % of the class scored 95 % . the difference between 55 % and 95 % is 40 % . the average will be 55 % + 0.3 ( 40 % ) = 67 % . the answer is c .\"" + }, + { + "Answer": 262, + "Options": "a ) 251 , b ) 260 , c ) 263 , d ) 269 , e ) 262", + "Correct": "e", + "Explanation": "there are 31 digits in 10 ^ 30 when we subtract 36 from it , there will be 30 digits left . 10 ^ 30 can be written as 9999999 . . . . ( 30 times ) + 1 so , 10 ^ 30 - 36 = 9999999 . . . . ( 30 times ) + 1 - 36 = 9999999 . . . . ( 30 times ) - 35 consider the last 2 digits , 99 - 35 = 64 the last 2 digits will be 64 . and our number would be 99999 . . . . . . 99964 with 2 less 9 s after subtraction . number of 9 s left are 28 and the last two digits are 64 the sum of the digits will be ( 28 * 9 ) + 6 + 4 = 262 answer : - e" + }, + { + "Answer": 63, + "Options": "a ) 2 , b ) 63 , c ) 15 , d ) 21 , e ) 35", + "Correct": "b", + "Explanation": "solution - simply substitute 3 and 7 in equation in the place of a and b respectively . 3 # 7 = 3 * 7 - 7 + 7 ^ 2 = 21 - 7 + 49 = 63 . ans b" + }, + { + "Answer": 0.16666666666666666, + "Options": "a ) 1 / 20 , b ) 1 / 6 , c ) 1 / 5 , d ) 4 / 21 , e ) 5 / 21", + "Correct": "b", + "Explanation": "\"this is how i used to calculate which i think works pretty well : if you let the average of the 20 other numbers equal a , can you write this equation for sum of the list ( s ) n + 20 a = s the question tells us that n = 4 a plug this back into the first equation and you get that the sum is 24 a 4 a + 20 a = 24 a therefore fraction w of n to the total would be 4 a / 24 a or 1 / 6 answer b\"" + }, + { + "Answer": 18, + "Options": "a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20", + "Correct": "c", + "Explanation": "142 + 110 = 252 / 14 = 18 ( remainder ) c" + }, + { + "Answer": 16, + "Options": "a ) 20 inches , b ) 77 inches , c ) 16 inches , d ) 97 inches , e ) 66 inches", + "Correct": "c", + "Explanation": "\"explanation : total length of scale in inches = ( 6 * 12 ) + 8 = 80 inches length of each of the 5 parts = 80 / 5 = 16 inches answer : c\"" + }, + { + "Answer": 1800, + "Options": "a ) 2160 , b ) 2350 , c ) 2000 , d ) 2300 , e ) 1800", + "Correct": "e", + "Explanation": "\"explanation : total exp = 5000 + 1500 + 4500 + 2500 + 2000 + 700 = 16200 exp in % = 100 - 10 = 90 % , 16200 = 90 % saving = 10 % = 16200 x 10 / 90 = rs . 1800 answer : e\"" + }, + { + "Answer": 0.7857142857142856, + "Options": "a ) 11 / 14 , b ) 13 / 18 , c ) 4 / 7 , d ) 3 / 7 , e ) 3 / 14", + "Correct": "a", + "Explanation": "if we use variable for total votes there will be too many fractions to manipulate with , so pick some smart # : let set total # of votes is 18 . 2 / 9 of the votes on a certain resolution have been counted - - > 4 counted and 18 - 4 = 14 votes left to be counted ; 3 / 4 of those counted are in favor of the resolution - - > 3 in favor and 1 against ; ratio of those who voted against to those who voted for to be 2 to 1 there should be total of 18 * 2 / 3 = 12 people who voted against , so in the remaining 14 votes there should be 12 - 1 = 11 people who voted against . thus e = 11 / 14 of the remaining votes must be against . answer : a ." + }, + { + "Answer": 53, + "Options": "a ) 53 , b ) 45 , c ) 65 , d ) 78 , e ) 64", + "Correct": "a", + "Explanation": "\"( x + x 1 + . . . x 14 ) / 15 = 40 53 option a\"" + }, + { + "Answer": 9.9, + "Options": "a ) 2 , b ) 5.5 , c ) 6.5 , d ) 3.2 , e ) 9.9", + "Correct": "e", + "Explanation": "eq of line = y = mx + c c = 10 x = 100 y = 100 m + 10 , substitute y by 1000 as given in question . 1000 = 100 m + 10 , m = 9.9 . correct option is e" + }, + { + "Answer": 2.000000000000014, + "Options": "a ) 10 , b ) 388 , c ) 37 , d ) 29 , e ) 2", + "Correct": "e", + "Explanation": "\"explanation : let the original price be rs . 100 . decreased by 30 % = 70 then increased 40 % on rs 70 = 70 + 28 = 98 net change in price = 100 - 98 = 2 answer : e\"" + }, + { + "Answer": 1264, + "Options": "a ) 1264 , b ) 1723 , c ) 1129 , d ) 2613 , e ) 1372", + "Correct": "a", + "Explanation": "\"a b has 62.5 % or ( 5 / 8 ) of the milk in a . therefore , let the quantity of milk in container a ( initially ) be 8 k . quantity of milk in b = 8 k - 5 k = 3 k . quantity of milk in container c = 8 k - 3 k = 5 k container : a b c quantity of milk : 8 k 3 k 5 k it is given that if 158 liters was transferred from container c to container b , then both the containers would have equal quantities of milk . 5 k - 158 = 3 k + 158 = > 2 k = 316 = > k = 158 the initial quantity of milk in a = 8 k = 8 * 158 = 1264 liters .\"" + }, + { + "Answer": 0.19, + "Options": "a ) 0.12 , b ) 0.15 , c ) 0.17 , d ) 0.19 , e ) 0.25", + "Correct": "d", + "Explanation": "the probability that they do not meet is represented by the total of the areas of the two outer triangles in the figure below , which is 0.81 . so the probability of a meeting is 1 - 0.81 = 0 . 19 . correct answer d" + }, + { + "Answer": 33, + "Options": "a ) 23 % , b ) 35 % , c ) 33 % , d ) 40 % , e ) 45 %", + "Correct": "c", + "Explanation": "\"we have a 11 litre solution containing 42 % of alcohol in the water . = > quantity of alcohol in the solution = 11 \u00d7 42 / 100 now 3 litre of water is added to the solution . = > total quantity of the new solution = 11 + 3 = 14 percentage of alcohol in the new solution = 11 \u00d7 42 / 100 14 \u00d7 100 = 11 \u00d7 4210014 \u00d7 100 = 11 \u00d7 3 / 100 = 33 % c\"" + }, + { + "Answer": 11.999999999999545, + "Options": "a ) 96 , b ) 75 , c ) 48 , d ) 25 , e ) 12", + "Correct": "e", + "Explanation": "\"when positive integer x is divided by positive integer y , the remainder is 1.44 - - > x = qy + 1.44 ; x / y = 96.12 - - > x = 96 y + 0.12 y ( so q above equals to 96 ) ; 0.12 y = 1.44 - - > y = 12 . answer : e .\"" + }, + { + "Answer": 270.00000000000006, + "Options": "a ) 180 , b ) 200 , c ) 250 , d ) 270 , e ) 300", + "Correct": "d", + "Explanation": "\"let x be the total number of pages in the book , then she finished 23 \u22c5 x pages . then she has x \u2212 23 \u22c5 x = 13 \u22c5 x pages left . 23 \u22c5 x \u2212 13 \u22c5 x = 90 13 \u22c5 x = 90 x = 270 . so answer is d .\"" + }, + { + "Answer": 175, + "Options": "a ) 17.5 , b ) 130 , c ) 175 , d ) 195 , e ) 220", + "Correct": "c", + "Explanation": "\"white : yellow = x : ( x + 50 ) = 7 : 11 - - > 11 x = 7 x + 350 - - > x = 87.5 . the total # of balls originally x + x = 87.5 + 87.5 = 175 . answer : c .\"" + }, + { + "Answer": 0.8, + "Options": "a ) 4 / 5 , b ) 7 / 11 , c ) 7 / 13 , d ) 7 / 15 , e ) 8 / 11", + "Correct": "a", + "Explanation": "let the required fraction be x . then 1 - x = 9 x 20 1 - x 2 = 9 x 20 20 - 20 x 2 = 9 x 20 x 2 + 9 x - 20 = 0 20 x 2 + 25 x - 16 x - 20 = 0 5 x ( 4 x + 5 ) - 4 ( 4 x + 5 ) = 0 ( 4 x + 5 ) ( 5 x - 4 ) = 0 x = 4 / 5 a )" + }, + { + "Answer": 18, + "Options": "a ) 8 , b ) 12 , c ) 18 , d ) 20 , e ) 24", + "Correct": "c", + "Explanation": "\"if the average of 10 - pound and 20 - pound boxes is 18 , the ratio of 10 - pound boxes : 20 - pound boxes is 1 : 4 . so out of 30 boxes , 6 are 10 - pound boxes and 24 are 20 - pound boxes . if the average of 10 and 20 - pound boxes is to be 15 , the ratio of 10 - pound boxes : 20 - pound boxes should be 1 : 1 . the number of 10 pound boxes remain the same so we still have 6 of them . to get a ratio of 1 : 1 , the number of 20 - pound boxes must be 6 . we need to remove 18 of the 20 - pound boxes . the answer is c .\"" + }, + { + "Answer": 8, + "Options": "a ) 3 , b ) 4 , c ) 8 , d ) 9 , e ) none of the above", + "Correct": "c", + "Explanation": "( x + 4 ) \u00d7 60 + x \u00d7 120 + ( x \u2212 4 ) \u00d7 180 / ( x + 4 ) + x + ( x \u2212 4 ) = 100 \u21d2 360 x \u2212 480 / 3 x = 100 \u21d2 60 x = 480 \u21d2 x = 8 answer c" + }, + { + "Answer": 50, + "Options": "a ) 40 , b ) 45 , c ) 50 , d ) 90 , e ) 2500", + "Correct": "c", + "Explanation": "first recognize you only need to consider the first two digits ( because the second two are just the first two flipped ) there are 90 possibilities for the first two digits of a 4 digit number , 10 - 99 inclusive . everything starting with a 1 , 3,5 , 7,9 will be odd , which is 5 / 9 ths of the combinations . 5 / 9 * 90 = 50 answer : c" + }, + { + "Answer": 2000, + "Options": "a ) 500 , b ) 1500 , c ) 2500 , d ) 2000 , e ) 1000", + "Correct": "d", + "Explanation": "\"to solve we will set up a proportion . we know that \u201c 100 million vehicles is to 100 accidents as 2 billion vehicles is to x accidents \u201d . to express everything in terms of \u201c millions \u201d , we can use 2,000 million rather than 2 billion . creating a proportion we have : 100 / 100 = 2,000 / x cross multiplying gives us : 100 x = 2,000 * 100 x = 20 * 100 = 2000 answer : d\"" + }, + { + "Answer": 10, + "Options": "a ) 12 , b ) 8 , c ) 4 , d ) 10 , e ) 16", + "Correct": "d", + "Explanation": "- 4 hours : 1,000 - 2 hours : 2,000 now : 4,000 + 2 hours : 8,000 + 4 hours : 16,000 + 6 hours : 32,000 + 8 hours : 64,000 + 10 hours : 128,000 answer : d" + }, + { + "Answer": 9, + "Options": "a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9", + "Correct": "e", + "Explanation": "\"36 ^ 10 = 6 ^ 24 ( 6 ^ 2 ) = 6 * 6 = 36 ( 6 ^ 3 ) = 36 * 6 = . 16 ( 6 ^ 4 ) = . 16 * 6 = . . 96 ( 6 ^ 5 ) = . . 96 * 6 = . . 76 ( 6 ^ 6 ) = . . 76 * 6 = . . . 56 ( 6 ^ 7 ) = . . . . 56 * 6 = . . . . 36 if you see there is a pattern here in tens digits 3 , 1,9 , 7,5 , 3,1 and so on . . . continue the pattern up to 6 ^ 24 ( dont actually calculate full values ) and answer is e : 9\"" + }, + { + "Answer": 4691130840, + "Options": "a ) 4691130840 , b ) 4686970743 , c ) 4691100843 , d ) 4586870843 , e ) none", + "Correct": "a", + "Explanation": "\"answer 469160 x 9999 = 469160 x ( 10000 - 1 ) = 4691600000 - 469160 = 4691130840 . option : a\"" + }, + { + "Answer": 3, + "Options": "a ) 3 , b ) 3.5 , c ) 3 , d ) 4.5 , e ) 5", + "Correct": "c", + "Explanation": "222 - 198 = 24 pounds lost in 4 months 24 / 4 = 6 , so joe is losing weight at a rate of 6 pounds per month . . . . in approximately how many months will he weigh 180 pounds ? a simple approach is to just list the weights . now : 198 lbs in 1 month : 192 lbs in 2 months : 186 lbs in 3 months : 180 lbs answer : c" + }, + { + "Answer": 5250, + "Options": "a ) 100 , b ) 250 , c ) 750 , d ) 5250 , e ) 5635", + "Correct": "d", + "Explanation": "\"6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 56 * 25 * 1 / 2 = 700 feet ^ 3 of milk must be removed , which equals to 700 * 7.5 = 5250 gallons . answer : d .\"" + }, + { + "Answer": 12, + "Options": "a ) 1 , b ) 8 , c ) 12 , d ) 9 , e ) 7", + "Correct": "c", + "Explanation": "\"3 * 4 = 12 quarters answer : c\"" + }, + { + "Answer": 220030, + "Options": "a ) 122443 , b ) 154546 , c ) 165454 , d ) 186545 , e ) 220030", + "Correct": "e", + "Explanation": "\"( 555 + 445 ) * 2 * 110 + 30 = 220000 + 30 = 220030 e\"" + }, + { + "Answer": 36, + "Options": "a ) 36 , b ) 77 , c ) 88 , d ) 99 , e ) 22", + "Correct": "a", + "Explanation": "let the number of rabbits and peacocks be ' r ' and ' p ' respectively . as each animal has only one head , so r + p = 60 - - - ( 1 ) each rabbit has 4 legs and each peacock has 2 legs . total number of legs of rabbits and peacocks , 4 r + 2 p = 192 - - - ( 2 ) multiplying equation ( 1 ) by 2 and subtracting it from equation ( 2 ) , we get = > 2 r = 72 = > r = 36 . answer : a" + }, + { + "Answer": 337, + "Options": "a ) 1 , b ) 100 , c ) 229 , d ) 329 , e ) 337", + "Correct": "e", + "Explanation": "using the formula : ( a + 1 ) ^ 2 - a ^ 2 = 2 a + 1 so , answer = 168 * 2 + 1 = 336 + 1 = 337 = answer = e" + }, + { + "Answer": 4, + "Options": "a ) a ) 4 , b ) b ) 1 , c ) c ) 2 , d ) d ) 3 , e ) e ) 5", + "Correct": "a", + "Explanation": "\"explanation : ( 1054 / 23 ) gives remainder 19 19 + 4 = 23 , so we need to add 4 answer : option a\"" + }, + { + "Answer": 11, + "Options": "a ) 10 , b ) 12 , c ) 15 , d ) 11 , e ) 20", + "Correct": "d", + "Explanation": "\"ab = ( a - 1 ) ( b - 1 ) y 10 = ( y - 1 ) ( 10 - 1 ) = 90 - - > y - 1 = 10 - - > y = 11 answer : d\"" + }, + { + "Answer": 50, + "Options": "a ) 35 , b ) 45 , c ) 55 , d ) 60 , e ) 50", + "Correct": "e", + "Explanation": "a - club has 200 members ( 1 / 2 of 400 ) b - club has 250 members ( 5 / 8 of 400 ) c - club has 300 members ( 3 / 4 of 400 ) we can create an equation to solve this : 200 + 250 + 150 = n + x + 2 y where n is the number of students , x is the number of students in two clubs , and y is the number of students in three clubs . the question provides y for us ( 150 ) . 750 = 400 + x + 300 x = 50 e" + }, + { + "Answer": 50.000000000000014, + "Options": "a ) a ) 25 , b ) b ) 40 , c ) c ) 32 , d ) d ) 50 , e ) e ) 28", + "Correct": "d", + "Explanation": "let the mother ' s present age be x years then the person ' s present age = 2 x / 5 ( 2 x / 5 ) + 10 = 1 / 2 ( x + 10 ) 2 ( 2 x + 50 ) = 5 ( x + 10 ) x = 50 answer is d" + }, + { + "Answer": 1, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "b", + "Explanation": "the equation that can be formed t is 13 x + 2 = 8 y + 5 . . 13 x - 3 = 8 y . . . as we can see x can take only odd values as the rhs will always be even . . also x can take values till 13 as 13 * 14 > 180 . . now we have to substitue x as 1 , 35 , 79 , 1113 . . . once we find 7 fitting in , any other value need not be checked as every 4 th value will give us answer so next value will be 15 . . ans 1 . . b" + }, + { + "Answer": 3000, + "Options": "a ) 2000 , b ) 3000 , c ) 3500 , d ) 3800 , e ) 4000", + "Correct": "b", + "Explanation": "not fail in english = 51 % not fail in hindi = 64 % not fail in both = 30 % ( 49 + 36 - 15 ) pass in english only = 51 - 30 = 21 21 / 100 * x = 630 x = 3000 answer : b" + }, + { + "Answer": 0.5357142857142857, + "Options": "a ) 6 / 11 , b ) 8 / 15 , c ) 9 / 20 , d ) 11 / 25 , e ) 15 / 28", + "Correct": "e", + "Explanation": "\"p ( neither pen is defective ) = 6 / 8 * 5 / 7 = 15 / 28 the answer is e .\"" + }, + { + "Answer": 3645, + "Options": "a ) 8100 , b ) 3388 , c ) 7767 , d ) 2009 , e ) 3645", + "Correct": "e", + "Explanation": "\"2880 * 9 / 8 * 9 / 8 = 3645 answer : e\"" + }, + { + "Answer": 600, + "Options": "a ) $ 500 , b ) $ 600 , c ) $ 700 , d ) $ 800 , e ) $ 900", + "Correct": "b", + "Explanation": "\"if linda spent 3 / 4 of her savings on furniture , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 150 . so 1 / 4 of her savings is $ 150 . so her original savings are 4 times $ 150 = $ 600 correct answer b\"" + }, + { + "Answer": 60, + "Options": "a ) 50 , b ) 40 , c ) 60 , d ) 100 , e ) 70", + "Correct": "c", + "Explanation": "\"we have x + x % of 150 = 150 x + x / 100 * 150 = 150 5 / 2 * x = 150 x = 150 * 2 / 5 = 60 answer is c\"" + }, + { + "Answer": 6, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8", + "Correct": "c", + "Explanation": "\"2 m = 18 - m 3 m = 18 m = 6 the answer is c .\"" + }, + { + "Answer": 42, + "Options": "a ) 35 , b ) 37 , c ) 39 , d ) 41 , e ) 42", + "Correct": "e", + "Explanation": "\"explanation : let b ' s age = x years . then , as age = ( x + 12 ) years . ( x + 12 + 10 ) = 2 ( x \u2014 10 ) hence x = 42 . present age of b = 42 years answer : option e\"" + }, + { + "Answer": 0.45, + "Options": "a ) 3 / 10 , b ) 7 / 10 , c ) 9 / 10 , d ) 9 / 20 , e ) 13 / 20", + "Correct": "d", + "Explanation": "\"( 1 / 2 ) x = ( 1 / 4 ) y ( 1 / 4 ) y + ( 1 / 5 ) y = ( 9 / 20 ) y the answer is d .\"" + }, + { + "Answer": 15, + "Options": "a ) 10 , b ) 9 , c ) 15 , d ) 6 , e ) 12", + "Correct": "c", + "Explanation": "2 x + 6 x + 8 x = 120 x = 7.5 2 x = 15 answer : c" + }, + { + "Answer": 6, + "Options": "a ) 8 , b ) 10 , c ) 9 , d ) 6 , e ) 5", + "Correct": "d", + "Explanation": "\"50 x + 78 = 54 ( x + 1 ) = > 4 x = 24 = > x = 6 answer : d\"" + }, + { + "Answer": 2900, + "Options": "a ) s . 2900 , b ) s . 3570 , c ) s . 4500 , d ) s . 4550 , e ) s . 2500", + "Correct": "a", + "Explanation": "\"sum of the salaries of the person for the months of january , february , march and april = 4 * 8000 = 32000 - - - - ( 1 ) sum of the salaries of the person for the months of february , march , april and may = 4 * 8900 = 35600 - - - - ( 2 ) ( 2 ) - ( 1 ) i . e . may - jan = 3600 salary of may is rs . 6500 salary of january = rs . 2900 answer : a\"" + }, + { + "Answer": 161, + "Options": "a ) 125 , b ) 126 , c ) 130 , d ) 148 , e ) 161", + "Correct": "e", + "Explanation": "\"3 * 15 + 3 * 16 + 3 * 19 + 11 = 45 + 48 + 57 + 11 = 161 the answer is e .\"" + }, + { + "Answer": 9900, + "Options": "a ) 110 , b ) 1100 , c ) 9900 , d ) 10000 , e ) 12100", + "Correct": "c", + "Explanation": "\"we know that p , q , r can only lie on a grid 10 x 11 let ' s start by fixing p ' x - coordinate : we have 10 possible places for it then we choose x - coordinate for r : since pr | | x - axis , r ' s x - coordinate can not coincide with p ' s x - coord , so we have only 9 possible choices left . then , we fix p ' s ( and r ' s too ) y - coordinate : 11 possible choices . finally , after we fixed p and r , q ' s x - coordinate must be the same as p ' s ( because p is the right angle and pr | | x - axis ) , so the only choice is for y - coordinate , and we have 10 possible choices left . so , total number of different triangles : 10 * 9 * 11 * 10 = 9,900 answer : c\"" + }, + { + "Answer": 67, + "Options": "a ) 16.5 kg , b ) 66.5 kg , c ) 26.5 kg , d ) 56.5 kg , e ) 86.5 kg", + "Correct": "b", + "Explanation": "\"let arun ' s weight be x kg . according to arun , 65 < x < 72 . according to arun ' s brother , 60 < x < 70 . according to arun ' s mother , x < 68 . the values satisfying all the above conditions are 66 and 67 . required average = ( 66 + 67 ) / 2 = 66.5 kg answer : b\"" + }, + { + "Answer": 111110, + "Options": "a ) 900 , b ) 8000 , c ) 1100 , d ) 111110 , e ) 14", + "Correct": "d", + "Explanation": "\"10 / 9 = 1 and 1000000 / 9 = 111111 = = > 111111 - 1 = 111110 . answer : d\"" + }, + { + "Answer": 0.16666666666666666, + "Options": "a ) 1 / 20 , b ) 1 / 6 , c ) 1 / 5 , d ) 4 / 21 , e ) 5 / 21", + "Correct": "b", + "Explanation": "\"series : a 1 , a 2 . . . . a 20 , n sum of a 1 + a 2 + . . . + a 20 = 20 * x ( x = average ) so , n = 4 * x hence , a 1 + a 2 + . . + a 20 + n = 24 x so , the fraction asked = 4 x / 24 x = 1 / 6 ; answer : b .\"" + }, + { + "Answer": 58, + "Options": "a ) 42 , b ) 43 , c ) 44 , d ) 45 , e ) 58", + "Correct": "e", + "Explanation": "\"let \u2018 x \u2019 be the average score after 12 th innings \u21d2 12 x = 11 \u00d7 ( x \u2013 2 ) + 80 \u2234 x = 58 answer e\"" + }, + { + "Answer": 120, + "Options": "a ) 120 , b ) 155 , c ) 180 , d ) 336 , e ) 456", + "Correct": "a", + "Explanation": "danny can divide his herd into 5 equal parts and also to 6 equal parts = > no of cows = multiple of 5 and 6 = multiple of 30 . only option a and c qualify . now 2 nd condition : but not to 9 equal parts : so it should not be a multiple of 9 . answer : a" + }, + { + "Answer": 16, + "Options": "a ) 29 , b ) 776 , c ) 66 , d ) 16 , e ) 99", + "Correct": "d", + "Explanation": "\"( 90 / 100 ) * 40 \u2013 ( 4 / 5 ) * 25 36 - 20 = 16 answer : d\"" + }, + { + "Answer": 250, + "Options": "a ) 210 , b ) 252 , c ) 250 , d ) 300 , e ) 420", + "Correct": "c", + "Explanation": "\"however the process of dividing the volume of box by the volume of a soap seems flawed but it does work in this case due to the numbers dimensions of the box = 25 * 42 * 60 dimensions of the soap = 6 * 6 * 7 placing the 7 inch side along 42 inch side we get 6 soaps in a line and in a similar way 5 along 25 and 6 along 60 we get = 5 x 5 x 10 = 250 so the question is why this particular arrangement , in order to maximize number of soaps we need to minimize the space wasted and this is the only config where we dont waste any space so we can expect the maximum number the answer is ( c )\"" + }, + { + "Answer": 4, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 10", + "Correct": "a", + "Explanation": "\"explanation : n = h . c . f . of ( 4665 - 1305 ) , ( 6905 - 4665 ) and ( 6905 - 1305 ) = h . c . f . of 3360 , 2240 and 5600 = 1120 . sum of digits in n = ( 1 + 1 + 2 + 0 ) = 4 answer is a\"" + }, + { + "Answer": 36, + "Options": "a ) 24 , b ) 28 , c ) 32 , d ) 36 , e ) 40", + "Correct": "d", + "Explanation": "\"since the distance remains the same ( we ' re just changing the rate and time ) , any increase in rate or time is met with a decrease in the other term . decreasing the time by 1 / 4 would give us : d = ( r ) ( t ) = ( 3 t / 4 ) ( x * r ) x = 4 / 3 since ( 3 t / 4 ) ( 4 r / 3 ) = ( r ) ( t ) = d 4 r / 3 = r + 12 r / 3 = 12 r = 36 the answer is d .\"" + }, + { + "Answer": 156, + "Options": "a ) $ 92 , b ) $ 96 , c ) $ 156 , d ) $ 120 , e ) $ 240", + "Correct": "c", + "Explanation": "\"eps actual > eps expected . each gets and additional . 12 per share . thus . 52 * 300 - - > $ 156 answer is c\"" + }, + { + "Answer": 0.3333333333333333, + "Options": "a ) $ 0.15 , b ) $ 0.20 , c ) $ 0.33 , d ) $ 0.40 , e ) $ 0.45", + "Correct": "c", + "Explanation": "\"on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.5 = 3 * x - - > x = $ 0.33 . answer : c .\"" + }, + { + "Answer": 5, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5", + "Correct": "e", + "Explanation": "solving for z algebraically in this problem would not be easy . instead , we can follow the hint in the question ( \u201c which of these integers \u2026 \u201d ) and test each answer choice : a . 2 / 0 = 2 / 1 + 2 / 25 incorrect ( division by zero ) b . 2 / 1 = 2 / 2 + 2 / 26 incorrect c . 2 / 2 = 2 / 3 + 2 / 27 incorrect d . 2 / 3 = 2 / 4 + 2 / 28 incorrect e . 2 / 4 = 2 / 5 + 2 / 30 correct the correct answer is e , because it contains the only value that makes the equation work . notice how quickly this strategy worked in this case" + }, + { + "Answer": 44.700000000000045, + "Options": "a ) 30 , b ) 35 , c ) 38 , d ) 40 , e ) 45", + "Correct": "e", + "Explanation": "sum of ages of class before replacement = 45 x 14 = 630 sum of ages of class without teacher = 630 - 15 = 615 sum of ages of class after replacement = 45 x 14.66 = 660 age of teacher = 660 - 615 = 45 answer : e" + }, + { + "Answer": 41.5, + "Options": "a ) 35.2 , b ) 36.1 , c ) 36.5 , d ) 41.5 , e ) none", + "Correct": "d", + "Explanation": "\"sol . therefore correct sum = ( 41 \u00d7 50 + 48 \u2013 23 ) = 2075 . therefore correct mean = 2075 / 50 = 41.5 . answer d\"" + }, + { + "Answer": 50, + "Options": "a ) 50 , b ) 74 , c ) 78 , d ) 80 , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : number of subjects = 6 average of marks in 6 subjects = 70 therefore total marks in 6 subjects = 70 * 6 = 420 now , no . of subjects = 5 total marks in 5 subjects = 74 * 5 = 370 therefore marks in 6 th subject = 420 \u2013 370 = 50 answer a\"" + }, + { + "Answer": 2000.0000000000002, + "Options": "a ) rs . 3000 , b ) rs . 3600 , c ) rs . 2000 , d ) rs . 4000 , e ) none of these", + "Correct": "c", + "Explanation": "\"let the amount with r be rs . r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 5000 - r ) = > 3 r = 10000 - 2 r = > 5 r = 10000 = > r = 2000 . answer : c\"" + }, + { + "Answer": 460, + "Options": "a ) $ 440 , b ) $ 450 , c ) $ 460 , d ) $ 470 , e ) $ 480", + "Correct": "c", + "Explanation": "\"avg = sum of observations / number of observations avg income = ( 250 + 400 + 750 + 400 + 500 ) / 5 = 460 answer is c\"" + }, + { + "Answer": 6191, + "Options": "a ) s . 4991 , b ) s . 5991 , c ) s . 6001 , d ) s . 6191 , e ) s . 7991", + "Correct": "d", + "Explanation": "\"total fr 5 mnths = ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs 34009 . reqd . sale = rs . [ ( 6700 * 6 ) - 34009 ] = rs . ( 40200 - 34009 ) = rs . 6191 . answer : d\"" + }, + { + "Answer": 32, + "Options": "a ) 25 , b ) 30 , c ) 32 , d ) 35 , e ) 40", + "Correct": "c", + "Explanation": "\"when a number n = a ^ x * b ^ y , where a and b are prime numbers , and x , y are positive integers , the number of divisors of n = ( x + 1 ) ( y + 1 ) therefore , the answer is c . 4 * 8 = 32\"" + }, + { + "Answer": 39, + "Options": "a ) 39 , b ) 35 , c ) 42 , d ) 40.5 , e ) 41", + "Correct": "a", + "Explanation": "\"explanation : let the average after 17 innings = x total runs scored in 17 innings = 17 x average after 16 innings = ( x - 3 ) total runs scored in 16 innings = 16 ( x - 3 ) total runs scored in 16 innings + 87 = total runs scored in 17 innings = > 16 ( x - 3 ) + 87 = 17 x = > 16 x - 48 + 87 = 17 x = > x = 39 answer : option a\"" + }, + { + "Answer": 16.666666666666668, + "Options": "a ) $ 16.7 , b ) $ 24 , c ) $ 30 , d ) $ 36 , e ) $ 40", + "Correct": "a", + "Explanation": "\"a its is . let price = x ( x - 1.25 ) 8 = 5 x x = 10 / 3 hence total money = 5 * 10 / 3 = 16.7\"" + }, + { + "Answer": 14.999999999999986, + "Options": "a ) 11 , b ) 13 , c ) 15 , d ) 18 , e ) 10", + "Correct": "c", + "Explanation": "\"required difference = [ 3 \u00bd % of rs . 9000 ] \u2013 [ 3 1 / 3 % of rs . 9000 ] = [ ( 7 / 20 - ( 10 / 3 ) ] % of rs . 9000 = 1 / 6 % of rs . 9000 = rs . [ ( 1 / 6 ) 8 ( 1 / 100 ) * 9000 ] = rs . 15 . answer is c .\"" + }, + { + "Answer": 0.6363636363636364, + "Options": "a ) 1 / 9 , b ) 1 / 6 , c ) 2 / 3 , d ) 4 / 9 , e ) 7 / 11", + "Correct": "e", + "Explanation": "\"her tips were 7 / 4 of her salary . let ' s say her salary = $ 4 this mean her tips = ( 7 / 4 ) ( $ 4 ) = $ 7 so , her total income = $ 4 + $ 7 = $ 11 what fraction of her income for the week came from tips $ 7 / $ 11 = 7 / 11 = e\"" + }, + { + "Answer": 9, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", + "Correct": "c", + "Explanation": "\"d = ( d - r ) / q = ( 83 - 2 ) / 9 = 81 / 9 = 9 c )\"" + }, + { + "Answer": 53.84615384615385, + "Options": "a ) 66.66 % , b ) 66.68 % , c ) 53.84 % , d ) 86.66 % , e ) 66.65 %", + "Correct": "c", + "Explanation": "\"excess of b ' s height over a ' s = [ ( 35 / ( 100 - 35 ) ] x 100 % = 53.84 % answer : c )\"" + }, + { + "Answer": 88, + "Options": "a ) 57 , b ) 67 , c ) 77 , d ) 88 , e ) 97", + "Correct": "d", + "Explanation": "\"money collected = ( 77.44 x 100 ) paise = 7744 paise . number of members = square root of 7744 = 88 . answer : option d\"" + }, + { + "Answer": 285, + "Options": "a ) 288 , b ) 278 , c ) 267 , d ) 285 , e ) 231", + "Correct": "d", + "Explanation": "\"since the month begins with a sunday , so there will be five sundays in the month . required average = [ ( 510 * 5 ) + ( 240 * 25 ) ] / 30 = 8550 / 30 = 285 . answer : d\"" + }, + { + "Answer": 140, + "Options": "a ) 120 , b ) 140 , c ) 160 , d ) 180 , e ) 200", + "Correct": "b", + "Explanation": "\"let the total number of ounces in the drink be x . % of orange = 15 % % of watermelon = 60 % % of grape = 100 % - 75 % = 25 % 0.25 x = 35 x = 140 therefore there are a total of 140 ounces in the drink . the answer is b .\"" + }, + { + "Answer": 26, + "Options": "a ) 26 , b ) 30 , c ) 28 , d ) 36 , e ) 42", + "Correct": "a", + "Explanation": "( ( 2 a + 16 ) + ( 3 a - 8 ) ) / 2 = ( 5 a + 8 ) / 2 = 69 a = 26 the answer is a ." + }, + { + "Answer": 42, + "Options": "a ) 701 , b ) 120 , c ) 42 , d ) 868 , e ) 1", + "Correct": "c", + "Explanation": "y = 42 , because : ( 55 + 48 + 507 + 2 + 684 + y ) / 6 = 223 ( 55 + 48 + 507 + 2 + 684 + y ) / 6 * 6 = 223 * 6 ( 55 + 48 + 507 + 2 + 684 + y ) - 1296 = 1338 - 1296 y = 42 so the correct answer is c , 42 ." + }, + { + "Answer": 2.5, + "Options": "a ) 1 / 2 , b ) 1 , c ) 2 , d ) 5 / 2 , e ) 4", + "Correct": "d", + "Explanation": "\"since ( m , n ) and ( m + 2 , n + k ) are two points on the line with the equation x = 2 y + 5 they should satisfy m = 2 n + 5 and m + 5 = 2 * ( n + k ) + 5 . by 1 st equation we have m - 2 n = 5 and by 2 nd equation m - 2 n = 2 k - - - > 5 = 2 k - - - > k = 5 / 2 . the answer is , therefore , ( d ) .\"" + }, + { + "Answer": 4900, + "Options": "a ) 4500 , b ) 4600 , c ) 4300 , d ) 4900 , e ) 5000", + "Correct": "d", + "Explanation": "sum of first n even numbers = n ( n + 1 ) = 4970 sum of first n odd numbers = n ^ 2 = 70 * 70 = 4900 ( here n = 70 ) answer : d" + }, + { + "Answer": 9, + "Options": "a ) 9 % , b ) 12 % , c ) 15 % , d ) 18 % , e ) 21 %", + "Correct": "a", + "Explanation": "\"the percent of alcohol in the solution is ( 0.05 ( 40 ) + 2.5 ) / 50 = 4.5 / 50 = 9 % the answer is a .\"" + }, + { + "Answer": 15, + "Options": "a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25", + "Correct": "c", + "Explanation": "pick 100 and x = all set with exactly two items 80 = 30 + 50 + 20 - ( x ) - 10 x = 10 so the answer is 10 + 5 / 100 = 15 % answer c" + }, + { + "Answer": 29, + "Options": "a ) 27 , b ) 29 , c ) 33 , d ) 39 , e ) 41", + "Correct": "b", + "Explanation": "\"explanation : in this type of question , its obvious we need to calculate the hcf , trick is hcf of ( 1255 - 8 ) and ( 1490 - 11 ) = hcf ( 1247 , 1479 ) = 29 option b\"" + }, + { + "Answer": 0.5, + "Options": "a ) 1 / 4 , b ) 1 / 2 , c ) 1 / 3 , d ) 1 / 5 , e ) 1 / 9", + "Correct": "b", + "Explanation": "explanation : the addition of two integer results in an odd number only if any one of the integers is an odd number . the probability of an odd among the two integer is 1 / 2 . hence , the required probability is 1 / 2 . answer : b" + }, + { + "Answer": 80, + "Options": "a ) 40 % , b ) 60 % , c ) 80 % , d ) 100 % , e ) 110 %", + "Correct": "c", + "Explanation": "we can assume the total weight of the mixture = 100 conc of a in the final mixture = 22 let weight of a in the mixture be x . conc given = 20 % = . 2 therefore , weight of b = 100 - x . conc given = 30 % = . 3 now , acc to the problem , . 2 x + . 3 ( 100 - x ) = 22 solving , we get x = 80 . since we assumed the weight of the mixture = 100 , therefore presence of a in the mixture = 80 % . answer : c" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "a", + "Explanation": "the answer is a , there is exactly one . since is the largest ( and only ) even prime number , any p larger than 2 is odd . then since 32 = 2 * 2 * 2 * 2 , all of which are even , this means that p must be the only odd prime factor ." + }, + { + "Answer": 550, + "Options": "a ) a ) 400 , b ) b ) 450 , c ) c ) 500 , d ) d ) 550 , e ) e ) 600", + "Correct": "d", + "Explanation": "\"10 * 160 = 1600 3 * 100 + 5 * 150 = 1050 1600 \u2013 1050 = 550 d\"" + }, + { + "Answer": 1, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 1 , e ) 5", + "Correct": "d", + "Explanation": "- 6 * a ^ 2 = 3 ( 4 a + 2 ) a = - 1 or - 1 a = - 1 = b answer : d" + }, + { + "Answer": 14.285714285714286, + "Options": "a ) 100 / 7 , b ) 5 , c ) 20 / 3 , d ) 8 , e ) 39 / 4", + "Correct": "a", + "Explanation": "20 % alcohol solution means ; in the 100 liter solution , 20 liters of solution is alcohol and 80 liters other solvents . if we addxliters of alcohol to the solution , the solution becomes 100 + xliters and alcohol , which was 20 liters , becomes 20 + x liters . according to the statement ; 20 + x = 30 % of ( 100 + x ) or 20 + x = ( 100 + x ) 3 / 10 200 + 10 x = 300 + 3 x 7 x = 100 x = 100 / 7 ans : a" + }, + { + "Answer": 9, + "Options": "a ) 9 , b ) 8 , c ) 6 , d ) 4 , e ) 3", + "Correct": "a", + "Explanation": "\"let the number be x . then , ( x + x 2 ) / 2 = 5 x = > x 2 - 9 x = 0 = > x ( x - 9 ) = 0 = > x = 0 or x = 9 so , the number is 9 . answer : a\"" + }, + { + "Answer": 74, + "Options": "a ) 74 kg , b ) 76.5 kg , c ) 85 kg , d ) 78 , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : total weight increased = ( 2 x 4.5 ) kg = 9 kg . weight of new person = ( 65 + 9 ) kg = 74 kg . answer : a\"" + }, + { + "Answer": 35, + "Options": "a ) 18 % , b ) 20 % , c ) 21 % , d ) 23 % , e ) can not be determined", + "Correct": "d", + "Explanation": "answer : d ." + }, + { + "Answer": 41.99999999999999, + "Options": "a ) $ 42 , b ) $ 44 , c ) $ 52 , d ) $ 60 , e ) $ 68", + "Correct": "a", + "Explanation": "\"started to test answer a if he had 42 , then he spent 13 2 / 3 at hardware store now he was left with 27 1 / 3 $ he spent 7 dollars on cleaning , thus he remained with 20 1 / 3 $ he then spent 1 / 2 of 20 1 / 3 or 10.5 , hence , right option is a .\"" + }, + { + "Answer": 14, + "Options": "a ) 18 , b ) 56 , c ) 12 , d ) 17 , e ) 14", + "Correct": "e", + "Explanation": "\"initial average age of the 10 persons be p . age of the new person q . sum of the ages of the initial 10 persons = 10 p new average = ( p - 3 ) 10 ( p - 3 ) = 10 p - 44 + q = > q = 14 answer : e\"" + }, + { + "Answer": 0.2, + "Options": "a ) 0.15 , b ) 0.20 , c ) 0.25 , d ) 0.30 , e ) 0.33", + "Correct": "b", + "Explanation": "rearrange the first set : a = { 5,4 , 3,2 } b = { 4,5 , 6,7 , 8 } as you can see numbers in each column ( the numbers of the same color ) give the sum of 9 . so there are 4 such pares possible , total # of pairs is 4 * 5 = 20 . q = favorable / total = 4 / 20 = 0.2 . answer : b . or : we can select any number from set a ( 4 / 4 = 1 ) but in this case we must select its matching pair from set b ( the number of the same color ) and since there are only one matching pair of this particular number in b then the probability of this is 1 / 5 . so , overall : q = 1 * 1 / 5 . answer : b ." + }, + { + "Answer": 300, + "Options": "a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500", + "Correct": "c", + "Explanation": "\"many approaches are possible . for example : consider numbers from 0 to 999 written as follows : 1 . 000 2 . 001 3 . 002 4 . 003 . . . . . . . . . 1000 . 999 we have 1000 numbers . we used 3 digits per number , hence used total of 3 * 1000 = 3000 digits . now , why should any digit have preferences over another ? we used each of 10 digits equal # of times , thus we used each digit ( including 3 ) 3000 / 10 = 300 times . answer : c .\"" + }, + { + "Answer": 2, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "c", + "Explanation": "\"n = 20 k + 11 2 n = 2 ( 20 k + 11 ) = 4 k * 10 + 22 = 4 k * 10 + 2 * 10 + 2 = 10 j + 2 the answer is c .\"" + }, + { + "Answer": 23, + "Options": "a ) 7 , b ) 13 , c ) 16 , d ) 21 , e ) 23", + "Correct": "e", + "Explanation": "\"general rule for such kind of problems : to maximize one quantity , minimize the others ; to minimize one quantity , maximize the others . thus to maximize the number of points of one particular player minimize the number of points of all other 11 players . minimum number of points for a player is 7 , so the minimum number of points of 11 players is 7 * 11 = 77 . therefore , the maximum number of points t for 12 th player is 100 - 77 = 23 . answer : e .\"" + }, + { + "Answer": 11, + "Options": "a ) 19 , b ) 18 , c ) 16 , d ) 11 , e ) 17", + "Correct": "d", + "Explanation": "\"sum of 10 even numbers = 10 * 11 = 110 average = 110 / 10 = 11 answer : d\"" + }, + { + "Answer": 38.666666666666664, + "Options": "a ) 35.29 kg , b ) 37.25 kg , c ) 42.45 kg , d ) 38.66 kg , e ) 29.78 kg", + "Correct": "d", + "Explanation": "\"total weight of 26 + 34 students = 26 * 50 + 34 * 30 = 2320 average weight of the class is = 2320 / 60 = 38.66 kg answer is d\"" + }, + { + "Answer": 50, + "Options": "a ) 20 % , b ) 30 % , c ) 40 % , d ) 50 % , e ) 60 %", + "Correct": "d", + "Explanation": "\"the is always the difference between our starting and ending points . in this case , it \u00e2 \u20ac \u2122 s 100 \u00e2 \u20ac \u201c 50 = 40 . the \u00e2 \u20ac \u0153 original \u00e2 \u20ac \u009d is our starting point ; in this case , it \u00e2 \u20ac \u2122 s 100 . ( 50 / 100 ) * 100 = ( 0.5 ) * 100 = 50 % . d\"" + }, + { + "Answer": 600, + "Options": "a ) 400 , b ) 500 , c ) 375 , d ) 450 , e ) 600", + "Correct": "e", + "Explanation": "a + b + c = 1800 a = 2 / 5 ( b + c ) ; b = 1 / 5 ( a + c ) a / ( b + c ) = 2 / 5 a = 1 / 6 * 3600 = > 600 answer : e" + }, + { + "Answer": 4, + "Options": "a ) 0 , b ) 1 , c ) 3 , d ) 4 , e ) 6", + "Correct": "d", + "Explanation": "\"i tried plugging in numbers x = 9 q + 5 x = 14 8 x = 112 8 x / 9 = 9 * 12 + 4 remainder is 4 . answer is d .\"" + }, + { + "Answer": 0.3333333333333333, + "Options": "a ) 1 / 3 , b ) 2 / 5 , c ) 1 / 4 , d ) 2 / 3 , e ) 4 / 5", + "Correct": "a", + "Explanation": "sum of the g . p . = ( first term - r * last term ) / 1 \u2013 r 40 / 3 = 9 \u2013 1 / 3 ( last term ) / 2 / 3 last term = ( - 40 / 3 * 2 / 3 + 9 ) * 3 = - 80 / 3 + 27 = 1 / 3 answer : a" + }, + { + "Answer": 105, + "Options": "a ) 105 , b ) 110 , c ) 120 , d ) 130 , e ) 140", + "Correct": "a", + "Explanation": "\"let the number of boys who passed = x . then , 39 x x + 15 x ( 120 - x ) = 120 x 36 24 x = 4320 - 1800 = > x = 2520 / 24 x = 105 . hence , the number of boys passed = 105 . answer : a\"" + }, + { + "Answer": 74, + "Options": "a ) 74 , b ) 69 , c ) 75 , d ) 85 , e ) 90", + "Correct": "a", + "Explanation": "\"explanation : average = ( 76 + 65 + 82 + 62 + 85 ) / 5 = 370 / 5 = 74 hence average = 74 answer : a\"" + }, + { + "Answer": 4, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "c", + "Explanation": "\"lets say 5 and 10 ounce packages be x and y respectively . given that , 5 x + 10 y = 70 and x = y + 2 . what is the value of y . substituting the x in first equation , 5 y + 10 + 10 y = 70 - > y = 60 / 15 . = 4 c\"" + }, + { + "Answer": 35, + "Options": "a ) 33 kg , b ) 31 kg , c ) 32 kg , d ) 36 kg , e ) 35 kg", + "Correct": "e", + "Explanation": "\"let a , b , c represent their respective weights . then , we have : a + b + c = ( 45 x 3 ) = 135 . . . . ( i ) a + b = ( 42 x 2 ) = 84 . . . . ( ii ) b + c = ( 43 x 2 ) = 86 . . . . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 170 . . . . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 35 b ' s weight = 35 kg . e\"" + }, + { + "Answer": 51, + "Options": "a ) 51 , b ) 45 , c ) 65 , d ) 78 , e ) 64", + "Correct": "a", + "Explanation": "\"( x + x 1 + . . . x 14 ) / 15 = 40 51 option a\"" + }, + { + "Answer": 14, + "Options": "a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16", + "Correct": "c", + "Explanation": "\"when x is divided by 9 , the remainder is 2 : so , the possible values of x are : 2 , 11 , 21 , 29 , etc . when x is divided by 7 , the remainder is 4 : so , the possible values of x are : 4 , 11,18 , . . . stop . since both lists include 11 , the smallest possible value of x is 11 . when y is divided by 11 , the remainder is 3 : so , the possible values of y are : 3 , 14 , 25 , etc . when y is divided by 13 , the remainder is 12 : so , the possible values of y are : 12 , 25 , . . . stop . since both lists include 25 , the smallest possible value of y is 25 since the smallest possible values of x and y are 11 and 25 respectively , the smallest possible value of y - x is 14 . so , c is the correct answer to the original question .\"" + }, + { + "Answer": 3.315, + "Options": "a ) $ 1.40 , b ) $ 2.40 , c ) $ 3.315 , d ) $ 4.40 , e ) $ 5.40", + "Correct": "c", + "Explanation": "\"manager wages per hour = $ 8.50 dishwasher wages per hour = half of manager ' s wages . = 1 / 2 ( $ 8.50 ) = = > $ 4.25 chef wages per hour = 22 % greater than dishwasher wages - - > 22 % of $ 4.25 = ( 22 * ( $ 4.25 ) ) / 100 - - > ( $ 93.5 ) / 100 - - > $ 0.935 therefore , chef wages per hour = $ 4.25 + $ 0.935 = = > $ 5.185 difference of wages between manager and chef = $ 8.50 - $ 5.185 = = > $ 3.315 answer : c\"" + }, + { + "Answer": 80, + "Options": "a ) 108 , b ) 80 , c ) 128 , d ) 135 , e ) 143", + "Correct": "b", + "Explanation": "\"let the 2 positive numbers x and y x + y = 18 - - 1 x ^ 2 - y ^ 2 = 36 = > ( x + y ) ( x - y ) = 36 - - 2 using equation 1 in 2 , we get = > x - y = 2 - - 3 solving equation 1 and 3 , we get x = 10 y = 8 product = 10 * 8 = 80 answer b\"" + }, + { + "Answer": 60, + "Options": "a ) 60 , b ) 120 , c ) 130 , d ) 140 , e ) 150", + "Correct": "a", + "Explanation": "solution : let xx be the number he chose , then 4 \u22c5 x \u2212 138 = 102 4 x = 240 x = 60 answer a" + }, + { + "Answer": 480.7, + "Options": "a ) a ) 125 , b ) b ) 175 , c ) c ) 481 , d ) d ) 375 , e ) e ) 524", + "Correct": "c", + "Explanation": "\"explanation : ? = ( 228 x 1265 / 100 ) \u00f7 6 = 288420 / 600 = 481 answer : option c\"" + }, + { + "Answer": 168.6, + "Options": "a ) 138.9 cms , b ) 149.2 cms , c ) 168.6 cms , d ) 159.2 cms , e ) 142.5 cms", + "Correct": "c", + "Explanation": "\"explanation : average height of the whole class = ( 40 \u00d7 169 + 10 \u00d7 167 / 50 ) = 168.6 cms answer c\"" + }, + { + "Answer": 0.2857142857142857, + "Options": "a ) 1 / 7 , b ) 7 / 12 , c ) 1 / 2 , d ) 2 / 7 , e ) 2 / 3", + "Correct": "d", + "Explanation": "\"same amount of water made bigger jar 1 / 7 full , then the same amount of water ( stored for a while in smaller jar ) were added to bigger jar , so bigger jar is 1 / 7 + 1 / 7 = 2 / 7 full . answer : d .\"" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "c", + "Explanation": "\"2 ( 3 x - 5 ) - 10 = 3 ( x - 2 ) - 5 3 x = 9 x = 3 the answer is c .\"" + }, + { + "Answer": 2, + "Options": "a ) 1 / 4 , b ) 56 / 27 , c ) 2 , d ) 3 , e ) 4", + "Correct": "c", + "Explanation": "soln : 28 = 1 * 28 2 * 14 4 * 7 sum of reciprocals = 1 + 1 / 28 + 1 / 2 + 1 / 14 + 1 / 4 + 1 / 7 = 56 / 28 = 2 answer : c" + }, + { + "Answer": 89.99999999999997, + "Options": "a ) 37.5 , b ) 75 , c ) 100 , d ) 150 , e ) 90", + "Correct": "e", + "Explanation": "nope , 150 . i can only get it by following pr ' s backsolving explanation . i hate that . original mixture has 20 % salt and 80 % water . total = x out of which salt = 0.2 x and water = 0.8 x now , 1 / 4 water evaporates and all salt remains . so what remains is 0.2 x salt and 0.6 x water . now 12 gallons salt is added and 6 gallons of water is added . so salt now becomes - > ( 0.2 x + 12 ) and water - - > ( 0.6 x + 6 ) amount of salt is 33.33 % of total . so amount of water is 66.66 % . so salt is half of the volume of water . so ( 0.2 x + 12 ) = ( 0.6 x + 6 ) / 2 = > 0.4 x + 24 = 0.6 x + 6 - > 0.2 x = 18 solving , x = 90 answer : e" + }, + { + "Answer": 625, + "Options": "a ) 325 , b ) 425 , c ) 625 , d ) 700 , e ) none of these", + "Correct": "c", + "Explanation": "as per question stem 2 / 5 m ( portion of men employees who are managers ) + 250 ( portion of female employees who are managers ) = 2 / 5 t ( portion of total number of employees who are managers ) , thus we get that 2 / 5 m + 250 = 2 / 5 t , or 2 / 5 ( t - m ) = 250 , from here we get that t - m = 625 , that would be total number of female employees and the answer ( c )" + }, + { + "Answer": 98, + "Options": "a ) 66 , b ) 74 , c ) 78 , d ) 98 , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : number of subjects = 6 average of marks in 6 subjects = 78 therefore total marks in 6 subjects = 78 * 6 = 468 now , no . of subjects = 5 total marks in 5 subjects = 74 * 5 = 370 therefore marks in 6 th subject = 468 \u2013 370 = 98 answer d\"" + }, + { + "Answer": 11, + "Options": "a ) 12 , b ) 11 , c ) 13 , d ) 15 , e ) 16", + "Correct": "b", + "Explanation": "\"let p = 3 , q = 5 then 2 * 3 + 5 = 11 so 2 p + q = 11 . answer : b\"" + }, + { + "Answer": 8, + "Options": "a ) 4 , b ) 8 , c ) 12 , d ) 16 , e ) 18", + "Correct": "b", + "Explanation": "sol . since the number is greater than the number obtained on reversing the digits , so the ten ' s is greater than the unit ' s digit . let the ten ' s and units digit be 2 x and x respectively . then , ( 10 \u00d7 2 x + x ) - ( 10 x + 2 x ) = 36 \u21d4 9 x = 36 \u21d4 x = 4 . \u2234 required difference = ( 2 x + x ) - ( 2 x - x ) = 2 x = 8 . answer b" + }, + { + "Answer": 41, + "Options": "a ) 23 , b ) 78 , c ) 27 , d ) 61 , e ) 41", + "Correct": "e", + "Explanation": "\"explanation : 40 + 5 * 12 / ( 180 / 3 ) = 40 + 5 * 12 / ( 60 ) = 40 + ( 5 * 12 ) / 60 = 40 + 1 = 41 . answer : e\"" + }, + { + "Answer": 154.75280898876406, + "Options": "a ) 743 , b ) 155 , c ) 852 , d ) 741 , e ) 785", + "Correct": "b", + "Explanation": "\"divisor * quotient + remainder = dividend divisor = ( dividend ) - ( remainder ) / quotient ( 13787 - 14 ) / 89 = 155 answer ( b )\"" + }, + { + "Answer": 60, + "Options": "a ) 20 liters , b ) 30 liters , c ) 50 liters , d ) 60 liters , e ) none of these", + "Correct": "d", + "Explanation": "explanation : quantity of milk = 60 * ( 2 / 3 ) = 40 liters quantity of water = 60 - 40 = 20 liters answer : d" + }, + { + "Answer": 20, + "Options": "a ) 17 inches , b ) 20 inches , c ) 15 inches , d ) 18 inches , e ) 19 inches", + "Correct": "b", + "Explanation": "\"explanation : total length of scale in inches = ( 6 * 12 ) + 8 = 80 inches length of each of the 4 parts = 80 / 4 = 20 inches answer : b\"" + }, + { + "Answer": 49, + "Options": "a ) 2 , b ) 4 , c ) 8 , d ) 49 , e ) 32", + "Correct": "d", + "Explanation": "lets assign variables to all the areas in venn diagram of three . three different units are dog , cat , snake = total = 79 only dog = d = 15 only cat = c = 10 only snake = s exactly dog and cat = 5 exactly dog and snake = x exactly cat and snake = y all three = 3 so 79 = 15 + 10 + 5 + 3 + x + y + s we need to know total snakes = x + y + s + 3 = 49 answer : d" + }, + { + "Answer": 35, + "Options": "a ) 30 , 10 , b ) 25 , 5 , c ) 29 , 9 , d ) 35 , 15 , e ) 20,10", + "Correct": "d", + "Explanation": "\"let their ages be x and ( x + 20 ) years . then , 5 ( x - 10 ) = ( x + 20 - 10 ) = > 4 x = 60 = > x = 15 their present ages are 35 years and 15 year . answer : d\"" + }, + { + "Answer": 40000, + "Options": "a ) $ 35,000 , b ) $ 40,000 , c ) $ 55,000 , d ) $ 65,000 , e ) $ 75,000", + "Correct": "b", + "Explanation": "another method is to get ratios say 30000 = a and we know the # of people are in 1 : 5 ratio average = ( 3 a * 1 + a * 5 ) / 6 = 8 a / 6 = 40000 answer is b . $ 40,000" + }, + { + "Answer": 3.8666666666666667, + "Options": "a ) 3.9 , b ) 4.6 , c ) 5.2 , d ) 6 , e ) 8.1", + "Correct": "a", + "Explanation": "\"eq of line = y = mx + c c = 20 x = 150 y = 150 m + 20 , substitute y by 600 as given in question . 600 = 150 m + 20 , m = 3.9 correct option is a\"" + }, + { + "Answer": 800, + "Options": "a ) 400 bc , b ) 400 b / c , c ) 800 bc , d ) 800 b / c , e ) 800 / bc", + "Correct": "c", + "Explanation": "\"2 cases * c cartons / case * b boxes / carton * 400 clips / box = 800 bc paper clips the answer is c .\"" + }, + { + "Answer": 6, + "Options": "a ) a ) 4 , b ) b ) 1 , c ) c ) 6 , d ) d ) 3 , e ) e ) 5", + "Correct": "c", + "Explanation": "\"explanation : ( 1052 / 23 ) gives remainder 17 17 + 6 = 23 , so we need to add 6 answer : option c\"" + }, + { + "Answer": 18.6, + "Options": "a ) 15.6 , b ) 16.0 , c ) 17.5 , d ) 18.6 , e ) 19.1", + "Correct": "d", + "Explanation": "\"a certain taxi company charges $ 3.00 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ? a . 15.60 b . 16.00 c . 17.50 d . 18.70 e . 19.10 1 / 5 miles = 0.2 miles . the cost of 8 miles long ride would be $ 3.00 for the first 0.2 miles plus ( 8 - 0.2 ) / 0.2 * 0.4 = $ 3.0 + $ 15.6 = $ 18.6 . answer : d .\"" + }, + { + "Answer": 0.3333333333333333, + "Options": "a ) 1 / 9 , b ) 1 / 6 , c ) 1 / 3 , d ) 4 / 9 , e ) 5 / 9", + "Correct": "c", + "Explanation": "\"her tips were 2 / 4 of her salary . let ' s say her salary = $ 4 this mean her tips = ( 2 / 4 ) ( $ 4 ) = $ 2 so , her total income = $ 4 + $ 2 = $ 6 what fraction of her income for the week came from tips $ 2 / $ 6 = 1 / 3 = c\"" + }, + { + "Answer": 165, + "Options": "a ) 75 , b ) 100 , c ) 125 , d ) 175 , e ) 165", + "Correct": "e", + "Explanation": "\"female = x male = 990 - x x / 2 + 990 - x / 4 = 1 / 3 * ( 990 ) = 330 x = 330 x / 2 = 165 is supposed to be the answer m is missing something correct option e\"" + }, + { + "Answer": 20, + "Options": "a ) 10 , b ) 50 , c ) 40 , d ) 20 , e ) 60", + "Correct": "d", + "Explanation": "d 20 amith \u2019 s age = a and daughter \u2019 s age = b then , a \u2013 5 = 3 ( b \u2013 5 ) = > a \u2013 3 b + 10 = 0 \u2026 \u2026 ( 1 ) and , a + 10 = 2 ( a + 10 ) = > a \u2013 2 b \u2013 10 = 0 \u2026 \u2026 ( 2 ) solving the 2 eqns , we will get a = 50 , b = 20 . therefore , amith \u2019 s age is 50 and his daughter \u2019 s age is 20" + }, + { + "Answer": 0.5555555555555556, + "Options": "a ) 15 / 2 , b ) 9 / 4 , c ) 5 / 9 , d ) 7 / 5 , e ) 9 / 7", + "Correct": "c", + "Explanation": "blue tin or red tin : 2 / 3 ( n ) red tin : ( 1 / 3 ) n blue tin : ( 1 / 4 ) n what the last statment meant , is it wants this fraction : ( # of cookies in green tin ) / ( # of cookies in red and green tin ) # of cookies in green tin = 2 n / 3 - n / 4 = 8 n - 3 n / 12 = 5 n / 12 # of cookies in red and green tin = n / 3 + 5 n / 12 = 9 n / 12 fraction q = 5 n / 12 * 12 / 9 n = 5 / 9 ( c )" + }, + { + "Answer": 23, + "Options": "a ) 19 , b ) 21 , c ) 23 , d ) 25 , e ) 27", + "Correct": "c", + "Explanation": "\"let the average age of the whole team be x years . 11 x - ( 26 + 29 ) = 9 ( x - 1 ) = > 11 x - 9 x = 46 = > 2 x = 46 = > x = 23 . so , average age of the team is 23 years . c\"" + }, + { + "Answer": 600, + "Options": "a ) 450 , b ) 300 , c ) 500 , d ) 600 , e ) 175", + "Correct": "d", + "Explanation": "\"let the maximum marks be x then , 33 % of x = 125 + 73 33 x / 100 = 198 x = 600 answer is d\"" + }, + { + "Answer": 0.07142857142857144, + "Options": "a ) 0 , b ) 1 / 14 , c ) 2 / 15 , d ) 1 / 10 , e ) 2 / 10", + "Correct": "b", + "Explanation": "suppose the water in each jug is l liters cx x ( 1 / 7 ) = l cx = 7 l liters cx is capacity of x cy x ( 2 / 3 ) = l cy = 3 l / 2 liters cy is capacity of y now , y is 3 l / 2 - l empty = l / 2 empty so , we can put only l / 2 water in jug y from jug x jug x ' s remaining water = l - l / 2 = l / 2 fraction of x which contains water = water / cx = ( l / 2 ) / 7 l = 1 / 14 answer will be b" + }, + { + "Answer": 240, + "Options": "a ) 120 , b ) 240 , c ) 360 , d ) 540 , e ) 720", + "Correct": "b", + "Explanation": "jason can select his seat in 2 ways ( two aisles ) his 1 st of 4 friends have 5 seats to select = > his 2 nd of remaining 3 friends will have 4 seat to chose from . . . and so on total ways e = > 2 * 5 * 4 * 3 * 2 * 1 = 240 . b" + }, + { + "Answer": 25, + "Options": "a ) 10 , b ) 25 , c ) 35 , d ) 40 , e ) 55", + "Correct": "b", + "Explanation": "\"0.037 * 10 ^ 5 can be written as 3700 148000 * 10 ^ ( - 3 ) can be written as 148 required = 3700 / 148 = 25 answer : b\"" + }, + { + "Answer": 55, + "Options": "a ) 190 , b ) 195 , c ) 200 , d ) 205 , e ) 55", + "Correct": "e", + "Explanation": "\"this question can be solved with the average formula and ' bunching . ' we ' re asked for the average of all of the multiples of 10 from 10 to 100 , inclusive . to start , we can figure out the total number of terms rather easily : 1 ( 10 ) = 10 2 ( 10 ) = 20 . . . 10 ( 10 ) = 100 so we know that there are 10 total numbers . we can now figure out the sum of those numbers with ' bunching ' : 10 + 100 = 110 20 + 90 = 110 30 + 80 = 110 etc . since there are 10 total terms , this pattern will create 5 ' pairs ' of 110 . thus , since the average = ( sum of terms ) / ( number of terms ) , we have . . . ( 5 ) ( 110 ) / ( 10 ) = 55 answer : e\"" + }, + { + "Answer": 123500.125, + "Options": "a ) 123,750 , b ) 164,850 , c ) 164,749 , d ) 149,700 , e ) 156,720", + "Correct": "a", + "Explanation": "\"find the number , upon sum of 3 digits of a number gives a reminder 2 when it is divided by 4 seeing the options after dividing and finding the reminder of 2 my answer was a\"" + }, + { + "Answer": 20000, + "Options": "a ) $ 20000 , b ) $ 15000 , c ) $ 12000 , d ) $ 10000 , e ) $ 9000", + "Correct": "a", + "Explanation": "\"since investment doubles in 70 / r years then for r = 8 it ' ll double in 70 / 8 = ~ 9 years ( we are not asked about the exact amount so such an approximation will do ) . thus in 18 years investment will double twice and become ( $ 5,000 * 2 ) * 2 = $ 20,000 ( after 9 years investment will become $ 5,000 * 2 = $ 10,000 and in another 9 years it ' ll become $ 10,000 * 2 = $ 20,000 ) . answer : a .\"" + }, + { + "Answer": 40000, + "Options": "a ) $ 35,000 , b ) $ 40,000 , c ) $ 55,000 , d ) $ 65,000 , e ) $ 75,000", + "Correct": "b", + "Explanation": "another method is to get ratios say 30000 = a and we know the # of people are in 1 : 5 ratio average = ( 3 a * 1 + a * 5 ) / 6 = 8 a / 6 = 40000 answer is b . $ 40,000" + }, + { + "Answer": 12, + "Options": "a ) 6 , b ) 12 , c ) 24 , d ) 36 , e ) 48", + "Correct": "b", + "Explanation": "\"q : if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer t that must divide n is : a 6 , b 12 , c 24 , d 36 , e 48 n ^ 2 is divisible by 72 , but it must also be greater than 72 . if n is an integer , then n ^ 2 must be a perfect square . the factorization of 72 is ( 8 ) ( 9 ) , so if it is multiplied by 2 , it will be ( 2 ) ( 8 ) ( 9 ) = ( 16 ) ( 9 ) = 144 , a perfect square . so n ^ 2 must be at least 144 or a multiple of 144 , which means that n must be 12 or a multiple of 12 . b\"" + }, + { + "Answer": 11, + "Options": "a ) 11 , b ) 14 , c ) 15 , d ) 13 , e ) 18", + "Correct": "a", + "Explanation": "\"age of the 15 th student = [ 15 * 15 - ( 14 * 5 + 16 * 9 ) ] = ( 225 - 214 ) = 11 years . answer a\"" + }, + { + "Answer": 360, + "Options": "a ) a . 150 , b ) b . 300 , c ) c . 600 , d ) d . 1,200 , e ) e . 360", + "Correct": "e", + "Explanation": "\"volume per box : 15 x 12 x 10 = 1,800 total volume : 1 , 080,000 number of boxes : total volume / volume per box = 1 , 080,000 / 1,800 = 600 price per month : number of boxes * price per box = 600 * 0.6 = 360 answer : e\"" + }, + { + "Answer": 70, + "Options": "a ) 40 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 80 %", + "Correct": "d", + "Explanation": "\"can be reduced to 4 y / 10 + 3 y / 10 = 7 y / 10 = 70 % answer d\"" + }, + { + "Answer": 164.98876404494382, + "Options": "a ) 743 , b ) 154 , c ) 852 , d ) 741 , e ) 165", + "Correct": "e", + "Explanation": "\"divisor * quotient + remainder = dividend divisor = ( dividend ) - ( remainder ) / quotient ( 14698 - 14 ) / 89 = 165 answer ( e )\"" + }, + { + "Answer": 49.99999999999996, + "Options": "a ) 20 % , b ) 25 % , c ) 50 % , d ) 75 % , e ) 60 %", + "Correct": "c", + "Explanation": "\"let original income = $ 100 expenditure = $ 75 savings = $ 25 new income = $ 120 new expenditure = $ 110 / 100 * 75 = $ 165 / 2 new savings = 120 - 165 / 2 = $ 75 / 2 increase in savings = 75 / 2 - 25 = $ 25 / 2 increase % = 25 / 2 * 1 / 25 * 100 = 50 % answer is c\"" + }, + { + "Answer": 33, + "Options": "a ) 27 , b ) 30 , c ) 33 , d ) 36 , e ) 39", + "Correct": "c", + "Explanation": "\"33 / 4 \u00f7 4 = 33 / 16 pounds in each container 33 / 16 pounds * 16 ounces / pound = 33 ounces in each container the answer is c .\"" + }, + { + "Answer": 7, + "Options": "a ) 5 , b ) 7 , c ) 8 , d ) 10 , e ) 11", + "Correct": "b", + "Explanation": "q = 7 is the correct answer . good solution buneul . b" + }, + { + "Answer": 14, + "Options": "a ) 9 , b ) 11 , c ) 13 , d ) 15 , e ) 14", + "Correct": "e", + "Explanation": "i am guessing the question is : ( 2 to the power x ) - ( 2 to the power ( x - 2 ) ) = 3 ( 2 to the power 12 ) 2 ^ x - 2 ^ ( x - 2 ) = 3 . 2 ^ 12 hence x = 14 . answer is e" + }, + { + "Answer": 0.2857142857142857, + "Options": "a ) 1 / 49 , b ) 2 / 7 , c ) 3 / 7 , d ) 16 / 49 , e ) 40 / 49", + "Correct": "b", + "Explanation": "\"the probability of drawing a pink gumball both times is the same . the probability that she drew two blue gumballs = 25 / 49 = ( 5 / 7 ) * ( 5 / 7 ) therefore probability that the next one she draws is pink = 2 / 7 option ( b )\"" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "c", + "Explanation": "\"x = ( y / 6 ) - ( 2 / 5 ) , and so y = 6 x + 12 / 5 . the slope is 6 . ( n + 18 - n ) / ( m + p - m ) = 6 p = 3 the answer is c .\"" + }, + { + "Answer": 14, + "Options": "a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18", + "Correct": "c", + "Explanation": "w = 30 ! 8 w = 30 x 29 x 28 x 27 x 26 x 25 x 24 x 24 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 09 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 out of these 30 , 27 , 24 , 21 , 18 , 15 , 12 , 09 , 06 , 3 are factors of 3 3 x 10 , 3 x 3 x 3 , 3 x 8 , 3 x 3 x 2 , 3 x 5 , 3 x 4 , 3 x 3 x 3 , 3 x 2 , 3 so we have a total of 14 three ' s . . . therefore the maximum value of k can be 14 ( c )" + }, + { + "Answer": 2, + "Options": "a ) 16 . , b ) 8 . , c ) 7 . , d ) 2 . , e ) - 2 .", + "Correct": "d", + "Explanation": "\"given a + b = 4 b + c = 5 c + d = 3 ( a + b ) - ( b + c ) + ( c + d ) = ( a + d ) = > 4 - 5 + 3 = 2 . option d . . .\"" + }, + { + "Answer": 50, + "Options": "a ) 36 , b ) 40 , c ) 44 , d ) 50 , e ) 52", + "Correct": "d", + "Explanation": "\"for 40 hrs = 40 * 16 = 640 excess = 920 - 640 = 280 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 280 / 28 = 70 / 7 = 10 total hrs = 40 + 10 = 50 answer d 50\"" + }, + { + "Answer": 42, + "Options": "a ) 40 , b ) 41 , c ) 42 , d ) 45 , e ) 43", + "Correct": "c", + "Explanation": "\"total age of all students = 20 \u00e3 \u2014 21 total age of all students + age of the teacher = 21 \u00e3 \u2014 22 age of the teacher = 21 \u00e3 \u2014 22 \u00e2 \u02c6 \u2019 21 \u00e3 \u2014 20 = 21 ( 22 \u00e2 \u02c6 \u2019 20 ) = 21 \u00e3 \u2014 2 = 42 answer is c .\"" + }, + { + "Answer": 81.1, + "Options": "a ) 9 , b ) 20 , c ) 55 , d ) 70 , e ) 80", + "Correct": "e", + "Explanation": "\"here ' s an approach that ' s based on number properties and a bit ofbrute forcemath : we ' re told that k and n are both integers . since k / n = 81.2 , we can say that k = 81.2 ( n ) n has tomultiply outthe . 2 so that k becomes an integer . with the answers that we have to work with , n has to be a multiple of 5 . eliminate a and e . with the remaining answers , we can test the answers and find the one that fits the rest of the info ( k / n = 81.2 and k / n has a remainder of 11 ) answer b : if n = 20 , then k = 1624 ; 1624 / 20 has a remainder of 4 not a match answer c : if n = 55 , then k = 4466 ; 4466 / 55 has a remainder of 11 match . final answer : e\"" + }, + { + "Answer": 8, + "Options": "a ) 1 , b ) 2 , c ) 4 , d ) 8 , e ) 16", + "Correct": "d", + "Explanation": "distribute the exponent . a ^ 5 * b ^ 5 = 128 y find the prime factorization of 96 . this is 2 ^ 5 * 2 ^ 2 . we need 2 ^ 3 ( or some other power of 2 that will give us a multiple of 2 ^ 5 as our second term ) . 2 ^ 3 = 8 the answer is d ." + }, + { + "Answer": 11, + "Options": "a ) 3 , b ) 7 , c ) 11 , d ) 21 , e ) 25", + "Correct": "c", + "Explanation": "\"jacob = x years , mike = x + 12 years 5 years from now , 2 ( x + 5 ) = x + 17 2 x + 10 = x + 17 x = 7 x + 4 = 11 years answer c\"" + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10", + "Correct": "a", + "Explanation": "old mix has 20 % oil . you add 2 kgs of 100 % oil . you get new mix with 30 % oil ( 70 % material b ) . w 1 / w 2 = ( 100 - 30 ) / ( 30 - 20 ) = 70 / 10 = 7 / 1 for every 7 parts of mix a , you have added 1 part of oil . since you have added 2 kgs oil , mix a must be 7 * 2 = 14 kgs . you already had 8 kgs of mix a , so extra mix a added must be 14 - 8 = 6 kgs . answer ( a )" + }, + { + "Answer": 680, + "Options": "a ) 600 , b ) 640 , c ) 680 , d ) 720 , e ) 760", + "Correct": "c", + "Explanation": "\"the number of seats in the theater is 15 + ( 15 + 2 ) + . . . + ( 15 + 38 ) = 20 ( 15 ) + 2 ( 1 + 2 + . . . + 19 ) = 20 ( 15 ) + 2 ( 19 ) ( 20 ) / 2 = 20 ( 15 + 19 ) = 20 ( 34 ) = 680 the answer is c .\"" + }, + { + "Answer": 15, + "Options": "a ) 14 , b ) 20 , c ) 22 , d ) 24 , e ) 15", + "Correct": "e", + "Explanation": "for a total of 51000 chips ( adding s 1 , s 2 , s 3 , s 4 ) total number of defective chips is 17 ( ( adding defective chips of s 1 , s 2 , s 3 , s 4 ) so ratio is 12 / 48000 or 1 every 4000 chips . keeping this ratio constant for 60000 chips number of defective chips will be ( 1 / 4000 ) * 60000 = 15 e" + }, + { + "Answer": 111.11111111111111, + "Options": "a ) 112.2 m , b ) 216.3 m , c ) 111.12 m , d ) 213.27 m , e ) 222.40 m", + "Correct": "c", + "Explanation": "c 111.12 m x runs 1000 m while y runs 900 m and z runs 800 m . the number of meters that z runs when y runs 1000 m , = ( 1000 * 800 ) / 900 = 8000 / 9 = 888.88 m . y can give z = 1000 - 888.88 = 111.12 m ." + }, + { + "Answer": 5.000000000000043, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "e", + "Explanation": "\"( 1053 / 23 ) gives a remainder 18 so we need to add 5 . the answer is e .\"" + }, + { + "Answer": 9000, + "Options": "a ) rs . 7000 , b ) rs . 8000 , c ) rs . 8500 , d ) rs . 9000 , e ) none", + "Correct": "d", + "Explanation": "\"answer average salary = 8000 + 5000 + 16000 + 7000 + 9000 / 5 = rs . 9000 correct option : d\"" + }, + { + "Answer": 181.78817648189806, + "Options": "a ) 183.62 , b ) 106.07 , c ) 106.04 , d ) 106.03 , e ) 186.01", + "Correct": "a", + "Explanation": "\"a = 3000 ( 51 / 50 ) 3 = 3183.62 3000 - - - - - - - - - - - 183.62 answer : a\"" + }, + { + "Answer": 7, + "Options": "a ) 7 , b ) 6 , c ) 5 , d ) 11 , e ) 13", + "Correct": "a", + "Explanation": "let the minimum whole number be 20 + 6 = 26 where 6 is the remainder . 26 when divided by 19 then leaves 7 . correct answer a ." + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 10 , c ) 12 , d ) 14 , e ) 15", + "Correct": "a", + "Explanation": "\"explanation : = > 3 ( 2 x + 9 ) = 57 = > 2 x + 9 = 19 = > x = 5 answer : option a\"" + }, + { + "Answer": 15.999999999999998, + "Options": "a ) 10 hrs , b ) 12 hrs , c ) 16 hrs , d ) 18 hrs , e ) 20 hrs", + "Correct": "c", + "Explanation": "\"1 / 20 + 1 / 30 = 1 / 12 1 + 1 / 3 = 4 / 3 1 - - - 12 4 / 3 - - - ? 4 / 3 * 12 = 16 hrs c\"" + }, + { + "Answer": 69, + "Options": "a ) 2 , b ) 4 , c ) 8 , d ) 69 , e ) 32", + "Correct": "d", + "Explanation": "\"lets assign variables to all the areas in venn diagram of three . three different units are dog , cat , snake = total = 99 only dog = d = 15 only cat = c = 10 only snake = s exactly dog and cat = 5 exactly dog and snake = x exactly cat and snake = y all three = 3 so 99 = 15 + 10 + 5 + 3 + x + y + s we need to know total snakes = x + y + s + 3 = 69 answer : d\"" + }, + { + "Answer": 9, + "Options": "a ) 7 % , b ) 9 % , c ) 11 % , d ) 12 % , e ) none of these", + "Correct": "b", + "Explanation": "we have , 12 % of x = 6 % of y = > 2 % of x = 1 % of y = > ( 2 x 9 ) % of x = ( 1 x 9 ) % of y thus , 18 % of x = 9 % of y . answer : b" + }, + { + "Answer": 14, + "Options": "a ) a ) 12 , b ) b ) 14 , c ) c ) 16 , d ) d ) 18 , e ) e ) 22", + "Correct": "b", + "Explanation": "\"d = ( d - r ) / q = ( 127 - 1 ) / 9 = 126 / 9 = 14 b )\"" + }, + { + "Answer": 458329, + "Options": "a ) 328359 , b ) 557321 , c ) 258327 , d ) 458329 , e ) 4422", + "Correct": "d", + "Explanation": "a ( a ( a ( a ( 1 ) ) ) ) = a ( a ( a ( 4 ) ) ) = a ( a ( 25 ) ) = a ( 676 ) = 677 ^ 2 = 458329 thus , the answer is d ." + }, + { + "Answer": 74, + "Options": "a ) 68 % , b ) 70 % , c ) 72 % , d ) 74 % , e ) 77 %", + "Correct": "d", + "Explanation": "\"70 % of the class scored 65 % and 30 % of the class scored 95 % . the difference between 65 % and 95 % is 30 % . the average will be 65 % + 0.3 ( 30 % ) = 74 % . the answer is d .\"" + }, + { + "Answer": 20, + "Options": "a ) 20 , b ) 40 , c ) 60 , d ) 80 , e ) none of these", + "Correct": "a", + "Explanation": "\"solution required number of student = h . c . f of 1020 and 860 = 20 . answer a\"" + }, + { + "Answer": 10, + "Options": "a ) 10 , b ) 12 , c ) 13 , d ) 14 , e ) 15", + "Correct": "a", + "Explanation": "\"100 - ( 100 - 80 ) - ( 100 - 75 ) - ( 100 - 85 ) - ( 100 - 70 ) = 100 - 20 - 25 - 15 - 30 = 100 - 90 = 10 answer : a\"" + }, + { + "Answer": 90, + "Options": "a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90", + "Correct": "e", + "Explanation": "numbers will be like 102 = > 201 = 102 + 99 203 = > 302 = 103 + 99 so the hundereth digit and units digit are consecutive where unit digit is bigger than hundred digit . there will be ninet pairs of such numbers for every pair there will 10 numbers like for 12 = > 102 , 112,132 , 142,152 , 162,172 , 182,192 . total = 9 * 10 = 90 hence e ." + }, + { + "Answer": 8, + "Options": "a ) 8 , b ) 7 , c ) 2 , d ) 6 , e ) 5", + "Correct": "a", + "Explanation": "suppose there are nn persons present in a function and every person shakes hand with every other person . then , total number of handshakes = nc 2 = n ( n \u2212 1 ) / 2 n ( n \u2212 1 ) = 28 \u00d7 2 n ( n \u2212 1 ) = 56 n = 8 answer a 8" + }, + { + "Answer": 170, + "Options": "a ) 121 , b ) 129 , c ) 138 , d ) 152 , e ) 170", + "Correct": "e", + "Explanation": "\"3 * 16 + 3 * 17 + 3 * 20 + 11 = 48 + 51 + 60 + 11 = 170 the answer is e .\"" + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) 13 , c ) 15 , d ) 18 , e ) 22", + "Correct": "a", + "Explanation": "\"x = - 2 and y = - 4 x - y = - 2 - ( - 4 ) = - 2 + 4 = 2 x * y = - 2 * - 4 = 8 now we apply it in the equation 5 ( x - y ) ^ 2 - xy = 5 ( 2 ) ^ 2 - 8 = = > 5 * 4 - 8 = 20 - 8 = 12 answer : a\"" + }, + { + "Answer": 310, + "Options": "a ) 250 , b ) 276 , c ) 280 , d ) 310 , e ) none", + "Correct": "d", + "Explanation": "\"since the month begins with sunday , to there will be five sundays in the month average required = ( 660 x 5 + 240 x 25 ) / 30 ) = 310 answer : option d\"" + }, + { + "Answer": 33, + "Options": "a ) 10 % , b ) 25 % , c ) 33 % , d ) 50 % , e ) 67 %", + "Correct": "c", + "Explanation": "each 48 - day period , senior representatives visit the home office 3 times while junior representatives visit 4 times , thus 33 % more . the answer is c ." + }, + { + "Answer": 3, + "Options": "a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 8", + "Correct": "b", + "Explanation": "\"i like to put the numbers in prime factors so it is easier and faster to visualize . 14 * n / 60 if we write the factors of 14 - - > 2 , 7 , and the factors of 60 - - > 2 , 2 , 3 , 5 , we have ( 2 * 7 * n ) / ( 2 ^ 2 * 3 * 5 ) simplifying 7 * n / ( 2 * 3 * 5 ) the only way the equation above has an integer value is if n has at least the factors 2 , 3 and 5 , so we can simplify again and we have the number 7 . the number could be 2 * 3 * 5 , or 2 * 3 * 5 * 2 , or 2 * 3 * 5 * . . . . . however to be less than 200 we can not add any prime number . 2 * 3 * 5 = 120 if we added the next prime factor 7 , we would have q = 2 * 3 * 5 * 7 = 840 thus , answer b .\"" + }, + { + "Answer": 40.5, + "Options": "a ) 32.5 , b ) 36.5 , c ) 40.5 , d ) 44.5 , e ) 48.5", + "Correct": "c", + "Explanation": "the point of intersection is ( - 9 , - 9 ) . the triangle has a base of length 9 and a height of 9 . area = ( 1 / 2 ) * base * height = ( 1 / 2 ) * 9 * 9 = 40.5 the answer is c ." + }, + { + "Answer": 4, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "d", + "Explanation": "\"if the average price is 54 , then mary has 7 oranges and 3 apples ( a ratio of 7 : 3 ) . for the average price to be 50 , the ratio should be 1 : 1 . mary must put back 4 oranges . the answer is d .\"" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "c", + "Explanation": "\"x = ( y / 3 ) - ( 2 / 5 ) , and so y = 3 x + 6 / 5 . the slope is 3 . ( n + 9 - n ) / ( m + p - m ) = 3 p = 3 the answer is c .\"" + }, + { + "Answer": 78, + "Options": "a ) 76 , b ) 68 , c ) 78 , d ) 66 , e ) 67", + "Correct": "c", + "Explanation": "1 + 2 + 3 + \u22ef + n = \u2211 n = n ( n + 1 ) / 2 1 + 2 + 3 + \u22ef + 12 = n ( n + 1 ) / 2 = ( 12 ( 12 + 1 ) ) / 2 = ( 12 \u00d7 13 ) / 2 = 6 \u00d7 13 = 78 answer is c" + }, + { + "Answer": 24, + "Options": "a ) 23 , b ) 24 , c ) 25 , d ) 26 , e ) 27", + "Correct": "b", + "Explanation": "\"average age of people = 30 so have total age = 210 before 7 years we have to deduct each person age by seven years 210 - 42 = 161 so average age would be 161 / 7 = 24 answer : b\"" + }, + { + "Answer": 90, + "Options": "a ) 90 % , b ) 87.5 % , c ) 66.7 % , d ) 50 % , e ) 36 %", + "Correct": "a", + "Explanation": "lets say there are total 100 employees then men = 46 & women = 54 unionized emp = 60 & non unionized emp = 40 men unionized = . 7 * 60 = 42 women unionized = 18 women non - unionized = 54 - 18 = 36 percentage of women non unionized = 36 / 40 * 100 = 90 % the answer is option a" + }, + { + "Answer": 72, + "Options": "a ) 18 , b ) 92 , c ) 72 , d ) 26 , e ) 19", + "Correct": "c", + "Explanation": "explanation : let the present age of person be x years . then , 6 ( x + 6 ) - 6 ( x - 6 ) = x < = > ( 6 x + 36 ) - ( 6 x - 36 ) = x < = > x = 72 . . answer : c" + }, + { + "Answer": 63, + "Options": "a ) 54 , b ) 59 , c ) 63 , d ) 71 , e ) 92", + "Correct": "c", + "Explanation": "total = 70 thrower = 49 rest = 70 - 49 = 21 left handed = 21 / 3 = 7 right handed = 14 if all thrower are right handed then total right handed is 49 + 14 = 63 so c . 63 is the right answer" + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 8 , c ) 7 , d ) 10 , e ) 11", + "Correct": "a", + "Explanation": "solution : log 255 = 251 / 2 = 5 answer is a" + }, + { + "Answer": 17, + "Options": "a ) 17 , b ) 39 , c ) 42 , d ) 45 , e ) none of the above", + "Correct": "a", + "Explanation": "let the average after 17 th inning = x . then , average after 16 th inning = ( x \u2013 3 ) . \u2234 16 ( x \u2013 3 ) + 65 = 17 x or x = ( 65 \u2013 48 ) = 17 . answer a" + }, + { + "Answer": 18, + "Options": "a ) 12 , b ) 16 , c ) 18 , d ) 24 , e ) 26", + "Correct": "c", + "Explanation": "\"explanation : suppose the boy got x sums right and 2 x sums wrong . then , x + 2 x = 54 3 x = 54 x = 18 . answer : c\"" + }, + { + "Answer": 0.23529411764705882, + "Options": "a ) 1 / 12 , b ) 4 / 17 , c ) 2 / 3 , d ) 1 1 / 9 , e ) 2 1 / 9", + "Correct": "b", + "Explanation": "total bought = 4 / 17 + 3 / 10 left part 9 / 30 - - - > 3 / 10 so used part 4 / 17 + 3 / 10 - 3 / 10 = 4 / 17 answer : b" + }, + { + "Answer": 89, + "Options": "a ) 87 , b ) 89 , c ) 90 , d ) 93 , e ) 95", + "Correct": "b", + "Explanation": "\"total score on 3 tests = 81 * 3 = 243 jerry wants the average to be = 83 hence total score on 4 tests should be = 83 * 4 = 332 score required on the fourth test = 332 - 243 = 89 option b\"" + }, + { + "Answer": 6, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "d", + "Explanation": "given that p is smallest integer greater than 300 - assume there is a 3 - digit that satisfies the above conditions . let the number be xyx ; question asks us the values of 2 x + y we can straight away cross out options a ) and d ) - sum of digits 3 or 6 implies it is divisible by 3 - - - > we know that p is a prime number coming to option b ) 2 x + y = 4 - - > only x = 2 and y = 0 satisfy this equation ( x > 2 will never give sum of digits = 4 ) ; but 202 is divisible by 2 ; we know that p is a prime number similarly option c ) 2 x + y = 5 - - > only x = 2 and y = 1 satisfy this equation ( x > 2 will never give sum of digits = 5 ) ; but 212 is divisible by 2 ; we know that p is a prime number therefore answer option should be e - - - > can be verified by taking 2 x + y = 7 - - - > x = 3 and y = 1 ; gives 313 d" + }, + { + "Answer": 3, + "Options": "a ) 4 , b ) 7 , c ) 8 , d ) 5 , e ) 3", + "Correct": "e", + "Explanation": "\"explanation : let the number be x . then , ( x - 5 ) / 7 = 7 = > x - 5 = 49 x = 54 . : ( x - 24 ) / 10 = ( 54 - 24 ) / 10 = 3 answer : option e\"" + }, + { + "Answer": 8, + "Options": "a ) 16.2 , b ) 4 , c ) 5 , d ) 500 , e ) 8", + "Correct": "e", + "Explanation": "\"answer let 45 x a = ( 40 x 900 ) / 100 \u2234 a = ( 40 x 9 ) / 45 = 8 correct option : e\"" + }, + { + "Answer": 585, + "Options": "a ) 910 , b ) 585 , c ) 785 , d ) 685 , e ) 885", + "Correct": "b", + "Explanation": "required numbers are 18,27 . . . . . 99 this is an a . p . in which a = 18 , d = 9 and l = 99 . let the number of terms in it be n . then t = 99 so a + ( n - 1 ) d = 99 . 18 + ( n - 1 ) * 9 = 99 , 18 + 9 n - 9 = 99 9 + 9 n = 99 9 n = 99 - 9 n = 90 / 9 then n = 10 . required sum = n / 2 ( a + l ) = 10 / 2 ( 18 + 99 ) = 585 answer is b ." + }, + { + "Answer": 6, + "Options": "a ) 5 , b ) 8 , c ) 7 , d ) 6 , e ) 9", + "Correct": "d", + "Explanation": "\"on dividing 899830 by 16 we get the remainder 6 , so 6 should be subtracted d\"" + }, + { + "Answer": 0.2857142857142857, + "Options": "a ) 3 / 14 , b ) 2 / 7 , c ) 9 / 14 , d ) 5 / 7 , e ) 11 / 14", + "Correct": "b", + "Explanation": "probability of an event = ( # of favorable outcomes ) / ( total # of outcomes ) . there are 5 numbers you can choose from ( 3 , 6 , 9 , 12 , 15 ) so that the sum to be divisible by 3 and there are total of 7 numbers so p = c 35 c 37 = 27 p = c 53 c 73 = 27 . answer : b ." + }, + { + "Answer": 61, + "Options": "a ) 31 , b ) 61 , c ) 50 , d ) 99 , e ) 101", + "Correct": "b", + "Explanation": "\"2 ^ 10 = 1.024 * 10 ^ 3 = > 2 ^ 100 = ( 1.024 ) ^ 10 * 10 ^ 60 therefore 61 digits would be my best guess b\"" + }, + { + "Answer": 15, + "Options": "a ) 12.5 % , b ) 13 % , c ) 16 % , d ) 15 % , e ) 19 %", + "Correct": "d", + "Explanation": "\"quantity x rate = price 1 x 1 = 1 0.68 x 1.25 = 0.85 decrease in price = ( 0.15 / 1 ) \u00d7 100 = 15 % d )\"" + }, + { + "Answer": 25, + "Options": "a ) 20 % , b ) 15 % , c ) 30 % , d ) 25 % , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : solution : 25 % of ( x - y ) = 15 % of ( x + y ) 25 ( x - y ) / 100 = 15 ( x + y ) / 100 5 ( x - y ) = 3 ( x + y ) x = 4 y . . ' . required percentage = ( y * 100 / x ) % = y * 100 / 4 y = 25 % answer : d\"" + }, + { + "Answer": 75, + "Options": "a ) 65 kg , b ) 70 kg , c ) 75 kg , d ) 80 kg , e ) 85 kg", + "Correct": "c", + "Explanation": "wt of abc = 84 * 3 = 252 kg wt of abcd = 80 * 4 = 320 kg wt of d = 68 kg wt of e = 71 kg wt of abcde = 320 + 71 = 391 kg wt of bcde = 79 * 4 = 316 kg wt of a = 391 - 316 = 75 kg answer : c" + }, + { + "Answer": 100, + "Options": "a ) 100 , b ) 350 , c ) 400 , d ) 450 , e ) 500", + "Correct": "a", + "Explanation": "total marks : 1500 for three exams 40 % of 1500 = 600 first exam marks = 45 % of 500 = 225 second exam marks = 55 % of 500 = 275 let x be the third exam marks 225 + 275 + x = 600 x = 100 answer : a" + }, + { + "Answer": 22, + "Options": "a ) 22 , b ) 23 , c ) 24 , d ) 26 , e ) 28", + "Correct": "a", + "Explanation": "\"let hens be x and cows be y now , feet : x * 2 + y * 4 = 140 heads : x * 1 + y * 1 = 46 implies , 2 x + 4 y = 140 and x + y = 46 solving these two equations , we get x = 22 and y = 24 therefore , hens are 22 . answer : a\"" + }, + { + "Answer": 62.4, + "Options": "a ) 68 , b ) 62.4 , c ) 86 , d ) 72.8 , e ) 108", + "Correct": "b", + "Explanation": "\"x is 20 % greater than 52 means x is 1.2 times 52 ( in other words 52 + 20 / 100 * 52 = 1.2 * 52 ) therefore , x = 1.2 * 88 = 62.4 answer : b\"" + }, + { + "Answer": 135, + "Options": "a ) 130 , b ) 132 , c ) 135 , d ) 136 , e ) 138", + "Correct": "c", + "Explanation": "let the required number be x . then , 43 x \u2013 34 x = 1215 or 9 x = 1215 or x = 135 . required number = 135 answer : c" + }, + { + "Answer": 50, + "Options": "a ) 55 , b ) 65 , c ) 50 , d ) 75 , e ) 85", + "Correct": "c", + "Explanation": "\"x ^ 2 + y ^ 2 should make you think of these formulas : ( x + y ) ( x + y ) = x ^ 2 + y ^ 2 + 2 xy we already know ( x + y ) = - 10 and x * y = 25 ( x + y ) ( x + y ) = ( - 10 ) ( - 10 ) = x ^ 2 + y ^ 2 + 2 * ( 25 ) x ^ 2 + y ^ 2 = 100 - 50 = 50 answer : c\"" + }, + { + "Answer": 23, + "Options": "a ) 7 , b ) 13 , c ) 16 , d ) 21 , e ) 23", + "Correct": "e", + "Explanation": "\"general rule for such kind of problems : to maximize one quantity , minimize the others ; to minimize one quantity , maximize the others . thus to maximize the number of points of one particular player minimize the number of points of all other 11 players . minimum number of points for a player is 7 , so the minimum number of points of 11 players is 7 * 11 = 77 . therefore , the maximum number of points l for 12 th player is 100 - 77 = 23 . answer : e .\"" + }, + { + "Answer": 6, + "Options": "a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 9", + "Correct": "c", + "Explanation": "logx ( y 3 ) = 2 : given x 2 = y 3 : rewrite in exponential form x 4 = y 6 : square both sides x 4 = y 6 : rewrite the above using the log base y logy ( x 4 ) = logy ( y 6 ) = 6 correct answer c" + }, + { + "Answer": 33.333333333333336, + "Options": "a ) 37.5 litres , b ) 36.67 litres , c ) 37.67 litres , d ) 36.5 litres , e ) 33.33 litres", + "Correct": "e", + "Explanation": "\"working formula . . . initial concentration * initial volume = final concentration * final volume . let x is the part removed from 100 lts . 36 % ( 1 - x / 100 ) ^ 2 = 16 % * 100 % ( 1 - x / 100 ) ^ 2 = 16 / 36 - - - - - - > ( 1 - x / 100 ) ^ 2 = ( 4 / 6 ) ^ 2 100 - x = 400 / 6 x = 33.33 . . . ans e\"" + }, + { + "Answer": 25.000000000000007, + "Options": "a ) 40 , b ) 25 , c ) 38 , d ) 50 , e ) 39", + "Correct": "b", + "Explanation": "\"let , father \u00e2 \u20ac \u2122 s current age is a years . then , man \u00e2 \u20ac \u2122 s current age = [ ( 2 / 5 ) a ] years . therefore , [ ( 2 / 5 ) a + 5 ] = ( 1 / 2 ) ( a + 5 ) 2 ( 2 a + 25 ) = 5 ( a + 8 ) a = 25 b\"" + }, + { + "Answer": 6.6000000000000005, + "Options": "a ) $ 1.56 , b ) $ 2.40 , c ) $ 3.80 , d ) $ 4.20 , e ) $ 6.60", + "Correct": "e", + "Explanation": "\"in 3 miles , initial 1 / 5 mile charge is $ 1 rest of the distance = 3 - ( 1 / 5 ) = 14 / 5 rest of the distance charge = 14 ( 0.4 ) = $ 5.6 ( as the charge is 0.4 for every 1 / 5 mile ) = > total charge for 3 miles = 1 + 5.6 = 6.6 answer is e .\"" + }, + { + "Answer": 194, + "Options": "a ) 179 , b ) 194 , c ) 269 , d ) 177 , e ) 191", + "Correct": "b", + "Explanation": "\"explanation : total runs scored by the batsman = 60 * 46 = 2760 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2760 \u00e2 \u20ac \u201c 2552 = 208 runs . let the highest score be x , hence the lowest score = x \u00e2 \u20ac \u201c 180 x + ( x - 180 ) = 208 2 x = 388 x = 194 runs answer : b\"" + }, + { + "Answer": 11, + "Options": "a ) 10.6 kg , b ) 10.8 kg , c ) 11 kg , d ) 14.9 kg , e ) none", + "Correct": "c", + "Explanation": "answer weight of new student = total weight of all 20 students - total weight of initial 19 students = ( 20 x 14.8 - 19 x 15 ) kg = 11 kg . correct option : c" + }, + { + "Answer": 16, + "Options": "a ) 11 , b ) 16 , c ) 13 , d ) 14 , e ) 15", + "Correct": "b", + "Explanation": "\"explanation : given that a + b = 16 + b + c = > a ? c = 16 + b ? b = 16 = > c is younger than a by 16 years answer : option b\"" + }, + { + "Answer": 39, + "Options": "a ) 36 , b ) 37 , c ) 38 , d ) 39 , e ) 35", + "Correct": "d", + "Explanation": "\"explanation : let the average after 17 th match is x then the average before 17 th match is x - 3 so 16 ( x - 3 ) + 87 = 17 x = > x = 87 - 48 = 39 option d\"" + }, + { + "Answer": 4.5, + "Options": "a ) $ 3.50 , b ) $ 4.00 , c ) $ 4.25 , d ) $ 4.50 , e ) $ 5.00", + "Correct": "d", + "Explanation": "let x be the value of the weekly allowance . ( 2 / 3 ) ( 2 / 5 ) x = 120 cents ( 4 / 15 ) x = 120 x = $ 4.50 the answer is d ." + }, + { + "Answer": 208, + "Options": "a ) $ 200 , b ) $ 204 , c ) $ 208 , d ) $ 212 , e ) $ 216", + "Correct": "c", + "Explanation": "\"let the shares for a , b , and c be x , 2 x , and 4 x respectively . 7 x = 364 x = 52 4 x = 208 the answer is c .\"" + }, + { + "Answer": 4166.666666666667, + "Options": "a ) rs . 4500 , b ) rs . 4000 , c ) rs . 4167 , d ) rs . 4200 , e ) rs . 3000", + "Correct": "c", + "Explanation": "income = rs . 100 expenditure = rs . 80 savings = rs . 20 present expenditure 80 + 80 * ( 10 / 100 ) = rs . 88 present savings = 100 \u2013 88 = rs . 12 if savings is rs . 12 , salary = rs . 100 if savings is rs . 500 , salary = 100 / 12 * 500 = 4167 answer : c" + }, + { + "Answer": 12, + "Options": "a ) - 3 , b ) 3 , c ) 5 , d ) - 12 , e ) 12", + "Correct": "e", + "Explanation": "\"a can not be the answer as all the three terms are in modulus and hence the answer will be non negative . | x - 4 | > = 0 - - > minimum occurs at x = 4 | x + 7 | > = 0 - - > minimum occurs at x = - 7 | x - 5 | > = 0 - - > minimum occurs at x = 5 x = - 7 - - > result = 11 + 0 + 12 = 23 . also any negative value will push the combined value of | x - 4 | + | x - 5 | to a value > 9 . x = 4 - - > result = 0 + 11 + 1 = 12 x = 5 - - > result = 1 + 12 + 0 = 13 x = 7 - - > result = 3 + 14 + 2 = 19 so minimum value of the expression occurs at x = 4 and the resultant value = 12 answer : e\"" + }, + { + "Answer": 0.46875, + "Options": "a ) 5 / 16 , b ) 1 / 2 , c ) 12 / 30 , d ) 15 / 32 , e ) 3 / 8", + "Correct": "d", + "Explanation": "the probability of the coin landing tails up either 3 or 4 times = p ( 3 t ) + p ( 4 t ) binomial distribution formula : nck p ^ k ( 1 - p ) ^ ( n - k ) p ( 3 t ) = 5 c 3 ( 1 / 2 ) ^ 3 ( 1 / 2 ) ^ 2 = 10 ( 1 / 2 ) ^ 5 p ( 4 t ) = 5 c 4 ( 1 / 2 ) ^ 4 ( 1 / 2 ) ^ 1 = 5 ( 1 / 2 ) ^ 5 = > p ( 3 t ) + p ( 4 t ) = 15 / 32 answer : d" + }, + { + "Answer": 700, + "Options": "a ) 0 , b ) 50 , c ) 450 , d ) 693 , e ) 500", + "Correct": "d", + "Explanation": "we can break this problem into two parts : 1 ) what is 1 / 10 percent of 7,000 ? 2 ) what is 1 / 10 of 7,000 ? to calculate 1 / 10 percent of 7,000 we must first remember to divide 1 / 10 by 100 . so we have : ( 1 / 10 ) / ( 100 ) to divide a number by 100 means to multiply it by 1 / 100 , so we have : 1 / 10 x 1 / 100 = 1 / 1,000 thus , 1 / 10 percent of 7,000 = 1 / 1,000 x 7,000 = 7 . now let ' s concentrate on part 2 . we need to calculate 1 / 10 of 7,000 . to do this we simply multiply 1 / 10 by 7,000 . 1 / 10 x 7,000 = 700 the answer to part 1 is 7 , and the answer to part 2 is 700 . their difference is 700 \u2013 7 = 693 . answer d ." + }, + { + "Answer": 400, + "Options": "a ) ( 400 ) , b ) ( 300 ) , c ) ( 040 ) , d ) ( 4030 ) , e ) ( 030 )", + "Correct": "a", + "Explanation": "assume that the equation of the line is y = mx + c , where m and c are the slope and y - intercept . you are also given that the line crosses the point ( - 12 , - 39 ) , this means that this point will also lie on the line above . thus you get - 39 = m * ( - 12 ) + c , with m = 3 / 4 as the slope is given to be 3 / 4 . after substituting the above values , you get c = - 30 . thus the equation of the line is y = 0.75 * x - 30 and the point where it will intersect the x - axis will be with y coordinate = 0 . put y = 0 in the above equation of the line and you will get , x = 40 . thus , the point e of intersection is ( 400 ) . a is the correct answer ." + }, + { + "Answer": 2900, + "Options": "a ) 2900 , b ) 7250 , c ) 2767 , d ) 1998 , e ) 2771", + "Correct": "a", + "Explanation": "\"explanation : a b c investment 3 x 4 x 5 x rate of return 6 y % 5 y % 4 y % return \\ inline \\ frac { 18 xy } { 100 } \\ inline \\ frac { 20 xy } { 100 } \\ inline \\ frac { 20 xy } { 100 } total = ( 18 + 20 + 20 ) = \\ inline \\ frac { 58 xy } { 100 } b ' s earnings - a ' s earnings = \\ inline \\ frac { 2 xy } { 100 } = 100 total earning = \\ inline \\ frac { 58 xy } { 100 } = 2900 answer : a ) rs . 2900\"" + }, + { + "Answer": 32, + "Options": "a ) 2 , b ) 4 , c ) 8 , d ) 16 , e ) 32", + "Correct": "e", + "Explanation": "x * ( 1 / 2 ) ^ 2 = 2 ^ 3 x = 2 ^ 2 * 2 ^ 3 = 2 ^ 5 = 32 the answer is e ." + }, + { + "Answer": 54.285714285714285, + "Options": "a ) 44.28 , b ) 54.28 , c ) 34.28 , d ) 64.28 , e ) 74.28", + "Correct": "b", + "Explanation": "\"sum of the marks for the class of 20 students = 20 * 40 = 800 sum of the marks for the class of 50 students = 50 * 60 = 3000 sum of the marks for the class of 70 students = 800 + 3000 = 3800 average marks of all the students = 3800 / 70 = 54.28 answer : b\"" + }, + { + "Answer": 0.06666666666666665, + "Options": "a ) 2 / 19 , b ) 3 / 29 , c ) 4 / 15 , d ) 1 / 15 , e ) 1 / 2", + "Correct": "d", + "Explanation": "first , there are 6 c 4 ways you can select 6 good bulbs from 4 good ones . second , there are 10 c 4 ways you select 4 bulbs from 10 ones in the box . then , the probability that neither bulb will be defective is : 6 c 4 / 10 c 4 = 15 / 210 = 1 / 15 answer is d" + }, + { + "Answer": 12, + "Options": "a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18", + "Correct": "b", + "Explanation": "there are 3 ! ways to make codes starting with 12 . there are 3 ! ways to make codes starting with 24 . the number of codes is 2 * 3 ! = 12 . the answer is b ." + }, + { + "Answer": 15, + "Options": "a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 19", + "Correct": "c", + "Explanation": "34 ! has 3 , 6 , 9 , . . . . 30 , 33 as factors , which are 11 multiples of 3 . we need to add 4 more to these 11 because of 9 , 18 , and 27 . the greatest integer of k is 15 . the answer is c ." + }, + { + "Answer": 8175, + "Options": "a ) 2480 , b ) 3490 , c ) 6785 , d ) 8255 , e ) 9255", + "Correct": "d", + "Explanation": "\"you ' ll never need a formula for the sums of squares on the actual gmat . you do n ' t need to use that formula here , though it ' s not all that straightforward to solve without one . two different approaches : 16 ^ 2 + 17 ^ 2 + 18 ^ 2 + . . . + 30 ^ 2 = ( 15 + 1 ) ^ 2 + ( 15 + 2 ) ^ 2 + ( 15 + 3 ) ^ 2 + . . . + ( 15 + 15 ) ^ 2 now we can expand each square ; they are all in the ( x + y ) ^ 2 = x ^ 2 + 2 xy + y ^ 2 pattern . = ( 15 ^ 2 + 2 * 15 + 1 ^ 2 ) + ( 15 ^ 2 + 4 * 15 + 2 ^ 2 ) + ( 15 ^ 2 + 6 * 15 + 3 ^ 2 ) + . . . + ( 15 ^ 2 + 30 * 15 + 15 ^ 2 ) now we have fifteen 15 ^ 2 terms , so adding these gives 15 * 15 ^ 2 = 15 ^ 3 = 3375 . we also have the entire sum 1 ^ 2 + 2 ^ 2 + . . . + 15 ^ 2 , which we know is equal to 1240 . finally adding the middle terms , we have : 2 * 15 + 4 * 15 + 6 * 15 + . . . + 30 * 15 = 15 ( 2 + 4 + 6 + . . . . + 30 ) = 15 * 2 * ( 1 + 2 + 3 + . . . + 15 ) = 15 * 2 * 8 * 15 = 3600 so the sum must be 3375 + 1240 + 3600 = 8215 alternatively , we can use a different factoring pattern . we want to find the value of 30 ^ 2 + 29 ^ 2 + . . . + 17 ^ 2 + 16 ^ 2 . well if we subtract 15 ^ 2 + 14 ^ 2 + . . . . + 2 ^ 2 + 1 ^ 2 from this , the answer will be 1240 less than what we want to find . so if we can find the value of 30 ^ 2 + 29 ^ 2 + . . . + 17 ^ 2 + 16 ^ 2 - ( 15 ^ 2 + 14 ^ 2 + . . . . + 2 ^ 2 + 1 ^ 2 ) then we can add 1240 to get the answer . now grouping the terms above to get differences of squares , we have = ( 30 ^ 2 - 15 ^ 2 ) + ( 29 ^ 2 - 14 ^ 2 ) + . . . + ( 16 ^ 2 - 1 ^ 2 ) and factoring each of these using x ^ 2 - y ^ 2 = ( x + y ) ( x - y ) , we have = 45 * 15 + 43 * 15 + 41 * 15 + . . . + 17 * 15 = 15 ( 45 + 43 + 41 + . . . + 17 ) in brackets we have an equally spaced sum with fifteen terms , which we can evaluate using the familiar formula . so the above equals 15 * 15 * 62 / 2 = 6975 and adding back the 1280 , we get the answer of 8255 . ( ans d )\"" + }, + { + "Answer": 40, + "Options": "a ) 38 , b ) 29 , c ) 27 , d ) 40 , e ) 91", + "Correct": "d", + "Explanation": "\"explanation : x \u00e2 \u20ac \u201c 3 / 8 x = 25 x = 40 answer : d\"" + }, + { + "Answer": 25, + "Options": "a ) 10 , b ) 25 , c ) 55 , d ) 35 , e ) 65", + "Correct": "b", + "Explanation": "you could pick 70 non - programmers , 2 male programmers , and 2 female programmers , and still not have 3 programmers of the same sex . but if you pick one more person , you must either pick a male or a female programmer , so the answer is 25 . b" + }, + { + "Answer": 18, + "Options": "a ) 11 , b ) 18 , c ) 14 , d ) 12 , e ) 10", + "Correct": "b", + "Explanation": "explanation : let somu ' s age be x and that of his father be 3 x . so , x - 9 = 3 x - 9 / 5 = x = 18 answer : option b" + }, + { + "Answer": 9, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10", + "Correct": "d", + "Explanation": "\"say there are ' a ' associate professors . so we have 2 a pencils and a charts . say there are ' b ' assistant professors . so we have b pencils and 2 b charts . total pencils are 10 so 2 a + b = 11 total charts are 11 so a + 2 b = 16 add both : 3 a + 3 b = 27 so a + b = 9 total number of people = 9 d\"" + }, + { + "Answer": 100, + "Options": "a ) 25 , b ) 50 , c ) 75 , d ) 100 , e ) 125", + "Correct": "d", + "Explanation": "let us assume k be the element we need to search then let array be n 1 , n 2 , n 3 . . . . . . . . . . . . . . n 100 now to prove that the element searched is not there in the array we have to compare the element k with every element in the array . so , totally we need 100 comparisons . answer : d" + }, + { + "Answer": 100, + "Options": "a ) 50 km , b ) 100 km , c ) 60 km , d ) 70 km , e ) 80 km", + "Correct": "b", + "Explanation": "\"let the actual distance travelled be x km . x / 10 = ( x + 20 ) / 12 12 x = 10 x + 200 2 x = 200 x = 100 km . answer : b\"" + }, + { + "Answer": 4082.4, + "Options": "a ) rs . 4082.40 , b ) rs . 1024.21 , c ) rs . 2810.6 , d ) rs . 3214 , e ) none of these", + "Correct": "a", + "Explanation": "explanation : length of the first carpet = ( 1.44 ) ( 6 ) = 8.64 cm area of the second carpet = 8.64 ( 1 + 40 / 100 ) 6 ( 1 + 25 / 100 ) = 51.84 ( 1.4 ) ( 5 / 4 ) sq m = ( 12.96 ) ( 7 ) sq m cost of the second carpet = ( 45 ) ( 12.96 x 7 ) = 315 ( 13 - 0.04 ) = 4095 - 12.6 = rs . 4082.40 answer is a" + }, + { + "Answer": 16.66666666666667, + "Options": "a ) 13.67 % , b ) 14.67 % , c ) 15.67 % , d ) 16.67 % , e ) 17.67 %", + "Correct": "d", + "Explanation": "\"let total % of work is 100 % total person = p 1 / 7 person are absent of total person . so absent person is 1 / 7 p ie p / 7 . left person is , p - p / 7 = 6 p / 7 . p person do the work 100 % 1 person do the work 100 * p % 6 p / 7 person do the work ( 100 * p * 7 ) / 6 p % = 116.67 % work increased for each person is = ( 116.67 - 100 ) % = 16.67 % answer : d\"" + }, + { + "Answer": 95, + "Options": "a ) a ) 78 , b ) b ) 82 , c ) c ) 95 , d ) d ) 91 , e ) e ) 85", + "Correct": "c", + "Explanation": "\"correct avg marks = 100 + ( 10 - 60 ) / 10 avg = 100 - 5 = 95 answer is c\"" + }, + { + "Answer": 199, + "Options": "a ) $ 150 , b ) $ 248.75 , c ) $ 199 , d ) $ 171.6 , e ) $ 190", + "Correct": "c", + "Explanation": "$ 9.95 * 20 = $ 199 . answer is c ." + }, + { + "Answer": 60, + "Options": "a ) a ) 40 , b ) b ) 60 , c ) c ) 80 , d ) d ) 120 , e ) e ) 140", + "Correct": "b", + "Explanation": "\"total number of students : 160 total girls : 160 * 5 / 8 = 100 total boys : 160 - 100 = 60 answer is b\"" + }, + { + "Answer": 25, + "Options": "a ) 14 % , b ) 25 % , c ) 28 % , d ) 34 % , e ) 50 %", + "Correct": "b", + "Explanation": "\"official solution : if we start with 40 gallons of a mixture that is 10 % grape juice , then we have : 50 \u00d7 0.10 = 5 gallons of grape juice . 50 \u00d7 0.90 = 45 gallons of other components . if we add 10 gallons of grape juice , we will end up with 15 gallons of grape juice and 45 gallons of other components , and we will have a total of 60 gallons of the mixture . so 15 / 60 of the new mixture is grape juice . now we convert this to a percent : percent grape juice = 25 / 100 = 25 % . the correct answer is choice ( b )\"" + }, + { + "Answer": 55.99999999999999, + "Options": "a ) 40 % , b ) 44 % , c ) 50 % , d ) 56 % , e ) 60 %", + "Correct": "d", + "Explanation": "paint : canvas cost is 4 : 1 . so , paint accounts for 80 % of cost and canvas accounts for 20 % . canvas , after decrease by 40 % will be ( 100 - 40 ) % of 20 % = > 60 % of 20 % = > 12 % of original paint , after decrease by 60 % will be ( 100 - 60 ) % of 80 % = > 40 % of 80 % = > 32 % of original new cost as a % of old cost = 32 + 12 = 44 % of original . so , overall cost saving = 100 - 44 = 56 % therefore , ( d )" + }, + { + "Answer": 14, + "Options": "a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18", + "Correct": "c", + "Explanation": "v = 30 ! 8 v = 30 x 29 x 28 x 27 x 26 x 25 x 24 x 24 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 09 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 out of these 30 , 27 , 24 , 21 , 18 , 15 , 12 , 09 , 06 , 3 are factors of 3 3 x 10 , 3 x 3 x 3 , 3 x 8 , 3 x 3 x 2 , 3 x 5 , 3 x 4 , 3 x 3 x 3 , 3 x 2 , 3 so we have a total of 14 three ' s . . . therefore the maximum value of k can be 14 ( c )" + }, + { + "Answer": 74, + "Options": "a ) 74 , b ) 76 , c ) 78 , d ) 80 , e ) 82", + "Correct": "a", + "Explanation": "\"a score of 58 was 2 standard deviations below the mean - - > 58 = mean - 2 d a score of 98 was 3 standard deviations above the mean - - > 98 = mean + 3 d solving above for mean e = 74 . answer : a .\"" + }, + { + "Answer": 499.99999999999994, + "Options": "a ) 400 , b ) 500 , c ) 505 , d ) none of these , e ) 506", + "Correct": "b", + "Explanation": "\"explanation : 35 / . 07 = 3500 / 7 = 500 option b\"" + }, + { + "Answer": 80, + "Options": "a ) 85 kg , b ) 90 kg , c ) 80 kg , d ) 75 kg , e ) 70 kg", + "Correct": "c", + "Explanation": "\"total weight increased = 20 x 2 kg = 40 kg . weight of new person = 40 + 40 kg = 80 kg answer : c\"" + }, + { + "Answer": 4.9956356288922485, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "d", + "Explanation": "\"0.0010101 * 10 ^ k > 100 we need to move the decimal point to the right 5 places to get 101.01 this is equivalent to multiplying by 10 ^ 5 . the answer is d .\"" + }, + { + "Answer": 9, + "Options": "a ) 1 : 2 , b ) 3 : 2 , c ) 9 : 1 , d ) 5 : 2 , e ) 6 : 5", + "Correct": "c", + "Explanation": "\"g = 19 w c = 9 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 19 w + 9 wx = x + 1 * 18 w 19 + 9 x = 18 ( x + 1 ) x = 1 / 9 ratio of gold with copper = 1 : 1 / 9 = 9 : 1 answer is c\"" + }, + { + "Answer": 2, + "Options": "a ) - 4 , b ) 4 , c ) - 2 , d ) 1 / 2 , e ) - 2", + "Correct": "e", + "Explanation": "as y = 0.5 mx + m , from 0 = 1 / 2 mx + m we get x = - 2 . hence , the correct answer choice is e ." + }, + { + "Answer": 900, + "Options": "a ) 450 , b ) 810 , c ) 900 , d ) 1000 , e ) 1100", + "Correct": "c", + "Explanation": "\"we want the sum of the digits from 0 to 99 , so i approximated : 0 - 9 - > 45 - > ( 9 + 0 ) * 10 / 2 40 - 49 - > 85 ( 13 + 4 ) * 10 / 2 90 - 99 - > 135 ( 18 + 9 ) * 10 / 2 we can see at a glance that theweightgoes up as the numbers go up ( meaning the difference between 85 and 45 is 40 , while 135 - 85 is 50 , this means that the second part of this sequence carries more weight for our result ) , so we know that the final answer has to be more than 850 ( 85 * 10 ) but close to it , and that ' s just r = 900 : the answer is c .\"" + }, + { + "Answer": 74.99999999999716, + "Options": "a ) 96 , b ) 75 , c ) 48 , d ) 25 , e ) 12", + "Correct": "b", + "Explanation": "\"x = qy + 9 , where q is the quotient x / y = ( q y + 9 ) / y = q + ( 9 / y ) = 96.12 = 96 + 0.12 = > q = 96 9 / y = 0.12 = > y = 75 answer is b .\"" + }, + { + "Answer": 180, + "Options": "a ) 300 , b ) 240 , c ) 220 , d ) 200 , e ) 180", + "Correct": "e", + "Explanation": "\"4 th term + 12 th term = 24 i . e . , ( a + 3 d ) + ( a + 11 d ) = 24 now , sum of first 15 terms = ( 15 / 2 ) * [ 2 a + ( 15 - 1 ) d ] = ( 15 / 2 ) * [ 2 a + 14 d ] = ( 15 / 2 ) * 24 - - - - - - - - - - - - - - - from ( 1 ) = 180 answer : e\"" + }, + { + "Answer": 3528, + "Options": "a ) 1236 , b ) 3528 , c ) 4096 , d ) 4608 , e ) 6561", + "Correct": "b", + "Explanation": "first digit . . 9 posibilities second digit , 8 possibilities third digit , 7 possibilities fourth digit , 7 possibilities . 9 * 8 * 7 * 7 = 3528 . b" + }, + { + "Answer": 37.5, + "Options": "a ) a : 45 , b ) b : 25 , c ) c : 37.5 , d ) d : 36 , e ) e : 42", + "Correct": "c", + "Explanation": "\"if you have a 37.5 liter capacity , you start with 37.5 l of a and 0 l of b . 1 st replacement after the first replacement you have 37.5 - 15 = 22.5 l of a and 15 l of b . the key is figuring out how many liters of a and b , respectively , are contained in the next 15 liters of mixture to be removed . the current ratio of a to total mixture is 22.5 / 37.5 ; expressed as a fraction this becomes ( 45 / 2 ) / ( 75 / 2 ) , or 45 / 2 * 2 / 75 . canceling the 2 s and factoring out a 5 leaves the ratio as 9 / 15 . note , no need to reduce further as we ' re trying to figure out the amount of a and b in 15 l of solution . 9 / 15 of a means there must be 6 / 15 of b . multiply each respective ratio by 15 to get 9 l of a and 6 l of b in the next 15 l removal . final replacement the next 15 l removal means 9 liters of a and 6 liters of b are removed and replaced with 15 liters of b . 22.5 - 9 = 13.5 liters of a . 15 liters of b - 6 liters + 15 more liters = 24 liters of b . test to the see if the final ratio = 9 / 16 ; 13.5 / 24 = ( 27 / 2 ) * ( 1 / 24 ) = 9 / 16 . choice c is correct .\"" + }, + { + "Answer": 61.904761904761905, + "Options": "a ) 61.90 % , b ) 52.20 % , c ) 56.20 % , d ) 70.45 % , e ) 74.41 %", + "Correct": "a", + "Explanation": "\"say a 100 families existed in 1904 then the number of families owning a computer in 1904 - 50 number of families owning computer in 1908 = 50 * 130 / 100 = 65 number of families in 1908 = 105 the percentage = 65 / 105 * 100 = 61.90 % . option : a\"" + }, + { + "Answer": 315.00000000000045, + "Options": "a ) 305 , b ) 315 , c ) 345 , d ) 325 , e ) 335", + "Correct": "b", + "Explanation": "let the number be x . then 4 / 15 of 5 / 7 of x - 4 / 9 of 2 / 5 of x = 8 \uf0f3 4 / 21 x - 8 / 45 x = 8 ( 4 / 21 - 8 / 45 ) x = 8 \uf0f3 ( 60 - 56 ) / 315 x = 8 \uf0f3 4 / 315 x = 8 x = ( 8 * 315 ) / 4 = 630 \uf0f3 1 / 2 x = 315 hence required number = 315 answer is b ." + }, + { + "Answer": 33, + "Options": "a ) 33 , b ) 32 , c ) 31 , d ) 30 , e ) 29", + "Correct": "a", + "Explanation": "yes there is a different way of arriving at that answer . . . . u can also use airthmetic progression to get the answer since the first term to be divisble by 3 is 102 . . take that as a . . the starting no and since 198 is the last digit to be divisible by 3 take that as n . . . since the difference is 3 take that as d no u have to find what term is 198 take that as nth term the formula for that is n = a + ( n - 1 ) * d 198 = 102 + ( n - 1 ) * 3 from this u get n = 33" + }, + { + "Answer": 17, + "Options": "a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19", + "Correct": "c", + "Explanation": "let p be the number of participants . pc 2 = 136 ( p ) ( p - 1 ) = 272 = 17 * 16 p = 17 the answer is c ." + }, + { + "Answer": 9, + "Options": "a ) 30 , b ) 18 , c ) 10 , d ) 9 , e ) 7", + "Correct": "d", + "Explanation": "\"( average production for n days ) * n = ( total production for n days ) - - > 40 n = ( total production for n days ) ; ( total production for n days ) + 90 = ( average production for n + 1 days ) * ( n + 1 ) - - > 40 n + 90 = 45 * ( n + 1 ) - - > n = 9 answer : d .\"" + }, + { + "Answer": 720, + "Options": "a ) $ 900 , b ) $ 720 , c ) $ 675 , d ) $ 450 , e ) $ 225", + "Correct": "b", + "Explanation": "to solve this question , it will be best to first express the given ratio using variable multipliers . thus , we have : household expenses : food : miscellaneous = 5 x : 4 x : x since we are told that the total amount allocated to these categories is $ 1,800 we can set up the equation : 5 x + 4 x + x = 1,800 10 x = 1,800 x = 180 thus , the total amount allocated to food is 4 x 180 = $ 720 . answer b ." + }, + { + "Answer": 2080, + "Options": "a ) 2080 , b ) 1700 , c ) 2350 , d ) 2500 , e ) 8000", + "Correct": "a", + "Explanation": "\"16 pounds and 4 ounces = 16 * 16 + 4 = 260 ounces . 13 tons = 13 * 2600 pound = 13 * 2600 * 16 ounces . hence the answer is ( 13 * 2600 * 16 ) / 260 = 2080 . answer : a .\"" + }, + { + "Answer": 0.7333333333333333, + "Options": "a ) 5 / 9 , b ) 3 / 15 , c ) 23 / 30 , d ) 22 / 30 , e ) 53 / 90", + "Correct": "d", + "Explanation": "let the total students be 30 given 2 / 5 of the students are females = 12 then males = 3 / 5 = 18 5 / 6 of the females are on honor roll = 10 males on the honor roll = 2 / 3 = 12 total students on honor roll = 12 + 10 = 22 fraction = 22 / 30 d" + }, + { + "Answer": 105.6, + "Options": "a ) 68 , b ) 70.4 , c ) 86 , d ) 105.6 , e ) 108", + "Correct": "d", + "Explanation": "\"x is 20 % greater than 88 means x is 1.2 times 88 ( in other words 88 + 20 / 100 * 88 = 1.2 * 88 ) therefore , x = 1.2 * 88 = 105.6 answer : d\"" + }, + { + "Answer": 14, + "Options": "a ) 12 , b ) 13 , c ) 14 , d ) 17 , e ) 23", + "Correct": "c", + "Explanation": "\"the range of a set of data is the difference between the highest and lowest values in the set in this set , highest number = 31 lowest number = 17 range = highest - lowest = 31 - 17 = 14 option c\"" + }, + { + "Answer": 4079, + "Options": "a ) 2988 , b ) 2776 , c ) 4079 , d ) 2871 , e ) 881", + "Correct": "c", + "Explanation": "x * ( 95 / 100 ) * ( 85 / 100 ) = 3294 x = 4079 answer : c" + }, + { + "Answer": 700, + "Options": "a ) 237 , b ) 287 , c ) 197 , d ) 287 , e ) 700", + "Correct": "e", + "Explanation": "\"explanation : let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 350 ) = 2 + 2 ( extra ) = > 2 x - 700 = x = > x = 700 . answer : e\"" + }, + { + "Answer": 1010, + "Options": "a ) 10 , b ) 11 , c ) 1001 , d ) 1011 , e ) 10001", + "Correct": "c", + "Explanation": "binary divison can provide a quick answer if you are comfortable with it . as option e is the biggest binary number we try with it first : 100010000 / 1001 = 10000 1000100000 / 1001 = 100000 so answer is option is c" + }, + { + "Answer": 4, + "Options": "a ) 2 , b ) 5 , c ) 4 , d ) 24 , e ) 35", + "Correct": "c", + "Explanation": "\"ab = 1 + 2 ( a + b ) 7 a = 1 + 2 a + 14 5 a = 15 a = 3 b - a = 7 - 3 = 4 c is the answer\"" + }, + { + "Answer": 0.25, + "Options": "a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 6 , e ) 1 / 12", + "Correct": "c", + "Explanation": "6 a / 100 = 12 a = 200 12 b / 100 = 6 b = 50 c = b / a = 50 / 200 = 1 / 4 the answer is c ." + }, + { + "Answer": 2.25, + "Options": "a ) 5 / 2 , b ) 8 / 3 , c ) 9 / 4 , d ) 10 / 3 , e ) 12 / 5", + "Correct": "c", + "Explanation": "\"the time it takes printer x is 15 hours . the combined rate of y and z is 1 / 10 + 1 / 20 = 3 / 20 the time it takes y and z is 20 / 3 the ratio of times is 15 / ( 20 / 3 ) = 3 * 15 / 20 = 9 / 4 the answer is c .\"" + }, + { + "Answer": 665, + "Options": "a ) 665 , b ) 127 , c ) 272 , d ) 287 , e ) 227", + "Correct": "a", + "Explanation": "\"let the total score be x . ( x + 92 - 85 ) / 8 = 84 . so , x + 7 = 672 = > x = 665 . answer : a\"" + }, + { + "Answer": 22, + "Options": "a ) 16 , b ) 18 , c ) 20 , d ) 22 , e ) 24", + "Correct": "d", + "Explanation": "\"( x + 3 ) ^ 2 / ( 3 x + 65 ) = 2 ( x + 3 ) ^ 2 = 2 ( 3 x + 65 ) x ^ 2 + 6 x + 9 = 6 x + 130 x ^ 2 - 121 = 0 ( x - 11 ) ( x + 11 ) = 0 x = 11 or x = - 11 the answer is d .\"" + }, + { + "Answer": 17, + "Options": "a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 17", + "Correct": "e", + "Explanation": "\"four wheeler = 17 * 4 = 68 ( max ) 2 wheel = 1 so no of 4 wheeler = 17 answer : e\"" + }, + { + "Answer": 10, + "Options": "a ) 30 , b ) 25 , c ) 15 , d ) 10 , e ) 5", + "Correct": "d", + "Explanation": "\"because the cord was extended to its full length at all items , the dog ran along a semi - circular path , from north to south . the circumference of a full circle is 2 * pi * r , but since we only care about the length of half the circle , the semi - circle path is pi * r . e = pi * r = 30 . round pi = 3 , then r = 10 . chord is about 10 feet long . d\"" + }, + { + "Answer": 10000, + "Options": "a ) $ 4096 , b ) $ 5904 , c ) $ 7892 , d ) $ 10052 , e ) $ 20736", + "Correct": "d", + "Explanation": "1 st - 20000 . 2 nd - 0.7 * 20000 = 14000 3 rd - 0.7 * 14000 = 9800 range = 20000 - 9800 = 10200 . answer : d ." + }, + { + "Answer": 6, + "Options": "a ) 5 % , b ) 6 % , c ) 8 % , d ) 10 % , e ) none of these", + "Correct": "b", + "Explanation": "si = 27160 - ( principal amount ) = 27160 - 22000 = 5160 . now , ( 10000 * 5 * r / 100 ) + ( 12000 * 3 * r / 100 ) = 5160 . 500 r + 360 r = 5160 . . . . . rate = 6 % . answer : b" + }, + { + "Answer": 14.999999999999979, + "Options": "a ) 11 , b ) 15 , c ) 18 , d ) 17 , e ) 19", + "Correct": "b", + "Explanation": "b 15 the number of bees was 15" + }, + { + "Answer": 117, + "Options": "a ) 222 , b ) 117 , c ) 278 , d ) 767 , e ) 298", + "Correct": "b", + "Explanation": "h . c . f of co - prime numbers is 1 . so , l . c . m = \\ inline \\ fn _ jvn \\ frac { 117 } { 1 } = 117 answer : b" + }, + { + "Answer": 1280, + "Options": "a ) 1280 , b ) 1270 , c ) 1260 , d ) 1250 , e ) none", + "Correct": "a", + "Explanation": "solution let x = the number required . a = 720 d = 7392 b = 125 h = 462 then by the conditions of the problem ( x + a ) / b = d / h therefore x = ( bd - ah ) / h restoring the numbers , x = [ ( 125.7392 ) - ( 720.462 ) ] / 462 = 1280 . answer a" + }, + { + "Answer": 551.9230769230769, + "Options": "a ) 500 , b ) 450 , c ) 552 , d ) 600 , e ) 400", + "Correct": "c", + "Explanation": "\"total = 500 ( 25 ) + 600 ( 27 ) number of installments = 52 average = total / number of installments = 552 approximately answer : c\"" + }, + { + "Answer": 48, + "Options": "a ) 20 cs , b ) cs / 2 , c ) 48 cs , d ) ( 2 cs ) / 12 , e ) ( 24 c ) / s", + "Correct": "c", + "Explanation": "\"ans : c solution : simple multiplication s students , c classes , 4 books / month = 48 books a year total number of books = 48 cs\"" + }, + { + "Answer": 9900, + "Options": "a ) 110 , b ) 1,100 , c ) 9,900 , d ) 10,000 , e ) 12,100", + "Correct": "c", + "Explanation": "\"p can take a total of 10 * 11 co - ordinates . for a given p , r can take a total of 9 co - ordinates and q can take a total of 10 co - ordinates . hence , total = 110 * 9 * 10 = 9900 ans : c\"" + }, + { + "Answer": 18, + "Options": "a ) 39 , b ) 18 , c ) 42 , d ) 40.5 , e ) 41.5", + "Correct": "b", + "Explanation": "\"let the average after 16 th inning = x then total run after 16 th inning = 16 x then total run after 17 th inning = 16 x + 50 then average run after 17 th inning = ( 16 x + 50 ) / 17 ( 16 x + 50 ) / 17 = x + 2 = > 16 x + 50 = 17 x + 34 = > x = 16 x = 16 ; average after 17 th inning = 16 + 2 = 18 answer : b\"" + }, + { + "Answer": 0.1, + "Options": "a ) 0.001 , b ) 0.01 , c ) 0.1 , d ) 1 , e ) 0", + "Correct": "c", + "Explanation": "explanation : 0.12 \u00f7 x 2 = 12 = > 0.12 / x 2 = 12 = > x 2 = 0.12 / 12 = 0.01 = > x = 0.1 answer : option c" + }, + { + "Answer": 25, + "Options": "a ) 12.5 % , b ) 20 % , c ) 25 % , d ) 50 % , e ) 100 %", + "Correct": "c", + "Explanation": "\"assume hours worked : 10 hours hourly wage : 10 $ weekly wage : 100 $ after decrease of 20 % in hourly wage would become 8 $ hours worked would have to be 12.5 hours in order to maintain weekly wage of 100 $ % increase in number of hours worked = ( 12.5 - 10 ) / 10 = 0.25 * 100 = 25 % answer is c\"" + }, + { + "Answer": 1.3333333333333333, + "Options": "a ) 0.75 , b ) 0.8 , c ) 1 , d ) 1.33 , e ) 1.75", + "Correct": "d", + "Explanation": "\"say the cost price of 60 pencils was $ 60 ( $ 1 per pencil ) and the selling price of 1 pencil was p . selling at a loss : 60 - 60 p = 20 p - - > p = 3 / 4 . ( cost price ) / ( selling price ) = 1 / ( 3 / 4 ) = 4 / 3 = 1.33 . answer : d .\"" + }, + { + "Answer": 0.04, + "Options": "a ) 2 / 125 , b ) 3 / 125 , c ) c ) 2 / 25 , d ) 3 / 25 , e ) 1 / 25", + "Correct": "e", + "Explanation": "\"p ( playing 2 or more instruments ) = 128 / 800 = 4 / 25 . then , the probability of playing exactly one instrument is given by : p ( playing 1 or more instruments ) - p ( playing 2 or more instruments ) = 1 / 5 - 4 / 25 = 1 / 25 . answer e .\"" + }, + { + "Answer": 76.1904761904762, + "Options": "a ) 8 % , b ) 15 % , c ) 45 % , d ) 52 % , e ) 76 %", + "Correct": "e", + "Explanation": "\"solution : this is a percent decrease problem . we will use the formula : percent change = ( new \u2013 old ) / old x 100 to calculate the final answer . we first set up the ratios of royalties to sales . the first ratio will be for the first 20 million in sales , and the second ratio will be for the next 108 million in sales . because all of the sales are in millions , we do not have to express all the trailing zeros in our ratios . first 20 million royalties / sales = 7 / 20 next 108 million royalties / sales = 9 / 108 = 1 / 12 because each ratio is not an easy number to use , we can simplify each one by multiplying each by the lcm of the two denominators , which is 60 . keep in mind that we are able to do this only because our answer choices are expressed in percents . first 20 million royalties / sales = ( 7 / 20 ) x 60 = 21 next 108 million royalties / sales = 9 / 108 = ( 1 / 12 ) x 60 = 5 we can plug 9 and 5 into our percent change formula : ( new \u2013 old ) / old x 100 [ ( 5 \u2013 21 ) / 21 ] x 100 - 1600 / 21 x 100 at this point we can stop and consider the answer choices . since we know that 1600 / 21 is just a bit less than \u00bd , we know that - 1600 / 21 x 100 is about a 76 % decrease . answer e .\"" + }, + { + "Answer": 0.012345679012345678, + "Options": "a ) 0.0123 , b ) 0.0625 , c ) 0.16 , d ) 0.25 , e ) 0.5", + "Correct": "a", + "Explanation": "\"( 1 / 9 ) \u00b2 = ( 1 / 9 ) ( 1 / 9 ) = 1 / 81 approach # 1 : use long division to divide 81 into 1 to get 1 / 81 = 0.0123 a\"" + }, + { + "Answer": 16, + "Options": "a ) 1 , b ) 4 , c ) 9 , d ) 13 , e ) 16", + "Correct": "e", + "Explanation": "\"number of cups flour needed for 3 ounces of butter = 4 number of cups flour needed for 1 ounce of butter = 4 / 3 number of cups flour needed for 12 ounces of butter = 4 / 3 * 12 = 16 answer e\"" + }, + { + "Answer": 96, + "Options": "a ) a ) 78 , b ) b ) 82 , c ) c ) 96 , d ) d ) 91 , e ) e ) 85", + "Correct": "c", + "Explanation": "\"correct avg marks = 100 + ( 10 - 50 ) / 10 avg = 100 - 4 = 96 answer is c\"" + }, + { + "Answer": 19.999999999999996, + "Options": "a ) 25 % , b ) 20 % , c ) 16.67 % , d ) 33.33 % , e ) none of these", + "Correct": "b", + "Explanation": "\"explanation : let us assume before increase the petrol will be rs . 100 . after increase it will be rs ( 100 + 25 ) i . e 125 . now , his consumption should be reduced to : - = 125 \u2212 100125 \u2217 100 . hence , the consumption should be reduced to 20 % . answer : b\"" + }, + { + "Answer": 45, + "Options": "a ) 10 , b ) 30 , c ) 45 , d ) 60 , e ) 90", + "Correct": "c", + "Explanation": "\"10 players are there . two players play one game with one another . so 10 c 2 = 10 * 9 / 2 = 45 so option c is correct\"" + }, + { + "Answer": 32, + "Options": "a ) 20 , b ) 10 , c ) 32 , d ) 40 , e ) 5", + "Correct": "c", + "Explanation": "\"arithmetic mean expression for p and q : ( p + q ) / 2 = 10 ; p + q = 20 - - - - eq 1 arithmetic mean expression for q and r : ( q + r ) / 2 = 20 ; q + r = 52 - - - - eq 2 subtracting eq 1 from eq 2 we get : r - p = 32 hence , the correct answer is c\"" + }, + { + "Answer": 19.999999999999996, + "Options": "a ) 8 , b ) 15 , c ) 20 , d ) 27 , e ) 39", + "Correct": "c", + "Explanation": "\"4 ^ 3 + 5 ^ 3 = 189 the number is 4 * 5 = 20 c\"" + }, + { + "Answer": 99.99999999999999, + "Options": "a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500", + "Correct": "a", + "Explanation": "\"0.037 * 10 ^ 5 can be written as 3600 74000 * 10 ^ ( - 3 ) can be written as 36 required = 3600 / 36 = 100 answer : a\"" + }, + { + "Answer": 144, + "Options": "a ) $ 130 , b ) $ 136 , c ) $ 144 , d ) $ 150 , e ) $ 160", + "Correct": "c", + "Explanation": "\"0.8 * ( 1.2 * 150 ) = $ 144 the answer is c .\"" + }, + { + "Answer": 9, + "Options": "a ) 7.9 s , b ) 2.5 s , c ) 7.5 s , d ) 9 s , e ) 7.4 s", + "Correct": "d", + "Explanation": "\"explanation : 90 km / hr = 90 * 5 / 18 = 25 m / s speed = distance / time ; v = d / t 25 = 225 / t t = 9 s answer : d\"" + }, + { + "Answer": 1200, + "Options": "a ) 1000 , b ) 1200 , c ) 1400 , d ) 1600 , e ) 1800", + "Correct": "b", + "Explanation": "\"let x be the number of eggs that were laid . ( 2 / 5 ) ( 3 / 4 ) ( 1 / 3 ) x = 120 ( 6 / 60 ) x = 120 x = 1200 the answer is b .\"" + }, + { + "Answer": 0.25, + "Options": "a ) 1 / 7 , b ) 1 / 5 , c ) 1 / 4 , d ) 1 / 3 , e ) 3 / 7", + "Correct": "c", + "Explanation": "\"1 lbs of raisin = $ 1 4 lbs of raisin = $ 4 1 lbs of nuts = $ 3 4 lbs of nuts = $ 12 total value of mixture = 12 + 4 = 16 fraction of the value of raisin = 4 / 16 = 1 / 4 ans : c\"" + }, + { + "Answer": 1, + "Options": "a ) 8 , b ) 5 , c ) 1 , d ) 3 , e ) 4", + "Correct": "c", + "Explanation": "\"6 * 15 * 11 = ( \u221a ( 6 + 2 ) ( 15 + 3 ) ) / ( 11 + 1 ) = ( \u221a 8 * 18 ) / 12 = ( \u221a 144 ) / 12 = 12 / 124 = 1 . answer is c\"" + }, + { + "Answer": 15, + "Options": "a ) 5 , b ) 8 , c ) 10 , d ) 15 , e ) 20", + "Correct": "d", + "Explanation": "explanation : let number of keepers be x . then , total number of feet = 2 x 50 + 4 x 45 + 4 x 8 + 2 x = 2 x + 312 . total number of heads = 50 + 45 + 8 + x = 103 + x . therefore ( 2 x + 312 ) = ( 103 + x ) + 224 or x = 15 . answer : d" + }, + { + "Answer": 1, + "Options": "a ) 6 , b ) 5 , c ) 1 , d ) 3 , e ) 2", + "Correct": "c", + "Explanation": "n + 1 = 6 a + 4 i . e . n + 1 = 10 , 16 , 22 , 28 , . . . etc . i . e . n = 9 , 15 , 21 , 27 , . . . etc . when n is divided by 2 remainder is always 1 answer : c" + }, + { + "Answer": 0.75, + "Options": "a ) 3 , b ) 1 , c ) 3 / 4 , d ) - 1 / 3 , e ) - 3", + "Correct": "c", + "Explanation": "the expression 9 / ( 5 + 3 / x ) = 1 should have been equal to something . if 9 / ( 5 + 3 / x ) = 1 = > 9 x / ( 5 x + 3 ) = 1 = > 9 x = 5 x + 3 = > 4 x = 3 = > x = 3 / 4 correct option : c" + }, + { + "Answer": 5400, + "Options": "a ) 54888 , b ) 2777 , c ) 5400 , d ) 1278 , e ) 2881", + "Correct": "c", + "Explanation": "\"100 x + 400 = 12 ( x \u2013 5 ) x = 50 100 * 50 + 400 = 5400 answer : c\"" + }, + { + "Answer": 254.54545454545453, + "Options": "a ) s . 254 , b ) s . 284 , c ) s . 290 , d ) s . 304 , e ) s . 380", + "Correct": "a", + "Explanation": "\"let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 560 but x = 120 % of y = 120 y / 100 = 12 y / 10 \u2234 12 y / 10 + y = 560 \u21d2 y [ 12 / 10 + 1 ] = 560 \u21d2 22 y / 10 = 560 \u21d2 22 y = 5600 \u21d2 y = 5600 / 22 = rs . 254 ( approx ) a )\"" + }, + { + "Answer": 406, + "Options": "a ) 426 , b ) 406 , c ) 401 , d ) 409 , e ) 405", + "Correct": "b", + "Explanation": "\"solution we know that ( 1 + 2 + 3 + . . . . . + 28 ) = n ( n + 1 ) / 2 therefore ( 1 + 2 + 3 + . . . . + 28 ) = ( 28 \u00d7 29 / 2 ) = 406 . answer b\"" + }, + { + "Answer": 35000, + "Options": "a ) 28000 , b ) 30000 , c ) 32000 , d ) 35000 , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : suppose b ' s investment = x . then a ' s investment = 3 x suppose bs period of investment = y , then a ' s period of investment = 2 y a : b = 3 x * 2 y : xy = 6 : 1 total profit * 1 / 7 = 5000 = > total profit = 5000 * 7 = 35000 . answer : option d\"" + }, + { + "Answer": 3, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 7", + "Correct": "d", + "Explanation": "mean = ( x + x + 2 + x + 4 + x + 7 + x + 22 ) / 5 = ( 5 x + 35 ) / 5 = x + 7 median = x + 4 thus mean - median = x + 7 - ( x + 4 ) = 3 answer = d" + }, + { + "Answer": 765.0000000000001, + "Options": "a ) 392 , b ) 229 , c ) 765 , d ) 493 , e ) 540", + "Correct": "c", + "Explanation": "\"c 765 ? = 5100 * ( 2 / 5 ) * ( 1 / 2 ) * ( 3 / 4 ) = 765\"" + }, + { + "Answer": 999.9999999999999, + "Options": "a ) 1000 , b ) 3889 , c ) 8908 , d ) 3780 , e ) 2709", + "Correct": "a", + "Explanation": "\"1120 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 1000 answer : a\"" + }, + { + "Answer": 16, + "Options": "a ) 10 , b ) 12 , c ) 16 , d ) 18 , e ) 20", + "Correct": "c", + "Explanation": "\"sp = 15 loss = cp 16 loss = cp \u2212 sp = cp \u2212 15 \u21d2 cp 16 = cp \u2212 15 \u21d2 15 cp 16 = 15 \u21d2 cp 16 = 1 \u21d2 cp = 16 c\"" + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10", + "Correct": "a", + "Explanation": "the word red has exactly 3 letters which are all different . therefore the number of words that can be formed = number of permutations of 3 letters taken all at a time . = p ( 3 , 3 ) = 3 ! = 3 x 2 \u00d7 1 = 6 answer : a" + }, + { + "Answer": 48, + "Options": "a ) 24 , b ) 25 , c ) 48 , d ) 50 , e ) none", + "Correct": "c", + "Explanation": "\"answer sum of 100 result = sum of 60 result + sum of 40 result . = 60 x 40 + 40 x 60 = 4800 / 100 correct option : c\"" + }, + { + "Answer": 24, + "Options": "a ) 18 , b ) 92 , c ) 27 , d ) 24 , e ) 19", + "Correct": "d", + "Explanation": "explanation : let the present age of person be x years . then , 4 ( x + 3 ) - 4 ( x - 3 ) = x < = > ( 4 x + 12 ) - ( 4 x - 12 ) = x < = > x = 24 . . answer : d" + }, + { + "Answer": 45, + "Options": "a ) 33 , b ) 54 , c ) 18 , d ) 45 , e ) 01", + "Correct": "d", + "Explanation": "\"explanation : as there is meal for 70 adults and 35 have their meal , the meal left can be catered to 35 adults . now , 70 adults = 90 children 7 adults = 9 children therefore , 35 adults = 45 children hence , the meal can be catered to 45 children . answer : d\"" + }, + { + "Answer": 5, + "Options": "a ) $ 5 , b ) $ 10 , c ) $ 12 , d ) $ 15 , e ) $ 20", + "Correct": "a", + "Explanation": "he lost $ 5 . the lady from the flower shop gave him $ 20 in change , but eventually got $ 20 back . she broke even . the man who got the haircut gave the barber nothing ( except counterfeit money ) but got $ 5 back from the barber . so the barber lost only $ 5 , and gave a free haircut ." + }, + { + "Answer": 0.125, + "Options": "a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 5 , d ) 1 / 6 , e ) 1 / 8", + "Correct": "e", + "Explanation": "\"the fraction of homes which are termite - infested but not collapsing is 3 / 8 * 1 / 3 = 1 / 8 the answer is e .\"" + }, + { + "Answer": 60, + "Options": "a ) 50 , b ) 65 , c ) 70 , d ) 61 , e ) 60", + "Correct": "e", + "Explanation": "\"let the actual distance traveled be x km . then , x / 12 = ( x + 20 ) / 16 x - 60 = > x = 60 km . answer : e\"" + }, + { + "Answer": 27, + "Options": "a ) 14 years , b ) 18 years , c ) 20 years , d ) 27 years , e ) 16 years", + "Correct": "d", + "Explanation": "\"let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . ( x + 29 ) + 2 = 2 ( x + 2 ) x + 31 = 2 x + 4 x = 27 . answer : d\"" + }, + { + "Answer": 90, + "Options": "a ) 60 , b ) 75 , c ) 90 , d ) 100 , e ) 110", + "Correct": "c", + "Explanation": "13 th result = sum of 25 results - sum of 24 results = 18 * 25 - 12 * 10 - 12 * 20 = 450 - 120 - 240 = 90 answer is c" + }, + { + "Answer": 80, + "Options": "a ) 90 , b ) 82 , c ) 80 , d ) 45 , e ) 36", + "Correct": "c", + "Explanation": "three - digit integers greater than 700 : 701 to 999 , inclusive . possible values for hundreds - digit - - > 7 , 89 possible values for tens - digit and ones - digit - - > 0 , 1 , 23 , 45 , 67 , 89 when hundreds - digit and tens - digit are the same : ( 3 x 1 x 10 ) - 3 = 27 - - - > we minus three to exclude 777 , 888 and 999 when hundreds - digit and ones - digit are the same : ( 3 x 10 x 1 ) - 3 = 27 - - - > we minus three to exclude 777 , 888 and 999 when tens - digit and hundreds - digit are the same : [ ( 3 x 10 x 1 ) - 3 ] - 1 = 26 - - - > we minus three to exclude 777 , 888 and 999 ; we minus one to exclude 700 t = 27 + 27 + 26 = 80 answer : c" + }, + { + "Answer": 30, + "Options": "a ) 30 , 10 , b ) 25 , 5 , c ) 29 , 9 , d ) 50 , 30 , e ) 20,10", + "Correct": "a", + "Explanation": "\"let their ages be x and ( x + 20 ) years . then , 5 ( x - 5 ) = ( x + 20 - 5 ) = > 4 x = 40 = > x = 10 their present ages are 30 years and 10 year . answer : a\"" + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 10 , c ) 15 , d ) 25 , e ) 35", + "Correct": "a", + "Explanation": "\"total applicants = 40 political science = 15 and non political science = 40 - 15 = 25 gpa > 3.0 = 20 and gpa < = 3.0 = 20 10 non political science students had gpa < = 3.0 - - > 15 non political science students had gpa > 3.0 gpa > 3.0 in political science = total - ( gpa > 3.0 in non political science ) w = 20 - 15 = 5 answer : a\"" + }, + { + "Answer": 0.3, + "Options": "a ) $ 4 , b ) $ 0.3 , c ) $ 1 , d ) $ 3 , e ) $ 1.65", + "Correct": "b", + "Explanation": "lets assume price of coffee in june = 100 x price of green tea in june = 100 x price of coffee in july = 200 x ( because of 100 % increase in price ) price of green tea in july = 30 x ( because of 70 % decrease in price ) price of 1.5 pound of coffee 1.5 pound of green tea in july will be = 300 x + 45 x = 345 x as per question 345 x = 3.45 $ x = 0.01 s so the price of tea in july = 30 x = 30 x 0.01 = 0.3 $ / pound answer b" + }, + { + "Answer": 71, + "Options": "a ) 69 , b ) 72 , c ) 75 , d ) 71 , e ) none of them", + "Correct": "d", + "Explanation": "\"total weight increased = ( 1.8 x 10 ) kg = 18 kg . : . weight of the new man = ( 53 + 18 ) kg = 71 kg . answer is d\"" + }, + { + "Answer": 769.9999999999994, + "Options": "a ) $ 770 , b ) $ 660 , c ) $ 700 , d ) $ 1100 , e ) $ 840", + "Correct": "a", + "Explanation": "let the original purchase price be x so original selling price at 10 % profit = 1.1 x if product is purchased at 10 % less of original = 0.9 x profit of 30 % on this price = 1.3 ( 0.9 x ) he would have received $ 49 more in second scenario = > 1.3 ( 0.9 x ) - 1.1 x = 49 = > 0.07 x = 49 = > x = $ 700 original purchase price = $ 700 hence , original selling price ( at 10 % of profit ) = 1.1 ( 700 ) = $ 770 option a" + }, + { + "Answer": 85, + "Options": "a ) 81 , b ) 82 , c ) 85 , d ) 90 , e ) 95", + "Correct": "c", + "Explanation": "since the numbers are co - prime , they contain only 1 as the common factor . also , the given two products have the middle number in common . so , middle number = h . c . f of 551 and 1073 = 29 ; first number = 551 / 29 = 19 third number = 1073 / 29 = 37 . required sum = 19 + 29 + 37 = 85 . answer : c" + }, + { + "Answer": 8195, + "Options": "a ) 2480 , b ) 3490 , c ) 6785 , d ) 8235 , e ) 9255", + "Correct": "d", + "Explanation": "\"you ' ll never need a formula for the sums of squares on the actual gmat . you do n ' t need to use that formula here , though it ' s not all that straightforward to solve without one . two different approaches : 16 ^ 2 + 17 ^ 2 + 18 ^ 2 + . . . + 30 ^ 2 = ( 15 + 1 ) ^ 2 + ( 15 + 2 ) ^ 2 + ( 15 + 3 ) ^ 2 + . . . + ( 15 + 15 ) ^ 2 now we can expand each square ; they are all in the ( x + y ) ^ 2 = x ^ 2 + 2 xy + y ^ 2 pattern . = ( 15 ^ 2 + 2 * 15 + 1 ^ 2 ) + ( 15 ^ 2 + 4 * 15 + 2 ^ 2 ) + ( 15 ^ 2 + 6 * 15 + 3 ^ 2 ) + . . . + ( 15 ^ 2 + 30 * 15 + 15 ^ 2 ) now we have fifteen 15 ^ 2 terms , so adding these gives 15 * 15 ^ 2 = 15 ^ 3 = 3375 . we also have the entire sum 1 ^ 2 + 2 ^ 2 + . . . + 15 ^ 2 , which we know is equal to 1240 . finally adding the middle terms , we have : 2 * 15 + 4 * 15 + 6 * 15 + . . . + 30 * 15 = 15 ( 2 + 4 + 6 + . . . . + 30 ) = 15 * 2 * ( 1 + 2 + 3 + . . . + 15 ) = 15 * 2 * 8 * 15 = 3600 so the sum must be 3375 + 1240 + 3600 = 8215 alternatively , we can use a different factoring pattern . we want to find the value of 30 ^ 2 + 29 ^ 2 + . . . + 17 ^ 2 + 16 ^ 2 . well if we subtract 15 ^ 2 + 14 ^ 2 + . . . . + 2 ^ 2 + 1 ^ 2 from this , the answer will be 1240 less than what we want to find . so if we can find the value of 30 ^ 2 + 29 ^ 2 + . . . + 17 ^ 2 + 16 ^ 2 - ( 15 ^ 2 + 14 ^ 2 + . . . . + 2 ^ 2 + 1 ^ 2 ) then we can add 1240 to get the answer . now grouping the terms above to get differences of squares , we have = ( 30 ^ 2 - 15 ^ 2 ) + ( 29 ^ 2 - 14 ^ 2 ) + . . . + ( 16 ^ 2 - 1 ^ 2 ) and factoring each of these using x ^ 2 - y ^ 2 = ( x + y ) ( x - y ) , we have = 45 * 15 + 43 * 15 + 41 * 15 + . . . + 17 * 15 = 15 ( 45 + 43 + 41 + . . . + 17 ) in brackets we have an equally spaced sum with fifteen terms , which we can evaluate using the familiar formula . so the above equals 15 * 15 * 62 / 2 = 6975 and adding back the 1260 , we get the answer of 8235 . ( ans d )\"" + }, + { + "Answer": 2, + "Options": "a ) 3 , b ) 2 , c ) 1 , d ) 0 , e ) 5", + "Correct": "b", + "Explanation": "\"explanation : let n = 4 q + 3 . then 2 n = 8 q + 6 = 4 ( 2 q + 1 ) + 2 . thus , when 2 n is divided by 4 , the remainder is 2 . answer : b\"" + }, + { + "Answer": 224, + "Options": "a ) 180 , b ) 130 , c ) 140 , d ) 160 , e ) 224", + "Correct": "e", + "Explanation": "\"white : yellow = x : ( x + 70 ) = 8 : 13 - - > 13 x = 8 x + 560 - - > x = 112 . the total # of balls originally x + x = 112 + 112 = 224 . answer : e .\"" + }, + { + "Answer": 44, + "Options": "a ) 21 , b ) 24 , c ) 44 , d ) 62 , e ) 70", + "Correct": "c", + "Explanation": "range = the difference between the greatest and the smallest numbers in the sequence . our sequence is odd and is a multiple of 7 . every number in that sequence can be represented like this : 11 * ( 2 n + 1 ) where n is any positive integer . range = 11 * ( 2 m + 1 ) - 11 * ( 2 n + 1 ) = 11 * 2 * ( m - n ) = 22 * ( m - n ) . m , n - any positive integers the answer must be divisible by 22 , which is only 44 . the correct answer is c" + }, + { + "Answer": 19, + "Options": "a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19", + "Correct": "e", + "Explanation": "\"242 + 100 = 342 / 18 = 19 ( remainder ) e\"" + }, + { + "Answer": 92, + "Options": "a ) 52 , b ) 92 , c ) 95 , d ) 88 , e ) 66", + "Correct": "b", + "Explanation": "\"right side = 15 seat left side = 15 - 3 ( 3 few seat in right side ) = 12 seat total = 15 + 12 = 27 people can seat in 27 seat = 27 * 3 = 81 people can seat in last seat = 11 total people can seat = 81 + 11 = 92 answer : b\"" + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10", + "Correct": "a", + "Explanation": "\"to get 40 points as end of season we need another 26 points or more from remaining 15 matches : option a = 6 * 3 + 9 * 1 = 27 hence option a - 6\"" + }, + { + "Answer": 1650, + "Options": "a ) 1245 , b ) 1345 , c ) 1455 , d ) 1577 , e ) 1665", + "Correct": "e", + "Explanation": "\"let the smaller number be x . then larger number = ( x + 1390 ) . x + 1390 = 6 x + 15 5 x = 1375 x = 275 large number = 275 + 1390 = 1665 e\"" + }, + { + "Answer": 10, + "Options": "a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16", + "Correct": "b", + "Explanation": "\"the daily production was raised by 5 units for n days , which has a weighting of 5 n . 5 n = 105 - 55 = 50 n = 10 the answer is b .\"" + }, + { + "Answer": 45, + "Options": "a ) 30 , b ) 36 , c ) 42 , d ) 45 , e ) 50", + "Correct": "d", + "Explanation": "\"10 c 2 = 45 the answer is d .\"" + }, + { + "Answer": 0.5, + "Options": "a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 5 , e ) 5 / 6", + "Correct": "a", + "Explanation": "x + y will be even if x and y are both even or both odd . p ( x and y are both even ) = 2 / 5 * 2 / 4 = 1 / 5 p ( x and y are both odd ) = 3 / 5 * 2 / 4 = 3 / 10 p ( x + y is even ) = 1 / 5 + 3 / 10 = 1 / 2 the answer is a ." + }, + { + "Answer": 4, + "Options": "a ) 4 , b ) 6 , c ) 10 , d ) 8 , e ) 13", + "Correct": "a", + "Explanation": "\"60 / 100 ) * 40 \u00e2 \u20ac \u201c ( 4 / 5 ) * 25 24 - 20 = 4 answer : a\"" + }, + { + "Answer": 6, + "Options": "a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15", + "Correct": "b", + "Explanation": "\"24 x + 21 y = 6 ( 4 x + 3 y ) which will be a minimum positive number when 4 x + 3 y = 1 . 4 ( 1 ) + 3 ( - 1 ) = 1 then 6 ( 4 x + 3 y ) can have a minimum positive value of 6 . the answer is b .\"" + }, + { + "Answer": 5.28, + "Options": "a ) 5.2 minutes , b ) 5.21 minutes , c ) 5.25 minutes , d ) 5.28 minutes , e ) 6 minutes", + "Correct": "d", + "Explanation": "let both of them meet after tt min 4500 m are covered by suresh in 60 m . in tt min he will cover 4500 t 604500 t 60 likewise , in tt min suresh ' s wife will cover 3750 t 603750 t 60 given , 4500 t 60 + 3750 t 60 = 7264500 t 60 + 3750 t 60 = 726 tt = 5.28 minutes option ( d ) is correct" + }, + { + "Answer": 30, + "Options": "a ) 39 , b ) 27 , c ) 30 , d ) 26 , e ) 29", + "Correct": "c", + "Explanation": "\"20 + 24 + 8 * 2 = 60 / 2 = 30 answer : c\"" + }, + { + "Answer": 66, + "Options": "a ) 66 , b ) 18 , c ) 16 , d ) 10 , e ) 15", + "Correct": "a", + "Explanation": "\"20 * 33 / 2 = 5 / 2 * 2 * x = > x = 66 answer : a\"" + }, + { + "Answer": 5000, + "Options": "a ) 13000 , b ) 7000 , c ) 10000 , d ) 5000 , e ) none of these", + "Correct": "d", + "Explanation": "explanation : profit = 5 , 00,000 \u00e2 \u02c6 \u2019 ( 1 , 50,000 + 75,000 ) = rs . 2 , 75,000 . since , such loom contributes equally to sales and manufacturing expenses . but the monthly charges are fixed at rs 75,000 . if one loan breaks down sales and expenses will decrease . new profit : - = > 500000 \u00e3 \u2014 ( 69 / 70 ) \u00e2 \u02c6 \u2019 150000 \u00e3 \u2014 ( 69 / 70 ) \u00e2 \u02c6 \u2019 75000 . = > rs 2 , 70,000 . decrease in profit = > 2 , 75,000 \u00e2 \u02c6 \u2019 2 , 70,000 = > rs . 5,000 . answer : d" + }, + { + "Answer": 127, + "Options": "a ) 124 , b ) 125 , c ) 126 , d ) 127 , e ) 128", + "Correct": "d", + "Explanation": "let the number of breads initial be x you should go in reverse order as left bread is 3 i . e x = ? after 1 st person ate a = x - ( x / 2 ) - ( 1 / 2 ) i . e a = ( 2 x - x ) / 2 - ( 1 / 2 ) i . e a = ( x / 2 ) - ( 1 / 2 ) i . e a = ( 2 x - 2 ) / 4 i . e a = ( x - 1 ) / 2 like wise - - - - after 2 nd person ate b = ( a - 1 ) / 2 like wise - - - - after 3 rd person ate c = ( b - 1 ) / 2 like wise - - - - after 4 th person ate d = ( c - 1 ) / 2 like wise - - - - after 5 th person ate e = ( d - 1 ) / 2 now as after 5 th person ate the value of remaining bread is - - - 3 therefore the value of e = 3 ; now go reverse from botom to top to get the value of x after calcuating value of d = 7 value of c = 15 value of b = 31 value of a = 63 value of x = 127 so the final answer is 127 breads were there answer : d" + }, + { + "Answer": 4.600000000000001, + "Options": "a ) 4.7 , b ) 4.8 , c ) 4.3 , d ) 4.6 , e ) 4.9", + "Correct": "d", + "Explanation": "explanation : in the given question we have taken average of 6 numbers taken 2 at a time which makes 3 numbers . = > 3.95 ( average of 1 st and 2 nd number ) = > 3.85 ( average of 3 rd and 4 th number ) = > 3.4 ( average of 5 th and 6 th number ) 3.95 = ( 3.4 + 3.85 + x ) / 3 x = 4.6 answer d" + }, + { + "Answer": 87, + "Options": "a ) 80 kg , b ) 87 kg , c ) 90 kg , d ) 100 kg , e ) 110 kg", + "Correct": "b", + "Explanation": "\"total weight increased = ( 8 x 4 ) kg = 32 kg . weight of new person = ( 55 + 32 ) kg = 87 kg . b )\"" + }, + { + "Answer": 67, + "Options": "a ) 70 , b ) 75 , c ) 67 , d ) 85 , e ) 90", + "Correct": "c", + "Explanation": "\"explanation : ( 55 + 67 + 76 + 82 + 55 / 5 ) = 67 option c\"" + }, + { + "Answer": 62, + "Options": "a ) 25 , b ) 32 , c ) 36 , d ) 48 , e ) 62", + "Correct": "e", + "Explanation": "make a venn diagram to get a clear picture . look at the diagram : each letter represents only one color . b represents the people who take only art . d represents people who take only art and bio etc . d + f = 20 ( people who take art and one other class ) b = 3 e ( people who take only art is 3 times the people who take bio and calculus ) 17 + 10 + 9 + b + d + e + f = 100 ( total people ) b + b / 3 = 44 b = 33 number of freshmen who take art = 33 + 20 + 9 = 62 answer e" + }, + { + "Answer": 10, + "Options": "a ) 1 : 8 , b ) 1 : 4 , c ) 2 : 1 , d ) 4 : 1 , e ) 10 : 1", + "Correct": "e", + "Explanation": "\"x = 5 y , y = 2 * z x : y , y : z 5 : 1 , 2 : 1 10 : 2 , 2 : 1 so , x : z = 10 : 1 ( e )\"" + }, + { + "Answer": 25, + "Options": "a ) 10 , b ) 25 , c ) 35 , d ) 46 , e ) 50", + "Correct": "b", + "Explanation": "i think we can use double - matrix method and solve using only one variable . our goal is to find the number of hardcover nonfiction books . let that number be x . we are given that all 140 books are either paperback fiction , paperback nonfiction , or hardcover nonfiction . this implies that number of hardcover fiction books is 0 . double - matrix : p = paperback ; h = hardcover ; f = fiction ; nf = nonfiction p h total f 2 x + 40 0 nf x + 20 x total 3 x + 60 x 160 3 x + 60 + x = 160 x = 25 answer ( b . )" + }, + { + "Answer": 400, + "Options": "a ) 400 , b ) 510 , c ) 500 , d ) none of these , e ) 506", + "Correct": "a", + "Explanation": "explanation : 100 / . 25 = 10000 / 25 = 400 option a" + }, + { + "Answer": 144, + "Options": "a ) 147 , b ) 142 , c ) 173 , d ) 144 , e ) 186", + "Correct": "d", + "Explanation": "a prime number ( or a prime ) is a natural number greater than 1 that has no positive divisors other than 1 and itself . here are the first few prime numbers : 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 , 53 , 59 , 61 , 67 , 71 , 73 , 79 , 83 , 89 , 97 , 101 , 103 , 107 , 109 , 113 , 127 , 131 , 137 , 139 , 149 , 151 , 157 , 163 , 167 , 173 , 179 , 181 , 191 , 193 , 197 , 199 , etc . immediate two prime numbers after 70 are - 71 and 73 sum = 71 + 73 = 144 answer - d" + }, + { + "Answer": 16, + "Options": "a ) 24 , b ) 22 , c ) 16 , d ) 18 , e ) 20", + "Correct": "c", + "Explanation": "\"we know that : x > 1 , y > 1 , and x + 3 y < 940 , and it is given that length means no of factors . for any value of x and y , the max no of factors can be obtained only if factor is smallest noall factors are equal . hence , lets start with smallest no 2 . 2 ^ 1 = 2 2 ^ 2 = 4 2 ^ 3 = 8 2 ^ 4 = 16 2 ^ 5 = 32 2 ^ 6 = 64 2 ^ 7 = 128 2 ^ 8 = 256 2 ^ 9 = 512 2 ^ 10 = 1024 ( opps / / it exceeds 1000 , so , x ca n ' t be 2 ^ 10 ) so , max value that x can take is 2 ^ 9 , for which haslength of integeris 9 . now , since x = 512 , x + 3 y < 940 so , 3 y < 428 = = > y < 428 / 3 so , y can take any value which is less than 428 / 3 . and to get the maximum no of factors of smallest integer , we can say y = 2 ^ 7 for 2 ^ 7 has length of integer is 7 . so , combined together : 9 + 7 = 16 . c\"" + }, + { + "Answer": 25, + "Options": "a ) 21 , b ) 22 , c ) 23 , d ) 25 , e ) 28", + "Correct": "d", + "Explanation": "\"let the average age of the whole team be x years . 11 x - ( 28 + 31 ) = 9 ( x - 1 ) = > 11 x - 9 x = 50 = > 2 x = 50 = > x = 25 . so , average age of the team is 25 years . d\"" + }, + { + "Answer": 161, + "Options": "a ) $ 120 , b ) $ 135 , c ) $ 161 , d ) $ 165 , e ) $ 192", + "Correct": "c", + "Explanation": "\"let the charge for first hour = x + 35 then charge for each additional hour = x x + 35 + 4 x = 350 = > 5 x = 315 = > x = 63 total charge for patient for 3 hours of therapy = x + 35 + x = 2 x + 35 = 161 $ answer c\"" + }, + { + "Answer": 85, + "Options": "a ) 75 . , b ) 85 . , c ) 90 . , d ) 94 . , e ) 100 .", + "Correct": "b", + "Explanation": "edit : given ( x 1 + x 2 . . . + x 6 ) / 6 = 80 ( x 1 + x 2 . . . + x 6 ) = 480 - - > eq 1 . now given avg length of one third ropes is 70 . that means out 6 / 3 = 2 ropes . let the avg length of two ropes be ( x 1 + x 2 ) / 2 = 70 . ( x 1 + x 2 ) = 140 . - - > eq 2 . now we are asked to find the average of the remaining i . e . ( x 3 + x 4 + x 5 + x 6 ) substitute eq 2 in eq 1 then we get 140 + x 3 + x 4 + x 5 + x 6 = 480 = > x 3 + x 4 + x 5 + x 6 = 340 now divide 340 by 4 we get 85 . = > ( x 3 + x 4 + x 5 + x 6 ) / 4 = 85 = avg length of remaining ropes . imo correct option is b ." + }, + { + "Answer": 39.599999999999994, + "Options": "a ) 39.6 , b ) 43 , c ) 40 , d ) 38 , e ) 29", + "Correct": "a", + "Explanation": "\"solution : average speed = 2 xy / x + y = 2 * 44 * 36 / 44 + 36 = 39.6 answer : a\"" + }, + { + "Answer": 55053, + "Options": "a ) 55287 , b ) 29887 , c ) 27768 , d ) 55053 , e ) 17191", + "Correct": "d", + "Explanation": "\"explanation : 120 * 456 + 333 = 55053 answer : d\"" + }, + { + "Answer": 8, + "Options": "a ) 1 , b ) 2 , c ) 4 , d ) 6 , e ) 8", + "Correct": "e", + "Explanation": "\"( 71 ) ( 73 ) = ( 72 - 1 ) ( 72 + 1 ) = 72 ^ 2 - 1 which is 1 less than a multiple of 9 . then the remainder will be 8 . the answer is e .\"" + }, + { + "Answer": 317, + "Options": "a ) 156 , b ) 162 , c ) 317 , d ) 324 , e ) 325", + "Correct": "c", + "Explanation": "\"buy as many $ 50 deals as possible . we can by 650 / 50 = 13 two dozen roses , thus total of 13 * 24 = 312 roses . we are left with 680 - 650 = $ 30 . we can buy 30 / 5.3 = ~ 5 roses for that amount . total = 312 + 5 = 317 . answer : c .\"" + }, + { + "Answer": 0.08333333333333334, + "Options": "a ) 0 , b ) 1 / 12 , c ) 2 / 15 , d ) 1 / 10 , e ) 2 / 10", + "Correct": "b", + "Explanation": "\"suppose the water in each jug is l liters cx x ( 1 / 6 ) = l cx = 6 l liters cx is capacity of x cy x ( 2 / 3 ) = l cy = 3 l / 2 liters cy is capacity of y now , y is 3 l / 2 - l empty = l / 2 empty so , we can put only l / 2 water in jug y from jug x jug x ' s remaining water = l - l / 2 = l / 2 fraction of x which contains water = water / cx = ( l / 2 ) / 6 l = 1 / 12 answer will be b\"" + }, + { + "Answer": 250, + "Options": "a ) 250 , b ) 125 , c ) 500 , d ) 100 , e ) 80", + "Correct": "a", + "Explanation": "( shimla + red delicious ) - ( red delicious + fuji ) = 250 shimla - fuji = 250 answer : a" + }, + { + "Answer": 500, + "Options": "a ) $ 490 , b ) $ 500 , c ) $ 510 , d ) $ 520 , e ) $ 530", + "Correct": "b", + "Explanation": "\"s . i for 5 years = $ 815 - $ 590 = $ 225 the s . i . is $ 45 / year s . i . for 2 years = $ 90 principal = $ 590 - $ 90 = $ 500 the answer is b .\"" + }, + { + "Answer": 1.25, + "Options": "a ) 1.05 , b ) 1.25 , c ) 1.45 , d ) 1.55 , e ) 1.65", + "Correct": "b", + "Explanation": "explanation : 1 | 1.5625 ( 1.25 | 1 | - - - - - - - 22 | 56 | 44 | - - - - - - - 245 | 1225 | 1225 | - - - - - - - | x | - - - - - - - 1.5625 = 1.25 . answer is b" + }, + { + "Answer": 4, + "Options": "a ) 20 % , b ) 18 % , c ) 4 % , d ) 12 % , e ) 14 %", + "Correct": "c", + "Explanation": "\"100 * 100 = 10000 80 * 120 = 9600 10000 - - - - - - - 400 100 - - - - - - - ? = 4 % answer : c\"" + }, + { + "Answer": 25, + "Options": "a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 29", + "Correct": "b", + "Explanation": "\"x / 2 y = 3 / 2 = > x = 6 y / 2 = 3 y = > ( 7 x + 4 y ) / ( x - 2 y ) = ( ( 7 * ( 3 y ) ) + 4 y ) / ( 3 y - 2 y ) = > 25 y / y = 25 answer : b\"" + }, + { + "Answer": 14, + "Options": "a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18", + "Correct": "c", + "Explanation": "\"explanation : let number of horses = number of men = x . then , number of legs = 4 x + 2 x ( x / 2 ) = 5 x . so , 5 x = 70 or x = 14 . answer : c\"" + }, + { + "Answer": 0.41666666666666663, + "Options": "a ) 0 , b ) 1 / 12 , c ) 5 / 12 , d ) 7 / 18 , e ) 4 / 9", + "Correct": "c", + "Explanation": "\"total # of outcomes is 6 * 6 = 36 ; favorable outcomes : a - b - - > prime 1 - 1 - - > 2 ; 1 - 2 - - > 3 ; 2 - 1 - - > 3 ; 1 - 4 - - > 5 ; 4 - 1 - - > 5 ; 2 - 3 - - > 5 ; 3 - 2 - - > 5 ; 1 - 6 - - > 7 ; 6 - 1 - - > 7 ; 2 - 5 - - > 7 ; 5 - 2 - - > 7 ; 3 - 4 - - > 7 ; 4 - 3 - - > 7 ; 6 - 5 - - > 11 ; 5 - 6 - - > 11 . total of 15 favorable outcomes t = 15 / 36 . answer : c .\"" + }, + { + "Answer": 6, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 12", + "Correct": "b", + "Explanation": "a + b = 6 ab 1 / a + 1 / b = ( b + a ) / ( ab ) = 6 . the answer is b ." + }, + { + "Answer": 0.3333333333333333, + "Options": "a ) 1 / 6 , b ) 1 / 5 , c ) 1 / 4 , d ) 1 / 3 , e ) 1 / 2", + "Correct": "d", + "Explanation": "\"let x be the fraction of her take - home pay that the worker saved . let p be the monthly pay . 12 xp = 6 ( 1 - x ) p 12 xp = 6 p - 6 xp 18 xp = 6 p x = 1 / 3 the answer is d .\"" + }, + { + "Answer": 95.99999999999999, + "Options": "a ) 124 % , b ) 120 % , c ) 96 % , d ) 80 % , e ) 64 %", + "Correct": "c", + "Explanation": "\"tim = 100 mary ' s income is 60 percent more than tims income ; mary ' s income = t + 0.6 t = 1.6 t = 1.6 * 100 = 160 tims income is 40 percent less than juans income . 100 is 40 % less than juan ' s income 100 = j - 0.4 j 100 = 0.6 j j = 100 / 0.6 = 1000 / 6 what percentage of juans income is marts income ( 160 / ( 1000 / 6 ) ) * 100 = ( 160 * 6 * 100 ) / 1000 = 96 % answer : c\"" + }, + { + "Answer": 7, + "Options": "a ) 7 , b ) 8 , c ) 10 , d ) 11 , e ) 13", + "Correct": "a", + "Explanation": "\"joan starts off with 100 $ . . which is to be tripled every month her monthly payments look like this : 100 , 300 , 900 , 2700 . . . . . . . . . upto 109300 this can be re written as : 100 x 1 , 100 x 3 , 100 x 9 , 100 x 27 . . . . . . 100 x 1093 so we have 1 , 3 , 9 , 27 . . . . . 109300 in gp we know that a = 1 , and r = 3 ( its easy to figure it out by looking at the question , but regardless of it being mentioned in the question we can still compute the value of r using the formula tn = a 3 ^ n - 1 . . . ) therefore to find the sum of n terms of a gp we use this formula : sn = a ( 1 - r ^ n ) / 1 - r using this and plugging in the information we get . . . 1093 = 1 - 3 ^ n / 1 - 3 ; 1 - 3 ^ n / - 2 cross multiplying we get 1093 x - 2 = 1 - 3 ^ n - 2186 = 1 - 3 ^ n - 2187 = - 3 ^ n 2187 = 3 ^ n ( negatives cancel out ) 2187 can also be re written as 3 ^ 7 therefore ; 3 ^ 7 = 3 ^ n thus n = 7 ( a )\"" + }, + { + "Answer": 25, + "Options": "a ) 28 , b ) 27 , c ) 26 , d ) 22 , e ) 25", + "Correct": "e", + "Explanation": "\"explanation : let the average score of the first 18 innings be n 18 n + 97 = 19 ( n + 4 ) = > n = 21 so , average score after 19 th innings = x + 4 = 25 . answer : e\"" + }, + { + "Answer": 1.8000000000000003, + "Options": "a ) 5 / 3 , b ) 7 / 4 , c ) 9 / 5 , d ) 11 / 6 , e ) 13 / 7", + "Correct": "c", + "Explanation": "\"the time it takes printer x is 12 hours . the combined rate of y and z is 1 / 10 + 1 / 20 = 3 / 20 the time it takes y and z is 20 / 3 the ratio of times is 12 / ( 20 / 3 ) = 3 * 12 / 20 = 9 / 5 the answer is c .\"" + }, + { + "Answer": 34, + "Options": "a ) 23 , b ) 34 , c ) 35 , d ) 41 , e ) 44", + "Correct": "b", + "Explanation": "\"let number of years taught by virginia = v number of years taught by adrienne = a number of years taught by dennis = d v + a + d = 75 v = a + 9 = > a = v - 9 v = d - 9 = > a = ( d - 9 ) - 9 = d - 18 d - 9 + d - 18 + d = 96 = > 3 d = 75 + 27 = 102 = > d = 34 answer b\"" + }, + { + "Answer": 80, + "Options": "a ) 68 , b ) 72 , c ) 76 , d ) 80 , e ) 84", + "Correct": "d", + "Explanation": "\"28 liters is 35 % of the capacity c . 28 = 0.35 c c = 28 / 0.35 = 80 liters . the answer is d .\"" + }, + { + "Answer": 10, + "Options": "a ) 10 , b ) 11 , c ) 12 , d ) 15 , e ) 16", + "Correct": "a", + "Explanation": "4 a 3 | 9 8 4 } = = > a + 8 = b = = > b - a = 8 13 b 7 | also , 13 b 7 is divisible by 11 = > ( 7 + 3 ) \u2013 ( b + 1 ) = ( 9 \u2013 b ) ( 9 \u2013 b ) = 0 b = 9 ( b = 9 and a = 1 ) = > ( a + b ) = 10 . answer a" + }, + { + "Answer": 9, + "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12", + "Correct": "b", + "Explanation": "since 19,683 is an odd number , it is not a multiple of 4 . this means that y must equal zero . since x - y = 9 and y = 0 , then x = 9 . the answer is b ." + }, + { + "Answer": 1100, + "Options": "a ) 1000 , b ) 2217 , c ) 1100 , d ) 2777 , e ) 2991", + "Correct": "c", + "Explanation": "\"1232 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 1100 answer : c\"" + }, + { + "Answer": 129, + "Options": "a ) 125 , b ) 127 , c ) 129 , d ) 131 , e ) 141", + "Correct": "c", + "Explanation": "\"explanation : in this type of question , its obvious we need to calculate the hcf , trick is hcf of ( 1428 - 9 ) and ( 2206 - 13 ) = hcf ( 1419 , 2193 ) = 129 option c\"" + }, + { + "Answer": 46.666666666666664, + "Options": "a ) 50.78 kg , b ) 49.32 kg , c ) 46.66 kg , d ) 69.15 kg , e ) 70.89 kg", + "Correct": "c", + "Explanation": "\"total weight of 40 + 20 students = 40 * 50 + 20 * 40 = 2000 + 800 average weight of the class is = 2800 / 60 = 46.66 kg answer is c\"" + }, + { + "Answer": 3, + "Options": "a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15", + "Correct": "a", + "Explanation": "\"d = ( d - r ) / q = ( 15 - 3 ) / 4 = 12 / 4 = 3 a )\"" + }, + { + "Answer": 30, + "Options": "a ) 26 , b ) 30 , c ) 36 , d ) 38 , e ) 40", + "Correct": "b", + "Explanation": "\"at 6 ' o clock , there would be 6 strikes . first strike , then a short interval , the second strike , then a short interval and so on till the 6 th strike . so there would be in all 5 intervals between 6 strikes . similarly , between 8 strikes , there would be 7 intervals . according to the question , the time spent in the strike and the interval is same . at 6 ' o clock , the 6 strikes and the 5 intervals together take 22 sec so each strike and each interval takes 2 secs . at 8 ' o clock , the 8 strikes and 7 intervals will take 2 * ( 8 + 7 ) = 30 secs b\"" + }, + { + "Answer": 1000, + "Options": "a ) 1 , b ) 10 , c ) 121 , d ) 100 , e ) 1000", + "Correct": "e", + "Explanation": "if m and n are whole numbers such that mn = 121 , the value of ( m - 1 ) n + 1 is : a . 1 b . 10 c . 121 d . 1000 sol . - we know that 112 = 121 . putting m = 11 and n = 2 , we get : ( m - 1 ) n + 1 = ( 11 - 1 ) ( 2 + 1 ) = 103 = 1000 . answer : e" + }, + { + "Answer": 19.1, + "Options": "a ) 15.6 , b ) 16.0 , c ) 17.5 , d ) 18.7 , e ) 19.1", + "Correct": "e", + "Explanation": "\"a certain taxi company charges $ 3.50 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ? a . 15.60 b . 16.00 c . 17.50 d . 18.70 e . 19.10 1 / 5 miles = 0.2 miles . the cost of 8 miles long ride would be $ 3.50 for the first 0.2 miles plus ( 8 - 0.2 ) / 0.2 * 0.4 = $ 3.5 + $ 15.6 = $ 18.7 . answer : e .\"" + }, + { + "Answer": 7.5, + "Options": "a ) 7.9 s , b ) 2.5 s , c ) 7.5 s , d ) 7.6 s , e ) 7.4 s", + "Correct": "c", + "Explanation": "\"explanation : 60 km / hr = 60 * 5 / 18 = 16.67 m / s speed = distance / time ; v = d / t 16.67 = 125 / t t = 7.5 s answer : c\"" + }, + { + "Answer": 6, + "Options": "a ) 3 , b ) 1 , c ) 2 , d ) 4 , e ) 6", + "Correct": "e", + "Explanation": "sum of digits = ( 5 + 1 + 7 + x + 3 + 2 + 4 ) = ( 22 + x ) , which must be divisible by 7 . x = 6 . e" + }, + { + "Answer": 184, + "Options": "a ) 130 , b ) 140 , c ) 156 , d ) 184 , e ) 196", + "Correct": "d", + "Explanation": "explanation : lcm of 5 , 6 , 9 and 12 is 180 required number = 180 + 4 = 184 answer : option d" + }, + { + "Answer": 7, + "Options": "a ) 3.5 , b ) 6 , c ) 8 , d ) 7 , e ) 4", + "Correct": "d", + "Explanation": "\"let the number be x . then , 3 ( 2 x + 9 ) = 69 2 x = 14 = > x = 7 answer : d\"" + }, + { + "Answer": 20, + "Options": "a ) 8 , b ) 14 , c ) 10 , d ) 20 , e ) 40", + "Correct": "d", + "Explanation": "n ^ ( n / 2 ) = 20 apply log n / 2 logn = log 20 nlogn = 2 log 20 = log 20 ^ 2 = log 400 logn = log 400 now apply antilog n = 400 / n now n = 20 . answer : d" + }, + { + "Answer": 4, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "d", + "Explanation": "units digit of 87 ^ 76 = 1 because 87 ^ 3 n + 1 has units place as 1 units digit of 14 ^ 87 = 4 because 14 ^ ( some odd no . ) has units place as 4 units digit of 41 ^ 14 = 1 because 41 ^ ( some even no . ) has units place as 1 units digit of 76 ^ 41 = 6 because 76 ^ ( any positive no . ) has units place as 6 so , units digit of the product is = ` ` 4 ` ` ( units digit of 1 * 4 * 1 * 6 ) answer : d" + }, + { + "Answer": 2, + "Options": "a ) 2 , b ) 5 , c ) 1 , d ) 6 , e ) 7", + "Correct": "a", + "Explanation": "the sum of the digits of the number is divisible by 3 , then the number is divisible by 3 . 1 + 8 + 9 + 4 + x = 22 + x least value of x may be 2 therefore 22 + 2 = 24 is divisible by 3 . a" + }, + { + "Answer": 100, + "Options": "a ) 90 % , b ) 99 % , c ) 100 % , d ) 101 % , e ) 110 %", + "Correct": "b", + "Explanation": "\"the total number of employees = n the average salary = x total salary to all emplyoees = xn after the total number of employees = n - 0.1 n = 0.9 n the average salary = x + 10 % of x = 1.1 x total salary to all emplyoees = 0.9 n ( 1.1 x ) total salary after as a % of total salary before w = [ 0.9 n ( 1.1 x ) ] / xn = 0.99 or 99 % = b\"" + }, + { + "Answer": 9.090909090909092, + "Options": "a ) 9.09 , b ) 10 , c ) 11 , d ) 12 , e ) 13", + "Correct": "a", + "Explanation": "let original hourly wage be x and let the no of hours worked be y total wage will be = x * y after the increment the wage will be = 1.1 x now we need to find number of hours worked so that x * y = 1.1 x * z i . e z = x * y / 1.1 x = 1 / 1.1 y % decrease = ( y - 1 / 1.1 y ) / y * 100 = 1 - 1 / 1.1 * 100 = 9.09 % thus my answer is a ." + }, + { + "Answer": 35, + "Options": "a ) 0 , b ) 10 , c ) 20 , d ) 30 , e ) 35", + "Correct": "e", + "Explanation": "\"i also was confused when i was looking forabove number : d as far as i understood , 35 is a factor of ab . in other words , the values of b ( units digits can be 5 or 0 . better to have option for 5 in this case to havebigger result ) . now let ' s try 35 x 1 ( a = 3 , b = 5 respectively we have = 15 ) . but we do n ' t have this number in answer choices , move on . ( avoid even multiples of 2,4 , 6,8 etc ( we will have 0 in units thus making our result 0 ) 35 x 3 = 105 ( a = 0 b = 5 respectively . hey ! that ' s 0 now . 35 x 5 = 175 ( a = 7 , b = 5 respectively . increasing trend , we have 35 now ) . this is the greatest possible value of b x a . imo e .\"" + }, + { + "Answer": 12, + "Options": "a ) 15 , b ) 12 , c ) 18 , d ) 10 , e ) 14", + "Correct": "b", + "Explanation": "6 x - 3 y = 3 * ( 2 x - y ) = 3 * 4 = 12 answer : b" + }, + { + "Answer": 18.444444444444443, + "Options": "a ) 18.44 , b ) 18.48 , c ) 18.42 , d ) 18.49 , e ) 18.41", + "Correct": "a", + "Explanation": "first we make the denominator 200 . i . e . , we are introducing an error of 11 which is 11189 = 11711189 = 117 th of the denominator . now 3486200 = 17.433486200 = 17.43 but this answer is less than actual answer . so we have to increase it by 1 / 17 th part of it . 117 \u00d7 17.43 \u2243 1117 \u00d7 17.43 \u2243 1 so final answer = 17.43 + 1 = 18.43 actual answer = 18.44 answer : a" + }, + { + "Answer": 7500, + "Options": "a ) $ 8500 , b ) $ 9500 , c ) $ 7000 , d ) $ 7500 , e ) $ 6500", + "Correct": "d", + "Explanation": "\"explanatory answer let the profit made during the year be $ 3 x therefore , $ x would have been shared equally and the remaining $ 2 x would have been shared in the ratio 6 : 4 . i . e . , 60 % of 2 x would go to mary and 40 % of 2 x would go to mike . hence , mary would get ( 60 - 40 ) % of 2 x more than mike or 20 % of 2 x = $ 1000 i . e . , ( 20 / 100 ) * 2 x = 1000 or 2 x = 5000 . hence , the profit made by the company during the year $ 3 x = $ 7500 . answer : d\"" + }, + { + "Answer": 50, + "Options": "a ) 45 % , b ) 48 % , c ) 50 % , d ) 58 % , e ) 65 %", + "Correct": "c", + "Explanation": "\"when the storm deposited 120 billion gallons , volume of water in the reservoir = 200 + 120 = 320 billion gallons if this is only 80 % of the capacity of the reservoir , the total capacity of the reservoir = 320 / 0.8 = 400 billion gallons therefore percentage of reservoir that was full before the storm = ( 200 / 400 ) * 100 = 50 % option c\"" + }, + { + "Answer": 33, + "Options": "a ) 480 , b ) 239 , c ) 270 , d ) 282 , e ) 112", + "Correct": "a", + "Explanation": "answer : a" + }, + { + "Answer": 400, + "Options": "a ) rs 200 , b ) rs 300 , c ) rs 400 , d ) rs 500 , e ) rs 600", + "Correct": "c", + "Explanation": "let c = x . then b = x / 2 and a = x / 4 a : b : c = 1 : 2 : 4 . c ' s share rs . [ ( 4 / 7 ) x 700 ) = 400 answer : c" + }, + { + "Answer": 32, + "Options": "a ) 19 , b ) 17 , c ) 32 , d ) 9 , e ) 8", + "Correct": "c", + "Explanation": "explanation : answer will be hcf of ( 150 - 50 , 230 - 5 , 175 - 25 ) hcf of ( 100 , 225 , 150 ) = 32 option c" + }, + { + "Answer": 27, + "Options": "a ) 24 miles , b ) 25 miles , c ) 26 miles , d ) 27 miles , e ) 28 miles", + "Correct": "d", + "Explanation": "the girls ran 27 + 9 = 36 laps . 36 x 3 / 4 = 108 / 4 , which reduces to 27 . the girls ran 27 miles correct answer d" + }, + { + "Answer": 640, + "Options": "a ) 80 , b ) 120 , c ) 160 , d ) 640 , e ) 760", + "Correct": "d", + "Explanation": "\"working inside out , ( 4 \u20ac 5 ) = 2 * 4 * 5 = 40 8 \u20ac 40 = 2 * 8 * 40 = 640 hence , answer is d\"" + }, + { + "Answer": 87111.11111111112, + "Options": "a ) 87111 , b ) 81007 , c ) 81008 , d ) 81066 , e ) 81022", + "Correct": "a", + "Explanation": "\"64000 * 7 / 6 * 7 / 6 = 87111 answer : a\"" + }, + { + "Answer": 44, + "Options": "a ) 36 , b ) 40 , c ) 44 , d ) 48 , e ) 52", + "Correct": "c", + "Explanation": "\"for 40 hrs = 40 * 16 = 640 excess = 752 - 640 = 112 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 112 / 28 = 28 / 7 = 4 total hrs = 40 + 4 = 44 answer c 44\"" + }, + { + "Answer": 62.6, + "Options": "a ) 75 , b ) 62.6 , c ) 87 , d ) 165 , e ) 11", + "Correct": "b", + "Explanation": "explanation : average = ( 72 + 60 + 35 + 62 + 84 ) / 5 = 313 / 5 = 62.6 . answer : b" + }, + { + "Answer": 0.625, + "Options": "a ) 5 / 8 , b ) 7 / 8 , c ) 6 / 8 , d ) 2 / 9 , e ) 1 / 7", + "Correct": "a", + "Explanation": "\"first notice the number of months for which he worked - march to sept i . e . 7 months avg of monthly totals in tips for months other than august = x tips in august = 10 x total tips for all months = 6 * x + 10 x = 16 x tips for august / total tips for all months = 10 x / 16 x = 5 / 8 answer : a\"" + }, + { + "Answer": 1620, + "Options": "a ) 1245 , b ) 1567 , c ) 1678 , d ) 1335 , e ) 1635", + "Correct": "e", + "Explanation": "\"let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 15 5 x = 1350 x = 270 large number = 270 + 1365 = 1635 e\"" + }, + { + "Answer": 7, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "e", + "Explanation": "\"( x + 2 ) \u00d7 40 + x \u00d7 120 + ( x \u2212 2 ) \u00d7 180 / ( x + 2 ) + x + ( x \u2212 2 ) = 100 \u21d2 340 x \u2212 280 / 3 x = 100 \u21d2 40 x = 280 \u21d2 x = 7 answer e\"" + }, + { + "Answer": 13.043478260869565, + "Options": "a ) 13 % , b ) 22.2 % , c ) 20 % , d ) 12.5 % , e ) 11.1 %", + "Correct": "a", + "Explanation": "\"welcome , just post the question and the choices let ' s see , the way i did it was 1 / 6 are clerical out of 3600 so 600 are clerical 600 reduced by 1 / 4 is 1200 * 1 / 4 so it reduced 150 people , so there is 450 clerical people left but since 150 people left , it also reduced from the total of 3600 so there are 3450 people total since 450 clerical left / 3450 people total you get ( a ) 13 % answer : a\"" + }, + { + "Answer": 77, + "Options": "a ) 65 , b ) 77 , c ) 75 , d ) 85 , e ) 90", + "Correct": "b", + "Explanation": "explanation : average = ( 76 + 65 + 82 + 67 + 95 ) / 5 = 385 / 5 = 77 hence average = 77 answer : b" + }, + { + "Answer": 627, + "Options": "a ) 630 , b ) 633 , c ) 150 , d ) 140 , e ) 627", + "Correct": "e", + "Explanation": "lcm = 630 630 - 3 = 627 answer : e" + }, + { + "Answer": 0.625, + "Options": "a ) 4 / 9 , b ) 5 / 4 , c ) 5 / 8 , d ) 5 / 9 , e ) 6 / 9", + "Correct": "c", + "Explanation": "\"income = salary ( s ) + tips = s + s * 5 / 3 = s * 8 / 3 tips = s * 8 / 3 fraction of his income came from tips = ( s * 5 / 3 ) / ( s * 8 / 3 ) = 5 / 8 answer : c\"" + }, + { + "Answer": 36.35, + "Options": "a ) $ 36.35 , b ) $ 26.35 , c ) $ 16.35 , d ) $ 46.35 , e ) $ 56.35", + "Correct": "a", + "Explanation": "$ 50 + $ 20 = $ 70 what they left with plus $ 10 to each $ 8 + $ 15.65 + $ 10 = $ 33.65 what they spent ( gifts are $ 5 + $ 5 ) $ 70 - $ 33.65 = $ 36.35 left correct answer a" + }, + { + "Answer": 5, + "Options": "a ) 3 , b ) 5 , c ) 6 , d ) 11 , e ) 16", + "Correct": "b", + "Explanation": "\"( m - 8 ) ( m - a ) = m ^ 2 - qm - 24 a = - 3 q = 8 + a = 5 = b\"" + }, + { + "Answer": 16, + "Options": "a ) 8 , b ) 16 , c ) 10 , d ) 11 , e ) 12", + "Correct": "b", + "Explanation": "\"let x be the number . always replace ` ` is ' ' with an equal sign ( 1 / 2 ) x + 5 = 13 ( 1 / 2 ) x = 13 - 5 ( 1 / 2 ) x = 8 x = 16 correct answer is b\"" + }, + { + "Answer": 12, + "Options": "a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 15", + "Correct": "c", + "Explanation": "\"d = ( d - r ) / q = ( 109 - 1 ) / 9 = 108 / 9 = 12 c\"" + }, + { + "Answer": 7.5, + "Options": "a ) 4.5 , b ) 5 , c ) 5.6 , d ) 7.5 , e ) 6.5", + "Correct": "d", + "Explanation": "\"if $ x $ is the number , x / 6 * 12 = 15 = > 2 x = 15 = > x = 7.5 d\"" + }, + { + "Answer": 20.000000000000114, + "Options": "a ) $ 13 , b ) $ 15 , c ) $ 20 , d ) $ 28 , e ) $ 48", + "Correct": "c", + "Explanation": "as given aram ' payment is [ 1 ] [ / 2 ] * fine - 4 i . e total fine = 2 * ( sam ' s payment + 4 ) now , as everything looks integer , fine should be able to divide by 4 and 3 . because joe ' s contribution has 1 / 4 of the fine and peter ' s contribution has 1 / 3 of the fine so , that leads me to following : options , aram ' s pay , total fine ( f ) , f / 4 , f / 3 a ) , 13 , 34 , no i . e 34 / 4 , no i . e 34 / 3 b ) , 14 , 38 , no , no c ) , 20 , 48 , yes yes , no need to further go on as we have got f / 4 and f / 3 correct , just for confirmation we go further d ) , 28 , 64 , yes , no e ) , 48 , 104 , yes , no correct answer is c" + }, + { + "Answer": 36.5, + "Options": "a ) 35.2 , b ) 36.1 , c ) 36.2 , d ) 36.4 , e ) none", + "Correct": "d", + "Explanation": "\"solution correct sum = ( 36 x 50 + 43 - 23 ) = 1820 . \u00e2 \u02c6 \u00b4 correct mean = 1820 / 50 = 36.4 . answer d\"" + }, + { + "Answer": 30.333333333333332, + "Options": "a ) 30.33 , b ) 34.44 , c ) 26.1 , d ) 28.0 , e ) 21.0", + "Correct": "a", + "Explanation": "\"explanation : let the two parts be ( 52 - x ) and x . then , 10 ( 52 - x ) + 22 x = 780 = > 12 x = 260 = > x = 21.66 . bigger part = ( 52 - x ) = 30.33 . answer : a ) 30.33\"" + }, + { + "Answer": 2400, + "Options": "a ) 3800 , b ) 3300 , c ) 2400 , d ) 4200 , e ) 1400", + "Correct": "c", + "Explanation": "c $ 2400 let the price of a saree and a shirt be $ x and $ y respectively . then , 2 x + 4 y = 1600 . . . . ( i ) and x + 6 y = 1600 . . . . ( ii ) divide equation ( i ) by 2 , we get the below equation . = > x + 2 y = 800 . - - - ( iii ) now subtract ( iii ) from ( ii ) x + 6 y = 1600 ( - ) x + 2 y = 800 - - - - - - - - - - - - - - - - 4 y = 800 - - - - - - - - - - - - - - - - therefore , y = 200 . now apply value of y in ( iii ) = > x + 2 x 200 = 800 = > x + 400 = 800 therefore x = 400 solving ( i ) and ( ii ) we get x = 400 , y = 200 . cost of 12 shirts = $ ( 12 x 200 ) = $ 2400 ." + }, + { + "Answer": 30, + "Options": "a ) a ) 12 , b ) b ) 15 , c ) c ) 16 , d ) d ) 17 , e ) e ) 30", + "Correct": "e", + "Explanation": "\"d = ( d - r ) / q = ( 271 - 1 ) / 9 = 270 / 9 = 30 e )\"" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "c", + "Explanation": "\"x = ( y / 5 ) - ( 2 / 5 ) , and so y = 5 x + 2 . the slope is 5 . ( n + 15 - n ) / ( m + p - m ) = 5 p = 3 the answer is c .\"" + }, + { + "Answer": 7, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", + "Correct": "a", + "Explanation": "since \u201c connection \u201d between y and 6 is 1 / 1 then lcm ( 6 , y ) = 6 y , which means that 6 and y are co - prime ( they do not share any common factor but 1 ) , because if the had any common factor but 1 then lcm ( 6 , y ) would be less than 6 y . so , we should check how many integers less than 20 are co - prime with 6 , which can be rephrased as how many integers less than 20 are not divisible by 2 or 3 ( 6 = 2 * 3 ) . there are ( 18 - 2 ) / 2 + 1 = 9 multiples of 2 in the range from 0 to 20 , not inclusive ; there are ( 18 - 3 ) / 3 + 1 = 6 multiples of 3 in the range from 0 to 20 , not inclusive ; there are 3 multiples of 6 in the range from 0 to 20 , not inclusive ( 6 , 12 , 18 ) - overlap of the above two sets ; total multiples of 2 or 6 in the range from 0 to 20 , not inclusive is 9 + 6 - 3 = 12 ; total integers in the range from 0 to 20 , not inclusive is 19 ; hence , there are total of 19 - 12 = 7 numbers which have no common factor with 6 other than 1 : 1 , 5 , 7 , 11 , 13 , 17 and 19 . answer : a ." + }, + { + "Answer": 0.3000000000000001, + "Options": "a ) 0.6 , b ) 0.5 , c ) 0.35 , d ) 0.3 , e ) none of them", + "Correct": "d", + "Explanation": "\"given expression = ( 0.8 ) ( power 3 ) - ( 0.5 ) ( power 3 ) / ( 0.8 ) ( power 2 ) + ( 0.8 x 0.5 ) + ( 0.5 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 0.8 - 0.5 ) = 0.30 answer is d .\"" + }, + { + "Answer": 2580, + "Options": "a ) $ 2160 , b ) $ 2370 , c ) $ 2580 , d ) $ 2790 , e ) $ 2950", + "Correct": "c", + "Explanation": "\"let x be the value of the item . 0.07 * ( x - 1000 ) = 110.60 x = 2580 the answer is c .\"" + }, + { + "Answer": 108, + "Options": "a ) 53 , b ) 108 , c ) 77 , d ) 107 , e ) 109", + "Correct": "d", + "Explanation": "explanation : let the present ages of the father and son be 2 x and x years respectively . then , ( 2 x - 18 ) = 3 ( x - 18 ) = > x = 36 required sum = ( 2 x + x ) = 108 years . answer : option d" + }, + { + "Answer": 3.3333333333333335, + "Options": "a ) 2 , b ) 5 / 3 , c ) 3 , d ) 10 / 3 , e ) 14 / 3", + "Correct": "d", + "Explanation": "if x is a prime number , and x - 1 is the median of the set { x - 1 , 3 x + 3 , 2 x - 4 } , then what is the average ( arithmetic mean ) of the set ? a . 2 b . 5 / 3 c . 3 d . 10 / 3 e . 14 / 3 solution : x - 1 is the median of the set , implies if we arrange the set in ascending order , the set would be [ 2 x - 4 , x - 1 , 3 x + 3 ] . this means that : 2 x - 4 < x - 2 < 3 x + 3 solving inequality gives x > - 2 and x < 3 . since x is prime number and the only prime number < 3 is 2 , so put x = 2 . hence set becomes : [ 0 , 1 , 9 ] and avg = 10 / 3 . d" + }, + { + "Answer": 179, + "Options": "a ) 179 , b ) 208 , c ) 210 , d ) 223 , e ) 229", + "Correct": "a", + "Explanation": "\"explanation : total runs scored by the batsman = 60 * 46 = 2760 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2760 \u2013 2552 = 208 runs . let the highest score be x , hence the lowest score = x \u2013 150 x + ( x - 150 ) = 208 2 x = 358 x = 179 runs answer a\"" + }, + { + "Answer": 100, + "Options": "a ) 103 , b ) 102 , c ) 100 , d ) 105 , e ) 106", + "Correct": "c", + "Explanation": "let the number of 50 - rupee notes = x then , the number of 70 - rupee notes = ( 100 \u2013 x ) 50 x + 70 ( 100 \u2013 x ) = 5000 : x = 100 answer : c" + }, + { + "Answer": 1, + "Options": "a ) 3 / 4 , b ) 1 , c ) 4 / 3 , d ) 2 , e ) 7 / 2", + "Correct": "b", + "Explanation": "\"slope = ( y 2 - y 1 ) / ( x 2 - x 1 ) = > k = ( k + 4 ) / ( 4 + 1 ) = > 5 k = k + 4 = > k = 1 ans b it is !\"" + }, + { + "Answer": 25, + "Options": "a ) 20 % , b ) 25 % , c ) 28.5 % , d ) 30 % , e ) 32 %", + "Correct": "b", + "Explanation": "\"1 st year income = i 1 st year savings = s 1 st year expense = e 1 2 nd year income = 1.25 i 2 nd year savings = 2 s ( 100 % increase ) 2 nd year expense = e 2 e 1 + e 2 = 2 e 1 e 2 = e 1 that means expenses are same during both years . with increase of 25 % income the savings increased by 100 % . or s = . 25 i or s = 25 % of income b is the answer\"" + }, + { + "Answer": 1200, + "Options": "a ) 1000 , b ) 1200 , c ) 1500 , d ) 2000 , e ) 1800", + "Correct": "b", + "Explanation": "solution : passed in none = 5 % passed in all = 5 % passed in four = 20 % 0 f 90 % = 18 % passed in three = 24.5 % passed in three = ( 100 - 5 - 5 - 22.5 - 24.5 - 18 ) = 25 % . but given 300 students passed in three . hence , 25 % = 300 . so , 100 % = 1200 . 1200 students must have appeared . answer : option b" + }, + { + "Answer": 24, + "Options": "a ) 22 , b ) 24 , c ) 28 , d ) 32 , e ) 44", + "Correct": "b", + "Explanation": "g ( z ) = 4 ^ 11 = 2 ^ 22 . so we have to find a product with atleast 22 2 ' s in it . in option 1 22 the total no of 2 ' s = [ 22 / 2 ] + [ 22 / 4 ] + [ 22 / 8 ] + [ 22 / 16 ] = 11 + 5 + 2 + 1 = 19 in option 2 24 the total no of 2 ' s = [ 24 / 2 ] + [ 24 / 4 ] + [ 24 / 8 ] + [ 24 / 16 ] = 12 + 6 + 3 + 1 = 22 . hence b" + }, + { + "Answer": 2, + "Options": "a ) 16 . , b ) 8 . , c ) 7 . , d ) 2 . , e ) - 2 .", + "Correct": "d", + "Explanation": "\"given a + b = 5 b + c = 6 c + d = 3 ( a + b ) - ( b + c ) + ( c + d ) = ( a + d ) = > 5 - 6 + 3 = 2 . option d . . .\"" + }, + { + "Answer": 15885.416666666668, + "Options": "a ) 15456 , b ) 14758 , c ) 15789 , d ) 13250 , e ) 12450", + "Correct": "c", + "Explanation": "\"let his total sales be x total sales - commission = $ 15000 x - [ ( 10 % of 5000 ) + 5 % of ( x - 5000 ) ] = 15000 95 x / 100 = 15000 x = 15789 approximately answer is c\"" + }, + { + "Answer": 57, + "Options": "a ) 57 , b ) 67 , c ) 77 , d ) 87 , e ) 97", + "Correct": "a", + "Explanation": "\"explanation : money collected = ( 32.49 x 100 ) paise = 3249 paise . \u2234 number of members = \u221a ( 3249 ) = 57 . answer : a\"" + }, + { + "Answer": 210, + "Options": "a ) 120 , b ) 150 , c ) 180 , d ) 210 , e ) 240", + "Correct": "d", + "Explanation": "( 6 ' ) ' = ( 3 * 6 - 3 ) ' = 15 ' = 15 * 15 - 15 = 210 answer d" + }, + { + "Answer": 1.5958333333333332, + "Options": "a ) 18.6 , b ) 9.3 , c ) 6.2 , d ) 3.1 , e ) 1.6", + "Correct": "e", + "Explanation": "number of passengers using kennedy airport = 38 / 3 = ~ 12.67 passengers using miami airport = 12.67 / 2 = ~ 6.3 passengers using logan airport = 6.3 / 4 = ~ 1.58 so e" + }, + { + "Answer": 160000.00000000003, + "Options": "a ) $ 10800 , b ) $ 18000 , c ) $ 160000 , d ) $ 1800 , e ) none", + "Correct": "c", + "Explanation": "\"[ 1 / ( x 1 / y 1 + x 2 / y 2 + x 3 / y 3 ) ] * total amount = balance amount [ 1 - ( 1 / 5 + 1 / 10 + 3 / 5 ) } * total salary = $ 16000 , = [ 1 - 9 / 10 ] * total salary = $ 16000 , total salary = $ 16000 * 10 = $ 160000 , correct answer ( c )\"" + }, + { + "Answer": 52.005494505494504, + "Options": "a ) 50 , b ) 52 , c ) 51 , d ) 53 , e ) none of the above", + "Correct": "b", + "Explanation": "\"required average marks = 60 \u00e3 \u2014 50 + 35 \u00e3 \u2014 60 + 45 \u00e3 \u2014 55 + 42 \u00e3 \u2014 45 / 60 + 35 + 45 + 42 = 3000 + 2100 + 2475 + 1890 / 182 = 9465 \u00e2 \u0081 \u201e 182 = 52 answer b\"" + }, + { + "Answer": 34, + "Options": "a ) a ) 46 , b ) b ) 34 , c ) c ) 66 , d ) d ) 76 , e ) e ) 74", + "Correct": "b", + "Explanation": "1 to 11 = 11 * 52 = 572 1 to 6 = 6 * 49 = 294 6 to 11 = 6 * 52 = 312 6 th = 294 + 312 \u2013 572 = 34 answer : b" + }, + { + "Answer": 20, + "Options": "a ) 20 , b ) 21 , c ) 25 , d ) 26 , e ) 27", + "Correct": "a", + "Explanation": "\"( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 138 + 2 * 131 a + b + c = \u221a 400 = 20 a\"" + }, + { + "Answer": 200, + "Options": "a ) 50 , b ) 100 , c ) 150 , d ) 200 , e ) 250", + "Correct": "d", + "Explanation": "\"explanation : let the number of 20 paise coins be x . then the no of 25 paise coins = ( 324 - x ) . 0.20 \u00d7 ( x ) + 0.25 ( 324 - x ) = 71 = > x = 200 . answer : d\"" + }, + { + "Answer": 28, + "Options": "a ) 91 , b ) 28 , c ) 56 , d ) 89 , e ) none of these", + "Correct": "b", + "Explanation": "\"solution required number of student = h . c . f of 1204 and 840 = 28 . answer b\"" + }, + { + "Answer": 44, + "Options": "a ) 15 , b ) 30 , c ) 31 , d ) 33 , e ) 44", + "Correct": "e", + "Explanation": "we have to find the number of terms that are divisible by 2 but not by 6 ( as the question asks for the even numbers only which are not divisible by 3 ) for 2 , 10 , 12,14 . . . 140 using ap formula , we can say 140 = 10 + ( n - 1 ) * 2 or n = 66 . for 6 , 12,18 , . . . 138 using ap formula , we can say 138 = 12 + ( n - 1 ) * 6 or n = 22 . hence , only divisible by 2 but not 3 = 66 - 22 = 44 . hence , answer e" + }, + { + "Answer": 57.74647887323944, + "Options": "a ) 57.75 % , b ) 54.54 % , c ) 63 % , d ) 70 % , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : number of runs made by running = 142 - ( 12 x 4 + 2 x 6 ) = 142 - ( 60 ) = 82 now , we need to calculate 82 is what percent of 142 . = > 82 / 142 * 100 = 57.75 % answer : a\"" + }, + { + "Answer": 0.1111111111111111, + "Options": "a ) 1 / 190 , b ) 1 / 20 , c ) 1 / 9 , d ) 1 / 10 , e ) 1 / 92", + "Correct": "c", + "Explanation": "\"the problem with your solution is that we do n ' t choose 1 shoe from 20 , but rather choose the needed one after we just took one and need the second to be the pair of it . so , the probability would simply be : 1 / 1 * 1 / 9 ( as after taking one at random there are 9 shoes left and only one is the pair of the first one ) = 1 / 9 answer : c .\"" + }, + { + "Answer": 24.242424242424242, + "Options": "a ) 25 % , b ) 20 % , c ) 24.2 % , d ) 33.33 % , e ) none of these", + "Correct": "c", + "Explanation": "explanation : let us assume before increase the petrol will be rs . 100 . after increase it will be rs ( 100 + 32 ) i . e 132 . now , his consumption should be reduced to : - = ( 132 \u2212 100 ) / 132 \u2217 100 . hence , the consumption should be reduced to 24.2 % . answer : c" + }, + { + "Answer": 25, + "Options": "a ) 25 , b ) 60 , c ) 50 , d ) 30 , e ) 40", + "Correct": "a", + "Explanation": "\"a 1 = 90 / 3 = 30 a 2 = a 1 - 5 = 25 sum of second list = 25 * 3 = 75 therefore the number = 75 - 50 = 25 a\"" + }, + { + "Answer": 1.794, + "Options": "a ) 2.91 , b ) 1.794 , c ) 1.338 , d ) 1.986 , e ) 1.999", + "Correct": "b", + "Explanation": "\"1.35 + . 123 + . 321 = 0 0 = 0 - 1.35 - 0.123 - 0.321 0 = - 1.794 answer : b\"" + }, + { + "Answer": 140, + "Options": "a ) 86 , b ) 160 , c ) 76 , d ) 140 , e ) 26", + "Correct": "d", + "Explanation": "\"given m + p + c = 60 * 3 = 180 - - - ( 1 ) m + p = 90 * 2 = 180 - - - ( 2 ) p + c = 70 * 2 = 140 - - - ( 3 ) where m , p and c are marks obtained by the student in mathematics , physics and chemistry . p = ( 2 ) + ( 3 ) - ( 1 ) = 180 + 140 - 180 = 140 answer : d\"" + }, + { + "Answer": 7, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9", + "Correct": "c", + "Explanation": "\"2 m = 21 - m 3 m = 21 m = 7 the answer is c .\"" + }, + { + "Answer": 500, + "Options": "a ) 300 , b ) 350 , c ) 400 , d ) 450 , e ) 500", + "Correct": "e", + "Explanation": "\"each term in set b is 20 more than the corresponding term in set a . the difference of the sums = 25 * 20 = 500 . the answer is e .\"" + }, + { + "Answer": 29.411764705882355, + "Options": "a ) 25 % , b ) 22.2 % , c ) 20 % , d ) 29.4 % , e ) 11.1 %", + "Correct": "d", + "Explanation": "\"welcome , just post the question and the choices let ' s see , the way i did it was 1 / 3 are clerical out of 3600 so 1200 are clerical 1200 reduced by 1 / 6 is 1200 * 1 / 6 so it reduced 200 people , so there is 1000 clerical people left but since 200 people left , it also reduced from the total of 3600 so there are 3400 people total since 1000 clerical left / 3400 people total you get ( a ) 29.4 % answer : d\"" + }, + { + "Answer": 96, + "Options": "a ) 68 , b ) 70.4 , c ) 96 , d ) 105.6 , e ) 108", + "Correct": "c", + "Explanation": "\"x is 20 % greater than 80 means x is 1.2 times 80 ( in other words 80 + 20 / 100 * 80 = 1.2 * 80 ) therefore , x = 1.2 * 80 = 96.00 answer : c\"" + }, + { + "Answer": 40, + "Options": "a ) 20 coins , b ) 30 coins , c ) 40 coins , d ) 25 coins , e ) none of these", + "Correct": "c", + "Explanation": "\"let number of each type of coin = x . then , 1 \u00d7 x + . 50 \u00d7 x + . 25 x = 70 \u21d2 1.75 x = 70 \u21d2 x = 40 coins answer c\"" + }, + { + "Answer": 435, + "Options": "a ) 10 , b ) 30 , c ) 435 , d ) 60 , e ) 90", + "Correct": "c", + "Explanation": "\"30 players are there . two players play one game with one another . so 30 c 2 = 30 * 29 / 2 = 435 so option c is correct\"" + }, + { + "Answer": 18, + "Options": "a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18", + "Correct": "e", + "Explanation": "\"legs 18 * 4 = 72 now half on their horses so remaining on the walk so 9 men 9 men has 18 legs so , 18 + 72 = 90 legs walking answer : e\"" + }, + { + "Answer": 15.5, + "Options": "a ) 5 , b ) 5.5 , c ) 6 , d ) 6.5 , e ) 7", + "Correct": "d", + "Explanation": "\"the total subtracted is ( 9 + 8 + . . . + 1 ) = ( 9 * 10 ) / 2 = 45 on average , each number will be reduced by 45 / 10 = 4.5 therefore , the overall average will be reduced by 4.5 the answer is d .\"" + }, + { + "Answer": 14, + "Options": "a ) 14 , b ) 20 , c ) 26 , d ) 28 , e ) 30", + "Correct": "a", + "Explanation": "\"solution let the number be x . then , 15 x - x = 196 \u2039 = \u203a 14 x = 196 x \u2039 = \u203a 14 . answer a\"" + }, + { + "Answer": 11, + "Options": "a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13", + "Correct": "c", + "Explanation": "86 + 50 d = 53 ( d + 1 ) . 3 d = 33 . d = 11 . the answer is c ." + }, + { + "Answer": 6470, + "Options": "a ) rs . 5870 , b ) rs . 5991 , c ) rs . 6470 , d ) rs . 6850 , e ) none of these", + "Correct": "c", + "Explanation": "\"explanation : total sale for 5 months = rs . ( 5420 + 5660 + 6200 + 6350 + 6500 ) = rs . 30,130 therefore , required sale = rs . [ ( 6100 * 6 ) \u2013 30,130 ] = rs . ( 36600 \u2013 30,130 ) = rs . 6470 answer c\"" + }, + { + "Answer": 5, + "Options": "a ) 6 . , b ) 2 . , c ) 3 . , d ) 5 . , e ) 4 .", + "Correct": "d", + "Explanation": "no strategy involved . simple question demanding fast calculation . 11 x 5 = 55 = > 79 - 55 = 24 = > 24 / 6 is an integer ans d . 5 . good luck" + }, + { + "Answer": 302.9802941364969, + "Options": "a ) 306.06 , b ) 306.02 , c ) 306.04 , d ) 306.09 , e ) 306.12", + "Correct": "c", + "Explanation": "\"a = 5000 ( 51 / 50 ) 3 = 5306.04 5000 - - - - - - - - - - - 306.04 answer : c\"" + }, + { + "Answer": 36, + "Options": "a ) 4 , b ) 8 , c ) 12 , d ) 24 , e ) 36", + "Correct": "e", + "Explanation": "explanation : total number of routes from bristol to carlisle = ( 6 x 3 x 2 ) = 36 . answer : e" + }, + { + "Answer": 48, + "Options": "a ) 52 , b ) 54 , c ) 48 , d ) 58 , e ) 60", + "Correct": "c", + "Explanation": "\"let n = total students in class total points for 1 / 3 class = 54 n / 3 = 18 n total points for 2 / 3 class = 45 * 2 n / 3 = 30 n total points for whole class = 18 n + 30 n = 48 n 48 n total class points / n total students = 48 grade point average for total class answer : c\"" + }, + { + "Answer": 7, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8", + "Correct": "d", + "Explanation": "since factors of ' 4 ' are { 1 , 2,4 } 4 ^ 3 = 64 number of factors / divisors of 64 = 2 ^ 6 we know that when a number is expressed as a product of the prime factors as below : n = a ^ x * b ^ y * c ^ z then no . of divisors = ( x + 1 ) * ( y + 1 ) * ( z + 1 ) then here ( 6 + 1 ) = 7 answer : d" + }, + { + "Answer": 38400, + "Options": "a ) 38400 , b ) 24000 , c ) 24936 , d ) 25640 , e ) none", + "Correct": "a", + "Explanation": "answer \u2235 60 % of p = 23040 \u2234 p = ( 23040 x 100 ) / 60 = 38400 correct option : a" + }, + { + "Answer": 36, + "Options": "a ) 96 , b ) 75 , c ) 36 , d ) 25 , e ) 12", + "Correct": "c", + "Explanation": "\"guys , one more simple funda . 5 / 2 = 2.5 now . 5 x 2 = 1 is the remainder 25 / 4 = 6.25 now . 25 x 4 = 1 is the remainder 32 / 5 = 6.4 now . 4 x 5 = 2 is the remainder given x / y = 96.25 and remainder is 9 so . 25 x y = 9 hence y = 36 ans c\"" + }, + { + "Answer": 33, + "Options": "a ) 27 , b ) 29 , c ) 28 , d ) 30 , e ) 33", + "Correct": "e", + "Explanation": "13605 \u00f7 87 = 156 , remainder = 33 hence 33 is the least number which can be subtracted from 13605 such that the remainder is divisible by 87 answer is e" + }, + { + "Answer": 40, + "Options": "a ) 75 , b ) 65 , c ) 85 , d ) 40 , e ) 80", + "Correct": "d", + "Explanation": "total increase in weight = 8 \u00d7 2.5 = 20 if x is the weight of the new person , total increase in weight = x \u2212 20 = > 20 = x - 20 = > x = 20 + 20 = 40 answer is d ." + }, + { + "Answer": 20.948616600790515, + "Options": "a ) 12 % , b ) 15 % , c ) 18 % , d ) 21 % , e ) 24 %", + "Correct": "d", + "Explanation": "\"let p be the original price per unit of gas . let x be the original gas consumption . let y be the reduced gas consumption . y * 1.1 * 1.15 * p = x * p y = x / ( 1.1 * 1.15 ) which is about 0.79 x which is a decrease of about 21 % . the answer is d .\"" + }, + { + "Answer": 5, + "Options": "a ) $ 5 , b ) $ 10 , c ) $ 15 , d ) $ 20 , e ) $ 25", + "Correct": "a", + "Explanation": "\"let q ' s hourly wage be x , then p ' s hourly wage is 1.5 x let t be the number of hours that q needs , then p needs t - 10 hours to do the job . since they both are paid an equal total amount of $ 300 : x * t = 1.5 x * ( t - 10 ) t = 30 hours and q ' s hourly wage is 300 / 30 = $ 10 p ' s hourly wage is 300 / ( t - 10 ) = $ 15 which is $ 5 per hour more . the answer is a .\"" + }, + { + "Answer": 54, + "Options": "a ) 35 , b ) 25 , c ) 45 , d ) 54 , e ) 52", + "Correct": "d", + "Explanation": "let the number be x . then , 1 / 3 of 1 / 4 of x = 15 x = 15 * 12 = 180 so , required number = ( 3 / 10 * 180 ) = 54 . answer : d" + }, + { + "Answer": 24, + "Options": "a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 26", + "Correct": "d", + "Explanation": "\"let x be the correct sums and ( 30 - x ) be the incorrect sums . 3 x - 2 ( 30 - x ) = 60 5 x = 120 x = 24 the answer is d .\"" + }, + { + "Answer": 8, + "Options": "a ) \u2013 29 , b ) \u2013 12 , c ) - 8 , d ) 29 , e ) 168", + "Correct": "c", + "Explanation": "\"explanation : = > y = x ^ 2 - 2 x - 8 = > y = ( x + 2 ) ( x - 4 ) = > x = - 2 , y = 4 product x = ( - 2 ) ( 4 ) = - 8 answer option - 8 answer : c\"" + }, + { + "Answer": 33.33333333333334, + "Options": "a ) 33.33 % , b ) 24.33 % , c ) 15.33 % , d ) 16.33 % , e ) 17.33 %", + "Correct": "a", + "Explanation": "\"let total % of work is 100 % total person = p 1 / 4 person are absent of total person . so absent person is 1 / 4 p ie p / 4 . left person is , p - p / 4 = 3 p / 4 . p person do the work 100 % 1 person do the work 100 * p % 3 p / 4 person do the work ( 100 * p * 4 ) / 3 p % = 133.33 % work increased for each person is = ( 133.33 - 100 ) % = 33.33 % answer : a\"" + }, + { + "Answer": 30, + "Options": "a ) 27 , b ) 29 , c ) 28 , d ) 30 , e ) 31", + "Correct": "d", + "Explanation": "\"13602 \u00f7 87 = 156 , remainder = 30 hence 30 is the least number which can be subtracted from 13602 such that the remainder is divisible by 87 answer is d\"" + }, + { + "Answer": 20.5, + "Options": "a ) 16.5 , b ) 17.5 , c ) 18.5 , d ) 19.5 , e ) 20.5", + "Correct": "e", + "Explanation": "let siri has x rs , then christine has 20 + x rs given x + ( 20 + x ) = 21 = > 2 x = 1 or x = 0.5 so christine and siri has 20.5 and 0.5 rs respectively . answer : e" + }, + { + "Answer": 34, + "Options": "a ) 37 , b ) 38 , c ) 39 , d ) 34 , e ) 41", + "Correct": "d", + "Explanation": "let present age of a be a and b be b a + 10 = 2 * ( b - 10 ) = > 2 b - a = 30 . . . . . . ( i ) a = b + 4 = > 2 b - b - 4 = 30 b = 34 so the present age of b is 34 years answer : d" + }, + { + "Answer": 984.4, + "Options": "a ) 347.4 , b ) 984.4 , c ) 877.4 , d ) 637.4 , e ) 667.4", + "Correct": "b", + "Explanation": "let the costs of each kg of mangos and each kg of rice be $ a and $ r respectively . 10 a = 24 r and 6 * 23 = 2 r a = 12 / 5 r and r = 69 a = 165.6 required total cost = 4 * 165.6 + 3 * 69 + 5 * 23 = 662.4 + 207 + 115 = $ 984.40 b" + }, + { + "Answer": 611, + "Options": "a ) 171 , b ) 281 , c ) 391 , d ) 491 , e ) 611", + "Correct": "e", + "Explanation": "\"sum s = n / 2 { 2 a + ( n - 1 ) d } = 11 / 2 { 2 * 50 + ( 11 - 1 ) * 1 } = 11 * 55 = 605 = x number of even number = ( 60 - 50 ) / 2 + 1 = 6 = y x + y = 605 + 6 = 611 e\"" + }, + { + "Answer": 85.71428571428571, + "Options": "a ) 12.5 % , b ) 85.7 % , c ) 80 % , d ) 11 % , e ) 1 %", + "Correct": "b", + "Explanation": "\"say y = 1 and x = 7 . then y = 1 is less than x = 7 by ( 7 - 1 ) / 7 * 100 = 6 / 7 * 100 = 85.7 % . answer : b .\"" + }, + { + "Answer": 391, + "Options": "a ) 343 , b ) 393 , c ) 363 , d ) 391 , e ) 409", + "Correct": "d", + "Explanation": "n = smallest number n + 6 = largest number ( n + n + 6 ) / 2 = 20 = > ( 2 n + 6 ) / 2 = 20 = > n + 3 = 20 = > n = 17 so product of n and n + 6 = ( 17 ) ( 23 ) = 391 answer - d" + }, + { + "Answer": 12, + "Options": "a ) $ 11.73 , b ) $ 12.00 , c ) $ 13.80 , d ) $ 14.00 , e ) $ 15.87", + "Correct": "b", + "Explanation": "\"if the amount spent excluding the gratuity was x , then x ( 1.15 ) = 207 = > x = 207 / 1.15 = 180 then the average price per person = 180 / 15 = 12 option ( b )\"" + }, + { + "Answer": 20, + "Options": "a ) 14 , b ) 20 , c ) 22 , d ) 24 , e ) 25", + "Correct": "b", + "Explanation": "i agree with your solution = 20 . but the question is : there are different combination to get 60000 chips . for example : 1 * s 3 + 2 * s 4 + 2 * s 2 . in this way , we ship 60000 chips with only 6 + 4 * 2 + 2 * 2 = 18 defective chips , better than the average of 20 . the question is to find the expected number q of defective chips , i guess it assume the minimum # , therefore it might not be 20 ." + }, + { + "Answer": 40, + "Options": "a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60", + "Correct": "a", + "Explanation": "\"number of pens = 640 number of pencils = 520 required number of students = h . c . f . of 640 and 520 = 40 answer is a\"" + }, + { + "Answer": 56.25, + "Options": "a ) 22.35 , b ) 33.25 , c ) 22.25 , d ) 51.35 , e ) 56.25", + "Correct": "e", + "Explanation": "explanation : total of 50 numbers = ( 50 \u00d7 56 ) = 2800 total of 48 numbers = ( 2800 - ( 45 + 55 ) ] = 2700 required average = 2700 / 48 = 56.25 answer : e" + }, + { + "Answer": 17, + "Options": "a ) 17 , b ) 19 , c ) 21 , d ) 13 , e ) 18", + "Correct": "a", + "Explanation": "\"( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 149 + 2 * 70 a + b + c = \u00e2 \u02c6 \u0161 289 = 17 answer a\"" + }, + { + "Answer": 106, + "Options": "a ) 106 , b ) 49 , c ) 68 , d ) 38 , e ) 55", + "Correct": "a", + "Explanation": "a 106 ( 11 * 9 ) + 7 = 106" + }, + { + "Answer": 990, + "Options": "a ) $ 880 , b ) $ 990 , c ) $ 1,000 , d ) $ 1,100 , e ) $ 1,210", + "Correct": "b", + "Explanation": "\"10 / 100 p = 110 > > p = 110 * 100 / 10 = 1100 1100 - 110 = 990 answer : b\"" + }, + { + "Answer": 693, + "Options": "a ) 0 , b ) 50 , c ) 450 , d ) 495 , e ) 694", + "Correct": "e", + "Explanation": "\"we can break this problem into two parts : 1 ) what is 1 / 10 percent of 6,000 ? 2 ) what is 1 / 10 of 6,000 ? to calculate 1 / 10 percent of 6,000 we must first remember to divide 1 / 10 by 100 . so we have : ( 1 / 10 ) / ( 100 ) to divide a number by 100 means to multiply it by 1 / 100 , so we have : 1 / 10 x 1 / 100 = 1 / 1,000 thus , 1 / 10 percent of 6,000 = 1 / 1,000 x 6,000 = 6 . now let ' s concentrate on part 2 . we need to calculate 1 / 10 of 5,000 . to do this we simply multiply 1 / 10 by 6,000 . 1 / 10 x 6,000 = 600 the answer to part 1 is 6 , and the answer to part 2 is 600 . their difference is 600 \u2013 6 = 694 . answer e .\"" + }, + { + "Answer": 17.142857142857142, + "Options": "a ) 17.14286 min , b ) 62 min , c ) 70.1346 min , d ) 74 min , e ) 76.1346 min", + "Correct": "a", + "Explanation": "x = time for type b prolems 2 x = time for type a problem total time = 3 hrs = 180 min 190 x + 10 * 2 x = 180 x = 180 / 210 x = 0.72 time taken for type a problem = 10 * 2 * 0.857143 = 17.14286 min answer : a" + }, + { + "Answer": 248, + "Options": "a ) $ 150 , b ) $ 248.75 , c ) $ 200 , d ) $ 171.6 , e ) $ 190", + "Correct": "b", + "Explanation": "$ 9.95 * 25 = $ 248.75 . answer is b ." + }, + { + "Answer": 500, + "Options": "a ) - 500 , b ) - 1000 , c ) - 999 , d ) - 1001 , e ) 500500", + "Correct": "a", + "Explanation": "one groups the first two terms and each successive two terms to obtain a sum of 500 expressions each of which is - 1 . the answer is - 500 correct answer a" + }, + { + "Answer": 545.3645294456946, + "Options": "a ) 550.87 , b ) 506.07 , c ) 506.04 , d ) 506.03 , e ) 306.01", + "Correct": "a", + "Explanation": "\"a = 9000 ( 51 / 50 ) 3 = 9550.87 9000 - - - - - - - - - - - 550.87 answer : a\"" + }, + { + "Answer": 1, + "Options": "a ) 3 hr . , b ) 5 hr . , c ) 2 hr . , d ) 7 hr . , e ) 1 hr .", + "Correct": "e", + "Explanation": "\"e 1 hr . let the duration of the flight be x hours . then , 600 / x - 600 / 0.5 x = 200 - - > 600 / x - 1200 / ( 2 x + 1 ) = 200 - - > x ( 2 x + 1 ) = 3 - - > 2 x ^ 2 + x - 3 = 0 - - > ( 2 x + 3 ) ( x - 1 ) = 0 - - > x = 1 hr .\"" + }, + { + "Answer": 859560, + "Options": "a ) 345466 , b ) 465767 , c ) 565676 , d ) 645469 , e ) 859622", + "Correct": "e", + "Explanation": "\"dividend = quotient * divisor + reminder 859622 / 456 gives quotient = 1885 and reminder = 62 . so , the next number divisible by 456 is 456 places infront of 456 * 1885 which means 456 \u2013 62 = 394 should be added to 859622 . e\"" + }, + { + "Answer": 25, + "Options": "a ) 9 % , b ) 11 % , c ) 15 % , d ) 25 % , e ) 90 %", + "Correct": "d", + "Explanation": "\"cost of 12 paper towels individually = 1 * 12 = 12 cost of a set of 12 paper towels = 9 cost of one roll = 9 / 12 = 3 / 4 = 0.75 savings per roll = 1 - . 75 = 0.25 % of savings is r = . 25 / 1 * 100 = 25 % d is the answer .\"" + }, + { + "Answer": 8, + "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12", + "Correct": "a", + "Explanation": "\"the total number of books the students borrowed is 20 * 2 = 40 . the students who borrowed zero , one , or two books borrowed 8 * 1 + 3 * 2 = 14 books . the 7 students who borrowed at least three books borrowed 40 - 14 = 26 books . if 6 of these students borrowed exactly 3 books , then the maximum that one student could have borrowed is 26 - 18 = 8 books . the answer is a .\"" + }, + { + "Answer": 9.25, + "Options": "a ) 9.25 , b ) 11.75 , c ) 13.25 , d ) 15.75 , e ) 17.25", + "Correct": "a", + "Explanation": "\"let x be the length of the size 8 shoe . then 0.3 x = 9 / 4 x = 90 / 12 = 15 / 2 inches the size 15 shoe has a length of 15 / 2 + 7 / 4 = 37 / 4 = 9.25 inches the answer is a .\"" + }, + { + "Answer": 625, + "Options": "a ) 2 , b ) 625 , c ) 8 , d ) 16 , e ) 32", + "Correct": "b", + "Explanation": "\"( x + y ) ^ 2 - ( x - y ) ^ 2 ( x + y + x - y ) ( x + y - x + y ) ( 2 x ) ( 2 y ) 4 xy 4 5 ^ 4 = 625 answer b\"" + }, + { + "Answer": 8, + "Options": "a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10", + "Correct": "d", + "Explanation": "we ' re told that by selling cakes at n dollars / cake , a baker will make $ 320 . reducing the price by 20 % and selling 2 more cakes will also make her $ 320 . we ' re asked for the original number of cakes that the baker intends to sell . $ 320 is a rather interesting number . based on the answer choices , we ' re almost certainly dealing with integer values for the number of cakes and the price per cake . as such , 6 is probably not going to be part of the solution ( either as 4 and 6 cakes or as 6 and 8 cakes ) . as such , we can avoid answers b and c . . . . let ' s test answer d : 8 cakes if . . . . original cakes = 8 8 ( n ) = $ 320 , so n = $ 40 / cake 20 % off = $ 8 off = 40 - 8 = $ 32 / cake + 2 more cakes = 8 + 2 = 10 cakes 10 ( 32 ) = $ 320 this is an exact match for what we were told , so this must be the answer . final answer : d" + }, + { + "Answer": 40, + "Options": "a ) 40 , b ) 44 , c ) 48 , d ) 52 , e ) 56", + "Correct": "a", + "Explanation": "\"the time to produce the first 60 cogs is 60 / 30 = 2 hours . the time to produce the next 60 cogs is 60 / 60 = 1 hour . the average output is 120 cogs / 3 hours = 40 cogs per hour . the answer is a .\"" + }, + { + "Answer": 6.995635628892249, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10", + "Correct": "b", + "Explanation": "\"0.00010101 * 10 ^ k > 1000 we need to move the decimal point to the right 7 places to get 1010.1 this is equivalent to multiplying by 10 ^ 7 . the answer is b .\"" + }, + { + "Answer": 31, + "Options": "a ) 30 kg , b ) 31 kg , c ) 37 kg , d ) 39 kg , e ) 41 kg", + "Correct": "b", + "Explanation": "\"let a , b , c represent their respective weights . then , we have : a + b + c = ( 45 x 3 ) = 135 . . . . ( i ) a + b = ( 40 x 2 ) = 80 . . . . ( ii ) b + c = ( 43 x 2 ) = 86 . . . . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 166 . . . . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 31 . b ' s weight = 31 kg b )\"" + }, + { + "Answer": 62.5, + "Options": "a ) 21 , b ) 20 , c ) 63 , d ) 30 , e ) 45", + "Correct": "c", + "Explanation": "\"let number is x . when 5 added to it , = ( x + 5 ) 2 multiplied to sum , = 2 * ( x + 5 ) now , = [ { 2 * ( x + 5 ) } / 5 ] and , = [ { 2 * ( x + 5 ) } / 5 ] - 5 according to question , [ { 2 * ( x + 5 ) } / 5 ] - 5 = half of 44 [ ( 2 x + 10 ) / 5 ) = 22 + 5 2 x + 10 = 27 * 5 2 x - 135 - 10 x = 125 / 2 = 62.5 = 63 so , required number is : 63 . answer : c\"" + }, + { + "Answer": 14, + "Options": "a ) 14 , b ) 20 , c ) 26 , d ) 28 , e ) 30", + "Correct": "a", + "Explanation": "let the number be x . then , 15 x - x = 196 < = > 14 x = 196 < = > x = 14 . answer : a" + }, + { + "Answer": 81, + "Options": "a ) 23 , b ) 78 , c ) 27 , d ) 61 , e ) 81", + "Correct": "e", + "Explanation": "\"explanation : 80 + 5 * 12 / ( 180 / 3 ) = 80 + 5 * 12 / ( 60 ) = 80 + ( 5 * 12 ) / 60 = 80 + 1 = 81 . answer : e\"" + }, + { + "Answer": 171.42857142857142, + "Options": "a ) 171.4 , b ) 171.5 , c ) 171.6 , d ) 171.7 , e ) none of the above", + "Correct": "a", + "Explanation": "lets assume the initial production was 100 litres of beer for 100 hr . with the 20 % increase the total amount of beer production will be 120 litres and with 30 % decrease in total hours will be reduced to 70 hr . 100 hr - - - - > 100 lts 1 hr - - - - - > 1 lts 70 hr - - - - - > 120 lts 1 hr - - - - - > 1.714 lts total increase in production for 1 hr = 171.4 % answer a" + }, + { + "Answer": 0.625, + "Options": "a ) 3 / 4 , b ) 1 / 2 , c ) 5 / 8 , d ) 1 , e ) 1 / 4", + "Correct": "c", + "Explanation": "sample space = 2 ^ 3 = 8 favourable events = { bgg } , { bgb } , { bbb } , { ggg } , { gbg } , probability = 5 / 8 = 5 / 8 . ans ( c ) ." + }, + { + "Answer": 37.10843373493976, + "Options": "a ) 37 , b ) 25 , c ) 48 , d ) 50 , e ) none", + "Correct": "a", + "Explanation": "\"answer sum of 83 result = sum of 55 result + sum of 28 result . = 30 x 20 + 20 x 30 = 3080 correct option : a\"" + }, + { + "Answer": 98, + "Options": "a ) 87 , b ) 89 , c ) 90 , d ) 98 , e ) 95", + "Correct": "d", + "Explanation": "\"total score on 3 tests = 90 * 3 = 270 jerry wants the average to be = 92 hence total score on 4 tests should be = 92 * 4 = 368 score required on the fourth test = 368 - 270 = 98 option d\"" + }, + { + "Answer": 8.36, + "Options": "a ) $ 3.36 , b ) $ 6.85 , c ) $ 8.36 , d ) $ 10.08 , e ) $ 11.85", + "Correct": "c", + "Explanation": "\"answer = c 2 * 2.44 + 4 * 0.87 = 2 ( 2.50 - 0.06 ) + 4 ( 1.00 - 0.13 ) = 5 + 4 - 0.12 - 0.52 = 9 - 0.64 = 8.36\"" + }, + { + "Answer": 20, + "Options": "a ) 35 , b ) 20 , c ) 40 , d ) 30 , e ) 67", + "Correct": "b", + "Explanation": "explanation : number is ( 5 * 12 ) - ( 4 * 10 ) = 60 - 40 = 20 answer : option b" + }, + { + "Answer": 1250, + "Options": "a ) 850 , b ) 1250 , c ) 1650 , d ) 2050 , e ) 2450", + "Correct": "b", + "Explanation": "\"each term in set b is 50 more than the corresponding term in set a . the difference of the sums = 25 * 50 = 1250 . the answer is b .\"" + }, + { + "Answer": 340.8, + "Options": "a ) 0.3408 , b ) 3.408 , c ) 34.08 , d ) 340.8 , e ) none of these", + "Correct": "d", + "Explanation": "\"solution 16 \u00d7 21.3 = ( 16 x 213 / 10 ) = ( 16 x 213 / 10 ) = 3408 / 10 = 340.8 . answer d\"" + }, + { + "Answer": 9, + "Options": "a ) 0 , b ) 3 , c ) 6 , d ) 9 , e ) 12", + "Correct": "d", + "Explanation": "\"from ( x + 3 ) ( y - 3 ) = 0 it follows that either x = - 3 or y = 3 . thus either x ^ 2 = 9 or y ^ 2 = 9 . now , if x ^ 2 = 9 , then the least value of y ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 9 + 0 = 9 . similarly if y ^ 2 = 9 , then the least value of x ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 0 + 9 = 9 . answer : d .\"" + }, + { + "Answer": 30.000000000000007, + "Options": "a ) 40 , b ) 45 , c ) 38 , d ) 50 , e ) 30", + "Correct": "e", + "Explanation": "\"let , father \u00e2 \u20ac \u2122 s current age is a years . then , man \u00e2 \u20ac \u2122 s current age = [ ( 2 / 5 ) a ] years . therefore , [ ( 2 / 5 ) a + 6 ] = ( 1 / 2 ) ( a + 6 ) 2 ( 2 a + 30 ) = 5 ( a + 6 ) a = 30 e\"" + }, + { + "Answer": 6, + "Options": "a ) $ 2.50 , b ) $ 3.00 , c ) $ 3.50 , d ) $ 6.00 , e ) $ 5.00", + "Correct": "d", + "Explanation": "\"number of wheels in truck = 18 number of wheels on its front axle = 2 number of wheels remaining = 16 number of axles remaining axles = 16 / 4 = 4 total number of axles = 5 t = 1.50 + 1.50 ( x \u2212 2 ) = 1.50 + 1.5 * 3 = 1.5 + 4.5 = 6 $ answer d\"" + }, + { + "Answer": 8, + "Options": "a ) 8 , b ) 13 , c ) 17 , d ) 15 , e ) none of these", + "Correct": "a", + "Explanation": "solution : let the fraction be x / y . when fraction is squared its numerator is reduced by 33 ( 1 / 3 ) and denominator is reduced by 20 % . according to question , ( x / y ) 2 * 33 ( 1 / 3 ) % / 20 % = 2 ( x / y ) . or , ( x / y ) 2 * ( 2 / 3 ) / ( 1 / 5 ) = 2 ( x / y ) . or , x / y = 3 / 5 . sum of numerator and denominator is , ( x + y ) = 3 + 5 = 8 . answer : option a" + }, + { + "Answer": 134, + "Options": "a ) 22 , b ) 134 , c ) 62 , d ) 122 , e ) 672", + "Correct": "b", + "Explanation": "\"factorise 2211 . . 3 * 11 * 67 . . so n has to be a multiple of largest prime number , 61 . . so n = 2 * 61 = 134 . . ans : b\"" + }, + { + "Answer": 22, + "Options": "a ) 20 . , b ) 21 . , c ) 22 . , d ) 23 . , e ) 24 .", + "Correct": "c", + "Explanation": "\"before solving it algebraically , let us prime factorize 1430 = 2 * 5 * 11 * 13 . since number of apples per person * total persons q = 1430 , the answer should be a factor of 1430 . only c is . and that ' s your answer . c\"" + }, + { + "Answer": 59, + "Options": "a ) 59 , b ) 57 , c ) 55 , d ) 58 , e ) 60", + "Correct": "a", + "Explanation": "\"we are asked to find integer solutions for x , y . there is no need to apply euclidian algorithm here , we can get particular solutions simply by plugging in some values . as y reaches 3 we get : y \u2019 = 3 and x \u2019 = 13 . we need only to solve for x . general solution for x will be : x = x \u2019 + bn = 13 + 17 n hence lower limit for n is n \u2265 0 . now we \u2019 ll find upper limit using given restriction x \u2264 1000 . plugging in general solution we \u2019 ll get : 13 + 17 n \u2264 1000 17 n \u2264 987 n \u2264 58 and our list of possible values of n has following representation : 0 , 1,2 , 3 , \u2026 . . , 58 total number of elements is 59 . answer : a\"" + }, + { + "Answer": 19, + "Options": "a ) $ 14.00 , b ) $ 16.00 , c ) $ 17.00 , d ) $ 19.00 , e ) $ 23.00", + "Correct": "d", + "Explanation": "\"first 3 shirts are sold for $ 20 , $ 22 and $ 25 = $ 67 . to get average price of $ 20 , total sale should be 10 * $ 20 = $ 200 so remaining 7 shirts to be sold for $ 200 - $ 67 = $ 133 answer should be 133 / 7 = $ 19.00 that is d\"" + }, + { + "Answer": 0.25, + "Options": "a ) 1 / 4 , b ) 7 / 12 , c ) 2 / 3 , d ) 7 / 8 , e ) 8 / 7", + "Correct": "a", + "Explanation": "let ' take the number of geese to be 100 . male = 50 . female = 50 . now the second part of the q , let ' s take the number migrated to be 20 . so we have 20 geese that migrated and out of that 20 % are male i . e 20 / 100 * 20 = 4 geese ( males ) and now we know out of the total 20 geese , 4 are male , then 16 have to be female . now the ratio part , male geese ratios = 4 / 50 = 2 / 25 . - a female geese ratios = 16 / 50 = 8 / 25 - b cross multiply equations a and b and you get = 1 / 4 . ans a" + }, + { + "Answer": 37, + "Options": "a ) 57 , b ) 67 , c ) 37 , d ) 87 , e ) 97", + "Correct": "c", + "Explanation": "\"money collected = ( 13.69 x 100 ) paise = 1369 paise numbers of members = 1369 squareroot = 37 answer c\"" + }, + { + "Answer": 132, + "Options": "a ) 99 , b ) 132 , c ) 16 , d ) 10 , e ) 15", + "Correct": "b", + "Explanation": "\"40 * 33 / 2 = 5 / 2 * 2 * x = > x = 132 answer : b\"" + }, + { + "Answer": 349, + "Options": "a ) 389 , b ) 356 , c ) 380 , d ) 350 , e ) 349", + "Correct": "e", + "Explanation": "\"x = 13 p + 11 and x = 17 q + 9 13 q + 11 = 17 q + 9 17 q - 13 q = 2 q = 2 + 13 q / 17 the least value of p for which q = 2 + 13 q / 17 is a whole number is p = 26 x = ( 13 * 26 * 11 ) = ( 338 + 11 ) = 349 . answer is e\"" + }, + { + "Answer": 5, + "Options": "a ) - 1 , b ) 3 , c ) 1 , d ) 2 , e ) 5", + "Correct": "e", + "Explanation": "\"if we solve the question , we get x = 5 . option : e\"" + }, + { + "Answer": 291.6666666666667, + "Options": "a ) 291.67 , b ) 105 , c ) 301.05 , d ) 288 , e ) 249.55", + "Correct": "a", + "Explanation": "\"system of equations a = ( 36 / 100 ) c ( 1 / 3 ) a = 35 - - > a = 105 substitution 105 = ( 36 / 100 ) c c = ( 100 / 36 ) 105 - you can do the ugly calculation 105 / 36 * 100 the correct answer is a . the correct answer is 291.67\"" + }, + { + "Answer": 2310, + "Options": "a ) 1155 , b ) 2310 , c ) 4620 , d ) 30030 , e ) 60060", + "Correct": "b", + "Explanation": "the integer should be divisible by : 10 , 11 , 12 , 13 , 14 and 15 , that is 5 * 211 , 3 * 2 ^ 2 , 13 , 2 * 7 , and 3 * 5 . the least common multiple of these integers is the product of 13 , 11 , 7 , 5 , 3 and 2 ^ 2 . then , r / 26 is ( 13 * 11 * 7 * 5 * 3 * 2 ^ 2 ) / 2 * 13 = 11 * 7 * 5 * 3 * 2 = 2310 . answer : b ." + }, + { + "Answer": 2, + "Options": "a ) 2 , b ) 20 , c ) 28 , d ) 14 , e ) 19", + "Correct": "a", + "Explanation": "\"number of statues = all the paint \u00f7 amount used per statue = 1 / 2 \u00f7 1 / 4 = 1 / 2 * 4 / 1 = 2 answer is a\"" + }, + { + "Answer": 8, + "Options": "a ) 10 , b ) 120 , c ) 15 , d ) 8 , e ) 16", + "Correct": "d", + "Explanation": "explanation : sum of first n natural numbers = n ( n + 1 ) / 2 hence , sum of first 15 natural numbers = ( 15 x 16 ) / 2 = 120 therefore , required average of = 120 / 15 = 8 answer : d" + }, + { + "Answer": 0.3611111111111111, + "Options": "a ) 3 / 8 , b ) 13 / 36 , c ) 17 / 36 , d ) 19 / 36 , e ) 23 / 36", + "Correct": "b", + "Explanation": "if you calculate 3 ^ a for 1 st roll , all 6 results will be 9 , 81 , 6561 , 729 , 9 , 81 . this result is the same for 2 nd roll . 9 , 81 , 6561 , 729 , 9 , 81 . about distance : if the first result is 9 and the second is also 9 , the distance is 9 - 9 = 0 which is smaller than 9 . if the first result is 9 and the second is 81 , the distance is 81 - 9 = 72 which is also smaller than b which has the value of 81 . if the first result is 81 and the second is 9 , the distance will be greater than b . distance 81 - 9 = 72 > 9 . on the first roll , the probability of getting result 9 is 2 / 6 . in this case no other alternative values for second roll which would make the distance greater than b . so probability is 0 . so next estimations are : probability of getting 81 on the first roll ( 2 / 6 ) * probability of getting 9 on the second roll ( 2 / 6 ) = 1 / 9 probability of getting 729 on the first roll ( 1 / 6 ) * probability of getting 9 , 81 on the second roll ( 4 / 6 ) = 1 / 9 probability of getting 6561 on the first roll ( 1 / 6 ) * probability of getting 9 , 81 , 729 on the first roll ( 5 / 6 ) = 5 / 36 all together : 1 / 9 + 1 / 9 + 5 / 36 = 13 / 36 = b" + }, + { + "Answer": 10, + "Options": "a ) $ 9 , b ) $ 3 , c ) $ 4 , d ) $ 10 , e ) $ 5", + "Correct": "d", + "Explanation": "\"my lunch = l , my friends lunch = l + 3 ( l ) + ( l + 3 ) = 17 l + l + 3 - 3 = 17 - 3 2 l = 14 l = 7 my friends lunch l + 3 = 7 + 3 = $ 10 , the answer is d\"" + }, + { + "Answer": 75, + "Options": "a ) a ) 110 , b ) b ) 122 , c ) c ) 90 , d ) d ) 85 , e ) e ) 75", + "Correct": "e", + "Explanation": "explanation : average of new numbers = 15 * 5 = 75 answer : option e" + }, + { + "Answer": 5, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "c", + "Explanation": "4 ltr - water 36 ltr - milk let x water be added then the new mixture must have 20 % water then 4 + x = 20 / 100 ( 40 + x ) x = 5 answer : c" + }, + { + "Answer": 40, + "Options": "a ) 16 , b ) 18 , c ) 24 , d ) 40 , e ) 12", + "Correct": "d", + "Explanation": "\"total time taken = x / 40 + 2 x / 20 hours = 5 x / 40 = x / 8 hours average speed = 5 x / ( x / 8 ) = 40 kmph answer : d\"" + }, + { + "Answer": 35.75, + "Options": "a ) $ 35.83 , b ) $ 35.84 , c ) $ 35.85 , d ) $ 35.86 , e ) $ 35.87", + "Correct": "c", + "Explanation": "solution they paid for food , sales tax and tip , hence total paid = $ 30 + 9.5 % * 30 + 10 % * 30 = $ 35.85 answer c" + }, + { + "Answer": 24, + "Options": "a ) 78 years , b ) 22 years , c ) 88 years , d ) 66 years , e ) 24 years", + "Correct": "e", + "Explanation": "\"let ' s son age is x , then father age is x + 26 . = > 2 ( x + 2 ) = ( x + 26 + 2 ) = > 2 x + 4 = x + 28 = > x = 24 years answer : e\"" + }, + { + "Answer": 23.333333333333336, + "Options": "a ) 17 litres , b ) 23.3 litres , c ) 11 litres , d ) 07 litres , e ) 38 litres", + "Correct": "b", + "Explanation": "\"262.85 ( 35 ) + 3 , 104.35 x = 1 , 399.45 ( 35 + x ) solve the equation . 262.85 ( 35 ) + 3 , 104.35 x = 1 , 399.45 ( 35 + x ) 9 , 199.75 + 3 , 104.35 x = 48980.75 + 1 , 399.45 x 9 , 199.75 + 1 , 704.9 x = 48980.75 1 , 704.9 x = 39,781 x \u2248 23.3 answer is b .\"" + }, + { + "Answer": 94.44444444444444, + "Options": "a ) 12.5 % , b ) 87.5 % , c ) 80 % , d ) 94.4 % , e ) 1 %", + "Correct": "d", + "Explanation": "\"say y = 1 and x = 18 . then y = 1 is less than x = 18 by ( 18 - 1 ) / 18 * 100 = 17 / 18 * 100 = 94.4 % . answer : d .\"" + }, + { + "Answer": 8.999999999999986, + "Options": "a ) 8 % , b ) 9 % , c ) 10 % , d ) 11 % , e ) 5 %", + "Correct": "b", + "Explanation": "say currently both a dozen eggs and 5 pounds of oranges cost $ 100 ( they are at the same price ) . so , to buy a dozen eggs and 5 pounds of oranges we need $ 100 . after the increase , the price of a dozen eggs will be $ 103 and the price of 5 pounds of oranges will be $ 106 . so after the increase , to buy a dozen eggs and 5 pounds of oranges we ' ll need $ 209 . increase = 9 % . answer : b ." + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "a", + "Explanation": "6 * 22 = 132 7 * 19 = 133 ` 1 a" + }, + { + "Answer": 14, + "Options": "a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16", + "Correct": "d", + "Explanation": "\"( x + 3 ) ^ 2 / ( 3 x + 29 ) = 2 ( x + 3 ) ^ 2 = 2 ( 3 x + 29 ) x ^ 2 + 6 x + 9 = 6 x + 58 x ^ 2 - 49 = 0 ( x - 7 ) ( x + 7 ) = 0 x = 7 or x = - 7 the answer is d .\"" + }, + { + "Answer": 900, + "Options": "a ) 850 , b ) 900 , c ) 750 , d ) 950 , e ) 800", + "Correct": "b", + "Explanation": "let the price of one apple = a and price of one orange = b price of 24 apples is equal to that of 28 oranges 24 a = 28 b = > 6 a = 7 b \u21d2 b = 6 a / 7 - - - - - ( equation 1 ) price of 45 apples and 60 oranges together is rs . 1350 = > 45 a + 60 b = 1350 = > 3 a + 4 b = 90 \u21d2 3 a + 4 ( 6 a ) / 7 = 90 ( \u2235 substituted the value of b from equation 1 ) \u21d2 a + 4 ( 2 a ) / 7 = 30 = > 7 a + 8 a = 30 \u00d7 7 = 210 = > 15 a = 210 \u21d2 a = 21015 = 423 = 14 b = 6 a 7 = ( 6 \u00d7 14 ) / 7 = 6 \u00d7 2 = 12 total price of 30 apples and 40 oranges = 30 a + 45 b = ( 30 \u00d7 14 ) + ( 40 \u00d7 12 ) = 420 + 480 = 900 answer is b ." + }, + { + "Answer": 7.000000000000001, + "Options": "a ) 4.37 % , b ) 5 % , c ) 6 % , d ) 8.75 % , e ) 7 %", + "Correct": "e", + "Explanation": "solution increase in 10 years = ( 297500 - 175000 ) = 122500 increase % = ( 122500 / 175000 \u00e3 \u2014 100 ) % = 70 % . required average = ( 70 / 10 ) % = 7 % . answer e" + }, + { + "Answer": 100, + "Options": "a ) $ 100 , b ) $ 104 , c ) $ 108 , d ) $ 112 , e ) $ 116", + "Correct": "a", + "Explanation": "\"let the price of the meal be x . after a 10 % sales tax addition , the price is 1.1 * x after a 20 % tip on this amount , the total is 1.2 * 1.1 * x = 1.32 x 1.32 x = 132 x = 100 the correct answer is a .\"" + }, + { + "Answer": 28, + "Options": "a ) 28 , b ) 19 , c ) 22 , d ) 20 , e ) 21", + "Correct": "a", + "Explanation": "\"let the total number of workers be x . then , 8000 x = ( 14000 * 7 ) + 6000 ( x - 7 ) = 2000 x = 56000 = x = 28 . answer : a\"" + }, + { + "Answer": 63, + "Options": "a ) 86.5 kg , b ) 62.5 kg , c ) 46.5 kg , d ) 26.5 kg , e ) 16.5 kg", + "Correct": "b", + "Explanation": "let arun ' s weight be x kg . according to arun , 61 < x < 72 . according to arun ' s brother , 60 < x < 70 . according to arun ' s mother , x < 64 . the values satisfying all the above conditions are 62 and 63 . required average = ( 62 + 63 ) / 2 = 62.5 kg answer : b" + }, + { + "Answer": 484, + "Options": "a ) $ 400 , b ) $ 489 , c ) $ 484 , d ) $ 365 , e ) % 342", + "Correct": "c", + "Explanation": "( 4 / 15 ) a = ( 2 / 5 ) b = > a = ( ( 2 / 5 ) * ( 15 / 4 ) ) b = > a = ( 3 / 2 ) b = > a / b = 3 / 2 a : b = 3 : 2 b ' s share = rs . ( 1210 * ( 2 / 5 ) ) = $ 484 option c" + }, + { + "Answer": 11, + "Options": "a ) - 3 , b ) 3 , c ) 5 , d ) 7 , e ) 11", + "Correct": "e", + "Explanation": "a can not be the answer as all the three terms are in modulus and hence the answer will be non negative . | x - 4 | > = 0 - - > minimum occurs at x = 4 | x + 6 | > = 0 - - > minimum occurs at x = - 6 | x - 5 | > = 0 - - > minimum occurs at x = 5 x = - 6 - - > result = 10 + 0 + 11 = 21 . also any negative value will push the combined value of | x - 4 | + | x - 5 | to a value > 9 . x = 4 - - > result = 0 + 10 + 1 = 11 x = 5 - - > result = 1 + 11 + 0 = 12 x = 6 - - > result = 2 + 12 + 1 = 15 so minimum value of the expression occurs at x = 4 and the resultant value = 11 answer : e" + }, + { + "Answer": 5000, + "Options": "a ) rs . 5000 , b ) rs . 25000 , c ) rs . 7500 , d ) rs . 8500 , e ) rs . 9500", + "Correct": "a", + "Explanation": "\"income = rs . 100 expenditure = rs . 80 savings = rs . 20 present expenditure 80 * ( 20 / 100 ) = rs . 96 present savings = 100 \u2013 96 = rs . 4 100 - - - - - - 4 ? - - - - - - - - - 200 = > 5000 answer : a\"" + }, + { + "Answer": 20, + "Options": "a ) 40 cm , b ) 20 cm , c ) 30 cm , d ) 25 cm , e ) 35 cm", + "Correct": "b", + "Explanation": "the total height of the 31 students = ( 20 * 20 ) + ( 11 * 20 ) = 400 + 220 = 620 cm the required average height = 620 / 31 = 20 cm answer : b" + }, + { + "Answer": 1.3999999999999997, + "Options": "a ) 1 / 3 , b ) 2 / 3 , c ) 5 / 7 , d ) 7 / 5 , e ) 3 / 2", + "Correct": "d", + "Explanation": "say the total number of players is 18 , 9 right - handed and 9 left - handed . on a certain day , two - thirds of the players were absent from practice - - > 12 absent and 6 present . of the players at practice that day , one - third were left - handed - - > 6 * 2 / 3 = 4 were left - handed and 2 right - handed . the number of right - handed players who were not at practice that day is 9 - 2 = 7 . the number of left - handed players who were not at practice that days is 9 - 4 = 5 . the ratio = 7 / 5 . answer : d" + }, + { + "Answer": 432, + "Options": "a ) 2134 , b ) 2234 , c ) 2540 , d ) 2560 , e ) 432", + "Correct": "e", + "Explanation": "432 e" + }, + { + "Answer": 1, + "Options": "a ) 10 , b ) 15 , c ) 35 , d ) 1 , e ) 45", + "Correct": "d", + "Explanation": "\"it ' s simple can be solved by elimination of answer choices . option b and c are too large , not possible . even ae are large to have correct choice . ans : d\"" + }, + { + "Answer": 110, + "Options": "a ) 1628.4 , b ) 110 , c ) 1492 , d ) 1496 , e ) none of these", + "Correct": "b", + "Explanation": "\"solution : let average expenditure of 10 people be x . then , 10 x = 8 * 10 + 2 * ( x + 4 ) ; or , 10 x = 10 * 10 + 2 x + 8 ; or , x = 11 ; so , total money spent = 11 * 10 = rs . 110 . answer : option b\"" + }, + { + "Answer": 0.8686868686868687, + "Options": "a ) 4 / 99 , b ) 2 / 25 , c ) 8 / 99 , d ) 49 / 100 , e ) 86 / 99", + "Correct": "e", + "Explanation": "\"interesting question ! also one that we should be able to answer very quickly be keeping an eye on our best friends , the answer choices . we know that x belongs to the set { 1 , 2 , 3 , . . . , 99 } . we want to know the probability c that x ( x + 1 ) is a multiple of either 4 or 5 . when will this happen ? if either x or ( x + 1 ) is a multiple of 4 or 5 . since 4 * 5 is 20 , let ' s look at the first 20 numbers to get a rough idea of how often this happens . out of the numbers from 1 to 20 : 4 , 5 , 6 , 8 , 9 , 10 , 11 , 12 , 13 , 15 , 16 , 17 , 20 so , 14 out of the first 20 numbers match our criteria . since : probability = ( # of desired outcomes ) / ( total # of possibilities ) , we guesstimate the answer to be 14 / 20 . since ( e ) is the only answer greater than 1 / 2 , we go with ( e ) .\"" + }, + { + "Answer": 2012, + "Options": "a ) 2010 , b ) 2011 , c ) 2012 , d ) 2013 , e ) 2014", + "Correct": "c", + "Explanation": "the cost of commodity x increases by 10 cents per year relative to commodity y . the price of x must gain 20 + 90 = $ 1.10 cents on commodity y , which will take 11 years . the answer is c ." + }, + { + "Answer": 15, + "Options": "a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16", + "Correct": "d", + "Explanation": "let the present ages of anand and bala be ' a ' and ' b ' respectively . a - 10 = 1 / 3 ( b - 10 ) - - - ( 1 ) b = a + 10 substituting b = a + 12 in first equation , a - 10 = 1 / 3 ( a + 0 ) = > 3 a - 30 = a = > 2 a = 30 = > a = 15 . answer : d" + }, + { + "Answer": 40.1, + "Options": "a ) 40.3 , b ) 40.4 , c ) 40.6 , d ) 40.8 , e ) none of the above", + "Correct": "a", + "Explanation": "\"sum of 10 numbers = 402 corrected sum of 10 numbers = 402 \u2013 13 + 31 \u2013 17 = 403 hence , new average = 403 \u2044 10 = 40.3 answer a\"" + }, + { + "Answer": 650, + "Options": "a ) $ 540 , b ) $ 580 , c ) $ 600 , d ) $ 650 , e ) $ 680", + "Correct": "d", + "Explanation": "given that a : ( b + c + d ) = 1 : 2 . hence a contributed 1 / 3 rd of the total price . given b : ( a + c + d ) = 1 : 4 hence b contributed 1 / 5 th of the total price . given c : ( a + b + d ) = 2 : 3 hence c contributed 2 / 5 th of the total price . thus the contribution made by a , b and c = 1 / 3 + 1 / 5 + 2 / 5 = 14 / 15 so , the remaining 1 / 15 th of the price is contributed by david . hence david ' s contribution = 1 / 15 \u00d7 9750 = $ 650 . the answer is d ." + }, + { + "Answer": 760, + "Options": "a ) 450 , b ) 760 , c ) 110 , d ) 180 , e ) 400", + "Correct": "b", + "Explanation": "\"by using the formula , t [ n ( n - 1 ) / 2 ] , where t = no . of games between two teams and n = total no . of teams , we get : 760 option b .\"" + }, + { + "Answer": 6, + "Options": "a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 2 , d ) 4 / 5 , e ) 6", + "Correct": "e", + "Explanation": "\"p ( b | a ) = p ( a \u00e2 \u02c6 \u00aa b ) / p ( a ) p ( b | a ) = ( 12 / 15 ) / ( 2 / 15 ) = 6 . e\"" + }, + { + "Answer": 81.81818181818181, + "Options": "a ) 71.11 , b ) 71.12 , c ) 71.1 , d ) 71.17 , e ) 81.81", + "Correct": "e", + "Explanation": "\"car travels first 160 km at 75 km / hr time taken to travel first 160 km = distancespeed = 160 / 75 car travels next 160 km at 90 km / hr time taken to travel next 160 km = distancespeed = 160 / 90 total distance traveled = 160 + 160 = 2 \u00d7 160 total time taken = 160 / 75 + 160 / 90 average speed = total distance traveled / total time taken = 320 / ( 160 / 75 + 160 / 90 ) = 81.81 km / hr answer : e\"" + }, + { + "Answer": 60, + "Options": "a ) 60 , b ) 78 , c ) 267 , d ) 29 , e ) 27", + "Correct": "a", + "Explanation": "\"a + b + c = 500 a + c = 200 b + c = 360 - - - - - - - - - - - - - - a + b + 2 c = 560 a + b + c = 500 - - - - - - - - - - - - - - - - c = 60 answer : a\"" + }, + { + "Answer": 20, + "Options": "a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22", + "Correct": "d", + "Explanation": "\"let n be the number of participants . the number of games is nc 2 = n * ( n - 1 ) / 2 = 190 n * ( n - 1 ) = 380 = 20 * 19 ( trial and error ) the answer is d .\"" + }, + { + "Answer": 12, + "Options": "a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15", + "Correct": "b", + "Explanation": "( 17.28 / x ) = 2 * 3.6 * 0.2 x = ( 17.28 / 1.44 ) = ( 1728 / 14 ) = 12 . option b" + }, + { + "Answer": 1000, + "Options": "a ) 600 , b ) 800 , c ) 1000 , d ) 1200 , e ) 1400", + "Correct": "c", + "Explanation": "\"each term in set b is 40 more than the corresponding term in set a . the difference of the sums = 25 * 40 = 1000 . the answer is c .\"" + }, + { + "Answer": 12, + "Options": "a ) 12.0 , b ) 30.0 , c ) 30.9 , d ) 40.0 , e ) 60.0", + "Correct": "a", + "Explanation": "the average of 5 numbers is 6.8 the sum of 5 numbers will be 6.8 x 5 = 34 the average of 5 number after one of the number is multiplied by 2 is 9.2 the sum of the numbers will now be 9.2 x 5 = 46 so the sum has increased by 46 - 34 = 12 let the number multiplied by 2 be n then , 2 n = n + 12 or n = 12 answer : - a" + }, + { + "Answer": 6, + "Options": "a ) $ 3 , b ) $ 6 , c ) $ 9 , d ) $ 12 , e ) $ 15", + "Correct": "b", + "Explanation": "\"let q ' s hourly wage be x , then p ' s hourly wage is 1.5 x let t be the number of hours that q needs , then p needs t - 10 hours to do the job . since they both are paid an equal total amount of $ 360 : x * t = 1.5 x * ( t - 10 ) t = 30 hours and q ' s hourly wage is 360 / 30 = $ 12 p ' s hourly wage is 360 / ( t - 10 ) = $ 18 which is $ 6 per hour more . the answer is b .\"" + }, + { + "Answer": 1000, + "Options": "a ) $ 500 , b ) $ 600 , c ) $ 700 , d ) $ 800 , e ) $ 1000", + "Correct": "e", + "Explanation": "\"if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 250 . so 1 / 4 of her savings is $ 250 . so her original savings are 4 times $ 250 = $ 1000 correct answer e\"" + }, + { + "Answer": 879.9999999999993, + "Options": "a ) $ 880 , b ) $ 950 , c ) $ 1100 , d ) $ 1240 , e ) $ 1360", + "Correct": "a", + "Explanation": "\"let p be the original purchase price of the product . bill originally sold the product for 1.1 * p . in the second scenario , the purchase price is 0.9 * p . a 30 % profit means the selling price would be 1.3 * 0.9 * p = 1.17 * p thus , according to the information in the question , 1.17 p - 1.1 p = 56 0.07 = 56 p = 800 the original selling price was 800 * 1.1 = 880 . the correct answer is a .\"" + }, + { + "Answer": 16, + "Options": "a ) 18 , b ) 25 , c ) 16 , d ) 72 , e ) 27", + "Correct": "c", + "Explanation": "\"to improve his average by 6 runs per innings he has to contribute 16 x 6 = 96 runs for the previous 16 innings . thus , the average after the 17 th innings = 112 - 96 = 16 . answer : c\"" + }, + { + "Answer": 184, + "Options": "a ) 164 , b ) 174 , c ) 184 , d ) 194 , e ) 204", + "Correct": "c", + "Explanation": "2 ( n + 1 ) ( 2 n + 1 ) / 3 ( 2 * 12 * 23 ) / 3 = 2 * 4 * 23 = 184 answer : c" + }, + { + "Answer": 5, + "Options": "a ) 8 , b ) 10 , c ) 9 , d ) 6 , e ) 5", + "Correct": "e", + "Explanation": "51 x + 69 = 54 ( x + 1 ) = > 3 x = 15 = > x = 5 answer : e" + }, + { + "Answer": 4, + "Options": "a ) 10 , b ) 99 , c ) 27 , d ) 4 , e ) 29", + "Correct": "d", + "Explanation": "\"let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 32 x = 4 ( 3 x + 5 ) 20 x = 20 x = 1 quantity of alcohol = ( 4 x 1 ) litres = 4 litres . answer : d\"" + }, + { + "Answer": 80, + "Options": "a ) 124 % , b ) b . 120 % , c ) 96 % , d ) 80 % , e ) 64 %", + "Correct": "d", + "Explanation": "\"even i got 96 % j = 100 t = 100 * 0.5 = 50 m = 50 * 1.6 = 80 if mary ' s income is x percent of j m = j * x / 100 x = m * 100 / j = 80 * 100 / 100 = 80 ans : d\"" + }, + { + "Answer": 11, + "Options": "a ) 9 years , b ) 11 years , c ) 14 years , d ) 21 years , e ) 25 years", + "Correct": "b", + "Explanation": "\"solution age of the 15 th student = [ 15 x 15 - ( 14 x 5 + 16 x 9 ) ] = ( 225 - 214 ) = 11 years . answer b\"" + }, + { + "Answer": 0.015625, + "Options": "a ) 0.0016 , b ) 0.0625 , c ) 0.16 , d ) 0.25 , e ) 0.0156", + "Correct": "e", + "Explanation": "( 1 / 4 ) ^ 3 = 1 / 64 = 0.0156 answer : e" + }, + { + "Answer": 72, + "Options": "a ) 79 , b ) 89 , c ) 95 , d ) 72.72 , e ) 97.2", + "Correct": "d", + "Explanation": "\"let the 6 courses that were taken last year be a 1 , a 2 , a 3 , a 4 , a 5 , a 6 a 1 + a 2 + a 3 + a 4 + a 5 + a 6 = 100 * 6 = 600 the year before , the 5 courses be b 1 , b 2 , b 3 , b 4 , b 5 b 1 + b 2 + b 3 + b 4 + b 5 = 40 * 5 = 200 student ' s average = ( 600 + 200 ) / 11 = 72.72 answer d\"" + }, + { + "Answer": 1015, + "Options": "a ) 1008 , b ) 1015 , c ) 1022 , d ) 1032 , e ) none of these", + "Correct": "b", + "Explanation": "\"explanation required number = ( l . c . m . of 12,16 , 18 , 21 , 28 ) + 7 = 1008 + 7 = 1015 answer b\"" + }, + { + "Answer": 16, + "Options": "a ) 10 , b ) 11 , c ) 12 , d ) 16 , e ) 14", + "Correct": "d", + "Explanation": "\"sum of 15 even numbers = 15 * 16 = 240 average = 240 / 15 = 16 answer : d\"" + }, + { + "Answer": 48, + "Options": "a ) 48 , b ) 50 , c ) 62 , d ) 78 , e ) 100", + "Correct": "a", + "Explanation": "milk quantity = 3 / 5 * 60 = 36 water quantity = 100 - 36 = 64 new ratio of m : w = 36 : 64 + x = 3 : 4 192 + 3 x = 144 x = 48 answer is a" + }, + { + "Answer": 100, + "Options": "a ) rs . 200 , b ) rs . 100 , c ) rs . 300 , d ) rs . 50 , e ) rs . 90", + "Correct": "b", + "Explanation": "\"a profit of rs . 500 is divided between x and y in the ratio of 1 / 2 : 1 / 3 or 3 : 2 . so profits are 300 and 200 . difference in profit share = 300 - 200 = 100 answer : b\"" + }, + { + "Answer": 4.210526315789474, + "Options": "a ) $ 4.31 , b ) $ 4.51 , c ) $ 4.21 , d ) $ 5.21 , e ) $ 5.61", + "Correct": "c", + "Explanation": "let money spent each year = $ 60 units bought first year = 20 units bought second year = 15 units bought third year = 12 units bought fourth year = 10 total number of units = 57 total money spent = 60 * 4 = 240 average = 240 / 57 = 4.21 answer : c" + }, + { + "Answer": 62.5, + "Options": "a ) 50 , b ) 26 , c ) 27 , d ) 62.5 , e ) 21", + "Correct": "d", + "Explanation": "\"let the length of each train be x m . then , distance covered = 2 x m . relative speed = 46 - 36 = 10 km / hr . = 10 * 5 / 18 = 25 / 9 m / sec . 2 x / 45 = 25 / 9 = > x = 65.5 . answer : d\"" + }, + { + "Answer": 39, + "Options": "a ) 19 , b ) 29 , c ) 39 , d ) 49 , e ) 59", + "Correct": "c", + "Explanation": "\"solution let the average after 17 th inning = x . then , average after 16 th inning = ( x - 3 ) average = 16 ( x - 3 ) + 87 = 17 x or x = ( 87 - 48 ) = 39 . answer c\"" + }, + { + "Answer": 77, + "Options": "a ) 79 , b ) 89 , c ) 95 , d ) 77.27 , e ) 97.2", + "Correct": "d", + "Explanation": "\"let the 6 courses that were taken last year be a 1 , a 2 , a 3 , a 4 , a 5 , a 6 a 1 + a 2 + a 3 + a 4 + a 5 + a 6 = 100 * 6 = 600 the year before , the 5 courses be b 1 , b 2 , b 3 , b 4 , b 5 b 1 + b 2 + b 3 + b 4 + b 5 = 50 * 5 = 250 student ' s average = ( 600 + 250 ) / 11 = 77.27 answer d\"" + }, + { + "Answer": 5.5, + "Options": "a ) $ 3.15 , b ) $ 4.45 , c ) $ 4.80 , d ) $ 5.5 , e ) $ 5.40", + "Correct": "d", + "Explanation": "\"let the fixed charge of jim \u2019 s taxi service = 2.35 $ and charge per 2 / 5 mile ( . 4 mile ) = . 35 $ total charge for a trip of 3.6 miles = 2.35 + ( 3.6 / . 4 ) * . 35 = 2.35 + 9 * . 35 = 5.5 $ answer d\"" + }, + { + "Answer": 5600, + "Options": "a ) s . 9800 , b ) s . 3800 , c ) s . 9800 , d ) s . 6800 , e ) s . 5600", + "Correct": "e", + "Explanation": "cost of the camel = p 10 camels = 24 horses 16 horses = 4 oxen 6 oxen = 4 elephants 10 elephants = rs . 140000 p = rs . [ ( 24 * 4 * 4 * 140000 ) / ( 10 * 16 * 6 * 10 ) ] p = rs . ( 53760000 / 9600 ) = > p = rs . 5600 answer : e" + }, + { + "Answer": 8, + "Options": "a ) 14 , b ) 13 , c ) 12 , d ) 8 , e ) 10", + "Correct": "d", + "Explanation": "the number = 2 a + 3 b < 20 when a = 1 , b = 1 , 2 , 3 , 4 , 5 - > 2 a = 2 ; 3 b = 3 , 6 , 9 - > the number = 5 , 8 , 11 - - > 3 numbers when a = 2 , b = 1 , 2,3 - > . . . . - - > 3 numbers when a = 3 , b = 1,2 , 3,4 - - > . . . . - - > 2 numbers total number is already 8 . look at the answer there is no number greater than 8 - - > we dont need to try any more answer must be d" + }, + { + "Answer": 10, + "Options": "a ) 30 , b ) 25 , c ) 15 , d ) 10 , e ) 5", + "Correct": "d", + "Explanation": "\"because the cord was extended to its full length at all items , the dog ran along a semi - circular path , from north to south . the circumference of a full circle is 2 * pi * r , but since we only care about the length of half the circle , the semi - circle path is pi * r . w = pi * r = 30 . round pi = 3 , then r = 10 . chord is about 10 feet long . d\"" + }, + { + "Answer": 0.4, + "Options": "a ) 1 / 2 , b ) 2 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 3 / 7", + "Correct": "d", + "Explanation": "\"x = 5 y + 5 , and thus y = x / 5 - 1 the slope is 1 / 5 . the slope of a line through points ( m , n ) and ( m + 2 , n + p ) is ( n + p - n ) / ( m + 2 - m ) = p / 2 p / 2 = 1 / 5 and thus p = 2 / 5 the answer is d .\"" + }, + { + "Answer": 1500, + "Options": "a ) 3387 , b ) 1000 , c ) 2866 , d ) 1500 , e ) 1121", + "Correct": "d", + "Explanation": "\"20 * 15 * 5 = 1500 answer : d\"" + }, + { + "Answer": 5.28, + "Options": "a ) 5.5 min . , b ) 6 min . , c ) 4.9 min . , d ) 5.28 min . , e ) 5 min .", + "Correct": "d", + "Explanation": "\"let both of them meet after t min 4500 m are covered by suresh in 60 m . in t min he will cover 4500 t / 60 likewise , in t min suresh ' s wife will cover 3750 t / 60 given , ( 4500 t / 60 ) + ( 3750 t / 60 ) = 726 t = 5.28 minutes answer : d\"" + }, + { + "Answer": 54.99999999999999, + "Options": "a ) 55 , b ) 100 , c ) 490 , d ) 500 , e ) 980", + "Correct": "a", + "Explanation": "\"average price for a pair of rackets = $ 9.8 total cost = $ 9.8 * x = $ 539 x = 55 pairs were sold . answer : a\"" + }, + { + "Answer": 0.25, + "Options": "a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6", + "Correct": "c", + "Explanation": "1 / 2 + 1 / 2 + 0 = 1 xy = 1 / 2 * 1 / 2 = 1 / 4 answer : c" + }, + { + "Answer": 6000, + "Options": "a ) 600 , b ) 1200 , c ) 1500 , d ) 3600 , e ) 6000", + "Correct": "e", + "Explanation": "\"sugar : flour = 5 : 2 = 25 : 10 ; flour : soda = 10 : 1 = 10 : 1 ; thus we have that sugar : flour : soda = 25 x : 10 x : 1 x . also given that 10 x / ( 1 x + 60 ) = 8 / 1 - - > x = 240 - - > sugar = 25 x = 6000 answer : e .\"" + }, + { + "Answer": 500, + "Options": "a ) 600 , b ) 500 , c ) 400 , d ) 300 , e ) 800", + "Correct": "b", + "Explanation": "\"the student got 125 marks and still failed by 40 marks = 125 + 40 = 165 therefore 33 % of the total marks = 165 100 % of the total = 165 * 100 / 33 = 55 max mark = 500 answer b\"" + }, + { + "Answer": 5, + "Options": "a ) 30 , b ) 18 , c ) 10 , d ) 9 , e ) 5", + "Correct": "e", + "Explanation": "\"( average production for n days ) * n = ( total production for n days ) - - > 60 n = ( total production for n days ) ; ( total production for n days ) + 90 = ( average production for n + 1 days ) * ( n + 1 ) - - > 60 n + 90 = 65 * ( n + 1 ) - - > n = 5 . or as 30 extra units increased the average for n + 1 days by 5 units per day then 30 / ( n + 1 ) = 5 - - > n = 5 . answer : e .\"" + }, + { + "Answer": 0.25, + "Options": "a ) 9 / 16 , b ) 1 / 2 , c ) 1 / 3 , d ) 1 / 4 , e ) 1 / 6", + "Correct": "d", + "Explanation": "remaining number of digits after three ' 0 ' digits = 4 constraint - no more ' 0 ' and no more ' 1 ' well , these four digits can be odd or even 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 16 ways to choose 3 odd digits out of total 4 digits = 4 c 3 = 4 4 * 1 / 16 = 1 / 4 d is the answer hi ! since we are talking about remaining 4 digits . each digit can either be odd or even ( total ways to select = 2 . desired outcome = 1 ) so let ' s say we want to choose first 3 digits as odd digits and last digit as even . the probability will be : - 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 16 but out of remaining 4 digit , any 3 can be odd and one even as there are no constraints in the question . therefore , total ways of choosing 3 odd digits out of 4 total digits = 4 c 3 so , the probability = 4 * 1 / 16 = 1 / 4 answer is d" + }, + { + "Answer": 13, + "Options": "a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14", + "Correct": "d", + "Explanation": "\"according to order of operations , inner brackets first where 6 \u00d7 4 \u00f7 3 is first calculated since it has a multiplication and a division . 6 \u00d7 4 \u00f7 3 = 24 \u00f7 3 = 8 hence 11 + sqrt ( - 4 + 6 \u00d7 4 \u00f7 3 ) = 11 + sqrt ( - 4 + 8 ) = 11 + sqrt ( 4 ) = 11 + 2 = 13 correct answer d ) 13\"" + }, + { + "Answer": 364, + "Options": "a ) 654 , b ) 584 , c ) 384 , d ) 364 , e ) 394", + "Correct": "d", + "Explanation": "the number of positive integer solutions for the equatio fx 1 + x 2 + \u22ef + xn = k ( k - 1 ) c ( n - 1 ) - where k is the number and n is number of variable in the equation . 15 - 1 c 4 - 1 = 14 c 3 = 364 answer : d" + }, + { + "Answer": 8000, + "Options": "a ) rs . 7000 , b ) rs . 8000 , c ) rs . 8500 , d ) rs . 9000 , e ) none", + "Correct": "b", + "Explanation": "\"answer average salary = 8000 + 5000 + 11000 + 7000 + 9000 / 5 = rs . 8000 correct option : b\"" + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 78 , c ) 8 , d ) 9 , e ) 10", + "Correct": "a", + "Explanation": "\"let the time for which car averages 60 mph = t 70 * ( t + 4 ) = 75 * 4 + 60 t = > 10 t = 20 = > t = 2 total duration of the trip = 4 + 2 = 6 answer a\"" + }, + { + "Answer": 840, + "Options": "a ) $ 840 , b ) $ 800 , c ) $ 1000 , d ) $ 700 , e ) $ 1500", + "Correct": "a", + "Explanation": "\"if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 210 . so 1 / 4 of her savings is $ 210 . so her original savings are 4 times $ 210 = $ 840 correct answer a\"" + }, + { + "Answer": 453, + "Options": "a ) 387 , b ) 429 , c ) 457 , d ) 499 , e ) 536", + "Correct": "c", + "Explanation": "\"sum of consecutive integers from 61 to 69 , inclusive = = = = > ( a 1 + an ) / 2 * # of terms = ( 61 + 69 ) / 2 * 9 = 65 * 9 = 585 sum of non - prime numbers b / w 60 and 70 , non inclusive = = = > 585 - 128 ( i . e . , 61 + 67 , being the prime # s in the range ) = 457 answer : c\"" + }, + { + "Answer": 10, + "Options": "a ) - 10 , b ) 10 , c ) - 19 , d ) 20 , e ) 21", + "Correct": "a", + "Explanation": "\"yes ! there is really a faster way to solve it . sum of consecutive odd or even integers = ( no . of odd or even ints ) * ( first int + last int ) / 2 here a = sum of even ints from 2 to 20 , inclusive number of even ints = 10 , first int + last int = 2 + 20 = 22 a = 10 * 22 / 2 = 110 b = sum of odd ints from 1 to 19 , inclusive number of odd ints = 10 , first int + last int = 1 + 19 = 20 a = 10 * 20 / 2 = 100 b - a = 100 - 110 = - 10 ans : a\"" + }, + { + "Answer": 13, + "Options": "a ) - 13 , b ) 13 , c ) 5 , d ) 7 , e ) 8", + "Correct": "b", + "Explanation": "\"a can not be the answer as all the three terms are in modulus and hence the answer will be non negative . | x - 4 | > = 0 - - > minimum occurs at x = 4 | x + 8 | > = 0 - - > minimum occurs at x = - 8 | x - 5 | > = 0 - - > minimum occurs at x = 5 x = - 8 - - > result = 12 + 0 + 13 = 25 . also any negative value will push the combined value of | x - 4 | + | x - 5 | to a value > 9 . x = 4 - - > result = 0 + 12 + 1 = 13 x = 5 - - > result = 1 + 13 + 0 = 14 x = 8 - - > result = 4 + 16 + 3 = 23 so minimum value of the expression occurs at x = 4 and the resultant value = 13 answer : b\"" + }, + { + "Answer": 36, + "Options": "a ) 37 , b ) 36 , c ) 39 , d ) 40 , e ) 41", + "Correct": "b", + "Explanation": "\"let present age of a be a and b be b a + 10 = 2 * ( b - 10 ) = > 2 b - a = 30 . . . . . . ( i ) a = b + 6 = > 2 b - b - 6 = 30 b = 36 so the present age of b is 36 years answer : b\"" + }, + { + "Answer": 200, + "Options": "a ) 200 m , b ) 250 m , c ) 450 m , d ) 350 m , e ) 270 m", + "Correct": "a", + "Explanation": "speed of a : speed of b = 5 \u2044 3 : 1 = 5 : 3 i . e . , in a race of 5 m , a runs 5 m and b runs 3 m i . e . , a gains 2 m over b in a race of 5 m = > a gains 80 m over b in a race of 52 \u00d7 80 = 200 m hence , winning point should be 200 m away from the starting point . answer : a" + }, + { + "Answer": 15, + "Options": "a ) 20 , b ) 18 , c ) 14 , d ) 15 , e ) 16", + "Correct": "d", + "Explanation": "easy way to go about this problem is we have 6 * 6 = 36 enteries in table the least number of enteries would be ( 36 - 6 ) / 2 since 6 enteries represent the distances between same points . alternatively this can be solved as combination problem . correct answer d" + }, + { + "Answer": 93, + "Options": "a ) 93 kg , b ) 50 kg , c ) 85 kg , d ) 80 kg , e ) 60 kg", + "Correct": "a", + "Explanation": "\"explanation : total increase in weight = 8 \u00e3 \u2014 3.5 = 28 if x is the weight of the new person , total increase in weight = x \u00e2 \u02c6 \u2019 65 = > 28 = x - 65 = > x = 28 + 65 = 93 answer : option a\"" + }, + { + "Answer": 36, + "Options": "a ) a ) 51 , b ) b ) 50 , c ) c ) 45 , d ) d ) 40 , e ) e ) 36", + "Correct": "e", + "Explanation": "\"explanation : let the number be x . then , x - ( x / 3 ) = 24 = > 2 x / 3 = 24 = > x = 36 answer : option e\"" + }, + { + "Answer": 43, + "Options": "a ) $ 21 , b ) $ 27 , c ) $ 31 , d ) $ 43 , e ) it can not be determined", + "Correct": "d", + "Explanation": "\"let ' s suppose that the price of a burger is bb , of a shake - ss and that of a cola is cc . we can then construct these equations : 3 b + 7 s + c = 120 4 b + 10 s + c = 158.5 subtracting the first equation from the second gives us b + 3 s = 38.5 now if we subtract the new equation two times from first or 3 times from second we will get b + s + c = 43 . in any case , there is no necessity to know each item ' s price , just the sum . answer : d\"" + }, + { + "Answer": 40, + "Options": "a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50", + "Correct": "d", + "Explanation": "\"i think we can use double - matrix method and solve using only one variable . our goal is to find the number of hardcover nonfiction books . let that number be x . we are given that all 140 books are either paperback fiction , paperback nonfiction , or hardcover nonfiction . this implies that number of hardcover fiction books is 0 . double - matrix : p = paperback ; h = hardcover ; f = fiction ; nf = nonfiction p h total f 2 x + 40 0 nf x + 20 x total 3 x + 60 x 220 3 x + 60 + x = 220 x = 40 answer ( d . )\"" + }, + { + "Answer": 49, + "Options": "a ) 20 , b ) 31 , c ) 42 , d ) 49 , e ) 64", + "Correct": "d", + "Explanation": "x + ( x - 14 ) = 84 - - > x = 49 . answer : d ." + }, + { + "Answer": 10, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 10", + "Correct": "e", + "Explanation": "\"( x + 2 ) \u00d7 30 + x \u00d7 120 + ( x \u2212 2 ) \u00d7 180 / ( x + 2 ) + x + ( x \u2212 2 ) = 100 \u21d2 330 x \u2212 300 / 3 x = 100 \u21d2 30 x = 300 \u21d2 x = 10 answer e\"" + }, + { + "Answer": 4, + "Options": "a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12", + "Correct": "a", + "Explanation": "\"while this question can be solved with a rather straight - forward algebra approach ( as the other posters have noted ) , it can also be solved by testing the answers . one of those numbers must be the total number of goals . . . from a tactical standpoint , it ' s best to test either answer b or answer d , so if the answer is not correct , then you would have a gauge for whether you should gohigherorlowerwith your next test . here , i ' ll start with answer a = 4 goals if . . . . total goals = 4 goals 5 th game = 2 goals 1 st 4 games = 2 goals avg . for 1 st 4 games = 2 / 4 = 0.5 goal / game avg . for all 5 games = 4 / 5 = 0.8 goals / game this is an exact match for what we ' re told in the prompt , so answer a must be the answer .\"" + }, + { + "Answer": 16, + "Options": "a ) $ 16 , b ) $ 14 , c ) $ 5 , d ) $ 15 , e ) $ 0", + "Correct": "a", + "Explanation": "\"1 / 5 x $ 120 = $ 24 for sandwich 1 / 6 x $ 120 = $ 20 for museum 1 / 2 x $ 120 = $ 60 for book $ 24 + $ 20 + $ 60 = $ 104 spent $ 120 - $ 104 = $ 16 left over correct answer a\"" + }, + { + "Answer": 0.09166666666666666, + "Options": "a ) 55 / 601 , b ) 601 / 55 , c ) 11 / 120 , d ) 120 / 11 , e ) 120 / 13", + "Correct": "c", + "Explanation": "\"given a + b = 55 , hcm and lcm is 5 and 120 axb = lcmx hcf 600 = 120 x 5 1 / a + 1 / b = a + b / ab = > 55 / 600 = > 11 / 120 answer : c\"" + }, + { + "Answer": 35, + "Options": "a ) 40 , b ) 45 , c ) 35 , d ) 50 , e ) 55", + "Correct": "c", + "Explanation": "a is one third of the sum of b and c . . or a = 1 / 3 ( b + c ) . . . but a + b + c = 60 so 1 / 3 ( b + c ) + b + c = 60 4 ( b + c ) / 3 = 60 b + c = 60 * 3 / 4 = 45 a = 60 - 45 = 15 2 ) b is one fifth of the sum of a and c or b = 1 / 5 ( a + c ) . . . but a + b + c = 60 so 1 / 5 ( a + c ) + a + c = 60 a + c = 60 * 5 / 6 = 50 but a = 15 , so c = 50 - 15 = 35 answer : c" + }, + { + "Answer": 0.6666666666666665, + "Options": "a ) 1 / 12 , b ) 1 / 9 , c ) 1 2 / 3 , d ) 2 / 3 , e ) 2 1 / 9", + "Correct": "d", + "Explanation": "\"total bought = 5 / 11 + 2 / 3 left part 25 / 55 - - - > 5 / 11 so used part 5 / 11 + 2 / 3 - 5 / 11 = 2 / 3 ans d\"" + }, + { + "Answer": 166, + "Options": "a ) 27556 , b ) 800 , c ) 796 , d ) 87 , e ) 166", + "Correct": "e", + "Explanation": "2 = 2 3 = 3 4 = 2 * 2 5 = 5 6 = 2 * 3 7 = 7 8 = 2 * 2 * 2 9 = 3 * 3 10 = 2 * 5 11 = 11 so ( x ^ 2 ) + 164 = ( 2 * 2 * 2 * 3 * 3 * 5 * 7 * 11 ) = 27720 . then ( x ^ 2 ) = 27556 . then x = 166 , which is option e ." + }, + { + "Answer": 0.6071428571428572, + "Options": "a ) 4 / 7 , b ) 9 / 14 , c ) 11 / 14 , d ) 17 / 28 , e ) 23 / 28", + "Correct": "d", + "Explanation": "\"p ( red or blue ) = 1 - p ( white ) - p ( green ) = 28 / 28 - 7 / 28 - 4 / 28 = 17 / 28 the answer is d .\"" + }, + { + "Answer": 70, + "Options": "a ) 70 m , b ) 72 m , c ) 80 m , d ) 82 m , e ) 84 m", + "Correct": "a", + "Explanation": "\"let the length of each train be x m . then , distance covered = 2 x m . relative speed = 50 - 36 = 14 km / hr . = 14 * 5 / 18 = 35 / 9 m / sec . 2 x / 36 = 35 / 9 = > x = 70 . answer : a\"" + }, + { + "Answer": 158, + "Options": "a ) 150 , b ) 152 , c ) 154 , d ) 158 , e ) 144", + "Correct": "d", + "Explanation": "\"d = d * q + r d = 17 * 9 + 5 d = 153 + 5 d = 158\"" + }, + { + "Answer": 50.90909090909091, + "Options": "a ) 52.6 , b ) 52.4 , c ) 52.1 , d ) 50.9 , e ) 52.9", + "Correct": "d", + "Explanation": "\"sum of the marks for the class of 25 students = 25 * 40 = 1000 sum of the marks for the class of 30 students = 30 * 60 = 1800 sum of the marks for the class of 55 students = 1000 + 1800 = 2800 average marks of all the students = 2800 / 55 = 50.9 . answer : d\"" + }, + { + "Answer": 0.16666666666666669, + "Options": "a ) 0 , b ) 1 / 15 , c ) 2 / 15 , d ) 1 / 6 , e ) 2 / 10", + "Correct": "d", + "Explanation": "\"suppose the water in each jug is l liters cx x ( 1 / 3 ) = l cx = 3 l liters cx is capacity of x cy x ( 2 / 3 ) = l cy = 3 l / 2 liters cy is capacity of y now , y is 3 l / 2 - l empty = l / 2 empty so , we can put only l / 2 water in jug y from jug x jug x ' s remaining water = l - l / 2 = l / 2 fraction of x which contains water = water / cx = ( l / 2 ) / 3 l = 1 / 6 answer will be d\"" + }, + { + "Answer": 35, + "Options": "a ) 30 , b ) 35 , c ) 40 , d ) 45 , e ) 55", + "Correct": "b", + "Explanation": "\"a 1 = 120 / 3 = 40 a 2 = a 1 - 5 = 35 sum of second list = 35 * 3 = 105 therefore the number = 105 - 70 = 35 b\"" + }, + { + "Answer": 60.000000000000014, + "Options": "a ) 60 , b ) 45 , c ) 38 , d ) 50 , e ) 39", + "Correct": "a", + "Explanation": "\"let , father \u00e2 \u20ac \u2122 s current age is a years . then , man \u00e2 \u20ac \u2122 s current age = [ ( 2 / 5 ) a ] years . therefore , [ ( 2 / 5 ) a + 12 ] = ( 1 / 2 ) ( a + 12 ) 2 ( 2 a + 60 ) = 5 ( a + 12 ) a = 60 a\"" + }, + { + "Answer": 25, + "Options": "a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 10", + "Correct": "c", + "Explanation": "quantity of milk in the mixture = 90 / 100 ( 50 ) = 45 litres . after adding water , milk would form 60 % of the mixture . hence , if quantity of mixture after adding x liters of water , ( 60 ) / 100 x = 45 = > x = 75 hence 75 - 50 = 25 litres of water must be added . answer : c" + }, + { + "Answer": 10, + "Options": "a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 15", + "Correct": "b", + "Explanation": "\"if the average of 10 - pound and 20 - pound boxes is 18 , the ratio of 10 - pound boxes : 20 - pound boxes is 1 : 4 . so out of 20 boxes , 4 are 10 - pound boxes and 16 are 20 - pound boxes . if the average of 10 and 20 - pound boxes is to be 16 , the ratio of 10 - pound boxes : 20 - pound boxes should be 2 : 3 . the number of 10 pound boxes remains the same so we still have 4 of them . to get a ratio of 2 : 3 , the number of 20 - pound boxes must be 6 . we need to remove 10 of the 20 - pound boxes . the answer is b .\"" + }, + { + "Answer": 33.33333333333333, + "Options": "a ) 30 , b ) 25 , c ) 33.33 , d ) 44.44 , e ) 28", + "Correct": "c", + "Explanation": "unscreened part = 30 - 20 = 10 . % unscreened part = 10 / 30 * 100 = 33.33 % answer c" + }, + { + "Answer": 360, + "Options": "a ) 180 % , b ) 360 % , c ) 200 % , d ) 220 % , e ) 250 %", + "Correct": "b", + "Explanation": "\"say john ' s wages last week were $ 100 , so he spent 0.10 * 100 = $ 10 on recreation ; this week ' s wages is 0.90 * 100 = $ 90 , so he spends 0.4 * 90 = $ 36 on recreation ; 36 / 10 = 3.60 , hence the amount he spends on recreation this week is 360 % of the amount he spent on recreation last week : 10 * 3.6 = 36 answer : b\"" + }, + { + "Answer": 10, + "Options": "a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12", + "Correct": "d", + "Explanation": "the line with slope 2 passing through ( 40 , 30 ) has x - intercept 40 \u2212 ( 30 / 2 ) . the line with slope 6 passing through ( 40 , 30 ) has x - intercept 40 \u2212 ( 30 / 6 ) . so the difference in the x - intercepts is ( 30 / 2 ) \u2212 ( 30 / 6 ) = 10 . correct answer d" + }, + { + "Answer": 18, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 18 , e ) 11", + "Correct": "d", + "Explanation": "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 47 5 x = 45 = > x = 9 hence , b ' s age = 2 x = 18 years . answer : d" + }, + { + "Answer": 200, + "Options": "a ) $ 110 , b ) $ 120 , c ) $ 180 , d ) $ 200 , e ) $ 260", + "Correct": "d", + "Explanation": "\"lets assume al have amount a in his bank account and eliot ' s bank account got e amount . we can form an equation from the first condition . a - e = 1 / 12 * ( a + e ) = = > 11 a = 13 e - - - - - - - - - - - - ( 1 ) second condition gives two different amounts , al ' s amount = 1.1 a and eliot ' s amount = 1.2 e 1.1 a = 20 + 1.2 e = = > 11 a = 200 + 12 e - - - - - - - ( 2 ) substituting ( 1 ) in ( 2 ) : 13 e = 200 + 12 e = = > e = 200 d\"" + }, + { + "Answer": 6, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "e", + "Explanation": "assume the answer choices as the value of z 9 / 9 = 1 ans e" + }, + { + "Answer": 9, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10", + "Correct": "d", + "Explanation": "\"x < y < z to find the least possible value for z - x ; we need to find the values for z and x that can be closest to each other . if x is some even number , then what could be minimum possible odd z . if x is some even number y - x > 5 ; y > x + 5 ; minimum value for y = x + 5 + 2 = x + 7 [ note : x + 5 is as even + odd = odd and nearest odd greater than x + 5 is x + 5 + 2 ] minimum value for z = y + 2 = x + 7 + 2 = x + 9 [ note : z = y + 2 because both z and y are odd . difference between two odd numbers is 2 ] d = z - x = x + 9 - x = 9 ans : d\"" + }, + { + "Answer": 20000, + "Options": "a ) $ 20000 , b ) $ 15000 , c ) $ 12000 , d ) $ 10000 , e ) $ 9000", + "Correct": "a", + "Explanation": "since investment doubles in 70 / r years , then for r = 8 it ' ll double in 70 / 8 = ~ 9 years ( we are not asked about the exact amount so such an approximation will do ) . thus in 18 years investment will double twice and become ( $ 5,000 * 2 ) * 2 = $ 20,000 ( after 9 years investment will become $ 5,000 * 2 = $ 10,000 and in another 9 years it ' ll become $ 10,000 * 2 = $ 20,000 ) . answer : a ." + }, + { + "Answer": 98.76543209876543, + "Options": "a ) 97.765 % , b ) 99.765 % , c ) 96.765 % , d ) 95.765 % , e ) 98.765 %", + "Correct": "e", + "Explanation": "\"let the number be x the right number is 9 x the wrong number is x / 9 error is ( 9 x - x / 9 ) = 80 x / 9 percentage of error is ( ( 80 x / 9 ) / 9 x ) * 100 = 98.765 % answer : e\"" + }, + { + "Answer": 60.000000000000014, + "Options": "a ) 40 , b ) 52 , c ) 60 , d ) 80 , e ) 98", + "Correct": "c", + "Explanation": "\"let the no of matches played more = x so , ( 120 + x ) * 52 / 100 = 33.6 + x by solving we get x = 60 answer : c\"" + }, + { + "Answer": 24, + "Options": "a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25", + "Correct": "d", + "Explanation": "\"let the average age of the whole team be x years . 11 x - ( 26 + 31 ) = 9 ( x - 1 ) 11 x - 9 x = 48 2 x = 48 x = 24 . the average age of the team is 24 years . the answer is d .\"" + }, + { + "Answer": 35, + "Options": "a ) 20 , b ) 35 , c ) 55 , d ) 65 , e ) 80", + "Correct": "b", + "Explanation": "\"the arithmetic mean of 4 equally weighted tests was 50 . so what we can assume is that we have 4 test scores , each 50 . he dropped his lowest score and the avg went to 55 . this means that the lowest score was not 50 and other three scores had given the lowest score 5 each to make it up to 50 too . when the lowest score was removed , the other 3 scores got their 5 back . so the lowest score was 3 * 5 = 15 less than 50 . so the lowest score = 50 - 15 = 35 answer ( b )\"" + }, + { + "Answer": 2, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "c", + "Explanation": "first thing i noticed was that all these numbers are prime . . . prime factorization gives the following step 1 : 2 * 1210 step 2 : 2 * 11 * 110 step 4 : 2 * 11 * 11 * 10 step 5 : 2 * 11 * 11 * 2 * 5 so he scored e = 2 11 - point baskets in my opinion . answer c" + }, + { + "Answer": 7, + "Options": "a ) 0 , b ) 1 , c ) 3 , d ) 4 , e ) 7", + "Correct": "e", + "Explanation": "\"i tried plugging in numbers x = 9 q + 5 x = 14 5 x = 70 5 x / 9 = 63 + 7 remainder is 7 . answer is e .\"" + }, + { + "Answer": 70.00000000000398, + "Options": "a ) 72 , b ) 71 , c ) 70 , d ) 30 , e ) 45", + "Correct": "c", + "Explanation": "\"when positive integer x is divided by positive integer y , the remainder is 7 - - > x = qy + 7 ; x / y = 86.1 - - > x = 86 y + 0.1 y ( so q above equals to 86 ) ; 0.1 y = 7 - - > y = 70 . answer : c .\"" + }, + { + "Answer": 5, + "Options": "a ) 16 . , b ) 8 . , c ) 5 . , d ) 2 . , e ) - 2 .", + "Correct": "c", + "Explanation": "\"given a + b = 11 = > a = 11 - b - - > eq 1 b + c = 9 c + d = 3 = > d = 3 - c - - > eq 2 then eqs 1 + 2 = > a + d = 11 - b + 3 - c = > 14 - ( b + c ) = > 14 - 9 = 5 . option c . . .\"" + }, + { + "Answer": 25, + "Options": "a ) 25 , b ) 26 , c ) 18 , d ) 19 , e ) 10", + "Correct": "a", + "Explanation": "let the six numbers be , a , b , c , d , e , f . a + b + c + d + e + f = 30 \u00d7 6 = 180 - - - - ( 1 ) a + b + c + d = 25 \u00d7 4 = 100 - - - - ( 2 ) d + e + f = 35 \u00d7 3 = 105 - - - - ( 3 ) add 2 nd and 3 rd equations and subtract 1 st equation from this . d = 25 answer : a" + }, + { + "Answer": 663, + "Options": "a ) 515 . , b ) 545 . , c ) 661 . , d ) 644 . , e ) 666 .", + "Correct": "c", + "Explanation": "\"answer is c : 661 solution : total number of students studying both are 423 + 240 - 134 = 529 ( subtracting the 134 since they were included in the both the other numbers already ) . so 80 % of total is 529 , so 100 % is approx . 661 .\"" + }, + { + "Answer": 40, + "Options": "a ) 40 , b ) 30 , c ) 25 , d ) data inadequate , e ) none of these .", + "Correct": "a", + "Explanation": "\"let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 60 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 60 + 20 ) / 2 = 40 . answer : a\"" + }, + { + "Answer": 45, + "Options": "a ) 88 , b ) 45 , c ) 36 , d ) 80 , e ) 12", + "Correct": "b", + "Explanation": "\"speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 240 + 210 = 450 m . time taken = 450 / 10 = 45 sec . answer : b\"" + }, + { + "Answer": 5, + "Options": "a ) 1 , b ) 3 , c ) 0 , d ) 5 , e ) 7", + "Correct": "d", + "Explanation": "1 * 3 * 5 * 7 . . . . . . . . . . . . . . . . . . . will end up in 5 in the units place answer : d" + }, + { + "Answer": 37, + "Options": "a ) 5 , b ) 10 , c ) 37 , d ) 40 , e ) 45", + "Correct": "c", + "Explanation": "solution - lets say , single hamburgersxand double hamburgersy given that , x + y = 50 and 1 x + 1.5 y = 68.50 . by solving the equations y = 37 . ans c ." + }, + { + "Answer": 32000, + "Options": "a ) $ 20000 , b ) $ 15000 , c ) $ 32000 , d ) $ 10000 , e ) $ 9000", + "Correct": "c", + "Explanation": "\"since investment doubles in 70 / r years then for r = 8 it ' ll double in 70 / 8 = ~ 9 years ( we are not asked about the exact amount so such an approximation will do ) . thus in 18 years investment will double twice and become ( $ 8,000 * 2 ) * 2 = $ 32,000 ( after 9 years investment will become $ 8,000 * 2 = $ 16,000 and in another 9 years it ' ll become $ 16,000 * 2 = $ 32,000 ) . answer : c .\"" + }, + { + "Answer": 34, + "Options": "a ) 37 , b ) 26 , c ) 34 , d ) 18 , e ) 11", + "Correct": "c", + "Explanation": "explanation : 24 + 26 + 6 * 3 = 68 / 2 = 34 answer : c" + }, + { + "Answer": 3, + "Options": "a ) 3 , b ) 2 , c ) 1 , d ) 0 , e ) 4", + "Correct": "a", + "Explanation": "\"| 9 - 4 | - | 12 - 14 | = | 5 | - | - 2 | = 5 - 2 = 3 correct answer a\"" + }, + { + "Answer": 400, + "Options": "a ) 400 , b ) 540 , c ) 100 , d ) 830 , e ) 420", + "Correct": "a", + "Explanation": "\"4 ^ k = 5 4 ^ 2 k = 5 ^ 2 4 ^ 2 k = 25 4 ^ ( 2 k + 2 ) = 4 ^ 2 k * 4 ^ 2 = 25 * 16 = 400 answer : a\"" + }, + { + "Answer": 3000, + "Options": "a ) 600 , b ) 1200 , c ) 1500 , d ) 1600 , e ) 3000", + "Correct": "e", + "Explanation": "sugar : flour = 5 : 4 = 25 : 20 ; flour : soda = 10 : 1 = 20 : 2 ; thus we have that sugar : flour : soda = 25 x : 20 x : 2 x . also given that 20 x / ( 2 x + 60 ) = 8 / 1 - - > x = 120 - - > sugar = 25 x = 3,000 answer : e ." + }, + { + "Answer": 48, + "Options": "a ) 20 , b ) 36 , c ) 48 , d ) 60 , e ) 72", + "Correct": "c", + "Explanation": "answer c . we know that sarah negotiated a discount of 20 % , so each of them paid $ 4 less . since there are three people , the 20 % of the original price amounts to $ 12 . 5 times 12 $ is 60 $ , so the original price , before sarah negotiated the discount , had been $ 60 . they paid $ 12 less than the base price , so they spent $ 48 ." + }, + { + "Answer": 8000, + "Options": "a ) 8000 , b ) 7540 , c ) 6500 , d ) 9100 , e ) 6000", + "Correct": "a", + "Explanation": "let the number of candidates appeared be x then , 7 % of x - 6 % of x = 80 1 % of x = 80 x = 80 * 100 = 8000 answer is a" + }, + { + "Answer": 13, + "Options": "a ) 13 , b ) 25 , c ) 87 , d ) 49 , e ) 63", + "Correct": "a", + "Explanation": "explanation : required numbers are 24 , 30 , 36 , 42 , . . . , 96 this is an a . p . in which a = 24 , d = 6 and l = 96 let the number of terms in it be n . then tn = 96 a + ( n - 1 ) d = 96 24 + ( n - 1 ) x 6 = 96 ( n - 1 ) x 6 = 72 ( n - 1 ) = 12 n = 13 required number of numbers = 13 . a )" + }, + { + "Answer": 20.000000000000004, + "Options": "a ) 0 , b ) 5 , c ) 10 , d ) 15 , e ) 20", + "Correct": "e", + "Explanation": "\"x = \u221a 5 and y also = \u221a 5 applying the function ( \u221a 5 + \u221a 5 ) ^ 2 - ( \u221a 5 - \u221a 5 ) ^ 2 = ( 2 \u221a 5 ) ^ 2 - 0 = 4 x 5 = 20 . note : alternative approach is the entire function is represented as x ^ 2 - y ^ 2 = ( x + y ) ( x - y ) which can be simplified as ( x + y + x - y ) ( x + y - ( x - y ) ) = ( 2 x ) ( 2 y ) = 4 xy . substituting x = \u221a 5 and y = \u221a 5 you get the answer 20 answer is e .\"" + }, + { + "Answer": 60, + "Options": "a ) 20 , b ) 40 , c ) 60 , d ) 90 , e ) 120", + "Correct": "c", + "Explanation": "\"let ( y / 20 ) x ( y / 180 ) = 1 y ^ 2 = 20 x 180 = 20 x 20 x 9 y = ( 20 x 3 ) = 60 the answer is c .\"" + }, + { + "Answer": 285, + "Options": "a ) 290 , b ) 304 , c ) 285 , d ) 270 , e ) 275", + "Correct": "c", + "Explanation": "\"in a month of 30 days beginning with a sunday , there will be 4 complete weeks and another two days which will be sunday and monday . hence there will be 5 sundays and 25 other days in a month of 30 days beginning with a sunday average visitors on sundays = 510 total visitors of 5 sundays = 510 \u00d7 5 average visitors on other days = 240 total visitors of other 25 days = 240 \u00d7 25 total visitors = ( 510 \u00d7 5 ) + ( 240 \u00d7 25 ) total days = 30 average number of visitors per day = ( ( 510 \u00d7 5 ) + ( 240 \u00d7 25 ) ) / 30 = ( ( 51 \u00d7 5 ) + ( 24 \u00d7 25 ) ) / 3 = ( 17 \u00d7 5 ) + ( 8 \u00d7 25 ) = 85 + 200 = 285 answer is c .\"" + }, + { + "Answer": 22, + "Options": "a ) 16 , b ) 18 , c ) 20 , d ) 22 , e ) 24", + "Correct": "d", + "Explanation": "\"let n be the number of participants . the number of games is nc 2 = n * ( n - 1 ) / 2 = 231 n * ( n - 1 ) = 462 = 22 * 21 ( trial and error ) the answer is d .\"" + }, + { + "Answer": 24, + "Options": "a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 24", + "Correct": "e", + "Explanation": "\"i am getting 12 . e . hope havent done any calculation errors . . approach . . let y = no . of days taken by y to do w widgets . then x will take y + 2 days . 1 / ( y + 2 ) + 1 / y = 5 / 12 ( 5 / 12 is because ( 5 / 4 ) w widgets are done in 3 days . so , x widgets will be done in 12 / 5 days or 5 / 12 th of a widget in a day ) solving , we have y = 4 = > x takes 6 days to doing x widgets . so , he will take 24 days to doing 4 w widgets . answer : e\"" + }, + { + "Answer": 350, + "Options": "a ) $ 310 , b ) $ 320 , c ) $ 330 , d ) $ 340 , e ) $ 350", + "Correct": "e", + "Explanation": "\"s . i for 5 years = $ 595 - $ 420 = $ 175 the s . i . is $ 35 / year s . i . for 2 years = $ 70 principal = $ 420 - $ 70 = $ 350 the answer is e .\"" + }, + { + "Answer": 15, + "Options": "a ) 5 , b ) 10 , c ) 15 , d ) 40 , e ) 50", + "Correct": "c", + "Explanation": "solution let the initial number of persons be x . then 16 x + 15 x 15 = 15.5 ( x + 20 ) = 0.5 x = 7.5 x = 15 . answer c" + }, + { + "Answer": 24, + "Options": "a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25", + "Correct": "d", + "Explanation": "\"10 * 19 - 26 + 76 = 240 240 / 10 = 24 the answer is d .\"" + }, + { + "Answer": 2570, + "Options": "a ) $ 1940 , b ) $ 2150 , c ) $ 2360 , d ) $ 2570 , e ) $ 2780", + "Correct": "d", + "Explanation": "let x be the value of the item . 0.07 * ( x - 1000 ) = 109.90 x = 2570 the answer is d ." + }, + { + "Answer": 10.080000000000002, + "Options": "a ) 9.5 , b ) 9.8 , c ) 10.1 , d ) 10.6 , e ) 11.2", + "Correct": "c", + "Explanation": "\"distance = 21 km time = 9 / 12 + 12 / 9 = ( 81 + 144 ) / 108 = 225 / 108 = 25 / 12 hours average speed = ( 21 * 12 ) / 25 = 10.1 km / h the answer is c .\"" + }, + { + "Answer": 7000, + "Options": "a ) 13000 , b ) 7000 , c ) 10000 , d ) 5000 , e ) none of these", + "Correct": "b", + "Explanation": "\"explanation : profit = 5 , 00,000 \u2212 ( 1 , 50,000 + 75,000 ) = rs . 2 , 75,000 . since , such loom contributes equally to sales and manufacturing expenses . but the monthly charges are fixed at rs 75,000 . if one loan breaks down sales and expenses will decrease . new profit : - = > 500000 \u00d7 ( 49 / 50 ) \u2212 150000 \u00d7 ( 49 / 50 ) \u2212 75000 . = > rs 2 , 68,000 . decrease in profit = > 2 , 75,000 \u2212 2 , 68,000 = > rs . 7,000 . answer : b\"" + }, + { + "Answer": 1800, + "Options": "a ) 1235 , b ) 1346 , c ) 1378 , d ) 1635 , e ) 1815", + "Correct": "e", + "Explanation": "\"let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 4 x + 15 3 x = 1350 x = 450 large number = 450 + 1365 = 1815 e\"" + }, + { + "Answer": 4, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "e", + "Explanation": "sum of all four pigs weigh = 60 kg it is possible that all four pigs are underweight . because the average is 15 kg which itself underweight . answer e" + }, + { + "Answer": 20, + "Options": "a ) 0 , b ) 12 , c ) 13 , d ) 20 , e ) 25", + "Correct": "d", + "Explanation": "12 * 35 = 420 420 % 21 = 20 answer : d" + }, + { + "Answer": 0.3, + "Options": "a ) 3 / 10 , b ) 1 / 2 , c ) 2 / 5 , d ) 3 / 7 , e ) 1 / 6", + "Correct": "a", + "Explanation": "\"here , s = { 1 , 2,3 , . . . . . . , 19,20 } e = event getting a multiple of 3 = { 3,6 , 9,12 , 15,18 } probability = 6 / 20 = 3 / 10 correct option is a\"" + }, + { + "Answer": 32, + "Options": "a ) 28 , b ) 29 , c ) 30 , d ) 31 , e ) 32", + "Correct": "e", + "Explanation": "1000 \u2212 64 = 936 . whatever xy is you finish with 36 = = > 3 + 6 = 9 therefore , 279 \u2212 9 = 270 and 270 / 9 = 30 now you add the last two digits ( 3 and 6 ) answer is 30 + 2 = 32 answer : e" + }, + { + "Answer": 7145, + "Options": "a ) 7400 , b ) 7145 , c ) 7200 , d ) 7323 , e ) 6030", + "Correct": "b", + "Explanation": "\"x * ( 85 / 100 ) * ( 75 / 100 ) = 4555 x = 7145 answer : b\"" + }, + { + "Answer": 22, + "Options": "a ) 24 , b ) 33 , c ) 22 , d ) 20 , e ) 21", + "Correct": "c", + "Explanation": "\"( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 252 + 2 * 116 a + b + c = \u00e2 \u02c6 \u0161 484 = 22 answer c\"" + }, + { + "Answer": 24, + "Options": "a ) 4 , b ) 14 , c ) 24 , d ) 34 , e ) 44", + "Correct": "c", + "Explanation": "\"according to order of operations , inner brackets first where 6 ? 4 ? 3 is first calculated since it has a multiplication and a division . 6 * 4 * 3 = 24 * 3 = 8 hence 22 + sqrt ( - 4 + 6 * 4 * 3 ) = 22 + sqrt ( - 4 + 8 ) = 22 + sqrt ( 4 ) = 22 + 2 = 24 correct answer c\"" + }, + { + "Answer": 104, + "Options": "a ) $ 100.00 , b ) $ 104.00 , c ) $ 110.00 , d ) $ 115.00 , e ) $ 119.00", + "Correct": "b", + "Explanation": "first 3 shirts are sold for $ 82 , $ 100 and $ 90 = $ 272 . to get average price of $ 100 , total sale should be 10 * $ 100 = $ 1000 so remaining 7 shirts to be sold for $ 1000 - $ 272 = $ 728 answer should be 728 / 7 = $ 104.00 that is b" + }, + { + "Answer": 5, + "Options": "a ) 5 kg , b ) 6.5 kg , c ) 7.5 kg , d ) 8 kg , e ) 9 kg", + "Correct": "a", + "Explanation": "explanation : expl : milk in 85 kg of mix = 85 * ( 27 / 34 ) = 135 / 2 kg . water in it = 85 - 135 / 2 = 35 / 2 kg . let x kg of water be added to it . then , ( 135 / 2 ) / ( 35 / 2 + x ) = 3 / 1 ; 135 / ( 35 + 2 x ) = 3 / 1 ; 105 + 6 x = 135 ; 6 x = 30 ; x = 5 the quantity of water to be added = 5 kg answer : a" + }, + { + "Answer": 6, + "Options": "a ) 2 , b ) 5 , c ) 7 , d ) 6 , e ) 35", + "Correct": "d", + "Explanation": "ab = 12 + 2 ( a + b ) 10 a = 12 + 2 a + 20 8 a = 32 a = 4 b - a = 10 - 4 = 6 d is the answer" + }, + { + "Answer": 4, + "Options": "a ) 6 , b ) 8 , c ) 4 , d ) 9 , e ) 2", + "Correct": "c", + "Explanation": "\"7 people visited 2 stores each for 14 visits . to maximize the number of stores that one person visited , let ' s assume that 3 people visited 1 store each . the number of remaining visits is 21 - 14 - 3 = 4 , which is the maximum that one person could have visited . the answer is c .\"" + }, + { + "Answer": 9996, + "Options": "a ) 4676 , b ) 4678 , c ) 8888 , d ) 9504 , e ) 9996", + "Correct": "e", + "Explanation": "\"largest 4 digit number = 9999 9999 \u00f7 12 = 833 , remainder = 3 hence largest 4 digit number exactly divisible by 12 = 9999 - 3 = 9996 answer : e\"" + }, + { + "Answer": 14.285714285714285, + "Options": "a ) 14.3 % . , b ) 70 % . , c ) 60 % . , d ) 68 % . , e ) 80 % .", + "Correct": "a", + "Explanation": "given ratio = 1 / 8 : 1 / 7 = 7 : 8 let first number be 7 x and the second number be 8 x . the second number is more than first number by 1 x . required percentage = 1 x / 7 x * 100 = 14.3 % . answer : a" + }, + { + "Answer": 104, + "Options": "a ) 104 , b ) 27 , c ) 99 , d ) 17 , e ) 80", + "Correct": "a", + "Explanation": "\"explanation : number of subjects = 6 average of marks in 6 subjects = 79 therefore total marks in 6 subjects = 79 * 6 = 474 now , no . of subjects = 5 total marks in 5 subjects = 74 * 5 = 370 therefore marks in 6 th subject = 474 \u2013 370 = 104 answer : a\"" + }, + { + "Answer": 0.9333333333333333, + "Options": "a ) 14 / 15 , b ) 15 / 16 , c ) 17 / 18 , d ) 9 / 10 , e ) 5 / 6", + "Correct": "a", + "Explanation": "the probability that he makes at least one of the three shots = 1 - ( the probability that he misses all of the shots ) the probability that he misses all shots = ( prob that he misses free throw ) * ( prob that he misses 3 - pointer ) * ( prob that he misses the professional 3 - pointer ) prob that he misses the free throw = 1 - 4 / 5 = 1 / 5 ; prob that he misses the 3 - pointer = 1 - 1 / 2 = 1 / 2 ; prob that he misses the professional 3 - pointer = 1 - 1 / 3 = 2 / 3 thus the probability that he misses all shots = ( 1 / 5 ) * ( 1 / 2 ) * ( 2 / 3 ) = 1 / 15 answer : 1 - 1 / 15 = 14 / 15 a" + }, + { + "Answer": 392, + "Options": "a ) 392 , b ) 412 . , c ) 432 . , d ) 502 , e ) 522", + "Correct": "a", + "Explanation": "\"solution 1 : given that number of pastries are equally divided in to 28 groups , so the answer should be a multiple of 28 . and in the given choices , only 392 is divisible by 28 with remainder 0 ( make sure others are no multiples of 28 ) . so this is good enough to stop here , but to verify , 392 / 28 = 14 and 392 / 49 = 8 , which confirms the second part of question , 14 - 8 , 6 pastry short of each customer . solution 2 : going mathematical , expressing in the equation form , let x be the number of pastries and , n be the number of customers in 28 groups . so , x = 28 * n , as per second statement , x = 49 * ( n - 6 ) solve the above 2 for n and then we get x as 392 . answer is a : 392 .\"" + }, + { + "Answer": 36, + "Options": "a ) 35 , b ) 38 , c ) 45 , d ) 36 , e ) 60", + "Correct": "d", + "Explanation": "\"explanation : if teacher ' s age is 15 years , there is no change in the average . but teacher has contributed 1 year to all the students along with maintaining his age at 16 . age of teacher = average age of all + total increase in age = 16 + ( 1 x 20 ) = 36 years answer : d\"" + }, + { + "Answer": 144, + "Options": "a ) t = 288 , b ) t = 144 , c ) t = 12 , d ) 48 , e ) 96", + "Correct": "b", + "Explanation": "4 white chess pieces can be arranged in 4 ! ways and 4 black pieces can be arranged in 3 ! ways . w _ w _ w _ w number of ways = 4 ! * 3 ! = 24 * 6 = 144 answer b" + }, + { + "Answer": 4, + "Options": "a ) 4 , b ) 2 , c ) 0 , d ) \u2212 2 , e ) \u2212 4", + "Correct": "a", + "Explanation": "\"slope = rise / run = 7 / 14 = 1 / 2 the equation of the line is y = ( 1 / 2 ) x + b 3 = ( 1 / 2 ) ( 10 ) + b b = - 2 the equation of the line is y = ( 1 / 2 ) x - 2 to find the x - intercept , let y = 0 : 0 = ( 1 / 2 ) x - 2 x = 4 the answer is a .\"" + }, + { + "Answer": 64, + "Options": "a ) 4 , b ) 24 , c ) 54 , d ) 64 , e ) 94", + "Correct": "d", + "Explanation": "\"from ( x + 8 ) ( y - 8 ) = 0 it follows that either , x = - 8 or y = 8 . thus either x ^ 2 = 64 or y ^ 2 = 64 . now , if x ^ 2 = 64 , then the least value of y ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 64 + 0 = 64 . similarly if y ^ 2 = 64 , then the least value of x ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 0 + 64 = 64 . answer : d .\"" + }, + { + "Answer": 14.999999999999991, + "Options": "a ) 3 % , b ) 5 % , c ) 10 % , d ) 15 % , e ) 18 %", + "Correct": "d", + "Explanation": "1990 dick saved = $ 1150 jane saved = $ 850 ( jane saved $ 150 less than she did the prior year ) jane saved approximately $ 150 / 1000 $ ( 15 % ) less in 1990 answer : d" + }, + { + "Answer": 0.35714285714285715, + "Options": "a ) 7 / 16 , b ) 7 / 15 , c ) 10 / 21 , d ) 17 / 35 , e ) 5 / 14", + "Correct": "e", + "Explanation": "\"let the total # of cups be 10 . # of small cups sold 3 / 5 * 10 = 6 ; # of large cups sold 10 - 6 = 4 ; let the price of small cup be $ 6 , then the price of larges cup would be 5 / 6 * 6 = $ 5 ; revenue from small cups : 6 * $ 6 = $ 36 ; revenue from large cups cups : 4 * $ 5 = $ 20 ; fraction of total revenue from large cups : 20 / ( 36 + 20 ) = 5 / 14 . answer : e\"" + }, + { + "Answer": 18.333333333333332, + "Options": "a ) 68.33 , b ) 18.33 , c ) 28.33 , d ) 48.33 , e ) 98.33", + "Correct": "b", + "Explanation": "explanation : present worth = amount - truediscount = 110 - 10 = rs . 100 si on rs . 100 for a certain time = rs . 10 si on rs . 100 for doube the time = rs . 20 truediscount on rs . 120 = 120 - 100 = rs . 20 truediscount on rs . 110 = = rs . 18.33 answer : b" + }, + { + "Answer": 14, + "Options": "a ) 30 , b ) 14 , c ) 10 , d ) 9 , e ) 7", + "Correct": "b", + "Explanation": "\"( average production for n days ) * n = ( total production for n days ) - - > 60 n = ( total production for n days ) ; ( total production for n days ) + 90 = ( average production for n + 1 days ) * ( n + 1 ) - - > 60 n + 90 = 62 * ( n + 1 ) - - > n = 14 . or as 30 extra units increased the average for n + 1 days by 2 units per day then 30 / ( n + 1 ) = 2 - - > n = 14 . answer : b .\"" + }, + { + "Answer": 77, + "Options": "a ) 76 kg , b ) 77 kg , c ) 76.5 kg , d ) data inadequate , e ) none of these", + "Correct": "b", + "Explanation": "\"total weight increases = 8 \u00d7 1.5 = 12 kg so the weight of new person = 65 + 12 = 77 kg answer b\"" + }, + { + "Answer": 260, + "Options": "a ) $ 220 , b ) $ 240 , c ) $ 260 , d ) $ 300 , e ) $ 320", + "Correct": "c", + "Explanation": "\"1.2 n + n = 572 2.2 n = 572 n = 260 the answer is c .\"" + }, + { + "Answer": 372.00000000000006, + "Options": "a ) s . 300 , b ) s . 360 , c ) s . 389 , d ) s . 368 , e ) s . 372", + "Correct": "e", + "Explanation": "( a = 2 / 3 b and b = 1 / 4 c ) = a / b = 2 / 3 and b / c = 1 / 4 a : b = 2 : 3 and b : c = 1 : 4 = 3 : 12 a : b : c = 2 : 3 : 12 a ; s share = 527 * 2 / 17 = rs . 62 b ' s share = 527 * 3 / 17 = rs . 93 c ' s share = 527 * 12 / 17 = rs . 372 . answer : e" + }, + { + "Answer": 30, + "Options": "a ) a ) 36 , b ) b ) 30 , c ) c ) 40 , d ) d ) 42 , e ) e ) 44", + "Correct": "b", + "Explanation": "\"let b be the number of blue hats and let g be the number of green hats . b + g = 85 . b = 85 - g . 6 b + 7 g = 540 . 6 ( 85 - g ) + 7 g = 540 . 510 - 6 g + 7 g = 540 . g = 540 - 510 = 30 . the answer is b .\"" + }, + { + "Answer": 2, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "a", + "Explanation": "\"if average of 3 is 6 so sum of 3 should be 18 3 recording can be from 0 - 10 inclusive to find one smallest other two should be highest so , lets assume three var are a , b , c say a is smallest and give b and c greatest readings say 8 and 8 so a has to be 2 a\"" + }, + { + "Answer": 4, + "Options": "a ) 5 , b ) 6 , c ) 8 , d ) 9 , e ) 4", + "Correct": "e", + "Explanation": "explanation : given exp . = a 2 + b 2 - 2 ab , where a = 287 and b = 269 = ( a - b ) 2 = ( 287 - 269 ) 2 = ( 182 ) = 324 answer is e" + }, + { + "Answer": 0.2222222222222222, + "Options": "a ) 1 / 3 , b ) 1 / 4 , c ) 3 / 8 , d ) 2 / 9 , e ) 5 / 18", + "Correct": "d", + "Explanation": "\"males who did not arrive on time are 1 / 4 * 2 / 3 = 1 / 6 of the attendees . females who did not arrive on time are 1 / 6 * 1 / 3 = 1 / 18 of the attendees . the fraction of all attendees who did not arrive on time is 1 / 6 + 1 / 18 = 2 / 9 the answer is d .\"" + }, + { + "Answer": 52.122093023255815, + "Options": "a ) 50.12 , b ) 52.12 , c ) 51.12 , d ) 53.12 , e ) none of the above", + "Correct": "b", + "Explanation": "\"required average marks = 50 \u00e3 \u2014 50 + 35 \u00e3 \u2014 60 + 45 \u00e3 \u2014 55 + 42 \u00e3 \u2014 45 / 50 + 35 + 45 + 42 = 2500 + 2100 + 2475 + 1890 / 172 = 8965 \u00e2 \u0081 \u201e 172 = 52.12 answer b\"" + }, + { + "Answer": 60, + "Options": "a ) 60 , b ) 62 , c ) 64 , d ) 66 , e ) 68", + "Correct": "a", + "Explanation": "the sum of the four smallest primes greater than 10 is 11 + 13 + 17 + 19 = 60 . the answer is a ." + }, + { + "Answer": 2400, + "Options": "a ) 2388 , b ) 3722 , c ) 2400 , d ) 2872 , e ) 1231", + "Correct": "c", + "Explanation": "explanation : let the amount with r be rs . r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 6000 - r ) = > 3 r = 12000 - 2 r = > 5 r = 12000 = > r = 2400 . answer : c" + }, + { + "Answer": 9, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9", + "Correct": "e", + "Explanation": "\"let bill run x on saturday , so he will run x + 4 on sunday . . julia will run 2 * ( x + 4 ) on sunday . . totai = x + x + 4 + 2 x + 8 = 32 . . 4 x + 12 = 32 . . x = 5 . . ans = x + 4 = 5 + 4 = 9 answer e\"" + }, + { + "Answer": 6500, + "Options": "a ) 5000 , b ) 2999 , c ) 2878 , d ) 2990 , e ) 6500", + "Correct": "e", + "Explanation": "\"income = rs . 100 expenditure = rs . 80 savings = rs . 20 present expenditure 80 * ( 20 / 100 ) = rs . 96 present savings = 100 \u00e2 \u20ac \u201c 96 = rs . 4 100 - - - - - - 4 ? - - - - - - - - - 260 = > 6500 answer : e\"" + }, + { + "Answer": 59.067961165048544, + "Options": "a ) 55.1 , b ) 51.1 , c ) 53.1 , d ) 52.1 , e ) 59.1", + "Correct": "e", + "Explanation": "sum of the marks for the class of 55 students = 55 * 60 = 3300 sum of the marks for the class of 48 students = 48 * 58 = 2784 sum of the marks for the class of 103 students = 3300 + 2784 = 6084 average marks of all the students = 6084 / 103 = 59.1 answer : e" + }, + { + "Answer": 0.16666666666666666, + "Options": "a ) 2 / 6 , b ) 1 / 6 , c ) 1 / 8 , d ) 1 / 3 , e ) 1 / 2", + "Correct": "b", + "Explanation": "let ' s call the boxes that contain $ 4 , $ 400 , and $ 4000 , respectively , box a , box b , box c . these are opened , respectively , by key a , key b , and key c . we want to know the probability of winning more than $ 4000 . notice that if the distribution of keys is : box a = key b box b = key a box c = key c then the contestant wins exactly $ 4000 , not more than $ 4000 . the only configuration that leads to winning more than $ 1000 is : box a = key a box b = key b box c = key c i . e . , getting all three keys correct . that ' s the only way to be more than $ 4000 . so , really , the question can be rephrased : what is the probability of guessing the order of keys so that each key matches the correct box ? well , for a set of three items , the number of possible permutations is 3 ! = 3 * 2 * 1 = 6 . of those 6 possible permutations , only one of them leads to all three keys being paired with the right box . so , the answer is probability = 1 / 6 answer : b" + }, + { + "Answer": 9, + "Options": "a ) 1 , b ) 3 , c ) 9 , d ) 6 , e ) 7", + "Correct": "c", + "Explanation": "\"let seventh observation = x . then , according to the question we have = > ( 96 + x ) / 7 = 15 = > x = 9 hence , the seventh observation is 9 . answer : c\"" + }, + { + "Answer": 16, + "Options": "a ) 16 , b ) 24 , c ) c is elder than a , d ) data inadequate , e ) none", + "Correct": "a", + "Explanation": "\"solution [ ( a + b ) - ( b + c ) ] = 16 \u00e2 \u20ac \u00b9 = \u00e2 \u20ac \u00ba a - c = 16 . answer a\"" + }, + { + "Answer": 3000, + "Options": "a ) 45645433 , b ) 46457457 , c ) 4675 , d ) 3000 , e ) 3432", + "Correct": "d", + "Explanation": "say the profit was $ x . mary ' s share = x / 6 ( half of the third ) + ( x - x / 3 ) * 0.7 harry share = x / 6 ( half of the third ) + ( x - x / 3 ) * 0.3 thus ( x - x / 3 ) * 0.7 - ( x - x / 3 ) * 0.3 = 800 - - > x = 3000 . answer is d" + }, + { + "Answer": 84, + "Options": "a ) 87 , b ) 16 , c ) 10 , d ) 84 , e ) 17", + "Correct": "d", + "Explanation": "\"average after 11 innings = 44 required number of runs = ( 44 * 11 ) - ( 40 * 10 ) = 484 - 400 = 84 . answer : d\"" + }, + { + "Answer": 36, + "Options": "a ) 20 cs , b ) cs / 2 , c ) 36 cs , d ) ( 2 cs ) / 12 , e ) ( 24 c ) / s", + "Correct": "c", + "Explanation": "\"ans : c solution : simple multiplication s students , c classes , 3 books / month = 36 books a year total number of books = 36 cs\"" + }, + { + "Answer": 200, + "Options": "a ) rs . 300 , b ) rs . 200 , c ) rs . 240 , d ) rs . 350 , e ) none of these", + "Correct": "b", + "Explanation": "\"z share = z , y = 1.2 z x = 1.25 \u00d7 1.2 z , x + y + z = 740 ( 1.25 \u00d7 1.2 + 1.2 + 1 ) z = 74 3.7 z = 740 , z = 200 answer : . b .\"" + }, + { + "Answer": 1, + "Options": "a ) 7 , b ) 8 , c ) 6 , d ) 3 , e ) 1", + "Correct": "e", + "Explanation": "add 64 + 37 = 101 now 101 divided by 5 so we get 1 as reaminder answer : e" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 5 , c ) 3 , d ) 4 , e ) 11", + "Correct": "a", + "Explanation": "\"let x = 296 q + 75 = ( 37 x 8 q + 37 x 2 ) + 1 = 37 ( 8 q + 2 ) + 1 thus , when the number is divided by 37 , the remainder is 1 . answer a\"" + }, + { + "Answer": 128, + "Options": "a ) 128 , b ) 142 , c ) 143 , d ) 141 , e ) 129", + "Correct": "e", + "Explanation": "\"minimum three digit number is 100 and maximum three digit number is 999 . the first three digit number that leaves remainder 5 when divided by 7 is 103 . 14 * 7 = 98 + 5 = 103 the second three digit number that leaves remainder 5 when divided by 7 is 110 . 15 * 7 = 105 + 5 = 110 the third three digit number that leaves remainder 5 when divided by 7 is 117 and so on the last three digit number that leaves remainder 5 when divided by 7 is 999 142 * 7 = 994 + 5 = 999 therefore , we identify the sequence 103 , 110,117 . . . . . 999 use the formula of last term last term = first term + ( n - 1 ) * common difference you will get the answer 129 that is definitely e .\"" + }, + { + "Answer": 183868020, + "Options": "a ) 194852714 , b ) 183941604 , c ) 183851704 , d ) 183951714 , e ) 183768244", + "Correct": "b", + "Explanation": "\"18396 x 9999 = 18396 x ( 10000 - 1 ) = 18396 x 10000 - 18396 x 1 = 183960000 - 18396 = 183941604 b\"" + }, + { + "Answer": 268, + "Options": "a ) 89 , b ) 49 , c ) 68 , d ) 268 , e ) 55", + "Correct": "d", + "Explanation": "d 268 ( 17 * 15 ) + 13 = 268" + }, + { + "Answer": 6000, + "Options": "a ) rs . 4000 , b ) rs . 6000 , c ) rs . 7500 , d ) rs . 6600 , e ) none", + "Correct": "b", + "Explanation": "solution let c = x . then , b = 4 x and 2 a = 3 x 4 x = 12 x or a = 6 x . \u2234 a : b : c = 6 x : 4 x : x = 6 : 4 : 1 . so b ' s capital = rs ( 16500 x 4 / 11 ) = rs . 6000 . answer b" + }, + { + "Answer": 52.5, + "Options": "a ) $ 37.00 , b ) $ 40.00 , c ) $ 45.50 , d ) $ 48.00 , e ) $ 52.50", + "Correct": "e", + "Explanation": "\"first 2 shirts are sold for $ 40 and $ 50 = $ 90 . to get average price of $ 50 , total sale should be 6 * $ 50 = $ 300 so remaining 4 shirts to be sold for $ 300 - $ 90 = $ 210 answer should be 210 / 4 = $ 52.50 that is e\"" + }, + { + "Answer": 3300, + "Options": "a ) s . 3300 , b ) s . 4570 , c ) s . 4500 , d ) s . 4550 , e ) s . 2500", + "Correct": "a", + "Explanation": "\"sum of the salaries of the person for the months of january , february , march and april = 4 * 8000 = 32000 - - - - ( 1 ) sum of the salaries of the person for the months of february , march , april and may = 4 * 8800 = 35200 - - - - ( 2 ) ( 2 ) - ( 1 ) i . e . may - jan = 3200 salary of may is rs . 6500 salary of january = rs . 3300 answer : a\"" + }, + { + "Answer": 0.22222222222222224, + "Options": "a ) 1 / 9 , b ) 2 / 9 , c ) 2 / 5 , d ) 3 / 5 , e ) 3 / 7", + "Correct": "b", + "Explanation": "probability of basket = 2 / 3 probability of no basket = 1 / 3 required probability = 3 * 2 / 3 * 1 / 3 * 1 / 3 = 2 / 9 b is the answer ." + }, + { + "Answer": 1, + "Options": "a ) - 5 , b ) 1 , c ) 4 , d ) 3 , e ) 2", + "Correct": "b", + "Explanation": "\"1 . subtract 1 from both sides : x + 1 - 1 = 2 - 1 2 . simplify both sides : x = 1 b\"" + }, + { + "Answer": 3.8499999999999996, + "Options": "a ) $ 1.85 , b ) $ 3.85 , c ) $ 4.85 , d ) $ 6.85 , e ) $ 5.85", + "Correct": "b", + "Explanation": "\"john spent and gave to his two friends a total of 2.25 + 2.20 + 2.20 = $ 6.65 money left 10.50 - 6.65 = $ 3.85 correct answer is b ) $ 3.85\"" + }, + { + "Answer": 63, + "Options": "a ) 61 , b ) 62 , c ) 65 , d ) 63 , e ) 64", + "Correct": "d", + "Explanation": "responding to a pm : to solve this question , i will make an equation in x and then make educated guesses . here ' s how : assuming x motorcycles were sold every month initially . ( 568000 / x + 1000 ) ( x - 8 ) = 594000 ( 568 / x + 1 ) ( x - 8 ) = 594 now 568 = 8 * 71 assuming x = 71 ( we have all integers so it is obvious that 568 / x should be an integer . we get 9 * 66 = 594 ( matches ) so he will sell 71 - 8 = 63 bikes this month answer ( d )" + }, + { + "Answer": 50, + "Options": "a ) 50 , b ) 2.5 , c ) 25 , d ) . 25 , e ) none of these", + "Correct": "a", + "Explanation": "explanation : 1 / 0.02 = ( 1 * 100 ) / 2 = 100 / 2 = 50 option a" + }, + { + "Answer": 14, + "Options": "a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 14", + "Correct": "e", + "Explanation": "\"solution let the toatl number of workers be x . then 8000 x = ( 10000 x 7 ) + 6000 ( x - 7 ) x = 14 . answer e\"" + }, + { + "Answer": 585, + "Options": "a ) 540 , b ) 585 , c ) 619 , d ) 649 , e ) 700", + "Correct": "b", + "Explanation": "\"before price increase price = d after 30 % price increase price = d + ( 20 / 100 ) * d = 1.2 d = 351 ( given ) i . e . d = 351 / 1.3 = $ 292,5 i . e . 2 d = 2 * 292.5 = 585 answer : option b\"" + }, + { + "Answer": 2, + "Options": "a ) 2 , b ) 4 , c ) 6 , d ) 9 , e ) 8", + "Correct": "a", + "Explanation": "let the number to be added be x , then ( 2 + x ) : ( 3 + x ) = 4 : 5 \u21d2 ( 2 + x ) / ( 5 + x ) = 4 / 5 5 ( 2 + x ) = 4 ( 3 + x ) 10 + 5 x = 12 + 4 x 5 x - 4 x = 12 - 10 x = 2 answer : 2" + }, + { + "Answer": 168, + "Options": "a ) 168 , b ) 667 , c ) 288 , d ) 1991 , e ) 111", + "Correct": "a", + "Explanation": "\"average of new numbers = ( 21 \u00d7 8 ) = 168 answer : a\"" + }, + { + "Answer": 12.599999999999998, + "Options": "a ) 12.6 . , b ) 14.4 . , c ) 15.8 . , d ) 16.2 . , e ) 16.4 .", + "Correct": "a", + "Explanation": "\"[ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 9.8 = 6 * 0 + 2 * 7.2 + 8 - 9.8 = 0 + 14.4 - 1.8 12.6 answer a\"" + }, + { + "Answer": 63, + "Options": "a ) 15 % , b ) 20 % , c ) 25 % , d ) 63 % , e ) 75 %", + "Correct": "d", + "Explanation": "initially 84 % and 16 % split 80 % is further divided as 25 % and 75 % q is asking about that 75 % let total be ' 100 ' then that 75 % is ( 3 / 4 ) \u2217 84 so , the required % is [ ( 3 / 4 ) \u2217 84 / 100 ] \u2217 100 = 63 % answer : d" + }, + { + "Answer": 15, + "Options": "a ) a ) 10 , b ) b ) 12 , c ) c ) 15 , d ) d ) 20 , e ) e ) 25", + "Correct": "c", + "Explanation": "the difference between the highest and lowest salaries is $ 100000 . so there are at least 2 people - say one with salary 0 and the other with 100 k . no salary will be outside this range . median = 50 k more than lowest . so median is right in the center of lowest and highest since lowest and highest differ by 100 k . in our example , median = 50 k . since there are more than 2 people , there would probably be a person at 50 k . mean = 20 k more than median so in our example , mean salary = 70 k on the number line , 0 . . . . . . . . 50 k ( median ) . . . . . . . . 100 k mean = 70 k so there must be people more toward 100 k to bring the mean up to 70 k . since we want to add minimum people , we will add people at 100 k to quickly make up the right side deficit . 0 and 50 k are ( 70 k + 20 k ) = 90 k away from 70 k . 100 k is 30 k away from 70 k . to bring the mean to 70 k , we will add two people at 100 k each to get : 0 . . . . 50 k . . . . . 100 k , 100 k , 100 k but when we add more people to the right of 70 k , the median will shift to the right . we need to keep the median at 50 k . so every time we add people to the right of 70 k , we need to add people at 50 k too to balance the median . 50 k is 20 k less than 70 k while 100 k is 30 k more than 70 k . to keep the mean same , we need to add 2 people at 100 k for every 3 people we add at 50 k . so if we add 3 people at 50 k and 2 people at 100 k , we get : 0 , . . . 50 k , 50 k , 50 k , 50 k , . . . 100 k , 100 k , 100 k , 100 k , 100 k the median is not at 50 k yet . add another 3 people at 50 k and another 2 at 100 k to get 0 , 50 k , 50 k , 50 k , 50 k , 50 k , 50 k , 50 k , 100 k , 100 k , 100 k , 100 k , 100 k , 100 k , 100 k now the median is 50 k and mean is 70 k . total number of people is 15 . answer ( c )" + }, + { + "Answer": 11, + "Options": "a ) $ 11.00 , b ) $ 1.25 , c ) $ 5.00 , d ) $ 6.00 , e ) $ 20.00", + "Correct": "a", + "Explanation": "\"a for me 9 people with 1 $ each - > maximum = 11\"" + }, + { + "Answer": 23, + "Options": "a ) 23 , b ) 21 , c ) 43 , d ) 56 , e ) 30", + "Correct": "a", + "Explanation": "\"xy = 120 and x 2 + y 2 = 289 . ( x + y ) 2 = x 2 + y 2 + 2 xy = 289 + ( 2 x 120 ) = 529 x + y = 529 = 23 . answer a\"" + }, + { + "Answer": 76, + "Options": "a ) 87 , b ) 16 , c ) 10 , d ) 76 , e ) 17", + "Correct": "d", + "Explanation": "\"average after 11 innings = 36 required number of runs = ( 36 * 11 ) - ( 32 * 10 ) = 396 - 320 = 76 . answer : d\"" + }, + { + "Answer": 162, + "Options": "a ) 160 , b ) 161 , c ) 162 , d ) 163 , e ) 164", + "Correct": "c", + "Explanation": "\"to minimize one quantity maximize other . 161 * 2 ( max possible amount of food a guest could consume ) = 322 pounds , so there must be more than 161 guests , next integer is 162 . answer : c .\"" + }, + { + "Answer": 0.9722222222222222, + "Options": "a ) 13 , b ) pi / 3 , c ) pi / 2 , d ) 35 / 36 , e ) 8 / 9", + "Correct": "d", + "Explanation": "small circle radius = a , so area = pi a ^ 2 large circle radius = 6 a , so area = 9 . pi a ^ 2 area of shaded region = 36 pi a ^ 2 - pi a ^ 2 = 35 pi a ^ 2 so , probability = ( 35 pi a ^ 2 ) / ( 36 pi a ^ 2 ) = 35 / 36 = answer = d" + }, + { + "Answer": 7.5, + "Options": "a ) 1 / 7 , b ) 3 , c ) 15 , d ) 15 / 2 , e ) 60 / 7", + "Correct": "d", + "Explanation": "x + y = 8 . . . equation 1 - 3 x + y = 7 . . . equation 2 adding both the equations - 2 x + 2 y = 15 = > y - x = 15 / 2 correct answer option d" + }, + { + "Answer": 0.5, + "Options": "a ) 1 / 2 , b ) 1 , c ) 2 , d ) 4 , e ) 8", + "Correct": "a", + "Explanation": "\"given : 6 / w + 6 / x = 6 / ywx = y find : ( w + x ) / 2 = ? 6 ( 1 / w + 1 / x ) = 6 ( 1 / y ) - divide both sides by 6 ( 1 / w + 1 / x ) = 1 / y ( x + w ) / wx = 1 / wx - sub ' d in y = wx x + w - 1 = 0 x + w = 1 therefore ( w + x ) / 2 = 1 / 2 ans : a\"" + }, + { + "Answer": 164483.66666666666, + "Options": "a ) 897 , b ) 164,850 , c ) 164,749 , d ) 149,700 , e ) 156,720", + "Correct": "b", + "Explanation": "\"explanatory answer step 1 : identify the series the smallest 3 digit number that will leave a remainder of 2 when divided by 3 is 101 . the next couple of numbers that will leave a remainder of 2 when divided by 3 are 104 and 107 . the largest 3 digit number that will leave a remainder of 2 when divided by 3 is 998 . it is evident that any number in the sequence will be a 3 digit positive integer of the form ( 3 n + 2 ) . so , the given numbers are in an arithmetic sequence with the first term being 101 and the last term being 998 and the common difference being 3 . step 2 : compute the sum sum of an arithmetic progression ( ap ) = [ first term + last term / 2 ] n we know the first term : 101 we know the last term : 998 . the only unknown is the number of terms , n . in an a . p . , the nth term an = a 1 + ( n - 1 ) * d in this case , therefore , 998 = 101 + ( n - 1 ) * 3 or 897 = ( n - 1 ) * 3 ( n - 1 ) = 299 or n = 300 . sum of the ap will therefore , be [ 101 + 998 / 2 ] \u2217 300 = 164,850 choice b is the correct answer .\"" + }, + { + "Answer": 7670, + "Options": "a ) rs . 5870 , b ) rs . 5991 , c ) rs . 6020 , d ) rs . 7670 , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : total sale for 5 months = rs . ( 5420 + 5660 + 6200 + 6350 + 6500 ) = rs . 30,130 therefore , required sale = rs . [ ( 6300 * 6 ) \u2013 30,130 ] = rs . ( 37800 \u2013 30,130 ) = rs . 7670 answer d\"" + }, + { + "Answer": 1.9999999999999998, + "Options": "a ) 25 / 6 , b ) 36 / 25 , c ) 2 , d ) 5 / 6 , e ) 25 / 36", + "Correct": "c", + "Explanation": "5 x = 6 y = > x / y = 6 / 5 1 / 3 * x to 1 / 5 * y = x / y * 5 / 3 = ( 6 / 5 ) * ( 5 / 3 ) = 2 ans : c" + }, + { + "Answer": 56.25, + "Options": "a ) 56.25 , b ) 52.9 , c ) 52.1 , d ) 52.3 , e ) 42.5", + "Correct": "a", + "Explanation": "\"sum of the marks for the class of 30 students = 30 * 50 = 1500 sum of the marks for the class of 50 students = 50 * 60 = 3000 sum of the marks for the class of 80 students = 1500 + 3000 = 4500 average marks of all the students = 4500 / 80 = 56.25 answer : a\"" + }, + { + "Answer": 1500, + "Options": "a ) 1000 , b ) 1250 , c ) 1500 , d ) 1600 , e ) 2000", + "Correct": "c", + "Explanation": "to begin , find the area of each of the two sections by multiplying the lengths of the sides : 30 feet \u00d7 40 feet = 1200 square feet 60 feet \u00d7 80 feet = 4800 square feet the total area that needs sod has an area of 1200 + 4800 = 6000 square feet . each individual square is 2 feet by 2 feet , so each has an area of 4 square feet . because all the numbers are even , there will be no waste when the squares of sod are placed . therefore , you just have to find the number of squares needed by dividing : 6000 \u00f7 4 = 1500 correct answer c ) 1500" + }, + { + "Answer": 4.5, + "Options": "a ) 4 , b ) 9 / 2 , c ) 7 , d ) 41 / 4 , e ) 25", + "Correct": "b", + "Explanation": "just forget about the value of b ^ 4 for the moment and let b ^ 2 = x . ( its better to work with power of 2 than 4 ) now we have equation as 4 x ^ 2 - 41 x + 100 = 0 , factoring them gives us 4 x ^ 2 - 16 x - 25 x + 100 = 0 . which can be solved as ( 4 x - 25 ) ( x - 4 ) , so x = 4 and 25 / 4 . so b ^ 2 = 4 and 25 / 4 so b = + 2 and minus 2 and + 5 / 2 and minus 5 / 2 the two greatest values are + 2 and + 5 / 2 . so their sum 2 + 5 / 2 = 9 / 2 = b" + }, + { + "Answer": 27, + "Options": "a ) 28 , b ) 27 , c ) 26 , d ) 22 , e ) 24", + "Correct": "b", + "Explanation": "explanation : let the average score of the first 18 innings be n 18 n + 99 = 19 ( n + 4 ) = > n = 23 so , average score after 19 th innings = x + 4 = 27 . answer : b" + }, + { + "Answer": 10, + "Options": "a ) 4.3 , b ) 5.6 , c ) 6.2 , d ) 10.0 , e ) 12.0", + "Correct": "d", + "Explanation": "\"for the total revenue to remain the same when the price is 1 / 10 , the number of products sold must 1 / 10 times . therefore increase in the number of products sold is 100 % = > the required ratio = 100 % / 10 % = 10.0 answer : d\"" + }, + { + "Answer": 0.1, + "Options": "a ) 1 / 4 , b ) 1 / 6 , c ) 1 / 8 , d ) 1 / 9 , e ) 1 / 10", + "Correct": "e", + "Explanation": "\"the fraction of homes which are termite - infested but not collapsing is 3 / 10 * 1 / 3 = 1 / 10 the answer is e .\"" + }, + { + "Answer": 20, + "Options": "a ) 12 , b ) 20 , c ) 18 , d ) 12 , e ) 81", + "Correct": "b", + "Explanation": "\"( 80 / 100 ) * 40 \u00e2 \u20ac \u201c ( 4 / 5 ) * 15 32 - 12 = 20 answer : b\"" + }, + { + "Answer": 750, + "Options": "a ) 250 / 3 , b ) 750 , c ) 400 , d ) 480 , e ) 600", + "Correct": "b", + "Explanation": "\"we know that x is 10 % , y is 30 % and w . avg = 25 % . what does this mean with respect to w . avg technique ? w . avg is 1 portion away from y and 3 portion away from x so for every 1 portion of x we will have to add 3 portions of y . if x = 250 then y = 750 answer : b\"" + }, + { + "Answer": 194, + "Options": "a ) 178 , b ) 182 , c ) 186 , d ) 190 , e ) 194", + "Correct": "e", + "Explanation": "\"j + k = 287 and so k = 287 - j j - 8 = 2 k j - 8 = 2 ( 287 - j ) 3 j = 582 j = 194 the answer is e .\"" + }, + { + "Answer": 0.045388, + "Options": "a ) 0.045388 , b ) 4.5388 , c ) 453.88 , d ) 473.88 , e ) none of these", + "Correct": "a", + "Explanation": "\"answer multiplying 3.242 x 14 = 4.5388 now divide 4.5388 by 100 so , 4.5388 \u00f7 100 = 0.045388 \u2234 shift the decimal two places to the left as 100 correct option : a\"" + }, + { + "Answer": 800, + "Options": "a ) 600 , b ) 700 , c ) 800 , d ) 900 , e ) none", + "Correct": "c", + "Explanation": "\"solution : let xx be the number i chose , then x / 5 \u2212 154 = 6 x / 5 = 160 x = 800 answer c\"" + }, + { + "Answer": 9600, + "Options": "a ) 9000 , b ) 9400 , c ) 9600 , d ) 9800 , e ) 9700", + "Correct": "c", + "Explanation": "greatest number of 4 digits is 9999 . l . c . m of 15 , 25 , 40 and 75 is 600 . on dividing 9999 by 600 , the remainder is 399 . required number = 9999 - 399 = 9600 answer : c" + }, + { + "Answer": 1.25, + "Options": "a ) 3 / 4 , b ) 5 / 4 , c ) 7 / 4 , d ) 9 / 4 , e ) 11 / 4", + "Correct": "b", + "Explanation": "x + 2 / y + 1 = 1 i . e , x - y + 1 = 0 ; - - - - - - - - ( 1 ) x + 4 / y + 2 = 1 / 2 i . e . , 2 x - y + 6 = 0 ; - - - - - - - - - ( 2 ) solving 1 and 2 . . . we get x = - 5 and y = - 4 answer is 5 / 4 . . . answer : b" + }, + { + "Answer": 26, + "Options": "a ) 23 , b ) 24 , c ) 25 , d ) 26 , e ) 27", + "Correct": "d", + "Explanation": "\"average age of people = 30 so have total age = 210 before 7 years we have to deduct each person age by seven years 210 - 32 = 182 so average age would be 182 / 7 = 26 answer : d\"" + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 7 , c ) 10 , d ) 12 , e ) 14", + "Correct": "a", + "Explanation": "\"let the number of cows be x and their legs be 4 x . let the number of chicken be y and their legs be 2 x . total number of legs = 4 x + 2 y . total number of heads = x + y . the number of legs was 10 more than twice the number of heads . therefore , 2 \u00d7 ( x + y ) + 10 = 4 x + 2 y . or , 2 x + 2 y + 10 = 4 x + 2 y . or , 2 x + 10 = 4 x [ subtracting 2 y from both sides ] . or , 10 = 4 x \u2013 2 x [ subtracting 2 x from both sides ] . or , 10 = 2 x . or , x = 5 [ dividing by 2 on both sides ] . therefore , the number of cows = 5 . correct answer : a ) 5\"" + }, + { + "Answer": 960, + "Options": "a ) 732 , b ) 990 , c ) 1098 , d ) 960 , e ) 1405", + "Correct": "d", + "Explanation": "\"total number of digits = ( no . of digits in 1 - digit page nos . + no . of digits in 2 - digit page nos . + no . of digits in 3 - digit page nos . ) = ( 1 x 9 + 2 x 90 + 3 x 257 ) = ( 9 + 180 + 771 ) = 960 . answer : d\"" + }, + { + "Answer": 16, + "Options": "a ) 18 , b ) 56 , c ) 16 , d ) 17 , e ) 14", + "Correct": "c", + "Explanation": "\"initial average age of the 10 persons be p . age of the new person q . sum of the ages of the initial 10 persons = 10 p new average = ( p - 3 ) 10 ( p - 3 ) = 10 p - 46 + q = > q = 16 answer : c\"" + }, + { + "Answer": 280.00000000000006, + "Options": "a ) 240 , b ) 260 , c ) 270 , d ) 280 , e ) 290", + "Correct": "d", + "Explanation": "let the number be x . then , ( ( 1 / 5 ) x + 4 ) = ( ( 1 / 4 ) x \u2212 10 ) < = > x / 20 < = > x = 14 * 20 = 280 . answer : d" + }, + { + "Answer": 0.19999999999999998, + "Options": "a ) 0.2 , b ) 0.5 , c ) 2.5 , d ) 1.8 , e ) none", + "Correct": "a", + "Explanation": "\"sol . ( x \u00d7 6 ) = ( 0.60 \u00d7 2 ) \u21d2 x = 0.60 / 6 = 0.2 . answer a\"" + }, + { + "Answer": 4, + "Options": "a ) 4 , b ) 0 , c ) 2 , d ) 3 , e ) 5", + "Correct": "a", + "Explanation": "\"power set is the set of subsets of { 1,2 } that is { { 1,2 } , { 1 } , { 2 } , f } answer : a\"" + }, + { + "Answer": 65, + "Options": "a ) 22 , b ) 77 , c ) 29 , d ) 65 , e ) 21", + "Correct": "d", + "Explanation": "64 + 5 * 12 / ( 180 / 3 ) = 64 + 5 * 12 / ( 60 ) = 64 + ( 5 * 12 ) / 60 = 64 + 1 = 65 . answer : d" + }, + { + "Answer": 35, + "Options": "a ) 35 , b ) 66 , c ) 77 , d ) 99 , e ) 91", + "Correct": "a", + "Explanation": "\"let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 1021 96 + 225 + 490 + 6 x = 1021 6 x = 210 = > x = 35 . answer : a\"" + }, + { + "Answer": 45, + "Options": "a ) 3 , b ) 35 , c ) 4 , d ) 45 , e ) 5", + "Correct": "d", + "Explanation": "joe lost his weigh 24 pounds during 6 months . that means that he lost 4 pounds per month . he should lose more 18 pounds to be 180 pounds . so it would take 18 / 4 = 4.5 months . correct answer is d" + }, + { + "Answer": 110, + "Options": "a ) a ) 90 , b ) b ) 100 , c ) c ) 110 , d ) d ) 130 , e ) e ) 140", + "Correct": "c", + "Explanation": "c . 110 sum of all lengths of all 5 pieces of wood = 128 * 5 = 640 3 rd piece ( sorted in increasing length ) length = 140 ( median ) for sum of first 2 wood length to become max , last two should be least . let 4 th , 5 th wood also have length 140 each . total of last 3 = 140 * 3 = 420 sum of first 2 = 640 - 420 = 220 each of these 2 will have length 220 / 2 = 110 answer c" + }, + { + "Answer": 2, + "Options": "a ) 3 , b ) 2 , c ) 4 , d ) 1 , e ) 5", + "Correct": "b", + "Explanation": "present age of 5 members = 5 x 17 + 3 x 5 = 100 years also , present ages of 5 members + age of the baby = 6 x 17 = 102 years age of the baby = 102 \u2013 100 = 2 years . answer : b" + }, + { + "Answer": 54, + "Options": "a ) $ 144 , b ) $ 90 , c ) $ 60 , d ) $ 54 , e ) $ 48", + "Correct": "d", + "Explanation": "the correct answer is d ." + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 12", + "Correct": "a", + "Explanation": "\"option ' a ' 29 / 11 = 2 and 79 / 11 = 7 = = > 7 - 2 = 5 numbers\"" + }, + { + "Answer": 15, + "Options": "a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16", + "Correct": "d", + "Explanation": "\"p / 3 + f / 4 = p / 3 + ( 48 - p ) / 4 = 12 + p / 2 p / 3 + f / 3 = ( p + f ) / 3 = 48 / 3 = 16 p / 4 + f / 4 = 12 p / 3 + f / 3 > p / 3 + f / 4 > p / 4 + f / 4 - - > 16 > 12 + p / 12 > 12 greatest possible q : 12 + p / 12 = 15 - - > p = 36 ( integer - - > good ) 15 or d is the answer\"" + }, + { + "Answer": 18, + "Options": "a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20", + "Correct": "d", + "Explanation": "\"10 + 8 = 18 the answer is d .\"" + }, + { + "Answer": 115, + "Options": "a ) a . 72 , b ) b . 115 , c ) c . 48 , d ) d . 46 , e ) e . 44", + "Correct": "b", + "Explanation": "\"at 6 : 00 it ' ll chime 6 times . if we assume that the time taken to chime is x , then time between chimes is also x . so you have 6 chimes , which is 6 x and 5 time intervals between chimes . this means that 11 x = 55 seconds . thus x = 5 seconds . by a similar logic , at 12 : 00 , there are 12 chimes and 11 intervals so the total time is ( 12 + 11 ) x = 23 x = 115 seconds . answer b\"" + }, + { + "Answer": 35.75, + "Options": "a ) 33.25 , b ) 35.75 , c ) 34.25 , d ) 35 , e ) none", + "Correct": "b", + "Explanation": "solution required average = ( 38.9 x 10 ) - ( 41 x 6 ) / 4 = 143 / 4 . = 35.75 answer b" + }, + { + "Answer": 18, + "Options": "a ) 15 , b ) 18 , c ) 19 , d ) 22 , e ) 23", + "Correct": "b", + "Explanation": "explanation : 60 - 6 = 54 , 190 - 10 = 180 highest number that divides 54 and 180 is hcf of numbers hcf of 54 nad 180 = 18 answer : b" + }, + { + "Answer": 1, + "Options": "a ) $ 1 , b ) $ 2 , c ) $ 3 , d ) $ 4 , e ) $ 5", + "Correct": "a", + "Explanation": "in order to divide the sum in 9 parts , the amount must be divisible by 9 divisibility rule of 9 : the sum of the digits must be divisible by 9 sum of digits of 143 = 8 and 9 is divisible by 9 . hence , we need to add 1 to this number for it to be divisible by 9 correct option : a" + }, + { + "Answer": 33, + "Options": "a ) 267 , b ) 7 , c ) 76 , d ) 8 , e ) 82", + "Correct": "a", + "Explanation": "answer : a" + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 7 , c ) 8 , d ) 9 , e ) 11", + "Correct": "a", + "Explanation": "\"29 / 11 = 2 and 79 / 11 = 7 = = > 7 - 2 = 5 numbers option ' a '\"" + }, + { + "Answer": 62.5, + "Options": "a ) 62.5 , b ) 77 , c ) 48 , d ) 99 , e ) 21", + "Correct": "a", + "Explanation": "\"speed on return trip = 150 % of 50 = 75 km / hr . average speed of trip = 50 + 75 / 2 = 125 / 2 = 62.5 km / hr answer : a\"" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 5 , c ) 6 , d ) 7 , e ) 8", + "Correct": "a", + "Explanation": "given , the remainders are same i . e . differences of that numbers are exactly divisible . hence , you have to find hcf ( x \u2013 y , y \u2013 z , z \u2013 x ) . 858 \u2013 794 = 64 ; 1351 \u2013 794 = 557 ; 1351 \u2013 858 = 493 . hcf of ( 64 , 557 , 493 ) = 1 . answer : a" + }, + { + "Answer": 140000.00000000003, + "Options": "a ) $ 10400 , b ) $ 14000 , c ) $ 144000 , d ) $ 1800 , e ) $ 140000", + "Correct": "e", + "Explanation": "\"[ 1 / ( x 1 / y 1 + x 2 / y 2 + x 3 / y 3 ) ] * total amount = balance amount [ 1 - ( 1 / 5 + 1 / 10 + 3 / 5 ) } * total salary = $ 14000 , = [ 1 - 9 / 10 ] * total salary = $ 14000 , total salary = $ 14000 * 10 = $ 140000 , correct answer ( e )\"" + }, + { + "Answer": 147.6923076923077, + "Options": "a ) rs . 117.69 , b ) rs . 147.69 , c ) rs . 137.69 , d ) rs . 157.69 , e ) rs . 127.69", + "Correct": "b", + "Explanation": "\"( p * 10 * 15 ) / 100 - ( p * 3.5 * 15 ) / 100 = 144 = > p = rs . 147.69 answer : b\"" + }, + { + "Answer": 900, + "Options": "a ) 300 , b ) 400 , c ) 900 , d ) 600 , e ) 700", + "Correct": "c", + "Explanation": "sum of first n odd natural nuber is = n ^ 2 so sum of the first 30 odd natural numbers = ( 30 ) ^ 2 = 900 ans 900 answer : c" + }, + { + "Answer": 36, + "Options": "a ) 33 , b ) 54 , c ) 36 , d ) 17 , e ) 01", + "Correct": "c", + "Explanation": "explanation : as there is meal for 70 adults and 42 have their meal , the meal left can be catered to 28 adults . now , 70 adults = 90 children 7 adults = 9 children therefore , 28 adults = 36 children hence , the meal can be catered to 36 children . answer : c" + }, + { + "Answer": 8, + "Options": "a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 0", + "Correct": "d", + "Explanation": "the units digit of powers of 3 , cycles in a group of 4 : { 3 , 9 , 7 , 1 } 53 has the form 4 k + 1 , so the units digit of 93 ^ 53 is 3 . the units digit of powers of 5 is always 5 . 3 + 5 = 8 , so the units digit is 8 . the answer is d ." + }, + { + "Answer": 0.6599999999999999, + "Options": "a ) 0.66 , b ) 0.72 , c ) 0.78 , d ) 0.84 , e ) 0.9", + "Correct": "a", + "Explanation": "\"let x be the total number of students . the number students who are younger than 25 is 0.6 * 0.4 x + 0.7 * 0.6 x = 0.66 x the answer is a .\"" + }, + { + "Answer": 9, + "Options": "a ) 8 , b ) 9 , c ) 12 , d ) 14 , e ) 16", + "Correct": "b", + "Explanation": "\"explanation : = > 3 ( 2 x + 13 ) = 93 = > 2 x + 13 = 31 = > x = 9 option b\"" + }, + { + "Answer": 0.5, + "Options": "a ) 1 / 2 , b ) 1 / 3 , c ) 2 / 3 , d ) 1 / 4 , e ) 1 / 5", + "Correct": "a", + "Explanation": "\"t - > a / b = 20 * 21 * \u2026 \u2026 * 39 / 21 * 22 * \u2026 . * 39 * 40 = 20 / 40 = 1 / 2 . therefore , the answer is a .\"" + }, + { + "Answer": 268.4, + "Options": "a ) 190 , b ) 284.6 , c ) 300 , d ) 268 , e ) 312", + "Correct": "d", + "Explanation": "\"so 12.2 * 22 = 268 . . imo option d is correct answer . .\"" + }, + { + "Answer": 750, + "Options": "a ) 740 , b ) 750 , c ) 760 , d ) 770 , e ) 775", + "Correct": "b", + "Explanation": "\"explanation : since the month begins with a sunday , so there will be five sundays in the month , required average = ( 1000 * 5 + 700 * 25 ) / 30 = 22500 / 30 = 750 answer : b ) 750\"" + }, + { + "Answer": 7, + "Options": "a ) 10.6 kg , b ) 10.8 kg , c ) 7 kg , d ) 14.9 kg , e ) none", + "Correct": "c", + "Explanation": "\"answer weight of new student = total weight of all 20 students - total weight of initial 19 students = ( 20 x 14.6 - 19 x 15 ) kg = 7 kg . correct option : c\"" + }, + { + "Answer": 18, + "Options": "a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20", + "Correct": "c", + "Explanation": "we know prime no . are 2 , 3 , 5 , 7 mulply by 1 is prime no 2 = 21 ( 2 * 1 ) = 73 ( 7 * 3 ) 2 = 21 ( 2 * 1 ) = 37 ( 3 * 7 ) 2 = 12 ( 1 * 2 ) = 43 ( 4 * 3 ) or 34 ( 3 * 4 ) or 26 ( 2 * 6 ) or 62 ( 6 * 2 ) . . . similarly for all prime no then u will got it . . . . 12,13 , 15,17 , 21,26 , 31,34 , 35,37 , 43,51 , 53,57 , 62,71 , 73,75 ans is 18 answer : c" + }, + { + "Answer": 9, + "Options": "a ) 9 , b ) 12 , c ) 11 , d ) 10 , e ) 3", + "Correct": "a", + "Explanation": "\"out of the 16 integers : 8 are odd and 8 are even . if we need to make sure that the product of all the integers withdrawn is even then we need to make sure that we have at least one even number . in the worst case : 1 . we will end up picking odd numbers one by one , so we will pick all 8 odd numbers first 2 . 9 th number will be the first even number so we need to withdraw at least 9 numbers to make sure that we get one even number and the product of all the integers picked is even . so , answer will be 9 . ( a )\"" + }, + { + "Answer": 8.981462409886715, + "Options": "a ) 7.98 , b ) 8.98 , c ) 9.98 , d ) 6.98 , e ) 8.12", + "Correct": "b", + "Explanation": "total cost = 5000 \u00d7 3 = 15000 total diesel used = 5000 / 8.50 + 5000 / 9 + 5000 / 9.50 = 588 + 555 + 527 = 1670 average cost per litre of diesel = 15000 / 1670 = 8.98 answer : b" + }, + { + "Answer": 70, + "Options": "a ) 7 , b ) 17 , c ) 70 , d ) 100 , e ) 107", + "Correct": "c", + "Explanation": "the sum of the ten numbers is 7 * 10 = 70 if each number is multiplied by 10 , the new sum is 10 * ( 70 ) . the average is then 10 * 7 = 70 the answer is c ." + }, + { + "Answer": 0.8333333333333334, + "Options": "a ) 1 / 2 , b ) 2 , c ) 1 / 3 , d ) 3 , e ) 5 / 6", + "Correct": "e", + "Explanation": "\"very easy question . 2 variables and 2 easy equations . xy = 25 - - - > x = 25 / y - ( i ) x / y = 36 - - - > replacing ( i ) here - - - > 25 / ( y ^ 2 ) = 36 - - - > y ^ 2 = 25 / 36 - - - > y = 5 / 6 or - 5 / 6 the question states that x and y are positive integers . therefore , y = 5 / 6 is the answer . answer e .\"" + }, + { + "Answer": 68.2, + "Options": "a ) 67 , b ) 26 , c ) 87 , d ) 26 , e ) 68", + "Correct": "e", + "Explanation": "\"average = ( 70 + 63 + 80 + 63 + 65 ) / 5 = 341 / 5 = 68.2 . answer : e\"" + }, + { + "Answer": 33, + "Options": "a ) 50 min , b ) 33 min , c ) 35 min , d ) 25 min , e ) 20 min", + "Correct": "b", + "Explanation": "\"clearly , the two will meet when they are 1000 m apart to be 20 + 13 = 33 km apart , they take 1 hour to be 1000 m apart , they take 33 * 1000 / 1000 = 33 min . answer is b\"" + }, + { + "Answer": 199, + "Options": "a ) 134 , b ) 178 , c ) 199 , d ) 166 , e ) 194", + "Correct": "c", + "Explanation": "the number of votes the winning candidate received was 979 + 53 + 79 + 105 / 4 = 304 . the second received 304 \u2013 53 = 251 the fourth place received 304 \u2013 105 = 199 . c" + }, + { + "Answer": 1.1, + "Options": "a ) 2.1 , b ) 1.3 , c ) 5.1 , d ) 2.3 , e ) 1.1", + "Correct": "e", + "Explanation": "e 1 : 1 ( approx ) explanation : we know that the probability of having a boy or having a girl is same and thus , half of the couples will stop after having a boy child . half of the others will have a girl and will have a baby again . out of those half of the couples , half will have a boy and will stop and half will have a girl again . this will keep on going like this . now , if there are x number of couples , there will be x boys . 1 / 2 have a boy and stop : 0 girls 1 / 4 have a girl , then a boy : x / 4 girls 1 / 8 have 2 girls , then a boy : 2 * x / 8 girls 1 / 16 have 3 girls , then a boy : 3 * x / 16 girls 1 / 32 have 4 girls , then a boy : 4 * x / 32 girls \u2026 total : x boys and 1 x 2 x 3 x 4 x \u2013 + \u2013 + \u2013 + \u2014 + \u2026 = ~ x therefore , the proportion of boys to girls will be extremely close to 1 : 1" + }, + { + "Answer": 44, + "Options": "a ) 57 , b ) 67 , c ) 77 , d ) 87 , e ) 44", + "Correct": "e", + "Explanation": "\"money collected = ( 19.36 x 100 ) paise = 1936 paise . number of members = square root of 1936 = 44 answer : option e\"" + }, + { + "Answer": 23.091725465041694, + "Options": "a ) 15 % , b ) 23 % , c ) 25 % , d ) 60 % , e ) 80 %", + "Correct": "b", + "Explanation": "\"listed selling price of chair = 77.95 $ discounted selling price of chair = 59.95 $ discount = 77.95 - 59.95 = 18 $ % decrease in price of chair = ( 18 / 77.95 ) * 100 % = 23 % approx answer b\"" + }, + { + "Answer": 5290, + "Options": "a ) 4236 , b ) 4306 , c ) 4336 , d ) 5336 , e ) none", + "Correct": "d", + "Explanation": "\"solution divisor = ( 5 \u00d7 46 ) = 230 . also . 10 \u00d7 q = 230 \u2039 = \u203a q = 23 . and , r = 46 . dividend = ( 230 \u00d7 23 + 46 ) = 5336 . answer d\"" + }, + { + "Answer": 91, + "Options": "a ) 55 , b ) 60 , c ) 73 , d ) 82 , e ) 91", + "Correct": "e", + "Explanation": "let the number of correct responses be x then the number of incorrect responses = 100 - x according to question x - 2 ( 100 - x ) = 73 ( subtracting twice of incorrect from correct ) 3 x = 273 x = 91 answer : e" + }, + { + "Answer": 11, + "Options": "a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15", + "Correct": "a", + "Explanation": "3 / 11 \u00d7 [ ( 1 + 1 / 3 ) ( 1 + 1 / 4 ) . . . . . . . ( 1 + 1 / 120 ) ] 3 / 11 \u00d7 [ 4 / 3 + 5 / 4 \u00d7 . . . . . . . . 121 / 120 ] 3 / 11 \u00d7 4 / 3 \u00d7 5 / 4 \u00d7 . . . . 121 / 120 121 / 11 = 11 . a" + }, + { + "Answer": 1998, + "Options": "a ) 1776 , b ) 1887 , c ) 1998 , d ) 2332 , e ) 2554", + "Correct": "c", + "Explanation": "\"there are 6 possible arrangements of the three numbers . then each number will be in the hundreds , tens , and ones place two times each . the sum is 2 ( 222 ) + 2 ( 333 ) + 2 ( 444 ) = 1998 the answer is c .\"" + }, + { + "Answer": 50.66666666666667, + "Options": "a ) 15 , b ) 30 , c ) 51 , d ) 63 , e ) 76", + "Correct": "c", + "Explanation": "\"we have to find the number of terms that are divisible by 2 but not by 6 ( as the question asks for the even numbers only which are not divisible by 3 ) for 2 , 10 , 12,14 . . . 160 using ap formula , we can say 160 = 10 + ( n - 1 ) * 2 or n = 76 . for 6 , 12,18 , . . . 156 using ap formula , we can say 156 = 12 + ( n - 1 ) * 6 or n = 25 . hence , only divisible by 2 but not 3 = 76 - 25 = 51 . hence , answer c\"" + }, + { + "Answer": 50, + "Options": "a ) 40 , b ) 44 , c ) 45 , d ) 46 , e ) 50", + "Correct": "e", + "Explanation": "answer e = 50 we have ( 10 ^ a ) - 74 , where the sum of the digits is 440 . 100 - 74 = 26 , so we already have 2 + 6 = 8 from the 440 . because we have a power of 10 , we will have numbers like 100 , 1000 , 10000 and so on . this minus 74 rests 26 and a lot of 9 s . e . g : 1000 - 74 = 9926 . so dividing the 432 / 9 = 48 , that ` s the number of 9 s . and we have 2 other numbers ( 2 and 6 ) wich were 00 before the subtraction . so we have 48 + 2 as an a = 50" + }, + { + "Answer": 0.001, + "Options": "a ) \u2212 100 , b ) 0.001 , c ) 0.25 , d ) 4 , e ) 8", + "Correct": "b", + "Explanation": "quickly we can spot that answer is neither integer nor negative . eliminate a , de by inversing and squaring 0.001 answer : b" + }, + { + "Answer": 1760, + "Options": "a ) 1760 , b ) 1700 , c ) 2350 , d ) 2500 , e ) 8000", + "Correct": "a", + "Explanation": "16 pounds and 4 ounces = 16 * 16 + 4 = 260 ounces . 13 tons = 13 * 2200 pound = 13 * 2200 * 16 ounces . hence the answer is ( 13 * 2200 * 16 ) / 260 = 1760 . answer : a ." + }, + { + "Answer": 9492.1875, + "Options": "a ) 3277 , b ) 2977 , c ) 9492 , d ) 6077 , e ) 17112", + "Correct": "c", + "Explanation": "\"explanation : 40,000 * ( 3 / 4 ) ^ 5 answer : c\"" + }, + { + "Answer": 0.41666666666666663, + "Options": "a ) 0 , b ) 1 / 12 , c ) 5 / 12 , d ) 7 / 18 , e ) 4 / 9", + "Correct": "c", + "Explanation": "\"total # of outcomes is 6 * 6 = 36 ; favorable outcomes : a - b - - > prime 1 - 1 - - > 2 ; 1 - 2 - - > 3 ; 2 - 1 - - > 3 ; 1 - 4 - - > 5 ; 4 - 1 - - > 5 ; 2 - 3 - - > 5 ; 3 - 2 - - > 5 ; 1 - 6 - - > 7 ; 6 - 1 - - > 7 ; 2 - 5 - - > 7 ; 5 - 2 - - > 7 ; 3 - 4 - - > 7 ; 4 - 3 - - > 7 ; 6 - 5 - - > 11 ; 5 - 6 - - > 11 . total of 15 favorable outcomes w = 15 / 36 . answer : c .\"" + }, + { + "Answer": 20000, + "Options": "a ) 7787 , b ) 8000 , c ) 1988 , d ) 1277 , e ) 20000", + "Correct": "e", + "Explanation": "\"x * 125 / 100 * 75 / 100 = 18750 x * 0.9375 = 18750 x = 18750 / 0.9375 = > 20000 answer : e\"" + }, + { + "Answer": 1529.4117647058824, + "Options": "a ) 1000 , b ) 1250 , c ) 1300 , d ) 1529.41 , e ) 1625", + "Correct": "d", + "Explanation": "\"300 gallons of water increases capacity by 30 % that means 30 % is 300 gallons , so 100 % would be = 300 * 100 / 30 = 1000 gallons now 1000 + 300 gallons is 85 % capacity of tank . so 100 % capacity would be = 1300 * 100 / 85 = 1529.41 d is the answer\"" + }, + { + "Answer": 33, + "Options": "a ) 36 , b ) 33 , c ) 44 , d ) 64 , e ) 56", + "Correct": "b", + "Explanation": "a = 5 x , b = 5 z therefore ( 5 x * 10 + 5 z ) - ( 10 x + z ) = ( 5 - 1 ) ( 10 x + z ) = . ( 10 x + z ) number should be divisible by 4 b" + }, + { + "Answer": 30, + "Options": "a ) 25 liters , b ) 27 liters , c ) 30 liters , d ) 32 liters , e ) 35 liters", + "Correct": "c", + "Explanation": "\"let x ltr water to be added 2 ltr alcohol to be represented as ( 20 ( 1 - 3 / 4 ( new soln . = 10 + x ) ) ) 2 = 5 % * ( 10 + x ) - - - - - - - - > x = 30 answer : c\"" + }, + { + "Answer": 0.16666666666666666, + "Options": "a ) 1 / 9 , b ) 4 / 6 , c ) 3 / 6 , d ) 1 / 2 , e ) 1 / 6", + "Correct": "e", + "Explanation": "let ' s call the boxes that contain $ 5 , $ 500 , and $ 5000 , respectively , box a , box b , box c . these are opened , respectively , by key a , key b , and key c . we want to know the probability of winning more than $ 5000 . notice that if the distribution of keys is : box a = key b box b = key a box c = key c then the contestant wins exactly $ 5000 , not more than $ 5000 . the only configuration that leads to winning more than $ 1000 is : box a = key a box b = key b box c = key c i . e . , getting all three keys correct . that ' s the only way to be more than $ 5000 . so , really , the question can be rephrased : what is the probability of guessing the order of keys so that each key matches the correct box ? well , for a set of three items , the number of possible permutations is 3 ! = 3 * 2 * 1 = 6 . of those 6 possible permutations , only one of them leads to all three keys being paired with the right box . so , the answer is probability = 1 / 6 answer : e" + }, + { + "Answer": 15, + "Options": "a ) 14 , b ) 15 , c ) 20 , d ) 22 , e ) 25", + "Correct": "b", + "Explanation": "\"b 15\"" + }, + { + "Answer": 7, + "Options": "a ) a ) 2 , b ) b ) 3 , c ) c ) 4 , d ) d ) 5 , e ) e ) 7", + "Correct": "e", + "Explanation": "49 / 7 = 7 e" + }, + { + "Answer": 48, + "Options": "a ) 22 , b ) 33 , c ) 44 , d ) 48 , e ) 99", + "Correct": "d", + "Explanation": "x / ( 12 p ) = even prime number x = even prime number * 11 p least value of x = lowest even prime number * 12 * lowest value of p = 2 * 12 * 2 = 48 answer d" + }, + { + "Answer": 28, + "Options": "a ) 10 , b ) 30 , c ) 28 , d ) 60 , e ) 90", + "Correct": "c", + "Explanation": "\"10 players are there . two players play one game with one another . so 8 c 2 = 8 * 7 / 2 = 28 so option c is correct\"" + }, + { + "Answer": 2.5, + "Options": "a ) 1.3 , b ) 1.7 , c ) 2.1 , d ) 2.5 , e ) 2.9", + "Correct": "d", + "Explanation": "\"let x be the number of liters of ethanol added to the gas tank . 0.05 ( 45 ) + x = 0.1 ( 45 + x ) 0.9 x = 4.5 - 2.25 = 2.25 x = 2.5 liters the answer is d .\"" + }, + { + "Answer": 95, + "Options": "a ) 24 , b ) 77 , c ) 297 , d ) 267 , e ) 95", + "Correct": "e", + "Explanation": "\"explanation : 42 - 23 = 19 19 x 5 = 95 answer : e\"" + }, + { + "Answer": 4, + "Options": "a ) a ) 6 , b ) b ) 4 , c ) c ) 8 , d ) d ) 10 , e ) e ) 12", + "Correct": "b", + "Explanation": "12 ( 84 ) + 92 x / 12 + x = 86 1008 + 92 x / 12 + x = 86 1008 + 92 x = 86 ( 12 + x ) 1008 + 92 x = 1032 + 86 x x ' s one side , numbers one side we get , 92 x - 86 x = 1032 - 1008 6 x = 24 hence , x = 4 answer b" + }, + { + "Answer": 28, + "Options": "a ) 16 , b ) 19 , c ) 15 , d ) 20 , e ) 28", + "Correct": "e", + "Explanation": "\"let the son ' s present age be x years . then , man ' s present age = ( x + 30 ) years . ( x + 30 ) + 2 = 2 ( x + 2 ) x + 32 = 2 x + 4 = > x = 28 . answer : e\"" + }, + { + "Answer": 18, + "Options": "a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19", + "Correct": "d", + "Explanation": "\"a two - digit integer ` ` ab ' ' can be expressed algebraically as 10 a + b . q - r = ( 10 a + b ) - ( 10 b + a ) = 9 ( a - b ) < 20 . the greatest multiple of 9 which is less than 20 is 18 . the answer is d .\"" + }, + { + "Answer": 99, + "Options": "a ) 108 , b ) 99 , c ) 128 , d ) 135 , e ) 143", + "Correct": "b", + "Explanation": "\"let the 2 positive numbers x and y x + y = 20 - - 1 x ^ 2 - y ^ 2 = 40 = > ( x + y ) ( x - y ) = 40 - - 2 using equation 1 in 2 , we get = > x - y = 2 - - 3 solving equation 1 and 3 , we get x = 11 y = 9 product = 11 * 9 = 99 answer b\"" + }, + { + "Answer": 60, + "Options": "a ) 33 , b ) 77 , c ) 60 , d ) 29 , e ) 11", + "Correct": "c", + "Explanation": "explanation : let the number of students who passed the examination be x number of students failed = ( 100 - x ) total marks of students who have passed = 70 x total marks of 100 students = 100 * 50 = 5000 total marks of students who have failed = 20 ( 100 \u2013 x ) 20 ( 100 \u2013 x ) + 70 x = 5000 2000 \u2013 20 x + 70 x = 5000 50 x = 3000 x = 60 answer : c" + }, + { + "Answer": 756, + "Options": "a ) 756 , b ) 750 , c ) 600 , d ) 760 , e ) none of these", + "Correct": "a", + "Explanation": "\"number of male employees = 1800 * 60 / 100 = 1080 required number of male employees who are less than 50 years old = 1080 * ( 100 - 30 ) % = 1080 * 70 / 100 = 756 . answer : a\"" + }, + { + "Answer": 86400, + "Options": "a ) 85,400 , b ) 86,400 , c ) 87,400 , d ) 88,400 , e ) 89,400", + "Correct": "b", + "Explanation": "\"this question can be modified so that the birth rate is given every m seconds and the death rate is given every n seconds . for this particular question : increase in the population every 2 seconds = 5 - 3 = 2 people . total 2 second interval in a day = 24 * 60 * 60 / 2 = 43,200 population increase = 43,200 * 2 = 86,400 . hence b .\"" + }, + { + "Answer": 7, + "Options": "a ) 7 , b ) 10 , c ) 12 , d ) 14 , e ) 15", + "Correct": "a", + "Explanation": "\"explanation : = > 3 ( 2 x + 9 ) = 69 = > 2 x + 9 = 23 = > x = 7 answer : option a\"" + }, + { + "Answer": 20, + "Options": "a ) 5 , b ) 9 , c ) 12 , d ) 20 , e ) 30", + "Correct": "d", + "Explanation": "in order x ! to be divisible by 1,000 , it should have at least 3 trailing zeros . a trailing 0 in factorial of a number is produced by 2 and 5 in it : 2 * 5 = 10 . so , we need 10 to be in x ! at least in power of 3 . 5 ! = 120 has 1 trailing zeros . 10 ! will have 2 trailing zeros . 15 ! will have 3 trailing zeros . 20 ! will have 5 trailing zeros . answer : d ." + }, + { + "Answer": 1080, + "Options": "a ) $ 1080 , b ) $ 1180 , c ) $ 1280 , d ) $ 1380 , e ) $ 1480", + "Correct": "a", + "Explanation": "a = 1 / 3 ( b + c ) = > c = 3 a - b - - - ( 1 ) b = 2 / 7 ( a + c ) = > c = 3.5 b - a - - ( b ) a - b = $ 30 a = 30 + b ( 1 ) = = = > c = 90 + 3 b - b = 2 b + 90 = = > 2 b - c = - 90 - - - ( 3 ) ( 2 ) = = = > c = 3.5 b - b - 30 = 2.5 b - 30 = = > 2.5 b - c = 30 - - - ( 4 ) from ( 4 ) and ( 3 ) 0.5 b = 120 b = $ 240 a = $ 270 c = 810 - 240 = $ 570 total amount = 270 + 240 + 570 = $ 1080 answer : a" + }, + { + "Answer": 17, + "Options": "a ) \u2013 5 , b ) 1 , c ) 13 , d ) 17 , e ) 551", + "Correct": "d", + "Explanation": "2 x - g = 11 . . . . g = 2 x - 11 4 x + g = 4 x + 2 x - 11 = 6 x - 11 6 x - 11 = - 5 . . . x = 1 6 x - 11 = 1 . . . x = 2 6 x - 11 = 13 . . . x = 4 6 x - 11 = 17 . . x is not integer 6 x - 11 = 551 . . x is not integer i think the choice e is 55 not 551 . otherwise both de can not be solution = d" + }, + { + "Answer": 0.111328125, + "Options": "a ) 57 / 512 , b ) 7 / 512 , c ) 55 / 512 , d ) 9 / 512 , e ) 11 / 512", + "Correct": "a", + "Explanation": "this is a fair dice with 8 fair sides , so the probability of the dice landing on any sides is equal . the question ask if the value of the dice is shown 3 at least once so the calculation of the first possible outcomes is 1 / 8 * 1 / 8 * 1 / 8 ( all of the dice thrown shown the value of 3 ) this is follow by the second possible outcomes if the dice thrown show the value of 3 2 times ( 1 / 8 * 1 / 8 * 7 / 8 ) * 7 here referring to any number besides 3 the third possible outcomes is that the dice show the value 3 one time ( 1 / 8 * 7 / 8 * 7 / 8 ) so the answer is 1 / 512 + 7 / 512 + 49 / 512 = 57 / 512 answer : a" + }, + { + "Answer": 11.05, + "Options": "a ) 12.0 , b ) 12.1 , c ) 12.2 , d ) 12.3 , e ) 11.0", + "Correct": "e", + "Explanation": "let say the factor is x , the at 7 pm quantity = 10 ( i . e . quantity @ 1 pm ) * x ^ 2 = 12.1 = > x ^ 2 = 1.21 or x = 1.1 = > @ 4 pm quantity = 10 x = 10 * 1.1 = 11 . answer e" + }, + { + "Answer": 33, + "Options": "a ) 5 , b ) 33 , c ) 20 , d ) 40 , e ) 45", + "Correct": "b", + "Explanation": "\"solution - lets say , single hamburgersxand double hamburgersy given that , x + y = 50 and 1 x + 1.5 y = 66.50 . by solving the equations y = 33 . ans b .\"" + }, + { + "Answer": 41.99999999999999, + "Options": "a ) 20 , b ) 24 , c ) 36 , d ) 42 , e ) 60", + "Correct": "d", + "Explanation": "\"let the capacity of the tank = c ( 3 / 4 ) c + 7 = ( 9 / 10 ) c = > ( 9 / 10 ) c - ( 3 / 4 ) c = 7 = > ( 3 / 20 ) c = 7 = > c = ( 7 * 20 ) / 3 = 46.66 number of gallons of gasoline that the tank currently holds = 3 / 4 * c + 7 = 34.99 + 7 = 41.99 = 42 answer d\"" + }, + { + "Answer": 110, + "Options": "a ) 100 , b ) 110 , c ) 120 , d ) 130 , e ) 140", + "Correct": "b", + "Explanation": "let the number of boys who passed = x . then , 39 x x + 15 x ( 120 - x ) = 120 x 37 24 x = 4440 - 1800 = > x = 2640 / 24 x = 110 . hence , the number of boys passed = 110 . answer : b" + }, + { + "Answer": 300, + "Options": "a ) 220 , b ) 250 , c ) 280 , d ) 300 , e ) 340", + "Correct": "d", + "Explanation": "\"let the total number of ounces in the drink be x . % of orange = 25 % % of watermelon = 40 % % of grape = 100 % - 65 % = 35 % 0.35 x = 105 x = 300 therefore there are a total of 300 ounces in the drink . the answer is d .\"" + }, + { + "Answer": 1, + "Options": "a ) 3 : 2 , b ) 1 : 1 , c ) 3 : 1 , d ) 5 : 2 , e ) 4 : 3", + "Correct": "b", + "Explanation": "\"g = 11 w c = 5 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 11 w + 5 wx = x + 1 * 8 w 11 + 5 x = 8 ( x + 1 ) x = 1 / 1 ratio of gold with copper = 1 : 1 = 1 : 1 answer is b\"" + }, + { + "Answer": 1216, + "Options": "a ) 1216 , b ) 1723 , c ) 1129 , d ) 2613 , e ) 1372", + "Correct": "a", + "Explanation": "a b has 62.5 % or ( 5 / 8 ) of the milk in a . therefore , let the quantity of milk in container a ( initially ) be 8 k . quantity of milk in b = 8 k - 5 k = 3 k . quantity of milk in container c = 8 k - 3 k = 5 k container : a b c quantity of milk : 8 k 3 k 5 k it is given that if 152 liters was transferred from container c to container b , then both the containers would have equal quantities of milk . 5 k - 152 = 3 k + 152 = > 2 k = 304 = > k = 152 the initial quantity of milk in a = 8 k = 8 * 152 = 1216 liters ." + }, + { + "Answer": 35, + "Options": "a ) 25 % , b ) 35 % , c ) 45 % , d ) 55 % , e ) 65 %", + "Correct": "b", + "Explanation": "\"to maximize the percentage of companies offering both , let ' s assume that all 35 % of companies which offer wireless internet also offer snacks . the answer is b .\"" + }, + { + "Answer": 156, + "Options": "a ) 156 , b ) 208 , c ) 210 , d ) 223 , e ) 229", + "Correct": "a", + "Explanation": "\"explanation : total runs scored by the batsman = 59 * 46 = 2714 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2714 \u2013 2552 = 162 runs . let the highest score be x , hence the lowest score = x \u2013 150 x + ( x - 150 ) = 162 2 x = 312 x = 156 runs answer a\"" + }, + { + "Answer": 6, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "e", + "Explanation": "\"3 ^ 2 y = 3 ^ 12 2 y = 12 , therefore y = 6 e\"" + }, + { + "Answer": 780, + "Options": "a ) 233 , b ) 600 , c ) 287 , d ) 780 , e ) 191", + "Correct": "d", + "Explanation": "\"explanation : total salary of 8 workers and supervisor together = 9 \u00e3 \u2014 430 = 3870 now total salary of 8 workers = 3870 \u00e2 \u02c6 \u2019 870 = 3000 total salary of 9 workers including the new supervisor = 9 \u00e3 \u2014 420 = 3780 salary of the new supervisor = 3780 \u00e2 \u02c6 \u2019 3000 = 780 answer : d\"" + }, + { + "Answer": 4.400000000000001, + "Options": "a ) 4.2 , b ) 4.4 , c ) 4.6 , d ) 5.6 , e ) 5.7", + "Correct": "b", + "Explanation": "\"sum of the remaining two numbers = ( 3.95 * 6 ) - [ ( 3.6 * 2 ) + ( 3.85 * 2 ) ] = 8.8 . required average = ( 8.8 / 2 ) = 4.4 . b\"" + }, + { + "Answer": 0.4, + "Options": "a ) 1 / 4 , b ) 1 / 2 , c ) 2 / 5 , d ) 1 , e ) 5 / 4", + "Correct": "c", + "Explanation": "\"min value of a / b will be when b is highest and a is lowest - - - > a = 30 and b = 50 so , a / b = 3 / 5 max value of a / b will be when b is lowest and a is highest - - - > a = 40 and b = 40 so , a / b = 1 range is 1 - ( 3 / 5 ) = 2 / 5 answer should be c .\"" + }, + { + "Answer": 10000, + "Options": "a ) 7787 , b ) 10000 , c ) 1988 , d ) 1277 , e ) 2081", + "Correct": "b", + "Explanation": "\"x * 105 / 100 * 95 / 100 = 9975 x * 0.9975 = 9975 x = 9975 / 0.9975 = > 10000 answer : b\"" + }, + { + "Answer": 60, + "Options": "a ) 60 , b ) 30 , c ) 12 , d ) 90 , e ) 120", + "Correct": "a", + "Explanation": "\"240 can be written as ( 2 ^ 4 ) * 3 * 5 . for k ^ 2 to be divisible by 240 it should contain at least 2 ^ 4 and 3 and 5 in its factors . we can leave out option c because 12 doesnt have 5 as one of its factor . now if we check for option b , 30 can be written as 2 * 3 * 5 , hence 30 ^ 2 will have 2 as the maximum power of 2 , so we can leave out this option too . option c is the right answer if we follow the same method as we followed for other two previous options . 60 = ( 2 ^ 2 ) * 3 * 5 ; 60 ^ 2 = ( 2 ^ 4 ) * ( 3 ^ 2 ) * ( 5 ^ 2 ) . so it shows that 60 ^ 2 is divisible by 240 and hence the answer . answer : a\"" + }, + { + "Answer": 220040, + "Options": "a ) 220044 , b ) 145778 , c ) 220400 , d ) 220014 , e ) 220040", + "Correct": "e", + "Explanation": "\"( 555 + 445 ) * 2 * 110 + 30 = 220000 + 30 = 220040 e\"" + }, + { + "Answer": 47.99999999999998, + "Options": "a ) 30 , b ) 36 , c ) 42 , d ) 46 , e ) 48", + "Correct": "e", + "Explanation": "\"let the total weight be x . sand content = ( 1 / 3 ) x water content = ( 1 / 2 ) x gravel = x - ( 1 / 3 ) x - ( 1 / 2 ) x = ( 1 / 6 ) x = 8 x = 48 then answer will be e = 48\"" + }, + { + "Answer": 7, + "Options": "a ) 5 , b ) 7 , c ) 10 , d ) 15 , e ) 18", + "Correct": "b", + "Explanation": "\"a = 2 m = m + 14 m = 14 a = 28 a = 4 b , and so b = 7 the answer is b .\"" + }, + { + "Answer": 38.46153846153846, + "Options": "a ) a ) 6.7 , b ) b ) 38.5 , c ) c ) 9.6 , d ) d ) 12.5 , e ) e ) 7.9", + "Correct": "b", + "Explanation": "\"amount salt in 100 kg solution = 10 * 100 / 100 = 10 kg let x kg of pure salt be added then ( 10 + x ) / ( 100 + x ) = 35 / 100 200 + 20 x = 700 + 7 x 13 x = 500 x = 28.5 answer is b\"" + }, + { + "Answer": 19, + "Options": "a ) 13 , b ) 15 , c ) 17 , d ) 19 , e ) 21", + "Correct": "d", + "Explanation": "\"y = 276 * a + 42 = ( 23 * 12 ) * a + 23 + 19 the answer is d .\"" + }, + { + "Answer": 2, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8", + "Correct": "a", + "Explanation": "\"f 200 / x leaves a reminder 2 then ( 200 - 2 ) i . e . 198 is divisible by x so ( 200 + 198 ) / x leaves a reminder rem ( 200 / x ) + rem ( 198 / x ) = > 2 + 0 = 2 answer : a\"" + }, + { + "Answer": 1, + "Options": "a ) 48 seconds , b ) 1 minute , 12 seconds , c ) 1 minute , 36 seconds , d ) 2 minutes , 14 seconds , e ) 4 minutes , 12 seconds", + "Correct": "c", + "Explanation": "\"if 5 / 7 of tub ' s content is drained 2 / 7 th of tub still needs to be drained . if it takes 4 minutes to drain 5 / 7 th of tub it takes 4 * ( 7 / 5 ) minutes to drain the entire tub and 4 * ( 7 / 5 ) * ( 2 / 7 ) min to drain 2 / 7 th of the tub which is 8 / 5 minutes or 1 3 / 5 minutes or 1 minute 36 seconds so answer is c\"" + }, + { + "Answer": 74.99999999999997, + "Options": "a ) 92 , b ) 90 , c ) 82 , d ) 78 , e ) 75", + "Correct": "e", + "Explanation": "i get 75 . a cube with 1 million liters cube would be a cube with the dimensions of 100 * 100 * 100 . 4 * 2 covers 8 sq liters so 100 / 8 = 12.5 . t = 12.5 * 6 = 75 . e" + }, + { + "Answer": 6, + "Options": "a ) 3 , b ) 6 , c ) 10 , d ) 12 , e ) 18", + "Correct": "b", + "Explanation": "= 3 c 2 x 2 = 6 can you explain your method . i solved it differently xyz , where z must be 5 . therefore 1 variation of digit in z . y can be any of the 3 possible choices . x can be any of the 2 possible choices . 2 + 3 + 1 = 6 b" + }, + { + "Answer": 30, + "Options": "a ) 20 % , b ) 30 % , c ) 60 % , d ) 50 % , e ) 33 %", + "Correct": "b", + "Explanation": "ok , i do not know whether it is exactly what you want to hear but i did it that way : first look at difference between revenue and variable cost = > take the bigger one ( b ) which gives you : 4.5 x - 1500 just plug in 2000 and 3000 . you get 7500 and 12000 ( difference 4500 ) . 4500 > 0.5 * 7500 so 30 % b" + }, + { + "Answer": 90, + "Options": "a ) 25 , b ) 90 , c ) 100 , d ) 140 , e ) it can not be determined from the information given", + "Correct": "b", + "Explanation": "\"the arithmetic mean of a and b = ( a + b ) / 2 = 45 - - a + b = 90 - - 1 similarly for b + c = 180 - - 2 subtracting 1 from 2 we have c - a = 90 ; answer : b\"" + }, + { + "Answer": 173, + "Options": "a ) 173 , b ) 685 , c ) 865 , d ) 495 , e ) 534", + "Correct": "a", + "Explanation": "\"let y x 240 = 173 x 240 then y = ( 173 x 240 ) / 240 = 173 answer : a\"" + }, + { + "Answer": 42, + "Options": "a ) a ) 35 , b ) b ) 34 , c ) c ) 42 , d ) d ) 25 , e ) e ) 26", + "Correct": "c", + "Explanation": "explanation : let the present age of p and q be 3 x and 4 x respectively . twelve years ago , p was half of q in age = > 2 ( 3 x \u2013 12 ) = ( 4 x \u2013 12 ) = > 6 x \u2013 24 = 4 x \u2013 12 = > 2 x = 12 = > x = 6 7 x = 7 * 6 = 42 answer : option c" + }, + { + "Answer": 75, + "Options": "a ) 74 , b ) n = 75 , c ) n = 175 , d ) n = 680 , e ) 690", + "Correct": "b", + "Explanation": "\"i solved this question by plugging in numbers from the answer choices . a . ) 74 starting with answer choice a , i immediately eliminated it because 74 is not even divisible by 5 . b . ) 75 i divide 75 / 5 and get 15 as an answer . i divide 75 / 34 and get a remainder of 7 . 15 - 7 = 8 so i know the correct answer isb\"" + }, + { + "Answer": 0.3, + "Options": "a ) 3 / 19 , b ) 3 / 11 , c ) 3 / 17 , d ) 3 / 10 , e ) 3 / 13", + "Correct": "d", + "Explanation": "explanation : 3 p 3 p = 6 , p = 3636 = 1212 and 3 q 3 q = 15 , q = 315315 = 1515 then p \u2013 q = 1 / 2 \u2013 1 / 5 = 3 / 10 answer : d" + }, + { + "Answer": 382.2307692307692, + "Options": "a ) 380 times , b ) 381 times , c ) 382 times , d ) 392 times , e ) 482 times", + "Correct": "c", + "Explanation": "\"time difference is 1 hr , 22 min , 49 sec = 4969 sec . so , light glows floor ( 4969 / 13 ) = 382 times . answer : c\"" + }, + { + "Answer": 40.00000000000002, + "Options": "a ) 3 / 80 , b ) 3 / 5 , c ) 40 , d ) 5 / 3 , e ) 80 / 3", + "Correct": "c", + "Explanation": "10 / 100 = 1 / 10 n = 2 ^ 1 / 10 n ^ b = 2 ^ 4 ( 2 ^ 1 / 10 ) ^ b = 2 ^ 4 b = 40 answer : c" + }, + { + "Answer": 91, + "Options": "a ) 91 , b ) 37 , c ) 99 , d ) 277 , e ) 19", + "Correct": "a", + "Explanation": "explanation : required number of students = h . c . f of 1001 and 910 = 9 answer : a ) 91" + }, + { + "Answer": 4690640889, + "Options": "a ) 4586970843 , b ) 4686970743 , c ) 4691100843 , d ) 4586870843 , e ) 4690640889", + "Correct": "e", + "Explanation": "answer 469111 x 9999 = 469111 x ( 10000 - 1 ) = 4691110000 - 469111 = 4690640889 . option : e" + }, + { + "Answer": 25, + "Options": "a ) 25 % , b ) 15 % , c ) 30 % , d ) 32 % , e ) 40 %", + "Correct": "a", + "Explanation": "\"required percentage = [ 100 * 20 / ( 100 - 20 ) ] % = 25 % answer is a\"" + }, + { + "Answer": 60, + "Options": "a ) 15 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 60 %", + "Correct": "e", + "Explanation": "\"sol . let the original consumption = 100 kg and new consumption = x kg . so , 100 x 2 = x \u00d7 5 = x = 40 kg . \u2234 reduction in consumption = 60 % . answer e\"" + }, + { + "Answer": 4, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "c", + "Explanation": "\"assume n = 29 remainder ( n / 24 ) = 4 n + 15 = 44 remainder ( 44 / 5 ) = 4 option c\"" + }, + { + "Answer": 105, + "Options": "a ) 190 , b ) 105 , c ) 200 , d ) 205 , e ) 210", + "Correct": "b", + "Explanation": "\"this question can be solved with the average formula and ' bunching . ' we ' re asked for the average of all of the multiples of 10 from 10 to 200 , inclusive . to start , we can figure out the total number of terms rather easily : 1 ( 10 ) = 10 2 ( 10 ) = 20 . . . 20 ( 10 ) = 200 so we know that there are 40 total numbers . we can now figure out the sum of those numbers with ' bunching ' : 10 + 200 = 210 20 + 190 = 210 30 + 180 = 210 etc . since there are 20 total terms , this pattern will create 10 ' pairs ' of 210 . thus , since the average = ( sum of terms ) / ( number of terms ) , we have . . . ( 10 ) ( 210 ) / ( 20 ) = 105 answer : b\"" + }, + { + "Answer": 1800, + "Options": "a ) 900 , b ) 1800 , c ) 2250 , d ) 1650 , e ) 1250", + "Correct": "b", + "Explanation": "\"4 a * 5 b = 30 * 30 = 900 20 ab = 900 i . e . 30 ab = 1800 answer : option b\"" + }, + { + "Answer": 12, + "Options": "a ) 4 , b ) 6 , c ) 8 , d ) 9 , e ) 12", + "Correct": "e", + "Explanation": "the exponents of x ^ 2 * y * z are 2 , 1 , and 1 . the number of factors is ( 2 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 12 the answer is e ." + }, + { + "Answer": 58, + "Options": "a ) 80 % , b ) 74 % , c ) 58 % , d ) 56 % , e ) 50 %", + "Correct": "c", + "Explanation": "2 students scored 80 % 5 students scored 60 % 3 students scored 40 % ( 2 ) ( 80 ) + 5 ( 60 ) + 3 ( 40 ) = 160 + 300 + 120 = 580 580 / 10 students = 58 - - > 58 % average answer : c" + }, + { + "Answer": 114.9999999999999, + "Options": "a ) 113 , b ) 114 , c ) 115 , d ) 116 , e ) 117", + "Correct": "c", + "Explanation": "\"12.4 * x + 26 = ( 6 + x ) 12 solve equation x = 115 answer : c\"" + }, + { + "Answer": 12, + "Options": "a ) 17 , b ) 15 , c ) 12 , d ) - 8 / 5 , e ) none", + "Correct": "c", + "Explanation": "answer \u221a 289 - \u221a 625 \u00f7 \u221a 25 = \u221a 17 x 17 - \u221a 25 x 25 \u00f7 \u221a 5 x 5 = 17 - 25 \u00f7 5 = 17 - 5 = 12 correct option : c" + }, + { + "Answer": 28, + "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 21 , e ) 28", + "Correct": "e", + "Explanation": "total marks of male = m total marks of female = f number of males = 8 number of females = f given : ( m + f ) / ( 8 + f ) = 90 - - - - - - - - - - - - - 1 also given , m / 8 = 83 thus m = 664 - - - - - - - - - 2 also , f / f = 92 thus f = 92 f - - - - - - - - - 3 put 2 and 3 in 1 : we get ( 664 + 92 f ) / ( 8 + f ) = 90 solving this we get f = 28 ans : e" + }, + { + "Answer": 53.794705707972525, + "Options": "a ) 10 , b ) 12 , c ) 14 , d ) 54 , e ) 18", + "Correct": "d", + "Explanation": "\"this one ' s easy . 1000 * 2 ^ t = 500,000 2 ^ t = 500 now gauging , since 2 ^ 8 = 256 , then 2 ^ 9 = 512 so t = 9 but be careful , ' t ' is in time intervals of 6 minutes so answer is 9 * 6 = 54 minutes answer ( d )\"" + }, + { + "Answer": 98, + "Options": "a ) 68 , b ) 78 , c ) 88 , d ) 98 , e ) 56", + "Correct": "d", + "Explanation": "2 + 3 = 2 * [ 3 + ( 2 - 1 ) ] = 8 3 + 7 = 3 * [ 7 + ( 3 - 1 ) ] = 27 4 + 5 = 4 * [ 5 + ( 4 - 1 ) ] = 32 5 + 8 = 5 * [ 8 + ( 5 - 1 ) ] = 60 6 + 7 = 6 * [ 7 + ( 6 - 1 ) ] = 72 therefore 7 + 8 = 7 * [ 8 + ( 7 - 1 ) ] = 98 x + y = x [ y + ( x - 1 ) ] = x ^ 2 + xy - x correct answer is d ) 98" + }, + { + "Answer": 2, + "Options": "a ) 10 , b ) 2 , c ) 4 , d ) 16 , e ) 18", + "Correct": "b", + "Explanation": "important : i notice that if we square x \u00b2 , we get x \u2074 , and if we square 1 / x \u00b2 , we get 1 / x \u2074 , so let ' s see what happens if we take the equation x \u00b2 + 1 / x \u00b2 = 2 andsquareboth sides : ( x \u00b2 + 1 / x \u00b2 ) \u00b2 = 4 so , ( x \u00b2 + 1 / x \u00b2 ) ( x \u00b2 + 1 / x \u00b2 ) = 4 expand to get : x \u2074 + 1 + 1 + 1 / x \u2074 = 4 simplify : x \u2074 + 1 / x \u2074 = 2 answer : b" + }, + { + "Answer": 460, + "Options": "a ) 443 , b ) 450 , c ) 460 , d ) 468 , e ) 475", + "Correct": "c", + "Explanation": "\"total number of installments = 52 payment per installment for the first 12 installments = 410 payment per installment for the remaining 32 installments = 410 + 65 = 475 average = ( 12 * 410 + 40 * 475 ) / 52 = 460 answer c\"" + }, + { + "Answer": 1.1000000000000085, + "Options": "a ) 2.1 % , b ) 8.1 % , c ) 5.1 % , d ) 6.1 % , e ) 1.1 %", + "Correct": "e", + "Explanation": "\"100 * 100 = 10000 86 * 115 = 9890 - - - - - - - - - - - 10000 - - - - - - - - - - - 110 100 - - - - - - - - - - - ? = > 1.1 % decrease answer : e\"" + }, + { + "Answer": 17, + "Options": "a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19", + "Correct": "c", + "Explanation": "\"explanation : let the number of persons be n \u00e2 \u02c6 \u00b4 total handshakes = nc 2 = 136 n ( n - 1 ) / 2 = 136 \u00e2 \u02c6 \u00b4 n = 17 answer : c\"" + }, + { + "Answer": 49, + "Options": "a ) 5 , b ) 10 , c ) 20 , d ) 40 , e ) 49", + "Correct": "e", + "Explanation": "\"solution - lets say , single hamburgersxand double hamburgersy given that , x + y = 50 and 1 x + 1.5 y = 74.50 . by solving the equations y = 49 . ans e .\"" + }, + { + "Answer": 10, + "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 12 , e ) 16", + "Correct": "c", + "Explanation": "\"m + tu + w + th = 4 * 48 = 192 tu + w + th + f = 4 * 40 = 160 m = 42 tu + w + th = 192 - 42 = 150 f = 160 \u2013 150 = 10 answer : c\"" + }, + { + "Answer": 60, + "Options": "a ) 60 , b ) 120 , c ) 160 , d ) 240 , e ) 840", + "Correct": "a", + "Explanation": "\"let a = first term , d = common difference . 4 th term = a + 3 d 12 th term = a + 11 d a + 3 d + a + 11 d = 8 2 a + 14 d = 8 a + 7 d = 4 . sum of the first 15 terms = 15 / 2 ( 2 a + 14 d ) = 15 ( a + 7 d ) = 15 ( 4 ) = 60 . ans ( a )\"" + }, + { + "Answer": 0.14285714285714285, + "Options": "a ) 5 / 6 , b ) 1 / 5 , c ) 1 / 6 , d ) 1 / 7 , e ) 1 / 24", + "Correct": "d", + "Explanation": "\"let x be the number of upgraded sensors on the satellite . the number of non - upgraded sensors per unit is x / 4 . the number of non - upgraded sensors on the whole satellite is 24 ( x / 4 ) = 6 x . the fraction of sensors which have been upgraded is x / ( x + 6 x ) = x / 7 x = 1 / 7 the answer is d .\"" + }, + { + "Answer": 70, + "Options": "a ) $ 160 , b ) $ 70 , c ) $ 90 , d ) $ 80 , e ) $ 55", + "Correct": "b", + "Explanation": "4 ibs and 5 clients - so total 9 people the bill $ 756 includes 20 % gratuity . . . so the actual cost of dinner was $ 630 now , the cost per person will be $ 630 / 9 which is $ 70 option b" + }, + { + "Answer": 345, + "Options": "a ) $ 150 , b ) $ 345 , c ) $ 365 , d ) $ 715 , e ) $ 730", + "Correct": "b", + "Explanation": "\"total weekly income over 5 weeks = $ 406 + $ 413 + $ 420 + $ 436 + $ 395 = $ 2070 for avg weekly income to be $ 500 over 7 weeks , we need total weekly income over 7 weeks = $ 3500 now , $ 3500 - $ 2070 = $ 1430 from this , we subtract base salary for 2 weeks i . e $ 370 * 2 = $ 740 therefore , commission = $ 1430 - $ 740 = $ 690 for 2 weeks avg weekly commission = $ 345 answer b\"" + }, + { + "Answer": 50, + "Options": "a ) 60 , b ) 80 , c ) 50 , d ) 100 , e ) 40", + "Correct": "c", + "Explanation": "let the total number of ounces in the drink be x % of orange = 25 % % of watermelon = 35 % % of grape = 100 % - 60 % = 40 % but this number is given as 20 ounces so 40 % of x = 20 and x = ( 20 ) ( 100 / 40 ) = ( 20 ) ( 5 / 2 ) x = 50 therefore there a total of 50 ounces in the drink . correct answer - c" + }, + { + "Answer": 360, + "Options": "a ) 300 , b ) 320 , c ) 340 , d ) 360 , e ) 380", + "Correct": "d", + "Explanation": "let alchemerion be a let son be s let father be f a = 3 * s f = 40 + ( 2 * a ) therefore 1240 = ( s + f + a ) 1240 = ( a / 3 ) + ( 40 + ( 2 * a ) ) + a a = 360 answer : d" + }, + { + "Answer": 50, + "Options": "a ) 50 km , b ) 56 km , c ) 70 km , d ) 80 km , e ) 90 km", + "Correct": "a", + "Explanation": "let the actual distance travelled be x km . then x / 10 = ( x + 20 ) / 14 - - > 14 x = 10 x + 200 - - > 4 x = 200 - - > x = 50 km . answer : a ." + }, + { + "Answer": 16, + "Options": "a ) 24 , b ) 18 , c ) 16 , d ) 12 , e ) 8", + "Correct": "c", + "Explanation": "\"4 machines do x units in 6 days we have x / 6 = > rate of the 4 machines we know that we need to have 2 x units in 3 days therefore , we need to get to 2 x / 3 rate of the machines . rate of one machine is x / 6 * 1 / 4 = x / 24 . now , we need to know how many machines need to work simultaneously , to get 2 x done in 3 days . 2 x / 3 work needs to be done by machines that work at x / 24 rate . let ' s assign a constant y for the number of machines : ( x / 24 ) * y = 2 x / 3 y = 2 x / 3 * 24 / x cancel 3 with 24 , and x with x and get - > 16 . answer choice c\"" + }, + { + "Answer": 36, + "Options": "a ) 20 lb , b ) 30 lb , c ) 10 lb , d ) 15 lb , e ) 36 lb", + "Correct": "e", + "Explanation": "sol . 36 \u00f7 3 = 12 . answer : e" + }, + { + "Answer": 5, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 5", + "Correct": "e", + "Explanation": "\"if 200 / x leaves a reminder 5 then ( 200 - 5 ) i . e . 195 is divisible by x so ( 200 + 195 ) / x leaves a reminder rem ( 200 / x ) + rem ( 195 / x ) = > 5 + 0 = 5 answer : e\"" + }, + { + "Answer": 2401, + "Options": "a ) 2401 , b ) 4 , c ) 8 , d ) 16 , e ) 32", + "Correct": "a", + "Explanation": "\"( x + y ) ^ 2 - ( x - y ) ^ 2 ( x + y + x - y ) ( x + y - x + y ) ( 2 x ) ( 2 y ) 4 xy 4 7 ^ 4 = 2401 answer a\"" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "a", + "Explanation": "answer : a . there is exactly one . the prime factorization of 14 is 14 = 2 * 7 , so n = 2 * 7 * p = 7 * 2 * p = 7 * 2 p , so 2 p is the only even number that divides n ." + }, + { + "Answer": 288, + "Options": "a ) 240 , b ) 248 , c ) 280 , d ) 288 , e ) 290", + "Correct": "d", + "Explanation": "let x be no . of passengers at beginning at , 1 st station is drops 1 / 3 rd so remaining 2 / 3 rd are in train only plus 280 i . e . , 2 x / 3 + 280 at 2 nd stop 1 / 2 of new total and 12 more i . e . , ( 2 x / 3 + 280 ) / 2 + 12 = 248 on solving above equation we get x as 288 answer : d" + }, + { + "Answer": 15, + "Options": "a ) 14 , b ) 20 , c ) 15 , d ) 32 , e ) 64", + "Correct": "c", + "Explanation": "\"by formula , ( a + b + c ) ^ 2 = a ^ 2 + b ^ 2 + c ^ 2 + 2 ( ab + bc + ca ) , since , a ^ 2 + b ^ 2 + c ^ 2 = 213 and ab + bc + ca = 6 , ( a + b + c ) ^ 2 = 213 + 2 ( 6 ) = 225 = 15 ^ 2 therefore : a + b + c = 15 answer : c\"" + }, + { + "Answer": 6, + "Options": "a ) 8 , b ) 10 , c ) 12 , d ) 6 , e ) 19", + "Correct": "d", + "Explanation": "\"2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 48 - 36 = 12 ab = 6 . answer : d\"" + }, + { + "Answer": 0.9523809523809524, + "Options": "a ) 22 / 21 , b ) 20 / 21 , c ) 23 / 21 , d ) 25 / 21 , e ) 28 / 21", + "Correct": "b", + "Explanation": "\"say x = y = 10 . in this case we would have : 30 x = 300 black - and - white films ; 6 y = 60 color films . y / x % = 10 / 10 % = 1 % of the black - and - white films , so 3 black - and - white films and all 60 color films , thus total of 63 films were selected . color films thus compose 60 / 63 = 20 / 21 of the selected films . answer : b\"" + }, + { + "Answer": 12, + "Options": "a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14", + "Correct": "c", + "Explanation": "\"solution let x be the number . always replace ` ` is ' ' with an equal sign ( 1 / 2 ) x + 5 = 11 ( 1 / 2 ) x + 5 - 5 = 11 - 5 ( 1 / 2 ) x = 6 2 \u00d7 ( 1 / 2 ) x = 6 \u00d7 2 x = 12 answer c\"" + }, + { + "Answer": 0.25, + "Options": "a ) - 4 , b ) 4 , c ) - 1 / 4 , d ) 1 / 4 , e ) 2", + "Correct": "d", + "Explanation": "as 4 y = mx + c , from 4 y = 0 m + m we get y = 1 / 4 . hence , the correct answer choice is d ." + }, + { + "Answer": 42, + "Options": "a ) 38 , b ) 42 , c ) 46 , d ) 49 , e ) 62", + "Correct": "b", + "Explanation": "according to remainder theorem when dfracf ( x ) x + adfracf ( x ) x + a , then the remainder is f ( \u2212 a ) f ( \u2212 a ) . in this case , as x + 3 x + 3 divides x 3 + 4 x 2 \u2212 7 x + 12 \u2013 kx 3 + 4 x 2 \u2212 7 x + 12 \u2013 k perfectly ( kk being the number to be subtracted ) , the remainder is 0 when the value of xx is substituted by - 3 . i . e . , ( \u2212 3 ) 3 + 4 ( \u2212 3 ) 2 \u2212 7 ( \u2212 3 ) + 12 \u2212 k = 0 ( \u2212 3 ) 3 + 4 ( \u2212 3 ) 2 \u2212 7 ( \u2212 3 ) + 12 \u2212 k = 0 or \u2212 27 + 36 + 21 + 12 = k \u2212 27 + 36 + 21 + 12 = k or k = k = 42 b" + }, + { + "Answer": 2944, + "Options": "a ) 2674 , b ) 2944 , c ) 2464 , d ) 2924 , e ) 2994", + "Correct": "b", + "Explanation": "explanation : 40 * 72 + 64 = 2944 answer : b" + }, + { + "Answer": 0.5, + "Options": "a ) 1 / 2 , b ) 1 , c ) 2 / 3 , d ) 3 / 5 , e ) 3 / 8", + "Correct": "a", + "Explanation": "sol . required probability = pg . ) x p ( b ) = ( 1 \u2014 d x ( 1 \u2014 i ) = : x 1 = 1 / 2 ans . ( a )" + }, + { + "Answer": 9.959919678390985, + "Options": "a ) 12.0 , b ) 12.1 , c ) 12.2 , d ) 10.0 , e ) 10.4", + "Correct": "d", + "Explanation": "the question says that bacteria increased by same fraction , not by same amount in 2 intervals of 3 hours . let x represent the amount of bacteria present at 4 : 00 pm . since the fractional increase must remain constant from 1 to 4 pm as it is from 4 pm to 7 pm : fractional increase from 1 pm to 4 pm = x / 8.0 fractional increase from 4 pm to 7 pm = 12.4 / x x \\ 8 = 12.4 \\ x x ^ 2 = 12.4 * 8 x = 10 answer : d" + }, + { + "Answer": 16500, + "Options": "a ) 21000 , b ) 19800 , c ) 16500 , d ) 15800 , e ) 8700", + "Correct": "c", + "Explanation": "given : the question tells us about the number of tickets sold in the first week at reduced price = 5400 . it also tells us that during the remaining weeks , the number of tickets sold at full price was 5 times the no . of tickets sold at reduced price . the total tickets sold was 25200 , and we are asked to find the number of tickets that where sold at full price . approach : the question asks us to find the number of ticket sold at full price . we know that the number of tickets sold at full price was 5 times the no . of tickets sold at reduced price in remaining weeks . hence , assuming tickets sold at reduced price in remaining weeks to be x would give us the no . of tickets sold at full price to be 5 x . tickets sold in first week + tickets sold in remaining weeks = total no . of tickets soldi . e . tickets sold in first week + tickets sold at full price in remaining weeks + tickets sold at reduced price in remaining weeks = total no . of tickets sold we know the no . of tickets sold during first week and the total no . of tickets sold . we will use this relation to get to our answer . working out : tickets sold in first week + tickets sold at full price in remaining weeks + tickets sold at reduced price in remaining weeks = total no . of tickets sold substituting values in the equation , we get 5400 + 5 x + x = 25200 x = 3300 tickets sold at full price = 5 x = 16500 answer : option c" + }, + { + "Answer": 144, + "Options": "a ) 144 % , b ) b . 120 % , c ) 96 % , d ) 80 % , e ) 64 %", + "Correct": "a", + "Explanation": "\"even i got 96 % j = 100 t = 100 * 0.9 = 90 m = 90 * 1.6 = 144 if mary ' s income is x percent of j m = j * x / 100 x = m * 100 / j = 144 * 100 / 100 = 144 ans : a\"" + }, + { + "Answer": 597, + "Options": "a ) 597 , b ) 608 , c ) 613 , d ) 616 , e ) 621", + "Correct": "a", + "Explanation": "\"the set s = { 5 , 13 , 21 , 29 , . . . . . . . . . . . . . . . . . . . . . } 1 st number = 8 * 0 + 5 = 5 2 nd number = 8 * 1 + 5 = 13 3 rd number = 8 * 2 + 5 = 21 75 th number = 8 * ( 75 - 1 ) + 5 = 597 answer = a\"" + }, + { + "Answer": 720, + "Options": "a ) 80 , b ) 720 , c ) 760 , d ) 840 , e ) 860", + "Correct": "b", + "Explanation": "\"working inside out , ( 4 \u20ac 5 ) = 2 * 4 * 5 = 40 9 \u20ac 40 = 2 * 9 * 40 = 720 hence , answer is b\"" + }, + { + "Answer": 2, + "Options": "a ) 2 , b ) 3 , c ) 5 , d ) 7 , e ) 9", + "Correct": "a", + "Explanation": "\"p \u00e3 \u00b7 44 = 432 = > p = 432 * 44 = 19008 p / 34 = 19008 / 34 = 559 , remainder = 2 a\"" + }, + { + "Answer": 75, + "Options": "a ) 75 , b ) 65 , c ) 43 , d ) 52 , e ) 78", + "Correct": "a", + "Explanation": "65 \u00f7 13 = 5 bags per student 5 x 15 = 75 nuts per student correct answer a" + }, + { + "Answer": 0.5, + "Options": "a ) 5 / 2 , b ) 1 / 2 , c ) 2 / 3 , d ) 2 / 5 , e ) 0", + "Correct": "b", + "Explanation": "we are given x = 1 \u2013 4 t and y = 2 t \u2013 2 , and we need to determine the value for t when x = y . we should notice that both x and y are already in terms of t . thus , we can substitute 1 \u2013 4 t for x and 2 t \u2013 2 for y in the equation x = y . this gives us : 1 \u2013 4 t = 2 t \u2013 2 3 = 6 t 1 / 2 = t the answer is b ." + }, + { + "Answer": 4, + "Options": "a ) 5 , b ) 6 , c ) 4 , d ) 9 , e ) 5.5", + "Correct": "c", + "Explanation": "explanation : unit digit in 795 = unit digit in [ ( 74 ) 23 x 73 ] = unit digit in [ ( unit digit in ( 2401 ) ) 23 x ( 343 ) ] = unit digit in ( 123 x 343 ) = unit digit in ( 343 ) = 3 unit digit in 358 = unit digit in [ ( 34 ) 14 x 32 ] = unit digit in [ unit digit in ( 81 ) 14 x 32 ] = unit digit in [ ( 1 ) 14 x 32 ] = unit digit in ( 1 x 9 ) = unit digit in ( 9 ) = 9 unit digit in ( 795 - 358 ) = unit digit in ( 343 - 9 ) = unit digit in ( 334 ) = 4 . so , answer c" + }, + { + "Answer": 33, + "Options": "a ) 18 , b ) 25 , c ) 20 , d ) 32 , e ) 33", + "Correct": "e", + "Explanation": "explanation : let first number be x . so , 2 nd no . = 4 x & 3 rd no . = 2 x . so , x + 4 x + 2 x = 77 \u00d7 3 = 231 7 x = 231 x = 231 / 7 hence , smallest number x = 33 answer : e" + }, + { + "Answer": 25, + "Options": "a ) 2 % , b ) 17 % , c ) 25 % , d ) 65 % , e ) 83 %", + "Correct": "c", + "Explanation": "\"new value \u2013 old value ) / old value x 100 we are given : february sales this year = 400 million february sales last year = 320 million we need to determine the percent increase between sales from last year to sales this year . thus , the new value = 400 million and the old value = 320 million . let \u2019 s plug them into our percent change formula . ( new value \u2013 old value ) / old value x 100 [ ( 400 \u2013 320 ) / 320 ] x 100 = 25 % . the answer is c .\"" + }, + { + "Answer": 26, + "Options": "a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28", + "Correct": "c", + "Explanation": "xy is 2 digit no . y - x = 4 ; ( 10 x + y ) * ( 2 x + 4 ) = 208 ; sub y = x + 4 ; we get 26 answer : c" + }, + { + "Answer": 24, + "Options": "a ) $ 4 , b ) $ 14 , c ) $ 5 , d ) $ 15 , e ) $ 24", + "Correct": "e", + "Explanation": "1 / 5 x $ 180 = $ 36 for sandwich 1 / 6 x $ 180 = $ 30 for museum 1 / 2 x $ 180 = $ 90 for book $ 36 + $ 30 + $ 90 = $ 156 spent $ 180 - $ 156 = $ 24 left over correct answer e" + }, + { + "Answer": 64, + "Options": "a ) 64 , b ) 68 , c ) 70 , d ) 79 , e ) 80", + "Correct": "a", + "Explanation": "let x = the less number 2 x = the greater number the sum of the numbers is 96 x + 2 x = 96 3 x = 96 x = 32 2 x = 64 option a" + }, + { + "Answer": 20, + "Options": "a ) 50 , b ) 10 , c ) 15 , d ) 25 , e ) 20", + "Correct": "e", + "Explanation": "since five times the number equals one hundred , then the number equals one hundred divided by five . therefore the number is 100 / 5 = 20 . correct answer e" + }, + { + "Answer": 144, + "Options": "a ) $ 144 , b ) $ 135 , c ) $ 90 , d ) $ 60 , e ) $ 54", + "Correct": "a", + "Explanation": "since 2 / 3 of the books in the collection were sold , 1 / 3 were not sold . the 36 unsold books represent 1 / 3 of the total number of books in the collection , and 2 / 3 of the total number of books equals 2 ( 36 ) or 72 . the total proceeds of the sale was 72 ( $ 2.00 ) or $ 144 . the best answer is therefore a . answer : a ." + }, + { + "Answer": 4, + "Options": "a ) \u2212 48 , b ) \u2212 2 , c ) 4 , d ) 46 , e ) 48", + "Correct": "c", + "Explanation": "\"a ( a - 4 ) = 21 and b ( b - 4 ) = 21 = > a , b must be integers and if a is - 3 or 7 , b will be 7 and - 3 respectively = > a + b = 4 ans : c\"" + }, + { + "Answer": 42500, + "Options": "a ) $ 27,500 , b ) $ 35,000 , c ) $ 37,500 , d ) $ 42,500 , e ) $ 50,000", + "Correct": "d", + "Explanation": "let x be the average of 40 customers 40 * x + 10 * 55000 = 50 * 45000 solving this we have x = 42500 answer is d ." + }, + { + "Answer": 33, + "Options": "a ) 28 , b ) 31 , c ) 33 , d ) 35 , e ) 38", + "Correct": "c", + "Explanation": "the numbers be 11 a and 11 b 11 a \u00d7 11 b = 363 ab = 3 co - primes with product 3 are ( 1 , 3 ) hence the numbers with hcf 11 and product 363 = ( 11 \u00d7 1 , 11 \u00d7 3 ) = ( 11 , 33 ) numbers are 11 and 33 the greater number = 33" + }, + { + "Answer": 36, + "Options": "a ) 10 , b ) 30 , c ) 36 , d ) 60 , e ) 90", + "Correct": "c", + "Explanation": "\"9 players are there . two players play one game with one another . so 9 c 2 = 9 x 8 / 2 = 36 so option c is correct\"" + }, + { + "Answer": 15, + "Options": "a ) 14 , b ) 12 , c ) 13 , d ) 15 , e ) 16", + "Correct": "d", + "Explanation": "\"let n be the number of persons in the party . number of hands shake = 105 ; total number of hands shake is given by nc 2 . now , according to the question , nc 2 = 105 ; or , n ! / [ 2 ! * ( n - 2 ) ! ] = 105 ; or , n * ( n - 1 ) / 2 = 105 ; or , n 2 - n = 210 ; or , n 2 - n - 210 = 0 ; or , n = 15 , - 14 ; but , we can not take negative value of n . so , n = 15 i . e . number of persons in the party = 15 . answer d\"" + }, + { + "Answer": 86, + "Options": "a ) 79 , b ) 86 , c ) 95 , d ) 72 , e ) 80", + "Correct": "b", + "Explanation": "\"age of the 15 th student = 20 * 15 - ( 14 * 5 + 16 * 9 ) = 300 - 214 = 86 years answer is b\"" + }, + { + "Answer": 0.75, + "Options": "a ) 1 / 2 , b ) 1 / 4 , c ) 3 / 4 , d ) 2 / 3 , e ) none of these", + "Correct": "c", + "Explanation": "explanation : a \u00e2 \u02c6 \u2014 b \u00e2 \u02c6 \u2014 c / b \u00e2 \u02c6 \u2014 c \u00e2 \u02c6 \u2014 d = 195 / 65 = > a / d = 3 d \u00e2 \u02c6 \u2014 e \u00e2 \u02c6 \u2014 f / c \u00e2 \u02c6 \u2014 d \u00e2 \u02c6 \u2014 e = 250 / 1000 = > f / c = 1 / 4 a / d * f / c = 3 * 1 / 4 = 3 / 4 answer : c" + }, + { + "Answer": 4.319999999999999, + "Options": "a ) 5.29 min , b ) 4.32 min , c ) 5.08 min , d ) 9.28 min , e ) 5.988 min", + "Correct": "b", + "Explanation": "\"clearly , the two will meet when they are 594 m apart . to be ( 4.5 + 3.75 ) = 8.25 km apart , they take 1 hour . to be 594 m apart , they take ( 100 / 825 * 594 / 1000 ) hrs = ( 594 / 8250 * 60 ) min = 4.32 min . answer : b\"" + }, + { + "Answer": 34.99999999999999, + "Options": "a ) 15 % , b ) 20 % , c ) 22.5 % , d ) 35 % , e ) 50 %", + "Correct": "d", + "Explanation": "4 miles on the highway = 4 / 34 gallons ; 4 miles in the city = 4 / 20 gallons ; total = 4 / 34 + 4 / 20 = 27 / 85 gallons . 8 miles on the highway = 4 / 17 gallons . the % change = ( 27 / 85 - 4 / 17 ) / ( 4 / 17 ) = 0.35 . answer : d ." + }, + { + "Answer": 15840, + "Options": "a ) 1250 , b ) 2489 , c ) 6398 , d ) 15840 , e ) 2487", + "Correct": "d", + "Explanation": "\"explanation : a 2 = 69696 = > a = 264 4 a = 1056 1056 * 15 = 15840 answer : d\"" + }, + { + "Answer": 14, + "Options": "a ) 14 , b ) 10 , c ) 8 , d ) 9.5 , e ) none of these", + "Correct": "a", + "Explanation": "\"answer : a ( 5 x 8 - 3 x 4 ) / 2 = 14\"" + }, + { + "Answer": 7, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "e", + "Explanation": "the class borrowed a total of 40 * 2 = 80 books . the 28 students who borrowed 0 , 1 , or 2 books borrowed a total of 12 + 14 * 2 = 40 . to maximize the number of books borrowed by 1 student , let ' s assume that 11 students borrowed 3 books and 1 student borrowed the rest . 80 - 40 - 3 * 11 = 7 the maximum number of books borrowed by any student is 7 . the answer is e ." + }, + { + "Answer": 60, + "Options": "a ) 15 , b ) 70 , c ) 20 , d ) 60 , e ) none", + "Correct": "d", + "Explanation": "\"sol . average = ( 42 + 45 + 48 + 51 + 54 + 57 + 60 + 63 + 66 + 69 + 72 + 75 + 78 / 13 ) = 780 / 5 = 60 . answer d\"" + }, + { + "Answer": 115, + "Options": "a ) 90 , b ) 115 , c ) 120 , d ) 130 , e ) 220", + "Correct": "b", + "Explanation": "\"orchestra seats - a balcony seats - b a + b = 355 and 12 a + 8 b = 3320 solving equations simultaneously ( multiply equation 1 with 8 and subtract from second equation ) 4 a = 3320 - 8 * 355 = 3320 - 2840 = 480 i . e . a = 120 and b = 355 - 120 = 235 more seats in balcony than orchestra = b - a = 235 - 120 = 115 answer : option b\"" + }, + { + "Answer": 8, + "Options": "a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16", + "Correct": "a", + "Explanation": "\"let ' s say age of richard isr age of david isd age of scott iss now richard is 6 years older than david , i . e . r = d + 6 david is 8 years older than scott i . e . d = s + 8 if in 8 years , richard will be twice as old as scott i . e . r + 8 = 2 x ( s + 8 ) i . e . r + 8 = 2 s + 16 i . e . r = 2 s + 8 but r = d + 6 = ( s + 8 ) + 6 = s + 14 therefore , 2 s + 8 = s + 14 i . e . s = 6 i . e . r = 20 i . e . d = 14 now , how old was david 6 years ago ? i . e . d - 6 = 14 - 6 = 8 years answer : option a\"" + }, + { + "Answer": 28, + "Options": "a ) 40 , b ) 44 , c ) 80 , d ) 88 , e ) 28", + "Correct": "e", + "Explanation": "\"according to the given conditions x + y = 16 and x ^ 2 + y ^ 2 = 200 now ( x + y ) ^ 2 = x ^ 2 + y ^ 2 + 2 xy so 16 ^ 2 = 200 + 2 xy so xy = 56 / 2 = 28 answer : e\"" + }, + { + "Answer": 5000, + "Options": "a ) 2788 , b ) 5000 , c ) 7282 , d ) 2782 , e ) 2729", + "Correct": "b", + "Explanation": "\"4 - - - 4000 5 - - - ? = > 5000 answer : b\"" + }, + { + "Answer": 10.344827586206897, + "Options": "a ) 16 , b ) 10.34 , c ) 12.46 , d ) 11.2 , e ) 14", + "Correct": "b", + "Explanation": "1 ) cost of repairing = 14.5 ( for one year ) , therefore for 2 years it would be $ 29 . 2 ) cost of new pair which will last for 2 years is $ 32 . percentage change formula = ( final value - initial value ) / ( initial value ) * 100 . in this case the final value would be the price of new shoeinitial value would be the cost of repairing the old shoe . i . e ( 32 - 29 ) / ( 29 ) * 100 = 10.34 % . ans is b" + }, + { + "Answer": 56, + "Options": "a ) 22 , b ) 56 , c ) 12 , d ) 36 , e ) 10", + "Correct": "b", + "Explanation": "8 * 7 = 56 . answer is b ." + }, + { + "Answer": 81, + "Options": "a ) 79 , b ) 89 , c ) 95 , d ) 81.81 , e ) 97.2", + "Correct": "d", + "Explanation": "\"let the 6 courses that were taken last year be a 1 , a 2 , a 3 , a 4 , a 5 , a 6 a 1 + a 2 + a 3 + a 4 + a 5 + a 6 = 100 * 6 = 600 the year before , the 5 courses be b 1 , b 2 , b 3 , b 4 , b 5 b 1 + b 2 + b 3 + b 4 + b 5 = 60 * 5 = 300 student ' s average = ( 600 + 300 ) / 11 = 81.81 answer d\"" + }, + { + "Answer": 0.9411764705882353, + "Options": "a ) 14 / 13 , b ) 13 / 17 , c ) 16 / 17 , d ) 13 / 18 , e ) none of these", + "Correct": "c", + "Explanation": "explanation : hcf of 4128 and 4386 4128 ) 4386 ( 1 4128 - - - - - 258 ) 4128 ( 16 4128 - - - - 0 hence hcf of 4128 and 4386 is 258 . 4128 / 258 = 16 4386 / 258 = 17 4128 / 4386 = 16 / 17 answer : option c" + }, + { + "Answer": 10, + "Options": "a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18", + "Correct": "a", + "Explanation": "\"4 n + 7 > 1 4 n > - 6 n > - ( 3 / 2 ) n > - 1.5 ( n = - 1 , 0 , 1 , 2 3 . . . . . . . . upto infinity ) from second constraint 4 n + 7 < 40 4 n < 33 n < 8 . 25 n = ( - infinity , . . . . . . . - 3 , - 2 , - 1 , 0 , 1 , 2 , . . . . . . . . . upto 8 ) combining the two - 1.5 < n < 8.25 n = 1 to 8 ( 48 integers ) and n = - 1 and 0 so 10 integers . a\"" + }, + { + "Answer": 147, + "Options": "a ) 145 , b ) 146 , c ) 147 , d ) 148 , e ) 149", + "Correct": "c", + "Explanation": "1 to 11 = 11 * 42 = 462 1 to 5 = 5 * 49 = 245 5 to 11 = 7 * 52 = 364 5 th = 245 + 364 \u2013 462 = 147 answer : c" + }, + { + "Answer": 0.4285714285714286, + "Options": "a ) 1 / 7 , b ) 2 / 7 , c ) 3 / 7 , d ) 4 / 7 , e ) 5 / 7", + "Correct": "c", + "Explanation": "water content can b in 1 st and second is 2 / 5 and 1 / 5 total : 3 / 5 . the total milk content is 7 / 5 . the ratio is ( ( 3 / 5 ) / ( 7 / 5 ) ) = 3 / 7 . answer : c" + }, + { + "Answer": 7, + "Options": "a ) 7 , b ) 6 , c ) 8 , d ) 9 , e ) 10", + "Correct": "a", + "Explanation": "\"we have : 1 ) x < y < z 2 ) y - x > 3 3 ) x = 2 k ( x is an even number ) 4 ) y = 2 n + 1 ( y is an odd number ) 5 ) z = 2 p + 1 ( z is an odd number ) 6 ) z - x = ? least value z - x = 2 p + 1 - 2 k = 2 p - 2 k + 1 = 2 ( p - k ) + 1 - that means that z - x must be an odd number . we are asked to find the least value , so we have to pick the least numbers since y is odd and x is even , y - x must be odd . since y - x > 3 , the least value for y - x must be 5 , the least value for x must be 2 , and , thus , the least possible value for y must be 7 ( y - 2 = 5 , y = 7 ) 2 < 7 < z , since z is odd , the least possible value for z is 9 z - x = 9 - 2 = 7 answer a\"" + }, + { + "Answer": 1950, + "Options": "a ) rs 1950 , b ) rs 2000 , c ) rs 745 , d ) rs 765 , e ) none", + "Correct": "a", + "Explanation": "required amount = 42900 / 22 = rs 1950 answer a" + }, + { + "Answer": 1, + "Options": "a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1", + "Correct": "e", + "Explanation": "\"on dividing 9671 by 5 , we get remainder = 1 . required number be subtracted = 1 answer : e\"" + }, + { + "Answer": 8, + "Options": "a ) 3 years , b ) 4 years , c ) 6 years , d ) 7 years , e ) 8 years", + "Correct": "e", + "Explanation": "\"let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 70 5 x = 40 x = 8 . age of the youngest child = x = 8 years . e )\"" + }, + { + "Answer": 30, + "Options": "a ) 22 , b ) 24 , c ) 26 , d ) 28 , e ) 30", + "Correct": "e", + "Explanation": "\"4 n + 7 > 1 4 n > - 6 n > - ( 3 / 2 ) n > - 1.5 ( n = - 1 , 0 , 1 , 2 3 . . . . . . . . upto infinity ) from second constraint 4 n + 7 < 120 4 n < 113 n < 28 . 25 n = ( - infinity , . . . . . . . - 3 , - 2 , - 1 , 0 , 1 , 2 , . . . . . . . . . upto 48 ) combining the two - 1.5 < n < 48.25 n = 1 to 28 ( 48 integers ) and n = - 1 and 0 so 30 integers . e is the answer\"" + }, + { + "Answer": 45, + "Options": "a ) 47 , b ) 45 , c ) 25 , d ) 37 , e ) 44", + "Correct": "b", + "Explanation": "the total of thirteen numbers = 13 x 9 = 117 the total of first 6 and last 6 numbers is = 6 x 5 + 6 x 7 = 72 so , the middle number is ( 117 - 72 ) = 45 b" + }, + { + "Answer": 145, + "Options": "a ) 90 , b ) 130 , c ) 150 , d ) 320 , e ) 145", + "Correct": "e", + "Explanation": "\"i ' ve been reading the website for a while and i ' m always keen to see different approaches so i would like to share one that works for me : short version : truck a travels for an hour . distance remaining = 1025 - 90 = 935 k ratio of speeds 9 : 8 - > 935 / 17 = 55 truck a = 90 + 55 * 9 = 585 truck b = 55 * 8 = 440 delta = 145 km answer e\"" + }, + { + "Answer": 275, + "Options": "a ) $ 245 , b ) $ 255 , c ) $ 265 , d ) $ 275 , e ) $ 285", + "Correct": "d", + "Explanation": "\"1.2 n + n = 605 2.2 n = 605 n = 275 the answer is d .\"" + }, + { + "Answer": 31, + "Options": "a ) 31 , b ) 33 , c ) 35 , d ) 37 , e ) 39", + "Correct": "a", + "Explanation": "total weight of the 4 dogs = ( 25 + 31 + 35 + 33 ) = 124 avg = 124 / 4 = 31 total weight of 5 dogs = 124 + y or 4 ( 31 ) + y average of 5 dogs as per question = 31 equation : 4 ( 31 ) + y = 5 ( 31 ) , or y = 31 . choose a" + }, + { + "Answer": 48, + "Options": "a ) 2 , b ) 48 , c ) 0 , d ) 10 , e ) 3", + "Correct": "b", + "Explanation": "3 x + y = 40 2 x - y = 20 5 x = 60 x = 12 y = 4 3 y ^ 2 = 3 * 16 = 48 answer is b" + }, + { + "Answer": 20, + "Options": "a ) 10 , b ) 20 , c ) 37 , d ) 26 , e ) 22", + "Correct": "b", + "Explanation": "let the initial number of persons be x . then , 16 x + 20 * 15 = 15.5 ( x + 20 ) < = > 0.5 x = 10 < = > x = 20 . answer : b" + }, + { + "Answer": 540, + "Options": "a ) 80 , b ) 120 , c ) 160 , d ) 540 , e ) 660", + "Correct": "d", + "Explanation": "\"working inside out , ( 4 \u20ac 5 ) = 3 * 4 * 5 = 60 3 \u20ac 60 = 3 * 3 * 60 = 540 hence , answer is d\"" + }, + { + "Answer": 3, + "Options": "a ) 6 , b ) 5 , c ) 2 , d ) 3 , e ) 4", + "Correct": "d", + "Explanation": "take the example of 16 . . . it has 3 positive divisors ( 1 , 2,4 , 8,16 ) now , take the example of 4 . . . it has only 3 divisors . . so d is the ans" + }, + { + "Answer": 239, + "Options": "a ) 249 , b ) 498 , c ) 239 , d ) 823 , e ) 1,002", + "Correct": "c", + "Explanation": "\"slope of 2 and a y - intercept of 2 y - coordinate is 480 y = 2 x + 2 478 = 2 x x = 239 answer : c . 239\"" + }, + { + "Answer": 168, + "Options": "a ) 108 , b ) 119 , c ) 128 , d ) 135 , e ) 168", + "Correct": "e", + "Explanation": "let the 2 positive numbers x and y x + y = 26 - - 1 x ^ 2 - y ^ 2 = 52 = > ( x + y ) ( x - y ) = 52 - - 2 using equation 1 in 2 , we get = > x - y = 2 - - 3 solving equation 1 and 3 , we get x = 14 y = 12 product = 14 * 12 = 168 answer e" + }, + { + "Answer": 337500, + "Options": "a ) $ 300000 , b ) $ 320000 , c ) $ 335000 , d ) $ 336500 , e ) $ 337500", + "Correct": "e", + "Explanation": "a = 7000 b = 8000 c = 9000 a share 7 parts , b share 8 parts & c share 9 parts total 24 parts - - - - - > 900000 - - - - > 1 part - - - - - - - > 37500 c share = 9 parts - - - - - > 337500 e" + }, + { + "Answer": 23, + "Options": "a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24", + "Correct": "d", + "Explanation": "\"let the average age of the whole team be x years . 11 x - ( 27 + 28 ) = 9 ( x - 1 ) 11 x - 9 x = 46 2 x = 46 x = 23 . the average age of the team is 23 years . the answer is d .\"" + }, + { + "Answer": 131, + "Options": "a ) 90 , b ) 131 , c ) 150 , d ) 320 , e ) 450", + "Correct": "b", + "Explanation": "i ' ve been reading the website for a while and i ' m always keen to see different approaches so i would like to share one that works for me : short version : truck a travels for an hour . distance remaining = 787 - 90 = 697 k ratio of speeds 9 : 8 - > 697 / 17 = 41 truck a = 90 + 41 * 9 = 459 truck b = 41 * 8 = 328 delta = 131 km answer b" + }, + { + "Answer": 0.12, + "Options": "a ) 3 / 25 , b ) 3 / 125 , c ) c ) 2 / 25 , d ) 3 / 25 , e ) 1 / 5", + "Correct": "a", + "Explanation": "\"p ( playing 2 or more instruments ) = 64 / 800 = 2 / 25 . then , the probability of playing exactly one instrument is given by : p ( playing 1 or more instruments ) - p ( playing 2 or more instruments ) = 1 / 5 - 2 / 25 = 3 / 25 . answer a .\"" + }, + { + "Answer": 2, + "Options": "a ) 1 / 2 , b ) 1 , c ) 2 , d ) 5 / 2 , e ) 4", + "Correct": "c", + "Explanation": "\"since ( m , n ) and ( m + 2 , n + k ) are two points on the line with the equation x = 2 y + 5 they should satisfy m = 2 n + 5 and m + 4 = 2 * ( n + k ) + 5 . by 1 st equation we have m - 2 n = 5 and by 2 nd equation m - 2 n = 2 k + 1 - - - > 5 = 2 k + 1 - - - > k = 2 . the answer is , therefore , ( c ) .\"" + }, + { + "Answer": 16500, + "Options": "a ) 21000 , b ) 19800 , c ) 16500 , d ) 15800 , e ) 8700", + "Correct": "c", + "Explanation": "given : the question tells us about the number of tickets sold in the first week at reduced price = 5400 . it also tells us that during the remaining weeks , the number of tickets sold at full price was 5 times the no . of tickets sold at reduced price . the total tickets sold was 25200 , and we are asked to find the number of tickets that where sold at full price . approach : the question asks us to find the number of ticket sold at full price . we know that the number of tickets sold at full price was 5 times the no . of tickets sold at reduced price in remaining weeks . hence , assuming tickets sold at reduced price in remaining weeks to be x would give us the no . of tickets sold at full price to be 5 x . tickets sold in first week + tickets sold in remaining weeks = total no . of tickets soldi . e . tickets sold in first week + tickets sold at full price in remaining weeks + tickets sold at reduced price in remaining weeks = total no . of tickets sold we know the no . of tickets sold during first week and the total no . of tickets sold . we will use this relation to get to our answer . working out : tickets sold in first week + tickets sold at full price in remaining weeks + tickets sold at reduced price in remaining weeks = total no . of tickets sold substituting values in the equation , we get 5400 + 5 x + x = 25200 x = 3300 tickets sold at full price = 5 x = 16500 answer : option c" + }, + { + "Answer": 2, + "Options": "a ) 2 , b ) b ) 1 , c ) c ) 5 , d ) d ) 21 , e ) e ) 28", + "Correct": "a", + "Explanation": "algebraic approach : let n be the smaller integer = > 1 / n + 1 / ( n + 4 ) = 1 or ( ( n + 4 ) + n ) / n ( n + 4 ) = 1 or n ^ 2 + 4 n = 2 n + 4 or n = 2 as n can not be - negative solve for n = > n = 2 . hence , a" + }, + { + "Answer": 33.333333333333336, + "Options": "a ) 17 % , b ) 25.6 % , c ) none % , d ) 33.3 % , e ) 50 %", + "Correct": "d", + "Explanation": "solution : let the current food expense be represented by rs . 100 . the cost of food rises 50 % . so , to buy same amount of food , they need to increase their expense , = ( 100 + 50 % of 100 ) = rs . 150 . but , they want to keep food expense the same , so they have to cut rs . by 50 to keep it to rs . = 100 . the % decrease in consumption is , ( 50 / 150 ) * 100 = 33.3 % . mental calculation method ; 100 - - - - - 50 % \u2191 - - - \u2192 150 - - - - - - x % \u2193 - - - \u2192 100 . here , x = ( 50 / 125 ) * 100 = 33.3 % . answer : option d" + }, + { + "Answer": 20, + "Options": "a ) 18 , b ) 82 , c ) 20 , d ) 27 , e ) 29", + "Correct": "c", + "Explanation": "\"let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 x / 2 = ( 73 - 63 ) = > x / 2 = 10 = > x = 20 . answer : c\"" + }, + { + "Answer": 59.99999999999999, + "Options": "a ) 50 , b ) 60 , c ) 490 , d ) 500 , e ) 980", + "Correct": "b", + "Explanation": "\"average price for a pair of rackets = $ 9.8 total cost = $ 9.8 * x = $ 588 x = 60 pairs were sold . answer : b\"" + }, + { + "Answer": 3, + "Options": "a ) 17 , b ) 15 , c ) 12 , d ) 8 , e ) 3", + "Correct": "e", + "Explanation": "\"f the number is x , then , x + 17 = 60 / x x 2 + 17 x - 60 = 0 ( x + 20 ) ( x - 3 ) = 0 x = 3 , - 20 , so x = 3 ( as 3 is positive ) answer : e\"" + }, + { + "Answer": 27, + "Options": "a ) 23 , b ) 27 , c ) 31 , d ) 35 , e ) 39", + "Correct": "b", + "Explanation": "\"m + h = 80 h = 80 - m 4 m + 5 h = 373 4 m + 5 * ( 80 - m ) = 373 m = 27 the answer is b .\"" + }, + { + "Answer": 5, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "d", + "Explanation": "\"minimuum should be 1 maximum should be 4 : 1 out of a or b to make the multiplication negative 3 out of c , d , e or f to make the multiplication negative . negative + negative < 0 answer : c maximum will be 5 . . you dont require both the multiplicatin to be negative for entire equation to be negative . . . any one a or b can be negative to make ab negative and it can still be more ( away from 0 ) than the multiplication of 4 other - ve numbers . . . actually by writing minimum required as 1 out of 6 , you are actually meaning s = 5 out of 6 also possible as you will see 5 or 1 will give you same equation . . ans d\"" + }, + { + "Answer": 100, + "Options": "a ) 100 , b ) 90 , c ) 80 , d ) 70 , e ) 60", + "Correct": "a", + "Explanation": "\"( 9 * 80 + x ) / 10 = 82 x = ( 10 * 82 ) - ( 9 * 80 ) x = 820 - 720 total score required 820 - 720 = 100 correct answer is a\"" + }, + { + "Answer": 47, + "Options": "a ) 48 , b ) 47 , c ) 46 , d ) 45 , e ) 44", + "Correct": "b", + "Explanation": "\"7 * 3 = 21 7 * 49 = 343 total multiples = ( 49 - 3 ) + 1 = 47 include 21 and 343 = 47 answer is b\"" + }, + { + "Answer": 58, + "Options": "a ) 50 , b ) 56 , c ) 58 , d ) 62 , e ) 66", + "Correct": "c", + "Explanation": "given that , total average e sold is 66 , male / female = 1 / 2 and female average is 70 . average of male members isx . ( 70 * f + x * m ) / ( m + f ) = 66 - > solving this equation after substituting 2 m = f , x = 58 . ans c ." + }, + { + "Answer": 19898, + "Options": "a ) 20198 , b ) 20098 , c ) 20000 , d ) 20088 , e ) 20085", + "Correct": "b", + "Explanation": "\"explanation : ( a + b ) 2 + ( a \u00e2 \u02c6 \u2019 b ) 2 = 2 ( a 2 + b 2 ) ( reference : basic algebraic formulas ) 1072 + 932 = ( 100 + 7 ) 2 + ( 100 \u00e2 \u02c6 \u2019 7 ) 2 = 2 ( 1002 + 72 ) = 2 ( 10000 + 49 ) = 20098 . answer : option b\"" + }, + { + "Answer": 4, + "Options": "a ) 14 % , b ) 4 % , c ) 15 % , d ) 5 % , e ) 25 %", + "Correct": "b", + "Explanation": "\"let ' s say there is a total of 100 students at this college . 50 percent of the total number of students are freshmen . # of freshmen = 50 % of 100 = 50 40 percent of the fresh - men are enrolled in the school of liberal arts . . . number of liberal arts freshmen = 40 % of 50 = 20 . . . and , of these , 20 percent are psychology majors . . . number of liberal arts freshmen who are psychology majors = 20 % of 20 = 4 what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts ? 4 / 100 = 4 % answer : b\"" + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) 18 , c ) 32 , d ) 40 , e ) 44", + "Correct": "a", + "Explanation": "lets take numbers here . assume that the total number of movie theaters in the town = 100 then number of movie theaters with 3 screens or less = 60 = > number of movie theaters with 4 screens or more = 40 movie theaters with 3 screens or less selling popcorn at more than $ 300 = 20 % of 60 = 12 number of movie theaters selling popcorn at $ 300 or less = 56 = > number of movie theaters selling popcorn at more than $ 300 = 100 - 56 = 44 of these 44 theaters , 12 are those with 3 screens or less therefore 12 ( 44 - 12 ) must be those with four screens or more a is the answer" + }, + { + "Answer": 585, + "Options": "a ) 585 km , b ) 767 km , c ) 276 km , d ) 178 km , e ) 176 km", + "Correct": "a", + "Explanation": "\"explanation : let us assume that trains meet after ' x ' hours distance = speed * time distance traveled by two trains = 20 x km and 25 x km resp . as one train travels 65 km more than the other , 25 x \u00e2 \u20ac \u201c 20 x = 65 5 x = 65 x = 13 hours as the two trains are moving towards each other , relative speed = 20 + 25 = 45 km / hr therefore , total distance = 45 * 13 = 585 km . answer : a\"" + }, + { + "Answer": 21, + "Options": "a ) 21 , b ) 42 , c ) 43 , d ) 44 , e ) 45", + "Correct": "a", + "Explanation": "\"n ( n - 1 ) / 2 = 7 * 6 / 2 = 21 answer : a\"" + }, + { + "Answer": 50.000000000000014, + "Options": "a ) 15 % , b ) 20 % , c ) 22.5 % , d ) 25 % , e ) 50 %", + "Correct": "e", + "Explanation": "\"4 miles on the highway = 4 / 40 gallons ; 4 miles in the city = 4 / 20 gallons ; total = 4 / 40 + 4 / 20 = 3 / 10 gallons . 8 miles on the highway = 8 / 40 gallons . the % change = ( 3 / 10 - 8 / 40 ) / ( 8 / 40 ) = 1 / 2 = 0.50 . answer : e .\"" + }, + { + "Answer": 5184, + "Options": "a ) 76 , b ) 5776 , c ) 304 , d ) 5184 , e ) none", + "Correct": "d", + "Explanation": "\"answer let \u221a n / 18 = 4 then \u221a n = 18 x 4 = 72 \u2234 n = 72 x 72 = 5184 . correct option : d\"" + }, + { + "Answer": 15.7625, + "Options": "a ) 9 % , b ) 9.27 % , c ) 27 % , d ) 15.76 % , e ) none of these", + "Correct": "d", + "Explanation": "actual increase in population = 5 % let , earlier population = 100 then the population after 3 years = 100 ( 1 + 5 / 100 ) ^ 3 = 115.7625 \u2234 required percentage = 15.7625 % answer : d" + }, + { + "Answer": 2250, + "Options": "a ) $ 1600 , b ) $ 1850 , c ) $ 2250 , d ) $ 2400 , e ) $ 2750", + "Correct": "c", + "Explanation": "let the value of the item be $ x , then 0.07 ( x \u2212 1000 ) = 87.5 - - > x \u2212 1000 = 1250 x \u2212 1000 = 1250 - - > x = 2250 . answer : c ." + }, + { + "Answer": 1152, + "Options": "a ) 1200 , b ) 1152 , c ) 1189 , d ) 1190 , e ) 100", + "Correct": "b", + "Explanation": "\"let x be the number i chose , then x / 6 \u2212 189 = 3 x / 6 = 192 x = 1152 answer is b .\"" + }, + { + "Answer": 15, + "Options": "a ) 12 , b ) 15 , c ) 16 , d ) 18 , e ) 20", + "Correct": "b", + "Explanation": "\"let the number of ducks be d and number of cows be c then , total number of legs = 2 d + 4 c = 2 ( d + 2 c ) total number of heads = c + d given that total number of legs are 28 more than twice the number of heads = > 2 ( d + 2 c ) = 30 + 2 ( c + d ) = > d + 2 c = 15 + c + d = > 2 c = 15 + c = > c = 15 i . e . , total number of cows = 15 answer is b .\"" + }, + { + "Answer": 50, + "Options": "a ) 40 meter , b ) 45 meter , c ) 50 meter , d ) 55 meter , e ) none of these", + "Correct": "c", + "Explanation": "\"explanation : let the length of each train is x meter distance will be x + x = 2 x relative speed = 46 - 36 = 10 km / hr = 10 * ( 5 / 18 ) = 25 / 9 m / sec distance = speed * time 2 x = 25 / 9 \u2217 36 2 x = 100 = > x = 50 so length of both the trains are 50 meters option c\"" + }, + { + "Answer": 33.33333333333333, + "Options": "a ) 66.66 % , b ) 66.68 % , c ) 66.766 % , d ) 33.33 % , e ) 66.65 %", + "Correct": "d", + "Explanation": "\"excess of b ' s height over a ' s = [ ( 25 / ( 100 - 25 ) ] x 100 % = 33.33 % answer : d )\"" + }, + { + "Answer": 14.879999999999995, + "Options": "a ) 20 % , b ) 18 % , c ) 15 % , d ) 12 % , e ) 14 %", + "Correct": "c", + "Explanation": "\"100 * 100 = 10000 76 * 112 = 8512 10000 - - - - - - - 1488 100 - - - - - - - ? = 15 % answer : c\"" + }, + { + "Answer": 0.6333333333333333, + "Options": "a ) 3 / 5 , b ) 7 / 15 , c ) 11 / 15 , d ) 19 / 30 , e ) 23 / 30", + "Correct": "d", + "Explanation": "\"p ( red or blue ) = 1 - p ( white ) - p ( green ) = 30 / 30 - 5 / 30 - 6 / 30 = 19 / 30 the answer is d .\"" + }, + { + "Answer": 77, + "Options": "a ) 67 , b ) 69 , c ) 77 , d ) 79 , e ) 81", + "Correct": "c", + "Explanation": "\"required average = 7 ( 1 + 2 + . . . . + 21 ) / 21 ( 7 / 21 ) x ( ( 21 x 22 ) / 2 ) ( because sum of first 21 natural numbers ) = 77 c\"" + }, + { + "Answer": 50, + "Options": "a ) 50 km , b ) 56 km , c ) 60 km , d ) 70 km , e ) 80 km", + "Correct": "a", + "Explanation": "\"let the actual distance travelled be x km . x / 10 = ( x + 20 ) / 14 14 x = 10 x + 200 4 x = 200 x = 50 km . answer : a\"" + }, + { + "Answer": 31, + "Options": "a ) 31 , b ) 25 , c ) 35 , d ) 45 , e ) 75", + "Correct": "a", + "Explanation": "\"out of 300 - 180 purchased for less than 100 $ 120 for more out of 300 - 120 responded as satisfied and 180 responded disatisfied out of 180 ( purchased less than 100 $ ) - 15 % = 27 responded as satisfied , so remaining satisfied are 120 - 27 = 93 so 93 is what percentage of 300 - 31 % so the answer should be a\"" + }, + { + "Answer": 58.7, + "Options": "a ) 58 kgs , b ) 58.85 kgs , c ) 58.7 kgs , d ) 59 kgs , e ) 59.85 kgs", + "Correct": "c", + "Explanation": "\"actual total weight is ( 20 x 58.4 - 56 + 62 ) = 1174 kgs actual average weight is 1174 / 20 = 58.7 kgs c\"" + }, + { + "Answer": 80, + "Options": "a ) 56 kg , b ) 80 kg , c ) 85 kg , d ) data inadequate , e ) none of these", + "Correct": "b", + "Explanation": "\"b 80 kg total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 60 + 20 ) kg = 80 kg .\"" + }, + { + "Answer": 1, + "Options": "a ) 1 , 20 , b ) 1 , 21 , c ) 1 , 22 , d ) 1 , 23 , e ) 1 , 24", + "Correct": "a", + "Explanation": "the number is 35 , when divided by 5 , 32 leaves remainder 0 , 21 respectively . so if 35 is divided by 2 , 35 leaves remainder 1 , 20 respectively . answer : a" + }, + { + "Answer": 80, + "Options": "a ) 60 , b ) 80 , c ) 40 , d ) 120 , e ) 160", + "Correct": "b", + "Explanation": "( 1 + 1 / 8 ) x - ( 1 - 1 / 4 ) x = 30 ( 9 / 8 ) x - ( 3 / 4 ) x = 30 x = 80 = q answer : b" + }, + { + "Answer": 28, + "Options": "a ) 23 years , b ) 28 years , c ) 21 years , d ) 20 years , e ) 19 years", + "Correct": "b", + "Explanation": "\"let present age of the son = x years then , present age the man = ( x + 30 ) years given that , in 2 years , man ' s age will be twice the age of his son \u00e2 \u2021 \u2019 ( x + 30 ) + 2 = 2 ( x + 2 ) \u00e2 \u2021 \u2019 x = 28 answer : b\"" + }, + { + "Answer": 3, + "Options": "a ) 100 , b ) 65 , c ) 25 , d ) 11 , e ) 3", + "Correct": "e", + "Explanation": "machine y produces 20 percent more widgets in an hour than machine x does in an hour . so if machine x produces 100 widgets , then machine y produces 120 widgets . ratio of 120 / 100 = 6 / 5 . this is their speed of work ( y : x ) . i . e . speed of their work ( x : y ) = 5 / 6 now , time is inversely proportional to speed . hence the ratio of the time spent ( x : y ) = 6 / 5 let us assume that they spend 6 x and 5 x hours . given that 6 x - 5 x = 60 so , x = 60 . hence 6 x = 6 * 60 = 360 hours . hence x takes 120 hours to produce 1080 widgets . so , in 1 hour , it can produce ( 1 * 1080 ) / 360 = 3 hence option ( e ) ." + }, + { + "Answer": 35, + "Options": "a ) 22 , b ) 35 , c ) 25 , d ) 99 , e ) 21", + "Correct": "b", + "Explanation": "\"let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 80 x - ( 5 * 20 ) = 90 ( x - 5 ) 350 = 10 x = > x = 35 . answer : b\"" + }, + { + "Answer": 150, + "Options": "a ) 150 , b ) 450 , c ) 500 , d ) 650 , e ) 700", + "Correct": "a", + "Explanation": "\"required number = ( 75 / 2 ) / ( 1 / 4 ) = ( 75 / 2 x 4 / 1 ) = 150 . answer : a\"" + }, + { + "Answer": 4, + "Options": "a ) 10 years , b ) 4 years , c ) 6 years , d ) 15 years , e ) 16 years", + "Correct": "b", + "Explanation": "\"let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 12 5 x = 10 x = 2 . hence , b ' s age = 2 x = 4 years . b )\"" + }, + { + "Answer": 792, + "Options": "a ) 792 , b ) 684 , c ) 492 , d ) 372 , e ) 340", + "Correct": "a", + "Explanation": "\"9 pages from 1 to 9 will require 9 digits . 90 pages from 10 to 99 will require 90 * 2 = 180 digits . 300 - ( 90 + 9 ) = 201 pages will require 201 * 3 = 603 digits . the total number of digits is 9 + 180 + 603 = 792 . the answer is a .\"" + }, + { + "Answer": 306, + "Options": "a ) a ) 426 , b ) b ) 306 , c ) c ) 207 , d ) d ) 204 , e ) e ) 297", + "Correct": "b", + "Explanation": "given ratio = 1 / 2 : 2 / 3 : 3 / 4 = 6 : 8 : 9 1 st part = 782 * 9 / 23 = rs . 306 . answer : b" + }, + { + "Answer": 167, + "Options": "a ) 158 , b ) 161 , c ) 164 , d ) 167 , e ) 170", + "Correct": "d", + "Explanation": "k - 32 = 9 t / 5 k = 9 t / 5 + 32 k = 9 ( 75 ) / 5 + 32 = 167 the answer is d ." + }, + { + "Answer": 989.9999999999997, + "Options": "a ) 99 , b ) 9.9 , c ) 990 , d ) 0.99 , e ) 0.099", + "Correct": "c", + "Explanation": "\"( 0.0077 ) ( 4.5 ) / ( 0.05 ) ( 0.1 ) ( 0.007 ) = 0.0077 * 450 / 5 * ( 0.1 ) ( 0.007 ) = 0.077 * 90 / 1 * 0.007 = 77 * 90 / 7 = 11 * 90 = 990 answer : c\"" + }, + { + "Answer": 60, + "Options": "a ) 54 , b ) 59 , c ) 60 , d ) 71 , e ) 92", + "Correct": "c", + "Explanation": "\"total = 70 thrower = 40 rest = 70 - 40 = 30 left handed = 30 / 3 = 10 right handed = 20 if all throwe 0 r are right handed then total right handed is 40 + 20 = 60 so c . 60 is the right answer\"" + }, + { + "Answer": 990, + "Options": "a ) rs . 692.80 , b ) rs . 820 , c ) rs . 990 , d ) rs . 1385 , e ) none", + "Correct": "c", + "Explanation": "\"answer income of the deceased = total income of 4 members - total income of remaining 3 members . = 735 x 4 - 650 x 3 rs . = 990 rs . correct option : c\"" + }, + { + "Answer": 210, + "Options": "a ) 210 kms , b ) 30 kms , c ) 20 kms , d ) 40 kms , e ) none of these", + "Correct": "a", + "Explanation": "if x is the distance , then difference in speeds = x / 5 - x / 7 = 12 2 x / 35 = 12 x = 12 * 35 / 2 = 210 kms . answer : a" + }, + { + "Answer": 416, + "Options": "a ) 351 , b ) 364 , c ) 416 , d ) 424 , e ) 450", + "Correct": "c", + "Explanation": "\"we ' re dealing with a sequence of consecutive odd integers : 11 to 41 , inclusive . we ' re asked for the sum of this group . 1 ) start with the sum of the smallest and the biggest : 11 + 41 = 52 2 ) now look at the ' next smallest ' and the ' next biggest ' : 13 + 39 = 52 now we have proof that there is no middle term . we have 8 bunches of 52 . 8 ( 52 ) = 416 c\"" + }, + { + "Answer": 2, + "Options": "a ) 2 , b ) 6 , c ) 5 , d ) 4 , e ) 3", + "Correct": "a", + "Explanation": "if x = 2 6.1 \u00d7 10 ^ 2 = 610 < 620 so , x = 2 answer : a" + }, + { + "Answer": 4, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "d", + "Explanation": "this is equivalent to : - 2 x * 4 y * 5 z = 16000 y = z ( given ) 2 x * 4 y * 5 y = 16000 2 x * y ^ 2 = 16000 / 20 2 x * y ^ 2 = 800 now from options given we will figure out which number will divide 800 and gives us a perfect square : - which gives us x = 4 as 2 * 4 * y ^ 2 = 800 y ^ 2 = 100 y = 10 number of red balls = 4 hence d" + }, + { + "Answer": 1.5, + "Options": "a ) 1.9 , b ) 1.7 , c ) 1.2 , d ) 1.5 , e ) 1.1", + "Correct": "d", + "Explanation": "\"speed of boat in still water ( b ) = 4.5 km / hr . speed of boat with stream ( down stream ) , d = b + u speed of boat against stream ( up stream ) , u = b \u2013 u it is given upstream time is twice to that of down stream . \u21d2 downstream speed is twice to that of upstream . so b + u = 2 ( b \u2013 u ) \u21d2 u = b / 3 = 1.5 km / hr . answer : d\"" + }, + { + "Answer": 11, + "Options": "a ) 8 , b ) 11 , c ) 13 , d ) 15 , e ) 16", + "Correct": "b", + "Explanation": "for divisibility by 11 , the difference of sums of digits at even and odd places must be either zero or divisible by 11 . for 8261955 , difference = ( 8 + 6 + 9 + 5 ) - ( 2 + 1 + 5 ) = 28 - 8 = 20 . the units digit is at odd place . so we add 2 to the number = > 8261955 + 2 = 8261957 now , ( 8 + 6 + 9 + 7 ) - ( 2 + 1 + 5 ) = 30 - 8 = 22 = > 22 is a multiple of 11 and hence 8261957 is also divisible by 11 b" + }, + { + "Answer": 0.3, + "Options": "a ) 1 / 17 , b ) 3 / 17 , c ) 1 / 10 , d ) 6 / 20 , e ) 3 / 10", + "Correct": "d", + "Explanation": "\"we have the ratio of a \u2019 s speed and b \u2019 s speed . this means , we know how much distance a covers compared with b in the same time . this is what the beginning of the race will look like : ( start ) a _________ b ______________________________ if a covers 20 meters , b covers 14 meters in that time . so if the race is 20 meters long , when a reaches the finish line , b would be 6 meters behind him . if we want the race to end in a dead heat , we want b to be at the finish line too at the same time . this means b should get a head start of 6 meters so that he doesn \u2019 t need to cover that . in that case , the time required by a ( to cover 20 meters ) would be the same as the time required by b ( to cover 14 meters ) to reach the finish line . so b should get a head start of 6 / 20 th of the race . answer ( d )\"" + }, + { + "Answer": 270, + "Options": "a ) $ 240 , b ) $ 250 , c ) $ 260 , d ) $ 270 , e ) $ 280", + "Correct": "d", + "Explanation": "1.2 n + n = 594 2.2 n = 594 n = 270 the answer is d ." + }, + { + "Answer": 4, + "Options": "a ) 10 , b ) 388 , c ) 4 , d ) 29 , e ) 22", + "Correct": "c", + "Explanation": "\"explanation : let the original price be rs . 100 . decreased by 20 % = 80 then increased 20 % on rs 80 = 80 + 16 = 96 net change in price = 100 - 96 = 4 answer : c\"" + }, + { + "Answer": 20, + "Options": "a ) 20 , b ) 25 , c ) 10 , d ) 30 , e ) 15", + "Correct": "a", + "Explanation": "chris present age = x after 10 years = x + 10 3 years back = x - 3 x + 10 = 3 ( x - 3 ) x = 20 answer is a" + }, + { + "Answer": 22, + "Options": "a ) 27 , b ) 25 , c ) 24 , d ) 21 , e ) 22", + "Correct": "e", + "Explanation": "\"2 multiples are . . . 10,12 , 14,16 , 18,20 , 22,24 , 26,28 , 30,32 , 34,36 , 38,40 , 42,44 , 46,48 , 50,52 , . . . , the answer is = 22 answer is e\"" + }, + { + "Answer": 131, + "Options": "a ) 154 , b ) 220 , c ) 129 , d ) 131 , e ) 224", + "Correct": "d", + "Explanation": "131 . these are the first 10 prime numbers ( 2 , 3 , 5 . . . ) prefixed with a 1 answer : d" + }, + { + "Answer": 0.25, + "Options": "a ) 1 / 6 , b ) 1 / 7 , c ) 1 / 8 , d ) 1 / 4 , e ) 1 / 3", + "Correct": "d", + "Explanation": "\"first notice the number of months for which he worked - march to sept i . e . 7 months avg of monthly totals in tips for months other than august = x tips in august = 2 x total tips for all months = 6 * x + 2 x = 8 x tips for august / total tips for all months = 2 x / 8 x = 1 / 4 answer : d\"" + }, + { + "Answer": 1.3, + "Options": "a ) 1.3 kg , b ) 1.5 kg , c ) 1.7 kg , d ) 1.9 kg , e ) none of these", + "Correct": "a", + "Explanation": "explanation : flower - nectar contains 50 % of non - water part . in honey this non - water part constitutes 65 % ( 100 - 35 ) . therefore 0.5 x amount of flower - nectar = 0.65 x amount of honey = 0.65 x 1 kg therefore amount of flower - nectar needed = ( 0.65 / 0.51 ) kg = 1.3 kgs answer : a" + }, + { + "Answer": 4.5, + "Options": "a ) $ 0.00 , b ) $ 4.50 , c ) $ 3.40 , d ) $ 5.00 , e ) $ 6.80", + "Correct": "b", + "Explanation": "\"0.85 * { original price } = $ 61.2 - - > { original price } = $ 72 . { final price } = $ 61.2 * 1.25 = $ 76.5 . the difference = $ 76.5 - $ 72 = $ 4.5 answer : b .\"" + }, + { + "Answer": 1020, + "Options": "a ) 1008 , b ) 1015 , c ) 1020 , d ) 1032 , e ) 1048", + "Correct": "c", + "Explanation": "\"required number = ( l . c . m . of 12 , 24 , 36 , 48,56 ) + 12 = 1008 + 12 = 1020 answer : option c\"" + }, + { + "Answer": 20, + "Options": "a ) 20 , b ) 99 , c ) 28 , d ) 27 , e ) 12", + "Correct": "a", + "Explanation": "numbers of students in section a = x numbers of students in section b and c = ( 100 \u2013 x ) x 70 + ( 100 \u2013 x ) 87.5 = 84 100 70 x + 87.5 100 \u2013 87.5 x = 8400 8750 \u2013 17.5 x = 8400 17.5 x = 8750 \u2013 8400 = > x = 20 . answer : a" + }, + { + "Answer": 56, + "Options": "a ) 66 , b ) 52 , c ) 58 , d ) 55 , e ) 56", + "Correct": "e", + "Explanation": "\"though 2 * ( 8 c 2 ) is the correct approcah to do this , but for people like me who find perm , comb n prob a nightmare , an easy approach can be used . the first guy has to play 2 matches with the rest of 7 , so he ' ll play 14 matches . similarly , second guy has to play with the rest of 6 as his 2 games with the first guy are already played . so he plays 12 matches . this continues like this and the total matches are 14 + 12 + 10 . . . + 2 14 + 12 + . . . + 2 = 2 ( 7 + 6 + . . . + 1 ) = 2 ( ( 7 * 8 ) / 2 ) = 7 * 8 = 56 . answer : e\"" + }, + { + "Answer": 225, + "Options": "a ) 200 , b ) 225 , c ) 50 , d ) 115 , e ) 150", + "Correct": "b", + "Explanation": "\"x + y = 250 x - y = 200 2 x = 50 x = 25 y = 225 answer is b\"" + }, + { + "Answer": 184, + "Options": "a ) 130 , b ) 140 , c ) 136 , d ) 184 , e ) 196", + "Correct": "d", + "Explanation": "\"explanation : lcm of 5 , 9 , 12 and 18 is 180 required number = 180 + 4 = 184 answer : option d\"" + }, + { + "Answer": 484, + "Options": "a ) rs 460 , b ) rs 484 , c ) rs 550 , d ) rs 664 , e ) none of these", + "Correct": "b", + "Explanation": "explanation : let a = abhinav , b = bhupathi . 4 / 15 a = 2 / 5 b = > a = ( 2 / 515 / 4 ) b = > a = 3 / 2 b = > a / b = 3 / 2 = > a : b = 3 : 2 b ' s share = rs . ( 12102 / 5 ) = rs . 484 . answer : b" + }, + { + "Answer": 22500, + "Options": "a ) 3277 , b ) 2977 , c ) 22500 , d ) 6077 , e ) 17112", + "Correct": "c", + "Explanation": "explanation : 40,000 * ( 3 / 4 ) ^ 2 answer : c" + }, + { + "Answer": 0.9677419354838709, + "Options": "a ) 1 / 130 , b ) 1 / 5 , c ) 3 / 13 , d ) 10 / 13 , e ) 30 / 31", + "Correct": "e", + "Explanation": "\"it ' s y / xpercentnot y / x . if x = 20 and y = 10 . then : 20 x = 400 black - and - white films ; 6 y = 60 color films . y / x % = 10 / 20 % = 0.5 % of the black - and - white films , so 2 black - and - white films and all 60 color films , thus total of 62 films were selected . color films thus compose e = 60 / 62 = 30 / 31 of the selected films . answer : e .\"" + }, + { + "Answer": 40, + "Options": "a ) 39 , b ) 35 , c ) 42 , d ) 40 , e ) 41.5", + "Correct": "d", + "Explanation": "\"let the average after 16 th inning = x then total run after 16 th inning = 16 x then total run after 17 th inning = 16 x + 200 then average run after 17 th inning = ( 16 x + 200 ) / 17 ( 16 x + 200 ) / 17 = x + 10 = > 16 x + 200 = 17 x + 170 x = 30 ; average after 17 th inning = 30 + 10 = 40 answer : d\"" + }, + { + "Answer": 35, + "Options": "a ) 25 % , b ) 35 % , c ) 45 % , d ) 70 % , e ) 80 %", + "Correct": "b", + "Explanation": "1 . we are given the following percentages : 30 ( 70 ) , 40 ( 60 ) , 25 ( 75 ) . there are two threads from here . first starts at 30 % and finishes there . second one starts at 70 , then 40 , and then 25 . we need a value that is divisible by 7 , 2 , and 5 at least once . lets pick a number now , say 700 . so say if non hawks are 700 ( this is 70 % of the total , so total = 1000 ) , then paddy warbs are 2 / 5 x 700 = 1400 / 5 = 280 . kingfishers , therefore , are 280 / 4 = 70 . lets add them up . 300 hawks + 280 peddy warbs + 70 kingsifhers = 650 . so all others are 1000 - 650 = 350 or 35 % of total birds . the main job here to to identify the smart number to start the question with . this can be time consuming , but once identified , this question can be solved fairly quickly . 2 . another method : if x is total - - > non hawks = 0.7 x - - > warbs = 0.4 ( 0.7 x ) - - > kfs = 0.25 ( 0.4 ( 0.7 x ) ) . our job is to find out r : ( 0.3 x + 0.28 x + 0.07 x ) / x . or 0.65 x / x = 0.65 . we need to find 1 - 0.65 = 0.35 or 35 % . b" + }, + { + "Answer": 40500, + "Options": "a ) 81000 , b ) 33888 , c ) 77678 , d ) 200988 , e ) 40500", + "Correct": "e", + "Explanation": "\"32000 * 9 / 8 * 9 / 8 = 40500 answer : e\"" + }, + { + "Answer": 13, + "Options": "a ) 8 , b ) 10 , c ) 14 , d ) 13 , e ) 16", + "Correct": "d", + "Explanation": "\"explanation : = > 3 ( 2 x + 7 ) = 99 = > 2 x + 7 = 33 = > x = 13 option d\"" + }, + { + "Answer": 14, + "Options": "a ) 15 , b ) 14 , c ) 13 , d ) 12 , e ) 11", + "Correct": "b", + "Explanation": "\"a / b + b / a = ( a 2 ] / ab a + b = + b 2 ) / ab = ( a 2 + b 2 + a + b ) / ab = [ ( a + b ) 2 - 2 ab - 8 / 1 = - 8 ab = 4 / 1 = 4 hence a / b + b / a = [ ( - 8 ) 2 - 2 ( 4 ) ] / 4 = 56 / 4 = 14 . answer : b\"" + }, + { + "Answer": 57, + "Options": "a ) 77 , b ) 57 , c ) 34 , d ) 65 , e ) 21", + "Correct": "b", + "Explanation": "step 1 : find the number of white t - shirts . 5 \u00d7 6 = 30 step 2 : find the number of blue t - shirts . 3 \u00d7 9 = 27 step 3 : find the total number of t - shirts . 30 + 27 = 57 darren bought 57 t - shirts . answer is b ." + }, + { + "Answer": 40, + "Options": "a ) 40 , b ) 42 , c ) 44 , d ) 46 , e ) 48", + "Correct": "a", + "Explanation": "\"let x be the number he chose , then 7 \u22c5 x \u2212 150 = 130 7 x = 280 x = 40 correct answer a\"" + }, + { + "Answer": 0.09, + "Options": "a ) 5 / 100 , b ) 6 / 100 , c ) 7 / 100 , d ) 8 / 100 , e ) 9 / 100", + "Correct": "e", + "Explanation": "( 1 - 1 / 10 ) ( 1 - 1 / 11 ) ( 1 - 1 / 12 ) . . . ( 1 - 1 / 99 ) ( 1 - 1 / 100 ) = ( 9 / 10 ) ( 10 / 11 ) ( 11 / 12 ) . . . ( 98 / 99 ) ( 99 / 100 ) = 9 / 100 : simplify correct answer e" + }, + { + "Answer": 7, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", + "Correct": "a", + "Explanation": "\"a simple and elegant solution . as addition of 39 , shifts mean by 2 , and addition of 15 , shifts mean by 1 to the other side , we have the mean lying between 3915 , and in a ratio of 2 : 1 39 - 15 = 24 24 divide by 3 is 8 . meaning mean of the n terms is 15 + 8 = 39 - 16 = 23 now , from first statement , when a person aged 39 is added to a group of n people , the average age increases by 2 . w * 23 + 39 = 25 * ( w + 1 ) w = 7 ans . ( a )\"" + }, + { + "Answer": 45, + "Options": "a ) a ) 51 , b ) b ) 50 , c ) c ) 45 , d ) d ) 40 , e ) e ) 36", + "Correct": "c", + "Explanation": "\"explanation : let the number be x . then , x - ( x / 3 ) = 30 = > 2 x / 3 = 30 = > x = 45 answer : option c\"" + }, + { + "Answer": 990.0000000000001, + "Options": "a ) 0.099 , b ) 0.0099 , c ) 9.9 , d ) 990 , e ) 99", + "Correct": "d", + "Explanation": "\"( 0.0077 ) ( 3.6 ) / ( 0.04 ) ( 0.1 ) ( 0.007 ) = 0.0077 * 360 / 4 * ( 0.1 ) ( 0.007 ) = 0.077 * 90 / 1 * 0.007 = 77 * 90 / 7 = 11 * 90 = 990 answer : d\"" + }, + { + "Answer": 33, + "Options": "a ) 22 , b ) 33 , c ) 77 , d ) 99 , e ) 27", + "Correct": "b", + "Explanation": "explanation : let the numbers be a , b , c , d given , a + b + c = 60 , b + c + d = 45 now , d = 18 thus , b + c + 18 = 45 \u21d2 b + c = 27 putting the value of b + c in a + b + c = 60 a + 27 = 60 \u21d2 a = 33 answer : b" + }, + { + "Answer": 30, + "Options": "a ) 12 , b ) 15 , c ) 20 , d ) 25 , e ) 30", + "Correct": "e", + "Explanation": "since the distance remains the same ( we ' re just changing the rate and time ) , any increase in rate or time is met with a decrease in the other term . decreasing the time by 1 / 4 would give us : d = ( r ) ( t ) = ( 3 t / 4 ) ( x * r ) x = 4 / 3 since ( 3 t / 4 ) ( 4 r / 3 ) = ( r ) ( t ) = d 4 r / 3 = r + 10 r / 3 = 10 r = 30 the answer is e ." + }, + { + "Answer": 150.00000000000003, + "Options": "a ) $ 60 , b ) $ 80 , c ) $ 90 , d ) $ 120 , e ) $ 150", + "Correct": "e", + "Explanation": "\"let ' s let t = total number of dollars spent at the supermarket . with this variable we can set up an equation and determine t . we are given that john spent 1 / 2 of his money on fresh fruits and vegetables , or ( 1 / 2 ) t , 1 / 3 on meat products , or ( 1 / 3 ) t , and 1 / 10 on bakery products , or ( 1 / 10 ) t . we are also given that he spent the remaining $ 10 on candy . since we know where all his money was allocated , we can sum these values together and set the sum to t . so we have : ( 1 / 2 ) t + ( 1 / 3 ) t + ( 1 / 10 ) t + 10 = t to get rid of the fractions we can multiply the entire equation by 30 , and we obtain : 15 t + 10 t + 3 t + 300 = 30 t 28 t + 300 = 30 t 300 = 2 t t = 150 john spent $ 90 at the supermarket . answer : e\"" + }, + { + "Answer": 50, + "Options": "a ) 50 , b ) 28 , c ) 160 , d ) 180 , e ) 18", + "Correct": "a", + "Explanation": "\"let the numbers be x and y . then , x + y = 5 and x - y = 10 x 2 - y 2 = ( x + y ) ( x - y ) = 5 * 10 = 50 . answer : a\"" + }, + { + "Answer": 1680, + "Options": "a ) 9632 , b ) 7896 , c ) 8741 , d ) 1683 , e ) 8523", + "Correct": "d", + "Explanation": "l . c . m of 5,6 , 7,8 = 840 required number is of the form of 840 k + 3 least value of k for which ( 840 k + 3 ) is divided by 9 is k = 2 required number = ( 840 * 2 + 3 ) = 1683 answer ( d )" + }, + { + "Answer": 88, + "Options": "a ) a ) 70 , b ) b ) 77 , c ) c ) 79 , d ) d ) 81 , e ) e ) 88", + "Correct": "e", + "Explanation": "\"required average = 8 ( 1 + 2 + . . . . + 21 ) / 21 ( 8 / 21 ) x ( ( 21 x 22 ) / 2 ) ( because sum of first 21 natural numbers ) = 88 e\"" + }, + { + "Answer": 1.1999999999999993, + "Options": "a ) 0.2 , b ) 1.2 , c ) 1.8 , d ) 2.2 , e ) 4.0", + "Correct": "b", + "Explanation": "\"since y * is defined as the greatest positive even integer less than or equal to y , then 9.2 * = 8 ( the greatest positive even integer less than or equal to 9.2 is 4 ) . hence , 9.2 \u2013 9.2 * = 9.2 - 8 = 1.2 answer : b .\"" + }, + { + "Answer": 160, + "Options": "a ) $ 100 , b ) $ 150 , c ) $ 160 , d ) $ 200 , e ) $ 250", + "Correct": "c", + "Explanation": "\"a : ( b + c ) = 2 : 3 a ' s share = 400 * 2 / 5 = $ 160 answer is c\"" + }, + { + "Answer": 10, + "Options": "a ) 5 , b ) 10 , c ) 8 , d ) 15 , e ) 20", + "Correct": "b", + "Explanation": "x + x ( xx ) put the value of x = 2 in the above expression we get , 2 + 2 ( 22 ) = 2 + 2 ( 2 \u00d7 2 ) = 2 + 2 ( 4 ) = 2 + 8 = 10 answer : b" + }, + { + "Answer": 25, + "Options": "a ) \u2212 1 , b ) 0 , c ) 1 , d ) 25 , e ) 29", + "Correct": "d", + "Explanation": "on solving the inner bracket we get 4 . then we get equation as - 1 x 4 where b = 4 and a = - 1 answer d" + }, + { + "Answer": 0.96, + "Options": "a ) 0.96 , b ) 9.4 , c ) 0.094 , d ) 94 , e ) none", + "Correct": "a", + "Explanation": "\"answer let a - 4 % of a = ab . \u21d2 ( 96 x a ) / 100 = ab \u2234 b = 0.96 correct option : a\"" + }, + { + "Answer": 1, + "Options": "a ) 2 , b ) 9 , c ) 6 , d ) 5 , e ) 1", + "Correct": "e", + "Explanation": "\"let x = 296 q + 75 = ( 37 * 8 q + 37 * 2 ) + 1 37 * ( 8 q + 2 ) + 1 thus when the number is divided by 37 the remainder is 1 answer ( e )\"" + }, + { + "Answer": 860, + "Options": "a ) 430 , b ) 516 , c ) 660 , d ) 860 , e ) none", + "Correct": "d", + "Explanation": "\"solution given expression = [ 860 / 100 x 50 + 50 / 100 x 860 ] = 430 + 430 = 860 . answer d\"" + }, + { + "Answer": 15, + "Options": "a ) 21 , b ) 20 , c ) 19 , d ) 16 , e ) 15", + "Correct": "e", + "Explanation": "\"marcella has 20 pairs of shoes and loses 9 shoes . to minimize the loss of identical pairs of shoes we want marcella to lose as many identical pairs as possible . this would yield 4 identical pairs and 1 additional shoe ( destroying 5 pairs of shoes ) . the 20 pairs of shoes minus the 5 ' destroyed ' pairs yields 15 pairs that still fulfill the requirements . answer : e\"" + }, + { + "Answer": 3, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "a", + "Explanation": "\"3 < x < 6 < y < 7 ; 3 < x y < 7 3 + y < x + 7 y - x < 4 . positive integer difference is 3 ( for example y = 6.5 and x = 3.5 ) answer : a .\"" + }, + { + "Answer": 26, + "Options": "a ) 22 , b ) 30 , c ) 99 , d ) 26 , e ) 27", + "Correct": "d", + "Explanation": "total age increased = ( 8 * 2 ) years = 8 years . sum of ages of two new men = ( 21 + 23 + 8 ) years = 52 years average age of two new men = ( 52 / 2 ) years = 26 years . answer : d" + }, + { + "Answer": 48, + "Options": "a ) 16 , b ) 24 , c ) 48 , d ) 96 , e ) 78", + "Correct": "c", + "Explanation": "solution required number = ( 2 \u00d7 4 \u00d7 6 ) = 48 . answer c" + }, + { + "Answer": 25, + "Options": "a ) 20 years , b ) 21 years , c ) 22 years , d ) 23 years , e ) 25 years", + "Correct": "e", + "Explanation": "\"explanation : let the average age of the whole team by x years . 11 x \u00e2 \u20ac \u201c ( 28 + 31 ) = 9 ( x - 1 ) 11 x \u00e2 \u20ac \u201c 9 x = 50 2 x = 50 x = 25 so , average age of the team is 25 years . answer e\"" + }, + { + "Answer": 285, + "Options": "a ) 280 , b ) 285 , c ) 290 , d ) 295 , e ) 275", + "Correct": "b", + "Explanation": "\"explanation : as the month begin with sunday , so there will be five sundays in the month . so result will be : = ( 510 \u00d7 5 + 240 \u00d7 25 / 30 ) = ( 8550 / 30 ) = 285 option b\"" + }, + { + "Answer": 54.285714285714285, + "Options": "a ) 50.78 kg , b ) 49.32 kg , c ) 61.67 kg , d ) 69.15 kg , e ) 54.28 kg", + "Correct": "e", + "Explanation": "\"total weight of 40 + 30 students = 40 * 50 + 30 * 60 = 2000 + 1800 average weight of the class is = 3800 / 70 = 54.28 kg answer is e\"" + }, + { + "Answer": 5, + "Options": "a ) 10 , b ) 5 , c ) 15 , d ) 20 , e ) 7", + "Correct": "b", + "Explanation": "\"so , according to a mean of a set of even numbers from 16 to 44 = ( 16 + 44 ) / 2 = 30 and mean of a set of even numbers from 14 to 56 = ( 14 + 56 ) / 2 = 35 difference = 35 - 30 = 5 answer : b .\"" + }, + { + "Answer": 228, + "Options": "a ) s . 130 , b ) s . 140 , c ) s . 150 , d ) s . 228 , e ) s . 282", + "Correct": "d", + "Explanation": "\"let the amount paid to a per week = x and the amount paid to b per week = y then x + y = 570 but x = 150 % of y = 150 y / 100 = 15 y / 10 \u2234 15 y / 10 + y = 570 \u21d2 y [ 15 / 10 + 1 ] = 570 \u21d2 25 y / 10 = 570 \u21d2 25 y = 5700 \u21d2 y = 5700 / 25 = rs . 228 d )\"" + }, + { + "Answer": 20, + "Options": "a ) 24 , b ) 12 , c ) 20 , d ) 4 , e ) 2", + "Correct": "c", + "Explanation": "the wording of the question is slightly misleading . when a question asks what is thefewestthatcouldhave been sold , it is suggesting that there could be many different quantities sold . in this question however , because we are told that exactly 64 frisbees have been sold and revenue was exactly $ 204 , there is only one possible solution for the number of $ 3 and $ 4 frisbees sold . to solve , we have 2 equations and 2 unknowns let x = number of $ 3 frisbees sold let y = number of $ 4 frisbees sold x + y = 60 3 x + 4 y = 200 x = 60 - y 3 ( 60 - y ) + 4 y = 200 180 - 3 y + 4 y = 200 y = 20 answer : c" + }, + { + "Answer": 23, + "Options": "a ) 7 , b ) 23 , c ) 12 , d ) 17 , e ) 25", + "Correct": "b", + "Explanation": "16 + 7 = 23 . answer is b ." + }, + { + "Answer": 37.1, + "Options": "a ) $ 2.10 , b ) $ 37.10 , c ) $ 37.16 , d ) $ 38.10 , e ) $ 38.80", + "Correct": "b", + "Explanation": "\"principal that is amount taken by laura at year beginning = 35 $ rate of interest = 6 % interest = ( 6 / 100 ) * 35 = 2.10 $ total amount that laura owes a year later = 35 + 2.1 = 37.1 $ answer b\"" + }, + { + "Answer": 12, + "Options": "a ) 4 % increase , b ) 12 % increase , c ) 10 % decrease , d ) 6 % increase , e ) none of these", + "Correct": "b", + "Explanation": "\"explanation : solution : let the original price be rs . 100 . new final price = 140 % of ( 80 % of 100 ) = rs . 140 / 100 * 80 / 100 * 100 = rs . 112 . . ' . increase = 12 % answer : b\"" + }, + { + "Answer": 12, + "Options": "a ) 4 , b ) 7 , c ) 8 , d ) 12 , e ) it can not be determined from the information given .", + "Correct": "d", + "Explanation": "a = ( 1 , 3,5 ) , sum of this = 9 b = ( 5 , 7,9 ) , sum of this = 21 , the differenct between 21 - 9 = 12 hence , 12 is the answer i . e . d" + }, + { + "Answer": 19, + "Options": "a ) 23 , b ) 28 , c ) 27 , d ) 19 , e ) 24", + "Correct": "d", + "Explanation": "\"let the average after the 16 th inning be p . so , the average after the 15 th inning will be ( p - 3 ) hence , 15 ( p - 30 ) + 64 = 16 p = > p = 19 . answer : d\"" + }, + { + "Answer": 6, + "Options": "a ) 5 , b ) 6 , c ) 8 , d ) 10 , e ) 50", + "Correct": "b", + "Explanation": "\"the no will be of the form 2 ^ n to achieve this . since any other form will have odd no in the prime factorization . hence we need to find solution of n for equation - 1 < 2 ^ n < 101 . 2 ^ 6 = 64 , 2 ^ 7 - 128 hence n can take values from 1 to 6 . hence ans - ( b ) 6\"" + }, + { + "Answer": 80, + "Options": "a ) 65 , b ) 80 , c ) 90 , d ) 115 , e ) 120", + "Correct": "b", + "Explanation": "we can use some form of the equation d = rt [ distance = rate * time ] rate of plane a : 200 mph rate of plane b : 300 mph plane a will be in the sky 40 minutes longer than plane b ( 2 / 3 of an hour ) time of plane a when b overtakes it : t + ( 2 / 3 ) use 2 / 3 of an hour since the rate is in hours time of plane b when b overtakes a : t at the time that b overtakes a , they will have travelled the same distance so rt is equal for each plane : 200 * ( t + 2 / 3 ) = 300 * t 200 t + 400 / 3 = 300 t 400 / 3 = 100 t 4 / 3 = t this is 1 and a third hour , so 60 minutes + 20 minutes = 80 minutes b" + }, + { + "Answer": 1394, + "Options": "a ) 1394 , b ) 1294 , c ) 1194 , d ) 1094 , e ) none of them", + "Correct": "a", + "Explanation": "here , ( 20 - 14 ) = 6 , ( 25 \u2013 19 ) = 6 , ( 35 - 29 ) = 6 and ( 40 - 34 ) = 6 . therefore , required number = ( l . c . m . of 2025 , 3540 ) \u2013 6 = 1394 . answer is a ." + }, + { + "Answer": 21, + "Options": "a ) 17 , b ) 21 , c ) 22 , d ) 24 , e ) 25", + "Correct": "b", + "Explanation": "average of 22 numbers = 0 . sum of 22 numbers ( 0 x 22 ) = 0 . it is quite possible that 21 of these numbers may be positive and if their sum is a then 22 nd number is ( - a ) answer is 21 ( b )" + }, + { + "Answer": 400, + "Options": "a ) 100 , b ) 300 , c ) 400 , d ) 3,000 , e ) 4,000", + "Correct": "c", + "Explanation": "\"straight pluggin in for me . as usual , i started with c and got the answer . lets ' back calculate and see what we get let us consider eggs processed each day to be 400 so initial ratio of eggs processed and rejected is 96 : 4 or 24 : 1 so out of 400 eggs , there will be 384 eggs processed and 16 rejected . now if the no . of eggs inspected remain and 12 more eggs get accepted that means there e = 384 + 12 = 396 eggs accepted and 4 rejected . . . and the ratio will be 99 : 1 bingo . . . this is what the questions says . . . . its always a good idea to start with c .\"" + }, + { + "Answer": 72, + "Options": "a ) 70 , b ) 72 , c ) 75 , d ) 78 , e ) 80", + "Correct": "b", + "Explanation": "\"income of 6 months = ( 6 \u00d7 75 ) \u2013 debt = 450 \u2013 debt income of the man for next 4 months = 4 \u00d7 60 + debt + 30 = 270 + debt \u2234 income of 10 months = 720 average monthly income = 720 \u00f7 10 = 72 answer b\"" + }, + { + "Answer": 150, + "Options": "a ) 150 , b ) 200 , c ) 250 , d ) 350 , e ) none", + "Correct": "a", + "Explanation": "\"sol . let the number of grils be x . then , number of boys = ( 600 - x ) . then , ( 11 3 / 4 \u00d7 600 ) \u21d4 11 x + 12 ( 600 - x ) \u21d4 x = 7200 - 7050 \u21d4 150 . answer a\"" + }, + { + "Answer": 18, + "Options": "a ) 25 , b ) 31 , c ) 27 , d ) 29 , e ) 18", + "Correct": "e", + "Explanation": "\"let the average after 17 innings = x total runs scored in 17 innings = 17 x average after 16 innings = ( x - 3 ) total runs scored in 16 innings = 16 ( x - 3 ) total runs scored in 16 innings + 66 = total runs scored in 17 innings = > 16 ( x - 3 ) + 66 = 17 x = > 16 x - 48 + 66 = 17 x = > x = 18 answer is e .\"" + }, + { + "Answer": 43.13380281690141, + "Options": "a ) 13.1 , b ) 43.1 , c ) 40.1 , d ) 23.1 , e ) 45.1", + "Correct": "b", + "Explanation": "given exp . = ( 14 ) ^ 2 x 5 ^ 3 \u00e3 \u00b7 568 = e = 196 x 125 \u00e3 \u00b7 568 43.1 b" + }, + { + "Answer": 50, + "Options": "a ) 50 % , b ) 32.5 % , c ) 37 % , d ) 37.5 % , e ) 40 %", + "Correct": "a", + "Explanation": "\"what % less of 12 is 6 let it be x % less , then = 12 ( 1 - x / 100 ) = 6 1 - x / 100 = 6 / 12 x = 100 / 2 x = 50 % ans a\"" + }, + { + "Answer": 57.224489795918366, + "Options": "a ) 57 , b ) 51 , c ) 59 , d ) 55 , e ) 52", + "Correct": "a", + "Explanation": "\"for 40 hrs = 40 * 14 = 560 excess = 982 - 560 = 422 for extra hours = . 75 ( 14 ) = 10.5 + 14 = 24.5 number of extra hrs = 422 / 24.5 = 17.2 = 17 approx . total hrs = 40 + 17 = 57 answer a\"" + }, + { + "Answer": 71, + "Options": "a ) 23 , b ) 71 , c ) 27 , d ) 61 , e ) 81", + "Correct": "b", + "Explanation": "\"explanation : 70 + 5 * 12 / ( 180 / 3 ) = 70 + 5 * 12 / ( 60 ) = 70 + ( 5 * 12 ) / 60 = 70 + 1 = 71 . answer : b\"" + }, + { + "Answer": 0.6153846153846154, + "Options": "a ) 30 / 25 , b ) 28 / 13 , c ) 28 / 29 , d ) 8 / 13 , e ) none of these", + "Correct": "d", + "Explanation": "explanation : we can do it easily by in two steps step 1 : we get the hcf of 368 and 598 which is 46 step 2 : divide both by 46 , we will get the answer 8 / 13 answer : option d" + }, + { + "Answer": 18, + "Options": "a ) 18 , b ) 40 , c ) 21 , d ) 43 , e ) 28", + "Correct": "a", + "Explanation": "\"( x ^ n + 1 ) will be divisible by ( x + 1 ) only when n is odd ; ( 19 ^ 19 + 1 ) will be divisible by ( 19 + 1 ) ; ( 19 ^ 19 + 1 ) + 18 when divided by 20 will give 18 as remainder . correct option : a\"" + }, + { + "Answer": 7, + "Options": "a ) 3 , b ) 6 , c ) 9 , d ) 8 , e ) 7", + "Correct": "e", + "Explanation": "\"a ' s + co + ca + cats = 16 . sa ' s + 1 + 1 + cats = 16 or sa ' s + cats = 14 . sa ' s ( 2 ) + 2 + 1 + cats * 4 = 45 sa ' s * 2 + cats * 4 = 42 or sa ' s + cats * 2 = 21 or 14 - cats + cat * 2 = 21 then cats = 7 e\"" + }, + { + "Answer": 1, + "Options": "a ) 3 , b ) 1 , c ) 16 , d ) 11 , e ) 15", + "Correct": "b", + "Explanation": "\"on dividing 9671 by 2 , we get remainder = 1 . required number be subtracted = 1 answer : b\"" + }, + { + "Answer": 18200, + "Options": "a ) 18500 , b ) 18200 , c ) 17500 , d ) 16500 , e ) 13500", + "Correct": "b", + "Explanation": "\"( 18000 + 200 ) / 90 * 90 = 18200 answer : b\"" + }, + { + "Answer": 176470, + "Options": "a ) 20,000 , b ) 176470 , c ) 10000 , d ) 13000 , e ) 56600", + "Correct": "b", + "Explanation": "x be the # of bees in the hive with the max # of bees . let other hives have same # of bees . so , x + 3 * ( 0.8 ) * x = 600,000 = > 3.4 x = 600,000 = > x = 176470 . b is the answer ." + }, + { + "Answer": 5.2, + "Options": "a ) 2.8 % , b ) 3.6 % , c ) 4.4 % , d ) 5.2 % , e ) 6.0 %", + "Correct": "d", + "Explanation": "\"let amount spent by jill = 100 clothing = 50 , food = 10 , others = 40 tax on clothing = 2 tax on others = 3.2 percentage = 5.2 / 100 = 5.2 % answer : d\"" + }, + { + "Answer": 6, + "Options": "a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10", + "Correct": "c", + "Explanation": "let x be the wholesale price . then 1.7 x = 34 and x = 34 / 1.7 = 20 . to achieve a 100 % markup , the price needs to be $ 40 . the retailer needs to increase the price by $ 6 more . the answer is c ." + }, + { + "Answer": 258, + "Options": "a ) a ) 258 , b ) b ) 65 , c ) c ) 58 , d ) d ) 62 , e ) e ) 48", + "Correct": "a", + "Explanation": "\"6 th number = sum of 1 st 6 no . s + sum of last 6 no . s - sum of 11 no . s answer = 6 * 88 + 6 * 65 - 11 * 60 = 258 answer is a\"" + }, + { + "Answer": 2400, + "Options": "a ) 2400 , b ) 2550 , c ) 5050 , d ) 6275 , e ) 11325", + "Correct": "a", + "Explanation": "\"set a contains 4 , 6 . . . 50 set b contains 104 , 106 . . . 150 number of terms in each set = 24 difference between corresponding terms in set a and b = 100 difference between sum of set b and set a = 100 * 24 = 2400 answer a\"" + }, + { + "Answer": 75, + "Options": "a ) 74 , b ) v = 75 , c ) v = 175 , d ) v = 680 , e ) 690", + "Correct": "b", + "Explanation": "i solved this question by plugging in numbers from the answer choices . a . ) 74 starting with answer choice a , i immediately eliminated it because 74 is not even divisible by 5 . b . ) 75 i divide 75 / 5 and get 15 as an answer . i divide 75 / 34 and get a remainder of 7 . 15 - 7 = 8 so i know the correct answer isb" + }, + { + "Answer": 50, + "Options": "a ) 55 , b ) 50 , c ) 40 . , d ) 30 . , e ) 25 .", + "Correct": "b", + "Explanation": "\"given there are 50 students , 80 % of 50 = 40 boys and remaining 10 girls . now here 80 % are boys and 20 % are girls . now question is asking about how many boys do we need to add , to make the girls percentage to 20 or 20 % . . if we add 50 to existing 40 then the count will be 90 and the girls number will be 10 as it . now boys are 90 % and girls are 10 % . ( out of 100 students = 90 boys + 10 girls ) . imo option b is correct .\"" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9", + "Correct": "a", + "Explanation": "\"1 / 5 = 0.2 . . ( a repeating pattern one digit long ) a\"" + }, + { + "Answer": 4, + "Options": "a ) 3 . , b ) 2 . , c ) 1 / 2 . , d ) 4 , e ) there is n ' t enough data to answer the question .", + "Correct": "d", + "Explanation": "answer is d : 4 x - y = ( x + y ) / 2 solving for x / y = 4" + }, + { + "Answer": 1, + "Options": "a ) 1 hour , b ) 2 hour , c ) 3 hour , d ) 4 hour , e ) 5 hour", + "Correct": "a", + "Explanation": "\"let the duration of the flight be x hours then 600 / x - 600 / x ( 1 / 2 ) = 200 = 600 / x - 1200 / 2 x + 1 = 200 = x ( 2 x + 1 ) = 3 = 2 xsquare + x - 3 = 0 = ( 2 x + 3 ) ( x - 1 ) = 0 = x = 1 hr ( neglecting the - ve value of x ) answer : option a\"" + }, + { + "Answer": 143547, + "Options": "a ) 223888 , b ) 143547 , c ) 2607778 , d ) 126997 , e ) 127811", + "Correct": "b", + "Explanation": "if the given number is a + b + c then a . b | a . c | a . b + a . c - b \u21d2 \u21d2 5 + 3 + 2 = 5.3 | 5.2 | 5.3 + 5.2 - 3 = 151022 \u21d2 \u21d2 9 + 2 + 4 = 9.2 | 9.4 | 9.2 + 9.4 - 2 = 183652 7 + 2 + 5 = 7.2 | 7.5 | 7.2 + 7.5 - 2 = 143547 answer : b" + }, + { + "Answer": 3600, + "Options": "a ) 76 , b ) 5776 , c ) 304 , d ) 3600 , e ) none", + "Correct": "d", + "Explanation": "\"answer let \u221a n / 15 = 4 then \u221a n = 15 x 4 = 60 \u2234 n = 60 x 60 = 3600 . correct option : d\"" + }, + { + "Answer": 4499, + "Options": "a ) a ) 3800 , b ) b ) 4200 , c ) c ) 4400 , d ) d ) 4500 , e ) e ) 4600", + "Correct": "d", + "Explanation": "\"x * ( 90 / 100 ) * ( 80 / 100 ) = 3240 x = 4500 answer : d\"" + }, + { + "Answer": 36.21, + "Options": "a ) 40 - 43 , b ) 39 - 42 , c ) 39 - 42 , d ) 38 - 41 , e ) 36 - 40", + "Correct": "e", + "Explanation": "\"2 % ( 35.5 ) = 0.71 12 % ( 35.5 ) = 4.26 total amount could have been 35.5 + 0.71 and 35.5 + 4.26 = > could have been between 36.21 and 39.76 = > approximately between 36 and 40 answer is e .\"" + }, + { + "Answer": 35, + "Options": "a ) $ 27 , b ) $ 29 , c ) $ 31 , d ) $ 33 , e ) $ 35", + "Correct": "e", + "Explanation": "the difference in the two prices is $ 1.70 - $ 1.20 = $ 0.50 for each color copy . each color copy will cost an extra $ 0.50 at print shop y . 70 * $ 0.50 = $ 35 the answer is e ." + }, + { + "Answer": 120, + "Options": "a ) 240 , b ) 75 , c ) 110 , d ) 120 , e ) 200", + "Correct": "d", + "Explanation": "\"adult + children = 240 let , children = y then , adult = y + 80 i . e . y + ( y + 80 ) = 240 i . e . y = 80 i . e . adult = 80 + 80 = 160 adults include only men and women i . e . men + women = 160 let women , w = x then men , m = x + 80 i . e . x + ( x + 20 ) = 2 x + 80 = 160 i . e . x = 40 i . e . men , m = 40 + 80 = 120 answer : option d\"" + }, + { + "Answer": 32.5, + "Options": "a ) 14 % , b ) 25 % , c ) 28 % , d ) 32.5 % , e ) 50 %", + "Correct": "d", + "Explanation": "\"official solution : if we start with 40 gallons of a mixture that is 10 % grape juice , then we have : 30 \u00d7 0.10 = 3 gallons of grape juice . 30 \u00d7 0.90 = 27 gallons of other components . if we add 10 gallons of grape juice , we will end up with 13 gallons of grape juice and 36 gallons of other components , and we will have a total of 40 gallons of the mixture . so 13 / 40 of the new mixture is grape juice . now we convert this to a percent : percent grape juice = 32,5 % . the correct answer is choice ( d )\"" + }, + { + "Answer": 24, + "Options": "a ) 16 , b ) 20 , c ) 24 , d ) 28 , e ) 32", + "Correct": "c", + "Explanation": "\"3.456789 ^ 12 has 6 * 12 = 72 decimal places . 10 ^ 48 moves the decimal place to the right 48 places . ( 10 ^ 4 * 3.456789 ) ^ 12 has 72 - 48 = 24 digits after the decimal point . the answer is c .\"" + }, + { + "Answer": 15120, + "Options": "a ) 15120 , b ) 14500 , c ) 14900 , d ) 14300 , e ) 14000", + "Correct": "a", + "Explanation": "total amount invested = 50000 assume that investment of c = x . then investment of b = 5000 + x , investment of a = 4000 + 5000 + x = 9000 + x x + 5000 + x + 9000 + x = 50000 \u21d2 3 x + 14000 = 50000 \u21d2 3 x = 50000 \u2013 14000 = 36000 \u21d2 x = 36000 / 3 = 12000 investment of c = x = 12000 investment of b = 5000 + x = 17000 investment of a = 9000 + x = 21000 ratio of the investment of a , b and c = 21000 : 17000 : 12000 = 21 : 17 : 12 share of a = total profit \u00d7 21 / 50 = 36000 \u00d7 21 / 50 = 15,120 answer is a ." + }, + { + "Answer": 0.08333333333333333, + "Options": "a ) 1 / 6 , b ) 1 / 8 , c ) 1 / 12 , d ) 1 / 4 , e ) 3 / 4", + "Correct": "c", + "Explanation": "o = 3 a p = 4 o = 12 a a = p / 12 the answer is c ." + }, + { + "Answer": 30, + "Options": "a ) 0 , b ) 10 , c ) 20 , d ) 30 , e ) 40", + "Correct": "d", + "Explanation": "\"( 3 ' ) ' = ( 3 * 3 - 3 ) ' = 6 ' = 6 * 6 - 6 = 30 answer d\"" + }, + { + "Answer": 550.0000000000001, + "Options": "a ) 280 , b ) 400 , c ) 540 , d ) 550 , e ) 840", + "Correct": "d", + "Explanation": "\"of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month : 2 / 3 * 3 / 4 = 1 / 2 survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year : ( 1 - 3 / 5 ) * 1 / 2 = 1 / 5 survived the first year . 110 geese survived the first year : 1 / 5 * ( total ) = 110 - - > ( total ) = 550 . answer : d .\"" + }, + { + "Answer": 285, + "Options": "a ) 250 , b ) 276 , c ) 280 , d ) 285 , e ) 295", + "Correct": "d", + "Explanation": "\"explanation : since the month begins with a sunday , to there will be five sundays in the month . required average = ( 510 \u00d7 5 + 240 \u00d7 25 / 30 ) = 8550 / 30 = 285 answer : d\"" + }, + { + "Answer": 75, + "Options": "a ) $ 75 , b ) $ 40 , c ) $ 50 , d ) $ 80 , e ) $ 100", + "Correct": "a", + "Explanation": "\"deargoodyear 2013 , i ' m happy to help . this is a relatively straightforward problem , not very challenging . btw , crazy eddiewas the actually name of an electronics chain on the east coast of the usa back in the 1970 s . manufacturing now is $ 50 . they now are making a 50 % profit , so the selling price must be $ 100 . they had this same selling price , $ 100 , before they made the change , and had a profit of 25 % , so the manufacturing must have been $ 75 . answer = ( a ) .\"" + }, + { + "Answer": 5, + "Options": "a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8", + "Correct": "b", + "Explanation": "\"z = n ( n - 3 ) z = 2 * n 2 n = n ( n - 3 ) = > 2 = n - 3 = > n = 5 answer b\"" + }, + { + "Answer": 4, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "d", + "Explanation": "d 4 now if you go on calculating 2 ^ 300 , you will lose so much time and it might not even be feasible to carry out so long of calculations . thus we will make use of a trick here . we will calculate the remainder of each power of 2 till we come across a pattern . 2 ^ 1 divided by 4 leaves the remainder 2 . 2 ^ 2 divided by 4 leaves the remainder 0 . 2 ^ 3 divided by 4 leaves the remainder 0 . 2 ^ 4 divided by 4 leaves the remainder 0 . you can see that all the following powers of two will be divisible by 4 . therefore the remainder when 2 ^ 300 is divided by 4 will be 0 only ." + }, + { + "Answer": 351, + "Options": "a ) 22 , b ) 28 , c ) 77 , d ) 99 , e ) 351", + "Correct": "e", + "Explanation": "if u can just keep an eye on the options 99 is the only multiple of 9 in options given . . so you can mark it wid in seconds . now coming to the process m ( d ) = 7 x and b ( d ) = 2 x now from the next line the new eqn becomes 7 x / ( 2 x + 6 ) = 13 / 4 solving it 28 x = 26 x + 78 x = 39 which means m ( d ) = 273 and b ( d ) = 78 so total initially is m ( d ) + b ( d ) = 351 e" + }, + { + "Answer": 6249, + "Options": "a ) 5999 , b ) 6788 , c ) 6250 , d ) 4559 , e ) 6989", + "Correct": "c", + "Explanation": "\"x * ( 90 / 100 ) * ( 80 / 100 ) = 4500 x = 6250 answer : c\"" + }, + { + "Answer": 17.5, + "Options": "a ) 12 % , b ) 14 % , c ) 16 % , d ) 20 % , e ) 17.5 %", + "Correct": "e", + "Explanation": "\"explanation : 100 * 100 = 10000 75 * 110 = 8250 10000 - - - - - - - 1750 100 - - - - - - - ? = 17.5 % e )\"" + }, + { + "Answer": 26, + "Options": "a ) 7 , b ) 33 , c ) 12 , d ) 17 , e ) 26", + "Correct": "e", + "Explanation": "16 + 10 = 26 . answer is e ." + }, + { + "Answer": 8, + "Options": "a ) 8 , b ) 18 , c ) 10 , d ) 12 , e ) 14", + "Correct": "a", + "Explanation": "\"we know dividend = divisor * quotient + remainder = = = > 507 = divisor * 61 + 19 = = = = = > 488 / 61 = divisor = = = > divisor = 8 ans - a\"" + }, + { + "Answer": 7000, + "Options": "a ) 4000 , b ) 5000 , c ) 6000 , d ) 7000 , e ) 8000", + "Correct": "d", + "Explanation": "total salary of raj and roshan = 2 x 4000 = 8000 total salary of raj roshan and thomas = 3 x 5000 = 15000 salary of thomas = 15000 - 8000 = rs . 7000 answer : d" + }, + { + "Answer": 90, + "Options": "a ) 27 , b ) 36 , c ) 29 , d ) 90 , e ) 11", + "Correct": "d", + "Explanation": "\"let the price of turban be x . thus , for one year the salary = ( 90 + x ) for 9 months he should earn 3434 ( 90 + x ) . now he gets one turban and rs . 45 . thus , 3434 ( 90 + x ) = 45 + x or 270 + 3 x = 180 + 4 x or x = 90 answer : d\"" + }, + { + "Answer": 2400, + "Options": "a ) 1287 , b ) 2887 , c ) 2000 , d ) 1129 , e ) 2400", + "Correct": "e", + "Explanation": "let money invested by raghu = rs . x money invested by trishul = 9 / 10 x = 0.9 x money invested by vishal = 9 / 10 x * 110 / 100 = 0.99 x also , x + 0.9 x + 0.99 x = 6936 = x = 6936 / 2.89 = 2000 therefore , amount invested by raghu is rs . 2400 . answer : e" + }, + { + "Answer": 81, + "Options": "a ) 91 , b ) 81 , c ) 1001 , d ) 1911 , e ) none", + "Correct": "b", + "Explanation": "olution required number of students . = h . c . f of 891 and 810 . \u00e2 \u20ac \u00b9 = \u00e2 \u20ac \u00ba 81 . answer b" + }, + { + "Answer": 488, + "Options": "a ) 246 , b ) 248 , c ) 492 , d ) 15,128 , e ) 30,256", + "Correct": "c", + "Explanation": "\"ok let ' s take a crack at this one . so basically we have 144 ^ 2 - 142 ^ 2 so then ( 144 + 142 ) ( 144 - 142 ) ( 246 ) ( 2 ) = 492 answer : c\"" + }, + { + "Answer": 500, + "Options": "a ) 250 , b ) 500 , c ) 450 , d ) 550 , e ) 650", + "Correct": "b", + "Explanation": "\"the number of chocolate bars is equal to 20 * 25 = 500 correct answer b\"" + }, + { + "Answer": 35.75, + "Options": "a ) 35.75 , b ) 36 , c ) 37 , d ) 38 , e ) 39", + "Correct": "a", + "Explanation": "\"james worked for 41 hours hence he earned 40 * x + 1 * 1.5 x = 41.5 x dollars ; we know that harry also earned the same 41.5 x dollars , out of which he earned 30 x dollars for thefirst 30 hoursplus 11.5 x additional dollars . since for each additional hour he gets 3 x dollars then he worked for 11.5 x / 2 x = 5.75 additional hours , so harry worked for total of 30 + 5.75 = 35.75 hours . answer : a .\"" + }, + { + "Answer": 42, + "Options": "a ) 20 , b ) 31 , c ) 42 , d ) 53 , e ) 64", + "Correct": "c", + "Explanation": "\"x + ( x - 14 ) = 70 - - > x = 42 . answer : c .\"" + }, + { + "Answer": 2, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "b", + "Explanation": "\"on dividing 165826 by 4 we get the remainder 2 , so 2 should be subtracted b\"" + }, + { + "Answer": 16, + "Options": "a ) 16 kmph , b ) 20 kmph , c ) 25 kmph , d ) 30 kmph , e ) 35 kmph", + "Correct": "a", + "Explanation": "\"total time taken = x / 40 + 2 x / 20 hours = 5 x / 40 = x / 8 hours average speed = 2 x / ( x / 8 ) = 16 kmph answer : a\"" + }, + { + "Answer": 9, + "Options": "a ) 9 , b ) 1 , c ) 2 , d ) 4 , e ) 8", + "Correct": "a", + "Explanation": "if x is 1 , 2 , 4 , or 8 , then gcd of x and y is 1 , 2 , 4 , and 8 respectively . so , by poe the answer must be a . still : if x is a multiple of 9 , then y is 8 greater than a multiple of 9 , so not a multiple of 9 , so both of them can not be divisive by 9 . answer : a ." + }, + { + "Answer": 10, + "Options": "a ) 6 , b ) 10 , c ) 18 , d ) 24 , e ) 27", + "Correct": "b", + "Explanation": "total students = 100 one half of the students are boys = 1 / 2 * 100 = 50 one fifth of the boys are under six feet tall = 1 / 5 * 50 = 10 . . . therefore number of boys in the class under six feet tall = 10 . . . answer b . . . . alternatively . . . number of boys in the class under six feet tall = 1 / 5 of 1 / 2 of total students = 1 / 5 * 1 / 2 * 100 = 10 . . . answer b" + }, + { + "Answer": 23.076923076923077, + "Options": "a ) 23 % , b ) 18.75 % , c ) 30 % , d ) 50 % , e ) 100 %", + "Correct": "a", + "Explanation": "\"explanatory answer let the wages earned by erica be $ 100 then , wages earned by robin and charles will be $ 130 and $ 160 respectively . charles earns $ 30 more than robin who earns $ 130 . therefore , charles ' wage is 30 / 130 * 100 = 23.07 % . correct choice is ( a )\"" + }, + { + "Answer": 40, + "Options": "a ) 25 , b ) 40 , c ) 64 , d ) 80 , e ) 96", + "Correct": "b", + "Explanation": "7 / 8 x - 3 / 4 x = 5 galls 1 / 8 * x = 5 gallons x = 40 gallons answer : b" + }, + { + "Answer": 0.4666666666666666, + "Options": "a ) 4 / 9 , b ) 5 / 11 , c ) 7 / 15 , d ) 9 / 22 , e ) 12 / 35", + "Correct": "c", + "Explanation": "\"# defective pens = 3 # good pens = 7 probability of the 1 st pen being good = 7 / 10 probability of the 2 nd pen being good = 6 / 9 total probability = 7 / 10 * 6 / 9 = 7 / 15 the answer is c .\"" + }, + { + "Answer": 39, + "Options": "a ) 19 , b ) 29 , c ) 39 , d ) 49 , e ) none of these", + "Correct": "c", + "Explanation": "\"explanation : let b ' s present age = x years . then , a ' s present age = ( x + 9 ) years . ( x + 9 ) + 10 = 2 ( x - 10 ) = > x + 19 = 2 x - 20 = > x = 39 . answer : c\"" + }, + { + "Answer": 180, + "Options": "a ) 48 , b ) 54 , c ) 72 , d ) 84 , e ) 180", + "Correct": "e", + "Explanation": "\"let the second number be x . then , first number = 2 x and third number = 2 x / 3 . 2 x + x + 2 x / 3 = 660 11 x / 3 = 660 x = 180 answer : e\"" + }, + { + "Answer": 13, + "Options": "a ) 15 , b ) 13 , c ) 11 , d ) 14 , e ) 18", + "Correct": "b", + "Explanation": "when x is divided by 17 , the remainder is 3 : so , the possible values of x are : 3 , 20 , 37,54 , etc . when x is divided by 19 , the remainder is 1 : so , the possible values of x are : 1,20 . . . stop . since both lists include 20 , the smallest possible value of x is 20 . when y is divided by 14 , the remainder is 5 : so , the possible values of y are : 5 , 19 , 33,47 etc . when y is divided by 21 , the remainder is 12 : so , the possible values of y are : 12 , 33 , . . . stop . since both lists include 33 , the smallest possible value of y is 33 since the smallest possible values of x and y are 20 and 33 respectively , the smallest possible value of y - x is 13 . so , b is the correct answer to the original question ." + }, + { + "Answer": 96000, + "Options": "a ) rs . 32000 , b ) rs . 96000 , c ) rs . 128000 , d ) rs . 500000 , e ) none of these", + "Correct": "b", + "Explanation": "solution : let the number of passenger traveling by first class be x . then , number of passenger traveling by second class will be 4 x . but the fare is in the ratio 3 : 1 in other words , if 3 y fare is collected per i class passenger , y would be collected per ii class passenger . fares of i class passengers : fares of ii class passengers = x * 3 y : 4 x * y = 3 : 4 the above ratio can be interpreted as follows . if total fare is 3 + 4 = 7 , then i class passengers should pay rs . 3 similarly , we can calculate the fare of i class passengers when total was 224000 total fare i class fare 7 3 224000 ? = 224000 * ( 3 / 7 ) = rs . 96000 . answer : option b" + }, + { + "Answer": 570, + "Options": "a ) 550 , b ) 570 , c ) 590 , d ) 610 , e ) 630", + "Correct": "b", + "Explanation": "\"the number of seats in the theater is 12 + ( 12 + 2 ) + . . . + ( 12 + 36 ) = 19 ( 12 ) + 2 ( 1 + 2 + . . . + 18 ) = 19 ( 12 ) + 2 ( 18 ) ( 19 ) / 2 = 19 ( 12 + 18 ) = 19 ( 30 ) = 570 the answer is b .\"" + }, + { + "Answer": 77.12, + "Options": "a ) 68.8 , b ) 73.6 , c ) 75.2 , d ) 77.12 , e ) 81.6", + "Correct": "d", + "Explanation": "\"degree of difficulty of dive = 3.2 scores are 6.0 , 7.5 , 8.1 , 8.5 and 9.0 we can drop 6.0 and 9.0 sum of the remaining scores = ( 7.5 + 8.1 + 8.5 ) = 24 point of value of the dive = 24.1 * 3.2 = 77.12 answer d\"" + }, + { + "Answer": 37, + "Options": "a ) 15 , b ) 21 , c ) 37 , d ) 19 , e ) 21", + "Correct": "c", + "Explanation": "\"total money = rs . 10350 . let 50 rupees note was x . then 500 rupees note = 54 - x now , 50 * x + 500 * ( 54 - x ) = 10350 50 x + 27000 - 500 x = 10350 - 450 x = - 16650 x = 37 . no . of 50 rupees note = 37 . answer : option c\"" + }, + { + "Answer": 18, + "Options": "a ) 18 , b ) 30 , c ) 35 , d ) 40 , e ) 45", + "Correct": "a", + "Explanation": "\"lots of ways to tackle this . 15 % of 180 = 27 1 / 3 of 27 = 9 so , 1 / 3 less than 27 is equal to 27 - 9 = 18 answer : a\"" + }, + { + "Answer": 24, + "Options": "a ) $ 10 , b ) $ 12 , c ) $ 13.20 , d ) $ 15 , e ) $ 24", + "Correct": "e", + "Explanation": "\"3 j + 2 s = 69 2 j + 3 s = 86 - - - - - - - - - - - - - - - - 5 j + 5 s = 155 - - - - ( divide by 5 ) - - - > j + s = 31 3 j + 2 s = j + 2 ( j + s ) = j + 62 = 69 - - - > j = 7 3 * 7 + 2 s = 69 21 + 2 s = 69 2 s = 48 s = 24 answer : e\"" + }, + { + "Answer": 770.0000000000001, + "Options": "a ) $ 700 , b ) $ 754 , c ) $ 770 , d ) $ 782 , e ) $ 893", + "Correct": "c", + "Explanation": "official solution : ( c ) if bill \u2019 s salary increased by 16 % he would earn $ 812 . algebraically , this can be written as : $ 812 = 1.16 s , where s is his current salary . then s = $ 812 / 1.16 = $ 700 . now that we know his current salary is $ 700 , we can calculate what his salary would be if it were increased by 10 % . we know that 10 % of $ 700 is $ 70 , so his salary would be : r = $ 700 + $ 70 = $ 770 . the correct answer is choice ( c ) ." + }, + { + "Answer": 0.20000000000000107, + "Options": "a ) - 0.1 , b ) 0 , c ) 0.05 , d ) 0.2 , e ) 0.3", + "Correct": "d", + "Explanation": "to find x , we first sum a , b , and c , then round to the tenths place . 5.45 + 2.95 + 3.74 = 12.14 , which rounds to 12.2 . to find y , we first round a , b , and c to the tenths place and them sum them . so 5.4 + 2.9 + 3.7 = 12.0 . we are looking for y - x , which gives us 12.2 - 12.0 = 0.2 , or answer choice d ." + }, + { + "Answer": 0.23333333333333334, + "Options": "a ) 7 / 30 , b ) 11 / 30 , c ) 13 / 30 , d ) 17 / 30 , e ) none", + "Correct": "a", + "Explanation": "answer given exp . = [ ( 4 x 5 x 6 ) + ( 5 x 6 ) + ( 2 x 6 ) + ( 2 x 3 ) ] / [ ( 2 x 3 x 4 x 5 x 6 ) ] = 168 / ( 24 x 30 ) = 7 / 30 correct option : a" + }, + { + "Answer": 0.09523809523809523, + "Options": "a ) 2 / 21 , b ) 2 / 19 , c ) 1 / 11 , d ) 1 / 7 , e ) 1 / 5", + "Correct": "a", + "Explanation": "let d be the full distance . let x be the fraction of the distance that b runs . let v be the speed at which b runs . the time should be the same for both runners . time = d / ( 21 v / 19 ) = xd / v ( 19 / 21 ) * d / v = x * d / v x = 19 / 21 b should have a head start of 2 / 21 of the full distance . the answer is a ." + }, + { + "Answer": 5000, + "Options": "a ) 8500 , b ) 3500 , c ) 4500 , d ) 5000 , e ) 1500", + "Correct": "d", + "Explanation": "( a + b ) - ( b + c ) = 5000 a - c = 5000 answer : d" + }, + { + "Answer": 66.66666666666666, + "Options": "a ) 75.56 % , b ) 66.66 % , c ) 70.05 % , d ) 80 % , e ) 85 %", + "Correct": "b", + "Explanation": "excess of q ' s height over p = ( 40 / ( 100 - 40 ) ) * 100 = = > 66.66 % answer b" + }, + { + "Answer": 16, + "Options": "a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19", + "Correct": "b", + "Explanation": "\"let p be the number of participants . pc 2 = 120 ( p ) ( p - 1 ) = 240 = 16 * 15 p = 16 the answer is b .\"" + }, + { + "Answer": 100, + "Options": "a ) $ 140 , b ) $ 100 , c ) $ 220 , d ) $ 240 , e ) $ 260", + "Correct": "b", + "Explanation": "10 $ per week ! an year has 52 weeks . annual charges per year = 52 * 10 = 520 $ 30 $ per month ! an year has 12 months . annual charges per year = 12 * 35 = 420 $ 520 - 420 = 100 ans b" + }, + { + "Answer": 270, + "Options": "a ) 292 , b ) 270 , c ) 192 , d ) 144 , e ) 168", + "Correct": "b", + "Explanation": "let no of passengers in the beginning be x after first station no passengers = ( x - x / 3 ) + 280 = 2 x / 3 + 280 after second station no passengers = 1 / 2 ( 2 x / 3 + 280 ) + 12 1 / 2 ( 2 x / 3 + 280 ) + 12 = 242 2 x / 3 + 280 = 2 * 230 = 460 - 280 = 180 2 x / 3 = 180 x = 270 . so the answer is option b ) 270 ." + }, + { + "Answer": 8.333333333333334, + "Options": "a ) 10 gallons , b ) 8.5 gallons , c ) 8 gallons , d ) 8.33 gallons , e ) 9.33 gallons", + "Correct": "d", + "Explanation": "in 125 gallons of the solution there are 0.2 \u2217 125 = 25 gallons of water . we want to add w gallons of water to 125 gallons of solution so that 25 + w gallons of water to be 25 % of new solution : 25 + w = 0.25 ( 125 + w ) - - > w = 253 \u2248 8.33 . answer : d" + }, + { + "Answer": 1499.9999999999998, + "Options": "a ) 1200 , b ) 3000 , c ) 1000 , d ) 3600 , e ) 1500", + "Correct": "e", + "Explanation": "\"let the additional invested amount for 8 % interest be x ; equation will be ; 3000 + 0.05 * 3000 + x + 0.08 x = 3000 + x + 0.06 ( 3000 + x ) 0.05 * 3000 + 0.08 x = 0.06 x + 0.06 * 3000 0.02 x = 3000 ( 0.06 - 0.05 ) x = 3000 * 0.01 / 0.02 = 1500 ans : ` ` e ' '\"" + }, + { + "Answer": 4, + "Options": "a ) 4 , b ) 8 , c ) 9 , d ) 10 , e ) 12", + "Correct": "a", + "Explanation": "just looking at the question , ( x + 2 ) ( y + 3 ) could be even * even , odd * even , or even * odd in order for the whole expression to be even . however , just looking at 4 xy , since x * y will always be an integer , it will always be divisible by 4 . 4 divided by 4 is 1 , hence preserving x * y . answer : a . 4" + }, + { + "Answer": 30, + "Options": "a ) 8 , b ) 30 , c ) 3 , d ) 7 , e ) 10", + "Correct": "b", + "Explanation": "cost of each apple = 2 dollars apples that benny can buy with the amount she has = 360 / 2 = 180 . apples that each kid gets evenly = 180 / 6 = 30 apples . so the answer is b = 30" + }, + { + "Answer": 14999.999999999998, + "Options": "a ) 7787 , b ) 8000 , c ) 15000 , d ) 1277 , e ) 2081", + "Correct": "c", + "Explanation": "\"x * 112 / 100 * 88 / 100 = 14784 x * 0.9856 = 14784 x = 14784 / 0.9856 = > 15000 answer : c\"" + }, + { + "Answer": 4916, + "Options": "a ) 4016 , b ) 4076 , c ) 4816 , d ) 4916 , e ) 5916", + "Correct": "d", + "Explanation": "\"total sale for 5 months = rs . ( 5266 + 5744 + 5864 + 6122 + 6588 ) = rs . 29584 . required sale = rs . [ ( 5750 x 6 ) - 34500 ] = rs . ( 34500 - 29584 ) = rs . 4916 . answer : d\"" + }, + { + "Answer": 19000, + "Options": "a ) s . 43000 , b ) s . 19000 , c ) s . 57000 , d ) s . 60000 , e ) s . 62000", + "Correct": "b", + "Explanation": "\"length ( l ) = 20 m , breadth ( b ) = 15 m and height ( h ) = 5 m total area of the hall to be covered with mat = 2 ( lb + bh + hl ) = 2 ( 20 * 15 + 15 * 5 + 5 * 20 ) = 2 ( 300 + 75 + 100 ) = 2 * 475 = 950 sq . m total expenditure = 20 * 950 = rs . 19000 b\"" + }, + { + "Answer": 30, + "Options": "a ) 25 , b ) 27 , c ) 30 , d ) 35 , e ) 42", + "Correct": "c", + "Explanation": "\"average in 5 matches = ( 2 * 27 + 3 * 32 ) / 2 + 3 = 54 + 96 / 5 = 30 answer is c\"" + }, + { + "Answer": 52, + "Options": "a ) 52 , b ) 45 , c ) 65 , d ) 78 , e ) 64", + "Correct": "a", + "Explanation": "\"( x + x 1 + . . . x 14 ) / 15 = 40 52 option a\"" + }, + { + "Answer": 216, + "Options": "a ) 400 , b ) 1728 , c ) 108 , d ) 216 , e ) 432", + "Correct": "d", + "Explanation": "the number of ways u can chose two digits from 9 digits is 9 c 2 = ( 9 * 8 ) / 2 . and the no of ways u can arrange two digits like asked is 4 c 2 = ( 4 * 3 ) / 2 . total ways is 36 * 6 = 216 . answer : d" + }, + { + "Answer": 0.3, + "Options": "a ) 0.0003 , b ) 0.03 , c ) 0.3 , d ) 3 , e ) 30", + "Correct": "c", + "Explanation": "\"x = 0.009 / 0.03 = 0.3 answer : c\"" + }, + { + "Answer": 0.25, + "Options": "a ) 1 / 4 , b ) 1 / 8 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4", + "Correct": "a", + "Explanation": "\"for n ( n + 1 ) to be a multiple of 8 , either n or n + 1 has to be a multiple of 8 . thus n must be of the form 8 k or 8 k - 1 . the probability is 2 / 8 = 1 / 4 . the answer is a .\"" + }, + { + "Answer": 2, + "Options": "a ) 5 : 2 , b ) 5 : 1 , c ) 4 : 3 , d ) 2 : 1 , e ) 3 : 1", + "Correct": "d", + "Explanation": "\"we ' re given a few facts to work with : 1 ) the average height of the females is 170 cm 2 ) the average height of the males is 185 cm 3 ) the average of the group is 180 cm we ' re asked for the ratio of men to women . w = number of women m = number of men ( 170 w + 185 m ) / ( w + m ) = 180 170 w + 185 m = 180 w + 180 m 5 m = 10 w m = 2 w m / w = 2 / 1 the ratio of men to women is 2 to 1 . d\"" + }, + { + "Answer": 2520, + "Options": "a ) 560 , b ) 380 , c ) 900 , d ) 2560 , e ) 2520", + "Correct": "e", + "Explanation": "the integer should be divisible by : 5 , 6 , 7 , 89 , and 10 . the least common multiple of these integers is lcm = 420 . answer : 5 * 3 ^ 2 * 7 * 2 ^ 3 the answer is e )" + }, + { + "Answer": 180, + "Options": "a ) 120 , b ) 150 , c ) 180 , d ) 240 , e ) 600", + "Correct": "c", + "Explanation": "this question was n ' t particularly grueling , but i think it ' s the first where i had the opportunity to solve it via theory andinspectionthat many on this board suggest as strategy on the gmat . it actually came to me by accident . basically , if we thought that the 3 packets of powder were included in the 12 ounces of water , that would mean we would need 150 packets of smoothie mix ( along with 12 ( 150 ) ounces of water for a total of 150 packets . however , we know , after a more careful reading of the stimulus , that the 3 ounces are not included in the 12 ounces . as such , the answer has to be less than 150 packets , since 150 would be too much powder considering you already have 150 ( 12 ) ounces of water and need less packets than water to make a smoothie . as such , the only answer less than 150 is 120 , a . does this make sense ? or am i way off base ? c" + }, + { + "Answer": 6, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9", + "Correct": "c", + "Explanation": "sol . let the ten \u2019 s digit be x and unit \u2019 s digit be y , then , ( 10 x + y ) - ( 10 y + x ) = 54 \u21d4 9 ( x - y ) = 54 \u21d4 x - y = 6 answer c" + }, + { + "Answer": 4991, + "Options": "a ) 4857 , b ) 4184 , c ) 4012 , d ) 4991 , e ) 5291", + "Correct": "d", + "Explanation": "\"let the sale in the sixth month = x then ( 6435 + 6927 + 6855 + 7230 + 6562 + x ) / 6 = 6500 = > 6435 + 6927 + 6855 + 7230 + 6562 + x = 6 \u00d7 6500 = > 34009 + x = 39000 = > x = 39000 \u2212 34009 = 4991 answer : d\"" + }, + { + "Answer": 400.00000000000034, + "Options": "a ) 220 , b ) 400 , c ) 500 , d ) 560 , e ) 590", + "Correct": "b", + "Explanation": "\"n * 50 = ( 320000 - 300000 ) = 20000 n = 20000 / 50 = 400 b\"" + }, + { + "Answer": 88, + "Options": "a ) 88 , b ) 56 , c ) 89 , d ) 86 , e ) 96", + "Correct": "a", + "Explanation": "\"explanation : in this type of question , its obvious we need to calculate the hcf , trick is hcf of ( 3815 - 31 ) and ( 4521 - 33 ) = hcf ( 3784 , 4488 ) = 88 option a\"" + }, + { + "Answer": 98910, + "Options": "a ) 897 , b ) 98,910 , c ) 64,749 , d ) 49,700 , e ) 56,720", + "Correct": "b", + "Explanation": "find the number , upon sum of 3 digits of a number gives a reminder 2 when it is divided by 5 seeing the options after dividing and finding the reminder of 2 my answer was b" + }, + { + "Answer": 45, + "Options": "a ) 40 , b ) 45 , c ) 27 , d ) 28 , e ) 22", + "Correct": "b", + "Explanation": "\"let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 70 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 70 + 20 ) / 2 = 45 . answer : b\"" + }, + { + "Answer": 3, + "Options": "a ) 3 , b ) 8 , c ) 9 , d ) 10 , e ) 11", + "Correct": "a", + "Explanation": "expanding we have 6 x ^ 2 - 21 x + 4 x - 14 6 x ^ 2 - 17 x - 14 taking coefficients , a = 6 , k = - 17 , n = - 14 therefore a - n + k = 6 - ( - 14 ) - 17 = 20 - 17 = 3 the answer is a ." + }, + { + "Answer": 13, + "Options": "a ) 2 , b ) 7 , c ) 11 , d ) 13 , e ) 17", + "Correct": "d", + "Explanation": "\"f ( 28 ) = 2 * 4 * 6 * 8 * 10 * 12 * 14 * 16 * 18 * 20 * 22 * 24 * 26 * 28 the greatest prime factor in this list is 13 . the answer is d .\"" + }, + { + "Answer": 16, + "Options": "a ) 11 . , b ) 12 . , c ) 13 . , d ) 14 . , e ) 16", + "Correct": "e", + "Explanation": "\"price of candy before price increase = 15 / 1.25 = 12 price of soda before price increase = 6 / 1.5 = 4 total price = 12 + 4 = 16 e is the answer\"" + }, + { + "Answer": 71.71428571428571, + "Options": "a ) 73.41 , b ) 72.28 , c ) 72.43 , d ) 73.43 , e ) can not be determined", + "Correct": "b", + "Explanation": "\"total marks = 35 x 72 = 2520 corrected total marks = 2520 - 46 + 56 = 2530 correct average = 2530 / 35 = 72.28 answer : b\"" + }, + { + "Answer": 2184, + "Options": "a ) 1888 , b ) 2999 , c ) 2834 , d ) 2777 , e ) 2184", + "Correct": "e", + "Explanation": "\"let the total number of votes polled in the election be 100 k . number of valid votes = 100 k - 20 % ( 100 k ) = 80 k let the number of votes polled in favour of a and b be a and b respectively . a - b = 15 % ( 100 k ) = > a = b + 15 k = > a + b = b + 15 k + b now , 2 b + 15 k = 80 k and hence b = 32.5 k it is given that 100 k = 6720 32.5 k = 32.5 k / 100 k * 6720 = 2184 the number of valid votes polled in favour of b is 2184 . answer : e\"" + }, + { + "Answer": 32, + "Options": "a ) 30 , b ) 20 , c ) 35 , d ) 32 , e ) 40", + "Correct": "d", + "Explanation": "let average is x 100 x + 400 = 5400 x = 50 let the number of student joined is y ( 100 + y ) * ( 50 - 10 ) = 5400 y = 35 answer : d" + }, + { + "Answer": 23, + "Options": "a ) 36 , b ) 39 , c ) 23 , d ) 45 , e ) none of the above", + "Correct": "c", + "Explanation": "\"let the average after 17 th inning = x . then , average after 16 th inning = ( x \u2013 4 ) . \u2234 16 ( x \u2013 4 ) + 87 = 17 x or x = ( 87 \u2013 64 ) = 23 . answer c\"" + }, + { + "Answer": 3, + "Options": "a ) 0 , b ) 1 , c ) 3 , d ) 4 , e ) 6", + "Correct": "c", + "Explanation": "\"i tried plugging in numbers x = 9 q + 5 x = 14 6 x = 84 6 x / 9 = 9 * 9 + 3 remainder is 3 . answer is c .\"" + }, + { + "Answer": 0.3, + "Options": "a ) 3 / 10 , b ) 3 / 20 , c ) 2 / 5 , d ) 1 / 2 , e ) 1 / 3", + "Correct": "a", + "Explanation": "s = { 1 , 23 , \u2026 . 20 } e = { 3 , 6 , 912 , 1518 } p ( e ) = 6 / 20 = 3 / 10 option a" + }, + { + "Answer": 74, + "Options": "a ) 74 kg , b ) 77 kg , c ) 76.5 kg , d ) data inadequate , e ) none of these", + "Correct": "a", + "Explanation": "\"total weight increases = 6 \u00d7 1.5 = 9 kg so the weight of new person = 65 + 9 = 74 kg answer a\"" + }, + { + "Answer": 234, + "Options": "a ) 234 , b ) 116 , c ) 117 , d ) 118 , e ) 119", + "Correct": "a", + "Explanation": "\"x : y : z = 100 : 45 : 50 20 : 9 : 10 9 - - - 54 39 - - - ? = > 234 answer : a\"" + }, + { + "Answer": 78.4, + "Options": "a ) 78.4 , b ) 91.0 , c ) 88.0 , d ) 70.4 , e ) 71.2", + "Correct": "a", + "Explanation": "\"12 % of 70 = ( 70 * 0.11 ) = 8.4 12 % greater than 70 = 70 + 8.4 = 78.4 answer is clearly a .\"" + }, + { + "Answer": 26, + "Options": "a ) 26 years , b ) 18 years , c ) 20 years , d ) 22 years , e ) none", + "Correct": "a", + "Explanation": "\"solution let the son ' s present age be x years . then , man ' s present age = ( x + 28 ) years . then \u00e2 \u20ac \u00b9 = \u00e2 \u20ac \u00ba ( x + 28 ) + 2 = 2 ( x + 2 ) \u00e2 \u20ac \u00b9 = \u00e2 \u20ac \u00ba x + 30 = 2 x + 4 x = 26 . answer a\"" + }, + { + "Answer": 0.5333333333333333, + "Options": "a ) 3 / 2 , b ) 3 / 4 , c ) 8 / 15 , d ) 1 / 2 , e ) 1 / 5", + "Correct": "c", + "Explanation": "\"let team b has 8 agents , so team a has 5 agents let each agent of team b picked up 5 calls , so total calls by team b = 40 so , each agent in team a picked up 7 calls , so total calls for team a = 35 fraction for team b = 40 / ( 40 + 35 ) = 8 / 15 = answer = c\"" + }, + { + "Answer": 0.9523809523809523, + "Options": "a ) 26 / 21 , b ) 28 / 21 , c ) 20 / 21 , d ) 40 / 21 , e ) 60 / 21", + "Correct": "c", + "Explanation": "\"say x = y = 10 . in this case we would have : 20 x = 200 black - and - white films ; 4 y = 40 color films . y / x % = 10 / 10 % = 1 % of the black - and - white films , so 2 black - and - white films and all 40 color films , thus total of 42 films were selected . color films thus compose 40 / 42 = 20 / 21 of the selected films . answer : c\"" + }, + { + "Answer": 18, + "Options": "a ) 16 , b ) 12 , c ) 18 , d ) 22 , e ) 08", + "Correct": "c", + "Explanation": "2 * 9 = 18 . answer is c ." + }, + { + "Answer": 23, + "Options": "a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25", + "Correct": "c", + "Explanation": "the nubmer which when divided by 7 leaves remainder 1 should be of the form 7 k + 1 this number when divided by 3 leaves remainder 2 . so , ( 7 k + 1 ) - 2 should be divisible by 3 or 7 k - 1 should be divisible by 3 . we now put the values of k starting from 0 to find first number divisible by 3 we find 1 st number at k = 1 thus smallest number will be 7 ( 1 ) + 1 = 8 now , next number will be = 8 + lcm of 37 i . e 29 now we will find number of all such values less than 500 by using the formula for last term of an a . p 8 + ( n - 1 ) 21 = 400 n = 23.42 or n = 23 answer : - c" + }, + { + "Answer": 33.0625, + "Options": "a ) 33.06 , b ) 34.1 , c ) 34.2 , d ) 24.6 , e ) none of these", + "Correct": "a", + "Explanation": "explanation : increase in the price of sugar = ( 12 + 3 ) = 15 % hence , price of the sugar on jan 1 , 1996 = > ( 25 * 115 * 115 ) / ( 100 * 100 ) = rs 33.06 . answer : a" + }, + { + "Answer": 75, + "Options": "a ) 50 , b ) 55 , c ) 60 , d ) 65 , e ) 75", + "Correct": "e", + "Explanation": "explanation : total weight increased is 3 * 10 = 30 . so weight of new person is 45 + 30 = 75 answer : option e" + }, + { + "Answer": 75, + "Options": "a ) 53 % , b ) 58 % , c ) 62.5 % , d ) 64 % , e ) 75 %", + "Correct": "e", + "Explanation": "\"last year revenue = 100 ( assume ) ; this year revenue = 90 ; projected revenue = 120 . actual / projected * 100 = 90 / 120 * 100 = 75 % . answer : e .\"" + }, + { + "Answer": 1733.3333333333333, + "Options": "a ) 1000 , b ) 1250 , c ) 1733.33 , d ) 1800 , e ) 2025", + "Correct": "c", + "Explanation": "300 gallons of water increases capacity by 30 % that means 30 % is 300 gallons , so 100 % would be = 300 * 100 / 30 = 1000 gallons now 1000 + 300 gallons is 75 % capacity of tank . so 100 % capacity would be = 1300 * 100 / 75 = 1733.33 c is the answer" + }, + { + "Answer": 37.5, + "Options": "a ) 37.9 , b ) 37.53 , c ) 37.5 , d ) 37.1 , e ) 37.4", + "Correct": "c", + "Explanation": "explanation : average speed = ( 2 xy ) / ( x + y ) km / hr = ( 2 * 50 * 30 ) / ( 50 + 30 ) km / hr . 37.5 km / hr . answer : c" + }, + { + "Answer": 6250, + "Options": "a ) 13000 , b ) 6250 , c ) 10000 , d ) 5000 , e ) none of these", + "Correct": "b", + "Explanation": "\"explanation : profit = 5 , 00,000 \u00e2 \u02c6 \u2019 ( 1 , 50,000 + 75,000 ) = rs . 2 , 75,000 . since , such loom contributes equally to sales and manufacturing expenses . but the monthly charges are fixed at rs 75,000 . if one loan breaks down sales and expenses will decrease . new profit : - = > 500000 \u00e3 \u2014 ( 55 / 56 ) \u00e2 \u02c6 \u2019 150000 \u00e3 \u2014 ( 55 / 56 ) \u00e2 \u02c6 \u2019 75000 . = > rs 2 , 68,750 decrease in profit = > 2 , 75,000 \u00e2 \u02c6 \u2019 2 , 68,750 = > rs . 6,250 answer : b\"" + }, + { + "Answer": 51.1875, + "Options": "a ) 60 - 65 , b ) 55 - 58 , c ) 51 - 59 , d ) 39 - 41 , e ) 38 - 40", + "Correct": "c", + "Explanation": "\"5 % ( 48.75 ) = 2.4375 20 % ( 48.75 ) = 9.75 total amount could have been 48.75 + 2.4375 and 48.75 + 9.75 = > could have been between 51.1875 and 58.5 = > approximately between 51 and 59 answer is c .\"" + }, + { + "Answer": 22, + "Options": "a ) 20 . , b ) 21 . , c ) 22 . , d ) 23 . , e ) 24 .", + "Correct": "c", + "Explanation": "\"before solving it algebraically , let us prime factorize 1430 = 2 * 5 * 11 * 13 . since number of apples per person * total persons f = 1430 , the answer should be a factor of 1430 . only c is . and that ' s your answer . c\"" + }, + { + "Answer": 32, + "Options": "a ) 87 , b ) 98 , c ) 32 , d ) 28 , e ) 37", + "Correct": "c", + "Explanation": "\"20 + 28 + 8 * 2 = 64 / 2 = 32 answer : c\"" + }, + { + "Answer": 24, + "Options": "a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25", + "Correct": "d", + "Explanation": "let the average age of the whole team be x years . 11 x - ( 27 + 30 ) = 9 ( x - 1 ) 11 x - 9 x = 48 2 x = 48 x = 24 . the average age of the team is 24 years . the answer is d ." + }, + { + "Answer": 3, + "Options": "a ) 12 , b ) 7 , c ) 9 , d ) 15 , e ) 3", + "Correct": "e", + "Explanation": "150 / 50 = 3 the answer is e ." + }, + { + "Answer": 144, + "Options": "a ) 2134 , b ) 2234 , c ) 2540 , d ) 2560 , e ) 144", + "Correct": "e", + "Explanation": "\"144 e\"" + }, + { + "Answer": 3, + "Options": "a ) - 5 , b ) - 4 , c ) 4 , d ) 3 , e ) 2", + "Correct": "d", + "Explanation": "\"1 . subtract 1 from both sides : x + 1 - 1 = 4 - 1 2 . simplify both sides : x = 3 d\"" + }, + { + "Answer": 1650, + "Options": "a ) 1650 , b ) 1324 , c ) 1245 , d ) 1300 , e ) 1635", + "Correct": "a", + "Explanation": "\"let the smaller number be x . then larger number = ( x + 1325 ) . x + 1325 = 5 x + 5 4 x = 1320 x = 330 large number = 330 + 1320 = 1650 answer : a\"" + }, + { + "Answer": 55, + "Options": "a ) 55 , b ) 42 , c ) 43 , d ) 44 , e ) 45", + "Correct": "a", + "Explanation": "\"n ( n - 1 ) / 2 = 11 * 10 / 2 = 55 answer : a\"" + }, + { + "Answer": 1000, + "Options": "a ) 220 , b ) 230 , c ) 500 , d ) 560 , e ) 1000", + "Correct": "e", + "Explanation": "\"n * 50 = ( 350000 - 300000 ) = 50000 n = 50000 / 50 = 1000 e\"" + }, + { + "Answer": 680, + "Options": "a ) 188 , b ) 216 , c ) 156 , d ) 680 , e ) 121", + "Correct": "d", + "Explanation": "\"25 % of x = x / 4 ; 20 % of 1000 = 20 / 100 * 1000 = 200 given that , x / 4 = 200 - 30 = > x / 4 = 170 = > x = 680 . answer : d\"" + }, + { + "Answer": 33, + "Options": "a ) 31 , b ) 32 , c ) 33 , d ) 34 , e ) 35", + "Correct": "c", + "Explanation": "\"14 x + 75 = 15 ( x + 3 ) x = 30 + 3 = 33 answer : c\"" + }, + { + "Answer": 1050, + "Options": "a ) 1050 , b ) 2770 , c ) 1550 , d ) 5102 , e ) 5000", + "Correct": "a", + "Explanation": "\"10 * 150 = 1500 3 * 100 + 1 * 150 = 450 1500 \u2013 450 = 1050 answer : a\"" + }, + { + "Answer": 6.5, + "Options": "a ) 8.5 , b ) 6.5 , c ) 5.5 , d ) 5.6 , e ) 4.4", + "Correct": "b", + "Explanation": "\"100 * 100 = 10000 85 * 110 = 9350 - - - - - - - - - - - 10000 - - - - - - - - - - - 650 100 - - - - - - - - - - - ? = > 6.5 % decrease answer : b\"" + }, + { + "Answer": 5.75, + "Options": "a ) $ 0.00 , b ) $ 5.75 , c ) $ 3.40 , d ) $ 5.00 , e ) $ 6.80", + "Correct": "b", + "Explanation": "\"0.85 * { original price } = $ 78.2 - - > { original price } = $ 92 . { final price } = $ 78.2 * 1.25 = $ 97.75 . the difference = $ 97.75 - $ 92 = $ 5.75 answer : b .\"" + }, + { + "Answer": 44, + "Options": "a ) 32 % , b ) 35 % , c ) 38 % , d ) 41 % , e ) 44 %", + "Correct": "e", + "Explanation": "\"the amount of chemical x in the solution is 20 + 0.3 ( 80 ) = 44 liters . 44 liters / 100 liters = 44 % the answer is e .\"" + }, + { + "Answer": 22.5, + "Options": "a ) 20.5 % , b ) 22.5 % , c ) 21.5 % , d ) 10.5 % , e ) 32.5 %", + "Correct": "b", + "Explanation": "\"total honda brand red cars = 90 / 100 * 500 = 450 total red cars = 60 / 100 * 900 = 540 no . of non - honda cars = 900 - 500 = 400 no . of non - honda red cars = 540 - 450 = 90 % of non - honda red cars = 90 / 400 * 100 = 22.5 % answer : b\"" + }, + { + "Answer": 10080, + "Options": "a ) 1080 , b ) 10080 , c ) 10025 , d ) 11080 , e ) 12080", + "Correct": "b", + "Explanation": "lcm = 180 180 ) 10000 ( 55 9900 - - - - - - - - - 100 10000 + 180 - 100 = 10080 answer : b" + }, + { + "Answer": 25, + "Options": "a ) 19 , b ) 21 , c ) 23 , d ) 25 , e ) 27", + "Correct": "d", + "Explanation": "\"let x be the correct sums and ( 30 - x ) be the incorrect sums . 3 x - 2 ( 30 - x ) = 65 5 x = 125 x = 25 the answer is d .\"" + }, + { + "Answer": 71, + "Options": "a ) 71 kg , b ) 77 kg , c ) 76.5 kg , d ) data inadequate , e ) none of these", + "Correct": "a", + "Explanation": "\"total weight increases = 4 \u00d7 1.5 = 6 kg so the weight of new person = 65 + 6 = 71 kg answer a\"" + }, + { + "Answer": 1100, + "Options": "a ) a ) 200 , b ) b ) 2000 , c ) c ) 800 , d ) d ) 2100 , e ) e ) 1100", + "Correct": "e", + "Explanation": "the total of ten numbers = 10 x 210 = 2100 the total of first 5 and last 4 numbers is = 5 x 40 + 4 x 200 = 1000 so , the middle number is ( 2100 - 1000 ) = 1100 e" + }, + { + "Answer": 15, + "Options": "a ) 11 , b ) 15 , c ) 12 , d ) 17 , e ) 19", + "Correct": "b", + "Explanation": "b 15 ( x + y ) \u00e2 \u20ac \u201c ( y + z ) = 15 x \u00e2 \u20ac \u201c z = 15" + }, + { + "Answer": 174.5, + "Options": "a ) 174.5 , b ) 173.5 , c ) 172.5 , d ) 171.5 , e ) 170.5", + "Correct": "a", + "Explanation": "\"the total height was 15 cm too much . the average height should be reduced by 15 cm / 30 = 0.5 cm the answer is a .\"" + }, + { + "Answer": 328, + "Options": "a ) 328 , b ) 262 , c ) 72 , d ) 205 , e ) 267", + "Correct": "a", + "Explanation": "a : b : c = 100 : 65 : 40 = 20 : 13 : 8 8 - - - - 64 41 - - - - ? = > rs . 328 answer : a" + }, + { + "Answer": 1481, + "Options": "a ) 1361 , b ) 1481 , c ) 1601 , d ) 1721 , e ) 1841", + "Correct": "b", + "Explanation": "\"x = 60 + 61 + . . . + 80 = 21 ( 70 ) = 1470 y = 11 x + y = 1481 the answer is b .\"" + }, + { + "Answer": 10, + "Options": "a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25", + "Correct": "b", + "Explanation": "let the quantity of alcohol and water be 2 x and 5 x 2 x / ( 5 x + 10 ) = 2 / 7 20 x = 4 ( 3 x + 5 ) x = 5 quantity of alcohol = 2 * 5 = 10 liters . answer is b" + }, + { + "Answer": 500, + "Options": "a ) 100 , b ) 200 , c ) 500 , d ) 1000 , e ) 5000", + "Correct": "c", + "Explanation": "5.4 * 10 ^ 6 / 10800 = = > 54 * 10 ^ 3 / 108 = = > 54000 / 108 = 500 answer : c" + }, + { + "Answer": 88.8, + "Options": "a ) 88.8 , b ) 91.0 , c ) 88.0 , d ) 70.9 , e ) 71.2", + "Correct": "a", + "Explanation": "\"11 % of 80 = ( 80 * 0.11 ) = 8.8 11 % greater than 80 = 80 + 8.8 = 88.8 answer is clearly a .\"" + }, + { + "Answer": 314.15, + "Options": "a ) $ 314.16 , b ) $ 314.17 , c ) $ 314.18 , d ) $ 314.19 , e ) $ 314.20", + "Correct": "a", + "Explanation": "\"if the last three digits of a whole number are divisible by 8 , then the entire number is divisible by 8 the last 3 digit 412 not divisible by a hence , we need to add 4 to this number for it to be divisible by 8 correct option : a\"" + }, + { + "Answer": 0.75, + "Options": "a ) 3 / 4 , b ) 1 / 4 , c ) 1 / 2 , d ) 1 , e ) none of them", + "Correct": "a", + "Explanation": "\"let the original fraction be x / y . then ( 115 % of x ) / ( 92 % of y ) = 15 / 16 = > ( 115 x / 92 y ) = 15 / 16 = ( ( 15 / 16 ) * ( 92 / 115 ) ) = 3 / 4 answer is a .\"" + }, + { + "Answer": 60, + "Options": "a ) 55 % , b ) 60 % , c ) 50 % , d ) 45 % , e ) 66 %", + "Correct": "b", + "Explanation": "\"i just wanted to mention a couple of things here : * this is a pure ratio question ; the number 2,500 is completely irrelevant , and you can ignore it if you like . when we increase something by 1 / 5 , we are multiplying it by 1 + 1 / 5 = 6 / 5 , so the answer here must be ( 1 / 2 ) * ( 6 / 5 ) = 3 / 5 = 60 % . answer : b\"" + }, + { + "Answer": 442, + "Options": "a ) a ) 442 , b ) b ) 490 , c ) c ) 380 , d ) d ) 450 , e ) e ) 690", + "Correct": "a", + "Explanation": "the only thing you have to do is a simple multiply we have : 17 * 26 = 442 correct answer is : a ) 442" + }, + { + "Answer": 65, + "Options": "a ) 86 , b ) 16 , c ) 76 , d ) 65 , e ) 26", + "Correct": "d", + "Explanation": "given m + p + c = 85 * 3 = 255 - - - ( 1 ) m + p = 90 * 2 = 180 - - - ( 2 ) p + c = 70 * 2 = 140 - - - ( 3 ) where m , p and c are marks obtained by the student in mathematics , physics and chemistry . p = ( 2 ) + ( 3 ) - ( 1 ) = 180 + 140 - 255 = 65 answer : d" + }, + { + "Answer": 10, + "Options": "a ) 10 % , b ) 12 % , c ) 14 % , d ) 16 % , e ) 18 %", + "Correct": "a", + "Explanation": "\"let ' s say there is a total of 100 students at this college . 40 percent of the total number of students are freshmen . # of freshmen = 40 % of 100 = 40 50 percent of the fresh - men are enrolled in the school of liberal arts . . . number of liberal arts freshmen = 50 % of 40 = 20 . . . and , of these , 50 percent are psychology majors . . . number of liberal arts freshmen who are psychology majors = 50 % of 20 = 10 what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts ? 10 / 100 = 10 % answer : a\"" + }, + { + "Answer": 3451.2195121951218, + "Options": "a ) 3451.21 , b ) 3029.0 , c ) 2993.03 , d ) 2984.36 , e ) none of these", + "Correct": "a", + "Explanation": "explanation : given exp . = 3500 - ( ( 1000 \u00f7 2050 ) * 100 ) = 3451.21 answer a" + }, + { + "Answer": 5, + "Options": "a ) 6 , b ) 8 , c ) 10 , d ) 5 , e ) 13", + "Correct": "d", + "Explanation": "\"joan starts off with 100 $ . . which is to be tripled every month her monthly payments look like this : 100 , 300 , 900 , 2700 . . . . . . . . . upto 12100 this can be re written as : 100 x 1 , 100 x 3 , 100 x 9 , 100 x 27 . . . . . . 100 x 121 so we have 1 , 3 , 9 , 27 . . . . . 12100 in gp we know that a = 1 , and r = 3 ( its easy to figure it out by looking at the question , but regardless of it being mentioned in the question we can still compute the value of r using the formula tn = a 3 ^ n - 1 . . . ) therefore to find the sum of n terms of a gp we use this formula : sn = a ( 1 - r ^ n ) / 1 - r 121 = 1 - 3 ^ n / 1 - 3 ; 1 - 3 ^ n / - 2 cross multiplying we get 121 x - 2 = 1 - 3 ^ n - 242 = 1 - 3 ^ n - 243 = - 3 ^ n 243 = 3 ^ n ( negatives cancel out ) 243 can also be re written as 3 ^ 5 therefore ; 3 ^ 5 = 3 ^ n thus n = 5 ( d )\"" + }, + { + "Answer": 355, + "Options": "a ) q = 350 , b ) q = 353 , c ) q = 354 , d ) q = 356 , e ) 357", + "Correct": "b", + "Explanation": "focus on the points where the number of digits q in squares change : 1 , 2 , 3 - single digit squares . first 2 digit number is 10 . 4 , 5 , . . . 9 - two digit squares . to get 9 , the last number with two digit square , think that first 3 digit number is 100 which is 10 ^ 2 . so 9 ^ 2 must be the last 2 digit square . 10 , 11 , 12 , . . . 31 - three digit squares . to get 31 , think of 1000 - the first 4 digit number . it is not a perfect square but 900 is 30 ^ 2 . 32 ^ 2 = 2 ^ 10 = 1024 , the first 4 digit square . 32 - 99 - four digit squares . to get 99 , think of 10000 - the first 5 digit number which is 100 ^ 2 . so number of digits in s ( 99 ) = 3 * 1 + 6 * 2 + 22 * 3 + 68 * 4 = 3 + 12 + 66 + 272 = 353 . b" + }, + { + "Answer": 181, + "Options": "a ) 178.27 cm , b ) 181.29 cm , c ) 978.29 cm , d ) 178.89 cm , e ) 176.29 cm", + "Correct": "b", + "Explanation": "\"calculated average height of 35 boys = 183 cm . wrong total height of 35 boys = 183 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 183 cm - ( 166 cm - 106 cm ) / 35 = 183 cm - 60 / 35 cm = 183 cm - 1.71 cm = 181.29 cm . answer : b\"" + }, + { + "Answer": 66, + "Options": "a ) 22 , b ) 77 , c ) 29 , d ) 66 , e ) 21", + "Correct": "d", + "Explanation": "\"65 + 5 * 12 / ( 180 / 3 ) = 65 + 5 * 12 / ( 60 ) = 65 + ( 5 * 12 ) / 60 = 65 + 1 = 66 . answer : d\"" + }, + { + "Answer": 2, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "a", + "Explanation": "\u201c in the county of veenapaniville , there are a total of 50 high schools , of three kinds : 25 public schools , 16 parochial schools , and 9 private independent schools . \u201d \u201c district a has 18 high schools total . \u201d \u201c district b has 17 high schools total , and only two of those are private independent schools . \u201d \u201c district c has an equal number of each of the three kinds of schools . \u201d hmm . that \u2019 s not a simple number . let \u2019 s put that on hold for a moment . so far , from the matrix it looks like we could figure out the missing number in the \u201c totals \u201d row . that number must be 15 , because 18 + 17 + 15 = 50 . now , go back to that last fact : \u201c district c has an equal number of each of the three kinds of schools . \u201d now that makes sense . district c has 15 schools , so it must have 5 of each kind : the question is asking : \u201c how many private independent schools are there in district a ? \u201d well , now that \u2019 s just a matter of adding across the \u201c private independent \u201d row . we know 2 + 2 + 5 = 9 , so the missing number must be 2 . there \u2019 s still a good deal of information we can \u2019 t figure out from the information given in the question , but we are able to answer the specific question asked here . there are 2 private independent schools in district a , so the answer = ( a ) ." + }, + { + "Answer": 3, + "Options": "a ) 10.6 kg , b ) 3 kg , c ) 11 kg , d ) 14.9 kg , e ) none", + "Correct": "b", + "Explanation": "\"answer weight of new student = total weight of all 20 students - total weight of initial 19 students = ( 20 x 14.4 - 19 x 15 ) kg = 3 kg . correct option : b\"" + }, + { + "Answer": 14.5, + "Options": "a ) 10.5 % , b ) 11.5 % , c ) 12.5 % , d ) 13.5 % , e ) 14.5 %", + "Correct": "e", + "Explanation": "quantity x rate = price 1 x 1 = 1 0.9 x 0.95 = 0.855 decrease in price = ( 0.145 / 1 ) \u00e3 \u2014 100 = 14.5 % answer = option e" + }, + { + "Answer": 74.99999999999997, + "Options": "a ) 92 , b ) 90 , c ) 82 , d ) 78 , e ) 75", + "Correct": "e", + "Explanation": "i get 75 . a cube with 1 million liters cube would be a cube with the dimensions of 100 * 100 * 100 . 4 * 2 covers 8 sq liters so 100 / 8 = 12.5 . r = 12.5 * 6 = 75 . e" + }, + { + "Answer": 259200, + "Options": "a ) 32,300 , b ) 172,800 , c ) 468,830 , d ) 338,200 , e ) 259,200", + "Correct": "e", + "Explanation": "\"every 2 seconds , 6 persons are added ( 7 - 1 ) . every second 3 persons are added . in a day 24 hrs = 24 * 60 minutes = 24 * 60 * 60 = 86400 seconds . 86400 * 3 = 259200 option e\"" + }, + { + "Answer": 6, + "Options": "a ) 7.9 s , b ) 6 s , c ) 7.5 s , d ) 7.6 s , e ) 7.4 s", + "Correct": "b", + "Explanation": "\"explanation : 90 km / hr = 90 * 5 / 18 = 25 m / s speed = distance / time ; v = d / t 25 = 150 / t t = 6 s answer : b\"" + }, + { + "Answer": 260, + "Options": "a ) 260 , b ) 620 , c ) 500 , d ) 520 , e ) 720", + "Correct": "a", + "Explanation": "\"let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 130 ) = 2 + 2 ( extra ) = > 2 x - 260 = x = > x = 260 . answer : a\"" + }, + { + "Answer": 3.333333333333333, + "Options": "a ) 5 / 2 , b ) 7 / 4 , c ) 8 / 5 , d ) 10 / 3 , e ) 12 / 5", + "Correct": "d", + "Explanation": "the time it takes printer x is 16 hours . the combined rate of y and z is 1 / 12 + 1 / 8 = 5 / 24 the time it takes y and z is 24 / 5 the ratio of times is 16 / ( 24 / 5 ) = 5 * 16 / 24 = 10 / 3 the answer is d ." + }, + { + "Answer": 5, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5", + "Correct": "e", + "Explanation": "unit digit in 15 ^ 100 = unit digit in [ ( 15 ^ 4 ) ^ 25 ] but unit digit in 15 ^ 4 = 5 unit digit 15 ^ 100 = 5 answer is e" + }, + { + "Answer": 180, + "Options": "a ) 180 , b ) 227 , c ) 268 , d ) 198 , e ) 176", + "Correct": "a", + "Explanation": "12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 12 / 29 * 435 = 180 answer : a" + }, + { + "Answer": 20, + "Options": "a ) 25 , b ) 35 , c ) 45 , d ) 55 , e ) 20", + "Correct": "e", + "Explanation": "assume total distance = 100 miles time taken for 80 miles = 80 / 80 = 1 hour time taken for the rest of the 20 miles = 20 / v hours . average speed = 50 therefore the total time needed = 2 hours . 2 = 1 + 20 / v hence v = 20 mph answer : e" + }, + { + "Answer": 64, + "Options": "a ) 18 , b ) 55 , c ) 63 , d ) 64 , e ) 70", + "Correct": "d", + "Explanation": "current age of the guy = a years . then , 8 ( a + 8 ) \u2013 8 ( a \u2013 8 ) = a ( 8 a + 64 ) \u2013 ( 8 a \u2013 64 ) = a a = 128 / 2 = 64 d" + }, + { + "Answer": 71.25, + "Options": "a ) 71.25 , b ) 52.9 , c ) 52.1 , d ) 52.3 , e ) 42.5", + "Correct": "a", + "Explanation": "\"sum of the marks for the class of 30 students = 30 * 40 = 1200 sum of the marks for the class of 50 students = 50 * 90 = 4500 sum of the marks for the class of 80 students = 1200 + 4500 = 5700 average marks of all the students = 5700 / 80 = 71.25 answer : a\"" + }, + { + "Answer": 900, + "Options": "a ) 600 , b ) 900 , c ) 1500 , d ) 1600 , e ) 1750", + "Correct": "b", + "Explanation": "\"sugar : flour = 3 : 8 = 15 : 40 ; flour : soda = 10 : 1 = 40 : 4 ; thus we have that sugar : flour : soda = 15 x : 40 x : 4 x . also given that 40 x / ( 4 x + 60 ) = 8 / 1 - - > x = 60 - - > sugar = 15 x = 900 . answer : b .\"" + }, + { + "Answer": 36, + "Options": "a ) 36 , b ) 38 , c ) 33 , d ) 32 , e ) 38", + "Correct": "a", + "Explanation": "j = 18 ; j = 2 b ; b = 18 / 2 = 9 ; twice as old so b = 9 ( now ) + ( 9 ) = 18 ; jacob is 18 + 18 = 36 answer : a" + }, + { + "Answer": 14100, + "Options": "a ) rs . 16003 , b ) rs . 16029 , c ) rs . 11288 , d ) rs . 14100 , e ) rs . 16011", + "Correct": "d", + "Explanation": "\"explanation : manager ' s monthly salary rs . ( 2100 * 21 - 1500 * 20 ) = rs . 14100 . answer : d\"" + }, + { + "Answer": 6, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "e", + "Explanation": "the ratio 1 : 2 : 3 represents 1 cup strawberries : 2 cups raspberries : 3 cups blueberries . 1 + 2 + 3 = 6 6 cups will be used for the pie . the answer is e" + }, + { + "Answer": 133, + "Options": "a ) 179 , b ) 208 , c ) 210 , d ) 133 , e ) 229", + "Correct": "d", + "Explanation": "\"explanation : total runs scored by the batsman = 58 * 46 = 2668 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2668 \u2013 2552 = 116 runs . let the highest score be x , hence the lowest score = x \u2013 150 x + ( x - 150 ) = 116 2 x = 266 x = 133 runs answer d\"" + }, + { + "Answer": 4000, + "Options": "a ) rs . 4007 , b ) rs . 4000 , c ) rs . 4028 , d ) rs . 4050 , e ) rs . 4032", + "Correct": "b", + "Explanation": "\"let p , q and r represent their respective monthly incomes . then , we have : p + q = ( 5050 * 2 ) = 10100 - - - ( i ) q + r = ( 6250 * 2 ) = 12500 - - - ( ii ) p + r = ( 5200 * 2 ) = 10400 - - - ( iii ) adding ( i ) , ( ii ) and ( iii ) , we get : 2 ( p + q + r ) = 33000 = p + q + r = 16500 - - - ( iv ) subtracting ( ii ) from ( iv ) , we get , p = 4000 . p ' s monthly income = rs . 4000 . answer : b\"" + }, + { + "Answer": 8400, + "Options": "a ) rs . 7000 , b ) rs . 8400 , c ) rs . 8500 , d ) rs . 9000 , e ) none", + "Correct": "b", + "Explanation": "\"answer average salary = 10000 + 5000 + 11000 + 7000 + 9000 / 5 = rs . 8400 correct option : b\"" + }, + { + "Answer": 724827405, + "Options": "a ) 724533811 , b ) 353654655 , c ) 545463251 , d ) 725117481 , e ) 477899932", + "Correct": "d", + "Explanation": "\"72519 x 9999 = 72519 x ( 10000 - 1 ) = 72519 x 10000 - 72519 x 1 = 725190000 - 72519 = 725117481 d\"" + }, + { + "Answer": 64, + "Options": "a ) 64 , b ) 130 , c ) 140 , d ) 160 , e ) 120", + "Correct": "a", + "Explanation": "\"white : yellow = x : ( x + 20 ) = 8 : 13 - - > 13 x = 8 x + 160 - - > x = 32 . the total # of balls originally x + x = 32 + 32 = 64 . answer : a .\"" + }, + { + "Answer": 25.75, + "Options": "a ) 22 , b ) 23 , c ) 24 , d ) 25 , e ) 26", + "Correct": "e", + "Explanation": "\"x + ( x + 3 ) + ( x + 6 ) + ( x + 7 ) = 120 4 x + 16 = 120 4 x = 104 x = 26 the answer is e .\"" + }, + { + "Answer": 180, + "Options": "a ) $ 120 , b ) $ 180 , c ) $ 310 , d ) $ 450 , e ) $ 640", + "Correct": "b", + "Explanation": "\"the volume of each box is 20 * 20 * 12 = 4800 cubic inches . number of boxes = 2 , 160,000 / 4800 = 450 boxes total cost = 450 \u00d7 $ 0.4 = $ 180 the answer is b .\"" + }, + { + "Answer": 91.42857142857143, + "Options": "a ) 91.4 kgs , b ) 88.5 kgs , c ) 86.5 kgs , d ) 67.5 kgs , e ) 88.2 kgs", + "Correct": "a", + "Explanation": "average weight = [ ( a + b + c + ( a + b ) + ( b + c ) + ( c + a ) + ( a + b + c ) ] / 7 = 4 ( a + b + c ) / 7 = 4 x 160 / 7 = 91.4 kgs answer : a" + }, + { + "Answer": 144, + "Options": "a ) 216 , b ) 180 , c ) 144 , d ) 108 , e ) 72", + "Correct": "c", + "Explanation": "\"there are several ways to find the least common multiple of two numbers . in this case , the most efficient method is to use the greatest common factor : ( a * b ) / ( gcf ab ) = lcm ab the greatest common factor of 12 and 16 is 4 . so , 12 # 16 = 12 * 16 / 4 = 48 . the greatest common factor of 18 and 24 is 6 . so , 18 # 24 = 18 * 24 / 6 = 72 finally , the greatest common factor of 48 and 72 is 24 . so , t = ( ( 12 # 16 ) # ( 18 # 24 ) ) = 48 # 72 = ( 48 * 72 ) / 24 = 2 * 72 = 144 the correct answer is c .\"" + }, + { + "Answer": 84, + "Options": "a ) $ 80 , b ) $ 81 , c ) $ 82 , d ) $ 83 , e ) $ 84", + "Correct": "e", + "Explanation": "let t be the total amount of money spent . 6 * 11 + ( t / 7 + 6 ) = t 72 = 6 t / 7 t = ( 7 * 72 ) / 6 = 84 the answer is e ." + }, + { + "Answer": 50, + "Options": "a ) 40 , b ) 50 , c ) 62 , d ) 45 , e ) 56", + "Correct": "b", + "Explanation": "\"let the average after 11 th inning = x then , average after 10 th inning = x - 5 10 ( x - 5 ) + 100 = 11 x x = 100 - 50 = 50 answer is b\"" + }, + { + "Answer": 5, + "Options": "a ) 10 , b ) 4 , c ) 21 , d ) 3 , e ) 5", + "Correct": "e", + "Explanation": "( 7 + 3 ) / 2 = 5 the correct answer is e" + }, + { + "Answer": 34.9, + "Options": "a ) 30 , b ) 25.4 , c ) 40 , d ) 35.25 , e ) 26.55", + "Correct": "d", + "Explanation": "\"explanation : correct sum = ( 36 * 20 + 25 - 40 ) = 705 correct mean = = 705 / 20 = 35.25 answer : d\"" + }, + { + "Answer": 80, + "Options": "a ) 75 kg , b ) 55 kg , c ) 45 kg , d ) 80 kg , e ) 25 kg", + "Correct": "d", + "Explanation": "\"explanation : total weight increased = ( 6 x 2.5 ) kg = 15 kg . weight of new person = ( 65 + 15 ) kg = 80 kg . answer : d\"" + }, + { + "Answer": 3.3333333333333335, + "Options": "a ) 1.26 , b ) 2.54 , c ) 5.23 , d ) 4.23 , e ) 3.33", + "Correct": "e", + "Explanation": "for the total revenue to remain the same when the price is 3 / 10 , the number of products sold must 3 / 10 times . therefore increase in the number of products sold is 100 % = > the required ratio = 100 % / 30 % = 3.33 answer : e" + }, + { + "Answer": 28.000000000000004, + "Options": "a ) 14 % , b ) 25 % , c ) 28 % , d ) 34 % , e ) 50 %", + "Correct": "c", + "Explanation": "\"mixture contains 4 gallons of grape juice out of 40 gallons after addition : 14 gallons of grape juice out of 50 gallons = = > 28 % answer c\"" + }, + { + "Answer": 155, + "Options": "a ) 155 , b ) 195 , c ) 200 , d ) 205 , e ) 210", + "Correct": "a", + "Explanation": "\"this question can be solved with the average formula and ' bunching . ' we ' re asked for the average of all of the multiples of 10 from 10 to 300 , inclusive . to start , we can figure out the total number of terms rather easily : 1 ( 10 ) = 10 2 ( 10 ) = 20 . . . 30 ( 10 ) = 300 so we know that there are 30 total numbers . we can now figure out the sum of those numbers with ' bunching ' : 10 + 300 = 310 20 + 290 = 310 30 + 280 = 310 etc . since there are 30 total terms , this pattern will create 15 ' pairs ' of 310 . thus , since the average = ( sum of terms ) / ( number of terms ) , we have . . . ( 15 ) ( 310 ) / ( 30 ) = 155 answer : a\"" + }, + { + "Answer": 1.2, + "Options": "a ) 1.12 , b ) 1.25 , c ) 1.20 , d ) 1.3 , e ) none", + "Correct": "c", + "Explanation": "\"sol . ( x \u00d7 5 ) = ( 0.75 \u00d7 8 ) \u21d2 x = 6 / 5 = 1.20 . answer c\"" + }, + { + "Answer": 7, + "Options": "a ) 3 : 2 , b ) 4 : 3 , c ) 5 : 1 , d ) 6 : 5 , e ) 7 : 1", + "Correct": "e", + "Explanation": "( x + y ) / ( x - y ) = 4 / 3 dividing numerator and denominator by y ( x / y ) + 1 / ( x / y ) - 1 = 4 / 3 let x / y be z z + 1 / z - 1 = 4 / 3 3 z + 3 = 4 z - 4 z = 7 x / y = 7 answer e" + }, + { + "Answer": 13.999928000575995, + "Options": "a ) 14 , b ) 44 , c ) 48 , d ) 50 , e ) 56", + "Correct": "a", + "Explanation": "let the capacity of the can be t litres . quantity of milk in the mixture before adding milk = 1 / 6 ( t - 2 ) after adding milk , quantity of milk in the mixture = 2 / 7 t . 2 t / 7 - 2 = 1 / 6 ( t - 2 ) 5 t = 84 - 14 = > t = 14 . answer : a" + }, + { + "Answer": 7, + "Options": "a ) 16.2 , b ) 7 , c ) 5 , d ) 500 , e ) none", + "Correct": "b", + "Explanation": "\"answer let 45 x a = ( 35 x 900 ) / 100 \u2234 a = ( 35 x 9 ) / 45 = 7 correct option : b\"" + }, + { + "Answer": 65, + "Options": "a ) 60 , b ) 62 , c ) 64 , d ) 65 , e ) 66", + "Correct": "d", + "Explanation": "\"sum of the deviations of the numbers in the set from the mean is always zero 54 , 55 , 57 , 58 , 59 , 62 , 62 , 63 , 65 mean is 60 so the list is - 6 - 5 - 3 - 2 - 1 + 2 + 2 + 3 + 5 . . . this shud total to zero but this is - 5 , hence we need a number that is 5 more than the mean to get a + 5 and make it zero hence the answer is 60 + 5 = 65 d\"" + }, + { + "Answer": 40, + "Options": "a ) 18 , b ) 21 , c ) 38 , d ) 40 , e ) 57", + "Correct": "d", + "Explanation": "\"5 / 6 * p have horseshoes , so p is a multiple of 6 . 2 / 3 * 5 / 6 * p = 5 / 9 * p are icelandic ponies with horseshoes , so p is a multiple of 9 . the minimum value of p is 18 . then h = p + 4 = 22 . the minimum number of horses and ponies is 40 . the answer is d .\"" + }, + { + "Answer": 6, + "Options": "a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8", + "Correct": "c", + "Explanation": "\"explanation : on dividing 427398 by 14 we get the remainder 6 , so 6 should be subtracted answer : option c\"" + }, + { + "Answer": 42, + "Options": "a ) 87 , b ) 42 , c ) 78 , d ) 76 , e ) 26", + "Correct": "b", + "Explanation": "5 x 6 x 2 x 50 25 100 250 x + 150 x + 200 x = 4200 600 x = 4200 x = 7 = > 6 x = 42 answer : b" + }, + { + "Answer": 35.064935064935064, + "Options": "a ) 20 % , b ) 24 % , c ) 30 % , d ) 35 % , e ) 79 %", + "Correct": "d", + "Explanation": "\"take it as original output = 100 . to meet demand increase by 10 % , then output = 110 . to meet holiday demand , new output increase by 40 % then output equals 154 to restore new holidy demand output to original 100 . final - initial / final * 100 = 54 / 154 * 100 = 35 % approxiamately . option d is correct .\"" + }, + { + "Answer": 1176, + "Options": "a ) 1176 , b ) 2209 , c ) 2878 , d ) 1210 , e ) 1560", + "Correct": "a", + "Explanation": "as expected , this question boils down to 2 equation , consider total number of balls in triangle = t and number of balls in last row = x . 1 + 2 + 3 + . . . + x = t x ( x + 1 ) / 2 = t - - - - ( a ) as mentioned in the question , side of a square will be ( x - 8 ) and total number of balls in square will be ( t + 424 ) ( x - 8 ) ^ 2 = t + 424 - - - - - ( b ) now the hardest part of the question will be to solve these 2 equations and this looks like time consuming but the easy way will be plug and play . also , we ' ve to find a value of t ( from 5 optiosn given below ) which can make a square of a a number . one we know this , it will be a cake walk . we can see that option a fits this criteria in eq ( b ) . add - 1176 + 424 = 1600 = 40 ^ 2 = ( x - 8 ) ^ 2 hence , x = 48 . cross check by putting in eq ( a ) = x ( x + 1 ) / 2 = t = > 48 * 49 / 2 = 1176 hence , answer is a ." + }, + { + "Answer": 36.75, + "Options": "a ) $ 2.10 , b ) $ 36.75 , c ) $ 37.16 , d ) $ 38.10 , e ) $ 38.80", + "Correct": "b", + "Explanation": "\"principal that is amount taken by laura at year beginning = 35 $ rate of interest = 5 % interest = ( 5 / 100 ) * 35 = 1.75 $ total amount that laura owes a year later = 35 + 1.75 = 36.75 $ answer b\"" + }, + { + "Answer": 42, + "Options": "a ) 25 , b ) 31 , c ) 27 , d ) 29 , e ) 42", + "Correct": "e", + "Explanation": "\"let the average after 17 innings = x total runs scored in 17 innings = 17 x average after 16 innings = ( x - 3 ) total runs scored in 16 innings = 16 ( x - 3 ) total runs scored in 16 innings + 90 = total runs scored in 17 innings = > 16 ( x - 3 ) + 90 = 17 x = > 16 x - 48 + 90 = 17 x = > x = 42 answer is e .\"" + }, + { + "Answer": 22, + "Options": "a ) 20 years , b ) 21 years , c ) 22 years , d ) 23 years , e ) 24 years", + "Correct": "c", + "Explanation": "\"explanation : let the average age of the whole team by x years . 11 x \u00e2 \u20ac \u201c ( 25 + 28 ) = 9 ( x - 1 ) 11 x \u00e2 \u20ac \u201c 9 x = 44 2 x = 44 x = 22 . so , average age of the team is 22 years . answer c\"" + }, + { + "Answer": 0.6, + "Options": "a ) $ 0.15 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.6", + "Correct": "e", + "Explanation": "\"on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.9 = 3 * x - - > x = $ 0.6 . answer : e .\"" + }, + { + "Answer": 20.666666666666668, + "Options": "a ) 30 , b ) 25 , c ) 20.67 , d ) 12.33 , e ) 19.48", + "Correct": "c", + "Explanation": "\"let the actual distance traveled is ' x ' km then by given conditions , we have x / 10 = ( x + 31 ) / 25 25 x = 10 x + 310 x = 20.67 km ans - c\"" + }, + { + "Answer": 1080, + "Options": "a ) 100 , b ) 1000 , c ) 1080 , d ) 1020 , e ) 1200", + "Correct": "c", + "Explanation": "\"0.9 * 600 = 0.5 * x x = 9 / 5 * 600 = 1080\"" + }, + { + "Answer": 15, + "Options": "a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 15", + "Correct": "e", + "Explanation": "\"ifno caris selected more than once then the number of clients = 15 / 3 = 5 but since every car is being selected three times so no . of clients must be thrice as well = 5 * 3 = 15 answer : option e\"" + }, + { + "Answer": 0.008416666666666666, + "Options": "a ) 0.008416667 , b ) 0.110773333 , c ) 0.12526234 , d ) 0.01072333 , e ) 0.12725002", + "Correct": "a", + "Explanation": "\"25.25 / 3000 = 2525 / 300000 = 0.008416667 answer : a\"" + }, + { + "Answer": 54, + "Options": "a ) 15 , b ) 30 , c ) 31 , d ) 33 , e ) 54", + "Correct": "e", + "Explanation": "\"we have to find the number of terms that are divisible by 2 but not by 6 ( as the question asks for the even numbers only which are not divisible by 3 ) for 2 , 10 , 12,14 . . . 170 using ap formula , we can say 170 = 10 + ( n - 1 ) * 2 or n = 81 . for 6 , 12,18 , . . . 168 using ap formula , we can say 168 = 12 + ( n - 1 ) * 6 or n = 27 . hence , only divisible by 2 but not 3 = 81 - 27 = 54 . hence , answer e\"" + }, + { + "Answer": 50.000000000001066, + "Options": "a ) 96 , b ) 75 , c ) 50 , d ) 25 , e ) 12", + "Correct": "c", + "Explanation": "\"by the definition of a remainder , the remainder here is equal to 8 / y . the remainder in decimal form is given as . 16 therefore , 8 / y = . 16 solve for y and get 50 . c\"" + }, + { + "Answer": 140.33333333333334, + "Options": "a ) 151 , b ) 140.33 , c ) 152 , d ) 148 , e ) none of the above", + "Correct": "b", + "Explanation": "\"corrected mean = 140 \u00d7 30 \u2212 135 + 145 / 30 = 4200 \u2212 135 + 145 / 30 = 4210 / 30 = 140.33 answer b\"" + }, + { + "Answer": 525, + "Options": "a ) 250 , b ) 350 , c ) 450 , d ) 550 , e ) 525", + "Correct": "e", + "Explanation": "\"the number of chocolate bars is equal to 21 * 25 = 525 correct answer e\"" + }, + { + "Answer": 24, + "Options": "a ) 23 years , b ) 22 years , c ) 24 years , d ) 20 years , e ) 19 years", + "Correct": "c", + "Explanation": "\"let present age of the son = x years then , present age the man = ( x + 26 ) years given that , in 2 years , man ' s age will be twice the age of his son \u00e2 \u2021 \u2019 ( x + 26 ) + 2 = 2 ( x + 2 ) \u00e2 \u2021 \u2019 x = 24 answer : c\"" + }, + { + "Answer": 0.45, + "Options": "a ) 1 / 15 , b ) 1 / 5 , c ) 9 / 20 , d ) 1 / 3 , e ) 2 / 5", + "Correct": "c", + "Explanation": "\"tot students = x 1 st year student = x / 2 - - - - > non majaor = 4 / 5 ( x / 2 ) - - - - - > maj = 1 / 5 ( x / 2 ) 2 nd year student = x / 2 - - - - > maj = 1 / 2 ( 1 / 5 ( x / 2 ) ) = 1 / 20 ( x ) - - - > non major = x / 2 - 1 / 20 ( x ) = 9 / 20 ( x ) hence 9 / 20 c\"" + }, + { + "Answer": 86, + "Options": "a ) 86 , b ) 38 , c ) 62 , d ) 122 , e ) 672", + "Correct": "a", + "Explanation": "factorise 1419 . . 3 * 11 * 43 . . so n has to be a multiple of largest prime number , 61 . . so n = 2 * 43 = 86 . . ans : a" + }, + { + "Answer": 92, + "Options": "a ) 104 , b ) 60 , c ) 92 , d ) 50 , e ) 25", + "Correct": "c", + "Explanation": "\"f ( x ) = 2 x ^ 2 + y f ( 2 ) = 50 = > 2 * ( 2 ) ^ 2 + y = 50 = > 8 + y = 50 = > y = 42 f ( 5 ) = 2 * ( 5 ) ^ 2 + 42 = 92 answer c\"" + }, + { + "Answer": 37.50819672131148, + "Options": "a ) 4 , b ) 33.8 , c ) 10 , d ) 30 , e ) 37.3", + "Correct": "e", + "Explanation": "annual increase is ( 500 + 30.5 - 12.6 ) * 6 = 3107.4 hence every year there is an increase of 107.4 for his saving to double he needs additional $ 4000 therefore $ 4000 / 107.4 = 37.3 correct option is e ) 37.3" + }, + { + "Answer": 14, + "Options": "a ) 7 , b ) 10 , c ) 12 , d ) 13 , e ) 14", + "Correct": "e", + "Explanation": "hi - the questions says | y | < = 13 so the values of y will range from 0 to 13 . so the values of y will be 0,1 , 2,3 , 4,5 , 6,7 , 8,9 , 10,11 , 12,13 . so 14 ( e ) is the answer . remember sign does n ' t matter for y as y will always be positive ." + }, + { + "Answer": 0.631578947368421, + "Options": "a ) 1 / 4 , b ) 3 / 4 , c ) 10 / 19 , d ) 11 / 19 , e ) 12 / 19", + "Correct": "e", + "Explanation": "saving = s , expenditure = e , income = i at the end of 12 months ; 12 s = 7 e = 7 ( i - s ) = > 19 s = 7 i = > savings = 7 / 19 i hence expenditure = 1 - ( 7 / 19 ) = 12 / 19 answer ( e )" + }, + { + "Answer": 32.625, + "Options": "a ) 26 , b ) 40 , c ) 29.25 , d ) 32.625 , e ) none of the above", + "Correct": "d", + "Explanation": "let the average expenditure of all the ninte be x then , 3 \u00d7 8 + x + 5 = 9 x \u21d2 x = 3.625 \u2234 total money spent = 9 x = 9 \u00d7 3.625 = 32.625 answer d" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 2 / 5 , c ) 1 / 2 , d ) 2 / 3 , e ) 6 / 5", + "Correct": "a", + "Explanation": "\"say , the tree grows by x feet every year . then , 4 + 6 x = ( 1 + 1 / 4 ) ( 4 + 4 x ) or , x = 1 answer a\"" + }, + { + "Answer": 724827405, + "Options": "a ) 233243413 , b ) 354545451 , c ) 343435451 , d ) 565656767 , e ) 725117481", + "Correct": "e", + "Explanation": "\"72519 x 9999 = 72519 x ( 10000 - 1 ) = 72519 x 10000 - 72519 x 1 = 725190000 - 72519 = 725117481 e\"" + }, + { + "Answer": 72000, + "Options": "a ) 81000 , b ) 85000 , c ) 75000 , d ) 72000 , e ) 77000", + "Correct": "d", + "Explanation": "let savings in national savings certificate = x and savings in public provident fund = ( 180000 - x ) 1 / 3 x = 1 / 2 ( 180000 \u2212 x ) \u21d2 2 x = 3 ( 180000 \u2212 x ) \u21d2 2 x = 540000 \u2212 3 x \u21d2 5 x = 540000 \u21d2 x = 540000 / 5 = 108000 savings in public provident fund = ( 180000 - 108000 ) = 72000 answer is d ." + }, + { + "Answer": 41, + "Options": "a ) 35 , b ) 37 , c ) 39 , d ) 41 , e ) 42", + "Correct": "d", + "Explanation": "\"explanation : let b ' s age = x years . then , as age = ( x + 11 ) years . ( x + 11 + 10 ) = 2 ( x \u2014 10 ) hence x = 41 . present age of b = 41 years answer : option d\"" + }, + { + "Answer": 17, + "Options": "a ) 19 , b ) 18 , c ) 16 , d ) 11 , e ) 17", + "Correct": "e", + "Explanation": "\"sum of 16 even numbers = 16 * 17 = 272 average = 272 / 16 = 17 answer : e\"" + }, + { + "Answer": 70, + "Options": "a ) 35 , b ) 48 , c ) 69 , d ) 70 , e ) 74", + "Correct": "d", + "Explanation": "5 * a 1 + 7 * b 1 = g 5 * a 2 + 7 * b 2 = g 5 * ( a 1 - a 2 ) = 7 * ( b 2 - b 1 ) since we are dealing with integers we can assume that a 1 - a 2 = 7 * q and b 2 - b 1 = 5 * q where q is integer , so whenever we get a pair for ( a ; b ) we can find another one by simply adding 7 to a and subtracting 5 from b or vice versa , subtracting 7 from a and adding 5 to b . lets check how it works for our numbers , starting from the largest : e ) 74 = 5 * 12 + 7 * 2 ( a 1 = 12 , b 1 = 2 ) , subtract 7 from a and add 5 to b respectively , so a 2 = 5 and b 2 = 7 , second pair - bad d ) 70 = 5 * 7 + 7 * 5 ( a 1 = 7 , b 1 = 5 ) , if we add 7 to a we will have to subtract 5 from b but b ca n ' t be 0 , so - no pair , if we subtract 7 from a , we ' ll get a = 0 which also is n ' t allowed - no pair , thus this is the only pair for ( a ; b ) that works , good ! , thus d is the answer" + }, + { + "Answer": 0.8999999999999999, + "Options": "a ) 0.0009 , b ) 0.09 , c ) 0.9 , d ) 9 , e ) 90", + "Correct": "c", + "Explanation": "\"x = 0.009 / 0.01 = 0.9 answer : c\"" + }, + { + "Answer": 75.6, + "Options": "a ) 76.5 , b ) 75.6 , c ) 73.5 , d ) 79 , e ) 77", + "Correct": "b", + "Explanation": "\"mean = ( sum of all no . in series ) / ( no . in series ) m 1 = 67 = ( x + 28 + 70 + 88 + 104 ) / ( 5 ) 67 x 5 = 290 + x x = 45 therefore mean of 2 nd series m 2 = ( x + 50 + 62 + 97 + 124 ) / 5 m 2 = 75.6 answer = b\"" + }, + { + "Answer": 48.53, + "Options": "a ) $ 30.14 , b ) 48.53 , c ) 34.66 , d ) 32.29 , e ) 33.16", + "Correct": "b", + "Explanation": "\"211 * 15 = 3165 / 100 = 31.65 211 + 31.65 = 242.65 242.65 / 5 = 48.53 answer : b\"" + }, + { + "Answer": 15.199999999999992, + "Options": "a ) 15.2 % , b ) 16.0 % , c ) 20.0 % , d ) 23.2 % , e ) 24.8 %", + "Correct": "a", + "Explanation": "y = 100 ( start with yy , it makes getting x easier ) . x = y * 1.2 = 120 z = y / 1.2 = 83.33 w = x * 0.8 = 96 then for the answer : ( w - z ) / z = ( 96 - 83.33 ) / 83.33 = 15.2 % answer : a" + }, + { + "Answer": 68, + "Options": "a ) 68 , b ) 70 , c ) 72 , d ) 74 , e ) 76", + "Correct": "a", + "Explanation": "\"k - 32 = 9 t / 5 k = 9 t / 5 + 32 k = 9 ( 20 ) / 5 + 32 = 68 the answer is a .\"" + }, + { + "Answer": 37, + "Options": "a ) 31 , b ) 33 , c ) 35 , d ) 37 , e ) 39", + "Correct": "d", + "Explanation": "\"the first number is 22 = 16 + 6 ( 1 ) . we can continue adding 6 to make a list : 22 , 28 , 34 , . . . the last number is 238 = 16 + 6 ( 37 ) there are 37 numbers in the list . the answer is d .\"" + }, + { + "Answer": 3.75, + "Options": "a ) $ 1.25 , b ) $ 2.50 , c ) $ 3.75 , d ) $ 4.70 , e ) $ 8.20", + "Correct": "c", + "Explanation": "let x be the cost of a bus ride . x + ( x + 235 ) = 985 2 x = 750 x = $ 3.75 the answer is c ." + }, + { + "Answer": 72, + "Options": "a ) 56 , b ) 60 , c ) 64 , d ) 68 , e ) 72", + "Correct": "e", + "Explanation": "\"let c be the capacity of the can . ( 5 / 8 ) * ( c - 8 ) + 8 = ( 2 / 3 ) * c 15 c - 120 + 192 = 16 c c = 72 the answer is e .\"" + }, + { + "Answer": 4, + "Options": "a ) 4 , b ) 6 , c ) 7 , d ) 8 , e ) 9", + "Correct": "a", + "Explanation": "division of total distance traveled will be 16 + 16 + 8 + 4 + 2 ans : a" + }, + { + "Answer": 30, + "Options": "a ) a ) 4.8 , b ) b ) 48 , c ) c ) 30 , d ) d ) 68 , e ) e ) 48", + "Correct": "c", + "Explanation": "explanation : 58164 / x = 1938.8 = > x = 58164 / 1938.8 = 30 answer : option c" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 8 , c ) 7 , d ) 6 , e ) 2", + "Correct": "a", + "Explanation": "6 * 22 = 132 7 * 19 = 133 - - - - - - - - - - - - - - 1 . answer : a" + }, + { + "Answer": 3700, + "Options": "a ) s . 3700 , b ) s . 4570 , c ) s . 4500 , d ) s . 4550 , e ) s . 2500", + "Correct": "a", + "Explanation": "\"sum of the salaries of the person for the months of january , february , march and april = 4 * 8000 = 32000 - - - - ( 1 ) sum of the salaries of the person for the months of february , march , april and may = 4 * 8700 = 34800 - - - - ( 2 ) ( 2 ) - ( 1 ) i . e . may - jan = 2800 salary of may is rs . 6500 salary of january = rs . 3700 answer : a\"" + }, + { + "Answer": 30, + "Options": "a ) 50 km , b ) 40 km , c ) 30 km , d ) 20 km , e ) none of these", + "Correct": "c", + "Explanation": "explanation : the actual distance jogged be d . = > d / 12 = ( d + 10 ) / 16 = > 16 d = 12 d + 120 = > 4 d = 120 = > d = 30 answer : c" + }, + { + "Answer": 11, + "Options": "a ) 10 , b ) 8 , c ) 9 , d ) 5 , e ) 11", + "Correct": "e", + "Explanation": "\"let possible value of x is 109 least possible value of x / 14 is 109 / 14 = > 7 quotient with remainder 11 thus answer is ( e ) 11\"" + }, + { + "Answer": 62.5, + "Options": "a ) 53 % , b ) 58 % , c ) 62.5 % , d ) 64 % , e ) 75 %", + "Correct": "c", + "Explanation": "\"last year revenue = 100 ( assume ) ; this year revenue = 75 ; projected revenue = 120 . actual / projected * 100 = 75 / 120 * 100 = 62.5 % . answer : c\"" + }, + { + "Answer": 720, + "Options": "a ) $ 24 million , b ) $ 120 million , c ) $ 644 million , d ) $ 540 million , e ) $ 720 million", + "Correct": "e", + "Explanation": "\"convert units to millions as answer is in millions 1996 imports = $ 1.44 bill = $ 1440 mill i . e . 1440 / 12 = $ 120 mill / month 1997 imports = $ 360 mill / 2 month i . e . $ 180 mill / month difference / month = 180 - 120 = 60 difference / year = $ 60 mill * 12 = $ 720 mill answer : e\"" + }, + { + "Answer": 34, + "Options": "a ) 20 , b ) 10 , c ) 34 , d ) 40 , e ) 5", + "Correct": "c", + "Explanation": "\"arithmetic mean expression for p and q : ( p + q ) / 2 = 10 ; p + q = 20 - - - - eq 1 arithmetic mean expression for q and r : ( q + r ) / 2 = 20 ; q + r = 54 - - - - eq 2 subtracting eq 1 from eq 2 we get : r - p = 34 hence , the correct answer is c\"" + }, + { + "Answer": 16, + "Options": "a ) 10 , b ) 16 , c ) 12 , d ) 14 , e ) 19", + "Correct": "b", + "Explanation": "\"we know that : x > 1 , y > 1 , and x + 3 y < 960 , and it is given that length means no of factors . for any value of x and y , the max no of factors can be obtained only if factor is smallest no all factors are equal . hence , lets start with smallest no 2 . 2 ^ 1 = 2 2 ^ 2 = 4 2 ^ 3 = 8 2 ^ 4 = 16 2 ^ 5 = 32 2 ^ 6 = 64 2 ^ 7 = 128 2 ^ 8 = 256 2 ^ 9 = 512 2 ^ 10 = 1024 ( it exceeds 960 , so , x ca n ' t be 2 ^ 10 ) so , max value that x can take is 2 ^ 9 , for which has length of integer is 9 . now , since x = 512 , x + 3 y < 960 so , 3 y < 448 = = > y < 448 / 3 so , y can take any value which is less than 448 / 3 . and to get the maximum no of factors of smallest integer , we can say y = 2 ^ 7 for 2 ^ 7 has length of integer is 7 . so , combined together : 9 + 7 = 16 . b\"" + }, + { + "Answer": 7, + "Options": "a ) 7 , b ) 9 , c ) 15 , d ) 25 , e ) 63", + "Correct": "a", + "Explanation": "\"perfect square , is just an integer that can be written as the square of some other integer . for example 16 = 4 ^ 2 , is a perfect square . now , 1575 = 3 ^ 2 * 5 ^ 2 * 7 , so if k = 7 then 1575 k = ( 3 * 5 * 7 ) ^ 2 , which is a perfect square ( basically the least positive value of k must complete only the power of 7 to even power as powers of other primes are already even ) . answer : a .\"" + }, + { + "Answer": 280, + "Options": "a ) $ 380 , b ) $ 540 , c ) $ 280 , d ) $ 1380 , e ) $ 1430", + "Correct": "c", + "Explanation": "difficulty level : 600 each month ' s budget = 12600 / 12 = 1050 budget for 6 months = 6 * 1050 = 6300 actual amount spent = 6580 amount spent over the budget = 6580 - 6300 = 280 answer ( c ) , regards ," + }, + { + "Answer": 40, + "Options": "a ) 9 , b ) 14 , c ) 28 , d ) 40 , e ) 60", + "Correct": "d", + "Explanation": "let the total weight be x . sand content = ( 1 / 4 ) x water content = ( 2 / 5 ) x gravel = x - ( 1 / 4 ) x - ( 2 / 5 ) x = ( 7 / 20 ) x = 14 x = 40 then answer will be d = 40" + }, + { + "Answer": 50, + "Options": "a ) 50 , b ) 18 , c ) 16 , d ) 12 , e ) 8", + "Correct": "a", + "Explanation": "\"6 machines do x units in 10 days we have x / 10 = > rate of the 6 machines we know that we need to have 5 x units in 6 days therefore , we need to get to 5 x / 6 rate of the machines . rate of one machine is x / 10 * 1 / 6 = x / 60 . now , we need to know how many machines need to work simultaneously , to get 5 x done in 6 days . 5 x / 6 work needs to be done by machines that work at x / 60 rate . let ' s assign a constant y for the number of machines : ( x / 60 ) * y = 5 x / 6 y = 5 x / 6 * 60 / x cancel 6 with 60 , and x with x and get - > 50 . answer choice a\"" + }, + { + "Answer": 1280, + "Options": "a ) 1287 , b ) 1285 , c ) 1283 , d ) 1280 , e ) 1281", + "Correct": "d", + "Explanation": "\"trees increase by 1 / 4 the number of trees in preceding year . hence , correct answer must be divisible by 4 . based on divisibility rules , if last 2 digits are divisible by 4 then the number is divisible by 4 . thus , we can eliminate a , b , c , e the answer to be d again , trees increase by 1 / 4 the number of trees in preceding year . hence , the number of trees increase by 5 / 4 times the number of trees the preceding year . if x = initial number of trees = 1280 year 1 = 5 / 4 x year 2 = ( 5 / 4 ) ( 5 / 4 ) x year 3 = ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) x year 4 = ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) x only for answer d : ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) 1280 = 3125 hence , correct answer = d\"" + }, + { + "Answer": 420, + "Options": "a ) rs . 480 , b ) rs . 520 , c ) rs . 420 , d ) rs . 460 , e ) none of these", + "Correct": "c", + "Explanation": "let d be the average daily expenditure original expenditure = 35 \u00d7 d new expenditure = 35 \u00d7 d + 42 new average expenditure will be : ( 35 \u00d7 d + 42 ) / 42 = d - 1 on solving , we get d = 12 therefore original expenditure = 35 \u00d7 12 = 420 answer : c" + }, + { + "Answer": 8, + "Options": "a ) 6 , b ) 8 , c ) 11 , d ) 12 , e ) 13", + "Correct": "b", + "Explanation": "let the number of donkeys be x and the number of pigs be y . then , 4 x + 2 y = 2 ( x + y ) = 16 or 2 x + ( 2 x + 2 y ) = ( 2 x + 2 y ) + 16 or 2 x = 16 or x = 8 . answer : b" + }, + { + "Answer": 8.333333333333334, + "Options": "a ) 10 glas , b ) 8.5 gals , c ) 8 gals , d ) 6.66 gals , e ) 8.33 gals", + "Correct": "e", + "Explanation": "\"in 125 gallons of the solution there are 0.2 \u2217 125 = 250 gallons of water . we want to add ww gallons of water to 125 gallons of solution so that 25 + w gallons of water to be 25 % of new solution : 25 + w = 0.25 ( 125 + w ) - - > w = 25 / 3 \u2248 8.33 answer : e .\"" + }, + { + "Answer": 24, + "Options": "a ) a ) 10 , b ) b ) 24 , c ) c ) 40 , d ) d ) 55 , e ) e ) 70", + "Correct": "b", + "Explanation": "\"total score of 16 students is 16 * 61.50 = 984 total score of 15 students is 15 * 64 = 960 so , the score of the person who left is 24 ( 984 - 960 ) answer will be ( b )\"" + }, + { + "Answer": 40, + "Options": "a ) 50 km , b ) 56 km , c ) 60 km , d ) 40 km , e ) 80 km", + "Correct": "d", + "Explanation": "\"let the actual distance travelled be x km . x / 10 = ( x + 20 ) / 15 15 x = 10 x + 200 5 x = 200 x = 40 km . answer : d\"" + }, + { + "Answer": 36, + "Options": "a ) $ 22 , b ) $ 24 , c ) $ 30 , d ) $ 36 , e ) $ 40", + "Correct": "d", + "Explanation": "\"d its is . let price = x ( x - 1.5 ) 8 = 6 x x = 6 hence total money = 6 * 6 = 36\"" + }, + { + "Answer": 6, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "d", + "Explanation": "if a door is closed at the start , it requires an odd number of people to operate to be open at the end . only the perfect squares have an odd number of factors . the doors which are open at the end are : 1 , 4 , 9 , 16 , 25 , 36 for a total of 6 doors . the answer is d ." + }, + { + "Answer": 1.2000000000000002, + "Options": "a ) 1.2 , b ) 0.2 , c ) 1.8 , d ) 2.2 , e ) 4.0", + "Correct": "a", + "Explanation": "since y * is defined as the greatest positive even integer less than or equal to y , then 7.2 * = 6 ( the greatest positive even integer less than or equal to 7.2 is 6 ) . hence , 7.2 \u2013 7.2 * = 7.2 - 6 = 1.2 answer : a ." + }, + { + "Answer": 93.33333333333333, + "Options": "a ) 94 , b ) 95 , c ) 93 , d ) 97 , e ) 98", + "Correct": "c", + "Explanation": "\"3 * 27 = 81 3 * 119 = 357 total multiples of 3 = ( 119 - 27 ) + 1 = 93 answer is c .\"" + }, + { + "Answer": 16.666666666666668, + "Options": "a ) 9 , b ) 16.66 , c ) 47 , d ) 48 3 / 5 , e ) 59", + "Correct": "b", + "Explanation": "\"you can plug in values . c = 5 / 9 * ( f - 32 ) f = 32 - - > c = 0 ; f = 32 + 30 = 62 - - > c = 5 / 9 * 30 = 16.66 . increase = 16.66 degrees . answer : b .\"" + }, + { + "Answer": 13500, + "Options": "a ) 8300 , b ) 8400 , c ) 13500 , d ) 8700 , e ) 9000", + "Correct": "c", + "Explanation": "9548 16862 = 3362 + x + 7314 x = 16862 - 3362 - - - - - = 13500 16862 - - - - - c )" + }, + { + "Answer": 375, + "Options": "a ) $ 1500 , b ) $ 150 , c ) $ 375 , d ) $ 200 , e ) $ 450", + "Correct": "c", + "Explanation": "let the shares of w , x , y , z are 1 a , 6 a , 2 a , 4 a 6 a - 2 a = 1500 4 a = $ 1500 , a = 375 w ' s share = 1 a = $ 375 answer is c" + }, + { + "Answer": 500, + "Options": "a ) 500 , b ) 387 , c ) 298 , d ) 267 , e ) 191", + "Correct": "a", + "Explanation": "\"explanation : given that the student got 125 marks and still he failed by 40 marks = > the minimum pass mark = 125 + 40 = 165 given that minimum pass mark = 33 % of the total mark answer : a ) 500\"" + }, + { + "Answer": 13.329999999999984, + "Options": "a ) 16.16 % , b ) 15.55 % , c ) 14.44 % , d ) 13.33 % , e ) 12.22 %", + "Correct": "d", + "Explanation": "\"( 100 % + 7 % ) * ( 100 % - 19 % ) = 1.07 * . 81 = 0.8667 1 - 0.8667 = 13.33 % lost = - 13.33 % the answer is d the organization has lost 13.33 % of its total volunteers from fall to spring .\"" + }, + { + "Answer": 44, + "Options": "a ) 0.33 , b ) 0.44 , c ) 0.55 , d ) 44 , e ) 55", + "Correct": "d", + "Explanation": "\"main thing to remember is answer is asked in cents , however when we calculate , it comes up as 0.44 $ just multiply by 100 , answer e = 44 . d\"" + }, + { + "Answer": 0.0144, + "Options": "a ) 0.0414 , b ) 0.144 , c ) 0.0144 , d ) 0.414 , e ) none of them", + "Correct": "c", + "Explanation": "= 144 / 0.144 = 14.4 / x = 144 x 1000 / 144 = 14.4 / x = x = 14.4 / 1000 = 0.0144 answer is c ." + }, + { + "Answer": 60, + "Options": "a ) 20 % , b ) 30 % , c ) 40 % , d ) 70 % , e ) 60 %", + "Correct": "e", + "Explanation": "\"the is always the difference between our starting and ending points . in this case , it \u2019 s 100 \u2013 40 = 60 . the \u201c original \u201d is our starting point ; in this case , it \u2019 s 100 . ( 60 / 100 ) * 100 = ( 0.6 ) * 100 = 60 % . e\"" + }, + { + "Answer": 10, + "Options": "a ) 7 liters , b ) 15 liters , c ) 10 liters , d ) 9 liters , e ) none of these", + "Correct": "c", + "Explanation": "\"explanation : number of liters of water in 150 liters of the mixture = 20 % of 150 = 20 / 100 * 150 = 30 liters . p liters of water added to the mixture to make water 25 % of the new mixture . total amount of water becomes ( 30 + p ) and total volume of mixture is ( 150 + p ) . ( 30 + p ) = 25 / 100 * ( 150 + p ) 120 + 4 p = 150 + p = > p = 10 liters . answer is c\"" + }, + { + "Answer": 30, + "Options": "a ) 120 , b ) 134 , c ) 127 , d ) 30 , e ) 650", + "Correct": "d", + "Explanation": "option ( b ) and ( c ) are ruled out as they are not divisilble by 5 and 6 . 120 is both divisible by 5 and 6 but also by 12 , so it wrong . 650 is divisible by 5 but not by 6 . hence , ( d ) is the answer , as it is both divisible by 5 or 6 but not by 12" + }, + { + "Answer": 7, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10", + "Correct": "b", + "Explanation": "\"say there are ' a ' associate professors . so we have 2 a pencils and a charts . say there are ' b ' assistant professors . so we have b pencils and 2 b charts . total pencils are 10 so 2 a + b = 10 total charts are 11 so a + 2 b = 11 add both : 3 a + 3 b = 21 so a + b = 7 total number of people = 7 answer : b\"" + }, + { + "Answer": 6, + "Options": "a ) 1 , b ) 6 , c ) 4 , d ) 7 , e ) 9", + "Correct": "b", + "Explanation": "if a number is divisible by 6 , it must be divisible by both 2 and 3 in 522 x , to this number be divisible by 2 , the value of x must be even . so it can be 2,4 or 6 from given options 552 x is divisible by 3 , if sum of its digits is a multiple of 3 . 5 + 5 + 2 + x = 12 + x , if put x = 2 , 12 + 2 = 14 not a multiple of 3 if put x = 4 , 12 + 6 = 18 is a multiple of 3 if put x = 6 , 12 + 2 = 14 not a multiple of 3 the value of x is 6 . b" + }, + { + "Answer": 12, + "Options": "a ) 9 , b ) 12 , c ) 15 , d ) 16 , e ) 18", + "Correct": "b", + "Explanation": "in 24 liters , red = 6 / 9 * 24 = 16 and blue = 8 so , 16 / ( 8 + x ) = 4 / 5 or , x = 12 ( answer b )" + }, + { + "Answer": 0.8686868686868687, + "Options": "a ) 4 / 99 , b ) 2 / 25 , c ) 8 / 99 , d ) 49 / 100 , e ) 86 / 99", + "Correct": "e", + "Explanation": "\"interesting question ! also one that we should be able to answer very quickly be keeping an eye on our best friends , the answer choices . we know that x belongs to the set { 1 , 2 , 3 , . . . , 99 } . we want to know the probability w that x ( x + 1 ) is a multiple of either 4 or 5 . when will this happen ? if either x or ( x + 1 ) is a multiple of 4 or 5 . since 4 * 5 is 20 , let ' s look at the first 20 numbers to get a rough idea of how often this happens . out of the numbers from 1 to 20 : 4 , 5 , 6 , 8 , 9 , 10 , 11 , 12 , 13 , 15 , 16 , 17 , 20 so , 14 out of the first 20 numbers match our criteria . since : probability = ( # of desired outcomes ) / ( total # of possibilities ) , we guesstimate the answer to be 14 / 20 . since ( e ) is the only answer greater than 1 / 2 , we go with ( e ) .\"" + }, + { + "Answer": 250, + "Options": "a ) rs . 220 , b ) rs . 250 , c ) rs . 280 , d ) rs . 300 , e ) rs . 320", + "Correct": "b", + "Explanation": "let the amount paid to m per week = x and the amount paid to n per week = y then x + y = 550 but x = 120 % of y = 120 y / 100 = 12 y / 10 \u2234 12 y / 10 + y = 550 \u21d2 y [ 12 / 10 + 1 ] = 550 \u21d2 22 y / 10 = 550 \u21d2 22 y = 5500 \u21d2 y = 5500 / 22 = 500 / 2 = rs . 250 b )" + }, + { + "Answer": 0.08333333333333331, + "Options": "a ) 5 / 36 , b ) 5 / 24 , c ) 1 / 12 , d ) 1 / 6 , e ) 1 / 4", + "Correct": "c", + "Explanation": "2 / 3 * ( 2 x - 1 ) / ( 3 x - 1 ) = 5 / 12 = > x = 3 so total gems = 9 and probability of ruby = 1 / 3 * 2 / 8 = 1 / 12 answer 1 / 12 c" + }, + { + "Answer": 125, + "Options": "a ) 72 , b ) 80 , c ) 125 , d ) 150 , e ) 100", + "Correct": "c", + "Explanation": "explanation : let the number of students be x . then , number of students above 8 years of age = ( 100 - 20 ) % of x = 80 % of x . 80 % of x = 60 + 2 / 3 of 60 80 / 100 x = 100 x = 125 . answer : option c" + }, + { + "Answer": 16, + "Options": "a ) 16 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 50 %", + "Correct": "a", + "Explanation": "\"let original salary be $ 100 salary after decreasing 40 % = 100 - 100 x 40 / 100 = $ 60 salary after increasing 40 % on $ 60 = 60 + 60 x 40 / 100 = $ 84 percentage of loss = 100 - 84 = 16 % answer : a\"" + }, + { + "Answer": 178, + "Options": "a ) 12 , b ) 142 , c ) 164 , d ) 178 , e ) 84", + "Correct": "d", + "Explanation": "\"explanation : average after 13 innings = 58 required number of runs = ( 58 * 13 ) \u2013 ( 48 * 12 ) = 754 \u2013 576 = 178 answer d\"" + }, + { + "Answer": 800, + "Options": "a ) 800 , b ) 840 , c ) 880 , d ) 920 , e ) 960", + "Correct": "a", + "Explanation": "\"let x be the number of eggs that were laid . ( 2 / 5 ) ( 3 / 4 ) ( 1 / 2 ) x = 120 ( 6 / 40 ) x = 120 x = 800 the answer is a .\"" + }, + { + "Answer": 1, + "Options": "a ) 0 , b ) 1 , c ) - 1 , d ) - 8 , e ) 8", + "Correct": "b", + "Explanation": "\"explanation : x = 3 y < = > 5 - q = 3 ( 3 q - 1 ) < = > 5 - q = 9 q - 3 < = > 8 q = 8 < = > q = 1 . answer : b\"" + }, + { + "Answer": 245, + "Options": "a ) 166 , b ) 105 , c ) 178 , d ) 177 , e ) 245", + "Correct": "e", + "Explanation": "\"x : y : z = 100 : 45 : 30 20 : 9 : 6 9 - - - 63 35 - - - ? = > 245 answer : e\"" + }, + { + "Answer": 59, + "Options": "a ) 58 kgs , b ) 58.85 kgs , c ) 58.95 kgs , d ) 59 kgs , e ) 59.85 kgs", + "Correct": "d", + "Explanation": "\"actual total weight is ( 20 x 58.4 - 56 + 68 ) = 1180 kgs actual average weight is 1180 / 20 = 59 kgs d\"" + }, + { + "Answer": 54, + "Options": "a ) 87 , b ) 54 , c ) 29 , d ) 30 , e ) 70", + "Correct": "b", + "Explanation": "b 54 7 ^ 2 + 2 ^ 2 + 1 ^ 1 6 ^ 2 + 3 ^ 2 + 3 ^ 2 2 ^ 2 + 5 ^ 2 + 5 ^ 2" + }, + { + "Answer": 22, + "Options": "a ) 20 . , b ) 21 . , c ) 22 . , d ) 23 . , e ) 24 .", + "Correct": "c", + "Explanation": "\"before solving it algebraically , let us prime factorize 1430 = 2 * 5 * 11 * 13 . since number of apples per person * total persons w = 1430 , the answer should be a factor of 1430 . only c is . and that ' s your answer . c\"" + }, + { + "Answer": 512, + "Options": "a ) 432 , b ) 640 , c ) 256 , d ) 512 , e ) none of these", + "Correct": "d", + "Explanation": "\"in case i : let the no . of children = x . hence , total no . of notebooks distributed 1 \u2044 8 x . x or x 2 \u2044 8 . . . . . . . ( i ) in case ii : no . of children = x \u2044 2 now , the total no . of notebooks = 16 \u00d7 x \u2044 2 . . . . . . . ( ii ) comparing ( i ) & ( ii ) , we get x 2 \u2044 8 = 8 x or , x = 64 hence , total no . of notebooks = 64 \u00d7 64 / 8 = 512 answer d\"" + }, + { + "Answer": 0.4, + "Options": "a ) 0.8 , b ) 0.4 , c ) 0.96 , d ) 0.69 , e ) 0.76", + "Correct": "b", + "Explanation": "\"given expression = ( 0.5 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.5 ) ( power 2 ) + ( 0.5 x 0.1 ) + ( 0.1 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 0.5 - 0.1 ) = 0.4 answer is b\"" + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 1 , c ) 0 , d ) 8 , e ) 7", + "Correct": "a", + "Explanation": "\"take any prime number greater than 3 and check - say p = 5 so , p ^ 2 + 17 = 25 + 17 = > 42 42 / 12 will have remainder as 6 say p = 7 so , p ^ 2 + 17 = 49 + 17 = > 66 66 / 12 will have remainder as 6 so answer will be ( a ) 6\"" + }, + { + "Answer": 87.5, + "Options": "a ) 90.5 % , b ) 87.5 % , c ) 80.5 % , d ) 77.5 % , e ) 70.5 %", + "Correct": "b", + "Explanation": "within 1 standard deviation of the mean - means in the range { mean - 1 * sd ; mean + 1 * sd } = { 10 - 1 * 0.212 ; 10 + 0.3 } = { 9.788 ; 10.212 } . from the 8 listed numbers , 7 are within this range so 6 / 8 = 87.5 % . answer : b ." + }, + { + "Answer": 8, + "Options": "a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8", + "Correct": "e", + "Explanation": "\"2 ( 2 x - 3 ) - 21 = 2 ( x - 4 ) - 3 2 x = 16 x = 8 the answer is e .\"" + }, + { + "Answer": 33, + "Options": "a ) 27 , b ) 37 , c ) 932 , d ) 12 , e ) 91", + "Correct": "a", + "Explanation": "answer : a" + }, + { + "Answer": 858, + "Options": "a ) 1217 , b ) 1219 , c ) 1210 , d ) 1212 , e ) 858", + "Correct": "e", + "Explanation": "\"\u03c0 ( 232 \u2013 162 ) = 858 answer : e\"" + }, + { + "Answer": 75, + "Options": "a ) 75 , b ) 37 , c ) 26 , d ) 97 , e ) 27", + "Correct": "a", + "Explanation": "\"average = ( 76 + 65 + 82 + 67 + 85 ) / 5 = 375 / 5 = 75 . answer : a\"" + }, + { + "Answer": 1680, + "Options": "a ) 1677 , b ) 1683 , c ) 2523 , d ) 3363 , e ) none of these", + "Correct": "b", + "Explanation": "explanation : l . c . m of 5 , 6 , 7 , 8 = 840 therefore required number is of the form 840 k + 3 . least value of k for which ( 840 k + 3 ) is divisible by 9 is k = 2 therefore required number = ( 840 x 2 + 3 ) = 1683 . answer : b" + }, + { + "Answer": 256, + "Options": "a ) 230 , b ) 240 , c ) 236 , d ) 256 , e ) 266", + "Correct": "d", + "Explanation": "\"explanation : lcm of 7 , 9 , 12 and 18 is 252 required number = 252 + 4 = 256 answer : option d\"" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 5 , c ) 7 , d ) 8 , e ) 9", + "Correct": "a", + "Explanation": "slope = ( 17 2 / 3 - 12 2 / 3 ) / ( 7 - 15 ) = - 5 / 8 y = mx + b = > 12 2 / 3 = - 15 * 5 / 8 + b = > b = 1 y = - 75 x / 8 + 22 only integer values work , and the only multiples of 8 between 7 and 15 for x value is 8 , thus 1 point . a" + }, + { + "Answer": 3, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 7", + "Correct": "b", + "Explanation": "2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 = 77 ( discard as sum is odd ) 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 = 98 ( sum is even ) least number = 3 b" + }, + { + "Answer": 5, + "Options": "a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 7", + "Correct": "c", + "Explanation": "\"let seventh observation = x . then , according to the question we have = > ( 72 + x ) / 7 = 11 = > x = 5 . hence , the seventh observation is 5 . answer : c\"" + }, + { + "Answer": 23, + "Options": "a ) 12 % , b ) 26 % , c ) 23 % , d ) 30 % , e ) 60 %", + "Correct": "c", + "Explanation": "\"in the first plot 15 % of 300 seeds germinated , so 0.15 x 300 = 45 seeds germinated . in the second plot , 35 % of 200 seeds germinated , so 0.35 x 200 = 70 seeds germinated . since 45 + 70 = 115 seeds germinated out of a total of 300 + 200 = 500 seeds , the percent of seeds that germinated is ( 115 / 500 ) x 100 % , or 23 % . answer : c .\"" + }, + { + "Answer": 13, + "Options": "a ) 11 , b ) 13 , c ) 15 , d ) 18 , e ) 19", + "Correct": "b", + "Explanation": "\"12 , 15 , 18 , 21 , 24 , 27 , 30 , 33 , 36 , 39 , 42 , 45,48 . 13 numbers . 10 / 3 = 3 and 50 / 3 = 16 = = > 16 - 3 = 13 . therefore 13 digits b )\"" + }, + { + "Answer": 70, + "Options": "a ) 70 , b ) 105 , c ) 178 , d ) 177 , e ) 169", + "Correct": "a", + "Explanation": "\"x : y : z = 100 : 45 : 30 20 : 9 : 6 9 - - - 18 35 - - - ? = > 70 answer : a\"" + }, + { + "Answer": 62024.8125, + "Options": "a ) 61,600 , b ) 64,850 , c ) 64,749 , d ) 49,700 , e ) 56,720", + "Correct": "a", + "Explanation": "\"find the number , upon sum of 3 digits of a number gives a reminder 2 when it is divided by 8 seeing the options after dividing an finding the reminder of 2 my answer was a\"" + }, + { + "Answer": 6, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "e", + "Explanation": "\"the lcm of 5 , 11 , and 13 is 715 . the next multiple is 2 * 715 = 1,430 . 1,430 + { remainder } = 1,430 + 3 = 1,433 , which is 6 less than 1,439 . answer : e .\"" + }, + { + "Answer": 858.5454545454545, + "Options": "a ) 419 , b ) 551 , c ) 601 , d ) 620 , e ) 858.54", + "Correct": "e", + "Explanation": "add 12 , 13 , 14 , 510 , 520 , 530 , 1,115 , 1,120 , and 1,125 , 2140 , 2345 grouping numbers together may quicken the addition sum = 9444 4959 / 11 = 858.54 . e" + }, + { + "Answer": 90, + "Options": "a ) 102 % , b ) 90 % , c ) 120 % , d ) 85 % , e ) 95 %", + "Correct": "b", + "Explanation": "\"easiest thing to do : assume that price is 100 price at the end of yr 1 : 100 + 20 = 120 price at the end of year 2 = 120 - 120 * 0.25 = 120 * 0.75 = 90 hence required answer = ( 90 / 100 ) * 100 % = 90 % answer is b .\"" + }, + { + "Answer": 16, + "Options": "a ) 11 , b ) 16 , c ) 13 , d ) 14 , e ) 15", + "Correct": "b", + "Explanation": "explanation : age of the 15 th student = [ 15 * 15 - ( 13 * 5 + 16 * 9 ) ] = 16 years . answer : b" + }, + { + "Answer": 334, + "Options": "a ) $ 160 , b ) $ 289 , c ) $ 334 , d ) $ 274 , e ) $ 286", + "Correct": "c", + "Explanation": "\"total number of days of stay = 23 charge of staying in first week = 18 * 7 = 126 $ charge of staying for additional days = ( 23 - 7 ) * 13 = 16 * 13 = 208 $ total charge = 126 + 208 = 334 $ answer c\"" + }, + { + "Answer": 50000, + "Options": "a ) $ 40,000 , b ) $ 50,000 , c ) $ 64,000 , d ) $ 66,667 , e ) $ 80,000", + "Correct": "b", + "Explanation": "equation is correct , so math must be a problem . 0.15 * 40,000 + 0.2 * ( x - 40,000 ) = 8,000 - - > 6,000 + 0.2 x - 8,000 = 8,000 - - > 0.2 x = 10,000 - - > x = 50,000 . answer : b ." + }, + { + "Answer": 9, + "Options": "a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 10", + "Correct": "c", + "Explanation": "solution let the numbers be x , x + 2 , x + 4 then x , ( x + 2 ) + ( x + 4 ) = x + 20 \u2039 = \u203a 2 x = 14 \u2039 = \u203a x = 7 . therefore middle number = x + 2 = 9 . answer c" + }, + { + "Answer": 18, + "Options": "a ) 8 , b ) 9 , c ) 16 , d ) 17 , e ) 18", + "Correct": "e", + "Explanation": "\"let the ages of children be x , ( x + 4 ) , ( x + 8 ) , ( x + 12 ) years . then , x + ( x + 4 ) + ( x + 8 ) + ( x + 12 ) = 48 4 x = 24 x = 6 x + 12 = 6 + 12 = 18 answer : e\"" + }, + { + "Answer": 42.5, + "Options": "a ) 27.5 % , b ) 33.3 % , c ) 35.5 % , d ) 42.5 % , e ) 47.5 %", + "Correct": "d", + "Explanation": "\"let x be the original number of each color so there are a total of 5 x candies . kaz eats all of the green candies and half of the orange ones . there are 0 green candies and 0.5 x orange candies remaining . he eats half of the remaining pieces of each color . there are 0.25 x orange candies , and 0.5 x each of red , yellow , and blue candies . he eats red and yellow candies in equal proportions . orange + blue + red + yellow = 0.75 x + red + yellow = 1.6 x red + yellow = 0.85 x red = 0.425 x , since red = yellow . the answer is d .\"" + }, + { + "Answer": 58.65, + "Options": "a ) 58 kgs , b ) 58.65 kgs , c ) 58.95 kgs , d ) 59 kgs , e ) 59.85 kgs", + "Correct": "b", + "Explanation": "\"actual total weight is ( 20 x 58.4 - 56 + 61 ) = 1173 kgs actual average weight is 1177 / 20 = 58.65 kgs b\"" + }, + { + "Answer": 53, + "Options": "a ) 53 , b ) 56 , c ) 60 , d ) 64 , e ) 68", + "Correct": "a", + "Explanation": "this question can be solved in a variety of ways : with algebra , by testing the answers and by using a great number property shortcut involving consecutive integers . we ' re given a few facts to work with : 1 ) there are 9 rows of tiles . 2 ) when going from ' left to right ' , each row contains two fewer tiles than the one next to it . 3 ) there are a total of 405 tiles we ' re asked how many tiles the left - most most row holds ( meaning the one with the most tiles ) . to start , 405 is divisible by 9 , so we can figure out the average number of tiles per row . that is 405 / 9 = 45 . since we ' re dealing with a set of 9 consecutive integers that differ by 2 each , we know that the ' 5 th row ' will have 45 tiles ( the average ) . then we just have to ' add 2 s ' until we get to the first row . . . 45 + 2 + 2 + 2 + 2 = 53 . final answer : a" + }, + { + "Answer": 13, + "Options": "a ) 8 , b ) 13 , c ) 16 , d ) 24 , e ) 27", + "Correct": "b", + "Explanation": "each group has 8 = 8 + 8 + 8 = 24 max 4 people are in 2 groups , subtract 4 people twice as they are counted twice each pair of groups has 5 in common , so in addition to the 4 people subtract 1 from each group ans : 8 + 8 + 8 - ( 2 ( 4 ) ) - 3 = 13 answer : b" + }, + { + "Answer": 4, + "Options": "a ) 4 kg , b ) 5 kg , c ) 8 kg , d ) 30 kg , e ) 35 kg", + "Correct": "a", + "Explanation": "exp . water in the given mixture = 10 * 20 / 100 = 2 kg , and spirit = ( 20 - 2 ) = 18 kg let x kg of water added , then , x + 2 / 20 + x * 100 = = 25 4 x + 8 = 20 + x , or x = 4 kg answer : a" + }, + { + "Answer": 3, + "Options": "a ) 1.8 , b ) 3 , c ) 6 , d ) 18 , e ) 60", + "Correct": "b", + "Explanation": "\"mean = median = ( first + last ) / 2 and sum = mean * number of terms h ( 18 ) = [ ( 2 + 18 ) / 2 ] * 9 = 90 h ( 10 ) = ( 2 + 10 ) / 2 ] * 5 = 30 h ( 18 ) / h ( 10 ) = ( 90 ) / ( 30 ) = 3 answer : b\"" + }, + { + "Answer": 480, + "Options": "a ) 160 , b ) 320 , c ) 480 , d ) 600 , e ) 720", + "Correct": "c", + "Explanation": "there are 2 ^ 5 = 32 possibilities for the true - false answers . however we need to remove two cases for ttttt and fffff . there are 4 * 4 = 16 possibilities for the multiple choice questions . the total number of possibilities is 30 * 16 = 480 . the answer is c ." + }, + { + "Answer": 398, + "Options": "a ) 370 , b ) 365 , c ) 398 , d ) 456 , e ) 460", + "Correct": "c", + "Explanation": "easy solution : n = dq 1 + 255 2 n = 2 dq 1 + 51 0 - ( 1 ) 2 n = dq 2 + 112 - ( 2 ) as ( 1 ) = ( 2 ) = 2 n d * ( q 2 - 2 q 1 ) = 398 d * some integer = 398 checking all options only ( c ) syncs with it . answer c" + }, + { + "Answer": 150, + "Options": "a ) 150 , b ) 153 , c ) 154 , d ) 155 , e ) 156", + "Correct": "a", + "Explanation": "\"explanation : let the number = x , then , x - ( 3 / 5 ) x = 60 , = > ( 2 / 5 ) x = 60 = > 2 x = 60 * 5 , = > x = 150 answer : option a\"" + }, + { + "Answer": 0.12500000000000003, + "Options": "a ) 0 , b ) 1 / 15 , c ) 2 / 15 , d ) 1 / 8 , e ) 2 / 10", + "Correct": "d", + "Explanation": "\"suppose the water in each jug is l liters cx x ( 1 / 4 ) = l cx = 4 l liters cx is capacity of x cy x ( 2 / 3 ) = l cy = 3 l / 2 liters cy is capacity of y now , y is 3 l / 2 - l empty = l / 2 empty so , we can put only l / 2 water in jug y from jug x jug x ' s remaining water = l - l / 2 = l / 2 fraction of x which contains water = water / cx = ( l / 2 ) / 4 l = 1 / 8 answer will be d\"" + }, + { + "Answer": 58.6, + "Options": "a ) 58.6 kgs , b ) 58.85 kgs , c ) 58.95 kgs , d ) 59 kgs , e ) 59.85 kgs", + "Correct": "a", + "Explanation": "actual total weight is ( 20 x 58.4 - 56 + 60 ) = 1172 kgs actual average weight is 1172 / 20 = 58.6 kgs a" + }, + { + "Answer": 12, + "Options": "a ) 14.0 , b ) 13.0 , c ) 12.0 , d ) 11.0 , e ) 10.0", + "Correct": "c", + "Explanation": "\"solution : h stopped 700 ft before reaching the final point , time taken to reach 4000 ft = 4000 / 800 = 5 hrs . this means she reached there at 11 : 00 . speed difference between them is 800 - 500 = 300 ft / hr so by the time h stops they have 1500 ft of distance so now here we use relative speed formula they both are travelling toward each other with speed of 1000 and 500 total 1500 ft / hr and distance bwn them is 1500 ft so time taken to meet = 1 hr from 11 : 00 means 12 : 00 is the answer . c\"" + }, + { + "Answer": 7, + "Options": "a ) $ 3 , b ) $ 5 , c ) $ 7 , d ) $ 9 , e ) $ 11", + "Correct": "c", + "Explanation": "let q ' s hourly wage be x , then p ' s hourly wage is 1.5 x let t be the number of hours that q needs , then p needs t - 10 hours to do the job . since they both are paid an equal total amount of $ 420 : x * t = 1.5 x * ( t - 10 ) t = 30 hours and q ' s hourly wage is 420 / 30 = $ 14 p ' s hourly wage is 420 / ( t - 10 ) = $ 21 which is $ 7 per hour more . the answer is c ." + }, + { + "Answer": 0.328125, + "Options": "a ) 0 , b ) 21 / 64 , c ) 1 , d ) 22 / 63 , e ) 23 / 65", + "Correct": "b", + "Explanation": "log ( a ( a ( a ^ 1 / 4 ) ^ 1 / 4 ) ^ 1 / 4 = > log ( a ( a ^ 1 + 1 / 4 ) ^ 1 / 4 ) ^ 1 / 4 = > log ( a ( a ^ 5 / 4 ) ^ 1 / 4 ) ^ 1 / 4 = > log ( a ( a ^ 5 / 16 ) ^ 1 / 4 = > log ( a ^ 1 + 5 / 16 ) ^ 1 / 4 = > log ( a ^ 21 / 16 ) ^ 1 / 4 = > log ( a ^ 21 / 64 ) = > 21 / 64 log ( a ) = > 21 / 64 answer : b" + }, + { + "Answer": 10, + "Options": "a ) 12 , b ) 14 , c ) 10 , d ) 16 , e ) 18", + "Correct": "c", + "Explanation": "now : mary = x , rahul = x + 30 in 20 years mary = x + 20 , rahul = x + 30 + 20 or 2 ( x + 20 ) x + 30 + 20 = 2 ( x + 20 ) x + 50 = 2 x + 40 50 - 40 = 2 x - x x = 10 mary is 10 years old answer : c" + }, + { + "Answer": 1, + "Options": "a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2", + "Correct": "d", + "Explanation": "\"the midpoint of ( 2,8 ) and ( 8 , - 2 ) is ( 5,3 ) . the slope of a line through ( 0 , - 2 ) and ( 5,3 ) is ( 3 - ( - 2 ) ) / ( 5 - 0 ) = 5 / 5 = 1 the answer is d .\"" + }, + { + "Answer": 6, + "Options": "a ) 2 , b ) 4 , c ) 10 , d ) 12 , e ) 11", + "Correct": "d", + "Explanation": "d" + }, + { + "Answer": 1.35, + "Options": "a ) 1.12 , b ) 1.16 , c ) 1.2 , d ) 1.35 , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : ( x * 5 ) = ( 0.75 * 9 ) x = 6.75 / 5 = 1.35 answer : d\"" + }, + { + "Answer": 355, + "Options": "a ) t = 350 , b ) t = 353 , c ) t = 354 , d ) t = 356 , e ) 357", + "Correct": "b", + "Explanation": "\"focus on the points where the number of digits in squares change : 1 , 2 , 3 - single digit squares . first 2 digit number is 10 . 4 , 5 , . . . 9 - two digit squares . to get 9 , the last number with two digit square , think that first 3 digit number is 100 which is 10 ^ 2 . so 9 ^ 2 must be the last 2 digit square . 10 , 11 , 12 , . . . 31 - three digit squares . to get 31 , think of 1000 - the first 4 digit number . it is not a perfect square but 900 is 30 ^ 2 . 32 ^ 2 = 2 ^ 10 = 1024 , the first 4 digit square . 32 - 99 - four digit squares . to get 99 , think of 10,000 - the first 5 digit number which is 100 ^ 2 . so number of digits in s ( 99 ) = 3 * 1 + 6 * 2 + 22 * 3 + 68 * 4 = 3 + 12 + 66 + 272 = 353 . b\"" + }, + { + "Answer": 42, + "Options": "a ) 42 , b ) 40 , c ) 30 , d ) 18 , e ) 11", + "Correct": "a", + "Explanation": "\"explanation : 26 + 30 + 7 * 4 = 84 / 2 = 42 answer : a\"" + }, + { + "Answer": 400, + "Options": "a ) 16 , b ) 80 , c ) 400 , d ) 180 , e ) 240", + "Correct": "c", + "Explanation": "prime digits 2 , 35 and 7 . three digit numbers _ _ _ 1 st place can be filled in 4 ways 2 nd place can be filled in 10 ways 3 rd place can be filled in 10 ways total = 4 * 10 * 10 = 400 ans : c" + }, + { + "Answer": 78, + "Options": "a ) 74 , b ) 75 , c ) 69 , d ) 78 , e ) 45", + "Correct": "d", + "Explanation": "\"solution : sum of 1 st 12 results = 12 * 14 sum of last 12 results = 12 * 17 13 th result = x ( let ) now , 12 * 14 + 12 * 17 + x = 25 * 18 or , x = 78 . answer : option d\"" + }, + { + "Answer": 253, + "Options": "a ) 145 , b ) 185 , c ) 253 , d ) 370 , e ) none", + "Correct": "c", + "Explanation": "solution let the number be x . then 2 x = 10 or x = 5 . so , the number is either 253 or 352 . since the number increases on reversing the digits , so the hundred ' s digit is smaller than the units digit . hence , required number = 253 . answer c" + }, + { + "Answer": 6, + "Options": "a ) 3 , b ) 5 , c ) 6 , d ) 8 , e ) 9", + "Correct": "c", + "Explanation": "\"explanation : on dividing 7538 by 14 we get the remainder 6 , so 6 should be subtracted option c\"" + }, + { + "Answer": 20, + "Options": "a ) 12 % , b ) 15 % , c ) 18 % , d ) 20 % , e ) 25 %", + "Correct": "d", + "Explanation": "\"fathers without full - time jobs are 1 / 4 * 2 / 5 = 2 / 20 of all the parents surveyed . mothers without full - time jobs are 1 / 6 * 3 / 5 = 1 / 10 of all the parents surveyed . the percent of parents without full - time jobs is 2 / 20 + 1 / 10 = 1 / 5 = 20 % the answer is d .\"" + }, + { + "Answer": 77, + "Options": "a ) 79 litres , b ) 78 litres , c ) 77 litres , d ) 152 liters , e ) 304 litres", + "Correct": "c", + "Explanation": "i guess it should be the ratio w , by volume ofsoaptowaterin the solutiondoubleswhereas the ratio , by volume ofalocoholtowaterremains thesameas before 2 : 50 : 100 = > 1 : 25 : 50 . if we add all the parts , we get 76 liters so we have 1 liters of soap , 25 liters of alcohol and 50 liters of water . now as per the question , soap : water doubles but alcohol to water remains the same . so soap becomes 2 liters , alcohol remains 25 liters and water remains at 50 liters . hence 77 liters - option c )" + }, + { + "Answer": 5.9, + "Options": "a ) 5.4 , b ) 5.9 , c ) 6.3 , d ) 6.7 , e ) 7.5", + "Correct": "b", + "Explanation": "let x be the length of the size 8 shoe . then 0.4 x = 9 / 5 x = 4.5 inches the size 15 shoe has a length of 4.5 + 7 / 5 = 5.9 inches the answer is b ." + }, + { + "Answer": 22, + "Options": "a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 26", + "Correct": "c", + "Explanation": "\"let the total number of workers be y . so sum of salary for all workers = sum of salary of 7 technician + sum of salary for other y - 7 workers . 7 x 1000 + 780 ( y - 7 ) = 850 y \u21d2 7000 + 780 y - 5460 = 850 y \u21d2 70 y = 1540 \u2234 y = 22 so total number of workers = 22 c\"" + }, + { + "Answer": 780, + "Options": "a ) 1628.4 , b ) 1534 , c ) 780 , d ) 1496 , e ) none of these", + "Correct": "c", + "Explanation": "\"solution : let average expenditure of 15 people be x . then , 15 x = 10 * 50 + 5 * ( x + 4 ) ; or , 15 x = 10 * 50 + 5 x + 20 ; or , x = 52 ; so , total money spent = 52 * 15 = rs . 780 . answer : option c\"" + }, + { + "Answer": 0.5714285714285714, + "Options": "a ) 4 / 7 , b ) 34 , c ) 1 , d ) 2 , e ) 3", + "Correct": "a", + "Explanation": "\"answer given exp . = 4 / 7 + { ( 2 q - p ) / ( 2 q + p ) } dividing numerator as well as denominator by q , exp = 1 / 7 + { 2 - p / q ) / ( 2 + p / q ) } = 1 / 7 + { ( 2 - 4 / 5 ) / ( 2 + 4 / 5 ) } = 1 / 7 + 6 / 14 = 1 / 7 + 3 / 7 = 4 / 7 correct option : a\"" + }, + { + "Answer": 28, + "Options": "a ) 16 , b ) 14 , c ) 28 , d ) 11 , e ) 9", + "Correct": "c", + "Explanation": "10 20 30 40 50 60 70 80 leave the top right - most number 8 start with bottom right - most number 5 80 * 30 + 70 = 2470 2470 * 20 + 60 = 49460 49460 * 10 + 50 = 494650 this is the number required now , do the successive division in the reverse order the sum of the remainders is 28 hence , the correct option is c" + }, + { + "Answer": 137, + "Options": "a ) 65 , b ) 66 , c ) 67 , d ) 131 , e ) 136", + "Correct": "e", + "Explanation": "\"the answer to the question is indeed e . the problem with above solutions is that they do not consider words like aa , bb , . . . the number of 1 letter words ( x ) that can be made from 68 letters is 68 ; the number of 2 letter words ( xx ) that can be made from 68 letters is 68 * 68 , since each x can take 68 values . total : 68 + 68 * 68 . similarly : the number of 1 letter words ( x ) that can be made from 67 letters is 67 ; the number of 2 letter words ( xx ) that can be made from 67 letters is 67 * 67 , since each x can take 67 values . total : 67 + 67 * 67 . the difference is ( 68 + 68 * 68 ) - ( 67 + 67 * 67 ) = 136 . answer : e .\"" + }, + { + "Answer": 43, + "Options": "a ) 43 , b ) 45 , c ) 47 , d ) 50 , e ) 52", + "Correct": "a", + "Explanation": "a number to be divisible by both 3 and 7 should be divisible by the least common multiple of 3 and 7 so by 21 . multiples of 21 between 100 and 999 , inclusive is ( last - first ) / multiple + 1 = ( 987 - 105 ) / 21 + 1 = 42 + 1 = 43 answer : a ." + }, + { + "Answer": 62.5, + "Options": "a ) 22.3 , b ) 33.2 , c ) 22.2 , d ) 51.3 , e ) 62.5", + "Correct": "e", + "Explanation": "\"explanation : total of 50 numbers = ( 50 \u00d7 62 ) = 3100 total of 48 numbers = ( 3100 - ( 45 + 55 ) ] = 3000 required average = 3000 / 48 = 62.5 answer : e\"" + }, + { + "Answer": 130, + "Options": "a ) 130 , b ) 80 , c ) 100 , d ) 120 , e ) 150", + "Correct": "a", + "Explanation": "let e 10 = x no . d 10 = y no . donald is having x + y notes mona carries 3 x + y again x = 2 y or donald x + y = 39 or 3 y = 39 y = 13 ; x = 26 , total notes they carry = 104 + 26 = 130 a" + }, + { + "Answer": 4, + "Options": "a ) 5 , b ) 7 , c ) 4 , d ) 11 , e ) 12", + "Correct": "c", + "Explanation": "39 / 11 = 1 and 79 / 11 = 7 = = > 7 - 3 = 4 numbers answer : c" + }, + { + "Answer": 4, + "Options": "a ) 4.5 , b ) 5 , c ) 5.5 , d ) 5.8 , e ) 4", + "Correct": "e", + "Explanation": "\"if $ x $ is the number , x / 6 * 12 = 8 = > 2 x = 8 = > x = 4.0 e\"" + }, + { + "Answer": 15000, + "Options": "a ) 7787 , b ) 8000 , c ) 15000 , d ) 1277 , e ) 2081", + "Correct": "c", + "Explanation": "\"x * 130 / 100 * 70 / 100 = 13650 x * 0.91 = 13650 x = 13650 / 0.91 = > 15000 answer : c\"" + }, + { + "Answer": 13200, + "Options": "a ) 10,000 , b ) 11.0 , c ) 12,000 , d ) 13,200 , e ) 14,000", + "Correct": "d", + "Explanation": "\"the average price of 25 products is $ 1,200 means that the total price of 25 products is 25 * 1,200 = $ 30,000 . next , since exactly 12 of the products sell for less than $ 1,000 , then let ' s make these 12 items to be at $ 400 each ( min possible ) . now , the remaining 12 items can not be priced less than $ 1,000 , thus the minimum possible price of each of these 12 items is $ 1,000 . thus the minimum possible value of 24 products is 12 * 400 + 12 * 1,000 = $ 16,800 . therefore , the greatest possible selling price of the most expensive product is $ 30,000 - $ 16,800 = $ 13,200 . answer : d .\"" + }, + { + "Answer": 0.75, + "Options": "a ) 2 / 3 , b ) 3 / 4 , c ) 4 / 5 , d ) 5 / 6 , e ) 7 / 8", + "Correct": "b", + "Explanation": "\"( 1 / 2 ) x = ( 1 / 4 ) y ( 1 / 4 ) y + ( 1 / 2 ) y = ( 3 / 4 ) y the answer is b .\"" + }, + { + "Answer": 65, + "Options": "a ) 75 kg , b ) 85 kg , c ) 95 kg , d ) 65 kg , e ) 55 kg", + "Correct": "d", + "Explanation": "the total weight increase = ( 8 x 2.5 ) kg = 20 kg weight of new person = ( 45 + 20 ) kg = 65 kg the answer is d ." + }, + { + "Answer": 65, + "Options": "a ) a ) 65 , b ) b ) 76 , c ) c ) 78 , d ) d ) 80 , e ) e ) 88", + "Correct": "a", + "Explanation": "\"explanation : average after 11 innings should be 35 so , required score = ( 11 * 35 ) - ( 10 * 32 ) = 385 - 320 = 65 answer : option a\"" + }, + { + "Answer": 18, + "Options": "a ) 4 , b ) 6 , c ) 18 , d ) 10 , e ) 12", + "Correct": "c", + "Explanation": "\"i am getting 12 . e . hope havent done any calculation errors . . approach . . let y = no . of days taken by y to do w widgets . then x will take y + 2 days . 1 / ( y + 2 ) + 1 / y = 5 / 12 ( 5 / 12 is because ( 5 / 4 ) w widgets are done in 3 days . so , x widgets will be done in 12 / 5 days or 5 / 12 th of a widget in a day ) solving , we have y = 4 = > x takes 6 days to doing x widgets . so , he will take 18 days to doing 3 w widgets . answer : c\"" + }, + { + "Answer": 85, + "Options": "a ) 80 , b ) 81 , c ) 82 , d ) 83 , e ) 85", + "Correct": "e", + "Explanation": "\"solution : mabel handled 90 transactions anthony handled 10 % more transactions than mabel anthony = 90 + 90 \u00d7 10 % = 90 + 90 \u00d7 0.10 = 90 + 9 = 99 cal handled 2 / 3 rds of the transactions than anthony handled cal = 2 / 3 \u00d7 99 = 66 jade handled 19 more transactions than cal . jade = 66 + 19 = 85 jade handled = 85 transactions . answer : e\"" + }, + { + "Answer": 90.4, + "Options": "a ) 88.8 , b ) 90.4 , c ) 88.0 , d ) 70.9 , e ) 71.2", + "Correct": "b", + "Explanation": "\"13 % of 80 = ( 80 * 0.13 ) = 10.4 11 % greater than 80 = 80 + 10.4 = 90.4 answer is clearly b .\"" + }, + { + "Answer": 0.6666666666666666, + "Options": "a ) 1 / 9 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6", + "Correct": "d", + "Explanation": "\"n ( n + 1 ) to be divisible by 3 either n or n + 1 must be a multiples of 3 . in each following group of numbers : { 1 , 2 , 3 } , { 4 , 5 , 6 } , { 7 , 8 , 9 } , . . . , { 97 , 98 , 99 } there are exactly 2 numbers out of 3 satisfying the above condition . for example in { 1 , 2 , 3 } n can be : 2 , or 3 . thus , the overall probability is 2 / 3 . answer : d .\"" + }, + { + "Answer": 10, + "Options": "a ) 13 , b ) 15 , c ) 16 , d ) 10 , e ) 18", + "Correct": "d", + "Explanation": "\"12 , 15 , 18 , 21 , 24 , 27 , 30 , 33 , 36 , 39 . 10 numbers . 10 / 3 = 3 and 40 / 3 = 13 = = > 13 - 3 = 10 . therefore 10 digits d )\"" + }, + { + "Answer": 129, + "Options": "a ) 65 , b ) 66 , c ) 67 , d ) 131 , e ) 128", + "Correct": "e", + "Explanation": "\"the answer to the question is indeed e . the problem with above solutions is that they do not consider words like aa , bb , . . . the number of 1 letter words ( x ) that can be made from 64 letters is 64 ; the number of 2 letter words ( xx ) that can be made from 64 letters is 64 * 64 , since each x can take 64 values . total : 64 + 64 * 64 . similarly : the number of 1 letter words ( x ) that can be made from 63 letters is 63 ; the number of 2 letter words ( xx ) that can be made from 63 letters is 63 * 63 , since each x can take 63 values . total : 63 + 63 * 63 . the difference is ( 64 + 64 * 64 ) - ( 63 + 63 * 63 ) = 128 . answer : e .\"" + }, + { + "Answer": 3.6000000000000014, + "Options": "a ) 4.2 , b ) 4.4 , c ) 3.6 , d ) 5.6 , e ) 5.7", + "Correct": "c", + "Explanation": "\"sum of the remaining two numbers = ( 3.95 * 6 ) - [ ( 4.4 * 2 ) + ( 3.85 * 2 ) ] = 7.20 . required average = ( 7.2 / 2 ) = 3.6 . c\"" + }, + { + "Answer": 47.5, + "Options": "a ) 45 % , b ) 47.5 % , c ) 35 % , d ) 32.5 % , e ) 30 %", + "Correct": "b", + "Explanation": "price = p initially price reduced by 25 % which means new price is 3 / 4 p now on this new price further 30 percent is reduced which means the new price is merely 70 percent of 3 / 4 p = = > ( 3 / 4 ) x ( 7 / 10 ) p = 21 / 40 p is the new price after both deduction which is 52.5 percent of the original value p . this implies this entire series of deduction is worth having discounted 47.5 % of p . so answer is b = 47.5 %" + }, + { + "Answer": 15, + "Options": "a ) 8 , b ) 10 , c ) 15 , d ) 14 , e ) 16", + "Correct": "c", + "Explanation": "\"ifno caris selected more than once then the number of clients = 10 / 2 = 5 but since every car is being selected three times so no . of clients must be thrice as well = 5 * 3 = 15 answer : option c\"" + }, + { + "Answer": 5, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "e", + "Explanation": "( x / 5 ) + 3 = 4 . subtracting both sides with 3 gives x / 5 = 1 multiplying both sides by 5 gives x = 5 answer : e" + }, + { + "Answer": 10, + "Options": "a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50", + "Correct": "a", + "Explanation": "\"( 1056 / 26 ) gives remainder 16 10 + 16 = 26 , so we need to add 10 a\"" + }, + { + "Answer": 0.6666666666666667, + "Options": "a ) 6 / 9 , b ) 5 / 3 , c ) 2 / 3 , d ) 4 / 3 , e ) 5 / 3", + "Correct": "c", + "Explanation": "let abi ' s monthly savings = s abi ' s monthly pay = p abi ' s monthly expenditure = p - s abi ' s savings by the end of the year from these monthly savings were six times the amount she spent per month 12 s = 6 * ( p - s ) = > 2 s = p - s = > p = 3 s abi ' s monthly expenditure = p - s = 3 s - s = 2 s fraction of her salary that abi spent each month = 2 s / 3 s = p - s / p = 2 / 3 . answer is c" + }, + { + "Answer": 0.3333333333333335, + "Options": "a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 6 , d ) 1 / 8 , e ) 1 / 9", + "Correct": "a", + "Explanation": "explanation : one - half ( 1 / 2 ) plus one - third ( 1 / 3 ) equals five - sixths ( 5 / 6 ) , so one - sixth ( 1 / 6 ) of the third worker ' s time should be budgeted to the project in order for the total time to be equivalent to that of one person working full - time . if x 2 - x - 6 = 0 , then ( x + 2 ) ( x - 3 ) = 0 , so x = - 2 or x = 3 . correct answer : a" + }, + { + "Answer": 17.931568569324174, + "Options": "a ) 10 , b ) 12 , c ) 14 , d ) 18 , e ) 20", + "Correct": "d", + "Explanation": "2000 ^ 12000 ^ 22000 ^ 32000 ^ 4 . . . . . . . 2000 ^ 9 population increases in this sequence taking 9 * 2 = 18 answer : d" + }, + { + "Answer": 7.48, + "Options": "a ) 6.6 kg , b ) 6.8 kg , c ) 7.48 kg , d ) 6.9 kg , e ) 7.8 kg", + "Correct": "c", + "Explanation": "\"880 * 8.5 7480.0 gm 7.48 kg answer : c\"" + }, + { + "Answer": 55, + "Options": "a ) 55 , b ) 56 , c ) 57 , d ) 58 , e ) 59", + "Correct": "a", + "Explanation": "\"20 x + 50 = 21 ( x \u2013 5 ) x = 55 answer : a\"" + }, + { + "Answer": 28, + "Options": "a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29", + "Correct": "d", + "Explanation": "\"let x be the number of students in the largest class . then x + ( x - 2 ) + ( x - 4 ) + ( x - 6 ) + ( x - 8 ) = 120 5 x - 20 = 120 5 x = 140 x = 28 the answer is d .\"" + }, + { + "Answer": 21, + "Options": "a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25", + "Correct": "a", + "Explanation": "\"explanation : let the number of workers = x given that average salary of all the workers = rs . 8000 then , total salary of all workers = 8000 x given that average salary of 7 technicians is rs . 12000 = > total salary of 7 technicians = 7 \u00d7 12000 = 84000 count of the rest of the employees = ( x - 7 ) average salary of the rest of the employees = rs . 6000 total salary of the rest of the employees = ( x - 7 ) ( 6000 ) 8000 x = 84000 + ( x - 7 ) ( 6000 ) = > 8 x = 84 + ( x - 7 ) ( 6 ) = > 8 x = 84 + 6 x - 42 = > 2 x = 42 = > x = 42 / 2 = 21 answer : option a\"" + }, + { + "Answer": 15, + "Options": "a ) 5 , b ) 8 , c ) 10 , d ) 12 , e ) 15", + "Correct": "e", + "Explanation": "\"let x be the amount of liquid q to be added . ( 3 / 8 ) * 40 + x = ( 6 / 11 ) * ( 40 + x ) 1320 + 88 x = 1920 + 48 x 40 x = 600 x = 15 the answer is e .\"" + }, + { + "Answer": 1500, + "Options": "a ) $ 1000 , b ) $ 1200 , c ) $ 1500 , d ) $ 1800 , e ) $ 2000", + "Correct": "c", + "Explanation": "let the shares of a , b , c and d be 5 x , 2 x , 4 x and 3 x respectively . then , 4 x - 3 x = 500 x = $ 500 d ' s share = 3 x = 3 * $ 500 = $ 1500 the answer is c ." + }, + { + "Answer": 20, + "Options": "a ) - 29 , b ) - 19 , c ) 20 , d ) 29 , e ) 39", + "Correct": "c", + "Explanation": "\"45 - [ 28 - { 37 - ( 15 - * ) } ] = 59 = > 45 - [ 28 - { 37 - 15 + * } ] = 59 45 - [ 28 - 37 + 15 - * ] = 59 = > 45 [ 43 - 37 - * ] = 59 45 - [ 6 - * ] = 59 = > 45 - 6 + * = 59 39 + * = 59 = > * = 59 - 39 = 20 answer : c\"" + }, + { + "Answer": 29, + "Options": "a ) 22 , b ) 29 , c ) 19 , d ) 5 , e ) 2", + "Correct": "b", + "Explanation": "\"( 4 ) 11 x ( 7 ) 5 x ( 11 ) 2 = ( 2 x 2 ) 11 x ( 7 ) 5 x ( 11 ) 2 = 211 x 211 x 75 x 112 = 222 x 75 x 112 total number of prime factors = ( 22 + 5 + 2 ) = 29 . answer b 29\"" + }, + { + "Answer": 234, + "Options": "a ) 230 , b ) 234 , c ) 250 , d ) 547 , e ) 484", + "Correct": "b", + "Explanation": "400 125 \\ / 300 / \\ 175 100 7 : 4 7 - > 150 11 - > ? = > 234 answer : b" + }, + { + "Answer": 24, + "Options": "a ) 12 , b ) 20 , c ) 30 , d ) 15 , e ) 24", + "Correct": "e", + "Explanation": "his savings in 1 year = 1 / 4 - ( 1 / 8 + 1 / 12 ) = 1 / 24 he can buy a new house in 24 years answer : e" + }, + { + "Answer": 46, + "Options": "a ) 53 , b ) 52 , c ) 51 , d ) 46 , e ) 49", + "Correct": "d", + "Explanation": "\"125 - 80 + 1 = 52 ' d ' is the answer\"" + }, + { + "Answer": 21, + "Options": "a ) 20 , b ) 23 , c ) 21 , d ) 25 , e ) 26", + "Correct": "c", + "Explanation": "this is maximum - minimum . hence , 39 - ( 1 + 1 + 1 + 1 + 1 + 1 + 1 ) = 32 and 39 - ( 1 + 2 + 3 + 4 + 5 + 6 + 7 ) = 11 . so , 32 - 11 = 21 . the correct answer is c ." + }, + { + "Answer": 1200.0000000000002, + "Options": "a ) 800 , b ) 500 , c ) 900 , d ) 1200 , e ) none", + "Correct": "d", + "Explanation": "\"answer 1.5 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ] = 1.5 x [ ( 36 x 48 x 250 ) / ( 12 x 9 x 5 ) ] = 1.5 x 4 x 4 x 50 = 1200 correct option : d\"" + }, + { + "Answer": 5.5, + "Options": "a ) 5 / 2 , b ) 10 / 3 , c ) 7 / 2 , d ) 14 / 3 , e ) 11 / 2", + "Correct": "e", + "Explanation": "\"for 2 z ^ 2 + 5 z = 12 roots are [ - 5 + sqrt ( 25 + 96 ) ] / 4 or [ - 5 - sqrt ( 25 + 96 ) ] / 4 = 1.5 or - 4 hence larger root 1.5 is 1.5 - ( - 4 ) = 5.5 = 11 / 2 greater than smaller root ( - 4 ) . hence option ( e ) .\"" + }, + { + "Answer": 125, + "Options": "a ) 125 , b ) 977 , c ) 289 , d ) 1077 , e ) 111", + "Correct": "a", + "Explanation": "let x = 1 and y = 1 f ( 1 + 1 ) = f ( 1 ) + f ( 1 ) + 7 x 1 x 1 + 4 \u21d2 \u21d2 f ( 2 ) = 19 let x = 2 and y = 2 f ( 2 + 2 ) = 19 + 19 + 7 x 2 x 2 + 4 \u21d2 \u21d2 f ( 4 ) = 70 let x = 1 and y = 4 f ( 1 + 4 ) = 4 + 70 + 28 + 4 = 106 f ( 2 ) + f ( 5 ) = 125 answer : a" + }, + { + "Answer": 16, + "Options": "a ) 16 , b ) 25 , c ) 35 , d ) 45 , e ) 55", + "Correct": "a", + "Explanation": "\"a 1 = 120 / 3 = 40 a 2 = a 1 - 8 = 32 sum of second list = 32 * 3 = 96 therefore the number = 96 - 80 = 16 answer : a\"" + }, + { + "Answer": 119.9999999999999, + "Options": "a ) 100 , b ) 120 , c ) 130 , d ) 140 , e ) 150", + "Correct": "b", + "Explanation": "\"let the total weight be x . sand content = ( 1 / 5 ) x water content = ( 3 / 4 ) x gravel = x - ( 1 / 5 ) x - ( 3 / 4 ) x = ( 1 / 20 ) x = 6 x = 120 then answer will be b = 120\"" + }, + { + "Answer": 0.1111111111111111, + "Options": "a ) 2 / 9 , b ) 5 / 7 , c ) 1 / 7 , d ) 1 / 9 , e ) 3 / 7", + "Correct": "d", + "Explanation": "total number of outcomes possible when a die is rolled = 6 ( \u2235 any one face out of the 6 faces ) hence , total number of outcomes possible when a die is rolled twice , n ( s ) = 6 \u00d7 6 = 36 e = getting a sum of 9 when the two dice fall = { ( 3 , 6 ) , { 4 , 5 } , { 5 , 4 } , ( 6 , 3 ) } hence , n ( e ) = 4 p ( e ) = n ( e ) / n ( s ) = 4 / 36 = 1 / 9 answer : option d" + }, + { + "Answer": 360, + "Options": "a ) 40 / 3 , b ) 40 , c ) 120 , d ) 360 , e ) 420", + "Correct": "d", + "Explanation": "case 1 : deposit = $ x ; rate of increase = r . interest yearned in 1 year = xr . deposit in 1 year = x + xr . interest yearned in 2 year = ( x + xr ) r . the difference a = ( x + xr ) r - xr = xr ^ 2 = 40 . case 2 : deposit = $ x ; rate of increase = 3 r . interest yearned in 1 year = x ( 3 r ) . deposit in 1 year = x + 3 xr . interest yearned in 2 year = ( x + 3 xr ) 3 r . the difference = ( x + 3 xr ) 3 r - 3 xr = 9 xr ^ 2 . since from case 1 we know that xr ^ 2 = 40 , then 9 xr ^ 2 = 9 * 40 = 360 . answer : d ." + }, + { + "Answer": 75, + "Options": "a ) 74 , b ) k = 75 , c ) k = 175 , d ) k = 680 , e ) 690", + "Correct": "b", + "Explanation": "\"i solved this question by plugging in numbers from the answer choices . a . ) 74 starting with answer choice a , i immediately eliminated it because 74 is not even divisible by 5 . b . ) 75 i divide 75 / 5 and get 15 as an answer . i divide 75 / 34 and get a remainder of 7 . 15 - 7 = 8 so i know the correct answer isb\"" + }, + { + "Answer": 673, + "Options": "a ) 560 , b ) 561 , c ) 562 , d ) 563 , e ) 673", + "Correct": "e", + "Explanation": "total price of 8 t - shirts = 8 * 526 = 4208 total price of 7 t - shirts = 7 * 505 = 3535 total price of 1 t - shirts = 4208 - 3535 = 673 average price of 3 t - shirts = 673 correct option answer : e" + }, + { + "Answer": 9, + "Options": "a ) 8 , b ) 10 , c ) 9 , d ) 14 , e ) 16", + "Correct": "c", + "Explanation": "\"explanation : = > 3 ( 2 x + 6 ) = 72 = > 2 x + 6 = 24 = > x = 9 option c\"" + }, + { + "Answer": 0.48, + "Options": "a ) 2 / 125 , b ) 12 / 25 , c ) c ) 2 / 25 , d ) 3 / 25 , e ) 1 / 5", + "Correct": "b", + "Explanation": "p ( playing 2 or more instruments ) = 96 / 800 = 3 / 25 . then , the probability of playing exactly one instrument is given by : p ( playing 1 or more instruments ) - p ( playing 2 or more instruments ) = 3 / 5 - 3 / 25 = 12 / 25 . answer b ." + }, + { + "Answer": 0.75, + "Options": "a ) 3 / 4 , b ) 5 / 6 , c ) 7 / 8 , d ) 5 / 8 , e ) 7 / 12", + "Correct": "a", + "Explanation": "let p be the capacity of jar x . the amount of water in jar y is 1 / 2 * p / 2 = p / 4 then the total amount in jar x is p / 2 + p / 4 = 3 p / 4 the answer is a ." + }, + { + "Answer": 0.19999999999999968, + "Options": "a ) 1 / 5 , b ) 2 / 3 , c ) 5 / 7 , d ) 7 / 5 , e ) 3 / 2", + "Correct": "a", + "Explanation": "say the total number of players is 18 , 9 right - handed and 9 left - handed . on a certain day , two - thirds of the players were absent from practice - - > 6 absent and 12 present . of the players at practice that day , one - third were left - handed - - > 12 * 1 / 3 = 4 were left - handed and 8 right - handed . the number of right - handed players who were not at practice that day is 9 - 8 = 1 . the number of left - handed players who were not at practice that days is 9 - 4 = 5 . the ratio = 1 / 5 . answer : a ." + }, + { + "Answer": 1360, + "Options": "a ) $ 1360 , b ) $ 1620 , c ) $ 1650 , d ) $ 680 , e ) $ 770", + "Correct": "a", + "Explanation": "\"for 200 - 80 - 20 = 100 pages only cost is 5 $ per page for the first time page is typed - 100 * 5 = 500 $ ; for 80 pages the cost is : first time 5 $ + 3 $ of the first revision - 80 * ( 5 + 3 ) = 640 $ ; for 20 pages the cost is : first time 5 $ + 3 $ of the first revision + 3 $ of the second revision - 20 ( 5 + 3 + 3 ) = 220 $ ; total : 500 + 640 + 220 = 1360 $ . answer : a .\"" + }, + { + "Answer": 3800, + "Options": "a ) rs . 6003 , b ) rs . 3800 , c ) rs . 1288 , d ) rs . 6108 , e ) rs . 6011", + "Correct": "b", + "Explanation": "\"explanation : manager ' s monthly salary rs . ( 1800 * 21 - 1700 * 20 ) = rs . 3800 . answer : b\"" + }, + { + "Answer": 198.69662921348313, + "Options": "a ) 199 , b ) 154 , c ) 852 , d ) 741 , e ) 785", + "Correct": "a", + "Explanation": "\"divisor * quotient + remainder = dividend divisor = ( dividend ) - ( remainder ) / quotient ( 17698 - 14 ) / 89 = 199 answer ( a )\"" + }, + { + "Answer": 10, + "Options": "a ) 14 years , b ) 12 years , c ) 56 years , d ) 10 years , e ) 55 years", + "Correct": "d", + "Explanation": "\"given that a + b = 10 + b + c = > a \u00e2 \u20ac \u201c c = 10 + b \u00e2 \u20ac \u201c b = 10 = > c is younger than a by 10 years answer : d\"" + }, + { + "Answer": 15, + "Options": "a ) 14.4 , b ) 14.7 , c ) 15.0 , d ) 15.3 , e ) 15.6", + "Correct": "c", + "Explanation": "\"let x be the factor by which the bacteria increases every three hours . at 4 : 00 pm , the amount of bacteria was 10 x and at 7 : 00 pm it was 10 x ^ 2 . 10 x ^ 2 = 22.5 x ^ 2 = 2.25 x = 1.5 at 4 : 00 pm , the amount of bacteria was 10 ( 1.5 ) = 15 grams . the answer is c .\"" + }, + { + "Answer": 12, + "Options": "a ) 10 , b ) 12 , c ) 15 , d ) 18 , e ) 20", + "Correct": "b", + "Explanation": "6 x ^ 2 + x - 12 = 6 x ^ 2 + 9 x - 8 x - 12 = > 3 x ( 2 x + 3 ) - 4 ( 2 x + 3 ) = > ( 2 x + 3 ) ( 3 x - 4 ) = ( ax + w ) ( cx + d ) hence a = 2 , w = c = 3 , d = - 4 so , 2 + 3 + 3 + | - 4 | = 2 + 3 + 3 + 4 = 12 answer b ." + }, + { + "Answer": 4400, + "Options": "a ) 4400 , b ) 3500 , c ) 8700 , d ) 9000 , e ) 8000", + "Correct": "a", + "Explanation": "\"x * ( 95 / 100 ) * ( 85 / 100 ) = 3553 x = 4400 answer a\"" + }, + { + "Answer": 35, + "Options": "a ) 25 , b ) 27 , c ) 30 , d ) 35 , e ) none", + "Correct": "d", + "Explanation": "solution excluded number = ( 27 x 5 ) - ( 25 x 4 ) = 135 - 100 = 35 . answer d" + }, + { + "Answer": 38, + "Options": "a ) 19 , b ) 29 , c ) 38 , d ) 49 , e ) 59", + "Correct": "c", + "Explanation": "\"let the average after 17 th inning = x then average after 16 th inning = ( x - 3 ) therefore 16 ( x - 3 ) + 86 = 17 x therefore x = 38 answer : c\"" + }, + { + "Answer": 200, + "Options": "a ) 150 , b ) 200 , c ) 250 , d ) 300 , e ) 350", + "Correct": "b", + "Explanation": "( 1 - ( 1 / 16 ) ) ( 1 - ( 1 / 15 ) ) ( 1 - ( 5 / 7 ) ) of income = 50 hence income = 200 answer : b" + }, + { + "Answer": 0.2857142857142857, + "Options": "a ) 2 / 7 , b ) 3 / 8 , c ) 9 / 16 , d ) 5 / 8 , e ) 16 / 9", + "Correct": "a", + "Explanation": "\"3 / 5 * 5 / 7 * 2 / 3 = 2 / 7 answer : a\"" + }, + { + "Answer": 220, + "Options": "a ) 130 , b ) 140 , c ) 150 , d ) 220 , e ) 280", + "Correct": "d", + "Explanation": "let the amount paid to a per week = x and the amount paid to b per week = y then x + y = 550 but x = 150 % of y = 150 y / 100 = 15 y / 10 \u2234 15 y / 10 + y = 550 \u21d2 y [ 15 / 10 + 1 ] = 550 \u21d2 25 y / 10 = 550 \u21d2 25 y = 5500 \u21d2 y = 5500 / 25 = rs . 220 d )" + }, + { + "Answer": 66.05504587155964, + "Options": "a ) 59 % , b ) 55 % , c ) 63 % , d ) 66 % , e ) 68 %", + "Correct": "d", + "Explanation": "\"say a 100 families existed in 1991 then the number of families owning a computer in 1991 - 60 number of families owning computer in 1993 = 60 * 120 / 100 = 72 number of families in 1993 = 109 the percentage = 72 / 109 * 100 = 66 % . answer : d\"" + }, + { + "Answer": 800, + "Options": "a ) $ 800 , b ) $ 1000 , c ) $ 600 , d ) $ 400 , e ) $ 500", + "Correct": "a", + "Explanation": "increase in house value = $ 28,000 - $ 20,000 = $ 8000 so , tax increase = 10 % of $ 8000 = $ 800 answer : a" + }, + { + "Answer": 0.75, + "Options": "a ) 0.65 , b ) 0.25 , c ) 0.75 , d ) 0.85 , e ) none", + "Correct": "c", + "Explanation": "\"sol . ( x \u00d7 2 ) = ( 0.25 \u00d7 6 ) \u21d2 x = 1.5 / 2 = 0.75 . answer c\"" + }, + { + "Answer": 324, + "Options": "a ) 534 , b ) 446 , c ) 354 , d ) 324 , e ) none of them", + "Correct": "d", + "Explanation": "= a ^ 2 + b ^ 2 - 2 ab where a = 287 and b = 269 = ( a - b ) ^ 2 = ( 287 - 269 ) ^ 2 = ( 18 ) ^ 2 = 324 answer is d" + }, + { + "Answer": 400, + "Options": "a ) 90 , b ) 120 , c ) 160 , d ) 360 , e ) 400", + "Correct": "e", + "Explanation": "\"if we exclude those cases and take the question at face value , then it seems straightforward . group # 1 = ( did n ' t like , did n ' t understand ) = 100 group # 2 = ( likeunderstood ) = 3 / 4 ( 1 / 4 ) n = 100 n = 400 answer = ( e )\"" + }, + { + "Answer": 3, + "Options": "a ) 3 , b ) 2 , c ) 1 , d ) 0 , e ) 4", + "Correct": "a", + "Explanation": "\"| 8 - 3 | - | 4 - 6 | = | 5 | - | - 2 | = 5 - 2 = 3 correct answer a\"" + }, + { + "Answer": 5, + "Options": "a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3", + "Correct": "c", + "Explanation": "\"x is an integer and 2.134 \u00d7 10 x is less than 240,000 , what is the greatest possible value for x ? for 2.134 \u00d7 10 x is less than 240,000 to remain true , the greatest number is 213,400 , which makes x = 5 c . 5\"" + }, + { + "Answer": 3, + "Options": "a ) 3 , b ) 5 , c ) 8 , d ) 13 , e ) 15", + "Correct": "a", + "Explanation": "\"total # of students = 40 avg # of books per student = 2 total # of books = 40 * 2 = 80 # of student borrowed at least 3 books = 40 - 2 - 12 - 10 = 16 # of books borrowed by above 16 students = 80 - ( 12 * 1 ) - ( 10 * 2 ) = 48 considering that 15 out of above 16 students borrowed only 3 books , # of books borrowed = 15 * 3 = 45 so maximum # of books borrowed by any single student = 48 - 45 = 3 option a\"" + }, + { + "Answer": 49.99999999999999, + "Options": "a ) 14.3 % , b ) 16.67 % , c ) 33 % , d ) 28.6 % , e ) 49.67 %", + "Correct": "e", + "Explanation": "the exam gives us a number that is easily divisible by 7 to pique our curiosity and tempt us into calculating actual numbers ( also because otherwise the ratio would be incorrect ) . since the question is about percentages , the actual numbers will be meaningless , as only the ratio of that number versus others will be meaningful . nonetheless , for those who are curious , each 1 / 7 portion represents ( 14210 / 7 ) 2,030 employees . this in turn means that 4,060 employees are journeymen and the remaining 10,150 are full time workers . if half the journeymen were laid off , that would mean 1 / 7 of the total current workforce would be removed . this statistic is what leads many students to think that since half the journeymen are left , the remaining journeymen would represent half of what they used to be , which means 1 / 7 of the total workforce . if 1 / 7 of the workforce is journeymen , and 1 / 7 is roughly 14.3 % , then answer choice a should be the right answer . in this case , though , it is merely the tempting trap answer choice . what changed between the initial statement and the final tally ? well , you let go of 1 / 7 of the workforce , so the total number of workers went down . the remaining workers are still 1 / 7 of the initial workers , but the group has changed . the new workforce is smaller than the original group , specifically 6 / 7 of it because 1 / 7 was eliminated . the remaining workers now account for 1 / 7 out of 6 / 7 of the force , which if we multiply by 7 gives us 1 out of 6 . this number as a percentage is answer choice b , 49.67 % . using the absolute numbers we calculated before , there were 4,060 journeymen employees out of 14,210 total . if 2,030 of them are laid off , then there are 2,030 journeyman employees left , but now out of a total of ( 14,210 - 2,030 ) 12,180 employees . 2,030 / 12,180 is exactly 1 / 6 , or 16.67 % . the answer will work with either percentages or absolute numbers , but the percentage calculation will be significantly faster and applicable to any similar situation . the underlying principle of percentages ( and , on a related note , ratios ) can be summed up in the brainteaser i like to ask my students : if you \u2019 re running a race and you overtake the 2 nd place runner just before the end , what position do you end up in ? the correct answer is 2 nd place . percentages , like ratios and other concepts of relative math , depend entirely on the context . whether 100 % more of something is better than 50 % more of something else depends on the context much more than the percentages quoted . when it comes to percentages on the gmat , the goal is to understand them enough to instinctively not fall into the traps laid out for you . e" + }, + { + "Answer": 33, + "Options": "a ) 26 , b ) 22 , c ) 25 , d ) 27 , e ) 33", + "Correct": "e", + "Explanation": "( 4 ) ^ 13 x ( 7 ) ^ 5 x ( 11 ) ^ 2 = ( 2 x 2 ) ^ 13 x ( 7 ) ^ 5 x ( 11 ) ^ 2 = 2 ^ 13 x 2 ^ 13 x 7 ^ 5 x 11 ^ 2 = 2 ^ 26 x 7 ^ 5 x 11 ^ 2 total number of prime factors = ( 26 + 5 + 2 ) = 33 . answer is e ." + }, + { + "Answer": 20, + "Options": "a ) 20 , b ) 25 , c ) 27 , d ) 22 , e ) 91", + "Correct": "a", + "Explanation": "\"let the son ' s present age be x years . then , man ' s present age = ( x + 22 ) years . ( x + 22 ) + 2 = 2 ( x + 2 ) x + 24 = 2 x + 4 = > x = 20 . answer : a\"" + }, + { + "Answer": 50, + "Options": "a ) 82 m , b ) 50 m , c ) 72 m , d ) 80 m , e ) none of these", + "Correct": "b", + "Explanation": "\"explanation : the relative speed of train is 46 - 36 = 10 km / hr = ( 10 x 5 ) / 18 = 25 / 9 m / s 10 \u00d7 518 = 259 m / s in 36 secs the total distance travelled is 36 x 25 / 9 = 100 m . therefore the length of each train is = 100 / 2 = 50 m . answer b\"" + }, + { + "Answer": 0.3333333333333333, + "Options": "a ) 1 / 6 , b ) 3 / 10 , c ) 1 / 3 , d ) 1 / 2 , e ) 2 / 3", + "Correct": "c", + "Explanation": "the car ends within a half mile of the sign indicating 2 1 / 2 miles means that the car will end in one mile interval , between the signs indicating 2 and 3 miles . now , it does n ' t matter where the car starts or what distance it travels , the probability will be p = ( favorable outcome ) / ( total # of outcomes ) = 1 / 3 ( as the car starts at random point end travels some distance afterwards we can consider its end point as the point where he randomly appeared , so the probability that the car appeared within 1 mile interval out of total 3 miles will be 1 / 3 ) . answer : c ." + }, + { + "Answer": 11, + "Options": "a ) 10 , b ) 7 , c ) 11 , d ) 5 , e ) 3", + "Correct": "c", + "Explanation": "t 4 + t 20 = t 8 + t 15 + t 12 = > a + 3 d + a + 19 d = a + 7 d + a + 14 d + a + 11 d = > a + 10 d = 0 = > t 11 = 0 i . e . 11 th term is zero . answer : c" + }, + { + "Answer": 3.6, + "Options": "a ) 2.4 , b ) 2.7 , c ) 3.0 , d ) 3.3 , e ) 3.6", + "Correct": "e", + "Explanation": "\"let x be the amount of pure alcohol required . 0.2 ( 6 ) + x = 0.5 ( x + 6 ) 0.5 x = 3 - 1.2 x = 3.6 liters the answer is e .\"" + }, + { + "Answer": 16, + "Options": "a ) 12 , b ) 16 , c ) 17 , d ) 19 , e ) 21", + "Correct": "b", + "Explanation": "the worst case scenario will be if we remove all 14 tablets of medicine b first . the next 2 tablets we remove have to be of medicine a , so to guarantee that at least two tablets of each kind will be taken we should remove minimum of 14 + 2 = 16 tablets . answer : b ." + }, + { + "Answer": 24, + "Options": "a ) 25 , b ) 24 , c ) 27 , d ) 28 , e ) 29", + "Correct": "b", + "Explanation": "\"present age = x before 7 yrs , y = x - 7 after 7 yrs , z = x + 7 by the qn , x + ( x - 7 ) = 27 2 x - 7 = 27 2 x = 27 + 7 x = 34 / 2 x = 17 z = x + 7 = 17 + 7 = 24 answer : b\"" + }, + { + "Answer": 799.9999999999999, + "Options": "a ) 1000 , b ) 800 , c ) 2889 , d ) 2777 , e ) 2991", + "Correct": "b", + "Explanation": "\"896 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 800 answer : b\"" + }, + { + "Answer": 42, + "Options": "a ) 34 , b ) 38 , c ) 36 , d ) 40 , e ) 42", + "Correct": "e", + "Explanation": "\"at 6 ' o clock , there would be 6 strikes . first strike , then a short interval , the second strike , then a short interval and so on till the 6 th strike . so there would be in all 5 intervals between 6 strikes . similarly , between 11 strikes , there would be 10 intervals . according to the question , the time spent in the strike and the interval is same . at 6 ' o clock , the 6 strikes and the 5 intervals together take 22 sec so each strike and each interval takes 2 secs . at 11 ' o clock , the 11 strikes and 10 intervals will take 2 * ( 11 + 10 ) = 42 secs e\"" + }, + { + "Answer": 13, + "Options": "a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15", + "Correct": "c", + "Explanation": "four wheeler = 13 * 4 = 52 ( max ) 2 wheel = 1 so no of 4 wheeler = 13 answer : c" + }, + { + "Answer": 80, + "Options": "a ) 60 , b ) 80 , c ) 40 , d ) 120 , e ) 160", + "Correct": "b", + "Explanation": "\"( 1 + 1 / 8 ) x - ( 1 - 1 / 4 ) x = 30 ( 9 / 8 ) x - ( 3 / 4 ) x = 30 x = 80 = w answer : b\"" + }, + { + "Answer": 9.6, + "Options": "a ) 9.6 , b ) 11 , c ) 11.5 , d ) 12 , e ) 12.5", + "Correct": "a", + "Explanation": "\"mean = 12 two standard deviations is 1.2 + 1.2 = 2.4 there could be two calues for this . mean + two standard deviations = 14.4 mean - two standard deviations = 9.6 answer choice has 9.6 and so a is the answer .\"" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 9 / 4 , c ) 16 / 25 , d ) 7 / 1 , e ) 7 / 2", + "Correct": "a", + "Explanation": "\"for a 2 nd degree equation ax 2 + bx _ c = 0 has equal roots the condition is b 2 - 4 ac = 0 in the given equation ( 4 k ) ^ 2 - 4 * 2 k * 2 = 0 by solving this equation we get k = 0 , k = 1 answer : a\"" + }, + { + "Answer": 14, + "Options": "a ) 4 , b ) 12 , c ) 14 , d ) 21 , e ) 28", + "Correct": "c", + "Explanation": "\"if a ^ 2 - b ^ 2 = 0 , then let ' s assume that a = b . a must equal the 4 th positive multiple of 4 , thus a = 28 , which also equals b . b is the second positive multiple of n , thus n = 28 / 2 = 14 . the answer is c .\"" + }, + { + "Answer": 318, + "Options": "a ) 156 , b ) 162 , c ) 318 , d ) 324 , e ) 325", + "Correct": "c", + "Explanation": "buy as many $ 50 deals as possible . we can by 650 / 50 = 13 two dozen roses , thus total of 13 * 24 = 312 roses . we are left with 680 - 650 = $ 30 . we can buy 30 / 4.5 = ~ 6 roses for that amount . total = 312 + 6 = 318 . answer : c ." + }, + { + "Answer": 2200, + "Options": "a ) 2200 , b ) 2550 , c ) 5050 , d ) 6275 , e ) 11325", + "Correct": "a", + "Explanation": "\"set a contains 8 , 10 , 12 . . . 50 set b contains 108 , 110 , 112 . . . 150 number of terms in each set = 22 difference between corresponding terms in set a and b = 100 difference between sum of set b and set a = 100 * 22 = 2200 answer a\"" + }, + { + "Answer": 8, + "Options": "a ) 9 , b ) 8 , c ) 0 , d ) 2 , e ) 1", + "Correct": "b", + "Explanation": "explanation : given , number is divisible by 8 only if ' a 16 ' is divisible by 8 . . : highest value of a is ' 8 ' . answer : option b" + }, + { + "Answer": 14.285714285714292, + "Options": "a ) 13.28 % , b ) 14.28 % , c ) 15.28 % , d ) 16.28 % , e ) 17.28 %", + "Correct": "b", + "Explanation": "\"let total % of work is 100 % total person = p 1 / 8 person are absent of total person . so absent person is 1 / 8 p ie p / 8 . left person is , p - p / 8 = 7 p / 8 . p person do the work 100 % 1 person do the work 100 * p % 7 p / 8 person do the work ( 100 * p * 8 ) / 7 p % = 114.28 % work increased for each person is = ( 114.28 - 100 ) % = 14.28 % answer : b\"" + }, + { + "Answer": 0.25, + "Options": "a ) 1 / 2 , b ) 1 / 4 , c ) 3 / 4 , d ) 2 / 3 , e ) none of these", + "Correct": "b", + "Explanation": "\"explanation : a \u00e2 \u02c6 \u2014 b \u00e2 \u02c6 \u2014 c / b \u00e2 \u02c6 \u2014 c \u00e2 \u02c6 \u2014 d = 65 / 65 = > a / d = 1 d \u00e2 \u02c6 \u2014 e \u00e2 \u02c6 \u2014 f / c \u00e2 \u02c6 \u2014 d \u00e2 \u02c6 \u2014 e = 250 / 1000 = > f / c = 1 / 4 a / d * f / c = 1 * 1 / 4 = 1 / 4 answer : b\"" + }, + { + "Answer": 0.1111111111111111, + "Options": "a ) 5 / 6 , b ) 1 / 5 , c ) 1 / 6 , d ) 1 / 9 , e ) 1 / 24", + "Correct": "d", + "Explanation": "let x be the number of upgraded sensors on the satellite . the number of non - upgraded sensors per unit is x / 3 . the number of non - upgraded sensors on the whole satellite is 24 ( x / 3 ) = 8 x . the fraction of sensors which have been upgraded is x / ( x + 8 x ) = x / 9 x = 1 / 9 the answer is d ." + }, + { + "Answer": 0.010000000000000002, + "Options": "a ) 0.0016 , b ) 0.0625 , c ) 0.16 , d ) 0.25 , e ) 0.01", + "Correct": "e", + "Explanation": "\"( 1 / 10 ) \u00b2 = ( 1 / 10 ) ( 1 / 10 ) = 1 / 100 approach # 1 : use long division to divide 100 into 1 to get 1 / 100 = 0.01 e\"" + }, + { + "Answer": 0.125, + "Options": "a ) 1 / 16 , b ) 1 / 8 , c ) 3 / 16 , d ) 3 / 8 , e ) 13 / 16", + "Correct": "b", + "Explanation": "s : simon t : theresa r : roger let theresa baked a . as per question , we have s = a + 2 n r = 2 a = n / 3 or a = n / 6 now , total = a + ( a + 2 n ) + 2 a = 8 n / 3 fraction , ( n / 3 ) / ( 8 n / 3 ) = 1 / 8 answer : b" + }, + { + "Answer": 17, + "Options": "a ) 33 , b ) 17 , c ) 49 , d ) 16 , e ) 23", + "Correct": "b", + "Explanation": "x - y - z = x - x / 4 - x / 7 = ( 28 - 7 - 4 ) x / 28 = 17 x / 28 17 is not divisible by 28 ( it ' s a prime # ) , so for least value , x = 28 answer - b" + }, + { + "Answer": 36, + "Options": "a ) 18 % , b ) 30 % , c ) 36 % , d ) 48 % , e ) 54 %", + "Correct": "c", + "Explanation": "\"given voters in ratio 2 : 1 let x has 200 votersy has 100 voters for x 72 % voted means 72 * 200 = 144 votes combined for xy has 300 voters and voted 60 % so total votes = 180 balance votes = 180 - 144 = 36 as y has 100 voters so 36 votes means 36 % of votes required ans c\"" + }, + { + "Answer": 62.5, + "Options": "a ) 23 , b ) 41 , c ) 48 , d ) 62 , e ) 86", + "Correct": "d", + "Explanation": "to get maximum vehicles we must take into consideration the minimum weight i . e 1600 pounds here since , 1 ton = 2000 pounds 50 tons will be 100,000 pounds from the answer choices : let max number of vehicles be 62 total weight will be = 62 * 1600 = 99200 pounds , which is lesser than the maximum weight allowed . ans : d" + }, + { + "Answer": 10, + "Options": "a ) 7.9 s , b ) 2.5 s , c ) 7.5 s , d ) 7.6 s , e ) 10 s", + "Correct": "e", + "Explanation": "\"explanation : 54 km / hr = 54 * 5 / 18 = 15 m / s speed = distance / time ; v = d / t 15 = 150 / t t = 10 s answer : e\"" + }, + { + "Answer": 104, + "Options": "a ) 123 , b ) 106 , c ) 100 , d ) 156 , e ) 104", + "Correct": "e", + "Explanation": "\"explanation : cash realised = rs . ( 104.25 - 0.25 ) = rs . 104 . answer : e\"" + }, + { + "Answer": 280.59999999999997, + "Options": "a ) 190 , b ) 284.6 , c ) 300 , d ) 280 , e ) 312", + "Correct": "d", + "Explanation": "\"so 12.2 * 23 = 280 . . imo option d is correct answer . .\"" + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9", + "Correct": "a", + "Explanation": "\"the numbers should be of the form 11 c + 3 . the minimum is 3 when c = 0 . the maximum is 47 when c = 4 . there are 5 such numbers . the answer is a .\"" + }, + { + "Answer": 3, + "Options": "a ) 3 , b ) 5 , c ) 7 , d ) 12 , e ) 15", + "Correct": "a", + "Explanation": "\"sol . let the number be x . then , x + 17 = 60 / x \u21d4 x 2 + 17 x - 60 = 0 \u21d4 ( x + 20 ) ( x - 3 ) = 0 \u21d4 x = 3 . answer a\"" + }, + { + "Answer": 220080, + "Options": "a ) 220880 , b ) 145778 , c ) 220081 , d ) 220080 , e ) 220030", + "Correct": "d", + "Explanation": "( 555 + 445 ) * 2 * 110 + 80 = 220000 + 80 = 220080 d" + }, + { + "Answer": 31, + "Options": "a ) 31 , b ) 39 , c ) 30 , d ) 33 , e ) 34", + "Correct": "a", + "Explanation": "explanation : let total participants be ( x + 1 ) then = > ( 1 / 5 ) * x + ( 5 / 6 ) * x = x + 1 = > 31 x / 30 = x + 1 = > x = 30 so total participants ( x + 1 ) = 31 hence ( a ) is the correct answer . answer : a" + }, + { + "Answer": 6084, + "Options": "a ) 6084 , b ) 6184 , c ) 5084 , d ) 6048 , e ) 6049", + "Correct": "a", + "Explanation": "\"1347 7431 - - - - - - - - - - - - 6084 answer : a\"" + }, + { + "Answer": 0.5, + "Options": "a ) 1 / 2 , b ) 1 , c ) 2 , d ) 4 , e ) 8", + "Correct": "a", + "Explanation": "\"given : 2 / w + 2 / x = 2 / ywx = y find : ( w + x ) / 2 = ? 2 ( 1 / w + 1 / x ) = 2 ( 1 / y ) - divide both sides by 2 ( 1 / w + 1 / x ) = 1 / y ( x + w ) / wx = 1 / wx - sub ' d in y = wx x + w - 1 = 0 x + w = 1 therefore ( w + x ) / 2 = 1 / 2 ans : a\"" + }, + { + "Answer": 4, + "Options": "a ) 3 , b ) 4 , c ) 6 , d ) 7 , e ) 8", + "Correct": "b", + "Explanation": "\"explanation : on dividing 427398 by 11 we get the remainder 4 , so 4 should be subtracted answer : option b\"" + }, + { + "Answer": 3250, + "Options": "a ) rs . 3250 , b ) rs . 3350 , c ) rs . 3450 , d ) rs . 3550 , e ) rs . 3650", + "Correct": "a", + "Explanation": "ratio of shares of a , b , c , d = ( 24 * 3 ) : ( 10 * 5 ) : ( 35 * 4 ) : ( 21 * 3 ) = 72 : 50 : 140 : 63 let total rent be rs . x . then , a \u2019 s share = rs . 72 x / 325 . therefore , 72 x / 325 = 720 = > x = 720 * 325 / 72 = 3250 . hence , total rent of the field is rs . 3250 . answer : a" + }, + { + "Answer": 9, + "Options": "a ) 4 . , b ) 9 . , c ) 12 . , d ) 16 . , e ) 64 .", + "Correct": "b", + "Explanation": "\"eq 1 : a - b - c + d = 12 eq 2 : a + b - c - d = 6 ( 1 ) subtract eq 1 from eq 2 a - b - c + d = 12 - a + b - c - d = 6 - - - - - - - - - - - - - - - - - - - - - - - - - 2 b + 2 d = 6 ( 2 ) simplify - b + d = 3 b - d = - 3 ( b - d ) ^ 2 = ( - 3 ) ^ 2 = 9 my answer : b\"" + }, + { + "Answer": 6.5, + "Options": "a ) 6.5 , b ) 5 , c ) 5.5 , d ) 5.8 , e ) 6", + "Correct": "a", + "Explanation": "\"if $ x $ is the number , x / 6 * 12 = 13 = > 2 x = 13 = > x = 6.5 a\"" + }, + { + "Answer": 68, + "Options": "a ) 86.5 kg , b ) 67.5 kg , c ) 46.5 kg , d ) 26.5 kg , e ) 16.5 kg", + "Correct": "b", + "Explanation": "\"let arun ' s weight be x kg . according to arun , 66 < x < 72 . according to arun ' s brother , 60 < x < 70 . according to arun ' s mother , x < 69 . the values satisfying all the above conditions are 67 and 68 . required average = ( 67 + 68 ) / 2 = 67.5 kg answer : b\"" + }, + { + "Answer": 1634, + "Options": "a ) 1235 , b ) 1456 , c ) 1634 , d ) 1678 , e ) 1635", + "Correct": "c", + "Explanation": "\"let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 20 5 x = 1345 x = 269 large number = 269 + 1365 = 1634 c\"" + }, + { + "Answer": 56.666666666666664, + "Options": "a ) 42.5 % , b ) 62.1 % , c ) 56.7 % , d ) 39.9 % , e ) 51.4 %", + "Correct": "c", + "Explanation": "\"total number of students = 50 + 100 = 150 number of students passed = ( 50 % of 50 + 40 % of 100 ) = 25 + 40 = 65 number of failures = 85 * 100 / 150 = 56.7 % answer is c\"" + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 9 , c ) 11 , d ) 13 , e ) 15", + "Correct": "a", + "Explanation": "\"( 5 ^ 5 ) ( 9 ^ 3 ) = 3 ( 15 ^ x ) = > 5 ^ 5 * 3 ^ 6 = 3 * 3 ^ x * 5 ^ x = > 5 ^ 5 * 3 ^ 6 = 3 ^ ( x + 1 ) * 5 ^ x value of x = 5 answer a\"" + }, + { + "Answer": 64, + "Options": "a ) 124 % , b ) b ) 64 % , c ) c ) 96 % , d ) d ) 80 % , e ) e ) 64 %", + "Correct": "b", + "Explanation": "\"m = ( 160 / 100 ) t t = ( 40 / 100 ) j = > m = ( 64 / 100 ) j answer b .\"" + }, + { + "Answer": 1800, + "Options": "a ) 2000 , b ) 1900 , c ) 1800 , d ) 1600 , e ) 1,500", + "Correct": "c", + "Explanation": "digit a can be filled in 9 ways ( excluding 0 ) digit b can be filled in 10 ways digit c can be filled in 10 ways digit d can be filled in 2 ways ( because of modulus a - d ) the answer will be 9 * 10 * 10 * 2 = 1800 ans c" + }, + { + "Answer": 423, + "Options": "a ) 395 , b ) 275 , c ) 355 , d ) 423 , e ) 365", + "Correct": "d", + "Explanation": "the mean of numbers 28 , x , 42 , 78 and 104 is 62 : 28 + x + 42 + 78 + 104 = 90 * 5 - - > x = 198 ; so , the mean of 128 , 255 , 511 , 1023 and x is ( 128 + 255 + 511 + 1023 + 198 ) / 5 = 423 . answer : d ." + }, + { + "Answer": 630, + "Options": "a ) 400 km , b ) 500 km , c ) 360 km , d ) 550 km , e ) 630 km", + "Correct": "e", + "Explanation": "\"sol . average speed of a tractor = 25 km / h the speed of a bus in an hour = 25 \u00d7 2 = 50 km the speed of a car in an hour = 9 / 5 * 50 = 90 km so , the distance covered by car in 7 h is 90 \u00d7 7 = 630 km ans . ( e )\"" + }, + { + "Answer": 1.4, + "Options": "a ) $ 0.60 , b ) $ 0.80 , c ) $ 1.00 , d ) $ 1.20 , e ) $ 1.40", + "Correct": "e", + "Explanation": "\"let price of a sundae = s price of ice cream bar = . 6 $ 125 * . 6 + 125 * s = 250 = > 125 * s = 175 = > s = 1.4 answer e\"" + }, + { + "Answer": 7, + "Options": "a ) 3 years , b ) 4 years , c ) 6 years , d ) 7 years , e ) 8 years", + "Correct": "d", + "Explanation": "\"let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 65 5 x = 35 x = 7 . age of the youngest child = x = 7 years . d )\"" + }, + { + "Answer": 10.999999999999998, + "Options": "a ) 12 , b ) 15 , c ) 10 , d ) 11 , e ) 13", + "Correct": "d", + "Explanation": "\"2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 31 - 9 = 22 ab = 11 . answer is d .\"" + }, + { + "Answer": 160, + "Options": "a ) 40 , b ) 60 , c ) 160 , d ) 100 , e ) 120", + "Correct": "c", + "Explanation": "xy + xz = 132 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 1 ) yz + yx = 152 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2 ) xz + zy = 180 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 3 ) re - writing equation 3 as follows : xz + zy = 152 + 28 xz + zy = yz + yx + 28 xz = yx + 28 . . . . . . . . . . . . . . . ( 4 ) adding ( 1 ) ( 4 ) 2 xz = 160 xz = 80 xyz has to be multiple of 80 , only 160 fits in answer = c" + }, + { + "Answer": 5, + "Options": "a ) 8 , b ) 7 , c ) 6 , d ) 5 , e ) 4", + "Correct": "d", + "Explanation": "14 ^ m = 2 ^ m * 7 ^ m . let ' s figure out how many 7 ' s are in the prime factorization of 40 ! the multiples of 7 are : 7 , 14 , 21 , 28 , 35 . thus 7 ^ 5 will divide 40 ! but 7 ^ 6 will not . clearly 2 ^ 5 will divide 40 ! so m = 5 is the largest possible integer . the answer is d ." + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "c", + "Explanation": "x = ( y / 7 ) - ( 2 / 5 ) , and so y = 7 x + 14 / 5 . the slope is 7 . ( n + 21 - n ) / ( m + p - m ) = 7 p = 3 the answer is c ." + }, + { + "Answer": 780, + "Options": "a ) $ 760 , b ) $ 750 , c ) $ 810 , d ) $ 800 , e ) $ 780", + "Correct": "e", + "Explanation": "50 pages typed 1 x 30 pages typed 2 x ( original + one revision ) 20 pages typed 3 x ( original + two revisions ) 50 ( 5 ) + 30 ( 5 + 4 ) + 20 ( 5 + 4 + 4 ) = 250 + 270 + 260 = 780 answer - e" + }, + { + "Answer": 83, + "Options": "a ) 81 % , b ) 82 % , c ) 83 % , d ) 84 % , e ) 85 %", + "Correct": "c", + "Explanation": "\"( 15 * 75 + 10 * 95 ) / 25 = 83 % the answer is c .\"" + }, + { + "Answer": 6, + "Options": "a ) 2 , b ) 3 , c ) 6 , d ) 7 , e ) 8", + "Correct": "c", + "Explanation": "one way of solving this is : speed of boat on still water ( lake ) = 5 kmph speed upstream = 4 kmph = speed in still water - speed of river = > speed of river = 1 kmph = > speed downstream = speed in still water + speed of river = 5 + 1 = 6 kmph ans is c" + }, + { + "Answer": 19, + "Options": "a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19", + "Correct": "e", + "Explanation": "\"let p be the number of participants . pc 2 = 171 ( p ) ( p - 1 ) = 342 = 19 * 18 p = 19 the answer is e .\"" + }, + { + "Answer": 100, + "Options": "a ) 5 , b ) 10 , c ) 50 , d ) 100 , e ) 1000", + "Correct": "d", + "Explanation": "a contest will consist of n questions , each of which is to be answered eithertrueorfalse . anyone who answers all n questions correctly will be a winner . what is the least value of n for which the probability is less than 1 / 1000 that a person who randomly guesses the answer to each question will be a winner ? a . 5 b . 10 c . 50 d . 100 e . 1000 soln : ans is b probability that one question is answered right is 1 / 2 . now for minimum number of questions needed to take probability less than 1 / 1000 is = > ( 1 / 2 ) ^ n < 1 / 1000 n = 10 satisfies this . d" + }, + { + "Answer": 25, + "Options": "a ) 25 , b ) 16 , c ) 18 , d ) 24 , e ) 26", + "Correct": "a", + "Explanation": "\"explanation : suppose the boy got x sums right and 2 x sums wrong . then , x + 2 x = 75 3 x = 75 x = 25 . answer : a\"" + }, + { + "Answer": 28, + "Options": "a ) 28 liters , b ) 27 liters , c ) 30 liters , d ) 32 liters , e ) 35 liters", + "Correct": "a", + "Explanation": "let x ltr water to be added 2 ltr alcohol to be represented as ( 20 ( 1 - 3 / 4 ( new soln . = 12 + x ) ) ) 2 = 5 % * ( 12 + x ) - - - - - - - - > x = 28 ans a" + }, + { + "Answer": 586, + "Options": "a ) s . 440 , b ) s . 586 , c ) s . 540 , d ) s . 740 , e ) s . 840", + "Correct": "b", + "Explanation": "\"s . i for 5 years = ( 1020 - 710 ) = rs . 310 . s . i . for 2 years = 310 / 5 * 2 = rs . 124 . principal = ( 710 - 124 ) = rs . 586 . answer : b\"" + }, + { + "Answer": 10, + "Options": "a ) 11 , b ) 10 , c ) 12 , d ) 17 , e ) 19", + "Correct": "b", + "Explanation": "\"b 10 ( x + y ) \u00e2 \u20ac \u201c ( y + z ) = 10 x \u00e2 \u20ac \u201c z = 10\"" + }, + { + "Answer": 20, + "Options": "a ) 17 years , b ) 20 years , c ) 29 years , d ) 10 years , e ) 12 years", + "Correct": "b", + "Explanation": "\"let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 52 5 x = 50 = > x = 10 hence , b ' s age = 2 x = 20 years . answer : b\"" + }, + { + "Answer": 50, + "Options": "a ) 20 , b ) 60 , c ) 50 , d ) 70 , e ) 80", + "Correct": "c", + "Explanation": "c 50 let the age before 10 years = x then , 125 x / 100 = x + 10 \u21d2 125 x = 100 x + 1000 \u21d2 x = 1000 / 25 = 40 present age = x + 10 = 40 + 10 = 50" + }, + { + "Answer": 19, + "Options": "a ) 17 , b ) 19 , c ) 21 , d ) 24 , e ) 25", + "Correct": "b", + "Explanation": "\"average of 20 numbers = 0 . sum of 20 numbers ( 0 x 20 ) = 0 . it is quite possible that 19 of these numbers may be positive and if their sum is a then 20 th number is ( - a ) answer is 19 ( b )\"" + }, + { + "Answer": 15, + "Options": "a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15", + "Correct": "e", + "Explanation": "\"if the average of 10 - pound and 20 - pound boxes is 18 , the ratio of 10 - pound boxes : 20 - pound boxes is 1 : 4 . so out of 20 boxes , 4 are 10 - pound boxes and 16 are 20 - pound boxes . if the average of 10 and 20 - pound boxes is to be 12 , the ratio of 10 - pound boxes : 20 - pound boxes should be 4 : 1 . the number of 10 pound boxes remains the same so we still have 4 of them . to get a ratio of 4 : 1 , the number of 20 - pound boxes must be 1 . we need to remove 15 of the 20 - pound boxes . the answer is e .\"" + }, + { + "Answer": 40, + "Options": "a ) 20 , b ) 25 , c ) 30 , d ) 40 , e ) 50", + "Correct": "d", + "Explanation": "\"let the list price be 2 x for min sale price , the first discount given should be 70 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 40 and 0.8 x = 32 so lowest sale price is 32 , which is 40 % of 80 hence , d is the answer\"" + }, + { + "Answer": 72, + "Options": "a ) 48 , b ) 57 , c ) 66 , d ) 72 , e ) 81", + "Correct": "d", + "Explanation": "\"( 4 ' ) ' = ( 3 * 4 - 3 ) ' = 9 ' = 9 * 9 - 9 = 72 answer d\"" + }, + { + "Answer": 17576, + "Options": "a ) 56678 , b ) 16789 , c ) 17576 , d ) 35142 , e ) none of these", + "Correct": "c", + "Explanation": "\"explanation : the first letter from the right can be chosen in 26 ways because there are 26 alphabets . having chosen this , the second letter can be chosen in 26 ways . = > the first two letters can be chosen in 26 * 26 = 676 wayshaving chosen the first two letters , the third letter can be chosen in 26 ways . = > all the three letters can be chosen in 676 * 26 = 17576 ways . it implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter . answer : c\"" + }, + { + "Answer": 292.79999999999995, + "Options": "a ) 190 , b ) 284.6 , c ) 300 , d ) 292 , e ) 312", + "Correct": "d", + "Explanation": "so 12.2 * 24 = 292 . . imo option d is correct answer . ." + }, + { + "Answer": 2, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "b", + "Explanation": "35 / 36 = 0.97222222222 . . . the answer is b ." + }, + { + "Answer": 25, + "Options": "a ) 25 % , b ) 35 % , c ) 45 % , d ) 55 % , e ) 65 %", + "Correct": "a", + "Explanation": "let abcdef be the regular hexagon with sides ab and ed parallel . p and q are mid points of af and ef resp . ae = root ( 3 ) * s ( s is side of hexagon ) then pq = ( root ( 3 ) * s ) / 2 mid point theorem now u know side of inner hexagon use formula area of hexagon = ( 3 * root ( 3 ) ) 2 * s ^ 2 and find diff in area of two hexagon multiply by 100 and divide the product by area of bigger hexagon ans 25 % answer : a" + }, + { + "Answer": 35, + "Options": "a ) 28 sec , b ) 16 sec , c ) 35 sec , d ) 18 sec , e ) 17 sec", + "Correct": "c", + "Explanation": "\"speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 240 + 110 = 350 m . time taken = 350 / 10 = 35 sec . answer : c\"" + }, + { + "Answer": 8, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) f = 8", + "Correct": "e", + "Explanation": "\"the combinations could be f { ( 1,240 ) , ( 2,120 ) , ( 3,80 ) , ( 4,60 ) , ( 5,48 ) , ( 6,40 ) , ( 8,30 ) , ( 10,24 ) , ( 12,20 ) , ) 15,16 ) , ( 16,15 ) , ( 20,12 ) , ( 24,10 ) , ( 30,8 ) , ( 40,6 ) , ( 48,5 ) , ( 60,4 ) , ( 80,3 ) , ( 120,2 ) , ( 240,1 ) } of these we are told 8 < = t < = 30 so we can remove these pairs , and we are left only with . { ( 8,30 , ( 10,24 ) , ( 12,20 ) , ( 15,16 ) , ( 16,15 ) , ( 20,12 ) , ( 24,10 ) , ( 30,8 ) } hence 8 . . e\"" + }, + { + "Answer": 50, + "Options": "a ) 100 , b ) 150 , c ) 50 , d ) 200 , e ) 250", + "Correct": "c", + "Explanation": "we have : ( 100 + 200 + 300 + x ) / 4 = 250 600 + x = 1000 x = 400 ( 300 + 150 + 100 + x + y ) / 5 = 200 550 + 400 + y = 1000 y = 50 answer is c" + }, + { + "Answer": 1249.9999999999998, + "Options": "a ) s 200 , b ) s 1250 , c ) s 300 , d ) s 450 , e ) s 550", + "Correct": "b", + "Explanation": "\"suppose the amount in the beginning was rs \u2019 x \u2019 money spent on clothes = rs 1 x / 3 balance = rs 2 x / 3 money spent on food = 1 / 5 of 2 x / 3 = rs 2 x / 15 balance = 2 x / 3 - 2 x / 15 = rs 8 x / 15 money spent on travel = 1 / 4 of 8 x / 15 = rs 2 x / 15 = 8 x / 15 - 2 x / 15 = 6 x / 15 = rs 2 x / 5 therefore 2 x / 5 = 500 = 1250 answer : b\"" + }, + { + "Answer": 4.8, + "Options": "a ) 5.29 min , b ) 5.28 min , c ) 5.08 min , d ) 4.8 min , e ) 5.988 min", + "Correct": "d", + "Explanation": "\"clearly , the two will meet when they are 660 m apart . to be ( 4.5 + 3.75 ) = 8.25 km apart , they take 1 hour . to be 660 m apart , they take ( 100 / 825 * 660 / 1000 ) hrs = ( 660 / 8250 * 60 ) min = 4.8 min . answer : d\"" + }, + { + "Answer": 25, + "Options": "a ) 25 , b ) 30 , c ) 35 , d ) 40 , e ) 45", + "Correct": "a", + "Explanation": "\"a 1 = 120 / 3 = 40 a 2 = a 1 - 5 = 35 sum of second list = 35 * 3 = 105 therefore the number = 105 - 80 = 25 a\"" + }, + { + "Answer": 0.25, + "Options": "a ) 0.0016 , b ) 0.0625 , c ) 0.16 , d ) 0.25 , e ) 0.5", + "Correct": "d", + "Explanation": "\"( 1 / 4 ) = 0.25 answer : d\"" + }, + { + "Answer": 7, + "Options": "a ) 3 , b ) 5 , c ) 4 , d ) 7 , e ) 2", + "Correct": "d", + "Explanation": "\"on dividing 5474827 by 12 we get the remainder 7 , so 7 should be subtracted d\"" + }, + { + "Answer": 1800, + "Options": "a ) 1800 , b ) 1992 , c ) 9921 , d ) 2798 , e ) 2789", + "Correct": "a", + "Explanation": "\"p = 18 ( 100 / 10 ) 2 = > p = 1800 answer : a\"" + }, + { + "Answer": 33, + "Options": "a ) 31 % . , b ) 71 % . , c ) 49 % . , d ) 33 % . , e ) 51 % .", + "Correct": "d", + "Explanation": "\"30 % of 2 litres = 0.6 litres 45 % of 6 litres = 2.7 litres therefore , total quantity of alcohol is 3.3 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 33 % d\"" + }, + { + "Answer": 0.13725490196078433, + "Options": "a ) 1 / 51 , b ) 4 / 51 , c ) 7 / 51 , d ) 3 / 44 , e ) 7 / 44", + "Correct": "c", + "Explanation": "\"we have the ratio of a \u2019 s speed and b \u2019 s speed . this means , we know how much distance a covers compared with b in the same time . this is what the beginning of the race will look like : ( start ) a _________ b ______________________________ if a covers 51 meters , b covers 44 meters in that time . so if the race is 51 meters long , when a reaches the finish line , b would be 7 meters behind him . if we want the race to end in a dead heat , we want b to be at the finish line too at the same time . this means b should get a head start of 7 meters so that he doesn \u2019 t need to cover that . in that case , the time required by a ( to cover 51 meters ) would be the same as the time required by b ( to cover 44 meters ) to reach the finish line . so b should get a head start of 7 / 51 th of the race . answer ( c )\"" + }, + { + "Answer": 3000.0000000000005, + "Options": "a ) 46457 , b ) 465745 , c ) 3000 , d ) 3456 , e ) 35346", + "Correct": "c", + "Explanation": "say the profit was $ x . john share = x / 6 ( half of the third ) + ( x - x / 3 ) * 0.7 mike ' s share = x / 6 ( half of the third ) + ( x - x / 3 ) * 0.3 thus ( x - x / 3 ) * 0.7 - ( x - x / 3 ) * 0.3 = 800 - - > x = 3000 . answer is c" + }, + { + "Answer": 7, + "Options": "a ) 2 , b ) 5 , c ) 9 , d ) 7 , e ) 6", + "Correct": "d", + "Explanation": "let the number be x x - 4 = 21 / x x ^ 2 - 4 x - 21 = 0 ( x - 7 ) ( x + 3 ) = 0 x = 7 correct answer d" + }, + { + "Answer": 65, + "Options": "a ) 76 , b ) 60 , c ) 65 , d ) 48 , e ) 52", + "Correct": "c", + "Explanation": "\"for 40 hrs = 40 * 16 = 640 excess = 1340 - 640 = 700 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 700 / 28 = 25 total hrs = 40 + 25 = 65 answer c 65\"" + }, + { + "Answer": 12, + "Options": "a ) 10 , b ) 12 , c ) 15 , d ) 18 , e ) 21", + "Correct": "b", + "Explanation": "\"2 oxen = 3 buffaloes = 4 cows also : 15 buffaloes + 8 oxen + 24 cows = 10 oxen + 8 oxen + 12 oxen = 30 oxen there is enough fodder for 1 oxen for 30 * 24 days . 40 cows + 15 buffaloes = 20 oxen + 10 oxen = 30 oxen the new total is equal to 60 oxen instead of 30 oxen . 30 * 24 / 60 oxen = 12 days the answer is b .\"" + }, + { + "Answer": 5870, + "Options": "a ) rs . 5870 , b ) rs . 5991 , c ) rs . 6020 , d ) rs . 6850 , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : total sale for 5 months = rs . ( 5420 + 5660 + 6200 + 6350 + 6500 ) = rs . 30,130 therefore , required sale = rs . [ ( 6000 * 6 ) \u2013 30,130 ] = rs . ( 36000 \u2013 30,130 ) = rs . 5870 answer a\"" + }, + { + "Answer": 4.8, + "Options": "a ) 2.8 % , b ) 3.6 % , c ) 4.4 % , d ) 5.2 % , e ) 4.8 %", + "Correct": "e", + "Explanation": "\"let amount spent by jill = 100 clothing = 50 , food = 20 , others = 30 tax on clothing = 2.4 tax on others = 2.4 percentage = 4.8 / 100 = 4.8 % answer : e\"" + }, + { + "Answer": 12, + "Options": "a ) 3 , b ) 6 , c ) 8 , d ) 12 , e ) 24", + "Correct": "d", + "Explanation": "for a quadratic equation ax ^ 2 + sx + c = 0 , we know that - s / a is sum of roots and c / a is product of roots . the quadratic equation here is x ^ 2 + sx + 72 = 0 , where product of roots is 72 . if we find all the factors of 72 , we have the answer . by prime factorization , we get 72 = 2 ^ 3 * 3 ^ 2 . we know that total factors are ( 3 + 1 ) * ( 2 + 1 ) = 12 ( reason : with 2 ^ n , we have n + 1 possibilities . n ^ 0 to n ^ n . so n + 1 ) = d" + }, + { + "Answer": 10150, + "Options": "a ) 10150 , b ) 7250 , c ) 2767 , d ) 1998 , e ) 2771", + "Correct": "a", + "Explanation": "\"explanation : a b c investment 3 x 4 x 5 x rate of return 6 y % 5 y % 4 y % return \\ inline \\ frac { 18 xy } { 100 } \\ inline \\ frac { 20 xy } { 100 } \\ inline \\ frac { 20 xy } { 100 } total = ( 18 + 20 + 20 ) = \\ inline \\ frac { 58 xy } { 100 } b ' s earnings - a ' s earnings = \\ inline \\ frac { 2 xy } { 100 } = 350 total earning = \\ inline \\ frac { 58 xy } { 100 } = 10150 answer : a ) rs . 10150\"" + }, + { + "Answer": 26, + "Options": "a ) 28 , b ) 27 , c ) 26 , d ) 22 , e ) 24", + "Correct": "c", + "Explanation": "\"explanation : let the average score of the first 18 innings be n 18 n + 98 = 19 ( n + 4 ) = > n = 22 so , average score after 19 th innings = x + 4 = 26 . answer : c\"" + }, + { + "Answer": 144.99999999999986, + "Options": "a ) 143 , b ) 144 , c ) 145 , d ) 146 , e ) 147", + "Correct": "c", + "Explanation": "12.4 * x + 26 = ( 7 + x ) 12 solve equation x = 145 answer : c" + }, + { + "Answer": 534, + "Options": "a ) 534 , b ) 1403 , c ) 1623 , d ) 1513 , e ) 1613", + "Correct": "a", + "Explanation": "137 - 731 and 276 - 672 similarly 435 - 534 answer : a" + }, + { + "Answer": 60, + "Options": "a ) 40 % , b ) 60 % , c ) 65 % , d ) 70 % , e ) 75 %", + "Correct": "b", + "Explanation": "number of runs made by running = 110 - ( 6 x 4 + 4 x 6 ) = 120 - ( 48 ) = 72 now , we need to calculate 60 is what percent of 120 . = > 72 / 120 * 100 = 60 % b" + }, + { + "Answer": 60, + "Options": "a ) 120 , b ) 30 , c ) 90 , d ) 60 , e ) 12", + "Correct": "d", + "Explanation": "240 can be written as ( 2 ^ 4 ) * 3 * 5 . for x ^ 2 to be divisible by 240 it should contain at least 2 ^ 4 and 3 and 5 in its factors . we can leave out option e because 12 doesnt have 5 as one of its factor . now if we check for option b , 30 can be written as 2 * 3 * 5 , hence 30 ^ 2 will have 2 as the maximum power of 2 , so we can leave out this option too . option d is the right answer if we follow the same method as we followed for other two previous options . 60 = ( 2 ^ 2 ) * 3 * 5 ; 60 ^ 2 = ( 2 ^ 4 ) * ( 3 ^ 2 ) * ( 5 ^ 2 ) . so it shows that 60 ^ 2 is divisible by 240 and hence the answer . answer : d" + }, + { + "Answer": 0.3076923076923077, + "Options": "a ) 1 / 2 , b ) 1 / 3 , c ) 4 / 13 , d ) 8 / 29 , e ) 6 / 33", + "Correct": "c", + "Explanation": "let the following be true : t makes x in time t then the following follows : n makes x in 4 t / 3 o makes x in 3 / 2 ( 4 t / 3 ) = 2 t m : n : o = 1 : 4 / 3 : 2 = 3 : 4 : 6 so n = 4 / ( 3 + 4 + 6 ) = 4 / 13 = c" + }, + { + "Answer": 31, + "Options": "a ) 17 , b ) 18 , c ) 34 , d ) 31 , e ) 36", + "Correct": "d", + "Explanation": "( ( 1 ^ m ) / ( 5 ^ m ) ) ( ( 1 ^ 16 ) / ( 4 ^ 16 ) ) = 1 / ( 2 ( 10 ) ^ 31 ) ( ( 1 / 5 ) ^ m ) * ( ( 1 / 2 ) ^ 32 ) = 1 / ( 2 * ( 2 * 5 ) ^ 31 ) ) 2 ^ 36 will cancel out , since 1 can be written as 1 ^ 35 , so ( 1 / 5 ) ^ m = ( 1 / 5 ) ^ 31 ( ( 1 / 5 ) ^ m ) * ( ( 1 / 2 ) ^ 32 ) = 1 / [ ( 2 ^ 32 ) * ( 5 ^ 31 ) ] so , m = 31 answer d" + }, + { + "Answer": 18, + "Options": "a ) 8 , b ) 12 , c ) 15 , d ) 17 , e ) 18", + "Correct": "e", + "Explanation": "\"let original strength = y then , 40 y + 18 x 32 = ( y + 18 ) x 36 \u00e2 \u2021 \u2019 40 y + 576 = 36 y + 648 \u00e2 \u2021 \u2019 4 y = 72 \u00e2 \u02c6 \u00b4 y = 18 e\"" + }, + { + "Answer": 280.00000000000006, + "Options": "a ) 160 , b ) 180 , c ) 200 , d ) 280 , e ) none", + "Correct": "d", + "Explanation": "\"answer let the number be n . then , ( n / 5 ) + 7 = ( n / 4 ) - 7 \u00e2 \u2021 \u2019 ( n / 4 ) - ( n / 5 ) = 14 \u00e2 \u2021 \u2019 ( 5 n - 4 n ) / 20 = 14 \u00e2 \u02c6 \u00b4 n = 280 option : d\"" + }, + { + "Answer": 0.948051948051948, + "Options": "a ) 730 / 77 , b ) 73 / 77 , c ) 7.3 / 77 , d ) 7.3 / 770 , e ) 7.3 / 77", + "Correct": "b", + "Explanation": "x / y = 0.04 / 1.5 y / x = 1.5 / 0.04 by componendo dividendo rule ( y + x ) / ( y - x ) = 1.54 / 1.46 ( y - x ) / ( y + x ) = 1.46 / 1.54 = 73 / 77 answer : b" + }, + { + "Answer": 16, + "Options": "a ) 20 , b ) 16 , c ) 8 , d ) 4 , e ) 2", + "Correct": "b", + "Explanation": "the x - axis is 8 units from the point p . thus the y - axis is 16 units from the point p . the answer is b ." + }, + { + "Answer": 7.5, + "Options": "a ) 6.5 , b ) 7.0 , c ) 7.5 , d ) 8.0 , e ) 8.5", + "Correct": "c", + "Explanation": "\"in one hour , the crow eats 1 / 30 of the nuts . ( 1 / 4 ) / ( 1 / 30 ) = 7.5 hours the answer is c .\"" + }, + { + "Answer": 6, + "Options": "a ) 29 , b ) 776 , c ) 66 , d ) 12 , e ) 6", + "Correct": "e", + "Explanation": "\"( 65 / 100 ) * 40 \u2013 ( 4 / 5 ) * 25 26 - 20 = 6 answer : e\"" + }, + { + "Answer": 0.75, + "Options": "a ) 1 / 4 , b ) 2 / 4 , c ) 3 / 4 , d ) 2 / 3 , e ) 1 / 3", + "Correct": "c", + "Explanation": "if original fraction is x / y , then 1.12 x / 0.98 y = 6 / 7 ( 8 / 7 ) * ( x / y ) = 6 / 7 x / y = 6 / 8 = 3 / 4 answer : c" + }, + { + "Answer": 150, + "Options": "a ) 100 , b ) 150 , c ) 160 , d ) 180 , e ) 199", + "Correct": "b", + "Explanation": "65 % of x = 20 % of 487.50 then , 65 / 100 * x = 20 / 100 * 4875 / 10 x = 150 answer is b" + }, + { + "Answer": 0.5555555555555556, + "Options": "a ) 0 , b ) 3 / 7 , c ) 2 / 5 , d ) 1 / 2 , e ) 5 / 9", + "Correct": "e", + "Explanation": "we will have a negative product only if 1 , 2 , 3 , 4 , or 5 are selected from set t . p ( negative product ) = 5 / 9 the answer is e ." + }, + { + "Answer": 2, + "Options": "a ) 2 , b ) 5 , c ) 11 , d ) 3 , e ) 4", + "Correct": "a", + "Explanation": "6 * 15 * 5 = ( \u221a ( 6 + 2 ) ( 15 + 3 ) ) / ( 5 + 1 ) = ( \u221a 8 * 18 ) / 6 = ( \u221a 144 ) / 6 = 12 / 6 = 2 answer is a" + }, + { + "Answer": 4.5, + "Options": "a ) 4.5 , b ) 5 , c ) 5.5 , d ) 5.8 , e ) 6", + "Correct": "a", + "Explanation": "\"if $ x $ is the number , x / 6 * 12 = 9 = > 2 x = 9 = > x = 4.5 a\"" + }, + { + "Answer": 540, + "Options": "a ) 545 , b ) 488 , c ) 542 , d ) 548 , e ) 560", + "Correct": "a", + "Explanation": "required number = ( l . c . m . of 12 , 15 , 20 , 54 ) + 5 = 540 + 5 = 545 . answer : a" + }, + { + "Answer": 49000, + "Options": "a ) 28000 , b ) 30000 , c ) 32000 , d ) 34000 , e ) 49000", + "Correct": "e", + "Explanation": "\"explanation : suppose b ' s investment = x . then a ' s investment = 3 x suppose bs period of investment = y , then a ' s period of investment = 2 y a : b = 3 x * 2 y : xy = 6 : 1 total profit * 1 / 7 = 7000 = > total profit = 7000 * 7 = 49000 . answer : option e\"" + }, + { + "Answer": 17, + "Options": "a ) 15 , b ) 21 , c ) 17 , d ) 19 , e ) 21", + "Correct": "c", + "Explanation": "\"total money = rs . 10350 . let 50 rupees note was x . then 500 rupees note = 36 - x now , 50 * x + 500 * ( 36 - x ) = 10350 50 x + 18000 - 500 x = 10350 - 450 x = - 7650 x = 17 . no . of 50 rupees note = 17 . answer : option c\"" + }, + { + "Answer": 33, + "Options": "a ) 35 , b ) 33 , c ) 28 , d ) 21 , e ) 15", + "Correct": "b", + "Explanation": "the smallest possible product is 33 which is 3 * 11 . all other products are too big . the answer is b ." + }, + { + "Answer": 58, + "Options": "a ) 56 , b ) 57 , c ) 58 , d ) 59 , e ) 60", + "Correct": "c", + "Explanation": "\"11 / 7 * 37 = 58.1 the answer is c .\"" + }, + { + "Answer": 7000, + "Options": "a ) 7000 , b ) 8000 , c ) 9000 , d ) 10000 , e ) 11000", + "Correct": "a", + "Explanation": "total rebecca = x + 15000 ; total = x + 15000 + 18000 ; x + 15000 / x + 33000 = 55 / 100 therefore x = 7000 a" + }, + { + "Answer": 16, + "Options": "a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20", + "Correct": "c", + "Explanation": "\"let the number of ducks be d and number of cows be c then , total number of legs = 2 d + 4 c = 2 ( d + 2 c ) total number of heads = c + d given that total number of legs are 32 more than twice the number of heads = > 2 ( d + 2 c ) = 32 + 2 ( c + d ) = > d + 2 c = 16 + c + d = > 2 c = 16 + c = > c = 16 i . e . , total number of cows = 16 answer is c .\"" + }, + { + "Answer": 6, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 6 , e ) 5", + "Correct": "d", + "Explanation": "d ) 6" + }, + { + "Answer": 3377, + "Options": "a ) 3327 , b ) 3237 , c ) 3337 , d ) 3377 , e ) none of these", + "Correct": "d", + "Explanation": "\"answer x = 13200 - 9823 = 3377 option : d\"" + }, + { + "Answer": 223.0072, + "Options": "a ) 219.5 , b ) 223.0 , c ) 235.01 , d ) 266.74 , e ) 669.0", + "Correct": "b", + "Explanation": "in the case we won the bet , we have : 1.28 * 5.23 * 3.25 * 2.0 * 5.00 = 219.50 we will win 223 so correct answer is b" + }, + { + "Answer": 500.0000000000001, + "Options": "a ) $ 900 , b ) $ 300 , c ) $ 500 , d ) $ 700 , e ) $ 800", + "Correct": "c", + "Explanation": "\"if linda spent 4 / 5 of her savings on furniture , the rest 5 / 5 - 4 / 5 = 1 / 5 on a tv but the tv cost her $ 100 . so 1 / 5 of her savings is $ 100 . so her original savings are 5 times $ 100 = $ 500 correct answer c\"" + }, + { + "Answer": 900, + "Options": "a ) 250 / 3 , b ) 500 / 3 , c ) 900 , d ) 480 , e ) 600", + "Correct": "c", + "Explanation": "\"we know that x is 10 % , y is 30 % and w . avg = 25 % . what does this mean with respect to w . avg technique ? w . avg is 1 portion away from y and 3 portion away from x so for every 1 portion of x we will have to add 3 portions of y . if x = 300 then y = 900 answer : c\"" + }, + { + "Answer": 13, + "Options": "a ) 11 , b ) 17 , c ) 13 , d ) 23 , e ) none of these", + "Correct": "c", + "Explanation": "\"explanatory answer when 242 is divided by a certain divisor the remainder obtained is 8 . let the divisor be d . when 242 is divided by d , let the quotient be ' x ' . the remainder is 8 . therefore , 242 = xd + 8 when 698 is divided by the same divisor the remainder obtained is 9 . let y be the quotient when 698 is divided by d . then , 698 = yd + 9 . when the sum of the two numbers , 242 and 698 , is divided by the divisor , the remainder obtained is 4 . 242 + 698 = 940 = xd + yd + 8 + 9 940 = xd + yd + 17 as xd and yd are divisible by d , the remainder when 940 is divided by d should have been 17 . however , because we know that the remainder is 4 , it would be possible only when 17 / d leaves a remainder of 4 . if the remainder obtained is 4 when 17 is divided by ' d ' , then ' d ' has to be 13 . choice c\"" + }, + { + "Answer": 84, + "Options": "a ) 60 , b ) 74 , c ) 84 , d ) 54 , e ) 104", + "Correct": "c", + "Explanation": "\"the number of positive integer solutions for the equatio fx 1 + x 2 + \u22ef + xn = k ( k - 1 ) c ( n - 1 ) - where k is the number and n is number of variable in the equation . 10 - 1 c 4 - 1 = 9 c 3 = 84 answer : c\"" + }, + { + "Answer": 20, + "Options": "a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22", + "Correct": "d", + "Explanation": "\"d = ( d - r ) / q = ( 122 - 2 ) / 6 = 122 / 6 = 20 d )\"" + }, + { + "Answer": 5, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8", + "Correct": "b", + "Explanation": "\"in one hour , the crow eats 1 / 20 of the nuts . ( 1 / 4 ) / ( 1 / 20 ) = 5 hours the answer is b .\"" + }, + { + "Answer": 45, + "Options": "a ) 45 , b ) 15 , c ) 25 , d ) 5 , e ) 30", + "Correct": "a", + "Explanation": "20 + 10 + 15 = 45 . answer is a" + }, + { + "Answer": 70.19999999999999, + "Options": "a ) 35.67 % , b ) 64.75 % , c ) 68.57 % , d ) 70.20 % , e ) none of these", + "Correct": "d", + "Explanation": "girls = 900 , boys = 1100 passed = ( 28 % of 1100 ) + ( 32 % of 900 ) = 308 + 288 = 596 failed = 2000 - 596 = 1404 failed % = [ ( 1404 / 2000 ) x 100 ] % = 70.2 % . answer : d" + }, + { + "Answer": 61, + "Options": "a ) $ 21 , b ) $ 27 , c ) $ 31 , d ) $ 61 , e ) it can not be determined", + "Correct": "d", + "Explanation": "\"let ' s suppose that the price of a burger is bb , of a shake - ss and that of a cola is cc . we can then construct these equations : 3 b + 7 s + c = 130 4 b + 10 s + c = 164.5 subtracting the first equation from the second gives us b + 3 s = 34.5 now if we subtract the new equation two times from first or 3 times from second we will get b + s + c = 61 . in any case , there is no necessity to know each item ' s price , just the sum . answer : d\"" + }, + { + "Answer": 2, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "b", + "Explanation": "\"the product of n and 5 = 5 n . . the difference between an integer n and the product of n and 5 = 5 n - n = 4 n . . the outcome of the binary operation of n is less than 10 ? so 4 n < 10 . . . max value that n can take as an integer is 2 answer : b\"" + }, + { + "Answer": 48, + "Options": "a ) 36 , b ) 48 , c ) 17 , d ) 6 , e ) 5", + "Correct": "b", + "Explanation": "\"sol . ( b ) the sum of roots = a + b = 8 product of roots = ab = 8 now , a 2 + b 2 = ( a + b ) 2 - 2 ab = 64 - 16 = 48 answer b\"" + }, + { + "Answer": 56000, + "Options": "a ) $ 40,000 , b ) $ 56,000 , c ) $ 64,000 , d ) $ 66,667 , e ) $ 80,000", + "Correct": "b", + "Explanation": "\"equation is correct , so math must be a problem . 0.12 * 40,000 + 0.2 * ( x - 40,000 ) = 8,000 - - > 4,800 + 0.2 x - 8,000 = 8,000 - - > 0.2 x = 11,200 - - > x = 56,000 . answer : b .\"" + }, + { + "Answer": 15, + "Options": "a ) 18 , b ) 19 , c ) 17 , d ) 16 , e ) 15", + "Correct": "e", + "Explanation": "let the total number of workers be y . so sum of salary for all workers = sum of salary of 5 technician + sum of salary for other y - 5 workers . 5 x 800 + 650 ( y - 5 ) = 700 y \u21d2 4000 + 650 y - 3250 = 700 y \u21d2 50 y = 750 \u2234 y = 15 so total number of workers = 15 e" + }, + { + "Answer": 120, + "Options": "a ) 75 , b ) 100 , c ) 120 , d ) 175 , e ) 225", + "Correct": "c", + "Explanation": "\"let m be the number of male participants and f be the number of female articipants in the meeting . thetotal number of participants is given as 720 . hence , we have m + f = 720 now , we have that half the female participants and one - quarter of the male participants are democrats . let d equal the number of the democrats . then we have the equation f / 2 + m / 4 = d now , we have that one - third of the total participants are democrats . hence , we have the equation d = 720 / 3 = 240 solving the three equations yields the solution f = 240 , m = 480 , and d = 240 . the number of female democratic participants equals half the female participants equals 240 / 2 = 120 . answer : c\"" + }, + { + "Answer": 79.99999999999999, + "Options": "a ) 10 , b ) 20 , c ) 30 , d ) 60 , e ) 80", + "Correct": "e", + "Explanation": "\"0.036 * 10 ^ 5 can be written as 3600 45000 * 10 ^ ( - 3 ) can be written as 45 required = 3600 / 45 = 80 answer : e\"" + }, + { + "Answer": 225, + "Options": "a ) 205 , b ) 215 , c ) 225 , d ) 260 , e ) 270", + "Correct": "c", + "Explanation": "\"average of the two areas = 500 / 2 = 250 one - fifth of the average of the two areas = 250 / 5 = 50 \u21d2 difference of the two areas = 50 let area of the smaller part = x hectares . then , area of the larger part = x + 50 hectares . = > x + x + 50 = 500 = > 2 x = 450 = > x = 225 answer : c\"" + }, + { + "Answer": 39, + "Options": "a ) 28 sec , b ) 16 sec , c ) 39 sec , d ) 18 sec , e ) 17 sec", + "Correct": "c", + "Explanation": "\"speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 240 + 150 = 390 m . time taken = 390 / 10 = 39 sec . answer : c\"" + }, + { + "Answer": 0.02857142857142857, + "Options": "a ) 1 / 70 , b ) 1 / 35 , c ) 2 / 35 , d ) 1 / 12 , e ) 1 / 7", + "Correct": "b", + "Explanation": "divisions are 0 1 / 7 2 / 7 3 / 7 4 / 7 5 / 7 6 / 7 1 1 / 5 2 / 5 3 / 5 4 / 5 5 / 5 expressing the same in terms of the lcm of 57 , i . e 35 0 7 / 35 14 / 35 21 / 35 28 / 35 35 / 35 5 / 35 10 / 35 15 / 35 20 / 35 25 / 35 30 / 35 by comparing the divisions with each other we can see 1 / 35 is the shortest possible distance between any two selected divisions . z = 1 / 35 answer is b ." + }, + { + "Answer": 75, + "Options": "a ) 65 , b ) 69 , c ) 72 , d ) 75 , e ) 79", + "Correct": "d", + "Explanation": "\"add all those marks and divide it by 5 becz they gave us 5 subjects for finding average marks we need to divide them add them 76 + 65 + 82 + 67 + 85 / 5 = 375 / 5 = 75 answer : d\"" + }, + { + "Answer": 10, + "Options": "a ) 6 , b ) 8 , c ) 10 , d ) 11 , e ) 13", + "Correct": "c", + "Explanation": "\"joan starts off with 100 $ . . which is to be tripled every month her monthly payments look like this : 100 , 300 , 900 , 2700 . . . . . . . . . upto 2952400 this can be re written as : 100 x 1 , 100 x 3 , 100 x 9 , 100 x 27 . . . . . . 100 x 29524 so we have 1 , 3 , 9 , 27 . . . . . 2652400 in gp we know that a = 1 , and r = 3 ( its easy to figure it out by looking at the question , but regardless of it being mentioned in the question we can still compute the value of r using the formula tn = a 3 ^ n - 1 . . . ) therefore to find the sum of n terms of a gp we use this formula : sn = a ( 1 - r ^ n ) / 1 - r using this and plugging in the information we get . . . 29524 = 1 - 3 ^ n / 1 - 3 ; 1 - 3 ^ n / - 2 cross multiplying we get 29524 x - 2 = 1 - 3 ^ n - 59048 = 1 - 3 ^ n - 59049 = - 3 ^ n 59049 = 3 ^ n ( negatives cancel out ) 59049 can also be re written as 3 ^ 10 therefore ; 3 ^ 10 = 3 ^ n thus n = 10 ( c )\"" + }, + { + "Answer": 5, + "Options": "a ) 3.0 , b ) 7.0 , c ) 5.0 , d ) 2.0 , e ) 1.0", + "Correct": "c", + "Explanation": "\"for the total revenue to remain the same when the price is one fifth , the number of products sold must five times . therefore increase in the number of products sold is 100 % = > the required ratio = 100 % / 20 % = 5.0 answer : c\"" + }, + { + "Answer": 17, + "Options": "a ) 8 , b ) 12 , c ) 15 , d ) 17 , e ) 18", + "Correct": "d", + "Explanation": "\"let original strength = y then , 40 y + 17 x 32 = ( y + 17 ) x 36 \u00e2 \u2021 \u2019 40 y + 544 = 36 y + 612 \u00e2 \u2021 \u2019 4 y = 68 \u00e2 \u02c6 \u00b4 y = 17 d\"" + }, + { + "Answer": 2, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "c", + "Explanation": "\"number = 5 * 2 + 0 = 10 4 ) 10 ( 2 8 - - - - - - - - 2 required number = 2 . answer : c\"" + }, + { + "Answer": 18, + "Options": "a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20", + "Correct": "c", + "Explanation": "first , let ' s translate the expression 21 # 36 , using the definition given : 21 # 36 = 21 \u00d7 24 \u00d7 27 \u00d7 30 \u00d7 33 \u00d7 36 we need the prime factorization of this product . let ' s factor out 3 from each multiple . 21 # 36 = 3 ^ 6 ( 7 \u00d7 8 \u00d7 9 \u00d7 10 \u00d7 11 \u00d7 12 ) now let ' s replace each consecutive integer with its prime factorization : 21 # 36 = 3 ^ 6 ( 7 \u00d7 2 ^ 3 \u00d7 3 ^ 2 \u00d7 ( 2 \u00d7 5 ) \u00d7 11 \u00d7 ( 2 ^ 2 \u00d7 3 ) ) let ' s group the prime bases : 21 # 36 = 2 ^ 6 \u00d7 3 ^ 9 \u00d7 5 \u00d7 7 \u00d7 11 the sum of the exponents is 6 + 9 + 1 + 1 + 1 = 18 the answer is c ." + }, + { + "Answer": 741, + "Options": "a ) rs 741 , b ) rs 5991 , c ) rs 6001 , d ) rs 6991 , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : total sale for 5 days = rs . ( 435 + 927 + 855 + 230 + 562 ) = rs . 3009 . required sale = rs . [ ( 625 x 6 ) - 3009 ] = rs . ( 3750 - 3009 ) = rs . 741 . answer : a\"" + }, + { + "Answer": 0.16, + "Options": "a ) 2 / 125 , b ) 4 / 25 , c ) c ) 2 / 25 , d ) 3 / 25 , e ) 1 / 5", + "Correct": "b", + "Explanation": "\"p ( playing 2 or more instruments ) = 32 / 800 = 1 / 25 . then , the probability of playing exactly one instrument is given by : p ( playing 1 or more instruments ) - p ( playing 2 or more instruments ) = 1 / 5 - 1 / 25 = 4 / 25 . answer b .\"" + }, + { + "Answer": 75, + "Options": "a ) 60 , b ) 70 , c ) 65 , d ) 75 , e ) 80", + "Correct": "d", + "Explanation": "lets assume that total number of students in class is 100 and required average be x . then from the given statement we can calculate : ( 10 * 95 ) + ( 20 * 90 ) + ( 70 * x ) = ( 100 * 80 ) 70 x = 8000 - ( 950 + 1800 ) = 5250 answer : d x = 75 ." + }, + { + "Answer": 484, + "Options": "a ) 484 , b ) 460 , c ) 550 , d ) 664 , e ) none of them", + "Correct": "a", + "Explanation": "4 / 15 a = 2 / 5 b a = ( 2 / 5 x 15 / 4 ) b a = 3 / 2 b a / b = 3 / 2 a : b = 3 : 2 . therefore , b ' s share = rs . ( 1210 x 2 / 5 ) = rs . 484 . answer is a ." + }, + { + "Answer": 5, + "Options": "a ) a ) 4 , b ) b ) 7 , c ) c ) 9 , d ) d ) 5 , e ) e ) 2", + "Correct": "d", + "Explanation": "10 - 5 = 5 . answer is d" + }, + { + "Answer": 21, + "Options": "a ) 31 , b ) 21 , c ) 41 , d ) 61 , e ) 51", + "Correct": "b", + "Explanation": "\"a ^ 2 + b ^ 2 should make you think of these formulas : ( a + b ) ( a + b ) = a ^ 2 + b ^ 2 + 2 ab we already know ( a + b ) = - 9 and a * b = 30 ( a + b ) ( a + b ) = ( - 9 ) ( - 9 ) = a ^ 2 + b ^ 2 + 2 * ( 30 ) a ^ 2 + b ^ 2 = 81 - 60 = 21 answer : b\"" + }, + { + "Answer": 102, + "Options": "a ) 104 , b ) 60 , c ) 52 , d ) 50 , e ) 102", + "Correct": "e", + "Explanation": "\"f ( x ) = 2 x ^ 2 + y f ( 2 ) = 60 = > 2 * ( 2 ) ^ 2 + y = 60 = > 8 + y = 60 = > y = 52 f ( 5 ) = 2 * ( 5 ) ^ 2 + 52 = 102 answer e\"" + }, + { + "Answer": 4, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 6", + "Correct": "d", + "Explanation": "\"as per question = > n = 7 p + 2 for some integer p hence 2 n = > 14 q + 4 = > remainder = > 4 for some integer q alternatively = > n = 2 > 2 n = > 4 = > 4 divided by 7 will leave a remainder 4 hence d\"" + }, + { + "Answer": 720, + "Options": "a ) 600 , b ) 720 , c ) 820 , d ) 800 , e ) 920", + "Correct": "b", + "Explanation": "\"0.6 * 600 = 0.5 * x x = 6 / 5 * 600 = 720\"" + }, + { + "Answer": 8, + "Options": "a ) 8 , b ) 7 , c ) 6 , d ) 5 , e ) 4", + "Correct": "a", + "Explanation": "let the time for which car averages 80 mph = t 65 * ( t + 4 ) = 50 * 4 + 80 t = > 15 t = 60 = > t = 4 total duration of the trip = 4 + 4 = 8 answer a" + }, + { + "Answer": 412.5, + "Options": "a ) 100.5 , b ) 200.5 , c ) 300.5 , d ) 350.5 , e ) 412.5", + "Correct": "e", + "Explanation": "\"6 x / 10 - x / 3 = 110 4 x / 15 = 110 x = 412.5 answer : e\"" + }, + { + "Answer": 0.2222222222222222, + "Options": "a ) 1 / 9 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 9 , e ) 2 / 3", + "Correct": "d", + "Explanation": "for n ( n + 1 ) to be a multiple of 9 , either n or n + 1 has to be a multiple of 9 . thus n must be of the form 9 k or 9 k - 1 . the probability is 2 / 9 . the answer is d ." + }, + { + "Answer": 1, + "Options": "a ) 3 / 7 , b ) 34 , c ) 1 , d ) 2 , e ) 3", + "Correct": "c", + "Explanation": "\"answer given exp . = 4 / 7 + { ( 2 q - p ) / ( 2 q + p ) } dividing numerator as well as denominator by q , exp = 4 / 7 + { 2 - p / q ) / ( 2 + p / q ) } = 4 / 7 + { ( 2 - 4 / 5 ) / ( 2 + 4 / 5 ) } = 4 / 7 + 6 / 14 = 4 / 7 + 3 / 7 = 7 / 7 = 1 . correct option : c\"" + }, + { + "Answer": 1.2857142857142856, + "Options": "a ) 0.75 , b ) 0.8 , c ) 1 , d ) 1.28 , e ) 1.35", + "Correct": "d", + "Explanation": "\"say the cost price of 70 pencils was $ 70 ( $ 1 per pencil ) and the selling price of 1 pencil was p . selling at a loss : 70 - 70 p = 20 p - - > p = 7 / 9 . ( cost price ) / ( selling price ) = 1 / ( 7 / 9 ) = 9 / 7 = 1.28 . answer : d .\"" + }, + { + "Answer": 1649.999999999999, + "Options": "a ) 1100 , b ) 2100 , c ) 1300 , d ) 1650 , e ) 1400", + "Correct": "d", + "Explanation": "\"4 x / 10 - x / 3 = 110 1 x / 15 = 110 x = 1650 answer : d\"" + }, + { + "Answer": 25, + "Options": "a ) 36 - 48 , b ) 50 - 34 , c ) 60 - 24 , d ) 42 - 42 , e ) 25 - 37", + "Correct": "e", + "Explanation": "\"in this problem , we are asked to find two numbers . therefore , we must let x be one of them . let x , then , be the first number . we are told that the other number is 12 more , x + 12 . the problem states that their sum is 62 : word problem = 62 the line over x + 12 is a grouping symbol called a vinculum . it saves us writing parentheses . we have : 2 x = 62 \u00e2 \u02c6 \u2019 12 = 50 . x = 50 / 2 = 25 . this is the first number . therefore the other number is x + 12 = 25 + 12 = 37 . the sum of 25 + 37 is 62 . e\"" + }, + { + "Answer": 0.3333333333333333, + "Options": "a ) 1 / 3 , b ) 2 / 5 , c ) 3 / 10 , d ) 3 / 7 , e ) 1 / 7", + "Correct": "a", + "Explanation": "\"here , s = [ 1 , 2 , 3 , 4 , \u2026 . , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 ] let e = event of getting a multiple of 3 = [ 3 , 6 , 9 , 12 , 15 , 18 , 21 , 24 , 27 ] p ( e ) = n ( e ) / n ( s ) = 9 / 27 = 1 / 3 the answer is a .\"" + }, + { + "Answer": 12, + "Options": "a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15", + "Correct": "d", + "Explanation": "2 ^ ( 2 w ) = 8 ^ ( w \u2212 4 ) 2 ^ ( 2 w ) = 2 ^ ( 3 * ( w \u2212 4 ) ) 2 ^ ( 2 w ) = 2 ^ ( 3 w - 12 ) let ' s equate the exponents as the bases are equal . 2 w = 3 w - 12 w = 12 the answer is d ." + }, + { + "Answer": 7000, + "Options": "a ) 7000 , b ) 700 , c ) 70000 , d ) 70 , e ) 7", + "Correct": "a", + "Explanation": "\"100889 - ( local value of 3 ) = 100889 - 3000 = 97889 local value of 7 in 97889 = 7000 a\"" + }, + { + "Answer": 42, + "Options": "a ) a ) 54 , b ) b ) 75 , c ) c ) 48 , d ) d ) 42 , e ) e ) 63", + "Correct": "d", + "Explanation": "let the numbers be 5 x , 6 x , 8 x . largest number = 8 x . smallest number = 5 x . third number = 6 x . 8 x + 5 x = 6 x + 49 7 x = 49 = > x = 7 6 x = 42 = > third number is 42 . answer : d" + }, + { + "Answer": 724, + "Options": "a ) 631 , b ) 731 , c ) 831 , d ) 849 , e ) 901", + "Correct": "b", + "Explanation": "\"3 ^ 0 + 2 = 3 3 ^ 2 + 2 = 11 3 ^ 4 + 2 = 83 3 ^ 6 + 2 = 731 the answer is b .\"" + }, + { + "Answer": 300, + "Options": "a ) 60 , b ) 120 , c ) 240 , d ) 275 , e ) 300", + "Correct": "e", + "Explanation": "let v denote the volume of feed one chicken consumes per day . then the total volume of feed in stock will be v \u2217 d \u2217 c where d is the number of days the feed will last if the number of chickens does not change and cc is the current number of chickens . from the question it follows that v ( d + 20 ) ( c \u2212 75 ) = vdc v ( d \u2212 15 ) ( c + 100 ) = vdc the first equation simplifies to 20 c \u2212 75 d = 1500 . the second equation simplifies to ( \u2212 15 ) c + 100 d = 1500 after dividing everything by 5 we get the linear system : 4 c \u2212 15 d = 300 ( \u2212 3 ) c + 20 d = 300 solving it we get c = 300 d = 60 answer : e" + }, + { + "Answer": 15, + "Options": "a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16", + "Correct": "d", + "Explanation": "t + b + c + 14 + 15 = 12 * 5 = 60 = > t + b + c = 60 - 29 = 31 t + b + c + 29 = 31 + 29 = 60 average = 60 / 4 = 15 answer d" + }, + { + "Answer": 144, + "Options": "a ) 216 , b ) 180 , c ) 144 , d ) 108 , e ) 72", + "Correct": "c", + "Explanation": "\"there are several ways to find the least common multiple of two numbers . in this case , the most efficient method is to use the greatest common factor : ( a * b ) / ( gcf ab ) = lcm ab the greatest common factor of 12 and 16 is 4 . so , 12 # 16 = 12 * 16 / 4 = 48 . the greatest common factor of 18 and 24 is 6 . so , 18 # 24 = 18 * 24 / 6 = 72 finally , the greatest common factor of 48 and 72 is 24 . so , q = ( ( 12 # 16 ) # ( 18 # 24 ) ) = 48 # 72 = ( 48 * 72 ) / 24 = 2 * 72 = 144 the correct answer is c .\"" + }, + { + "Answer": 90, + "Options": "a ) 84 , b ) 89 , c ) 90 , d ) 92 , e ) 95", + "Correct": "c", + "Explanation": "set x = { 11 , 13 , 17 , . . . . . . . . . . . . . , 83 , 89 , 97 } set y = { 7 , 21 , 35 , . . . . . . . . . . . . . . . , 77 , 91 , } combining two sets , say set z set z = { 7 , 11 , 13 , 17,21 , . . . . . . . . . . . . . . . . . . . , 77 , 83 , 89 , 91 , 97 } range = max value - min value range ( z ) = 97 - 7 = 90 oa c is the answer ." + }, + { + "Answer": 163, + "Options": "a ) 130 , b ) 141 , c ) 152 , d ) 163 , e ) 174", + "Correct": "d", + "Explanation": "\"3 / 10 * p are ponies with horseshoes , so p is a multiple of 10 . 5 / 8 * 3 / 10 * p = 3 / 16 * p are icelandic ponies with horseshoes , so p is a multiple of 16 . the minimum value of p is 80 . then h = p + 3 = 83 . the minimum number of horses and ponies is 163 . the answer is d .\"" + }, + { + "Answer": 24, + "Options": "a ) 4 % increase , b ) 24 % increase , c ) 10 % decrease , d ) 6 % increase , e ) none of these", + "Correct": "b", + "Explanation": "\"explanation : solution : let the original price be rs . 100 . new final price = 155 % of ( 80 % of 100 ) = rs . 155 / 100 * 80 / 100 * 100 = rs . 124 . . ' . increase = 24 % answer : b\"" + }, + { + "Answer": 9, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 12", + "Correct": "c", + "Explanation": "\"27 ^ c > 3 ^ 24 converting into the same bases : 27 ^ c > 27 ^ 8 therefore for the equation to hold true , c > 8 or c = 9 option c\"" + }, + { + "Answer": 205, + "Options": "a ) 190 , b ) 195 , c ) 200 , d ) 205 , e ) 210", + "Correct": "d", + "Explanation": "\"we ' re asked for the average of all of the multiples of 10 from 10 to 400 , inclusive . to start , we can figure out the total number of terms rather easily : 1 ( 10 ) = 10 2 ( 10 ) = 20 . . . 40 ( 10 ) = 400 so we know that there are 40 total numbers . we can now figure out the sum of those numbers with ' bunching ' : 10 + 400 = 410 20 + 390 = 410 30 + 380 = 410 etc . since there are 40 total terms , this pattern will create 20 ' pairs ' of 410 . thus , since the average = ( sum of terms ) / ( number of terms ) , we have . . . ( 20 ) ( 410 ) / ( 40 ) = 410 / 2 = 205 final answer : d\"" + }, + { + "Answer": 27, + "Options": "a ) 0.27 , b ) 0.027 , c ) 27 , d ) 0.0027 , e ) 2.7 e - 06", + "Correct": "c", + "Explanation": "\"99 * 0.27 = 26.73 approx . 27 answer : c\"" + }, + { + "Answer": 163, + "Options": "a ) 150 , b ) 200 , c ) 250 , d ) 163 , e ) none", + "Correct": "d", + "Explanation": "\"sol . let the number of grils be x . then , number of boys = ( 652 - x ) . then , ( 11 3 / 4 \u00d7 652 ) \u21d4 11 x + 12 ( 652 - x ) \u21d4 x = 7824 - 7661 \u21d4 163 . answer d\"" + }, + { + "Answer": 58000, + "Options": "a ) $ 40,000 , b ) $ 56,000 , c ) $ 64,000 , d ) $ 58,000 , e ) $ 80,000", + "Correct": "d", + "Explanation": "\"equation is correct , so math must be a problem . 0.11 * 40,000 + 0.2 * ( x - 40,000 ) = 8,000 - - > 4,400 + 0.2 x - 8,000 = 8,000 - - > 0.2 x = 11,600 - - > x = 58,000 . answer : d .\"" + }, + { + "Answer": 8, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 12", + "Correct": "d", + "Explanation": "answer = d = 8 if least = - 4 , then largest = 9 range = 9 - 1 = 8" + }, + { + "Answer": 20, + "Options": "a ) 15 , b ) 18 , c ) 13 , d ) 19 , e ) 20", + "Correct": "e", + "Explanation": "\"avg = ( 10 + 15 + 20 + 25 + 30 ) / 5 = 100 / 5 = > 20 answer e\"" + }, + { + "Answer": 369.63, + "Options": "a ) 369.63 , b ) 372.33 , c ) 702.33 , d ) 702 , e ) none of them", + "Correct": "a", + "Explanation": ". 3 33 333 3.33 - - - - - - - - - - 369.63 - - - - - - - - - - answer is a" + }, + { + "Answer": 41, + "Options": "a ) 25 , b ) 28 , c ) 30 , d ) 35 , e ) 41", + "Correct": "e", + "Explanation": "required sum = ( 2 + 3 + 5 + 7 + 11 + 13 ) = 41 note : 1 is not a prime number option e" + }, + { + "Answer": 7, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 12 , e ) 15", + "Correct": "b", + "Explanation": "\"the lcm of 9 , 11 and 17 is 1,683 . the next multiple is 2 * 1,683 = 3,366 . 3,366 + { remainder } = 3,366 + 8 = 3,374 , which is 7 less than 3,381 . answer : b .\"" + }, + { + "Answer": 7, + "Options": "a ) 7 , b ) 20 , c ) 28 , d ) 14 , e ) 19", + "Correct": "a", + "Explanation": "\"number of statues = all the paint \u00f7 amount used per statue = 7 / 16 \u00f7 1 / 16 = 7 / 16 * 16 / 1 = 7 / 1 = 7 answer is a .\"" + }, + { + "Answer": 1, + "Options": "a ) 3 , b ) 1 , c ) 1 / 3 , d ) - 1 / 3 , e ) - 3", + "Correct": "b", + "Explanation": "\"the expression 5 / ( 4 + 1 / x ) = 1 should have been equal to something . if 5 / ( 4 + 1 / x ) = 1 = > 5 x / ( 4 x + 1 ) = 1 = > 5 x = 4 x + 1 = > x = 1 correct option : b\"" + }, + { + "Answer": 44, + "Options": "a ) 44 , b ) 48 , c ) 45 , d ) 43 , e ) 50", + "Correct": "a", + "Explanation": "\"total age = 22 * 21 tot age of all stu + age of the teacher = 23 * 22 age of the teacher = 23 * 22 - 22 * 21 = 44 answer a\"" + }, + { + "Answer": 1, + "Options": "a ) 0 , b ) 1 , c ) 36 , d ) 118 , e ) 420", + "Correct": "b", + "Explanation": "\"6 + 2 + 4 + 9 + 3 + 8 = 32 , so this number is not divisible by 3 and thus not divisible by 18 . therefore , k = 0 6 ^ k - k ^ 6 = 1 - 0 = 1 the answer is b .\"" + }, + { + "Answer": 495, + "Options": "a ) 540 km , b ) 495 km , c ) 276 km , d ) 178 km , e ) 176 km", + "Correct": "b", + "Explanation": "\"explanation : let us assume that trains meet after ' x ' hours distance = speed * time distance traveled by two trains = 20 x km and 25 x km resp . as one train travels 55 km more than the other , 25 x \u00e2 \u20ac \u201c 20 x = 55 5 x = 55 x = 11 hours as the two trains are moving towards each other , relative speed = 20 + 25 = 45 km / hr therefore , total distance = 45 * 11 = 495 km . answer : b\"" + }, + { + "Answer": 19, + "Options": "a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20", + "Correct": "d", + "Explanation": "\"10 + 9 = 19 the answer is d .\"" + }, + { + "Answer": 1125, + "Options": "a ) 1025 , b ) 1075 , c ) 1125 , d ) 1175 , e ) 1225", + "Correct": "c", + "Explanation": "\"let x be the number of eggs that were laid . ( 2 / 5 ) ( 4 / 5 ) ( 1 / 3 ) x = 120 ( 8 / 75 ) x = 120 x = 1125 the answer is c .\"" + }, + { + "Answer": 11, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", + "Correct": "e", + "Explanation": "\"p is a positive even integer with a positive units digit - - > the units digit of p can be 2 , 4 , 6 , or 8 - - > in order the units digit of p ^ 3 - p ^ 2 to be 0 , the units digit of p ^ 3 and p ^ 2 must be the same . thus the units digit of p can be 0 , 1 , 5 or 6 . intersection of values is 6 , thus the units digit of p + 5 is 6 + 5 = 11 . answer : e .\"" + }, + { + "Answer": 7, + "Options": "a ) 2 a , b ) a / 2 , c ) 6 a , d ) 7 a , e ) 9 a", + "Correct": "d", + "Explanation": "ratio 1 : 3 a = x ratio 2 : 4 a = y x + y = 7 a answer is d" + }, + { + "Answer": 3, + "Options": "a ) 30 , b ) 18 , c ) 10 , d ) 9 , e ) 3", + "Correct": "e", + "Explanation": "\"( average production for n days ) * n = ( total production for n days ) - - > 70 n = ( total production for n days ) ; ( total production for n days ) + 90 = ( average production for n + 1 days ) * ( n + 1 ) - - > 70 n + 90 = 75 * ( n + 1 ) - - > n = 3 . answer : e .\"" + }, + { + "Answer": 12, + "Options": "a ) 2 , b ) 12 , c ) 3 , d ) 8 , e ) 4", + "Correct": "b", + "Explanation": "4 * ( 9 ) ^ 1 / 2 = 4 * 3 = 12 b is the answer" + }, + { + "Answer": 640, + "Options": "a ) 640 , b ) 500 , c ) 3000 , d ) 1000 , e ) 2000", + "Correct": "a", + "Explanation": "( p * 5 * 15 ) / 100 - ( p * 3.5 * 15 ) / 100 = 144 75 p / 100 \u00e2 \u20ac \u201c 52.5 p / 100 = 144 22.5 p = 144 * 100 = > p = rs . 640 answer a" + }, + { + "Answer": 285, + "Options": "a ) 187 , b ) 279 , c ) 280 , d ) 285 , e ) 262", + "Correct": "d", + "Explanation": "\"since the month begins with a sunday , so there will be five sundays in the month . required average = [ ( 510 * 5 ) + ( 240 * 25 ) ] / 30 = 8550 / 30 = 285 . answer : d\"" + }, + { + "Answer": 28, + "Options": "a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29", + "Correct": "d", + "Explanation": "present age = x before 7 yrs , y = x - 7 after 7 yrs , z = x + 7 by the qn , x + ( x - 7 ) = 35 2 x - 7 = 35 2 x = 35 + 7 x = 42 / 2 x = 21 z = x + 7 = 21 + 7 = 28 answer : d" + }, + { + "Answer": 18, + "Options": "a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20", + "Correct": "d", + "Explanation": "\"the point of intersection is ( - 6 , - 6 ) . the triangle has a base of length 6 and a height of 6 . area = ( 1 / 2 ) * base * height = ( 1 / 2 ) * 6 * 6 = 18 the answer is d .\"" + }, + { + "Answer": 13, + "Options": "a ) 22 kg , b ) 21.6 kg , c ) 22.4 kg , d ) 13 kg , e ) none of these", + "Correct": "d", + "Explanation": "\"exp . the total weight of 29 students = 29 * 28 the total weight of 30 students = 30 * 27.5 weight of the new student = ( 30 * 27.5 \u2013 29 * 28 ) = 825 - 812 = 13 answer : d\"" + }, + { + "Answer": 12, + "Options": "a ) 10.5 , b ) 11 , c ) 11.5 , d ) 12 , e ) 12.5", + "Correct": "d", + "Explanation": "the value which isexactlytwo sd less than the mean is : mean - 2 * sd = 15 - 2 * 1.5 = 12 . answer : d ." + }, + { + "Answer": 37.5, + "Options": "a ) $ 37.5 , b ) $ 64 , c ) $ 75 , d ) $ 96 , e ) can not be determined", + "Correct": "a", + "Explanation": "\"solution : 5 x + 4 y + 2 z = 80 7 x + 4 y + 2 z = 70 adding both the equations = 12 x + 8 y + 4 z = 150 3 x + 2 y + 1 z = 37.5 ans a\"" + }, + { + "Answer": 40000, + "Options": "a ) 40000 , b ) 24000 , c ) 26682 , d ) 29973 , e ) 12312", + "Correct": "a", + "Explanation": "\"x * ( 80 / 100 ) = 32000 x = 400 * 100 x = 40000 answer : a\"" + }, + { + "Answer": 75, + "Options": "a ) 12.5 % , b ) 75 % , c ) 80 % , d ) 11 % , e ) 1 %", + "Correct": "b", + "Explanation": "\"say y = 1 and x = 4 . then y = 1 is less than x = 4 by ( 4 - 1 ) / 4 * 100 = 3 / 4 * 100 = 75 % . answer : b .\"" + }, + { + "Answer": 2, + "Options": "a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8", + "Correct": "b", + "Explanation": "n = 30 k + 16 2 n = 2 ( 30 k + 16 ) = 4 k * 15 + 32 = 4 k * 15 + 2 * 15 + 2 = 15 j + 2 the answer is b ." + }, + { + "Answer": 25, + "Options": "a ) 9 % , b ) 11 % , c ) 15 % , d ) 25 % , e ) 90 %", + "Correct": "d", + "Explanation": "\"cost of 12 paper towels individually = 1 * 12 = 12 cost of a set of 12 paper towels = 9 cost of one roll = 9 / 12 = 3 / 4 = 0.75 savings per roll = 1 - . 75 = 0.25 % of savings is t = . 25 / 1 * 100 = 25 % d is the answer .\"" + }, + { + "Answer": 50, + "Options": "a ) 32 , b ) 37 , c ) c . 40 , d ) 43 , e ) 50", + "Correct": "e", + "Explanation": "note that both median and range do not restrict too many numbers in the set . range is only concerned with the smallest and greatest . median only cares about the middle . quick check of each option starting from the largest : ( e ) 50 range of 20 means the smallest integer will be 30 . so 20 can not lie in between and hence can not be the median . ( d ) 43 range of 20 means the smallest integer will be 23 . so 20 can not lie in between and hence can not be the median . ( c ) 40 range of 20 means the smallest integer will be 20 . 20 can lie in between such as : 20 , 20 , 20 , 20 , 20 , 20 , 20 , 20 , 20 , 50 this is possible . hence it is the greatest such number . answer ( e )" + }, + { + "Answer": 589.5691609977324, + "Options": "a ) 221 , b ) 287 , c ) 400 , d ) 589 , e ) 171", + "Correct": "d", + "Explanation": "\"explanation : 650 = p ( 21 / 20 ) 2 p = 589.56 answer : d\"" + }, + { + "Answer": 50, + "Options": "a ) 30 % , b ) 50 % , c ) 60 % , d ) 80 % , e ) 90 %", + "Correct": "b", + "Explanation": "\"number of runs made by running = 110 - ( 3 x 4 + 8 x 6 ) = 120 - ( 60 ) = 60 now , we need to calculate 60 is what percent of 120 . = > 60 / 120 * 100 = 50 % b\"" + }, + { + "Answer": 100.89999999999999, + "Options": "a ) 10.09 , b ) 1.06 , c ) 10.06 , d ) 100.9 , e ) 100.6", + "Correct": "d", + "Explanation": "\"= 4.036 / 0.04 = 403.6 / 4 = 100.9 answer is d .\"" + }, + { + "Answer": 13, + "Options": "a ) - 11 , b ) - 12 , c ) - 13 , d ) - 14 , e ) - 15", + "Correct": "c", + "Explanation": "\"- x 2 - ( k + 7 ) x - 8 = - ( x - 2 ) ( x - 4 ) : given - x 2 - ( k + 7 ) x - 8 = - x 2 + 6 x - 8 - ( k + 7 ) = 6 : two polynomials are equal if their corresponding coefficients are equal . k = - 13 : solve the above for k correct answer c\"" + }, + { + "Answer": 18, + "Options": "a ) 18 , b ) 56 , c ) 12 , d ) 17 , e ) 14", + "Correct": "a", + "Explanation": "\"initial average age of the 10 persons be p . age of the new person q . sum of the ages of the initial 10 persons = 10 p new average = ( p - 3 ) 10 ( p - 3 ) = 10 p - 48 + q = > q = 18 answer : a\"" + }, + { + "Answer": 14, + "Options": "a ) 10 , b ) 12 , c ) 14 , d ) 8 , e ) 9", + "Correct": "c", + "Explanation": "\"explanation : on dividing 10154 by 30 we get the remainder 14 , so 14 should be subtracted option c\"" + }, + { + "Answer": 26, + "Options": "a ) 25 , b ) 31 , c ) 26 , d ) 29 , e ) 39", + "Correct": "c", + "Explanation": "\"let the average after 17 innings = x total runs scored in 17 innings = 17 x average after 16 innings = ( x - 3 ) total runs scored in 16 innings = 16 ( x - 3 ) total runs scored in 16 innings + 74 = total runs scored in 17 innings = > 16 ( x - 3 ) + 74 = 17 x = > 16 x - 48 + 74 = 17 x = > x = 26 answer is c\"" + }, + { + "Answer": 216, + "Options": "a ) 122 , b ) 210 , c ) 216 , d ) 217 , e ) 225", + "Correct": "c", + "Explanation": "we should determine which 5 digits from given 6 , would form the 5 digit number divisible by 3 . we have six digits : 0 , 1 , 2 , 3 , 4 , 5 . their sum = 15 . for a number to be divisible by 3 the sum of the digits must be divisible by 3 . as the sum of the six given numbers is 15 ( divisible by 3 ) only 5 digits good to form our 5 digit number would be 15 - 0 = { 1 , 2 , 3 , 4 , 5 } and 15 - 3 = { 0 , 1 , 2 , 4 , 5 } . meaning that no other 5 from given six will total the number divisible by 3 . second step : we have two set of numbers : 1 , 2 , 3 , 4 , 5 and 0 , 1 , 2 , 4 , 5 . how many 5 digit numbers can be formed using these two sets : 1 , 2 , 3 , 4 , 5 - - > 5 ! as any combination of these digits would give us 5 digit number divisible by 3 . 5 ! = 120 . 0 , 1 , 2 , 4 , 5 - - > here we can not use 0 as the first digit , otherwise number wo n ' t be any more 5 digit and become 4 digit . so , desired # would be total combinations 5 ! , minus combinations with 0 as the first digit ( combination of 4 ) 4 ! - - > 5 ! - 4 ! = 4 ! ( 5 - 1 ) = 4 ! * 4 = 96 120 + 96 = 216 = q answer : c ." + }, + { + "Answer": 178, + "Options": "a ) 168.58 cm , b ) 158.58 cm , c ) 179.29 cm , d ) 168.58 cm , e ) 178.58 cm", + "Correct": "e", + "Explanation": "\"calculated average height of 35 boys = 180 cm . wrong total height of 35 boys = 180 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 156 cm . correct total height of 35 boys = 180 * 35 cm - 156 cm + 106 cm = 180 * 35 cm - 156 cm + 106 cm / 35 = 180 cm - 50 / 35 cm = 180 cm - 1.42 cm = 178.58 cm . answer : e\"" + }, + { + "Answer": 1.7276978417266187, + "Options": "a ) $ 1.63 , b ) $ 1.64 , c ) $ 1.68 , d ) $ 1.73 , e ) $ 1.76", + "Correct": "d", + "Explanation": "( 1365 * 1.89 + 720 * 1.42 ) / ( 1365 + 720 ) = ~ 1.73 option ( d )" + }, + { + "Answer": 206, + "Options": "a ) 200 , b ) 202 , c ) 204 , d ) 206 , e ) 208", + "Correct": "d", + "Explanation": "\"35 * 190 = 6650 . the other 5 onions weigh a total of 1030 grams . the average weight is 1030 / 5 = 206 grams . the answer is d .\"" + }, + { + "Answer": 14, + "Options": "a ) 14 , b ) 19 , c ) 27 , d ) 18 , e ) 15", + "Correct": "a", + "Explanation": "explanation : let mudit ' s present age be ' m ' years . m + 16 = 3 ( m - 4 ) = > 2 m = 28 = > m = 14 years . answer : a" + }, + { + "Answer": 220, + "Options": "a ) 220 , b ) 200 , c ) 140 , d ) 80 , e ) 60", + "Correct": "a", + "Explanation": "the ratio of present ages of father and son is 7 : 4 , so suppose the present ages are 7 x and 4 x , respectively . 10 years later , the ages of father and son , respectively , shall be 7 x + 10 and 4 x + 10 . the ratio of ages 10 years later is given to be 5 : 3 . this means ( 7 x + 10 ) / ( 4 x + 10 ) = 5 / 3 solving we get x = 20 . so present age of father is 7 x = 140 and present age of son is 4 x = 80 . the sum of present ages is thus 220 . ans a" + }, + { + "Answer": 48, + "Options": "a ) 20 , b ) 24 , c ) 30 , d ) 32 , e ) 48", + "Correct": "e", + "Explanation": "\"4 * 1 * 4 - ( - 2 * 1 * 16 ) = 16 + 32 = 48 ans : e\"" + }, + { + "Answer": 100, + "Options": "a ) 90 % , b ) 99 % , c ) 100 % , d ) 101 % , e ) 110 %", + "Correct": "b", + "Explanation": "\"the total number of employees = n the average salary = x total salary to all emplyoees = xn after the total number of employees = n - 0.1 n = 0.9 n the average salary = x + 10 % of x = 1.1 x total salary to all emplyoees = 0.9 n ( 1.1 x ) total salary after as a % of total salary before q = [ 0.9 n ( 1.1 x ) ] / xn = 0.99 or 99 % = b\"" + }, + { + "Answer": 180000.00000000003, + "Options": "a ) $ 10800 , b ) $ 18000 , c ) $ 180000 , d ) $ 1800 , e ) none", + "Correct": "c", + "Explanation": "\"[ 1 / ( x 1 / y 1 + x 2 / y 2 + x 3 / y 3 ) ] * total amount = balance amount [ 1 - ( 1 / 5 + 1 / 10 + 3 / 5 ) } * total salary = $ 18000 , = [ 1 - 9 / 10 ] * total salary = $ 18000 , total salary = $ 18000 * 10 = $ 180000 , correct answer ( c )\"" + }, + { + "Answer": 44, + "Options": "a ) $ 36 , b ) $ 44 , c ) $ 52 , d ) $ 60 , e ) $ 68", + "Correct": "b", + "Explanation": "\"started to test answer b if he had 44 , then he spent 11 at hardware store now he was left with 33 $ he spent 9 dollars on cleaning , thus he remained with 24 $ he then spent 1 / 2 of 24 , or 12 , and was left with 12 . hence , the only option that can be right is b\"" + }, + { + "Answer": 1, + "Options": "a ) 1 / 4 , b ) 1 / 2 , c ) 1 , d ) 2 , e ) 3", + "Correct": "c", + "Explanation": "13 - 13 w = 13 w 26 w = 13 w = 1 / 2 2 w * 2 = 1 / 2 * 2 = 1 answer : c" + }, + { + "Answer": 179, + "Options": "a ) 170 , b ) 179 , c ) 37 , d ) 67 , e ) 32", + "Correct": "b", + "Explanation": "\"divisor = ( dividend \u2013 remainder / quotient ) = ( 15968 - 37 ) / 89 = 179 answer b 179\"" + }, + { + "Answer": 26.25, + "Options": "a ) 22.25 , b ) 99 , c ) 26.25 , d ) 66 , e ) 887", + "Correct": "c", + "Explanation": "\"total time taken = x / 70 + 2 x / 20 hours = 4 x / 35 hours average speed = 3 x / ( 4 x / 35 ) = 26.25 kmph answer : c\"" + }, + { + "Answer": 16, + "Options": "a ) 68 , b ) 66 , c ) 565 , d ) 16 , e ) 35", + "Correct": "d", + "Explanation": "128 is the total sum of money . as we have 13 10 dollar bills so the closest we can get to 128 using the 10 dollar bills is by using 12 * 10 dollar bils 128 - 120 = 8 so now we need to get 8 from either 5 dollar bills or 1 dollar bills 8 - 5 ( use only 1 5 dollar bill ) = 3 so we can get 3 from using 3 $ 1 bills . hence 16 ( 12 + 1 + 3 ) answer is d" + }, + { + "Answer": 15.5, + "Options": "a ) 19 , b ) 19.5 , c ) 20 , d ) 20.5 , e ) 21", + "Correct": "d", + "Explanation": "\"the total subtracted is ( 9 + 8 + . . . + 1 ) = ( 9 * 10 ) / 2 = 45 on average , each number will be reduced by 45 / 10 = 4.5 therefore , the overall average will be reduced by 4.5 the answer is d .\"" + }, + { + "Answer": 1.65, + "Options": "a ) 1.12 , b ) 1.65 , c ) 1.2 , d ) 1.3 , e ) none of these", + "Correct": "b", + "Explanation": "\"explanation : ( x * 5 ) = ( 0.75 * 11 ) x = 8.25 / 5 = 1.65 answer : b\"" + }, + { + "Answer": 36, + "Options": "a ) 24 , b ) 25 , c ) 28 , d ) 32 , e ) 36", + "Correct": "e", + "Explanation": "\"9 c 2 = 36 the answer is e\"" + }, + { + "Answer": 120, + "Options": "a ) $ 120 , b ) $ 125 , c ) $ 130 , d ) $ 135 , e ) $ 140", + "Correct": "a", + "Explanation": "\"the difference in the two prices is $ 2.75 - $ 1.25 = $ 1.50 for each color copy . each color copy will cost an extra $ 1.50 at print shop y . 80 * $ 1.50 = $ 120 the answer is a .\"" + }, + { + "Answer": 3.125, + "Options": "a ) 25.0 % , b ) 8.3 % , c ) 3.1 % , d ) 2.7 % , e ) 1.0 %", + "Correct": "c", + "Explanation": "c . each cat gets 1 / 4 as much food as a dog . a dog gets 1 / 8 of the food . 1 / 4 of 1 / 8 is 1 / 32 , which is about 3.1 % , so the answer is c ." + }, + { + "Answer": 20, + "Options": "a ) 62 , b ) 45 , c ) 28 , d ) 20 , e ) 25", + "Correct": "d", + "Explanation": "explanation : total runs scored = ( 36 x 5 ) = 180 . let the runs scored by e be x . then , runs scored by d = x + 5 ; runs scored by a = x + 8 ; runs scored by b = x + x + 5 = 2 x + 5 ; runs scored by c = ( 107 - b ) = 107 - ( 2 x + 5 ) = 102 - 2 x . so , total runs = ( x + 8 ) + ( 2 x + 5 ) + ( 102 - 2 x ) + ( x + 5 ) + x = 3 x + 120 . therefore 3 x + 120 = 180 3 x = 60 x = 20 . answer : option d" + }, + { + "Answer": 12, + "Options": "a ) 12 kg , b ) 13 kg , c ) 22 kg , d ) 14 kg , e ) 15 kg", + "Correct": "a", + "Explanation": "25 % = 5 kg 100 % = 20 kg 60 % of 20 kg = 12 kg 12 kg answer : a" + }, + { + "Answer": 0.4166666666666667, + "Options": "a ) 12 / 5 , b ) 5 / 12 , c ) 6 / 4 , d ) 2 / 3 , e ) 4 / 7", + "Correct": "b", + "Explanation": "\"here n ( s ) = ( 6 * 6 ) = 36 let e = event of getting a total more than 7 = { ( 2,6 ) , ( 3,5 ) , ( 3,6 ) , ( 4,4 ) , ( 4,5 ) , ( 4,6 ) , ( 5,3 ) , ( 5,4 ) , ( 5,5 ) , ( 5,6 ) , ( 6,2 ) , ( 6,3 ) , ( 6,4 ) , ( 6,5 ) , ( 6,6 ) } p ( e ) = n ( e ) / n ( s ) = 15 / 36 = 5 / 12 option b\"" + }, + { + "Answer": 66.66666666666666, + "Options": "a ) 35 , b ) 64 , c ) 66.67 , d ) 60 , e ) 84", + "Correct": "c", + "Explanation": "number of boys attending the college : 0.75 * 160 = 120 number of girls not attending the college : 0.40 * 200 = 80 number of girls attending the college : 200 - 80 = 120 total attending = 120 + 120 = 240 total people = 160 + 200 = 360 % of people attending = 240 / 360 = 66.67 % . c is the correct answer" + }, + { + "Answer": 600, + "Options": "a ) $ 600 , b ) $ 700 , c ) $ 800 , d ) $ 900 , e ) $ 1000", + "Correct": "a", + "Explanation": "0.1 x = 0.08 ( 2000 - x ) + 92 0.18 x = 252 x = 1400 then the amount invested at 8 % is $ 2000 - $ 1400 = $ 600 the answer is a ." + }, + { + "Answer": 73, + "Options": "a ) a ) 87 , b ) b ) 99 , c ) c ) 68 , d ) d ) 82 , e ) e ) 73", + "Correct": "e", + "Explanation": "average = ( 76 + 65 + 82 + 67 + 75 ) / 5 = 365 / 5 = 73 . answer : e" + }, + { + "Answer": 139, + "Options": "a ) 65 , b ) 66 , c ) 67 , d ) 131 , e ) 138", + "Correct": "e", + "Explanation": "\"the answer to the question is indeed e . the problem with above solutions is that they do not consider words like aa , bb , . . . the number of 1 letter words ( x ) that can be made from 69 letters is 69 ; the number of 2 letter words ( xx ) that can be made from 69 letters is 69 * 69 , since each x can take 69 values . total : 69 + 69 * 69 . similarly : the number of 1 letter words ( x ) that can be made from 68 letters is 68 ; the number of 2 letter words ( xx ) that can be made from 68 letters is 68 * 68 , since each x can take 68 values . total : 68 + 68 * 68 . the difference is ( 69 + 69 * 69 ) - ( 68 + 68 * 68 ) = 138 . answer : e .\"" + }, + { + "Answer": 3168, + "Options": "a ) rs . 3168 , b ) rs . 2520 , c ) rs . 2880 , d ) rs . 3360 , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : let c ' s investment = rs . x b ' s investment = rs . ( x - 3000 ) a ' s investment = rs . ( x - 3000 + 6000 ) = rs . ( x + 3000 ) now , ( a + b + c ) ' s investment = rs . 90000 = > x + ( x - 3000 ) + ( x + 3000 ) = 90000 = > 3 x = 90000 = > x = 30000 hence , a ' s investment = rs . 33000 b ' s investment = rs . 27000 c ' s investment = rs . 30000 ratio of the capitals of a , b and c = 33000 : 27000 : 30000 = 11 : 9 : 10 a ' s share = rs . [ ( 11 / 30 ) \u00e3 \u2014 8640 ] = rs . 3168 answer : option a\"" + }, + { + "Answer": 74, + "Options": "a ) 44 % , b ) 48 % , c ) 52 % , d ) 42 % , e ) 74 %", + "Correct": "e", + "Explanation": "\"first calculate the distance , b has covered with his speed in the time , in which a reached 40 % of the race . then add the remaining distance as head start for b to win the race . its best to apply ratios concept here . since a ' s speed is 20 / 13 of b , therefore , b ' s speed is 13 / 20 of a distance covered by b = speed x time = ( 13 / 20 ) x ( 0.4 ) = 0.26 ( which means b would have covered 0.26 of the race length during the time in which a has covered 0.4 of the race length . therefore to win , b needs a headstart of ( 1 - 0.26 = ) 0.74 of the race length . so the answer is e\"" + }, + { + "Answer": 7, + "Options": "a ) 7 , b ) 9 , c ) 10 , d ) 11 , e ) 12", + "Correct": "a", + "Explanation": "( n + 2 ) ! / n ! = 72 rewrite as : [ ( n + 2 ) ( n + 1 ) ( n ) ( n - 1 ) ( n - 2 ) . . . . ( 3 ) ( 2 ) ( 1 ) ] / [ ( n ) ( n - 1 ) ( n - 2 ) . . . . ( 3 ) ( 2 ) ( 1 ) ] = 132 cancel out terms : ( n + 2 ) ( n + 1 ) = 72 from here , we might just test the answer choices . since ( 9 ) ( 8 ) = 72 , we can see that n = 7 a" + }, + { + "Answer": 4, + "Options": "a ) 10 , b ) 8 , c ) 6 , d ) 4 , e ) 2", + "Correct": "d", + "Explanation": "\"( ( 90 \u03b8 33 ) \u03b8 17 ) the remainder of 90 divided by 33 is 24 ; the remainder of 24 divided by 17 is 7 ; ( 99 \u03b8 ( 33 \u03b8 17 ) ) the remainder of 33 divided by 17 is 16 ; 7 - 3 = 4 . answer : d .\"" + }, + { + "Answer": 12, + "Options": "a ) 5 % , b ) 8 % , c ) 10 % , d ) 12 % , e ) 15 %", + "Correct": "d", + "Explanation": "\"let x be the amount of gasoline the driver buys originally . let y be the new amount of gasoline the driver should buy . let p be the original price per liter . ( 1.25 * p ) y = 1.1 ( p * x ) y = ( 1.1 / 1.25 ) * x = 0.88 x which is a reduction of 12 % . the answer is d .\"" + }, + { + "Answer": 42, + "Options": "a ) 11 , b ) 66 , c ) 18 , d ) 16 , e ) 42", + "Correct": "e", + "Explanation": "\"explanation : age of the 16 th student = [ 16 * 16 - ( 14 * 5 + 16 * 9 ) ] = ( 256 - 214 ) = 42 years . answer : e\"" + }, + { + "Answer": 540, + "Options": "a ) 400 km , b ) 500 km , c ) 360 km , d ) 540 km , e ) 600 km", + "Correct": "d", + "Explanation": "\"sol . average speed of a tractor = 25 km / h the speed of a bus in an hour = 25 \u00d7 2 = 50 km the speed of a car in an hour = 9 / 5 * 50 = 90 km so , the distance covered by car in 6 h is 90 \u00d7 6 = 540 km ans . ( d )\"" + }, + { + "Answer": 12, + "Options": "a ) 11 , b ) 12 , c ) 77 , d ) 33 , e ) 88", + "Correct": "b", + "Explanation": "\"add the numbers of highlighters . 6 + 2 + 4 = 12 . answer is b .\"" + }, + { + "Answer": 37, + "Options": "a ) 19 , b ) 29 , c ) 37 , d ) 49 , e ) 59", + "Correct": "c", + "Explanation": "\"let the average after 17 th inning = x then average after 16 th inning = ( x - 3 ) therefore 16 ( x - 3 ) + 85 = 17 x therefore x = 37 answer : c\"" + }, + { + "Answer": 25.925925925925924, + "Options": "a ) 49.66 % , b ) 52.66 % , c ) 28.22 % , d ) 33.33 % , e ) 25.92 %", + "Correct": "e", + "Explanation": "\"say a 100 families existed in 1998 then the number of families owning a computer in 1998 - 20 number of families owning computer in 2002 = 20 * 140 / 100 = 28 number of families in 2002 = 108 the percentage = 28 / 108 * 100 = 25.92 % . answer : e\"" + }, + { + "Answer": 900, + "Options": "a ) 998 , b ) 297 , c ) 999 , d ) 902 , e ) 900", + "Correct": "e", + "Explanation": "\"last term = first term + ( total no . of terms - 1 ) consecutive difference s is a set of 100 consecutive multiples of 8 . if the smallest number in s is 108 , then the greatest number in s is first term = 102 ; total terms = 100 ; difference = 3 108 + ( 99 ) 8 = 900 ans e\"" + }, + { + "Answer": 225, + "Options": "a ) 179 , b ) 208 , c ) 210 , d ) 225 , e ) 229", + "Correct": "d", + "Explanation": "\"explanation : total runs scored by the batsman = 62 * 46 = 2852 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2852 \u2013 2552 = 300 runs . let the highest score be x , hence the lowest score = x \u2013 150 x + ( x - 150 ) = 300 2 x = 450 x = 225 runs answer d\"" + }, + { + "Answer": 4, + "Options": "a ) 4 % increase , b ) 10 % increase , c ) 10 % decrease , d ) 6 % increase , e ) none of these", + "Correct": "a", + "Explanation": "explanation : solution : let the original price be rs . 100 . new final price = 130 % of ( 80 % of 100 ) = rs . 130 / 100 * 80 / 100 * 100 = rs . 104 . . ' . increase = 4 % answer : a" + }, + { + "Answer": 0.4, + "Options": "a ) 1 / 7 , b ) 2 / 5 , c ) 1 / 2 , d ) 7 / 12 , e ) 2 / 3", + "Correct": "b", + "Explanation": "\"same amount of water made bigger jar 1 / 5 full , then the same amount of water ( stored for a while in smaller jar ) were added to bigger jar , so bigger jar is 1 / 5 + 1 / 5 = 2 / 5 full . answer : b .\"" + }, + { + "Answer": 1.6, + "Options": "a ) 1.2 kg , b ) 1.5 kg , c ) 1.7 kg , d ) 1.6 kg , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : flower - nectar contains 50 % of non - water part . in honey this non - water part constitutes 80 % ( 100 - 20 ) . therefore 0.5 x amount of flower - nectar = 0.80 x amount of honey = 0.80 x 1 kg therefore amount of flower - nectar needed = ( 0.80 / 0.51 ) kg = 1.6 kgs answer : d\"" + }, + { + "Answer": 10000, + "Options": "a ) 3377 , b ) 2899 , c ) 2500 , d ) 2778 , e ) 10000", + "Correct": "e", + "Explanation": "\"a : b : c = 2 / 3 : 1 / 6 : 1 / 6 = 4 : 1 : 1 x * 2 / 100 * 2 / 3 = 200 a capital = 15000 * 2 / 3 = 10000 answer : e\"" + }, + { + "Answer": 49.99999999999999, + "Options": "a ) 50 , b ) 100 , c ) 490 , d ) 500 , e ) 980", + "Correct": "a", + "Explanation": "\"average price for a pair of rackets = $ 9.8 total cost = $ 9.8 * x = $ 490 x = 50 pairs were sold . answer : a\"" + }, + { + "Answer": 10, + "Options": "a ) 5 , b ) 7 , c ) 8 , d ) 10 , e ) 12", + "Correct": "d", + "Explanation": "pounds of apples = x pounds of oranges = 5 x x + 5 x = 12 6 x = 12 x = 12 / 6 = 2 oranges = 5 x = 5 * 2 = 10 answer : d" + }, + { + "Answer": 7, + "Options": "a ) 7 , b ) 4 , c ) 5 , d ) 6 , e ) 3", + "Correct": "a", + "Explanation": "\"let x = 7.1 and y = 14.1 greatest possible difference = 14.1 - 7.1 = 7 answer a\"" + }, + { + "Answer": 3, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8", + "Correct": "b", + "Explanation": "if 100 / x leaves a reminder 3 then ( 100 - 3 ) i . e . 97 is divisible by x so ( 100 + 97 ) / x leaves a reminder rem ( 100 / x ) + rem ( 97 / x ) = > 3 + 0 = 3 answer : b" + }, + { + "Answer": 60, + "Options": "a ) 45 % , b ) 500 / 11 , c ) 600 / 11 , d ) 55 % , e ) 60 %", + "Correct": "e", + "Explanation": "\"explanation : number of runs made by running , = > 125 \u2212 ( 5 \u00d7 4 + 5 \u00d7 6 ) . = > 125 - 50 = > 75 hence , the required percentage is : - = > 75 / 125 * 100 = > 60 % answer : e\"" + }, + { + "Answer": 102, + "Options": "a ) $ 122 , b ) $ 152 , c ) $ 202 , d ) $ 107 , e ) $ 102", + "Correct": "e", + "Explanation": "explanatory answer let the sums of money received by a , b and c be x , y and z respectively . then x - 5 : y - 8 : z - 4 is 2 a : 8 a : 6 a when $ 5 , $ 8 and $ 4 are removed , we are removing a total of $ 17 from $ 1100 . therefore , 2 a + 8 a + 6 a = 1100 - 17 = 1093 i . e . , 16 a = 1093 or a = 68 . we know that z - 6 = 16 a = 6 * 16 = 96 therefore , z = 96 + 6 = $ 102 the correct choice is ( e )" + }, + { + "Answer": 79, + "Options": "a ) 80 , b ) 79 , c ) 78 , d ) 81 , e ) 82", + "Correct": "b", + "Explanation": "max no of girls = hcf of 2923 and 3239 = 79 answer : b" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 6 , e ) 7", + "Correct": "c", + "Explanation": "\"d = ( d - r ) / q = ( 23 - 2 ) / 7 = 21 / 7 = 3 c\"" + }, + { + "Answer": 144, + "Options": "a ) rs . 129 , b ) rs . 144 , c ) rs . 156 , d ) rs . 168 , e ) rs . 178", + "Correct": "b", + "Explanation": "ratio of initial investments = 1 / 2 : 1 / 3 : 1 / 4 = 6 : 4 : 3 . let their initial investments be 6 x , 2 x and 3 x respectively . a : b : c = ( 6 x * 2 + 3 x * 10 ) : ( 4 x * 12 ) : ( 3 x * 12 ) = 42 : 48 : 36 = 7 : 8 : 6 . therefore , b \u2019 s share = rs . 378 * 8 / 21 = rs . 144 . answer : b" + }, + { + "Answer": 12, + "Options": "a ) 10 , b ) 12 , c ) 15 , d ) 18 , e ) 20", + "Correct": "b", + "Explanation": "6 x ^ 2 + x - 12 = 6 x ^ 2 + 9 x - 8 x - 12 = > 3 x ( 2 x + 3 ) - 4 ( 2 x + 3 ) = > ( 2 x + 3 ) ( 3 x - 4 ) = ( hx + b ) ( cx + d ) hence h = 2 , b = c = 3 , d = - 4 so , 2 + 3 + 3 + | - 4 | = 2 + 3 + 3 + 4 = 12 answer b ." + }, + { + "Answer": 56, + "Options": "a ) $ 44 , b ) $ 48 , c ) $ 52 , d ) $ 56 , e ) $ 60", + "Correct": "d", + "Explanation": "\"p = ( 2 / 8 ) * p + 42 ( 6 / 8 ) * p = 42 p = 56 the answer is d .\"" + }, + { + "Answer": 7550, + "Options": "a ) 5100 , b ) 7550 , c ) 10100 , d ) 15500 , e ) 20100", + "Correct": "b", + "Explanation": "\"my solution is : first 50 even integers : 2 4 6 8 < . . . > integers from 102 to 200 102 104 106 108 < . . . > we notice that each integer from the second set is 100 more than the respective integer in the first set . since we have 50 even integers from 102 to 200 , then : r = 2550 + ( 100 * 50 ) = 7550 . b\"" + }, + { + "Answer": 5, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "d", + "Explanation": "let the present ages of bipin , alok , chandan are b , a , c respectively given conditions are 1 ) b = 6 a 2 ) ( b + 10 ) = 2 * ( c + 10 ) 3 ) chandans present age = c = 10 years therefore b = 30 so a = 5 answer : d" + }, + { + "Answer": 80, + "Options": "a ) 36 liters , b ) 40 liters , c ) 45 liters , d ) 54 liters , e ) 80 liters", + "Correct": "e", + "Explanation": "\"a big container is 30 % full with water and after 36 liters of water is added , the container becomes 75 % full . hence these 36 liters account for 45 % of the container , which means that the capacity of it is 36 / 0.45 = 80 liters . or : if the capacity of the container is x liters then : 0.3 x + 36 = 0.75 x - - > x = 80 liters . answer : e .\"" + }, + { + "Answer": 13, + "Options": "a ) 12 , b ) 13 , c ) 14 , d ) 16 , e ) 15", + "Correct": "b", + "Explanation": "\"let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 92 ( x - 5 ) 72 x - ( 5 * 40 ) = 92 ( x - 5 ) 260 = 20 x = > x = 13 answer : b\"" + }, + { + "Answer": 0.027777777777777776, + "Options": "a ) 41 / 50 , b ) 1 / 221 , c ) 1 / 216 , d ) 1 / 36 , e ) 1 / 42", + "Correct": "d", + "Explanation": "toguaranteethat jim will get some monetary payoff he must score the maximum score of 6 + 6 = 12 , because if he gets even one less than that so 11 , someone can get 12 and jim will get nothing . p ( 12 ) = 1 / 6 ^ 2 = 1 / 36 . answer : d" + }, + { + "Answer": 300, + "Options": "a ) 150 , b ) 280 , c ) 310 , d ) 420 , e ) 300", + "Correct": "e", + "Explanation": "\"many approaches are possible . for example : consider numbers from 0 to 999 written as follows : 1 . 000 2 . 001 3 . 002 4 . 003 . . . . . . . . . 1000 . 999 we have 1000 numbers . we used 3 digits per number , hence used total of 3 * 1000 = 3000 digits . now , why should any digit have preferences over another ? we used each of 10 digits equal # of times , thus we used each digit ( including 6 ) 3000 / 10 = 300 times . answer : e .\"" + }, + { + "Answer": 30, + "Options": "a ) 25 , b ) 30 , c ) 35 , d ) 40 , e ) 45", + "Correct": "b", + "Explanation": "\"the time to produce the first 60 cogs is 60 / 20 = 3 hours . the time to produce the next 60 cogs is 60 / 60 = 1 hour . the average output is 120 cogs / 4 hours = 30 cogs per hour . the answer is b .\"" + }, + { + "Answer": 500, + "Options": "a ) 339 , b ) 500 , c ) 288 , d ) 277 , e ) 112", + "Correct": "b", + "Explanation": "sol : let a , b be the numbers . a + b = 45 ab + baab + ba = 2.05 \u21d2 a 2 + b 2 ab \u21d2 a 2 + b 2 ab = 2.05 \u21d2 ( a + b ) 2 \u2212 2 abab = 2.05 \u21d2 ( a + b ) 2 \u2212 2 abab = 2.05 \u21d2 ( a + b ) 2 \u21d2 ( a + b ) 2 = 2.05 ab + 2 ab = 4.05 ab \u21d2 \u21d2 ab = 4524 . 054524.05 = 500 answer : b" + }, + { + "Answer": 25.00000000000001, + "Options": "a ) 50 % , b ) 40 % , c ) 25 % , d ) 20 % , e ) 10 %", + "Correct": "c", + "Explanation": "\"looking at the ratio we can take total number of people q = 20 . . ans 5 / 20 or 25 % c\"" + }, + { + "Answer": 5, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "e", + "Explanation": "\"let number of apples = a number of oranges = b a + b = 10 - - - 1 . 56 = ( . 5 a + . 6 b ) / 10 = > 56 = 5 a + 6 b - - - - 2 solving 1 and 2 , we get a = 4 b = 6 let the number of oranges put back = c 52 * ( 10 - c ) = 50 * 4 + 60 ( 6 - c ) = > c = 5 answer e\"" + }, + { + "Answer": 5, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 6 , e ) 5", + "Correct": "e", + "Explanation": "\"explanation : 39 + 18 = 57 / 13 = 5 ( remainder ) answer : e\"" + }, + { + "Answer": 11500, + "Options": "a ) rs . 11,300 , b ) rs . 11,500 , c ) rs . 11,302 , d ) rs . 11,301 , e ) rs . 11,303", + "Correct": "b", + "Explanation": "explanation : manager ' s monthly salary = rs . ( 1900 x 25 - 1500 x 24 ) = rs . 11,500 answer : b" + }, + { + "Answer": 18.400000000000002, + "Options": "a ) $ 58.40 , b ) $ 40 . 00 , c ) $ 24.60 , d ) $ 18.40 , e ) $ 16.00", + "Correct": "d", + "Explanation": "the tourist must pay tax on $ 730 - $ 500 = $ 230 . thus the amount to be paid is 0.08 * $ 230 = $ 18.40 . answer : d ." + }, + { + "Answer": 4000, + "Options": "a ) rs . 2000 , b ) rs . 3000 , c ) rs . 4000 , d ) rs . 4500 , e ) rs . 5000", + "Correct": "c", + "Explanation": "let p , q and r represent their respective monthly incomes . then , we have : p + q = ( 5050 x 2 ) = 10100 . . . . ( i ) q + r = ( 6250 x 2 ) = 12500 . . . . ( ii ) m + o = ( 5200 x 2 ) = 10400 . . . . ( iii ) adding ( i ) , ( ii ) and ( iii ) , we get : 2 ( m + n + o ) = 33000 or m + n + o = 16500 . . . . ( iv ) subtracting ( ii ) from ( iv ) , we get m = 4000 . m ' s monthly income = rs . 4000 c" + }, + { + "Answer": 60, + "Options": "a ) 500 % , b ) 250 % , c ) 500 / 3 % , d ) 125 % , e ) 60 %", + "Correct": "e", + "Explanation": "\"let ' s take values of x , y , z which can satisfy given equations . let z = 200 , so y becomes 100 ( since y is 50 % less than z ) , x becomes 120 ( since 20 % more than y ) now req is ( x / z ) * 100 = ( 120 / 200 ) * 100 = 60 % answer : e\"" + }, + { + "Answer": 270, + "Options": "a ) 240 , b ) 270 , c ) 295 , d ) 360 , e ) none", + "Correct": "b", + "Explanation": "\"solution let the numbers be x and ( x + 1365 ) . then , x + 1365 = 6 x + 15 \u21d4 5 x = 1350 \u21d4 x = 270 . answer b\"" + }, + { + "Answer": 21, + "Options": "a ) 19 , b ) 20 , c ) 21 , d ) 22 , e ) 23", + "Correct": "c", + "Explanation": "\"10 + 11 = 21 the answer is c .\"" + }, + { + "Answer": 5, + "Options": "a ) 8 , b ) 7 , c ) 6 , d ) 5 , e ) 4", + "Correct": "d", + "Explanation": "\"let x be the number of canoes . then 3 x / 4 is the number of kayaks . 11 x + ( 3 x / 4 ) * 16 = 460 11 x + 12 x = 460 23 x = 460 x = 20 ( canoes ) 3 x / 4 = 15 ( kayaks ) there were 20 - 15 = 5 more canoes rented out . the answer is d .\"" + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) 13 , c ) 16.6 , d ) 17 , e ) 23", + "Correct": "a", + "Explanation": "answer of set w is 12 ." + }, + { + "Answer": 55, + "Options": "a ) 35 , b ) 45 , c ) 55 , d ) 65 , e ) 75", + "Correct": "c", + "Explanation": "11 c 2 = 55 the answer is c ." + }, + { + "Answer": 110, + "Options": "a ) $ 60 , b ) $ 64 , c ) $ 75 , d ) $ 110 , e ) can not be determined", + "Correct": "d", + "Explanation": "solution : 6 x + 4 y + 2 z = 80 4 x + 2 y + 2 z = 140 adding both the equations = 10 x + 6 y + 4 z = 220 5 x + 3 y + 2 z = 110 ans d" + }, + { + "Answer": 0.06, + "Options": "a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 10 , d ) 3 / 50 , e ) 1 / 20", + "Correct": "d", + "Explanation": "perhaps it is also easy to just translate the % into fractions : 6 % : 6 / 100 = 3 / 50 7 % : 7 / 100 8 % : 8 / 100 = 4 / 50 = 2 / 25 9 % : 9 / 100 only 3 / 50 exists in the answer choices , so ans d" + }, + { + "Answer": 19, + "Options": "a ) 19 , b ) 21 , c ) 23 , d ) 25 , e ) 27", + "Correct": "a", + "Explanation": "let the three numbers be x , x + 2 , and x + 4 . 3 x = 2 ( x + 4 ) + 7 x = 15 and then the third number is x + 4 = 19 . the answer is a ." + }, + { + "Answer": 160, + "Options": "a ) 150 % , b ) 170 % , c ) 175 % , d ) 160 % , e ) 180 %", + "Correct": "d", + "Explanation": "\"say vartan ' s wages last week were $ 100 , so he spent 0.20 * 100 = $ 20 on recreation ; this week ' s wages is 0.8 * 100 = $ 80 , so he spends 0.4 * 80 = $ 32 on recreation ; 32 / 20 = 1.6 , hence the amount he spends on recreation this week is 160 % of the amount he spent on recreation last week : 20 * 1.6 = 32 answer : d\"" + }, + { + "Answer": 3, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8", + "Correct": "a", + "Explanation": "2 x 3 x 8 x cube + 27 x cube = 945 35 x cube = 945 x cube = 27 = > x = 3 . answer : a" + }, + { + "Answer": 20, + "Options": "a ) 15 , b ) 18 , c ) 20 , d ) 25 , e ) 30", + "Correct": "c", + "Explanation": "1 ^ 2 + 2 ^ 2 + 3 ^ 2 + - - - - - + n ^ 2 = n ( n + 1 ) ( 2 n + 1 ) / 6 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + - - - - - + 7 ^ 2 = 7 * 8 * 156 = 140 required average is = 140 / 7 = 20 answer is c" + }, + { + "Answer": 820, + "Options": "a ) 872 , b ) 820 , c ) 837 , d ) 840 , e ) 83", + "Correct": "b", + "Explanation": "\"25 % of x = x / 4 ; 15 % of 1500 = 15 / 100 * 1500 = 225 given that , x / 4 = 225 - 20 = > x / 4 = 205 = > x = 820 . answer : b\"" + }, + { + "Answer": 0.25, + "Options": "a ) 1 / 5 , b ) 2 / 8 , c ) 1 / 3 , d ) 2 / 3 , e ) 7 / 9", + "Correct": "b", + "Explanation": "number x has to be chosen from numbers 1 - 9 ( 8 / x ) > x = > 8 > x ^ 2 = > x ^ 2 - 8 < 0 x can have 2 values only 1 , 2 therefore , probability = 2 / 8 answer b" + }, + { + "Answer": 2.25, + "Options": "a ) 3 , b ) 6 , c ) 1 / 9 , d ) 1 / 3 , e ) 9 / 4", + "Correct": "e", + "Explanation": "\"explanation : solution : given x = k / y ^ 2 , where k is constant . now , y = 3 and x = 1 gives k = 9 . . ' . x = 9 / y ^ 2 = > x = 9 / 2 ^ 2 = 9 / 4 answer : e\"" + }, + { + "Answer": 31, + "Options": "a ) 39 , b ) 40 , c ) 31 , d ) 42 , e ) 43", + "Correct": "c", + "Explanation": "\"solution start with 5 pens . mike gives you 20 pens : 5 + 20 = 25 pens . cindy doubles the number of pens you have : 25 \u00e3 \u2014 2 = 50 pens . sharon takes 19 pens from you : 50 - 19 = 31 pens . so you have 31 at the end . correct answer : c\"" + }, + { + "Answer": 150, + "Options": "a ) 150 , b ) 175 , c ) 200 , d ) 225 , e ) 300", + "Correct": "a", + "Explanation": "\"for an ap the mean or average of series is average of first and last term . so , average of numbers between 200 to 400 , inclusive = ( 200 + 400 ) / 2 = 300 average of numbers between 100 to 200 , inclusive = ( 100 + 200 ) / 2 = 150 difference = 300 - 150 = 150 answer is a\"" + }, + { + "Answer": 28500, + "Options": "a ) s . 28500 , b ) s . 50000 , c ) s . 57000 , d ) s . 60000 , e ) s . 62000", + "Correct": "a", + "Explanation": "\"length ( l ) = 20 m , breadth ( b ) = 15 m and height ( h ) = 5 m total area of the hall to be covered with mat = 2 ( lb + bh + hl ) = 2 ( 20 * 15 + 15 * 5 + 5 * 20 ) = 2 ( 300 + 75 + 100 ) = 2 * 475 = 950 sq . m total expenditure = 30 * 950 = rs . 28,500 a\"" + }, + { + "Answer": 16, + "Options": "a ) 24 , b ) 26 , c ) 30 , d ) 16 , e ) 40", + "Correct": "d", + "Explanation": "\"let the number of coins one son got be x and the number of coins another got be y . total = x + y . x ^ 2 - y ^ 2 = 16 ( x - y ) - - > x + y = 16 . answer : d .\"" + }, + { + "Answer": 60, + "Options": "a ) 48 , b ) 54 , c ) 72 , d ) 60 , e ) 27", + "Correct": "d", + "Explanation": "\"let the second number be x . then , first number = 2 x and third number = 2 x / 3 . 2 x + x + 2 x / 3 = 220 11 x / 3 = 220 x = 60 answer : d\"" + }, + { + "Answer": 0.4444444444444444, + "Options": "a ) 2 / 7 , b ) 4 / 9 , c ) 16 / 25 , d ) 7 / 1 , e ) 7 / 2", + "Correct": "b", + "Explanation": "\"for a 2 nd degree equation ax 2 + bx _ c = 0 has equal roots the condition is b 2 - 4 ac = 0 in the given equation ( 6 k ) ^ 2 - 4 * 2 k * 2 = 0 by solving this equation we get k = 0 , k = 4 / 9 answer : b\"" + }, + { + "Answer": 122, + "Options": "a ) $ 122 , b ) $ 150 , c ) $ 176 , d ) $ 200 , e ) $ 250", + "Correct": "a", + "Explanation": "\"a : ( b + c ) = 1 : 2 a ' s share = 366 * 1 / 3 = $ 122 answer is a\"" + }, + { + "Answer": 66, + "Options": "a ) 41 , b ) 42 , c ) 43 , d ) 66 , e ) 45", + "Correct": "d", + "Explanation": "\"n ( n - 1 ) / 2 = 12 * 11 / 2 = 66 answer : d\"" + }, + { + "Answer": 22.400000000000002, + "Options": "a ) 21.2 % , b ) 21.6 % , c ) 22.0 % , d ) 22.4 % , e ) 22.8 %", + "Correct": "d", + "Explanation": "the total amount of alcohol is 0.25 ( 8 ) + 0.12 ( 2 ) = 2.24 liters . the percentage is 2.24 / 10 = 22.4 / 100 which is 22.4 % the answer is d ." + }, + { + "Answer": 11, + "Options": "a ) 11 , b ) 14 , c ) 18 , d ) 20 , e ) 29", + "Correct": "a", + "Explanation": "when dividing 5264 by 17 , we get the remainder 11 , so 11 should be subtracted . the answer is a ." + }, + { + "Answer": 315, + "Options": "a ) $ 150 , b ) $ 245 , c ) $ 365 , d ) $ 315 , e ) $ 730", + "Correct": "d", + "Explanation": "\"total weekly income over 5 weeks = $ 406 + $ 413 + $ 420 + $ 436 + $ 395 = $ 2070 for avg weekly income to be $ 500 over 7 weeks , we need total weekly income over 7 weeks = $ 3500 now , $ 3500 - $ 2070 = $ 1430 from this , we subtract base salary for 2 weeks i . e $ 350 * 2 = $ 700 therefore , commission = $ 1430 - $ 800 = $ 630 for 2 weeks avg weekly commission = $ 315 answer d\"" + }, + { + "Answer": 9, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10", + "Correct": "d", + "Explanation": "\"the daily production was raised by 5 units for n days , which has a weighting of 5 n . 5 n = 100 - 55 = 45 n = 9 the answer is d .\"" + }, + { + "Answer": 140, + "Options": "a ) 39 , b ) 140 , c ) 42 , d ) 40.5 , e ) 41.5", + "Correct": "b", + "Explanation": "\"let the average after 16 th inning = x then total run after 16 th inning = 16 x then total run after 17 th inning = 16 x + 300 then average run after 17 th inning = ( 16 x + 300 ) / 17 ( 16 x + 300 ) / 17 = x + 10 = > 16 x + 300 = 17 x + 170 x = 130 average after 17 th inning = 130 + 10 = 140 answer : b\"" + }, + { + "Answer": 512, + "Options": "a ) 357 , b ) 834 , c ) 500 , d ) 512 , e ) 216", + "Correct": "d", + "Explanation": "d 512 the cube that remains will be 8 x 8 x 8 . this will make a total of 512 . this is because , when a layer is taken , it will be taken from all sides of the cube which will reduce the dimension be two and not one ." + }, + { + "Answer": 7, + "Options": "a ) a ) 7 , b ) b ) 12 , c ) c ) 15 , d ) d ) 18 , e ) e ) 20", + "Correct": "a", + "Explanation": "\"explanation : 2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 30 - 16 = 14 ab = 7 answer : a\"" + }, + { + "Answer": 70, + "Options": "a ) 42 , b ) 43 , c ) 70 , d ) 45 , e ) 46", + "Correct": "c", + "Explanation": "\"let \u2018 x \u2019 be the average score after 12 th innings \u21d2 12 x = 11 \u00d7 ( x \u2013 2 ) + 92 \u2234 x = 70 answer c\"" + }, + { + "Answer": 42, + "Options": "a ) 21 , b ) 42 , c ) 24 , d ) 40 , e ) 45", + "Correct": "b", + "Explanation": "16,800 / 42 = 400 400 = ( 20 ) ^ 2 ans - 42 answer : b" + }, + { + "Answer": 30, + "Options": "a ) 70 , b ) 45 , c ) 50 , d ) 46 , e ) 30", + "Correct": "e", + "Explanation": "\"% of boy attending the college = 100 - 30 = 70 % number of boys attending the college : 0.70 * 300 = 210 total people = 300 + 240 = 540 total number of students attending the college : 0.70 * 540 = 378 number of girls attending the college = 378 - 210 = 168 number of girls not attending the college = 240 - 168 = 72 % of girls not attending = 72 / 240 = 30 % . e is the correct answer\"" + }, + { + "Answer": 15, + "Options": "a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18", + "Correct": "b", + "Explanation": "\"d = ( d - r ) / q = ( 95 - 5 ) / 6 = 90 / 6 = 15 b\"" + }, + { + "Answer": 90, + "Options": "a ) 40 , b ) 60 , c ) 70 , d ) 80 , e ) 90", + "Correct": "e", + "Explanation": "e 90 1080 apples = 90 dozens the required number of boxes = 90 . answer : e" + }, + { + "Answer": 720, + "Options": "a ) s . 440 , b ) s . 500 , c ) s . 720 , d ) s . 740 , e ) s . 840", + "Correct": "c", + "Explanation": "s . i for 5 years = ( 1020 - 820 ) = rs . 200 . s . i . for 2 years = 200 / 4 * 2 = rs . 100 . principal = ( 820 - 100 ) = rs . 720 . answer : c" + }, + { + "Answer": 0.6363636363636364, + "Options": "a ) 10 / 16 , b ) 6 / 16 , c ) 7 / 11 , d ) 6 / 10 , e ) 4 / 10", + "Correct": "c", + "Explanation": "\"w = m + 4 w + m = 18 m + 4 + m = 18 2 m = 14 m = 7 w = 11 ratio : 7 : 11 ans : c\"" + }, + { + "Answer": 12, + "Options": "a ) 22 , b ) 77 , c ) 15 , d ) 12 , e ) 88", + "Correct": "d", + "Explanation": "( 80 / 100 ) * 40 \u2013 ( 4 / 5 ) * 25 32 - 20 = 12 answer : d" + }, + { + "Answer": 35, + "Options": "a ) 31 % . , b ) 71 % . , c ) 49 % . , d ) 29 % . , e ) 35 % .", + "Correct": "e", + "Explanation": "\"25 % of 2 litres = 0.5 litres 50 % of 6 litres = 3.0 litres therefore , total quantity of alcohol is 3.5 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 35 % answer : e\"" + }, + { + "Answer": 8, + "Options": "a ) 6 , b ) 7 , c ) 5 , d ) 8 , e ) 18", + "Correct": "d", + "Explanation": "so , the numbers should be from 10 , 000,000 to 100 , 000,000 the following two cases are possible for the sum of the digits to be 2 : 1 . two 1 ' s and the rest are 0 ' s : 10 , 000,001 10 , 000,010 10 , 000,100 10 , 001,000 10 , 010,000 10 , 100,000 11 , 000,000 7 numbers . 2 . one 2 and the rest are 0 ' s : 20 , 000,000 1 number . total = 8 numbers . answer : d" + }, + { + "Answer": 74, + "Options": "a ) 58 kg , b ) 60 kg , c ) 64 kg , d ) 70 kg , e ) 74", + "Correct": "e", + "Explanation": "\"sol . for 9 kg zinc , mixture melted = ( 9 + 11 ) kg . for 33.3 kg zinc , mixture , melted = [ 20 / 9 x 33.3 ] kg = 74 kg . answer e\"" + }, + { + "Answer": 0.8, + "Options": "a ) 3 / 4 , b ) 1 , c ) 4 / 5 , d ) 2 , e ) 7 / 2", + "Correct": "c", + "Explanation": "slope = ( y 2 - y 1 ) / ( x 2 - x 1 ) = > k = ( k + 4 ) / ( 5 + 1 ) = > 6 k = k + 4 = > k = 4 / 5 ans c it is !" + }, + { + "Answer": 30.33125, + "Options": "a ) $ 30.14 , b ) 45.14 , c ) 34.66 , d ) 32.29 , e ) 30.33", + "Correct": "e", + "Explanation": "\"211 * 15 = 3165 / 100 = 31.65 211 + 31.65 = 242.65 242.65 / 8 = 30.33 answer : e\"" + }, + { + "Answer": 4, + "Options": "a ) 4 , b ) 2 , c ) 0 , d ) \u2212 2 , e ) \u2212 4", + "Correct": "a", + "Explanation": "\"slope = rise / run = 11 / 22 = 1 / 2 the equation of the line is y = ( 1 / 2 ) x + b 3 = ( 1 / 2 ) ( 10 ) + b b = - 2 the equation of the line is y = ( 1 / 2 ) x - 2 to find the x - intercept , let y = 0 : 0 = ( 1 / 2 ) x - 2 x = 4 the answer is a .\"" + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 8 , c ) 10 , d ) 4 , e ) 12", + "Correct": "a", + "Explanation": "\"let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 12 = > 2 x = 12 = > x = 6 a\"" + }, + { + "Answer": 0.28, + "Options": "a ) 2 / 125 , b ) 3 / 125 , c ) c ) 2 / 25 , d ) 3 / 25 , e ) 7 / 25", + "Correct": "e", + "Explanation": "\"p ( playing 2 or more instruments ) = 96 / 800 = 3 / 25 . then , the probability of playing exactly one instrument is given by : p ( playing 1 or more instruments ) - p ( playing 2 or more instruments ) = 2 / 5 - 3 / 25 = 7 / 25 . answer e .\"" + }, + { + "Answer": 18, + "Options": "a ) $ 10 , b ) $ 12 , c ) $ 13.20 , d ) $ 15 , e ) $ 18", + "Correct": "e", + "Explanation": "\"3 j + 2 s = 69 2 j + 3 s = 76 - - - - - - - - - - - - - - - - 5 j + 5 s = 145 - - - - ( divide by 5 ) - - - > j + s = 29 3 j + 2 s = j + 2 ( j + s ) = j + 58 = 69 - - - > j = 11 3 * 11 + 2 s = 69 33 + 2 s = 69 2 s = 36 s = 18 answer : e\"" + }, + { + "Answer": 1080, + "Options": "a ) 8521 , b ) 1080 , c ) 368 , d ) 8979 , e ) 6584", + "Correct": "b", + "Explanation": "factors of 12 = 2 * 2 * 3 factors of 27 = 3 * 3 * 3 factors of 40 = 2 * 2 * 2 * 5 thus the l . c . m is 2 ^ 3 * 3 ^ 3 * 5 = 1080 the answer is b" + }, + { + "Answer": 135, + "Options": "a ) 75 , b ) 100 , c ) 125 , d ) 135 , e ) 225", + "Correct": "d", + "Explanation": "\"let m be the number of male participants and f be the number of female articipants in the meeting . thetotal number of participants is given as 810 . hence , we have m + f = 810 now , we have that half the female participants and one - quarter of the male participants are democrats . let d equal the number of the democrats . then we have the equation f / 2 + m / 4 = d now , we have that one - third of the total participants are democrats . hence , we have the equation d = 810 / 3 = 270 solving the three equations yields the solution f = 270 , m = 540 , and d = 270 . the number of female democratic participants equals half the female participants equals 270 / 2 = 135 . answer : d\"" + }, + { + "Answer": 12960, + "Options": "a ) a ) 13050 , b ) b ) 12960 , c ) c ) 10025 , d ) d ) 11080 , e ) e ) 12080", + "Correct": "b", + "Explanation": "the largest five digit numbers are 13050 , 12960,12080 13050 is not divisible by 12 12960 is divisible by 18 , 12 and 15 answer : b" + }, + { + "Answer": 20, + "Options": "a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 50 %", + "Correct": "b", + "Explanation": "\"pass percentage = 100 - ( 20 + 70 - 10 ) = 100 - 80 = 20 answer : b\"" + }, + { + "Answer": 11, + "Options": "a ) 5 , b ) 11 , c ) 13 , d ) 21 , e ) 23", + "Correct": "b", + "Explanation": "factor out 221 221 = 13 * 17 thus pq = 13 & pr = 17 or vice versa thus p = 1 , q = 3 & r = 7 sum = 1 + 3 + 7 = 11 answer : b" + }, + { + "Answer": 105, + "Options": "a ) 18 , b ) 36 , c ) 72 , d ) 90 , e ) 105", + "Correct": "e", + "Explanation": "\"let kate charge for x hours , then pat charged for 2 x and mat - for 6 x . so , 2 x + 6 x + x = 189 - total hours charged for , x = 21 . mat charged 6 x - x or 5 x for more hours than kate , or for 105 hours . e is correct\"" + }, + { + "Answer": 20, + "Options": "a ) 14 , b ) 15 , c ) 18 , d ) 20 , e ) 22", + "Correct": "d", + "Explanation": "\"the rate of 10 machines is rate = job / time = x / 4 units per day - - > the rate of 1 machine 1 / 10 * ( x / 4 ) = x / 40 units per day ; now , again as { time } * { combined rate } = { job done } then 6 * ( m * x / 40 ) = 3 x - - > m = 20 . answer : d .\"" + }, + { + "Answer": 7, + "Options": "a ) a ) 4 , b ) b ) 7 , c ) c ) 9 , d ) d ) 5 , e ) e ) 2", + "Correct": "b", + "Explanation": "9 - 2 = 7 . answer is b" + }, + { + "Answer": 0.11111111111111116, + "Options": "a ) 1 / 9 , b ) 1 / 6 , c ) 2 / 9 , d ) 1 / 4 , e ) 1 / 2", + "Correct": "a", + "Explanation": "age of boys q : 4 , 6 , 7 sum of ages taken 2 at a time : 10 , 13,11 ages of girls : 5 , 8 , 9 sum of ages taken 2 at a time : 13 , 17,14 9 combinations of sum between sets ( 10 , 12,11 ) ( 13 , 17,14 ) = 23 , 27,24 - 16 , 30,17 - 24 , 28,25 prob ( even ) = 5 / 9 prob ( odd ) = 4 / 9 answer = 5 / 9 - 4 / 9 = 1 / 9" + }, + { + "Answer": 20, + "Options": "a ) 22 , b ) 20 , c ) 24 , d ) 26 , e ) 28", + "Correct": "b", + "Explanation": "( 2 x + y ) * ( 2 z + w ) = 4 + 2 ( 8 ) = 20 answer : b" + }, + { + "Answer": 37, + "Options": "a ) 35 , b ) 37 , c ) 39 , d ) 41 , e ) 42", + "Correct": "b", + "Explanation": "explanation : let b ' s age = x years . then , as age = ( x + 7 ) years . ( x + 7 + 10 ) = 2 ( x \u2014 10 ) hence x = 37 . present age of b = 37 years answer : option b" + }, + { + "Answer": 4, + "Options": "a ) 5 , b ) 6 , c ) 4 , d ) 8 , e ) 9", + "Correct": "c", + "Explanation": "explanation : unit digit in 34 = 1 unit digit in ( 34 ) 16 = 1 unit digit in 365 = unit digit in [ ( 34 ) 16 x 3 ] = ( 1 x 3 ) = 3 unit digit in 659 = 6 unit digit in 74 unit digit in ( 74 ) 17 is 1 . unit digit in 771 = unit digit in [ ( 74 ) 17 x 73 ] = ( 1 x 3 ) = 3 required digit = unit digit in ( 3 x 6 x 3 ) = 4 . answer is c" + }, + { + "Answer": 90, + "Options": "a ) 76 kg , b ) 76.5 kg , c ) 90 kg , d ) data inadequate , e ) none of these", + "Correct": "c", + "Explanation": "\"explanation : total weight increased = ( 5 x 10.00 ) kg = 50 kg . weight of new person = ( 40 + 50 ) kg = 90 kg . answer : c\"" + }, + { + "Answer": 74.99999999999999, + "Options": "a ) 45 , b ) 27 , c ) 28 , d ) 26 , e ) 75", + "Correct": "e", + "Explanation": "\"sol : 45 if x persons were there in total , then x \u00d7 ( 1 \u2013 1 / 3 ) \u00d7 ( 1 \u2013 2 / 5 ) \u00d7 ( 1 \u2013 2 / 3 ) = 10 x \u00d7 2 / 3 \u00d7 3 / 5 \u00d7 1 / 3 = 10 x = 75 answer : e\"" + }, + { + "Answer": 27, + "Options": "a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29", + "Correct": "c", + "Explanation": "\"let x be the number of students in the largest class . then x + ( x - 2 ) + ( x - 4 ) + ( x - 6 ) + ( x - 8 ) = 115 5 x - 20 = 115 5 x = 135 x = 27 the answer is c .\"" + }, + { + "Answer": 80, + "Options": "a ) 80 m , b ) 180 m , c ) 100 m , d ) 60 m , e ) of these", + "Correct": "a", + "Explanation": "let the lengths of the three ropes be 4 k , 5 k and 6 k respectively . 4 k + 6 k = 5 k + 100 = > 5 k = 100 = > k = 20 therefore the weight of the lightest boy = 4 k = 4 ( 20 ) = 80 m answer : a" + }, + { + "Answer": 514.1899999999999, + "Options": "a ) $ 514.16 , b ) $ 514.17 , c ) $ 514.18 , d ) $ 514.19 , e ) $ 514.20", + "Correct": "b", + "Explanation": "\"this is equivalent to finding the first number that is divisible by 9 that occurs after 51416 . in order to divide the sum in 9 parts , the amount must be divisible by 9 divisibility rule of 9 : the sum of the digits must be divisible by 9 sum of digits of 51416 = 17 and 18 is divisible by 9 . hence , we need to add 1 to this number for it to be divisible by 9 correct option : b\"" + }, + { + "Answer": 80, + "Options": "a ) 76 , b ) 77 , c ) 78 , d ) 79 , e ) 80", + "Correct": "e", + "Explanation": "\"let x be the number of students in the class . let p be the average of the rest of the class . 84 x = ( 1 / 4 ) 96 x + ( 3 / 4 ) ( p ) x 336 = 96 + 3 p 3 p = 240 p = 80 . the answer is e .\"" + }, + { + "Answer": 2.7, + "Options": "a ) 2.215 . , b ) 2.5 . , c ) 2.6 , d ) 2.7 , e ) 3.5 .", + "Correct": "d", + "Explanation": "\"the ant walks an average of 600 meters in 10 minutes 600 meters in 5 / 30 hours the beetle walks 25 % less distance = 600 - 150 = 450 meters in 10 minutes 0.450 km in 5 / 30 = 5 / 30 hours speed = 0.450 * 30 / 5 = 2.7 km / h i guess option d should be 2.7\"" + }, + { + "Answer": 12, + "Options": "a ) 10 hours , b ) 12 hours , c ) 14 hours , d ) 16 hours , e ) none of these", + "Correct": "b", + "Explanation": "\"explanation : speed of the boat = 6 km / hr speed downstream = ( 6 + 2 ) = 8 km / hr speed upstream = ( 6 - 2 ) = 4 km / hr distance travelled downstream = distance travelled upstream = 32 km total time taken = time taken downstream + time taken upstream = ( 32 / 8 ) + ( 32 / 4 ) = ( 32 / 8 ) + ( 64 / 8 ) = ( 96 / 8 ) = 12 hr . answer : option b\"" + }, + { + "Answer": 35.999999999999986, + "Options": "a ) 16 , b ) 20 , c ) 36 , d ) 44 , e ) 48", + "Correct": "c", + "Explanation": "\"lets say x ounces of p is mixed with q . = > 66 - x ounces of q is present in the mixture ( as the total = 66 ounces ) given total almond weight = 15 ounces ( 20 x / 100 ) + ( 25 / 100 ) ( 66 - x ) = 15 = > x = 30 = > 66 - 30 = 36 ounces of q is present in the mixture . answer is c .\"" + }, + { + "Answer": 36.54, + "Options": "a ) 36.54 , b ) 36.58 , c ) 36.23 , d ) 36.14 , e ) 36.81", + "Correct": "a", + "Explanation": "\"explanation : correct sum = ( 36 * 50 + 48 - 21 ) = 1827 . correct mean = = 1827 / 50 = 36.54 answer : a ) 36.54\"" + }, + { + "Answer": 30.06993006993007, + "Options": "a ) 20 % , b ) 24 % , c ) 30 % , d ) 32 % , e ) 79 %", + "Correct": "c", + "Explanation": "\"the original output increases by 10 % and then 30 % . total % change = a + b + ab / 100 total % change = 10 + 30 + 10 * 30 / 100 = 43 % now , you want to change it to 0 , so , 0 = 43 + x + 43 x / 100 x = - 43 ( 100 ) / 143 = 30 % approximately answer is c\"" + }, + { + "Answer": 25, + "Options": "a ) 15 , b ) 45 , c ) 35 , d ) 25 , e ) 55", + "Correct": "d", + "Explanation": "let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 95 ( x - 5 ) 80 x - ( 5 * 20 ) = 95 ( x - 5 ) 375 = 15 x = > x = 25 answer : d" + }, + { + "Answer": 400, + "Options": "a ) 400 , b ) 300 , c ) 500 , d ) 610 , e ) 175", + "Correct": "a", + "Explanation": "\"let the maximum marks be x then , 33 % of x = 92 + 40 33 x / 100 = 132 x = 400 answer is a\"" + }, + { + "Answer": 0.3333333333333332, + "Options": "a ) 1 / 5 , b ) 1 / 4 , c ) 1 / 3 , d ) 2 / 5 , e ) 3 / 7", + "Correct": "c", + "Explanation": "\"x : 0.5 % is 0.1 % - points from 0.6 % . y : 0.8 % is 0.2 % - points from 0.6 % . therefore the ratio of products checked by y : x is 1 : 2 . thus , worker y checked 1 / 3 of the products . the answer is c .\"" + }, + { + "Answer": 3000.0000000000005, + "Options": "a ) $ 9000 , b ) $ 3000 , c ) $ 6000 , d ) $ 7000 , e ) $ 8000", + "Correct": "b", + "Explanation": "\"if linda spent 5 / 6 of her savings on furniture , the rest 6 / 6 - 5 / 6 = 1 / 6 on a tv but the tv cost her $ 500 . so 1 / 6 of her savings is $ 500 . so her original savings are 6 times $ 500 = $ 3000 correct answer b\"" + }, + { + "Answer": 0.45, + "Options": "a ) 0 , b ) 2 / 15 , c ) 2 / 5 , d ) 9 / 20 , e ) 5 / 6", + "Correct": "d", + "Explanation": "\"we need to determine the result of 1 / 3 + 1 / 2 - 5 / 6 + 1 / 5 + 1 / 4 - 9 / 20 let \u2019 s add the given fractions in two groups . in the group of the first three fractions , notice that 1 / 3 and 1 / 2 share a common denominator of 6 with 5 / 6 . 1 / 2 + 1 / 3 = 3 / 6 + 2 / 6 = 5 / 6 thus , 5 / 6 \u2013 5 / 6 = 0 looking at the 2 nd group of the fractions ( 1 / 5 , 1 / 4 , and 9 / 20 ) , notice that 1 / 5 and 1 / 4 share a common denominator of 20 with 9 / 20 . 1 / 5 + 1 / 4 = 4 / 20 + 5 / 20 = 9 / 20 thus , 9 / 20 \u2013 9 / 20 = 0 . thus , the result of 1 / 3 + 1 / 2 \u2013 5 / 6 + 1 / 5 + 1 / 4 \u2013 9 / 20 is 9 / 20 . answer : d\"" + }, + { + "Answer": 86, + "Options": "a ) 38 , b ) 27 , c ) 99 , d ) 17 , e ) 86", + "Correct": "e", + "Explanation": "\"explanation : number of subjects = 6 average of marks in 6 subjects = 76 therefore total marks in 6 subjects = 76 * 6 = 456 now , no . of subjects = 5 total marks in 5 subjects = 74 * 5 = 370 therefore marks in 6 th subject = 456 \u2013 370 = 86 answer : e\"" + }, + { + "Answer": 301, + "Options": "a ) 106 , b ) 301 , c ) 309 , d ) 400 , e ) 450", + "Correct": "b", + "Explanation": "explanation : clearly , the required number would be such that it leaves a remainder of 1 when divided by 3 , 4 , 5 , or 6 and no remainder when divided by 7 . thus , the number must be of the form ( l . c . m of 3 , 4 , 5 , 6 ) x + 1 i . e . , ( 60 x + 1 ) and a multiple of 7 . clearly , for x = 5 , the number is a multiple of 7 . so the number is 301 . answer : b ) 301" + }, + { + "Answer": 0.8, + "Options": "a ) 3 / 2 , b ) 3 / 4 , c ) 4 / 5 , d ) 1 / 2 , e ) 1 / 5", + "Correct": "c", + "Explanation": "let team b has 8 agents , so team a has 5 agents let each agent of team b picked up 5 calls , so total calls by team b = 40 so , each agent in team a picked up 2 calls , so total calls for team a = 10 fraction for team b = 40 / ( 40 + 10 ) = 4 / 5 = answer = c" + }, + { + "Answer": 120, + "Options": "a ) 6 , b ) 24 , c ) 72 , d ) 96 , e ) 120", + "Correct": "e", + "Explanation": "\"use the slot method for all the possible arrangements : we have 5 options for the 1 st slot , 4 for the 2 nd , 3 for 3 rd , 2 for 4 th and 1 for the 5 th , giving the total number of arrangements = 5 * 4 * 3 * 2 * 1 = 120 , e is the correct answer .\"" + }, + { + "Answer": 5500, + "Options": "a ) 5500 , b ) 2999 , c ) 2878 , d ) 2990 , e ) 2771", + "Correct": "a", + "Explanation": "\"income = rs . 100 expenditure = rs . 80 savings = rs . 20 present expenditure 80 * ( 20 / 100 ) = rs . 96 present savings = 100 \u00e2 \u20ac \u201c 96 = rs . 4 100 - - - - - - 4 ? - - - - - - - - - 220 = > 5500 answer : a\"" + }, + { + "Answer": 4, + "Options": "a ) $ 2.50 , b ) $ 3.00 , c ) $ 3.50 , d ) $ 4.00 , e ) $ 5.00", + "Correct": "d", + "Explanation": "\"number of wheels in truck = 18 number of wheels on its front axle = 2 number of wheels remaining = 16 number of axles remaining axles = 16 / 4 = 4 total number of axles = 5 t = 2.50 + 0.50 ( x \u2212 2 ) = 2.50 + . 5 * 3 = 2.5 + 1.5 = 4 $ answer d\"" + }, + { + "Answer": 2.855999999999767, + "Options": "a ) s . 2.04 , b ) s . 2.08 , c ) s . 2.02 , d ) s . 2.86 , e ) s . 2.42", + "Correct": "d", + "Explanation": "\"c . i . when interest is compounded yearly = [ 7000 * ( 1 + 4 / 100 ) * ( 1 + ( 1 / 2 * 4 ) / 100 ] = 7000 * 26 / 25 * 51 / 50 = rs . 7425.6 c . i . when interest is compounded half - yearly = [ 7000 * ( 1 + 2 / 100 ) 2 ] = ( 7000 * 51 / 50 * 51 / 50 * 51 / 50 ) = rs . 7428.46 difference = ( 7428.46 - 7425.6 ) = rs . 2.86 . answer : d\"" + }, + { + "Answer": 102, + "Options": "a ) 124 % , b ) 102 % , c ) 96 % , d ) 80 % , e ) 64 %", + "Correct": "b", + "Explanation": "juan ' s income = 100 ( assume ) ; tim ' s income = 60 ( 40 percent less than juan ' s income ) ; mary ' s income = 102 ( 70 percent more than tim ' s income ) . thus , mary ' s income ( 102 ) is 102 % of juan ' s income ( 100 ) . answer : b ." + }, + { + "Answer": 400, + "Options": "a ) $ 360 , b ) $ 380 , c ) $ 400 , d ) $ 420 , e ) $ 440", + "Correct": "c", + "Explanation": "\"s . i for 5 years = $ 680 - $ 480 = $ 200 the s . i . is $ 40 / year s . i . for 2 years = $ 80 principal = $ 480 - $ 80 = $ 400 the answer is c .\"" + }, + { + "Answer": 22, + "Options": "a ) 11 , b ) 25 , c ) 27 , d ) 22 , e ) 91", + "Correct": "d", + "Explanation": "\"let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . ( x + 24 ) + 2 = 2 ( x + 2 ) x + 26 = 2 x + 4 = > x = 22 . answer : d\"" + }, + { + "Answer": 9, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10", + "Correct": "d", + "Explanation": "\"we want to minimize z \u2212 xz \u2212 x , so we need to maximize xx . say z = 11 = oddz = 11 = odd , then max value of yy will be 9 ( as yy is also odd ) . now , since y \u2212 5 > xy \u2212 5 > x - - > 9 \u2212 5 > x 9 \u2212 5 > x - - > 4 > x 4 > x , then max value of xx is 2 ( as xx is even ) . hence , the least possible value of z \u2212 xz \u2212 x is 11 - 2 = 9 . answer : d .\"" + }, + { + "Answer": 75, + "Options": "a ) 70 , b ) 75 , c ) 80 , d ) 85 , e ) 60", + "Correct": "b", + "Explanation": "\"explanation : ( 65 + 67 + 76 + 82 + 855 ) = 75 answer : option b\"" + }, + { + "Answer": 24, + "Options": "a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 26", + "Correct": "d", + "Explanation": "\"312 = 24 * 13 = 26 * 12 there are 24 people in the group today . the answer is d .\"" + }, + { + "Answer": 210, + "Options": "a ) $ 110 , b ) $ 120 , c ) $ 180 , d ) $ 220 , e ) $ 210", + "Correct": "e", + "Explanation": "\"lets assume al have amount a in his bank account and eliot ' s bank account got e amount . we can form an equation from the first condition . a - e = 1 / 12 * ( a + e ) = = > 11 a = 13 e - - - - - - - - - - - - ( 1 ) second condition gives two different amounts , al ' s amount = 1.1 a and eliot ' s amount = 1.2 e 1.1 a = 21 + 1.2 e = = > 11 a = 210 + 12 e - - - - - - - ( 2 ) substituting ( 1 ) in ( 2 ) : 13 e = 210 + 12 e = = > e = 210 e\"" + }, + { + "Answer": 23.076923076923073, + "Options": "a ) 16 % , b ) 23.07 % , c ) 25 % , d ) 30 % , e ) 35 %", + "Correct": "b", + "Explanation": "\"x * y = constt . let x = y = 100 in beginning i . e . x * y = 100 * 100 = 10000 x ( 100 ) - - - becomes - - - > 1.3 x ( 130 ) i . e . 130 * new ' y ' = 10000 i . e . new ' y ' = 10000 / 130 = 76.92 i . e . y decreases from 100 to 76.92 i . e . decrease of 23.07 % b\"" + }, + { + "Answer": 249.99999999999997, + "Options": "a ) rs . 150 , b ) rs . 190 , c ) rs . 200 , d ) rs . 250 , e ) rs . 300", + "Correct": "d", + "Explanation": "\"let the amount paid to a per week = x and the amount paid to b per week = y then x + y = 550 but x = 120 % of y = 120 y / 100 = 12 y / 10 \u2234 12 y / 10 + y = 550 \u21d2 y [ 12 / 10 + 1 ] = 550 \u21d2 22 y / 10 = 550 \u21d2 22 y = 5500 \u21d2 y = 5500 / 22 = 500 / 2 = rs . 250 d )\"" + }, + { + "Answer": 3159, + "Options": "a ) 1888 , b ) 2999 , c ) 3159 , d ) 2777 , e ) 2991", + "Correct": "c", + "Explanation": "\"let the total number of votes polled in the election be 100 k . number of valid votes = 100 k - 20 % ( 100 k ) = 80 k let the number of votes polled in favour of a and b be a and b respectively . a - b = 15 % ( 100 k ) = > a = b + 15 k = > a + b = b + 15 k + b now , 2 b + 15 k = 80 k and hence b = 32.5 k it is given that 100 k = 9720 32.5 k = 32.5 k / 100 k * 9720 = 3159 the number of valid votes polled in favour of b is 3159 . answer : c\"" + }, + { + "Answer": 25, + "Options": "a ) 25 , b ) 46 , c ) 88 , d ) 13 , e ) 12", + "Correct": "a", + "Explanation": "\"total score of the batsman in 20 matches = 600 . total score of the batsman in the next 10 matches = 150 . total score of the batsman in the 30 matches = 750 . average score of the batsman = 750 / 30 = 25 . answer : a\"" + }, + { + "Answer": 7, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9", + "Correct": "c", + "Explanation": "\"sa ' s + co + ca + cats = 14 . sa ' s + 1 + 1 + cats = 14 or sa ' s + cats = 12 . sa ' s ( 2 ) + 2 + 1 + cats * 4 = 41 sa ' s * 2 + cats * 4 = 38 or sa ' s + cats * 2 = 19 or 12 - cats + cat * 2 = 19 then cats = 7 c\"" + }, + { + "Answer": 23, + "Options": "a ) t = 21 , b ) t = 22 , c ) t = 23 , d ) 24 , e ) 27", + "Correct": "c", + "Explanation": "\"squaring on both sides , x ^ 2 + ( 1 / x ) ^ 2 + 2 ( x ) ( 1 / x ) = 5 ^ 2 x ^ 2 + ( 1 / x ) ^ 2 = 23 answer : c\"" + }, + { + "Answer": 20, + "Options": "a ) a ) 12 , b ) b ) 15 , c ) c ) 16 , d ) d ) 17 , e ) e ) 20", + "Correct": "e", + "Explanation": "\"d = ( d - r ) / q = ( 181 - 1 ) / 9 = 180 / 9 = 20 e )\"" + }, + { + "Answer": 450, + "Options": "a ) 450 km , b ) 500 km , c ) 360 km , d ) 550 km , e ) 600 km", + "Correct": "a", + "Explanation": "\"sol . average speed of a tractor = 25 km / h the speed of a bike in an hour = 25 \u00d7 2 = 50 km the speed of a car in an hour = 9 / 5 * 50 = 90 km so , the distance covered by car in 5 h is 90 \u00d7 5 = 450 km ans . ( a )\"" + }, + { + "Answer": 360, + "Options": "a ) 360 , b ) 350 , c ) 340 , d ) 370 , e ) 380", + "Correct": "a", + "Explanation": "let x be the number of parts the woodworker normally makes daily . in 24 days he makes 24 \u22c5 x pieces . his new daily production rate is x + 5 pieces and in 22 days he made 22 \u22c5 ( x + 5 ) parts . this is 80 more than 24 \u22c5 x . therefore the equation is : 24 \u22c5 x + 80 = 22 ( x + 5 ) 30 = 2 x x = 15 normally he makes 15 parts a day and in 24 days he makes 15 \u22c5 24 = 360 parts . so answer is a ." + }, + { + "Answer": 28, + "Options": "a ) 28 , b ) 12 , c ) - 28 , d ) 12 , e ) 0", + "Correct": "c", + "Explanation": "add how he has already borrowed and how much he is going to borrow - 20 + - 8 correct answer c ) - 28" + }, + { + "Answer": 2, + "Options": "a ) 2 , b ) 9 , c ) 6 , d ) 4 , e ) 0", + "Correct": "a", + "Explanation": "\"let the ages of children be x , ( x + 8 ) , ( x + 16 ) , ( x + 24 ) and ( x + 32 ) years . then , x + ( x + 8 ) + ( x + 16 ) + ( x + 24 ) + ( x + 32 ) = 90 5 x = 10 x = 2 . age of the youngest child = x = 2 years . answer : a\"" + }, + { + "Answer": 469, + "Options": "a ) 240 , b ) 369 , c ) 469 , d ) 520 , e ) 599", + "Correct": "c", + "Explanation": "case 1 : numbers starting with 8 followed by even number the hundreds digit can take 4 numbers ( 0,2 , 4,6 ) so 4 ways the unit digit can take remaining 3 even numbers left after using 2 , to be even so 3 ways . the tens digit can take remaining 7 numbers left after using 3 numbers so 7 ways total = 4 * 3 * 7 = 84 case 2 : numbers starting with 8 followed by odd number the hundreds digit can take 5 numbers ( 1 , 3,5 , 7,9 ) so 5 ways the unit digit can take remaining 4 even numbers ( 0,2 , 4,6 ) to be even so 4 ways . the tens digit can take remaining 7 numbers left after using 3 numbers so 7 ways total = 5 * 4 * 7 = 140 case 3 : numbers starting with 9 followed by even number the hundreds digit can take 5 numbers ( 0 , 2,4 , 6,8 ) so 5 ways the unit digit can take remaining 4 even numbers left after using 1 , to be even so 3 ways . the tens digit can take remaining 7 numbers left after using 3 numbers so 7 ways total = 5 * 3 * 7 = 105 case 4 : numbers starting with 9 followed by odd number the hundreds digit can take 4 numbers ( 1,3 , 5,7 ) so 4 ways the unit digit can take 5 numbers ( 0 , 2,4 , 6,8 ) to be even so 5 ways . the tens digit can take remaining 7 numbers left after using 3 numbers so 7 ways total = 4 * 5 * 7 = 140 hence 84 + 140 + 105 + 140 = 469 , correct answer is c" + }, + { + "Answer": 50, + "Options": "a ) 25 , b ) 50 , c ) 75 , d ) 100 , e ) 4", + "Correct": "b", + "Explanation": "\"substitute y by 25 in x + 2 y = 100 x + 2 ( 25 ) = 100 x + 50 = 100 if we substitute x by 50 in x + 50 = 100 , we have 50 + 50 = 100 . hence x = 50 correct answer b\"" + }, + { + "Answer": 0.15384615384615385, + "Options": "a ) 1 / 4 , b ) 4 / 15 , c ) 2 / 13 , d ) 4 / 11 , e ) 4 / 5", + "Correct": "c", + "Explanation": "\"let avg for 11 mos . = 10 therefore , dec = 20 year total = 11 * 10 + 20 = 130 answer = 20 / 130 = 2 / 13 = c\"" + }, + { + "Answer": 2.333333333333333, + "Options": "a ) 1 / 3 , b ) 2 / 3 , c ) 4 / 3 , d ) 5 / 3 , e ) 7 / 3", + "Correct": "e", + "Explanation": "( 2 / 3 ) g = ( 1 / 5 ) ( b + g ) 10 g = 3 b + 3 g 7 g = 3 b b / g = 7 / 3 . the answer is e ." + }, + { + "Answer": 7, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10", + "Correct": "b", + "Explanation": "min no could be = 7 ( 1024 ) let jaya has two digits number = 10 and amitabh has two digits number = 24 after appending = 1024 which is perfect square of 32 and sum of four digits number 1024 = 7 answer : b" + }, + { + "Answer": 5, + "Options": "a ) 2 litres , b ) 5 litres , c ) 7 litres , d ) 11 litres , e ) none of these", + "Correct": "b", + "Explanation": "in mixture , quantity of pure milk / quantity of water = 3 \u2212 0 / 3.6 \u2212 3 = 3 / 0.6 = 5 / 1 since in every 5 litres of milk , he adds 1 litre of water . \u2234 in every 25 litres of milk , he adds 5 litres of water . answer b" + }, + { + "Answer": 78, + "Options": "a ) 45 , b ) 65 , c ) 75 , d ) 78 , e ) 90", + "Correct": "d", + "Explanation": "\"a + b + c = 3 * 84 = 252 a + b + c + d = 4 * 80 = 320 - - - - ( i ) so , d = 68 & e = 68 + 6 = 74 b + c + d + e = 79 * 4 = 316 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 320 \u2013 316 = 4 a = e + 4 = 74 + 4 = 78 d\"" + }, + { + "Answer": 180, + "Options": "a ) $ 60 , b ) $ 90 , c ) $ 120 , d ) $ 150 , e ) $ 180", + "Correct": "e", + "Explanation": "5 : 4 = 15 : 12 and 3 : 2 = 18 : 12 . an increase in $ 45 increases the ratio by 3 : 12 . therefore an increase in $ 15 increases the ratio by 1 : 12 . therefore , january ' s bill was 12 ( $ 15 ) = $ 180 . the answer is e ." + }, + { + "Answer": 8, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 8", + "Correct": "e", + "Explanation": "\"( 1056 / 28 ) gives remainder 20 20 + 8 = 28 , so we need to add 8 e\"" + }, + { + "Answer": 18, + "Options": "a ) \u2013 108 , b ) \u2013 44 , c ) 10 , d ) - 18 , e ) 18", + "Correct": "d", + "Explanation": "# p = 2 p + 20 - - - > # ( # p ) = 2 ( 2 p + 20 ) + 20 = 4 p + 60 and thus # ( 4 p + 60 ) = 2 ( 4 p + 60 ) + 20 = 8 p + 140 = - 4 - - - > 8 p = - 144 - - - > p = - 18 , d is the correct answer ." + }, + { + "Answer": 41, + "Options": "a ) 32 , b ) 41 , c ) 45 , d ) 48 , e ) 50", + "Correct": "b", + "Explanation": "\"sum of ages of class before replacement = 30 x 10 = 300 sum of ages of class without teacher = 300 - 11 = 289 sum of ages of class after replacement = 30 x 11 = 330 age of teacher = 330 - 289 = 41 answer : b\"" + }, + { + "Answer": 30, + "Options": "a ) 1 , b ) 10 , c ) 30 , d ) 20 , e ) 21", + "Correct": "c", + "Explanation": "\"this is a solution from beatthegmat : even numbers : ( 60 - 2 ) / 2 + 1 = 30 even integers . ( 60 + 2 ) / 2 = 31 is the average of the even set . sum = avg * ( # of elements ) = 31 * 30 = 930 = a odd numbers : ( 59 - 1 ) / 2 + 1 = 30 odd integers . ( 59 + 1 ) / 2 = 30 is the average of the odd set . sum = avg * ( # of elements ) = 30 * 30 = 900 = b a - b = 930 - 900 = 30 . answer : c\"" + }, + { + "Answer": 10, + "Options": "a ) 50 , b ) 78 , c ) 267 , d ) 29 , e ) 10", + "Correct": "e", + "Explanation": "\"a + b + c = 500 a + c = 200 b + c = 310 - - - - - - - - - - - - - - a + b + 2 c = 510 a + b + c = 500 - - - - - - - - - - - - - - - - c = 10 answer : e\"" + }, + { + "Answer": 4.4, + "Options": "a ) 2.8 % , b ) 3.6 % , c ) 4.4 % , d ) 5.2 % , e ) 6.0 %", + "Correct": "c", + "Explanation": "\"let amount spent by jill = 100 clothing = 50 , food = 20 , others = 30 tax on clothing = 2 tax on others = 2.4 percentage = 4.4 / 100 4.4 % answer : c\"" + }, + { + "Answer": 80.00000000000001, + "Options": "a ) 25 minutes , b ) 10 minutes , c ) 20 minutes , d ) 80 minutes , e ) 60 minutes", + "Correct": "d", + "Explanation": "\"lets take number of minutesx . given that , 8 + 0.25 x = 12 + 0.2 x - > 0.05 x = 2 - > x = 80 minutes ans d\"" + }, + { + "Answer": 16, + "Options": "a ) 18 % , b ) 72 % , c ) 32 % , d ) 16 % , e ) 52 %", + "Correct": "d", + "Explanation": "100 * 100 = 10000 70 * 120 = 8400 10000 - - - - - - - 1600 100 - - - - - - - ? = 16 % answer : d" + }, + { + "Answer": 0.16666666666666666, + "Options": "a ) 1 / 9 , b ) 1 / 6 , c ) 1 / 2 , d ) 1 / 3 , e ) 32 / 36", + "Correct": "b", + "Explanation": "a dice is composed of 6 numbers - 12 , 34 , 56 . when trowing 2 dices - there are 36 options ( 6 x 6 = 36 ) . if we want the sum of two dices to be < 5 there are those options : ( 11 ) , ( 12 ) , ( 21 ) , ( 13 ) , ( 31 ) , ( 22 ) - total of 6 options . therefore - the probability to have a sum which is smaller than 5 is 6 / 36 = 1 / 6 . answer : b" + }, + { + "Answer": 22, + "Options": "a ) 22 , b ) 28 , c ) 32 , d ) 48 , e ) 92", + "Correct": "a", + "Explanation": "\"let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . ( x + 24 ) + 2 = 2 ( x + 2 ) x + 26 = 2 x + 4 = > x = 22 . answer is a .\"" + }, + { + "Answer": 120, + "Options": "a ) a ) 40 , b ) b ) 60 , c ) c ) 80 , d ) d ) 120 , e ) e ) 140", + "Correct": "d", + "Explanation": "total number of students : 160 total girls : 160 * 1 / 4 = 40 total boys : 160 - 40 = 120 answer is d" + }, + { + "Answer": 0.2, + "Options": "a ) 1 / 17 , b ) 3 / 17 , c ) 1 / 10 , d ) 4 / 20 , e ) 3 / 10", + "Correct": "d", + "Explanation": "\"we have the ratio of a \u2019 s speed and b \u2019 s speed . this means , we know how much distance a covers compared with b in the same time . this is what the beginning of the race will look like : ( start ) a _________ b ______________________________ if a covers 20 meters , b covers 16 meters in that time . so if the race is 20 meters long , when a reaches the finish line , b would be 4 meters behind him . if we want the race to end in a dead heat , we want b to be at the finish line too at the same time . this means b should get a head start of 4 meters so that he doesn \u2019 t need to cover that . in that case , the time required by a ( to cover 20 meters ) would be the same as the time required by b ( to cover 16 meters ) to reach the finish line . so b should get a head start of 4 / 20 th of the race . answer ( d )\"" + }, + { + "Answer": 16, + "Options": "a ) 16 , b ) 14 , c ) 18 , d ) 10 , e ) 20", + "Correct": "a", + "Explanation": "\"we know that : x > 1 , y > 1 , and x + 3 y < 980 , and it is given that length means no of factors . for any value of x and y , the max no of factors can be obtained only if factor is smallest no all factors are equal . hence , lets start with smallest no 2 . 2 ^ 1 = 2 2 ^ 2 = 4 2 ^ 3 = 8 2 ^ 4 = 16 2 ^ 5 = 32 2 ^ 6 = 64 2 ^ 7 = 128 2 ^ 8 = 256 2 ^ 9 = 512 2 ^ 10 = 1024 ( it exceeds 1000 , so , x ca n ' t be 2 ^ 10 ) so , max value that x can take is 2 ^ 9 , for which has length of integer is 9 . now , since x = 512 , x + 3 y < 980 so , 3 y < 468 = = > y < 156 so , y can take any value which is less than 162 . and to get the maximum no of factors of smallest integer , we can say y = 2 ^ 7 for 2 ^ 7 has length of integer is 7 . so , combined together : 9 + 7 = 16 . a\"" + }, + { + "Answer": 60.00000011175871, + "Options": "a ) 65 , b ) 60.003662 , c ) 80.2 , d ) 85 , e ) 90", + "Correct": "b", + "Explanation": "\"first , we have to find a . we know that after t = 2 minutes the temperature f = 120 degrees . hence : 120 = 120 * ( 2 ^ - 2 a ) + 60 60 = 120 * ( 2 ^ - 2 a ) 60 / 120 = 2 ^ - 2 a 1 / 2 = 2 ^ - 2 a 2 ^ - 1 = 2 ^ - 2 a - 1 = - 2 a 1 / 2 = a now we need to find f after t = 30 minutes : f = 120 * ( 2 ^ - 1 / 2 * 30 ) + 60 f = 120 * ( 2 ^ - 15 ) + 60 f = 120 * ( 1 / 2 ^ 15 ) + 60 f = 120 * 1 / 32768 + 60 f = 0.003662 + 60 = 60.003662 answer b !\"" + }, + { + "Answer": 2, + "Options": "a ) 6 , b ) 1 , c ) 0 , d ) 2 , e ) 7", + "Correct": "d", + "Explanation": "\"every prime number greater than 3 can be written 6 n + 1 or 6 n - 1 . if p = 6 n + 1 , then p ^ 2 + 13 = 36 n ^ 2 + 12 n + 1 + 13 = 36 n ^ 2 + 12 n + 12 + 2 if p = 6 n - 1 , then p ^ 2 + 13 = 36 n ^ 2 - 12 n + 1 + 13 = 36 n ^ 2 - 12 n + 12 + 2 when divided by 12 , it must leave a remainder of 2 . the answer is d .\"" + }, + { + "Answer": 25, + "Options": "a ) 25 , b ) 30 , c ) 35 , d ) 40 , e ) 45", + "Correct": "a", + "Explanation": "\"d = ( d - r ) / q = ( 127 - 2 ) / 5 = 125 / 5 = 25 a\"" + }, + { + "Answer": 80, + "Options": "a ) 77 % , b ) 78 % , c ) 79 % , d ) 80 % , e ) 81 %", + "Correct": "d", + "Explanation": "\"( 15 * 70 + 10 * 95 ) / 25 = 80 % the answer is d .\"" + }, + { + "Answer": 26048, + "Options": "a ) 720 , b ) 864 , c ) 900 , d ) 936 , e ) 26048", + "Correct": "e", + "Explanation": "total number of four letter passwords = 8 * 8 * 8 * 8 * 8 = 32768 - - - - - - ( 1 ) total number of passwords in which no letter repeats = 8 c 5 * 5 ! = 56 * 120 = 6720 - - - - - - ( 2 ) therefore required value = ( 1 ) - ( 2 ) = 32768 - 6720 = 26048 e" + }, + { + "Answer": 101, + "Options": "a ) 125 , b ) 111 , c ) 129 , d ) 101 , e ) 141", + "Correct": "d", + "Explanation": "\"explanation : in this type of question , its obvious we need to calculate the hcf , trick is hcf of ( 4351 - 8 ) and ( 5161 - 10 ) = hcf ( 4343 , 5151 ) = 101 option d\"" + }, + { + "Answer": 20, + "Options": "a ) 20 inches , b ) 77 inches , c ) 66 inches , d ) 97 inches , e ) 66 inches", + "Correct": "a", + "Explanation": "\"explanation : total length of scale in inches = ( 6 * 12 ) + 8 = 80 inches length of each of the 4 parts = 80 / 4 = 20 inches answer : a\"" + }, + { + "Answer": 8, + "Options": "a ) 3 , b ) 2 , c ) 4 , d ) 8 , e ) 6", + "Correct": "d", + "Explanation": "\"explanation : on dividing 50248 by 20 we get the remainder 8 , so 8 should be subtracted option d\"" + }, + { + "Answer": 24, + "Options": "a ) 22 , b ) 23 , c ) 24 , d ) 26 , e ) 28", + "Correct": "c", + "Explanation": "\"let hens be x and cows be y now , feet : x * 2 + y * 4 = 144 heads : x * 1 + y * 1 = 48 implies , 2 x + 4 y = 144 and x + y = 48 solving these two equations , we get x = 24 and y = 24 therefore , hens are 26 . answer : c\"" + }, + { + "Answer": 33, + "Options": "a ) 47 , b ) 37 , c ) 39 , d ) 43 , e ) 33", + "Correct": "e", + "Explanation": "\"average score before 10 th innings = 60 - 3 \u00d7 10 = 30 average score after 10 th innings = > 30 + 3 = 33 answer : e\"" + }, + { + "Answer": 200.89999999999998, + "Options": "a ) 200.9 , b ) 2.06 , c ) 20.06 , d ) 100.9 , e ) 200.6", + "Correct": "a", + "Explanation": "\"= 8.036 / 0.04 = 803.6 / 4 = 200.9 answer is a .\"" + }, + { + "Answer": 1.84, + "Options": "a ) $ 1 , b ) $ 1.84 , c ) $ 1.98 , d ) $ 2.34 , e ) $ 2.56", + "Correct": "b", + "Explanation": "ordering the data from least to greatest , we get : $ 1.61 , $ 1.75 , $ 1.79 , $ 1.84 , $ 1.96 , $ 2.09 , $ 2.11 the median gasoline price is $ 1.84 . ( there were 3 states with higher gasoline prices and 3 with lower prices . ) b" + }, + { + "Answer": 8, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", + "Correct": "b", + "Explanation": "\"102 * n ^ 2 < = 8100 n ^ 2 < = 8100 / 102 which will be less than 81 since 8100 / 100 = 81 which is the square of 9 next closest value of n where n ^ 2 < = 81 is 8 ans b\"" + }, + { + "Answer": 80, + "Options": "a ) 12 , b ) 18 , c ) 24 , d ) 28 , e ) 80", + "Correct": "e", + "Explanation": "slope = change in vertical direction / change in horizontal direction = 4 / 3 change in vertical direction = 4 x = ab change in horizontal direction = 3 x = bc ab ^ 2 + bc ^ 2 = 100 ^ 2 16 x ^ 2 + 9 x ^ 2 = 10000 25 x ^ 2 = 400 x ^ 2 = 400 x = 20 therefore ab = 20 * 4 = 80 answer : e" + }, + { + "Answer": 10000, + "Options": "a ) 100 , b ) 1000 , c ) 10000 , d ) 100000 , e ) none", + "Correct": "c", + "Explanation": "let c be the cost of producing and selling x books let r be the revenue made for selling x books r = selling price of 1 book \u00d7 number of books sold r = 9 x c = fixed cost + variable cost variable cost = fee charged for 1 book \u00d7 number of books sold variable cost = 4 x c = 50000 + 4 x r = c 9 x = 50000 + 4 x 9 x - 4 x = 50000 + 4 x - 4 x 5 x = 50000 x = 10000 since 5 \u00d7 10000 = 50000 the break even point is to sell 10000 books . answer c" + }, + { + "Answer": 84, + "Options": "a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %", + "Correct": "d", + "Explanation": "\"16 % ________________________________________________ m + s 34 % ________________________________________________ m 34 % ________________________________________________ m - s 16 % since 68 % lies one standard deviation from mean m , = > 50 % of 68 % lies on either side as it is symmetric about m . thus 16 % lie below m - s and 16 % lie above m + s now below m + s = 16 + 34 + 34 = 84 % hence d\"" + }, + { + "Answer": 1, + "Options": "a ) - 2 , b ) 0 , c ) 1 , d ) 2 , e ) 3", + "Correct": "c", + "Explanation": "( x ) = x ( 2 \u2212 x ) ( p + 1 ) = ( p + 1 ) ( 2 - p - 1 ) = ( 1 - p ) ( p + 1 ) we are given that p + 1 = ( p + 1 ) therefore ( 1 - p ) ( p + 1 ) = ( p + 1 ) or ( p + 1 ) + ( p - 1 ) ( p + 1 ) = 0 ( p + 1 ) ( p - 1 ) = 0 p = - 1 , p = 1 option c" + }, + { + "Answer": 150, + "Options": "a ) 25 % , b ) 50 % , c ) 75 % , d ) 100 % , e ) 150 %", + "Correct": "e", + "Explanation": "dolphin once in 3 min ; beluga once in 6 min ; so , dolphin comes up 2 times frequently than beluga , which is 150 % ( 6 - 3 ) / 2 * 100 . answer : e ." + }, + { + "Answer": 878, + "Options": "a ) 741 , b ) 752 , c ) 878 , d ) 785 , e ) 458", + "Correct": "c", + "Explanation": "\"solution : sum of 1 st 12 results = 12 * 14 sum of last 12 results = 12 * 17 13 th result = x ( let ) now , 12 * 14 + 12 * 17 + x = 25 * 50 or , x = 878 . answer : option c\"" + }, + { + "Answer": 4400, + "Options": "a ) s . 9800 , b ) s . 3800 , c ) s . 9800 , d ) s . 4400 , e ) s . 6880", + "Correct": "d", + "Explanation": "\"cost of the camel = p 10 camels = 24 horses 16 horses = 4 oxen 6 oxen = 4 elephants 10 elephants = rs . 110000 p = rs . [ ( 24 * 4 * 4 * 110000 ) / ( 10 * 16 * 6 * 10 ) ] p = rs . ( 42240000 / 9600 ) = > p = rs . 4400 answer : d\"" + }, + { + "Answer": 0.13227513227513227, + "Options": "a ) 35 / 189 , b ) 33 / 129 , c ) 25 / 189 , d ) 24 / 113 , e ) 20 / 189", + "Correct": "c", + "Explanation": "p ( kyle will solve ) = 1 / 3 p ( david will not solve ) = 1 - 2 / 7 = 5 / 7 p ( catherine will solve ) = 5 / 9 p = ( 1 / 3 ) * ( 5 / 7 ) * ( 5 / 9 ) = 25 / 189 answer : c" + }, + { + "Answer": 36, + "Options": "a ) 32 kmph , b ) 33 kmph , c ) 34 kmph , d ) 35 kmph , e ) 36 kmph", + "Correct": "e", + "Explanation": "\"avg speed = total distance / total time . total distance traveled = 100 + 50 = 150 km ; time taken for uphill journey = 100 / 30 = 10 / 3 ; time taken for down hill journey = 50 / 60 = 5 / 6 ; avg speed = 150 / ( 10 / 3 + 5 / 6 ) = 36 kmph answer : e\"" + }, + { + "Answer": 40, + "Options": "a ) 40 , b ) 50 , c ) 90 , d ) 140 , e ) it can not be determined from the information given .", + "Correct": "a", + "Explanation": "\"- ( a + b = 100 ) b + c = 140 c - a = 40 a . 40\"" + }, + { + "Answer": 0.36, + "Options": "a ) 0.28 , b ) 0.36 , c ) 0.45 , d ) 0.56 , e ) 0.7", + "Correct": "b", + "Explanation": "p ( b | a ) = p ( a n b ) / p ( a ) p ( a n b ) = p ( b | a ) \u00d7 p ( a ) p ( a n b ) = 0.2 \u00d7 0.18 p ( a n b ) = 0.36 b )" + }, + { + "Answer": 83, + "Options": "a ) 79 , b ) 81 , c ) 83 , d ) 85 , e ) 87", + "Correct": "c", + "Explanation": "\"let x be the height of the first person . then the heights are x , x + 2 , x + 4 , and x + 10 . 4 x + 16 = 4 ( 77 ) = 308 x = 73 and the fourth person has a height of 73 + 10 = 83 inches the answer is c .\"" + }, + { + "Answer": 0.2, + "Options": "a ) 0.15 , b ) 0.20 , c ) 0.25 , d ) 0.30 , e ) 0.33", + "Correct": "b", + "Explanation": "the total number of pairs t , b possible is 4 * 5 = 20 . out of these 20 pairs only 4 sum up to 9 : ( 2 , 7 ) ; ( 3 , 6 ) , ( 4 , 5 ) and ( 5 , 4 ) . the probability thus is 4 / 20 = 0.2 . answer : b ." + }, + { + "Answer": 450, + "Options": "a ) 400 , b ) 420 , c ) 430 , d ) 450 , e ) 510", + "Correct": "d", + "Explanation": "\"let no . of non - officers be x 15 * 420 + x * 110 = ( x + 15 ) 120 x = 450 d\"" + }, + { + "Answer": 4, + "Options": "a ) 4 . , b ) 8 . , c ) 12 . , d ) 16 . , e ) 64 .", + "Correct": "a", + "Explanation": "\"eq 1 : a - b - c + d = 13 eq 2 : a + b - c - d = 9 ( 1 ) subtract eq 1 from eq 2 a - b - c + d = 13 - a + b - c - d = 9 - - - - - - - - - - - - - - - - - - - - - - - - - 2 b + 2 d = 4 ( 2 ) simplify - b + d = 2 b - d = - 2 ( b - d ) ^ 2 = ( - 2 ) ^ 2 = 4 my answer : a\"" + }, + { + "Answer": 3327, + "Options": "a ) 3327 , b ) 3237 , c ) 3337 , d ) 2337 , e ) none of these", + "Correct": "a", + "Explanation": "\"answer x = 13200 - 9873 = 3327 option : a\"" + }, + { + "Answer": 12, + "Options": "a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18", + "Correct": "b", + "Explanation": "\"legs 12 * 4 = 48 now half on their horses so remaining on the walk so 6 men 6 men has 12 legs so , 12 + 48 = 60 legs walking answer : b\"" + }, + { + "Answer": 29, + "Options": "a ) 25 , b ) 76 , c ) 29 , d ) 12 , e ) 20", + "Correct": "c", + "Explanation": "explanation : let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 985 96 + 225 + 490 + 6 x = 985 6 x = 174 = > x = 29 . answer : c" + }, + { + "Answer": 10, + "Options": "a ) 11 , b ) 13 , c ) 14 , d ) 12 , e ) 10", + "Correct": "e", + "Explanation": "\"explanation : let somu ' s age be x and that of his father be 3 x . so , x - 5 = 3 x - 5 / 5 = x = 10 answer : option e\"" + }, + { + "Answer": 58, + "Options": "a ) 50 , b ) 56 , c ) 58 , d ) 62 , e ) 66", + "Correct": "c", + "Explanation": "\"given that , total average w sold is 66 , male / female = 1 / 2 and female average is 70 . average of male members isx . ( 70 * f + x * m ) / ( m + f ) = 66 - > solving this equation after substituting 2 m = f , x = 58 . ans c .\"" + }, + { + "Answer": 12, + "Options": "a ) 1 : 8 , b ) 1 : 4 , c ) 2 : 1 , d ) 4 : 1 , e ) 12 : 1", + "Correct": "e", + "Explanation": "\"x = 6 y , y = 2 * z x : y , y : z 6 : 1 , 2 : 1 12 : 2 , 2 : 1 so , x : z = 12 : 1 ( e )\"" + }, + { + "Answer": 91, + "Options": "a ) 87 , b ) 91 , c ) 100 , d ) 96 , e ) 101", + "Correct": "b", + "Explanation": "\"number of pens = 1001 number of pencils = 910 required number of students = h . c . f . of 1001 and 910 = 91 answer is b\"" + }, + { + "Answer": 38.666666666666664, + "Options": "a ) 33 , b ) 36 , c ) 39 , d ) 42 , e ) 45", + "Correct": "c", + "Explanation": "\"the first number is 22 = 16 + 6 ( 1 ) . we can continue adding 6 to make a list : 22 , 28 , 34 , . . . the last number is 250 = 16 + 6 ( 39 ) there are 39 numbers in the list . the answer is c .\"" + }, + { + "Answer": 10, + "Options": "a ) 15 , b ) 10 , c ) 9 , d ) 6 , e ) 4", + "Correct": "b", + "Explanation": "\"we can first set up our ratio using variable multipliers . we are given that a fruit - salad mixture consists of apples , peaches , and grapes , in the ratio of 6 : 5 : 2 , respectively , by weight . thus , we can say : apples : peaches : grapes = 12 x : 8 x : 7 x we are given that 54 pounds of the mixture is prepared so we can set up the following question and determine a value for x : 12 x + 8 x + 7 x = 54 27 x = 54 x = 2 now we can determine the number of pounds of apples and of grapes . pounds of grapes = ( 7 ) ( 2 ) = 14 pounds of apples = ( 12 ) ( 2 ) = 24 thus we know that there are 24 - 14 = 10 more pounds of apples than grapes . answer is b .\"" + }, + { + "Answer": 150, + "Options": "a ) s . 150 , b ) s . 200 , c ) s . 250 , d ) s . 350 , e ) s . 400", + "Correct": "a", + "Explanation": "\"let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 330 but x = 120 % of y = 120 y / 100 = 12 y / 10 \u00e2 \u02c6 \u00b4 12 y / 10 + y = 330 \u00e2 \u2021 \u2019 y [ 12 / 10 + 1 ] = 330 \u00e2 \u2021 \u2019 22 y / 10 = 330 \u00e2 \u2021 \u2019 22 y = 3300 \u00e2 \u2021 \u2019 y = 3300 / 22 = 300 / 2 = rs . 150 a )\"" + }, + { + "Answer": 520, + "Options": "a ) 540 , b ) 520 , c ) 619 , d ) 649 , e ) 700", + "Correct": "b", + "Explanation": "\"before price increase price = d after 30 % price increase price = d + ( 30 / 100 ) * d = 1.3 d = 338 ( given ) i . e . d = 338 / 1.3 = $ 260 i . e . 2 d = 2 * 260 = 520 answer : option b\"" + }, + { + "Answer": 68, + "Options": "a ) 30 , b ) 80 , c ) 20 , d ) 68 , e ) 26", + "Correct": "d", + "Explanation": "\"let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 . x / 2 = ( 79 - 45 ) = > x / 2 = 34 = > x = 68 . answer : d\"" + }, + { + "Answer": 50000, + "Options": "a ) 26799 , b ) 24000 , c ) 50000 , d ) 29973 , e ) 12312", + "Correct": "c", + "Explanation": "\"x * ( 90 / 100 ) = 45000 x = 500 * 100 x = 50000 answer : c\"" + }, + { + "Answer": 66, + "Options": "a ) 58 , b ) 62 , c ) 66 , d ) 70 , e ) 74", + "Correct": "c", + "Explanation": "12 c 2 = 66 the answer is c ." + }, + { + "Answer": 800, + "Options": "a ) $ 830 , b ) $ 800 , c ) $ 770 , d ) $ 730 , e ) $ 700", + "Correct": "b", + "Explanation": "1 . 15 bills spent 2 . number of $ 10 bills is one more or one less than number of $ 50 bills . so , 2 choices 1 . 7 * 10 + 8 * 50 = $ 470 2 . 8 * 10 + 7 * 50 = $ 430 least money lost implies most money spent . i . e $ 470 therefore , lost money = 1270 - 470 = 800 . answer b" + }, + { + "Answer": 20, + "Options": "a ) 12 , b ) 20 , c ) 48 , d ) 55 , e ) 60", + "Correct": "b", + "Explanation": "say farmer has n goat and he is good for d days . : - we have 3 equations given in question : - ( n - 5 ) * d + 4 = ( n + 10 ) * ( d - 3 ) = n * d solving these : ( you can solve 1 st and 3 rd and 2 nd and 3 rd together ) we get : 10 d - 3 n = 30 4 n - 5 d = 20 = > n = 20 ans b it is !" + }, + { + "Answer": 9, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 12", + "Correct": "c", + "Explanation": "\"27 ^ y > 3 ^ 24 converting into the same bases : 27 ^ y > 27 ^ 8 therefore for the equation to hold true , y > 8 or y = 9 option c\"" + }, + { + "Answer": 0.13333333333333333, + "Options": "a ) 0 , b ) 2 / 15 , c ) 2 / 5 , d ) 9 / 20 , e ) 5 / 6", + "Correct": "b", + "Explanation": "\"we need to determine the result of 1 / 3 + 1 / 2 - 5 / 6 + 1 / 5 + 1 / 4 - 9 / 20 let \u2019 s add the given fractions in two groups . in the group of the first three fractions , notice that 1 / 3 and 1 / 2 share a common denominator of 6 with 5 / 6 . 1 / 2 + 1 / 3 = 3 / 6 + 2 / 6 = 5 / 6 thus , 5 / 6 \u2013 5 / 6 = 0 looking at the 2 nd group of the fractions ( 1 / 5 , 1 / 4 , and 9 / 20 ) , notice that 1 / 5 and 1 / 4 share a common denominator of 20 with 9 / 20 . 1 / 5 + 1 / 4 = 4 / 20 + 5 / 20 = 9 / 20 thus , 9 / 20 \u2013 9 / 20 = 0 . thus , the result of 1 / 3 + 1 / 2 \u2013 5 / 6 + 1 / 5 + 1 / 4 \u2013 9 / 20 is 2 / 15 . answer : b\"" + }, + { + "Answer": 15, + "Options": "a ) 4 , b ) 12 , c ) 15 , d ) 20 , e ) 24", + "Correct": "c", + "Explanation": "\"you could set - up a quick table and brute force the answer . a 4 * 50 200 1800 - 200 1600 26 61.54 b 12 * 50 600 1800 - 600 1200 18 66.67 c 15 * 50 750 1800 - 750 1050 15 70.00 d 20 * 50 1000 1800 - 1000 800 10 80.00 e 24 * 50 1200 1800 - 1200 600 6 100.00 answer is c\"" + }, + { + "Answer": 0.56, + "Options": "a ) 0.44 , b ) 0.5 , c ) 0.56 , d ) 0.62 , e ) 0.68", + "Correct": "c", + "Explanation": "\"let x be the total number of students . the number students who are younger than 25 is 0.5 * 0.4 x + 0.6 * 0.6 x = 0.56 x the answer is c .\"" + }, + { + "Answer": 0.5, + "Options": "a ) 1 / 45 , b ) 1 / 2 , c ) 1 / 8 , d ) 2 / 3 , e ) 2 / 11", + "Correct": "b", + "Explanation": "let us say probability of a occuring is a . let us say probability of b occuring is b . a = 2 b probability ( either a or b or both ) = 5 times probability ( a and b ) a * ( 1 - b ) + b * ( 1 - a ) + ab = 5 * ab substituting a = 2 b in the second equation : 2 b * ( 1 - b ) + b * ( 1 - 2 b ) + 2 b * b = 5 * 2 b * b 3 b - 2 b ^ 2 = 110 b ^ 2 3 b = 12 b ^ 2 b = 3 / 12 = 1 / 4 so , a = 2 b = 1 / 2" + }, + { + "Answer": 0.71875, + "Options": "a ) 3 / 8 , b ) 1 / 2 , c ) 11 / 16 , d ) 23 / 32 , e ) 3 / 4", + "Correct": "d", + "Explanation": "\"the answer isc : 11 / 16 . the key to this problem is remembering that the median for a consecutive set of numbers is equivalent to its mean . for example , the mean and median of a set consisting of x , x + 1 , x + 2 , . . . , y will always be ( x + y ) / 2 . for set s , consisting of numbers ( a , a + 1 , . . . , b ) , the median is given to be 3 / 4 * b : ( a + b ) / 2 = ( 3 / 4 ) * b a = b / 2 for set q , consisting of numbers ( b , b + 1 , . . . , c ) , the median is given to be 7.5 / 8 * c : ( b + c ) / 2 = ( 7.5 / 8 ) * c b = ( 7 / 8 ) * c for set r , consisting of numbers ( a , a + 1 , . . . c ) , the median needs to be found : a = b / 2 = ( 7 / 8 * c ) / 2 = ( 7 / 16 ) * c median = ( a + c ) / 2 = ( 7 / 16 * c + c ) / 2 = ( 23 / 16 ) * c / 2 = ( 23 / 32 ) * c ( answer d )\"" + }, + { + "Answer": 699.9999999999999, + "Options": "a ) 700 , b ) 300 , c ) 1000 , d ) 360 , e ) 2400", + "Correct": "a", + "Explanation": "let the additional invested amount for 8 % interest be x ; equation will be ; 1400 + 0.05 * 2400 + x + 0.08 x = 1400 + x + 0.06 ( 2400 + x ) 0.05 * 1400 + 0.08 x = 0.06 x + 0.06 * 1400 0.02 x = 1400 ( 0.06 - 0.05 ) x = 1400 * 0.01 / 0.02 = 700 ans : a" + }, + { + "Answer": 1, + "Options": "a ) 1 coin , b ) 2 coins , c ) 3 coins , d ) 4 coins , e ) coins", + "Correct": "a", + "Explanation": "he would need to add one coin more so 12005 is fully divisible by 7 and each would get 1715 coins . so the correct answer is a" + }, + { + "Answer": 570, + "Options": "a ) 420 , b ) 550 , c ) 490 , d ) 570 , e ) 457", + "Correct": "d", + "Explanation": "\"10 * 162 = 1620 3 * 100 + 5 * 150 = 1050 1620 \u2013 1050 = 570 answer : d\"" + }, + { + "Answer": 65, + "Options": "a ) 50 , b ) 88 , c ) 65 , d ) 55 , e ) 22", + "Correct": "c", + "Explanation": "\"let the length of each train be x m . then , distance covered = 2 x m . relative speed = 49 - 36 = 13 km / hr . = 13 * 5 / 18 = 65 / 18 m / sec . 2 x / 36 = 65 / 18 = > x = 65 . answer : c\"" + }, + { + "Answer": 11, + "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12", + "Correct": "d", + "Explanation": "solution let the number pf papers be x . then , 63 x + 20 + 2 = 65 x 65 x - 63 x = 22 2 x = 22 x = 11 . answer d" + }, + { + "Answer": 11, + "Options": "a ) 11 , b ) 14 , c ) 13 , d ) 15 , e ) 16", + "Correct": "a", + "Explanation": "\"let p = 2 , q = 7 then 2 * 2 + 7 = 11 so 2 p + q = 11 . answer : a\"" + }, + { + "Answer": 383, + "Options": "a ) 263 , b ) 293 , c ) 323 , d ) 353 , e ) 383", + "Correct": "e", + "Explanation": "sum of consecutive integers from 51 to 59 , inclusive = = = = > ( a 1 + an ) / 2 * # of terms = ( 51 + 59 ) / 2 * 9 = 55 * 9 = 495 sum of non - prime numbers b / w 50 and 60 , non inclusive = = = > 495 - 112 ( i . e . , 53 + 59 , being the prime # s in the range ) = 383 answer : e" + }, + { + "Answer": 110, + "Options": "a ) 85.5 , b ) 86.5 , c ) 87.5 , d ) 110 , e ) 89.5", + "Correct": "d", + "Explanation": "\"total increase in weight = 10 \u00d7 5 = 50 if x is the weight of the new person , total increase in weight = x \u2212 60 = > 50 = x - 60 = > x = 50 + 60 = 110 answer : d\"" + }, + { + "Answer": 3, + "Options": "a ) 1 / 2 , b ) 2 / 3 , c ) 3 , d ) 4 / 5 , e ) 4 / 7", + "Correct": "c", + "Explanation": "p ( b | a ) = p ( a \u00e2 \u02c6 \u00aa b ) / p ( a ) p ( b | a ) = ( 6 / 15 ) / ( 2 / 15 ) = 3 . c" + }, + { + "Answer": 27, + "Options": "a ) - 4 , b ) 4 , c ) 10 , d ) 27 , e ) 40", + "Correct": "d", + "Explanation": "the fastest approach has already been shown . here ' s one more option . given : x + y = 9 x \u2013 y = 3 add the two equations to get : 2 x = 12 , which means x = 6 if x = 6 , we can plug that value into either equation , to conclude that y = 3 if x = 6 and y = 3 , then x \u00b2 - y \u00b2 = 6 \u00b2 - 3 \u00b2 = 27 answer : d" + }, + { + "Answer": 6, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "d", + "Explanation": "\"when you choose ( and then eat ) the first apple , the probability of that apple being red is 9 / 10 . so if we do the activity 1 times , the probability of it being red is 9 / 10 . for 2 times , it is ( 9 / 10 ) * ( 8 / 9 ) for 3 times , it is ( 9 / 10 ) * ( 8 / 9 ) * ( 7 / 8 ) you can notice that the numerator of the first term cancels with the denominator of the second . so we can see that the probability becomes 0.5 when the last term is 5 / 6 & it becomes less than 0.5 when the last term is 4 / 5 . 9 accounts for n = 1 , so 4 will account for n = 6 , answer . d\"" + }, + { + "Answer": 55, + "Options": "a ) 68 , b ) 42 , c ) 55 , d ) 18 , e ) 44", + "Correct": "c", + "Explanation": "\"2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 210 - 100 = 110 ab = 55 . answer : c\"" + }, + { + "Answer": 18, + "Options": "a ) 22 , b ) 21 , c ) 20 , d ) 19 , e ) 18", + "Correct": "e", + "Explanation": "solution simple out of 150 10 % are male i . e 15 and 20 % are female i . e 30 , so total homeowner is 45 . now min number homeowner is 15 and max is 30 so question ask us to find least and 18 has least value among all option . so ans is 18 . ans : e" + }, + { + "Answer": 22, + "Options": "a ) 23 , b ) 24 , c ) 25 , d ) 22 , e ) 27", + "Correct": "d", + "Explanation": "\"average age of people = 30 so have total age = 210 before 7 years we have to deduct each person age by seven years 210 - 56 = 154 so average age would be 154 / 7 = 22 answer : d\"" + }, + { + "Answer": 75.00000000000001, + "Options": "a ) $ 75 , b ) $ 80 , c ) $ 90 , d ) $ 120 , e ) $ 180", + "Correct": "a", + "Explanation": "\"let ' s let t = total number of dollars spent at the supermarket . with this variable we can set up an equation and determine t . we are given that john spent 1 / 2 of his money on fresh fruits and vegetables , or ( 1 / 2 ) t , 1 / 3 on meat products , or ( 1 / 3 ) t , and 1 / 10 on bakery products , or ( 1 / 10 ) t . we are also given that he spent the remaining $ 5 on candy . since we know where all his money was allocated , we can sum these values together and set the sum to t . so we have : ( 1 / 2 ) t + ( 1 / 3 ) t + ( 1 / 10 ) t + 5 = t to get rid of the fractions we can multiply the entire equation by 30 , and we obtain : 15 t + 10 t + 3 t + 150 = 30 t 28 t + 150 = 30 t 150 = 2 t t = 75 john spent $ 7 at the supermarket . answer : a\"" + }, + { + "Answer": 25, + "Options": "a ) 72 , b ) 80 , c ) 25 , d ) 150 , e ) 100", + "Correct": "c", + "Explanation": "\"explanation : let the number of students be x . then , number of students above 8 years of age = ( 100 - 20 ) % of x = 80 % of x . 80 % of x = 12 + 2 / 3 of 12 80 / 100 x = 20 x = 25 . answer : option c\"" + }, + { + "Answer": 50, + "Options": "a ) 40 , b ) 44 , c ) 45 , d ) 46 , e ) 50", + "Correct": "e", + "Explanation": "answer e = 50 we have ( 10 ^ w ) - 74 , where the sum of the digits is 440 . 100 - 74 = 26 , so we already have 2 + 6 = 8 from the 440 . because we have a power of 10 , we will have numbers like 100 , 1000 , 10000 and so on . this minus 74 rests 26 and a lot of 9 s . e . g : 1000 - 74 = 9926 . so dividing the 432 / 9 = 48 , that ` s the number of 9 s . and we have 2 other numbers ( 2 and 6 ) wich were 00 before the subtraction . so we have 48 + 2 as an w = 50" + }, + { + "Answer": 295, + "Options": "a ) 24 , b ) 77 , c ) 295 , d ) 267 , e ) 29", + "Correct": "c", + "Explanation": "\"explanation : 65 - 6 = 59 59 x 5 = 295 answer : c\"" + }, + { + "Answer": 16, + "Options": "a ) 16 , b ) 28 , c ) 32 , d ) 36 , e ) 38", + "Correct": "a", + "Explanation": "solution let the ten digits be x . then , units digit = 6 x therefore x + 6 x = 7 \u2039 = \u203a 7 x = 7 \u2039 = \u203a x = 1 . so , ten ' s digit = 1 , unit ' s digit = 6 . hence , the required number is 16 . answer a" + }, + { + "Answer": 432, + "Options": "a ) 384 , b ) 432 , c ) 207 , d ) 269 , e ) 208", + "Correct": "b", + "Explanation": "average mark scored by all the three boys = [ 64 / 100 ( 900 ) + 36 / 100 ( 900 ) + 44 / 100 ( 900 ) ] / 3 = 432 answer : b" + }, + { + "Answer": 2, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "a", + "Explanation": "\"when a certain number x is divided by 63 , the remainder is 11 . what is the remainder when x is divided by 9 ? putting a value say x = 11 we get remainder as 11 when divided by 63 . when 11 divided by 9 we get 2 as remainder . a is the answer .\"" + }, + { + "Answer": 0.038903999999999994, + "Options": "a ) 0.045388 , b ) 4.5388 , c ) 453.88 , d ) 473.88 , e ) 0.038904", + "Correct": "e", + "Explanation": "answer multiplying 3.242 x 12 = 3.8904 now divide 3.8904 by 100 so , 3.8904 \u00f7 100 = 0.038904 \u2234 shift the decimal two places to the left as 100 correct option : e" + }, + { + "Answer": 15, + "Options": "a ) [ 45 ] , b ) [ 30 ] , c ) [ 15 ] , d ) [ 5 ] , e ) [ 50 ]", + "Correct": "c", + "Explanation": "\"[ 5 ] * [ 6 ] = 15 * 3 = 45 = [ 15 ] the answer is c .\"" + }, + { + "Answer": 1998, + "Options": "a ) 1997 , b ) 1998 , c ) 1999 , d ) 2000 , e ) none of these", + "Correct": "b", + "Explanation": "suppose in \u2018 n \u2019 years the price of comodity x will be more by 40 paise than that of commodity y . \u2234 420 + 40 n \u2013 630 \u2013 15 n = 40 or , 25 n \u2013 210 = 40 or , 25 n = 250 or , n = 250 \u2044 25 = 10 years . answer b" + }, + { + "Answer": 3.25, + "Options": "a ) 3.5 , b ) 3.35 , c ) 3.45 , d ) 3.25 , e ) 3.55", + "Correct": "d", + "Explanation": "\"assume she has $ 200 to spend . tax clothing = 45 % = $ 90 = $ 4.5 food = 45 % = $ 90 = $ 0.00 items = 10 % = $ 20 = $ 2.00 total tax = $ 6.50 % of total amount = 6.5 / 200 * 100 = 3.25 % answer d\"" + }, + { + "Answer": 8.000000000000007, + "Options": "a ) 10 % , b ) 12.5 % , c ) 8 % , d ) 12 % , e ) 6.66 %", + "Correct": "c", + "Explanation": "explanatory answer let the price of 1 litre of gasoline be $ x and let ron initially buy ' y ' litres of gasoline . therefore , he would have spent $ xy on gasoline . when the price of gasoline increases by 25 % , the new price per litre of gasoline is 1.25 x . ron intends to increase the amount he spends on gasoline by 15 % . i . e . , he is willing to spend xy + 15 % of xy = 1.15 xy let the new quantity of gasoline that he can get be ' q ' . then , 1.25 x * q = 1.15 xy or q = 1.15 xy / 1.25 x = 0.92 y . as the new quantity that he can buy is 0.92 y , he gets 0.08 y lesser than what he used to get earlier . or a reduction of 8 % . the correct choice is ( c )" + }, + { + "Answer": 250, + "Options": "a ) rs . 300 , b ) rs . 200 , c ) rs . 250 , d ) rs . 350 , e ) none of these", + "Correct": "c", + "Explanation": "\"z share = z , y = 1.2 z x = 1.25 \u00e3 \u2014 1.2 z , x + y + z = 925 ( 1.25 \u00e3 \u2014 1.2 + 1.2 + 1 ) z = 925 3.7 z = 925 , z = 250 answer : . c\"" + }, + { + "Answer": 4, + "Options": "a ) 6 rs , b ) 2 rs , c ) 4 rs , d ) 9 rs , e ) 3 rs", + "Correct": "c", + "Explanation": "\"5 m = xw = 8 b 5 m + xw + 8 b - - - - - 60 rs . 5 m + 5 m + 5 m - - - - - 60 rs . 15 m - - - - - - 60 rs . = > 1 m = 4 rs . answer : c\"" + }, + { + "Answer": 2984, + "Options": "a ) 2984 , b ) 2983 , c ) 2982 , d ) 2981 , e ) none of these", + "Correct": "a", + "Explanation": "option a" + }, + { + "Answer": 26, + "Options": "a ) 92 , b ) 43 , c ) 71 , d ) 26 , e ) 31", + "Correct": "d", + "Explanation": "\"( x ^ n + 1 ) will be divisible by ( x + 1 ) only when n is odd ; ( 27 ^ 27 + 1 ) will be divisible by ( 27 + 1 ) ; ( 27 ^ 27 + 1 ) + 26 when divided by 28 will give 26 as remainder . correct option : d\"" + }, + { + "Answer": 20, + "Options": "a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 50 %", + "Correct": "c", + "Explanation": "raja ' s salary less than ram ' s by 25 / ( 100 + 25 ) * 100 % = 20 % answer is c" + }, + { + "Answer": 0.08999999999999998, + "Options": "a ) 0.0009 , b ) 0.09 , c ) 0.9 , d ) 9 , e ) 90", + "Correct": "b", + "Explanation": "x = 0.009 / 0.1 = 0.09 answer : b" + }, + { + "Answer": 121, + "Options": "a ) 121 , b ) 421 , c ) 143 , d ) 176 , e ) 84", + "Correct": "a", + "Explanation": "\"explanation : average after 16 innings = 31 required number of runs = ( 31 * 16 ) \u2013 ( 25 * 15 ) = 496 \u2013 375 = 121 answer a\"" + }, + { + "Answer": 88320, + "Options": "a ) 87801 , b ) 87811 , c ) 87862 , d ) 11803 , e ) 87803", + "Correct": "e", + "Explanation": "x + 1315 + 9211 - 1569 = 11901 = x + 1315 + 9211 = 11901 + 1569 = x + 10526 = 13470 = x = 98329 - 10526 = 87803 answer is e" + }, + { + "Answer": 1.3, + "Options": "a ) 1.9 , b ) 1.7 , c ) 1.3 , d ) 1.5 , e ) 1.1", + "Correct": "c", + "Explanation": "\"speed of boat in still water ( b ) = 3.9 km / hr . speed of boat with stream ( down stream ) , d = b + u speed of boat against stream ( up stream ) , u = b \u2013 u it is given upstream time is twice to that of down stream . \u21d2 downstream speed is twice to that of upstream . so b + u = 2 ( b \u2013 u ) \u21d2 u = b / 3 = 1.3 km / hr . answer : c\"" + }, + { + "Answer": 117, + "Options": "a ) 115 , b ) 116 , c ) 117 , d ) 118 , e ) 119", + "Correct": "c", + "Explanation": "\"x : y : z = 100 : 45 : 50 20 : 9 : 10 9 - - - 27 39 - - - ? = > 117 answer : c\"" + }, + { + "Answer": 119.4, + "Options": "a ) 160 kg , b ) 175 kg , c ) 180.7 kg , d ) 119.4 kg , e ) 190.8 kg", + "Correct": "d", + "Explanation": "\"total weight increased = ( 7 x 6.2 ) kg = 43.4 kg . weight of new person = ( 76 + 43.4 ) kg = 119.4 kg option d\"" + }, + { + "Answer": 4184.615384615385, + "Options": "a ) rs . 6184.5 , b ) rs . 4184.5 , c ) rs . 5700 , d ) rs . 4284.5 , e ) rs . 5184.5", + "Correct": "b", + "Explanation": "\"cost of the camel = p 10 camels = 24 horses 26 horses = 4 oxen 6 oxen = 4 elephants 10 elephants = rs . 170000 p = rs . [ ( 24 * 4 * 4 * 170000 ) / ( 10 * 26 * 6 * 10 ) ] p = rs . ( 65280000 / 15600 ) = > p = rs . 4184.5 answer : b\"" + }, + { + "Answer": 69.33333333333333, + "Options": "a ) 33.25 , b ) 32.25 , c ) 65 , d ) 67 , e ) 69", + "Correct": "e", + "Explanation": "explanation : = ( 56 \u00d7 7 ) \u2212 ( 46 \u00d7 4 ) / 3 = ( 392 \u2212 184 ) / 3 = 69 answer : option e" + }, + { + "Answer": 100, + "Options": "a ) 98 , b ) 99 , c ) 100 , d ) 97 , e ) 95", + "Correct": "b", + "Explanation": "\"10 * 2 = 20 10 * 100 = 1000 total multiples = ( 100 - 2 ) + 1 = 99 answer b\"" + }, + { + "Answer": 9, + "Options": "a ) 17 : 3 , b ) 9 : 1 , c ) 3 : 17 , d ) 5 : 3 , e ) 11 : 2", + "Correct": "b", + "Explanation": "\"rom the beginning ; initially milk to water is 12 l : 8 l remove half 6 - 4 add 10 l milk 16 - 4 remove half 8 - 2 add 10 l milk 18 - 2 18 : 2 = 9 : 1 answer : b\"" + }, + { + "Answer": 189, + "Options": "a ) 3 , b ) 7 , c ) 21 , d ) 189 , e ) 198", + "Correct": "d", + "Explanation": "in that case , the sophie prime numbers greater than 6 are 7 , 11,23 , 47,59 , . . which yields units digit as 1 , 3,7 and 9 product would be 1 x 3 x 7 x 9 = 189 answer should be d" + }, + { + "Answer": 6.5, + "Options": "a ) 10 , b ) 388 , c ) 6.5 , d ) 29 , e ) 22", + "Correct": "c", + "Explanation": "\"explanation : let the original price be rs . 100 . decreased by 15 % = 85 then increased 10 % on rs 85 = 85 + 8.5 = 93.5 net change in price = 100 - 93.5 = 6.5 answer : c\"" + }, + { + "Answer": 10000, + "Options": "a ) 981 , b ) 1000 , c ) 1011 , d ) 10000 , e ) 1110", + "Correct": "d", + "Explanation": "the number of codes possible if leading zero is allowed = 10 * 10 * 10 * 10 * 10 = 10 ^ 5 the number of codes possible if leading zero is not allowed = 9 * 10 * 10 * 10 * 10 = 9 * 10 ^ 4 the difference = 10 ^ 5 - 9 * 10 ^ 4 = 10 ^ 4 ( 10 - 9 ) = 10 ^ 4 . answer : d . similar questions to practice : hope it helps ." + }, + { + "Answer": 79012.34567901235, + "Options": "a ) 81000 , b ) 81007 , c ) 81008 , d ) 79012.3 , e ) 81022", + "Correct": "d", + "Explanation": "\"64000 * 10 / 9 * 10 / 9 = 79012.3 answer : d\"" + }, + { + "Answer": 4500, + "Options": "a ) 2788 , b ) 4500 , c ) 7282 , d ) 2782 , e ) 2729", + "Correct": "b", + "Explanation": "\"4 - - - 3600 5 - - - ? = > 4500 answer : b\"" + }, + { + "Answer": 9, + "Options": "a ) 9 , b ) 10 , c ) 12 , d ) 14 , e ) 15", + "Correct": "a", + "Explanation": "\"explanation : = > 3 ( 2 x + 9 ) = 81 = > 2 x + 9 = 27 = > x = 9 answer : option a\"" + }, + { + "Answer": 4800, + "Options": "a ) s . 9800 , b ) s . 3800 , c ) s . 9800 , d ) s . 4800 , e ) s . 6880", + "Correct": "d", + "Explanation": "\"cost of the camel = p 10 camels = 24 horses 16 horses = 4 oxen 6 oxen = 4 elephants 10 elephants = rs . 120000 p = rs . [ ( 24 * 4 * 4 * 120000 ) / ( 10 * 16 * 6 * 10 ) ] p = rs . ( 46080000 / 9600 ) = > p = rs . 4800 answer : d\"" + }, + { + "Answer": 22, + "Options": "a ) 20 years , b ) 21 years , c ) 22 years , d ) 24 years , e ) none of these", + "Correct": "c", + "Explanation": "\"explanation : let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years = > ( x + 24 ) + 2 = 2 ( x + 2 ) = > x + 26 = 2 x + 4 so , x = 22 option c\"" + }, + { + "Answer": 1, + "Options": "a ) 11 , b ) 1 , c ) 2 , d ) 3 , e ) 21", + "Correct": "b", + "Explanation": "\"let 100 + 11 = 111 111 divided evenly by eleven leaves a remainder of one . correct answer is b .\"" + }, + { + "Answer": 21, + "Options": "a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24", + "Correct": "b", + "Explanation": "\"solution let the toatl number of workers be x . then 8000 x = ( 12000 x 7 ) + 6000 ( x - 7 ) 2000 x = 42000 x = 21 . answer b\"" + }, + { + "Answer": 259, + "Options": "a ) 259 , b ) 498 , c ) 676 , d ) 823 , e ) 1,002", + "Correct": "a", + "Explanation": "\"slope of 2 and a y - intercept of 2 y - coordinate is 520 y = 2 x + 2 518 = 2 x x = 259 answer : a . 259\"" + }, + { + "Answer": 1.7056626506024097, + "Options": "a ) $ 1.63 , b ) $ 1.71 , c ) $ 1.68 , d ) $ 1.72 , e ) $ 1.76", + "Correct": "b", + "Explanation": "\"( 1325 * 1.89 + 750 * 1.38 ) / ( 1325 + 750 ) = ~ 1.71 option ( b )\"" + }, + { + "Answer": 99935, + "Options": "a ) 100555 , b ) 100775 , c ) 100885 , d ) 100995 , e ) 100665", + "Correct": "b", + "Explanation": "\"smallest number of six digits is 100000 . required number must be divisible by l . c . m . of 25,35 , 45,15 i . e 1575 , on dividing 100000 by 1575 , we get 800 as remainder . therefore , required number = 100000 + ( 1575 \u00e2 \u20ac \u201c 800 ) = 100775 . answer is b .\"" + }, + { + "Answer": 63, + "Options": "a ) 38 , b ) 47 , c ) 50 , d ) 53 , e ) 63", + "Correct": "e", + "Explanation": "\"if you list the amount eaten each hour , you ' ll get an equally spaced list , increasing by 3 each hour . in any equally spaced list , the median equals the mean . here , the mean is 540 / 9 = 60 , so the median is also 60 , and that is the amount eaten in the 5 th hour . we need to add 3 to find the total eaten in the next hour , so the answer is 63 . option e .\"" + }, + { + "Answer": 400, + "Options": "a ) s . 150 , b ) s . 200 , c ) s . 250 , d ) s . 350 , e ) s . 400", + "Correct": "e", + "Explanation": "\"let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 880 but x = 120 % of y = 120 y / 100 = 12 y / 10 \u00e2 \u02c6 \u00b4 12 y / 10 + y = 880 \u00e2 \u2021 \u2019 y [ 12 / 10 + 1 ] = 880 \u00e2 \u2021 \u2019 22 y / 10 = 880 \u00e2 \u2021 \u2019 22 y = 8800 \u00e2 \u2021 \u2019 y = 8800 / 22 = 800 / 2 = rs . 400 e )\"" + }, + { + "Answer": 0.509090909090909, + "Options": "a ) 1 / 25 , b ) 28 / 55 , c ) 2 / 35 , d ) 2 / 55 , e ) 1 / 75", + "Correct": "b", + "Explanation": "\"first , there are 9 c 3 ways you can select 3 good pencils from 4 good ones . second , there are 11 c 3 ways you select 3 pencils from 6 ones in the box . then , the probability that neither pen will be defective is : 9 c 3 / 11 c 3 = 84 / 165 = 28 / 55 answer is b\"" + }, + { + "Answer": 5300, + "Options": "a ) 2177 , b ) 2876 , c ) 4500 , d ) 5300 , e ) 6711", + "Correct": "d", + "Explanation": "sum of the salaries of the person for the months of january , february , march and april = 4 * 8000 = 32000 - - - - ( 1 ) sum of the salaries of the person for the months of february , march , april and may = 4 * 8300 = 33200 - - - - ( 2 ) ( 2 ) - ( 1 ) i . e . may - jan = 1200 salary of may is rs . 6500 salary of january = rs . 5300 . answer : d" + }, + { + "Answer": 170, + "Options": "a ) 100 , b ) 170 , c ) 150 , d ) 180 , e ) 199", + "Correct": "b", + "Explanation": "\"65 % of x = 20 % of 552.50 then , 65 / 100 * x = 20 / 100 * 5525 / 10 x = 170 answer is b\"" + }, + { + "Answer": 864, + "Options": "a ) 2134 , b ) 2234 , c ) 2540 , d ) 2560 , e ) 864", + "Correct": "e", + "Explanation": "\"5184 e\"" + }, + { + "Answer": 2000, + "Options": "a ) 1500 , b ) 1600 , c ) 1750 , d ) 1900 , e ) 2000", + "Correct": "e", + "Explanation": "let the price of basic computer be c and the price of the printer be p : c + p = $ 2,500 . the price of the enhanced computer will be c + 500 and total price for that computer and the printer will be 2,500 + 500 = $ 3,000 . now , we are told that the price of the printer is 1 / 6 of that new total price : p = 1 / 6 * $ 3,000 = $ 500 . plug this value in the first equation : c + 500 = $ 2,500 - - > c = $ 2000 answer : e ." + }, + { + "Answer": 50, + "Options": "a ) 60 % , b ) 70 % , c ) 80 % , d ) 90 % , e ) 50 %", + "Correct": "e", + "Explanation": "say john ' s wages last week were $ 100 , so he spent 0.30 * 100 = $ 30 on recreation ; this week ' s wages is 0.75 * 100 = $ 75 , so he spends 0.2 * 75 = $ 15 on recreation ; 15 / 30 = 0.50 , hence the amount he spends on recreation this week is 50 % of the amount he spent on recreation last week : 30 * 0.5 = 15 answer : e" + }, + { + "Answer": 1, + "Options": "a ) 1 % , b ) 2 % , c ) 1.5 % , d ) 3 % , e ) 4 %", + "Correct": "a", + "Explanation": "the percent increase is ( 20000 - 10000 ) / 10000 = 10000 / 10000 = 1 % so the approximate answer is a" + }, + { + "Answer": 5, + "Options": "a ) 6 , b ) 10 , c ) 12 , d ) 5 , e ) 8", + "Correct": "d", + "Explanation": "d 5" + }, + { + "Answer": 14045, + "Options": "a ) s . 14991 , b ) s . 49930 , c ) s . 14045 , d ) s . 14999 , e ) s . 14578", + "Correct": "c", + "Explanation": "total sale for 4 months = rs . ( 5700 + 8550 + 6855 + 3850 ) = rs . 24955 required sale = rs . [ ( 7800 x 5 ) - 24955 ] = rs . ( 39000 - 24955 ) = rs . 14045 option c" + }, + { + "Answer": 28, + "Options": "a ) 48 , b ) 28 , c ) 36 , d ) 72 , e ) 27", + "Correct": "b", + "Explanation": "\"to improve his average by 8 runs per innings he has to contribute 14 x 8 = 112 runs for the previous 14 innings . thus , the average after the 15 th innings = 140 - 112 = 28 . answer : b\"" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 5 , c ) 7 , d ) 8 , e ) 9", + "Correct": "a", + "Explanation": "\"slope = ( 17 2 / 3 - 12 2 / 3 ) / ( 16 - 22 ) = - 5 / 6 y = mx + b = > 12 2 / 3 = - 22 * 5 / 6 + b = > b = 31 y = - 5 x / 6 + 31 only integer values work , and the only multiples of 6 between 16 and 22 for x values is 18 , thus 1 point . a\"" + }, + { + "Answer": 120, + "Options": "a ) 6 , b ) 36 , c ) 48 , d ) 60 , e ) 120", + "Correct": "e", + "Explanation": "\"let total no of students in the class be n so , we are told that n is divisible by both 15 24 so , lets find the least common multiple of 15 24 , ie 120 so our answer is ( e ) 120\"" + }, + { + "Answer": 4.0000000000000036, + "Options": "a ) 4.0 % , b ) 5.0 % , c ) 6.0 % , d ) 7.0 % , e ) 8.0 %", + "Correct": "a", + "Explanation": "quantity x rate = price 1 x 1 = 1 0.8 x 1.20 = 0.960 decrease in price = ( 0.040 / 1 ) \u00e3 \u2014 100 = 4.0 % answer = option a" + }, + { + "Answer": 18.999999999999993, + "Options": "a ) 25 % , b ) 19 % , c ) 30 % , d ) 22.5 % , e ) 15 %", + "Correct": "b", + "Explanation": "consider base price - $ 100 25 % increase = 1.40 * 100 = $ 140 then a 15 % decrease on new price = 0.85 * 140 = $ 119 so final price of radio - $ 119 therefore a 19 % increase correct option - b" + }, + { + "Answer": 9.237333333333334, + "Options": "a ) 0.092 , b ) 0.92 , c ) 9.2 , d ) 92 , e ) 920", + "Correct": "c", + "Explanation": "\"w ( 69.28 \u00d7 0.004 ) / 0.03 1 . 0.004 = 4 \u00d7 10 ^ ( - 3 ) 2 . 0.03 = 3 \u00d7 10 ^ ( - 2 ) 3 . ( a \u00d7 b ) / c = a \u00d7 ( b / c ) 4 . 0.004 / 0.03 = 4 \u00d7 10 ^ ( - 3 ) / ( 3 \u00d7 10 ^ ( - 2 ) ) = 4 \u00d7 10 ^ ( - 3 - ( - 2 ) ) / 3 = 4 \u00d7 10 ^ ( - 1 ) / 3 = ( 4 / 3 ) \u00d7 10 ^ ( - 1 ) = 1.333 \u00d7 10 ^ ( - 1 ) therefore , ( 69.28 \u00d7 0.004 ) / 0.03 = 69.28 \u00d7 ( 0.004 / 0.03 ) = 69.28 \u00d7 1.33 \u00d7 10 ^ ( - 1 ) = 69.28 \u00d7 1.33 / 10 = 6.928 * 1.33 now , 7 \u00d7 2 = 14 7 \u00d7 1 = 7 or better : 6.9 \u00d7 1 = 6.9 6.9 \u00d7 2 = 13.8 hence , 6.9 < 6.928 \u00d7 1.33 < 13.8 9.2 is the only answer that satisfies this condition . c\"" + }, + { + "Answer": 14, + "Options": "a ) 6 , b ) 12 , c ) 14 , d ) 18 , e ) 20", + "Correct": "c", + "Explanation": "required number is divisible by 72 as well as by 112 , if it is divisible by their lcm , which is 1008 . now , 1008 when divided by 72 , gives quotient = 14 . therefore , required number = 14 . answer : c" + }, + { + "Answer": 72, + "Options": "a ) 72 min , b ) 62 min , c ) 70 min , d ) 74 min , e ) 76 min", + "Correct": "a", + "Explanation": "\"x = time for type b prolems 2 x = time for type a problem total time = 3 hrs = 180 min 150 x + 50 * 2 x = 180 x = 180 / 250 x = 0.72 time taken for type a problem = 50 * 2 * 0.72 = 72 min answer : a\"" + }, + { + "Answer": 249.99999999999994, + "Options": "a ) rs 200 , b ) rs 250 , c ) rs 300 , d ) rs 450 , e ) rs 550", + "Correct": "b", + "Explanation": "\"suppose the amount in the beginning was rs \u2019 x \u2019 money spent on clothes = rs 1 x / 3 balance = rs 2 x / 3 money spent on food = 1 / 5 of 2 x / 3 = rs 2 x / 15 balance = 2 x / 3 - 2 x / 15 = rs 8 x / 15 money spent on travel = 1 / 4 of 8 x / 15 = rs 2 x / 15 = 8 x / 15 - 2 x / 15 = 6 x / 15 = rs 2 x / 5 therefore 2 x / 5 = 100 = 250 answer : b\"" + }, + { + "Answer": 180.83333333333331, + "Options": "a ) a ) 165 , b ) b ) 220 , c ) c ) 310 , d ) d ) 185 , e ) e ) 181", + "Correct": "e", + "Explanation": "loan amount : rs . 15000 / - @ 11.5 % interest per month = 15000 / - * 11.5 % = rs . 1725 interest for one day = 1725 / 30 = 57.50 interest for 7 days is = 57.50 * 7 = 403 fd amount is = rs . 10000 / - @ 9.5 % interest per month = 10000 * 9.5 % = 950 / - interest for 7 days = 950 / 30 * 7 = 222 interest amount to be paid by sam = 403 - 222 = 181 / - for 7 days answer is e" + }, + { + "Answer": 2, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "c", + "Explanation": "\"apparently it ' s d = x ^ 2 - x ^ 3 instead of d = x ^ 2 - d ^ 3 . in this case : the x - intercept is the value ( s ) of x for d = 0 . 0 = x ^ 2 - x ^ 3 ; 0 = x ^ 2 ( 1 - x ) ; x = 0 or x = 1 . answer : c .\"" + }, + { + "Answer": 5, + "Options": "a ) 5 % decrease , b ) 5 % increase , c ) 10 % decrease , d ) 15 % decrease , e ) none of these", + "Correct": "b", + "Explanation": "we have , receipts = price x sales therefore , net % change in receipts = ( x + y + xy / 100 ) % = [ - 30 + 50 + ( - 30 x 50 ) / 100 ] % = 5 % increase . answer : b" + }, + { + "Answer": 49, + "Options": "a ) 20 , b ) 49 , c ) 22 , d ) 23 , e ) none", + "Correct": "b", + "Explanation": "\"sol . let the total number of workers be x . then , 8000 x = ( 20000 \u00d7 7 ) + 6000 ( x \u2013 7 ) \u2039 = \u203a 2000 x = 98000 \u2039 = \u203a x = 49 . answer b\"" + }, + { + "Answer": 0.7499999999999999, + "Options": "a ) 1 / 3 , b ) 3 / 2 , c ) 3 / 4 , d ) 3 , e ) 3 / 5", + "Correct": "c", + "Explanation": "\"should be a sub - 600 level q . . volume = { 3 / 5 } / { 4 / 5 } = 3 / 4 c\"" + }, + { + "Answer": 60, + "Options": "a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80", + "Correct": "c", + "Explanation": "\"total people at party = 150 women = 70 so men 150 - 70 = 80 no . of pple who tried appetizer = 150 - 60 ( given info ) = 90 no of women who tried appetizer = 30 so remaining ppl ( men ) who tried the appetizer = 90 - 30 = 60 correct option c\"" + }, + { + "Answer": 47.99999999999999, + "Options": "a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 48", + "Correct": "e", + "Explanation": "\"0.036 * 10 ^ 5 can be written as 3600 75000 * 10 ^ ( - 3 ) can be written as 75 required = 3600 / 75 = 48 answer : e\"" + }, + { + "Answer": 9999.99999999988, + "Options": "a ) rs . 15000 , b ) rs . 12000 , c ) rs . 10000 , d ) rs . 20000 , e ) none of these", + "Correct": "c", + "Explanation": "in simple words s . i = ptr / 100 = ( p * 1 * 10 ) / 100 p / 10 here amount a = p + s . i = p + p / 10 = 11 p / 10 . . . . now for compound interest when calculated half yearly amount = p [ 1 + r / 200 ] ^ 2 t = p [ 1 + 10 / 200 ] ^ 2 * 1 = 441 p / 400 here its given in the question dat diff btwn simple interest and compound interest half yearly . . . is 25 = > 441 p / 400 - 11 p / 10 = 25 = > p / 400 = 25 = > p = 400 * 25 = 10000 so sum = 10000 answer : c" + }, + { + "Answer": 8205, + "Options": "a ) 2480 , b ) 3490 , c ) 6785 , d ) 8225 , e ) 9255", + "Correct": "d", + "Explanation": "\"you ' ll never need a formula for the sums of squares on the actual gmat . you do n ' t need to use that formula here , though it ' s not all that straightforward to solve without one . two different approaches : 16 ^ 2 + 17 ^ 2 + 18 ^ 2 + . . . + 30 ^ 2 = ( 15 + 1 ) ^ 2 + ( 15 + 2 ) ^ 2 + ( 15 + 3 ) ^ 2 + . . . + ( 15 + 15 ) ^ 2 now we can expand each square ; they are all in the ( x + y ) ^ 2 = x ^ 2 + 2 xy + y ^ 2 pattern . = ( 15 ^ 2 + 2 * 15 + 1 ^ 2 ) + ( 15 ^ 2 + 4 * 15 + 2 ^ 2 ) + ( 15 ^ 2 + 6 * 15 + 3 ^ 2 ) + . . . + ( 15 ^ 2 + 30 * 15 + 15 ^ 2 ) now we have fifteen 15 ^ 2 terms , so adding these gives 15 * 15 ^ 2 = 15 ^ 3 = 3375 . we also have the entire sum 1 ^ 2 + 2 ^ 2 + . . . + 15 ^ 2 , which we know is equal to 1240 . finally adding the middle terms , we have : 2 * 15 + 4 * 15 + 6 * 15 + . . . + 30 * 15 = 15 ( 2 + 4 + 6 + . . . . + 30 ) = 15 * 2 * ( 1 + 2 + 3 + . . . + 15 ) = 15 * 2 * 8 * 15 = 3600 so the sum must be 3375 + 1240 + 3600 = 8215 alternatively , we can use a different factoring pattern . we want to find the value of 30 ^ 2 + 29 ^ 2 + . . . + 17 ^ 2 + 16 ^ 2 . well if we subtract 15 ^ 2 + 14 ^ 2 + . . . . + 2 ^ 2 + 1 ^ 2 from this , the answer will be 1240 less than what we want to find . so if we can find the value of 30 ^ 2 + 29 ^ 2 + . . . + 17 ^ 2 + 16 ^ 2 - ( 15 ^ 2 + 14 ^ 2 + . . . . + 2 ^ 2 + 1 ^ 2 ) then we can add 1240 to get the answer . now grouping the terms above to get differences of squares , we have = ( 30 ^ 2 - 15 ^ 2 ) + ( 29 ^ 2 - 14 ^ 2 ) + . . . + ( 16 ^ 2 - 1 ^ 2 ) and factoring each of these using x ^ 2 - y ^ 2 = ( x + y ) ( x - y ) , we have = 45 * 15 + 43 * 15 + 41 * 15 + . . . + 17 * 15 = 15 ( 45 + 43 + 41 + . . . + 17 ) in brackets we have an equally spaced sum with fifteen terms , which we can evaluate using the familiar formula . so the above equals 15 * 15 * 62 / 2 = 6975 and adding back the 1250 , we get the answer of 8225 . ( ans d )\"" + }, + { + "Answer": 0.3125, + "Options": "a ) 1 / 2 , b ) 1 / 4 , c ) 3 / 8 , d ) 3 / 16 , e ) 5 / 16", + "Correct": "e", + "Explanation": "one possible case is : girl - girl - girl - boy - boy the probability of this is 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 32 there are 5 c 3 = 10 such cases so we should multiply by 10 . p ( two boys and three girls ) = 10 / 32 = 5 / 16 the answer is e ." + }, + { + "Answer": 8.799999999999997, + "Options": "a ) 5 kg , b ) 6.625 kg , c ) 6.25 kg , d ) 6.35 kg , e ) 8.8 kg", + "Correct": "e", + "Explanation": "sodium chloride in 100 kg = 1 / 5 x 100 = 20 kg ammonium in 100 kg = 4 / 5 x 100 = 80 kg now 80 is 25 parts out of ( 25 + 9 ) = 34 parts . hence 9 parts = 9 / 25 x 80 = 28.8 amount to be added = 28.8 - 20 = 8.8 kg answer : e" + }, + { + "Answer": 72, + "Options": "a ) 24 , b ) 72 , c ) 297 , d ) 267 , e ) 29", + "Correct": "b", + "Explanation": "\"explanation : 17 - 5 = 12 12 x 6 = 72 answer : b\"" + }, + { + "Answer": 232, + "Options": "a ) $ 208 , b ) $ 216 , c ) $ 224 , d ) $ 232 , e ) $ 240", + "Correct": "d", + "Explanation": "let the shares for a , b , and c be x , 2 x , and 4 x respectively . 7 x = 406 x = 58 4 x = 232 the answer is d ." + }, + { + "Answer": 167, + "Options": "a ) a ) 130 , b ) b ) 134 , c ) c ) 148 , d ) d ) 158 , e ) e ) 167", + "Correct": "e", + "Explanation": "\"d = d * q + r d = 18 * 9 + 5 d = 162 + 5 d = 167 answer e\"" + }, + { + "Answer": 15, + "Options": "a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 30 %", + "Correct": "b", + "Explanation": "initially the mixture contains 20 % of 15 = 15 * ( 20 / 100 ) = 3 lts of alcohol after mixing another 5 lts of water . . . the total liquid is 20 lts . . so alcohol percentage = ( 3 / 20 ) * 100 = 15 % answer : b" + }, + { + "Answer": 5.5, + "Options": "a ) 5 / 2 , b ) 10 / 3 , c ) 7 / 2 , d ) 14 / 3 , e ) 11 / 2", + "Correct": "e", + "Explanation": "\"for 2 c ^ 2 + 5 c = 12 roots are [ - 5 + sqrt ( 25 + 96 ) ] / 4 or [ - 5 - sqrt ( 25 + 96 ) ] / 4 = 1.5 or - 4 hence larger root 1.5 is 1.5 - ( - 4 ) = 5.5 = 11 / 2 greater than smaller root ( - 4 ) . hence option ( e ) .\"" + }, + { + "Answer": 360, + "Options": "a ) $ 260 , b ) $ 360 , c ) $ 160 , d ) $ 460 , e ) $ 560", + "Correct": "b", + "Explanation": "\"a = 1 / 3 ( b + c ) = > c = 3 a - b - - - ( 1 ) b = 2 / 7 ( a + c ) = > c = 3.5 b - a - - ( b ) a - b = $ 10 a = 10 + b ( 1 ) = = = > c = 30 + 3 b - b = 2 b + 30 = = > 2 b - c = - 30 - - - ( 3 ) ( 2 ) = = = > c = 3.5 b - b - 10 = 2.5 b - 10 = = > 2.5 b - c = 10 - - - ( 4 ) from ( 4 ) and ( 3 ) 0.5 b = 40 b = $ 80 a = $ 90 c = 270 - 80 = $ 190 total amount = 90 + 80 + 190 = $ 360 answer : b\"" + }, + { + "Answer": 60, + "Options": "a ) 52 , b ) 56 , c ) 60 , d ) 64 , e ) 68", + "Correct": "c", + "Explanation": "\"let c be the capacity of the can . ( 5 / 8 ) * ( c - 20 ) + 20 = ( 3 / 4 ) * c 5 c - 100 + 160 = 6 c c = 60 the answer is c .\"" + }, + { + "Answer": 7, + "Options": "a ) 3 , b ) 7 , c ) 11 , d ) 21 , e ) 24", + "Correct": "b", + "Explanation": "solution h . c . f . of 2436 and 1001 is 7 . also , h . c . f . of 105 and 7 is 7 . \u2234 h . c . f . of 105 , 1001 and 2436 is 7 . answer b" + }, + { + "Answer": 12, + "Options": "a ) 5 , b ) 10 , c ) 12 , d ) 40 , e ) 50", + "Correct": "c", + "Explanation": "solution let the initial number of persons be x . then 16 x + 12 x 15 = 15.5 ( x + 20 ) = 0.5 x = 6 x = 12 . answer c" + }, + { + "Answer": 6, + "Options": "a ) 0.5 , b ) 1 , c ) 1.5 , d ) 2 , e ) 6", + "Correct": "e", + "Explanation": "let ' s say c = 3 , b = 2 , a = 2 so that our 1 st expression holds true . now , ibsert those numbers in the second expression and we ' ll get 6 answer e ( hopefully ) ) )" + }, + { + "Answer": 612, + "Options": "a ) $ 255 , b ) $ 275 , c ) $ 510 , d ) $ 612 , e ) $ 2,550", + "Correct": "d", + "Explanation": "total no . of boxes = 3060000 / ( 20 \u00d7 20 \u00d7 15 ) = 510 total cost = 510 \u00d7 $ 1.20 = $ 612 answer d" + }, + { + "Answer": 6, + "Options": "a ) 0 , b ) 6 , c ) 11 , d ) 9 , e ) 7", + "Correct": "b", + "Explanation": "\"1271 * 1275 * 1277 * 1285 = ( 1272 - 2 ) ( 1272 + 3 ) ( 1284 - 7 ) ( 1284 + 1 ) = ( multiple of 12 - 1 ) ( multiple of 12 + 3 ) ( multiple of 12 - 7 ) ( multiple of 12 + 1 ) now , if we expand this expression all terms but the last one will have a multiple of 12 in them , thus will leave no remainder upon division by 12 , the last term will be ( - 2 ) ( 3 ) ( - 7 ) ( 1 ) = 42 . thus the question becomes : what is the remainder upon division of 42 by 12 ? the answer to this question is 6 . answer : b\"" + }, + { + "Answer": 611, + "Options": "a ) 654 , b ) 655 , c ) 611 , d ) 657 , e ) 658", + "Correct": "c", + "Explanation": "\"total cost 940 940 * 35 / 100 = 329 so the cut in amount is 329 the less amount to be spend is 940 - 329 = 611 answer : c\"" + }, + { + "Answer": 1400, + "Options": "a ) $ 1200 , b ) $ 1500 , c ) $ 1400 , d ) $ 1250 , e ) $ 1350", + "Correct": "c", + "Explanation": "\"50 pages typed 1 x 20 pages typed 2 x ( original + one revision ) 30 pages typed 3 x ( original + two revisions ) 50 ( 10 ) + 20 ( 10 + 5 ) + 30 ( 10 + 5 + 5 ) = 500 + 300 + 600 = 1400 answer - c\"" + }, + { + "Answer": 19, + "Options": "a ) 19 , b ) 25 , c ) 35 , d ) 45 , e ) 55", + "Correct": "a", + "Explanation": "\"a 1 = 120 / 3 = 40 a 2 = a 1 - 7 = 33 sum of second list = 33 * 3 = 99 therefore the number = 99 - 80 = 19 answer : a\"" + }, + { + "Answer": 58.888888888888886, + "Options": "a ) 50.78 kg , b ) 49.32 kg , c ) 61.67 kg , d ) 58.88 kg , e ) 70.89 kg", + "Correct": "d", + "Explanation": "\"total weight of 50 + 40 students = 50 * 50 + 40 * 70 = 2500 + 2800 average weight of the class is = 5300 / 90 = 58.88 kg answer is d\"" + }, + { + "Answer": 8, + "Options": "a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14", + "Correct": "b", + "Explanation": "\"let dan ' s present age be x . x + 20 = 7 ( x - 4 ) 6 x = 48 x = 8 the answer is b .\"" + }, + { + "Answer": 40.00000000000001, + "Options": "a ) 40 , b ) 45 , c ) 38 , d ) 50 , e ) 39", + "Correct": "a", + "Explanation": "a 40 let , father \u2019 s current age is a years . then , man \u2019 s current age = [ ( 2 / 5 ) a ] years . therefore , [ ( 2 / 5 ) a + 8 ] = ( 1 / 2 ) ( a + 8 ) 2 ( 2 a + 40 ) = 5 ( a + 8 ) a = 40" + }, + { + "Answer": 10, + "Options": "a ) 18 , b ) 56 , c ) 12 , d ) 17 , e ) 10", + "Correct": "e", + "Explanation": "\"initial average age of the 10 persons be p . age of the new person q . sum of the ages of the initial 10 persons = 10 p new average = ( p - 3 ) 10 ( p - 3 ) = 10 p - 40 + q = > q = 10 answer : e\"" + }, + { + "Answer": 0.2857142857142857, + "Options": "a ) 1 / 7 , b ) 3 / 14 , c ) 1 / 2 , d ) 2 / 7 , e ) 3 / 4", + "Correct": "d", + "Explanation": "\"for n ( n + 1 ) to be a multiple of 7 , either n or n + 1 has to be a multiple of 7 . thus n must be of the form 7 k or 7 k - 1 . the probability is 2 / 7 . the answer is d .\"" + }, + { + "Answer": 182, + "Options": "a ) 178.27 cm , b ) 182.29 cm , c ) 978.29 cm , d ) 178.89 cm , e ) 176.29 cm", + "Correct": "b", + "Explanation": "\"calculated average height of 35 boys = 184 cm . wrong total height of 35 boys = 184 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 184 cm - ( 166 cm - 106 cm ) / 35 = 184 cm - 60 / 35 cm = 184 cm - 1.71 cm = 182.29 cm . answer : b\"" + }, + { + "Answer": 40, + "Options": "a ) 25 , b ) 40 , c ) 35 , d ) 30 , e ) 28", + "Correct": "b", + "Explanation": "\"as half the circle shape consist of 27 - 7 = 20 boys , so total number of boys in full circle = 2 * 20 = 40 answer : b\"" + }, + { + "Answer": 17.820424948594926, + "Options": "a ) 18 % , b ) 20 % , c ) 25 % , d ) 60 % , e ) 80 %", + "Correct": "a", + "Explanation": "listed selling price of chair = 72.95 $ discounted selling price of chair = 59.95 $ discount = 72.95 - 59.95 = 13 $ % decrease in price of chair = ( 13 / 72.95 ) * 100 % = 18 % approx answer a" + }, + { + "Answer": 0.8599999999999998, + "Options": "a ) 0.68 , b ) 0.086 , c ) 0.86 , d ) 0.068 , e ) none of them", + "Correct": "c", + "Explanation": "\"given expression = ( 0.96 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.96 ) ( power 2 ) + ( 0.96 x 0.1 ) + ( 0.1 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 0.96 - 0.1 ) = 0.86 answer is c .\"" + }, + { + "Answer": 25, + "Options": "a ) 88 , b ) 27 , c ) 36 , d ) 80 , e ) 25", + "Correct": "e", + "Explanation": "\"speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 150 + 100 = 250 m . time taken = 250 / 10 = 25 sec . answer : e\"" + }, + { + "Answer": 6, + "Options": "a ) 2 , b ) 4 , c ) 12 , d ) 7 , e ) 6", + "Correct": "e", + "Explanation": "since there are 5 colors , if you take 5 plates , you could still have 1 plate per color and not have a match . therefore , upon taking the 6 th plate , you will definitely have a match since the 6 th plate will form at least a pair with the 1 st 5 so 5 + 1 = 6 answer is e" + }, + { + "Answer": 1015, + "Options": "a ) 1008 , b ) 1015 , c ) 1022 , d ) 1032 , e ) none", + "Correct": "b", + "Explanation": "\"solution required numbers = ( l . c . m of 12 , 16,18 , 21,28 ) + 7 \u2039 = \u203a 1008 + 7 = 1015 . answer b\"" + }, + { + "Answer": 176, + "Options": "a ) 175 , b ) 176 , c ) 177 , d ) 178 , e ) 179", + "Correct": "b", + "Explanation": "b = d * q + r b = 14 * 12 + 8 b = 168 + 8 b = 176" + }, + { + "Answer": 19, + "Options": "a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19", + "Correct": "e", + "Explanation": "\"let n be the number of participants . the number of games is nc 2 = n * ( n - 1 ) / 2 = 171 n * ( n - 1 ) = 342 = 19 * 18 ( trial and error ) the answer is e .\"" + }, + { + "Answer": 76.4, + "Options": "a ) 76.5 , b ) 58 , c ) 39.8 , d ) 90.3 , e ) 66.67", + "Correct": "a", + "Explanation": "\"mean = ( sum of all no . in series ) / ( no . in series ) m 1 = 62 = ( x + 28 + 50 + 78 + 104 ) / ( 5 ) 62 x 5 = 260 + x x = 50 therefore mean of 2 nd series m 2 = ( x + 48 + 62 + 98 + 124 ) / 5 m 2 = 76.5 answer = a\"" + }, + { + "Answer": 191.25, + "Options": "a ) 191 , b ) 192 , c ) 193 , d ) 212 , e ) 213", + "Correct": "b", + "Explanation": "\"total movies submitted are 765 . as per question we need to take 1 / 4 of 765 to be considered for top 10 movies = 191.25 approximate the value we 192 . answer : option b is the correct answer . .\"" + }, + { + "Answer": 340, + "Options": "a ) 180 , b ) 220 , c ) 260 , d ) 300 , e ) 340", + "Correct": "e", + "Explanation": "each child takes a total of 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 = 11 * 12 / 2 = 66 apples . the total number of apples taken by 10 children is 10 * 66 = 660 the number of apples left in the end is 1000 - 660 = 340 apples . the answer is e ." + }, + { + "Answer": 0.3125, + "Options": "a ) 1 / 3 , b ) \u00bc , c ) 9 / 25 , d ) 5 / 16 , e ) 0", + "Correct": "d", + "Explanation": "\"prime digits are : 2 , 3 , 5 , 7 total number of 2 digit # s with both digits prime are : 4 * 4 = 16 out of these numbers divisible by 3 = 33 , 27 , 57 , 72 and 75 . i had to find the numbers manually using the 4 numbers above . = > prob = 5 / 16 . ans d . took me 3 : 20 mins .\"" + }, + { + "Answer": 4000.000000000002, + "Options": "a ) 3000 , b ) 4000 , c ) 5000 , d ) 5500 , e ) 6000", + "Correct": "b", + "Explanation": "investment in 12 % stock be x then investment 15 % stock = ( 12000 - x ) 12 / 120 * x + 15 / 125 * ( 12000 - x ) = 1360 x = 4000 answer b" + }, + { + "Answer": 7, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10", + "Correct": "b", + "Explanation": "42.24 = 14 k + km / 50 . . . we can rewrite the number as follows : 42 + 0.24 = 14 k + km / 50 . . . . . . . . since k is integer , then 42 = 14 k . . . . . . . . . . k = 3 0.24 = km / 50 . . . . . . 24 / 100 = 3 m / 50 . . . . . . m = 4 k + m = 3 + 4 = 7 answer : b" + }, + { + "Answer": 30, + "Options": "a ) 15 , b ) 30 , c ) 35 , d ) 45 , e ) 55", + "Correct": "b", + "Explanation": "\"let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 80 x - ( 5 * 30 ) = 90 ( x - 5 ) 300 = 10 x = > x = 30 answer : b\"" + }, + { + "Answer": 100, + "Options": "a ) a ) 100 , b ) b ) 110 , c ) c ) 120 , d ) d ) 130 , e ) e ) 140", + "Correct": "a", + "Explanation": "\"a + b + c = 450 a + c = 200 b + c = 350 - - - - - - - - - - - - - - a + b + 2 c = 550 a + b + c = 450 - - - - - - - - - - - - - - - - c = 100 answer : a\"" + }, + { + "Answer": 749.9999999999999, + "Options": "a ) $ 750 , b ) $ 350 , c ) $ 650 , d ) $ 550 , e ) $ 850", + "Correct": "a", + "Explanation": "\"if linda spent 2 / 3 of her savings on furniture , the rest 3 / 3 - 2 / 3 = 1 / 3 on a tv but the tv cost her $ 250 . so 1 / 3 of her savings is $ 250 . so her original savings are 3 times $ 250 = $ 750 correct answer a\"" + }, + { + "Answer": 35, + "Options": "a ) 40 , b ) 15 , c ) 35 , d ) 20 , e ) 25", + "Correct": "c", + "Explanation": "so , according to a mean of a set of even numbers from 20 to 60 = ( 20 + 60 ) / 2 = 40 and mean of a set of even numbers from 10 to 140 = ( 10 + 140 ) / 2 = 75 difference = 75 - 40 = 35 answer : c ." + }, + { + "Answer": 20, + "Options": "a ) 20 , b ) 40 , c ) - 20 , d ) 0 , e ) - 40", + "Correct": "c", + "Explanation": "\"there will be two cases x + 10 = 10 and x + 10 = - 10 solve for x = > x = 10 - 10 = > x = 0 or x = - 10 - 10 = > x = - 20 the sum of both values will be 0 + - 20 = - 20 answer is c\"" + }, + { + "Answer": 34, + "Options": "a ) 25 , b ) 34 , c ) 39 , d ) 21 , e ) 11", + "Correct": "b", + "Explanation": "\"add the numbers of doughnuts . 12 + 12 + 10 = 34 . answer is b .\"" + }, + { + "Answer": 799.9999999999993, + "Options": "a ) 80 , b ) 110 , c ) 160 , d ) 800 , e ) 400", + "Correct": "d", + "Explanation": "we start by creating a variable for the total number of students in the math course . we can say : t = total number of students in the math course next , we can use variable t in an equation that we translate from the given information . we are given that , of the final grades received by the students in a certain math course , 1 / 5 are a ' s , 1 / 4 are b ' s , 1 / 2 are c ' s , and the remaining 40 grades are d ' s . since this represents all the grades in the class , it represents all the students in the class . thus we know : # a \u2019 s + # b \u2019 s + # c \u2019 s + # d \u2019 s = total number of students in the class 1 / 5 ( t ) + \u00bc ( t ) + \u00bd ( t ) + 40 = t we can multiply the entire equation by 20 to cancel out the denominators of the fractions and we have : 4 t + 5 t + 10 t + 800 = 20 t 19 t + 800 = 20 t 800 = t there are a total of 800 students in the math class . answer is d ." + }, + { + "Answer": 9, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10", + "Correct": "d", + "Explanation": "to get 40 points as end of season we need another 32 points or more from remaining 15 matches : option a = 6 * 3 + 9 * 1 = 27 option b = 7 * 3 + 8 * 1 = 29 option c = 8 * 3 + 7 * 1 = 31 option d = 9 * 3 + 6 * 1 = 33 hence option d - 9" + }, + { + "Answer": 6, + "Options": "a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8", + "Correct": "c", + "Explanation": "explanation : on dividing 427398 by 12 we get the remainder 6 , so 6 should be subtracted answer : option c" + }, + { + "Answer": 41.60000000000002, + "Options": "a ) $ 41.60 , b ) $ 45.00 , c ) $ 50.75 , d ) $ 55.75 , e ) $ 61.25", + "Correct": "a", + "Explanation": "looking at the values / percentage , its clear that company x costlier than company y just observed the oa ; they have 4 distinct numbers after decimal point total calculation of company x gives . 00 + . 00 + . 50 = . 50 at the decimal total calculation of company y gives . 00 + . 90 + . 00 = . 90 at the decimal there difference provides . 60 at the decimal ; only 41.60 fits in answer = a" + }, + { + "Answer": 40.44166666666667, + "Options": "a ) $ 30.14 , b ) 40.44 , c ) 34.66 , d ) 32.29 , e ) 33.16", + "Correct": "b", + "Explanation": "\"211 * 15 = 3165 / 100 = 31.65 211 + 31.65 = 242.65 242.65 / 6 = 40.44 answer : b\"" + }, + { + "Answer": 1000, + "Options": "a ) 800 , b ) 900 , c ) 1000 , d ) 1100 , e ) none of these", + "Correct": "c", + "Explanation": "as per question stem 2 / 5 m ( portion of men employees who are managers ) + 400 ( portion of female employees who are managers ) = 2 / 5 t ( portion of total number of employees who are managers ) , thus we get that 2 / 5 m + 400 = 2 / 5 t , or 2 / 5 ( t - m ) = 400 , from here we get that t - m = 1000 , that would be total number of female employees and the answer ( c )" + }, + { + "Answer": 10, + "Options": "a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 14", + "Correct": "b", + "Explanation": "in one hour , the crow eats 1 / 40 of the nuts . ( 1 / 4 ) / ( 1 / 40 ) = 10 hours the answer is b ." + }, + { + "Answer": 6, + "Options": "a ) 2 pm , b ) 9 pm , c ) 3 pm , d ) 6 pm , e ) 7 pm", + "Correct": "d", + "Explanation": "a day has 24 hrs . assume x hours have passed . remaining time is ( 24 - x ) 24 \u2212 x = 2 / 6 x \u21d2 x = 18 time is 6 pm answer : d" + }, + { + "Answer": 35, + "Options": "a ) 35 , b ) 42 , c ) 45 , d ) 49 , e ) 54", + "Correct": "a", + "Explanation": "\"first step will be to break down all the numbers into their prime factors . 105 = 3 * 5 * 7 21 = 7 * 3 35 = 7 * 5 45 = 3 * 3 * 5 so , ( 105 ) ^ 3 = 3 * 7 * 7 * 5 * 3 * 3 * 5 * b therefore ( 3 * 5 * 7 ) ^ 3 = 3 ^ 3 * 5 ^ 2 * 7 ^ 2 * b therefore , b = 3 ^ 3 * 5 ^ 3 * 7 ^ 3 / 3 ^ 3 * 5 ^ 2 * 7 ^ 2 b = 5 * 7 = 35 correct answer a .\"" + }, + { + "Answer": 100, + "Options": "a ) $ 100 , b ) $ 220 , c ) $ 280 , d ) $ 300 , e ) $ 360", + "Correct": "a", + "Explanation": "\"total value of the prize = $ 400 number of people = 20 2 / 5 of 400 ( = $ 160 ) should be distributed among 3 / 5 of 20 ( = 12 people ) with each getting $ 20 each . remaining money = 400 - 160 = $ 240 . now in order to ' maximize ' 1 prize , we need to minimise the others and we have been given that each should get $ 20 . thus , minimising the remaining 7 people ( = 20 - 12 - 1 . ' - 1 ' to exclude 1 that needs to be maximised ) = 7 * 20 = 140 . thus the maximum award can be = 240 - 140 = $ 100 , hence a is the correct answer .\"" + }, + { + "Answer": 179, + "Options": "a ) 178.27 cm , b ) 179.29 cm , c ) 978.29 cm , d ) 178.89 cm , e ) 176.29 cm", + "Correct": "b", + "Explanation": "\"calculated average height of 35 boys = 181 cm . wrong total height of 35 boys = 181 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 181 cm - ( 166 cm - 106 cm ) / 35 = 181 cm - 60 / 35 cm = 181 cm - 1.71 cm = 179.29 cm . answer : b\"" + }, + { + "Answer": 399.6, + "Options": "a ) 362.33 , b ) 399.6 , c ) 702.33 , d ) 702 , e ) none of them", + "Correct": "b", + "Explanation": "\". 3 33 333 33.3 - - - - - - - - - - 399.6 - - - - - - - - - - answer is b\"" + }, + { + "Answer": 22, + "Options": "a ) 3 , b ) 5 , c ) 6 , d ) 22 , e ) 18", + "Correct": "d", + "Explanation": "\"x can be written as 82 k + 5 or x = 5 , 87,169 , etc . x + 17 = 82 k + 5 + 17 = 82 k + 22 or x + 17 = 22,104 , 186 etc . when divided by 41 , we will get the remainder 22 . d\"" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 8 , e ) 9", + "Correct": "c", + "Explanation": "let number of apples = a number of oranges = b a + b = 15 - - - 1 . 48 = ( . 4 a + . 6 b ) / 15 = > 48 = 4 a + 6 b - - - - 2 solving 1 and 2 , we get a = 9 b = 6 let the number of oranges put back = c 45 * ( 15 - c ) = 40 * 9 + 60 ( 6 - c ) = > c = 3 answer c" + }, + { + "Answer": 100, + "Options": "a ) 100 , b ) 200 , c ) 10 ^ 4 , d ) 10 ^ 5 , e ) 10 ^ 6", + "Correct": "a", + "Explanation": "if richter scale reading goes from x - 1 to x it will be 10 if richter scale reading goes from 3 to 4 it will be 10 if richter scale reading goes from 4 to 5 it will be 10 so it will from 3 to 5 i . e 4,5 = 10 * 10 = 10 ^ 2 answer is a" + }, + { + "Answer": 46, + "Options": "a ) 12 liters , b ) 32 liters , c ) 46 liters , d ) 50 liters , e ) 34 liters", + "Correct": "c", + "Explanation": "\"milk = 3 / 5 * 115 = 69 liters water = 46 liters 69 : ( 46 + p ) = 3 : 4 138 + 3 p = 276 = > p = 46 46 liters of water are to be added for the ratio become 3 : 4 . answer : c\"" + }, + { + "Answer": 0.22857142857142856, + "Options": "a ) 7 / 25 , b ) 3 / 25 , c ) 8 / 35 , d ) 2 / 13 , e ) 3 / 17", + "Correct": "c", + "Explanation": "p ( a n b ) = p ( a ) . p ( b ) p ( a n b ) = 4 / 7 . 2 / 5 p ( a n b ) = 8 / 35 . c" + }, + { + "Answer": 0.0049999999999999975, + "Options": "a ) $ 0.25 , b ) $ 0.12 , c ) $ 0.05 , d ) $ 0.003 , e ) $ 0.005", + "Correct": "e", + "Explanation": "\"cost per capsule in r is 6.25 / 250 = 0.625 / 25 = 0.025 cost per capsule in t is 3.00 / 100 = 0.03 the difference is 0.005 the answer is e\"" + }, + { + "Answer": 0.64, + "Options": "a ) 2 / 7 , b ) 9 / 4 , c ) 16 / 25 , d ) 7 / 1 , e ) 7 / 2", + "Correct": "c", + "Explanation": "for a 2 nd degree equation ax 2 + bx _ c = 0 has equal roots the condition is b 2 - 4 ac = 0 in the given equation ( 5 k ) ^ 2 - 4 * 2 k * 2 = 0 by solving this equation we get k = 0 , k = 16 / 25 answer : c" + }, + { + "Answer": 26, + "Options": "a ) 16 days , b ) 26 days , c ) 27 days , d ) 28 days , e ) 29 days", + "Correct": "b", + "Explanation": "the bacteria doubles each day , so after 29 days , the dish was half full . after 28 days , the dish was one quarter full . after 27 days , the dish was one eighth full . after 26 days , the dish was one sixteenth full . the answer is b ." + }, + { + "Answer": 2.857142857142857, + "Options": "a ) 3 / 2 , b ) 5 / 4 , c ) 10 / 3 , d ) 20 / 7 , e ) 25 / 9", + "Correct": "d", + "Explanation": "n = 3 d / 5 j = n / 6 = d / 10 the average of november and january is ( n + j ) / 2 = 7 d / 10 / 2 = 7 d / 20 d is 20 / 7 times the average of november and january . the answer is d ." + }, + { + "Answer": 2, + "Options": "a ) 123 , b ) 127 , c ) 2 , d ) 305 , e ) 505", + "Correct": "c", + "Explanation": "\"explanation : required number = h . c . f . of ( 1557 - 7 ) and ( 2037 - 5 ) = h . c . f . of 1550 and 2032 = 2 . answer : c\"" + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) 14 , c ) 18 , d ) 24 , e ) 23", + "Correct": "a", + "Explanation": "now : rosy = x , david = x + 18 in 6 years rosy = x + 6 , david = x + 18 + 6 or 2 ( x + 6 ) x + 24 = 2 x + 12 x = 12 rosy is 12 years old answer : a" + }, + { + "Answer": 65, + "Options": "a ) 39 , b ) 40 , c ) 65 , d ) 42 , e ) 43", + "Correct": "c", + "Explanation": "solution start with 20 pens . mike gives you 22 pens : 20 + 22 = 42 pens . cindy doubles the number of pens you have : 42 \u00e3 \u2014 2 = 84 pens . sharon takes 19 pens from you : 84 - 19 = 65 pens . so you have 65 at the end . correct answer : c" + }, + { + "Answer": 133, + "Options": "a ) 121 , b ) 133 , c ) 145 , d ) 150 , e ) 165", + "Correct": "b", + "Explanation": "let x , x + 2 and x + 4 be three integers . the sum of the first x and third x + 4 is given by x + ( x + 4 ) 131 less than three times the second 3 ( x + 2 ) is given by 3 ( x + 2 ) - 131 ` ` the sum of the first and third is 131 less than three times the second ' ' gives x + ( x + 4 ) = 3 ( x + 2 ) - 131 solve for x and find all three numbers x = 129 , x + 2 = 131 , x + 4 = 133 as an exercise , check that the sum of the first and third is 131 less than three times b" + }, + { + "Answer": 74, + "Options": "a ) 74 , b ) 76 , c ) 78 , d ) 80 , e ) 82", + "Correct": "a", + "Explanation": "\"a score of 58 was 2 standard deviations below the mean - - > 58 = mean - 2 d a score of 98 was 3 standard deviations above the mean - - > 98 = mean + 3 d solving above for mean t = 74 . answer : a .\"" + }, + { + "Answer": 7, + "Options": "a ) 13 , b ) 15 , c ) 16 , d ) 7 , e ) 18", + "Correct": "d", + "Explanation": "\"12 , 15 , 18 , 21 , 24 , 27 , 30 . 7 numbers . 10 / 3 = 3 and 31 / 3 = 10 = = > 10 - 3 = 7 . therefore 7 digits d )\"" + }, + { + "Answer": 28, + "Options": "a ) 28 , b ) 25 , c ) 35 , d ) 45 , e ) 55", + "Correct": "a", + "Explanation": "\"a 1 = 120 / 3 = 40 a 2 = a 1 - 4 = 36 sum of second list = 36 * 3 = 108 therefore the number = 108 - 80 = 28 answer : a\"" + }, + { + "Answer": 75625, + "Options": "a ) 75625 , b ) 68225 , c ) 72325 , d ) 71225 , e ) 72225", + "Correct": "a", + "Explanation": "explanation : 121 \u00d7 5 ^ 4 = 121 \u00d7 ( 10 / 2 ) ^ 4 = ( 121 \u00d7 10000 ) / 16 = 7.5625 \u00d7 10000 = 75625 answer is a" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 8", + "Correct": "a", + "Explanation": "if the number is divisible by 6 , then the sum of the digits must also be divisible by both 3 and 2 . only 1 yields such a number . answer : a" + }, + { + "Answer": 784, + "Options": "a ) 652 , b ) 589 , c ) 456 , d ) 620 , e ) 784", + "Correct": "e", + "Explanation": "mean = ( 8 + 16 + 24 + 32 + 40 + 48 ) / 6 = 28 median = ( 24 + 32 ) / 2 = 28 product = 28 * 28 = 784 option e" + }, + { + "Answer": 17.1, + "Options": "a ) 17.1 , b ) 17.3 , c ) 17.5 , d ) 17.7 , e ) 17.2", + "Correct": "a", + "Explanation": "\"29.94 / 1.45 = 299.4 / 14.5 = ( 2994 / 14.5 ) x 1 / 10 ) [ here , substitute 171 in the place of 2994 / 14.5 ] = 171 / 10 = 17.1 answer is a .\"" + }, + { + "Answer": 140, + "Options": "a ) 140 , b ) 100 , c ) 125 , d ) 175 , e ) 225", + "Correct": "a", + "Explanation": "\"female = x male = 840 - x x / 2 + 840 - x / 4 = 1 / 3 * ( 840 ) = 280 x = 280 x / 2 = 140 is supposed to be the answer m is missing something correct option a\"" + }, + { + "Answer": 11000, + "Options": "a ) rs . 10000 , b ) rs . 11000 , c ) rs . 12000 , d ) rs . 9000 , e ) rs . 8500", + "Correct": "b", + "Explanation": "explanation total income of 3 members = rs . ( 8000 + 15000 + 6000 ) = rs . 29000 . required income = rs . [ ( 10000 x 4 ) \u2013 29000 ] = rs . ( 40000 \u2013 29000 ) = rs . 11000 . answer b" + }, + { + "Answer": 12, + "Options": "a ) - 12 , b ) 12 , c ) - 1 / 12 , d ) 1 / 12 , e ) 3", + "Correct": "b", + "Explanation": "( 3 / 2 ) x - 3 = 15 = > 3 x - 6 = 30 = > 3 x = 36 = > x = 12 answer : b" + }, + { + "Answer": 9.295068031549134, + "Options": "a ) $ 4.50 , b ) $ 5.10 , c ) $ 9.30 , d ) $ 5.50 , e ) $ 5.60", + "Correct": "c", + "Explanation": "\"i tried using time / rate approach : - initial price difference = 9.80 - 3.20 = 6.60 price of corn increasing by 5 x price of wheat decreasing by x ( 1.4 ) - x = . 4 x since both the quantities are moving towards reducing the price gap hence : - relative increase = 5 x + . 4 x let t be the time by which gap is filled so , 6.6 = t ( 5.4 x ) - > t = ( 6.6 ) / 5.4 x final price = 3.20 + 5 x * t - > 3.20 + 5 * 6.6 / 5.4 = 9.3 answer c .\"" + }, + { + "Answer": 690, + "Options": "a ) 233 , b ) 690 , c ) 287 , d ) 771 , e ) 191", + "Correct": "b", + "Explanation": "\"explanation : total salary of 8 workers and supervisor together = 9 \u00e3 \u2014 430 = 3870 now total salary of 8 workers = 3870 \u00e2 \u02c6 \u2019 870 = 3000 total salary of 9 workers including the new supervisor = 9 \u00e3 \u2014 410 = 3690 salary of the new supervisor = 3690 \u00e2 \u02c6 \u2019 3000 = 690 answer : b\"" + }, + { + "Answer": 10, + "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12", + "Correct": "c", + "Explanation": "6 + 4 = 10 correct answer is c ) 10" + }, + { + "Answer": 128, + "Options": "a ) 128 , b ) 142 , c ) 143 , d ) 141 , e ) 129", + "Correct": "e", + "Explanation": "\"explanatory answer step 1 : find the first and last term of the series the smallest 3 - digit positive integer that leaves a remainder of 5 when divided by 7 is 103 . the largest 3 - digit positive integer that leaves a remainder of 5 when divided by 7 is 999 . the series of numbers that satisfy the condition that the number should leave a remainder of 5 when divided by 7 is an a . p ( arithmetic progression ) with the first term being 103 and the last term being 999 . the common difference of the sequence is 7 . step 2 : compute the number of terms in an a . p , the last term l = a + ( n - 1 ) * d , where ' a ' is the first term , ' n ' is the number of terms of the series and ' d ' is the common difference . therefore , 999 = 103 + ( n - 1 ) * 7 or 999 - 103 = ( n - 1 ) * 7 or 896 = ( n - 1 ) * 7 so , n - 1 = 128 or n = 129 choice e is the correct answer .\"" + }, + { + "Answer": 18, + "Options": "a ) 6 , b ) 12 , c ) 18 , d ) 32 , e ) 48", + "Correct": "c", + "Explanation": "\"3.456789 ^ 9 has 6 * 9 = 54 decimal places . 10 ^ 36 moves the decimal place to the right 36 places . ( 10 ^ 4 * 3.456789 ) ^ 9 has 54 - 36 = 18 digits after the decimal point . the answer is c .\"" + }, + { + "Answer": 60, + "Options": "a ) 25 , b ) 34 , c ) 50 , d ) 60 , e ) 100", + "Correct": "d", + "Explanation": "orange juice concentrate : water : : 1 : 3 total quantity of orange juice = 200 * 6 = 1200 oz so orange juice concentrate : water : : 300 oz : 900 oz no . of 5 oz can = 300 oz / 5 oz = 60 answer d , 60 cans" + }, + { + "Answer": 15, + "Options": "a ) 9 , b ) 12 , c ) 15 , d ) 18 , e ) 21", + "Correct": "c", + "Explanation": "if the average of 10 - pound and 20 - pound boxes is 18 , the ratio of 10 - pound boxes : 20 - pound boxes is 1 : 4 . so out of 30 boxes , 6 are 10 - pound boxes and 24 are 20 - pound boxes . if the average of 10 and 20 - pound boxes is to be 16 , the ratio of 10 - pound boxes : 20 - pound boxes should be 2 : 3 . the number of 10 pound boxes remain the same so we still have 6 of them . to get a ratio of 2 : 3 , the number of 20 - pound boxes must be 9 . we need to remove 15 of the 20 - pound boxes . the answer is c ." + }, + { + "Answer": 160, + "Options": "a ) $ 160 , b ) $ 220 , c ) $ 280 , d ) $ 300 , e ) $ 360", + "Correct": "a", + "Explanation": "total value of the prize = $ 500 number of people = 20 2 / 5 of 500 ( = $ 200 ) should be distributed among 3 / 5 of 20 ( = 12 people ) with each getting $ 20 each . remaining money = 500 - 200 = $ 300 . now in order to ' maximize ' 1 prize , we need to minimise the others and we have been given that each should get $ 20 . thus , minimising the remaining 7 people ( = 20 - 12 - 1 . ' - 1 ' to exclude 1 that needs to be maximised ) = 7 * 20 = 140 . thus the maximum award can be = 300 - 140 = $ 160 , hence a is the correct answer ." + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 3 , c ) 2 , d ) 1 , e ) 0", + "Correct": "a", + "Explanation": "\"3 \u201d 3 = 9 - 3 = 6 answer : a\"" + }, + { + "Answer": 63, + "Options": "a ) 58 , b ) 59 , c ) 60 , d ) 62 , e ) 63", + "Correct": "e", + "Explanation": "\"let x be the number he chose , then 4 \u22c5 x \u2212 142 = 110 4 x = 252 x = 63 correct answer e\"" + }, + { + "Answer": 16, + "Options": "a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20", + "Correct": "c", + "Explanation": "\"144 = 16 * 9 = 18 * 8 there are 16 people in the group today . the answer is c .\"" + }, + { + "Answer": 7.9865771812080535, + "Options": "a ) 7.59 , b ) 7.79 , c ) 7.99 , d ) 8.19 , e ) 8.39", + "Correct": "c", + "Explanation": "distance = 17 km time = 7 / 10 + 10 / 7 = ( 49 + 100 ) / 70 = 149 / 70 hours average speed = ( 17 * 70 ) / 149 = 7.99 km / h the answer is c ." + }, + { + "Answer": 18, + "Options": "a ) 21 , b ) 20 , c ) 19 , d ) 18 , e ) 15", + "Correct": "d", + "Explanation": "marcella has 23 pairs of shoes and loses 9 shoes . to minimize the loss of identical pairs of shoes we want marcella to lose as many identical pairs as possible . this would yield 4 identical pairs and 1 additional shoe ( destroying 5 pairs of shoes ) . the 23 pairs of shoes minus the 5 ' destroyed ' pairs yields 20 pairs that still fulfill the requirements . answer : d" + }, + { + "Answer": 2400, + "Options": "a ) rs . 2400 , b ) rs . 2490 , c ) rs . 2500 , d ) rs . 2550 , e ) rs . 2600", + "Correct": "a", + "Explanation": "let the price of a saree and a shirt be rs . x and rs . y respectively . then , 2 x + 4 y = 1600 . . . . ( i ) and x + 6 y = 1600 . . . . ( ii ) divide equation ( i ) by 2 , we get the below equation . = > x + 2 y = 800 . - - - ( iii ) now subtract ( iii ) from ( ii ) x + 6 y = 1600 ( - ) x + 2 y = 800 - - - - - - - - - - - - - - - - 4 y = 800 - - - - - - - - - - - - - - - - therefore , y = 200 . now apply value of y in ( iii ) = > x + 2 x 200 = 800 = > x + 400 = 800 therefore x = 400 solving ( i ) and ( ii ) we get x = 400 , y = 200 . cost of 12 shirts = rs . ( 12 x 200 ) = rs . 2400 . a" + }, + { + "Answer": 89.6, + "Options": "a ) $ 54.00 , b ) $ 89.60 , c ) $ 90.00 , d ) $ 100.80 , e ) $ 154.80", + "Correct": "b", + "Explanation": "\"correct answer : b the tourist must pay tax on $ 1720 - $ 600 = $ 1120 . thus , the amount of tax he has to pay is 0.08 ( $ 1120 ) = $ 89.60 . the correct answer is b .\"" + }, + { + "Answer": 7, + "Options": "a ) 0 , b ) 1 , c ) 5 , d ) 7 , e ) 9", + "Correct": "d", + "Explanation": "\"i looked for patterns : ^ 2 - units digit 9 ^ 3 - units digit 7 ^ 4 - units digit 1 ^ 5 - units digit 3 hence , we can see that when raised to a power which is multiple of 4 , the units digit is 1 , and when to an even power not multiple of 4 , the units digit is 9 and we can then see : ^ 16 - units digit 1 , or ^ 18 - units digit 9 and ^ 19 - units digit 7 therefore , g = when divided by 10 , the remainder must be 7 . d\"" + }, + { + "Answer": 1620, + "Options": "a ) 1456 , b ) 1563 , c ) 1546 , d ) 1643 , e ) 1635", + "Correct": "e", + "Explanation": "\"let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 15 5 x = 1350 x = 270 large number = 270 + 1365 = 1635 e\"" + }, + { + "Answer": 9, + "Options": "a ) 5 , b ) 7 , c ) 9 , d ) 12 , e ) 14", + "Correct": "c", + "Explanation": "\"let the number of cows be x and their legs be 4 x . let the number of chicken be y and their legs be 2 x . total number of legs = 4 x + 2 y . total number of heads = x + y . the number of legs was 18 more than twice the number of heads . therefore , 2 \u00d7 ( x + y ) + 18 = 4 x + 2 y . or , 2 x + 2 y + 18 = 4 x + 2 y . or , 2 x + 18 = 4 x [ subtracting 2 y from both sides ] . or , 18 = 4 x \u2013 2 x [ subtracting 2 x from both sides ] . or , 18 = 2 x . or , x = 9 [ dividing by 2 on both sides ] . therefore , the number of cows = 9 . correct answer : c ) 9\"" + }, + { + "Answer": 8, + "Options": "a ) 5 , b ) 6 , c ) 8 , d ) 9 , e ) 10", + "Correct": "c", + "Explanation": "\"the lcm of 5 , 7 , and 9 is 315 . the next multiple is 2 * 315 = 630 . 630 + { remainder } = 630 + 4 = 634 , which is 8 less than 642 . answer : c .\"" + }, + { + "Answer": 320, + "Options": "a ) $ 320 , b ) $ 160 , c ) $ 200 , d ) $ 410 , e ) $ 325", + "Correct": "a", + "Explanation": "p = 2 j ; q = p + 20 ; a = 1.15 ( q ) p + j + q + r - 1200 = 11 p + 0.5 p + p + 20 + 1.15 ( p + 20 ) = 1211 p + 0.5 p + p + 20 + 1.15 p + 23 = 1211 p + 0.5 p + p + 1.15 p + 43 = 1211 p + 0.5 p + p + 1.15 p = 1168 3.65 p = 1168 p = 320 answer : a" + }, + { + "Answer": 2.9365079365079367, + "Options": "a ) 195 / 63 , b ) 145 / 63 , c ) 155 / 63 , d ) 125 / 63 , e ) 185 / 63", + "Correct": "e", + "Explanation": "\"( \u221a 1.21 ) / ( \u221a 0.81 ) + ( \u221a 1.44 ) / ( \u221a 0.49 ) 11 / 9 + 12 / 7 = > ( 77 + 108 ) / 63 = > 185 / 63 answer is e .\"" + }, + { + "Answer": 8, + "Options": "a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 0", + "Correct": "d", + "Explanation": "\"the units digit of powers of 3 , cycles in a group of 4 : { 3 , 9 , 7 , 1 } 49 has the form 4 k + 1 , so the units digit of 93 ^ 49 is 3 . the units digit of powers of 5 is always 5 . 3 + 5 = 8 , so the units digit is 8 . the answer is d .\"" + }, + { + "Answer": 10.4, + "Options": "a ) 8.6 , b ) 9.8 , c ) 10.4 , d ) 11.2 , e ) 12.6", + "Correct": "c", + "Explanation": "\"let x be the length of the size 8 shoe . then 0.2 x = 9 / 5 x = 9 inches the size 15 shoe has a length of 9 + 7 / 5 = 10.4 inches the answer is c .\"" + }, + { + "Answer": 1.7999999999999998, + "Options": "a ) 1.5 , b ) 1.8 , c ) 2.1 , d ) 2.4 , e ) 2.7", + "Correct": "b", + "Explanation": "\"let x be the amount of pure alcohol required . 0.35 ( 6 ) + x = 0.5 ( x + 6 ) 0.5 x = 3 - 2.1 x = 1.8 liters the answer is b .\"" + }, + { + "Answer": 0.5, + "Options": "a ) 1 / 2 , b ) 1 / 4 , c ) 3 / 4 , d ) 2 / 3 , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : a \u2217 b \u2217 c / b \u2217 c \u2217 d = 130 / 65 = > a / d = 2 d \u2217 e \u2217 f / c \u2217 d \u2217 e = 250 / 1000 = > f / c = 14 a / d * f / c = 2 * 1 / 4 = 1 / 2 answer : a\"" + }, + { + "Answer": 512, + "Options": "a ) 430 , b ) 450 , c ) 460 , d ) 480 , e ) 512", + "Correct": "e", + "Explanation": "let suppose total number of students in class are x . then from the question we can conclude it that , x \u2217 18 x = x 2 \u2217 16 = > x = 64 total notebooks , = 18 x 2 = ( 18 \u2217 64 \u2217 64 ) = 512 e" + }, + { + "Answer": 0.33333333333333337, + "Options": "a ) 1 / 49 , b ) 4 / 7 , c ) 3 / 7 , d ) 1 / 3 , e ) 40 / 49", + "Correct": "d", + "Explanation": "\"the probability of drawing a pink gumball both times is the same . the probability that she drew two blue gumballs = 16 / 36 = ( 2 / 3 ) * ( 2 / 3 ) therefore probability that the next one she draws is pink = 1 / 3 option ( d )\"" + }, + { + "Answer": 142, + "Options": "a ) 104 , b ) 60 , c ) 52 , d ) 50 , e ) 142", + "Correct": "e", + "Explanation": "\"f ( x ) = 2 x ^ 2 + y f ( 2 ) = 100 = > 2 * ( 2 ) ^ 2 + y = 100 = > 8 + y = 100 = > y = 92 f ( 5 ) = 2 * ( 5 ) ^ 2 + 92 = 142 answer e\"" + }, + { + "Answer": 10000, + "Options": "a ) 10200 , b ) 10000 , c ) 9500 , d ) 9000 , e ) none", + "Correct": "b", + "Explanation": "explanation : = > one - legged = 5 % of 10000 = 500 = > remaining = 10000 - 500 = 9500 = > barefooted = 9500 / 2 = 4750 = > remaining people = 9500 - 4750 = 4750 = > hence required number of shoes = 4750 * 2 + 500 * 1 = 10000 hence ( b ) is the correct answer . answer : b" + }, + { + "Answer": 104.99999999999997, + "Options": "a ) 37.5 , b ) 75 , c ) 105 , d ) 150 , e ) 175", + "Correct": "c", + "Explanation": "\"nope , 150 . i can only get it by following pr ' s backsolving explanation . i hate that . original mixture has 20 % salt and 80 % water . total = x out of which salt = 0.2 x and water = 0.8 x now , 1 / 4 water evaporates and all salt remains . so what remains is 0.2 x salt and 0.6 x water . now 14 gallons salt is added and 7 gallons of water is added . so salt now becomes - > ( 0.2 x + 14 ) and water - - > ( 0.6 x + 7 ) amount of salt is 33.33 % of total . so amount of water is 66.66 % . so salt is half of the volume of water . so ( 0.2 x + 14 ) = ( 0.6 x + 7 ) / 2 = > 0.2 x = 21 solving , x = 105 answer : c\"" + }, + { + "Answer": 888, + "Options": "a ) 246 , b ) 248 , c ) 892 , d ) 15,128 , e ) 20,256", + "Correct": "c", + "Explanation": "\"# of 2 - letter codes possible from 224 different signs = 224 * 224 . # of 2 - letter codes possible from 222 different signs = 222 * 222 . the difference = 224 ^ 2 - 222 ^ 2 = ( 224 - 222 ) ( 224 + 222 ) = 892 . answer : c .\"" + }, + { + "Answer": 4, + "Options": "a ) 8 , b ) 7 , c ) 6 , d ) 5 , e ) 4", + "Correct": "e", + "Explanation": "1 runs once ( one game ) 4 runs twice ( two game ) 5 runs three times ( three games ) so we have ( 1 * 1 + 4 * 2 + 5 * 3 ) / 6 = 24 / 6 = 4 . ans : e ." + }, + { + "Answer": 2.2222222222222223, + "Options": "a ) 7 / 9 , b ) 20 / 9 , c ) 7 / 20 , d ) 9 / 20 , e ) 11 / 20", + "Correct": "b", + "Explanation": "\"1 / r = 1 / x + 1 / y 1 / r = 1 / 4 + 1 / 5 = 9 / 20 r = 20 / 9 the answer is b .\"" + }, + { + "Answer": 528, + "Options": "a ) 627 , b ) 528 soldiers , c ) 626 , d ) 657 , e ) 673", + "Correct": "b", + "Explanation": "assume x soldiers join the fort . 1200 soldiers have provision for 1200 ( days for which provisions last them ) ( rate of consumption of each soldier ) = ( 1200 ) ( 30 ) ( 3 ) kg . also provisions available for ( 1200 + x ) soldiers is ( 1200 + x ) ( 25 ) ( 2.5 ) k as the same provisions are available = > ( 1200 ) ( 30 ) ( 3 ) = ( 1200 + x ) ( 25 ) ( 2.5 ) x = [ ( 1200 ) ( 30 ) ( 3 ) ] / ( 25 ) ( 2.5 ) - 1200 = > x = 528 . answer : b" + }, + { + "Answer": 140, + "Options": "a ) 140 , b ) 143 , c ) 144 , d ) 145 , e ) 150", + "Correct": "a", + "Explanation": "\"explanation : let the number = x , then , x - ( 3 / 5 ) x = 56 , = > ( 2 / 5 ) x = 56 = > 2 x = 56 * 5 , = > x = 140 answer : option a\"" + }, + { + "Answer": 93, + "Options": "a ) 87 , b ) 89 , c ) 90 , d ) 93 , e ) 95", + "Correct": "d", + "Explanation": "\"total score on 3 tests = 85 * 3 = 255 jerry wants the average to be = 87 hence total score on 4 tests should be = 87 * 4 = 348 score required on the fourth test = 348 - 255 = 93 option d\"" + }, + { + "Answer": 32, + "Options": "a ) a ) 32 , b ) b ) 35 , c ) c ) 39 , d ) d ) 40 , e ) e ) 45", + "Correct": "a", + "Explanation": "\"x \u2013 3 / 8 x = 20 x = 32 answer : a\"" + }, + { + "Answer": 350, + "Options": "a ) 350 , b ) 420 , c ) 510 , d ) 320 , e ) 280", + "Correct": "a", + "Explanation": "lcm = 2 * 5 * 5 * 7 = 350 . answer is a" + }, + { + "Answer": 528, + "Options": "a ) $ 24 million , b ) $ 120 million , c ) $ 144 million , d ) $ 240 million , e ) $ 528 million", + "Correct": "e", + "Explanation": "\"convert units to millions as answer is in millions 1996 imports = $ 1.20 bill = $ 1200 mill i . e . 1200 / 12 = $ 100 mill / month 1997 imports = $ 288 mill / 2 month i . e . $ 144 mill / month difference / month = 144 - 100 = 44 difference / year = $ 44 mill * 12 = $ 528 mill answer : e\"" + }, + { + "Answer": 2, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "b", + "Explanation": "\"let x be the amount of liquid q to be added . ( 2 / 5 ) * 25 + x = ( 4 / 9 ) * ( 25 + x ) 450 + 45 x = 500 + 20 x 25 x = 50 x = 2 the answer is b .\"" + }, + { + "Answer": 6, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8", + "Correct": "c", + "Explanation": "4 x + 2.8 y = 42 - - > multiply by 2.5 ( to get the integers ) - - > 10 x + 7 y = 105 - - > only one positive integers solutions x = 6 and y = 5 ( how to solve : 7 y must have the last digit of 5 in order the last digit of the sum to be 5 ) . answer : c ." + }, + { + "Answer": 40, + "Options": "a ) 30 , b ) 40 , c ) 36 , d ) 56 , e ) 66", + "Correct": "b", + "Explanation": "\"explanation : lcm of 6 , 9 , 12 and 18 is 36 required number = 36 + 4 = 40 answer : option b\"" + }, + { + "Answer": 40, + "Options": "a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60", + "Correct": "c", + "Explanation": "let number of pounds of 5 $ candy to be used be w 6 = ( 20 * 8 + 5 * w ) / ( 20 + w ) = > 120 + 6 w = 160 + 5 w = > w = 40 answer c" + }, + { + "Answer": 42.857142857142854, + "Options": "a ) 42.85 % , b ) 66.68 % , c ) 66.766 % , d ) 86.66 % , e ) 66.65 %", + "Correct": "a", + "Explanation": "excess of b ' s height over a ' s = [ ( 30 / ( 100 - 30 ) ] x 100 % = 42.85 % answer : a )" + }, + { + "Answer": 315, + "Options": "a ) 315 , b ) 339 , c ) 288 , d ) 299 , e ) 111", + "Correct": "a", + "Explanation": "explanation : let the areas of the two parts be x and ( 700 - x ) hectares therefore , so , the two parts are 385 and 315 . hence , area of the smaller = 315 hectares answer : a ) 315" + }, + { + "Answer": 17.7, + "Options": "a ) 17.1 , b ) 17.3 , c ) 17.5 , d ) 17.7 , e ) 17.2", + "Correct": "d", + "Explanation": "\"29.94 / 1.45 = 299.4 / 14.5 = ( 2994 / 14.5 ) x 1 / 10 ) [ here , substitute 177 in the place of 2994 / 14.5 ] = 177 / 10 = 17.7 answer is d .\"" + }, + { + "Answer": 25, + "Options": "a ) 12.5 % , b ) 20 % , c ) 25 % , d ) 50 % , e ) 100 %", + "Correct": "c", + "Explanation": "correct answer : c solution : c . we can set up equations for income before and after the wage reduction . initially , the employee earns w wage and works h hours per week . after the reduction , the employee earns . 8 w wage and works x hours . by setting these equations equal to each other , we can determine the increase in hours worked : wh = . 8 wx ( divide both sides by . 8 w ) 1.25 h = x we know that the new number of hours worked t will be 25 % greater than the original number . the answer is c ." + }, + { + "Answer": 0.3, + "Options": "a ) 9 / 10 , b ) 6 / 10 , c ) 2 / 10 , d ) 3 / 10 , e ) 5 / 10", + "Correct": "d", + "Explanation": "\"explanation : here , s = { 1 , 2 , 3 , 4 , . . . . , 19 , 20 } = > n ( s ) = 20 let e = event of getting a multiple of 4 or 15 = multiples od 4 are { 4 , 8 , 12 , 16 , 20 } and multiples of 15 means multiples of 3 and 5 = { 3 , 6 , 9 , 12 , 15 , 18 , 5 , 10 , 15 , 20 } . = the common multiple is only ( 15 ) . = > e = n ( e ) = 6 required probability = p ( e ) = n ( e ) / n ( s ) = 6 / 20 = 3 / 10 . answer is d\"" + }, + { + "Answer": 1, + "Options": "a ) 1 / 2 , b ) 1 , c ) 2 , d ) 5 / 2 , e ) 4", + "Correct": "b", + "Explanation": "\"the equation of the line can be re written as y = ( 1 / 2 ) x - 5 / 2 . slope = 1 / 2 , which means for every 1 unit increase in the y co - ordinate , x will increase by 2 units . hence k = 1 . answer : b\"" + }, + { + "Answer": 240.00000000000003, + "Options": "a ) $ 100 , b ) $ 150 , c ) $ 125 , d ) $ 200 , e ) $ 240", + "Correct": "e", + "Explanation": "\"a : ( b + c ) = 2 : 3 a ' s share = 600 * 2 / 5 = $ 240 answer is e\"" + }, + { + "Answer": 8, + "Options": "a ) 8 , b ) 9 , c ) 7 , d ) 6 , e ) 3", + "Correct": "a", + "Explanation": "\"explanation : on dividing 427398 by 10 we get the remainder 8 , so 8 should be subtracted option a\"" + }, + { + "Answer": 2400, + "Options": "a ) 480 , b ) 1600 , c ) 1920 , d ) 2080 , e ) 2400", + "Correct": "e", + "Explanation": "given info : no . of students enrolled in school x is = 7 % more than previous year ' s strength = 7 x / 100 no . of students enrolled in school y is = 3 % more than previous year ' s strength = 3 y / 100 given that ` ` this year ' ' school x have 40 students more than school y . so the increase in strength can be written as 7 x / 100 = 40 + 3 y / 100 7 x = 4000 + 3 y . . . . . . . . . . . . . . . . . . . . ( 1 ) and total students on previous year are x + y = 4000 . . . . . . . . . . . . . . . . . . . . . . ( 2 ) equating & solving we get , y = 2400 ans is e" + }, + { + "Answer": 9, + "Options": "a ) 17 : 3 , b ) 9 : 1 , c ) 3 : 17 , d ) 5 : 3 , e ) 11 : 2", + "Correct": "b", + "Explanation": "\"he 20 litre mixture contains milk and water in the ratio of 3 : 2 . therefore , there will be 12 litres of milk in the mixture and 8 litres of water in the mixture . step 1 . when 10 litres of the mixture is removed , 6 litres of milk is removed and 4 litres of water is removed . therefore , there will be 6 litres of milk and 4 litres of water left in the container . it is then replaced with pure milk of 10 litres . now the container will have 16 litres of milk and 4 litres of water . step 2 . when 10 litres of the new mixture is removed , 8 litres of milk and 2 litres of water is removed . the container will have 8 litres of milk and 2 litres of water in it . now 10 litres of pure milk is added . therefore , the container will have 18 litres of milk and 2 litres of water in it at the end of the second step . therefore , the ratio of milk and water is 18 : 2 or 9 : 1 . shortcut . we are essentially replacing water in the mixture with pure milk . let w _ o be the amount of water in the mixture originally = 8 litres . let w _ r be the amount of water in the mixture after the replacements have taken place . then , { w _ r } / { w _ o } = ( 1 - r / m ) ^ n where r is the amount of the mixture replaced by milk in each of the steps , m is the total volume of the mixture and n is the number of times the cycle is repeated . hence , { w _ r } / { w _ o } \u00a0 = ( 1 / 2 ) ^ 2 \u00a0 = 1 / 4 therefore , tw _ r \u00a0 = { w _ o } / 4 = 8 / 4 \u00a0 = 2 litres . b\"" + }, + { + "Answer": 252, + "Options": "a ) $ 252 , b ) $ 135 , c ) $ 90 , d ) $ 60 , e ) $ 54", + "Correct": "a", + "Explanation": "\"since 2 / 3 of the books in the collection were sold , 1 / 3 were not sold . the 36 unsold books represent 1 / 3 of the total number of books in the collection , and 2 / 3 of the total number of books equals 2 ( 36 ) or 72 . the total proceeds of the sale was 72 ( $ 3.50 ) or $ 252 . the best answer is therefore a . answer : a .\"" + }, + { + "Answer": 30, + "Options": "a ) 31 , b ) 35 , c ) 29 , d ) 25 , e ) 30", + "Correct": "e", + "Explanation": "total score of the batsman in 35 matches = 1260 . total score of the batsman in the next 14 matches = 210 . total score of the batsman in the 30 matches = 1470 . average score of the batsman = 1470 / 49 = 30 . answer : e" + }, + { + "Answer": 23, + "Options": "a ) 16 , b ) 23 , c ) 19 , d ) 20 , e ) 22", + "Correct": "b", + "Explanation": "\"we need to find the median which is the third value when the numbers are in increasing order . since k < m < r < s < t , the median would be r . the average of the positive integers is 18 which means that in effect , all numbers are equal to 18 . if the largest number is 40 , it is 22 more than 18 . we need r to be maximum so k and m should be as small as possible to get the average of 16 . since all the numbers are positive integers , k and m can not be less than 1 and 2 respectively . 1 is 17 less than 18 and 2 is 16 less than 18 which means k and m combined are 33 less than the average . 40 is already 22 more than 18 and hence we only have 33 - 22 = 11 extra to distribute between r and s . since s must be greater than r , r can be 18 + 5 = 23 and s can be 18 + 6 = 24 . so r is 23 answer ( b )\"" + }, + { + "Answer": 56, + "Options": "a ) 52 , b ) 54 , c ) 56 , d ) 58 , e ) 60", + "Correct": "c", + "Explanation": "\"basically , the question asks how many 4 digit numbers ( including those in the form 0 xxx , 00 xx , and 000 x ) have digits which add up to 5 . think about the question this way : we know that there is a total of 5 to be spread among the 4 digits , we just have to determine the number of ways it can be spread . let x represent a sum of 1 , and | represent a seperator between two digits . as a result , we will have 5 x ' s ( digits add up to the 5 ) , and 3 | ' s ( 3 digit seperators ) . so , for example : xx | x | x | x = 2111 | | xxx | xx = 0032 etc . there are 8 c 3 ways to determine where to place the separators . hence , the answer is 8 c 3 = 56 . c\"" + }, + { + "Answer": 232, + "Options": "a ) $ 140 , b ) $ 160 , c ) $ 220 , d ) $ 232 , e ) $ 260", + "Correct": "d", + "Explanation": "\"10 $ per week ! an year has 52 weeks . annual charges per year = 52 * 10 = 520 $ 30 $ per month ! an year has 12 months . annual charges per year = 12 * 24 = 288 $ 520 - 288 = 232 ans d\"" + }, + { + "Answer": 25, + "Options": "a ) 5 % , b ) 10 % , c ) 20 % , d ) 25 % , e ) 33 %", + "Correct": "d", + "Explanation": "let x be the original price of one ticket . the total original cost is 3 x . the new cost is 4 y , where y is the discounted price of one ticket . 3 x = 4 y y = 3 x / 4 = 0.75 x which is a discount of 25 % . the answer is d ." + }, + { + "Answer": 19.999999999999243, + "Options": "a ) 96 , b ) 75 , c ) 48 , d ) 25 , e ) 20", + "Correct": "e", + "Explanation": "by the definition of a remainder , the remainder here is equal to 3 / y . the remainder in decimal form is given as . 15 therefore , 3 / y = . 15 solve for y and get 20 . e" + }, + { + "Answer": 16, + "Options": "a ) 16 , b ) 18 , c ) 19 , d ) 22 , e ) 24", + "Correct": "a", + "Explanation": "\"explanation : 10 * 15 + 36 \u2013 26 = 160 / 10 = 16 a )\"" + }, + { + "Answer": 117.6, + "Options": "a ) 68 , b ) 70.4 , c ) 86 , d ) 105.6 , e ) 117.6", + "Correct": "e", + "Explanation": "\"x = 98 * 1.2 = 117.6 so the answer is e .\"" + }, + { + "Answer": 10, + "Options": "a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14", + "Correct": "a", + "Explanation": "since average price of a pencil = 2 \u2234 price of 75 pencils = 150 \u2234 price of 30 pens = ( 450 \u2013 150 ) = 300 \u2234 average price of a pen = 360 \u2044 60 = 10 answer a" + }, + { + "Answer": 259, + "Options": "a ) 264 , b ) 259 , c ) 269 , d ) 270 , e ) 282", + "Correct": "b", + "Explanation": "this question includes a number of great number property shortcuts that you can take advantage of : 1 ) the question asks for the smallest number that , when increased by 5 is divisible by 8 , 11 and 24 . since the answers are numbers , we can test the answers . 2 ) any number that is divisible by 24 is also divisible by 8 , so we really just need to consider the 11 and the 24 . 3 ) to be divisible by 24 , the end number must be even . since we ' re adding 5 to get to that end number , the starting number must be odd . the last shortcut allows us to eliminate answers a , d and e . between answers b and c , testing b first will prove that , when increased by 5 , the end sum is divisible by both 11 and 24 . final answer : b" + }, + { + "Answer": 3, + "Options": "a ) 5 , b ) 3 , c ) 6 , d ) 2 , e ) 1", + "Correct": "b", + "Explanation": "use elimination method to find the correct option . you find that of all the options 3 is the correct value for y answer : b" + }, + { + "Answer": 0.8235294117647058, + "Options": "a ) 7 / 16 , b ) 7 / 15 , c ) 10 / 21 , d ) 14 / 17 , e ) 1 / 2", + "Correct": "d", + "Explanation": "let the total # of cups be 10 . # of small cups sold 1 / 5 * 10 = 2 ; # of large cups sold 10 - 2 = 8 ; let the price of small cup be $ 6 , then the price of larges cup would be 7 / 6 * 6 = $ 7 ; revenue from small cups : 2 * $ 6 = $ 12 ; revenue from large cups cups : 8 * $ 7 = $ 56 ; fraction of total revenue from large cups : 56 / ( 56 + 12 ) = 14 / 17 . answer : d ." + }, + { + "Answer": 0.11111111111111109, + "Options": "a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 6 , d ) 1 / 9 , e ) 1 / 12", + "Correct": "d", + "Explanation": "\"4 a / 100 = 12 a = 300 12 b / 100 = 4 b = 100 / 3 c = b / a = 100 / ( 3 * 300 ) = 1 / 9 the answer is d .\"" + }, + { + "Answer": 3, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "a", + "Explanation": "\"3 years answer : a\"" + }, + { + "Answer": 0.3125, + "Options": "a ) 1 / 3 , b ) \u00bc , c ) 9 / 25 , d ) 5 / 16 , e ) 0", + "Correct": "d", + "Explanation": "prime digits are : 2 , 3 , 5 , 7 total number of 2 digit # s with both digits prime are : 4 * 4 = 16 out of these numbers divisible by 3 = 33 , 27 , 57 , 72 and 75 . i had to find the numbers manually using the 4 numbers above . = > prob = 5 / 16 . ans d . took me 3 : 20 mins ." + }, + { + "Answer": 650, + "Options": "a ) a ) 400 , b ) b ) 650 , c ) c ) 500 , d ) d ) 550 , e ) e ) 600", + "Correct": "b", + "Explanation": "\"10 * 170 = 1700 3 * 100 + 5 * 150 = 1050 1700 \u2013 1050 = 650 b\"" + }, + { + "Answer": 4937, + "Options": "a ) 4637 , b ) 4737 , c ) 4937 , d ) 5937 , e ) 5978", + "Correct": "c", + "Explanation": "\"total sale for 5 months = rs . ( 5266 + 5768 + 5922 + 5678 + 6029 ) = rs . 28663 . required sale = rs . [ ( 5600 x 6 ) - 28663 ] = rs . ( 33600 - 28663 ) = rs . 4937 . answer : c\"" + }, + { + "Answer": 164, + "Options": "a ) 160 , b ) 161 , c ) 162 , d ) 163 , e ) 164", + "Correct": "e", + "Explanation": "to minimize one quantity maximize other . 163 * 2 ( max possible amount of food a guest could consume ) = 326 pounds , so there must be more than 163 guests , next integer is 164 . answer : e ." + }, + { + "Answer": 22, + "Options": "a ) 18 , b ) 20 , c ) 22 , d ) 23 , e ) 25", + "Correct": "c", + "Explanation": "let the total number of workers be y . so sum of salary for all workers = sum of salary of 7 technician + sum of salary for other y - 7 workers . 7 x 1000 + 780 ( y - 7 ) = 850 y \u21d2 7000 + 780 y - 5460 = 850 y \u21d2 70 y = 1540 \u2234 y = 22 so total number of workers = 22 c" + }, + { + "Answer": 62, + "Options": "a ) 62 kg , b ) 60 kg , c ) 70 kg , d ) 72 kg , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : let the weight of student be x kg . given , difference in average weight = 3 kg = > ( 80 - x ) / 6 = 3 = > x = 62 answer : a\"" + }, + { + "Answer": 4.2, + "Options": "a ) 20 / 21 , b ) 23 / 25 , c ) 24 / 23 , d ) 22 / 5 , e ) 21 / 5", + "Correct": "e", + "Explanation": "description : = > 9 x = 2 ( x + 2 ) + 9 + 2 ( x + 4 ) = > 9 x = 4 x + 21 = > 5 x = 21 x = 21 / 5 answer e" + }, + { + "Answer": 54, + "Options": "a ) 54 , b ) 33 , c ) 44 , d ) 66 , e ) 99", + "Correct": "a", + "Explanation": "\"x / ( 9 p ) = odd prime number x = odd prime number * 9 p least value of x = lowest odd prime number * 9 * lowest value of p = 3 * 9 * 2 = 54 answer a\"" + }, + { + "Answer": 400, + "Options": "a ) rs . 200 , b ) rs . 300 , c ) rs . 400 , d ) rs . 600 , e ) rs . 500", + "Correct": "c", + "Explanation": "let saiji = x . then , annie = x / 2 and maya = x / 4 . therefore , maya : annie : saiji = x / 4 : x / 2 : x = 1 : 2 : 4 . therefore , saiji \u2019 s share = rs . 900 * 4 / 9 = rs . 400 . answer : c" + }, + { + "Answer": 24, + "Options": "a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28", + "Correct": "a", + "Explanation": "let x be the number of students in the largest class . then x + ( x - 2 ) + ( x - 4 ) + ( x - 6 ) + ( x - 8 ) = 100 5 x - 20 = 100 5 x = 120 x = 24 the answer is a ." + }, + { + "Answer": 8, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8", + "Correct": "e", + "Explanation": "\"if n = 8 mark sold 1 box and ann sold 6 boxes total 7 < 8 answer : e\"" + }, + { + "Answer": 4, + "Options": "a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10", + "Correct": "b", + "Explanation": "2 ( 3 x - 5 ) - 19 = 3 ( x - 4 ) - 5 3 x = 12 x = 4 the answer is b ." + }, + { + "Answer": 0.9756097560975611, + "Options": "a ) 40 / 41 , b ) 20 / 41 , c ) 30 / 41 , d ) 60 / 41 , e ) 80 / 41", + "Correct": "a", + "Explanation": "\"say x = y = 10 . in this case we would have : 20 x = 200 black - and - white films ; 8 y = 80 color films . y / x % = 10 / 10 % = 1 % of the black - and - white films , so 2 black - and - white films and all 80 color films , thus total of 82 films were selected . color films thus compose 80 / 82 = 40 / 41 of the selected films . answer : a\"" + }, + { + "Answer": 130, + "Options": "a ) 130 , b ) 100 , c ) 125 , d ) 175 , e ) 225", + "Correct": "a", + "Explanation": "\"let m be the number of male participants and f be the number of female articipants in the meeting . thetotal number of participants is given as 780 . hence , we have m + f = 780 now , we have that half the female participants and one - quarter of the male participants are democrats . let d equal the number of the democrats . then we have the equation f / 2 + m / 4 = d now , we have that one - third of the total participants are democrats . hence , we have the equation d = 780 / 3 = 260 solving the three equations yields the solution f = 260 , m = 520 , and d = 260 . the number of female democratic participants equals half the female participants equals 260 / 2 = 130 . answer : a\"" + }, + { + "Answer": 0.008333333333333333, + "Options": "a ) 719 / 720 , b ) 1 / 120 , c ) 2 / 233 , d ) 3 / 543 , e ) 1 / 720", + "Correct": "b", + "Explanation": "5 ties and 5 shirts . . . red tie can take any of 5 shirts . . orange can take any of the remaining 4 shirts yellow any of remaining 3 . . and so on till last indigo chooses the 1 remaining . . total ways = 5 * 4 * 3 * 2 * 1 = 120 out of this 120 , only 1 way will have same colour tie and shirt . . prob = 1 / 120 b" + }, + { + "Answer": 60, + "Options": "a ) 55 , b ) 56 , c ) 57 , d ) 58 , e ) 60", + "Correct": "e", + "Explanation": "\"20 x + 45 = 21 ( x \u2013 5 ) x = 60 answer : e\"" + }, + { + "Answer": 3, + "Options": "a ) a ) 9 , b ) b ) 3 , c ) c ) 12 , d ) d ) 6 , e ) e ) 10", + "Correct": "b", + "Explanation": "a no . divisible by 36 means it is div by 49 . to be div by 4 last 2 digits to be multiple of 4 so , f could be either 2 or 6 only similarly for a number to be div by 9 its sum must be multiple of 9 first . filtering we find q could be either 1 , 47 only . to be divisible by 9 only 1 works . ( if we choose f = 6 then q have to be 6 but as per condition qf are distinct ) so q = 1 f = 2 ans : - 3 . b" + }, + { + "Answer": 50, + "Options": "a ) 50 % , b ) 85 % , c ) 25 % , d ) 75 % , e ) none of above", + "Correct": "a", + "Explanation": "\"explanation : actually it means 25 is what percent of 50 , which can be calculated as , ( 25 / 50 ) * 100 = 25 * 2 = 50 answer : option a\"" + }, + { + "Answer": 20, + "Options": "a ) 23 years , b ) 22 years , c ) 21 years , d ) 20 years , e ) 19 years", + "Correct": "d", + "Explanation": "\"let present age of the son = x years then , present age the man = ( x + 22 ) years given that , in 2 years , man ' s age will be twice the age of his son \u00e2 \u2021 \u2019 ( x + 22 ) + 2 = 2 ( x + 2 ) \u00e2 \u2021 \u2019 x = 20 answer : d\"" + }, + { + "Answer": 6, + "Options": "a ) 8 , b ) 13 , c ) 28 , d ) 6 , e ) 2", + "Correct": "d", + "Explanation": "d" + }, + { + "Answer": 240, + "Options": "a ) 1628.4 , b ) 1534 , c ) 1492 , d ) 240 , e ) none of these", + "Correct": "d", + "Explanation": "\"solution : let average expenditure of 10 people be x . then , 10 x = 20 * 5 + 5 * ( x + 4 ) ; or , 10 x = 20 * 5 + 5 x + 20 ; or , x = 24 ; so , total money spent = 24 * 10 = rs . 240 . answer : option d\"" + }, + { + "Answer": 15, + "Options": "a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16", + "Correct": "d", + "Explanation": "w : x : y = 100 : 30 : 20 20 : 6 : 4 20 - - - 10 30 - - - ? = > 15 answer : d" + }, + { + "Answer": 16, + "Options": "a ) 10 , b ) 16 , c ) 37 , d ) 29 , e ) 22", + "Correct": "b", + "Explanation": "\"explanation : let the original price be rs . 100 . decreased by 30 % = 70 then increased 20 % on rs 70 = 70 + 14 = 84 net change in price = 100 - 84 = 16 answer : b\"" + }, + { + "Answer": 160, + "Options": "a ) 120 , b ) 100 , c ) 135 , d ) 140 , e ) 160", + "Correct": "e", + "Explanation": "line k passes through the origin and has slope 1 / 4 means that its equation is y = 1 / 4 * x . thus : ( x , 8 ) = ( 32 , 8 ) and ( 20 , y ) = ( 20,5 ) - - > x * y = 32 * 5 = 160 . answer : e" + }, + { + "Answer": 28, + "Options": "a ) 16 , b ) 10 , c ) 28 , d ) 4 , e ) 2", + "Correct": "c", + "Explanation": "at least 20 golf tees for each member of his foursome = total of at least 4 * 20 = 80 tees . 2 packages of the generic golf tees , that are packaged by the dozen = 2 * 12 = 24 tees . so , bill must by at least 16 aero tees . they come by the pair , hence he must by at least 56 / 2 = 28 packages of aero flight tees . answer : c ." + }, + { + "Answer": 888, + "Options": "a ) $ 24 million , b ) $ 120 million , c ) $ 144 million , d ) $ 240 million , e ) $ 888 million", + "Correct": "e", + "Explanation": "\"convert units to millions as answer is in millions 1996 imports = $ 1.44 bill = $ 1440 mill i . e . 1440 / 12 = $ 120 mill / month 1997 imports = $ 388 mill / 2 month i . e . $ 194 mill / month difference / month = 194 - 120 = 74 difference / year = $ 74 mill * 12 = $ 988 mill answer : e\"" + }, + { + "Answer": 0.4166666666666667, + "Options": "a ) 5 / 12 , b ) 12 / 5 , c ) 25 / 144 , d ) 144 / 25 , e ) 146 / 25", + "Correct": "a", + "Explanation": "\"let the number be x . then , 2 / 3 x = 25 / 216 * 1 / x x 2 = 25 / 216 * 3 / 2 = 25 / 144 x = 5 / 12 answer : a\"" + }, + { + "Answer": 11.11111111111111, + "Options": "a ) 2.5 % , b ) 11 % , c ) 5 % , d ) 15 % , e ) 25 %", + "Correct": "b", + "Explanation": "\"50 % of ( x - y ) = 40 % of ( x + y ) ( 50 / 100 ) ( x - y ) = ( 40 / 100 ) ( x + y ) 5 ( x - y ) = 4 ( x + y ) x = 9 y x = 9 y therefore required percentage = ( ( y / x ) x 100 ) % = ( ( y / 9 y ) x 100 ) = 11 % answer is b .\"" + }, + { + "Answer": 4.25, + "Options": "a ) 2.25 , b ) 3.25 , c ) 4.25 , d ) 5.25 , e ) 6.25", + "Correct": "c", + "Explanation": "\"squaring on both sides ( x + 1 / x ) ^ 2 = 2.5 ^ 2 x ^ 2 + 1 / x ^ 2 = 6.25 - 2 x ^ 2 + 1 / x ^ 2 = 4.25 answer : c\"" + }, + { + "Answer": 0.41666666666666663, + "Options": "a ) 1 / 4 , b ) 1 / 3 , c ) 5 / 13 , d ) 5 / 12 , e ) 1 / 2", + "Correct": "d", + "Explanation": "for the product of 2 numbers to be negative either of them must be positive or negative : p ( positive , negative ) = 2 / 6 * 3 / 6 = 6 / 36 ; p ( negative , positive ) = 3 / 6 * 3 / 6 = 9 / 36 p = 6 / 36 + 9 / 36 p = 15 / 36 p = 5 / 12 answer : d" + }, + { + "Answer": 20.999999999996362, + "Options": "a ) 27 , b ) 25 , c ) 26 , d ) 21 , e ) 24", + "Correct": "d", + "Explanation": "\"172835 / 136 = 1270 and reminder = 115 . 136 - 115 = 21 so , the next number divisible by 115 is 21 places in front of 172835 which means 21 + 172835 = 172856 21 should be added to 172835 d\"" + }, + { + "Answer": 27, + "Options": "a ) 24 , b ) 27 , c ) 30 , d ) 33 , e ) 36", + "Correct": "b", + "Explanation": "the first number is 22 = 16 + 6 ( 1 ) . we can continue adding 6 to make a list : 22 , 28 , 34 , . . . the last number is 278 = 16 + 6 ( 27 ) there are 27 numbers in the list . the answer is b ." + }, + { + "Answer": 8.424908424908429, + "Options": "a ) 19 % , b ) 15 % , c ) 25 % , d ) 40 % , e ) 8.4 %", + "Correct": "e", + "Explanation": "\"cost of food ( c ) = food consumed per student ( f ) * number of students ( n ) * price of food ( p ) originally , c = fnp when number of students decrease by 8 % , and the price of food increases by 20 % , c = f ( new ) * ( 0.91 n ) * ( 1.2 p ) = > f ( new ) = f / ( 0.91 * 1.2 ) = > f ( new ) = 0.915 f therefore the new cost of food must be 91.5 % of the old cost , or the cost of food must decrease by 8.4 % ( option e )\"" + }, + { + "Answer": 4500, + "Options": "a ) 4500 , b ) 4600 , c ) 4680 , d ) 4710 , e ) none", + "Correct": "a", + "Explanation": "sol . required average = ( 4375 x 12 ) - ( 4000 x 3 ) / 9 \u21d4 52500 - 12000 / 9 \u21d4 40500 / 9 = 4500 . answer a" + }, + { + "Answer": 80, + "Options": "a ) 18 , b ) 36 , c ) 80 , d ) 90 , e ) 108", + "Correct": "c", + "Explanation": "\"let kate charge for x hours , then pat charged for 2 x and mat - for 6 x . so , 2 x + 6 x + x = 144 - total hours charged for , x = 16 . mat charged 6 x - x or 5 x for more hours than kate , or for 80 hours . c is correct\"" + }, + { + "Answer": 1000, + "Options": "a ) $ 1000 , b ) $ 1050 , c ) $ 1100 , d ) $ 1150 , e ) $ 1200", + "Correct": "a", + "Explanation": "sum of ratio terms = 2 + 8 = 10 x = 5000 * 2 / 10 = $ 1000 answer is a" + }, + { + "Answer": 75, + "Options": "a ) 74 , b ) 75 , c ) 76 , d ) 77 , e ) 78", + "Correct": "b", + "Explanation": "ans : b ( 75 ) lets say class u indeed has 4 children , b has 6 children and c has 5 children . now , if the average of class u is 65 , hence total marks awarded in the class = 65 * 4 = 260 similarly , class b = 80 * 6 = 480 class c = 77 * 5 = 385 total marks provided = u + b + c = 260 + 480 + 385 = 1125 avg . marks = 1125 / 15 ( total no . of students ) = 75 = b" + }, + { + "Answer": 80, + "Options": "a ) 10 , b ) 30 , c ) 40 , d ) 70 , e ) 80", + "Correct": "e", + "Explanation": "we know that to find the last two digits , we need to find the remainder we get when we divide the product by 100 . remainder of ( 63 * 35 * 37 * 82 * 71 * 41 ) / 100 note that we can simplify this expression by canceling out the 5 and 2 in the numerator and denominator . but before we do that , here is an important note : note : we can not just cancel off the common terms in the numerator and denominator to get the remainder . but , if we want to cancel off to simplify the question , we can do it , provided we remember to multiply it back again . so say , we want to find the remainder when 14 is divided by 10 i . e . 14 / 10 ( remainder 4 ) . but we cancel off the common 2 to get 7 / 5 . the remainder here will be 2 which is not the same as the remainder obtained by dividing 14 by 10 . but if we multiply 2 back by 2 ( the number we canceled off ) , the remainder will become 2 * 2 = 4 which is correct . take another example to reinforce this \u2013 what is the remainder when 85 is divided by 20 ? it is 5 . we might rephrase it as \u2013 what is the remainder when 17 is divided by 4 ( cancel off 5 from the numerator and the denominator ) . the remainder in this case is 1 . we multiply the 5 back to 1 to get the remainder as 5 which is correct . so keeping this very important point in mind , let \u2019 s go ahead and cancel the common 5 and 2 . we need the remainder of ( 63 * 7 * 37 * 41 * 71 * 41 * 5 * 2 ) / 10 * 5 * 2 remainder of ( 63 * 7 * 37 * 41 * 71 * 41 ) / 10 now using concept 2 , let \u2019 s write the numbers in form of multiples of 10 remainder of ( 60 + 3 ) * 7 * ( 30 + 7 ) * ( 40 + 1 ) * ( 70 + 1 ) * ( 40 + 1 ) / 10 remainder of 3 * 7 * 7 * 1 * 1 * 1 / 10 remainder of 147 / 10 = 7 now remember , we had canceled off 10 so to get the actual remainder so we need to multiply by 10 : 7 * 10 = 70 . when 63 * 35 * 37 * 82 * 71 * 41 is divided by 100 , the remainder is 70 . so the last two digits of 63 * 35 * 37 * 82 * 71 * 41 must be 80 . answer ( e )" + }, + { + "Answer": 12.4864, + "Options": "a ) 9 % , b ) 9.27 % , c ) 27 % , d ) 12.48 % , e ) none of these", + "Correct": "d", + "Explanation": "\"actual increase in population = 4 % let , earlier population = 100 then the population after 3 years = 100 ( 1 + 4 / 100 ) ^ 3 = 112.4864 \u2234 required percentage = 12.48 % answer : d\"" + }, + { + "Answer": 20, + "Options": "a ) and 20 , b ) and 24 , c ) and 22 , d ) and 29 , e ) of these", + "Correct": "a", + "Explanation": "\"let the age of jill 6 years ago be x , age of henry be 2 x x + 6 + 2 x + 6 = 33 x = 7 present ages will be 13 and 20 answer : a\"" + }, + { + "Answer": 113, + "Options": "a ) 72 , b ) 76 , c ) 100 , d ) 113 , e ) 112", + "Correct": "d", + "Explanation": "\"diver = ( 5 * 3 ) + 3 = 18 3 * quotient = 18 quotient = 6 dividend = ( divisor * quotient ) + remainder dividend = ( 18 * 6 ) + 5 = 113 d\"" + }, + { + "Answer": 2100, + "Options": "a ) 2000 , b ) 2100 , c ) 2150 , d ) 2200 , e ) 2500", + "Correct": "b", + "Explanation": "the fastest way in an ap is to find the average and multiply with total integers . . between 34 and 135 , the smallest multiple of 4 is 36 and largest = 132 . . average = ( 36 + 132 ) / 2 = 84 . . total numbers = ( 132 - 36 ) / 4 + 1 = 24 + 1 = 25 . . sum = 25 * 84 = 2100 ans b" + }, + { + "Answer": 7, + "Options": "a ) 5 , b ) 7 , c ) 9 , d ) 10 , e ) 11", + "Correct": "b", + "Explanation": "\"expanding we have 6 x ^ 2 - 9 x + 4 x - 6 6 x ^ 2 - 5 x - 6 taking coefficients , a = 6 , k = - 5 , n = - 6 therefore a - n + k = 6 - ( - 6 ) - 5 = 12 - 5 = 7 the answer is b .\"" + }, + { + "Answer": 30, + "Options": "a ) 30 , b ) 35 , c ) 40 , d ) 45 , e ) 50", + "Correct": "a", + "Explanation": "\"let x be the original number of apples . on day one , the vendor throws away ( 0.2 ) ( 0.5 ) x = 0.1 x . the remaining apples are ( 0.8 ) ( 0.5 ) x = 0.4 x . on day two , the vendor throws away ( 0.5 ) ( 0.4 ) x = 0.2 x . the vendor throws away a total of 0.1 x + 0.2 x = 0.3 x . the vendor throws away 30 percent of the apples . the answer is a .\"" + }, + { + "Answer": 2407, + "Options": "a ) 2407 , b ) 2408 , c ) 2409 , d ) 2405 , e ) 32", + "Correct": "a", + "Explanation": "2407 ^ 1 + 1 ^ 2407 = 2408 answer : a" + }, + { + "Answer": 50, + "Options": "a ) 25 , b ) 66 , c ) 77 , d ) 50 , e ) 91", + "Correct": "d", + "Explanation": "\"let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 1111 96 + 225 + 490 + 6 x = 1111 6 x = 300 = > x = 50 . answer : d\"" + }, + { + "Answer": 32, + "Options": "a ) 64 , b ) 32 , c ) 46 , d ) 75 , e ) 47", + "Correct": "b", + "Explanation": "b 32 the total of three numbers must be 48 x 3 = 144 . the total of two numbers must be 56 x 2 = 112 . therefore , 144 - 112 = 32 ." + }, + { + "Answer": 0.11111111111111112, + "Options": "a ) 1 / 4 , b ) 1 / 9 , c ) 9 / 16 , d ) 5 / 8 , e ) 16 / 9", + "Correct": "b", + "Explanation": "\"2 / 5 * 5 / 9 * 1 / 2 = 1 / 9 answer : b\"" + }, + { + "Answer": 19872, + "Options": "a ) 20072 , b ) 20062 , c ) 10072 , d ) 20172 , e ) 10272", + "Correct": "a", + "Explanation": "\"explanation : ( a + b ) 2 + ( a \u00e2 \u02c6 \u2019 b ) 2 = 2 ( a 2 + b 2 ) ( reference : basic algebraic formulas ) 1062 + 942 = ( 100 + 6 ) 2 + ( 100 \u00e2 \u02c6 \u2019 6 ) 2 = 2 ( 1002 + 62 ) = 2 ( 10000 + 36 ) = 20072 . answer : option a\"" + }, + { + "Answer": 3120, + "Options": "a ) 1040 , b ) 2080 , c ) 3120 , d ) 4160 , e ) none of these", + "Correct": "c", + "Explanation": "\"number of male employees = 6400 * 65 / 100 = 4160 required number of male employees who are less than 50 years old = 4160 * ( 100 - 25 ) % = 4160 * 75 / 100 = 3120 . answer : c\"" + }, + { + "Answer": 0.14285714285714285, + "Options": "a ) 1 / 7 , b ) 3 / 4 , c ) 4 / 5 , d ) 5 / 4 , e ) 3 / 2", + "Correct": "a", + "Explanation": "\"a / b = 4 / 5 m / x = ( 1 / 5 ) * 5 / ( 7 / 4 ) * 4 = 1 / 7 the answer is a .\"" + }, + { + "Answer": 37, + "Options": "a ) 41 , b ) 42 , c ) 32 , d ) 37 , e ) 39", + "Correct": "d", + "Explanation": "lcm of 3 , 5 , 7 and 8 = 840 28523 \u00f7 840 = 33 remainder = 803 hence the least number which should be added = 840 - 803 = 37 answer : option d" + }, + { + "Answer": 40, + "Options": "a ) 25 , b ) 40 , c ) 77 , d ) 99 , e ) 91", + "Correct": "b", + "Explanation": "\"let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 1051 96 + 225 + 490 + 6 x = 1051 6 x = 240 = > x = 40 . answer : b\"" + }, + { + "Answer": 3150, + "Options": "a ) rs . 1050 , b ) rs . 1400 , c ) rs . 3150 , d ) rs . 4200 , e ) none", + "Correct": "c", + "Explanation": "explanation : area of 4 walls of the room = [ 2 ( l + b ) \u00d7 h ] m 2 area of 4 walls of new room = [ 2 ( 3 l + 3 b ) \u00d7 3 h ] m 2 = 9 [ 2 ( l + b ) \u00d7 h ] m 2 cost of painting the 4 walls of new room = rs . ( 9 \u00d7 350 ) = rs . 3150 correct option : c" + }, + { + "Answer": 18, + "Options": "a ) 12 , b ) 29 , c ) 27 , d ) 18 , e ) 99", + "Correct": "d", + "Explanation": "\"explanation : let the number be x . therefore , 3 ( 2 x + 5 ) = 123 6 x + 15 = 123 6 x = 108 x = 18 answer : d\"" + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 4 , c ) 1 , d ) 0 , e ) can not be determined", + "Correct": "a", + "Explanation": "\"sol . ( a ) number = 899 q + 63 , where q is quotient = 31 \u00d7 29 q + ( 58 + 5 ) = 29 [ 31 q + 2 ] + 5 \u2234 remainder = 5 answer a\"" + }, + { + "Answer": 18, + "Options": "a ) $ 12 , b ) $ 14 , c ) $ 16 , d ) $ 18 , e ) $ 20", + "Correct": "d", + "Explanation": "\"average price per book = ( 1280 + 880 ) / ( 65 + 55 ) = 2160 / 120 = $ 18 the answer is d .\"" + }, + { + "Answer": 1542.857142857143, + "Options": "a ) 1235 , b ) 1557.9 , c ) 1378 , d ) 1635 , e ) 1489", + "Correct": "b", + "Explanation": "\"let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 8 x + 15 7 x = 1350 x = 192.9 large number = 192.9 + 1365 = 1557.9 b\"" + }, + { + "Answer": 12, + "Options": "a ) 8 , b ) 10 , c ) 12 , d ) 16 , e ) 24", + "Correct": "c", + "Explanation": "if a ^ 2 - b ^ 2 = 0 , then let ' s assume that a = b . a must equal the 4 th positive multiple of 4 , thus a = 24 , which also equals b . b is the second positive multiple of n , thus n = 24 / 2 = 12 . the answer is c ." + }, + { + "Answer": 14, + "Options": "a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16", + "Correct": "c", + "Explanation": "\"the total number of books the students borrowed is 20 * 2 = 40 . the students who borrowed zero , one , or two books borrowed 10 * 1 + 5 * 2 = 20 books . the 3 students who borrowed at least three books borrowed 40 - 20 = 20 books . if 2 of these students borrowed exactly 3 books , then the maximum that one student could have borrowed is 20 - 6 = 14 books . the answer is c .\"" + }, + { + "Answer": 8, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) g = 8", + "Correct": "e", + "Explanation": "\"the combinations could be { ( 1,240 ) , ( 2,120 ) , ( 3,80 ) , ( 4,60 ) , ( 5,48 ) , ( 6,40 ) , ( 8,30 ) , ( 10,24 ) , ( 12,20 ) , ) 15,16 ) , ( 16,15 ) , ( 20,12 ) , ( 24,10 ) , ( 30,8 ) , ( 40,6 ) , ( 48,5 ) , ( 60,4 ) , ( 80,3 ) , ( 120,2 ) , ( 240,1 ) } of these we are told 8 < = t < = 30 so we can remove these pairs , and we are left only with . { ( 8,30 , ( 10 , 24 ) , ( 12,20 ) , ( 15,16 ) , ( 16,15 ) , ( 20,12 ) , ( 24,10 ) , ( 30,8 ) } hence 8 . . e\"" + }, + { + "Answer": 20, + "Options": "a ) 32 , b ) 37 , c ) c . 40 , d ) 20 , e ) 50", + "Correct": "d", + "Explanation": "\"note that both median and range do not restrict too many numbers in the set . range is only concerned with the smallest and greatest . median only cares about the middle . quick check of each option starting from the largest : ( e ) 50 range of 20 means the smallest integer will be 30 . so 20 can not lie in between and hence can not be the median . ( d ) 43 range of 20 means the smallest integer will be 23 . so 20 can not lie in between and hence can not be the median . ( c ) 40 range of 20 means the smallest integer will be 20 . 20 can lie in between such as : 20 , 20 , 20 , 20 , 20 , 20 , 20 , 20 , 20 , 20 this is possible . hence it is the greatest such number . answer ( d )\"" + }, + { + "Answer": 121, + "Options": "a ) 90 , b ) 100 , c ) 120 , d ) 160 , e ) 121", + "Correct": "e", + "Explanation": "\"solution : let x be the number he chose , then 2 * x * 140 = 102 2 x = 242 x = 121 correct answer e\"" + }, + { + "Answer": 48, + "Options": "a ) 20 , b ) 36 , c ) 48 , d ) 60 , e ) 84", + "Correct": "c", + "Explanation": "first , we have to understand what linearly means . it ' s not a straight ratio ( since 6 : 30 does not equal 24 : 60 ) . we need to look at the increases in each measurement to see what the scalar actually is . from 6 to 24 we have an increase of 18 . from 30 to 60 we have an increase of 30 . therefore , the increase ratio is 18 : 30 or 3 : 5 . in other words , for every 3 that p increases , s increases by 5 . we know that s is 100 . to get from 60 to 100 , we went up by 40 , or 8 jumps of 5 ; therefore , p will go up by 8 jumps of 3 . 24 + 8 ( 3 ) = 24 + 24 = 48 = c" + }, + { + "Answer": 2500, + "Options": "a ) 2500 , b ) 2550 , c ) 5050 , d ) 6275 , e ) 11325", + "Correct": "a", + "Explanation": "\"set a contains 2,4 , 6 . . . 50 set b contains 102 , 104 , 106 . . . 150 number of terms in each set = 25 difference between corresponding terms in set a and b = 100 difference between sum of set b and set a = 100 * 25 = 2500 answer a\"" + }, + { + "Answer": 18, + "Options": "a ) 100 , b ) 65 , c ) 25 , d ) 11 , e ) 18", + "Correct": "e", + "Explanation": "\"machine y produces 20 percent more widgets in an hour than machine x does in an hour . so if machine x produces 100 widgets , then machine y produces 120 widgets . ratio of 120 / 100 = 6 / 5 . this is their speed of work ( y : x ) . i . e . speed of their work ( x : y ) = 5 / 6 now , time is inversely proportional to speed . hence the ratio of the time spent ( x : y ) = 6 / 5 let us assume that they spend 6 x and 5 x hours . given that 6 x - 5 x = 10 so , x = 10 . hence 6 x = 6 * 10 = 60 hours . hence x takes 120 hours to produce 1080 widgets . so , in 1 hour , it can produce ( 1 * 1080 ) / 60 = 18 hence option ( e ) .\"" + }, + { + "Answer": 0.045374000000000005, + "Options": "a ) 0.045374 , b ) 4.5388 , c ) 453.88 , d ) 473.88 , e ) none of these", + "Correct": "a", + "Explanation": "\"answer multiplying 3.241 x 14 = 4.5374 now divide 4.5374 by 100 so , 4.5374 \u00f7 100 = 0.045374 \u2234 shift the decimal two places to the left as 100 correct option : a\"" + }, + { + "Answer": 5, + "Options": "a ) 0 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "d", + "Explanation": "explanation : p + q = \u03b1 \u2013 2 and pq = \u2013 \u03b1 \u2013 1 ( p + q ) 2 = p 2 + q 2 + 2 pq , thus ( \u03b1 \u2013 2 ) 2 = p 2 + q 2 + 2 ( \u2013 \u03b1 \u2013 1 ) p 2 + q 2 = \u03b1 2 \u2013 4 \u03b1 + 4 + 2 \u03b1 + 2 p 2 + q 2 = \u03b1 2 \u2013 2 \u03b1 + 6 p 2 + q 2 = \u03b1 2 \u2013 2 \u03b1 + 1 + 5 p 2 + q 2 = ( \u03b1 \u2013 1 ) 2 + 5 thus , minimum value of p 2 + q 2 is 5 . answer : d" + }, + { + "Answer": 21, + "Options": "a ) a ) 21 , b ) b ) 34 , c ) c ) 45 , d ) d ) 25 , e ) e ) 26", + "Correct": "a", + "Explanation": "explanation : let the present age of p and q be 3 x and 4 x respectively . six years ago , p was half of q in age = > 2 ( 3 x \u2013 6 ) = ( 4 x \u2013 6 ) = > 6 x \u2013 12 = 4 x \u2013 6 = > 2 x = 6 = > x = 3 7 x = 7 * 3 = 21 answer : option a" + }, + { + "Answer": 66, + "Options": "a ) 22 , b ) 0 , c ) 49 , d ) 58 , e ) 66", + "Correct": "e", + "Explanation": "it is clear that 22 x 48 = 10 x 55 + k + 11 x 40 \u21d2 \u21d2 k = 66 answer : e" + }, + { + "Answer": 40, + "Options": "a ) 50 km , b ) 58 km , c ) 60 km , d ) 40 km , e ) 65 km", + "Correct": "d", + "Explanation": "\"let the actual distance traveled be x km . then , x / 8 = ( x + 20 ) / 12 3 x - 2 x = 40 = > x = 40 km . answer : d\"" + }, + { + "Answer": 0.75, + "Options": "a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4", + "Correct": "e", + "Explanation": "\"let p be the number of progressives in the country as a whole . in each province , the number of traditionalists is p / 12 the total number of traditionalists is 4 p / 12 = p / 3 . the total population is p + p / 3 = 4 p / 3 p / ( 4 p / 3 ) = 3 / 4 the answer is e .\"" + }, + { + "Answer": 2100, + "Options": "a ) 1287 , b ) 2887 , c ) 2100 , d ) 1129 , e ) 1192", + "Correct": "c", + "Explanation": "\"let money invested by raghu = rs . x money invested by trishul = 9 / 10 x = 0.9 x money invested by vishal = 9 / 10 x * 110 / 100 = 0.99 x also , x + 0.9 x + 0.99 x = 6069 = x = 6069 / 2.89 = 2100 therefore , amount invested by raghu is rs . 2100 . answer : c\"" + }, + { + "Answer": 500, + "Options": "a ) 300 , b ) 400 , c ) 500 , d ) 600 , e ) 700", + "Correct": "c", + "Explanation": "a + b = 45 a / b + b / a = 2.05 = > ( a ^ 2 + b ^ 2 ) / ab = 2.05 = > ( ( a + b ) ^ 2 \u2212 2 ab ) / ab = 2.05 = > ( a + b ) ^ 2 = 2.05 ab + 2 ab = 4.05 ab = > ab = 45 ^ 2 / 4.05 = 500 answer : c" + }, + { + "Answer": 25, + "Options": "a ) 20 , b ) 25 , c ) 55 , d ) 65 , e ) 80", + "Correct": "b", + "Explanation": "\"the arithmetic mean of 4 equally weighted tests was 40 . so what we can assume is that we have 4 test scores , each 40 . he dropped his lowest score and the avg went to 45 . this means that the lowest score was not 40 and other three scores had given the lowest score 5 each to make it up to 40 too . when the lowest score was removed , the other 3 scores got their 5 back . so the lowest score was 3 * 5 = 15 less than 40 . so the lowest score = 40 - 15 = 25 answer ( b )\"" + }, + { + "Answer": 48, + "Options": "a ) 48 , b ) 47 , c ) 46 , d ) 49 , e ) 52", + "Correct": "a", + "Explanation": "\"let their ages are 9 x , 15 x and 25 x respectively . difference between the ages of patrick and monica = 25 x - 9 x = 16 x where 49 x = 147 or x = 3 so diff in ages = 16 x = 16 * 3 = 48 yrs answer : a\"" + }, + { + "Answer": 6.04, + "Options": "a ) 5 , b ) 6 , c ) 9 , d ) 10 , e ) 11", + "Correct": "b", + "Explanation": "\"250 = 10 * 25 500 = 20 * 25 the even multiples are 25 multiplied by 10 , 12 , 14 , 16 , 18 , and 20 for a total of 6 . the answer is b .\"" + }, + { + "Answer": 3, + "Options": "a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 8", + "Correct": "b", + "Explanation": "\"i like to put the numbers in prime factors so it is easier and faster to visualize . 14 * n / 60 if we write the factors of 14 - - > 2 , 7 , and the factors of 60 - - > 2 , 2 , 3 , 5 , we have ( 2 * 7 * n ) / ( 2 ^ 2 * 3 * 5 ) simplifying 7 * n / ( 2 * 3 * 5 ) the only way the equation above has an integer value is if n has at least the factors 2 , 3 and 5 , so we can simplify again and we have the number 7 . the number could be 2 * 3 * 5 , or 2 * 3 * 5 * 2 , or 2 * 3 * 5 * . . . . . however to be less than 200 we can not add any prime number . 2 * 3 * 5 = 120 if we added the next prime factor 7 , we would have c = 2 * 3 * 5 * 7 = 840 thus , answer b\"" + }, + { + "Answer": 80, + "Options": "a ) \u2212 220 , b ) \u2212 100 , c ) 100 , d ) \u2212 80 , e ) it can not be determined from the information given", + "Correct": "d", + "Explanation": "\"question : a - c = ? ( a + b ) / 2 = 110 = = = > a + b = 220 ( b + c ) / 2 = 150 = = = > b + c = 300 ( a + b ) - ( b + c ) = 220 - 300 = = = > a + b - b - c = - 80 = = = > a - c = - 80 answer : d\"" + }, + { + "Answer": 125, + "Options": "a ) 100 , b ) 110 , c ) 125 , d ) 130 , e ) 145", + "Correct": "c", + "Explanation": "\"let the number of boys who passed = x . then , 39 x x + 15 x ( 120 - x ) = 120 x 40 24 x = 4800 - 1800 = > x = 3000 / 24 x = 125 hence , the number of boys passed = 125 . answer : c\"" + }, + { + "Answer": 24, + "Options": "a ) 16 , b ) 19 , c ) 15 , d ) 24 , e ) 10", + "Correct": "d", + "Explanation": "\"let the son ' s present age be x years . then , man ' s present age = ( x + 26 ) years . ( x + 26 ) + 2 = 2 ( x + 2 ) x + 28 = 2 x + 4 = > x = 24 . answer : d\"" + }, + { + "Answer": 16, + "Options": "a ) 4 , b ) 8 , c ) 16 , d ) 32 , e ) 64", + "Correct": "c", + "Explanation": "\"by formula , ( a + b + c ) ^ 2 = a ^ 2 + b ^ 2 + c ^ 2 + 2 ( ab + bc + ca ) , since , a ^ 2 + b ^ 2 + c ^ 2 = 250 and ab + bc + ca = 3 , ( a + b + c ) ^ 2 = 250 + 2 ( 3 ) = 256 = 16 ^ 2 therefore : a + b + c = 16 answer : c\"" + }, + { + "Answer": 10, + "Options": "a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50", + "Correct": "a", + "Explanation": "explanation : clue : answer will be 5 % of 1000 - 4 % of 1000 answer : option a" + }, + { + "Answer": 0.25, + "Options": "a ) 1 / 3 , b ) 2 / 5 , c ) 1 / 4 , d ) 1 / 6 , e ) 3 / 4", + "Correct": "c", + "Explanation": "\"the fraction of homes which are termite - infested but not collapsing is 3 / 4 * 1 / 3 = 1 / 4 the answer is c .\"" + }, + { + "Answer": 4100, + "Options": "a ) 4100 , b ) 3590 , c ) 2800 , d ) 3700 , e ) 3600", + "Correct": "a", + "Explanation": "a 4100" + }, + { + "Answer": 20, + "Options": "a ) 1 , b ) 4 , c ) 9 , d ) 13 , e ) 20", + "Correct": "e", + "Explanation": "\"solving through algebra route : 2 b + 5 f = x amount if we multiply this equation with 4 we get : 8 b + 20 f = 4 x therefore , we got 8 ounces of butter and 4 x amount of quantity when we use 20 ounces of floor . ans : e\"" + }, + { + "Answer": 10, + "Options": "a ) 30 , b ) 25 , c ) 15 , d ) 10 , e ) 5", + "Correct": "d", + "Explanation": "\"because the cord was extended to its full length at all items , the dog ran along a semi - circular path , from north to south . the circumference of a full circle is 2 * pi * r , but since we only care about the length of half the circle , the semi - circle path is pi * r . l = pi * r = 30 . round pi = 3 , then r = 10 . chord is about 10 feet long . d\"" + }, + { + "Answer": 6, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "e", + "Explanation": "the question can be done in seconds if you understand the properties of factors of a number . note that every distinct factor of a number which is not a perfect square has a complementary factor . for example , factors of 6 : 1 , 2 , 3 , 6 1 has a complementary factor 6 such that 1 * 6 = 6 ( the original number ) 2 has a complementary factor 3 such that 2 * 3 = 6 ( the original number ) so if you have a number , n , which is not a perfect square , and start multiplying its factors , you will get n to a certain power . the power will half of the number of factors . for example , 6 has 4 factors and when you multiply all 4 factors , you get 6 ^ 2 ( 2 is half of 4 ) . so if you know that the product of all factors is x ^ 3 , it means there must have been twice the number of factors i . e . 3 * 2 = 6 factors . e )" + }, + { + "Answer": 18, + "Options": "a ) 10 years , b ) 12 years , c ) 14 years , d ) 18 years , e ) 16 years", + "Correct": "d", + "Explanation": "\"let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 47 5 x = 45 x = 9 . hence , b ' s age = 2 x = 19 years . d )\"" + }, + { + "Answer": 36.5, + "Options": "a ) 35.22 , b ) 36.12 , c ) 36.22 , d ) 36.42 , e ) none", + "Correct": "d", + "Explanation": "\"solution correct sum = ( 36 x 50 + 44 - 23 ) = 1821 . \u00e2 \u02c6 \u00b4 correct mean = 1821 / 50 = 36.42 . answer d\"" + }, + { + "Answer": 10, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", + "Correct": "d", + "Explanation": "\"let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 27 5 x = 25 = > x = 5 hence , b ' s age = 2 x = 10 years . answer : d\"" + }, + { + "Answer": 54, + "Options": "a ) 38 , b ) 47 , c ) 50 , d ) 53 , e ) 54", + "Correct": "e", + "Explanation": "if you list the amount eaten each hour , you ' ll get an equally spaced list , increasing by 4 each hour . in any equally spaced list , the median equals the mean . here , the mean is 450 / 9 = 50 , so the median is also 50 , and that is the amount eaten in the 5 th hour . we need to add 4 to find the total eaten in the next hour , so the answer is 54 option e ." + }, + { + "Answer": 0.6923076923076923, + "Options": "a ) 4 / 9 , b ) 5 / 4 , c ) 9 / 13 , d ) 5 / 9 , e ) 6 / 9", + "Correct": "c", + "Explanation": "\"income = salary ( s ) + tips = s + s * 9 / 4 = s * 13 / 4 tips = s * 9 / 4 fraction of his income came from tips = ( s * 9 / 4 ) / ( s * 13 / 4 ) = 9 / 13 answer : c\"" + }, + { + "Answer": 19, + "Options": "a ) 25 , b ) 23 , c ) 19 , d ) 18 , e ) 17", + "Correct": "c", + "Explanation": "explanation : sum of the present ages of husband , wife and child = ( 23 * 2 + 5 * 2 ) + 1 = 57 years . required average = ( 57 / 3 ) = 19 years . answer : c" + }, + { + "Answer": 8000, + "Options": "a ) rs . 8000 , b ) rs . 8400 , c ) rs . 7500 , d ) rs . 7800 , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : 8820 - - - - 441 100 - - - - ? = > 5 % x * 105 / 100 * 105 / 100 = 8820 x * 1.1025 = 8820 x = 8820 / 1.1025 = > 8000 answer is a\"" + }, + { + "Answer": 6, + "Options": "a ) 4.5 , b ) 5 , c ) 5.5 , d ) 5.8 , e ) 6", + "Correct": "e", + "Explanation": "\"if $ x $ is the number , x / 6 * 12 = 12 = > 2 x = 12 = > x = 6 e\"" + }, + { + "Answer": 12, + "Options": "a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12", + "Correct": "e", + "Explanation": "\"rx * ( t + 2 ) = w ry * ( t ) = w . also , w / ( t + 2 ) + w / t = ( 5 w / 4 ) * ( 1 / 3 ) or 1 / t + 1 / ( t + 2 ) = 5 / 12 - - > ( 3 + 2 ) / 12 = 1 / 4 + 1 / 6 thus , t = 4 . replacing , rx = w / 6 , w / 6 * t = 2 w or t = 12 days . answer : e\"" + }, + { + "Answer": 20, + "Options": "a ) 20 , b ) 10 , c ) 30 , d ) 40 , e ) 5", + "Correct": "a", + "Explanation": "arithmetic mean expression for p and q : ( p + q ) / 2 = 10 ; p + q = 20 - - - - eq 1 arithmetic mean expression for q and r : ( q + r ) / 2 = 20 ; q + r = 40 - - - - eq 2 subtracting eq 1 from eq 2 we get : r - p = 20 hence , the correct answer is a" + }, + { + "Answer": 10, + "Options": "a ) 12 , b ) 10 , c ) c is elder than a , d ) data inadequate , e ) none", + "Correct": "b", + "Explanation": "\"solution [ ( a + b ) - ( b + c ) ] = 10 \u00e2 \u20ac \u00b9 = \u00e2 \u20ac \u00ba a - c = 10 . answer b\"" + }, + { + "Answer": 4.5, + "Options": "a ) 8 , b ) 4.5 , c ) 3.2 , d ) 7 , e ) 3", + "Correct": "b", + "Explanation": "divide 9 / 4 by 1 / 2 = 9 / 4 \u00f7 1 / 2 = 9 / 4 * 2 / 1 = 18 / 4 = 4.5 . answer is b ." + }, + { + "Answer": 18.333333333333332, + "Options": "a ) 18.2 , b ) 20 , c ) 25 , d ) 26 , e ) 28", + "Correct": "a", + "Explanation": "1 . firstly find the mean : mean = ( 75 + 83 + 96 + 100 + 121 + 125 ) \u00f7 6 = 600 \u00f7 6 = 100 2 . next find the variance . to calculate the variance , take each difference , square it , and then average the result : ( 75 - 100 ) 2 + ( 83 - 100 ) 2 + ( 96 - 100 ) 2 + ( 100 - 100 ) 2 + ( 121 - 100 ) 2 + ( 125 - 100 ) 2 = ( - 25 ) 2 + ( - 17 ) 2 + ( - 4 ) 2 + ( 0 ) 2 + ( 21 ) 2 + ( 25 ) 2 = 625 + 289 + 16 + 0 + 441 + 625 = 1996 so the variance = 1996 \u00f7 6 = 332.66 . . . 3 . the standard deviation is just the square root of the variance = \u221a ( 332.66 . . . ) = 18.2 correct to 1 decimal places answer is a" + }, + { + "Answer": 18, + "Options": "a ) 15 , b ) 18 , c ) 20 , d ) 22 , e ) none", + "Correct": "b", + "Explanation": "\"sol . average = ( 8 + 12 + 16 + 20 + 24 + 28 / 6 ) = 108 / 6 = 18 answer b\"" + }, + { + "Answer": 86400, + "Options": "a ) 32,300 , b ) 172,800 , c ) 468,830 , d ) 86,400 , e ) 259,200", + "Correct": "d", + "Explanation": "\"every 2 seconds , 2 persons are added ( 8 - 6 ) . every second 1 persons are added . in a day 24 hrs = 24 * 60 minutes = 24 * 60 * 60 = 86400 seconds . 86400 * 1 = 86400 option d\"" + }, + { + "Answer": 50, + "Options": "a ) 26 , b ) 32 , c ) 38 , d ) 44 , e ) 50", + "Correct": "e", + "Explanation": "\"p - 7 = 3 ( k - 7 ) and so p = 3 k - 14 p + 2 = 2 ( k + 2 ) ( 3 k - 14 ) + 2 = 2 k + 4 k = 16 p = 34 p + k = 50 the answer is e .\"" + }, + { + "Answer": 16807, + "Options": "a ) 7 , b ) 49 , c ) 343 , d ) 2401 , e ) 16,807", + "Correct": "e", + "Explanation": "\"x * ( 1 / 7 ) ^ 2 = 7 ^ 3 x = 7 ^ 2 * 7 ^ 3 = 7 ^ 5 = 16,807 the answer is e .\"" + }, + { + "Answer": 20, + "Options": "a ) 50 % , b ) 30 % , c ) 25 % , d ) 20 % , e ) 90 %", + "Correct": "d", + "Explanation": "\"explanation : actually it means 2 is what percent of 10 , which can be calculated as , ( 2 / 10 ) * 100 = 2 * 10 = 20 answer : option d\"" + }, + { + "Answer": 15, + "Options": "a ) 15 , b ) 8 , c ) 4 , d ) 10 , e ) 3", + "Correct": "a", + "Explanation": "\"2 ab = ( a ( power 2 ) + b ( power 2 ) - ( a - b ) ( power 2 ) = 39 - 9 = 30 ab = 15 . answer is a .\"" + }, + { + "Answer": 120, + "Options": "a ) 36 liters , b ) 40 liters , c ) 45 liters , d ) 54 liters , e ) 120 liters", + "Correct": "e", + "Explanation": "\"a big container is 30 % full with water and after 54 liters of water is added , the container becomes 75 % full . hence these 54 liters account for 45 % of the container , which means that the capacity of it is 54 / 0.45 = 120 liters . or : if the capacity of the container is x liters then : 0.3 x + 54 = 0.75 x - - > x = 120 liters . answer : e\"" + }, + { + "Answer": 28, + "Options": "a ) 15 , b ) 28 , c ) 16 , d ) 12 , e ) 73", + "Correct": "b", + "Explanation": "\"( 80 / 100 ) * 60 \u00e2 \u20ac \u201c ( 4 / 5 ) * 25 48 - 20 = 28 answer : b\"" + }, + { + "Answer": 2.999999999999986, + "Options": "a ) a . 1 , b ) b . 2 , c ) c . 3 , d ) d . 4 , e ) e . 8", + "Correct": "c", + "Explanation": "if r were a multiple of 15 , the quotient r / 15 would be an integer . the fact that it ' s a decimal tells us that 15 goes into r eight whole times and some decimal part of a time . this decimal part , 0.2 is the remainder divided by the divisor . let b be the remainder . b / 15 = 0.2 = 1 / 5 b = ( 15 ) * ( 1 / 5 ) = 3 answer = ( c )" + }, + { + "Answer": 2.0833333333333335, + "Options": "a ) 4 / 15 , b ) 1 / 2 , c ) 15 / 22 , d ) 25 / 12 , e ) 11 / 4", + "Correct": "d", + "Explanation": "\"the time it takes printer x is 15 hours . the combined rate of y and z is 1 / 12 + 1 / 18 = 5 / 36 the time it takes y and z is 36 / 5 the ratio of times is 15 / ( 36 / 5 ) = 5 * 15 / 36 = 25 / 12 the answer is d .\"" + }, + { + "Answer": 9, + "Options": "a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9", + "Correct": "e", + "Explanation": "10 / 11 = 0.9090909090 . . . the odd - numbered decimal places are 9 . the answer is e ." + }, + { + "Answer": 10, + "Options": "a ) 11 , b ) 10 , c ) 12 , d ) 13 , e ) 14", + "Correct": "b", + "Explanation": "\"t 5 + t 21 = t 8 + t 15 + t 13 = > a + 4 d + a + 20 d = a + 7 d + a + 14 d + a + 12 d = > a + 9 d = 0 = > t 10 = 0 i . e . 10 th term is zero . answer : b\"" + }, + { + "Answer": 130, + "Options": "a ) 101 , b ) 116 , c ) 130 , d ) n = 131 , e ) n = 141", + "Correct": "d", + "Explanation": "sorry the answer n = 131 is d ." + }, + { + "Answer": 9, + "Options": "a ) 1 , b ) 3 , c ) 7 , d ) 9 , e ) can not be determined", + "Correct": "d", + "Explanation": "ab and cd are two digit integers , their sum can give us only one three digit integer of a kind of jjj it ' s 111 . so , a = 1 . 1 b + cd = 111 now , c can not be less than 9 , because no to digit integer with first digit 1 ( mean that it ' s < 20 ) can be added to two digit integer less than 90 to have the sum 111 ( if cd < 90 meaning c < 9 cd + 1 b < 111 ) - - > c = 9 answer : d ." + }, + { + "Answer": 160, + "Options": "a ) 140 , b ) 121 , c ) 110 , d ) 160 , e ) none", + "Correct": "d", + "Explanation": "\"explanation : average amount paid by 7 persons = rs . 80 increase in average due to rs . 70 paid extra by the 8 th men = rs . 70 / 7 = rs . 10 therefore , average expenditure of 8 friends = rs . 80 + rs . 10 = rs . 90 therefore , amount paid by the 11 th men = rs . 90 + rs . 70 = rs . 160 correct option : d\"" + }, + { + "Answer": 0.14285714285714285, + "Options": "a ) 6 / 7 , b ) 1 / 7 , c ) 5 / 7 , d ) 3 / 2 , e ) 4 / 7", + "Correct": "b", + "Explanation": "answer : option b a / b = 4 / 1 = > a = 4 b ( a - 3 b ) / ( 2 a - b ) = ( 4 b - 3 b ) / ( 8 b - b ) = b / 7 b = > 1 / 7" + }, + { + "Answer": 31, + "Options": "a ) 23 , b ) 43 , c ) 21 , d ) 31 , e ) 43", + "Correct": "d", + "Explanation": "sol . let a , b , c represent their individual wgts . then , a + b + c = ( 45 * 3 ) kg = 135 kg a + b = ( 40 * 2 ) kg = 80 kg & b + c = ( 43 * 2 ) kg = 86 kg b = ( a + b ) + ( b + c ) - ( a + b + c ) = ( 80 + 86 - 135 ) kg = 31 kg . answer d" + }, + { + "Answer": 28, + "Options": "a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28", + "Correct": "e", + "Explanation": "there are 8 integers from - 3 to 4 inclusive . 8 c 2 = 28 . the answer is e ." + }, + { + "Answer": 26, + "Options": "a ) 21 , b ) 20 , c ) 26 , d ) 30 , e ) 45", + "Correct": "c", + "Explanation": "\"let number is x . when 20 added to it , = ( x + 20 ) 2 multiplied to sum , = 2 * ( x + 20 ) now , = [ { 2 * ( x + 20 ) } / 2 ] and , = [ { 2 * ( x + 20 ) } / 2 ] - 2 according to question , [ { 2 * ( x + 20 ) } / 2 ] - 2 = half of 88 [ ( 2 x + 40 ) / 2 ) = 44 + 2 2 x + 40 = 46 * 2 x + 20 = 46 x = 46 - 20 x = 26 so , required number is : 26 . answer : c\"" + }, + { + "Answer": 0.1428571428571428, + "Options": "a ) 1 / 4 , b ) 4 / 5 , c ) 1 / 5 , d ) 1 / 6 , e ) 1 / 7", + "Correct": "e", + "Explanation": "if s is an integer and we know that the average speed is 2.8 , s must be = 2 . that meanss + 1 = 3 . this implies that the ratio of time for s = 2 is 1 / 4 of the total time . the formula for distance / rate is d = rt . . . so the distance travelled when s = 2 is 2 t . the distance travelled for s + 1 = 3 is 3 * 4 t or 12 t . therefore , total distance covered while the sun was shining over him is e = 2 / 14 = 1 / 7 . answer : e" + }, + { + "Answer": 98, + "Options": "a ) 96 % , b ) 98 % , c ) 95 % , d ) 97 % , e ) 96 %", + "Correct": "b", + "Explanation": "\"let the number be x the right number is 5 x the wrong number is x / 10 error is ( 5 x - x / 10 ) = 49 x / 10 percentage of error is ( ( 49 x / 10 ) / 5 x ) * 100 = 98 % answer : b\"" + }, + { + "Answer": 5, + "Options": "a ) 3 , b ) 3.5 , c ) 4 , d ) 4.5 , e ) 5", + "Correct": "e", + "Explanation": "\"0 . [ u ] 325 [ / u = 0.325325325 . . . . . every 3 rd digit is 5 and every multiple of 3 will be the digit 5 . since 81 is multiple of 3 , the 81 st digit is 5 . answer e\"" + }, + { + "Answer": 2, + "Options": "a ) 2 d , b ) d , c ) 2 d + 2 , d ) 8 d , e ) 2 d + 4", + "Correct": "b", + "Explanation": "concept : standard deviation is defined as average deviation of terms in the set from the mean value of the set . i . e . 1 ) it depends on the separation between the successive terms of the set 2 ) if a constant value is added / subtracted in every terms of set then the separation between successive terms does not change hence s . d . remains constant e . g . { 1 , 2 , 3 , 4 , 5 } will have same standard deviation as { 1 + 10 , 2 + 10 , 3 + 10 , 4 + 10 , 5 + 10 } 3 ) if a constant value is multiplied in every terms then the separation between succesive terms gets multiplied by the constant hence s . d . remains gets multiplied by same number e . g . { 0.7 , 1.4 , 2.1 , 2.8 , 3.5 } will have standard deviation = 0.7 * standard deviation of set { 1 , 2 , 3 , 4 , 5 } when 2 is added in each term of set { a , b , c } then the new set { a + 2 , b + 2 , c + 2 } will remain same as the previous standard deviation i . e . d answer : b" + }, + { + "Answer": 416.6666666666667, + "Options": "a ) 412.16 , b ) 150 , c ) 400 , d ) 416.67 , e ) 420.34", + "Correct": "d", + "Explanation": "\"system of equations a = ( 36 / 100 ) c ( 1 / 2 ) a = 75 - - > a = 150 substitution 150 = ( 36 / 100 ) c c = ( 100 / 36 ) 150 calculate 150 / 36 * 100 the correct answer is d - the correct answer will be slightly smaller than 513 . therefore , the correct answer is 475 .\"" + }, + { + "Answer": 8, + "Options": "a ) a ) 2 , b ) b ) 4 , c ) c ) 6 , d ) d ) 8 , e ) e ) 18", + "Correct": "d", + "Explanation": "6 , 6,6 , 7,8 , 8,8 , 8,8 , 9,9 so you will observer that the median of the list is 8 . ans d" + }, + { + "Answer": 512, + "Options": "a ) 412 , b ) 502 , c ) 512 , d ) 522 , e ) none", + "Correct": "c", + "Explanation": "\"answer let 62976 / n = 123 then n = 62976 / 123 = 512 . option : c\"" + }, + { + "Answer": 0.6, + "Options": "a ) $ 0.60 , b ) $ 0.80 , c ) $ 1.00 , d ) $ 1.20 , e ) $ 1.60", + "Correct": "a", + "Explanation": "\"let price of a sundae = s price of ice cream bar = . 4 $ 200 * . 4 + 200 * s = 200 = > 200 * s = 200 = > s = 0.6 answer a\"" + }, + { + "Answer": 350, + "Options": "a ) a ) 300 , b ) b ) 350 , c ) c ) 450 , d ) d ) 470 , e ) e ) 500", + "Correct": "b", + "Explanation": "\"explanation : 10 * 150 = 1500 4 * 100 + 5 * 150 = 1150 1500 \u2013 1150 = 350 b\"" + }, + { + "Answer": 57, + "Options": "a ) 57 , b ) 59 , c ) 63 , d ) 71 , e ) 92", + "Correct": "a", + "Explanation": "\"total = 70 thrower = 31 rest = 70 - 31 = 39 left handed = 39 / 3 = 13 right handed = 26 if all thrower are right handed then total right handed is 31 + 26 = 57 so a . 57 is the right answer\"" + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25", + "Correct": "a", + "Explanation": "speed of the train = ( 54 * 5 / 18 ) m / sec = 15 m / sec . length of the train = ( speed x time ) time = ( length of the train / speed ) = ( 75 / 15 ) = 5 sec answer : a" + }, + { + "Answer": 3.999999999999936, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "d", + "Explanation": "\"( 1077 / 23 ) gives a remainder 19 so we need to add 4 . the answer is d .\"" + }, + { + "Answer": 4, + "Options": "a ) 1 : 2 , b ) 3 : 2 , c ) 4 : 1 , d ) 5 : 2 , e ) 6 : 5", + "Correct": "c", + "Explanation": "\"g = 19 w c = 9 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 19 w + 9 wx = x + 1 * 17 w 19 + 9 x = 17 ( x + 1 ) x = 1 / 4 ratio of gold with copper = 1 : 1 / 4 = 4 : 1 answer is c\"" + }, + { + "Answer": 55, + "Options": "a ) 50 , b ) 88 , c ) 66 , d ) 55 , e ) 22", + "Correct": "d", + "Explanation": "\"let the length of each train be x m . then , distance covered = 2 x m . relative speed = 47 - 36 = 11 km / hr . = 11 * 5 / 18 = 55 / 18 m / sec . 2 x / 36 = 55 / 18 = > x = 55 . answer : d\"" + }, + { + "Answer": 93, + "Options": "a ) 90 , b ) 93 , c ) 56 , d ) 80.5 , e ) 78", + "Correct": "b", + "Explanation": "\"total increase in weight = 8 \u00d7 6 = 48 if x is the weight of the new person , total increase in weight = x \u2212 45 = > 48 = x - 45 = > x = 48 + 45 = 93 answer : b\"" + }, + { + "Answer": 91, + "Options": "a ) 31 , b ) 35 , c ) 50 , d ) 91 , e ) 101", + "Correct": "d", + "Explanation": "2 ^ 10 = 1.024 * 10 ^ 3 = > 2 ^ 100 = ( 1.024 ) ^ 10 * 10 ^ 90 therefore 91 digits would be my best guess d" + }, + { + "Answer": 358, + "Options": "a ) 328 , b ) 348 , c ) 358 , d ) 362 , e ) data inadequate", + "Correct": "c", + "Explanation": "explanation : let the total number of sweets be ( 25 x + 8 ) . then , ( 25 x + 8 ) - 22 is divisible by 28 ( 25 x - 14 ) is divisible by 28 28 x - ( 3 x + 14 ) is divisible by 28 ( 3 x + 14 ) is divisible by 28 x = 14 . therefore total number of sweets = ( 25 x 14 + 8 ) = 358 . answer : c" + }, + { + "Answer": 46, + "Options": "a ) 40 , b ) 41 , c ) 46 , d ) 42 , e ) 49", + "Correct": "c", + "Explanation": "\"total age of all students = 23 \u00e3 \u2014 22 total age of all students + age of the teacher = 24 \u00e3 \u2014 23 age of the teacher = 24 \u00e3 \u2014 23 \u00e2 \u02c6 \u2019 23 \u00e3 \u2014 22 = 23 ( 24 \u00e2 \u02c6 \u2019 22 ) = 23 \u00e3 \u2014 2 = 46 answer is c .\"" + }, + { + "Answer": 2, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "c", + "Explanation": "the equation of line a is y = - x + 2 the equation of line b is y = 5 x - 10 5 x - 10 = - x + 2 x = 2 y = 0 the point of intersection is ( 2,0 ) and then a + b = 2 . the answer is c ." + }, + { + "Answer": 5.5, + "Options": "a ) 5 / 2 , b ) 10 / 3 , c ) 7 / 2 , d ) 14 / 3 , e ) 11 / 2", + "Correct": "e", + "Explanation": "\"for 2 q ^ 2 + 5 q = 12 roots are [ - 5 + sqrt ( 25 + 96 ) ] / 4 or [ - 5 - sqrt ( 25 + 96 ) ] / 4 = 1.5 or - 4 hence larger root 1.5 is 1.5 - ( - 4 ) = 5.5 = 11 / 2 greater than smaller root ( - 4 ) . hence option ( e ) .\"" + }, + { + "Answer": 4, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 7", + "Correct": "d", + "Explanation": "\"mean = ( x + x + 2 + x + 4 + x + 7 + x + 27 ) / 5 = ( 5 x + 40 ) / 5 = x + 8 median = x + 4 thus mean - median = x + 8 - ( x + 4 ) = 4 answer = d\"" + }, + { + "Answer": 84, + "Options": "a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %", + "Correct": "d", + "Explanation": "\"16 % ________________________________________________ m + g 34 % ________________________________________________ m 34 % ________________________________________________ m - g 16 % since 68 % lies one standard deviation from mean m , = > 50 % of 68 % lies on either side as it is symmetric about m . thus 16 % lie below m - g and 16 % lie above m + g now below m + g = 16 + 34 + 34 = 84 % hence d\"" + }, + { + "Answer": 600, + "Options": "a ) 300 , b ) 600 , c ) 800 , d ) 1000 , e ) 900", + "Correct": "b", + "Explanation": "explanation : let their maximum marks be x . then , 35 % of x = 185 + 25 = > 35 / 100 x = 210 x = ( 210100 / 35 ) x = 600 . answer : b" + }, + { + "Answer": 35, + "Options": "a ) 25 % , b ) 28 % , c ) 30 % , d ) 32.5 % , e ) 35 %", + "Correct": "e", + "Explanation": "\"1 st year income = i 1 st year savings = s 1 st year expense = e 1 2 nd year income = 1.35 i 2 nd year savings = 2 s ( 100 % increase ) 2 nd year expense = e 2 e 1 + e 2 = 2 e 1 e 2 = e 1 that means expenses are same during both years . with increase of 35 % income the savings increased by 100 % . or s = . 35 i or s = 35 % of income e is the answer\"" + }, + { + "Answer": 144, + "Options": "a ) 114 , b ) 120 , c ) 134 , d ) 144 , e ) none of these", + "Correct": "d", + "Explanation": "explanation : the ratio of their initial investment = 1 / 2 : 1 / 3 : 1 / 4 = 6 : 4 : 3 let ' s take the initial investment of p , q and r as 6 x , 4 x and 3 x respectively a : b : c = ( 6 x * 2 + 3 x * 10 ) : 4 x * 12 : 3 x * 12 = ( 12 + 30 ) : 4 * 12 : 3 * 12 = ( 4 + 10 ) : 4 * 4 : 12 = 14 : 16 : 12 = 7 : 8 : 6 b ' s share = 378 * ( 8 / 21 ) = 18 * 8 = 144 . answer : option d" + }, + { + "Answer": 122, + "Options": "a ) 22 , b ) 38 , c ) 62 , d ) 122 , e ) 672", + "Correct": "d", + "Explanation": "\"same logic but with application of factorials . 2 * 4 * 6 * 8 * . . . * n = 2 ( 1 * 2 * 3 * 4 * . . . n / 2 ) = 2 * ( n / 2 ) ! now we have : 2 * ( n / 2 ) ! / 2013 = 2 * ( n / 2 ) ! / ( 3 \u00d7 11 \u00d7 61 ) for the expression 2 * ( n / 2 ) ! to be divisible by 2013 min value of n / 2 should be 61 . so n / 2 = 61 = > n = 122 answer d .\"" + }, + { + "Answer": 1.7777777777777777, + "Options": "a ) 2 / 7 , b ) 9 / 4 , c ) 16 / 25 , d ) 7 / 1 , e ) 16 / 9", + "Correct": "e", + "Explanation": "for a 2 nd degree equation ax 2 + bx _ c = 0 has equal roots the condition is b 2 - 4 ac = 0 in the given equation ( 3 k ) ^ 2 - 4 * 2 k * 2 = 0 by solving this equation we get k = 0 , k = 16 / 9 answer : e" + }, + { + "Answer": 60, + "Options": "a ) 60 , b ) 50 , c ) 66 , d ) 54 , e ) none", + "Correct": "a", + "Explanation": "sol . let the total original sale be rs . 100 . then , original number of visitors = 100 . new number of visitors = 120 / 0.75 = 160 . \u2234 increase % = 60 % . answer a" + }, + { + "Answer": 18.333333333333332, + "Options": "a ) 18.20 , b ) 18.33 , c ) 18 , d ) 18.3 , e ) none of these", + "Correct": "b", + "Explanation": "\"explanation : present worth = amount - truediscount = 110 - 10 = rs . 100 si on rs . 100 for a certain time = rs . 10 si on rs . 100 for doube the time = rs . 20 truediscount on rs . 120 = 120 - 100 = rs . 20 truediscount on rs . 110 = ( 110 x 20 / 120 ) = rs . 18.33 answer : b\"" + }, + { + "Answer": 115.38461538461537, + "Options": "a ) 45 % , b ) 65 % , c ) 85 % , d ) 115 % , e ) 125 %", + "Correct": "d", + "Explanation": "\"let x be the number of new biographies added to the library . let b be the original number of biographies , so the original number of books was 5 b . 0.35 ( 5 b + x ) = b + x 0.75 b = 0.65 x x = 1.15 b the answer is d .\"" + }, + { + "Answer": 56.333333333333336, + "Options": "a ) 56.33 , b ) 34.89 , c ) 23.67 , d ) 54.65 , e ) 43.98", + "Correct": "a", + "Explanation": "average marks of batch 1 = 45 students in batch 1 = 40 total marks of batch 1 = 40 * 45 average marks of batch 2 = 55 students in batch 2 = 50 total marks of batch 2 = 50 \u00d7 55 average marks of batch 3 = 65 students in batch 3 = 60 total marks of batch 3 = 65 \u00d7 60 total students = 40 + 60 + 50 = 150 average marks of all the students = ( ( 40 * 45 ) + ( 50 \u00d7 55 ) + ( 65 \u00d7 60 ) ) / 150 = 169 / 3 = 56.333 answer is a ." + }, + { + "Answer": 91, + "Options": "a ) 52 , b ) 49 , c ) 91 , d ) 88 , e ) 66", + "Correct": "c", + "Explanation": "right side = 15 seat left side = 15 - 3 ( 3 few seat in right side ) = 12 seat total = 15 + 12 = 27 people can seat in 27 seat = 27 * 3 = 81 people can seat in last seat = 10 total people can seat = 81 + 10 = 91 answer : c" + }, + { + "Answer": 7, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "e", + "Explanation": "\"let x = 4.1 and y = 11.1 greatest possible difference = 11.1 - 4.1 = 7 answer e\"" + }, + { + "Answer": 10, + "Options": "a ) 22 , b ) 10 , c ) 25 , d ) 99 , e ) 21", + "Correct": "b", + "Explanation": "\"let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 80 x - ( 5 * 70 ) = 90 ( x - 5 ) 100 = 10 x = > x = 10 . answer : b\"" + }, + { + "Answer": 21, + "Options": "a ) 19 , b ) 20 , c ) 21 , d ) 22 , e ) 23", + "Correct": "c", + "Explanation": "\"y = 276 * a + 44 = ( 23 * 12 ) * a + 23 + 21 the answer is c .\"" + }, + { + "Answer": 26, + "Options": "a ) 21 , b ) 22 , c ) 23 , d ) 26 , e ) 28", + "Correct": "d", + "Explanation": "\"let the average age of the whole team be x years . 11 x - ( 29 + 32 ) = 9 ( x - 1 ) = > 11 x - 9 x = 52 = > 2 x = 52 = > x = 26 . so , average age of the team is 26 years . d\"" + }, + { + "Answer": 2, + "Options": "a ) - 5 , b ) - 4 , c ) 4 , d ) 3 , e ) 2", + "Correct": "e", + "Explanation": "\"1 . subtract 1 from both sides : x + 1 - 1 = 3 - 1 2 . simplify both sides : x = 2 e\"" + }, + { + "Answer": 23, + "Options": "a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24", + "Correct": "d", + "Explanation": "\"check two extreme cases : jane = 18 , child = 9 , years ago = 32 - 18 = 14 - - > child ' s age now = 9 + 14 = 23 ; jane = 20 , child = 10 , years ago = 32 - 20 = 12 - - > child ' s age now = 10 + 12 = 22 . answer : d .\"" + }, + { + "Answer": 7, + "Options": "a ) 0 , b ) 1 , c ) 5 , d ) 7 , e ) 9", + "Correct": "d", + "Explanation": "\"i looked for patterns : ^ 2 - units digit 9 ^ 3 - units digit 7 ^ 4 - units digit 1 ^ 5 - units digit 3 hence , we can see that when raised to a power which is multiple of 4 , the units digit is 1 , and when to an even power not multiple of 4 , the units digit is 9 and we can then see : ^ 16 - units digit 1 , or ^ 18 - units digit 9 and ^ 19 - units digit 7 therefore , r = when divided by 10 , the remainder must be 7 . d\"" + }, + { + "Answer": 1, + "Options": "a ) - 3 , b ) - 1 , c ) - 1 / 3 , d ) 0 , e ) 1", + "Correct": "e", + "Explanation": "\"the midpoint of ( 2,8 ) and ( 6 , - 4 ) is ( 4,2 ) . the slope of a line through ( 0 , - 2 ) and ( 4,2 ) is ( 2 - ( - 2 ) ) / ( 4 - 0 ) = 4 / 4 = 1 the answer is e .\"" + }, + { + "Answer": 35, + "Options": "a ) 20 , b ) 25 , c ) b = 30 , d ) b = 35 , e ) b = 40", + "Correct": "d", + "Explanation": "\"suppose the population of the country in current year is 1000 . so annual increase is 1000 + 39.4 - 19.4 = 1020 hence every year there is an increase of 2 % . 2000 = 1000 ( 1 + ( 2 / 100 ) ) ^ n n = 35 answer is d .\"" + }, + { + "Answer": 88, + "Options": "a ) 55 , b ) 60 , c ) 73 , d ) 82 , e ) 88", + "Correct": "e", + "Explanation": "\"let the number of correct responses be x then the number of incorrect responses = 100 - x according to question x - 2 ( 100 - x ) = 64 ( subtracting twice of incorrect from correct ) 3 x = 264 x = 88 answer : e\"" + }, + { + "Answer": 890, + "Options": "a ) 340 , b ) 330 , c ) 320 , d ) 310 , e ) 890", + "Correct": "e", + "Explanation": "number of rhinos = 8000 watering area = 10,000 acres number of rhino to increase by 10 percent , then number of rhino = 8800 grazing area for a rhino = 100 total grazing area for 8800 rhinos = 8800 * 100 = 8 , 80,000 total area required for the wildlife preserve = 8 , 80,000 + 10,000 = 8 , 90,000 = 890 * 1000 answer e" + }, + { + "Answer": 112, + "Options": "a ) $ 112.00 , b ) $ 64.80 , c ) $ 90.00 , d ) $ 100.80 , e ) $ 154.80", + "Correct": "a", + "Explanation": "\"correct answer : a the tourist must pay tax on $ 1720 - $ 600 = $ 1120 . thus , the amount of tax he has to pay is 0.1 ( $ 1120 ) = $ 112 . the correct answer is a .\"" + }, + { + "Answer": 35, + "Options": "a ) 78 years , b ) 22 years , c ) 88 years , d ) 35 years , e ) 65 years", + "Correct": "d", + "Explanation": "\"let ' s son age is x , then father age is x + 37 . = > 2 ( x + 2 ) = ( x + 37 + 2 ) = > 2 x + 4 = x + 39 = > x = 35 years answer : d\"" + }, + { + "Answer": 960, + "Options": "a ) 960 , b ) 1000 , c ) 1020 , d ) 1080 , e ) 1075", + "Correct": "a", + "Explanation": "0.8 * 600 = 0.5 * x x = 8 / 5 * 600 = 960" + }, + { + "Answer": 24, + "Options": "a ) 4 , b ) 52 , c ) 16 , d ) 24 , e ) 64", + "Correct": "d", + "Explanation": "\"by formula , ( a + b + c ) ^ 2 = a ^ 2 + b ^ 2 + c ^ 2 + 2 ( ab + bc + ca ) , since , a ^ 2 + b ^ 2 + c ^ 2 = 560 and ab + bc + ca = 8 , ( a + b + c ) ^ 2 = 560 + 2 ( 8 ) = 576 = 24 ^ 2 therefore : a + b + c = 24 answer : d\"" + }, + { + "Answer": 12.5, + "Options": "a ) 10.5 , b ) 11 , c ) 11.5 , d ) 12 , e ) 12.5", + "Correct": "e", + "Explanation": "\"the value which isexactlytwo sd less than the mean is : mean - 2 * sd = 15.5 - 2 * 1.5 = 12.5 . answer : e .\"" + }, + { + "Answer": 1184, + "Options": "a ) 1184 , b ) 1723 , c ) 1129 , d ) 2613 , e ) 1372", + "Correct": "a", + "Explanation": "\"a 1184 b has 62.5 % or ( 5 / 8 ) of the milk in a . therefore , let the quantity of milk in container a ( initially ) be 8 k . quantity of milk in b = 8 k - 5 k = 3 k . quantity of milk in container c = 8 k - 3 k = 5 k container : a b c quantity of milk : 8 k 3 k 5 k it is given that if 148 liters was transferred from container c to container b , then both the containers would have equal quantities of milk . 5 k - 148 = 3 k + 148 = > 2 k = 296 = > k = 148 the initial quantity of milk in a = 8 k = 8 * 148 = 1184 liters .\"" + }, + { + "Answer": 5290, + "Options": "a ) 5336 , b ) 4306 , c ) 4236 , d ) 4336 , e ) none", + "Correct": "a", + "Explanation": "sol . divisor = ( 5 \u00d7 46 ) = 230 . also , 10 \u00d7 q = 230 \u21d2 q = 23 . and , r = 46 . dividend = ( 230 \u00d7 23 + 46 ) = 5336 . answer a" + }, + { + "Answer": 62, + "Options": "a ) 54 , b ) 59 , c ) 63 , d ) 71 , e ) 62", + "Correct": "e", + "Explanation": "\"total = 70 thrower = 46 rest = 70 - 46 = 24 left handed = 24 / 3 = 8 right handed = 16 if all thrower are right handed then total right handed is 46 + 16 = 62 so e . 62 is the right answer\"" + }, + { + "Answer": 13, + "Options": "a ) 10 , b ) 11 , c ) 13 , d ) 15 , e ) 16", + "Correct": "c", + "Explanation": "here n = 18 = 2 \u00d7 32 \u03d5 ( 18 ) = 18 ( 1 \u2212 12 ) ( 1 \u2212 13 ) = 6 so 56 when divided by 18 , remainder is 1 . so we can write the given expression 5100 = ( 56 ) 16 \u00d7 54 = ( 1 ) 16 \u00d7 54 = 52 \u00d7 52 = 7 \u00d7 7 = 49 now 49 when divided by 18 , remainder is 13 . c" + }, + { + "Answer": 2, + "Options": "a ) 16 . , b ) 8 . , c ) 7 . , d ) 2 . , e ) - 2 .", + "Correct": "d", + "Explanation": "\"given a + b = 4 b + c = 7 c + d = 5 ( a + b ) - ( b + c ) + ( c + d ) = ( a + d ) = > 4 - 7 + 5 = 2 . option d . . .\"" + }, + { + "Answer": 0.27999999999999997, + "Options": "a ) 0.06 , b ) 0.12 , c ) 0.21 , d ) 0.29 , e ) 0.28", + "Correct": "e", + "Explanation": "the probability that eachdoesn ' thit is : 0.5 , 0.8 , and 0.7 . when we have multiple independent events , we multiply the probabilities : . 5 * . 8 * . 7 = 0.28 . option : e" + }, + { + "Answer": 20000, + "Options": "a ) $ 20000 , b ) $ 15000 , c ) $ 12000 , d ) $ 10000 , e ) $ 9000", + "Correct": "a", + "Explanation": "\"since investment doubles in 70 / r years then for r = 4 it ' ll double in 70 / 4 = ~ 18 years ( we are not asked about the exact amount so such an approximation will do ) . thus in 36 years investment will double twice and become ( $ 5,000 * 2 ) * 2 = $ 20,000 ( after 18 years investment will become $ 5,000 * 2 = $ 10,000 and in another 18 years it ' ll become $ 10,000 * 2 = $ 20,000 ) . answer : a .\"" + }, + { + "Answer": 0.041666666666666664, + "Options": "a ) 1 / 32 , b ) 1 / 28 , c ) 1 / 24 , d ) 1 / 16 , e ) 1 / 14", + "Correct": "c", + "Explanation": "there are 3 single digit multiple of 3 , that is , 3 , 69 . there are 8 prime nos less than 20 - 23 , 57 , 1113 , 1719 total outcome - 8 * 3 = 24 favourable outcome = 1 ( 9 * 5 ) hence required probability = 1 / 24 . answer c ." + }, + { + "Answer": 0.2, + "Options": "a ) 1 / 10 , b ) 1 / 5 , c ) 2 / 5 , d ) 3 / 5 , e ) 3 / 10", + "Correct": "b", + "Explanation": "p 2 \u2013 13 p + 40 = h so ( p \u2013 8 ) ( p \u2013 5 ) = h for q to be negative , the expressions ( p \u2013 8 ) and ( p \u2013 5 ) must have opposite signs . which integers on the number line will yield opposite signs for the expressions ( p \u2013 8 ) and ( p \u2013 5 ) ? those integers in the range 5 < p < 8 ( notice 5 and 8 are not included because they would both yield a value of zero and zero is a nonnegative integer ) . that means that there are only two integer values for p , 6 and 7 , that would yield a negative q . with a total of 10 possible p values , only 2 yield a negative q , so the probability is 2 / 10 or 1 / 5 . the correct answer is b ." + }, + { + "Answer": 0.3333333333333333, + "Options": "a ) 5 / 12 , b ) 12 / 5 , c ) 1 / 3 , d ) 144 / 25 , e ) 146 / 25", + "Correct": "c", + "Explanation": "let the number be x . then , 2 / 3 x = 16 / 216 * 1 / x x 2 = 16 / 216 * 3 / 2 = 16 / 144 = 1 / 9 x = 1 / 3 answer : c" + }, + { + "Answer": 13, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 13 , e ) 10", + "Correct": "d", + "Explanation": "we have : 1 ) x < y < z 2 ) y - x > 9 3 ) x = 2 k ( x is an even number ) 4 ) y = 2 n + 1 ( y is an odd number ) 5 ) z = 2 p + 1 ( z is an odd number ) 6 ) z - x = ? least value z - x = 2 p + 1 - 2 k = 2 p - 2 k + 1 = 2 ( p - k ) + 1 - that means that z - x must be an odd number . we can eliminate answer choices a , c and e we are asked to find the least value , so we have to pick the least numbers since y is odd and x is even , y - x must be odd . since y - x > 9 , the least value for y - x must be 11 , the least value for x must be 2 , and , thus , the least possible value for y must be 13 ( y - 2 = 11 , y = 13 ) 2 < 13 < z , since z is odd , the least possible value for z is 15 z - x = 15 - 2 = 13 answer d" + }, + { + "Answer": 15, + "Options": "a ) 15 , b ) 17 , c ) 19 , d ) 21 , e ) 26", + "Correct": "a", + "Explanation": "let the three integers be x , x + 2 and x + 4 . then , 3 x = 2 ( x + 4 ) + 3 x = 11 . third integer = x + 4 = 15 . option a" + }, + { + "Answer": 54, + "Options": "a ) 18 , b ) 28 , c ) 48 , d ) 38 , e ) 54", + "Correct": "e", + "Explanation": "let x = the number sought . then x / 9 + x + 9 = 69 . and x = 54 . e" + }, + { + "Answer": 10.000000000000014, + "Options": "a ) 20 % , b ) 10 % , c ) 25 % , d ) 18 % , e ) 30 %", + "Correct": "b", + "Explanation": "\"let the original price be $ 100 new final price = 120 % of ( 75 % of $ 100 ) = 120 / 100 * 75 / 100 * 100 = $ 90 decrease is 10 % answer is b\"" + }, + { + "Answer": 55, + "Options": "a ) 75 kg , b ) 85 kg , c ) 95 kg , d ) 65 kg , e ) 55 kg", + "Correct": "e", + "Explanation": "\"the total weight increase = ( 8 x 2.5 ) kg = 20 kg weight of new person = ( 35 + 20 ) kg = 55 kg the answer is e .\"" + }, + { + "Answer": 86400, + "Options": "a ) 86,400 , b ) 172,800 , c ) 468,830 , d ) 338,200 , e ) 259,200", + "Correct": "a", + "Explanation": "\"every 2 seconds , 2 persons are added ( 4 - 2 ) . every second 1 person are added . in a day 24 hrs = 24 * 60 minutes = 24 * 60 * 60 = 86400 seconds . 86400 * 1 = 86400 option a\"" + }, + { + "Answer": 8, + "Options": "a ) 7 , b ) 9 , c ) 8 , d ) 11 , e ) 10", + "Correct": "c", + "Explanation": "\"explanation : let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 22 \u21d2 5 x = 20 \u21d2 x = 4 . hence , b ' s age = 2 x = 8 years . answer : c\"" + }, + { + "Answer": 800, + "Options": "a ) 700 , b ) 300 , c ) 250 , d ) 550 , e ) 800", + "Correct": "e", + "Explanation": "let the price of a pant and a t - shirt be rs . x and rs . y respectively . then , 3 x + 6 y = 1500 . . . . ( i ) and x + 12 y = 1500 . . . . ( ii ) divide equation ( i ) by 3 , we get the below equation . = x + 2 y = 500 . - - - ( iii ) now subtract ( iii ) from ( ii ) x + 12 y = 1500 ( - ) x + 2 y = 500 - - - - - - - - - - - - - - - - 10 y = 1000 - - - - - - - - - - - - - - - - cost of 8 t - shirts = 8 * 100 = 800 answer : e" + }, + { + "Answer": 290, + "Options": "a ) rs . 260 , b ) rs . 270 , c ) rs . 280 , d ) rs . 290 , e ) rs . 300", + "Correct": "d", + "Explanation": "let b gets rs x . then we can say a gets rs ( x + 40 ) and c gets rs ( x + 70 ) . x + 40 + x + x + 70 = 770 3 x = 660 x = 220 . b \u00e2 \u20ac \u2122 s share = rs ( 220 + 70 ) = rs . 290 d" + }, + { + "Answer": 16, + "Options": "a ) 15 , b ) 16 , c ) 11 , d ) 18 , e ) 13", + "Correct": "b", + "Explanation": "\"let the population of two villages be equal after p years then , 74000 - 1200 p = 42000 + 800 p 2000 p = 32000 p = 16 answer is b .\"" + }, + { + "Answer": 66.66666666666666, + "Options": "a ) 12.5 % , b ) 66.6 % , c ) 80 % , d ) 11 % , e ) 1 %", + "Correct": "b", + "Explanation": "\"say y = 1 and x = 3 . then y = 1 is less than x = 3 by ( 3 - 1 ) / 3 * 100 = 2 / 3 * 100 = 66.6 % . answer : b .\"" + }, + { + "Answer": 300, + "Options": "a ) 450 , b ) 300 , c ) 500 , d ) 610 , e ) 175", + "Correct": "b", + "Explanation": "\"let the maximum marks be x then , 33 % of x = 59 + 40 33 x / 100 = 99 x = 300 answer is b\"" + }, + { + "Answer": 16, + "Options": "a ) 20 % , b ) 16 % , c ) 15 % , d ) 12 % , e ) 10 %", + "Correct": "b", + "Explanation": "\"let x be the amount of gasoline the driver buys originally . let y be the new amount of gasoline the driver should buy . let p be the original price per liter . ( 1.25 * p ) y = 1.05 ( p * x ) y = ( 1.05 / 1.25 ) x = 0.84 x which is a reduction of 16 % . the answer is b .\"" + }, + { + "Answer": 10, + "Options": "a ) 8 % , b ) 10 % , c ) 2 % , d ) 5 % , e ) 6 %", + "Correct": "b", + "Explanation": "actual price = 100 + 10 = $ 110 saving = 10 / 110 * 100 = 100 / 11 = 10 % approximately answer is b" + }, + { + "Answer": 96, + "Options": "a ) 72 , b ) 84 , c ) 88 , d ) 96 , e ) 108", + "Correct": "d", + "Explanation": "r = j + 8 = k + 4 r + 2 = 3 ( j + 2 ) ( j + 8 ) + 2 = 3 j + 6 j = 2 r = 10 k = 6 in 2 years ( r + 2 ) ( k + 2 ) = 12 * 8 = 96 the answer is d ." + }, + { + "Answer": 8, + "Options": "a ) 2 liters , b ) 3 liters , c ) 8 liters , d ) 5 liters , e ) 7 liters", + "Correct": "c", + "Explanation": "number of liters of water in 120 liters of the mixture = 20 % of 120 = 20 / 100 * 120 = 24 liters . p liters of water added to the mixture to make water 25 % of the new mixture . total amount of water becomes ( 24 + p ) and total volume of mixture is ( 120 + p ) . ( 24 + p ) = 25 / 100 * ( 120 + p ) 96 + 4 p = 120 + p p = 8 liters . answer : c" + }, + { + "Answer": 18.8, + "Options": "a ) 18 , b ) 18.8 , c ) 19 , d ) 17.8 , e ) 17.9", + "Correct": "b", + "Explanation": "at the non - discounted price , each friend would pay $ 20 , as $ 100 divided by 5 friends is $ 20 per friend . but if the bill is 6 % off , then each friend would pay 6 % less . 6 % of $ 20 is $ 1.2 , so each friend saves $ 1.2 and pays the remaining 18.8 correct option : option b" + }, + { + "Answer": 0.75, + "Options": "a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4", + "Correct": "e", + "Explanation": "\"let p be the number of progressives in the country as a whole . in each province , the number of traditionalists is p / 15 the total number of traditionalists is 5 p / 15 = p / 3 . the total population is p + p / 3 = 4 p / 3 p / ( 4 p / 3 ) = 3 / 4 the answer is e .\"" + }, + { + "Answer": 25, + "Options": "a ) 5 % , b ) 7 % , c ) 9 % , d ) 11 % , e ) 25 %", + "Correct": "e", + "Explanation": "\"explanation : the difference of two successive amounts must be the simple interest in 1 year on the lower amount of money . s . i = 22050 / - - 17640 / - = rs . 4410 / - rate of interest = ( 4410 / 17640 ) \u00d7 ( 100 / 1 ) = > 25 % answer : option e\"" + }, + { + "Answer": 294, + "Options": "a ) 294 , b ) 306 , c ) 318 , d ) 338 , e ) 362", + "Correct": "a", + "Explanation": "\"859722 / 456 = 1885 with a remainder of 162 . we need to add 456 - 162 = 294 the answer is a .\"" + }, + { + "Answer": 100, + "Options": "a ) 150 . , b ) 145 . , c ) 100 . , d ) 30 . , e ) 25 .", + "Correct": "c", + "Explanation": "\"given there are 100 students , 90 % of 50 = 90 boys and remaining 10 girls . now here 90 % are boys and 10 % are girls . now question is asking about how many boys do we need to add , to make the girls percentage to 5 or 5 % . . if we add 1000 to existing 90 then the count will be 190 and the girls number will be 10 as it . now boys are 95 % and girls are 5 % . ( out of 200 students = 190 boys + 10 girls ) . imo option c is correct .\"" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 7 , c ) 3 , d ) 9 , e ) 2", + "Correct": "c", + "Explanation": "total age of 4 members , 10 years ago = ( 24 x 4 ) years = 96 years . total age of 4 members now = [ 96 + ( 10 x 4 ) ] years = 136 years . total age of 6 members now = ( 24 x 6 ) years = 144 years . sum of the ages of 2 children = ( 144 - 136 ) years = 8 years . let the age of the younger child be years . then , age of the elder child = years . so , age of younger child = 3 years . answer : c" + }, + { + "Answer": 33, + "Options": "a ) 7 , b ) 6 , c ) 78 , d ) 9 , e ) 1", + "Correct": "a", + "Explanation": "answer : a" + }, + { + "Answer": 30, + "Options": "a ) 10 , b ) 20 , c ) 30 % , d ) 40 , e ) 50", + "Correct": "c", + "Explanation": "let the sample be 100 . given 60 % are not first year i . e . there could be second year ( x ) and more than 2 years ( y ) possibility . 60 % = ( x ) + y given 30 % = second year ( x ) club both , we get y = 30 % . answer : option c is correct answer ." + }, + { + "Answer": 45, + "Options": "a ) 40 , b ) 45 , c ) 55 , d ) 45 , e ) 50", + "Correct": "d", + "Explanation": "\"a 1 = 120 / 3 = 40 a 2 = a 1 - 5 = 35 sum of second list = 35 * 3 = 105 therefore the number = 105 - 60 = 45 d\"" + }, + { + "Answer": 49, + "Options": "a ) 24 , b ) 26 , c ) 30 , d ) 49 , e ) 40", + "Correct": "d", + "Explanation": "\"let the number of coins one son got be x and the number of coins another got be y . total = x + y . x ^ 2 - y ^ 2 = 49 ( x - y ) - - > x + y = 49 . answer : d .\"" + }, + { + "Answer": 300, + "Options": "a ) 512 , b ) 300 , c ) 294 , d ) 264 , e ) 385", + "Correct": "b", + "Explanation": "\"many approaches are possible . for example : consider numbers from 0 to 999 written as follows : 1 . 000 2 . 001 3 . 002 4 . 003 . . . . . . . . . 1000 . 999 we have 1000 numbers . we used 3 digits per number , hence used total of 3 * 1000 = 3000 digits . now , why should any digit have preferences over another ? we used each of 10 digits equal # of times , thus we used each digit ( including 4 ) 3000 / 10 = 300 times . answer : b .\"" + }, + { + "Answer": 565.7142857142857, + "Options": "a ) 1217 , b ) 1219 , c ) 1210 , d ) 565.7 , e ) 1312", + "Correct": "d", + "Explanation": "\"\u03c0 ( 182 \u2013 122 ) = 565.7 answer : d\"" + }, + { + "Answer": 12, + "Options": "a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14", + "Correct": "d", + "Explanation": "l = r l = 3 c r = c + 24 3 c = c + 24 c = 12 the answer is d ." + }, + { + "Answer": 27, + "Options": "a ) 27 % , b ) 26 % , c ) 29 % , d ) 30 % , e ) 60 %", + "Correct": "a", + "Explanation": "\"in the first plot 25 % of 300 seeds germinated , so 0.25 x 300 = 75 seeds germinated . in the second plot , 30 % of 200 seeds germinated , so 0.30 x 200 = 60 seeds germinated . since 75 + 60 = 135 seeds germinated out of a total of 300 + 200 = 500 seeds , the percent of seeds that germinated is ( 135 / 500 ) x 100 % , or 27 % . answer : a .\"" + }, + { + "Answer": 45, + "Options": "a ) 20 % , b ) 30 % , c ) 40 % , d ) 50 % , e ) 45 %", + "Correct": "e", + "Explanation": "\"the is always the difference between our starting and ending points . in this case , it \u00e2 \u20ac \u2122 s 100 \u00e2 \u20ac \u201c 55 = 45 . the \u00e2 \u20ac \u0153 original \u00e2 \u20ac \u009d is our starting point ; in this case , it \u00e2 \u20ac \u2122 s 100 . ( 45 / 100 ) * 100 = ( 0.45 ) * 100 = 45 % . e\"" + }, + { + "Answer": 26, + "Options": "a ) 19 , b ) 26 , c ) 20 , d ) 32 , e ) 21", + "Correct": "b", + "Explanation": "\"age of b = age of ( a + b + c ) \u00e2 \u20ac \u201c age of ( a + c ) = 28 \u00e3 \u2014 3 \u00e2 \u20ac \u201c 29 \u00e3 \u2014 2 = 84 \u00e2 \u20ac \u201c 58 = 26 years b\"" + }, + { + "Answer": 625, + "Options": "a ) 24 , b ) 120 , c ) 625 , d ) 720 , e ) 1024", + "Correct": "c", + "Explanation": "\"5 choices for each of the 4 questions , thus total f of 5 * 5 * 5 * 5 = 5 ^ 4 = 625 ways to answer all of them . answer : c .\"" + }, + { + "Answer": 50, + "Options": "a ) 2 % , b ) 17 % , c ) 50 % , d ) 65 % , e ) 83 %", + "Correct": "c", + "Explanation": "\"new value \u2013 old value ) / old value x 100 we are given : february sales this year = 480 million february sales last year = 320 million we need to determine the percent increase between sales from last year to sales this year . thus , the new value = 480 million and the old value = 320 million . let \u2019 s plug them into our percent change formula . ( new value \u2013 old value ) / old value x 100 [ ( 480 \u2013 320 ) / 320 ] x 100 = 50 % . the answer is c .\"" + }, + { + "Answer": 8.78048780487805, + "Options": "a ) 9.28 , b ) 8.48 , c ) 8.78 , d ) 8.98 , e ) 9.18", + "Correct": "c", + "Explanation": "\"distance = 18 km time = 8 / 10 + 10 / 8 = ( 64 + 100 ) / 80 = 164 / 80 = 41 / 20 hours average speed = ( 18 * 20 ) / 41 = 8.78 km / h the answer is c .\"" + }, + { + "Answer": 724797420, + "Options": "a ) 456578972 , b ) 436567874 , c ) 725087484 , d ) 725117481 , e ) 357889964", + "Correct": "c", + "Explanation": "\"72516 x 9999 = 72516 x ( 10000 - 1 ) = 72516 x 10000 - 72516 x 1 = 725160000 - 72516 = 725087484 c\"" + }, + { + "Answer": 40.825, + "Options": "a ) 41 - 44 , b ) 39 - 41 , c ) 38 - 40 , d ) 37 - 39 , e ) 36 - 37", + "Correct": "a", + "Explanation": "\"15 % ( 35.5 ) = 5.325 25 % ( 35.5 ) = 8.875 total amount could have been 35.5 + 5.325 and 35.5 + 8.875 = > could have been between 40.825 and 44.375 = > approximately between 41 and 44 answer is a .\"" + }, + { + "Answer": 191, + "Options": "a ) 167 , b ) 175 , c ) 183 , d ) 191 , e ) 199", + "Correct": "d", + "Explanation": "\"let n - 1 = 2 a . 2 + 4 + . . . + 2 a = 2 * ( 1 + 2 + . . . + a ) = 2 * ( a ) ( a + 1 ) / 2 = ( a ) ( a + 1 ) = 95 * 96 then a = 95 and n = 191 . the answer is d .\"" + }, + { + "Answer": 0.75, + "Options": "a ) 5 / 3 , b ) 3 / 9 , c ) 3 / 2 , d ) 3 / 5 , e ) 3 / 4", + "Correct": "e", + "Explanation": "let julie ' s monthly savings = s julie ' s monthly pay = p julie ' s monthly expenditure = p - s julie ' s savings by the end of the year from these monthly savings were four times the amount she spent per month 12 s = 4 * ( p - s ) = > 3 s = p - s = > p = 4 s julie ' s monthly expenditure = p - s = 4 s - s = 3 s fraction of her salary that julie spent each month = 3 s / 4 s = p - s / p = 3 / 4 . answer is e" + }, + { + "Answer": 56, + "Options": "a ) 65 , b ) 62 , c ) 61 , d ) 56 , e ) 58", + "Correct": "d", + "Explanation": "\"basically , the question asks how many 4 digit numbers ( including those in the form 0 xxx , 00 xx , and 000 x ) have digits which add up to 5 . think about the question this way : we know that there is a total of 5 to be spread among the 4 digits , we just have to determine the number of ways it can be spread . let x represent a sum of 1 , and | represent a seperator between two digits . as a result , we will have 5 x ' s ( digits add up to the 5 ) , and 3 | ' s ( 3 digit seperators ) . so , for example : xx | x | x | x = 2111 | | xxx | xx = 0032 etc . there are 8 c 3 ways to determine where to place the separators . hence , the answer is 8 c 3 = 56 . d\"" + }, + { + "Answer": 10.5, + "Options": "a ) 4.5 , b ) 8.9 , c ) 10.5 , d ) 4.5 , e ) 5.6", + "Correct": "c", + "Explanation": "sum of 8 numbers = 8 * 8 = 64 if 4 is added from each of five of the numbers , we added 4 * 5 = 20 from the total sum sum of 8 number after adding 4 from each of five of the numbers = 64 + 20 = 84 new average = 84 / 8 = 10.5 answer c" + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 11 , e ) 12", + "Correct": "a", + "Explanation": "\"answer = a = 5 if least = - 3 , then largest = 6 range = 6 - 1 = 5\"" + }, + { + "Answer": 4, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "b", + "Explanation": "let x be the number of canoes . then 2 x / 3 is the number of kayaks . 14 x + ( 2 x / 3 ) * 15 = 288 14 x + 10 x = 288 24 x = 288 x = 12 ( canoes ) 2 x / 3 = 8 ( kayaks ) there were 12 - 8 = 4 more canoes rented out . the answer is b ." + }, + { + "Answer": 87.5, + "Options": "a ) 85.5 , b ) 86.5 , c ) 87.5 , d ) 88.5 , e ) 89.5", + "Correct": "c", + "Explanation": "\"total increase in weight = 9 \u00d7 2.5 = 22.5 if x is the weight of the new person , total increase in weight = x \u2212 65 = > 22.5 = x - 65 = > x = 22.5 + 65 = 87.5 answer : c\"" + }, + { + "Answer": 115, + "Options": "a ) 107 , b ) 109 , c ) 111 , d ) 113 , e ) 115", + "Correct": "e", + "Explanation": "\"the least number which when divided by different divisors leaving the same remainder in each case = lcm ( different divisors ) + remainder left in each case . hence the required least number = lcm ( 38 , 3 ) + 1 = 115 . answer : e\"" + }, + { + "Answer": 19, + "Options": "a ) 13 , b ) 15 , c ) 17 , d ) 19 , e ) 21", + "Correct": "d", + "Explanation": "let x be the number of cans in row 1 . the total number of cans is x + ( x + 3 ) + . . . + ( x + 27 ) = 10 x + 3 ( 1 + 2 + . . . + 9 ) = 10 x + 3 ( 9 ) ( 10 ) / 2 = 10 x + 135 since the total is less than 150 , x must equal 1 . the number of cans in the 7 th row is 1 + 3 ( 6 ) = 19 the answer is d ." + }, + { + "Answer": 132, + "Options": "a ) 96 , b ) 108 , c ) 120 , d ) 132 , e ) 144", + "Correct": "d", + "Explanation": "\"( 5 ' ) ' = ( 3 * 5 - 3 ) ' = 12 ' = 12 * 12 - 12 = 132 answer d\"" + }, + { + "Answer": 1441, + "Options": "a ) 1439 , b ) 1440 , c ) 1459 , d ) 1449 , e ) 1500", + "Correct": "a", + "Explanation": "lcm = 1440 1440 - 1 = 1439 answer : a" + }, + { + "Answer": 0.5, + "Options": "a ) 1 / 2 , b ) 1 , c ) 3 , d ) 4 , e ) 5", + "Correct": "a", + "Explanation": "that quadratic is factored as follows : 2 x \u00b2 + 9 x \u2212 5 = ( 2 x \u2212 1 ) ( x + 5 ) . lesson 17 . now , it is easy to see that the second factor will be 0 when x = \u2212 5 . as for the value of x that will make 2 x \u2212 1 = 0 , we must solve that little equation . ( lesson 9 . ) we have : 2 x = 1 x = 1 2 the solutions are : x = 1 / 2 or \u2212 5 a" + }, + { + "Answer": 21.05263157894737, + "Options": "a ) 10 , b ) 15 , c ) 21 , d ) 18 , e ) 19", + "Correct": "c", + "Explanation": "multiples of 19 = 114 , 133,152 , - - - - - , 494 number of multiples of 19 = > 494 - 114 / 19 + 1 = 21 answer is c" + }, + { + "Answer": 37.5, + "Options": "a ) 35.5 , b ) 36.5 , c ) 37.5 , d ) 38.5 , e ) 39.5", + "Correct": "c", + "Explanation": "let the present age of q be x the age of q years back ( to be defined ) is x / 3 as the age of p will be x by then . years passed = x - x / 3 = 2 x / 3 ( subtracting age of q ) so p acurrent age is x + 2 x / 3 and q current age is x adding them to 100 we get x = 37.5 answer : c" + }, + { + "Answer": 0.9677419354838709, + "Options": "a ) 1 / 130 , b ) 1 / 5 , c ) 3 / 13 , d ) 10 / 13 , e ) 30 / 31", + "Correct": "e", + "Explanation": "\"it ' s y / xpercentnot y / x . if x = 20 and y = 10 . then : 20 x = 400 black - and - white films ; 6 y = 60 color films . y / x % = 10 / 20 % = 0.5 % of the black - and - white films , so 2 black - and - white films and all 60 color films , thus total of 62 films were selected . color films thus compose r = 60 / 62 = 30 / 31 of the selected films . answer : e .\"" + }, + { + "Answer": 13, + "Options": "a ) 13.0 , b ) 13.3 , c ) 13.6 , d ) 13.9 , e ) 14.2", + "Correct": "a", + "Explanation": "\"let x be the factor by which the bacteria increases every three hours . at 4 : 00 pm , the amount of bacteria was 10 x and at 7 : 00 pm it was 10 x ^ 2 . 10 x ^ 2 = 16.9 x ^ 2 = 1.69 x = 1.3 at 4 : 00 pm , the amount of bacteria was 10 ( 1.3 ) = 13 grams . the answer is a .\"" + }, + { + "Answer": 12.5, + "Options": "a ) 8 , b ) 12.5 , c ) 16 , d ) 24 , e ) 36", + "Correct": "b", + "Explanation": "\"i ' m going to focus on denominator only . . ( 2 ^ 25 ) . ( ( 3 ^ 4 ) ^ k = 18 ^ 25 ( 2 ^ 25 ) . ( ( 3 ^ 4 k ) = ( 2 . 3 ^ 2 ) ^ 25 ( 2 ^ 25 ) . ( ( 3 ^ 4 k ) = ( 2 ^ 25 ) . ( 3 ^ 2 ) ^ 25 hence 4 k = 50 k = 12,5 answer b i hope it ' s quite clear\"" + }, + { + "Answer": 0.8, + "Options": "a ) 4 / 5 , b ) 4 / 7 , c ) 5 , d ) 5 / 7 , e ) none", + "Correct": "a", + "Explanation": "\"let the required fraction be x . then 1 - x = 9 x 20 1 - x 2 = 9 x 20 20 - 20 x 2 = 9 x 20 x 2 + 9 x - 20 = 0 20 x 2 + 25 x - 16 x - 20 = 0 5 x ( 4 x + 5 ) - 4 ( 4 x + 5 ) = 0 ( 4 x + 5 ) ( 5 x - 4 ) = 0 x = 4 / 5 option a\"" + }, + { + "Answer": 0.5, + "Options": "a ) 1.7 , b ) 0.5 , c ) 1.1 , d ) 1.5 , e ) 1.9", + "Correct": "b", + "Explanation": "\"m = 1.5 s = x ds = 1.5 + x us = 1.5 + x 1.5 + x = ( 1.5 - x ) 2 1.5 + x = 3 - 2 x 3 x = 1.5 x = 0.5 answer : b\"" + }, + { + "Answer": 0.7777777777777778, + "Options": "a ) 10 / 16 , b ) 6 / 16 , c ) 4 / 16 , d ) 7 / 9 , e ) 4 / 10", + "Correct": "d", + "Explanation": "\"w = m + 2 w + m = 16 m + 2 + m = 16 2 m = 14 m = 7 w = 9 ratio : 7 : 9 ans : d\"" + }, + { + "Answer": 405, + "Options": "a ) 435 hectares . , b ) 425 hectares . , c ) 445 hectares . , d ) 415 hectares . , e ) 405 hectares .", + "Correct": "e", + "Explanation": "\"let the areas of the parts be x hectares and ( 900 - x ) hectares . difference of the areas of the two parts = x - ( 900 - x ) = 2 x - 900 one - fifth of the average of the two areas = 1 / 5 [ x + ( 900 \u2212 x ) ] / 2 = 1 / 5 \u00d7 ( 900 / 2 ) = 450 / 5 = 90 given that difference of the areas of the two parts = one - fifth of the average of the two areas = > 2 x - 900 = 90 = > 2 x = 990 \u21d2 x = 990 / 2 = 495 hence , area of smaller part = ( 900 - x ) = ( 900 \u2013 495 ) = 405 hectares . answer is e .\"" + }, + { + "Answer": 34, + "Options": "a ) 25 , b ) 31 , c ) 27 , d ) 29 , e ) 34", + "Correct": "e", + "Explanation": "\"let the average after 17 innings = x total runs scored in 17 innings = 17 x average after 16 innings = ( x - 3 ) total runs scored in 16 innings = 16 ( x - 3 ) total runs scored in 16 innings + 82 = total runs scored in 17 innings = > 16 ( x - 3 ) + 82 = 17 x = > 16 x - 48 + 82 = 17 x = > x = 34 answer is e .\"" + }, + { + "Answer": 1, + "Options": "a ) 5 , b ) 4 , c ) 1 , d ) 2 , e ) 10", + "Correct": "c", + "Explanation": "\"7 * 7 * 7 * 7 / 100 = 2401 / 100 = 24 reminder 1 answer : c\"" + }, + { + "Answer": 324, + "Options": "a ) 234 , b ) 267 , c ) 324 , d ) 356 , e ) 577", + "Correct": "c", + "Explanation": "given equation is in the form ( a + b ) 2 \u2212 4 ab where a = 422 and b = 404 hence answer = ( a + b ) 2 \u2212 4 ab = ( a \u2212 b ) 2 = ( 422 \u2212 404 ) 2 = 182 = 324 c" + }, + { + "Answer": 15, + "Options": "a ) 15 , b ) 25 , c ) 30 , d ) 35 , e ) 40", + "Correct": "a", + "Explanation": "\"let b : y : g = 3 x : 7 x : 8 x . 3 x + 7 x + 8 x = 18 x = 54 - - > x = 3 . g - b = 8 x - 3 x = 5 x = 15 . the answer is a .\"" + }, + { + "Answer": 155, + "Options": "a ) 155 , b ) 160 , c ) 175 , d ) 190 , e ) 195", + "Correct": "a", + "Explanation": "250 = n ( exactly 1 channel ) + n ( exactly 2 channels ) + n ( exactly 3 channels ) 250 = n ( exactly 1 channel ) + 90 + n ( exactly 3 channels ) let ' s find the value of n ( exactly 3 channels ) = x 250 = n ( a ) + n ( b ) + n ( c ) - n ( a and b ) - n ( b and c ) - n ( c and a ) + n ( a and b and c ) note that each of n ( a and b ) is the sum of ' number of people watching exactly two channels a and b ' and ' number of people watching all three channels ' . 250 = 116 + 127 + 107 - n ( exactly 2 channels ) - 3 x + x 250 = 116 + 127 + 107 - 90 - 2 x x = 25 250 = n ( exactly 1 channel ) + 90 + 25 n ( exactly 1 channel ) = 155 answer ( a )" + }, + { + "Answer": 12, + "Options": "a ) 9 , b ) 10 , c ) 12 , d ) 14 , e ) 18", + "Correct": "c", + "Explanation": "\"the rate of 6 machines is rate = job / time = x / 5 units per day - - > the rate of 1 machine 1 / 6 * ( x / 5 ) = x / 30 units per day ; now , again as { time } * { combined rate } = { job done } then 10 * ( m * x / 30 ) = 4 x - - > m = 12 . answer : c .\"" + }, + { + "Answer": 100, + "Options": "a ) 25 % , b ) 50 % , c ) 75 % , d ) 100 % , e ) 200 %", + "Correct": "d", + "Explanation": "mean of s is ( - 4 - 1 + 0 + 6 + 9 ) / 5 = 2 ; in order the increase to be minimal we should replace two smallest elements of s , which are - 4 and - 1 , with two smallest primes , which are 2 and 3 . hence our new set will be { 2 , 3 , 0 , 6 , 9 } - - > new mean is ( 2 + 3 + 0 + 6 + 9 ) / 5 = 4 . percent increase = ( 4 - 2 ) / 2 * 100 = 100 % . answer : d ." + }, + { + "Answer": 129600, + "Options": "a ) 129,500 , b ) 129,600 , c ) 129,700 , d ) 129,800 , e ) 129,900", + "Correct": "b", + "Explanation": "\"this question can be modified so that the birth rate is given every m seconds and the death rate is given every n seconds . for this particular question : increase in the population every 2 seconds = 6 - 3 = 3 people . total 2 second interval in a day = 24 * 60 * 60 / 2 = 43,200 population increase = 43,200 * 3 = 129,600 . hence b .\"" + }, + { + "Answer": 39, + "Options": "a ) 39 , b ) 40 , c ) 44 , d ) 48 , e ) 52", + "Correct": "a", + "Explanation": "x x + 4 x + 8 x + 12 x + 16 x + 20 x + 24 x + 28 8 x + 112 = 360 8 x = 248 x = 31 3 rd question = 31 + 8 = 31 + 8 = 39 answer a" + }, + { + "Answer": 72, + "Options": "a ) 20 cs , b ) cs / 2 , c ) 72 cs , d ) ( 2 cs ) / 12 , e ) ( 24 c ) / s", + "Correct": "c", + "Explanation": "\"ans : c solution : simple multiplication s students , c classes , 6 books / month = 72 books a year total number of books = 72 cs\"" + }, + { + "Answer": 40, + "Options": "a ) 25 , b ) 40 , c ) 90 , d ) 140 , e ) it can not be determined from the information given .", + "Correct": "b", + "Explanation": "\"- ( a + b = 80 ) b + c = 120 c - a = 40 b . 40\"" + }, + { + "Answer": 3, + "Options": "a ) 2.1 , b ) 2.4 , c ) 2.7 , d ) 3.0 , e ) 3.3", + "Correct": "d", + "Explanation": "\"let x be the amount of pure alcohol required . 0.25 ( 6 ) + x = 0.5 ( x + 6 ) 0.5 x = 3 - 1.5 x = 3 liters the answer is d .\"" + }, + { + "Answer": 7550, + "Options": "a ) 5100 , b ) 7550 , c ) 10100 , d ) 15500 , e ) 20100", + "Correct": "b", + "Explanation": "first 50 even integers : 2 4 6 8 < . . . > integers from 102 to 200 102 104 106 108 < . . . > we notice that each integer from the second set is 100 more than the respective integer in the first set . since we have 50 even integers from 102 to 200 , then : 2550 + ( 100 * 50 ) = 7550 ; answer : b" + }, + { + "Answer": 26, + "Options": "a ) 15 , b ) 37 , c ) 55 , d ) 26 , e ) 73", + "Correct": "d", + "Explanation": "using the elimination method the option that fits this description is 26 6 - 2 = 4 ( unit ' s digit that exceeds its ten ' s digit by 3 ) 26 * 8 = 208 ( the product of the given number and the sum of its digits is equal to 175 ) answer : d" + }, + { + "Answer": 0.07142857142857142, + "Options": "a ) 1 / 14 , b ) 3 / 35 , c ) 5 / 37 , d ) 2 / 35 , e ) none", + "Correct": "a", + "Explanation": "\"answer we have , m x n = 5 x 210 = 1050 \u00e2 \u02c6 \u00b4 1 / m + 1 / n = ( m + n ) / mn = 75 / 1050 = 1 / 14 correct option : a\"" + }, + { + "Answer": 0.5, + "Options": "a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 5 / 6 , e ) 7 / 8", + "Correct": "a", + "Explanation": "( 1 / 2 ) x = ( 1 / 4 ) y ( 1 / 4 ) y + ( 1 / 4 ) y = ( 1 / 2 ) y the answer is a ." + }, + { + "Answer": 0.5599999999999999, + "Options": "a ) 0.86 , b ) 0.56 , c ) 0.96 , d ) 0.69 , e ) 0.76", + "Correct": "b", + "Explanation": "\"given expression = ( 0.66 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.66 ) ( power 2 ) + ( 0.66 x 0.1 ) + ( 0.1 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 0.66 - 0.1 ) = 0.56 answer is b\"" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9", + "Correct": "b", + "Explanation": "the given number = 7 y 86038 sum of the odd places = 8 + 0 + 8 + 7 = 23 sum of the even places = 3 + 6 + y ( sum of the odd places ) - ( sum of even places ) = number ( exactly divisible by 11 ) 23 - ( 9 + y ) = divisible by 11 14 \ufffd y = divisible by 11 . y must be 3 , to make given number divisible by 11 . b" + }, + { + "Answer": 230, + "Options": "a ) 100 , b ) 230 , c ) 150 , d ) 180 , e ) 199", + "Correct": "b", + "Explanation": "\"65 % of x = 20 % of 747.50 then , 65 / 100 * x = 20 / 100 * 7475 / 10 x = 230 answer is b\"" + }, + { + "Answer": 3400, + "Options": "a ) 3600 , b ) 3890 , c ) 88798 , d ) 3400 , e ) 2891", + "Correct": "d", + "Explanation": "\"explanation : manager ' s monthly salary rs . ( 1400 * 21 - 1300 * 20 ) = rs . 3400 . answer : d\"" + }, + { + "Answer": 20, + "Options": "a ) 10 , b ) 12 , c ) 20 , d ) 18 , e ) 21", + "Correct": "c", + "Explanation": "sp = 19 loss = cp 20 loss = cp \u2212 sp = cp \u2212 19 \u21d2 cp 20 = cp \u2212 19 \u21d2 19 cp 20 = 19 \u21d2 cp 20 = 1 \u21d2 cp = 20 c" + }, + { + "Answer": 3.75, + "Options": "a ) 5 / 3 , b ) 5 / 4 , c ) 10 / 3 , d ) 15 / 4 , e ) 15 / 2", + "Correct": "d", + "Explanation": "\"n = 2 d / 5 j = n / 3 = 2 d / 15 the average of november and january is ( n + j ) / 2 = 8 d / 15 / 2 = 4 d / 15 d is 15 / 4 times the average of november and january . the answer is d .\"" + }, + { + "Answer": 600, + "Options": "a ) 600 , b ) 288 , c ) 2768 , d ) 287 , e ) 191", + "Correct": "a", + "Explanation": "\"s . i for 5 years = ( 1020 - 720 ) = rs . 300 . s . i . for 2 years = 300 / 5 * 2 = rs . 120 . principal = ( 720 - 120 ) = rs . 600 . answer : a\"" + }, + { + "Answer": 81, + "Options": "a ) 91 , b ) 51 , c ) 81 , d ) 71 , e ) 61", + "Correct": "c", + "Explanation": "any number between 1000 and 10000 is of 4 digits . the unit \u2019 s place can be filled up by 45 or 6 , that is , in 3 ways . similarly , the ten \u2019 s place can be filled up by 4 or 5 or 6 , that is in 3 ways . the hundred \u2019 s place can be filled up by 4 , 5 or 6 , that is in 3 ways and the thousand \u2019 s place can . be filled up by 4 or 5 or 6 , that is , in 3 ways . hence the required numbers = 3 x 3 x 3 x 3 = 81 answer : c" + }, + { + "Answer": 33, + "Options": "a ) 11 , b ) 22 , c ) 77 , d ) 33 , e ) 88", + "Correct": "d", + "Explanation": "\"add the numbers of highlighters . 10 + 15 + 8 = 33 . answer is d .\"" + }, + { + "Answer": 2, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "a", + "Explanation": "if x , y , and z are consecutive numbers and x > y > z , then y = z + 1 and x = z + 2 . 2 x + 3 y + 3 z = 5 y + 8 2 z + 4 + 3 z + 3 + 3 z = 5 z + 5 + 8 3 z = 6 z = 2 the answer is a ." + }, + { + "Answer": 60, + "Options": "a ) 52 , b ) 46 , c ) 60 , d ) 50 , e ) 35", + "Correct": "c", + "Explanation": "\"line k passes through the origin and has slope 1 / 2 means that its equation is y = 1 / 2 * x . thus : ( x , 6 ) = ( 12 , 6 ) and ( 10 , y ) = ( 10,5 ) - - > x * y = 12 * 5 = 60 . answer : c\"" + }, + { + "Answer": 27.500000000000004, + "Options": "a ) 31 % . , b ) 71 % . , c ) 27.5 % . , d ) 29 % . , e ) 51 % .", + "Correct": "c", + "Explanation": "\"25 % of 3 litres = 0.75 litres 40 % of 5 litres = 2 litres therefore , total quantity of alcohol is 2.75 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 27.5 % c\"" + }, + { + "Answer": 123.2, + "Options": "a ) 68 , b ) 70.4 , c ) 123.2 , d ) 105.6 , e ) 108", + "Correct": "c", + "Explanation": "\"x = 88 * 1.4 = 123.2 so the answer is c .\"" + }, + { + "Answer": 16, + "Options": "a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 16", + "Correct": "e", + "Explanation": "\"since average price of a pencil = 2 \u2234 price of 75 pencils = 150 \u2234 price of 30 pens = ( 630 \u2013 150 ) = 480 \u2234 average price of a pen = 480 \u2044 60 = 16 answer e\"" + }, + { + "Answer": 240, + "Options": "a ) 200 , b ) 240 , c ) 50 , d ) 115 , e ) 150", + "Correct": "b", + "Explanation": "\"x + y = 280 x - y = 200 2 x = 80 x = 40 y = 240 answer is b\"" + }, + { + "Answer": 18.333333333333332, + "Options": "a ) $ 18.33 , b ) $ 22.33 , c ) $ 28.33 , d ) $ 26.23 , e ) $ 16.23", + "Correct": "a", + "Explanation": "s . i . on $ ( 110 - 10 ) for a certain time = $ 10 . s . i . on $ 100 for double the time = $ 20 . t . d . on $ 120 = $ ( 120 - 100 ) = $ 20 . t . d . on $ 110 = $ ( 20 / 120 * 100 ) = $ 18.33 answer : a" + }, + { + "Answer": 18, + "Options": "a ) 12 , b ) 13 , c ) 15 , d ) 18 , e ) 20", + "Correct": "d", + "Explanation": "let the two integers equal x and y , and then create the following equation and simplify : xy + 4 = 40 xy = 36 so x and y are a pair of integers that equal 36 . try adding all possible combinations of two integers that multiply out to 36 : 1 \u00d7 36 = 36 1 + 36 = 37 2 \u00d7 18 = 36 2 + 18 = 20 3 \u00d7 12 = 36 3 + 12 = 15 4 \u00d7 9 = 36 4 + 9 = 13 6 \u00d7 6 = 36 6 + 6 = 12 this list of sums includes 12 , 13 , 15 , and 20 , but not 18 . thus , no pair of integers both satisfies the original equation and adds up to 18 correct answer d ) 18" + }, + { + "Answer": 65, + "Options": "a ) 65 kg , b ) 90 kg , c ) 85 kg , d ) data inadequate , e ) none of these", + "Correct": "a", + "Explanation": "\"a 65 kg total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 64 + 20 ) kg = 65 kg .\"" + }, + { + "Answer": 60.5, + "Options": "a ) 40 , b ) 60.5 , c ) 52 , d ) 55 , e ) 36", + "Correct": "b", + "Explanation": "explanation : let the average after 22 nd innings = x then average after 21 th innings = ( x - 3.5 ) therefore 21 ( x - 3.5 ) + 134 = 22 x therefore x = 60.5 answer : b" + }, + { + "Answer": 59.23076923076923, + "Options": "a ) 52.6 , b ) 52.4 , c ) 52.1 , d ) 59 , e ) 52.9", + "Correct": "d", + "Explanation": "\"sum of the marks for the class of 25 students = 25 * 50 = 1250 sum of the marks for the class of 40 students = 40 * 65 = 2600 sum of the marks for the class of 65 students = 1250 + 2600 = 3850 average marks of all the students = 4850 / 65 = 59 . answer : d\"" + }, + { + "Answer": 30, + "Options": "a ) 49 , b ) 30 , c ) 29 , d ) 31 , e ) 32", + "Correct": "b", + "Explanation": "\"explanation : divide the given number by 99 and find the remainder . if you subtract the remainder from the given number then it is exactly divisible by 99 . 99 ) 12702 ( 128 99 280 198 822 792 30 required number is 30 . answer is b\"" + }, + { + "Answer": 48, + "Options": "a ) 48 , b ) 70.4 , c ) 86 , d ) 105.6 , e ) 108", + "Correct": "a", + "Explanation": "\"x is 20 % greater than 40 means x is 1.2 times 40 ( in other words 40 + 20 / 100 * 40 = 1.2 * 40 ) therefore , x = 1.2 * 40 = 48 answer : a\"" + }, + { + "Answer": 770, + "Options": "a ) 770 , b ) 780 , c ) 790 , d ) 800 , e ) 810", + "Correct": "a", + "Explanation": "\"the number of seats in the theater is 14 + ( 14 + 2 ) + . . . + ( 14 + 42 ) = 22 ( 14 ) + 2 ( 1 + 2 + . . . + 21 ) = 22 ( 14 ) + 2 ( 21 ) ( 22 ) / 2 = 22 ( 14 + 21 ) = 22 ( 35 ) = 770 the answer is a .\"" + }, + { + "Answer": 12, + "Options": "a ) 20 lb , b ) 18 lb , c ) 12 lb , d ) 15 lb , e ) 5 lb", + "Correct": "c", + "Explanation": "\"sol . 12 \u00f7 1 = 12 . answer : c\"" + }, + { + "Answer": 620, + "Options": "a ) 620 , b ) 610 , c ) 630 , d ) 625 , e ) 635", + "Correct": "a", + "Explanation": "\"let the price of one apple = a and price of one orange = b the price of 80 apples is equal to that of 120 oranges 80 a = 120 b = > 2 a = 3 b \u21d2 b = 2 a / 3 - - - - - ( equation 1 ) price of 60 apples and 75 oranges together is rs . 1320 = > 60 a + 75 b = 1320 = > 4 a + 5 b = 88 \u21d2 4 a + 5 ( 2 a ) / 3 = 88 ( \u2235 substituted the value of b from equation 1 ) = > 12 a + 10 a = 88 \u00d7 3 = > 6 a + 5 a = 44 \u00d7 3 = > 11 a = 44 \u00d7 3 = > a = 4 \u00d7 3 = 12 b = 2 a / 3 = ( 2 \u00d7 12 ) / 3 = 8 total price of 25 apples and 40 oranges = 25 a + 40 b = ( 25 \u00d7 12 ) + ( 40 \u00d7 8 ) = 300 + 320 = 620 answer is a .\"" + }, + { + "Answer": 18, + "Options": "a ) 20 inches , b ) 77 inches , c ) 66 inches , d ) 18 inches , e ) 66 inches", + "Correct": "d", + "Explanation": "\"explanation : total length of scale in inches = ( 7 * 12 ) + 6 = 90 inches length of each of the 5 parts = 90 / 5 = 18 inches answer : d\"" + }, + { + "Answer": 2.25, + "Options": "a ) $ 2.25 , b ) $ 2.75 , c ) $ 3.00 , d ) $ 3.50 , e ) $ 3.75", + "Correct": "a", + "Explanation": "\"let x be the value of the weekly allowance . ( 2 / 3 ) ( 2 / 5 ) x = 60 cents ( 4 / 15 ) x = 60 x = $ 2.25 the answer is a .\"" + }, + { + "Answer": 91, + "Options": "a ) 91 , b ) 30 , c ) 45 , d ) 60 , e ) 90", + "Correct": "a", + "Explanation": "\"10 players are there . two players play one game with one another . so 14 c 2 = 14 * 13 / 2 = 91 so option a is correct\"" + }, + { + "Answer": 35, + "Options": "a ) 30 , b ) 35 , c ) 37 , d ) 41 , e ) 43", + "Correct": "b", + "Explanation": "explanation : let a ' s age 10 years ago = x years . then , b ' s age 10 years ago = 2 x years . ( x + 10 ) / ( 2 x + lo ) = 3 / 4 = > x = 5 . so , the total of their present ages = ( x + 10 + 2 x + 10 ) = ( 3 x + 20 ) = 35 years . answer : option b" + }, + { + "Answer": 2, + "Options": "a ) 24 , b ) 12 , c ) 6 , d ) 4 , e ) 2", + "Correct": "e", + "Explanation": "\"the greatest common divisor of 12 and 16 is 4 . hence 12 * 16 = 4 ( note that * here denotes the function not multiplication ) . the greatest common divisor of 18 and 12 is 6 . hence 18 * 12 = 6 . hence ( ( 12 * 16 ) * ( 18 * 12 ) ) = 4 * 6 . the greatest common divisor of 4 and 6 is 2 . answer ; e .\"" + }, + { + "Answer": 80, + "Options": "a ) 76 , b ) 80 , c ) 85 , d ) 87 , e ) 89", + "Correct": "b", + "Explanation": "\"explanation : average = total runs / no . of innings = 36 so , total = average x no . of innings = 36 x 10 = 360 . now increase in avg = 4 runs . so , new avg = 36 + 4 = 40 runs total runs = new avg x new no . of innings = 40 x 11 = 440 runs made in the 11 th inning = 440 - 360 = 80 answer : b\"" + }, + { + "Answer": 134, + "Options": "a ) 130 , b ) 132 , c ) 134 , d ) 136 , e ) 138", + "Correct": "c", + "Explanation": "\"let the required number be x . then , 43 x \u2013 34 x = 1206 or 9 x = 1206 or x = 134 . required number = 134 . answer : c\"" + }, + { + "Answer": 81.5, + "Options": "a ) 81 , b ) 81.5 , c ) 82 , d ) 84.5 , e ) none of these", + "Correct": "b", + "Explanation": "explanation : let the number of students in classes x , y and z be a , b and c respectively . then total of x = 83 a total of y = 76 b total of z = 85 c and , ( 83 a + 76 b ) / ( a + b ) = 79 . i . e 4 a = 3 b . also , ( 76 b + 85 c ) / ( b + c ) = 81 . i . e 4 c = 5 b . hence , b = ( 4 / 3 ) a , c = ( 5 / 4 ) b = ( 5 / 4 ) x ( 4 / 3 ) a = ( 5 / 3 ) a . average of x , y and z = ( 83 a + 76 b + 85 c ) / ( a + b + c ) . = > 83 a + 76 \u2217 ( 4 / 3 ) a + 85 \u2217 ( 5 / 3 ) a / a + ( 4 / 3 ) a + ( 5 / 3 ) a . = > 978 / 12 = > 81.5 answer : b" + }, + { + "Answer": 14, + "Options": "a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18", + "Correct": "c", + "Explanation": "answer is c . numbers in format of 3 ^ k in the series from 1 to 30 inclusive r are : 3 * 1 , 3 * 2 , 3 * 3 , 3 * 4 , 3 * 5 , 3 * 3 * 2 , 3 * 7 , 3 * 8 , 3 * 3 * 3 , 3 * 10 . total number of 3 = 13 . so k = 14 ." + }, + { + "Answer": 33, + "Options": "a ) 33 , b ) 30 , c ) 36 , d ) 28 , e ) 26", + "Correct": "a", + "Explanation": "explanation : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - solution 1 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - assume that the number of boys = b and number of girls is g number of boys + number of girls = 41 = > b + g = 41 - - - - - - - - - - - - ( equation 1 ) given that each boy got rs . 12 and each girl got rs . 8 and total amount = rs . 460 = > 12 b + 8 g = 460 - - - - - - - - ( equation 2 ) now we need solve equation 1 and equation 2 to get b and g ( equation 1 ) \u00d7 8 = > 8 b + 8 g = 8 \u00d7 41 = 328 \u2212 \u2212 \u2212 \u2212 \u2212 \u2212 \u2212 \u2212 ( equation 3 ) ( equation 2 ) - ( equation 3 ) = 4 b = 460 - 328 = 132 = > b = 1324 = 33 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - solution 2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - given that amount received by a boy = rs . 12 and amount received by a girl = rs . 8 total amount = 460 given that number of boys + number of girls = 41 hence mean amount = 460 / 41 by the rule of alligation , we have amount received by a boy amount received by a girl 12 8 mean amount 460 / 41 460 / 41 - 8 = 132 / 41 12 - 460 / 41 = 32 / 41 number of boys : number of girls = 132 / 41 : 32 / 41 = 132 : 32 = 66 : 16 = 33 : 8 given that number of boys + number of girls = 41 hence number of boys = 41 \u00d7 3341 = 33 answer : option a" + }, + { + "Answer": 29, + "Options": "a ) 29 , b ) 27 , c ) 28 , d ) 24 , e ) 21", + "Correct": "a", + "Explanation": "\"( 4 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 2 = ( 2 x 2 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 2 = 2 ^ 11 x 2 ^ 11 x 7 ^ 5 x 11 ^ 2 = 2 ^ 22 x 7 ^ 5 x 11 ^ 2 total number of prime factors = ( 22 + 5 + 2 ) = 29 . answer is a .\"" + }, + { + "Answer": 10000, + "Options": "a ) 4676 , b ) 4678 , c ) 9950 , d ) 9504 , e ) 9936", + "Correct": "c", + "Explanation": "\"largest 4 digit number = 9999 9999 \u00f7 50 = 199 , remainder = 49 hence largest 4 digit number exactly divisible by 50 = 9999 - 49 = 9950 answer : c\"" + }, + { + "Answer": 86, + "Options": "a ) 86 , b ) 90 , c ) 92 , d ) 94 , e ) 96", + "Correct": "a", + "Explanation": "\"divisor = ( 6 * 3 ) + 2 = 20 5 * quotient = 20 quotient = 4 . dividend = ( divisor * quotient ) + remainder dividend = ( 20 * 4 ) + 6 = 86 . a\"" + }, + { + "Answer": 15, + "Options": "a ) a ) 2 , b ) b ) 6 , c ) c ) 8 , d ) d ) 15 , e ) e ) 20", + "Correct": "d", + "Explanation": "two ways to do it . . . a = 8 x + 3 . . b = 6 y + 5 . . 1 ) convenient way . . take x and y as 0 , and you will get a * b as 3 * 5 = 15 answer : d" + }, + { + "Answer": 20, + "Options": "a ) 10 , b ) 15 , c ) 20 , d ) 30 , e ) 35", + "Correct": "c", + "Explanation": "1995 - let the value be z 1996 - x % increase - z ( 1 + x / 100 ) 1997 - x % decrease - z ( 1 + x / 100 ) ( 1 - x / 100 ) from 95 to 97 decrease is 4 % hence , [ z - { z ( 1 + x / 100 ) ( 1 - x / 100 ) } ] / z = 4 / 100 solving x = 20 % c is the answer" + }, + { + "Answer": 642987, + "Options": "a ) $ 642986 , b ) $ 642987 , c ) $ 642988 , d ) $ 642989 , e ) $ 642990", + "Correct": "b", + "Explanation": "to find the least amount the man should add to his saving account to split the money evenly among his 9 children , he needs to make the total divisible by 9 simply add the individual digits of the total = 6 + 4 + 2 + 9 + 8 + 6 = 35 if you add 1 , the number is divisible by 9 ( 35 + 1 ) correct option : b" + }, + { + "Answer": 72.41379310344827, + "Options": "a ) 71.11 , b ) 71.12 , c ) 72.4 , d ) 71.17 , e ) 71.13", + "Correct": "c", + "Explanation": "\"car travels first 160 km at 75 km / hr time taken to travel first 160 km = distancespeed = 160 / 75 car travels next 160 km at 70 km / hr time taken to travel next 160 km = distancespeed = 160 / 70 total distance traveled = 160 + 160 = 2 \u00d7 160 total time taken = 160 / 75 + 160 / 70 average speed = total distance traveled / total time taken = 320 / ( 160 / 75 + 160 / 70 ) = 72.4 km / hr answer : c\"" + }, + { + "Answer": 10.5, + "Options": "a ) a ) 10.5 , b ) b ) 12 , c ) c ) 15 , d ) d ) 18 , e ) e ) 20", + "Correct": "a", + "Explanation": "\"explanation : 2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 25 - 4 = 21 ab = 10.5 answer : a\"" + }, + { + "Answer": 0.6666666666666666, + "Options": "a ) 1 / 6 , b ) 1 / 4 , c ) 1 / 2 , d ) 1 / 3 , e ) 2 / 3", + "Correct": "e", + "Explanation": "at least questions are best solved by taking the opposite scenario and subtracting it from 1 . probability of choosing no vowel from set 1 is 2 / 5 and set 2 is 5 / 6 . multiply these to get 1 / 3 . therefore , probability of picking at least one vowel = 1 - 1 / 3 = 2 / 3 . answer = e" + }, + { + "Answer": 12, + "Options": "a ) a ) 36 , b ) b ) 12 , c ) c ) 18 , d ) d ) 64 , e ) e ) 10", + "Correct": "b", + "Explanation": "x + ( xx ) put the value of x = 2 in the above expression we get , 3 + ( 33 ) = 3 + ( 3 \u00d7 3 ) = 3 + ( 9 ) = 3 + 9 = 12 b" + }, + { + "Answer": 108, + "Options": "a ) 84 , b ) 96 , c ) 100 , d ) 108 , e ) 120", + "Correct": "d", + "Explanation": "\"r = j + 6 = k + 3 r + 2 = 2 ( j + 2 ) ( j + 6 ) + 2 = 2 j + 4 j = 4 r = 10 k = 7 in 2 years ( r + 2 ) ( k + 2 ) = 12 * 9 = 108 the answer is d .\"" + }, + { + "Answer": 391, + "Options": "a ) 171 , b ) 281 , c ) 391 , d ) 591 , e ) 601", + "Correct": "c", + "Explanation": "\"sum s = n / 2 { 2 a + ( n - 1 ) d } = 11 / 2 { 2 * 30 + ( 11 - 1 ) * 1 } = 11 * 35 = 385 = x number of even number = ( 40 - 30 ) / 2 + 1 = 6 = y x + y = 385 + 6 = 391 c\"" + }, + { + "Answer": 23, + "Options": "a ) 19 , b ) 35 , c ) 20 , d ) 32 , e ) 23", + "Correct": "e", + "Explanation": "age of b = age of ( a + b + c ) \u00e2 \u20ac \u201c age of ( a + c ) = 27 \u00e3 \u2014 3 \u00e2 \u20ac \u201c 29 \u00e3 \u2014 2 = 81 \u00e2 \u20ac \u201c 58 = 23 years e" + }, + { + "Answer": 16.4, + "Options": "a ) 12.6 . , b ) 14.4 . , c ) 15.8 . , d ) 16.2 . , e ) 16.4 .", + "Correct": "e", + "Explanation": "\"[ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 6.0 = 6 * 0 + 2 * 7.2 + 8 - 6.0 = 0 + 14.4 + 2 16.4 answer e\"" + }, + { + "Answer": 16, + "Options": "a ) $ 14 , b ) $ 16 , c ) $ 22 , d ) $ 24 , e ) $ 26", + "Correct": "b", + "Explanation": "\"10 $ per week ! an year has 52 weeks . annual charges per year = 52 * 10 = 520 $ 30 $ per month ! an year has 12 months . annual charges per year = 12 * 42 = 504 $ 520 - 504 = 16 ans b\"" + }, + { + "Answer": 125, + "Options": "a ) 110 , b ) 125 , c ) 75 , d ) 170 , e ) 195", + "Correct": "b", + "Explanation": "\"lcm of 8 , 12 , 15 and 20 = 120 required number = 120 + 5 = 125 answer : option b\"" + }, + { + "Answer": 0.2222222222222222, + "Options": "a ) 1 / 2 , b ) 2 , c ) 2 / 9 , d ) 3 , e ) 1 / 6", + "Correct": "c", + "Explanation": "\"very easy question . 2 variables and 2 easy equations . xy = 4 - - - > x = 4 / y - ( i ) x / y = 81 - - - > replacing ( i ) here - - - > 4 / ( y ^ 2 ) = 81 - - - > y ^ 2 = 4 / 81 - - - > y = 2 / 9 or - 2 / 9 the question states that x and y are positive integers . therefore , y = 2 / 9 is the answer . answer c .\"" + }, + { + "Answer": 8, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 5", + "Correct": "c", + "Explanation": "since cake is a 3 d object , it will have length , breadth , height . . . first cut across length now we will get 2 pieces then cut across breadth we will get 4 parts in total now . . . now cut across height , finally we will get 8 parts . . . answer : c" + }, + { + "Answer": 59, + "Options": "a ) 87 , b ) 16 , c ) 10 , d ) 76 , e ) 59", + "Correct": "e", + "Explanation": "average after 11 innings = 19 required number of runs = ( 19 * 11 ) - ( 15 * 10 ) = 209 - 150 = 59 . answer : e" + }, + { + "Answer": 15, + "Options": "a ) 12 , b ) 15 , c ) c is elder than a , d ) data inadequate , e ) none", + "Correct": "b", + "Explanation": "\"solution [ ( a + b ) - ( b + c ) ] = 15 \u00e2 \u20ac \u00b9 = \u00e2 \u20ac \u00ba a - c = 15 . answer b\"" + }, + { + "Answer": 40, + "Options": "a ) 46 , b ) 47 , c ) 48 , d ) 49 , e ) 40", + "Correct": "e", + "Explanation": "\"mother + daughter + child = 160 kg daughter + child = 60 kg mother = 160 - 60 = 100 kg child = 1 / 5 th of mother = ( 1 / 5 ) * 100 = 20 kg so now daughter = 120 - ( mother + child ) = 160 - ( 100 + 20 ) = 40 kg answer : e\"" + }, + { + "Answer": 20, + "Options": "a ) 39 , b ) 35 , c ) 20 , d ) 40.5 , e ) 41.5", + "Correct": "c", + "Explanation": "\"let the average after 16 th inning = x then total run after 16 th inning = 16 x then total run after 17 th inning = 16 x + 100 then average run after 17 th inning = ( 16 x + 100 ) / 17 ( 16 x + 100 ) / 17 = x + 5 = > 16 x + 100 = 17 x + 85 = > x = 15 x = 15 ; average after 17 th inning = 15 + 5 = 20 answer : c\"" + }, + { + "Answer": 40, + "Options": "a ) 20 % , b ) 30 % , c ) 40 % , d ) 70 % , e ) 80 %", + "Correct": "c", + "Explanation": "the is always the difference between our starting and ending points . in this case , it \u2019 s 100 \u2013 60 = 40 . the \u201c original \u201d is our starting point ; in this case , it \u2019 s 100 . ( 40 / 100 ) * 100 = ( 0.4 ) * 100 = 40 % . c" + }, + { + "Answer": 396.00000000000006, + "Options": "a ) s . 300 , b ) s . 360 , c ) s . 396 , d ) s . 368 , e ) s . 323", + "Correct": "c", + "Explanation": "\"( a = 2 / 3 b and b = 1 / 4 c ) = a / b = 2 / 3 and b / c = 1 / 4 a : b = 2 : 3 and b : c = 1 : 4 = 3 : 12 a : b : c = 2 : 3 : 12 a ; s share = 561 * 2 / 17 = rs . 66 b ' s share = 561 * 3 / 17 = rs . 99 c ' s share = 561 * 12 / 17 = rs . 396 . answer : c\"" + }, + { + "Answer": 30, + "Options": "a ) 25 , b ) 30 , c ) 45 , d ) 60 , e ) 65", + "Correct": "b", + "Explanation": "explanation : let their ages 10 years ago is x , 2 x and 3 x years . 10 + 2 x + 10 + 3 x + 10 = 90 hence x = 10 b \ufffd s present age = ( 2 x + 10 ) = 30 years answer : option b" + }, + { + "Answer": 0.41666666666666663, + "Options": "a ) 0 , b ) 1 / 12 , c ) 5 / 12 , d ) 7 / 18 , e ) 4 / 9", + "Correct": "c", + "Explanation": "\"total # of outcomes is 6 * 6 = 36 ; favorable outcomes : a - b - - > prime 1 - 1 - - > 2 ; 1 - 2 - - > 3 ; 2 - 1 - - > 3 ; 1 - 4 - - > 5 ; 4 - 1 - - > 5 ; 2 - 3 - - > 5 ; 3 - 2 - - > 5 ; 1 - 6 - - > 7 ; 6 - 1 - - > 7 ; 2 - 5 - - > 7 ; 5 - 2 - - > 7 ; 3 - 4 - - > 7 ; 4 - 3 - - > 7 ; 6 - 5 - - > 11 ; 5 - 6 - - > 11 . total of 15 favorable outcomes e = 15 / 36 . answer : c .\"" + }, + { + "Answer": 34, + "Options": "a ) 30 , b ) 29 , c ) 34 , d ) 21 , e ) 20", + "Correct": "c", + "Explanation": "c list of consecutive numbers that has an ' f ' in the spelling" + }, + { + "Answer": 15, + "Options": "a ) $ 10 , b ) $ 12 , c ) $ 13.20 , d ) $ 15 , e ) $ 16.80", + "Correct": "d", + "Explanation": "\"3 j + 2 s = 69 2 j + 3 s = 71 - - - - - - - - - - - - - - - - 5 j + 5 s = 140 - - - - ( divide by 5 ) - - - > j + s = 28 3 j + 2 s = j + 2 ( j + s ) = j + 56 = 69 - - - > j = 13 3 * 13 + 2 s = 69 39 + 2 s = 69 2 s = 30 s = 15 answer : d\"" + }, + { + "Answer": 94.28571428571429, + "Options": "a ) 94.2 kgs , b ) 88.5 kgs , c ) 86.5 kgs , d ) 67.5 kgs , e ) 88.2 kgs", + "Correct": "a", + "Explanation": "\"average weight = [ ( a + b + c + ( a + b ) + ( b + c ) + ( c + a ) + ( a + b + c ) ] / 7 = 4 ( a + b + c ) / 7 = 4 x 165 / 7 = 94.2 kgs answer : a\"" + }, + { + "Answer": 10, + "Options": "a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14", + "Correct": "c", + "Explanation": "\"l = r l = 3 c r = c + 20 3 c = c + 20 c = 10 the answer is c .\"" + }, + { + "Answer": 84, + "Options": "a ) 62 , b ) 68 , c ) 76 , d ) 84 , e ) 96", + "Correct": "d", + "Explanation": "\"we see that h will be a maximum h = 140 when t - 3 = 0 , that is when t = 3 . at t = 5 , h = - 14 ( 5 - 3 ) ^ 2 + 140 = - 14 ( 4 ) + 140 = 84 the answer is d .\"" + }, + { + "Answer": 17.446043165467625, + "Options": "a ) 16.8 % , b ) 17.4 % , c ) 17.9 % , d ) 18.5 % , e ) 19.1 %", + "Correct": "b", + "Explanation": "\"given : selling price of an apple = 23 - - > cost price = 23 / 1.15 = 20 selling price of an orange = 10 - - > cost price = 10 / 1.25 = 8 a > o 23 * ( a ) + 10 * ( o ) = 653 653 - 23 * ( a ) has to be divisible by 10 - - > units digit has to be 0 values of a can be 1 , 11 , 21 , 31 , . . . . - - > 1 can not be the value between 11 and 21 , if a = 11 , o = 30 - - > not possible if a = 21 , o = 17 - - > possible cost price = 20 * 21 + 8 * 17 = 420 + 136 = 556 profit = 653 - 556 = 97 profit % x = ( 97 / 556 ) * 100 = 17.4 % answer : b\"" + }, + { + "Answer": 1561, + "Options": "a ) 1560 , b ) 1561 , c ) 1559 , d ) 1557 , e ) none of the above", + "Correct": "b", + "Explanation": "we need a number that is a multiple of 7 that will give a remainder of 1 when divided by 2 , 3 , 4 , 5 , and 6 . the least common multiple of these numbers is 60 . so , we need a multiple of 7 that is 1 greater than a multiple of 60 . answer b" + }, + { + "Answer": 0.4583333333333333, + "Options": "a ) 1 / 140 , b ) 1 / 180 , c ) 11 / 24 , d ) 10 / 15 , e ) 57 / 120", + "Correct": "c", + "Explanation": "\"required probability = p ( x ) + p ( y ) + p ( z ) ( all the events are mutually exclusive ) . = 1 / 4 + 1 / 8 + 1 / 12 = 11 / 24 answer : c\"" + }, + { + "Answer": 192.5, + "Options": "a ) 191 , b ) 193 , c ) 195 , d ) 212 , e ) 213", + "Correct": "b", + "Explanation": "\"total movies submitted are 770 . as per question we need to take 1 / 4 of 770 to be considered for top 10 movies = 192.25 approximate the value we 193 imo option b is the correct answer . . .\"" + }, + { + "Answer": 128, + "Options": "a ) 149 , b ) 190 , c ) 128 , d ) 178 , e ) 190", + "Correct": "c", + "Explanation": "\"to improve his average by 8 runs per innings he has to contribute 9 x 8 = 72 runs for the previous 8 innings . thus , the average after the 9 th innings = 200 - 72 = 128 . answer : c\"" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 6", + "Correct": "c", + "Explanation": "\"as per question = > n = 7 p + 1 for some integer p hence 3 n = > 21 q + 3 = > remainder = > 6 for some integer q alternatively = > n = 2 > 3 n = > 3 = > 3 divided by 7 will leave a remainder 3 hence c\"" + }, + { + "Answer": 7, + "Options": "a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9", + "Correct": "d", + "Explanation": "explanation : let number of family members be x . then , total number of feet = 2 x 4 + 4 x 3 + 4 x 18 + 2 x = 2 x + 92 . total number of heads = 4 + 3 + 18 + x = 25 + x . therefore ( 2 x + 92 ) = ( 25 + x ) + 74 or x = 7 . answer : d" + }, + { + "Answer": 84, + "Options": "a ) 66 , 78 , b ) 70 , 82 , c ) 94 , 106 , d ) 84 , 96 , e ) none", + "Correct": "d", + "Explanation": "\"solution out of the given numbers , the two with h . c . f . 12 and difference 12 are 84 and 96 answer d\"" + }, + { + "Answer": 75, + "Options": "a ) 65 , b ) 75 , c ) 60 , d ) 55 , e ) 50", + "Correct": "b", + "Explanation": "\"4 th term + 12 th term = 10 i . e . , ( a + 3 d ) + ( a + 11 d ) = 10 now , sum of first 15 terms = ( 15 / 2 ) * [ 2 a + ( 15 - 1 ) d ] = ( 15 / 2 ) * [ 2 a + 14 d ] = ( 15 / 2 ) * 10 - - - - - - - - - - - - - - - from ( 1 ) = 75 answer : b\"" + }, + { + "Answer": 2000, + "Options": "a ) 2000 , b ) 1700 , c ) 2350 , d ) 2500 , e ) 8000", + "Correct": "a", + "Explanation": "\"16 pounds and 4 ounces = 16 * 16 + 4 = 260 ounces . 13 tons = 13 * 2500 pound = 13 * 2500 * 16 ounces . hence the answer is ( 13 * 2500 * 16 ) / 260 = 2000 . answer : a .\"" + }, + { + "Answer": 70.19999999999999, + "Options": "a ) 35.67 % , b ) 64.75 % , c ) 68.57 % , d ) 70.20 % , e ) none of these", + "Correct": "d", + "Explanation": "girls = 900 , boys = 1100 passed = ( 28 % of 1100 ) + ( 32 % of 900 ) = 308 + 288 = 596 failed = 2000 - 596 = 1404 failed % = [ ( 1404 / 2000 ) x 100 ] % = 70.2 % . answer : d" + }, + { + "Answer": 12, + "Options": "a ) 10 , b ) 11 , c ) 12 , d ) 14 , e ) 16", + "Correct": "c", + "Explanation": "c 12 12 men can complete a work in 18 days . six days after they started working , 4 more men joined them . how many days will all of them together complete the remaining work ?" + }, + { + "Answer": 1980, + "Options": "a ) 1980 , b ) 1982 , c ) 1930 , d ) 1988 , e ) 1680", + "Correct": "a", + "Explanation": "\"= ( 28 + 48 / 69 ) \u00d7 69 = ( 1932 + 48 ) / 69 \u00d7 69 = 1980 / 69 \u00d7 69 = 1980 answer is a .\"" + }, + { + "Answer": 152, + "Options": "a ) 131 , b ) 135 , c ) 139 , d ) 152 , e ) 188", + "Correct": "d", + "Explanation": "lets say j is the weight of jack and s is the wt of his sister . if he loses 32 pounds , he s twice as heavy as his sister . j - 32 = 2 * s also , together they weight 212 pounds j + s = 212 solvong the 2 equation , we get j = 152 pounds ! d" + }, + { + "Answer": 3, + "Options": "a ) 3 , b ) 12 , c ) 18 , d ) 24 , e ) 27", + "Correct": "a", + "Explanation": "total students = 36 one third of the students are boys = 1 / 3 * 36 = 12 one fourth of the boys are under six feet tall = 1 / 4 * 12 = 3 . . . therefore number of boys in the class under six feet tall = 3 . . . answer a . . . . alternatively . . . number of boys in the class under six feet tall = 1 / 4 of 1 / 3 of total students = 1 / 4 * 1 / 3 * 36 = 3 . . . answer a" + }, + { + "Answer": 56.52173913043478, + "Options": "a ) 46.2 % , b ) 54.54 % , c ) 63 % , d ) 56.52 % , e ) none of these", + "Correct": "d", + "Explanation": "explanation : number of runs made by running = 138 - ( 12 x 4 + 2 x 6 ) = 138 - ( 60 ) = 78 now , we need to calculate 72 is what percent of 138 . = > 78 / 138 * 100 = 56.52 % answer : d" + }, + { + "Answer": 39.2, + "Options": "a ) $ 39.00 , b ) $ 39.10 , c ) $ 39.25 , d ) $ 39.30 , e ) $ 39.20", + "Correct": "e", + "Explanation": "in 8 miles , initial 1 / 5 mile charge is $ 8 rest of the distance = 8 - ( 1 / 5 ) = 39 / 5 rest of the distance charge = 39 ( 0.8 ) = $ 31.2 ( as the charge is 0.8 for every 1 / 5 mile ) = > total charge for 4 miles = 8 + 31.2 = 39.2 answer is e" + }, + { + "Answer": 15, + "Options": "a ) a ) 10 , b ) b ) 12 , c ) c ) 15 , d ) d ) 20 , e ) e ) 25", + "Correct": "c", + "Explanation": "the difference between the highest and lowest salaries is $ 100000 . so there are at least 2 people - say one with salary 0 and the other with 100 k . no salary will be outside this range . median = 50 k more than lowest . so median is right in the center of lowest and highest since lowest and highest differ by 100 k . in our example , median = 50 k . since there are more than 2 people , there would probably be a person at 50 k . mean = 20 k more than median so in our example , mean salary = 70 k on the number line , 0 . . . . . . . . 50 k ( median ) . . . . . . . . 100 k mean = 70 k so there must be people more toward 100 k to bring the mean up to 70 k . since we want to add minimum people , we will add people at 100 k to quickly make up the right side deficit . 0 and 50 k are ( 70 k + 20 k ) = 90 k away from 70 k . 100 k is 30 k away from 70 k . to bring the mean to 70 k , we will add two people at 100 k each to get : 0 . . . . 50 k . . . . . 100 k , 100 k , 100 k but when we add more people to the right of 70 k , the median will shift to the right . we need to keep the median at 50 k . so every time we add people to the right of 70 k , we need to add people at 50 k too to balance the median . 50 k is 20 k less than 70 k while 100 k is 30 k more than 70 k . to keep the mean same , we need to add 2 people at 100 k for every 3 people we add at 50 k . so if we add 3 people at 50 k and 2 people at 100 k , we get : 0 , . . . 50 k , 50 k , 50 k , 50 k , . . . 100 k , 100 k , 100 k , 100 k , 100 k the median is not at 50 k yet . add another 3 people at 50 k and another 2 at 100 k to get 0 , 50 k , 50 k , 50 k , 50 k , 50 k , 50 k , 50 k , 100 k , 100 k , 100 k , 100 k , 100 k , 100 k , 100 k now the median is 50 k and mean is 70 k . total number of people is 15 . answer ( c )" + }, + { + "Answer": 42, + "Options": "a ) 30 , b ) 36 , c ) 42 , d ) 48 , e ) 54", + "Correct": "c", + "Explanation": "\"the cost of annie ' s ride was 2.5 + 5 + ( 0.25 * 22 ) = $ 13 let x be the distance of mike ' s ride . the cost of mike ' s ride is 2.5 + ( 0.25 * x ) = 13 0.25 * x = 10.5 x = 42 miles the answer is c .\"" + }, + { + "Answer": 94, + "Options": "a ) 22 , b ) 38 , c ) 62 , d ) 94 , e ) 672", + "Correct": "d", + "Explanation": "\"factorise 1551 . . 3 * 11 * 47 . . so n has to be a multiple of largest prime number , 61 . . so n = 2 * 47 = 94 . . ans : d\"" + }, + { + "Answer": 40, + "Options": "a ) 2.5 % , b ) 40 % , c ) 5 % , d ) 15 % , e ) 25 %", + "Correct": "b", + "Explanation": "\"70 % of ( x - y ) = 30 % of ( x + y ) ( 70 / 100 ) ( x - y ) = ( 30 / 100 ) ( x + y ) 7 ( x - y ) = 3 ( x + y ) 4 x = 10 y x = 5 / 2 y therefore required percentage = ( ( y / x ) x 100 ) % = ( ( y / ( 5 / 2 ) y ) x 100 ) = 40 % answer is b .\"" + }, + { + "Answer": 8123.076923076918, + "Options": "a ) 8120 , b ) 8123 , c ) 8222 , d ) 8322 , e ) 8422", + "Correct": "b", + "Explanation": "\"let salary be x total spent = ( x / 3 + x / 4 + x / 5 ) = ( 47 / 60 ) * x left = ( x - 47 x / 60 ) = ( 13 / 60 ) * x given , ( 13 / 60 ) * x = 1760 x = ( 1760 * 60 ) / 13 = 8123.077 = 8123 ( approax ) answer : b\"" + }, + { + "Answer": 200, + "Options": "a ) s . 80 , b ) s . 85 , c ) s . 90 , d ) s . 100 , e ) s . 200", + "Correct": "e", + "Explanation": "9 / 12 = 3 / 4 * 600 = 450 400 - - - - - - - - - - - - - 50 1 / 4 - - - - - - - - 50 1 - - - - - - - - - ? = > rs . 200 answer : e" + }, + { + "Answer": 36, + "Options": "a ) 2134 , b ) 2234 , c ) 2540 , d ) 2560 , e ) 36", + "Correct": "e", + "Explanation": "\"36 e\"" + }, + { + "Answer": 8, + "Options": "a ) 12 , b ) 9 , c ) 8 , d ) 6 , e ) 5", + "Correct": "c", + "Explanation": "let the total length of the pencil be x cm . black part is 1 / 8 of the length so x / 8 . so the remaining part is x - x / 8 = = > 8 x / 8 - x / 8 = = > 7 x / 8 cm . white part = 1 / 2 * 7 x / 8 = 7 x / 16 cm . so the remaining part is 7 x / 8 - 7 x / 16 = = > 14 x / 16 - 7 x / 16 = 7 x / 16 which is equal to 3 1 / 2 . 7 x / 16 = 7 / 2 cross multiply and we get x = 16 / 2 = 8 cm . so the total length of the pencil is 8 cm . the correct answer is option c ) 8 ." + }, + { + "Answer": 20, + "Options": "a ) 21 , b ) 20 , c ) 19 , d ) 16 , e ) 15", + "Correct": "b", + "Explanation": "\"greatest number of paired shoes means greatest number of lost pairs 9 shoes have 4 pairs and 1 extra shoes of a pair . so a otal of 5 pairs she loses leftover pair = 20 answer : b\"" + }, + { + "Answer": 200, + "Options": "a ) 125 , b ) 160 , c ) 200 , d ) 250 , e ) 320", + "Correct": "c", + "Explanation": "\"let the total number of ounces in the drink be x . % of orange = 25 % % of watermelon = 40 % % of grape = 100 % - 65 % = 35 % 0.35 x = 70 x = 200 therefore there are a total of 200 ounces in the drink . the answer is c .\"" + }, + { + "Answer": 23.076923076923077, + "Options": "a ) 18.75 % , b ) 23 % , c ) 30 % , d ) 50 % , e ) 100 %", + "Correct": "b", + "Explanation": "let wage of erica = 10 wage of robin = 1.3 * 10 = 13 wage of charles = 1.6 * 10 = 16 percentage by which wage earned by charles is more than that earned by robin = ( 16 - 13 ) / 13 * 100 % = 3 / 13 * 100 % = 23 % answer b" + }, + { + "Answer": 6, + "Options": "a ) 3 years , b ) 4 years , c ) 6 years , d ) 7 years , e ) 8 years", + "Correct": "c", + "Explanation": "\"let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 60 5 x = 30 x = 6 . age of the youngest child = x = 6 years . c )\"" + }, + { + "Answer": 50, + "Options": "a ) 57.5 litres , b ) 56.67 litres , c ) 57.67 litres , d ) 56.5 litres , e ) 50 litres", + "Correct": "e", + "Explanation": "\"working formula . . . initial concentration * initial volume = final concentration * final volume . let x is the part removed from 100 lts . 36 % ( 1 - x / 100 ) ^ 2 = 9 % * 100 % ( 1 - x / 100 ) ^ 2 = 9 / 36 - - - - - - > ( 1 - x / 100 ) ^ 2 = ( 3 / 6 ) ^ 2 100 - x = 300 / 6 x = 50 ans e\"" + }, + { + "Answer": 4650, + "Options": "a ) rs . 6003 , b ) rs . 6029 , c ) rs . 4650 , d ) rs . 6108 , e ) rs . 6011", + "Correct": "c", + "Explanation": "\"explanation : manager ' s monthly salary rs . ( 1650 * 21 - 1500 * 20 ) = rs . 4650 . answer : c\"" + }, + { + "Answer": 6.357615894039731, + "Options": "a ) 5.35 % , b ) 6.35 % , c ) 7.35 % , d ) 8.35 % , e ) 9.35 %", + "Correct": "b", + "Explanation": "\"cost of kit = $ 75.50 if filters are purchased individually - $ 7.35 * 3 + $ 12.05 * 3 + $ 12.50 = $ 70.70 amount saved = $ 75.50 - $ 70.70 = $ 4.80 required % age = ( $ 4.80 / $ 75.50 ) * 100 = 6.35 % so , the correct answer is b .\"" + }, + { + "Answer": 0.041666666666666664, + "Options": "a ) 1 / 32 , b ) 1 / 28 , c ) 1 / 24 , d ) 1 / 16 , e ) 1 / 14", + "Correct": "c", + "Explanation": "\"there are 3 single digit multiple of 3 , that is , 3 , 6,9 . there are 8 prime nos less than 20 - 2,3 , 5,7 , 11,13 , 17,19 total outcome - 8 * 3 = 24 favourable outcome = 1 ( 9 * 5 ) hence required probability e = 1 / 24 . answer c .\"" + }, + { + "Answer": 360, + "Options": "a ) 360 , b ) 420 , c ) 510 , d ) 320 , e ) 280", + "Correct": "a", + "Explanation": "\"lcm = 2 * 2 * 2 * 3 * 3 * 5 = 360 . answer is a\"" + }, + { + "Answer": 15, + "Options": "a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 35", + "Correct": "b", + "Explanation": "number in black are given and in red are calculated . now , since x + 3 x = 100 , then x = 25 and therefore = 25 \u2212 10 = 15 answer : b ." + }, + { + "Answer": 140, + "Options": "a ) 90 , b ) 110 , c ) 120 , d ) 140 , e ) 220", + "Correct": "d", + "Explanation": "\"orchestra seats - a balcony seats - b a + b = 360 and 12 a + 8 b = 3320 solving equations simultaneously ( multiply equation 1 with 8 and subtract from second equation ) 4 a = 3320 - 8 * 360 = 3320 - 2880 = 440 i . e . a = 110 and b = 360 - 110 = 250 more seats in balcony than orchestra = b - a = 250 - 110 = 140 answer : option d\"" + }, + { + "Answer": 8, + "Options": "a ) 4 , b ) 18 , c ) 29 , d ) 8 , e ) 116", + "Correct": "d", + "Explanation": "ans is 8 my approach was : ( 56 ^ 2 + 56 ^ 2 ) / 28 ^ 2 = 56 ( 56 + 56 ) / 28 * 28 = 56 * 112 / 28 * 28 = 2 * 4 = 8 d" + }, + { + "Answer": 90, + "Options": "a ) 90 , b ) 110 , c ) 140 , d ) 130 , e ) 120", + "Correct": "a", + "Explanation": "let number of notes of each denomination be x . then x + 5 x + 10 x = 480 16 x = 480 x = 30 . hence , total number of notes = 3 x = 90 . a" + }, + { + "Answer": 24.242424242424242, + "Options": "a ) 20 % , b ) 24 % , c ) 30 % , d ) 32 % , e ) 79 %", + "Correct": "b", + "Explanation": "\"let initial output is o then after 10 % increase it will be 1.1 o and after 20 % increase on this new output the latest output will be 1.1 o * 1.20 = 1.32 o now we have to decrease the output by some percentage so that the new output is same as the starting output ( o ) so , 1.32 o * ( 1 - x / 100 ) = o = > x = 24.24 % so , answer will be b\"" + }, + { + "Answer": 13, + "Options": "a ) 7 , b ) 9 , c ) 13 , d ) 14 , e ) 18", + "Correct": "c", + "Explanation": "79 is the remainder , therefore the number ( a * b * c ) or multiple of the number we need is 79 less than 233 hence 233 - 79 = 154 therefore , 154 is either a number we want or it is a multiple of the number we want but the largest factor of 154 is 77 because 77 * 2 = 154 but 77 is less than 79 hence it can not be a number thus 154 is the number we want a * b * c = 154 now factorize 154 = 1 * 2 * 7 * 11 all are prime also we know 1 < a < b < c thus a = 2 and c = 11 therefore a + c = 2 + 11 = 13 answer : c" + }, + { + "Answer": 12, + "Options": "a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18", + "Correct": "b", + "Explanation": "\"if the average of 10 - pound and 20 - pound boxes is 18 , the ratio of 10 - pound boxes : 20 - pound boxes is 1 : 4 . so out of 20 boxes , 4 are 10 - pound boxes and 16 are 20 - pound boxes . if the average of 10 and 20 - pound boxes is to be 15 , the ratio of 10 - pound boxes : 20 - pound boxes should be 1 : 1 . the number of 10 pound boxes remains the same so we still have 4 of them . to get a ratio of 1 : 1 , the number of 20 - pound boxes must be 4 . we need to remove 12 of the 20 - pound boxes . the answer is b .\"" + }, + { + "Answer": 51999.99999999999, + "Options": "a ) $ 40,000 , b ) $ 52,000 , c ) $ 64,000 , d ) $ 66,667 , e ) $ 80,000", + "Correct": "b", + "Explanation": "\"equation is correct , so math must be a problem . 0.14 * 40,000 + 0.2 * ( x - 40,000 ) = 8,000 - - > 5,600 + 0.2 x - 8,000 = 8,000 - - > 0.2 x = 10,400 - - > x = 52,000 . answer : b .\"" + }, + { + "Answer": 119.99999999999996, + "Options": "a ) 120 , b ) 75 , c ) 100 , d ) 150 , e ) 175", + "Correct": "a", + "Explanation": "\"nope , 150 . i can only get it by following pr ' s backsolving explanation . i hate that . original mixture has 20 % salt and 80 % water . total = x out of which salt = 0.2 x and water = 0.8 x now , 1 / 4 water evaporates and all salt remains . so what remains is 0.2 x salt and 0.6 x water . now 16 gallons salt is added and 8 gallons of water is added . so salt now becomes - > ( 0.2 x + 16 ) and water - - > ( 0.6 x + 8 ) amount of salt is 33.33 % of total . so amount of water is 66.66 % . so salt is half of the volume of water . so ( 0.2 x + 16 ) = ( 0.6 x + 8 ) / 2 = > 0.2 x = 24 solving , x = 120 answer : a\"" + }, + { + "Answer": 0.94, + "Options": "a ) 0.94 , b ) 9.4 , c ) 0.094 , d ) 94 , e ) none", + "Correct": "a", + "Explanation": "\"answer let a - 6 % of a = ab . \u21d2 ( 94 x a ) / 100 = ab \u2234 b = 0.94 correct option : a\"" + }, + { + "Answer": 560, + "Options": "a ) 90 , b ) 120 , c ) 160 , d ) 360 , e ) 560", + "Correct": "e", + "Explanation": "\"if we exclude those cases and take the question at face value , then it seems straightforward . group # 1 = ( did n ' t like , did n ' t understand ) = 120 group # 2 = ( likeunderstood ) = 3 / 4 ( 1 / 4 ) n = 560 n = 480 answer = ( e )\"" + }, + { + "Answer": 870, + "Options": "a ) 870 , b ) 600 , c ) 287 , d ) 771 , e ) 191", + "Correct": "a", + "Explanation": "\"explanation : total salary of 8 workers and supervisor together = 9 \u00e3 \u2014 430 = 3870 now total salary of 8 workers = 3870 \u00e2 \u02c6 \u2019 870 = 3000 total salary of 9 workers including the new supervisor = 9 \u00e3 \u2014 430 = 3870 salary of the new supervisor = 3870 \u00e2 \u02c6 \u2019 3000 = 870 answer : a\"" + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) 15 , c ) 18 , d ) 21 , e ) 24", + "Correct": "a", + "Explanation": "the list should be wmwmw . hence , from women 2 ! and men 3 ! , we get ( 2 ! ) ( 3 ! ) = 12 . therefore , the correct answer is a ." + }, + { + "Answer": 285, + "Options": "a ) $ 200 , b ) $ 220 , c ) $ 285 , d ) $ 300 , e ) $ 360", + "Correct": "c", + "Explanation": "\"total value of the prize = $ 600 number of people = 15 2 / 5 of 600 ( = $ 240 ) should be distributed among 3 / 5 of 15 ( = 9 people ) with each getting $ 15 each . remaining money = 600 - 240 = $ 360 . now in order to ' maximize ' 1 prize , we need to minimise the others and we have been given that each should get $ 15 . thus , minimising the remaining 5 people ( = 15 - 9 - 1 . ' - 1 ' to exclude 1 that needs to be maximised ) = 5 * 15 = 75 . thus the maximum award can be = 360 - 75 = $ 285 , hence c is the correct answer .\"" + }, + { + "Answer": 3775, + "Options": "a ) 3775 , b ) 3665 , c ) 3456 , d ) 3459 , e ) 3569", + "Correct": "a", + "Explanation": "sn = ( 1 + 2 + 3 + . . . + 50 + 51 + 52 + . . . + 100 ) - ( 1 + 2 + 3 + . . . + 50 ) = ( 50 x 101 ) - ( 25 x 51 ) = ( 5050 - 1275 ) = 3775 . option a" + }, + { + "Answer": 44, + "Options": "a ) 23 , b ) 37 , c ) 28 , d ) 44 , e ) 81", + "Correct": "d", + "Explanation": "explanation : formula n ( a \u00e2 \u02c6 \u00aa b ) = n ( a ) + n ( b ) \u00e2 \u02c6 \u2019 n ( a \u00e2 \u02c6 \u00a9 b ) fail in hindi or english = 34 + 44 \u00e2 \u20ac \u201c 22 = 56 therefore students who passed = 100 \u00e2 \u20ac \u201c 56 = 44 . answer : d" + }, + { + "Answer": 1994, + "Options": "a ) 1992 , b ) 1993 , c ) 1994 , d ) 1995 , e ) 1996", + "Correct": "e", + "Explanation": "let the no of years it takes is x . 540 + 30 x = 780 - 10 x - - > 40 x = 240 and x = 6 . thus , it happens in 1996 . e ." + }, + { + "Answer": 0.4666666666666667, + "Options": "a ) 7 / 15 , b ) 1 / 5 , c ) 4 / 15 , d ) 1 / 3 , e ) 2 / 5", + "Correct": "a", + "Explanation": "tot students = x 1 st year student = x / 2 - - - - > non majaor = 4 / 5 ( x / 2 ) - - - - - > maj = 1 / 5 ( x / 2 ) 2 nd year student = x / 2 - - - - > maj = 1 / 3 ( 1 / 5 ( x / 2 ) ) = 1 / 30 ( x ) - - - > non major = x / 2 - 1 / 30 ( x ) = 7 / 15 ( x ) hence 7 / 15 a" + }, + { + "Answer": 480, + "Options": "a ) 125 , b ) 280 , c ) 384 , d ) 480 , e ) 500", + "Correct": "d", + "Explanation": "\"explanation : let the number be x . 5 * x / 6 = 5 * x / 16 + 250 25 * x / 48 = 250 x = 480 answer d\"" + }, + { + "Answer": 132, + "Options": "a ) 132 , b ) 39 , c ) 42 , d ) 65 , e ) 156", + "Correct": "a", + "Explanation": "\"here 156 has three two ' s two three ' s and one 11 rest of them must be in w so w = 11 * 3 * 4 = 132 smash a\"" + }, + { + "Answer": 256, + "Options": "a ) 2 , b ) 4 , c ) 8 , d ) 256 , e ) 32", + "Correct": "d", + "Explanation": "\"( x + y ) ^ 2 - ( x - y ) ^ 2 ( x + y + x - y ) ( x + y - x + y ) ( 2 x ) ( 2 y ) 4 xy 4 4 ^ 4 = 256 answer d\"" + }, + { + "Answer": 0.8686868686868687, + "Options": "a ) 4 / 99 , b ) 2 / 25 , c ) 8 / 99 , d ) 49 / 100 , e ) 86 / 99", + "Correct": "e", + "Explanation": "\"interesting question ! also one that we should be able to answer very quickly be keeping an eye on our best friends , the answer choices . we know that x belongs to the set { 1 , 2 , 3 , . . . , 99 } . we want to know the probability r that x ( x + 1 ) is a multiple of either 4 or 5 . when will this happen ? if either x or ( x + 1 ) is a multiple of 4 or 5 . since 4 * 5 is 20 , let ' s look at the first 20 numbers to get a rough idea of how often this happens . out of the numbers from 1 to 20 : 4 , 5 , 6 , 8 , 9 , 10 , 11 , 12 , 13 , 15 , 16 , 17 , 20 so , 14 out of the first 20 numbers match our criteria . since : probability = ( # of desired outcomes ) / ( total # of possibilities ) , we guesstimate the answer to be 14 / 20 . since ( e ) is the only answer greater than 1 / 2 , we go with ( e ) .\"" + }, + { + "Answer": 3, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "b", + "Explanation": "first of all if you are down to just 3 pieces and you know that if the offending piece is less or more active , then it takes exactly 1 measurement to find out the offending piece . so you know you have to reduce the problem to three . now when you are down to either a or b after measurement 1 , you need the next measurement to ( a ) reduce the problem set to 3 and ( b ) to know whether anser is more or less . now you can not compare a group of 4 to 4 , as in the best case it will only reduce the problem to 4 elements which is not good enough . if you have to choose a set of 3 to compare , you can not pick any 3 on the same side from the same set ( a or b ) because if you do this , a quick check will show you that in every choice there is a case where you can only get down to 4 elements . eg . if you weighed { 1 , 23 } v / s { 5 , 910 } and they were equal you ' re problem would only reduce to { 46 , 78 } the easiest way to solve this then is to compare 3 to 3 , and make sure each side has elements from both ab such that whatever the measurement outcome in the worst case the problem reduces to 3 elements only . which is why the sets { 1 , 59 } and { 2 , 67 } or { a , b , c } { a , b , b } . the extra element from c is just taken to make the problem symmetric so to say , we have 8 elements and we make it 9 , to compose 3 sets of 3 each . = b" + }, + { + "Answer": 60, + "Options": "a ) 20 cs , b ) cs / 2 , c ) 60 cs , d ) ( 2 cs ) / 12 , e ) ( 24 c ) / s", + "Correct": "c", + "Explanation": "\"ans : c solution : simple multiplication s students , c classes , 5 books / month = 60 books a year total number of books = 60 cs\"" + }, + { + "Answer": 17, + "Options": "a ) 14 , b ) 17 , c ) 11 , d ) 19 , e ) 99", + "Correct": "b", + "Explanation": "\"let the son ' s present age be x years . then , ( 44 - x ) = x x = 22 . son ' s age 5 years back = ( 22 - 5 ) = 17 years answer : b\"" + }, + { + "Answer": 40.00000000000001, + "Options": "a ) 16 , b ) 20 , c ) 32 , d ) 40 , e ) 48", + "Correct": "d", + "Explanation": "lets say x ounces of p is mixed with q . = > 65 - x ounces of q is present in the mixture ( as the total = 65 ounces ) given total almond weight = 15 ounces ( 20 x / 100 ) + ( 25 / 100 ) ( 65 - x ) = 15 = > x = 25 = > 65 - 25 = 40 ounces of q is present in the mixture . answer is d ." + }, + { + "Answer": 0.3125, + "Options": "a ) 1 / 3 , b ) \u00bc , c ) 9 / 25 , d ) 5 / 16 , e ) 0", + "Correct": "d", + "Explanation": "\"prime digits are : 2 , 3 , 5 , 7 total number of 2 digit # s with both digits prime are : 4 * 4 = 16 out of these numbers divisible by 3 = 33 , 27 , 57 , 72 and 75 . i had to find the numbers manually using the 4 numbers above . = > prob = 5 / 16 . ans d . took me 3 : 20 mins .\"" + }, + { + "Answer": 6, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "d", + "Explanation": "\"3 < x < 6 < y < 10 ; 3 < x y < 10 3 + y < x + 10 y - x < 7 . positive integer difference is 6 ( for example y = 9.5 and x = 3.5 ) answer : d .\"" + }, + { + "Answer": 22500, + "Options": "a ) rs . 16003 , b ) rs . 16029 , c ) rs . 22500 , d ) rs . 16108 , e ) rs . 16011", + "Correct": "c", + "Explanation": "\"explanation : manager ' s monthly salary rs . ( 2500 * 21 - 1500 * 20 ) = rs . 22500 . answer : c\"" + }, + { + "Answer": 4, + "Options": "a ) 10 , b ) 12 , c ) 16 , d ) 20 , e ) 4", + "Correct": "e", + "Explanation": "let original strength = y then , 40 y + 12 x 32 = ( y + 12 ) x 34 \u00e2 \u2021 \u2019 40 y + 384 = 34 y + 408 \u00e2 \u2021 \u2019 6 y = 24 \u00e2 \u02c6 \u00b4 y = 4 e" + }, + { + "Answer": 25, + "Options": "a ) \u2212 2 % , b ) 2 % , c ) 22 % , d ) 25 % , e ) can not be determined", + "Correct": "d", + "Explanation": "as per question = > price was simple 10 percent greater hence x [ 1 + 10 / 100 ] must be the final price . equating the two we get = > x [ 110 / 100 ] = x [ 1 + p / 100 ] [ 88 / 100 ] = > 44 p + 4400 = 5500 = > 44 p = 1100 = > p = 1100 / 44 = > 100 / 4 = > 25 . so p must be 25 answer : d" + }, + { + "Answer": 9, + "Options": "a ) 6 , b ) 5 , c ) 9 , d ) 13 , e ) 15", + "Correct": "c", + "Explanation": "\"explanation : unit digit in ( 4137 ) 754 = unit digit in { [ ( 4137 ) 4 ] 188 x ( 4137 ) 2 } = unit digit in { 292915317923361 x 17114769 } = ( 1 x 9 ) = 9 c\"" + }, + { + "Answer": 16, + "Options": "a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18", + "Correct": "d", + "Explanation": "\"legs 16 * 4 = 64 now half on their horses so remaining on the walk so 8 men 8 men has 16 legs so , 16 + 64 = 80 legs walking answer : d\"" + }, + { + "Answer": 34, + "Options": "a ) 33 , b ) 34 , c ) 26 , d ) 28 , e ) 19", + "Correct": "b", + "Explanation": "\"explanation : let the two parts be ( 54 - x ) and x . then , 10 ( 54 - x ) + 22 x = 780 = > 12 x = 240 = > x = 20 . bigger part = ( 54 - x ) = 34 . answer : b ) 34\"" + }, + { + "Answer": 70, + "Options": "a ) 65 , b ) 68 , c ) 72 , d ) 70 , e ) 58", + "Correct": "d", + "Explanation": "\"as half the circle shape consist of 45 - 10 = 35 boys , so total number of boys in full circle = 2 * 35 = 70 answer : d\"" + }, + { + "Answer": 20, + "Options": "a ) 10 , b ) 20 , c ) 60 , d ) 120 , e ) 600", + "Correct": "b", + "Explanation": "since the numbers must be distinct and increasing from left to right , the only arrangements we could come - up with are : 245 _ - - > 4 246 _ - - > 3 247 _ - - > 2 248 _ - - > 1 256 _ - - > 3 257 _ - - > 2 258 _ - - > 1 267 _ - - > 2 268 _ - - > 1 number of integers = 20 b" + }, + { + "Answer": 11, + "Options": "a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14", + "Correct": "b", + "Explanation": "\"125 + 40 = 165 / 15 = 11 ( remainder ) b\"" + }, + { + "Answer": 300, + "Options": "a ) a . 150 , b ) b . 300 , c ) c . 600 , d ) d . 1,200 , e ) e . 2,400", + "Correct": "b", + "Explanation": "\"volume per box : 15 x 12 x 10 = 1,800 total volume : 1 , 080,000 number of boxes : total volume / volume per box = 1 , 080,000 / 1,800 = 600 price per month : number of boxes * price per box = 600 * 0.5 = 300 answer : b\"" + }, + { + "Answer": 5, + "Options": "a ) 0 , b ) 3 , c ) 5 , d ) 11 , e ) 13", + "Correct": "c", + "Explanation": "\"let the number be x and on dividing x by 5 , we get k as quotient and 3 as remainder . x = 5 k + 3 x 2 = ( 5 k + 3 ) 2 = ( 25 k 2 + 30 k + 9 ) = 5 ( 5 k 2 + 6 k + 1 ) + 4 on dividing x 2 by 5 , we get 4 as remainder . answer : c\"" + }, + { + "Answer": 47.33333333333333, + "Options": "a ) 15 , b ) 30 , c ) 31 , d ) 33 , e ) 47", + "Correct": "e", + "Explanation": "\"we have to find the number of terms that are divisible by 2 but not by 6 ( as the question asks for the even numbers only which are not divisible by 3 ) for 2 , 10 , 12,14 . . . 150 using ap formula , we can say 150 = 10 + ( n - 1 ) * 2 or n = 71 . for 6 , 12,18 , . . . 96 using ap formula , we can say 150 = 12 + ( n - 1 ) * 6 or n = 24 . hence , only divisible by 2 but not 3 = 71 - 24 = 47 . hence , answer e\"" + }, + { + "Answer": 11, + "Options": "a ) 1 , b ) 4 , c ) 9 , d ) 11 , e ) no such integers exist", + "Correct": "d", + "Explanation": "first note that we must have 1 / a < 1 , so a > 1 . since 1 / a > 1 / b > 1 / c , we must also have 1 / a > 1 / 3 ; so a < 3 . thus , a / 2 . now 1 / b + 1 / c = 1 / 2 where 2 < b < c . similar to before , 1 / b > 1 / 4 , so b < 4 . thus , b = 3 . with a = 2 and b = 3 we have 1 / 2 + 1 / 3 + 1 / c = 1 , which is satisfied when c = 6 . to conclude , a + b + c = 2 + 3 + 6 = 11 . correct answer d" + }, + { + "Answer": 84, + "Options": "a ) 276 , b ) 84 , c ) 88 , d ) 90 , e ) 342", + "Correct": "b", + "Explanation": "\"required number = ( lcm of 5 , 10 , 15 and 20 ) + 24 = 60 + 24 = 84 option b\"" + }, + { + "Answer": 9, + "Options": "a ) 12 , b ) 10 , c ) 7 , d ) 9 , e ) 8", + "Correct": "d", + "Explanation": "\"let the number of students who wrote the exam be x . total marks of students = 60 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 60 x - ( 5 * 44 ) = 80 ( x - 5 ) 180 = 20 x = > x = 9 answer : d\"" + }, + { + "Answer": 20, + "Options": "a ) 20 , b ) 25 , c ) 55 , d ) 65 , e ) 80", + "Correct": "a", + "Explanation": "the arithmetic mean of 4 equally weighted tests was 35 . so what we can assume is that we have 4 test scores , each 35 . he dropped his lowest score and the avg went to 40 . this means that the lowest score was not 35 and other three scores had given the lowest score 5 each to make it up to 35 too . when the lowest score was removed , the other 3 scores got their 5 back . so the lowest score was 3 * 5 = 15 less than 35 . so the lowest score = 35 - 15 = 20 answer ( a )" + }, + { + "Answer": 56, + "Options": "a ) 64 , b ) 62 , c ) 63 , d ) 61 , e ) 56", + "Correct": "e", + "Explanation": "\"basically , the question asks how many 4 digit numbers ( including those in the form 0 xxx , 00 xx , and 000 x ) have digits which add up to 5 . think about the question this way : we know that there is a total of 5 to be spread among the 4 digits , we just have to determine the number of ways it can be spread . let x represent a sum of 1 , and | represent a seperator between two digits . as a result , we will have 5 x ' s ( digits add up to the 5 ) , and 3 | ' s ( 3 digit seperators ) . so , for example : xx | x | x | x = 2111 | | xxx | xx = 0032 etc . there are 8 c 3 ways to determine where to place the separators . hence , the answer is 8 c 3 = 56 . e\"" + }, + { + "Answer": 0.1428571428571428, + "Options": "a ) 1 / 4 , b ) 4 / 5 , c ) 1 / 5 , d ) 1 / 6 , e ) 1 / 7", + "Correct": "e", + "Explanation": "if s is an integer and we know that the average speed is 2.8 , s must be = 2 . that meanss + 1 = 3 . this implies that the ratio of time for s = 2 is 1 / 4 of the total time . the formula for distance / rate is d = rt . . . so the distance travelled when s = 2 is 2 t . the distance travelled for s + 1 = 3 is 3 * 4 t or 12 t . therefore , total distance covered while the sun was shining over him is q = 2 / 14 = 1 / 7 . answer : e" + }, + { + "Answer": 2, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 1 , e ) 2", + "Correct": "e", + "Explanation": "solve by simultaneous equations . my answer is e . x = 4 y = 2" + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 7 , c ) 8 , d ) 9 , e ) 10", + "Correct": "a", + "Explanation": "a - 7 10 ! is divisible by 5 there are 4 numbers between 10 ! and 10 ! + 20 that are divisible by 5 . hence 5" + }, + { + "Answer": 0.33333333333333337, + "Options": "a ) 5 / 24 , b ) 6 / 24 , c ) 7 / 24 , d ) 8 / 24 , e ) 1 / 3", + "Correct": "e", + "Explanation": "\"p = 3 / 6 , q = 3 / 18 = > q = 1 / 6 therefore p - q = ( 1 / 2 ) - ( 1 / 6 ) = 1 / 3 answer : e\"" + }, + { + "Answer": 5, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 12 , e ) 24", + "Correct": "b", + "Explanation": "let # of colors needed be nn , then it must be true that n + c 2 n \u2265 12 n + cn 2 - # of ways to choose the pair of different colors from nn colors when order does n ' t matter ) - - > n + n ( n \u2212 1 ) / 2 \u2265 12 - - > 2 n + n ( n \u2212 1 ) \u2265 24 - - > n is an integer ( it represents # of colors ) n \u2265 5 - - > nmin = 5 answer : b ." + }, + { + "Answer": 35, + "Options": "a ) 25 , b ) 27 , c ) 30 , d ) 35 , e ) 37", + "Correct": "d", + "Explanation": "solution excluded number = ( 27 \u00d7 5 ) - ( 25 \u00d7 4 ) = 135 - 100 = 35 . answer d" + }, + { + "Answer": 23, + "Options": "a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25", + "Correct": "c", + "Explanation": "\"let the average age of the whole team be x years . 11 x - ( 24 + 31 ) = 9 ( x - 1 ) 11 x - 9 x = 46 2 x = 46 x = 23 . the average age of the team is 23 years . the answer is c .\"" + }, + { + "Answer": 0.65, + "Options": "a ) 1 / 6 , b ) 2 / 9 , c ) 6 / 20 , d ) 13 / 20 , e ) 3 / 4", + "Correct": "d", + "Explanation": "\"method - 1 there are 9 fine pieces of pen and 3 defective in a lot of 16 pens i . e . probability of first pen not being defective = ( 13 / 16 ) i . e . probability of second pen not being defective = ( 12 / 15 ) [ 15 pen remaining with 12 defective remaining considering that first was defective ] probability of both pen being non - defective = ( 12 / 15 ) * ( 13 / 16 ) = 13 / 20 answer : option d\"" + }, + { + "Answer": 260, + "Options": "a ) 250 , b ) 260 , c ) 270 , d ) 280 , e ) 285", + "Correct": "b", + "Explanation": "a eats more than b if b eats 1 times than the ratio of a and b is a : b is 2.6 : 1 or 13 : 5 and as b eat 4 times less the c the the ratio of b : c is 5 : 20 the the least number of times all three has eat is the lcm of a , b , c that is 260 . . answer : b" + }, + { + "Answer": 78, + "Options": "a ) 78 , b ) 58 , c ) 390 , d ) 310 , e ) 66", + "Correct": "a", + "Explanation": "\"x is common to both the series . so , x is not going to make a difference to the average . only the remaining 4 numbers will contribute to the difference in average between the two series . sum of the 4 numbers , excluding x , of the first series is 28 + 42 + 78 + 104 = 252 sum of the 4 numbers , excluding x , of the second series is 48 + 62 + 98 + 124 = 332 the difference between the sum of the two sets of numbers = 332 - 252 = 80 the sum of the second series is 80 more than the sum of the first series . if the sum of the second series is 80 more , the average of the second series will be 80 / 5 = 16 more than the first series . therefore , the average of the second series = 62 + 16 = 78 . answer a\"" + }, + { + "Answer": 10, + "Options": "a ) 6 rs , b ) 2 rs , c ) 4 rs , d ) 9 rs , e ) 10 rs", + "Correct": "e", + "Explanation": "\"5 m = xw = 8 b 5 m + xw + 8 b - - - - - 150 rs . 5 m + 5 m + 5 m - - - - - 150 rs . 15 m - - - - - - 150 rs . = > 1 m = 10 rs . answer : e\"" + }, + { + "Answer": 14.000000000000002, + "Options": "a ) 6 % , b ) 14 % , c ) 37 1 / 2 % , d ) 60 % , e ) 75 %", + "Correct": "b", + "Explanation": "\"just plug and chug . since the question asks for percents , pick 100 . ( but any number will do . ) 100 / 10 + 100 / 25 = 10 + 4 = 14 14 is 14 % of 100 = b\"" + }, + { + "Answer": 690, + "Options": "a ) 690 , b ) 860 , c ) 560 , d ) 875 , e ) 880", + "Correct": "a", + "Explanation": "\"50 % of x = x / 2 ; 25 % of 1500 = 25 / 100 * 1500 = 375 given that , x / 2 = 375 - 30 = > x / 2 = 345 = > x = 690 . answer : a\"" + }, + { + "Answer": 150, + "Options": "a ) 52 , b ) 75 , c ) 92 , d ) 136 , e ) 150", + "Correct": "e", + "Explanation": "w 1 / w 2 = ( a 2 - aavg ) / ( aavg - a 1 ) = ( 44 - 40 ) / ( 40 - 36 ) = 4 / 4 = 1 / 1 = number of microtron stocks / number of dynaco stocks so for every 1 microtron stock , she sold 1 dynaco stock . so out of 300 total stocks , ( 1 / 1 ) th i . e . 300 / 2 = 150 must be dynaco stock . answer ( e )" + }, + { + "Answer": 33, + "Options": "a ) 78 years , b ) 22 years , c ) 33 years , d ) 66 years , e ) 65 years", + "Correct": "c", + "Explanation": "\"let ' s son age is x , then father age is x + 35 . = > 2 ( x + 2 ) = ( x + 35 + 2 ) = > 2 x + 4 = x + 37 = > x = 33 years answer : c\"" + }, + { + "Answer": 24, + "Options": "a ) 89 , b ) 20 , c ) 36 , d ) 24 , e ) 34", + "Correct": "d", + "Explanation": "\"speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 120 + 120 = 360 m . time taken = 240 / 10 = 24 sec . answer : option d\"" + }, + { + "Answer": 10, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", + "Correct": "d", + "Explanation": "\"101 * n ^ 2 < = 12100 n ^ 2 < = 12100 / 101 which will be less than 121 since 12100 / 100 = 121 which is the square of 9 next closest value of n where n ^ 2 < = 121 is 10 ans d\"" + }, + { + "Answer": 30, + "Options": "a ) 15 , b ) 30 , c ) 60 , d ) 90 , e ) 120", + "Correct": "b", + "Explanation": "\"k ^ 3 = 120 * x = 2 ^ 3 * 3 * 5 * x the factors of k must at minimum include 2 * 3 * 5 = 30 . the answer is b .\"" + }, + { + "Answer": 8, + "Options": "a ) 12 , b ) 16 , c ) 34 , d ) 38 , e ) 8", + "Correct": "e", + "Explanation": "s + j = 40 s = 4 * j j = 8 answer : e" + }, + { + "Answer": 45, + "Options": "a ) 34 , b ) 50 , c ) 32 , d ) 28 , e ) 45", + "Correct": "e", + "Explanation": "brother ' s age = 10 x + y so sister ' s age = 10 y + x . . after 29 years , 10 x + y + 29 = 2 * ( 10 y + x + 29 ) . . . . so 29 + 19 y = 8 x . . . check for odd values of y , y = 1 satisfies the eqn with x = 6 . . . so ages are 61 and 16 and ans as found correctly by u is e . . 45" + }, + { + "Answer": 10000, + "Options": "a ) 40000 , b ) 60000 , c ) 10000 , d ) 25000 , e ) 50000", + "Correct": "c", + "Explanation": "\"if value of business = x total sell ( 1 x / 3 ) ( 3 / 5 ) = 2000 - > x = 10000 answer : c\"" + }, + { + "Answer": 6303, + "Options": "a ) 5307 , b ) 5647 , c ) 5927 , d ) 6297 , e ) 6557", + "Correct": "d", + "Explanation": "\"when increased by 3 , the number must include at least 2 ^ 2 * 3 ^ 2 * 5 ^ 2 * 7 = 6300 the answer is d .\"" + }, + { + "Answer": 13.5, + "Options": "a ) 10.5 , b ) 11 , c ) 11.5 , d ) 12 , e ) 13.5", + "Correct": "e", + "Explanation": "\"the value which isexactlytwo sd less than the mean is : mean - 2 * sd = 16.5 - 2 * 1.5 = 13.5 . answer : e .\"" + }, + { + "Answer": 11, + "Options": "a ) 11 , b ) 12 , c ) 14 , d ) 15 , e ) 16", + "Correct": "a", + "Explanation": "\"3 / 11 \u00d7 [ ( 1 + 1 / 3 ) ( 1 + 1 / 4 ) . . . . . . . ( 1 + 1 / 120 ) ] 3 / 11 \u00d7 [ 4 / 3 + 5 / 4 \u00d7 . . . . . . . . 121 / 120 ] 3 / 11 \u00d7 4 / 3 \u00d7 5 / 4 \u00d7 . . . . 121 / 120 121 / 11 = 11 . a )\"" + }, + { + "Answer": 0.5416666666666666, + "Options": "a ) 7 / 24 , b ) 11 / 24 , c ) 13 / 24 , d ) 17 / 24 , e ) 19 / 24", + "Correct": "c", + "Explanation": "the given expression = 1 / ( 2 \u00e3 \u2014 3 ) + 1 / ( 3 \u00e3 \u2014 4 ) + 1 / ( 4 \u00e3 \u2014 5 ) + . . . . . . + 1 / ( 23 \u00e3 \u2014 24 ) = ( 1 / 2 - 1 / 3 ) + ( 1 / 3 - 1 / 4 ) + ( 1 / 4 - 1 / 5 ) + . . . . . . . . . . + ( 1 / 23 - 1 / 24 ) = 1 / 2 - 1 / 24 = 11 / 24 thus , the fraction we should add = 1 - 11 / 24 = 13 / 24 the answer is c ." + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1", + "Correct": "a", + "Explanation": "1 ^ 3 = 1 2 ^ 3 = 8 3 ^ 3 = 27 4 ^ 3 = 64 the two numbers are 1 and 4 . the answer is a ." + }, + { + "Answer": 97200, + "Options": "a ) 81000 , b ) 97200 , c ) 27772 , d ) 29889 , e ) 22312", + "Correct": "b", + "Explanation": "76800 * 9 / 8 * 9 / 8 = 97200 . answer : b" + }, + { + "Answer": 79, + "Options": "a ) 65 , b ) 69 , c ) 72 , d ) 79 , e ) none", + "Correct": "d", + "Explanation": "\"sol . average = 96 + 65 + 82 + 67 + 85 / 5 ) = ( 395 / 5 ) = 79 . answer d\"" + }, + { + "Answer": 12, + "Options": "a ) 17 years , b ) 19 years , c ) 29 years , d ) 10 years , e ) 12 years", + "Correct": "e", + "Explanation": "\"let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 32 5 x = 30 = > x = 6 hence , b ' s age = 2 x = 12 years . answer : e\"" + }, + { + "Answer": 3399.999999999999, + "Options": "a ) 3200 , b ) 3400 , c ) 3600 , d ) 3800 , e ) 4000", + "Correct": "b", + "Explanation": "\"if his salary is x , then x - x * ( 2 / 5 + 3 / 10 + 1 / 8 ) = 1400 x ( 1 - 33 / 40 ) = 1400 x = 1400 * 40 / 7 = rs 8000 expenditure on food and conveyance = 8000 * 3 / 10 + 8000 * 1 / 8 = 2400 + 1000 = 3400 answer : b\"" + }, + { + "Answer": 28, + "Options": "a ) 25 , b ) 24 , c ) 23 , d ) 21 , e ) 28", + "Correct": "e", + "Explanation": "let a and b be the two numbers ( a + b ) ^ 2 = a ^ 2 + 2 ab + b ^ 2 given ( a + b ) = 8 a ^ 2 + b ^ 2 = 120 so , 8 ^ 2 = 120 + 2 ab 2 ab = 120 - 64 2 ab = 56 ab = 28 ans e" + }, + { + "Answer": 200, + "Options": "a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 550", + "Correct": "b", + "Explanation": "\"explanation : since the month begins with a sunday , so there will be five sundays in the month , required average = ( 500 * 5 + 140 * 25 ) / 30 = 6000 / 30 = 200 answer : b ) 200\"" + }, + { + "Answer": 90, + "Options": "a ) 75 kg , b ) 55 kg , c ) 45 kg , d ) 85 kg , e ) 90 kg", + "Correct": "e", + "Explanation": "\"explanation : total weight increased = ( 8 x 3.5 ) kg = 28 kg . weight of new person = ( 62 + 28 ) kg = 90 kg . answer : e\"" + }, + { + "Answer": 32, + "Options": "a ) 32 , b ) 48 , c ) 45 , d ) 72 , e ) 18", + "Correct": "a", + "Explanation": "\"ages of p and mi = 3 x : 5 x ages of mi and mo = 3 x : 5 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 25 x sum = 49 x = 98 x = 2 difference if ages of pa and mo = 25 x - 9 x = 16 x = 16 * 2 = 32 answer a\"" + }, + { + "Answer": 330, + "Options": "a ) 330 , b ) 360 , c ) 380 , d ) 400 , e ) 420", + "Correct": "a", + "Explanation": "\"unit place increased by 3 . so 6 , 16,26 , . . . . 96 . total 10 * 3 = 30 increased . ten ' s place increased by 30 . so 60,61 , . . . 69 . total 10 * 30 = 300 increased . so total varies = 300 + 30 = 330 . answer : a\"" + }, + { + "Answer": 44.44444444444444, + "Options": "a ) 20 , b ) 25 , c ) 33 1 / 3 , d ) 44 4 / 9 , e ) 80", + "Correct": "d", + "Explanation": "\"let x = 100 so y = 180 we want percentage change . so , ( 100 - 180 ) / 180 = - 44.44 % = 44 4 / 9 % lesser than y . hence option ( d ) .\"" + }, + { + "Answer": 30, + "Options": "a ) 25 , b ) 28 , c ) 30 , d ) 35 , e ) 40", + "Correct": "c", + "Explanation": "\"let b : y : g = 3 x : 7 x : 8 x . 3 x + 7 x + 8 x = 18 x = 108 - - > x = 6 . g - b = 8 x - 3 x = 5 x = 30 . the answer is c .\"" + }, + { + "Answer": 15, + "Options": "a ) 10 , b ) 15 , c ) 17 , d ) 19 , e ) 21", + "Correct": "b", + "Explanation": "\"let us calculate both the length and width of the room in centimeters . length = 7 meters and 20 centimeters = 720 cm width = 4 meters and 32 centimeters = 432 cm as we want the least number of square tiles required , it means the length of each square tile should be as large as possible . further , the length of each square tile should be a factor of both the length and width of the room . hence , the length of each square tile will be equal to the hcf of the length and width of the room = hcf of 720 and 432 = 144 thus , the number of square tiles required = ( 720 x 432 ) / ( 144 x 144 ) = 5 x 3 = 15 answer : b\"" + }, + { + "Answer": 7, + "Options": "a ) 5 , b ) 7 , c ) 6 , d ) 8 , e ) 9", + "Correct": "b", + "Explanation": "b 7" + }, + { + "Answer": 377.8020134228188, + "Options": "a ) 125 , b ) 175 , c ) 225 , d ) 375 , e ) 524", + "Correct": "d", + "Explanation": "explanation : ? = ( 178 x 1265 / 100 ) \u00f7 6 = 2250 / 600 = 375 answer : option d" + }, + { + "Answer": 2400, + "Options": "a ) 2160 , b ) 2350 , c ) 2000 , d ) 2300 , e ) 2400", + "Correct": "e", + "Explanation": "\"explanation : total exp = 5000 + 1500 + 4500 + 2500 + 2000 + 6100 = 21600 exp in % = 100 - 10 = 90 % , 21600 = 90 % saving = 10 % = 21600 x 10 / 90 = rs . 2400 answer : e\"" + }, + { + "Answer": 7.4074074074074066, + "Options": "a ) 19 % , b ) 15 % , c ) 25 % , d ) 40 % , e ) 7.4 %", + "Correct": "e", + "Explanation": "\"cost of food ( c ) = food consumed per student ( f ) * number of students ( n ) * price of food ( p ) originally , c = fnp when number of students decrease by 8 % , and the price of food increases by 20 % , c = f ( new ) * ( 0.9 n ) * ( 1.2 p ) = > f ( new ) = f / ( 0.9 * 1.2 ) = > f ( new ) = 0.9259 f therefore the new cost of food must be 92.59 % of the old cost , or the cost of food must decrease by 7.4 % ( option e )\"" + }, + { + "Answer": 10.999999999999991, + "Options": "a ) 11 , b ) 13 , c ) 14 , d ) 18 , e ) 10", + "Correct": "a", + "Explanation": "\"required difference = [ 3 \u00bd % of rs . 6600 ] \u2013 [ 3 1 / 3 % of rs . 6600 ] = [ ( 7 / 20 - ( 10 / 3 ) ] % of rs . 6600 = 1 / 6 % of rs . 6600 = rs . [ ( 1 / 6 ) 8 ( 1 / 100 ) * 6600 ] = rs . 11 . answer is a .\"" + }, + { + "Answer": 60, + "Options": "a ) 36 , b ) 60 , c ) 84 , d ) 72 , e ) 86", + "Correct": "b", + "Explanation": "detailed solution any multiple of 12 should be a multiple of 4 and 3 . first , let us look at the constraint for a number being a multiple of 3 . sum of the digits should be a multiple of 3 . sum of all numbers from 2 to 7 is 27 . so , if we have to drop a digit and still retain a multiple of 3 , we should drop either 3 or 6 . so , the possible 5 digits are 2 , 4 , 5 , 6 , 7 or 2 , 3 , 4 , 5 , 7 . when the digits are 2 , 4 , 5 , 6 , 7 . the last two digits possible for the number to be a multiple of 4 are 24 , 64 , 52 , 72 , 56 , 76 . for each of these combinations , there are 6 different numbers possible . so , with this set of 5 digits we can have 36 different numbers . when the digits are 2 , 3 , 4 , 5 , 7 . the last two digits possible for the number to be a multiple of 4 are 32 , 52 , 72 , 24 . for each of these combinations , there are 6 different numbers possible . so , with this set of 5 digits we can have 24 different numbers . overall , there are 60 different 5 - digit numbers possible . correct answer : b" + }, + { + "Answer": 7992, + "Options": "a ) 6992 , b ) 6982 , c ) 7982 , d ) 7972 , e ) 7992", + "Correct": "e", + "Explanation": "\"explanation : ( local value of 8 ) - ( face value of 8 ) = ( 8000 - 8 ) = 7992 e )\"" + }, + { + "Answer": 33.333333333333314, + "Options": "a ) 3 / 80 , b ) 3 / 5 , c ) 4 , d ) 100 / 3 , e ) 80 / 3", + "Correct": "d", + "Explanation": "\"15 / 100 = 3 / 20 n = 2 ^ 3 / 20 n ^ b = 2 ^ 5 ( 2 ^ 3 / 20 ) ^ b = 2 ^ 5 b = 100 / 3 answer : d\"" + }, + { + "Answer": 23, + "Options": "a ) 21 , b ) 22 , c ) 20 , d ) 18 , e ) 23", + "Correct": "e", + "Explanation": "\"explanation : let the son ' s present age be x years . then , man ' s present age = ( x + 25 ) years = > ( x + 25 ) + 2 = 2 ( x + 2 ) = > x + 27 = 2 x + 4 so , x = 23 . answer : e\"" + }, + { + "Answer": 18, + "Options": "a ) 3 , b ) 6 , c ) 18 , d ) 12 , e ) 16", + "Correct": "c", + "Explanation": "m ^ 2 is divisible by 48 so m ^ 2 must be multiple of 48 . if the value of m is multiples of 18 then it will satisfy the condition . if we if m is 12 or 24 or 36 then it ans is c but if m = 54 then answer should be 16 . is the question right ? or am i missing some thing ? c" + }, + { + "Answer": 8, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) p = 8", + "Correct": "e", + "Explanation": "\"the combinations could be p { ( 1,240 ) , ( 2,120 ) , ( 3,80 ) , ( 4,60 ) , ( 5,48 ) , ( 6,40 ) , ( 8,30 ) , ( 10,24 ) , ( 12,20 ) , ) 15,16 ) , ( 16,15 ) , ( 20,12 ) , ( 24,10 ) , ( 30,8 ) , ( 40,6 ) , ( 48,5 ) , ( 60,4 ) , ( 80,3 ) , ( 120,2 ) , ( 240,1 ) } of these we are told 8 < = t < = 30 so we can remove these pairs , and we are left only with . { ( 8,30 , ( 10,24 ) , ( 12,20 ) , ( 15,16 ) , ( 16,15 ) , ( 20,12 ) , ( 24,10 ) , ( 30,8 ) } hence 8 . e\"" + }, + { + "Answer": 16.2, + "Options": "a ) 12.6 . , b ) 14.4 . , c ) 15.8 . , d ) 16.2 . , e ) 16.4 .", + "Correct": "d", + "Explanation": "\"[ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 6.2 = 6 * 0 + 2 * 7.2 + 8 - 6.2 = 0 + 14.4 + 1.8 16.2 answer d\"" + }, + { + "Answer": 36, + "Options": "a ) 28 , b ) 30 , c ) 32 , d ) 34 , e ) 36", + "Correct": "e", + "Explanation": "\"let x be the number of blueberries in each blue box . then there are x + 15 strawberries in each red box . x + ( x + 15 ) = 87 x = 36 the answer is e .\"" + }, + { + "Answer": 1511.7142857142858, + "Options": "a ) 1400 , b ) 141.71 , c ) 1210 , d ) 1511.71 , e ) 1500", + "Correct": "d", + "Explanation": "\"\u03c0 ( 252 \u2013 122 ) = 1511.71 answer : d\"" + }, + { + "Answer": 0.3333333333333333, + "Options": "a ) 1 / 5 , b ) 2 / 3 , c ) 2 / 5 , d ) 3 / 5 , e ) 1 / 3", + "Correct": "e", + "Explanation": "we do n ' t need to get into calculations for solving this question . we can use the concept of weighted averages . we know that if the average speed for the entire marathon was 5 mph , she ran at 6 mph for a longer duration . 2 1 3 - - 5 - - - - 6 this shows that you can divide the entire journey in 3 equal parts . thus , 2 / 3 part she ran at 6 mph and 1 / 3 part she ran at 3 mph . answer : e" + }, + { + "Answer": 69, + "Options": "a ) 65 , b ) 69 , c ) 72 , d ) 75 , e ) none", + "Correct": "b", + "Explanation": "sol . average = 66 + 65 + 77 + 62 + 75 / 5 ) = ( 345 / 5 ) = 69 . answer b" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9", + "Correct": "a", + "Explanation": "\"1 / 6 = 0.1666666 . . . ( a repeating pattern one digit long ) a\"" + }, + { + "Answer": 12, + "Options": "a ) 10 years , b ) 12 years , c ) 14 years , d ) 15 years , e ) 16 years", + "Correct": "b", + "Explanation": "\"let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 32 5 x = 30 x = 6 . hence , b ' s age = 2 x = 12 years . b )\"" + }, + { + "Answer": 90000, + "Options": "a ) 150000 , b ) 90000 , c ) 85000 , d ) 190000 , e ) 250000", + "Correct": "b", + "Explanation": "\"if value of business = x total sell ( 2 x / 3 ) ( 3 / 4 ) = 45000 - > x = 150000 answer : b\"" + }, + { + "Answer": 150, + "Options": "a ) 10 , b ) 50 , c ) 150 , d ) 200 , e ) 300", + "Correct": "c", + "Explanation": "recognize that 25 is a factor of 7500 . if we take this out , we have two parts to the equation : - x ^ 2300 x one part of the equation brings our value down , whereas the other part brings our value up . at this point , we can test the numbers in the answer choice . notice that they are very straight forward to square , and multiplication by 300 is very easy . a ) 10 - 3000 - 100 = 2900 b ) 50 - 15000 - 2500 = 12500 c ) 150 - 45000 - 22500 = 22500 d ) 200 - 60000 - 40000 = 20000 e ) 300 - recognize that this is zero therefore , answer is 150 . hope this helps those - like myself - who have n ' t thought about calculus for over half a decade . c" + }, + { + "Answer": 746, + "Options": "a ) 746 , b ) 750 , c ) 789 , d ) 678 , e ) 897", + "Correct": "a", + "Explanation": "\"required number = ( lcm of 8 , 14 , 26 and 28 ) + 18 = 728 + 18 = 746 option a\"" + }, + { + "Answer": 1.8, + "Options": "a ) 2 / 1 , b ) 4 / 1 , c ) 2 / 3 , d ) 9 / 5 , e ) 3 / 2", + "Correct": "d", + "Explanation": "\"given that milk / water = 4 x / x and 4 x + x = 45 - - > x = 9 . thus milk = 4 x = 36 liters and water = x = 9 liters . new ratio = 36 / ( 9 + 11 ) = 36 / 20 = 9 / 5 . answer : d .\"" + }, + { + "Answer": 108, + "Options": "a ) 108 , b ) 120 , c ) 134 , d ) 144 , e ) none of these", + "Correct": "a", + "Explanation": "explanation : the ratio of their initial investment = 1 / 2 : 1 / 3 : 1 / 4 = 6 : 4 : 3 let ' s take the initial investment of p , q and r as 6 x , 4 x and 3 x respectively a : b : c = ( 6 x * 2 + 3 x * 10 ) : 4 x * 12 : 3 x * 12 = ( 12 + 30 ) : 4 * 12 : 3 * 12 = ( 4 + 10 ) : 4 * 4 : 12 = 14 : 16 : 12 = 7 : 8 : 6 r ' s share = 378 * ( 6 / 21 ) = 108 . answer : option a" + }, + { + "Answer": 26, + "Options": "a ) 67 , b ) 26 , c ) 99 , d ) 26 , e ) 91", + "Correct": "d", + "Explanation": "answer : d" + }, + { + "Answer": 42, + "Options": "a ) 36 , b ) 42 , c ) 48 , d ) 54 , e ) 60", + "Correct": "b", + "Explanation": "k ^ 3 = 168 * x = 2 ^ 3 * 3 * 7 * x the factors of k must at minimum include 2 * 3 * 7 = 42 . the answer is b ." + }, + { + "Answer": 6, + "Options": "a ) 0 , b ) 5 , c ) 2 , d ) 3 , e ) 6", + "Correct": "e", + "Explanation": "unit digit in 14 ^ 100 = unit digit in [ ( 14 ^ 4 ) ^ 25 ] but unit digit in 14 ^ 4 = 6 unit digit 14 ^ 100 = 6 answer is e" + }, + { + "Answer": 29.160000000000004, + "Options": "a ) 26.34 litres , b ) 27.36 liters , c ) 28 litres , d ) 29.16 litres , e ) can not be determined", + "Correct": "d", + "Explanation": "solution amount of milk left after 3 operations [ 40 ( 1 - 4 / 40 ) 3 ] litres = ( 40 x 9 / 10 x 9 / 10 x 9 / 10 ) = 29.16 litres answer d" + }, + { + "Answer": 116.19999999999999, + "Options": "a ) 108.6 , b ) 110.4 , c ) 112.6 , d ) 114.8 , e ) 116.2", + "Correct": "e", + "Explanation": "\"let x be the original weight of the grapes . the weight of the grape pulp was 0.1 x . since the grape pulp is 83 % of the raisins , 0.1 x = 0.83 ( 14 kg ) . then x = 8.3 * 14 = 116.2 kg . the answer is e .\"" + }, + { + "Answer": 14, + "Options": "a ) 14 , b ) 19 , c ) 33 , d ) 38 , e ) 56", + "Correct": "a", + "Explanation": "\"explanation : let the son ' s present age be x years . then , ( 38 - x ) = x x = 19 . son ' s age 5 years back = ( 19 - 5 ) = 14 years . answer : a\"" + }, + { + "Answer": 180, + "Options": "a ) 12 , b ) 180 , c ) 24 , d ) 28 , e ) 40", + "Correct": "b", + "Explanation": "\"slope = change in vertical direction / change in horizontal direction = 4 / 3 change in vertical direction = 4 x = ab change in horizontal direction = 3 x = bc ab ^ 2 + bc ^ 2 = 225 ^ 2 16 x ^ 2 + 9 x ^ 2 = 225 ^ 2 25 x ^ 2 = 225 ^ 2 x ^ 2 = 25 * 9 ^ 2 x = 45 therefore ab = 45 * 4 = 180 answer : b\"" + }, + { + "Answer": 10.46, + "Options": "a ) $ 3.36 , b ) $ 6.85 , c ) $ 8.46 , d ) $ 10.46 , e ) $ 11.85", + "Correct": "d", + "Explanation": "\"answer = d 2 * 3.49 + 4 * 0.87 = 2 ( 3.50 - 0.01 ) + 4 ( 1.00 - 0.13 ) = 7 + 4 - 0.02 - 0.52 = 11 - 0.54 = 10.46\"" + }, + { + "Answer": 8.999999999999998, + "Options": "a ) 6 , b ) 9 , c ) 12 , d ) 15 , e ) 18", + "Correct": "b", + "Explanation": "\"( v * ) * = ( v - v / 3 ) - ( v - v / 3 ) / 3 4 = 2 v / 3 - 2 v / 9 = 4 v / 9 v = 9 the answer is b .\"" + }, + { + "Answer": 163, + "Options": "a ) 163 , b ) 785 , c ) 852 , d ) 456 , e ) 852", + "Correct": "a", + "Explanation": "\"divisor * quotient + remainder = dividend divisor = ( dividend ) - ( remainder ) / quotient ( 12401 - 13 ) / 76 = 163 answer ( a )\"" + }, + { + "Answer": 80, + "Options": "a ) 78 , b ) 56 , c ) 80 , d ) 27 , e ) 40", + "Correct": "c", + "Explanation": "\"sum of the marks for the 10 students = 10 * 40 = 400 . the marks of each student are doubled , the sum also will be doubled . the new sum = 400 * 2 = 800 . so , the new average = 800 / 10 = 80 . answer : c\"" + }, + { + "Answer": 14.000000000000002, + "Options": "a ) 13.7 , b ) 14.0 , c ) 14.3 , d ) 14.6 , e ) 14.9", + "Correct": "b", + "Explanation": "\"let x be the factor by which the bacteria increases every three hours . at 4 : 00 pm , the amount of bacteria was 10 x and at 7 : 00 pm it was 10 x ^ 2 . 10 x ^ 2 = 19.6 x ^ 2 = 1.96 x = 1.4 at 4 : 00 pm , the amount of bacteria was 10 ( 1.4 ) = 14 grams . the answer is b .\"" + }, + { + "Answer": 165.63333333333333, + "Options": "a ) 380 times , b ) 142 times , c ) 382 times , d ) 392 times , e ) 165 times", + "Correct": "e", + "Explanation": "\"time difference is 1 hr , 22 min , 49 sec = 4969 sec . so , light glows floor ( 4969 / 30 ) = 165 times . answer : e\"" + }, + { + "Answer": 33, + "Options": "a ) 14 years , b ) 18 years , c ) 20 years , d ) 22 years , e ) 33 years", + "Correct": "e", + "Explanation": "\"let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . ( x + 35 ) + 2 = 2 ( x + 2 ) x + 37 = 2 x + 4 x = 33 . answer : e\"" + }, + { + "Answer": 120, + "Options": "a ) $ 120 , b ) $ 40 , c ) $ 80 , d ) $ 100 , e ) $ 140", + "Correct": "a", + "Explanation": "to determine how much extra he would need to pay , you have to add all 4 weeks of gb usage ( 2 + 3 + 5 + 10 = 20 ) . to determine the extra amount of gb usage , you have to subtract the the original amount of gb ( 8 ) allowed on his plan . 20 - 8 = 12 to determine the extra cost on his cell phone plan , you have to multiply $ 10.00 per extra usage ( 12 ) for a total of $ 120.00 . the correct answer is a" + }, + { + "Answer": 11.904761904761905, + "Options": "a ) 11 , b ) 12 , c ) 14 , d ) 16 , e ) 18", + "Correct": "b", + "Explanation": "\"explanation : as the division is by 2 , 3 , 7 together , the numbers are to be divisible by : 2 * 3 * 7 = 42 the limits are 100 and 600 the first number divisible is 42 * 3 = 126 to find out the last number divisible by 42 within 600 : 600 / 42 = 14.28 hence , 42 * 14 = 588 is the last number divisible by 42 within 600 hence , total numbers divisible by 2 , 3 , 7 together are ( 14 \u2013 2 ) = 12 answer : b\"" + }, + { + "Answer": 47500, + "Options": "a ) s . 43000 , b ) s . 50000 , c ) s . 57000 , d ) s . 60000 , e ) s . 47500", + "Correct": "e", + "Explanation": "\"length ( l ) = 20 m , breadth ( b ) = 15 m and height ( h ) = 5 m total area of the hall to be covered with mat = 2 ( lb + bh + hl ) = 2 ( 20 * 15 + 15 * 5 + 5 * 20 ) = 2 ( 300 + 75 + 100 ) = 2 * 475 = 950 sq . m total expenditure = 50 * 950 = rs . 47500 e\"" + }, + { + "Answer": 8, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10", + "Correct": "c", + "Explanation": "say there are ' a ' associate professors . so we have 2 a pencils and a charts . say there are ' b ' assistant professors . so we have b pencils and 2 b charts . total pencils are 10 so 2 a + b = 10 total charts are 11 so a + 2 b = 14 add both : 3 a + 3 b = 24 so a + b = 8 total number of people = 8 c" + }, + { + "Answer": 14.11111111111111, + "Options": "a ) 20 , b ) 14 , c ) 16 , d ) 5 , e ) 8", + "Correct": "b", + "Explanation": "median is the middle number of a sorted distribution . in case of even number of items , median will be the average of middle two values . the question asks fora new number that will cause the median of new set at 9 . mentionable that given set is already sorted and number of items of new set will be 7 + 1 = 8 . to get median 9 , the sum of 4 th 5 th term should be 18 and it ' s 5 + 14 . so to keep the median 9 , the new item should be > = 14 . the answer is b" + }, + { + "Answer": 66.66666666666666, + "Options": "a ) 12.5 % , b ) 40 % , c ) 67 % , d ) 125 % , e ) none", + "Correct": "c", + "Explanation": "\"solution 2 : 3 = 2 / 3 = ( 2 / 3 x 100 ) % . = 66.6 % . answer c\"" + }, + { + "Answer": 0.05714285714285714, + "Options": "a ) 2 / 69 , b ) 2 / 60 , c ) 2 / 63 , d ) 2 / 35 , e ) 2 / 38", + "Correct": "d", + "Explanation": "\"explanation : let a be the event that x is selected and b is the event that y is selected . p ( a ) = 1 / 7 , p ( b ) = 2 / 5 . let c be the event that both are selected . p ( c ) = p ( a ) \u00e3 \u2014 p ( b ) as a and b are independent events : = ( 1 / 7 ) \u00e3 \u2014 ( 2 / 5 ) = 2 / 35 answer : d ) 2 / 35\"" + }, + { + "Answer": 11, + "Options": "a ) 11 , 1315 , b ) 7 , 2 , 10 , c ) 7 , 9 , 10 , d ) 7 , 9 , 11 , e ) 7 , 9 , 29", + "Correct": "a", + "Explanation": "explanation : let the three consecutive odd integers be x , x + 2 and x + 4 respectively . x + 4 + x + 2 = x + 17 = > x = 11 hence three consecutive odd integers are 11 , 13 and 15 answer : a" + }, + { + "Answer": 133, + "Options": "a ) 133 , b ) 168 , c ) 189 , d ) 190 , e ) 200", + "Correct": "a", + "Explanation": "\"solution average of 7 people after the last one enters = 151 . \u00e2 \u02c6 \u00b4 required weight = ( 7 x 151 ) - ( 6 x 154 ) = 1057 - 924 = 133 . answer a\"" + }, + { + "Answer": 0.25, + "Options": "a ) 1.5 , b ) 0.5 , c ) 6.25 , d ) 0.25 , e ) 6.0", + "Correct": "d", + "Explanation": "\"since z * is defined as the greatest positive even integer less than or equal to z , then 6.25 * = 6 ( the greatest positive even integer less than or equal to 6.25 is 6 ) . hence , 6.25 \u2013 6.25 * = 6.25 - 6 = 0.25 answer : d .\"" + }, + { + "Answer": 63.58823529411765, + "Options": "a ) 62.12 , b ) 63 , c ) 63.33 , d ) 64 , e ) 65", + "Correct": "c", + "Explanation": "at the non - discounted price , each friend would pay $ 66.66 , as $ 400 divided by 6 friends is $ 66.66 per friend . but if the bill is 5 % off , then each friend would pay 5 % less . 5 % of $ 66.66 is $ 3.33 , so each friend saves $ 3.33 and pays the remaining $ 63.33 correct option : option c" + }, + { + "Answer": 75, + "Options": "a ) 80 kg , b ) 85 kg , c ) 75 kg , d ) 100 kg , e ) 110 kg", + "Correct": "c", + "Explanation": "\"total weight increased = ( 8 x 5 ) kg = 40 kg . weight of new person = ( 35 + 40 ) kg = 75 kg . answer : c\"" + }, + { + "Answer": 51.2, + "Options": "a ) 51.2 , b ) 59.5 , c ) 52.8 , d ) 52.5 , e ) 52.1", + "Correct": "a", + "Explanation": "\"sum of the marks for the class of 22 students = 22 * 40 = 880 sum of the marks for the class of 28 students = 28 * 60 = 1680 sum of the marks for the class of 50 students = 880 + 1680 = 2560 average marks of all the students = 2560 / 50 = 51.2 answer : a\"" + }, + { + "Answer": 18, + "Options": "a ) - 29 , b ) - 19 , c ) 18 , d ) 29 , e ) 39", + "Correct": "c", + "Explanation": "\"45 - [ 28 - { 37 - ( 15 - * ) } ] = 57 = > 45 - [ 28 - { 37 - 15 + * } ] = 57 45 - [ 28 - 37 + 15 - * ] = 57 = > 45 [ 43 - 37 - * ] = 57 45 - [ 6 - * ] = 57 = > 45 - 6 + * = 57 39 + * = 57 = > * = 57 - 39 = 18 answer : c\"" + }, + { + "Answer": 27, + "Options": "a ) 21 , b ) 24 , c ) 27 , d ) 36 , e ) 45", + "Correct": "c", + "Explanation": "let the 3 consecutive odd numbers each divisible by 3 be x , x + 3 , x + 6 given , x + x + 3 + x + 6 = 72 3 x = 63 x = 21 the numbers are 21 , 24 , 27 therefore the largest number is 27 answer c ." + }, + { + "Answer": 13.33333333333333, + "Options": "a ) 3 / 80 , b ) 3 / 5 , c ) 4 , d ) 5 / 3 , e ) 40 / 3", + "Correct": "e", + "Explanation": "\"15 / 100 = 3 / 20 n = 3 ^ 3 / 20 n ^ b = 3 ^ 2 ( 3 ^ 3 / 20 ) ^ b = 3 ^ 2 b = 40 / 3 answer : e\"" + }, + { + "Answer": 2010, + "Options": "a ) 2010 , b ) 2011 , c ) 2012 , d ) 2013 , e ) 2014", + "Correct": "a", + "Explanation": "\"the cost of commodity x increases by 10 cents per year relative to commodity y . the price of x must gain 20 + 70 = 90 cents on commodity y , which will take 9 years . the answer is a .\"" + }, + { + "Answer": 7, + "Options": "a ) 7 , b ) 9 , c ) 10 , d ) 11 , e ) 12", + "Correct": "a", + "Explanation": "since ( ii ) holds for every real number x , it will remain valid if we replace x with - x . therefore , f ( 1 - x ) = 3 + f ( - x ) . now , from ( i ) , 10 = f ( x ) + f ( 1 - x ) = f ( x ) + 3 + f ( - x ) so that f ( x ) + f ( - x ) = 10 - 3 = 7 . ( observe that f ( x ) = 3 x + 4 satisfies the conditions in the problem . ) correct answer a" + }, + { + "Answer": 216, + "Options": "a ) 220 , b ) 65 , c ) 216 , d ) 219 , e ) 230", + "Correct": "c", + "Explanation": "12 * 18 = 216 . answer is c ." + }, + { + "Answer": 168, + "Options": "a ) 8 , b ) 64 , c ) 168 , d ) 102 , e ) 144", + "Correct": "c", + "Explanation": "\"if 80 % of the packages weigh at least 25 pounds this means that 20 % of the packages weigh less than 25 pounds let t = total number of packages so , 20 % of t = # of packages that weigh less than 25 pounds 48 packages weigh less than 25 pounds great . so , 20 % of t = 48 rewrite to get : 0.2 t = 48 solve : t = 240 90 % of the packages weigh less than 75 pounds so , 90 % oft = number of packages that weigh less than 75 pounds 90 % of 240 = 216 , so 216 packages weigh less than 75 pounds of those 216 packages that weigh less than 75 pounds , 48 packages weigh less than 25 pounds . so , the number of packages that weight between 25 and 75 pounds = 216 - 48 = 168 = c\"" + }, + { + "Answer": 5, + "Options": "a ) 0 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "e", + "Explanation": "0 . [ u ] 125 [ / u = 0.425425425 . . . . . every 3 rd digit is 5 and every multiple of 3 will be the digit 5 . since 81 is multiple of 3 , the 81 st digit is 5 . answer e" + }, + { + "Answer": 18, + "Options": "a ) 8 , b ) 10 , c ) 12 , d ) 15 , e ) 18", + "Correct": "e", + "Explanation": "\"when a number n = a ^ x * b ^ y , where a and b are prime numbers , and x , y are positive integers , the number of divisors of n = ( x + 1 ) ( y + 1 ) therefore , the answer is e . 3 * 6 = 18\"" + }, + { + "Answer": 174, + "Options": "a ) 172 , b ) 173 , c ) 174 , d ) 175 , e ) none of the above", + "Correct": "c", + "Explanation": "total runs = 40 \u00d7 50 = 2000 let his highest score be = x then his lowest score = x \u2013 172 now 200 \u2212 x \u2212 ( x \u2212 172 ) / 38 = 48 \u21d2 2 x = 2172 \u2013 1824 \u21d2 x = 174 answer c" + }, + { + "Answer": 14, + "Options": "a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14", + "Correct": "e", + "Explanation": "= 17 - 3 = 14 answer e" + }, + { + "Answer": 0.21052631578947367, + "Options": "a ) 4 / 19 , b ) 1 / 9 , c ) 2 / 3 , d ) 1 1 / 9 , e ) 2 1 / 9", + "Correct": "a", + "Explanation": "\"total bought = 4 / 19 + 2 / 13 left part 4 / 26 - - - > 2 / 13 so used part 4 / 19 + 2 / 13 - 2 / 13 = 4 / 19 answer : a\"" + }, + { + "Answer": 1232, + "Options": "a ) 1232 , b ) 1723 , c ) 1129 , d ) 2613 , e ) 1372", + "Correct": "a", + "Explanation": "\"a b has 62.5 % or ( 5 / 8 ) of the milk in a . therefore , let the quantity of milk in container a ( initially ) be 8 k . quantity of milk in b = 8 k - 5 k = 3 k . quantity of milk in container c = 8 k - 3 k = 5 k container : a b c quantity of milk : 8 k 3 k 5 k it is given that if 154 liters was transferred from container c to container b , then both the containers would have equal quantities of milk . 5 k - 154 = 3 k + 154 = > 2 k = 308 = > k = 154 the initial quantity of milk in a = 8 k = 8 * 154 = 1232 liters .\"" + }, + { + "Answer": 80, + "Options": "a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80", + "Correct": "e", + "Explanation": "total people at party = 170 women = 70 so men 170 - 70 = 100 no . of pple who tried appetizer = 170 - 60 ( given info ) = 110 no of women who tried appetizer = 30 so remaining ppl ( men ) who tried the appetizer = 110 - 30 = 80 correct option e" + }, + { + "Answer": 2, + "Options": "a ) 2 , b ) 5 , c ) 8 , d ) 1 , e ) 3", + "Correct": "a", + "Explanation": "number = 7 * 5 + 0 = 35 11 ) 35 ( 3 33 - - - - - - - - 2 required number = 2 . answer : a" + }, + { + "Answer": 1170, + "Options": "a ) $ 880 , b ) $ 990 , c ) $ 1,000 , d ) $ 1,170 , e ) $ 1,210", + "Correct": "d", + "Explanation": "10 / 100 p = 130 > > p = 130 * 100 / 10 = 1300 1300 - 130 = 1170 answer : d" + }, + { + "Answer": 27474, + "Options": "a ) 27488 , b ) 27424 , c ) 27474 , d ) 27784 , e ) 27468", + "Correct": "c", + "Explanation": "c 27474 x + 3699 + 1985 - 2047 = 31111 x + 3699 + 1985 = 31111 + 2047 x + 5684 = 33158 x = 33158 - 5684 = 27474 ." + }, + { + "Answer": 17, + "Options": "a ) 17 , b ) 25 , c ) 26 , d ) 27 , e ) 28", + "Correct": "a", + "Explanation": "the question simplfies to ( 8 \u00d7 10 ^ 10 ) ( 10 ^ 6 ) = > 8 * 10 ^ 16 = > will contain 16 zeros + 1 digit 8 = > 17 ans a" + }, + { + "Answer": 10, + "Options": "a ) 12.5 % , b ) 10 % , c ) 15 % , d ) 17 % , e ) 19 %", + "Correct": "b", + "Explanation": "\"quantity x rate = price 1 x 1 = 1 0.72 x 1.25 = 0.9 decrease in price = ( 0.1 / 1 ) \u00d7 100 = 10 % b )\"" + }, + { + "Answer": 15, + "Options": "a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16", + "Correct": "d", + "Explanation": "\"the total number of books the students borrowed is 25 * 2 = 50 . the students who borrowed zero , one , or two books borrowed 11 * 1 + 6 * 2 = 23 books . the 5 students who borrowed at least three books borrowed 50 - 23 = 27 books . if 4 of these students borrowed exactly 3 books , then the maximum that one student could have borrowed is 27 - 12 = 15 books . the answer is d .\"" + }, + { + "Answer": 484, + "Options": "a ) $ 310 , b ) $ 395 , c ) $ 484 , d ) $ 512 , e ) $ 542", + "Correct": "c", + "Explanation": "4 / 15 a = 2 / 5 b a = 2 / 5 * 15 / 4 b a = 3 / 2 b a / b = 3 / 2 a : b = 3 : 2 b ' s share = 1210 * 2 / 5 = $ 484 answer is c" + }, + { + "Answer": 2120, + "Options": "a ) $ 2,040 , b ) $ 2,120 , c ) $ 1,960 , d ) $ 1,920 , e ) $ 1,400", + "Correct": "b", + "Explanation": "in order to maximize the amount of money that the gambler kept , we should maximize # of $ 20 chips lost and minimize # of $ 100 chips lost , which means that # of $ 20 chips lost must be 2 more than # of $ 100 chips lost . so , if # of $ 20 chips lost is x then # of $ 100 chips lost should be x - 2 . now , given that total # of chips lost is 16 : x + x - 2 = 16 - - > x = 9 : 9 $ 20 chips were lost and 9 - 2 = 7 $ 100 chips were lost . total worth of chips lost is 9 * 20 + 7 * 100 = $ 880 , so the gambler kept $ 3,000 - $ 880 = $ 2,120 . answer : b ." + }, + { + "Answer": 0.29, + "Options": "a ) 0.52 , b ) 0.29 , c ) 0.48 , d ) 0.64 , e ) 0.46", + "Correct": "b", + "Explanation": "\"given exp . = 0.3 * 0.8 + ( 0.1 * 0.5 ) = 0.24 + 0.05 = 0.29 answer is b .\"" + }, + { + "Answer": 0.6666666666666666, + "Options": "a ) 2 / 3 , b ) 3 / 5 , c ) 2 / 7 , d ) 3 / 7 , e ) 4 / 9", + "Correct": "a", + "Explanation": "\"p ( b | a ) = p ( a \u222a b ) / p ( a ) p ( b | a ) = ( 4 / 17 ) / ( 6 / 17 ) = 4 / 6 = 2 / 3 . a\"" + }, + { + "Answer": 0.5625, + "Options": "a ) 15 / 16 , b ) 9 / 16 , c ) 1 / 2 , d ) 1 / 4 , e ) 1 / 8", + "Correct": "b", + "Explanation": "the probability of not getting an e after spinning the spinner two times is 3 / 4 * 3 / 4 = 9 / 16 ( so getting any of the remaining 3 letters out of 4 ) . answer : b ." + }, + { + "Answer": 100, + "Options": "a ) 300 , b ) 100 , c ) 150 , d ) 170 , e ) 270", + "Correct": "b", + "Explanation": "n th term of a . p . is given by a + ( n - 1 ) d 4 th term = a + 3 d 12 th term = a + 11 d given a + 3 d + a + 11 d = 20 - - > 2 a + 14 d = 20 - - > a + 7 d = 10 sum of n term of a . p = n / 2 [ 2 a + ( n - 1 ) d ] subsitiuing n = 10 . . . we get 10 / 2 [ 2 a + 14 d ] = 10 [ a + 7 d ] = 10 * 10 = 100 . . . answer is b . . ." + }, + { + "Answer": 116.71232876712328, + "Options": "a ) 119 , b ) 185 , c ) 190 , d ) 116 , e ) 200", + "Correct": "d", + "Explanation": "\"total production of salt by the company in that year = 3000 + 3100 + 3200 + . . . . + 4100 = 42600 . average monthly production of salt for that year = 42600 / 365 \u00e2 \u2030 \u02c6 116 answer : d\"" + }, + { + "Answer": 7, + "Options": "a ) 3 , b ) 5 , c ) 7 , d ) 8 , e ) 9", + "Correct": "c", + "Explanation": "\"explanation : on dividing 652543 by 12 we get the remainder 7 , so 7 should be subtracted option c\"" + }, + { + "Answer": 825, + "Options": "a ) s . 800 , b ) s . 810 , c ) s . 825 , d ) s . 900 , e ) s . 920", + "Correct": "c", + "Explanation": "\"2475 * 1 / 3 = 825 option c\"" + }, + { + "Answer": 30, + "Options": "a ) 40 , b ) 50 , c ) 62 , d ) 30 , e ) 56", + "Correct": "d", + "Explanation": "\"let the average after 11 th inning = x then , average after 10 th inning = x - 5 10 ( x - 5 ) + 80 = 11 x x = 80 - 50 = 30 answer is d\"" + }, + { + "Answer": 2, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "c", + "Explanation": "\"apparently it ' s s = x ^ 2 - x ^ 3 instead of s = x ^ 2 - s ^ 3 . in this case : the x - intercept is the value ( s ) of x for s = 0 . 0 = x ^ 2 - x ^ 3 ; 0 = x ^ 2 ( 1 - x ) ; x = 0 or x = 1 . answer : c .\"" + }, + { + "Answer": 45, + "Options": "a ) 40 , b ) 50 , c ) 62 , d ) 45 , e ) 56", + "Correct": "d", + "Explanation": "\"let the average after 11 th inning = x then , average after 10 th inning = x - 5 10 ( x - 5 ) + 95 = 11 x x = 95 - 50 = 45 answer is d\"" + }, + { + "Answer": 400.90000000000003, + "Options": "a ) 40.09 , b ) 4.06 , c ) 40.06 , d ) 400.9 , e ) 400.6", + "Correct": "d", + "Explanation": "= 16.036 / 0.04 = 1603.6 / 4 = 400.9 answer is d ." + }, + { + "Answer": 0.84, + "Options": "a ) 9 / 25 , b ) 10 / 25 , c ) 6 / 10 , d ) 2 / 3 , e ) 21 / 25", + "Correct": "e", + "Explanation": "\"simply look at the question from the other side . what is the probability that you can \u2019 t row the canoe ? this would be 2 / 5 x 2 / 5 = 4 / 25 . using the idea that the probability of something happening is 1 \u2013 the probability that it doesn \u2019 t happen , you can use the following equation to reach the right answer r : 1 \u2013 4 / 25 = 21 / 25 . answer choice e .\"" + }, + { + "Answer": 16, + "Options": "a ) 10 , b ) 12 , c ) 16 , d ) 24 , e ) 32", + "Correct": "c", + "Explanation": "\"if a ^ 2 - b ^ 2 = 0 , then let ' s assume that a = b . a must equal the 4 th positive multiple of 4 , thus a = 32 , which also equals b . b is the second positive multiple of n , thus n = 32 / 2 = 16 . the answer is c .\"" + }, + { + "Answer": 26.897352853986263, + "Options": "a ) 27 , b ) 12 , c ) 14 , d ) 16 , e ) 18", + "Correct": "a", + "Explanation": "this one ' s easy . 1000 * 2 ^ t = 500,000 2 ^ t = 500 now gauging , since 2 ^ 8 = 256 , then 2 ^ 9 = 512 so t = 9 but be careful , ' t ' is in time intervals of 3 minutes so answer is 9 * 3 = 27 minutes answer ( a )" + }, + { + "Answer": 56, + "Options": "a ) 36 , b ) 46 , c ) 56 , d ) 66 , e ) 96", + "Correct": "c", + "Explanation": "8 ! / ( 8 - 2 ) ! = 8 ! / 6 ! = 8 * 7 = 56 . hence , the correct answer is c ." + }, + { + "Answer": 105500, + "Options": "a ) $ 135875 , b ) $ 52700 , c ) $ 127900 , d ) $ 105500 , e ) $ 105000", + "Correct": "d", + "Explanation": "there are 5 people inheriting the money . we have to take the total of the inheritance and divide it by 5 for each person receiving money . $ 527500 / 5 = $ 105500 . therefore the correct answer is d ." + }, + { + "Answer": 355, + "Options": "a ) r = 350 , b ) r = 353 , c ) r = 354 , d ) r = 356 , e ) 357", + "Correct": "b", + "Explanation": "\"focus on the points where the number of digits in squares change : 1 , 2 , 3 - single digit squares . first 2 digit number is 10 . 4 , 5 , . . . 9 - two digit squares . to get 9 , the last number with two digit square , think that first 3 digit number is 100 which is 10 ^ 2 . so 9 ^ 2 must be the last 2 digit square . 10 , 11 , 12 , . . . 31 - three digit squares . to get 31 , think of 1000 - the first 4 digit number . it is not a perfect square but 900 is 30 ^ 2 . 32 ^ 2 = 2 ^ 10 = 1024 , the first 4 digit square . 32 - 99 - four digit squares . to get 99 , think of 10,000 - the first 5 digit number which is 100 ^ 2 . so number of digits in s ( 99 ) = 3 * 1 + 6 * 2 + 22 * 3 + 68 * 4 = 3 + 12 + 66 + 272 = r = 353 . b\"" + }, + { + "Answer": 8, + "Options": "a ) 8 , b ) 4 , c ) 16 , d ) 32 , e ) 64", + "Correct": "a", + "Explanation": "\"2 ^ ab = 2 ^ 2 therefore ab = 2 either a = 1 or 2 or b = 2 or 1 therefore 2 ^ a * 2 ^ b = 2 ^ ( a + b ) = 2 ^ 3 = 8 a\"" + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 17 , c ) 13 , d ) 23 , e ) none of these", + "Correct": "a", + "Explanation": "\"let that divisor be x since remainder is 4 or 8 it means divisor is greater than 8 . now 242 - 4 = 238 = kx ( k is an integer and 234 is divisble by x ) similarly 698 - 8 = 690 = lx ( l is an integer and 689 is divisible by x ) adding both 698 and 242 = ( 238 + 690 ) + 4 + 8 = x ( k + l ) + 12 when we divide this number by x then remainder will be equal to remainder of ( 12 divided by x ) = 7 hence x = 12 - 7 = 5 hence a\"" + }, + { + "Answer": 3200, + "Options": "a ) rs . 3200 , b ) rs . 3600 , c ) rs . 2400 , d ) rs . 4000 , e ) none of these", + "Correct": "a", + "Explanation": "\"let the amount with r be rs . r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 8000 - r ) = > 3 r = 16000 - 2 r = > 5 r = 16000 = > r = 3200 . answer : a\"" + }, + { + "Answer": 33.22222222222222, + "Options": "a ) 31 , b ) 33 , c ) 35 , d ) 36 , e ) 23", + "Correct": "b", + "Explanation": "\"multiples of 9 = 9 , 18,27 , - - - - - 297 number of multiples of 15 = > 9 * 33 = 297 answer is b\"" + }, + { + "Answer": 48.550000000000004, + "Options": "a ) a ) 48.55 , b ) b ) 49 , c ) c ) 51 , d ) d ) 61 , e ) e ) 62", + "Correct": "a", + "Explanation": "required average = ( 50.25 x 16 + 45.15 x 8 ) / ( 16 + 8 ) = ( 804 + 361.20 ) / 24 = 1165.20 / 24 = 48.55 kg answer is a" + }, + { + "Answer": 204, + "Options": "a ) 190 , b ) 204 , c ) 220 , d ) 230 , e ) none of these", + "Correct": "b", + "Explanation": "explanation : 1 / 2 : 2 / 3 : 3 / 4 = 6 : 8 : 9 first part = 782 \u2217 6 / 23 = 204 option b" + }, + { + "Answer": 1, + "Options": "a ) 0 , b ) - 1 , c ) 1 , d ) 2 , e ) 3", + "Correct": "c", + "Explanation": "21 m + 21 n - 21 = - 21 m + 21 n + 21 42 m = 42 = > m = 1 c" + }, + { + "Answer": 200, + "Options": "a ) 30 % , b ) 33 1 / 2 % , c ) 40 % , d ) 60 % , e ) 200 %", + "Correct": "e", + "Explanation": "original visual range = 50 km new visual range = 150 km percent increase in the visual range by using the telescope = ( 150 - 50 ) / 50 * 100 % = 2 * 100 % = 200 % answer e" + }, + { + "Answer": 12, + "Options": "a ) 12 min , b ) 18 min , c ) 16 min , d ) 20 min , e ) 26 min", + "Correct": "a", + "Explanation": "\"in 1 hr , the bus covers 50 km without stoppages and 40 km with stoppages . stoppage time = time take to travel ( 50 - 40 ) km i . e 10 km at 50 km / hr . stoppage time = 10 / 50 hrs = 12 min answer : a\"" + }, + { + "Answer": 20, + "Options": "a ) 40 , b ) 26 , c ) 20 , d ) 28 , e ) 22", + "Correct": "c", + "Explanation": "\"let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 20 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 20 + 20 ) / 2 = 20 . answer : c\"" + }, + { + "Answer": 1110, + "Options": "a ) 900 , b ) 1000 , c ) 1110 , d ) 1200 , e ) 1400", + "Correct": "c", + "Explanation": "\"10 / 9 = 1 and 10000 / 9 = 1111 = = > 1111 - 1 = 1110 . therefore 1110 answer : c\"" + }, + { + "Answer": 40, + "Options": "a ) 15 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 40 %", + "Correct": "e", + "Explanation": "sol . let the original consumption = 100 kg and new consumption = x kg . so , 100 x 3 = x \u00d7 5 = x = 60 kg . \u2234 reduction in consumption = 40 % . answer e" + }, + { + "Answer": 39.5, + "Options": "a ) 30 , b ) 33.6 , c ) 39.8 , d ) 44.9 , e ) none", + "Correct": "c", + "Explanation": "\"sol . there are five prime numbers between 30 and 50 . they are 31 , 37 , 41 , 43 and 47 \u2234 required average = [ 31 + 37 + 41 + 43 + 47 / 5 ] = 199 / 5 = 39.8 answer c\"" + }, + { + "Answer": 2030, + "Options": "a ) $ 2,040 , b ) $ 2,120 , c ) $ 1,960 , d ) $ 1,920 , e ) $ 2,030", + "Correct": "e", + "Explanation": "\"in order to maximize the amount of money that the gambler kept , we should maximize # of $ 30 chips lost and minimize # of $ 100 chips lost , which means that # of $ 30 chips lost must be 2 more than # of $ 100 chips lost . so , if # of $ 30 chips lost is x then # of $ 100 chips lost should be x - 2 . now , given that total # of chips lost is 16 : x + x - 2 = 16 - - > x = 9 : 9 $ 30 chips were lost and 9 - 2 = 7 $ 100 chips were lost . total worth of chips lost is 9 * 30 + 7 * 100 = $ 970 , so the gambler kept $ 3,000 - $ 970 = $ 2,030 . answer : e\"" + }, + { + "Answer": 80, + "Options": "a ) 95 , b ) 90 , c ) 85 , d ) 80 , e ) 75", + "Correct": "d", + "Explanation": "\"let x be the number of students in the school . 0.2 x students went to the trip and took more than 100 $ . they compose ( 100 - 75 ) = 25 % of all students who went to the trip . therefore the toal of 0.2 x / 0.25 = 0.8 x students went to the camping which is 80 % . the answer is d\"" + }, + { + "Answer": 63.61904761904762, + "Options": "a ) 60 , b ) 68 , c ) 65 , d ) 64 , e ) 61", + "Correct": "d", + "Explanation": "\"for 40 hrs = 40 * 12 = 480 excess = 976 - 480 = 496 for extra hours = . 75 ( 12 ) = 9 + 12 = 21 number of extra hrs = 496 / 21 = 23.62 total hrs = 40 + 23.62 = 63.62 = 64 approx . answer d 64\"" + }, + { + "Answer": 6.849999999999994, + "Options": "a ) 2 % , b ) 8.85 % , c ) 5.85 % , d ) 6.85 % , e ) 1 %", + "Correct": "d", + "Explanation": "\"100 * 100 = 10000 81 * 115 = 9315 - - - - - - - - - - - 10000 - - - - - - - - - - - 685 100 - - - - - - - - - - - ? = > 6.85 % decrease answer : d\"" + }, + { + "Answer": 66.66666666666667, + "Options": "a ) 33.33 % , b ) 25 % , c ) 75 % , d ) 66.66 % , e ) none of these", + "Correct": "d", + "Explanation": "\"using formula ( x / ( 100 - x ) * 100 ) where x is percentage decrease ( here it is 40 % ) = > 40 / ( 100 - 40 ) * 100 = 66.66 % answer : d\"" + }, + { + "Answer": 52.06214689265537, + "Options": "a ) 50.15 , b ) 52.06 , c ) 51.25 , d ) 53.06 , e ) none of the above", + "Correct": "b", + "Explanation": "\"required average marks = 55 \u00e3 \u2014 50 + 35 \u00e3 \u2014 60 + 45 \u00e3 \u2014 55 + 42 \u00e3 \u2014 45 / 55 + 35 + 45 + 42 = 2750 + 2100 + 2475 + 1890 / 162 = 9215 \u00e2 \u0081 \u201e 177 = 52.06 answer b\"" + }, + { + "Answer": 129.9999999999999, + "Options": "a ) 65 km , b ) 100 km , c ) 120 km , d ) 130 km , e ) 75 km", + "Correct": "d", + "Explanation": "let total distance be = x km . then , 3 x / 5 + 7 x / 20 + 6.5 = x ; 12 x + 7 x + 130 = 20 x ; x = 130 hence total distance = 130 km . answer d" + }, + { + "Answer": 34, + "Options": "a ) 39 , b ) 33 , c ) 34 , d ) 30 , e ) 36", + "Correct": "c", + "Explanation": "explanation : numbers divisible by 4 are 16,20 , 24,28 , 32,36 , 40,44 , 48,52 , , , average = ( 16 + 20 + 24 + 28 + 32 + 36 + 40 + 44 + 48 + 52 ) / 10 = 340 / 10 = 34 answer : c" + }, + { + "Answer": 10, + "Options": "a ) 10 . , b ) 8 . , c ) 7 . , d ) 2 . , e ) - 2 .", + "Correct": "a", + "Explanation": "\"given a + b = 16 = > a = 16 - b - - > eq 1 b + c = 9 c + d = 3 = > d = 3 - c - - > eq 2 then eqs 1 + 2 = > a + d = 16 - b + 3 - c = > 19 - ( b + c ) = > 19 - 9 = 10 . option a . . .\"" + }, + { + "Answer": 160, + "Options": "a ) 177 , b ) 150 , c ) 817 , d ) 160 , e ) 616", + "Correct": "d", + "Explanation": "a + b + c = 880 4 a = 5 b = 10 c = x a : b : c = 1 / 4 : 1 / 5 : 1 / 10 = 5 : 4 : 2 2 / 11 * 880 = rs . 160 answer : d" + }, + { + "Answer": 1.3333333333333333, + "Options": "a ) 2 / 1 , b ) 4 / 3 , c ) 2 / 3 , d ) 3 / 4 , e ) 3 / 2", + "Correct": "b", + "Explanation": "given that milk / water = 4 x / x and 4 x + x = 45 - - > x = 9 . thus milk = 4 x = 36 liters and water = x = 9 liters . new ratio = 36 / ( 9 + 18 ) = 36 / 27 = 4 / 3 . answer : b ." + }, + { + "Answer": 19, + "Options": "a ) 19 , b ) 20 , c ) 32 , d ) 41 , e ) 53", + "Correct": "a", + "Explanation": "\"( 1056 / 25 ) gives remainder 6 19 + 6 = 23 , so we need to add 19 a\"" + }, + { + "Answer": 6, + "Options": "a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 7", + "Correct": "d", + "Explanation": "the number of bars of chocolate that can be placed in the little boxes of 9 bars is the first number that is divisible by 9 that occurs before 853845 . in order to divide the sum in 9 parts , the amount must be divisible by 9 divisibility rule of 9 : the sum of the digits must be divisible by 9 sum of digits of 853845 = 33 and 27 is divisible by 9 . hence , we need to remove 6 to this number for it to be divisible by 9 correct option : d" + }, + { + "Answer": 117, + "Options": "a ) 115 , b ) 117 , c ) 116 , d ) 114 , e ) 112", + "Correct": "b", + "Explanation": "explanation : length = 6 m 24 cm = 624 cm width = 4 m 32 cm = 432 cm hcf of 624 and 432 = 48 number of square tiles required = ( 624 x 432 ) / ( 48 x 48 ) = 13 x 9 = 117 . answer is b" + }, + { + "Answer": 20, + "Options": "a ) 20 , b ) 99 , c ) 27 , d ) 22 , e ) 29", + "Correct": "a", + "Explanation": "\"let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 16 x = 4 ( 3 x + 5 ) 4 x = 20 x = 5 quantity of alcohol = ( 4 x 5 ) litres = 20 litres . answer : a\"" + }, + { + "Answer": 120, + "Options": "a ) 300 , b ) 120 , c ) 150 , d ) 170 , e ) 270", + "Correct": "b", + "Explanation": "\"n th term of a . p . is given by a + ( n - 1 ) d 4 th term = a + 3 d 12 th term = a + 11 d given a + 3 d + a + 11 d = 20 - - > 2 a + 14 d = 20 - - > a + 7 d = 10 sum of n term of a . p = n / 2 [ 2 a + ( n - 1 ) d ] subsitiuing n = 12 . . . we get 12 / 2 [ 2 a + 14 d ] = 15 [ a + 7 d ] = 12 * 10 = 120 . . . answer is b . . .\"" + }, + { + "Answer": 300, + "Options": "a ) a ) 300 , b ) b ) 150 , c ) c ) 130 , d ) d ) 90 , e ) e ) 210", + "Correct": "a", + "Explanation": "let x be the total number of pages in the book , then she finished 2 / 3 * x pages . then she has x \u2212 2 / 3 * x = 1 / 3 * x pages left . 2 / 3 * x \u2212 1 / 3 * x = 100 1 / 3 * x = 100 x = 300 so the book is 300 pages long . answer is a ." + }, + { + "Answer": 66, + "Options": "a ) 50 , b ) 48 , c ) 65 , d ) 66 , e ) 72", + "Correct": "d", + "Explanation": "\"average in 25 matches = ( 10 * 60 + 15 * 70 ) / 10 + 15 = 66 answer is d\"" + }, + { + "Answer": 36, + "Options": "a ) 15 , b ) 30 , c ) 36 , d ) 40 , e ) 45", + "Correct": "c", + "Explanation": "\"lots of ways to tackle this . 30 % of 180 = 54 1 / 3 of 45 = 18 so , 1 / 3 less than 54 is equal to 54 - 18 = 36 answer : c\"" + }, + { + "Answer": 100, + "Options": "a ) 100 , b ) 110 , c ) 120 , d ) 130 , e ) 140", + "Correct": "a", + "Explanation": "\"let the number of boys who passed = x . then , 39 x x + 15 x ( 120 - x ) = 120 x 35 24 x = 4200 - 1800 = > x = 2400 / 24 x = 100 . hence , the number of boys passed = 100 . answer : a\"" + }, + { + "Answer": 93, + "Options": "a ) 38 , b ) 47 , c ) 50 , d ) 53 , e ) 93", + "Correct": "e", + "Explanation": "\"if you list the amount eaten each hour , you ' ll get an equally spaced list , increasing by 3 each hour . in any equally spaced list , the median equals the mean . here , the mean is 450 / 5 = 90 , so the median is also 90 , and that is the amount eaten in the 2 nd hour . we need to add 3 to find the total eaten in the next hour , so the answer is 93 option e\"" + }, + { + "Answer": 6000, + "Options": "a ) s . 9800 , b ) s . 3800 , c ) s . 9800 , d ) s . 6000 , e ) s . 6880", + "Correct": "d", + "Explanation": "\"cost of the camel = p 10 camels = 24 horses 16 horses = 4 oxen 6 oxen = 4 elephants 10 elephants = rs . 150000 p = rs . [ ( 24 * 4 * 4 * 150000 ) / ( 10 * 16 * 6 * 10 ) ] p = rs . ( 57600000 / 9600 ) = > p = rs . 6000 answer : d\"" + }, + { + "Answer": 27, + "Options": "a ) 23 , b ) 24 , c ) 25 , d ) 26 , e ) 27", + "Correct": "e", + "Explanation": "\"average age of people = 30 so have total age = 210 before 7 years we have to deduct each person age by seven years 210 - 21 = 189 so average age would be 189 / 7 = 27 answer : e\"" + }, + { + "Answer": 0.16666666666666666, + "Options": "a ) 1 / 6 , b ) 1 / 3 , c ) 2 / 3 , d ) 1 / 4 , e ) 4", + "Correct": "a", + "Explanation": "= > ( ( 2 ^ 5 ) * ( ( 3 ^ 2 ) ^ 2 ) / ( ( 2 ^ 3 ) ^ 2 ) * ( 3 ^ 5 ) ) = > ( ( 2 ^ 5 ) * ( 3 ^ 4 ) ) / ( ( 2 ^ 6 ) * ( 3 ^ 5 ) ) = > 1 / ( 2 * 3 ) = > 1 / 6 option a is answer" + }, + { + "Answer": 10, + "Options": "a ) 11 , b ) 12 , c ) 10 , d ) 2 , e ) 7", + "Correct": "c", + "Explanation": "1 2 3 4 5 6 7 8 leave the top right - most number 8 start with bottom right - most number 5 8 * 3 + 7 = 31 31 * 2 + 6 = 68 68 * 1 + 5 = 73 this is the number required now , do the successive division in the reverse order the sum of the remainders is 10 hence , the correct option is c" + }, + { + "Answer": 20, + "Options": "a ) 12.5 % , b ) 13 % , c ) 15 % , d ) 17 % , e ) 20 %", + "Correct": "e", + "Explanation": "\"quantity x rate = price 1 x 1 = 1 0.64 x 1.25 = 0.8 decrease in price = ( 0.2 / 1 ) \u00d7 100 = 20 % e )\"" + }, + { + "Answer": 36, + "Options": "a ) 25 , b ) 43 , c ) 14 , d ) 36 , e ) 12", + "Correct": "d", + "Explanation": "john ' s age = 10 x + y so wilson ' s age = 10 y + x . . after 21 years , 10 x + y + 21 = 2 * ( 10 y + x + 21 ) . . . . so 21 + 19 y = 8 x . . . check for odd values of y , y = 1 satisfies the eqn with x = 5 . . . so ages are 51 and 15 and ans as found correctly by u is d . . 36" + }, + { + "Answer": 58, + "Options": "a ) $ 58 , b ) $ 42 , c ) $ 65 , d ) $ 48 , e ) $ 62", + "Correct": "a", + "Explanation": "avg = sum of observations / number of observations avg income = ( 45 + 50 + 60 + 65 + 70 ) / 5 = 58 answer is a" + }, + { + "Answer": 0.4166666666666667, + "Options": "a ) 5 / 12 , b ) 1 / 15 , c ) 2 / 13 , d ) 2 / 15 , e ) 1 / 17", + "Correct": "a", + "Explanation": "first , there are 7 c 3 ways you can select 3 good pencils from 4 good ones . second , there are 9 c 3 ways you select 3 pencils from 6 ones in the box . then , the probability that neither pen will be defective is : 7 c 3 / 9 c 3 = 35 / 84 = 5 / 12 answer is a" + }, + { + "Answer": 0.11499999999999999, + "Options": "a ) 23 / 200 , b ) 11 / 100 , c ) 7 / 50 , d ) 3 / 20 , e ) 4 / 25", + "Correct": "a", + "Explanation": "males who did not arrive on time are 1 / 8 * 3 / 5 = 3 / 40 of the attendees . females who did not arrive on time are 1 / 10 * 2 / 5 = 2 / 50 of the attendees . the fraction of all attendees who did not arrive on time is 3 / 40 + 2 / 50 = 23 / 200 the answer is a ." + }, + { + "Answer": 5, + "Options": "a ) a ) 7 , b ) b ) 5 , c ) c ) 9 , d ) d ) 8 , e ) e ) none of the above", + "Correct": "b", + "Explanation": "sol . 30 lines per page total 150 lines = 150 / 30 = 5 answer : b" + }, + { + "Answer": 684, + "Options": "a ) s . 684 , b ) s . 500 , c ) s . 540 , d ) s . 740 , e ) s . 840", + "Correct": "a", + "Explanation": "\"s . i for 5 years = ( 1020 - 780 ) = rs . 240 . s . i . for 2 years = 240 / 5 * 2 = rs . 96 . principal = ( 780 - 96 ) = rs . 684 answer : a\"" + }, + { + "Answer": 480, + "Options": "a ) 400 , b ) 420 , c ) 480 , d ) 450 , e ) 510", + "Correct": "c", + "Explanation": "\"let no . of non - officers be x 15 * 440 + x * 110 = ( x + 15 ) 120 x = 480 c\"" + }, + { + "Answer": 25, + "Options": "a ) 15 % , b ) 25 % , c ) 0.125 % , d ) 0.2083 % , e ) none", + "Correct": "b", + "Explanation": "\"this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 480 / 3840 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 50 ) = 25 % the correct answer is ( b ) .\"" + }, + { + "Answer": 690, + "Options": "a ) 732 , b ) 990 , c ) 109 , d ) 130 , e ) 690", + "Correct": "e", + "Explanation": "\"total number of digits = ( no . of digits in 1 - digit page nos . + no . of digits in 2 - digit page nos . + no . of digits in 3 - digit page nos . ) = ( 1 x 9 + 2 x 90 + 3 x 167 ) = ( 9 + 180 + 501 ) = 690 . answer : e\"" + }, + { + "Answer": 30, + "Options": "a ) 10 , b ) 30 , c ) 20 , d ) 15 , e ) 16", + "Correct": "b", + "Explanation": "\"number of liters of water in 150 liters of the mixture = 10 % of 150 = 10 / 100 * 150 = 15 liters . p liters of water added to the mixture to make water 25 % of the new mixture . total amount of water becomes ( 15 + p ) and total volume of mixture is ( 150 + p ) . ( 15 + p ) = 25 / 100 * ( 150 + p ) 60 + 4 p = 150 + p p = 30 liters . answer : b\"" + }, + { + "Answer": 7992, + "Options": "a ) 2992 , b ) 7992 , c ) 2877 , d ) 2077 , e ) 6229", + "Correct": "b", + "Explanation": "explanation : 8000 \u00e2 \u20ac \u201c 8 = 7992 answer : b" + }, + { + "Answer": 16, + "Options": "a ) 8 , b ) 16 , c ) 10 , d ) 11 , e ) 12", + "Correct": "b", + "Explanation": "\"12 + 4 = 16 correct answer is b ) 16\"" + }, + { + "Answer": 21.842857142857145, + "Options": "a ) 21.84 , b ) 22.84 , c ) 23.84 , d ) 24.84 , e ) 25.84", + "Correct": "a", + "Explanation": "\"dinner bill of 7 person = 139 + 10 % tip so , 10 % of 139 = ( 139 * 10 ) / 100 = 13.9 so , the actual total amount = 139 + 13.9 = $ 152.9 so per head bill = 152.9 / 7 = $ 21.84 answer : a\"" + }, + { + "Answer": 6, + "Options": "a ) 1 : 8 , b ) 1 : 4 , c ) 2 : 1 , d ) 6 : 1 , e ) 8 : 1", + "Correct": "d", + "Explanation": "\"x = 3 y , y = 2 * z x : y , y : z 3 : 1 , 2 : 1 6 : 2 , 2 : 1 so , x : z = 6 : 1 ( d )\"" + }, + { + "Answer": 474232, + "Options": "a ) 6623 , b ) 43036 , c ) 51515 , d ) 474232 , e ) 2025", + "Correct": "d", + "Explanation": "dividend = ? ? = d * q + r ? = 800 * 594 + - 968 ? = 475,200 + - 968 ? = 474,232" + }, + { + "Answer": 576, + "Options": "a ) 572 , b ) 573 , c ) 574 , d ) 575 , e ) 576", + "Correct": "e", + "Explanation": "\"sum of 1 st n odd no . s = 1 + 3 + 5 + 7 + . . . = n ^ 2 so , sum of 1 st 24 odd numbers = 24 ^ 2 = 576 answer : e\"" + }, + { + "Answer": 650, + "Options": "a ) 650 , b ) 640 , c ) 630 , d ) 620 , e ) 610", + "Correct": "a", + "Explanation": "a = 4 d = 7 \u2013 4 = 3 sum of first 20 terms , s 20 answer is a" + }, + { + "Answer": 25, + "Options": "a ) 25 , b ) 35 , c ) 38 , d ) 40 , e ) 45", + "Correct": "a", + "Explanation": "\"10 play kabadi = > n ( a ) = 10 , 5 play both gmaes . = > n ( anb ) = 5 15 play kho kho only , = > n ( b ) = n ( b only ) + n ( anb ) = 15 + 5 = 20 total = > n ( aub ) = n ( a ) + n ( b ) - n ( anb ) = 10 + 20 - 5 = 25 answer : a\"" + }, + { + "Answer": 180, + "Options": "a ) 504 , b ) 532 , c ) 210 , d ) 180 , e ) 280", + "Correct": "d", + "Explanation": "lcm of 7 , 8 and 9 is 504 , thus 523 rbc must be divisible by 504 . 523 rbc = 523000 + rbc 523000 divided by 504 gives a remainder of 352 . hence , 352 + rbc = k * 504 . k = 1 rbc = 152 - - > r * b * c = 10 k = 2 rbc = 656 - - > r * b * c = 180 as rbc is three digit number k can not be more than 2 . two answers ? well only one is listed in answer choices , so d . answer : d ." + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "c", + "Explanation": "\"28160 = 1 * 5 * 8 ^ 3 * 11 the factors of 8 must come from the purple point value , so there are 3 purple chips . the answer is c .\"" + }, + { + "Answer": 100.00000000000001, + "Options": "a ) 100 , b ) 12 , c ) 15 , d ) 18 , e ) 19", + "Correct": "a", + "Explanation": "\"2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 281 - 81 = 200 = > ab = 100 answer : a\"" + }, + { + "Answer": 70.76923076923077, + "Options": "a ) 50.78 kg , b ) 49.32 kg , c ) 70.76 kg , d ) 69.15 kg , e ) 70.89 kg", + "Correct": "c", + "Explanation": "\"total weight of 60 + 70 students = 60 * 60 + 70 * 80 = 3600 + 5600 average weight of the class is = 9200 / 130 = 70.76 kg answer is c\"" + }, + { + "Answer": 44.00000000000003, + "Options": "a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 44 %", + "Correct": "e", + "Explanation": "\"say a recliner is actually worth $ 100 if she sells 100 recliners then she earns $ 10000 after the discount of 20 % , she will earn $ 80 per recliner and she sells 80 % more ie . , 180 recliners hence her sales tields 180 * 80 = $ 14400 increase in sales = 14400 - 10000 = $ 4400 so % increase = 4400 * 100 / 10000 = 44 % e is the answer\"" + }, + { + "Answer": 6, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8", + "Correct": "d", + "Explanation": "given k is an integer 121 < k ^ 2 < 225 11 < | k | < 15 k = - 12 , - 13 , - 1412 , 1314 answer : d" + }, + { + "Answer": 36.45, + "Options": "a ) 76.55 , b ) 36.35 , c ) 46.15 , d ) 16.05 , e ) 20", + "Correct": "b", + "Explanation": "\"explanation : correct sum = ( 36 * 40 + 34 - 20 ) = 1454 correct mean = = 1454 / 40 = 36.35 answer : b\"" + }, + { + "Answer": 1312.5, + "Options": "a ) 1000 , b ) 1312.5 , c ) 1400 , d ) 1600 , e ) 1625", + "Correct": "b", + "Explanation": "\"300 gallons of water increases capacity by 40 % that means 40 % is 300 gallons , so 100 % would be = 300 * 100 / 40 = 750 gallons now 750 + 300 gallons is 80 % capacity of tank . so 100 % capacity would be = 1050 * 100 / 80 = 1312.5 b is the answer\"" + }, + { + "Answer": 30.580000000000002, + "Options": "a ) 32.84 , b ) 22.84 , c ) 30.58 , d ) 24.84 , e ) 30.84", + "Correct": "c", + "Explanation": "\"dinner bill of 5 person = 139 + 10 % tip so , 10 % of 139 = ( 139 * 10 ) / 100 = 13.9 so , the actual total amount = 139 + 13.9 = $ 152.9 so per head bill = 152.9 / 5 = $ 30.58 answer : c\"" + }, + { + "Answer": 0.18666666666666662, + "Options": "a ) 6 / 25 , b ) 11 / 50 , c ) 14 / 75 , d ) 23 / 100 , e ) 31 / 150", + "Correct": "c", + "Explanation": "\"males who did not arrive on time are 1 / 5 * 3 / 5 = 3 / 25 of the attendees . females who did not arrive on time are 1 / 6 * 2 / 5 = 1 / 15 of the attendees . the fraction of all attendees who did not arrive on time is 3 / 25 + 1 / 15 = 14 / 75 the answer is c .\"" + }, + { + "Answer": 1, + "Options": "a ) 4 , b ) 3 , c ) 2 , d ) 1 , e ) 0", + "Correct": "d", + "Explanation": "\"( 1 ) x = 7 y + 3 ( 2 ) 2 x = 18 y + 2 ( 2 ) - ( 1 ) : x = 11 y - 1 11 y - x = 1 the answer is d .\"" + }, + { + "Answer": 0.17142857142857143, + "Options": "a ) 2 / 35 , b ) 2 / 3 , c ) 6 / 35 , d ) 5 / 7 , e ) 7 / 5", + "Correct": "c", + "Explanation": "\"let a be the event that ram is selected and b is the event that ravi is selected . p ( a ) = 6 / 7 p ( b ) = 1 / 5 let c be the event that both are selected . p ( c ) = p ( a ) x p ( b ) as a and b are independent events : = 6 / 7 x 1 / 5 = 6 / 35 answer : c\"" + }, + { + "Answer": 14.139999999999986, + "Options": "a ) - 16.16 % , b ) - 15.15 % , c ) - 14.14 % , d ) - 13.13 % , e ) - 12.12 %", + "Correct": "c", + "Explanation": "\"( 100 % + 6 % ) * ( 100 % - 19 % ) = 1.06 * . 81 = 0.8586 . 1 - 0.8586 = 14.14 % lost = - 14.14 % the answer is c the organization has lost 14.14 % of its total volunteers from fall to spring .\"" + }, + { + "Answer": 28, + "Options": "a ) 41 , b ) 28 , c ) 43 , d ) 44 , e ) 45", + "Correct": "b", + "Explanation": "\"n ( n - 1 ) / 2 = 8 * 7 / 2 = 28 answer : b\"" + }, + { + "Answer": 26.999999999999993, + "Options": "a ) 15 , b ) 18 , c ) 21 , d ) 24 , e ) 27", + "Correct": "e", + "Explanation": "( v * ) * = ( v - v / 3 ) - ( v - v / 3 ) / 3 12 = 2 v / 3 - 2 v / 9 = 4 v / 9 v = 27 the answer is e ." + }, + { + "Answer": 6991, + "Options": "a ) s . 1991 , b ) s . 2991 , c ) s . 3991 , d ) s . 4991 , e ) s . 6991", + "Correct": "e", + "Explanation": "\"explanation : total sale for 5 months = rs . ( 8435 + 8927 + 8855 + 9230 + 8562 ) = rs . 44009 . required sale = rs . [ ( 8500 x 6 ) \u00e2 \u20ac \u201c 44009 ] = rs . ( 51000 \u00e2 \u20ac \u201c 44009 ) = rs . 6991 . answer e\"" + }, + { + "Answer": 300, + "Options": "a ) 200 , b ) 300 , c ) 400 , d ) 500 , e ) 470", + "Correct": "b", + "Explanation": "1 . the numbers in which 7 occurs only once . e . g 7 , 17 , 78 , 217 , 743 etc this means that 7 is one of the digits and the remaining two digits will be any of the other 9 digits ( i . e 0 to 9 with the exception of 7 ) you have 1 * 9 * 9 = 81 such numbers . however , 7 could appear as the first or the second or the third digit . therefore , there will be 3 * 81 = 243 numbers ( 1 - digit , 2 - digits and 3 - digits ) in which 7 will appear only once . in each of these numbers , 7 is written once . therefore , 243 times . 2 . the numbers in which 7 will appear twice . e . g 772 or 377 or 747 or 77 in these numbers , one of the digits is not 7 and it can be any of the 9 digits ( 0 to 9 with the exception of 7 ) . there will be 9 such numbers . however , this digit which is not 7 can appear in the first or second or the third place . so there are 3 * 9 = 27 such numbers . in each of these 27 numbers , the digit 7 is written twice . therefore , 7 is written 54 times . 3 . the number in which 7 appears thrice - 777 - 1 number . 7 is written thrice in it . therefore , the total number of times the digit 7 is written between 1 and 999 is 243 + 54 + 3 = 300 option b" + }, + { + "Answer": 75, + "Options": "a ) 98 , b ) 78 , c ) 76 , d ) 87 , e ) 75", + "Correct": "e", + "Explanation": "\"average = ( 76 + 65 + 82 + 67 + 85 ) / 5 = 375 / 5 = 75 . answer : e\"" + }, + { + "Answer": 54, + "Options": "a ) 48 % , b ) 52 % , c ) 54 % , d ) 60 % , e ) 70 %", + "Correct": "c", + "Explanation": "\"we have a 24 litre solution containing 90 % of alcohol in the water . = > quantity of alcohol in the solution = 24 \u00e3 \u2014 90 / 100 now 16 litre of water is added to the solution . = > total quantity of the new solution = 24 + 16 = 40 percentage of alcohol in the new solution = 24 \u00e3 \u2014 90 / 100 40 \u00e3 \u2014 100 = 24 \u00e3 \u2014 9010040 \u00e3 \u2014 100 = 24 \u00e3 \u2014 2.25 / 100 = 54 % c\"" + }, + { + "Answer": 56.5, + "Options": "a ) 54.5 , b ) 56.5 , c ) 59.2 , d ) 61 , e ) 62", + "Correct": "b", + "Explanation": "explanation : solution : assume karthik ' s weight be x kg . according to karthik , 55 < x < 62 according to karthik ; s brother , 50 < x < 60 . according to karthik ' s mother , x < 58 . the values satisfying all the above conditions are 56 and 57 . . ' . required average = ( 56 + 57 ) / 2 = 56.5 . answer : b" + }, + { + "Answer": 98.68, + "Options": "a ) $ 94.03 , b ) $ 96.75 , c ) $ 98.68 , d ) $ 102.07 , e ) $ 105.3", + "Correct": "c", + "Explanation": "\"there can be 2 cases 1 ) 25 + 25 + 10 + 5 = $ 98.68 or 2 ) 25 + 25 + 25 = $ 96.60 c\"" + }, + { + "Answer": 38, + "Options": "a ) 42 , b ) 36 , c ) 46 , d ) 38 , e ) 40", + "Correct": "d", + "Explanation": "\"at 6 ' o clock , there would be 6 strikes . first strike , then a short interval , the second strike , then a short interval and so on till the 6 th strike . so there would be in all 5 intervals between 6 strikes . similarly , between 10 strikes , there would be 9 intervals . according to the question , the time spent in the strike and the interval is same . at 6 ' o clock , the 6 strikes and the 5 intervals together take 22 sec so each strike and each interval takes 2 secs . at 12 ' o clock , the 10 strikes and 9 intervals will take 2 * ( 10 + 9 ) = 38 secs d d\"" + }, + { + "Answer": 21, + "Options": "a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22", + "Correct": "d", + "Explanation": "\"d = ( d - r ) / q = ( 171 - 3 ) / 8 = 168 / 8 = 21 d\"" + }, + { + "Answer": 780, + "Options": "a ) 780 , b ) 200 , c ) 210 , d ) 220 , e ) 230", + "Correct": "a", + "Explanation": "\"or , if there are n persons then no . of shakehands = nc 2 = 40 c 2 = 780 answer : a\"" + }, + { + "Answer": 24.5, + "Options": "a ) 18.5 , b ) 21.5 , c ) 24.5 , d ) 27.5 , e ) 30.5", + "Correct": "c", + "Explanation": "\"the point of intersection is ( - 7 , - 7 ) . the triangle has a base of length 7 and a height of 7 . area = ( 1 / 2 ) * base * height = ( 1 / 2 ) * 7 * 7 = 24.5 the answer is c .\"" + }, + { + "Answer": 7, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 7", + "Correct": "e", + "Explanation": "16 ^ y = 4 ^ 2 y = 4 ^ 14 2 y = 14 y = 7 the answer is e ." + }, + { + "Answer": 15, + "Options": "a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19", + "Correct": "a", + "Explanation": "\"let p be the number of participants . pc 2 = 105 ( p ) ( p - 1 ) = 210 = 15 * 14 p = 15 the answer is a .\"" + }, + { + "Answer": 0.5714285714285714, + "Options": "a ) 2 / 7 , b ) 3 / 7 , c ) 4 / 7 , d ) 9 / 14 , e ) 11 / 14", + "Correct": "c", + "Explanation": "let x be the amount of jam at the beginning . after lunch , the remaining jam was ( 2 / 3 ) x . after dinner , the remaining jam was ( 6 / 7 ) ( 2 / 3 ) x = ( 4 / 7 ) x . the answer is c ." + }, + { + "Answer": 98.77, + "Options": "a ) $ 94.03 , b ) $ 96.75 , c ) $ 98.78 , d ) $ 98.77 , e ) $ 105.3", + "Correct": "d", + "Explanation": "\"there can be 2 cases 1 ) 25 + 25 + 10 + 5 = $ 98.77 or 2 ) 25 + 25 + 25 = $ 96.75 d\"" + }, + { + "Answer": 0.2, + "Options": "a ) 1 / 10 , b ) 1 / 5 , c ) 2 / 5 , d ) 3 / 5 , e ) 3 / 10", + "Correct": "b", + "Explanation": "p 2 \u2013 13 p + 40 = s so ( p \u2013 8 ) ( p \u2013 5 ) = s for q to be negative , the expressions ( p \u2013 8 ) and ( p \u2013 5 ) must have opposite signs . which integers on the number line will yield opposite signs for the expressions ( p \u2013 8 ) and ( p \u2013 5 ) ? those integers in the range 5 < p < 8 ( notice 5 and 8 are not included because they would both yield a value of zero and zero is a nonnegative integer ) . that means that there are only two integer values for p , 6 and 7 , that would yield a negative q . with a total of 10 possible p values , only 2 yield a negative q , so the probability is 2 / 10 or 1 / 5 . the correct answer is b ." + }, + { + "Answer": 2, + "Options": "a ) 0 , b ) 2 , c ) 5 , d ) 7 , e ) 9", + "Correct": "b", + "Explanation": "sol . let the number be 5 x 2 . clearly , it is divisible by 2 . now , 5 + x + 2 = ( 7 + x ) must be divisible by 3 . so , x = 2 . answer b" + }, + { + "Answer": 240, + "Options": "a ) 120 , b ) 240 , c ) 360 , d ) 720 , e ) 1440", + "Correct": "b", + "Explanation": "x - x - x - x - x - - > there are 4 odd digits from 1 to 7 , inclusive thus options for the first and the last x ' s are : 4 - x - x - 3 . other x ' s can take following values : 4 - 5 - 4 - 3 - - > 4 * 5 * 4 * 3 = 240 . answer : b ." + }, + { + "Answer": 16.666666666666664, + "Options": "a ) 7.5 % , b ) 9.1 % , c ) 10.9 % , d ) 16.67 % , e ) 15 %", + "Correct": "d", + "Explanation": "reduce in consumption = r / ( 100 + r ) * 100 % = 20 / 120 * 100 = 16.67 % answer is d" + }, + { + "Answer": 800, + "Options": "a ) 800 , b ) 500 , c ) 505 , d ) none of these , e ) 506", + "Correct": "a", + "Explanation": "\"explanation : 64 / . 08 = 6400 / 8 = 800 option a\"" + }, + { + "Answer": 4.5, + "Options": "a ) 1.5 , b ) 4.5 , c ) 7.5 , d ) 9.5 , e ) 8.7", + "Correct": "b", + "Explanation": "explanation : ( a / b ) x \u2212 2 = ( b / a ) x \u2212 7 \u21d2 ( a / b ) x \u2212 2 = ( a / b ) \u2212 ( x \u2212 7 ) \u21d2 x \u2212 2 = \u2212 ( x \u2212 7 ) \u21d2 x \u2212 2 = \u2212 x + 7 \u21d2 x \u2212 2 = \u2212 x + 7 \u21d2 2 x = 9 \u21d2 x = 92 = 4.5 option b" + }, + { + "Answer": 102, + "Options": "a ) 87 , b ) 89 , c ) 90 , d ) 93 , e ) 102", + "Correct": "e", + "Explanation": "total score on 3 tests = 94 * 3 = 282 jerry wants the average to be = 96 hence total score on 4 tests should be = 96 * 4 = 384 score required on the fourth test = 384 - 282 = 102 option e" + }, + { + "Answer": 199.99999999999997, + "Options": "a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500", + "Correct": "b", + "Explanation": "\"0.036 * 10 ^ 5 can be written as 3600 18000 * 10 ^ ( - 3 ) can be written as 18 required = 3600 / 18 = 200 answer : b\"" + }, + { + "Answer": 5500, + "Options": "a ) 2788 , b ) 5500 , c ) 7282 , d ) 2782 , e ) 2729", + "Correct": "b", + "Explanation": "4 - - - 4400 5 - - - ? = > 5500 answer : b" + }, + { + "Answer": 4200, + "Options": "a ) rs . 3601 , b ) rs . 3618 , c ) rs . 4200 , d ) rs . 3619 , e ) rs . 3610", + "Correct": "c", + "Explanation": "\"manager ' s monthly salary = rs . ( 1950 * 16 - 1800 * 15 ) = rs . 4200 answer : c\"" + }, + { + "Answer": 4, + "Options": "a ) 6 , b ) 4 , c ) 0 , d ) 8 , e ) 7", + "Correct": "b", + "Explanation": "\"every prime number greater than 3 can be written 6 n + 1 or 6 n - 1 . if p = 6 n + 1 , then p ^ 2 + 15 = 36 n ^ 2 + 12 n + 1 + 15 = 36 n ^ 2 + 12 n + 12 + 4 if p = 6 n - 1 , then p ^ 2 + 15 = 36 n ^ 2 - 12 n + 1 + 15 = 36 n ^ 2 - 12 n + 12 + 4 when divided by 12 , it must leave a remainder of 4 . the answer is b .\"" + }, + { + "Answer": 56, + "Options": "a ) 9 , b ) 31 , c ) 56 , d ) 72 , e ) 90", + "Correct": "c", + "Explanation": "age of the 15 th student = 18 * 15 - ( 14 * 5 + 16 * 9 ) = 270 - 214 = 56 years answer is c" + }, + { + "Answer": 140, + "Options": "a ) s . 240 , b ) s . 140 , c ) s . 340 , d ) s . 50 , e ) s . 90", + "Correct": "b", + "Explanation": "\"a profit of rs . 700 is divided between x and y in the ratio of 1 / 2 : 1 / 3 or 3 : 2 . so profits are 300 and 200 . difference in profit share = 420 - 280 = 140 answer : b\"" + }, + { + "Answer": 2.666666666666667, + "Options": "a ) 4 / 3 , b ) 5 / 3 , c ) 7 / 3 , d ) 8 / 3 , e ) 10 / 3", + "Correct": "d", + "Explanation": "let the number of quarts that should be added to get the required ratio = x so total quarts of water = ( x + 4 ) but the original number of quarts of alcohol remains the same , so we have : 4 / ( x + 4 ) = 3 / 5 cross - multiply : now we have 20 = 3 x + 12 = > 3 x = 20 - 12 = > x = 8 / 3 answer - d" + }, + { + "Answer": 1, + "Options": "a ) 0.5 , b ) 1 , c ) 1.5 , d ) 2 , e ) 3", + "Correct": "b", + "Explanation": "\"let x be the number of desks and bookcases that are placed along the library wall . 2 x + 1.5 x < 15 3.5 x < 15 since x is a non negative integer , the largest number x can be is 4 . when x is 4 , the desks and bookcases take up 3.5 * 4 = 14 m = q , leaving 1 m of empty space . thus , i believe the answer is b ) 1\"" + }, + { + "Answer": 3, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 3 , e ) 7", + "Correct": "d", + "Explanation": "cant think of a straight approach but here is how i solved it : k is divided by 5 and remainder is 2 . this means k = 5 n + 2 ( n is an integer ) so the possible values of k = { 2 , 7 , 12 , 17 , 22 , 27 , 32 , 37 } ( less than 39 ) secondly , if k is divided by 6 , the remainder is 5 = > k = 6 m + 5 so the possible value set for k = { 5 , 11 , 17 , 23 , 29,35 } ( less than 39 ) 17 is the only common number in both the sets . hence k = 17 answer : d" + }, + { + "Answer": 202, + "Options": "a ) 179 , b ) 202 , c ) 210 , d ) 223 , e ) 229", + "Correct": "b", + "Explanation": "\"explanation : total runs scored by the batsman = 61 * 46 = 2806 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2806 \u2013 2552 = 254 runs . let the highest score be x , hence the lowest score = x \u2013 150 x + ( x - 150 ) = 254 2 x = 404 x = 202 runs answer b\"" + }, + { + "Answer": 26, + "Options": "a ) 26 , b ) 32 , c ) 35 , d ) 30 , e ) 45", + "Correct": "a", + "Explanation": "\"explanation : hcf ( 408 , 216 ) = 24 the number of boys or girls that can be placed in a section = 24 . thus the total number of sections is given by 408 / 24 + 216 / 24 = 17 + 9 = 26 answer : a\"" + }, + { + "Answer": 7.333333333333333, + "Options": "a ) 7.33 % , b ) 9 % , c ) 9.67 % , d ) 11 % , e ) 11.5 %", + "Correct": "a", + "Explanation": "\"we have an 11 litre solution containing 16 % of alcohol in the water . = > quantity of alcohol in the solution = 11 \u00e3 \u2014 16 / 100 now 13 litre of water is added to the solution . = > total quantity of the new solution = 11 + 13 = 24 percentage of alcohol in the new solution = 11 \u00e3 \u2014 16 / 100 24 \u00e3 \u2014 100 = 11 \u00e3 \u2014 1610024 \u00e3 \u2014 100 = 11 \u00e3 \u2014 0.67 / 100 = 7.33 % a\"" + }, + { + "Answer": 57, + "Options": "a ) 36 , b ) 57 , c ) 44 , d ) 48 , e ) 52", + "Correct": "b", + "Explanation": "\"for 40 hrs = 40 * 16 = 640 excess = 1116 - 640 = 476 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 476 / 28 = 17 total hrs = 40 + 17 = 57 answer b 57\"" + }, + { + "Answer": 30, + "Options": "a ) 21 % , b ) 22.5 % , c ) 25 % , d ) 30 % , e ) 40 %", + "Correct": "d", + "Explanation": "\"1 st year income = i 1 st year savings = s 1 st year expense = e 1 2 nd year income = 1.3 i 2 nd year savings = 2 s ( 100 % increase ) 2 nd year expense = e 2 e 1 + e 2 = 2 e 1 e 2 = e 1 that means expenses are same during both years . with increase of 30 % income the savings increased by 100 % . or s = . 3 i or s = 30 % of income d is the answer\"" + }, + { + "Answer": 17, + "Options": "a ) 8 , b ) 14 , c ) 15 , d ) 17 , e ) 30", + "Correct": "d", + "Explanation": "\"within one standard deviation of the average age means 31 + / - 7 23 - - 31 - - 39 number of dif . ages - 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 total = 17 d\"" + }, + { + "Answer": 9, + "Options": "a ) 17 : 3 , b ) 9 : 1 , c ) 3 : 17 , d ) 5 : 3 , e ) 11 : 2", + "Correct": "b", + "Explanation": "he 20 litre mixture contains milk and water in the ratio of 3 : 2 . therefore , there will be 12 litres of milk in the mixture and 8 litres of water in the mixture . step 1 . when 10 litres of the mixture is removed , 6 litres of milk is removed and 4 litres of water is removed . therefore , there will be 6 litres of milk and 4 litres of water left in the container . it is then replaced with pure milk of 10 litres . now the container will have 16 litres of milk and 4 litres of water . step 2 . when 10 litres of the new mixture is removed , 8 litres of milk and 2 litres of water is removed . the container will have 8 litres of milk and 2 litres of water in it . now 10 litres of pure milk is added . therefore , the container will have 18 litres of milk and 2 litres of water in it at the end of the second step . therefore , the ratio of milk and water is 18 : 2 or 9 : 1 . shortcut . we are essentially replacing water in the mixture with pure milk . let w _ o be the amount of water in the mixture originally = 8 litres . let w _ r be the amount of water in the mixture after the replacements have taken place . then , { w _ r } / { w _ o } = ( 1 - r / m ) ^ n where r is the amount of the mixture replaced by milk in each of the steps , m is the total volume of the mixture and n is the number of times the cycle is repeated . hence , { w _ r } / { w _ o } \u00a0 = ( 1 / 2 ) ^ 2 \u00a0 = 1 / 4 therefore q , w _ r \u00a0 = { w _ o } / 4 = 8 / 4 \u00a0 = 2 litres . b" + }, + { + "Answer": 26, + "Options": "a ) 9 , b ) 11 , c ) 15 , d ) 12 , e ) 26", + "Correct": "e", + "Explanation": "\"age of the 15 th student = 16 * 15 - ( 14 * 5 + 16 * 9 ) = 240 - 214 = 26 years answer is e\"" + }, + { + "Answer": 1.4000000000000004, + "Options": "a ) $ 1.40 , b ) $ 2.50 , c ) $ 4.10 , d ) $ 4.70 , e ) $ 8.20", + "Correct": "a", + "Explanation": "\"let x be the cost of a bus ride . x + ( x + 685 ) = 965 2 x = 280 x = $ 1.40 the answer is a .\"" + }, + { + "Answer": 6, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "d", + "Explanation": "let , average commission = x no . of items sold = y total commission = xy new commission = xy + 1000 new average = ( xy + 1000 ) / ( y + 1 ) = 150 + x i . e . ( xy + 1000 ) = ( y + 1 ) * ( 150 + x ) i . e . ( xy + 1000 ) = ( xy + x + 150 y + 150 ) i . e . ( 850 ) = ( x + 150 y ) new commission = 250 = 150 + x i . e . x = 100 i . e . y = 5 new sales = y + 1 = 6 answer : option d" + }, + { + "Answer": 10, + "Options": "a ) 10 , b ) 12 , c ) 15 , d ) 17 , e ) 18", + "Correct": "a", + "Explanation": "\"let original strength = y then , 40 y + 10 x 32 = ( y + 10 ) x 36 \u00e2 \u2021 \u2019 40 y + 320 = 36 y + 360 \u00e2 \u2021 \u2019 4 y = 40 \u00e2 \u02c6 \u00b4 y = 10 a\"" + }, + { + "Answer": 49, + "Options": "a ) 35 , b ) 42 , c ) 45 , d ) 49 , e ) 54", + "Correct": "d", + "Explanation": "\"a = 105 = 3 * 5 * 7 a ^ 3 = 21 \u00d7 25 \u00d7 45 \u00d7 b = > a ^ 3 = ( 7 * 3 ) x ( 5 * 5 ) x ( 3 ^ 2 * 5 ) x b = > a ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x b = > ( 3 * 5 * 7 ) ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x b b = 7 ^ 2 = 49 answer d\"" + }, + { + "Answer": 300, + "Options": "a ) a ) 300 , b ) b ) 350 , c ) c ) 450 , d ) d ) 470 , e ) e ) 500", + "Correct": "a", + "Explanation": "\"explanation : 10 * 150 = 1500 3 * 100 + 6 * 150 = 1200 1500 \u2013 1200 = 300 a\"" + }, + { + "Answer": 0.36000000000000004, + "Options": "a ) 0.05 , b ) 0.36 , c ) 0.2 , d ) 0.25 , e ) 0.6", + "Correct": "b", + "Explanation": "\"index for females = ( 25 - 8 ) / 25 = 17 / 25 = 0.68 index for males = ( 25 - 17 / 25 = 8 / 25 = 0.32 index for females exceeds males by 0.68 - 0.32 = 0.36 answer : b\"" + }, + { + "Answer": 475, + "Options": "a ) 62 , b ) 171 , c ) 475 , d ) 513 , e ) 684", + "Correct": "c", + "Explanation": "\"total automobile instalment credit = 57 * 3 = 171 total consumer instalment credit = 171 \u2217 100 / 36 = 475 ; answer = c . 475\"" + }, + { + "Answer": 68, + "Options": "a ) 39 , b ) 68 , c ) 54 , d ) 57 , e ) 60", + "Correct": "b", + "Explanation": "\"g + h = 92 . . . 1 ; g / 4 + h / 3 = 25 . . . . 2 or 3 g + 4 h = 25 * 12 = 300 g = 92 - h or 3 ( 92 - h ) + 4 h = 300 h = 300 - 276 = 24 then g = 92 - 24 = 68 b\"" + }, + { + "Answer": 20298, + "Options": "a ) 20200 , b ) 20000 , c ) 40400 , d ) 40000 , e ) 44000", + "Correct": "a", + "Explanation": "\"a = 100 , tn = 300 a + ( n - 1 ) d = 300 = > n = 101 sn = n / 2 ( a + l ) = 101 / 2 ( 100 + 300 ) sn = 20200 answer : a\"" + }, + { + "Answer": 32, + "Options": "a ) 18 , b ) 32 , c ) 27 , d ) 26 , e ) 19", + "Correct": "b", + "Explanation": "\"explanation : let the present age of person be x years . then , 4 ( x + 4 ) - 4 ( x - 4 ) = x < = > ( 4 x + 16 ) - ( 4 x - 16 ) = x < = > x = 32 . . answer : b\"" + }, + { + "Answer": 110, + "Options": "a ) 100 minute , b ) 110 minute , c ) 120 minute , d ) 130 minute , e ) 140 minute", + "Correct": "b", + "Explanation": "total journey = 440 * 2 = 880 a meet b 20 yards from top in getting down it means he has covered 440 + 20 = 460 yards while b is 420 yards . so he is 40 yards ahead of b which is equals to 5 minute . so 40 yards in 5 min 880 yards will be in 5 * 880 / ( 40 ) = 110 minute answer : b" + }, + { + "Answer": 56, + "Options": "a ) 22 , b ) 27 , c ) 28 , d ) 26 , e ) 56", + "Correct": "e", + "Explanation": "\"explanation : if teacher ' s age is 15 years , there is no change in the average . but teacher has contributed 1 year to all the students along with maintaining his age at 16 . age of teacher = average age of all + total increase in age = 16 + ( 1 x 40 ) = 56 years answer : e\"" + }, + { + "Answer": 9, + "Options": "a ) 9 , b ) 7 , c ) 8 , d ) 5 , e ) 3", + "Correct": "a", + "Explanation": "let the number be x . then , ( x + x 2 ) / 2 = 5 x = > x 2 - 9 x = 0 = > x ( x - 9 ) = 0 = > x = 0 or x = 9 so , the number is 9 . answer : a" + }, + { + "Answer": 22, + "Options": "a ) 1 , b ) 6 , c ) 7 , d ) 8 , e ) 22", + "Correct": "e", + "Explanation": "explanation : x + y = 24 xy = 23 ( x - y ) 2 = ( x + y ) 2 - 4 xy ( x - y ) 2 = 576 - 92 = > ( x - y ) = 22 answer : e" + }, + { + "Answer": 42, + "Options": "a ) 40 , b ) 48 , c ) 45 , d ) 42 , e ) 22", + "Correct": "d", + "Explanation": "\"though 2 * ( 7 c 2 ) is the correct approcah to do this , but for people like me who find perm , comb n prob a nightmare , an easy approach can be used . the first guy has to play 2 matches with the rest of 6 , so he ' ll play 12 matches . similarly , second guy has to play with the rest of 5 as his 2 games with the first guy are already played . so he plays 10 matches . this continues like this and the total matches are 12 + 10 + 8 . . . + 2 12 + 10 + . . . + 2 = 2 ( 6 + 5 + . . . + 1 ) = 2 ( ( 6 * 7 ) / 2 ) = 6 * 7 = 42 . answer : d\"" + }, + { + "Answer": 23, + "Options": "a ) 19 , b ) 35 , c ) 20 , d ) 32 , e ) 23", + "Correct": "e", + "Explanation": "\"age of b = age of ( a + b + c ) \u00e2 \u20ac \u201c age of ( a + c ) = 29 \u00e3 \u2014 3 \u00e2 \u20ac \u201c 32 \u00e3 \u2014 2 = 87 \u00e2 \u20ac \u201c 64 = 23 years e\"" + }, + { + "Answer": 16, + "Options": "a ) 9 , b ) 12 , c ) 15 , d ) 16 , e ) 18", + "Correct": "d", + "Explanation": "\"in 24 liters , red = 5 / 8 * 24 = 15 and blue = 9 so , 15 / ( 9 + x ) = 3 / 5 or , x = 16 ( answer d )\"" + }, + { + "Answer": 22, + "Options": "a ) 17 litres , b ) 22 litres , c ) 11 litres , d ) 07 litres , e ) 38 litres", + "Correct": "b", + "Explanation": "262.85 ( 33 ) + 3 , 104.35 x = 1 , 399.45 ( 33 + x ) solve the equation . 262.85 ( 33 ) + 3 , 104.35 x = 1 , 399.45 ( 33 + x ) 8 , 674.05 + 3 , 104.35 x = 46181.85 + 1 , 369.45 x 8 , 674.05 + 1 , 704.9 x = 46181.85 1 , 704.9 x = 37 , 507.8 x = 22 answer is b ." + }, + { + "Answer": 12.99999999999999, + "Options": "a ) 11 , b ) 13 , c ) 14 , d ) 18 , e ) 10", + "Correct": "b", + "Explanation": "\"required difference = [ 3 \u00bd % of rs . 7800 ] \u2013 [ 3 1 / 3 % of rs . 7800 ] = [ ( 7 / 20 - ( 10 / 3 ) ] % of rs . 7800 = 1 / 6 % of rs . 7800 = rs . [ ( 1 / 6 ) 8 ( 1 / 100 ) * 7800 ] = rs . 13 . answer is b .\"" + }, + { + "Answer": 27, + "Options": "a ) 38 , b ) 40 , c ) 27 , d ) 43 , e ) 56", + "Correct": "c", + "Explanation": "explanation : let x be the number of questions answered correctly . hence , number of questions whose answer were wrong = ( 70 \u2013 x ) 3 * x + ( 70 \u2013 x ) * ( - 1 ) = 38 4 x = 38 + 70 = 108 x = 27 answer c" + }, + { + "Answer": 37.275, + "Options": "a ) 40 - 42 , b ) 39 - 41 , c ) 38 - 40 , d ) 37 - 38 , e ) 36 - 37", + "Correct": "d", + "Explanation": "5 % ( 35.5 ) = 1.775 8 % ( 35.5 ) = 2.84 total amount could have been 35.5 + 1.775 and 35.5 + 2.84 = > could have been between 37.275 and 38.34 = > approximately between 37 and 38 answer is b . d" + }, + { + "Answer": 480, + "Options": "a ) 480 , b ) 120 , c ) 160 , d ) 240 , e ) 360", + "Correct": "a", + "Explanation": "working inside out , ( 4 \u20ac 5 ) = 2 * 4 * 5 = 40 6 \u20ac 40 = 2 * 6 * 40 = 480 hence , answer is a" + }, + { + "Answer": 173, + "Options": "a ) 174 cm , b ) 173 cm , c ) 172 cm , d ) 171 cm , e ) 170 cm", + "Correct": "b", + "Explanation": "\"the total height was 40 cm too much . the average height should be reduced by 40 cm / 20 = 2 cm the answer is b .\"" + }, + { + "Answer": 16, + "Options": "a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20", + "Correct": "c", + "Explanation": "j - 6 = 3 ( t - 6 ) , so j = 3 t - 12 j + 4 = 2 ( t + 4 ) ( 3 t - 12 ) + 4 = 2 t + 8 t = 16 the answer is c ." + }, + { + "Answer": 3000, + "Options": "a ) $ 2000 , b ) $ 6000 , c ) $ 4000 , d ) $ 1333 , e ) $ 3000", + "Correct": "e", + "Explanation": "explanatory answer let the profit made during the year be $ 3 x therefore , $ x would have been shared equally and the remaining $ 2 x would have been shared in the ratio 7 : 3 . i . e . , 70 % of 2 x would go to mary and 30 % of 2 x would go to mike . hence , mary would get ( 70 - 30 ) % of 2 x more than mike or 40 % of 2 x = $ 800 i . e . , ( 40 / 100 ) * 2 x = 800 or 2 x = 2000 . hence , the profit made by the company during the year $ 3 x = $ 3000 . the correct choice is ( e )" + }, + { + "Answer": 35, + "Options": "a ) 25 % , b ) 35 % , c ) 45 % , d ) 70 % , e ) 80 %", + "Correct": "b", + "Explanation": "\"1 . we are given the following percentages : 30 ( 70 ) , 40 ( 60 ) , 25 ( 75 ) . there are two threads from here . first starts at 30 % and finishes there . second one starts at 70 , then 40 , and then 25 . we need a value that is divisible by 7 , 2 , and 5 at least once . lets pick a number now , say 700 . so say if non hawks are 700 ( this is 70 % of the total , so total = 1000 ) , then paddy warbs are 2 / 5 x 700 = 1400 / 5 = 280 . kingfishers , therefore , are 280 / 4 = 70 . lets add them up . 300 hawks + 280 peddy warbs + 70 kingsifhers = 650 . so all others are 1000 - 650 = 350 or 35 % of total birds . the main job here to to identify the smart number to start the question with . this can be time consuming , but once identified , this question can be solved fairly quickly . 2 . another method : if x is total - - > non hawks = 0.7 x - - > warbs = 0.4 ( 0.7 x ) - - > kfs = 0.25 ( 0.4 ( 0.7 x ) ) . our job is to find out w : ( 0.3 x + 0.28 x + 0.07 x ) / x . or 0.65 x / x = 0.65 . we need to find 1 - 0.65 = 0.35 or 35 % . b\"" + }, + { + "Answer": 29.999999999999996, + "Options": "a ) 20 , b ) 30 , c ) 36 , d ) 40 , e ) 60", + "Correct": "b", + "Explanation": "let the capacity of the tank = c ( 3 / 4 ) c + 5 = ( 9 / 10 ) c = > ( 9 / 10 ) c - ( 3 / 4 ) c = 5 = > ( 3 / 20 ) c = 5 = > c = ( 5 * 20 ) / 3 = 33.33 number of gallons of gasoline that the tank currently holds = 3 / 4 * c + 5 = 24.99 + 5 = 29.99 = 30 answer b" + }, + { + "Answer": 5, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8", + "Correct": "b", + "Explanation": "let x be the number and y be the quotient . then , x = 357 * y + 39 = ( 17 * 21 * y ) + ( 17 * 2 ) + 5 = 17 * ( 21 y + 2 ) + 5 . required remainder = 5 . answer : b" + }, + { + "Answer": 0.3333333333333333, + "Options": "a ) 1 / 5 , b ) 1 / 6 , c ) 1 / 3 , d ) 1 / 6 , e ) 1 / 3", + "Correct": "c", + "Explanation": "here , g and h are events q ( g | h ) = q ( gnh ) / q ( h ) = 0.9 / 0.9 = 1 q ( g | h ) = q ( gnh ) / q ( g ) = 0.9 / 0.30 = 1 / 3 answer is c" + }, + { + "Answer": 5995, + "Options": "a ) 6100 , b ) 5100 , c ) 550 , d ) 598 , e ) 5995", + "Correct": "e", + "Explanation": "\"explanation : = 6000 \u2212 ( 105 / 21 ) = 6000 \u2212 5 = 5995 option e\"" + }, + { + "Answer": 82, + "Options": "a ) 76 , b ) 78 , c ) 80 , d ) 82 , e ) 84", + "Correct": "d", + "Explanation": "\"let x be the height of the first person . then the heights are x , x + 2 , x + 4 , and x + 10 . 4 x + 16 = 4 ( 76 ) = 304 x = 72 and the fourth person has a height of 72 + 10 = 82 inches the answer is d .\"" + }, + { + "Answer": 114, + "Options": "a ) 90 , b ) 100 , c ) 110 , d ) 114 , e ) 130", + "Correct": "d", + "Explanation": "explanation : 3 / 5 of 390 - 4 / 7 of 210 = 234 - 120 = 114 . answer : d" + }, + { + "Answer": 65, + "Options": "a ) 500 % , b ) 250 % , c ) 65 % , d ) 125 % , e ) 60 %", + "Correct": "c", + "Explanation": "\"z = 100 ; y = 50 so x = 65 x as % of z = 65 / 100 * 100 = > 65 % answer will be ( c )\"" + }, + { + "Answer": 1, + "Options": "a ) 0.01 , b ) 1 , 000,000 , c ) 0.001 , d ) 1,000 , e ) 1.0 e - 05", + "Correct": "b", + "Explanation": "given that 10,000 microns = 1 decimeter = 10,000 , 000,000 angstroms so , 1 micron = 10,000 , 000,000 / 10,000 = 1 , 000,000 answer : b" + }, + { + "Answer": 28, + "Options": "a ) 28 , b ) 10 , c ) 30 , d ) 40 , e ) 5", + "Correct": "a", + "Explanation": "\"arithmetic mean expression for p and q : ( p + q ) / 2 = 10 ; p + q = 20 - - - - eq 1 arithmetic mean expression for q and r : ( q + r ) / 2 = 20 ; q + r = 48 - - - - eq 2 subtracting eq 1 from eq 2 we get : r - p = 28 hence , the correct answer is a\"" + }, + { + "Answer": 117, + "Options": "a ) 110 , b ) 124 , c ) 96 , d ) 117 , e ) 127", + "Correct": "d", + "Explanation": "\"length = 6 m 24 cm = 624 cm width = 4 m 32 cm = 432 cm hcf of 624 and 432 = 48 number of square tiles required = ( 624 * 432 ) / ( 48 * 48 ) = 13 * 9 = 117 answer : d\"" + }, + { + "Answer": 2017, + "Options": "a ) 2017 , b ) 2088 , c ) 270 , d ) 1881 , e ) 1781", + "Correct": "a", + "Explanation": "f ( f ( 0 ) ) + f ( 0 ) = 2 ( 0 ) + 3 \u21d2 \u21d2 f ( 1 ) = 3 - 1 = 2 , f ( 1 ) = 2 f ( f ( 1 ) ) + f ( 1 ) = 2 ( 1 ) + 3 \u21d2 \u21d2 f ( 2 ) = 5 - 2 = 3 , f ( 2 ) = 3 f ( f ( 2 ) ) + f ( 2 ) = 2 ( 2 ) + 3 \u21d2 \u21d2 f ( 3 ) = 7 - 3 = 4 , f ( 3 ) = 4 . . . . . . . . . . . . . . f ( 2016 ) = 2017 ans : a" + }, + { + "Answer": 28, + "Options": "a ) 28 , b ) 32 , c ) 35 , d ) 30 , e ) 45", + "Correct": "a", + "Explanation": "\"explanation : hcf ( 408 , 264 ) = 24 the number of boys or girls that can be placed in a section = 24 . thus the total number of sections is given by 408 / 24 + 264 / 24 = 17 + 11 = 28 answer : a\"" + }, + { + "Answer": 32, + "Options": "a ) 26 , b ) 28 , c ) 30 , d ) 32 , e ) 34", + "Correct": "d", + "Explanation": "\"let x be the number of blueberries in each blue box . then there are x + 12 strawberries in each red box . x + ( x + 12 ) = 76 x = 32 the answer is d .\"" + }, + { + "Answer": 8000, + "Options": "a ) 7600 , b ) 8000 , c ) 8400 , d ) data inadequate , e ) none of these", + "Correct": "b", + "Explanation": "\"solution let the number of candidates appeared from each state be x . then , 7 % of x - 6 % of x = 80 \u21d4 1 % of x = 80 \u21d4 x = 80 \u00d7 100 = 8000 . answer b\"" + }, + { + "Answer": 1499.9999999999998, + "Options": "a ) s 200 , b ) s 1500 , c ) s 300 , d ) s 450 , e ) s 550", + "Correct": "b", + "Explanation": "\"suppose the amount in the beginning was rs \u2019 x \u2019 money spent on clothes = rs 1 x / 3 balance = rs 2 x / 3 money spent on food = 1 / 5 of 2 x / 3 = rs 2 x / 15 balance = 2 x / 3 - 2 x / 15 = rs 8 x / 15 money spent on travel = 1 / 4 of 8 x / 15 = rs 2 x / 15 = 8 x / 15 - 2 x / 15 = 6 x / 15 = rs 2 x / 5 therefore 2 x / 5 = 100 = 1500 answer : b\"" + }, + { + "Answer": 120, + "Options": "a ) 120 , b ) 160 , c ) 190 , d ) 200 , e ) 400", + "Correct": "a", + "Explanation": "let the total number of ounces in the drink be x . % of orange = 15 % % of watermelon = 60 % % of grape = 100 % - 75 % = 25 % 0.25 x = 30 x = 120 therefore there are a total of 120 ounces in the drink . the answer is a ." + }, + { + "Answer": 0.3408, + "Options": "a ) 0.3408 , b ) 3.408 , c ) 34.08 , d ) 340.8 , e ) none of these", + "Correct": "a", + "Explanation": "\"solution 0.16 \u00d7 2.13 = ( 16 / 100 x 213 / 100 ) = ( 16 x 213 / 10000 ) = 3408 / 10000 = 0.3408 . answer a\"" + }, + { + "Answer": 8800, + "Options": "a ) rs . 7000 , b ) rs . 8000 , c ) rs . 8800 , d ) rs . 9000 , e ) none", + "Correct": "c", + "Explanation": "\"answer average salary = 8000 + 5000 + 15000 + 7000 + 9000 / 5 = rs . 8800 correct option : c\"" + }, + { + "Answer": 26, + "Options": "a ) 22 , b ) 28 , c ) 27 , d ) 19 , e ) 11", + "Correct": "d", + "Explanation": "answer : d" + }, + { + "Answer": 37, + "Options": "a ) 33 kg , b ) 31 kg , c ) 32 kg , d ) 36 kg , e ) 37 kg", + "Correct": "e", + "Explanation": "\"let a , b , c represent their respective weights . then , we have : a + b + c = ( 45 x 3 ) = 129 . . . . ( i ) a + b = ( 40 x 2 ) = 80 . . . . ( ii ) b + c = ( 43 x 2 ) = 86 . . . . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 166 . . . . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 37 . b ' s weight = 37 kg . e\"" + }, + { + "Answer": 6, + "Options": "a ) a ) 10 , b ) b ) 8 , c ) c ) 6 , d ) d ) 4 , e ) e ) 2", + "Correct": "c", + "Explanation": "\"x = 12 - 2 y x = 12 - 6 . x = 6 answer : c\"" + }, + { + "Answer": 96, + "Options": "a ) 92 , b ) 39 , c ) 87 , d ) 96 , e ) none", + "Correct": "d", + "Explanation": "sum of three number is = 88 * 3 = 264 let three numbers are a , b , c and a is the highest and c is the lowest then , 2 b = a so b = a / 2 and 3 c = a so c = a / 3 we can write , a + b + c = 264 a + a / 2 + a / 3 = 264 11 a / 6 = 264 a = 144 so , c = 144 / 3 = 48 so there difference is = 144 - 48 = 96 answer d" + }, + { + "Answer": 2.361111111111111, + "Options": "a ) $ 1.09 , b ) $ 1.67 , c ) $ 2.25 , d ) $ 2.36 , e ) $ 2.50", + "Correct": "d", + "Explanation": "\"total cost of parking for 9 hours = 9 $ for the first 2 hours and then 1.75 for ( 9 - 2 ) hours = 9 + 7 * 1.75 = 21.25 thus the average parking price = 21.25 / 9 = 2.36 $ d is the correct answer .\"" + }, + { + "Answer": 31, + "Options": "a ) 34 kg , b ) 40 kg , c ) 42 kg , d ) 41 kg , e ) 31 kg", + "Correct": "e", + "Explanation": "\". let a , b , c represent their individual wgts . then , a + b + c = ( 45 * 3 ) kg = 135 kg a + b = ( 40 * 2 ) kg = 80 kg & b + c = ( 43 * 2 ) kg = 86 kg b = ( a + b ) + ( b + c ) - ( a + b + c ) = ( 80 + 86 - 135 ) kg = 31 kg . answer is e .\"" + }, + { + "Answer": 80, + "Options": "a ) 70 , b ) 78 , c ) 80 , d ) 84 , e ) 90", + "Correct": "c", + "Explanation": "otal increase in marks = x x 1 = x 2 2 x / 2 = ( 82 - 62 ) x / 2 = 40 x = 80 . c" + }, + { + "Answer": 63, + "Options": "a ) 63 , b ) 6973 , c ) 5994 , d ) 6084 , e ) none of these", + "Correct": "a", + "Explanation": "( place value of 7 ) - ( face value of 7 ) = ( 70 - 7 ) = 63 answer : option a" + }, + { + "Answer": 10, + "Options": "a ) 50 km , b ) 76 km , c ) 18 km , d ) 10 km , e ) 97 km", + "Correct": "d", + "Explanation": "\"let the actual distance traveled be x km . then , x / 5 = ( x + 20 ) / 15 10 x - 100 = > x = 10 km . answer : d\"" + }, + { + "Answer": 81, + "Options": "a ) 70 kg , b ) 80 kg , c ) 81 kg , d ) 90 kg , e ) 91 kg", + "Correct": "c", + "Explanation": "\"total weight increased = ( 8 x 2 ) kg = 16 kg . weight of new person = ( 65 + 16 ) kg = 81 kg . c )\"" + }, + { + "Answer": 4, + "Options": "a ) 4 kg , b ) 21.6 kg , c ) 22.4 kg , d ) 21 kg , e ) none of these", + "Correct": "a", + "Explanation": "\"exp . the total weight of 29 students = 29 * 28 the total weight of 30 students = 30 * 27.2 weight of the new student = ( 30 * 27.2 \u2013 29 * 28 ) = 816 - 812 = 4 answer : a\"" + }, + { + "Answer": 75, + "Options": "a ) 70 , b ) 72 , c ) 75 , d ) 78 , e ) 80", + "Correct": "c", + "Explanation": "\"income of 6 months = ( 6 \u00d7 80 ) \u2013 debt = 480 \u2013 debt income of the man for next 4 months = 4 \u00d7 60 + debt + 30 = 270 + debt \u2234 income of 10 months = 750 average monthly income = 750 \u00f7 10 = 75 answer c\"" + }, + { + "Answer": 1000, + "Options": "a ) rs . 1000 , b ) rs . 2000 , c ) rs . 1500 , d ) rs . 3000 , e ) rs . 3100", + "Correct": "a", + "Explanation": "\"income = rs . 100 expenditure = rs . 75 savings = rs . 25 present expenditure 75 + 75 * ( 10 / 100 ) = rs . 82.5 present savings = 100 \u2013 82.50 = rs . 17.50 if savings is rs . 17.50 , salary = rs . 100 if savings is rs . 175 , salary = 100 / 17.5 * 175 = 1000 answer : a\"" + }, + { + "Answer": 3.4499999999999993, + "Options": "a ) $ 2.55 , b ) $ 2.85 , c ) $ 3.15 , d ) $ 3.45 , e ) $ 3.75", + "Correct": "d", + "Explanation": "\"x = 3 x / 5 + 1 / 3 * 2 x / 5 + 92 4 x / 15 = 92 x = 345 = $ 3.45 the answer is d .\"" + }, + { + "Answer": 12000, + "Options": "a ) 12028 , b ) 12000 , c ) 12019 , d ) 12197 , e ) 18000", + "Correct": "c", + "Explanation": "[ 1300 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 600 x = 18000 answer : c" + }, + { + "Answer": 33, + "Options": "a ) 21 , b ) 35 , c ) 33 , d ) 60 , e ) 65", + "Correct": "c", + "Explanation": "the total number of the people in the room must be a multiple of both 7 and 11 ( in order 3 / 7 and 5 / 11 of the number to be an integer ) , thus the total number of the people must be a multiple of lcm of 7 and 11 , which is 77 . since , the total number of the people in the room is greater than 50 and less than 100 , then there are 77 people in the room . therefore there are 3 / 7 * 77 = 33 people in the room under the age of 21 . answer : c ." + }, + { + "Answer": 9, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", + "Correct": "c", + "Explanation": "100 x - ( 10 x + x ) - - - - - - - - - - - 89 x = 801 x = 9 c" + }, + { + "Answer": 4.340259786868312, + "Options": "a ) 2 \u221a 2 , b ) 2 \u221a 3 , c ) 3 \u221a 2 , d ) 3 \u221a 3 , e ) 13 / 3", + "Correct": "e", + "Explanation": "\"( \u221a 96 + \u221a 486 ) / \u221a 54 = ( 4 \u221a 6 + 9 \u221a 6 ) / 3 \u221a 6 = 13 \u221a 6 / 3 \u221a 6 = 13 / 3 hence , the correct answer is e .\"" + }, + { + "Answer": 184, + "Options": "a ) 187 , b ) 197 , c ) 184 , d ) 219 , e ) 227", + "Correct": "c", + "Explanation": "let ' n ' is the smallest number which divided by 13 and 15 leaves respective remainders of 2 and 4 . required number = ( lcm of 13 and 15 ) - ( common difference of divisors and remainders ) = ( 195 ) - ( 11 ) = 184 . answer : c" + }, + { + "Answer": 420, + "Options": "a ) $ 420 , b ) $ 382 , c ) $ 385 , d ) $ 392 , e ) $ 399", + "Correct": "a", + "Explanation": "\"( 406 / 116 ) 120 = 420 in this case long division does not take much time . ( 406 / 116 ) = 3.5 35 * 12 = 420 ( 350 + 70 ) answer a\"" + }, + { + "Answer": 300, + "Options": "a ) 210 , b ) 280 , c ) 300 , d ) 320 , e ) 340", + "Correct": "c", + "Explanation": "\"let the maximum marks be x then , 60 % of x = 160 + 20 60 x / 100 = 180 60 x = 180 * 100 = 18000 x = 300 answer is c\"" + }, + { + "Answer": 216000, + "Options": "a ) 215,000 , b ) 216,000 , c ) 217,000 , d ) 218,000 , e ) 219,000", + "Correct": "b", + "Explanation": "this question can be modified so that the birth rate is given every m seconds and the death rate is given every n seconds . for this particular question : increase in the population every 2 seconds = 7 - 2 = 5 people . total 2 second interval in a day = 24 * 60 * 60 / 2 = 43,200 population increase = 43,200 * 5 = 216,000 . hence b ." + }, + { + "Answer": 50.000013888888894, + "Options": "a ) 50 , b ) 99 , c ) 77 , d ) 26 , e ) 23", + "Correct": "a", + "Explanation": "\"let the length of each train be x m . then , distance covered = 2 x m . relative speed = 46 - 36 = 10 km / hr . = 10 * 5 / 18 = 25 / 9 m / sec . 2 x / 36 = 25 / 9 = > x = 50 . answer : a\"" + }, + { + "Answer": 22, + "Options": "a ) 17 , b ) 22 , c ) 21 , d ) 24 , e ) 25", + "Correct": "b", + "Explanation": "\"average of 23 numbers = 0 . sum of 23 numbers ( 0 x 23 ) = 0 . it is quite possible that 22 of these numbers may be positive and if their sum is a then 23 rd number is ( - a ) answer is 22 ( b )\"" + }, + { + "Answer": 21, + "Options": "a ) 5 inches , b ) 6 inches , c ) 9 inches , d ) 10 inches , e ) 21 inches", + "Correct": "e", + "Explanation": "total rainfall in 2 weeks = 35 inches . assume the rainfall in second week = 1 . x rainfall in first week = x total rainfall = 2.5 x = 35 inches x = 14 and 1.5 x = 21 rainfall during second week = 21 inches option e" + }, + { + "Answer": 47, + "Options": "a ) 47 , b ) 46 , c ) 54 , d ) 58 , e ) 62", + "Correct": "a", + "Explanation": "\"orange + mango - apple = 7 mango + apple - orange = 10 apple = 40 orange + mango + apple = 4 40 + 10 + 4 - 7 = 47 like apple answer : a\"" + }, + { + "Answer": 18, + "Options": "a ) 20 , b ) 18 , c ) 17 , d ) 22 , e ) 23", + "Correct": "b", + "Explanation": "x = - 6 and y = - 3 x - y = - 6 - ( - 3 ) = - 6 + 3 = - 3 x * y = - 6 * - 3 = 18 now we apply it in the equation 4 ( x - y ) ^ 2 - xy = 4 ( - 3 ) ^ 2 - 18 = = > 4 * 9 - 18 = 36 - 18 = 18 answer : b" + }, + { + "Answer": 90, + "Options": "a ) 90 , b ) 80 , c ) 70 , d ) 60 , e ) 50", + "Correct": "a", + "Explanation": "\"4 th term + 12 th term = 12 i . e . , ( a + 3 d ) + ( a + 11 d ) = 12 now , sum of first 15 terms = ( 15 / 2 ) * [ 2 a + ( 15 - 1 ) d ] = ( 15 / 2 ) * [ 2 a + 14 d ] = ( 15 / 2 ) * 12 - - - - - - - - - - - - - - - from ( 1 ) = 90 answer : a\"" + }, + { + "Answer": 1288, + "Options": "a ) 246 , b ) 248 , c ) 1292 , d ) 15,128 , e ) 30,256", + "Correct": "c", + "Explanation": "\"# of 2 - letter codes possible from 324 different signs = 324 * 324 . # of 2 - letter codes possible from 322 different signs = 322 * 322 . the difference = 324 ^ 2 - 322 ^ 2 = ( 324 - 322 ) ( 324 + 322 ) = 1292 . answer : c .\"" + }, + { + "Answer": 5, + "Options": "a ) $ 2.50 , b ) $ 3.00 , c ) $ 3.50 , d ) $ 4.00 , e ) $ 5.00", + "Correct": "e", + "Explanation": "number of wheels in truck = 18 number of wheels on its front axle = 2 number of wheels remaining = 16 number of axles remaining axles = 16 / 4 = 4 total number of axles = 5 t = 3.50 + 0.50 ( x \u2212 2 ) = 3.50 + . 5 * 3 = 3.5 + 1.5 = 5 $ answer e" + }, + { + "Answer": 71.96261682242991, + "Options": "a ) 72 , b ) 34 , c ) 78 , d ) 37 , e ) 27", + "Correct": "a", + "Explanation": "lets say the family income is 100 in may , bil earned 70 family income is 30 in june , bil earned 10 % more than may , so it is ( 70 + 10 * 70 / 100 = 77 ) family income is same 30 in june bil ' s income percent is 77 * 100 / 107 ~ 72 ans is a" + }, + { + "Answer": 57, + "Options": "a ) 5.7 , b ) 57 , c ) 570 , d ) 0.57 , e ) 0.057", + "Correct": "b", + "Explanation": "given 7125 / 1.25 = 5700 712.5 / 12.5 = 71.25 / 1.25 = 7125 * 1 / 1.25 * 100 = 5700 / 100 = 57 answer : b" + }, + { + "Answer": 700, + "Options": "a ) 0 , b ) 50 , c ) 450 , d ) 693 , e ) 500", + "Correct": "d", + "Explanation": "we can break this problem into two parts : 1 ) what is 1 / 10 percent of 7,000 ? 2 ) what is 1 / 10 of 7,000 ? to calculate 1 / 10 percent of 7,000 we must first remember to divide 1 / 10 by 100 . so we have : ( 1 / 10 ) / ( 100 ) to divide a number by 100 means to multiply it by 1 / 100 , so we have : 1 / 10 x 1 / 100 = 1 / 1,000 thus , 1 / 10 percent of 7,000 = 1 / 1,000 x 7,000 = 7 . now let ' s concentrate on part 2 . we need to calculate 1 / 10 of 7,000 . to do this we simply multiply 1 / 10 by 7,000 . 1 / 10 x 7,000 = 700 the answer to part 1 is 7 , and the answer to part 2 is 700 . their difference is 700 \u2013 7 = 693 . answer d ." + }, + { + "Answer": 6000, + "Options": "a ) 100 , b ) 250 , c ) 750 , d ) 5625 , e ) 6000", + "Correct": "e", + "Explanation": "6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 64 * 25 * 1 / 2 = 800 feet ^ 3 of milk must be removed , which equals to 800 * 7.5 = 6000 gallons . answer : e ." + }, + { + "Answer": 54.99999999999995, + "Options": "a ) 53 , b ) 54 , c ) 55 , d ) 56 , e ) 57", + "Correct": "c", + "Explanation": "\"12.4 * x + 26 = ( 4 + x ) 12 solve equation x = 55 answer : c\"" + }, + { + "Answer": 10, + "Options": "a ) 12 , b ) 11 , c ) 10 , d ) 27 , e ) 22", + "Correct": "c", + "Explanation": "explanation : total employees = \\ inline \\ frac { ( 25 - 10 ) \\ times 20 } { 10 } = 30 hence number of educated employees = 30 - 20 = 10 answer : c ) 10" + }, + { + "Answer": 8, + "Options": "a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 0", + "Correct": "d", + "Explanation": "3,8 and 7 have a power cycle of 4 , i . e . the units digit in each case will repeat after every 4 th power . for eg : 3 ^ 1 = 3 , 3 ^ 2 = 9 , 3 ^ 3 = 27 , 3 ^ 4 = 81 , 3 ^ 5 = 243 all the powers given ( 1 ! + 2 ! + . . . . ) , are multiples of 4 . it is so because the last 2 digits of the total sum will be 00 , for each one of them , which make them divisible by 4 . thus , the given problem boils down to 3 ^ 4 + 8 ^ 4 + 7 ^ 4 = 1 + 6 + 1 = 8 thus , the units digit is 8 . answer : d" + }, + { + "Answer": 3.0751133491652576, + "Options": "a ) 195 / 63 , b ) 145 / 63 , c ) 155 / 63 , d ) 125 / 63 , e ) 3.075", + "Correct": "e", + "Explanation": "\"( \u221a 1.5 ) / ( \u221a 0.81 ) + ( \u221a 1.44 ) / ( \u221a 0.49 ) = > 3.075 answer is e .\"" + }, + { + "Answer": 12765, + "Options": "a ) 12765 , b ) 121227 , c ) 26887 , d ) 19977 , e ) 26992", + "Correct": "a", + "Explanation": "assume c takes 20 days . now b takes 4 / 5 ( 20 ) = 16 days . a takes 3 / 4 ( 16 ) = 12 now their efficiencies ratio = 1 / 20 : 1 / 16 : 1 / 12 = 12 : 15 : 20 b ' s share in the profit of rs . 40000 = 15 / 47 ( 40000 ) = rs . 12765 answer : a" + }, + { + "Answer": 5, + "Options": "a ) 5 kg , b ) 11 kg , c ) 30 kg , d ) 36.5 kg , e ) 71 kg", + "Correct": "a", + "Explanation": "\"after two persons leave the group the average remains the same . that means the weight of the two persons = 40 + 30 = 70 so , the average the two persons = 35 that gives the answer 40 - 35 = 5 answer a\"" + }, + { + "Answer": 69, + "Options": "a ) a . 72 , b ) b . 50 , c ) c . 48 , d ) d . 69 , e ) e . 44", + "Correct": "d", + "Explanation": "\"at 6 : 00 it ' ll chime 6 times . if we assume that the time taken to chime is x , then time between chimes is also x . so you have 6 chimes , which is 6 x and 5 time intervals between chimes . this means that 11 x = 33 seconds . thus x = 3 seconds . by a similar logic , at 12 : 00 , there are 12 chimes and 11 intervals so the total time is ( 12 + 11 ) x = 23 x = 69 seconds . answer d\"" + }, + { + "Answer": 29.999999999999996, + "Options": "a ) 33 , b ) 30 , c ) 38 , d ) 37 , e ) 27", + "Correct": "b", + "Explanation": "explanation : pool : kerosene 3 : 2 ( initially ) 2 : 3 ( after replacement ) \\ frac { remaining \\ : ( or \\ : left ) \\ : quantity } { initial \\ : quantity } = \\ left ( 1 - \\ frac { replaced \\ : quantity } { total \\ : quantity } \\ right ) ( for petrol ) \\ frac { 2 } { 3 } = \\ left ( 1 - \\ frac { 10 } { k } \\ right ) \\ rightarrow \\ frac { 1 } { 3 } = \\ frac { 10 } { k } \\ rightarrow k = 30 l therefore the total quantity of the mixture in the container is 30 liters . answer : b ) 30" + }, + { + "Answer": 25, + "Options": "a ) 12.5 % , b ) 20 % , c ) 25 % , d ) 50 % , e ) 100 %", + "Correct": "c", + "Explanation": "\"correct answer : c solution : c . we can set up equations for income before and after the wage reduction . initially , the employee earns w wage and works h hours per week . after the reduction , the employee earns . 8 w wage and works x hours . by setting these equations equal to each other , we can determine the increase in hours worked : wh = . 8 wx ( divide both sides by . 8 w ) 1.25 h = x we know that the new number of hours worked will be q = 25 % greater than the original number . the answer is c .\"" + }, + { + "Answer": 192, + "Options": "a ) 172 , b ) 180 , c ) 192 , d ) 200 , e ) 216", + "Correct": "c", + "Explanation": "\"r = j + 8 = k + 4 r + 4 = 2 ( j + 4 ) ( j + 8 ) + 4 = 2 j + 8 j = 4 r = 12 k = 8 in 4 years ( r + 4 ) ( k + 4 ) = 16 * 12 = 192 the answer is c .\"" + }, + { + "Answer": 1260, + "Options": "a ) 5040 , b ) 2520 , c ) 1890 , d ) 1260 , e ) 630", + "Correct": "d", + "Explanation": "the integer should be divisible by : 2 , 3 , 4 , 5 , 6 , 7 , 8 and 9 , that is 2 , 3 , 2 ^ 2 , 5 , 2 * 3 , 7 , 2 ^ 3 and 3 ^ 2 . the least common multiple of these integers is the product of 7 , 5 , 3 ^ 2 and 2 ^ 3 . then , l / 2 is ( 7 * 5 * 3 ^ 2 * 2 ^ 3 ) / 2 = 7 * 5 * 9 * 4 = 1260 . answer : d ." + }, + { + "Answer": 90, + "Options": "a ) \u2212 220 , b ) \u2212 100 , c ) \u2212 90 , d ) 135 , e ) it can not be determined from the information given", + "Correct": "c", + "Explanation": "\"question : a - c = ? ( a + b ) / 2 = 115 = = = > a + b = 230 ( b + c ) / 2 = 160 = = = > b + c = 320 ( a + b ) - ( b + c ) = 230 - 320 = = = > a + b - b - c = - 90 = = = > a - c = - 90 answer : c\"" + }, + { + "Answer": 37, + "Options": "a ) 42 , b ) 37 , c ) 44 , d ) 45 , e ) 46", + "Correct": "b", + "Explanation": "\"let \u2018 x \u2019 be the average score after 12 th innings \u21d2 12 x = 11 \u00d7 ( x \u2013 3 ) + 70 \u2234 x = 37 answer b\"" + }, + { + "Answer": 13, + "Options": "a ) 10 , b ) 11 , c ) 13 , d ) 15 , e ) 16", + "Correct": "c", + "Explanation": "\"here n = 18 = 2 \u00d7 32 \u03d5 ( 18 ) = 18 ( 1 \u2212 12 ) ( 1 \u2212 13 ) = 6 so 56 when divided by 18 , remainder is 1 . so we can write the given expression 5100 = ( 56 ) 16 \u00d7 54 = ( 1 ) 16 \u00d7 54 = 52 \u00d7 52 = 7 \u00d7 7 = 49 now 49 when divided by 18 , remainder is 13 . c\"" + }, + { + "Answer": 250, + "Options": "a ) 100 , b ) 150 , c ) 200 , d ) 250 , e ) 350", + "Correct": "d", + "Explanation": "\"a + b + c = 900 a + c = 400 b + c = 750 - - - - - - - - - - - - - - a + b + 2 c = 1150 a + b + c = 900 - - - - - - - - - - - - - - - - c = 250 answer : d\"" + }, + { + "Answer": 47, + "Options": "a ) 20 , b ) 31 , c ) 42 , d ) 47 , e ) 64", + "Correct": "d", + "Explanation": "\"x + ( x - 10 ) = 84 - - > x = 47 . answer : d .\"" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9", + "Correct": "a", + "Explanation": "solution ( 1000 + n ) > ( 1000 n ) clearly , n = 1 . answer a" + }, + { + "Answer": 34, + "Options": "a ) 12 , b ) 25 , c ) 34 , d ) 29 , e ) 27", + "Correct": "c", + "Explanation": "sum of all the 11 numbers = 11 * 22 = 242 sum of the first 6 of them = 6 * 19 = 114 sum of the last 6 of them = 6 * 27 = 162 so , the 8 th number = 242 + 114 - 162 = 34 . answer : c" + }, + { + "Answer": 8, + "Options": "a ) 24 , b ) 8 , c ) 12 , d ) 4 , e ) 2", + "Correct": "b", + "Explanation": "\"in this question however , because we are told that exactly 64 frisbees have been sold and revenue was exactly $ 204 , there is only one possible solution for the number of $ 3 and $ 4 frisbees sold . to solve , we have 2 equations and 2 unknowns let x = number of $ 3 frisbees sold let y = number of $ 4 frisbees sold x + y = 64 3 x + 4 y = 200 x = 64 - y 3 ( 64 - y ) + 4 y = 200 192 - 3 y + 4 y = 200 y = 8 answer : b\"" + }, + { + "Answer": 23, + "Options": "a ) 17 , b ) 23 , c ) 21 , d ) 24 , e ) 25", + "Correct": "b", + "Explanation": "\"average of 24 numbers = 0 . sum of 24 numbers ( 0 x 24 ) = 0 . it is quite possible that 23 of these numbers may be positive and if their sum is a then 24 th number is ( - a ) answer is 23 ( b )\"" + }, + { + "Answer": 21, + "Options": "a ) 21 , b ) 20 , c ) 19 , d ) 16 , e ) 15", + "Correct": "a", + "Explanation": "\"marcella has 26 pairs of shoes and loses 9 shoes . to minimize the loss of identical pairs of shoes we want marcella to lose as many identical pairs as possible . this would yield 4 identical pairs and 1 additional shoe ( destroying 5 pairs of shoes ) . the 26 pairs of shoes minus the 5 ' destroyed ' pairs yields 21 pairs that still fulfill the requirements . answer : a\"" + }, + { + "Answer": 400, + "Options": "a ) 250 , b ) 350 , c ) 450 , d ) 400 , e ) 650", + "Correct": "d", + "Explanation": "\"the number of chocolate bars is equal to 16 * 25 = 400 correct answer d\"" + }, + { + "Answer": 10, + "Options": "a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25", + "Correct": "b", + "Explanation": "explanation : let number of keepers be x . then , total number of feet = 2 x 60 + 4 x 35 + 4 x 6 + 2 x = 2 x + 284 . total number of heads = 60 + 35 + 6 + x = 101 + x . therefore ( 2 x + 284 ) = ( 101 + x ) + 193 or x = 10 . answer : b" + }, + { + "Answer": 35, + "Options": "a ) 18 % , b ) 20 % , c ) 21 % , d ) 25 % , e ) can not be determined", + "Correct": "d", + "Explanation": "answer : d ." + }, + { + "Answer": 5, + "Options": "a ) a ) 4 , b ) b ) 3 , c ) c ) 2 , d ) d ) 5 , e ) e ) 6", + "Correct": "d", + "Explanation": "\"explanation : 725 = 36 x 20 + r 725 = 720 + r r = 725 - 720 = 5 answer : option d\"" + }, + { + "Answer": 13, + "Options": "a ) 9 , b ) 13 , c ) 15 , d ) 16 , e ) 18", + "Correct": "b", + "Explanation": "\"in 32 liters , red = 5 / 8 * 32 = 20 and blue = 12 so , 20 / ( 12 + x ) = 4 / 5 or , x = 13 ( answer b )\"" + }, + { + "Answer": 0.5, + "Options": "a ) 1 / 2 , b ) 1 , c ) 2 , d ) 4 , e ) 8", + "Correct": "a", + "Explanation": "\"given : 5 / w + 5 / x = 5 / ywx = y find : ( w + x ) / 2 = ? 5 ( 1 / w + 1 / x ) = 5 ( 1 / y ) - divide both sides by 5 ( 1 / w + 1 / x ) = 1 / y ( x + w ) / wx = 1 / wx - sub ' d in y = wx x + w - 1 = 0 x + w = 1 therefore ( w + x ) / 2 = 1 / 2 ans : a\"" + }, + { + "Answer": 0.39999999999999997, + "Options": "a ) $ 015 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45", + "Correct": "d", + "Explanation": "\"on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.6 = 3 * x - - > x = $ 0.4 . answer : d .\"" + }, + { + "Answer": 54, + "Options": "a ) 23 , b ) 54 , c ) 28 , d ) 40 , e ) 81", + "Correct": "b", + "Explanation": "\"explanation : formula n ( a \u00e2 \u02c6 \u00aa b ) = n ( a ) + n ( b ) \u00e2 \u02c6 \u2019 n ( a \u00e2 \u02c6 \u00a9 b ) fail in hindi or english = 25 + 48 \u00e2 \u20ac \u201c 27 = 46 therefore students who passed = 100 \u00e2 \u20ac \u201c 46 = 54 . answer : b\"" + }, + { + "Answer": 125, + "Options": "a ) $ 125 , b ) $ 150 , c ) $ 200 , d ) $ 250 , e ) $ 450", + "Correct": "a", + "Explanation": "\"cavg = average contribution before john cavg * 1.5 = 75 , therefore the average cont is $ 50 before john . if he needs to increase the average contribution by $ 25 , he must put in $ 25 for each of the 2 people . so $ 50 . but , he also has to put in the average for himself ( the threeth person ) , so add $ 75 . so $ 125 is your answer . answer a\"" + }, + { + "Answer": 39, + "Options": "a ) 39 , b ) 49 , c ) 58 , d ) 113 , e ) 131", + "Correct": "a", + "Explanation": "you have 6 digits : 2 , 3 , 4 , 6 , 7 , 8 each digit needs to be used to make two 3 digit numbers . this means that we will use each of the digits only once and in only one of the numbers . the numbers need to be as close to each other as possible . the numbers can not be equal so the greater number needs to be as small as possible and the smaller number needs to be as large as possible to be close to each other . the first digit ( hundreds digit ) of both numbers should be consecutive integers now let ' s think about the next digit ( the tens digit ) . to minimize the difference between the numbers , the tens digit of the greater number should be as small as possible and the tens digit of the smaller number should be as large as possible . so let ' s not use 2 and 8 in the hundreds places and reserve them for the tens places . now what are the options ? try and make a pair with ( 3 * * and 4 * * ) . make the 3 * * number as large as possible and make the 4 * * number as small as possible . 387 and 426 ( difference is 39 ) or try and make a pair with ( 6 * * and 7 * * ) . make the 6 * * number as large as possible and make the 7 * * number as small as possible . we get 684 and 723 ( difference is 39 ) a" + }, + { + "Answer": 7.777777777777779, + "Options": "a ) 8 , b ) 9 , c ) 7.77 , d ) 10 , e ) 11", + "Correct": "c", + "Explanation": "total rebecca = x + 20 ; total = x + 20 + 10 x + 20 / x + 30 = 55 / 100 therefore x = 7.77 c" + }, + { + "Answer": 37, + "Options": "a ) 15 , b ) 28 , c ) 37 , d ) 42 , e ) 60", + "Correct": "c", + "Explanation": "take lcm of 4,5 and 6 = 60 now 4 x = 60 = > x = 15 5 y = 60 = > y = 12 6 z = 60 = > z = 10 115 + 12 + 10 = 37 . option c ." + }, + { + "Answer": 24, + "Options": "a ) 5 inches , b ) 6 inches , c ) 9 inches , d ) 10 inches , e ) 24 inches", + "Correct": "e", + "Explanation": "\"total rainfall in 2 weeks = 40 inches . assume the rainfall in second week = 1 . x rainfall in first week = x total rainfall = 2.5 x = 40 inches x = 16 and 1.5 x = 24 rainfall during second week = 24 inches option e\"" + }, + { + "Answer": 4, + "Options": "a ) 2 , b ) 4 , c ) 3 , d ) 5 , e ) 6", + "Correct": "b", + "Explanation": "\"t = the number of cups of tea c = the number of cups of hot chocolate t + c = 22 t - c = 8 - > t = 15 . c = 7 . mo drinks 5 cups of tea a day then number of days that are not rainy = 15 / 5 = 3 so number of rainy days = 7 - 3 = 4 b is the answer .\"" + }, + { + "Answer": 2999.9999999999995, + "Options": "a ) $ 3000 , b ) $ 3200 , c ) $ 3300 , d ) $ 3400 , e ) $ 4000", + "Correct": "a", + "Explanation": "\"explanatory answer let the profit made during the year be $ 3 x therefore , $ x would have been shared equally and the remaining $ 2 x would have been shared in the ratio 6.5 : 3.5 i . e . , 65 % of 2 x would go to mary and 35 % of 2 x would go to mike . hence , mary would get ( 65 - 35 ) % of 2 x more than mike or 30 % of 2 x = $ 600 i . e . , ( 30 / 100 ) * 2 x = 600 or 2 x = 2000 . hence , the profit made by the company during the year $ 3 x = $ 3000 . answer : a\"" + }, + { + "Answer": 15, + "Options": "a ) 15 , b ) 16 , c ) 18 , d ) 20 , e ) 24", + "Correct": "a", + "Explanation": "24,000 = 6,000 ( 1 + x ) ^ 10 4 = ( 1 + x ) ^ 10 = 2 ^ 2 ( 1 + x ) ^ 10 = ( ( 1 + x ) ^ 5 ) ^ 2 = 2 ^ 2 therefore , ( 1 + x ) ^ 5 = 2 48,000 = 6000 ( 1 + x ) ^ n ( 1 + x ) ^ n = 8 ( 1 + x ) ^ n = 2 ^ 3 ( 1 + x ) ^ n = ( ( 1 + x ) ^ 5 ) ^ 3 = ( 1 + x ) ^ 15 therefore , n = 15 . the answer is a ." + }, + { + "Answer": 0.3333333333333333, + "Options": "a ) 1 / 7 , b ) 2 / 7 , c ) 1 / 3 , d ) 7 / 12 , e ) 2 / 3", + "Correct": "c", + "Explanation": "\"same amount of water made bigger jar 1 / 6 full , thenthe same amount of water ( stored for a while in smaller jar ) were added to bigger jar , so bigger jar is 1 / 6 + 1 / 6 = 2 / 6 = 1 / 3 full . answer : c .\"" + }, + { + "Answer": 25, + "Options": "a ) 33.33 % , b ) 25 % , c ) 75 % , d ) 66.66 % , e ) none of these", + "Correct": "b", + "Explanation": "using formula ( x / ( 100 - x ) * 100 ) where x is percentage decrease ( here it is 20 % ) = > 20 / ( 100 - 20 ) * 100 = 25 % answer : b" + }, + { + "Answer": 65, + "Options": "a ) 240 , b ) 65 , c ) 110 , d ) 130 , e ) 200", + "Correct": "b", + "Explanation": "adult + children = 200 let , children = y then , adult = y + 20 i . e . y + ( y + 20 ) = 200 i . e . y = 900 i . e . adult = 90 + 20 = 110 adults include only men and women i . e . men + women = 110 let women , w = x then men , m = x + 20 i . e . x + ( x + 20 ) = 2 x + 20 = 110 i . e . x = 45 i . e . men , m = 45 + 20 = 65 answer : option b" + }, + { + "Answer": 4.285714285714286, + "Options": "a ) 30 / 7 , b ) 30 / 98 , c ) 60 / 147 , d ) 50 / 294 , e ) 52 / 294", + "Correct": "a", + "Explanation": "required fraction = l . c . m of 6 / 7 , 5 / 14 , 10 / 21 = ( l . c . m of 6 , 5 , 10 ) / ( h . c . f of 7 , 14 , 21 ) = 30 / 7 answer : a" + }, + { + "Answer": 10, + "Options": "a ) 5 % , b ) 10 % , c ) 15 % , d ) 20 % , e ) it can not be determined", + "Correct": "b", + "Explanation": "\"solution : let the total number of flags be 100 ( even number ) let the total number of ' blue ' flags alone be ' a ' let the total number of ' red ' flags alone be ' b ' let the total number of ' both ' flags be ' c ' we have given , total number of blue flags = 60 % = 60 = a + c total number of red flags = 50 % = 50 = b + c total number of flags = a + b + c = 100 ( since all the flags have been utilized ) so , substituting for c in the third equation , we have , 60 - c + c + 50 - c = 100 c = 10 option b .\"" + }, + { + "Answer": 200, + "Options": "a ) 200 , b ) 300 , c ) 400 , d ) 500 , e ) 600", + "Correct": "a", + "Explanation": "\"20 % is an equal distance between 10 % and 30 % . thus there should be equal parts of both solutions . we should add 200 ml of solution y . the answer is a .\"" + }, + { + "Answer": 200, + "Options": "a ) 12.5 % , b ) 40 % , c ) 80 % , d ) 200 % , e ) none", + "Correct": "d", + "Explanation": "\"solution 6 : 3 = 6 / 3 = ( 6 / 3 x 100 ) % . = 200 % . answer d\"" + }, + { + "Answer": 88, + "Options": "a ) 80 kg , b ) 85 kg , c ) 90 kg , d ) 88 kg , e ) 110 kg", + "Correct": "d", + "Explanation": "\"total weight increased = ( 8 x 6 ) kg = 48 kg . weight of new person = ( 40 + 48 ) kg = 88 kg . answer : d\"" + }, + { + "Answer": 18, + "Options": "a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 18", + "Correct": "e", + "Explanation": "\"p \u00e3 \u00b7 44 = 432 = > p = 432 * 44 = 19008 p / 30 = 19008 / 30 = 633 , remainder = 18 e\"" + }, + { + "Answer": 25, + "Options": "a ) 60 , b ) 52 , c ) 5 , d ) 25 , e ) 125", + "Correct": "d", + "Explanation": "let the numbers be a , b , c , d , e , f , g d + e + f + g = 15 * 4 = 60 e + f + g = 55 , 60 - 55 = 5 so the fourth number is 5 . the square is 25 . the answer is option d ." + }, + { + "Answer": 24.000000000000007, + "Options": "a ) 16 , b ) 20 , c ) 24 , d ) 28 , e ) 32", + "Correct": "c", + "Explanation": "\"since the distance remains the same ( we ' re just changing the rate and time ) , any increase in rate or time is met with a decrease in the other term . decreasing the time by 1 / 3 would give us : d = ( r ) ( t ) = ( 2 t / 3 ) ( x * r ) x = 3 / 2 since ( 2 t / 3 ) ( 3 r / 2 ) = ( r ) ( t ) = d 3 r / 2 = r + 12 r / 2 = 12 r = 24 the answer is c .\"" + }, + { + "Answer": 900, + "Options": "a ) 450 , b ) 810 , c ) 900 , d ) 1000 , e ) 1100", + "Correct": "c", + "Explanation": "\"we want the sum of the digits from 0 to 99 , so i approximated : 0 - 9 - > 45 - > ( 9 + 0 ) * 10 / 2 40 - 49 - > 85 ( 13 + 4 ) * 10 / 2 90 - 99 - > 135 ( 18 + 9 ) * 10 / 2 we can see at a glance that theweightgoes up as the numbers go up ( meaning the difference between 85 and 45 is 40 , while 135 - 85 is 50 , this means that the second part of this sequence carries more weight for our result ) , so we know that the final answer has to be more than 850 ( 85 * 10 ) but close to it , and that ' s just q = 900 : the answer is c .\"" + }, + { + "Answer": 117, + "Options": "a ) 115 , b ) 121 , c ) 117 , d ) 119 , e ) 121", + "Correct": "c", + "Explanation": "\"total money = rs . 10350 . let 50 rupees note was x . then 500 rupees note = 126 - x now , 50 * x + 500 * ( 126 - x ) = 10350 50 x + 63000 - 500 x = 10350 - 450 x = - 52650 x = 117 . no . of 50 rupees note = 117 . answer : option c\"" + }, + { + "Answer": 145, + "Options": "a ) 75 , b ) 100 , c ) 125 , d ) 175 , e ) 145", + "Correct": "e", + "Explanation": "\"let m be the number of male participants and f be the number of female articipants in the meeting . thetotal number of participants is given as 870 . hence , we have m + f = 870 now , we have that half the female participants and one - quarter of the male participants are democrats . let d equal the number of the democrats . then we have the equation f / 2 + m / 4 = d now , we have that one - third of the total participants are democrats . hence , we have the equation d = 870 / 3 = 290 solving the three equations yields the solution f = 290 , m = 580 , and d = 290 . the number of female democratic participants equals half the female participants equals 290 / 2 = 145 . answer : e\"" + }, + { + "Answer": 14, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 14", + "Correct": "e", + "Explanation": "\"let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 37 5 x = 35 = > x = 7 hence , b ' s age = 2 x = 14 years . answer : e\"" + }, + { + "Answer": 66.66666666666666, + "Options": "a ) 40 % , b ) 50 % , c ) 60 % , d ) 66.66 % , e ) 70 %", + "Correct": "d", + "Explanation": "\"explanation : number of runs made by running = 150 - ( 5 x 4 + 5 x 6 ) = 150 - ( 50 ) = 100 now , we need to calculate 100 is what percent of 150 . = > 100 / 150 * 100 = 66.66 % option d\"" + }, + { + "Answer": 20, + "Options": "a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24", + "Correct": "a", + "Explanation": "220 = 20 * 11 = 22 * 10 there are 20 people in the group today . the answer is a ." + }, + { + "Answer": 8, + "Options": "a ) 36 , b ) 24 , c ) 17 , d ) 8 , e ) 5", + "Correct": "d", + "Explanation": "\"sol . ( b ) the sum of roots = a + b = 4 product of roots = ab = 4 now , a 2 + b 2 = ( a + b ) 2 - 2 ab = 16 - 8 = 8 answer d\"" + }, + { + "Answer": 5, + "Options": "a ) 3 , b ) 5 , c ) 6 , d ) 11 , e ) 16", + "Correct": "b", + "Explanation": "\"( m - 8 ) ( m - a ) = m ^ 2 - sm - 24 a = - 3 s = 8 + a = 5 = d = b\"" + }, + { + "Answer": 0.6666666666666664, + "Options": "a ) 2 / 3 , b ) 5 / 6 , c ) 7 / 8 , d ) 4 / 5 , e ) 5 / 8", + "Correct": "a", + "Explanation": "x : 0.5 % is 0.2 % - points from 0.7 % . y : 0.8 % is 0.1 % - points from 0.7 % . therefore the ratio of products checked by y : x is 2 : 1 . thus , worker y checked 2 / 3 of the products . the answer is a ." + }, + { + "Answer": 44, + "Options": "a ) a ) 44 , b ) b ) 77 , c ) c ) 79 , d ) d ) 81 , e ) e ) 82", + "Correct": "a", + "Explanation": "\"required average = 7 ( 1 + 2 + . . . . + 21 ) / 21 ( 4 / 21 ) x ( ( 21 x 22 ) / 2 ) ( because sum of first 21 natural numbers ) = 44 a\"" + }, + { + "Answer": 24, + "Options": "a ) 22 , b ) 24 , c ) 28 , d ) 32 , e ) 44", + "Correct": "b", + "Explanation": "g ( a ) = 4 ^ 11 = 2 ^ 22 . so we have to find a product with atleast 22 2 ' s in it . in option 1 22 the total no of 2 ' s = [ 22 / 2 ] + [ 22 / 4 ] + [ 22 / 8 ] + [ 22 / 16 ] = 11 + 5 + 2 + 1 = 19 in option 2 24 the total no of 2 ' s = [ 24 / 2 ] + [ 24 / 4 ] + [ 24 / 8 ] + [ 24 / 16 ] = 12 + 6 + 3 + 1 = 22 . hence b" + }, + { + "Answer": 0.3888888888888889, + "Options": "a ) 1 / 4 , b ) 4 / 15 , c ) 1 / 3 , d ) 7 / 18 , e ) 4 / 5", + "Correct": "d", + "Explanation": "\"let avg for 11 mos . = 10 therefore , dec = 70 year total = 11 * 10 + 70 = 180 answer = 70 / 180 = 7 / 18 = d\"" + }, + { + "Answer": 11, + "Options": "a ) 9 , b ) 11 , c ) 15 , d ) 12 , e ) 20", + "Correct": "b", + "Explanation": "\"age of the 15 th student = 15 * 15 - ( 14 * 5 + 16 * 9 ) = 225 - 214 = 11 years answer is b\"" + }, + { + "Answer": 15, + "Options": "a ) 15 , b ) 20 , c ) 25 , d ) 13 , e ) 42", + "Correct": "a", + "Explanation": "\"x + y = 20 x - y = 10 2 x = 30 x = 15 answer is a\"" + }, + { + "Answer": 12, + "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 12 , e ) 14", + "Correct": "d", + "Explanation": "let x be molly ' s present age . x + 18 = 5 ( x - 6 ) x = 12 the answer is d ." + }, + { + "Answer": 945.0000000000013, + "Options": "a ) 670 , b ) 750 , c ) 945 , d ) 375 , e ) 315", + "Correct": "c", + "Explanation": "\"let no . be x 4 / 15 * 5 / 7 * x - 4 / 9 * 2 / 5 * x = 8 by further solving 20 x / 105 - 8 x / 45 = 8 4 x / 315 = 24 x = 1890 we have to find x / 2 = 1890 / 2 = 945 answer : c\"" + }, + { + "Answer": 3, + "Options": "a ) 1.5 , b ) 2 , c ) 2.4 , d ) 2.7 , e ) 3", + "Correct": "e", + "Explanation": "\"let x be the number of liters of ethanol added to the gas tank . 0.05 ( 54 ) + x = 0.1 ( 54 + x ) 0.9 x = 5.4 - 2.7 = 2.7 x = 3 liters the answer is e .\"" + }, + { + "Answer": 100, + "Options": "a ) 100 kg , b ) 102.5 kg , c ) 85 kg , d ) data inadequate , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : total weight increased = ( 10 x 3.5 ) kg = 35 kg . weight of new person = ( 65 + 35 ) kg = 100 kg . answer : a\"" + }, + { + "Answer": 92, + "Options": "a ) a ) 78 , b ) b ) 82 , c ) c ) 92 , d ) d ) 91 , e ) e ) 85", + "Correct": "c", + "Explanation": "\"correct avg marks = 100 + ( 10 - 90 ) / 10 avg = 100 - 8 = 92 answer is c\"" + }, + { + "Answer": 66, + "Options": "a ) 65 , b ) 66 , c ) 67 , d ) 71 , e ) 72", + "Correct": "b", + "Explanation": "( xn + 1 ) will be divisible by ( x + 1 ) only when n is odd . ( 67 ^ 67 + 1 ) will be divisible by ( 67 + 1 ) ( 67 ^ 67 + 1 ) + 66 , when divided by 68 will give 66 as remainder . b )" + }, + { + "Answer": 230, + "Options": "a ) 100 , b ) 230 , c ) 300 , d ) 400 , e ) 500", + "Correct": "b", + "Explanation": "since 170 students answered yes only for subject m , then the remaining 330 students who answered yes for subject m , also answered yes for subject r . so , 330 students answered yes for both subjects . if 320 students answered yes for both subjects , then 400 - 330 = 70 students answered yes only for subject r . so , we have that : 200 students answered yes only for subject m ; 70 students answered yes only for subject r ; 300 students answered yes for both subjects ; therefore 800 - ( 200 + 70 + 300 ) = 230 students did not answer yes for either subject . answer : b ." + }, + { + "Answer": 78, + "Options": "a ) 70 , b ) 72 , c ) 75 , d ) 78 , e ) 80", + "Correct": "d", + "Explanation": "\"income of 6 months = ( 6 \u00d7 85 ) \u2013 debt = 510 \u2013 debt income of the man for next 4 months = 4 \u00d7 60 + debt + 30 = 270 + debt \u2234 income of 10 months = 780 average monthly income = 780 \u00f7 10 = 78 answer d\"" + }, + { + "Answer": 9, + "Options": "a ) 14 , b ) 13 , c ) 9 , d ) 7 , e ) 5", + "Correct": "c", + "Explanation": "c . 9 30 - 3 = 27 27 - 10 - 18 = - 9 then 9 are in the intersection between 4 years experience and degree . answer c" + }, + { + "Answer": 58, + "Options": "a ) 54 , b ) 58 , c ) 63 , d ) 71 , e ) 92", + "Correct": "b", + "Explanation": "\"total = 70 thrower = 34 rest = 70 - 34 = 36 left handed = 36 / 3 = 12 right handed = 24 if all thrower are right handed then total right handed is 34 + 24 = 58 so b . 58 is the right answer\"" + }, + { + "Answer": 31, + "Options": "a ) 31 , b ) 0.31 , c ) 0.0031 , d ) 0.00031 , e ) 3.1 e - 05", + "Correct": "a", + "Explanation": "\"99 * 0.31 = 30.69 approx . 31 answer : a\"" + }, + { + "Answer": 30, + "Options": "a ) 40 , b ) 44 , c ) 80 , d ) 88 , e ) 30", + "Correct": "e", + "Explanation": "sol . let the numbers be x and y . then , ( x + y ) = 30 and x 2 + y 2 = 840 . now , 2 xy = ( x + y ) 2 - ( x 2 + y 2 ) = ( 30 ) 2 - 840 = 900 - 840 = 60 xy = 30 . answer e" + }, + { + "Answer": 12, + "Options": "a ) 10 , b ) 12 , c ) 15 , d ) 18 , e ) 20", + "Correct": "b", + "Explanation": "this is the hard one , definitely a 700 + level question . we need numbers a , b , c , and d such that 6 x ^ 2 + x - 12 = ( ax + b ) ( cx + d ) this means that ac = 6 , bd = \u2013 12 , and ad + bc = 1 . the a & c pair could be ( 1 , 6 ) or ( 2 , 3 ) , in some order . the absolute values of the b & d pair could be ( 1 , 12 ) or ( 2 , 6 ) or ( 3 , 4 ) , and of course , in each case , one of the two would have to be negative . after some trial and error , we find : 6 x ^ 2 + x - 12 = ( 2 x + 3 ) ( 3 x - 4 ) thus , we see : | a | + | b | + | c | + | d | = 2 + 3 + 3 + 4 = 12 answer = b" + }, + { + "Answer": 200, + "Options": "a ) 104 , b ) 114 , c ) 315 , d ) 200 , e ) 335", + "Correct": "d", + "Explanation": "let the numbers be x and y . then x + y = 30 and x - y = 10 x = 20 ; y = 10 xy = 20 * 10 = 200 answer : d" + }, + { + "Answer": 63, + "Options": "a ) 48 , b ) 24 , c ) 56 , d ) 63 , e ) 14", + "Correct": "d", + "Explanation": "60 \u00d7 3 / 4 = 45 , 60 \u00d7 8 / 5 = 96 45 \u2013 96 + ? = 12 = > 96 + 12 = 108 \u2013 45 = 63 [ 63 + 45 = 108 \u2013 96 = 12 ] option d" + }, + { + "Answer": 70, + "Options": "a ) 90 , b ) 95 , c ) 70 , d ) 105 , e ) 110", + "Correct": "c", + "Explanation": "10 and 190 inclusive would mean there are 15 terms . no need to add up all the terms and further divide by 15 since the terms are evenly spaced in ascending order from 10 , 20 , 30 . . . . . . . . 160 the middle term is the average which is the tenth term = 70 c is the answer ." + }, + { + "Answer": 85, + "Options": "a ) 85 , b ) 36 , c ) 72 , d ) 90 , e ) 108", + "Correct": "a", + "Explanation": "\"85 all u do is do 2 : 1 : 6 = > 2 x + x + 6 x = 153 = > x = 17 34 : 17 : 102 102 - 17 = 85 answer a\"" + }, + { + "Answer": 75, + "Options": "a ) 75 , b ) 50 , c ) 60 , d ) 70 , e ) 80", + "Correct": "a", + "Explanation": "according to order of operations , inner brackets first . hence | 9 - 8 ( 3 - 12 ) | - | 5 - 11 | = | 9 - 8 * ( - 9 ) | - | 5 - 11 | according to order of operations , multiplication within absolute value signs ( which may be considered as brackets when it comes to order of operations ) next . hence = | 9 + 72 | - | 5 - 11 | = | 81 | - | - 6 | = 81 - 6 = 75 correct answer a ) 75" + }, + { + "Answer": 93, + "Options": "a ) 79 , b ) 93 , c ) 88 , d ) 88 , e ) 75", + "Correct": "b", + "Explanation": "\"average = ( 96 + 95 + 82 + 97 + 95 ) / 5 = 465 / 5 = 93 . answer : b\"" + }, + { + "Answer": 0.33333333333333337, + "Options": "a ) 1 / 3 , b ) 2 / 10 , c ) 1 / 50 , d ) 1 / 500 , e ) 2 / 500", + "Correct": "a", + "Explanation": "\"let x be the difference then . 5 - 1 / 3 = x 5 / 10 - 1 / 3 = x x = 1 / 3 ans a\"" + }, + { + "Answer": 50, + "Options": "a ) 50 % , b ) 80 % , c ) 40 % , d ) 90 % , e ) 100 %", + "Correct": "a", + "Explanation": "\"explanation : actually it means 10 is what percent of 20 , which can be calculated as , ( 10 / 20 ) * 100 = 10 * 5 = 50 answer : option a\"" + }, + { + "Answer": 10, + "Options": "a ) 4 . , b ) 6 . , c ) 7 . , d ) 10 . , e ) 8 .", + "Correct": "d", + "Explanation": "\"total teams = 18 bad teams = ( 2 / 3 ) * 18 = 12 rich teams = 9 so maximum value that the both rich and bad can take will be 9 . so e = 10 can not be that value . ans d .\"" + }, + { + "Answer": 27, + "Options": "a ) and 27 , b ) and 24 , c ) and 22 , d ) and 29 , e ) of these", + "Correct": "a", + "Explanation": "\"let the age of jill 5 years ago be x , age of henry be 2 x x + 5 + 2 x + 5 = 43 x = 11 present ages will be 16 and 27 answer : a\"" + }, + { + "Answer": 92, + "Options": "a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %", + "Correct": "e", + "Explanation": "\"this is easiest to solve with a bell - curve histogram . m here is equal to \u00b5 in the gaussian normal distribution and thus m = 50 % of the total population . so , if 84 % is one st . dev , then on either side of m we have 84 / 2 = 42 % . so , 84 % are to the right and left of m ( = 50 % ) . in other words , our value m + d = 50 + 42 = 92 % goingfrom the mean m , to the right of the distributionin the bell shaped histogram . . this means that 92 % of the values are below m + d . like i said , doing it on a bell - curve histogram is much easier to fullygethow this works , or you could apply gmat percentile jargon / theory to it e\"" + }, + { + "Answer": 1600, + "Options": "a ) r = 200 , b ) r = 600 , c ) r = 800 , d ) r = 1600 , e ) r = 50", + "Correct": "d", + "Explanation": "original cost c 1 = t 1 * b 1 ^ 4 new cost c 2 = t 2 * b 2 ^ 4 . . . . only b is doubled so t 2 = t 1 and b 2 = 2 b 1 c 2 = t 2 * ( 2 b 1 ) ^ 4 = 16 ( t 1 * b 1 ^ 4 ) = 16 c 1 16 times c 1 = > 1600 % of c 1 ans d = 1600" + }, + { + "Answer": 0.5044955044955045, + "Options": "a ) 500 / 1001 , b ) 503 / 1001 , c ) 303 / 1001 , d ) 301 / 1001 , e ) 505 / 1001", + "Correct": "e", + "Explanation": "6 c 4 / 14 c 4 + ( 6 c 2 * 8 c 2 ) / 14 c 4 + 8 c 4 / 14 c 4 = 505 / 1001 case 1 : only 4 positive no . case 2 : 2 positive and 2 negative no . case 3 : 4 negative no . answer : e" + }, + { + "Answer": 2, + "Options": "a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1", + "Correct": "d", + "Explanation": "f ( x ) + 3 f ( 8 - x ) = x : given f ( 2 ) + 3 f ( 6 ) = 2 : x = 2 above f ( 6 ) + 3 f ( 2 ) = 6 : x = 6 above f ( 6 ) = 6 - 3 f ( 2 ) : solve equation c for f ( 6 ) f ( 2 ) + 3 ( 6 - 3 f ( 2 ) ) = 2 : substitute f ( 2 ) = 2 : solve above equation . correct answer is d ) 2" + }, + { + "Answer": 60, + "Options": "a ) 20 coins , b ) 30 coins , c ) 40 coins , d ) 60 coins , e ) none of these", + "Correct": "d", + "Explanation": "\"let number of each type of coin = x . then , 1 \u00d7 x + . 50 \u00d7 x + . 25 x = 105 \u21d2 1.75 x = 105 \u21d2 x = 60 coins answer d\"" + }, + { + "Answer": 4, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 11 , e ) 4", + "Correct": "e", + "Explanation": "\"answer = e = 4 if least = - 4 , then largest = 5 range = 5 - 1 = 4\"" + }, + { + "Answer": 95.42857142857143, + "Options": "a ) 95 , b ) 95.42 , c ) 95.45 , d ) 94 , e ) 93", + "Correct": "b", + "Explanation": "the sum of 7 weights = weights of [ a + b + c + ( a + b ) + ( b + c ) + ( c + a ) + ( a + b + c ) ] = weights of [ 4 * ( a + b + c ) = 4 * 167 = 668 therefore the average weight of 7 readings is 668 / 7 = 95.428 answer : b" + }, + { + "Answer": 30, + "Options": "a ) 20 % , b ) 30 % , c ) 40 % , d ) 50 % , e ) 60 %", + "Correct": "b", + "Explanation": "\"the is always the difference between our starting and ending points . in this case , it \u00e2 \u20ac \u2122 s 100 \u00e2 \u20ac \u201c 70 = 30 . the \u00e2 \u20ac \u0153 original \u00e2 \u20ac \u009d is our starting point ; in this case , it \u00e2 \u20ac \u2122 s 100 . ( 30 / 100 ) * 100 = ( 0.3 ) * 100 = 30 % . b\"" + }, + { + "Answer": 14, + "Options": "a ) 23 , b ) 19 , c ) 22 , d ) 20 , e ) 14", + "Correct": "e", + "Explanation": "\"let the total number of workers be x . then , 8000 x = ( 10000 * 7 ) + 6000 ( x - 7 ) = 2000 x = 28000 = x = 14 . answer : e\"" + }, + { + "Answer": 360, + "Options": "a ) $ 200 , b ) $ 360 , c ) $ 400 , d ) $ 500 , e ) $ 600", + "Correct": "b", + "Explanation": "\"c for cost . p price per person . c = 3 * p c = 4 * p - 120 substituting the value of p from the first equation onto the second we get p = 120 . plugging in the value of p in the first equation , we get c = 360 . which leads us to answer choice b\"" + }, + { + "Answer": 128, + "Options": "a ) 128 % , b ) b . 120 % , c ) 96 % , d ) 80 % , e ) 64 %", + "Correct": "a", + "Explanation": "even i got 96 % j = 100 t = 100 * 0.8 = 80 m = 80 * 1.6 = 128 if mary ' s income is x percent of j m = j * x / 100 x = m * 100 / j = 128 * 100 / 100 = 128 ans : a" + }, + { + "Answer": 40, + "Options": "a ) 40 min , b ) 62 min , c ) 70 min , d ) 74 min , e ) 76 min", + "Correct": "a", + "Explanation": "\"x = time for type b prolems 2 x = time for type a problem total time = 3 hrs = 180 min 175 x + 25 * 2 x = 180 x = 180 / 225 x = 0.8 time taken for type a problem = 25 * 2 * 0.8 = 40 min answer : a\"" + }, + { + "Answer": 0.0625, + "Options": "a ) 1 / 16 , b ) 1 / 4 , c ) 1 , d ) 4 , e ) 8", + "Correct": "a", + "Explanation": "\"2 a / 100 = 8 a = 400 8 b / 100 = 2 b = 25 c = b / a = 25 / 400 = 1 / 16 the answer is a .\"" + }, + { + "Answer": 252, + "Options": "a ) $ 120 , b ) $ 135 , c ) $ 150 , d ) $ 165 , e ) $ 252", + "Correct": "e", + "Explanation": "\"let the charge for first hour = x + 30 then charge for each additional hour = x x + 30 + 4 x = 400 = > 5 x = 370 = > x = 74 total charge for patient for 3 hours of therapy = x + 30 + 2 x = 3 x + 30 = 252 $ answer e\"" + }, + { + "Answer": 6, + "Options": "a ) 0 , b ) 5 , c ) 6 , d ) 10 , e ) 12", + "Correct": "c", + "Explanation": "x = 1 * 2 * 3 * 4 * 5 * . . . . . . * 49 * 50 = 50 ! y = 100 ^ k 100 = 10 ^ 2 = 2 ^ 2 * 5 ^ 2 on prime factorization of x , power of 5 will always be greater than power of 2 concept : in every factorial value ( x ! ) , on prime factorization , the power of bigger prime number > the power of smaller prime number also , power of any prime number in any factorial can be calculated by following understanding power of prime x in n ! = [ n / x ] + [ n / x ^ 2 ] + [ n / x ^ 3 ] + [ n / x ^ 4 ] + . . . and so on where , [ x ] = greatest integer less than or equal to x and the explanation of terms is as follows [ n / x ] = no . of integers that are multiple of x from 1 to n [ n / x ^ 2 ] = no . of integers that are multiple of x ^ 2 from 1 to n whose first power has been counted in previous step and second is being counted at this step [ n / x ^ 3 ] = no . of integers that are multiple of x ^ 3 from 1 to n whose first two powers have been counted in previous two step and third power is counted at this step and so on . . . . . where [ n / x ] is greatest integer value of ( n / x ) less than or equal to ( n / x ) i . e . [ 100 / 3 ] = [ 33.33 ] = 33 i . e . [ 100 / 9 ] = [ 11.11 ] = 11 etc . power of 5 in x = [ 50 / 5 ] + [ 50 / 5 ^ 2 ] + [ 50 / 5 ^ 3 ] . . . = 10 + 2 + 0 = 12 power of 2 in x = [ 50 / 2 ] + [ 50 / 2 ^ 2 ] + [ 50 / 2 ^ 3 ] . . . = 25 + 12 + 6 + 3 + 1 = 47 i . e . x = 50 ! = 2 ^ 47 * 5 ^ 12 * . . . = 10 ^ 12 * . . . = 100 ^ 6 * . . . i . e . x is divisible by a 6 th power of 100 at the most i . e . y = 100 ^ k = 100 ^ 6 i . e . k = 6 answer : option c" + }, + { + "Answer": 22.5, + "Options": "a ) 20.5 , b ) 21.5 , c ) 22.5 , d ) 23.5 , e ) 24.5", + "Correct": "c", + "Explanation": "( 38 seconds + 7 seconds ) / 2 = 22.5 seconds correct option is : c" + }, + { + "Answer": 35, + "Options": "a ) 35 , b ) 40 , c ) 45 , d ) 50 , e ) 55", + "Correct": "a", + "Explanation": "\"let x be the number of blueberries in each blue box . then there are x + 30 strawberries in each red box . x + ( x + 30 ) = 100 x = 35 the answer is a .\"" + }, + { + "Answer": 362, + "Options": "a ) 124 , b ) 97 , c ) 117 , d ) 229 , e ) 362", + "Correct": "e", + "Explanation": "total jellybeans in 34 bags = 34 * 117 = 3978 total jellybeans in 35 bags = 35 * 124 = 4340 number of jellybeans in new bag = 3978 - 4340 = 362 jellybeans answer is e" + }, + { + "Answer": 800, + "Options": "a ) 450 , b ) 300 , c ) 800 , d ) 610 , e ) 175", + "Correct": "c", + "Explanation": "\"let the maximum marks be x then , 33 % of x = 175 + 89 33 x / 100 = 264 x = 800 answer is c\"" + }, + { + "Answer": 475, + "Options": "a ) 475 , b ) 350 , c ) 450 , d ) 550 , e ) 650", + "Correct": "a", + "Explanation": "\"the number of chocolate bars is equal to 19 * 25 = 475 correct answer a\"" + }, + { + "Answer": 64, + "Options": "a ) 54 , b ) 59 , c ) 63 , d ) 64 , e ) 92", + "Correct": "d", + "Explanation": "\"total = 70 thrower = 52 rest = 70 - 52 = 18 left handed = 18 / 3 = 6 right handed = 12 if all thrower are right handed then total right handed is 52 + 12 = 64 so d . 64 is the right answer\"" + }, + { + "Answer": 14, + "Options": "a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15", + "Correct": "d", + "Explanation": "\"100 - ( 100 - 84 ) - ( 100 - 75 ) - ( 100 - 85 ) - ( 100 - 70 ) = 100 - 16 - 25 - 15 - 30 = 100 - 86 = 14 answer : d\"" + }, + { + "Answer": 1, + "Options": "a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1", + "Correct": "e", + "Explanation": "let us say x sheets are used to create paper boats and y sheets are used to create paper planes . since total 80 paper toys are to be created , 8 x + 6 y = 80 . = > 8 x = 80 - 6 y = > x = 10 - ( 6 / 8 ) y = > x = 10 - ( 3 / 4 ) y to minimize x , we need to maximize y . and y needs to be multiple of 4 . y = 4 , x = 10 - ( 3 / 4 ) 4 = 7 y = 8 , x = 10 - ( 3 / 4 ) 8 = 4 y = 12 , x = 10 - ( 3 / 4 ) 12 = 1 beyond this , x will become negative for greater values of y . so , minimum 1 sheet is required to be used for creating paper boats . answer : e" + }, + { + "Answer": 8, + "Options": "a ) 4 kg , b ) 8 kg , c ) 7 kg , d ) 3 kg , e ) 9 kg", + "Correct": "b", + "Explanation": "b 8 kg 8 kg : 16 / 2" + }, + { + "Answer": 24, + "Options": "a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25", + "Correct": "d", + "Explanation": "\"( 1056 / 27 ) gives remainder 3 24 + 3 = 27 , so we need to add 24 d\"" + }, + { + "Answer": 5, + "Options": "a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9", + "Correct": "c", + "Explanation": "let the numerator be x and denominator be y . then = > x = y + 4 and 6 + x = 3 * y = > 6 + y + 4 = 3 * y = > 2 y = 10 = > y = 5 option c" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 6", + "Correct": "a", + "Explanation": "\"( - 2 ) ^ ( 2 m ) = 4 ^ m and 2 ^ ( 3 - m ) = 4 ^ ( ( 3 - m ) / 2 ) therefore , m = ( 3 - m ) / 2 2 m = 3 - m m = 1 answer a\"" + }, + { + "Answer": 60, + "Options": "a ) 22 , b ) 60 , c ) 28 , d ) 76 , e ) 21", + "Correct": "b", + "Explanation": "explanation : the least number of trees that are required = lcm ( 4 , 5 , 6 ) = 60 . answer : b" + }, + { + "Answer": 144, + "Options": "a ) 143 , b ) 144 , c ) 145 , d ) 146 , e ) 147", + "Correct": "b", + "Explanation": "let total runs done by a batsman in 12 innings be x therefore , x / 12 = 24 that means x = 12 * 24 = 288 runs for 15 innings , avg was doubled i . e . . 48.00 therefore , ( x + y ) / 15 = 48 where y is the no of runs done in last 3 innings y = 432 therefore average is 432 / 3 = 144 answer : b" + }, + { + "Answer": 100, + "Options": "a ) 40 , b ) 44 , c ) 100 , d ) 88 , e ) 48", + "Correct": "c", + "Explanation": "\"according to the given conditions x + y = 20 and x ^ 2 + y ^ 2 = 200 now ( x + y ) ^ 2 = x ^ 2 + y ^ 2 + 2 xy so 20 ^ 2 = 200 + 2 xy so xy = 200 / 2 = 100 answer : c\"" + }, + { + "Answer": 3, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 6 , e ) 3", + "Correct": "e", + "Explanation": "\"explanation : 39 + 16 = 55 / 13 = 3 ( remainder ) answer : e\"" + }, + { + "Answer": 12, + "Options": "a ) 8 , b ) 12 , c ) 9 , d ) 6 , e ) 5", + "Correct": "b", + "Explanation": "\"52 x + 78 = 54 ( x + 1 ) = > 2 x = 24 = > x = 12 answer : b\"" + }, + { + "Answer": 4, + "Options": "a ) 4 , b ) 8 , c ) 16 , d ) 1911 , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : required number of students = h . c . f of 1048 and 828 = 4 . answer : a\"" + }, + { + "Answer": 83.99999999999999, + "Options": "a ) 124 % , b ) b ) 120 % , c ) c ) 96 % , d ) d ) 80 % , e ) e ) 84 %", + "Correct": "e", + "Explanation": "\"m = ( 140 / 100 ) t t = ( 60 / 100 ) j = > m = ( 84 / 100 ) j answer e .\"" + }, + { + "Answer": 0.7584126790364585, + "Options": "a ) 0.72 , b ) 0.74 , c ) 0.76 , d ) 0.78 , e ) 0.82", + "Correct": "c", + "Explanation": "x is the initial quantity of impurities in that gold . after a cycle of purification the quantity of impurities left would be x 1 = x - 1 / 16 x i . e . x 1 = 15 / 16 x same thing for x 2 , x 3 , x 4 , respectively representing the quantity of impurities left after 2 , 3 , 4 cycles of purification . so we have : x 1 = 15 / 16 x x 2 = 15 / 16 x 1 x 3 = 15 / 16 x 2 x 4 = 15 / 16 x 3 by multiplying both ends of the equations we get : x 1 * x 2 * x 3 * x 4 = ( 15 / 16 ) ^ 4 x * x 1 * x 2 * x 3 simplification leaves us with : x 4 = ( 15 / 16 ) ^ 4 x x 4 is the quantity of impurities left after four cycles . so the cumulative quantity of impurities ( q 4 ) which has been removed after 4 cycles is : q 4 = x - x 4 = x - ( 15 / 16 ) ^ 4 x i . e . q 4 = x ( 1 - ( 15 / 16 ) ^ 4 ) in this case , given x was : x = ( 1 - 16 / 24 ) * 10 g = 3.33 g ( remember we had 16 / 24 pure gold ) so we have q 4 = 3.33 * ( 1 - ( 15 / 16 ) ^ 4 ) = 3.33 * ( 1 - ( 50625 / 65536 ) ) = 3.33 * ( 14911 / 65536 ) = 0.757 rounded gives q 4 = 0.76 answer : c" + }, + { + "Answer": 62, + "Options": "a ) 104 , b ) 60 , c ) 62 , d ) 50 , e ) 25", + "Correct": "c", + "Explanation": "\"f ( x ) = 2 x ^ 2 + y f ( 2 ) = 20 = > 2 * ( 2 ) ^ 2 + y = 20 = > 8 + y = 20 = > y = 12 f ( 5 ) = 2 * ( 5 ) ^ 2 + 12 = 62 answer c\"" + }, + { + "Answer": 45, + "Options": "a ) 75 , b ) 45 , c ) 87 , d ) 165 , e ) 11", + "Correct": "b", + "Explanation": "\"explanation : average = ( 36 + 35 + 42 + 57 + 55 ) / 5 = 225 / 5 = 45 . answer : b\"" + }, + { + "Answer": 99, + "Options": "a ) 99 , b ) 100 , c ) 87 , d ) 95 , e ) 90", + "Correct": "a", + "Explanation": "detailed solution 10 students have scored 600 marks amongst them , and no one is allowed to score lesser than 40 or higher than 100 . the idea now is to maximize what the highest scorer gets . the 5 least scores have an average of 55 , which means that they have scored 55 x 5 = 275 marks amongst them . this leaves 325 marks to be shared amongst the top 5 students . lets call them a , b , c , d and e . now , in order to maximize what the top scorer \u201c e \u201d gets , all the others have to get the least possible scores ( and at the same time , they should also get distinct integers . ) the least possible score of the top 5 should be at least equal to the highest of the bottom 5 . now we want to make sure that the highest of the bottom 5 is the least possible . this can be done by making all scores equal to 55 . if some scores are less than 55 , some other scores have to be higher than 55 to compensate and make the average 55 . thus the highest score is the least only when the range is 0 . so now , we have the lowest value that the top 5 can score , which is 55 . the others have to get distinct integer scores , and as few marks as possible , so that \u201c e \u201d gets the maximum . so , 55 + 56 + 57 + 58 + e = 325 e = 99 marks . answer choice ( a )" + }, + { + "Answer": 143547, + "Options": "a ) 253547 , b ) 143681 , c ) 143547 , d ) 147614 , e ) 255547", + "Correct": "c", + "Explanation": "c 143547" + }, + { + "Answer": 4, + "Options": "a ) 1 : 1 , b ) 3 : 1 , c ) 4 : 5 , d ) 4 : 3 , e ) 4 : 1", + "Correct": "e", + "Explanation": "explanation : 80 x = 20 y x : y = 80 : 20 = 4 : 1 answer : e" + }, + { + "Answer": 115, + "Options": "a ) $ 115 , b ) $ 135 , c ) $ 150 , d ) $ 165 , e ) $ 192", + "Correct": "a", + "Explanation": "\"let the charge for first hour = x + 25 then charge for each additional hour = x x + 25 + 4 x = 250 = > 5 x = 225 = > x = 45 total charge for patient for 3 hours of therapy = x + 25 + x = 2 x + 25 = 115 $ answer a\"" + }, + { + "Answer": 4, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "c", + "Explanation": "\"8 people visited 2 stores each for 16 visits . to maximize the number of stores that one person visited , let ' s assume that 3 people visited 1 store each . the number of remaining visits is 23 - 16 - 3 = 4 , which is the maximum that one person could have visited . the answer is c .\"" + }, + { + "Answer": 12, + "Options": "a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18", + "Correct": "b", + "Explanation": "1 x 12 ounce can of concentrate + 4 x 12 ounce cans of water = 60 ounces of the mixture . 60 ounces of mixture gives ( 60 / 6 ) = 10 servings . thus 1 x 12 ounce can of concentrate is used to produce 10 servings of the mixture . to make 120 servings of the mixture , we need 120 / 10 = 12 cans of the concentrate . the answer is b ." + }, + { + "Answer": 5, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "d", + "Explanation": "minimuum should be 1 maximum should be 4 : 1 out of a or b to make the multiplication negative 3 out of c , d , e or f to make the multiplication negative . negative + negative < 0 answer : c maximum will be 5 . . you dont require both the multiplicatin to be negative for entire equation to be negative . . . any one a or b can be negative to make ab negative and it can still be more ( away from 0 ) than the multiplication of 4 other - ve numbers . . . actually by writing minimum required as 1 out of 6 , you are actually meaning 5 out of 6 also possible as you will see a = 5 or 1 will give you same equation . . ans d" + }, + { + "Answer": 70.6, + "Options": "a ) 71.6 , b ) 70.6 , c ) 80.6 , d ) 60.6 , e ) 50.6", + "Correct": "b", + "Explanation": "explanation : average = ( 56 + 60 + 72 + 85 + 80 ) / 5 = 70.6 . answer : b ) 70.6" + }, + { + "Answer": 103, + "Options": "a ) 100 , b ) 102 , c ) 103 , d ) 150 , e ) 46", + "Correct": "c", + "Explanation": "\"n th term of a . p = a + ( n - 1 ) * d = 3 + ( 21 - 1 ) * 5 , = 3 + 100 = 103 . answer : c\"" + }, + { + "Answer": 0.9677419354838709, + "Options": "a ) 1 / 130 , b ) 1 / 5 , c ) 3 / 13 , d ) 10 / 13 , e ) 30 / 31", + "Correct": "e", + "Explanation": "\"it ' s y / xpercentnot y / x . if x = 20 and y = 10 . then : 20 x = 400 black - and - white films ; 6 y = 60 color films . y / x % = 10 / 20 % = 0.5 % of the black - and - white films , so 2 black - and - white films and all 60 color films , thus total of 62 films were selected . color films thus compose w 60 / 62 = 30 / 31 of the selected films . answer : e .\"" + }, + { + "Answer": 999.9999999999998, + "Options": "a ) s 200 , b ) s 1000 , c ) s 300 , d ) s 450 , e ) s 550", + "Correct": "b", + "Explanation": "\"suppose the amount in the beginning was rs \u2019 x \u2019 money spent on clothes = rs 1 x / 3 balance = rs 2 x / 3 money spent on food = 1 / 5 of 2 x / 3 = rs 2 x / 15 balance = 2 x / 3 - 2 x / 15 = rs 8 x / 15 money spent on travel = 1 / 4 of 8 x / 15 = rs 2 x / 15 = 8 x / 15 - 2 x / 15 = 6 x / 15 = rs 2 x / 5 therefore 2 x / 5 = 400 = 1000 answer : b\"" + }, + { + "Answer": 4, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8", + "Correct": "c", + "Explanation": "\"f 100 / x leaves a reminder 4 then ( 100 - 4 ) i . e . 96 is divisible by x so ( 100 + 96 ) / x leaves a reminder rem ( 100 / x ) + rem ( 96 / x ) = > 4 + 0 = 4 answer : c\"" + }, + { + "Answer": 14, + "Options": "a ) 7 , b ) 14 , c ) 49 , d ) 21 , e ) none of these", + "Correct": "b", + "Explanation": "\"explanation \u221a ( 14 ) ^ 2 = ? or , ? = 14 answer b\"" + }, + { + "Answer": 25, + "Options": "a ) 0 , b ) 25 , c ) 50 , d ) 30 , e ) 40", + "Correct": "b", + "Explanation": "let the original salary = $ 100 new final salary = 150 % of ( 50 % of rs . 100 ) = $ ( ( 150 / 100 ) * ( 50 / 100 ) * 100 ) = $ 75 . decrease = 25 % answer option b ) 25 ." + }, + { + "Answer": 0.16666666666666666, + "Options": "a ) 1 / 20 , b ) 1 / 6 , c ) 1 / 5 , d ) 4 / 21 , e ) 5 / 21", + "Correct": "b", + "Explanation": "\"this is how i used to calculate which i think works pretty well : if you let the average of the 20 other numbers equal a , can you write this equation for sum of the list ( s ) n + 20 a = s the question tells us that n = 4 a plug this back into the first equation and you get that the sum is 24 a 4 a + 20 a = 24 a therefore fraction u of n to the total would be 4 a / 24 a or 1 / 6 answer b\"" + }, + { + "Answer": 32.00000000000001, + "Options": "a ) 10 , b ) 12 , c ) 15 , d ) 18 , e ) 32", + "Correct": "e", + "Explanation": "\"2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 80 - 16 = 64 = > ab = 32 answer : e\"" + }, + { + "Answer": 7, + "Options": "a ) 6 , b ) 5 , c ) 4 , d ) 7 , e ) 2", + "Correct": "d", + "Explanation": "can be solved without much calculations . you are given that ( - 2 , - 3 ) is the center of the circle . point ( 6 , - 3 ) lies inside the circle - - - > the radius is lesser than distance of ( - 2 , - 3 ) from ( 6 , - 3 ) - - - > lesser than 8 units but the radius will also be greater than the distance of ( - 2 , - 3 ) from ( - 2,3 ) - - - - > greater than 6 units . thus the radius is > 6 but < 8 and as it is an integer , the only possible value of radius = 7 units . d is the correct answer ." + }, + { + "Answer": 130, + "Options": "a ) 130 , b ) 152 , c ) 225 , d ) 260 , e ) 180", + "Correct": "a", + "Explanation": "\"let the total journey be x km then , ( 3 x / 5 ) + ( 7 x / 20 ) + 6.5 = x 12 x + 7 x + 20 * 6.5 = 20 x x = 130 km answer is a\"" + }, + { + "Answer": 90, + "Options": "a ) 90 , b ) 65 , c ) 85 , d ) 95 , e ) 80", + "Correct": "a", + "Explanation": "\"total increase in weight = 8 \u00d7 2.5 = 20 if x is the weight of the new person , total increase in weight = x \u2212 70 = > 20 = x - 70 = > x = 20 + 70 = 90 answer is a .\"" + }, + { + "Answer": 7, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8", + "Correct": "d", + "Explanation": "it is so better to start with 2 and check whether sum of two primes is primes is even . 1 ) 2 ( 6 times ) 2 ) 2 ( 3 times ) + 3 ( 2 times ) 3 ) 2 ( 2 times ) + 3 + 5 4 ) 2 + 3 + 7 5 ) 2 + 5 + 5 6 ) 3 ( 4 times ) 7 ) 5 + 7 answer : d" + }, + { + "Answer": 18, + "Options": "a ) 18 , b ) 92 , c ) 27 , d ) 26 , e ) 19", + "Correct": "a", + "Explanation": "\"explanation : let the present age of person be x years . then , 3 ( x + 3 ) - 3 ( x - 3 ) = x < = > ( 3 x + 9 ) - ( 3 x - 9 ) = x < = > x = 18 . . answer : a ) 18\"" + }, + { + "Answer": 755, + "Options": "a ) 750 , b ) 752 , c ) 754 , d ) 755 , e ) 756", + "Correct": "d", + "Explanation": "\"sum of the deviations of the numbers in the set from the mean is always zero 744 , 745 , 747 , 748 , 749 , 752 , 752 , 753 , 755 mean is 750 so the list is - 6 - 5 - 3 - 2 - 1 + 2 + 2 + 3 + 5 . . . this shud total to zero but this is - 5 , hence we need a number that is 5 more than the mean to get a + 5 and make it zero hence the answer is 750 + 5 = 755 d\"" + }, + { + "Answer": 12, + "Options": "a ) 6 , b ) 12 , c ) 24 , d ) 36 , e ) 48", + "Correct": "b", + "Explanation": "\"possible values of n = 12 , 24 , 36 and 48 . but it is 12 that can divide all the possible values of n . if we consider 48 , it will not divide 12 , 24 and 36 . hence , 12 is the value that must divide n . answer : b\"" + }, + { + "Answer": 17.05, + "Options": "a ) $ 17.05 , b ) $ 17.55 , c ) $ 17.15 , d ) $ 17.35 , e ) $ 17.25", + "Correct": "a", + "Explanation": "\"john spent and gave to his two friends a total of 1.05 + 1.00 + 1.00 = $ 3.05 money left 20.10 - 3.05 = $ 17.05 answer : a\"" + }, + { + "Answer": 1625, + "Options": "a ) 1000 , b ) 1250 , c ) 1300 , d ) 1600 , e ) 1625", + "Correct": "e", + "Explanation": "\"since pumping in additional 300 gallons of water will increase the amount of water in the pool by 30 % , then initially the pool is filled with 1,000 gallons of water . so , we have that 1,000 + 300 = 0.8 * { total } - - > { total } = 1,625 . answer : e .\"" + }, + { + "Answer": 500, + "Options": "a ) 300 , b ) t = 400 , c ) t = 500 , d ) 600 , e ) none of these", + "Correct": "c", + "Explanation": "\"{ managers } = { female managers } + { male managers } ; we are told that the total number of managers in the company is 2 / 5 of all the employees , thus { managers } = 2 / 5 ( m + f ) , where m and f are number of female and male employees , respectively . also , we know that 2 / 5 of all male employees are managers : { male managers } = 2 / 5 * mas well as there are total of 200 female managers : { female managers } = 200 ; thus : 2 / 5 ( m + f ) = 200 + 2 / 5 * m - - > f = 500 . answer : c .\"" + }, + { + "Answer": 61, + "Options": "a ) 23 , b ) 78 , c ) 27 , d ) 61 , e ) 81", + "Correct": "d", + "Explanation": "\"explanation : 60 + 5 * 12 / ( 180 / 3 ) = 60 + 5 * 12 / ( 60 ) = 60 + ( 5 * 12 ) / 60 = 60 + 1 = 61 . answer : d\"" + }, + { + "Answer": 500, + "Options": "a ) 300 , b ) y = 400 , c ) y = 500 , d ) y = 600 , e ) none of these", + "Correct": "c", + "Explanation": "\"{ managers } = { female managers } + { male managers } ; we are told that the total number of managers in the company is 2 / 5 of all the employees , thus { managers } = 2 / 5 ( m + f ) , where m and f are number of female and male employees , respectively . also , we know that 2 / 5 of all male employees are managers : { male managers } = 2 / 5 * mas well as there are total of 200 female managers : { female managers } = 200 ; thus : 2 / 5 ( m + f ) = 200 + 2 / 5 * m - - > f = 500 . answer : c .\"" + }, + { + "Answer": 2, + "Options": "a ) 2 , b ) 4 , c ) 8 , d ) 16 , e ) 32", + "Correct": "a", + "Explanation": "4 \u00f8 2 = 2 ^ 4 / 2 ^ 2 = 4 4 \u00f8 3 = 2 ^ 4 / 2 ^ 3 = 2 the answer is a ." + }, + { + "Answer": 64, + "Options": "a ) 23 , b ) 32 , c ) 44 , d ) 15 , e ) 64", + "Correct": "e", + "Explanation": "the 3 inch side should be aligned to the 12 inch side ( 4 layer ) 7 inch side should be aligned to the 14 inch side . ( 2 layer ) and 2 inch side should be aligned to the 16 inch side . ( 8 layer ) maximum number of rectangles = 4 * 2 * 8 = 64 answer is e" + }, + { + "Answer": 20, + "Options": "a ) 30 % , b ) 25 % , c ) 75 % , d ) 20 % , e ) none of these", + "Correct": "d", + "Explanation": "explanation : solution : babji is less than ashis by ( 25 / ( 100 + 25 ) * 100 ) % = 20 % answer : d" + }, + { + "Answer": 0.72, + "Options": "a ) 0.9 , b ) 0.72 , c ) 0.45 , d ) 0.35 , e ) 0.28", + "Correct": "b", + "Explanation": "\"let x be the total number of students . the number students who are younger than 25 is 0.6 * 0.4 x + 0.8 * 0.6 x = 0.72 x the answer is b .\"" + }, + { + "Answer": 2, + "Options": "a ) 0 , b ) 2 , c ) 3 , d ) 6 , e ) 7", + "Correct": "b", + "Explanation": "\"n = 22 k + 12 2 n = 2 ( 22 k + 12 ) = 4 * 11 k + 24 = 4 * 11 k + 2 * 11 + 2 = 11 j + 2 . the answer is b .\"" + }, + { + "Answer": 65, + "Options": "a ) 52.5 , b ) 52.9 , c ) 52.1 , d ) 52.3 , e ) 65", + "Correct": "e", + "Explanation": "\"sum of the marks for the class of 30 students = 30 * 40 = 1200 sum of the marks for the class of 50 students = 50 * 80 = 4000 sum of the marks for the class of 80 students = 1200 + 4000 = 5200 average marks of all the students = 5200 / 80 = 65 answer : e\"" + }, + { + "Answer": 25, + "Options": "a ) 1 , b ) 13 , c ) 26 , d ) 25 , e ) 1014", + "Correct": "d", + "Explanation": "x = 14 + 16 + . . . + 62 = ( largest + smallest ) / 2 * ( # of terms ) = ( 14 + 62 ) / 2 * 25 = 38 * 25 . gcd of 25 and 39 * 25 is 25 . answer : d ." + }, + { + "Answer": 4, + "Options": "a ) 2.0 , b ) 4.0 , c ) 5.0 , d ) 6.0 , e ) 8.0", + "Correct": "b", + "Explanation": "\"for the total revenue to remain the same when the price is one fourth , the number of products sold must four times . therefore increase in the number of products sold is 100 % = > the required ratio = 100 % / 25 % = 4.0 answer : b\"" + }, + { + "Answer": 74, + "Options": "a ) 87 , b ) 74 , c ) 10 , d ) 76 , e ) 17", + "Correct": "b", + "Explanation": "\"average after 11 innings = 34 required number of runs = ( 34 * 11 ) - ( 30 * 10 ) = 374 - 300 = 74 . answer : b\"" + }, + { + "Answer": 7, + "Options": "a ) 5.5 kg , b ) 11 kg , c ) 30 kg , d ) 36.5 kg , e ) 7 kg", + "Correct": "e", + "Explanation": "\"after two persons leave the group the average remains the same . that means the weight of the two persons = 44 + 30 = 74 so , the average the two persons = 37 that gives the answer 44 - 37 = 7 answer e\"" + }, + { + "Answer": 72, + "Options": "a ) 62 , b ) 72 , c ) 82 , d ) 92 , e ) 62", + "Correct": "b", + "Explanation": "\"a 2 - b 2 = 8 : given a 4 + b 4 - 2 a 2 b 2 = 82 : square both sides and expand . a * b = 2 : given a 2 b 2 = 22 : square both sides . a 4 + b 4 - 2 ( 4 ) = 82 : substitute a 4 + b 4 = 72 correct answer b\"" + }, + { + "Answer": 47.99999999999818, + "Options": "a ) 96 , b ) 75 , c ) 48 , d ) 25 , e ) 12", + "Correct": "c", + "Explanation": "\"when positive integer x is divided by positive integer y , the remainder is 5.76 - - > x = qy + 5.76 ; x / y = 96.12 - - > x = 96 y + 0.12 y ( so q above equals to 96 ) ; 0.12 y = 5.76 - - > y = 48 . answer : c .\"" + }, + { + "Answer": 0.5555555555555556, + "Options": "a ) 1 / 12 , b ) 1 / 9 , c ) 2 / 3 , d ) 5 / 9 , e ) 2 1 / 9", + "Correct": "d", + "Explanation": "\"total bought = 5 / 9 + 1 / 3 left part 8 / 24 - - - > 1 / 3 so used part 5 / 9 + 1 / 3 - 1 / 3 = 5 / 9 answer : d\"" + }, + { + "Answer": 25, + "Options": "a ) 47 , b ) 25 , c ) 37 , d ) 33 , e ) 29", + "Correct": "b", + "Explanation": "\"before you tackle this question you must first understand that the question is comprised of two key parts , 1 st is finding out how manytermsis in that sequence and 2 nd whatactual number valuethat term is . in an arithmetic progression , in this case consecutive odd integers 1 , 3 , 5 , . . . . , there are two set of rules . rule # 1 ( arithmetic sequence ) : xn = a + d ( n - 1 ) identifies what the actual # in the sequence would be . each number in the sequence has a term such as 1 ( is the first term ) , 3 ( is the second term ) and so on . so if i were to ask you to find out what the 10 th term is of that sequence you would use that formula to find that value . a = 1 ( first term ) d = 2 ( the common difference ) remember in the sequence 1 , 3 , 5 , 7 the common difference is always 2 * on a side note we use n - 1 because we do n ' t have d in the first term , therefore if we were solving for the first term we would get 0 as n - 1 and 0 times d would give us 0 , leaving only the first term . this works regardless what your first term is in any sequence . but remember the question askswhat is thevalueof n if the sum of the consecutive odd integers from 1 to n equals 169 ? which means we first need a consecutive sequence that sums up to 169 and than find what the value of the n is , in this case it would be the last number in that sequence . in order to find that we first need to knowhow many terms ( how many of the n there is ) in order to be able to plug n in this formula given we know what the sum is . for that to happen we need to use rule # 2 . rule # 2 ( summing an arithmetic series ) : 169 = n / 2 ( 2 a + ( n - 1 ) d ) . given the question gives us what the sum is ( 169 in this case ) we would simply use this formula to solve for n . once we solve for n ( 13 in this case ) we can simply plug n into the first formula ( rule 1 ) and find the value . it feels very confusing and difficult at first , but once you identify the steps all you need to do is plug and play . we have the sum ( 169 ) of a sequence , the number of terms in that sequence is ( unknown ) . rule # 2 tells us how many numbers there are in that sequence and rule # 1 gives us what that last term is .\"" + }, + { + "Answer": 28.571428571428573, + "Options": "a ) a ) 6.7 , b ) b ) 1.3 , c ) c ) 9.6 , d ) d ) 12.5 , e ) e ) 28.6", + "Correct": "e", + "Explanation": "\"amount salt in 100 kg solution = 10 * 100 / 100 = 10 kg let x kg of pure salt be added then ( 10 + x ) / ( 100 + x ) = 30 / 100 100 + 10 x = 300 + 3 x 7 x = 200 x = 28.6 answer is e\"" + }, + { + "Answer": 2, + "Options": "a ) 10 , b ) 8 , c ) 5 , d ) 4 , e ) 2", + "Correct": "e", + "Explanation": "15 = 3 * 5 since 15 is not a perfect square , no of ways = 2 answer e" + }, + { + "Answer": 4, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "d", + "Explanation": "\"solve for x : 5 x + 3 = 10 x - 17 20 = 5 x 4 = x correct answer d ) 4\"" + }, + { + "Answer": 9.333333333333334, + "Options": "a ) 28 / 3 , b ) 27 / 3 , c ) 26 / 3 , d ) 25 / 3 , e ) 24 / 3", + "Correct": "a", + "Explanation": "take alternative no . 1 / 2 , 43 16 / 4 = 4 15 / 5 = 3 56 / 6 = 28 / 3 hence ans is 28 / 3 answer : a" + }, + { + "Answer": 450, + "Options": "a ) 540 km , b ) 767 km , c ) 276 km , d ) 450 km , e ) 176 km", + "Correct": "d", + "Explanation": "explanation : let us assume that trains meet after ' x ' hours distance = speed * time distance traveled by two trains = 20 x km and 25 x km resp . as one train travels 50 km more than the other , 25 x \u00e2 \u20ac \u201c 20 x = 50 5 x = 50 x = 10 hours as the two trains are moving towards each other , relative speed = 20 + 25 = 45 km / hr therefore , total distance = 45 * 10 = 450 km . answer : d" + }, + { + "Answer": 1027.1999999999998, + "Options": "a ) 347.4 , b ) 987.4 , c ) 877.2 , d ) 1027.2 , e ) 1667.2", + "Correct": "d", + "Explanation": "\"let the costs of each kg of mangos and each kg of rice be $ a and $ r respectively . 10 a = 24 r and 6 * 24 = 2 r a = 12 / 5 r and r = 72 a = 144 required total cost = 4 * 144 + 3 * 72 + 5 * 24 = 691.2 + 216 + 120 = $ 1027.20 d\"" + }, + { + "Answer": 18, + "Options": "a ) 10 , b ) 12 , c ) 15 , d ) 18 , e ) 20", + "Correct": "d", + "Explanation": "\"given : n = 20 ! n = 20 ! . the highest power k for which 2 ^ k is a factor of n can be found with the above formula : k = 20 / 2 + 20 / 4 + 20 / 8 + 20 / 16 = 10 + 5 + 2 + 1 = 18 answer : d .\"" + }, + { + "Answer": 724827405, + "Options": "a ) 455465473 , b ) 654676854 , c ) 667676753 , d ) 725117481 , e ) 764534522", + "Correct": "d", + "Explanation": "\"72519 x 9999 = 72519 x ( 10000 - 1 ) = 72519 x 10000 - 72519 x 1 = 725190000 - 72519 = 725117481 d\"" + }, + { + "Answer": 17, + "Options": "a ) 17 , b ) 34 , c ) 54 , d ) 64 , e ) 112", + "Correct": "a", + "Explanation": "3 * 5 = 15 15 + 2 = 17 17 * 3 = 51 51 + 2 = 53 answer : a" + }, + { + "Answer": 15000, + "Options": "a ) 5000 , b ) 10000 , c ) 15000 , d ) 2778 , e ) 1991", + "Correct": "c", + "Explanation": "a : b : c = 2 / 3 : 1 / 6 : 1 / 6 = 4 : 1 : 1 x * 2 / 100 * 2 / 3 = 300 a ' s capital = 22500 * 2 / 3 = 15000 answer : c" + }, + { + "Answer": 3, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "d", + "Explanation": "\"easier to start with numbers that are of the form 14 p + 3 - - - > 17,31 , 45,59 , 73,87 . out of these 3 ( 31 , 59,87 ) are also of the form 4 q + 3 . thus 3 is the answer . d is the correct answer .\"" + }, + { + "Answer": 0.5, + "Options": "a ) 0 , b ) 1 / 2 , c ) 2 / 9 , d ) 1 / 3 , e ) 1", + "Correct": "b", + "Explanation": "\"if he is to ride 2 times and since he can choose any of the 2 cars each time , total number of ways is = 2 * 2 = 4 now the number of ways if he is to choose a different car each time is = 2 * 1 = 2 so the probability is = 2 / 4 = 1 / 2 answer : b\"" + }, + { + "Answer": 2.5, + "Options": "a ) 3 , b ) 2.5 , c ) 2.25 , d ) 1.5 , e ) 4", + "Correct": "b", + "Explanation": "\"m = 7.5 s = x ds = 7.5 + x us = 7.5 - x 7.5 + x = ( 7.5 - x ) 2 7.5 + x = 15 - 2 x 3 x = 7.5 x = 2.5 answer : b\"" + }, + { + "Answer": 2.4499999999999993, + "Options": "a ) $ 2.45 , b ) $ 2.54 , c ) $ 2.35 , d ) $ 2.48 , e ) $ 2.49", + "Correct": "a", + "Explanation": "\"john spent and gave to his two friends a total of 3.25 + 2.20 + 2.20 = $ 7.65 money left 10.10 - 7.65 = $ 2.45 answer : a\"" + }, + { + "Answer": 15, + "Options": "a ) 36 , b ) 24 , c ) 15 , d ) 6 , e ) 5", + "Correct": "c", + "Explanation": "\"sol . ( b ) the sum of roots = a + b = 5 product of roots = ab = 5 now , a 2 + b 2 = ( a + b ) 2 - 2 ab = 25 - 10 = 15 answer c\"" + }, + { + "Answer": 440, + "Options": "a ) 123 , b ) 213 , c ) 440 , d ) 550 , e ) 540", + "Correct": "c", + "Explanation": "400 ( x - 40 ) \u2265 40000 x - 40 \u2265 400 x \u2265 440 answer : option c" + }, + { + "Answer": 6, + "Options": "a ) 6 , 030,053 , b ) 6 , 030,054 , c ) 6 , 030,055 , d ) 6 , 042,091 , e ) 6 , 030,057", + "Correct": "d", + "Explanation": "\"interesting problem . i think key is to notice that all the given answer choices differs in last two digits . therefore , our entire focus should be to figure out how the given terms contribute to last two digits of total . 1000 ^ 2 - > 00 1001 ^ 1 - > 01 . . . 1006 ^ 2 - > 36 total - > * 91 answer d .\"" + }, + { + "Answer": 70000, + "Options": "a ) 67000 , b ) 70000 , c ) 76500 , d ) 77200 , e ) 85200", + "Correct": "b", + "Explanation": "explanation : ( 112 x 54 ) = 112 x ( 10 / 2 ) 4 = 112 x 10 4 / 2 4 = 1120000 / 16 = 70000 answer is b" + }, + { + "Answer": 20, + "Options": "a ) 5 % , b ) 7 % , c ) 9 % , d ) 11 % , e ) 20 %", + "Correct": "e", + "Explanation": "\"explanation : the difference of two successive amounts must be the simple interest in 1 year on the lower amount of money . s . i = 21168 / - - 17640 / - = rs . 3528 / - rate of interest = ( 3528 / 17640 ) \u00d7 ( 100 / 1 ) = > 20 % answer : option e\"" + }, + { + "Answer": 35, + "Options": "a ) 0 , b ) 15 , c ) 20 , d ) 25 , e ) 35", + "Correct": "e", + "Explanation": "i also was confused when i was looking forabove number : d as far as i understood , 25 is a factor of ab . in other words , the values of b ( units digits can be 5 or 0 . better to have option for 5 in this case to havebigger result ) . now let ' s try 25 x 1 ( a = 2 , b = 5 respectively we have = 10 ) . but we do n ' t have this number in answer choices , move on . ( avoid even multiples of 2,4 , 6,8 etc ( we will have 0 in units thus making our result 0 ) 25 x 3 = 75 ( a = 7 b = 5 respectively . hey ! that ' s 35 . this is the greatest possible value of b x a imo e ." + }, + { + "Answer": 0.08999999999999998, + "Options": "a ) 0.09 , b ) 0.08 , c ) 0.1 , d ) 0.07 , e ) none of them", + "Correct": "a", + "Explanation": "\"given expression = ( 0.15 ) ( power 3 ) - ( 0.06 ) ( power 3 ) / ( 0.15 ) ( power 2 ) + ( 0.15 x 0.06 ) + ( 0.06 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 0.15 - 0.06 ) = 0.09 answer is a .\"" + }, + { + "Answer": 2, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "c", + "Explanation": "\"assume x is quotient here , n = 12 x + 8 - - - - - - - - - - ( 1 ) and n = 6 x + ? we can also write equation ( 1 ) as : n = ( 12 x + 6 ) + 2 . ie 6 ( 2 x + 1 ) + 2 ie the first term is perfectly divisible by 6 . so , the remainder left is 2 . so , answer ( c ) is right choice .\"" + }, + { + "Answer": 0.1111111111111111, + "Options": "a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 5 , d ) 1 / 9 , e ) 1 / 3", + "Correct": "d", + "Explanation": "\"given x = k / y 2 , where k is a constant . now , y = 2 and x = 1 gives k = 4 . x = 4 / y 2 = > x = 4 / 62 , when y = 6 = > x = 4 / 36 = 1 / 9 . answer : d\"" + }, + { + "Answer": 56, + "Options": "a ) 56 , b ) 57 , c ) 58 , d ) 59 , e ) 60", + "Correct": "a", + "Explanation": "\"basically , the question asks how many 4 digit numbers ( including those in the form 0 xxx , 00 xx , and 000 x ) have digits which add up to 5 . think about the question this way : we know that there is a total of 5 to be spread among the 4 digits , we just have to determine the number of ways it can be spread . let x represent a sum of 1 , and | represent a seperator between two digits . as a result , we will have 5 x ' s ( digits add up to the 5 ) , and 3 | ' s ( 3 digit seperators ) . so , for example : xx | x | x | x = 2111 | | xxx | xx = 0032 etc . there are 8 c 3 ways to determine where to place the separators . hence , the answer is 8 c 3 = 56 . a\"" + }, + { + "Answer": 250, + "Options": "a ) rs . 200 , b ) rs . 250 , c ) rs . 300 , d ) rs . 350 , e ) rs . 370", + "Correct": "b", + "Explanation": "\"let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 550 but x = 120 % of y = 120 y / 100 = 12 y / 10 \u2234 12 y / 10 + y = 550 \u21d2 y [ 12 / 10 + 1 ] = 550 \u21d2 22 y / 10 = 550 \u21d2 22 y = 5500 \u21d2 y = 5500 / 22 = 500 / 2 = rs . 250 b )\"" + }, + { + "Answer": 750, + "Options": "a ) 450 , b ) 550 , c ) 650 , d ) 750 , e ) 850", + "Correct": "d", + "Explanation": "\"each term in set b is 30 more than the corresponding term in set a . the difference of the sums = 25 * 30 = 750 . the answer is d .\"" + }, + { + "Answer": 576, + "Options": "a ) 125 , b ) 280 , c ) 384 , d ) 400 , e ) 576", + "Correct": "e", + "Explanation": "explanation : let the number be x . 5 * x / 6 = 5 * x / 16 + 300 25 * x / 48 = 300 x = 576 answer e" + }, + { + "Answer": 5, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "e", + "Explanation": "we have to work with multiples of 20 and 25 . first , we must know the limits of this multiples , so : 105 / 25 = 4 . . . . so the max is 4 105 / 20 = 5 . . . so the max is 5 105 - 100 = 5 answer : e" + }, + { + "Answer": 2.5, + "Options": "a ) 5 , b ) 5 / 2 , c ) - 1 / 6 , d ) - 1 / 5 , e ) - 5", + "Correct": "b", + "Explanation": "\"any x and y satisfying x / y = 7 / 3 should give the same value for ( x + y ) / ( x - y ) . say x = 7 and y = 3 , then ( x + y ) / ( x - y ) = ( 7 + 3 ) / ( 7 - 3 ) = 5 / 2 . answer : b .\"" + }, + { + "Answer": 190, + "Options": "a ) 190 , b ) 120 , c ) 150 , d ) 199 , e ) 110", + "Correct": "a", + "Explanation": "solution we know that ( 1 + 2 + 3 + . . . . . + 19 ) = n ( n + 1 ) / 2 therefore ( 1 + 2 + 3 + . . . . + 19 ) = ( 19 \u00d7 20 / 2 ) = 190 . answer a" + }, + { + "Answer": 5, + "Options": "a ) 4 , b ) 3 , c ) 2 , d ) 5 , e ) 6", + "Correct": "d", + "Explanation": "explanation : 689 = 36 x 19 + r 689 = 684 + r r = 689 - 684 = 5 answer : option d" + }, + { + "Answer": 23, + "Options": "a ) 20 , b ) 23 , c ) 27 , d ) 150 , e ) 255", + "Correct": "b", + "Explanation": "\"explanation : we know ( x + y ) 2 = x 2 + y 2 + 2 xy = > ( x + y ) 2 = 289 + 2 ( 120 ) = > ( x + y ) = 529 \u2212 \u2212 \u2212 \u221a = 23 option b\"" + }, + { + "Answer": 165, + "Options": "a ) a ) 145 , b ) b ) 148 , c ) c ) 165 , d ) d ) 153 , e ) e ) 158", + "Correct": "c", + "Explanation": "\"d = d * q + r d = 18 * 9 + 3 d = 162 + 3 d = 165 answer : c\"" + }, + { + "Answer": 16, + "Options": "a ) 16 , b ) 12 , c ) 18 , d ) 22 , e ) 08", + "Correct": "a", + "Explanation": "2 * 8 = 16 . answer is a ." + }, + { + "Answer": 62.99999999999999, + "Options": "a ) 35 , b ) 45 , c ) 25 , d ) 63 , e ) 55", + "Correct": "d", + "Explanation": "\"a : b : c = 10 \u00d7 7 : 12 \u00d7 5 : 15 \u00d7 3 = 2 \u00d7 7 : 12 \u00d7 1 : 3 \u00d7 3 = 14 : 12 : 9 amount that c should pay = 245 \u00d7 9 / 35 = 7 \u00d7 9 = 63 answer is d\"" + }, + { + "Answer": 28000, + "Options": "a ) 28029 , b ) 28000 , c ) 28001 , d ) 28012 , e ) 28129", + "Correct": "b", + "Explanation": "suppose b invested rs . x for y months . then , a invested rs . 3 x for 2 y months . so , a : b = ( 3 x * 2 y ) : ( x * y ) = 6 xy : xy = 6 : 1 . b ' s profit : total profit = 1 : 7 . let the total profit be rs . x then , 1 / 7 = 4000 / x or x = 28000 . answer : b" + }, + { + "Answer": 0.4666666666666667, + "Options": "a ) 1 / 3 , b ) 3 / 5 , c ) 7 / 15 , d ) 11 / 30 , e ) 17 / 30", + "Correct": "c", + "Explanation": "\"p ( red or blue ) = 1 - p ( white ) - p ( green ) = 15 / 15 - 5 / 15 - 3 / 15 = 7 / 15 the answer is c .\"" + }, + { + "Answer": 11, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 11", + "Correct": "e", + "Explanation": "one way of solving this is : speed of boat on still water ( lake ) = 10 kmph speed upstream = 9 kmph = speed in still water - speed of river = > speed of river = 1 kmph = > speed downstream = speed in still water + speed of river = 10 + 1 = 11 kmph ans is e" + }, + { + "Answer": 73, + "Options": "a ) 56 , b ) 65 , c ) 73 , d ) 89 , e ) 90", + "Correct": "c", + "Explanation": "\"a + b + c = 3 * 50 = 150 a + b + c + d = 4 * 53 = 212 - - - - ( i ) so , d = 62 & e = 62 + 3 = 65 b + c + d + e = 51 * 4 = 204 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 212 \u2013 204 = 8 a = e + 8 = 65 + 8 = 73 answer : c\"" + }, + { + "Answer": 2000, + "Options": "a ) 2400 , b ) 2403 , c ) 3998 , d ) 2539 , e ) 2000", + "Correct": "e", + "Explanation": "\"e 2000 let the amount with r be $ r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 5000 - r ) = > 3 r = 10000 - 2 r = > 5 r = 10000 = > r = 2000 .\"" + }, + { + "Answer": 30, + "Options": "a ) 24 , b ) 30 , c ) 48 , d ) 60 , e ) 120", + "Correct": "b", + "Explanation": "paint one of the faces red and make it the top face . 5 options for the bottom face . now , four side faces can be painted in ( 4 - 1 ) ! = 3 ! = 6 ways ( circular arrangements of 4 colors ) . total = 5 * 6 = 30 . answer : b ." + }, + { + "Answer": 36.4, + "Options": "a ) $ 36.4 , b ) $ 37.10 , c ) $ 37.16 , d ) $ 38.10 , e ) $ 38.80", + "Correct": "a", + "Explanation": "\"principal that is amount taken by laura at year beginning = 35 $ rate of interest = 4 % interest = ( 4 / 100 ) * 35 = 1.4 $ total amount that laura owes a year later = 35 + 1.4 = 36.4 $ answer a\"" + }, + { + "Answer": 15, + "Options": "a ) 21 , b ) 20 , c ) 15 , d ) 10 , e ) 9", + "Correct": "c", + "Explanation": "\"number start between 10 to 40 is 30 numbers half of them is even . . which is 15 answer : c\"" + }, + { + "Answer": 8, + "Options": "a ) 3 , b ) 5 , c ) 8 , d ) 13 , e ) 15", + "Correct": "c", + "Explanation": "\"total # of students = 35 avg # of books per student = 2 total # of books = 35 * 2 = 70 # of student borrowed at least 3 books = 35 - 2 - 12 - 10 = 11 # of books borrowed by above 11 students = 70 - ( 12 * 1 ) + ( 10 * 2 ) = 38 considering that 10 out of above 11 students borrowed only 3 books , # of books borrowed = 10 * 3 = 30 so maximum # of books borrowed by any single student = 38 - 30 = 8 option c\"" + }, + { + "Answer": 65, + "Options": "a ) $ 20 , b ) $ 65 , c ) $ 50 , d ) $ 80 , e ) $ 100", + "Correct": "b", + "Explanation": "\"deargoodyear 2013 , i ' m happy to help . this is a relatively straightforward problem , not very challenging . btw , crazy eddiewas the actually name of an electronics chain on the east coast of the usa back in the 1970 s . manufacturing now is $ 50 . they now are making a 50 % profit , so the selling price must be $ 100 . they had this same selling price , $ 100 , before they made the change , and had a profit of 35 % , so the manufacturing must have been $ 65 . answer = ( b ) .\"" + }, + { + "Answer": 50, + "Options": "a ) 25 % , b ) 32.5 % , c ) 37 % , d ) 50 % , e ) 40 %", + "Correct": "d", + "Explanation": "what % less of 14 is 7 let it be x % less , then = 14 ( 1 - x / 100 ) = 7 1 - x / 100 = 7 / 14 x = 100 / 2 x = 50 % ans d" + }, + { + "Answer": 4, + "Options": "a ) 4 , b ) 6 , c ) 10 , d ) 16 , e ) 18", + "Correct": "a", + "Explanation": "a = 2 m = m + 8 m = 8 a = 16 a = 4 b , and so b = 4 the answer is a ." + }, + { + "Answer": 70, + "Options": "a ) $ 20 , b ) $ 40 , c ) $ 50 , d ) $ 70 , e ) $ 100", + "Correct": "d", + "Explanation": "\"deargoodyear 2013 , i ' m happy to help . this is a relatively straightforward problem , not very challenging . btw , crazy eddiewas the actually name of an electronics chain on the east coast of the usa back in the 1970 s . manufacturing now is $ 50 . they now are making a 50 % profit , so the selling price must be $ 100 . they had this same selling price , $ 100 , before they made the change , and had a profit of 30 % , so the manufacturing must have been $ 70 . answer = ( d ) .\"" + }, + { + "Answer": 8, + "Options": "a ) 8 , b ) 12 , c ) 16 , d ) 24 , e ) 36", + "Correct": "a", + "Explanation": "\"i ' m going to focus on denominator only . . ( 2 ^ 16 ) . ( ( 3 ^ 4 ) ^ k = 18 ^ 16 ( 2 ^ 16 ) . ( ( 3 ^ 4 k ) = ( 2 . 3 ^ 2 ) ^ 16 ( 2 ^ 16 ) . ( ( 3 ^ 4 k ) = ( 2 ^ 24 ) . ( 3 ^ 2 ) ^ 16 hence 4 k = 32 k = 8 answer a i hope it ' s quite clear\"" + }, + { + "Answer": 13, + "Options": "a ) 10 , b ) 15 , c ) 13 , d ) 11 , e ) 9", + "Correct": "c", + "Explanation": "\"age of the 25 th student = 25 * 25 - ( 10 * 22 + 14 * 28 ) = 625 - 612 = 13 years answer is c\"" + }, + { + "Answer": 6, + "Options": "a ) 12 , b ) 6 , c ) 9 , d ) 15 , e ) 7", + "Correct": "b", + "Explanation": "360 / 60 = 6 the answer is b ." + }, + { + "Answer": 69, + "Options": "a ) 65 , b ) 67 , c ) 68 , d ) 69 , e ) 50", + "Correct": "d", + "Explanation": "explanation : let the sum of current ages of 6 persons = x given average age of 6 person after 2 years = 43 = > x + 6 ( 2 ) / 6 = 43 = > x + 12 = 258 = x = 246 let the seventh ' s person age will be y given current average age of 7 persons = 45 [ sum of current 6 person ' s age ( x ) + seventh person ' s age ( y ) ] / 7 = 45 = > 246 + y = 45 ( 7 ) = > y = 315 - 246 = > y = 69 hence seventh person ' s age = 69 hence ( d ) is the correct answer . answer : d" + }, + { + "Answer": 2025, + "Options": "a ) 3000 , b ) 4200 , c ) 2025 , d ) 1205 , e ) 3251", + "Correct": "c", + "Explanation": "\"1800 * 9 / 8 * 9 / 8 = 2025 answer : c\"" + }, + { + "Answer": 11, + "Options": "a ) 4 , b ) 6 , c ) 11 , d ) 12 , e ) 15", + "Correct": "c", + "Explanation": "\"the question basically asks how many positive odd integers less than 110 are odd multiples of 5 so we have 5 , 15,25 , 35,45 , . . and 105 = 11 ans c\"" + }, + { + "Answer": 20, + "Options": "a ) 20 , b ) 28 , c ) 30 , d ) 35 , e ) 40", + "Correct": "a", + "Explanation": "\"let b : y : g = 3 x : 7 x : 8 x . 3 x + 7 x + 8 x = 18 x = 72 - - > x = 4 . g - b = 8 x - 3 x = 5 x = 20 . the answer is a .\"" + }, + { + "Answer": 5, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "e", + "Explanation": "solve for x : 5 x + 3 = 10 x - 22 25 = 5 x 5 = x correct answer e ) 5" + }, + { + "Answer": 39, + "Options": "a ) 67 sec , b ) 89 sec , c ) 39 sec , d ) 87 sec , e ) 45 sec", + "Correct": "c", + "Explanation": "\"speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 270 + 120 = 390 m . time taken = 390 / 10 = 39 sec . answer : c\"" + }, + { + "Answer": 30, + "Options": "a ) - 30 , b ) + 30 , c ) 0 , d ) 27 , e ) 47", + "Correct": "b", + "Explanation": "the absolute values of + 47 and - 27 are 47 and 27 respectively ; and their difference = 47 \u2013 27 = 30 . ( + 47 ) + ( - 27 ) = + 30 answer : b" + }, + { + "Answer": 800, + "Options": "a ) 800 , b ) 900 , c ) 100 , d ) 1000 , e ) 950", + "Correct": "a", + "Explanation": "\"to solve we will set up a proportion . we know that \u201c 100 million vehicles is to 40 accidents as 2 billion vehicles is to x accidents \u201d . to express everything in terms of \u201c millions \u201d , we can use 2,000 million rather than 2 billion . creating a proportion we have : 100 / 40 = 2,000 / x cross multiplying gives us : 100 x = 2,000 * 40 x = 20 * 40 = 800 answer : a\"" + }, + { + "Answer": 3.0892857142857144, + "Options": "a ) 195 / 63 , b ) 145 / 63 , c ) 155 / 63 , d ) 3.089 , e ) 185 / 63", + "Correct": "d", + "Explanation": "\"( \u221a 1.21 ) / ( \u221a 0.64 ) + ( \u221a 1.44 ) / ( \u221a 0.49 ) 11 / 8 + 12 / 7 = > 3.089 answer is d\"" + }, + { + "Answer": 4, + "Options": "a ) 8 , b ) can not be determined , c ) 4 , d ) 6 , e ) 9", + "Correct": "b", + "Explanation": "yes , the correct answer is b" + }, + { + "Answer": 75, + "Options": "a ) 20 , b ) 25 , c ) 40 , d ) 45 , e ) 75", + "Correct": "e", + "Explanation": "\"there are 5 days so the sum of temperature can be 60 * 5 = 300 lowest is 45 . to find the maximum range we can say the temperature was the lowest for 4 of the 5 days so 4 * 45 = 180 . on the fifth day it is 300 - 180 = 120 range is therefore 120 - 45 = 75 answer e\"" + }, + { + "Answer": 26, + "Options": "a ) 21 , b ) 26 , c ) 27 , d ) 22 , e ) 29", + "Correct": "b", + "Explanation": "explanation : total of the 9 digits - 9 * 18 = 162 total of the 4 digits - 4 * 8 = 32 total of the remaining 5 digits - 162 - 32 = 130 average of the remaining 3 numbers = 130 / 5 = 26 answer : b" + }, + { + "Answer": 8, + "Options": "a ) 2 , b ) 8 , c ) 6 , d ) 9 , e ) 0", + "Correct": "b", + "Explanation": "\"any power of anything ending in 5 always has a units digit of 5 . so the first term has a units digit of 5 . 2 nd part 3 ^ 45 has a units digit of 3 therefore , the second term has a units digit of 3 . of course 5 + 3 = 8 , so something with a units digit of 5 plus something with a units digit of 3 answer = b\"" + }, + { + "Answer": 2052, + "Options": "a ) 4038 , b ) 8076 , c ) 2052 , d ) 4845.6 , e ) none of these", + "Correct": "c", + "Explanation": "\"\u2235 amount , he have spent in 1 month on clothes transport = amount spent on saving per month \u2235 amount , spent on clothes and transport = 24624 \u2044 12 = 2052 answer c\"" + }, + { + "Answer": 0.65, + "Options": "a ) 4 / 5 , b ) 8 / 15 , c ) 11 / 15 , d ) 9 / 20 , e ) 13 / 20", + "Correct": "e", + "Explanation": "\"( 1 / 2 ) x = ( 1 / 4 ) y ( 1 / 4 ) y + ( 2 / 5 ) y = ( 13 / 20 ) y the answer is e .\"" + }, + { + "Answer": 11.709999999999994, + "Options": "a ) 16.16 % , b ) 15.25 % , c ) 14.14 % , d ) 13.33 % , e ) 11.71 %", + "Correct": "e", + "Explanation": "\"( 100 % + 9 % ) * ( 100 % - 19 % ) = 1.09 * . 81 = 0.8829 . 1 - 0.8829 = 11.71 % lost = - 11.71 % the answer is e the organization has lost 11.71 % of its total volunteers from fall to spring .\"" + }, + { + "Answer": 66.9, + "Options": "a ) 35.67 % , b ) 66.90 % , c ) 68.57 % , d ) 69.57 % , e ) none of these", + "Correct": "b", + "Explanation": "\"girls = 900 , boys = 1100 passed = ( 34 % of 1100 ) + ( 32 % of 900 ) = 374 + 288 = 662 failed = 2000 - 662 = 1338 failed % = [ ( 1338 / 2000 ) x 100 ] % = 66.9 % . answer : b\"" + }, + { + "Answer": 30, + "Options": "a ) 50 , b ) 78 , c ) 30 , d ) 29 , e ) 27", + "Correct": "c", + "Explanation": "\"a + b + c = 500 a + c = 200 b + c = 330 - - - - - - - - - - - - - - a + b + 2 c = 530 a + b + c = 500 - - - - - - - - - - - - - - - - c = 30 answer : c\"" + }, + { + "Answer": 25.000000000000533, + "Options": "a ) 96 , b ) 75 , c ) 48 , d ) 25 , e ) 12", + "Correct": "d", + "Explanation": "\"by the definition of a remainder , the remainder here is equal to 4 / y . the remainder in decimal form is given as . 16 therefore , 4 / y = . 16 solve for y and get 25 . d\"" + }, + { + "Answer": 8, + "Options": "a ) 8 liters , b ) 10 liters , c ) 12 liters , d ) 15 liters , e ) 18 liters", + "Correct": "a", + "Explanation": "\"1 st ratio = 3 : 2 2 nd ratio = 3 : 5 difference of cross products ratio = 3 * 5 - 3 * 2 = 9 common factor of the 1 st ratio = ( quantity replaced / sum of terms in 1 st ratio ) + ( quantity replaced * term a in 2 nd ratio / difference ) = ( 5 / 5 ) + ( 5 * 3 / 9 ) = 1 + 5 / 3 = 2.67 quantity of a = 3 * 2.67 = 8 liters approximately answer is a\"" + }, + { + "Answer": 10, + "Options": "a ) 5 , b ) 8 , c ) 10 , d ) 20 , e ) 25", + "Correct": "c", + "Explanation": "\"50 = 2 * 5 ^ 2 if 50 divides n ^ 2 , then n must be divisible by 2 * 5 = 10 the answer is c .\"" + }, + { + "Answer": 25, + "Options": "a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29", + "Correct": "a", + "Explanation": "\"present age = x before 7 yrs , y = x - 7 after 7 yrs , z = x + 7 by the qn , x + ( x - 7 ) = 29 2 x - 7 = 29 2 x = 29 + 7 x = 36 / 2 x = 18 z = x + 7 = 18 + 7 = 25 answer : a\"" + }, + { + "Answer": 0.2222222222222222, + "Options": "a ) 1 / 9 , b ) 2 / 9 , c ) 4 / 9 , d ) 3 / 9 , e ) 2 / 27", + "Correct": "b", + "Explanation": "\"we just need to find the factor thats all , w - > quadrupled - > 4 w d - > doubled - > 2 d z - > tripled - > 3 z hence , z ^ 2 = 9 z ^ 2 w is in numerator , and d * z in denominator . hence , additional factor being introduced = 4 / 2 * 9 = 4 / 18 = 2 / 9 = b\"" + }, + { + "Answer": 60, + "Options": "a ) 32 , b ) 60 , c ) 27 , d ) 29 , e ) 21", + "Correct": "b", + "Explanation": "let the number of boys be x . number of girls is 120 - x . total number of chocolates received by boys and girls = 2 x + 3 ( 120 - x ) = 300 = > 360 - x = 300 = > x = 60 . so , the number of boys or girls is 60 . answer : b" + }, + { + "Answer": 20, + "Options": "a ) 30 , b ) 40 , c ) 20 , d ) 10 , e ) 25", + "Correct": "c", + "Explanation": "milk : water = 3 : 2 after adding 10 liters of water milk : water = 2 : 3 olny water patrs increase when mixture of water milk : wate = 3 : 2 = 2 * ( 3 : 2 ) = 6 : 4 after adding 10 liters of water milk : water = 2 : 3 = 3 * ( 2 : 3 ) = 6 : 9 option ' c '" + }, + { + "Answer": 15, + "Options": "a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 19", + "Correct": "c", + "Explanation": "\"35 ! has 3 , 6 , 9 , . . . . 30 , 33 as factors , which are 11 multiples of 3 . we need to add 4 more to these 11 because of 9 , 18 , and 27 . the greatest integer of k is 15 . the answer is c .\"" + }, + { + "Answer": 2.4479999999994106, + "Options": "a ) s . 2.04 , b ) s . 2.08 , c ) s . 2.02 , d ) s . 2.83 , e ) s . 2.45", + "Correct": "e", + "Explanation": "\"c . i . when interest is compounded yearly = [ 6000 * ( 1 + 4 / 100 ) * ( 1 + ( 1 / 2 * 4 ) / 100 ] = 6000 * 26 / 25 * 51 / 50 = rs . 6364.8 c . i . when interest is compounded half - yearly = [ 6000 * ( 1 + 2 / 100 ) 2 ] = ( 6000 * 51 / 50 * 51 / 50 * 51 / 50 ) = rs . 6367.25 difference = ( 6367.25 - 6364.8 ) = rs . 2.45 . answer : e\"" + }, + { + "Answer": 990, + "Options": "a ) 600 , b ) 700 , c ) 990 , d ) 900 , e ) none", + "Correct": "c", + "Explanation": "\"solution : let x be the number i chose , then x / 9 \u00e2 \u02c6 \u2019 100 = 10 x / 9 = 110 x = 990 answer c\"" + }, + { + "Answer": 2000.0000000000002, + "Options": "a ) 2000 , b ) 500 , c ) 900 , d ) 1600 , e ) none", + "Correct": "a", + "Explanation": "\"answer 2.5 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ] = 2.5 x [ ( 36 x 48 x 250 ) / ( 12 x 9 x 5 ) ] = 2.5 x 4 x 4 x 50 = 2000 correct option : a\"" + }, + { + "Answer": 25, + "Options": "a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 40 %", + "Correct": "b", + "Explanation": "clearly , the retailer gets 1 dozen out of 4 dozens free . equivalent discount = 1 / 4 * 100 = 25 % . answer b ) 25 %" + }, + { + "Answer": 9, + "Options": "a ) $ 9 , b ) $ 12 , c ) $ 13.20 , d ) $ 15 , e ) $ 16.80", + "Correct": "a", + "Explanation": "3 j + 2 s = 69 2 j + 3 s = 61 - - - - - - - - - - - - - - - - 5 j + 5 s = 130 - - - - ( divide by 5 ) - - - > j + s = 26 3 j + 2 s = j + 2 ( j + s ) = j + 52 = 69 - - - > j = 17 3 * 17 + 2 s = 69 51 + 2 s = 69 2 s = 18 s = 9 answer : a" + }, + { + "Answer": 877.4, + "Options": "a ) rs . 849.40 , b ) rs . 877.40 , c ) rs . 901.60 , d ) rs . 815.20 , e ) none of these", + "Correct": "b", + "Explanation": "let the costs of each kg of apples and each kg of rice be rs . a and rs . r respectively . 10 a = 24 r and 6 * 20.50 = 2 r a = 12 / 5 r and r = 61.5 a = 147.6 required total cost = 4 * 147.6 + 3 * 61.5 + 5 * 20.5 = 590.4 + 184.5 + 102.5 = rs . 877.40 answer : b" + }, + { + "Answer": 12.5, + "Options": "a ) 12.5 % , b ) 13 % , c ) 13.15 % , d ) 14 % , e ) 15 %", + "Correct": "a", + "Explanation": "\"quantity x rate = price 1 x 1 = 1 0.7 x 1.25 = 0.875 decrease in price = ( 0.125 / 1 ) \u00d7 100 = 12.5 % a )\"" + }, + { + "Answer": 2, + "Options": "a ) x = 2 , b ) x = 5 , c ) x = 8 , d ) 10 , e ) 11", + "Correct": "a", + "Explanation": "really hard . but let ' s start with few concepts : 1 . square of an odd integer will be odd . 2 . difference of odd and odd will be even . 3 . any odd integer can be expressed as difference of two squares . 4 . an even integer can be expressed as difference of two squares only if that even integer is a multiple of 4 . assume two odd integers to be ( 2 x - 1 ) and ( 2 x + 1 ) . difference of their squares = ( 2 x + 1 ) ^ 2 - ( 2 x - 1 ) ^ 2 = 4 x ^ 2 + 1 + 4 x - ( 4 x ^ 2 + 1 - 4 x ) = 4 x ^ 2 + 1 + 4 x - 4 x ^ 2 - 1 + 4 x = 8 x now root of 8 x needs to be an integer such that it is equal to the sum of the digits of the two odd integers . 8 = 2 ^ 3 , so x needs to be such that itcompletesa perfect square . if we find x , we can find the value of 2 x + 1 ( larger integer ) and then sum of its digits . let ' s check the options , starting with c . for sum to be 8 , few possibilities are : 17 , 35 , 53 , 71 if we take 17 , the pair is 15 and 17 , meaning x = 8 . 8 x = 64 root of 64 = 4 but 4 is not equal to 1 + 5 + 1 + 7 . reject . if we take 35 , the pair is 33 and 35 , meaning x = 17 . 8 x = 8 * 17 reject since perfect square is not possible . if we take 53 , the pair is 51 and 53 , meaning x = 26 . 8 x = 8 * 26 reject since perfect square is not possible . if we take 71 , the pair is 69 and 71 , meaning x = 35 . 8 x = 8 * 35 reject since perfect square is not possible . i tried each option and the possibilities and then got lost . then , it occurred to me that i was only checking 2 - digit integers . what about 3 - digits ? starting with option a , only 2 - digit odd integer whose sum is 2 is 101 . if we take 101 , the pair is 99 and 101 , meaning x = 50 . 8 x = 8 * 50 = 400 root of 400 = 20 which is indeed equal to 9 + 9 + 1 + 1 . answer ( a ) ." + }, + { + "Answer": 87, + "Options": "a ) 55 , b ) 60 , c ) 73 , d ) 81 , e ) 87", + "Correct": "e", + "Explanation": "\"let the number of correct responses be x then the number of incorrect responses = 100 - x according to question x - 2 ( 100 - x ) = 61 ( subtracting twice of incorrect from correct ) 3 x = 261 x = 87 answer : e\"" + }, + { + "Answer": 14, + "Options": "a ) $ 14 , b ) $ 2 , c ) $ 10 , d ) $ 6 , e ) $ 8", + "Correct": "a", + "Explanation": "sale price ( sp ) = 210 + markup ( mp ) - - > mp = sp - 210 and given mp = sp / 4 ( 25 % is 1 / 4 th ) so sp / 4 = sp - 210 3 sp / 4 = 210 sp = 280 now a discount of 20 % is given so new sp is . 8 * 280 = 224 profit = 224 - 210 = 14 answer is a" + }, + { + "Answer": 33, + "Options": "a ) 50 , b ) 72 , c ) 25 , d ) 92 , e ) 33", + "Correct": "e", + "Explanation": "\"a 2 - b 2 = 5 : given a 4 + b 4 - 2 a 2 b 2 = 52 : square both sides and expand . a * b = 2 : given a 2 b 2 = 22 : square both sides . a 4 + b 4 - 2 ( 4 ) = 25 : substitute a 4 + b 4 = 33 correct answer e\"" + }, + { + "Answer": 4800, + "Options": "a ) 4500 , b ) 4250 , c ) 4350 , d ) 4800 , e ) 4150", + "Correct": "d", + "Explanation": "\"explanation : to solve this use the formula of ap , sn = ( n / 2 ) ( a + l ) . . . . . . . . . . . . . . . . ( 1 ) to find n , use = > tn = a + ( n - 1 ) d = > 79 = 1 + ( n - 1 ) 2 = > n = 40 use value of n in ( 1 ) then , sn = ( 40 / 2 ) ( 1 + 79 ) = 1600 ans : - 3 ( sn ) = 4800 answer : d\"" + }, + { + "Answer": 26.470588235294116, + "Options": "a ) 24 , b ) 25 , c ) 23 , d ) 22 , e ) 26.5", + "Correct": "e", + "Explanation": "step 1 ) took lcm of 25 and 30 . . came as 150 . step 2 ) 150 distance between b to c . . . do 150 / 30 hence 5 gallons used step 3 ) twice distance . . hence 150 * 2 = 300 . . . do as above . . 300 / 25 = 12 gallons used step 4 ) total gallons . . 5 + 12 = 17 gallons step ) total miles = 150 + 300 = 450 miles hence . . average of whole journey = 450 / 17 which comes to 26.5 answer : e" + }, + { + "Answer": 2, + "Options": "a ) 2 , b ) 3 , c ) 5 , d ) 8 , e ) 10", + "Correct": "a", + "Explanation": "any odd number square will give odd number only . . similarly wen we add 2 odd numbers we will get even number . . wen we multiply 2 even owe will get even nuber . . so the result of the above expression is an even number only . . hence it is divisible by 2 . . . answer : a" + }, + { + "Answer": 50, + "Options": "a ) 50 , b ) 60 , c ) 75 , d ) 80 , e ) 85", + "Correct": "a", + "Explanation": "\"( x + x 1 + . . . x 14 ) / 15 = 40 50 option a\"" + }, + { + "Answer": 25, + "Options": "a ) 5 % , b ) 10 % , c ) 15 % , d ) 25 % , e ) none", + "Correct": "d", + "Explanation": "solution required percentage \u2039 = \u203a [ 20 / ( 100 - 20 ) x 100 ] % \u2039 = \u203a 25 % answer d" + }, + { + "Answer": 191.4, + "Options": "a ) 151 , b ) 149 , c ) 152 , d ) 191.4 , e ) none of the above", + "Correct": "d", + "Explanation": "\"corrected mean = 190 \u00d7 25 \u2212 130 + 165 / 25 = 4750 + 35 / 25 = 4785 / 25 = 191.4 answer d\"" + }, + { + "Answer": 1.6666666666666667, + "Options": "a ) 1.78 , b ) 1.667 , c ) 1.15 , d ) 1.5 , e ) 1.2", + "Correct": "b", + "Explanation": "m = 5 s = x ds = 5 + x us = 5 - x 5 + x = ( 5 - x ) 2 5 + x = 10 - 2 x 3 x = 5 x = 1.667 answer : b" + }, + { + "Answer": 6.46, + "Options": "a ) $ 3.36 , b ) $ 6.46 , c ) $ 8.46 , d ) $ 10.08 , e ) $ 11.85", + "Correct": "b", + "Explanation": "answer = b 2 * 1.49 + 4 * 0.87 = 2 ( 1.50 - 0.01 ) + 4 ( 1.00 - 0.13 ) = 3 + 4 - 0.02 - 0.52 = 7 - 0.54 = 6.46" + }, + { + "Answer": 1800, + "Options": "a ) $ 1500 , b ) $ 1600 , c ) $ 1700 , d ) $ 1800 , e ) $ 1900", + "Correct": "d", + "Explanation": "\"if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 450 . so 1 / 4 of her savings is $ 450 . so her original savings are 4 times $ 450 = $ 1800 correct answer d\"" + }, + { + "Answer": 650, + "Options": "a ) 278 , b ) 277 , c ) 278 , d ) 450 , e ) 650", + "Correct": "e", + "Explanation": "\"10 * 150 = 1500 1 * 100 + 5 * 150 = 850 1500 \u2013 850 = 650 answer : e\"" + }, + { + "Answer": 29, + "Options": "a ) 21 , b ) 25 , c ) 29 , d ) 33 , e ) 37", + "Correct": "c", + "Explanation": "\"29 / 4 \u00f7 4 = 29 / 16 pounds in each container 29 / 16 pounds * 16 ounces / pound = 29 ounces in each container the answer is c .\"" + }, + { + "Answer": 45, + "Options": "a ) [ 25 ] , b ) [ 135 ] , c ) [ 30 ] , d ) [ 90 ] , e ) [ 45 ]", + "Correct": "e", + "Explanation": "[ 9 ] * [ 10 ] = 27 * 5 = 135 = 3 * 45 = [ 45 ] the answer is e ." + }, + { + "Answer": 0.41666666666666663, + "Options": "a ) 0 , b ) 1 / 12 , c ) 5 / 12 , d ) 7 / 18 , e ) 4 / 9", + "Correct": "c", + "Explanation": "\"total # of outcomes is 6 * 6 = 36 ; favorable outcomes : a - b - - > prime 1 - 1 - - > 2 ; 1 - 2 - - > 3 ; 2 - 1 - - > 3 ; 1 - 4 - - > 5 ; 4 - 1 - - > 5 ; 2 - 3 - - > 5 ; 3 - 2 - - > 5 ; 1 - 6 - - > 7 ; 6 - 1 - - > 7 ; 2 - 5 - - > 7 ; 5 - 2 - - > 7 ; 3 - 4 - - > 7 ; 4 - 3 - - > 7 ; 6 - 5 - - > 11 ; 5 - 6 - - > 11 . total of 15 favorable outcomes q = 15 / 36 . answer : c .\"" + }, + { + "Answer": 78.5, + "Options": "a ) 76 kg , b ) 77 kg , c ) 78.5 kg , d ) data inadequate , e ) none of these", + "Correct": "c", + "Explanation": "\"total weight increases = 9 \u00d7 1.5 = 13.5 kg so the weight of new person = 65 + 13.5 = 78.5 kg answer c\"" + }, + { + "Answer": 1199.9999999999998, + "Options": "a ) 1000 , b ) 2217 , c ) 1200 , d ) 2777 , e ) 2991", + "Correct": "c", + "Explanation": "\"1344 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 1200 answer : c\"" + }, + { + "Answer": 128, + "Options": "a ) 128 , b ) 142 , c ) 143 , d ) 141 , e ) 129", + "Correct": "e", + "Explanation": "\"minimum three digit number is 100 and maximum three digit number is 999 . the first three digit number that leaves remainder 5 when divided by 7 is 103 . 14 * 7 = 98 + 5 = 103 the second three digit number that leaves remainder 5 when divided by 7 is 110 . 15 * 7 = 105 + 5 = 110 the third three digit number that leaves remainder 5 when divided by 7 is 117 and so on the last three digit number that leaves remainder 5 when divided by 7 is 999 142 * 7 = 994 + 5 = 999 therefore , we identify the sequence 103 , 110,117 . . . . . 999 use the formula of last term last term = first term + ( n - 1 ) * common difference you will get the answer 129 that is definitely e .\"" + }, + { + "Answer": 11, + "Options": "a ) 20 , b ) 18 , c ) 16 , d ) 11 , e ) 5", + "Correct": "d", + "Explanation": "\"add these two equations 4 x + 4 y = 22 divide by 2 ( to get 2 x + 2 y ) answer will be d . 11\"" + }, + { + "Answer": 19500, + "Options": "a ) 9500 , b ) 17500 , c ) 18200 , d ) 19500 , e ) 6750", + "Correct": "d", + "Explanation": "total salary paid to thomas in one week : 4550 / - salary for one day : 4550 / 7 = 650 / - total for one month = 650 / - * 30 days = 19500 / - answer is option ( d )" + }, + { + "Answer": 0.5, + "Options": "a ) 1 / 2 , b ) 2 / 5 , c ) 3 / 5 , d ) 3 / 10 , e ) 7 / 10", + "Correct": "a", + "Explanation": "the fraction of birds that are male parrots is ( 2 / 3 ) ( 3 / 5 ) = 2 / 5 . the fraction of birds that are male toucans is ( 1 / 4 ) ( 2 / 5 ) = 1 / 10 . the total fraction of male birds is 2 / 5 + 1 / 10 = 1 / 2 . the answer is a ." + }, + { + "Answer": 24, + "Options": "a ) $ 24 , b ) $ 80 , c ) $ 90 , d ) $ 120 , e ) $ 180", + "Correct": "a", + "Explanation": "\"let ' s let t = total number of dollars spent at the supermarket . with this variable we can set up an equation and determine t . we are given that john spent 1 / 4 of his money on fresh fruits and vegetables , or ( 1 / 4 ) t , 1 / 3 on meat products , or ( 1 / 3 ) t , and 1 / 6 on bakery products , or ( 1 / 6 ) t . we are also given that he spent the remaining $ 6 on candy . since we know where all his money was allocated , we can sum these values together and set the sum to t . so we have : ( 1 / 4 ) t + ( 1 / 3 ) t + ( 1 / 6 ) t + 6 = t to get rid of the fractions we can multiply the entire equation by 12 , and we obtain : 3 t + 4 t + 2 t + 72 = 12 t 9 t + 72 = 12 t 72 = 3 t t = 24 john spent $ 24 at the supermarket . answer : a\"" + }, + { + "Answer": 3, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "a", + "Explanation": "anything power by 10 we got 10 and some zeros after that . ( i . e , 1000000000000000 . . . . ) on that , we minus 7 means , we must get last two digits is 93 . and 93 is divided by 6 , we get reminder 3 . answer : a" + }, + { + "Answer": 7.5, + "Options": "a ) 7.5 kg , b ) 11 kg , c ) 30 kg , d ) 36.5 kg , e ) 71 kg", + "Correct": "a", + "Explanation": "\"after two persons leave the group the average remains the same . that means the weight of the two persons = 45 + 30 = 75 so , the average the two persons = 37.5 that gives the answer 45 - 37.5 = 7.5 answer a\"" + }, + { + "Answer": 8, + "Options": "a ) 16 . , b ) 8 . , c ) 7 . , d ) 2 . , e ) - 2 .", + "Correct": "b", + "Explanation": "\"given a + b = 14 = > a = 14 - b - - > eq 1 b + c = 9 c + d = 3 = > d = 3 - c - - > eq 2 then eqs 1 + 2 = > a + d = 14 - b + 3 - c = > 17 - ( b + c ) = > 17 - 9 = 8 . option b . . .\"" + }, + { + "Answer": 101, + "Options": "a ) 75 kg , b ) 65 kg , c ) 55 kg , d ) 85 kg , e ) 101 kg", + "Correct": "e", + "Explanation": "\"total weight increased = ( 8 x 4.5 ) kg = 36 kg . weight of new person = ( 65 + 36 ) kg = 101 kg . answer : e\"" + }, + { + "Answer": 30, + "Options": "a ) 25 , b ) 30 , c ) 90 , d ) 140 , e ) it can not be determined from the information given", + "Correct": "b", + "Explanation": "\"the arithmetic mean of a and b = ( a + b ) / 2 = 45 - - a + b = 90 - - 1 similarly for b + c = 120 - - 2 subtracting 1 from 2 we have c - a = 30 ; answer : b\"" + }, + { + "Answer": 9, + "Options": "a ) 9 , b ) 10 , c ) 12 , d ) 14 , e ) 16", + "Correct": "a", + "Explanation": "\"let ' s say age of richard isr age of david isd age of scott iss now richard is 6 years older than david , i . e . r = d + 6 david is 8 years older than scott i . e . d = s + 8 if in 8 years , richard will be twice as old as scott i . e . r + 8 = 2 x ( s + 8 ) i . e . r + 8 = 2 s + 16 i . e . r = 2 s + 8 but r = d + 6 = ( s + 8 ) + 6 = s + 14 therefore , 2 s + 8 = s + 14 i . e . s = 6 i . e . r = 20 i . e . d = 14 now , how old was david 5 years ago ? i . e . d - 5 = 14 - 5 = 9 years answer : option a\"" + }, + { + "Answer": 72, + "Options": "a ) 3 , b ) 6 , c ) 9 , d ) 72 , e ) 14", + "Correct": "d", + "Explanation": "let the number of each size of jar = wthen 1 / 4 w + 1 / 2 w + w = 42 1 3 / 4 w = 42 w = 24 the total number of jars = 3 w = 72 answer : d" + }, + { + "Answer": 216, + "Options": "a ) 216 , b ) 82 , c ) 80 , d ) 45 , e ) 36", + "Correct": "a", + "Explanation": "three digit number can have only following 3 patterns : a . all digits are distinct ; b . two digits are alike and third is different ; c . all three digits are alike . we need to calculate b . b = total - a - c total numbers from 700 to 999 = 299 ( 3 - digit numbers greater than 700 ) ; a . all digits are distinct = 3 * 9 * 8 = 216 answer : a" + }, + { + "Answer": 17.3, + "Options": "a ) 17.1 , b ) 17.3 , c ) 17.5 , d ) 17.7 , e ) 17.2", + "Correct": "b", + "Explanation": "\"29.94 / 1.45 = 299.4 / 14.5 = ( 2994 / 14.5 ) x 1 / 10 ) [ here , substitute 173 in the place of 2994 / 14.5 ] = 173 / 10 = 17.3 answer is b .\"" + }, + { + "Answer": 1, + "Options": "a ) 1 / 2 , b ) 1 / 4 , c ) 3 / 4 , d ) 2 / 3 , e ) 1", + "Correct": "e", + "Explanation": "\"explanation : a \u00e2 \u02c6 \u2014 b \u00e2 \u02c6 \u2014 c / b \u00e2 \u02c6 \u2014 c \u00e2 \u02c6 \u2014 d = 130 / 65 = > a / d = 2 d \u00e2 \u02c6 \u2014 e \u00e2 \u02c6 \u2014 f / c \u00e2 \u02c6 \u2014 d \u00e2 \u02c6 \u2014 e = 250 / 500 = > f / c = 1 / 2 a / d * f / c = 2 * 1 / 2 = 1 answer : e\"" + }, + { + "Answer": 23, + "Options": "a ) 20 , b ) 23 , c ) 169 , d ) 172 , e ) 198", + "Correct": "b", + "Explanation": "\"explanation : let the number be x and y . we know that , ( x + y ) 2 = ( x 2 + y 2 ) + 2 xy = 289 + 2 \u00d7 120 = 289 + 240 = 529 \u21d2 x + y = \u221a 529 = 23 correct option : b\"" + }, + { + "Answer": 3.6999999999999993, + "Options": "a ) 2.3 , b ) 2.6 , c ) 3.6 , d ) 3.7 , e ) 4.6", + "Correct": "d", + "Explanation": "sum of the remaining two numbers = ( 2.80 * 6 ) - [ ( 2.4 * 2 ) + ( 2.3 * 2 ) ] = 16.80 - ( 4.8 + 4.6 ) = 16.80 - 9.40 = 7.40 required average = ( 7.4 / 2 ) = 3.7 answer : d" + }, + { + "Answer": 81.00000000000001, + "Options": "a ) 63 , b ) 72 , c ) 81 , d ) 90 , e ) 99", + "Correct": "c", + "Explanation": "\"let x be the original weight . the weight of the grape pulp was 0.09 x . since the grape pulp is 81 % of the raisins , 0.09 x = 0.81 ( 9 kg ) . then x = 9 * 9 = 81 kg . the answer is c .\"" + }, + { + "Answer": 120, + "Options": "a ) 20 coins , b ) 50 coins , c ) 100 coins , d ) 120 coins , e ) none of these", + "Correct": "d", + "Explanation": "\"let number of each type of coin = x . then , 1 \u00d7 x + . 50 \u00d7 x + . 25 x = 210 \u21d2 1.75 x = 210 \u21d2 x = 120 coins answer d\"" + }, + { + "Answer": 5776, + "Options": "a ) 76 , b ) 5776 , c ) 304 , d ) 1296 , e ) none", + "Correct": "b", + "Explanation": "\"answer let \u221a n / 19 = 4 then \u221a n = 19 x 4 = 76 \u2234 n = 76 x 76 = 5776 . correct option : b\"" + }, + { + "Answer": 1150, + "Options": "a ) 1105 , b ) 1245 , c ) 1275 , d ) 1215 , e ) 1150", + "Correct": "e", + "Explanation": "\"$ 25 per packet of gasket in case a customer orders less than 10 in case a customer orders > 10 price per gasket = 25 * 4 / 5 = 20 a certain week the supplier sold 60 gasket 1 . he sold 20 % of the gaskets to x = 10 gaskets = 25 * 10 = 250 2 . he sold 30 % of the gaskets to y = 15 gaskets = 25 * 10 + 20 * 5 = 350 3 . he sold remaining 50 % to z = 25 gaskets = 25 * 10 = 250 + 20 * 15 = 550 thus , total money earned 250 + 350 + 550 = 1150 answer is e\"" + }, + { + "Answer": 3, + "Options": "a ) 5 , b ) 0 , c ) 1 , d ) 2 , e ) 3", + "Correct": "e", + "Explanation": "\"remainder will be number / 100 here as the divisor is two digit number = 12 . hence checking for the last two digits = 5 * 7 * 9 = 15 thus remainder = 3 . answer : e\"" + }, + { + "Answer": 87, + "Options": "a ) 75 , b ) 65 , c ) 87 , d ) 95 , e ) 80", + "Correct": "c", + "Explanation": "\"total increase in weight = 8 \u00d7 2.5 = 20 if x is the weight of the new person , total increase in weight = x \u2212 67 = > 20 = x - 67 = > x = 20 + 67 = 87 answer is c .\"" + }, + { + "Answer": 80, + "Options": "a ) 80 , b ) 8 , c ) 15 , d ) 21 , e ) 35", + "Correct": "a", + "Explanation": "\"solution - simply substitute 3 and 8 in equation in the place of a and b respectively . 3 # 8 = 3 * 8 - 8 + 8 ^ 2 = 24 - 8 + 64 = 80 . ans a\"" + }, + { + "Answer": 8, + "Options": "a ) 3 , b ) z = 4 , c ) z = 5 , d ) z = 6 , e ) z = 8", + "Correct": "e", + "Explanation": "\"the combinations could be { ( 1,240 ) , ( 2,120 ) , ( 3,80 ) , ( 4,60 ) , ( 5,48 ) , ( 6,40 ) , ( 8,30 ) , ( 10,24 ) , ( 12,20 ) , ) 15,16 ) , ( 16,15 ) , ( 20,12 ) , ( 24,10 ) , ( 30,8 ) , ( 40,6 ) , ( 48,5 ) , ( 60,4 ) , ( 80,3 ) , ( 120,2 ) , ( 240,1 ) } of these we are told 8 < = t < = 30 so we can remove these pairs , and we are left only with . { ( 8,30 , ( 10,24 ) , ( 12,20 ) , ( 15,16 ) , ( 16,15 ) , ( 20,12 ) , ( 24,10 ) , ( 30,8 ) } hence 8 . e\"" + }, + { + "Answer": 5, + "Options": "a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8", + "Correct": "b", + "Explanation": "\"f = n ( n - 3 ) f = 2 * n 2 n = n ( n - 3 ) = > 2 = n - 3 = > n = 5 answer b\"" + }, + { + "Answer": 27, + "Options": "a ) 27 , b ) 16 , c ) 38 , d ) 61 , e ) 83", + "Correct": "a", + "Explanation": "using the elimination method the option that fits this description is 27 7 - 2 = 5 ( unit ' s digit that exceeds its ten ' s digit by 3 ) 27 * 9 = 243 ( the product of the given number and the sum of its digits is equal to 175 ) answer : a" + }, + { + "Answer": 14.5, + "Options": "a ) 14.5 , b ) 13.5 , c ) 12.5 , d ) 17.5 , e ) 11.5", + "Correct": "a", + "Explanation": "explanation : given : 240 - 80 / 60 - 40 * 10 = ? substituting the coded symbols for mathematical operations , we get , 240 / 80 * 60 / 40 + 10 = ? 3 * 1.5 + 10 = 14.5 answer : a" + }, + { + "Answer": 861, + "Options": "a ) 427 , b ) 859 , c ) 869 , d ) 861 , e ) none of these", + "Correct": "d", + "Explanation": "\"solution required number = ( l . c . m . of 24 , 32 , 36 , 54 ) - 3 = 864 - 3 = 861 . answer d\"" + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 5 , c ) 4 , d ) 3 , e ) 2", + "Correct": "a", + "Explanation": "\"can be solved without much calculations . you are given that ( - 2 , - 3 ) is the center of the circle . point ( 5 , - 3 ) lies inside the circle - - - > the radius is lesser than distance of ( - 2 , - 3 ) from ( 5 , - 3 ) - - - > lesser than 7 units but the radius will also be greater than the distance of ( - 2 , - 3 ) from ( - 2,2 ) - - - - > greater than 5 units . thus the radius is > 5 but < 7 and as it is an integer , the only possible value of radius = 6 units . a is the correct answer .\"" + }, + { + "Answer": 75, + "Options": "a ) 20.23 , b ) 20.13 , c ) 75 , d ) 20.93 , e ) 10.93", + "Correct": "c", + "Explanation": "a : b = 1 : 3 b : c = 1 : 5 a : b : c = 1 : 3 : 15 15 / 19 * 95 = 75 answer : c" + }, + { + "Answer": 72, + "Options": "a ) 29 , b ) 72 , c ) 39 , d ) 37 , e ) 75", + "Correct": "b", + "Explanation": "\"average = ( 61 + 65 + 82 + 67 + 85 ) / 5 = 72 answer : b\"" + }, + { + "Answer": 7525, + "Options": "a ) 7500 , b ) 7525 , c ) 7550 , d ) 8000 , e ) none of these", + "Correct": "b", + "Explanation": "explanation : as per bodmas rule first we will solve the terms in the bracket then other . = 7500 + ( 25 ) = 7525 option b" + }, + { + "Answer": 0.5, + "Options": "a ) 1 / 2 , b ) 1 , c ) 2 , d ) 4 , e ) 8", + "Correct": "a", + "Explanation": "given : 7 / w + 7 / x = 7 / ywx = y find : ( w + x ) / 2 = ? 7 ( 1 / w + 1 / x ) = 7 ( 1 / y ) - divide both sides by 7 ( 1 / w + 1 / x ) = 1 / y ( x + w ) / wx = 1 / wx - sub ' d in y = wx x + w - 1 = 0 x + w = 1 therefore ( w + x ) / 2 = 1 / 2 ans : a" + }, + { + "Answer": 0.17857142857142858, + "Options": "a ) 7 / 72 , b ) 1 / 6 , c ) 7 / 36 , d ) 5 / 28 , e ) 21 / 36", + "Correct": "d", + "Explanation": "probability = no : of desired outcomes / total no : of outcomes . you are picking two slips out of 8 slips . so total no : of outcomes = 8 c 2 = 28 desired outcome : sum of the numbers on the two slips is equal to one of the numbers left in the box . how many such outcomes are there ? if you look at the numbers closely , you will see that the following pair of numbers will give you the desired outcome . ( 12 ) ( 23 ) ( 35 ) ( 58 ) ( 813 ) . there are 5 such pairs . if the two numbers which i pick is from any of these 5 pairs , then i get my desired outcome . so no : of desired outcomes = 5 probability = 5 / 28 answer : d" + }, + { + "Answer": 4.999999999999999, + "Options": "a ) - 1 , b ) 0 , c ) 5 , d ) 2 , e ) 3", + "Correct": "c", + "Explanation": "answer x = 1 + \u221a 2 \u2234 x 4 - 4 x 3 + 4 x 2 + 5 = x 2 ( x 2 - 4 x + 4 ) + 4 = x 2 ( x - 2 ) 2 + 4 = ( 1 + \u221a 2 ) 2 ( 1 + \u221a 2 - 2 ) 2 + 4 = ( \u221a 2 + 1 ) 2 ( \u221a 2 - 1 ) 2 + 4 = [ ( \u221a 2 ) 2 - ( 1 ) 2 ] 2 + 4 = ( 2 - 1 ) 2 = 1 + 4 = 5 correct option : c" + }, + { + "Answer": 50, + "Options": "a ) 25 , b ) 50 , c ) 90 , d ) 140 , e ) it can not be determined from the information given", + "Correct": "b", + "Explanation": "\"the arithmetic mean of a and b = ( a + b ) / 2 = 45 - - a + b = 90 - - 1 similarly for b + c = 140 - - 2 subtracting 1 from 2 we have c - a = 50 ; answer : b\"" + }, + { + "Answer": 120, + "Options": "a ) 6 , b ) 36 , c ) 120 , d ) 60 , e ) 72", + "Correct": "c", + "Explanation": "\"let total no of students in the class be n so , we are told that n is divisible by both 10 24 so , lets find the least common multiple of 10 24 , ie 120 so our answer is ( c ) 120\"" + }, + { + "Answer": 25, + "Options": "a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 25", + "Correct": "e", + "Explanation": "let initially each was having x bullets they shot 4 bullets so 5 x - 20 = x x = 5 so each was having 5 bullets . total was 25 . answer : e" + }, + { + "Answer": 4691, + "Options": "a ) 4857 , b ) 4184 , c ) 4012 , d ) 4691 , e ) 5291", + "Correct": "d", + "Explanation": "\"let the sale in the sixth month = x then ( 6735 + 6927 + 6855 + 7230 + 6562 + x ) / 6 = 6500 = > 6735 + 6927 + 6855 + 7230 + 6562 + x = 6 \u00d7 6500 = > 34309 + x = 39000 = > x = 39000 \u2212 34309 = 4691 answer : d\"" + }, + { + "Answer": 0.5, + "Options": "a ) 4 / 9 , b ) 1 / 2 , c ) 2 / 3 , d ) 1 / 3 , e ) 5 / 6", + "Correct": "b", + "Explanation": "j be the number of juniors and s be the number of seniors . there are 2 / 3 as many juniors as seniors 23 \u2217 s = j j / s = 23 going on trip = j 4 + 23 \u2217 s fraction = ( j 4 + 23 s ) / ( j + s ) = ( 2 / 3 * 1 / 4 + 2 / 3 ) / ( 2 / 3 + 1 ) = 1 / 2 fraction not on trip = 1 / 2 answer : b" + }, + { + "Answer": 12557, + "Options": "a ) s . 12557 , b ) s . 14993 , c ) s . 15560 , d ) s . 12589 , e ) s . 12500", + "Correct": "a", + "Explanation": "\"total sale for 5 months = rs . ( 4000 + 6524 + 5689 + 7230 + 6000 ) = rs . 29443 required sale = rs . [ ( 7000 x 6 ) - 29443 ] = rs . ( 42000 - 29443 ) = rs . 12557 . option a\"" + }, + { + "Answer": 62.5, + "Options": "a ) 62.50 % , b ) 60 % , c ) 70 % , d ) 65 % , e ) 66 / 3 %", + "Correct": "a", + "Explanation": "i just wanted to mention a couple of things here : * this is a pure ratio question ; the number 2000 is completely irrelevant , and you can ignore it if you like . when we increase something by 1 / 4 , we are multiplying it by 1 + 1 / 4 = 5 / 4 , so the answer here must be ( 1 / 2 ) * ( 5 / 4 ) = 5 / 8 = 62.50 % . answer : a" + }, + { + "Answer": 9.237333333333334, + "Options": "a ) 0.092 , b ) 0.92 , c ) 9.2 , d ) 92 , e ) 920", + "Correct": "c", + "Explanation": "f ( 69.28 \u00d7 0.004 ) / 0.03 1 . 0.004 = 4 \u00d7 10 ^ ( - 3 ) 2 . 0.03 = 3 \u00d7 10 ^ ( - 2 ) 3 . ( a \u00d7 b ) / c = a \u00d7 ( b / c ) 4 . 0.004 / 0.03 = 4 \u00d7 10 ^ ( - 3 ) / ( 3 \u00d7 10 ^ ( - 2 ) ) = 4 \u00d7 10 ^ ( - 3 - ( - 2 ) ) / 3 = 4 \u00d7 10 ^ ( - 1 ) / 3 = ( 4 / 3 ) \u00d7 10 ^ ( - 1 ) = 1.333 \u00d7 10 ^ ( - 1 ) therefore , ( 69.28 \u00d7 0.004 ) / 0.03 = 69.28 \u00d7 ( 0.004 / 0.03 ) = 69.28 \u00d7 1.33 \u00d7 10 ^ ( - 1 ) = 69.28 \u00d7 1.33 / 10 = 6.928 * 1.33 now , 7 \u00d7 2 = 14 7 \u00d7 1 = 7 or better : 6.9 \u00d7 1 = 6.9 6.9 \u00d7 2 = 13.8 hence , 6.9 < 6.928 \u00d7 1.33 < 13.8 9.2 is the only answer that satisfies this condition . c" + }, + { + "Answer": 8640, + "Options": "a ) 8600 , b ) 8610 , c ) 8620 , d ) 8630 , e ) 8640", + "Correct": "e", + "Explanation": "explanation : lcm of 27 - 18 - 16 - 15 is 2160 . after dividing 9999 by 2160 we get 1359 remainder . so answer will be 9999 - 1359 = 8640 option e" + }, + { + "Answer": 23, + "Options": "a ) 7 , b ) 13 , c ) 16 , d ) 21 , e ) 23", + "Correct": "e", + "Explanation": "\"general rule for such kind of problems : to maximize one quantity , minimize the others ; to minimize one quantity , maximize the others . thus to maximize the number of points of one particular player minimize the number of points of all other 11 players . minimum number of points for a player is 7 , so the minimum number of points of 11 players is 7 * 11 = 77 . therefore , the maximum number of points w for 12 th player is 100 - 77 = 23 . answer : e .\"" + }, + { + "Answer": 85, + "Options": "a ) 75 . , b ) 85 . , c ) 90 . , d ) 94 . , e ) 100 .", + "Correct": "b", + "Explanation": "edit : given ( x 1 + x 2 . . . + x 6 ) / 6 = 80 ( x 1 + x 2 . . . + x 6 ) = 480 - - > eq 1 . now given avg length of one third strings is 70 . that means out 6 / 3 = 2 strings . let the avg length of two strings be ( x 1 + x 2 ) / 2 = 70 . ( x 1 + x 2 ) = 140 . - - > eq 2 . now we are asked to find the average of the remaining i . e . ( x 3 + x 4 + x 5 + x 6 ) substitute eq 2 in eq 1 then we get 140 + x 3 + x 4 + x 5 + x 6 = 480 = > x 3 + x 4 + x 5 + x 6 = 340 now divide 340 by 4 we get 85 . = > ( x 3 + x 4 + x 5 + x 6 ) / 4 = 85 = avg length of remaining strings . imo correct option is b ." + }, + { + "Answer": 40000, + "Options": "a ) 40 , b ) 40000 , c ) 500 , d ) 5,000 , e ) 100,000", + "Correct": "b", + "Explanation": "if the palindrome must be even , it must begin and end in 2,4 6 and 8 ( 4 ways ) e . g 222212222,444414444 . the middle number in the nine - digit could be 0 - 9 ( 10 ways ) , e . g 22522 , 22822 the 2 nd and fourth numbers , the 3 rd and 5 th and 4 th and 6 th could must also be same i . e 0 - 9 ( 10 ways ) e . g 242343242 , 648565846 we thus have , 4 * 10 * 10 * 10 * 10 = 40000 b" + }, + { + "Answer": 1, + "Options": "a ) $ 1 , b ) $ 27 , c ) $ 31 , d ) $ 41 , e ) it can not be determined", + "Correct": "a", + "Explanation": "let ' s suppose that the price of a burger is bb , of a shake - ss and that of a cola is cc . we can then construct these equations : 3 b + 7 s + c = 110 4 b + 10 s + c = 164.5 subtracting the first equation from the second gives us b + 3 s = 54.5 now if we subtract the new equation two times from first or 3 times from second we will get b + s + c = 11 . in any case , there is no necessity to know each item ' s price , just the sum . answer : a" + }, + { + "Answer": 0.5833333333333334, + "Options": "a ) 7 / 12 , b ) 29 / 60 , c ) 17 / 30 , d ) 19 / 30 , e ) 11 / 15", + "Correct": "a", + "Explanation": "\"let s assume the platinum card spending limit = x gold card spending limit will be = x / 2 balance on gold card is = x / 2 * 1 / 3 = x / 6 platinum card unspent limit is = x - 1 / 4 x = 3 / 4 x so if gold card balance is transferred then the rest unspent will be 3 / 4 x - x / 6 = 7 / 12 x so the ans is a\"" + }, + { + "Answer": 5, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "e", + "Explanation": "if the average price is 52 , then mary has 6 oranges and 4 apples ( a ratio of 3 : 2 ) . for the average price to be 44 , the ratio should be 1 : 4 . mary must put back 5 oranges . the answer is e ." + }, + { + "Answer": 420, + "Options": "a ) rs . 450 , b ) rs . 320 , c ) rs . 550 , d ) rs . 420 , e ) none", + "Correct": "d", + "Explanation": "\"solution : let the original average expenditure be rs . x then , 42 ( x - 1 ) - 35 x = 42 . = > 7 x = 84 = > x = 12 therefore original expenditure , = rs . ( 35 \u00d7 12 ) = rs . 420 . answer : option d\"" + }, + { + "Answer": 62, + "Options": "a ) 22 , b ) 77 , c ) 29 , d ) 62 , e ) 21", + "Correct": "d", + "Explanation": "\"61 + 5 * 12 / ( 180 / 3 ) = 61 + 5 * 12 / ( 60 ) = 61 + ( 5 * 12 ) / 60 = 61 + 1 = 62 . answer : d\"" + }, + { + "Answer": 50, + "Options": "a ) 30 % , b ) 33 1 / 2 % , c ) 40 % , d ) 60 % , e ) 50 %", + "Correct": "e", + "Explanation": "\"original visual range = 100 km new visual range = 150 km percent increase in the visual range by using the telescope = ( 150 - 100 ) / 100 * 100 % = 1 / 2 * 100 % = 50 % answer e\"" + }, + { + "Answer": 17.5, + "Options": "a ) 17.1 , b ) 17.3 , c ) 17.5 , d ) 17.7 , e ) 17.2", + "Correct": "c", + "Explanation": "\"29.94 / 1.45 = 299.4 / 14.5 = ( 2994 / 14.5 ) x 1 / 10 ) [ here , substitute 175 in the place of 2994 / 14.5 ] = 175 / 10 = 17.5 answer is c .\"" + }, + { + "Answer": 91440, + "Options": "a ) 30240 , b ) 60480 , c ) 91440 , d ) 98240 , e ) 101040", + "Correct": "c", + "Explanation": "case 1 : all digits distinct select 5 digits out of 10 in 10 c 5 ways and arrange them in 5 ! ways which gives us 10 c 5 x 5 ! = 30240 case 2 : two digits are same , other 3 are distinct e . g . 45722 select a digit which is to be repeated in 10 c 1 ways , select other 3 digits in 9 c 3 ways and arrange them in 5 ! / 2 ! ways to get 10 c 1 x 9 c 3 x 5 ! / 2 ! = 50400 ways case 3 : two digits repeated and one other digit e . g . 33448 select 2 digits to be repeated in 10 c 2 ways , select the single digit in 8 c 1 ways and arrange them all in 5 ! / 2 ! . 2 ! ways to get 10 c 2 x 8 c 1 x 5 ! / 2 ! . 2 ! = 10800 sum of all = 30240 + 50400 + 10800 = 91440 ways ans : c" + }, + { + "Answer": 0.6666666666666666, + "Options": "a ) - 2 , b ) 0 , c ) 1 / 2 , d ) 1 , e ) 2 / 3", + "Correct": "e", + "Explanation": "x = 3 y + 5 , and thus y = x / 3 - 5 / 3 the slope is 1 / 3 . the slope of a line through points ( m , n ) and ( m + 2 , n + p ) is ( n + p - n ) / ( m + 2 - m ) = p / 2 p / 2 = 1 / 3 and thus p = 2 / 3 the answer is e ." + }, + { + "Answer": 26, + "Options": "a ) 22 , b ) 23 , c ) 24 , d ) 25 , e ) 26", + "Correct": "e", + "Explanation": "\"10 * 20 - 26 + 86 = 260 260 / 10 = 26 the answer is e .\"" + }, + { + "Answer": 750, + "Options": "a ) 300 , b ) 375 , c ) 400 , d ) 500 , e ) 750", + "Correct": "e", + "Explanation": "as per the question 400 = 2 a / 5 thus - a which is the total amount = 1000 the amount thus left = 600 she then deposited 1 / 4 of 600 = 150 total amount in her account = 750 answer e" + }, + { + "Answer": 1800, + "Options": "a ) 1800 , b ) 2888 , c ) 1200 , d ) 2699 , e ) 2771", + "Correct": "a", + "Explanation": "\"p - - - 10 - - - - 900 p - - - 5 - - - - - 450 3 p - - - 5 - - - - - 1350 - - - - - - = > 1800 answer : a\"" + }, + { + "Answer": 12, + "Options": "a ) - 1 , b ) 6 , c ) 7 , d ) 12 , e ) 14", + "Correct": "d", + "Explanation": "denote | x - 6 | as y : y ^ 2 + y = 20 - - > y = - 5 or y = 4 . discard the first solution since y = | x - 6 | , so it ' s an absolute value and thus can not be negative . y = | x - 6 | = 4 - - > x = 10 or x = - 2 . the sum = 12 . answer : d ." + }, + { + "Answer": 120, + "Options": "a ) 27 , b ) 33 , c ) 54 , d ) 81 , e ) 120", + "Correct": "e", + "Explanation": "answer is the lcm of 5 and 24 = 120 answer e" + }, + { + "Answer": 175, + "Options": "a ) 166 , b ) 105 , c ) 175 , d ) 177 , e ) 169", + "Correct": "c", + "Explanation": "\"x : y : z = 100 : 45 : 30 20 : 9 : 6 9 - - - 45 35 - - - ? = > 175 answer : c\"" + }, + { + "Answer": 110, + "Options": "a ) 90 , b ) 100 , c ) 110 , d ) 120 , e ) 130", + "Correct": "c", + "Explanation": "\"let x be the number he chose , then 3 \u22c5 x \u2212 220 = 110 3 x = 330 x = 110 correct answer c\"" + }, + { + "Answer": 2704, + "Options": "a ) 2135 , b ) 6551 , c ) 2704 , d ) 6466 , e ) 1113", + "Correct": "c", + "Explanation": "given exp . = [ ( a + b ) 2 - 4 ab ] , where a = 476 and b = 424 = [ ( 476 + 424 ) 2 - 4 x 476 x 424 ] = [ ( 900 ) 2 - 807296 ] = 810000 - 807296 = 2704 . correct option is c" + }, + { + "Answer": 66.66666666666666, + "Options": "a ) 30 % , b ) 33 1 / 2 % , c ) 40 % , d ) 60 % , e ) 66 2 / 3 %", + "Correct": "e", + "Explanation": "\"original visual range = 90 km new visual range = 150 km percent increase in the visual range by using the telescope = ( 150 - 90 ) / 90 * 100 % = 2 / 3 * 100 % = 66.67 % answer e\"" + }, + { + "Answer": 549.9999999999995, + "Options": "a ) $ 180 , b ) $ 280 , c ) $ 420 , d ) $ 550 , e ) $ 700", + "Correct": "d", + "Explanation": "\"let p be the original purchase price of the product . bill originally sold the product for 1.1 * p . in the second scenario , the purchase price is 0.9 * p . a 30 % profit means the selling price would be 1.3 * 0.9 * p = 1.17 * p thus , according to the information in the question , 1.17 p - 1.1 p = 35 0.07 = 35 p = 500 the original selling price was 500 * 1.1 = 550 . the correct answer is d .\"" + }, + { + "Answer": 6, + "Options": "a ) 5 , b ) 6 , c ) 8 , d ) 10 , e ) 50", + "Correct": "b", + "Explanation": "the no will be of the form 2 ^ n to achieve this . since any other form will have odd no in the prime factorization . hence we need to find solution of n for equation - 1 < 2 ^ n < 101 . 2 ^ 6 = 64 , 2 ^ 7 - 128 hence n can take values from 1 to 6 . hence answer : b" + }, + { + "Answer": 2000, + "Options": "a ) 1500 , b ) 1992 , c ) 9921 , d ) 2798 , e ) 2000", + "Correct": "e", + "Explanation": "\"p = 20 ( 100 / 10 ) 2 = > p = 2000 answer : e\"" + }, + { + "Answer": 2, + "Options": "a ) 3 , b ) 2 , c ) 5 , d ) 6 , e ) 1", + "Correct": "b", + "Explanation": "\"on dividing 433124 by 17 we get the remainder 15 , so 2 should be added b\"" + }, + { + "Answer": 80, + "Options": "a ) 85 kg , b ) 90 kg , c ) 83 kg , d ) 80 kg , e ) 82 kg", + "Correct": "d", + "Explanation": "\"total weight increased = 25 x 1 kg = 25 kg . weight of new person = 55 + 25 kg = 80 kg answer : d\"" + }, + { + "Answer": 525, + "Options": "a ) 400 , b ) 420 , c ) 430 , d ) 450 , e ) 525", + "Correct": "e", + "Explanation": "\"let no . of non - officers be x 15 * 470 + x * 110 = ( x + 15 ) 120 x = 525 e\"" + }, + { + "Answer": 282, + "Options": "a ) 280 , b ) 282 , c ) 284 , d ) 286 , e ) 288", + "Correct": "b", + "Explanation": "\"the least number which when divided by different divisors leaving the same remainder in each case = lcm ( different divisors ) + remainder left in each case . hence the required least number = lcm ( 31 , 9 ) + 3 = 282 . answer : b\"" + }, + { + "Answer": 500, + "Options": "a ) 350 , b ) 500 , c ) 650 , d ) 235 , e ) 450", + "Correct": "b", + "Explanation": "b" + }, + { + "Answer": 190, + "Options": "a ) 190 , b ) 200 , c ) 210 , d ) 220 , e ) 230", + "Correct": "a", + "Explanation": "\"1 st person will shake hand with 19 people 2 nd person will shake hand with 18 people 3 rd person will shake hand with 17 people . . . . . . total no . of handshakes = 19 + 18 + 17 + . . . + 3 + 2 + 1 = 19 * ( 19 + 1 ) / 2 = 190 or , if there are n persons then no . of shakehands = nc 2 = 20 c 2 = 190 answer : a\"" + }, + { + "Answer": 120, + "Options": "a ) a . 150 , b ) b . 300 , c ) c . 600 , d ) d . 120 , e ) e . 200", + "Correct": "d", + "Explanation": "volume per box : 15 x 12 x 10 = 1,800 total volume : 1 , 080,000 number of boxes : total volume / volume per box = 1 , 080,000 / 1,800 = 600 price per month : number of boxes * price per box = 600 * 0.2 = 120 answer : d" + }, + { + "Answer": 240, + "Options": "a ) s . 250 , b ) s . 280 , c ) s . 290 , d ) s . 299 , e ) s . 240", + "Correct": "e", + "Explanation": "\"let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 528 but x = 120 % of y = 120 y / 100 = 12 y / 10 \u2234 12 y / 10 + y = 528 \u21d2 y [ 12 / 10 + 1 ] = 528 \u21d2 22 y / 10 = 528 \u21d2 22 y = 5280 \u21d2 y = 5280 / 22 = 480 / 2 = rs . 240 e\"" + }, + { + "Answer": 22, + "Options": "a ) 22 , b ) 24 , c ) 26 , d ) 28 , e ) 30", + "Correct": "a", + "Explanation": "\"( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 222 + 2 * 131 a + b + c = \u221a 484 = 22 a\"" + }, + { + "Answer": 265, + "Options": "a ) $ 150 , b ) $ 245 , c ) $ 365 , d ) $ 715 , e ) $ 265", + "Correct": "e", + "Explanation": "\"total weekly income over 5 weeks = $ 406 + $ 413 + $ 420 + $ 436 + $ 395 = $ 2070 for avg weekly income to be $ 500 over 7 weeks , we need total weekly income over 7 weeks = $ 3500 now , $ 3500 - $ 2070 = $ 1430 from this , we subtract base salary for 2 weeks i . e $ 450 * 2 = $ 900 therefore , commission = $ 1430 - $ 900 = $ 530 for 2 weeks avg weekly commission = $ 265 answer e\"" + }, + { + "Answer": 899.9999999999998, + "Options": "a ) 360 , b ) 900 , c ) 540 , d ) 640 , e ) 720", + "Correct": "b", + "Explanation": "\"too many words and redundant info there . ( i ) 1 / 3 of the pieces of art are displayed , hence 2 / 3 of the pieces of art are not displayed . ( ii ) 1 / 6 of the pieces on display are sculptures , hence 5 / 6 of the pieces on display are paintings . ( iii ) 1 / 3 of the pieces not on display are paintings , hence 2 / 3 of the pieces not on display are sculptures . 400 sculptures are not on display , so according to ( iii ) 2 / 3 * { not on display } = 400 - - > { not on display } = 600 . according to ( i ) 2 / 3 * { total } = 600 - - > { total } = 900 . answer : b .\"" + }, + { + "Answer": 0.29411764705882354, + "Options": "a ) 5 / 17 , b ) 1 / 5 , c ) 1 / 4 , d ) 1 / 3 , e ) 3 / 7", + "Correct": "a", + "Explanation": "\"1 lbs of raisin = $ 1 5 lbs of raisin = $ 5 1 lbs of nuts = $ 3 4 lbs of nuts = $ 12 total value of mixture = 12 + 5 = 17 fraction of the value of raisin = 5 / 17 = 1 / 5 ans : a\"" + }, + { + "Answer": 7175, + "Options": "a ) 256 , b ) 512 , c ) 768 , d ) 1024 , e ) 7168", + "Correct": "e", + "Explanation": "0.7 * 2 ^ 10 = 0.7 * 1024 = 716.8 the answer is e ." + }, + { + "Answer": 29.25, + "Options": "a ) 29.25 , b ) 29.28 , c ) 29.27 , d ) 29.22 , e ) 29.21", + "Correct": "a", + "Explanation": "average of 9 = x 9 x = 8 * 3 + x * 2 x = 3.25 total = 9 * 3.25 = 29.25 . answer : a" + }, + { + "Answer": 20, + "Options": "a ) 18 , b ) 20 , c ) 24 , d ) 30 , e ) 40", + "Correct": "b", + "Explanation": "\"exp . multiples of 5 between 6 and 34 are 10 , 15,20 , 25,30 average = ( 10 + 15 + 20 + 25 + 30 ) / 5 = 5 ( 10 + 30 ) / 2 * 5 = 40 / 2 = 20 answer : b\"" + }, + { + "Answer": 1.5, + "Options": "a ) 1.2 kg , b ) 1.5 kg , c ) 1.7 kg , d ) 1.9 kg , e ) none of these", + "Correct": "b", + "Explanation": "\"explanation : flower - nectar contains 50 % of non - water part . in honey this non - water part constitutes 75 % ( 100 - 25 ) . therefore 0.5 x amount of flower - nectar = 0.75 x amount of honey = 0.75 x 1 kg therefore amount of flower - nectar needed = ( 0.75 / 0.51 ) kg = 1.5 kgs answer : b\"" + }, + { + "Answer": 85, + "Options": "a ) 75 , b ) 80 , c ) 85 , d ) 90 , e ) 95", + "Correct": "c", + "Explanation": "answer = c please refer diagram below 95 - 10 = 85" + }, + { + "Answer": 0.1388888888888889, + "Options": "a ) 1 / 18 , b ) 1 / 12 , c ) 1 / 9 , d ) 1 / 6 , e ) 5 / 36", + "Correct": "e", + "Explanation": "there are 5 ways to roll an 8 : 2 and 6 , 6 and 2 , 3 and 5 , 5 and 3 , 4 and 4 ( 4 and 4 is counted just once ) . there are 6 * 6 = 36 ways to roll two six - sided dice . the dice are fair , so the probability of rolling an 8 is 5 / 36 . e" + }, + { + "Answer": 1, + "Options": "a ) - 1 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "b", + "Explanation": "a = 3 , b = - 6 , c = 3 x 1,2 = ( 6 \u00b1 \u221a ( ( - 6 ) 2 - 4 \u00d7 3 \u00d7 3 ) ) / ( 2 \u00d7 3 ) = ( 6 \u00b1 \u221a ( 36 - 36 ) ) / 6 = ( 6 \u00b1 0 ) / 6 x 1 = x 2 = 1 b" + }, + { + "Answer": 4728, + "Options": "a ) 4722 , b ) 4725 , c ) 4728 , d ) 4731 , e ) 4733", + "Correct": "a", + "Explanation": "\"here smallest number means lcm hence lcm of 27,35 , 25,21 = 3 ^ 3 x 5 ^ 2 x 7 = 4725 therefore required number is 4725 - 3 = 4722 ans - a\"" + }, + { + "Answer": 80, + "Options": "a ) 27 , b ) 48 , c ) 80 , d ) 72 , e ) 18", + "Correct": "c", + "Explanation": "\"ages of p and mi = 3 x : 5 x ages of mi and mo = 3 x : 5 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 25 x sum = 49 x = 245 x = 5 difference if ages of pa and mo = 25 x - 9 x = 16 x = 16 * 5 = 80 answer c\"" + }, + { + "Answer": 20, + "Options": "a ) 11 , b ) 12 , c ) 14 , d ) 15 , e ) 20", + "Correct": "e", + "Explanation": "7 c 2 - 1 = 20 answer is e" + }, + { + "Answer": 50, + "Options": "a ) 22 , b ) 33 , c ) 22 , d ) 41 , e ) 50", + "Correct": "e", + "Explanation": "\"explanation : total of 50 numbers = ( 50 \u00d7 50 ) = 2500 total of 48 numbers = ( 2500 - ( 45 + 55 ) ] = 2400 required average = 2400 / 48 = 50 answer : e\"" + }, + { + "Answer": 9035, + "Options": "a ) $ 4035 , b ) $ 4036 , c ) $ 9035 , d ) $ 16140 , e ) $ 36140", + "Correct": "c", + "Explanation": "the ak company plans to make a profit of $ 30 , 500000 and it needs to earn the fixed costs of $ 50 , 200000 , so it needs to earn $ 80 , 700000 on top of the costs for the production of the 20000 cars . therefore , price of each car needs to be the unit costs plus $ 80 , 700000 / 20000 . after removing the 0 ' s , we end with the unit costs plus $ 8070 / 2 , which is $ 5000 plus $ 4035 . therefore , answer c is correct ." + }, + { + "Answer": 180, + "Options": "a ) 120 , b ) 150 , c ) 180 , d ) 240 , e ) 600", + "Correct": "c", + "Explanation": "\"this question was n ' t particularly grueling , but i think it ' s the first where i had the opportunity to solve it via theory andinspectionthat many on this board suggest as strategy on the gmat . it actually came to me by accident . basically , if we thought that the 3 packets of powder were included in the 12 ounces of water , that would mean we would need 150 packets of smoothie mix ( along with 12 ( 150 ) ounces of water for a total of 150 packets . however , we know , after a more careful reading of the stimulus , that the 3 ounces are not included in the 12 ounces . as such , the answer has to be less than 150 packets , since 150 would be too much powder considering you already have 150 ( 12 ) ounces of water and need less packets than water to make a smoothie . as such , the only answer less than 150 is 120 , a . does this make sense ? or am i way off base ? c\"" + }, + { + "Answer": 150, + "Options": "a ) 149 , b ) 150 , c ) 151 , d ) 166 , e ) none", + "Correct": "b", + "Explanation": "solution required numbers are 102 , 018114 , . . . . 996 . this is an a . p with a = 102 , d = 6 . let the number of its terms be n . then a + ( n - 1 ) d \u2039 = \u203a 102 + ( n - 1 ) \u00d7 6 = 996 \u2039 = \u203a n = 150 . answer b" + }, + { + "Answer": 784, + "Options": "a ) 729 , b ) 754 , c ) 784 , d ) 783 , e ) 108", + "Correct": "c", + "Explanation": "\"7 ^ k = 2 7 ^ 4 k = 2 ^ 4 7 ^ 4 k = 16 7 ^ ( 4 k + 2 ) = 7 ^ 4 k * 7 ^ 2 = 16 * 49 = 784 answer : c\"" + }, + { + "Answer": 2.05, + "Options": "a ) $ 2.15 , b ) $ 2.05 , c ) $ 2.45 , d ) $ 2.25 , e ) $ 2.85", + "Correct": "b", + "Explanation": "\"john spent and gave to his two friends a total of 1.05 + 1.00 + 1.00 = $ 3.05 money left 5.10 - 3.05 = $ 2.05 answer : b\"" + }, + { + "Answer": 1488, + "Options": "a ) $ 1124 million , b ) $ 1120 million , c ) $ 1144 million , d ) $ 1240 million , e ) $ 1488 million", + "Correct": "e", + "Explanation": "convert units to millions as answer is in millions 1996 imports = $ 1.44 bill = $ 1440 mill i . e . 1440 / 12 = $ 120 mill / month 1997 imports = $ 488 mill / 2 month i . e . $ 244 mill / month difference / month = 244 - 120 = 124 difference / year = $ 124 mill * 12 = $ 1488 mill answer : e" + }, + { + "Answer": 6, + "Options": "a ) 1.5 , b ) 3.0 , c ) 3.9 , d ) 4.0 , e ) 6.0", + "Correct": "e", + "Explanation": "initial avg is 6.8 so the summation of the nos is 6.8 * 5 = 34 now the new avg is 9.2 so summation will be 9.2 * 5 = 46 . so change in summation is 12 . this comes when a number is multiplied by 3 . in the original sum we already have that number added once . to bring additional 12 increment by multiplying by 3 , we get a total increase of 18 . thus , 6 is multiplied by 3 . answer : e" + }, + { + "Answer": 10200, + "Options": "a ) s . 10,000 , b ) s . 10,200 , c ) s . 10,400 , d ) s . 10,700 , e ) s . 10,800", + "Correct": "b", + "Explanation": "let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 3 x = 36000 x = 12000 a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . b ' s share = rs . ( 30000 x 17 / 50 ) = rs . 10,200 . b" + }, + { + "Answer": 92, + "Options": "a ) 75 kg . , b ) 80 kg . , c ) 86 kg . , d ) 90 kg . , e ) 92 kg .", + "Correct": "e", + "Explanation": "\"the new average will be = ( 94 * 7 + 110 + 60 ) / 9 = 92 kgs e is the answer\"" + }, + { + "Answer": 106, + "Options": "a ) 85 , b ) 80 , c ) 95 , d ) 90 , e ) 106", + "Correct": "e", + "Explanation": "\"total increase in weight = 12 \u00d7 4 = 48 if x is the weight of the new person , total increase in weight = x \u2212 58 = > 48 = x - 58 = > x = 48 + 58 = 106 answer : e\"" + }, + { + "Answer": 150, + "Options": "a ) 30 % , b ) 33 1 / 2 % , c ) 40 % , d ) 60 % , e ) 150 %", + "Correct": "e", + "Explanation": "\"original visual range = 60 km new visual range = 150 km percent increase in the visual range by using the telescope = ( 150 - 60 ) / 60 * 100 % = 3 / 2 * 100 % = 150 % answer e\"" + }, + { + "Answer": 0.0063, + "Options": "a ) 0.063 , b ) 0.0063 , c ) 0.63 , d ) 0.00063 , e ) 63", + "Correct": "b", + "Explanation": "9 * 7 = 63 sum of decimal places = 4 so , 0.9 * 0.007 = 0.0063 answer : b" + }, + { + "Answer": 4, + "Options": "a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1", + "Correct": "b", + "Explanation": "since x is an integer , ( - 3 ) ^ ( 2 x ) is always positive . so , 3 ^ 2 x = 3 ^ ( 12 - x ) 2 x = 12 - x 3 x = 12 x = 4 answer : b" + }, + { + "Answer": 5290, + "Options": "a ) 5336 , b ) 5242 , c ) 6524 , d ) 3526 , e ) 4526", + "Correct": "a", + "Explanation": "\"divisor = ( 5 * 46 ) = 230 10 * quotient = 230 quotient = 230 / 10 = 23 . dividend = ( divisor * quotient ) + remainder = ( 230 * 23 ) + 46 = ( 5290 + 46 ) = 5336 . answer is a\"" + }, + { + "Answer": 25, + "Options": "a ) 20 , b ) 25 , c ) 30 , d ) 35 , e ) 45", + "Correct": "b", + "Explanation": "x + y = 45 x - y = 5 adding 2 x = 50 = = > x = 25 and y = 45 - 25 = 20 bigger number is x = 25 answer b ." + }, + { + "Answer": 4, + "Options": "a ) 4 , b ) 3 , c ) 5 , d ) 6 , e ) 7", + "Correct": "a", + "Explanation": "\"let seventh observation = x . then , according to the question we have = > ( 66 + x ) / 7 = 10 = > x = 4 . hence , the seventh observation is 4 . answer : a\"" + }, + { + "Answer": 11, + "Options": "a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13", + "Correct": "c", + "Explanation": "\"the smallest amount that the company can spend is the lcm of 350 and 200 , which is 1400 for each , which is total 2800 . the number of 1 st type of computers which costing $ 350 = 1400 / 350 = 4 . the number of 2 nd type of computers which costing $ 200 = 1400 / 200 = 7 . total = 4 + 7 = 11 answer is c .\"" + }, + { + "Answer": 0.1111111111111111, + "Options": "a ) 1 / 6 , b ) 7 / 216 , c ) 4 / 36 , d ) 9 / 216 , e ) 11 / 216", + "Correct": "c", + "Explanation": "the total possible number of combination if the dice is thrown 2 times is 36 . there are 4 possible outcomes that the sum of the number is 5 which is ( 2 + 3 ) ( 3 + 2 ) ( 1 + 4 ) and ( 4 + 1 ) answer : c" + }, + { + "Answer": 1.0833333333333333, + "Options": "a ) 1 / 140 , b ) 11 / 12 , c ) 14 / 8 , d ) 13 / 12 , e ) 57 / 120", + "Correct": "d", + "Explanation": "required probability = p ( x ) + p ( y ) + p ( z ) ( all the events are mutually exclusive ) . = 1 / 2 + 1 / 4 + 1 / 3 = 13 / 12 answer : d" + }, + { + "Answer": 72, + "Options": "a ) 48 , b ) 54 , c ) 72 , d ) 84 , e ) 27", + "Correct": "c", + "Explanation": "let the second number be x . then , first number = 2 x and third number = 2 x / 3 . 2 x + x + 2 x / 3 = 264 11 x / 3 = 264 x = 72 answer : c" + }, + { + "Answer": 7, + "Options": "a ) 0 , b ) 1 , c ) 5 , d ) 7 , e ) 9", + "Correct": "d", + "Explanation": "\"i looked for patterns : ^ 2 - units digit 9 ^ 3 - units digit 7 ^ 4 - units digit 1 ^ 5 - units digit 3 hence , we can see that when raised to a power which is multiple of 4 , the units digit is 1 , and when to an even power not multiple of 4 , the units digit is 9 and we can then see : ^ 16 - units digit 1 , or ^ 18 - units digit 9 and ^ 19 - units digit 7 therefore , w = when divided by 10 , the remainder must be 7 . d\"" + }, + { + "Answer": 7, + "Options": "a ) 6 rs , b ) 7 rs , c ) 8 rs , d ) 4 rs , e ) 1 rs", + "Correct": "b", + "Explanation": "\"5 m = xw = 8 b 5 m + xw + 8 b - - - - - 105 rs . 5 m + 5 m + 5 m - - - - - 105 rs . 15 m - - - - - - 105 rs . = > 1 m = 7 rs . answer : b\"" + }, + { + "Answer": 5.5, + "Options": "a ) 5 / 2 , b ) 10 / 3 , c ) 7 / 2 , d ) 14 / 3 , e ) 11 / 2", + "Correct": "e", + "Explanation": "\"for 2 b ^ 2 + 5 b = 12 roots are [ - 5 + sqrt ( 25 + 96 ) ] / 4 or [ - 5 - sqrt ( 25 + 96 ) ] / 4 = 1.5 or - 4 hence larger root 1.5 is 1.5 - ( - 4 ) = 5.5 = 11 / 2 greater than smaller root ( - 4 ) . hence option ( e ) .\"" + }, + { + "Answer": 1.0034602076124568, + "Options": "a ) 290 / 289 , b ) 1 / 289 , c ) 290 / 90 , d ) 290 / 19 , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : if the numbers are a , b , then ab = 17 , as 17 is a prime number , so a = 1 , b = 17 . 1 / a 2 + 1 / b 2 = 1 / 1 ( 2 ) + 1 / 17 ( 2 ) = 290 / 289 option a\"" + }, + { + "Answer": 498, + "Options": "a ) 249 , b ) 498 , c ) 676 , d ) 823 , e ) 1,002", + "Correct": "b", + "Explanation": "\"slope of 2 and a y - intercept of 2 y - coordinate is 998 y = 2 x + 2 996 = 2 x x = 498 answer : b . 498\"" + }, + { + "Answer": 59, + "Options": "a ) 54 , b ) 59 , c ) 63 , d ) 71 , e ) 92", + "Correct": "b", + "Explanation": "\"37 are throwers and right handed 1 / 3 of remaining 33 , i . e 11 are left handed and remaining are right handed . basically , out of 70 , only 11 are left handed and remaining 70 - 11 = 59 are right handed . b is the answer\"" + }, + { + "Answer": 500, + "Options": "a ) q = 300 , b ) q = 400 , c ) q = 500 , d ) q = 600 , e ) none of these", + "Correct": "c", + "Explanation": "{ managers } = { female managers } + { male managers } ; we are told that the total number of managers in the company is 2 / 5 of all the employees , thus { managers } = 2 / 5 ( m + f ) , where m and f are number of female and male employees , respectively . also , we know that 2 / 5 of all male employees are managers : { male managers } = 2 / 5 * mas well as there are total of 200 female managers : { female managers } = 200 ; thus : 2 / 5 ( m + f ) = 200 + 2 / 5 * m - - > f = 500 . answer : c ." + }, + { + "Answer": 86, + "Options": "a ) 40 , b ) 44 , c ) 80 , d ) 86 , e ) 90", + "Correct": "d", + "Explanation": "\"sol . let the numbers be x and y . then , ( x + y ) = 24 and x 2 + y 2 = 404 . now , 2 xy = ( x + y ) 2 - ( x 2 + y 2 ) = ( 24 ) 2 - 404 = 576 - 404 = 172 xy = 86 . answer d\"" + }, + { + "Answer": 1.1111111111111112, + "Options": "a ) 10 / 9 , b ) 1 / 289 , c ) 290 / 90 , d ) 290 / 19 , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : if the numbers are a , b , then ab = 3 , as 3 is a prime number , so a = 1 , b = 3 . 1 / a 2 + 1 / b 2 = 1 / 1 ( 2 ) + 1 / 3 ( 2 ) = 10 / 9 option a\"" + }, + { + "Answer": 12, + "Options": "a ) 7 , b ) 9 , c ) 11 , d ) 12 , e ) 21", + "Correct": "d", + "Explanation": "lcm of two prime numbers will basically be multiple of those numbers . lcm = 10 = 2 * 5 , both of which are prime . now we know x > y , so x = 5 and y = 2 . 2 x + y = 2 * 5 + 2 = 10 + 2 = 12 . answer : d" + }, + { + "Answer": 56, + "Options": "a ) a - 56 , b ) b - 57 , c ) c - 58 , d ) d - 59 , e ) e - 60", + "Correct": "a", + "Explanation": "let the number of black balls = x and the number of white balls = 6 x then , total number of balls in the box = x + 6 x = 7 x i . e . , the total number of balls must be a multiple of 7 from the given choices , only 56 is the multiple of 7 . hence , 56 are the number of balls in the box . answer is a ." + }, + { + "Answer": 5, + "Options": "a ) 3 . , b ) 4 . , c ) 5 . , d ) 7 . , e ) 8 .", + "Correct": "c", + "Explanation": "given to find the positive divisors of 120 and condition is that divisors have to be multiple of 4 but not including 120 . consider factors of 120 4 * 30 6 * 20 15 * 8 24 * 5 60 * 2 total we get 5 different ways and all are part of 4 . answer : c is correct option ." + }, + { + "Answer": 5, + "Options": "a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 8", + "Correct": "c", + "Explanation": "\"explanation : seventh observation = ( 7 \u00d7 \u00d7 11 - 6 \u00d7 \u00d7 12 ) = 5 correct option : c\"" + }, + { + "Answer": 28350, + "Options": "a ) $ 24960 , b ) $ 25920 , c ) $ 28080 , d ) $ 28350 , e ) $ 29160", + "Correct": "d", + "Explanation": "\"from 9 : 00 in the morning to 5 : 55 in the afternoon , inclusive there are 9 * 12 = 108 five - minute intervals , thus total of 108 * 30 tickets were sold . say x student and 3 x regular tickets were sold , then x + 3 x = 108 * 30 - - > x = 27 * 30 and 3 x = 3 * ( 27 * 30 ) = 27 * 90 . therefore , the total revenue from ticket sales that day was 27 * 30 * 5 + 27 * 90 * 10 = $ 28,350 . answer : d .\"" + }, + { + "Answer": 460, + "Options": "a ) rs . 480 , b ) rs . 960 , c ) rs . 960 , d ) rs . 460 , e ) rs . 560", + "Correct": "d", + "Explanation": "explanation : average price of a goat = rs . 60 total price of 8 goats = 8 * 60 = rs . 480 but total price of 2 cows and 8 goats = rs . 1400 total price of 2 cows is = 1400 - 480 = 980 average price of a cow = 980 / 2 = rs . 460 answer : option d" + }, + { + "Answer": 2, + "Options": "a ) 1 , b ) 2 , c ) 345 , d ) 445 , e ) 235", + "Correct": "b", + "Explanation": "1 = 6,2 = 36,3 = 363,4 = 364,5 = 365 , then 36 = ? 36 = 2 check the second eqn . answer : b" + }, + { + "Answer": 272.72727272727275, + "Options": "a ) s . 200.72 , b ) s . 250.72 , c ) s . 272.72 , d ) s . 300.72 , e ) s . 310.72", + "Correct": "c", + "Explanation": "\"let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 600 but x = 120 % of y = 120 y / 100 = 12 y / 10 \u2234 12 y / 10 + y = 600 \u21d2 y [ 12 / 10 + 1 ] = 600 \u21d2 22 y / 10 = 600 \u21d2 22 y = 6000 \u21d2 y = 6000 / 22 = rs . 272.72 c\"" + }, + { + "Answer": 84, + "Options": "a ) 124 % , b ) 120 % , c ) 96 % , d ) 80 % , e ) 84 %", + "Correct": "e", + "Explanation": "\"juan ' s income = 100 ( assume ) ; tim ' s income = 60 ( 40 percent less than juan ' s income ) ; mary ' s income = 84 ( 40 percent more than tim ' s income ) . thus , mary ' s income ( 84 ) is 84 % of juan ' s income ( 100 ) . answer : e .\"" + }, + { + "Answer": 1.12, + "Options": "a ) $ 1.00 , b ) $ 1.12 , c ) $ 1.20 , d ) $ 1.32 , e ) $ 1.40", + "Correct": "b", + "Explanation": "phil = x sal = 0.8 x kim = ( 1.4 ) * 0.8 x = 1.12 x x + 0.8 x = 1.8 - - > x = 1 kim = 1.12 answer : b" + }, + { + "Answer": 2240, + "Options": "a ) $ 2,240 , b ) $ 2,120 , c ) $ 1,960 , d ) $ 1,920 , e ) $ 1,400", + "Correct": "a", + "Explanation": "\"in order to maximize the amount of money that the gambler kept , we should maximize # of $ 20 chips lost and minimize # of $ 100 chips lost , which means that # of $ 20 chips lost must be 2 more than # of $ 100 chips lost . so , if # of $ 20 chips lost is x then # of $ 100 chips lost should be x - 2 . now , given that total # of chips lost is 14 : x + x - 2 = 14 - - > x = 8 : 8 $ 20 chips were lost and 8 - 2 = 6 $ 100 chips were lost . total worth of chips lost is 8 * 20 + 6 * 100 = $ 760 , so the gambler kept $ 3,000 - $ 760 = $ 2,240 . answer : a .\"" + }, + { + "Answer": 84, + "Options": "a ) 56 , b ) 70 , c ) 84 , d ) 96 , e ) 120", + "Correct": "c", + "Explanation": "\"k ^ 3 = 336 * x = 2 ^ 4 * 3 * 7 * x the factors of k must at minimum include 2 ^ 2 * 3 * 7 = 84 . the answer is c .\"" + }, + { + "Answer": 20, + "Options": "a ) 5 % , b ) 10 % , c ) 15 % , d ) 20 % , e ) it can not be determined", + "Correct": "d", + "Explanation": "\"solution : let the total number of flags be 100 ( even number ) let the total number of ' blue ' flags alone be ' a ' let the total number of ' red ' flags alone be ' b ' let the total number of ' both ' flags be ' c ' we have given , total number of blue flags = 60 % = 60 = a + c total number of red flags = 55 % = 55 = b + c total number of flags = a + b + c = 100 ( since all the flags have been utilized ) so , substituting for c in the third equation , we have , 60 - c + c + 60 - c = 100 c = 20 option d .\"" + }, + { + "Answer": 10, + "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12", + "Correct": "c", + "Explanation": "let x be the number . always replace ` ` is ' ' with an equal sign ( 1 / 2 ) x + 6 = 11 ( 1 / 2 ) x = 11 - 6 ( 1 / 2 ) x = 5 x = 10 correct answer is c" + }, + { + "Answer": 10, + "Options": "a ) 8 , b ) 12 , c ) 10 , d ) 16 , e ) 18", + "Correct": "c", + "Explanation": "n ^ ( n / 2 ) = 10 apply log n / 2 logn = log 10 nlogn = 2 log 10 = log 10 ^ 2 = log 100 logn = log 100 now apply antilog n = 100 / n now n = 10 . answer : c" + }, + { + "Answer": 56, + "Options": "a ) 48 , b ) 50 , c ) 56 , d ) 62 , e ) 64", + "Correct": "c", + "Explanation": "1 to 11 = 11 * 50 = 550 1 to 6 = 6 * 49 = 294 6 to 11 = 6 * 52 = 312 6 th = 294 + 312 \u2013 550 = 56 c" + }, + { + "Answer": 1408, + "Options": "a ) 1218 , b ) 1212 , c ) 1408 , d ) 2707 , e ) 2591", + "Correct": "c", + "Explanation": "\"\u03c0 ( 232 \u2013 92 ) = 1408 answer : c\"" + }, + { + "Answer": 0.4666666666666667, + "Options": "a ) 11 / 30 , b ) 29 / 60 , c ) 17 / 30 , d ) 19 / 30 , e ) 7 / 15", + "Correct": "e", + "Explanation": "i think e - 7 / 15 is the correct answer . here goes : lets assume originally the number of beds = x after the new tower , the total combined no of beds = 2 x so old = x , new = x now 1 / 3 of x are occupied and 1 / 5 of x are occupied which simplifies to ( 1 / 5 ) x we are shifting 1 / 3 of x to the new ward so there will now be : 1 / 3 of x plus 1 / 5 of x occupied in the new ward . add them up to get 8 / 15 of x there are x beds in new tower so ratio is : ( 8 / 15 ) x / x = 8 / 15 of x subtract that from 15 / 15 of x and you get the number of un - occupied beds to total capacity of new towerb = 7 / 15 . e" + }, + { + "Answer": 11.6, + "Options": "a ) 10.5 , b ) 11 , c ) 11.6 , d ) 12 , e ) 12.5", + "Correct": "c", + "Explanation": "\"mean = 16.2 two standard deviations is 2.3 + 2.3 = 4.6 there could be two calues for this . mean + two standard deviations = 20.8 mean - two standard deviations = 11.6 answer choice has 11.6 and so c is the answer .\"" + }, + { + "Answer": 1200, + "Options": "a ) rs . 600 , b ) rs . 900 , c ) 1200 rupees , d ) rs . 1500 , e ) none", + "Correct": "c", + "Explanation": "solution 22.22 let the sum be rs . x . now , s . i . = rs . 600 , t = 10 years . rate = % = ( 100 x 600 / x x 10 ) % = ( 6000 / x ) % s . i . for first 5 years = rs . ( x x 5 x 6000 / x x 100 ) = rs . 300 . s . i . for first 5 years = rs . ( 3 x x 5 x 6000 / x x 100 ) = rs . 900 . \u2234 total interest = rs . 1200 . answer c" + }, + { + "Answer": 0.5, + "Options": "a ) 1 / 2 , b ) 1 / 3 , c ) 2 / 3 , d ) 1 / 4 , e ) 1 / 5", + "Correct": "a", + "Explanation": "\"w - > a / b = 20 * 21 * \u2026 \u2026 * 39 / 21 * 22 * \u2026 . * 39 * 40 = 20 / 40 = 1 / 2 . therefore , the answer is a .\"" + }, + { + "Answer": 7, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9", + "Correct": "c", + "Explanation": "description : = > 8 x = 2 ( x + 2 ) + 5 + 3 ( x + 4 ) = > 3 x = 21 , x = 7 = > x + 4 = 11 x = 11 - 4 = 7 answer c" + }, + { + "Answer": 1578, + "Options": "a ) 1572 , b ) 1782 , c ) 1992 , d ) 2122 , e ) 2342", + "Correct": "a", + "Explanation": "\"when increased by 3 , the number must include at least 3 ^ 2 * 5 ^ 2 * 7 = 1575 the answer is a .\"" + }, + { + "Answer": 5.333333333333333, + "Options": "a ) 16 / 3 , b ) 7 / 3 , c ) 5 / 2 , d ) 4 / 3 , e ) 3", + "Correct": "a", + "Explanation": "let x be the # of cups going into the 8 cup bottle . so . . . . x / 8 = ( ( 8 - x ) / 4 ) 64 - 8 x = 4 x 64 = 12 x x = 16 / 3 . answer : a" + }, + { + "Answer": 44.99999999999999, + "Options": "a ) 45 , b ) 27 , c ) 28 , d ) 26 , e ) 91", + "Correct": "a", + "Explanation": "sol : 45 if x persons were there in total , then x \u00d7 ( 1 \u2013 1 / 3 ) \u00d7 ( 1 \u2013 2 / 5 ) \u00d7 ( 1 \u2013 2 / 3 ) = 6 x \u00d7 2 / 3 \u00d7 3 / 5 \u00d7 1 / 3 = 6 x = 6 \u00d7 5 \u00d7 3 / 2 = 45 answer : a" + }, + { + "Answer": 15, + "Options": "a ) 9 years , b ) 11 years , c ) 15 years , d ) 21 years , e ) 25 years", + "Correct": "c", + "Explanation": "\"solution age of the 15 th student = [ 15 x 15 - ( 14 x 7 + 16 x 7 ) ] = ( 225 - 210 ) = 15 years . answer c\"" + }, + { + "Answer": 50, + "Options": "a ) 10 . , b ) 25 . , c ) 30 . , d ) 38 , e ) 50 .", + "Correct": "e", + "Explanation": "total distance - 1000 km time ratio a : b - 3 : 1 speed ratio a : b - 3 : 1 so distance ( speed * time ) ratio will be - 3 * 3 : 1 * 1 - 9 : 1 so total distance traveled by b - 100 km time taken by b ( 18 : 00 - 16 : 00 = 2 ) - 2 hours speed of b - 50 kmph answer : e" + }, + { + "Answer": 20, + "Options": "a ) 25 , b ) 76 , c ) 29 , d ) 12 , e ) 20", + "Correct": "e", + "Explanation": "\"explanation : let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 931 96 + 225 + 490 + 6 x = 931 6 x = 120 = > x = 20 . answer : e\"" + }, + { + "Answer": 93, + "Options": "a ) 80 kg , b ) 93 kg , c ) 70 kg , d ) 75 kg , e ) 85 kg", + "Correct": "b", + "Explanation": "\"since the average has increased by 1.5 kg , the weight of the man who stepped in must be equal to 68 + 10 x 2.5 68 + 25 = 93 kg ans : ' b '\"" + }, + { + "Answer": 24, + "Options": "a ) 1 , b ) 4 , c ) 9 , d ) 13 , e ) 24", + "Correct": "e", + "Explanation": "\"solving through algebra route : 3 b + 4 f = x amount if we multiply this equation with 6 we get : 18 b + 24 f = 6 x therefore , we got 18 ounces of butter and 6 x amount of quantity when we use 24 ounces of floor . ans : e\"" + }, + { + "Answer": 55.88235294117647, + "Options": "a ) 46.2 % , b ) 54.54 % , c ) 55.88 % , d ) 70 % , e ) none of these", + "Correct": "c", + "Explanation": "\"explanation : number of runs made by running = 136 - ( 12 x 4 + 2 x 6 ) = 136 - ( 60 ) = 76 now , we need to calculate 72 is what percent of 136 . = > 76 / 136 * 100 = 55.88 % answer : c\"" + }, + { + "Answer": 97, + "Options": "a ) 97 , b ) 168 , c ) 189 , d ) 190 , e ) 200", + "Correct": "a", + "Explanation": "\"solution average of 7 people after the last one enters = 151 . \u00e2 \u02c6 \u00b4 required weight = ( 7 x 151 ) - ( 6 x 160 ) = 1057 - 960 = 97 . answer a\"" + }, + { + "Answer": 0.5454545454545454, + "Options": "a ) 5 / 11 , b ) 6 / 11 , c ) 4 / 11 , d ) 7 / 11 , e ) 8 / 11", + "Correct": "b", + "Explanation": "explanation : given expression = 1 / ( 2 \u00d7 3 ) + 1 / ( 3 \u00d7 4 ) + 1 / ( 4 \u00d7 5 ) + . . . . . . + 1 / ( 21 \u00d7 22 ) = ( 1 / 2 - 1 / 3 ) + ( 1 / 3 - 1 / 4 ) + ( 1 / 4 - 1 / 5 ) + . . . . . . . . . . = ( 1 / 21 - 1 / 22 ) = 1 / 2 - 1 / 22 = 10 / 22 = 5 / 11 thus , least fraction to be added = 1 - 5 / 11 = 6 / 11 answer : option b" + }, + { + "Answer": 28672, + "Options": "a ) 44648 , b ) 27844 , c ) 28642 , d ) 16864 , e ) 32458", + "Correct": "c", + "Explanation": "we can have 7 digits ( 1 , 2,3 , 5,6 , 8,9 ) for the first place ( ten thousand ' s place ) . and similarly 8 digits for thousand ' s , hundred ' s , tenth ' s and unit digit . ( 0,1 , 2,3 , 5,6 , 8,9 ) so in total 7 * 8 * 8 * 8 * 8 = 28672 hence c" + }, + { + "Answer": 15, + "Options": "a ) 19 , b ) 18 , c ) 17 , d ) 16 , e ) 15", + "Correct": "e", + "Explanation": "we ' re asked to deal with the positive integers less than 20 . there are only 19 numbers in that group ( 1 to 19 , inclusive ) . we ' re asked to find all of the numbers that fit one ( or more ) of the given descriptions . looking at the answer choices , we have every value form 15 to 19 , inclusive , so most ( if not all ) of the numbers from 1 to 19 fit one ( or more ) of the descriptions . how long would it take you to find the ones that do n ' t fit . . . . . ? the first several should be pretty easy to find - the prompt wants us to focus on multiples of 2 and 9 ( and sums of those multiples ) . so what odd numbers are less than 9 ? 1 , 3 , 5 , 7 none of these values fit the given descriptions . that ' s 4 out of 19 that we know for sure do not fit . 19 - 4 = 15 = e" + }, + { + "Answer": 36, + "Options": "a ) 45 kg , b ) 38 kg , c ) 66 kg , d ) 36 kg , e ) of these", + "Correct": "d", + "Explanation": "let the weights of the three boys be 4 k , 5 k and 6 k respectively . 4 k + 6 k = 5 k + 45 = > 5 k = 45 = > k = 9 therefore the weight of the lightest boy = 4 k = 4 ( 9 ) = 36 kg . answer : d" + }, + { + "Answer": 126, + "Options": "a ) 107 , b ) 126 , c ) 117 , d ) 136 , e ) 147", + "Correct": "b", + "Explanation": "let us calculate both the length and width of the room in centimeters . length = 6 meters and 72 centimeters = 672 cm width = 4 meters and 32 centimeters = 432 cm as we want the least number of square tiles required , it means the length of each square tile should be as large as possible . further , the length of each square tile should be a factor of both the length and width of the room . hence , the length of each square tile will be equal to the hcf of the length and width of the room = hcf of 672 and 432 = 48 thus , the number of square tiles required = ( 672 x 432 ) / ( 48 x 48 ) = 14 x 9 = 126 answer : b" + }, + { + "Answer": 0.8686868686868687, + "Options": "a ) 4 / 99 , b ) 2 / 25 , c ) 8 / 99 , d ) 49 / 100 , e ) 86 / 99", + "Correct": "e", + "Explanation": "interesting question ! also one that we should be able to answer very quickly be keeping an eye on our best friends , the answer choices . we know that x belongs to the set { 1 , 2 , 3 , . . . , 99 } . we want to know the probability q that x ( x + 1 ) is a multiple of either 4 or 5 . when will this happen ? if either x or ( x + 1 ) is a multiple of 4 or 5 . since 4 * 5 is 20 , let ' s look at the first 20 numbers to get a rough idea of how often this happens . out of the numbers from 1 to 20 : 4 , 5 , 6 , 8 , 9 , 10 , 11 , 12 , 13 , 15 , 16 , 17 , 20 so , 14 out of the first 20 numbers match our criteria . since : probability = ( # of desired outcomes ) / ( total # of possibilities ) , we guesstimate the answer to be 14 / 20 . since ( e ) is the only answer greater than 1 / 2 , we go with ( e ) ." + }, + { + "Answer": 5184, + "Options": "a ) 2450 , b ) 2560 , c ) 2650 , d ) 3500 , e ) 5184", + "Correct": "e", + "Explanation": "\"given exp . = ( 12 ) 3 x 64 = ( 12 ) 3 x 64 = ( 12 ) 2 x 62 = ( 72 ) 2 = 5184 432 12 x 62 e\"" + }, + { + "Answer": 0.52, + "Options": "a ) 0.4 , b ) 0.44 , c ) 0.48 , d ) 0.52 , e ) 0.56", + "Correct": "d", + "Explanation": "\"let x be the total number of students . the number students who are younger than 25 is 0.4 * 0.4 x + 0.6 * 0.6 x = 0.52 x the answer is d .\"" + }, + { + "Answer": 4, + "Options": "a ) 1 , b ) 2 , c ) 4 , d ) 6 , e ) 8", + "Correct": "c", + "Explanation": "this one took me bout 3 1 / 2 min . just testin numbers and what not . first notice that n is positive . save time by noticing thati worked out one solution where n = 0 only to find that thats not an option : p . 1 - 7 stands for ^ 1 thru 7 1 : 7 * 1 = 7 2 : 7 * 7 = 9 3 : 7 * 9 = 3 4 : 7 * 3 = 1 5 : 7 * 1 = 7 6 : 7 * 7 = 9 7 : 7 * 9 = 3 pattern repeats every @ 5 . notice every ^ 4 or multiple of 4 is always going to be 1 . this is just for future notice for similar problems . so 7 ^ 4 n + 3 - - - > if n = 1 then its ( ( 7 ^ 7 ) * 6 ) ) / 10 which can say is going to be 3 * 8 - - > 18 / 10 - - > r = 8 now from here if id double check just to make sure . 7 ^ 4 ( 2 ) + 3 * 6 ^ 2 - - - > 7 ^ 11 * 36 or we can just say again 7 ^ 11 * 6 ( b / c we are only interested in the units digit ) . since ^ 12 is going to be 1 that means ^ 11 is going to be 3 ( as taken from our pattern ) so again 3 * 6 = 18 / 10 - - - > r = 4 . c or j in this problem ." + }, + { + "Answer": 40, + "Options": "a ) 7 , b ) 14 , c ) 21 , d ) 28 , e ) 40", + "Correct": "e", + "Explanation": "5 c + 6 p = 94 we need to maximize p to minimize c so that the eq is also satisfied try substitution for cp to solve so that eqn is satisfied the least value of c for which equation gets satisfied is 5 i . e . 5 * 8 + 6 * 9 = 40 + 54 = 94 hence e is the answer" + }, + { + "Answer": 20, + "Options": "a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20", + "Correct": "e", + "Explanation": "\"y = 264 * a + 42 = ( 22 * 12 ) * a + 22 + 20 the answer is e .\"" + }, + { + "Answer": 0.12500000000000006, + "Options": "a ) 1 / 9 , b ) 1 / 8 , c ) 1 / 7 , d ) 7 / 8 , e ) 8 / 7", + "Correct": "b", + "Explanation": "let p = total cost of the rental van . the original share per person is p / 9 . the new share per person is p / 8 . p / 8 = p / 9 * 9 / 8 = ( 1 + 1 / 8 ) * original share the answer is b ." + }, + { + "Answer": 38, + "Options": "a ) 67 sec , b ) 89 sec , c ) 38 sec , d ) 87 sec , e ) 45 sec", + "Correct": "c", + "Explanation": "\"speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 260 + 120 = 380 m . time taken = 380 / 10 = 38 sec . answer : c\"" + }, + { + "Answer": 18, + "Options": "a ) 15 , b ) 18 , c ) 20 , d ) 22 , e ) 17", + "Correct": "b", + "Explanation": "x = the number of blue pens y = the number of black pens z = the number of red pens from the first sentence we have equation # 1 : x + y + z = 31 . . . he has 5 more black pens than red pens . . . equation # 2 : y = 5 + z . . . twice as many blue pens as black pens . . . equation # 3 : x = 2 y solve equation # 1 for z : z = y - 5 now , we can replace both x and z with y in equation # 1 2 y + y + ( y - 5 ) = 31 4 y - 5 = 31 4 y = 36 y = 9 there are 9 black pens . this is 5 more than the number of red pens , so z = 4 . hence the answer is . x = 18 , and just for check 18 + 9 + 4 = 31 . answer = 18 , ( b )" + }, + { + "Answer": 12000, + "Options": "a ) rs . 16003 , b ) rs . 16029 , c ) rs . 1288 , d ) rs . 16108 , e ) rs . 12000", + "Correct": "e", + "Explanation": "\"explanation : manager ' s monthly salary rs . ( 2000 * 21 - 1500 * 20 ) = rs . 12000 . answer : e\"" + }, + { + "Answer": 8, + "Options": "a ) 12 % , b ) 14 % , c ) 16 % , d ) 20 % , e ) 8 %", + "Correct": "e", + "Explanation": "\"explanation : 100 * 100 = 10000 80 * 115 = 9200 10000 - - - - - - - 800 100 - - - - - - - ? = 8 % e )\"" + }, + { + "Answer": 32, + "Options": "a ) 28 , b ) 29 , c ) 30 , d ) 31 , e ) 32", + "Correct": "e", + "Explanation": "\"let x be the number of students in the largest class . then x + ( x - 2 ) + ( x - 4 ) + ( x - 6 ) + ( x - 8 ) = 140 5 x - 20 = 140 5 x = 160 x = 32 the answer is e .\"" + }, + { + "Answer": 40, + "Options": "a ) 22 , b ) 88 , c ) 77 , d ) 40 , e ) 99", + "Correct": "d", + "Explanation": "\"in 1 hr , the bus covers 60 km without stoppages and 20 km with stoppages . stoppage time = time take to travel ( 60 - 20 ) km i . e 40 km at 60 km / hr . stoppage time = 40 / 60 hrs = 40 min . answer : d\"" + }, + { + "Answer": 0.75, + "Options": "a ) 3 / 8 , b ) 1 / 2 , c ) 11 / 16 , d ) 5 / 7 , e ) 3 / 4", + "Correct": "e", + "Explanation": "\"the answer isc : 11 / 16 . the key to this problem is remembering that the median for a consecutive set of numbers is equivalent to its mean . for example , the mean and median of a set consisting of x , x + 1 , x + 2 , . . . , y will always be ( x + y ) / 2 . for set s , consisting of numbers ( a , a + 1 , . . . , b ) , the median is given to be 3 / 4 * b : ( a + b ) / 2 = ( 3 / 4 ) * b a = b / 2 for set q , consisting of numbers ( b , b + 1 , . . . , c ) , the median is given to be 8 / 8 * c : ( b + c ) / 2 = ( 8 / 8 ) * c b = ( 1 ) * c for set r , consisting of numbers ( a , a + 1 , . . . c ) , the median needs to be found : a = b / 2 = ( 1 * c ) / 2 = ( 1 / 2 ) * c median = ( a + c ) / 2 = ( 1 / 2 * c + c ) / 2 = ( 3 / 2 ) * c / 2 = ( 3 / 4 ) * c ( answer e )\"" + }, + { + "Answer": 176, + "Options": "a ) a ) 130 , b ) b ) 134 , c ) c ) 148 , d ) d ) 176 , e ) e ) 160", + "Correct": "d", + "Explanation": "\"d = d * q + r d = 19 * 9 + 5 d = 171 + 5 d = 176 answer d\"" + }, + { + "Answer": 5184, + "Options": "a ) 2128 , b ) 3458 , c ) 4207 , d ) 5184 , e ) 8104", + "Correct": "d", + "Explanation": "all three digits are different and first digit is not zero . so first digit can be filled in 8 ways . and , second digit can be filled in 9 ways . and , third digit can be filled in 9 ways . and , fourth digit can be filled in 8 ways . total ways = 8 * 9 * 9 * 8 = 5184 hence option ( d ) ." + }, + { + "Answer": 4, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "c", + "Explanation": "let us understand the meaning of | a | > 2 mod is very easy concept if you solve mod question by considering as a distance . when a mod is written as | x - ( a ) | = b , this means the distance from point ' a ' ( both side left and right of ' a ' on number line ) is b . | x - ( a ) | < b means the distance is between the two extreme distance ( left and right side of ' a ' on number line , considering the max distance is ' b ' from ' a ' - as per this scenario . . . . . hence the value of ' a ' must be between these two extremes . | x - ( a ) | > b means the distance is greater than the distance of ' b ' . . i . e the value of a could be anywhere more than ' b ' ( i . e . current case ) . now come to the question . first its given | a | > 2 = = > a > 2 i . e . a can have any value bigger than 2 ( i . e . 3 , 4 , 5 \u2026 ) . now , lets move to equation a + 2 b = 32 = = > b = ( 32 \u2013 a ) / 2 = = > b = 16 \u2013 ( a / 2 ) . according to question , b is an integer , hence to make \u2018 b \u2019 integer a must be divisible by 2 . minimum possible value of \u2018 a \u2019 that is divisible by 2 is 4 ( a is greater than 2 so the next number that is divisible by 2 is 4 ) . so the answer is c ( value 4 ) ." + }, + { + "Answer": 315, + "Options": "a ) $ 315 , b ) $ 245 , c ) $ 365 , d ) $ 715 , e ) $ 730", + "Correct": "a", + "Explanation": "total weekly income over 5 weeks = $ 406 + $ 413 + $ 420 + $ 436 + $ 495 = $ 2170 for avg weekly income to be $ 500 over 7 weeks , we need total weekly income over 7 weeks = $ 3500 now , $ 3500 - $ 2170 = $ 1330 from this , we subtract base salary for 2 weeks i . e $ 350 * 2 = $ 700 therefore , commission = $ 1330 - $ 700 = $ 730 for 2 weeks avg weekly commission = $ 315 answer a" + }, + { + "Answer": 165, + "Options": "a ) 165 , b ) 161 , c ) 162 , d ) 163 , e ) 164", + "Correct": "a", + "Explanation": "\"to minimize one quantity maximize other . 164 * 2.5 ( max possible amount of food a guest could consume ) = 410 pounds , so there must be more than 164 guests , next integer is 165 . answer : a .\"" + }, + { + "Answer": 39.99999999999998, + "Options": "a ) 3 / 80 , b ) 3 / 5 , c ) 40 , d ) 5 / 3 , e ) 80 / 3", + "Correct": "c", + "Explanation": "\"15 / 100 = 3 / 20 n = 2 ^ 3 / 20 n ^ b = 2 ^ 6 ( 2 ^ 3 / 20 ) ^ b = 2 ^ 6 b = 40 answer : c\"" + }, + { + "Answer": 2.9166666666666665, + "Options": "a ) 3 / 5 , b ) 1 / 7 , c ) 12 / 35 , d ) 31 / 12 , e ) 35 / 12", + "Correct": "e", + "Explanation": "\"1 / r = 1 / x + 1 / y 1 / r = 1 / 5 + 1 / 7 = 12 / 35 r = 35 / 12 the answer is e .\"" + }, + { + "Answer": 7.225, + "Options": "a ) 6.6 kg , b ) 7.225 kg , c ) 6.7 kg , d ) 6.9 kg , e ) 7.8 kg", + "Correct": "b", + "Explanation": "850 * 8.5 7225.0 gm 7.225 kg answer : b" + }, + { + "Answer": 26, + "Options": "a ) 23 years , b ) 22 years , c ) 21 years , d ) 20 years , e ) 26 years", + "Correct": "e", + "Explanation": "\"let present age of the son = x years then , present age the man = ( x + 28 ) years given that , in 2 years , man ' s age will be twice the age of his son \u00e2 \u2021 \u2019 ( x + 28 ) + 2 = 2 ( x + 2 ) \u00e2 \u2021 \u2019 x = 26 answer : e\"" + }, + { + "Answer": 10, + "Options": "a ) 7 , b ) 8 , c ) 10 , d ) 12 , e ) 14", + "Correct": "c", + "Explanation": "\"option ' c ' 10 / 9 = 1 and 100 / 9 = 11 = = > 11 - 1 = 10 . therefore 10 digits .\"" + }, + { + "Answer": 9, + "Options": "a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9", + "Correct": "e", + "Explanation": "\"7 in power repeats pattern of 4 : 7 - 9 - 3 - 1 . as 75 = 4 * 18 + 3 then the last digit of 7 ^ 75 is the same as the last digit of 7 ^ 3 , which is 3 . units digit of 7 ^ 75 + 6 will be : 3 + 6 = 9 . answer is e\"" + }, + { + "Answer": 25, + "Options": "a ) 5 % , b ) 10 % , c ) 15 % , d ) 20 % , e ) 25 %", + "Correct": "e", + "Explanation": "\"solution : let the total number of flags be 100 ( even number ) let the total number of ' blue ' flags alone be ' a ' let the total number of ' red ' flags alone be ' b ' let the total number of ' both ' flags be ' c ' we have given , total number of blue flags = 60 % = 60 = a + c total number of red flags = 65 % = 65 = b + c total number of flags = a + b + c = 100 ( since all the flags have been utilized ) so , substituting for c in the third equation , we have , 60 - c + c + 65 - c = 100 c = 25 option e .\"" + }, + { + "Answer": 90.4, + "Options": "a ) 67 , b ) 26 , c ) 87 , d ) 26 , e ) 90", + "Correct": "e", + "Explanation": "\"average = ( 96 + 95 + 82 + 87 + 92 ) / 5 = 452 / 5 = 90 . answer : e\"" + }, + { + "Answer": 32, + "Options": "a ) 20 , b ) 22 , c ) 26 , d ) 30 , e ) 32", + "Correct": "e", + "Explanation": "\"women = 2 / 5 * 80 = 32 married = 1 / 2 * 80 = 40 unmarried = 40 max ( un - married women ) = 32 e\"" + }, + { + "Answer": 16, + "Options": "a ) 11 , b ) 12 , c ) 14 , d ) 16 , e ) 18", + "Correct": "d", + "Explanation": "\"let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 32 = > 2 x = 32 = > x = 16 d\"" + }, + { + "Answer": 1, + "Options": "a ) 1.5 kg , b ) 2 kg , c ) . 5 kg , d ) 1 kg , e ) none of these", + "Correct": "d", + "Explanation": "explanation : by the rule of alligation , we have percentage concentration of manganese in the mixture : 20 percentage concentration of manganese in pure iron : 0 percentage concentration of manganese in the final mixture 10 10 - 0 = 10 20 - 10 = 10 = > quantity of the mixture : quantity of iron = 10 : 10 = 1 : 1 given that quantity of the mixture = 1 kg hence quantity of iron to be added = 1 kg answer : option d" + }, + { + "Answer": 11.999999999999998, + "Options": "a ) 0 , b ) 5 , c ) 12 , d ) 15 , e ) 20", + "Correct": "c", + "Explanation": "\"x = \u221a 3 and y also = \u221a 3 applying the function ( \u221a 3 + \u221a 3 ) ^ 2 - ( \u221a 3 - \u221a 3 ) ^ 2 = ( 2 \u221a 3 ) ^ 2 - 0 = 4 x 3 = 12 . note : alternative approach is the entire function is represented as x ^ 2 - y ^ 2 = ( x + y ) ( x - y ) which can be simplified as ( x + y + x - y ) ( x + y - ( x - y ) ) = ( 2 x ) ( 2 y ) = 4 xy . substituting x = \u221a 3 and y = \u221a 3 you get the answer 12 . answer c\"" + }, + { + "Answer": 12, + "Options": "a ) 11.0 , b ) 12.0 , c ) 13.0 , d ) 14.0 , e ) 15.0", + "Correct": "b", + "Explanation": "solution : h stopped 1000 ft before reaching the final point , time taken to reach 4000 ft = 4000 / 800 = 5 hrs . this means she reached there at 11 : 00 . speed difference between them is 800 - 500 = 300 ft / hr so by the time h stops they have 1500 ft of distance so now here we use relative speed formula they both are travelling toward each other with speed of 1000 and 500 total 1500 ft / hr and distance bwn them is 1500 ft so time taken to meet = 1 hr from 11 : 00 means 12 : 00 is the answer . b" + }, + { + "Answer": 12.5, + "Options": "a ) 6.7 , b ) 1.3 , c ) 9.6 , d ) 12.5 , e ) 7.9", + "Correct": "d", + "Explanation": "\"amount salt in 100 kg solution = 10 * 100 / 100 = 10 kg let x kg of pure salt be added then ( 10 + x ) / ( 100 + x ) = 20 / 100 100 + 10 x = 200 + 2 x 8 x = 100 x = 12.5 answer is d\"" + }, + { + "Answer": 396, + "Options": "a ) $ 396 , b ) $ 400 , c ) $ 404 , d ) $ 408 , e ) $ 412", + "Correct": "a", + "Explanation": "\"the service cost of 4 vans and 2 trucks is 6 * 2.30 $ 13.80 the fuel in 4 vans is 4 * 65 = 260 liters the fuel in 2 trucks is 2 * 65 * 2.2 = 286 liters the total fuel ( vans + trucks ) = 546 liters the total fuel cost is 546 * 0.7 = $ 382.20 the total cost is $ 382.20 + $ 13.80 = $ 396 the answer is a .\"" + }, + { + "Answer": 1632, + "Options": "a ) 1234 , b ) 1265 , c ) 1350 , d ) 1467 , e ) 1647", + "Correct": "e", + "Explanation": "\"let the smaller number be x . then larger number = ( x + 1375 ) . x + 1375 = 6 x + 15 5 x = 1360 x = 272 large number = 272 + 1375 = 1647 e\"" + }, + { + "Answer": 2800.0000000000005, + "Options": "a ) 800 , b ) 500 , c ) 2800 , d ) 1600 , e ) none", + "Correct": "c", + "Explanation": "answer 3.5 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ] = 3.5 x [ ( 36 x 48 x 250 ) / ( 12 x 9 x 5 ) ] = 3.5 x 4 x 4 x 50 = 2800 correct option : c" + }, + { + "Answer": 78, + "Options": "a ) 29 , b ) 78 , c ) 39 , d ) 37 , e ) 75", + "Correct": "b", + "Explanation": "\"average = ( 91 + 65 + 82 + 67 + 85 ) / 5 = 78 answer : b\"" + }, + { + "Answer": 5969.7231730930225, + "Options": "a ) 5969.72 , b ) 8877.72 , c ) 2877.72 , d ) 2678.72 , e ) 1011.72", + "Correct": "a", + "Explanation": "8000 - - - - 1261 100 - - - - ? = > 15.76 % x * 115.76 / 100 * 115.76 / 100 = 8000 x * 1.34 = 8000 x = 8000 / 1.34 = > 5969.72 answer : a" + }, + { + "Answer": 2, + "Options": "a ) 7 , b ) 1 , c ) 2 , d ) 9 , e ) 8", + "Correct": "c", + "Explanation": "using the elimination method substitute options for x and find the correct option . answer : c" + }, + { + "Answer": 20, + "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 20", + "Correct": "e", + "Explanation": "\"total marks of male = m total marks of female = f number of males = 8 number of females = f given : ( m + f ) / ( 8 + f ) = 90 - - - - - - - - - - - - - 1 also given , m / 8 = 85 thus m = 680 - - - - - - - - - 2 also , f / f = 92 thus f = 92 f - - - - - - - - - 3 put 2 and 3 in 1 : we get ( 680 + 92 f ) / ( 8 + f ) = 90 solving this we get f = 20 ans : e\"" + }, + { + "Answer": 100, + "Options": "a ) 50 , b ) 26 , c ) 27 , d ) 28 , e ) 100", + "Correct": "e", + "Explanation": "\"let the length of each train be x m . then , distance covered = 2 x m . relative speed = 46 - 36 = 10 km / hr . = 10 * 5 / 18 = 25 / 9 m / sec . 2 x / 72 = 25 / 9 = > x = 100 . answer : e\"" + }, + { + "Answer": 500, + "Options": "a ) 500 , b ) 650 , c ) 400 , d ) 575 , e ) 610", + "Correct": "a", + "Explanation": "\"let the maximum marks be x then , 40 % of x = 150 + 50 40 x / 100 = 200 x = 500 answer is a\"" + }, + { + "Answer": 500, + "Options": "a ) $ 200 , b ) $ 500 , c ) $ 600 , d ) $ 800 , e ) $ 1,200", + "Correct": "b", + "Explanation": "suppose total money spent = x not spend ( money he still has ) = x - 800 x + x - 800 = 1800 x = 1300 money not spend = 1300 - 800 = 500 answer : b" + }, + { + "Answer": 40, + "Options": "a ) 30 , b ) 35 , c ) 40 , d ) 45 , e ) 50", + "Correct": "c", + "Explanation": "let age of the son before 8 years = x then , age of kamal before 8 years ago = 4 x after 8 years , kamal will be twice as old as his son \u21d2 4 x + 16 = 2 ( x + 16 ) \u21d2 x = 8 present age of kamal = 4 x + 8 = 4 \u00d7 8 + 8 = 40 answer is c ." + }, + { + "Answer": 6, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9", + "Correct": "b", + "Explanation": "\"6 years answer : b\"" + }, + { + "Answer": 3500, + "Options": "a ) 1900 , b ) 3500 , c ) 4000 , d ) 2000 , e ) 2500", + "Correct": "b", + "Explanation": "let the number of 50 \u2013 rupee notes be x . then , the number of 100 - rupee notes = ( 85 \u2013 x ) 50 x + 100 ( 85 \u2013 x ) = 5000 x + 2 ( 85 \u2013 x ) = 100 = x = 70 so , required amount = rs . ( 50 x 70 ) = rs . 3500 answer : b" + }, + { + "Answer": 453.51473922902494, + "Options": "a ) 221 , b ) 287 , c ) 453 , d ) 288 , e ) 171", + "Correct": "c", + "Explanation": "explanation : 500 = p ( 21 / 20 ) 2 p = 453.51 answer : c" + }, + { + "Answer": 0.5625, + "Options": "a ) 3 , b ) 6 , c ) 1 / 9 , d ) 1 / 3 , e ) 9 / 16", + "Correct": "e", + "Explanation": "\"explanation : solution : given x = k / y ^ 2 , where k is constant . now , y = 3 and x = 1 gives k = 9 . . ' . x = 9 / y ^ 2 = > x = 9 / 4 ^ 2 = 9 / 16 answer : e\"" + }, + { + "Answer": 58, + "Options": "a ) 12 liters , b ) 32 liters , c ) 41 liters , d ) 50 liters , e ) 58 liters", + "Correct": "e", + "Explanation": "\"milk = 3 / 5 * 145 = 87 liters water = 58 liters 87 : ( 58 + p ) = 3 : 4 174 + 3 p = 348 = > p = 58 58 liters of water are to be added for the ratio become 3 : 4 . answer : e\"" + }, + { + "Answer": 12, + "Options": "a ) 11 , b ) 15 , c ) 12 , d ) 17 , e ) 19", + "Correct": "c", + "Explanation": "\"c 12 ( x + y ) \u2013 ( y + z ) = 12 x \u2013 z = 12\"" + }, + { + "Answer": 18.700000000000003, + "Options": "a ) 15.60 , b ) 16.0 , c ) 17.8 , d ) 18.7 , e ) 19.1", + "Correct": "d", + "Explanation": "first 1 / 5 minute charge = 3.10 cents rest of the minute = 8 - ( 1 / 5 ) = 39 / 5 charge for the rest of the minute = 39 * 0.4 = 15.6 total charge = 3.10 + 15.6 = 18.7 cents answer is d ." + }, + { + "Answer": 0.2222222222222222, + "Options": "a ) 1 / 9 , b ) 2 / 9 , c ) 4 / 9 , d ) 3 / 9 , e ) 2 / 27", + "Correct": "b", + "Explanation": "\"we just need to find the factor thats all , w - > quadrupled - > 4 w f - > doubled - > 2 f z - > tripled - > 3 z hence , z ^ 2 = 9 z ^ 2 w is in numerator , and f * z in denominator . hence , additional factor being introduced = 4 / 2 * 9 = 4 / 18 = 2 / 9 = b\"" + }, + { + "Answer": 6, + "Options": "a ) 6 rs , b ) 2 rs , c ) 4 rs , d ) 9 rs , e ) 3 rs", + "Correct": "a", + "Explanation": "\"5 m = xw = 8 b 5 m + xw + 8 b - - - - - 90 rs . 5 m + 5 m + 5 m - - - - - 90 rs . 15 m - - - - - - 90 rs . = > 1 m = 6 rs . answer : a\"" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 17 , c ) 18 , d ) 77 , e ) 26", + "Correct": "a", + "Explanation": "\"answer : 1 option : a\"" + }, + { + "Answer": 0.5, + "Options": "a ) 1 / 2 , b ) 1 / 3 , c ) 2 / 3 , d ) 1 / 4 , e ) 1 / 5", + "Correct": "a", + "Explanation": "\"e - > a / b = 20 * 21 * \u2026 \u2026 * 39 / 21 * 22 * \u2026 . * 39 * 40 = 20 / 40 = 1 / 2 . therefore , the answer is a .\"" + }, + { + "Answer": 22, + "Options": "a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24", + "Correct": "c", + "Explanation": "check two extreme cases : jane = 20 , child = 10 , years ago = 32 - 20 = 12 - - > child ' s age now = 10 + 12 = 22 ; jane = 22 , child = 11 , years ago = 32 - 22 = 10 - - > child ' s age now = 11 + 10 = 21 . answer : c ." + }, + { + "Answer": 7, + "Options": "a ) 5 , b ) 7 , c ) 11 , d ) 13 , e ) 17", + "Correct": "b", + "Explanation": "if we break down what the stem is asking what is the sum of all mult of 50 between 300 and 600 . using arithmetic progression to find n : 600 = 300 + ( n - 1 ) 50 300 + 50 = 50 n 350 = 50 n = > n = 7 the sum would be : 11 * mean mean = [ 600 + 300 ] / 2 = 450 7 * 450 = 4950 b" + }, + { + "Answer": 50, + "Options": "a ) 20 % , b ) 30 % , c ) 40 % , d ) 50 % , e ) 70 %", + "Correct": "d", + "Explanation": "\"to maximize the percentage of companies offering both , let ' s assume that all 50 % of companies which offer wireless internet also offer snacks . the answer is d .\"" + }, + { + "Answer": 32.72727272727272, + "Options": "a ) 32 kmph , b ) 33 kmph , c ) 34 kmph , d ) 35 kmph , e ) 36 kmph", + "Correct": "b", + "Explanation": "\"avg speed = total distance / total time . total distance traveled = 100 + 50 = 150 km ; time taken for uphill journey = 100 / 30 = 10 / 3 ; time taken for down hill journey = 50 / 40 = 5 / 4 ; avg speed = 150 / ( 10 / 3 + 5 / 4 ) = 33 kmph answer : b\"" + }, + { + "Answer": 7.448077718958487, + "Options": "a ) $ 4.50 , b ) $ 5.10 , c ) $ 5.30 , d ) $ 7.50 , e ) $ 5.60", + "Correct": "d", + "Explanation": "\"i tried using time / rate approach : - initial price difference = 7.80 - 3.20 = 4.60 price of corn increasing by 5 x price of wheat decreasing by x ( 1.4 ) - x = . 4 x since both the quantities are moving towards reducing the price gap hence : - relative increase = 5 x + . 4 x let t be the time by which gap is filled so , 4.6 = t ( 5.4 x ) - > t = ( 4.6 ) / 5.4 x final price = 3.20 + 5 x * t - > 3.20 + 5 * 4.6 / 5.4 = 7.5 answer d .\"" + }, + { + "Answer": 0.32653061224489793, + "Options": "a ) 2 / 7 , b ) 16 / 49 , c ) 16 / 25 , d ) 7 / 1 , e ) 7 / 2", + "Correct": "b", + "Explanation": "\"for a 2 nd degree equation ax 2 + bx _ c = 0 has equal roots the condition is b 2 - 4 ac = 0 in the given equation ( 7 k ) ^ 2 - 4 * 2 k * 2 = 0 by solving this equation we get k = 0 , k = 16 / 49 answer : b\"" + }, + { + "Answer": 6720, + "Options": "a ) 6720 , b ) 7720 , c ) 7820 , d ) 7950 , e ) 8120", + "Correct": "a", + "Explanation": "first ring can be worn in 4 ways ( on any of the four fingers ) ; second ring can be worn in 5 ways ( as it can go on any of four fingers - 4 ways ; plus it can go below the first one - 1 ) ; third ring can be worn in 6 ways ( the same logic as for the second ring ) ; fourth ring can be worn in 7 ways ; fifth ring can be worn in 8 ways ; total : 4 * 5 * 6 * 7 * 8 = 6720 . ans : a" + }, + { + "Answer": 0.09090909090909091, + "Options": "a ) 1 / 11 , b ) 1 / 20 , c ) 1 / 19 , d ) 1 / 10 , e ) 1 / 9", + "Correct": "a", + "Explanation": "the problem with your solution is that we do n ' t choose 1 shoe from 12 , but rather choose the needed one after we just took one and need the second to be the pair of it . so , the probability would simply be : 1 / 1 * 1 / 11 as after taking one at random there are 11 shoes left and only one is the pair of the first one ) = 1 / 11 answer : a ." + }, + { + "Answer": 90.9090909090909, + "Options": "a ) 12.5 % , b ) 90.9 , c ) 91.7 , d ) 11 % , e ) 1 %", + "Correct": "b", + "Explanation": "\"say y = 1 and x = 11 . then y = 1 is less than x = 11 by ( 11 - 1 ) / 11 * 100 = 10 / 11 * 100 = 90.9 % . answer : b .\"" + }, + { + "Answer": 1.6800000000000637, + "Options": "a ) 2 , b ) 4.3 , c ) 1.68 , d ) 1.5 , e ) 3.2", + "Correct": "c", + "Explanation": "since ravi ' s 4 days average income for form filling is defined as the greatest positive even integer less than or equal to his avg income , then avg income for form filling = 1024 ( the greatest positive even integer less than or equal to 1025.68 is 1024 ) . hence the difference = 1025.68 - 1024 = 1.68 answer : c ." + }, + { + "Answer": 60, + "Options": "a ) 60 min , b ) 50 min , c ) 70 min , d ) 65 min , e ) 80 min", + "Correct": "a", + "Explanation": "a 60 min roy will be able to consume all the five tablets in an hour . tablet 1 will be taken in 0 min . tablet 2 will be taken in 15 min . tablet 3 will be taken in 30 min . tablet 4 will be taken in 45 min . tablet 5 will be taken in 60 min ." + }, + { + "Answer": 119, + "Options": "a ) 100 , b ) 110 , c ) 119 , d ) 120 , e ) 112", + "Correct": "c", + "Explanation": "we just enter this root into the equation in order to recieve an equation to find the answer ! 2 * 7 ^ 2 + 3 * 7 - k = 0 k = 98 + 21 = 119 the answer is c" + }, + { + "Answer": 23, + "Options": "a ) a . 72 , b ) b . 50 , c ) c . 48 , d ) d . 46 , e ) e . 23", + "Correct": "e", + "Explanation": "\"at 6 : 00 it ' ll chime 6 times . if we assume that the time taken to chime is x , then time between chimes is also x . so you have 6 chimes , which is 6 x and 5 time intervals between chimes . this means that 11 x = 11 seconds . thus x = 1 seconds . by a similar logic , at 12 : 00 , there are 12 chimes and 11 intervals so the total time is ( 12 + 11 ) x = 23 x = 23 seconds . answer e\"" + }, + { + "Answer": 32, + "Options": "a ) 10 , b ) 32 , c ) 15 , d ) 18 , e ) 19", + "Correct": "b", + "Explanation": "\"2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 100 - 36 = 64 = > ab = 32 answer : b\"" + }, + { + "Answer": 14, + "Options": "a ) s . 13 , b ) s . 12 , c ) s . 15 , d ) s . 22 , e ) s . 14", + "Correct": "e", + "Explanation": "total members in the group = 7 average amount = rs . 20 total amount with them = 7 * 20 = rs . 140 one number has rs . 56 . so , the amount with remaining 6 people = 140 - 56 = rs . 84 the average amount with them = 84 / 6 = rs . 14 . answer : e" + }, + { + "Answer": 96, + "Options": "a ) 88 , b ) 90 , c ) 96 , d ) 98 , e ) 102", + "Correct": "c", + "Explanation": "2 multiples - choice questions can be answered in = 4 x 4 = 16 ways 3 true - false questions can be answered in = 2 x 2 x 2 = 8 ways but out of the 8 ways , 2 ways [ ( true - true - true ) ( false - false - false ) ] will contain same answers thus 3 true - false questions can be answered in = 2 x 2 x 2 = 6 ways total ways to answer the quiz = 16 x 6 = 96 answer c" + }, + { + "Answer": 77, + "Options": "a ) 73 , b ) 74 , c ) 75 , d ) 76 , e ) 77", + "Correct": "e", + "Explanation": "we need to take gcd which is 2 thus all the rooms will have 2 students of the same dept 1 ) 72 / 2 = 36 2 ) 58 / 2 = 29 3 ) 24 / 2 = 12 total no . of min rooms reqd = 36 + 12 + 29 = 77 answer : e" + }, + { + "Answer": 77.5, + "Options": "a ) 45 % , b ) 40 % , c ) 35 % , d ) 77.5 % , e ) 30 %", + "Correct": "d", + "Explanation": "\"price = p initially price reduced by 25 % which means new price is 3 / 4 p now on this new price further 70 percent is reduced which means the new price is merely 30 percent of 3 / 4 p = = > ( 3 / 4 ) x ( 3 / 10 ) p = 9 / 40 p is the new price after both deduction which is 22.5 percent of the original value p . this implies this entire series of deduction is worth having discounted 77.5 % of p . so answer is d = 77.5 %\"" + }, + { + "Answer": 44, + "Options": "a ) 50 , b ) 45 , c ) 44 , d ) 60 , e ) 65", + "Correct": "c", + "Explanation": "\"explanation : required number = lcm of ( 9 , 6 , 12 and 18 ) + 8 = 36 + 8 = 44 answer : option c\"" + }, + { + "Answer": 0.1428571428571428, + "Options": "a ) 1 / 8 , b ) 1 / 6 , c ) 1 / 7 , d ) 1 / 5 , e ) 1 / 4", + "Correct": "c", + "Explanation": "if s is an integer and we know that the average speed is 2.8 , s must be = 2 . that meanss + 1 = 3 . this implies that the ratio of time for s = 2 is 1 / 4 of the total time . the formula for distance / rate is d = rt . . . so the distance travelled when s = 2 is 2 t . the distance travelled for s + 1 = 3 is 3 * 4 t or 12 t . therefore , total distance covered while the sun was shining over him is 2 / 14 = 1 / 7 . answer : c" + }, + { + "Answer": 549.9999999999998, + "Options": "a ) $ 500 , b ) $ 550 , c ) $ 600 , d ) $ 650 , e ) $ 700", + "Correct": "b", + "Explanation": "bob earned 2000 * ( 1 + 0.12 ) in total by fund a and earned 1000 * ( 1 + 0.3 ) ^ 2 in total by fund b . so 2000 * ( 1.12 ) - 1000 * ( 1.69 ) = 550 . the answer is , therefore , ( b ) ." + }, + { + "Answer": 100.27397260273973, + "Options": "a ) 100 , b ) 105 , c ) 109 , d ) 120 , e ) 90", + "Correct": "a", + "Explanation": "\"total production of salt by the company in that year = 2500 + 2600 + 2700 + . . . . + 3600 = 36600 . average monthly production of salt for that year = 36600 / 365 \u00e2 \u2030 \u02c6 100 answer : a\"" + }, + { + "Answer": 35, + "Options": "a ) 37 kg , b ) 35 kg , c ) 85 kg , d ) 45 kg , e ) 25 kg", + "Correct": "b", + "Explanation": "7 / 20 * 100 = 35 answer : b" + }, + { + "Answer": 0.98, + "Options": "a ) 0.98 , b ) 9.4 , c ) 0.094 , d ) 94 , e ) none", + "Correct": "a", + "Explanation": "answer let a - 2 % of a = ab . \u21d2 ( 98 x a ) / 100 = ab \u2234 b = 0.98 correct option : a" + }, + { + "Answer": 7.499999999999996, + "Options": "a ) 7.5 % , b ) 5 % , c ) 12 % , d ) 8 % , e ) 10 %", + "Correct": "a", + "Explanation": "total price including tax is $ 98.90 perfume cost before tax is = 92 ie 92 * 7.5 % + 98.90 answer is 7.5 %" + }, + { + "Answer": 11, + "Options": "a ) 11 , b ) 12 , c ) 10 , d ) 22 , e ) 44", + "Correct": "a", + "Explanation": "detailed solution number should be a multiple of 3 and 4 . so , the sum of the digits should be a multiple of 3 . we can either have all seven digits as 3 , or have three 2 ' s and four 3 ' s , or six 2 ' s and a 3 . ( the number of 2 ' s should be a multiple of 3 ) . for the number to be a multiple of 4 , the last 2 digits should be 32 . now , let us combine these two . all seven 3 ' s - no possibility . three 2 ' s and four 3 ' s - the first 5 digits should have two 2 ' s and three 3 ' s in some order . no of possibilities = 5 ! 3 ! 2 ! = 10 six 2 ' s and one 3 - the first 5 digits should all be 2 ' s . so , there is only one number 2222232 . so , there are a total of 10 + 1 = 11 solutions . correct answer : a ." + }, + { + "Answer": 20, + "Options": "a ) 20 liters , b ) 40 liters , c ) 45 liters , d ) 54 liters , e ) 60 liters", + "Correct": "a", + "Explanation": "\"a big container is 30 % full with water and after 9 liters of water is added , the container becomes 75 % full . hence these 9 liters account for 45 % of the container , which means that the capacity of it is 9 / 0.45 = 20 liters . or : if the capacity of the container is x liters then : 0.3 x + 9 = 0.75 x - - > x = 20 liters . answer : a .\"" + }, + { + "Answer": 5, + "Options": "a ) 8 , b ) 10 , c ) 5 , d ) 14 , e ) 7", + "Correct": "c", + "Explanation": "\"explanation : = > 3 ( 2 x + 15 ) = 75 = > 2 x + 15 = 25 = > x = 5 option c\"" + }, + { + "Answer": 3675, + "Options": "a ) 3675 , b ) 3575 , c ) 3475 , d ) 3375 , e ) 3275", + "Correct": "a", + "Explanation": "explanation : to solve this use the formula of ap , sn = ( n / 2 ) ( a + l ) . . . . . . . . . . . . . . . . ( 1 ) to find n , use = > tn = a + ( n - 1 ) d = > 69 = 1 + ( n - 1 ) 2 = > n = 35 use value of n in ( 1 ) then , sn = ( 35 / 2 ) ( 1 + 69 ) = 1225 ans : - 3 ( sn ) = 3675 answer : a" + }, + { + "Answer": 407, + "Options": "a ) a ) 407 , b ) b ) 518 , c ) c ) 519 , d ) d ) 521 , e ) e ) 525", + "Correct": "a", + "Explanation": "a very helpful rule to know in arithmetic is the rule that in evenly spaced sets , average = median . because the average will equal the median in these sets , then we quickly know that the median of this set of consecutive odd integer numbers is 414 . there are 8 numbers in the set , and in a set with an even number of terms the median is just the average of the two most median terms ( here the 4 th and 5 th numbers in the set ) . this means that numbers 4 and 5 in this set are 413 and 415 . because we know that number 4 is 413 , we know that the smallest number is 3 odd numbers below this , which means that it is 3 * 2 = 6 below this ( every odd number is every other number ) . therefore 413 - 6 = 407 , answer choice a" + }, + { + "Answer": 45.000000000000014, + "Options": "a ) 15 % , b ) 20 % , c ) 22.5 % , d ) 45 % , e ) 50 %", + "Correct": "d", + "Explanation": "\"4 miles on the highway = 4 / 38 gallons ; 4 miles in the city = 4 / 20 gallons ; total = 4 / 38 + 4 / 20 = 29 / 95 gallons . 8 miles on the highway = 8 / 38 gallons . the % change = ( 29 / 95 - 8 / 38 ) / ( 8 / 38 ) = 0.45 . answer : d .\"" + }, + { + "Answer": 85, + "Options": "a ) 75 . , b ) 85 . , c ) 90 . , d ) 94 . , e ) 100 .", + "Correct": "b", + "Explanation": "edit : given ( x 1 + x 2 . . . + x 6 ) / 6 = 80 ( x 1 + x 2 . . . + x 6 ) = 480 - - > eq 1 . now given avg length of one third wires is 70 . that means out 6 / 3 = 2 wires . let the avg length of two wires be ( x 1 + x 2 ) / 2 = 70 . ( x 1 + x 2 ) = 140 . - - > eq 2 . now we are asked to find the average of the remaining i . e . ( x 3 + x 4 + x 5 + x 6 ) substitute eq 2 in eq 1 then we get 140 + x 3 + x 4 + x 5 + x 6 = 480 = > x 3 + x 4 + x 5 + x 6 = 340 now divide 340 by 4 we get 85 . = > ( x 3 + x 4 + x 5 + x 6 ) / 4 = 85 = avg length of remaining wires . imo correct option is b ." + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "a", + "Explanation": "when 15 is divided by u , the remainder is 4 i . e . 4 mangoes left over after grouping , so u must be greater than 4 . it also means that 11 is completely divisible by u . factors of 11 are 1 and 11 . out of these , u could be 11 . answer ( a )" + }, + { + "Answer": 144, + "Options": "a ) 216 , b ) 180 , c ) 144 , d ) 108 , e ) 72", + "Correct": "c", + "Explanation": "\"there are several ways to find the least common multiple of two numbers . in this case , the most efficient method is to use the greatest common factor : ( a * b ) / ( gcf ab ) = lcm ab the greatest common factor of 12 and 16 is 4 . so , 12 # 16 = 12 * 16 / 4 = 48 . the greatest common factor of 18 and 24 is 6 . so , 18 # 24 = 18 * 24 / 6 = 72 finally , the greatest common factor of 48 and 72 is 24 . so , w = ( ( 12 # 16 ) # ( 18 # 24 ) ) = 48 # 72 = ( 48 * 72 ) / 24 = 2 * 72 = 144 the correct answer is c .\"" + }, + { + "Answer": 50, + "Options": "a ) 40 , b ) 45 , c ) 48 , d ) 50 , e ) 55", + "Correct": "d", + "Explanation": "let d be the distance and let v be the speed in the second half . the total time = t 1 + t 2 d / 60 = d / 150 + ( d / 2 ) / v d / 100 = d / 2 v and so v = 50 km / hr the answer is d ." + }, + { + "Answer": 1.2000000000000002, + "Options": "a ) 0.2 , b ) 1.2 , c ) 1.8 , d ) 2.2 , e ) 4.0", + "Correct": "b", + "Explanation": "since s * is defined as the greatest positive even integer less than or equal to s , then 5.2 * = 4 ( the greatest positive even integer less than or equal to 5.2 is 4 ) . hence , 5.2 \u2013 5.2 * = 5.2 - 4 = 1.2 answer : b ." + }, + { + "Answer": 32, + "Options": "a ) 30 , b ) 31 , c ) 32 , d ) 35 , e ) 36", + "Correct": "c", + "Explanation": "let their present ages be 5 x , 7 x and 8 x . 7 years ago , sum of their ages was 59 . sum of their present ages = 59 + ( 3 x 7 ) = 80 sum of their present ages given is 5 x + 7 x + 8 x = 20 x 20 x = 80 = > x = 80 20 = 4 age of the eldest one = 8 x = 8 x 4 = 32 years . c" + }, + { + "Answer": 399, + "Options": "a ) a ) 399 , b ) b ) 418 , c ) c ) 519 , d ) d ) 521 , e ) e ) 525", + "Correct": "a", + "Explanation": "\"a very helpful rule to know in arithmetic is the rule that in evenly spaced sets , average = median . because the average will equal the median in these sets , then we quickly know that the median of this set of consecutive odd integer numbers is 414 . there are 16 numbers in the set , and in a set with an even number of terms the median is just the average of the two most median terms ( here the 7 th and 8 th numbers in the set ) . this means that numbers 7 and 8 in this set are 413 and 415 . because we know that number 7 is 413 , we know that the smallest number is 7 odd numbers below this , which means that it is 7 * 2 = 14 below this ( every odd number is every other number ) . therefore 413 - 14 = 399 , answer choice a .\"" + }, + { + "Answer": 6.529411764705882, + "Options": "a ) 39 / 6 , b ) 62 / 11 , c ) 11 / 61 , d ) 21 / 61 , e ) 20 / 61", + "Correct": "a", + "Explanation": "let the retail price be = x selling price of z = 0.7 x selling price of x = 0.85 * 0.7 x = 0.60 x selling price of y = ( ( 0.7 x + 0.6 x ) / 2 ) * 0.60 = 0.65 x * 0.60 = 0.39 x 0.39 x = k * 0.60 x k = 0.39 / 0.6 = 39 / 6 answer : a" + }, + { + "Answer": 102, + "Options": "a ) 150 , b ) 122 , c ) 30 , d ) 120 , e ) 102", + "Correct": "e", + "Explanation": "30 x + 40 = 31 ( x \u00e2 \u20ac \u201c 2 ) x = 102 e" + }, + { + "Answer": 187.5, + "Options": "a ) $ 178.50 , b ) $ 182.50 , c ) $ 185.50 , d ) $ 187.50 , e ) $ 200", + "Correct": "d", + "Explanation": "\"0.75 * ( 1.25 * 200 ) = $ 187.50 the answer is d .\"" + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 4 , c ) 5 , d ) 1 , e ) 2", + "Correct": "a", + "Explanation": "( x / 4 ) - ( ( x - 3 ) / 6 ) = 1 = > ( 3 x - 2 ( x - 3 ) ) / 12 = 1 = > 3 x - 2 x + 6 = 12 = > x = 6 . answer is a" + }, + { + "Answer": 659.9999999999994, + "Options": "a ) $ 480 , b ) $ 570 , c ) $ 660 , d ) $ 720 , e ) $ 850", + "Correct": "c", + "Explanation": "\"let p be the original purchase price of the product . bill originally sold the product for 1.1 * p . in the second scenario , the purchase price is 0.9 * p . a 30 % profit means the selling price would be 1.3 * 0.9 * p = 1.17 * p thus , according to the information in the question , 1.17 p - 1.1 p = 42 0.07 = 42 p = 600 the original selling price was 600 * 1.1 = 660 . the correct answer is c .\"" + }, + { + "Answer": 24, + "Options": "a ) 24 , b ) 32 , c ) 36 , d ) 42 , e ) 45", + "Correct": "a", + "Explanation": "explanation : let the numbers be 4 x , 5 x and 6 x . therefore , ( 4 x + 5 x + 6 x ) / 3 = 20 15 x = 60 x = 4 largest number = 6 x = 24 . answer a" + }, + { + "Answer": 14, + "Options": "a ) 14 , b ) 19 , c ) 38 , d ) 33 , e ) 35", + "Correct": "a", + "Explanation": "et son ' s present age is = x then 38 - x = x x = 19 son ' s age 5 years back is 19 - 5 = 14 years . answer : a" + }, + { + "Answer": 2880, + "Options": "a ) 288 , b ) 320 , c ) 2,880 , d ) 3,200 , e ) 28,800", + "Correct": "c", + "Explanation": "to solve we will set up a proportion . we know that \u201c 100 million vehicles is to 96 accidents as 3 billion vehicles is to x accidents \u201d . to express everything in terms of \u201c millions \u201d , we can use 3,000 million rather than 3 billion . creating a proportion we have : 100 / 96 = 3,000 / x cross multiplying gives us : 100 x = 3,000 * 96 x = 30 * 96 = 2,880 correct answer is c ." + }, + { + "Answer": 16.000000000000004, + "Options": "a ) 3 / 80 , b ) 3 / 5 , c ) 4 , d ) 16 , e ) 80 / 3", + "Correct": "d", + "Explanation": "\"25 / 100 = 1 / 4 n = 2 ^ 1 / 4 n ^ b = 2 ^ 4 ( 2 ^ 1 / 4 ) ^ b = 2 ^ 4 b = 16 answer : d\"" + }, + { + "Answer": 25, + "Options": "a ) 20 , b ) 25 , c ) 30 , d ) 35 , e ) 40", + "Correct": "b", + "Explanation": "firstly we have 20 friends and money wiill be distribute each of them 5 rupee then 5 more friends it means total no frnd = 25 each recv 4 rupee which means all recv 1 less rupee answer : b" + }, + { + "Answer": 45, + "Options": "a ) 45 kg , b ) 50 kg , c ) 53 kg , d ) 55 kg , e ) none of these", + "Correct": "a", + "Explanation": "\"solution weight of the teacher = ( 35.4 \u00d7 25 - 35 \u00d7 24 ) kg = 45 kg . answer a\"" + }, + { + "Answer": 5, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8", + "Correct": "b", + "Explanation": "let the number off boys in the group originally be x . total weight of the boys = 35 x after the boy weighing 40 kg joins the group , total weight of boys = 35 x + 40 so 35 x + 40 = 36 ( x + 1 ) = > x = 5 . answer : b" + }, + { + "Answer": 32.72727272727273, + "Options": "a ) 72 min , b ) 62 min , c ) 70 min , d ) 32.72727 min , e ) 76 min", + "Correct": "d", + "Explanation": "\"x = time for type b prolems 2 x = time for type a problem total time = 3 hrs = 180 min 180 x + 20 * 2 x = 180 x = 180 / 220 x = 0.818182 time taken for type a problem = 20 * 2 * 0.818182 = 32.72727 min answer : d\"" + }, + { + "Answer": 68, + "Options": "a ) 16 % , b ) 32 % , c ) 68 % , d ) 84 % , e ) 92 %", + "Correct": "c", + "Explanation": "\"this is easiest to solve with a bell - curve histogram . m here is equal to \u00b5 in the gaussian normal distribution and thus m = 50 % of the total population . so , if 36 % is one st . dev , then on either side of m we have 36 / 2 = 18 % . so , 18 % are to the right and left of m ( = 50 % ) . in other words , our value m + d = 50 + 18 = 68 % goingfrom the mean m , to the right of the distributionin the bell shaped histogram . . this means that 68 % of the values are below m + d . like i said , doing it on a bell - curve histogram is much easier to fullygethow this works , or you could apply gmat percentile jargon / theory to it c\"" + }, + { + "Answer": 79.36000000000001, + "Options": "a ) 68.8 , b ) 73.6 , c ) 75.2 , d ) 76.8 , e ) 79.36", + "Correct": "e", + "Explanation": "\"degree of difficulty of dive = 3.2 scores are 6.0 , 7.5 , 8.8 , 8.5 and 9.0 we can drop 6.0 and 9.0 sum of the remaining scores = ( 7.5 + 8.8 + 8.5 ) = 24.8 point of value of the dive = 24 * 3.2 = 79.36 answer e\"" + }, + { + "Answer": 4, + "Options": "a ) 4 , b ) 3 , c ) 2 , d ) 7 , e ) 6", + "Correct": "a", + "Explanation": "( 3 ! * 5 ! + 4 ! * 3 ! ) / 2 = 3 ! ( 5 ! + 4 ! ) / 2 = 6 ( 120 + 24 ) / 2 = 432 100 th digit of the above product will be equal to 4 answer a" + }, + { + "Answer": 1, + "Options": "a ) a . 0 , b ) b . 1 , c ) c . 3 , d ) d . 4 , e ) e . 5", + "Correct": "b", + "Explanation": "92 p \u00d7 5 p + t + 11 t \u00d7 6 pt - - 1 = b" + }, + { + "Answer": 10, + "Options": "a ) 10 , b ) 20 , c ) 40 , d ) 60 , e ) 120", + "Correct": "a", + "Explanation": "\"method 1 : take the first amateur . he plays a game with each of the other four i . e . 4 games . now take the second one . he has already played a game with the first one . he plays 3 games with the rest of the 3 amateurs i . e . 3 more games are played . now take the third amateur . he has already played a game each with the first and the second amateur . now he plays 2 games with the remaining 2 amateurs so 2 more games are played . now go on to the fourth amateur . he has already played 3 games with the first 3 amateurs . he just needs to play a game with the last one i . e . 1 more game is played . the last amateur has already played 4 games . total no of games = 4 + 3 + 2 + 1 = 10 method 2 : each person is one participant of 4 games . so there are in all 4 * 5 = 20 instances of one participant games . but each game has 2 participants so total number of games = 20 / 2 = 10 answer : a .\"" + }, + { + "Answer": 25, + "Options": "a ) 23 % , b ) 17 % , c ) 11 % , d ) 10 % , e ) 25 %", + "Correct": "e", + "Explanation": "\"e 10 % 100 - [ ( 100 - 75 ) + ( 100 - 90 ) + ( 100 - 85 ) + ( 100 - 75 ) ] = 100 - ( 25 + 10 + 15 + 25 ) = 100 - 75\"" + }, + { + "Answer": 32, + "Options": "a ) 16 , b ) 20 , c ) 32 , d ) 44 , e ) 48", + "Correct": "c", + "Explanation": "\"lets say x ounces of p is mixed with q . = > 67 - x ounces of q is present in the mixture ( as the total = 67 ounces ) given total almond weight = 15 ounces ( 20 x / 100 ) + ( 25 / 100 ) ( 67 - x ) = 15 = > x = 35 = > 67 - 35 = 32 ounces of q is present in the mixture . answer is c .\"" + }, + { + "Answer": 144, + "Options": "a ) 72 , b ) 88 , c ) 112 , d ) 122 , e ) 144", + "Correct": "e", + "Explanation": "case 1 : numbers starting with 1 1 _ _ the unit digit can take 4 numbers ( 3,5 , 7,9 ) to be odd so 4 ways . the tens digit can take remaining 8 numbers left after using 2 numbers so 8 ways . total = 8 * 4 = 32 case 2 : numbers starting with 2 2 _ _ the unit digit can take 5 numbers ( 1 , 3,5 , 7,9 ) to be odd so 5 ways . the tens digit can take remaining 8 numbers left after using 2 numbers so 8 ways . total = 8 * 5 = 40 case 3 : numbers starting with 3 3 _ _ the unit digit can take 4 numbers ( 1,5 , 7,9 ) to be odd so 4 ways . the tens digit can take remaining 8 numbers left after using 2 numbers so 8 ways . total = 8 * 4 = 32 case 4 : numbers starting with 4 4 _ _ the unit digit can take 5 numbers ( 1 , 3,5 , 7,9 ) to be odd so 5 ways . the tens digit can take remaining 8 numbers left after using 2 numbers so 8 ways . total = 8 * 5 = 40 hence 32 + 40 + 32 + 40 = 144 , correct answer is e" + }, + { + "Answer": 20, + "Options": "a ) 20 % increase , b ) 10 % increase , c ) 10 % decrease , d ) 6 % increase , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : solution : let the original price be rs . 100 . new final price = 150 % of ( 80 % of 100 ) = rs . 150 / 100 * 80 / 100 * 100 = rs . 120 . . ' . increase = 20 % answer : a\"" + }, + { + "Answer": 171, + "Options": "a ) 171 , b ) 175 , c ) 180 , d ) 190 , e ) 200", + "Correct": "a", + "Explanation": "sum s = n / 2 { 2 a + ( n - 1 ) d } = 11 / 2 { 2 * 10 + ( 11 - 1 ) * 1 } = 11 * 15 = 165 = x number of even number = ( 20 - 10 ) / 2 + 1 = 6 = y x + y = 165 + 6 = 171 a" + }, + { + "Answer": 266, + "Options": "a ) 266 , b ) 268 , c ) 270 , d ) 272 , e ) 274", + "Correct": "a", + "Explanation": "\"the least number which when divided by different divisors leaving the same remainder in each case = lcm ( different divisors ) + remainder left in each case . hence the required least number = lcm ( 33 , 8 ) + 2 = 266 . answer : a\"" + }, + { + "Answer": 70, + "Options": "a ) $ 60 , b ) $ 70 , c ) $ 75 , d ) $ 96 , e ) can not be determined", + "Correct": "b", + "Explanation": "\"solution : 3 x + 4 y + 2 z = 90 7 x + 2 y + 2 z = 50 adding both the equations = 10 x + 6 y + 4 z = 140 5 x + 3 y + 2 z = 70 ans b\"" + }, + { + "Answer": 12, + "Options": "a ) 12 days , b ) 12 1 / 4 days , c ) 14 days , d ) 24 1 / 2 days , e ) none of these", + "Correct": "a", + "Explanation": "let total money be rs . x a ' s 1 day ' s wages = rs . x / 21 , b ' s 1 day ' s wages = rs . x / 28 ( a + b ) ' s 1 day ' s wages = rs . ( x / 21 + x / 28 ) = rs . x / 12 ; money is sufficient to pay the wages of both for 12 days . correct option : a" + }, + { + "Answer": 50, + "Options": "a ) 50 , b ) 80 , c ) 120 , d ) 150 , e ) 100", + "Correct": "a", + "Explanation": "\"explanation : let the number of students be x . then , number of students above 8 years of age = ( 100 - 20 ) % of x = 80 % of x . 80 % of x = 24 + 2 / 3 of 24 80 / 100 x = 40 x = 50 . answer : option a\"" + }, + { + "Answer": 23, + "Options": "a ) r = 21 , b ) r = 22 , c ) r = 23 , d ) 24 , e ) 27", + "Correct": "c", + "Explanation": "\"squaring on both sides , x ^ 2 + ( 1 / x ) ^ 2 + 2 ( x ) ( 1 / x ) = 5 ^ 2 x ^ 2 + ( 1 / x ) ^ 2 = 23 answer : c\"" + }, + { + "Answer": 120, + "Options": "a ) 100 , b ) 110 , c ) 120 , d ) 130 , e ) 140", + "Correct": "c", + "Explanation": "\"let the number of boys who passed = x . then , 39 x x + 15 x ( 120 - x ) = 120 x 39 24 x = 4680 - 1800 = > x = 2880 / 24 x = 120 . hence , the number of boys passed = 120 . answer : c\"" + }, + { + "Answer": 81000, + "Options": "a ) 81000 , b ) 22887 , c ) 26877 , d ) 26771 , e ) 17121", + "Correct": "a", + "Explanation": "64000 * 9 / 8 * 9 / 8 = 81000 answer : a" + }, + { + "Answer": 7, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "e", + "Explanation": "the smallest amount that the company can spend is the lcm of 375 and 150 , which is 750 for each , which is total 1500 . the number of 1 st type of computers which costing $ 375 = 750 / 375 = 2 . the number of 2 nd type of computers which costing $ 150 = 750 / 150 = 5 . total = 2 + 5 = 7 answer is e ." + }, + { + "Answer": 360, + "Options": "a ) 360 , b ) 252 , c ) 280 , d ) 300 , e ) 420", + "Correct": "a", + "Explanation": "\"however the process of dividing the volume of box by the volume of a soap seems flawed but it does work in this case due to the numbers dimensions of the box = 30 * 42 * 60 dimensions of the soap = 5 * 6 * 7 we get = 6 x 6 x 10 = 360 so the question is why this particular arrangement , in order to maximize number of soaps we need to minimize the space wasted and this is the only config where we dont waste any space so we can expect the maximum number the answer is ( a )\"" + }, + { + "Answer": 16, + "Options": "a ) 4 . , b ) 8 . , c ) 12 . , d ) 16 , e ) 64", + "Correct": "d", + "Explanation": "a - b - c + d = 13 - - equation 1 a + b - c - d = 5 - - equation 2 adding 1 and 2 , we get 2 a - 2 c = 18 = > a - c = 9 - - equation 3 using equation 3 in 2 , we get b - d = 5 - 9 = - 4 = > ( b - d ) ^ 2 = 16 answer d" + }, + { + "Answer": 2400.0000000000005, + "Options": "a ) 800 , b ) 500 , c ) 900 , d ) 1600 , e ) 2400", + "Correct": "e", + "Explanation": "\"answer 3 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ] = 3 x [ ( 36 x 48 x 250 ) / ( 12 x 9 x 5 ) ] = 3 x 4 x 4 x 50 = 2400 correct option : e\"" + }, + { + "Answer": 46, + "Options": "a ) 42 , b ) 46 , c ) 50 , d ) 54 , e ) 58", + "Correct": "b", + "Explanation": "j = 2 f = 2 ( s + 9 ) = 2 s + 18 j - 6 = 5 * ( s - 6 ) ( 2 s + 18 ) - 6 = 5 s - 30 s = 14 and so j = 46 the answer is b ." + }, + { + "Answer": 10.218563187844456, + "Options": "a ) $ 4.50 , b ) $ 10.2 , c ) $ 5.30 , d ) $ 5.50 , e ) $ 5.60", + "Correct": "b", + "Explanation": "i tried using time / rate approach : - initial price difference = 10.80 - 3.20 = 7.60 price of corn increasing by 5 x price of wheat decreasing by x ( 1.4 ) - x = . 4 x since both the quantities are moving towards reducing the price gap hence : - relative increase = 5 x + . 4 x let t be the time by which gap is filled so , 7.6 = t ( 5.4 x ) - > t = ( 7.6 ) / 5.4 x final price = 3.20 + 5 x * t - > 3.20 + 5 * 7.6 / 5.4 = 10.2 answer b ." + }, + { + "Answer": 17, + "Options": "a ) 9 , b ) 11 , c ) 13 , d ) 15 , e ) 17", + "Correct": "e", + "Explanation": "\"d = ( d - r ) / q = ( 172 - 2 ) / 10 = 170 / 10 = 17 e\"" + }, + { + "Answer": 120, + "Options": "a ) 80 , b ) 90 , c ) 100 , d ) 110 , e ) 120", + "Correct": "e", + "Explanation": "\"48 liters is 40 % of the capacity c . 48 = 0.4 c c = 48 / 0.4 = 120 liters . the answer is e .\"" + }, + { + "Answer": 0.38095238095238093, + "Options": "a ) 2 / 3 , b ) 3 / 4 , c ) 7 / 19 , d ) 8 / 21 , e ) 10 / 21", + "Correct": "d", + "Explanation": "total balls are 21 and neither black nor white . so favor case will be only 8 c 1 and total case 21 c 1 probability will be 8 c 1 / 21 c 1 = 8 / 21 answer : d" + }, + { + "Answer": 36, + "Options": "a ) 48 , b ) 64 , c ) 36 , d ) 72 , e ) 27", + "Correct": "c", + "Explanation": "\"to improve his average by 5 runs per innings he has to contribute 12 x 5 = 60 runs for the previous 12 innings . thus , the average after the 13 th innings = 96 - 60 = 36 . answer : c\"" + }, + { + "Answer": 60, + "Options": "a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90", + "Correct": "b", + "Explanation": "explanation : clearly , x % of 150 = 150 - x [ as x is number of boys ] = > x + x / 100 \u2217 150 = 150 = > 5 / 2 x = 150 = > x = 60 option b" + }, + { + "Answer": 15, + "Options": "a ) 35 , b ) 30 , c ) 25 , d ) 20 , e ) 15", + "Correct": "e", + "Explanation": "a 1 = 120 / 3 = 40 a 2 = a 1 - 5 = 35 sum of second list = 35 * 3 = 105 therefore the number = 105 - 90 = 15 e" + }, + { + "Answer": 25, + "Options": "a ) 25 , b ) 42 , c ) 45 , d ) 49 , e ) 54", + "Correct": "a", + "Explanation": "\"first step will be to break down all the numbers into their prime factors . 105 = 3 * 5 * 7 21 = 7 * 3 49 = 7 * 7 45 = 3 * 3 * 5 so , ( 105 ) ^ 3 = 3 * 7 * 7 * 7 * 3 * 3 * 5 * b therefore ( 3 * 5 * 7 ) ^ 3 = 3 ^ 3 * 5 * 7 ^ 3 * b therefore , b = 3 ^ 3 * 5 ^ 3 * 7 ^ 3 / 3 ^ 3 * 5 * 7 ^ 3 b = 5 ^ 2 = 25 correct answer a .\"" + }, + { + "Answer": 1.6666666666666667, + "Options": "a ) 25 / 9 , b ) 9 / 5 , c ) 5 / 3 , d ) 3 / 5 , e ) 9 / 25", + "Correct": "c", + "Explanation": "\"sqrt ( 5 x / 3 ) to be perfect square x has to 5 / 3 ans : c\"" + }, + { + "Answer": 53.99999999999999, + "Options": "a ) 20 , b ) 24 , c ) 36 , d ) 40 , e ) 54", + "Correct": "e", + "Explanation": "\"let the capacity of the tank = c ( 3 / 4 ) c + 9 = ( 9 / 10 ) c = > ( 9 / 10 ) c - ( 3 / 4 ) c = 9 = > ( 3 / 20 ) c = 9 = > c = ( 9 * 20 ) / 3 = 60 number of gallons of gasoline that the tank currently holds = 3 / 4 * c + 9 = 45 + 9 = 54 answer e\"" + }, + { + "Answer": 18, + "Options": "a ) 18 , b ) 36 , c ) 72 , d ) 0 , e ) 1", + "Correct": "a", + "Explanation": "12 / 99 = 12 1212 / 99 = 24 121212 / 99 = 36 . . . 121212 . . . ( 300 ) / 99 = ( 12 * 300 ) % 99 = 36 if they say 300 digits then ( 12 * 150 ) % 99 = 18 answer : a" + }, + { + "Answer": 19, + "Options": "a ) 19 , b ) 20 , c ) 21 , d ) 22 , e ) 23", + "Correct": "a", + "Explanation": "avg = sum of the value / no . of the value 18 = ( sum of the first 17 innings score + 1 ) / 18 ( 18 * 18 - 1 ) = sum of the first 17 innings score sum of the first 17 innings score = 323 ave upto 17 innings = 323 / 17 = 19 answer : a" + }, + { + "Answer": 129, + "Options": "a ) 90 , b ) 129 , c ) 120 , d ) 160 , e ) 200", + "Correct": "b", + "Explanation": "\"solution : let x be the number he chose , then 2 * x * 148 = 110 2 x = 258 x = 129 correct answer b\"" + }, + { + "Answer": 45, + "Options": "a ) 22 , b ) 389 , c ) 38 , d ) 45 , e ) 01", + "Correct": "d", + "Explanation": "let there be x voters and k votes goes to loser then 0.8 x - 120 = k + ( k + 200 ) k + 200 = 0.41 x \\ inline \\ rightarrow k = 1440 and ( k + 200 ) = 1640 therefore \\ inline \\ frac { 1440 } { 3200 } \\ times 100 = 45 % answer : d ) 45 %" + }, + { + "Answer": 120, + "Options": "a ) 80 , b ) 100 , c ) 110 , d ) 120 , e ) 140", + "Correct": "d", + "Explanation": "we have numbers { 01 , 23 , 45 , 67 , 89 } now we would decide the cases on behalf of value of hundred place digit . and accordingly choose unit ' s digit and ten ' s digit . value of hundred place digit must be choosen in such a manner that there should exist a greater digit for ten ' s place and a smaller digit for unit place . thus we can have values of hundred ' s digit from 12 , 34 , 56 , 78 only now starting from hundred ' s digit = 8 : hundred ' s digit possible values for ten ' s digit possible values for unit digit total ways 8 9 01 , 23 , 45 , 67 1 * 1 * 8 = 8 7 89 0 , 12 , 34 , 56 1 * 2 * 7 = 14 6 7 , 89 01 , 23 , 45 1 * 3 * 6 = 18 5 67 , 89 0 , 12 , 34 1 * 4 * 5 = 20 4 5 , 67 , 89 01 , 23 1 * 5 * 4 = 20 3 45 , 67 , 89 0 . 1.2 1 * 6 * 3 = 18 2 3 , 45 , 67 , 89 01 1 * 7 * 2 = 14 1 23 , 45 , 67 , 89 0 1 * 8 * 1 = 8 so , total no of cases = 8 + 14 + 18 + 20 + 20 + 18 + 14 + 8 = 120 hence total no of possible 3 digit numbers = 120 answer : d" + }, + { + "Answer": 76, + "Options": "a ) 70 , b ) 76 , c ) 78 , d ) 80 , e ) 88", + "Correct": "b", + "Explanation": "\"explanation : average after 11 innings should be 36 so , required score = ( 11 * 36 ) - ( 10 * 32 ) = 396 - 320 = 76 answer : option b\"" + }, + { + "Answer": 25, + "Options": "a ) 47 , b ) 25 , c ) 37 , d ) 33 , e ) 29", + "Correct": "b", + "Explanation": "\"before you tackle this question you must first understand that the question is comprised of two key parts , 1 st is finding out how manytermsis in that sequence and 2 nd whatactual number valuethat term is . in an arithmetic progression , in this case consecutive odd integers 1 , 3 , 5 , . . . . , there are two set of rules . rule # 1 ( arithmetic sequence ) : xn = a + d ( n - 1 ) identifies what the actual # in the sequence would be . each number in the sequence has a term such as 1 ( is the first term ) , 3 ( is the second term ) and so on . so if i were to ask you to find out what the 10 th term is of that sequence you would use that formula to find that value . a = 1 ( first term ) d = 2 ( the common difference ) remember in the sequence 1 , 3 , 5 , 7 the common difference is always 2 * on a side note we use n - 1 because we do n ' t have d in the first term , therefore if we were solving for the first term we would get 0 as n - 1 and 0 times d would give us 0 , leaving only the first term . this works regardless what your first term is in any sequence . but remember the question askswhat is thevalueof n if the sum of the consecutive odd integers from 1 to n equals 169 ? which means we first need a consecutive sequence that sums up to 169 and than find what the value of the n is , in this case it would be the last number in that sequence . in order to find that we first need to knowhow many terms ( how many of the n there is ) in order to be able to plug n in this formula given we know what the sum is . for that to happen we need to use rule # 2 . rule # 2 ( summing an arithmetic series ) : 169 = n / 2 ( 2 a + ( n - 1 ) d ) . given the question gives us what the sum is ( 169 in this case ) we would simply use this formula to solve for n . once we solve for n ( 13 in this case ) we can simply plug n into the first formula ( rule 1 ) and find the value . it feels very confusing and difficult at first , but once you identify the steps all you need to do is plug and play . we have the sum ( 169 ) of a sequence , the number of terms in that sequence is ( unknown ) . rule # 2 tells us how many numbers there are in that sequence and rule # 1 gives us what that last term is .\"" + }, + { + "Answer": 900, + "Options": "a ) 278 , b ) 900 , c ) 278 , d ) 450 , e ) 772", + "Correct": "b", + "Explanation": "\"10 * 150 = 1500 3 * 100 + 2 * 150 = 600 1500 \u2013 600 = 900 answer : b\"" + }, + { + "Answer": 174, + "Options": "a ) 170 , b ) 172 , c ) 174 , d ) 176 , e ) 178", + "Correct": "c", + "Explanation": "\"the least number which when divided by different divisors leaving the same remainder in each case = lcm ( different divisors ) + remainder left in each case . hence the required least number = lcm ( 31 , 5 ) + 4 = 174 . answer : c\"" + }, + { + "Answer": 39, + "Options": "a ) 12 , b ) 39 , c ) 43 , d ) 52 , e ) 34", + "Correct": "b", + "Explanation": "\"let the average after 17 th inning = x . then , average after 16 th inning = ( x - 3 ) . : . 16 ( x - 3 ) + 87 = 17 x or x = ( 87 - 48 ) = 39 . ans : b\"" + }, + { + "Answer": 1025, + "Options": "a ) 256 , b ) 512 , c ) 768 , d ) 1024 , e ) 1536", + "Correct": "d", + "Explanation": "\"0.1 * 2 ^ 10 = 0.1 * 1024 = 102.4 the answer is d .\"" + }, + { + "Answer": 2, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "b", + "Explanation": "\"i solved the second degree equation and found it like this : x ^ 2 - mx - 15 = 0 ( x - 5 ) ( x + 3 ) = 0 x = 5 or x = - 3 substituting both values for x in the equation we find : x ^ 2 - mx - 15 = > ( - 3 ) ^ 2 - m ( - 3 ) = 15 = > 9 + 3 m = 15 = > 3 m = 15 - 9 = 6 = > m = 2 and with 5 , using a similar process we end up with : ( 5 ) ^ 2 - m ( 5 ) = 15 - 5 m = 15 - 25 = - 10 m = 2 ao , ans b\"" + }, + { + "Answer": 1125.0000000000002, + "Options": "a ) 1125 % , b ) 956 % , c ) 417 % , d ) 3788 % , e ) 219 %", + "Correct": "a", + "Explanation": "what percent is x greater than 4 / 7 if ( 1 / 7 ) ( x ) = 1 ? = > x = 7 % change = [ ( 7 - 4 / 7 ) / ( 4 / 7 ) ] * 100 = ( 49 / 4 - 1 ) * 100 = 45 * 25 = 1125 % ans , a" + }, + { + "Answer": 1, + "Options": "a ) 125 / 64 , b ) 25 / 16 , c ) 1 , d ) 4 / 5 , e ) 64 / 125", + "Correct": "c", + "Explanation": "a nice fast approach is the first find a pair of numbers that satisfy the given equation : 4 a = 5 b here ' s one pair : a = 5 and b = 4 what is the ratio of a / 5 to b / 4 ? in other words , what is the value of ( a / 5 ) / ( b / 4 ) ? plug in values to get : ( a / 5 ) / ( b / 4 ) = ( 5 / 5 ) / ( 4 / 4 ) = 1 / 1 = 1 c" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "c", + "Explanation": "solution let x = the number required . by the conditions , x + 1 : x + 5 = a + 5 : x + 13 subtracting terms , ( art . 385,2 . ) x + 1 : 4 = x + 5 : 8 therefore 8 x + 8 = 4 x + 20 . and x = 3 . answer c" + }, + { + "Answer": 55, + "Options": "a ) 45 % , b ) 55 % , c ) 35 % , d ) 32.5 % , e ) 30 %", + "Correct": "b", + "Explanation": "\"price = p initially price reduced by 25 % which means new price is 3 / 4 p now on this new price further 40 percent is reduced which means the new price is merely 60 percent of 3 / 4 p = = > ( 3 / 4 ) x ( 3 / 5 ) p = 9 / 20 p is the new price after both deduction which is 45 percent of the original value p . this implies this entire series of deduction is worth having discounted 55 % of p . so answer is b = 55 %\"" + }, + { + "Answer": 9, + "Options": "a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9", + "Correct": "e", + "Explanation": "the units digit of the exponents of 7 repeat in a cycle of four , which is { 7,9 , 3,1 } . the number 25 has the form 4 n + 1 so the units digit is 7 inside the bracket . the exponent 50 has the form 4 n + 2 , so the units digit is 9 . the answer is e ." + }, + { + "Answer": 92, + "Options": "a ) 92 , b ) 82 , c ) 72 , d ) 62 , e ) 52", + "Correct": "a", + "Explanation": "( 9 * 82 + x ) / 10 = 83 x = ( 10 * 83 ) - ( 9 * 82 ) x = 830 - 738 total score required 830 - 738 = 92 correct answer is a" + }, + { + "Answer": 880, + "Options": "a ) $ 900 , b ) $ 880 , c ) $ 1000 , d ) $ 700 , e ) $ 1500", + "Correct": "b", + "Explanation": "\"if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 220 . so 1 / 4 of her savings is $ 220 . so her original savings are 4 times $ 220 = $ 880 correct answer b\"" + }, + { + "Answer": 1, + "Options": "a ) 0.01 , b ) 1 , 000,000 , c ) 0.001 , d ) 1,000 , e ) 1.0 e - 05", + "Correct": "b", + "Explanation": "given that 10,000 microns = 1 decimeter = 10,000 , 000,000 angstroms so , 1 micron = 10,000 , 000,000 / 10,000 = 1 , 000,000 answer : b" + }, + { + "Answer": 15, + "Options": "a ) 22 , b ) 15 , c ) 28 , d ) 26 , e ) 9", + "Correct": "b", + "Explanation": "as the eldest son ' s age is 3 times that of the youngest , eldest son ' s age should be a multiple of 3 . from the given options take 15 as the eldest son ' s age . then youngest son ' s age becomes 5 . but eldest sons age is 2 more than the sum of the remaining two sons . so sum of the remaining two sons is 13 . so the age of the middle son is 13 - 5 = 8 . which satisfies another condition in the question that the difference between the two sons age is 3 . so answer is 15 . answer : b" + }, + { + "Answer": 37.5, + "Options": "a ) 22.3 , b ) 33.2 , c ) 22.2 , d ) 11.3 , e ) 37.5", + "Correct": "e", + "Explanation": "\"explanation : total of 50 numbers = ( 50 \u00d7 38 ) = 1900 ( 50 \u00d7 38 ) = 1900 total of 48 numbers = ( 1900 - ( 45 + 55 ) ] = 1800 required average = 180048 = 2256 = 37.5 answer : e\"" + }, + { + "Answer": 48.00000000010186, + "Options": "a ) 44 , b ) 43 , c ) 42 , d ) 41 , e ) 48", + "Correct": "e", + "Explanation": "\"1782452 / 92 = 19374 and reminder = 44 . 92 - 44 = 48 so , the next number divisible by 92 is 48 places in front of 1782452 which means 48 + 1782452 = 1782500 48 should be added to 1782452 e\"" + }, + { + "Answer": 14, + "Options": "a ) 1 : 8 , b ) 1 : 4 , c ) 2 : 1 , d ) 14 : 1 , e ) 18 : 1", + "Correct": "d", + "Explanation": "x = 7 y , y = 2 * z x : y , y : z 7 : 1 , 2 : 1 14 : 2 , 2 : 1 so , x : z = 14 : 1 ( d )" + }, + { + "Answer": 13, + "Options": "a ) 9 , b ) 12 , c ) 13 , d ) 14 , e ) 17", + "Correct": "c", + "Explanation": "because 16 ^ 2 = 256 , y the next perfect square to begin with two 2 s can not be 3 - digit . let ' s try 4 - digit . 40 ^ 2 = 1600 and 50 ^ 2 = 2500 . so , if there is a 4 - digit perfect square to begin with two 2 s it must be between 41 ^ 2 and 49 ^ 2 . test the middle number 45 ^ 2 = 2025 . test larger number : 46 ^ 2 = 2116 . test next number : 47 ^ 2 = 2209 . bingo ! the sum of the digits = 2 + 2 + 0 + 9 = 13 . answer : c ." + }, + { + "Answer": 6, + "Options": "a ) 6 % , b ) 25 % , c ) 37 1 / 2 % , d ) 60 % , e ) 75 %", + "Correct": "a", + "Explanation": "just plug and chug . since the question asks for percents , pick 100 . ( but any number will do . ) 100 / 50 + 100 / 25 = 2 + 4 = 6 6 is 6 % of 100 . answer : a" + }, + { + "Answer": 2011, + "Options": "a ) 2008 , b ) 2009 , c ) 2010 , d ) 2011 , e ) 2012", + "Correct": "d", + "Explanation": "let the commodity p costs 40 paise more than the commodity q after n years . price of the commodity p in 2001 = rs . 4.20 since the price of the commodity p increases by rs 0.40 every year , price of the commodity p after n years from 2001 = rs . 4.20 + ( n \u00d7 . 40 ) price of the commodity q in 2001 = rs . 6.30 since the price of the commodity q increases by rs 0.15 every year , price of the commodity q after n years from 2001 = rs . 6.30 + ( n \u00d7 . 15 ) since the commodity p costs rs . 0.40 more that the commodity q after n years from 2001 , 4.20 + ( n \u00d7 . 40 ) = 6.30 + ( n \u00d7 . 15 ) + 0.40 = > ( 40 n - . 15 n ) = 6.30 - 4.20 + 0.40 = 2.5 = > . 25 n = 2.5 = > n = 2.5 / . 25 = 10 = > commodity p costs rs . 0.40 more that the commodity q after 10 years from 2001 . i . e . , in 2011 answer : d" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "a", + "Explanation": "explanation : 1 \u00e3 \u2014 2 + 2 \u00e3 \u2014 1 = ( 2 \u00e3 \u2014 1 - 3 \u00e3 \u2014 2 + 1 \u00e3 \u2014 2 ) + ( 2 \u00e3 \u2014 2 - 3 \u00e3 \u2014 1 + 2 \u00e3 \u2014 1 ) = ( 2 - 6 + 2 + 4 - 3 + 2 ) = 1 . answer : a" + }, + { + "Answer": 52.5, + "Options": "a ) 82.5 , b ) 52.9 , c ) 52.2 , d ) 52.5 , e ) 52.7", + "Correct": "d", + "Explanation": "\"sum of the marks for the class of 30 students = 30 * 40 = 1200 sum of the marks for the class of 50 students = 50 * 60 = 3000 sum of the marks for the class of 80 students = 1200 + 3000 = 4200 average marks of all the students = 4200 / 80 = 52.5 answer : d\"" + }, + { + "Answer": 270, + "Options": "a ) $ 270 , b ) $ 250 , c ) $ 240 , d ) $ 220 , e ) $ 200", + "Correct": "a", + "Explanation": "original price = x sold to collector at 1.2 x re - buy price = 1.2 x * 0.5 = 0.6 x therefore , x - 0.6 x = 100 ; x = 250 second selling price = 1.8 * 0.6 * 250 = 270 answer : a" + }, + { + "Answer": 1499.9999999999998, + "Options": "a ) 1500 , b ) 2777 , c ) 2889 , d ) 27670 , e ) 2771", + "Correct": "a", + "Explanation": "\"1680 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 1500 . answer : a\"" + }, + { + "Answer": 34, + "Options": "a ) 36 , b ) 35 , c ) 34 , d ) 38 , e ) 40", + "Correct": "c", + "Explanation": "at 6 ' o clock , there would be 6 strikes . first strike , then a short interval , the second strike , then a short interval and so on till the 6 th strike . so there would be in all 5 intervals between 6 strikes . similarly , between 9 strikes , there would be 8 intervals . according to the question , the time spent in the strike and the interval is same . at 6 ' o clock , the 6 strikes and the 5 intervals together take 22 sec so each strike and each interval takes 2 secs . at 12 ' o clock , the 9 strikes and 8 intervals will take 2 * ( 9 + 8 ) = 34 secs c" + }, + { + "Answer": 36, + "Options": "a ) 81 , b ) 63 , c ) 54 , d ) 36 , e ) 90", + "Correct": "d", + "Explanation": "nc 2 = 36 = > n * ( n - 1 ) / 2 = 36 by middle term factor and n can not be negative = > n = 9 nc 7 = 9 c 7 = 9 ! / 7 ! * ( 9 - 7 ) ! = 9 * 8 * 7 ! / 7 ! * 2 = 36 so , answer is d ." + }, + { + "Answer": 16.666666666666664, + "Options": "a ) 17.5 litres , b ) 16.67 litres , c ) 17.67 litres , d ) 16.5 litres , e ) 16 litres", + "Correct": "b", + "Explanation": "\"in 100 l mixture we have 36 l milk and 64 l water . hence m and w are in the ratio of 9 : 16 . x l of solution has been removed . hence we have 36 - 9 / 25 x of milk and 64 - 16 / 25 x of water . for calculation simplicity multiply and divide 9 / 25 x by 4 we get 36 / 100 x since this procedure is repeated 2 times . this was my equation 25 = 36 * ( 36 - 36 / 100 x ) ^ 2 ) / ( 36 ) ^ 2 by solving it . we get x = 100 / 6 or 50 / 3 or 16.67 answer : b\"" + }, + { + "Answer": 14, + "Options": "a ) 2.25 , b ) 3.25 , c ) 4.25 , d ) 14 , e ) 6.25", + "Correct": "d", + "Explanation": "\"squaring on both sides ( x + 1 / x ) ^ 2 = 4 ^ 2 x ^ 2 + 1 / x ^ 2 = 16 - 2 x ^ 2 + 1 / x ^ 2 = 14 answer : d\"" + }, + { + "Answer": 17, + "Options": "a ) 15 , b ) 16 , c ) 18 , d ) 19 , e ) 17", + "Correct": "e", + "Explanation": "solve the first equation 2 x + 4 = 4 ( x - 2 ) to obtain . x = 6 substitute x by 6 ( same solution ) in the second equation and solve for k . - 6 + k = 2 ( 6 ) - 1 solve for k . k = 17 correct answer e" + }, + { + "Answer": 10, + "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 12 , e ) 15", + "Correct": "c", + "Explanation": "explanation : its a bit funny sum . if you see the first sentence actually it saying that the numbers are in a . p . now as the first two numbers product is 85 so if you take factor 85 you get 5 and 17 . . now as per option 17 can not be the middle number so from intuition and seeing the option only 10 could be the middle number where 8.5 is the first number and 11.5 is the last answer : c" + }, + { + "Answer": 100, + "Options": "a ) 80 , b ) 90 , c ) 100 , d ) 120 , e ) 140", + "Correct": "c", + "Explanation": "\"let the number of candidate who passed = y then , 39 y + 15 ( 120 - y ) = 120 x 35 \u21d2 24 y = 4200 - 1800 \u2234 y = 2400 / 24 = 100 c\"" + }, + { + "Answer": 164, + "Options": "a ) 288 , b ) 262 , c ) 72 , d ) 205 , e ) 164", + "Correct": "e", + "Explanation": "\"a : b : c = 100 : 65 : 40 = 20 : 13 : 8 8 - - - - 32 41 - - - - ? = > rs . 164 answer : e\"" + }, + { + "Answer": 0.5833333333333334, + "Options": "a ) 5 / 24 , b ) 7 / 12 , c ) 7 / 24 , d ) 8 / 24 , e ) 9 / 24", + "Correct": "b", + "Explanation": "\"p = 3 / 4 , q = 3 / 18 = > q = 1 / 6 therefore p - q = ( 3 / 4 ) - ( 1 / 6 ) = 7 / 12 answer : b\"" + }, + { + "Answer": 35, + "Options": "a ) 35 , b ) 50 , c ) 100 , d ) 120 , e ) 150", + "Correct": "a", + "Explanation": "\"6 th result = sum of 11 results - sum of 10 results = 11 * 20 - 5 * 15 - 5 * 22 = 220 - 75 - 110 = 35 answer is a\"" + }, + { + "Answer": 0.8333333333333334, + "Options": "a ) 0 , b ) 2 / 15 , c ) 2 / 5 , d ) 9 / 20 , e ) 5 / 6", + "Correct": "e", + "Explanation": "we need to determine the result of 1 / 3 + 1 / 2 - 5 / 6 + 1 / 5 + 1 / 4 - 9 / 20 let \u2019 s add the given fractions in two groups . in the group of the first three fractions , notice that 1 / 3 and 1 / 2 share a common denominator of 6 with 5 / 6 . 1 / 2 + 1 / 3 = 3 / 6 + 2 / 6 = 5 / 6 thus , 5 / 6 \u2013 5 / 6 = 0 looking at the 2 nd group of the fractions ( 1 / 5 , 1 / 4 , and 9 / 20 ) , notice that 1 / 5 and 1 / 4 share a common denominator of 20 with 9 / 20 . 1 / 5 + 1 / 4 = 4 / 20 + 5 / 20 = 9 / 20 thus , 9 / 20 \u2013 9 / 20 = 0 . thus , the result of 1 / 3 + 1 / 2 \u2013 5 / 6 + 1 / 5 + 1 / 4 \u2013 9 / 20 is 5 / 6 . answer : e" + }, + { + "Answer": 250, + "Options": "a ) 250 , b ) 277 , c ) 278 , d ) 200 , e ) 288", + "Correct": "a", + "Explanation": "\"explanation : let the number of 20 paise coins be x . then the no of 25 paise coins = ( 334 - x ) . 0.20 * ( x ) + 0.25 ( 334 - x ) = 71 = > x = 250 . . answer : a ) 250\"" + }, + { + "Answer": 169, + "Options": "a ) 160 , b ) 161 , c ) 162 , d ) 163 , e ) 169", + "Correct": "e", + "Explanation": "\"to minimize one quantity maximize other . 168 * 2 ( max possible amount of food a guest could consume ) = 336 pounds , so there must be more than 168 guests , next integer is 169 . answer : e .\"" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 2 , c ) 5 , d ) 6 , e ) 8", + "Correct": "a", + "Explanation": "\"( 929 / 30 ) gives remainder 29 29 + 1 = 30 , so we need to add 1 answer : a\"" + }, + { + "Answer": 8, + "Options": "a ) 5 , b ) 7 , c ) 9 , d ) 8 , e ) 12", + "Correct": "d", + "Explanation": "\"29 / 11 = 2 and 119 / 11 = 10 = = > 10 - 2 = 8 numbers answer : d\"" + }, + { + "Answer": 6, + "Options": "a ) 4 hours , b ) 5 hours , c ) 6 hours , d ) 7 hours , e ) none of these", + "Correct": "c", + "Explanation": "let a and be together take x hours to complete the work . then , a alone takes ( x + 8 ) hrs and b alone takes ( x + 9 / 2 ) hrs to complete the work . then , 1 / ( x + 8 ) + 1 / ( x + 9 / 2 ) = 1 / x , 1 / ( x + 8 ) + 2 / ( 2 x + 9 ) = 1 / x x ( 4 x + 25 ) = ( x + 8 ) ( 2 x + 9 ) 2 x ^ 2 = 72 , x ^ 2 = 36 , x = 6 correct option : c" + }, + { + "Answer": 33, + "Options": "a ) 8 , b ) 10 , c ) 12 , d ) 12 , e ) 16", + "Correct": "a", + "Explanation": "answer : a" + }, + { + "Answer": 0.14285714285714285, + "Options": "a ) 1 / 7 , b ) 3 , c ) 12 / 3 , d ) 6 / 6 , e ) 1", + "Correct": "a", + "Explanation": "answer a is impossible because the invers of 1 / x is x , and the only way to have something other than a natural number is to input something other than a natural number . with the specification that only natural numbers may be used 1 / 7 is not a possibility for f ( f ( x ) )" + }, + { + "Answer": 52, + "Options": "a ) 32 , b ) 42 , c ) 52 , d ) 62 , e ) 72", + "Correct": "c", + "Explanation": "5 x \u2212 28 subtraction is built backwards , multiply the unknown by 5 5 x \u2212 28 = 232 is translates to equals + 28 + 28 add 28 to both sides 5 x = 260 the variable ismultiplied by 5 5 5 divide both sides by 5 x = 52 the number is 52 . correct answer c" + }, + { + "Answer": 1348.2857142857142, + "Options": "a ) 1217 , b ) 1348.2 , c ) 1210 , d ) 1212 , e ) 1312", + "Correct": "b", + "Explanation": "\u03c0 ( 232 \u2013 102 ) = 1348.2 answer : b" + }, + { + "Answer": 23, + "Options": "a ) 12 % , b ) 14 % , c ) 16 % , d ) 20 % , e ) 23 %", + "Correct": "e", + "Explanation": "\"explanation : 100 * 100 = 10000 70 * 110 = 7700 10000 - - - - - - - 2300 100 - - - - - - - ? = 23 % e )\"" + }, + { + "Answer": 20, + "Options": "a ) 20 , b ) 87 , c ) 266 , d ) 288 , e ) 11", + "Correct": "a", + "Explanation": "we know that average of n consecutive numbes average = n \u00d7 ( n + 1 ) 2 n = ( n + 1 ) 2 n \u00d7 ( n + 1 ) 2 n = ( n + 1 ) 2 if the given n is sufficiently large , the average does not change much even though we exclude one or two numbers from it . so the approximate number of observations is almost double to the average ( remember : the average of consecutive numbers almost lies in the middle ) the approximate average is 800 / 39 = approx 20 . so the initial numbers may be nearer to 40 . in this question it is actually 40 as from the denominator of the new average 800 / 39 . the initial numbers are 40 . sum of 40 consecutive numbers = 40 \u00d7 ( 40 + 1 ) 2 = 82040 \u00d7 ( 40 + 1 ) 2 = 820 sum of 39 numbers = average x numbenumber of observations = 80039 \u00d7 3980039 \u00d7 39 = 800 so the number excluded = 820 - 800 = 20 answer : a" + }, + { + "Answer": 3153, + "Options": "a ) 2327 , b ) 2757 , c ) 3147 , d ) 3587 , e ) 3997", + "Correct": "c", + "Explanation": "\"when increased by 3 , the number must include at least 2 * 3 ^ 2 * 5 ^ 2 * 7 = 3150 the answer is c .\"" + }, + { + "Answer": 17.5, + "Options": "a ) 25.5 % , b ) 21.5 % , c ) 17.5 % , d ) 13.5 % , e ) 9.5 %", + "Correct": "c", + "Explanation": "\"fathers without full - time jobs are 1 / 4 * 2 / 5 = 2 / 20 of all the parents surveyed . mothers without full - time jobs are 1 / 8 * 3 / 5 = 3 / 40 of all the parents surveyed . the percent of parents without full - time jobs is 2 / 20 + 3 / 40 = 7 / 40 = 17.5 % the answer is c .\"" + }, + { + "Answer": 24, + "Options": "a ) 24 , b ) 55 , c ) 77 , d ) 99 , e ) 01", + "Correct": "a", + "Explanation": "let the sum be rs . x , then it becomes rs . 4 x in eight years rs . 3 x is the interest on x for eight years . r = ( 100 * 3 x ) / ( x * 8 ) = 300 / 8 % if the sum becomes ten times itself , then interest is 9 x . the required time period = ( 100 * 9 x ) / ( x * 300 / 8 ) = ( 100 * 9 x * 8 ) / ( x * 300 ) = 24 years . answer : a" + }, + { + "Answer": 1.04, + "Options": "a ) 290 / 289 , b ) 26 / 25 , c ) 290 / 90 , d ) 290 / 19 , e ) none of these", + "Correct": "b", + "Explanation": "\"explanation : if the numbers are a , b , then ab = 5 , as 17 is a prime number , so a = 1 , b = 5 . 1 / a 2 + 1 / b 2 = 1 / 1 ( 2 ) + 1 / 5 ( 2 ) = 26 / 25 option b\"" + }, + { + "Answer": 72, + "Options": "a ) 62 kg , b ) 60 kg , c ) 70 kg , d ) 72 kg , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : let the weight of student be x kg . given , difference in average weight = 4 kg = > ( 92 - x ) / 5 = 4 = > x = 72 answer : d\"" + }, + { + "Answer": 499.99999999999955, + "Options": "a ) 80 , b ) 110 , c ) 160 , d ) 500 , e ) 400", + "Correct": "d", + "Explanation": "\"we start by creating a variable for the total number of students in the math course . we can say : t = total number of students in the math course next , we can use variable t in an equation that we translate from the given information . we are given that , of the final grades received by the students in a certain math course , 1 / 5 are a ' s , 1 / 4 are b ' s , 1 / 2 are c ' s , and the remaining 25 grades are d ' s . since this represents all the grades in the class , it represents all the students in the class . thus we know : # a \u2019 s + # b \u2019 s + # c \u2019 s + # d \u2019 s = total number of students in the class 1 / 5 ( t ) + \u00bc ( t ) + \u00bd ( t ) + 25 = t we can multiply the entire equation by 20 to cancel out the denominators of the fractions and we have : 4 t + 5 t + 10 t + 500 = 20 t 19 t + 500 = 20 t 500 = t there are a total of 500 students in the math class . answer is d .\"" + }, + { + "Answer": 4, + "Options": "a ) 8 , b ) 5 , c ) 11 , d ) 3 , e ) 4", + "Correct": "e", + "Explanation": "\"6 * 15 * 2 = ( \u221a ( 6 + 2 ) ( 15 + 3 ) ) / ( 2 + 1 ) = ( \u221a 8 * 18 ) / 3 = ( \u221a 144 ) / 3 = 12 / 3 = 4 . answer is e\"" + }, + { + "Answer": 39, + "Options": "a ) 39 , b ) 40 , c ) 41 , d ) 42 , e ) 43", + "Correct": "a", + "Explanation": "\"solution start with 7 pens . mike gives you 22 pens : 7 + 22 = 29 pens . cindy doubles the number of pens you have : 29 \u00d7 2 = 58 pens . sharon takes 19 pens from you : 58 - 19 = 39 pens . so you have 39 at the end . correct answer : a\"" + }, + { + "Answer": 55.000000000000014, + "Options": "a ) 40 , b ) 55 , c ) 68 , d ) 80 , e ) 98", + "Correct": "b", + "Explanation": "\"let the no of matches played more = x so , ( 120 + x ) * 52 / 100 = 36 + x by solving we get x = 55 answer : b\"" + }, + { + "Answer": 5.199999999999999, + "Options": "a ) $ 5.20 , b ) $ 4.45 , c ) $ 4.80 , d ) $ 5.05 , e ) $ 5.40", + "Correct": "a", + "Explanation": "let the fixed charge of jim \u2019 s taxi service = 2.05 $ and charge per 2 / 5 mile ( . 4 mile ) = . 35 $ total charge for a trip of 3.6 miles = 2.05 + ( 3.6 / . 4 ) * . 35 = 2.05 + 9 * . 35 = 5.2 $ answer a" + }, + { + "Answer": 49, + "Options": "a ) 35 , b ) 42 , c ) 45 , d ) 49 , e ) 54", + "Correct": "d", + "Explanation": "\"a = 105 = 3 * 5 * 7 a ^ 3 = 21 \u00d7 25 \u00d7 45 \u00d7 w = > a ^ 3 = ( 7 * 3 ) x ( 5 * 5 ) x ( 3 ^ 2 * 5 ) x w = > a ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x w = > ( 3 * 5 * 7 ) ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x w w = 7 ^ 2 = 49 answer d\"" + }, + { + "Answer": 42.857142857142854, + "Options": "a ) 42.85 , b ) 40 , c ) 35 , d ) 41 , e ) 39", + "Correct": "a", + "Explanation": "\"step 1 ) took lcm of 40 and 50 . . came as 200 . step 2 ) 200 distance between b to c . . . do 200 / 50 hence 4 gallons used step 3 ) twice distance . . hence 200 * 2 = 400 . . . do as above . . 400 / 40 = 10 gallons used step 4 ) total gallons . . 4 + 10 = 14 gallons step ) total miles = 200 + 400 = 600 miles hence . . average of whole journey = 600 / 14 which comes to 42.85 answer : a\"" + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) 11 , c ) 10 , d ) 9 , e ) 8", + "Correct": "a", + "Explanation": "\"let the time for which car averages 75 mph = t 65 * ( t + 4 ) = 45 * 4 + 75 t = > 10 t = 80 = > t = 8 total duration of the trip = 8 + 4 = 12 answer a\"" + }, + { + "Answer": 22, + "Options": "a ) 21 , b ) 22 , c ) 23 , d ) 25 , e ) 28", + "Correct": "b", + "Explanation": "let the average age of the whole team be x years . 11 x - ( 25 + 28 ) = 9 ( x - 1 ) = > 11 x - 9 x = 44 = > 2 x = 44 = > x = 22 . so , average age of the team is 22 years . b" + }, + { + "Answer": 806.6666666666666, + "Options": "a ) a ) 333 , b ) b ) 383 , c ) c ) 402 , d ) d ) 433 , e ) e ) 804", + "Correct": "e", + "Explanation": "here ' s the calculation for that case , assume monthly payment is x . after 1 st month : ( 2000 ) ( 1.1 ) - x = 2200 - x after 2 nd month : ( 2200 - x ) ( 1.1 ) - x = 2420 - 2.21 x after 3 rd month : ( 2420 - 2.21 x ) ( 1.1 ) - x = 2662 - 3.31 x now , the amount after the last payment in 3 rd month must bring the total to 0 . hence : 2662 - 3.31 x = 0 x = 2662 / 3.31 = 804 answer e" + }, + { + "Answer": 2.5, + "Options": "a ) 5 / 2 , b ) 7 / 2 , c ) 10 / 3 , d ) 15 / 4 , e ) 25 / 3", + "Correct": "a", + "Explanation": "\"n = 3 d / 5 j = n / 3 = d / 5 the average of november and january is ( n + j ) / 2 = 4 d / 5 / 2 = 2 d / 5 d is 5 / 2 times the average of november and january . the answer is a .\"" + }, + { + "Answer": 3.84, + "Options": "a ) 5.29 min , b ) 3.84 min , c ) 5.08 min , d ) 9.28 min , e ) 5.988 min", + "Correct": "b", + "Explanation": "\"clearly , the two will meet when they are 528 m apart . to be ( 4.5 + 3.75 ) = 8.25 km apart , they take 1 hour . to be 528 m apart , they take ( 100 / 825 * 528 / 1000 ) hrs = ( 528 / 8250 * 60 ) min = 3.84 min . answer : b\"" + }, + { + "Answer": 840, + "Options": "a ) 600 , b ) 620 , c ) 500 , d ) 520 , e ) 840", + "Correct": "e", + "Explanation": "\"let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 420 ) = 2 + 2 ( extra ) = > 2 x - 840 = x = > x = 840 . answer : e\"" + }, + { + "Answer": 33.333333333333336, + "Options": "a ) 31 , b ) 46 , c ) 88 , d ) 33.33 , e ) 12", + "Correct": "d", + "Explanation": "\"total score of the batsman in 20 matches = 800 . total score of the batsman in the next 10 matches = 200 . total score of the batsman in the 30 matches = 1000 . average score of the batsman = 1000 / 30 = 33.33 answer : d\"" + }, + { + "Answer": 4, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 6 , e ) 4", + "Correct": "e", + "Explanation": "\"explanation : 39 + 17 = 56 / 13 = 4 ( remainder ) answer : e\"" + }, + { + "Answer": 30, + "Options": "a ) 20 , b ) 30 , c ) 10 , d ) 40 , e ) 15", + "Correct": "b", + "Explanation": "( grade 1 + grade 2 ) - ( grade 2 + grade 5 ) = 30 grade 1 - grade 5 = 30 answer : b" + }, + { + "Answer": 21, + "Options": "a ) 14 , b ) 16 , c ) 18 , d ) 10 , e ) 21", + "Correct": "e", + "Explanation": "\"while this question can be solved with a rather straight - forward algebra approach ( as the other posters have noted ) , it can also be solved by testing the answers . one of those numbers must be the total number of goals . . . from a tactical standpoint , it ' s best to test either answer b or answer d , so if the answer is not correct , then you would have a gauge for whether you should gohigherorlowerwith your next test . here , i ' ll start with answer e = 21 goals if . . . . total goals = 21 goals 5 th game = 5 goals 1 st 4 games = 16 goals avg . for 1 st 4 games = 16 / 4 = 4 goal / game avg . for all 5 games = 21 / 5 = 4.2 goals / game this is an exact match for what we ' re told in the prompt , so answer e must be the answer .\"" + }, + { + "Answer": 36.5, + "Options": "a ) 36.7 , b ) 36.1 , c ) 36.5 , d ) 36.9 , e ) 36.3", + "Correct": "a", + "Explanation": "\"correct sum = ( 36 * 50 + 60 - 23 ) = 1837 . correct mean = 1837 / 50 = 36.7 answer : a\"" + }, + { + "Answer": 15, + "Options": "a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19", + "Correct": "a", + "Explanation": "\"explanation : let the number of persons be n \u00e2 \u02c6 \u00b4 total handshakes = nc 2 = 105 n ( n - 1 ) / 2 = 105 \u00e2 \u02c6 \u00b4 n = 15 answer : a\"" + }, + { + "Answer": 78, + "Options": "a ) 78 kg . , b ) 70 kg . , c ) 75 kg . , d ) 70 kg . , e ) 72 kg .", + "Correct": "a", + "Explanation": "\"the new average will be = ( 76 * 7 + 110 + 60 ) / 9 = 78 kgs a is the answer\"" + }, + { + "Answer": 50, + "Options": "a ) 20 . , b ) 45 . , c ) 50 . , d ) 30 . , e ) 25 .", + "Correct": "c", + "Explanation": "given there are 50 students , 84 % of 50 = 42 boys and remaining 8 girls . now here 84 % are boys and 16 % are girls . now question is asking about how many boys do we need to add , to make the girls percentage to 5 or 8 % . . if we add 50 to existing 45 then the count will be 92 and the girls number will be 8 as it . now boys are 92 % and girls are 8 % . ( out of 100 students = 92 boys + 8 girls ) . imo option c is correct ." + }, + { + "Answer": 120, + "Options": "a ) 12.5 % , b ) 40 % , c ) 120 % , d ) 125 % , e ) none", + "Correct": "c", + "Explanation": "\"solution 6 : 5 = 6 / 5 = ( 6 / 5 x 100 ) % . = 120 % . answer c\"" + }, + { + "Answer": 8, + "Options": "a ) 2 , b ) 5 , c ) 6 , d ) 8 , e ) 10", + "Correct": "d", + "Explanation": "\"explanation : unit digit in the given product = unit digit in ( 4 * 8 * 3 * 3 ) = 8 answer : d\"" + }, + { + "Answer": 676, + "Options": "a ) 515 . , b ) 678 . , c ) 618 . , d ) 644 . , e ) 666 .", + "Correct": "b", + "Explanation": "\"answer is b : 678 solution : total number of students studying both are 450 + 226 - 134 = 542 ( subtracting the 134 since they were included in the both the other numbers already ) . so 80 % of total is 542 , so 100 % is approx . 678 .\"" + }, + { + "Answer": 8, + "Options": "a ) 8 , b ) 15 , c ) 14 , d ) 12 , e ) 10", + "Correct": "a", + "Explanation": "since the number is greater than the number obtained on reversing the digits , so the ten ' s digit is greater than the unit ' s digit . let the ten ' s and unit ' s digits be 2 x and x respectively . then , ( 10 * 2 x + x ) - ( 10 x + 2 x ) = 36 9 x = 36 x = 4 required difference = ( 2 x + x ) - ( 2 x - x ) = 2 x = 8 . answer a" + }, + { + "Answer": 15, + "Options": "a ) 8 % , b ) 15 % , c ) 45 % , d ) 52 % , e ) 56 %", + "Correct": "b", + "Explanation": "\"first ratio = 3 / 20 = 15 % second ratio = ( 3 + 12 ) / ( 9 + 108 ) = 15 / 117 = 12,8 % decrease = 2,2 % 2,2 % / 15 % = 15 % approximately . answer : b\"" + }, + { + "Answer": 2.5, + "Options": "a ) 31 \u2044 5 , b ) 16 \u2044 5 , c ) 20 \u2044 9 , d ) 5 / 2 , e ) 5 \u2044 16", + "Correct": "d", + "Explanation": "\"say x / 3 / 9 * 5 / 6 = x * 9 / 3 * 5 / 6 = x * 5 / 2 d\"" + }, + { + "Answer": 22, + "Options": "a ) 20 . , b ) 21 . , c ) 22 . , d ) 23 . , e ) 24 .", + "Correct": "c", + "Explanation": "\"before solving it algebraically , let us prime factorize 1430 = 2 * 5 * 11 * 13 . since number of apples per person * total persons s = 1430 , the answer should be a factor of 1430 . only c is . and that ' s your answer . c\"" + }, + { + "Answer": 6, + "Options": "a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 2", + "Correct": "b", + "Explanation": "age of sobha ' s father when sobha was born = 38 age of sobha ' s mother when sobha was born = 36 \u2212 4 = 32 required difference of age = 38 \u2212 32 = 6 answer is b ." + }, + { + "Answer": 28, + "Options": "a ) 25 , b ) 30 , c ) 28 , d ) 36 , e ) 42", + "Correct": "c", + "Explanation": "\"( ( 2 a + 16 ) + ( 3 a - 8 ) ) / 2 = ( 5 a + 8 ) / 2 = 74 a = 28 the answer is c .\"" + }, + { + "Answer": 462, + "Options": "a ) 450 , b ) 451 , c ) 460 , d ) 462 , e ) none", + "Correct": "d", + "Explanation": "\"solution on dividing 457 by 11 , remainder is 6 . required number is either 451 or 462 nearest to 456 is = 462 . answer d\"" + }, + { + "Answer": 20.011399999999995, + "Options": "a ) 20.0015 , b ) 20.0105 , c ) 20.0115 , d ) 20.0114 , e ) none", + "Correct": "d", + "Explanation": "solution given expression = ( 12.1212 + 17.0005 ) - 9.1103 = ( 29.1217 - 9.1103 ) = 20.0114 . answer d" + }, + { + "Answer": 121, + "Options": "a ) 123 , b ) 121 , c ) 277 , d ) 267 , e ) 120", + "Correct": "b", + "Explanation": "\"let xx be the number he chose , then 2 \u00e2 \u2039 \u2026 x \u00e2 \u02c6 \u2019 138 = 104 2 \u00e2 \u2039 \u2026 x \u00e2 \u02c6 \u2019 138 = 104 x = 121 answer : b\"" + }, + { + "Answer": 25, + "Options": "a ) 20 % , b ) 30 % , c ) 40 % , d ) 25 % , e ) 60 %", + "Correct": "d", + "Explanation": "\"the is always the difference between our starting and ending points . in this case , it \u00e2 \u20ac \u2122 s 100 \u00e2 \u20ac \u201c 75 = 25 . the \u00e2 \u20ac \u0153 original \u00e2 \u20ac \u009d is our starting point ; in this case , it \u00e2 \u20ac \u2122 s 100 . ( 25 / 100 ) * 100 = ( 0.25 ) * 100 = 25 % . d\"" + }, + { + "Answer": 7, + "Options": "a ) 1 , b ) 2 , c ) 4 , d ) 5 , e ) 7", + "Correct": "e", + "Explanation": "( 55 ) ( 57 ) = ( 56 - 1 ) ( 56 + 1 ) = 56 ^ 2 - 1 which is 1 less than a multiple of 8 . then the remainder will be 7 . the answer is e ." + }, + { + "Answer": 10, + "Options": "a ) 30 , b ) 25 , c ) 15 , d ) 10 , e ) 5", + "Correct": "d", + "Explanation": "because the cord was extended to its full length at all items , the dog ran along a semi - circular path , from north to south . the circumference of a full circle is 2 * pi * r , but since we only care about the length of half the circle , the semi - circle path is pi * r . q = pi * r = 30 . round pi = 3 , then r = 10 . chord is about 10 feet long . d" + }, + { + "Answer": 19.999999999999716, + "Options": "a ) 20 , b ) 22 , c ) 23 , d ) 24 , e ) 25", + "Correct": "a", + "Explanation": "\"when positive integer x is divided by positive integer y , the remainder is 8 - - > x = qy + 8 ; x / y = 76.4 - - > x = 76 y + 0.4 y ( so q above equals to 76 ) ; 0.4 y = 8 - - > y = 20 . answer : a .\"" + }, + { + "Answer": 0.25, + "Options": "a ) 60 / 120 , b ) 15 / 120 , c ) 30 / 120 , d ) 80 / 120 , e ) 40 / 120", + "Correct": "c", + "Explanation": "\"number of people whose age is less than 20 is given by 120 - 90 = 30 probability p that a person selected at random from the group is less than 20 is gieven by 30 / 120 = 0.25 correct answer c\"" + }, + { + "Answer": 450, + "Options": "a ) 300 , b ) 350 , c ) 400 , d ) 450 , e ) 500", + "Correct": "d", + "Explanation": "\"22 % is 12 % - points higher than 10 % but 8 % - points lower than 30 % . thus there should be 2 parts of solution x for 3 parts of solution y . we should add 450 ml of solution y . the answer is d .\"" + }, + { + "Answer": 99, + "Options": "a ) 85 , b ) 86 , c ) 88 , d ) 90 , e ) 99", + "Correct": "e", + "Explanation": "when the student weighs 90 pounds the average weight is x - 1 pounds ; when the student weighs 110 pounds the average weight is x + 4 pounds . so , the increase in total weight of 110 - 90 = 20 pounds corresponds to the increase in average weight of ( x + 4 ) - ( x - 1 ) = 5 pounds , which means that there are 20 / 5 = 4 students ( including the new one ) . so , initially there were 5 student . total weight = 5 x + 90 = 6 ( x - 1 ) - - > x = 96 pounds . answer : e ." + }, + { + "Answer": 200, + "Options": "a ) 50 , b ) 100 , c ) 200 , d ) 300 , e ) 400", + "Correct": "c", + "Explanation": "since 500 = 2 ^ 2 * 5 ^ 3 then a number can not have 2 and / or 5 as a factor . the odd numbers do not have 2 as a factor and there are 250 odd numbers from 1 to 500 . we then need to eliminate the 50 numbers that end with 5 , that is 5 , 15 , 25 , . . . , 495 . there are a total of 250 - 50 = 200 such numbers between 1 and 500 . the answer is c ." + }, + { + "Answer": 0.4166666666666667, + "Options": "a ) 5 / 19 , b ) 5 / 12 , c ) 5 / 28 , d ) 5 / 10 , e ) 5 / 11", + "Correct": "b", + "Explanation": "\"explanation : here n ( s ) = ( 6 x 6 ) = 36 let e = event of getting a total more than 7 = { ( 2,6 ) , ( 3,5 ) , ( 3,6 ) , ( 4,4 ) , ( 4,5 ) , ( 4,6 ) , ( 5,3 ) , ( 5,4 ) , ( 5,5 ) , ( 5,6 ) , ( 6,2 ) , ( 6,3 ) , ( 6,4 ) , ( 6,5 ) , ( 6,6 ) } therefore , p ( e ) = n ( e ) / n ( s ) = 15 / 36 = 5 / 12 . answer : b ) 5 / 12\"" + }, + { + "Answer": 78000, + "Options": "a ) rs . 78000 , b ) rs . 48000 , c ) rs . 6000 , d ) rs . 82000 , e ) rs . 32000", + "Correct": "a", + "Explanation": "6 : 1 2 : 1 - - - - - - 12 : 1 1 - - - - - 6000 13 - - - - - ? = > rs . 78,000 answer : a" + }, + { + "Answer": 17576, + "Options": "a ) 1700 , b ) 7570 , c ) 1576 , d ) 17576 , e ) 500", + "Correct": "d", + "Explanation": "the first letter from the right can be chosen in 26 ways because there are 26 alphabets . having chosen this , the second letter can be chosen in 26 ways . = > the first two letters can be chosen in 26 \u00e3 \u2014 26 = 67626 \u00e3 \u2014 26 = 676 ways having chosen the first two letters , the third letter can be chosen in 26 ways . = > all the three letters can be chosen in 676 \u00e3 \u2014 26 = 17576676 \u00e3 \u2014 26 = 17576 ways . it implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter . answer d" + }, + { + "Answer": 16, + "Options": "a ) 8 , b ) 16 , c ) 24 , d ) 36 , e ) 40", + "Correct": "b", + "Explanation": "\"since 64 \u00f7 k = 4 and 64 \u00f7 16 = 4 , then k = 16 correct answer b\"" + }, + { + "Answer": 191, + "Options": "a ) 165 , b ) 185 , c ) 190 , d ) 191 , e ) 199", + "Correct": "d", + "Explanation": "\"191 answer is d\"" + }, + { + "Answer": 140, + "Options": "a ) $ 124 , b ) $ 132 , c ) $ 140 , d ) $ 148 , e ) $ 156", + "Correct": "c", + "Explanation": "\"let the price of the meal be x . after a 10 % sales tax addition , the price is 1.1 * x after a 20 % tip on this amount , the total is 1.2 * 1.1 * x = 1.32 x 1.32 x = 184.80 x = 140 the correct answer is c .\"" + }, + { + "Answer": 98.6, + "Options": "a ) 75 kg , b ) 50 kg , c ) 85 kg , d ) 80 kg , e ) 98.6 kg", + "Correct": "e", + "Explanation": "\"explanation : total increase in weight = 8 \u00e3 \u2014 4.2 = 33.6 if x is the weight of the new person , total increase in weight = x \u00e2 \u02c6 \u2019 65 = > 33.6 = x - 65 = > x = 33.6 + 65 = 98.6 answer : option e\"" + }, + { + "Answer": 1350, + "Options": "a ) $ 1250 , b ) $ 1350 , c ) $ 1150 , d ) $ 1360 , e ) $ 1370", + "Correct": "b", + "Explanation": "\"50 pages typed 1 x 30 pages typed 2 x ( original + one revision ) 20 pages typed 3 x ( original + two revisions ) 50 ( 10 ) + 30 ( 10 + 5 ) + 20 ( 10 + 5 + 5 ) = 500 + 450 + 400 = 1350 answer - b\"" + }, + { + "Answer": 700, + "Options": "a ) $ 600 , b ) $ 700 , c ) $ 800 , d ) $ 900 , e ) $ 1000", + "Correct": "b", + "Explanation": "\"0.1 x = 0.08 ( 2000 - x ) + 74 0.18 x = 234 x = 1300 then the amount invested at 8 % is $ 2000 - $ 1300 = $ 700 the answer is b .\"" + }, + { + "Answer": 3.571428571428581, + "Options": "a ) 3.57 % , b ) 5.9 % , c ) 11.1 % , d ) 12.5 % , e ) 23.6 %", + "Correct": "a", + "Explanation": "\"opening = 28 closing = 29 rise in price = 1 so , percent increase = 1 / 28 * 100 = 3.57 answer : a\"" + }, + { + "Answer": 19, + "Options": "a ) 8 , b ) 10 , c ) 12 , d ) 19 , e ) 16", + "Correct": "d", + "Explanation": "the bookman had 10 hardback ad 55 - 10 = 45 paperback copies ; 14 copies were sold , hence 55 - 14 = 41 copies were left . let # of paperback copies left be p then 10 p + 20 ( 41 - p ) = 560 - - > 10 p = 260 - - > p = 26 # of paperback copies sold is 45 - 26 = 19 answer : d" + }, + { + "Answer": 15, + "Options": "a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16", + "Correct": "d", + "Explanation": "\"p / 3 + f / 4 = p / 3 + ( 48 - p ) / 4 = 12 + p / 2 p / 3 + f / 3 = ( p + f ) / 3 = 48 / 3 = 16 p / 4 + f / 4 = 12 p / 3 + f / 3 > p / 3 + f / 4 > p / 4 + f / 4 - - > 16 > 12 + p / 12 > 12 greatest possible r : 12 + p / 12 = 15 - - > p = 36 ( integer - - > good ) 15 or d is the answer\"" + }, + { + "Answer": 21, + "Options": "a ) rs . 18.95 , b ) rs 16 , c ) rs . 21 , d ) rs . 25.71 , e ) none of these", + "Correct": "c", + "Explanation": "answer total earning for the week = sum of earning of first four days + sum of earning of last four days - earning of 4 th day = 4 x 18 + 4 x 22 - 13 = rs . 147 \u00e2 \u02c6 \u00b4 average earning = 147 / 7 = rs . 21 correct option : c" + }, + { + "Answer": 4, + "Options": "a ) 1 , b ) 2 , c ) 4 , d ) 6 , e ) none of them", + "Correct": "c", + "Explanation": "\"unit digit in 3 ^ 4 = 1 = > unit digit in ( 3 ^ 4 ) ^ 16 = 1 therefore , unit digit in 3 ^ 65 = unit digit in [ ( 3 ^ 4 ) ^ 16 x 3 ] = ( 1 x 3 ) = 3 unit digit in 6 ^ 59 = 6 unit digit in 7 ^ 4 = 1 = > unit digit in ( 7 ^ 4 ) ^ 17 is 1 unit digit in 7 ^ 71 = unit digit in [ ( 7 ^ 4 ) ^ 17 x 7 ^ 3 ] = ( ( 1 x 3 ) = 3 therefore , required digit = unit digit in ( 3 x 6 x 3 ) = 4 answer is c\"" + }, + { + "Answer": 550, + "Options": "a ) 278 , b ) 277 , c ) 278 , d ) 450 , e ) 550", + "Correct": "e", + "Explanation": "\"10 * 150 = 1500 2 * 100 + 5 * 150 = 950 1500 \u2013 1050 = 550 answer : e\"" + }, + { + "Answer": 64, + "Options": "a ) 58 kg , b ) 60 kg , c ) 64 kg , d ) 70 kg , e ) none", + "Correct": "c", + "Explanation": "sol . for 9 kg zinc , mixture melted = ( 9 + 11 ) kg . for 28.8 kg zinc , mixture , melted = [ 20 / 9 x 28.8 ] kg = 64 kg . answer c" + }, + { + "Answer": 95.5, + "Options": "a ) 60 kg , b ) 95.5 kg , c ) 80 kg , d ) 85 kg , e ) 90 kg", + "Correct": "b", + "Explanation": "\"total weight increased = ( 5 x 5.5 ) kg = 27.5 kg . weight of new person = ( 68 + 27.5 ) kg = 95.5 kg option b\"" + }, + { + "Answer": 36, + "Options": "a ) 65 degrees , b ) 73 degrees , c ) 36 degrees , d ) 34 degrees , e ) 74 degrees", + "Correct": "c", + "Explanation": "\"m + tu + w + th = 4 * 48 = 192 tu + w + th + f = 4 * 46 = 184 m = 44 tu + w + th = 192 - 44 = 148 f = 184 \u2013 148 = 36 answer : c\"" + }, + { + "Answer": 1.8, + "Options": "a ) 1.8 , b ) 1.6 , c ) 2.775 . , d ) 1.9 , e ) 3.5 .", + "Correct": "a", + "Explanation": "the ant walks an average of 1000 meters in 30 minutes 1000 meters in 1 / 2 hours the beetle walks 10 % less distance = 1000 - 10 = 900 meters in 30 minutes 0.900 km in 30 / 60 = 1 / 2 hours speed = 0.900 * 2 = 1.8 km / h i guess option a should be 1.8" + }, + { + "Answer": 1096, + "Options": "a ) 1005 , b ) 1045 , c ) 1075 , d ) 1015 , e ) 1096", + "Correct": "e", + "Explanation": "\"$ 25 per packet of gasket in case a customer orders less than 10 in case a customer orders > 10 price per gasket = 20 * 4 / 5 = 16 a certain week the supplier sold 60 gasket 1 . he sold 20 % of the gaskets to x = 12 gaskets = 20 * 10 + 16 * 2 = 200 + 32 = 232 2 . he sold 15 % of the gaskets to y = 9 gaskets = 20 * 9 = 180 3 . he sold remaining 65 % to z = 39 gaskets = 20 * 10 = 200 + 16 * 29 = 684 thus , total money earned 232 + 180 + 684 = 1096 answer is e\"" + }, + { + "Answer": 42, + "Options": "a ) 42 , b ) 64 , c ) 36 , d ) 72 , e ) 27", + "Correct": "a", + "Explanation": "\"to improve his average by 6 runs per innings he has to contribute 8 x 6 = 48 runs for the previous 8 innings . thus , the average after the 9 th innings = 90 - 48 = 42 . answer : a\"" + }, + { + "Answer": 140, + "Options": "a ) 90 , b ) 130 , c ) 150 , d ) 140 , e ) 450", + "Correct": "d", + "Explanation": "\"i ' ve been reading the website for a while and i ' m always keen to see different approaches so i would like to share one that works for me : short version : truck a travels for an hour . distance remaining = 940 - 90 = 850 k ratio of speeds 9 : 8 - > 850 / 17 = 50 truck a = 90 + 50 * 9 = 540 truck b = 50 * 8 = 400 delta = 140 km answer d\"" + }, + { + "Answer": 24, + "Options": "a ) 24 , b ) 37 , c ) 28 , d ) 40 , e ) 81", + "Correct": "a", + "Explanation": "\"explanation : formula n ( a \u00e2 \u02c6 \u00aa b ) = n ( a ) + n ( b ) \u00e2 \u02c6 \u2019 n ( a \u00e2 \u02c6 \u00a9 b ) fail in hindi or english = 32 + 56 \u00e2 \u20ac \u201c 12 = 76 therefore students who passed = 100 \u00e2 \u20ac \u201c 76 = 24 . answer : a\"" + }, + { + "Answer": 39, + "Options": "a ) 22 , b ) 33 , c ) 55 , d ) 77 , e ) 39", + "Correct": "e", + "Explanation": "\"let f = pure fuji , g = pure gala and c - cross pollinated . c = 10 % of x where x is total trees . c = . 1 x also 3 x / 4 = f and c + f = 221 = > . 1 x + 3 / 4 x = 221 = > x = 260 260 - 221 = pure gala = 39 . e\"" + }, + { + "Answer": 2, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "c", + "Explanation": "\"apparently it ' s q = x ^ 2 - x ^ 3 instead of q = x ^ 2 - q ^ 3 . in this case : the x - intercept is the value ( s ) of x for q = 0 . 0 = x ^ 2 - x ^ 3 ; 0 = x ^ 2 ( 1 - x ) ; x = 0 or x = 1 . answer : c .\"" + }, + { + "Answer": 13, + "Options": "a ) 16 , b ) 18 , c ) 13 , d ) 20 , e ) 22", + "Correct": "c", + "Explanation": "\"we need to find the median which is the third value when the numbers are in increasing order . since k < m < r < s < t , the median would be r . the average of the positive integers is 10 which means that in effect , all numbers are equal to 10 . if the largest number is 20 , it is 10 more than 20 . we need r to be maximum so k and m should be as small as possible to get the average of 10 . since all the numbers are positive integers , k and m can not be less than 1 and 2 respectively . 1 is 9 less than 10 and 2 is 8 less than 10 which means k and m combined are 17 less than the average . 20 is already 10 more than 10 and hence we only have 17 - 10 = 7 extra to distribute between r and s . since s must be greater than r , r can be 10 + 3 = 13 and s can be 10 + 4 = 14 . so r is 13 . answer ( c )\"" + }, + { + "Answer": 30, + "Options": "a ) 30 , b ) 50 , c ) 15 , d ) 12 , e ) 20", + "Correct": "a", + "Explanation": "\"let the actual distance traveled be x km . then , x / 10 = ( x + 15 ) / 15 x - 30 = > x = 30 km . answer : a\"" + }, + { + "Answer": 8.965784284662087, + "Options": "a ) 9 , b ) 12 , c ) 14 , d ) 16 , e ) 18", + "Correct": "a", + "Explanation": "\"this one ' s easy . 1000 * 2 ^ t = 500,000 2 ^ t = 500 now gauging , since 2 ^ 8 = 256 , then 2 ^ 9 = 512 so t = 9 but be careful , ' t ' is in time intervals of 1 minutes so answer is 9 * 1 = 9 minutes answer ( a )\"" + }, + { + "Answer": 300, + "Options": "a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500", + "Correct": "c", + "Explanation": "\"a + b + c = 1000 a + c = 700 b + c = 600 - - - - - - - - - - - - - - a + b + 2 c = 1300 a + b + c = 1000 - - - - - - - - - - - - - - - - c = 300 answer : c\"" + }, + { + "Answer": 9, + "Options": "a ) 9 , b ) 12 , c ) 16 , d ) 24 , e ) 36", + "Correct": "a", + "Explanation": "\"i ' m going to focus on denominator only . . ( 2 ^ 18 ) . ( ( 3 ^ 4 ) ^ k = 18 ^ 18 ( 2 ^ 18 ) . ( ( 3 ^ 4 k ) = ( 2 . 3 ^ 2 ) ^ 18 ( 2 ^ 18 ) . ( ( 3 ^ 4 k ) = ( 2 ^ 24 ) . ( 3 ^ 2 ) ^ 18 hence 4 k = 36 k = 9 answer a i hope it ' s quite clear\"" + }, + { + "Answer": 1, + "Options": "a ) 8 , b ) 6 , c ) 1 , d ) 4 , e ) 2", + "Correct": "c", + "Explanation": "explanation : let the original number be pq i . e . , ( 10 p + q ) . after interchanging the digits , the new number becomes qp i . e . , ( 10 q + p ) . the question states that the average of 9 numbers has become 1 less than the original average . therefore , the sum of the original 9 numbers will be 9 * 1 more than the sum of the 9 numbers with the digits interchanged . i . e . , 10 p + q = 10 q + p + 9 = > 9 a - 9 b = 9 = > a - b = 1 . answer : c" + }, + { + "Answer": 7991, + "Options": "a ) s . 4991 , b ) s . 5991 , c ) s . 6001 , d ) s . 6991 , e ) s . 7991", + "Correct": "e", + "Explanation": "\"total fr 5 mnths = ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs 34009 . reqd . sale = rs . [ ( 7000 * 6 ) - 34009 ] = rs . ( 42000 - 34009 ) = rs . 7991 . answer : e\"" + }, + { + "Answer": 18, + "Options": "a ) 5 inches , b ) 6 inches , c ) 9 inches , d ) 10 inches , e ) 18 inches", + "Correct": "e", + "Explanation": "\"total rainfall in 2 weeks = 18 inches . assume the rainfall in second week = 1 . x rainfall in first week = x total rainfall = 2.5 x = 18 inches x = 12 and 1.5 x = 18 rainfall during second week = 18 inches option e\"" + }, + { + "Answer": 7, + "Options": "a ) - 3 , b ) 3 , c ) 5 , d ) 7 , e ) 8", + "Correct": "d", + "Explanation": "\"a can not be the answer as all the three terms are in modulus and hence the answer will be non negative . | x - 4 | > = 0 - - > minimum occurs at x = 4 | x + 2 | > = 0 - - > minimum occurs at x = - 2 | x - 5 | > = 0 - - > minimum occurs at x = 5 x = - 2 - - > result = 6 + 0 + 7 = 13 . also any negative value will push the combined value of | x - 4 | + | x - 5 | to a value > 9 . x = 4 - - > result = 0 + 6 + 1 = 7 x = 5 - - > result = 1 + 7 + 0 = 8 x = 2 - - > result = 2 + 4 + 3 = 9 so minimum value of the expression occurs at x = 4 and the resultant value = 7 answer : d\"" + }, + { + "Answer": 97, + "Options": "a ) 75 kg , b ) 65 kg , c ) 55 kg , d ) 97 kg , e ) 25 kg", + "Correct": "d", + "Explanation": "\"total weight increased = ( 8 x 4 ) kg = 32 kg . weight of new person = ( 65 + 32 ) kg = 97 kg . answer : d\"" + }, + { + "Answer": 40, + "Options": "a ) 36 , b ) 42 , c ) 40 , d ) 46 , e ) none", + "Correct": "c", + "Explanation": "\"17 ( p + 1 ) = 29 ( q + 1 ) - - > ( p + 1 ) / ( q + 1 ) = 29 / 17 - - > the least positive value of p + 1 is 25 , so the least value of p is 24 and the least positive value of q + 1 is 17 , so the least value of q is 16 - - > the least value of p + q is 24 + 16 = 40 . answer : c .\"" + }, + { + "Answer": 0.16666666666666666, + "Options": "a ) 1 / 3 , b ) 1 / 6 , c ) 2 / 3 , d ) 2 / 5 , e ) 3 / 7", + "Correct": "b", + "Explanation": "number of ways you can choose 2 from 4 = 4 c 2 = 6 e = event of getting the 2 numbers is more than 6 = ( 3,4 ) = 1 probability = 1 / 6 answer is b" + }, + { + "Answer": 75, + "Options": "a ) 76 kg , b ) 76.5 kg , c ) 75 kg , d ) data inadequate , e ) none of these", + "Correct": "c", + "Explanation": "\"explanation : total weight increased = ( 10 x 2.5 ) kg = 25 kg . weight of new person = ( 50 + 25 ) kg = 75 kg . answer : c\"" + }, + { + "Answer": 80, + "Options": "a ) 60 kg , b ) 50 kg , c ) 92 kg , d ) 80 kg , e ) 70 kg", + "Correct": "d", + "Explanation": "total weight increased = 2 * 20 = 40 kg weight of the new man = 40 + 40 = 80 kg answer is d" + }, + { + "Answer": 134, + "Options": "a ) 134 , b ) 120 , c ) 218 , d ) 140 , e ) 145", + "Correct": "a", + "Explanation": "a + b + c = 645 a = 3 b 3 b + b + b - 25 = 645 5 b = 670 b = 134 answer : a" + }, + { + "Answer": 25, + "Options": "a ) 4 . , b ) 8 . , c ) 12 . , d ) 25 . , e ) 64 .", + "Correct": "d", + "Explanation": "\"eq 1 : a - b - c + d = 13 eq 2 : a + b - c - d = 3 ( 1 ) subtract eq 1 from eq 2 a - b - c + d = 13 - a + b - c - d = 3 - - - - - - - - - - - - - - - - - - - - - - - - - 2 b + 2 d = 10 ( 2 ) simplify - b + d = 5 b - d = - 5 ( b - d ) ^ 2 = ( - 5 ) ^ 2 = 25 my answer : d\"" + }, + { + "Answer": 25, + "Options": "a ) 66.66 % , b ) 66.68 % , c ) 66.766 % , d ) 86.66 % , e ) 25 %", + "Correct": "e", + "Explanation": "\"excess of b ' s height over a ' s = [ ( 20 / ( 100 - 20 ) ] x 100 % = 25 % answer : e )\"" + }, + { + "Answer": 6, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8", + "Correct": "c", + "Explanation": "2 ways to solve this problem . . summation ( x ) = n ( n - 1 ) / 2 n ( n - 1 ) / 2 = 15 ; n ^ 2 - n - 30 = 0 ans : 6 answer : c" + }, + { + "Answer": 64, + "Options": "a ) 57 kg , b ) 60 kg , c ) 64 kg , d ) 62 kg , e ) 66 kg", + "Correct": "c", + "Explanation": "the sailor weighing 56 kg is replaced and the average is increased by 1 kg . hence , the weight of the new sailor is ( 56 + increase in total weight ) = 56 + 1 x 8 = 56 + 8 = 64 kg . answer : c" + }, + { + "Answer": 14.999999999999996, + "Options": "a ) 45 , b ) 27 , c ) 15 , d ) 26 , e ) 91", + "Correct": "c", + "Explanation": "sol : if x sweets were there in total , then x \u00d7 ( 1 \u2013 1 / 3 ) \u00d7 ( 1 \u2013 2 / 5 ) \u00d7 ( 1 \u2013 2 / 3 ) = 2 x \u00d7 2 / 3 \u00d7 3 / 5 \u00d7 1 / 3 = 2 x = 15 answer : c" + }, + { + "Answer": 20, + "Options": "a ) 22 , b ) 25 , c ) 24 , d ) 20 , e ) 28", + "Correct": "d", + "Explanation": "\"explanation : let the number of hens be x and the number of cows be y . then , x + y = 60 . . . . ( i ) and 2 x + 4 y = 200 x + 2 y = 100 . . . . ( ii ) solving ( i ) and ( ii ) we get : x = 20 , y = 40 . the required answer = 20 . answer : d\"" + }, + { + "Answer": 10, + "Options": "a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25", + "Correct": "b", + "Explanation": "\"assume she has $ 200 to spend . tax clothing = 50 % = $ 100 = $ 10.00 food = 25 % = $ 50 = $ 0.00 items = 25 % = $ 50 = $ 10.00 total tax = $ 20.00 % of total amount = 20 / 200 * 100 = 10 % answer b\"" + }, + { + "Answer": 171, + "Options": "a ) 62 , b ) 181 , c ) 170 , d ) 171 , e ) 50", + "Correct": "d", + "Explanation": "\"a 2 - b 2 = 11 : given a 4 + b 4 - 2 a 2 b 2 = 112 : square both sides and expand . a * b = 2 : given a 2 b 2 = 52 : square both sides . a 4 + b 4 - 2 ( 25 ) = 121 : substitute a 4 + b 4 = 171 correct answer d\"" + }, + { + "Answer": 100, + "Options": "a ) 90 % , b ) 99 % , c ) 100 % , d ) 101 % , e ) 110 %", + "Correct": "b", + "Explanation": "\"let the number of employees before jul 1 be 100 then av sal 1 = total 1 / 100 after jul 1 employees = 90 av sal 2 = total 2 / 90 now from the question av 2 = av 1 + 10 % total 2 / 90 = total 1 / 100 + 1 / 10 * total 1 / 100 total 2 / 90 = 11 total 1 / 1000 total 2 = 99 total 1 / 100 now percent = total 2 / total 1 * 100 = 99 total 1 / total 1 = 99 answer : b\"" + }, + { + "Answer": 0.001, + "Options": "a ) 1 / 1000 , b ) 1 / 506 , c ) 253 / 500 , d ) 253 / 1000 , e ) none of these", + "Correct": "a", + "Explanation": "given exp . = ( a ^ 2 + b ^ 2 - ab ) / ( a ^ 3 + b ^ 3 ) = 1 / ( a + b ) = 1 / ( 753 + 247 ) = 1 / 1000 answer : a" + }, + { + "Answer": 14.980000000000004, + "Options": "a ) 20 % , b ) 18 % , c ) 15 % , d ) 12 % , e ) 14 %", + "Correct": "c", + "Explanation": "\"100 * 100 = 10000 78 * 109 = 8502 10000 - - - - - - - 1200 100 - - - - - - - ? = 15 % answer : c\"" + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16", + "Correct": "a", + "Explanation": "let no . of buffaloes be x & no . of ducks be y buffaloes have 4 legs while ducks have 2 4 x + 2 y = 2 * ( x + y ) + 24 = > 4 x + 2 y - 2 x - 2 y = 24 = > x = 12 number of buffaloes in the group = 12 answer : a" + }, + { + "Answer": 1, + "Options": "a ) 0 , b ) 1 , c ) 3 , d ) 5 , e ) 6", + "Correct": "b", + "Explanation": "57 / 5000 = 57 / ( 5 * 10 ^ 3 ) = ( 57 / 5 ) * 10 ^ - 3 = 11.4 * 10 ^ - 3 = . 0114 thousandths digit = 1 answer b" + }, + { + "Answer": 85, + "Options": "a ) 75 , b ) 65 , c ) 85 , d ) 95 , e ) 80", + "Correct": "c", + "Explanation": "\"total increase in weight = 8 \u00d7 2.5 = 20 if x is the weight of the new person , total increase in weight = x \u2212 65 = > 20 = x - 65 = > x = 20 + 65 = 85 answer is c .\"" + }, + { + "Answer": 8, + "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12", + "Correct": "a", + "Explanation": "lcm of 12 , 2030 is 120 . so the number is in the form of 120 x + 3 which is divisible by 11 , by placing x = 3 , we get 363 which is divisible by 11 and the multiple of 120 when 3 is subtracted from 363 . so the no . is 363 . so when 30 is added to it and is divided by 11 we get remainder as 8 answer : a" + }, + { + "Answer": 105, + "Options": "a ) 100 , b ) 99 , c ) 98 , d ) 102 , e ) 104", + "Correct": "e", + "Explanation": "\"g ( 106 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 * 101 * 103 * 105 g ( 103 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 * 101 * 103 g ( 106 ) - g ( 103 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 * 101 * 103 * 105 - 1 * 3 * 5 * 7 * 9 * . . . * 99 * 101 * 103 = 1 * 3 * 5 * 7 * 9 * . . . * 103 * ( 105 - 1 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 * 101 * 103 * 104 hence : e\"" + }, + { + "Answer": 99.9, + "Options": "a ) 99.9 , b ) 91.0 , c ) 88.0 , d ) 70.9 , e ) 71.2", + "Correct": "a", + "Explanation": "\"11 % of 90 = ( 90 * 0.11 ) = 9.9 11 % greater than 90 = 90 + 9.9 = 99.9 answer is clearly a .\"" + }, + { + "Answer": 40, + "Options": "a ) 40 , b ) 99 , c ) 88 , d ) 77 , e ) 66", + "Correct": "a", + "Explanation": "\"let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 60 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 60 + 20 ) / 2 = 40 . answer : a\"" + }, + { + "Answer": 21, + "Options": "a ) 7 , b ) 14 , c ) 21 , d ) 28 , e ) 35", + "Correct": "c", + "Explanation": "1029 = 7 x 7 x 7 x 3 n must include at least 7 , 2 * 7 , and 3 * 7 . the answer is c ." + }, + { + "Answer": 2000, + "Options": "a ) $ 1000 , b ) $ 2000 , c ) $ 3000 , d ) $ 4000 , e ) $ 5000", + "Correct": "b", + "Explanation": "a certain percentage of questions in the quant section of the gmat are just ' math questions ' - you ' ll use a formula , do some calculations and you ' ll have the answer . this is one of those types of questions . you still have to write everything down and stay organized , but the work involved is relatively straight - forward . here , we ' re told that the current annual deductible is $ 3000 and that the deductible is to be increased by 2 / 3 . we ' re asked how much more will the deductible cost a family next year . original deductible = $ 3000 increase in deductible = 2 / 3 the answer is calculated by the equation : $ 3000 \u00d7 2 / 3 = $ 2000 . b" + }, + { + "Answer": 5, + "Options": "a ) 15 , b ) 10 , c ) 5 , d ) 20 , e ) 25", + "Correct": "c", + "Explanation": "\"the q talks of total capacity , normal level , present level , shortage etc . . so it is all about not going wrong in these terms 6 mg = 60 % of total . . total = 6 / . 6 = 10 mg . . normal level = 1 / 2 of 10 = 5 mg . . shortage of normal level = 10 - 5 = 5 mg . . c\"" + }, + { + "Answer": 500, + "Options": "a ) $ 500 , b ) $ 520 , c ) $ 540 , d ) $ 560 , e ) $ 580", + "Correct": "a", + "Explanation": "s . i for 5 years = $ 850 - $ 600 = $ 250 the s . i . is $ 50 / year s . i . for 2 years = $ 100 principal = $ 600 - $ 100 = $ 500 the answer is a ." + }, + { + "Answer": 0.1388888888888889, + "Options": "a ) 1 / 12 , b ) 5 / 36 , c ) 1 / 6 , d ) 1 / 3 , e ) 17 / 36", + "Correct": "b", + "Explanation": "no . of possible outcomes = 6 * 6 = 36 no . of outcomes that result a total of 8 ( as a is 8 spaces behind b ) = 5 ( ( 2,6 ) , ( 3,5 ) , ( 4,4 ) , ( 5,3 ) , ( 6,2 ) ) so , the probability = 5 / 36 ( option b )" + }, + { + "Answer": 38, + "Options": "a ) 36 , b ) 38 , c ) 40 , d ) 42 , e ) 44", + "Correct": "b", + "Explanation": "\"let b be the number of blue hats and let g be the number of green hats . b + g = 85 . b = 85 - g . 6 b + 7 g = 548 . 6 ( 85 - g ) + 7 g = 548 . 510 - 6 g + 7 g = 548 . g = 548 - 510 = 38 . the answer is b .\"" + }, + { + "Answer": 20, + "Options": "a ) 11 , b ) 13 , c ) 14 , d ) 12 , e ) 20", + "Correct": "e", + "Explanation": "\"explanation : let somu ' s age be x and that of his father be 3 x . so , x - 10 = 3 x - 10 / 5 = x = 20 answer : option e\"" + }, + { + "Answer": 96, + "Options": "a ) 57 , b ) 67 , c ) 77 , d ) 87 , e ) 96", + "Correct": "e", + "Explanation": "\"explanation : money collected = ( 92.16 x 100 ) paise = 9216 paise . \u2234 number of members = \u221a ( 9216 ) = 96 . answer : e\"" + }, + { + "Answer": 20, + "Options": "a ) 50 km , b ) 76 km , c ) 20 km , d ) 16 km , e ) 97 km", + "Correct": "c", + "Explanation": "\"let the actual distance traveled be x km . then , x / 5 = ( x + 20 ) / 10 5 x - 100 = > x = 20 km . answer : c\"" + }, + { + "Answer": 824777405, + "Options": "a ) 724533811 , b ) 353654655 , c ) 825107481 , d ) 725117481 , e ) 477899932", + "Correct": "c", + "Explanation": "\"82519 x 9999 = 82519 x ( 10000 - 1 ) = 82519 x 10000 - 82519 x 1 = 825190000 - 82519 = 825107481 c\"" + }, + { + "Answer": 44, + "Options": "a ) 35 , b ) 40 , c ) 44 , d ) 45 , e ) 56", + "Correct": "c", + "Explanation": "\"we just enter this root into the equation in order to recieve an equation to find the answer ! 2 * 4 ^ 2 + 3 * 4 - k = 0 k = 32 + 12 = 44 the answer is c\"" + }, + { + "Answer": 1.55, + "Options": "a ) 140 / 217 , b ) 156 / 185 , c ) 217 / 140 , d ) 263 / 149 , e ) 241 / 163", + "Correct": "c", + "Explanation": "the way to approach this problem is 8 < a < 15 and 6 < b < 21 minimum possible value of a is 9 and maximum is 14 minimum possible value of b is 7 and maximum is 20 range = max a / min b - min a / max b ( highest - lowest ) 14 / 7 - 9 / 20 = 217 / 140 hence c" + }, + { + "Answer": 1782, + "Options": "a ) 1234 , b ) 1345 , c ) 1456 , d ) 1797 , e ) 1635", + "Correct": "d", + "Explanation": "\"let the smaller number be x . then larger number = ( x + 1500 ) . x + 1500 = 6 x + 15 5 x = 1485 x = 297 large number = 297 + 1500 = 1797 d\"" + }, + { + "Answer": 78, + "Options": "a ) 56 , b ) 70 , c ) 78 , d ) 80 , e ) 85", + "Correct": "c", + "Explanation": "let boys = 3 x and girls = 2 x . number of those who get less than 90 % mark = ( 80 % of 3 x ) + ( 75 % of 2 x ) = ( 80 / 100 ) * 3 x + ( 75 / 100 * 2 x ) = 39 x / 10 required percentage = ( 39 x / 10 * 1 / 5 x * 100 ) % = 78 % . answer : c" + }, + { + "Answer": 24, + "Options": "a ) a ) 16 , b ) b ) 18 , c ) c ) 19 , d ) d ) 22 , e ) e ) 24", + "Correct": "e", + "Explanation": "\"explanation : 10 * 23 + 36 \u2013 26 = 240 = > 240 / 10 = 24 e )\"" + }, + { + "Answer": 80, + "Options": "a ) 75 kg , b ) 55 kg , c ) 80 kg , d ) 85 kg , e ) 25 kg", + "Correct": "c", + "Explanation": "\"explanation : total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 60 + 20 ) kg = 80 kg . answer : c\"" + }, + { + "Answer": 48.12698412698413, + "Options": "a ) 36 , b ) 40 , c ) 44 , d ) 48 , e ) 52", + "Correct": "d", + "Explanation": "\"for 40 hrs = 40 * 18 = 720 excess = 976 - 720 = 252 for extra hours = . 75 ( 18 ) = 13.5 + 18 = 31.5 number of extra hrs = 252 / 31.5 = 8 total hrs = 40 + 8 = 48 answer d 48\"" + }, + { + "Answer": 56, + "Options": "a ) 57 , b ) 56 , c ) 55 , d ) 54 , e ) 53", + "Correct": "b", + "Explanation": "\"basically , the question asks how many 4 digit numbers ( including those in the form 0 xxx , 00 xx , and 000 x ) have digits which add up to 5 . think about the question this way : we know that there is a total of 5 to be spread among the 4 digits , we just have to determine the number of ways it can be spread . let x represent a sum of 1 , and | represent a seperator between two digits . as a result , we will have 5 x ' s ( digits add up to the 5 ) , and 3 | ' s ( 3 digit seperators ) . so , for example : xx | x | x | x = 2111 | | xxx | xx = 0032 etc . there are 8 c 3 ways to determine where to place the separators . hence , the answer is 8 c 3 = 56 . b\"" + }, + { + "Answer": 100, + "Options": "a ) 400 , b ) 300 , c ) 200 , d ) 100 , e ) 150", + "Correct": "d", + "Explanation": "c = rs . 1000 / - d = rs . 1500 / - c share 2 parts & d share 3 parts total 5 parts - - - - - > rs . 500 / - - - - - > 1 part - - - - - - - > rs . 100 / - d share = 3 parts - - - - - > rs . 300 / - d" + }, + { + "Answer": 63, + "Options": "a ) 63 , b ) 64 , c ) 65 , d ) 66 , e ) 67", + "Correct": "a", + "Explanation": "\"a two - digit integer ` ` ab ' ' can be expressed algebraically as 10 a + b . q - r = ( 10 a + b ) - ( 10 b + a ) = 9 ( a - b ) < 70 . the greatest multiple of 9 which is less than 70 is 63 . the answer is a .\"" + }, + { + "Answer": 2.333333333333333, + "Options": "a ) 5 / 3 , b ) 2 / 7 , c ) 7 / 3 , d ) 1 / 7 , e ) 1 / 4", + "Correct": "c", + "Explanation": "7 liter of forset green have 4 liter of blue and 3 liter of yellow suppose we add x liter of yellow to make it a verdant green so the ratio of blue to yellow in verdant green is \u00be so the equation is blue / yellow = 4 / ( 3 + x ) = \u00be 9 + 3 x = 16 = > x = 7 / 3 answer : c" + }, + { + "Answer": 17, + "Options": "a ) 10 , b ) 12 , c ) 17 , d ) 18 , e ) 20", + "Correct": "c", + "Explanation": "\"sp = 16 loss = cp 17 loss = cp \u2212 sp = cp \u2212 16 \u21d2 cp 17 = cp \u2212 16 \u21d2 16 cp 17 = 16 \u21d2 cp 17 = 1 \u21d2 cp = 17 c\"" + }, + { + "Answer": 3153, + "Options": "a ) 2927 , b ) 3147 , c ) 3387 , d ) 3567 , e ) 3797", + "Correct": "b", + "Explanation": "\"when increased by 3 , the number must include at least 2 * 3 ^ 2 * 5 ^ 2 * 7 = 3150 the answer is b .\"" + }, + { + "Answer": 20, + "Options": "a ) 9 , b ) 13 , c ) 16 , d ) 20 , e ) 25", + "Correct": "d", + "Explanation": "let original hourly wage be x and let the no of hours worked be y total wage will be = x * y after the increment the wage will be = 1.25 x now we need to find number of hours worked so that x * y = 1.25 x * z i . e z = 4 / 5 y % decrease = ( y - 4 / 5 y ) / y * 100 = 100 / 5 = 20 % . thus my answer is d" + }, + { + "Answer": 76, + "Options": "a ) 11 , b ) 37 , c ) 36 , d ) 76 , e ) 33", + "Correct": "d", + "Explanation": "if we strike out 3 zeros , we are in effect reducing two zeroes . so we need 74 steps to reduce 148 zeroes . there are 2 zeroes and 151 ones left now . the remaining zeroes can be reduced in 2 steps . hence the answer is 76 . answer : d" + }, + { + "Answer": 75, + "Options": "a ) 45 , b ) 65 , c ) 75 , d ) 89 , e ) 90", + "Correct": "c", + "Explanation": "\"a + b + c = 3 * 84 = 252 a + b + c + d = 4 * 80 = 320 - - - - ( i ) so , d = 68 & e = 68 + 3 = 71 b + c + d + e = 79 * 4 = 316 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 320 \u2013 316 = 4 a = e + 4 = 71 + 4 = 75 c\"" + }, + { + "Answer": 580, + "Options": "a ) 540 , b ) 570 , c ) 619 , d ) 649 , e ) 580", + "Correct": "e", + "Explanation": "\"before price increase price = d after 30 % price increase price = d + ( 30 / 100 ) * d = 1.3 d = 377 ( given ) i . e . d = 377 / 1.3 = $ 290 i . e . 2 d = 2 * 290 = 580 answer : option e\"" + }, + { + "Answer": 2, + "Options": "a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 9", + "Correct": "a", + "Explanation": "8 , 86 , x , - 4 , - 12 i guess each differ in d range of 2 8 - 8 = 0 8 - 6 = 2 6 - 2 = 4 2 - 6 = - 4 - 4 - 8 = - 12 answer : a" + }, + { + "Answer": 2007, + "Options": "a ) 2003 , b ) 2004 , c ) 2005 , d ) 2006 , e ) 2007", + "Correct": "e", + "Explanation": "\"she must gain at least 70 points , now she has 32 and every year gives her two more points : one for age and one for additional year of employment , so 32 + 2 * ( # of years ) = 70 - - > ( # of years ) = 19 - - > 1988 + 19 = 2007 . answer : e .\"" + }, + { + "Answer": 33.33333333333333, + "Options": "a ) 25 % , b ) 33 1 / 3 % , c ) 50 % , d ) 66 2 / 3 % , e ) 75 %", + "Correct": "b", + "Explanation": "\"general formula for percent increase or decrease , ( percent change ) : percent = change / original \u2217 100 so , the time between maintenance checks increased by 60 \u2212 45 / 45 \u2217 100 = 33 1 / 3 answer : b .\"" + }, + { + "Answer": 67, + "Options": "a ) 61 % , b ) 63 % , c ) 65 % , d ) 67 % , e ) 69 %", + "Correct": "d", + "Explanation": "74 + 84 + x = 3 * 75 x = 67 the answer is d ." + }, + { + "Answer": 21, + "Options": "a ) 20 years , b ) 21 years , c ) 22 years , d ) 23 years , e ) 24 years", + "Correct": "b", + "Explanation": "\"explanation : let the average age of the whole team by x years . 11 x \u00e2 \u20ac \u201c ( 24 + 27 ) = 9 ( x - 1 ) 11 x \u00e2 \u20ac \u201c 9 x = 42 2 x = 42 x = 21 . so , average age of the team is 21 years . answer b\"" + }, + { + "Answer": 15.555555555555555, + "Options": "a ) 9 , b ) 15.55 , c ) 47 , d ) 48 3 / 5 , e ) 59", + "Correct": "b", + "Explanation": "you can plug in values . c = 5 / 9 * ( f - 32 ) f = 32 - - > c = 0 ; f = 32 + 28 = 60 - - > c = 5 / 9 * 28 = 15.55 . increase = 15.55 degrees . answer : b ." + }, + { + "Answer": 56.7, + "Options": "a ) $ 55.70 , b ) $ 56.20 , c ) $ 56.70 , d ) $ 57.20 , e ) $ 57.70", + "Correct": "c", + "Explanation": "1.05 * $ 54 = $ 56.70 the answer is c ." + }, + { + "Answer": 300, + "Options": "a ) 150 , b ) 300 , c ) 450 , d ) 490 , e ) 620", + "Correct": "b", + "Explanation": "x / 10 students are > 4 yrs 20 students are < 3 yrs x / 10 + 20 = 50 x / 10 = 30 x = 300 answer : b" + }, + { + "Answer": 6.25, + "Options": "a ) 25 / 4 , b ) 25 / 2 , c ) 20 / 4 , d ) 35 / 4 , e ) 25 / 3", + "Correct": "a", + "Explanation": "3 p + 4 q = ? divided by q , 3 ( p / q ) + 4 = x 3 * ( 3 / 4 ) + 4 = 25 / 4 answer : a" + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) 15 , c ) 18 , d ) 21 , e ) 24", + "Correct": "a", + "Explanation": "\"first arrange 3 women . 3 women can be arranged in 3 places in 3 ! ways . now w blank w blankw we have to fill the two blanks with 2 men . we can arrange 2 persons in 2 places in 2 ! ways . 3 ! * 2 ! = 12 ways . a is the answer\"" + }, + { + "Answer": 0.72, + "Options": "a ) 0.86 , b ) 0.68 , c ) 0.96 , d ) 0.69 , e ) 0.72", + "Correct": "e", + "Explanation": "\"given expression = ( 0.82 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.82 ) ( power 2 ) + ( 0.82 x 0.1 ) + ( 0.1 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 0.82 - 0.1 ) = 0.72 answer is e\"" + }, + { + "Answer": 15.799999999999999, + "Options": "a ) 12.6 . , b ) 14.4 . , c ) 15.8 . , d ) 16.2 . , e ) 16.4", + "Correct": "c", + "Explanation": "[ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 6.6 = 6 * 0 + 2 * 7.2 + 8 - 6.6 = 0 + 14.4 + 1.4 15.8 answer c" + }, + { + "Answer": 16, + "Options": "a ) 15.1 , b ) 15.4 , c ) 15.7 , d ) 16.0 , e ) 16.3", + "Correct": "d", + "Explanation": "let x be the factor by which the bacteria increases every three hours . at 4 : 00 pm , the amount of bacteria was 10 x and at 7 : 00 pm it was 10 x ^ 2 . 10 x ^ 2 = 25.6 x ^ 2 = 2.56 x = 1.6 at 4 : 00 pm , the amount of bacteria was 10 ( 1.6 ) = 16 grams . the answer is d ." + }, + { + "Answer": 36.5, + "Options": "a ) 35.24 , b ) 36.16 , c ) 36.24 , d ) 36.46 , e ) none", + "Correct": "d", + "Explanation": "\"solution correct sum = ( 36 x 50 + 46 - 23 ) = 1823 . \u00e2 \u02c6 \u00b4 correct mean = 1823 / 50 = 36.46 . answer d\"" + }, + { + "Answer": 40.5, + "Options": "a ) 45 , b ) 47.3 , c ) 39.8 , d ) 45.5 , e ) 40.5", + "Correct": "e", + "Explanation": "total weight of boys in class 15 x 48 = 720 kg total weight of all student in the class room 25 x 45 = 1125 kg total no of girls in the class 1125 - 720 = 405 kg average weight of girls 405 / 10 = 40.5 kg correct ans is e" + }, + { + "Answer": 36, + "Options": "a ) 48 , 36 , b ) 36 , 48 , c ) 32 , 48 , d ) 48 , 32 , e ) 32 , 42", + "Correct": "b", + "Explanation": "2 x = 84 \u2212 12 = 72 . x = 72 / 2 = 36 . this is the first number . therefore the other number is x + 12 = 36 + 12 = 48 . the sum of 36 + 48 is 84 . answer is b ." + }, + { + "Answer": 42, + "Options": "a ) 36 - 48 , b ) 50 - 34 , c ) 60 - 24 , d ) 42 - 54 , e ) 21 - 63", + "Correct": "d", + "Explanation": "\"in this problem , we are asked to find two numbers . therefore , we must let x be one of them . let x , then , be the first number . we are told that the other number is 12 more , x + 12 . the problem states that their sum is 96 : word problem = 96 the line over x + 12 is a grouping symbol called a vinculum . it saves us writing parentheses . we have : 2 x = 96 \u00e2 \u02c6 \u2019 12 = 84 . x = 84 / 2 = 42 . this is the first number . therefore the other number is x + 12 = 42 + 12 = 54 . the sum of 42 + 54 is 96 . d\"" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9", + "Correct": "b", + "Explanation": "\"we have equation 2 n + 5 m = 50 we have factor 2 in first number and we have factor 5 in second number . lcm ( 2 , 5 ) = 10 so we can try some numbers and we should start from 5 because it will be less list than for 2 2 * 5 = 10 and n should be equal 20 4 * 5 = 20 and n should be equal 15 6 * 5 = 30 and n should be equal 10 8 * 5 = 40 and n should be equal 5 10 * 5 = 50 and n should be equal 0 third variant give us the mininal difference n - m = 10 - 6 = 4 and there is some mistake in my way of thinking because we do n ' t have such answer ) if we change the task and will seek for difference between m and n than minimal result q will be 8 - 5 = 3 and answer b\"" + }, + { + "Answer": 11, + "Options": "a ) 13 , b ) 15 , c ) 12 , d ) 10 , e ) 11", + "Correct": "e", + "Explanation": "first payment - - $ 400 total amount to be repaid - - $ 819200 first month payment - - $ 400 second month payment - - $ 400 * 2 = $ 800 third month payment - - $ 800 * 2 = $ 1600 fourth month payment - - $ 1600 * 2 = $ 3200 fifth month payment - - $ 3200 * 2 = $ 6400 sixth month payment - - $ 6400 * 2 = $ 12800 seventh month payment - - $ 25600 * 2 = $ 51200 eight month payment - - $ 51200 * 2 = $ 102400 ninth month payment - - $ 102400 * 2 = $ 204800 tenth month payment - - $ 204800 * 2 = $ 409600 eleventh month payment - - $ 409600 * 2 = $ 819200 answer is e" + }, + { + "Answer": 31, + "Options": "a ) 31 , b ) 67 , c ) 88 , d ) 69 , e ) 12", + "Correct": "a", + "Explanation": "total score of the batsman in 20 matches = 800 . total score of the batsman in the next 10 matches = 130 . total score of the batsman in the 30 matches = 930 . average score of the batsman = 930 / 30 = 31 . answer : a" + }, + { + "Answer": 3600.0000000000005, + "Options": "a ) rs . 3000 , b ) rs . 3600 , c ) rs . 2400 , d ) rs . 4000 , e ) none of these", + "Correct": "b", + "Explanation": "\"let the amount with r be rs . r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 9000 - r ) = > 3 r = 18000 - 2 r = > 5 r = 18000 = > r = 3600 . answer : b\"" + }, + { + "Answer": 198, + "Options": "a ) 182 , b ) 186 , c ) 190 , d ) 194 , e ) 198", + "Correct": "e", + "Explanation": "\"j + k = 293 and so k = 293 - j j - 8 = 2 k j - 8 = 2 ( 293 - j ) 3 j = 594 j = 198 the answer is e .\"" + }, + { + "Answer": 40, + "Options": "a ) 40 m , b ) 72 m , c ) 80 m , d ) 82 m , e ) 84 m", + "Correct": "a", + "Explanation": "\"let the length of each train be x m . then , distance covered = 2 x m . relative speed = 44 - 36 = 8 km / hr . = 8 * 5 / 18 = 20 / 9 m / sec . 2 x / 36 = 20 / 9 = > x = 40 . answer : a\"" + }, + { + "Answer": 6, + "Options": "a ) 2 , b ) 5 , c ) 6 , d ) 8 , e ) 9", + "Correct": "c", + "Explanation": "each of the 59 members in lourdes school class is required to sign up for a minimum of one and a maximum of three academic clubs . total = g 1 + g 2 + g 3 - ( # in exactly 2 ) - 2 * ( # in 3 sets ) 59 = 22 + 27 + 28 - ( 6 ) - 2 x so , # in 3 sets = 6 = c" + }, + { + "Answer": 80, + "Options": "a ) 80 , b ) 90 , c ) 110 , d ) 120 , e ) 130", + "Correct": "b", + "Explanation": "\"if on a test three people answered 90 % of the questions correctly and two people answered 80 % correctly , then the average for the group is not 85 % but rather 3 \u00d7 90 + 2 \u00d7 805 = 4305 = 86.3 \u00d7 90 + 2 \u00d7 805 = 4305 = 86 . here , 90 has a weight of 3 = > it occurs 3 times . whereas 80 has a weight of 2 = > it occurs 2 times . so the average is closer to 90 than to 80 as we have just calculated . b\"" + }, + { + "Answer": 86, + "Options": "a ) 79 , b ) 89 , c ) 95 , d ) 86.36 , e ) 97.2", + "Correct": "d", + "Explanation": "\"let the 6 courses that were taken last year be a 1 , a 2 , a 3 , a 4 , a 5 , a 6 a 1 + a 2 + a 3 + a 4 + a 5 + a 6 = 100 * 6 = 600 the year before , the 5 courses be b 1 , b 2 , b 3 , b 4 , b 5 b 1 + b 2 + b 3 + b 4 + b 5 = 70 * 5 = 350 student ' s average = ( 600 + 350 ) / 11 = 86.36 answer d\"" + }, + { + "Answer": 116.66666666666667, + "Options": "a ) 116 , b ) 84 , c ) 40 , d ) 28 , e ) 20", + "Correct": "a", + "Explanation": "\"almonds : walnuts = 5 : 1 total mixture has 6 parts in a 140 pound mixture , almonds are 5 / 6 ( total mixture ) = 5 / 6 * 140 = 116 pounds answer ( a )\"" + }, + { + "Answer": 0.26, + "Options": "a ) 0.52 , b ) 0.26 , c ) 0.48 , d ) 0.64 , e ) 0.46", + "Correct": "b", + "Explanation": "\"given exp . = 0.4 * 0.5 + ( 0.3 * 0.2 ) = 0.2 + 0.06 = 0.26 answer is b .\"" + }, + { + "Answer": 8, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8", + "Correct": "e", + "Explanation": "\"4 x + 2.8 y = 42 - - > multiply by 2.5 ( to get the integers ) - - > 10 x + 7 y = 105 - - > only one positive integers solutions x = 8 and y = 5 ( how to solve : 7 y must have the last digit of 5 in order the last digit of the sum to be 5 ) . answer : e .\"" + }, + { + "Answer": 40000, + "Options": "a ) $ 40000 , b ) $ 15000 , c ) $ 12000 , d ) $ 10000 , e ) $ 9000", + "Correct": "a", + "Explanation": "since investment doubles in 70 / r years then for r = 8 it ' ll double in 70 / 8 = ~ 9 years ( we are not asked about the exact amount so such an approximation will do ) . thus in 18 years investment will double twice and become ( $ 10,000 * 2 ) * 2 = $ 40,000 ( after 9 years investment will become $ 10,000 * 2 = $ 20,000 and in another 9 years it ' ll become $ 20,000 * 2 = $ 40,000 ) . answer : a ." + }, + { + "Answer": 6000, + "Options": "a ) 5000 , b ) 2999 , c ) 6000 , d ) 2990 , e ) 2771", + "Correct": "c", + "Explanation": "\"income = rs . 100 expenditure = rs . 80 savings = rs . 20 present expenditure 80 * ( 20 / 100 ) = rs . 96 present savings = 100 \u00e2 \u20ac \u201c 96 = rs . 4 100 - - - - - - 4 ? - - - - - - - - - 240 = > 6000 answer : c\"" + }, + { + "Answer": 25, + "Options": "a ) 9 % , b ) 11 % , c ) 15 % , d ) 25 % , e ) 90 %", + "Correct": "d", + "Explanation": "cost of 12 paper towels individually = 1 * 12 = 12 cost of a set of 12 paper towels = 9 cost of one roll = 9 / 12 = 3 / 4 = 0.75 savings per roll = 1 - . 75 = 0.25 % of savings is q = . 25 / 1 * 100 = 25 % d is the answer ." + }, + { + "Answer": 6, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "d", + "Explanation": "suppose anoop joined after 3 months . then , 20000 * 12 = 40000 * ( 12 \u2013 x ) = > = > x = 6 . answer : d" + }, + { + "Answer": 204, + "Options": "a ) 204.6 cm , b ) 404.6 cm , c ) 224.6 cm , d ) 205.6 cm , e ) 256.6 cm", + "Correct": "a", + "Explanation": "total height = 180 * 35 = 6300 cm . total height of those who left = 120 * 7 = 840 total height of those who joined = 140 * 7 = 980 new average = [ 6300 - 120 + 980 ] / 35 = 7160 / 35 cm . = 204.6 cm answer : a" + }, + { + "Answer": 6, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "e", + "Explanation": "\"if the average price is 56 , then mary has 8 oranges and 2 apples ( a ratio of 4 : 1 ) . for the average price to be 50 , the ratio should be 1 : 1 . mary must put back 6 oranges . the answer is e .\"" + }, + { + "Answer": 55, + "Options": "a ) 24 , b ) 55 , c ) 297 , d ) 267 , e ) 29", + "Correct": "b", + "Explanation": "explanation : 21 - 10 = 11 11 x 5 = 55 answer : b" + }, + { + "Answer": 4.449999999999999, + "Options": "a ) 4.7 , b ) 4.45 , c ) 4.2 , d ) 4.1 , e ) 4.9", + "Correct": "b", + "Explanation": "explanation : sum of the remaining two numbers = ( 3.9 * 6 ) - [ ( 3.4 * 2 ) + ( 3.85 * 2 ) ] = 23.40 - ( 6.8 + 7.7 ) = 23.40 - 14.5 = 8.90 . required average = ( 8.9 / 2 ) = 4.45 . answer : b ) 4.45" + }, + { + "Answer": 33, + "Options": "a ) 33 kg , b ) 31 kg , c ) 32 kg , d ) 36 kg , e ) 37 kg", + "Correct": "a", + "Explanation": "\"a 33 kg let a , b , c represent their respective weights . then , we have : a + b + c = ( 45 x 3 ) = 135 . . . . ( i ) a + b = ( 41 x 2 ) = 82 . . . . ( ii ) b + c = ( 43 x 2 ) = 86 . . . . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 168 . . . . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 33 . b ' s weight = 33 kg . a\"" + }, + { + "Answer": 2, + "Options": "a ) - 2 , b ) - 1 , c ) 0 , d ) 2 , e ) none of the above", + "Correct": "d", + "Explanation": "let us transform the formula : q = ( x \u2013 5 ) \u00b2 + ( x + 1 ) \u00b2 \u2013 6 = x \u00b2 \u2013 10 x + 25 + x \u00b2 + 2 x + 1 \u2013 6 = 2 x \u00b2 \u2013 8 x + 20 = 2 \u00d7 ( x \u00b2 \u2013 4 x + 10 ) = 2 \u00d7 ( ( x \u00b2 \u2013 4 x + 4 ) + 6 ) = 2 \u00d7 ( ( x \u2013 2 ) \u00b2 + 6 ) any square is greater or equal 0 . therefore the formula possess the least value when ( x \u2013 2 ) \u00b2 = 0 . x \u2013 2 = 0 x = 2 the correct answer is choice ( d ) ." + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 3 , c ) 2 , d ) 0 , e ) 5", + "Correct": "a", + "Explanation": "\"1024 \u00e3 \u00b7 25 = 40 with remainder = 24 24 + 1 = 25 . hence 1 should be added to 1024 so that the sum will be divisible by 25 answer : option a\"" + }, + { + "Answer": 7, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9", + "Correct": "c", + "Explanation": "we have ( 3 + 11 + 7 + 9 + 15 + 13 + 8 + 19 + 17 + 21 + 14 + x ) / 12 = 12 137 + x = 144 x = 7 answer is c" + }, + { + "Answer": 3.0035428163476343, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "c", + "Explanation": "the sum is a little more than ( 2 / 3 ) + ( 8 / 6 ) + ( 2 / 4 ) = 2.5 . correct answer c" + }, + { + "Answer": 108, + "Options": "a ) 108 , b ) 135 , c ) 139 , d ) 147 , e ) 188", + "Correct": "a", + "Explanation": "\"lets say j is the weight of jack and s is the wt of his sister . if he loses 8 pounds , he s twice as heavy as his sister . j - 12 = 2 * s also , together they weight 156 pounds j + s = 156 solvong the 2 equation , we get j = 108 pounds ! a\"" + }, + { + "Answer": 40, + "Options": "a ) 39 , b ) 41 , c ) 40 , d ) 42 , e ) 43", + "Correct": "c", + "Explanation": "total age of all students = 19 \u00e3 \u2014 20 total age of all students + age of the teacher = 20 \u00e3 \u2014 21 age of the teacher = 20 \u00e3 \u2014 21 \u00e2 \u02c6 \u2019 20 \u00e3 \u2014 19 = 20 ( 21 \u00e2 \u02c6 \u2019 19 ) = 20 \u00e3 \u2014 2 = 40 answer is c ." + }, + { + "Answer": 2, + "Options": "a ) 4 / 5 , b ) 1 , c ) 2 , d ) 5 , e ) 8", + "Correct": "c", + "Explanation": "\"( m , n ) m = x n = y m = n / 2 - 2 / 5 10 m = 5 n - 4 ( multiplied by 10 to simplify equation ) ( m + p , n + 4 ) m + p = x n + 4 = y m + p = ( n + 4 ) / 2 - 2 / 5 multiplied by 10 again 10 m + 10 p = 5 n + 20 - 4 use both equations to solve for p and you get 10 p = 20 p = 2 answer : c\"" + }, + { + "Answer": 24, + "Options": "a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25", + "Correct": "d", + "Explanation": "\"10 + 14 = 24 the answer is d .\"" + }, + { + "Answer": 155, + "Options": "a ) 86 , b ) 165 , c ) 76 , d ) 155 , e ) 26", + "Correct": "d", + "Explanation": "\"given m + p + c = 55 * 3 = 165 - - - ( 1 ) m + p = 90 * 2 = 180 - - - ( 2 ) p + c = 70 * 2 = 140 - - - ( 3 ) where m , p and c are marks obtained by the student in mathematics , physics and chemistry . p = ( 2 ) + ( 3 ) - ( 1 ) = 180 + 140 - 165 = 155 answer : d\"" + }, + { + "Answer": 175, + "Options": "a ) 150 % , b ) 175 percent , c ) 200 % , d ) 250 % , e ) 350 %", + "Correct": "b", + "Explanation": "let z be the percentt x * z / 100 = 2 x - y zx = 7 y * 100 z = 700 y / 4 y z = 350 / 2 z = 175 % answer : b" + }, + { + "Answer": 886.0759493670886, + "Options": "a ) 1000 , b ) 812.88 , c ) 827.78 , d ) 826.82 , e ) 886.08", + "Correct": "e", + "Explanation": "\"1120 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 886.08 answer : e\"" + }, + { + "Answer": 1.4, + "Options": "a ) 25 / 9 , b ) 9 / 5 , c ) 5 / 3 , d ) 7 / 5 , e ) 9 / 25", + "Correct": "d", + "Explanation": "sqrt ( 7 x / 5 ) to be perfect square x has to 7 / 5 ans : d" + }, + { + "Answer": 0.5625, + "Options": "a ) 9 / 18 , b ) 9 / 16 , c ) 9 / 11 , d ) 9 / 12 , e ) 9 / 13", + "Correct": "b", + "Explanation": "( 1 ) put 1 white in first bag , and all the remaining ball in second bag . probability = 12 \u00d7 0 + 12 \u00d7 51612 \u00d7 0 + 12 \u00d7 516 = 532532 ( 2 ) to maximize , we put 1 red in the first bag , and all the remaining in the second . probability = 12 \u00d7 1 + 12 \u00d7 43212 \u00d7 1 + 12 \u00d7 432 = 9 / 16 answer : b" + }, + { + "Answer": 50, + "Options": "a ) 50 m , b ) 72 m , c ) 80 m , d ) 82 m , e ) 92 m", + "Correct": "a", + "Explanation": "\"let the length of each train be x metres . then , distance covered = 2 x metres . relative speed = ( 46 - 36 ) km / hr = ( 10 x ( 5 / 18 ) m / sec = ( 25 / 9 ) m / sec ( 2 x / 36 ) = ( 25 / 9 ) 2 x = 100 x = 50 . a\"" + }, + { + "Answer": 21, + "Options": "a ) 19 , b ) 18 , c ) 16 , d ) 11 , e ) 21", + "Correct": "e", + "Explanation": "\"sum of 20 even numbers = 20 * 21 = 420 average = 420 / 20 = 21 answer : e\"" + }, + { + "Answer": 71.99999999999999, + "Options": "a ) 72 , b ) 60 , c ) 32 , d ) 96 , e ) 65", + "Correct": "a", + "Explanation": "explanation : let the larger number be x . then , x - 48 = 1 / 3 x x - x / 3 = 48 = > 2 x / 3 = 48 = > x = 72 answer : option a" + }, + { + "Answer": 80, + "Options": "a ) 88 % , b ) 90 % , c ) 80 % , d ) 87 % , e ) 20 %", + "Correct": "c", + "Explanation": "a b c d 90 100 80 100 a d 90 - - - - - 100 360 - - - - - - ? = 400 500 - - - - - - 400 100 - - - - - - - ? = > 80 % answer : c" + }, + { + "Answer": 12, + "Options": "a ) 8 , b ) 12 , c ) 20 , d ) 24 , e ) 28", + "Correct": "b", + "Explanation": "if all the tables seated 4 , the number of customers could be 4 * 40 = 160 . 212 - 160 = 52 , so 52 / 2 = 26 tables must be tables seating 6 people . the number of tables seating 4 people is 40 - 26 = 14 . the number of new tables is 26 - 14 = 12 more than the number of old tables . the answer is b ." + }, + { + "Answer": 39, + "Options": "a ) 39 , b ) 49 , c ) 58 , d ) 113 , e ) 131", + "Correct": "a", + "Explanation": "you have 6 digits : 2 , 3 , 4 , 6 , 7 , 8 each digit needs to be used to make two 3 digit numbers . this means that we will use each of the digits only once and in only one of the numbers . the numbers need to be as close to each other as possible . the numbers can not be equal so the greater number needs to be as small as possible and the smaller number needs to be as large as possible to be close to each other . the first digit ( hundreds digit ) of both numbers should be consecutive integers now let ' s think about the next digit ( the tens digit ) . to minimize the difference between the numbers , the tens digit of the greater number should be as small as possible and the tens digit of the smaller number should be as large as possible . so let ' s not use 2 and 8 in the hundreds places and reserve them for the tens places . now what are the options ? try and make a pair with ( 3 * * and 4 * * ) . make the 3 * * number as large as possible and make the 4 * * number as small as possible . 387 and 426 ( difference is 39 ) or try and make a pair with ( 6 * * and 7 * * ) . make the 6 * * number as large as possible and make the 7 * * number as small as possible . we get 684 and 723 ( difference is 39 ) a" + }, + { + "Answer": 34, + "Options": "a ) 25 , b ) 30 , c ) 28 , d ) 34 , e ) 42", + "Correct": "d", + "Explanation": "\"( ( 2 a + 16 ) + ( 3 a - 8 ) ) / 2 = ( 5 a + 8 ) / 2 = 89 a = 34 the answer is d .\"" + }, + { + "Answer": 600, + "Options": "a ) $ 600 , b ) $ 700 , c ) $ 800 , d ) $ 900 , e ) $ 1000", + "Correct": "a", + "Explanation": "0.1 x = 0.08 ( 2000 - x ) + 92 0.18 x = 252 x = 1400 then the amount invested at 8 % is $ 2000 - $ 1400 = $ 600 the answer is a ." + }, + { + "Answer": 2, + "Options": "a ) 1 , b ) 3 , c ) 5 , d ) 2 , e ) 9", + "Correct": "d", + "Explanation": "answer d ( a + b ) ( a - b ) = 25 5 cases for ( a + b ) , ( a - b ) 25 , 1 5 , 5 answer d" + }, + { + "Answer": 7, + "Options": "a ) 6.6 , b ) 6.7 , c ) 6.8 , d ) 7.0 , e ) 6.9", + "Correct": "d", + "Explanation": "old set s - total is avg * no of elements = 6.2 * 10 = 62 if one number is increased by 8 then total increased to 62 + 8 = 70 new avg - 70 / 10 = 7.0 . hence answer is d ." + }, + { + "Answer": 400, + "Options": "a ) 100 , b ) 300 , c ) 400 , d ) 3,000 , e ) 4,000", + "Correct": "c", + "Explanation": "\"straight pluggin in for me . as usual , i started with c and got the answer . lets ' back calculate and see what we get let us consider eggs processed each day to be 400 so initial ratio of eggs processed and rejected is 96 : 4 or 24 : 1 so out of 400 eggs , there will be 384 eggs processed and 16 rejected . now if the no . of eggs inspected remain and 12 more eggs get accepted that means there t = 384 + 12 = 396 eggs accepted and 4 rejected . . . and the ratio will be 99 : 1 bingo . . . this is what the questions says . . . . its always a good idea to start with c .\"" + }, + { + "Answer": 4, + "Options": "a ) \u2212 48 , b ) \u2212 5 , c ) 4 , d ) 46 , e ) 48", + "Correct": "c", + "Explanation": "i . e . if a = 6 then b = - 2 or if a = - 2 then b = 6 but in each case a + b = - 2 + 6 = 4 answer : option c" + }, + { + "Answer": 1999.3333333333333, + "Options": "a ) 2010 , b ) 2011 , c ) 2012 , d ) 2013 , e ) 2014", + "Correct": "c", + "Explanation": "\"the price of commodity x increases 25 cents each year relative to commodity y . the price difference is $ 2.10 and commodity x needs to be 65 cents more than commodity y . $ 2.75 / 25 cents = 11 years the answer is 2001 + 11 years = 2012 . the answer is c .\"" + }, + { + "Answer": 2610, + "Options": "a ) $ 2420 , b ) $ 2610 , c ) $ 2860 , d ) $ 3050 , e ) $ 3270", + "Correct": "b", + "Explanation": "\"let x be the value of the item . 0.07 * ( x - 1000 ) = 112.70 x = 2610 the answer is b .\"" + }, + { + "Answer": 2, + "Options": "a ) 4 , b ) 1 , c ) 2 , d ) 3 , e ) 5", + "Correct": "c", + "Explanation": "\"explanation : ( 1056 / 23 ) gives remainder 21 21 + 2 = 23 , so we need to add 2 answer : option c\"" + }, + { + "Answer": 1014, + "Options": "a ) 1008 , b ) 1014 , c ) 1022 , d ) 1032 , e ) 1043", + "Correct": "b", + "Explanation": "\"required number = ( l . c . m of 12 , 16 , 18 , 21,28 ) + 6 = 1008 + 6 = 1014 answer : b\"" + }, + { + "Answer": 93.33333333333333, + "Options": "a ) 92.33 % , b ) 91.33 % , c ) 95.33 % , d ) 93.33 % , e ) 94.33 %", + "Correct": "d", + "Explanation": "\"let the number be x the right number is 3 x the wrong number is x / 5 error is ( 3 x - x / 5 ) = 14 x / 5 percentage of error is ( ( 14 x / 5 ) / 3 x ) * 100 = 93.33 % answer : d\"" + }, + { + "Answer": 120, + "Options": "a ) 150 , b ) 155 , c ) 140 , d ) 120 , e ) 165", + "Correct": "d", + "Explanation": "let x be the correct answer and y be the wrong answer so the total number of questions is ( x + y ) = 150 . . . . . ( 1 ) = > 4 x - 2 y = 420 . . . . . ( 2 ) by solving ( 1 ) & ( 2 ) , we get = > 6 x = 720 hence x = 120 therefore , number of correct answers are 120 . answer d" + }, + { + "Answer": 6, + "Options": "a ) a ) 4 , b ) b ) 3 , c ) c ) 2 , d ) d ) 5 , e ) e ) 6", + "Correct": "e", + "Explanation": "\"explanation : 690 = 36 x 19 + r 690 = 684 + r r = 690 - 684 = 6 answer : option e\"" + }, + { + "Answer": 30, + "Options": "a ) 22 , b ) 30 , c ) 77 , d ) 20 , e ) 99", + "Correct": "b", + "Explanation": "\"in 1 hr , the bus covers 60 km without stoppages and 30 km with stoppages . stoppage time = time take to travel ( 60 - 30 ) km i . e 30 km at 60 km / hr . stoppage time = 30 / 60 hrs = 30 min . answer : b\"" + }, + { + "Answer": 295, + "Options": "a ) 250 , b ) 276 , c ) 280 , d ) 295 , e ) none", + "Correct": "d", + "Explanation": "\"since the month begins with sunday , to there will be five sundays in the month average required = ( 570 x 5 + 240 x 25 ) / 30 ) = 295 answer : option d\"" + }, + { + "Answer": 24, + "Options": "a ) 24 , b ) 16 , c ) 12 , d ) 8 , e ) 4", + "Correct": "a", + "Explanation": "n - not rented trucks ; r - rented trucks n + r = 24 n + r / 2 = 12 r = 24 a" + }, + { + "Answer": 87, + "Options": "a ) 32 , b ) 45 , c ) 59 , d ) 73 , e ) 87", + "Correct": "e", + "Explanation": "( x + y ) = 36 and both x an y are prime . the only values of x and y can be 17 and 19 ( x = 17 and y = 19 ) 4 x + y = 4 * 17 + 19 = 87 correct option : e" + }, + { + "Answer": 228, + "Options": "a ) 740 , b ) 228 , c ) 690 , d ) 780 , e ) 458", + "Correct": "b", + "Explanation": "\"solution : sum of 1 st 12 results = 12 * 14 sum of last 12 results = 12 * 17 13 th result = x ( let ) now , 12 * 14 + 12 * 17 + x = 25 * 24 or , x = 228 . answer : option b\"" + }, + { + "Answer": 4.600000000000001, + "Options": "a ) 2.3 , b ) 2.5 , c ) 3.5 , d ) 3.6 , e ) 4.6", + "Correct": "e", + "Explanation": "\"sum of the remaining two numbers = ( 3.95 * 6 ) - [ ( 3.4 * 2 ) + ( 3.85 * 2 ) ] = 23.70 - ( 6.8 + 7.7 ) = 23.70 - 14.5 = 9.20 . required average = ( 9.2 / 2 ) = 4.6 . e\"" + }, + { + "Answer": 7, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", + "Correct": "a", + "Explanation": "a simple and elegant solution . as addition of 39 , shifts mean by 2 , and addition of 15 , shifts mean by 1 to the other side , we have the mean lying between 3915 , and in a ratio of 2 : 1 39 - 15 = 24 24 divide by 3 is 8 . meaning mean of the n terms is 15 + 8 = 39 - 16 = 23 now , from first statement , when a person aged 39 is added to a group of n people , the average age increases by 2 . e * 23 + 39 = 25 * ( e + 1 ) e = 7 ans . ( a )" + }, + { + "Answer": 27, + "Options": "a ) 88 , b ) 77 , c ) 33 , d ) 44 , e ) 27", + "Correct": "e", + "Explanation": "explanation : let the present age be ' x ' years . then father ' s present age is 3 x + 3 years . three years hence ( 3 x + 3 ) + 3 = 2 ( x + 3 ) + 8 x = 8 hence father ' s present age = 3 x + 3 = [ ( 3 x 8 ) + 3 ] = 27 years . answer : e" + }, + { + "Answer": 77, + "Options": "a ) 272 , b ) 77 , c ) 168 , d ) 56 , e ) 59", + "Correct": "b", + "Explanation": "explanation : 15 - 2 + 4 \u00f7 1 / 2 \u00d7 8 = 15 - 2 + 4 \u00d7 2 \u00d7 8 = 15 - 2 + 64 = 77 answer : option b" + }, + { + "Answer": 5, + "Options": "a ) 1 , b ) 2 , c ) 5 , d ) 19 , e ) 20", + "Correct": "c", + "Explanation": "\"when positive integer n is divided by 2 , the remainder is 1 i . e . , n = 2 x + 1 values of n can be one of { 1 , 3 , 5 , 7 , 9 , 11 , 13 , 15 , 17,19 , . . . . . . . . . . . . . . 31 , 33,35 . . . . . . . . . . . . . . . . . . } similarly , when n is divided by 7 , the remainder is 5 . . i . e . , n = 7 y + 5 values of n can be one of { 5 , 12 , 19 , 26 , 33 , 40 , 47 , 54 , 61 . . . . . . . . } combining both the sets we get n = { 19 , 52 , . . . . . . . . . . . } what is the smallest positive integer p , such that ( n + p ) is a multiple of 21 or 21 x in case of n = 5 p = 5 so for min value of p , we take min value of n . c is the answer .\"" + }, + { + "Answer": 11, + "Options": "a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15", + "Correct": "a", + "Explanation": "\"100 - ( 100 - 81 ) - ( 100 - 75 ) - ( 100 - 85 ) - ( 100 - 70 ) = 100 - 19 - 25 - 15 - 30 = 100 - 89 = 11 answer : a\"" + }, + { + "Answer": 28.000000000000004, + "Options": "a ) 31 % . , b ) 71 % . , c ) 49 % . , d ) 29 % . , e ) 28 % .", + "Correct": "e", + "Explanation": "\"20 % of 2 litres = 0.4 litres 40 % of 6 litres = 2.4 litres therefore , total quantity of alcohol is 2.8 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 28 % answer : e\"" + }, + { + "Answer": 1620, + "Options": "a ) 1234 , b ) 1540 , c ) 1650 , d ) 1632 , e ) 1635", + "Correct": "e", + "Explanation": "\"let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 15 5 x = 1350 x = 270 large number = 270 + 1365 = 1635 e\"" + }, + { + "Answer": 230, + "Options": "a ) $ 190 , b ) $ 210 , c ) $ 230 , d ) $ 250 , e ) $ 270", + "Correct": "c", + "Explanation": "j + k = 600 so k = 600 - j 2 j = k + 90 2 j = ( 600 - j ) + 90 3 j = 690 j = 230 the answer is c ." + }, + { + "Answer": 0.2, + "Options": "a ) 5 / 6 , b ) 1 / 5 , c ) 1 / 6 , d ) 1 / 7 , e ) 1 / 24", + "Correct": "b", + "Explanation": "\"let x be the number of upgraded sensors on the satellite . the number of non - upgraded sensors per unit is x / 6 . the number of non - upgraded sensors on the whole satellite is 24 ( x / 6 ) = 4 x . the fraction of sensors which have been upgraded is x / ( x + 4 x ) = x / 5 x = 1 / 5 the answer is b .\"" + }, + { + "Answer": 495, + "Options": "a ) 400 , b ) 420 , c ) 430 , d ) 495 , e ) 510", + "Correct": "d", + "Explanation": "let no . of non - officers be x 15 * 450 + x * 110 = ( x + 15 ) 120 x = 495 d" + }, + { + "Answer": 105, + "Options": "a ) 10 , b ) 30 , c ) 105 , d ) 60 , e ) 90", + "Correct": "c", + "Explanation": "15 players are there . two players play one game with one another . so 15 c 2 = 15 x 14 / 2 = 105 so option c is correct" + }, + { + "Answer": 135, + "Options": "a ) 90 , b ) 130 , c ) 135 , d ) 320 , e ) 450", + "Correct": "c", + "Explanation": "\"i ' ve been reading the website for a while and i ' m always keen to see different approaches so i would like to share one that works for me : short version : truck a travels for an hour . distance remaining = 855 - 90 = 765 k ratio of speeds 9 : 8 - > 765 / 17 = 45 truck a = 90 + 45 * 9 = 495 truck b = 45 * 8 = 360 delta = 135 km answer c\"" + }, + { + "Answer": 749.9999999999999, + "Options": "a ) s 200 , b ) s 750 , c ) s 300 , d ) s 450 , e ) s 550", + "Correct": "b", + "Explanation": "\"suppose the amount in the beginning was rs \u2019 x \u2019 money spent on clothes = rs 1 x / 3 balance = rs 2 x / 3 money spent on food = 1 / 5 of 2 x / 3 = rs 2 x / 15 balance = 2 x / 3 - 2 x / 15 = rs 8 x / 15 money spent on travel = 1 / 4 of 8 x / 15 = rs 2 x / 15 = 8 x / 15 - 2 x / 15 = 6 x / 15 = rs 2 x / 5 therefore 2 x / 5 = 300 = 750 answer : b\"" + }, + { + "Answer": 21, + "Options": "a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22", + "Correct": "d", + "Explanation": "\"from right 16 , from left 6 total = 16 + 6 - 1 = 21 answer : d\"" + }, + { + "Answer": 7550, + "Options": "a ) 5100 , b ) 7550 , c ) 10100 , d ) 15500 , e ) 20100", + "Correct": "b", + "Explanation": "\"my solution is : first 50 even integers : 2 4 6 8 < . . . > integers from 102 to 200 102 104 106 108 < . . . > we notice that each integer from the second set is 100 more than the respective integer in the first set . since we have 50 even integers from 102 to 200 , then : w = 2550 + ( 100 * 50 ) = 7550 . b\"" + }, + { + "Answer": 123.75, + "Options": "a ) 143 , b ) 150 , c ) 123.75 , d ) 140.55 , e ) none", + "Correct": "c", + "Explanation": "solution y = 125 + 10 % of 125 = 125 + 12.50 = 137.50 . x = 137.50 - 10 % of 137.50 = 137.50 - 13.75 = 123.75 . answer c" + }, + { + "Answer": 1600, + "Options": "a ) 200 , b ) 600 , c ) 800 , d ) 1600 , e ) 50", + "Correct": "d", + "Explanation": "\"original cost c 1 = t 1 * b 1 ^ 4 new cost c 2 = t 2 * b 2 ^ 4 . . . . only b is doubled so t 2 = t 1 and b 2 = 2 b 1 c 2 = t 2 * ( 2 b 1 ) ^ 4 = 16 ( t 1 * b 1 ^ 4 ) = 16 c 1 16 times c 1 = > 1600 % of c 1 ans d = 1600\"" + }, + { + "Answer": 45, + "Options": "a ) a 17 , b ) b ) 28 , c ) c ) 35 , d ) d ) 45 , e ) e ) 80", + "Correct": "d", + "Explanation": "it is finding the minimum range between all their scores , if all test taker scores are between 0 and maximum range we will have : a - 0 and 17 b - 0 and 28 c - 0 and 35 d - 0 and 45 therefore the minimum range is 45 , it cant be any lower however you play with the numbers . d" + }, + { + "Answer": 1000, + "Options": "a ) $ 2000 , b ) $ 5000 , c ) $ 8000 , d ) $ 1500 , e ) $ 1000", + "Correct": "e", + "Explanation": "\"let the shares of a , b , c , d are 5 x , 3 x , 2 x , 3 x 5 x - 3 x = 1000 x = 500 c ' s share = 2 x = $ 1000 answer is e\"" + }, + { + "Answer": 42, + "Options": "a ) 20 , b ) 21 , c ) 42 , d ) 23 , e ) 24", + "Correct": "c", + "Explanation": "\"solution let the toatl number of workers be x . then 8000 x = ( 18000 x 7 ) + 6000 ( x - 7 ) x = 42 answer c\"" + }, + { + "Answer": 83.99999999999999, + "Options": "a ) 23 , b ) 87 , c ) 84 , d ) 26 , e ) 19", + "Correct": "c", + "Explanation": "given total sum = rs . 427 and given that 3 times a \u2019 s share , 4 times b \u2019 s share and 7 times c \u2019 s share are all equal . = > 3 a = 4 b = 7 c but given = > a + b + c = 427 now express a and b in terms of c i . e = > ( 7 c / 3 ) + ( 7 c / 4 ) + c = 427 = > c = 84 answer : c" + }, + { + "Answer": 17, + "Options": "a ) \u2013 5 , b ) 1 , c ) 13 , d ) 17 , e ) 551", + "Correct": "d", + "Explanation": "2 x - t = 11 . . . . t = 2 x - 11 4 x + t = 4 x + 2 x - 11 = 6 x - 11 6 x - 11 = - 5 . . . x = 1 6 x - 11 = 1 . . . x = 2 6 x - 11 = 13 . . . x = 4 6 x - 11 = 17 . . x is not integer 6 x - 11 = 551 . . x is not integer i think the choice e is 55 not 551 . otherwise both de can not be solution = d" + }, + { + "Answer": 58293485180, + "Options": "a ) 58210607666 , b ) 58310607896 , c ) 58295817036 , d ) 58591650836 , e ) 58310692816", + "Correct": "c", + "Explanation": "\"582964 x 99999 = 582964 x ( 10000 - 1 ) = 582964 x 100000 - 582964 x 1 = 58296400000 - 582964 = 58295817036 c\"" + }, + { + "Answer": 40, + "Options": "a ) 36 liters , b ) 40 liters , c ) 45 liters , d ) 54 liters , e ) 60 liters", + "Correct": "b", + "Explanation": "\"a big container is 30 % full with water and after 18 liters of water is added , the container becomes 75 % full . hence these 18 liters account for 45 % of the container , which means that the capacity of it is 18 / 0.45 = 40 liters . or : if the capacity of the container is x liters then : 0.3 x + 18 = 0.75 x - - > x = 40 liters . answer : b .\"" + }, + { + "Answer": 15, + "Options": "a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15", + "Correct": "e", + "Explanation": "\"explanation : age of the 15 th student = [ 15 * 15 - ( 14 * 7 + 16 * 7 ) ] = 15 years . answer : e\"" + }, + { + "Answer": 543.95, + "Options": "a ) a ) 125 , b ) b ) 175 , c ) c ) 225 , d ) d ) 375 , e ) e ) 544", + "Correct": "e", + "Explanation": "\"explanation : ? = ( 258 x 1265 / 100 ) \u00f7 6 = 326370 / 600 = 544 answer : option e\"" + }, + { + "Answer": 35, + "Options": "a ) 40 , b ) 45 , c ) 35 , d ) 30 , e ) 25", + "Correct": "c", + "Explanation": "( 1 / 5 ) ^ m ( 1 / 4 ) ^ 18 = 1 / { 2 ( 10 ) ^ 35 } 2 ( 10 ) ^ 35 / 4 ^ 18 = 5 ^ m [ 2 ( 2 ^ 35 ) ( 5 ^ 35 ) ] / [ 2 ^ 36 ] = 5 ^ m 5 ^ 35 = 5 ^ m n = 35 c" + }, + { + "Answer": 25, + "Options": "a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28", + "Correct": "b", + "Explanation": "10 ^ m = n * ( 2 ^ 2 ) ( 2 * 5 ) ^ m = n * ( 2 ^ 2 ) ( 2 ^ m ) * ( 5 ^ m ) = n * ( 2 ^ 2 ) now equate both side we get m = 2 and ( 5 ^ m ) = n ( 5 ^ 2 ) = n = > n = 25 answer : b" + }, + { + "Answer": 19, + "Options": "a ) 30 , b ) 19 , c ) 10 , d ) 9 , e ) 7", + "Correct": "b", + "Explanation": "\"( average production for n days ) * n = ( total production for n days ) - - > 50 n = ( total production for n days ) ; ( total production for n days ) + 90 = ( average production for n + 1 days ) * ( n + 1 ) - - > 50 n + 90 = 52 * ( n + 1 ) - - > n = 19 . or as 40 extra units increased the average for n + 1 days by 2 units per day then 40 / ( n + 1 ) = 2 - - > n = 19 . answer : b .\"" + }, + { + "Answer": 1, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "b", + "Explanation": "the equation that can be formed e is 13 x + 2 = 8 y + 5 . . 13 x - 3 = 8 y . . . as we can see x can take only odd values as the rhs will always be even . . also x can take values till 13 as 13 * 14 > 180 . . now we have to substitue x as 1 , 35 , 79 , 1113 . . . once we find 7 fitting in , any other value need not be checked as every 4 th value will give us answer so next value will be 15 . . ans 1 . . b" + }, + { + "Answer": 0.32, + "Options": "a ) $ 015 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.32 , e ) $ 0.45", + "Correct": "d", + "Explanation": "\"on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.48 = 3 * x - - > x = $ 0.32 . answer : d .\"" + }, + { + "Answer": 0.027777777777777773, + "Options": "a ) 1 / 36 , b ) 1 / 30 , c ) 5 / 36 , d ) 1 / 24 , e ) 1 / 28", + "Correct": "a", + "Explanation": "explanation : the probability that sumit actually sees a shark , given that he claimed to have seen one . = > p ( he actually sees the shark and reports truth ) / p ( he claims of seeing a shark ) . = > p ( sees the shark ) p ( reports truth ) / ( p ( he sees a shark ) p ( reports truth ) + p ( does n ' t see ) p ( reports false ) . = > ( 1 / 8 \u00d7 1 / 6 ) / ( 1 / 8 \u00d7 1.6 + 7 / 8 \u00d7 5 / 6 ) = > 1 / 36 . answer : a" + }, + { + "Answer": 113, + "Options": "a ) 115 kg . , b ) 118 kg . , c ) 113 kg . , d ) 110 kg . , e ) 112 kg .", + "Correct": "c", + "Explanation": "the new average will be = ( 121 * 7 + 110 + 60 ) / 9 = 113 kgs c is the answer" + }, + { + "Answer": 110, + "Options": "a ) 130 , b ) 120 , c ) 110 , d ) 180 , e ) 150", + "Correct": "c", + "Explanation": "\"given m + p + c = 70 * 3 = 210 - - - ( 1 ) m + p = 90 * 2 = 180 - - - ( 2 ) p + c = 70 * 2 = 140 - - - ( 3 ) where m , p and c are marks obtained by the student in mathematics , physics and chemistry . p = ( 2 ) + ( 3 ) - ( 1 ) = 180 + 140 - 210 = 110 answer : c\"" + }, + { + "Answer": 30.069930069930077, + "Options": "a ) 20 % , b ) 24 % , c ) 30 % , d ) 32 % , e ) 79 %", + "Correct": "c", + "Explanation": "take it as original output = 100 . to meet demand increase by 10 % , then output = 110 . to meet holiday demand , new output increase by 30 % then output equals 143 to restore new holidy demand output to original 100 . final - initial / final * 100 = 43 / 143 * 100 = 30 % approxiamately . option c is correct ." + }, + { + "Answer": 7, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8", + "Correct": "d", + "Explanation": "64 ^ k > 4 ^ 19 4 ^ ( 3 k ) > 4 ^ 19 3 k > 19 k = 7 the answer is d ." + }, + { + "Answer": 5, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "e", + "Explanation": "= 10 \u2217 9 \u2217 8 \u2217 7 \u2217 6 \u2217 5 ! \u2212 2 \u2217 5 ! \u2217 5 \u2217 4 \u2217 3 \u2217 2 \u2217 1 = 5 ! \u2217 10 \u2217 3 \u2217 8 ( 125 ) = 5 \u2217 ( 2 \u2217 2 ) \u2217 3 \u2217 2 \u2217 ( 5 \u2217 2 ) \u2217 24 \u2217 5 \u2217 5 \u2217 5 = 5 \u2217 2 \u2217 5 \u2217 2 \u2217 5 \u2217 2 \u2217 5 \u2217 2 \u2217 24 \u2217 5 \u2217 3 = 10 ^ 4 \u2217 2 ^ 4 \u2217 5 \u2217 3 = 10 ^ 4 \u2217 5 \u2217 2 \u2217 12 \u2217 3 = 10 ^ 5 \u2217 36 answer : e" + }, + { + "Answer": 1197, + "Options": "a ) 867 , b ) 1179 , c ) 1196 , d ) 1098 , e ) 1197", + "Correct": "e", + "Explanation": "e 1197 let the three digit numbers be 100 a + 10 b + c a = b + 2 c = b - 2 a + b + c = 3 b = 27 = > b = 9 so a = 11 and b = 7 hence the three digit number is : 1197" + }, + { + "Answer": 24, + "Options": "a ) $ 22 , b ) $ 24 , c ) $ 30 , d ) $ 36 , e ) $ 40", + "Correct": "b", + "Explanation": "\"b its is . let price = x ( x - 1 ) 8 = 6 x x = 4 hence total money = 6 * 4 = 24\"" + }, + { + "Answer": 53.99999999999999, + "Options": "a ) 54 , b ) 45 , c ) 25 , d ) 15 , e ) 55", + "Correct": "a", + "Explanation": "\"a : b : c = 10 \u00d7 7 : 12 \u00d7 5 : 15 \u00d7 3 = 2 \u00d7 7 : 12 \u00d7 1 : 3 \u00d7 3 = 14 : 12 : 9 amount that c should pay = 210 \u00d7 9 / 35 = 6 \u00d7 9 = 54 answer is a\"" + }, + { + "Answer": 0.14285714285714288, + "Options": "a ) 2 / 35 , b ) 2 / 3 , c ) 7 / 35 , d ) 1 / 7 , e ) 7 / 5", + "Correct": "d", + "Explanation": "\"let a be the event that ram is selected and b is the event that ravi is selected . p ( a ) = 5 / 7 p ( b ) = 1 / 5 let c be the event that both are selected . p ( c ) = p ( a ) x p ( b ) as a and b are independent events : = 5 / 7 x 1 / 5 = 1 / 7 answer : d\"" + }, + { + "Answer": 56.5, + "Options": "a ) a ) 59 , b ) b ) 61 , c ) c ) 56 , d ) d ) 65 , e ) e ) 67", + "Correct": "c", + "Explanation": "\"formula = \u221a a \u00d7 b a = 49 and b = 64 \u221a 49 \u00d7 64 = 7 \u00d7 8 = 56 c\"" + }, + { + "Answer": 100, + "Options": "a ) 100 , b ) 50 , c ) 150 , d ) 200 , e ) 75", + "Correct": "a", + "Explanation": "\"let the number be x then , 3 x / 5 - ( 50 % of x ) = 10 3 x / 5 - 50 x / 100 = 10 x = 100 answer is a\"" + }, + { + "Answer": 40, + "Options": "a ) 80 , b ) 40 , c ) 50 , d ) 60 , e ) 20", + "Correct": "b", + "Explanation": "since 2 + 3 = 5 & 7 + 8 = 15 any combination with these no be will give u desirable result . . . so total no in 100 will be 20 & that ' s why in 200 , it will be 40 answer : b" + }, + { + "Answer": 9, + "Options": "a ) 12 , b ) 15 , c ) 10 , d ) 18 , e ) 9", + "Correct": "e", + "Explanation": "\"2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 27 - 9 = 18 ab = 9 . answer is e .\"" + }, + { + "Answer": 86, + "Options": "a ) 75 , b ) 78 , c ) 80 , d ) 82 , e ) 86", + "Correct": "e", + "Explanation": "\"divisor = ( 6 * 3 ) + 2 = 20 5 * quotient = 20 quotient = 4 . dividend = ( divisor * quotient ) + remainder dividend = ( 20 * 4 ) + 6 = 86 e )\"" + }, + { + "Answer": 11, + "Options": "a ) 11 , b ) 5 , c ) 9 , d ) 8 , e ) 10", + "Correct": "a", + "Explanation": "50 employees . counting every different attendand to the courses we have : accounting : 22 finance : 14 marketing : 15 which would add up to 51 different attendands , which is not possible . now 10 have taken exactly 2 courses , which means that there are 10 less different attendands . say that 10 of the finance attentands also attended accounting . 51 - 10 = 41 1 person has taken all three courses . as above , we subtract him from the number of different attendands . since this time the person took all three courses , we have to substract him two times . 41 - 2 = 39 . answer : a" + }, + { + "Answer": 1554, + "Options": "a ) 1210 , b ) 1221 , c ) 1332 , d ) 1443 , e ) 1554", + "Correct": "e", + "Explanation": "there are 6 possible arrangements of the three numbers . then each number will be in the hundreds , tens , and ones place two times each . the sum is 2 ( 111 ) + 2 ( 222 ) + 2 ( 444 ) = 1554 the answer is e ." + }, + { + "Answer": 75, + "Options": "a ) 74 , b ) x = 75 , c ) x = 175 , d ) x = 680 , e ) 690", + "Correct": "b", + "Explanation": "\"i solved this question by plugging in numbers from the answer choices . a . ) 74 starting with answer choice a , i immediately eliminated it because 74 is not even divisible by 5 . b . ) 75 i divide 75 / 5 and get 15 as an answer . i divide 75 / 34 and get a remainder of 7 . 15 - 7 = 8 so i know the correct answer isb\"" + }, + { + "Answer": 10, + "Options": "a ) 1 , b ) 22 , c ) 23 , d ) 10 , e ) 25", + "Correct": "d", + "Explanation": "let 1 = x 2 = 2 x 3 = 4 x 4 = 8 x 5 = 16 x 6 = 32 x 7 = 64 x now given 2 x * 6 x + 5 x / 4 x - 56 x i can write it as = 2 x * ( 2 x + 4 x ) + ( x + 4 x ) / 4 x - ( 64 x - 8 x ) now by putting the values i get = 2 * ( 2 + 3 ) + ( 8 + 1 ) / 3 - ( 7 - 4 ) = 2 * 5 + 9 / 3 - 3 = 10 + 9 / 3 - 3 = 10 + 3 - 3 = 10 answer : d" + }, + { + "Answer": 9.237333333333334, + "Options": "a ) 0.092 , b ) 0.92 , c ) 9.2 , d ) 92 , e ) 920", + "Correct": "c", + "Explanation": "\"a ( 69.28 \u00d7 0.004 ) / 0.03 1 . 0.004 = 4 \u00d7 10 ^ ( - 3 ) 2 . 0.03 = 3 \u00d7 10 ^ ( - 2 ) 3 . ( a \u00d7 b ) / c = a \u00d7 ( b / c ) 4 . 0.004 / 0.03 = 4 \u00d7 10 ^ ( - 3 ) / ( 3 \u00d7 10 ^ ( - 2 ) ) = 4 \u00d7 10 ^ ( - 3 - ( - 2 ) ) / 3 = 4 \u00d7 10 ^ ( - 1 ) / 3 = ( 4 / 3 ) \u00d7 10 ^ ( - 1 ) = 1.333 \u00d7 10 ^ ( - 1 ) therefore , ( 69.28 \u00d7 0.004 ) / 0.03 = 69.28 \u00d7 ( 0.004 / 0.03 ) = 69.28 \u00d7 1.33 \u00d7 10 ^ ( - 1 ) = 69.28 \u00d7 1.33 / 10 = 6.928 * 1.33 now , 7 \u00d7 2 = 14 7 \u00d7 1 = 7 or better : 6.9 \u00d7 1 = 6.9 6.9 \u00d7 2 = 13.8 hence , 6.9 < 6.928 \u00d7 1.33 < 13.8 9.2 is the only answer that satisfies this condition . c\"" + }, + { + "Answer": 9, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9", + "Correct": "e", + "Explanation": "\"if n = 9 mark sold 1 box and ann sold 7 boxes total 8 < 9 answer : e\"" + }, + { + "Answer": 10, + "Options": "a ) 10 , b ) 910 , c ) 1001 , d ) 1911 , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : required number of students = h . c . f of 890 and 630 = 10 . answer : a\"" + }, + { + "Answer": 38.15, + "Options": "a ) $ 2.10 , b ) $ 37.10 , c ) $ 37.16 , d ) $ 38.10 , e ) $ 38.15", + "Correct": "e", + "Explanation": "principal that is amount taken by laura at year beginning = 35 $ rate of interest = 9 % interest = ( 9 / 100 ) * 35 = 3.15 $ total amount that laura owes a year later = 35 + 3.15 = 38.15 $ answer e" + }, + { + "Answer": 30, + "Options": "a ) 36 - 48 , b ) 50 - 34 , c ) 60 - 24 , d ) 30 - 42 , e ) 21 - 63", + "Correct": "d", + "Explanation": "\"in this problem , we are asked to find two numbers . therefore , we must let x be one of them . let x , then , be the first number . we are told that the other number is 12 more , x + 12 . the problem states that their sum is 72 : word problem = 72 the line over x + 12 is a grouping symbol called a vinculum . it saves us writing parentheses . we have : 2 x = 72 \u00e2 \u02c6 \u2019 12 = 60 . x = 60 / 2 = 30 . this is the first number . therefore the other number is x + 12 = 30 + 12 = 42 . the sum of 30 + 42 is 72 . d\"" + }, + { + "Answer": 4, + "Options": "a ) 8,5 , b ) 4,0 , c ) 1,4 , d ) 0,8 , e ) 8,0", + "Correct": "b", + "Explanation": "\"since the given number is divisible by 5 , so 0 or 5 must come in place of $ . but , a number ending with 5 is never divisible by 8 . so , 0 will replace $ . now , the number formed by the last three digits is 4 * 0 , which becomes divisible by 8 , if * is replaced by 4 . hence , digits in place of * and $ are 4 and 0 respectively . answer b 4,0\"" + }, + { + "Answer": 4000, + "Options": "a ) 2788 , b ) 4000 , c ) 7282 , d ) 2782 , e ) 2729", + "Correct": "b", + "Explanation": "\"4 - - - 3200 5 - - - ? = > 4000 answer : b\"" + }, + { + "Answer": 9, + "Options": "a ) 1 , b ) 9 , c ) - 1 , d ) 5 / 4 , e ) - 4 / 5", + "Correct": "b", + "Explanation": "\"we ' re given the equation 5 - 5 / x = 4 + 4 / x . we ' re asked for the value of x . the common - denominator of these 4 numbers is x , so we need to multiply both sides of the equation by x , giving us . . . 5 x - 5 x / x = 4 x + 4 x / x we can then eliminate that denominator , which gives us . . . . 5 x - 5 = 4 x + 4 9 = x b\"" + }, + { + "Answer": 28, + "Options": "a ) 21 , b ) 28 , c ) 34 , d ) 32 , e ) 76", + "Correct": "b", + "Explanation": "required number of trees = 24 / 36 * 42 = 28 . answer : b" + }, + { + "Answer": 0.47619047619047616, + "Options": "a ) 1 / 140 , b ) 10 / 21 , c ) 27 / 410 , d ) 11 / 21 , e ) 57 / 120", + "Correct": "b", + "Explanation": "\"required probability = p ( x ) + p ( y ) + p ( z ) ( all the events are mutually exclusive ) . = 1 / 4 + 1 / 12 + 1 / 7 = 10 / 21 answer : b\"" + }, + { + "Answer": 107, + "Options": "a ) 366 , b ) 107 , c ) 102 , d ) 192 , e ) 122", + "Correct": "b", + "Explanation": "\"cash realised = rs . ( 107.25 - 0.25 ) = rs . 107 . answer : b\"" + }, + { + "Answer": 2100, + "Options": "a ) 2100 , b ) 2550 , c ) 5050 , d ) 6275 , e ) 11325", + "Correct": "a", + "Explanation": "\"set a contains 10 , 12,14 , 16 . . . 50 set b contains 110 , 112 , 114 . . . 150 number of terms in each set = 21 difference between corresponding terms in set a and b = 100 difference between sum of set b and set a = 100 * 21 = 2100 answer a\"" + }, + { + "Answer": 11, + "Options": "a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 11", + "Correct": "e", + "Explanation": "5 < x < 21 , 7 < x < 18 , 2 < x < 13 9 < x < 12 x < 13 from above : 10 < x < 12 - - > x = 11 . answer : e ." + }, + { + "Answer": 24, + "Options": "a ) 9 , b ) 12 , c ) 15 , d ) 16 , e ) 24", + "Correct": "e", + "Explanation": "\"in 24 liters , red = 4 / 6 * 24 = 16 and blue = 8 so , 16 / ( 8 + x ) = 3 / 6 or , x = 24 ( answer e )\"" + }, + { + "Answer": 168, + "Options": "a ) 154 , b ) 248 , c ) 360 , d ) 424 , e ) 168", + "Correct": "e", + "Explanation": "136 = 2 ^ 3 * 17 ; 144 = 2 ^ 4 * 3 ^ 2 h . c . f = 2 ^ 3 = 8 since h . c . f is the product of lowest powers of common factors , so the third number must have ( 2 ^ 3 ) as its factor . since l . c . m is the product of highest powers of common prime factors , so the third number must have 3 and 7 as its factors . third number = 2 ^ 3 * 3 * 7 = 168 answer : e" + }, + { + "Answer": 2, + "Options": "a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8", + "Correct": "b", + "Explanation": "first of all , the units digit of ( 33 ) ^ 43 is the same as that of 3 ^ 43 and the units digit of ( 43 ) ^ 32 is the same as that of 3 ^ 32 . so , we need to find the units digit of 3 ^ 43 + 3 ^ 33 . next , the units digit of 3 in positive integer power repeats in blocks of four { 3 , 9 , 7 , 1 } : 3 ^ 1 = 3 ( the units digit is 3 ) 3 ^ 2 = 9 ( the units digit is 9 ) 3 ^ 3 = 27 ( the units digit is 7 ) 3 ^ 4 = 81 ( the units digit is 1 ) 3 ^ 5 = 243 ( the units digit is 3 again ! ) . . . thus : the units digit of 3 ^ 43 is the same as the units digit of 3 ^ 3 , so 7 ( 43 divided by the cyclicity of 4 gives the remainder of 3 ) . the units digit of 3 ^ 33 is the same as the units digit of 3 ^ 1 , so 3 ( 33 divided by the cyclicity of 4 gives the remainder of 1 ) . therefore the units digit of ( 33 ) ^ 43 + ( 43 ) ^ 32 is 7 + 5 = 2 . answer : b ." + }, + { + "Answer": 200, + "Options": "a ) 200 , b ) 220 , c ) 240 , d ) 322 , e ) 342", + "Correct": "a", + "Explanation": "\"required number = ( lcm of 15 , 30 , 45 and 60 ) + 20 = 180 + 20 = 200 option a\"" + }, + { + "Answer": 160, + "Options": "a ) $ 120 , b ) $ 130 , c ) $ 140 , d ) $ 150 , e ) $ 160", + "Correct": "e", + "Explanation": "joe had $ 100 in his left and $ 100 in his right pocket at the end . so , he had $ 120 in his left pocket ( and $ 80 in his right pocket ) before moving $ 20 from his left to his right pocket . thus , he had $ 160 in his left pocket originally ( solve x \u2212 x / 4 = 120 ) . correct answer e" + }, + { + "Answer": 70, + "Options": "a ) 45 % , b ) 70 % , c ) 35 % , d ) 32.5 % , e ) 30 %", + "Correct": "b", + "Explanation": "\"price = p initially price reduced by 25 % which means new price is 3 / 4 p now on this new price further 60 percent is reduced which means the new price is merely 40 percent of 3 / 4 p = = > ( 3 / 4 ) x ( 2 / 5 ) p = 6 / 20 p is the new price after both deduction which is 30 percent of the original value p . this implies this entire series of deduction is worth having discounted 70 % of p . so answer is b = 70 %\"" + }, + { + "Answer": 1767, + "Options": "a ) 1767 , b ) 1800 , c ) 1812 , d ) 1890 , e ) none", + "Correct": "a", + "Explanation": "solving for 1225 = 52 \u00d7 72 sum of divisors = ( ap + 1 \u2013 1 ) / ( a \u2013 1 ) \u00d7 ( bq + 1 \u2013 1 ) / ( b \u2013 1 ) here a = 5 , b = 7 prime factors p = 2 and q = 2 sum of divisors = ( 53 \u2013 1 ) / ( 5 \u2013 1 ) \u00d7 ( 73 \u2013 1 ) / ( 7 \u2013 1 ) = ( 124 / 4 ) \u00d7 ( 342 / 6 ) = ( 31 \u00d7 57 ) = 1767 option a" + }, + { + "Answer": 50, + "Options": "a ) 30 , b ) 35 , c ) 40 , d ) 50 , e ) 60", + "Correct": "d", + "Explanation": "\"when a number n = a ^ x * b ^ y , where a and b are prime numbers , and x , y are positive integers , the number of divisors of n = ( x + 1 ) ( y + 1 ) therefore , the answer is d . 5 * 10 = 50\"" + }, + { + "Answer": 10, + "Options": "a ) 10 , b ) 12 , c ) 14 , d ) 17 , e ) 18", + "Correct": "a", + "Explanation": "\"2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 29 - 9 = 20 ab = 10 a )\"" + }, + { + "Answer": 1122, + "Options": "a ) 1012 , b ) 1011 , c ) 1212 , d ) 1122 , e ) 1021", + "Correct": "d", + "Explanation": "v 50 w 196 x y 269 z 123 in 1 st row and 1 st column v + 196 + 269 = v + 50 + w w = 415 again , in 2 nd column and 3 rd row 50 + x + z = 269 + z + 123 x = 342 as sum of each row column and diagonal are same . so , 269 + 342 + 415 = 1026 415 + y + 123 = 1026 y = 488 269 + z + 123 = 1026 z = 634 y + z = 488 + 634 = 1122 answer : d" + }, + { + "Answer": 80, + "Options": "a ) 20 coins , b ) 30 coins , c ) 40 coins , d ) 80 coins , e ) none of these", + "Correct": "d", + "Explanation": "let number of each type of coin = x . then , 1 \u00d7 x + . 50 \u00d7 x + . 25 x = 140 \u21d2 1.75 x = 140 \u21d2 x = 80 coins answer d" + }, + { + "Answer": 20, + "Options": "a ) 20 , b ) 12 , c ) 13 , d ) 14 , e ) 16", + "Correct": "a", + "Explanation": "\"amount of salt = 8.0 assume x gallons of water are added . 8.0 / 80 + x = 8 / 100 800 = 8 x + 640 8 x = 160 x = 20 correct option : a\"" + }, + { + "Answer": 182, + "Options": "a ) 187.89 cm , b ) 182.29 cm , c ) 123.98 cm , d ) 149.98 cm , e ) 146.89 cm", + "Correct": "b", + "Explanation": "\"calculated average height of 35 boys = 184 cm . wrong total height of 35 boys = 184 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 183 cm - ( 166 cm + 106 cm ) / 35 = 184 cm - 60 / 35 cm = 184 cm - 1.71 cm = 182.29 cm . answer : b\"" + }, + { + "Answer": 12, + "Options": "a ) $ 12 , b ) $ 14 , c ) $ 5 , d ) $ 15 , e ) $ 0", + "Correct": "a", + "Explanation": "\"1 / 5 x $ 90 = $ 15 for sandwich 1 / 6 x $ 90 = $ 45 for museum 1 / 2 x $ 90 = $ 78 for book $ 15 + $ 45 + $ 18 = $ 78 spent $ 90 - $ 78 = $ 12 left over correct answer a\"" + }, + { + "Answer": 18, + "Options": "a ) 10 , b ) 12 , c ) 13 , d ) 15 , e ) 18", + "Correct": "e", + "Explanation": "\"let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 36 = > 2 x = 36 = > x = 18 e\"" + }, + { + "Answer": 1584, + "Options": "a ) 1254 , b ) 1376 , c ) 1456 , d ) 1599 , e ) 1635", + "Correct": "d", + "Explanation": "\"let the smaller number be x . then larger number = ( x + 1335 ) . x + 1335 = 6 x + 15 5 x = 1320 x = 264 large number = 264 + 1335 = 1599 d\"" + }, + { + "Answer": 20, + "Options": "a ) \u2013 29 , b ) \u2013 12 , c ) 12 , d ) 20 , e ) 168", + "Correct": "d", + "Explanation": "\"explanation : = > y = x ^ 2 - 9 x + 20 = > y = ( x - 4 ) ( x - 5 ) = > x = 4 , y = 5 product y = ( 4 ) ( 5 ) = 20 answer option 20 answer : d\"" + }, + { + "Answer": 14, + "Options": "a ) 14 , b ) 12 , c ) 16 , d ) 8 , e ) 6", + "Correct": "a", + "Explanation": "\"explanation : let the number of ducks be d and number of cows be c then , total number of legs = 2 d + 4 c = 2 ( d + 2 c ) total number of heads = c + d given that total number of legs are 28 more than twice the number of heads = > 2 ( d + 2 c ) = 28 + 2 ( c + d ) = > d + 2 c = 14 + c + d = > 2 c = 14 + c = > c = 14 i . e . , total number of cows = 14 answer : a\"" + }, + { + "Answer": 4, + "Options": "a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10", + "Correct": "b", + "Explanation": "let x be the wholesale price . then 1.9 x = 76 and x = 76 / 1.9 = 40 . to achieve a 100 % markup , the price needs to be $ 80 . the retailer needs to increase the price by $ 4 more . the answer is b ." + }, + { + "Answer": 42, + "Options": "a ) 42 , b ) 45 , c ) 34 , d ) 76 , e ) 25", + "Correct": "a", + "Explanation": "a 42" + }, + { + "Answer": 40, + "Options": "a ) 10 , b ) 20 , c ) 40 , d ) 60 , e ) 120", + "Correct": "c", + "Explanation": "\"each person is one participant of 4 games . so there are in all 16 * 5 = 80 instances of one participant games . but each game has 2 participants so total number of games = 80 / 2 = 40 c\"" + }, + { + "Answer": 37, + "Options": "a ) 22 , b ) 37 , c ) 99 , d ) 38 , e ) 27", + "Correct": "b", + "Explanation": "\"total age increased = ( 15 * 2 ) years = 30 years . sum of ages of two new men = ( 21 + 23 + 30 ) years = 74 years average age of two new men = ( 74 / 2 ) years = 37 years . answer : b\"" + }, + { + "Answer": 432, + "Options": "a ) 400 , b ) 430 , c ) 435 , d ) 405 , e ) none of these", + "Correct": "c", + "Explanation": "explanation : sum of first n natural numbers = 1 + 2 + 3 + . . . . . n = n ( n + 1 ) / 2 substitute n = 29 . so s 20 = 29 \u00e3 \u2014 30 / 2 = 435 correct option : c" + }, + { + "Answer": 60, + "Options": "a ) 15 % , b ) 20 % , c ) 25 % , d ) 60 % , e ) 75 %", + "Correct": "d", + "Explanation": "initially 80 % and 20 % split 80 % is further divided as 25 % and 75 % q is asking about that 75 % let total be ' 100 ' then that 75 % is ( 3 / 4 ) \u2217 80 so , the required % is [ ( 3 / 4 ) \u2217 80 / 100 ] \u2217 100 = 60 % answer : d" + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14", + "Correct": "a", + "Explanation": "\"explanation : l = r l = 3 c r = c + 12 we can substitute r for l in the second equation : r = 3 c . if r is equal to both 3 c and c + 12 , we can say 3 c = c + 12 , and solve for c . 3 c = c + 12 2 c = 12 c = 6 answer : ( a )\"" + }, + { + "Answer": 57, + "Options": "a ) 15 , b ) 21 , c ) 17 , d ) 37 , e ) 57", + "Correct": "e", + "Explanation": "\"total money = rs . 10350 . let 50 rupees note was x . then 500 rupees note = 72 - x now , 50 * x + 500 * ( 72 - x ) = 10350 50 x + 36000 - 500 x = 10350 - 450 x = - 25650 x = 57 . no . of 50 rupees note = 57 . answer : option e\"" + }, + { + "Answer": 625, + "Options": "a ) 24 , b ) 120 , c ) 625 , d ) 720 , e ) 1024", + "Correct": "c", + "Explanation": "\"5 choices for each of the 4 questions , thus total w of 5 * 5 * 5 * 5 = 5 ^ 4 = 625 ways to answer all of them . answer : c .\"" + }, + { + "Answer": 14, + "Options": "a ) s . 14 , b ) s . 18 , c ) s . 12 , d ) s . 11 , e ) s . 10", + "Correct": "a", + "Explanation": "\"average price per book = ( 600 + 240 ) / ( 40 + 20 ) = 840 / 60 = rs . 14 answer : a\"" + }, + { + "Answer": 8200, + "Options": "a ) rs . 7000 , b ) rs . 8200 , c ) rs . 8500 , d ) rs . 9000 , e ) none", + "Correct": "b", + "Explanation": "\"answer average salary = 9000 + 5000 + 11000 + 7000 + 9000 / 5 = rs . 8200 correct option : b\"" + }, + { + "Answer": 6000, + "Options": "a ) 500 , b ) 2000 , c ) 5000 , d ) 6000 , e ) 7000", + "Correct": "d", + "Explanation": "\"total sale for 5 months = rs . ( 7435 + 7920 + 7855 + 8230 + 7560 ) = rs . 39000 . required sale = rs . [ ( 7500 x 6 ) - 39000 ] = rs . ( 45000 - 39000 ) = rs . 6000 answer : option d\"" + }, + { + "Answer": 93, + "Options": "a ) 75 , b ) 95 , c ) 93 , d ) 165 , e ) 11", + "Correct": "c", + "Explanation": "\"explanation : average = ( 96 + 95 + 82 + 97 + 95 ) / 5 = 465 / 5 = 93 . answer : c\"" + }, + { + "Answer": 6100, + "Options": "a ) 2177 , b ) 2876 , c ) 4500 , d ) 2981 , e ) 6100", + "Correct": "e", + "Explanation": "\"sum of the salaries of the person for the months of january , february , march and april = 4 * 8000 = 32000 - - - - ( 1 ) sum of the salaries of the person for the months of february , march , april and may = 4 * 8100 = 32400 - - - - ( 2 ) ( 2 ) - ( 1 ) i . e . may - jan = 400 salary of may is rs . 6500 salary of january = rs . 6100 . answer : e\"" + }, + { + "Answer": 0.5555555555555556, + "Options": "a ) 2 / 3 , b ) 3 / 5 , c ) 4 / 7 , d ) 5 / 9 , e ) none of these", + "Correct": "d", + "Explanation": "let the numerator and denominator of the fraction be ' n ' and ' d ' respectively . d = 2 n - 1 ( n + 1 ) / ( d + 1 ) = 3 / 5 5 n + 5 = 3 d + 3 5 n + 5 = 3 ( 2 n - 1 ) + 3 = > n = 5 d = 2 n - 1 = > d = 9 hence the fraction is : 5 / 9 answer : d" + }, + { + "Answer": 0.3333333333333333, + "Options": "a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 5 , d ) 1 / 6 , e ) 2 / 3", + "Correct": "b", + "Explanation": "number of ways you can choose 2 from 4 = 4 c 2 = 6 e = event of getting the 2 numbers product is more than 15 = ( 3,7 ) , ( 5,7 ) = 2 probability = 2 / 6 = 1 / 3 answer is b" + }, + { + "Answer": 48, + "Options": "a ) 8 , b ) 64 , c ) 48 , d ) 102 , e ) 144", + "Correct": "c", + "Explanation": "\"if 80 % of the packages weigh at least 25 pounds this means that 20 % of the packages weigh less than 25 pounds let t = total number of packages so , 20 % of t = # of packages that weigh less than 25 pounds 48 packages weigh less than 25 pounds great . so , 20 % of t = 48 rewrite to get : 0.2 t = 48 solve : t = 240 40 % of the packages weigh less than 75 pounds so , 40 % oft = number of packages that weigh less than 75 pounds 40 % of 240 = 96 , so 96 packages weigh less than 75 pounds of those 96 packages that weigh less than 75 pounds , 48 packages weigh less than 25 pounds . so , the number of packages that weight between 25 and 75 pounds = 96 - 48 = 48 = c\"" + }, + { + "Answer": 1600, + "Options": "a ) e = 200 , b ) e = 600 , c ) e = 800 , d ) e = 1600 , e ) 50", + "Correct": "d", + "Explanation": "\"original cost e , c 1 = t 1 * b 1 ^ 4 new cost c 2 = t 2 * b 2 ^ 4 . . . . only b is doubled so t 2 = t 1 and b 2 = 2 b 1 c 2 = t 2 * ( 2 b 1 ) ^ 4 = 16 ( t 1 * b 1 ^ 4 ) = 16 c 1 16 times c 1 = > 1600 % of c 1 ans d = 1600\"" + }, + { + "Answer": 107.99999999999999, + "Options": "a ) 96 , b ) 100 , c ) 104 , d ) 108 , e ) 112", + "Correct": "d", + "Explanation": "\"1 / 12 + 1 / 4 + 1 / 9 + 1 / 6 = ( 3 + 9 + 4 + 6 ) / 36 = 11 / 18 let x be the number of passengers on the ship . 42 = ( 7 / 18 ) x x = 108 the answer is d .\"" + }, + { + "Answer": 120, + "Options": "a ) $ 60 , b ) $ 80 , c ) $ 100 , d ) $ 120 , e ) $ 140", + "Correct": "d", + "Explanation": "\"5 : 4 = 15 : 12 and 3 : 2 = 18 : 12 . an increase in $ 30 increases the ratio by 3 : 12 . therefore an increase in $ 10 increases the ratio by 1 : 12 . therefore , january ' s bill was 12 ( $ 10 ) = $ 120 . the answer is d .\"" + }, + { + "Answer": 312, + "Options": "a ) $ 92 , b ) $ 312 , c ) $ 104 , d ) $ 120 , e ) $ 240", + "Correct": "b", + "Explanation": "eps actual > eps expected . each gets and additional . 12 per share . thus . 52 * 600 - - > $ 312 answer is b" + }, + { + "Answer": 9, + "Options": "a ) a ) 4 , b ) b ) 7 , c ) c ) 9 , d ) d ) 5 , e ) e ) 2", + "Correct": "c", + "Explanation": "13 - 4 = 9 . answer is c" + }, + { + "Answer": 45, + "Options": "a ) 18 , b ) 28 , c ) 45 , d ) 38 , e ) 59", + "Correct": "c", + "Explanation": "\"let x = the number sought . then x / 3 + x + 3 = 63 . and x = 45 . c\"" + }, + { + "Answer": 42, + "Options": "a ) 40 , b ) 42 , c ) 44 , d ) 46 , e ) 48", + "Correct": "b", + "Explanation": "let x be the original number of apples . on day one , the vendor throws away ( 0.2 ) ( 0.7 ) x = 0.14 x . the remaining apples are ( 0.8 ) ( 0.7 ) x = 0.56 x . on day two , the vendor throws away ( 0.5 ) ( 0.56 ) x = 0.28 x . the vendor throws away a total of 0.14 x + 0.28 x = 0.42 x . the vendor throws away 42 percent of the apples . the answer is b ." + }, + { + "Answer": 53, + "Options": "a ) 53 , b ) 55 , c ) 59 , d ) 71 , e ) 92", + "Correct": "a", + "Explanation": "\"total = 61 thrower = 37 rest = 61 - 37 = 24 left handed = 24 / 3 = 8 right handed = 16 if all thrower are right handed then total right handed is 37 + 16 = 53 so a . 53 is the right answer\"" + }, + { + "Answer": 43, + "Options": "a ) 47 , b ) 37 , c ) 39 , d ) 43 , e ) 42", + "Correct": "d", + "Explanation": "\"average score before 15 th innings = 85 - 3 \u00d7 15 = 40 average score after 15 th innings = > 40 + 3 = 43 answer : d\"" + }, + { + "Answer": 0.5833333333333334, + "Options": "a ) 5 / 12 , b ) 7 / 12 , c ) 25 / 144 , d ) 144 / 25 , e ) 146 / 25", + "Correct": "b", + "Explanation": "\"let the number be x . then , 2 / 3 x = 49 / 216 * 1 / x x 2 = 49 / 216 * 3 / 2 = 49 / 144 x = 7 / 12 answer : b\"" + }, + { + "Answer": 1178, + "Options": "a ) rs . 1178 , b ) rs . 820 , c ) rs . 990 , d ) rs . 1385 , e ) none", + "Correct": "a", + "Explanation": "\"answer income of the deceased = total income of 4 members - total income of remaining 3 members . = 782 x 4 - 650 x 3 rs . = 1178 rs . correct option : a\"" + }, + { + "Answer": 3, + "Options": "a ) 0 , b ) 3 , c ) 1 , d ) 2 , e ) 4", + "Correct": "b", + "Explanation": "\"remainder will be number / 100 here as the divisor is two digit number = 12 . hence checking for the last two digits = 5 * 7 * 9 = 15 thus remainder = 3 . answer : b\"" + }, + { + "Answer": 7, + "Options": "a ) 20 , b ) 21 , c ) 22 , d ) 7 , e ) 24", + "Correct": "d", + "Explanation": "\"solution let the toatl number of workers be x . then 8000 x = ( 8000 x 7 ) + 6000 ( x - 7 ) x = 7 . answer d\"" + }, + { + "Answer": 90, + "Options": "a ) 90 , b ) 100 , c ) 105 , d ) 110 , e ) 125", + "Correct": "a", + "Explanation": "\"explanation : since the month begins with a sunday , so there will be five sundays in the month , required average = ( 140 * 5 + 80 * 25 ) / 30 = 2700 / 30 = 90 answer : a ) 90\"" + }, + { + "Answer": 40, + "Options": "a ) 20 , b ) 25 , c ) 30 , d ) 40 , e ) 50", + "Correct": "d", + "Explanation": "\"let the list price be 2 x for min sale price , the first discount given should be 50 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 40 and 0.8 x = 32 so lowest sale price is 32 , which is 40 % of 80 hence , d is the answer\"" + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 3 , c ) 1 , d ) 6 , e ) 2", + "Correct": "a", + "Explanation": "on dividing 228712 by 9 we get the remainder 4 , so 5 should be subtracted a" + }, + { + "Answer": 24, + "Options": "a ) 20 , b ) 24 , c ) 36 , d ) 40 , e ) 60", + "Correct": "b", + "Explanation": "\"let the capacity of the tank = c ( 3 / 4 ) c + 4 = ( 9 / 10 ) c = > ( 9 / 10 ) c - ( 3 / 4 ) c = 4 = > ( 3 / 20 ) c = 4 = > c = ( 4 * 20 ) / 3 = 26.66 number of gallons of gasoline that the tank currently holds = 3 / 4 * c + 4 = 19.99 + 4 = 23.99 = 24 answer b\"" + }, + { + "Answer": 281, + "Options": "a ) 135 , b ) 237 , c ) 281 , d ) 300 , e ) 380", + "Correct": "c", + "Explanation": "\"the number of liters in each can = hcf of 50 , 144 and 368 = 2 liters . number of cans of maaza = 50 / 2 = 25 number of cans of pepsi = 144 / 2 = 72 number of cans of sprite = 368 / 2 = 184 the total number of cans required = 25 + 72 + 184 = 281 cans . answer : c\"" + }, + { + "Answer": 24, + "Options": "a ) 24 , b ) 66 , c ) 9 , d ) 7 , e ) 01", + "Correct": "a", + "Explanation": "answer : 24 explanation : let the smallest of these number be x . the other two numbers are ( x + 2 ) and ( x + 4 ) . x + ( x + 2 ) + ( x + 4 ) = ( x + ( x + 2 ) + ( x + 4 ) ) / 3 + 44 3 x + 3 * ( x + 2 ) + 3 * ( x + 4 ) = x + ( x + 2 ) + ( x + 4 ) + 132 9 x + 18 = 3 x + 138 6 x = 120 x = 20 therefore , the largest number is 24 . answer : a" + }, + { + "Answer": 5591, + "Options": "a ) s . 4991 , b ) s . 5591 , c ) s . 6001 , d ) s . 6991 , e ) s . 7991", + "Correct": "b", + "Explanation": "\"total fr 5 mnths = ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs 34009 . reqd . sale = rs . [ ( 6600 * 6 ) - 34009 ] = rs . ( 39600 - 34009 ) = rs . 5591 . answer : b\"" + }, + { + "Answer": 91, + "Options": "a ) 91 , b ) 910 , c ) 1001 , d ) 1911 , e ) none", + "Correct": "a", + "Explanation": "\"olution required number of students . = h . c . f of 1001 and 910 . \u2039 = \u203a 91 . answer a\"" + }, + { + "Answer": 10, + "Options": "a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 10", + "Correct": "e", + "Explanation": "\"explanation : on dividing 427398 by 13 we get the remainder 10 , so 10 should be subtracted answer : option e\"" + }, + { + "Answer": 81, + "Options": "a ) 24 , b ) 26 , c ) 30 , d ) 81 , e ) 40", + "Correct": "d", + "Explanation": "let the number of coins one son got be x and the number of coins another got be y . total = x + y . x ^ 2 - y ^ 2 = 81 ( x - y ) - - > x + y = 81 . answer : d ." + }, + { + "Answer": 4, + "Options": "a ) $ 3.00 , b ) $ 9.00 , c ) $ 2.00 , d ) $ 4.00 , e ) $ 7.00", + "Correct": "d", + "Explanation": "d . $ 4.00" + }, + { + "Answer": 53.846153846153854, + "Options": "a ) 33.33 % , b ) 25 % , c ) 75 % , d ) 53.85 % , e ) none of these", + "Correct": "d", + "Explanation": "\"using formula ( x / ( 100 - x ) * 100 ) where x is percentage decrease ( here it is 35 % ) = > 35 / ( 100 - 35 ) * 100 = 53.85 % answer : d\"" + }, + { + "Answer": 7, + "Options": "a ) 22 kg , b ) 21.6 kg , c ) 22.4 kg , d ) 21 kg , e ) 7 kg", + "Correct": "e", + "Explanation": "\"exp . the total weight of 29 students = 29 * 28 the total weight of 30 students = 30 * 27.3 weight of the new student = ( 30 * 27.3 \u2013 29 * 28 ) = 819 - 812 = 7 answer : e\"" + }, + { + "Answer": 3, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 9", + "Correct": "a", + "Explanation": "\"sol . lie purchases 6 a bananas mere for 4096 of rs 40 or , rs 16 . reduced price per do 3 a\"" + }, + { + "Answer": 240, + "Options": "a ) a . 150 , b ) b . 300 , c ) c . 600 , d ) d . 240 , e ) e . 200", + "Correct": "d", + "Explanation": "\"volume per box : 15 x 12 x 10 = 1,800 total volume : 1 , 080,000 number of boxes : total volume / volume per box = 1 , 080,000 / 1,800 = 600 price per month : number of boxes * price per box = 600 * 0.4 = 240 answer : d\"" + }, + { + "Answer": 4, + "Options": "a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10", + "Correct": "b", + "Explanation": "let x be the wholesale price . then 1.8 x = 36 and x = 36 / 1.8 = 20 . to achieve a 100 % markup , the price needs to be $ 40 . the retailer needs to increase the price by $ 4 more . the answer is b ." + }, + { + "Answer": 7, + "Options": "a ) 2 , b ) 4 , c ) 8 , d ) 7 , e ) 32", + "Correct": "d", + "Explanation": "you are considering a case when cat dogs and rabbit are not exactly equal to 12 . the solution shall be 60 = 30 + 40 + 16 - 12 - 2 x and hence x shall be 7 . answer d" + }, + { + "Answer": 57000, + "Options": "a ) rs . 50000 , b ) rs . 52000 , c ) rs . 57000 , d ) rs . 60000 , e ) rs . 67000", + "Correct": "c", + "Explanation": "\"length ( l ) = 20 m , breadth ( b ) = 15 m and height ( h ) = 5 m total area of the hall to be covered with mat = 2 ( lb + bh + hl ) = 2 ( 20 * 15 + 15 * 5 + 5 * 20 ) = 2 ( 300 + 75 + 100 ) = 2 * 475 = 950 sq . m total expenditure = 60 * 950 = rs . 57000 c\"" + }, + { + "Answer": 58.9, + "Options": "a ) 58 kgs , b ) 58.85 kgs , c ) 58.9 kgs , d ) 59 kgs , e ) 59.85 kgs", + "Correct": "c", + "Explanation": "\"actual total weight is ( 20 x 58.4 - 56 + 66 ) = 1178 kgs actual average weight is 1178 / 20 = 58.9 kgs c\"" + }, + { + "Answer": 504, + "Options": "a ) 512 , b ) 508 , c ) 451 , d ) 516 , e ) 451", + "Correct": "b", + "Explanation": "\"prime factorization of 36 = 2 x 2 x 3 x 3 prime factorization of 56 = 2 x 2 x 2 x 7 gcf = 4 lcm = 504 sum = 508 ans : b\"" + }, + { + "Answer": 2500, + "Options": "a ) 1287 , b ) 2887 , c ) 2500 , d ) 1129 , e ) 1192", + "Correct": "c", + "Explanation": "\"let money invested by raghu = rs . x money invested by trishul = 9 / 10 x = 0.9 x money invested by vishal = 9 / 10 x * 110 / 100 = 0.99 x also , x + 0.9 x + 0.99 x = 7225 = x = 7225 / 2.89 = 2500 therefore , amount invested by raghu is rs . 2500 . answer : c\"" + }, + { + "Answer": 0.35714285714285715, + "Options": "a ) 1 / 12 , b ) 5 / 14 , c ) 2 / 13 , d ) 2 / 15 , e ) 1 / 17", + "Correct": "b", + "Explanation": "\"first , there are 6 c 3 ways you can select 3 good pencils from 4 good ones . second , there are 8 c 3 ways you select 3 pencils from 6 ones in the box . then , the probability that neither pen will be defective is : 6 c 3 / 8 c 3 = 20 / 56 = 5 / 14 answer is b\"" + }, + { + "Answer": 20.48, + "Options": "a ) 22.48 % , b ) 20.48 % , c ) 24.48 % , d ) 25.48 % , e ) 26.48 %", + "Correct": "b", + "Explanation": "let the total money = 300 a ' s part = 100 b ' s part = 200 after 2 years a ' s part = 73.46 ( as it depreciates by 14.29 % per annum ) after 2 years b ' s part = 288 ( using the compound interest formula , a = p ( 1 + r / n ) ^ nt ) , where p = 200 , r = 0.2 , n = 1 , t = 2 ) so , after 2 years total amount = 361.46 therefore % increase in money = ( 361.46 - 300 ) * 100 / 300 = 20.48 % answer : b" + }, + { + "Answer": 26, + "Options": "a ) 22 , b ) 23 , c ) 26 , d ) 29 , e ) 31", + "Correct": "c", + "Explanation": "\"total age of 15 persons = 15 * 10 = 150 years average age of 16 persons = 11 years total age of 16 persons = 16 * 11 = 176 years age of the teacher = 176 - 150 = 26 years answer is c\"" + }, + { + "Answer": 60, + "Options": "a ) 60 , b ) 27 , c ) 28 , d ) 26 , e ) 91", + "Correct": "a", + "Explanation": "sol : if x birds were there in total , then x \u00d7 ( 1 \u2013 1 / 3 ) \u00d7 ( 1 \u2013 2 / 5 ) \u00d7 ( 1 \u2013 2 / 3 ) = 8 x \u00d7 2 / 3 \u00d7 3 / 5 \u00d7 1 / 3 = 8 x = 60 answer : a" + }, + { + "Answer": 18, + "Options": "a ) a ) 12 , b ) b ) 14 , c ) c ) 16 , d ) d ) 18 , e ) e ) 22", + "Correct": "d", + "Explanation": "\"d = ( d - r ) / q = ( 199 - 1 ) / 11 = 198 / 11 = 18 d )\"" + }, + { + "Answer": 2319, + "Options": "a ) 2289 , b ) 2310 , c ) 2333 , d ) 2456 , e ) 2309", + "Correct": "b", + "Explanation": "remainder when 2304 is divided by 21 = 15 so , no . should added to make 15 to 21 = 6 no . = 2304 + 6 = 2310 answer b" + }, + { + "Answer": 4, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8", + "Correct": "c", + "Explanation": "24 x + 20 y = 4 ( 6 x + 5 y ) which will be a minimum positive number when 6 x + 5 y = 1 . 6 ( 1 ) + 5 ( - 1 ) = 1 then 4 ( 6 x + 5 y ) can have a minimum positive value of 4 . the answer is c ." + }, + { + "Answer": 125, + "Options": "a ) 125 , b ) 126 , c ) 130 , d ) 148 , e ) 151", + "Correct": "a", + "Explanation": "\"we have : 3 * 11 = 33 3 * 12 = 36 3 * 15 = 45 all of this is : ( 33 + 36 + 45 ) + 11 = 114 + 11 = 125 correct answer a\"" + }, + { + "Answer": 27, + "Options": "a ) 15 , b ) 23 , c ) 27 , d ) 46 , e ) 32", + "Correct": "c", + "Explanation": "daughter ' s age = 10 x + y so mother ' s age = 10 y + x . . after 13 years , 10 x + y + 13 = 2 * ( 10 y + x + 13 ) . . . . so 13 + 19 y = 8 x . . . check for odd values of y , y = 1 satisfies the eqn with x = 4 . . . so ages are 41 and 14 and ans as found correctly by u is c . . 27" + }, + { + "Answer": 97, + "Options": "a ) 76 kg , b ) 80 kg , c ) 85 kg , d ) 97 kg , e ) none", + "Correct": "d", + "Explanation": "\"solution total weight increased = ( 10 x 3.2 ) kg = 32 kg . weight of new person = ( 65 + 32 ) kg = 97 kg . answer d\"" + }, + { + "Answer": 81, + "Options": "a ) 76 , b ) 81 , c ) 85 , d ) 87 , e ) 89", + "Correct": "b", + "Explanation": "\"explanation : average = total runs / no . of innings = 37 so , total = average x no . of innings = 37 x 10 = 370 . now increase in avg = 4 runs . so , new avg = 37 + 4 = 41 runs total runs = new avg x new no . of innings = 41 x 11 = 451 runs made in the 11 th inning = 451 - 370 = 81 answer : b\"" + }, + { + "Answer": 1.3333333333333333, + "Options": "a ) 1.33 , b ) 2.33 , c ) 3.33 , d ) 4.33 , e ) 1.45", + "Correct": "a", + "Explanation": "\"for the total revenue to remain the same when the price is 3 / 4 , the number of products sold must 3 / 4 times . therefore increase in the number of products sold is 100 % = > the required ratio = 100 % / 75 % = 1.33 answer : a\"" + }, + { + "Answer": 35, + "Options": "a ) 35 % , b ) 48 % , c ) 52 % , d ) 42 % , e ) 46 %", + "Correct": "a", + "Explanation": "first calculate the distance , b has covered with his speed in the time , in which a reached 80 % of the race . then add the remaining distance as head start for b to win the race . its best to apply ratios concept here . since a ' s speed is 15 / 13 of b , therefore , b ' s speed is 13 / 15 of a distance covered by b = speed x time = ( 13 / 15 ) x ( 0.75 ) = 0.65 % ( which means b would have covered 0.65 of the race length during the time in which a has covered 0.75 of the race length . therefore to win , b needs a headstart of ( 1 - 0.65 = ) 0.35 of the race length . so the answer is a" + }, + { + "Answer": 11000, + "Options": "a ) 12000 , b ) 11000 , c ) 10000 , d ) 13000 , e ) 15000", + "Correct": "b", + "Explanation": "the average price of 20 products is $ 1,200 means that the total price of 20 products is 20 * 1,200 = $ 24,000 . next , since exactly 10 of the products sell for less than $ 1,000 , then let ' s make these 10 items to be at $ 400 each ( min possible ) . now , the remaining 9 items can not be priced less than $ 1,000 , thus the minimum possible price of each of these 9 items is $ 1,000 . thus the minimum possible value of 19 products is 10 * 400 + 9 * 1,000 = $ 13,000 . therefore , the greatest possible selling price of the most expensive product is $ 24,000 - $ 13,000 = $ 11,000 . answer : b ." + }, + { + "Answer": 0.2, + "Options": "a ) 1 / 2 , b ) 1 / 5 , c ) 2 / 3 , d ) 2 / 5 , e ) 1 / 7", + "Correct": "b", + "Explanation": "\"first , there are 4 c 3 ways you can select 3 good pencils from 4 good ones . second , there are 6 c 3 ways you select 3 pencils from 6 ones in the box . then , the probability that neither pen will be defective is : 4 c 3 / 6 c 3 = 4 / 20 = 1 / 5 answer is b\"" + }, + { + "Answer": 75, + "Options": "a ) 50 , b ) 40 , c ) 60 , d ) 100 , e ) 75", + "Correct": "e", + "Explanation": "\"we have x + x % of 300 = 300 x + x / 100 * 300 = 300 4 * x = 300 x = 75 answer is e\"" + }, + { + "Answer": 0.5466666666666666, + "Options": "a ) $ 015 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.55", + "Correct": "e", + "Explanation": "\"on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.82 = 3 * x - - > x = $ 0.55 . answer : e .\"" + }, + { + "Answer": 4050, + "Options": "a ) 8100 , b ) 3388 , c ) 7767 , d ) 4050 , e ) 2288", + "Correct": "d", + "Explanation": "\"3200 * 9 / 8 * 9 / 8 = 4050 answer : d\"" + }, + { + "Answer": 45, + "Options": "a ) 30 , b ) 45 , c ) 50 , d ) 80 , e ) 100", + "Correct": "b", + "Explanation": "consider john ' s points as x so bill ' s points are x + 20 so sue ' s points are 2 x + 40 total of all three students is 4 x + 60 , but this total is given as 160 x = 25 so bill ' s points = 25 + 20 = 45 correct answer option b" + }, + { + "Answer": 305, + "Options": "a ) 250 , b ) 305 , c ) 280 , d ) 285 , e ) none", + "Correct": "b", + "Explanation": "\"since the month begins with sunday , to there will be five sundays in the month average required = ( 630 x 5 + 240 x 25 / 30 ) = 305 answer : option b\"" + }, + { + "Answer": 2999.9999999999995, + "Options": "a ) $ 3500 , b ) $ 3400 , c ) $ 3300 , d ) $ 3200 , e ) $ 3000", + "Correct": "e", + "Explanation": "\"explanatory answer let the profit made during the year be $ 3 x therefore , $ x would have been shared equally and the remaining $ 2 x would have been shared in the ratio 9 : 1 . i . e . , 90 % of 2 x would go to mary and 10 % of 2 x would go to mike . hence , mary would get ( 90 - 10 ) % of 2 x more than mike or 80 % of 2 x = $ 1600 i . e . , ( 60 / 100 ) * 2 x = 1600 or 2 x = 2000 . hence , the profit made by the company during the year $ 3 x = $ 3000 . answer : e\"" + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9", + "Correct": "a", + "Explanation": "\"5 years answer : a\"" + }, + { + "Answer": 4.949999999999999, + "Options": "a ) $ 3.15 , b ) $ 4.95 , c ) $ 4.80 , d ) $ 5.05 , e ) $ 5.40", + "Correct": "b", + "Explanation": "let the fixed charge of jim \u00e2 \u20ac \u2122 s taxi service = 2.25 $ and charge per 2 / 5 mile ( . 4 mile ) = . 3 $ total charge for a trip of 3.6 miles = 2.25 + ( 3.6 / . 4 ) * . 3 = 2.25 + 9 * . 3 = 4.95 $ answer b" + }, + { + "Answer": 21000, + "Options": "a ) 21000 , b ) 30000 , c ) 32000 , d ) 34000 , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : suppose b ' s investment = x . then a ' s investment = 3 x suppose bs period of investment = y , then a ' s period of investment = 2 y a : b = 3 x * 2 y : xy = 6 : 1 total profit * 1 / 7 = 3000 = > total profit = 3000 * 7 = 21000 . answer : option a\"" + }, + { + "Answer": 82, + "Options": "a ) 16 % , b ) 32 % , c ) 48 % , d ) 82 % , e ) 92 %", + "Correct": "d", + "Explanation": "\"this is easiest to solve with a bell - curve histogram . m here is equal to \u00b5 in the gaussian normal distribution and thus m = 50 % of the total population . so , if 64 % is one st . dev , then on either side of m we have 64 / 2 = 32 % . so , 32 % are to the right and left of m ( = 50 % ) . in other words , our value m + d = 50 + 32 = 82 % goingfrom the mean m , to the right of the distributionin the bell shaped histogram . . this means that 82 % of the values are below m + d . like i said , doing it on a bell - curve histogram is much easier to fullygethow this works , or you could apply gmat percentile jargon / theory to it d\"" + }, + { + "Answer": 37.5, + "Options": "a ) 50 , b ) 37.5 , c ) 27 , d ) 28 , e ) 21", + "Correct": "b", + "Explanation": "let the length of each train be x m . then , distance covered = 2 x m . relative speed = 46 - 36 = 10 km / hr . = 10 * 5 / 18 = 25 / 9 m / sec . 2 x / 27 = 25 / 9 = > x = 37.5 . answer : b" + }, + { + "Answer": 60, + "Options": "a ) $ 65 , b ) $ 55 , c ) $ 50 , d ) $ 60 , e ) $ 45", + "Correct": "d", + "Explanation": "call the fine f . joe paid ( 1 / 4 ) f + 4 and peter paid ( 1 / 3 ) f \u2013 4 , leaving ( 1 / 2 ) f \u2013 5 left . if we add those three up , they should add up to f . f = [ ( 1 / 4 ) f + 7 ] + [ ( 1 / 3 ) f \u2013 7 ] + [ ( 1 / 2 ) f \u2013 12 ] f = ( 1 / 4 ) f + ( 1 / 3 ) f + ( 1 / 2 ) f \u2013 12 multiply all terms by 12 to clear the fractions . 12 f = 3 f + 4 f + 6 f \u2013 144 12 f = 13 f \u2013 144 \u2013 f = \u2013 144 f = 144 well , if the fine cost $ 144 , then sam paid the part not covered by joe or peter . half the fine is $ 72 , and sam paid $ 12 less than this : $ 60 . answer = d" + }, + { + "Answer": 2350, + "Options": "a ) 2160 , b ) 2350 , c ) 2000 , d ) 2300 , e ) none of these", + "Correct": "b", + "Explanation": "explanation : total exp = 5000 + 1500 + 4500 + 2500 + 2000 + 5650 = 21150 exp in % = 100 - 10 = 90 % , 21150 = 90 % saving = 10 % = 21150 x 10 / 90 = rs . 2350 answer : b" + }, + { + "Answer": 375, + "Options": "a ) a ) 220 , b ) b ) 490 , c ) c ) 375 , d ) d ) 450 , e ) e ) 690", + "Correct": "c", + "Explanation": "\"the only thing you have to do is a simple multiply we have : 15 * 25 = 375 correct answer is : c ) 375\"" + }, + { + "Answer": 72, + "Options": "a ) 68 , b ) 69 , c ) 70 , d ) 71 , e ) 72", + "Correct": "e", + "Explanation": "\"the time to produce the first 60 cogs is 60 / 90 = 2 / 3 hours . the time to produce the next 60 cogs is 60 / 60 = 1 hour . the average output is 120 cogs / ( 5 / 3 ) hours = 72 cogs per hour . the answer is e .\"" + }, + { + "Answer": 20, + "Options": "a ) 6 , b ) 8 , c ) 9 , d ) 20 , e ) 14", + "Correct": "d", + "Explanation": "two ways to do it . . 1 ) straight logic . . only 20 fits in . . d" + }, + { + "Answer": 12, + "Options": "a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16", + "Correct": "c", + "Explanation": "\"let x be the amount of liquid q to be added . ( 2 / 5 ) * 30 + x = ( 4 / 7 ) * ( 30 + x ) 420 + 35 x = 600 + 20 x 15 x = 180 x = 12 the answer is c .\"" + }, + { + "Answer": 59, + "Options": "a ) 59 , b ) 88 , c ) 77 , d ) 26 , e ) 18", + "Correct": "a", + "Explanation": "the probability that paul correctly picks the winner = ( a ' s chances of winning ) x ( pauls picking the winner corectly ) + ( a ' s chances of loosing ) x ( paul picks wrongly ) = 23 \u00d7 23 + 13 \u00d7 13 = 59 answer : a" + }, + { + "Answer": 7, + "Options": "a ) 8 , b ) 7 , c ) 5 , d ) 4 , e ) 3", + "Correct": "b", + "Explanation": "because we have to maximize the pair of matched socks , we will remove 2 pairs ( 4 socks ) out of 10 pairs 1 sock from the 3 th pair . thus the no of matching socks pair remaining = 10 - 3 = 7 answer b" + }, + { + "Answer": 19, + "Options": "a ) 23 , b ) 20 , c ) 11 , d ) 19 , e ) 2", + "Correct": "d", + "Explanation": "soln : { 18 } + { 16 } = 18 * { 16 } + { 16 } = 19 * { 16 } answer : d" + }, + { + "Answer": 25, + "Options": "a ) 11 , b ) 25 , c ) 27 , d ) 22 , e ) 91", + "Correct": "b", + "Explanation": "let the son ' s present age be x years . then , man ' s present age = ( x + 27 ) years . ( x + 27 ) + 2 = 2 ( x + 2 ) x + 29 = 2 x + 4 = > x = 25 . answer : b" + }, + { + "Answer": 0.051871999999999995, + "Options": "a ) 0.045388 , b ) 4.5388 , c ) 0.051872 , d ) 473.88 , e ) none of these", + "Correct": "c", + "Explanation": "\"answer multiplying 3.242 x 16 = 5.1872 now divide 5.1872 by 100 so , 5.1872 \u00f7 100 = 0.051872 \u2234 shift the decimal two places to the left as 100 correct option : c\"" + }, + { + "Answer": 200, + "Options": "a ) 57 , b ) 177 , c ) 178 , d ) 377 , e ) 200", + "Correct": "e", + "Explanation": "lets say she sales x items so her commission will be : x * 1500 * 15 / 100 = 225 x salary difference is : 90000 - 45000 = 45000 so commission must at least be equal to salary difference i . e . x = 45000 / 225 = 200 ( approx ) . hence answer is e" + }, + { + "Answer": 196.66666666666666, + "Options": "a ) $ 28 , b ) $ 82 , c ) $ 110 , d ) $ 138 , e ) $ 196", + "Correct": "e", + "Explanation": "\"by the question , the equation would be 150 p - 86 * 150 - 16500 = 0 p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component . solving the equation , we get p = $ 196 . answer e for me .\"" + }, + { + "Answer": 2000, + "Options": "a ) 8981 , b ) 3799 , c ) 1200 , d ) 2693 , e ) 2000", + "Correct": "e", + "Explanation": "\"p - - - 10 - - - - 1000 p - - - 5 - - - - - 500 3 p - - - 5 - - - - - 1500 - - - - - - = > 2000 answer : e\"" + }, + { + "Answer": 80, + "Options": "a ) 56 , b ) 70 , c ) 90 , d ) 98 , e ) 80", + "Correct": "e", + "Explanation": "total = 180 television = 115 radio = 110 magazine = 130 all the three = 180 - 115 - 110 - 130 + 85 + 75 + 95 = 80 answer e" + }, + { + "Answer": 18, + "Options": "a ) 18 , b ) 16 , c ) 17 , d ) 15 , e ) 19", + "Correct": "a", + "Explanation": "\"the bottom row has x bricks x + x - 1 + x - 2 + x - 3 + x - 4 = 100 5 x - 10 = 100 5 x = 90 x = 18 answer : a\"" + }, + { + "Answer": 28, + "Options": "a ) 28 , b ) 37 , c ) 29 , d ) 237 , e ) 212", + "Correct": "a", + "Explanation": "average age ( present ) of 7 members = 29 years 5 years ago , average age of 7 members was 29 - 5 = 24 years . since , the youngest member was not born 5 years ago . therefore , average age of remaining 6 members is increased by 246246 = 4 years . therefore , 5 years ago , average age of 6 members was 24 + 4 = 28 years . answer : a" + }, + { + "Answer": 35, + "Options": "a ) 10 , b ) 20 , c ) 35 , d ) 45 , e ) 50", + "Correct": "c", + "Explanation": "\"i think we can use double - matrix method and solve using only one variable . our goal is to find the number of hardcover nonfiction books . let that number be x . we are given that all 140 books are either paperback fiction , paperback nonfiction , or hardcover nonfiction . this implies that number of hardcover fiction books is 0 . double - matrix : p = paperback ; h = hardcover ; f = fiction ; nf = nonfiction p h total f 2 x + 40 0 nf x + 20 x total 3 x + 60 x 200 3 x + 60 + x = 200 x = 35 answer ( c . )\"" + }, + { + "Answer": 2, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "a", + "Explanation": "\"t = the number of cups of tea c = the number of cups of hot chocolate t + c = 26 t - c = 14 - > t = 20 . c = 6 . mo drinks 4 cups of tea a day then number of days that are not rainy = 20 / 4 = 5 so number of rainy days = 7 - 5 = 2 a is the answer .\"" + }, + { + "Answer": 75, + "Options": "a ) 18 , b ) 36 , c ) 75 , d ) 90 , e ) 108", + "Correct": "c", + "Explanation": "75 all u do is do 2 : 1 : 6 = > 2 x + x + 6 x = 135 = > x = 15 30 : 15 : 90 90 - 15 = 75 answer c" + }, + { + "Answer": 14, + "Options": "a ) 18 , b ) 21 , c ) 13 , d ) 16 , e ) 14", + "Correct": "e", + "Explanation": "\"( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 52 + 2 * 72 a + b + c = \u00e2 \u02c6 \u0161 196 = 14 answer e\"" + }, + { + "Answer": 2, + "Options": "a ) 10 : 7 , b ) 9 : 8 , c ) 2 : 1 , d ) 13 : 11 , e ) 14 : 8", + "Correct": "c", + "Explanation": "correct option : ( c ) use rule of alligation , to determine the ratio the required ratio of soybean and peas = 6 : 3 = 2 : 1" + }, + { + "Answer": 5.5, + "Options": "a ) 5 / 2 , b ) 10 / 3 , c ) 7 / 2 , d ) 14 / 3 , e ) 11 / 2", + "Correct": "e", + "Explanation": "for 2 a ^ 2 + 5 a = 12 roots are [ - 5 + sqrt ( 25 + 96 ) ] / 4 or [ - 5 - sqrt ( 25 + 96 ) ] / 4 = 1.5 or - 4 hence larger root 1.5 is 1.5 - ( - 4 ) = 5.5 = 11 / 2 greater than smaller root ( - 4 ) . hence option ( e ) ." + }, + { + "Answer": 2, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "b", + "Explanation": "if x + 1 / x = p = = > x ^ 2 + 1 / x ^ 2 = p ^ 2 - 2 ans = 2 ^ 2 - 2 = 2 answer : b" + }, + { + "Answer": 1637, + "Options": "a ) 1637 , b ) 1456 , c ) 1567 , d ) 1678 , e ) 1635", + "Correct": "a", + "Explanation": "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 5 5 x = 1360 x = 272 large number = 272 + 1365 = 1637 a" + }, + { + "Answer": 1, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "b", + "Explanation": "set x = to amount of money for bonuses , and y to be the amount of each individual bonus . x = 5 * y + 2 . 3 x = 15 * y + 6 3 x = 3 * 5 * y + 6 3 x = 5 ( 3 ( y + 1 ) ) + 1 remainder is then 1 , so option b ." + }, + { + "Answer": 4690910862, + "Options": "a ) 4586970843 , b ) 4686970743 , c ) 4690910862 , d ) 4586870843 , e ) none", + "Correct": "c", + "Explanation": "\"answer 469138 x 9999 = 469138 x ( 10000 - 1 ) = 4691380000 - 469138 = 4690910862 . option : c\"" + }, + { + "Answer": 49, + "Options": "a ) 35 , b ) 42 , c ) 45 , d ) 49 , e ) 54", + "Correct": "d", + "Explanation": "\"a = 105 = 3 * 5 * 7 a ^ 3 = 21 \u00d7 25 \u00d7 45 \u00d7 e = > a ^ 3 = ( 7 * 3 ) x ( 5 * 5 ) x ( 3 ^ 2 * 5 ) x e = > a ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x e = > ( 3 * 5 * 7 ) ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x e e = 7 ^ 2 = 49 answer d\"" + }, + { + "Answer": 1.3999999999999997, + "Options": "a ) 1 / 3 , b ) 2 / 3 , c ) 7 / 5 , d ) 5 / 7 , e ) 3 / 2", + "Correct": "c", + "Explanation": "\"say the total number of players is 18 , 9 right - handed and 9 left - handed . on a certain day , two - thirds of the players were absent from practice - - > 12 absent and 6 present . of the players at practice that day , one - third were right - handed - - > 6 * 1 / 3 = 2 were right - handed and 4 left - handed . the number of right - handed players who were not at practice that day is 9 - 2 = 7 . the number of left - handed players who were not at practice that days is 9 - 4 = 5 . the ratio = 7 / 5 . answer : c .\"" + }, + { + "Answer": 7, + "Options": "a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 12", + "Correct": "b", + "Explanation": "\"option ' b ' 32 / 9 = 3 and 97 / 9 = 10 = = > 10 - 3 = 7 numbers\"" + }, + { + "Answer": 8, + "Options": "a ) 2 , b ) 4 , c ) 8 , d ) 10 , e ) 12", + "Correct": "c", + "Explanation": "\"the x - axis is 4 units from the point p . thus the y - axis is 8 units from the point p . the answer is c .\"" + }, + { + "Answer": 125, + "Options": "a ) 50 , b ) 75 , c ) 150 , d ) 125 , e ) 100", + "Correct": "d", + "Explanation": "\"since the month begin with sunday , so there will be five sundays in the month required average = ( 150 * 5 + 120 * 25 ) / 30 = 3750 / 30 = 125 answer is d\"" + }, + { + "Answer": 0.3333333333333333, + "Options": "a ) 1 / 3 , b ) 2 / 5 , c ) 3 / 10 , d ) 3 / 7 , e ) 1 / 7", + "Correct": "a", + "Explanation": "\"here , s = [ 1 , 2 , 3 , 4 , \u2026 . , 19 , 20 , 21 ] let e = event of getting a multiple of 3 = [ 3 , 6 , 9 , 12 , 15 , 18 , 21 ] p ( e ) = n ( e ) / n ( s ) = 7 / 21 = 1 / 3 the answer is a .\"" + }, + { + "Answer": 0.4, + "Options": "a ) 1 / 5 , b ) 3 / 10 , c ) 2 / 5 , d ) 1 / 2 , e ) 3 / 5", + "Correct": "c", + "Explanation": "\"p ( both apples are not spoiled ) = 4 c 2 / 5 c 2 = 4 * 3 / 5 * 4 = 3 / 5 p ( one of the apple spoiled ) = 1 - 3 / 5 = 2 / 5 answer is c .\"" + }, + { + "Answer": 360, + "Options": "a ) 40 / 3 , b ) 40 , c ) 120 , d ) 360 , e ) 420", + "Correct": "d", + "Explanation": "case 1 : deposit = $ x ; rate of increase = r . interest yearned in 1 year = xr . deposit in 1 year = x + xr . interest yearned in 2 year = ( x + xr ) r . the difference w = ( x + xr ) r - xr = xr ^ 2 = 40 . case 2 : deposit = $ x ; rate of increase = 3 r . interest yearned in 1 year = x ( 3 r ) . deposit in 1 year = x + 3 xr . interest yearned in 2 year = ( x + 3 xr ) 3 r . the difference = ( x + 3 xr ) 3 r - 3 xr = 9 xr ^ 2 . since from case 1 we know that xr ^ 2 = 40 , then 9 xr ^ 2 = 9 * 40 = 360 . answer : d ." + }, + { + "Answer": 11, + "Options": "a ) 6 , b ) 9 , c ) 12 , d ) 11 , e ) 48", + "Correct": "d", + "Explanation": "if 3 machines can do the work in 44 hr then 4 machines can do the work in 3 / 4 * 44 = 33 hrs . hence time saved will be 11 hr option d is the correct answer" + }, + { + "Answer": 3, + "Options": "a ) 3 , b ) 0 , c ) 1 , d ) 2 , e ) 4", + "Correct": "a", + "Explanation": "\"since f ( n ) = f ( n - 1 ) - n then : f ( 6 ) = f ( 5 ) - 6 and f ( 5 ) = f ( 4 ) - 5 . as given that f ( 4 ) = 14 then f ( 5 ) = 14 - 5 = 9 - - > substitute the value of f ( 5 ) back into the first equation : f ( 6 ) = f ( 5 ) - 6 = 9 - 6 = 3 . answer : a . questions on funtions to practice :\"" + }, + { + "Answer": 255, + "Options": "a ) 237 , b ) 246 , c ) 255 , d ) 264 , e ) 273", + "Correct": "c", + "Explanation": "lcm ( 8 , 11,24 ) = 24 x 11 = 264 so the least divisible number is 264 , and the number we are looking for is 264 - 9 = 255 . the answer is c ." + }, + { + "Answer": 7500, + "Options": "a ) 7500 , b ) 5000 , c ) 5400 , d ) 7000 , e ) 8500", + "Correct": "a", + "Explanation": "let average is x 100 x + 500 = 125 ( x \u2013 10 ) x = 70 100 * 70 + 500 = 7500 answer : a" + }, + { + "Answer": 80, + "Options": "a ) 18 , b ) 80 , c ) 72 , d ) 90 , e ) 108", + "Correct": "b", + "Explanation": "\"80 all u do is do 2 : 1 : 6 = > 2 x + x + 6 x = 144 = > x = 16 32 : 16 : 96 96 - 16 = 80 answer b\"" + }, + { + "Answer": 0.6, + "Options": "a ) a ) 0.9 , b ) b ) 0.6 , c ) c ) 0.45 , d ) d ) 0.3 , e ) e ) 0.25", + "Correct": "b", + "Explanation": "percent of students who are 25 years old or older is 0.5 * 48 + 0.2 * 52 = ~ 34 , so percent of people who are less than 25 years old is 100 - 3 = 66 . answer : b ." + }, + { + "Answer": 7070, + "Options": "a ) rs . 7070 , b ) rs . 5991 , c ) rs . 6020 , d ) rs . 6850 , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : total sale for 5 months = rs . ( 5420 + 5660 + 6200 + 6350 + 6500 ) = rs . 30,130 therefore , required sale = rs . [ ( 6200 * 6 ) \u2013 30,130 ] = rs . ( 37200 \u2013 30,130 ) = rs . 7070 answer a\"" + }, + { + "Answer": 25, + "Options": "a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25", + "Correct": "e", + "Explanation": "\"the multiples of 4 are from 4 * 4 up to 4 * 28 . 28 - 4 + 1 = 25 . the answer is e .\"" + }, + { + "Answer": 60, + "Options": "a ) 3 , b ) 60 , c ) 9 , d ) 12 , e ) 14", + "Correct": "b", + "Explanation": "let the number of each size of jar = wthen 1 / 4 w + 1 / 2 w + w = 35 1 3 / 4 w = 35 w = 20 the total number of jars = 3 w = 60 answer : b" + }, + { + "Answer": 416, + "Options": "a ) 404 , b ) 408 , c ) 412 , d ) 416 , e ) 420", + "Correct": "d", + "Explanation": "the number of seats in the theater is 14 + ( 14 + 3 ) + . . . + ( 14 + 36 ) = 13 ( 14 ) + 3 ( 1 + 2 + . . . + 12 ) = 13 ( 14 ) + 3 ( 12 ) ( 13 ) / 2 = 13 ( 14 + 18 ) = 13 ( 32 ) = 416 the answer is d ." + }, + { + "Answer": 80, + "Options": "a ) 21 , b ) 27 , c ) 26 , d ) 80 , e ) 28", + "Correct": "d", + "Explanation": "\"given m + p + c = 80 * 3 = 240 - - - ( 1 ) m + p = 90 * 2 = 180 - - - ( 2 ) p + c = 70 * 2 = 140 - - - ( 3 ) where m , p and c are marks obtained by the student in mathematics , physics and chemistry . p = ( 2 ) + ( 3 ) - ( 1 ) = 180 + 140 - 240 = 80 . answer : d\"" + }, + { + "Answer": 38.000000000000014, + "Options": "a ) 25 % , b ) 28 % , c ) 32 % , d ) 38 % , e ) 40 %", + "Correct": "d", + "Explanation": "\"given voters in ratio 2 : 1 let x has 200 votersy has 100 voters for x 62 % voted means 62 * 200 = 124 votes combined for xy has 300 voters and voted 54 % so total votes = 162 balance votes = 162 - 124 = 38 as y has 100 voters so 38 votes means 38 % of votes required ans d\"" + }, + { + "Answer": 0.8333333333333334, + "Options": "a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 5 , e ) 5 / 6", + "Correct": "e", + "Explanation": "because we see h willbring 1 / 3 of his booksto the new home - - > try to pick a number that isdivisible by 3 . before : assume h = 30 books h = 1 / 2 m - - > m = 60 books after : h ' = 1 / 3 h = 10 books m ' = 1 / 2 m = 30 books total = 40 books m ' = 40 = 5 / 6 * 60 ratio : 5 / 6 ans : e" + }, + { + "Answer": 4, + "Options": "a ) 10 , b ) 4 , c ) 8 , d ) 6 , e ) 5", + "Correct": "b", + "Explanation": "\"number = 8 * 8 + 0 = 64 5 ) 64 ( 12 60 - - - - - - - - 4 required number = 4 . answer : b\"" + }, + { + "Answer": 40, + "Options": "a ) 35 , b ) 36 , c ) 40 , d ) 42 , e ) 45", + "Correct": "c", + "Explanation": "the question is finding y such that ( 50 - y ) ! is a multiple of 50 . that means we need to have 2 * 5 ^ 2 in ( 50 - y ) ! 10 ! is the smallest factorial number with 2 * 5 ^ 2 as a factor . 50 - y = 10 y = 40 the answer is c ." + }, + { + "Answer": 10, + "Options": "a ) 11 , b ) 82 , c ) 10 , d ) 28 , e ) 23", + "Correct": "c", + "Explanation": "\"explanation : total employees = \\ inline \\ frac { ( 25 - 10 ) \\ times 20 } { 10 } = 30 hence number of educated employees = 30 - 20 = 10 answer : c\"" + }, + { + "Answer": 0.041666666666666664, + "Options": "a ) 1 / 32 , b ) 1 / 28 , c ) 1 / 24 , d ) 1 / 16 , e ) 1 / 14", + "Correct": "c", + "Explanation": "\"there are 3 single digit multiple of 3 , that is , 3 , 6,9 . there are 8 prime nos less than 20 - 2,3 , 5,7 , 11,13 , 17,19 total outcome - 8 * 3 = 24 favourable outcome = 1 ( 9 * 5 ) hence required probability r = 1 / 24 . answer c .\"" + }, + { + "Answer": 50, + "Options": "a ) 50 % , b ) 25 % , c ) 250 % , d ) 75 % , e ) 80 %", + "Correct": "a", + "Explanation": "\"r + w + p = 150 s + l = 150 1 / 3 * 150 = 50 short - stemmed white = 20 short - stemmed pink = 15 = > short - stemmed red = 15 15 / p = 15 / r = > r = p so total long stemmed = 100 and long stemmed red + long stemmed pink = 100 so long stemmed red / long stemmed = ? total white = 20 ( as no long stemmed white ) = > r + r + 20 = 150 = > r = 130 and r = 65 long stemmed r = 65 - 15 = 50 so long stemmed red / r = 50 / 100 = 50 % answer - a\"" + }, + { + "Answer": 18, + "Options": "a ) 20 , b ) 16 , c ) 22 , d ) 18 , e ) 24", + "Correct": "d", + "Explanation": "smallest gumballs = ( 19 - 16 ) + ( 19 - 12 ) + 19 = 29 largest gumballs = ( 25 - 16 ) + ( 25 - 12 ) + 25 = 47 difference = 47 - 29 = 18 d" + }, + { + "Answer": 958.9041095890411, + "Options": "a ) 939.6 , b ) 958.9 , c ) 927.78 , d ) 926.82 , e ) 902.1", + "Correct": "b", + "Explanation": "\"1120 = p [ 1 + ( 7 * 12 / 5 ) / 100 ] p = 958.90 answer : b\"" + }, + { + "Answer": 22, + "Options": "a ) 22 , b ) 27 , c ) 18 , d ) 12 , e ) 81", + "Correct": "a", + "Explanation": "\"( 80 / 100 ) * 40 \u00e2 \u20ac \u201c ( 2 / 5 ) * 25 32 - 10 = 22 answer : a\"" + }, + { + "Answer": 15, + "Options": "a ) 8 , b ) 14 , c ) 15 , d ) 18 , e ) 30", + "Correct": "c", + "Explanation": "\"within one standard deviation of the average age means 31 + / - 7 23 - - 30 - - 37 number of dif . ages - 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 total = 15 c\"" + }, + { + "Answer": 4.85, + "Options": "a ) $ 3.85 , b ) $ 4.85 , c ) $ 5.85 , d ) $ 2.85 , e ) $ 1.85", + "Correct": "b", + "Explanation": "\"john spent and gave to his two friends a total of 1.25 + 1.20 + 1.20 = $ 3.65 money left 8.50 - 3.65 = $ 4.85 correct answer is b ) $ 4.85\"" + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 8 , c ) 11 , d ) 12 , e ) 14", + "Correct": "a", + "Explanation": "\"in 4 hr journey = 55 * 4 = 220 mph let in the next additional hour journey = 70 * x = 70 x mph so , ( 220 + 70 x ) / ( 4 + x ) = 60 = > 220 + 70 x = 240 + 60 x = > 10 x = 20 = > x = 2 h so the trip is ( 4 + x ) = > 6 hours long answer : a\"" + }, + { + "Answer": 5, + "Options": "a ) 2 . , b ) 4 . , c ) 5 . , d ) 7 . , e ) 9 .", + "Correct": "c", + "Explanation": "\"ad = ( a + 1 ) ( d + 1 ) - 11 0 = a + d - 10 a + d = 10 a = d ( as they are twin brothers ) a = d = 5 c is the answer\"" + }, + { + "Answer": 500, + "Options": "a ) s . 80 , b ) s . 85 , c ) s . 90 , d ) s . 500 , e ) s . 120", + "Correct": "d", + "Explanation": "\"9 / 12 = 3 / 4 * 500 = 375 250 - - - - - - - - - - - - - 125 1 / 4 - - - - - - - - 125 1 - - - - - - - - - ? = > rs . 500 answer : d\"" + }, + { + "Answer": 60, + "Options": "a ) 36 liters , b ) 40 liters , c ) 45 liters , d ) 54 liters , e ) 60 liters", + "Correct": "e", + "Explanation": "\"a big container is 30 % full with water and after 27 liters of water is added , the container becomes 75 % full . hence these 27 liters account for 45 % of the container , which means that the capacity of it is 27 / 0.45 = 60 liters . or : if the capacity of the container is x liters then : 0.3 x + 27 = 0.75 x - - > x = 60 liters . answer : e .\"" + }, + { + "Answer": 0.17857142857142858, + "Options": "a ) 7 / 72 , b ) 1 / 6 , c ) 5 / 28 , d ) 15 / 36 , e ) 21 / 36", + "Correct": "c", + "Explanation": "probability = no : of desired outcomes / total no : of outcomes . you are picking two slips out of 8 slips . so total no : of outcomes = 8 c 2 = 28 desired outcome : sum of the numbers on the two slips is equal to one of the numbers left in the box . how many such outcomes are there ? if you look at the numbers closely , you will see that the following pair of numbers will give you the desired outcome . ( 3,5 ) ( 5,8 ) ( 8,13 ) ( 13,21 ) ( 21,34 ) . there are 7 such pairs . if the two numbers which i pick is from any of these 5 pairs , then i get my desired outcome . so no : of desired outcomes = 5 probability = 5 / 28 answer : c" + }, + { + "Answer": 21, + "Options": "a ) 18 , b ) 15 , c ) 17 , d ) 19 , e ) 21", + "Correct": "e", + "Explanation": "\"ab = ( a - 1 ) ( b - 1 ) x 9 = ( x - 1 ) ( 9 - 1 ) = 160 - - > x - 1 = 20 - - > x = 21 answer : e\"" + }, + { + "Answer": 17550, + "Options": "a ) 11,550 , b ) 14,550 , c ) 17,550 , d ) 20,550 , e ) 23,550", + "Correct": "c", + "Explanation": "\"2 + 4 + 6 + 8 + . . . + 100 = 2550 302 + 304 + . . . + 400 = 50 ( 300 ) + ( 2 + 4 + . . . + 100 ) = 15,000 + 2550 = 17,550 the answer is c .\"" + }, + { + "Answer": 1.0999999999999999, + "Options": "a ) 1.9 , b ) 1.7 , c ) 1.2 , d ) 1.5 , e ) 1.1", + "Correct": "e", + "Explanation": "speed of boat in still water ( b ) = 3.3 km / hr . speed of boat with stream ( down stream ) , d = b + u speed of boat against stream ( up stream ) , u = b \u2013 u it is given upstream time is twice to that of down stream . \u21d2 downstream speed is twice to that of upstream . so b + u = 2 ( b \u2013 u ) \u21d2 u = b / 3 = 1.1 km / hr . answer : e" + }, + { + "Answer": 348, + "Options": "a ) 270 , b ) 279 , c ) 348 , d ) 371 , e ) 372", + "Correct": "c", + "Explanation": "\"12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 12 / 29 * 841 = 348 answer : c\"" + }, + { + "Answer": 8, + "Options": "a ) 8 , b ) 7 , c ) 15 , d ) 21 , e ) 25", + "Correct": "a", + "Explanation": "\"jacob = x years , michael = x + 13 years 9 years from now , 2 ( x + 9 ) = x + 22 2 x + 18 = x + 22 x = 4 x + 4 = 8 years answer a\"" + }, + { + "Answer": 93, + "Options": "a ) 93 , b ) 67 , c ) 77 , d ) 87 , e ) 97", + "Correct": "a", + "Explanation": "\"money collected = ( 86.49 x 100 ) paise = 8649 paise numbers of members = 8649 squareroot = 93 answer a\"" + }, + { + "Answer": 39.476190476190474, + "Options": "a ) 28.32 , b ) 39 , c ) 38.78 , d ) 29 , e ) 39.47", + "Correct": "e", + "Explanation": "explanation : total sum of 63 numbers = ( 65 * 40 ) - ( 83 + 30 ) = 2600 - 113 = 2487 average = 2487 / 63 = 39.47 answer : e" + }, + { + "Answer": 19, + "Options": "a ) 29 , b ) 39 , c ) 19 , d ) 49 , e ) 59", + "Correct": "c", + "Explanation": "a + b + c + d = 17 4 + 2 + 6 + 5 = 17 d = 5 d + e + f + g = 17 5 + 3 + 8 + 1 = 17 g = 1 g + h + i = 17 1 + 9 + 7 = 17 g = 1 , h = 9 . answer : c" + }, + { + "Answer": 2590, + "Options": "a ) $ 2380 , b ) $ 2590 , c ) $ 2760 , d ) $ 2940 , e ) $ 3150", + "Correct": "b", + "Explanation": "\"let x be the value of the item . 0.07 * ( x - 1000 ) = 111.30 x = 2590 the answer is b .\"" + }, + { + "Answer": 2.5, + "Options": "a ) 1.5 liters , b ) 2.5 liters , c ) 3.5 liters , d ) 4.5 liters , e ) 5.5 liters", + "Correct": "b", + "Explanation": "solution a = 50 % solution solution b = 30 % solution 30 % - 45 % = 15 % solution b 50 % - 45 % = 5 % solution a so the ratio is 3 : 1 for 30 % : 50 % solutions 3 / 4 * 10 liter = 7.5 for 30 % solution and 2.5 for 50 % solution . . answer : b" + }, + { + "Answer": 302, + "Options": "a ) $ 160 , b ) $ 176 , c ) $ 282 , d ) $ 302 , e ) $ 286", + "Correct": "d", + "Explanation": "\"total number of days of stay = 23 charge of staying in first week = 18 * 7 = 126 $ charge of staying for additional days = ( 23 - 7 ) * 11 = 16 * 11 = 176 $ total charge = 126 + 176 = 302 $ answer d\"" + }, + { + "Answer": 100011, + "Options": "a ) 100011 , b ) 111111 , c ) 101111 , d ) 1011111 , e ) 211111", + "Correct": "a", + "Explanation": "\"smallest number of 6 digits is 100000 . on dividing 100000 by 111 , we get 100 as remainder . number to be added = ( 111 - 100 ) - 11 . hence , required number = 100011 answer a 100011\"" + }, + { + "Answer": 14, + "Options": "a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17", + "Correct": "b", + "Explanation": "sol . let the present age of kareem \u2019 s son be x years . then , kareem \u2019 s age = 3 x years after 10 years , kareem \u2019 s age = 3 x + 10 years and kareem \u2019 s son \u2019 s age = x + 10 years \u2234 ( 3 x + 10 ) + ( x + 10 ) = 76 = > 4 x = 56 = > x = 14 \u2234 kareem \u2019 s present age = 3 x = 3 \u00d7 14 = 42 years kareem \u2019 s son \u2019 s age = x = 14 years . answer b" + }, + { + "Answer": 600, + "Options": "a ) 250 / 3 , b ) 500 / 3 , c ) 400 , d ) 480 , e ) 600", + "Correct": "e", + "Explanation": "we know that x is 10 % , y is 30 % and w . avg = 25 % . what does this mean with respect to w . avg technique ? w . avg is 1 portion away from y and 3 portion away from x so for every 1 portion of x we will have to add 3 portions of y . if x = 200 then y = 600 answer : e" + }, + { + "Answer": 90, + "Options": "a ) 50 yards , b ) 60 yards , c ) 70 yards , d ) 80 yards , e ) 90 yards", + "Correct": "e", + "Explanation": ". the other team is extra information . 150 \u2013 60 = 90 he got 90 yards running . correct answer e" + }, + { + "Answer": 199, + "Options": "a ) 233 , b ) 299 , c ) 333 , d ) 199 , e ) 339", + "Correct": "d", + "Explanation": "eq of line = y = mx + c m = 4 , c = 4 y = 4 x + 4 , substitute y by 800 as given in question . 800 = 4 x + 4 , x = 199 . correct option is d" + }, + { + "Answer": 840, + "Options": "a ) 600 , b ) 700 , c ) 840 , d ) 900 , e ) none of these", + "Correct": "c", + "Explanation": "explanation : let p ' s capital = p , q ' s capital = q and r ' s capital = r then 4 p = 6 q = 10 r = > 2 p = 3 q = 5 r = > q = 2 p / 3 r = 2 p / 5 p : q : r = p : 2 p / 3 : 2 p / 5 = 15 : 10 : 6 r ' s share = 4340 * ( 6 / 31 ) = 140 * 6 = 840 . answer : option c" + }, + { + "Answer": 25, + "Options": "a ) 30 , b ) 28 , c ) 27 , d ) 25 , e ) 26", + "Correct": "d", + "Explanation": "\"4 n + 7 > 1 4 n > - 6 n > - ( 3 / 2 ) n > - 1.5 ( n = - 1 , 0 , 1 , 2 3 . . . . . . . . upto infinity ) from second constraint 4 n + 7 < 100 4 n < 93 n < 23 . 25 n = ( - infinity , . . . . . . . - 3 , - 2 , - 1 , 0 , 1 , 2 , . . . . . . . . . upto 23 ) combining the two - 1.5 < n < 23.25 n = 1 to 23 ( 23 integers ) and n = - 1 and 0 so 25 integers . d is the answer\"" + }, + { + "Answer": 30, + "Options": "a ) 20 , b ) 10 , c ) 30 , d ) 40 , e ) 5", + "Correct": "c", + "Explanation": "\"arithmetic mean expression for p and q : ( p + q ) / 2 = 10 ; p + q = 20 - - - - eq 1 arithmetic mean expression for q and r : ( q + r ) / 2 = 20 ; q + r = 50 - - - - eq 2 subtracting eq 1 from eq 2 we get : r - p = 30 hence , the correct answer is c\"" + }, + { + "Answer": 25600, + "Options": "a ) rs . 18000 , b ) rs . 20000 , c ) rs . 25600 , d ) rs . 32000 , e ) none of these", + "Correct": "c", + "Explanation": "let the monthly salaries of ram and shyam be rs . r and rs . s respectively . 10 / 100 r = 8 / 100 s r = 4 / 5 s monthly salary of abhinav = ( 1.92 lakhs ) / 12 = rs . 0.16 lakhs s = 2 ( 0.16 lakhs ) = 0.32 lakhs r = 4 / 5 ( 0.32 lakhs ) = rs . 25600 answer : c" + }, + { + "Answer": 1.7, + "Options": "a ) 1.2 kg , b ) 1.5 kg , c ) 1.7 kg , d ) 1.9 kg , e ) none of these", + "Correct": "c", + "Explanation": "\"explanation : flower - nectar contains 50 % of non - water part . in honey this non - water part constitutes 85 % ( 100 - 15 ) . therefore 0.5 x amount of flower - nectar = 0.85 x amount of honey = 0.85 x 1 kg therefore amount of flower - nectar needed = ( 0.85 / 0.51 ) kg = 1.7 kgs answer : c\"" + }, + { + "Answer": 2, + "Options": "a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1", + "Correct": "d", + "Explanation": "let the second integer be x and the fourth be a . then [ 3 x + x + ( x + 2 ) + a ] / 4 = 16 = > 5 x + 2 + a = 64 = > 5 x + a = 62 = > a = 62 - 5 x from the above equation we can see that a is minimum when x is maximum , provided both are positive the maximum value that x can take in the above equation while still keeping a positive is x = 12 this gives us a = 62 - 60 = 2 therefore the minimum value that the fourth integer can have is 2 . option d ." + }, + { + "Answer": 560, + "Options": "a ) 80 , b ) 120 , c ) 160 , d ) 240 , e ) 560", + "Correct": "e", + "Explanation": "\"working inside out , ( 4 \u20ac 5 ) = 2 * 4 * 5 = 40 7 \u20ac 40 = 2 * 3 * 40 = 560 hence , answer is e\"" + }, + { + "Answer": 13.33744, + "Options": "a ) 11.34 , b ) 12.34 , c ) 13.34 , d ) 14.34 , e ) 15.34", + "Correct": "c", + "Explanation": "5.6 + 10.3 = 15.9 i . e . . 15.9 - 2.56 = 13.34 so ur answer is 9 ^ 13.34 answer : c" + }, + { + "Answer": 500, + "Options": "a ) 8 , b ) 55 , c ) 87 , d ) 90 , e ) 2", + "Correct": "b", + "Explanation": "b" + }, + { + "Answer": 0.25, + "Options": "a ) 1 / 7 , b ) 2 / 7 , c ) 1 / 2 , d ) 7 / 12 , e ) 1 / 4", + "Correct": "e", + "Explanation": "\"same amount of water made bigger jar 1 / 8 full , then the same amount of water ( stored for a while in smaller jar ) were added to bigger jar , so bigger jar is 1 / 8 + 1 / 8 = 1 / 4 full . answer : e .\"" + }, + { + "Answer": 45.714285714285715, + "Options": "a ) 46 , b ) 40 , c ) 44 , d ) 48 , e ) 49", + "Correct": "a", + "Explanation": "\"for 40 hrs = 40 * 20 = 800 excess = 1000 - 800 = 200 for extra hours = . 75 ( 20 ) = 15 + 20 = 35 number of extra hrs = 200 / 35 = 5.71 = 6 approx . total hrs = 40 + 6 = 46 answer a 46\"" + }, + { + "Answer": 4, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "b", + "Explanation": "\"10 ^ m = 2 ^ m * 5 ^ m . let ' s figure out how many 5 ' s are in the prime factorization of 20 ! the multiples of 5 are : 5 , 10 , 15 , 20 . thus 5 ^ 4 will divide 20 ! but 5 ^ 5 will not . clearly 2 ^ 4 will divide 20 ! so m = 4 is the largest possible integer . the answer is b .\"" + }, + { + "Answer": 4, + "Options": "a ) 3 , b ) 1 , c ) 16 , d ) 4 , e ) 15", + "Correct": "d", + "Explanation": "\"on dividing 9679 by 15 , we get remainder = 4 . required number be subtracted = 4 answer : d\"" + }, + { + "Answer": 33, + "Options": "a ) 33 , 13 , b ) 25 , 5 , c ) 29 , 9 , d ) 50 , 30 , e ) 20,10", + "Correct": "a", + "Explanation": "let their ages be x and ( x + 20 ) years . then , 5 ( x - 8 ) = ( x + 20 - 8 ) = > 4 x = 52 = > x = 13 their present ages are 33 years and 13 year . answer : a" + }, + { + "Answer": 25, + "Options": "a ) 9 % , b ) 11 % , c ) 15 % , d ) 25 % , e ) 90 %", + "Correct": "d", + "Explanation": "\"cost of 12 paper towels individually = 1 * 12 = 12 cost of a set of 12 paper towels = 9 cost of one roll = 9 / 12 = 3 / 4 = 0.75 savings per roll = 1 - . 75 = 0.25 % of savings is = . 25 / 1 * 100 = 25 % d is the answer .\"" + }, + { + "Answer": 5, + "Options": "a ) 3 , b ) 1 , c ) 5 , d ) 11 , e ) 15", + "Correct": "c", + "Explanation": "\"on dividing 3830 by 15 , we get remainder = 5 . required number be subtracted = 5 answer : c\"" + }, + { + "Answer": 4, + "Options": "a ) 3 , b ) 4 , c ) 2 , d ) 1 , e ) 7", + "Correct": "b", + "Explanation": "7 ^ ( x - y ) = 343 = 7 ^ 3 = > x - y = 3 - - - - - - - - - - - - - - - - - - - - - - - - - - - ( equation 1 ) 7 ^ ( x + y ) = 16807 = 7 ^ 5 = > x + y = 5 - - - - - - - - - - - - - - - - - - - - - - - - - - - ( equation 2 ) ( equation 1 ) + ( equation 2 ) = > 2 x = 3 + 5 = 8 = > x = 8 / 2 = 4 answer is b" + }, + { + "Answer": 3399.999999999999, + "Options": "a ) $ 8600 , b ) $ 2400 , c ) $ 1000 , d ) $ 3000 , e ) $ 3400", + "Correct": "e", + "Explanation": "remaining part of salary left = 1 - ( 2 / 5 + 3 / 10 + 1 / 8 ) = 1 - ( 33 / 40 ) = 7 / 40 let the monthly salary be $ x then , 7 / 40 of x = $ 1400 x = ( 1400 * 40 / 7 ) = $ 8600 expenditure on food = $ ( 3 / 10 * 800 ) = $ 2400 expenditure on conveyance = $ ( 1 / 8 * 8000 ) = $ 1000 $ 2400 + $ 1000 = $ 3400 so the answer is option e ) $ 3400" + }, + { + "Answer": 10, + "Options": "a ) 21 , b ) 20 , c ) 11 , d ) 10 , e ) 9", + "Correct": "d", + "Explanation": "number start between 25 to 45 is 20 numbers half of them is even . . which is 10 answer : d" + }, + { + "Answer": 439.99999999999966, + "Options": "a ) $ 200 , b ) $ 260 , c ) $ 320 , d ) $ 380 , e ) $ 440", + "Correct": "e", + "Explanation": "\"let p be the original purchase price of the product . bill originally sold the product for 1.1 * p . in the second scenario , the purchase price is 0.9 * p . a 30 % profit means the selling price would be 1.3 * 0.9 * p = 1.17 * p thus , according to the information in the question , 1.17 p - 1.1 p = 28 0.07 = 28 p = 400 the original selling price was 400 * 1.1 = 440 . the correct answer is e .\"" + }, + { + "Answer": 140, + "Options": "a ) 140 , b ) 165 , c ) 150 , d ) 142 , e ) 174", + "Correct": "a", + "Explanation": "let the number be x . then , 4 * x / 5 \u2013 ( 65 % of x ) = 21 4 x / 5 \u2013 65 x / 100 = 21 5 x = 2100 x = 140 . answer a 140" + }, + { + "Answer": 8, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", + "Correct": "b", + "Explanation": "\"101 * n ^ 2 < = 8100 n ^ 2 < = 8100 / 101 which will be less than 81 since 8100 / 100 = 81 which is the square of 9 next closest value of n where n ^ 2 < = 81 is 8 ans b\"" + }, + { + "Answer": 13541, + "Options": "a ) 12455 , b ) 14153 , c ) 14256 , d ) 13541 , e ) 14541", + "Correct": "d", + "Explanation": "conversion of hexa decimal to decimal ( e 78 ) = ( 8 * 16 ^ 0 ) + ( 7 * 16 ^ 1 ) + ( 14 * 16 ^ 2 ) = 8 + 112 + 3584 = 3704 conversion of decimal to radix 7 3704 / 7 : reminder : 1 and dividend : 529 529 / 7 : reminder : 4 and dividend : 75 75 / 7 : reminder : 5 and dividend : 10 10 / 7 : reminder : 3 and dividend : 1 1 / 7 : reminder 1 then finally result is : 13541 answer : d" + }, + { + "Answer": 2, + "Options": "a ) 29 , b ) 776 , c ) 2 , d ) 12 , e ) 99", + "Correct": "c", + "Explanation": "\"( 55 / 100 ) * 40 \u2013 ( 4 / 5 ) * 25 22 - 20 = 2 answer : c\"" + }, + { + "Answer": 1600, + "Options": "a ) 1209 , b ) 1615 , c ) 1245 , d ) 1300 , e ) 1635", + "Correct": "b", + "Explanation": "\"let the smaller number be x . then larger number = ( x + 1515 ) . x + 1515 = 16 x + 15 15 x = 1500 x = 100 large number = 100 + 1515 = 1615 answer : b\"" + }, + { + "Answer": 7, + "Options": "a ) $ 5 , b ) $ 7 , c ) $ 6 , d ) $ 8 , e ) $ 9", + "Correct": "b", + "Explanation": "if large doll costs $ 5 , then he can buy 350 / 5 = 70 large dolls and 350 / 3 = 116 small dolls . difference is more than 20 . discard . if large doll costs $ 7 , then he can buy 350 / 7 = 50 large dolls and 350 / 5 = 70 small dolls . difference is 20 , which is we wanted . answer b ." + }, + { + "Answer": 20000, + "Options": "a ) 62,000 , b ) 85,500 , c ) 95,500 , d ) 100,500 , e ) 100,000", + "Correct": "a", + "Explanation": "\"since investment doubles in 70 / r years then for r = 8 it ' ll double in 70 / 8 = ~ 9 years ( we are not asked about the exact amount so such an approximation will do ) . thus in 18 years investment will double twice and become ( $ 5,000 * 2 ) * 2 = $ 20,000 ( after 9 years investment will become $ 5,000 * 2 = $ 10,000 and in another 9 years it ' ll become $ 10,000 * 2 = $ 20,000 ) . answer : a .\"" + }, + { + "Answer": 6, + "Options": "a ) 2 . , b ) 6 . , c ) 5 . , d ) 7 . , e ) 9 .", + "Correct": "b", + "Explanation": "ad = ( a + 1 ) ( d + 1 ) - 13 0 = a + d - 12 a + d = 12 a = d ( as they are twin brothers ) a = d = 6 b is the answer" + }, + { + "Answer": 30, + "Options": "a ) 26 , b ) 32 , c ) 18 , d ) 20 , e ) 30", + "Correct": "e", + "Explanation": "i simply looked at the 3 different possible scores for each individual test : 18 , 32,26 we have to find the minimum range : 32 - 18 = 14 32 - 26 = 6 26 - 18 = 8 the find the minimum range , you have to make the set of the 5 scores as small as possible . which means that 4 of the 5 scores of each individual person is zero . 6 * 5 = 30 answer : e" + }, + { + "Answer": 1, + "Options": "a ) 0 , b ) 1 , c ) 37 , d ) 118 , e ) 513", + "Correct": "b", + "Explanation": "\"at first we should understand whether 759325 divisible by 15 . 15 is equal to 3 * 5 so 759325 should be divisible on these integers 759325 is divisible by 5 because of last digit 5 but not divisible by 3 because sum of its digits does n ' t divisible by 3 : 7 + 5 + 9 + 3 + 2 + 5 = 31 and 31 does n ' t divisible by 3 so 759325 can be divisible by 15 ^ k only if k = 0 and 15 ^ k = 1 so 3 ^ k - k ^ 3 = 1 - 0 = 1 answer is b\"" + }, + { + "Answer": 0.125, + "Options": "a ) 1 / 3 , b ) 1 / 6 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 5", + "Correct": "d", + "Explanation": "\"must be once on heads and twice on tails 1 / 2 * 1 / 2 * 1 / 2 = 1 / 8 answer : d\"" + }, + { + "Answer": 160, + "Options": "a ) 80 , b ) 120 , c ) 160 , d ) 270 , e ) 110", + "Correct": "c", + "Explanation": "\"sum of the marks for the 10 students = 10 * 80 = 800 . the marks of each student are doubled , the sum also will be doubled . the new sum = 800 * 2 = 1600 . so , the new average = 1600 / 10 = 160 . answer : c\"" + }, + { + "Answer": 13, + "Options": "a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15", + "Correct": "c", + "Explanation": "100 - ( 100 - 83 ) - ( 100 - 75 ) - ( 100 - 85 ) - ( 100 - 70 ) = 100 - 17 - 25 - 15 - 30 = 100 - 87 = 13 answer : c" + }, + { + "Answer": 0.625, + "Options": "a ) 1 / 4 , b ) 3 / 8 , c ) 1 / 2 , d ) 5 / 8 , e ) 59 / 94", + "Correct": "e", + "Explanation": "\"n ( n + 1 ) ( n + 2 ) will be divisible by 8 when n is a multiple of 2 or when ( n + 1 ) is a multiple of 8 . thus when n is even , this whole expression will be divisible by 8 . from 1 to 96 , there are 47 even integers . now when ( n + 1 ) is multiple by 8 , we have 12 such values for ( n + 1 ) probability that n ( n + 1 ) ( n + 2 ) will be divisible by 8 = ( 47 + 12 ) / 94 = 59 / 94 = 5 / 8 ans is e\"" + }, + { + "Answer": 8, + "Options": "a ) a ) 10 , b ) b ) 8 , c ) c ) 6 , d ) d ) 4 , e ) e ) 2", + "Correct": "b", + "Explanation": "x = 10 - 2 y x = 10 - 2 . x = 8 answer : b" + }, + { + "Answer": 25, + "Options": "a ) 10 , b ) 25 , c ) 50 , d ) 75 , e ) 100", + "Correct": "b", + "Explanation": "\"surprisingly no one answered this easy one . property of a set of consecutive integerz . mean = median = ( first element + last element ) / 2 = ( second element + last but one element ) / 2 = ( third element + third last element ) / 2 etc . etc . so mean = median = 50 / 2 = 25 answer is b\"" + }, + { + "Answer": 1, + "Options": "a ) 3 , b ) 2 , c ) 1 , d ) 1 / 2 , e ) 1 / 3", + "Correct": "c", + "Explanation": "since a , b and c are positive integers less than 4 we have the following possibilities : 4 ^ a = 416 , or 64 3 ^ b = 39 , or 27 2 ^ c = 24 , or 8 trial and error gives us quite quick the solution of 4 ^ a = 64 3 ^ b = 9 2 ^ c = 4 64 + 9 + 4 = 77 i . e . c = 2 and b = 2 - - - - > b / c = 1 / 1 = 1 the correct answer is c" + }, + { + "Answer": 15, + "Options": "a ) 28 , b ) 27 , c ) 11 , d ) 15 , e ) 19", + "Correct": "d", + "Explanation": "explanation : let ' k ' be the total number of sweets . given total number of students = 112 if sweets are distributed among 112 children , let number of sweets each student gets = ' l ' = > k / 112 = l . . . . ( 1 ) but on that day students absent = 32 = > remaining = 112 - 32 = 80 then , each student gets ' 6 ' sweets extra . = > k / 80 = l + 6 . . . . ( 2 ) from ( 1 ) k = 112 l substitute in ( 2 ) , we get 112 l = 80 l + 480 32 l = 480 l = 15 therefore , 15 sweets were each student originally supposed to get . answer : d" + }, + { + "Answer": 10500, + "Options": "a ) 7000 , b ) 10500 , c ) 14000 , d ) 12000 , e ) 3500", + "Correct": "b", + "Explanation": "to determine the amount of calories allowed per day , you need to subtract 500 from 2000 , for a total of 1500 to determine the amount of calories allowed per week , you need to multiply the daily amount allowed ( 1500 ) by the number of days in a week ( 7 ) for a total of 10500 the correct answer is b" + }, + { + "Answer": 0.125, + "Options": "a ) 1 / 4 , b ) 1 / 8 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4", + "Correct": "b", + "Explanation": "\"because n ( n + 1 ) is always an even product of even * odd or odd * even factors , there is a probability of 1 that that it will be divisible by 2 , and , thus , a probability of 1 / 2 that it will be divisible by 4 and , thus , a probability of 1 / 4 that it will be divisible by 8 and , thus , a probability of 1 / 8 that it will be divisible by 16 1 * 1 / 8 = 1 / 8 answer : b\"" + }, + { + "Answer": 5.25, + "Options": "a ) 21 / 4 , b ) 35 , c ) 28 , d ) 26 , e ) 21", + "Correct": "a", + "Explanation": "x / y = 2 / 5 - > 1 ( x + 3 ) / 2 y = 1 / 3 - > 2 divide 1 by 2 : = > 2 x / ( x + 3 ) = 6 / 5 = > 10 x = 6 x + 18 = > x = 3 / 2 = > y = 5 / 2 * 3 / 2 = 15 / 4 so x + y = 21 / 4 the answer is a" + }, + { + "Answer": 24, + "Options": "a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28", + "Correct": "c", + "Explanation": "the bacteria doubles each day , so after 29 days , the dish was half full . after 28 days , the dish was one quarter full . after 27 days , the dish was one eighth full . after 26 days , the dish was one sixteenth full . after 25 days , the dish was 1 / 32 full . after 24 days , the dish was 1 / 64 full . the answer is c ." + }, + { + "Answer": 14, + "Options": "a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 14", + "Correct": "e", + "Explanation": "concept : a number will be divisible by 3 if sum of all the digits of the number is divisible by 3 here the possible sum of the two distinct digits can be 3 , 6 , 9 and 12 only in order to satisfy the given condition if sum of digits = 3 , no . = 12 , 21 - - - 2 cases if sum of digits = 6 , no . = 15 , 24 , 42 , 51 - - - 4 cases if sum of digits = 9 , no . = 27 , 36 , 45 , 54 , 63 , 72 - - - 6 cases if sum of digits = 12 , no . = 57 , 75 - - - 2 cases total cases = 2 + 4 + 6 + 2 = 14 cases answer : option e" + }, + { + "Answer": 450, + "Options": "a ) 400 , b ) 450 , c ) 500 , d ) 550 , e ) 600", + "Correct": "b", + "Explanation": "\"10 * 150 = 1500 3 * 100 + 5 * 150 = 1050 1500 \u2013 1050 = 450 b\"" + }, + { + "Answer": 50, + "Options": "a ) 20 , b ) 40 , c ) 60 , d ) 80 , e ) 50", + "Correct": "e", + "Explanation": "say , if speed is 60 , 300 / 50 = 6 hrs and 300 / 60 = 5 hrs ( a reduction of 1 hr - > correct answer ) answer ( e )" + }, + { + "Answer": 15, + "Options": "a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16", + "Correct": "d", + "Explanation": "p / 3 + f / 4 = p / 3 + ( 48 - p ) / 4 = 12 + p / 2 p / 3 + f / 3 = ( p + f ) / 3 = 48 / 3 = 16 p / 4 + f / 4 = 12 p / 3 + f / 3 > p / 3 + f / 4 > p / 4 + f / 4 - - > 16 > 12 + p / 12 > 12 greatest possible w : 12 + p / 12 = 15 - - > p = 36 ( integer - - > good ) 15 or d is the answer" + }, + { + "Answer": 385, + "Options": "a ) $ 374 , b ) $ 382 , c ) $ 385 , d ) $ 392 , e ) $ 399", + "Correct": "c", + "Explanation": "\"soln : - ( 406 / 116 ) 110 = 385 in this case long division does not take much time . ( 406 / 116 ) = 3.5 35 * 11 = 385 ( 350 + 35 ) answer : c\"" + }, + { + "Answer": 66, + "Options": "a ) a ) 66 , b ) b ) 77 , c ) c ) 79 , d ) d ) 81 , e ) e ) 82", + "Correct": "a", + "Explanation": "\"required average = 6 ( 1 + 2 + . . . . + 21 ) / 21 ( 6 / 21 ) x ( ( 21 x 22 ) / 2 ) ( because sum of first 21 natural numbers ) = 66 a\"" + }, + { + "Answer": 42, + "Options": "a ) 42 , b ) 84 , c ) 48 , d ) 24 , e ) 43", + "Correct": "a", + "Explanation": "let the numbers be x and x + 2 . then , ( x + 2 ) 2 - x 2 = 84 4 x + 4 = 84 4 x = 80 x = 20 . the required sum = x + ( x + 2 ) = 2 x + 2 = 42 . answer a 42" + }, + { + "Answer": 24.000000000000004, + "Options": "a ) 6 % , b ) 24 % , c ) 37 1 / 2 % , d ) 60 % , e ) 75 %", + "Correct": "b", + "Explanation": "\"just plug and chug . since the question asks for percents , pick 100 . ( but any number will do . ) 100 / 5 + 100 / 25 = 20 + 4 = 24 24 is 24 % of 100 = b\"" + }, + { + "Answer": 2018, + "Options": "a ) 2018 , b ) 2088 , c ) 270 , d ) 1881 , e ) 1781", + "Correct": "a", + "Explanation": "\"f ( f ( 0 ) ) + f ( 0 ) = 2 ( 0 ) + 3 \u21d2 \u21d2 f ( 1 ) = 3 - 1 = 2 , f ( 1 ) = 2 f ( f ( 1 ) ) + f ( 1 ) = 2 ( 1 ) + 3 \u21d2 \u21d2 f ( 2 ) = 5 - 2 = 3 , f ( 2 ) = 3 f ( f ( 2 ) ) + f ( 2 ) = 2 ( 2 ) + 3 \u21d2 \u21d2 f ( 3 ) = 7 - 3 = 4 , f ( 3 ) = 4 . . . . . . . . . . . . . . f ( 2017 ) = 2018 ans : a\"" + }, + { + "Answer": 0.7999999999999998, + "Options": "a ) 1.8 , b ) 1.4 , c ) 1.2 , d ) 1.0 , e ) 0.8", + "Correct": "e", + "Explanation": "in 4 gallons of the solution there are 0.9 \u2217 4 = 3.80 gallons of glycerin . we want to add ww gallons of water to 4 gallons of solution so that these 3.6 gallons of glycerin to be 75 % of new solution : 0.9 \u2217 4 = 0.75 ( 4 + w ) - - > w = 0.8 answer : e ." + }, + { + "Answer": 82265.625, + "Options": "a ) 81000 , b ) 81007 , c ) 81008 , d ) 81066 , e ) 82265.6", + "Correct": "e", + "Explanation": "\"65000 * 9 / 8 * 9 / 8 = 82265.6 answer : e\"" + }, + { + "Answer": 0.33333333333333326, + "Options": "a ) 1 / 12 , b ) 1 / 9 , c ) 2 / 3 , d ) 1 / 3 , e ) 2 1 / 9", + "Correct": "d", + "Explanation": "\"total bought = 3 / 8 + 1 / 3 left part 15 / 40 - - - > 3 / 8 so used part 3 / 8 + 1 / 3 - 3 / 8 = 1 / 3 ans d\"" + }, + { + "Answer": 42, + "Options": "a ) 54 sec , b ) 48 sec , c ) 42 sec , d ) 70 sec , e ) 60 sec", + "Correct": "c", + "Explanation": "at 6 ' 0 clock , clock ticks 6 times . so , there must be 5 intervals between clock ticks . time between first and last ticks = 30 sec so , 1 interval = 30 / 5 = 6 sec so 6 ' o clock 5 * 6 = 30 sec 7 ' o clock 6 * 6 = 36 sec 8 ' o clock 7 * 6 = 42 sec so , 42 sec at 8 ' o clock . answer : c" + }, + { + "Answer": 72, + "Options": "a ) 72 , b ) 75 , c ) 81 , d ) 84 , e ) 88", + "Correct": "a", + "Explanation": "9 * 8 = 72 the answer is a ." + }, + { + "Answer": 58, + "Options": "a ) 20 , b ) 36 , c ) 48 , d ) 50 , e ) 58", + "Correct": "e", + "Explanation": "\"production during these 5 days = total production in a month - production in first 25 days . = 30 x 68 - 25 x 70 = 290 \u2234 average for last 5 days = 290 / 5 = 58 e\"" + }, + { + "Answer": 1.75, + "Options": "a ) 3.42 , b ) 6.16 , c ) 8.32 , d ) 2.0 , e ) 1.75", + "Correct": "e", + "Explanation": "this is a good question to understand the difference between mean and median . mean : average of all the numbers . ( sum of all the elements divided by the number of elements ) median : arrange the elements of the set in increasing order . if the number of terms is odd , the middle term is the median . if the number of terms is even , the average of middle two terms is the median coming to this question , mean = ( 22 + 25 + 30 + 40 ) / 4 = 29.25 median = ( 25 + 30 ) / 2 = 27.5 total = 1.75 option e" + }, + { + "Answer": 8.5, + "Options": "a ) 7.5 , b ) 8.5 , c ) 9 , d ) 9.5 , e ) 10", + "Correct": "b", + "Explanation": "let son ' s present age be a years . then , ( 25 \u2212 a ) = a \u21d2 2 a = 25 \u21d2 a = 25 / 2 = 12.5 son ' s age 4 years back = 12.5 - 4 = 8.5 answer : b" + }, + { + "Answer": 4.5, + "Options": "a ) $ 3.15 , b ) $ 4.5 , c ) $ 4.80 , d ) $ 5.05 , e ) $ 5.40", + "Correct": "b", + "Explanation": "\"let the fixed charge of jim \u2019 s taxi service = 2.25 $ and charge per 2 / 5 mile ( . 4 mile ) = . 25 $ total charge for a trip of 3.6 miles = 2.25 + ( 3.6 / . 4 ) * . 25 = 2.25 + 9 * . 25 = 4.5 $ answer b\"" + }, + { + "Answer": 60, + "Options": "a ) a ) 60 , b ) b ) 150 , c ) c ) 130 , d ) d ) 90 , e ) e ) 210", + "Correct": "a", + "Explanation": "let x be the total number of pages in the book , then she finished 2 / 3 * x pages . then she has x \u2212 2 / 3 * x = 1 / 3 * x pages left . 2 / 3 * x \u2212 1 / 3 * x = 20 1 / 3 * x = 20 x = 60 so the book is 270 pages long . answer is a ." + }, + { + "Answer": 26, + "Options": "a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28", + "Correct": "c", + "Explanation": "26 answer : c" + }, + { + "Answer": 14, + "Options": "a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15", + "Correct": "d", + "Explanation": "\"four wheeler = 14 * 4 = 56 ( max ) 2 wheel = 1 so no of 4 wheeler = 14 answer : d\"" + }, + { + "Answer": 400, + "Options": "a ) 420 , b ) 400 , c ) 430 , d ) 410 , e ) 450", + "Correct": "b", + "Explanation": "\"explanation : average price of a goat = rs . 70 total price of 8 goats = 10 * 70 = rs . 700 but total price of 2 cows and 8 goats = rs . 1500 total price of 2 cows is = 1500 - 700 = 800 average price of a cow = 800 / 2 = rs . 400 answer : b\"" + }, + { + "Answer": 9, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10", + "Correct": "d", + "Explanation": "\"x < y < z to find the least possible value for z - x ; we need to find the values for z and x that can be closest to each other . if x is some even number , then what could be minimum possible odd z . if x is some even number y - x > 5 ; y > x + 5 ; minimum value for y = x + 5 + 2 = x + 7 [ note : x + 5 is as even + odd = odd and nearest odd greater than x + 5 is x + 5 + 2 ] minimum value for z = y + 2 = x + 7 + 2 = x + 9 [ note : z = y + 2 because both z and y are odd . difference between two odd numbers is 2 ] f = z - x = x + 9 - x = 9 ans : d\"" + }, + { + "Answer": 180, + "Options": "a ) 180 , b ) 185 , c ) 190 , d ) 160 , e ) 165", + "Correct": "a", + "Explanation": "1 - 60 5 - 15 - 25 - 35 - 45 are valid multiples of 5 . add them 5 + 15 + 25 + 35 + 45 + 55 = 180 a" + }, + { + "Answer": 0.625, + "Options": "a ) 1 / 4 , b ) 3 / 8 , c ) 1 / 2 , d ) 5 / 8 , e ) 3 / 4", + "Correct": "d", + "Explanation": "for w total numbers 8 * 12 there are 12 numbers divisible by 8 - > 3 * 12 ( if 8 is an example - ( 6 , 78 ) , ( 7 , 89 ) , ( 8 , 910 ) ) and 12 numbers divisible by 4 but not divisible by 8 - > 2 * 12 ( if 4 is an example ( 2 , 34 ) and ( 4 , 56 ) ) the answer 5 / 8 - > d" + }, + { + "Answer": 0.3333333333333333, + "Options": "a ) 1 / 3 , b ) 2 / 5 , c ) 3 / 10 , d ) 3 / 7 , e ) 1 / 7", + "Correct": "a", + "Explanation": "here , s = [ 1 , 2 , 3 , 4 , \u2026 . , 19 , 20 , 21 , 22 , 23 , 24 ] let e = event of getting a multiple of 3 = [ 3 , 6 , 9 , 12 , 15 , 18 , 21 , 24 ] p ( e ) = n ( e ) / n ( s ) = 8 / 24 = 1 / 3 the answer is a ." + }, + { + "Answer": 72, + "Options": "a ) 33 , b ) 54 , c ) 18 , d ) 17 , e ) 72", + "Correct": "e", + "Explanation": "\"explanation : as there is meal for 70 adults and 14 have their meal , the meal left can be catered to 56 adults . now , 70 adults = 90 children 7 adults = 9 children therefore , 56 adults = 72 children hence , the meal can be catered to 72 children . answer : e\"" + }, + { + "Answer": 36, + "Options": "a ) 10 % , b ) 20 % , c ) 25 % , d ) 36 % , e ) 50 %", + "Correct": "d", + "Explanation": "let original salary be $ 100 salary after decreasing 60 % = 100 - 100 x 60 / 100 = $ 40 salary after increasing 60 % on $ 40 = 40 + 40 x 60 / 100 = $ 64 percentage of loss = 100 - 64 = 36 % answer : d" + }, + { + "Answer": 44, + "Options": "a ) 44 , b ) 5 , c ) 10 , d ) 15 , e ) 20", + "Correct": "a", + "Explanation": "x = \u221a 11 and y also = \u221a 11 applying the function ( \u221a 11 + \u221a 11 ) ^ 2 - ( \u221a 11 - \u221a 11 ) ^ 2 = ( 2 \u221a 11 ) ^ 2 - 0 = 4 x 11 = 44 . note : alternative approach is the entire function is represented as x ^ 2 - y ^ 2 = ( x + y ) ( x - y ) which can be simplified as ( x + y + x - y ) ( x + y - ( x - y ) ) = ( 2 x ) ( 2 y ) = 4 xy . substituting x = \u221a 11 and y = \u221a 11 you get the answer 44 . answer a" + }, + { + "Answer": 4200, + "Options": "a ) 3800 , b ) 4500 , c ) 5200 , d ) 3400 , e ) 4200", + "Correct": "e", + "Explanation": "\"following the above formula , we have the total marks = 120 * 35 = 4200 answer is e\"" + }, + { + "Answer": 35, + "Options": "a ) a ) 35 , b ) b ) 34 , c ) c ) 50 , d ) d ) 67 , e ) e ) 100", + "Correct": "a", + "Explanation": "\"its a . total juice rquired = 280 * 6 = 1680 ounce 12 ounce concentate makes = 12 * 4 = 48 ounce juice total cans required = 1680 / 48 = 35 . answer a\"" + }, + { + "Answer": 5, + "Options": "a ) 5 % , b ) 10 % , c ) 15 % , d ) 20 % , e ) it can not be determined", + "Correct": "a", + "Explanation": "\"solution : let the total number of flags be 100 ( even number ) let the total number of ' blue ' flags alone be ' a ' let the total number of ' red ' flags alone be ' b ' let the total number of ' both ' flags be ' c ' we have given , total number of blue flags = 60 % = 60 = a + c total number of red flags = 45 % = 45 = b + c total number of flags = a + b + c = 100 ( since all the flag have been utilized ) so , substituting for c in the third equation , we have , 60 - c + c + 45 - c = 100 c = 5 option a .\"" + }, + { + "Answer": 255, + "Options": "a ) 190 , b ) 255 , c ) 200 , d ) 205 , e ) 210", + "Correct": "b", + "Explanation": "this question can be solved with the average formula and ' bunching . ' we ' re asked for the average of all of the multiples of 10 from 10 to 500 , inclusive . to start , we can figure out the total number of terms rather easily : 1 ( 10 ) = 10 2 ( 10 ) = 20 . . . 50 ( 10 ) = 500 so we know that there are 50 total numbers . we can now figure out the sum of those numbers with ' bunching ' : 10 + 500 = 510 20 + 490 = 510 30 + 480 = 510 etc . since there are 50 total terms , this pattern will create 25 ' pairs ' of 510 . thus , since the average = ( sum of terms ) / ( number of terms ) , we have . . . ( 25 ) ( 510 ) / ( 50 ) = 255 final answer : b" + }, + { + "Answer": 1500, + "Options": "a ) 1500 , b ) 2677 , c ) 1997 , d ) 2677 , e ) 1971", + "Correct": "a", + "Explanation": "p = 15 ( 100 / 10 ) 2 = > p = 1500 answer : a" + }, + { + "Answer": 0.3333333333333333, + "Options": "a ) 1 / 4 , b ) 1 / 3 , c ) 3 / 8 , d ) 2 / 3 , e ) 1 / 2", + "Correct": "b", + "Explanation": "let assume that 1 st bottle capacity = 1 litre ; therefore , it contain 1 / 2 litre oil and 1 / 2 litre water . ( i . e ) water = 1 / 2 litre oil = 1 / 2 litre 2 nd bottle is twice the capacity i . e . 2 litre capacity it means , 1 / 2 litre filled with oil and 1 ( 1 / 2 ) litre filled with water . i . e . oil = 1 / 2 liter water = 1 ( 1 / 2 ) litre in total the third bottle will contain , 1 litre oil and 2 litre water . i . e . , oil = 1 litre water = 2 liter therefore , oil proportion is 1 / 3 answer : b" + }, + { + "Answer": 0.043478260869565216, + "Options": "a ) 1 / 190 , b ) 1 / 23 , c ) 1 / 19 , d ) 1 / 10 , e ) 1 / 9", + "Correct": "b", + "Explanation": "\"the problem with your solution is that we do n ' t choose 1 shoe from 24 , but rather choose the needed one after we just took one and need the second to be the pair of it . so , the probability would simply be : 1 / 1 * 1 / 23 ( as after taking one at random there are 23 shoes left and only one is the pair of the first one ) = 1 / 23 answer : b\"" + }, + { + "Answer": 120, + "Options": "a ) 26 , b ) 39 , c ) 120 , d ) 65 , e ) 156", + "Correct": "c", + "Explanation": "\"here 156 has three two ' s two three ' s and one 10 rest of them must be in w so w = 10 * 3 * 4 = 120 smash c\"" + }, + { + "Answer": 23, + "Options": "a ) 17 , b ) 19 , c ) 21 , d ) 23 , e ) 25", + "Correct": "d", + "Explanation": "\"total classes = 5 total students = 95 . average = 19 if the classes had average number of students : 19 19 19 19 19 given case = 23 21 19 17 15 hence number of students in the largest class = 23 correct option : d\"" + }, + { + "Answer": 10, + "Options": "a ) 3 , b ) 4 , c ) 10 , d ) 6 , e ) 7", + "Correct": "c", + "Explanation": "\"let x = 6.1 and y = 16.1 greatest possible difference = 16.1 - 6.1 = 10 answer c\"" + }, + { + "Answer": 19, + "Options": "a ) $ 13 , b ) $ 15 , c ) $ 17 , d ) $ 19 , e ) $ 21", + "Correct": "d", + "Explanation": "average price per book = ( 1380 + 900 ) / ( 65 + 55 ) = 2280 / 120 = $ 19 the answer is d ." + }, + { + "Answer": 38, + "Options": "a ) 20 , b ) 36 , c ) 48 , d ) 38 , e ) 59", + "Correct": "d", + "Explanation": "\"production during these 5 days = total production in a month - production in first 25 days . = 30 x 48 - 25 x 50 = 190 \u2234 average for last 5 days = 190 / 5 = 38 d\"" + }, + { + "Answer": 550, + "Options": "a ) 300 , b ) 600 , c ) 550 , d ) 1000 , e ) 900", + "Correct": "c", + "Explanation": "\"explanation : let their maximum marks be x . then , 40 % of x = 200 + 20 = > 40 / 100 x = 220 x = ( 22000 / 40 ) x = 550 . answer : c\"" + }, + { + "Answer": 8, + "Options": "a ) 25 , b ) 8 , c ) 27 , d ) 29 , e ) 39", + "Correct": "b", + "Explanation": "\"let the average after 17 innings = x total runs scored in 17 innings = 17 x average after 16 innings = ( x - 3 ) total runs scored in 16 innings = 16 ( x - 3 ) total runs scored in 16 innings + 56 = total runs scored in 17 innings = > 16 ( x - 3 ) + 56 = 17 x = > 16 x - 48 + 56 = 17 x = > x = 8 answer is b .\"" + }, + { + "Answer": 1.222222222222222, + "Options": "a ) 1 , b ) 4 / 3 , c ) 17 / 5 , d ) 11 / 9 , e ) 4", + "Correct": "d", + "Explanation": "we have two equations : 2 x + y = 6 x + 2 y = 5 notice that something nice happens when we add them . we get : 3 x + 3 y = 11 divide both sides by 3 to get : x + y = 11 / 3 so , ( x + y ) / 3 = 11 / 9 answer : d" + }, + { + "Answer": 4, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "e", + "Explanation": "this question asks what is . . . ( the answer ) , so we know that the answer will be consistent . as such , we can test values to quickly get the solution . we ' re told that m and n are positive integers and m = 15 n - 1 . we ' re asked for the remainder when m is divided by 5 . if . . . . n = 1 m = 14 14 / 5 = 2 remainder 4 final answer : e" + }, + { + "Answer": 500, + "Options": "a ) 350 , b ) 400 , c ) 500 , d ) 550 , e ) 590", + "Correct": "c", + "Explanation": "\"n * 50 = ( 325000 - 300000 ) = 25000 n = 25000 / 50 = 500 c\"" + }, + { + "Answer": 1, + "Options": "a ) 1 / 2 , b ) 1 , c ) 2 , d ) 5 / 2 , e ) 4", + "Correct": "b", + "Explanation": "step 1 : analyze the question for any question involving the equation of a line , a good place to start is the slope - intercept form of the line , y = mx 1 b . remember that if you have two points on a line , you can derive the entire equation , and if you have an equation of the line , you can calculate any points on that line . step 2 : state the task we are solving for k , which is the amount by which the y - coordinate increases when the x - coordinate increases by 2 . step 3 : approach strategically the slope of a line is the ratio between the change in y and the change in x . in other words , every time the x - coordinate increases by 1 , the y - coordinate increases by the amount of the slope . the equation of the line in the question stem is defined as x = 2 y + 5 . we must isolate y to have slope - intercept form : so the slope of this line is 1 / 2 . this means that for every change of + 1 in the x direction , there is a change of + 1 / 2 in the y direction . then we know that , because there is an increase in 2 units in the x direction when moving from m to m + 2 , there must be a change of 1 unit in the y direction when moving from n to n + k . so k = 1 . since there are variables that eventually cancel ( m and n are not part of the answers ) , we can pick numbers . let \u2019 s say that you choose the y - coordinate of the point ( m , n ) to be 0 to allow for easier calculations . using the equation we \u2019 re given to relate x - and y - coordinates , we can calculate the x - coordinate : so ( m , n ) is the point ( 5 , 0 ) . now we \u2019 ll plug our values of m and n into the next point : ( m + 2 , n + k ) . that yields ( 7 , k ) . all we have to do is plug an x - coordinate of 7 into the equation to solve for k , the y - coordinate : answer is b" + }, + { + "Answer": 0.25, + "Options": "a ) - 4 , b ) - 1 / 4 , c ) 0 , d ) 1 / 4 , e ) 4", + "Correct": "d", + "Explanation": "we ' re told that 625 ^ ( - x ) + 25 ^ ( - 2 x ) + 5 ^ ( - 4 x ) = 15 . we ' re asked for the value of x . since each of the calculated terms must be positive ( regardless of what the exponent is ) , we can use thebasesto our advantage . . . . . with answer a , we ' d have 625 ^ 4 , which is much bigger than 15 ( and we ' d be adding to that big number ) . eliminate a . with answer e , we ' d have 625 ^ ( - 4 ) , which would create a tiny fraction ( and we ' d add some other fractions to it , so the total would be much too small ) . eliminate e . with answer d , we ' d have 625 ^ ( - 1 / 4 ) , which will also be a fraction ( just not as tiny as the one in answer e ) , but the total would still be too small . eliminate d . with answer c , anything to the ' 0 power ' is 1 , so we ' d have 1 + 1 + 1 = 3 . this is not 15 . eliminate c . d" + }, + { + "Answer": 2704, + "Options": "a ) 76 , b ) 5776 , c ) 304 , d ) 2704 , e ) none", + "Correct": "d", + "Explanation": "\"answer let \u221a n / 13 = 4 then \u221a n = 13 x 4 = 52 \u2234 n = 52 x 52 = 2704 . correct option : d\"" + }, + { + "Answer": 29, + "Options": "a ) 29 , b ) 34 , c ) 44 , d ) 54 , e ) 64", + "Correct": "a", + "Explanation": "odd prime number less than 125 : 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 , 53 , 59 , 61 , 67 , 71 , 73 , 79 , 83 , 89 , 97 , 101 , 103 , 107 , 109 , 113 there is 29 the odd prime number answer is a" + }, + { + "Answer": 2.4, + "Options": "a ) 5 / 12 , b ) 7 / 12 , c ) 12 / 5 , d ) 7 / 5 , e ) 11 / 5", + "Correct": "c", + "Explanation": "\"1 / r = 1 / x + 1 / y 1 / r = 1 / 4 + 1 / 6 = 5 / 12 r = 12 / 5 the answer is c .\"" + }, + { + "Answer": 25, + "Options": "a ) 87 , b ) 27 , c ) 25 , d ) 26 , e ) 24", + "Correct": "c", + "Explanation": "\"let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 80 x - ( 5 * 40 ) = 90 ( x - 5 ) 250 = 10 x = > x = 25 answer : c\"" + }, + { + "Answer": 13, + "Options": "a ) - 4 , b ) - 2 , c ) 11 , d ) 13 , e ) 22", + "Correct": "d", + "Explanation": "\"the equation that can be formed is : 3 x - 16 = 36 - x or , 4 x = 52 or , x = 13 . answer : d\"" + }, + { + "Answer": 60, + "Options": "a ) 36 , b ) 46 , c ) 56 , d ) 59 , e ) 60", + "Correct": "e", + "Explanation": "5 ! / ( 5 - 3 ) ! = 5 ! / 2 ! = 5 * 4 * 3 = 60 . hence , the correct answer is e ." + }, + { + "Answer": 34, + "Options": "a ) 32 , b ) 33 , c ) 34 , d ) 45 , e ) 44", + "Correct": "c", + "Explanation": "x person , y chocolates 1 st equation = = > ( y - 1 ) / x = 1 2 nd equation = = > y / ( x - 1 ) = 2 solving we get x = 3 , y = 4 answer : c" + }, + { + "Answer": 244, + "Options": "a ) 190 , b ) 284.6 , c ) 300 , d ) 244 , e ) 312", + "Correct": "d", + "Explanation": "\"so 12.2 * 20 = 244 . . imo option d is correct answer . .\"" + }, + { + "Answer": 60.000000000000014, + "Options": "a ) 2 minutes , b ) 10 minutes , c ) 20 minutes , d ) 40 minutes , e ) 60 minutes", + "Correct": "e", + "Explanation": "lets take number of minutesx . given that , 9 + 0.25 x = 12 + 0.2 x - > 0.05 x = 2 - > x = 60 minutes ans e" + }, + { + "Answer": 40, + "Options": "a ) 20 inches , b ) 77 inches , c ) 66 inches , d ) 97 inches , e ) 40 inches", + "Correct": "e", + "Explanation": "explanation : total length of scale in inches = ( 6 * 12 ) + 8 = 80 inches length of each of the 2 parts = 80 / 2 = 40 inches answer : e" + }, + { + "Answer": 0.9999999999999858, + "Options": "a ) 1 % decrease , b ) 2 % increase , c ) 3 % decrease , d ) 4 % decrease , e ) none of these", + "Correct": "a", + "Explanation": "\"since tax consumption = revenue . therefore , net % change in revenue = ( x + y + xy / 100 ) % = [ - 10 + 10 + ( - 10 x 10 ) / 100 ] % or - 1 % . therefore , revenue decreased by 1 % . answer : a\"" + }, + { + "Answer": 89, + "Options": "a ) 88 ab , b ) - 89 ab , c ) 89 ab , d ) - 88 a , e ) - 88 b", + "Correct": "c", + "Explanation": "answer : c" + }, + { + "Answer": 4086, + "Options": "a ) 6084 , b ) 3788 , c ) 4086 , d ) 2721 , e ) 1812", + "Correct": "c", + "Explanation": "explanation : 1345 5431 - - - - - - - - - - - - 4086 answer : c" + }, + { + "Answer": 3, + "Options": "a ) 6 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "c", + "Explanation": "( a \u2013 b ) \u2013 ( c + d ) = 9 and ( c \u2013 d ) \u2013 ( a + b ) = 3 = > ( a \u2013 c ) \u2013 ( b + d ) = 9 and ( c \u2013 a ) \u2013 ( b + d ) = 3 = > ( b + d ) = ( a \u2013 c ) \u2013 9 and ( b + d ) = ( c \u2013 a ) \u2013 3 = > ( a \u2013 c ) \u2013 9 = ( c \u2013 a ) \u2013 3 = > 2 ( a \u2013 c ) = 6 = > ( a \u2013 c ) = 3 answer : c" + }, + { + "Answer": 27, + "Options": "a ) 27 , b ) 32 , c ) 35 , d ) 30 , e ) 45", + "Correct": "a", + "Explanation": "\"explanation : hcf ( 408 , 240 ) = 24 the number of boys or girls that can be placed in a section = 24 . thus the total number of sections is given by 408 / 24 + 240 / 24 = 17 + 10 = 27 answer : a\"" + }, + { + "Answer": 0.2222222222222222, + "Options": "a ) 1 / 9 , b ) 2 / 9 , c ) 4 / 9 , d ) 3 / 9 , e ) 2 / 27", + "Correct": "b", + "Explanation": "we just need to find the factor thats all , w - > quadrupled - > 4 w m - > doubled - > 2 m z - > tripled - > 3 z hence , z ^ 2 = 9 z ^ 2 w is in numerator , and m * z in denominator . hence , additional factor being introduced = 4 / 2 * 9 = 4 / 18 = 2 / 9 = b" + }, + { + "Answer": 0.25, + "Options": "a ) 1 / 4 , b ) 2 / 7 , c ) 5 / 12 , d ) 1 / 2 , e ) 7 / 12", + "Correct": "a", + "Explanation": "total savings = s amount spent on stereo = ( 1 / 4 ) s amount spent on television = ( 1 - 2 / 3 ) ( 1 / 4 ) s = ( 1 / 3 ) * ( 1 / 4 ) * s = ( 1 / 12 ) s ( stereo + tv ) / total savings = s ( 1 / 4 + 1 / 12 ) / s = 1 / 4 answer : a" + }, + { + "Answer": 125, + "Options": "a ) 12.5 % , b ) 40 % , c ) 80 % , d ) 125 % , e ) none", + "Correct": "d", + "Explanation": "\"solution 5 : 4 = 5 / 4 = ( 5 / 4 x 100 ) % . = 125 % . answer d\"" + }, + { + "Answer": 158, + "Options": "a ) 96 , b ) 106 , c ) 158 , d ) 116 , e ) 122", + "Correct": "c", + "Explanation": "\"average = total runs / no . of innings = 32 so , total = average x no . of innings = 32 * 20 = 640 now increase in avg = 4 runs . so , new avg = 32 + 6 = 38 runs total runs = new avg x new no . of innings = 38 * 21 = 798 runs made in the 11 th inning = 798 - 640 = 158 answer : c\"" + }, + { + "Answer": 100, + "Options": "a ) 0 , b ) 25 , c ) 50 , d ) 75 , e ) 100", + "Correct": "e", + "Explanation": "first even minus first odd = 2 - 1 = 1 ; the sum of first 2 even integers minus the sum of first 2 odd integers = ( 2 + 4 ) - ( 1 + 3 ) = 2 ; the sum of first 3 even integers minus the sum of first 3 odd integers = ( 2 + 4 + 6 ) - ( 1 + 3 + 5 ) = 3 ; we can see the patterns here , so the sum of first 100 positive even integers minus the sum of first 100 positive odd integers will be 100 . answer : e ." + }, + { + "Answer": 179.99999999999991, + "Options": "a ) $ 120 , b ) $ 150 , c ) $ 180 , d ) $ 210 , e ) $ 240", + "Correct": "c", + "Explanation": "\"3 : 2 = 9 : 6 and 5 : 3 = 10 : 6 . an increase in $ 30 increases the ratio by 1 : 6 . therefore , january ' s bill was 6 ( $ 30 ) = $ 180 . the answer is c .\"" + }, + { + "Answer": 0.8888888888888888, + "Options": "a ) 3 / 2 , b ) 3 / 4 , c ) 8 / 9 , d ) 1 / 2 , e ) 1 / 5", + "Correct": "c", + "Explanation": "\"let team b has 8 agents , so team a has 5 agents let each agent of team b picked up 5 calls , so total calls by team b = 40 so , each agent in team a picked up 1 calls , so total calls for team a = 5 fraction for team b = 40 / ( 40 + 5 ) = 8 / 9 = answer = c\"" + }, + { + "Answer": 37, + "Options": "a ) 50 min , b ) 40 min , c ) 35 min , d ) 37 min , e ) 20 min", + "Correct": "d", + "Explanation": "\"clearly , the two will meet when they are 1000 m apart to be 20 + 17 = 37 km apart , they take 1 hour to be 1000 m apart , they take 37 * 1000 / 1000 = 37 min . answer is d\"" + }, + { + "Answer": 72, + "Options": "a ) 72 , b ) 44 , c ) 80 , d ) 88 , e ) 48", + "Correct": "a", + "Explanation": "\"according to the given conditions x + y = 18 and x ^ 2 + y ^ 2 = 180 now ( x + y ) ^ 2 = x ^ 2 + y ^ 2 + 2 xy so 18 ^ 2 = 180 + 2 xy so xy = 144 / 2 = 72 answer : a\"" + }, + { + "Answer": 62, + "Options": "a ) 49 , b ) 53 , c ) 56 , d ) 59 , e ) 62", + "Correct": "e", + "Explanation": "let s be the number of small jars and let l be the number of large jars . s + l = 100 . l = 100 - s . 3 s + 5 l = 376 . 3 s + 5 ( 100 - s ) = 376 . - 2 s + 500 = 376 . 2 s = 124 . s = 62 . the answer is e ." + }, + { + "Answer": 1636, + "Options": "a ) 1235 , b ) 1456 , c ) 1567 , d ) 1636 , e ) 1635", + "Correct": "d", + "Explanation": "\"let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 10 5 x = 1355 x = 271 large number = 271 + 1365 = 1636 d\"" + }, + { + "Answer": 1, + "Options": "a ) 2 , b ) 7 , c ) 6 , d ) 1 , e ) 9", + "Correct": "d", + "Explanation": "\"explanation : 45 + 31 = 76 / 15 = 1 ( remainder ) answer : d\"" + }, + { + "Answer": 360000, + "Options": "a ) a - 352000 , b ) b - 356000 , c ) c - 360000 , d ) d - 348000 , e ) e - 340000", + "Correct": "c", + "Explanation": "he is saving \u00e2 \u00a3 500 per month . he needs \u00e2 \u00a3 45000 and it takes \u00e2 \u00a3 45000 / \u00e2 \u00a3 500 = 90 months to save the money . in 90 months , he earns 90 * \u00e2 \u00a3 4000 = \u00e2 \u00a3 36000 . answer : c" + }, + { + "Answer": 60, + "Options": "a ) 60 , b ) 70 , c ) 75 , d ) 84 , e ) 90", + "Correct": "a", + "Explanation": "there were 36 * 5 = 180 total votes made . if each voter picked 3 coaches , there were 180 / 3 = 60 voters . a" + }, + { + "Answer": 101.99999999999999, + "Options": "a ) 96 , b ) 98 , c ) 100 , d ) 102 , e ) 104", + "Correct": "d", + "Explanation": "\"let x be the original weight of the grapes . the weight of the grape pulp was 0.1 x . since the grape pulp is 85 % of the raisins , 0.1 x = 0.85 ( 12 kg ) . then x = 8.5 * 12 = 102 kg . the answer is d .\"" + }, + { + "Answer": 18, + "Options": "a ) 10 , b ) 12 , c ) 18 , d ) 19 , e ) 20", + "Correct": "c", + "Explanation": "\"sp = 17 loss = cp 18 loss = cp \u2212 sp = cp \u2212 17 \u21d2 cp 18 = cp \u2212 17 \u21d2 17 cp 18 = 17 \u21d2 cp 18 = 1 \u21d2 cp = 18 c\"" + }, + { + "Answer": 10, + "Options": "a ) 8 , b ) 9 , c ) 11 , d ) 7 , e ) 10", + "Correct": "e", + "Explanation": "10 because after 10 wickets , the innings is complete . answer : e" + }, + { + "Answer": 256, + "Options": "a ) 256 , b ) 4 , c ) \u221a 2 , d ) 16 , e ) none", + "Correct": "a", + "Explanation": "answer ? ) 1 / 2 = ( 5568 / 87 ) 1 / 3 + ( 72 x 2 ) 1 / 2 = ( 64 ) 1 / 3 + ( 144 ) 1 / 2 \u2234 ? = ( 4 + 12 ) 2 = 256 correct option : a" + }, + { + "Answer": 82, + "Options": "a ) 42 , b ) 43 , c ) 44 , d ) 82 , e ) 46", + "Correct": "d", + "Explanation": "\"let \u2018 x \u2019 be the average score after 12 th innings \u21d2 12 x = 11 \u00d7 ( x \u2013 4 ) + 115 \u2234 x = 82 answer d\"" + }, + { + "Answer": 60, + "Options": "a ) 60 % , b ) 40 % , c ) 80 % , d ) 125 % , e ) none", + "Correct": "a", + "Explanation": "\"solution 3 : 5 = 3 / 5 = ( 3 / 5 x 100 ) % . = 60 % . answer a\"" + }, + { + "Answer": 400.000000000039, + "Options": "a ) 300 , b ) 375 , c ) 400 , d ) 460 , e ) 500", + "Correct": "c", + "Explanation": "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 142.07 here 142 is the quotient . given that remainder = 28 so , 142.07 = 142 + 28 / j so , j = 400 answer - c" + }, + { + "Answer": 16500, + "Options": "a ) 16000 , b ) 16500 , c ) 17000 , d ) 17500 , e ) 18000", + "Correct": "b", + "Explanation": "total number of preferred shares = 1200 face value = rs . 50 dividend paid on preferred shares is 10 % dividend per share = 50 \u00d7 10 / 100 = rs . 5 total dividend = 1200 \u00d7 5 = 6000 total number of common shares = 3000 face value = rs . 50 semi - annual dividend of 3 \u00bd % is declared on common shares . semi - annual dividend per share = 50 \u00d7 7 / 2 \u00d7 100 = rs . 74 total semi - annual dividend = 7 / 4 \u00d7 3000 = rs . 5250 annual dividend = rs . 5250 \u00d7 2 = rs . 10500 total dividend on all all shares ( preferred and common ) = 6000 + 10500 = rs . 16500 answer is b ." + }, + { + "Answer": 108.45000000000003, + "Options": "a ) 108.45 , b ) 110.45 , c ) 106.45 , d ) 109.45 , e ) none of them", + "Correct": "a", + "Explanation": "= 12.05 * ( 5.4 / 0.6 ) = ( 12.05 * 9 ) = 108.45 answer is a ." + }, + { + "Answer": 9, + "Options": "a ) 5 , b ) 7 , c ) 8 , d ) q = 9 , e ) 10", + "Correct": "d", + "Explanation": "mode of list ii = 3 median q of list ii = 4 + 6 / 2 = 5 sum of mode + mean = 3 + 5 = 8 now to make 8 as the median we need to find a value of y such that if the no . of terms in list 1 are odd then y = 8 else if even then 7 + y / 2 = 8 here its even so 7 + y / 2 = 8 from this y = 9 ( d )" + }, + { + "Answer": 19, + "Options": "a ) - 29 , b ) - 19 , c ) 19 , d ) 29 , e ) 39", + "Correct": "c", + "Explanation": "\"45 - [ 28 - { 37 - ( 15 - * ) } ] = 58 = > 45 - [ 28 - { 37 - 15 + * } ] = 58 45 - [ 28 - 37 + 15 - * ] = 58 = > 45 [ 43 - 37 - * ] = 58 45 - [ 6 - * ] = 58 = > 45 - 6 + * = 58 39 + * = 58 = > * = 58 - 39 = 19 answer : c\"" + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 10 , c ) 15 , d ) 25 , e ) 35", + "Correct": "a", + "Explanation": "\"total applicants = 40 political science = 15 and non political science = 40 - 15 = 25 gpa > 3.0 = 20 and gpa < = 3.0 = 20 10 non political science students had gpa < = 3.0 - - > 15 non political science students had gpa > 3.0 gpa > 3.0 in political science = total - ( gpa > 3.0 in non political science ) r = 20 - 15 = 5 answer : a\"" + }, + { + "Answer": 150, + "Options": "a ) 210 , b ) 150 , c ) 280 , d ) 300 , e ) 420", + "Correct": "b", + "Explanation": "\"however the process of dividing the volume of box by the volume of a soap seems flawed but it does work in this case due to the numbers dimensions of the box = 25 * 42 * 60 dimensions of the soap = 5 * 12 * 7 placing the 7 inch side along 42 inch side we get 6 soaps in a line and in a similar way 5 along 25 and 6 along 60 we get = 5 x 6 x 5 = 150 so the question is why this particular arrangement , in order to maximize number of soaps we need to minimize the space wasted and this is the only config where we dont waste any space so we can expect the maximum number the answer is ( b )\"" + }, + { + "Answer": 900, + "Options": "a ) 872 , b ) 738 , c ) 900 , d ) 840 , e ) 83", + "Correct": "c", + "Explanation": "\"25 % of x = x / 4 ; 15 % of 1600 = 15 / 100 * 1600 = 240 given that , x / 4 = 240 - 15 = > x / 4 = 225 = > x = 900 . answer : c\"" + }, + { + "Answer": 4687.5, + "Options": "a ) 100 , b ) 250 , c ) 750 , d ) 4687.5 , e ) 5635.5", + "Correct": "d", + "Explanation": "\"6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 50 * 25 * 1 / 2 = 625 feet ^ 3 of milk must be removed , which equals to 625 * 7.5 = 4687.5 gallons . answer : d .\"" + }, + { + "Answer": 20, + "Options": "a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) none of them", + "Correct": "b", + "Explanation": "reduction in consumption = [ ( ( r / ( 100 + r ) ) * 100 ] % = [ ( 25 / 125 ) * 100 ] % = 20 % . answer is b ." + }, + { + "Answer": 12, + "Options": "a ) 4 , b ) 6 , c ) 12 , d ) 16 , e ) 24", + "Correct": "c", + "Explanation": "since the phone number must be even , the unit ' s digit can be either 2 or 8 . when the unit ' s digit is 2 - - > number of possibilities is 3 ! = 6 when the unit ' s digit is 8 - - > number of possibilities is 3 ! = 6 largest number of extensions = 6 + 6 = 12 answer : c" + }, + { + "Answer": 35.89743589743589, + "Options": "a ) 20 % , b ) 24 % , c ) 28 % , d ) 32 % , e ) 36 %", + "Correct": "e", + "Explanation": "\"let p be the original price per unit of gas . let x be the original gas consumption . let y be the reduced gas consumption . y * 1.2 * 1.3 * p = x * p y = x / ( 1.2 * 1.3 ) which is about 0.64 x which is a decrease of about 36 % . the answer is e .\"" + }, + { + "Answer": 8, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", + "Correct": "b", + "Explanation": "\"2 m = 24 - m 3 m = 24 m = 8 the answer is b .\"" + }, + { + "Answer": 24, + "Options": "a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 24", + "Correct": "e", + "Explanation": "ifno caris selected more than once then the number of clients = 16 / 2 = 8 but since every car is being selected three times so no . of clients must be thrice as well = 8 * 3 = 24 answer : option e" + }, + { + "Answer": 4.285714285714286, + "Options": "a ) 30 / 7 , b ) 30 / 9 , c ) 30 / 2 , d ) 30 / 3 , e ) 30 / 6", + "Correct": "a", + "Explanation": "\"required fraction = l . c . m of 6 / 7 , 5 / 14 , 10 / 21 = ( l . c . m of 6 , 5 , 10 ) / ( h . c . f of 7 , 14 , 21 ) = 30 / 7 answer : a\"" + }, + { + "Answer": 2, + "Options": "a ) 5 : 2 , b ) 2 : 1 , c ) 11 : 7 , d ) 13 : 9 , e ) none of these", + "Correct": "b", + "Explanation": "solution let the present ages of the father and son be 7 x and 3 x years respectively . then , 7 x 3 x = 756 \u21d4 21 x 2 = 756 \u21d4 x 2 = 36 \u21d4 x = 6 . \u2234 required ratio = ( 7 x + 6 ) : ( 3 x + 6 ) = 48 : 24 = 2 : 1 . answer b" + }, + { + "Answer": 0.8, + "Options": "a ) 0.8 , b ) 1.0 , c ) 1.2 , d ) 1.4 , e ) 1.6", + "Correct": "a", + "Explanation": "first , get the middle coordinate between ( 46 ) and ( 62 ) . x = 4 + ( 6 - 4 ) / 2 = 5 y = 2 + ( 6 - 2 ) / 2 = 4 second , get the slope of ( 54 ) and ( 00 ) . m = 4 - 0 / 5 - 0 = 4 / 5 = 0.8 answer : a" + }, + { + "Answer": 5, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 9 , e ) 5", + "Correct": "e", + "Explanation": "\"as per question = > n = 11 p + 1 for some integer p hence 5 n = > 55 q + 5 = > remainder = > 5 for some integer q hence e\"" + }, + { + "Answer": 18, + "Options": "a ) 17 years , b ) 19 years , c ) 18 years , d ) 10 years , e ) 12 years", + "Correct": "c", + "Explanation": "\"let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 47 5 x = 45 = > x = 9 hence , b ' s age = 2 x = 18 years . answer : c\"" + }, + { + "Answer": 65818408915, + "Options": "a ) 65842158943 , b ) 65839570421 , c ) 65821141683 , d ) 66821785904 , e ) 65821041783", + "Correct": "e", + "Explanation": "\"658217 x 99999 = 658217 x ( 100000 - 1 ) = 658217 x 100000 - 658217 x 1 = 65821700000 - 658217 = 65821041783 e\"" + }, + { + "Answer": 139, + "Options": "a ) 130 , b ) 132 , c ) 134 , d ) 136 , e ) 139", + "Correct": "e", + "Explanation": "\"let the required number be x . then , 43 x \u2013 34 x = 1251 or 9 x = 1251 or x = 139 . required number = 139 . answer : e\"" + }, + { + "Answer": 16, + "Options": "a ) 15 , b ) 11 , c ) 18 , d ) 16 , e ) 20", + "Correct": "d", + "Explanation": "d 16 let the present ages of peter and jacob be ' a ' and ' b ' respectively . a - 10 = 1 / 3 ( b - 10 ) - - - ( 1 ) b = a + 12 substituting b = a + 12 in first equation , a - 10 = 1 / 3 ( a + 2 ) = > 3 a - 30 = a + 2 = > 2 a = 32 = > a = 16 ." + }, + { + "Answer": 120.00000000000003, + "Options": "a ) $ 60 , b ) $ 80 , c ) $ 90 , d ) $ 120 , e ) $ 180", + "Correct": "d", + "Explanation": "let ' s let t = total number of dollars spent at the supermarket . with this variable we can set up an equation and determine t . we are given that john spent 1 / 2 of his money on fresh fruits and vegetables , or ( 1 / 2 ) t , 1 / 3 on meat products , or ( 1 / 3 ) t , and 1 / 10 on bakery products , or ( 1 / 10 ) t . we are also given that he spent the remaining $ 8 on candy . since we know where all his money was allocated , we can sum these values together and set the sum to t . so we have : ( 1 / 2 ) t + ( 1 / 3 ) t + ( 1 / 10 ) t + 8 = t to get rid of the fractions we can multiply the entire equation by 30 , and we obtain : 15 t + 10 t + 3 t + 240 = 30 t 28 t + 240 = 30 t 240 = 2 t t = 120 john spent $ 90 at the supermarket . answer : d" + }, + { + "Answer": 0.5, + "Options": "a ) 3 / 2 , b ) - 1 / 2 , c ) - 1 , d ) 1 / 2 , e ) 2 / 3", + "Correct": "d", + "Explanation": "here is my solution . 5 ^ ( x + 1 ) * 4 ^ ( y - 1 ) = 25 ^ x * 64 ^ y here rhs 25 ^ x * 64 ^ y = 5 ^ ( 2 x ) * 4 ^ ( 3 y ) equating powers on both sides - - > x + 1 = 2 x , thus x = 1 and 2 y - 1 = 3 y giving y = - 1 / 2 so , x + y = 1 / 2 option : d" + }, + { + "Answer": 7, + "Options": "a ) 0 , b ) 1 , c ) 5 , d ) 7 , e ) 9", + "Correct": "d", + "Explanation": "i looked for patterns : ^ 2 - units digit 9 ^ 3 - units digit 7 ^ 4 - units digit 1 ^ 5 - units digit 3 hence , we can see that when raised to a power which is multiple of 4 , the units digit is 1 , and when to an even power not multiple of 4 , the units digit is 9 and we can then see : ^ 16 - units digit 1 , or ^ 18 - units digit 9 and ^ 19 - units digit 7 therefore , e = when divided by 10 , the remainder must be 7 . d" + }, + { + "Answer": 22.5, + "Options": "a ) 71.5 , b ) 11.5 , c ) 81.5 , d ) 11.5 , e ) 22.5", + "Correct": "e", + "Explanation": "explanation : middle numbers = [ ( 10.5 x 6 + 11.4 x 6 ) - 9.9 x 11 ] = 22.5 . answer : e" + }, + { + "Answer": 384, + "Options": "a ) 164 , b ) 224 , c ) 280 , d ) 384 , e ) 476", + "Correct": "d", + "Explanation": "\"there are 2 ^ 3 = 8 possibilities for the true - false answers . however we need to remove two cases for ttt and fff . there are 4 * 4 * 4 = 64 possibilities for the multiple choice questions . the total number of possibilities is 6 * 64 = 384 . the answer is d .\"" + }, + { + "Answer": 144, + "Options": "a ) 26 , b ) 39 , c ) 42 , d ) 144 , e ) 156", + "Correct": "d", + "Explanation": "\"here 156 has three two ' s two three ' s and one 13 rest of them must be in w so w = 12 * 3 * 4 = 144 smash d\"" + }, + { + "Answer": 20, + "Options": "a ) 17 , b ) 20 , c ) 21 , d ) 24 , e ) 25", + "Correct": "b", + "Explanation": "\"average of 21 numbers = 0 . sum of 21 numbers ( 0 x 21 ) = 0 . it is quite possible that 20 of these numbers may be positive and if their sum is a then 21 st number is ( - a ) answer is 20 ( b )\"" + }, + { + "Answer": 225, + "Options": "a ) 648 , b ) 300 , c ) 252 , d ) 225 , e ) 26", + "Correct": "d", + "Explanation": "there are 100 numbers which begin with 600 next , in every 10 numbers such as 100 to 110 , 110 to 120 , 120 to 130 6 comes at least once . number of such intervals = end limit - first no . / interval . our range of numbers is 100 - 1000 1000 - 100 = 900 / 10 = 90 number of 10 s interval in this is 90 . so 90 ' 6 s ' so far we have calculated 190 . the total now comes to 280 . the nearest to which is 225 . hence d ." + }, + { + "Answer": 24, + "Options": "a ) 24 , b ) 25 , c ) 48 , d ) 50 , e ) none", + "Correct": "a", + "Explanation": "\"answer sum of 50 result = sum of 30 result + sum of 20 result . = 30 x 20 + 20 x 30 = 1200 correct option : a\"" + }, + { + "Answer": 5040, + "Options": "a ) 5050 , b ) 5020 , c ) 5040 , d ) 5030 , e ) 5075", + "Correct": "c", + "Explanation": "\"let the total amount be rs . x the , x / 14 - x / 18 = 80 = = > 2 x / 126 = 80 = = > x / 63 = 63 x 80 = 5040 . hence the total amount is 5040 . answer c .\"" + }, + { + "Answer": 25, + "Options": "a ) 2 , b ) 3 , c ) 1 , d ) 10 , e ) 25", + "Correct": "e", + "Explanation": "explanation : 2 ^ 3 = 2 * 2 * 2 = 8 5 ^ 2 = 5 * 5 = 25 6 ^ 1 = 6 * 1 = 6 hence 5 ^ 2 is the largest one answer : e" + }, + { + "Answer": 22, + "Options": "a ) 36 - 48 , b ) 22 - 34 , c ) 60 - 24 , d ) 42 - 42 , e ) 21 - 63", + "Correct": "b", + "Explanation": "\"in this problem , we are asked to find two numbers . therefore , we must let x be one of them . let x , then , be the first number . we are told that the other number is 12 more , x + 12 . the problem states that their sum is 56 : word problem = 56 the line over x + 12 is a grouping symbol called a vinculum . it saves us writing parentheses . we have : 2 x = 56 \u00e2 \u02c6 \u2019 12 = 44 . x = 44 / 2 = 22 . this is the first number . therefore the other number is x + 12 = 22 + 12 = 34 . the sum of 22 + 34 is 56 . b\"" + }, + { + "Answer": 221.2357, + "Options": "a ) 229.3657 , b ) 229.7563 , c ) 229.6357 , d ) 229.5637 , e ) 221.2357", + "Correct": "e", + "Explanation": "217 2.017 0.217 + 2.0017 - - - - - - - - 221.2357 - - - - - - - - - answer is e ." + }, + { + "Answer": 6, + "Options": "a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12", + "Correct": "b", + "Explanation": "\"let dan ' s present age be x . x + 18 = 8 ( x - 3 ) 7 x = 42 x = 6 the answer is b .\"" + }, + { + "Answer": 19, + "Options": "a ) 20 , b ) 24 , c ) 19 , d ) 28 , e ) 30", + "Correct": "c", + "Explanation": "\"( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 99 + 2 * 131 a + b + c = \u221a 361 = 19 c\"" + }, + { + "Answer": 19, + "Options": "a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20", + "Correct": "d", + "Explanation": "11 yellow + 7 purple + after that we have only one option that is to be blue so answer is 19 answer : d" + }, + { + "Answer": 36, + "Options": "a ) 12 , b ) 15 , c ) 18 , d ) 36 , e ) 24", + "Correct": "d", + "Explanation": "the list should be wmwmw . hence , from women 3 ! and men 3 ! , we get ( 3 ! ) ( 3 ! ) = 36 . therefore , the correct answer is d ." + }, + { + "Answer": 1764, + "Options": "a ) 1764 , b ) 1774 , c ) 1784 , d ) 1794 , e ) 1754", + "Correct": "a", + "Explanation": "\"sum of 1 st n odd no . s = 1 + 3 + 5 + 7 + . . . = n ^ 2 so , sum of 1 st 42 odd numbers = 42 ^ 2 = 1764 answer : a\"" + }, + { + "Answer": 12, + "Options": "a ) 10 , b ) 11 , c ) 12 , d ) can not be determined , e ) none of the above", + "Correct": "c", + "Explanation": "\"since average price of a pencil = 2 \u2234 price of 75 pencils = 150 \u2234 price of 30 pens = ( 510 \u2013 150 ) = 360 \u2234 average price of a pen = 360 \u2044 60 = 12 answer c\"" + }, + { + "Answer": 4, + "Options": "a ) 0.039 , b ) 0.235 , c ) 0.25 , d ) 4 , e ) 5", + "Correct": "d", + "Explanation": "solution given expression = ( a + b ) \u00b2 - ( a - b ) \u00b2 / ab = 4 ab / ab = 4 . answer d" + }, + { + "Answer": 7391, + "Options": "a ) s . 4991 , b ) s . 5991 , c ) s . 6001 , d ) s . 6991 , e ) s . 7391", + "Correct": "e", + "Explanation": "\"total fr 5 mnths = ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs 34009 . reqd . sale = rs . [ ( 6900 * 6 ) - 34009 ] = rs . ( 41400 - 34009 ) = rs . 7391 . answer : e\"" + }, + { + "Answer": 0.675, + "Options": "a ) 1 / 5 , b ) 2 / 8 , c ) 5 / 9 , d ) 27 / 40 , e ) 15 / 30", + "Correct": "d", + "Explanation": "the amount spent by the company on raw material is 1 / 4 , so remaining is 3 / 4 . 1 / 10 of the remaining is spent on machinery , 1 / 10 * 3 / 4 = 3 / 40 total amount spent on raw material and machinery is 1 / 4 + 3 / 40 to make the denominator common we use 40 , so 1 / 4 is 10 / 40 10 / 40 + 3 / 40 = 13 / 40 is spent on raw material and machinery remaining 27 / 40 is left with the company answer is d" + }, + { + "Answer": 7.999999999999999, + "Options": "a ) 12 , b ) 8 , c ) 16 , d ) 6 , e ) 2", + "Correct": "b", + "Explanation": "given that x = y = z . so , x = y , x = 2 z , y = 2 z . given xyz = 256 = > ( 2 z ) * ( 2 z ) * z = 256 = > 4 z ^ 3 = 256 = > z = 4 then x = 2 z = 2 ( 4 ) = 8 answer : b" + }, + { + "Answer": 31, + "Options": "a ) 31 , b ) 32 , c ) 43 , d ) 45 , e ) 26", + "Correct": "a", + "Explanation": "\"explanation : 4 \u00e3 \u2014 5 + 5 \u00e3 \u2014 4 = ( 2 \u00e3 \u2014 4 - 3 \u00e3 \u2014 5 + 4 \u00e3 \u2014 5 ) + ( 2 \u00e3 \u2014 5 - 3 \u00e3 \u2014 4 + 5 \u00e3 \u2014 4 ) = ( 8 - 15 + 20 + 10 - 12 + 20 ) = 31 . answer : a\"" + }, + { + "Answer": 69930, + "Options": "a ) 699990 , b ) 99990 , c ) 99980 , d ) 69300 , e ) none of these", + "Correct": "d", + "Explanation": "explanation : required difference = 70000 - 700 = 69300 answer is d" + }, + { + "Answer": 22.666666666666668, + "Options": "a ) 17 litres , b ) 22.67 litres , c ) 11 litres , d ) 07 litres , e ) 38.67 litres", + "Correct": "b", + "Explanation": "\"262.85 ( 34 ) + 3 , 104.35 x = 1 , 399.45 ( 34 + x ) solve the equation . 262.85 ( 34 ) + 3 , 104.35 x = 1 , 399.45 ( 34 + x ) 8936.9 + 3 , 104.35 x = 47 , 581.3 + 1 , 399.45 x 8936.9 + 1 , 704.9 x = 47 , 581.3 1 , 704.9 x = 38 , 644.40 x \u2248 22.67 answer is b .\"" + }, + { + "Answer": 60, + "Options": "a ) 48 , b ) 50 , c ) 60 , d ) 75 , e ) 100", + "Correct": "c", + "Explanation": "this can be solve in two steps and without any complex calculation . given : equation of line s as y = ( 4 / 3 ) x - 100 . so the line intercept the axes at ( 0 , - 100 ) and ( 75,0 ) . this can be considered a right angle triangle with right angle at ( 0,0 ) . so base = 100 , height = 75 and hypotenuse = 125 ( by pythagoras triplet ) so a perpendicular from the ( 0,0 ) to hypotenuse will be the answer . area of triangle = 0.5 * 100 * 75 = 0.5 * 125 * x = > x = 60 ; so answer is 60 = c" + }, + { + "Answer": 5.15, + "Options": "a ) $ 5.15 , b ) $ 4.45 , c ) $ 4.80 , d ) $ 5.05 , e ) $ 5.40", + "Correct": "a", + "Explanation": "\"let the fixed charge of jim \u00e2 \u20ac \u2122 s taxi service = 2 $ and charge per 2 / 5 mile ( . 4 mile ) = . 35 $ total charge for a trip of 3.6 miles = 2 + ( 3.6 / . 4 ) * . 35 = 2 + 9 * . 35 = 5.15 $ answer a\"" + }, + { + "Answer": 2, + "Options": "a ) 1 , b ) 2 , c ) 6 , d ) 8 , e ) 9", + "Correct": "b", + "Explanation": "let the ten ' s and unit digit be x and 8 respectively . x then , 10 x + 8 + 18 = 10 x 8 + x x x 10 x 2 + 8 + 18 x = 80 + x 2 9 x 2 + 18 x - 72 = 0 x 2 + 2 x - 8 = 0 ( x + 4 ) ( x - 2 ) = 0 x = 2 option b" + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) 15 , c ) 16 , d ) 17 , e ) 18", + "Correct": "a", + "Explanation": "\"12 , 15 , 18 , 21 , 24 , 27 , 30 , 33 , 36 , 39 , 42 , 45 , . 12 numbers . 10 / 3 = 3 and 47 / 3 = 15 = = > 15 - 3 = 12 . therefore 12 digits a )\"" + }, + { + "Answer": 5.400000000000006, + "Options": "a ) $ 14 , b ) $ 5.4 , c ) $ 4.4 , d ) $ 1.2 , e ) $ 5.0", + "Correct": "b", + "Explanation": "\"sale price ( sp ) = 81 + markup ( mp ) - - > mp = sp - 81 and given mp = sp / 4 ( 25 % is 1 / 4 th ) so sp / 4 = sp - 81 3 sp / 4 = 81 sp = 108 now a discount of 20 % is given so new sp is . 8 * 108 = 86.4 profit = 86.4 - 81 = 5.4 $ answer is b\"" + }, + { + "Answer": 30.76923076923077, + "Options": "a ) 18.75 % , b ) 23 % , c ) 30 % , d ) 31 % , e ) 100 %", + "Correct": "d", + "Explanation": "\"let wage of erica = 10 wage of robin = 1.3 * 10 = 13 wage of charles = 1.7 * 10 = 17 percentage by which wage earned by charles is more than that earned by robin = ( 17 - 13 ) / 13 * 100 % = 4 / 13 * 100 % = 31 % answer d\"" + }, + { + "Answer": 0.08571428571428572, + "Options": "a ) 3 / 35 , b ) 2 / 3 , c ) 7 / 35 , d ) 5 / 7 , e ) 7 / 5", + "Correct": "a", + "Explanation": "\"let a be the event that ram is selected and b is the event that ravi is selected . p ( a ) = 3 / 7 p ( b ) = 1 / 5 let c be the event that both are selected . p ( c ) = p ( a ) x p ( b ) as a and b are independent events : = 3 / 7 x 1 / 5 = 3 / 35 answer : a\"" + }, + { + "Answer": 540, + "Options": "a ) 540 km , b ) 767 km , c ) 276 km , d ) 178 km , e ) 176 km", + "Correct": "a", + "Explanation": "\"explanation : let us assume that trains meet after ' x ' hours distance = speed * time distance traveled by two trains = 20 x km and 25 x km resp . as one train travels 60 km more than the other , 25 x \u2013 20 x = 60 5 x = 60 x = 12 hours as the two trains are moving towards each other , relative speed = 20 + 25 = 45 km / hr therefore , total distance = 45 * 12 = 540 km . answer : a\"" + }, + { + "Answer": 23, + "Options": "a ) 12 , b ) 27 , c ) 23 , d ) 28 , e ) 11", + "Correct": "c", + "Explanation": "let the numbers be x , x + 1 , x + 2 , x + 3 , x + 4 , x + 5 and x + 6 , then ( x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) + ( x + 4 ) + ( x + 5 ) + ( x + 6 ) ) / 7 = 20 . or 7 x + 21 = 140 or 7 x = 119 or x = 17 . latest number = x + 6 = 23 . answer : c" + }, + { + "Answer": 6, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9", + "Correct": "b", + "Explanation": "let qt + t + q = x add 1 on both sides : qt + t + q + 1 = x + 1 tq + 1 ) + q + 1 = x + 1 ( q + 1 ) ( t + 1 ) = x + 1 minimum value of ( q + 1 ) = 2 minimum value of ( t + 1 ) = 2 hence x + 1 can not be prime substitute x from the given options : 6 + 1 = 7 - - > prime - - > qt + t + s can not be 6 answer : b" + }, + { + "Answer": 26.961111111111112, + "Options": "a ) $ 30.14 , b ) 45.14 , c ) 34.66 , d ) 26.96 , e ) 33.16", + "Correct": "d", + "Explanation": "\"211 * 15 = 3165 / 100 = 31.65 211 + 31.65 = 242.65 242.65 / 9 = 26.96 answer : d\"" + }, + { + "Answer": 7.8500000000000005, + "Options": "a ) $ 7.85 , b ) $ 11.30 , c ) $ 13.20 , d ) $ 17.80 , e ) $ 22.10", + "Correct": "a", + "Explanation": "pa = price of a pb = price of b ta = time for a to complete the job tb = time for b to complete the job given pa = 1.4 pb ta + 20 = tb pa * ta = pb * tb = 550 1.4 pb * ( tb - 20 ) = pb * tb 1.4 pb tb - pb tb = 1.4 pb * 20 0.4 pbtb = 28 pb tb = 28 / 0.4 = 70 pb = 550 / 70 ~ 7.85 a" + }, + { + "Answer": 0.2777777777777778, + "Options": "a ) 5 / 18 , b ) 6 / 24 , c ) 7 / 24 , d ) 8 / 24 , e ) 9 / 24", + "Correct": "a", + "Explanation": "\"p = 4 / 8 , q = 4 / 18 = > q = 2 / 9 therefore p - q = ( 1 / 2 ) - ( 2 / 9 ) = 5 / 18 answer : a\"" + }, + { + "Answer": 7, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "e", + "Explanation": "\"in 21 liters of drink a , there are 12 liters of milk and 9 liters of juice . with 12 liters of milk , we need a total of 16 liters of juice to make drink b . we need to add 7 liters of juice . the answer is e .\"" + }, + { + "Answer": 100011, + "Options": "a ) 100009 , b ) 100010 , c ) 100011 , d ) 100015 , e ) 100017", + "Correct": "c", + "Explanation": "the smallest 6 - digit number 100000 . 111 ) 100000 ( 900 999 - - - - - 100 - - - required number = 100000 + ( 111 - 100 ) = 100011 option c" + }, + { + "Answer": 2.8124999999999996, + "Options": "a ) $ 2.40 , b ) $ 2.80 , c ) $ 3.20 , d ) $ 3.60 , e ) $ 4.80", + "Correct": "b", + "Explanation": "total allowance = x amount spent at the arcade = 3 / 5 x amount remaining = 2 / 5 x amount spent at the toy store = 2 / 5 * 1 / 3 x = 2 / 15 x amount remaining = 2 / 5 x - 2 / 15 x = 4 / 15 x now , 4 / 15 x = $ 0.8 therefore , x = $ 2.80 . answer b" + }, + { + "Answer": 75, + "Options": "a ) 65 , b ) 69 , c ) 75 , d ) none of these , e ) can not be determined", + "Correct": "c", + "Explanation": "\"solution : average = ( 76 + 65 + 82 + 67 + 85 ) / 5 = 375 / 5 = 75 . hence , average = 75 . answer : option c\"" + }, + { + "Answer": 10.000000000000009, + "Options": "a ) 10 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 35 %", + "Correct": "a", + "Explanation": "\"1990 dick saved = $ 2200 jane saved = $ 1800 ( jane saved $ 200 less than she did the prior year ) jane saved approximately $ 200 / 2000 $ ( 10 % ) less in 1990 answer : a\"" + }, + { + "Answer": 4, + "Options": "a ) 3 , b ) 4 , c ) 2 , d ) 1 , e ) 5", + "Correct": "b", + "Explanation": "here is my solution . 7 ^ ( 3 x - 1 ) * 3 ^ ( 4 y - 3 ) = 49 ^ x * 27 ^ y here rhs 49 ^ x * 27 ^ y = 7 ^ ( 2 x ) * 3 ^ ( 3 y ) equating powers on both sides - - > 3 x - 1 = 2 x , thus x = 1 and 4 y - 3 = 3 y giving y = 3 so , x + y = 4 option : b" + }, + { + "Answer": 62, + "Options": "a ) 87 , b ) 16 , c ) 62 , d ) 76 , e ) 17", + "Correct": "c", + "Explanation": "\"average after 11 innings = 22 required number of runs = ( 33 * 11 ) - ( 18 * 10 ) = 242 - 180 = 62 . answer : c\"" + }, + { + "Answer": 147, + "Options": "a ) 35 , b ) 42 , c ) 45 , d ) 147 , e ) 54", + "Correct": "d", + "Explanation": "\"first step will be to break down all the numbers into their prime factors . 105 = 3 * 5 * 7 21 = 7 * 3 25 = 5 * 5 15 = 3 * 5 so , ( 105 ) ^ 3 = 3 * 7 * 5 * 5 * 3 * 5 * b therefore ( 3 * 5 * 7 ) ^ 3 = 3 ^ 2 * 5 ^ 3 * 7 * b therefore , b = 3 ^ 3 * 5 ^ 3 * 7 ^ 3 / 3 ^ 2 * 5 ^ 3 * 7 b = 3 * 7 ^ 2 = 3 * 49 = 147 correct answer d .\"" + }, + { + "Answer": 1, + "Options": "a ) 4 , b ) 3 , c ) 2 , d ) 1 , e ) 0", + "Correct": "d", + "Explanation": "we get 2 quadratic equations here . . 1 ) x ^ 2 - x - 1 = 0 . . . . . . . roots 2 , - 1 2 ) x ^ 2 + x - 1 = 0 . . . . . . . . roots - 2 , 1 inserting each root in given equation , it can be seen that - 1 and - 2 do not satisfy the equations . so value of x for given equation . . . . x = 2 or x = 1 i guess range is 2 - 1 = 1 d" + }, + { + "Answer": 728, + "Options": "a ) 727 , b ) 728 , c ) 758 , d ) 748 , e ) 792", + "Correct": "b", + "Explanation": "from 1 to 99 = 19 integers having 1 from 101 to 199 = all are having 1 similarly 201 - 299 , 301 - 399 , 401 - 499 , . . . . . so on , will have 19 integers having 1 answer = 1000 - ( 19 * 9 + 99 + 2 ) / / 2 is added for 100 and 1000 = 728 answer : b" + }, + { + "Answer": 12, + "Options": "a ) 24 , b ) 18 , c ) 16 , d ) 12 , e ) 8", + "Correct": "d", + "Explanation": "\"4 machines do x units in 6 days we have x / 6 = > rate of the 4 machines we know that we need to have 4 x units in 6 days therefore , we need to get to 4 x / 6 rate of the machines . rate of one machine is x / 6 * 1 / 4 = x / 24 . now , we need to know how many machines need to work simultaneously , to get 3 x done in 6 days . 3 x / 6 work needs to be done by machines that work at x / 24 rate . let ' s assign a constant y for the number of machines : ( x / 24 ) * y = 3 x / 6 y = 3 x / 6 * 24 / x cancel 6 with 24 , and x with x and get - > 12 . answer choice d\"" + }, + { + "Answer": 43, + "Options": "a ) 42 , b ) 43 , c ) 44 , d ) 45 , e ) 46", + "Correct": "b", + "Explanation": "\"let \u2018 x \u2019 be the average score after 12 th innings \u21d2 12 x = 11 \u00d7 ( x \u2013 2 ) + 65 \u2234 x = 43 answer b\"" + }, + { + "Answer": 4, + "Options": "a ) 4 , b ) 7 , c ) 8 , d ) 5 , e ) 3", + "Correct": "a", + "Explanation": "\"explanation : let the number be x . then , ( x - 5 ) / 7 = 7 = > x - 5 = 49 x = 54 . : ( x - 14 ) / 10 = ( 54 - 14 ) / 10 = 4 answer : option a\"" + }, + { + "Answer": 3, + "Options": "a ) 2 , b ) 4 , c ) 5 , d ) 3 , e ) 7", + "Correct": "d", + "Explanation": "\"ratio 1 : 3 w = x ratio 2 : 3 w = 2 y x = 2 y ( x + y ) / y = ( 2 y + y ) / y = y ( 2 + 1 ) / y = 3 answer is d\"" + }, + { + "Answer": 20.833333333333332, + "Options": "a ) 15 % , b ) 25 % , c ) 12.5 % , d ) 20.83 % , e ) none", + "Correct": "d", + "Explanation": "\"only trick n this question is to ignore 60 % information as farm tax is levied uniformly in the village and that includes mr william ' s land . what percentage of tax mr william paid ? this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 500 / 4000 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 60 ) = 20.833 % and the answer is not there in the options . the correct answer is ( d ) .\"" + }, + { + "Answer": 87, + "Options": "a ) 56 , b ) 65 , c ) 75 , d ) 89 , e ) 87", + "Correct": "e", + "Explanation": "\"a + b + c = 3 * 60 = 180 a + b + c + d = 4 * 65 = 260 - - - - ( i ) so , d = 80 & e = 80 + 3 = 83 b + c + d + e = 64 * 4 = 256 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 260 \u2013 256 = 4 a = e + 4 = 83 + 4 = 87 answer : e\"" + }, + { + "Answer": 37.89473684210526, + "Options": "a ) 38 kmph , b ) 33 kmph , c ) 34 kmph , d ) 35 kmph , e ) 36 kmph", + "Correct": "a", + "Explanation": "\"avg speed = total distance / total time . total distance traveled = 100 + 50 = 150 km ; time taken for uphill journey = 100 / 30 = 10 / 3 ; time taken for down hill journey = 50 / 80 = 5 / 8 ; avg speed = 150 / ( 10 / 3 + 5 / 8 ) = 38 kmph answer : a\"" + }, + { + "Answer": 5, + "Options": "a ) a . 5 , b ) b . 8 , c ) c . 10 , d ) d . 12 , e ) e . 16", + "Correct": "a", + "Explanation": "\"you might think of this in a management context - we can use the principle of ' person - hours ' to solve any problem where we have identical workers . so , using simpler numbers , suppose you know that 6 identical employees , working simultaneously , would finish a job in 5 hours . then that job requires 6 * 5 = 30 total hours of person - work . if instead you wanted the job done in 3 hours , you ' d assign 30 / 3 = 10 employees to do the job , because you want to get a total of 30 hours of work from the employees . we can solve this problem identically . if 15 machines ( identical ones , i assume ) work simultaneously for 36 days , they will do a total of 15 * 36 machine - days of work . so the job requires 15 * 36 days of machine work in total . we instead want the job done in 1 / 4 less time , so in 27 days . so we ' ll need 15 * 36 / 27 = 20 machines , or 5 additional machines . a\"" + }, + { + "Answer": 0.4, + "Options": "a ) 0.2 , b ) 0.3 , c ) 0.4 , d ) 0.5 , e ) 0.6", + "Correct": "c", + "Explanation": "\"we are selecting from non - negative single digit integers , so from { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } . these 10 digits represent the total number of outcomes . hence , the total number of outcomes is 10 . we need to find the probability that the median of the set will increase but the range still remains the same . the median of the set is ( 3 + 6 ) / 2 = 4.5 , thus the number selected must be 5 or greater . for the range to remain the same , the number must be between 2 and 8 inclusive . to satisfy both conditions , the number selected must be 5 , 6 , 7 , or 8 . the probability is 4 / 10 = 0.4 the answer is c .\"" + }, + { + "Answer": 12, + "Options": "a ) 2 , b ) 8 , c ) 12 , d ) 21 , e ) 35", + "Correct": "c", + "Explanation": "\"solution - simply substitute 2 and 3 in equation in the place of a and b respectively . 2 # 3 = 2 * 3 - 3 + 3 ^ 2 = 6 - 3 + 9 = 12 . ans c\"" + }, + { + "Answer": 56, + "Options": "a ) 56 , b ) 52 , c ) 51 , d ) 50 , e ) 49", + "Correct": "a", + "Explanation": "125 - 70 + 1 = 56 ' a ' is the answer" + }, + { + "Answer": 1, + "Options": "a ) 0 , b ) 1 , c ) 42 , d ) 118 , e ) 242", + "Correct": "b", + "Explanation": "\"4 + 3 + 5 + 9 + 6 + 1 = 28 , so this number is not divisible by 3 and thus not divisible by 21 . therefore , k = 0 7 ^ k - k ^ 7 = 1 - 0 = 1 the answer is b .\"" + }, + { + "Answer": 110, + "Options": "a ) 85 , b ) 86.5 , c ) 90 , d ) 88.5 , e ) 110", + "Correct": "e", + "Explanation": "\"total increase in weight = 10 x 4 = 40 if x is the weight of the new person , total increase in weight = x \u2212 70 = > 40 = x - 70 = > x = 40 + 70 = 110 answer : e\"" + }, + { + "Answer": 27, + "Options": "a ) 25 , b ) 27 , c ) 29 , d ) 31 , e ) 32", + "Correct": "b", + "Explanation": "explanation : let the numbers are x , x + 2 , x + 4 , x + 6 , then = > x + ( x + 2 ) + ( x + 4 ) + ( x + 6 ) / 4 = 24 = > 4 x + 12 ) / 4 = 24 = > x + 3 = 24 = > x = 21 so largest number is 21 + 6 = 27 option b" + }, + { + "Answer": 1800, + "Options": "a ) 1600 , b ) 1800 , c ) 1900 , d ) 2000 , e ) 2500", + "Correct": "b", + "Explanation": "tax for the year 1996 = 2108 surcharge add : 200 ie 2000 - 200 = 1800 1800 * 6 % = 108 + 2000 = 2108 so the answer is b" + }, + { + "Answer": 40.00000000000002, + "Options": "a ) 10 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 40 %", + "Correct": "e", + "Explanation": "\"given voters in ratio 2 : 1 let x has 200 votersy has 100 voters for x 76 % voted means 76 * 200 = 152 votes combined for xy has 300 voters and voted 64 % so total votes = 192 balance votes = 192 - 152 = 40 as y has 100 voters so 40 votes means 40 % of votes required ans e\"" + }, + { + "Answer": 10, + "Options": "a ) 8 , b ) 6 , c ) 10 , d ) 4 , e ) 3", + "Correct": "c", + "Explanation": "4 ^ 2 * 4 ^ 2 * 4 ^ 2 * 4 ^ 2 * 4 ^ 2 = 4 ^ ( 2 + 2 + 2 + 2 + 2 ) = 4 ^ 10 answer : 10 option : c" + }, + { + "Answer": 24, + "Options": "a ) 17 , b ) 24 , c ) 21 , d ) 23 , e ) 25", + "Correct": "b", + "Explanation": "\"average of 25 numbers = 0 . sum of 25 numbers ( 0 x 25 ) = 0 . it is quite possible that 24 of these numbers may be positive and if their sum is a then 25 th number is ( - a ) answer is 24 ( b )\"" + }, + { + "Answer": 2450, + "Options": "a ) 2984 , b ) 2983 , c ) 2982 , d ) 2450 , e ) none of these", + "Correct": "d", + "Explanation": "\"2500 - 50 = 2450 answer : d\"" + }, + { + "Answer": 180.83333333333331, + "Options": "a ) a ) 165 , b ) b ) 220 , c ) c ) 310 , d ) d ) 185 , e ) e ) 181", + "Correct": "e", + "Explanation": "loan amount : rs . 15000 / - @ 11.5 % interest per month = 15000 / - * 11.5 % = rs . 1725 interest for one day = 1725 / 30 = 57.50 interest for 7 days is = 57.50 * 7 = 403 fd amount is = rs . 10000 / - @ 9.5 % interest per month = 10000 * 9.5 % = 950 / - interest for 7 days = 950 / 30 * 7 = 222 interest amount to be paid by solomon = 403 - 222 = 181 / - for 7 days answer is e" + }, + { + "Answer": 31, + "Options": "a ) 88 , b ) 27 , c ) 36 , d ) 31 , e ) 12", + "Correct": "d", + "Explanation": "\"speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 190 + 120 = 310 m . time taken = 310 / 10 = 31 sec . answer : d\"" + }, + { + "Answer": 61.47540983606557, + "Options": "a ) 69.55 $ , b ) 50.63 $ , c ) 60.95 $ , d ) 52.15 $ , e ) 53.15 $", + "Correct": "c", + "Explanation": "\"let x is the cost of the food 1.07 x is the gross bill after including sales tax 1.15 * 1.07 x = 75 x = 60.95 hence , the correct option is c\"" + }, + { + "Answer": 188, + "Options": "a ) a ) 188 , b ) b ) 65 , c ) c ) 58 , d ) d ) 62 , e ) e ) 48", + "Correct": "a", + "Explanation": "\"6 th number = sum of 1 st 6 no . s + sum of last 6 no . s - sum of 11 no . s answer = 6 * 58 + 6 * 65 - 11 * 50 = 188 answer is a\"" + }, + { + "Answer": 300000, + "Options": "a ) $ 180,000 , b ) $ 202,000 , c ) $ 220,000 , d ) $ 300,000 , e ) $ 2 , 200,000", + "Correct": "d", + "Explanation": "answer : d , ( with different approach ) : the 200 paid is 0.2 % of the additional amount above 200,000 . let it be x now 0.2 % of x = 200 therefore x = 100,000 total = 200,000 + x = 300,000" + }, + { + "Answer": 1495, + "Options": "a ) 1234 , b ) 1345 , c ) 1456 , d ) 1567 , e ) 1499", + "Correct": "e", + "Explanation": "\"let the smaller number be x . then larger number = ( x + 1200 ) . x + 1200 = 5 x + 4 4 x = 1196 x = 299 large number = 299 + 1200 = 1499 e\"" + }, + { + "Answer": 991, + "Options": "a ) 901 , b ) 989 , c ) 990 , d ) 991 , e ) 1,001", + "Correct": "d", + "Explanation": "james = ( 0.5 / 100 ) * 2000 = 10 votes to win = ( 50 / 100 ) * total votes + 1 = ( 50 / 100 ) * 2000 + 1 = 1001 remaining voted needed to win election = 1001 - 10 = 991 answer : option d" + }, + { + "Answer": 44, + "Options": "a ) 22 , b ) 33 , c ) 44 , d ) 66 , e ) 99", + "Correct": "c", + "Explanation": "\"x / ( 11 p ) = even prime number x = even prime number * 11 p least value of x = lowest even prime number * 11 * lowest value of p = 2 * 11 * 2 = 44 answer c\"" + }, + { + "Answer": 9, + "Options": "a ) 5 , b ) 7 , c ) 8 , d ) r = 9 , e ) 10", + "Correct": "d", + "Explanation": "mode of list ii = 3 median r of list ii = 4 + 6 / 2 = 5 sum of mode + mean = 3 + 5 = 8 now to make 8 as the median we need to find a value of y such that if the no . of terms in list 1 are odd then y = 8 else if even then 7 + y / 2 = 8 here its even so 7 + y / 2 = 8 from this y = 9 ( d )" + }, + { + "Answer": 193.33333333333334, + "Options": "a ) $ 28 , b ) $ 82 , c ) $ 110 , d ) $ 138 , e ) $ 194", + "Correct": "e", + "Explanation": "\"by the question , the equation would be 150 p - 84 * 150 - 16500 = 0 p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component . solving the equation , we get p = $ 194 . answer e for me .\"" + }, + { + "Answer": 12, + "Options": "a ) 6 , b ) 12 , c ) 14 , d ) 16 , e ) 28", + "Correct": "b", + "Explanation": "\"equate the fat : 0.1 x + 0.35 * 8 = 0.2 ( x + 8 ) - - > x = 12 . answer : b .\"" + }, + { + "Answer": 7, + "Options": "a ) 3 , b ) 7 , c ) 17 , d ) 31 , e ) 38", + "Correct": "b", + "Explanation": "adding all the numbers we get 137 + x given - ( 137 + x ) / 12 = 12 137 + x = 12 * 12 x = 144 - 137 x = 7 answer : b" + }, + { + "Answer": 24.000000000000007, + "Options": "a ) 17 litres , b ) 24 litres , c ) 11 litres , d ) 07 litres , e ) 38 litres", + "Correct": "b", + "Explanation": "\"262.85 ( 36 ) + 3 , 104.35 x = 1 , 399.45 ( 36 + x ) solve the equation . 262.85 ( 36 ) + 3 , 104.35 x = 1 , 399.45 ( 36 + x ) 9 , 462.6 + 3 , 104.35 x = 50 , 380.2 + 1 , 399.45 x 9 , 462.6 + 1 , 704.9 x = 50 , 380.2 1 , 704.9 x = 40 , 917.6 x = 24 answer is b .\"" + }, + { + "Answer": 3.0277777777777777, + "Options": "a ) $ 1.09 , b ) $ 1.67 , c ) $ 2.25 , d ) $ 2.37 , e ) $ 3.03", + "Correct": "e", + "Explanation": "total cost of parking for 9 hours = 15 $ for the first 2 hours and then 1.75 for ( 9 - 2 ) hours = 15 + 7 * 1.75 = 27.25 thus the average parking price = 27.25 / 9 = 3.03 $ e is the correct answer ." + }, + { + "Answer": 6, + "Options": "a ) 3 , b ) 6 , c ) 14 , d ) 17 , e ) 20", + "Correct": "b", + "Explanation": "\"the objective here is that 70 % of the fruit in the box should be apples . now , there are 14 apples at start and there is no talk of removing any apples , so number of apples should remain 14 and they should constitute 70 % of total fruit , so total fruit = 14 / 0.7 = 20 so we should have 20 - 14 = 6 oranges . right now , there are 12 oranges , so to get to 6 oranges , we should remove 12 - 6 = 6 oranges . answer b\"" + }, + { + "Answer": 55, + "Options": "a ) 55 , b ) 65 , c ) 75 , d ) 85 , e ) 95", + "Correct": "a", + "Explanation": "\"let the marks obtained by the student in physics , chemistry and mathematics be p , c and m respectively . p + c + m = 110 + p c + m = 110 average mark obtained by the student in chemistry and mathematics = ( c + m ) / 2 = 110 / 2 = 55 . answer : a\"" + }, + { + "Answer": 3200, + "Options": "a ) 1600 , b ) 3200 , c ) 800 , d ) 400 , e ) 200", + "Correct": "b", + "Explanation": "\"to solve we will set up a proportion . we know that \u201c 100 million vehicles is to 80 accidents as 4 billion vehicles is to x accidents \u201d . to express everything in terms of \u201c millions \u201d , we can use 4,000 million rather than 4 billion . creating a proportion we have : 100 / 80 = 4,000 / x cross multiplying gives us : 100 x = 4,000 * 80 x = 40 * 80 = 3200 answer : b\"" + }, + { + "Answer": 6, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9", + "Correct": "b", + "Explanation": "let bill run x on saturday , so he will run x + 4 on sunday . . julia will run 2 * ( x + 4 ) on sunday . . totai = x + x + 4 + 2 x + 8 = 20 . . 4 x + 12 = 20 . . x = 2 . . ans = x + 4 = 2 + 4 = 6 answer b" + }, + { + "Answer": 0.5, + "Options": "a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6", + "Correct": "a", + "Explanation": "= > log ( 8 ) ^ 1 / 2 / log 8 = 1 / 2 log 8 / log 8 = 1 / 2 answer a" + }, + { + "Answer": 48, + "Options": "a ) 15 , b ) 30 , c ) 35 , d ) 40 , e ) 48", + "Correct": "e", + "Explanation": "\"lots of ways to tackle this . 40 % of 180 = 72 1 / 3 of 72 = 24 so , 1 / 3 less than 72 is equal to 72 - 24 = 48 answer : e\"" + }, + { + "Answer": 3, + "Options": "a ) - 3 , b ) 3 , c ) - 4 , d ) 4 , e ) - 5", + "Correct": "b", + "Explanation": "\"( 1 ) x = 9 y + 4 ( 2 ) 2 x = 14 y + 1 ( 2 ) - ( 1 ) : x = 5 y - 3 5 y - x = 3 the answer is b .\"" + }, + { + "Answer": 5, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8", + "Correct": "b", + "Explanation": "\"total subjects = 4 + 3 + 3 = 10 max subjects by 1 teacher = 2 so , min of teachers required = 10 / 2 = 5 answer : b\"" + }, + { + "Answer": 25.25, + "Options": "a ) 18 % , b ) 72 % , c ) 32 % , d ) 25.25 % , e ) 52.25 %", + "Correct": "d", + "Explanation": "\"100 * 100 = 10000 65 * 115 = 7475 10000 - - - - - - - 2525 100 - - - - - - - ? = 25.25 % answer : d\"" + }, + { + "Answer": 16, + "Options": "a ) 4 , b ) 8 , c ) 12 , d ) 16 , e ) 32", + "Correct": "d", + "Explanation": "there are 4 flavors of pizza and each can be : 1 . without cheese and mushrooms ; 2 . with cheese ; 3 . with mushrooms ; 4 . with cheese and mushrooms . so , the total number of pizza varieties is 4 * 4 = 16 . answer : d ." + }, + { + "Answer": 15, + "Options": "a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15", + "Correct": "e", + "Explanation": "\"explanation : given that a + b = 15 + b + c = > a ? c = 15 + b ? b = 15 = > c is younger than a by 15 years answer : option e\"" + }, + { + "Answer": 34, + "Options": "a ) 24 , b ) 25 , c ) 34 , d ) 39 , e ) 43", + "Correct": "c", + "Explanation": "explanation : 306 \u00e3 \u00b7 ? \u00e3 \u2014 15 = 405 - 270 = 135 ( 306 \u00e3 \u2014 15 ) / ? = 135 ? = ( 306 \u00e3 \u2014 15 ) / 135 = 34 answer : option c" + }, + { + "Answer": 60, + "Options": "a ) 60 , b ) 25 , c ) 50 , d ) 75 , e ) 100", + "Correct": "a", + "Explanation": "\"surprisingly no one answered this easy one . property of a set of consecutive integerz . mean = median = ( first element + last element ) / 2 = ( second element + last but one element ) / 2 = ( third element + third last element ) / 2 etc . etc . so mean = median = 120 / 2 = 60 answer is a\"" + }, + { + "Answer": 16, + "Options": "a ) 12 , b ) 16 , c ) 18 , d ) 24 , e ) 26", + "Correct": "b", + "Explanation": "\"explanation : suppose the boy got x sums right and 2 x sums wrong . then , x + 2 x = 48 3 x = 48 x = 16 . answer : b\"" + }, + { + "Answer": 68, + "Options": "a ) 70 , b ) 75 , c ) 80 , d ) 85 , e ) 68", + "Correct": "e", + "Explanation": "\"explanation : ( 50 + 60 + 70 + 80 + 80 / 5 ) = 68 option e\"" + }, + { + "Answer": 400, + "Options": "a ) 425 , b ) 375 , c ) 350 , d ) 400 , e ) 500", + "Correct": "d", + "Explanation": "explanation : average price of a hen = rs . 50 total price of 10 hens = 10 * 50 = rs . 500 but total price of 5 goats and 10 hens = rs . 2500 total price of 5 goats is = 2500 - 500 = 2000 average price of a goat = 2000 / 5 = rs . 400 answer : d" + }, + { + "Answer": 13, + "Options": "a ) 3 , b ) 6 , c ) 8 , d ) 12 , e ) 13", + "Correct": "e", + "Explanation": "\"m ^ 2 is divisible by 48 so m ^ 2 must be multiple of 48 . if the value of m is multiples of 13 then it will satisfy the condition . if we if m is 12 or 24 or 36 then it ans is e but if m = 39 then answer should be 16 . is the question right ? or am i missing some thing ? e\"" + }, + { + "Answer": 7, + "Options": "a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 13", + "Correct": "b", + "Explanation": "315 = 3 * 3 * 5 * 7 thus k must include numbers at least up to the number 7 . the answer is b ." + }, + { + "Answer": 450, + "Options": "a ) 250 , b ) 420 , c ) 440 , d ) 650 , e ) 450", + "Correct": "e", + "Explanation": "given exp . = ( 15 ) ^ 2 x 8 ^ 3 \u00e3 \u00b7 256 = a = 225 x 512 \u00e3 \u00b7 256 = 450 e" + }, + { + "Answer": 166, + "Options": "a ) 85 , b ) 91 , c ) 115 , d ) 133 , e ) 166", + "Correct": "e", + "Explanation": "since there is only one even prime number ( 2 ) , and the sum of two odd numbers is even , the product of these two numbers must be even . correct answer e" + }, + { + "Answer": 120, + "Options": "a ) 120 , b ) 346 , c ) 356 , d ) 366 , e ) 396", + "Correct": "a", + "Explanation": "6 ! / 6 - 3 ) ! = 6 ! / 3 ! = 6 * 5 * 4 = 120 . hence , the correct answer is a ." + }, + { + "Answer": 88, + "Options": "a ) 95 , b ) 90 , c ) 88 , d ) 80 , e ) 75", + "Correct": "c", + "Explanation": "\"let x be the number of students in the school . 0.22 x students went to the trip and took more than 100 $ . they compose ( 100 - 75 ) = 25 % of all students who went to the trip . therefore the toal of 0.22 x / 0.25 = 0.88 x students went to the camping which is 88 % . the answer is c\"" + }, + { + "Answer": 2, + "Options": "a ) 2 : 1 , b ) 14 : 3 , c ) 7 : 2 , d ) 1 : 2 , e ) none", + "Correct": "a", + "Explanation": "solution : ( a + b + c ) = 3 + 4 + 7 = 14 and c = 7 then , ( a + b + c ) : c = 2 : 1 . answer : option a" + }, + { + "Answer": 0.7, + "Options": "a ) $ 0.60 , b ) $ 0.70 , c ) $ 0.80 , d ) $ 0.90 , e ) $ 1.00", + "Correct": "b", + "Explanation": "1 st day fine - 0.05 2 nd day fine - 0.05 * 2 = 0.1 ( as doubling gives lower value ) 3 rd day fine - 0.1 * 2 = 0.2 ( as doubling gives lower value ) 4 th day fine - 0.2 * 2 = 0.4 ( as doubling gives lower value we add 0.3 this time ) 5 th day fine - 0.4 + 0.3 = 0.7 ( as doubling gives higher value we add 0.3 this time ) answer : b ." + }, + { + "Answer": 920, + "Options": "a ) $ 900 , b ) $ 800 , c ) $ 1000 , d ) $ 920 , e ) $ 1500", + "Correct": "d", + "Explanation": "\"if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 230 . so 1 / 4 of her savings is $ 230 . so her original savings are 4 times $ 230 = $ 920 correct answer d\"" + }, + { + "Answer": 2, + "Options": "a ) 2 , b ) 4 , c ) 5 , d ) 500 , e ) none", + "Correct": "a", + "Explanation": "answer let 45 x a = ( 10 x 900 ) / 100 \u2234 a = ( 10 x 9 ) / 45 = 2 correct option : a" + }, + { + "Answer": 7, + "Options": "a ) 4 metres , b ) 5 metres , c ) 7 metres , d ) 6 metres , e ) 8 metres", + "Correct": "c", + "Explanation": "let radius of inner circle = r 1 radius of outer circle = r 2 also r 1 = 1 / 3 * r 2 3 * r 1 = r 2 circumference of inner circle = 2 * pi * r 1 circumference of outer circle = 2 * pi * r 2 = 6 * pi * r 1 ( since r 2 = 3 * r 1 ) 2 * pi * r 1 + 6 * pi * r 1 = 88 ( as per question ) r 1 = 3.5 m r 2 = 3 * 3.5 = 10.5 m width of road = 10.5 - 3.5 = 7 m ans . answer : c" + }, + { + "Answer": 0.5625000000000001, + "Options": "a ) 3 / 8 , b ) 8 / 15 , c ) 9 / 16 , d ) 12 / 25 , e ) 16 / 27", + "Correct": "c", + "Explanation": "\"6 a / 100 = 8 a = 400 / 3 8 b / 100 = 6 b = 75 c = b / a = 75 * 3 / 400 = 9 / 16 the answer is c .\"" + }, + { + "Answer": 36, + "Options": "a ) 21 , b ) 36 , c ) 39 , d ) 60 , e ) 65", + "Correct": "b", + "Explanation": "\"the total number of the people in the room must be a multiple of both 8 and 12 ( in order 3 / 7 and 5 / 13 of the number to be an integer ) , thus the total number of the people must be a multiple of lcm of 8 and 12 , which is 96 . since , the total number of the people in the room is greater than 50 and less than 100 , then there are 96 people in the room . therefore there are 3 / 8 * 96 = 36 people in the room under the age of 21 . answer : b .\"" + }, + { + "Answer": 20, + "Options": "a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30", + "Correct": "c", + "Explanation": "\"let x be the number of blueberries in each blue box . then there are x + 10 strawberries in each red box . x + ( x + 10 ) = 50 x = 20 the answer is c .\"" + }, + { + "Answer": 4.5, + "Options": "a ) \u2013 3 , b ) 9 / 2 , c ) 1 , d ) 2 , e ) 3", + "Correct": "b", + "Explanation": "x = 3 y 2 a - 3 y = 3 ( 3 b - y ) 2 a - 3 y = 9 b - 3 y 2 a = 9 b a / b = 9 / 2 answer : b" + }, + { + "Answer": 3075, + "Options": "a ) 3072 , b ) 512 , c ) 768 , d ) 1024 , e ) 1536", + "Correct": "a", + "Explanation": "\"0.3 * 2 ^ 10 = 0.3 * 1024 = 307.2 the answer is a .\"" + }, + { + "Answer": 95.99999999999999, + "Options": "a ) 92 , b ) 96 , c ) 100 , d ) 104 , e ) 108", + "Correct": "b", + "Explanation": "let x be the original weight . the weight of the grape pulp was 0.07 x . since the grape pulp is 84 % of the raisins , 0.07 x = 0.84 ( 8 ) . then x = 12 * 8 = 96 kg . the answer is b ." + }, + { + "Answer": 4, + "Options": "a ) 4 , b ) 2 , c ) 0 , d ) \u2212 2 , e ) \u2212 4", + "Correct": "a", + "Explanation": "\"slope = rise / run = 6 / 12 = 1 / 2 the equation of the line is y = ( 1 / 2 ) x + b 3 = ( 1 / 2 ) ( 10 ) + b b = - 2 the equation of the line is y = ( 1 / 2 ) x - 2 to find the x - intercept , let y = 0 : 0 = ( 1 / 2 ) x - 2 x = 4 the answer is a .\"" + }, + { + "Answer": 22550, + "Options": "a ) 14,550 , b ) 18,550 , c ) 22,550 , d ) 26,550 , e ) 30,550", + "Correct": "c", + "Explanation": "\"2 + 4 + 6 + 8 + . . . + 100 = 2550 402 + 404 + . . . + 500 = 50 ( 400 ) + ( 2 + 4 + . . . + 100 ) = 20,000 + 2550 = 22,550 the answer is c .\"" + }, + { + "Answer": 6, + "Options": "a ) 10 , b ) 9 , c ) 8 , d ) 7 , e ) 6", + "Correct": "e", + "Explanation": "\"let x be the number of canoes . then 3 x / 4 is the number of kayaks . 9 x + ( 3 x / 4 ) * 12 = 432 9 x + 9 x = 432 18 x = 432 x = 24 ( canoes ) 3 x / 4 = 18 ( kayaks ) there were 24 - 18 = 6 more canoes rented out . the answer is e .\"" + }, + { + "Answer": 99.5, + "Options": "a ) 74 kg , b ) 78.5 kg , c ) 99.5 kg , d ) data inadequate , e ) none of these", + "Correct": "c", + "Explanation": "\"total weight increased = ( 7 x 3.5 ) kg = 24.5 kg . weight of new person = ( 75 + 24.5 ) kg = 99.5 kg . answer : option c\"" + }, + { + "Answer": 8, + "Options": "a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8", + "Correct": "e", + "Explanation": "\"explanation : on dividing 427398 by 10 we get the remainder 8 , so 8 should be subtracted answer : option e\"" + }, + { + "Answer": 17, + "Options": "a ) 8 , b ) 16 , c ) 17 , d ) 18 , e ) 34", + "Correct": "c", + "Explanation": "minimum age = average - 1 standard deviation = 10 - 8 = 2 maximum age = average + 1 standard deviation = 10 + 8 = 18 maximum number of different ages of the applicants = 18 - 2 + 1 = 17 answer c" + }, + { + "Answer": 92, + "Options": "a ) a . 72 , b ) b . 50 , c ) c . 92 , d ) d . 46 , e ) e . 44", + "Correct": "c", + "Explanation": "at 6 : 00 it ' ll chime 6 times . if we assume that the time taken to chime is x , then time between chimes is also x . so you have 6 chimes , which is 6 x and 5 time intervals between chimes . this means that 11 x = 44 seconds . thus x = 4 seconds . by a similar logic , at 12 : 00 , there are 12 chimes and 11 intervals so the total time is ( 12 + 11 ) x = 23 x = 92 seconds . answer c" + }, + { + "Answer": 35, + "Options": "a ) 35 , b ) 36 , c ) 37 , d ) 38 , e ) 39", + "Correct": "a", + "Explanation": "\"42 x = 21 x + 1.5 x ( h - 21 ) = = > 42 = 21 + 1.5 ( h - 21 ) = = > h - 21 = 21 / 1.5 = 14 = > h = 35 answer is a\"" + }, + { + "Answer": 4, + "Options": "a ) 1 , b ) 4 / 3 , c ) 17 / 5 , d ) 18 / 5 , e ) 4", + "Correct": "e", + "Explanation": "\"we have two equations : 2 x + y = 26 x + 2 y = 10 notice that something nice happens when we add them . we get : 3 x + 3 y = 36 divide both sides by 3 to get : x + y = 12 so , ( x + y ) / 3 = 12 / 3 = 4 answer : e\"" + }, + { + "Answer": 34, + "Options": "a ) 34 , b ) 76 , c ) 29 , d ) 12 , e ) 20", + "Correct": "a", + "Explanation": "\"explanation : let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 1015 96 + 225 + 490 + 6 x = 1015 6 x = 204 = > x = 34 . answer : a\"" + }, + { + "Answer": 14700, + "Options": "a ) 14700 , b ) 14703 , c ) 37798 , d ) 13777 , e ) 14778", + "Correct": "a", + "Explanation": "explanation : let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 < = > 3 x = 36000 < = > x = 12000 . a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . a ' s share = rs . ( 35000 * 21 / 50 ) = rs . 14,700 . answer : a ) 14700" + }, + { + "Answer": 1200, + "Options": "a ) $ 1200 , b ) $ 1300 , c ) $ 1400 , d ) $ 1800 , e ) $ 1900", + "Correct": "a", + "Explanation": "\"if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 300 . so 1 / 4 of her savings is $ 300 . so her original savings are 4 times $ 300 = $ 1200 correct answer a\"" + }, + { + "Answer": 214.21, + "Options": "a ) $ 214.16 , b ) $ 214.17 , c ) $ 214.18 , d ) $ 214.19 , e ) $ 214.24", + "Correct": "e", + "Explanation": "\"if the last three digits of a whole number are divisible by 8 , then the entire number is divisible by 8 the last 3 digit 418 not divisible by a hence , we need to add 6 to this number for it to be divisible by 8 correct option : e\"" + }, + { + "Answer": 50, + "Options": "a ) 23 , b ) 37 , c ) 28 , d ) 40 , e ) 50", + "Correct": "e", + "Explanation": "\"explanation : formula n ( a \u00e2 \u02c6 \u00aa b ) = n ( a ) + n ( b ) \u00e2 \u02c6 \u2019 n ( a \u00e2 \u02c6 \u00a9 b ) fail in hindi or english = 25 + 50 \u00e2 \u20ac \u201c 25 = 50 therefore students who passed = 100 \u00e2 \u20ac \u201c 50 = 50 . answer : e\"" + }, + { + "Answer": 28000, + "Options": "a ) 28000 , b ) 30000 , c ) 32000 , d ) 34000 , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : suppose b ' s investment = x . then a ' s investment = 3 x suppose bs period of investment = y , then a ' s period of investment = 2 y a : b = 3 x * 2 y : xy = 6 : 1 total profit * 1 / 7 = 4000 = > total profit = 4000 * 7 = 28000 . answer : option a\"" + }, + { + "Answer": 0.84, + "Options": "a ) 9 / 25 , b ) 10 / 25 , c ) 6 / 10 , d ) 2 / 3 , e ) 21 / 25", + "Correct": "e", + "Explanation": "simply look at the question from the other side . what is the probability that you can \u2019 t row the canoe ? this would be 2 / 5 x 2 / 5 = 4 / 25 . using the idea that the probability j of something happening is 1 \u2013 the probability that it doesn \u2019 t happen , you can use the following equation to reach the right answer : 1 \u2013 4 / 25 = 21 / 25 . answer choice e ." + }, + { + "Answer": 0.1111111111111111, + "Options": "a ) 7 / 45 , b ) 2 / 45 , c ) 1 / 9 , d ) 8 / 45 , e ) 9 / 45", + "Correct": "c", + "Explanation": "explanation : hcf of fractions = hcf of numerators / lcm of denominators = ( hcf of 2 , 4 , 6 ) / ( lcm of 3 , 9 , 18 ) = 2 / 18 = 1 / 9 answer : option c" + }, + { + "Answer": 156, + "Options": "a ) 12 , b ) 39 , c ) 54 , d ) 156 , e ) none", + "Correct": "d", + "Explanation": "\"sol . required mean proportional = \u221a 234 x 104 = \u221a 13 x 9 x 2 x 13 x 8 = ( 13 x 3 x 4 ) = 156 . answer d\"" + }, + { + "Answer": 72, + "Options": "a ) 15 , b ) 30 , c ) 36 , d ) 72 , e ) 46", + "Correct": "d", + "Explanation": "explanation : originally , let number of women = x . then , number of men = 2 x . so , in city y , we have : ( 2 x - 16 ) = ( x + 8 ) or x = 24 . therefore total number of passengers in the beginning = ( x + 2 x ) = 3 x = 72 . answer : d" + }, + { + "Answer": 0.5, + "Options": "a ) 1 / 8 , b ) 1 / 7 , c ) 1 / 2 , d ) 1 / 4 , e ) 1 / 6", + "Correct": "c", + "Explanation": "first notice the number of months for which he worked - march to sept i . e . 7 months avg of monthly totals in tips for months other than august = x tips in august = 6 x total tips for all months = 6 * x + 6 x = 12 x tips for august / total tips for all months = 6 x / 12 x = 1 / 2 answer : c" + }, + { + "Answer": 2, + "Options": "a ) a ) 2.12 , b ) b ) 2.2 , c ) c ) 1.25 , d ) d ) 1.3 , e ) e ) 2.0", + "Correct": "e", + "Explanation": "( x * 3 ) = ( 0.75 * 8 ) x = 6 / 3 x = 2 answer = e" + }, + { + "Answer": 105300, + "Options": "a ) 81000 , b ) 81028 , c ) 105300 , d ) 29889 , e ) 22312", + "Correct": "c", + "Explanation": "83200 * 9 / 8 * 9 / 8 = 105300 . answer : c" + }, + { + "Answer": 280, + "Options": "a ) 280 , b ) 216 , c ) 2240 , d ) 246 , e ) 2520", + "Correct": "a", + "Explanation": "the way i solved it is a b c ( hundreds , tens , units ) c can be 0 2 4 6 8 ( any of the 5 digits ) a can be anything except ( d or 0 ) so 8 possibilities b can be anything execpt ( a d c ) so 7 possibilities total ways are 7 * 8 * 5 = 280 ans : a" + }, + { + "Answer": 46, + "Options": "a ) 46 , b ) 47 , c ) 48 , d ) 49 , e ) 50", + "Correct": "a", + "Explanation": "mother + daughter + child = 130 kg daughter + child = 60 kg mother = 130 - 60 = 70 kg child = 1 / 5 th of mother = ( 1 / 5 ) * 70 = 14 kg so now daughter = 130 - ( mother + child ) = 130 - ( 70 + 14 ) = 46 kg answer : a" + }, + { + "Answer": 382.50000000000006, + "Options": "a ) 0.3825 , b ) 3.825 , c ) 38.25 , d ) 382.5 , e ) 0.0382", + "Correct": "d", + "Explanation": "( 0.625 * 0.0729 * 28.9 ) / ( 0.0017 ) * 0.025 * 8.1 = { ( 625 / 1000 ) * ( 729 / 10000 ) * ( 289 / 10 ) } / { ( 17 / 10000 ) * ( 25 / 1000 ) * ( 81 / 10 ) = 382.5 answer : d" + }, + { + "Answer": 3, + "Options": "a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 8", + "Correct": "b", + "Explanation": "\"14 n / 60 must be an integer . = > 7 n / 30 must be an integer . hence n must be a multiple of 2 * 3 * 5 . = > n has 3 different prime integers and can not have more than 3 different prime integers because 2 * 3 * 5 * 7 = 210 > 200 answer : b\"" + }, + { + "Answer": 3, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "b", + "Explanation": "the product of 4 integers is negative thus an odd number of integers need to be negative to have a negative product we are asked at most how many are required . so , the highest odd integer before 6 , i . e . 3 correct option : b" + }, + { + "Answer": 16875, + "Options": "a ) 3277 , b ) 2977 , c ) 16875 , d ) 6077 , e ) 17112", + "Correct": "c", + "Explanation": "\"explanation : 40,000 ( 34 ) 3 = 1687540,000 ( 34 ) 3 = 16875 answer : c\"" + }, + { + "Answer": 9, + "Options": "a ) 17 : 3 , b ) 9 : 1 , c ) 3 : 17 , d ) 5 : 3 , e ) 11 : 2", + "Correct": "b", + "Explanation": "\"he 20 litre mixture contains milk and water in the ratio of 3 : 2 . therefore , there will be 12 litres of milk in the mixture and 8 litres of water in the mixture . step 1 . when 10 litres of the mixture is removed , 6 litres of milk is removed and 4 litres of water is removed . therefore , there will be 6 litres of milk and 4 litres of water left in the container . it is then replaced with pure milk of 10 litres . now the container will have 16 litres of milk and 4 litres of water . step 2 . when 10 litres of the new mixture is removed , 8 litres of milk and 2 litres of water is removed . the container will have 8 litres of milk and 2 litres of water in it . now 10 litres of pure milk is added . therefore , the container will have 18 litres of milk and 2 litres of water in it at the end of the second step . therefore , the ratio of milk and water is 18 : 2 or 9 : 1 . shortcut . we are essentially replacing water in the mixture with pure milk . let w _ o be the amount of water in the mixture originally = 8 litres . let w _ r be the amount of water in the mixture after the replacements have taken place . then , { w _ r } / { w _ o } = ( 1 - r / m ) ^ n where r is the amount of the mixture replaced by milk in each of the steps , m is the total volume of the mixture and n is the number of times the cycle is repeated . hence , { w _ r } / { w _ o } \u00a0 = ( 1 / 2 ) ^ 2 \u00a0 = 1 / 4 therefore r , w _ r \u00a0 = { w _ o } / 4 = 8 / 4 \u00a0 = 2 litres . b\"" + }, + { + "Answer": 34, + "Options": "a ) 35 , b ) 34 , c ) 20 , d ) 35 , e ) 342", + "Correct": "b", + "Explanation": "\"required number = ( lcm of 2 , 6 , 12 and 24 ) + 12 = 24 + 10 = 34 option b\"" + }, + { + "Answer": 108, + "Options": "a ) 366 , b ) 106 , c ) 108 , d ) 192 , e ) 122", + "Correct": "c", + "Explanation": "\"cash realised = rs . ( 108.25 - 0.25 ) = rs . 108 . answer : c\"" + }, + { + "Answer": 0.11111111111111116, + "Options": "a ) 1 / 9 , b ) 1 / 6 , c ) 2 / 9 , d ) 1 / 4 , e ) 1 / 2", + "Correct": "a", + "Explanation": "age of boys w : 4 , 6 , 7 sum of ages taken 2 at a time : 10 , 1311 ages of girls : 5 , 8 , 9 sum of ages taken 2 at a time : 13 , 1714 9 combinations of sum between sets ( 10 , 1211 ) ( 13 , 1714 ) = 23 , 2724 - 16 , 3017 - 24 , 2825 prob ( even ) = 5 / 9 prob ( odd ) = 4 / 9 answer = 5 / 9 - 4 / 9 = 1 / 9" + }, + { + "Answer": 5.5, + "Options": "a ) 3.8 , b ) 10 , c ) 5 , d ) 5.5 , e ) 7.5", + "Correct": "d", + "Explanation": "\"given expression = ( 18 - 4.25 / 2.5 = 13.75 / 2.5 = 137.5 / 25 = 5.5 answer is d .\"" + }, + { + "Answer": 3427, + "Options": "a ) 3427 , b ) 3237 , c ) 3337 , d ) 2337 , e ) none of these", + "Correct": "a", + "Explanation": "\"answer x = 13200 - 9773 = 3427 option : a\"" + }, + { + "Answer": 725, + "Options": "a ) 705 , b ) 735 , c ) 685 , d ) 665 , e ) 725", + "Correct": "e", + "Explanation": "5 + 6 = > 5 \u00e3 \u2014 6 = 30 = > 30 \u00e3 \u2014 10 + 5 = 305 6 + 7 = > 6 \u00e3 \u2014 7 = 42 = > 42 \u00e3 \u2014 10 + 5 = 425 7 + 8 = > 7 \u00e3 \u2014 8 = 56 = > 56 \u00e3 \u2014 10 + 5 = 565 then 8 + 9 = > 8 \u00e3 \u2014 9 = 72 = > 72 \u00e3 \u2014 10 + 5 = 725 answer : e" + }, + { + "Answer": 2, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 6", + "Correct": "c", + "Explanation": "\"i tried plugging in numbers x = 9 q + 5 x = 14 4 x = 56 4 x / 9 = 9 * 6 + 2 remainder is 2 . answer is c\"" + }, + { + "Answer": 69, + "Options": "a ) 65 % , b ) 67 % , c ) 69 % , d ) 72 % , e ) 75 %", + "Correct": "c", + "Explanation": "\"70 % of the class scored 60 % and 30 % of the class scored 90 % . the difference between 60 % and 90 % is 30 % . the average will be 60 % + 0.3 ( 30 % ) = 69 % . the answer is c .\"" + }, + { + "Answer": 75, + "Options": "a ) 60 % , b ) 65 % , c ) 70 % , d ) 75 % , e ) 80 %", + "Correct": "d", + "Explanation": "\"this question is a weighted average question with a series of dependent variables . the remaining portion of the class represents 100 % - 25 % - 50 % = 25 % of the class converting the portions of the class population to decimal weights , we find : class average = 0.25 x 80 + 0.50 x 65 + 0.25 x 90 = 75 the class average is 75 % final answer d ) 75 %\"" + }, + { + "Answer": 10, + "Options": "a ) 30 , b ) 25 , c ) 15 , d ) 10 , e ) 5", + "Correct": "d", + "Explanation": "\"because the cord was extended to its full length at all items , the dog ran along a semi - circular path , from north to south . the circumference of a full circle is 2 * pi * r , but since we only care about the length of half the circle , the semi - circle path is pi * r . s = pi * r = 30 . round pi = 3 , then r = 10 . chord is about 10 feet long . d\"" + }, + { + "Answer": 48, + "Options": "a ) 14 , b ) 24 , c ) 28 , d ) 48 , e ) 96", + "Correct": "d", + "Explanation": "first , look for all 4 digits without repeat that add up to 28 . to avoid repetition , start with the highest numbers first . start from the largest number possible 9874 . then the next largest number possible is 9865 . after this , you ' ll realize no other solution . clearly the solution needs to start with a 9 ( cuz otherwise 8765 is the largest possible , but only equals 26 ) . with a 9 , you also need an 8 ( cuz otherwise 9765 is the largest possible , but only equals 27 ) . with 98 __ only 74 and 65 work . so you have two solutions . each can be rearranged in 4 ! = 24 ways . so d = 24 + 24 = 48 . d" + }, + { + "Answer": 205, + "Options": "a ) 192 , b ) 195 , c ) 200 , d ) 205 , e ) 208", + "Correct": "d", + "Explanation": "it will be easier if you draw a table for this one . let t be the total trout . total speckled trout ( st ) = 645 if female speckled trout = fst then male speckled trout = 45 + 2 fst therefore 45 + 2 fst + fst = 645 we solve and get fst = 200 and mst = 445 ratio of fst to mrt = 4 : 3 we have fst = 200 solve ratio to get mrt = 150 now ratio of mrt to t = 3 : 20 we have mrt = 150 solve ratio to get t = 1000 now unless youve drawn the table it might get a little complex . from above we have mst and mrt mst + mrt = 445 + 150 = 595 so t - 595 = total female trouts 1000 - 595 = 405 female trouts we have from above that fst = 200 so ( whew ! ) frt = 405 - 200 = 205 answer is d" + }, + { + "Answer": 42, + "Options": "a ) 21 , b ) 42 , c ) 63 , d ) 72 , e ) 168", + "Correct": "b", + "Explanation": "\"let ( y / 21 ) x ( y / 84 ) = 1 y ^ 2 = 21 x 84 = 21 x 21 x 4 y = ( 21 x 2 ) = 42 the answer is b .\"" + }, + { + "Answer": 36, + "Options": "a ) 32 , b ) 36 , c ) 40 , d ) 44 , e ) 48", + "Correct": "b", + "Explanation": "\"the cost of annie ' s ride was 2.5 + 5 + ( 0.25 * 16 ) = $ 11.50 let x be the distance of mike ' s ride . the cost of mike ' s ride is 2.5 + ( 0.25 * x ) = 11.5 0.25 * x = 9 x = 36 miles the answer is b .\"" + }, + { + "Answer": 5812.5, + "Options": "a ) 100 , b ) 250 , c ) 750 , d ) 5812.5 , e ) 5835.5", + "Correct": "d", + "Explanation": "\"6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 62 * 25 * 1 / 2 = 775 feet ^ 3 of milk must be removed , which equals to 775 * 7.5 = 5812.5 gallons . answer : d .\"" + }, + { + "Answer": 14.285714285714285, + "Options": "a ) 50.5 % , b ) 44.4 % , c ) 22.2 % , d ) 14.3 % , e ) 25 %", + "Correct": "d", + "Explanation": "\"20 % of ( x - y ) = 15 % of ( x + y ) 20 / 100 ( x - y ) = 15 / 100 ( x + y ) 5 x = 35 y required percentage = y / x * 100 = 5 y / 35 y * 100 = 14.28 % answer is d\"" + }, + { + "Answer": 36, + "Options": "a ) 35 hrs , b ) 36 hrs , c ) 37 hrs , d ) 38 hrs , e ) 39 hrs", + "Correct": "b", + "Explanation": "if a tap could fill entire tank in 18 hrs due to leakage , tap can fill entire tank in 12 hrs without leakage . tank emptied in 0 ne hr by leakage = 1 / 12 - 1 / 18 = ( 6 - 4 ) / 72 = 2 / 72 = 1 / 36 . full tank can be emptied in 36 hrs . answer : b" + }, + { + "Answer": 240, + "Options": "a ) 280 , b ) 300 , c ) 240 , d ) 350 , e ) 400", + "Correct": "c", + "Explanation": "jill earns 4 dollars / hour and the hourly tip is ( 3 / 20 ) * 40 . jill thus earns 4 * 8 + 8 * 2 * 3 per day ( or 4 ( 8 ) + 6 ( 8 ) = 10 ( 8 ) = 80 ) . jill has worked for 3 days - > 80 * 3 = 240 . this matches answer choice c ." + }, + { + "Answer": 455, + "Options": "a ) 455 , b ) 525 , c ) 1400 , d ) 180 , e ) 560", + "Correct": "a", + "Explanation": "\"by using the formula , t [ n ( n - 1 ) / 2 ] , where t = no . of games between two teams and n = total no . of teams , we get : 455 option a .\"" + }, + { + "Answer": 25, + "Options": "a ) 21 , b ) 20 , c ) 25 , d ) 30 , e ) 45", + "Correct": "c", + "Explanation": "\"let number is x . when 10 added to it , = ( x + 10 ) 7 multiplied to sum , = 7 * ( x + 10 ) now , = [ { 7 * ( x + 10 ) } / 5 ] and , = [ { 7 * ( x + 10 ) } / 5 ] - 5 according to question , [ { 7 * ( x + 10 ) } / 5 ] - 5 = half of 88 [ ( 7 x + 70 ) / 5 ) = 44 + 5 7 x + 70 = 49 * 5 x + 10 = 7 * 5 x + 10 = 35 x = 35 - 10 x = 25 so , required number is : 25 . answer : c\"" + }, + { + "Answer": 103, + "Options": "a ) 74 , b ) 75 , c ) 103 , d ) 78 , e ) 45", + "Correct": "c", + "Explanation": "\"solution : sum of 1 st 12 results = 12 * 14 sum of last 12 results = 12 * 17 13 th result = x ( let ) now , 12 * 14 + 12 * 17 + x = 25 * 19 or , x = 103 . answer : option c\"" + }, + { + "Answer": 20, + "Options": "a ) 20 , b ) 60 , c ) 108 , d ) 144 , e ) 180", + "Correct": "a", + "Explanation": "the number of ornaments = a ten more than 1 / 6 of the ornaments in her collection are handmade = > handmade = 10 + a / 6 1 / 2 of the handmade ornaments are antiques = > handmade ornaments = 1 / 2 * ( 10 + a / 6 ) = 5 + a / 12 1 / 3 of the ornaments in her collection are handmade antiques = > handmade ornaments = a / 3 = > 5 + a / 12 = a / 3 = > a = 200 ans : a" + }, + { + "Answer": 90, + "Options": "a ) 240 , b ) 75 , c ) 110 , d ) 90 , e ) 200", + "Correct": "d", + "Explanation": "\"adult + children = 240 let , children = y then , adult = y + 40 i . e . y + ( y + 40 ) = 240 i . e . y = 100 i . e . adult = 100 + 40 = 140 adults include only men and women i . e . men + women = 140 let women , w = x then men , m = x + 40 i . e . x + ( x + 40 ) = 2 x + 40 = 140 i . e . x = 54 i . e . men , m = 54 + 40 = 90 answer : option d\"" + }, + { + "Answer": 2, + "Options": "a ) $ 1 , b ) $ 2 , c ) $ 3 , d ) $ 4 , e ) $ 5", + "Correct": "b", + "Explanation": "\"the average price of a shirt is : $ 360 / 20 = $ 18 . the average price of a sweater is : $ 900 / 45 = $ 20 . the difference in price is : $ 20 - $ 18 = $ 2 . the answer is b .\"" + }, + { + "Answer": 3267.97385620915, + "Options": "a ) 3,108 , b ) 3,100 , c ) 3,108 , d ) 3,124 , e ) 3,250", + "Correct": "e", + "Explanation": "\"to maximize number of hot dogs with 300 $ total number of hot dogs bought in 250 - pack = 22.95 * 13 = 298.35 $ amount remaining = 300 - 298.35 = 1.65 $ this amount is too less to buy any 8 - pack . greatest number of hot dogs one can buy with 300 $ = 250 * 13 = 3250 answer e\"" + }, + { + "Answer": 30, + "Options": "a ) $ 10 , b ) $ 20 , c ) $ 30 , d ) $ 40 , e ) $ 50", + "Correct": "c", + "Explanation": "2 \u00d7 ( 10 + 5 ) = 2 \u00d7 10 + 2 \u00d7 5 = 20 + 10 = 30 dollars correct answer is c ) $ 30" + }, + { + "Answer": 40, + "Options": "a ) 67 sec , b ) 89 sec , c ) 36 sec , d ) 87 sec , e ) 40 sec", + "Correct": "e", + "Explanation": "\"speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 280 + 120 = 400 m . time taken = 400 / 10 = 40 sec . answer : e\"" + }, + { + "Answer": 39, + "Options": "a ) 16 years , b ) 88 years , c ) 39 years , d ) 66 years , e ) 77 years", + "Correct": "c", + "Explanation": "\"let b ' s age = x years . then , as age = ( x + 9 ) years . ( x + 9 + 10 ) = 2 ( x \u2014 10 ) hence x = 39 . present age of b = 39 years answer : c\"" + }, + { + "Answer": 300, + "Options": "a ) 250 , b ) 150 , c ) 300 , d ) 400 , e ) 450", + "Correct": "c", + "Explanation": "there are 600 numbers from 401 to 1000 ( inclusive ) . half of the numbers are odd , so there are 300 odd numbers . the answer is c ." + }, + { + "Answer": 65, + "Options": "a ) 22 , b ) 98 , c ) 28 , d ) 29 , e ) 22", + "Correct": "b", + "Explanation": "answer : b" + }, + { + "Answer": 60000, + "Options": "a ) 75000 , b ) 160000 , c ) 170000 , d ) 60000 , e ) 70000", + "Correct": "d", + "Explanation": "if value of business = x total sell ( 2 x / 3 ) ( 3 / 4 ) = 30000 - > x = 60000 answer : d" + }, + { + "Answer": 6.666666666666665, + "Options": "a ) 1.4 % , b ) 5.9 % , c ) 11.1 % , d ) 6.67 % , e ) 23.6 %", + "Correct": "d", + "Explanation": "\"opening = 15 closing = 16 rise in price = 1 so , percent increase = 1 / 15 * 100 = 6.67 answer : d\"" + }, + { + "Answer": 10, + "Options": "a ) 7 , b ) 8.5 , c ) 10 , d ) 12 , e ) 14", + "Correct": "c", + "Explanation": "explanation : 2 ab = ( a 2 + b 2 ) \u2212 ( a \u2212 b ) 2 = > 2 ab = 29 - 9 = 20 = > ab = 10 option c" + }, + { + "Answer": 663, + "Options": "a ) $ 255 , b ) $ 275 , c ) $ 510 , d ) $ 1,250 , e ) $ 663", + "Correct": "e", + "Explanation": "\"total no . of boxes = 3060000 / ( 20 \u00d7 20 \u00d7 15 ) = 510 total cost = 510 \u00d7 $ 1.30 = $ 663 answer e\"" + }, + { + "Answer": 0.96, + "Options": "a ) a ) 0.96 , b ) b ) 1.2 , c ) c ) 1.25 , d ) d ) 1.3 , e ) e ) 0.8", + "Correct": "a", + "Explanation": "\"( x * 5 ) = ( 0.6 * 8 ) x = 4.8 / 5 x = 0.96 answer = a\"" + }, + { + "Answer": 5, + "Options": "a ) 20 , b ) 18 , c ) 11 , d ) 5 , e ) 50", + "Correct": "d", + "Explanation": "add these two equations 8 x + 4 y = 20 divide by 2 ( to get 2 x + y ) answer will be d . 10" + }, + { + "Answer": 36, + "Options": "a ) 35 , b ) 36 , c ) 37 , d ) 38 , e ) 39", + "Correct": "b", + "Explanation": "\"42 x = 24 x + 1.5 x ( h - 24 ) = = > 42 = 24 + 1.5 ( h - 24 ) = = > h - 24 = 18 / 1.5 = 12 = > h = 36 answer is b\"" + }, + { + "Answer": 18, + "Options": "a ) 12 , b ) 15 , c ) 17 , d ) 18 , e ) 21", + "Correct": "d", + "Explanation": "\"the worst case scenario will be if we remove all 16 tablets of medicine b first . the next 2 tablets we remove have to be of medicine a , so to guarantee that at least two tablets of each kind will be taken we should remove minimum of 16 + 2 = 18 tablets . answer : d .\"" + }, + { + "Answer": 66.66666666666666, + "Options": "a ) 62 , b ) 63 , c ) 64 , d ) 66.66 , e ) 65", + "Correct": "d", + "Explanation": "given : - violets - c / 3 carnations - c tulip - c / 12 rose - c / 12 total flowers in terms of c = c / 3 + c + c / 12 + c / 12 = 18 c / 12 percentage of carnations = c / 3 c / 2 * 100 = 66.66 % answer d" + }, + { + "Answer": 56.25, + "Options": "a ) 33.25 % , b ) 40.25 % , c ) 50.25 % , d ) 55.25 % , e ) 56.25 %", + "Correct": "e", + "Explanation": "\"i just wanted to mention a couple of things here : * this is a pure ratio question ; the number 500 is completely irrelevant , and you can ignore it if you like . when we increase something by 1 / 8 , we are multiplying it by 1 + 1 / 8 = 9 / 8 , so the answer here must be ( 1 / 2 ) * ( 9 / 8 ) = 9 / 16 = 56.25 % . answer is e\"" + }, + { + "Answer": 92, + "Options": "a ) 38 , b ) 27 , c ) 92 , d ) 17 , e ) 80", + "Correct": "c", + "Explanation": "\"explanation : number of subjects = 6 average of marks in 6 subjects = 77 therefore total marks in 6 subjects = 77 * 6 = 462 now , no . of subjects = 5 total marks in 5 subjects = 74 * 5 = 370 therefore marks in 6 th subject = 462 \u2013 370 = 92 answer : c\"" + }, + { + "Answer": 316, + "Options": "a ) 156 , b ) 162 , c ) 316 , d ) 324 , e ) 325", + "Correct": "c", + "Explanation": "\"buy as many $ 50 deals as possible . we can by 650 / 50 = 13 two dozen roses , thus total of 13 * 24 = 312 roses . we are left with 680 - 650 = $ 30 . we can buy 30 / 7.3 = ~ 4 roses for that amount . total = 312 + 4 = 316 . answer : c .\"" + }, + { + "Answer": 20, + "Options": "a ) a ) 36 , b ) b ) 20 , c ) c ) 40 , d ) d ) 42 , e ) e ) 44", + "Correct": "b", + "Explanation": "let b be the number of blue hats and let g be the number of green hats . b + g = 85 . b = 85 - g . 6 b + 7 g = 530 . 6 ( 85 - g ) + 7 g = 530 . 510 - 6 g + 7 g = 530 . g = 530 - 510 = 20 . the answer is b ." + }, + { + "Answer": 14.949999999999989, + "Options": "a ) 16.16 % , b ) 15.15 % , c ) 14.95 % , d ) 13.33 % , e ) 12.52 %", + "Correct": "c", + "Explanation": "\"( 100 % + 5 % ) * ( 100 % - 19 % ) = 1.05 * . 81 = 0.8505 . 1 - 0.8505 = 14.95 % lost = - 14.95 % the answer is c the organization has lost 14.95 % of its total volunteers from fall to spring .\"" + }, + { + "Answer": 693, + "Options": "a ) 693 , b ) 656 , c ) 691 , d ) 9890 , e ) 10000", + "Correct": "a", + "Explanation": "( local value of 7 ) - ( face value of 7 ) = ( 700 - 7 ) = 693 a" + }, + { + "Answer": 34, + "Options": "a ) 28 , b ) 30 , c ) 32 , d ) 34 , e ) 36", + "Correct": "d", + "Explanation": "the cost of annie ' s ride was 2.5 + 5 + ( 0.25 * 14 ) = $ 11 let x be the distance of mike ' s ride . the cost of mike ' s ride is 2.5 + ( 0.25 * x ) = 11 0.25 * x = 8.5 x = 34 miles the answer is d ." + }, + { + "Answer": 0.4, + "Options": "a ) 3 / 10 , b ) 2 / 5 , c ) 1 / 2 , d ) 2 / 3 , e ) 6 / 5", + "Correct": "b", + "Explanation": "say , the tree grows by x feet every year . then , 4 + 6 x = ( 1 + 1 / 7 ) ( 4 + 4 x ) or , x = 2 / 5 answer b" + }, + { + "Answer": 50, + "Options": "a ) 50 , b ) 88 , c ) 77 , d ) 66 , e ) 51", + "Correct": "a", + "Explanation": "\"a + b + c = 500 a + c = 200 b + c = 350 - - - - - - - - - - - - - - a + b + 2 c = 550 a + b + c = 500 - - - - - - - - - - - - - - - - c = 50 answer : a\"" + }, + { + "Answer": 49, + "Options": "a ) 35 , b ) 42 , c ) 45 , d ) 49 , e ) 54", + "Correct": "d", + "Explanation": "\"a = 105 = 3 * 5 * 7 a ^ 3 = 21 \u00d7 25 \u00d7 45 \u00d7 d = > a ^ 3 = ( 7 * 3 ) x ( 5 * 5 ) x ( 3 ^ 2 * 5 ) x d = > a ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x d = > ( 3 * 5 * 7 ) ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x d d = 7 ^ 2 = 49 answer d\"" + }, + { + "Answer": 100, + "Options": "a ) 25 , b ) 28 , c ) 30 , d ) 34 , e ) 100", + "Correct": "e", + "Explanation": "required sum = ( 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 ) = 100 note : 1 is not a prime number option e" + }, + { + "Answer": 23, + "Options": "a ) 11 , b ) 23 , c ) 27 , d ) 22 , e ) 91", + "Correct": "b", + "Explanation": "\"let the son ' s present age be x years . then , man ' s present age = ( x + 25 ) years . ( x + 25 ) + 2 = 2 ( x + 2 ) x + 27 = 2 x + 4 = > x = 23 . answer : b\"" + }, + { + "Answer": 4005, + "Options": "a ) 2017 , b ) 2647 , c ) 2147 , d ) 2045 , e ) 4005", + "Correct": "e", + "Explanation": "\"solution we know that ( 1 + 2 + 3 + . . . . . + 89 ) = n ( n + 1 ) / 2 therefore ( 1 + 2 + 3 + . . . . + 89 ) = ( 89 \u00d7 90 / 2 ) = 4005 . answer e\"" + }, + { + "Answer": 46, + "Options": "a ) 76 sec , b ) 67 sec , c ) 98 sec , d ) 46 sec , e ) 23 sec", + "Correct": "d", + "Explanation": "\"speed of train relative to jogger = 46 - 10 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 340 + 120 = 460 m . time taken = 460 / 10 = 46 sec . answer : d\"" + }, + { + "Answer": 16, + "Options": "a ) 22 , b ) 20 , c ) 16 , d ) 18 , e ) 14", + "Correct": "c", + "Explanation": "forget conventional ways of solving math questions . in ps , ivy approach is the easiest and quickest way to find the answer . after x years passes david \u2019 s age will be ( 40 + x ) years old , and his daughter \u2019 s age will be ( 12 + x ) years old . since the david \u2019 s age is twice his daughter \u2019 s age ( 40 + x ) = 2 * ( 12 + x ) - - - > 40 + x = 24 + 2 x - - - > x = 16 the answer is ( c ) ." + }, + { + "Answer": 1, + "Options": "a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1", + "Correct": "e", + "Explanation": "( 400 ) ( 7,000 ) = ( 2,800 ) ( 100 ^ x ) = > ( 400 ) ( 7,000 ) / 2,800 = 100 ^ x = > 100 = 100 ^ x = > 100 ^ 1 = 100 ^ x since , base is same so powers will be same too . so , x = 1 answer will be e" + }, + { + "Answer": 2.3999999999999995, + "Options": "a ) $ 2.40 , b ) $ 3.00 , c ) $ 3.20 , d ) $ 3.60 , e ) $ 4.80", + "Correct": "a", + "Explanation": "\"total allowance = x amount spent at the arcade = 3 / 5 x amount remaining = 2 / 5 x amount spent at the toy store = 2 / 5 * 1 / 3 x = 2 / 15 x amount remaining = 2 / 5 x - 2 / 15 x = 4 / 15 x now , 4 / 15 x = $ 0.64 therefore , x = $ 2.40 . answer a\"" + }, + { + "Answer": 25, + "Options": "a ) and 25 , b ) and 24 , c ) and 22 , d ) and 29 , e ) of these", + "Correct": "a", + "Explanation": "let the age of jill 7 years ago be x , age of henry be 2 x x + 7 + 2 x + 7 = 41 x = 9 present ages will be 16 and 25 answer : a" + }, + { + "Answer": 24, + "Options": "a ) 14 , b ) 20 , c ) 18 , d ) 24 , e ) 21", + "Correct": "d", + "Explanation": "\"let the actual distance traveled be x km . then , x / 4 = ( x + 6 ) / 5 x - 24 = > x = 24 km . answer : d\"" + }, + { + "Answer": 8102, + "Options": "a ) 6084 , b ) 3788 , c ) 2077 , d ) 8082 , e ) 1812", + "Correct": "d", + "Explanation": "\"explanation : 1239 9321 - - - - - - - - - - - - 8082 answer : d\"" + }, + { + "Answer": 5, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9", + "Correct": "b", + "Explanation": "\"sol . let the ten \u2019 s digit be x and unit \u2019 s digit be y , then , ( 10 x + y ) - ( 10 y + x ) = 45 \u21d4 9 ( x - y ) = 45 \u21d4 x - y = 5 answer b\"" + }, + { + "Answer": 520, + "Options": "a ) 90 , b ) 120 , c ) 160 , d ) 360 , e ) 520", + "Correct": "e", + "Explanation": "if we exclude those cases and take the question at face value , then it seems straightforward . group # 1 = ( did n ' t like , did n ' t understand ) = 130 group # 2 = ( like understood ) = 3 / 4 ( 1 / 4 ) n = 130 n = 520 answer = ( e )" + }, + { + "Answer": 330, + "Options": "a ) $ 374 , b ) $ 330 , c ) $ 385 , d ) $ 392 , e ) $ 399", + "Correct": "b", + "Explanation": "\"( 348 / 116 ) 110 = 330 in this case long division does not take much time . ( 348 / 116 ) = 3 3 * 110 = 330 ( 300 + 30 ) answer b\"" + }, + { + "Answer": 350, + "Options": "a ) $ 160 , b ) $ 350 , c ) $ 282 , d ) $ 274 , e ) $ 286", + "Correct": "b", + "Explanation": "\"total number of days of stay = 23 charge of staying in first week = 18 * 7 = 126 $ charge of staying for additional days = ( 23 - 7 ) * 14 = 16 * 14 = 224 $ total charge = 126 + 224 = 350 $ answer b\"" + }, + { + "Answer": 6, + "Options": "a ) 0 , b ) 1 , c ) 6 , d ) 3 , e ) 5", + "Correct": "c", + "Explanation": "unit digit in 4 ^ 100 = unit digit in [ ( 4 ^ 4 ) ^ 25 ] but unit digit in 4 ^ 4 = 6 unit digit 4 ^ 100 = 6 answer is c" + }, + { + "Answer": 3900, + "Options": "a ) rs . 3900 , b ) rs . 3990 , c ) rs . 4000 , d ) rs . 4100 , e ) rs . 4200", + "Correct": "a", + "Explanation": "\"let the cost of a chair and that of a table be rs . x and rs . y respectively . then , 10 x = 4 y or y = 5 x . 2 15 x + 2 y = 4000 15 x + 2 x 5 x = 4000 2 20 x = 4000 x = 200 . so , y = 5 x 200 = 500 . 2 hence , the cost of 12 chairs and 3 tables = 12 x + 3 y = rs . ( 2400 + 1500 ) = rs . 3900 . a\"" + }, + { + "Answer": 2, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "c", + "Explanation": "\"n = 28 k + 15 2 n = 2 ( 28 k + 15 ) = 4 k * 14 + 30 = 4 k * 14 + 2 * 14 + 2 = 14 j + 2 the answer is c .\"" + }, + { + "Answer": 50, + "Options": "a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80", + "Correct": "b", + "Explanation": "\"25 / 2 \u00f7 4 = 25 / 8 pounds in each container 25 / 8 pounds * 16 ounces / pound = 50 ounces in each container the answer is b .\"" + }, + { + "Answer": 0.031746031746031744, + "Options": "a ) 2 / 69 , b ) 2 / 60 , c ) 2 / 63 , d ) 2 / 29 , e ) 2 / 10", + "Correct": "c", + "Explanation": "\"explanation : let a be the event that x is selected and b is the event that y is selected . p ( a ) = 1 / 7 , p ( b ) = 2 / 9 . let c be the event that both are selected . p ( c ) = p ( a ) \u00d7 p ( b ) as a and b are independent events : = ( 1 / 7 ) \u00d7 ( 2 / 9 ) = 2 / 63 answer : c ) 2 / 63\"" + }, + { + "Answer": 15, + "Options": "a ) 17 , b ) 16 , c ) 15 , d ) 14 , e ) 13", + "Correct": "c", + "Explanation": "the total number of cars is 51 . so each showroom has 17 cars ( since the number of cars in each showrooms should be equal 51 / 3 = 17 ) . moreover that the number of model f is maximum means that the numbers of model g and h should be minimum . since each model must be represented by at least one car in every showroom that minimum number should be 1 . so maximum number of model f is 17 - 2 = 15 . the answer is ( c )" + }, + { + "Answer": 81, + "Options": "a ) 33 , b ) 54 , c ) 81 , d ) 17 , e ) 01", + "Correct": "c", + "Explanation": "\"explanation : as there is meal for 70 adults and 7 have their meal , the meal left can be catered to 63 adults . now , 70 adults = 90 children 7 adults = 9 children therefore , 63 adults = 81 children hence , the meal can be catered to 81 children . answer : c\"" + }, + { + "Answer": 19, + "Options": "a ) 0 , b ) 1 , c ) 10 , d ) 19 , e ) 20", + "Correct": "d", + "Explanation": "solution average of 20 numbers = 0 . \u2234 sum of 20 numbers = ( 0 \u00d7 20 ) = 0 . it is quite possible that 19 of these number may be positive and if their sum is a , then 20 th number is ( - a ) . answer d" + }, + { + "Answer": 1599.9999999999998, + "Options": "a ) 1600 , b ) 2777 , c ) 2889 , d ) 27670 , e ) 2771", + "Correct": "a", + "Explanation": "\"1792 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 1600 . answer : a\"" + }, + { + "Answer": 500, + "Options": "a ) r = 300 , b ) r = 400 , c ) r = 500 , d ) 600 , e ) none of these", + "Correct": "c", + "Explanation": "\"{ managers } = { female managers } + { male managers } ; we are told that the total number of managers in the company is 2 / 5 of all the employees , thus { managers } = 2 / 5 ( m + f ) , where m and f are number of female and male employees , respectively . also , we know that 2 / 5 of all male employees are managers : { male managers } = 2 / 5 * mas well as there are total of 200 female managers : { female managers } = 200 ; thus : 2 / 5 ( m + f ) = 200 + 2 / 5 * m - - > f = 500 . answer : c .\"" + }, + { + "Answer": 130, + "Options": "a ) 130 , b ) 140 , c ) 136 , d ) 156 , e ) 166", + "Correct": "a", + "Explanation": "\"explanation : lcm of 6 , 7 , 9 and 18 is 126 required number = 126 + 4 = 130 answer : option a\"" + }, + { + "Answer": 18, + "Options": "a ) 22 , b ) 23 , c ) 18 , d ) 26 , e ) 28", + "Correct": "c", + "Explanation": "\"let hens be x and cows be y now , feet : x * 2 + y * 4 = 140 heads : x * 1 + y * 1 = 44 implies , 2 x + 4 y = 140 and x + y = 44 solving these two equations , we get x = 18 and y = 26 therefore , hens are 26 . answer : c\"" + }, + { + "Answer": 0.4, + "Options": "a ) 2 / 3 , b ) 2 / 5 , c ) 3 / 4 , d ) 3 / 7 , e ) 5 / 8", + "Correct": "b", + "Explanation": "the line y = - x + 4 intersects the rectangle and these three points of intersection ( 0,0 ) , ( 0,4 ) and ( 4,0 ) form a triangle . the points below the line y = - x + 4 satisfy x + y < 4 . the area of this triangle is ( 1 / 2 ) ( 4 ) ( 4 ) = 8 the area of the rectangle is 20 . p ( x + y < 4 ) = 8 / 20 = 2 / 5 the answer is b ." + }, + { + "Answer": 60, + "Options": "a ) 50 liters , b ) 55 liters , c ) 60 liters , d ) 70 liters , e ) 75 liters", + "Correct": "c", + "Explanation": "\"quantity of milk = 60 x 2 litres = 40 litres . 3 quantity of water in it = ( 60 - 40 ) litres = 20 litres . new ratio = 1 : 2 let quantity of water to be added further be x litres . then , milk : water = 40 . 20 + x now , 40 = 1 20 + x 2 20 + x = 80 x = 60 . quantity of water to be added = 60 liters . c\"" + }, + { + "Answer": 0.25, + "Options": "a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4", + "Correct": "a", + "Explanation": "\"because n ( n + 1 ) is always an even product of even * odd or odd * even factors , there is a probability of 1 that that it will be divisible by 2 , and , thus , a probability of 1 / 2 that it will be divisible by 4 and , thus , a probability of 1 / 4 that it will be divisible by 8 1 * 1 / 4 = 1 / 4 answer : a\"" + }, + { + "Answer": 2, + "Options": "a ) 1 , b ) 1 / 2 , c ) 2 , d ) 4 , e ) - 1 / 2", + "Correct": "c", + "Explanation": "substituted option c i . e x = 2 . inequality satisfied . this eliminates all options except answer is c" + }, + { + "Answer": 4900, + "Options": "a ) rs . 3601 , b ) rs . 3618 , c ) rs . 4900 , d ) rs . 3619 , e ) rs . 3610", + "Correct": "c", + "Explanation": "\"manager ' s monthly salary = rs . ( 2500 * 25 - 2400 * 24 ) = rs . 4900 answer : c\"" + }, + { + "Answer": 12.5, + "Options": "a ) 12 % , b ) 12.5 % , c ) 13.5 % , d ) 13 % , e ) 14 %", + "Correct": "b", + "Explanation": "explanation : the original profit is : - = > 70000 \u2212 42000 \u2212 12000 = 16000 . if 7.14 % of 14 i . e . one of the machines closed throughout the year , then the change in profit will be : - = > ( 13 / 14 ) \u00d7 [ 70000 \u2212 42000 ] . = > 14000 . thus , decrease in the profit % is : - = > ( 2000 / 16000 ) \u00d7 100 . = > 12.5 % . answer : b" + }, + { + "Answer": 80, + "Options": "a ) 80 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %", + "Correct": "a", + "Explanation": "\"this is easiest to solve with a bell - curve histogram . m here is equal to \u00b5 in the gaussian normal distribution and thus m = 50 % of the total population . so , if 60 % is one st . dev , then on either side of m we have 60 / 2 = 30 % . so , 30 % are to the right and left of m ( = 50 % ) . in other words , our value m + d = 50 + 30 = 80 % goingfrom the mean m , to the right of the distributionin the bell shaped histogram . . this means that 80 % of the values are below m + d . like i said , doing it on a bell - curve histogram is much easier to fullygethow this works , or you could apply gmat percentile jargon / theory to it a\"" + }, + { + "Answer": 18, + "Options": "a ) 20 , b ) 18 , c ) 16 , d ) 19 , e ) 17", + "Correct": "b", + "Explanation": "p 1 = rs . 16 per kg , p 2 = rs . 22 per kg , q 1 = 8 kg , q 2 = 4 kg now , p = ( p 1 q 1 + p 2 q 2 ) / ( q 1 + q 2 ) average price of the mixture = 8 * 16 + 4 * 22 / 12 = 128 + 88 / 12 = 216 / 12 = 18 answer : b" + }, + { + "Answer": 504, + "Options": "a ) 336 , b ) 346 , c ) 356 , d ) 366 , e ) 504", + "Correct": "e", + "Explanation": "9 ! / ( 9 - 3 ) ! = 9 ! / 6 ! = 9 * 8 * 7 = 504 . hence , the correct answer is e ." + }, + { + "Answer": 34.080000000000005, + "Options": "a ) 0.3408 , b ) 3.408 , c ) 34.08 , d ) 340.8 , e ) none of these", + "Correct": "c", + "Explanation": "\"solution 1.6 \u00d7 21.3 = ( 16 / 10 x 213 / 10 ) = ( 16 x 213 / 100 ) = 3408 / 100 = 34.08 . answer c\"" + }, + { + "Answer": 66, + "Options": "a ) 22 , b ) 33 , c ) 44 , d ) 66 , e ) 99", + "Correct": "d", + "Explanation": "x / ( 11 p ) = odd prime number x = odd prime number * 11 p least value of x = lowest odd prime number * 11 * lowest value of p = 3 * 11 * 2 = 66 answer d" + }, + { + "Answer": 117, + "Options": "a ) rs . 115 , b ) rs . 116 , c ) rs . 117 , d ) rs . 118 , e ) none", + "Correct": "c", + "Explanation": "solution : let the average expenditure of all the nine be x . then , 12 \u00d7 8 + ( x + 8 ) = 9 x . therefore , x = 13 . total money spent , = 9 x = rs . ( 9 \u00d7 13 ) = rs . 117 answer : option c" + }, + { + "Answer": 4, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9", + "Correct": "a", + "Explanation": "\"sol . let the ten \u2019 s digit be x and unit \u2019 s digit be y , then , ( 10 x + y ) - ( 10 y + x ) = 36 \u21d4 9 ( x - y ) = 36 \u21d4 x - y = 4 answer a\"" + }, + { + "Answer": 4, + "Options": "a ) 5 , b ) 6 , c ) 4 , d ) 3 , e ) 2", + "Correct": "c", + "Explanation": "solution : npr = ncr \ufffd r ! 6 pr = 15 * r ! 360 = 15 * r ! r ! = 360 / 15 = 24 r ! = 4 * 3 * 2 * 1 = > r ! = 4 ! therefore , r = 4 . answer : option c" + }, + { + "Answer": 16, + "Options": "a ) 18 , b ) 82 , c ) 16 , d ) 27 , e ) 29", + "Correct": "c", + "Explanation": "\"let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 x / 2 = ( 73 - 65 ) = > x / 2 = 8 = > x = 16 . answer : c\"" + }, + { + "Answer": 80, + "Options": "a ) 10 % , b ) 20 % , c ) 60 % , d ) 80 % , e ) 50 %", + "Correct": "d", + "Explanation": "\"pass percentage = 100 - ( 25 + 35 - 40 ) = 100 - 20 = 80 answer : d\"" + }, + { + "Answer": 54, + "Options": "a ) 54 , b ) 55 , c ) 53 , d ) 56 , e ) 57", + "Correct": "a", + "Explanation": "solution : ( x ^ n + 1 ) is divisible by ( x + 1 ) , when n is odd . . ' . ( 55 ^ 55 + 1 ) is divisible by ( 55 + 1 ) = 56 . when ( 55 ^ 55 + 1 ) + 54 is divided by 56 , the remainder is 54 . answer a" + }, + { + "Answer": 24, + "Options": "a ) 22 , b ) 24 , c ) 28 , d ) 32 , e ) 44", + "Correct": "b", + "Explanation": "\"g ( a ) = 4 ^ 11 = 2 ^ 22 . so we have to find a product with atleast 22 2 ' s in it . in option 1 22 the total no of 2 ' s = [ 22 / 2 ] + [ 22 / 4 ] + [ 22 / 8 ] + [ 22 / 16 ] = 11 + 5 + 2 + 1 = 19 in option 2 24 the total no of 2 ' s = [ 24 / 2 ] + [ 24 / 4 ] + [ 24 / 8 ] + [ 24 / 16 ] = 12 + 6 + 3 + 1 = 22 . hence b\"" + }, + { + "Answer": 230, + "Options": "a ) 115 , b ) 230 , c ) 460 , d ) 575 , e ) 690", + "Correct": "b", + "Explanation": "the lcm of n and m is 690 = 2 * 3 * 5 * 23 . m is not divisible by 2 , thus 2 goes to n n is not divisible by 3 , thus 3 goes to m . from above : n must be divisible by 2 and not divisible by 3 : n = 2 * . . . in order n to be a 3 - digit number it must take all other primes too : n = 2 * 5 * 23 = 230 . answer : b ." + }, + { + "Answer": 84, + "Options": "a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %", + "Correct": "d", + "Explanation": "\"d the prompt says that 68 % of the population lies between m - d and m + d . thus , 32 % of the population is less than m - d or greater than m + d . since the population is symmetric , half of this 32 % is less than m - d and half is greater than m + d . thus , f = ( 68 + 16 ) % or ( 100 - 16 ) % of the population is less than m + d . d\"" + }, + { + "Answer": 16, + "Options": "a ) 12 , b ) 29 , c ) 27 , d ) 16 , e ) 99", + "Correct": "d", + "Explanation": "\"explanation : let the number be x . therefore , 3 ( 2 x + 5 ) = 111 6 x + 15 = 111 6 x = 96 x = 16 answer : d\"" + }, + { + "Answer": 3.200000000000273, + "Options": "a ) rs . 2.20 , b ) rs . 3.20 , c ) rs . 4.20 , d ) rs . 5.20 , e ) rs . 3.25", + "Correct": "b", + "Explanation": "p 9 r / 100 ) ^ 2 = 2000 ( 4 / 100 ) ^ 2 = rs . 3.20 answer : b" + }, + { + "Answer": 3.3333333333333335, + "Options": "a ) 9 / 4 , b ) 3 / 2 , c ) 4 / 3 , d ) 2 / 3 , e ) 10 / 3", + "Correct": "e", + "Explanation": "\"sq rt ( 10 x / 3 ) = x = > 10 x / 3 = x ^ 2 = > x = 10 / 3 ans - e\"" + }, + { + "Answer": 14, + "Options": "a ) 4 , b ) 7 , c ) 12 , d ) 14 , e ) 28", + "Correct": "d", + "Explanation": "if there were only people , there would be exactly twice the number of legs as heads . each dog contributes two extra legs over and above this number . so 28 extra legs means 14 dogs . correct answer d" + }, + { + "Answer": 137, + "Options": "a ) 96 , b ) 106 , c ) 128 , d ) 137 , e ) 122", + "Correct": "d", + "Explanation": "\"average = total runs / no . of innings = 32 so , total = average x no . of innings = 32 * 20 = 640 now increase in avg = 4 runs . so , new avg = 32 + 5 = 37 runs total runs = new avg x new no . of innings = 37 * 21 = 777 runs made in the 11 th inning = 777 - 640 = 137 answer : d\"" + }, + { + "Answer": 588, + "Options": "a ) 654 , b ) 655 , c ) 656 , d ) 588 , e ) 658", + "Correct": "d", + "Explanation": "\"total cost 840 840 * 30 / 100 = 252 so the cut in amount is 252 the less amount to be spend is 840 - 252 = 588 answer : d\"" + }, + { + "Answer": 28, + "Options": "a ) 1 , b ) 4 , c ) 9 , d ) 13 , e ) 28", + "Correct": "e", + "Explanation": "\"solving through algebra route : 3 b + 4 f = x amount if we multiply this equation with 7 we get : 21 b + 28 f = 7 x therefore , we got 21 ounces of butter and 7 x amount of quantity when we use 28 ounces of floor . ans : e\"" + }, + { + "Answer": 36, + "Options": "a ) 40 , b ) 36 , c ) 32 , d ) 28 , e ) 24", + "Correct": "b", + "Explanation": "\"let c be the capacity of the can . ( 4 / 7 ) * ( c - 8 ) + 8 = ( 2 / 3 ) * c 12 c - 96 + 168 = 14 c 2 c = 72 c = 36 the answer is b .\"" + }, + { + "Answer": 34, + "Options": "a ) a ) 25 , b ) b ) 34 , c ) c ) 50 , d ) d ) 67 , e ) e ) 100", + "Correct": "b", + "Explanation": "\"its b . total juice rquired = 272 * 6 = 1632 ounce 12 ounce concentate makes = 12 * 4 = 48 ounce juice total cans required = 1632 / 48 = 34 . answer b\"" + }, + { + "Answer": 1, + "Options": "a ) 2 : 9 , b ) 2 : 7 , c ) 1 : 6 , d ) 1 : 1 , e ) 1 : 3", + "Correct": "d", + "Explanation": "\"( 10 / 100 ) a + ( 2 / 100 ) b = ( 6 / 100 ) ( a + b ) 4 a = 4 b = > a / b = 1 / 1 answer is d .\"" + }, + { + "Answer": 7, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10", + "Correct": "b", + "Explanation": "\"i got two equations : 3 x - 2 y = 25 x + y = 7 3 x - 2 ( 7 - x ) = 25 3 x - 14 + 2 x = 25 5 x = 39 x = 7.8 or between 7 and 8 . ( ans b )\"" + }, + { + "Answer": 386, + "Options": "a ) 366 , b ) 236 , c ) 367 , d ) 365 , e ) 386", + "Correct": "e", + "Explanation": "\"explanation : the least number which when divided by different divisors leaving the same remainder in each case = lcm ( different divisors ) + remainder left in each case . hence the required least number = lcm ( 35 , 11 ) + 1 = 386 . answer : e\"" + }, + { + "Answer": 75, + "Options": "a ) 55 , b ) 65 , c ) 75 , d ) 85 , e ) 95", + "Correct": "c", + "Explanation": "\"let the marks obtained by the student in physics , chemistry and mathematics be p , c and m respectively . p + c + m = 150 + p c + m = 150 average mark obtained by the student in chemistry and mathematics = ( c + m ) / 2 = 150 / 2 = 75 . answer : c\"" + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9", + "Correct": "a", + "Explanation": "\"lets say 5 and 10 ounce packages be x and y respectively . given that , 5 x + 10 y = 85 and x = y + 2 . what is the value of y . substituting the x in first equation , 5 y + 10 + 10 y = 85 - > y = 75 / 15 . = 5 a\"" + }, + { + "Answer": 30, + "Options": "a ) 30 , b ) 54 , c ) 72 , d ) 84 , e ) 27", + "Correct": "a", + "Explanation": "\"let the second number be x . then , first number = 2 x and third number = 2 x / 3 . 2 x + x + 2 x / 3 = 110 11 x / 3 = 110 x = 30 answer : a\"" + }, + { + "Answer": 50.96666666666667, + "Options": "a ) 21.84 , b ) 50.96 , c ) 53.84 , d ) 24.84 , e ) 50.26", + "Correct": "b", + "Explanation": "\"dinner bill of 3 person = 139 + 10 % tip so , 10 % of 139 = ( 139 * 10 ) / 100 = 13.9 so , the actual total amount = 139 + 13.9 = $ 152.9 so per head bill = 152.9 / 3 = $ 50.96 answer : b\"" + }, + { + "Answer": 5, + "Options": "a ) 1 % , b ) 2 % , c ) 4 % , d ) 5 % , e ) 6 %", + "Correct": "d", + "Explanation": "let x be the amount of gasoline the driver buys originally . let y be the new amount of gasoline the driver should buy . let p be the original price per liter . ( 1.2 * p ) y = 1.14 ( p * x ) y = ( 1.14 / 1.2 ) x = 0.95 x which is a reduction of 5 % . the answer is d ." + }, + { + "Answer": 23, + "Options": "a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25", + "Correct": "c", + "Explanation": "\"explanation : let the numbers be x , x + 1 , x + 2 , x + 3 , x + 4 , x + 5 and x + 6 , then ( x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) + ( x + 4 ) + ( x + 5 ) + ( x + 6 ) ) / 7 = 20 . or 7 x + 21 = 140 or 7 x = 119 or x = 17 . latest number = x + 6 = 23 . answer : c\"" + }, + { + "Answer": 13, + "Options": "a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13", + "Correct": "e", + "Explanation": "\"according to order of operations , inner brackets first where 6 \u00d7 4 \u00f7 3 is first calculated since it has a multiplication and a division . 6 \u00d7 4 \u00f7 3 = 24 \u00f7 3 = 8 hence 11 + sqrt ( - 4 + 6 \u00d7 4 \u00f7 3 ) = 11 + sqrt ( - 4 + 8 ) = 11 + sqrt ( 4 ) = 11 + 2 = 13 correct answer e ) 13\"" + }, + { + "Answer": 34.66428571428572, + "Options": "a ) $ 30.14 , b ) 45.14 , c ) 34.66 , d ) 32.29 , e ) 33.16", + "Correct": "c", + "Explanation": "\"211 * 15 = 3165 / 100 = 31.65 211 + 31.65 = 242.65 242.65 / 7 = 34.66 answer : c\"" + }, + { + "Answer": 74671.875, + "Options": "a ) 81000 , b ) 81007 , c ) 74671.875 , d ) 81066 , e ) 81022", + "Correct": "c", + "Explanation": "\"59000 * 9 / 8 * 9 / 8 = 74671.875 answer : c\"" + }, + { + "Answer": 160, + "Options": "a ) 12 , b ) 28 , c ) 160 , d ) 180 , e ) 18", + "Correct": "c", + "Explanation": "\"let the numbers be x and y . then , x + y = 20 and x - y = 8 x 2 - y 2 = ( x + y ) ( x - y ) = 20 * 8 = 160 . answer : c\"" + }, + { + "Answer": 12, + "Options": "a ) a ) 23 , b ) b ) 21 , c ) c ) 52 , d ) d ) 56 , e ) e ) 12", + "Correct": "e", + "Explanation": "\"let the total number of workers be x . then , 9000 x = ( 12000 * 6 ) + 6000 ( x - 6 ) = > 3000 x = 36000 = x = 12 . answer : e\"" + }, + { + "Answer": 43.75, + "Options": "a ) 22.35 , b ) 33.25 , c ) 22.25 , d ) 11.35 , e ) 43.75", + "Correct": "e", + "Explanation": "\"explanation : total of 50 numbers = ( 50 \u00d7 44 ) = 2200 total of 48 numbers = ( 2200 - ( 45 + 55 ) ] = 2100 required average = 2100 / 48 = 43.75 answer : e\"" + }, + { + "Answer": 0.3, + "Options": "a ) 3 / 10 , b ) 1 / 70 , c ) 3 / 14 , d ) 1 / 10 , e ) 11 / 14", + "Correct": "a", + "Explanation": "the fraction is nothing but the probability . . number to choose 3 out of 6 = 6 c 3 number to choose a and b and 2 from remaining 4 = 4 c 2 . . prob of a and b choosen = 4 c 2 / 6 c 3 = 3 / 10 answer : a" + }, + { + "Answer": 60.00000000000001, + "Options": "a ) 60 % , b ) 50 % , c ) 55 % , d ) 40 % , e ) 33.3 %", + "Correct": "a", + "Explanation": "increase = 192000 - 120000 = 72000 % increase = 72000 * 100 / 120000 = 60 % answer : option a" + }, + { + "Answer": 64, + "Options": "a ) 58 , b ) 60 , c ) 62 , d ) 64 , e ) 66", + "Correct": "d", + "Explanation": "\"18 x + 100 = 19 ( x + 2 ) x = 62 + 2 = 64 answer : d\"" + }, + { + "Answer": 4, + "Options": "a ) 1 , b ) 2 , c ) 4 , d ) - 2 , e ) - 4", + "Correct": "c", + "Explanation": "focus on the transition points and plug in the values . a > 6 so a could be 7 , 8 , 9 , 10 , 11 etc look at a = 7 7 + b < 11 b < 4 b could be 3 , 2 , 1 , 0 , - 1 etc when b is 3 , we get a - b = 4 this must be the smallest value because as a increases , b reduces so a - b increases . take another example . a = 11 so b < 0 . a - b will give a value greater than 11 . answer ( c ) ." + }, + { + "Answer": 11, + "Options": "a ) 4 , b ) 7 , c ) 8 , d ) 11 , e ) 12", + "Correct": "d", + "Explanation": "given that x = 8 ! = 2 ^ 7 \u2217 3 ^ 2 \u2217 5 \u2217 7 x . hence , x = 2 ^ 7 \u2217 3 ^ 2 \u2217 5 ^ 1 \u2217 7 ^ 1 = 2 ^ i \u2217 3 ^ k \u2217 5 ^ m \u2217 7 p , since i , k , m , and p are positive integers , then we can equate the exponents , so we have that i = 7 , k = 2 , m = 1 , and p = 1 therefore , i + k + m + p = 7 + 2 + 1 + 1 = 11 answer : d ." + }, + { + "Answer": 4, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 4", + "Correct": "e", + "Explanation": "n = h . c . f . of ( 4665 - 1305 ) , ( 6905 - 4665 ) and ( 6905 - 1305 ) = h . c . f . of 3360 , 2240 and 5600 = 1120 . sum of digits in n = ( 1 + 1 + 2 + 0 ) = 4 answer : e" + }, + { + "Answer": 3.3749999999999996, + "Options": "a ) $ 2.40 , b ) $ 3.00 , c ) $ 3.40 , d ) $ 3.60 , e ) $ 4.80", + "Correct": "c", + "Explanation": "\"total allowance = x amount spent at the arcade = 3 / 5 x amount remaining = 2 / 5 x amount spent at the toy store = 2 / 5 * 1 / 3 x = 2 / 15 x amount remaining = 2 / 5 x - 2 / 15 x = 4 / 15 x now , 4 / 15 x = $ 0.9 therefore , x = $ 3.40 . answer c\"" + }, + { + "Answer": 84, + "Options": "a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %", + "Correct": "d", + "Explanation": "\"16 % ________________________________________________ m + f 34 % ________________________________________________ m 34 % ________________________________________________ m - f 16 % since 68 % lies one standard deviation from mean m , = > 50 % of 68 % lies on either side as it is symmetric about m . thus 16 % lie below m - f and 16 % lie above m + f now below m + f = 16 + 34 + 34 = 84 % hence d\"" + }, + { + "Answer": 70, + "Options": "a ) 70 , b ) 65 , c ) 80 , d ) 140 , e ) 60", + "Correct": "a", + "Explanation": "\"answer let the number be x . then , x - 40 = 100 - x \u00e2 \u2021 \u2019 2 x = 100 + 40 = 140 \u00e2 \u2021 \u2019 2 x = 140 \u00e2 \u02c6 \u00b4 x = 70 correct option : a\"" + }, + { + "Answer": 5, + "Options": "a ) 4 , b ) 7 , c ) 5 , d ) 3 , e ) 6", + "Correct": "c", + "Explanation": "\"answer dividing numerator as well as denominator by b , we get given exp . = ( 5 a + 4 b ) / ( 5 a - 4 b ) = ( 5 a / b + 4 ) / ( 5 a / b - 4 ) since a / b = 6 / 5 this implies that = [ ( 5 * 6 ) / 5 + 4 ] / [ ( 5 * 6 ) / 5 - 4 ) ] = ( 6 + 4 ) / ( 6 - 4 ) = 5 option : c\"" + }, + { + "Answer": 6, + "Options": "a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12", + "Correct": "b", + "Explanation": "\"i am getting 12 . e . hope havent done any calculation errors . . approach . . let y = no . of days taken by y to do w widgets . then x will take y + 2 days . 1 / ( y + 2 ) + 1 / y = 5 / 12 ( 5 / 12 is because ( 5 / 4 ) w widgets are done in 3 days . so , x widgets will be done in 12 / 5 days or 5 / 12 th of a widget in a day ) solving , we have y = 4 = > x takes 6 days to doing x widgets . answer : b\"" + }, + { + "Answer": 3, + "Options": "a ) 4 , b ) 5 , c ) 3 , d ) 8 , e ) 9", + "Correct": "c", + "Explanation": "sum of digits = ( 7 + 6 + 1 + x + 8 + 2 + 9 ) = ( 33 + x ) , which must be divisible by 9 . x = 3 . c )" + }, + { + "Answer": 200, + "Options": "a ) 150 , b ) 200 , c ) 240 , d ) 300 , e ) 480", + "Correct": "b", + "Explanation": "\"the first digit and last digit are the same so the 2 possibilities are 6 or 8 . the second and third digits can be any number from 0 to 9 . the total number of palindromic integers is 2 * 10 * 10 = 200 the answer is b .\"" + }, + { + "Answer": 56, + "Options": "a ) 40 , b ) 56 , c ) 60 , d ) 62 , e ) 70", + "Correct": "b", + "Explanation": "\"when a number n = a ^ x * b ^ y , where a and b are prime numbers , and x , y are positive integers , the number of divisors of n = ( x + 1 ) ( y + 1 ) therefore , the answer is b . 7 * 8 = 56\"" + }, + { + "Answer": 0.5, + "Options": "a ) 1 / 3 , b ) 2 / 3 , c ) 1 / 4 , d ) 1 / 2 , e ) 3 / 5", + "Correct": "d", + "Explanation": "no of ways of selecting a gender - 2 c 1 no of ways of selecting any 2 children out of 4 = 4 c 2 total possible outcomes - 2 ^ 4 ( each child can be either a girl or a boy ) probability = 2 c 1 * 4 c 2 / 2 ^ 4 = 2 * 4 / 2 * 2 * 2 * 2 = 8 / 16 = 1 / 2 ans = d" + }, + { + "Answer": 3, + "Options": "a ) 3 , b ) 2 , c ) 4 , d ) 1 , e ) 5", + "Correct": "a", + "Explanation": "\"let possible value of x is 91 least possible value of x / 8 is 91 / 8 = > 11 quotient with remainder 3 thus answer is ( a ) 3\"" + }, + { + "Answer": 400, + "Options": "a ) 600 , b ) 450 , c ) 350 , d ) 550 , e ) 400", + "Correct": "e", + "Explanation": "let the interval is x . prize of 2 nd and 3 rd is 2000 - x and 2000 - 2 x 2000 + 2000 - x + 2000 - 2 x = 4800 x = 400 answer : e" + }, + { + "Answer": 11, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", + "Correct": "e", + "Explanation": "total subjects = 9 + 7 + 6 = 22 max subjects by 1 teacher = 2 so , min of teachers required = 22 / 2 = 11 answer : e" + }, + { + "Answer": 1236, + "Options": "a ) 1236 , b ) 1365 , c ) 1200 , d ) 1526 , e ) 1325", + "Correct": "a", + "Explanation": "r - 1 a - 2 n - 3 d - 6 so for mango the code is 1236 answer : a" + }, + { + "Answer": 18, + "Options": "a ) 18 , b ) 12 , c ) 9 , d ) 4.5 , e ) 3", + "Correct": "a", + "Explanation": "\"the x - axis is 9 units from the point p . thus the y - axis is 18 units from the point p . the answer is a .\"" + }, + { + "Answer": 81.81818181818183, + "Options": "a ) 66.66 % , b ) 81.81 % , c ) 66.766 % , d ) 86.66 % , e ) 66.65 %", + "Correct": "b", + "Explanation": "\"excess of b ' s height over a ' s = [ ( 45 / ( 100 - 45 ) ] x 100 % = 81.81 % answer : b )\"" + }, + { + "Answer": 4, + "Options": "a ) 2 . , b ) 4 . , c ) 5 . , d ) 7 , e ) 9 .", + "Correct": "b", + "Explanation": "\"ad = ( a + 1 ) ( d + 1 ) - 9 0 = a + d - 8 a + d = 8 a = d ( as they are twin brothers ) a = d = 4 b is the answer\"" + }, + { + "Answer": 4, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "d", + "Explanation": "the lcm of 5,9 and 11 is 495 . the next multiple is 2 * 495 = 990 . 990 + { remainder } = 990 + 3 = 993 , which is 4 less than 997 . answer : d ." + }, + { + "Answer": 98.75, + "Options": "a ) $ 94.03 , b ) $ 96.75 , c ) $ 98.75 , d ) $ 102.07 , e ) $ 105.3", + "Correct": "c", + "Explanation": "\"there can be 2 cases 1 ) 25 + 25 + 10 + 5 = $ 98.75 or 2 ) 25 + 25 + 25 = $ 96.75 c\"" + }, + { + "Answer": 7, + "Options": "a ) 3 , b ) 5 , c ) 9 , d ) 7 , e ) 8", + "Correct": "d", + "Explanation": "d 7 let the number of cows be x and their legs be 4 x . let the number of chicken be y and their legs be 2 x . total number of legs = 4 x + 2 y . total number of heads = x + y . the number of legs was 14 more than twice the number of heads . therefore , 2 \u00d7 ( x + y ) + 14 = 4 x + 2 y . or , 2 x + 2 y + 14 = 4 x + 2 y . or , 2 x + 14 = 4 x [ subtracting 2 y from both sides ] . or , 14 = 4 x \u2013 2 x [ subtracting 2 x from both sides ] . or , 14 = 2 x . or , x = 7 [ dividing by 2 on both sides ] . therefore , the number of cows = 7 ." + }, + { + "Answer": 32, + "Options": "a ) 32 , b ) 29 , c ) 28 , d ) 30 , e ) 31", + "Correct": "a", + "Explanation": "\"13604 \u00f7 87 = 156 , remainder = 32 hence 32 is the least number which can be subtracted from 13604 such that the remainder is divisible by 87 answer is a\"" + }, + { + "Answer": 3.333333333333333, + "Options": "a ) 10 / 3 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "a", + "Explanation": "x * 2 = 5 * 4 / 3 x * 2 = 20 / 3 x = 10 / 3 answer : a" + }, + { + "Answer": 68, + "Options": "a ) 64 , b ) 68 , c ) 65 , d ) 66 , e ) 67", + "Correct": "b", + "Explanation": "sum of all the 17 numbers = 17 * 59 = 1,003 sum of the first 9 of them = 9 * 56 = 504 sum of the last 9 of them = 9 * 63 = 567 so , the 8 th number = 504 + 567 - 1,003 = 68 . answer : b" + }, + { + "Answer": 2, + "Options": "a ) 2 , b ) - 2 , c ) 3 , d ) - 3 , e ) 4", + "Correct": "a", + "Explanation": "\"( 1 ) x = 10 y + 3 ( 2 ) 2 x = 21 y + 1 ( 2 ) - ( 1 ) : x = 11 y - 2 11 y - x = 2 the answer is a .\"" + }, + { + "Answer": 39, + "Options": "a ) $ 21 , b ) $ 27 , c ) $ 31 , d ) $ 39 , e ) it can not be determined", + "Correct": "d", + "Explanation": "\"let ' s suppose that the price of a burger is bb , of a shake - ss and that of a cola is cc . we can then construct these equations : 3 b + 7 s + c = 120 4 b + 10 s + c = 160.5 subtracting the first equation from the second gives us b + 3 s = 40.5 now if we subtract the new equation two times from first or 3 times from second we will get b + s + c = 39 . in any case , there is no necessity to know each item ' s price , just the sum . answer : d\"" + }, + { + "Answer": 6, + "Options": "a ) 6 , 8 , b ) 9 , 12 , c ) 12 , 16 , d ) 16 , 20 , e ) none", + "Correct": "a", + "Explanation": "solution let the numbers be 3 x and 4 x . then , ( 4 x ) 2 = 8 x ( 3 x ) 2 - 224 \u2039 = \u203a 16 x 2 = 72 x 2 - 224 \u2039 = \u203a 56 x 2 = 224 . \u2039 = \u203a x 2 = 4 . \u2039 = \u203a x = 2 . so , the numbers are 6 and 8 . answer a" + }, + { + "Answer": 650, + "Options": "a ) $ 550 , b ) $ 650 , c ) $ 750 , d ) $ 850 , e ) $ 950", + "Correct": "b", + "Explanation": "\"0.1 x = 0.08 ( 2000 - x ) + 83 0.18 x = 243 x = 1350 then the amount invested at 8 % is $ 2000 - $ 1350 = $ 650 the answer is b .\"" + }, + { + "Answer": 21, + "Options": "a ) 22 , b ) 21 , c ) 88 , d ) 76 , e ) 29", + "Correct": "b", + "Explanation": "answer : b ) 21" + }, + { + "Answer": 0.6666666666666666, + "Options": "a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4", + "Correct": "d", + "Explanation": "\"for n ( n + 1 ) to be a multiple of 3 , either n or n + 1 has to be a multiple of 3 . thus n must be of the form 3 k or 3 k - 1 , but not 3 k + 1 . the probability is 2 / 3 . the answer is d .\"" + }, + { + "Answer": 12, + "Options": "a ) 23 , b ) 11 , c ) 2 , d ) 10 , e ) 12", + "Correct": "e", + "Explanation": "total products to be stored 212 the big box can store 50 small box can store 40 storing 212 products in big box 212 / 50 = 4 r 12 least number of toys that will be left unboxed = 12 answer : e" + }, + { + "Answer": 12.28070175438597, + "Options": "a ) 19 % , b ) 12.3 % , c ) 25 % , d ) 40 % , e ) 9.4 %", + "Correct": "b", + "Explanation": "cost of food ( c ) = food consumed per student ( f ) * number of students ( n ) * price of food ( p ) originally , c = fnp when number of students decrease by 5 % , and the price of food increases by 20 % , c = f ( new ) * ( 0.95 n ) * ( 1.2 p ) = > f ( new ) = f / ( 0.95 * 1.2 ) = > f ( new ) = 0.877 f therefore the new cost of food must be 87.7 % of the old cost , or the cost of food must decrease by 12.28 % ( optionb )" + }, + { + "Answer": 650, + "Options": "a ) 280 , b ) 400 , c ) 540 , d ) 650 , e ) 840", + "Correct": "d", + "Explanation": "\"of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month : 2 / 3 * 3 / 4 = 1 / 2 survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year : ( 1 - 3 / 5 ) * 1 / 2 = 1 / 5 survived the first year . 130 geese survived the first year : 1 / 5 * ( total ) = 130 - - > ( total ) = 650 . answer : d .\"" + }, + { + "Answer": 44.99999999999999, + "Options": "a ) 36 , b ) 39 , c ) 42 , d ) 45 , e ) 48", + "Correct": "d", + "Explanation": "\"( v * ) * = ( v - v / 3 ) - ( v - v / 3 ) / 3 20 = 2 v / 3 - 2 v / 9 = 4 v / 9 v = 45 the answer is d .\"" + }, + { + "Answer": 8, + "Options": "a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 13", + "Correct": "b", + "Explanation": "let the number be xy . given xy \u2013 yx = 36 . this means the number is greater is than the number got on reversing the digits . this shows that the ten \u2019 s digit x > unit digit y . also given ratio between digits is 1 : 2 = > x = 2 y ( 10 x + y ) \u2013 ( 10 y + x ) = 36 = > x \u2013 y = 4 = > 2 y \u2013 y = 4 . hence , ( x + y ) \u2013 ( x \u2013 y ) = 3 y \u2013 y = 2 y = 8 b" + }, + { + "Answer": 995456, + "Options": "a ) 444440 , b ) 610000 , c ) 666640 , d ) 995456 , e ) 880000", + "Correct": "d", + "Explanation": "n = 4 * 4 * 4 * 4 = 256 < x > = ( 5555 + 2222 ) / 2 = 3888.5 sum = number of integers x average value n * < x > = 256 * 3888.5 = 711040 answer = d" + }, + { + "Answer": 2, + "Options": "a ) 10 , b ) 12 , c ) 16 , d ) 2 , e ) 22", + "Correct": "d", + "Explanation": "\"let original strength = y then , 40 y + 2 x 32 = ( y + 2 ) x 36 \u00e2 \u2021 \u2019 40 y + 64 = 36 y + 72 \u00e2 \u2021 \u2019 4 y = 8 \u00e2 \u02c6 \u00b4 y = 2 d\"" + }, + { + "Answer": 11, + "Options": "a ) 10.5 , b ) 11 , c ) 11.5 , d ) 12 , e ) 12.5", + "Correct": "b", + "Explanation": "\"the value which isexactlytwo sd less than the mean is : mean - 2 * sd = 14.0 - 2 * 1.5 = 11 . answer : b .\"" + }, + { + "Answer": 2, + "Options": "a ) 24 , b ) 12 , c ) 6 , d ) 4 , e ) 2", + "Correct": "e", + "Explanation": "the greatest common divisor of 16 and 20 is 4 . hence 16 * 20 = 4 ( note that * here denotes the function not multiplication ) . the greatest common divisor of 18 and 24 is 6 . hence 18 * 24 = 6 . hence ( ( 16 * 20 ) * ( 18 * 24 ) ) = 4 * 6 . the greatest common divisor of 4 and 6 is 2 . answer ; e ." + }, + { + "Answer": 5, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "c", + "Explanation": "\"the class borrowed a total of 40 * 2 = 80 books . the 26 students who borrowed 0 , 1 , or 2 books borrowed a total of 12 + 12 * 2 = 36 . to maximize the number of books borrowed by 1 student , let ' s assume that 13 students borrowed 3 books and 1 student borrowed the rest . 80 - 36 - 3 * 13 = 5 the maximum number of books borrowed by any student is 5 . the answer is c .\"" + }, + { + "Answer": 64, + "Options": "a ) 33.25 , b ) 89 , c ) 64 , d ) 68 , e ) 90", + "Correct": "c", + "Explanation": "explanation : = ( 48 \u00d7 12 ) \u2212 ( 40 \u00d7 8 ) / 4 = ( 576 \u2212 320 ) / 4 = 64 answer : option c" + }, + { + "Answer": 34.285714285714285, + "Options": "a ) 34 , b ) 25 , c ) 48 , d ) 50 , e ) none", + "Correct": "a", + "Explanation": "answer sum of 70 result = sum of 40 result + sum of 30 result . = 40 x 30 + 30 x 40 = 2400 / 70 correct option : a" + }, + { + "Answer": 0.4242424242424242, + "Options": "a ) 1 / 6 , b ) 2 / 33 , c ) 14 / 33 , d ) 9 / 16 , e ) 3 / 44", + "Correct": "c", + "Explanation": "\"method - 1 there are 9 fine pieces of pen and 4 defective in a lot of 12 pens i . e . probability of first pen not being defective = ( 8 / 12 ) i . e . probability of second pen not being defective = ( 7 / 11 ) [ 11 pen remaining with 8 defective remaining considering that first was defective ] probability of both pen being non - defective = ( 8 / 12 ) * ( 7 / 11 ) = 14 / 33 answer : option c\"" + }, + { + "Answer": 104, + "Options": "a ) 102 % , b ) 105 % , c ) 120 % , d ) 135 % , e ) 104 %", + "Correct": "e", + "Explanation": "\"easiest thing to do : assume that price is 100 price at the end of yr 1 : 100 + 30 = 130 price at the end of year 2 = 130 - 130 * 0.20 = 130 * 0.80 = 104 hence required answer = ( 104 / 100 ) * 100 % = 104 % answer is e .\"" + }, + { + "Answer": 301, + "Options": "a ) 201 , b ) 394 , c ) 302 , d ) 301 , e ) 294", + "Correct": "d", + "Explanation": "d = d * q + r d = 21 * 14 + 7 d = 294 + 7 d = 301" + }, + { + "Answer": 40, + "Options": "a ) 40 , b ) 20 , c ) 25 , d ) 30 , e ) 35", + "Correct": "a", + "Explanation": "250 employees : 90 male , 160 female 40 managers , 210 associates 160 male associates implies 50 female associates which means the remaining 40 females must be managers a . 40" + }, + { + "Answer": 265, + "Options": "a ) 24 , b ) 77 , c ) 297 , d ) 265 , e ) 29", + "Correct": "d", + "Explanation": "\"explanation : 61 - 6 = 53 53 x 5 = 265 answer : d\"" + }, + { + "Answer": 63, + "Options": "a ) 21 , b ) 63 , c ) 3969 , d ) 147 , e ) 167", + "Correct": "b", + "Explanation": "\"answer let ( y / 21 ) x ( y / 189 ) = 1 then , y 2 = 21 x 189 = 21 x 21 x 9 \u2234 y = ( 21 x 3 ) = 63 . option : b\"" + }, + { + "Answer": 0.2, + "Options": "a ) 0.01 , b ) 0.02 , c ) 0.03 , d ) 0.1 , e ) 0.2", + "Correct": "e", + "Explanation": "rounding off the values : x = 13.17 y = 7.69 z = 11.55 a = 13.17 + 7.69 + 11.55 = 32.41 x + y + z = 13.165 + 7.686 + 11.545 = 32.206 b = 32.21 a - b = 0.2 option e" + }, + { + "Answer": 810, + "Options": "a ) s . 800 , b ) s . 810 , c ) s . 820 , d ) s . 900 , e ) s . 920", + "Correct": "b", + "Explanation": "\"2430 * 1 / 3 = 810 option b\"" + }, + { + "Answer": 46.8, + "Options": "a ) 79 , b ) 99 , c ) 47 , d ) 89 , e ) 45", + "Correct": "c", + "Explanation": "average = ( 45 + 35 + 52 + 47 + 55 ) / 5 = 234 / 5 = 47 . answer : c" + }, + { + "Answer": 5, + "Options": "a ) 2 , b ) 5 , c ) 7 , d ) 24 , e ) 35", + "Correct": "b", + "Explanation": "\"ab = 10 + 2 ( a + b ) 9 a = 10 + 2 a + 18 7 a = 28 a = 4 b - a = 9 - 4 = 5 b is the answer\"" + }, + { + "Answer": 1350, + "Options": "a ) $ 880 , b ) $ 990 , c ) $ 1,350 , d ) $ 1,100 , e ) $ 1,210", + "Correct": "c", + "Explanation": "\"10 / 100 p = 150 > > p = 150 * 100 / 10 = 1500 1500 - 150 = 1350 answer : c\"" + }, + { + "Answer": 90, + "Options": "a ) 90 , b ) 98 , c ) 106 , d ) 120 , e ) 136", + "Correct": "a", + "Explanation": "we see that h will be a maximum h = 150 when t - 3 = 0 , that is when t = 3 . at t = 5 , h = - 15 ( 5 - 3 ) ^ 2 + 150 = - 15 ( 4 ) + 150 = 90 the answer is a ." + }, + { + "Answer": 6, + "Options": "a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 7", + "Correct": "d", + "Explanation": "let seventh observation = x . then , according to the question we have = > ( 78 + x ) / 7 = 12 = > x = 6 . hence , the seventh observation is 6 . answer : d" + }, + { + "Answer": 4550, + "Options": "a ) 4554 , b ) 4657 , c ) 8457 , d ) 3458 , e ) 5254", + "Correct": "a", + "Explanation": "let man , s age be xy the woman ' s age is yx then 10 x + y - 10 y - x = 1 / 11 ( 10 x + y + 10 y + x ) 9 x - 9 y = x + y 8 x = 10 y x / y = 10 / 8 = 5 / 4 so xy = 54 and yx = 45 answer : a" + }, + { + "Answer": 45, + "Options": "a ) 57 , b ) 67 , c ) 45 , d ) 47 , e ) 97", + "Correct": "c", + "Explanation": "\"money collected = ( 20.25 x 100 ) paise = 2025 paise numbers of members = 2025 squareroot = 45 answer c\"" + }, + { + "Answer": 88, + "Options": "a ) 40 , b ) 44 , c ) 80 , d ) 88 , e ) 48", + "Correct": "d", + "Explanation": "\"according to the given conditions x + y = 24 and x ^ 2 + y ^ 2 = 400 now ( x + y ) ^ 2 = x ^ 2 + y ^ 2 + 2 xy so 24 ^ 2 = 400 + 2 xy so xy = 176 / 2 = 88 answer : d\"" + }, + { + "Answer": 42, + "Options": "a ) 45 , b ) 48 , c ) 51 , d ) 42 , e ) 54", + "Correct": "d", + "Explanation": "let the numbers be 3 x , 3 x + 3 and 3 x + 6 . then , 3 x + ( 3 x + 3 ) + ( 3 x + 6 ) = 117 9 x = 108 x = 12 largest number = 3 x + 6 = 42 answer : d" + }, + { + "Answer": 12, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 12", + "Correct": "e", + "Explanation": "\"say the number of people having birthdays on wednesday is x and the number of people having birthdays on each of the other 6 days is y . then x + 6 y = 50 . now , plug options for x . only a and e give an integer value for y . but only for e x > y as needed . answer : e .\"" + }, + { + "Answer": 53.33, + "Options": "a ) 53.33 , b ) 46.33 , c ) 15.36 , d ) 15.45 , e ) 15.48", + "Correct": "a", + "Explanation": "320 \u00e3 \u00b7 2 \u00e3 \u00b7 3 = 320 \u00e3 \u2014 1 / 2 \u00e3 \u2014 1 / 3 = 160 / 3 = 53.33 correct answer : a" + }, + { + "Answer": 263.6363636363636, + "Options": "a ) s . 263 , b ) s . 283 , c ) s . 293 , d ) s . 300 , e ) s . 383", + "Correct": "a", + "Explanation": "\"let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 580 but x = 120 % of y = 120 y / 100 = 12 y / 10 \u2234 12 y / 10 + y = 580 \u21d2 y [ 12 / 10 + 1 ] = 580 \u21d2 22 y / 10 = 580 \u21d2 22 y = 5800 \u21d2 y = 5800 / 22 = rs . 263 a )\"" + }, + { + "Answer": 5, + "Options": "a ) 11 , b ) 12 , c ) 5 , d ) 14 , e ) 18", + "Correct": "c", + "Explanation": "5 answer : c" + }, + { + "Answer": 0.20833333333333334, + "Options": "a ) 5 / 24 , b ) 6 / 24 , c ) 7 / 24 , d ) 8 / 24 , e ) 9 / 24", + "Correct": "a", + "Explanation": "\"p = 3 / 8 , q = 3 / 18 = > q = 1 / 6 therefore p - q = ( 3 / 8 ) - ( 1 / 6 ) = 5 / 24 answer : a\"" + }, + { + "Answer": 1000, + "Options": "a ) $ 200 , b ) $ 300 , c ) $ 400 , d ) $ 500 , e ) $ 1000", + "Correct": "e", + "Explanation": "\"c for cost . p price per person . c = 4 * p c = 5 * p - 250 substituting the value of p from the first equation onto the second we get p = 250 . plugging in the value of p in the first equation , we get c = 1000 . which leads us to answer choice e\"" + }, + { + "Answer": 26, + "Options": "a ) 33 , b ) 82 , c ) 99 , d ) 89 , e ) 27", + "Correct": "d", + "Explanation": "answer : d" + }, + { + "Answer": 750, + "Options": "a ) 750 , b ) 277 , c ) 878 , d ) 450 , e ) 272", + "Correct": "a", + "Explanation": "\"10 * 150 = 1500 3 * 100 + 3 * 150 = 750 1500 \u2013 750 = 750 answer : a\"" + }, + { + "Answer": 5, + "Options": "a ) 5 % , b ) 6 % , c ) 7 % , d ) 8 % , e ) 9 %", + "Correct": "a", + "Explanation": "\"the difference of two successive amounts must be the simple interest in 1 year on the lower amount of money . s . i = 18522 / - - 17640 / - = rs . 882 / - rate of interest = ( 882 / 17640 ) \u00d7 ( 100 / 1 ) = > 8820 / 1764 = 5 % principal = amount / ( 1 + r / 100 ) n = 17640 / ( 1 + 5 / 100 ) 2 = 17640 / ( 21 / 20 \u00d7 21 / 20 ) = 17640 / ( 1.05 \u00d7 1.05 ) = 17640 / 1.1025 = 16000 thus the principal is rs . 16000 / - and the rate of interest is 5 % a\"" + }, + { + "Answer": 16, + "Options": "a ) 12 , b ) 16 , c ) 20 , d ) 24 , e ) 28", + "Correct": "b", + "Explanation": "let dan ' s present age be x . x + 16 = 4 ( x - 8 ) 3 x = 48 x = 16 the answer is b ." + }, + { + "Answer": 4970, + "Options": "a ) 4520 , b ) 4350 , c ) 4210 , d ) 4100 , e ) 4970", + "Correct": "e", + "Explanation": "\"explanation : = 5020 \u2212 ( 1004 / 2008 \u00d7 100 ) = 5020 \u2212 50 = 4970 option e\"" + }, + { + "Answer": 36, + "Options": "a ) 20 min , b ) 25 min , c ) 26 min , d ) 36 min , e ) 30 min", + "Correct": "d", + "Explanation": "50 % of 60 = 30 % or 0.30 2 hr x 60 min = 120 min 120 min x 0.30 = 36 min it will take 36 min longer to print them with only 50 printers . answer is d" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 10 , c ) 11 , d ) 19 , e ) none of these", + "Correct": "a", + "Explanation": "solution required number of student = h . c . f of 1802 and 1203 = 1 . answer a" + }, + { + "Answer": 22, + "Options": "a ) 12 , b ) 18 , c ) 22 , d ) 28 , e ) 36", + "Correct": "c", + "Explanation": "\"3.456789 ^ 11 has 6 * 11 = 66 decimal places . 10 ^ 44 moves the decimal place to the right 44 places . ( 10 ^ 4 * 3.456789 ) ^ 11 has 66 - 44 = 22 digits after the decimal point . the answer is c .\"" + }, + { + "Answer": 55, + "Options": "a ) a ) 10 , b ) b ) 25 , c ) c ) 40 , d ) d ) 55 , e ) e ) 70", + "Correct": "d", + "Explanation": "total score of 16 students is 16 * 62.50 = 1000 total score of 15 students is 15 * 63 = 945 so , the score of the person who left is 55 ( 1000 - 945 ) answer will be ( d )" + }, + { + "Answer": 2, + "Options": "a ) 3 , b ) 2 , c ) 9 , d ) 8 , e ) 7", + "Correct": "b", + "Explanation": "there are total 40 workers . one - fourth of the workers in palabras bookstore have read the latest book by j . saramago , so 10 have read saramago . 5 / 8 of the workers have read the latest book by h . kureishi . so ( 5 / 8 ) * 40 = 25 have read kureishi the number of workers that have read neither book is one less than the number of the workers that have read the latest saramago book and have not read the latest kureishi book if b workers have read both books , 20 - b have read saramago but not kureishi . so , ( 10 - b - 1 ) have read neither . total = n ( a ) + n ( b ) - both + neither 40 = 10 + 25 - b + ( 10 - b - 1 ) b = 2 answer ( b )" + }, + { + "Answer": 14, + "Options": "a ) 10 , b ) 20 , c ) 28 , d ) 14 , e ) 19", + "Correct": "d", + "Explanation": "number of statues = all the paint \u00f7 amount used per statue = 7 / 8 \u00f7 1 / 16 = 7 / 8 * 16 / 1 = 112 / 8 = 14 . answer is d ." + }, + { + "Answer": 200, + "Options": "a ) $ 200 , b ) $ 275 , c ) $ 510 , d ) $ 1,250 , e ) $ 2,550", + "Correct": "a", + "Explanation": "\"the volume of each box is 20 * 20 * 12 = 4800 cubic inches . number of boxes = 2 , 400,000 / 4800 = 500 boxes total cost = 500 \u00d7 $ 0.4 = $ 200 the answer is a .\"" + }, + { + "Answer": 1.875, + "Options": "a ) 15 / 8 , b ) 3 / 8 , c ) 5 / 8 , d ) 7 / 15 , e ) 8 / 15", + "Correct": "a", + "Explanation": "\"1 / r = 1 / x + 1 / y 1 / r = 1 / 3 + 1 / 5 = 8 / 15 r = 15 / 8 the answer is a .\"" + }, + { + "Answer": 1, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "b", + "Explanation": "\"number = 269 * 68 + 0 = 18292 67 ) 18292 ( 273 18291 - - - - - - - - 1 required number = 1 . answer : b\"" + }, + { + "Answer": 3, + "Options": "a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : on dividing 427398 by 15 we get the remainder 3 , so 3 should be subtracted answer : option a\"" + }, + { + "Answer": 12, + "Options": "a ) 13 , b ) 12 , c ) 16 , d ) 17 , e ) 18", + "Correct": "b", + "Explanation": "\"12 , 15 , 18 , 21 , 24 , 27 , 30 , 33 , 36 , 39 , 42 , 45 . 12 numbers . 10 / 3 = 3 and 46 / 3 = 15 = = > 15 - 3 = 12 . therefore 12 digits b )\"" + }, + { + "Answer": 990, + "Options": "a ) 732 , b ) 990 , c ) 1098 , d ) 1305 , e ) 1605", + "Correct": "b", + "Explanation": "\"explanation : total number of digits = ( no . of digits in 1 - digit page nos . + no . of digits in 2 - digit page nos . + no . of digits in 3 - digit page nos . ) = ( 1 x 9 + 2 x 90 + 3 x 267 ) = ( 9 + 180 + 801 ) = 990 . answer : b\"" + }, + { + "Answer": 4, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 3 , e ) 2", + "Correct": "a", + "Explanation": "1 / 5 ^ m * 1 / 4 ^ 2 = 1 / 2 ^ 4 * 5 ^ 4 2 ^ 4 * 5 ^ 4 / 2 ^ 4 = 5 ^ m or 5 ^ 4 = 5 ^ m therefore m = 4 a" + }, + { + "Answer": 16, + "Options": "a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16", + "Correct": "e", + "Explanation": "frank is 15 years younger then john - - > f + 15 = j ; in 5 years john will be twice as old as frank ( in 3 year john will be j + 3 years old and frank will be f + 3 years old ) - - > j + 3 = 2 * ( f + 3 ) - - > ( f + 15 ) + 3 = 2 * ( f + 3 ) - - > f = 12 ; in 4 years frank will be 12 + 4 = 16 years old . answer : e ." + }, + { + "Answer": 150, + "Options": "a ) 72 , b ) 80 , c ) 120 , d ) 40 , e ) 150", + "Correct": "e", + "Explanation": "\"explanation : let the number of students be x . then , number of students above 8 years of age = ( 100 - 20 ) % of x = 80 % of x . 80 % of x = 72 + 2 / 3 of 72 80 / 100 x = 120 x = 150 . answer : option e\"" + }, + { + "Answer": 7, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", + "Correct": "a", + "Explanation": "the units digit of 734 ^ 99 is 4 because 4 raised to the power of an odd integer ends in 4 . the units digit of 347 ^ 83 is 3 because powers of 7 end in 7 , 9 , 3 , or 1 cyclically . since 83 is in the form 4 n + 3 , the units digit is 3 . then 4 + 3 = 7 . the answer is a ." + }, + { + "Answer": 600, + "Options": "a ) 90 , b ) 120 , c ) 160 , d ) 360 , e ) 600", + "Correct": "e", + "Explanation": "\"if we exclude those cases and take the question at face value , then it seems straightforward . group # 1 = ( did n ' t like , did n ' t understand ) = 150 group # 2 = ( likeunderstood ) = 3 / 4 ( 1 / 4 ) n = 150 n = 600 answer = ( e )\"" + }, + { + "Answer": 36, + "Options": "a ) 26 , b ) 36 , c ) 16 , d ) 06 , e ) 40", + "Correct": "b", + "Explanation": "explanation : let ' s call : a = 123456789101112131415161718192021222324252627282930313233343536373839404142434481 = > a = b * 100 + 81 [ with b = 1234567 . . . . . 424344 ] we have : b x 100 is divisible by 45 because : - sum of all digits in b = 1 + 2 + 3 + . . . . + 44 = ( 1 + 44 ) + ( 2 + 43 ) + . . . . + ( 22 + 23 ) ( 22 pairs ) = 22 * 45 = > b divisible for 9 since b is divisible by 9 , b * 100 will be divisible by 9 * 5 = 45 81 divided 45 gives a remainder of 36 therefore , a divided by 45 reminder 36 answer : b" + }, + { + "Answer": 0.6761904761904762, + "Options": "a ) 1 / 140 , b ) 1 / 180 , c ) 71 / 105 , d ) 21 / 113 , e ) 57 / 120", + "Correct": "c", + "Explanation": "\"required probability = p ( x ) + p ( y ) + p ( z ) ( all the events are mutually exclusive ) . = 1 / 7 + 1 / 3 + 1 / 5 = 71 / 105 answer : c\"" + }, + { + "Answer": 80, + "Options": "a ) 40 , b ) 80 , c ) 70 , d ) 60 , e ) 50", + "Correct": "b", + "Explanation": "\"200 men do the rest of the work in 100 - 20 = 80 days 100 men can do the rest of the work in 80 * 200 / 100 = 160 days required number of days = 160 - 80 = 80 days answer is b\"" + }, + { + "Answer": 5, + "Options": "a ) 7.9 s , b ) 2.5 s , c ) 5 s , d ) 7.6 s , e ) 7.4 s", + "Correct": "c", + "Explanation": "explanation : 72 km / hr = 72 * 5 / 18 = 20 m / s speed = distance / time ; v = d / t 20 = 100 / t t = 5 s answer : c" + }, + { + "Answer": 28, + "Options": "a ) 0 , b ) 12 , c ) 13 , d ) 20 , e ) 28", + "Correct": "e", + "Explanation": "\"12 * 49 = 588 588 % 21 = 28 answer : e\"" + }, + { + "Answer": 2.2499999999999996, + "Options": "a ) $ 2.25 , b ) $ 3.00 , c ) $ 3.25 , d ) $ 3.65 , e ) $ 4.80", + "Correct": "a", + "Explanation": "\"x = 3 x / 5 + 1 / 3 * 2 x / 5 + 60 4 x / 15 = 60 x = 225 = $ 2.25 the answer is a .\"" + }, + { + "Answer": 10, + "Options": "a ) 10 , b ) 8 , c ) 6 , d ) 5 , e ) 7", + "Correct": "a", + "Explanation": "\"let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 27 5 x = 25 x = 5 . hence , b ' s age = 2 x = 10 years answer : a\"" + }, + { + "Answer": 9936, + "Options": "a ) 4676 , b ) 4678 , c ) 8888 , d ) 9504 , e ) 9936", + "Correct": "e", + "Explanation": "\"largest 4 digit number = 9999 9999 \u00f7 72 = 138 , remainder = 63 hence largest 4 digit number exactly divisible by 88 = 9999 - 63 = 9936 answer : e\"" + }, + { + "Answer": 26, + "Options": "a ) 16 , b ) 26 , c ) 36 , d ) 46 , e ) 56", + "Correct": "b", + "Explanation": "substitute x by 10 in the given expression and evaluate 30 - | - ( 10 ) + 6 | = 30 - | - 10 + 6 | = 30 - | - 4 | = 30 - 4 = 26 correct answer b ) 26" + }, + { + "Answer": 5, + "Options": "a ) 8 , b ) 9 , c ) 5 , d ) 7 , e ) 10", + "Correct": "c", + "Explanation": "cost of each apple = 4 dollars apples that benny can buy with the amount she has = 360 / 4 = 90 . apples that each kid gets evenly = 90 / 18 = 5 apples . so the answer is c = 5" + }, + { + "Answer": 58, + "Options": "a ) 50 , b ) 56 , c ) 58 , d ) 62 , e ) 66", + "Correct": "c", + "Explanation": "\"given that , total average r sold is 66 , male / female = 1 / 2 and female average is 70 . average of male members isx . ( 70 * f + x * m ) / ( m + f ) = 66 - > solving this equation after substituting 2 m = f , x = 58 . ans c .\"" + }, + { + "Answer": 100, + "Options": "a ) 33.33 % , b ) 100 % , c ) 75 % , d ) 66.66 % , e ) none of these", + "Correct": "b", + "Explanation": "\"using formula ( x / ( 100 - x ) * 100 ) where x is percentage decrease ( here it is 25 % ) = > 50 ( 100 - 50 ) * 100 = 100 % answer : b\"" + }, + { + "Answer": 1375, + "Options": "a ) 1375 , b ) 1376 , c ) 1875 , d ) 1365 , e ) 1345", + "Correct": "a", + "Explanation": "\"explanation : 20 * 66 + 55 = 1375 answer : a\"" + }, + { + "Answer": 13.2, + "Options": "a ) 66 / 5 , b ) 13 , c ) 17 , d ) 21 , e ) 23", + "Correct": "a", + "Explanation": "let bucket a be a and bucket b be b scenario 1 a - 6 = 1 / 3 ( b + 6 ) - - - - > 3 a - 18 = b + 6 scenario 2 b - 6 = 1 / 2 ( a + 6 ) - - - - - > 2 b - 12 = a + 6 from scenario 1 , b = 3 a - 24 substitute b with this information in stmt 2 2 ( 3 a - 24 ) - 12 = a + 6 - - - - - - > 6 a - 48 - 12 = a + 6 - - - - - - > 6 a - a = 60 + 6 - - - > 5 a = 66 a = 66 / 5 , answer choice a" + }, + { + "Answer": 12.46, + "Options": "a ) $ 3.36 , b ) $ 6.85 , c ) $ 8.46 , d ) $ 10.08 , e ) $ 12.46", + "Correct": "e", + "Explanation": "\"answer = e 2 * 2.49 + 4 * 1.87 = 2 ( 2.50 - 0.01 ) + 4 ( 2.00 - 0.13 ) = 5 + 8 - 0.02 - 0.52 = 13 - 0.54 = 12.46\"" + }, + { + "Answer": 40, + "Options": "a ) 40 % , b ) 48 % , c ) 54 % , d ) 58 % , e ) 65 %", + "Correct": "a", + "Explanation": "when the storm deposited 110 billion gallons , volume of water in the reservoir = 220 + 110 = 360 billion gallons if this is only 60 % of the capacity of the reservoir , the total capacity of the reservoir = 330 / 0.6 = 550 billion gallons therefore percentage of reservoir that was full before the storm = ( 220 / 550 ) * 100 = 40 % option a" + }, + { + "Answer": 11110, + "Options": "a ) 900 , b ) 11110 , c ) 1100 , d ) 1200 , e ) 1400", + "Correct": "b", + "Explanation": "\"10 / 9 = 1 and 100000 / 9 = 11111 = = > 11111 - 1 = 11110 . answer : b\"" + }, + { + "Answer": 5, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 12 , e ) 24", + "Correct": "b", + "Explanation": "\"let ' s start with 4 minimum number of colors so single color code we can make 4 nos . now if we need to make 2 color combination out of 4 we can do so in 4 ! / 2 ! * 2 ! or 4 * 3 / 2 or 6 so total we can make 4 + 6 = 10 color combinations but we have 12 boxes so let ' s look at 5 we get 5 single color codes and out 5 color choices , we can choose 2 in 5 ! / 2 ! * 3 ! ways or 10 ways . so total we can have 5 + 10 = 15 color combinations . so , minimum number we need will be 5 ans is b . . . . . . .\"" + }, + { + "Answer": 9.000000000000002, + "Options": "a ) 9 , b ) 8 , c ) 7 , d ) 6 , e ) 5", + "Correct": "a", + "Explanation": "log 9 ( x 3 ) = log 2 ( 8 ) : given log 2 ( 23 ) = 3 : simplify right hand side of given equation . log 9 ( x 3 ) = 3 : rewrite the above equation log 9 ( x 3 ) = log 9 ( 93 ) : rewite 3 as a log base 9 . x 3 = 93 : obtain algebraic equation from eqaution d . x = 9 : solve above for x correct answer a" + }, + { + "Answer": 0.45454545454545453, + "Options": "a ) 10 / 16 , b ) 6 / 16 , c ) 4 / 16 , d ) 5 / 11 , e ) 4 / 10", + "Correct": "d", + "Explanation": "\"w = m + 6 w + m = 16 m + 6 + m = 16 2 m = 10 m = 5 w = 11 ratio : 5 : 11 ans : d\"" + }, + { + "Answer": 1991, + "Options": "a ) s . 1991 , b ) s . 2991 , c ) s . 3991 , d ) s . 4991 , e ) s . 5991", + "Correct": "a", + "Explanation": "\"explanation : total sale for 5 months = rs . ( 3435 + 3927 + 3855 + 4230 + 3562 ) = rs . 19009 . required sale = rs . [ ( 3500 x 6 ) \u00e2 \u20ac \u201c 19009 ] = rs . ( 21000 \u00e2 \u20ac \u201c 19009 ) = rs . 1991 . answer a\"" + }, + { + "Answer": 11, + "Options": "a ) 5 , b ) 7 , c ) 10 , d ) 12 , e ) 11", + "Correct": "e", + "Explanation": "explanation : let the number of pigs be x and the number of hens be y . then , 4 x + 2 y = 2 ( x + y ) + 22 4 x + 2 y = 2 x + 2 y + 22 2 x = 22 x = 11 answer : e" + }, + { + "Answer": 10, + "Options": "a ) 20 , b ) 18 , c ) 11 , d ) 10 , e ) 5", + "Correct": "d", + "Explanation": "add these two equations 2 x + 4 y = 20 divide by 2 ( to get x + 2 y ) answer will be d . 10" + }, + { + "Answer": 4, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8", + "Correct": "a", + "Explanation": "\"a + b + c = 18 b + c + d = 15 a + d = 11 a \u2013 d = 3 a + d = 11 2 d = 8 d = 4 answer : a\"" + }, + { + "Answer": 5100, + "Options": "a ) rs . 4500 , b ) rs . 4700 , c ) rs . 4800 , d ) rs . 5000 , e ) rs . 5100", + "Correct": "e", + "Explanation": "\"total sale for 5 months = rs . ( 6400 + 7000 + 6800 + 7200 + 6500 ) = rs . 33900 required sale = rs . [ ( 6500 x 6 ) - 34009 ] = rs . ( 39000 - 33900 ) = rs . 5100 answer : e\"" + }, + { + "Answer": 28, + "Options": "a ) $ 5 , b ) $ 10 , c ) $ 14 , d ) $ 28 , e ) $ 29", + "Correct": "d", + "Explanation": "\"bill = fixed charge + charge of calls made in jan , bill = fixed charge ( let , y ) + charge of calls made in jan ( let , x ) = $ 52 in feb , bill = fixed charge ( let , y ) + charge of calls made in feb ( then , 2 x ) = $ 76 i . e . x + y = 52 and 2 x + y = 76 take the difference if two equations i . e . ( 2 x + y ) - ( x + y ) = 76 - 52 i . e . x = 24 i . e . fixed monthly charge , y = 28 answer : option d\"" + }, + { + "Answer": 9, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 10 , e ) 9", + "Correct": "e", + "Explanation": "6 * 1024 + 4 * 64 + 2 = 6144 + 256 + 2 = 6402 in binary code 6402 base 10 = 11001 000000 10 in base 2 . so 9 zeros are there . answer : e" + }, + { + "Answer": 484.76847061839544, + "Options": "a ) 489.66 , b ) 406.07 , c ) 406.04 , d ) 306.03 , e ) 306.01", + "Correct": "a", + "Explanation": "\"a = 8000 ( 51 / 50 ) 3 = 8489.66 8000 - - - - - - - - - - - 489.66 answer : a\"" + }, + { + "Answer": 37.33333333333333, + "Options": "a ) 15 , b ) 30 , c ) 31 , d ) 37 , e ) 46", + "Correct": "d", + "Explanation": "\"we have to find the number of terms that are divisible by 2 but not by 6 ( as the question asks for the even numbers only which are not divisible by 3 ) for 2 , 10 , 12,14 . . . 120 using ap formula , we can say 120 = 10 + ( n - 1 ) * 2 or n = 56 . for 6 , 12,18 , . . . 120 using ap formula , we can say 120 = 12 + ( n - 1 ) * 6 or n = 19 . hence , only divisible by 2 but not 3 = 56 - 19 = 37 . hence , answer d\"" + }, + { + "Answer": 50, + "Options": "a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50", + "Correct": "e", + "Explanation": "0.037 * 10 ^ 5 can be written as 3700 74000 * 10 ^ ( - 3 ) can be written as 74 required = 3700 / 74 = 50 answer : e" + }, + { + "Answer": 40, + "Options": "a ) 18 , b ) 28 , c ) 40 , d ) 38 , e ) 59", + "Correct": "c", + "Explanation": "\"let x = the number sought . then x / 2 + x + 2 = 62 . x = 40 . c\"" + }, + { + "Answer": 9, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", + "Correct": "c", + "Explanation": "\"14 n + 34 = 16 ( n + 1 ) 2 n = 18 n = 9 the answer is c .\"" + }, + { + "Answer": 0.525, + "Options": "a ) \u00bd , b ) 21 / 40 , c ) 1 / 50 , d ) 1 / 500 , e ) 2 / 500", + "Correct": "b", + "Explanation": "\"let x be the difference then . 65 - 1 / 8 = x 65 / 100 - 1 / 8 = x x = 21 / 40 ans b\"" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "a", + "Explanation": "\"0 < x < 7 , 0 < x < 15 , 5 > x > \u2013 1 3 > x > 0 x < 2 from above : 0 < x < 2 - - > x = 1 . answer : a .\"" + }, + { + "Answer": 2, + "Options": "a ) 7 , b ) 6 , c ) 5 , d ) 2 , e ) 3", + "Correct": "d", + "Explanation": "explanation : the equation for this problem can be made as : 5 x + 7 y = 38 where x is the number of watermelons and y is the number of pineapples . now test for 2 , 3 and 4 : for y = 2 5 x + 14 = 38 x is not an integer for y = 3 5 x = 17 x not an integer for y = 4 x = 2 so 4 pineapples and 2 watermelons can be bought by 38 rs . answer : d" + }, + { + "Answer": 58, + "Options": "a ) 42 , b ) 32 , c ) 48 , d ) 28 , e ) 58", + "Correct": "e", + "Explanation": "x / 87 = 24 . x = 24 * 87 . so correct answer would be , ( 24 * 87 ) / 36 = 58 . answer : e" + }, + { + "Answer": 0.6666666666666666, + "Options": "a ) 4 / 7 , b ) 5 / 9 , c ) 2 / 3 , d ) 10 / 11 , e ) none of these", + "Correct": "c", + "Explanation": "explanation : let the required fraction be a / b . then \u21d2 a / b + 1 = 1 / 2 \u21d2 2 a \u2013 b = 1 - - - - ( 1 ) \u21d2 a + 1 / b = 1 \u21d2 a \u2013 b = \u2013 1 \u21d2 a \u2013 b = \u2013 1 - - - - - - - ( 2 ) solving ( 1 ) & ( 2 ) we get a = 2 , b = 3 fraction = a / b = 2 / 3 correct option : c" + }, + { + "Answer": 242.38423530919772, + "Options": "a ) 244.83 , b ) 306.07 , c ) 306.04 , d ) 306.03 , e ) 306.01", + "Correct": "a", + "Explanation": "\"a = 4000 ( 51 / 50 ) 3 = 4244.832 4000 - - - - - - - - - - - 244.83 answer : a\"" + }, + { + "Answer": 14, + "Options": "a ) 14 , b ) 15 , c ) 25 , d ) 13 , e ) 42", + "Correct": "a", + "Explanation": "x + y = 10 x - y = 18 2 x = 28 x = 14 answer is a" + }, + { + "Answer": 7, + "Options": "a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3", + "Correct": "a", + "Explanation": "\"on dividing 964807 by 15 we get the remainder 7 , so 7 should be subtracted a\"" + }, + { + "Answer": 1, + "Options": "a ) 2 hrs , b ) 3 hrs , c ) 1 hrs , d ) 1 1 / 2 hrs , e ) 2 1 / 2 hrs", + "Correct": "c", + "Explanation": "sol . distance between ramgarh and devgarh = ( 60 * 65 ) / 60 = 60 average speed of the bus is increased by 5 km / hr then the speed of the bus = 60 km / hr required time = 60 / 60 = 1 hr c" + }, + { + "Answer": 153, + "Options": "a ) 165 , b ) 185 , c ) 153 , d ) 198 , e ) 199", + "Correct": "c", + "Explanation": "\"153 answer is c\"" + }, + { + "Answer": 75, + "Options": "a ) 75 , b ) 150 , c ) 300 , d ) 600 , e ) 700", + "Correct": "a", + "Explanation": "\"required number = ( 75 / 2 ) / ( 1 / 2 ) = ( 75 / 2 x 2 / 1 ) = 75 answer : a\"" + }, + { + "Answer": 45, + "Options": "a ) 23 , b ) 45 , c ) 15 , d ) 28 , e ) 18", + "Correct": "b", + "Explanation": "a : b : c = 10 * 7 : 12 * 5 : 15 * 3 = 2 * 7 : 12 * 1 : 3 * 3 = 14 : 12 : 9 amount that c should pay = 175 * ( 9 / 35 ) = 5 * 9 = 45 answer is b" + }, + { + "Answer": 0.22727272727272727, + "Options": "a ) 1 / 6 , b ) 5 / 22 , c ) 6 / 11 , d ) 9 / 16 , e ) 3 / 4", + "Correct": "b", + "Explanation": "\"method - 1 there are 9 fine pieces of pen and 6 defective in a lot of 12 pens i . e . probability of first pen not being defective = ( 6 / 12 ) i . e . probability of second pen not being defective = ( 5 / 11 ) [ 11 pen remaining with 5 defective remaining considering that first was defective ] probability of both pen being non - defective = ( 6 / 12 ) * ( 5 / 11 ) = 5 / 22 answer : option b\"" + }, + { + "Answer": 0.4, + "Options": "a ) 0.2 , b ) 0.3 , c ) 0.4 , d ) 0.5 , e ) 0.6", + "Correct": "c", + "Explanation": "we are selecting from non - negative single digit integers , so from { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } . these 10 digits represent the total number of outcomes . hence , the total number of outcomes is 10 . we need to find the probability that the median of the set will increase but the range still remains the same . the median of the set is ( 3 + 5 ) / 2 = 4 , thus the number selected must be 5 or greater . for the range to remain the same , the number must be between 2 and 8 inclusive . to satisfy both conditions , the number selected must be 5 , 6 , 7 , or 8 . the probability is 4 / 10 = 0.4 the answer is c ." + }, + { + "Answer": 16, + "Options": "a ) 0 , b ) 9 , c ) 12 , d ) 16 , e ) 18", + "Correct": "d", + "Explanation": "\"from ( x + 4 ) ( y - 4 ) = 0 it follows that either x = - 4 or y = 4 . thus either x ^ 2 = 16 or y ^ 2 = 16 . now , if x ^ 2 = 16 , then the least value of y ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 16 + 0 = 16 . similarly if y ^ 2 = 16 , then the least value of x ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 0 + 16 = 16 . answer : d .\"" + }, + { + "Answer": 2015, + "Options": "a ) 2015 , b ) 2088 , c ) 270 , d ) 1881 , e ) 1781", + "Correct": "a", + "Explanation": "\"f ( f ( 0 ) ) + f ( 0 ) = 2 ( 0 ) + 3 \u21d2 \u21d2 f ( 1 ) = 3 - 1 = 2 , f ( 1 ) = 2 f ( f ( 1 ) ) + f ( 1 ) = 2 ( 1 ) + 3 \u21d2 \u21d2 f ( 2 ) = 5 - 2 = 3 , f ( 2 ) = 3 f ( f ( 2 ) ) + f ( 2 ) = 2 ( 2 ) + 3 \u21d2 \u21d2 f ( 3 ) = 7 - 3 = 4 , f ( 3 ) = 4 . . . . . . . . . . . . . . f ( 2014 ) = 2015 ans : a\"" + }, + { + "Answer": 51, + "Options": "a ) 23 , b ) 78 , c ) 27 , d ) 51 , e ) 81", + "Correct": "d", + "Explanation": "\"explanation : 50 + 5 * 12 / ( 180 / 3 ) = 50 + 5 * 12 / ( 60 ) = 50 + ( 5 * 12 ) / 60 = 50 + 1 = 51 . answer : d\"" + }, + { + "Answer": 1.9249999999999998, + "Options": "a ) $ 1.75 , b ) $ 1.93 , c ) $ 2.00 , d ) $ 2.15 , e ) $ 2.30", + "Correct": "b", + "Explanation": "this question can be solved with a handful of different algebra approaches ( as has been shown in the various posts ) . since the question asks for the price of the largest pot , and the answers are prices , we can test the answers . we ' re told that there are 6 pots and that each pot costs 25 cents more than the next . the total price of the pots is $ 8.25 . we ' re asked for the price of the largest ( most expensive ) pot . since the total price is $ 7.80 ( a 25 - cent increment ) and the the difference in sequential prices of the pots is 25 cents , the largest pot probably has a price that is a 25 - cent increment . from the answer choices , i would then test answer c first ( since answers b and d are not in 25 - cent increments ) . if . . . . the largest pot = $ 1.75 the other 5 pots are . . . . 1.75 1.50 1.25 1.00 0.75 total = $ 7.80 so this must be the answer . b" + }, + { + "Answer": 17, + "Options": "a ) 10 , b ) 12 , c ) 17 , d ) 22 , e ) 30", + "Correct": "c", + "Explanation": "bunuel , my answer for exactly 2 people was 17 and this was my approach : 100 % = ( a + b + c ) - ( anb + anc + bnc ) - 5 % + 22 % which leads me to x = 100 % = ( 50 + 30 + 20 ) - ( at least 2 people ) - 5 % + 22 % . c" + }, + { + "Answer": 6, + "Options": "a ) $ 5 , b ) $ 10 , c ) $ 14 , d ) $ 6 , e ) $ 28", + "Correct": "d", + "Explanation": "\"bill = fixed charge + charge of calls made in jan , bill = fixed charge ( let , y ) + charge of calls made in jan ( let , x ) = $ 48 in feb , bill = fixed charge ( let , y ) + charge of calls made in feb ( then , 2 x ) = $ 90 i . e . x + y = 48 and 2 x + y = 90 take the difference if two equations i . e . ( 2 x + y ) - ( x + y ) = 90 - 48 i . e . x = 42 i . e . fixed monthly charge , y = 6 answer : option d\"" + }, + { + "Answer": 14, + "Options": "a ) 16 , b ) 17 , c ) 18 , d ) 14 , e ) 13", + "Correct": "d", + "Explanation": "\"since 56 / k = 4 and 56 / 14 = 4 , then k = 14 correct answer d\"" + }, + { + "Answer": 83.99999999999996, + "Options": "a ) 75 , b ) 90 , c ) 45 , d ) 80 , e ) 84", + "Correct": "e", + "Explanation": "e 84 explanation : let us assume that jack lived for p years . p / 6 + p / 12 + p / 7 + 5 + p / 2 + 4 = x = > p = 84 . therefore , jack lived for 84 years ." + }, + { + "Answer": 2125, + "Options": "a ) 1500 , b ) 1600 , c ) 1750 , d ) 1900 , e ) 2125", + "Correct": "e", + "Explanation": "\"let the price of basic computer be c and the price of the printer be p : c + p = $ 2,500 . the price of the enhanced computer will be c + 500 and total price for that computer and the printer will be 2,500 + 500 = $ 3,000 . now , we are told that the price of the printer is 1 / 8 of that new total price : p = 1 / 8 * $ 3,000 = $ 375 . plug this value in the first equation : c + 375 = $ 2,500 - - > c = $ 2,125 . answer : e .\"" + }, + { + "Answer": 431, + "Options": "a ) 401 , b ) 411 , c ) 421 , d ) 431 , e ) 441", + "Correct": "d", + "Explanation": "\"x = 10 + 11 + . . . + 30 = 21 ( 20 ) = 420 y = 11 x + y = 431 the answer is d .\"" + }, + { + "Answer": 111, + "Options": "a ) 101 , b ) 107 , c ) 111 , d ) 117 , e ) 121", + "Correct": "c", + "Explanation": "let the numbers be 37 a and 37 b . then , 37 a x 37 b = 4107 ab = 3 . now , co - primes with product 3 are ( 1 , 3 ) . so , the required numbers are ( 37 x 1 , 37 x 3 ) i . e . , ( 37 , 111 ) . greater number = 111 . answer : option c" + }, + { + "Answer": 1631, + "Options": "a ) 1235 , b ) 1456 , c ) 1567 , d ) 1678 , e ) 1631", + "Correct": "e", + "Explanation": "\"let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 35 5 x = 1330 x = 266 large number = 266 + 1365 = 1631 e\"" + }, + { + "Answer": 2, + "Options": "a ) 8 , b ) 2 , c ) 6 , d ) 7 , e ) 1", + "Correct": "b", + "Explanation": "explanation : let n = 4 * q + 3 . then , 2 * n = 8 * q + 6 = 4 ( 2 * q + 1 ) + 2 . thus when 2 * n is divided by 4 , the reminder is 2 . answer : b ) 2" + }, + { + "Answer": 3456, + "Options": "a ) 2925 , b ) 3456 , c ) 4581 , d ) 3683 , e ) 1308", + "Correct": "b", + "Explanation": "6 ^ k = 4 6 ^ 2 k = 4 ^ 2 6 ^ 2 k = 16 6 ^ ( 2 k + 3 ) = 6 ^ 2 k * 6 ^ 3 = 16 * 216 = 3456 answer : b" + }, + { + "Answer": 775.5724667489372, + "Options": "a ) 120 , b ) 180 , c ) 772 , d ) 720 , e ) 1,440", + "Correct": "c", + "Explanation": "\"diameter of car tire = 13 inches radius of car tire = 6.5 inches = 6.5 * 2.54 cm = 16.51 cm circumference of the car tire = 2 * pi * 16.51 = 2 * 3.14 * 16.51 = 103.68 cm distance traveled by car = . 5 mile = . 5 * 1.6 km = . 8 km = 800 m = 8 * 10 ^ 4 cm number of revolutions = distance traveled / circumference of tire = 8 * 10 ^ 4 / 103.68 = 771.60 since the answer choices are far apart we should use estimation in this question . ideally , in the gmat the conversion between units would be provided . answer c\"" + }, + { + "Answer": 5, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 12 , e ) 24", + "Correct": "b", + "Explanation": "\"back - solving is the best way to solve this problem . you basically need 12 combinations ( including single colors ) if we start from option 1 - > 1 = > 4 c 2 + 4 = 10 ( not enough ) 2 = > 5 c 2 + 5 = 15 ( enough ) since the minimum number is asked . it should be 5 . answer - b\"" + }, + { + "Answer": 8100312, + "Options": "a ) 8100312 , b ) 8100313 , c ) 8100412 , d ) 8200312 , e ) 8300312", + "Correct": "a", + "Explanation": "take 2 outside as common we get 2 ( 1 + 2 * 1 ^ 2 + 3 * 1 ^ 3 + . . . . . . . . . 2012 * 1 ^ 2012 ) then 2 ( 1 + 2 + . . . . . 2012 ) we get 8100312 answer : a" + }, + { + "Answer": 14, + "Options": "a ) 4 , b ) 6 , c ) 9 , d ) 14 , e ) 20", + "Correct": "d", + "Explanation": "based on the original number of shares , the range would be : 112 - 45 = 67 however , the prompt tells us that two of the values in the table are going to change . after the changes , the values will be : v 68 w 112 x 36 y 117 z 45 now the range is 117 - 36 = 81 the increase in the range requires us to compare thenewrange to theoldrange : 81 - 67 = 14 d" + }, + { + "Answer": 32.5, + "Options": "a ) 35.2 , b ) 32.5 , c ) 36.5 , d ) 39.1 , e ) none", + "Correct": "b", + "Explanation": "\"sol . therefore correct sum = ( 32 \u00d7 50 + 48 \u2013 23 ) = 1625 . therefore correct mean = 1625 / 50 = 32.5 . answer b\"" + }, + { + "Answer": 0.17999999999999997, + "Options": "a ) 0.00018 , b ) 0.09 , c ) 0.018 , d ) 0.18 , e ) 90", + "Correct": "d", + "Explanation": "\"x = 0.009 / 0.18 = 0.05 answer : d\"" + }, + { + "Answer": 20, + "Options": "a ) 10 % , b ) 14.28 % , c ) 15 % , d ) 16 % , e ) 20 %", + "Correct": "e", + "Explanation": "let total % of work is 100 % total person = p 1 / 6 person are absent of total person . so absent person is 1 / 6 p ie p / 6 . left person is , p - p / 6 = 5 p / 6 . p person do the work 100 % 1 person do the work 100 * p % 5 p / 6 person do the work ( 100 * p * 6 ) / 5 p % = 120.00 % work increased for each person is = ( 120 - 100 ) % = 20 % answer : e" + }, + { + "Answer": 35, + "Options": "a ) 35 , b ) 30 , c ) 25 , d ) data inadequate , e ) none of these .", + "Correct": "a", + "Explanation": "\"let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 60 and c - p = 10 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 60 + 10 ) / 2 = 35 . answer : a\"" + }, + { + "Answer": 173, + "Options": "a ) 173 , b ) 185 , c ) 197 , d ) 209 , e ) 221", + "Correct": "a", + "Explanation": "\"sum of consecutive integers from 21 to 29 , inclusive = = = = > ( a 1 + an ) / 2 * # of terms = ( 21 + 29 ) / 2 * 9 = 25 * 9 = 225 sum of non - prime numbers b / w 20 and 30 , non inclusive = = = > 225 - 52 ( i . e . , 23 + 29 , being the prime # s in the range ) = 173 answer : a\"" + }, + { + "Answer": 41, + "Options": "a ) 20 , b ) 31 , c ) 41 , d ) 53 , e ) 64", + "Correct": "c", + "Explanation": "\"x + ( x - 22 ) = 60 - - > x = 41 . answer : c .\"" + }, + { + "Answer": 50.95890410958904, + "Options": "a ) 51 , b ) 53 , c ) 55 , d ) 56 , e ) 57", + "Correct": "a", + "Explanation": "total production of salt by the company in that year = 1000 + 1100 + 1200 + . . . . + 2100 = 18600 . average monthly production of salt for that year = 18600 / 365 \u00e2 \u2030 \u02c6 51 answer : a" + }, + { + "Answer": 25, + "Options": "a ) 25 liters , b ) 27 liters , c ) 30 liters , d ) 32 liters , e ) 35 liters", + "Correct": "a", + "Explanation": "\"let x ltr water to be added 2 ltr alcohol to be represented as ( 20 ( 1 - 3 / 4 ( new soln . = 15 + x ) ) ) 2 = 5 % * ( 15 + x ) - - - - - - - - > x = 25 ans a\"" + }, + { + "Answer": 32, + "Options": "a ) 64 and 15,625 , b ) 32 and 3,125 , c ) 64 and 15,620 , d ) 64 and 15,635 , e ) 64 and 16,625", + "Correct": "b", + "Explanation": "1 , 00,000 = 10 ^ 5 = 10 x 10 x 10 x 10 x 10 = ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) = ( 2 ^ 5 ) x ( 5 ^ 5 ) = 32 x 3125 so the numbers are 32 and 3,125 answer : b" + }, + { + "Answer": 936, + "Options": "a ) 720 , b ) 864 , c ) 900 , d ) 936 , e ) 1296", + "Correct": "d", + "Explanation": "total number of four letter passwords = 6 * 6 * 6 * 6 = 1296 - - - - - - ( 1 ) total number of passwords in which no letter repeats = 6 c 4 * 4 ! = 15 * 24 = 360 - - - - - - ( 2 ) therefore required value v = ( 1 ) - ( 2 ) = 1296 - 360 = 936 . d" + }, + { + "Answer": 78, + "Options": "a ) 70 , b ) 72 , c ) 75 , d ) 78 , e ) none of the above", + "Correct": "d", + "Explanation": "\"income of 6 months = ( 6 \u00d7 85 ) \u2013 debt = 510 \u2013 debt income of the man for next 4 months = 4 \u00d7 60 + debt + 30 = 270 + debt \u2234 income of 10 months = 780 average monthly income = 780 \u00f7 10 = 78 answer d\"" + }, + { + "Answer": 0.5, + "Options": "a ) 0.1 , b ) 0.3 , c ) 0.5 , d ) 0.7 , e ) 0.9", + "Correct": "c", + "Explanation": "\"first , get the middle coordinate between ( 0,2 ) and ( 12,8 ) . . . x = 0 + ( 12 - 0 ) / 2 = 6 y = 2 + ( 8 - 2 ) / 2 = 5 second , get the slope of ( 6,5 ) and ( 4,4 ) . m = 5 - 4 / 6 - 4 = 1 / 2 = 0.5 answer : c\"" + }, + { + "Answer": 8, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10", + "Correct": "c", + "Explanation": "let the total money be $ x b ' s 1 day work = $ x / 12 c ' s 1 day work = $ x / 24 a + b 1 day work = $ x / 8 money is sufficient to pay the wages of both for 8 days answer is c" + }, + { + "Answer": 200, + "Options": "a ) 100 , b ) 200 , c ) 350 , d ) 50 , e ) 250", + "Correct": "b", + "Explanation": "jonathan = matthew + zac = 550 strawberries j + m = 350 m + z = 250 use j + m = 350 to plug into the original formula ( j + m ) + z = 550 350 + z = 550 subtract 350 from each side z = 200 answer : b" + }, + { + "Answer": 1.0000000000000044, + "Options": "a ) 2 : 5 , b ) 2 : 3 , c ) 2 : 4 , d ) 1 : 1 , e ) 2 : 9", + "Correct": "d", + "Explanation": "\"let the ratio be k : 1 . then , k * 16.2 + 1 * 15.4 = ( k + 1 ) * 15.8 = ( 16.2 - 15.8 ) k = ( 15.8 - 15.4 ) = k = 0.4 / 0.4 = 1 / 1 required ratio = 1 / 1 : 1 = 1 : 1 . answer : d\"" + }, + { + "Answer": 8, + "Options": "a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 15", + "Correct": "a", + "Explanation": "\"explanation : = > 3 ( 2 x + 9 ) = 75 = > 2 x + 9 = 25 = > x = 8 answer : option a\"" + }, + { + "Answer": 70000, + "Options": "a ) 70000 , b ) 80000 , c ) 90000 , d ) 90090 , e ) 100000", + "Correct": "a", + "Explanation": "\"( 112 x 54 ) = 112 x 10 4 = 112 x 104 = 1120000 = 70000 2 24 16 a )\"" + }, + { + "Answer": 2, + "Options": "a ) 2 , b ) 3.25 , c ) 4.25 , d ) 5.25 , e ) 6.25", + "Correct": "a", + "Explanation": "\"squaring on both sides ( x + 1 / x ) ^ 2 = 2 ^ 2 x ^ 2 + 1 / x ^ 2 = 4 - 2 x ^ 2 + 1 / x ^ 2 = 2 answer : a\"" + }, + { + "Answer": 0.5454545454545454, + "Options": "a ) 1 / 6 , b ) 2 / 9 , c ) 6 / 11 , d ) 9 / 16 , e ) 3 / 4", + "Correct": "c", + "Explanation": "\"# defective pens = 3 # good pens = 9 probability of the 1 st pen being good = # of favorable outcomes / # of total outcomes = 9 / 12 probability of the 2 nd pen being good = # of remaining favorable outcomes / # of total remaining outcomes = 8 / 11 total probability = 9 / 12 * 8 / 11 = 6 / 11 answer will be c\"" + }, + { + "Answer": 12, + "Options": "a ) 25 , b ) 76 , c ) 29 , d ) 12 , e ) 20", + "Correct": "d", + "Explanation": "\"explanation : let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 883 96 + 225 + 490 + 6 x = 883 6 x = 72 = > x = 12 . answer : d\"" + }, + { + "Answer": 0.5833333333333334, + "Options": "a ) 2 / 3 , b ) 5 / 6 , c ) 7 / 12 , d ) 11 / 12 , e ) 17 / 24", + "Correct": "c", + "Explanation": "\"( 1 / 2 ) x = ( 1 / 4 ) y ( 1 / 4 ) y + ( 1 / 3 ) y = ( 7 / 12 ) y the answer is c .\"" + }, + { + "Answer": 64, + "Options": "a ) 95 , b ) 90 , c ) 85 , d ) 80 , e ) 64", + "Correct": "e", + "Explanation": "\"let x be the number of students in the school . 0.16 x students went to the trip and took more than 100 $ . they compose ( 100 - 75 ) = 25 % of all students who went to the trip . therefore the toal of 0.16 x / 0.25 = 0.64 x students went to the camping which is 64 % . the answer is e\"" + }, + { + "Answer": 98, + "Options": "a ) a ) 70 , b ) b ) 76 , c ) c ) 78 , d ) d ) 98 , e ) e ) 88", + "Correct": "d", + "Explanation": "\"explanation : average after 11 innings should be 38 so , required score = ( 11 * 38 ) - ( 10 * 32 ) = 418 - 320 = 98 answer : option d\"" + }, + { + "Answer": 625, + "Options": "a ) 24 , b ) 120 , c ) 625 , d ) 720 , e ) 1024", + "Correct": "c", + "Explanation": "\"5 choices for each of the 4 questions , thus total r of 5 * 5 * 5 * 5 = 5 ^ 4 = 625 ways to answer all of them . answer : c .\"" + }, + { + "Answer": 0.05714285714285714, + "Options": "a ) 1 / 35 , b ) 3 / 35 , c ) 5 / 37 , d ) 2 / 35 , e ) none", + "Correct": "d", + "Explanation": "answer we have , m x n = 6 x 210 = 1260 \u2234 1 / m + 1 / n = ( m + n ) / mn = 72 / 1260 = 4 / 70 = 2 / 35 correct option : d" + }, + { + "Answer": 0.4375, + "Options": "a ) 0.44 , b ) 0.55 , c ) 0.65 , d ) 0.75 , e ) 0.85", + "Correct": "a", + "Explanation": "\"number of people whose age is less than 20 is given by 160 - 90 = 70 probability p that a person selected at random from the group is less than 20 is gieven by 70 / 160 = 0.4375 ~ 0.44 correct answer a\"" + }, + { + "Answer": 1799.9999999999995, + "Options": "a ) 360 , b ) 1800 , c ) 540 , d ) 640 , e ) 720", + "Correct": "b", + "Explanation": "\"too many words and redundant info there . ( i ) 1 / 3 of the pieces of art are displayed , hence 2 / 3 of the pieces of art are not displayed . ( ii ) 1 / 6 of the pieces on display are sculptures , hence 5 / 6 of the pieces on display are paintings . ( iii ) 1 / 3 of the pieces not on display are paintings , hence 2 / 3 of the pieces not on display are sculptures . 800 sculptures are not on display , so according to ( iii ) 2 / 3 * { not on display } = 800 - - > { not on display } = 1200 . according to ( i ) 2 / 3 * { total } = 1200 - - > { total } = 1800 . answer : b .\"" + }, + { + "Answer": 6.9, + "Options": "a ) 6.6 , b ) 6.7 , c ) 6.8 , d ) 6.85 , e ) 6.9", + "Correct": "e", + "Explanation": "\"old set s - total is avg * no of elements = 6.2 * 10 = 62 if one number is increased by 7 then total increased to 62 + 7 = 69 new avg - 69 / 10 = 6.9 . hence answer is e .\"" + }, + { + "Answer": 0.08000000000000002, + "Options": "a ) 7 / 25 , b ) 3 / 25 , c ) 8 / 25 , d ) 2 / 25 , e ) 3 / 17", + "Correct": "d", + "Explanation": "\"p ( a n b ) = p ( a ) . p ( b ) p ( a n b ) = 1 / 5 . 2 / 5 p ( a n b ) = 2 / 25 . d\"" + }, + { + "Answer": 45, + "Options": "a ) 15 , b ) 3 , c ) 5 , d ) 45 , e ) none of these", + "Correct": "d", + "Explanation": "reqd no . = 2 \u00e2 \u0081 \u201e 5 \u00e3 \u2014 300 - 3 \u00e2 \u0081 \u201e 5 \u00e3 \u2014 125 = 120 - 75 = 45 answer d" + }, + { + "Answer": 280.00000000000006, + "Options": "a ) $ 180 , b ) $ 250 , c ) $ 260 , d ) $ 280 , e ) $ 300", + "Correct": "d", + "Explanation": "\"if 40 books constitute 1 / 3 rd of the total , then 2 / 3 rd of the total = 80 books amount received for sold books = 80 * 3.5 = $ 280 answer : d\"" + }, + { + "Answer": 1, + "Options": "a ) 27 / 8 , b ) 8 / 27 , c ) 1 , d ) 9 / 4 , e ) 81 / 64", + "Correct": "c", + "Explanation": "\"a nice fast approach is the first find a pair of numbers that satisfy the given equation : 2 a = 3 b here ' s one pair : a = 3 and b = 2 what is the ratio of a / 3 to b / 3 ? in other words , what is the value of ( a / 3 ) / ( b / 2 ) ? plug in values to get : ( a / 3 ) / ( b / 2 ) = ( 3 / 3 ) / ( 2 / 2 ) = 1 / 1 = 1 c\"" + }, + { + "Answer": 72, + "Options": "a ) 48 , b ) 66 , c ) 72 , d ) 78 , e ) 90", + "Correct": "c", + "Explanation": "total number of 5 digit numbers that can be formed = 5 ! = 120 . total number of 5 digit numbers in which 3 and 4 are adjacent = 48 . this can be calculated by taking 3 and 4 as a pair and considering positions where they can appear . number of 5 digit numbers in which 3 and 4 are not adjacent = total number of 5 digit numbers - total number of 5 digit numbers in which 3 and 4 are adjacent . ans = 120 - 48 = 72 c" + }, + { + "Answer": 195, + "Options": "a ) 134 , b ) 178 , c ) 195 , d ) 166 , e ) 194", + "Correct": "c", + "Explanation": "c 195 the number of votes the winning candidate received was 963 + 53 + 79 + 105 / 4 = 300 . the second received 300 \u2013 53 = 247 , the third received 300 \u2013 105 = 195 ." + }, + { + "Answer": 39, + "Options": "a ) 39 kg , b ) 32 kg , c ) 33 kg , d ) 34 kg , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : let a , b , c represent their respective weights . then , we have : a + b + c = ( 45 x 3 ) = 135 \u2026 . ( i ) a + b = ( 40 x 2 ) = 80 \u2026 . ( ii ) b + c = ( 47 x 2 ) = 94 \u2026 . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 174 \u2026 . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 39 . b \u2019 s weight = 39 kg . answer : a\"" + }, + { + "Answer": 90, + "Options": "a ) 85 , b ) 77 , c ) 33 , d ) 90 , e ) 75", + "Correct": "d", + "Explanation": "\"sum of the marks for the 30 students = 30 * 45 = 1350 . the marks of each student are doubled , the sum also will be doubled . the new sum = 1350 * 2 = 2700 . so , the new average = 2700 / 30 = 90 . answer : d\"" + }, + { + "Answer": 33.33333333333333, + "Options": "a ) 10 % , b ) 12 % , c ) 15 % , d ) 17 % , e ) 33 %", + "Correct": "e", + "Explanation": "\"lets assume that candidate got 25 % votes and total votes is 100 . candidate won = 25 remaining = 75 to get 50 % , candidate requires 25 votes from 100 which is 25 % and 25 votes from 75 . 25 / 75 = 33.33 % which is approx 33 % . hence the answer is e\"" + }, + { + "Answer": 52, + "Options": "a ) $ 92 , b ) $ 96 , c ) $ 52 , d ) $ 120 , e ) $ 240", + "Correct": "c", + "Explanation": "\"eps actual > eps expected . each gets and additional . 12 per share . thus . 52 * 100 - - > $ 52 answer is c\"" + }, + { + "Answer": 108, + "Options": "a ) 72 , b ) 84 , c ) 90 , d ) 96 , e ) 108", + "Correct": "e", + "Explanation": "r = j + 6 = k + 3 r + 4 = 2 ( j + 4 ) ( j + 6 ) + 4 = 2 j + 8 j = 2 r = 8 k = 5 in 4 years ( r + 4 ) ( k + 4 ) = 12 * 9 = 108 the answer is e ." + }, + { + "Answer": 36.5, + "Options": "a ) 35.2 , b ) 36.1 , c ) 36.5 , d ) 39.1 , e ) none of these", + "Correct": "c", + "Explanation": "\"solution correct sum = ( 36 \u00d7 50 + 48 - 23 ) = 1525 . \u2234 correct mean = 1825 / 50 = 36.5 answer c\"" + }, + { + "Answer": 125, + "Options": "a ) 75 , b ) 100 , c ) 125 , d ) 175 , e ) 225", + "Correct": "c", + "Explanation": "\"let m be the number of male participants and f be the number of female articipants in the meeting . thetotal number of participants is given as 750 . hence , we have m + f = 750 now , we have that half the female participants and one - quarter of the male participants are democrats . let d equal the number of the democrats . then we have the equation f / 2 + m / 4 = d now , we have that one - third of the total participants are democrats . hence , we have the equation d = 750 / 3 = 250 solving the three equations yields the solution f = 250 , m = 500 , and d = 250 . the number of female democratic participants equals half the female participants equals 250 / 2 = 125 . answer : c\"" + }, + { + "Answer": 124.11, + "Options": "a ) $ 124.11 , b ) $ 124.12 , c ) $ 124.13 , d ) $ 124.14 , e ) $ 124.15", + "Correct": "a", + "Explanation": "this is equivalent to finding the first number that is divisible by 9 that occurs after 12415 . in order to divide the sum in 9 parts , the amount must be divisible by 9 divisibility rule of 9 : the sum of the digits must be divisible by 9 sum of digits of 12415 = 13 and 9 is divisible by 9 . hence , we need to remove 4 to this number for it to be divisible by 9 correct option : a" + }, + { + "Answer": 10, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 10", + "Correct": "e", + "Explanation": "\"let bill run x on saturday , so he will run x + 4 on sunday . . julia will run 2 * ( x + 4 ) on sunday . . totai = x + x + 4 + 2 x + 8 = 36 . . 4 x + 12 = 36 . . x = 6 . . ans = x + 4 = 6 + 4 = 10 answer e\"" + }, + { + "Answer": 1035, + "Options": "a ) 1030 , b ) 1034 , c ) 1035 , d ) 1037 , e ) 1040", + "Correct": "c", + "Explanation": "\"let sn = ( 1 + 2 + 3 + . . . + 45 ) . this is an a . p . in which a = 1 , d = 1 , n = 45 . sn = n [ 2 a + ( n - 1 ) d ] = 45 x [ 2 x 1 + ( 45 - 1 ) x 1 ] = 45 x 46 = ( 45 x 23 ) 2 2 2 = 45 x ( 20 + 3 ) = 45 x 20 + 45 x 3 = 900 + 135 = 1035 . c )\"" + }, + { + "Answer": 2400, + "Options": "a ) 600 , b ) 1200 , c ) 1500 , d ) 1600 , e ) 2400", + "Correct": "e", + "Explanation": "\"sugar : flour = 5 : 5 = 10 : 10 ; flour : soda = 10 : 1 = 10 : 1 ; thus we have that sugar : flour : soda = 10 x : 10 x : 1 x . also given that 10 x / ( 1 x + 60 ) = 8 / 1 - - > x = 240 - - > sugar = 10 x = 2400 answer : e .\"" + }, + { + "Answer": 94, + "Options": "a ) 94 kg , b ) 85 kg , c ) 90 kg , d ) 100 kg , e ) 110 kg", + "Correct": "a", + "Explanation": "\"total weight increased = ( 8 x 3 ) kg = 24 kg . weight of new person = ( 70 + 24 ) kg = 94 kg . answer : a\"" + }, + { + "Answer": 1.5, + "Options": "a ) 1.0 , b ) 1.9 , c ) 1.6 , d ) 1.5 , e ) 1.1", + "Correct": "d", + "Explanation": "\"m = 4.5 s = x ds = 4.5 + x us = 4.5 + x 4.5 + x = ( 4.5 - x ) 2 4.5 + x = 9 - 2 x 3 x = 4.5 x = 1.5 answer : d\"" + }, + { + "Answer": 60, + "Options": "a ) 60 , b ) 10 , c ) 19 , d ) 20 , e ) 21", + "Correct": "a", + "Explanation": "\"this is a solution from beatthegmat : even numbers : ( 120 - 2 ) / 2 + 1 = 60 even integers . ( 120 + 2 ) / 2 = 61 is the average of the even set . sum = avg * ( # of elements ) = 61 * 60 = 3660 = a odd numbers : ( 119 - 1 ) / 2 + 1 = 60 odd integers . ( 119 + 1 ) / 2 = 60 is the average of the odd set . sum = avg * ( # of elements ) = 60 * 60 = 3600 = b a - b = 3660 - 3600 = 60 . answer : a\"" + }, + { + "Answer": 54.54545454545454, + "Options": "a ) 55 , b ) 56 , c ) 34 , d ) 78 , e ) 23", + "Correct": "a", + "Explanation": "lets say the family income is 100 in may , lee earned 50 family income is 50 in june , lee earned 20 % more than may , so it is ( 50 + 20 * 50 / 100 = 60 ) family income is same 50 in june lee ' s income percent is 60 * 100 / 110 ~ 55 ans is a" + }, + { + "Answer": 299.1, + "Options": "a ) $ 287.50 , b ) $ 290.40 , c ) $ 293.30 , d ) $ 296.20 , e ) $ 299.10", + "Correct": "e", + "Explanation": "\"the service cost of 3 vans and 2 trucks is 5 * 2.10 $ 10.50 the fuel in 3 vans is 3 * 65 = 195 liters the fuel in 2 trucks is 2 * 65 * 2.2 = 286 liters the total fuel ( vans + trucks ) = 481 liters the total fuel cost is 481 * 0.6 = $ 288.60 the total cost is $ 288.60 + $ 10.50 = $ 299.10 the answer is e .\"" + }, + { + "Answer": 20, + "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 20", + "Correct": "e", + "Explanation": "\"let x be the number . always replace ` ` is ' ' with an equal sign ( 1 / 2 ) x + 7 = 17 ( 1 / 2 ) x = 17 - 7 ( 1 / 2 ) x = 20 x = 20 correct answer is e\"" + }, + { + "Answer": 921.0526315789474, + "Options": "a ) 1000 , b ) 912.88 , c ) 927.78 , d ) 926.82 , e ) 921.05", + "Correct": "e", + "Explanation": "1120 = p [ 1 + ( 9 * 12 / 5 ) / 100 ] p = 921.05 answer : e" + }, + { + "Answer": 84.99999999999993, + "Options": "a ) 82 , b ) 83 , c ) 84 , d ) 85 , e ) 86", + "Correct": "d", + "Explanation": "\"12.4 x + 26 / ( 5 + x ) = 12 12.4 x + 26 = 60 + 12 x x = 34 / 0.4 = 85 answer : d\"" + }, + { + "Answer": 16, + "Options": "a ) 8 , b ) 12 , c ) 13 , d ) 14 , e ) 16", + "Correct": "e", + "Explanation": "amount of salt = 6.4 assume x gallons of water are added . 6.4 / 64 + x = 8 / 100 640 = 8 x + 512 8 x = 128 x = 16 correct option : e" + }, + { + "Answer": 63, + "Options": "a ) 63 , b ) 24 , c ) 17 , d ) 6 , e ) 5", + "Correct": "a", + "Explanation": "\"sol . ( b ) the sum of roots = a + b = 9 product of roots = ab = 9 now , a 2 + b 2 = ( a + b ) 2 - 2 ab = 81 - 18 = 63 answer a\"" + }, + { + "Answer": 5.9956356288922485, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "d", + "Explanation": "0.00010101 * 10 ^ k > 100 we need to move the decimal point to the right 6 places to get 101.01 this is equivalent to multiplying by 10 ^ 6 . the answer is d ." + }, + { + "Answer": 13, + "Options": "a ) 13 , b ) 14 , c ) 16 , d ) 17 , e ) 19", + "Correct": "a", + "Explanation": "\"12 , 15 , 18 , 21 , 24 , 27 , 30 , 33 , 36 , 39 , 42 , 45,48 . 13 numbers . 10 / 3 = 3 and 50 / 3 = 16 = = > 16 - 3 = 13 . therefore 13 digits . a )\"" + }, + { + "Answer": 4599, + "Options": "a ) a ) 3800 , b ) b ) 4200 , c ) c ) 4400 , d ) d ) 4500 , e ) e ) 4600", + "Correct": "e", + "Explanation": "\"x * ( 90 / 100 ) * ( 80 / 100 ) = 3312 x = 4600 answer : e\"" + }, + { + "Answer": 2499, + "Options": "a ) rs . 2500 , b ) rs . 2300 , c ) rs . 2200 , d ) rs . 1400 , e ) rs . 1600", + "Correct": "a", + "Explanation": "explanation : price of 357 apples = rs . 1517.25 price of 1 apple = rs . 1517.25 / 357 price of 49 dozens apples = rs ( 49 \u00d7 12 \u00d7 1517.25 / 357 ) \u2248 rs . 2500 answer : option a" + }, + { + "Answer": 55, + "Options": "a ) 10 , b ) 25 , c ) 55 , d ) 75 , e ) 100", + "Correct": "c", + "Explanation": "surprisingly no one answered this easy one . property of a set of consecutive integerz . mean = median = ( first element + last element ) / 2 = ( second element + last but one element ) / 2 = ( third element + third last element ) / 2 etc . etc . so mean = median = 110 / 2 = 55 answer is c" + }, + { + "Answer": 316, + "Options": "a ) 156 , b ) 162 , c ) 316 , d ) 324 , e ) 325", + "Correct": "c", + "Explanation": "\"buy as many $ 50 deals as possible . we can by 650 / 50 = 13 two dozen roses , thus total of 13 * 24 = 312 roses . we are left with 680 - 650 = $ 30 . we can buy 30 / 6.3 = ~ 4 roses for that amount . total = 312 + 4 = 316 . answer : c .\"" + }, + { + "Answer": 56, + "Options": "a ) 15 , b ) 25 , c ) 35 , d ) 45 , e ) 56", + "Correct": "e", + "Explanation": "\"let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 8 ) students = 90 ( x - 8 ) 80 x - ( 8 * 20 ) = 90 ( x - 8 ) 560 = 10 x = > x = 56 answer : e\"" + }, + { + "Answer": 6, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8", + "Correct": "c", + "Explanation": "\"64 ^ k > 4 ^ 17 4 ^ ( 3 k ) > 4 ^ 17 3 k > 17 k = 6 the answer is c .\"" + }, + { + "Answer": 1, + "Options": "a ) 22 kg , b ) 1 kg , c ) 22.4 kg , d ) 21 kg , e ) none of these", + "Correct": "b", + "Explanation": "\"exp . the total weight of 29 students = 29 * 28 the total weight of 30 students = 30 * 27.1 weight of the new student = ( 30 * 27.1 \u2013 29 * 28 ) = 813 - 812 = 1 answer : b\"" + }, + { + "Answer": 9, + "Options": "a ) 1 , b ) 6 , c ) 3 , d ) 0 , e ) 9", + "Correct": "e", + "Explanation": "as the unit place digit of 3 to the power of 1 is 3 , to the power of 2 is 9 . to the power of 3 is 7 , to the power of 4 is 1 and it ' ll be repeated again in the same order . . . . so the unit place digit of 3 to the power of 34 is 9 . . answer : e" + }, + { + "Answer": 11, + "Options": "a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 19", + "Correct": "a", + "Explanation": "( x + 5 ) * 150 + x * 85 = 1455 = > x = 3 total lens = 3 + ( 3 + 5 ) = 11 answer a" + }, + { + "Answer": 114, + "Options": "a ) 22 , b ) 38 , c ) 114 , d ) 122 , e ) 672", + "Correct": "c", + "Explanation": "\"factorise 1881 . . 3 * 11 * 57 . . so n has to be a multiple of largest prime number , 61 . . so n = 2 * 57 = 114 . . ans : c\"" + }, + { + "Answer": 39, + "Options": "a ) 9 years , b ) 19 years , c ) 29 years , d ) 39 years , e ) none", + "Correct": "d", + "Explanation": "\"solution let b ' s present age = x years . then , a ' s present age \u2039 = \u203a ( x + 9 ) years . \u2234 ( x + 9 ) + 10 = 2 ( x - 10 ) \u2039 = \u203a x + 19 = 2 x - 20 \u2039 = \u203a x = 39 . answer d\"" + }, + { + "Answer": 10, + "Options": "a ) 7 , b ) 8 , c ) 10 , d ) 11 , e ) 12", + "Correct": "c", + "Explanation": "p is a positive even integer with a positive units digit - - > the units digit of p can be 2 , 4 , 6 , or 8 - - > in order the units digit of p ^ 3 - p ^ 2 to be 0 , the units digit of p ^ 3 and p ^ 2 must be the same . thus the units digit of p can be 0 , 1 , 5 or 6 . intersection of values is 6 , thus the units digit of p + 4 is 6 + 4 = 10 . answer : c ." + }, + { + "Answer": 105, + "Options": "a ) 366 , b ) 106 , c ) 102 , d ) 105 , e ) 122", + "Correct": "d", + "Explanation": "\"cash realised = rs . ( 105.25 - 0.25 ) = rs . 106 . answer : d\"" + }, + { + "Answer": 21, + "Options": "a ) 22 , b ) 21 , c ) 45 , d ) 27 , e ) 25", + "Correct": "b", + "Explanation": "list down possibilities : from only 1 box all the way to all 6 if only one of the boxes has a green ball , it can be any of the 6 boxes . so , we have 6 possibilities . if two of the boxes have green balls and then there are 5 consecutive sets of 2 boxes . 12 , 23 , 34 , 45 , 56 . if 3 of the boxes have green balls , there are 4 possibilities : 123 , 234 , 345 , 456 . if 4 boxes have green balls , there are 3 possibilities : 1234 , 2345 , 3456 . if 5 boxes have green balls , there are 2 possibilities : 12345 , 23456 . if all 6 boxes have green balls , there is just 1 possibility . total number of possibilities = 6 + 5 + 4 + 3 + 2 + 1 = 21 . ans : b" + }, + { + "Answer": 830, + "Options": "a ) rs . 832 , b ) rs . 830 , c ) rs . 822 , d ) rs . 812 , e ) rs . 810", + "Correct": "b", + "Explanation": "\"let the total amount in the partnership be ' x ' . then a ' s share = x / 3 b ' s share = x / 4 c ' s share = x / 5 d ' s share = x - ( x / 3 + x / 4 + x / 5 ) = 13 x / 60 a : b : c : d = x / 3 : x / 4 : x / 5 : 13 x / 60 = 20 : 15 : 12 : 13 a ' s share in the profit of rs . 2490 = 20 ( 2490 / 60 ) = rs . 830 . answer : b\"" + }, + { + "Answer": 100, + "Options": "a ) 100 , b ) 1000 , c ) . 001 , d ) . 0001 , e ) . 01", + "Correct": "a", + "Explanation": "( . 02 ) 2 + ( 0.52 ) 2 + ( 0.035 ) 2 / ( 0.002 ) 2 + ( 0.052 ) 2 + ( 0.0035 ) 2 = a 2 + b 2 + c 2 / ( a / 10 ) 2 + ( b / 10 ) 2 + ( c / 10 ) 2 where a = . 02 , b = . 52 , c = . 035 = 100 ( a 2 + b 2 + c 2 ) / a 2 + b 2 + c 2 = 100 answer : a" + }, + { + "Answer": 8, + "Options": "a ) 8 s , b ) 2.5 s , c ) 7.5 s , d ) 7.6 s , e ) 7.4 s", + "Correct": "a", + "Explanation": "\"explanation : 72 km / hr = 72 * 5 / 18 = 20 m / s speed = distance / time ; v = d / t 20 = 160 / t t = 8 s answer : a\"" + }, + { + "Answer": 1008, + "Options": "a ) 896 , b ) 1008 , c ) 1120 , d ) 1024 , e ) none of these", + "Correct": "b", + "Explanation": "the smallest four digit number is 1000 . if 1000 is divided by 112 , the remainder is 104 . 112 - 104 = 8 , if 8 is added to 1000 , it will become the smallest four digit number and a multiple of 112 . answer : b" + }, + { + "Answer": 11, + "Options": "a ) 11 , b ) 15 , c ) 6 , d ) 8 , e ) 76", + "Correct": "a", + "Explanation": "\"explanation : age of the 15 th student = [ 15 * 15 - ( 14 * 5 + 16 * 9 ) ] = ( 225 - 214 ) = 11 years . answer : a ) 11\"" + }, + { + "Answer": 70, + "Options": "a ) 32 , b ) 35 , c ) 30 , d ) 40 , e ) 70", + "Correct": "e", + "Explanation": "assume the current age = a a - x / 4 = 28 ( i ) a + x / 4 = 4 x or a = 15 x / 4 ( ii ) putting the value of a from ( ii ) in ( i ) 15 x / 4 - x / 4 = 28 or 14 x / 4 = 28 therefore x = 8 and a = 30 5 x years from now , age will be 30 + 5 * 8 = 70 option e" + }, + { + "Answer": 15, + "Options": "a ) - 29 , b ) - 19 , c ) 15 , d ) 29 , e ) 39", + "Correct": "c", + "Explanation": "\"45 - [ 28 - { 37 - ( 15 - * ) } ] = 54 = > 45 - [ 28 - { 37 - 15 + * } ] = 54 45 - [ 28 - 37 + 15 - * ] = 54 = > 45 [ 43 - 37 - * ] = 54 45 - [ 6 - * ] = 54 = > 45 - 6 + * = 54 39 + * = 54 = > * = 54 - 39 = 19 answer : c\"" + }, + { + "Answer": 2, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "b", + "Explanation": "\"29 / 3 = 58 / 6 = 10 - 87 / 6 = 15 - prime numbers between 10 and 15 are 11 and 13 - sign signifies that the number is marginally less . answer b\"" + }, + { + "Answer": 16, + "Options": "a ) 18 , b ) 8 , c ) 12 , d ) 16 , e ) none of these", + "Correct": "d", + "Explanation": "105 - 57 = 48 57 - 25 = 32 105 - 25 = 80 the h . c . f of 32 , 48 and 80 is 16 . answer : d" + }, + { + "Answer": 1620, + "Options": "a ) 1235 , b ) 1456 , c ) 1567 , d ) 1678 , e ) 1635", + "Correct": "e", + "Explanation": "\"let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 15 5 x = 1350 x = 270 large number = 270 + 1365 = 1635 e\"" + }, + { + "Answer": 20.000000000000014, + "Options": "a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 50 %", + "Correct": "c", + "Explanation": "\"say a recliner is actually worth $ 100 if she sells 100 recliners then she earns $ 10000 after the discount of 20 % , she will earn $ 80 per recliner and she sells 50 % more ie . , 150 recliners hence her sales yields 150 * 80 = $ 12000 increase in sales = 12000 - 10000 = $ 2000 so % increase = 2000 * 100 / 10000 = 20 % c is the answer\"" + }, + { + "Answer": 19928, + "Options": "a ) 20120 , b ) 11500 , c ) 20128 , d ) 20660 , e ) 20228", + "Correct": "c", + "Explanation": "explanation : ( a + b ) 2 + ( a \u00e2 \u02c6 \u2019 b ) 2 = 2 ( a 2 + b 2 ) ( reference : basic algebraic formulas ) 1082 + 922 = ( 100 + 8 ) 2 + ( 100 \u00e2 \u02c6 \u2019 8 ) 2 = 2 ( 1002 + 82 ) = 2 ( 10000 + 64 ) = 20128 . answer : option c" + }, + { + "Answer": 37, + "Options": "a ) 34 , b ) 35 , c ) 36 , d ) 37 , e ) 38", + "Correct": "d", + "Explanation": "1 + 1 + 1 = 3 3 factorial = 6 6 to the power 1 + 1 = 6 ^ 2 = 36 36 + 1 = 37 answer : d" + }, + { + "Answer": 25, + "Options": "a ) 25 m , b ) 50 m , c ) 72 m , d ) 80 m , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : the relative speed of train is 46 - 36 = 10 km / hr = ( 10 x 5 ) / 18 = 25 / 9 m / s 10 \u00d7 518 = 259 m / s in 18 secs the total distance traveled is 18 x 25 / 9 = 50 m . therefore the length of each train is = 50 / 2 = 25 m . answer a\"" + }, + { + "Answer": 1600.0000000000002, + "Options": "a ) 800 , b ) 500 , c ) 900 , d ) 1600 , e ) none", + "Correct": "d", + "Explanation": "\"answer 2 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ] = 2 x [ ( 36 x 48 x 250 ) / ( 12 x 9 x 5 ) ] = 2 x 4 x 4 x 50 = 1600 correct option : d\"" + }, + { + "Answer": 5.4, + "Options": "a ) $ 3.15 , b ) $ 4.45 , c ) $ 4.80 , d ) $ 5.05 , e ) $ 5.40", + "Correct": "e", + "Explanation": "\"let the fixed charge of jim \u2019 s taxi service = 2.25 $ and charge per 2 / 5 mile ( . 4 mile ) = . 35 $ total charge for a trip of 3.6 miles = 2.25 + ( 3.6 / . 4 ) * . 35 = 2.25 + 9 * . 35 = 5.4 $ answer e\"" + }, + { + "Answer": 120, + "Options": "a ) $ 100 , b ) $ 120 , c ) $ 280 , d ) $ 300 , e ) $ 360", + "Correct": "b", + "Explanation": "\"total value of the prize = $ 1200 number of people = 40 2 / 5 of 1200 ( = $ 480 ) should be distributed among 3 / 5 of 40 ( = 24 people ) with each getting $ 40 each . remaining money = 1200 - 480 = $ 720 . now in order to ' maximize ' 1 prize , we need to minimise the others and we have been given that each should get $ 40 . thus , minimising the remaining 15 people ( = 40 - 24 - 1 . ' - 1 ' to exclude 1 that needs to be maximised ) = 15 * 40 = 600 . thus the maximum award can be = 720 - 600 = $ 120 , hence b is the correct answer .\"" + }, + { + "Answer": 1500, + "Options": "a ) 1200 , b ) 1300 , c ) 1400 , d ) 1500 , e ) 1600", + "Correct": "d", + "Explanation": "\"let x be the number of eggs that were laid . ( 2 / 5 ) ( 4 / 5 ) ( 1 / 4 ) x = 120 ( 8 / 100 ) x = 120 x = 1500 the answer is d .\"" + }, + { + "Answer": 208, + "Options": "a ) 2.08 % , b ) 20.8 % , c ) 208 % , d ) 0.208 % , e ) none of these", + "Correct": "c", + "Explanation": "\"explanation : while calculation in terms of percentage we need to multiply by 100 , so 2.08 * 100 = 208 answer : option c\"" + }, + { + "Answer": 23, + "Options": "a ) 7 , b ) 13 , c ) 16 , d ) 21 , e ) 23", + "Correct": "e", + "Explanation": "\"general rule for such kind of problems : to maximize one quantity , minimize the others ; to minimize one quantity , maximize the others . thus to maximize the number of points of one particular player minimize the number of points of all other 11 players . minimum number of points for a player is 7 , so the minimum number of points of 11 players is 7 * 11 = 77 . therefore , the maximum number of points e for 12 th player is 100 - 77 = 23 . answer : e .\"" + }, + { + "Answer": 2009, + "Options": "a ) 2003 , b ) 2009 , c ) 2005 , d ) 2006 , e ) 2007", + "Correct": "b", + "Explanation": "she must gain at least 70 points , now she has 31 and every year gives her two more points : one for age and one for additional year of employment , so 32 + 2 * ( # of years ) = 70 - - > ( # of years ) = 19 - - > 1990 + 19 = 2009 . answer : b ." + }, + { + "Answer": 41, + "Options": "a ) 39 , b ) 41 , c ) 45 , d ) 42 , e ) 50", + "Correct": "b", + "Explanation": "\"age of the 15 th student = 17 * 15 - ( 14 * 5 + 16 * 9 ) = 255 - 214 = 41 years answer is b\"" + }, + { + "Answer": 4675, + "Options": "a ) 2988 , b ) 2776 , c ) 4400 , d ) 4675 , e ) 881", + "Correct": "d", + "Explanation": "\"x * ( 95 / 100 ) * ( 80 / 100 ) = 3553 x = 4675 answer : d\"" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 6", + "Correct": "a", + "Explanation": "she eat as follow mon - 1 tue - 2 wed - 3 thr - 5 fri - 1 ( since she had more than 4 previous day ) sat - 6 sunday - 1 ( since she had more than 4 previous day ) so 30 th day of month she will have 1 . answer is a" + }, + { + "Answer": 49.050000000000004, + "Options": "a ) 49.05 , b ) 42.25 , c ) 50 , d ) 51.25 , e ) 52.25", + "Correct": "a", + "Explanation": "\"explanation : average weight of 26 boys = 50.25 total weight of 26 boys = 50.25 \u00d7 26 average weight of remaining 8 boys = 45.15 total weight of remaining 8 boys = 45.15 \u00d7 8 total weight of all boys in the class = ( 50.25 \u00d7 26 ) + ( 45.15 \u00d7 8 ) total boys = 26 + 8 = 34 average weight of all the boys = ( 50.25 \u00d7 26 ) + ( 45.15 \u00d7 8 ) / 34 = 49.05 answer : option a\"" + }, + { + "Answer": 9, + "Options": "a ) 18 , b ) 16 , c ) 13 , d ) 9 , e ) 11", + "Correct": "d", + "Explanation": "lcm of 20 = 20 1 / 4 marking are ( table of 5 ) 0 . . . . . . 5 . . . . . . 10 . . . . . 15 . . . . . . 20 ( total = 5 ) 1 / 5 marking are ( table of 4 ) 0 . . . . . . . 4 . . . . . . 8 . . . . . . 12 . . . . . . . . 16 . . . . . . 20 ( total = 6 ) overlapping markings are 0 . . . . . . . . 20 ( total = 2 ) total markings = 5 + 6 - 2 = 9 answer = d" + }, + { + "Answer": 302.9802941364969, + "Options": "a ) 272.22 , b ) 128.29 , c ) 306.04 , d ) 198.39 , e ) 212.22", + "Correct": "c", + "Explanation": "\"explanation : a = 5000 ( 51 / 50 ) 3 = 5306.04 5000 - - - - - - - - - - - 306.04 answer : c\"" + }, + { + "Answer": 36, + "Options": "a ) 25 , b ) 27 , c ) 30 , d ) 35 , e ) 36", + "Correct": "e", + "Explanation": "average in 5 matches = ( 2 * 30 + 3 * 40 ) / 2 + 3 = 60 + 120 / 5 = 180 / 5 = 36 answer is e" + }, + { + "Answer": 45, + "Options": "a ) 33 , b ) 45 , c ) 26 , d ) 28 , e ) 19", + "Correct": "b", + "Explanation": "\"explanation : let the two parts be ( 60 - x ) and x . then , 10 ( 60 - x ) + 22 x = 780 = > 12 x = 180 = > x = 15 . bigger part = ( 60 - x ) = 45 . answer : b ) 45\"" + }, + { + "Answer": 9376, + "Options": "a ) 8476 , b ) 7376 , c ) 9376 , d ) 7378 , e ) 9466", + "Correct": "c", + "Explanation": "c 9376 looking at the last digit , the last digit must be either 0 , 1 , 5 or 6 . then looking at the last two digits , the last two digits must be either 0001 , 25 or 76 . then looking at the last three digits , the last three digits must be either 00001 , 625 or 376 . then looking at the last four digits , the last four digits must be either 0000001 , 0625 or 9376 . out of those , only 9376 is a 4 digit number" + }, + { + "Answer": 6, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "d", + "Explanation": "for solving this type of tasks we can use such approach 15 / 3 = 5 15 / 3 ^ 2 = 1 and remainder and 3 ^ 3 is more than 15 so we stop on second exponent 5 + 1 = 6 so maximum value of k = 6 and answer is d" + }, + { + "Answer": 20, + "Options": "a ) 21 , b ) 20 , c ) 11 , d ) 10 , e ) 9", + "Correct": "b", + "Explanation": "\"number start between 15 to 55 is 40 numbers half of them is even . . which is 20 answer : b\"" + }, + { + "Answer": 55, + "Options": "a ) 54 , b ) 55 , c ) 60 , d ) 65 , e ) 70", + "Correct": "b", + "Explanation": "let n = total students in class total points for 1 / 3 class = 45 n / 3 = 15 n total points for 2 / 3 class = 60 * 2 n / 3 = 40 n total points for whole class = 15 n + 40 n = 55 n 63 n total class points / n total students = 55 grade point average for total class answer : b" + }, + { + "Answer": 19, + "Options": "a ) 21 , b ) 20 , c ) 19 , d ) 16 , e ) 15", + "Correct": "c", + "Explanation": "\"marcella has 24 pairs of shoes and loses 9 shoes . to minimize the loss of identical pairs of shoes we want marcella to lose as many identical pairs as possible . this would yield 4 identical pairs and 1 additional shoe ( destroying 5 pairs of shoes ) . the 24 pairs of shoes minus the 5 ' destroyed ' pairs yields 19 pairs that still fulfill the requirements . answer : c\"" + }, + { + "Answer": 90, + "Options": "a ) 90 kg , b ) 55 kg , c ) 45 kg , d ) 85 kg , e ) 25 kg", + "Correct": "a", + "Explanation": "\"explanation : total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 70 + 20 ) kg = 90 kg . answer : a\"" + }, + { + "Answer": 0.2222222222222222, + "Options": "a ) 1 / 9 , b ) 2 / 9 , c ) 4 / 9 , d ) 3 / 9 , e ) 2 / 27", + "Correct": "b", + "Explanation": "\"we just need to find the factor thats all , w - > quadrupled - > 4 w h - > doubled - > 2 h z - > tripled - > 3 z hence , z ^ 2 = 9 z ^ 2 w is in numerator , and h * z in denominator . hence , additional factor being introduced = 4 / 2 * 9 = 4 / 18 = 2 / 9 = b\"" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9", + "Correct": "b", + "Explanation": "\"we have equation 2 n + 5 m = 50 we have factor 2 in first number and we have factor 5 in second number . lcm ( 2 , 5 ) = 10 so we can try some numbers and we should start from 5 because it will be less list than for 2 2 * 5 = 10 and n should be equal 20 4 * 5 = 20 and n should be equal 15 6 * 5 = 30 and n should be equal 10 8 * 5 = 40 and n should be equal 5 10 * 5 = 50 and n should be equal 0 third variant give us the mininal difference n - m = 10 - 6 = 4 and there is some mistake in my way of thinking because we do n ' t have such answer ) if we change the task and will seek for difference between m and n than minimal result w will be 8 - 5 = 3 and answer b\"" + }, + { + "Answer": 8, + "Options": "a ) 4 , b ) 8 , c ) 6 , d ) 7 , e ) 5", + "Correct": "b", + "Explanation": "lets make factorization of 225 and 216 . . 225 = 5 x 5 x 3 x 3 x 3 216 = 2 x 2 x 2 x 3 x 3 x 3 h would have to have 3 two ' s , 225 has 3 threes and and so does 216 but they can be the same three threes so we count them only once . . . 225 has 2 fives . . . so we had them together and we get 3 + 3 + 2 = 8 ( b ) ( answer ) . . ." + }, + { + "Answer": 3460, + "Options": "a ) 3460 , b ) 685 , c ) 865 , d ) 495 , e ) 534", + "Correct": "a", + "Explanation": "\"let y x 12 = 173 x 240 then y = ( 173 x 240 ) / 12 = 3460 answer : a\"" + }, + { + "Answer": 8.75, + "Options": "a ) 5.75 , b ) 6.75 , c ) 7.75 , d ) 8.75 , e ) 9.75", + "Correct": "d", + "Explanation": "man has rs . x he leaves - 1 st shop wid rs . ( 2 x - 10 ) 2 nd shop wid rs . [ 2 ( 2 x - 10 ) - 10 ] 3 rd shop wid rs . { 2 [ 2 ( 2 x - 10 ) - 10 ] - 10 } = 0 ( since he has no money left ) so solving the eqn x = 8.75 answer : d" + }, + { + "Answer": 0.2025, + "Options": "a ) 0.2022 , b ) 0.2012 , c ) 0.2025 , d ) 0.2021 , e ) 0.2029", + "Correct": "c", + "Explanation": "four tenths = 0.4 five thousandths = 0.005 the average is ( 0.4 + 0.005 ) / 2 = 0.2025 answer : c" + }, + { + "Answer": 51, + "Options": "a ) 55 kg , b ) 53 kg , c ) 49 kg , d ) 52 kg , e ) 51 kg", + "Correct": "e", + "Explanation": "\"explanation let a , b , c represent their respective weights . then , we have : a + b + c = ( 43 x 3 ) = 129 \u00e2 \u20ac \u00a6 . ( i ) a + b = ( 48 x 2 ) = 96 \u00e2 \u20ac \u00a6 . ( ii ) b + c = ( 42 x 2 ) = 84 \u00e2 \u20ac \u00a6 . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 180 \u00e2 \u20ac \u00a6 . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 51 . b \u00e2 \u20ac \u2122 s weight = 51 kg . answer e\"" + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 15 , c ) 21 , d ) 27 , e ) 39", + "Correct": "a", + "Explanation": "\"2 ^ 3 + 3 ^ 3 = 35 therefore product is 2 * 3 = 6 a\"" + }, + { + "Answer": 125, + "Options": "a ) 50 , b ) 125 , c ) 200 , d ) 1,000 , e ) 2,000", + "Correct": "b", + "Explanation": "y = 50 % of 25 % 0 f x = x / 8 and y / 100 of x = 100 y / 100 * 8 y = 100 y = 125 answer - b" + }, + { + "Answer": 800, + "Options": "a ) rs . 500 , b ) rs . 600 , c ) rs . 800 , d ) rs . 900 , e ) rs . 700", + "Correct": "c", + "Explanation": "for 1 year interest = 1200 - 1120 = 80 for 4 year 320 then sum = 1120 - 320 = 800 answer : c" + }, + { + "Answer": 93, + "Options": "a ) 84 , b ) 93 , c ) 90 , d ) 92 , e ) 95", + "Correct": "b", + "Explanation": "\"set x = { 11 , 13 , 17 , . . . . . . . . . . . . . , 83 , 89 , 97 } set y = { 4 , 8 , 12 , . . . . . . . . . . . . . . . , 88 , 92 , 96 } combining two sets , say set z set z = { 4,8 , 11 , 12,13 , 17 , . . . . . . . . . . . . . . . . . . . , 83 , 88 , 89 , 92 , 96 , 97 } range = max value - min value range ( z ) = 97 - 4 = 93 oa b is the answer .\"" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "c", + "Explanation": "\"xy = 3 as x + y = 3 x 2 y 3 + y 2 x 3 = 27 x 2 y 2 ( y + x ) = 27 substituting x + y x 2 y 2 = 9 xy = 3 answer : c\"" + }, + { + "Answer": 32, + "Options": "a ) 13 , b ) 26 , c ) 32 , d ) 48 , e ) 56", + "Correct": "c", + "Explanation": "juan - - > laurence = x messages ; juan - - > keith = 8 x messages ( juan sends keith eight times as many messages as he sends laurence ) ; laurence - - > missy = 4.5 x = 18 ( laurence sends missy 4.5 times as many messages as he receives from juan ) . 4.5 x = 18 - - > x = 4 - - > 8 x = 32 . answer : c ." + }, + { + "Answer": 19.999999999999872, + "Options": "a ) 96 , b ) 75 , c ) 48 , d ) 20 , e ) 12", + "Correct": "d", + "Explanation": "\"guys , one more simple funda . 5 / 2 = 2.5 now . 5 x 2 = 1 is the remainder 25 / 4 = 6.25 now . 25 x 4 = 1 is the remainder 32 / 5 = 6.4 now . 4 x 5 = 2 is the remainder given x / y = 96.45 and remainder is 9 so . 45 x y = 9 hence y = 20 ans d\"" + }, + { + "Answer": 80, + "Options": "a ) 15 % , b ) 80 % , c ) 20 % , d ) 22 % , e ) 24 %", + "Correct": "b", + "Explanation": "new annual salary = $ 25000 salary increase = $ 5000 . original salary = $ 25000 - $ 5000 . = $ 20000 % increase = ( $ 15000 / $ 75000 ) * 100 = 80 % hence b ." + }, + { + "Answer": 11.1, + "Options": "a ) 10.5 , b ) 11 , c ) 11.1 , d ) 12 , e ) 12.5", + "Correct": "c", + "Explanation": "\"mean = 14.5 two standard deviations is 1.7 + 1.7 = 3.4 there could be two calues for this . mean + two standard deviations = 17.9 mean - two standard deviations = 11.1 answer choice has 11.1 and so c is the answer .\"" + }, + { + "Answer": 1, + "Options": "a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2", + "Correct": "d", + "Explanation": "first , plot the point ( 3 , 4 ) on a graph . a slope of 2 means \u201c up 2 , over 1 , \u201d so plot this point on a graph , too . here \u2019 s the resulting graph : y over 1 up 2 ( 1 , 0 ) ( 2 , 2 ) ( 3 , 4 ) ( 4 , 6 ) x the line passes through the x - axis at 1 , making the correct answer d ) 1" + }, + { + "Answer": 28, + "Options": "a ) 27 , b ) 29 , c ) 28 , d ) 30 , e ) 31", + "Correct": "c", + "Explanation": "\"13600 \u00f7 87 = 156 , remainder = 28 hence 28 is the least number which can be subtracted from 13600 such that the remainder is divisible by 87 answer is c\"" + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 11 , e ) 12", + "Correct": "a", + "Explanation": "\"answer = a = 5 if least = - 5 , then largest = 6 range = 6 - 1 = 5\"" + }, + { + "Answer": 1200, + "Options": "a ) 600 bc , b ) 600 b / c , c ) 1200 bc , d ) 1200 b / c , e ) 1200 / bc", + "Correct": "c", + "Explanation": "2 cases * c cartons / case * b boxes / carton * 600 clips / box = 1200 bc paper clips the answer is c ." + }, + { + "Answer": 9, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 9 , e ) 8", + "Correct": "d", + "Explanation": "\"fastly i reduce 60 % till it gets closer to our required 2000 candidates step ( 1 ) 40000 accepted . step ( 2 ) another 40 % of 40000 = 16000 accepted . here it is quiet observable that if we further deduct candidate by 60 % it would change our probablity of easy going 2000 candidate . so i would get to second stage of recruitment where 50 % is accepted step ( 3 ) 50 % of 16000 = 8000 step ( 4 ) 50 % of 8000 = 4000 step ( 5 ) 50 % of 4000 = 2000 step ( 6 ) 50 % of 2000 = 1000 step ( 7 ) 50 % of 1000 = 500 last step of accepting 70 % of 500 = 350 ( our target ) total 8 steps required . ans d\"" + }, + { + "Answer": 74, + "Options": "a ) 40 , b ) 74 , c ) 60 , d ) 70 , e ) 80", + "Correct": "b", + "Explanation": "\"according to order of operations , inner brackets first . hence | 8 - 8 ( 3 - 12 ) | - | 5 - 11 | = | 8 - 8 * ( - 9 ) | - | 5 - 11 | according to order of operations , multiplication within absolute value signs ( which may be considered as brackets when it comes to order of operations ) next . hence = | 8 + 72 | - | 5 - 11 | = | 80 | - | - 6 | = 80 - 6 = 74 correct answer b ) 74\"" + }, + { + "Answer": 2, + "Options": "a ) 2 , b ) 1 / 2 , c ) - 1 / 2 , d ) - 2 , e ) - 12", + "Correct": "d", + "Explanation": "f ( a ) = - 1 / 3 = - 1 / a , and thus a = 3 f ( ab ) = 1 / 6 , and thus ab = - 6 3 b = - 6 b = - 2 the answer is d ." + }, + { + "Answer": 17.666666666666664, + "Options": "a ) 17.72 , b ) 18.52 , c ) 19.63 , d ) 16.53 , e ) 15.63", + "Correct": "a", + "Explanation": "explanation : sum of first 11 prime no . which are odd = 195 average = 195 / 11 = 17.72 answer : a" + }, + { + "Answer": 15, + "Options": "a ) 5 inches , b ) 6 inches , c ) 9 inches , d ) 10 inches , e ) 15 inches", + "Correct": "e", + "Explanation": "\"total rainfall in 2 weeks = 25 inches . assume the rainfall in second week = 1 . x rainfall in first week = x total rainfall = 2.5 x = 25 inches x = 10 and 1.5 x = 15 rainfall during second week = 9 inches option e\"" + }, + { + "Answer": 14999.999999999995, + "Options": "a ) $ 8000 , b ) $ 10000 , c ) $ 15000 , d ) $ 12000 , e ) $ 12500", + "Correct": "c", + "Explanation": "\"explanatory answer let the profit made during the year be $ 3 x therefore , $ x would have been shared equally and the remaining $ 2 x would have been shared in the ratio 5.5 : 4.5 i . e . , 55 % of 2 x would go to mary and 45 % of 2 x would go to mike . hence , mary would get ( 55 - 45 ) % of 2 x more than mike or 10 % of 2 x = $ 1000 i . e . , ( 60 / 100 ) * 2 x = 1000 or 2 x = 10000 . hence , the profit made by the company during the year $ 3 x = $ 15000 . answer : c\"" + }, + { + "Answer": 9, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 9 , e ) 6", + "Correct": "d", + "Explanation": "\"the product of 10 integers is negative thus an odd number of integers need to be negative to have a negative product we are asked at most how many are required . so , the highest odd integer before 6 , i . e . 9 correct option : d\"" + }, + { + "Answer": 42, + "Options": "a ) 42 , b ) 32 , c ) 48 , d ) 28 , e ) 38", + "Correct": "a", + "Explanation": "\"x / 63 = 24 . x = 24 * 63 . so correct answer would be , ( 24 * 63 ) / 36 = 42 . answer : a\"" + }, + { + "Answer": 150, + "Options": "a ) 48 , b ) 150 , c ) 72 , d ) 84 , e ) 27", + "Correct": "b", + "Explanation": "\"let the second number be x . then , first number = 2 x and third number = 2 x / 3 . 2 x + x + 2 x / 3 = 550 11 x / 3 = 550 x = 150 answer : b\"" + }, + { + "Answer": 5, + "Options": "a ) 7 , b ) 8 , c ) 5 , d ) 6 , e ) 2", + "Correct": "c", + "Explanation": "atleast 9 green breads are needed to make a necklace , so irrespective of the combinations of white and orange beads , the number of necklaces that can be formed will be 45 / 9 = 5 answer : - c" + }, + { + "Answer": 32.142857142857146, + "Options": "a ) 24 , b ) 32 , c ) 48 , d ) 50 , e ) none", + "Correct": "b", + "Explanation": "\"answer sum of 70 result = sum of 45 result + sum of 25 result . = 45 x 25 + 25 x 45 = 2250 / 70 correct option : b\"" + }, + { + "Answer": 31, + "Options": "a ) 30 , b ) 31 , c ) 32 , d ) 33 , e ) 34", + "Correct": "b", + "Explanation": "n ( a u b u c ) = n ( a ) + n ( b ) + n ( c ) - n ( a intersection b ) - n ( a intersection c ) - n ( c intersection b ) + n ( a intersection b - intersection c ) hence , total no . of students = 10 + 20 + 5 - 4 - 0 - 2 + 2 = 31 . answer : b" + }, + { + "Answer": 25, + "Options": "a ) rs . 25 , b ) rs . 22.50 , c ) rs . 20 , d ) rs . 17.50 , e ) none of these", + "Correct": "a", + "Explanation": "\"let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 961 96 + 225 + 490 + 6 x = 961 6 x = 150 = > x = 25 . answer : a\"" + }, + { + "Answer": 1430, + "Options": "a ) 1209 , b ) 1324 , c ) 1441 , d ) 1300 , e ) 1635", + "Correct": "c", + "Explanation": "\"let the smaller number be x . then larger number = ( x + 1311 ) . x + 1311 = 11 x + 11 10 x = 1300 x = 130 large number = 130 + 1311 = 1441 answer : c\"" + }, + { + "Answer": 20, + "Options": "a ) 20 coins , b ) 30 coins , c ) 28 coins , d ) 25 coins , e ) none of these", + "Correct": "a", + "Explanation": "\"let number of each type of coin = x . then , 1 \u00d7 x + . 50 \u00d7 x + . 25 x = 35 \u21d2 1.75 x = 35 \u21d2 x = 20 coins answer a\"" + }, + { + "Answer": 10, + "Options": "a ) 10 , b ) 17 , c ) 18 , d ) 19 , e ) 20", + "Correct": "a", + "Explanation": "\"two digit numbers : 5 at tens place : 50 , 52,54 , 56,58 7 at tens place : 70 , 72,74 , 76,78 if 5 and 7 is at units place , the number cant be even total : 5 + 5 = 10 answer a\"" + }, + { + "Answer": 106.25, + "Options": "a ) 109 % , b ) 106.25 % , c ) 120 % , d ) 115 % , e ) 110 %", + "Correct": "b", + "Explanation": "\"easiest thing to do : assume that price is 100 price at the end of yr 1 : 100 + 25 = 125 price at the end of year 2 = 125 - 125 * 0.15 = 125 * 0.85 = 106.25 hence required answer = ( 106.25 / 100 ) * 100 % = 106.25 % answer is b .\"" + }, + { + "Answer": 495, + "Options": "a ) rs . 485 , b ) rs . 495 / - , c ) rs . 575 , d ) rs . 685 , e ) rs . 592", + "Correct": "b", + "Explanation": "a : b : c = 3 : 2 : 5 total parts = 10 c ' s share is = 5 parts 10 - - - - - > rs . 960 / - 3 - - - - - > rs . 480 / - a ' s total = 480 + 15 = rs . 495 / - b )" + }, + { + "Answer": 400, + "Options": "a ) rs . 300 , b ) rs . 400 , c ) rs . 480 , d ) rs . 500 , e ) rs . 520", + "Correct": "b", + "Explanation": "p : q = 5 : 4 , q : r = 9 : 10 = ( 9 x 4 / 9 ) : ( 10 x 4 / 9 ) = 4 : 40 / 9 . so , p : q : r = 5 : 4 : 40 / 9 = 45 : 36 : 40 sum of ratio terms is = ( 45 + 36 + 40 ) = 121 . r share of amount is rs ( 1210 x 40 / 121 ) = rs . 400 . b" + }, + { + "Answer": 150, + "Options": "a ) 120 , b ) 140 , c ) 150 , d ) 180 , e ) 200", + "Correct": "c", + "Explanation": "\"let the total number of ounces in the drink be x . % of orange = 35 % % of watermelon = 35 % % of grape = 100 % - 70 % = 30 % 0.30 x = 45 x = 150 therefore there are a total of 150 ounces in the drink . the answer is c .\"" + }, + { + "Answer": 53.999999999999986, + "Options": "a ) 45 , b ) 48 , c ) 51 , d ) 54 , e ) 57", + "Correct": "d", + "Explanation": "\"( v * ) * = ( v - v / 3 ) - ( v - v / 3 ) / 3 24 = 2 v / 3 - 2 v / 9 = 4 v / 9 v = 54 the answer is d .\"" + }, + { + "Answer": 1.6, + "Options": "a ) 4 / 5 , b ) 6 / 5 , c ) 7 / 5 , d ) 8 / 5 , e ) 9 / 5", + "Correct": "d", + "Explanation": "w / x = 2 / 3 = > x = 3 / 2 w and w / y = 6 / 15 = > y = 15 / 6 w ( x + y ) / y = ( 3 / 2 w + 15 / 6 w ) / 15 / 6 w = 4 w / ( 15 / 6 w ) = 8 / 5 correct option : d" + }, + { + "Answer": 200, + "Options": "a ) 160 , b ) 200 , c ) 240 , d ) 300 , e ) 480", + "Correct": "b", + "Explanation": "the first digit and last digit are the same so the 2 possibilities are 6 or 8 . the second and third digits can be any number from 0 to 9 . the total number of palindromic integers is 2 * 10 * 10 = 200 the answer is b ." + }, + { + "Answer": 15593.999999999996, + "Options": "a ) $ 15594 . , b ) $ 15322 . , c ) $ 14786 . , d ) $ 14543 . , e ) $ 12988 .", + "Correct": "a", + "Explanation": "whenever you have a question in which a value is increased by x % and then increased by y % then the overall effective increase = ( x + y + xy / 100 ) % the effective increase = 13 + 20 + ( 13 \u00d7 20 / 100 ) = 35.6 % this is a little more 33 % or 1 / 3 the original value . the quickest way to solve this question is to use approximation . 11500 + 1 / 3 ( 12000 ) = 15500 therefore option a is the answer . i selected 12000 because it ' s value is a little more 11500 and it ' s easier to divide by 3 ( ie to calculate 1 / 3 or 33 % ) ." + }, + { + "Answer": 8.371572875253811, + "Options": "a ) $ 8.40 , b ) $ 5.10 , c ) $ 5.30 , d ) $ 5.50 , e ) $ 5.60", + "Correct": "a", + "Explanation": "\"i tried using time / rate approach : - initial price difference = 8.80 - 3.20 = 5.60 price of corn increasing by 5 x price of wheat decreasing by x ( 1.4 ) - x = . 4 x since both the quantities are moving towards reducing the price gap hence : - relative increase = 5 x + . 4 x let t be the time by which gap is filled so , 5.6 = t ( 5.4 x ) - > t = ( 5.6 ) / 5.4 x final price = 3.20 + 5 x * t - > 3.20 + 5 * 5.6 / 5.4 = 8.4 answer a .\"" + }, + { + "Answer": 28.000000000000025, + "Options": "a ) 28 % , b ) 32 % , c ) 35 % , d ) 45 % , e ) 52 %", + "Correct": "a", + "Explanation": "let the price of the product be $ 100 and let original sale be 100 pieces then , total revenue = 100 * 100 = $ 10000 new revenue = 80 * 160 = $ 12800 increase in revenue = 2800 * 100 / 10000 = 28 % answer is a" + }, + { + "Answer": 135, + "Options": "a ) 124 , b ) 135 , c ) 146 , d ) 157 , e ) 168", + "Correct": "b", + "Explanation": "initially the number of gold coins and silver coins is 2 k and 6 k . after adding gold coins , the number of coins is 3 k and 6 k . thus k = 15 and the total number of coins is 9 k = 135 . the answer is b ." + }, + { + "Answer": 400, + "Options": "a ) 280 , b ) 400 , c ) 420 , d ) 480 , e ) 520", + "Correct": "b", + "Explanation": "\"let the maximum marks be x then , 35 % of x = 100 + 40 35 x / 100 = 140 35 x = 140 * 100 = 14000 x = 400 answer is b\"" + }, + { + "Answer": 0.4166666666666667, + "Options": "a ) 5 / 12 , b ) 5 / 15 , c ) 5 / 10 , d ) 5 / 11 , e ) 5 / 13", + "Correct": "a", + "Explanation": "\"a / d = ( 3 / 4 ) * ( 7 / 9 ) * ( 5 / 7 ) = > 5 / 12 answer : a\"" + }, + { + "Answer": 12, + "Options": "a ) 8 , b ) 12 , c ) 15 , d ) 17 , e ) 18", + "Correct": "b", + "Explanation": "\"let original strength = y then , 40 y + 12 x 32 = ( y + 12 ) x 36 \u21d2 40 y + 384 = 36 y + 432 \u21d2 4 y = 48 \u2234 y = 12 b\"" + }, + { + "Answer": 25, + "Options": "a ) 40 , b ) 30 , c ) 25 , d ) data inadequate , e ) none of these .", + "Correct": "c", + "Explanation": "\"let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 30 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 30 + 20 ) / 2 = 25 . answer : c\"" + }, + { + "Answer": 675, + "Options": "a ) 675 , b ) 725 , c ) 895 , d ) 1025 , e ) none of these", + "Correct": "a", + "Explanation": "\"solution : dividing each side by 25 , we obtain ( 25 x / 675 ) = ( 675 / 25 ) therefore : x = 27 check : 25 x = 675 ( 25 * 27 ) = 675 675 = 675 answer : a\"" + }, + { + "Answer": 0.2, + "Options": "a ) 1 / 5 , b ) 1 / 6 , c ) 1 / 6 , d ) 1 / 4 , e ) 1 / 2", + "Correct": "a", + "Explanation": "here , x and y are events z ( x | y ) = z ( xny ) / z ( y ) = 0.10 / 0.10 = 1 q ( g | h ) = z ( xny ) / z ( x ) = 0.4 / 0.02 = 1 / 5 answer is a" + }, + { + "Answer": 44.44444444444444, + "Options": "a ) 44.4 , b ) 44.8 , c ) 1 , d ) 19 , e ) 44.11", + "Correct": "a", + "Explanation": "explanation : 20 + 0.25 \u00d7 d = 24 + 0.16 d solving we get d = 44.4 answer : a" + }, + { + "Answer": 48, + "Options": "a ) 44 , b ) 46 , c ) 48 , d ) 50 , e ) 52", + "Correct": "c", + "Explanation": "$ 24 = 4 * $ 6 the number of doughnuts is 4 * 12 = 48 the answer is c ." + }, + { + "Answer": 19, + "Options": "a ) 13 , b ) 15 , c ) 17 , d ) 19 , e ) 21", + "Correct": "d", + "Explanation": "\"let x be the number of cans in row 1 . the total number of cans is x + ( x + 3 ) + . . . + ( x + 24 ) = 9 x + 3 ( 1 + 2 + . . . + 8 ) = 9 x + 3 ( 8 ) ( 9 ) / 2 = 9 x + 108 since the total is less than 120 , x must equal 1 . the number of cans in the 7 th row is 1 + 3 ( 6 ) = 19 the answer is d .\"" + }, + { + "Answer": 32, + "Options": "a ) 22 , b ) 30 , c ) 99 , d ) 38 , e ) 32", + "Correct": "e", + "Explanation": "\"total age increased = ( 10 * 2 ) years = 20 years . sum of ages of two new men = ( 21 + 23 + 20 ) years = 64 years average age of two new men = ( 64 / 2 ) years = 32 years . answer : e\"" + }, + { + "Answer": 5, + "Options": "a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8", + "Correct": "b", + "Explanation": "\"q = n ( n - 3 ) q = 2 * n 2 n = n ( n - 3 ) = > 2 = n - 3 = > n = 5 answer b\"" + }, + { + "Answer": 16, + "Options": "a ) 11 , b ) 13 , c ) 14 , d ) 16 , e ) 10", + "Correct": "d", + "Explanation": "\"explanation : let somu ' s age be x and that of his father be 3 x . so , x - 8 = 3 x - 8 / 5 = x = 16 answer : option d\"" + }, + { + "Answer": 27, + "Options": "a ) 27 , b ) 35 , c ) 39 , d ) 60 , e ) 65", + "Correct": "a", + "Explanation": "\"the total number of the people in the room must be a multiple of both 7 and 9 ( in order 3 / 7 and 5 / 9 of the number to be an integer ) , thus the total number of the people must be a multiple of lcm of 7 and 9 , which is 63 . since , the total number of the people in the room is greater than 50 and less than 100 , then there are 91 people in the room . therefore there are 3 / 7 * 63 = 27 people in the room under the age of 21 . answer : a .\"" + }, + { + "Answer": 88.49858755935034, + "Options": "a ) 78 , b ) 68 , c ) 88 , d ) 97 , e ) 37", + "Correct": "c", + "Explanation": "\"c 88 from the given alternatives , 88 \u00d7 89 = 7832 \u2234 smaller number = 88\"" + }, + { + "Answer": 800.0000000000001, + "Options": "a ) 80 , b ) 800 , c ) 8000 , d ) 80000 , e ) none of these", + "Correct": "b", + "Explanation": "\"solution therefore = 3.6 x 0.48 x 2.50 / 0.12 x 0.09 x 0.5 = 36 x 48 x 250 / 12 x 9 x 5 = 800 answer b\"" + }, + { + "Answer": 9.333333333333332, + "Options": "a ) 7.33 cm , b ) 6.33 cm , c ) 5.33 cm , d ) 9.33 cm , e ) 8.33 cm", + "Correct": "d", + "Explanation": "( 1 / 8 ) p + ( 1 / 2 ) p + ( 7 / 2 ) = p on solving the above for p we get 9.333 now checking for the answer : 9.333 / 8 = 1.166 cm 9.333 / 2 = 4.665 cm now 1.166 + 4.665 + ( 7 / 2 ) = 9.33 cm answer : d" + }, + { + "Answer": 34, + "Options": "a ) 34 , b ) 55 , c ) 66 , d ) 81 , e ) 21", + "Correct": "a", + "Explanation": "\"m + tu + w + th = 4 * 48 = 192 tu + w + th + f = 4 * 46 = 184 m = 42 tu + w + th = 192 - 42 = 150 f = 184 \u2013 150 = 34 . answer : a\"" + }, + { + "Answer": 17.700000000000003, + "Options": "a ) 15.6 , b ) 16.0 , c ) 17.7 , d ) 18.7 , e ) 19.1", + "Correct": "c", + "Explanation": "\"a certain taxi company charges $ 2.10 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ? a . 15.60 b . 16.00 c . 17.50 d . 18.70 e . 19.10 1 / 5 miles = 0.2 miles . the cost of 8 miles long ride would be $ 2.10 for the first 0.2 miles plus ( 8 - 0.2 ) / 0.2 * 0.4 = $ 2.1 + $ 15.6 = $ 17.7 . answer : c .\"" + }, + { + "Answer": 20, + "Options": "a ) 12 , b ) 18 , c ) 24 , d ) 20 , e ) 40", + "Correct": "d", + "Explanation": "\"slope = change in vertical direction / change in horizontal direction = 4 / 3 change in vertical direction = 4 x = ab change in horizontal direction = 3 x = bc ab ^ 2 + bc ^ 2 = 25 ^ 2 16 x ^ 2 + 9 x ^ 2 = 625 25 x ^ 2 = 625 x ^ 2 = 25 x = 5 therefore ab = 5 * 4 = 20 answer : d\"" + }, + { + "Answer": 5000, + "Options": "a ) 4000 , b ) 4500 , c ) 5055 , d ) 5000 , e ) 2500", + "Correct": "d", + "Explanation": "\"first recognize you only need to consider the first four digits ( because the second four are just the first four flipped ) there are 9000 possibilities for the first four digits of a 8 digit number , 1000 - 9999 inclusive . everything starting with a 1 , 3,5 , 7,9 will be odd , which is 5 / 9 ths of the combinations . 5 / 9 * 9000 = 5000 answer : d\"" + }, + { + "Answer": 80, + "Options": "a ) 70 , b ) 75 , c ) 20 , d ) 80 , e ) 60", + "Correct": "d", + "Explanation": "explanation : 100 \u00e2 \u20ac \u201c 20 = 80 answer : d" + }, + { + "Answer": 37, + "Options": "a ) 37 , b ) 38 , c ) 39 , d ) 40 , e ) 41", + "Correct": "a", + "Explanation": "\"let present age of a be a and b be b a + 10 = 2 * ( b - 10 ) = > 2 b - a = 30 . . . . . . ( i ) a = b + 7 = > 2 b - b - 7 = 30 b = 37 so the present age of b is 37 years answer : a\"" + }, + { + "Answer": 11, + "Options": "a ) 11 , b ) 12 , c ) 13 , d ) 15 , e ) 18", + "Correct": "a", + "Explanation": "ab = ( a - 1 ) ( b - 1 ) y 12 = ( y - 1 ) ( 12 - 1 ) = 110 - - > y - 1 = 10 - - > y = 11 answer : a" + }, + { + "Answer": 19, + "Options": "a ) 11 , b ) 15 , c ) 12 , d ) 19 , e ) 20", + "Correct": "d", + "Explanation": "\"d 19 ( x + y ) \u00e2 \u20ac \u201c ( y + z ) = 19 x \u00e2 \u20ac \u201c z = 19\"" + }, + { + "Answer": 35.99999999999999, + "Options": "a ) 30 , b ) 33 , c ) 36 , d ) 39 , e ) 42", + "Correct": "c", + "Explanation": "\"( v * ) * = ( v - v / 3 ) - ( v - v / 3 ) / 3 16 = 2 v / 3 - 2 v / 9 = 4 v / 9 v = 36 the answer is c .\"" + }, + { + "Answer": 10000, + "Options": "a ) $ 10000 , b ) $ 11000 , c ) $ 12000 , d ) $ 10500 , e ) $ 11500", + "Correct": "a", + "Explanation": "let t be the tier price , p be total price = 30000 per the given conditions : 0.25 t + 0.15 ( p - t ) = 5500 0.25 t + 0.15 * 30000 - 0.15 t = 5500 0.10 t + 4500 = 5500 0.10 t = 5500 - 4500 = 1000 t = 1000 / 0.10 = 10000 answer a" + }, + { + "Answer": 653, + "Options": "a ) 515 . , b ) 545 . , c ) 618 . , d ) 649 . , e ) 666 .", + "Correct": "d", + "Explanation": "\"answer is d : 649 solution : total number of students studying both are 423 + 230 - 134 = 519 ( subtracting the 134 since they were included in the both the other numbers already ) . so 80 % of total is 519 , so 100 % is approx . 649 .\"" + }, + { + "Answer": 55, + "Options": "a ) 46 , b ) 47 , c ) 48 , d ) 55 , e ) 50", + "Correct": "d", + "Explanation": "\"the standard deviation ( { sd } ) = 2 ; 3 standard deviations below the mean is greater than 48 : { mean } - 3 * { sd } > 48 ; { mean } - 6 > 48 ; { mean } > 54 . answer : d .\"" + }, + { + "Answer": 68, + "Options": "a ) 50 , b ) 52 , c ) 49 , d ) 68 , e ) 74", + "Correct": "d", + "Explanation": "\"sum of 5 integer ( a , b , c , d , e ) = 5 * 60 = 300 e - a = 10 i . e . e = a + 10 for e to be maximum remaining 4 must be as small as possible since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers i . e . a + a + a + a + ( a + 10 ) = 300 i . e . 5 a = 290 i . e . a = 58 i . e . largest e = 58 + 10 = 68 answer : option d\"" + }, + { + "Answer": 2809, + "Options": "a ) 2709 , b ) 2809 , c ) 2909 , d ) 3009 , e ) 3109", + "Correct": "b", + "Explanation": "\"sum of 1 st n odd no . s = 1 + 3 + 5 + 7 + . . . = n ^ 2 so , sum of 1 st 53 odd numbers = 53 ^ 2 = 2809 answer : b\"" + }, + { + "Answer": 15, + "Options": "a ) 25 , b ) 13 , c ) 17 , d ) 24 , e ) 15", + "Correct": "e", + "Explanation": "5 + 2 \u00e2 \u20ac \u00a2 ( 8 \u00e2 \u20ac \u201c 3 ) = 5 + 2 ( 5 ) = 5 + 2 * 5 = 5 + 10 = 15 correct answer e" + }, + { + "Answer": 1, + "Options": "a ) a ) 4 , b ) b ) 1 , c ) c ) 2 , d ) d ) 3 , e ) e ) 5", + "Correct": "b", + "Explanation": "\"explanation : ( 1057 / 23 ) gives remainder 22 22 + 1 = 23 , so we need to add 1 answer : option b\"" + }, + { + "Answer": 1000, + "Options": "a ) 3323 , b ) 1000 , c ) 2877 , d ) 2992 , e ) 7111", + "Correct": "b", + "Explanation": "20 * 10 * 5 = 1000 answer : b" + }, + { + "Answer": 796, + "Options": "a ) 50 , b ) 200 , c ) 380 , d ) 798 , e ) 400", + "Correct": "d", + "Explanation": "1 / 20 % of 8000 = 4 1 / 10 of 8000 = 800 800 - 2 = 798 ans : d" + }, + { + "Answer": 10.000000000000009, + "Options": "a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 30 %", + "Correct": "a", + "Explanation": "\"1990 dick saved = $ 5500 jane saved = $ 4500 ( jane saved $ 500 less than she did the prior year ) jane saved approximately $ 500 / 5000 $ ( 10 % ) less in 1990 answer : a\"" + }, + { + "Answer": 2, + "Options": "a ) a ) 4 , b ) b ) 7 , c ) c ) 9 , d ) d ) 5 , e ) e ) 2", + "Correct": "e", + "Explanation": "7 - 5 = 2 . answer is e" + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) 14 , c ) 18 , d ) 22 , e ) 24", + "Correct": "a", + "Explanation": "\"d = ( d - r ) / q = ( 109 - 1 ) / 9 = 108 / 9 = 12 a )\"" + }, + { + "Answer": 4.799999999999999, + "Options": "a ) $ 2.40 , b ) $ 3.00 , c ) $ 3.20 , d ) $ 3.60 , e ) $ 4.80", + "Correct": "e", + "Explanation": "\"total allowance = x amount spent at the arcade = 3 / 5 x amount remaining = 2 / 5 x amount spent at the toy store = 2 / 5 * 1 / 3 x = 2 / 15 x amount remaining = 2 / 5 x - 2 / 15 x = 4 / 15 x now , 4 / 15 x = $ 1.28 therefore , x = $ 4.80 . answer e\"" + }, + { + "Answer": 13.333333333333332, + "Options": "a ) 50 km , b ) 56 km , c ) 13.3 km , d ) 70 km , e ) 80 km", + "Correct": "c", + "Explanation": "\"let the actual distance travelled be x km . x / 10 = ( x + 20 ) / 25 25 x = 10 x + 200 15 x = 200 x = 13.3 km . answer : c\"" + }, + { + "Answer": 100, + "Options": "a ) 36 liters , b ) 40 liters , c ) 45 liters , d ) 54 liters , e ) 100 liters", + "Correct": "e", + "Explanation": "\"a big container is 30 % full with water and after 45 liters of water is added , the container becomes 75 % full . hence these 45 liters account for 45 % of the container , which means that the capacity of it is 45 / 0.45 = 100 liters . or : if the capacity of the container is x liters then : 0.3 x + 45 = 0.75 x - - > x = 100 liters . answer : e .\"" + }, + { + "Answer": 200, + "Options": "a ) 160 , b ) 200 , c ) 240 , d ) 300 , e ) 480", + "Correct": "b", + "Explanation": "the first digit and last digit are the same so the 2 possibilities are 6 or 8 . the second and third digits can be any number from 0 to 9 . the total number of palindromic integers is 2 * 10 * 10 = 200 the answer is b ." + }, + { + "Answer": 125, + "Options": "a ) a ) 110 , b ) b ) 122 , c ) c ) 120 , d ) d ) 125 , e ) e ) 145", + "Correct": "d", + "Explanation": "\"explanation : average of new numbers = 25 * 5 = 125 answer : option d\"" + }, + { + "Answer": 899.9999999999999, + "Options": "a ) 900 , b ) 2217 , c ) 2889 , d ) 2777 , e ) 2991", + "Correct": "a", + "Explanation": "\"1008 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 900 answer : a\"" + }, + { + "Answer": 3, + "Options": "a ) $ 1.40 , b ) $ 3 , c ) $ 3.40 , d ) $ 4.40 , e ) $ 5.40", + "Correct": "b", + "Explanation": "\"manager wages per hour = $ 7.50 dishwasher wages per hour = half of manager ' s wages . = 1 / 2 ( $ 7.50 ) = = > $ 3.75 chef wages per hour = 20 % greater than dishwasher wages - - > 20 % of $ 3.75 = ( 20 * ( $ 3.75 ) ) / 100 - - > ( $ 75 ) / 100 - - > $ 0.75 therefore , chef wages per hour = $ 3.75 + $ 0.75 = = > $ 4.5 difference of wages between manager and chef = $ 7.50 - $ 4.5 = = > $ 3 answer : b\"" + }, + { + "Answer": 145, + "Options": "a ) 145 , b ) 168 , c ) 189 , d ) 190 , e ) 200", + "Correct": "a", + "Explanation": "\"solution average of 7 people after the last one enters = 151 . \u00e2 \u02c6 \u00b4 required weight = ( 7 x 151 ) - ( 6 x 152 ) = 1057 - 912 = 145 . answer a\"" + }, + { + "Answer": 8, + "Options": "a ) 22 , b ) 67 , c ) 88 , d ) 12 , e ) 8", + "Correct": "e", + "Explanation": "\"( 70 / 100 ) * 40 \u2013 ( 4 / 5 ) * 25 = 8 answer : e\"" + }, + { + "Answer": 8, + "Options": "a ) 1 , b ) 3 , c ) 5 , d ) 8 , e ) 11", + "Correct": "d", + "Explanation": "27 is 3 * 3 * 3 then a 3 + 1 = 4 b 3 + 3 = 6 c 3 + 5 = 8 d 3 + 8 = 11 e 3 + 11 = 14 here d is the only addition that gives a prime number ." + }, + { + "Answer": 476, + "Options": "a ) 120 , b ) 239 , c ) 476 , d ) 523 , e ) 526", + "Correct": "c", + "Explanation": "let the smaller number be x . then , larger number = ( 2395 + x ) therefore 2395 + x = ( 6 x + 15 ) \u2039 = \u203a 5 x = 2380 \u2039 = \u203a x = 476 . answer : c" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 6 , e ) 7", + "Correct": "c", + "Explanation": "\"d = ( d - r ) / q = ( 22 - 1 ) / 7 = 21 / 7 = 3 c\"" + }, + { + "Answer": 1013, + "Options": "a ) 1008 , b ) 1013 , c ) 1022 , d ) 1032 , e ) 1043", + "Correct": "b", + "Explanation": "\"required number = ( l . c . m of 12 , 16 , 18 , 21,28 ) + 5 = 1008 + 5 = 1013 answer : b\"" + }, + { + "Answer": 1, + "Options": "a ) 7 / 5 , b ) 5 / 7 , c ) 1 , d ) 49 / 25 , e ) it can not be determined", + "Correct": "c", + "Explanation": "ratio = 7 k / 5 k = 7 / 5 , 14 / 10 , etc . x is multiplied by y and y is multiplied by x - - > ( 7 k * 9 k ) / ( 9 k * 7 k ) = 1 answer : c" + }, + { + "Answer": 10, + "Options": "a ) 10 , b ) - 2 , c ) 11 , d ) 13 , e ) 22", + "Correct": "a", + "Explanation": "the equation that can be formed is : 3 x - 14 = 26 - x or , 4 x = 40 or , x = 10 . a answer ." + }, + { + "Answer": 9500, + "Options": "a ) s . 9500 , b ) s . 50000 , c ) s . 57000 , d ) s . 60000 , e ) s . 62000", + "Correct": "a", + "Explanation": "length ( l ) = 20 m , breadth ( b ) = 15 m and height ( h ) = 5 m total area of the hall to be covered with mat = 2 ( lb + bh + hl ) = 2 ( 20 * 15 + 15 * 5 + 5 * 20 ) = 2 ( 300 + 75 + 100 ) = 2 * 475 = 950 sq . m total expenditure = 10 * 950 = rs . 9500 a" + }, + { + "Answer": 290, + "Options": "a ) 300 , b ) 276 , c ) 290 , d ) 285 , e ) none", + "Correct": "c", + "Explanation": "\"since the month begins with sunday , to there will be five sundays in the month average required = ( 540 x 5 + 240 x 25 ) / 30 ) = 290 answer : option c\"" + }, + { + "Answer": 12, + "Options": "a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15", + "Correct": "b", + "Explanation": "\"explanation : given that a + b = 12 + b + c = > a \u2013 c = 12 + b \u2013 b = 12 = > c is younger than a by 12 years answer : option b\"" + }, + { + "Answer": 12, + "Options": "a ) 6 , b ) 12 , c ) 24 , d ) 36 , e ) 48", + "Correct": "b", + "Explanation": "\"q : if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer v that must divide n is : a 6 , b 12 , c 24 , d 36 , e 48 n ^ 2 is divisible by 72 , but it must also be greater than 72 . if n is an integer , then n ^ 2 must be a perfect square . the factorization of 72 is ( 8 ) ( 9 ) , so if it is multiplied by 2 , it will be ( 2 ) ( 8 ) ( 9 ) = ( 16 ) ( 9 ) = 144 , a perfect square . so n ^ 2 must be at least 144 or a multiple of 144 , which means that n must be 12 or a multiple of 12 . b\"" + }, + { + "Answer": 468, + "Options": "a ) 198 , b ) 288 , c ) 363 , d ) 396 , e ) 468", + "Correct": "e", + "Explanation": "i will go with e ( pending elements to match is 2 ^ 2 * 3 ^ 2 * 13 ^ 1 = 468" + }, + { + "Answer": 700, + "Options": "a ) 450 , b ) 300 , c ) 500 , d ) 610 , e ) 700", + "Correct": "e", + "Explanation": "\"let the maximum marks be x then , 33 % of x = 175 + 56 33 x / 100 = 231 x = 700 answer is e\"" + }, + { + "Answer": 91, + "Options": "a ) 91 , b ) 910 , c ) 1001 , d ) 1911 , e ) none of these", + "Correct": "a", + "Explanation": "\"solution required number of student = h . c . f of 1001 and 910 = 91 . answer a\"" + }, + { + "Answer": 70, + "Options": "a ) 70 , b ) 60 , c ) 55 , d ) 65 , e ) 85", + "Correct": "a", + "Explanation": "hear , 10 students had average score of 80 , so , 80 x 10 = 800 and 10 students had average score of 60 , so , 60 x 10 = 600 total no of student are 20 ( 800 + 600 ) / 20 = 70 correct ans is a" + }, + { + "Answer": 0.1111111111111111, + "Options": "a ) 3 , b ) 6 , c ) 1 / 9 , d ) 1 / 3 , e ) 9", + "Correct": "c", + "Explanation": "\"explanation : solution : given x = k / y ^ 2 , where k is constant . now , y = 3 and x = 1 gives k = 9 . . ' . x = 9 / y ^ 2 = > x = 9 / 9 ^ 2 = 1 / 9 answer : c\"" + }, + { + "Answer": 72.5, + "Options": "a ) a ) 59 , b ) b ) 61 , c ) c ) 63 , d ) d ) 72 , e ) e ) 67", + "Correct": "d", + "Explanation": "\"formula = \u221a a \u00d7 b a = 64 and b = 81 \u221a 64 \u00d7 81 = 8 \u00d7 9 = 72 d\"" + }, + { + "Answer": 6, + "Options": "a ) 16 . , b ) 8 . , c ) 7 . , d ) 6 . , e ) - 2 .", + "Correct": "d", + "Explanation": "\"given a + b = 12 = > a = 12 - b - - > eq 1 b + c = 9 c + d = 3 = > d = 3 - c - - > eq 2 then eqs 1 + 2 = > a + d = 12 - b + 3 - c = > 15 - ( b + c ) = > 15 - 9 = 6 . option d . . .\"" + }, + { + "Answer": 4, + "Options": "a ) $ 1 , b ) $ 2 , c ) $ 3 , d ) $ 4 , e ) $ 5", + "Correct": "d", + "Explanation": "the average price of a shirt is : $ 400 / 25 = $ 16 . the average price of a sweater is : $ 1500 / 75 = $ 20 . the difference in price is : $ 20 - $ 16 = $ 4 . the answer is d ." + }, + { + "Answer": 10, + "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12", + "Correct": "c", + "Explanation": "average of the first ' n ' natural numbers = ( n + 1 ) / 2 we get ( 19 + 1 ) / 2 = 10 answer : c" + }, + { + "Answer": 2, + "Options": "a ) 0 , b ) 2 , c ) 1 , d ) 3 , e ) 4", + "Correct": "b", + "Explanation": "\"assume x is quotient here , n = 18 x + 11 - - - - - - - - - - ( 1 ) and n = 9 x + ? we can also write equation ( 1 ) as : n = ( 18 x + 9 ) + 2 . ie 9 ( 2 x + 1 ) + 2 ie the first term is perfectly divisible by 6 . so , the remainder left is 2 . so , answer ( b ) is right choice .\"" + }, + { + "Answer": 3, + "Options": "a ) 0 , b ) 2 , c ) 3 , d ) 5 , e ) 7", + "Correct": "c", + "Explanation": "i think the answer should be c . thoose are p - values that satisfy given restriction : - 2 , 0 , 2 ( note , a fraction can be also a perfect square ) - - > 16 * 100 , 16 * 1 , 16 / 100" + }, + { + "Answer": 39, + "Options": "a ) 37 , b ) 38 , c ) 39 , d ) 40 , e ) 41", + "Correct": "c", + "Explanation": "\"let present age of a be a and b be b a + 10 = 2 * ( b - 10 ) = > 2 b - a = 30 . . . . . . ( i ) a = b + 9 = > 2 b - b - 9 = 30 b = 39 so the present age of b is 39 years answer : c\"" + }, + { + "Answer": 43.75, + "Options": "a ) 2 % , b ) 17 % , c ) 44 % , d ) 65 % , e ) 83 %", + "Correct": "c", + "Explanation": "\"new value \u2013 old value ) / old value x 100 we are given : february sales this year = 460 million february sales last year = 320 million we need to determine the percent increase between sales from last year to sales this year . thus , the new value = 460 million and the old value = 320 million . let \u2019 s plug them into our percent change formula . ( new value \u2013 old value ) / old value x 100 [ ( 460 \u2013 320 ) / 320 ] x 100 \u2248 44 % . the answer is c .\"" + }, + { + "Answer": 0.6, + "Options": "a ) 2 / 5 , b ) 3 / 4 , c ) 4 / 5 , d ) 5 / 4 , e ) 3 / 5", + "Correct": "e", + "Explanation": "a / b = 4 / 5 m / x = ( 3 / 5 ) * 5 / ( 5 / 4 ) * 4 = 3 / 5 the answer is e ." + }, + { + "Answer": 10, + "Options": "a ) 13 , b ) 12 , c ) 10 , d ) 16 , e ) 14", + "Correct": "c", + "Explanation": "c 10" + }, + { + "Answer": 2376, + "Options": "a ) 2673 , b ) 2763 , c ) 2637 , d ) 2736 , e ) 2376", + "Correct": "e", + "Explanation": "\"= 24 - 1 = 23 = ( decrement each digit of the number obtained from 9 ) here we got 23 . now = 9 - 2 = 7 and 9 - 3 = 6 . so we have 76 just write these numbers together . that is we have 23 and 76 . hence answer is 2376 answer is e .\"" + }, + { + "Answer": 60, + "Options": "a ) 57 , b ) 60 , c ) 63 , d ) 66 , e ) 69", + "Correct": "b", + "Explanation": "\"m + h = 90 h = 90 - m 4 m + 5 h = 390 4 m + 5 * ( 90 - m ) = 390 m = 60 the answer is b .\"" + }, + { + "Answer": 49, + "Options": "a ) 51 , b ) 56 , c ) 49 , d ) 17 , e ) 7", + "Correct": "c", + "Explanation": "\"133 + 16 = 149 dividing 149 evenly into whole numbers is 2 and leaves 49 remaining . the correct answer is c .\"" + }, + { + "Answer": 1, + "Options": "a ) 2 , b ) - 2 , c ) 1 , d ) - 1 , e ) 5", + "Correct": "c", + "Explanation": "if we solve the question , we get x = 1 . option : c" + }, + { + "Answer": 5050, + "Options": "a ) 3043 , b ) 5050 , c ) 5176 , d ) 9356 , e ) 4890", + "Correct": "b", + "Explanation": "b 5050 you must have noticed that 50 pairs of n ^ 2 \u2013 ( n - 1 ) ^ 2 exist . n ^ 2 \u2013 ( n - 1 ) ^ 2 = n + ( n \u2013 1 ) in such case , we may as well write 100 ^ 2 - 99 ^ 2 + 98 ^ 2 - 97 ^ 2 + 96 ^ 2 - 95 ^ 2 + . . . + 2 ^ 2 - 1 ^ 2 as 100 + 99 + 98 + . . . + 2 + 1 = ( 100 x 101 ) / 2 = 5050" + }, + { + "Answer": 35, + "Options": "a ) 20 , b ) r = 25 , c ) r = 30 , d ) r = 35 , e ) 40", + "Correct": "d", + "Explanation": "\"suppose the population of the country in current year is 1000 . so annual increase is 1000 + 39.4 - 19.4 = 1020 hence every year there is an increase of 2 % . 2000 = 1000 ( 1 + ( 2 / 100 ) ) ^ n n = 35 answer is d .\"" + }, + { + "Answer": 46.6, + "Options": "a ) 12.8 , b ) 24.2 , c ) 46.6 , d ) 72.1 , e ) 96.8", + "Correct": "c", + "Explanation": "arithmetic mean = sum / total numbers sum = 43.1 * 8 = 344.8 sum of half of these numbers is 158.4 . so , 4 numbers sum is 158.4 . rest 4 numbers sum = 344.8 - 158.4 = 186.4 arithmetic mean of the 4 nos = 186.4 / 4 = 46.6 hence , c is the answer ." + }, + { + "Answer": 50, + "Options": "a ) 25 % , b ) 33 1 / 3 % , c ) 50 % , d ) 66 2 / 3 % , e ) 75 %", + "Correct": "c", + "Explanation": "general formula for percent increase or decrease , ( percent change ) : percent = change / original \u2217 100 so , the time between maintenance checks increased by 45 \u2212 30 / 30 \u2217 100 = 50 answer : c ." + }, + { + "Answer": 48, + "Options": "a ) 33 , b ) 37 , c ) 54 , d ) 99 , e ) 48", + "Correct": "e", + "Explanation": "the number of students with first division = 30 % of 300 = 30 / 100 \u00d7 300 = 9000 / 100 = 90 and , the number of students with second division = 54 % of 300 = 54 / 100 \u00d7 300 = 16200 / 100 = 162 therefore , the number of students who just passed = 300 \u2013 ( 90 + 162 ) = 48 answer : e" + }, + { + "Answer": 3, + "Options": "a ) 6 rs , b ) 7 rs , c ) 8 rs , d ) 4 rs , e ) 3 rs", + "Correct": "e", + "Explanation": "\"5 m = xw = 8 b 5 m + xw + 8 b - - - - - 45 rs . 5 m + 5 m + 5 m - - - - - 45 rs . 15 m - - - - - - 45 rs . = > 1 m = 3 rs . answer : e\"" + }, + { + "Answer": 89.6, + "Options": "a ) 89.6 , b ) 91.0 , c ) 88.0 , d ) 70.9 , e ) 71.2", + "Correct": "a", + "Explanation": "\"12 % of 80 = ( 80 * 0.12 ) = 9.6 12 % greater than 80 = 80 + 9.6 = 89.6 answer is clearly a .\"" + }, + { + "Answer": 80, + "Options": "a ) 25 , b ) 35 , c ) 75 , d ) 80 , e ) 90", + "Correct": "d", + "Explanation": "\"a + b + c = 3 * 84 = 252 a + b + c + d = 4 * 80 = 320 - - - - ( i ) so , d = 68 & e = 68 + 8 = 76 b + c + d + e = 79 * 4 = 316 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 320 \u00e2 \u20ac \u201c 316 = 4 a = e + 4 = 76 + 4 = 80 d\"" + }, + { + "Answer": 342.8571428571429, + "Options": "a ) 120 , b ) 300 , c ) 401.36 , d ) 350.15 , e ) 342.86", + "Correct": "e", + "Explanation": "\"system of equations a = ( 35 / 100 ) c ( 1 / 3 ) a = 40 - - > a = 120 substitution 120 = ( 35 / 100 ) c c = ( 100 / 35 ) 120 answer - 120 / 35 * 100 the correct answer is e . - 342.86\"" + }, + { + "Answer": 35, + "Options": "a ) 18 % , b ) 20 % , c ) 21 % , d ) 40 % , e ) can not be determined", + "Correct": "d", + "Explanation": "answer : d ." + }, + { + "Answer": 16, + "Options": "a ) 14 years , b ) 12 years , c ) 56 years , d ) 16 years , e ) 55 years", + "Correct": "d", + "Explanation": "\"given that a + b = 16 + b + c = > a \u00e2 \u20ac \u201c c = 16 + b \u00e2 \u20ac \u201c b = 16 = > c is younger than a by 16 years answer : d\"" + }, + { + "Answer": 1614, + "Options": "a ) 1254 , b ) 1376 , c ) 1456 , d ) 1555 , e ) 1629", + "Correct": "e", + "Explanation": "\"let the smaller number be x . then larger number = ( x + 1360 ) . x + 1360 = 6 x + 15 5 x = 1345 x = 269 large number = 269 + 1360 = 1629 e\"" + }, + { + "Answer": 1, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "b", + "Explanation": "solution : we write the given equation like this ( 2 a - 1 ) x = 2 ( b - 1 ) the following cases are possible : if 2 a - 1 \u2260 0 , i . e . a \u2260 1 / 2 , the equation has single solution x = 2 ( b - 1 ) / ( 2 a - 1 ) if a = 1 / 2 and b = 1 , the equation gets the kind 0 . x = 0 and every x is solution if a = 1 / 2 and b \u2260 1 , we get 0 . x = 2 ( b - 1 ) , where 2 ( b - 1 ) \u2260 0 in this case the equation has no solution . if b = 7 and a \u2260 1 / 2 the single solution is x = 2 ( 7 - 1 ) / ( 2 a - 1 ) = 12 / ( 2 a - 1 ) if a is whole number , then 2 a - 1 is also whole number and the solution x = 12 / ( 2 a - 1 ) is natural number when 2 a - 1 is positive divisor of 12 . to have a as whole number , the divisor of 12 mu be odd . but the only whole positive odd numbers divisible by 12 are 1 and 3 . therefore 2 a - 1 = 3 < = > a = 2 or 2 a - 1 = 1 < = > a = 1 a = 2 or 2 a - 1 = 1 < = > a = 1 answer b" + }, + { + "Answer": 15, + "Options": "a ) 25 , b ) 20 , c ) 15 , d ) 13 , e ) 14", + "Correct": "c", + "Explanation": "let the number of keepers be x then , total number of heads = ( 50 + 45 + 8 + x ) = ( 103 + x ) . total number of feet = ( 45 + 8 ) x 4 + ( 50 + x ) x 2 = ( 312 + 2 x ) . ( 312 + 2 x ) - ( 103 + x ) = 224 = = > x = 15 . hence , number of keepers = 15 . answer c ." + }, + { + "Answer": 140.78099890167377, + "Options": "a ) 140 , b ) 141 , c ) 142 , d ) 143 , e ) 144", + "Correct": "b", + "Explanation": "next year total population = [ 150 ^ 2 + 90 ^ 2 ] ^ . 5 = 174.92 = 175 man decreased by 10 % so total man = 150 * . 9 = 135 women will be = 175 - 135 = 40 so population after two years = [ 135 ^ 2 + 40 ^ 2 ] ^ . 5 = 140.80 = 141 so population after two year = 141 answer : b" + }, + { + "Answer": 25, + "Options": "a ) 47 , b ) 25 , c ) 37 , d ) 33 , e ) 29", + "Correct": "b", + "Explanation": "\"before you tackle this question you must first understand that the question is comprised of two key parts , 1 st is finding out how manytermsis in that sequence and 2 nd whatactual number valuethat term is . in an arithmetic progression , in this case consecutive odd integers 1 , 3 , 5 , . . . . , there are two set of rules . rule # 1 ( arithmetic sequence ) : xn = a + d ( n - 1 ) identifies what the actual # in the sequence would be . each number in the sequence has a term such as 1 ( is the first term ) , 3 ( is the second term ) and so on . so if i were to ask you to find out what the 10 th term is of that sequence you would use that formula to find that value . a = 1 ( first term ) d = 2 ( the common difference ) remember in the sequence 1 , 3 , 5 , 7 the common difference is always 2 * on a side note we use n - 1 because we do n ' t have d in the first term , therefore if we were solving for the first term we would get 0 as n - 1 and 0 times d would give us 0 , leaving only the first term . this works regardless what your first term is in any sequence . but remember the question askswhat is thevalueof n if the sum of the consecutive odd integers from 1 to n equals 169 ? which means we first need a consecutive sequence that sums up to 169 and than find what the value of the n is , in this case it would be the last number in that sequence . in order to find that we first need to knowhow many terms ( how many of the n there is ) in order to be able to plug n in this formula given we know what the sum is . for that to happen we need to use rule # 2 . rule # 2 ( summing an arithmetic series ) : 169 = n / 2 ( 2 a + ( n - 1 ) d ) . given the question gives us what the sum is ( 169 in this case ) we would simply use this formula to solve for n . once we solve for n ( 13 in this case ) we can simply plug n into the first formula ( rule 1 ) and find the value . it feels very confusing and difficult at first , but once you identify the steps all you need to do is plug and play . we have the sum ( 169 ) of a sequence , the number of terms in that sequence is ( unknown ) . rule # 2 tells us how many numbers there are in that sequence and rule # 1 gives us what that last term is .\"" + }, + { + "Answer": 5.999999999999999, + "Options": "a ) 6 , b ) 5 , c ) 4 , d ) 3 , e ) 8", + "Correct": "a", + "Explanation": "let us first find the fraction of green , blue and yellow balls 1 / 4 + 1 / 8 + 1 / 12 = 6 / 24 + 3 / 24 + 2 / 24 , common denominator = 11 / 24 , add numerators the fraction of white balls is given by 24 / 24 - 11 / 24 = 13 / 24 so the fraction 13 / 24 corresponds to 26 balls . if x is the total number of balls then ( 13 / 24 ) of x = 26 balls or ( 13 / 24 ) ? x = 26 x = 26 ? ( 24 / 13 ) = 48 , total number of balls the fraction of blue balls is 1 / 8 of x . the number of blue balls is given by ( 1 / 8 ) of 48 = 6 balls . correct answer a" + }, + { + "Answer": 100, + "Options": "a ) 50 , b ) 100 , c ) 150 , d ) 200 , e ) 250", + "Correct": "b", + "Explanation": "\"15 % is 5 % - points higher than 10 % but 15 % - points lower than 30 % . thus there should be 3 parts of solution x for 1 part of solution y . we should add 100 ml of solution y . the answer is b .\"" + }, + { + "Answer": 859560, + "Options": "a ) 565771 , b ) 456578 , c ) 676885 , d ) 788090 , e ) 859622", + "Correct": "e", + "Explanation": "\"dividend = quotient * divisor + reminder 859622 / 456 gives quotient = 1885 and reminder = 62 . so , the next number divisible by 456 is 456 places infront of 456 * 1885 which means 456 \u2013 62 = 394 should be added to 859622 . e\"" + }, + { + "Answer": 25, + "Options": "a ) 14 , b ) 20 , c ) 26 , d ) 25 , e ) 30", + "Correct": "d", + "Explanation": "\"solution let the number be x . then , 16 x - x = 375 \u2039 = \u203a 15 x = 375 x \u2039 = \u203a 25 . answer d\"" + }, + { + "Answer": 24, + "Options": "a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 24", + "Correct": "e", + "Explanation": "let the number of each size of jar = wthen 1 / 4 w + 1 / 2 w + w = 14 1 3 / 4 w = 14 w = 8 the total number of jars = 3 w = 24 answer : e" + }, + { + "Answer": 500, + "Options": "a ) $ 200 , b ) $ 400 , c ) $ 600 , d ) $ 800 , e ) $ 500", + "Correct": "e", + "Explanation": "suppose total money spent = x not spend ( money he still has ) = x - 600 x + x - 600 = 1600 x = 1100 money not spend = 1100 - 600 = 500 answer : e" + }, + { + "Answer": 400, + "Options": "a ) rs . 600 , b ) rs . 500 , c ) rs . 400 , d ) rs . 800 , e ) rs . 900", + "Correct": "c", + "Explanation": "solution : a : b : c = ( 800 * 2 ) : ( 1000 * 2 ) : ( 12000 * 2 ) = 4 : 5 : 6 . so c ' s share = rs . ( 1000 * 6 / 15 ) = rs . 400 . answer : option c" + }, + { + "Answer": 1.5, + "Options": "a ) 0 and 0.5 , b ) 0.5 and 1 , c ) 1 and 1.5 , d ) 1.5 and 2 , e ) 2 and 2.5", + "Correct": "d", + "Explanation": "trial and error would probably be the easiest way to solve this problem . when x is large enough positive number , then because of the exponents ( 5 > 4 ) , lhs will be more than rhs ( as you increase the positive value of x the distance between the values of lhs and rhs will increase ) . try x = 1 - - > lhs = 3 ^ 5 = 81 * 3 = 243 and rhs = 4 ^ 4 = 64 * 4 = 256 , so ( 1 + 2 x ) ^ 5 < ( 1 + 3 x ) ^ 4 . as you can see lhs is still slightly less than than rhs . so , the value of x for which ( 1 + 2 x ) ^ 5 = ( 1 + 3 x ) ^ 4 is slightly more than 1 . answer : d ." + }, + { + "Answer": 24, + "Options": "a ) 8 , b ) 64 , c ) 24 , d ) 102 , e ) 144", + "Correct": "c", + "Explanation": "\"if 80 % of the packages weigh at least 25 pounds this means that 20 % of the packages weigh less than 25 pounds let t = total number of packages so , 20 % of t = # of packages that weigh less than 25 pounds 48 packages weigh less than 25 pounds great . so , 20 % of t = 48 rewrite to get : 0.2 t = 48 solve : t = 240 30 % of the packages weigh less than 75 pounds so , 30 % oft = number of packages that weigh less than 75 pounds 30 % of 240 = 72 , so 72 packages weigh less than 75 pounds of those 72 packages that weigh less than 75 pounds , 48 packages weigh less than 25 pounds . so , the number of packages that weight between 25 and 75 pounds = 72 - 48 = 24 = c\"" + }, + { + "Answer": 4, + "Options": "a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 7", + "Correct": "c", + "Explanation": "solution : let the marks obtained in five subjects be 6 x , 7 x , 8 x , 9 x and 10 x . total marks obtained = 40 x max . marks of the five subjects = 40 x / 0.6 [ 40 x is 60 % of total marks ] max . marks in each subject = 40 x / 0.6 * 5 = 13.33 x hence , % of each subject = 6 x * 100 / 13.33 = 45.01 % or , 7 x * 100 / 13.33 = 52.51 in same way other percentage are 60.01 % , 67.52 % , 75.01 % . hence , number of subjects in which he gets more than 50 % marks = 4 . answer : option c" + }, + { + "Answer": 0.95, + "Options": "a ) 0.95 , b ) 9.4 , c ) 0.094 , d ) 94 , e ) none", + "Correct": "a", + "Explanation": "\"answer let a - 5 % of a = ab . \u21d2 ( 95 x a ) / 100 = ab \u2234 b = 0.95 correct option : a\"" + }, + { + "Answer": 9.600000000000001, + "Options": "a ) 9.6 , b ) 10.6 , c ) 11.0 , d ) 9.4 , e ) 8.1", + "Correct": "a", + "Explanation": "a 9.60 let us assume that originally jansi had x rupees and y 20 paise coins . going shopping she had ( 100 x + 20 y ) paise . she returned with only ( 100 y + 20 x ) paise . this last sum , as we know , is one - third of the original and therefore 3 ( 100 y + 20 x ) = 100 x + 20 y simplifying we have x = 7 y if y is 1 thenx is 7 . assuming this so jansi had 7.20 rupees when she set out for shopping . this is wrong because jansi actually had about 15 rupees . let us see now what we get if y = 2 . then x = 14 . the original sum was 14.40 rupees which accords with the condition of the problem . if we assume that y = 3 then the sum will be too big \u2014 21.60 rupees . therefore the only suitable answer is 14.40 rupees . after shopping jansi had 2 one rupee notes and 14 twenty paise coins . this is actually l / 3 rd of the original sum 1,440 : 3 = 480 . jansi ' s purchases , therefore , cost 14.40 \u2014 4.80 = rs 9.60" + }, + { + "Answer": 16, + "Options": "a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19", + "Correct": "b", + "Explanation": "\"explanation : let the number of persons be n \u2234 total handshakes = nc 2 = 120 n ( n - 1 ) / 2 = 120 \u2234 n = 16 answer : option b\"" + }, + { + "Answer": 39.99999999999849, + "Options": "a ) 96 , b ) 75 , c ) 40 , d ) 25 , e ) 12", + "Correct": "c", + "Explanation": "\"by the definition of a remainder , the remainder here is equal to 6 / y . the remainder in decimal form is given as . 15 therefore , 6 / y = . 15 solve for y and get 40 . c\"" + }, + { + "Answer": 24, + "Options": "a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28", + "Correct": "c", + "Explanation": "\"let p be the number of participants . pc 2 = 276 ( p ) ( p - 1 ) = 552 = 24 * 23 p = 24 the answer is c .\"" + }, + { + "Answer": 0.26666666666666666, + "Options": "a ) 4 / 15 , b ) 3 / 12 , c ) 3 / 11 , d ) 3 / 10 , e ) 3 / 14", + "Correct": "a", + "Explanation": "let veena paid x , so akshitha paid 3 x / 4 , and lasya paid 2 x , so total bill paid is given by x + ( 3 x / 4 ) + 2 x = 1 , we get i . e . x = 4 / 15 answer : a" + }, + { + "Answer": 80, + "Options": "a ) 12.5 % , b ) 87.5 % , c ) 80 % , d ) 11 % , e ) 1 %", + "Correct": "c", + "Explanation": "\"say y = 1 and x = 5 . then y = 1 is less than x = 5 by ( 5 - 1 ) / 5 * 100 = 4 / 5 * 100 = 80 % . answer : c .\"" + }, + { + "Answer": 50, + "Options": "a ) 50 % , b ) 58 % , c ) 62.5 % , d ) 64 % , e ) 75 %", + "Correct": "a", + "Explanation": "last year revenue = 100 ( assume ) ; this year revenue = 70 ; projected revenue = 140 . actual / projected * 100 = 70 / 140 * 100 = 50 % . answer : a ." + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 5 , c ) 9 , d ) 15 , e ) 30", + "Correct": "a", + "Explanation": "withoutusing the formula , we can see that today the restaurant served 30 customers above the average . the total amount above the average must equal total amount below the average . this additional 30 customers must offset the \u201c deficit \u201d below the average of 90 created on the x days the restaurant served only 60 customers per day . 30 / 30 = 1 day . choice ( a ) . withthe formula , we can set up the following : 90 = ( 60 x + 120 ) / ( x + 1 ) 90 x + 90 = 60 x + 120 30 x = 30 x = 1 answer choice ( a )" + }, + { + "Answer": 48.326530612244895, + "Options": "a ) 27 , b ) 48 , c ) 45 , d ) 72 , e ) 18", + "Correct": "b", + "Explanation": "\"ages of p and mi = 3 x + 5 x ages of mi and mo = 3 x : 5 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 25 x sum = 47 x = 148 x = 3 difference if ages of pa and mo = 25 x - 9 x = 16 x = 16 * 3 = 48 answer b\"" + }, + { + "Answer": 18, + "Options": "a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 21", + "Correct": "b", + "Explanation": "solution start with 15 baseball cards . maria takes half of one more than the number of baseball cards you have . so maria takes half of 15 + 1 which is 8 , so you ' re left with 15 - 8 = 7 . peter takes 1 baseball card from you : 7 - 1 = 6 baseball cards . paul triples the number of baseball cards you have : 6 \u00d7 3 = 18 baseball cards . so you have 18 at the end . correct answer : b" + }, + { + "Answer": 0.0625, + "Options": "a ) 1 / 16 , b ) 7 / 8 , c ) 9 / 64 , d ) 5 / 64 , e ) 3 / 64", + "Correct": "a", + "Explanation": "p ( xavier will solve ) = 1 / 4 p ( yvonne will solve ) = 2 / 3 p ( zelda will not solve ) = 1 - 5 / 8 = 3 / 8 . now , we need to multiply all this ps to find an answer : p = ( 1 / 4 ) * ( 2 / 3 ) * ( 3 / 8 ) = 1 / 16 . ans . a ." + }, + { + "Answer": 0.6666666666666666, + "Options": "a ) 2 / 3 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 6 , e ) 2 / 5", + "Correct": "a", + "Explanation": "you can simply use sets concept in this question . the formula total = n ( a ) + n ( b ) - n ( a and b ) is applicable here too . set 1 : number 1 or larger set 2 : number 15 or smaller 1 = p ( set 1 ) + p ( set 2 ) - p ( set 1 and set 2 ) ( combined probability is 1 because every number will be either 12 or moreor 20 or less or both ) 2 / 3 + p ( set 2 ) - 1 / 3 = 1 p ( set 2 ) = 2 / 3 answer a" + }, + { + "Answer": 33.33333333333333, + "Options": "a ) 33.33 % , b ) 25 % , c ) 75 % , d ) 66.66 % , e ) none of these", + "Correct": "a", + "Explanation": "\"using formula ( x / ( 100 - x ) * 100 ) where x is percentage decrease ( here it is 25 % ) = > 25 ( 100 - 25 ) * 100 = 33.33 % answer : a\"" + }, + { + "Answer": 79.16666666666667, + "Options": "a ) 8 % , b ) 15 % , c ) 45 % , d ) 52 % , e ) 79 %", + "Correct": "e", + "Explanation": "\"solution : this is a percent decrease problem . we will use the formula : percent change = ( new \u2013 old ) / old x 100 to calculate the final answer . we first set up the ratios of royalties to sales . the first ratio will be for the first 20 million in sales , and the second ratio will be for the next 108 million in sales . because all of the sales are in millions , we do not have to express all the trailing zeros in our ratios . first 20 million royalties / sales = 8 / 20 next 108 million royalties / sales = 9 / 108 = 1 / 12 because each ratio is not an easy number to use , we can simplify each one by multiplying each by the lcm of the two denominators , which is 60 . keep in mind that we are able to do this only because our answer choices are expressed in percents . first 20 million royalties / sales = ( 8 / 20 ) x 60 = 24 next 108 million royalties / sales = 9 / 108 = ( 1 / 12 ) x 60 = 5 we can plug 24 and 5 into our percent change formula : ( new \u2013 old ) / old x 100 [ ( 5 \u2013 24 ) / 24 ] x 100 - 475 / 6 x 100 at this point we can stop and consider the answer choices . since we know that 475 / 6 is just a bit less than \u00bd , we know that - 475 / 6 x 100 is about a 79 % decrease . answer e .\"" + }, + { + "Answer": 612, + "Options": "a ) 756 , b ) 612 , c ) 492 , d ) 372 , e ) 250", + "Correct": "b", + "Explanation": "9 pages from 1 to 9 will require 9 digits . 90 pages from 10 to 99 will require 90 * 2 = 180 digits . 240 - ( 90 + 9 ) = 141 pages will require 141 * 3 = 423 digits . the total number of digits is 9 + 180 + 423 = 612 . the answer is b ." + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 10 , c ) 15 , d ) 25 , e ) 35", + "Correct": "a", + "Explanation": "\"total applicants = 40 political science = 15 and non political science = 40 - 15 = 25 gpa > 3.0 = 20 and gpa < = 3.0 = 20 10 non political science students had gpa < = 3.0 - - > 15 non political science students had gpa > 3.0 gpa > 3.0 in political science = total - ( gpa > 3.0 in non political science ) e = 20 - 15 = 5 answer : a\"" + }, + { + "Answer": 70.00000000000001, + "Options": "a ) 40 , b ) 52 , c ) 68 , d ) 70 , e ) 98", + "Correct": "d", + "Explanation": "let the no of matches played more = x so , ( 120 + x ) * 52 / 100 = 28.8 + x by solving we get x = 70 answer : d" + }, + { + "Answer": 2, + "Options": "a ) 2 . , b ) 4 . , c ) 5 . , d ) 6 . , e ) 9 .", + "Correct": "a", + "Explanation": "y = x ^ 2 - 1 w ^ 3 = 3 ^ 2 - 1 w ^ 3 = 8 w = 2 answer a" + }, + { + "Answer": 30, + "Options": "a ) 30 , b ) 20 , c ) 25 , d ) 40 , e ) 50", + "Correct": "a", + "Explanation": "x scores 60 while y score 40 and z scores 30 . the number of points that z scores when y scores 120 = ( 120 * 30 ) / 40 = 90 . in x game of 100 points , y gives ( 120 - 90 ) = 30 points to c . a" + }, + { + "Answer": 48, + "Options": "a ) 20 , b ) 36 , c ) 48 , d ) 50 , e ) 59", + "Correct": "c", + "Explanation": "production during these 5 days = total production in a month - production in first 25 days . = 30 x 58 - 25 x 60 = 240 \u2234 average for last 5 days = 240 / 5 = 48 c" + }, + { + "Answer": 255, + "Options": "a ) $ 260 , b ) $ 255 , c ) $ 285 , d ) $ 290 , e ) $ 275", + "Correct": "b", + "Explanation": "\"if 30 books constitute 1 / 3 rd of the total , then 2 / 3 rd of the total = 60 books amount received for sold books = 60 * 4.25 = $ 255 answer : b\"" + }, + { + "Answer": 3, + "Options": "a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 8", + "Correct": "b", + "Explanation": "\"i like to put the numbers in prime factors so it is easier and faster to visualize . 14 * n / 60 if we write the factors of 14 - - > 2 , 7 , and the factors of 60 - - > 2 , 2 , 3 , 5 , we have ( 2 * 7 * n ) / ( 2 ^ 2 * 3 * 5 ) simplifying 7 * n / ( 2 * 3 * 5 ) the only way the equation above has an integer value is if n has at least the factors 2 , 3 and 5 , so we can simplify again and we have the number 7 . the number could be 2 * 3 * 5 , or 2 * 3 * 5 * 2 , or 2 * 3 * 5 * . . . . . however to be less than 200 we can not add any prime number . 2 * 3 * 5 = 120 if we added the next prime factor 7 , we would have s = 2 * 3 * 5 * 7 = 840 thus , answer b\"" + }, + { + "Answer": 62, + "Options": "a ) 71 , b ) 62 , c ) 53 , d ) 35 , e ) 45", + "Correct": "b", + "Explanation": "explanation : let the number be 10 x + y . \u2234 x + y = 8 . . . . . ( i ) 10 x + y - ( 10 y + x ) = 36 \u2234 9 ( x - y ) = 3 \u2234 x - y = 4 . . . . . . . ( ii ) from equation ( i ) and ( ii ) : x = 6 , y = 2 \u2234 number = 62 answer : option b" + }, + { + "Answer": 1249, + "Options": "a ) 1134 , b ) 1238 , c ) 1348 , d ) 1500 , e ) 1249", + "Correct": "e", + "Explanation": "population of seventh village = 7 * 1000 - ( 803 + 900 + 1100 + 1023 + 945 + 980 ) = 1249 answer is e" + }, + { + "Answer": 0.25, + "Options": "a ) - 4 , b ) - 1 / 4 , c ) 0 , d ) 1 / 4 , e ) 4", + "Correct": "d", + "Explanation": "\"we ' re told that 625 ^ ( - x ) + 25 ^ ( - 2 x ) + 5 ^ ( - 4 x ) = 15 . we ' re asked for the value of x . since each of the calculated terms must be positive ( regardless of what the exponent is ) , we can use thebasesto our advantage . . . . . with answer a , we ' d have 625 ^ 4 , which is much bigger than 15 ( and we ' d be adding to that big number ) . eliminate a . with answer e , we ' d have 625 ^ ( - 4 ) , which would create a tiny fraction ( and we ' d add some other fractions to it , so the total would be much too small ) . eliminate e . with answer d , we ' d have 625 ^ ( - 1 / 4 ) , which will also be a fraction ( just not as tiny as the one in answer e ) , but the total would still be too small . eliminate d . with answer c , anything to the ' 0 power ' is 1 , so we ' d have 1 + 1 + 1 = 3 . this is not 15 . eliminate c . d\"" + }, + { + "Answer": 5, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "d", + "Explanation": "\"minimuum should be 1 maximum should be 4 : 1 out of a or b to make the multiplication negative 3 out of c , d , e or f to make the multiplication negative . negative + negative < 0 answer : c maximum will be 5 . . you dont require both the multiplicatin to be negative for entire equation to be negative . . . any one a or b can be negative to make ab negative and it can still be more ( away from 0 ) than the multiplication of 4 other - ve numbers . . . actually by writing minimum required as 1 out of 6 , you are actually meaning 5 out of 6 also possible as you will see d = 5 or 1 will give you same equation . . ans d\"" + }, + { + "Answer": 540, + "Options": "a ) 540 , b ) 570 , c ) 619 , d ) 649 , e ) 700", + "Correct": "a", + "Explanation": "\"before price increase price = c after 30 % price increase price = c + ( 30 / 100 ) * c = 1.3 c = 351 ( given ) i . e . c = 351 / 1.3 = $ 270 i . e . 2 c = 2 * 270 = 540 answer : option a\"" + }, + { + "Answer": 195, + "Options": "a ) $ 28 , b ) $ 82 , c ) $ 110 , d ) $ 138 , e ) $ 195", + "Correct": "e", + "Explanation": "by the question , the equation would be 150 p - 85 * 150 - 16500 = 0 p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component . solving the equation , we get p = $ 195 . answer e for me ." + }, + { + "Answer": 42, + "Options": "a ) 31 , b ) 42 , c ) 29 , d ) 97 , e ) 27", + "Correct": "b", + "Explanation": "total score of the batsman in 30 matches = 1500 . total score of the batsman in the next 15 matches = 390 . total score of the batsman in the 30 matches = 1890 . average score of the batsman = 1890 / 45 = 42 . answer : b" + }, + { + "Answer": 2316.375, + "Options": "a ) 2240 , b ) 2250 , c ) 2310 , d ) 2330 , e ) 2332", + "Correct": "e", + "Explanation": "\"the fastest way in an ap is to find the average and multiply with total integers . . between 63 and 151 , the smallest multiple of 4 is 64 and largest = 148 . . average = ( 64 + 148 ) / 2 = 106 . . total numbers = ( 148 - 64 ) / 4 + 1 = 21 + 1 = 22 . . sum = 22 * 106 = 2332 ans e\"" + }, + { + "Answer": 68, + "Options": "a ) 57 , b ) 68 , c ) 77 , d ) 87 , e ) 97", + "Correct": "b", + "Explanation": "\"explanation : money collected = ( 46.24 x 100 ) paise = 4624 paise . \u2234 number of members = \u221a ( 4624 ) = 68 . answer : b\"" + }, + { + "Answer": 7, + "Options": "a ) 2 . , b ) 4 . , c ) 5 . , d ) 7 . , e ) 9 .", + "Correct": "d", + "Explanation": "\"ad = ( a + 1 ) ( d + 1 ) - 15 0 = a + d - 14 a + d = 14 a = d ( as they are twin brothers ) a = d = 7 d is the answer\"" + }, + { + "Answer": 15, + "Options": "a ) - 4 , b ) - 2 , c ) 15 , d ) 13 , e ) 22", + "Correct": "c", + "Explanation": "\"the equation that can be formed is : 2 x - 19 = 26 - x or , 3 x = 45 or , x = 15 . c answer .\"" + }, + { + "Answer": 115, + "Options": "a ) 100 , b ) 110 , c ) 115 , d ) 125 , e ) 140", + "Correct": "c", + "Explanation": "\"let the number of boys who passed = x . then , 39 x x + 15 x ( 120 - x ) = 120 x 38 24 x = 4560 - 1800 = > x = 2760 / 24 x = 115 . hence , the number of boys passed = 115 . answer : c\"" + }, + { + "Answer": 33, + "Options": "a ) 15 , b ) 28 , c ) 33 , d ) 42 , e ) 60", + "Correct": "c", + "Explanation": "\"take lcm of 2,5 and 8 = 40 now 2 x = 40 = > x = 20 5 y = 40 = > y = 8 8 z = 40 = > z = 5 20 + 8 + 5 = 33 . option c .\"" + }, + { + "Answer": 12, + "Options": "a ) 6 rs , b ) 2 rs , c ) 4 rs , d ) 9 rs , e ) 12 rs", + "Correct": "e", + "Explanation": "\"5 m = xw = 8 b 5 m + xw + 8 b - - - - - 180 rs . 5 m + 5 m + 5 m - - - - - 180 rs . 15 m - - - - - - 180 rs . = > 1 m = 12 rs . answer : e\"" + }, + { + "Answer": 85, + "Options": "a ) 57 , b ) 67 , c ) 77 , d ) 85 , e ) 97", + "Correct": "d", + "Explanation": "\"explanation : money collected = ( 72.25 x 100 ) paise = 7225 paise . \u2234 number of members = \u221a ( 7225 ) = 85 . answer : d\"" + }, + { + "Answer": 50, + "Options": "a ) 40 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 80 %", + "Correct": "b", + "Explanation": "\"can be reduced to y / 5 + 3 y / 10 = 2 y / 5 = 50 % b\"" + }, + { + "Answer": 1, + "Options": "a ) 1.7 , b ) 1.4 , c ) 1.1 , d ) 1.5 , e ) 1", + "Correct": "e", + "Explanation": "\"m = 3 s = x ds = 3 + x us = 3 + x 3 + x = ( 3 - x ) 2 3 + x = 6 - 2 x 3 x = 3 x = 1 answer : e\"" + }, + { + "Answer": 0.42857142857142855, + "Options": "a ) 25 / 9 , b ) 3 / 7 , c ) 5 / 3 , d ) 3 / 5 , e ) 9 / 25", + "Correct": "b", + "Explanation": "\"sqrt ( 3 x / 7 ) to be perfect square x has to 3 / 7 ans : b\"" + }, + { + "Answer": 8.933535963686566, + "Options": "a ) 6 , b ) 8 , c ) 10 , d ) 9 , e ) 13", + "Correct": "d", + "Explanation": "joan starts off with 100 $ . . which is to be tripled every month her monthly payments look like this : 100 , 300 , 900 , 2700 . . . . . . . . . upto 914800 this can be re written as : 100 x 1 , 100 x 3 , 100 x 9 , 100 x 27 . . . . . . 100 x 9148 so we have 1 , 3 , 9 , 27 . . . . . 914800 in gp we know that a = 1 , and r = 3 ( its easy to figure it out by looking at the question , but regardless of it being mentioned in the question we can still compute the value of r using the formula tn = a 3 ^ n - 1 . . . ) therefore to find the sum of n terms of a gp we use this formula : sn = a ( 1 - r ^ n ) / 1 - r using this and plugging in the information we get . . . 9148 = 1 - 3 ^ n / 1 - 3 ; 1 - 3 ^ n / - 2 cross multiplying we get 9148 x - 2 = 1 - 3 ^ n - 19682 = 1 - 3 ^ n - 19682 = - 3 ^ n 19683 = 3 ^ n ( negatives cancel out ) 19863 can also be re written as 3 ^ 9 therefore ; 3 ^ 9 = 3 ^ n thus n = 9 ( d )" + }, + { + "Answer": 76, + "Options": "a ) 73 , b ) 74 , c ) 75 , d ) 76 , e ) 77", + "Correct": "d", + "Explanation": "let x be the number of students in the class . let p be the average of the rest of the class . 80 x = ( 1 / 4 ) 92 x + ( 3 / 4 ) ( p ) x 320 = 92 + 3 p 3 p = 228 p = 76 . the answer is d ." + }, + { + "Answer": 11.6, + "Options": "a ) 58 / 9 , b ) 58 / 5 , c ) 58 / 7 , d ) 58 / 2 , e ) 58 / 1", + "Correct": "b", + "Explanation": "let p / q = a , then ( a - 1 / a ) = 21 / 10 \u21d2 a 2 \u2212 1 = a . 2110 \u21d2 a 2 \u2212 1 = a . 2110 \u21d2 10 a 2 \u2212 21 a \u2212 10 \u21d2 10 a 2 \u2212 21 a \u2212 10 = 0 roots of the equation = \u2212 b \u00b1 b 2 \u2212 4 ac \u2212 \u2212 \u2212 \u2212 \u2212 \u2212 \u2212 \u221a 2 a \u2212 b \u00b1 b 2 \u2212 4 ac 2 a a = 21 \u00b1 441 + 400 \u2212 \u2212 \u2212 \u2212 \u2212 \u2212 \u2212 \u2212 \u221a 2021 \u00b1 441 + 40020 a = 21 \u00b1 292021 \u00b1 2920 = 5 / 2 or - 2 / 5 for a = 5 / 2 , 4 p / q + 4 q / p = 58 / 5 for a = - 2 / 5 , 4 p / q + 4 q / p = - 58 / 5 answer : b" + }, + { + "Answer": 80, + "Options": "a ) 30 , b ) 80 , c ) 20 , d ) 25 , e ) 26", + "Correct": "b", + "Explanation": "\"let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 . x / 2 = ( 85 - 45 ) = > x / 2 = 40 = > x = 80 . answer : b\"" + }, + { + "Answer": 24, + "Options": "a ) 20 , b ) 10 , c ) 30 , d ) 24 , e ) 5", + "Correct": "d", + "Explanation": "\"arithmetic mean expression for p and q : ( p + q ) / 2 = 10 ; p + q = 20 - - - - eq 1 arithmetic mean expression for q and r : ( q + r ) / 2 = 20 ; q + r = 44 - - - - eq 2 subtracting eq 1 from eq 2 we get : r - p = 24 hence , the correct answer is d\"" + }, + { + "Answer": 26, + "Options": "a ) 16 , b ) 19 , c ) 15 , d ) 26 , e ) 10", + "Correct": "d", + "Explanation": "\"let the son ' s present age be x years . then , man ' s present age = ( x + 28 ) years . ( x + 28 ) + 2 = 2 ( x + 2 ) x + 30 = 2 x + 4 = > x = 26 . answer : d\"" + }, + { + "Answer": 56, + "Options": "a ) 23 , b ) 37 , c ) 56 , d ) 40 , e ) 81", + "Correct": "c", + "Explanation": "\"explanation : formula n ( a \u00e2 \u02c6 \u00aa b ) = n ( a ) + n ( b ) \u00e2 \u02c6 \u2019 n ( a \u00e2 \u02c6 \u00a9 b ) fail in hindi or english = 30 + 42 \u00e2 \u20ac \u201c 28 = 44 therefore students who passed = 100 \u00e2 \u20ac \u201c 44 = 56 . answer : c\"" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9", + "Correct": "b", + "Explanation": "\"d = ( d - r ) / q = ( 52 - 4 ) / 16 = 48 / 16 = 3 b )\"" + }, + { + "Answer": 5.65, + "Options": "a ) $ 3.15 , b ) $ 4.45 , c ) $ 4.80 , d ) $ 5.65 , e ) $ 5.40", + "Correct": "d", + "Explanation": "\"let the fixed charge of jim \u00e2 \u20ac \u2122 s taxi service = 2.5 $ and charge per 2 / 5 mile ( . 4 mile ) = . 35 $ total charge for a trip of 3.6 miles = 2.5 + ( 3.6 / . 4 ) * . 35 = 2.5 + 9 * . 35 = 5.65 $ answer d\"" + }, + { + "Answer": 465, + "Options": "a ) 400 , b ) 465 , c ) 430 , d ) 450 , e ) 510", + "Correct": "b", + "Explanation": "\"let no . of non - officers be x 15 * 430 + x * 110 = ( x + 15 ) 120 x = 465 b\"" + }, + { + "Answer": 87.8, + "Options": "a ) 67 , b ) 26 , c ) 88 , d ) 90 , e ) 75", + "Correct": "c", + "Explanation": "\"average = ( 90 + 92 + 85 + 87 + 85 ) / 5 = 439 / 5 = 87.8 . answer : c\"" + }, + { + "Answer": 5, + "Options": "a ) 5 years , b ) 4 years , c ) 6 years , d ) 7 years , e ) 8 years", + "Correct": "a", + "Explanation": "\"let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 55 5 x = 25 x = 5 . age of the youngest child = x = 5 years . a )\"" + }, + { + "Answer": 1500, + "Options": "a ) 220 , b ) 230 , c ) 500 , d ) 1500 , e ) 590", + "Correct": "d", + "Explanation": "n * 50 = ( 375000 - 300000 ) = 75000 n = 75000 / 50 = 1500 d" + }, + { + "Answer": 385, + "Options": "a ) a ) 70 , b ) b ) 35 , c ) c ) 385 , d ) d ) 280 , e ) e ) 140", + "Correct": "c", + "Explanation": "it is the lcm of 5 , 7 and 11 which is 385 . the answer is c ." + }, + { + "Answer": 31, + "Options": "a ) 23 kg , b ) 43 kg , c ) 21 kg , d ) 31 kg , e ) 43 kg", + "Correct": "d", + "Explanation": "sol . let a , b , c represent their individual wgts . then , a + b + c = ( 45 * 3 ) kg = 135 kg a + b = ( 40 * 2 ) kg = 80 kg & b + c = ( 43 * 2 ) kg = 86 kg b = ( a + b ) + ( b + c ) - ( a + b + c ) = ( 80 + 86 - 135 ) kg = 31 kg . answer d" + }, + { + "Answer": 24, + "Options": "a ) 12 , b ) 24 , c ) 18 , d ) 27 , e ) 25", + "Correct": "b", + "Explanation": "if father ' s age is f and son ' s age is s , then f = 3 s and f - 8 = 4 * ( s - 8 ) 3 s - 5 = 4 s - 32 s = 24 f = 72 years answer : b" + }, + { + "Answer": 38000, + "Options": "a ) s . 43000 , b ) s . 50000 , c ) s . 57000 , d ) s . 38000 , e ) s . 62000", + "Correct": "d", + "Explanation": "\"length ( l ) = 20 m , breadth ( b ) = 15 m and height ( h ) = 5 m total area of the hall to be covered with mat = 2 ( lb + bh + hl ) = 2 ( 20 * 15 + 15 * 5 + 5 * 20 ) = 2 ( 300 + 75 + 100 ) = 2 * 475 = 950 sq . m total expenditure = 40 * 950 = rs . 38000 d\"" + }, + { + "Answer": 480, + "Options": "a ) 96 , b ) 240 , c ) e = 256 , d ) e = 384 , e ) e = 480", + "Correct": "e", + "Explanation": "\"most test takers would recognize thesystemof equations in this prompt and just do algebra to get to the solution ( and that ' s fine ) . the wording of the prompt and the ' spread ' of the answer choices actually provide an interesting ' brute force ' shortcut that you can take advantage of to eliminate the 4 wrong answers . . . . we ' re told that there are 2 types of boxes : those that hold 12 glasses and those that hold 16 glasses . since the average number of boxes is 15 , we know that there must be at least some of each . we ' re also told that that there are 16 more of the larger boxes . this means , at the minimum , we have . . . 1 small box and 17 large boxes = 1 ( 12 ) + 17 ( 16 ) = 12 + 272 = 284 glasses at the minimum since the question asks for the total number of glasses , we can now eliminate answers a , b and c . . . . the difference in the number of boxes must be 16 though , so we could have . . . . 2 small boxes and 18 large boxes 3 small boxes and 19 large boxes etc . with every additional small box + large box that we add , we add 12 + 16 = 28 more glasses . thus , we can justadd 28 suntil we hit the correct answer . . . . 284 + 28 = 312 312 + 28 = 340 340 + 28 = 368 368 + 28 = 396 at this point , we ' ve ' gone past ' answer d , so the correct answer must be answer e . . . . . but here ' s the proof . . . . 396 + 28 = 424 424 + 28 = 452 452 + 28 = 480 final answer : e\"" + }, + { + "Answer": 10.500000000000002, + "Options": "a ) 10.5 , b ) 11 , c ) 12 , d ) 13 , e ) 15", + "Correct": "a", + "Explanation": "leak admits 9 / 4 tonnes water in 11 / 2 min = 11 / 2 * 4 / 9 = 22 / 9 leak admits 9 / 22 tonne of water in 5 min in 1 min in thrws 1 / 5 tonne of water = 9 / 22 - 1 / 5 = 23 / 110 92 / 23 / 11 min = 440 min 22 / 3 min = 7 / 22 / 22 / 3 = > 10.5 km / hr answer a" + }, + { + "Answer": 300, + "Options": "a ) 250 , b ) 260 , c ) 300 , d ) 285 , e ) none", + "Correct": "c", + "Explanation": "\"since the month begins with sunday , to there will be five sundays in the month average required = ( 600 x 5 + 240 x 25 ) / 30 ) = 300 answer : option c\"" + }, + { + "Answer": 40, + "Options": "a ) 40 km , b ) 76 km , c ) 18 km , d ) 16 km , e ) 97 km", + "Correct": "a", + "Explanation": "\"let the actual distance traveled be x km . then , x / 10 = ( x + 40 ) / 20 10 x - 400 = > x = 40 km . answer : a\"" + }, + { + "Answer": 140, + "Options": "a ) 75 , b ) 100 , c ) 125 , d ) 140 , e ) 225", + "Correct": "d", + "Explanation": "\"let m be the number of male participants and f be the number of female articipants in the meeting . thetotal number of participants is given as 840 . hence , we have m + f = 840 now , we have that half the female participants and one - quarter of the male participants are democrats . let d equal the number of the democrats . then we have the equation f / 2 + m / 4 = d now , we have that one - third of the total participants are democrats . hence , we have the equation d = 840 / 3 = 280 solving the three equations yields the solution f = 280 , m = 560 , and d = 280 . the number of female democratic participants equals half the female participants equals 280 / 2 = 140 . answer : d\"" + }, + { + "Answer": 32, + "Options": "a ) 65 degrees , b ) 32 degrees , c ) 37 degrees , d ) 34 degrees , e ) 74 degrees", + "Correct": "b", + "Explanation": "\"m + tu + w + th = 4 * 48 = 192 tu + w + th + f = 4 * 46 = 184 m = 40 tu + w + th = 192 - 40 = 152 f = 184 \u2013 152 = 32 answer : b\"" + }, + { + "Answer": 16, + "Options": "a ) 16 , b ) 17 , c ) 18 , d ) 14 , e ) 13", + "Correct": "a", + "Explanation": "since 64 / k = 4 and 64 / 16 = 4 , then k = 16 correct answer a" + }, + { + "Answer": 464, + "Options": "a ) 354 , b ) 225 , c ) 654 , d ) 741 , e ) 464", + "Correct": "e", + "Explanation": "\"1 ^ 3 + 3 ^ 2 = 1 + 9 = 10 3 ^ 3 + 5 ^ 2 = 27 + 25 = 52 5 ^ 3 + 7 ^ 2 = 125 + 49 = 174 and 7 ^ 3 + 11 ^ 2 = 343 + 121 = 464 answer : e\"" + }, + { + "Answer": 40, + "Options": "a ) 30 , b ) 35 , c ) 38 , d ) 40 , e ) 45", + "Correct": "d", + "Explanation": "10 play kabadi = > n ( a ) = 10 , 5 play both gmaes . = > n ( anb ) = 5 30 play kho kho only , = > n ( b ) = n ( b only ) + n ( anb ) = 30 + 5 = 35 total = > n ( aub ) = n ( a ) + n ( b ) - n ( anb ) = 10 + 35 - 5 = 40 answer : d" + }, + { + "Answer": 124, + "Options": "a ) 123 , b ) 267 , c ) 277 , d ) 124 , e ) 120", + "Correct": "d", + "Explanation": "\"let xx be the number he chose , then 2 \u00e2 \u2039 \u2026 x \u00e2 \u02c6 \u2019 138 = 110 x = 124 answer : d\"" + }, + { + "Answer": 40, + "Options": "a ) 28 , b ) 32 , c ) 36 , d ) 40 , e ) 44", + "Correct": "d", + "Explanation": "the average of the numbers in set s is 12 . if we increase the mean by 25 % , the new mean is 15 . thus , on average , 5 numbers increase by 5 . therefore n = 15 + 25 = 40 the answer is d ." + }, + { + "Answer": 2000, + "Options": "a ) 1800 , b ) 2000 , c ) 1640 , d ) 2200 , e ) 2400", + "Correct": "b", + "Explanation": "following the above formula , we have the total marks = 50 * 40 = 2000 answer is b" + }, + { + "Answer": 42.75, + "Options": "a ) 41.5 % , b ) 42.75 % , c ) 43 % , d ) 45 % , e ) 45.75 %", + "Correct": "b", + "Explanation": "\"we have a 9 litre solution containing 57 % of alcohol in the water . = > quantity of alcohol in the solution = 9 \u00e3 \u2014 57 / 100 now 3 litre of water is added to the solution . = > total quantity of the new solution = 9 + 3 = 12 percentage of alcohol in the new solution = 9 \u00e3 \u2014 57 / 100 12 \u00e3 \u2014 100 = 9 \u00e3 \u2014 5710012 \u00e3 \u2014 100 = 9 \u00e3 \u2014 4.75 / 100 = 42.75 % b\"" + }, + { + "Answer": 174, + "Options": "a ) 179 , b ) 367 , c ) 269 , d ) 177 , e ) 174", + "Correct": "e", + "Explanation": "\"explanation : total runs scored by the batsman = 60 * 46 = 2760 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2760 \u00e2 \u20ac \u201c 2552 = 208 runs . let the highest score be x , hence the lowest score = x \u00e2 \u20ac \u201c 140 x + ( x - 140 ) = 208 2 x = 348 x = 174 runs answer : e\"" + }, + { + "Answer": 487.9979508110673, + "Options": "a ) 487 , b ) 488 , c ) 489 , d ) 457 , e ) 495", + "Correct": "b", + "Explanation": "here from equation 1 we will get m ^ 2 - 8 m + 1 = 0 m ^ 2 = 8 m - 1 m = ( 8 m - 1 ) / m . . . . . . . . . ( 1 ) m = 8 - 1 / m so m + 1 / m = 8 now in equation 2 m ^ 3 + 1 / m ^ 3 ( m + 1 / m ) ( m ^ 2 - m * 1 / m + 1 / m ^ 2 ) ( m + 1 / m ) ( m ^ 2 - 1 + 1 / m ^ 2 ) ( m + 1 / m ) ( m ^ 2 + 1 / m ^ 2 - 1 ) ( m + 1 / m ) { ( m + 1 / m ) ^ 2 - 2 m * 1 / m - 1 } { since a ^ 2 + b ^ 2 = ( a + b ) ^ 2 - 2 ab } ( m + 1 / m ) { ( m + 1 / m ) ^ 2 - 2 - 1 } now putting the value of m from equation 1 8 ( 8 ^ 2 - 2 - 1 ) 8 ( 64 - 3 ) = 488 answer : b" + }, + { + "Answer": 10, + "Options": "a ) 3 , b ) 9 , c ) 10 , d ) 12 , e ) 14", + "Correct": "c", + "Explanation": "when we look at the two equations , we can relize some similarity , so lets work on it . . 3 a \u2013 2 b \u2013 2 c = 32 can be written as \u221a 3 a ^ 2 - \u221a ( 2 b + 2 c ) ^ 2 = 32 { \u221a 3 a - \u221a ( 2 b + 2 c ) } { \u221a 3 a + \u221a ( 2 b + 2 c ) } = 32 . . or 4 * \u221a 3 a + \u221a ( 2 b + 2 c ) = 32 . . or \u221a 3 a + \u221a ( 2 b + 2 c ) = 8 . . now lets work on these two equations 1 ) \u221a 3 a - \u221a ( 2 b + 2 c ) = 4 . . 2 ) \u221a 3 a + \u221a ( 2 b + 2 c ) = 8 . . a ) add the two eq . . \u221a 3 a + \u221a ( 2 b + 2 c ) + \u221a 3 a - \u221a ( 2 b + 2 c ) = 12 . . 2 \u221a 3 a = 12 . . or \u221a 3 a = 6 . . 3 a = 36 . . a = 12 . b ) subtract 1 from 2 . . \u221a 3 a + \u221a ( 2 b + 2 c ) - \u221a 3 a + \u221a ( 2 b + 2 c ) = 4 . . 2 \u221a ( 2 b + 2 c ) = 4 . . \u221a ( 2 b + 2 c ) = 2 . . 2 b + 2 c = 4 . . or b + c = 2 . . from a and b a + b + c = 12 + 2 = 14 . . c" + }, + { + "Answer": 125, + "Options": "a ) a ) 145 , b ) b ) 148 , c ) c ) 150 , d ) d ) 125 , e ) e ) 158", + "Correct": "d", + "Explanation": "\"d = d * q + r d = 15 * 8 + 5 d = 120 + 5 d = 125 answer : d\"" + }, + { + "Answer": 720, + "Options": "a ) 237 , b ) 287 , c ) 197 , d ) 287 , e ) 720", + "Correct": "e", + "Explanation": "\"explanation : let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 360 ) = 2 + 2 ( extra ) = > 2 x - 720 = x = > x = 720 . answer : e\"" + }, + { + "Answer": 106, + "Options": "a ) 366 , b ) 106 , c ) 102 , d ) 192 , e ) 122", + "Correct": "b", + "Explanation": "\"cash realised = rs . ( 106.25 - 0.25 ) = rs . 106 . answer : b\"" + }, + { + "Answer": 71, + "Options": "a ) 75 , b ) 72 , c ) 71 , d ) 76 , e ) 73", + "Correct": "c", + "Explanation": "let the number of 45 - rupee notes = x then , the number of 95 - rupee notes = ( 90 \u2013 x ) 45 x + 95 ( 90 \u2013 x ) = 5000 : x = 71 answer : c" + }, + { + "Answer": 12000, + "Options": "a ) 12002 , b ) 12000 , c ) 12028 , d ) 12020 , e ) 12013", + "Correct": "b", + "Explanation": "\"[ 1000 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 600 x = 12000 answer : b\"" + }, + { + "Answer": 15, + "Options": "a ) 15 , b ) 19 , c ) 11 , d ) 18 , e ) 13", + "Correct": "a", + "Explanation": "\"let the population of two villages be equal after p years then , 72000 - 1200 p = 42000 + 800 p 2000 p = 30000 p = 15 answer is a .\"" + }, + { + "Answer": 7, + "Options": "a ) 9 years , b ) 11 years , c ) 14 years , d ) 7 years , e ) 25 years", + "Correct": "d", + "Explanation": "\"solution age of the 15 th student = [ 15 x 15 - ( 14 x 3 + 16 x 11 ) ] = ( 225 - 218 ) = 7 years . answer d\"" + }, + { + "Answer": 83.33333333333334, + "Options": "a ) 12.5 % , b ) 83.3 % , c ) 80 % , d ) 11 % , e ) 1 %", + "Correct": "b", + "Explanation": "say y = 1 and x = 6 . then y = 1 is less than x = 6 by ( 6 - 1 ) / 6 * 100 = 5 / 6 * 100 = 83.3 % . answer : b ." + }, + { + "Answer": 1.7000000000000002, + "Options": "a ) 2 , b ) 1.7 , c ) 1.9 , d ) 1.8 , e ) 2.1", + "Correct": "b", + "Explanation": "solution let 5 th reading be x ( 2 + 2.1 + 2 + 2.2 + x ) / 5 = 2 8.3 + x = 10 x = 1.7 answer b" + }, + { + "Answer": 28, + "Options": "a ) 15 , b ) 16 , c ) 28 , d ) 56 , e ) 64", + "Correct": "c", + "Explanation": "\"number of ways 2 teams can be selected out of 8 teams : c 8 / 2 = 8 \u2217 7 / 2 = 28 ans : ' ' c ' '\"" + }, + { + "Answer": 7, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10", + "Correct": "b", + "Explanation": "38500 = 2 * 2 * 5 * 5 * 5 * 7 * 11 john participated 7 times . the answer is b ." + }, + { + "Answer": 0.3433333333333333, + "Options": "a ) 103 / 300 , b ) 103 / 200 , c ) 112 / 300 , d ) 154 / 140 , e ) 100 / 300", + "Correct": "a", + "Explanation": "let the numbers be a and b . then , a + b = 45 and ab = 3 * 100 = 300 . required sum = 1 / a + 1 / b = ( a + b ) / ab = 103 / 300 answer : a" + }, + { + "Answer": 9.090909090909088, + "Options": "a ) 9 % , b ) 12 % , c ) 15 % , d ) 17 % , e ) 20 %", + "Correct": "a", + "Explanation": "\"let me try a simpler one . lets assume that candidate got 45 % votes and total votes is 100 . candidate won = 45 remaining = 55 to get 50 % , candidate requires 5 votes from 100 which is 5 % and 5 votes from 55 . 5 / 55 = 1 / 11 = . 09 = 9 % which is approx 9 % . hence the answer is a .\"" + }, + { + "Answer": 17, + "Options": "a ) 17 , b ) 27 , c ) 37 , d ) 47 , e ) 57", + "Correct": "a", + "Explanation": "( 1056 / 29 ) gives remainder 12 17 + 12 = 29 , so we need to add 17 a" + }, + { + "Answer": 11, + "Options": "a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 19", + "Correct": "a", + "Explanation": "( x + 5 ) * 150 + x * 85 = 1455 = > x = 3 total lens = 3 + ( 3 + 5 ) = 11 answer a" + }, + { + "Answer": 15, + "Options": "a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15", + "Correct": "e", + "Explanation": "20 / 2 = 10 10 / 2 = 5 ans : 10 + 5 = 15 answer : e" + }, + { + "Answer": 11000, + "Options": "a ) $ 11500 , b ) $ 11000 , c ) $ 12000 , d ) $ 12100 , e ) $ 12500", + "Correct": "b", + "Explanation": "let t be the tier price , p be total price = 18000 per the given conditions : 0.12 t + 0.09 ( p - t ) = 1950 0.12 t + 0.09 * 18000 - 0.09 t = 1950 0.03 t + 1620 = 1950 0.03 t = 1950 - 1620 = 330 t = 330 / 0.03 = 11000 answer b" + }, + { + "Answer": 192, + "Options": "a ) 192 , b ) 203 , c ) 214 , d ) 225 , e ) 236", + "Correct": "a", + "Explanation": "let x be the middle integer . then the largest is 3 x and the smallest is 3 x - 23 . 3 x - 23 + x + 3 x = 33 x = 8 the three integers are 1 , 8 , and 24 . the product is 1 * 8 * 24 = 192 the answer is a ." + }, + { + "Answer": 55, + "Options": "a ) 20 , b ) 25 , c ) 55 , d ) 65 , e ) 80", + "Correct": "c", + "Explanation": "\"the arithmetic mean of 4 equally weighted tests was 70 . so what we can assume is that we have 4 test scores , each 70 . he dropped his lowest score and the avg went to 75 . this means that the lowest score was not 70 and other three scores had given the lowest score 5 each to make it up to 70 too . when the lowest score was removed , the other 3 scores got their 5 back . so the lowest score was 3 * 5 = 15 less than 70 . so the lowest score = 70 - 15 = 55 answer ( c )\"" + }, + { + "Answer": 5, + "Options": "a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8", + "Correct": "b", + "Explanation": "\"v = n ( n - 3 ) v = 2 * n 2 n = n ( n - 3 ) = > 2 = n - 3 = > n = 5 answer b\"" + }, + { + "Answer": 51, + "Options": "a ) 53 , b ) 52 , c ) 51 , d ) 50 , e ) 49", + "Correct": "c", + "Explanation": "\"125 - 75 + 1 = 51 ' c ' is the answer\"" + }, + { + "Answer": 37, + "Options": "a ) 11 , b ) 17 , c ) 13 , d ) 23 , e ) 37", + "Correct": "e", + "Explanation": "let that divisor be x since remainder is 15 or 27 it means divisor is greater than 27 . now 242 - 15 = 227 = kx ( k is an integer and 234 is divisble by x ) similarly 698 - 27 = 671 = lx ( l is an integer and 689 is divisible by x ) adding both 698 and 242 = ( 227 + 671 ) + 15 + 27 = x ( k + l ) + 42 when we divide this number by x then remainder will be equal to remainder of ( 42 divided by x ) = 5 hence x = 42 - 5 = 37 hence e" + }, + { + "Answer": 36, + "Options": "a ) 24 , b ) 72 , c ) 144 , d ) 36 , e ) 420", + "Correct": "d", + "Explanation": "the left window will have permutations of the 3 fiction books , so the number of possibilities for that window is permutations = 3 ! = ( 3 ) ( 2 ) ( 1 ) = 6 the right window will have permutations of the 3 non - fiction books , so the number of possibilities for that window is permutations = 3 ! = ( 3 ) ( 2 ) ( 1 ) = 6 any of the 24 displays of the left window could be combined with any of the 6 displays of the right window , so the total number of configurations is 6 * 6 = 36 answer : d ." + }, + { + "Answer": 0.6904761904761905, + "Options": "a ) 11 / 30 , b ) 29 / 42 , c ) 17 / 30 , d ) 19 / 30 , e ) 11 / 15", + "Correct": "b", + "Explanation": "\"let s assume the platinum card spending limit = x gold card spending limit will be = x / 2 balance on gold card is = x / 2 * 1 / 3 = x / 6 platinum card unspent limit is = x - 1 / 7 x = 6 / 7 x so if gold card balance is transferred then the rest unspent will be 6 / 7 x - x / 6 = 29 / 42 x so the ans is b\"" + }, + { + "Answer": 0.14285714285714285, + "Options": "a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 5 , d ) 1 / 6 , e ) 1 / 7", + "Correct": "e", + "Explanation": "\"the fraction of homes which are termite - infested but not collapsing is 3 / 7 * 1 / 3 = 1 / 7 the answer is e .\"" + }, + { + "Answer": 10, + "Options": "a ) - 3 , b ) 3 , c ) 5 , d ) 7 , e ) 10", + "Correct": "e", + "Explanation": "\"a can not be the answer as all the three terms are in modulus and hence the answer will be non negative . | x - 4 | > = 0 - - > minimum occurs at x = 4 | x + 5 | > = 0 - - > minimum occurs at x = - 5 | x - 5 | > = 0 - - > minimum occurs at x = 5 x = - 5 - - > result = 9 + 0 + 10 = 19 . also any negative value will push the combined value of | x - 4 | + | x - 5 | to a value > 9 . x = 4 - - > result = 0 + 9 + 1 = 10 x = 5 - - > result = 1 + 10 + 0 = 11 so minimum value of the expression occurs at x = 4 and the resultant value = 10 answer : e\"" + }, + { + "Answer": 24.25, + "Options": "a ) 18.25 , b ) 20.75 , c ) 22.25 , d ) 24.25 , e ) 26.75", + "Correct": "d", + "Explanation": "\"let x be the length of the size 8 shoe . then 0.1 x = 9 / 4 x = 90 / 4 inches the size 15 shoe has a length of 90 / 4 + 7 / 4 = 97 / 4 = 24.25 inches the answer is d .\"" + }, + { + "Answer": 28, + "Options": "a ) 15 min , b ) 18 min , c ) 16 min , d ) 20 min , e ) 28 min", + "Correct": "e", + "Explanation": "\"in 1 hr , the bus covers 75 km without stoppages and 40 km with stoppages . stoppage time = time take to travel ( 75 - 40 ) km i . e 35 km at 75 km / hr . stoppage time = 35 / 75 hrs = 28 min answer : e\"" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "c", + "Explanation": "@ ( n ) = 5 n - n we need to find the largest positive integer such that 5 n - n < 14 . then 4 n < 14 and n < 3.5 . the largest possible integer is n = 3 . the answer is c ." + }, + { + "Answer": 3, + "Options": "a ) - 9 , b ) - 5 , c ) - 3 , d ) - 1 , e ) 5", + "Correct": "c", + "Explanation": "\"x ^ 2 \u2013 4 x = 5 i . e . x ^ 2 \u2013 4 x - 5 = 0 i . e . x ^ 2 \u2013 5 x + x - 5 = 0 i . e . ( x - 5 ) ( x + 1 ) = 0 i . e . x = 5 or - 1 i . e . x - 2 = 5 - 2 or - 1 - 2 i . e . x - 2 = 3 or - 3 answer : option c\"" + }, + { + "Answer": 552, + "Options": "a ) 674 , b ) 604 , c ) 552 , d ) 372 , e ) 250", + "Correct": "c", + "Explanation": "\"9 pages from 1 to 9 will require 9 digits . 90 pages from 10 to 99 will require 90 * 2 = 180 digits . 220 - ( 90 + 9 ) = 121 pages will require 121 * 3 = 363 digits . the total number of digits is 9 + 180 + 363 = 552 . the answer is c .\"" + }, + { + "Answer": 25, + "Options": "a ) 9 % , b ) 11 % , c ) 15 % , d ) 25 % , e ) 90 %", + "Correct": "d", + "Explanation": "\"cost of 12 paper towels individually = 1 * 12 = 12 cost of a set of 12 paper towels = 9 cost of one roll = 9 / 12 = 3 / 4 = 0.75 savings per roll = 1 - . 75 = 0.25 % of savings is w = . 25 / 1 * 100 = 25 % d is the answer .\"" + }, + { + "Answer": 0.35294117647058826, + "Options": "a ) 6 / 17 , b ) 4 / 15 , c ) 1 / 3 , d ) 4 / 11 , e ) 4 / 5", + "Correct": "a", + "Explanation": "\"let avg for 11 mos . = 10 therefore , dec = 60 year total = 11 * 10 + 60 = 170 answer = 60 / 170 = 6 / 17 = a\"" + }, + { + "Answer": 4, + "Options": "a ) 6 , b ) 4 , c ) 8 , d ) 5 , e ) 3", + "Correct": "b", + "Explanation": "\"explanation : on dividing 101054 by 10 we get the remainder 4 , so 4 should be subtracted option b\"" + }, + { + "Answer": 0.006, + "Options": "a ) 0.008 , b ) 0.1 , c ) 0.12 , d ) 0.006 , e ) 0.007", + "Correct": "d", + "Explanation": "suppose machine x produce 1000 units total defective = 9 machine y then produces = 1500 units total defective = 6 probability = 15 / 2500 = 0.006 answer : d" + }, + { + "Answer": 4, + "Options": "a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 10", + "Correct": "b", + "Explanation": "the ratio of shadow to height is constant , so if x is the length of the shadow , then 2.5 / 5 = 2 / x and x = 4 . correct answer b" + }, + { + "Answer": 2, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "c", + "Explanation": "\"apparently it ' s a = x ^ 2 - x ^ 3 instead of a = x ^ 2 - a ^ 3 . in this case : the x - intercept is the value ( s ) of x for a = 0 . 0 = x ^ 2 - x ^ 3 ; 0 = x ^ 2 ( 1 - x ) ; x = 0 or x = 1 . answer : c .\"" + }, + { + "Answer": 25, + "Options": "a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25", + "Correct": "e", + "Explanation": "solution : we know that the average value is 20 therefore ( a + b + c ) / 3 = 20 so a + b + c = 60 and b = a + 13 therefore a + ( a + 13 ) + c = 60 the least value of c is when c = b so take c = a + 13 hence , a + ( a + 13 ) + ( a + 13 ) = 60 i . e . , a = 34 / 3 a non integer therefore c is not equal to b so take c = b + 1 therefore c = a + 14 a + ( a + 13 ) + ( a + 14 ) = 60 i . e . , a = 33 / 3 = 11 hence , a = 11 , b = 24 , and c = 25 answer : e" + }, + { + "Answer": 21, + "Options": "a ) 3 , b ) 6 , c ) 12 , d ) 23 , e ) 21", + "Correct": "e", + "Explanation": "2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 22 = > 4 x 2 ^ 2 n = 4 ^ 22 = 2 ^ 44 = > 2 ^ 2 x 2 ^ 2 n = 2 ^ 44 = > 2 ^ ( 2 n + 2 ) = 2 ^ 44 = > 2 n + 2 = 44 = > n = 21 so . answer will be e ." + }, + { + "Answer": 10, + "Options": "a ) 5 , b ) 6 , c ) 10 , d ) 15 , e ) 20", + "Correct": "c", + "Explanation": "\"if a ^ 2 - b ^ 2 = 0 , then let ' s assume that a = b . a must equal the 4 th positive multiple of 4 , thus a = 20 , which also equals b . b is the second positive multiple of n , thus n = 20 / 2 = 10 . the answer is c .\"" + }, + { + "Answer": 48, + "Options": "a ) 12 , b ) 15 , c ) 18 , d ) 21 , e ) 48", + "Correct": "e", + "Explanation": "the list should be wmwmw . hence , from women 4 ! and men 2 ! , we get ( 4 ! ) ( 2 ! ) = 48 . therefore , the correct answer is e ." + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1", + "Correct": "a", + "Explanation": "( 8000 ) ( 6000 ) = ( 480 ) ( 10 ^ y ) = > ( 8000 ) ( 6000 ) / 480 = 10 ^ y = > 100000 = 100 ^ y = > 10 ^ 5 = 10 ^ y since , base is same so powers will be same too . so , y = 5 answer will be a" + }, + { + "Answer": 2, + "Options": "a ) 1 , b ) 3 , c ) 4 , d ) 2 , e ) 6", + "Correct": "d", + "Explanation": "obviously , it is in the formula a ^ 2 - b ^ 2 = ( a + b ) ( a - b ) so k is 2 option d" + }, + { + "Answer": 30, + "Options": "a ) 2 % , b ) 17 % , c ) 30 % , d ) 65 % , e ) 83 %", + "Correct": "c", + "Explanation": "\"new value \u2013 old value ) / old value x 100 we are given : february sales this year = 416 million february sales last year = 320 million we need to determine the percent increase between sales from last year to sales this year . thus , the new value = 416 million and the old value = 320 million . let \u2019 s plug them into our percent change formula . ( new value \u2013 old value ) / old value x 100 [ ( 416 \u2013 320 ) / 320 ] x 100 = 30 % the answer is c .\"" + }, + { + "Answer": 32.72727272727273, + "Options": "a ) 55.42 % , b ) 52.25 % , c ) 56.23 % , d ) 30.70 % , e ) 32.72 %", + "Correct": "e", + "Explanation": "\"say a 100 families existed in 2000 then the number of families owning a computer in 2000 - 30 number of families owning computer in 2000 = 30 * 120 / 100 = 36 number of families in 2004 = 110 the percentage = 36 / 110 * 100 = 32.72 % . option : e\"" + }, + { + "Answer": 7, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8", + "Correct": "d", + "Explanation": "\"64 ^ k > 4 ^ 20 4 ^ ( 3 k ) > 4 ^ 20 3 k > 20 k = 7 the answer is d .\"" + }, + { + "Answer": 17.9, + "Options": "a ) 17.1 , b ) 17.3 , c ) 17.5 , d ) 17.7 , e ) 17.9", + "Correct": "e", + "Explanation": "29.94 / 1.45 = 299.4 / 14.5 = ( 2994 / 14.5 ) x 1 / 10 ) [ here , substitute 179 in the place of 2994 / 14.5 ] = 179 / 10 = 17.9 answer is e ." + }, + { + "Answer": 2.4, + "Options": "a ) 2 \u221a 2 , b ) 2 \u221a 3 , c ) 3 \u221a 2 , d ) 3 \u221a 3 , e ) 12 / 5", + "Correct": "e", + "Explanation": "\"( \u221a 27 + \u221a 243 ) / \u221a 75 = ( 3 \u221a 3 + 9 \u221a 3 ) / 5 \u221a 3 = 12 \u221a 3 / 5 \u221a 3 = 12 / 5 . hence , the correct answer is e\"" + }, + { + "Answer": 2, + "Options": "a ) 1 , b ) 0 , c ) 2 , d ) - 1 , e ) can not be determined", + "Correct": "c", + "Explanation": "median of the set = ( - 6 + 6 ) / 2 = 0 as per statement , mean of the set = 0 mean of the set | y | - | x | + 23 - 21 = 0 ( where x is negative n y is positive ) | y | - | x | = - 2 so the absolute difference between two numbers is 2 answer c" + }, + { + "Answer": 397, + "Options": "a ) 356 , b ) 366 , c ) 363 , d ) 396 , e ) 408", + "Correct": "d", + "Explanation": "\"there are 46 digits in 10 ^ 45 when we subtract 46 from it , there will be 45 digits left . 10 ^ 45 can be written as 9999999 . . . . ( 45 times ) + 1 so , 10 ^ 45 - 46 = 9999999 . . . . ( 45 times ) + 1 - 46 = 9999999 . . . . ( 45 times ) - 45 consider the last 2 digits , 99 - 45 = 54 the last 2 digits will be 54 . and our number would be 99999 . . . . . . 99954 with 2 less 9 s after subtraction . number of 9 s left are 43 and the last two digits are 54 the sum of the digits will be ( 43 * 9 ) + 5 + 4 = 396 answer : - d\"" + }, + { + "Answer": 25, + "Options": "a ) 25 , b ) 125 , c ) 625 , d ) 1625 , e ) none of these", + "Correct": "a", + "Explanation": "solution 5 a = 3125 \u21d4 5 a = 5 a \u21d4 a = 5 . \u2234 5 ( a - 3 ) = 5 ( 5 - 3 ) = 52 = 25 . answer a" + }, + { + "Answer": 25, + "Options": "a ) 47 , b ) 25 , c ) 37 , d ) 33 , e ) 29", + "Correct": "b", + "Explanation": "\"before you tackle this question you must first understand that the question is comprised of two key parts , 1 st is finding out how manytermsis in that sequence and 2 nd whatactual number valuethat term is . in an arithmetic progression , in this case consecutive odd integers 1 , 3 , 5 , . . . . , there are two set of rules . rule # 1 ( arithmetic sequence ) : xn = a + d ( n - 1 ) identifies what the actual # in the sequence would be . each number in the sequence has a term such as 1 ( is the first term ) , 3 ( is the second term ) and so on . so if i were to ask you to find out what the 10 th term is of that sequence you would use that formula to find that value . a = 1 ( first term ) d = 2 ( the common difference ) remember in the sequence 1 , 3 , 5 , 7 the common difference is always 2 * on a side note we use n - 1 because we do n ' t have d in the first term , therefore if we were solving for the first term we would get 0 as n - 1 and 0 times d would give us 0 , leaving only the first term . this works regardless what your first term is in any sequence . but remember the question askswhat is thevalueof n if the sum of the consecutive odd integers from 1 to n equals 169 ? which means we first need a consecutive sequence that sums up to 169 and than find what the value of the n is , in this case it would be the last number in that sequence . in order to find that we first need to knowhow many terms ( how many of the n there is ) in order to be able to plug n in this formula given we know what the sum is . for that to happen we need to use rule # 2 . rule # 2 ( summing an arithmetic series ) : 169 = n / 2 ( 2 a + ( n - 1 ) d ) . given the question gives us what the sum is ( 169 in this case ) we would simply use this formula to solve for n . once we solve for n ( 13 in this case ) we can simply plug n into the first formula ( rule 1 ) and find the value . it feels very confusing and difficult at first , but once you identify the steps all you need to do is plug and play . we have the sum ( 169 ) of a sequence , the number of terms in that sequence is ( unknown ) . rule # 2 tells us how many numbers there are in that sequence and rule # 1 gives us what that last term is .\"" + }, + { + "Answer": 12, + "Options": "a ) 18 , b ) 24 , c ) 16 , d ) 12 , e ) 10", + "Correct": "d", + "Explanation": "log 4 x + log 4 ( 1 / 6 ) = 1 / 2 = > log 4 [ x x 1 / 6 ] = 1 / 2 = > log 4 [ x / 6 ] = 1 / 2 = > 41 / 2 = x / 6 = > 2 = x / 6 therefore , x = 12 answer : d" + }, + { + "Answer": 77.99999999999999, + "Options": "a ) 124 % , b ) b ) 120 % , c ) c ) 78 % , d ) d ) 80 % , e ) e ) 64 %", + "Correct": "c", + "Explanation": "\"m = ( 130 / 100 ) t t = ( 60 / 100 ) j = > m = ( 78 / 100 ) j answer c .\"" + }, + { + "Answer": 0.15000000000000036, + "Options": "a ) 1.5 , b ) 0.15 , c ) 6.25 , d ) 0.25 , e ) 6.0", + "Correct": "b", + "Explanation": "\"since z * is defined as the greatest positive even integer less than or equal to z , then 6.15 * = 6 ( the greatest positive even integer less than or equal to 6.15 is 6 ) . hence , 6.15 \u2013 6.15 * = 6.15 - 6 = 0.15 answer : b .\"" + }, + { + "Answer": 59.999999999997726, + "Options": "a ) 96 , b ) 60 , c ) 48 , d ) 25 , e ) 12", + "Correct": "b", + "Explanation": "\"guys , one more simple funda . 5 / 2 = 2.5 now . 5 x 2 = 1 is the remainder 25 / 4 = 6.25 now . 25 x 4 = 1 is the remainder 32 / 5 = 6.4 now . 4 x 5 = 2 is the remainder given x / y = 96.15 and remainder is 9 so . 15 x y = 9 hence y = 60 ans b\"" + }, + { + "Answer": 12, + "Options": "a ) 5 inches , b ) 6 inches , c ) 9 inches , d ) 10 inches , e ) 12 inches", + "Correct": "e", + "Explanation": "\"total rainfall in 2 weeks = 20 inches . assume the rainfall in second week = 1.5 x rainfall in first week = x total rainfall = 2.5 x = 20 inches x = 8 and 1.5 x = 12 rainfall during second week = 12 inches option e\"" + }, + { + "Answer": 0.041666666666666664, + "Options": "a ) 1 / 32 , b ) 1 / 28 , c ) 1 / 24 , d ) 1 / 16 , e ) 1 / 14", + "Correct": "c", + "Explanation": "\"there are 3 single digit multiple of 3 , that is , 3 , 6,9 . there are 8 prime nos less than 20 - 2,3 , 5,7 , 11,13 , 17,19 total outcome - 8 * 3 = 24 favourable outcome = 1 ( 9 * 5 ) hence required probability q = 1 / 24 . answer c .\"" + }, + { + "Answer": 40, + "Options": "a ) 34 , b ) 43 , c ) 40 , d ) 38 , e ) 29", + "Correct": "c", + "Explanation": "\"solution : average speed = 2 xy / x + y = 2 * 60 * 30 / 60 + 30 = 40 answer : c\"" + }, + { + "Answer": 133, + "Options": "a ) 135 , b ) 137 , c ) 142 , d ) 130 , e ) 133", + "Correct": "e", + "Explanation": "\"the number of liters in each can = hcf of 20 , 144 and 368 = 4 liters . number of cans of maaza = 20 / 4 = 5 number of cans of pepsi = 144 / 4 = 36 number of cans of sprite = 368 / 4 = 92 the total number of cans required = 5 + 36 + 92 = 133 cans . answer : e\"" + }, + { + "Answer": 7, + "Options": "a ) 93 , b ) 7 , c ) 54 , d ) 9 , e ) 6", + "Correct": "b", + "Explanation": "on dividing 62571 by 99 we get the remainder 7 , so 7 should be subtracted . answer is b" + }, + { + "Answer": 10, + "Options": "a ) 10 , b ) 21 , c ) 22 , d ) 23 , e ) 24", + "Correct": "a", + "Explanation": "let the brother ' s present age be x years . then , man ' s present age = ( x + 12 ) years . ( x + 12 ) + 2 = 2 ( x + 2 ) x + 14 = 2 x + 4 x = 10 . answer : a" + }, + { + "Answer": 200, + "Options": "a ) 200 , b ) 84 , c ) 40 , d ) 28 , e ) 20", + "Correct": "a", + "Explanation": "\"almonds : walnuts = 5 : 2 total mixture has 7 parts in a 280 pound mixture , almonds are 5 / 7 ( total mixture ) = 5 / 7 * 280 = 200 pounds answer ( a )\"" + }, + { + "Answer": 192, + "Options": "a ) 168 , b ) 176 , c ) 184 , d ) 192 , e ) 200", + "Correct": "d", + "Explanation": "the 1 st digit can be filled up by the numbers : { 1 , 8,9 } = 3 ways the 2 nd digit can be filled up by the numbers : { 0,1 , 8,9 } = 4 ways the 3 rd digit can be filled up by the numbers : { 0,1 , 8,9 } = 4 ways the 4 th digit can be filled up by the numbers : { 0,1 , 8,9 } = 4 ways the total number of such four - digit numbers is 3 * 4 * 4 * 4 = 192 the answer is d ." + }, + { + "Answer": 79.8, + "Options": "a ) 73 kg , b ) 79.8 kg , c ) 86 kg , d ) data inadequate , e ) none of these", + "Correct": "b", + "Explanation": "\"total weight increased = ( 6 x 1.8 ) kg = 10.8 kg . weight of new person = ( 69 + 10.8 ) kg = 79.8 kg . answer : option b\"" + }, + { + "Answer": 2006, + "Options": "a ) 2003 , b ) 2004 , c ) 2005 , d ) 2006 , e ) 2007", + "Correct": "d", + "Explanation": "\"she must gain at least 70 points , now she has 30 and every year gives her two more points : one for age and one for additional year of employment , so 30 + 2 * ( # of years ) = 70 - - > ( # of years ) = 20 - - > 1986 + 20 = 2006 . answer : d .\"" + }, + { + "Answer": 196.25, + "Options": "a ) 191 , b ) 197 , c ) 193 , d ) 212 , e ) 213", + "Correct": "b", + "Explanation": "\"total movies submitted are 785 . as per question we need to take 1 / 4 of 785 to be considered for top 10 movies = 196.25 approximate the value we 197 . imo option b is the correct answer . . .\"" + }, + { + "Answer": 0.16666666666666669, + "Options": "a ) 1 / 6 , b ) 2 / 10 , c ) 1 / 50 , d ) 1 / 500 , e ) 2 / 500", + "Correct": "a", + "Explanation": "\"let x be the difference then . 5 - 1 / 3 = x 5 / 10 - 1 / 3 = x x = 1 / 6 ans a\"" + }, + { + "Answer": 61.666666666666664, + "Options": "a ) 50.78 kg , b ) 49.32 kg , c ) 61.67 kg , d ) 69.15 kg , e ) 70.89 kg", + "Correct": "c", + "Explanation": "\"total weight of 50 + 70 students = 50 * 50 + 70 * 70 = 7400 average weight of the class is = 7400 / 120 = 61.67 kg answer is c\"" + }, + { + "Answer": 2, + "Options": "a ) - 9 , b ) - 5 , c ) - 3 , d ) - 1 , e ) 2", + "Correct": "e", + "Explanation": "x ^ 2 \u2013 3 x = 18 i . e . x ^ 2 \u2013 3 x - 18 = 0 i . e . x ^ 2 \u2013 6 x + 3 x - 18 = 0 i . e . ( x - 6 ) ( x + 3 ) = 0 i . e . x = 6 or - 3 i . e . x - 4 = 6 - 4 or - 3 - 4 i . e . x - 4 = 2 or - 7 answer : option e" + }, + { + "Answer": 23, + "Options": "a ) 23 , b ) 3 , c ) 15 , d ) 52 / 7 , e ) 60 / 7", + "Correct": "a", + "Explanation": "4 x + y = 8 . . . equation 1 3 x - 4 y = 5 . . . equation 2 adding both the equations 7 x - 3 y = 23 correct answer option a" + }, + { + "Answer": 22, + "Options": "a ) 23 , b ) 22 , c ) 44 , d ) 33 , e ) 55", + "Correct": "b", + "Explanation": "b 22" + }, + { + "Answer": 46, + "Options": "a ) 46 , b ) 55 , c ) 43 , d ) 39 , e ) 54", + "Correct": "a", + "Explanation": "\"explanation : if teacher ' s age is 15 years , there is no change in the average . but teacher has contributed 1 year to all the students along with maintaining his age at 16 . age of teacher = average age of all + total increase in age = 16 + ( 1 x 30 ) = 46 years answer : a\"" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "a", + "Explanation": "to test a number n on whether it is a prime number , take square root ( n ) . consider as it is if it is a natural number . otherwise , increase the sq . root to the next natural no . then divide given no . by all prime numbers below the sq . root obtained . if the no . is divisible by any of the prime numbers , then it is not a prime number ; else it is . square root of 200 or 220 is less than 15 so , lets check if any number between 200 and 220 is not divisible by prime numbers 2 , 35 , 711 ( < 15 ) . that ' s it . out : 201 , 202 , 203 , 204 , 205 , 206 , 207 , 208 , 209 , 210 , 212 , 213 , 214 , 215 , 216 , 217 , 218 , 219 only 211 is a prime number in the given range correct option : a" + }, + { + "Answer": 6324, + "Options": "a ) 7349 , b ) 6300 , c ) 6325 , d ) 6939 , e ) 2989", + "Correct": "c", + "Explanation": "\"x * ( 90 / 100 ) * ( 80 / 100 ) = 4554 x = 6325 answer : c\"" + }, + { + "Answer": 1600, + "Options": "a ) w = 200 , b ) w = 600 , c ) w = 800 , d ) w = 1600 , e ) w = 50", + "Correct": "d", + "Explanation": "\"original cost w , c 1 = t 1 * b 1 ^ 4 new cost c 2 = t 2 * b 2 ^ 4 . . . . only b is doubled so t 2 = t 1 and b 2 = 2 b 1 c 2 = t 2 * ( 2 b 1 ) ^ 4 = 16 ( t 1 * b 1 ^ 4 ) = 16 c 1 16 times c 1 = > 1600 % of c 1 ans d = 1600\"" + }, + { + "Answer": 49.99999999999999, + "Options": "a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 80", + "Correct": "c", + "Explanation": "\"let the total weight be x . sand content = ( 1 / 2 ) x water content = ( 1 / 5 ) x gravel = x - ( 1 / 2 ) x - ( 1 / 5 ) x = ( 3 / 10 ) x = 15 x = 50 then answer will be c = 50\"" + }, + { + "Answer": 1.52, + "Options": "a ) $ 2.5 , b ) $ 2.55 , c ) $ 1.52 , d ) $ 3.25 , e ) $ 3.0", + "Correct": "c", + "Explanation": "finding the harmonic mean here . hm = 4 / ( 1 / 12 + 1 / 13 + 1 / 18 + 1 / 21 ) = 15.18 c" + }, + { + "Answer": 2300, + "Options": "a ) 2160 , b ) 2350 , c ) 2000 , d ) 2300 , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : total exp = 5000 + 1500 + 4500 + 2500 + 2000 + 5200 = 20700 exp in % = 100 - 10 = 90 % , 20700 = 90 % saving = 10 % = 20700 x 10 / 90 = rs . 2300 answer : d\"" + }, + { + "Answer": 71, + "Options": "a ) 71 , b ) 69 , c ) 75 , d ) 85 , e ) 90", + "Correct": "a", + "Explanation": "\"explanation : average = ( 76 + 65 + 82 + 47 + 85 ) / 5 = 355 / 5 = 71 hence average = 71 answer : a\"" + }, + { + "Answer": 24, + "Options": "a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25", + "Correct": "d", + "Explanation": "\"the multiples of 4 are from 4 * 3 up to 4 * 26 . 26 - 3 + 1 = 24 . the answer is d .\"" + }, + { + "Answer": 49.00000000000007, + "Options": "a ) 56 kg , b ) 52 kg , c ) 44 kg , d ) 49 kg , e ) none of these", + "Correct": "d", + "Explanation": "explanation : by the rule of alligation , we have cost of 1 kg of 1 st kind rice cost of 1 kg of 2 nd kind rice 6.6 9.6 price of 1 kg of the mixture 8.2 9.6 - 8.2 = 1.4 8.2 - 6.6 = 1.6 quantity of 1 st kind rice : quantity of 2 nd kind rice = 1.4 : 1.6 = 7 : 8 quantity of 1 st kind rice : 56 = 7 : 8 = > quantity of 1 st kind rice = 56 \u00d7 78 = 49 answer : option d" + }, + { + "Answer": 2.6, + "Options": "a ) $ 2.6 , b ) $ 2.40 , c ) $ 3.40 , d ) $ 4.40 , e ) $ 5.40", + "Correct": "a", + "Explanation": "manager wages per hour = $ 6.50 dishwasher wages per hour = half of manager ' s wages . = 1 / 2 ( $ 6.50 ) = = > $ 3.25 chef wages per hour = 20 % greater than dishwasher wages - - > 20 % of $ 3.25 = ( 20 * ( $ 3.25 ) ) / 100 - - > ( $ 65 ) / 100 - - > $ 0.65 therefore , chef wages per hour = $ 3.25 + $ 0.65 = = > $ 3.9 difference of wages between manager and chef = $ 6.50 - $ 3.9 = = > $ 2.6 answer : a" + }, + { + "Answer": 150, + "Options": "a ) $ 140 , b ) $ 145 , c ) $ 150 , d ) $ 155 , e ) $ 160", + "Correct": "c", + "Explanation": "0.75 * ( 1.25 * 160 ) = $ 150 the answer is c ." + }, + { + "Answer": 318, + "Options": "a ) a ) 318 , b ) b ) 65 , c ) c ) 58 , d ) d ) 62 , e ) e ) 48", + "Correct": "a", + "Explanation": "6 th number = sum of 1 st 6 no . s + sum of last 6 no . s - sum of 11 no . s answer = 6 * 98 + 6 * 65 - 11 * 60 = 318 answer is a" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "a", + "Explanation": "7 ^ 16 can be written as ( 7 ^ 4 ) ^ 3 if we divide 7 ^ 4 by 100 the reminder is 1 so , ( 7 ^ 4 ) ^ 3 by 100 , the reminder is 1 ^ 3 = 1 answer : a" + }, + { + "Answer": 49.5, + "Options": "a ) 49.5 , b ) 41.5 , c ) 45.5 , d ) 40.5 , e ) 47.5", + "Correct": "a", + "Explanation": "\"explanation : numbers divisible by 9 are 18,27 , 36,45 , 54,63 , 72,81 , average = ( 18 + 27 + 36 + 45 + 54 + 63 + 72 + 81 , ) / 8 = 396 / 8 = 49.5 answer : a\"" + }, + { + "Answer": 18, + "Options": "a ) 10 , b ) 11 , c ) 18 , d ) 20 , e ) 24", + "Correct": "c", + "Explanation": "\"sum of 17 even numbers = 17 * 18 = 306 average = 306 / 17 = 18 answer : c\"" + }, + { + "Answer": 1, + "Options": "a ) \u2013 16 , b ) \u2013 11 , c ) \u2013 4 , d ) 4 , e ) 1", + "Correct": "e", + "Explanation": "\"1 * ( - 3 ) = 1 * ( - 3 ) - 2 ( 1 + ( - 3 ) ) = - 3 + 4 = 1 option ( e )\"" + }, + { + "Answer": 0.15499999999999997, + "Options": "a ) 47 / 200 , b ) 31 / 200 , c ) 17 / 100 , d ) 11 / 100 , e ) 7 / 50", + "Correct": "b", + "Explanation": "\"males who did not arrive on time are 1 / 8 * 3 / 5 = 3 / 40 of the attendees . females who did not arrive on time are 1 / 5 * 2 / 5 = 2 / 25 of the attendees . the fraction of all attendees who did not arrive on time is 3 / 40 + 2 / 25 = 31 / 200 the answer is b .\"" + }, + { + "Answer": 16, + "Options": "a ) 16 , b ) 8 , c ) 12 , d ) 9 , e ) 7", + "Correct": "a", + "Explanation": "\"4 * 4 = 16 quarters answer : a\"" + }, + { + "Answer": 0.625, + "Options": "a ) 1 / 8 , b ) 2 / 3 , c ) 5 / 8 , d ) 4 / 7 , e ) 3 / 7", + "Correct": "c", + "Explanation": "\"at least twice , but not more than 4 timesmeans exactly 2 times , 3 times , 4 times the probability of getting exactly k results out of n flips is nck / 2 ^ n 4 c 2 / 2 ^ 4 + 4 c 3 / 2 ^ 4 = 10 / 16 = 5 / 8 option : c\"" + }, + { + "Answer": 49.99999999999997, + "Options": "a ) 50 . , b ) 45 . , c ) 40 . , d ) 30 . , e ) 25 .", + "Correct": "a", + "Explanation": "given there are 50 students in the forestside summer camp , 90 % of 50 = 45 boys and remaining 5 girls . now here 90 % are boys and 10 % are girls . now question is asking about how many boys do we need to add , to make the girls percentage to 5 or 5 % . . if we add 50 to existing 45 then the count will be 95 and the girls number will be 5 as it . now boys are 95 % and girls are 5 % . ( out of 100 students = 95 boys + 5 girls ) . imo option a is correct ." + }, + { + "Answer": 12, + "Options": "a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18", + "Correct": "b", + "Explanation": "\"d = ( d - r ) / q = ( 109 - 1 ) / 9 = 108 / 9 = 12 b )\"" + }, + { + "Answer": 0.6, + "Options": "a ) a ) 0.6 , b ) b ) 0.8 , c ) c ) 0.85 , d ) d ) 0.5 , e ) e ) none", + "Correct": "a", + "Explanation": "\"( x * 10 ) = ( 0.75 * 8 ) x = 6 / 10 x = 0.6 answer = a\"" + }, + { + "Answer": 37.25, + "Options": "a ) 35.29 kg , b ) 37.25 kg , c ) 42.45 kg , d ) 55.12 kg , e ) 29.78 kg", + "Correct": "b", + "Explanation": "total weight of 36 + 44 students = 36 * 44 + 44 * 35 = 2980 average weight of the class is = 2980 / 80 = 37.25 kg answer is b" + }, + { + "Answer": 0.005025125628140704, + "Options": "a ) 1 / 190 , b ) 1 / 20 , c ) 1 / 199 , d ) 1 / 10 , e ) 1 / 9", + "Correct": "c", + "Explanation": "\"the problem with your solution is that we do n ' t choose 1 shoe from 200 , but rather choose the needed one after we just took one and need the second to be the pair of it . so , the probability would simply be : 1 / 1 * 1 / 199 ( as after taking one at random there are 199 shoes left and only one is the pair of the first one ) = 1 / 199 answer : c .\"" + }, + { + "Answer": 233.33333333333331, + "Options": "a ) 400 % , b ) 80 % , c ) 233 % , d ) 60 % , e ) none of the above", + "Correct": "c", + "Explanation": "let x be the index in the year 2000 . after the decrease it becomes 0.3 x now for 0.3 x to reach 1 x it has to raise by 0.7 x . the increase needs to be 0.7 x / 0.3 x * 100 = 233.3 % answer c" + }, + { + "Answer": 10550, + "Options": "a ) $ 10500 , b ) $ 11000 , c ) $ 13000 , d ) $ 13500 , e ) $ 14,000", + "Correct": "a", + "Explanation": "given : for incomes over $ 5,000 , an 8 % tax is imposed on the first $ 5,000 , and a 10 % tax is imposed on the portion of the total income in excess of $ 5000 . if perry paid $ 950 in income tax last month , then what was perry ' s income ? for first 5000 , 8 % tax then we get 400 $ as tax . now perry paid 950 $ tax . . . we need to check which option is going to yield 550 $ on the remaining amount . a . $ 10,500 - 5000 = 5500 , then we get 10 % tax , we get 550 $ . . . ( $ 10,500 - 5000 - here already for 5000 $ we have calculated the tax and we need to tally for the remaining amount ) 550 + 400 = 950 $ . . . hence this is the option . answer : option a ." + }, + { + "Answer": 19.99999999999999, + "Options": "a ) 3 / 80 , b ) 3 / 5 , c ) 20 , d ) 5 / 3 , e ) 80 / 3", + "Correct": "c", + "Explanation": "\"15 / 100 = 3 / 20 n = 2 ^ 3 / 20 n ^ b = 2 ^ 3 ( 2 ^ 3 / 20 ) ^ b = 2 ^ 3 b = 20 answer : c\"" + }, + { + "Answer": 22500, + "Options": "a ) 3277 , b ) 2977 , c ) 22500 , d ) 6077 , e ) 17112", + "Correct": "c", + "Explanation": "explanation : 40,000 * ( 3 / 4 ) ^ 2 answer : c" + }, + { + "Answer": 54, + "Options": "a ) 42 , b ) 46 , c ) 50 , d ) 54 , e ) 58", + "Correct": "d", + "Explanation": "p - 5 = 3 ( k - 5 ) and so p = 3 k - 10 p + 6 = 2 ( k + 6 ) ( 3 k - 10 ) + 6 = 2 k + 12 k = 16 p = 38 p + k = 54 the answer is d ." + }, + { + "Answer": 0.2, + "Options": "a ) 1 / 20 , b ) 1 / 6 , c ) 1 / 5 , d ) 4 / 21 , e ) 5 / 21", + "Correct": "c", + "Explanation": "\"series : a 1 , a 2 . . . . a 20 , n sum of a 1 + a 2 + . . . + a 20 = 20 * x ( x = average ) so , n = 5 * x hence , a 1 + a 2 + . . + a 20 + n = 25 x so , the fraction asked = 5 x / 25 x = 1 / 5 answer c\"" + }, + { + "Answer": 64, + "Options": "a ) a ) 32 , b ) b ) 24 , c ) c ) 64 , d ) d ) 40 , e ) e ) 45", + "Correct": "c", + "Explanation": "\"x \u2013 3 / 8 x = 40 x = 64 answer : c\"" + }, + { + "Answer": 1000, + "Options": "a ) a ) 1000 , b ) b ) 3000 , c ) c ) 3500 , d ) d ) 2500 , e ) e ) 2250", + "Correct": "a", + "Explanation": "for 20 staffs : 300 * 100 * 20 = 60000 for driver and cleaning staff : 300 * 100 * 2 = 6000 from petty cash : 1000 answer is a" + }, + { + "Answer": 305, + "Options": "a ) 190 , b ) 284.6 , c ) 300 , d ) 305 , e ) 312", + "Correct": "d", + "Explanation": "\"to maximize the distance that suv could be driven on 25 gallons of gasoline , we need consider only highway driving . max distance = 25 * 12.2 = 305 answer d\"" + }, + { + "Answer": 8, + "Options": "a ) 6 rs , b ) 2 rs , c ) 4 rs , d ) 9 rs , e ) 8 rs", + "Correct": "e", + "Explanation": "\"5 m = xw = 8 b 5 m + xw + 8 b - - - - - 120 rs . 5 m + 5 m + 5 m - - - - - 120 rs . 15 m - - - - - - 120 rs . = > 1 m = 8 rs . answer : e\"" + }, + { + "Answer": 5, + "Options": "a ) 9 , b ) 4 , c ) 2 , d ) 1 , e ) 5", + "Correct": "e", + "Explanation": "step 1 convert fraction to decimal with two decimal places 1 / 2 = 0.50 then convert to scientific number = 5 * 10 ^ - 1 step 2 multiply 5 ^ 10 by 10 ^ - 10 step 3 5 has the sequence 5 , 25 , 125 answer is e" + }, + { + "Answer": 9, + "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12", + "Correct": "b", + "Explanation": "let he have x pant . by fundamental principle total no . of ways in which he can dress = 8 x 8 x = 72 x = 9 pants answer b" + }, + { + "Answer": 25, + "Options": "a ) 25 % , b ) 15 % , c ) 45 % , d ) 33 % , e ) 55 %", + "Correct": "a", + "Explanation": "machine a : 1 item in 4 minutes - - > 1 / 4 items in 1 minute ; machine b : 1 item in 5 minutes - - > 1 / 5 items in 1 minute . in the same time period , machine a produces ( 1 / 4 - 1 / 5 ) / ( 1 / 5 ) * 100 = ~ 25 % more items than machine b . answer : a ." + }, + { + "Answer": 17, + "Options": "a ) 32 , b ) 48 , c ) 67 , d ) 17 , e ) 26", + "Correct": "d", + "Explanation": "divisor = dividend - remainder divided by the quotient divisor = 76 - 8 divided by 4 divisor = 68 / 4 divisor = 17" + }, + { + "Answer": 48, + "Options": "a ) 20 , b ) 24 , c ) 36 , d ) 48 , e ) 60", + "Correct": "d", + "Explanation": "\"let the capacity of the tank = c ( 3 / 4 ) c + 8 = ( 9 / 10 ) c = > ( 9 / 10 ) c - ( 3 / 4 ) c = 8 = > ( 3 / 20 ) c = 8 = > c = ( 8 * 20 ) / 3 = 53.33 number of gallons of gasoline that the tank currently holds = 3 / 4 * c + 8 = 39.99 + 8 = 47.99 = 48 answer d\"" + }, + { + "Answer": 208, + "Options": "a ) 200 , b ) 208 , c ) 400 , d ) 500 , e ) 100", + "Correct": "b", + "Explanation": "\"let x be the number i chose , then x / 2 \u2212 100 = 4 x / 2 = 104 x = 208 answer is b .\"" + }, + { + "Answer": 20, + "Options": "a ) 25 % , b ) 33 1 / 3 % , c ) 50 % , d ) 66 2 / 3 % , e ) 20 %", + "Correct": "e", + "Explanation": "\"general formula for percent increase or decrease , ( percent change ) : percent = change / original \u2217 100 so , the time between maintenance checks increased by 60 \u2212 50 / 50 \u2217 100 = 20 answer : e .\"" + }, + { + "Answer": 1.9832, + "Options": "a ) 1.9328 , b ) 1.9832 , c ) 1.9823 , d ) 1.9382 , e ) none of them", + "Correct": "b", + "Explanation": "sum of decimal places = ( 2 + 2 ) = 4 2.68 * 0.74 = 1.9832 . answer is b ." + }, + { + "Answer": 72, + "Options": "a ) 25 , b ) 40 , c ) 64 , d ) 72 , e ) 96", + "Correct": "d", + "Explanation": "\"7 / 8 x - 3 / 4 x = 9 galls 1 / 8 * x = 9 gallons x = 72 gallons answer d\"" + }, + { + "Answer": 19, + "Options": "a ) 12 , b ) 29 , c ) 27 , d ) 19 , e ) 99", + "Correct": "d", + "Explanation": "explanation : let the number be x . therefore , 3 ( 2 x + 5 ) = 129 6 x + 15 = 129 6 x = 114 x = 19 answer : d" + }, + { + "Answer": 154, + "Options": "a ) 198 , b ) 154 , c ) 199 , d ) 102 , e ) 105", + "Correct": "b", + "Explanation": "\"last term = first term + ( total no . of terms - 1 ) consecutive difference s is a set of 50 consecutive multiples of 2 . if the smallest number in s is 56 , then the greatest number in s is first term = 56 ; total terms = 50 ; difference = 2 56 + ( 49 ) 2 = 154 ans b\"" + }, + { + "Answer": 990, + "Options": "a ) 732 , b ) 990 , c ) 1098 , d ) 1305 , e ) none of these", + "Correct": "b", + "Explanation": "solution total number of digits = ( no . of digits in 1 - digits page nos . + no . of digits in 2 - digits page nos . + no . of digits i 3 - digits page nos . ) = ( 1 * 9 + 2 * 90 + 3 * 267 ) = ( 9 + 180 + 801 ) = 990 . answer b" + }, + { + "Answer": 75, + "Options": "a ) 22 , b ) 75 , c ) 25 , d ) 70 , e ) 11", + "Correct": "b", + "Explanation": "weight of 1 st box = 200 weight of 3 rd box = ( 125 / 100 ) * 200 = 250 weight of 2 nd box = ( 120 / 100 ) * 250 = 300 weight of 4 th box = 350 weight of 5 th box = ( 10 / 7 ) * 350 = 500 average of 4 highest weighted boxes = ( 500 + 350 + 300 + 250 ) / 4 = 350 average of 4 lightest boxes = ( 350 + 300 + 250 + 200 ) / 4 = 275 therefore difference = 350 - 275 = 75 answer : b" + }, + { + "Answer": 288, + "Options": "a ) 125 , b ) 288 , c ) 384 , d ) 400 , e ) 500", + "Correct": "b", + "Explanation": "\"explanation : let the number be x . 5 * x / 6 = 5 * x / 16 + 150 25 * x / 48 = 150 x = 288 answer b\"" + }, + { + "Answer": 40, + "Options": "a ) 40 minutes , b ) 15 minutes , c ) 12 minutes , d ) 10 minutes , e ) 3 minutes", + "Correct": "a", + "Explanation": "let the movie size be 400 u . given , a + c = 4 hrs . a + c = 100 u / hr and a + b + c = 2.5 hrs or 400 / 2.5 = 160 u / hr b alone = 160 - 100 = 60 u / hr trailer = 40 times smaller or 400 / 10 = 40 u b will take 40 / 60 hrs or 40 minutes . ans a" + }, + { + "Answer": 100, + "Options": "a ) 100 , b ) 175 , c ) 200 , d ) 125 , e ) 300", + "Correct": "a", + "Explanation": "for an ap the mean or average of series is average of first and last term . so , average of numbers between 100 to 400 , inclusive = ( 100 + 400 ) / 2 = 250 average of numbers between 50 to 250 , inclusive = ( 50 + 250 ) / 2 = 150 difference = 250 - 150 = 100 answer is a" + }, + { + "Answer": 123.2, + "Options": "a ) $ 54.00 , b ) $ 64.80 , c ) $ 90.00 , d ) $ 100.80 , e ) $ 123.20", + "Correct": "e", + "Explanation": "\"correct answer : e the tourist must pay tax on $ 1720 - $ 600 = $ 1120 . thus , the amount of tax he has to pay is 0.11 ( $ 1120 ) = $ 123.20 . the correct answer is e .\"" + }, + { + "Answer": 144, + "Options": "a ) 125 , b ) 127 , c ) 129 , d ) 131 , e ) 144", + "Correct": "e", + "Explanation": "\"explanation : in this type of question , its obvious we need to calculate the hcf , trick is hcf of ( 6215 - 23 ) and ( 7373 - 29 ) = hcf ( 6192 , 7344 ) = 144 option e\"" + }, + { + "Answer": 7, + "Options": "a ) 4 , b ) 7 , c ) 6 , d ) 9 , e ) 8", + "Correct": "b", + "Explanation": "\"let the ages of children be x , ( x + 2 ) , ( x + 4 ) , ( x + 6 ) and ( x + 8 ) years . then , x + ( x + 2 ) + ( x + 4 ) + ( x + 6 ) + ( x + 8 ) = 50 5 x = 55 - 20 = 35 x = 7 . age of the youngest child = x = 7 years . answer : b\"" + }, + { + "Answer": 0.24999999999999994, + "Options": "a ) 1 / 4 , b ) 19 / 16 , c ) 15 / 16 , d ) 9 / 13 , e ) 0", + "Correct": "a", + "Explanation": "we need to simplify the expression using pemdas . parentheses exponents multiplication anddivision addition andsubtraction the calculation of an equation or expression must be carried out in the following order : 1 ) operations within parentheses ( or absolute value bars or radicals ) 2 ) exponents 3 ) multiplication and division from left to right 4 ) addition and subtraction from left to right the answer is a ." + }, + { + "Answer": 37, + "Options": "a ) 37 sec , b ) 89 sec , c ) 36 sec , d ) 87 sec , e ) 45 sec", + "Correct": "a", + "Explanation": "\"speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 250 + 120 = 370 m . time taken = 370 / 10 = 37 sec . answer : a\"" + }, + { + "Answer": 49.99999999999999, + "Options": "a ) 14.3 % , b ) 16.67 % , c ) 33 % , d ) 28.6 % , e ) 49.67 %", + "Correct": "e", + "Explanation": "the exam gives us a number that is easily divisible by 7 to pique our curiosity and tempt us into calculating actual numbers ( also because otherwise the ratio would be incorrect ) . since the question is about percentages , the actual numbers will be meaningless , as only the ratio of that number versus others will be meaningful . nonetheless , for those who are curious , each 1 / 7 portion represents ( 14210 / 7 ) 2,030 employees . this in turn means that 4,060 employees are journeymen and the remaining 10,150 are full time workers . if half the journeymen were laid off , that would mean 1 / 7 of the total current workforce would be removed . this statistic is what leads many students to think that since half the journeymen are left , the remaining journeymen would represent half of what they used to be , which means 1 / 7 of the total workforce . if 1 / 7 of the workforce is journeymen , and 1 / 7 is roughly 14.3 % , then answer choice a should be the right answer . in this case , though , it is merely the tempting trap answer choice . what changed between the initial statement and the final tally ? well , you let go of 1 / 7 of the workforce , so the total number of workers went down . the remaining workers are still 1 / 7 of the initial workers , but the group has changed . the new workforce is smaller than the original group , specifically 6 / 7 of it because 1 / 7 was eliminated . the remaining workers now account for 1 / 7 out of 6 / 7 of the force , which if we multiply by 7 gives us 1 out of 6 . this number as a percentage is answer choice b , 49.67 % . using the absolute numbers we calculated before , there were 4,060 journeymen employees out of 14,210 total . if 2,030 of them are laid off , then there are 2,030 journeyman employees left , but now out of a total of ( 14,210 - 2,030 ) 12,180 employees . 2,030 / 12,180 is exactly 1 / 6 , or 16.67 % . the answer will work with either percentages or absolute numbers , but the percentage calculation will be significantly faster and applicable to any similar situation . the underlying principle of percentages ( and , on a related note , ratios ) can be summed up in the brainteaser i like to ask my students : if you \u2019 re running a race and you overtake the 2 nd place runner just before the end , what position do you end up in ? the correct answer is 2 nd place . percentages , like ratios and other concepts of relative math , depend entirely on the context . whether 100 % more of something is better than 50 % more of something else depends on the context much more than the percentages quoted . when it comes to percentages on the gmat , the goal is to understand them enough to instinctively not fall into the traps laid out for you . e" + }, + { + "Answer": 2.5, + "Options": "a ) 1 , b ) 1.5 , c ) 2 , d ) 2.5 , e ) 3", + "Correct": "d", + "Explanation": "8 ounces * 8 times / day = 64 ounces of water = 64 * 0.0078125 = 0.5 gallon . 5 days need 0.5 * 5 = 2.5 gallons . correct option : 2.5 answer : d" + }, + { + "Answer": 9.237333333333334, + "Options": "a ) 0.092 , b ) 0.92 , c ) 9.2 , d ) 92 , e ) 920", + "Correct": "c", + "Explanation": "\"( 69.28 \u00d7 0.004 ) / 0.03 1 . 0.004 = 4 \u00d7 10 ^ ( - 3 ) 2 . 0.03 = 3 \u00d7 10 ^ ( - 2 ) 3 . ( a \u00d7 b ) / c = a \u00d7 ( b / c ) 4 . 0.004 / 0.03 = 4 \u00d7 10 ^ ( - 3 ) / ( 3 \u00d7 10 ^ ( - 2 ) ) = 4 \u00d7 10 ^ ( - 3 - ( - 2 ) ) / 3 = 4 \u00d7 10 ^ ( - 1 ) / 3 = ( 4 / 3 ) \u00d7 10 ^ ( - 1 ) = 1.333 \u00d7 10 ^ ( - 1 ) therefore , ( 69.28 \u00d7 0.004 ) / 0.03 = 69.28 \u00d7 ( 0.004 / 0.03 ) = 69.28 \u00d7 1.33 \u00d7 10 ^ ( - 1 ) = 69.28 \u00d7 1.33 / 10 = 6.928 * 1.33 now , 7 \u00d7 2 = 14 7 \u00d7 1 = 7 or better : 6.9 \u00d7 1 = 6.9 6.9 \u00d7 2 = 13.8 hence , 6.9 < 6.928 \u00d7 1.33 < 13.8 9.2 is the only answer that satisfies this condition . answer : c\"" + }, + { + "Answer": 0.7272727272727273, + "Options": "a ) 3 / 5 , b ) 5 / 7 , c ) 8 / 11 , d ) 11 / 15 , e ) 13 / 20", + "Correct": "c", + "Explanation": "p ( 2 cherry ) = 3 / 11 * 2 / 10 = 6 / 110 p ( 2 orange ) = 4 / 11 * 3 / 10 = 12 / 110 p ( 2 lemon ) = 4 / 11 * 3 / 10 = 12 / 110 p ( 2 of the same flavor ) = 30 / 110 p ( 2 different flavors ) = 1 - 30 / 110 = 80 / 110 = 8 / 11 the answer is c ." + }, + { + "Answer": 9, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10", + "Correct": "d", + "Explanation": "\"x < y < z to find the least possible value for z - x ; we need to find the values for z and x that can be closest to each other . if x is some even number , then what could be minimum possible odd z . if x is some even number y - x > 5 ; y > x + 5 ; minimum value for y = x + 5 + 2 = x + 7 [ note : x + 5 is as even + odd = odd and nearest odd greater than x + 5 is x + 5 + 2 ] minimum value for z = y + 2 = x + 7 + 2 = x + 9 [ note : z = y + 2 because both z and y are odd . difference between two odd numbers is 2 ] a = z - x = x + 9 - x = 9 ans : d\"" + }, + { + "Answer": 8, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10", + "Correct": "c", + "Explanation": "\"the average daily production was raised by 5 units for n days , which has a weighting of 5 n . 5 n = 95 - 55 = 40 n = 8 the answer is c .\"" + }, + { + "Answer": 28.57142857142857, + "Options": "a ) 25 % , b ) 20 % , c ) 16.67 % , d ) 28.6 % , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : let us assume before increase the petrol will be rs . 100 . after increase it will be rs ( 100 + 40 ) i . e 140 . now , his consumption should be reduced to : - = ( 140 \u2212 100 ) / 140 \u2217 100 . hence , the consumption should be reduced to 28.6 % . answer : d\"" + }, + { + "Answer": 4.200000000000001, + "Options": "a ) 4.2 , b ) 4.4 , c ) 4.6 , d ) 5.6 , e ) 5.7", + "Correct": "a", + "Explanation": "\"sum of the remaining two numbers = ( 3.95 * 6 ) - [ ( 3.8 * 2 ) + ( 3.85 * 2 ) ] = 8.4 . required average = ( 8.4 / 2 ) = 4.2 . a\"" + }, + { + "Answer": 120, + "Options": "a ) 110 , b ) 122 , c ) 120 , d ) 125 , e ) 145", + "Correct": "c", + "Explanation": "\"explanation : average of new numbers = 24 * 5 = 120 answer : option c\"" + }, + { + "Answer": 384.00000000000006, + "Options": "a ) s . 300 , b ) s . 360 , c ) s . 389 , d ) s . 384 , e ) s . 323", + "Correct": "d", + "Explanation": "\"( a = 2 / 3 b and b = 1 / 4 c ) = a / b = 2 / 3 and b / c = 1 / 4 a : b = 2 : 3 and b : c = 1 : 4 = 3 : 12 a : b : c = 2 : 3 : 12 a ; s share = 544 * 2 / 17 = rs . 64 b ' s share = 544 * 3 / 17 = rs . 96 c ' s share = 544 * 12 / 17 = rs . 384 . answer : d\"" + }, + { + "Answer": 0.5, + "Options": "a ) 0 , b ) 1 / 3 , c ) 2 / 5 , d ) 1 / 2 , e ) 3 / 5", + "Correct": "d", + "Explanation": "we will have a negative product only if 1 , 2 , 3 , or 4 are selected from set t . p ( negative product ) = 4 / 8 = 1 / 2 the answer is d ." + }, + { + "Answer": 29, + "Options": "a ) 87 , b ) 98 , c ) 30 , d ) 29 , e ) 37", + "Correct": "d", + "Explanation": "\"20 + 22 + 8 * 2 = 58 / 2 = 29 answer : d\"" + }, + { + "Answer": 1050, + "Options": "a ) 872 , b ) 738 , c ) 837 , d ) 840 , e ) 1050", + "Correct": "e", + "Explanation": "\"20 % of x = x / 5 ; 15 % of 1500 = 15 / 100 * 1500 = 225 given that , x / 5 = 225 - 15 = > x / 5 = 210 = > x = 1050 . answer : e\"" + }, + { + "Answer": 78, + "Options": "a ) 50 , b ) 52 , c ) 69 , d ) 78 , e ) 84", + "Correct": "d", + "Explanation": "\"sum of 5 integer ( a , b , c , d , e ) = 5 * 70 = 350 e - a = 10 i . e . e = a + 10 for e to be maximum remaining 4 must be as small as possible since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers i . e . a + a + a + a + ( a + 10 ) = 350 i . e . 5 a = 340 i . e . a = 68 i . e . largest e = 68 + 10 = 78 answer : option d\"" + }, + { + "Answer": 7776, + "Options": "a ) 6 , b ) 36 , c ) 216 , d ) 1296 , e ) 7776", + "Correct": "e", + "Explanation": "\"x * ( 1 / 6 ) ^ 2 = 6 ^ 3 x = 6 ^ 2 * 6 ^ 3 = 6 ^ 5 = 7776 the answer is e .\"" + }, + { + "Answer": 3.999999999999936, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "d", + "Explanation": "\"( 1054 / 23 ) gives a remainder 19 so we need to add 4 . the answer is d .\"" + }, + { + "Answer": 300, + "Options": "a ) 100 , b ) 200 , c ) 300 , d ) 350 , e ) 400", + "Correct": "c", + "Explanation": "\"7 x / 10 - x / 3 = 110 11 x / 30 = 110 x = 300 answer : c\"" + }, + { + "Answer": 8000, + "Options": "a ) 7000 , b ) 8000 , c ) 8800 , d ) 8900 , e ) 9000", + "Correct": "b", + "Explanation": "\"state a and state b had an equal number of candidates appeared . in state a , 6 % candidates got selected from the total appeared candidates in state b , 7 % candidates got selected from the total appeared candidates but in state b , 80 more candidates got selected than state a from these , it is clear that 1 % of the total appeared candidates in state b = 80 = > total appeared candidates in state b = 80 x 100 = 8000 = > total appeared candidates in state a = total appeared candidates in state b = 8000\"" + }, + { + "Answer": 27, + "Options": "a ) 22 , b ) 33 , c ) 55 , d ) 27 , e ) 88", + "Correct": "d", + "Explanation": "\"let f = pure fuji , g = pure gala and c - cross pollinated . c = 10 % of x where x is total trees . c = . 1 x also 3 x / 4 = f and c + f = 153 = > . 1 x + 3 / 4 x = 153 = > x = 180 180 - 153 = pure gala = 27 . d\"" + }, + { + "Answer": 273, + "Options": "a ) 115 , b ) 273 , c ) 117 , d ) 118 , e ) 119", + "Correct": "b", + "Explanation": "\"x : y : z = 100 : 45 : 50 20 : 9 : 10 9 - - - 63 39 - - - ? = > 273 answer : b\"" + }, + { + "Answer": 0.30337078651685395, + "Options": "a ) 21 / 29 , b ) 27 / 89 , c ) 89 / 21 , d ) 29 / 21 , e ) none", + "Correct": "b", + "Explanation": "1 / [ 3 + ( 1 / ( 3 + 1 / ( 3 - 1 / 3 ) ) ) ] = > 1 / [ 3 + 1 / ( 3 + 1 / ( 8 / 3 ) ) ] = > 1 / [ 3 + 1 / ( 3 + 3 / 8 ) ] = > 1 / [ 3 + 8 / 27 ] = > 1 / ( 89 / 27 ) = > 27 / 89 b" + }, + { + "Answer": 3, + "Options": "a ) 9 , b ) 2 , c ) 3 , d ) 7 , e ) 12", + "Correct": "c", + "Explanation": "\"2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 31 - 25 = 6 ab = 3 . answer : c\"" + }, + { + "Answer": 5, + "Options": "a ) 2 , b ) 5 , c ) 6 , d ) 7 , e ) 8", + "Correct": "b", + "Explanation": "solution : let the two digit number be xy . 4 ( x + y ) + 3 = 10 x + y . . . . . . . ( 1 ) 10 x + y + 18 = 10 y + x . . . . ( 2 ) solving 1 st equation we get 2 x - y = 1 . . . . . ( 3 ) solving 2 nd equation we get y - x = 2 . . . . . ( 4 ) solving 3 and 4 , we get x = 3 and y = 5 answer : b" + }, + { + "Answer": 30, + "Options": "a ) 30 , b ) 19 , c ) 22 , d ) 3 , e ) 90", + "Correct": "a", + "Explanation": "answer is 30 no of digits between 311 and 401 ( exclusive ) = 401 - 311 - 1 = 89 no intergers divisble by 3 = ~ 89 / 3 ~ 30 divsiblivity rule for 3 is sum of all digits must be divisble by 3 . it does n ' t matter if hundred digit and tens digits are switched . e . g 372 is divisble by 3 ( becae 3 + 7 + 2 = 12 ( divisble by 3 ) ) switch digits 732 also divisble by 3 ( becae 7 + 3 + 2 = 12 ( divisble by 3 ) ) divsiblivity rule for 3 is sum of all digits must be divisble by 3 . it does n ' t matter if hundred digit and tens digits are switched . you have right . so it is enough to proceed like usual to find the numbers in a given range that are divisible by 3 . so 399 - 312 / 3 + 1 = 30 . answer : a" + }, + { + "Answer": 99, + "Options": "a ) - 99 % , b ) - 100 % , c ) + 99 % , d ) + 100 % , e ) none", + "Correct": "a", + "Explanation": "solution : actual result = 10 x by mistake it has been divided by 10 = x / 10 % change = [ 10 x - ( 10 / x ) / 10 x ] * 100 = 99 = - 99 % . since , actual value is greater than the wrong value . alternatively , let , x = 10 actual result = 10 * 10 = 100 wrong result = 10 / 10 = 1 . change = ( 1 - 100 ) = - 99 % change = - 99 % . answer : option a" + }, + { + "Answer": 3, + "Options": "a ) 1 / 6 , b ) 1 / 3 , c ) 10 / 21 , d ) 1 / 2 , e ) 3 / 1", + "Correct": "e", + "Explanation": "assume x = 3002 ( 1.2 x ) / ( 0.5 x - 406 ) = 3602.4 / ( 3002 * 0.5 - 406 ) = 3602.4 / 1095 = = 3 / 1 e" + }, + { + "Answer": 1010, + "Options": "a ) 1008 , b ) 1010 , c ) 1022 , d ) 1032 , e ) 1043", + "Correct": "b", + "Explanation": "required number = ( l . c . m of 12 , 16 , 18 , 21,28 ) + 2 = 1008 + 2 = 1010 answer : b" + }, + { + "Answer": 0.09523809523809523, + "Options": "a ) 2 / 69 , b ) 2 / 21 , c ) 2 / 23 , d ) 2 / 29 , e ) 2 / 10", + "Correct": "b", + "Explanation": "explanation : let a be the event that x is selected and b is the event that y is selected . p ( a ) = 1 / 3 , p ( b ) = 2 / 7 . let c be the event that both are selected . p ( c ) = p ( a ) \u00e3 \u2014 p ( b ) as a and b are independent events : = ( 1 / 3 ) \u00e3 \u2014 ( 2 / 7 ) = 2 / 21 answer : b ) 2 / 21" + }, + { + "Answer": 0.3333333333333333, + "Options": "a ) 1 / 12 , b ) 1 / 8 , c ) 1 / 6 , d ) 1 / 3 , e ) 2 / 3", + "Correct": "d", + "Explanation": "\"let us say probability of a occurring is a . let us say probability of b occurring is b . a = 2 b probability ( either a or b or both ) = 8 times probability ( a and b ) a * ( 1 - b ) + b * ( 1 - a ) + ab = 8 * ab substituting a = 2 b in the second equation : 2 b * ( 1 - b ) + b * ( 1 - 2 b ) + 2 b * b = 8 * 2 b * b 3 b - 2 b ^ 2 = 16 b ^ 2 3 b = 18 b ^ 2 b = 3 / 18 = 1 / 6 so , a = 2 b = 1 / 3 answer : d\"" + }, + { + "Answer": 65, + "Options": "a ) - 5 , b ) 8 , c ) - 6 , d ) - 3 , e ) - 8", + "Correct": "b", + "Explanation": "answer : b" + }, + { + "Answer": 49.99999999999999, + "Options": "a ) 10 , b ) 12 , c ) 50 , d ) 18 , e ) 19", + "Correct": "c", + "Explanation": "2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 164 - 64 = 100 = > ab = 50 answer : c" + }, + { + "Answer": 640, + "Options": "a ) a ) 220 , b ) b ) 490 , c ) c ) 380 , d ) d ) 450 , e ) e ) 640", + "Correct": "e", + "Explanation": "\"the only thing you have to do is a simple multiply we have : 20 * 32 = 640 correct answer is : e ) 640\"" + }, + { + "Answer": 22500, + "Options": "a ) 18000 , b ) 22500 , c ) 24000 , d ) 26000 , e ) 32000", + "Correct": "b", + "Explanation": "z = 25 - - > y received 2 / 5 fewer votes than z - - > y = z - 2 / 5 * z = 15 ; x received 1 / 2 more votes than y - - > x = y + 1 / 2 * y = 22,5 . answer : b ." + }, + { + "Answer": 25920, + "Options": "a ) $ 24960 , b ) $ 25920 , c ) $ 28080 , d ) $ 28500 , e ) $ 29160", + "Correct": "b", + "Explanation": "from 9 : 00 in the morning to 4 : 55 in the afternoon , inclusive there are 8 * 12 = 96 five - minute intervals , thus total of 96 * 30 tickets were sold . say x student and 3 x regular tickets were sold , then x + 3 x = 96 * 30 - - > x = 24 * 30 and 3 x = 3 * ( 24 * 30 ) = 24 * 90 . therefore , the total revenue from ticket sales that day was 24 * 30 * 6 + 24 * 90 * 10 = $ 25,920 . answer : b ." + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 7 , c ) 10 , d ) 12 , e ) 14", + "Correct": "a", + "Explanation": "\"let the number of cows be x and their legs be 4 x . let the number of chicken be y and their legs be 2 x . total number of legs = 4 x + 2 y . total number of heads = x + y . the number of legs was 12 more than twice the number of heads . therefore , 2 \u00d7 ( x + y ) + 14 = 4 x + 2 y . or , 2 x + 2 y + 12 = 4 x + 2 y . or , 2 x + 12 = 4 x [ subtracting 2 y from both sides ] . or , 12 = 4 x \u2013 2 x [ subtracting 2 x from both sides ] . or , 12 = 2 x . or , x = 6 [ dividing by 2 on both sides ] . therefore , the number of cows = 6 . correct answer : a ) 6\"" + }, + { + "Answer": 10, + "Options": "a ) 5 , b ) 10 , c ) 12 , d ) 14 , e ) 15", + "Correct": "b", + "Explanation": "\"2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 29 - 9 = 20 ab = 10 . b )\"" + }, + { + "Answer": 5, + "Options": "a ) 5 : 2 , b ) 5 : 1 , c ) 4 : 3 , d ) 4 : 1 , e ) 3 : 1", + "Correct": "b", + "Explanation": "\"we ' re given a few facts to work with : 1 ) the average height of the females is 170 cm 2 ) the average height of the males is 182 cm 3 ) the average of the group is 180 cm we ' re asked for the ratio of men to women . w = number of women m = number of men ( 170 w + 182 m ) / ( w + m ) = 180 170 w + 182 m = 180 w + 180 m 2 m = 10 w m = 5 w m / w = 5 / 1 the ratio of men to women is 5 to 1 . b\"" + }, + { + "Answer": 0.023809523809523808, + "Options": "a ) 3 / 14 , b ) 2 / 7 , c ) 1 / 3 , d ) 1 / 42 , e ) 12 / 21", + "Correct": "d", + "Explanation": "both dice addition result is 13 = ( 6 + 7 ) probability that the number on first die is 6 = 1 / 6 probability that the number on second die is 7 = 1 / 7 probability that both dice addition result is 13 = 1 / 6 * 1 / 7 = 1 / 42 d" + }, + { + "Answer": 7, + "Options": "a ) 35 , b ) 7 , c ) 45 , d ) 49 , e ) 54", + "Correct": "b", + "Explanation": "first step will be to break down all the numbers into their prime factors . 105 = 3 * 5 * 7 21 = 7 * 3 25 = 5 * 5 315 = 3 * 3 * 5 * 7 so , ( 105 ) ^ 3 = 3 * 7 * 5 * 5 * 3 * 3 * 5 * 7 * b therefore ( 3 * 5 * 7 ) ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 ^ 2 * b therefore , b = 3 ^ 3 * 5 ^ 3 * 7 ^ 3 / 3 ^ 3 * 5 ^ 3 * 7 ^ 2 b = 7 correct answer b ." + }, + { + "Answer": 0.0625, + "Options": "a ) 1 / 16 , b ) 7 / 8 , c ) 9 / 64 , d ) 5 / 64 , e ) 3 / 64", + "Correct": "a", + "Explanation": "\"p ( xavier will solve ) = 1 / 3 p ( yvonne will solve ) = 1 / 2 p ( zelda will not solve ) = 1 - 5 / 8 = 3 / 8 . now , we need to multiply all this ps to find an answer : p = ( 1 / 3 ) * ( 1 / 2 ) * ( 3 / 8 ) = 1 / 16 . ans . a .\"" + }, + { + "Answer": 78.4, + "Options": "a ) $ 54.00 , b ) $ 78.40 , c ) $ 90.00 , d ) $ 100.80 , e ) $ 154.80", + "Correct": "b", + "Explanation": "correct answer : b the tourist must pay tax on $ 1720 - $ 600 = $ 1120 . thus , the amount of tax he has to pay is 0.07 ( $ 1120 ) = $ 78.40 . the correct answer is b ." + }, + { + "Answer": 26, + "Options": "a ) 22 , b ) 278 , c ) 267 , d ) 176 , e ) 971", + "Correct": "d", + "Explanation": "answer : d" + }, + { + "Answer": 179, + "Options": "a ) 187.89 cm , b ) 179.29 cm , c ) 123.98 cm , d ) 149.98 cm , e ) 146.89 cm", + "Correct": "b", + "Explanation": "\"calculated average height of 35 boys = 181 cm . wrong total height of 35 boys = 181 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 181 cm - ( 166 cm - 106 cm ) / 35 = 181 cm - ( 166 cm - 106 cm ) / 35 = 181 cm - 60 / 35 cm = 181 cm - 1.71 cm = 179.29 cm . answer : b\"" + }, + { + "Answer": 659.9999999999999, + "Options": "a ) 100 , b ) 200 , c ) 300 , d ) 350 , e ) 660", + "Correct": "e", + "Explanation": "\"5 x / 10 - x / 3 = 110 1 x / 6 = 110 x = 660 answer : e\"" + }, + { + "Answer": 20, + "Options": "a ) 19 , b ) 35 , c ) 20 , d ) 32 , e ) 21", + "Correct": "c", + "Explanation": "\"c 20 age of b = age of ( a + b + c ) \u2013 age of ( a + c ) = 26 \u00d7 3 \u2013 29 \u00d7 2 = 78 \u2013 58 = 20 years\"" + }, + { + "Answer": 80000, + "Options": "a ) 26799 , b ) 24000 , c ) 80000 , d ) 29973 , e ) 12312", + "Correct": "c", + "Explanation": "\"x * ( 80 / 100 ) = 64000 x = 800 * 100 x = 80000 answer : c\"" + }, + { + "Answer": 11000, + "Options": "a ) 12000 , b ) 11000 , c ) 10000 , d ) 13000 , e ) 15000", + "Correct": "b", + "Explanation": "the average price of 20 products is $ 1,200 means that the total price of 20 products is 20 * 1,200 = $ 24,000 . next , since exactly 10 of the products sell for less than $ 1,000 , then let ' s make these 10 items to be at $ 400 each ( min possible ) . now , the remaining 9 items can not be priced less than $ 1,000 , thus the minimum possible price of each of these 9 items is $ 1,000 . thus the minimum possible value of 19 products is 10 * 400 + 9 * 1,000 = $ 13,000 . therefore , the greatest possible selling price of the most expensive product is $ 24,000 - $ 13,000 = $ 11,000 . answer : b ." + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) 24 , c ) data inadequate , d ) none of these , e ) 34", + "Correct": "a", + "Explanation": "\"solution ( a + b ) - ( b + c ) = 12 \u21d4 a - c = 12 . answer a\"" + }, + { + "Answer": 9020, + "Options": "a ) 4520 , b ) 9100 , c ) 9150 , d ) 8120 , e ) 9020", + "Correct": "e", + "Explanation": "\"( 9000 + 20 ) / 90 * 90 = 9020 answer : e\"" + }, + { + "Answer": 125, + "Options": "a ) 123 , b ) 267 , c ) 125 , d ) 267 , e ) 120", + "Correct": "c", + "Explanation": "\"let xx be the number he chose , then 2 \u00e2 \u2039 \u2026 x \u00e2 \u02c6 \u2019 138 = 112 x = 125 answer : c\"" + }, + { + "Answer": 4028, + "Options": "a ) 4028 , b ) 4026 , c ) 4248 , d ) 4538 , e ) 9028", + "Correct": "a", + "Explanation": "\"= ( 45 + 23 / 89 ) \u00d7 89 = ( 4005 + 23 ) / 89 \u00d7 89 = 4028 / 89 \u00d7 89 = 4028 answer is a .\"" + }, + { + "Answer": 32, + "Options": "a ) 45 , b ) 32 , c ) 47 , d ) 48 , e ) 49", + "Correct": "b", + "Explanation": "the total present age of father and two sons is 3 x 24 = 72 yrs the total present age of sons is ( 15 + 5 ) x 2 = 40 years so , present age of father is 72 \u00e2 \u20ac \u201c 40 = 32 yrs answer b" + }, + { + "Answer": 0.52, + "Options": "a ) $ 0.52 , b ) $ 0.80 , c ) $ 1.00 , d ) $ 1.20 , e ) $ 1.60", + "Correct": "a", + "Explanation": "let price of a sundae = s price of ice cream bar = . 6 $ 225 * . 6 + 125 * s = 200 = > 125 * s = 65 = > s = 0.52 answer a" + }, + { + "Answer": 220050, + "Options": "a ) 145646 , b ) 236578 , c ) 645353 , d ) 456546 , e ) 220050", + "Correct": "e", + "Explanation": "\"( 555 + 445 ) * 2 * 110 + 50 = 220000 + 50 = 220050 e\"" + }, + { + "Answer": 30, + "Options": "a ) 30 , b ) 40 , c ) 45 , d ) 50 , e ) 56", + "Correct": "a", + "Explanation": "when a number n = a ^ x * b ^ y , where a and b are prime numbers , and x , y are positive integers , the number of divisors of n = ( x + 1 ) ( y + 1 ) therefore , the answer is a . 5 * 6 = 30" + }, + { + "Answer": 24, + "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 21 , e ) 24", + "Correct": "e", + "Explanation": "\"total marks of male = m total marks of female = f number of males = 8 number of females = f given : ( m + f ) / ( 8 + f ) = 90 - - - - - - - - - - - - - 1 also given , m / 8 = 84 thus m = 672 - - - - - - - - - 2 also , f / f = 92 thus f = 92 f - - - - - - - - - 3 put 2 and 3 in 1 : we get ( 672 + 92 f ) / ( 8 + f ) = 90 solving this we get f = 24 ans : e\"" + }, + { + "Answer": 4, + "Options": "a ) 4 , b ) 7 , c ) 8 , d ) 16 , e ) none of these", + "Correct": "a", + "Explanation": "49 \u00e3 \u2014 49 = 7 ? or , 7 ( 2 ) \u00e3 \u2014 7 ( 2 ) = 7 ? or 7 ( 4 ) = 7 ? or , ? = 4 answer a" + }, + { + "Answer": 16, + "Options": "a ) 12 , b ) 16 , c ) 20 , d ) 24 , e ) 28", + "Correct": "b", + "Explanation": "\"11 x + 60 = 12 ( x + 4 ) x = 12 + 4 = 16 answer : b\"" + }, + { + "Answer": 7, + "Options": "a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 9", + "Correct": "d", + "Explanation": "\"the units digit of 73 ^ 351 will be the same as the units digit of 3 ^ 351 3 ^ 1 = 3 - - > the units digit is 3 ; 3 ^ 2 = 9 - - > the units digit is 9 ; 3 ^ 3 = 27 - - > the units digit is 7 ; 3 ^ 4 = 81 - - > the units digit is 1 ; 3 ^ 5 = 243 - - > the units digit is 3 again ; . . . so , as you can see the units digit repeats in blocks of 4 : { 3 , 9 , 7 , 1 } , { 3 , 9 , 7 , 1 } , . . . now , since 351 = 348 + 3 = ( multiple of 4 ) + 3 , then the units digit of 3 ^ 351 will be the third number in the pattern thus 7 . answer : d .\"" + }, + { + "Answer": 22.142857142857142, + "Options": "a ) 21 , b ) 20 , c ) 22 , d ) 30 , e ) 45", + "Correct": "c", + "Explanation": "let number is x . when 5 added to it , = ( x + 5 ) 7 multiplied to sum , = 7 * ( x + 5 ) now , = [ { 7 * ( x + 5 ) } / 5 ] and , = [ { 7 * ( x + 5 ) } / 5 ] - 5 according to question , [ { 7 * ( x + 10 ) } / 5 ] - 5 = half of 66 [ ( 7 x + 35 ) / 5 ) = 33 + 5 7 x + 35 = 38 * 5 x = 155 / 7 x = 22.14 = 22 so , required number is : 22 . answer : c" + }, + { + "Answer": 191.66666666666666, + "Options": "a ) $ 28 , b ) $ 82 , c ) $ 110 , d ) $ 138 , e ) $ 193", + "Correct": "e", + "Explanation": "\"by the question , the equation would be 150 p - 83 * 150 - 16500 = 0 p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component . solving the equation , we get p = $ 193 . answer e for me .\"" + }, + { + "Answer": 1830, + "Options": "a ) 1839 , b ) 2830 , c ) 1830 , d ) 1831 , e ) 1835", + "Correct": "c", + "Explanation": "\"solution we know that ( 1 + 2 + 3 + . . . . . + 60 ) = n ( n + 1 ) / 2 therefore ( 1 + 2 + 3 + . . . . + 60 ) = ( 60 \u00d7 61 / 2 ) = 1830 . answer c\"" + }, + { + "Answer": 2, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "b", + "Explanation": "assume number of respective animals are x , y , z . x + y + z = 20 - - - ( 1 ) as the total number of animal has to be 20 amt of milk will be 4 x + ( 1 / 2 ) y + ( 1 / 4 ) z = 20 - - - ( 2 ) solving equation 1 and 2 we get 15 x + y = 60 - - - - ( 3 ) since buffalo gives 4 litre and total milk is 20 , x < 5 but from eq 3 , x can not be more than 4 ; further if x = 1 or 2 ; y > 20 . . . not possible , since total animal is 20 thus , x = 3 , y = 15 , z = 2 2 goats answer : b" + }, + { + "Answer": 35, + "Options": "a ) 40 , b ) 50 , c ) 62 , d ) 45 , e ) 35", + "Correct": "e", + "Explanation": "\"let the average after 11 th inning = x then , average after 10 th inning = x - 5 10 ( x - 5 ) + 85 = 11 x x = 85 - 50 = 35 answer is e\"" + }, + { + "Answer": 89100, + "Options": "a ) 89100 , b ) 81028 , c ) 27772 , d ) 29889 , e ) 22312", + "Correct": "a", + "Explanation": "70400 * 9 / 8 * 9 / 8 = 89100 . answer : a" + }, + { + "Answer": 10, + "Options": "a ) 5 , b ) 8 , c ) 4 , d ) 10 , e ) 3", + "Correct": "d", + "Explanation": "\"2 ab = ( a ( power 2 ) + b ( power 2 ) - ( a - b ) ( power 2 ) = 29 - 9 = 20 ab = 10 . answer is d .\"" + }, + { + "Answer": 7, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 0 , e ) 1", + "Correct": "a", + "Explanation": "\"39 + 20 = 59 / 13 = 7 ( remainder ) answer : a\"" + }, + { + "Answer": 50, + "Options": "a ) a + 5 , b ) a + 10 , c ) a + 25 , d ) a + 50 , e ) 2 a + 5", + "Correct": "d", + "Explanation": "in case of consecutive integers or integers in arithmetic progression mean = median i . e . median = a / 5 = mean = third integer first integer = a / 5 - 4 second integer = a / 5 - 2 third integer = a / 5 fourth integer = a / 5 + 2 fifth integer = a / 5 + 4 i . e . sixth integer = a / 5 + 6 seventh integer = a / 5 + 8 eighth integer = a / 5 + 10 ninth integer = a / 5 + 12 tenth integer = a / 5 + 14 now mean of next 5 integers = median = a / 5 + 5 i . e . sum of next 5 integers = ( a / 5 + 10 ) * 5 = a + 50 answer : option d" + }, + { + "Answer": 64.8, + "Options": "a ) 23 , b ) 87 , c ) 26 , d ) 64.8 , e ) 01", + "Correct": "d", + "Explanation": "explanation : the number is 1 / 3 of 1 / 4 is = 15 then 1 / 3 \u00e3 \u2014 1 / 4 = 18 number is 216 then 216 \u00e3 \u2014 3 / 10 = 64.8 answer : d" + }, + { + "Answer": 0.3125, + "Options": "a ) 1 / 3 , b ) \u00bc , c ) 9 / 25 , d ) 5 / 16 , e ) 0", + "Correct": "d", + "Explanation": "\"prime digits are : 2 , 3 , 5 , 7 total number of 2 digit # s with both digits prime are : 4 * 4 = 16 out of these numbers divisible by 3 = 33 , 27 , 57 , 72 and 75 . i had to find the numbers manually using the 4 numbers above . = > prob = 5 / 16 . ans d . took me 3 : 20 mins .\"" + }, + { + "Answer": 170, + "Options": "a ) 170 , b ) 130 , c ) 150 , d ) 120 , e ) 180", + "Correct": "a", + "Explanation": "\"explanation : 690 - 10 = 680 , 875 \u2013 25 = 850 highest number that can divide 680 and 850 exactly is hcm of the numbers . hcf of 680 and 850 = 170 answer : a\"" + }, + { + "Answer": 61376, + "Options": "a ) 61376 , b ) 54411 , c ) 612314 , d ) 64170 , e ) 64171", + "Correct": "a", + "Explanation": "the three digit natural numbers divisible by 8 are 104 , 112 , 120 , \u2026 . 992 . let sndenote their sum . that is , sn = 104 112 120 128 , 992 g + + + + + . now , the sequence 104 , 112 , 120 , g , 992 forms an a . p . a = 104 , d = 8 , l = 992 n = l - a / d n = 112 s 112 = n / 2 ( a + l ) = 61376 option a" + }, + { + "Answer": 0.5, + "Options": "a ) 1 / 5 , b ) 1 / 2 , c ) 2 / 3 , d ) 1 / 4 , e ) 2 / 5", + "Correct": "b", + "Explanation": "\"x : 0.5 % is 0.15 % - points from 0.65 % . y : 0.8 % is 0.15 % - points from 0.65 % . therefore the ratio of products checked by y : x is 1 : 1 . thus , worker y checked 1 / 2 of the products . the answer is b .\"" + }, + { + "Answer": 13, + "Options": "a ) 0 , b ) 2 , c ) 12 , d ) 13 , e ) 15", + "Correct": "d", + "Explanation": "the range q of a set is the difference between the largest and smallest elements of a set . without x , the difference between the largest and smallest elements of a set is 14 - 3 = 11 < 12 , which means that in order 12 to be the range of the set x must be either the smallest element so that 14 - x = 12 - - - > x = 2 or x must the largest element so that x - 3 = 12 - - > x = 15 . the the difference between the greatest possible value of x and least possible value of x is 15 - 2 = 13 . answer : d ." + }, + { + "Answer": 16.98888888888889, + "Options": "a ) 21.84 , b ) 12.84 , c ) 16.98 , d ) 24.84 , e ) 15.84", + "Correct": "c", + "Explanation": "\"dinner bill of 9 person = 139 + 10 % tip so , 10 % of 139 = ( 139 * 10 ) / 100 = 13.9 so , the actual total amount = 139 + 13.9 = $ 152.9 so per head bill = 152.9 / 9 = $ 16.98 answer : c\"" + }, + { + "Answer": 7, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 7", + "Correct": "e", + "Explanation": "\"9 ^ y = 3 ^ 2 y = 3 ^ 14 2 y = 14 y = 7 the answer is e .\"" + }, + { + "Answer": 540, + "Options": "a ) 540 , b ) 570 , c ) 619 , d ) 649 , e ) 700", + "Correct": "a", + "Explanation": "\"before price increase price = b after 30 % price increase price = b + ( 30 / 100 ) * b = 1.3 b = 351 ( given ) i . e . b = 351 / 1.3 = $ 270 i . e . 2 b = 2 * 270 = 540 answer : option a\"" + }, + { + "Answer": 2000, + "Options": "a ) 1287 , b ) 2887 , c ) 2000 , d ) 1129 , e ) 1192", + "Correct": "c", + "Explanation": "\"let money invested by raghu = rs . x money invested by trishul = 9 / 10 x = 0.9 x money invested by vishal = 9 / 10 x * 110 / 100 = 0.99 x also , x + 0.9 x + 0.99 x = 5780 = x = 5780 / 2.89 = 2000 therefore , amount invested by raghu is rs . 2000 . answer : c\"" + }, + { + "Answer": 93, + "Options": "a ) 52 , b ) 49 , c ) 95 , d ) 88 , e ) 93", + "Correct": "e", + "Explanation": "\"right side = 15 seat left side = 15 - 3 ( 3 few seat in right side ) = 12 seat total = 15 + 12 = 27 people can seat in 27 seat = 27 * 3 = 81 people can seat in last seat = 12 total people can seat = 81 + 12 = 93 answer : e\"" + }, + { + "Answer": 4100, + "Options": "a ) 256 , b ) 512 , c ) 4096 , d ) 1024 , e ) 1536", + "Correct": "c", + "Explanation": "\"0.4 * 2 ^ 10 = 0.4 * 1024 = 409.6 the answer is c .\"" + }, + { + "Answer": 36, + "Options": "a ) 34 , b ) 35 , c ) 36 , d ) 37 , e ) 38", + "Correct": "c", + "Explanation": "\"( 6 ^ 3 ) ^ 16 * 6 ^ 2 / 215 ( 215 + 1 ) ^ 16 * 6 ^ 2 / 215 1 ^ 16 * 6 ^ 2 / 215 = 36 answer : c\"" + }, + { + "Answer": 35, + "Options": "a ) 15 , b ) 25 , c ) 35 , d ) 45 , e ) 55", + "Correct": "c", + "Explanation": "\"let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 50 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 50 + 20 ) / 2 = 35 . answer : c\"" + }, + { + "Answer": 3, + "Options": "a ) 8 , b ) 10 , c ) 3 , d ) 6 , e ) 5", + "Correct": "c", + "Explanation": "\"46 x + 78 = 54 ( x + 1 ) = > 8 x = 24 = > x = 3 answer : c\"" + }, + { + "Answer": 48, + "Options": "a ) 20 , b ) 36 , c ) 48 , d ) 60 , e ) 72", + "Correct": "c", + "Explanation": "answer c . we know that saren negotiated a discount of 20 % , so each of them paid $ 4 less . since there are three people , the 20 % of the original price amounts to $ 12 . 5 times 12 $ is 60 $ , so the original price , before saren negotiated the discount , had been $ 60 . they paid $ 12 less than the base price , so they spent $ 48 ." + }, + { + "Answer": 50, + "Options": "a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70", + "Correct": "c", + "Explanation": "\"let number of pounds of 5 $ candy to be used be w 6 = ( 25 * 8 + 5 * w ) / ( 25 + w ) = > 150 + 6 w = 200 + 5 w = > w = 50 answer c\"" + }, + { + "Answer": 2075, + "Options": "a ) 300 , b ) 2075 , c ) 800 , d ) 1000 , e ) 3900", + "Correct": "b", + "Explanation": "\"explanation : let their maximum marks be x . then , 20 % of x = 390 + 25 = > 20 / 100 x = 415 x = ( 41500 / 20 ) x = 2075 . answer : b\"" + }, + { + "Answer": 8870, + "Options": "a ) rs . 5870 , b ) rs . 5991 , c ) rs . 8870 , d ) rs . 6850 , e ) none of these", + "Correct": "c", + "Explanation": "\"explanation : total sale for 5 months = rs . ( 5420 + 5660 + 6200 + 6350 + 6500 ) = rs . 30,130 therefore , required sale = rs . [ ( 6500 * 6 ) \u2013 30,130 ] = rs . ( 39000 \u2013 30,130 ) = rs . 8870 answer c\"" + }, + { + "Answer": 1, + "Options": "a ) 16 / 14 , b ) 8 / 7 , c ) 1 , d ) 7 / 8 , e ) 64 / 49", + "Correct": "c", + "Explanation": "\"a nice fast approach is the first find a pair of numbers that satisfy the given equation : 7 a = 8 b here ' s one pair : a = 8 and b = 7 what is the ratio of a / 8 to b / 7 ? in other words , what is the value of ( a / 8 ) / ( b / 7 ) ? plug in values to get : ( a / 8 ) / ( b / 7 ) = ( 8 / 8 ) / ( 7 / 7 ) = 1 / 1 = 1 c\"" + }, + { + "Answer": 49.69230769230769, + "Options": "a ) 45 % , b ) 49 % , c ) 50 % , d ) 51 % , e ) 62 %", + "Correct": "c", + "Explanation": "total number of votes polled = 4136 + 7636 + 11628 = 23400 required percentage = 11628 * 100 / 23400 = 50 % answer is c" + }, + { + "Answer": 5.303030303030298, + "Options": "a ) 19 % , b ) 15 % , c ) 25 % , d ) 40 % , e ) 5.3 %", + "Correct": "e", + "Explanation": "\"cost of food ( c ) = food consumed per student ( f ) * number of students ( n ) * price of food ( p ) originally , c = fnp when number of students decrease by 12 % , and the price of food increases by 20 % , c = f ( new ) * ( 0.88 n ) * ( 1.2 p ) = > f ( new ) = f / ( 0.88 * 1.2 ) = > f ( new ) = 0.9469 f therefore the new cost of food must be 94.69 % of the old cost , or the cost of food must decrease by 5.3 % ( option e )\"" + }, + { + "Answer": 92, + "Options": "a ) 50 , b ) 40 , c ) 60 , d ) 92 , e ) 70", + "Correct": "d", + "Explanation": "\"we have x + x % of 1150 = 1150 x + x / 100 * 1150 = 1150 25 / 2 * x = 1150 x = 1150 * 2 / 25 = 92 answer is d\"" + }, + { + "Answer": 2705, + "Options": "a ) 2505 , b ) 2509 , c ) 2705 , d ) 2508 , e ) none of them", + "Correct": "c", + "Explanation": "3005 - 3000 + 10 = 3005 - ( 3000 / 10 ) = 3005 - 300 = 2705 . answer is c" + }, + { + "Answer": 114.28571428571429, + "Options": "a ) 110 , b ) 114.28 , c ) 140 , d ) 160 , e ) 214", + "Correct": "b", + "Explanation": "white : yellow = x : ( x + 50 ) = 8 : 15 - - > 15 x = 8 x + 400 - - > x = 57.14 . the total # of balls originally x + x = 57.14 + 57.14 = 114.28 . answer : b ." + }, + { + "Answer": 109, + "Options": "a ) 110 , b ) 100 , c ) 109 , d ) 218 , e ) 210", + "Correct": "c", + "Explanation": "answer let the number be x . then , x - 68 = 150 - x \u00e2 \u2021 \u2019 2 x = 150 + 68 = 218 \u00e2 \u2021 \u2019 2 x = 218 \u00e2 \u02c6 \u00b4 x = 109 correct option : c" + }, + { + "Answer": 171, + "Options": "a ) 163 , b ) 171 , c ) 179 , d ) 185 , e ) 191", + "Correct": "b", + "Explanation": "\"let n - 1 = 2 a . 2 + 4 + . . . + 2 a = 2 * ( 1 + 2 + . . . + a ) = 2 * ( a ) ( a + 1 ) / 2 = ( a ) ( a + 1 ) = 85 * 86 then a = 85 and n = 171 . the answer is b .\"" + }, + { + "Answer": 25.483333333333334, + "Options": "a ) 21.84 , b ) 22.84 , c ) 23.84 , d ) 24.84 , e ) 25.48", + "Correct": "e", + "Explanation": "dinner bill of 6 person = 139 + 10 % tip so , 10 % of 139 = ( 139 * 10 ) / 100 = 13.9 so , the actual total amount = 139 + 13.9 = $ 152.9 so per head bill = 152.9 / 6 = $ 25.48 answer : e" + }, + { + "Answer": 33, + "Options": "a ) 35 , b ) 33 , c ) 48 , d ) 50 , e ) 52", + "Correct": "b", + "Explanation": "production during these 5 days = total production in a month - production in first 25 days . = 30 x 58 - 25 x 63 = 165 \u00e2 \u02c6 \u00b4 average for last 5 days = 165 / 5 = 33 b" + }, + { + "Answer": 20, + "Options": "a ) 9 % , b ) 15 % , c ) 20 % , d ) 50 % , e ) 100 %", + "Correct": "c", + "Explanation": "\"let ' s plug in somenicenumbers and see what ' s needed . let ' s say the employee used to make $ 1 / hour and worked 100 hours / week so , the total weekly income was $ 100 / week after the 25 % wage increase , the employee makes $ 1.25 / hour we want the employee ' s income to remain at $ 100 / week . so , we want ( $ 1.25 / hour ) ( new # of hours ) = $ 100 divide both sides by 1.25 to get : new # of hours = 100 / 1.25 \u2248 80 hours so , the number of hours decreases from 100 hours to ( approximately ) 80 hours . this represents a 20 % decrease ( approximately ) . answer : c\"" + }, + { + "Answer": 7, + "Options": "a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 11", + "Correct": "c", + "Explanation": "\"425897 / 456 = 933 with a remainder of 449 . we need to add 456 - 449 = 7 the answer is c .\"" + }, + { + "Answer": 10, + "Options": "a ) 5 , b ) 7 , c ) 9 , d ) 10 , e ) 12", + "Correct": "d", + "Explanation": "\"option ' d ' 15 / 5 = 3 and 65 / 5 = 13 = = > 13 - 3 = 10 numbers\"" + }, + { + "Answer": 81, + "Options": "a ) 80 , b ) 81 , c ) 82 , d ) 83 , e ) 84", + "Correct": "b", + "Explanation": "solution : mabel handled 90 transactions anthony handled 10 % more transactions than mabel anthony = 90 + 90 \u00d7 10 % = 90 + 90 \u00d7 0.10 = 90 + 9 = 99 cal handled 2 / 3 rds of the transactions than anthony handled cal = 2 / 3 \u00d7 99 = 66 jade handled 15 more transactions than cal . jade = 66 + 15 = 81 jade handled = 81 transactions . answer : b" + }, + { + "Answer": 480, + "Options": "a ) 96 , b ) 240 , c ) 56 , d ) 384 , e ) 480", + "Correct": "e", + "Explanation": "\"1 small box and 17 large boxes = 1 ( 12 ) + 17 ( 16 ) = 12 + 272 = 284 glasses at the minimum since the question asks for the total number of glasses , we can now eliminate answers a , b and c . . . . the difference in the number of boxes must be 16 though , so we could have . . . . 2 small boxes and 18 large boxes 3 small boxes and 19 large boxes etc . with every additional small box + large box that we add , we add 12 + 16 = 28 more glasses . thus , we can just ` ` add 28 s ' ' until we hit the correct answer . . . . 284 + 28 = 312 312 + 28 = 340 340 + 28 = 368 368 + 28 = 396 at this point , we ' ve ' gone past ' answer d , so the correct answer must be answer e . . . . . but here ' s the proof . . . . 396 + 28 = 424 424 + 28 = 452 452 + 28 = 480 final answer : e\"" + }, + { + "Answer": 318.1818181818182, + "Options": "a ) s . 200.18 , b ) s . 240.18 , c ) s . 290.18 , d ) s . 300.18 , e ) s . 318.18", + "Correct": "e", + "Explanation": "\"let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 700 but x = 120 % of y = 120 y / 100 = 12 y / 10 \u2234 12 y / 10 + y = 700 \u21d2 y [ 12 / 10 + 1 ] = 700 \u21d2 22 y / 10 = 700 \u21d2 22 y = 7000 \u21d2 y = 7000 / 22 = rs . 318.18 e )\"" + }, + { + "Answer": 1, + "Options": "a ) $ 1 , b ) $ 2 , c ) $ 3 , d ) $ 4 , e ) $ 6", + "Correct": "a", + "Explanation": "to find the least amount deepak should add to his saving account to split the money evenly among his 6 best friends , he needs to make the total divisible by 6 simply add the individual digits of the total = 4 + 4 + 9 + 7 + 7 + 4 = 35 if you add 1 , the number is divisible by 6 ( 35 + 1 ) correct option : a" + }, + { + "Answer": 20, + "Options": "a ) 30 , 10 , b ) 25 , 5 , c ) 29 , 9 , d ) 50 , 30 , e ) 20 , 8", + "Correct": "e", + "Explanation": "\"let their ages be x and ( x + 12 ) years . then , 5 ( x - 5 ) = ( x + 12 - 5 ) = > 4 x = 32 = > x = 8 their present ages are 20 years and 8 year . answer : e\"" + }, + { + "Answer": 400, + "Options": "a ) $ 350 , b ) $ 375 , c ) $ 400 , d ) $ 425 , e ) $ 450", + "Correct": "c", + "Explanation": "\"avg = sum of observations / number of observations avg income = ( 300 + 150 + 750 + 200 + 600 ) / 5 = 400 answer is c\"" + }, + { + "Answer": 27, + "Options": "a ) 22 , b ) 99 , c ) 27 , d ) 66 , e ) 887", + "Correct": "c", + "Explanation": "total time taken = x / 90 + 2 x / 20 hours = x / 9 hours average speed = 3 x / ( x / 9 ) = 27 kmph answer : c" + }, + { + "Answer": 40, + "Options": "a ) 40 , b ) 110 , c ) 120 , d ) 130 , e ) 220", + "Correct": "a", + "Explanation": "\"orchestra seats - a balcony seats - b a + b = 340 and 12 a + 8 b = 3320 solving equations simultaneously ( multiply equation 1 with 8 and subtract from second equation ) 4 a = 3320 - 8 * 340 = 3320 - 2720 = 600 i . e . a = 150 and b = 340 - 150 = 190 more seats in balcony than orchestra = b - a = 190 - 150 = 40 answer : option a\"" + }, + { + "Answer": 3, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "b", + "Explanation": "8 people visited 2 stores each for 16 visits . to maximize the number of stores that one person visited , let ' s assume that 3 people visited 1 store each . the number of remaining visits is 22 - 16 - 3 = 3 , which is the maximum that one person could have visited . the answer is b ." + }, + { + "Answer": 144, + "Options": "a ) 12 , b ) 144 , c ) 18 , d ) 21 , e ) 24", + "Correct": "b", + "Explanation": "the list should be wmwmw . hence , from women 3 ! and men 4 ! , we get ( 3 ! ) ( 4 ! ) = 144 . therefore , the correct answer is b ." + }, + { + "Answer": 5, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "c", + "Explanation": "\"p ( choosing a red apple 5 times in a row ) = 8 / 9 * 7 / 8 * 6 / 7 * 5 / 6 * 4 / 5 = 4 / 9 < 0.5 the answer is c .\"" + }, + { + "Answer": 179, + "Options": "a ) 167 , b ) 173 , c ) 179 , d ) 185 , e ) 193", + "Correct": "c", + "Explanation": "\"let n - 1 = 2 a . 2 + 4 + . . . + 2 a = 2 * ( 1 + 2 + . . . + a ) = 2 * ( a ) ( a + 1 ) / 2 = ( a ) ( a + 1 ) = 89 * 90 then a = 89 and n = 179 . the answer is c .\"" + }, + { + "Answer": 105, + "Options": "a ) 75 kg , b ) 65 kg , c ) 55 kg , d ) 85 kg , e ) 105 kg", + "Correct": "e", + "Explanation": "\"total weight increased = ( 8 x 5 ) kg = 40 kg . weight of new person = ( 65 + 40 ) kg = 105 kg . answer : e\"" + }, + { + "Answer": 27, + "Options": "a ) 3 , b ) 6 , c ) 12 , d ) 27 , e ) 24", + "Correct": "d", + "Explanation": "\"2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 28 = > 4 x 2 ^ 2 n = 4 ^ 28 = 2 ^ 56 = > 2 ^ 2 x 2 ^ 2 n = 2 ^ 56 = > 2 ^ ( 2 n + 2 ) = 2 ^ 56 = > 2 n + 2 = 56 = > n = 27 so . answer will be d .\"" + }, + { + "Answer": 74.99999999999997, + "Options": "a ) 92 , b ) 90 , c ) 82 , d ) 78 , e ) 75", + "Correct": "e", + "Explanation": "i get 75 . a cube with 1 million liters cube would be a cube with the dimensions of 100 * 100 * 100 . 4 * 2 covers 8 sq liters so 100 / 8 = 12.5 . y = 12.5 * 6 = 75 . e" + }, + { + "Answer": 3, + "Options": "a ) 6 , b ) 3 , c ) 5 , d ) - 1 , e ) none", + "Correct": "b", + "Explanation": "answer dividing numerator as well as denominator by b , we get given exp . = ( 3 a + 2 b ) / ( 3 a - 2 b ) = ( 3 a / b + 2 ) / ( 3 a / b - 2 ) = [ ( 3 x 4 ) / 3 + 2 ] / [ ( 3 x 4 ) / 3 - 2 ] = ( 4 + 2 ) / ( 4 - 2 ) = 3 option : b" + }, + { + "Answer": 150000.00000000003, + "Options": "a ) $ 150000 , b ) $ 18000 , c ) $ 180000 , d ) $ 1800 , e ) none", + "Correct": "a", + "Explanation": "[ 1 / ( x 1 / y 1 + x 2 / y 2 + x 3 / y 3 ) ] * total amount = balance amount [ 1 - ( 1 / 5 + 1 / 10 + 3 / 5 ) } * total salary = $ 15000 , = [ 1 - 9 / 10 ] * total salary = $ 15000 , total salary = $ 15000 * 10 = $ 150000 , correct answer ( a )" + }, + { + "Answer": 85.71428571428574, + "Options": "a ) 18 % , b ) 30 % , c ) 52 % , d ) 63 % , e ) 85.71 %", + "Correct": "e", + "Explanation": "let profit be x and cars sold be y originally profit / car = x / y now it is 1.3 x / 0.7 y = 13 / 7 ( x / y ) increase in profit per car = ( ( 6 / 7 ) ( x / y ) ) / ( x / y ) * 100 = 85.71 % answer = e" + }, + { + "Answer": 6.524582562663163, + "Options": "a ) $ 4.50 , b ) $ 5.10 , c ) $ 5.30 , d ) $ 5.50 , e ) $ 6.50", + "Correct": "e", + "Explanation": "\"i tried using time / rate approach : - initial price difference = 6.80 - 3.20 = 3.60 price of corn increasing by 5 x price of wheat decreasing by x ( 1.4 ) - x = . 4 x since both the quantities are moving towards reducing the price gap hence : - relative increase = 5 x + . 4 x let t be the time by which gap is filled so , 3.6 = t ( 5.4 x ) - > t = ( 3.6 ) / 5.4 x final price = 3.20 + 5 x * t - > 3.20 + 5 * 3.6 / 5.4 = 6.5 answer e .\"" + }, + { + "Answer": 500, + "Options": "a ) 8390 , b ) 3016 , c ) 2808 , d ) 3890 , e ) 2080", + "Correct": "b", + "Explanation": "b" + }, + { + "Answer": 35, + "Options": "a ) 37 , b ) 38 , c ) 39 , d ) 35 , e ) 41", + "Correct": "d", + "Explanation": "\"let present age of a be a and b be b a + 10 = 2 * ( b - 10 ) = > 2 b - a = 30 . . . . . . ( i ) a = b + 5 = > 2 b - b - 5 = 30 b = 35 so the present age of b is 35 years answer : d\"" + }, + { + "Answer": 999, + "Options": "a ) 732 , b ) 990 , c ) 999 , d ) 1305 , e ) 1405", + "Correct": "c", + "Explanation": "total number of digits = ( no . of digits in 1 - digit page nos . + no . of digits in 2 - digit page nos . + no . of digits in 3 - digit page nos . ) = ( 1 x 9 + 2 x 90 + 3 x 270 ) = ( 9 + 180 + 810 ) = 999 . answer : c" + }, + { + "Answer": 180, + "Options": "a ) 187.89 cm , b ) 180.29 cm , c ) 123.98 cm , d ) 149.98 cm , e ) 146.89 cm", + "Correct": "b", + "Explanation": "\"calculated average height of 35 boys = 182 cm . wrong total height of 35 boys = 182 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 182 cm - ( 166 cm - 106 cm ) / 35 = 182 cm - ( 166 cm - 106 cm ) / 35 = 182 cm - 60 / 35 cm = 182 cm - 1.71 cm = 180.29 cm . answer : b\"" + }, + { + "Answer": 84, + "Options": "a ) 74 , b ) 84 , c ) 94 , d ) 104 , e ) 114", + "Correct": "b", + "Explanation": "if money with anusha = a , babu = b & esha = e , then a + b + e = 378 - - - ( i ) & 12 a = 8 b = 6 e , so b = 3 a / 2 & e = 2 a substituting these values of b & e in ( i ) , a + ( 3 a / 2 ) + 2 a = 378 , on solving , a = 84 so , b = 126 , e = 168 answer : b" + }, + { + "Answer": 3900, + "Options": "a ) rs . 3900 , b ) rs . 4900 , c ) rs . 4980 , d ) rs . 5000 , e ) rs . 5900", + "Correct": "a", + "Explanation": "let the cost of a chair and that of a table be rs . x and rs . y respectively . then , 10 x = 4 y or y = 5 x . 2 15 x + 2 y = 4000 15 x + 2 x 5 x = 4000 2 20 x = 4000 x = 200 . so , y = 5 x 200 = 500 . 2 hence , the cost of 12 chairs and 3 tables = 12 x + 3 y = rs . ( 2400 + 1500 ) = rs . 3900 . a )" + }, + { + "Answer": 13, + "Options": "a ) 9 years , b ) 13 years , c ) 14 years , d ) 21 years , e ) 25 years", + "Correct": "b", + "Explanation": "\"solution age of the 15 th student = [ 15 x 15 - ( 14 x 6 + 16 x 8 ) ] = ( 225 - 212 ) = 13 years . answer b\"" + }, + { + "Answer": 75, + "Options": "a ) 66 % , b ) 75 % , c ) 70 % , d ) 50 % , e ) 82 %", + "Correct": "b", + "Explanation": "total percentage = ( 250 + 500 ) / 1000 = 0.75 b" + }, + { + "Answer": 24, + "Options": "a ) 1 , b ) 8 , c ) 12 , d ) 9 , e ) 24", + "Correct": "e", + "Explanation": "6 * 4 = 24 quarters answer : e" + }, + { + "Answer": 2400, + "Options": "a ) 2500 , b ) 2700 , c ) 2200 , d ) 2900 , e ) 2400", + "Correct": "e", + "Explanation": "let the price of a saree and a shirt be rs . x and rs . y respectively . then , 2 x + 4 y = 1600 . . . . ( i ) and x + 6 y = 1600 . . . . ( ii ) divide equation ( i ) by 2 , we get the below equation . = > x + 2 y = 800 . - - - ( iii ) now subtract ( iii ) from ( ii ) x + 6 y = 1600 ( - ) x + 2 y = 800 - - - - - - - - - - - - - - - - 4 y = 800 - - - - - - - - - - - - - - - - therefore , y = 200 . now apply value of y in ( iii ) = > x + 2 x 200 = 800 = > x + 400 = 800 therefore x = 400 solving ( i ) and ( ii ) we get x = 400 , y = 200 . cost of 12 shirts = rs . ( 12 x 200 ) = rs . 2400 . answer is e ." + }, + { + "Answer": 15, + "Options": "a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16", + "Correct": "d", + "Explanation": "\"p / 3 + f / 4 = p / 3 + ( 48 - p ) / 4 = 12 + p / 2 p / 3 + f / 3 = ( p + f ) / 3 = 48 / 3 = 16 p / 4 + f / 4 = 12 p / 3 + f / 3 > p / 3 + f / 4 > p / 4 + f / 4 - - > 16 > 12 + p / 12 > 12 greatest possible y : 12 + p / 12 = 15 - - > p = 36 ( integer - - > good ) 15 or d is the answer\"" + }, + { + "Answer": 98.73, + "Options": "a ) $ 98.73 , b ) $ 96.75 , c ) $ 98.78 , d ) $ 102.07 , e ) $ 105.3", + "Correct": "a", + "Explanation": "there can be 2 cases 1 ) 25 + 25 + 10 + 5 = $ 98.73 or 2 ) 25 + 25 + 25 = $ 96.75 a" + }, + { + "Answer": 66, + "Options": "a ) 81 , b ) 48 , c ) 66 , d ) 69 , e ) none of these", + "Correct": "c", + "Explanation": "solution : let the percentage marks in qa = ( 10 a + b ) % let the percentage marks in di = ( 10 b + a ) % let the percentage marks in va = x % . now , according to the question , we have , [ ( 10 a + b ) + x + ( 10 b + a ) ] / 3 = x \u2192 11 a + 11 b + x = 3 x . or , x = 11 ( a + b ) / 2 . clearly , we can see that the percentage of the va section will be a multiple of 11 . so , required answer will be 66 . answer : option c" + }, + { + "Answer": 45, + "Options": "a ) 45 , b ) 88 , c ) 66 , d ) 55 , e ) 22", + "Correct": "a", + "Explanation": "\"let the length of each train be x m . then , distance covered = 2 x m . relative speed = 45 - 36 = 9 km / hr . = 9 * 5 / 18 = 5 / 2 m / sec . 2 x / 36 = 5 / 2 = > x = 45 . answer : a\"" + }, + { + "Answer": 10, + "Options": "a ) 4 , b ) 10 , c ) 11 , d ) 12 , e ) 15", + "Correct": "b", + "Explanation": "the question basically asks how many positive odd integers less than 100 are odd multiples of 5 so we have 5,15 , 25,35 , 45,55 , 65,75 , 85,95 = 10 ans b" + }, + { + "Answer": 1295, + "Options": "a ) 2984 , b ) 2983 , c ) 2982 , d ) 1295 , e ) none of these", + "Correct": "d", + "Explanation": "\"1345 - 50 = 1295 answer : d\"" + }, + { + "Answer": 163, + "Options": "a ) 160 , b ) 161 , c ) 162 , d ) 163 , e ) 164", + "Correct": "d", + "Explanation": "\"to minimize one quantity maximize other . 162 * 2 ( max possible amount of food a guest could consume ) = 324 pounds , so there must be more than 162 guests , next integer is 163 . answer : d .\"" + }, + { + "Answer": 45, + "Options": "a ) 33 , b ) 36 , c ) 41 , d ) 45 , e ) 50", + "Correct": "d", + "Explanation": "possible solutions are diff of 0 - - 111222 , . . . . . . . . , 999 = 9 diff of 1 - - 123 , 234 , . . . . . , 789 = 7 x 2 = 14 diff of 2 - - 135 , 246 . . . . . . . 579 = 5 x 2 = 10 diff of 3 - - 147 , 258369 = 3 x 2 = 6 diff of 4 - - 159 = 1 x 2 = 2 last 210 , 420 , 630840 = 4 so total is 9 + 14 + 10 + 6 + 2 + 4 = 45 . answer : d" + }, + { + "Answer": 180, + "Options": "a ) 180 , b ) 45 , c ) 60 , d ) 90 , e ) 135", + "Correct": "a", + "Explanation": "we can start with the known quantity and then go on to find the others . shiny igneous ricks are 40 . these are ( 2 / 3 ) of total igneous rocks . ( 2 / 3 ) * total igneous rocks = 40 total igneous rocks = 40 * ( 3 / 2 ) = 60 total sedimentary rocks = 2 * total igneous rocks = 2 * 60 = 120 total number of rocks = 60 + 120 = 180 answer ( a )" + }, + { + "Answer": 88.66666666666667, + "Options": "a ) 88.33 , b ) 84.33 , c ) 88.66 , d ) 84.66 , e ) none of these", + "Correct": "c", + "Explanation": "total passed student = 40 + 45 + 48 = 133 133 is 88.66 % of 150 answer : c" + }, + { + "Answer": 28, + "Options": "a ) 25 , b ) 28 , c ) 31 , d ) 34 , e ) 37", + "Correct": "b", + "Explanation": "the middle number is 60 . let the smallest number be x . then the largest number is 2 x + 20 . to make x as small as possible , let ' s make the remaining numbers as large as possible . so the second largest = the largest = 2 x + 20 . the second smallest should be equal to the median . the numbers are x , 60 , 60 , 2 x + 20 , 2 x + 20 . x + 60 + 60 + 2 x + 20 + 2 x + 20 = 5 * 60 = 300 5 x = 140 x = 28 the answer is b ." + }, + { + "Answer": 7, + "Options": "a ) a ) 7 , b ) b ) 12 , c ) c ) 15 , d ) d ) 18 , e ) e ) 20", + "Correct": "a", + "Explanation": "\"explanation : 2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 50 - 36 = 14 ab = 7 . answer : a\"" + }, + { + "Answer": 400, + "Options": "a ) 150 , b ) 250 , c ) 400 , d ) 450 , e ) 550", + "Correct": "c", + "Explanation": "\"let the price of a pant and a t - shirt be rs . x and rs . y respectively . then , 3 x + 6 y = 750 . . . . ( i ) and x + 12 y = 750 . . . . ( ii ) divide equation ( i ) by 3 , we get the below equation . = x + 2 y = 250 . - - - ( iii ) now subtract ( iii ) from ( ii ) x + 12 y = 750 ( - ) x + 2 y = 250 - - - - - - - - - - - - - - - - 10 y = 500 - - - - - - - - - - - - - - - - y = 50 cost of 8 t - shirts = 8 * 50 = 400 answer : c\"" + }, + { + "Answer": 455, + "Options": "a ) 443 , b ) 455 , c ) 465 , d ) 468 , e ) 475", + "Correct": "b", + "Explanation": "\"total number of installments = 65 payment per installment for the first 20 installments = 410 payment per installment for the remaining 45 installments = 410 + 65 = 475 average = ( 20 * 410 + 45 * 475 ) / 65 = 455 answer b\"" + }, + { + "Answer": 11, + "Options": "a ) 3 , b ) 4 , c ) 7 , d ) 11 , e ) 12", + "Correct": "d", + "Explanation": "let 7 numbers are a , b , c , d , e , f , g . given avg of first 4 nums are 4 . . . i . e ( a + b + c + d ) / 4 = 4 a + b + c + d = 16 given avg of last 4 nums are also 4 . . i . e . ( d + e + f + g ) / 4 = 4 d + e + f + g = 16 e + f + g = 16 - d given avg of 7 nums are 3 . . . . i . e ( a + b + c + d + e + f + g ) / 7 = 3 a + b + c + d + e + f + g = 21 16 + 16 - d = 21 d = 32 - 21 d = 11 answer : d" + }, + { + "Answer": 2504, + "Options": "a ) 2500 , b ) 550 , c ) 2600 , d ) 2650 , e ) none of these", + "Correct": "a", + "Explanation": "solution : let the original price = y , after first change , it becomes , y * ( 1 + ( x / 100 ) ) after second change , it becomes y * ( 1 + ( x / 100 ) ) ( 1 - ( x / 100 ) ) = y ( 1 - ( x / 100 ) ^ 2 ) thus , x 2 * y = 106 - - - - - - - ( 1 ) x 2 = 106 / y now , y ( 1 - ( 106 / 10000 y ) ) 2 = 2304 ( similar to above ) y ( 1 - 100 / y ) 2 = 2304 y = 2500 . answer : option a" + }, + { + "Answer": 35, + "Options": "a ) 25 % , b ) 35 % , c ) 45 % , d ) 70 % , e ) 80 %", + "Correct": "b", + "Explanation": "\"since the problem does n ' t depend on the number of birds in reserve you can suppose that there are 100 birds . from them 100 * 0.3 = 30 are hawks . so , there are 70 non - hawks . there are 0.4 * 70 = 28 paddyfield - warblers . therefore , there are 0.25 * 28 = 7 kingfishers . the total number of birds in the nature reserve that are not hawks , paddyfield - warblers , or kingfishers is 100 - 30 - 28 - 7 = 35 . the answer is b\"" + }, + { + "Answer": 10, + "Options": "a ) 30 , b ) 25 , c ) 15 , d ) 10 , e ) 5", + "Correct": "d", + "Explanation": "\"because the cord was extended to its full length at all items , the dog ran along a semi - circular path , from north to south . the circumference of a full circle is 2 * pi * r , but since we only care about the length of half the circle , the semi - circle path is pi * r . pi * r = 30 . round pi = 3 , then r = 10 . chord is about 10 feet long answer : d\"" + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 1", + "Correct": "a", + "Explanation": "the sum is 66 . adding 6 to 66 = 66 + 6 = 72 . 72 is exactly divisible by 9 leaving 0 as the reminder = 8 . so the answer is a = 6" + }, + { + "Answer": 671, + "Options": "a ) 171 , b ) 181 , c ) 191 , d ) 201 , e ) 671", + "Correct": "e", + "Explanation": "11 + 12 * 1 = 23 23 + 12 * 2 = 47 47 + 12 * 3 = 83 83 + 12 * 4 = 131 131 + 12 * 5 = 191 191 + 12 * 6 = 263 263 + 12 * 7 = 347 347 + 12 * 8 = 443 443 + 12 * 9 = 551 551 + 12 * 10 = 671 answer : e" + }, + { + "Answer": 70, + "Options": "a ) 58 kg , b ) 60 kg , c ) 64 kg , d ) 70 kg , e ) none", + "Correct": "d", + "Explanation": "\"sol . for 9 kg zinc , mixture melted = ( 9 + 11 ) kg . for 31.5 kg zinc , mixture , melted = [ 20 / 9 x 31.5 ] kg = 70 kg . answer d\"" + }, + { + "Answer": 18, + "Options": "a ) 16 , b ) 14 , c ) 15 , d ) 18 , e ) 20", + "Correct": "d", + "Explanation": "\"explanation : let the son ' s present age be x years . then , man ' s present age = ( x + 20 ) years = > ( x + 20 ) + 2 = 2 ( x + 2 ) = > x + 22 = 2 x + 4 so , x = 18 . answer : d\"" + }, + { + "Answer": 4082.4, + "Options": "a ) rs . 3642.40 , b ) rs . 3868.80 , c ) rs . 4216.20 , d ) rs . 4082.40 , e ) none of these", + "Correct": "d", + "Explanation": "\"length of the first carpet = ( 1.44 ) ( 6 ) = 8.64 cm area of the second carpet = 8.64 ( 1 + 40 / 100 ) 6 ( 1 + 25 / 100 ) = 51.84 ( 1.4 ) ( 5 / 4 ) sq m = ( 12.96 ) ( 7 ) sq m cost of the second carpet = ( 45 ) ( 12.96 * 7 ) = 315 ( 13 - 0.04 ) = 4095 - 12.6 = rs . 4082.40 answer : d\"" + }, + { + "Answer": 0.01488095238095238, + "Options": "a ) 3 / 168 , b ) 5 / 168 , c ) 7 / 168 , d ) 5 / 336 , e ) 7 / 336", + "Correct": "d", + "Explanation": "the probability that jill and sandy will make a basket but jack will miss is 5 / 6 * 1 / 7 * 1 / 8 = 5 / 336 . the answer is d ." + }, + { + "Answer": 1, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "b", + "Explanation": "abc = a ( b ^ 3 ) = 180 on solving abc = a ( b ^ 3 ) we get c = b ^ 2 and for a ( b ^ 3 ) = 180 , there is only one possibility a = 180 and b = 1 so c = 1 ^ 2 = 1 answer : b" + }, + { + "Answer": 13, + "Options": "a ) 19 , b ) 18 , c ) 16 , d ) 13 , e ) 17", + "Correct": "d", + "Explanation": "\"sum of 12 even numbers = 12 * 13 = 156 average = 156 / 12 = 13 answer : d\"" + }, + { + "Answer": 15, + "Options": "a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16", + "Correct": "d", + "Explanation": "\"p / 3 + f / 4 = p / 3 + ( 48 - p ) / 4 = 12 + p / 2 p / 3 + f / 3 = ( p + f ) / 3 = 48 / 3 = 16 p / 4 + f / 4 = 12 p / 3 + f / 3 > p / 3 + f / 4 > p / 4 + f / 4 - - > 16 > 12 + p / 12 > 12 greatest possible h : 12 + p / 12 = 15 - - > p = 36 ( integer - - > good ) 15 or d is the answer\"" + }, + { + "Answer": 38, + "Options": "a ) 38 , b ) 43 , c ) 44 , d ) 45 , e ) 46", + "Correct": "a", + "Explanation": "\"let \u2018 x \u2019 be the average score after 12 th innings \u21d2 12 x = 11 \u00d7 ( x \u2013 2 ) + 60 \u2234 x = 38 answer a\"" + }, + { + "Answer": 20, + "Options": "a ) 10 , b ) 30 , c ) 20 , d ) 15 , e ) 17", + "Correct": "c", + "Explanation": "\"number of liters of water in 150 liters of the mixture = 15 % of 150 = 15 / 100 * 150 = 22.5 liters . p liters of water added to the mixture to make water 25 % of the new mixture . total amount of water becomes ( 22.5 + p ) and total volume of mixture is ( 150 + p ) . ( 22.5 + p ) = 25 / 100 * ( 150 + p ) 90 + 4 p = 150 + p p = 20 liters . answer : c\"" + }, + { + "Answer": 0.2857142857142857, + "Options": "a ) 2 / 7 , b ) 5 / 7 , c ) 3 / 7 , d ) 4 / 7 , e ) 1 / 7", + "Correct": "a", + "Explanation": "\"there are 9 years from 1962 - 1970 , inclusive . let ' s say the average circulation every year between 1962 - 1970 inclusive is x . so the total circulation is 9 x from 1962 - 1970 , inclusive . in 1961 , the circulation is 4 x . so total circulation for 1961 - 1970 is 4 x + 9 x = 13 x . ratio of circulation in 1961 to total circulation during 1961 - 1970 is 4 x to 14 x or 4 / 14 = 2 / 7 answer : a\"" + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) 24 , c ) 48 , d ) 52 , e ) 37", + "Correct": "a", + "Explanation": "let x be the amount peter picked . then mary and lucy picked 2 x and x + 2 x , respectively . so x + 2 x + x + 2 = 26 4 x = 24 x = 6 so 2 x = 2 * 6 = 12 correct answer is a ) 12" + }, + { + "Answer": 9, + "Options": "a ) 9 , b ) 8 , c ) 7 , d ) 6 , e ) 5", + "Correct": "a", + "Explanation": "\"number = ( 779 x a ) + 47 , where ` ` a ' ' is the quotient = ( 19 x 41 x a ) + ( 19 x 2 ) + 9 = 19 x ( 41 a + 2 ) + 9 = 19 x ( new quotient ) + 9 \\ inline \\ fn _ jvn \\ therefore required remainder = 9 answer : a\"" + }, + { + "Answer": 4, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 10 , e ) 4", + "Correct": "e", + "Explanation": "let no of cows be x , no of hens be y . so heads = x + y legs = 4 x + 2 y now , 4 x + 2 y = 2 ( x + y ) + 8 2 x = 8 x = 4 . answer : e" + }, + { + "Answer": 73, + "Options": "a ) 70 , b ) 75 , c ) 73 , d ) 85 , e ) 90", + "Correct": "c", + "Explanation": "\"explanation : ( 55 + 67 + 76 + 82 + 85 / 5 ) = 73 option c\"" + }, + { + "Answer": 1310, + "Options": "a ) 1320 , b ) 6530 , c ) 6630 , d ) 6730 , e ) 6830", + "Correct": "a", + "Explanation": "1370 - 50 * ( 5 ^ 0 ) = 1320 1320 - 50 * ( 5 ^ 1 ) = 1070 1070 - 50 * ( 5 ^ 2 ) = - 180 - 180 - 50 * ( 5 ^ 3 ) = - 6430 answer : a ." + }, + { + "Answer": 77, + "Options": "a ) 77 , b ) 79 , c ) 85 , d ) 87 , e ) 89", + "Correct": "a", + "Explanation": "\"explanation : average = total runs / no . of innings = 33 so , total = average x no . of innings = 33 x 10 = 330 . now increase in avg = 4 runs . so , new avg = 33 + 4 = 37 runs total runs = new avg x new no . of innings = 37 x 11 = 407 runs made in the 11 th inning = 407 - 330 = 77 answer : a\"" + }, + { + "Answer": 54, + "Options": "a ) 54 , b ) 27 , c ) 30 , d ) 35 , e ) 42", + "Correct": "a", + "Explanation": "\"average in 5 matches = ( 2 * 60 + 3 * 50 ) / 2 + 3 = 120 + 150 / 5 = 270 / 5 = 54 answer is a\"" + }, + { + "Answer": 7, + "Options": "a ) 1 , b ) 2 , c ) 4 , d ) 5 , e ) 7", + "Correct": "e", + "Explanation": "\"( 63 ) ( 65 ) = ( 64 - 1 ) ( 64 + 1 ) = 64 ^ 2 - 1 which is 1 less than a multiple of 8 . then the remainder will be 7 . the answer is e .\"" + }, + { + "Answer": 3000, + "Options": "a ) 3089 , b ) 3098 , c ) 3057 , d ) 3000 , e ) 3012", + "Correct": "d", + "Explanation": "a : b : c = 5 : 6 : 4 let the total profit = 100 - 30 = 70 5 / 15 * 70 = 70 / 3 a share = 70 / 3 + 30 = 160 / 3 b + c share = 100 - 160 / 3 = 140 / 3 a - ( b + c ) = 160 / 3 - 140 / 3 = 20 / 3 20 / 3 - - - - 200 100 - - - - ? = > 3000 answer : d" + }, + { + "Answer": 20, + "Options": "a ) $ 15 , b ) $ 20 , c ) $ 25 , d ) $ 18 , e ) $ 30", + "Correct": "b", + "Explanation": "\"a : ( b + c ) = 1 : 4 a ' s share = 100 * 1 / 5 = $ 20 answer is b\"" + }, + { + "Answer": 10, + "Options": "a ) 16 , b ) 10 , c ) 18 , d ) 19 , e ) 20", + "Correct": "b", + "Explanation": "two digit numbers : 5 at tens place : 50 , 52,54 , 56,58 9 at tens place : 90 , 92,94 , 96,98 if 5 and 9 is at units place , the number cant be even total : 5 + 5 = 10 answer b" + }, + { + "Answer": 27.77777777777778, + "Options": "a ) 15 % , b ) 25 % , c ) 15.125 % , d ) 27.78 % , e ) none", + "Correct": "d", + "Explanation": "\"only trick n this question is to ignore 45 % information as farm tax is levied uniformly in the village and that includes mr william ' s land . what percentage of tax mr william paid ? this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 480 / 3840 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 45 ) = 27.78 % and the answer is not there in the options . the correct answer is ( d ) .\"" + }, + { + "Answer": 4, + "Options": "a ) 4 , b ) 6 , c ) 5 , d ) 1 , e ) 2", + "Correct": "a", + "Explanation": "using the rule on the divisibility of nine , we add the digits of 1049 together to get 14 . since we are doing addition , the next number that is divisible by nine would be 18 . therefore , our answer 4 ( option a )" + }, + { + "Answer": 98, + "Options": "a ) a ) 78 , b ) b ) 82 , c ) c ) 98 , d ) d ) 91 , e ) e ) 85", + "Correct": "c", + "Explanation": "\"correct avg marks = 100 + ( 10 - 70 ) / 30 avg = 100 - 2 = 98 answer is c\"" + }, + { + "Answer": 22, + "Options": "a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28", + "Correct": "b", + "Explanation": "\"let x be the correct sums and ( 30 - x ) be the incorrect sums . 3 x - 2 ( 30 - x ) = 50 5 x = 110 x = 22 the answer is b .\"" + }, + { + "Answer": 8, + "Options": "a ) 3 , b ) 6 , c ) 8 , d ) 12 , e ) 16", + "Correct": "c", + "Explanation": "\"m ^ 2 is divisible by 48 so m ^ 2 must be multiple of 48 . if the value of m is multiples of 8 then it will satisfy the condition . if we if m is 12 or 24 or 36 then it ans is c but if m = 48 then answer should be 16 . is the question right ? or am i missing some thing ? c\"" + }, + { + "Answer": 1410, + "Options": "a ) rs . 692.80 , b ) rs . 820 , c ) rs . 990 , d ) rs . 1410 , e ) none", + "Correct": "d", + "Explanation": "answer income of the deceased = total income of 4 members - total income of remaining 3 members . = 840 x 4 - 650 x 3 rs . = 1410 rs . correct option : d" + }, + { + "Answer": 37.97402597402597, + "Options": "a ) 34 , b ) 43 , c ) 40 , d ) 38 , e ) 29", + "Correct": "d", + "Explanation": "\"solution : average speed = 2 xy / x + y = 2 * 43 * 34 / 43 + 34 = 2924 / 77 = 37.974 . . . = 38 answer : d\"" + }, + { + "Answer": 5, + "Options": "a ) 1 , b ) 4 , c ) 5 , d ) 6 , e ) 8", + "Correct": "c", + "Explanation": "2 : 5 : 13 2 x 5 x 13 x 15 7.5 2.5 30 x + 37.5 x + 32.5 x = 100 x / 20 x average = 5 answer : c" + }, + { + "Answer": 20, + "Options": "a ) $ 14 , b ) $ 16 , c ) $ 18 , d ) $ 20 , e ) $ 22", + "Correct": "d", + "Explanation": "\"the difference in the two prices is $ 1.70 - $ 1.20 = $ 0.50 for each color copy . each color copy will cost an extra $ 0.50 at print shop y . 40 * $ 0.50 = $ 20 the answer is d .\"" + }, + { + "Answer": 91.66666666666666, + "Options": "a ) 91.6 % , b ) 87.5 % , c ) 80 % , d ) 11 % , e ) 1 %", + "Correct": "a", + "Explanation": "\"say y = 1 and x = 12 . then y = 1 is less than x = 12 by ( 12 - 1 ) / 12 * 100 = 11 / 12 * 100 = 91.6 % . answer : a .\"" + }, + { + "Answer": 12.5, + "Options": "a ) 13.5 , b ) 14 , c ) 15 , d ) 12.5 , e ) none", + "Correct": "d", + "Explanation": "solution : at present the total age of the family = 5 * 20 = 100 . the total age of the family at the time of the birth of the youngest member , = [ 100 \u2212 10 \u2212 ( 10 * 4 ) ] = 50 . therefore , average age of the family at the time of birth of the youngest member , = 50 / 4 = 12.5 . answer : option d" + }, + { + "Answer": 9, + "Options": "a ) 4 , b ) 9 , c ) 11 , d ) 12 , e ) 15", + "Correct": "b", + "Explanation": "\"the question basically asks how many positive odd integers less than 90 are odd multiples of 5 so we have 5 , 15,25 , 35,45 , 55,65 , 75,85 = 9 ans b\"" + }, + { + "Answer": 0.5555555555555556, + "Options": "a ) 4 / 10 , b ) 4 / 9 , c ) 1 / 2 , d ) 6 / 10 , e ) 5 / 9", + "Correct": "e", + "Explanation": "first of all let us find out what is the maximum sum we will get by adding digits of numbers from 1 to 90 . that will be 17 ( 8 + 9 + 17 ) why did i calculate this ? i will come to that in a moment . so to get an odd digit by carrying out the operation # , the sum of the digits of the integer should be 1 , 3 , 5 , 7 , 9 , 10 , 12 , 14 , and 16 ( why not 18 ? because we know the maximum sum can be 17 ) number of integers , whose digits add to 1 : 1 and 10 = 2 number of integers , whose digits add to 3 : 3 , 12 , 21 , 30 = 4 number of integers , whose digits add to 5 : 5 , 14 , 23 , 32 , 41 , 50 = 6 number of integers , whose digits add to 7 : 7 , 16 , 25 , 34 , 43 , 52 , 61 , 70 = 8 number of integers , whose digits add to 9 : 10 multiples of 9 up to 90 = 10 number of integers , whose digits add to 10 : 19 , 28 , 37 , 46 , 55 , 64 , 73 , 82 = 8 number of integers , whose digits add to 12 : 39 , 48 , 57 , 66 , 75 , 84 = 6 number of integers , whose digits add to 14 : 59 , 68 , 77 , 86 = 4 number of integers , whose digits add to 16 : 79 , 88 = 2 so in total there are 2 + 4 + 6 + 8 + 10 + 8 + 6 + 4 + 2 = 50 such numbers probability = 50 / 90 = 5 / 9 correct answer e" + }, + { + "Answer": 11, + "Options": "a ) 5 , b ) 8 , c ) 10 , d ) 11 , e ) 17", + "Correct": "d", + "Explanation": "\"official solution : ( b ) we know that a # b = 100 and a # b = 4 a \u00b2 + 4 b \u00b2 + 8 ab . so 4 a \u00b2 + 4 b \u00b2 + 8 ab = 100 we can see that 4 a \u00b2 + 4 b \u00b2 + 8 ab is a well - known formula for ( 2 a + 2 b ) \u00b2 . therefore ( 2 a + 2 b ) \u00b2 = 100 . ( 2 a + 2 b ) is non - negative number , since both a and b are non - negative numbers . so we can conclude that 2 ( a + b ) = 10 . ( a + b ) + 6 = 10 / 2 + 6 = 11 . the correct answer is d .\"" + }, + { + "Answer": 900, + "Options": "a ) 450 , b ) 810 , c ) 900 , d ) 1000 , e ) 1100", + "Correct": "c", + "Explanation": "\"we want the sum of the digits from 0 to 99 , so i approximated : 0 - 9 - > 45 - > ( 9 + 0 ) * 10 / 2 40 - 49 - > 85 ( 13 + 4 ) * 10 / 2 90 - 99 - > 135 ( 18 + 9 ) * 10 / 2 we can see at a glance that theweightgoes up as the numbers go up ( meaning the difference between 85 and 45 is 40 , while 135 - 85 is 50 , this means that the second part of this sequence carries more weight for our result ) , so we know that the final answer has to be more than 850 ( 85 * 10 ) but close to it , and that ' s just t = 900 : the answer is c .\"" + }, + { + "Answer": 1.5, + "Options": "a ) 3 / 2 , b ) 12 / 5 , c ) 16 / 5 , d ) 15 / 4 , e ) 20 / 3", + "Correct": "a", + "Explanation": "there are two ways to calculate area of pqs . area remains same , so both are equal . 2 * 3 / 2 = pr * 4 / 2 pr = 3 / 2 a" + }, + { + "Answer": 7, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 25 , e ) 26", + "Correct": "a", + "Explanation": "\"explanation : 3 \u00e3 \u2014 2 + 2 \u00e3 \u2014 3 = ( 2 \u00e3 \u2014 3 - 3 \u00e3 \u2014 2 + 2 \u00e3 \u2014 3 ) + ( 2 \u00e3 \u2014 2 - 3 \u00e3 \u2014 3 + 2 \u00e3 \u2014 3 ) = ( 6 + 4 - 9 + 6 ) = 7 . answer : a\"" + }, + { + "Answer": 989.9999999999992, + "Options": "a ) $ 850 , b ) $ 990 , c ) $ 1050 , d ) $ 1180 , e ) $ 1340", + "Correct": "b", + "Explanation": "\"let p be the original purchase price of the product . bill originally sold the product for 1.1 * p . in the second scenario , the purchase price is 0.9 * p . a 30 % profit means the selling price would be 1.3 * 0.9 * p = 1.17 * p thus , according to the information in the question , 1.17 p - 1.1 p = 63 0.07 = 63 p = 900 the original selling price was 900 * 1.1 = 990 . the correct answer is b .\"" + }, + { + "Answer": 0.25, + "Options": "a ) 1 / 12 , b ) 1 / 6 , c ) 1 / 4 , d ) 1 / 3 , e ) 1 / 2", + "Correct": "c", + "Explanation": "roots of the equation ( x - 5 ) ( x + 10 ) ( 2 x - 5 ) = 0 are x = - 5 , x = - 10 andx = 5 / 2 = 2.5 . so , three solutions present in our set of 12 distinct numbers , therefore p = 3 / 12 = 1 / 4 . answer : c ." + }, + { + "Answer": 19, + "Options": "a ) a ) 16 , b ) b ) 18 , c ) c ) 19 , d ) d ) 22 , e ) e ) 24", + "Correct": "c", + "Explanation": "\"explanation : 10 * 18 + 36 \u2013 26 = 190 = > 190 / 10 = 19 c )\"" + }, + { + "Answer": 8215, + "Options": "a ) 2480 , b ) 3490 , c ) 6785 , d ) 8215 , e ) 9255", + "Correct": "d", + "Explanation": "\"sum of square of n numbers is found using the formula [ n ( n + 1 ) ( 2 n + 1 ) ] / 6 we have sum of 1 st 15 numbers = 1240 we need to find sum of squares from 16 to 30 which is = sum of squares of 1 st 30 + ve integers - sum of squares of 1 st 15 + ve integers . we will get d - 8215 ; answer : d\"" + }, + { + "Answer": 70, + "Options": "a ) 50.78 kg , b ) 49.32 kg , c ) 61.67 kg , d ) 70 kg , e ) 70.89 kg", + "Correct": "d", + "Explanation": "\"total weight of 50 + 50 students = 50 * 60 + 50 * 80 = 3000 + 4000 average weight of the class is = 7000 / 100 = 70 kg answer is d\"" + }, + { + "Answer": 158, + "Options": "a ) 150 , b ) 200 , c ) 250 , d ) 158 , e ) none", + "Correct": "d", + "Explanation": "\"sol . let the number of grils be x . then , number of boys = ( 632 - x ) . then , ( 11 3 / 4 \u00d7 632 ) \u21d4 11 x + 12 ( 632 - x ) \u21d4 x = 7584 - 7426 \u21d4 158 . answer d\"" + }, + { + "Answer": 181, + "Options": "a ) 187.89 cm , b ) 181.29 cm , c ) 123.98 cm , d ) 149.98 cm , e ) 146.89 cm", + "Correct": "b", + "Explanation": "\"calculated average height of 35 boys = 183 cm . wrong total height of 35 boys = 183 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 183 cm - ( 166 cm - 106 cm ) / 35 = 183 cm - 60 / 35 cm = 183 cm - 1.71 cm = 181.29 cm . answer : b\"" + }, + { + "Answer": 0.1666666666666668, + "Options": "a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 5 , d ) 1 / 6 , e ) 1 / 8", + "Correct": "d", + "Explanation": "\"x : 0.5 % is 0.05 % - points from 0.55 % . y : 0.8 % is 0.25 % - points from 0.55 % . therefore the ratio of products checked by y : x is 1 : 5 . thus , worker y checked 1 / 6 of the products . the answer is d .\"" + }, + { + "Answer": 54, + "Options": "a ) 45 , b ) 54 , c ) 34 , d ) 58 , e ) 56", + "Correct": "b", + "Explanation": "x - 9 = 5 ( y - 9 ) & x = 3 y x - 9 = 5 x / 3 - 45 x = 54 answer : b" + }, + { + "Answer": 1.2, + "Options": "a ) $ 0.60 , b ) $ 0.80 , c ) $ 1.00 , d ) $ 1.20 , e ) $ 1.60", + "Correct": "d", + "Explanation": "\"let price of a sundae = s price of ice cream bar = . 6 $ 125 * . 6 + 125 * s = 225 = > 125 * s = 150 = > s = 1.2 answer d\"" + }, + { + "Answer": 11.000000000000014, + "Options": "a ) 1 , b ) 11 , c ) 21 , d ) 31 , e ) 41", + "Correct": "b", + "Explanation": "l . c . m . of 5 , 6 , 4 and 3 = 60 . on dividing 1789 by 60 , the remainder is 49 . number to be added = ( 60 - 49 ) = 11 b )" + }, + { + "Answer": 1376, + "Options": "a ) 1376 , b ) 1800 , c ) 1400 , d ) 2500 , e ) 100", + "Correct": "a", + "Explanation": "\"let x be the number i chose , then x / 8 \u2212 160 = 12 x / 8 = 172 x = 1376 answer is a .\"" + }, + { + "Answer": 8, + "Options": "a ) 8 , b ) 12 , c ) 14 , d ) 16 , e ) 18", + "Correct": "a", + "Explanation": "legs 8 * 4 = 32 now half on their horses so remaining on the walk so 4 men 4 men has 8 legs so , 8 + 32 = 40 legs walking answer : a" + }, + { + "Answer": 8, + "Options": "a ) 10 , b ) 8 , c ) 40 , d ) 60 , e ) 120", + "Correct": "b", + "Explanation": "\"each person is one participant of 4 games . so there are in all 4 * 4 = 16 instances of one participant games . but each game has 2 participants so total number of games = 16 / 2 = 8 b\"" + }, + { + "Answer": 20, + "Options": "a ) 14 , b ) 20 , c ) 26 , d ) 28 , e ) 30", + "Correct": "b", + "Explanation": "\"solution let the number be x . then , 15 x - x = 280 \u2039 = \u203a 14 x = 280 x \u2039 = \u203a 20 . answer b\"" + }, + { + "Answer": 25, + "Options": "a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28", + "Correct": "b", + "Explanation": "\"let x be the number of students in the largest class . then x + ( x - 2 ) + ( x - 4 ) + ( x - 6 ) + ( x - 8 ) = 105 5 x - 20 = 105 5 x = 125 x = 25 the answer is b .\"" + }, + { + "Answer": 2, + "Options": "a ) $ 2.00 , b ) $ 3.00 , c ) $ 3.50 , d ) $ 4.00 , e ) $ 5.00", + "Correct": "a", + "Explanation": "\"number of wheels in truck = 18 number of wheels on its front axle = 2 number of wheels remaining = 16 number of axles remaining axles = 16 / 4 = 4 total number of axles = 5 t = 0.50 + 0.50 ( x \u2212 2 ) = 0.50 + . 5 * 3 = 0.5 + 1.5 = 2 $ answer a\"" + }, + { + "Answer": 0.1, + "Options": "a ) 0.1 , b ) 0.55 , c ) 0.65 , d ) 0.75 , e ) 0.85", + "Correct": "a", + "Explanation": "number of people whose age is less than 20 is given by 100 - 90 = 10 probability p that a person selected at random from the group is less than 20 is given by 10 / 100 = 0.1 correct answer a" + }, + { + "Answer": 16, + "Options": "a ) 15 , b ) 57 , c ) 16 , d ) 16 , e ) 73", + "Correct": "c", + "Explanation": "\"( 80 / 100 ) * 45 \u00e2 \u20ac \u201c ( 4 / 5 ) * 25 36 - 20 = 16 answer : c\"" + }, + { + "Answer": 0.28571428571428575, + "Options": "a ) 7 / 25 , b ) 3 / 25 , c ) 8 / 25 , d ) 2 / 7 , e ) 3 / 17", + "Correct": "d", + "Explanation": "\"p ( a n b ) = p ( a ) . p ( b ) p ( a n b ) = 5 / 7 . 2 / 5 p ( a n b ) = 2 / 7 . d\"" + }, + { + "Answer": 1000, + "Options": "a ) 100 cu . m , b ) 1000 cu . m , c ) 10000 cu . m , d ) 2000 cu . m , e ) 4000 cu . m", + "Correct": "b", + "Explanation": "\"20 * 10 * 5 = 1000 answer : b\"" + }, + { + "Answer": 120, + "Options": "a ) \u2212 120 , b ) \u2212 100 , c ) 100 , d ) 135 , e ) it can not be determined from the information given", + "Correct": "a", + "Explanation": "\"a + b = 220 b + c = 340 a - c = - 120 . imo option a .\"" + }, + { + "Answer": 1, + "Options": "a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2", + "Correct": "d", + "Explanation": "the midpoint of ( 2,8 ) and ( 14,4 ) is ( 8,6 ) . the slope of a line through ( 0 , - 2 ) and ( 8,6 ) is ( 6 - ( - 2 ) ) / ( 8 - 0 ) = 8 / 8 = 1 the answer is d ." + }, + { + "Answer": 60, + "Options": "a ) 50 kg , b ) 60 kg , c ) 55 kg , d ) 57 kg , e ) 62 kg", + "Correct": "b", + "Explanation": "\"explanation let a , b , c represent their respective weights . then , we have : a + b + c = ( 60 x 3 ) = 180 \u00e2 \u20ac \u00a6 . ( i ) a + b = ( 70 x 2 ) = 140 \u00e2 \u20ac \u00a6 . ( ii ) b + c = ( 50 x 2 ) = 100 \u00e2 \u20ac \u00a6 . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 240 \u00e2 \u20ac \u00a6 . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 60 . b \u00e2 \u20ac \u2122 s weight = 60 kg . answer b\"" + }, + { + "Answer": 2000, + "Options": "a ) 2160 , b ) 2350 , c ) 2000 , d ) 2300 , e ) none of these", + "Correct": "c", + "Explanation": "\"explanation : total exp = 5000 + 1500 + 4500 + 2500 + 2000 + 2500 = 18000 exp in % = 100 - 10 = 90 % , 18000 = 90 % saving = 10 % = 18000 x 10 / 90 = rs . 2000 answer : c\"" + }, + { + "Answer": 16000, + "Options": "a ) 1600 , b ) 8000 , c ) 16000 , d ) 12000 , e ) 18000", + "Correct": "c", + "Explanation": "explanation : place value = local value face value = absolute value the place value of 4 in 564823 is 4 x 1000 = 4000 the face value of 4 in 564823 is nothing but 4 . = > 4000 x 4 = 16000 answer : option c" + }, + { + "Answer": 49, + "Options": "a ) 10 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 49 %", + "Correct": "e", + "Explanation": "\"let original salary be $ 100 salary after decreasing 70 % = 100 - 100 x 70 / 100 = $ 30 salary after increasing 70 % on $ 30 = 30 + 30 x 70 / 100 = $ 51 percentage of loss = 100 - 51 = 49 % answer : e\"" + }, + { + "Answer": 80, + "Options": "a ) 60 , b ) 80 , c ) 40 , d ) 120 , e ) 160", + "Correct": "b", + "Explanation": "\"( 1 + 1 / 8 ) x - ( 1 - 1 / 4 ) x = 30 ( 9 / 8 ) x - ( 3 / 4 ) x = 30 x = 80 = e answer : b\"" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "a", + "Explanation": "answer is a . this is very similar to the 32 ^ 32 ^ 32 - 3 divided by 7 question ." + }, + { + "Answer": 26, + "Options": "a ) 40 , b ) 26 , c ) 27 , d ) 28 , e ) 22", + "Correct": "b", + "Explanation": "\"let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 32 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 32 + 20 ) / 2 = 26 . answer : b\"" + }, + { + "Answer": 0.5, + "Options": "a ) 3 , b ) 2 , c ) 1 / 2 , d ) 1 / 3 , e ) 1 / 4", + "Correct": "c", + "Explanation": "\"x = 4 y + 5 , and thus y = x / 4 - 5 / 4 the slope is 1 / 4 . the slope of a line through points ( m , n ) and ( m + 2 , n + p ) is ( n + p - n ) / ( m + 2 - m ) = p / 2 p / 2 = 1 / 4 and thus p = 1 / 2 the answer is c .\"" + }, + { + "Answer": 64, + "Options": "a ) 62 kg , b ) 60 kg , c ) 64 kg , d ) 72 kg , e ) none of these", + "Correct": "c", + "Explanation": "explanation : let the weight of student be x kg . given , difference in average weight = 8 kg = > ( 96 - x ) / 4 = 8 = > x = 64 answer : c" + }, + { + "Answer": 4, + "Options": "a ) 5 , b ) 4 , c ) 7 , d ) 8 , e ) 9", + "Correct": "b", + "Explanation": "\"going down = 16 m going up = 8 - - > total = 24 going down = 8 - - > total = 32 going up = 4 - - > total = 36 going down = 4 - - > total = 40 going up = 2 - - > total = 42 going down = 2 - - > total = 44 going up = 1 - - > total = 45 ( caught ) no of bounce = 4 answer : b\"" + }, + { + "Answer": 80, + "Options": "a ) 70 , b ) 80 , c ) 90 , d ) 92 , e ) 94", + "Correct": "b", + "Explanation": "\"if on a test three people answered 90 % of the questions correctly and two people answered 80 % correctly , then the average for the group is not 85 % but rather 3 \u00d7 90 + 2 \u00d7 805 = 4305 = 86.3 \u00d7 90 + 2 \u00d7 805 = 4305 = 86 . here , 90 has a weight of 3 = > it occurs 3 times . whereas 80 has a weight of 2 = > it occurs 2 times . so the average is closer to 90 than to 80 as we have just calculated . b\"" + }, + { + "Answer": 16, + "Options": "a ) $ 5 , b ) $ 10 , c ) $ 14 , d ) $ 16 , e ) $ 28", + "Correct": "d", + "Explanation": "\"bill = fixed charge + charge of calls made in jan , bill = fixed charge ( let , y ) + charge of calls made in jan ( let , x ) = $ 46 in feb , bill = fixed charge ( let , y ) + charge of calls made in feb ( then , 2 x ) = $ 76 i . e . x + y = 46 and 2 x + y = 76 take the difference if two equations i . e . ( 2 x + y ) - ( x + y ) = 76 - 46 i . e . x = 30 i . e . fixed monthly charge , y = 16 answer : option d\"" + }, + { + "Answer": 37, + "Options": "a ) 22 , b ) 77 , c ) 26 , d ) 37 , e ) 88", + "Correct": "d", + "Explanation": "\"16 x + 85 = 17 ( x + 3 ) x = 34 + 3 = 37 answer : d\"" + }, + { + "Answer": 37, + "Options": "a ) 1 , b ) 19 , c ) 29 , d ) 30 , e ) 37", + "Correct": "e", + "Explanation": "\"total of integers = 76 * 4 = 3004 lowest of the least possible integer is when the middle 2 intergers are at the maximum or equal to the highest possible integer . but all integers are distinct . so if the largest integer is 90 , then the middle 2 will be 88 and 89 lowest of least possible integer = 304 - ( 90 + 89 + 88 ) = 304 - 267 = 37 answer : e\"" + }, + { + "Answer": 21, + "Options": "a ) 15 , b ) 18 , c ) 21 , d ) 25 , e ) 31", + "Correct": "c", + "Explanation": "let the total number of workers be x 8000 x = 12000 * 7 + 6000 ( x - 7 ) x = 21 answer is c" + }, + { + "Answer": 150, + "Options": "a ) $ 100 , b ) $ 150 , c ) $ 200 , d ) $ 250 , e ) $ 450", + "Correct": "b", + "Explanation": "\"cavg = average contribution before john cavg * 1.5 = 75 , therefore the average cont is $ 50 before john . if he needs to increase the average contribution by $ 25 , he must put in $ 25 for each of the 3 people . so $ 75 . but , he also has to put in the average for himself ( the fourth person ) , so add $ 75 . so $ 150 is your answer . answer b\"" + }, + { + "Answer": 19, + "Options": "a ) 10 , b ) 12 , c ) 19 , d ) 18 , e ) 20", + "Correct": "c", + "Explanation": "\"sp = 18 loss = cp 19 loss = cp \u2212 sp = cp \u2212 18 \u21d2 cp 19 = cp \u2212 18 \u21d2 18 cp 19 = 18 \u21d2 cp 19 = 1 \u21d2 cp = 19 c\"" + }, + { + "Answer": 4, + "Options": "a ) 7 , b ) 4 , c ) 5 , d ) 3 , e ) 6", + "Correct": "b", + "Explanation": "we need 3 factors of 2 , so n must be at least 4 . therefore , the answer is b ." + }, + { + "Answer": 6250, + "Options": "a ) 5000 , b ) 2999 , c ) 2878 , d ) 6250 , e ) 2771", + "Correct": "d", + "Explanation": "\"income = rs . 100 expenditure = rs . 80 savings = rs . 20 present expenditure 80 * ( 20 / 100 ) = rs . 96 present savings = 100 \u00e2 \u20ac \u201c 96 = rs . 4 100 - - - - - - 4 ? - - - - - - - - - 250 = > 6250 answer : d\"" + }, + { + "Answer": 81, + "Options": "a ) 80 % , b ) 81 % , c ) 82 % , d ) 83 % , e ) 84 %", + "Correct": "b", + "Explanation": "\"( 15 * 75 + 10 * 90 ) / 25 = 81 % the answer is b .\"" + }, + { + "Answer": 31.25, + "Options": "a ) 22 % , b ) 24 % , c ) 25 % , d ) 27 % , e ) 31 %", + "Correct": "e", + "Explanation": "\"total sales = 800 comission = ( 20 / 100 ) * 500 + ( 50 / 100 ) * 300 = 100 + 150 = 250 % comission = ( 250 / 800 ) * 100 = 31.3 ~ 31 % answer is e\"" + }, + { + "Answer": 24, + "Options": "a ) 4 , b ) 12 , c ) 15 , d ) 20 , e ) 24", + "Correct": "e", + "Explanation": "\"you could set - up a quick table and brute force the answer . a 4 * 50 200 1800 - 200 1600 26 61.54 b 12 * 50 600 1800 - 600 1200 18 66.67 c 15 * 50 750 1800 - 750 1050 15 70.00 d 20 * 50 1000 1800 - 1000 800 10 80.00 e 24 * 50 1200 1800 - 1200 600 6 100.00 answer is e\"" + }, + { + "Answer": 39, + "Options": "a ) 26 , b ) 29 , c ) 39 , d ) 42 , e ) 43", + "Correct": "c", + "Explanation": "39 option ' c '" + }, + { + "Answer": 50, + "Options": "a ) 50 , b ) 55 , c ) 65 , d ) 72 , e ) 78", + "Correct": "a", + "Explanation": "( x + x 1 + . . . x 14 ) / 15 = 40 50 option a" + }, + { + "Answer": 15, + "Options": "a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18", + "Correct": "b", + "Explanation": "1000 + 200 x = 4000 x = 15 cars . the answer is b ." + }, + { + "Answer": 1099.9999999999998, + "Options": "a ) 1100 , b ) 3000 , c ) 1000 , d ) 3600 , e ) 2400", + "Correct": "a", + "Explanation": "\"let the additional invested amount for 8 % interest be x ; equation will be ; 2200 + 0.05 * 2200 + x + 0.08 x = 2200 + x + 0.06 ( 2200 + x ) 0.05 * 2200 + 0.08 x = 0.06 x + 0.06 * 2200 0.02 x = 2200 ( 0.06 - 0.05 ) x = 2200 * 0.01 / 0.02 = 1100 ans : ` ` a ' '\"" + }, + { + "Answer": 20, + "Options": "a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50", + "Correct": "b", + "Explanation": "let there be 4 x lbs of p in x and x lbs of v in x let there be y lbs of p in y and 5 y lbs of v in y now total p is 4 x + y = 24 and total q is x + 5 y = 25 solving the two equations , we get x = 5 and y = 4 mixture x has 4 x lbs of p = 4 x = 4 * 5 = 20 lbs answer : b" + }, + { + "Answer": 1, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5", + "Correct": "b", + "Explanation": "explanation : average of 10 numbers = 0 sum of 10 numbers = ( 0 x 10 ) = 0 . it is quite possible that 9 of these numbers may be negative and if there sum is - a , then 10 th number is ( a ) . answer : b" + }, + { + "Answer": 230, + "Options": "a ) 200 , b ) 230 , c ) 50 , d ) 115 , e ) 150", + "Correct": "b", + "Explanation": "\"x + y = 260 x - y = 200 2 x = 60 x = 30 y = 230 answer is b\"" + }, + { + "Answer": 28, + "Options": "a ) 48 , b ) 64 , c ) 28 , d ) 72 , e ) 27", + "Correct": "c", + "Explanation": "to improve his average by 4 runs per innings he has to contribute 16 x 4 = 64 runs for the previous 16 innings . thus , the average after the 17 th innings = 92 - 64 = 28 . answer : c" + }, + { + "Answer": 28, + "Options": "a ) 22 , b ) 24 , c ) 26 , d ) 20 , e ) 28", + "Correct": "e", + "Explanation": "\"explanation : let number of hens = h and number of cows = c number of heads = 48 = > h + c = 48 - - - ( equation 1 ) number of feet = 136 = > 2 h + 4 c = 136 = > h + 2 c = 68 - - - ( equation 2 ) ( equation 2 ) - ( equation 1 ) gives 2 c - c = 68 - 48 = > c = 20 substituting the value of c in equation 1 , we get h + 20 = 48 = > h = 48 - 20 = 28 i . e . , number of hens = 28 answer : e\"" + }, + { + "Answer": 128, + "Options": "a ) 128 , b ) 75 , c ) 69 , d ) 78 , e ) 45", + "Correct": "a", + "Explanation": "\"solution : sum of 1 st 12 results = 12 * 14 sum of last 12 results = 12 * 17 13 th result = x ( let ) now , 12 * 14 + 12 * 17 + x = 25 * 20 or , x = 128 . answer : option a\"" + }, + { + "Answer": 60, + "Options": "a ) 33 , b ) 37 , c ) 54 , d ) 60 , e ) 01", + "Correct": "d", + "Explanation": "\"the number of students with first division = 26 % of 300 = 26 / 100 \u00d7 300 = 7800 / 100 = 78 and , the number of students with second division = 54 % of 300 = 54 / 100 \u00d7 300 = 16200 / 100 = 162 therefore , the number of students who just passed = 300 \u2013 ( 78 + 162 ) = 60 answer : d\"" + }, + { + "Answer": 0.6666666666666666, + "Options": "a ) 2 / 3 , b ) 2 / 7 , c ) 1 / 2 , d ) 7 / 12 , e ) 1 / 7", + "Correct": "a", + "Explanation": "same amount of water made bigger jar 1 / 3 full , thenthe same amount of water ( stored for a while in smaller jar ) were added to bigger jar , so bigger jar is 1 / 3 + 1 / 3 = 2 / 3 full . answer : a ." + }, + { + "Answer": 64.00000000000001, + "Options": "a ) 64 % , b ) 120 % , c ) 96 % , d ) 80 % , e ) 64 %", + "Correct": "a", + "Explanation": "\"juan ' s income = 100 ( assume ) ; tim ' s income = 40 ( 60 percent less than juan ' s income ) ; mary ' s income = 64 ( 60 percent more than tim ' s income ) . thus , mary ' s income ( 64 ) is 64 % of juan ' s income ( 100 ) . answer : a .\"" + }, + { + "Answer": 160, + "Options": "a ) 150 , b ) 152 , c ) 154 , d ) 158 , e ) 160", + "Correct": "e", + "Explanation": "d = d * q + r d = 17 * 9 + 7 d = 153 + 7 d = 160 answer e" + }, + { + "Answer": 4, + "Options": "a ) 5 , b ) 4 , c ) 1 , d ) 2 , e ) 3", + "Correct": "b", + "Explanation": "\"if we solve the question , we get x = 4 . option : b\"" + }, + { + "Answer": 18, + "Options": "a ) 18 , b ) 12 , c ) 15 , d ) 17 , e ) 19", + "Correct": "a", + "Explanation": "explanation : 1 to 9 = 8 * 9 = 72 1 to 5 = 5 * 10 = 50 5 to 9 = 5 * 8 = 40 5 th = 50 + 40 = 90 \u2013 72 = 18 option a" + }, + { + "Answer": 89.99999999999999, + "Options": "a ) a ) 90 , b ) b ) 150 , c ) c ) 130 , d ) d ) 190 , e ) e ) 210", + "Correct": "a", + "Explanation": "\"let x be the total number of pages in the book , then she finished 2 / 3 * x pages . then she has x \u2212 2 / 3 * x = 1 / 3 * x pages left . 2 / 3 * x \u2212 1 / 3 * x = 30 1 / 3 * x = 30 x = 90 so the book is 90 pages long . answer is a .\"" + }, + { + "Answer": 0.9986095661846496, + "Options": "a ) 3252 / 3257 , b ) 3456 / 3461 , c ) 3591 / 3596 , d ) 3346 / 3351 , e ) 3453 / 3458", + "Correct": "c", + "Explanation": "let 3252 / 3257 be the original fraction . notice that it is a positive proper fraction . hence adding the same constant to both the numerator and the denominator will increase the fraction as the fraction will move closer to one . hence we just have to pick the number that adds the greatest value to both the numerator and the denominator . options can be re - written as ( x - 5 ) x = > 1 - ( 5 / x ) a ) 1 - ( 5 / 3257 ) b ) 1 - ( 5 / 3461 ) c ) 1 - ( 5 / 3596 ) d ) 1 - ( 5 / 3351 ) e ) 1 - ( 5 / 3458 ) answer : c" + }, + { + "Answer": 120, + "Options": "a ) 72 min , b ) 62 min , c ) 70 min , d ) 74 min , e ) 120 min", + "Correct": "e", + "Explanation": "\"x = time for type b prolems 2 x = time for type a problem total time = 3 hrs = 180 min 100 x + 100 * 2 x = 180 x = 180 / 300 x = 0.6 time taken for type a problem = 100 * 2 * 0.6 = 120 min answer : e\"" + }, + { + "Answer": 135, + "Options": "a ) 135 , b ) 136 , c ) 137 , d ) 138 , e ) 139", + "Correct": "b", + "Explanation": "total 35 pins are there and 4 sides of card board . . . so 35 x 4 = 140 now in the rectangle 4 vertices have 4 pins which is common to the sides . . . . so 140 - 4 = 136 answer : b" + }, + { + "Answer": 4753, + "Options": "a ) 1617 , b ) 4753 , c ) 1417 , d ) 4353 , e ) none of these", + "Correct": "b", + "Explanation": "explanation : ncr = n ! / ( r ) ! ( n \u2212 r ) ! 98 c 96 = 98 ! / ( 96 ) ! ( 2 ) ! = 98 \u2217 97 * 96 ! / ( 96 ) ! ( 2 ) ! = 98 * 97 / 2 \u2217 1 = 4753 option b" + }, + { + "Answer": 164, + "Options": "a ) 116 , b ) 132 , c ) 148 , d ) 164 , e ) 180", + "Correct": "d", + "Explanation": "3 / 10 * p are ponies with horseshoes , so p is a multiple of 10 . 5 / 8 * 3 / 10 * p = 3 / 16 * p are icelandic ponies with horseshoes , so p is a multiple of 16 . the minimum value of p is 80 . then h = p + 4 = 84 . the minimum number of horses and ponies is 164 . the answer is d ." + }, + { + "Answer": 20, + "Options": "a ) 10 , b ) 20 , c ) 40 , d ) 60 , e ) 120", + "Correct": "b", + "Explanation": "\"method 2 : each person is one participant of 4 games . so there are in all 8 * 5 = 40 instances of one participant games . but each game has 2 participants so total number of games = 40 / 2 = 20 b\"" + }, + { + "Answer": 38, + "Options": "a ) 20 % , b ) 35 % , c ) 38 % , d ) 65 % , e ) 135 %", + "Correct": "c", + "Explanation": "let the initial price be 100 1 st increase = 20 % the price now is 120 2 nd increase of 15 % on 120 = 18 final price = 138 , total increase = 38 % answer : c" + }, + { + "Answer": 6, + "Options": "a ) 0 , b ) 1 , c ) 4 , d ) 5 , e ) 6", + "Correct": "e", + "Explanation": "let there be a rows . then 5 a + 6 = 12 ( a - 3 ) [ equating the number of students ] = > a = 6 and total number of students = 36 therefore 6 students much sit in each row such that each row has an equal number of students and all students are seated . option ( e )" + }, + { + "Answer": 104, + "Options": "a ) 30 , b ) 104 , c ) 20 , d ) 25 , e ) 26", + "Correct": "b", + "Explanation": "\"let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 . x / 2 = ( 85 - 33 ) = > x / 2 = 52 = > x = 104 . answer : b\"" + }, + { + "Answer": 500, + "Options": "a ) 450 , b ) 300 , c ) 500 , d ) 610 , e ) 175", + "Correct": "c", + "Explanation": "\"let the maximum marks be x then , 33 % of x = 125 + 40 33 x / 100 = 165 x = 500 answer is c\"" + }, + { + "Answer": 2088, + "Options": "a ) 46 , b ) 248 , c ) 2092 , d ) 15,128 , e ) 30,256", + "Correct": "c", + "Explanation": "# of 2 - letter codes possible from 524 different signs = 524 * 524 . # of 2 - letter codes possible from 522 different signs = 522 * 522 . the difference = 524 ^ 2 - 522 ^ 2 = ( 524 - 522 ) ( 524 + 522 ) = 2092 . answer : c ." + }, + { + "Answer": 400, + "Options": "a ) 200 bc , b ) 200 b / c , c ) 400 bc , d ) 400 b / c , e ) 400 / bc", + "Correct": "c", + "Explanation": "\"2 cases * c cartons / case * b boxes / carton * 200 clips / box = 400 bc paper clips the answer is c .\"" + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 24 , c ) 30 , d ) 32 , e ) 48", + "Correct": "a", + "Explanation": "4 * 1 * 1 - ( - 2 * 1 * 1 ) = 4 + 2 = 6 ans : a" + }, + { + "Answer": 7.3500000000000005, + "Options": "a ) 7.35 , b ) 6.25 , c ) 8.15 , d ) 6.95 , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : 2.205 / 0.3 = 22.05 / 3 = 7.35 . answer : option a\"" + }, + { + "Answer": 3.2999999999999994, + "Options": "a ) $ 2.70 , b ) $ 3.00 , c ) $ 3.30 , d ) $ 3.60 , e ) $ 3.90", + "Correct": "c", + "Explanation": "\"x = 3 x / 5 + 1 / 3 * 2 x / 5 + 88 4 x / 15 = 88 x = 330 = $ 3.30 the answer is c .\"" + }, + { + "Answer": 30, + "Options": "a ) 21 , b ) 35 , c ) 39 , d ) 30 , e ) 65", + "Correct": "d", + "Explanation": "\"the total number of the people in the room must be a multiple of both 7 and 10 ( in order 3 / 7 and 5 / 10 of the number to be an integer ) , thus the total number of the people must be a multiple of lcm of 7 and 10 , which is 70 . since , the total number of the people in the room is greater than 50 and less than 100 , then there are 70 people in the room . therefore there are 3 / 7 * 70 = 30 people in the room under the age of 21 . answer : d .\"" + }, + { + "Answer": 0.4, + "Options": "a ) 2 / 5 , b ) 3 / 5 , c ) 4 / 5 , d ) 6 / 5 , e ) 7 / 5", + "Correct": "a", + "Explanation": "a no . is divisible by 4 if last two digit is divisible by 4 so numbers ending with 2428 , 4852 , 5664 , 6884 are divisible by 4 last two places are fixed by 2428 , 4852 , 5664 , 6884 so remaining 3 places can be filled in 3 ! ways for each total = 8 * 3 ! = 48 = n ( e ) n ( s ) = 5 c 4 = 120 p = 48 / 120 = 2 / 5 answer : a" + }, + { + "Answer": 48, + "Options": "a ) 500 % , b ) 48 % , c ) 500 / 3 % , d ) 125 % , e ) 60 %", + "Correct": "b", + "Explanation": "\"z = 100 ; y = 40 so x = 48 x as % of z = 48 / 100 * 100 = > 48 % answer will be ( b )\"" + }, + { + "Answer": 3, + "Options": "a ) 0 , b ) 2 , c ) 2.5 , d ) 4.67 , e ) 3", + "Correct": "e", + "Explanation": "\"spotting the pattern of equations both are in form of ( x + c ) ^ 2 so a 1 = ( x + 2 ) ^ 2 a 2 = ( 2 x - 3 ) ^ 2 l 1 = x + 2 l 2 = 2 x - 3 p 1 = 4 ( x + 2 ) p 2 = 4 ( 2 x - 3 ) p 1 + p 2 = 32 4 ( x + 2 ) + 4 ( 2 x - 3 ) = 32 . . . . . . . . . . . . . . > x = 3 answer : e\"" + }, + { + "Answer": 71.42857142857143, + "Options": "a ) 47 % , b ) 59 % , c ) 71 % , d ) 83 % , e ) 95 %", + "Correct": "c", + "Explanation": "\"let x be the number of new biographies added to the library . let b be the original number of biographies , so the original number of books was 5 b . 0.3 ( 5 b + x ) = b + x 0.5 b = 0.7 x x = 0.71 b the answer is c .\"" + }, + { + "Answer": 27, + "Options": "a ) 19 , b ) 20 , c ) 21 , d ) 27 , e ) 29", + "Correct": "d", + "Explanation": "3 + 16 + 33 + n + 1 = 20 x 4 = 80 = > n + 53 = 80 = > n = 27 answer d" + }, + { + "Answer": 194, + "Options": "a ) 165 , b ) 185 , c ) 190 , d ) 198 , e ) 194", + "Correct": "e", + "Explanation": "194 answer is e" + }, + { + "Answer": 16, + "Options": "a ) 11 , b ) 12 , c ) 16 , d ) 14 , e ) 15", + "Correct": "c", + "Explanation": "\"- x 2 - ( k + 10 ) x - 8 = - ( x - 2 ) ( x - 4 ) : given - x 2 - ( k + 10 ) x - 8 = - x 2 + 6 x - 8 - ( k + 10 ) = 6 : two polynomials are equal if their corresponding coefficients are equal . k = - 16 : solve the above for k correct answer c\"" + }, + { + "Answer": 19808, + "Options": "a ) 20018 , b ) 20028 , c ) 20108 , d ) 10008 , e ) 20008", + "Correct": "e", + "Explanation": "\"explanation : ( a + b ) 2 + ( a \u00e2 \u02c6 \u2019 b ) 2 = 2 ( a 2 + b 2 ) ( reference : basic algebraic formulas ) 1022 + 982 = ( 100 + 2 ) 2 + ( 100 \u00e2 \u02c6 \u2019 2 ) 2 = 2 ( 1002 + 22 ) = 2 ( 10000 + 4 ) = 20008 . answer : option e\"" + }, + { + "Answer": 20, + "Options": "a ) 20 , b ) 11 , c ) 12 , d ) 13 , e ) 14", + "Correct": "a", + "Explanation": "\"since average price of a pencil = 2 \u2234 price of 75 pencils = 150 \u2234 price of 30 pens = ( 750 \u2013 150 ) = 600 \u2234 average price of a pen = 600 \u2044 60 = 20 answer a\"" + }, + { + "Answer": 440, + "Options": "a ) 90 , b ) 120 , c ) 160 , d ) 360 , e ) 440", + "Correct": "e", + "Explanation": "\"if we exclude those cases and take the question at face value , then it seems straightforward . group # 1 = ( did n ' t like , did n ' t understand ) = 110 group # 2 = ( like understood ) = 3 / 4 ( 1 / 4 ) n = 110 n = 440 answer = ( e )\"" + }, + { + "Answer": 0.14699999999999996, + "Options": "a ) 0.184 , b ) 0.16 , c ) 0.18 , d ) 0.147 , e ) 0.148", + "Correct": "d", + "Explanation": "total no . of sides = 10 sides that are red = 3 probability that the die lands with red side up = 3 / 10 therefore , probability that the die does not land with red side up = 1 - 3 / 10 = 7 / 10 probability that kumar rolls the die 3 times and the die lands with a red side up for the first time on the third roll = ( 1 st roll - non red face ) x ( 2 nd roll - non red face ) x ( 3 rd roll - red face ) = ( 7 / 10 ) x ( 7 / 10 ) x ( 3 / 10 ) = 128 / 1000 = 0.147 d" + }, + { + "Answer": 38.4375, + "Options": "a ) 31355 , b ) 38.44 , c ) 29.55 , d ) 97.66 , e ) 45.66", + "Correct": "b", + "Explanation": "total score of the batsman in 25 matches = 1125 . total score of the batsman in the next 7 matches = 105 . total score of the batsman in the 32 matches = 1230 . average score of the batsman = 1230 / 32 = 38.44 . answer : b" + }, + { + "Answer": 440, + "Options": "a ) 510 , b ) 520 , c ) 530 , d ) 540 , e ) 440", + "Correct": "e", + "Explanation": "\"let the maximum marks be x then , 50 % of x = 200 + 20 50 x / 100 = 220 50 x = 220 * 100 = 22000 x = 440 answer is e\"" + }, + { + "Answer": 12, + "Options": "a ) 20 % , b ) 19 % , c ) 15 % , d ) 12 % , e ) 24 %", + "Correct": "d", + "Explanation": "\"answer : option d 100 * 100 = 10000 80 * 110 = 8800 10000 - - - - - - - 1200 100 - - - - - - - ? = 12 %\"" + }, + { + "Answer": 1875, + "Options": "a ) 1875 , b ) 1250 , c ) 1300 , d ) 1600 , e ) 1625", + "Correct": "a", + "Explanation": "\"300 gallons of water increases capacity by 25 % that means 25 % is 300 gallons , so 100 % would be = 300 * 100 / 25 = 1200 gallons now 1200 + 300 gallons is 80 % capacity of tank . so 100 % capacity would be = 1500 * 100 / 80 = 1875 a is the answer\"" + }, + { + "Answer": 168, + "Options": "a ) 26 , b ) 39 , c ) 42 , d ) 65 , e ) 168", + "Correct": "e", + "Explanation": "here 156 has three two ' s two three ' s and one 14 rest of them must be in w so w = 14 * 3 * 4 = 168 smash e" + }, + { + "Answer": 54, + "Options": "a ) 36 , b ) 40 , c ) 44 , d ) 48 , e ) 54", + "Correct": "e", + "Explanation": "for 40 hrs = 40 * 16 = 640 excess = 1032 - 640 = 392 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 392 / 28 = 98 / 7 = 14 total hrs = 40 + 14 = 54 answer e 52" + }, + { + "Answer": 2800, + "Options": "a ) rs . 3000 , b ) rs . 3600 , c ) rs . 2400 , d ) rs . 2800 , e ) none of these", + "Correct": "d", + "Explanation": "\"let the amount with r be rs . r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 7000 - r ) = > 3 r = 14000 - 2 r = > 5 r = 14000 = > r = 2800 . answer : d\"" + }, + { + "Answer": 95, + "Options": "a ) 95 kg , b ) 90 kg , c ) 85 kg , d ) data inadequate , e ) none of these", + "Correct": "a", + "Explanation": "\"a 95 kg total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 75 + 20 ) kg = 95 kg .\"" + }, + { + "Answer": 2560, + "Options": "a ) $ 1,600 , b ) $ 1,850 , c ) $ 2,250 , d ) $ 2,440 , e ) $ 2,560", + "Correct": "e", + "Explanation": "\"let x be the value of the item . 0.07 * ( x - 1000 ) = 109.20 x = 2560 the answer is e .\"" + }, + { + "Answer": 50, + "Options": "a ) 20 % , b ) 50 % , c ) 55 % , d ) 75 % , e ) 80 %", + "Correct": "b", + "Explanation": "\"r + w + p = 120 s + l = 120 1 / 3 * 120 = 40 short - stemmed white = 20 short - stemmed pink = 10 = > short - stemmed red = 10 10 / p = 10 / r = > r = p so total long stemmed = 80 and long stemmed red + long stemmed pink = 80 so long stemmed red / long stemmed = ? total white = 20 ( as no long stemmed white ) = > r + r + 20 = 120 = > 2 r = 100 and r = 50 long stemmed r = 50 - 10 = 40 so long stemmed red / r = 40 / 80 = 50 % answer - b\"" + }, + { + "Answer": 3, + "Options": "a ) 3 , b ) 5 , c ) 6 , d ) 8 , e ) 9", + "Correct": "a", + "Explanation": "\"sol . let the ten \u2019 s digit be x and unit \u2019 s digit be y , then , ( 10 x + y ) - ( 10 y + x ) = 27 \u21d4 9 ( x - y ) = 27 \u21d4 x - y = 3 answer a\"" + }, + { + "Answer": 0.4444444444444444, + "Options": "a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 4 / 9", + "Correct": "e", + "Explanation": "so not a vowel in set - 1 : 4 / 6 and not a vowel in ser - 2 : 5 / 6 now , 4 / 6 \u2217 5 / 6 = 5 / 9 this is for not a vowel . then for at least one vowel will be = 1 \u2212 5 / 9 = 4 / 9 answer will be e ." + }, + { + "Answer": 5, + "Options": "a ) 2 , b ) 4 , c ) 5 , d ) 7 , e ) 8", + "Correct": "c", + "Explanation": "p \u00f7 44 = 432 = > p = 432 * 44 = 19008 p / 31 = 19008 / 31 = 613 , remainder = 5 c" + }, + { + "Answer": 14, + "Options": "a ) 11 , b ) 13 , c ) 14 , d ) 12 , e ) 10", + "Correct": "c", + "Explanation": "\"explanation : let somu ' s age be x and that of his father be 3 x . so , x - 7 = 3 x - 7 / 5 = x = 14 answer : option c\"" + }, + { + "Answer": 12, + "Options": "a ) 11 , b ) 12 , c ) 28 , d ) 27 , e ) 19", + "Correct": "b", + "Explanation": "let the number of boys be x . then , ( 3 / 4 ) x = 18 or x = 18 x ( 4 / 3 ) = 24 . if total number of students is y , then ( 2 / 3 ) y = 24 or y = 24 x ( 3 / 2 ) = 36 . therefore number of girls in the class = ( 36 - 24 ) = 12 . answer : b" + }, + { + "Answer": 75625, + "Options": "a ) 34545 , b ) 46576 , c ) 67887 , d ) 57687 , e ) 75625", + "Correct": "e", + "Explanation": "121 \u00d7 54 = 121 \u00d7 ( 102 ) 4 = 121 \u00d7 1000016 = 7.5625 \u00d7 10000 = 75625 e" + }, + { + "Answer": 156, + "Options": "a ) 26 , b ) 39 , c ) 42 , d ) 65 , e ) 156", + "Correct": "e", + "Explanation": "\"here 156 has three two ' s two three ' s and one 13 rest of them must be in w so w = 13 * 3 * 4 = 156 answer : e\"" + }, + { + "Answer": 2976, + "Options": "a ) 2976 , b ) 2989 , c ) 2789 , d ) 2888 , e ) 2098", + "Correct": "a", + "Explanation": "\"let x be the number i chose , then x / 12 \u2212 240 = 8 x / 12 = 248 x = 2976 answer is a .\"" + }, + { + "Answer": 0.19999999999999998, + "Options": "a ) $ 0.15 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45", + "Correct": "b", + "Explanation": "\"on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.3 = 3 * x - - > x = $ 0.2 . answer : b .\"" + }, + { + "Answer": 0.5, + "Options": "a ) 1 / 2 , b ) 1 , c ) 2 , d ) 4 , e ) 8", + "Correct": "a", + "Explanation": "\"given : 3 / w + 3 / x = 3 / ywx = y find : ( w + x ) / 2 = ? 3 ( 1 / w + 1 / x ) = 3 ( 1 / y ) - divide both sides by 3 ( 1 / w + 1 / x ) = 1 / y ( x + w ) / wx = 1 / wx - sub ' d in y = wx x + w - 1 = 0 x + w = 1 therefore ( w + x ) / 2 = 1 / 2 ans : a\"" + }, + { + "Answer": 260, + "Options": "a ) 100 , b ) 260 , c ) 360 , d ) 400 , e ) 500", + "Correct": "b", + "Explanation": "\"since 140 students answered yes only for subject m , then the remaining 360 students who answered yes for subject m , also answered yes for subject r . so , 360 students answered yes for both subjects . if 360 students answered yes for both subjects , then 400 - 360 = 40 students answered yes only for subject r . so , we have that : 200 students answered yes only for subject m ; 40 students answered yes only for subject r ; 300 students answered yes for both subjects ; therefore 800 - ( 200 + 40 + 300 ) = 260 students did not answer yes for either subject . answer : b .\"" + }, + { + "Answer": 22030, + "Options": "a ) 1220 , b ) 1250 , c ) 2030 , d ) 22030 , e ) 1350", + "Correct": "d", + "Explanation": "required number = ( 555 + 445 ) * 2 * 110 + 30 = 220000 + 30 = 220030 . answer : d" + }, + { + "Answer": 2, + "Options": "a ) 36 , b ) 25 , c ) 2 , d ) 5 , e ) 3", + "Correct": "c", + "Explanation": "to find : x - 3 / x . let it be t . = > x - 3 / x = t = > ( x ^ 2 + 9 / x ^ 2 ) - 2 * x * 3 / x = t ^ 2 ( squaring both sides ) . = > ( 10 ) - 2 * 3 = 4 = > t ^ 2 = 4 . thus t = 2 or t = - 2 . answer c" + }, + { + "Answer": 13, + "Options": "a ) 23 , b ) 20 , c ) 13 , d ) 5 , e ) 2", + "Correct": "c", + "Explanation": "\"soln : { 12 } + { 10 } = 12 * { 10 } + { 10 } = 13 * { 10 } answer : c\"" + }, + { + "Answer": 600, + "Options": "a ) a ) 400 , b ) b ) 450 , c ) c ) 500 , d ) d ) 550 , e ) e ) 600", + "Correct": "e", + "Explanation": "\"10 * 150 = 1650 3 * 100 + 5 * 150 = 1050 1650 \u2013 1050 = 600 e\"" + }, + { + "Answer": 72900, + "Options": "a ) 81000 , b ) 81028 , c ) 27772 , d ) 72900 , e ) 22312", + "Correct": "d", + "Explanation": "57600 * 9 / 8 * 9 / 8 = 72900 . answer : d" + }, + { + "Answer": 26, + "Options": "a ) 45 , b ) 26 , c ) 44 , d ) 40 , e ) 46", + "Correct": "b", + "Explanation": "\"n th term of a . p = a + ( n - 1 ) * d = 8 + ( 10 - 1 ) * 2 , = 8 + 18 = 26 . answer : b\"" + }, + { + "Answer": 0.3, + "Options": "a ) 3 , b ) - 3 , c ) 10 / 3 , d ) 3 / 10 , e ) - 10 / 3", + "Correct": "d", + "Explanation": "( 10 x + 2 ) / 4 - ( 3 x - 6 ) / 18 = ( 2 x + 4 ) / 3 = > 18 ( 10 x + 2 ) / 4 - ( 3 x - 6 ) = 18 ( 2 x + 4 ) / 3 = > 4.5 ( 10 x + 2 ) - 3 x + 6 = 6 ( 2 x + 4 ) = > 45 x + 9 - 3 x + 6 = 12 x + 24 = > 45 x - 3 x - 12 x = 24 - 9 - 6 = > 30 x = 9 = > x = 9 / 30 = > x = 3 / 10 answer : d" + }, + { + "Answer": 64, + "Options": "a ) $ 60 , b ) $ 52 , c ) $ 63 , d ) $ 64 , e ) $ 68", + "Correct": "d", + "Explanation": "formula for vol of a cyl is pi * r ^ 2 * h so vy = 64 * vy y when half filled will cost 32 times x so ans is d" + }, + { + "Answer": 13, + "Options": "a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 13", + "Correct": "e", + "Explanation": "so i can write this as in - 3 i + 4 < = 15 or in - 3 i < = 11 so n can have - 8 to 14 = 13 true values . . . . e" + }, + { + "Answer": 26, + "Options": "a ) 20 , b ) 26 , c ) 24 , d ) 22 , e ) 30", + "Correct": "b", + "Explanation": "\"total # of codes possible is 3 * 3 * 3 = 27 . oit of those 27 codes only the product of 333 will be odd , the remaining 26 will have either 2 or 4 in them , which ensures that their product will be even . therefore the number of codes where the product of the digits is even = ( total ) - ( restriction ) = 27 - 1 = 26 . answer : b\"" + }, + { + "Answer": 144, + "Options": "a ) 216 , b ) 180 , c ) 144 , d ) 108 , e ) 72", + "Correct": "c", + "Explanation": "there are several ways to find the least common multiple of two numbers . in this case , the most efficient method is to use the greatest common factor : ( a * b ) / ( gcf ab ) = lcm ab the greatest common factor of 12 and 16 is 4 . so , 12 # 16 = 12 * 16 / 4 = 48 . the greatest common factor of 18 and 24 is 6 . so , 18 # 24 = 18 * 24 / 6 = 72 finally , the greatest common factor of 48 and 72 is 24 . so , e = ( ( 12 # 16 ) # ( 18 # 24 ) ) = 48 # 72 = ( 48 * 72 ) / 24 = 2 * 72 = 144 the correct answer is c ." + }, + { + "Answer": 2, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 6", + "Correct": "b", + "Explanation": "( - 2 ) ^ ( 2 m ) = 4 ^ m and 2 ^ ( 6 - m ) = 4 ^ ( ( 6 - m ) / 2 ) therefore , m = ( 6 - m ) / 2 2 m = 6 - m m = 2 answer b" + }, + { + "Answer": 18.333333333333332, + "Options": "a ) rs . 20 , b ) rs . 21.81 , c ) rs . 22 , d ) rs . 18.33 , e ) none", + "Correct": "d", + "Explanation": "\"solution s . i . on rs . ( 110 - 10 ) for a certain time = rs . 10 . s . i . on rs . 100 for double the time = rs . 20 . t . d . on rs . 120 = rs . ( 120 - 100 ) = rs . 20 . t . d . on rs . 110 = rs . ( 20 / 120 x 120 ) = rs . 18.33 . answer d\"" + }, + { + "Answer": 2000, + "Options": "a ) 3000 , b ) 4000 , c ) 2400 , d ) 2000 , e ) none of these", + "Correct": "d", + "Explanation": "original price = 1120 \u00d7 100 \u2044 70 \u00d7 100 \u2044 80 = 2000 answer d" + }, + { + "Answer": 19, + "Options": "a ) 33 , b ) 40 , c ) 49 , d ) 19 , e ) 61", + "Correct": "d", + "Explanation": "x - y + z = - 3 x / 4 + x + 3 x / 7 = ( - 21 + 28 + 12 ) x / 28 = 19 x / 28 19 is not divisible by 28 ( it ' s a prime # ) , so for least value , x = 28 answer - d" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 5 , c ) 3 , d ) 2 , e ) 6", + "Correct": "c", + "Explanation": "log 10 5 + log 10 ( 5 x + 1 ) = log 10 ( x + 5 ) + 1 log 10 5 + log 10 ( 5 x + 1 ) = log 10 ( x + 5 ) + log 10 10 log 10 [ 5 ( 5 x + 1 ) ] = log 10 [ 10 ( x + 5 ) ] 5 ( 5 x + 1 ) = 10 ( x + 5 ) 5 x + 1 = 2 x + 10 3 x = 9 = > x = 3 answer c" + }, + { + "Answer": 300, + "Options": "a ) 300 cm , b ) 15 cm , c ) 20 cm , d ) 10 cm , e ) 40 cm", + "Correct": "a", + "Explanation": "let their heights of x cm and ( x + 20 ) cm respectively . then , ( x + 20 ) - 10 = 3 ( x - 10 ) \u21d4 x + 10 = 3 x - 30 \u21d4 2 x = 40 \u2234 present height of taller tree = ( 20 + 10 ) = 30 cm . answer : 30 cm" + }, + { + "Answer": 40, + "Options": "a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 50 %", + "Correct": "d", + "Explanation": "\"pass percentage = 100 - ( 35 + 45 - 20 ) = 100 - 60 = 40 answer : d\"" + }, + { + "Answer": 88, + "Options": "a ) $ 85 , b ) $ 88 , c ) $ 91 , d ) $ 94 , e ) $ 97", + "Correct": "b", + "Explanation": "let t be the total amount of money spent . 7 * 10 + ( t / 8 + 7 ) = t 77 = 7 t / 8 t = ( 8 * 77 ) / 7 = 88 the answer is b ." + }, + { + "Answer": 150, + "Options": "a ) 210 , b ) 252 , c ) 280 , d ) 150 , e ) 420", + "Correct": "d", + "Explanation": "\"however the process of dividing the volume of box by the volume of a soap seems flawed but it does work in this case due to the numbers dimensions of the box = 25 * 42 * 60 dimensions of the soap = 10 * 6 * 7 we get = 5 x 6 x 5 = 150 so the question is why this particular arrangement , in order to maximize number of soaps we need to minimize the space wasted and this is the only config where we dont waste any space so we can expect the maximum number the answer is ( d )\"" + }, + { + "Answer": 19.846153846153847, + "Options": "a ) 18.75 , b ) 19.85 , c ) 20.32 , d ) 20.9 , e ) 21.0", + "Correct": "b", + "Explanation": "average age of university = ( ( 8 x 21 ) + ( 5 x 18 ) ) / 13 = 19.85 answer : b" + }, + { + "Answer": 40, + "Options": "a ) 25 , b ) 28 , c ) 30 , d ) 35 , e ) 40", + "Correct": "e", + "Explanation": "\"let b : y : g = 3 x : 7 x : 8 x . 3 x + 7 x + 8 x = 18 x = 144 - - > x = 8 . g - b = 8 x - 3 x = 5 x = 40 . the answer is e .\"" + }, + { + "Answer": 40, + "Options": "a ) 40 , b ) 44 , c ) 80 , d ) 88 , e ) 48", + "Correct": "a", + "Explanation": "\"according to the given conditions x + y = 22 and x ^ 2 + y ^ 2 = 404 now ( x + y ) ^ 2 = x ^ 2 + y ^ 2 + 2 xy so 22 ^ 2 = 404 + 2 xy so xy = 80 / 2 = 40 answer : a\"" + }, + { + "Answer": 500, + "Options": "a ) 300 , b ) w = 400 , c ) w = 500 , d ) w = 600 , e ) none of these", + "Correct": "c", + "Explanation": "\"{ managers } = { female managers } + { male managers } ; we are told that the total number of managers in the company is 2 / 5 of all the employees , thus { managers } = 2 / 5 ( m + f ) , where m and f are number of female and male employees , respectively . also , we know that 2 / 5 of all male employees are managers : { male managers } = 2 / 5 * mas well as there are total of 200 female managers : { female managers } = 200 ; thus : 2 / 5 ( m + f ) = 200 + 2 / 5 * m - - > f = 500 . answer : c .\"" + }, + { + "Answer": 42, + "Options": "a ) 10 , b ) 42 , c ) 14 , d ) 15 , e ) 60", + "Correct": "b", + "Explanation": "a : b 5 : 6 a + b = 77 5 x + 6 x = 77 x = 7 then two numbers are 35,42 . the bigger number is 42 answer : b" + }, + { + "Answer": 200, + "Options": "a ) 70 , b ) 80 , c ) 100 , d ) 140 , e ) 200", + "Correct": "e", + "Explanation": "according to the information in the question the maximum range would be between 400 and 700 ( 300 ) . the minimum range would be the greatest range for any one individual , which is listed in the problem as 100 . so the difference between these would be 300 - 100 or 200 . answer : e" + }, + { + "Answer": 17, + "Options": "a ) 12 , b ) 14 , c ) 17 , d ) 15 , e ) 16", + "Correct": "c", + "Explanation": "let p = 3 , q = 11 then 2 * 3 + 11 = 17 so 2 p + q = 17 . answer : c" + }, + { + "Answer": 0.1111111111111111, + "Options": "a ) 1 / 12 , b ) 1 / 6 , c ) 2 / 7 , d ) 1 / 3 , e ) 1 / 9", + "Correct": "e", + "Explanation": "totalsample spacefrom two fair six - sided dice is 36 . there are six possible ways to be 5 i . e . ( 1 + 4 ) , ( 2 + 3 ) , ( 3 + 2 ) , ( 4 + 1 ) so , total probability is 4 / 36 or 1 / 9 . answer is e ." + }, + { + "Answer": 363650, + "Options": "a ) 367300 , b ) 363580 , c ) 363650 , d ) 373650 , e ) 386750", + "Correct": "c", + "Explanation": "as per given data , p = 415600 , r 1 = 25 % incresed , r 2 = 30 % decreased population of the city at the end of the second year = p ( 1 + r 1 / 100 ) ( 1 - r 2 / 100 ) = 415600 ( 1 + 25 / 100 ) ( 1 - 30 / 100 ) = 363650 answer : c" + }, + { + "Answer": 134.8, + "Options": "a ) 134.8 , b ) 141.2 , c ) 147.2 , d ) 152.3 , e ) 160.1", + "Correct": "a", + "Explanation": "earning of the company from apple = 150 / 100 x 230 = 345 earning of the company from guava = 170 / 100 x 210 = 357 earning of the company from grape = 130 / 100 x 310 = 403 earning of the company from orange = 100 / 100 x 270 = 270 total earning of the company = 345 + 357 + 403 + 270 = 1375 total juice sold = 1020 average earning per 100 gallon of juice sold = ( 1375 / 1020 ) x 100 = $ 134.8 answer : a" + }, + { + "Answer": 0.5, + "Options": "a ) 4 / 2 , b ) 3 / 2 , c ) 1 / 2 , d ) 5 / 2 , e ) 7 / 2", + "Correct": "c", + "Explanation": "\"should be a sub - 600 level q . . volume = { 1 / 7 } / { 2 / 7 } = 1 / 2 c\"" + }, + { + "Answer": 84, + "Options": "a ) 28 , b ) 236 , c ) 288 , d ) 84 , e ) 26", + "Correct": "d", + "Explanation": "explanation : if each number is multiplied by k , then the new average increases by k times . so new average = 84 answer : d" + }, + { + "Answer": 0.7200000000000001, + "Options": "a ) 25 / 6 , b ) 36 / 25 , c ) 18 / 25 , d ) 5 / 6 , e ) 25 / 36", + "Correct": "c", + "Explanation": "\"5 x = 3 y = > x / y = 3 / 5 1 / 5 * x to 1 / 6 * y = x / y * 6 / 5 = ( 3 / 5 ) * ( 6 / 5 ) = 18 / 25 ans : c\"" + }, + { + "Answer": 100, + "Options": "a ) 0 , b ) 98 , c ) 99 , d ) 100 , e ) 90", + "Correct": "d", + "Explanation": "\"g ( 101 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 * 101 g ( 99 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 g ( 101 ) - g ( 99 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 * 101 - 1 * 3 * 5 * 7 * 9 * . . . * 99 = 1 * 3 * 5 * 7 * 9 * . . . * 99 * ( 101 - 1 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 * 100 hence : d\"" + }, + { + "Answer": 100, + "Options": "a ) 82 m , b ) 50 m , c ) 72 m , d ) 100 m , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : the relative speed of train is 46 - 36 = 10 km / hr = ( 10 x 5 ) / 18 = 25 / 9 m / s 10 \u00d7 518 = 259 m / s in 72 secs the total distance traveled is 72 x 25 / 9 = 200 m . therefore the length of each train is = 200 / 2 = 100 m . answer d\"" + }, + { + "Answer": 270.00000000000006, + "Options": "a ) 140 , b ) 320 , c ) 745 , d ) 270 , e ) 350", + "Correct": "d", + "Explanation": "let x be the total number of pages in the book , then she finished 23 \u22c5 x pages . then she has x \u2212 23 \u22c5 x = 13 \u22c5 xpages left . 23 \u22c5 x \u2212 13 \u22c5 x = 90 13 \u22c5 x = 90 x = 270 so the book is 270 pages long . correct answer is d ) 270" + }, + { + "Answer": 16, + "Options": "a ) 8 , b ) 12 , c ) 16 , d ) 20 , e ) 24", + "Correct": "c", + "Explanation": "\"the number of zeroes at the end of 70 ! will be less than the number of zeroes at the end of 140 ! hence it is sufficient to calculate the number of zeroes at the end of 70 ! the number of zeroes = [ 70 / 5 ] + [ 70 / 25 ] + [ 70 / 125 ] = 14 + 2 + 0 = 16 the answer is c .\"" + }, + { + "Answer": 60, + "Options": "a ) 95 , b ) 90 , c ) 85 , d ) 80 , e ) 60", + "Correct": "e", + "Explanation": "\"let x be the number of students in the school . 0.15 x students went to the trip and took more than 100 $ . they compose ( 100 - 75 ) = 25 % of all students who went to the trip . therefore the toal of 0.15 x / 0.25 = 0.6 x students went to the camping which is 60 % . the answer is e\"" + }, + { + "Answer": 94, + "Options": "a ) 80 , b ) 88 , c ) 94 , d ) 112 , e ) 124", + "Correct": "c", + "Explanation": "\"we see that h will be a maximum h = 150 when t - 3 = 0 , that is when t = 3 . at t = 5 , h = - 14 ( 5 - 3 ) ^ 2 + 150 = - 14 ( 4 ) + 150 = 94 the answer is c .\"" + }, + { + "Answer": 40.38461538461539, + "Options": "a ) 50.12 % , b ) 40.52 % , c ) 40.56 % , d ) 40.38 % , e ) 40.14 %", + "Correct": "d", + "Explanation": "\"say a 100 families existed in 1994 then the number of families owning a computer in 1994 - 40 number of families owning computer in 1998 = 35 * 120 / 100 = 42 number of families in 1998 = 104 the percentage = 42 / 104 * 100 = 40.38 % . option : d\"" + }, + { + "Answer": 0.11428571428571428, + "Options": "a ) 4 / 35 , b ) 2 / 3 , c ) 7 / 35 , d ) 5 / 7 , e ) 7 / 5", + "Correct": "a", + "Explanation": "let a be the event that ram is selected and b is the event that ravi is selected . p ( a ) = 4 / 7 p ( b ) = 1 / 5 let c be the event that both are selected . p ( c ) = p ( a ) x p ( b ) as a and b are independent events : = 4 / 7 x 1 / 5 = 4 / 35 answer : a" + }, + { + "Answer": 76, + "Options": "a ) 84 , b ) 64 , c ) 76 , d ) 72 , e ) none", + "Correct": "c", + "Explanation": "answer let the original number be n . so from question n - 3 n / 4 = 19 \u21d2 4 n - 3 n = 76 \u2234 n = 76 option : c" + }, + { + "Answer": 36.666666666666664, + "Options": "a ) 31 , b ) 36.67 , c ) 88 , d ) 13 , e ) 12", + "Correct": "b", + "Explanation": "\"total score of the batsman in 20 matches = 800 . total score of the batsman in the next 10 matches = 300 . total score of the batsman in the 30 matches = 1100 . average score of the batsman = 1100 / 30 = 36.67 . answer : b\"" + }, + { + "Answer": 22, + "Options": "a ) 22 , b ) 36 , c ) 39 , d ) 21 , e ) 11", + "Correct": "a", + "Explanation": "\"add the numbers of doughnuts . 6 + 8 + 8 = 22 . answer is a .\"" + }, + { + "Answer": 40000, + "Options": "a ) 26799 , b ) 24000 , c ) 26682 , d ) 29973 , e ) 40000", + "Correct": "e", + "Explanation": "\"x * ( 90 / 100 ) = 36000 x = 400 * 100 x = 40000 answer : e\"" + }, + { + "Answer": 16, + "Options": "a ) 11 , b ) 12 , c ) 13 , d ) 16 , e ) 17", + "Correct": "d", + "Explanation": "\"four wheeler = 16 * 4 = 64 ( max ) 2 wheel = 1 so no of 4 wheeler = 16 answer : d\"" + }, + { + "Answer": 15, + "Options": "a ) 22 , b ) 27 , c ) 15 , d ) 99 , e ) 21", + "Correct": "c", + "Explanation": "\"let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 80 x - ( 5 * 60 ) = 90 ( x - 5 ) 150 = 10 x = > x = 15 . answer : c\"" + }, + { + "Answer": 724787425, + "Options": "a ) 345434667 , b ) 246465757 , c ) 465767867 , d ) 725077485 , e ) 645354643", + "Correct": "d", + "Explanation": "\"72515 x 9999 = 72515 x ( 10000 - 1 ) = 72515 x 10000 - 72515 x 1 = 725150000 - 72515 = 725077485 d\"" + }, + { + "Answer": 16, + "Options": "a ) $ 14 , b ) $ 16 , c ) $ 18 , d ) $ 20 , e ) $ 22", + "Correct": "b", + "Explanation": "\"average price per book = ( 1080 + 840 ) / ( 65 + 55 ) = 1920 / 120 = $ 16 the answer is b .\"" + }, + { + "Answer": 174.25, + "Options": "a ) 174.75 cm , b ) 174.25 cm , c ) 173.75 cm , d ) 173.25 cm , e ) 172.75 cm", + "Correct": "b", + "Explanation": "the total height was 15 cm too much . the average height should be reduced by 15 cm / 20 = 0.75 cm the answer is b ." + }, + { + "Answer": 20, + "Options": "a ) 11 , b ) 13 , c ) 15 , d ) 18 , e ) 20", + "Correct": "e", + "Explanation": "\"the rate of 5 machines is rate = job / time = x / 4 units per day - - > the rate of 1 machine 1 / 5 * ( x / 4 ) = x / 20 units per day ; now , again as { time } * { combined rate } = { job done } then 2 * ( m * x / 20 ) = 2 x - - > m = 20 . answer : e .\"" + }, + { + "Answer": 9, + "Options": "a ) 9 , b ) 10 , c ) 12 , d ) 14 , e ) 16", + "Correct": "a", + "Explanation": "\"ifno caris selected more than once then the number of clients = 12 / 4 = 3 but since every car is being selected three times so no . of clients must be thrice as well = 3 * 3 = 9 answer : option a\"" + }, + { + "Answer": 1500, + "Options": "a ) 1500 , b ) 3100 , c ) 4400 , d ) 6200 , e ) 7400", + "Correct": "a", + "Explanation": "\"each term in set b is 60 more than the corresponding term in set a . the difference of the sums = 25 * 60 = 1500 . the answer is a .\"" + }, + { + "Answer": 287, + "Options": "a ) 288 , b ) 287 , c ) 72 , d ) 205 , e ) 267", + "Correct": "b", + "Explanation": "\"a : b : c = 100 : 65 : 40 = 20 : 13 : 8 8 - - - - 56 41 - - - - ? = > rs . 287 answer : b\"" + }, + { + "Answer": 1.6163438256658595, + "Options": "a ) $ 1.62 , b ) $ 1.64 , c ) $ 1.68 , d ) $ 1.72 , e ) $ 1.76", + "Correct": "a", + "Explanation": "\"( 1375 * 1.75 + 690 * 1.35 ) / ( 1375 + 690 ) = ~ 1.62 option ( a )\"" + }, + { + "Answer": 1210, + "Options": "a ) 2989 , b ) 2789 , c ) 1210 , d ) 1288 , e ) 1211", + "Correct": "c", + "Explanation": "\"\u03c0 ( 232 \u2013 122 ) = 1210 answer : c\"" + }, + { + "Answer": 54, + "Options": "a ) 52.2 , b ) 59.5 , c ) 52.8 , d ) 52.5 , e ) 54.0", + "Correct": "e", + "Explanation": "\"sum of the marks for the class of 12 students = 12 * 40 = 480 sum of the marks for the class of 28 students = 28 * 60 = 1680 sum of the marks for the class of 40 students = 480 + 1680 = 2160 average marks of all the students = 2160 / 40 = 54 answer : e\"" + }, + { + "Answer": 36, + "Options": "a ) 14 % , b ) 25 % , c ) 28 % , d ) 36 % , e ) 50 %", + "Correct": "d", + "Explanation": "official solution : if we start with 40 gallons of a mixture that is 10 % grape juice , then we have : 40 \u00d7 0.20 = 8 gallons of grape juice . 40 \u00d7 0.80 = 32 gallons of other components . if we add 10 gallons of grape juice , we will end up with 18 gallons of grape juice and 32 gallons of other components , and we will have a total of 50 gallons of the mixture . so 18 / 50 of the new mixture is grape juice . now we convert this to a percent : percent grape juice = 18 / 50 = 36 / 100 = 36 % . the correct answer is choice ( d )" + }, + { + "Answer": 0.010101010101010102, + "Options": "a ) 1 / 99 , b ) 1 / 6 , c ) 5 / 18 , d ) 13 / 18 , e ) 5 / 6", + "Correct": "a", + "Explanation": "probability of not getting the same flavor - > fouvarable - > cherry - orange [ 4 c 1 * 3 c 1 [ or simply 4 * 3 ] or cherry - lemon [ 4 * 4 ] or orange - lemon [ 3 * 4 ] prob = ( 4 * 3 + 4 * 4 + 3 * 4 ) / 9 c 2 = 40 / 3960 = 1 / 99 answer - > a" + }, + { + "Answer": 10, + "Options": "a ) $ 160 , b ) $ 96 , c ) $ 90 , d ) $ 10 , e ) $ 55", + "Correct": "d", + "Explanation": "7 teenagers - so total 7 people the bill $ 840 includes 20 % gratuity . . . so the actual cost of dinner was $ 700 now , the cost per person will be $ 700 / 7 which is $ 10 option d" + }, + { + "Answer": 39.99680025597952, + "Options": "a ) 25 , b ) 35 , c ) 45 , d ) 60 , e ) 40", + "Correct": "e", + "Explanation": "\"speed of the train = ( 63 * 5 / 18 ) m / sec = 35 / 2 m / sec . distance travelled = ( speed x time ) time = ( distance travelled / speed ) distance travelled = length of the train + length of the tunnel = 415 + 285 = 700 m time = ( 700 / 35 / 2 ) = 40 sec answer : e\"" + }, + { + "Answer": 1584, + "Options": "a ) 1584 , b ) 7640 , c ) 5640 , d ) 7240 , e ) 6780", + "Correct": "a", + "Explanation": "s is a set of all natural numbers less than 120 such that hcf of any element in s and 120 is 1 . such numbers are , s = { 1 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 , 53 , 59 , 61 , 67 , 71 , 73 , 79 , 83 , 89 , 97 , 101 , 103 , 107 , 109 , 113 } sum of s = 1584 . answer : a" + }, + { + "Answer": 180, + "Options": "a ) 60 , b ) 90 , c ) 120 , d ) 150 , e ) 180", + "Correct": "e", + "Explanation": "since the balls are all of different colors , let ' s permute them and then decide how many balls we put in each box . for example , arrange in a row the balls , then decide : two balls go into the first box , next two in the second box , and the last ball goes to the third box . since in each box there must be at least one ball , we have the possibilities of ( 2 , 2,1 ) , ( 2 , 1,2 ) , ( 1 , 2,2 ) or ( 3 , 1,1 ) , ( 1 , 3,1 ) , ( 1 , 1,3 ) balls in the three boxes . for the 2 , 2,1 type arrangements , we have [ 6 ! / ( 2 ! 2 ! 1 ! ) ] * 3 = 100 possibilities . inside a box , it does n ' t matter the order of the balls . for the 3 , 1,1 type arrangements , we have [ 6 ! / ( 3 ! 1 ! 1 ! ) ] * 3 = 80 possibilities . total of 100 + 80 = 180 possibilities . answer e ." + }, + { + "Answer": 183, + "Options": "a ) 187.89 cm , b ) 183.29 cm , c ) 123.98 cm , d ) 149.98 cm , e ) 146.89 cm", + "Correct": "b", + "Explanation": "\"calculated average height of 35 boys = 185 cm . wrong total height of 35 boys = 180 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 185 cm - ( 166 cm - 106 cm ) / 35 = 185 cm - 60 / 35 cm = 185 cm - 1.71 cm = 183.29 cm . answer : b\"" + }, + { + "Answer": 9, + "Options": "a ) 1 , b ) 7 . , c ) 2 . , d ) 3 , e ) 9", + "Correct": "e", + "Explanation": "a number ending in a 0 is divisible by 2 . a number ending in 2 zeroes is divisible by 4 . a number ending in 3 zeroes is divisible by 8 . a number ending in 4 zeroes in divisible by 16 . given the obscene number , you should immediately be convinced that you will need to focus on a very small part of it . 65,985 , 241,545 , 898,754 , 582,556 , 898,522 , 454,889 = 65,985 , 241,545 , 898,754 , 582,556 , 898,522 , 450,000 + 4,889 the first number is divisible by 16 . you just have to find the remainder when you divide 5287 by 16 . that will be the remainder when you divide the original number by 16 . 4889 / 16 gives remainder 9 . answer ( e )" + }, + { + "Answer": 900, + "Options": "a ) 600 , b ) 700 , c ) 800 , d ) 900 , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : let p ' s capital = p , q ' s capital = q and r ' s capital = r then 4 p = 6 q = 10 r = > 2 p = 3 q = 5 r = > q = 2 p / 3 r = 2 p / 5 p : q : r = p : 2 p / 3 : 2 p / 5 = 15 : 10 : 6 r ' s share = 4650 * ( 6 / 31 ) = 150 * 6 = 900 . answer : option d\"" + }, + { + "Answer": 17, + "Options": "a ) 17 , b ) 12 , c ) 13 , d ) 14 , e ) 15", + "Correct": "a", + "Explanation": "\"explanation : age of the 15 th student = [ 15 * 15 - ( 14 * 8 + 16 * 6 ) ] = 17 years . answer : a\"" + }, + { + "Answer": 0.9615384615384615, + "Options": "a ) 50 / 52 , b ) 55 / 52 , c ) 60 / 52 , d ) 40 / 52 , e ) 30 / 52", + "Correct": "a", + "Explanation": "\"say x = y = 10 . in this case we would have : 40 x = 400 black - and - white films ; 10 y = 100 color films . y / x % = 10 / 10 % = 1 % of the black - and - white films , so 4 black - and - white films and all 100 color films , thus total of 104 films were selected . color films thus compose 100 / 104 = 50 / 52 of the selected films . answer : a\"" + }, + { + "Answer": 14, + "Options": "a ) 14 , b ) 27 , c ) 21 , d ) 18 , e ) 11", + "Correct": "a", + "Explanation": "\"( a + b ) - ( b + c ) = 14 a - c = 14 . c is younger than a by 14 years . answer : a\"" + }, + { + "Answer": 19, + "Options": "a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19", + "Correct": "e", + "Explanation": "explanation : let the number of persons be n \u00e2 \u02c6 \u00b4 total handshakes = nc 2 = 171 n ( n - 1 ) / 2 = 171 \u00e2 \u02c6 \u00b4 n = 19 answer : option e" + }, + { + "Answer": 130, + "Options": "a ) 65 km , b ) 100 km , c ) 120 km , d ) 130 km , e ) 140 km", + "Correct": "d", + "Explanation": "explanation : let the journey be x km then , 3 x / 5 + 7 x / 20 + 6.5 = x 12 x + 7 x + 130 = 20 x x = 130 km answer : option d" + }, + { + "Answer": 269, + "Options": "a ) 249 , b ) 498 , c ) 676 , d ) 269 , e ) 1,002", + "Correct": "d", + "Explanation": "\"slope of 2 and a y - intercept of 2 y - coordinate is 540 y = 2 x + 2 538 = 2 x x = 269 answer : d . 269\"" + }, + { + "Answer": 45.6, + "Options": "a ) 47 , b ) 45.6 , c ) 44 , d ) 48 , e ) 49", + "Correct": "b", + "Explanation": "\"explanation : total marks obtained by a class of 25 students = 3 * 95 + 3 * 0 + 19 * 45 = 1140 average marks of whole class = 1140 / 25 = 45.6 answer : option b\"" + }, + { + "Answer": 48600, + "Options": "a ) $ 24960 , b ) $ 25920 , c ) $ 28080 , d ) $ 38500 , e ) $ 48600", + "Correct": "e", + "Explanation": "\"from 9 : 00 in the morning to 5 : 55 in the afternoon , inclusive there are 9 * 12 = 108 five - minute intervals , thus total of 108 * 50 tickets were sold . say x student and 3 x regular tickets were sold , then x + 3 x = 108 * 50 - - > x = 27 * 50 and 3 x = 3 * ( 27 * 50 ) = 27 * 150 . therefore , the total revenue from ticket sales that day was 27 * 50 * 6 + 27 * 150 * 10 = $ 48,600 . answer : e .\"" + }, + { + "Answer": 72, + "Options": "a ) 70 , b ) 71 , c ) 72 , d ) 73 , e ) 74", + "Correct": "c", + "Explanation": "explanation : let the second number is x , then first is 2 x , and third is 1 / 3 ( 2 x ) = > 2 x + x + 2 x / 3 = 264 < = > 11 x / 3 = 264 = > x = 72 answer : option c" + }, + { + "Answer": 10, + "Options": "a ) 7 , b ) 10 , c ) 20 , d ) 32 , e ) 35", + "Correct": "b", + "Explanation": "\"on dividing 105829 by 21 we get the remainder 10 , so 10 should be subtracted answer is b\"" + }, + { + "Answer": 65, + "Options": "a ) 30 , b ) 65 , c ) 60 , d ) 55 , e ) 56", + "Correct": "b", + "Explanation": "\"explanation : if teacher ' s age is 14 years , there is no change in the average . but teacher has contributed 1 year to all the students along with maintaining his age at 15 . age of teacher = average age of all + total increase in age = 15 + ( 1 x 50 ) = 65 years answer : b\"" + }, + { + "Answer": 720, + "Options": "a ) $ 200 , b ) $ 300 , c ) $ 400 , d ) $ 720 , e ) $ 600", + "Correct": "d", + "Explanation": "\"c for cost . p price per person . c = 3 * p c = 4 * p - 240 substituting the value of p from the first equation onto the second we get p = 240 . plugging in the value of p in the first equation , we get c = 720 . which leads us to answer choice d\"" + }, + { + "Answer": 12, + "Options": "a ) 6 , b ) 12 , c ) 24 , d ) 36 , e ) 48", + "Correct": "b", + "Explanation": "\"q : if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer w that must divide n is : a 6 , b 12 , c 24 , d 36 , e 48 n ^ 2 is divisible by 72 , but it must also be greater than 72 . if n is an integer , then n ^ 2 must be a perfect square . the factorization of 72 is ( 8 ) ( 9 ) , so if it is multiplied by 2 , it will be ( 2 ) ( 8 ) ( 9 ) = ( 16 ) ( 9 ) = 144 , a perfect square . so n ^ 2 must be at least 144 or a multiple of 144 , which means that n must be 12 or a multiple of 12 . b\"" + }, + { + "Answer": 10011, + "Options": "a ) 10101 , b ) 10110 , c ) 11100 , d ) 11001 , e ) 11011", + "Correct": "a", + "Explanation": "according to order of operations , 10 ? 2 ? 5 ( division and multiplication ) is done first from left to right 10 / 2 = 5 * 2 = 10 hence 10111 - 10 * 2 * 5 = 10111 - 10 = 10101 correct answer a" + }, + { + "Answer": 26, + "Options": "a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28", + "Correct": "d", + "Explanation": "\"364 = 26 * 14 = 28 * 13 there are 26 people in the group today . the answer is d .\"" + }, + { + "Answer": 50, + "Options": "a ) 25 , b ) 50 , c ) 60 , d ) 75 , e ) none", + "Correct": "b", + "Explanation": "explanation : let the number be a , then a / 5 \u2212 5 = 5 \u21d2 a / 5 = 10 \u21d2 a = 50 correct option : b" + }, + { + "Answer": 12, + "Options": "a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16", + "Correct": "c", + "Explanation": "( x + 3 ) ^ 2 / ( 2 x + 15 ) = 3 ( x + 3 ) ^ 2 = 3 ( 2 x + 15 ) x ^ 2 + 6 x + 9 = 6 x + 45 x ^ 2 - 36 = 0 ( x - 6 ) ( x + 6 ) = 0 x = 6 or x = - 6 the answer is c ." + }, + { + "Answer": 2, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "b", + "Explanation": "explanation : since the number of carbons is 2 , only two copies can be obtained . answer : b" + }, + { + "Answer": 17, + "Options": "a ) 8 , b ) 16 , c ) 17 , d ) 18 , e ) 34", + "Correct": "c", + "Explanation": "\"minimum age = average - 1 standard deviation = 30 - 8 = 22 maximum age = average + 1 standard deviation = 30 + 8 = 38 maximum number of different ages of the applicants = 38 - 22 + 1 = 17 answer c\"" + }, + { + "Answer": 15.512820512820513, + "Options": "a ) rs 13.51 , b ) rs 15.51 , c ) rs 16.51 , d ) rs 14.51 , e ) rs 17.51", + "Correct": "b", + "Explanation": "let cost of pencil = rs x cost of notebook = rs y cost of 8 dozen pencils are 96 x cost of 2 dozen pencils are 24 y cost of 3 pencils are 3 x cost of 4 notebooks are 4 y equations are 96 x + 24 y = 520 - - - - - 1 3 x + 4 y = 60 - - - - - 2 multiplying 6 with equation ( 2 ) and then subtracting eqn ( 1 ) - eqn ( 2 ) , we get 96 x + 24 y = 520 18 x + 24 y = 360 after solving the equations , we get x = 2.05 y = 13.46 cost of 1 pencil and 1 notebook is 2.05 + 13.46 = rs 15.51 answer : b" + }, + { + "Answer": 28, + "Options": "a ) 33 , b ) 67 , c ) 28 , d ) 31 , e ) 35", + "Correct": "c", + "Explanation": "let present age of p and q be 3 x 3 x and 4 x 4 x respectively . eight years ago , p was half of q ' s age \u00e2 \u2021 \u2019 ( 3 x \u00e2 \u02c6 \u2019 8 ) = 1 / 2 ( 4 x \u00e2 \u02c6 \u2019 8 ) \u00e2 \u2021 \u2019 6 x \u00e2 \u02c6 \u2019 16 = 4 x \u00e2 \u02c6 \u2019 8 \u00e2 \u2021 \u2019 2 x = 8 \u00e2 \u2021 \u2019 x = 4 total of their present ages = 3 x + 4 x = 7 x = 7 \u00e3 \u2014 4 = 28 c" + }, + { + "Answer": 6.6, + "Options": "a ) 2.3 , b ) 6.6 , c ) 3.6 , d ) 4.5 , e ) 4.6", + "Correct": "b", + "Explanation": "\"sum of the remaining two numbers = ( 4.6 * 6 ) - [ ( 3.4 * 2 ) + ( 3.8 * 2 ) ] = 27.60 - ( 6.8 + 7.6 ) = 27.60 - 14.40 = 13.20 . required average = ( 13.2 / 2 ) = 6.6 . answer : b\"" + }, + { + "Answer": 5, + "Options": "a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 10", + "Correct": "b", + "Explanation": "\"sol . on dividing 13924 by 97 , we get remainder = 5 . \u2234 required number to be subtracted = 5 . answer b\"" + }, + { + "Answer": 360, + "Options": "a ) 300 km , b ) 320 km , c ) 360 km , d ) 390 km , e ) 400 km", + "Correct": "c", + "Explanation": "\"sol . average speed of a tractor = 25 km / h the speed of a bus in an hour = 25 \u00d7 2 = 50 km the speed of a car in an hour = 9 / 5 * 50 = 90 km so , the distance covered by car in 4 h is 90 \u00d7 4 = 360 km ans . ( c )\"" + }, + { + "Answer": 100, + "Options": "a ) 120 , b ) 100 , c ) 125 , d ) 150 , e ) none of these", + "Correct": "b", + "Explanation": "explanation : solution : let the number be x . then , x - 3 / 4 x = 100 = > x / 4 = 100 = > x = 400 . 25 % of x = 25 % of 400 = 25 / 100 * 400 = 100 . answer : b" + }, + { + "Answer": 740, + "Options": "a ) 200 , b ) 740 , c ) 780 , d ) 500 , e ) 100", + "Correct": "b", + "Explanation": "\"let x be the number i chose , then x / 4 \u2212 175 = 10 x / 4 = 185 x = 740 answer is b .\"" + }, + { + "Answer": 19, + "Options": "a ) 17 , b ) 19 , c ) 20 , d ) 21 , e ) 22", + "Correct": "b", + "Explanation": "the answer will be 19 . explanation : 78 = 2 * 3 * 13 now multiples of 78 , 156 . . . . 780 , now 1000 - 780 = 220 only two more muktiples of 78 can exists . so total number of 3 digit multiples of 78 are 9 + 2 = 11 91 = 13 * 7 - - total number of three digit multiples - - 9 no remember we have a common multiples as well n - - 13 * 7 * 6 = 91 * 6 = 546 so total number of multiples - - 11 + 9 - 1 = 19 . hence answer is 19 . b" + }, + { + "Answer": 132, + "Options": "a ) 68 , b ) 132 , c ) 86 , d ) 105.6 , e ) 108", + "Correct": "b", + "Explanation": "\"x = 88 * 1.5 = 132 so the answer is b .\"" + }, + { + "Answer": 57, + "Options": "a ) a ) 99 , b ) b ) 84 , c ) c ) 72 , d ) d ) 57 , e ) e ) 67", + "Correct": "d", + "Explanation": "a ) 99 = 9 * 11 b ) 84 = 4 * 7 * 3 c ) 72 = 9 * 11 d ) 65 = 5 * 13 e ) 57 = 19 * 3 since 19 is not there in first 15 positive numbers it is the only possibility d )" + }, + { + "Answer": 900, + "Options": "a ) 450 , b ) 810 , c ) 900 , d ) 1000 , e ) 1100", + "Correct": "c", + "Explanation": "we want the sum of the digits from 0 to 99 , so i approximated : 0 - 9 - > 45 - > ( 9 + 0 ) * 10 / 2 40 - 49 - > 85 ( 13 + 4 ) * 10 / 2 90 - 99 - > 135 ( 18 + 9 ) * 10 / 2 we can see at a glance that theweightgoes up as the numbers go up ( meaning the difference between 85 and 45 is 40 , while 135 - 85 is 50 , this means that the second part of this sequence carries more weight for our result ) , so we know that the final answer has to be more than 850 ( 85 * 10 ) but close to it , and that ' s just e = 900 : the answer is c ." + }, + { + "Answer": 0.97, + "Options": "a ) 0.97 , b ) 9.4 , c ) 0.094 , d ) 94 , e ) none", + "Correct": "a", + "Explanation": "\"answer let a - 3 % of a = ab . \u21d2 ( 97 x a ) / 100 = ab \u2234 b = 0.97 correct option : a\"" + }, + { + "Answer": 4, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "c", + "Explanation": "\"when a certain number x is divided by 61 , the remainder is 24 . what is the remainder when x is divided by 5 ? putting a value say x = 24 we get remainder as 24 when divided by 61 . when 24 divided by 5 we get 4 as remainder . c is the answer .\"" + }, + { + "Answer": 1008.2442067736184, + "Options": "a ) 120 , b ) 180 , c ) 1003 , d ) 1000 , e ) 1,440", + "Correct": "c", + "Explanation": "\"diameter of car tire = 10 inches radius of car tire = 5 inches = 5 * 2.54 cm = 12.7 cm circumference of the car tire = 2 * pi * 12.7 = 2 * 3.14 * 12.7 = 79.76 cm distance traveled by car = . 5 mile = . 5 * 1.6 km = . 8 km = 800 m = 8 * 10 ^ 4 cm number of revolutions = distance traveled / circumference of tire = 8 * 10 ^ 4 / 79.76 = 1003 since the answer choices are far apart we should use estimation in this question . ideally , in the gmat the conversion between units would be provided . answer c\"" + }, + { + "Answer": 15, + "Options": "a ) 15 % , b ) 20 % , c ) 10 % , d ) 25 % , e ) 30 %", + "Correct": "a", + "Explanation": "let original salary be $ 100 increased salary = 10 % of ( 150 % of $ 100 ) = ( 10 / 100 ) * ( 150 / 100 ) * 100 = $ 15 increase = 15 % correct option is a" + }, + { + "Answer": 54, + "Options": "a ) 57 , b ) 54 , c ) 77 , d ) 87 , e ) 97", + "Correct": "b", + "Explanation": "money collected = ( 29.16 x 100 ) paise = 29.16 paise numbers of members = 2916 squareroot = 54 answer b" + }, + { + "Answer": 86, + "Options": "a ) 56 kg , b ) 90 kg , c ) 86 kg , d ) data inadequate , e ) none of these", + "Correct": "c", + "Explanation": "\"c 86 kg total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 66 + 20 ) kg = 86 kg .\"" + }, + { + "Answer": 3030, + "Options": "a ) 3111 , b ) 300 , c ) 3029 , d ) 3030 , e ) 3003", + "Correct": "d", + "Explanation": "required sum = 3000 + 30 = 3030 answer is d" + }, + { + "Answer": 48.792857142857144, + "Options": "a ) 48.79286 , b ) 42.25 , c ) 50.87364 , d ) 51.25 , e ) 52.25474", + "Correct": "a", + "Explanation": "\"explanation : average weight of 20 boys = 50.25 total weight of 20 boys = 50.25 \u00d7 20 average weight of remaining 8 boys = 45.15 total weight of remaining 8 boys = 45.15 \u00d7 8 total weight of all boys in the class = ( 50.25 \u00d7 20 ) + ( 45.15 \u00d7 8 ) total boys = 20 + 8 = 28 average weight of all the boys = ( 50.25 \u00d7 20 ) + ( 45.15 \u00d7 8 ) / 28 = answer : option a\"" + }, + { + "Answer": 3.67200000000048, + "Options": "a ) s . 2.04 , b ) s . 2.08 , c ) s . 3.67 , d ) s . 2.83 , e ) s . 2.42", + "Correct": "c", + "Explanation": "c . i . when interest is compounded yearly = [ 9000 * ( 1 + 4 / 100 ) * ( 1 + ( 1 / 2 * 4 ) / 100 ] = 9000 * 26 / 25 * 51 / 50 = rs . 9547.2 c . i . when interest is compounded half - yearly = [ 9000 * ( 1 + 2 / 100 ) 2 ] = ( 9000 * 51 / 50 * 51 / 50 * 51 / 50 ) = rs . 9550.87 difference = ( 9550.87 - 9547.2 ) = rs . 3.67 . answer : c" + }, + { + "Answer": 150, + "Options": "a ) $ 130 , b ) $ 140 , c ) $ 150 , d ) $ 160 , e ) $ 170", + "Correct": "c", + "Explanation": "let the price of the meal be x . after a 10 % sales tax addition , the price is 1.1 * x after a 20 % tip on this amount , the total is 1.2 * 1.1 * x = 1.32 x 1.32 x = 198 x = $ 150 the correct answer is c ." + }, + { + "Answer": 46, + "Options": "a ) 15 % , b ) 18 % , c ) 25 % , d ) 36 % , e ) 46 %", + "Correct": "e", + "Explanation": "\"given voters in ratio 2 : 1 let x has 200 votersy has 100 voters for x 64 % voted means 64 * 200 = 128 votes combined for xy has 300 voters and voted 58 % so total votes = 174 balance votes = 174 - 128 = 46 as y has 100 voters so 46 votes means 46 % of votes required ans e\"" + }, + { + "Answer": 3, + "Options": "a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3", + "Correct": "e", + "Explanation": "\"x is an integer and 2.134 \u00d7 10 x is less than 21,000 , what is the greatest possible value for x ? for 2.134 \u00d7 10 x is less than 21,000 to remain true , the greatest number is 2,134 , which makes x = 3 e . 3\"" + }, + { + "Answer": 23, + "Options": "a ) 87 , b ) 67 , c ) 23 , d ) 75 , e ) 25", + "Correct": "c", + "Explanation": "let the initial number of members in the group be n . initial total weight of all the members in the group = n ( 48 ) from the data , 48 n + 78 + 93 = 51 ( n + 2 ) = > 51 n - 48 n = 69 = > n = 23 therefore there were 23 members in the group initially . answer : c" + }, + { + "Answer": 11, + "Options": "a ) $ 10 , b ) $ 7 , c ) $ 8.5 , d ) $ 9 , e ) $ 11", + "Correct": "e", + "Explanation": "5 toys - > total cost = 5 * avg cost = 5 * 10 = 50 sixth toy cost = 16 total cost for 6 toys = 50 + 16 = 66 am = 66 / 6 = 11 hence e" + }, + { + "Answer": 1, + "Options": "a ) 3 : 2 , b ) 1 : 1 , c ) 3 : 1 , d ) 5 : 2 , e ) 4 : 3", + "Correct": "b", + "Explanation": "\"g = 10 w c = 6 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 10 w + 6 wx = x + 1 * 8 w 10 + 6 x = 8 ( x + 1 ) x = 1 / 1 ratio of gold with copper = 1 : 1 = 1 : 1 answer is b\"" + }, + { + "Answer": 0.42857142857142855, + "Options": "a ) 1 / 9 , b ) 1 / 6 , c ) 3 / 7 , d ) 4 / 9 , e ) 5 / 9", + "Correct": "c", + "Explanation": "\"her tips were 3 / 4 of her salary . let ' s say her salary = $ 4 this mean her tips = ( 3 / 4 ) ( $ 4 ) = $ 3 so , her total income = $ 4 + $ 3 = $ 7 what fraction of her income for the week came from tips $ 3 / $ 7 = 3 / 7 = c\"" + }, + { + "Answer": 61, + "Options": "a ) 65 , b ) 61 , c ) 59 , d ) 63 , e ) 64", + "Correct": "b", + "Explanation": "\"age of the 20 th student = 20 * 20 - ( 9 * 11 + 10 * 24 ) = 400 - 339 = 61 years answer is b\"" + }, + { + "Answer": 300, + "Options": "a ) s . 80 , b ) s . 85 , c ) s . 90 , d ) s . 300 , e ) s . 120", + "Correct": "d", + "Explanation": "\"9 / 12 = 3 / 4 * 500 = 375 300 - - - - - - - - - - - - - 75 1 / 4 - - - - - - - - 75 1 - - - - - - - - - ? = > rs . 300 answer : d\"" + }, + { + "Answer": 51, + "Options": "a ) 51 , b ) 37 , c ) 54 , d ) 99 , e ) 01", + "Correct": "a", + "Explanation": "\"the number of students with first division = 29 % of 300 = 29 / 100 \u00d7 300 = 8700 / 100 = 87 and , the number of students with second division = 54 % of 300 = 54 / 100 \u00d7 300 = 16200 / 100 = 162 therefore , the number of students who just passed = 300 \u2013 ( 87 + 162 ) = 51 answer : a\"" + }, + { + "Answer": 28, + "Options": "a ) 20 , b ) 25 , c ) 28 , d ) 20 , e ) 42", + "Correct": "c", + "Explanation": "\"x + y = 20 x - y = 36 2 x = 56 x = 28 answer is c\"" + }, + { + "Answer": 9, + "Options": "a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9", + "Correct": "e", + "Explanation": "the tens digit of 6 in integer power starting from 2 ( 6 ^ 1 has no tens digit ) repeats in a pattern of 5 : { 3 , 1 , 9 , 7 , 5 } : the tens digit of 6 ^ 2 = 36 is 3 . the tens digit of 6 ^ 3 = 216 is 1 . the tens digit of 6 ^ 4 = . . . 96 is 9 . the tens digit of 6 ^ 5 = . . . 76 is 7 . the tens digit of 6 ^ 6 = . . . 56 is 5 . the tens digit of 6 ^ 7 = . . . 36 is 3 again . etc . . . 19 has the form 5 n + 4 , so the tens digit of 6 ^ 19 is 9 . the answer is e ." + }, + { + "Answer": 100, + "Options": "a ) 50 , b ) 100 , c ) 110 , d ) 120 , e ) 130", + "Correct": "b", + "Explanation": "2 bats + 3 ball = 1300 - - - ( 1 ) 3 bats + 3 ball = 1200 - - - ( 2 ) subtracting 2 nd from 1 st , we get - bats + ball = 100 = > ball - bats = 100 b" + }, + { + "Answer": 0.6, + "Options": "a ) 0 , b ) 1 / 3 , c ) 2 / 5 , d ) 1 / 2 , e ) 3 / 5", + "Correct": "e", + "Explanation": "answer e . total # of outcomes : 5 * 5 = 25 # of outcomes where product is - ve : ( - 6,1 ) , ( - 6,2 ) , ( - 6,3 ) . . . hence , total : 15 probability : 15 / 25 = 3 / 5" + }, + { + "Answer": 8.38, + "Options": "a ) $ 8.38 , b ) $ 6.85 , c ) $ 8.46 , d ) $ 10.08 , e ) $ 11.85", + "Correct": "a", + "Explanation": "\"answer = a 2 * 2.45 + 4 * 0.87 = 2 ( 2.50 - 0.05 ) + 4 ( 1.00 - 0.13 ) = 5 + 4 - 0.1 - 0.52 = 9 - 0.62 = 8.38\"" + }, + { + "Answer": 11, + "Options": "a ) 11 , 42 , b ) 12 , 24 , c ) 15 , 42 , d ) 16 , 19 , e ) 33 , 44", + "Correct": "a", + "Explanation": "a 11 , 42 let the age of priya = x years then , the age of her father = ( x + 31 ) years atq , ( x + 8 ) + ( x + 31 + 8 ) = 69 2 x + 47 = 69 2 x = 69 \u2013 47 = 22 x = 11 the age of priya = 11 years the age of her father = 11 + 31 = 42 years" + }, + { + "Answer": 3, + "Options": "a ) 2 , b ) 4 , c ) 3 , d ) 5 , e ) 6", + "Correct": "c", + "Explanation": "\"cant think of a straight approach but here is how i solved it : k is divided by 5 and remainder is 2 . this means k = 5 n + 2 ( n is an integer ) so the possible values of k = { 2 , 7 , 12 , 17 , 22 , 27 , 32 , 37 } ( less than 38 ) secondly , if k is divided by 6 , the remainder is 5 = > k = 6 m + 5 so the possible value set for k = { 5 , 11 , 17 , 23 , 29,35 } ( less than 38 ) 17 is the only common number in both the sets . hence k = 17 answer : c\"" + }, + { + "Answer": 14, + "Options": "a ) 4 % , b ) 10 % , c ) 14 % , d ) 15 % , e ) 18 %", + "Correct": "c", + "Explanation": "let cost of prod for 1 ticket = 1 so cop for n tickets = n so for selling n tickets , sp = 1.2 * n = 1.2 n so sp of 1 ticket = 1.2 sp of 95 % tickets = 1.2 * 0.95 n so profit % = ( 1.2 * 0.95 n - n ) / n * 100 = 0.14 * 100 = 14 % answer - c" + }, + { + "Answer": 8, + "Options": "a ) 2 , b ) 5 , c ) 8 , d ) 9 , e ) 10", + "Correct": "c", + "Explanation": "explanation : let the numbers be x , x + 2 , x + 4 , x + 6 and x + 8 . then , ( x + ( x + 2 ) + ( x + 4 ) + ( x + 6 ) + ( x + 8 ) ) / 5 = 55 5 x + 20 = 275 x = 255 / 5 = 51 . so , required difference = ( 51 + 8 ) 51 = 8 answer : c" + }, + { + "Answer": 42, + "Options": "a ) a ) 47 , b ) b ) 45.6 , c ) c ) 42 , d ) d ) 48 , e ) e ) 49", + "Correct": "c", + "Explanation": "\"explanation : total marks obtained by a class of 25 students = 3 * 95 + 5 * 0 + 17 * 45 = 1050 average marks of whole class = 1050 / 25 = 42 answer : option c\"" + }, + { + "Answer": 52.25308641975309, + "Options": "a ) 50.25 , b ) 52.25 , c ) 51.25 , d ) 53.25 , e ) none of the above", + "Correct": "b", + "Explanation": "\"required average marks = 40 \u00d7 50 + 35 \u00d7 60 + 45 \u00d7 55 + 42 \u00d7 45 / 40 + 35 + 45 + 42 = 2000 + 2100 + 2475 + 1890 / 162 = 8465 \u2044 162 = 52.25 answer b\"" + }, + { + "Answer": 2000, + "Options": "a ) 500 , b ) 1000 , c ) 6000 , d ) 7000 , e ) 2000", + "Correct": "e", + "Explanation": "\"total sale for 5 months = rs . ( 3435 + 3920 + 3855 + 4230 + 3560 ) = rs . 19000 . required sale = rs . [ ( 3500 x 6 ) - 19000 ] = rs . ( 21000 - 19000 ) = rs . 2000 answer : option e\"" + }, + { + "Answer": 6, + "Options": "a ) 5 , b ) 7 , c ) 6 , d ) 11 , e ) 12", + "Correct": "c", + "Explanation": "\"option ' c ' 45 / 12 = 3 and 110 / 12 = 9 = = > 9 - 3 = 6 numbers\"" + }, + { + "Answer": 97, + "Options": "a ) 15 , b ) 21 , c ) 17 , d ) 19 , e ) 97", + "Correct": "e", + "Explanation": "\"total money = rs . 10350 . let 50 rupees note was x . then 500 rupees note = 108 - x now , 50 * x + 500 * ( 108 - x ) = 10350 50 x + 54000 - 500 x = 10350 - 450 x = - 43650 x = 97 . no . of 50 rupees note = 97 . answer : option e\"" + }, + { + "Answer": 55.00000000000001, + "Options": "a ) 45 % , b ) 48 % , c ) 55 % , d ) 58 % , e ) 65 %", + "Correct": "c", + "Explanation": "\"when the storm deposited 120 billion gallons , volume of water in the reservoir = 220 + 120 = 340 billion gallons if this is only 85 % of the capacity of the reservoir , the total capacity of the reservoir = 340 / 0.85 = 400 billion gallons therefore percentage of reservoir that was full before the storm = ( 220 / 400 ) * 100 = 55 % option c\"" + }, + { + "Answer": 724807415, + "Options": "a ) 345434667 , b ) 246465757 , c ) 465767867 , d ) 725097483 , e ) 645354643", + "Correct": "d", + "Explanation": "\"72518 x 9999 = 72517 x ( 10000 - 1 ) = 72517 x 10000 - 72517 x 1 = 725170000 - 72517 = 725097483 d\"" + }, + { + "Answer": 3800, + "Options": "a ) a ) 3800 , b ) b ) 4200 , c ) c ) 4400 , d ) d ) 4500 , e ) e ) 4600", + "Correct": "a", + "Explanation": "\"x * ( 90 / 100 ) * ( 85 / 100 ) = 2907 x = 3800 answer : a\"" + }, + { + "Answer": 26, + "Options": "a ) 24 , b ) 34 , c ) 29 , d ) 35 , e ) 26", + "Correct": "e", + "Explanation": "let the five numbers be a , b , c , d , e . then their average is ( a + b + c + d + e ) / 5 = 20 a + b + c = 48 ( 48 + d + e ) / 5 = 20 48 + d + e = 100 d + e = 52 average = 52 / 2 = 26 ans e" + }, + { + "Answer": 9.2727, + "Options": "a ) 9 % , b ) 9.27 % , c ) 27 % , d ) 12 % , e ) none of these", + "Correct": "b", + "Explanation": "\"actual increase in population = 3 % let , earlier population = 100 then the population after 3 years = 100 ( 1 + 3 / 100 ) ^ 3 = 109.2727 \u2234 required percentage = 9.27 % answer : b\"" + }, + { + "Answer": 183, + "Options": "a ) 178.27 cm , b ) 183.29 cm , c ) 978.29 cm , d ) 178.89 cm , e ) 176.29 cm", + "Correct": "b", + "Explanation": "\"calculated average height of 35 boys = 185 cm . wrong total height of 35 boys = 185 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 185 cm - ( 166 cm - 106 cm ) / 35 = 185 cm - 60 / 35 cm = 185 cm - 1.71 cm = 183.29 cm . answer : b\"" + }, + { + "Answer": 2.4722222222222223, + "Options": "a ) $ 1.09 , b ) $ 1.67 , c ) $ 2.225 , d ) $ 2.47 , e ) $ 2.50", + "Correct": "d", + "Explanation": "\"total cost of parking for 10 hours = 10 $ for the first 2 hours and then 1.75 for ( 9 - 2 ) hours = 10 + 7 * 1.75 = 22.25 thus the average parking price = 22.25 / 9 = 2.47 $ d is the correct answer .\"" + }, + { + "Answer": 1680, + "Options": "a ) 2377 , b ) 1683 , c ) 2677 , d ) 9972 , e ) 1611", + "Correct": "b", + "Explanation": "\"explanation : l . c . m . of 5 , 6 , 7 , 8 = 840 . { \\ color { blue } \\ therefore } required number is of the form 840 k + 3 least value of k for which ( 840 k + 3 ) is divisible by 9 is k = 2 . { \\ color { blue } \\ therefore } required number = ( 840 x 2 + 3 ) = 1683 . answer : b ) 1683\"" + }, + { + "Answer": 3, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "b", + "Explanation": "solution : b . for 1 pizza 10 $ . for 2 pizza 10 $ + 9.6 $ ( 4 % off ) = 19.6 , for 3 pizza 19.6 + 9.2 ( 8 % off ) = 28.8 , for 4 pizza 28.8 + 8.8 ( 12 % off ) = 37.6 . so he have 37 so he cant eat 4 th pizza ." + }, + { + "Answer": 11, + "Options": "a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15", + "Correct": "a", + "Explanation": "\"four wheeler = 11 * 4 = 44 ( max ) 2 wheel = 1 so no of 4 wheeler = 11 answer : a\"" + }, + { + "Answer": 100, + "Options": "a ) 100 , b ) 25 , c ) 40 , d ) 45 , e ) 75", + "Correct": "a", + "Explanation": "\"average = 60 , sum of temperatures = 60 * 5 = 300 as the min temperature is 40 , max would be 300 - 4 * 40 = 140 - - > the range = 140 ( max ) - 40 ( min ) = 100 answer : a\"" + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 10 , c ) 12 , d ) 14 , e ) 15", + "Correct": "a", + "Explanation": "\"explanation : = > 3 ( 2 x + 9 ) = 63 = > 2 x + 9 = 21 = > x = 6 answer : option a\"" + }, + { + "Answer": 0.6363636363636364, + "Options": "a ) 4 / 9 , b ) 5 / 4 , c ) 5 / 8 , d ) 5 / 9 , e ) 7 / 11", + "Correct": "e", + "Explanation": "\"income = salary ( s ) + tips = s + s * 7 / 4 = s * 11 / 4 tips = s * 7 / 4 fraction of his income came from tips = ( s * 7 / 4 ) / ( s * 11 / 4 ) = 7 / 11 answer : e\"" + }, + { + "Answer": 15, + "Options": "a ) 14 years , b ) 12 years , c ) 56 years , d ) 66 years , e ) 15 years", + "Correct": "e", + "Explanation": "\"given that a + b = 15 + b + c = > a \u00e2 \u20ac \u201c c = 15 + b \u00e2 \u20ac \u201c b = 15 = > c is younger than a by 15 years answer : e\"" + }, + { + "Answer": 3, + "Options": "a ) 3 , b ) 2 , c ) 1 , d ) 0 , e ) 4", + "Correct": "a", + "Explanation": "remainder will be number / 100 here as the divisor is two digit number = 12 . hence checking for the last two digits = 5 * 7 * 9 = 15 thus remainder = 3 . answer : a" + }, + { + "Answer": 64, + "Options": "a ) 25 , b ) 40 , c ) 64 , d ) 80 , e ) 96", + "Correct": "c", + "Explanation": "\"7 / 8 x - 3 / 4 x = 8 galls 1 / 8 * x = 8 gallons x = 64 gallons answer c\"" + }, + { + "Answer": 300, + "Options": "a ) rs . 300 , b ) rs . 200 , c ) rs . 240 , d ) rs . 350 , e ) none of these", + "Correct": "a", + "Explanation": "\"z share = z , y = 1.2 z x = 1.25 \u00e3 \u2014 1.2 z , x + y + z = 111 ( 1.25 \u00e3 \u2014 1.2 + 1.2 + 1 ) z = 1110 3.7 z = 1110 , z = 300 answer : . a\"" + }, + { + "Answer": 18.75, + "Options": "a ) 16.75 % , b ) 17.75 % , c ) 18.75 % , d ) 19.75 % , e ) none of these", + "Correct": "c", + "Explanation": "the amount of the final mixture is given by 50 ml + 30 ml = 80 ml the amount of alcohol is equal to the amount of alcohol in pure water ( which is 0 ) plus the amount of alcohol in the 30 % solution . let x be the percentage of alcohol in the final solution . hence 0 + 30 % 50 ml = x ( 80 ) solve for x x = 0.1817 = 18.75 % answer c" + }, + { + "Answer": 0.17647058823529413, + "Options": "a ) 1 / 14 , b ) 1 / 17 , c ) 3 / 14 , d ) 3 / 17 , e ) 1 / 31", + "Correct": "d", + "Explanation": "\"let x be the fraction of the distance that b runs . let v be the speed at which b runs . the time should be the same for both runners . time = d / ( 17 v / 14 ) = xd / v ( 14 / 17 ) * d / v = x * d / v x = 14 / 17 b should have a head start of 3 / 17 of the full distance . the answer is d .\"" + }, + { + "Answer": 260, + "Options": "a ) 238 , b ) 277 , c ) 278 , d ) 260 , e ) 288", + "Correct": "d", + "Explanation": "\"explanation : let the number of 20 paise coins be x . then the no of 25 paise coins = ( 336 - x ) . 0.20 * ( x ) + 0.25 ( 336 - x ) = 71 = > x = 260 . . answer : d ) 260\"" + }, + { + "Answer": 6, + "Options": "a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8", + "Correct": "d", + "Explanation": "\"the number of members is 7 k + 4 = 8 j + 4 the only number in this range which satisfies this is 60 . 60 / 9 = 6 ( 9 ) + 6 the answer is d .\"" + }, + { + "Answer": 6, + "Options": "a ) $ 4 , b ) $ 6 , c ) $ 7 , d ) $ 9 , e ) $ 3", + "Correct": "b", + "Explanation": "\"b $ 6 5 m = xw = 8 b 5 m + xw + 8 b - - - - - $ 90 rs . 5 m + 5 m + 5 m - - - - - $ 90 rs . 15 m - - - - - - $ 90 = > 1 m = $ 6 .\"" + }, + { + "Answer": 60, + "Options": "a ) 60 m , b ) 72 m , c ) 80 m , d ) 82 m , e ) 84 m", + "Correct": "a", + "Explanation": "\"let the length of each train be x m . then , distance covered = 2 x m . relative speed = 48 - 36 = 12 km / hr . = 12 * 5 / 18 = 10 / 3 m / sec . 2 x / 36 = 10 / 3 = > x = 60 . answer : a\"" + }, + { + "Answer": 92, + "Options": "a ) 92 , b ) 60 , c ) 73 , d ) 82 , e ) 91", + "Correct": "a", + "Explanation": "\"let the number of correct responses be x then the number of incorrect responses = 100 - x according to question x - 2 ( 100 - x ) = 76 ( subtracting twice of incorrect from correct ) 3 x = 276 x = 92 answer : a\"" + }, + { + "Answer": 1600, + "Options": "a ) 2400 , b ) 2403 , c ) 3998 , d ) 2539 , e ) 1600", + "Correct": "e", + "Explanation": "\"e 1600 let the amount with r be $ r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 4000 - r ) = > 3 r = 8000 - 2 r = > 5 r = 8000 = > r = 1600 .\"" + }, + { + "Answer": 34, + "Options": "a ) 10 , b ) 11 , c ) 12 , d ) 34 , e ) 15", + "Correct": "d", + "Explanation": "\"- > x ^ 4 + ( 1 / x ^ 4 ) = ( x ^ 2 ) ^ 2 + ( 1 / x ^ 2 ) ^ 2 = ( x ^ 2 + 1 / x ^ 2 ) ^ 2 - 2 x ^ 2 ( 1 / x ^ 2 ) = 6 ^ 2 - 2 = 34 . thus , the answer is d .\"" + }, + { + "Answer": 584638125, + "Options": "a ) 542622125 , b ) 584632125 , c ) 544638125 , d ) 584638125 , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : 935421 \u00d7 625 = 935421 \u00d7 54 = 935421 \u00d7 ( 10 / 2 ) 4 = ( 935421 \u00d7 10000 ) / 16 = 584638125 . answer : option d\"" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "a", + "Explanation": "my friend , every single odd number greater than can be written either as 4 v + 1 or as 4 v + 3 . if you divide any odd number by 4 , you will get a remainder of either 1 or 3 . that ' s not a rule unique to prime numbers at all . the 6 v + 1 or 6 v - 1 rule is basically every odd number that is not divisible by three , so it narrows the search a little . here ' s how i thought about the problem . first , eliminate all the even numbers and the odd multiples of 5 in that range . that leaves us with : { 201 , 203 , 207 , 209 , 211 , 213 , 217 , 219 } eliminate the four multiples of 3 . notice that 21 is a multiple of 3 , so 210 is also a multiple of 3 . if we add or subtract 3 or 9 , we get more multiples of three . when we eliminate those , we are left with . { 203 , 209 , 211 , 217 } now , notice that a cool thing about this range is that 210 is also a multiple 7 ( again , because 21 is a multiple of 7 ) . this means that 210 - 7 = 203 210 + 7 = 217 those two numbers are also multiples of 7 , so eliminate them from the list . now , we are left with { 209 , 211 } . we ' ve already checked all the prime numbers less than 10 , so we know that neither of these numbers is divisible by anything less than 10 . we have to check 11 now . we know that 22 is a multiple of 11 , so 220 is also a multiple of 11 . this means that 220 - 11 = 209 is also a multiple of 11 . we can eliminate this from the list also . that leaves us with just 211 . there ' s no zero option in the question , so this must be a prime number . answer = ( a )" + }, + { + "Answer": 756.6666666666666, + "Options": "a ) 756.7 , b ) 751.7 , c ) 753.7 , d ) 752.7 , e ) 722.7", + "Correct": "a", + "Explanation": "\"explanation : total of the 20 digits - 20 * 500 = 10000 total of the 14 digits - 14 * 390 = 5460 total of the remaining 6 digits - 10000 - 5460 = 4540 average of the remaining 6 numbers = 4540 / 6 = 756.7 answer : a\"" + }, + { + "Answer": 4, + "Options": "a ) 4 , b ) 34 , c ) 1 , d ) 2 , e ) 3", + "Correct": "a", + "Explanation": "\"answer given exp . = 25 / 7 + { ( 2 q - p ) / ( 2 q + p ) } dividing numerator as well as denominator by q , exp = 25 / 7 + { 2 - p / q ) / ( 2 + p / q ) } = 25 / 7 + { ( 2 - 4 / 5 ) / ( 2 + 4 / 5 ) } = 25 / 7 + 6 / 14 = 25 / 7 + 3 / 7 = 28 / 7 = 4 correct option : a\"" + }, + { + "Answer": 5437.5, + "Options": "a ) 100 , b ) 250 , c ) 750 , d ) 5437.5 , e ) 5635.5", + "Correct": "d", + "Explanation": "\"6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 58 * 25 * 1 / 2 = 725 feet ^ 3 of milk must be removed , which equals to 725 * 7.5 = 5437.5 gallons . answer : d .\"" + }, + { + "Answer": 15, + "Options": "a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16", + "Correct": "d", + "Explanation": "explanation : i ) let the ages of the five members at present be a , b , c , d & e years . and the age of the new member be f years . ii ) so the new average of five members ' age = ( a + b + c + d + f ) / 5 - - - - - - - ( 1 ) iii ) their corresponding ages 3 years ago = ( a - 3 ) , ( b - 3 ) , ( c - 3 ) , ( d - 3 ) & ( e - 3 ) years so their average age 3 years ago = ( a + b + c + d + e - 15 ) / 5 = x - - - - - ( 2 ) = = > a + b + c + d + e = 5 x + 15 = = > a + b + c + d = 5 x + 15 - e - - - - - - ( 3 ) iv ) substituting this value of a + b + c + d = 5 x + 15 - e in ( 1 ) above , the new average is : ( 5 x + 15 - e + f ) / 5 equating this to the average age of x years , 3 yrs , ago as in ( 2 ) above , ( 5 x + 15 - e + f ) / 5 = x = = > ( 5 x + 15 - e + f ) = 5 x solving e - f = 15 years . thus the difference of ages between replaced and new member = 15 years . answer : d" + }, + { + "Answer": 58.00000000000001, + "Options": "a ) 58 kg , b ) 60 kg , c ) 64 kg , d ) 70 kg , e ) none", + "Correct": "a", + "Explanation": "\"sol . for 9 kg zinc , mixture melted = ( 9 + 11 ) kg . for 26.1 kg zinc , mixture , melted = [ 20 / 9 x 26.1 ] kg = 58 kg . answer a\"" + }, + { + "Answer": 3, + "Options": "a ) 8 h , b ) 3 h , c ) 6 h , d ) 3 h , e ) 1 h", + "Correct": "b", + "Explanation": "explanation : time ( when x was 30 km ahead of y ) = ( 120 - 30 ) / 20 = 4.5 h time ( when y was 30 km ahead of x ) = ( 120 + 30 ) / 20 = 7.5 h thus , required difference in time = 3 h answer : b" + }, + { + "Answer": 150, + "Options": "a ) 90 , b ) 120 , c ) 150 , d ) 180 , e ) 200", + "Correct": "c", + "Explanation": "number of ways of selecting 2 fiction books = 5 c 2 number of ways of selecting 2 non fiction books = 6 c 2 5 c 2 * 6 c 2 = 10 * 15 = 150 answer : c" + }, + { + "Answer": 12, + "Options": "a ) 11 , b ) 13 , c ) 14 , d ) 12 , e ) 10", + "Correct": "d", + "Explanation": "\"explanation : let somu ' s age be x and that of his father be 3 x . so , x - 6 = 3 x - 6 / 5 = x = 12 answer : option d\"" + }, + { + "Answer": 163, + "Options": "a ) 150 , b ) 152 , c ) 154 , d ) 163 , e ) 144", + "Correct": "d", + "Explanation": "\"d = d * q + r d = 17 * 9 + 10 d = 153 + 10 d = 163 answer d\"" + }, + { + "Answer": 28, + "Options": "a ) 1 , b ) 28 , c ) 12 , d ) 9 , e ) 7", + "Correct": "b", + "Explanation": "\"7 * 4 = 28 quarters answer : b\"" + }, + { + "Answer": 40, + "Options": "a ) 40 , b ) 50 , c ) 65 , d ) 70 , e ) 90", + "Correct": "a", + "Explanation": "\"let the original # be x then 1.25 x \u2212 0.7 x = 22 - - > x = 40 answer : a .\"" + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) 15 , c ) 10 , d ) 18 , e ) 13", + "Correct": "a", + "Explanation": "\"2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 33 - 9 = 24 ab = 12 . answer is a .\"" + }, + { + "Answer": 5, + "Options": "a ) 1 , b ) 6 , c ) 7 , d ) 5 , e ) 8", + "Correct": "d", + "Explanation": "x * 1 = 3 * 5 / 3 x = 5 answer : d" + }, + { + "Answer": 24, + "Options": "a ) s . 10 , b ) s . 24 , c ) s . 30 , d ) s . 40 , e ) s . 50", + "Correct": "b", + "Explanation": "total earning for the week = sum of earning of first four days + sum of earning of last four days - earning of 4 th day = 4 x 25 + 4 x 22 - 20 = rs . 168 \u00e2 \u02c6 \u00b4 average earning = 168 / 7 = rs . 24 b" + }, + { + "Answer": 23, + "Options": "a ) 23 , b ) 25 , c ) 26 , d ) 27 , e ) 29", + "Correct": "a", + "Explanation": "\"x / 2 y = 3 / 2 = > x = 6 y / 2 = 3 y = > ( 7 x + 2 y ) / ( x - 2 y ) = ( ( 7 * ( 3 y ) ) + 2 y ) / ( 3 y - 2 y ) = > 23 y / y = 23 answer : a\"" + }, + { + "Answer": 7.000000000000001, + "Options": "a ) 4.37 % , b ) 5 % , c ) 6 % , d ) 8.75 % , e ) 7 %", + "Correct": "e", + "Explanation": "solution increase in 10 years = ( 297500 - 175000 ) = 122500 increase % = ( 122500 / 175000 \u00e3 \u2014 100 ) % = 70 % . required average = ( 70 / 10 ) % = 7 % . answer e" + }, + { + "Answer": 490, + "Options": "a ) 471 , b ) 490 , c ) 480 , d ) 453 , e ) 456", + "Correct": "b", + "Explanation": "average mark scored by all the three boys = [ 59 / 100 ( 700 ) + 55 / 100 ( 700 ) + 99 / 100 ( 700 ) + 67 / 100 ( 700 ) ] / 4 ( 413 + 385 + 693 + 469 ) / 4 = 490 answer : b" + }, + { + "Answer": 1, + "Options": "a ) 47 , b ) 65 , c ) 1 , d ) 35 , e ) 65", + "Correct": "c", + "Explanation": "\"it ' s simple can be solved by elimination of answer choices . option b and d are too large , not possible . even ae are large to have correct choice . ans : c\"" + }, + { + "Answer": 320, + "Options": "a ) 3.20 % , b ) 30.2 % , c ) 320.00 % , d ) 0.320 % , e ) none of these", + "Correct": "c", + "Explanation": "explanation : while calculation in terms of percentage we need to multiply by 100 , so 3.20 * 100 = 320 answer : option c" + }, + { + "Answer": 200, + "Options": "a ) 288 , b ) 266 , c ) 288 , d ) 200 , e ) 111", + "Correct": "d", + "Explanation": "25 + 25 = 50 25 % - - - - - - 50 100 % - - - - - ? = > 200 answer : d" + }, + { + "Answer": 18, + "Options": "a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 26", + "Correct": "a", + "Explanation": "smallest gumballs = ( 19 - 17 ) + ( 19 - 12 ) + 19 = 28 largest gumballs = ( 25 - 17 ) + ( 25 - 12 ) + 25 = 46 difference = 46 - 28 = 18 a" + }, + { + "Answer": 0.6666666666666666, + "Options": "a ) 3 , b ) 1 / 3 , c ) 2 / 3 , d ) 3 / 5 , e ) 4 / 5", + "Correct": "c", + "Explanation": "should be a sub - 600 level q . . volume = { 2 / 7 } / { 3 / 7 } = 2 / 3 c" + }, + { + "Answer": 127.5, + "Options": "a ) $ 21.25 m , b ) $ 25.5 m , c ) $ 106.25 m , d ) $ 127.5 m , e ) $ 153 m", + "Correct": "d", + "Explanation": "2 / 10 * 1 / 6 * ( total ) = 4.25 1 / 30 * ( total ) = 4.25 ( total ) = 4.25 * 30 = 127.5 answer : d ." + }, + { + "Answer": 25, + "Options": "a ) 47 , b ) 25 , c ) 37 , d ) 33 , e ) 29", + "Correct": "b", + "Explanation": "\"before you tackle this question you must first understand that the question is comprised of two key parts , 1 st is finding out how manytermsis in that sequence and 2 nd whatactual number valuethat term is . in an arithmetic progression , in this case consecutive odd integers 1 , 3 , 5 , . . . . , there are two set of rules . rule # 1 ( arithmetic sequence ) : xn = a + d ( n - 1 ) identifies what the actual # in the sequence would be . each number in the sequence has a term such as 1 ( is the first term ) , 3 ( is the second term ) and so on . so if i were to ask you to find out what the 10 th term is of that sequence you would use that formula to find that value . a = 1 ( first term ) d = 2 ( the common difference ) remember in the sequence 1 , 3 , 5 , 7 the common difference is always 2 * on a side note we use n - 1 because we do n ' t have d in the first term , therefore if we were solving for the first term we would get 0 as n - 1 and 0 times d would give us 0 , leaving only the first term . this works regardless what your first term is in any sequence . but remember the question askswhat is thevalueof n if the sum of the consecutive odd integers from 1 to n equals 169 ? which means we first need a consecutive sequence that sums up to 169 and than find what the value of the n is , in this case it would be the last number in that sequence . in order to find that we first need to knowhow many terms ( how many of the n there is ) in order to be able to plug n in this formula given we know what the sum is . for that to happen we need to use rule # 2 . rule # 2 ( summing an arithmetic series ) : 169 = n / 2 ( 2 a + ( n - 1 ) d ) . given the question gives us what the sum is ( 169 in this case ) we would simply use this formula to solve for n . once we solve for n ( 13 in this case ) we can simply plug n into the first formula ( rule 1 ) and find the value . it feels very confusing and difficult at first , but once you identify the steps all you need to do is plug and play . we have the sum ( 169 ) of a sequence , the number of terms in that sequence is ( unknown ) . rule # 2 tells us how many numbers there are in that sequence and rule # 1 gives us what that last term is .\"" + }, + { + "Answer": 7899593, + "Options": "a ) 2455835 , b ) 2789255 , c ) 6868575 , d ) 7899657 , e ) 1023666", + "Correct": "d", + "Explanation": "\"according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 7899665 - 12 * 3 * 2 = 7899665 - 8 = 7899657 correct answer d\"" + }, + { + "Answer": 0.5, + "Options": "a ) 3 , b ) 1 / 2 , c ) 1 / 3 , d ) - 1 / 3 , e ) - 3", + "Correct": "b", + "Explanation": "\"the expression 9 / ( 1 + 4 / x ) = 1 should have been equal to something . if 9 / ( 1 + 4 / x ) = 1 = 1 = > 9 x / ( x + 4 ) = 1 = > 9 x = x + 4 = > 8 x = 4 = > x = 1 / 2 correct option : b\"" + }, + { + "Answer": 1340, + "Options": "a ) 1340 , b ) 1445 , c ) 1375 , d ) 1415 , e ) 1455", + "Correct": "a", + "Explanation": "$ 25 per packet of gasket in case a customer orders less than 10 in case a customer orders > 10 price per gasket = 25 * 4 / 5 = 20 a certain week the supplier sold 60 gasket 1 . he sold 15 % of the gaskets to x = 9 gaskets = 25 * 9 = 225 2 . he sold 15 % of the gaskets to y = 9 gaskets = 25 * 9 = 225 3 . he sold remaining 70 % to z = 42 gaskets = 25 * 10 = 250 + 20 * 32 = 890 thus , total money earned 225 + 225 + 890 = 1340 answer is a" + }, + { + "Answer": 140, + "Options": "a ) 140 , b ) 100 , c ) 85 , d ) 160 , e ) 190", + "Correct": "a", + "Explanation": "\"sum of the marks for the 25 students = 25 * 70 = 1750 . the marks of each student are doubled , the sum also will be doubled . the new sum = 1750 * 2 = 3500 . so , the new average = 3500 / 25 = 140 . answer : a\"" + }, + { + "Answer": 11, + "Options": "a ) 9 , b ) 11 , c ) 13 , d ) 15 , e ) 17", + "Correct": "b", + "Explanation": "\"the daily production was raised by 5 units for n days , which has a weighting of 5 n . 5 n = 110 - 55 = 55 n = 11 the answer is b .\"" + }, + { + "Answer": 10, + "Options": "a ) 12 , b ) 8 , c ) 4 , d ) 10 , e ) 16", + "Correct": "d", + "Explanation": "- 4 hours : 1,000 - 2 hours : 2,000 now : 4,000 + 2 hours : 8,000 + 4 hours : 16,000 + 6 hours : 32,000 + 8 hours : 64,000 + 10 hours : 128,000 answer : d" + }, + { + "Answer": 10, + "Options": "a ) 10 , b ) 99 , c ) 27 , d ) 22 , e ) 29", + "Correct": "a", + "Explanation": "\"let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 20 x = 4 ( 3 x + 5 ) 8 x = 20 x = 2.5 quantity of alcohol = ( 4 x 2.5 ) litres = 10 litres . answer : a\"" + }, + { + "Answer": 3991, + "Options": "a ) 4991 , b ) 5991 , c ) 3991 , d ) 6542 , e ) 6995", + "Correct": "c", + "Explanation": "\"total sale for 5 months = rs . ( 5435 + 5927 + 5855 + 6230 + 5562 ) = rs . 29009 . required sale = rs . [ ( 5500 x 6 ) - 29009 ] = rs . ( 33000 - 29009 ) = rs . 3991 answer : option c\"" + }, + { + "Answer": 1, + "Options": "a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1", + "Correct": "e", + "Explanation": "from the coordinates of the foci , c = 5 and the major axis is the y axis . from the length of the major axis , we obtain a = 7 . also b 2 = a 2 - c 2 = 24 . the equation of the ellipse is given by x 2 / 24 + y 2 / 49 = 1 correct answer is e ) 1" + }, + { + "Answer": 4, + "Options": "a ) a . 4 , b ) b . 8 , c ) c . 10 , d ) d . 12 , e ) e . 16", + "Correct": "a", + "Explanation": "you might think of this in a management context - we can use the principle of ' person - hours ' to solve any problem where we have identical workers . so , using simpler numbers , suppose you know that 6 identical employees , working simultaneously , would finish a job in 5 hours . then that job requires 6 * 5 = 30 total hours of person - work . if instead you wanted the job done in 3 hours , you ' d assign 30 / 3 = 10 employees to do the job , because you want to get a total of 30 hours of work from the employees . we can solve this problem identically . if 12 machines ( identical ones , i assume ) work simultaneously for 40 days , they will do a total of 12 * 40 machine - days of work . so the job requires 12 * 40 days of machine work in total . we instead want the job done in 1 / 4 less time , so in 30 days . so we ' ll need 12 * 40 / 30 = 16 machines , or 4 additional machines . a" + }, + { + "Answer": 20, + "Options": "a ) 11 . , b ) 20 . , c ) 13 . , d ) 14 . , e ) 14.5", + "Correct": "b", + "Explanation": "\"price of candy before price increase = 20 / 1.25 = 16 price of soda before price increase = 6 / 1.5 = 4 total price = 16 + 4 = 20 b is the answer\"" + }, + { + "Answer": 48, + "Options": "a ) 36 , b ) 48 , c ) 72 , d ) 96 , e ) 108", + "Correct": "b", + "Explanation": "the number of photographs either framed by jack or taken by octavia = { jack } + { octavia } - { overlap } = 36 + 36 - 24 = 48 ( { overlap } is green box ) . answer : b" + }, + { + "Answer": 1.3333333333333333, + "Options": "a ) 1 / 3 , b ) 2 / 3 , c ) 4 / 3 , d ) 5 / 3 , e ) none of these", + "Correct": "c", + "Explanation": "explanation : ( p + q ) / ( p - q ) = ( p / q + 1 ) / ( p / q - 1 ) = ( 7 + 1 ) / ( 7 - 1 ) = 4 / 3 . answer : c" + }, + { + "Answer": 2880, + "Options": "a ) 2880 . , b ) 4860 . , c ) 5780 , d ) 5760 , e ) 6380 .", + "Correct": "a", + "Explanation": "normal day = 400 kw / h stormy day = 400 * 1.2 = 480 kw / h 3 windmills for 2 hours on stormy day 480 * 3 * 2 = 2880 answer : a" + }, + { + "Answer": 17, + "Options": "a ) \u2013 5 , b ) 1 , c ) 13 , d ) 17 , e ) 551", + "Correct": "d", + "Explanation": "2 x - j = 11 . . . . j = 2 x - 11 4 x + j = 4 x + 2 x - 11 = 6 x - 11 6 x - 11 = - 5 . . . x = 1 6 x - 11 = 1 . . . x = 2 6 x - 11 = 13 . . . x = 4 6 x - 11 = 17 . . x is not integer 6 x - 11 = 551 . . x is not integer i think the choice e is 55 not 551 . otherwise both de can not be solution = d" + }, + { + "Answer": 30, + "Options": "a ) 20 , b ) 30 , c ) 55 , d ) 65 , e ) 80", + "Correct": "b", + "Explanation": "\"the arithmetic mean of 4 equally weighted tests was 45 . so what we can assume is that we have 4 test scores , each 45 . he dropped his lowest score and the avg went to 50 . this means that the lowest score was not 45 and other three scores had given the lowest score 5 each to make it up to 45 too . when the lowest score was removed , the other 3 scores got their 5 back . so the lowest score was 3 * 5 = 15 less than 45 . so the lowest score = 45 - 15 = 30 answer ( b )\"" + }, + { + "Answer": 50, + "Options": "a ) 40 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 80 %", + "Correct": "b", + "Explanation": "\"can be reduced to 2 y / 10 + 3 y / 10 = y / 2 = 50 % answer b\"" + }, + { + "Answer": 15, + "Options": "a ) 0 , b ) 5 , c ) 10 , d ) 15 , e ) 25", + "Correct": "d", + "Explanation": "you should notice that 55 * 2 = 110 so 11,000 is divisible by 55 : 55 * 200 = 11,000 ( or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55 ) - - > b * a = 0 * 0 = 0 . next number divisible by 55 is 11,000 + 55 = 11,055 : b * a = 5 * 5 = 15 ( next number wo n ' t have 110 as the first 3 digits so we have only two options 0 and 25 ) . answer : e . ! please post ps questions in the ps subforum : gmat - problem - solving - ps - 140 / please post ds questions in the ds subforum : gmat - data - sufficiency - ds - 141 / no posting of ps / ds questions is allowed in the mainmath forum . d" + }, + { + "Answer": 1750.0000000000018, + "Options": "a ) rs . 1700 , b ) rs . 1720 , c ) rs . 1750 , d ) rs . 1850 , e ) rs . 2000", + "Correct": "c", + "Explanation": "c . i . = rs . 4000 x 1 + 10 2 - 4000 100 = rs . 4000 x 11 x 11 - 4000 10 10 = rs . 840 . sum = rs . 420 x 100 = rs . 1750 . 3 x 8 c" + }, + { + "Answer": 276, + "Options": "a ) 256 , b ) 266 , c ) 276 , d ) 286 , e ) 296", + "Correct": "c", + "Explanation": "the sum of n natural numbers = n * ( n + 1 ) / 2 = 23 * 24 / 2 = 276 the answer is c ." + }, + { + "Answer": 9, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9", + "Correct": "e", + "Explanation": "description : = > 11 x = 4 ( x + 2 ) + 16 + 3 ( x + 4 ) = > 11 x = 7 x + 36 = > 4 x = 36 x = 9 answer e" + }, + { + "Answer": 14.444444444444445, + "Options": "a ) 9 , b ) 14.44 , c ) 47 , d ) 48 3 / 5 , e ) 59", + "Correct": "b", + "Explanation": "\"you can plug in values . c = 5 / 9 * ( f - 32 ) f = 32 - - > c = 0 ; f = 32 + 26 = 58 - - > c = 5 / 9 * 26 = 14.44 . increase = 14.44 degrees . answer : b .\"" + }, + { + "Answer": 23, + "Options": "a ) 23 , b ) 25 , c ) 30 , d ) 22 , e ) 40", + "Correct": "a", + "Explanation": "\"let the average of the whole team be x years . 11 x - ( 26 + 29 ) = 9 ( x - 1 ) = 11 x - 9 x = 46 = 2 x = 46 = > x = 23 so , average age of the team is 23 years . answer a\"" + }, + { + "Answer": 499.9999999999999, + "Options": "a ) s 200 , b ) s 500 , c ) s 300 , d ) s 450 , e ) s 550", + "Correct": "b", + "Explanation": "suppose the amount in the beginning was rs \u2019 x \u2019 money spent on clothes = rs 1 x / 3 balance = rs 2 x / 3 money spent on food = 1 / 5 of 2 x / 3 = rs 2 x / 15 balance = 2 x / 3 - 2 x / 15 = rs 8 x / 15 money spent on travel = 1 / 4 of 8 x / 15 = rs 2 x / 15 = 8 x / 15 - 2 x / 15 = 6 x / 15 = rs 2 x / 5 therefore 2 x / 5 = 200 = 500 answer : b" + }, + { + "Answer": 5, + "Options": "a ) 12.5 % , b ) 13 % , c ) 5 % , d ) 17 % , e ) 19 %", + "Correct": "c", + "Explanation": "quantity x rate = price 1 x 1 = 1 0.76 x 1.25 = 0.95 decrease in price = ( 0.05 / 1 ) \u00d7 100 = 5 % c )" + }, + { + "Answer": 0.3125, + "Options": "a ) 1 / 3 , b ) \u00bc , c ) 9 / 25 , d ) 5 / 16 , e ) 0", + "Correct": "d", + "Explanation": "\"prime digits are : 2 , 3 , 5 , 7 total number of 2 digit # s with both digits prime are : 4 * 4 = 16 out of these numbers divisible by 3 = 33 , 27 , 57 , 72 and 75 . i had to find the numbers manually using the 4 numbers above . = > prob = 5 / 16 . ans d . took me 3 : 20 mins .\"" + }, + { + "Answer": 0.02857142857142857, + "Options": "a ) 1 / 70 , b ) 1 / 35 , c ) 2 / 35 , d ) 1 / 12 , e ) 1 / 7", + "Correct": "b", + "Explanation": "divisions are 0 1 / 7 2 / 7 3 / 7 4 / 7 5 / 7 6 / 7 1 1 / 5 2 / 5 3 / 5 4 / 5 5 / 5 expressing the same in terms of the lcm of 57 , i . e 35 0 7 / 35 14 / 35 21 / 35 28 / 35 35 / 35 5 / 35 10 / 35 15 / 35 20 / 35 25 / 35 30 / 35 by comparing the divisions with each other we can see 1 / 35 is the shortest possible distance between any two selected divisions . x = 1 / 35 answer is b ." + }, + { + "Answer": 0.7999999999999998, + "Options": "a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 5 , d ) 3 / 4 , e ) 4 / 5", + "Correct": "e", + "Explanation": "\"x : 0.5 % is 0.24 % - points from 0.74 % . y : 0.8 % is 0.06 % - points from 0.74 % . therefore the ratio of products checked by y : x is 4 : 1 . thus , worker y checked 4 / 5 of the products . the answer is e .\"" + }, + { + "Answer": 65, + "Options": "a ) 50 , b ) 100 , c ) 65 , d ) 500 , e ) 980", + "Correct": "c", + "Explanation": "\"average price for a pair of rackets = $ 9.8 total cost = $ 9.8 * x = $ 637 x = 65 pairs were sold . answer : c\"" + }, + { + "Answer": 264, + "Options": "a ) 264 . , b ) 428 , c ) 464 . , d ) 622 , e ) 642", + "Correct": "a", + "Explanation": "given - 3 x + 4 y = 28 - - - eq 1 3 x - 2 y = 8 - - eq 2 sum both eqns we get 2 y = 36 = > y = 18 sub 2 y in eq 2 = > 3 x - 36 = 8 . = > x = 44 / 3 now xy = 44 / 3 * 18 = 264 . option a is correct answer ." + }, + { + "Answer": 75, + "Options": "a ) 40 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 75 %", + "Correct": "e", + "Explanation": "\"can be reduced to 9 y / 20 + 6 y / 20 = 15 y / 20 = 75 % answer e\"" + }, + { + "Answer": 30, + "Options": "a ) 30 , b ) 40 , c ) 45 , d ) 25 , e ) 20", + "Correct": "a", + "Explanation": "\"as half the circle shape consist of 20 - 5 = 15 boys , so total number of boys in full circle = 2 * 15 = 30 answer : a\"" + }, + { + "Answer": 1, + "Options": "a ) 0.5 , b ) 1 , c ) 1.5 , d ) 2 , e ) 3", + "Correct": "b", + "Explanation": "\"let x be the number of desks and bookcases that are placed along the library wall . 2 x + 1.5 x < 15 3.5 x < 15 since x is a non negative integer , the largest number x can be is 4 . when x is 4 , the desks and bookcases take up 3.5 * 4 = 14 m , leaving 1 m of empty space . thus , i believe the answer is b ) 1\"" + }, + { + "Answer": 11, + "Options": "a ) 23 , b ) 19 , c ) 17 , d ) 13 , e ) 11", + "Correct": "e", + "Explanation": "f ( 24 ) = 2 * 4 * 6 * 8 * 10 * 12 * 14 * 16 * 18 * 20 * 22 * 24 = 2 ^ 12 * ( 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 * 11 ) - - > the greatest prime factor is 11 . answer : e ." + }, + { + "Answer": 20, + "Options": "a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20", + "Correct": "e", + "Explanation": "\"let the number of ducks be d and number of cows be c then , total number of legs = 2 d + 4 c = 2 ( d + 2 c ) total number of heads = c + d given that total number of legs are 40 more than twice the number of heads = > 2 ( d + 2 c ) = 40 + 2 ( c + d ) = > d + 2 c = 20 + c + d = > 2 c = 20 + c = > c = 20 i . e . , total number of cows = 20 answer is e .\"" + }, + { + "Answer": 120, + "Options": "a ) 90 , b ) 100 , c ) 120 , d ) 160 , e ) 200", + "Correct": "c", + "Explanation": "\"solution : let x be the number he chose , then 2 * x * 138 = 102 2 x = 240 x = 120 correct answer c\"" + }, + { + "Answer": 64.4980619863884, + "Options": "a ) 78 , b ) 64 , c ) 88 , d ) 67 , e ) 37", + "Correct": "b", + "Explanation": "\"b 4160 from the given alternatives , 64 \u00d7 65 = 4160 \u2234 smaller number = 64\"" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 4 , c ) 3 , d ) 5 , e ) 8", + "Correct": "c", + "Explanation": "let number of packs of three = t let number of packs of two = w 3 t + 2 w = 17 now , we need to test for values of w . since sum 17 is odd and 2 w will always be even , therefore w ca n ' t be even . now , we can test for values w = 1 , 3 and 5 2 * 4 + 3 * 3 = 8 + 9 = 17 answer c" + }, + { + "Answer": 1, + "Options": "a ) 3 , b ) 1 , c ) 1 / 3 , d ) - 1 / 3 , e ) - 3", + "Correct": "b", + "Explanation": "\"the expression 4 / ( 1 + 3 / x ) = 1 should have been equal to something . if 4 / ( 1 + 3 / x ) = 1 = > 4 x / ( x + 3 ) = 1 = > 4 x = x + 3 = > 3 x = 3 = > x = 1 correct option : b\"" + }, + { + "Answer": 1900, + "Options": "a ) 1900 , b ) 3600 , c ) 2400 , d ) 180 , e ) 5400", + "Correct": "a", + "Explanation": "\"1 st team : 190 2 nd team : 180 3 rd team : 170 similarly the last team will play 0 therefore ( 190 + 180 + 170 . . . . 10 ) 10 ( 19 + 18 + 17 + 16 . . . . 1 ) 10 ( n ( n + 1 ) / 2 ) = 10 ( 19 * 20 / 2 ) = 1900 answer : a\"" + }, + { + "Answer": 8, + "Options": "a ) 5 , b ) 7 , c ) 8 , d ) 13 , e ) 17", + "Correct": "c", + "Explanation": "\"if we break down what the stem is asking what is the sum of all mult of 30 between 390 and 600 . using arithmetic progression to find n : 600 = 390 + ( n - 1 ) 30 210 + 30 = 30 n 240 = 3 n = > n = 8 the sum would be : 8 * mean mean = [ 600 + 390 ] / 2 = 495 8 * 495 c\"" + }, + { + "Answer": 210, + "Options": "a ) 166 , b ) 105 , c ) 178 , d ) 177 , e ) 210", + "Correct": "e", + "Explanation": "\"x : y : z = 100 : 45 : 30 20 : 9 : 6 9 - - - 54 35 - - - ? = > 210 answer : e\"" + }, + { + "Answer": 24200.000000000004, + "Options": "a ) 24500 , b ) 24400 , c ) 24300 , d ) 24200 , e ) 24100", + "Correct": "d", + "Explanation": "explanation : expenditure = 20000 x 1.1 x 1.1 = 24200 answer : option d" + }, + { + "Answer": 50, + "Options": "a ) 15 % , b ) 25 % , c ) 50 % , d ) 0.2083 % , e ) none", + "Correct": "c", + "Explanation": "\"this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 480 / 3840 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 25 ) = 50 % the correct answer is ( c ) .\"" + }, + { + "Answer": 3500, + "Options": "a ) 13000 , b ) 7000 , c ) 10000 , d ) 3500 , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : profit = 5 , 00,000 \u00e2 \u02c6 \u2019 ( 1 , 50,000 + 75,000 ) = rs . 2 , 75,000 . since , such loom contributes equally to sales and manufacturing expenses . but the monthly charges are fixed at rs 75,000 . if one loan breaks down sales and expenses will decrease . new profit : - = > 500000 \u00e3 \u2014 ( 99 / 100 ) \u00e2 \u02c6 \u2019 150000 \u00e3 \u2014 ( 99 / 100 ) \u00e2 \u02c6 \u2019 75000 . = > rs 2 , 68,000 . decrease in profit = > 2 , 75,000 \u00e2 \u02c6 \u2019 2 , 71,500 = > rs . 3,500 . answer : d\"" + }, + { + "Answer": 3, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "b", + "Explanation": "( 1 ) x = 11 y + 4 ( 2 ) 2 x = 24 y + 1 let ' s subtract equation ( 1 ) from equation ( 2 ) . 13 y - 3 = x 13 y - x = 3 the answer is b ." + }, + { + "Answer": 18, + "Options": "a ) 16 , b ) 18 , c ) 20 , d ) 22 , e ) 24", + "Correct": "b", + "Explanation": "\"180 = 18 * 10 = 20 * 9 there are 18 people in the group today . the answer is b .\"" + }, + { + "Answer": 85, + "Options": "a ) 18 , b ) 17 , c ) 76 , d ) 85 , e ) 86", + "Correct": "d", + "Explanation": "\"let the number of wickets taken till the last match be x . then , ( 12.4 x + 26 ) / ( x + 5 ) = 12 = 12.4 x + 26 = 12 x + 60 = 0.4 x = 34 = x = 340 / 4 = 85 . answer : d\"" + }, + { + "Answer": 15, + "Options": "a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15", + "Correct": "e", + "Explanation": "solution average = 5 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 75 / 5 . = 15 answer e" + }, + { + "Answer": 100, + "Options": "a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 100", + "Correct": "e", + "Explanation": "\"total people at party = 180 women = 70 so men 180 - 70 = 110 no . of pple who tried appetizer = 180 - 50 ( given info ) = 130 no of women who tried appetizer = 30 so remaining ppl ( men ) who tried the appetizer = 130 - 30 = 100 correct option e\"" + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9", + "Correct": "a", + "Explanation": "\"let x be the number of canoes . then 2 x / 3 is the number of kayaks . 15 x + ( 2 x / 3 ) * 18 = 405 15 x + 12 x = 405 27 x = 405 x = 15 ( canoes ) 2 x / 3 = 10 ( kayaks ) there were 15 - 10 = 5 more canoes rented out . the answer is a .\"" + }, + { + "Answer": 10, + "Options": "a ) 12 , b ) 10 , c ) 15 , d ) 17 , e ) 20", + "Correct": "b", + "Explanation": "each employee will get a gift worth of = $ 4 total employees = 4000 / 4 = 1000 total blocks = 1000 / 100 = 10 correct option is b" + }, + { + "Answer": 392, + "Options": "a ) 351 , b ) 392 , c ) 410 , d ) 424 , e ) 450", + "Correct": "b", + "Explanation": "\"we ' re dealing with a sequence of consecutive odd integers : 15 to 41 , inclusive . we ' re asked for the sum of this group . 1 ) start with the sum of the smallest and the biggest : 15 + 41 = 56 2 ) now look at the ' next smallest ' and the ' next biggest ' : 17 + 39 = 56 now we have proof that there is no middle term . we have 7 bunches of 56 . 7 ( 56 ) = 392 b\"" + }, + { + "Answer": 141, + "Options": "a ) a ) 145 , b ) b ) 141 , c ) c ) 150 , d ) d ) 153 , e ) e ) 158", + "Correct": "b", + "Explanation": "\"d = d * q + r d = 17 * 8 + 5 d = 136 + 5 d = 141 answer : b\"" + }, + { + "Answer": 8, + "Options": "a ) 14 , b ) 6 , c ) 7 , d ) 8 , e ) 10", + "Correct": "d", + "Explanation": "d 8 emma has 8 dollars . daya has 25 % more dollars than emma . daya = 8 + 8 x 25 % = 8 + 8 x . 25 = 8 + 2 = 10 jeff has 2 / 5 of what daya has . = 10 x 2 / 5 = 4 brenda has 4 more dollars than jeff . = 4 + 4 = 8 brenda has 8 dollars . the correct answer is d ." + }, + { + "Answer": 46, + "Options": "a ) 20 , b ) 30 , c ) 36 , d ) 46 , e ) 54", + "Correct": "d", + "Explanation": "\"the cost of annie ' s ride was 2.5 + 5 + ( 0.25 * 26 ) = $ 14 let x be the distance of mike ' s ride . the cost of mike ' s ride is 2.5 + ( 0.25 * x ) = 14 0.25 * x = 11.5 x = 46 miles the answer is d .\"" + }, + { + "Answer": 102, + "Options": "a ) 160 kg , b ) 175 kg , c ) 180 kg , d ) 102 kg , e ) 190 kg", + "Correct": "d", + "Explanation": "\"total weight increased = ( 6 x 4.5 ) kg = 27 kg . weight of new person = ( 75 + 27 ) kg = 102 kg option d\"" + }, + { + "Answer": 48, + "Options": "a ) 24 , b ) 48 , c ) 50 , d ) 60 , e ) none", + "Correct": "b", + "Explanation": "answer average number of t . v . sets = ( 20 + 30 + 60 + 80 + 50 ) / 5 = 48 correct option : b" + }, + { + "Answer": 21, + "Options": "a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25", + "Correct": "a", + "Explanation": "\"281 + 160 = 441 / 21 = 21 ( remainder ) a\"" + }, + { + "Answer": 240, + "Options": "a ) 16 , b ) 128 , c ) 240 , d ) 512 , e ) none", + "Correct": "c", + "Explanation": "\"solution required numbers are 2 , 4 , 6 , . . 30 . this is an a . p containing 15 terms . required sum = n / 2 ( first term + last term ) \u2039 = \u203a 15 / 2 ( 2 + 30 ) \u2039 = \u203a 240 . answer c\"" + }, + { + "Answer": 10, + "Options": "a ) 25 , b ) 10 , c ) 90 , d ) 14 , e ) it can not be determined from the information given", + "Correct": "b", + "Explanation": "\"the arithmetic mean of a and b = ( a + b ) / 2 = 45 - - a + b = 90 - - 1 similarly for b + c = 100 - - 2 subtracting 1 from 2 we have c - a = 10 ; answer : b\"" + }, + { + "Answer": 12, + "Options": "a ) 11 , b ) 12 , c ) 17 , d ) 19 , e ) 21", + "Correct": "b", + "Explanation": "\"let original strength = y then , 40 y + 12 x 32 = ( y + 12 ) x 36 \u21d2 40 y + 384 = 36 y + 432 \u21d2 4 y = 48 \u2234 y = 12 b\"" + }, + { + "Answer": 7, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", + "Correct": "a", + "Explanation": "101 * n ^ 2 < = 6400 n ^ 2 < = 6400 / 101 which will be less than 81 since 6400 / 100 = 64 which is the square of 9 next closest value of n where n ^ 2 < = 64 is 7 ans a" + }, + { + "Answer": 2500, + "Options": "a ) rs . 2500 , b ) rs . 1000 , c ) rs . 1500 , d ) rs . 2000 , e ) none", + "Correct": "a", + "Explanation": "sol . let the shares of a , b , c and d be rs . 5 x , rs . 2 x , rs . 4 x and rs . 3 x respectively . then , 4 x - 3 x = 500 \u21d4 x = 500 . \u2234 a ' s share = rs . 5 x = rs . ( 5 x 500 ) = rs . 2500 . answer a" + }, + { + "Answer": 109, + "Options": "a ) 366 , b ) 106 , c ) 102 , d ) 109 , e ) 122", + "Correct": "d", + "Explanation": "\"cash realised = rs . ( 109.25 - 0.25 ) = rs . 109 . answer : d\"" + }, + { + "Answer": 36, + "Options": "a ) 36 , b ) 42 , c ) 44 , d ) 46 , e ) none", + "Correct": "a", + "Explanation": "\"17 ( p + 1 ) = 21 ( q + 1 ) - - > ( p + 1 ) / ( q + 1 ) = 21 / 17 - - > the least positive value of p + 1 is 21 , so the least value of p is 20 and the least positive value of q + 1 is 17 , so the least value of q is 16 - - > the least value of p + q is 20 + 16 = 36 . answer : a .\"" + }, + { + "Answer": 0.4, + "Options": "a ) 1 / 3 , b ) 2 / 5 , c ) 3 / 4 , d ) 3 / 2 , e ) 2 / 3", + "Correct": "b", + "Explanation": "\"a / b = 4 / 5 m / x = ( 2 / 5 ) * 5 / ( 5 / 4 ) * 4 = 2 / 5 the answer is b .\"" + }, + { + "Answer": 0.7857142857142856, + "Options": "a ) 11 / 14 , b ) 13 / 18 , c ) 4 / 7 , d ) 3 / 7 , e ) 3 / 14", + "Correct": "a", + "Explanation": "\"if we use variable for total votes there will be too many fractions to manipulate with , so pick some smart # : let set total # of votes is 18 . 2 / 9 of the votes on a certain resolution have been counted - - > 4 counted and 18 - 4 = 14 votes left to be counted ; 3 / 4 of those counted are in favor of the resolution - - > 3 in favor and 1 against ; ratio of those who voted against to those who voted for to be 2 to 1 there should be total of 18 * 2 / 3 = 12 people who voted against , so in the remaining 14 votes there should be 12 - 1 = 11 people who voted against . thus q = 11 / 14 of the remaining votes must be against . answer : a .\"" + }, + { + "Answer": 2, + "Options": "a ) - 1 , b ) 1 , c ) 2 , d ) - 1 , e ) 0", + "Correct": "c", + "Explanation": "explanation : if x 2 + kx - 3 is divisible by ( x - 1 ) then x = 1 ( 1 ) 2 + 1 ( k ) - 3 = 0 1 + k - 3 = 0 k = 2 answer : option c" + }, + { + "Answer": 7, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", + "Correct": "a", + "Explanation": "( x - 10 ) ( y - 5 ) ( z - 2 ) = 1000 put x = 0 y = - 5 z = 12 then ( 0 - 10 ) ( - 5 - 5 ) ( 12 - 2 ) = 1000 ( - 10 ) ( - 10 ) ( 10 ) = 1000 1000 = 1000 answer : a" + }, + { + "Answer": 31, + "Options": "a ) $ 21 , b ) $ 27 , c ) $ 31 , d ) $ 41 , e ) it can not be determined", + "Correct": "c", + "Explanation": "\"let ' s suppose that the price of a burger is bb , of a shake - ss and that of a cola is cc . we can then construct these equations : 3 b + 7 s + c = 120 4 b + 10 s + c = 164.5 subtracting the first equation from the second gives us b + 3 s = 44.5 now if we subtract the new equation two times from first or 3 times from second we will get b + s + c = 31 . in any case , there is no necessity to know each item ' s price , just the sum . answer : c\"" + }, + { + "Answer": 210, + "Options": "a ) 100 , b ) 210 , c ) 150 , d ) 180 , e ) 199", + "Correct": "b", + "Explanation": "\"65 % of x = 20 % of 682.50 then , 65 / 100 * x = 20 / 100 * 6825 / 10 x = 210 answer is b\"" + }, + { + "Answer": 71, + "Options": "a ) 40 , b ) 50 , c ) 60 , d ) 71 , e ) 80", + "Correct": "d", + "Explanation": "\"according to order of operations , inner brackets first . hence | 5 - 8 ( 3 - 12 ) | - | 5 - 11 | = | 5 - 8 * ( - 9 ) | - | 5 - 11 | according to order of operations , multiplication within absolute value signs ( which may be considered as brackets when it comes to order of operations ) next . hence = | 5 + 72 | - | 5 - 11 | = | 77 | - | - 6 | = 77 - 6 = 71 correct answer d ) 71\"" + }, + { + "Answer": 15, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 15", + "Correct": "e", + "Explanation": "\"we have : 1 ) x < y < z 2 ) y - x > 11 3 ) x = 2 k ( x is an even number ) 4 ) y = 2 n + 1 ( y is an odd number ) 5 ) z = 2 p + 1 ( z is an odd number ) 6 ) z - x = ? least value z - x = 2 p + 1 - 2 k = 2 p - 2 k + 1 = 2 ( p - k ) + 1 - that means that z - x must be an odd number . we are asked to find the least value , so we have to pick the least numbers since y is odd and x is even , y - x must be odd . since y - x > 11 , the least value for y - x must be 13 , the least value for x must be 2 , and , thus , the least possible value for y must be 15 ( y - 2 = 13 , y = 15 ) 2 < 15 < z , since z is odd , the least possible value for z is 17 z - x = 17 - 2 = 15 answer e\"" + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 4 , e ) 3", + "Correct": "a", + "Explanation": "\"since 24 / k = 4 and 24 / 6 = 4 , then k = 6 correct answer a\"" + }, + { + "Answer": 3, + "Options": "a ) 2 , b ) 3 , c ) 12 , d ) 43 , e ) 57", + "Correct": "b", + "Explanation": "57 % unsatisfied . so ~ 43 % satisfied but 100 % should be an integer only and since the above percentages are approximations 100 % should be as close as possible to an integer . now substitute value [ 1 ] if 43 % is 2 what is 100 % - > 200 / 43 is not giving a number which is closest to an integer . [ 2 ] if 43 % is 3 what is 100 % - > 300 / 43 [ 43 * 7 = 301 ] . . . therefore closest possible to an integer . [ it also satisfies the least possible and hence we need not check for other choices which are greater than 3 ] therefore ans is b ." + }, + { + "Answer": 100, + "Options": "a ) 72 , b ) 80 , c ) 120 , d ) 100 , e ) 150", + "Correct": "d", + "Explanation": "\"let the number of students be x . then , number of students above 8 years of age = ( 100 - 20 ) % of x = 80 % of x . 80 % of x = 48 + 2 / 3 of 48 ( 80 / 100 ) x = 80 x = 100 . answer d\"" + }, + { + "Answer": 84, + "Options": "a ) 82 , b ) 84 , c ) 86 , d ) 88 , e ) 90", + "Correct": "b", + "Explanation": "\"let x be the height of the first person . then the heights are x , x + 2 , x + 4 , and x + 10 . 4 x + 16 = 4 ( 78 ) = 312 x = 74 and the fourth person has a height of 74 + 10 = 84 inches the answer is b .\"" + }, + { + "Answer": 0.041666666666666664, + "Options": "a ) 1 / 32 , b ) 1 / 28 , c ) 1 / 24 , d ) 1 / 16 , e ) 1 / 14", + "Correct": "c", + "Explanation": "\"there are 3 single digit multiple of 3 , that is , 3 , 6,9 . there are 8 prime nos less than 20 - 2,3 , 5,7 , 11,13 , 17,19 total outcome - 8 * 3 = 24 favourable outcome = 1 ( 9 * 5 ) hence required probability w = 1 / 24 . answer c .\"" + }, + { + "Answer": 360, + "Options": "a ) 350 , b ) 260 , c ) 360 , d ) 380 , e ) 285", + "Correct": "c", + "Explanation": "a eats more than b if b eats 1 times than the ratio of a and b is a : b is 1.8 : 1 or 9 : 5 and as b eat 8 times less the c the the ratio of b : c is 5 : 40 the the least number of times all three has eat is the lcm of a , b , c that is 360 . . answer : c" + }, + { + "Answer": 62, + "Options": "a ) 62 , b ) 74 , c ) 78 , d ) 80 , e ) none of these", + "Correct": "a", + "Explanation": "explanation : number of subjects = 6 average of marks in 6 subjects = 72 therefore total marks in 6 subjects = 72 * 6 = 432 now , no . of subjects = 5 total marks in 5 subjects = 74 * 5 = 370 therefore marks in 6 th subject = 432 \u2013 370 = 62 answer a" + }, + { + "Answer": 30, + "Options": "a ) 20 , b ) 30 , c ) 50 , d ) 80 , e ) 100", + "Correct": "b", + "Explanation": "full time employee who have not worked for at least one year = a full time employee who have worked for at least one year = b non full time employee who have worked for at least one year = c non full time employee who have not worked for at least one year = d a + b + c + d = 150 a + b = 80 i . e . c + d = 70 b + c = 100 i . e . a + d = 50 d = 20 i . e . c = 70 - 20 = 50 i . e . b = 100 - 50 = 50 i . e . a = 80 - 50 = 30 b = 30 answer : option b" + }, + { + "Answer": 58.333333333333336, + "Options": "a ) 8 % , b ) 15 % , c ) 45 % , d ) 52 % , e ) 58 %", + "Correct": "e", + "Explanation": "\"solution : this is a percent decrease problem . we will use the formula : percent change = ( new \u2013 old ) / old x 100 to calculate the final answer . we first set up the ratios of royalties to sales . the first ratio will be for the first 20 million in sales , and the second ratio will be for the next 108 million in sales . because all of the sales are in millions , we do not have to express all the trailing zeros in our ratios . first 20 million royalties / sales = 4 / 20 = 1 / 5 next 108 million royalties / sales = 9 / 108 = 1 / 12 because each ratio is not an easy number to use , we can simplify each one by multiplying each by the lcm of the two denominators , which is 60 . keep in mind that we are able to do this only because our answer choices are expressed in percents . first 20 million royalties / sales = ( 4 / 20 ) x 60 = 12 next 108 million royalties / sales = 9 / 108 = ( 1 / 12 ) x 60 = 5 we can plug 12 and 5 into our percent change formula : ( new \u2013 old ) / old x 100 [ ( 5 \u2013 12 ) / 12 ] x 100 - 175 / 3 x 100 at this point we can stop and consider the answer choices . since we know that 175 / 3 is just a bit less than \u00bd , we know that - 175 / 3 x 100 is about a 58 % decrease . answer e .\"" + }, + { + "Answer": 21, + "Options": "a ) a ) 14 , b ) b ) 67 , c ) c ) 56 , d ) d ) 21 , e ) e ) 34", + "Correct": "d", + "Explanation": "let the son ' s present age be x years . then , ( 52 - x ) = x 2 x = 52 . x = 26 . son ' s age 5 years back ( 26 - 5 ) = 21 years . answer : d" + }, + { + "Answer": 10, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10", + "Correct": "e", + "Explanation": "\"let number of apples = a number of oranges = b a + b = 20 - - - 1 . 56 = ( . 4 a + . 6 b ) / 20 = > 56 = 4 a + 6 b - - - - 2 solving 1 and 2 , we get a = 4 b = 16 let the number of oranges put back = c 52 * ( 20 - c ) = 40 * 4 + 60 ( 16 - c ) = > c = 10 answer e\"" + }, + { + "Answer": 22.65126050420168, + "Options": "a ) 32.25 , b ) 21.45 , c ) 45 , d ) 22.45 , e ) 22", + "Correct": "d", + "Explanation": "average = ( 20 * 2 + 21 * 3 + 22 * 6 + 23 * 4 + 24 * 3 + 25 * 2 ) / 20 = 22.45 answer : d" + }, + { + "Answer": 6, + "Options": "a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 9", + "Correct": "c", + "Explanation": "\"18 = 2 * 3 ^ 2 if 18 divides n ^ 2 , then n must be divisible by 2 * 3 = 6 the answer is c .\"" + }, + { + "Answer": 38.46153846153846, + "Options": "a ) 15 % , b ) 162 \u2044 3 % , c ) 20 % , d ) 38.46 % , e ) 24 %", + "Correct": "d", + "Explanation": "new annual salary = $ 90,000 salary increase = $ 25,000 . original salary = $ 90,000 - $ 25,000 . = $ 75,000 % increase = ( $ 25,000 / $ 65,000 ) * 100 = 38.46 % hence d ." + }, + { + "Answer": 8, + "Options": "a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 9", + "Correct": "d", + "Explanation": "\"total subjects = 11 + 8 + 5 = 24 max subjects by 1 teacher = 3 so , min of teachers required = 24 / 3 = 8 answer : d\"" + }, + { + "Answer": 40, + "Options": "a ) 40 , b ) \u2013 60 , c ) 60 , d ) 75 , e ) 100", + "Correct": "a", + "Explanation": "absolute value will turn negatives into their positive ' equivalents ' , and will leave positives unchanged , so | - 2 | = 2 , | - 25 | = 25 , and | 5 | = 5 . getting rid of our absolute values we have : | - 2 | ( | - 25 | - | 5 | ) = ( 2 ) ( 25 - 5 ) = 2 * 20 = 40" + }, + { + "Answer": 15, + "Options": "a ) 10 , b ) 11 , c ) 13 , d ) 14 , e ) 15", + "Correct": "e", + "Explanation": "\"let number of apples = a number of oranges = b a + b = 30 - - - 1 . 56 = ( . 4 a + . 6 b ) / 30 = > 56 = 4 a + 6 b - - - - 2 solving 1 and 2 , we get a = 6 b = 24 let the number of oranges put back = c 52 * ( 30 - c ) = 40 * 6 + 60 ( 24 - c ) = > c = 15 answer e\"" + }, + { + "Answer": 4832, + "Options": "a ) 4832 , b ) 4855 , c ) 4825 , d ) 4895 , e ) 4862", + "Correct": "a", + "Explanation": "explanation : f ( 1 ) = 0 f ( 2 ) = f ( 1 + 1 ) = f ( 1 ) + f ( 1 ) + 4 ( 9 \u00d7 1 \u00d7 1 \u2013 1 ) = 0 + 0 + 4 \u00d7 8 = 32 f ( 4 ) = f ( 2 + 2 ) = f ( 2 ) + f ( 2 ) + 4 ( 9 \u00d7 2 \u00d7 2 \u2013 1 ) = 32 + 32 + 4 \u00d7 35 = 204 f ( 8 ) = f ( 4 + 4 ) = f ( 4 ) + f ( 4 ) + 4 ( 9 \u00d7 4 \u00d7 4 \u2013 1 ) = 204 + 204 + 4 \u00d7 143 = 980 f ( 16 ) = f ( 8 + 8 ) = f ( 8 ) + f ( 8 ) + 4 ( 9 \u00d7 8 \u00d7 8 \u2013 1 ) = 980 + 980 + 4 \u00d7 575 = 4260 f ( 17 ) = f ( 1 + 16 ) = f ( 16 ) + f ( 1 ) + 4 ( 9 \u00d7 16 \u00d7 1 \u2013 1 ) = 4260 + 0 + 4 \u00d7 143 = 4832 answer : a" + }, + { + "Answer": 16, + "Options": "a ) 7 , b ) 8 , c ) 15 , d ) 16 , e ) 23", + "Correct": "d", + "Explanation": "given 2 ^ 16 * 25 ^ s = 5 * 10 ^ 2 = > 2 ^ 16 * 5 ^ ( 2 s ) = 2 ^ m * 5 ^ ( m + 1 ) ans d on comparing the power of 2 = > m = 16" + }, + { + "Answer": 91, + "Options": "a ) 23 , b ) 78 , c ) 27 , d ) 91 , e ) 81", + "Correct": "d", + "Explanation": "\"explanation : 90 + 5 * 12 / ( 180 / 3 ) = 90 + 5 * 12 / ( 60 ) = 90 + ( 5 * 12 ) / 60 = 90 + 1 = 91 . answer : d\"" + }, + { + "Answer": 100, + "Options": "a ) 92 , b ) 90 , c ) 82 , d ) 78 , e ) 100", + "Correct": "e", + "Explanation": "the question say : a welder received an order to make a 1 million liter cube - shaped tank . ( 1 cubic meter = 1,000 liters ) in other words , the tank is going to have a volume of 1000 cubic meters . that would equal 1 million liters . a cube with a volume of 1000 cubic meters must be ( 10 meters ) x ( 10 meters ) x ( 10 meters ) . the question does n ' t specify whether this tank should have a closed top or an open top . ( the real gmat is good about specifying things like that . ) here , we are going to assume a closed top , only because if the top is open , we do n ' t use enough metal - - - we get an answer smaller than any of the answer choices . a closed - top cube , a full cube , has 6 sides , each of which is ( 10 meters ) x ( 10 meters ) . that ' s a total surface area of 600 sq m . the question tells us : he has only 2 x 3 meter sheets of metal that can be cut . each sheet has an area of 6 sq m . how many of these need to fill up 600 sq m ? 600 / 6 = 100 . he needs 100 sheets . answer = e" + }, + { + "Answer": 9, + "Options": "a ) - 4 , b ) 9 , c ) 11 , d ) 13 , e ) 22", + "Correct": "b", + "Explanation": "\"the equation that can be formed is : 3 x - 10 = 26 - x or , 4 x = 36 or , x = 9 . b answer .\"" + }, + { + "Answer": 6, + "Options": "a ) 6 , 030,053 , b ) 6 , 030,054 , c ) 6 , 030,055 , d ) 6 , 020,030 , e ) 6 , 030,057", + "Correct": "d", + "Explanation": "interesting problem . i think key is to notice that all the given answer choices differs in last two digits . therefore , our entire focus should be to figure out how the given terms contribute to last two digits of total . 1000 ^ 2 - > 00 1001 ^ 1 - > 01 . . . 1004 ^ 2 - > 16 total - > * 30 answer d ." + }, + { + "Answer": 0.8, + "Options": "a ) 3 / 5 , b ) 4 / 5 , c ) 5 / 6 , d ) 5 / 12 , e ) 7 / 12", + "Correct": "b", + "Explanation": "the 6 people consist of three sets of 2 siblings . the number of ways to choose 2 people is 6 c 2 = 15 . the number of ways to choose 2 from the first group of siblings is 2 c 2 = 1 . the number of ways to choose 2 from the second group of siblings is 2 c 2 = 1 . the number of ways to choose 2 from the third group of siblings is 2 c 2 = 1 . the number of ways to choose 2 people who are siblings is 1 + 1 + 1 = 3 . the number of ways to choose 2 people who are not siblings is 15 - 3 = 12 . p ( the two people are not siblings ) = 12 / 15 = 4 / 5 the answer is b ." + }, + { + "Answer": 2, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "a", + "Explanation": "2 years answer : a" + }, + { + "Answer": 20, + "Options": "a ) 18 min , b ) 17 min , c ) 19 min , d ) 20 min , e ) 21 min", + "Correct": "d", + "Explanation": "\"in 1 hr , the bus covers 60 km without stoppages and 40 km with stoppages . stoppage time = time take to travel ( 60 - 40 ) km i . e 20 km at 60 km / hr . stoppage time = 20 / 60 hrs = 20 min . answer : d\"" + }, + { + "Answer": 200, + "Options": "a ) 96 , b ) 200 , c ) 128 , d ) 116 , e ) 122", + "Correct": "b", + "Explanation": "\"average = total runs / no . of innings = 32 so , total = average x no . of innings = 32 * 20 = 640 now increase in avg = 4 runs . so , new avg = 32 + 8 = 40 runs total runs = new avg x new no . of innings = 40 * 21 = 840 runs made in the 11 th inning = 840 - 640 = 200 answer : b\"" + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 7 , c ) 9 , d ) 10 , e ) 11", + "Correct": "a", + "Explanation": "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 17 5 x = 15 x = 3 . hence , b ' s age = 2 x = 6 years . answer : option a" + }, + { + "Answer": 18.75, + "Options": "a ) 22.75 , b ) 33.25 , c ) 22.25 , d ) 11.75 , e ) 18.75", + "Correct": "e", + "Explanation": "\"explanation : total of 50 numbers = ( 50 \u00d7 20 ) = 1000 total of 48 numbers = ( 1000 - ( 45 + 55 ) ] = 900 required average = 900 / 48 = 18.75 answer : e\"" + }, + { + "Answer": 66, + "Options": "a ) 60 , b ) 62 , c ) 66 , d ) 72 , e ) 78", + "Correct": "c", + "Explanation": "= > ( 6767 + 1 ) is divisible by ( 67 + 1 ) = > ( 6767 + 1 ) is divisible by 68 = > ( 6767 + 1 ) \u00f7 68 gives a remainder of 0 = > [ ( 6767 + 1 ) + 66 ] \u00f7 68 gives a remainder of 66 = > ( 6767 + 67 ) \u00f7 68 gives a remainder of 66 c" + }, + { + "Answer": 4, + "Options": "a ) 1.7 , b ) 2.67 , c ) 1.2 , d ) 1.5 , e ) 4", + "Correct": "e", + "Explanation": "\"m = 12 s = x ds = 12 + x us = 12 + x 12 + x = ( 12 - x ) 2 12 + x = 24 - 2 x 3 x = 12 x = 4 answer : e\"" + }, + { + "Answer": 2, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "a", + "Explanation": "if average of 3 is 4 so sum of 3 should be 12 3 recording can be from 0 - 10 inclusive to find one smallest other two should be highest so , lets assume three var are a , b , c say a is smallest and give b and c greatest readings say 5 and 5 so a has to be 2 a" + }, + { + "Answer": 10, + "Options": "a ) 6 , b ) 9 , c ) 10 , d ) 12 , e ) 15", + "Correct": "c", + "Explanation": "this is an inverse proportional problem . . . . . . 5 pipes in 12 days ; so for 4 days , it will be = 12 x 5 / 4 = 15 so , q = 15 - 5 = 10 . c" + }, + { + "Answer": 129, + "Options": "a ) 129 kg , b ) 134 kg , c ) 180 kg , d ) 185 kg , e ) 190 kg", + "Correct": "a", + "Explanation": "\"total weight increased = ( 4 x 8.5 ) kg = 34 kg . weight of new person = ( 95 + 34 ) kg = 129 kg option a\"" + }, + { + "Answer": 20, + "Options": "a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60", + "Correct": "a", + "Explanation": "\"let number of pounds of 5 $ candy to be used be w 6 = ( 10 * 8 + 5 * w ) / ( 10 + w ) = > 60 + 6 w = 80 + 5 w = > w = 20 answer a\"" + }, + { + "Answer": 2, + "Options": "a ) 1 , b ) 2 , c ) 345 , d ) 445 , e ) 235", + "Correct": "b", + "Explanation": "1 = 6,2 = 36,3 = 363,4 = 364,5 = 365 , then 36 = ? 36 = 2 check the second eqn . answer : b" + }, + { + "Answer": 1100, + "Options": "a ) 1234 , b ) 1110 , c ) 1456 , d ) 1200 , e ) 1600", + "Correct": "b", + "Explanation": "\"let the smaller number be x . then larger number = ( x + 1365 ) . x + 1000 = 10 x + 10 9 x = 990 x = 110 large number = 110 + 1000 = 1110 b\"" + }, + { + "Answer": 159, + "Options": "a ) 158 cms , b ) 158.5 cms , c ) 159 cms , d ) 159.5 cms , e ) none", + "Correct": "c", + "Explanation": "explanation : average height of the whole class = ( 36 \u00d7 160 + 10 \u00d7 156 / 40 ) = 159 cms answer c" + }, + { + "Answer": 75000, + "Options": "a ) 55000 , b ) 75000 , c ) 65000 , d ) 190000 , e ) 250000", + "Correct": "b", + "Explanation": "\"if value of business = x total sell ( 2 x / 3 ) ( 3 / 4 ) = 15000 - > x = 75000 answer : b\"" + }, + { + "Answer": 6, + "Options": "a ) 116 yards , b ) 226 yards , c ) 97 yards , d ) 115.74 yards , e ) 1 yard", + "Correct": "d", + "Explanation": "d" + }, + { + "Answer": 20, + "Options": "a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30", + "Correct": "c", + "Explanation": "\"the q talks of total capacity , normal level , present level , shortage etc . . so it is all about not going wrong in these terms 30 mg = 75 % of total . . total = 30 / . 75 = 40 mg . . normal level = 1 / 2 of 40 = 20 mg . . shortage of normal level = 40 - 20 = 20 mg . . c\"" + }, + { + "Answer": 6, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "d", + "Explanation": "let , average commission = x no . of items sold = y total commission = xy new commission = xy + 1000 new average = ( xy + 1000 ) / ( y + 1 ) = 150 + x i . e . ( xy + 1000 ) = ( y + 1 ) * ( 150 + x ) i . e . ( xy + 1000 ) = ( xy + x + 150 y + 150 ) i . e . ( 850 ) = ( x + 150 y ) new commission = 250 = 150 + x i . e . x = 100 i . e . y = 5 new sales = y + 1 = 6 answer : option d" + }, + { + "Answer": 80, + "Options": "a ) 60 , b ) 80 , c ) 98 , d ) 89 , e ) 91", + "Correct": "b", + "Explanation": "if on a test three people answered 90 % of the questions correctly and two people answered 80 % correctly , then the average for the group is not 85 % but rather 3 \u00d7 90 + 2 \u00d7 805 = 4305 = 86.3 \u00d7 90 + 2 \u00d7 805 = 4305 = 86 . here , 90 has a weight of 3 = > it occurs 3 times . whereas 80 has a weight of 2 = > it occurs 2 times . so the average is closer to 90 than to 80 as we have just calculated . b" + }, + { + "Answer": 50, + "Options": "a ) $ 20 , b ) $ 40 , c ) $ 50 , d ) $ 80 , e ) $ 100", + "Correct": "c", + "Explanation": "\"deargoodyear 2013 , i ' m happy to help . this is a relatively straightforward problem , not very challenging . btw , crazy eddiewas the actually name of an electronics chain on the east coast of the usa back in the 1970 s . manufacturing now is $ 50 . they now are making a 50 % profit , so the selling price must be $ 100 . they had this same selling price , $ 100 , before they made the change , and had a profit of 50 % , so the manufacturing must have been $ 50 . answer = ( c ) .\"" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9", + "Correct": "b", + "Explanation": "\"the tens digit of 6 in integer power starting from 2 ( 6 ^ 1 has no tens digit ) repeats in a pattern of 5 : { 3 , 1 , 9 , 7 , 5 } : the tens digit of 6 ^ 2 = 36 is 3 . the tens digit of 6 ^ 3 = 216 is 1 . the tens digit of 6 ^ 4 = . . . 96 is 9 . the tens digit of 6 ^ 5 = . . . 76 is 7 . the tens digit of 6 ^ 6 = . . . 56 is 5 . the tens digit of 6 ^ 7 = . . . 36 is 3 again . etc . . . 22 has the form 5 n + 2 , so the tens digit of 6 ^ 22 is 3 . the answer is b .\"" + }, + { + "Answer": 540, + "Options": "a ) $ 250 , b ) $ 340 , c ) $ 640 , d ) $ 440 , e ) $ 540", + "Correct": "e", + "Explanation": "\"a = 1 / 3 ( b + c ) = > c = 3 a - b - - - ( 1 ) b = 2 / 7 ( a + c ) = > c = 3.5 b - a - - ( b ) a - b = $ 15 a = 15 + b ( 1 ) = = = > c = 45 + 3 b - b = 2 b + 45 = = > 2 b - c = - 45 - - - ( 3 ) ( 2 ) = = = > c = 3.5 b - b - 15 = 2.5 b - 15 = = > 2.5 b - c = 15 - - - ( 4 ) from ( 4 ) and ( 3 ) 0.5 b = 60 b = $ 120 a = $ 135 c = 405 - 120 = $ 285 total amount = 135 + 120 + 285 = $ 540 answer : e\"" + }, + { + "Answer": 0.5714285714285714, + "Options": "a ) 3 / 7 , b ) 5 / 7 , c ) 6 / 7 , d ) 1 / 7 , e ) 4 / 7", + "Correct": "e", + "Explanation": "first notice the number of months for which he worked - march to sept i . e . 7 months avg of monthly totals in tips for months other than august = x tips in august = 8 x total tips for all months = 6 * x + 8 x = 14 x tips for august / total tips for all months = 8 x / 14 x = 4 / 7 answer : e" + }, + { + "Answer": 87, + "Options": "a ) 44 % , b ) 48 % , c ) 52 % , d ) 42 % , e ) 87 %", + "Correct": "e", + "Explanation": "\"first calculate the distance , b has covered with his speed in the time , in which a reached 20 % of the race . then add the remaining distance as head start for b to win the race . its best to apply ratios concept here . since a ' s speed is 20 / 13 of b , therefore , b ' s speed is 13 / 20 of a distance covered by b = speed x time = ( 13 / 20 ) x ( 0.2 ) = 0.13 % ( which means b would have covered 0.13 of the race length during the time in which a has covered 0.2 of the race length . therefore to win , b needs a headstart of ( 1 - 0.13 = ) 0.87 of the race length . so the answer is e\"" + }, + { + "Answer": 20, + "Options": "a ) 20 , b ) 50 , c ) 60 , d ) 80 , e ) 100", + "Correct": "a", + "Explanation": "total cost for n products = fixed cost for n products + n * marginal cost - - > $ 16,000 = $ 12,000 + n * $ 200 - - > n = 20 . answer : a ." + }, + { + "Answer": 24, + "Options": "a ) 22 , b ) 21 , c ) 88 , d ) 37 , e ) 24", + "Correct": "e", + "Explanation": "\"explanation : lot the total number of workers be v then , 8 ooov = ( 12000 * 8 ) + 6000 ( v - 8 ) < = > 2000 v = 48000 < = > v = 24 answer : e ) 24\"" + }, + { + "Answer": 70807, + "Options": "a ) 70,592 , b ) 64,850 , c ) 64,749 , d ) 149,700 , e ) 156,720", + "Correct": "a", + "Explanation": "\"find the number , upon sum of 3 digits of a number gives a reminder 2 when it is divided by 7 seeing the options after dividing an finding the reminder of 2 my answer was a\"" + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) 15 , c ) 17 , d ) 19 , e ) 21", + "Correct": "a", + "Explanation": "\"the worst case scenario will be if we remove all 15 tablets of medicine b first . the next 2 tablets we remove have to be of medicine a , so to guarantee that at least two tablets of each kind will be taken we should remove minimum of 10 + 2 = 12 tablets . answer : a .\"" + }, + { + "Answer": 4, + "Options": "a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 9", + "Correct": "b", + "Explanation": "\"explanation : on dividing 42739 by 15 we get the remainder 4 , so 4 should be subtracted option b\"" + }, + { + "Answer": 60, + "Options": "a ) $ 48 , b ) $ 54 , c ) $ 60 , d ) $ 66 , e ) $ 72", + "Correct": "c", + "Explanation": "\"the difference in the two prices is $ 2.75 - $ 1.25 = $ 1.50 for each color copy . each color copy will cost an extra $ 1.50 at print shop y . 40 * $ 1.50 = $ 60 the answer is c .\"" + }, + { + "Answer": 10, + "Options": "a ) 4 , b ) 6 , c ) 5 , d ) 3 , e ) 10", + "Correct": "e", + "Explanation": "\"solution : 5 ^ 2 * 5 ^ 2 * 5 ^ 2 * 5 ^ 2 * 5 ^ 2 = 5 ^ ( 2 + 2 + 2 + 2 + 2 ) = 5 ^ 10 answer : e\"" + }, + { + "Answer": 0.6, + "Options": "a ) 1 / 5 , b ) 2 / 5 , c ) 3 / 5 , d ) 4 / 5 , e ) 5 / 5", + "Correct": "c", + "Explanation": "here ' s how to subtract 1 / 5 from 4 / 5 : 4 / 5 \u2212 1 / 5 since our denominators match , we can subtract the numerators . 4 \u2212 1 = 3 so the answer is : 3 / 5 answer : c" + }, + { + "Answer": 27, + "Options": "a ) 23 , b ) 24 , c ) 25 , d ) 26 , e ) 27", + "Correct": "e", + "Explanation": "a two - digit integer ` ` ab ' ' can be expressed algebraically as 10 a + b . q - r = ( 10 a + b ) - ( 10 b + a ) = 9 ( a - b ) < 30 . the greatest multiple of 9 which is less than 30 is 27 . the answer is e ." + }, + { + "Answer": 200, + "Options": "a ) 20 , b ) 50 , c ) 200 , d ) 100 , e ) 400", + "Correct": "c", + "Explanation": "the equation can be reduced to intercept form as | x / 10 | + | y / 10 | = 1 , so these are lines in four quadrants with x and y intercept as 10 , so it is a rhombus with diagonals of 20 each and hence area = 1 / 2 * d 1 * d 2 = 1 / 2 * 20 * 20 = 200 . answer c ." + }, + { + "Answer": 110.5, + "Options": "a ) 102 % , b ) 105 % , c ) 110.5 % , d ) 112.5 % , e ) 100 %", + "Correct": "c", + "Explanation": "easiest thing to do : assume that price is 100 price at the end of yr 1 : 100 + 30 = 130 price at the end of year 2 = 130 - 130 * 0.15 = 130 * 0.85 = 110.5 hence required answer = ( 110.5 / 100 ) * 100 % = 110.5 % answer is c ." + }, + { + "Answer": 60.00000000000002, + "Options": "a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80", + "Correct": "c", + "Explanation": "let the number be x . ( 5 / 4 ) * x = ( 4 / 5 ) * x + 27 25 x = 16 x + 540 9 x = 540 x = 60 the answer is c ." + }, + { + "Answer": 8, + "Options": "a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 0", + "Correct": "d", + "Explanation": "\"any power of anything ending in 5 always has a units digit of 5 . so the first term has a units digit of 5 . done . the second term takes a little more work . we can ignore the tens digit , and just treat this base as 3 . here is the units digit patter for the powers of 3 . 3 ^ 45 has a units digit of 3 of course 5 + 3 = 8 , d\"" + }, + { + "Answer": 80, + "Options": "a ) $ 20 , b ) $ 40 , c ) $ 50 , d ) $ 80 , e ) $ 100", + "Correct": "d", + "Explanation": "cost + profit = income ( selling price ) profit now = 0.5 x or x - 50 0.5 x = x - 50 50 = 0.5 x x = 100 $ is selling price so , profit before was 0.2 * 100 = 20 $ cost = 100 - 20 = 80 $ answer : d" + }, + { + "Answer": 724827405, + "Options": "a ) 434539873 , b ) 355797990 , c ) 435453490 , d ) m = 725117481 , e ) 873430134", + "Correct": "d", + "Explanation": "\"72519 x 9999 = 72519 x ( 10000 - 1 ) = 72519 x 10000 - 72519 x 1 = 725190000 - 72519 = 725117481 d\"" + }, + { + "Answer": 35, + "Options": "a ) 20 , b ) x = 25 , c ) x = 30 , d ) x = 35 , e ) 40", + "Correct": "d", + "Explanation": "\"suppose the population of the country in current year is 1000 . so annual increase is 1000 + 39.4 - 19.4 = 1020 hence every year there is an increase of 2 % . 2000 = 1000 ( 1 + ( 2 / 100 ) ) ^ n n = 35 answer is d .\"" + }, + { + "Answer": 6, + "Options": "a ) 0 , b ) 1 , c ) 3 , d ) 4 , e ) 6", + "Correct": "e", + "Explanation": "lets take the number as y when y is divided by 9 the remainder is 5 hence y can be written as y = 9 k + 5 multiplying by 3 will give 3 y = 27 k + 15 we can also write 3 y = 27 k + 9 + 6 now 27 k and 9 are divisible by 9 leaving the remainder as 6 hence e is the answer ." + }, + { + "Answer": 557, + "Options": "a ) 557 , b ) 608 , c ) 613 , d ) 616 , e ) 621", + "Correct": "a", + "Explanation": "\"the set s = { 5 , 13 , 21 , 29 , . . . . . . . . . . . . . . . . . . . . . } 1 st number = 8 * 0 + 5 = 5 2 nd number = 8 * 1 + 5 = 13 3 rd number = 8 * 2 + 5 = 21 70 th number = 8 * ( 70 - 1 ) + 5 = 557 answer = a\"" + }, + { + "Answer": 8, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) none", + "Correct": "c", + "Explanation": "solution : since f ( x ) is a linear function whose slope is 1 , a positive number , it is strictly increasing for all x . therefore its maximal value is reached for the largest value of x , x = 13 and f ( x ) = 13 - 5 = 8 . answer c" + }, + { + "Answer": 24, + "Options": "a ) 24 , b ) 10 , c ) 8 , d ) 9.5 , e ) none of these", + "Correct": "a", + "Explanation": "\"answer : a ( 5 x 12 - 3 x 4 ) / 2 = 24\"" + }, + { + "Answer": 22.5, + "Options": "a ) 22.5 , b ) 99 , c ) 24 , d ) 66 , e ) 887", + "Correct": "a", + "Explanation": "\"total time taken = x / 30 + 2 x / 20 hours = 2 x / 15 hours average speed = 3 x / ( 2 x / 15 ) = 22.5 kmph answer : a\"" + }, + { + "Answer": 30, + "Options": "a ) 27 , b ) 30 , c ) 29 , d ) 10 , e ) 11", + "Correct": "b", + "Explanation": "\"let the price of turban be x . thus , for one year the salary = ( 90 + x ) for 9 months he should earn 3434 ( 90 + x ) . now he gets one turban and rs . 60 . thus , 3434 ( 90 + x ) = 60 + x or 270 + 3 x = 240 + 4 x or x = 30 answer : b\"" + }, + { + "Answer": 47.99999999999999, + "Options": "a ) $ 44 , b ) $ 48 , c ) $ 52 , d ) $ 56 , e ) $ 60", + "Correct": "b", + "Explanation": "\"p = ( 2 / 6 ) * p + 32 ( 4 / 6 ) * p = 32 p = 48 the answer is b .\"" + }, + { + "Answer": 83.83561643835617, + "Options": "a ) 80 , b ) 85 , c ) 83 , d ) 95 , e ) 00", + "Correct": "c", + "Explanation": "\"total production of salt by the company in that year = 2000 + 2100 + 2200 + . . . . + 3100 = 30600 . average monthly production of salt for that year = 30600 / 365 \u00e2 \u2030 \u02c6 84 answer : c\"" + }, + { + "Answer": 8, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9", + "Correct": "d", + "Explanation": "\"14 n + 32 = 16 ( n + 1 ) 2 n = 16 n = 8 the answer is d .\"" + }, + { + "Answer": 330, + "Options": "a ) 354 , b ) 357 , c ) 330 , d ) 370 , e ) 360", + "Correct": "c", + "Explanation": "we know that ( 10 ^ 38 ) is ending 00 , so ( 10 ^ 38 ) \u2013 85 = 9 . . . . 9915 total number of digits in ( 10 ^ 38 ) \u2013 85 is 38 , or 36 digits of 9 and two digits 1 and 5 . answer choice is 36 * 9 + 6 = 330 answer is c 330" + }, + { + "Answer": 27, + "Options": "a ) 26 , b ) 27 , c ) 88 , d ) 99 , e ) 12", + "Correct": "b", + "Explanation": "sum of the 10 numbers = 230 if each number is increased by 4 , the total increase = 4 * 10 = 40 the new sum = 230 + 40 = 270 the new average = 270 / 10 = 27 . answer : b" + }, + { + "Answer": 14, + "Options": "a ) 6 , b ) 7 , c ) 13 , d ) 14 , e ) 29", + "Correct": "d", + "Explanation": "first i figured out the percentage change from the immediate previous amount for each of the period . thus it comes - 0 - 6 days = = > 0 % 7 - 13 days = = > 10 % ( 90 % of the price ) 14 - 29 days = = > 17 % ( approx ) ( went from 90 % to 75 % ) 30 days or more = = > 20 % ( went from 75 % to 60 % ) if the passenger had to pay the extra amount , she had to pay = ( 210 + 1050 ) = 1260 now 210 is somehow between 10 % and 20 % of 1260 . so 17 % is the choice here . correct ans : 14 days answer : d" + }, + { + "Answer": 13, + "Options": "a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14", + "Correct": "d", + "Explanation": "\"158 + 50 = 208 / 16 = 13 ( remainder ) d\"" + }, + { + "Answer": 18, + "Options": "a ) 20 , b ) 24 , c ) 26 , d ) 18 , e ) 30", + "Correct": "d", + "Explanation": "\"( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 62 + 2 * 131 a + b + c = \u221a 324 = 18 d\"" + }, + { + "Answer": 21, + "Options": "a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25", + "Correct": "a", + "Explanation": "\"the multiples of 4 are from 4 * 3 up to 4 * 23 . 23 - 3 + 1 = 21 . the answer is a .\"" + }, + { + "Answer": 103.5, + "Options": "a ) 103.5 rs , b ) 104.5 rs , c ) 105.5 rs , d ) 106.5 rs , e ) 107.5 rs", + "Correct": "a", + "Explanation": "for 1 st km : rs . 13.50 ramaining distance : 13 - 1 = 12 km 1 / 3 km costs 2.5 rs 1 km costs ( 2.5 * 3 ) remaining 12 km costs ( 2.5 * 3 ) * 12 = 90 rs total cost = 90 + 13.5 = 103.5 rs answer : a" + }, + { + "Answer": 4.6, + "Options": "a ) 4.6 , b ) 3.0 , c ) 4.1 , d ) 3.2 , e ) 2.9", + "Correct": "a", + "Explanation": "w = 0.50 f = 0.25 s = 1.00 b = w + 2 f + 3 s = 4.00 they pay , he pays 4 , net loss 0 fifth bundle = 2 they pay , he pays 5 , net loss 3 dollars 3 / 5 = 60 cents . charging 60 more cents on each bundle will be safe . answer : a" + }, + { + "Answer": 6, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "d", + "Explanation": "p ( choosing a red apple 6 times in a row ) = 10 / 11 * 9 / 10 * 8 / 9 * 7 / 8 * 6 / 7 * 5 / 6 = 5 / 11 < 0.5 the answer is d ." + }, + { + "Answer": 540, + "Options": "a ) 540 , b ) 570 , c ) 619 , d ) 649 , e ) 700", + "Correct": "a", + "Explanation": "\"before price increase price = x after 30 % price increase price = x + ( 30 / 100 ) * x = 1.3 x = 351 ( given ) i . e . x = 351 / 1.3 = $ 270 i . e . 2 x = 2 * 270 = 540 answer : option a\"" + }, + { + "Answer": 15, + "Options": "a ) 15 , b ) 30 , c ) 45 , d ) 60 , e ) 75", + "Correct": "a", + "Explanation": "no oa yet : my method : max points : a b c d e f 15 12 9 6 3 0 = 45 points min points a b c d e f 5 5 5 5 5 5 = 30 45 - 30 = 15 points = = = = > ( a ) ans" + }, + { + "Answer": 3, + "Options": "a ) 3 , b ) 20 , c ) 28 , d ) 14 , e ) 19", + "Correct": "a", + "Explanation": "\"number of statues = all the paint \u00f7 amount used per statue = 3 / 6 \u00f7 1 / 6 = 3 / 6 * 6 / 1 = 3 / 1 = 3 answer is a .\"" + }, + { + "Answer": 48.550000000000004, + "Options": "a ) 47.55 kg , b ) 48 kg , c ) 48.55 kg , d ) 49.25 kg , e ) 59.25 kg", + "Correct": "c", + "Explanation": "\"16 * 50.25 + 8 * 45.15 / 24 = 48.55 answer : c\"" + }, + { + "Answer": 27, + "Options": "a ) 25 liters , b ) 27 liters , c ) 30 liters , d ) 32 liters , e ) 35 liters", + "Correct": "b", + "Explanation": "\"let x ltr water to be added 2 ltr alcohol to be represented as ( 20 ( 1 - 3 / 4 ( new soln . = 13 + x ) ) ) 2 = 5 % * ( 13 + x ) - - - - - - - - > x = 27 ans b\"" + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) 16 , c ) 18 , d ) 24 , e ) 26", + "Correct": "a", + "Explanation": "\"explanation : suppose the boy got x sums right and 2 x sums wrong . then , x + 2 x = 36 3 x = 36 x = 12 . answer : a\"" + }, + { + "Answer": 500.90000000000003, + "Options": "a ) 50.09 , b ) 5.06 , c ) 50.06 , d ) 100.9 , e ) 500.9", + "Correct": "e", + "Explanation": "\"= 20.036 / 0.04 = 2003.6 / 4 = 500.9 answer is e .\"" + }, + { + "Answer": 6791, + "Options": "a ) s . 4991 , b ) s . 5991 , c ) s . 6001 , d ) s . 6791 , e ) s . 7991", + "Correct": "d", + "Explanation": "\"total fr 5 mnths = ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs 34009 . reqd . sale = rs . [ ( 6800 * 6 ) - 34009 ] = rs . ( 40800 - 34009 ) = rs . 6791 . answer : d\"" + }, + { + "Answer": 4, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "d", + "Explanation": "when 17 is divided by x , the remainder is 1 i . e . 1 orange left over after grouping , so x must be greater than 1 . it also means that 16 is completely divisible by x . factors of 16 are 1 , 2 , 4 , 8 , 16 . out of these , x can be 2 , 4 , 8 , and 16 . answer ( d ) ." + }, + { + "Answer": 7, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 10 , e ) 11", + "Correct": "b", + "Explanation": "\"the lcm of 7 , 9 , and 11 is 693 . the next multiple is 2 * 693 = 1386 . 1386 + { remainder } = 1386 + 5 = 1391 , which is 7 less than 1398 . answer : b .\"" + }, + { + "Answer": 137, + "Options": "a ) 130 , b ) 132 , c ) 134 , d ) 137 , e ) 138", + "Correct": "d", + "Explanation": "\"let the required number be x . then , 43 x \u2013 34 x = 1233 or 9 x = 1233 or x = 137 . required number = 137 . answer : d\"" + }, + { + "Answer": 100000, + "Options": "a ) 100000 , b ) 69842 , c ) 39684 , d ) 30158 , e ) none", + "Correct": "a", + "Explanation": "answer given expression = [ ( 69842 ) 2 - ( 30158 ) 2 ] / [ ( 69842 - 30158 ) ] = [ ( 69842 - 30158 ) ( 69842 + 30158 ) ] / ( 60842 - 30158 ) = 100000 correct option : a" + }, + { + "Answer": 15.999999999999998, + "Options": "a ) 10 hrs , b ) 12 hrs , c ) 16 hrs , d ) 18 hrs , e ) 20 hrs", + "Correct": "c", + "Explanation": "1 / 20 + 1 / 30 = 1 / 12 1 + 1 / 3 = 4 / 3 1 - - - 12 4 / 3 - - - ? 4 / 3 * 12 = 16 hrs c" + }, + { + "Answer": 24, + "Options": "a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28", + "Correct": "c", + "Explanation": "\"the time to produce the first 60 cogs is 60 / 15 = 4 hours . the time to produce the next 60 cogs is 60 / 60 = 1 hour . the average output is 120 cogs / 5 hours = 24 cogs per hour . the answer is c .\"" + }, + { + "Answer": 4.05, + "Options": "a ) $ 4.85 , b ) $ 4.15 , c ) $ 4.65 , d ) $ 4.55 , e ) $ 4.05", + "Correct": "e", + "Explanation": "\"john spent and gave to his two friends a total of 1.05 + 1.00 + 1.00 = $ 3.05 money left 7.10 - 3.05 = $ 4.05 answer : e\"" + }, + { + "Answer": 11, + "Options": "a ) 3 , b ) 5 , c ) 8 , d ) 11 , e ) 15", + "Correct": "d", + "Explanation": "\"total # of students = 32 avg # of books per student = 2 total # of books = 32 * 2 = 64 # of student borrowed at least 3 books = 32 - 2 - 12 - 10 = 8 # of books borrowed by above 8 students = 60 - ( 12 * 1 ) + ( 10 * 2 ) = 32 considering that 7 out of above 8 students borrowed only 3 books , # of books borrowed = 7 * 3 = 21 so maximum # of books borrowed by any single student = 32 - 21 = 11 option d\"" + }, + { + "Answer": 22, + "Options": "a ) a ) 16 , b ) b ) 18 , c ) c ) 19 , d ) d ) 22 , e ) e ) 24", + "Correct": "d", + "Explanation": "\"explanation : 10 * 21 + 36 \u2013 26 = 220 = > 220 / 10 = 22 d )\"" + }, + { + "Answer": 20, + "Options": "a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25", + "Correct": "d", + "Explanation": "let the number of people who eat oranges be x . then , total number of people = x + ( x / 2 ) + ( x / 2 ) = 2 x = > 2 x - 10 = x = > x = 10 = > total number of people were 2 x = 20 option d" + }, + { + "Answer": 45, + "Options": "a ) 22 , b ) 88 , c ) 77 , d ) 20 , e ) 45", + "Correct": "e", + "Explanation": "\"in 1 hr , the bus covers 60 km without stoppages and 15 km with stoppages . stoppage time = time take to travel ( 60 - 15 ) km i . e 45 km at 60 km / hr . stoppage time = 45 / 60 hrs = 45 min . answer : e\"" + }, + { + "Answer": 9, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 6 , e ) 5", + "Correct": "c", + "Explanation": "( ( ( 13 ! ) ^ 16 ) - ( ( 13 ! ) ^ 8 ) ) / ( ( ( 13 ! ) ^ 8 ) + ( ( 13 ! ) ^ 4 ) ) = a solving it , we get a / ( ( 13 ! ) ^ 4 ) = ( ( 13 ! ) ^ 4 - 1 ) last digit of ( 13 ! ) ^ 4 will be 0 . so last digit of ( ( 13 ! ) ^ 4 - 1 ) will be 9 . answer : c" + }, + { + "Answer": 2200, + "Options": "a ) 1287 , b ) 2200 , c ) 2000 , d ) 1129 , e ) 1192", + "Correct": "b", + "Explanation": "\"let money invested by raghu = rs . x money invested by trishul = 9 / 10 x = 0.9 x money invested by vishal = 9 / 10 x * 110 / 100 = 0.99 x also , x + 0.9 x + 0.99 x = 6358 = x = 6358 / 2.89 = 2200 therefore , amount invested by raghu is rs . 2200 . answer : b\"" + }, + { + "Answer": 3, + "Options": "a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 8", + "Correct": "b", + "Explanation": "\"i like to put the numbers in prime factors so it is easier and faster to visualize . 14 * n / 60 if we write the factors of 14 - - > 2 , 7 , and the factors of 60 - - > 2 , 2 , 3 , 5 , we have ( 2 * 7 * n ) / ( 2 ^ 2 * 3 * 5 ) simplifying 7 * n / ( 2 * 3 * 5 ) the only way the equation above has an integer value is if n has at least the factors 2 , 3 and 5 , so we can simplify again and we have the number 7 . the number could be 2 * 3 * 5 , or 2 * 3 * 5 * 2 , or 2 * 3 * 5 * . . . . . however to be less than 200 we can not add any prime number . 2 * 3 * 5 = 120 if we added the next prime factor 7 , we would have a = 2 * 3 * 5 * 7 = 840 thus , answer b\"" + }, + { + "Answer": 0.88891111, + "Options": "a ) rs . 0.7889 , b ) rs . 0.8889 , c ) rs . 0.9889 , d ) rs . 1.8889 , e ) rs . 2.8889", + "Correct": "b", + "Explanation": "if payment per hr is increased by 33.33 % , then 11.11 % decrease in income if earlier he is getting rs 1 hr per hr and working for 1 hr , income = rs 1 now he is getting rs 1.3333 per hr and working for 0.66667 hrs , income = rs . 0.8889 answer : b" + }, + { + "Answer": 19, + "Options": "a ) 6 , b ) 12 , c ) 19 , d ) 24 , e ) 27", + "Correct": "c", + "Explanation": "38 * 2 / 3 * 3 / 4 = 19 answer : c" + }, + { + "Answer": 8, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8", + "Correct": "e", + "Explanation": "\"one way of solving this is : speed of boat on still water ( lake ) = 7 kmph speed upstream = 6 kmph = speed in still water - speed of river = > speed of river = 1 kmph = > speed downstream = speed in still water + speed of river = 7 + 1 = 8 kmph ans is e\"" + }, + { + "Answer": 11, + "Options": "a ) 10 , b ) 12 , c ) 11 , d ) 13 , e ) 14", + "Correct": "c", + "Explanation": "r + g + b = 28 g = 12 r + g < 24 = > r + 12 < 24 = > r < 12 = > at most 11 red balls answer : c" + }, + { + "Answer": 0.4, + "Options": "a ) 1 / 4 , b ) 2 / 5 , c ) 9 / 16 , d ) 5 / 8 , e ) 16 / 9", + "Correct": "b", + "Explanation": "\"3 / 4 * 4 / 5 * 2 / 3 = 2 / 5 answer : b\"" + }, + { + "Answer": 0.08333333333333334, + "Options": "a ) 1 / 12 , b ) 1 / 16 , c ) 1 / 19 , d ) 1 / 14 , e ) 1 / 13", + "Correct": "a", + "Explanation": "\"x * ( 120 / 100 ) - - - - - - - - - - - - - - - - = 2 / 15 y * ( 75 / 100 ) x / y = 1 / 12 answer : a\"" + }, + { + "Answer": 52, + "Options": "a ) 13 , b ) 52 , c ) 39 , d ) 26 , e ) 35", + "Correct": "b", + "Explanation": "w is divided by 13 so that is multiple of 14 as 13 , 26,39 . . . w + 3 is divided by 11 the remainder is 0 so it is divisible by 11 . consider from option let us take the number is 13 it is divisible by 14 but 13 + 3 is not divisible by 11 so it is not answers so let us take 2 nd option 52 which is divisible by 13 and 52 + 3 = 55 is divisible by 11 so ans is b" + }, + { + "Answer": 250, + "Options": "a ) 300 , b ) 200 , c ) 250 , d ) 150 , e ) 160", + "Correct": "c", + "Explanation": "basically , this question is asking you to figure out how many students are being double - counted . a - club has 200 members ( 1 / 2 of 400 ) b - club has 250 members ( 5 / 8 of 400 ) c - club has 300 members ( 3 / 4 of 400 ) we can create an equation to solve this : 200 + 250 + 300 = n + x + 2 y where n is the number of students , x is the number of students in two clubs , and y is the number of students in three clubs . the question provides y for us ( 50 ) . 750 = 400 + x + 100 x = 250 c" + }, + { + "Answer": 10, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", + "Correct": "d", + "Explanation": "\"solution let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . \u2234 ( 2 x + 2 ) + 2 x + x = 27 \u21d4 5 x = 25 \u21d4 x = 5 . hence , b ' s age = 2 x = 10 years . answer d\"" + }, + { + "Answer": 5, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8", + "Correct": "b", + "Explanation": "by remainder theorem remainder = { [ ( 2 ^ 3 ) ^ 1551 * 2 ^ 2 ] / 9 } = [ { ( - 1 ) ^ 1551 * 4 } / 9 ] = 5 answer : b" + }, + { + "Answer": 190, + "Options": "a ) $ 28 , b ) $ 82 , c ) $ 110 , d ) $ 190 , e ) $ 192", + "Correct": "d", + "Explanation": "\"this question can be solved easily using a equation model . 150 * p = 16200 ( fixed cost ) + 150 * 80 + 150 * 2 . = 16200 + 12000 + 300 = 28500 p = $ 190 . d\"" + }, + { + "Answer": 0.41666666666666663, + "Options": "a ) 3 / 10 , b ) 4 / 11 , c ) 5 / 12 , d ) 6 / 13 , e ) 7 / 15", + "Correct": "c", + "Explanation": "p ( neither pen is defective ) = 6 / 9 * 5 / 8 = 5 / 12 the answer is c ." + }, + { + "Answer": 63, + "Options": "a ) 75 , b ) 63 , c ) 83 , d ) 94 , e ) 39", + "Correct": "b", + "Explanation": "using elimination method find which of the options fit the description of the number . . . from the option only 63 meets this description sum of digits - - - 6 + 3 = 9 difference of digits - - - 6 - 3 = 3 answer b ." + }, + { + "Answer": 2, + "Options": "a ) 2 , b ) 6 , c ) 5 , d ) 4 , e ) 3", + "Correct": "a", + "Explanation": "\"if x = 3 2.13 \u00d7 10 ^ 3 = 2130 > 2,100 so , x = 2 answer : a\"" + }, + { + "Answer": 13, + "Options": "a ) 15 , b ) 25 , c ) 13 , d ) 45 , e ) 75", + "Correct": "c", + "Explanation": "\"out of 300 - 180 purchased for less than 100 $ 120 for more out of 300 - 120 responded as satisfied and 180 responded disatisfied out of 180 ( purchased less than 100 $ ) - 45 % = 81 responded as satisfied , so remaining satisfied are 120 - 81 = 39 so 39 is what percentage of 300 - 13 % so the answer should be c\"" + }, + { + "Answer": 68, + "Options": "a ) 43 , b ) 56 , c ) 68 , d ) 87 , e ) 92", + "Correct": "c", + "Explanation": "\"sol . monthly rent per square feet = 2244 / ( 18 * 22 ) & annual rent per square feet = 12 * ( 2244 / ( 18 * 22 ) ) = 68 c\"" + }, + { + "Answer": 18, + "Options": "a ) 18 . , b ) 2 . , c ) 6 . , d ) 4 . , e ) 10 .", + "Correct": "a", + "Explanation": "let v and v ' be the original and the changed volume now v = pir ^ 2 h v ' = pi ( 3 r ) ^ 2 ( 2 h ) v ' = 18 v a ) 18" + }, + { + "Answer": 51.25, + "Options": "a ) 52.6 , b ) 52.4 , c ) 52.1 , d ) 51.2 , e ) 52.9", + "Correct": "d", + "Explanation": "\"sum of the marks for the class of 35 students = 35 * 40 = 1400 sum of the marks for the class of 45 students = 45 * 60 = 2700 sum of the marks for the class of 80 students = 1400 + 2700 = 4100 average marks of all the students = 4100 / 80 = 51.2 . answer : d\"" + }, + { + "Answer": 11, + "Options": "a ) 3 , b ) 6 , c ) 8 , d ) 11 , e ) 16", + "Correct": "d", + "Explanation": "\"m ^ 2 is divisible by 33 so m ^ 2 must be multiple of 48 . if the value of m is multiples of 11 then it will satisfy the condition . if we if m is 12 or 24 or 36 then it ans is d but if m = 33 then answer should be 16 . is the question right ? or am i missing some thing ? d\"" + }, + { + "Answer": 150, + "Options": "a ) 16 , b ) 24 , c ) 60 , d ) 120 , e ) 150", + "Correct": "e", + "Explanation": "answer = e = 150 no of 4 person committees that can be formed = 5 c 2 * 6 c 2 = 150 answer e" + }, + { + "Answer": 2800, + "Options": "a ) 2800 , b ) 3799 , c ) 1200 , d ) 2693 , e ) 1732", + "Correct": "a", + "Explanation": "\"p - - - 10 - - - - 1400 p - - - 5 - - - - - 700 3 p - - - 5 - - - - - 2100 - - - - - - = > 2800 answer : a\"" + }, + { + "Answer": 942.8571428571427, + "Options": "a ) 100 , b ) 200 , c ) 300 , d ) 350 , e ) 943", + "Correct": "e", + "Explanation": "\"45 x / 100 - x / 3 = 110 7 x / 60 = 110 x = 943 answer : e\"" + }, + { + "Answer": 9, + "Options": "a ) 2 / 18 , b ) 6 / 3 , c ) 30 / 2 , d ) 18 / 2 , e ) 6 / 18", + "Correct": "d", + "Explanation": "a / ( b / c ) = ( a * c ) / b the expression will have the largest value when numerator ( a * c ) is the largest . = ( 6 * 3 ) / 2 = 18 / 2 answer d" + }, + { + "Answer": 39, + "Options": "a ) 39 , b ) 88 , c ) 26 , d ) 87 , e ) 11", + "Correct": "a", + "Explanation": "\"explanation : consider the avg for first 16 innings is x . then total runs scored till 16 innings is 16 x . total runs after 17 innings = 16 x + 87 . thus , 16 x + 8717 = x + 316 x + 8717 = x + 3 \u21d2 x = 36 so his average after 17 innings = 39 . answer : a\"" + }, + { + "Answer": 64, + "Options": "a ) 64 , b ) 32 , c ) 16 , d ) 4 , e ) 1", + "Correct": "a", + "Explanation": "1 / 2 the square root of x is cube root of y . if y = 64 . . then 1 / 2 the square root of y = 4 and cube of y is 64 . option a ." + }, + { + "Answer": 1.5, + "Options": "a ) 2.5 , b ) 1.5 , c ) 1 , d ) 3.5 , e ) 4.5", + "Correct": "b", + "Explanation": "\"let x = the youngest child . each of the other four children will then be x + 1 , x + 2 , x + 3 we know that the sum of their ages is 12 so , x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) = 12 therefore the youngest child is 1.5 years old answer : b\"" + }, + { + "Answer": 0.25, + "Options": "a ) 0.0016 , b ) 0.0625 , c ) 0.16 , d ) 0.25 , e ) 0.5", + "Correct": "d", + "Explanation": "\"( 1 / 2 ) \u00b2 = ( 1 / 2 ) ( 1 / 2 ) = 1 / 4 approach # 1 : use long division to divide 4 into 1 to get 1 / 4 = 0.25 d\"" + }, + { + "Answer": 28, + "Options": "a ) [ 22 ] , b ) [ 44 ] , c ) [ 45 ] , d ) [ 28 ] , e ) [ 10 ]", + "Correct": "d", + "Explanation": "[ 6 ] * [ 3 ] = ( 6 / 2 + 1 ) ( 3 * 2 + 1 ) = [ 28 ] . ans - d" + }, + { + "Answer": 150, + "Options": "a ) 50 , b ) 100 , c ) 150 , d ) 92 , e ) 25", + "Correct": "c", + "Explanation": "a 2 - b 2 = 10 : given a 4 + b 4 - 2 a 2 b 2 = 102 : square both sides and expand . a * b = 5 : given a 2 b 2 = 52 : square both sides . a 4 + b 4 - 2 ( 25 ) = 100 : substitute a 4 + b 4 = 150 correct answer c" + }, + { + "Answer": 489.99999999999994, + "Options": "a ) 390 , b ) 490 , c ) 400 , d ) 460 , e ) none of these", + "Correct": "b", + "Explanation": "number of male employees = 2800 * 25 / 100 = 700 required number of male employees who are less than 50 years old = 700 * ( 100 - 30 ) % = 700 * 70 / 100 = 490 . answer : b" + }, + { + "Answer": 90, + "Options": "a ) 32 , b ) 81 , c ) 60 , d ) 27 , e ) 90", + "Correct": "e", + "Explanation": "explanation : let the number be 3 + 1 / 2 [ 1 / 3 ( a / 5 ) ] = a / 15 = > 3 = a / 30 = > a = 90 answer : e" + }, + { + "Answer": 188, + "Options": "a ) $ 120 , b ) $ 135 , c ) $ 150 , d ) $ 165 , e ) $ 188", + "Correct": "e", + "Explanation": "\"let the charge for first hour = x + 20 then charge for each additional hour = x x + 20 + 4 x = 300 = > 5 x = 280 = > x = 56 total charge for patient for 3 hours of therapy = x + 20 + 2 x = 3 x + 20 = 188 $ answer e\"" + }, + { + "Answer": 2.6, + "Options": "a ) 2 \u221a 2 , b ) 13 / 5 , c ) 3 \u221a 2 , d ) 3 \u221a 3 , e ) \u221a 2", + "Correct": "b", + "Explanation": "( \u221a 112 + \u221a 567 ) / \u221a 175 = ( 4 \u221a 7 + 9 \u221a 7 ) / 5 \u221a 7 = 13 / 5 hence , the correct answer is b ." + }, + { + "Answer": 35, + "Options": "a ) 25 , b ) 28 , c ) 30 , d ) 35 , e ) 40", + "Correct": "d", + "Explanation": "let b : y : g = 3 x : 7 x : 8 x . 3 x + 7 x + 8 x = 18 x = 126 - - > x = 7 . g - b = 8 x - 3 x = 5 x = 35 . the answer is d ." + }, + { + "Answer": 266.6666666666667, + "Options": "a ) 40 , b ) 200 , c ) 266 , d ) 267 , e ) 600", + "Correct": "d", + "Explanation": "in order not to lose money because of the change ben ' s total commission must beat least $ 75,000 - $ 45,000 = $ 30,000 , so total sales must beat least $ 30,000 / 0.15 = $ 200,000 . which means that he must makeat least $ 200,000 / 750 = 800 / 3 = 266.6 sales , so 267 sales . answer : d ." + }, + { + "Answer": 1608, + "Options": "a ) 1235 , b ) 1345 , c ) 1678 , d ) 1767 , e ) 1623", + "Correct": "e", + "Explanation": "\"let the smaller number be x . then larger number = ( x + 1355 ) . x + 1355 = 6 x + 15 5 x = 1340 x = 268 large number = 268 + 1355 = 1623 e\"" + }, + { + "Answer": 245, + "Options": "a ) 200 , b ) 245 , c ) 50 , d ) 115 , e ) 150", + "Correct": "b", + "Explanation": "\"x + y = 290 x - y = 200 2 x = 90 x = 45 y = 245 answer is b\"" + }, + { + "Answer": 166, + "Options": "a ) 165 , b ) 166 , c ) 190 , d ) 198 , e ) 199", + "Correct": "b", + "Explanation": "\"166 answer is b\"" + }, + { + "Answer": 1035, + "Options": "a ) 1035 , b ) 1280 , c ) 2070 , d ) 2140 , e ) none", + "Correct": "a", + "Explanation": "solution we know that ( 1 + 2 + 3 + . . . . . + 45 ) = n ( n + 1 ) / 2 therefore ( 1 + 2 + 3 + . . . . + 45 ) = ( 45 \u00d7 46 / 2 ) = 1035 . answer a" + }, + { + "Answer": 222, + "Options": "a ) 222 , b ) 224 , c ) 226 , d ) 228 , e ) 230", + "Correct": "a", + "Explanation": "\"a = d * q + r a = 13 * 17 + 1 a = 221 + 1 a = 222\"" + }, + { + "Answer": 130, + "Options": "a ) 125 km , b ) 130 km , c ) 135 km , d ) 140 km , e ) none", + "Correct": "b", + "Explanation": "\"sol . let the total journey be x km . then 3 x / 5 + 7 x / 20 + 6.5 = x \u21d4 12 x + 7 x + 20 * 6.5 = 20 x \u21d4 x = 130 km . answer b\"" + }, + { + "Answer": 750, + "Options": "a ) 650 , b ) 700 , c ) 750 , d ) 800 , e ) none of these", + "Correct": "c", + "Explanation": "as per question stem 2 / 5 m ( portion of men employees who are managers ) + 200 ( portion of female employees who are managers ) = 2 / 5 t ( portion of total number of employees who are managers ) , thus we get that 2 / 5 m + 300 = 2 / 5 t , or 2 / 5 ( t - m ) = 300 , from here we get that t - m = 750 , that would be total number of female employees and the answer ( c )" + }, + { + "Answer": 25, + "Options": "a ) 25 , b ) 36 , c ) 39 , d ) 21 , e ) 11", + "Correct": "a", + "Explanation": "\"add the numbers of doughnuts . 9 + 7 + 9 = 25 . answer is a .\"" + }, + { + "Answer": 3, + "Options": "a ) 5 , b ) 3 , c ) 2 , d ) 1 , e ) 0", + "Correct": "b", + "Explanation": "6 \u201d 3 = 9 - 6 = 3 answer : b" + }, + { + "Answer": 1, + "Options": "a ) 5 / 12 , b ) 12 / 5 , c ) 25 / 144 , d ) 144 / 25 , e ) 1", + "Correct": "e", + "Explanation": "\"let the number be x . then , 2 / 3 x = 144 / 216 * 1 / x x 2 = 144 / 216 * 3 / 2 = 144 / 144 x = 1 answer : e\"" + }, + { + "Answer": 33, + "Options": "a ) 85 , b ) 74 , c ) 67 , d ) 33 , e ) 28", + "Correct": "d", + "Explanation": "\"( 6 * 70 ) + 47 + x > 500 420 + 47 + x > 500 467 + x > 500 = > x > 33 option d\"" + }, + { + "Answer": 66.66666666666666, + "Options": "a ) 66.66 % , b ) 66.68 % , c ) 66.766 % , d ) 86.66 % , e ) 66.65 %", + "Correct": "a", + "Explanation": "\"excess of b ' s height over a ' s = [ ( 40 / ( 100 - 40 ) ] x 100 % = 66.66 % answer : a ) 66.66 %\"" + }, + { + "Answer": 2, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "b", + "Explanation": "\"25 / 3 = 8 . xxx 84 / 6 = 14 . xxx so we need to find prime numbers between 8 ( exclusive ) - 13 ( inclusive ) there are 2 prime numbers 1113 hence answer will be ( b ) 2 b\"" + }, + { + "Answer": 15, + "Options": "a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 19", + "Correct": "c", + "Explanation": "\"the smallest amount that the company can spend is the lcm of 400 and 350 , which is 2800 for each , which is total 5600 . the number of 1 st type of computers which costing $ 400 = 2800 / 400 = 7 . the number of 2 nd type of computers which costing $ 350 = 2800 / 350 = 8 . total = 7 + 8 = 15 answer is c .\"" + }, + { + "Answer": 0.6, + "Options": "a ) 3 / 5 , b ) 3 / 7 , c ) 4 / 7 , d ) 5 / 6 , e ) 7 / 12", + "Correct": "a", + "Explanation": "\"the 6 people consist of two sets of 3 siblings . the number of ways to choose 2 people is 6 c 2 = 15 . the number of ways to choose 2 from the first group of siblings is 3 c 2 = 3 . the number of ways to choose 2 from the second group of siblings is 3 c 2 = 3 . the number of ways to choose 2 people who are siblings is 3 + 3 = 6 . the number of ways to choose 2 people who are not siblings is 15 - 6 = 9 . p ( the two people are not siblings ) = 9 / 15 = 3 / 5 the answer is a .\"" + }, + { + "Answer": 0.15, + "Options": "a ) 27 / 4 , b ) 27 / 8 , c ) 3 / 4 , d ) 3 / 20 , e ) 1 / 4", + "Correct": "d", + "Explanation": "say a = 2 . then : a / b = 1 / 3 - - > b = 6 ; b / c = 2 - - > c = 3 ; c / d = 1 / 2 - - > d = 6 ; d / e = 3 - - > e = 2 ; e / f = 1 / 10 - - > f = 20 . abc / def = ( 2 * 6 * 3 ) / ( 6 * 2 * 20 ) = 3 / 20 . answer : d ." + }, + { + "Answer": 49, + "Options": "a ) 35 , b ) 42 , c ) 45 , d ) 49 , e ) 54", + "Correct": "d", + "Explanation": "\"a = 105 = 3 * 5 * 7 a ^ 3 = 21 \u00d7 25 \u00d7 45 \u00d7 z = > a ^ 3 = ( 7 * 3 ) x ( 5 * 5 ) x ( 3 ^ 2 * 5 ) x z = > a ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x z = > ( 3 * 5 * 7 ) ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x z z = 7 ^ 2 = 49 answer d\"" + }, + { + "Answer": 40, + "Options": "a ) 20 , b ) 40 , c ) 60 , d ) 80 , e ) 120", + "Correct": "b", + "Explanation": "\"let ( y / 20 ) x ( y / 80 ) = 1 y ^ 2 = 20 x 80 = 20 x 20 x 4 y = ( 20 x 2 ) = 40 the answer is b .\"" + }, + { + "Answer": 160, + "Options": "a ) $ 120 , b ) $ 140 , c ) $ 150 , d ) $ 160 , e ) $ 180", + "Correct": "d", + "Explanation": "\"let the price of the meal be x . after a 10 % sales tax addition , the price is 1.1 * x after a 20 % tip on this amount , the total is 1.2 * 1.1 * x = 1.32 x 1.32 x = $ 211.20 x = $ 160 the correct answer is d .\"" + }, + { + "Answer": 0.6333333333333333, + "Options": "a ) 17 / 30 , b ) 19 / 30 , c ) 11 / 15 , d ) 7 / 15 , e ) 2 / 5", + "Correct": "b", + "Explanation": "let x be the number of students in the school . the number of males who speak a foreign language is ( 3 / 5 ) ( 1 / 2 ) x = ( 3 / 10 ) x the number of females who speak a foreign language is ( 2 / 3 ) ( 1 / 2 ) x = ( 1 / 3 ) x the total number of students who speak a foreign language is ( 3 / 10 ) x + ( 1 / 3 ) x = ( 19 / 30 ) x the answer is b ." + }, + { + "Answer": 23, + "Options": "a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 25", + "Correct": "d", + "Explanation": "\"number of members in the team = 11 let the average age of of the team = x = > ( sum of ages of all 11 members ) / 11 = x = > sum of the ages of all 11 members = 11 x age of the captain = 26 age of the wicket keeper = 26 + 3 = 29 sum of the ages of 9 members of the team excluding captain and wicket keeper = 11 x \u2212 26 \u2212 29 = 11 x \u2212 55 average age of 9 members of the team excluding captain and wicket keeper = ( 11 x \u2212 55 ) / 9 given that ( 11 x \u2212 55 ) / 9 = ( x \u2212 1 ) \u21d2 11 x \u2212 55 = 9 ( x \u2212 1 ) \u21d2 11 x \u2212 55 = 9 x \u2212 9 \u21d2 2 x = 46 \u21d2 x = 46 / 2 = 23 years answer is d .\"" + }, + { + "Answer": 0.07692307692307693, + "Options": "a ) 1 / 190 , b ) 1 / 20 , c ) 1 / 19 , d ) 1 / 13 , e ) 1 / 9", + "Correct": "d", + "Explanation": "\"the problem with your solution is that we do n ' t choose 1 shoe from 14 , but rather choose the needed one after we just took one and need the second to be the pair of it . so , the probability would simply be : 1 / 1 * 1 / 13 ( as after taking one at random there are 13 shoes left and only one is the pair of the first one ) = 1 / 13 answer : d .\"" + }, + { + "Answer": 24.99999999999905, + "Options": "a ) 96 , b ) 75 , c ) 48 , d ) 25 , e ) 12", + "Correct": "d", + "Explanation": "\"when positive integer x is divided by positive integer y , the remainder is 3 - - > x = qy + 3 ; x / y = 96.12 - - > x = 96 y + 0.12 y ( so q above equals to 96 ) ; 0.12 y = 3 - - > y = 25 . answer : d .\"" + }, + { + "Answer": 100, + "Options": "a ) $ 100 , b ) $ 150 , c ) $ 200 , d ) $ 250 , e ) $ 450", + "Correct": "a", + "Explanation": "\"cavg = average contribution before john cavg * 1.5 = 75 , therefore the average cont is $ 50 before john . if he needs to increase the average contribution by $ 25 , he must put in $ 25 for each of the 1 people . so $ 25 . but , he also has to put in the average for himself ( the twoth person ) , so add $ 75 . so $ 100 is your answer . answer a\"" + }, + { + "Answer": 345, + "Options": "a ) $ 374 , b ) $ 382 , c ) $ 345 , d ) $ 392 , e ) $ 399", + "Correct": "c", + "Explanation": "\"( 348 / 116 ) 115 = 345 in this case long division does not take much time . ( 348 / 116 ) = 3 3 * 115 = 345 ( 300 + 45 ) answer c\"" + }, + { + "Answer": 960, + "Options": "a ) 233 , b ) 960 , c ) 287 , d ) 771 , e ) 191", + "Correct": "b", + "Explanation": "explanation : total salary of 8 workers and supervisor together = 9 \u00e3 \u2014 430 = 3870 now total salary of 8 workers = 3870 \u00e2 \u02c6 \u2019 870 = 3000 total salary of 9 workers including the new supervisor = 9 \u00e3 \u2014 440 = 3960 salary of the new supervisor = 3960 \u00e2 \u02c6 \u2019 3000 = 960 answer : b" + }, + { + "Answer": 5, + "Options": "a ) 3 , b ) 5 , c ) 6 , d ) 11 , e ) 16", + "Correct": "b", + "Explanation": "( m - 8 ) ( m - a ) = m ^ 2 - hm - 24 a = - 3 h = 8 + a = 5 = b" + }, + { + "Answer": 12.5, + "Options": "a ) 5 % , b ) 7.5 % , c ) 10 % , d ) 12.5 % , e ) 15 %", + "Correct": "d", + "Explanation": "\"let x be the original number of each color . kaz eats all of the green candies and half of the orange ones . there are 0 green candies and 0.5 x orange candies remaining . he eats half of the remaining pieces of each color . there are 0.25 x orange candies , and 0.5 x each of red , yellow , and blue candies . he eats red and yellow candies in equal proportions . orange + blue + red + yellow = 0.75 x + red + yellow = x red + yellow = 0.25 x red = 0.125 x , since red = yellow . the answer is d .\"" + }, + { + "Answer": 5, + "Options": "a ) 10 , b ) 8 , c ) 12 , d ) 15 , e ) 5", + "Correct": "e", + "Explanation": "average = ( 2 + 7 + 6 + x ) / 4 = 5 x = 5 answer is e" + }, + { + "Answer": 60, + "Options": "a ) 40 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 80 %", + "Correct": "c", + "Explanation": "\"can be reduced to 3 y / 10 + 3 y / 10 = 3 y / 5 = 60 % c\"" + }, + { + "Answer": 54, + "Options": "a ) a ) 51 , b ) b ) 50 , c ) c ) 45 , d ) d ) 54 , e ) e ) 36", + "Correct": "d", + "Explanation": "\"explanation : let the number be x . then , x - ( x / 3 ) = 36 = > 2 x / 3 = 36 = > x = 54 answer : option d\"" + }, + { + "Answer": 3.25, + "Options": "a ) 13 / 4 , b ) 6 / 5 , c ) 7 / 5 , d ) 8 / 5 , e ) 9 / 5", + "Correct": "a", + "Explanation": "\"w / x = 1 / 3 = > x = 3 w and w / y = 3 / 4 = > y = ( 4 / 3 ) w ( x + y ) / y = ( 3 w + 4 / 3 w ) / ( 4 / 3 w ) = ( 13 / 3 w ) / ( 4 / 3 w ) = 13 / 4 correct option : a\"" + }, + { + "Answer": 18, + "Options": "a ) 11 , b ) 25 , c ) 27 , d ) 18 , e ) 91", + "Correct": "d", + "Explanation": "\"let the son ' s present age be x years . then , man ' s present age = ( x + 20 ) years . ( x + 20 ) + 2 = 2 ( x + 2 ) x + 22 = 2 x + 4 = > x = 18 . answer : d\"" + }, + { + "Answer": 70, + "Options": "a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80", + "Correct": "d", + "Explanation": "35 / 2 \u00f7 4 = 35 / 8 pounds in each container 35 / 8 pounds * 16 ounces / pound = 70 ounces in each container the answer is d ." + }, + { + "Answer": 74, + "Options": "a ) 66 , b ) 74 , c ) 78 , d ) 80 , e ) none of these", + "Correct": "b", + "Explanation": "\"explanation : number of subjects = 6 average of marks in 6 subjects = 74 therefore total marks in 6 subjects = 74 * 6 = 444 now , no . of subjects = 5 total marks in 5 subjects = 74 * 5 = 370 therefore marks in 6 th subject = 444 \u2013 370 = 74 answer b\"" + }, + { + "Answer": 780, + "Options": "a ) 600 , b ) 780 , c ) 800 , d ) 900 , e ) none of these", + "Correct": "b", + "Explanation": "\"explanation : let p ' s capital = p , q ' s capital = q and r ' s capital = r then 4 p = 6 q = 10 r = > 2 p = 3 q = 5 r = > q = 2 p / 3 r = 2 p / 5 p : q : r = p : 2 p / 3 : 2 p / 5 = 15 : 10 : 6 r ' s share = 4030 * ( 6 / 31 ) = 130 * 6 = 780 . answer : option b\"" + }, + { + "Answer": 12, + "Options": "a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14", + "Correct": "c", + "Explanation": "if n = 12 mark sold 1 box and ann sold 10 boxes total 11 < 12 answer : c" + }, + { + "Answer": 50, + "Options": "a ) 150 , b ) 70 , c ) 50 , d ) 1500 , e ) 500", + "Correct": "c", + "Explanation": "given that 10 rabbits were caught and tagged in the first sample , and 10 were caught in the second sample of which 2 had tags , then 2 / 10 approximates the fraction of the population of tagged rabbits in the forest . proportion : a / x = c / d a = rabbits tagged first sample c / d = the fraction of the population of tagged rabbits in the forest x = the population of rabbits in the forest proportion : 10 / x = 1 / 5 x = ( 1 ) ( 10 ) ( 5 ) = 50 . there are approximately 50 rabbits in the forest . answer is c" + }, + { + "Answer": 4, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "e", + "Explanation": "a number is divisible by 5 , if its last digit is divisible by 5 let ' s look into the sum of last digits of each term of the given expression 1 ^ 1 = 1 2 ^ 2 = 4 3 ^ 3 = 7 4 ^ 4 = 6 5 ^ 5 = 5 6 ^ 6 = 6 7 ^ 7 = 3 adding all these numbers we get 32 which gives a remainder of 4 when divided by 7 . so answer must be 4 . bunuel , can you please confirm the answer of this question . yes , the oa is c . clicked the wrong button when posting . edited . thank you . e" + }, + { + "Answer": 43, + "Options": "a ) 43 , b ) 44 , c ) 45 , d ) 46 , e ) 47", + "Correct": "a", + "Explanation": "a + b + c = 144 a + b + c + d = 188 d = 44 e = 47 b + c + d + e = 192 b + c = 101 a = 43 answer : a" + }, + { + "Answer": 0.2, + "Options": "a ) 1 / 10 , b ) 1 / 8 , c ) 1 / 5 , d ) 1 / 4 , e ) 1 / 2", + "Correct": "c", + "Explanation": "total number of combinations possible = 10 ! / 2 ! 10 ! / 2 ! total favorable combinations = 9 ! 9 ! - we have considered the two is as one element . since we have two is , they can interchange their positions , without affecting the code . probability = 9 ! / ( 10 ! / 2 ! ) = 9 ! \u2217 2 ! / 10 ! = 1 / 59 ! / ( 10 ! / 2 ! ) = 9 ! \u2217 2 ! / 10 ! = 1 / 5 ans : c" + }, + { + "Answer": 33.33333333333333, + "Options": "a ) 20 % , b ) 75 % , c ) 50 % , d ) 33.3 % , e ) 80 %", + "Correct": "d", + "Explanation": "r + w + p = 90 s + l = 90 1 / 3 * 90 = 30 short - stemmed white = 15 short - stemmed pink = 10 = > short - stemmed red = 5 10 / p = 5 / r = > r = p / 2 , p = 2 r so total long stemmed = 60 and long stemmed red + long stemmed pink = 60 so long stemmed red / long stemmed = ? total white = 15 ( as no long stemmed white ) = > r + 2 r + 15 = 90 = > 3 r = 75 and r = 25 long stemmed r = 25 - 5 = 20 so long stemmed red / r = 20 / 60 = 33.3 % answer - d" + }, + { + "Answer": 16, + "Options": "a ) 16 , b ) 11 , c ) 10 , d ) 20 , e ) 9", + "Correct": "a", + "Explanation": "take the example of 6 . . . it has 4 positive divisors ( 1,2 , 3,4 ) now , take the example of 216 . . . it has 16 divisors . . so a is the ans" + }, + { + "Answer": 12000, + "Options": "a ) 12000 , b ) 13000 , c ) 14000 , d ) 15000 , e ) 16000", + "Correct": "a", + "Explanation": "\"the average price of 25 products is $ 1,200 means that the total price of 25 products is 25 * 1,200 = $ 30,000 . next , since exactly 10 of the products sell for less than $ 1,000 , then let ' s make these 10 items to be at $ 400 each ( min possible ) . now , the remaining 14 items can not be priced less than $ 1,000 , thus the minimum possible price of each of these 14 items is $ 1,000 . thus the minimum possible value of 24 products is 10 * 400 + 14 * 1,000 = $ 18,000 . therefore , the greatest possible selling price of the most expensive product is $ 30,000 - $ 18,000 = $ 12,000 . answer : a .\"" + }, + { + "Answer": 620, + "Options": "a ) 620 , b ) 530 , c ) 450 , d ) 470 , e ) 500", + "Correct": "a", + "Explanation": "solution let expenditure on friday be x ( 450 + 600 + 400 + 500 + x + 550 + 300 ) / 7 = 500 2800 + x = 3500 x = 700 pen + notebook + earphone = 700 earphone = 700 - 80 = 620 answer a" + }, + { + "Answer": 2, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "c", + "Explanation": "\"51 / 13 = 4 - 89 / 9 = 10 - prime numbers between 4 and 10 are 5 and 7 - sign signifies that the number is marginally less . answer c\"" + }, + { + "Answer": 1, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 1", + "Correct": "e", + "Explanation": "explanation : on dividing 5026 by 5 we get the remainder 1 , so 1 should be subtracted option e" + }, + { + "Answer": 0.7857142857142856, + "Options": "a ) 11 / 14 , b ) 13 / 18 , c ) 4 / 7 , d ) 3 / 7 , e ) 3 / 14", + "Correct": "a", + "Explanation": "\"if we use variable for total votes there will be too many fractions to manipulate with , so pick some smart # : let set total # of votes is 18 . 2 / 9 of the votes on a certain resolution have been counted - - > 4 counted and 18 - 4 = 14 votes left to be counted ; 3 / 4 of those counted are in favor of the resolution - - > 3 in favor and 1 against ; ratio of those who voted against to those who voted for to be 2 to 1 there should be total of 18 * 2 / 3 = 12 people who voted against , so in the remaining 14 votes there should be 12 - 1 = 11 people who voted against . thus x = 11 / 14 of the remaining votes must be against . answer : a .\"" + }, + { + "Answer": 11, + "Options": "a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14", + "Correct": "b", + "Explanation": "f ( 2 x + 1 ) = 2 f ( x ) + 1 : given f ( 3 ) = 2 f ( 1 ) + 1 : x = 1 in a f ( 1 ) = 2 f ( 0 ) + 1 : x = 0 in a f ( 3 ) = 11 : substitute correct answer b" + }, + { + "Answer": 40, + "Options": "a ) 45 , b ) 40 , c ) 39 , d ) 37 , e ) 38", + "Correct": "b", + "Explanation": "\"explanation : let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 . x / 2 = ( 83 - 63 ) = > x / 2 = 20 = > x = 40 . answer : b\"" + }, + { + "Answer": 181.42857142857142, + "Options": "a ) 185 , b ) 183.22 , c ) 184.96 , d ) 181.43 , e ) 182.78", + "Correct": "d", + "Explanation": "( sum of the 20 weights ) / 20 = 180 sum of the 20 weights = 3600 new sum = 3600 + 210 = 3810 new average = 3810 / 21 = 181.43 ans : d" + }, + { + "Answer": 663, + "Options": "a ) 663 , b ) 720 , c ) 625 , d ) 640 , e ) none", + "Correct": "a", + "Explanation": "solution : 663 explanation : for an ideal case , the batsman will hit a six on each ball . but if he hits six on the last ball of the over , the strike will change in the next over . thus , the best he can do in the last ball is run 3 runs so that he retains the strike even in the next over . thus the total runs that he can score in each over : 6 * 5 + 3 = 33 but this will have to go like it only till the 19 th over . in the last over , he can hit a six in the last ball as well as that will be the last ball of the match . thus runs for the last over will be 6 * 6 = 36 . hence the maximum runs = 33 * 19 + 36 = 663 answer a" + }, + { + "Answer": 58, + "Options": "a ) 50 , b ) 58 , c ) 49 , d ) 48 , e ) 44", + "Correct": "b", + "Explanation": "sum of 5 integer ( a , b , c , d , e ) = 5 * 50 = 250 e - a = 10 i . e . e = a + 10 for e to be maximum remaining 4 must be as small as possible since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers i . e . a + a + a + a + ( a + 10 ) = 250 i . e . 5 a = 240 i . e . a = 48 i . e . largest e = 48 + 10 = 58 answer : option b" + }, + { + "Answer": 257, + "Options": "a ) 264 , b ) 257 , c ) 269 , d ) 270 , e ) 282", + "Correct": "b", + "Explanation": "\"lcm ( 8 , 11,24 ) = 24 x 11 = 264 so the least divisible number is 264 , and the number we are looking for is 264 - 7 = 257 . the answer is b .\"" + }, + { + "Answer": 17, + "Options": "a ) 17 , b ) 19 , c ) 21 , d ) 23 , e ) 25", + "Correct": "a", + "Explanation": "\"let n = total students in class total points for 1 / 3 class = 15 n / 3 = 5 n total points for 2 / 3 class = 18 * 2 n / 3 = 12 n total points for whole class = 5 n + 12 n = 17 n 17 n total class points / n total students = 17 grade point average for total class answer : a\"" + }, + { + "Answer": 26.000000000000004, + "Options": "a ) 24 , b ) 26 , c ) 30 , d ) 46 , e ) 50", + "Correct": "b", + "Explanation": "oranges = ( oranges + kiwi + x ) * 0.3 24 = ( 30 + 24 + x ) * 0.3 x = 26 . answer : b ." + }, + { + "Answer": 57, + "Options": "a ) 47 , b ) 114 , c ) 74 , d ) 67 , e ) 57", + "Correct": "e", + "Explanation": "answer let the number be x . then , x - 44 = 70 - x \u00e2 \u2021 \u2019 2 x = 70 + 44 = 114 \u00e2 \u2021 \u2019 2 x = 114 \u00e2 \u02c6 \u00b4 x = 57 correct option : e" + }, + { + "Answer": 4, + "Options": "a ) 4 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 50 %", + "Correct": "a", + "Explanation": "\"let original salary be $ 100 salary after decreasing 20 % = 100 - 100 x 20 / 100 = $ 80 salary after increasing 20 % on $ 80 = 80 + 80 x 20 / 100 = $ 96 percentage of loss = 100 - 96 = 4 % answer : a\"" + }, + { + "Answer": 159, + "Options": "a ) 150 , b ) 152 , c ) 154 , d ) 159 , e ) 144", + "Correct": "d", + "Explanation": "\"d = d * q + r d = 17 * 9 + 6 d = 153 + 6 d = 159 answer d\"" + }, + { + "Answer": 800, + "Options": "a ) s . 800 , b ) s . 810 , c ) s . 820 , d ) s . 900 , e ) s . 920", + "Correct": "a", + "Explanation": "\"2400 * 1 / 3 = 800 option a\"" + }, + { + "Answer": 8270, + "Options": "a ) rs . 5870 , b ) rs . 8270 , c ) rs . 6020 , d ) rs . 6850 , e ) none of these", + "Correct": "b", + "Explanation": "\"explanation : total sale for 5 months = rs . ( 5420 + 5660 + 6200 + 6350 + 6500 ) = rs . 30,130 therefore , required sale = rs . [ ( 6400 * 6 ) \u2013 30,130 ] = rs . ( 38400 \u2013 30,130 ) = rs . 8270 answer b\"" + }, + { + "Answer": 384, + "Options": "a ) 351 , b ) 384 , c ) 410 , d ) 424 , e ) 450", + "Correct": "b", + "Explanation": "\"we ' re dealing with a sequence of consecutive odd integers : 9 to 39 , inclusive . we ' re asked for the sum of this group . 1 ) start with the sum of the smallest and the biggest : 9 + 39 = 48 2 ) now look at the ' next smallest ' and the ' next biggest ' : 11 + 37 = 48 now we have proof that there is no middle term . we have 8 bunches of 48 8 ( 48 ) = 384 b\"" + }, + { + "Answer": 18, + "Options": "a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19", + "Correct": "d", + "Explanation": "\"if the number of participants is 3 ( say a , b , c ) the number of games played will be 2 ( a plays against b and c ) + 1 ( b plays against c ) = 3 using the same logic , if the number of participants is n , the number of games played will be ( n - 1 ) + ( n - 2 ) + ( n - 3 ) + . . . 3 + 2 + 1 given that this sum = 153 = 1 + 2 + 3 + . . . ( n - 1 ) sum of first m positive integers is given by m ( m + 1 ) / 2 . so sum of first ( n - 1 ) positive integers is ( n - 1 ) * n / 2 153 = ( n - 1 ) * n / 2 ( n - 1 ) * n = 306 17 * 18 = 306 ( we know that 15 ^ 2 = 225 so the two consecutive numbers must be greater than 15 . also , 20 ^ 2 = 400 so the two numbers must be less than 20 . the pair of numbers in between 15 and 20 whose product ends with 6 is 17 and 18 ) so n = 18 answer ( d )\"" + }, + { + "Answer": 18, + "Options": "a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22", + "Correct": "c", + "Explanation": "let the present ages of son and father be x and ( 42 - x ) years respectively . then , ( 42 - x ) - 6 = 4 ( x - 6 ) 36 - x = 4 x - 24 x = 12 the son ' s age after 6 years will be 18 . the answer is c ." + }, + { + "Answer": 3.8000000000000007, + "Options": "a ) 4.2 , b ) 4.4 , c ) 4.6 , d ) 3.8 , e ) 5.7", + "Correct": "d", + "Explanation": "\"sum of the remaining two numbers = ( 3.95 * 6 ) - [ ( 4.2 * 2 ) + ( 3.85 * 2 ) ] = 7.60 . required average = ( 7.6 / 2 ) = 3.8 . d\"" + }, + { + "Answer": 0.0625, + "Options": "a ) 0.0016 , b ) 0.0625 , c ) 0.16 , d ) 0.25 , e ) 0.5", + "Correct": "b", + "Explanation": "\"1 / 4 = 25 / 100 = > ( 25 / 100 ) ^ 2 = 625 / 10000 = 0.0625 answer : b\"" + }, + { + "Answer": 12, + "Options": "a ) 7 , b ) 14 , c ) 12 , d ) 6 / 7 , e ) 5", + "Correct": "c", + "Explanation": "we ' re given the equation 5 + 7 / x = 6 - 5 / x . we ' re asked for the value of x . the common - denominator of these 4 numbers is x , so we need to multiply both sides of the equation by x , giving us . . . 5 x + 7 x / x = 6 x - 5 x / x we can then eliminate that denominator , which gives us . . . . 5 x + 7 = 6 x - 5 12 = x c" + }, + { + "Answer": 20, + "Options": "a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 20", + "Correct": "e", + "Explanation": "the question basically asks how many minutes it takes for a population to increase by factor 1000 ( 1000000 / 1000 = 1000 ) . now you know that every two minutes the population doubles , i . e . is multiplied by 2 . so the equation becomes : 2 ^ x > = 1000 , where x represents the number of times the population doubles . a lot of people remember that 2 ^ 10 = 1024 . i . e . the population has to double 10 times . since it takes the population 2 minutes to double once it takes 10 * 2 minutes = 20 minutes to double nine times . thus , solution e = 20 is correct ." + }, + { + "Answer": 20, + "Options": "a ) 20 km , b ) 56 km , c ) 60 km , d ) 70 km , e ) 80 km", + "Correct": "a", + "Explanation": "\"let the actual distance travelled be x km . x / 10 = ( x + 20 ) / 14 20 x = 10 x + 200 10 x = 200 x = 20 km . answer : a\"" + }, + { + "Answer": 21, + "Options": "a ) a ) 12 , b ) b ) 15 , c ) c ) 16 , d ) d ) 17 , e ) e ) 21", + "Correct": "e", + "Explanation": "\"d = ( d - r ) / q = ( 190 - 1 ) / 9 = 189 / 9 = 21 e )\"" + }, + { + "Answer": 99, + "Options": "a ) 57 , b ) 67 , c ) 77 , d ) 99 , e ) 97", + "Correct": "d", + "Explanation": "\"money collected = ( 98.01 x 100 ) paise = 9801 paise . number of members = square root of 9801 = 99 . answer : option d\"" + }, + { + "Answer": 9, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", + "Correct": "c", + "Explanation": "\"101 * n ^ 2 < = 10000 n ^ 2 < = 10000 / 101 which will be less than 100 since 10000 / 100 = 100 which is the square of 9 next closest value of n where n ^ 2 < = 100 is 9 ans c\"" + }, + { + "Answer": 192, + "Options": "a ) 190 , b ) 191 , c ) 192 , d ) 193 , e ) 194", + "Correct": "c", + "Explanation": "divide as ( 1 - 100 ) ( 100 - 200 ) . . . . ( 900 - 1000 ) total 192 answer : c" + }, + { + "Answer": 9, + "Options": "a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 9", + "Correct": "e", + "Explanation": "\"the bookman had 10 hardback ad 55 - 10 = 45 paperback copies ; 14 copies were sold , hence 55 - 14 = 41 copies were left . let # of paperback copies left be p then 10 p + 20 ( 41 - p ) = 460 - - > 10 p = 360 - - > p = 36 # of paperback copies sold is 45 - 36 = 9 answer : e\"" + }, + { + "Answer": 8, + "Options": "a ) 8 , b ) 20 , c ) 28 , d ) 14 , e ) 19", + "Correct": "a", + "Explanation": "\"number of statues = all the paint \u00f7 amount used per statue = 1 / 2 \u00f7 1 / 16 = 8 / 16 * 16 / 1 = 8 / 1 = 8 answer is a .\"" + }, + { + "Answer": 4, + "Options": "a ) 2 % , b ) 3 % , c ) 4 % , d ) 5 % , e ) 6 %", + "Correct": "c", + "Explanation": "\"let x be the amount of gasoline the driver buys originally . let y be the new amount of gasoline the driver should buy . let p be the original price per liter . ( 1.25 * p ) y = 1.2 ( p * x ) y = ( 1.2 / 1.25 ) x = 0.96 x which is a reduction of 4 % . the answer is c .\"" + }, + { + "Answer": 2249.9999999999995, + "Options": "a ) 360 , b ) 2250 , c ) 540 , d ) 640 , e ) 720", + "Correct": "b", + "Explanation": "too many words and redundant info there . ( i ) 1 / 3 of the pieces of art are displayed , hence 2 / 3 of the pieces of art are not displayed . ( ii ) 1 / 6 of the pieces on display are sculptures , hence 5 / 6 of the pieces on display are paintings . ( iii ) 1 / 3 of the pieces not on display are paintings , hence 2 / 3 of the pieces not on display are sculptures . 1000 sculptures are not on display , so according to ( iii ) 2 / 3 * { not on display } = 1000 - - > { not on display } = 1500 . according to ( i ) 2 / 3 * { total } = 1500 - - > { total } = 2250 . answer : b ." + }, + { + "Answer": 50, + "Options": "a ) 50 % , b ) 12 % , c ) 8 % , d ) 6 % , e ) 5 %", + "Correct": "a", + "Explanation": "let the annual bonus be x . a corporation double its annual bonus . so new bonus = 2 x . increase = 2 x - x = x the increase is what percent of the employees \u2019 new bonus = ( x / 2 x ) * 100 = 50 % hence a ." + }, + { + "Answer": 4, + "Options": "a ) 18 , b ) 12 , c ) 69 , d ) 32 , e ) 4", + "Correct": "e", + "Explanation": "explanation : unit digit in 3 ^ 4 = 1 unit digit in ( 3 ^ 4 ) 16 = 1 unit digit in 3 ^ 65 = unit digit in [ ( 3 ^ 4 ) 16 x 3 ] = ( 1 x 3 ) = 3 unit digit in 6 ^ 59 = 6 unit digit in 7 ^ 4 unit digit in ( 7 ^ 4 ) 17 is 1 . unit digit in 7 ^ 71 = unit digit in [ ( 7 ^ 4 ) 17 x 73 ] = ( 1 x 3 ) = 3 required digit = unit digit in ( 3 x 6 x 3 ) = 4 e" + }, + { + "Answer": 5, + "Options": "a ) 91 , b ) 10 , c ) 6 , d ) 5 , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : required number of students = h . c . f of 1345 and 775 = 5 . answer : d\"" + }, + { + "Answer": 0.3333333333333333, + "Options": "a ) 4 / 12 , b ) 4 / 17 , c ) 4 / 15 , d ) 4 / 11 , e ) 4 / 03", + "Correct": "a", + "Explanation": "\"explanation : let the positive number be x . then , 2 / 3 x = 16 / 216 * 1 / x x 2 = 16 / 216 * 3 / 2 = 16 / 144 x = \u221a 16 / 144 = 4 / 12 . answer : a\"" + }, + { + "Answer": 1620, + "Options": "a ) 1235 , b ) 1346 , c ) 1378 , d ) 1635 , e ) 1489", + "Correct": "d", + "Explanation": "\"let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 15 5 x = 1350 x = 270 large number = 270 + 1365 = 1635 d\"" + }, + { + "Answer": 991, + "Options": "a ) 901 , b ) 989 , c ) 990 , d ) 991 , e ) 1,001", + "Correct": "d", + "Explanation": "james = ( 0.5 / 100 ) * 2000 = 10 votes to win = ( 50 / 100 ) * total votes + 1 = ( 50 / 100 ) * 2000 + 1 = 1001 remaining voted needed to win election = 1001 - 10 = 991 answer : option d" + }, + { + "Answer": 2, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "b", + "Explanation": "\"on dividing 3832 by 5 , we get remainder = 2 . required number be subtracted = 2 answer : b\"" + }, + { + "Answer": 180, + "Options": "a ) s . 280 , b ) s . 180 , c ) s . 380 , d ) s . 50 , e ) s . 90", + "Correct": "b", + "Explanation": "a profit of rs . 900 is divided between x and y in the ratio of 1 / 2 : 1 / 3 or 3 : 2 . so profits are 540 and 360 . difference in profit share = 540 - 360 = 180 answer : b" + }, + { + "Answer": 10, + "Options": "a ) 7 , b ) 9 , c ) 8 , d ) 11 , e ) 10", + "Correct": "e", + "Explanation": "\"explanation : let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 27 \u21d2 5 x = 25 \u21d2 x = 5 . hence , b ' s age = 2 x = 10 years . answer : e\"" + }, + { + "Answer": 540, + "Options": "a ) 540 , b ) 520 , c ) 140 , d ) 560 , e ) 240", + "Correct": "a", + "Explanation": "3 + 5 + 8 = 16 2880 / 16 = 180 so y ' s share = 3 * 180 = 540 answer : a" + }, + { + "Answer": 54, + "Options": "a ) 42 , b ) 46 , c ) 50 , d ) 54 , e ) 58", + "Correct": "d", + "Explanation": "\"p - 3 = 3 ( k - 3 ) and so p = 3 k - 6 p + 9 = 2 ( k + 9 ) ( 3 k - 6 ) + 9 = 2 k + 18 k = 15 p = 39 p + k = 54 the answer is d .\"" + }, + { + "Answer": 15, + "Options": "a ) 7 , b ) 8 , c ) 14 , d ) 15 , e ) 20", + "Correct": "d", + "Explanation": "is there other way than just listing ? 25 34 43 52 59 61 68 70 77 86 95 106 115 124 133 15 ways . . d" + }, + { + "Answer": 48.68076923076923, + "Options": "a ) 48.68077 , b ) 42.25983 , c ) 50 , d ) 51.25388 , e ) 52.25", + "Correct": "a", + "Explanation": "\"explanation : average weight of 18 boys = 50.25 total weight of 18 boys = 50.25 \u00d7 18 average weight of remaining 8 boys = 45.15 total weight of remaining 8 boys = 45.15 \u00d7 8 total weight of all boys in the class = ( 50.25 \u00d7 18 ) + ( 45.15 \u00d7 8 ) total boys = 18 + 8 = 26 average weight of all the boys = ( 50.25 \u00d7 18 ) + ( 45.15 \u00d7 8 ) / 26 = 48.68077 answer : option a\"" + }, + { + "Answer": 0.375, + "Options": "a ) 1 / 8 , b ) 1 / 4 , c ) 1 / 2 , d ) 3 / 8 , e ) 5 / 8", + "Correct": "d", + "Explanation": "one possible case is : girl - boy - boy the probability of this is 1 / 2 * 1 / 2 * 1 / 2 = 1 / 8 there are 3 c 2 = 3 such cases so we should multiply by 3 . p ( one girl and two boys ) = 3 / 8 the answer is d ." + }, + { + "Answer": 7.4, + "Options": "a ) 6.8 , b ) 7.4 , c ) 7.7 , d ) 8.2 , e ) 8.6", + "Correct": "b", + "Explanation": "\"let x be the length of the size 8 shoe . then 0.3 x = 9 / 5 x = 90 / 15 = 6 inches the size 15 shoe has a length of 6 + 7 / 5 = 7.4 inches the answer is b .\"" + }, + { + "Answer": 59, + "Options": "a ) 55 , b ) 56 , c ) 57 , d ) 58 , e ) 59", + "Correct": "e", + "Explanation": "\"20 x + 46 = 21 ( x \u2013 5 ) x = 59 answer : e\"" + }, + { + "Answer": 8, + "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12", + "Correct": "a", + "Explanation": "\"let x be the number . always replace ` ` is ' ' with an equal sign ( 1 / 2 ) x + 7 = 11 ( 1 / 2 ) x = 11 - 7 ( 1 / 2 ) x = 4 x = 8 correct answer is a\"" + }, + { + "Answer": 3.5000000000000004, + "Options": "a ) 3 , b ) 4.5 , c ) 4 , d ) 3.5 , e ) 5", + "Correct": "d", + "Explanation": "\"assume she has $ 200 to spend . tax clothing = 25 % = $ 50 = $ 5 food = 25 % = $ 50 = $ 0.00 items = 50 % = $ 100 = $ 2.00 total tax = $ 20.00 % of total amount = 7 / 200 * 100 = 3.5 % answer d\"" + }, + { + "Answer": 225, + "Options": "a ) 225 , b ) 425 , c ) 520 , d ) 600 , e ) 700", + "Correct": "a", + "Explanation": "required number = ( 75 / 2 ) / ( 1 / 6 ) = ( 75 / 2 x 6 / 1 ) = 225 . answer : a" + }, + { + "Answer": 440.00000000000006, + "Options": "a ) rs . 400 , b ) rs . 440 , c ) rs . 150 , d ) rs . 460 , e ) rs . 520", + "Correct": "b", + "Explanation": "soln : - 460 / 115 ) 110 = 385 in this case long division does not take much time . ( 4 / 1 ) 110 = rs . 440 answer : b" + }, + { + "Answer": 8, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 12", + "Correct": "b", + "Explanation": "let the number be xy . given xy \u2013 yx = 36 . this means the number is greater is than the number got on reversing the digits . this shows that the ten \u2019 s digit x > unit digit y . also given ratio between digits is 1 : 2 = > x = 2 y ( 10 x + y ) \u2013 ( 10 y + x ) = 36 = > x \u2013 y = 4 = > 2 y \u2013 y = 4 . hence , ( x + y ) \u2013 ( x \u2013 y ) = 3 y \u2013 y = 2 y = 8 b" + }, + { + "Answer": 120, + "Options": "a ) \u2212 120 , b ) \u2212 100 , c ) 100 , d ) 135 , e ) it can not be determined from the information given", + "Correct": "a", + "Explanation": "\"question : a - c = ? ( a + b ) / 2 = 100 = = = > a + b = 200 ( b + c ) / 2 = 160 = = = > b + c = 320 ( a + b ) - ( b + c ) = 200 - 320 = = = > a + b - b - c = - 120 = = = > a - c = - 120 answer : a\"" + }, + { + "Answer": 19.99999999999999, + "Options": "a ) 3 / 80 , b ) 3 / 5 , c ) 20 , d ) 5 / 3 , e ) 80 / 3", + "Correct": "c", + "Explanation": "\"20 / 100 = 1 / 5 n = 2 ^ 1 / 5 n ^ b = 2 ^ 4 ( 2 ^ 1 / 5 ) ^ b = 2 ^ 4 b = 20 answer : c\"" + }, + { + "Answer": 20, + "Options": "a ) 18 , b ) 20 , c ) 24 , d ) 30 , e ) 32", + "Correct": "b", + "Explanation": "\"solution average = ( 10 + 15 + 20 + 25 + 30 / 5 ) = 100 / 2 = 20 answer b\"" + }, + { + "Answer": 25, + "Options": "a ) $ 25 , b ) $ 26 , c ) $ 27 , d ) $ 28 , e ) $ 30", + "Correct": "a", + "Explanation": "\"formula for vol of a cyl is pi * r ^ 2 * h so vy = 125 * vy y when half filled will cost 25 times x so ans is a\"" + }, + { + "Answer": 3.75, + "Options": "a ) $ 0.00 , b ) $ 1.00 , c ) $ 3.75 , d ) $ 5.00 , e ) $ 6.80", + "Correct": "c", + "Explanation": "\"0.85 * { original price } = $ 51 - - > { original price } = $ 60 . { final price } = $ 51 * 1.25 = $ 63.75 . the difference = $ 63.75 - 60 $ = $ 3.75 . answer : c .\"" + }, + { + "Answer": 2991, + "Options": "a ) 1991 , b ) 2991 , c ) 3991 , d ) 4521 , e ) 5991", + "Correct": "b", + "Explanation": "\"total sale for 5 months = rs . ( 4435 + 4927 + 4855 + 5230 + 4562 ) = rs . 24009 . required sale = rs . [ ( 4500 x 6 ) - 24009 ] = rs . ( 27000 - 24009 ) = rs . 2991 answer : option b\"" + }, + { + "Answer": 11988, + "Options": "a ) 11982 , b ) 11984 , c ) 11985 , d ) 11988 , e ) 11986", + "Correct": "d", + "Explanation": "n = 3 * 3 * 3 = 27 = ( 555 + 333 ) / 2 = 444 sum = number of integers x average value n * = 27 * 444 = 11988 answer = d" + }, + { + "Answer": 157, + "Options": "a ) 157 , b ) 168 , c ) 189 , d ) 190 , e ) 200", + "Correct": "a", + "Explanation": "\"solution average of 7 people after the last one enters = 151 . \u00e2 \u02c6 \u00b4 required weight = ( 7 x 151 ) - ( 6 x 150 ) = 1057 - 900 = 157 . answer a\"" + }, + { + "Answer": 1200, + "Options": "a ) 800 , b ) 900 , c ) 1000 , d ) 1100 , e ) 1200", + "Correct": "e", + "Explanation": "\"0.2 x = 4 ( 860 - 800 ) 0.2 x = 240 x = 1200 answer e\"" + }, + { + "Answer": 120, + "Options": "a ) 55 , b ) 65 , c ) 119 , d ) 109 , e ) 115", + "Correct": "c", + "Explanation": "\"a + b + c + d = 200 a + b = 80 c + d = 120 greatest possible = 119 ( just less than 1 ) answer = c\"" + }, + { + "Answer": 510, + "Options": "a ) 400 , b ) 420 , c ) 430 , d ) 450 , e ) 510", + "Correct": "e", + "Explanation": "\"let no . of non - officers be x 15 * 460 + x * 110 = ( x + 15 ) 120 x = 510 e\"" + }, + { + "Answer": 85, + "Options": "a ) 17 , b ) 98 , c ) 88 , d ) 85 , e ) 83", + "Correct": "d", + "Explanation": "let the number of wickets taken till the last match be x . then , ( 12.4 x + 26 ) / ( x + 5 ) = 12 = 12.4 x + 26 = 12 x + 60 = 0.4 x = 34 = x = 340 / 4 = 85 . answer : d" + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 10 , c ) 15 , d ) 25 , e ) 35", + "Correct": "a", + "Explanation": "\"total applicants = 40 political science = 15 and non political science = 40 - 15 = 25 gpa > 3.0 = 20 and gpa < = 3.0 = 20 10 non political science students had gpa < = 3.0 - - > 15 non political science students had gpa > 3.0 gpa > 3.0 in political science = total - ( gpa > 3.0 in non political science ) t = 20 - 15 = 5 answer : a\"" + }, + { + "Answer": 1, + "Options": "a ) 36 / 25 , b ) 10 / 12 , c ) 1 , d ) 1 / 5 , e ) 25 / 36", + "Correct": "c", + "Explanation": "\"a nice fast approach is the first find a pair of numbers that satisfy the given equation : 5 a = 6 b here ' s one pair : a = 6 and b = 5 what is the ratio of a / 6 to b / 5 ? in other words , what is the value of ( a / 6 ) / ( b / 5 ) ? plug in values to get : ( a / 6 ) / ( b / 5 ) = ( 6 / 6 ) / ( 5 / 5 ) = 1 / 1 = 1 c\"" + }, + { + "Answer": 970, + "Options": "a ) 970.3 liters , b ) 1000.45 liters , c ) 879.65 liters , d ) 1020.56 liters , e ) 910.95 liters", + "Correct": "a", + "Explanation": "amount of milk left after 3 operations = 1000 ( 1 - 10 / 1000 ) ^ 3 = 1000 * 99 / 100 * 99 / 100 * 99 / 100 = 970.3 liters answer is a" + }, + { + "Answer": 3600.000000000001, + "Options": "a ) rs . 2400 , b ) rs . 3000 , c ) rs . 3600 , d ) rs . 4800 , e ) none of these", + "Correct": "c", + "Explanation": "solution a : b : c = ( 16000 x 3 + 11000 x 9 ) : ( 12000 x 3 + 17000 x 9 ) : ( 21000 x 6 ) = 147 : 180 : 126 = 7 : 9 : 6 . \u2234 difference of b and c \u2019 s shares = rs . ( 26400 x 9 / 22 - 26400 x 6 / 22 ) = rs . 3600 . answer c" + }, + { + "Answer": 8, + "Options": "a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16", + "Correct": "a", + "Explanation": "\"let dan ' s present age be x . x + 16 = 6 ( x - 4 ) 5 x = 40 x = 8 the answer is a .\"" + }, + { + "Answer": 3, + "Options": "a ) 22 , b ) 11 , c ) 9 , d ) 6 , e ) 3", + "Correct": "e", + "Explanation": "18 ^ a ) * 9 ^ ( 3 a \u2013 1 ) = ( 2 ^ 3 ) ( 3 ^ b ) = 2 ^ a . 9 ^ a . 9 ^ ( 3 a \u2013 1 ) = ( 2 ^ 3 ) ( 3 ^ b ) just compare powers of 2 from both sides ( no need to calculate powers of 3 , 9 as value of b is not asked ) answer = 3 answer : e" + }, + { + "Answer": 80, + "Options": "a ) 70 , b ) 80 , c ) 85 , d ) 90 , e ) 95", + "Correct": "b", + "Explanation": "\"if on a test three people answered 90 % of the questions correctly and two people answered 80 % correctly , then the average for the group is not 85 % but rather 3 \u00d7 90 + 2 \u00d7 805 = 4305 = 86.3 \u00d7 90 + 2 \u00d7 805 = 4305 = 86 . here , 90 has a weight of 3 = > it occurs 3 times . whereas 80 has a weight of 2 = > it occurs 2 times . so the average is closer to 90 than to 80 as we have just calculated . b\"" + }, + { + "Answer": 78, + "Options": "a ) 78 , b ) 79 , c ) 85 , d ) 87 , e ) 89", + "Correct": "a", + "Explanation": "\"explanation : average = total runs / no . of innings = 34 so , total = average x no . of innings = 34 x 10 = 340 . now increase in avg = 4 runs . so , new avg = 34 + 4 = 38 runs total runs = new avg x new no . of innings = 38 x 11 = 418 runs made in the 11 th inning = 418 - 340 = 78 answer : a\"" + }, + { + "Answer": 18, + "Options": "a ) 22 , b ) 18 , c ) 99 , d ) 77 , e ) 24", + "Correct": "b", + "Explanation": "a : b = 2 : 3 b : c = 2 : 5 a : b : c = 4 : 6 : 15 6 / 25 * 75 = 18 answer : b" + }, + { + "Answer": 22, + "Options": "a ) 15 , b ) 25 , c ) 35 , d ) 22 , e ) 55", + "Correct": "d", + "Explanation": "\"a 1 = 120 / 3 = 40 a 2 = a 1 - 6 = 34 sum of second list = 34 * 3 = 102 therefore the number = 102 - 80 = 22 answer : d\"" + }, + { + "Answer": 174, + "Options": "a ) 174 cm , b ) 173 cm , c ) 172 cm , d ) 171 cm , e ) 170 cm", + "Correct": "a", + "Explanation": "\"the total height was 20 cm too much . the average height should be reduced by 20 cm / 20 = 1 cm the answer is a .\"" + }, + { + "Answer": 2000, + "Options": "a ) 2000 , b ) 8076 , c ) 9691.2 , d ) 4845.6 , e ) none of these", + "Correct": "a", + "Explanation": "\"\u2235 amount , he have spent in 1 month on clothes transport = amount spent on saving per month \u2235 amount , spent on clothes and transport = 24000 \u2044 12 = 2000 answer a\"" + }, + { + "Answer": 6800, + "Options": "a ) rs . 9800 , b ) rs . 3800 , c ) rs . 9800 , d ) rs . 6800 , e ) rs . 6880", + "Correct": "d", + "Explanation": "\"cost of the camel = p 10 camels = 24 horses 16 horses = 4 oxen 6 oxen = 4 elephants 10 elephants = rs . 170000 p = rs . [ ( 24 * 4 * 4 * 170000 ) / ( 10 * 16 * 6 * 10 ) ] p = rs . ( 65280000 / 9600 ) = > p = rs . 6800 answer : d\"" + }, + { + "Answer": 81.1, + "Options": "a ) 9 , b ) 20 , c ) 55 , d ) 70 , e ) 81", + "Correct": "e", + "Explanation": "\"here ' s an approach that ' s based on number properties and a bit ofbrute forcemath : we ' re told that k and n are both integers . since k / n = 81.2 , we can say that k = 81.2 ( n ) n has tomultiply outthe . 2 so that k becomes an integer . with the answers that we have to work with , n has to be a multiple of 5 . eliminate a and e . with the remaining answers , we can test the answers and find the one that fits the rest of the info ( k / n = 81.2 and k / n has a remainder of 11 ) answer b : if n = 20 , then k = 1624 ; 1624 / 20 has a remainder of 4 not a match answer c : if n = 55 , then k = 4466 ; 4466 / 55 has a remainder of 11 match . final answer : e\"" + }, + { + "Answer": 56, + "Options": "a ) 50 , b ) 40 , c ) 56 , d ) 16 , e ) 20", + "Correct": "c", + "Explanation": "\"let the actual distance traveled be x km . then , x / 8 = ( x + 14 ) / 10 2 x - 112 = > x = 56 km . answer : c\"" + }, + { + "Answer": 56.99999999999999, + "Options": "a ) 40 % , b ) 45 % , c ) 57 % , d ) 58 % , e ) 60 %", + "Correct": "c", + "Explanation": "tot no of votes = ( 1136 + 7636 + 11628 ) = 20400 req = > ( 11628 / 20400 * 100 ) = > 57 % answer c" + }, + { + "Answer": 28000, + "Options": "a ) 23477 , b ) 28000 , c ) 28877 , d ) 1987 , e ) 1771", + "Correct": "b", + "Explanation": "\"explanation : suppose b invested rs . x for y months . then , a invested rs . 3 x for 2 y months . so , a : b = ( 3 x * 2 y ) : ( x * y ) = 6 xy : xy = 6 : 1 . b ' s profit : total profit = 1 : 7 . let the total profit be rs . x then , 1 / 7 = 4000 / x or x = 28000 . answer : b ) 28000\"" + }, + { + "Answer": 36, + "Options": "a ) 15 min , b ) 18 min , c ) 16 min , d ) 20 min , e ) 36 min", + "Correct": "e", + "Explanation": "in 1 hr , the bus covers 100 km without stoppages and 40 km with stoppages . stoppage time = time take to travel ( 100 - 40 ) km i . e 60 km at 100 km / hr . stoppage time = 60 / 100 hrs = 36 min answer : e" + }, + { + "Answer": 0.041666666666666664, + "Options": "a ) 2 / 5 , b ) 1 / 4 , c ) 1 / 2 , d ) 1 / 24 , e ) 1 / 25", + "Correct": "d", + "Explanation": "ped = 3 / 5 = 12 / 20 sur = 1 / 4 = 4 / 20 gp = 1 - ( 12 / 20 + 4 / 20 ) = 1 - 16 / 20 = 4 / 20 hsur = ( 1 / 4 ) ( 4 / 20 ) = 1 / 20 if gp doubled = > ( 2 ) ( 4 ) = 8 ; then , total = 12 + 4 + 8 = 24 , and 1 is hsur = > proportion = 1 / 24 . answer : d" + }, + { + "Answer": 80, + "Options": "a ) 12 % , b ) 18 % , c ) 80 % , d ) 20 % , e ) 15 %", + "Correct": "c", + "Explanation": "let the annual bonus be x . a corporation triples its annual bonus . so new bonus = 5 x . increase = 5 x - x = 4 x the increase is what percent of the employees \u2019 new bonus = ( 4 x / 5 x ) * 100 = 80 % hence c ." + }, + { + "Answer": 4, + "Options": "a ) 4 years , b ) 8 years , c ) 10 years , d ) none of these , e ) can not be determined", + "Correct": "a", + "Explanation": "\"explanation let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 50 5 x = 20 x = 4 . age of the youngest child = x = 4 years . answer a\"" + }, + { + "Answer": 705, + "Options": "a ) 705 , b ) 655 , c ) 656 , d ) 657 , e ) 658", + "Correct": "a", + "Explanation": "total cost 940 940 * 25 / 100 = 235 so the cut in amount is 235 the less amount to be spend is 940 - 235 = 705 answer : a" + }, + { + "Answer": 40.5, + "Options": "a ) 40.46 , b ) 36.1 , c ) 36.5 , d ) 39.1 , e ) none", + "Correct": "a", + "Explanation": "\"sol . therefore correct sum = ( 40 \u00d7 50 + 48 \u2013 23 ) = 2023 . therefore correct mean = 2023 / 50 = 40.46 . answer a\"" + }, + { + "Answer": 175, + "Options": "a ) 174 , b ) 150 , c ) 180 , d ) 175 , e ) 190", + "Correct": "a", + "Explanation": "each set has 12 even and 13 odd numbered questions leading to total 96 even and 104 odd questions . 96 + 3 / 4 \u00e2 \u02c6 \u2014 104 = 96 + 78 = 17496 + 3 / 4 \u00e2 \u02c6 \u2014 104 = 96 + 78 = 174 answer : a" + }, + { + "Answer": 306, + "Options": "a ) $ 306 , b ) $ 275 , c ) $ 510 , d ) $ 1,250 , e ) $ 2,550", + "Correct": "a", + "Explanation": "\"total no . of boxes = 3060000 / ( 20 \u00d7 20 \u00d7 15 ) = 510 total cost = 510 \u00d7 $ 0.6 = $ 306 answer a\"" + }, + { + "Answer": 10, + "Options": "a ) 3 years , b ) 4 years , c ) 6 years , d ) 7 years , e ) 10 years", + "Correct": "e", + "Explanation": "\"let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 80 5 x = 50 x = 10 . age of the youngest child = x = 10 years . e )\"" + }, + { + "Answer": 220010, + "Options": "a ) 220010 , b ) 145778 , c ) 220110 , d ) 235467 , e ) 220001", + "Correct": "a", + "Explanation": "\"( 555 + 445 ) * 2 * 110 + 10 = 220000 + 10 = 220010 a\"" + }, + { + "Answer": 500, + "Options": "a ) $ 200 , b ) $ 400 , c ) $ 600 , d ) $ 800 , e ) $ 500", + "Correct": "e", + "Explanation": "suppose total money spent = x not spend ( money he still has ) = x - 600 x + x - 600 = 1600 x = 1100 money not spend = 1100 - 600 = 500 answer : e" + }, + { + "Answer": 10, + "Options": "a ) 5 : 2 , b ) 5 : 1 , c ) 4 : 3 , d ) 4 : 1 , e ) 10 : 1", + "Correct": "e", + "Explanation": "we ' re given a few facts to work with : 1 ) the average height of the females is 170 cm 2 ) the average height of the males is 181 cm 3 ) the average of the group is 180 cm we ' re asked for the ratio of men to women . w = number of women m = number of men ( 170 w + 181 m ) / ( w + m ) = 180 170 w + 181 m = 180 w + 180 m 1 m = 10 w m / w = 10 / 1 the ratio of men to women is 10 to 1 . e" + }, + { + "Answer": 25, + "Options": "a ) 2.5 % , b ) 10 % , c ) 5 % , d ) 15 % , e ) 25 %", + "Correct": "e", + "Explanation": "\"50 % of ( x - y ) = 30 % of ( x + y ) ( 50 / 100 ) ( x - y ) = ( 30 / 100 ) ( x + y ) 5 ( x - y ) = 3 ( x + y ) 2 x = 8 y x = 4 y therefore required percentage = ( ( y / x ) x 100 ) % = ( ( y / 4 y ) x 100 ) = 25 % answer is e .\"" + }, + { + "Answer": 220060, + "Options": "a ) 145646 , b ) 236578 , c ) 645353 , d ) 456546 , e ) 220060", + "Correct": "e", + "Explanation": "\"( 555 + 445 ) * 2 * 110 + 60 = 220000 + 60 = 220060 e\"" + }, + { + "Answer": 0.0625, + "Options": "a ) 2 / 7 , b ) 3 / 7 , c ) 1 / 16 , d ) 1 / 14 , e ) 1 / 12", + "Correct": "c", + "Explanation": "\"because n ( n + 1 ) is always an even product of even * odd or odd * even factors , there is a probability of 1 that that it will be divisible by 2 , and , thus , a probability of 1 / 2 that it will be divisible by 4 and , thus , a probability of 1 / 4 that it will be divisible by 8 and , thus , a probability of 1 / 8 that it will be divisible by 16 and , thus , a probability of 1 / 16 that it will be divisible by 32 1 * 1 / 16 = 1 / 16 answer : c\"" + }, + { + "Answer": 20, + "Options": "a ) 8 , b ) 12 , c ) 16 , d ) 20 , e ) 24", + "Correct": "d", + "Explanation": "we ' re asked how old jim is now . we ' re given three facts to work with : 1 ) today , jim is twice as old as fred 2 ) today , sam is 4 years younger than fred 3 ) four years ago , jim was 8 times as old as sam . let ' s test answer d : 20 if . . . . jim is currently 20 years old . . . . fred is 10 years old sam is 6 years old 4 years ago , jim was 16 and sam was 2 , so jim was 8 times sam ' s age . this is an exact match for what we were told , so this must be the answer . d" + }, + { + "Answer": 10.000000000000009, + "Options": "a ) 5 , b ) 6 , c ) 8 , d ) 9 , e ) 10", + "Correct": "e", + "Explanation": "a has 10 yellows 20 reds total = 30 so b has 1.2 x 20 = 24 reds 0.9 x 10 = 9 yellows total = 33 difference = 3 / 30 = 10 % answer : e" + }, + { + "Answer": 18, + "Options": "a ) 11 , b ) 18 , c ) 13 , d ) 23 , e ) none of these", + "Correct": "b", + "Explanation": "\"let that divisor be x since remainder is 12 or 16 it means divisor is greater than 16 . now 242 - 12 = 230 = kx ( k is an integer and 234 is divisble by x ) similarly 698 - 16 = 682 = lx ( l is an integer and 689 is divisible by x ) adding both 698 and 242 = ( 230 + 682 ) + 12 + 16 = x ( k + l ) + 28 when we divide this number by x then remainder will be equal to remainder of ( 28 divided by x ) = 10 hence x = 28 - 10 = 18 hence b\"" + }, + { + "Answer": 12800, + "Options": "a ) 12800 , b ) 13000 , c ) 11500 , d ) 12500 , e ) 12000", + "Correct": "a", + "Explanation": "b claims 2 / 7 of the profit a claims remaining 5 / 7 of the profit = > a : b = 5 / 7 : 2 / 7 = 5 : 2 let the money contributed by b = b then a : b = 16000 \u00d7 8 : b \u00d7 4 therefore , 16000 \u00d7 8 : b \u00d7 4 = 5 : 2 16000 \u00d7 8 \u00d7 2 = b \u00d7 4 \u00d7 5 16000 \u00d7 2 \u00d7 2 = b \u00d7 5 3200 \u00d7 2 \u00d7 2 = b b = 12800 answer is a ." + }, + { + "Answer": 200, + "Options": "a ) s . 150 , b ) s . 200 , c ) s . 250 , d ) s . 350 , e ) s . 400", + "Correct": "b", + "Explanation": "\"let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 440 but x = 120 % of y = 120 y / 100 = 12 y / 10 \u00e2 \u02c6 \u00b4 12 y / 10 + y = 440 \u00e2 \u2021 \u2019 y [ 12 / 10 + 1 ] = 440 \u00e2 \u2021 \u2019 22 y / 10 = 440 \u00e2 \u2021 \u2019 22 y = 4400 \u00e2 \u2021 \u2019 y = 4400 / 22 = 400 / 2 = rs . 200 b )\"" + }, + { + "Answer": 4, + "Options": "a ) 4 , b ) 12 , c ) 14 , d ) 16 , e ) 28", + "Correct": "a", + "Explanation": "\"equate the fat : 0.1 x + 0.25 * 8 = 0.2 ( x + 8 ) - - > x = 4 . answer : a .\"" + }, + { + "Answer": 6.97, + "Options": "a ) 6.6 kg , b ) 6.8 kg , c ) 6.7 kg , d ) 6.97 kg , e ) 7.8 kg", + "Correct": "d", + "Explanation": "\"820 * 8.5 6970.0 gm 6.97 kg answer : d\"" + }, + { + "Answer": 22, + "Options": "a ) 7 , b ) 33 , c ) 22 , d ) 17 , e ) 25", + "Correct": "c", + "Explanation": "16 + 6 = 22 . answer is c ." + }, + { + "Answer": 14, + "Options": "a ) 11 , b ) 12 , c ) 14 , d ) 19 , e ) 15", + "Correct": "c", + "Explanation": "\"- x 2 - ( k + 8 ) x - 8 = - ( x - 2 ) ( x - 4 ) : given - x 2 - ( k + 8 ) x - 8 = - x 2 + 6 x - 8 - ( k + 8 ) = 6 : two polynomials are equal if their corresponding coefficients are equal . k = - 14 : solve the above for k correct answer c\"" + }, + { + "Answer": 3, + "Options": "a ) b / 2 , b ) b , c ) 3 b / 2 , d ) 2 b , e ) 3 b", + "Correct": "e", + "Explanation": "lets do it by picking up numbers . let arthur carry 2 crumbs per trip , this means amy carries 3 crumbs per trip . also let arthur make 2 trips and so amy makes 4 trips . thus total crumbs carried by arthur ( b ) = 2 x 2 = 4 , total crumbs carried by amy = 3 x 4 = 12 . 12 is 3 times 4 , so e" + }, + { + "Answer": 26, + "Options": "a ) 30 , b ) 26 , c ) 11 , d ) 31 , e ) 32", + "Correct": "b", + "Explanation": "detailed solution let the total students be ( n + 1 ) let total badges be x let the average of \u2018 n \u2019 students be y the student who got 1 / 6 th of x = 5 y or y = x / 30 therefore \u2018 n \u2019 students got 1 / 30 th of total share each or n * x / 30 + 1 * x / 6 = x nx + 5 x = 30 x n + 5 = 30 or n = 25 total = n + 1 = 26 correct answer : b" + }, + { + "Answer": 14, + "Options": "a ) 14 , b ) 10 , c ) 9 , d ) 6 , e ) 5", + "Correct": "a", + "Explanation": "# of people times the # of hours : 4 * 7 = 28 - - > 4 lawyers do 28 worksin 7 hours . 3 * 14 / 3 = 14 - - > 3 assistants do 14 worksin 4 hours so , since the amount of work the assistants do is half the work the lawyers do , the time will be double , soans a" + }, + { + "Answer": 36, + "Options": "a ) 0 , b ) 16 , c ) 25 , d ) 36 , e ) 49", + "Correct": "d", + "Explanation": "from ( x + 6 ) ( y - 6 ) = 0 it follows that either x = - 6 or y = 6 . thus either x ^ 2 = 36 or y ^ 2 = 36 . now , if x ^ 2 = 36 , then the least value of y ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 36 + 0 = 36 . similarly if y ^ 2 = 36 , then the least value of x ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 0 + 36 = 36 . answer : d ." + }, + { + "Answer": 9, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", + "Correct": "c", + "Explanation": "let x be the larger number and y be the smaller number . x - y = 6 x + 2 ( y ) = 15 solve by substitution : y = x - 6 x + 2 ( x - 6 ) = 15 x + 2 x - 12 = 15 3 x = 27 x = 9 the larger number is 9 , so answer c is correct ." + }, + { + "Answer": 27.200000000000003, + "Options": "a ) 31 % . , b ) 71 % . , c ) 49 % . , d ) 27.2 % . , e ) 51 % .", + "Correct": "d", + "Explanation": "\"16 % of 2 litres = 0.32 litres 40 % of 6 litres = 2.4 litres therefore , total quantity of alcohol is 2.72 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 27.2 % answer : d\"" + }, + { + "Answer": 120, + "Options": "a ) 10 , b ) 45 , c ) 95 , d ) 120 , e ) none of these", + "Correct": "d", + "Explanation": "explanation : 3 prize among 10 students can be distributed in 10 c 3 ways = 120 ways . answer : d" + }, + { + "Answer": 71, + "Options": "a ) 69 % , b ) 71 % , c ) 73 % , d ) 75 % , e ) 77 %", + "Correct": "b", + "Explanation": "\"72 + 82 + x = 3 * 75 x = 71 the answer is b .\"" + }, + { + "Answer": 66, + "Options": "a ) 33 , b ) 77 , c ) 48 , d ) 66 , e ) 21", + "Correct": "d", + "Explanation": "\"speed on return trip = 120 % of 60 = 72 km / hr . average speed of trip = 60 + 72 / 2 = 132 / 2 = 66 km / hr answer : d\"" + }, + { + "Answer": 20.000000000000007, + "Options": "a ) 16 , b ) 18 , c ) 20 , d ) 22 , e ) 24", + "Correct": "c", + "Explanation": "\"let the number be x . ( 5 / 4 ) * x = ( 4 / 5 ) * x + 9 25 x = 16 x + 180 9 x = 180 x = 20 the answer is c .\"" + }, + { + "Answer": 192, + "Options": "a ) 176 , b ) 180 , c ) 184 , d ) 188 , e ) 192", + "Correct": "e", + "Explanation": "\"j + k = 284 and so k = 284 - j j - 8 = 2 k j - 8 = 2 ( 284 - j ) 3 j = 576 j = 192 the answer is e .\"" + }, + { + "Answer": 28, + "Options": "a ) 14 years , b ) 28 years , c ) 20 years , d ) 22 years , e ) none", + "Correct": "b", + "Explanation": "\"solution let the son ' s present age be x years . then , man ' s present age = ( x + 30 ) years . then \u00e2 \u20ac \u00b9 = \u00e2 \u20ac \u00ba ( x + 30 ) + 2 = 2 ( x + 2 ) \u00e2 \u20ac \u00b9 = \u00e2 \u20ac \u00ba x + 32 = 2 x + 4 x = 28 . answer b\"" + }, + { + "Answer": 7, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "e", + "Explanation": "as you see 5 ! till 10 ! each unit digit is zero . so 1 ! + 2 ! + 3 ! + 4 ! = 33 so unit digit 3 + 0 = 3 n = 3 n ^ n = 3 ^ 3 = 27 so last digit is 7 . answer : e" + }, + { + "Answer": 6.5, + "Options": "a ) 6.5 , b ) 6.7 , c ) 6.8 , d ) 6.85 , e ) 6.9", + "Correct": "a", + "Explanation": "\"old set s - total is avg * no of elements = 6.2 * 10 = 62 if one number is increased by 3 then total increased to 62 + 3 = 65 new avg - 65 / 10 = 6.5 . hence answer is a .\"" + }, + { + "Answer": 18, + "Options": "a ) a ) 8 , b ) b ) 10 , c ) c ) 12 , d ) d ) 14 , e ) e ) 18", + "Correct": "e", + "Explanation": "first , let ' s graph the lines y = 2 and x = 2 at this point , we need to find the points where the line y = 10 - x intersects the other two lines . for the vertical line , we know that x = 2 , so we ' ll plug x = 2 into the equation y = 10 - x to get y = 10 - 2 = 8 perfect , when x = 2 , y = 8 , so one point of intersection is ( 28 ) for the horizontal line , we know that y = 2 , so we ' ll plug y = 2 into the equation y = 10 - x to get 2 = 10 - x . solve to get : x = 8 so , when y = 2 , x = 8 , so one point of intersection is ( 82 ) now add these points to our graph and sketch the line y = 10 - x at this point , we can see that we have the following triangle . the base has length 6 and the height is 6 area = ( 1 / 2 ) ( base ) ( height ) = ( 1 / 2 ) ( 6 ) ( 6 ) = 18 answer : e" + }, + { + "Answer": 4, + "Options": "a ) 1 , b ) 2 , c ) 4 , d ) 6 , e ) 8", + "Correct": "c", + "Explanation": "\"this one took me bout 3 1 / 2 min . just testin numbers and what not . first notice that n is positive . save time by noticing thati worked out one solution where n = 0 only to find that thats not an option : p . 1 - 7 stands for ^ 1 thru 7 1 : 7 * 1 = 7 2 : 7 * 7 = 9 3 : 7 * 9 = 3 4 : 7 * 3 = 1 5 : 7 * 1 = 7 6 : 7 * 7 = 9 7 : 7 * 9 = 3 pattern repeats every @ 5 . notice every ^ 4 or multiple of 4 is always going to be 1 . this is just for future notice for similar problems . so 7 ^ 4 n + 3 - - - > if n = 1 then its ( ( 7 ^ 7 ) * 6 ) ) / 10 which can say is going to be 3 * 8 - - > 18 / 10 - - > r = 8 now from here if id double check just to make sure . 7 ^ 4 ( 2 ) + 3 * 6 ^ 2 - - - > 7 ^ 11 * 36 or we can just say again 7 ^ 11 * 6 ( b / c we are only interested in the units digit ) . since ^ 12 is going to be 1 that means ^ 11 is going to be 3 ( as taken from our pattern ) so again 3 * 6 = 18 / 10 - - - > r = 8 . c or j in this problem .\"" + }, + { + "Answer": 0.0625, + "Options": "a ) 1 / 8 , b ) 1 / 4 , c ) 1 / 16 , d ) 1 / 32 , e ) 1 / 2", + "Correct": "c", + "Explanation": "must be twice on heads and twice on tails 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 16 answer : c" + }, + { + "Answer": 80, + "Options": "a ) 124 % , b ) 120 % , c ) 96 % , d ) 80 % , e ) 64 %", + "Correct": "d", + "Explanation": "\"juan ' s income = 100 ( assume ) ; tim ' s income = 50 ( 50 percent less than juan ' s income ) ; mary ' s income = 80 ( 60 percent more than tim ' s income ) . thus , mary ' s income ( 80 ) is 80 % of juan ' s income ( 100 ) . answer : d .\"" + }, + { + "Answer": 24, + "Options": "a ) 18 metres , b ) 16 metres , c ) 38 metres , d ) 42 metres , e ) 24 metres", + "Correct": "e", + "Explanation": "a little reflection will show that chalk marks will touch the ground together for the first time after the wheels have passed over a distance which is the lcm of 2 2 / 5 metres and 3 3 / 7 metres . lcm of 12 / 5 metres and 24 / 7 metres = 24 metres . answer is e" + }, + { + "Answer": 9.090909090909093, + "Options": "a ) 9.1 litres , b ) 10 litres , c ) 8 litres , d ) 12 litres , e ) 6 litres", + "Correct": "a", + "Explanation": "working formula . . . initial concentration * initial volume = final concentration * final volume . let x is the part removed from 100 lts . 30.25 % ( 1 - x / 100 ) ^ 2 = 25 % * 100 % ( 1 - x / 100 ) ^ 2 = 25 / 30.25 - - - - - - > ( 1 - x / 100 ) ^ 2 = ( 5 / 5.5 ) ^ 2 100 - x = 500 / 5.5 x = 9.1 . . . ans a" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "c", + "Explanation": "\"x = ( y / 4 ) - ( 2 / 5 ) , and so y = 4 x + 8 / 5 . the slope is 4 . ( n + 12 - n ) / ( m + p - m ) = 3 p = 3 the answer is c .\"" + }, + { + "Answer": 60, + "Options": "a ) 48 , b ) 50 , c ) 60 , d ) 75 , e ) 100", + "Correct": "c", + "Explanation": "this can be solve in two steps and without any complex calculation . given : equation of line a as y = ( 4 / 3 ) x - 100 . so the line intercept the axes at ( 0 , - 100 ) and ( 750 ) . this can be considered a right angle triangle with right angle at ( 00 ) . so base = 100 , height = 75 and hypotenuse = 125 ( by pythagoras triplet ) so a perpendicular from the ( 00 ) to hypotenuse will be the answer . area of triangle = 0.5 * 100 * 75 = 0.5 * 125 * x = > x = 60 ; so answer is 60 = c" + }, + { + "Answer": 13, + "Options": "a ) 8 , b ) 13 , c ) 15 , d ) 18 , e ) 30", + "Correct": "b", + "Explanation": "\"within one standard deviation of the average age means 31 + / - 7 25 - - 31 - - 37 number of dif . ages - 25 26 27 28 29 30 31 32 33 34 35 36 37 total = 13 b\"" + }, + { + "Answer": 649, + "Options": "a ) 515 , b ) 545 , c ) 618 . , d ) 644 . , e ) 666", + "Correct": "d", + "Explanation": "\"solution : total number of students studying both are 423 + 226 - 134 = 515 ( subtracting the 134 since they were included in the both the other numbers already ) . so 80 % of total is 515 , so 100 % is approx . 644 . answer is d : 644\"" + }, + { + "Answer": 16.5, + "Options": "a ) 16.5 , b ) 10 , c ) 8 , d ) 9.5 , e ) none of these", + "Correct": "a", + "Explanation": "\"answer : a ( 5 x 9 - 3 x 4 ) / 2 = 16.5\"" + }, + { + "Answer": 175.5, + "Options": "a ) 176.5 cm , b ) 175.5 cm , c ) 174.5 cm , d ) 173.5 cm , e ) 172.5 cm", + "Correct": "b", + "Explanation": "\"the total height was 45 cm too much . the average height should be reduced by 45 cm / 30 = 1.5 cm the answer is b .\"" + }, + { + "Answer": 40.20000000000002, + "Options": "a ) 60.2 degrees c , b ) 50.2 degrees c , c ) 40.2 degrees c , d ) 70.2 degrees c , e ) none of these", + "Correct": "c", + "Explanation": "explanation : mon + tue + wed temperature = 3 x 36.3 = 108.9 tue + wed temperature = 108.9 \u2013 39 = 69.9 tue + wed + thu temperature = 3 x 36.7 = 110.1 so , thursday \u2019 s temperature = 110.1 \u2013 69.9 = 40.2 degrees c answer : c" + }, + { + "Answer": 500, + "Options": "a ) 400 , b ) 450 , c ) 500 , d ) 900 , e ) 2500", + "Correct": "c", + "Explanation": "\"first recognize you only need to consider the first three digits ( because the second three are just the first three flipped ) there are 900 possibilities for the first three digits of a 6 digit number , 100 - 999 inclusive . everything starting with a 1 , 3,5 , 7,9 will be odd , which is 5 / 9 ths of the combinations . 5 / 9 * 900 = 500 answer : c\"" + }, + { + "Answer": 2400, + "Options": "a ) 2400 , b ) 2403 , c ) 3998 , d ) 2539 , e ) 1930", + "Correct": "a", + "Explanation": "\"a 2400 let the amount with r be $ r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 6000 - r ) = > 3 r = 12000 - 2 r = > 5 r = 12000 = > r = 2400 .\"" + }, + { + "Answer": 331.26666666666665, + "Options": "a ) 380 times , b ) 381 times , c ) 382 times , d ) 392 times , e ) 331 times", + "Correct": "e", + "Explanation": "\"time difference is 1 hr , 22 min , 49 sec = 4969 sec . so , light glows floor ( 4969 / 15 ) = 331 times . answer : e\"" + }, + { + "Answer": 740, + "Options": "a ) rs . 440 , b ) rs . 500 , c ) rs . 540 , d ) rs . 740 , e ) rs . 840", + "Correct": "d", + "Explanation": "\"s . i for 5 years = ( 1020 - 820 ) = rs . 200 . s . i . for 2 years = 200 / 5 * 2 = rs . 80 . principal = ( 820 - 80 ) = rs . 740 . answer : d\"" + }, + { + "Answer": 49.18032786885246, + "Options": "a ) 39.55 $ , b ) 40.63 $ , c ) 41.63 $ , d ) 42.15 $ , e ) 48.7 $", + "Correct": "e", + "Explanation": "\"let x is the cost of the food 1.07 x is the gross bill after including sales tax 1.15 * 1.07 x = 60 x = 48.7 hence , the correct option is e\"" + }, + { + "Answer": 10000, + "Options": "a ) rs . 8000 , b ) rs . 9000 , c ) rs . 9800 , d ) rs . 9900 , e ) rs . 10000", + "Correct": "e", + "Explanation": "sol . income in first year = * x 42000 = rs . 24000 expenses in second year = \\ x 21000 = rs . 35000 total savings = total income - total expenses = ( 42000 + 24000 ) - ( 21000 + 35000 ) = 66000 - s 6000 = rs . 10000 e" + }, + { + "Answer": 23, + "Options": "a ) 23 years , b ) 20 years , c ) 25 years , d ) 22 years , e ) 28 years", + "Correct": "a", + "Explanation": "\"a 23 years let the average age of the whole team by x years . 11 x - ( 26 + 29 ) = 9 ( x - 1 ) 11 x - 9 x = 46 2 x = 46 x = 23 . so , average age of the team is 23 years\"" + }, + { + "Answer": 544, + "Options": "a ) - 544 , b ) 584 , c ) 544 , d ) 345 , e ) none of these", + "Correct": "c", + "Explanation": "\"= > - 24 * ( 30 - 1 ) + 1240 ; = > - ( 24 * 30 ) + 24 + 1240 ; = > - 720 + 1264 = 544 . correct option : c\"" + }, + { + "Answer": 0.4, + "Options": "a ) 0.2 , b ) 0.3 , c ) 0.4 , d ) 0.5 , e ) 0.6", + "Correct": "c", + "Explanation": "\"we are selecting from non - negative single digit integers , so from { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } . these 10 digits represent the total number of outcomes . hence , the total number of outcomes is 10 . we need to find the probability that the median of the set will increase but the range still remains the same . the median of the set is ( 3 + 4 ) / 2 = 3.5 , thus the number selected must be 4 or greater . for the range to remain the same , the number must be between 2 and 7 inclusive . to satisfy both conditions , the number selected must be 4 , 5 , 6 , or 7 . the probability is 4 / 10 = 0.4 the answer is c .\"" + }, + { + "Answer": 62, + "Options": "a ) 59 , b ) 60 , c ) 61 , d ) 62 , e ) 63", + "Correct": "d", + "Explanation": "\"let x be the number he chose , then 6 \u22c5 x \u2212 250 = 122 6 x = 372 x = 62 correct answer d\"" + }, + { + "Answer": 36000, + "Options": "a ) 240000 , b ) 300000 , c ) 168000 , d ) 36000 , e ) 24,000", + "Correct": "d", + "Explanation": "explanatory answer let the percentage of the total votes secured by party d be x % then the percentage of total votes secured by party r = ( x - 12 ) % as there are only two parties contesting in the election , the sum total of the votes secured by the two parties should total up to 100 % i . e . , x + x - 12 = 100 2 x - 12 = 100 or 2 x = 112 or x = 56 % . if party d got 56 % of the votes , then party got ( 56 - 12 ) = 44 % of the total votes . 44 % of the total votes = 132,000 i . e . , 44 / 100 * t = 132,000 = > t = 132000 * 100 / 44 = 300,000 votes . the margin by which party r lost the election = 12 % of the total votes = 12 % of 300,000 = 36,000 . the correct choice is ( d )" + }, + { + "Answer": 625, + "Options": "a ) 24 , b ) 120 , c ) 625 , d ) 720 , e ) 1024", + "Correct": "c", + "Explanation": "\"5 choices for each of the 4 questions , thus total e of 5 * 5 * 5 * 5 = 5 ^ 4 = 625 ways to answer all of them . answer : c .\"" + }, + { + "Answer": 300, + "Options": "a ) s . 150 , b ) s . 200 , c ) s . 250 , d ) s . 350 , e ) s . 300", + "Correct": "e", + "Explanation": "\"let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 660 but x = 120 % of y = 120 y / 100 = 12 y / 10 \u00e2 \u02c6 \u00b4 12 y / 10 + y = 660 \u00e2 \u2021 \u2019 y [ 12 / 10 + 1 ] = 660 \u00e2 \u2021 \u2019 22 y / 10 = 660 \u00e2 \u2021 \u2019 22 y = 6600 \u00e2 \u2021 \u2019 y = 6600 / 22 = 600 / 2 = rs . 300 e\"" + }, + { + "Answer": 350, + "Options": "a ) a ) 350 , b ) b ) 346 , c ) c ) 358 , d ) d ) 336 , e ) e ) 364", + "Correct": "a", + "Explanation": "x + x ( xx ) put the value of x = 7 in the above expression we get , 7 + 7 ( 77 ) = 7 + 7 ( 7 \u00e3 \u2014 7 ) = 7 + 7 ( 49 ) = 7 + 343 = 350 the answer is ( a )" + }, + { + "Answer": 4, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "b", + "Explanation": "\"the class borrowed a total of 40 * 2 = 80 books . the 25 students who borrowed 0 , 1 , or 2 books borrowed a total of 12 + 11 * 2 = 34 . to maximize the number of books borrowed by 1 student , let ' s assume that 14 students borrowed 3 books and 1 student borrowed the rest . 80 - 34 - 3 * 14 = 4 the maximum number of books borrowed by any student is 4 . the answer is b .\"" + }, + { + "Answer": 12, + "Options": "a ) 16 , b ) 12 , c ) 2 , d ) 6 , e ) 14", + "Correct": "b", + "Explanation": "t ^ 2 - kt - 48 = ( t - 8 ) ( t + m ) where m is any positive integer . if 48 / 8 = 6 , then we know as a matter of fact that : m = + 6 and thus k = 8 - 6 = 12 t ^ 2 - kt - m = ( t - a ) ( t + m ) where a > m t ^ 2 + kt - m = ( t - a ) ( t + m ) where a < m t ^ 2 - kt + m = ( t - a ) ( t - m ) t ^ 2 + kt + m = ( t + a ) ( t + m ) b" + }, + { + "Answer": 2000, + "Options": "a ) 2000 , b ) 2550 , c ) 5050 , d ) 6275 , e ) 11325", + "Correct": "a", + "Explanation": "set a contains 12,14 , 16 . . . 50 set b contains 112 , 114 , 116 . . . 150 number of terms in each set = 20 difference between corresponding terms in set a and b = 100 difference between sum of set b and set a = 100 * 20 = 2000 answer a" + }, + { + "Answer": 4, + "Options": "a ) 4 , b ) 1 / 5 , c ) - 1 / 6 , d ) - 1 / 5 , e ) - 5", + "Correct": "a", + "Explanation": "\"any x and y satisfying x / y = 5 / 3 should give the same value for ( x + y ) / ( x - y ) . say x = 5 and y = 3 , then ( x + y ) / ( x - y ) = ( 5 + 3 ) / ( 5 - 3 ) = 4 . answer : a .\"" + }, + { + "Answer": 140, + "Options": "a ) 130 , b ) 155 , c ) 490 , d ) 140 , e ) 160", + "Correct": "d", + "Explanation": "explanation : x - 35 = 80 x / 100 = > x = 175 = > 4 x / 5 = 4 x 175 / 5 = 140 . answer d" + }, + { + "Answer": 341.6666666666667, + "Options": "a ) 140 , b ) 240 , c ) 260 , d ) 280 , e ) 340", + "Correct": "e", + "Explanation": "explanation : since the month begins with a sunday , so there will be five sundays in the month , required average = ( 415 * 5 + 325 * 25 ) / 30 = 10200 / 30 = 340 answer : e ) 340" + }, + { + "Answer": 0.16666666666666666, + "Options": "a ) 1 / 20 , b ) 1 / 6 , c ) 1 / 5 , d ) 4 / 21 , e ) 5 / 21", + "Correct": "b", + "Explanation": "this is how i used to calculate which i think works pretty well : if you let the average of the 20 other numbers equal a , can you write this equation for sum of the list ( s ) n + 20 a = s the question tells us that n = 4 a plug this back into the first equation and you get that the sum is 24 a 4 a + 20 a = 24 a therefore fraction q of n to the total would be 4 a / 24 a or 1 / 6 answer b" + }, + { + "Answer": 19, + "Options": "a ) 14 , b ) 17 , c ) 11 , d ) 19 , e ) 99", + "Correct": "d", + "Explanation": "\"let the son ' s present age be x years . then , ( 48 - x ) = x x = 24 . son ' s age 5 years back = ( 24 - 5 ) = 19 years answer : d\"" + }, + { + "Answer": 40, + "Options": "a ) 0 , b ) 60 , c ) - 80 , d ) 40 , e ) 80", + "Correct": "d", + "Explanation": "\"there will be two cases x - 20 = 40 and x - 20 = - 40 solve for x = > x = 40 + 20 = > x = 60 or x = - 40 + 20 = > x = - 20 the sum of both values will be 60 + - 20 = 40 answer is d\"" + }, + { + "Answer": 250, + "Options": "a ) $ 240 , b ) $ 350 , c ) $ 217 , d ) $ 250 , e ) $ 340", + "Correct": "d", + "Explanation": "answer is ( d ) . if mathew is left with about $ 350 after all expenses each month , he would need to divide the total expense budget to london ( $ 3000 ) by 12 months to determine how much he would need to put away every single month to hit his target . $ 3000 / 12 = $ 250 ." + }, + { + "Answer": 190, + "Options": "a ) 125 , b ) 135 , c ) 140 , d ) 165 , e ) 190", + "Correct": "e", + "Explanation": "\"j + k = 281 and so k = 281 - j j - 8 = 2 k j - 8 = 2 ( 281 - j ) 3 j = 570 j = 190 the answer is e .\"" + }, + { + "Answer": 300, + "Options": "a ) 300 , b ) 320 , c ) 330 , d ) 350 , e ) 375", + "Correct": "a", + "Explanation": "\"explanation : average price of a goat = rs . 90 total price of 5 goats = 5 * 90 = rs . 450 but total price of 2 cows and 5 goats = rs . 1050 total price of 2 cows is = 1050 - 450 = 600 average price of a cow = 600 / 2 = rs . 300 answer : a\"" + }, + { + "Answer": 576, + "Options": "a ) 576 , b ) 520 , c ) 504 , d ) 432 , e ) 348", + "Correct": "a", + "Explanation": "a number not to be a multiple of 10 should not have the units digit of 0 . xxx 9 options for the first digit ( from 1 to 9 inclusive ) . 8 options for the third digit ( from 1 to 9 inclusive minus the one we used for the first digit ) . 8 options for the second digit ( from 0 to 9 inclusive minus 2 digits we used for the first and the third digits ) 9 * 8 * 8 = 576 . answer : a ." + }, + { + "Answer": 8.4, + "Options": "a ) 3 , b ) 3.75 , c ) 4.5 , d ) 8.4 , e ) 9", + "Correct": "d", + "Explanation": "05 grass seed contains 5 % herbicide and its amount is 3 pound 20 grass seed contains 20 % herbicide and its amount is x when these two types of grass seeds are mixed , their average becomes 15 % thus we have 3 ( 1 ) + x ( 20 ) / ( x + 3 ) = 15 3 + 20 x = 15 x + 45 5 x = 42 or x = 8.4 d" + }, + { + "Answer": 2013, + "Options": "a ) 222 , b ) 2787 , c ) 2013 , d ) 2778 , e ) 10222", + "Correct": "c", + "Explanation": "\"put n = 0 then f ( f ( 0 ) ) + f ( 0 ) = 2 ( 0 ) + 3 \u21d2 \u21d2 f ( 1 ) + 1 = 3 \u21d2 \u21d2 f ( 1 ) = 2 put n = 1 f ( f ( 1 ) ) + f ( 1 ) = 2 ( 1 ) + 3 \u21d2 \u21d2 f ( 2 ) + 2 = 5 \u21d2 \u21d2 f ( 2 ) = 3 put n = 2 f ( f ( 2 ) ) + f ( 2 ) = 2 ( 2 ) + 3 \u21d2 \u21d2 f ( 3 ) + 3 = 7 \u21d2 \u21d2 f ( 3 ) = 4 . . . . . . f ( 2012 ) = 2013 answer : c\"" + }, + { + "Answer": 72, + "Options": "a ) 57 , b ) 67 , c ) 72 , d ) 87 , e ) 97", + "Correct": "c", + "Explanation": "\"explanation : money collected = ( 51.84 x 100 ) paise = 5184 paise . \u2234 number of members = \u221a ( 5184 ) = 72 . answer : c\"" + }, + { + "Answer": 8, + "Options": "a ) 8 , b ) 13 , c ) 12 , d ) 20 , e ) 22", + "Correct": "a", + "Explanation": "4 * 2 * 1 = 8 at one ' s place only 5 will come and at ten ' s place 4 and 7 can be placed , and at 100 th place rest of the 4 digits can come . . . so the answer is 8 answer : a" + }, + { + "Answer": 128, + "Options": "a ) 128 , b ) 142 , c ) 143 , d ) 141 , e ) 129", + "Correct": "e", + "Explanation": "\"minimum three digit number is 100 and maximum three digit number is 999 . the first three digit number that leaves remainder 5 when divided by 7 is 103 . 14 * 7 = 98 + 5 = 103 the second three digit number that leaves remainder 5 when divided by 7 is 110 . 15 * 7 = 105 + 5 = 110 the third three digit number that leaves remainder 5 when divided by 7 is 117 and so on the last three digit number that leaves remainder 5 when divided by 7 is 999 142 * 7 = 994 + 5 = 999 therefore , we identify the sequence 103 , 110,117 . . . . . 999 use the formula of last term last term = first term + ( n - 1 ) * common difference you will get the answer 129 that is definitely e .\"" + }, + { + "Answer": 17, + "Options": "a ) a ) 17 , b ) b ) 18 , c ) c ) 19 , d ) d ) 22 , e ) e ) 24", + "Correct": "a", + "Explanation": "\"explanation : 10 * 16 + 36 \u2013 26 = 170 = > 170 / 10 = 17 a )\"" + }, + { + "Answer": 11, + "Options": "a ) 10 , b ) 12 , c ) 11 , d ) 13 , e ) 14", + "Correct": "c", + "Explanation": "\"ab = ( a - 1 ) ( b - 1 ) x 20 = ( x - 1 ) ( 20 - 1 ) = 190 - - > x - 1 = 10 - - > x = 11 answer : c\"" + }, + { + "Answer": 40, + "Options": "a ) 87 , b ) 40 , c ) 37 , d ) 28 , e ) 26", + "Correct": "b", + "Explanation": "a . m . of 75 numbers = 35 sum of 75 numbers = 75 * 35 = 2625 total increase = 75 * 5 = 375 increased sum = 2625 + 375 = 3000 increased average = 3000 / 75 = 40 . answer : b" + }, + { + "Answer": 4327, + "Options": "a ) 3327 , b ) 4327 , c ) 3337 , d ) 2337 , e ) none of these", + "Correct": "b", + "Explanation": "answer x = 13200 - 8873 = 4327 option : b" + }, + { + "Answer": 0.06666666666666667, + "Options": "a ) 1 / 190 , b ) 1 / 20 , c ) 1 / 19 , d ) 1 / 10 , e ) 1 / 15", + "Correct": "e", + "Explanation": "\"the problem with your solution is that we do n ' t choose 1 shoe from 16 , but rather choose the needed one after we just took one and need the second to be the pair of it . so , the probability would simply be : 1 / 1 * 1 / 15 ( as after taking one at random there are 15 shoes left and only one is the pair of the first one ) = 1 / 15 answer : e .\"" + }, + { + "Answer": 1200, + "Options": "a ) 1200 , b ) 380 , c ) 3800 , d ) 2180 , e ) 3180", + "Correct": "a", + "Explanation": "let the number of boys = x , number of girls = y 40 y / 100 = 120 y = 300 120 = 2 / 3 * 20 x / 100 = 2 x / 15 x = 900 total = x + y = 300 + 900 = 1200 answer : a" + }, + { + "Answer": 0.28, + "Options": "a ) 1 / 18 , b ) 7 / 18 , c ) 7 / 25 , d ) 3 / 25 , e ) 1 / 25", + "Correct": "c", + "Explanation": "\"we have the ratio of a \u2019 s speed and b \u2019 s speed . this means , we know how much distance a covers compared with b in the same time . this is what the beginning of the race will look like : ( start ) a _________ b ______________________________ if a covers 25 meters , b covers 18 meters in that time . so if the race is 25 meters long , when a reaches the finish line , b would be 7 meters behind him . if we want the race to end in a dead heat , we want b to be at the finish line too at the same time . this means b should get a head start of 7 meters so that he doesn \u2019 t need to cover that . in that case , the time required by a ( to cover 25 meters ) would be the same as the time required by b ( to cover 18 meters ) to reach the finish line . so b should get a head start of 7 / 25 th of the race . answer ( c )\"" + }, + { + "Answer": 200, + "Options": "a ) 238 , b ) 277 , c ) 278 , d ) 200 , e ) 288", + "Correct": "d", + "Explanation": "\"explanation : let the number of 20 paise coins be x . then the no of 25 paise coins = ( 324 - x ) . 0.20 * ( x ) + 0.25 ( 324 - x ) = 71 = > x = 200 . . answer : d ) 200\"" + }, + { + "Answer": 32, + "Options": "a ) 30 % , b ) 32 % , c ) 35 % , d ) 38 % , e ) 40 %", + "Correct": "b", + "Explanation": "\"the amount of chemical x in the solution is 20 + 0.15 ( 80 ) = 32 liters . 32 liters / 100 liters = 32 % the answer is b .\"" + }, + { + "Answer": 2, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5", + "Correct": "c", + "Explanation": "\"{ total } = { even } + { multiple of 5 } - { both } + { nether } . since { neither } = 0 ( allare even or multiple of 5 ) then : 12 = 4 + 10 - { both } + 0 ; { both } = 2 ( so 1 number is both even and multiple of 5 , so it must be a multiple of 10 ) . answer : c .\"" + }, + { + "Answer": 230, + "Options": "a ) s . 250 , b ) s . 280 , c ) s . 290 , d ) s . 299 , e ) s . 230", + "Correct": "e", + "Explanation": "\"let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 506 but x = 120 % of y = 120 y / 100 = 12 y / 10 \u2234 12 y / 10 + y = 506 \u21d2 y [ 12 / 10 + 1 ] = 506 \u21d2 22 y / 10 = 506 \u21d2 22 y = 5060 \u21d2 y = 5060 / 22 = 460 / 2 = rs . 230 e\"" + }, + { + "Answer": 9, + "Options": "a ) 9 years , b ) 11 years , c ) 14 years , d ) 21 years , e ) 9 years", + "Correct": "e", + "Explanation": "\"solution age of the 15 th student = [ 15 x 15 - ( 14 x 4 + 16 x 10 ) ] = ( 225 - 216 ) = 9 years . answer e\"" + }, + { + "Answer": 205, + "Options": "a ) 288 , b ) 262 , c ) 72 , d ) 205 , e ) 267", + "Correct": "d", + "Explanation": "\"a : b : c = 100 : 65 : 40 = 20 : 13 : 8 8 - - - - 40 41 - - - - ? = > rs . 205 answer : d\"" + }, + { + "Answer": 1.25, + "Options": "a ) 2 hours , b ) 2.25 hours , c ) 1 hour , d ) 1.25 hours , e ) not enough information", + "Correct": "d", + "Explanation": "each train is averaging 40 km / hour in an opposite direction . after 1 hour , they will be 80 km apart , and after 1.25 hours , they will be 100 km apart . ( 80 * 1.25 = 100 ) answer is d" + }, + { + "Answer": 2.9166666666666545, + "Options": "a ) 2.2 , b ) 8.2 , c ) 2.9 , d ) 2.1 , e ) 2.6", + "Correct": "c", + "Explanation": "\"xz = y 2 10 ( 0.48 z ) = 10 ( 2 x 0.70 ) = 101.40 0.48 z = 1.40 z = 140 = 35 = 2.9 ( approx . ) 48 12 answer : c\"" + }, + { + "Answer": 642, + "Options": "a ) 756 , b ) 642 , c ) 492 , d ) 372 , e ) 250", + "Correct": "b", + "Explanation": "\"9 pages from 1 to 9 will require 9 digits . 90 pages from 10 to 99 will require 90 * 2 = 180 digits . 250 - ( 90 + 9 ) = 151 pages will require 151 * 3 = 453 digits . the total number of digits is 9 + 180 + 453 = 642 . the answer is b .\"" + }, + { + "Answer": 27.638888888888896, + "Options": "a ) 25.7 miles , b ) 26.2 miles , c ) 27.6 miles , d ) 27.9 miles , e ) 29.9 miles", + "Correct": "c", + "Explanation": "for sad : saddaily = $ 34.95 / day sadmile = $ 0.23 / mile for ral : raldaily = $ 25.00 / day ralmile = $ 1.31 / mile we want the raltotal = sadtotal , so we get ( raldaily * days ) + ( ralmile * miles ) = ( saddaily * days ) + ( sadmile * miles ) = > miles = ( ( saddaily * days ) - ( raldaily * days ) ) / ( ralmiles - sadmiles ) = ( ( saddaily - raldaily ) * days ) / ( ralmiles - sadmiles ) miles = ( ( $ 34.95 * 3 ) - ( $ 25.00 * 3 ) ) / ( $ 1.31 - $ 0.23 ) = 27.6 miles c . 27.6 miles" + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 1 , c ) 0 , d ) 8 , e ) 7", + "Correct": "a", + "Explanation": "every prime number greater than 3 can be written 6 n + 1 or 6 n - 1 . if p = 6 n + 1 , then p ^ 2 + 16 = 36 n ^ 2 + 12 n + 1 + 16 = 36 n ^ 2 + 12 n + 12 + 5 if p = 6 n - 1 , then p ^ 2 + 16 = 36 n ^ 2 - 12 n + 1 + 16 = 36 n ^ 2 - 12 n + 12 + 5 when divided by 12 , it must leave a remainder of 5 . the answer is a ." + }, + { + "Answer": 66, + "Options": "a ) 68 , b ) 70.4 , c ) 86 , d ) 66 , e ) 108", + "Correct": "d", + "Explanation": "x is 20 % greater than 55 means x is 1.2 times 55 ( in other words 55 + 20 / 100 * 55 = 1.2 * 55 ) therefore , x = 1.2 * 55 = 66 answer : d" + }, + { + "Answer": 724827405, + "Options": "a ) 354517481 , b ) 457687783 , c ) 246567689 , d ) 725117481 , e ) 565776879", + "Correct": "d", + "Explanation": "\"72519 x 9999 = 72519 x ( 10000 - 1 ) = 72519 x 10000 - 72519 x 1 = 725190000 - 72519 = 725117481 d\"" + }, + { + "Answer": 43, + "Options": "a ) 41 , b ) 39 , c ) 43 , d ) 45 , e ) 47", + "Correct": "c", + "Explanation": "option ' c '" + }, + { + "Answer": 80, + "Options": "a ) 80 , b ) 120 , c ) 130 , d ) 140 , e ) 150", + "Correct": "a", + "Explanation": "\"solution : let xx be the number he chose , then 3 \u22c5 x \u2212 138 = 102 3 x = 240 x = 80 answer a\"" + }, + { + "Answer": 6, + "Options": "a ) - 1 , b ) 6 , c ) 7 , d ) 12 , e ) 14", + "Correct": "b", + "Explanation": "\"first of all | x - 3 | ^ 2 = ( x - 3 ) ^ 2 , so we have : ( x - 3 ) ^ 2 + | x - 3 | = 20 . when x < 3 , x - 3 is negative , thus | x - 3 | = - ( x - 3 ) . in this case we ' ll have ( x - 3 ) ^ 2 - ( x - 3 ) = 20 - - > x = - 1 or x = 8 . discard x = 8 because it ' s not in the range we consider ( < 3 ) . when x > = 3 , x - 3 is non - negative , thus | x - 3 | = x - 3 . in this case we ' ll have ( x - 3 ) ^ 2 + ( x - 3 ) = 20 - - > x = - 2 or x = 7 . discard x = - 2 because it ' s not in the range we consider ( > = 3 ) . thus there are two solutions : x = - 1 and x = 7 - - > the sum = 6 . answer : b .\"" + }, + { + "Answer": 34, + "Options": "a ) 30 , b ) 34 , c ) 40 , d ) 50 , e ) 60", + "Correct": "b", + "Explanation": "explanation : ( a + b ) , five years ago = ( 15 * 2 ) = 30 years . ( a + b ) , now = ( 30 + 5 * 2 ) years = 40 years . ( a + b + c ) , now = ( 20 x 3 ) years = 60 years . c , now = ( 60 - 40 ) years = 20 years . c , after 14 years = ( 20 + 14 ) years = 34 years . answer : b" + }, + { + "Answer": 7, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8", + "Correct": "d", + "Explanation": "so we can start with 2 and check whether sum of two primes is primes is even . 1 ) 2 ( 6 times ) 2 ) 2 ( 3 times ) + 3 ( 2 times ) 3 ) 2 ( 2 times ) + 3 + 5 4 ) 2 + 3 + 7 5 ) 2 + 5 + 5 6 ) 3 ( 4 times ) 7 ) 5 + 7 answer : d" + }, + { + "Answer": 82, + "Options": "a ) 80 , b ) 82 , c ) 84 , d ) 86 , e ) 88", + "Correct": "b", + "Explanation": "\"let x be the number he chose , then 5 \u22c5 x \u2212 275 = 135 5 x = 410 x = 82 correct answer b\"" + }, + { + "Answer": 36, + "Options": "a ) 36 , b ) 34 , c ) 32 , d ) 30 , e ) 28", + "Correct": "a", + "Explanation": "\"let c be the capacity of the can . ( 3 / 5 ) * ( c - 6 ) + 6 = ( 2 / 3 ) * c 9 c - 54 + 90 = 10 c c = 36 the answer is a .\"" + }, + { + "Answer": 1, + "Options": "a ) 3 , b ) 4 , c ) 2 , d ) 1 , e ) 5", + "Correct": "d", + "Explanation": "\"7 ^ 16 can be written as ( 7 ^ 4 ) ^ 4 if we divide 7 ^ 4 by 100 the reminder is 1 so , ( 7 ^ 4 ) ^ 4 by 100 , the reminder is 1 ^ 4 = 1 answer : d\"" + }, + { + "Answer": 425, + "Options": "a ) 250 , b ) 350 , c ) 425 , d ) 550 , e ) 650", + "Correct": "c", + "Explanation": "\"the number of chocolate bars is equal to 17 * 25 = 425 correct answer c\"" + }, + { + "Answer": 6, + "Options": "a ) 12 , b ) 18 , c ) 15 , d ) 6 , e ) 9", + "Correct": "d", + "Explanation": "explanation : = > y = x ^ 2 + 5 x + 6 = > y = ( x + 2 ) ( x + 3 ) = > x = - 2 , x = - 3 product x = ( - 2 ) ( - 3 ) = 6 answer option 6 answer : d" + }, + { + "Answer": 5.6, + "Options": "a ) $ 3.15 , b ) $ 4.45 , c ) $ 4.80 , d ) $ 5.05 , e ) $ 5.6", + "Correct": "e", + "Explanation": "\"let the fixed charge of jim \u2019 s taxi service = 2.45 $ and charge per 2 / 5 mile ( . 4 mile ) = . 35 $ total charge for a trip of 3.6 miles = 2.45 + ( 3.6 / . 4 ) * . 35 = 2.45 + 9 * . 35 = 5.6 $ answer e\"" + }, + { + "Answer": 22.5, + "Options": "a ) 12.5 % , b ) 16.7 % , c ) 22.5 % , d ) 27.5 % , e ) 33.3 %", + "Correct": "c", + "Explanation": "let x be the original number of each color so there are a total of 5 x candies . kaz eats all of the green candies and half of the orange ones . there are 0 green candies and 0.5 x orange candies remaining . he eats half of the remaining pieces of each color . there are 0.25 x orange candies , and 0.5 x each of red , yellow , and blue candies . he eats red and yellow candies in equal proportions . orange + blue + red + yellow = 0.75 x + red + yellow = 1.2 x red + yellow = 0.45 x red = 0.225 x , since red = yellow . the answer is c ." + }, + { + "Answer": 90, + "Options": "a ) 50 , b ) 60 , c ) 90 , d ) 48 , e ) 67", + "Correct": "c", + "Explanation": "c $ 90 let number of notes of each denomination be x . then x + 5 x + 10 x = 480 16 x = 480 x = 30 . hence , total number of notes = 3 x = 90 ." + }, + { + "Answer": 3334, + "Options": "a ) 2468 , b ) 2789 , c ) 2987 , d ) 3334 , e ) 3568", + "Correct": "d", + "Explanation": "if sum of the digits is divisible by 3 , the number is divisible by 3 . therefore , required number of non - negative integers is equal to count of numbers less than 10000 which are divisible by 3 . such numbers are ( 3 , 6 , 9 , . . . , 9999 ) ( arithmetic progression with first term = 3 , last term = 9999 , common difference = 3 ) . count of such numbers = 9999 3 = 3333 99993 = 3333 but zero is also divisible by 3 . this makes our total count 3334 d" + }, + { + "Answer": 25, + "Options": "a ) 10 % , b ) 15 % , c ) 25 % , d ) 35 % , e ) 40 %", + "Correct": "c", + "Explanation": "\"let x be the original number of each color . kaz eats all of the green candies and half of the orange ones . there are 0 green candies and 0.5 x orange candies remaining . he eats half of the remaining pieces of each color . there are 0.25 x orange candies , and 0.5 x each of red , yellow , and blue candies . he eats red and yellow candies in equal proportions . orange + blue + red + yellow = 0.75 x + red + yellow = 1.25 x red + yellow = 0.5 x red = 0.25 x , since red = yellow . the answer is c .\"" + }, + { + "Answer": 89, + "Options": "a ) - 32 , b ) - 30 , c ) 34 , d ) - 24 , e ) - 10", + "Correct": "c", + "Explanation": "answer : c" + }, + { + "Answer": 2, + "Options": "a ) 91 , b ) 2 , c ) 1001 , d ) 1911 , e ) none of these", + "Correct": "b", + "Explanation": "\"explanation : required number of students = h . c . f of 1234 and 874 = 2 . answer : b\"" + }, + { + "Answer": 60, + "Options": "a ) \u2212 60 , b ) \u2212 100 , c ) 100 , d ) 135 , e ) it can not be determined from the information given", + "Correct": "a", + "Explanation": "\"a + b = 240 b + c = 300 a - c = - 60 . imo option a .\"" + }, + { + "Answer": 23, + "Options": "a ) 23 % . , b ) 71 % . , c ) 49 % . , d ) 29 % . , e ) 51 % .", + "Correct": "a", + "Explanation": "\"25 % of 2 litres = 0.5 litres 30 % of 6 litres = 1.8 litres therefore , total quantity of alcohol is 2.3 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 23 % answer : a\"" + }, + { + "Answer": 450, + "Options": "a ) 250 / 3 , b ) 500 / 3 , c ) 400 , d ) 450 , e ) 600", + "Correct": "d", + "Explanation": "\"we know that x is 10 % , y is 30 % and w . avg = 25 % . what does this mean with respect to w . avg technique ? w . avg is 1 portion away from y and 3 portion away from x so for every 1 portion of x we will have to add 3 portions of y . if x = 150 then y = 450 answer : d\"" + }, + { + "Answer": 25, + "Options": "a ) a ) 10 , b ) b ) 25 , c ) c ) 40 , d ) d ) 55 , e ) e ) 70", + "Correct": "b", + "Explanation": "\"total score of 16 students is 16 * 62.50 = 1000 total score of 15 students is 15 * 65 = 975 so , the score of the person who left is 25 ( 1000 - 975 ) answer will be ( b )\"" + }, + { + "Answer": 66.66666666666414, + "Options": "a ) 96 , b ) 75 , c ) 66.7 , d ) 25 , e ) 12", + "Correct": "c", + "Explanation": "\"when positive integer x is divided by positive integer y , the remainder is 8 - - > x = qy + 8 ; x / y = 96.12 - - > x = 96 y + 0.12 y ( so q above equals to 96 ) ; 0.12 y = 8 - - > y = 66.7 . answer : c .\"" + }, + { + "Answer": 4691530800, + "Options": "a ) 4586970843 , b ) 4686970743 , c ) 4691100843 , d ) 4586870843 , e ) 4691530800", + "Correct": "e", + "Explanation": "\"answer 469200 x 9999 = 469200 x ( 10000 - 1 ) = 4692000000 - 469200 = 4691100843 . option : e\"" + }, + { + "Answer": 10, + "Options": "a ) 12 years , b ) 10 years , c ) 8 years , d ) 14 years , e ) 16 years", + "Correct": "b", + "Explanation": "\"c age x , then b age is 2 x so a age is 2 x + 2 . ( 2 x + 2 ) + 2 x + x = 27 5 x = 25 x = 5 so b is 2 x = 2 ( 5 ) 2 x 5 = 10 answer : b\"" + }, + { + "Answer": 447.5, + "Options": "a ) 447.5 , b ) 450 , c ) 465 , d ) 468 , e ) 475", + "Correct": "a", + "Explanation": "total number of installments = 52 payment per installment for the first 22 installments = 410 payment per installment for the remaining 30 installments = 410 + 65 = 475 average = ( 22 * 410 + 30 * 475 ) / 52 = 447.50 answer a" + }, + { + "Answer": 380, + "Options": "a ) 370 , b ) 365 , c ) 380 , d ) 456 , e ) 460", + "Correct": "c", + "Explanation": "\"easy solution : n = dq 1 + 241 2 n = 2 dq 1 + 482 - ( 1 ) 2 n = dq 2 + 102 - ( 2 ) as ( 1 ) = ( 2 ) = 2 n d * ( q 2 - 2 q 1 ) = 380 d * some integer = 380 checking all options only ( c ) syncs with it . answer c\"" + }, + { + "Answer": 6, + "Options": "a ) 10 , b ) 6 , c ) 4 , d ) 0 , e ) it can not be determined", + "Correct": "b", + "Explanation": "it is essential to recognize that the remainder when an integer is divided by 10 is simply the units digit of that integer . to help see this , consider the following examples : 4 / 10 is 0 with a remainder of 4 14 / 10 is 1 with a remainder of 4 5 / 10 is 0 with a remainder of 5 105 / 10 is 10 with a remainder of 5 it is also essential to remember that the s is a positive integer and multiple of 2 . any integer that is a multiple of 2 is an even number . so , s must be a positive even integer . with these two observations , the question can be simplified to : what is the units digit of 4 raised to an even positive integer ? the units digit of 4 raised to an integer follows a specific repeating pattern : 4 ^ 1 = 4 4 ^ 2 = 16 4 ^ 3 = 64 4 ^ 4 = 256 4 ^ ( odd number ) - - > units digit of 4 4 ^ ( even number ) - - > units digit of 6 there is a clear pattern regarding the units digit . 4 raised to any odd integer has a units digit of 4 while 4 raised to any even integer has a units digit of 6 . since s must be an even integer , the units digit of p = 4 ^ s will always be 6 . consequently , the remainder when p = 4 ^ s is divided by 10 will always be 6 . in case this is too theoretical , consider the following examples : s = 2 - - > p = 4 ^ z = 16 - - > s / 10 = 1 with a remainder of 6 s = 4 - - > p = 4 ^ z = 256 - - > s / 10 = 25 with a remainder of 6 s = 6 - - > p = 4 ^ z = 4096 - - > s / 10 = 409 with a remainder of 6 s = 8 - - > p = 4 ^ z = 65536 - - > s / 10 = 6553 with a remainder of 6 answer : b ." + }, + { + "Answer": 49, + "Options": "a ) 40 , b ) 49 , c ) 80 , d ) 88 , e ) 90", + "Correct": "b", + "Explanation": "\"sol . let the numbers be x and y . then , ( x + y ) = 22 and x 2 + y 2 = 386 . now , 2 xy = ( x + y ) 2 - ( x 2 + y 2 ) = ( 22 ) 2 - 386 = 484 - 386 = 98 xy = 49 . answer b\"" + }, + { + "Answer": 5, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 6", + "Correct": "d", + "Explanation": "\"( - 2 ) ^ ( 2 m ) = 4 ^ m and 2 ^ ( 15 - m ) = 4 ^ ( ( 15 - m ) / 2 ) therefore , m = ( 15 - m ) / 2 2 m = 15 - m m = 5 answer d\"" + }, + { + "Answer": 216, + "Options": "a ) $ 200 , b ) $ 208 , c ) $ 216 , d ) $ 224 , e ) $ 232", + "Correct": "c", + "Explanation": "\"let the shares for a , b , and c be x , 2 x , and 4 x respectively . 7 x = 378 x = 54 4 x = 216 the answer is c .\"" + }, + { + "Answer": 4.0000000000000036, + "Options": "a ) 10 % , b ) 8 % , c ) 6 % , d ) 4 % , e ) 2 %", + "Correct": "d", + "Explanation": "\"let x be the amount of money paid for the first purchase . the second time , the customer paid 0.8 ( 1.2 x ) = 0.96 x . the difference is 4 % . the answer is d .\"" + }, + { + "Answer": 248, + "Options": "a ) 248 , b ) 120 , c ) 252 , d ) 250 , e ) 350", + "Correct": "a", + "Explanation": "amount left = 0.5 x \u2212 4 for fifth store this is zero . so x = 8 . that means he entered fifth store with 8 . now for fourth store , amount left = 8 so 0.5 x \u2212 4 = 8 \u21d2 x = 24 for third store , amount left = 24 so 12 x \u2212 4 = 24 \u21d2 x = 56 for second store , amount left = 56 so 0.5 x \u2212 4 = 56 \u21d2 x = 120 for first store , amount left = 120 so 0.5 x \u2212 4 = 120 \u21d2 x = 248 so he entered first store with 248 . answer : a" + }, + { + "Answer": 0.5000000000000001, + "Options": "a ) 1 / 2 , b ) 2 / 7 , c ) 3 / 2 , d ) 4 / 7 , e ) none of them", + "Correct": "a", + "Explanation": "original share of 1 person = 1 / 3 new share of 1 person = 1 / 2 increase = ( 1 / 2 - 1 / 3 = 1 / 6 ) therefore , required fraction = ( 1 / 6 ) / ( 1 / 3 ) = ( 1 / 6 ) x ( 3 / 1 ) = 1 / 2 answer is a ." + }, + { + "Answer": 300, + "Options": "a ) 300 , b ) 400 , c ) 500 , d ) 600 , e ) 700", + "Correct": "a", + "Explanation": "\"required number = ( 75 / 2 ) / ( 1 / 8 ) = ( 75 / 2 x 8 / 1 ) = 300 . answer : a\"" + }, + { + "Answer": 64, + "Options": "a ) 22 , b ) 77 , c ) 64 , d ) 19 , e ) 17", + "Correct": "c", + "Explanation": "\"explanation : average after 11 innings = 24 required number of runs = ( 24 * 11 ) \u2013 ( 20 * 10 ) = 264 \u2013 200 = 64 answer : c\"" + }, + { + "Answer": 159, + "Options": "a ) 79 , b ) 80 , c ) 81 , d ) 157 , e ) 159", + "Correct": "e", + "Explanation": "\"the number of terms in this set would be : n = ( k - 1 ) / 2 ( as k is odd ) last term : k - 1 average would be first term + last term / 2 = ( 2 + k - 1 ) / 2 = ( k + 1 ) / 2 also average : sum / number of terms = 79 * 80 / ( ( k - 1 ) / 2 ) = 158 * 80 / ( k - 1 ) ( k + 1 ) / 2 = 158 * 80 / ( k - 1 ) - - > ( k - 1 ) ( k + 1 ) = 158 * 160 - - > k = 159 answer e .\"" + }, + { + "Answer": 45, + "Options": "a ) 40 , b ) 48 , c ) 43 , d ) 45 , e ) 41", + "Correct": "d", + "Explanation": "ele , the circus elephant , is currently three times older than lyn , the circus lion . ele = 3 * lyn usually , ages are integers so there is a good possibility that the age of ele is 45 ( the only option that is a multiple of 3 ) . then age of lyn would be 15 . in 15 yrs , ele would be 60 and lyn would be 30 - so lyn would be half as old as ele . answer ( d )" + }, + { + "Answer": 28, + "Options": "a ) 28 years , b ) 22 years , c ) 23 years , d ) 24 years , e ) 26 years", + "Correct": "a", + "Explanation": "\"explanation : let ' s son age is x , then father age is x + 30 . = > 2 ( x + 2 ) = ( x + 30 + 2 ) = > 2 x + 4 = x + 32 = > x = 28 years option a\"" + }, + { + "Answer": 60, + "Options": "a ) 18 , b ) 82 , c ) 60 , d ) 27 , e ) 29", + "Correct": "c", + "Explanation": "\"let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 x / 2 = ( 83 - 53 ) = > x / 2 = 30 = > x = 60 . answer : c\"" + }, + { + "Answer": 51, + "Options": "a ) 36 , b ) 40 , c ) 44 , d ) 48 , e ) 51", + "Correct": "e", + "Explanation": "\"for 40 hrs = 40 * 16 = 640 excess = 948 - 640 = 308 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 308 / 28 = 77 / 7 = 11 total hrs = 40 + 11 = 51 answer e 51\"" + }, + { + "Answer": 32500, + "Options": "a ) $ 30000 , b ) $ 32500 , c ) $ 35120 , d ) $ 41520 , e ) $ 25460", + "Correct": "b", + "Explanation": "let his total sales be x total sales - commission = $ 31100 x - [ ( 5 % of 10000 ) + 4 % of ( x - 10000 ) ] = 31100 x - 500 - ( x - 10000 ) / 25 = 31100 x = 32500 answer is b" + }, + { + "Answer": 54, + "Options": "a ) 0 , b ) 1 , c ) 27 , d ) 54 , e ) can not be determined", + "Correct": "d", + "Explanation": "\"factorization of 45 = 3 * 3 * 5 factorization of 80 = 5 * 2 ^ 4 means the smallest value of k is \\ sqrt { 3 ^ 2 * 5 * 2 ^ 4 } = 3 * 5 * 2 ^ 2 k ^ 3 = 3 ^ 3 * 5 ^ 3 * 2 ^ 6 * x = 3 ^ 3 * 2 * 4000 * x where x can be any integer k ^ 3 / 4000 = 3 ^ 3 * 2 * x = 54 x which obviously has different units digit depending on x answer : d\"" + }, + { + "Answer": 1.4210526315789473, + "Options": "a ) 11 / 12 , b ) 13 / 17 , c ) 13 / 19 , d ) 12 / 19 , e ) 27 / 19", + "Correct": "e", + "Explanation": "make r = 10 p = 0.6 r = 6 q = 0.8 p = 4.8 s = 0.6 p = 3.6 for that we get s = 7.6 and q 10.8 so 10.8 / 7.6 = 2.7 / 1.9 ans : e" + }, + { + "Answer": 13, + "Options": "a ) 12 , b ) 14 , c ) 13 , d ) 15 , e ) 16", + "Correct": "c", + "Explanation": "\"let p = 3 , q = 7 then 2 * 3 + 7 = 13 so 2 p + q = 13 . answer : c\"" + }, + { + "Answer": 0.5833333333333334, + "Options": "a ) 4 / 7 , b ) 5 / 9 , c ) 6 / 11 , d ) 7 / 12 , e ) 8 / 15", + "Correct": "d", + "Explanation": "\"# defective pens = 2 # good pens = 7 probability of the 1 st pen being good = 7 / 9 probability of the 2 nd pen being good = 6 / 8 total probability = 7 / 9 * 6 / 8 = 7 / 12 the answer is d .\"" + }, + { + "Answer": 110.00000000000001, + "Options": "a ) $ 50 , b ) $ 100 , c ) $ 110 , d ) $ 600 , e ) $ 300", + "Correct": "c", + "Explanation": "let the lowest price be x . therefore , highest price is x + 100 . now price of each variety is increased by 10 % . therefore the price will remain arranged in the same order as before . or lowest price = 1.1 x and highest = 1.1 * ( x + 100 ) or range = highest - lowest = 1.1 * ( x + 100 ) - 1.1 x = 110 , hence , c" + }, + { + "Answer": 1534, + "Options": "a ) 1534 , b ) 2999 , c ) 2834 , d ) 2777 , e ) 2991", + "Correct": "a", + "Explanation": "\"let the total number of votes polled in the election be 100 k . number of valid votes = 100 k - 20 % ( 100 k ) = 80 k let the number of votes polled in favour of a and b be a and b respectively . a - b = 15 % ( 100 k ) = > a = b + 15 k = > a + b = b + 15 k + b now , 2 b + 15 k = 80 k and hence b = 32.5 k it is given that 100 k = 4720 32.5 k = 32.5 k / 100 k * 4720 = 1534 the number of valid votes polled in favour of b is 1534 . answer : a\"" + }, + { + "Answer": 28, + "Options": "a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28", + "Correct": "e", + "Explanation": "\"20 + 24 + 6 * 2 = 56 / 2 = 28 answer : e\"" + }, + { + "Answer": 9, + "Options": "a ) 5 , b ) 9 , c ) 10 , d ) 13 , e ) 17", + "Correct": "b", + "Explanation": "official solution : ( b ) we know that a # b = 100 and a # b = 4 a \u00b2 + 4 b \u00b2 + 8 ab . so 4 a \u00b2 + 4 b \u00b2 + 8 ab = 100 we can see that 4 a \u00b2 + 4 b \u00b2 + 8 ab is a well - known formula for ( 2 a + 2 b ) \u00b2 . therefore ( 2 a + 2 b ) \u00b2 = 100 . ( 2 a + 2 b ) is non - negative number , since both a and b are non - negative numbers . so we can conclude that 2 ( a + b ) = 10 . ( a + b ) + 4 = 10 / 2 + 4 = 9 . the correct answer is b ." + }, + { + "Answer": 89.6, + "Options": "a ) 90 % , b ) 80 % , c ) 70 % , d ) 60 % , e ) 40 %", + "Correct": "a", + "Explanation": "the problem asks for the approximate chance that no more than 1 / 3 of the original investment is lost . we can apply the \u201c 1 \u2013 x \u201d technique : what \u2019 s the chance that more than 1 / 3 of the original investment is lost ? there are two outcomes we have to separately measure : ( a ) all 3 investments become worthless . ( b ) 2 of the 3 investments become worthless , while 1 doesn \u2019 t . outcome ( a ) : the probability is ( 0.2 ) ( 0.2 ) ( 0.2 ) = 0.008 , or a little less than 1 % . outcome ( b ) : call the investments x , y , and z . the probability that x retains value , while y and z become worthless , is ( 0.8 ) ( 0.2 ) ( 0.2 ) = 0.032 . now , we have to do the same thing for the specific scenarios in which y retains value ( while x and z don \u2019 t ) and in which z retains value ( while x and y don \u2019 t ) . each of those scenarios results in the same math : 0.032 . thus , we can simply multiply 0.032 by 3 to get 0.096 , or a little less than 10 % . the sum of these two probabilities is 0.008 + 0.096 = 0.104 , or a little more than 10 % . finally , subtracting from 100 % and rounding , we find that the probability we were looking for is approximately 90 % . the correct answer is a . this problem illustrates the power of diversification in financial investments . all else being equal , it \u2019 s less risky to hold a third of your money in three uncorrelated ( independent ) but otherwise equivalent investments than to put all your eggs in one of the baskets . that said , be wary of historical correlations ! housing price changes in different us cities were not so correlated \u2014 and then they became highly correlated during the recent housing crisis ( they all fell together ) , fatally undermining spreadsheet models that assumed that these price changes were independent ." + }, + { + "Answer": 62.5, + "Options": "a ) 23 , b ) 41 , c ) 48 , d ) 62 , e ) 86", + "Correct": "d", + "Explanation": "to get maximum vehicles we must take into consideration the minimum weight i . e 1600 pounds here since , 1 ton = 2000 pounds 50 tons will be 100,000 pounds from the answer choices : let max number of vehicles be 62 total weight will be = 62 * 1600 = 99200 pounds , which is lesser than the maximum weight allowed . ans : d" + }, + { + "Answer": 25400, + "Options": "a ) 2840 , b ) 5680 , c ) 6840 , d ) 25400 , e ) 28400", + "Correct": "d", + "Explanation": "bank balance is doubled with accumulation of interest tp 5080 . . this means interest is 5080 / 2 = 2540 for entire year . . although since interest is 10 % of avg monthly balance , it becomes 25400 . . d" + }, + { + "Answer": 66, + "Options": "a ) 66 , b ) 75 , c ) 80 , d ) 85 , e ) 90", + "Correct": "a", + "Explanation": "\"explanation : ( 40 + 60 + 70 + 80 + 80 / 5 ) = 66 option a\"" + }, + { + "Answer": 3, + "Options": "a ) 2 , b ) 5 , c ) 6 , d ) 3 , e ) 8", + "Correct": "d", + "Explanation": "\"cant think of a straight approach but here is how i solved it : k is divided by 5 and remainder is 2 . this means k = 5 n + 2 ( n is an integer ) so the possible values of k = { 2 , 7 , 12 , 17 , 22 } ( less than 24 ) secondly , if k is divided by 6 , the remainder is 5 = > k = 6 m + 5 so the possible value set for k = { 5 , 11 , 17 , 23 } ( less than 24 ) 17 is the only common number in both the sets . hence k = 17 answer : d\"" + }, + { + "Answer": 12, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 12", + "Correct": "e", + "Explanation": "\"let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 32 5 x = 30 = > x = 6 hence , b ' s age = 2 x = 12 years . answer : e\"" + }, + { + "Answer": 64, + "Options": "a ) 124 % , b ) b . 120 % , c ) 64 % , d ) 80 % , e ) 64 %", + "Correct": "c", + "Explanation": "\"even i got 96 % j = 100 t = 100 * 0.4 = 40 m = 40 * 1.6 = 64 if mary ' s income is x percent of j m = j * x / 100 x = m * 100 / j = 64 * 100 / 100 = 64 ans : c\"" + }, + { + "Answer": 84, + "Options": "a ) 70 , b ) 72 , c ) 75 , d ) 78 , e ) 84", + "Correct": "e", + "Explanation": "\"income of 6 months = ( 6 \u00d7 95 ) \u2013 debt = 570 \u2013 debt income of the man for next 4 months = 4 \u00d7 60 + debt + 30 = 270 + debt \u2234 income of 10 months = 840 average monthly income = 840 \u00f7 10 = 84 answer e\"" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 1.5 , c ) 1.8 , d ) 2.4 , e ) 3", + "Correct": "a", + "Explanation": "\"let x be the number of liters of ethanol added to the gas tank . 0.05 ( 18 ) + x = 0.1 ( 18 + x ) 0.9 x = 1.8 - 0.9 x = 1 liter the answer is a .\"" + }, + { + "Answer": 7.4074074074074066, + "Options": "a ) 7.5 % , b ) 7.41 % , c ) 10.9 % , d ) 12.6 % , e ) 15 %", + "Correct": "b", + "Explanation": "reduce in consumption = r / ( 100 + r ) * 100 % = 8 / 108 * 100 = 7.41 % answer is b" + }, + { + "Answer": 3240, + "Options": "a ) rs . 3240 , b ) rs . 2520 , c ) rs . 2880 , d ) rs . 3360 , e ) none of these", + "Correct": "a", + "Explanation": "explanation : let c ' s investment = rs . x b ' s investment = rs . ( x - 3000 ) a ' s investment = rs . ( x - 3000 + 6000 ) = rs . ( x + 3000 ) now , ( a + b + c ) ' s investment = rs . 72000 = > x + ( x - 3000 ) + ( x + 3000 ) = 72000 = > 3 x = 72000 = > x = 24000 hence , a ' s investment = rs . 27000 b ' s investment = rs . 21000 c ' s investment = rs . 24000 ratio of the capitals of a , b and c = 27000 : 21000 : 24000 = 9 : 7 : 8 a ' s share = rs . [ ( 9 / 24 ) \u00d7 8640 ] = rs . 3240 answer : option a" + }, + { + "Answer": 0.16666666666666666, + "Options": "a ) 1 / 20 , b ) 1 / 6 , c ) 1 / 5 , d ) 4 / 21 , e ) 5 / 21", + "Correct": "b", + "Explanation": "\"this is how i used to calculate which i think works pretty well : if you let the average of the 20 other numbers equal a , can you write this equation for sum of the list ( s ) n + 20 a = s the question tells us that n = 4 a plug this back into the first equation and you get that the sum is 24 a 4 a + 20 a = 24 a therefore fraction e of n to the total would be 4 a / 24 a or 1 / 6 answer b\"" + }, + { + "Answer": 0.1, + "Options": "a ) 0.2 , b ) 0.3 , c ) 0.1 , d ) 0.5 , e ) none", + "Correct": "c", + "Explanation": "\"sol . ( x \u00d7 4 ) = ( 0.20 \u00d7 2 ) \u21d2 x = 0.4 / 4 = 0.1 . answer c\"" + }, + { + "Answer": 510, + "Options": "a ) 158 , b ) 597 , c ) 599 , d ) 402 , e ) 510", + "Correct": "e", + "Explanation": "\"last term = first term + ( total no . of terms - 1 ) consecutive difference s is a set of 85 consecutive multiples of 5 . if the smallest number in s is 90 , then the greatest number in s is first term = 90 ; total terms = 85 ; difference = 5 90 + ( 84 ) 5 = 510 ans e\"" + }, + { + "Answer": 7028, + "Options": "a ) 7028 , b ) 4028 , c ) 3128 , d ) 3256 , e ) 5264", + "Correct": "a", + "Explanation": "( 7000 + 28 ) / 100 * 100 = 7028 answer : a" + }, + { + "Answer": 19, + "Options": "a ) 3 , b ) 6 , c ) 19 , d ) 23 , e ) 24", + "Correct": "c", + "Explanation": "\"2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 20 = > 4 x 2 ^ 2 n = 4 ^ 20 = 2 ^ 40 = > 2 ^ 2 x 2 ^ 2 n = 2 ^ 40 = > 2 ^ ( 2 n + 2 ) = 2 ^ 40 = > 2 n + 2 = 40 = > n = 19 so . answer will be c .\"" + }, + { + "Answer": 129.5, + "Options": "a ) 110.6 , b ) 129.5 , c ) 130.5 , d ) 86 , e ) 88", + "Correct": "b", + "Explanation": "\"diver = ( 8 * 3 ) + 3 = 27 6 * quotient = 27 quotient = 4.5 dividend = ( divisor * quotient ) + remainder dividend = ( 27 * 4.5 ) + 8 = 129.5 b\"" + }, + { + "Answer": 0.5714285714285715, + "Options": "a ) 3 / 7 , b ) 4 / 7 , c ) 5 / 7 , d ) 7 / 11 , e ) 9 / 11", + "Correct": "b", + "Explanation": "let a be the event \u2018 the number on the card drawn is even \u2019 and b be the event \u2018 the number on the card drawn is greater than 3 \u2019 . we have to find p ( a | b ) . now , the sample space of the experiment is s = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 } then a = { 2 , 4 , 6 , 8 , 10 } , b = { 4 , 5 , 6 , 7 , 8 , 9 , 10 } and a n b = { 4 , 6 , 8 , 10 } also p ( a ) = 5 / 2 , p ( b ) = 7 / 10 and p ( a n b ) = 4 / 10 then p ( a | b ) = p ( a n b ) / p ( b ) = ( 4 / 10 ) / ( 7 / 10 ) = 4 / 7 b )" + }, + { + "Answer": 74, + "Options": "a ) 74 , b ) 76 , c ) 78 , d ) 80 , e ) 82", + "Correct": "a", + "Explanation": "\"a score of 58 was 2 standard deviations below the mean - - > 58 = mean - 2 d a score of 98 was 3 standard deviations above the mean - - > 98 = mean + 3 d solving above for mean w = 74 . answer : a .\"" + }, + { + "Answer": 8, + "Options": "a ) 20 , b ) 36 , c ) 8 , d ) 50 , e ) 59", + "Correct": "c", + "Explanation": "\"production during these 5 days = total production in a month - production in first 25 days . = 30 x 43 - 25 x 50 = 40 \u2234 average for last 5 days = 40 / 5 = 8 c\"" + }, + { + "Answer": 1699.9999999999998, + "Options": "a ) 1700 , b ) 2777 , c ) 2889 , d ) 27670 , e ) 2771", + "Correct": "a", + "Explanation": "\"1904 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 1700 . answer : a\"" + }, + { + "Answer": 11, + "Options": "a ) 11 , b ) 15 , c ) 12 , d ) 17 , e ) 19", + "Correct": "a", + "Explanation": "\"a 11 ( x + y ) \u00e2 \u20ac \u201c ( y + z ) = 11 x \u00e2 \u20ac \u201c z = 11\"" + }, + { + "Answer": 36.5, + "Options": "a ) 35.24 , b ) 36.16 , c ) 36.22 , d ) 36.48 , e ) none", + "Correct": "d", + "Explanation": "\"solution correct sum = ( 36 x 50 + 47 - 23 ) = 1824 . \u00e2 \u02c6 \u00b4 correct mean = 1824 / 50 = 36.48 . answer d\"" + }, + { + "Answer": 62, + "Options": "a ) 54 , b ) 58 , c ) 62 , d ) 66 , e ) 70", + "Correct": "c", + "Explanation": "n = 4 k + 1 = 7 j + 3 let ' s start at 1 = 4 ( 0 ) + 1 and keep adding 4 until we find a number in the form 7 j + 3 . 1 , 5 , 9 , 13 , 17 = 7 ( 2 ) + 3 the next such number is 17 + 4 * 7 = 45 . 17 + 45 = 62 the answer is c ." + }, + { + "Answer": 189, + "Options": "a ) 179 , b ) 367 , c ) 189 , d ) 177 , e ) 191", + "Correct": "c", + "Explanation": "\"explanation : total runs scored by the batsman = 60 * 46 = 2760 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2760 \u00e2 \u20ac \u201c 2552 = 208 runs . let the highest score be x , hence the lowest score = x \u00e2 \u20ac \u201c 170 x + ( x - 170 ) = 208 2 x = 378 x = 189 runs answer : c\"" + }, + { + "Answer": 855220, + "Options": "a ) 854542 , b ) 856945 , c ) 758965 , d ) 855220 , e ) 826450", + "Correct": "d", + "Explanation": "\"( 855000 + 220 ) / 900 * 900 = 855000 + 220 = 855220 answer : d\"" + }, + { + "Answer": 5.199999999999999, + "Options": "a ) 6 , b ) 5.2 , c ) 4 , d ) 3 , e ) 2", + "Correct": "b", + "Explanation": "if a + b = 4.6 assuming a and b are positive then a * b < 10 ( they could be either 1,2 , 3,4 ) therefore a * b = c 2 * b = c a + b = 4.6 three simple equations - divide the 1 st / 2 nd - - > a = 2 plug it the 3 rd - - > b = 2.6 - - > c = 5.2 ( answer b )" + }, + { + "Answer": 11000, + "Options": "a ) $ 11500 , b ) $ 11000 , c ) $ 12000 , d ) $ 12100 , e ) $ 12500", + "Correct": "b", + "Explanation": "let t be the tier price , p be total price = 18000 per the given conditions : 0.12 t + 0.09 ( p - t ) = 1950 0.12 t + 0.09 * 18000 - 0.09 t = 1950 0.03 t + 1620 = 1950 0.03 t = 1950 - 1620 = 330 t = 330 / 0.03 = 11000 answer b" + }, + { + "Answer": 3, + "Options": "a ) 3 , b ) 5 , c ) 6 , d ) 10 , e ) 18", + "Correct": "a", + "Explanation": "# of boxes of cookies mary sold = x ann sold 5 times more = 5 x x + 5 x = 18 6 x = 18 x = 18 / 6 = 3 answer : a" + }, + { + "Answer": 19, + "Options": "a ) 12 , b ) 19 , c ) 26 , d ) 33 , e ) 40", + "Correct": "b", + "Explanation": "8 x + 75 = 9 ( x + 7 ) x = 12 + 7 = 19 answer : b" + }, + { + "Answer": 800, + "Options": "a ) s . 80 , b ) s . 85 , c ) s . 90 , d ) s . 800 , e ) s . 120", + "Correct": "d", + "Explanation": "\"9 / 12 = 3 / 4 * 1000 = 750 550 - - - - - - - - - - - - - 200 1 / 4 - - - - - - - - 200 1 - - - - - - - - - ? = > rs . 800 answer : d\"" + }, + { + "Answer": 100, + "Options": "a ) 600 , b ) 100 , c ) 800 , d ) 900 , e ) none", + "Correct": "b", + "Explanation": "solution : let x be the number i chose , then x / 4 \u00e2 \u02c6 \u2019 18 = 7 x / 4 = 25 x = 100 answer b" + }, + { + "Answer": 96, + "Options": "a ) $ 88 , b ) $ 96 , c ) $ 100 , d ) $ 106 , e ) $ 110", + "Correct": "b", + "Explanation": "\"0.8 * ( 1.2 * 100 ) = $ 96 the answer is b .\"" + }, + { + "Answer": 28, + "Options": "a ) 31 , b ) 46 , c ) 28 , d ) 13 , e ) 12", + "Correct": "c", + "Explanation": "\"total score of the batsman in 20 matches = 800 . total score of the batsman in the next 30 matches = 600 . total score of the batsman in the 50 matches = 1400 . average score of the batsman = 1400 / 50 = 28 . answer : c\"" + }, + { + "Answer": 0.19999999999999996, + "Options": "a ) 0.05 , b ) 0.0625 , c ) 0.2 , d ) 0.25 , e ) 0.6", + "Correct": "c", + "Explanation": "index for females = ( 20 - 8 ) / 20 = 3 / 5 = 0.6 index for males = ( 20 - 12 / 20 = 2 / 5 = 0.4 index for females exceeds males by 0.6 - 0.4 = 0.2 answer : c" + }, + { + "Answer": 9, + "Options": "a ) 3 , b ) 4 , c ) 8 , d ) 9 , e ) 13", + "Correct": "d", + "Explanation": "let number of packs of four = f let number of packs of nine = n 4 f + 9 n = 97 now , we need to test for values of n . since sum 97 is odd and 4 f will always be even , n ca n ' t be even . now , we can test for values e = 2 , 4 and 6 4 * 4 + 9 * 9 = 16 + 81 = 97 answer d" + }, + { + "Answer": 1, + "Options": "a ) 4 , b ) 5 , c ) 1 , d ) 2 , e ) 3", + "Correct": "c", + "Explanation": "\"on dividing 531742 by 3 we get the remainder 1 , so 1 should be subtracted c\"" + }, + { + "Answer": 600, + "Options": "a ) rs . 500 , b ) rs . 600 , c ) rs . 650 , d ) rs . 760 , e ) rs . 800", + "Correct": "b", + "Explanation": "first selling price = 110 % - - - - - > x rupees = sold at for rs . 60 / - = 120 % - - - - - > x + 60 rupees ~ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 10 % - - - - - - - - > 60 100 % - - - - - - - > rs . 600 / - option ' b '" + }, + { + "Answer": 28.000000000000004, + "Options": "a ) 0 , b ) 5 , c ) 10 , d ) 15 , e ) 28", + "Correct": "e", + "Explanation": "\"x = \u221a 7 and y also = \u221a 7 applying the function ( \u221a 7 + \u221a 7 ) ^ 2 - ( \u221a 7 - \u221a 7 ) ^ 2 = ( 2 \u221a 7 ) ^ 2 - 0 = 4 x 7 = 28 . note : alternative approach is the entire function is represented as x ^ 2 - y ^ 2 = ( x + y ) ( x - y ) which can be simplified as ( x + y + x - y ) ( x + y - ( x - y ) ) = ( 2 x ) ( 2 y ) = 4 xy . substituting x = \u221a 7 and y = \u221a 7 you get the answer 28 . answer e\"" + }, + { + "Answer": 10.5, + "Options": "a ) 10 , b ) 10.5 , c ) 11 , d ) 11.5 , e ) 12", + "Correct": "b", + "Explanation": "\"the total subtracted is ( 9 + 8 + . . . + 1 ) = ( 9 * 10 ) / 2 = 45 on average , each number will be reduced by 45 / 10 = 4.5 therefore , the overall average will be reduced by 4.5 the answer is b .\"" + }, + { + "Answer": 37.5, + "Options": "a ) 30 % , b ) 32 % , c ) 35 % , d ) 37.5 % , e ) 40 %", + "Correct": "d", + "Explanation": "\"x * y = constt . let x = y = 100 in beginning i . e . x * y = 100 * 100 = 10000 x ( 100 ) - - - becomes - - - > 1.6 x ( 120 ) i . e . 160 * new ' y ' = 10000 i . e . new ' y ' = 10000 / 160 = 62.5 i . e . y decreases from 100 to 62.5 i . e . decrease of 37.5 % answer : option d\"" + }, + { + "Answer": 1600, + "Options": "a ) $ 1500 , b ) $ 1600 , c ) $ 1700 , d ) $ 1800 , e ) $ 1900", + "Correct": "b", + "Explanation": "if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 400 . so 1 / 4 of her savings is $ 400 . so her original savings are 4 times $ 400 = $ 1600 correct answer b" + }, + { + "Answer": 65500, + "Options": "a ) 65500 $ , b ) 125800 $ , c ) 125900 $ , d ) 6500 $ , e ) 122500 $", + "Correct": "a", + "Explanation": "solution c ( 100 ) = 600 * 100 + 5500 = 125500 $ answer a" + }, + { + "Answer": 150, + "Options": "a ) a ) 150 , b ) b ) 140 , c ) c ) 130 , d ) d ) 120 , e ) e ) 110", + "Correct": "a", + "Explanation": "\"a + b + c = 400 a + c = 200 b + c = 350 - - - - - - - - - - - - - - a + b + 2 c = 550 a + b + c = 400 - - - - - - - - - - - - - - - - c = 150 answer : a\"" + }, + { + "Answer": 990, + "Options": "a ) 990 , b ) 99.0 , c ) 9.9 , d ) 0.99 , e ) 0.099", + "Correct": "a", + "Explanation": "\"( 0.0066 ) ( 3.6 ) / ( 0.04 ) ( 0.1 ) ( 0.006 ) = 0.0060 * 360 / 4 * ( 0.1 ) ( 0.006 ) = 0.066 * 90 / 1 * 0.006 = 66 * 90 / 6 = 11 * 90 = 990 answer : a\"" + }, + { + "Answer": 15.999999999999986, + "Options": "a ) 11 , b ) 13 , c ) 14 , d ) 18 , e ) 16", + "Correct": "e", + "Explanation": "required difference = [ 3 \u00bd % of rs . 9600 ] \u2013 [ 3 1 / 3 % of rs . 9600 ] = [ ( 7 / 20 - ( 10 / 3 ) ] % of rs . 9600 = 1 / 6 % of rs . 9600 = rs . [ ( 1 / 6 ) 8 ( 1 / 100 ) * 9600 ] = rs . 16 . answer is e ." + }, + { + "Answer": 900, + "Options": "a ) $ 700 , b ) $ 800 , c ) $ 900 , d ) $ 1100 , e ) $ 1200", + "Correct": "c", + "Explanation": "\"0.1 x = 0.08 ( 2000 - x ) + 38 0.18 x = 198 x = 1100 then the amount invested at 8 % is $ 2000 - $ 1100 = $ 900 the answer is c .\"" + }, + { + "Answer": 74, + "Options": "a ) 12 , b ) 18 , c ) 25 , d ) 74 , e ) 88", + "Correct": "d", + "Explanation": "number of runs scored more to increase the ratio by 1 is 26 - 14 = 12 to raise the average by one ( from 14 to 15 ) , he scored 12 more than the existing average . therefore , to raise the average by five ( from 14 to 19 ) , he should score 12 x 5 = 60 more than the existing average . thus he should score 14 + 60 = 74 . answer d" + }, + { + "Answer": 518.984375, + "Options": "a ) 511 , b ) 519 , c ) 256 , d ) 255 , e ) 1023", + "Correct": "b", + "Explanation": "there are 520 players , only 1 person wins , 519 players lose . in order to lose , you must have lost a game . 519 games . ans - b" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "c", + "Explanation": "( 7 w + 6 ) / 6 + ( 9 w + 8 ) / 2 = 22 or , [ 7 w + 6 + 3 ( 9 w + 8 ) ] / 6 = 22 or , 7 w + 6 + 27 w + 24 = 132 or , 34 w + 30 = 132 or , 34 w = 132 - 30 or , 34 w = 102 or , w = 102 / 34 therefore , w = 3 answer : c" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "c", + "Explanation": "x can have at most 3 prime factors , namely the prime factors 2 and 3 , plus one other . if x had more than this number of prime factors , then ( 6 ) ( x ^ 2 ) would have more than 3 prime factors . the answer is c ." + }, + { + "Answer": 5, + "Options": "a ) 8 % , b ) 10 % , c ) 2 % , d ) 5 % , e ) 6 %", + "Correct": "d", + "Explanation": "\"actual price = 200 + 10 = $ 210 saving = 10 / 210 * 100 = 100 / 21 = 5 % approximately answer is d\"" + }, + { + "Answer": 11, + "Options": "a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14", + "Correct": "b", + "Explanation": "we can determine quickly that total number should range between 49 / 8 < = n < = 49 / 1.5 , so ans should be between 6 and 33 . now solving the expression 8 a + 1.5 b = 49 decreasing 49 in multiple of 8 and checking divisibility of that number by 1.5 . this way we get 2 red giants , 22 white dwarfs we get 49 , but 2 + 22 = 24 and 24 is not an option . next we get 5 red giants and 6 white dwarfs to get 49 , 5 * 8 + 6 * 1.5 = 49 hence total number is 5 + 6 = 11 ans b" + }, + { + "Answer": 900, + "Options": "a ) 900 , b ) 1000 , c ) 1100 , d ) 1200 , e ) 1300", + "Correct": "a", + "Explanation": "a = b + 300 . a = 4 ( b - 600 ) . 4 ( b - 600 ) = b + 300 . 3 b = 2700 . b = 900 . the answer is a ." + }, + { + "Answer": 2700, + "Options": "a ) rs . 3601 , b ) rs . 3618 , c ) rs . 2700 , d ) rs . 3619 , e ) rs . 3610", + "Correct": "c", + "Explanation": "\"manager ' s monthly salary = rs . ( 1700 * 11 - 1600 * 10 ) = rs . 2700 answer : c\"" + }, + { + "Answer": 0.6666666666666666, + "Options": "a ) 2 / 3 , b ) 3 / 8 , c ) 1 / 2 , d ) 5 / 8 , e ) 3 / 4", + "Correct": "a", + "Explanation": "i get 5 / 8 as well 1 to 96 inclusive means we have 48 odd and 48 even integers e o e / 6 = integer , therefore we have 48 / 96 numbers divisible by 6 o e o / 6 = not integer we can not forget multiples of 6 from 1 to 96 we have 16 numbers that are multiple of 8 therefore , 48 / 96 + 16 / 96 = 64 / 96 = 2 / 3 answer : a" + }, + { + "Answer": 10, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10", + "Correct": "e", + "Explanation": "\"the numbers should be of the form 5 c + 3 . the minimum is 3 when c = 0 . the maximum is 48 when c = 9 . there are 10 such numbers . the answer is e .\"" + }, + { + "Answer": 84, + "Options": "a ) 84 , b ) 68 , c ) 85 , d ) 75 , e ) 42", + "Correct": "a", + "Explanation": "explanation total marks of 5 students = ( 65 + 75 + 55 + 72 + 69 ) = 336 required marks = [ ( 70 x 6 ) \u2013 336 ] = ( 420 \u2013 336 ) = 84 answer a" + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14", + "Correct": "a", + "Explanation": "t 7 + t 23 = t 8 + t 15 + t 13 = > a + 6 d + a + 22 d = a + 7 d + a + 14 d + a + 12 d = > a + 5 d = 0 = > t 6 = 0 i . e . 6 th term is zero . answer : a" + }, + { + "Answer": 3, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8", + "Correct": "b", + "Explanation": "\"f 200 / x leaves a reminder 3 then ( 200 - 3 ) i . e . 197 is divisible by x so ( 200 + 197 ) / x leaves a reminder rem ( 200 / x ) + rem ( 197 / x ) = > 3 + 0 = 3 answer : b\"" + }, + { + "Answer": 20, + "Options": "a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 20", + "Correct": "e", + "Explanation": "\"explanation : let the number of persons be n \u00e2 \u02c6 \u00b4 total handshakes = nc 2 = 190 n ( n - 1 ) / 2 = 190 \u00e2 \u02c6 \u00b4 n = 20 answer : option e\"" + }, + { + "Answer": 3, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "d", + "Explanation": "\"remainder will be number / 100 here as the divisor is two digit number = 12 . hence checking for the last two digits = 5 * 7 * 9 = 15 thus remainder = 3 . answer : d\"" + }, + { + "Answer": 66.66666666666667, + "Options": "a ) 8 % , b ) 15 % , c ) 45 % , d ) 52 % , e ) 67 %", + "Correct": "e", + "Explanation": "solution : this is a percent decrease problem . we will use the formula : percent change = ( new \u2013 old ) / old x 100 to calculate the final answer . we first set up the ratios of royalties to sales . the first ratio will be for the first 20 million in sales , and the second ratio will be for the next 108 million in sales . because all of the sales are in millions , we do not have to express all the trailing zeros in our ratios . first 20 million royalties / sales = 5 / 20 = 1 / 4 next 108 million royalties / sales = 9 / 108 = 1 / 12 because each ratio is not an easy number to use , we can simplify each one by multiplying each by the lcm of the two denominators , which is 60 . keep in mind that we are able to do this only because our answer choices are expressed in percents . first 20 million royalties / sales = ( 5 / 20 ) x 12 = 3 next 108 million royalties / sales = 9 / 108 = ( 1 / 12 ) x 12 = 1 we can plug 15 and 5 into our percent change formula : ( new \u2013 old ) / old x 100 [ ( 1 \u2013 3 ) / 3 ] x 100 - 200 / 3 x 100 at this point we can stop and consider the answer choices . since we know that 200 / 3 is just a bit less than \u00bd , we know that - 200 / 3 x 100 is about a 67 % decrease . answer e ." + }, + { + "Answer": 15, + "Options": "a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16", + "Correct": "d", + "Explanation": "w + b + c + 14 + 15 = 12 * 5 = 60 = > w + b + c = 60 - 29 = 31 w + b + c + 29 = 31 + 29 = 60 average = 60 / 4 = 15 answer d" + }, + { + "Answer": 63, + "Options": "a ) 85 , b ) 74 , c ) 67 , d ) 63 , e ) 28", + "Correct": "d", + "Explanation": "\"( 6 * 65 ) + 47 + x > 500 390 + 47 + x > 500 437 + x > 500 = > x > 63 option d\"" + }, + { + "Answer": 82, + "Options": "a ) 80 , b ) 81 , c ) 82 , d ) 83 , e ) 84", + "Correct": "c", + "Explanation": "\"solution : mabel handled 90 transactions anthony handled 10 % more transactions than mabel anthony = 90 + 90 \u00d7 10 % = 90 + 90 \u00d7 0.10 = 90 + 9 = 99 cal handled 2 / 3 rds of the transactions than anthony handled cal = 2 / 3 \u00d7 99 = 66 jade handled 16 more transactions than cal . jade = 66 + 16 = 82 jade handled = 82 transactions . answer : c\"" + }, + { + "Answer": 6, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 11 , e ) 12", + "Correct": "b", + "Explanation": "since - 4 is the least integer in list a , then 7 is the largest integer in that list . thus the range of the positive integers in the list is 7 - 1 = 6 . answer : b ." + }, + { + "Answer": 0.75, + "Options": "a ) 1 / 4 , b ) 3 / 8 , c ) 1 / 2 , d ) 5 / 8 , e ) 3 / 4", + "Correct": "e", + "Explanation": "\"i get 5 / 8 as well 1 to 96 inclusive means we have 48 odd and 48 even integers e o e / 4 = integer , therefore we have 48 / 96 numbers divisible by 8 o e o / 4 = not integer we can not forget multiples of 8 from 1 to 96 we have 24 numbers that are multiple of 4 therefore , 48 / 96 + 24 / 96 = 72 / 96 = 3 / 4 answer : e\"" + }, + { + "Answer": 20, + "Options": "a ) 20 , b ) 21 , c ) 23 , d ) 25 , e ) 26", + "Correct": "a", + "Explanation": "y = 288 * a + 44 = ( 24 * 12 ) * a + 24 + 20 the answer is a ." + }, + { + "Answer": 19, + "Options": "a ) 12 , b ) 15 , c ) 17 , d ) 19 , e ) 21", + "Correct": "d", + "Explanation": "\"the worst case scenario will be if we remove all 17 tablets of medicine b first . the next 2 tablets we remove have to be of medicine a , so to guarantee that at least two tablets of each kind will be taken we should remove minimum of 17 + 2 = 19 tablets . answer : d .\"" + }, + { + "Answer": 5625, + "Options": "a ) 100 , b ) 250 , c ) 750 , d ) 5625 , e ) 5635", + "Correct": "d", + "Explanation": "\"6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 60 * 25 * 1 / 2 = 750 feet ^ 3 of milk must be removed , which equals to 750 * 7.5 = 5625 gallons . answer : d .\"" + }, + { + "Answer": 54000, + "Options": "a ) $ 54,000 , b ) $ 56,000 , c ) $ 64,000 , d ) $ 66,667 , e ) $ 80,000", + "Correct": "a", + "Explanation": "\"equation is correct , so math must be a problem . 0.13 * 40,000 + 0.2 * ( x - 40,000 ) = 8,000 - - > 5,200 + 0.2 x - 8,000 = 8,000 - - > 0.2 x = 10,800 - - > x = 54,000 . answer : a .\"" + }, + { + "Answer": 98, + "Options": "a ) 78 , b ) 82 , c ) 98 , d ) 91 , e ) 85", + "Correct": "c", + "Explanation": "\"correct avg marks = 100 + ( 10 - 50 ) / 20 avg = 100 - 2 = 98 answer is c\"" + }, + { + "Answer": 280, + "Options": "a ) $ 140 , b ) $ 160 , c ) $ 220 , d ) $ 240 , e ) $ 280", + "Correct": "e", + "Explanation": "\"10 $ per week ! an year has 52 weeks . annual charges per year = 52 * 10 = 520 $ 30 $ per month ! an year has 12 months . annual charges per year = 12 * 20 = 240 $ 520 - 240 = 280 ans e\"" + }, + { + "Answer": 36, + "Options": "a ) 3 , b ) 6 , c ) 9 , d ) 36 , e ) 14", + "Correct": "d", + "Explanation": "let the number of each size of jar = wthen 1 / 4 w + 1 / 2 w + w = 21 1 3 / 4 w = 21 w = 12 the total number of jars = 3 w = 36 answer : d" + }, + { + "Answer": 1, + "Options": "a ) 64 / 81 , b ) 8 / 9 , c ) 1 , d ) 9 / 8 , e ) 81 / 64", + "Correct": "c", + "Explanation": "\"if ab \u2260 0 then a and b has two integer sets of pair if a = 9 then b = 8 and if a = - 9 then b = - 8 also in fraction if a = 1 / 8 then b = 1 / 9 any of the pair we check the ratio 8 a / 9 b = 1 answer : c\"" + }, + { + "Answer": 305, + "Options": "a ) 265 , b ) 275 , c ) 285 , d ) 295 , e ) 305", + "Correct": "e", + "Explanation": "\"the number of seats in the theater is 17 + ( 17 + 3 ) + . . . + ( 17 + 27 ) = 10 ( 17 ) + 3 ( 1 + 2 + . . . + 9 ) = 10 ( 17 ) + 3 ( 9 ) ( 10 ) / 2 = 170 + 135 = 305 the answer is e .\"" + }, + { + "Answer": 36, + "Options": "a ) 4 , b ) 36 , c ) 8 , d ) 10 , e ) 12", + "Correct": "b", + "Explanation": "i am getting 12 . e . hope havent done any calculation errors . . approach . . let y = no . of days taken by y to do w widgets . then x will take y + 2 days . 1 / ( y + 2 ) + 1 / y = 5 / 12 ( 5 / 12 is because ( 5 / 4 ) w widgets are done in 3 days . so , x widgets will be done in 12 / 5 days or 5 / 12 th of a widget in a day ) solving , we have y = 4 = > x takes 6 days to doing x widgets . so , he will take 36 days to doing 6 w widgets . answer : b" + }, + { + "Answer": 150, + "Options": "a ) 60 , b ) 90 , c ) 120 , d ) 150 , e ) 240", + "Correct": "d", + "Explanation": "let x be the number of timeshare condos available at playa del mar . then number of timeshare condos available at sunset beach = 3 / 5 x we know , x + 2 / 5 x = 350 hence , x = 250 . so , number of timeshare condos available at playa del mar = 250 the difference between the number of condos available at sunset beach and the number of condos available at playa del mar = x - 2 / 5 x = 3 / 5 x = 3 / 5 ( 250 ) = 150 the correct answer is d" + }, + { + "Answer": 40, + "Options": "a ) 25 litres , b ) 35 litres , c ) 30 litres , d ) 40 litres , e ) none of these", + "Correct": "d", + "Explanation": "x / 5 + 22 = 3 x / 4 = > x = 40 litres answer : d" + }, + { + "Answer": 1632, + "Options": "a ) 1235 , b ) 1456 , c ) 1567 , d ) 1632 , e ) 1635", + "Correct": "d", + "Explanation": "\"let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 30 5 x = 1335 x = 267 large number = 267 + 1365 = 1632 d\"" + }, + { + "Answer": 2, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "b", + "Explanation": "\"28 / 3 = 9 . xxx 86 / 6 = 14 . xxx so we need to find prime numbers between 9 ( exclusive ) - 13 ( inclusive ) there are 2 prime numbers 1113 hence answer will be ( b ) 2 b\"" + }, + { + "Answer": 175, + "Options": "a ) $ 100 , b ) $ 175 , c ) $ 200 , d ) $ 250 , e ) $ 450", + "Correct": "b", + "Explanation": "cavg = average contribution before john cavg * 1.5 = 75 , therefore the average cont is $ 50 before john . if he needs to increase the average contribution by $ 25 , he must put in $ 25 for each of the 4 people . so $ 100 . but , he also has to put in the average for himself ( the fiveth person ) , so add $ 75 . so $ 175 is your answer . answer b" + }, + { + "Answer": 0.8, + "Options": "a ) a ) 1.12 , b ) b ) 1.2 , c ) c ) 1.25 , d ) d ) 0.9 , e ) e ) 0.8", + "Correct": "e", + "Explanation": "\"( x * 5 ) = ( 0.5 * 8 ) x = 4 / 5 x = 0.8 answer = e\"" + }, + { + "Answer": 95, + "Options": "a ) 75 kg , b ) 85 kg , c ) 95 kg , d ) 65 kg , e ) 55 kg", + "Correct": "c", + "Explanation": "\"the total weight increase = ( 8 x 2.5 ) kg = 20 kg weight of new person = ( 75 + 20 ) kg = 95 kg the answer is c .\"" + }, + { + "Answer": 0.0020000000000000018, + "Options": "a ) $ 0.25 , b ) $ 0.12 , c ) $ 0.05 , d ) $ 0.03 , e ) $ 0.002", + "Correct": "e", + "Explanation": "cost per capsule in r is 5.25 / 250 = 0.525 / 25 = 0.021 cost per capsule in t is 2.99 / 130 = 0.023 the difference is 0.002 the answer is e" + }, + { + "Answer": 83, + "Options": "a ) 16 % , b ) 32 % , c ) 83 % , d ) 84 % , e ) 92 %", + "Correct": "c", + "Explanation": "\"this is easiest to solve with a bell - curve histogram . m here is equal to \u00b5 in the gaussian normal distribution and thus m = 50 % of the total population . so , if 66 % is one st . dev , then on either side of m we have 66 / 2 = 33 % . so , 33 % are to the right and left of m ( = 50 % ) . in other words , our value m + d = 50 + 33 = 83 % goingfrom the mean m , to the right of the distributionin the bell shaped histogram . . this means that 83 % of the values are below m + d . like i said , doing it on a bell - curve histogram is much easier to fullygethow this works , or you could apply gmat percentile jargon / theory to it c\"" + }, + { + "Answer": 8, + "Options": "a ) 8 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "a", + "Explanation": "unit digit in the given product = unit digit in 6 * 2 * 1 * 4 = 8 answer is a" + }, + { + "Answer": 190, + "Options": "a ) 191 , b ) 190 , c ) 193 , d ) 212 , e ) 213", + "Correct": "b", + "Explanation": "\"total movies submitted are 760 . as per question we need to take 1 / 4 of 760 to be considered for top 10 movies = 190 approximate the value we 190 . imo option b is the correct answer . . .\"" + }, + { + "Answer": 36, + "Options": "a ) 22 , b ) 65 , c ) 12 , d ) 36 , e ) 10", + "Correct": "d", + "Explanation": "4 * 9 = 36 . answer is d ." + }, + { + "Answer": 125127405, + "Options": "a ) 125177481 , b ) 353654655 , c ) 545463251 , d ) 725117481 , e ) 477899932", + "Correct": "a", + "Explanation": "\"12519 x 9999 = 12519 x ( 10000 - 1 ) = 12519 x 10000 - 12519 x 1 = 125190000 - 12519 = 125177481 a\"" + }, + { + "Answer": 786858, + "Options": "a ) 786845 , b ) 786857 , c ) 786858 , d ) 786859 , e ) 786860", + "Correct": "c", + "Explanation": "\"( 875 233 / 899 ) \u00d7 899 ( 786625 + 233 ) / 899 \u00d7 899 786858 / 899 \u00d7 899 786858 c\"" + }, + { + "Answer": 620, + "Options": "a ) $ 430 , b ) $ 620 , c ) $ 650 , d ) $ 680 , e ) $ 770", + "Correct": "b", + "Explanation": "\"for 100 - 40 - 10 = 50 pages only cost is 5 $ per page for the first time page is typed - 50 * 5 = 250 $ ; for 40 pages the cost is : first time 5 $ + 2 $ of the first revision - 40 * ( 5 + 2 ) = 280 $ ; for 10 pages the cost is : first time 5 $ + 2 $ of the first revision + 2 $ of the second revision - 10 ( 5 + 2 + 2 ) = 90 $ ; total : 250 + 280 + 90 = 620 $ . answer : b .\"" + }, + { + "Answer": 180, + "Options": "a ) 120 , b ) 150 , c ) 180 , d ) 210 , e ) 240", + "Correct": "c", + "Explanation": "they can make a team of 3 men and 2 women . the number of ways to do this is 6 c 3 * 4 c 2 = 20 * 6 = 120 they can make a team of 2 men and 3 women . the number of ways to do this is 6 c 2 * 4 c 3 = 15 * 4 = 60 the total number of distinct groups is 180 . the answer is c ." + }, + { + "Answer": 0.16666666666666663, + "Options": "a ) 1 / 6 , b ) 4 / 7 , c ) 3 / 7 , d ) 16 / 49 , e ) 40 / 49", + "Correct": "a", + "Explanation": "\"the probability of drawing a pink gumball both times is the same . the probability that she drew two blue gumballs = 25 / 36 = ( 5 / 6 ) * ( 5 / 6 ) therefore probability that the next one she draws is pink = 1 / 6 option ( a )\"" + }, + { + "Answer": 23, + "Options": "a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25", + "Correct": "c", + "Explanation": "\"let n be the number of participants . the number of games is nc 2 = n * ( n - 1 ) / 2 = 253 n * ( n - 1 ) = 506 = 23 * 22 ( trial and error ) the answer is c .\"" + }, + { + "Answer": 81, + "Options": "a ) $ 69 , b ) $ 72 , c ) $ 75 , d ) $ 78 , e ) $ 81", + "Correct": "e", + "Explanation": "p = ( 2 / 9 ) * p + 63 ( 7 / 9 ) * p = 63 p = 81 the answer is e ." + }, + { + "Answer": 38, + "Options": "a ) 28 sec , b ) 16 sec , c ) 38 sec , d ) 18 sec , e ) 17 sec", + "Correct": "c", + "Explanation": "\"speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 240 + 140 = 380 m . time taken = 380 / 10 = 38 sec . answer : c\"" + }, + { + "Answer": 540, + "Options": "a ) 540 , b ) 570 , c ) 619 , d ) 649 , e ) 700", + "Correct": "a", + "Explanation": "\"before price increase price = a after 30 % price increase price = a + ( 30 / 100 ) * a = 1.3 a = 351 ( given ) i . e . a = 351 / 1.3 = $ 270 i . e . 2 a = 2 * 270 = 540 answer : option a\"" + }, + { + "Answer": 2375, + "Options": "a ) 2200 , b ) 2295 , c ) 2375 , d ) 2380 , e ) 2385", + "Correct": "c", + "Explanation": "n = ( 4 * 5 - 1 ) * 5 * 5 * 5 = 2375 where 4 cases of first digit { 2,4 , 6,8 } 5 cases of second digit { 0 , 2,4 , 6,8 } 1 case of 22 for two leftmost digit 5 cases of third digit { 1 , 3,5 , 7,9 } 5 cases of fourth digit { 1 , 3,5 , 7,9 } 5 cases of fifth digit { 1 , 3,5 , 7,9 } c" + }, + { + "Answer": 45, + "Options": "a ) 25 , b ) 66 , c ) 77 , d ) 99 , e ) 45", + "Correct": "e", + "Explanation": "\"let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 1081 96 + 225 + 490 + 6 x = 1081 6 x = 270 = > x = 45 . answer : e\"" + }, + { + "Answer": 30, + "Options": "a ) 30 , 10 , b ) 2010 , c ) 3515 , d ) 5117 , e ) 20,17", + "Correct": "a", + "Explanation": "let their ages be x and ( x + 20 ) years ( x - 5 ) * 5 = ( x + 20 - 5 ) after solving this we get x = 10 years the age of elder one = 10 + 20 = 30 years so the present ages are 30 and 10 years answer : a" + }, + { + "Answer": 1.5200000000000102, + "Options": "a ) 0.2 % , b ) 0.8 % , c ) 1.2 % , d ) 1.52 % , e ) 2 %", + "Correct": "d", + "Explanation": "( 100 % + 8 % ) * ( 100 % - 6 % ) = 1.08 * 0.94 = 1.0152 = 101.52 % . the net percentage change in the price of the stock is ( + ) 1.52 % the answer is d" + }, + { + "Answer": 8, + "Options": "a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12", + "Correct": "d", + "Explanation": "there are twice as many girls as boys in the class - - > g = 2 b . each girl writes 3 more letters than each boy - - > boys write x letters , girls write x + 3 letters . boys write 24 letters - - > bx = 24 . girls write 90 - 24 = 66 letters - - > ( 2 b ) ( x + 3 ) = 66 - - > 2 bx + 6 b = 66 - - > 2 * 24 + 6 b = 66 - - > b = 3 . bx = 24 - - > 3 x = 24 - - > x = 8 . answer : d ." + }, + { + "Answer": 4, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "b", + "Explanation": "9 - 3 * 3 6 - 2 * 3 3 - 1 * 3 hence max of 3 ^ 4 is allowed . imo b ." + }, + { + "Answer": 46, + "Options": "a ) 35 , b ) 37 , c ) 46 , d ) 48 , e ) 50", + "Correct": "c", + "Explanation": "sum of all the 13 results = 13 * 60 = 780 sum of the first 7 of them = 7 * 57 = 399 sum of the last 7 of them = 7 * 61 = 427 so , the 8 th number = 427 + 399 - 780 = 46 . c" + }, + { + "Answer": 44, + "Options": "a ) 22 , b ) 33 , c ) 44 , d ) 66 , e ) 99", + "Correct": "c", + "Explanation": "\"x / ( 11 p ) = even prime number x = even prime number * 11 p least value of x = lowest even prime number * 11 * lowest value of p = 2 * 11 * 2 = 44 answer c\"" + }, + { + "Answer": 4263, + "Options": "a ) 4264 , b ) 2776 , c ) 4400 , d ) 2871 , e ) 881", + "Correct": "a", + "Explanation": "\"x * ( 95 / 100 ) * ( 85 / 100 ) = 3443 x = 4264 answer : a\"" + }, + { + "Answer": 48, + "Options": "a ) 25 , b ) 48 , c ) 64 , d ) 80 , e ) 96", + "Correct": "b", + "Explanation": "\"7 / 8 x - 3 / 4 x = 6 galls 1 / 8 * x = 6 gallons x = 48 gallons answer b\"" + }, + { + "Answer": 65, + "Options": "a ) 86.5 kg , b ) 64.5 kg , c ) 46.5 kg , d ) 26.5 kg , e ) 16.5 kg", + "Correct": "b", + "Explanation": "\"let arun ' s weight be x kg . according to arun , 63 < x < 72 . according to arun ' s brother , 60 < x < 70 . according to arun ' s mother , x < 66 . the values satisfying all the above conditions are 64 and 65 . required average = ( 64 + 65 ) / 2 = 64.5 kg answer : b\"" + }, + { + "Answer": 1070, + "Options": "a ) 347 , b ) 987 , c ) 1070 , d ) 1371 , e ) 1667", + "Correct": "c", + "Explanation": "\"let the costs of each kg of mangos and each kg of rice be $ a and $ r respectively . 10 a = 24 r and 6 * 25 = 2 r a = 12 / 5 r and r = 75 a = 180 required total cost = 4 * 180 + 3 * 75 + 5 * 25 = 720 + 225 + 125 = $ 1070 c\"" + }, + { + "Answer": 9, + "Options": "a ) 12 , b ) 16 , c ) 18 , d ) 9 , e ) 12", + "Correct": "d", + "Explanation": "\"explanation : suppose the boy got x sums right and 2 x sums wrong . then , x + 2 x = 27 3 x = 27 x = 9 . answer : d\"" + }, + { + "Answer": 98.56, + "Options": "a ) rs . 48 , b ) rs . 98.56 , c ) rs . 66.56 , d ) rs . 66.58 , e ) none of these", + "Correct": "b", + "Explanation": "explanation : given that simple interest for 2 years is rs . 800 i . e . , simple interest for 1 st year is rs . 400 and simple interest for 2 nd year is also rs . 400 compound interest for 1 st year will be 400 and compound interest for 2 nd year will be 832 - 400 = 432 you can see that compound interest for 2 nd year is more than simple interest for 2 nd year by 432 - 400 = rs . 32 i . e , rs . 32 is the interest obtained for rs . 400 for 1 year rate , r = 100 \u00d7 si / pt = ( 100 \u00d7 32 ) / ( 400 \u00d7 1 ) = 8 % difference between compound and simple interest for the 3 rd year = simple interest obtained for rs . 832 = prt / 100 = ( 832 \u00d7 8 \u00d7 1 ) / 100 = rs . 66.56 total difference between the compound and simple interest for 3 years = 32 + 66.56 = rs . 98.56 answer : option b" + }, + { + "Answer": 128, + "Options": "a ) 67 , b ) 128 , c ) 191 , d ) 197 , e ) 260", + "Correct": "b", + "Explanation": "a prime number is a number that has only two factors : 1 and itself . therefore , a prime number is divisible by two numbers only . let ' s list the numbers from 61 to 69 . 61 , 62 , 63 , 64 , 65 , 66 , 67 , 68 , 69 immediately we can eliminate the even numbers because they are divisible by 2 and thus are not prime . we are now left with : 61 , 63 , 65 , 67 , 69 we can next eliminate 65 because 65 is a multiple of 5 . we are now left with 61 , 63 , 67 , 69 . to eliminate any remaining values , we would look at those that are multiples of 3 . if you don \u2019 t know an easy way to do this , just start with a number that is an obvious multiple of 3 , such as 60 , and then keep adding 3 . we see that 60 , 63 , 66 , 69 are all multiples of 3 and therefore are not prime . thus , we can eliminate 63 and 69 from the list because they are not prime . finally , we are left with 61 and 67 , and we must determine whether they are divisible by 7 . they are not , and therefore they must be both prime . thus , the sum q of 61 and 67 is 128 . answer b ." + }, + { + "Answer": 0.33333333333333337, + "Options": "a ) 1 / 2 , b ) 1 , c ) 1 / 3 , d ) 3 / 4 , e ) 2", + "Correct": "c", + "Explanation": "\"sol . required probability = pg . ) x p ( b ) = ( 1 \u2014 d x ( 1 \u2014 i ) = : x 1 = 1 / 3 ans . ( c )\"" + }, + { + "Answer": 300000, + "Options": "a ) $ 180,000 , b ) $ 202,000 , c ) $ 220,000 , d ) $ 300,000 , e ) $ 2 , 200,000", + "Correct": "d", + "Explanation": "answer : d , ( with different approach ) : the 200 paid is 0.2 % of the additional amount above 200,000 . let it be x now 0.2 % of x = 200 therefore x = 100,000 total = 200,000 + x = 300,000" + }, + { + "Answer": 3, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "b", + "Explanation": "25 ^ 5 \u00d7 5 ^ ( - 1 ) = ( 125 ) ^ x ( 5 ^ 2 ) ^ 5 \u00d7 5 ^ ( - 1 ) = 5 ^ 3 x 5 ^ 10 x 5 ^ ( - 1 ) = 5 ^ 3 x ; since all of the bases are the same now , we can equate the exponents in the next step 10 - 1 = 3 x 9 = 3 x x = 3 ans . b ) 3" + }, + { + "Answer": 77, + "Options": "a ) 11 , b ) 22 , c ) 77 , d ) 33 , e ) 88", + "Correct": "c", + "Explanation": "\"add the numbers of highlighters . 24 + 28 + 25 = 77 . answer is c .\"" + }, + { + "Answer": 0.7931034482758621, + "Options": "a ) 17 / 23 , b ) 23 / 29 , c ) 29 / 35 , d ) 31 / 37 , e ) 33 / 39", + "Correct": "b", + "Explanation": "\"let the numerator be x . then the denominator is x + 6 . x + 1 / x + 7 = 4 / 5 . 5 x + 5 = 4 x + 28 . x = 23 . the original fraction is 23 / 29 . the answer is b .\"" + }, + { + "Answer": 80, + "Options": "a ) 80 , b ) 81 , c ) 82 , d ) 83 , e ) 84", + "Correct": "a", + "Explanation": "explanation : if n = 1 , then the set t 1 = { 1 , 23 , 45 } , and it does not have 6 or any multiples . n = 2 to n = 6 has 6 in the set . n = 7 , has the set t 7 = { 7 , 89 , 1011 } , and no 6 or multiples . so 1 in every 6 members do not have 6 or multiples of 6 . so , till n = 96 , there are 16 sets of \u201c 6 members \u201d ( 16 * 6 = 96 ) and 16 sets do not have 6 or its multiples , while the remaining 80 sets have . answer : a" + }, + { + "Answer": 1453.3333333333335, + "Options": "a ) 1628.4 , b ) 1534 , c ) 1453 , d ) 1496 , e ) none of these", + "Correct": "c", + "Explanation": "\"solution : let average expenditure of 20 people be x . then , 20 x = 12 * 70 + 8 * ( x + 4 ) ; or , 20 x = 12 * 70 + 8 x + 32 ; or , x = 72.667 ; so , total money spent = 72.67 * 20 = rs . 1453.4 . answer : option c\"" + }, + { + "Answer": 46080, + "Options": "a ) 32256 , b ) 24000 , c ) 44936 , d ) 46080 , e ) none", + "Correct": "d", + "Explanation": "\"answer \u2235 50 % of p = 23040 \u2234 p = ( 23040 x 100 ) / 50 = 46080 correct option : d\"" + }, + { + "Answer": 24, + "Options": "a ) 2 , b ) 8 , c ) 15 , d ) 24 , e ) 35", + "Correct": "d", + "Explanation": "\"solution - simply substitute 3 and 4 in equation in the place of a and b respectively . 3 # 4 = 3 * 4 - 4 + 4 ^ 2 = 12 - 4 + 16 = 24 . ans d\"" + }, + { + "Answer": 16, + "Options": "a ) 16 , b ) 8 , c ) 9 , d ) 10 , e ) 11", + "Correct": "a", + "Explanation": "\"let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 42 5 x = 40 = > x = 8 hence , b ' s age = 2 x = 16 years . answer : a\"" + }, + { + "Answer": 22000, + "Options": "a ) $ 27000 , b ) $ 22000 , c ) $ 33000 , d ) $ 16000 , e ) $ 43000", + "Correct": "b", + "Explanation": "let the lowest bonus be x . therefore , highest bonus is x + 20000 . now bonus of each employee is increased by 10 % . therefore the bonus will remain arranged in the same order as before . or lowest bonus = 1.1 x and highest = 1.1 * ( x + 20000 ) or range = highest - lowest = 1.1 * ( x + 20000 ) - 1.1 x = 22000 , hence , b" + }, + { + "Answer": 53, + "Options": "a ) 36 , b ) 40 , c ) 44 , d ) 48 , e ) 53", + "Correct": "e", + "Explanation": "\"for 40 hrs = 40 * 16 = 640 excess = 1004 - 640 = 364 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 364 / 28 = 13 total hrs = 40 + 13 = 53 answer e 53\"" + }, + { + "Answer": 19, + "Options": "a ) 3 , b ) 6 , c ) 14 , d ) 19 , e ) 20", + "Correct": "d", + "Explanation": "\"the objective here is that 70 % of the fruit in the box should be apples . now , there are 14 apples at start and there is no talk of removing any apples , so number of apples should remain 14 and they should constitute 70 % of total fruit , so total fruit = 14 / 0.7 = 20 so we should have 20 - 14 = 6 oranges . right now , there are 25 oranges , so to get to 6 oranges , we should remove 25 - 6 = 19 oranges . answer d\"" + }, + { + "Answer": 2, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "b", + "Explanation": "\"13 / 3 = 4 . xxx 83 / 6 = 13 . xxx so we need to find prime numbers between 4 ( exclusive ) - 12 ( inclusive ) there are 2 prime numbers 7 11 hence answer will be ( b ) 2 b\"" + }, + { + "Answer": 786, + "Options": "a ) 586 , b ) 766 , c ) 796 , d ) 786 , e ) 686", + "Correct": "d", + "Explanation": "\"explanation : 18 * 43 + 12 = 786 answer : d\"" + }, + { + "Answer": 0.8888888888888888, + "Options": "a ) 8 / 9 , b ) 11 / 12 , c ) 8 / 13 , d ) 11 / 13 , e ) 12 / 13", + "Correct": "a", + "Explanation": "we can take some easy numbers and make calculations simpler . let r ( rex ' s income ) = 100 q ( niall ' s income ) = 40 % r = 40 s ( sam ' s income ) = 75 % q = ( 3 / 4 ) * 40 = 30 now , if rex gives 40 % to niall - - > q = 40 + 40 = 80 60 % given to sam - - > s = 30 + 60 = 90 the ratio is : q / s = 80 / 90 = 8 / 9 = a" + }, + { + "Answer": 500, + "Options": "a ) 50 , b ) 100 , c ) 250 , d ) 450 , e ) 500", + "Correct": "e", + "Explanation": "2 a * 4 b = 10 * 10 = 100 8 ab = 100 i . e . 40 ab = 500 answer : option e" + }, + { + "Answer": 20, + "Options": "a ) s . 17 , b ) s . 18 , c ) s . 12 , d ) s . 20 , e ) s . 10", + "Correct": "d", + "Explanation": "\"average price per book = ( 1200 + 480 ) / ( 52 + 32 ) = 1680 / 84 = rs . 20 answer : d\"" + }, + { + "Answer": 208, + "Options": "a ) 26 , b ) 39 , c ) 42 , d ) 208 , e ) 156", + "Correct": "d", + "Explanation": "\"here 156 has three two ' s two three ' s and one 13 rest of them must be in w so w = 13 * 4 * 4 = 208 smash d\"" + }, + { + "Answer": 7, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "e", + "Explanation": "\"3 < x < 6 < y < 11 ; 3 < x y < 11 3 + y < x + 11 y - x < 8 . positive integer difference is 7 ( for example y = 10.5 and x = 3.5 ) answer : e .\"" + }, + { + "Answer": 5, + "Options": "a ) a ) 20 , b ) b ) 25 , c ) c ) 15 , d ) d ) 22 , e ) e ) 5", + "Correct": "e", + "Explanation": "chris present age = x after 20 years = x + 20 5 years back = x - 5 x + 20 = 5 ( x - 5 ) x = 5 answer is e" + }, + { + "Answer": 115, + "Options": "a ) a ) 110 , b ) b ) 122 , c ) c ) 120 , d ) d ) 115 , e ) e ) 145", + "Correct": "d", + "Explanation": "\"explanation : average of new numbers = 23 * 5 = 115 answer : option d\"" + }, + { + "Answer": 6.800000000000001, + "Options": "a ) $ 6.80 , b ) $ 6.50 , c ) $ 16.80 , d ) $ 6.85 , e ) $ 61.80", + "Correct": "a", + "Explanation": "\"in 4 miles , initial 1 / 5 mile charge is $ 3 rest of the distance = 4 - ( 1 / 5 ) = 19 / 5 rest of the distance charge = 19 ( 0.2 ) = $ 3.8 ( as the charge is 0.2 for every 1 / 5 mile ) = > total charge for 4 miles = 3 + 3.8 = 6.8 answer is a\"" + }, + { + "Answer": 18, + "Options": "a ) 14 years , b ) 12 years , c ) 56 years , d ) 66 years , e ) 18 years", + "Correct": "e", + "Explanation": "\"given that a + b = 182 + b + c = > a \u00e2 \u20ac \u201c c = 18 + b \u00e2 \u20ac \u201c b = 18 = > c is younger than a by 18 years answer : e\"" + }, + { + "Answer": 16, + "Options": "a ) 16 , b ) 127 , c ) 235 , d ) 305 , e ) 505", + "Correct": "a", + "Explanation": "\"explanation : required number = h . c . f . of ( 1657 - 9 ) and ( 2037 - 5 ) = h . c . f . of 1648 and 2032 = 16 . answer : a\"" + }, + { + "Answer": 1199.9999999999998, + "Options": "a ) 1200 , b ) 3000 , c ) 1000 , d ) 3600 , e ) 2400", + "Correct": "a", + "Explanation": "\"let the additional invested amount for 8 % interest be x ; equation will be ; 2400 + 0.05 * 2400 + x + 0.08 x = 2400 + x + 0.06 ( 2400 + x ) 0.05 * 2400 + 0.08 x = 0.06 x + 0.06 * 2400 0.02 x = 2400 ( 0.06 - 0.05 ) x = 2400 * 0.01 / 0.02 = 1200 ans : ` ` a ' '\"" + }, + { + "Answer": 4, + "Options": "a ) 2 , b ) 4 , c ) 8 , d ) 12 , e ) 14", + "Correct": "b", + "Explanation": "explanation : let the ten digit be x , unit digit is y . then ( 10 x + y ) - ( 10 y + x ) = 36 = > 9 x - 9 y = 36 = > x - y = 4 . option b" + }, + { + "Answer": 29, + "Options": "a ) 25 , b ) 27 , c ) 30 , d ) 29 , e ) 42", + "Correct": "d", + "Explanation": "\"average in 10 matches = ( 6 * 27 + 4 * 32 ) / 6 + 4 = 162 + 128 / 10 = 290 / 10 = 29 answer is d\"" + }, + { + "Answer": 24, + "Options": "a ) 24 , b ) 33 , c ) 55 , d ) 77 , e ) 88", + "Correct": "a", + "Explanation": "let f = pure fuji , g = pure gala and c - cross pollinated . c = 10 % of x where x is total trees . c = . 1 x also 3 x / 4 = f and c + f = 136 = > . 1 x + 3 / 4 x = 136 = > x = 160 160 - 136 = pure gala = 24 . a" + }, + { + "Answer": 0.17777777777777776, + "Options": "a ) 1 / 6 , b ) 2 / 15 , c ) 3 / 20 , d ) 7 / 30 , e ) 8 / 45", + "Correct": "e", + "Explanation": "\"males who did not arrive on time are 1 / 5 * 1 / 3 = 1 / 15 of the attendees . females who did not arrive on time are 1 / 6 * 2 / 3 = 1 / 9 of the attendees . the fraction of all attendees who did not arrive on time is 1 / 15 + 1 / 9 = 8 / 45 the answer is e .\"" + }, + { + "Answer": 5, + "Options": "a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 11", + "Correct": "b", + "Explanation": "\"the smallest amount that the company can spend is the lcm of 300 and 200 , which is 600 for each , which is total 1200 . the number of 1 st type of computers which costing $ 300 = 600 / 300 = 2 . the number of 2 nd type of computers which costing $ 200 = 600 / 200 = 3 . total = 2 + 3 = 5 answer is b .\"" + }, + { + "Answer": 3, + "Options": "a ) 6 , b ) 1 , c ) 3 , d ) 8 , e ) 7", + "Correct": "c", + "Explanation": "\"every prime number greater than 3 can be written 6 n + 1 or 6 n - 1 . if p = 6 n + 1 , then p ^ 2 + 14 = 36 n ^ 2 + 12 n + 1 + 14 = 36 n ^ 2 + 12 n + 12 + 3 if p = 6 n - 1 , then p ^ 2 + 14 = 36 n ^ 2 - 12 n + 1 + 14 = 36 n ^ 2 - 12 n + 12 + 3 when divided by 12 , it must leave a remainder of 3 . the answer is c .\"" + }, + { + "Answer": 6, + "Options": "a ) 9 , b ) 12 , c ) 20 , d ) 10 , e ) 0", + "Correct": "d", + "Explanation": "d" + }, + { + "Answer": 22, + "Options": "a ) 22 , b ) 24 , c ) 26 , d ) 20 , e ) 28", + "Correct": "a", + "Explanation": "\"explanation : let number of hens = h and number of cows = c number of heads = 42 = > h + c = 42 - - - ( equation 1 ) number of feet = 124 = > 2 h + 4 c = 124 = > h + 2 c = 62 - - - ( equation 2 ) ( equation 2 ) - ( equation 1 ) gives 2 c - c = 62 - 42 = > c = 20 substituting the value of c in equation 1 , we get h + 22 = 42 = > h = 42 - 20 = 22 i . e . , number of hens = 22 answer : a\"" + }, + { + "Answer": 1644, + "Options": "a ) 1235 , b ) 1345 , c ) 1678 , d ) 1767 , e ) 1659", + "Correct": "e", + "Explanation": "\"let the smaller number be x . then larger number = ( x + 1385 ) . x + 1385 = 6 x + 15 5 x = 1370 x = 274 large number = 274 + 1385 = 1659 e\"" + }, + { + "Answer": 1.7999999999999998, + "Options": "a ) $ 1.80 , b ) $ 2.00 , c ) $ 2.40 , d ) $ 2.70 , e ) $ 3.00", + "Correct": "a", + "Explanation": "the price in 1970 was 150 percent of its price in 1960 , means that the percent increase was 50 % from 1960 to 1970 ( and from 1970 to 1980 ) . therefore the price in 1980 = $ 1.2 * 1.5 = $ 1.8 . answer : a ." + }, + { + "Answer": 14, + "Options": "a ) 7 , b ) 9 , c ) 8 , d ) 14 , e ) 10", + "Correct": "d", + "Explanation": "explanation : let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 37 \u21d2 5 x = 35 \u21d2 x = 7 . hence , b ' s age = 2 x = 14 years . answer : d" + }, + { + "Answer": 6, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9", + "Correct": "b", + "Explanation": "let ct + t + c = x add 1 on both sides : ct + t + c + 1 = x + 1 t ( c + 1 ) + c + 1 = x + 1 ( c + 1 ) ( t + 1 ) = x + 1 minimum value of ( c + 1 ) = 2 minimum value of ( t + 1 ) = 2 hence x + 1 can not be prime substitute x from the given options : 6 + 1 = 7 - - > prime - - > ct + t + s can not be 6 answer : b" + }, + { + "Answer": 56, + "Options": "a ) 56 , b ) 18 , c ) 24 , d ) 19 , e ) 12", + "Correct": "a", + "Explanation": "\"total time taken = x / 40 + 2 x / 20 hours = 5 x / 40 = x / 8 hours average speed = 7 x / ( x / 8 ) = 56 kmph answer : a\"" + }, + { + "Answer": 28, + "Options": "a ) 36 , b ) 35 , c ) 28 , d ) 33 , e ) 21", + "Correct": "c", + "Explanation": "\"explanation : total of the 6 digits - 6 * 16 = 96 total of the 4 digits - 4 * 10 = 40 total of the remaining 2 digits - 96 - 40 = 56 average of the remaining 2 numbers = 56 / 2 = 28 answer : c\"" + }, + { + "Answer": 665, + "Options": "a ) 665 , b ) 376 , c ) 998 , d ) 1277 , e ) 1991", + "Correct": "a", + "Explanation": "explanation : let the total score be x . ( x + 92 - 85 ) / 8 = 84 . so , x + 7 = 672 = > x = 665 . answer : a ) 665" + }, + { + "Answer": 1638, + "Options": "a ) 1245 , b ) 1345 , c ) 1455 , d ) 1577 , e ) 1653", + "Correct": "e", + "Explanation": "\"let the smaller number be x . then larger number = ( x + 1380 ) . x + 1380 = 6 x + 15 5 x = 1365 x = 273 large number = 273 + 1380 = 1653 e\"" + }, + { + "Answer": 13, + "Options": "a ) 5 , b ) 8 , c ) 10 , d ) 13 , e ) 17", + "Correct": "d", + "Explanation": "official solution : ( b ) we know that a # b = 100 and a # b = 4 a \u00b2 + 4 b \u00b2 + 8 ab . so 4 a \u00b2 + 4 b \u00b2 + 8 ab = 100 we can see that 4 a \u00b2 + 4 b \u00b2 + 8 ab is a well - known formula for ( 2 a + 2 b ) \u00b2 . therefore ( 2 a + 2 b ) \u00b2 = 100 . ( 2 a + 2 b ) is non - negative number , since both a and b are non - negative numbers . so we can conclude that 2 ( a + b ) = 10 . ( a + b ) + 8 = 10 / 2 + 8 = 13 . the correct answer is d" + }, + { + "Answer": 30, + "Options": "a ) a ) 25 , b ) b ) 34 , c ) c ) 50 , d ) d ) 67 , e ) e ) 30", + "Correct": "e", + "Explanation": "\"its e . total juice rquired = 240 * 6 = 1440 ounce 12 ounce concentate makes = 12 * 4 = 48 ounce juice total cans required = 1440 / 48 = 30 . answer e\"" + }, + { + "Answer": 3200, + "Options": "a ) 4038 , b ) 8076 , c ) 3200 , d ) 4845.6 , e ) none of these", + "Correct": "c", + "Explanation": "\"\u2235 amount , he have spent in 1 month on clothes transport = amount spent on saving per month \u2235 amount , spent on clothes and transport = 38400 \u2044 12 = 3200 answer c\"" + }, + { + "Answer": 660, + "Options": "a ) 660 , b ) 700 , c ) 800 , d ) 900 , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : let p ' s capital = p , q ' s capital = q and r ' s capital = r then 4 p = 6 q = 10 r = > 2 p = 3 q = 5 r = > q = 2 p / 3 r = 2 p / 5 p : q : r = p : 2 p / 3 : 2 p / 5 = 15 : 10 : 6 r ' s share = 3410 * ( 6 / 31 ) = 110 * 6 = 660 . answer : option a\"" + }, + { + "Answer": 6, + "Options": "a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12", + "Correct": "b", + "Explanation": "let y produce w widgets in y days hence , in 1 day y will produce w / y widgets . also , x will produce w widgets in y + 2 days ( given , x takes two more days ) hence , in 1 day x will produce w / y + 2 widgets . hence together x and y in 1 day will produce { w / y + w / y + 2 } widgets . together x and y in 3 days will produce = 3 * [ { w / y + w / y + 2 } ] widgets . it is given that in 3 days together they produce ( 5 / 4 ) w widgets . equating , 3 * [ { w / y + w / y + 2 } ] = ( 5 / 4 ) w take out w common and move 3 to denominator of rhs w { 1 / y + 1 / ( y + 2 ) } = ( 5 / 12 ) w canceling w from both sides { 1 / y + 1 / ( y + 2 ) } = 5 / 12 2 y + 2 / y ( y + 2 ) = 5 / 12 24 y + 24 = 5 y ^ 2 + 10 y 5 y ^ 2 - 14 y - 24 = 0 5 y ^ 2 - 20 y + 6 y - 24 = 0 5 y ( y - 4 ) + 6 ( y - 4 ) = 0 ( 5 y + 6 ) + ( y - 4 ) = 0 y = - 6 / 5 or y = 4 discarding y = - 6 / 5 as no of days can not be negative y = 4 hence it takes y , 4 days to produce w widgets . therefore , it will take x ( 4 + 2 ) = 6 days to produce w widgets . hence it will take x 1 * 6 = 6 days to produce 1 w widgets . answer : b" + }, + { + "Answer": 100, + "Options": "a ) 20 coins , b ) 30 coins , c ) 50 coins , d ) 100 coins , e ) none of these", + "Correct": "d", + "Explanation": "\"let number of each type of coin = x . then , 1 \u00d7 x + . 50 \u00d7 x + . 25 x = 175 \u21d2 1.75 x = 175 \u21d2 x = 100 coins answer d\"" + }, + { + "Answer": 8.450000000000001, + "Options": "a ) $ 6.45 , b ) $ 8.35 , c ) $ 8.75 , d ) $ 8.85 , e ) $ 8.45", + "Correct": "e", + "Explanation": "john spent and gave to his two friends a total of 3.25 + 2.20 + 2.20 = $ 7.65 money left 16.10 - 7.65 = $ 8.45 answer : e" + }, + { + "Answer": 5, + "Options": "a ) 2 , b ) 6 , c ) 7 , d ) 8 , e ) 5", + "Correct": "e", + "Explanation": "let amount of 10 $ be x . then amount of 5 $ be 2 x . now 5 * 2 x + 10 * x = 100 . thus x = 5 . answer : e" + }, + { + "Answer": 0.5, + "Options": "a ) 0.05 , b ) 0.0625 , c ) 0.5 , d ) 0.25 , e ) 0.6", + "Correct": "c", + "Explanation": "\"index for females = ( 20 - 5 ) / 20 = 3 / 4 = 0.75 index for males = ( 20 - 15 / 20 = 1 / 4 = 0.25 index for females exceeds males by 0.75 - 0.25 = 0.5 answer : c\"" + }, + { + "Answer": 33.33333333333333, + "Options": "a ) 50.12 % , b ) 52.66 % , c ) 56.33 % , d ) 33.33 % , e ) 74.12 %", + "Correct": "d", + "Explanation": "say a 100 families existed in 1998 then the number of families owning a computer in 1998 - 30 number of families owning computer in 2002 = 30 * 120 / 100 = 36 number of families in 2002 = 108 the percentage = 36 / 108 * 100 = 33.33 % . option : d" + }, + { + "Answer": 40, + "Options": "a ) 40 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 80 %", + "Correct": "a", + "Explanation": "\"soln : - can be reduced to y / 10 + 3 y / 10 = 2 y / 5 = 40 % answer : a\"" + }, + { + "Answer": 36.1, + "Options": "a ) 36.7 , b ) 36.1 , c ) 36.5 , d ) 36.9 , e ) 36.3", + "Correct": "e", + "Explanation": "\"correct sum = ( 36 * 50 + 58 - 43 ) = 1815 . correct mean = 1815 / 50 = 36.3 answer : e\"" + }, + { + "Answer": 200, + "Options": "a ) 240 , b ) 300 , c ) 200 , d ) 400 , e ) 480", + "Correct": "c", + "Explanation": "{ total } = { retirees } + { bridge players } - { both } + { neither } x = 5 / 20 * x + x / 2 - 3 / 20 * x + 120 20 x = 5 x + 10 x - 3 x + 120 * 20 ( multiply by 20 ) 12 x = 120 * 20 x = 200 . answer : c" + }, + { + "Answer": 50, + "Options": "a ) 40 , b ) 30 , c ) 25 , d ) 50 , e ) none of these .", + "Correct": "d", + "Explanation": "let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 80 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 80 + 20 ) / 2 = 50 . answer : d" + }, + { + "Answer": 2011, + "Options": "a ) 2010 . , b ) 2011 . , c ) 2012 . , d ) 2013 . , e ) 2014 .", + "Correct": "b", + "Explanation": "\"the cost of commodity x increases by 10 cents per year relative to commodity y . the price of x must gain 20 + 80 = $ 1.00 cents on commodity y , which will take 10 years . the answer is b .\"" + }, + { + "Answer": 25, + "Options": "a ) 15 , b ) 25 , c ) 35 , d ) 45 , e ) 55", + "Correct": "b", + "Explanation": "\"a 1 = 120 / 3 = 40 a 2 = a 1 - 5 = 35 sum of second list = 35 * 3 = 105 therefore the number = 105 - 80 = 25 answer : b\"" + }, + { + "Answer": 84, + "Options": "a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %", + "Correct": "d", + "Explanation": "d the prompt says that 68 % of the population lies between m - d and m + d . thus , 32 % of the population is less than m - d or greater than m + d . since the population is symmetric , half of this 32 % is less than m - d and half is greater than m + d . thus , e = ( 68 + 16 ) % or ( 100 - 16 ) % of the population is less than m + d . d" + }, + { + "Answer": 650, + "Options": "a ) 600 , b ) 625 , c ) 650 , d ) 675 , e ) 700", + "Correct": "c", + "Explanation": "p = q + 1150 . p = 4 ( q - 200 ) . 4 ( q - 200 ) = q + 1150 . 3 q = 1950 . q = 650 . the answer is c ." + }, + { + "Answer": 81, + "Options": "a ) 78 , b ) 79 , c ) 80 , d ) 81 , e ) 82", + "Correct": "d", + "Explanation": "if ramesh attempts ' x ' questions correct and ' y ' questions wrong , then x + y = 108 - - - ( i ) & x - ( 1 / 3 ) y = 0 - - - ( ii ) on solving x = 27 , y = 81 answer : d" + }, + { + "Answer": 14999.99999999999, + "Options": "a ) 15000 , b ) 25000 , c ) 7500 , d ) 14500 , e ) none of these", + "Correct": "a", + "Explanation": "let the amount be x . from the question , x \u00d7 14 \u00d7 6 / 1200 \u2212 x \u00d7 8 \u00d7 8 / 1200 = 250 \u2234 x = 15000 answer a" + }, + { + "Answer": 8, + "Options": "a ) 15 , b ) 12 , c ) 8 , d ) 6 , e ) 4", + "Correct": "c", + "Explanation": "we can first set up our ratio using variable multipliers . we are given that a fruit - salad mixture consists of apples , peaches , and grapes , in the ratio of 6 : 5 : 2 , respectively , by weight . thus , we can say : apples : peaches : grapes = 6 x : 5 x : 2 x we are given that 39 pounds of the mixture is prepared so we can set up the following question and determine a value for x : 9 x + 6 x + 5 x = 40 20 x = 40 x = 2 now we can determine the number of pounds of apples and of grapes . pounds of grapes = ( 5 ) ( 2 ) = 10 pounds of apples = ( 9 ) ( 2 ) = 18 thus we know that there are 18 \u2013 10 = 8 more pounds of apples than grapes . answer is c ." + }, + { + "Answer": 20, + "Options": "a ) 18 , b ) 20 , c ) 24 , d ) 30 , e ) 32", + "Correct": "b", + "Explanation": "\"solution average = ( 10 + 15 + 20 + 25 + 30 / 5 ) = 100 / 5 = 20 . answer b\"" + }, + { + "Answer": 32, + "Options": "a ) 0.32 , b ) 0.44 , c ) 32 , d ) 44 , e ) 55", + "Correct": "c", + "Explanation": "\"a dozen eggs cost as much as a pound of rice - - > 12 eggs = 1 pound of rice = 24 cents ; a half - liter of kerosene costs as much as 8 eggs - - > 8 eggs = 1 / 2 liters of kerosene . how many cents does a liter of kerosene cost - - > 1 liter of kerosene = 16 eggs = 16 / 12 * 24 = 32 cents . answer : c .\"" + }, + { + "Answer": 600, + "Options": "a ) 750 , b ) 600 , c ) 650 , d ) 550 , e ) 500", + "Correct": "b", + "Explanation": "\"let the maximum marks be x then , 30 % of x = 150 + 30 30 x / 100 = 180 30 x = 180 * 100 = 18000 x = 600 answer is b\"" + }, + { + "Answer": 50, + "Options": "a ) a ) 36 , b ) b ) 50 , c ) c ) 40 , d ) d ) 42 , e ) e ) 44", + "Correct": "b", + "Explanation": "\"let b be the number of blue hats and let g be the number of green hats . b + g = 85 . b = 85 - g . 6 b + 7 g = 560 . 6 ( 85 - g ) + 7 g = 560 . 510 - 6 g + 7 g = 560 . g = 560 - 510 = 50 . the answer is b .\"" + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9", + "Correct": "a", + "Explanation": "explanation : number of questions attempted correctly = ( 70 % of 10 + 40 % of 30 + 60 % of 35 ) = 7 + 12 + 21 = 40 . questions to be answered correctly for 60 % = 60 % of total quotations = 60 % of 75 = 45 . he would have to answer 45 - 40 = 5 answer : a" + }, + { + "Answer": 2.3333333333333335, + "Options": "a ) 25 / 9 , b ) 7 / 3 , c ) 5 / 3 , d ) 3 / 5 , e ) 9 / 25", + "Correct": "b", + "Explanation": "\"sqrt ( 7 x / 3 ) to be perfect square x has to 7 / 3 ans : b\"" + }, + { + "Answer": 1.161290322580645, + "Options": "a ) 32 / 31 , b ) 33 / 31 , c ) 34 / 31 , d ) 36 / 31 , e ) 0 / 31", + "Correct": "d", + "Explanation": "connie has a 1 6 chance of winning 6 dollars her first turn . she has a 5 / 6 1 / 6 chance of winning 1 dollar her second turn . next , she has a 25 36 1 / 6 chance of winning 1 / 6 dollars her third turn . generalizing , connie ' s expected earnings form a geometric series with initial term 1 / 6 * 6 = 1 and common ratio 5 / 6 * 1 / 6 = 5 / 36 . hence , connie ' s expected earnings are 1 / 1 - 5 / 36 = 36 / 31 correct answer d" + }, + { + "Answer": 13, + "Options": "a ) 11 , b ) 12 , c ) 13 , d ) 16 , e ) 18", + "Correct": "c", + "Explanation": "\"let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 26 = > 2 x = 26 = > x = 13 c\"" + }, + { + "Answer": 2, + "Options": "a ) 3 , b ) 5 , c ) 4 , d ) 2 , e ) 1", + "Correct": "d", + "Explanation": "because a + b = 1 , 2 a + 2 b = 2 ( a + b ) = 2 \u00d7 1 = 2 . correct answer d" + }, + { + "Answer": 2220, + "Options": "a ) 2210 , b ) 2220 , c ) 2230 , d ) 2240 , e ) 2250", + "Correct": "b", + "Explanation": "\"there are 6 possible arrangements of the three numbers . then each number will be in the hundreds , tens , and ones place two times each . the sum is 2 ( 222 ) + 2 ( 333 ) + 2 ( 555 ) = 2220 the answer is b .\"" + }, + { + "Answer": 40.5, + "Options": "a ) 43.25 , b ) 43 , c ) 38 , d ) 40.5 , e ) 36", + "Correct": "d", + "Explanation": "sum of last 4 matches = ( ( 10 \u00d7 45 ) \u2013 ( 6 \u00d7 48 ) = 162 average = 162 / 4 = 40.5 answer : d" + }, + { + "Answer": 172, + "Options": "a ) 168 , b ) 172 , c ) 182 , d ) 140 , e ) 160", + "Correct": "b", + "Explanation": "first we need to figure out what numbers are exactly divisible by 7 , 12,10 . this will be the set { lcm , lcmx 2 , lcmx 3 , . . . } lcm ( 7 , 12,10 ) = 42 * 10 = 420 the numbers which will leave remainder 4 will be { 420 + 4 , 420 x 2 + 4 , , . . . } the largest such number less than or equal to 1856 is 420 * 4 + 4 or 1684 to obtain this you need to subtract 172 . b" + }, + { + "Answer": 4, + "Options": "a ) 5 , b ) 8 , c ) 10 , d ) 4 , e ) 17", + "Correct": "d", + "Explanation": "chicken - ch cows - c sheep - s ch + c = 6 s c > ch and c > s each cow has 4 legs and 1 head each chicken has 2 legs and 1 head so 5 c + 3 ch = 100 ( sum of legs and head ) there are 2 possible solutions to this equation c = 11 and ch = 9 or c = 14 and ch = 10 since from first equation where ch + c = 6 s the sum of ch and c should be divisbile by 6 . 20 is not so the only possible solution is c = 14 and ch = 10 . so s = 4 answer : d" + }, + { + "Answer": 14, + "Options": "a ) 11 , b ) 12 , c ) 14 , d ) 16 , e ) 18", + "Correct": "c", + "Explanation": "\"let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 28 = > 2 x = 28 = > x = 14 c\"" + }, + { + "Answer": 20, + "Options": "a ) 22 , b ) 23 , c ) 24 , d ) 20 , e ) 28", + "Correct": "d", + "Explanation": "\"explanation : let the number of hens be x and the number of cows be y . then , x + y = 50 . . . . ( i ) and 2 x + 4 y = 160 x + 2 y = 80 . . . . ( ii ) solving ( i ) and ( ii ) we get : x = 20 , y = 30 the required answer = 20 . answer : d\"" + }, + { + "Answer": 6.015384615384615, + "Options": "a ) 5 , b ) 6 , c ) 9 , d ) 10 , e ) 11", + "Correct": "b", + "Explanation": "\"650 = 10 * 65 1300 = 20 * 65 the even multiples are 65 multiplied by 10 , 12 , 14 , 16 , 18 , and 20 for a total of 6 . the answer is b .\"" + }, + { + "Answer": 7, + "Options": "a ) 7 , b ) 11 , c ) 13 , d ) 15 , e ) 17", + "Correct": "a", + "Explanation": "\"( 2 to the power x ) - ( 2 to the power ( x - 2 ) ) = 3 ( 2 to the power 5 ) 2 ^ x - 2 ^ ( x - 2 ) = 3 . 2 ^ 5 hence x = 7 . answer is a\"" + }, + { + "Answer": 80.76923076923075, + "Options": "a ) 80.78 % , b ) 80.76 % , c ) 80.72 % , d ) 80.79 % , e ) 80.74 %", + "Correct": "b", + "Explanation": "explanation : number of students appeared from school ' p ' = 100 , say number of students qualified from school ' p ' = 70 and number of students appeared from school ' q ' = 130 number of students qualified from school ' q ' = 50 % more than those qualified from school ' p ' . = 70 + 35 = 105 % of students qualified to the number of students appeared from school b = 105 / 130 * 100 = 80.76 % answer : b" + }, + { + "Answer": 81, + "Options": "a ) 73 , b ) 75 , c ) 77 , d ) 79 , e ) 81", + "Correct": "e", + "Explanation": "let x be the height of the first person . then the heights are x , x + 2 , x + 4 , and x + 10 . 4 x + 16 = 4 ( 75 ) = 300 x = 71 and the fourth person has a height of 71 + 10 = 81 inches the answer is e ." + }, + { + "Answer": 20, + "Options": "a ) 11 , b ) 12 , c ) 13 , d ) 20 , e ) 25", + "Correct": "d", + "Explanation": "\"four wheeler = 20 * 4 = 80 ( max ) 2 wheel = 1 so no of 4 wheeler = 20 answer : d\"" + }, + { + "Answer": 1200, + "Options": "a ) 1880 , b ) 2160 , c ) 1200 , d ) 8400 , e ) 1210", + "Correct": "c", + "Explanation": "\"50 % of x = x / 2 ; 25 % of 2500 = 25 / 100 * 2500 = 625 given that , x / 2 = 625 - 25 = > x / 2 = 600 = > x = 1200 . answer : c\"" + }, + { + "Answer": 70, + "Options": "a ) 10 % , b ) 20 % , c ) 30 % , d ) 70 % , e ) 50 %", + "Correct": "d", + "Explanation": "\"pass percentage = 100 - ( 30 + 35 - 35 ) = 100 - 30 = 70 answer : d\"" + }, + { + "Answer": 21, + "Options": "a ) 76 , b ) 21 , c ) 26 , d ) 28 , e ) 11", + "Correct": "b", + "Explanation": "\"explanation : lot the total number of workers be v then , 8 ooov = ( 12000 * 7 ) + 6000 ( v - 7 ) < = > 2000 v = 42000 < = > v = 21 . answer : b\"" + }, + { + "Answer": 123, + "Options": "a ) 123 , b ) 267 , c ) 277 , d ) 267 , e ) 120", + "Correct": "a", + "Explanation": "\"let xx be the number he chose , then 2 \u00e2 \u2039 \u2026 x \u00e2 \u02c6 \u2019 138 = 108 x = 123 answer : a\"" + }, + { + "Answer": 4, + "Options": "a ) 5 , b ) 4 , c ) 6 , d ) 3 , e ) 2", + "Correct": "b", + "Explanation": "\"let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 8 = > 2 x = 8 = > x = 4 b\"" + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) 16 , c ) 18 , d ) 24 , e ) 26", + "Correct": "a", + "Explanation": "\"log 8 x + log 8 ( 1 / 6 ) = 1 / 3 = > ( log x / log 8 ) + ( log 1 / 6 / log 8 ) = log ( 81 / 3 ) = log 2 = > log x = log 2 \u2013 log 1 / 6 = log ( 2 * 6 / 1 ) = log 12 answer : a\"" + }, + { + "Answer": 10, + "Options": "a ) 10 , b ) 44 , c ) 80 , d ) 88 , e ) 90", + "Correct": "a", + "Explanation": "\"sol . let the numbers be x and y . then , ( x + y ) = 12 and x 2 + y 2 = 124 . now , 2 xy = ( x + y ) 2 - ( x 2 + y 2 ) = ( 12 ) 2 - 124 = 144 - 124 = 20 xy = 10 . answer a\"" + }, + { + "Answer": 1225, + "Options": "a ) 190 , b ) 200 , c ) 1225 , d ) 220 , e ) 230", + "Correct": "c", + "Explanation": "total no . of handshakes = 49 + 48 + 47 + . . . + 3 + 2 + 1 = 19 * ( 19 + 1 ) / 2 = 1225 or , if there are n persons then no . of shakehands = nc 2 = 50 c 2 = 1225 answer : c" + }, + { + "Answer": 0.24, + "Options": "a ) 6 / 25 , b ) 3 / 25 , c ) 8 / 25 , d ) 2 / 13 , e ) 3 / 17", + "Correct": "a", + "Explanation": "\"p ( a n b ) = p ( a ) . p ( b ) p ( a n b ) = 3 / 5 . 2 / 5 p ( a n b ) = 6 / 25 . a\"" + }, + { + "Answer": 9, + "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10", + "Correct": "d", + "Explanation": "\"x < y < z to find the least possible value for z - x ; we need to find the values for z and x that can be closest to each other . if x is some even number , then what could be minimum possible odd z . if x is some even number y - x > 5 ; y > x + 5 ; minimum value for y = x + 5 + 2 = x + 7 [ note : x + 5 is as even + odd = odd and nearest odd greater than x + 5 is x + 5 + 2 ] minimum value for z = y + 2 = x + 7 + 2 = x + 9 [ note : z = y + 2 because both z and y are odd . difference between two odd numbers is 2 ] q = z - x = x + 9 - x = 9 ans : d\"" + }, + { + "Answer": 0.2857142857142857, + "Options": "a ) 2 / 5 , b ) 3 / 4 , c ) 4 / 5 , d ) 5 / 4 , e ) 2 / 7", + "Correct": "e", + "Explanation": "\"a / b = 4 / 5 m / x = ( 2 / 5 ) * 5 / ( 7 / 4 ) * 4 = 2 / 7 the answer is e .\"" + }, + { + "Answer": 25, + "Options": "a ) 25 % , b ) 15 % , c ) 20 % , d ) 40 % , e ) 45 %", + "Correct": "a", + "Explanation": "ratio of 2 bedroom apartment : 1 bedroom apartment = 700 : 2100 - - - - - > 1 : 3 let total number of apartments be x no . of 2 bedroom apartment = ( 1 / 4 ) * x percentage of apartments in the building are two - bedroom apartments - - - - > ( 1 / 4 ) * 100 - - - > 25 % answer : a" + }, + { + "Answer": 35, + "Options": "a ) 35 , b ) 37 , c ) 39 , d ) 41 , e ) 42", + "Correct": "a", + "Explanation": "\"explanation : let b ' s age = x years . then , as age = ( x + 5 ) years . ( x + 5 + 10 ) = 2 ( x \u2014 10 ) hence x = 35 . present age of b = 35 years answer : option a\"" + }, + { + "Answer": 189, + "Options": "a ) 185 , b ) 186 , c ) 177 , d ) 168 , e ) 189", + "Correct": "e", + "Explanation": "\"2 ^ 3 + 7 ^ 2 = 57 3 ^ 3 + 6 ^ 2 = 63 5 ^ 3 + 9 ^ 2 = 206 and 5 ^ 3 + 8 ^ 2 = 189 answer : e\"" + }, + { + "Answer": 113, + "Options": "a ) 32 , b ) 90 , c ) 113 , d ) 92 , e ) 81", + "Correct": "c", + "Explanation": "\"a 2 - b 2 = 9 : given a 4 + b 4 - 2 a 2 b 2 = 92 : square both sides and expand . a * b = 4 : given a 2 b 2 = 42 : square both sides . a 4 + b 4 - 2 ( 16 ) = 81 : substitute a 4 + b 4 = 113 correct answer c\"" + }, + { + "Answer": 9, + "Options": "a ) 3.5 , b ) 6 , c ) 8 , d ) 7 , e ) 9", + "Correct": "e", + "Explanation": "\"let the number be x . then , 3 ( 2 x + 9 ) = 81 2 x = 18 = > x = 9 answer : e\"" + }, + { + "Answer": 259200, + "Options": "a ) 32,300 , b ) 172,800 , c ) 468,830 , d ) 338,200 , e ) 259,200", + "Correct": "e", + "Explanation": "\"every 2 seconds , 6 persons are added ( 9 - 3 ) . every second 3 persons are added . in a day 24 hrs = 24 * 60 minutes = 24 * 60 * 60 = 86400 seconds . 86400 * 3 = 259200 option e\"" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "c", + "Explanation": "30 , 870,000 = 2 ^ 4 * 5 ^ 4 * 3087 = 2 ^ 4 * 3 * 5 ^ 4 * 1029 = 2 ^ 4 * 3 ^ 2 * 5 ^ 4 * 343 = 2 ^ 4 * 3 ^ 2 * 5 ^ 4 * 7 ^ 3 the answer is c ." + }, + { + "Answer": 28, + "Options": "a ) 16 , b ) 28 , c ) 41 , d ) 54 , e ) 65", + "Correct": "b", + "Explanation": "you can just write out the pattern and count : rgwbyrgwbyrgwby . . . but to save time a good test taker will just look for a pattern . min # is 3 , because w is the third one . then every 5 beads another white comes , so it must be 3 + 5 + 5 + 5 . . and so on . . . 3 + 5 = 8 3 + 5 + 5 = 13 3 + 5 + 5 + 5 = 18 3 + 5 + 5 + 5 + 5 = 23 so you see it ends in either 8 or 3 . pick an answer that ends in either 8 or 3 . only one answer does , b ." + }, + { + "Answer": 0.04999999999999999, + "Options": "a ) 0.68 , b ) 0.08 , c ) 0.05 , d ) 0.06 , e ) none of them", + "Correct": "c", + "Explanation": "\"given expression = ( 0.15 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.15 ) ( power 2 ) + ( 0.15 x 0.1 ) + ( 0.1 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 0.15 - 0.1 ) = 0.05 answer is c .\"" + }, + { + "Answer": 54, + "Options": "a ) $ 54.00 , b ) $ 57.00 , c ) $ 58.00 , d ) $ 60.50 , e ) $ 63.00", + "Correct": "a", + "Explanation": "first 2 shirts are sold for $ 38 and $ 42 = $ 80 . to get average price of $ 50 , total sale should be 7 * $ 50 = $ 350 so remaining 5 shirts to be sold for $ 350 - $ 80 = $ 270 answer should be 270 / 5 = $ 54.00 that is a" + }, + { + "Answer": 1440, + "Options": "a ) $ 880 , b ) $ 990 , c ) $ 1,000 , d ) $ 1,100 , e ) $ 1,440", + "Correct": "e", + "Explanation": "\"10 / 100 p = 160 > > p = 160 * 100 / 10 = 1600 1600 - 160 = 1440 answer : e\"" + }, + { + "Answer": 30, + "Options": "a ) 29 , b ) 30 , c ) 31 , d ) 32 , e ) 33", + "Correct": "b", + "Explanation": "solution : 3 ! + 15 + 9 = 30 explanation : 3 ! = 3 * 2 * 1 = 6 6 + 15 + 9 = 30 answer b" + }, + { + "Answer": 160, + "Options": "a ) 300 , b ) 120 , c ) 150 , d ) 160 , e ) 270", + "Correct": "d", + "Explanation": "\"n th term of a . p . is given by a + ( n - 1 ) d 4 th term = a + 3 d 12 th term = a + 11 d given a + 3 d + a + 11 d = 20 - - > 2 a + 14 d = 20 - - > a + 7 d = 10 sum of n term of a . p = n / 2 [ 2 a + ( n - 1 ) d ] subsitiuing n = 16 . . . we get 15 / 2 [ 2 a + 14 d ] = 16 [ a + 7 d ] = 16 * 10 = 160 . . . answer is d . . .\"" + }, + { + "Answer": 8, + "Options": "a ) a ) 8 , b ) b ) 15 , c ) c ) 16 , d ) d ) 17 , e ) e ) 18", + "Correct": "a", + "Explanation": "\"d = ( d - r ) / q = ( 73 - 1 ) / 9 = 72 / 9 = 8 a )\"" + }, + { + "Answer": 10, + "Options": "a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16", + "Correct": "b", + "Explanation": "explanation : let the number of articles of types p , q and r be 3 a , 2 a and 3 a respectively . thus , we get , ( 200 x 3 a ) + ( 90 x 2 a ) + ( 60 x 3 a ) = 4800 960 a = 4800 a = 5 hence , the number of articles of type \u201c q \u201d = 2 x 5 = 10 answer b" + }, + { + "Answer": 859, + "Options": "a ) 427 , b ) 859 , c ) 869 , d ) 4320 , e ) none of these", + "Correct": "b", + "Explanation": "solution required number = ( l . c . m . of 24 , 32 , 36 , 54 ) - 5 = 864 - 5 = 859 . answer b" + }, + { + "Answer": 400, + "Options": "a ) 300 , b ) 375 , c ) 400 , d ) 500 , e ) 575", + "Correct": "c", + "Explanation": "\"as per the question 200 = 2 a / 5 thus - a which is the total amount = 500 the amount thus left = 300 she then deposited 1 / 3 of 300 = 100 total amount in her account = 400 answer c\"" + }, + { + "Answer": 18, + "Options": "a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20", + "Correct": "c", + "Explanation": "\"1536 \u00f7 21 = 73 reminder - 3 3 + 18 = 21 hence 18 should be added to 1536 so that the sum will be divisible by 21 answer : c\"" + }, + { + "Answer": 7, + "Options": "a ) 7 , b ) 5 , c ) 0 , d ) 3 , e ) 9", + "Correct": "a", + "Explanation": "let n = 7 ( leaves a remainder of 7 when divided by 19 ) 18 n = 18 ( 7 ) = 126 , which leaves a remainder of 0 when divided by 9 . difference = 7 - 0 = 7 . answer a" + }, + { + "Answer": 35, + "Options": "a ) 50 min , b ) 40 min , c ) 35 min , d ) 25 min , e ) 20 min", + "Correct": "c", + "Explanation": "\"clearly , the two will meet when they are 1000 m apart to be 20 + 15 = 35 km apart , they take 1 hour to be 1000 m apart , they take 35 * 1000 / 1000 = 35 min . answer is c\"" + }, + { + "Answer": 45, + "Options": "a ) 45 , b ) 46 , c ) 47 , d ) 48 , e ) 49", + "Correct": "a", + "Explanation": "weight of the teacher = ( 35.4 x 25 - 35 x 24 ) kg = 45 kg . answer : a" + }, + { + "Answer": 18, + "Options": "a ) 18 , b ) 6 , c ) 14 , d ) 17 , e ) 20", + "Correct": "a", + "Explanation": "\"the objective here is that 70 % of the fruit in the box should be apples . now , there are 14 apples at start and there is no talk of removing any apples , so number of apples should remain 14 and they should constitute 70 % of total fruit , so total fruit = 14 / 0.7 = 20 so we should have 20 - 14 = 6 oranges . right now , there are 24 oranges , so to get to 6 oranges , we should remove 24 - 6 = 18 oranges . answer a\"" + }, + { + "Answer": 96, + "Options": "a ) 124 % , b ) 120 % , c ) 96 % , d ) 80 % , e ) 64 %", + "Correct": "c", + "Explanation": "\"juan ' s income = 100 ( assume ) ; tim ' s income = 60 ( 40 percent less than juan ' s income ) ; mary ' s income = 96 ( 60 percent more than tim ' s income ) . thus , mary ' s income ( 96 ) is 96 % of juan ' s income ( 100 ) . answer : c\"" + }, + { + "Answer": 274, + "Options": "a ) 249 , b ) 498 , c ) 676 , d ) 823 , e ) 274", + "Correct": "e", + "Explanation": "\"slope of 2 and a y - intercept of 2 y - coordinate is 550 y = 2 x + 2 548 = 2 x x = 274 answer : e . 274\"" + }, + { + "Answer": 0.5, + "Options": "a ) 1 / 2 , b ) 2 , c ) 1 / 3 , d ) 3 , e ) 1 / 6", + "Correct": "a", + "Explanation": "\"very easy question . 2 variables and 2 easy equations . xy = 4 - - - > x = 4 / y - ( i ) x / y = 16 - - - > replacing ( i ) here - - - > 4 / ( y ^ 2 ) = 16 - - - > y ^ 2 = 4 / 16 = 1 / 4 - - - > y = 1 / 2 or - 1 / 2 the question states that x and y are positive integers . therefore , y = 1 / 2 is the answer . answer a .\"" + }, + { + "Answer": 16, + "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 16", + "Correct": "e", + "Explanation": "\"total marks of male = m total marks of female = f number of males = 8 number of females = f given : ( m + f ) / ( 8 + f ) = 90 - - - - - - - - - - - - - 1 also given , m / 8 = 86 thus m = 688 - - - - - - - - 2 also , f / f = 92 thus f = 92 f - - - - - - - - - 3 put 2 and 3 in 1 : we get ( 688 + 92 f ) / ( 8 + f ) = 90 solving this we get f = 16 ans : e\"" + }, + { + "Answer": 37.8, + "Options": "a ) $ 2.10 , b ) $ 37.10 , c ) $ 37.16 , d ) $ 37.8 , e ) $ 38.80", + "Correct": "d", + "Explanation": "\"principal that is amount taken by laura at year beginning = 35 $ rate of interest = 8 % interest = ( 8 / 100 ) * 35 = 2.8 $ total amount that laura owes a year later = 35 + 2.8 = 37.8 $ answer d\"" + }, + { + "Answer": 600, + "Options": "a ) a ) 600 , b ) b ) 350 , c ) c ) 450 , d ) d ) 470 , e ) e ) 500", + "Correct": "a", + "Explanation": "explanation : 10 * 150 = 1500 3 * 100 + 4 * 150 = 900 1500 \u2013 900 = 600 a" + }, + { + "Answer": 840, + "Options": "a ) $ 850 , b ) $ 840 , c ) $ 860 , d ) $ 870 , e ) $ 880", + "Correct": "b", + "Explanation": "\"50 pages typed 1 x 40 pages typed 2 x ( original + one revision ) 10 pages typed 3 x ( original + two revisions ) 50 ( 6 ) + 40 ( 6 + 4 ) + 10 ( 6 + 4 + 4 ) = 300 + 400 + 140 = 840 answer - b\"" + }, + { + "Answer": 54.00000000000001, + "Options": "a ) 33 , b ) 54 , c ) 18 , d ) 17 , e ) 01", + "Correct": "b", + "Explanation": "\"explanation : as there is meal for 70 adults and 28 have their meal , the meal left can be catered to 42 adults . now , 70 adults = 90 children 7 adults = 9 children therefore , 42 adults = 54 children hence , the meal can be catered to 54 children . answer : b\"" + }, + { + "Answer": 3.6666666666666665, + "Options": "a ) 5 , b ) 11 / 3 , c ) - 1 / 6 , d ) - 1 / 5 , e ) - 5", + "Correct": "b", + "Explanation": "\"any x and y satisfying x / y = 7 / 4 should give the same value for ( x + y ) / ( x - y ) . say x = 7 and y = 4 , then ( x + y ) / ( x - y ) = ( 7 + 4 ) / ( 7 - 4 ) = 11 / 3 . answer : b .\"" + }, + { + "Answer": 8, + "Options": "a ) $ 1.56 , b ) $ 2.40 , c ) $ 3.80 , d ) $ 4.20 , e ) $ 8.00", + "Correct": "e", + "Explanation": "\"in 3 miles , initial 1 / 5 mile charge is $ 1 rest of the distance = 3 - ( 1 / 5 ) = 14 / 5 rest of the distance charge = 14 ( 0.5 ) = $ 7 ( as the charge is 0.5 for every 1 / 5 mile ) = > total charge for 3 miles = 1 + 7 = 8 answer is e .\"" + }, + { + "Answer": 27.380952380952383, + "Options": "a ) 50 % , b ) 51.22 % , c ) 5.26 % , d ) 7.20 % , e ) 27.38 %", + "Correct": "e", + "Explanation": "\"say a 100 families existed in 1956 then the number of families owning a computer in 1956 - 25 number of families owning computer in 1960 = 25 * 115 / 100 = 28.75 number of families in 1960 = 105 the percentage = 28.75 / 105 * 100 = 27.38 % . option : e\"" + }, + { + "Answer": 123, + "Options": "a ) 288 , b ) 262 , c ) 72 , d ) 123 , e ) 267", + "Correct": "d", + "Explanation": "\"a : b : c = 100 : 65 : 40 = 20 : 13 : 8 8 - - - - 24 41 - - - - ? = > rs . 123 answer : d\"" + }, + { + "Answer": 24, + "Options": "a ) 6 , b ) 7 , c ) 12 , d ) 16 , e ) 24", + "Correct": "e", + "Explanation": "number of ways first - place medal can be awarded to four contestants = 8 number of ways second - place medal can be awarded to contestants after awarding first - place medal = 3 therefore number of possibilities = 8 * 3 = 24 answer : e" + }, + { + "Answer": 90, + "Options": "a ) 120 , b ) 60 , c ) 36 , d ) 90 , e ) 54", + "Correct": "d", + "Explanation": "120 and 60 are both divisible by 6 and 15 but also by 12 . so they are not the right answer . 36 and 54 are both clearly not divisible by 15 ( not correct ) 90 is both divisible by 6 and 15 but not by 12 . answer : ( d ) 90" + }, + { + "Answer": 2, + "Options": "a ) 2 . , b ) 4 . , c ) 5 . , d ) 6 . , e ) 7 .", + "Correct": "a", + "Explanation": "let x be the number of guests . number of muffins prepared = 5 x + 2 number of muffins eaten + number of muffins remaining = number of muffins prepared 6 ( x - 1 ) + 6 = 5 x + 2 6 x = 5 x + 2 x = 2 answer : a" + }, + { + "Answer": 0.35, + "Options": "a ) 1 / 17 , b ) 3 / 17 , c ) 1 / 10 , d ) 7 / 20 , e ) 3 / 10", + "Correct": "d", + "Explanation": "\"we have the ratio of a \u2019 s speed and b \u2019 s speed . this means , we know how much distance a covers compared with b in the same time . this is what the beginning of the race will look like : ( start ) a _________ b ______________________________ if a covers 20 meters , b covers 13 meters in that time . so if the race is 20 meters long , when a reaches the finish line , b would be 7 meters behind him . if we want the race to end in a dead heat , we want b to be at the finish line too at the same time . this means b should get a head start of 7 meters so that he doesn \u2019 t need to cover that . in that case , the time required by a ( to cover 20 meters ) would be the same as the time required by b ( to cover 13 meters ) to reach the finish line . so b should get a head start of 7 / 20 th of the race . answer ( d )\"" + }, + { + "Answer": 9600, + "Options": "a ) 9600 , b ) 5200 , c ) 362 , d ) 958 , e ) 258", + "Correct": "a", + "Explanation": "explanation : largest number of four digits = 9999 lcm of 15 , 25 , 40 and 75 = 600 9999 \u00f7 600 = 16 , remainder = 399 hence , largest number of four digits which is divisible by 15 , 25 , 40 and 75 = 9999 - 399 = 9600 answer : a" + }, + { + "Answer": 72, + "Options": "a ) 40 , b ) 56 , c ) 72 , d ) 81 , e ) 104", + "Correct": "c", + "Explanation": "in the range 800 - 900 : 1 choice for the first digit : 8 ; 5 choices for the third digit : 1 , 3 , 5 , 7 , 9 ( as the number is odd ) ; 8 choices for the second digit : 10 digits - first digit - third digit = 8 digits . 1 * 5 * 8 = 40 . in the range 900 - 999 : 1 choice for the first digit : 9 ; 4 choices for the third digit : 1 , 3 , 5 , 7 ( 9 is out as it ' s the first digit ) ; 8 choices for the second digit : 10 digits - first digit - third digit = 8 digits . 1 * 4 * 8 = 32 . total : 40 + 32 = 72 . answer : c" + }, + { + "Answer": 8, + "Options": "a ) 12 , b ) 27 , c ) 8 , d ) 12 , e ) 81", + "Correct": "c", + "Explanation": "\"( 80 / 100 ) * 40 \u00e2 \u20ac \u201c ( 4 / 5 ) * 30 32 - 24 = 8 answer : c\"" + }, + { + "Answer": 6, + "Options": "a ) 4 , b ) 6 , c ) 11 , d ) 12 , e ) 15", + "Correct": "b", + "Explanation": "\"the odd numbers less than 60 are 1 , 3,5 , . . . 59 some of them are equal to product of 5 and odd number hence odd multiples of 5 which are less than 60 are 5,15 , 25,35 , 45,55 ( total = 6 ) ; answer : b\"" + }, + { + "Answer": 48, + "Options": "a ) 20 , b ) 36 , c ) 48 , d ) 60 , e ) 84", + "Correct": "c", + "Explanation": "first , we have to understand what linearly means . it ' s not a straight ratio ( since 6 : 30 does not equal 24 : 60 ) . we need to look at the increases in each measurement to see what the scalar actually is . from 6 to 24 we have an increase of 18 . from 30 to 60 we have an increase of 30 . therefore , the increase ratio is 18 : 30 or 3 : 5 . in other words , for every 3 that t increases , s increases by 5 . we know that s is 100 . to get from 60 to 100 , we went up by 40 , or 8 jumps of 5 ; therefore , t will go up by 8 jumps of 3 . 24 + 8 ( 3 ) = 24 + 24 = 48 = c" + }, + { + "Answer": 72, + "Options": "a ) 72 , b ) 64 , c ) 84 , d ) 12 , e ) 92", + "Correct": "a", + "Explanation": "let the numbers be x and ( 184 - x ) . then , ( x / 3 ) - ( 184 - x ) / 7 = 8 7 x - 3 ( 184 - x ) = 168 10 x = 720 , x = 72 . hence the correct answer is option a ) 72 ." + }, + { + "Answer": 7550, + "Options": "a ) 5100 , b ) 7550 , c ) 10100 , d ) 15500 , e ) 20100", + "Correct": "b", + "Explanation": "\"my solution is : first 50 even integers : 2 4 6 8 < . . . > integers from 102 to 200 102 104 106 108 < . . . > we notice that each integer from the second set is 100 more than the respective integer in the first set . since we have 50 even integers from 102 to 200 , then : q = 2550 + ( 100 * 50 ) = 7550 . b\"" + }, + { + "Answer": 145, + "Options": "a ) rs . 130 , b ) rs . 145 , c ) rs . 154 , d ) rs . 160 , e ) rs . 164", + "Correct": "b", + "Explanation": "let y gets rs x . then we can say x gets rs ( x + 20 ) and y gets rs ( x + 35 ) . x + 20 + x + x + 35 = 385 3 x = 330 x = 110 . r \u2019 s share = rs ( 110 + 35 ) = rs . 145 b" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 2", + "Correct": "a", + "Explanation": "case 1 n = 5,8 , 11,14 , 17,20 case 2 m = 5 , 9,13 , 17,21 therefore n = 17 remainder of 17 / 16 will be 1 a" + }, + { + "Answer": 43, + "Options": "a ) 18 , b ) 22 , c ) 42 , d ) 43 , e ) 45", + "Correct": "d", + "Explanation": "explanation : numbers from 1 to 60 , which are divisible by 6 are : 6 , 1218 , 24 , 30 , 3642 , 48 , 54 , 60 . there are 10 such numbers . numbers from 1 to 60 , the sum of whose digits is 6 are : 6 , 15 , 24 , 33 , 42 , 51 , 60 . there are 7 such numbers of which 4 are common to the above ones . so , there are 3 such uncommon numbers . numbers from 1 to 60 , which have 6 as one of the digits are 6 , 16 , 26 , 36 , 46 , 56 , 60 . clearly , there are 4 such uncommon numbers . so , numbers ' not connected with 6 ' = 60 - ( 10 + 3 + 4 ) = 43 . answer : d" + }, + { + "Answer": 26.666666666666668, + "Options": "a ) 25.66 % , b ) 26.66 % , c ) 27.66 % , d ) 28.66 % , e ) 29.66 %", + "Correct": "b", + "Explanation": "\"cost of kit = $ 67.50 if filters are purchased individually - $ 7.45 * 2 + $ 10.05 * 2 + $ 14.50 = $ 49.50 amount saved = $ 67.50 - $ 49.50 = $ 18 required % age = ( $ 18 / $ 67.50 ) * 100 = 26.66 % so , the correct answer is b .\"" + }, + { + "Answer": 18, + "Options": "a ) 10 , b ) 12 , c ) 15 , d ) 18 , e ) 20", + "Correct": "d", + "Explanation": "20 ! = 1 * 2 * 3 * 4 * 5 . . . * 19 * 20 ( this is 20 factorial written as 20 ! ) n = 1 * 2 * 3 * 4 * 5 * 6 * 7 . . . . . * 19 * 20 how many 2 s are there in n ? one 2 from 2 two 2 s from 4 one two from 6 three 2 s from 8 and so on . . . when you count them all , you get 18 . answer : d" + }, + { + "Answer": 16, + "Options": "a ) 18 km , b ) 16 km , c ) 12 km , d ) 24 km , e ) 25 km", + "Correct": "b", + "Explanation": "\"explanation : let the journey be x km then , 1 x / 2 + 1 x / 4 + 4 = x 3 x + 16 = 4 x x = 16 km answer : option b\"" + }, + { + "Answer": 30, + "Options": "a ) 15 , b ) 30 , c ) 35 , d ) 40 , e ) 45", + "Correct": "b", + "Explanation": "\"lots of ways to tackle this . 25 % of 180 = 45 1 / 3 of 45 = 15 so , 1 / 3 less than 45 is equal to 45 - 15 = 30 answer : b\"" + }, + { + "Answer": 67, + "Options": "a ) 66 kg , b ) 67 kg , c ) 68 kg , d ) 69 kg , e ) none of these", + "Correct": "b", + "Explanation": "explanation : let arun \u2019 s weight by x kg . according to arun , 65 < x < 72 according to arun \u2019 s brother , 60 < x < 70 . according to arun \u2019 s mother , x < = 68 the values satisfying all the above conditions are 66 , 67 and 68 . required average = [ 66 + 67 + 68 / 3 ] = [ 201 / 3 ] = 67 kg answer b" + }, + { + "Answer": 250, + "Options": "a ) 250 , b ) 275 , c ) 325 , d ) 350 , e ) 400", + "Correct": "a", + "Explanation": "\"this problem is a general word translation . we first define variables and then set up equations . we can define the following variables : f = the weight of the first lift s = the weight of the second lift we are given that the total weight of joe ' s two lifts was 450 pounds . we sum the two variables to obtain : f + s = 450 we are also given that twice the weight of his first lift was 300 pounds more than the weight of his second lift . we express this as : 2 f = 300 + s 2 f \u2013 300 = s we can now plug in ( 2 f \u2013 300 ) for s into the first equation , so we have : f + 2 f \u2013 300 = 450 3 f = 750 f = 250 answer is a .\"" + }, + { + "Answer": 30, + "Options": "a ) 23 minutes , b ) 30 minutes , c ) 43 minutes , d ) 23 minutes , e ) 33 minutes", + "Correct": "b", + "Explanation": "distance travelled by ramu = 45 * 4 = 180 km somu travelled the same distance in 6 hours . his speed = 180 / 6 = 30 km / hr hence in the conditional case , ramu ' s speed = 45 - 9 = 36 km / hr and somu ' s speed = 30 + 10 = 40 km / hr . therefore travel time of ramu and somu would be 5 hours and 4.5 hours respectively . hence difference in the time taken = 0.5 hours = 30 minutes . answer : b" + }, + { + "Answer": 6, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8", + "Correct": "c", + "Explanation": "\"4 x + 2.8 y = 42 - - > multiply by 2.5 ( to get the integers ) - - > 10 x + 7 y = 105 - - > only one positive integers solutions x = 6 and y = 5 ( how to solve : 7 y must have the last digit of 5 in order the last digit of the sum to be 5 ) . answer : c .\"" + }, + { + "Answer": 28, + "Options": "a ) 24 , b ) 28 , c ) 32 , d ) 36 , e ) 40", + "Correct": "b", + "Explanation": "\"in 84 liters of drink a , there are 48 liters of milk and 36 liters of juice . with 48 liters of milk , we need a total of 64 liters of juice to make drink b . we need to add 28 liters of juice . the answer is b .\"" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9", + "Correct": "b", + "Explanation": "\"we have equation 2 n + 5 m = 50 we have factor 2 in first number and we have factor 5 in second number . lcm ( 2 , 5 ) = 10 so we can try some numbers and we should start from 5 because it will be less list than for 2 2 * 5 = 10 and n should be equal 20 4 * 5 = 20 and n should be equal 15 6 * 5 = 30 and n should be equal 10 8 * 5 = 40 and n should be equal 5 10 * 5 = 50 and n should be equal 0 third variant give us the mininal difference n - m = 10 - 6 = 4 and there is some mistake in my way of thinking because we do n ' t have such answer ) if we change the task and will seek for difference between m and n than minimal result r will be 8 - 5 = 3 and answer b\"" + }, + { + "Answer": 155, + "Options": "a ) 150 , b ) 200 , c ) 155 , d ) 350 , e ) none", + "Correct": "c", + "Explanation": "\"sol . let the number of grils be x . then , number of boys = ( 620 - x ) . then , ( 11 3 / 4 \u00d7 620 ) \u21d4 11 x + 12 ( 620 - x ) \u21d4 x = 7440 - 7285 \u21d4 155 . answer c\"" + }, + { + "Answer": 34, + "Options": "a ) 50 min , b ) 40 min , c ) 34 min , d ) 25 min , e ) 20 min", + "Correct": "c", + "Explanation": "clearly , the two will meet when they are 1000 m apart to be 20 + 14 = 34 km apart , they take 1 hour to be 1000 m apart , they take 34 * 1000 / 1000 = 34 min . answer is c" + }, + { + "Answer": 4, + "Options": "a ) 4 , b ) - 4 , c ) - 3 , d ) - 6 , e ) 1", + "Correct": "a", + "Explanation": "x ^ 2 + 2 x - 24 = ( x + 6 ) ( x - 4 ) = 0 then x = - 6 or x = 4 . x ^ 2 - 5 x + 4 = ( x - 4 ) ( x - 1 ) = 0 then x = 4 or x = 1 . thus x = 4 . the answer is a ." + }, + { + "Answer": 285, + "Options": "a ) 250 , b ) 276 , c ) 280 , d ) 285 , e ) none", + "Correct": "d", + "Explanation": "sol . since the month begins with a sunday , so there will be five sundays in the month . \u2234 required average = [ 510 x 5 + 240 x 25 / 30 ] = 8550 / 30 = 285 answer d" + }, + { + "Answer": 75, + "Options": "a ) 10 , b ) 25 , c ) 50 , d ) 75 , e ) 100", + "Correct": "d", + "Explanation": "\"surprisingly no one answered this easy one . property of a set of consecutive integerz . mean = median = ( first element + last element ) / 2 = ( second element + last but one element ) / 2 = ( third element + third last element ) / 2 etc . etc . so mean = median = 150 / 2 = 75 answer is d\"" + }, + { + "Answer": 30.000000000000004, + "Options": "a ) 15 % , b ) 20 % , c ) 22.5 % , d ) 25 % , e ) 30 %", + "Correct": "e", + "Explanation": "\"4 miles on the highway = 4 / 32 gallons ; 4 miles in the city = 4 / 20 gallons ; total = 4 / 32 + 4 / 20 = 13 / 40 gallons . 8 miles on the highway = 8 / 30 gallons . the % change = ( 13 / 40 - 8 / 32 ) / ( 8 / 32 ) = 0.30 . answer : e .\"" + }, + { + "Answer": 4, + "Options": "a ) 6 years , b ) 9 years , c ) 5 years , d ) 4 years , e ) 6 years", + "Correct": "d", + "Explanation": "\"4 years answer : d\"" + }, + { + "Answer": 11, + "Options": "a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13", + "Correct": "c", + "Explanation": "7 m - 20 = 2 m so , 5 m = 20 so , m + 7 = 11 answer : c" + }, + { + "Answer": 4, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "b", + "Explanation": "\"sol . = ( 2 \u00d7 1 + 1 ) = 3 , = ( 2 \u00d7 3 + 1 ) = 7 , = ( 2 \u00d7 4 + 1 ) = 9 , which is not prime . therefore n = 4 . answer b\"" + }, + { + "Answer": 20, + "Options": "a ) 20 % , b ) 25 % , c ) 40 % , d ) 50 % , e ) 80 %", + "Correct": "a", + "Explanation": "two hundred multiples of seven will have 100 even and 100 odd numbers 300 multiples of eight will have all even ( being multiple of 8 ) probability of number selected being odd = total odd numbers / total available numbers probability = 100 / 500 = 0.2 = 20 % answer : option a" + }, + { + "Answer": 6.25, + "Options": "a ) 93.5 , b ) 90 , c ) 6.75 , d ) 6.25 , e ) 2", + "Correct": "d", + "Explanation": "\"let , p = 400 then j = ( 75 / 100 ) * 400 = 300 also j = ( 80 / 100 ) * t i . e . t = 300 * 100 / 80 = 375 and t = [ 1 - ( x / 100 ) ] * p i . e . 100 - x = 100 * t / p = 100 * 375 / 400 = 93.75 i . e . x = 6.25 answer : option d\"" + }, + { + "Answer": 44, + "Options": "a ) 0.33 , b ) 0.44 , c ) 0.55 , d ) 44 , e ) 55", + "Correct": "d", + "Explanation": "\"main thing to remember is answer is asked in cents , however when we calculate , it comes up as 0.44 $ just multiply by 100 , answer q = 44 . d\"" + }, + { + "Answer": 24, + "Options": "a ) 22 , b ) 18 , c ) 26 , d ) 24 , e ) 32", + "Correct": "d", + "Explanation": "\"( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 276 + 2 * 150 a + b + c = \u00e2 \u02c6 \u0161 576 = 24 answer d\"" + }, + { + "Answer": 20, + "Options": "a ) 20 % , b ) 23 % , c ) 15 % , d ) 18 % , e ) 16 %", + "Correct": "a", + "Explanation": "fathers without full - time jobs are 1 / 4 * 3 / 5 = 3 / 20 of all the parents surveyed . mothers without full - time jobs are 1 / 8 * 2 / 5 = 1 / 20 of all the parents surveyed . the percent of parents without full - time jobs is 3 / 20 + 1 / 20 = 1 / 5 = 20 % the answer is a ." + }, + { + "Answer": 4991, + "Options": "a ) 4551 , b ) 4771 , c ) 4991 , d ) 4881 , e ) 4661", + "Correct": "c", + "Explanation": "\"let the sale in the sixth month = x then ( 6435 + 6927 + 6855 + 7230 + 6562 + x ) / 6 = 6500 = > 6435 + 6927 + 6855 + 7230 + 6562 + x = 6 \u00d7 6500 = > 34009 + x = 39000 = > x = 39000 \u2212 34009 = 4991 answer is c .\"" + }, + { + "Answer": 7700, + "Options": "a ) rs . 7700 , b ) rs . 3618 , c ) rs . 3600 , d ) rs . 3619 , e ) rs . 3610", + "Correct": "a", + "Explanation": "\"manager ' s monthly salary = rs . ( 2700 * 26 - 2500 * 25 ) = rs . 7700 answer : a\"" + }, + { + "Answer": 15, + "Options": "a ) 14 , b ) 12 , c ) 13 , d ) 15 , e ) 16", + "Correct": "d", + "Explanation": "\"let n be the number of persons in the party . number of hands shake = 105 ; total number of hands shake is given by nc 2 . now , according to the question , nc 2 = 105 ; or , n ! / [ 2 ! * ( n - 2 ) ! ] = 105 ; or , n * ( n - 1 ) / 2 = 105 ; or , n 2 - n = 210 ; or , n 2 - n - 210 = 0 ; or , n = 15 , - 14 ; but , we can not take negative value of n . so , n = 15 i . e . number of persons in the party = 15 . option d\"" + }, + { + "Answer": 8.000000000000002, + "Options": "a ) 0 , b ) 8 , c ) 10 , d ) 15 , e ) 20", + "Correct": "b", + "Explanation": "\"x = \u221a 2 and y also = \u221a 2 applying the function ( \u221a 2 + \u221a 2 ) ^ 2 - ( \u221a 2 - \u221a 2 ) ^ 2 = ( 2 \u221a 2 ) ^ 2 - 0 = 4 x 2 = 8 . note : alternative approach is the entire function is represented as x ^ 2 - y ^ 2 = ( x + y ) ( x - y ) which can be simplified as ( x + y + x - y ) ( x + y - ( x - y ) ) = ( 2 x ) ( 2 y ) = 4 xy . substituting x = \u221a 2 and y = \u221a 2 you get the answer 8 . answer b\"" + }, + { + "Answer": 6400, + "Options": "a ) 76 , b ) 6400 , c ) 304 , d ) 1296 , e ) none", + "Correct": "b", + "Explanation": "\"answer let \u221a n / 20 = 4 then \u221a n = 20 x 4 = 80 \u2234 n = 80 x 80 = 6400 . correct option : b\"" + }, + { + "Answer": 0.037037037037037035, + "Options": "a ) 1 / 190 , b ) 1 / 20 , c ) 1 / 19 , d ) 1 / 27 , e ) 1 / 9", + "Correct": "d", + "Explanation": "\"the problem with your solution is that we do n ' t choose 1 shoe from 28 but rather choose the needed one after we just took one and need the second to be the pair of it . so , the probability would simply be : 1 / 1 * 1 / 27 ( as after taking one at random there are 27 shoes left and only one is the pair of the first one ) = 1 / 27 answer : d\"" + }, + { + "Answer": 40, + "Options": "a ) 22 , b ) 88 , c ) 40 , d ) 87 , e ) 17", + "Correct": "c", + "Explanation": "explanation : sum of the present ages of a , b and c = ( 27 \u00d7 3 + 3 \u00d7 3 ) years = 90 years . sum of the present ages of b and c = ( 20 \u00d7 2 + 5 \u00d7 2 ) years = 50 years . a ' s present age = 90 \u2013 50 = 40 years . answer : c" + }, + { + "Answer": 91.66666666666666, + "Options": "a ) 90.1 , b ) 91.7 , c ) 97.1 , d ) 101.1 , e ) 107.1", + "Correct": "b", + "Explanation": "explanation : in such a case the middle number ( c ) is the average \u2234 c = 20 and d = 22 and e = 24 required percentage = 22 / 24 x 100 = 91.7 answer : option b" + }, + { + "Answer": 12, + "Options": "a ) 3 , b ) 6 , c ) 8 , d ) 12 , e ) 16", + "Correct": "d", + "Explanation": "\"m ^ 2 is divisible by 48 so m ^ 2 must be multiple of 48 . if the value of m is multiples of 12 then it will satisfy the condition . if we if m is 12 or 24 or 36 then it ans is d but if m = 48 then answer should be 16 . is the question right ? or am i missing some thing ? d\"" + }, + { + "Answer": 0.39999999999999997, + "Options": "a ) $ 015 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45", + "Correct": "d", + "Explanation": "\"on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.6 = 3 * x - - > x = $ 0.4 . answer : d .\"" + }, + { + "Answer": 50, + "Options": "a ) 50 . , b ) 45 . , c ) 40 . , d ) 30 . , e ) 25 .", + "Correct": "a", + "Explanation": "given there are 50 students in the seaside summer camp , 90 % of 50 = 45 boys and remaining 5 girls . now here 90 % are boys and 10 % are girls . now question is asking about how many boys do we need to add , to make the girls percentage to 5 or 5 % . . if we add 50 to existing 45 then the count will be 95 and the girls number will be 5 as it . now boys are 95 % and girls are 5 % . ( out of 100 students = 95 boys + 5 girls ) . imo option a is correct ." + }, + { + "Answer": 5625, + "Options": "a ) 2379 , b ) 2889 , c ) 5625 , d ) 9000 , e ) 28311", + "Correct": "c", + "Explanation": "let their prices be 3 x , 5 x and 7 x . then , 2 x + 6 x + 8 x = ( 15000 * 3 ) or x = 2812.5 . cost of cheapest item = 2 x = rs . 5625 . answer : c" + }, + { + "Answer": 30, + "Options": "a ) 30 , b ) 81 , c ) 60 , d ) 27 , e ) 11", + "Correct": "a", + "Explanation": "\"explanation : let the number be 1 + 1 / 2 [ 1 / 3 ( a / 5 ) ] = a / 15 = > 1 = a / 30 = > a = 30 answer : a\"" + }, + { + "Answer": 50, + "Options": "a ) 50 km , b ) 16 km , c ) 18 km , d ) 29 km , e ) 19 km", + "Correct": "a", + "Explanation": "\"let the actual distance traveled be x km . then , x / 10 = ( x + 20 ) / 14 4 x - 200 = > x = 50 km . answer : a\"" + }, + { + "Answer": 1296, + "Options": "a ) 1294 , b ) 1295 , c ) 1296 , d ) 1297 , e ) 1298", + "Correct": "c", + "Explanation": "\"sum of 1 st n odd no . s = 1 + 3 + 5 + 7 + . . . = n ^ 2 so , sum of 1 st 36 odd numbers = 36 ^ 2 = 1296 answer : c\"" + }, + { + "Answer": 210, + "Options": "a ) 190 , b ) 200 , c ) 210 , d ) 220 , e ) 225", + "Correct": "c", + "Explanation": "\"though 2 * ( 15 c 2 ) is the correct approcah to do this , but for people like me who find perm , comb n prob a nightmare , an easy approach can be used . the first guy has to play 2 matches with the rest of 14 , so he ' ll play 28 matches . similarly , second guy has to play with the rest of 13 as his 2 games with the first guy are already played . so he plays 26 matches . this continues like this and the total matches are 28 + 26 + 24 . . . + 2 28 + 26 + . . . + 2 = 2 ( 14 + 13 + . . . + 1 ) = 2 ( ( 14 * 15 ) / 2 ) = 14 * 15 = 210 . answer : c\"" + }, + { + "Answer": 20, + "Options": "a ) 25.5 , b ) 2.5 , c ) 25 , d ) 20 , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : 1 / 0.05 = ( 1 * 100 ) / 5 = 100 / 5 = 20 option d\"" + }, + { + "Answer": 54, + "Options": "a ) 22 , b ) 54 , c ) 88 , d ) 37 , e ) 29", + "Correct": "b", + "Explanation": "\"explanation : lot the total number of workers be v then , 8 ooov = ( 18000 * 9 ) + 6000 ( v - 9 ) < = > 2000 v = 108000 < = > v = 54 answer : b ) 54\"" + }, + { + "Answer": 1000, + "Options": "a ) 1500 , b ) 1992 , c ) 9921 , d ) 1000 , e ) 2789", + "Correct": "d", + "Explanation": "\"p = 10 ( 100 / 10 ) 2 = > p = 1000 answer : d\"" + }, + { + "Answer": 144, + "Options": "a ) 107 , b ) 144 , c ) 175 , d ) 165 , e ) 130", + "Correct": "b", + "Explanation": "\"let us calculate both the length and width of the room in centimeters . length = 7 meters and 68 centimeters = 768 cm width = 4 meters and 32 centimeters = 432 cm as we want the least number of square tiles required , it means the length of each square tile should be as large as possible . further , the length of each square tile should be a factor of both the length and width of the room . hence , the length of each square tile will be equal to the hcf of the length and width of the room = hcf of 768 and 432 = 48 thus , the number of square tiles required = ( 768 x 432 ) / ( 48 x 48 ) = 16 x 9 = 144 answer : b\"" + }, + { + "Answer": 0.6666666666666666, + "Options": "a ) 5 / 3 , b ) 4 / 3 , c ) 2 / 3 , d ) 1 / 3 , e ) 1 / 5", + "Correct": "c", + "Explanation": "explanation : 1 \u00f7 [ 1 + 1 \u00f7 { 1 + 1 \u00f7 ( 1 \u00f7 1 ) } ] = 1 \u00f7 [ 1 + 1 \u00f7 { 1 + 1 \u00f7 1 } ] = 1 \u00f7 [ 1 + 1 \u00f7 { 1 + 1 } ] = 1 \u00f7 [ 1 + 1 \u00f7 2 ] = 1 \u00f7 [ 1 + ( 1 / 2 ) ] = 1 \u00f7 3 / 2 = 1 \u00d7 3 / 2 = 1 \u00d7 2 / 3 = 2 / 3 answer : option c" + }, + { + "Answer": 2, + "Options": "a ) 3 / 4 , b ) 1 , c ) 4 / 3 , d ) 2 , e ) 7 / 2", + "Correct": "d", + "Explanation": "\"slope = ( y 2 - y 1 ) / ( x 2 - x 1 ) = > k = ( k + 4 ) / ( 2 + 1 ) = > 3 k = k + 4 = > k = 2 ans d it is !\"" + }, + { + "Answer": 3200, + "Options": "a ) 2400 , b ) 2403 , c ) 3200 , d ) 2539 , e ) 1930", + "Correct": "c", + "Explanation": "\"c 3200 let the amount with r be $ r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 8000 - r ) = > 3 r = 16000 - 2 r = > 5 r = 16000 = > r = 3200 .\"" + }, + { + "Answer": 57.14285714285714, + "Options": "a ) 57 % , b ) 22.2 % , c ) 20 % , d ) 12.5 % , e ) 11.1 %", + "Correct": "a", + "Explanation": "\"let ' s see , the way i did it was 16 / 25 are clerical out of 3600 so 2304 are clerical 2304 reduced by 1 / 4 is 2304 * 1 / 4 so it reduced 576 people , so there is 1728 clerical people left but since 576 people left , it also reduced from the total of 3600 so there are 3024 people total since 1728 clerical left / 3024 people total you get ( a ) 57 %\"" + }, + { + "Answer": 270, + "Options": "a ) 240 , b ) 250 , c ) 260 , d ) 270 , e ) none", + "Correct": "d", + "Explanation": "\"solution let the numbers be x and x ( x + 1365 ) . then , x + 1365 = 6 x + 15 \u2039 = \u203a 5 x = 1350 . \u2039 = \u203a x = 270 . answer d\"" + }, + { + "Answer": 27, + "Options": "a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29", + "Correct": "c", + "Explanation": "\"present age = x before 7 yrs , y = x - 7 after 7 yrs , z = x + 7 by the qn , x + ( x - 7 ) = 33 2 x - 7 = 33 2 x = 33 + 7 x = 40 / 2 x = 20 z = x + 7 = 20 + 7 = 27 answer : c\"" + }, + { + "Answer": 7, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", + "Correct": "a", + "Explanation": "\"a simple and elegant solution . as addition of 39 , shifts mean by 2 , and addition of 15 , shifts mean by 1 to the other side , we have the mean lying between 3915 , and in a ratio of 2 : 1 39 - 15 = 24 24 divide by 3 is 8 . meaning mean of the n terms is 15 + 8 = 39 - 16 = 23 now , from first statement , when a person aged 39 is added to a group of n people , the average age increases by 2 . t * 23 + 39 = 25 * ( t + 1 ) t = 7 ans . ( a )\"" + }, + { + "Answer": 20, + "Options": "a ) rs 18.95 , b ) rs 16 , c ) rs 20 , d ) rs 25.71 , e ) none of these", + "Correct": "c", + "Explanation": "total earning for the week = rs ( 4 \u00d7 18 + 4 \u00d7 22 - 20 ) = rs 140 average earning = rs 140 / 7 = rs 20 . answer : c" + }, + { + "Answer": 370000, + "Options": "a ) $ 80,000 , b ) $ 130,000 , c ) $ 240,000 , d ) $ 370,000 , e ) $ 320,000", + "Correct": "d", + "Explanation": "for sake of ease , let ' s say there are 10 employees : 7 marketers , 1 engineers , and 2 manager . average company salary * number of employees = total company salary > > > $ 80,000 * 10 = $ 800,000 subtract the combined salaries for the marketers ( 7 * $ 50,000 ) and the engineers ( $ 80,000 ) > > > $ 800,000 - $ 350,000 - $ 80,000 = $ 370,000 . the correct answer is d ." + }, + { + "Answer": 1.825873786407767, + "Options": "a ) $ 1.63 , b ) $ 1.64 , c ) $ 1.68 , d ) $ 1.72 , e ) $ 1.83", + "Correct": "e", + "Explanation": "\"( 1370 * 1.99 + 690 * 1.50 ) / ( 1370 + 690 ) = ~ 1.83 - option ( e )\"" + }, + { + "Answer": 1984, + "Options": "a ) 2984 , b ) 2983 , c ) 2982 , d ) 2981 , e ) 1984", + "Correct": "e", + "Explanation": "2034 - 50 = 1984 answer : e" + }, + { + "Answer": 1.5, + "Options": "a ) 3 / 2 , b ) 3 / 3 , c ) 2 / 4 , d ) 4 / 4 , e ) 4 / 5", + "Correct": "a", + "Explanation": "if we substitute y = 4 x , we have y 2 + 4 y - 96 = 0 , so y = - 4 or y = 8 . the first does not map to a real solution , while the second maps to x = 3 / 2 correct answer a" + }, + { + "Answer": 38, + "Options": "a ) 23 , b ) 32 , c ) 38 , d ) 41 , e ) 44", + "Correct": "c", + "Explanation": "\"let number of years taught by virginia = v number of years taught by adrienne = a number of years taught by dennis = d v + a + d = 96 v = a + 9 = > a = v - 9 v = d - 9 = > a = ( d - 9 ) - 9 = d - 18 d - 9 + d - 18 + d = 87 = > 3 d = 87 + 27 = 114 = > d = 38 answer c\"" + }, + { + "Answer": 27, + "Options": "a ) 23 , b ) 27 , c ) 32 , d ) 72 , e ) 46", + "Correct": "b", + "Explanation": "let the ten ' s digit be x and unit ' s digit be y . then 10 x + y = 3 ( x + y ) = = > 7 x - 2 y = 0 = = > 7 x - 2 y = 0 - - - - > ( i ) 10 + y + 45 = 10 y + x = = > y - x = 5 = = = > - 2 x + 2 y = 10 - - - - - - ( ii ) by adding ( i ) and ( ii ) we get 5 x = 10 so x = 2 and y = 7 so the required number is 27 . so the correct option is b ) 27 ." + }, + { + "Answer": 100, + "Options": "a ) 90 , b ) 100 , c ) 110 , d ) 120 , e ) 130", + "Correct": "b", + "Explanation": "x / 2 + 6 + 3 + 1 + 4 sqrt ( x ) = x x / 2 + 10 + 4 sqrt ( x ) = x 4 sqrt ( x ) = x / 2 - 10 squaring on both sides 16 x = x \u00b2 / 4 + 100 - 10 x simplifying x \u00b2 - 104 x + 400 = 0 x = 100 , 4 x = 4 is not possible therefore x = 100 answer : b" + }, + { + "Answer": 35, + "Options": "a ) 0 , b ) 15 , c ) 25 , d ) 30 , e ) 35", + "Correct": "e", + "Explanation": "\"i also was confused when i was looking forabove number : d as far as i understood , 15 is a factor of ab . in other words , the values of b ( units digits can be 5 or 0 . better to have option for 5 in this case to havebigger result ) . now let ' s try 15 x 1 ( a = 1 , b = 5 respectively we have = 5 ) . to ensure , let ' s check ( avoid even multiples of 2,4 , 6,8 etc ( we will have 0 in units thus making our result 0 ) 15 x 3 = 45 ( a = 4 b = 5 respectively . hey ! that ' s 20 . but we do n ' t have this number in answer choices , move on ) . 15 x 5 = 75 ( a = 7 , b = 5 respectively . increasing trend , we have 35 now ) 15 x 7 = 105 ( a = 0 , b = 5 . have 0 now . can create a pattern ) imo e .\"" + }, + { + "Answer": 629, + "Options": "a ) 605 , b ) 608 , c ) 613 , d ) 616 , e ) 629", + "Correct": "e", + "Explanation": "\"the set s = { 5 , 13 , 21 , 29 , . . . . . . . . . . . . . . . . . . . . . } 1 st number = 8 * 0 + 5 = 5 2 nd number = 8 * 1 + 5 = 13 3 rd number = 8 * 2 + 5 = 21 79 th number = 8 * ( 79 - 1 ) + 5 = 629 answer = e\"" + }, + { + "Answer": 125, + "Options": "a ) 115 , b ) 125 , c ) 135 , d ) 145 , e ) 155", + "Correct": "b", + "Explanation": "\"sum of the 30 numbers = 30 * 25 = 750 if each number is multiplied by 5 , the sum also gets multiplied by 5 and the average also gets multiplied by 5 . thus , the new average = 25 * 5 = 125 . answer : b\"" + }, + { + "Answer": 21, + "Options": "a ) 7 , b ) 14 , c ) 49 , d ) 21 , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation \u221a ( 21 ) ^ 2 = ? or , ? = 21 answer d\"" + }, + { + "Answer": 12, + "Options": "a ) 8 , b ) 7 , c ) 12 , d ) 9 , e ) none of the above", + "Correct": "c", + "Explanation": "ans is c : 39 pounds - - > 6 days 117 pounds - - > x days x = 117 * 6 / 39 = 18 the animal has already consumed food in 6 days so the the number of days for it ' s total consumption be 117 pounds is 18 - 6 = 12" + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 5 , c ) 8 , d ) 13 , e ) 15", + "Correct": "a", + "Explanation": "\"total # of students = 42 avg # of books per student = 2 total # of books = 42 * 2 = 84 # of student borrowed at least 3 books = 42 - 2 - 12 - 10 = 18 # of books borrowed by above 18 students = 84 - ( 12 * 1 ) + ( 10 * 2 ) = 52 considering that 17 out of above 18 students borrowed only 3 books , # of books borrowed = 17 * 3 = 51 so maximum # of books borrowed by any single student = 52 - 51 = 1 option a\"" + }, + { + "Answer": 7, + "Options": "a ) 7 , b ) 8 , c ) 6 , d ) 5 , e ) 4", + "Correct": "a", + "Explanation": "explanation : let the higher number be n and x be the number erased . then ( ( n ( n + 1 ) / 2 ) + x ) / ( n + 1 ) = 35 * 7 / 17 = 602 / 17 hence , n = 69 and x = 7 satisfy the above conditions . answer : a" + }, + { + "Answer": 3108, + "Options": "a ) 3100 , b ) 2500 , c ) 2545 , d ) 5800 , e ) 3108", + "Correct": "e", + "Explanation": "on dividing 3105 by 21 , we get 18 as remainder . number to be added to 3105 = ( 21 - 18 ) - 3 . hence , required number = 3105 + 3 = 3108 . answer e" + }, + { + "Answer": 8, + "Options": "a ) \u2212 48 , b ) \u2212 2 , c ) 8 , d ) 9 , e ) 48", + "Correct": "c", + "Explanation": "\"i . e . if a = - 1 then b = 9 or if a = 9 then b = - 1 but in each case a + b = - 1 + 9 = 8 answer : option c\"" + }, + { + "Answer": 24, + "Options": "a ) 15 , b ) 18 , c ) 21 , d ) 24 , e ) 27", + "Correct": "d", + "Explanation": "let x be the rainfall in the first week . then 1.5 x was the rainfall in the second week . 2.5 x = 40 x = 16 the rainfall during the second week was 1.5 * 16 = 24 inches the answer is d ." + }, + { + "Answer": 37.5, + "Options": "a ) a : 45 , b ) b : 25 , c ) c : 37.5 , d ) d : 36 , e ) e : 42", + "Correct": "c", + "Explanation": "if you have a 37.5 liter capacity , you start with 37.5 l of a and 0 l of b . 1 st replacement after the first replacement you have 37.5 - 15 = 22.5 l of a and 15 l of b . the key is figuring out how many liters of a and b , respectively , are contained in the next 15 liters of mixture to be removed . the current ratio of a to total mixture is 22.5 / 37.5 ; expressed as a fraction this becomes ( 45 / 2 ) / ( 75 / 2 ) , or 45 / 2 * 2 / 75 . canceling the 2 s and factoring out a 5 leaves the ratio as 9 / 15 . note , no need to reduce further as we ' re trying to figure out the amount of a and b in 15 l of solution . 9 / 15 of a means there must be 6 / 15 of b . multiply each respective ratio by 15 to get 9 l of a and 6 l of b in the next 15 l removal . final replacement the next 15 l removal means 9 liters of a and 6 liters of b are removed and replaced with 15 liters of b . 22.5 - 9 = 13.5 liters of a . 15 liters of b - 6 liters + 15 more liters = 24 liters of b . test to the see if the final ratio = 9 / 16 ; 13.5 / 24 = ( 27 / 2 ) * ( 1 / 24 ) = 9 / 16 . choice c is correct ." + }, + { + "Answer": 0.225, + "Options": "a ) 0.225 , b ) 0.228 , c ) 0.254 , d ) 0.256 , e ) none", + "Correct": "a", + "Explanation": "\"sol . ( x \u00d7 4 ) = ( 0.45 \u00d7 2 ) \u21d2 x = 0.9 / 4 = 0.225 . answer a\"" + }, + { + "Answer": 1.8, + "Options": "a ) 1.12 , b ) 1.16 , c ) 1.8 , d ) 1.3 , e ) none of these", + "Correct": "c", + "Explanation": "\"explanation : ( x * 5 ) = ( 0.75 * 12 ) x = 9 / 5 = 1.80 answer : c\"" + }, + { + "Answer": 295.45454545454544, + "Options": "a ) s . 200.45 , b ) s . 250.45 , c ) s . 295.45 , d ) s . 300.45 , e ) s . 310.45", + "Correct": "c", + "Explanation": "\"let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 650 but x = 120 % of y = 120 y / 100 = 12 y / 10 \u2234 12 y / 10 + y = 650 \u21d2 y [ 12 / 10 + 1 ] = 650 \u21d2 22 y / 10 = 650 \u21d2 22 y = 6500 \u21d2 y = 6500 / 22 = rs . 295.45 c )\"" + }, + { + "Answer": 320, + "Options": "a ) 400 km , b ) 320 km , c ) 360 km , d ) 550 km , e ) 600 km", + "Correct": "b", + "Explanation": "sol . average speed of a tractor = 25 km / h the speed of a bike in an hour = 25 \u00d7 2 = 50 km the speed of a car in an hour = 8 / 5 * 50 = 80 km so , the distance covered by car in 4 h is 80 \u00d7 4 = 320 km ans . ( b )" + }, + { + "Answer": 859560, + "Options": "a ) 456456 , b ) 576834 , c ) 562783 , d ) 634567 , e ) 859622", + "Correct": "e", + "Explanation": "\"dividend = quotient * divisor + reminder 859622 / 456 gives quotient = 1885 and reminder = 62 . so , the next number divisible by 456 is 456 places infront of 456 * 1885 which means 456 \u2013 62 = 394 should be added to 859622 . e\"" + }, + { + "Answer": 450, + "Options": "a ) 450 , b ) 616 , c ) 672 , d ) 900 , e ) 1024", + "Correct": "a", + "Explanation": "remainder = 0.40 - - > 40 / 100 - - > can be written as ( 40 / 4 ) / ( 100 / 4 ) = 10 / 25 so remainders can be 10 , 20 , 30 , 40 , . . . . . 90 . we need the sum of only 2 digit remainders - - > 10 + 20 + 30 + 40 + 50 + 60 + 70 + 80 + 90 = 450 answer : a" + }, + { + "Answer": 4, + "Options": "a ) 3 , b ) 1 , c ) 2 , d ) 4 , e ) 5", + "Correct": "d", + "Explanation": "\"let possible value of x is 76 least possible value of x / 18 is 76 / 18 = > 4 quotient with remainder 4 thus answer is ( d ) 4\"" + }, + { + "Answer": 54.166666666666664, + "Options": "a ) 54.2 % , b ) 58 % , c ) 62.5 % , d ) 64 % , e ) 75 %", + "Correct": "a", + "Explanation": "\"last year revenue = 100 ( assume ) ; this year revenue = 65 ; projected revenue = 120 . actual / projected * 100 = 65 / 120 * 100 = 54.2 % . answer : a .\"" + }, + { + "Answer": 110, + "Options": "a ) 101 , b ) 66 , c ) 110 , d ) 160 , e ) 12", + "Correct": "c", + "Explanation": "\"explanation : age of the 18 th student = [ 18 * 18 - ( 14 * 5 + 16 * 9 ) ] = ( 324 - 214 ) = 110 years . answer : c\"" + }, + { + "Answer": 17, + "Options": "a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19", + "Correct": "c", + "Explanation": "\"d = ( d - r ) / q = ( 123 - 4 ) / 7 = 119 / 7 = 17 c\"" + }, + { + "Answer": 0.75, + "Options": "a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4", + "Correct": "e", + "Explanation": "\"let p be the number of progressives in the country as a whole . in each province , the number of traditionalists is p / 18 the total number of traditionalists is 6 p / 18 = p / 3 . the total population is p + p / 3 = 4 p / 3 p / ( 4 p / 3 ) = 3 / 4 the answer is e .\"" + }, + { + "Answer": 6000, + "Options": "a ) 6500 , b ) 2000 , c ) 4500 , d ) 3000 , e ) 6000", + "Correct": "e", + "Explanation": "let the amounts be x , y , z in ascending order of value . as the interest rate and interest accrued are same for 2 years 6 years and 11 years i . e . 2 x = 6 y = 11 z = k . l . c . m . of 2 , 611 = 66 so x : y : z : = 33000 : 11000 : 6000 the amount deposited for 11 years = 6000 answer : e" + }, + { + "Answer": 25.00000000000001, + "Options": "a ) 50 % , b ) 40 % , c ) 25 % , d ) 20 % , e ) 10 %", + "Correct": "c", + "Explanation": "looking at the ratio we can take total number of people = 20 . . ans 5 / 20 or 25 % c" + }, + { + "Answer": 10.4, + "Options": "a ) 15.5 , b ) 15.4 , c ) 15.25 , d ) 10.4 , e ) 15.6", + "Correct": "d", + "Explanation": "total age of 20 men = 15.6 x 20 = 312 now , total age of 25 men = 364 . total age of five men added later = 364 - 312 = 52 . hence , the total average of five men = 52 / 5 = 10.4 answer : d" + }, + { + "Answer": 11, + "Options": "a ) 11 years , b ) 17 years , c ) 67 years , d ) 14 years , e ) 12 years", + "Correct": "a", + "Explanation": "\"age of the 15 th student = [ 15 * 15 - ( 14 * 5 + 16 * 9 ) ] = ( 225 - 214 ) = 11 years . answer : a\"" + }, + { + "Answer": 2570, + "Options": "a ) $ 1940 , b ) $ 2150 , c ) $ 2360 , d ) $ 2570 , e ) $ 2780", + "Correct": "d", + "Explanation": "let x be the value of the item . 0.07 * ( x - 1000 ) = 109.90 x = 2570 the answer is d ." + }, + { + "Answer": 7, + "Options": "a ) 1 , b ) 2 , c ) 5 , d ) 7 , e ) 20", + "Correct": "d", + "Explanation": "when positive integer n is divided by 3 , the remainder is 1 i . e . , n = 3 x + 1 values of n can be one of { 1 , 4 , 7 , 10 , 13 , 16 , 19 , 22 . . . . . . . . . . . . . . 49 , 52 , 59 . . . . . . . . . . . . . . . . . . } similarly , when n is divided by 5 , the remainder is 5 . . i . e . , n = 5 y + 4 values of n can be one of { 4 , 9 , 14 , 19 , . . . } combining both the sets we get n = { 4,19 , 52 , . . . . . . . . . . . } what is the smallest positive integer p , such that ( n + p ) is a multiple of 11 or 11 x in case of n = 4 p = 7 so for min value of p , we take min value of n . d is the answer ." + }, + { + "Answer": 33.33333333333333, + "Options": "a ) 50.5 % , b ) 44.4 % , c ) 22.2 % , d ) 33.3 % , e ) 25 %", + "Correct": "d", + "Explanation": "\"40 % of ( x - y ) = 20 % of ( x + y ) 40 / 100 ( x - y ) = 20 / 100 ( x + y ) x = 3 y required percentage = y / x * 100 = y / 3 y * 100 = 33.3 % answer is d\"" + }, + { + "Answer": 5, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "c", + "Explanation": "\"3 < x < 6 < y < 9 ; 3 < x y < 9 3 + y < x + 9 y - x < 6 . positive integer difference is 5 ( for example y = 8.5 and x = 3.5 ) answer : c .\"" + }, + { + "Answer": 23400, + "Options": "a ) $ 23400 , b ) $ 25920 , c ) $ 28080 , d ) $ 28500 , e ) $ 29160", + "Correct": "a", + "Explanation": "\"from 9 : 00 in the morning to 6 : 00 in the afternoon , inclusive there are 9 * 10 = 90 five - minute intervals , thus total of 54 * 30 tickets were sold . say x student and 2 x regular tickets were sold , then x + 2 x = 90 * 30 - - > x = 30 * 30 and 2 x = 2 * ( 30 * 30 ) = 30 * 60 . therefore , the total revenue from ticket sales that day was 30 * 30 * 6 + 30 * 60 * 10 = $ 23,400 . answer : a .\"" + }, + { + "Answer": 0.4117647058823529, + "Options": "a ) 5 / 17 , b ) 7 / 17 , c ) 4 / 17 , d ) 3 / 17 , e ) 5", + "Correct": "b", + "Explanation": "# of basic stereos was 2 / 3 of total and # of deluxe stereos was 1 / 3 of total , let ' s assume total = 15 , then basic = 10 and deluxe = 5 . now , if time needed to produce one deluxe stereo is 1 unit than time needed to produce one basic stereo would be 7 / 5 units . total time for basic would be 10 * 1 = 10 and total time for deluxe would be 5 * 7 / 5 = 7 - - > total time for both of them would be 10 + 7 = 17 - - > deluxe / total = 7 / 17 . b" + }, + { + "Answer": 70, + "Options": "a ) 18 , b ) 36 , c ) 72 , d ) 70 , e ) 108", + "Correct": "d", + "Explanation": "\"70 all u do is do 2 : 1 : 6 = > 2 x + x + 6 x = 126 = > x = 14 28 : 14 : 84 84 - 14 = 70 answer d\"" + }, + { + "Answer": 760, + "Options": "a ) 237 , b ) 287 , c ) 760 , d ) 287 , e ) 720", + "Correct": "c", + "Explanation": "\"explanation : let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 380 ) = 2 + 2 ( extra ) = > 2 x - 760 = x = > x = 760 . answer : c\"" + }, + { + "Answer": 62, + "Options": "a ) 53 , b ) 62 , c ) 51 , d ) 50 , e ) 49", + "Correct": "b", + "Explanation": "\"135 - 74 + 1 = 62 ' b ' is the answer\"" + }, + { + "Answer": 1804, + "Options": "a ) 1804 , b ) 1816 , c ) 1824 , d ) 1828 , e ) 1832", + "Correct": "a", + "Explanation": "\"the fastest way in an ap is to find the average and multiply with total integers . . between 38 and 127 , the smallest multiple of 4 is 40 and largest = 124 . . average = ( 40 + 124 ) / 2 = 164 / 2 = 82 . . total numbers = ( 124 - 40 ) / 4 + 1 = = 84 / 4 + 1 = 27 + 1 = 22 . . sum = 82 * 22 = 1804 ans a\"" + }, + { + "Answer": 49.9, + "Options": "a ) 40.9 kg , b ) 42.9 kg , c ) 49.9 kg , d ) 39.9 kg , e ) none of these", + "Correct": "c", + "Explanation": "here one boy is excluded and final average of the group decreases . \u2234 change in average is ( \u2013 ) ve = \u2013 0.1 kg . using the formula sum of the quantities excluded = ( changein no . ofquantities \u00d7 origina laverage ) + ( changeinaverage \u00d7 final no . ofquantities ) \u21d2 weight of the boy who left = ( 1 \u00d7 45 ) \u2013 ( \u2013 0.1 \u00d7 49 ) = 49.9 kg answer c" + }, + { + "Answer": 1.8, + "Options": "a ) 4 / 5 , b ) 6 / 5 , c ) 7 / 5 , d ) 8 / 5 , e ) 9 / 5", + "Correct": "e", + "Explanation": "\"w / x = 1 / 3 = > x = 3 w and w / y = 4 / 15 = > y = 15 / 4 w ( x + y ) / y = ( 3 w + 15 / 4 w ) / ( 15 / 4 w ) = ( 27 / 4 w ) / ( 15 / 4 w ) = 9 / 5 correct option : e\"" + }, + { + "Answer": 36, + "Options": "a ) 4 , b ) 8 , c ) 12 , d ) 36 , e ) 32", + "Correct": "d", + "Explanation": "6 flavours * 6 choices = 6 c 1 * 6 c 1 = 6 * 6 = 36 = d" + }, + { + "Answer": 1.7142857142857142, + "Options": "a ) 12 / 7 , b ) 4 / 1 , c ) 2 / 3 , d ) 3 / 4 , e ) 3 / 2", + "Correct": "a", + "Explanation": "\"given that milk / water = 4 x / x and 4 x + x = 45 - - > x = 9 . thus milk = 4 x = 36 liters and water = x = 9 liters . new ratio = 36 / ( 9 + 12 ) = 36 / 21 = 12 / 7 . answer : a .\"" + }, + { + "Answer": 78, + "Options": "a ) a ) 96 , b ) b ) 108 , c ) c ) 110 , d ) d ) 78 , e ) of these", + "Correct": "d", + "Explanation": "\"let the greater and the smaller number be g and s respectively . gs = 2496 g + s exceeds g - s by 64 i . e . , g + s - ( g - s ) = 64 i . e . , 2 s = 64 = > s = 32 . g = 2496 / s = 78 . answer : d\"" + }, + { + "Answer": 625.0000000000001, + "Options": "a ) 280 , b ) 400 , c ) 540 , d ) 625 , e ) 840", + "Correct": "d", + "Explanation": "of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month : 2 / 3 * 3 / 4 = 1 / 2 survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year : ( 1 - 3 / 5 ) * 1 / 2 = 1 / 5 survived the first year . 120 geese survived the first year : 1 / 5 * ( total ) = 125 - - > ( total ) = 625 . answer : d ." + }, + { + "Answer": 25300, + "Options": "a ) 10000 , b ) 12000 , c ) 23000 , d ) 25300 , e ) 45000", + "Correct": "d", + "Explanation": "explanation : salary of the manager = ( 56 * 8800 - 55 * 8500 ) = 25300 answer : d" + }, + { + "Answer": 0.4166666666666667, + "Options": "a ) 5 / 7 , b ) 4 / 7 , c ) 5 / 12 , d ) 4 / 7 , e ) 1 / 6", + "Correct": "c", + "Explanation": "here n ( s ) = ( 6 * 6 ) = 36 let e = event of getting a total more than 7 = { ( 2,6 ) , ( 3,5 ) , ( 3,6 ) , ( 4,4 ) , ( 4,5 ) , ( 4,6 ) , ( 5,3 ) , ( 5,4 ) , ( 5,5 ) , ( 5,6 ) , ( 6,2 ) , ( 6,3 ) , ( 6,4 ) , ( 6,5 ) , ( 6,6 ) } p ( e ) = n ( e ) / n ( s ) = 15 / 36 = 5 / 12 option c" + }, + { + "Answer": 10, + "Options": "a ) a ) 9 , b ) b ) 5 , c ) c ) 7 , d ) d ) 10 , e ) e ) none of the above", + "Correct": "d", + "Explanation": "sol . apples 250 each carries 25 = 250 / 25 = 10 answer : d" + }, + { + "Answer": 36.5, + "Options": "a ) 36.5 , b ) 35 , c ) 34 , d ) 33 , e ) 32.5", + "Correct": "a", + "Explanation": "\"correct sum = ( 36 * 50 + 48 - 23 ) = 1825 . correct mean = 1825 / 50 = 36.5 answer a\"" + }, + { + "Answer": 0.18, + "Options": "a ) 0.52 , b ) 0.42 , c ) 0.18 , d ) 0.64 , e ) 0.46", + "Correct": "c", + "Explanation": "\"given exp . = 0.3 * 0.3 + ( 0.3 * 0.3 ) = 0.09 + 0.09 = 0.18 answer is c .\"" + }, + { + "Answer": 0.08333333333333333, + "Options": "a ) 1 / 12 , b ) 1 / 6 , c ) 1 / 4 , d ) 1 / 3 , e ) 1 / 2", + "Correct": "a", + "Explanation": "x = - 2.5 prob = 1 / 12 answer - a" + }, + { + "Answer": 2, + "Options": "a ) 10 , b ) 4 , c ) 2 , d ) 14 , e ) 16", + "Correct": "c", + "Explanation": "\"number of pens = 848 number of pencils = 630 required number of students = h . c . f . of 848 and 630 = 2 answer is c\"" + }, + { + "Answer": 26, + "Options": "a ) 20 years , b ) 21 years , c ) 22 years , d ) 23 years , e ) 26 years", + "Correct": "e", + "Explanation": "\"explanation : let the average age of the whole team by x years . 11 x \u00e2 \u20ac \u201c ( 29 + 32 ) = 9 ( x - 1 ) 11 x \u00e2 \u20ac \u201c 9 x = 52 2 x = 52 x = 26 . so , average age of the team is 26 years . answer e\"" + }, + { + "Answer": 3500, + "Options": "a ) 3600 , b ) 3890 , c ) 88798 , d ) 2789 , e ) 3500", + "Correct": "e", + "Explanation": "\"explanation : manager ' s monthly salary rs . ( 1500 * 21 - 1400 * 20 ) = rs . 3500 . answer : e\"" + }, + { + "Answer": 36, + "Options": "a ) 21 , b ) 35 , c ) 36 , d ) 60 , e ) 65", + "Correct": "c", + "Explanation": "\"the total number of the people in the room must be a multiple of both 7 and 12 ( in order 3 / 7 and 5 / 12 of the number to be an integer ) , thus the total number of the people must be a multiple of lcm of 7 and 12 , which is 84 . since , the total number of the people in the room is greater than 50 and less than 100 , then there are 84 people in the room . therefore there are 3 / 7 * 84 = 36 people in the room under the age of 21 . answer : c .\"" + }, + { + "Answer": 15, + "Options": "a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16", + "Correct": "d", + "Explanation": "r + b + c + 14 + 15 = 12 * 5 = 60 = > r + b + c = 60 - 29 = 31 r + b + c + 29 = 31 + 29 = 60 average = 60 / 4 = 15 answer d" + }, + { + "Answer": 0.36, + "Options": "a ) 3 , b ) 6 , c ) 1 / 9 , d ) 1 / 3 , e ) 9 / 25", + "Correct": "e", + "Explanation": "\"explanation : solution : given x = k / y ^ 2 , where k is constant . now , y = 3 and x = 1 gives k = 9 . . ' . x = 9 / y ^ 2 = > x = 9 / 5 ^ 2 = 9 / 25 answer : e\"" + }, + { + "Answer": 1.6666666666666667, + "Options": "a ) 9 / 4 , b ) 3 / 2 , c ) 4 / 3 , d ) 5 / 3 , e ) 1 / 2", + "Correct": "d", + "Explanation": "\"sq rt ( 5 x / 3 ) = x = > 5 x / 3 = x ^ 2 = > x = 5 / 3 ans - d\"" + }, + { + "Answer": 2011, + "Options": "a ) 2010 , b ) 2001 , c ) 2012 , d ) 2011 , e ) 2009", + "Correct": "d", + "Explanation": "\"suppose commodity x will cost 40 paise more than y after z years . then , ( 4.20 + 0.40 z ) - ( 6.30 + 0.15 z ) = 0.40 0.25 z = 0.40 + 2.10 z = 2.50 / 0.25 = 250 / 25 = 10 . therefore , x will cost 40 paise more than y 10 years after 2001 i . e . , 2011 . answer is d .\"" + }, + { + "Answer": 2, + "Options": "a ) - 1 , b ) 0 , c ) 1 , d ) 2 , e ) 4", + "Correct": "d", + "Explanation": "\"since f ( n ) = f ( n - 1 ) - n then : f ( 6 ) = f ( 5 ) - 6 and f ( 5 ) = f ( 4 ) - 5 . as given that f ( 4 ) = 13 then f ( 5 ) = 13 - 5 = 8 - - > substitute the value of f ( 5 ) back into the first equation : f ( 6 ) = f ( 5 ) - 6 = 8 - 6 = 2 . answer : d . questions on funtions to practice :\"" + }, + { + "Answer": 80, + "Options": "a ) 25 , b ) 80 , c ) 90 , d ) 140 , e ) it can not be determined from the information given", + "Correct": "b", + "Explanation": "\"the arithmetic mean of a and b = ( a + b ) / 2 = 45 - - a + b = 90 - - 1 similarly for b + c = 170 - - 2 subtracting 1 from 2 we have c - a = 80 ; answer : b\"" + }, + { + "Answer": 7.359999999999999, + "Options": "a ) 6.6 kg , b ) 6.8 kg , c ) 6.7 kg , d ) 6.9 kg , e ) 7.36 kg", + "Correct": "e", + "Explanation": "\"800 * 9.2 7360.0 gm 7.36 kg answer : e\"" + }, + { + "Answer": 3, + "Options": "a ) 4 , b ) 3 , c ) 2 , d ) 0 , e ) 5", + "Correct": "b", + "Explanation": "\"1022 \u00e3 \u00b7 25 = 40 with remainder = 22 22 + 3 = 25 . hence 3 should be added to 1022 so that the sum will be divisible by 25 answer : option b\"" + }, + { + "Answer": 64, + "Options": "a ) 22 , b ) 77 , c ) 29 , d ) 64 , e ) 21", + "Correct": "d", + "Explanation": "\"63 + 5 * 12 / ( 180 / 3 ) = 63 + 5 * 12 / ( 60 ) = 63 + ( 5 * 12 ) / 60 = 63 + 1 = 64 . answer : d\"" + }, + { + "Answer": 10, + "Options": "a ) 5 , b ) 6 , c ) 9 , d ) 10 , e ) 15", + "Correct": "d", + "Explanation": "since the starting point is given as the $ 4000 scholarship , assume $ 4000 scholarships to be x by the given information , $ 2500 scholarships = 2 x and $ 1250 scholarships = 6 x gievn : total $ 1250 scholarships = $ 75000 6 x * 1250 = 75000 solve for x = 10 option d" + }, + { + "Answer": 33, + "Options": "a ) 0.33 , b ) 0.44 , c ) 33 , d ) 44 , e ) 55", + "Correct": "c", + "Explanation": "\"a dozen eggs cost as much as a pound of rice - - > 12 eggs = 1 pound of rice = 33 cents ; a half - liter of kerosene costs as much as 6 eggs - - > 6 eggs = 1 / 2 liters of kerosene . how many cents does a liter of kerosene cost - - > 1 liter of kerosene = 12 eggs = 12 / 12 * 33 = 33 cents . answer : c .\"" + }, + { + "Answer": 66, + "Options": "a ) 18 , b ) 82 , c ) 66 , d ) 27 , e ) 77", + "Correct": "c", + "Explanation": "\"let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 x / 2 = ( 73 - 40 ) = > x / 2 = 33 = > x = 66 . answer : c\"" + }, + { + "Answer": 0.625, + "Options": "a ) 1 / 4 , b ) 3 / 8 , c ) 1 / 2 , d ) 5 / 8 , e ) 3 / 4", + "Correct": "d", + "Explanation": "\"total nos of ways in which we can choose n = 96 n ( n + 1 ) ( n + 2 ) will be divisible by 8 ? case 1 : n = odd then n + 2 = odd & n + 1 will be even i . e this needs get divided by 8 , hence is a multiple of 8 so we have 8 . . 96 = 12 multiples to fill the n + 1 pos hence 12 ways case 2 : n is even then n + 2 will be even & the product will be divisible by 24 & thus 8 so nos of values that can be used for n = 2 . . . . 96 ( all even nos ) i . e 48 nos total = 48 + 12 = 60 ways so reqd p = 60 / 96 = 5 / 8 ; answer : d\"" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 3 , c ) 7 , d ) 5 , e ) 6", + "Correct": "b", + "Explanation": "as per question = > n = 8 p + 1 for some integer p hence 3 n = > 24 q + 3 = > remainder = > 3 for some integer q hence b" + }, + { + "Answer": 47.368421052631575, + "Options": "a ) 35.7 % , b ) 39.8 % , c ) 43.2 % , d ) 47.4 % , e ) 51.2 %", + "Correct": "d", + "Explanation": "\"y = 1.9 x x = y / 1.9 = 10 y / 19 x is 9 / 19 less which is 47.4 % less than y . the answer is d .\"" + }, + { + "Answer": 107, + "Options": "a ) 107 kg , b ) 80 kg , c ) 120 kg , d ) 90 kg , e ) 100", + "Correct": "a", + "Explanation": "\"solution total weight increased = ( 10 x 4.2 ) kg = 42 kg . weight of new person = ( 65 + 42 ) kg = 107 kg . answer a\"" + }, + { + "Answer": 24, + "Options": "a ) 6 , b ) 36 , c ) 48 , d ) 24 , e ) 72", + "Correct": "d", + "Explanation": "\"let total no of students in the class be n so , we are told that n is divisible by both 8 24 so , lets find the least common multiple of 8 24 , ie 24 so our answer is ( d ) 24\"" + }, + { + "Answer": 1.6, + "Options": "a ) $ 0.60 , b ) $ 0.80 , c ) $ 1.00 , d ) $ 1.20 , e ) $ 1.60", + "Correct": "e", + "Explanation": "\"let price of a sundae = s price of ice cream bar = . 6 $ 125 * . 6 + 125 * s = 275 = > 125 * s = 200 = > s = 1.6 answer e\"" + }, + { + "Answer": 40, + "Options": "a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80", + "Correct": "a", + "Explanation": "\"let the average after 6 th inning = x then , average after 5 th inning = x - 2 5 ( x - 2 ) + 50 = 6 x x = 10 - 50 = 40 answer is a\"" + }, + { + "Answer": 45, + "Options": "a ) 45 , b ) 40 , c ) 35 , d ) 50 , e ) 55", + "Correct": "a", + "Explanation": "\"basically , this question is asking you to figure out how many students are being double - counted . a - club has 180 members ( 1 / 2 of 360 ) b - club has 225 members ( 5 / 8 of 360 ) c - club has 270 members ( 3 / 4 of 360 ) we can create an equation to solve this : 180 + 225 + 270 = n + x + 2 y where n is the number of students , x is the number of students in two clubs , and y is the number of students in three clubs . the question provides y for us ( 135 ) . 180 + 225 + 270 = 360 + x + 270 x = 405 - 360 = 45 a\"" + }, + { + "Answer": 14, + "Options": "a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 14", + "Correct": "e", + "Explanation": "\"substitute y by 2 in x + 5 y = 24 x + 5 ( 2 ) = 24 x + 10 = 24 if we substitute x by 14 in x + 10 = 24 , we have 14 + 10 = 24 . hence x = 14 correct answer e\"" + }, + { + "Answer": 33.33333333333333, + "Options": "a ) 18.75 % , b ) 33 % , c ) 30 % , d ) 50 % , e ) 100 %", + "Correct": "b", + "Explanation": "\"let wage of erica = 10 wage of robin = 1.2 * 10 = 12 wage of charles = 1.6 * 10 = 16 percentage by which wage earned by charles is more than that earned by robin = ( 16 - 12 ) / 12 * 100 % = 4 / 12 * 100 % = 33 % answer b\"" + }, + { + "Answer": 2, + "Options": "a ) 3 : 2 , b ) 4 : 3 , c ) 8 : 7 , d ) 5 : 8 , e ) 2 : 1", + "Correct": "e", + "Explanation": "let the two numbers be x and y . ( 1 / 10 ) * x + y = ( 6 / 5 ) * y ( 1 / 10 ) * x = ( 1 / 5 ) * y x / y = 2 / 1 = 2 / 1 the answer is e ." + }, + { + "Answer": 12, + "Options": "a ) 16 , b ) 12 , c ) 18 , d ) 22 , e ) 08", + "Correct": "b", + "Explanation": "2 * 6 = 12 . answer is b ." + }, + { + "Answer": 27550, + "Options": "a ) 23,550 , b ) 27,550 , c ) 31,550 , d ) 35,550 , e ) 39,550", + "Correct": "b", + "Explanation": "\"2 + 4 + 6 + 8 + . . . + 100 = 2550 502 + 504 + . . . + 600 = 50 ( 500 ) + ( 2 + 4 + . . . + 100 ) = 25,000 + 2550 = 27,550 the answer is b .\"" + }, + { + "Answer": 22, + "Options": "a ) - 4 , b ) - 2 , c ) 11 , d ) 13 , e ) 22", + "Correct": "e", + "Explanation": "\"the equation that can be formed is : 3 x - 18 = 70 - x or , 4 x = 88 or , x = 22 . e answer .\"" + }, + { + "Answer": 24.242424242424242, + "Options": "a ) 16 % , b ) 20 % , c ) 24 % , d ) 28 % , e ) 32 %", + "Correct": "c", + "Explanation": "\"let p be the original price per unit of gas . let x be the original gas consumption . let y be the reduced gas consumption . y * 1.1 * 1.2 * p = x * p y = x / ( 1.1 * 1.2 ) which is about 0.76 x which is a decrease of about 24 % . the answer is c .\"" + }, + { + "Answer": 0.16666666666666666, + "Options": "a ) 5 / 6 , b ) 1 / 5 , c ) 1 / 6 , d ) 1 / 7 , e ) 1 / 24", + "Correct": "c", + "Explanation": "\"let x be the number of upgraded sensors on the satellite . the number of non - upgraded sensors per unit is x / 6 . the number of non - upgraded sensors on the whole satellite is 30 ( x / 6 ) = 5 x . the fraction of sensors which have been upgraded is x / ( x + 5 x ) = x / 6 x = 1 / 6 the answer is c .\"" + }, + { + "Answer": 48, + "Options": "a ) 6 , b ) 36 , c ) 48 , d ) 60 , e ) 72", + "Correct": "c", + "Explanation": "\"let total no of students in the class be n so , we are told that n is divisible by both 16 24 so , lets find the least common multiple of 16 24 , ie 48 so our answer is ( c ) 48\"" + }, + { + "Answer": 290, + "Options": "a ) $ 150 , b ) $ 290 , c ) $ 365 , d ) $ 715 , e ) $ 730", + "Correct": "b", + "Explanation": "\"total weekly income over 5 weeks = $ 556 + $ 413 + $ 420 + $ 436 + $ 395 = $ 2220 for avg weekly income to be $ 500 over 7 weeks , we need total weekly income over 7 weeks = $ 3500 now , $ 3500 - $ 2220 = $ 1280 from this , we subtract base salary for 2 weeks i . e $ 350 * 2 = $ 700 therefore , commission = $ 1280 - $ 700 = $ 580 for 2 weeks avg weekly commission = $ 290 answer b\"" + }, + { + "Answer": 1.5999999999999999, + "Options": "a ) 1.9 , b ) 1.7 , c ) 1.2 , d ) 1.5 , e ) 1.6", + "Correct": "e", + "Explanation": "\"speed of boat in still water ( b ) = 4.8 km / hr . speed of boat with stream ( down stream ) , d = b + u speed of boat against stream ( up stream ) , u = b \u2013 u it is given upstream time is twice to that of down stream . \u21d2 downstream speed is twice to that of upstream . so b + u = 2 ( b \u2013 u ) \u21d2 u = b / 3 = 1.6 km / hr . answer : e\"" + }, + { + "Answer": 50, + "Options": "a ) 12 liters , b ) 32 liters , c ) 41 liters , d ) 50 liters , e ) 34 liters", + "Correct": "d", + "Explanation": "\"milk = 3 / 5 * 125 = 75 liters water = 50 liters 75 : ( 50 + p ) = 3 : 4 150 + 3 p = 400 = > p = 50 50 liters of water are to be added for the ratio become 3 : 4 . answer : d\"" + }, + { + "Answer": 24, + "Options": "a ) 30 , b ) 80 , c ) 20 , d ) 25 , e ) 24", + "Correct": "e", + "Explanation": "let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 . x / 2 = ( 35 - 23 ) = > x / 2 = 12 = > x = 24 . answer : e" + }, + { + "Answer": 25, + "Options": "a ) 23 , b ) 28 , c ) 25 , d ) 19 , e ) 11", + "Correct": "c", + "Explanation": "explanation : given r \u2013 q = q \u2013 t and r + t = 50 which gives q = 25 as the difference between r & q and q & t is same so answer is 25 years answer : c" + }, + { + "Answer": 3, + "Options": "a ) 3 , b ) 5 , c ) 6 , d ) 8 , e ) 9", + "Correct": "a", + "Explanation": "\"24 x + 21 y = 3 ( 8 x + 7 y ) which will be a minimum positive number when 8 x + 7 y = 1 . 8 ( 1 ) + 7 ( - 1 ) = 1 then 3 ( 8 x + 7 y ) can have a minimum positive value of 3 . the answer is a .\"" + }, + { + "Answer": 95, + "Options": "a ) 95 , b ) 106 , c ) 122 , d ) 116 , e ) 122", + "Correct": "a", + "Explanation": "\"average = total runs / no . of innings = 32 so , total = average x no . of innings = 32 * 20 = 640 now increase in avg = 4 runs . so , new avg = 32 + 3 = 35 runs total runs = new avg x new no . of innings = 35 * 21 = 735 runs made in the 11 th inning = 735 - 640 = 95 answer : a\"" + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 8 , c ) 10 , d ) 11 , e ) 13", + "Correct": "a", + "Explanation": "\"joan starts off with 100 $ . . which is to be tripled every month her monthly payments look like this : 100 , 300 , 900 , 2700 . . . . . . . . . upto 36400 this can be re written as : 100 x 1 , 100 x 3 , 100 x 9 , 100 x 27 . . . . . . 100 x 364 so we have 1 , 3 , 9 , 27 . . . . . 36400 in gp we know that a = 1 , and r = 3 ( its easy to figure it out by looking at the question , but regardless of it being mentioned in the question we can still compute the value of r using the formula tn = a 3 ^ n - 1 . . . ) therefore to find the sum of n terms of a gp we use this formula : sn = a ( 1 - r ^ n ) / 1 - r using this and plugging in the information we get . . . 364 = 1 - 3 ^ n / 1 - 3 ; 1 - 3 ^ n / - 2 cross multiplying we get 364 x - 2 = 1 - 3 ^ n - 728 = 1 - 3 ^ n - 729 = - 3 ^ n 729 = 3 ^ n ( negatives cancel out ) 729 can also be re written as 3 ^ 6 therefore ; 3 ^ 6 = 3 ^ n thus n = 6 ( a )\"" + }, + { + "Answer": 40, + "Options": "a ) 32 , b ) 40 , c ) 48 , d ) 54 , e ) 60", + "Correct": "b", + "Explanation": "\"16 liters is 40 % of the capacity c . 16 = 0.4 c c = 16 / 0.4 = 40 liters . the answer is b .\"" + }, + { + "Answer": 130, + "Options": "a ) 120 , b ) 130 , c ) 110 , d ) 150 , e ) 180", + "Correct": "b", + "Explanation": "let x be the correct answer and y be the wrong answer so the total number of questions is ( x + y ) = 150 = > 4 x - 2 y = 480 = > 6 x = 780 hence x = 130 answer : b" + }, + { + "Answer": 390, + "Options": "a ) 370 , b ) 365 , c ) 390 , d ) 456 , e ) 460", + "Correct": "c", + "Explanation": "\"easy solution : n = dq 1 + 251 2 n = 2 dq 1 + 502 - ( 1 ) 2 n = dq 2 + 112 - ( 2 ) as ( 1 ) = ( 2 ) = 2 n d * ( q 2 - 2 q 1 ) = 390 d * some integer = 390 checking all options only ( c ) syncs with it . answer c\"" + }, + { + "Answer": 40, + "Options": "a ) 15 min , b ) 18 min , c ) 16 min , d ) 20 min , e ) 40 min", + "Correct": "e", + "Explanation": "\"in 1 hr , the bus covers 120 km without stoppages and 40 km with stoppages . stoppage time = time take to travel ( 120 - 40 ) km i . e 80 km at 120 km / hr . stoppage time = 80 / 120 hrs = 40 min answer : e\"" + }, + { + "Answer": 4.000000000000002, + "Options": "a ) 4.2 , b ) 4.4 , c ) 4.6 , d ) 5.6 , e ) 4", + "Correct": "e", + "Explanation": "\"sum of the remaining two numbers = ( 3.95 * 6 ) - [ ( 4 * 2 ) + ( 3.85 * 2 ) ] = 8 required average = ( 8 / 2 ) = 4 e\"" + }, + { + "Answer": 6, + "Options": "a ) 4.37 % , b ) 5 % , c ) 6 % , d ) 8.75 % , e ) none of these", + "Correct": "c", + "Explanation": "solution increase in 10 year = ( 80000 - 50000 ) = 30000 . increase % = ( 30000 / 50000 x 100 ) % = 60 % \u00e2 \u02c6 \u00b4 required average = ( 60 / 10 ) % = 6 % answer c" + }, + { + "Answer": 8, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9", + "Correct": "d", + "Explanation": "\"lets say 5 and 10 ounce packages be x and y respectively . given that , 5 x + 10 y = 130 and x = y + 2 . what is the value of y . substituting the x in first equation , 5 y + 10 + 10 y = 130 - > y = 120 / 15 . = 8 d\"" + }, + { + "Answer": 0.16666666666666666, + "Options": "a ) 1 / 3 , b ) 1 / 6 , c ) 6 , d ) 3 , e ) 2", + "Correct": "b", + "Explanation": "explanation : x = y < = > 1 / q = ( 2 / q ) - 6 < = > 1 / q = 6 < = > q = 1 / 6 . answer : b" + }, + { + "Answer": 114.28571428571428, + "Options": "a ) 30 % , b ) 33 1 / 2 % , c ) 40 % , d ) 60 % , e ) 114.28 %", + "Correct": "e", + "Explanation": "\"original visual range = 70 km new visual range = 150 km percent increase in the visual range by using the telescope = ( 150 - 70 ) / 70 * 100 % = 8 / 7 * 100 % = 114.28 % answer e\"" + }, + { + "Answer": 3, + "Options": "a ) 5 , b ) 4 , c ) 7 , d ) 3 , e ) 8", + "Correct": "d", + "Explanation": "\"( 6 * 75 ) + 47 + x > 500 450 + 47 + x > 500 497 + x > 500 = > x > 3 option d\"" + }, + { + "Answer": 35, + "Options": "a ) $ 35 , b ) $ 36 , c ) $ 37 , d ) $ 38 , e ) $ 39", + "Correct": "a", + "Explanation": "\"p = ( 2 / 5 ) * p + 21 ( 3 / 5 ) * p = 21 p = 35 the answer is a .\"" + }, + { + "Answer": 450, + "Options": "a ) 350 , b ) 250 , c ) 450 , d ) 550 , e ) 650", + "Correct": "c", + "Explanation": "\"the number of chocolate bars is equal to 18 ? 25 = 450 correct answer c\"" + }, + { + "Answer": 3108, + "Options": "a ) 1208 , b ) 3108 , c ) 241 , d ) 217 , e ) 3147", + "Correct": "b", + "Explanation": "\"sol . on dividing 3105 by 21 , we get 18 as remainder . number to be added to 3105 = ( 21 - 18 ) - 3 . hence , required number = 3105 + 3 = 3108 . option b\"" + }, + { + "Answer": 540, + "Options": "a ) 5.04 % , b ) 50.4 % , c ) 209 % , d ) 540 % , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : while calculation in terms of percentage we need to multiply by 100 , so 5.40 * 100 = 540 answer : option d\"" + }, + { + "Answer": 96, + "Options": "a ) 96 % , b ) 95 % , c ) 2400 % , d ) 200 % , e ) 400 %", + "Correct": "a", + "Explanation": "lets take a number 20 20 / 5 = 4 20 * 5 = 100 diff = 100 - 4 = 96 % answer : a" + }, + { + "Answer": 4.870967741935484, + "Options": "a ) 0 , b ) 156 / 31 , c ) 123 / 31 , d ) 151 / 31 , e ) none", + "Correct": "d", + "Explanation": "solution : both fractions should be reduced before performing arithmetic operations . we get 3 * 27 / 31 + 3.27 / 3.31 = 3 * 27 / 31 + 27 / 31 = 4 * 27 / 31 = 151 / 31 answer d" + }, + { + "Answer": 35, + "Options": "a ) 25 % , b ) 35 % , c ) 45 % , d ) 70 % , e ) 80 %", + "Correct": "b", + "Explanation": "\"1 . we are given the following percentages : 30 ( 70 ) , 40 ( 60 ) , 25 ( 75 ) . there are two threads from here . first starts at 30 % and finishes there . second one starts at 70 , then 40 , and then 25 . we need a value that is divisible by 7 , 2 , and 5 at least once . lets pick a number now , say 700 . so say if non hawks are 700 ( this is 70 % of the total , so total = 1000 ) , then paddy warbs are 2 / 5 x 700 = 1400 / 5 = 280 . kingfishers , therefore , are 280 / 4 = 70 . lets add them up . 300 hawks + 280 peddy warbs + 70 kingsifhers = 650 . so all others are 1000 - 650 = 350 or 35 % of total birds . the main job here to to identify the smart number to start the question with . this can be time consuming , but once identified , this question can be solved fairly quickly . 2 . another method : if x is total - - > non hawks = 0.7 x - - > warbs = 0.4 ( 0.7 x ) - - > kfs = 0.25 ( 0.4 ( 0.7 x ) ) . our job is to find out e : ( 0.3 x + 0.28 x + 0.07 x ) / x . or 0.65 x / x = 0.65 . we need to find 1 - 0.65 = 0.35 or 35 % . b\"" + }, + { + "Answer": 121, + "Options": "a ) 21 , b ) 41 , c ) t = 121 , d ) 241 , e ) 481", + "Correct": "c", + "Explanation": "or u can just use the answer choices here . since the answers are already arranged in ascending order , the first number which gives remainder t as 1 for all three is the correct answer . in the given question , the first number which gives a remainder of 1 for 6,8 and 10 is 121 . c" + }, + { + "Answer": 71, + "Options": "a ) 71 , b ) 70 , c ) 72 , d ) 73 , e ) 36", + "Correct": "a", + "Explanation": "lcm = 72 72 - 1 = 71 answer : a" + }, + { + "Answer": 20, + "Options": "a ) 40 , b ) 20 , c ) 60 , d ) 80 , e ) 65", + "Correct": "b", + "Explanation": "\"number of pens = 1200 number of pencils = 820 required number of students = h . c . f . of 1200 and 820 = 20 answer is b\"" + }, + { + "Answer": 40, + "Options": "a ) 20 , b ) 25 , c ) 30 , d ) 40 , e ) 50", + "Correct": "d", + "Explanation": "\"let the list price be 2 x for min sale price , the first discount given should be 50 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 40 and 0.8 x = 32 so lowest sale price is 32 , which w is 40 % of 80 hence , d is the answer\"" + }, + { + "Answer": 15, + "Options": "a ) 5 % , b ) 7 % , c ) 9 % , d ) 15 % , e ) 12 %", + "Correct": "d", + "Explanation": "\"explanation : the difference of two successive amounts must be the simple interest in 1 year on the lower amount of money . s . i = 20286 / - - 17640 / - = rs . 2646 / - rate of interest = ( 2646 / 17640 ) \u00d7 ( 100 / 1 ) = > 15 % answer : option d\"" + }, + { + "Answer": 50, + "Options": "a ) 50 , b ) 47 , c ) 48 , d ) 49 , e ) 46", + "Correct": "a", + "Explanation": "solution 5 years ago average age of a , b , c , d = 45 years = > 5 years ago total age of a , b , c , d = 45 x 4 = 180 years = > total present age of a , b , c , d = 180 + 5 x 4 = 200 years if e ' s present age is x years = 200 + x / 5 = 50 x = 50 years . answer a" + }, + { + "Answer": 17, + "Options": "a ) $ 13 , b ) $ 15 , c ) $ 17 , d ) $ 19 , e ) $ 21", + "Correct": "c", + "Explanation": "\"average price per book = ( 1180 + 860 ) / ( 65 + 55 ) = 2040 / 120 = $ 17 the answer is c .\"" + }, + { + "Answer": 9, + "Options": "a ) 5 , b ) 8 , c ) 9 , d ) 10 , e ) 11", + "Correct": "c", + "Explanation": "\"expanding we have 6 x ^ 2 - 3 x + 4 x - 2 6 x ^ 2 + x - 2 taking coefficients , a = 6 , k = 1 , n = - 2 therefore a - n + k = 6 - ( - 2 ) + 1 = 8 + 1 = 9 the answer is c .\"" + }, + { + "Answer": 50, + "Options": "a ) 90 , b ) 95 , c ) 70 , d ) 85 , e ) 50", + "Correct": "e", + "Explanation": "so addition of all term - 10 , 20 , 30 , . . . . . . . 90 so average = ( 10 + 20 + 30 + 40 + 50 + 60 + 70 + 80 + 90 ) / 9 = ( 450 ) / 9 = 50 hence , the correct answer is e ." + }, + { + "Answer": 0.39999999999999997, + "Options": "a ) 0.4 , b ) 0.0625 , c ) 0.2 , d ) 0.25 , e ) 0.6", + "Correct": "a", + "Explanation": "\"index for females = ( 20 - 6 ) / 20 = 7 / 10 = 0.7 index for males = ( 20 - 14 / 20 = 3 / 10 = 0.3 index for females exceeds males by 0.7 - 0.3 = 0.4 answer : a\"" + }, + { + "Answer": 8, + "Options": "a ) 6 , b ) 8 , c ) 10 , d ) 14 , e ) 15", + "Correct": "b", + "Explanation": "\"let the number be xy . given xy \u2013 yx = 36 . this means the number is greater is than the number got on reversing the digits . this shows that the ten \u2019 s digit x > unit digit y . also given ratio between digits is 1 : 2 = > x = 2 y ( 10 x + y ) \u2013 ( 10 y + x ) = 36 = > x \u2013 y = 4 = > 2 y \u2013 y = 4 . hence , ( x + y ) \u2013 ( x \u2013 y ) = 3 y \u2013 y = 2 y = 8 b\"" + }, + { + "Answer": 40, + "Options": "a ) 45 % , b ) 40 % , c ) 25 % , d ) 28 % , e ) 33.33 %", + "Correct": "b", + "Explanation": "i year best is to give a number to his income , say 100 . . and let saving be x . . so expenditure = 100 - x next year - income = 140 savings = 2 x expenditure = 140 - 2 x . . now 140 - 2 x + 100 - x = 2 ( 100 - x ) . . . 240 - 3 x = 200 - 2 x . . . . . . . . . . . . . . . . x = 40 . . . saving % = 40 / 100 * 100 = 40 % answer : b" + }, + { + "Answer": 1626, + "Options": "a ) 1636 , b ) 1346 , c ) 1378 , d ) 1635 , e ) 1489", + "Correct": "a", + "Explanation": "\"let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 10 5 x = 1355 x = 271 large number = 271 + 1365 = 1636 a\"" + }, + { + "Answer": 6, + "Options": "a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8", + "Correct": "d", + "Explanation": "( ( 90 \u03b8 33 ) \u03b8 17 ) the remainder of 90 divided by 33 is 24 ; the remainder of 24 divided by 17 is 7 ; ( 97 \u03b8 ( 33 \u03b8 17 ) ) the remainder of 33 divided by 17 is 16 ; the remainder of 97 divided by 16 is 1 . 7 - 1 = 6 . answer : d ." + }, + { + "Answer": 1, + "Options": "a ) 1,000 , b ) 100 , c ) 1 , 000,000 , d ) 10 , e ) 10,000", + "Correct": "c", + "Explanation": "\"given that 1,000 microns = 1 decimeter = 1,000 , 000,000 angstroms so , 1 micron = 1,000 , 000,000 / 1,000 = 1 , 000,000 answer : c\"" + }, + { + "Answer": 13.99999999999999, + "Options": "a ) 14 , b ) 24 , c ) 34 , d ) 12 , e ) 13", + "Correct": "a", + "Explanation": "\"required difference = [ 3 1 / 2 % of $ 8400 ] \u2013 [ 3 1 / 3 % of $ 8400 ] = [ ( 7 / 20 ) - ( 10 / 3 ) ] % of $ 8400 = 1 / 6 % of $ 8400 = $ [ ( 1 / 6 ) * ( 1 / 100 ) * 8400 ] = $ 14 . answer a .\"" + }, + { + "Answer": 1600, + "Options": "a ) q = 200 , b ) q = 600 , c ) q = 800 , d ) q = 1600 , e ) q = 50", + "Correct": "d", + "Explanation": "\"original cost c 1 = t 1 * b 1 ^ 4 new cost c 2 = t 2 * b 2 ^ 4 . . . . only b is doubled so t 2 = t 1 and b 2 = 2 b 1 c 2 = t 2 * ( 2 b 1 ) ^ 4 = 16 ( t 1 * b 1 ^ 4 ) = 16 c 1 16 times c 1 = > 1600 % of c 1 ans d = 1600\"" + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 12 , c ) 10 , d ) 15 , e ) 18", + "Correct": "a", + "Explanation": "\"a = 2 m = m + 12 m = 12 a = 24 a = 4 b , and so b = 6 the answer is a .\"" + }, + { + "Answer": 89.99999999999999, + "Options": "a ) 124 % , b ) b ) 120 % , c ) c ) 96 % , d ) d ) 90 % , e ) e ) 64 %", + "Correct": "d", + "Explanation": "m = ( 150 / 100 ) t t = ( 60 / 100 ) j = > m = ( 90 / 100 ) j answer d ." + }, + { + "Answer": 29, + "Options": "a ) 27 , b ) 29 , c ) 28 , d ) 30 , e ) 31", + "Correct": "b", + "Explanation": "\"13601 \u00f7 87 = 156 , remainder = 29 hence 29 is the least number which can be subtracted from 13601 such that the remainder is divisible by 87 answer is b\"" + }, + { + "Answer": 1200, + "Options": "a ) 1250 , b ) 1300 , c ) 1375 , d ) 1200 , e ) none of them", + "Correct": "d", + "Explanation": "let 4207 - x = 3007 then x = 4207 - 3007 = 1200 answer is d" + }, + { + "Answer": 375, + "Options": "a ) 177 , b ) 150 , c ) 817 , d ) 716 , e ) 375", + "Correct": "e", + "Explanation": "a + b + c = 590 5 a = 3 b = 7 c = x a : b : c = 1 / 5 : 1 / 3 : 1 / 7 = 21 : 35 : 15 15 / 71 * 1775 = rs . 375 answer : e" + }, + { + "Answer": 4, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "c", + "Explanation": "\"n ^ ( n / 2 ) = 4 apply log n / 2 logn = log 4 nlogn = 2 log 4 = log 4 ^ 2 = log 16 logn = log 16 now apply antilog n = 16 / n now n = 4 . answer : c\"" + }, + { + "Answer": 7, + "Options": "a ) 5 , b ) 8 , c ) 7 , d ) 10 , e ) 3", + "Correct": "c", + "Explanation": "\"2 ab = ( a ( power 2 ) + b ( power 2 ) - ( a - b ) ( power 2 ) = 23 - 9 = 14 ab = 7 . answer is c .\"" + }, + { + "Answer": 77, + "Options": "a ) 22 , b ) 28 , c ) 59 , d ) 77 , e ) 84", + "Correct": "d", + "Explanation": "required sum = ( 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 ) = 77 note : 1 is not a prime number option d" + }, + { + "Answer": 41, + "Options": "a ) 67 sec , b ) 89 sec , c ) 36 sec , d ) 87 sec , e ) 41 sec", + "Correct": "e", + "Explanation": "\"speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 290 + 120 = 410 m . time taken = 410 / 10 = 41 sec . answer : e\"" + }, + { + "Answer": 30, + "Options": "a ) 30 , b ) 32 , c ) 35 , d ) 38 , e ) 40", + "Correct": "a", + "Explanation": "\"the rate of 20 machines is rate = job / time = x / 4 units per day - - > the rate of 1 machine 1 / 20 * ( x / 4 ) = x / 80 units per day ; now , again as { time } * { combined rate } = { job done } then 8 * ( m * x / 80 ) = 3 x - - > m = 30 . answer : a .\"" + }, + { + "Answer": 220, + "Options": "a ) 220 , b ) 364 , c ) 410 , d ) 424 , e ) 450", + "Correct": "a", + "Explanation": "we ' re dealing with a sequence of consecutive odd integers : 13 to 31 , inclusive . we ' re asked for the sum of this group . 1 ) start with the sum of the smallest and the biggest : 13 + 31 = 44 2 ) now look at the ' next smallest ' and the ' next biggest ' : 15 + 29 = 44 now we have proof that there is no middle term . we have 5 bunches of 44 5 ( 44 ) = 220 a" + }, + { + "Answer": 1.2500000000000002, + "Options": "a ) 1 / 4 , b ) 3 / 4 , c ) 5 / 4 , d ) 6 / 4 , e ) 7 / 4", + "Correct": "c", + "Explanation": "\"should be a sub - 600 level q . . volume = { 5 / 9 } / { 4 / 9 } = 5 / 4 c\"" + }, + { + "Answer": 0.5555555555555556, + "Options": "a ) 5 / 9 , b ) 3 / 2 , c ) 1 / 2 , d ) 5 / 6 , e ) 6 / 5", + "Correct": "a", + "Explanation": "p : the probability that x * y is even , then p = 1 - p ( x * y is odd ) p ( x * y odd ) = p ( x odd ) * p ( y odd ) = 4 / 6 * 4 / 6 = 16 / 36 = 4 / 9 and p = 1 - 4 / 9 = 5 / 9 option : a" + }, + { + "Answer": 0.22222222222222215, + "Options": "a ) 0 , b ) 1 / 9 , c ) 2 / 9 , d ) 1 / 3 , e ) 1", + "Correct": "c", + "Explanation": "\"probability = ( favorable cases ) / ( total number of cases ) total number of ways in which a person can ride car = 3 * 3 * 3 = 27 ( in first ride he has 3 options to sit , in second right again he has 3 seats available to sit and so on ) number of favorable cases , i . e . , when he rides on different cars ; he can choose seat car in 3 ways in his 1 st ride . he can choose seat car in 2 ways in his 2 nd ride . he can choose seat car in 1 ways in his 3 rd ride . so , 3 * 2 * 1 = 6 ways thus , probability of choosing different seats = 6 / 27 = 2 / 9 answer : c\"" + }, + { + "Answer": 299.9999999999999, + "Options": "a ) 300 , b ) 75 , c ) 100 , d ) 150 , e ) 175", + "Correct": "a", + "Explanation": "\"nope , 150 . i can only get it by following pr ' s backsolving explanation . i hate that . original mixture has 20 % salt and 80 % water . total = x out of which salt = 0.2 x and water = 0.8 x now , 1 / 4 water evaporates and all salt remains . so what remains is 0.2 x salt and 0.6 x water . now 40 gallons salt is added and 20 gallons of water is added . so salt now becomes - > ( 0.2 x + 40 ) and water - - > ( 0.6 x + 20 ) amount of salt is 33.33 % of total . so amount of water is 66.66 % . so salt is half of the volume of water . so ( 0.2 x + 40 ) = ( 0.6 x + 20 ) / 2 = > 0.4 x + 80 = 0.6 x + 20 = > 0.2 x = 60 solving , x = 300 answer : a\"" + }, + { + "Answer": 40, + "Options": "a ) 28 % , b ) 32 % , c ) 36 % , d ) 40 % , e ) 44 %", + "Correct": "d", + "Explanation": "the amount of chemical x in the solution is 20 + 0.25 ( 80 ) = 40 liters . 40 liters / 100 liters = 40 % the answer is d ." + }, + { + "Answer": 10, + "Options": "a ) 5 % , b ) 7 % , c ) 9 % , d ) 10 % , e ) 12 %", + "Correct": "d", + "Explanation": "explanation : the difference of two successive amounts must be the simple interest in 1 year on the lower amount of money . s . i = 19404 / - - 17640 / - = rs . 1764 / - rate of interest = ( 1764 / 17640 ) \u00d7 ( 100 / 1 ) = > 10 % answer : option d" + }, + { + "Answer": 20, + "Options": "a ) 14 years , b ) 18 years , c ) 20 years , d ) 22 years , e ) 16 years", + "Correct": "c", + "Explanation": "\"let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . ( x + 22 ) + 2 = 2 ( x + 2 ) x + 24 = 2 x + 4 x = 20 . answer : c\"" + }, + { + "Answer": 80, + "Options": "a ) 40 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 80 %", + "Correct": "e", + "Explanation": "\"can be reduced to y / 2 + 3 y / 10 = 4 y / 5 = 80 % e\"" + }, + { + "Answer": 30, + "Options": "a ) 14 , b ) 20 , c ) 26 , d ) 28 , e ) 30", + "Correct": "e", + "Explanation": "solution let the number be x . then , 11 x - x = 300 \u2039 = \u203a 10 x = 300 x \u2039 = \u203a 30 . answer e" + }, + { + "Answer": 52, + "Options": "a ) 42 , b ) 32 , c ) 48 , d ) 52 , e ) 38", + "Correct": "d", + "Explanation": "\"x / 78 = 24 . x = 24 * 78 . so correct answer would be , ( 24 * 78 ) / 36 = 52 . answer : d\"" + }, + { + "Answer": 3.3333333333333353, + "Options": "a ) 7 / 3 , b ) 5 / 3 , c ) 10 / 3 , d ) 3 / 7 , e ) 11 / 5", + "Correct": "c", + "Explanation": "c . p of 1 kg of cheaper rice = rs 3.10 c . p of 1 kg of expensive rice = rs 3.75 the mixture be worth for 1 kg = rs 3.25 by the alligation rule : quantity of cheaper rice / quantity of expensive rice = ( 3.75 - 3.25 ) / ( 3.25 - 3.10 ) = ( 0.50 ) / ( 0.15 ) = 10 / 3 c" + }, + { + "Answer": 39, + "Options": "a ) 39 , b ) 88 , c ) 266 , d ) 278 , e ) 221", + "Correct": "a", + "Explanation": "explanation : assume his initial average = xx his total runs after 16 innings = 16 xx after scoring 87 runs his average got increased by 3 to xx + 3 so his total runs after 17 innings = 17 \u00d7 ( xx + 3 ) but it was given that the difference in the total scores after 16 innings and 17 innings = 87 therefore 17 \u00d7 ( x + 3 ) \u2212 16 x = 87 \u21d2 x = 3617 \u00d7 ( x + 3 ) \u2212 16 x = 87 \u21d2 x = 36 his new average = 36 + 3 = 39 answer : a" + }, + { + "Answer": 0.3333333333333333, + "Options": "a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 3 / 4 , e ) 1", + "Correct": "b", + "Explanation": "let y - z = t - - - > since y is halfway between x and z and x > y we have x - y = t . moreover x - z = ( x - y ) + ( y - z ) = 2 t . similarly since x is halfway between w and z , we have a - x = 2 t . so y - x = - t , y - a = - 3 t . - - - > ( y - x ) / ( y - a ) = 1 / 3 . the answer is ( b ) ." + }, + { + "Answer": 615, + "Options": "a ) $ 600 , b ) $ 575 , c ) $ 550 , d ) $ 580 , e ) $ 615", + "Correct": "e", + "Explanation": "a + b + c = 1230 given ratio 9 : 10 : 11 let us say the shares of a , b , c deducting 5 , 1015 be a , b , c a + b + c = 1230 - 30 = 1200 = 30 k c share = ( 1200 x 30 ) / 60 = 600 c = charlie share = 600 + 15 = 615 option e" + }, + { + "Answer": 1999.6666666666667, + "Options": "a ) 2008 , b ) 2009 , c ) 2010 , d ) 2011 , e ) 2012", + "Correct": "b", + "Explanation": "\"the price of commodity x increases 25 cents each year relative to commodity y . the price difference is $ 2.10 and commodity x needs to be 10 cents less than commodity y . $ 2.00 / 25 cents = 8 years the answer is 2001 + 8 years = 2009 . the answer is b .\"" + }, + { + "Answer": 567, + "Options": "a ) 567 , b ) 167 , c ) 267 , d ) 467 , e ) 667", + "Correct": "a", + "Explanation": "here , a : b : c : d = 1 / 12 : 1 / 13 : 1 / 15 : 1 / 2 1 ) l . c . m of 12 : 13 : 15 : 2 is 780 2 ) find the number of books each friend received - - - - - - - - - ( to find no . of books each friend has , multiply the ratio with the l . c . m . calculated ) a = ( 1 / 12 ) x 780 = 65 b = ( 1 / 13 ) x 780 = 60 c = ( 1 / 15 ) x 780 = 52 d = ( 1 / 2 ) x 780 = 390 3 ) total number of toys = ( 65 x + 60 x + 52 x + 390 x ) = 567 x minimum number of pens ( x ) = 1 therefore , total number of items = 567 items . correct option : a" + }, + { + "Answer": 101, + "Options": "a ) 101 kg , b ) 103.4 kg , c ) 105 kg , d ) data inadequate , e ) none of these", + "Correct": "a", + "Explanation": "\"total weight increased = ( 4 x 1.5 ) kg = 6 kg . weight of new person = ( 95 + 6 ) kg = 101 kg . answer : option a\"" + }, + { + "Answer": 40, + "Options": "a ) 29 , b ) 88 , c ) 40 , d ) 28 , e ) 27", + "Correct": "c", + "Explanation": "explanation : 3 / 4 x = 30 = > x = 40 answer : c" + }, + { + "Answer": 26, + "Options": "a ) 25 , b ) 26 , c ) 39 , d ) 21 , e ) 11", + "Correct": "b", + "Explanation": "\"add the numbers of doughnuts . 12 + 6 + 8 = 26 . answer is b .\"" + }, + { + "Answer": 51, + "Options": "a ) 51 , b ) 50 , c ) 45 , d ) 40 , e ) 36", + "Correct": "a", + "Explanation": "explanation : let the number be x . then , x - ( x / 3 ) = 34 = > 2 x / 3 = 34 = > x = 51 answer : option a" + }, + { + "Answer": 19, + "Options": "a ) 19 min , b ) 19 hrs , c ) 52 min , d ) 126 min , e ) 52 min", + "Correct": "a", + "Explanation": "let the correct time to complete the journey be x min distance covered in ( x + 11 ) min . at 40 kmph distance covered in ( x + 5 ) min . at 50 kmph ( x + 11 ) / 60 * 40 = ( x + 5 ) / 60 * 50 x = 19 min answer ( a )" + }, + { + "Answer": 0.625, + "Options": "a ) 1 / 4 , b ) 3 / 8 , c ) 1 / 2 , d ) 5 / 8 , e ) 3 / 4", + "Correct": "d", + "Explanation": "for e total numbers 8 * 12 there are 12 numbers divisible by 8 - > 3 * 12 ( if 8 is an example - ( 6 , 78 ) , ( 7 , 89 ) , ( 8 , 910 ) ) and 12 numbers divisible by 4 but not divisible by 8 - > 2 * 12 ( if 4 is an example ( 2 , 34 ) and ( 4 , 56 ) ) the answer 5 / 8 - > d" + }, + { + "Answer": 11, + "Options": "a ) 9 , b ) 11 , c ) 13 , d ) 15 , e ) 17", + "Correct": "b", + "Explanation": "\"( 2 to the power x ) - ( 2 to the power ( x - 2 ) ) = 3 ( 2 to the power 9 ) 2 ^ x - 2 ^ ( x - 2 ) = 3 . 2 ^ 9 hence x = 11 . answer is b\"" + }, + { + "Answer": 73, + "Options": "a ) 50 , b ) 52 , c ) 59 , d ) 68 , e ) 73", + "Correct": "e", + "Explanation": "\"sum of 5 integer ( a , b , c , d , e ) = 5 * 65 = 325 e - a = 10 i . e . e = a + 10 for e to be maximum remaining 4 must be as small as possible since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers i . e . a + a + a + a + ( a + 10 ) = 325 i . e . 5 a = 315 i . e . a = 63 i . e . largest e = 63 + 10 = 73 answer : option e\"" + }, + { + "Answer": 750, + "Options": "a ) $ 450 , b ) $ 500 , c ) $ 750 , d ) $ 800 , e ) $ 840", + "Correct": "c", + "Explanation": "let the shares of a , b , c , d are x , 3 x , 4 x , 2 x 4 x - 2 x = 500 x = 250 b ' s share = 3 x = $ 750 answer is c" + }, + { + "Answer": 29.999999999999996, + "Options": "a ) 8 , b ) 15 , c ) 21 , d ) 30 , e ) 39", + "Correct": "d", + "Explanation": "5 ^ 3 + 6 ^ 3 = 341 number is 5 * 6 = 30 d" + }, + { + "Answer": 5, + "Options": "a ) 16.2 , b ) 4 , c ) 5 , d ) 500 , e ) none", + "Correct": "c", + "Explanation": "\"answer let 45 x a = ( 25 x 900 ) / 100 \u2234 a = ( 25 x 9 ) / 45 = 5 correct option : c\"" + }, + { + "Answer": 2, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "c", + "Explanation": "you have | x + 3 | - | 4 - x | = | 8 + x | first , look at the three values independently of their absolute value sign , in other words : | x + 3 | - | 4 - x | = | 8 + x | ( x + 3 ) - ( 4 - x ) = ( 8 + x ) now , you ' re looking at x < - 8 , s \u1ed1 x is a number less than - 8 . let ' s pretend x = - 10 here to make things a bit easier to understand . when x = - 10 i . ) ( x + 3 ) ( - 10 + 3 ) ( - 7 ) ii . ) ( 4 - x ) ( 4 - [ - 10 ] ) ( double negative , s \u1ed1 \u00ed t becomes positive ) ( 4 + 10 ) ( 14 ) iii . ) ( 8 + x ) ( 8 + - 10 ) ( - 2 ) in other words , when x < - 8 , ( x + 3 ) and ( 8 + x ) are negative . to solve problems like this , we need to check for the sign change . here is how i do it step by step . i . ) | x + 3 | - | 4 - x | = | 8 + x | ii . ) ignore absolute value signs ( for now ) and find the values of x which make ( x + 3 ) , ( 4 - x ) and ( 8 + x ) = to zero as follows : ( x + 3 ) x = - 3 ( - 3 + 3 ) = 0 ( 4 - x ) x = 4 ( 4 - 4 ) = 0 ( 8 + x ) x = - 8 ( 8 + - 8 ) = 1 c" + }, + { + "Answer": 60, + "Options": "a ) 200 km , b ) 50 km , c ) 20 km , d ) 60 km , e ) 80 km", + "Correct": "d", + "Explanation": "not really . when you solve the 2 equation above , you get , 6 t - 4 / 3 = 5 r / 6 from simplifying equation 1 4 t - 2 = r / 2 from simplifying equation 2 you can now multiply equation 2 by 5 to get 5 ( 4 t - 2 = r / 2 ) = 20 t - 10 = 5 r / 2 and then subtract this new equation from equation 1 to get t = 3 , followed by r = 20 to give you distance q = r * t = 20 * 3 = 60 km . d" + }, + { + "Answer": 0.1836734693877551, + "Options": "a ) 3 , b ) 6 , c ) 1 / 9 , d ) 1 / 3 , e ) 9 / 49", + "Correct": "e", + "Explanation": "explanation : solution : given x = k / y ^ 2 , where k is constant . now , y = 3 and x = 1 gives k = 9 . . ' . x = 9 / y ^ 2 = > x = 9 / 7 ^ 2 = 9 / 49 answer : e" + }, + { + "Answer": 14, + "Options": "a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16", + "Correct": "c", + "Explanation": "\"look at the below representation of the problem : steel chrome total a 3 3 60 > > no . of type a machines = 60 / 6 = 10 b 6 5 44 > > no . of type b machines = 44 / 11 = 4 so the answer is 14 i . e c . hope its clear .\"" + }, + { + "Answer": 6, + "Options": "a ) $ 14 , b ) $ 5 , c ) $ 10 , d ) $ 6 , e ) $ 8", + "Correct": "d", + "Explanation": "sale price ( sp ) = 90 + markup ( mp ) - - > mp = sp - 90 and given mp = sp / 4 ( 25 % is 1 / 4 th ) so sp / 4 = sp - 90 3 sp / 4 = 90 sp = 120 now a discount of 20 % is given so new sp is . 8 * 120 = 96 profit = 96 - 90 = 6.0 $ answer is d" + }, + { + "Answer": 35, + "Options": "a ) q = 20 , b ) q = 25 , c ) q = 30 , d ) q = 35 , e ) 40", + "Correct": "d", + "Explanation": "suppose the population of the country in current year is 1000 . so annual increase is 1000 + 39.4 - 19.4 = 1020 hence every year there is an increase of 2 % . 2000 = 1000 ( 1 + ( 2 / 100 ) ) ^ n n = 35 answer is d" + }, + { + "Answer": 7, + "Options": "a ) 4 , b ) 7 , c ) 11 , d ) 12 , e ) 15", + "Correct": "b", + "Explanation": "\"the question basically asks how many positive odd integers less than 70 are odd multiples of 5 so we have 5,15 , 25,35 , 45,55 and 65 = 7 ans b\"" + }, + { + "Answer": 20182390830, + "Options": "a ) 20183198166 , b ) 20194181766 , c ) 20175292556 , d ) 20132191166 , e ) 20153198166", + "Correct": "a", + "Explanation": "\"201834 x 99999 = 201834 x ( 100000 - 1 ) = 201834 x 100000 - 201834 x 1 = 20183400000 - 201834 = 20183198166 a\"" + }, + { + "Answer": 1330, + "Options": "a ) $ 1120 , b ) $ 1190 , c ) $ 1260 , d ) $ 1330 , e ) $ 1400", + "Correct": "d", + "Explanation": "\"95 % remains to be paid so the remaining amount is 19 * 70 = $ 1330 . the answer is d .\"" + }, + { + "Answer": 37, + "Options": "a ) 37 , b ) 168 , c ) 189 , d ) 190 , e ) 200", + "Correct": "a", + "Explanation": "\"solution average of 7 people after the last one enters = 151 . \u00e2 \u02c6 \u00b4 required weight = ( 7 x 151 ) - ( 6 x 170 ) = 1057 - 1020 = 37 . answer a\"" + }, + { + "Answer": 87, + "Options": "a ) 87 , b ) 97 , c ) 67 , d ) 57 , e ) 46", + "Correct": "a", + "Explanation": "\"87 answer is a\"" + }, + { + "Answer": 6, + "Options": "a ) - 30 , b ) - 20 , c ) - 6 , d ) 5 , e ) 20", + "Correct": "c", + "Explanation": "here x and y are integers . x ^ 2 = y xy = 27 . substitute x ^ 2 = y in xy = > x ^ 3 = 27 . here x 3 is positive , x is also positive . x = 3 then y = 9 . x - y = - 6 so option c is correct" + }, + { + "Answer": 40, + "Options": "a ) 13 , b ) 18 , c ) 40 , d ) 82 , e ) 43", + "Correct": "c", + "Explanation": "\"let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 x / 2 = ( 83 - 63 ) = > x / 2 = 20 = > x = 40 answer : c\"" + }, + { + "Answer": 762.0000000000001, + "Options": "a ) 392 , b ) 229 , c ) 753 , d ) 493 , e ) 762", + "Correct": "e", + "Explanation": "\"e 762 ? = 5080 * ( 2 / 5 ) * ( 1 / 2 ) * ( 3 / 4 ) = 762\"" + }, + { + "Answer": 214.18, + "Options": "a ) $ 214.16 , b ) $ 214.17 , c ) $ 214.18 , d ) $ 214.19 , e ) $ 214.20", + "Correct": "a", + "Explanation": "\"if the last three digits of a whole number are divisible by 8 , then the entire number is divisible by 8 the last 3 digit 415 not divisible by a hence , we need to add 1 to this number for it to be divisible by 8 correct option : a\"" + }, + { + "Answer": 40, + "Options": "a ) 20 , b ) 25 , c ) 30 , d ) 40 , e ) 50", + "Correct": "d", + "Explanation": "\"let the list price be 2 x for min sale price , the first discount given should be 50 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 40 and 0.8 x = 32 so lowest sale price is 32 , which y is 40 % of 80 hence , d is the answer\"" + }, + { + "Answer": 5120, + "Options": "a ) 5113 , b ) 5117 , c ) 5120 , d ) 8119 , e ) 10115", + "Correct": "c", + "Explanation": "\"trees increase by 1 / 4 the number of trees in preceding year . hence , correct answer must be divisible by 4 . based on divisibility rules , if last 2 digits are divisible by 4 then the number is divisible by 4 . thus , we can eliminate a , b , d , e the answer to be c again , trees increase by 1 / 4 the number of trees in preceding year . hence , the number of trees increase by 5 / 4 times the number of trees the preceding year . if x = initial number of trees = 5120 year 1 = 5 / 4 x year 2 = ( 5 / 4 ) ( 5 / 4 ) x year 3 = ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) x year 4 = ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) x only for answer d : ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) 5120 = 12500 hence , correct answer = c\"" + }, + { + "Answer": 100, + "Options": "a ) 125 , b ) 150 , c ) 100 , d ) 130 , e ) 140", + "Correct": "c", + "Explanation": "total = 200 not working = 100 having family = 75 like to sing in shower = 125 working = 200 - 100 = 100 not having family = 200 - 75 = 125 like to sing in shower = 125 largest possible number is the lowest possible among the above thus 100 c" + }, + { + "Answer": 61, + "Options": "a ) 54 , b ) 59 , c ) 61 , d ) 71 , e ) 92", + "Correct": "c", + "Explanation": "\"total = 70 thrower = 43 rest = 70 - 43 = 27 left handed = 27 / 3 = 9 right handed = 18 if all thrower are right handed then total right handed is 43 + 18 = 61 so c . 61 is the right answer\"" + }, + { + "Answer": 126, + "Options": "a ) rs . 126 , b ) rs . 132 , c ) rs . 120 , d ) rs . 114 , e ) none of these", + "Correct": "a", + "Explanation": "let the train fare between the two places for one person be rs . t bus fare between the two places for two persons rs . 4 / 3 t = > 6 / 2 ( 4 / 3 t ) + 8 ( t ) = 1512 = > 12 t = 1512 = > t = 126 . answer : a" + }, + { + "Answer": 72, + "Options": "a ) 40 , b ) 50 , c ) 72 , d ) 70 , e ) 80", + "Correct": "c", + "Explanation": "\"according to order of operations , inner brackets first . hence | 6 - 8 ( 3 - 12 ) | - | 5 - 11 | = | 6 - 8 * ( - 9 ) | - | 5 - 11 | according to order of operations , multiplication within absolute value signs ( which may be considered as brackets when it comes to order of operations ) next . hence = | 6 + 72 | - | 5 - 11 | = | 78 | - | - 6 | = 78 - 6 = 72 correct answer c ) 72\"" + }, + { + "Answer": 71.42857142857142, + "Options": "a ) 20 % , b ) 305 , c ) 50 % , d ) 71.4 % , e ) 60 %", + "Correct": "d", + "Explanation": "\"explanation : number of pages increased = 100 now , the number of pages of book = 240 number of pages of the books before increase = 240 \u2013 100 = 140 % increase in the number of pages in the book = 100 / 140 x 100 % = 71.4 % d\"" + }, + { + "Answer": 0.358, + "Options": "a ) 0.853 , b ) 0.358 , c ) 3.58 , d ) 8.35 , e ) none", + "Correct": "b", + "Explanation": "answer 3 / 10 + 5 / 100 + 8 / 1000 = 0.3 + 0.05 + 0.008 = 0.358 correct option : b" + }, + { + "Answer": 5, + "Options": "a ) 6 , b ) 4 , c ) 3 , d ) 5 , e ) 2", + "Correct": "d", + "Explanation": "if a = 1 , r = 2 then a = 1 , b = 2 , c = 4 then abs ( a + b - c ) = 1 if a = 1 , r = 3 then a = 1 , a = 3 , a = 9 then abs ( 1 + 3 - 9 ) = 5 if a = 2 , r = 2 , then a = 2 , b = 4 , c = 8 then abs ( 2 + 4 - 8 ) = 2 if a = 1 , r = - 2 then a = 1 , b = - 2 , c = 4 the abs ( 1 - 2 - 4 ) = 5 if a = 1 , r = - 3 then a = 1 , b = - 3 , c = 9 then abs ( 1 - 3 - 9 ) = 11 if a = 2 , r = - 2 then a = 2 , b = - 4 , c = - 8 then abs ( 2 - 4 - 8 ) = 10 so total 5 abs ( ) values answer : d" + }, + { + "Answer": 361, + "Options": "a ) 341 , b ) 351 , c ) 361 , d ) 371 , e ) 381", + "Correct": "c", + "Explanation": "\"sum of 1 st n odd no . s = 1 + 3 + 5 + 7 + . . . = n ^ 2 so , sum of 1 st 19 odd numbers = 19 ^ 2 = 361 answer : c\"" + }, + { + "Answer": 10.588235294117647, + "Options": "a ) 11.5 , b ) 9.5 , c ) 13.5 , d ) 10.6 , e ) 14.5", + "Correct": "d", + "Explanation": "\"step 1 ) took lcm of 10 and 12 . . came as 30 . just multiplied by 10 . . . ( to make easy calculation ) step 2 ) 300 distance between b to c . . . do 300 / 12 hence 25 gallons used step 3 ) twice distance . . hence 300 * 2 = 600 . . . do as above . . 600 / 10 = 60 gallons used step 4 ) total gallons . . 25 + 60 = 85 gallons step ) total miles = 300 + 600 = 900 miles hence . . average of whole journey = 900 / 85 which comes to 10.6 answer : d\"" + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9", + "Correct": "a", + "Explanation": "\"let bill run x on saturday , so he will run x + 4 on sunday . . julia will run 2 * ( x + 4 ) on sunday . . totai = x + x + 4 + 2 x + 8 = 16 . . 4 x + 12 = 16 . . x = 1 . . ans = x + 4 = 1 + 4 = 5 answer a\"" + }, + { + "Answer": 11, + "Options": "a ) 6 , b ) 7 , c ) 11 , d ) 8 , e ) 10", + "Correct": "c", + "Explanation": "\"we have : 1 ) x < y < z 2 ) y - x > 5 3 ) x = 2 k ( x is an even number ) 4 ) y = 2 n + 1 ( y is an odd number ) 5 ) z = 2 p + 1 ( z is an odd number ) 6 ) z - x = ? least value z - x = 2 p + 1 - 2 k = 2 p - 2 k + 1 = 2 ( p - k ) + 1 - that means that z - x must be an odd number . we can eliminate answer choices a , c and e we are asked to find the least value , so we have to pick the least numbers since y is odd and x is even , y - x must be odd . since y - x > 7 the least value for y - x must be 11 , the least value for x must be 2 , and , thus , the least possible value for y must be 11 ( y - 2 = 9 , y = 11 ) 2 < 11 < z , since z is odd , the least possible value for z is 13 z - x = 13 - 2 = 11 answer c\"" + }, + { + "Answer": 3.694512960621597, + "Options": "a ) 3.6 kg , b ) 3.696 kg , c ) 36 kg , d ) 36.9 kg , e ) 3.06 kg", + "Correct": "b", + "Explanation": "\"external radius = 4 cm , internal radius = 3 cm . volume of iron = ( 22 / 7 x [ ( 4 ) ^ 2 - ( 3 ) ^ 2 ] x 21 ) cm ^ 3 ( 22 / 7 x 7 x 1 x 21 ) cm ^ 3 462 cm ^ 3 . weight of iron = ( 462 x 8 ) gm = 3696 gm = 3.696 kg . answer b\"" + }, + { + "Answer": 75.5, + "Options": "a ) 76 kg , b ) 77 kg , c ) 75.5 kg , d ) data inadequate , e ) none of these", + "Correct": "c", + "Explanation": "\"total weight increases = 7 \u00d7 1.5 = 10.5 kg so the weight of new person = 65 + 10.5 = 75.5 kg answer c\"" + }, + { + "Answer": 85, + "Options": "a ) 55 , b ) 65 , c ) 75 , d ) 85 , e ) 95", + "Correct": "d", + "Explanation": "\"let the marks obtained by the student in physics , chemistry and mathematics be p , c and m respectively . p + c + m = 170 + p c + m = 170 average mark obtained by the student in chemistry and mathematics = ( c + m ) / 2 = 170 / 2 = 85 . answer : d\"" + }, + { + "Answer": 240, + "Options": "a ) 200 , b ) 220 , c ) 240 , d ) 260 , e ) 280", + "Correct": "c", + "Explanation": "22 * 200 = 4400 . the other 3 onions weigh a total of 720 grams . the average weight is 720 / 3 = 240 grams . the answer is c ." + }, + { + "Answer": 120.00000000000003, + "Options": "a ) s . 220 , b ) s . 120 , c ) s . 320 , d ) s . 50 , e ) s . 90", + "Correct": "b", + "Explanation": "\"a profit of rs . 600 is divided between x and y in the ratio of 1 / 2 : 1 / 3 or 3 : 2 . so profits are 360 and 240 . difference in profit share = 360 - 240 = 120 answer : b\"" + }, + { + "Answer": 57.14285714285714, + "Options": "a ) 30 % , b ) 50 % , c ) 57 % , d ) 62 % , e ) 75 %", + "Correct": "c", + "Explanation": "total number of votes polled = ( 1000 + 2000 + 4000 ) = 7000 required percentage = 4000 / 7000 * 100 = 57 % ( approximately ) answer : option c" + }, + { + "Answer": 64, + "Options": "a ) 24 , b ) 26 , c ) 30 , d ) 64 , e ) 40", + "Correct": "d", + "Explanation": "\"let the number of coins one son got be x and the number of coins another got be y . total = x + y . x ^ 2 - y ^ 2 = 64 ( x - y ) - - > x + y = 64 . answer : d .\"" + }, + { + "Answer": 300.9, + "Options": "a ) 30.09 , b ) 300.9 , c ) 30.06 , d ) 100.9 , e ) 300.6", + "Correct": "b", + "Explanation": "\"= 12.036 / 0.04 = 1203.6 / 4 = 300.9 answer is b .\"" + }, + { + "Answer": 24, + "Options": "a ) 24 % , b ) 26 % , c ) 28 % , d ) 30 % , e ) 32 %", + "Correct": "a", + "Explanation": "\"the amount of chemical x in the solution is 20 + 0.05 ( 80 ) = 24 liters . 24 liters / 100 liters = 24 % the answer is a .\"" + }, + { + "Answer": 74, + "Options": "a ) 74 , b ) 76 , c ) 78 , d ) 80 , e ) 82", + "Correct": "a", + "Explanation": "\"a score of 58 was 2 standard deviations below the mean - - > 58 = mean - 2 d a score of 98 was 3 standard deviations above the mean - - > 98 = mean + 3 d solving above for mean r = 74 . answer : a .\"" + }, + { + "Answer": 7999.999999999999, + "Options": "a ) 8008 , b ) 8000 , c ) 8022 , d ) 8021 , e ) 8022", + "Correct": "b", + "Explanation": "\"x * 110 / 100 * 90 / 100 = 7920 x * 0.99 = 7920 x = 7920 / 0.99 = > 8000 answer : b\"" + }, + { + "Answer": 720, + "Options": "a ) 720 , b ) 700 , c ) 800 , d ) 900 , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : let p ' s capital = p , q ' s capital = q and r ' s capital = r then 4 p = 6 q = 10 r = > 2 p = 3 q = 5 r = > q = 2 p / 3 r = 2 p / 5 p : q : r = p : 2 p / 3 : 2 p / 5 = 15 : 10 : 6 r ' s share = 3720 * ( 6 / 31 ) = 120 * 6 = 720 . answer : option a\"" + }, + { + "Answer": 184, + "Options": "a ) 184 , b ) 367 , c ) 269 , d ) 177 , e ) 191", + "Correct": "a", + "Explanation": "\"explanation : total runs scored by the batsman = 60 * 46 = 2760 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2760 \u00e2 \u20ac \u201c 2552 = 208 runs . let the highest score be x , hence the lowest score = x \u00e2 \u20ac \u201c 160 x + ( x - 160 ) = 208 2 x = 368 x = 184 runs answer : a\"" + }, + { + "Answer": 14, + "Options": "a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15", + "Correct": "d", + "Explanation": "\"explanation : given that a + b = 14 + b + c = > a ? c = 14 + b ? b = 14 = > c is younger than a by 14 years answer : option d\"" + }, + { + "Answer": 20, + "Options": "a ) 10 , b ) 15 , c ) 20 , d ) 36 , e ) 50", + "Correct": "c", + "Explanation": "200 = 2 ^ 3 * 5 ^ 2 if 200 divides n ^ 2 , then n must be divisible by 2 ^ 2 * 5 = 20 the answer is c ." + }, + { + "Answer": 100000, + "Options": "a ) 100555 , b ) 100775 , c ) 100885 , d ) 100995 , e ) 100665", + "Correct": "b", + "Explanation": "smallest number of six digits is 100000 . required number must be divisible by l . c . m . of 25,35 , 45,15 i . e 1575 , on dividing 100000 by 1575 , we get 800 as remainder . therefore , required number = 100000 + ( 1575 \u00e2 \u20ac \u201c 800 ) = 100775 . answer is b ." + }, + { + "Answer": 25, + "Options": "a ) 25 % , b ) 15 % , c ) 20 % , d ) 40 % , e ) 45 %", + "Correct": "a", + "Explanation": "ratio of 2 bedroom apartment : 1 bedroom apartment = 700 : 2100 - - - - - > 1 : 3 let total number of apartments be x no . of 2 bedroom apartment = ( 1 / 4 ) * x percentage of apartments in the building are two - bedroom apartments - - - - > ( 1 / 4 ) * 100 - - - > 25 % answer : a" + }, + { + "Answer": 28, + "Options": "a ) 36 , b ) 28 , c ) 42 , d ) 45 , e ) none of the above", + "Correct": "b", + "Explanation": "\"let the average after 17 th inning = x . then , average after 16 th inning = ( x \u2013 3 ) . \u2234 16 ( x \u2013 3 ) + 76 = 17 x or x = ( 76 \u2013 48 ) = 28 . answer b\"" + }, + { + "Answer": 4, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "d", + "Explanation": "\"find the pattern of the remainders after each power : ( 2 ^ 1 ) / 7 remainder 2 ( 2 ^ 2 ) / 7 remainder 4 ( 2 ^ 3 ) / 7 remainder 1 - - > this is where the cycle ends ( 2 ^ 4 ) / 7 remainder 2 - - > this is where the cycle begins again ( 2 ^ 5 ) / 7 remainder 4 continuing the pattern to ( 2 ^ 14 ) / 7 gives us a remainder of 4 final answer : d ) 4\"" + }, + { + "Answer": 1299.9999999999998, + "Options": "a ) 1200 , b ) 3000 , c ) 1300 , d ) 3600 , e ) 2400", + "Correct": "c", + "Explanation": "\"let the additional invested amount for 8 % interest be x ; equation will be ; 2600 + 0.05 * 2600 + x + 0.08 x = 2600 + x + 0.06 ( 2600 + x ) 0.05 * 2600 + 0.08 x = 0.06 x + 0.06 * 2600 0.02 x = 2600 ( 0.06 - 0.05 ) x = 2600 * 0.01 / 0.02 = 1300 ans : ` ` c ' '\"" + }, + { + "Answer": 480, + "Options": "a ) 96 , b ) 240 , c ) w = 256 , d ) w = 384 , e ) w = 480", + "Correct": "e", + "Explanation": "\"most test takers would recognize thesystemof equations in this prompt and just do algebra to get to the solution ( and that ' s fine ) . the wording of the prompt and the ' spread ' of the answer choices actually provide an interesting ' brute force ' shortcut that you can take advantage of to eliminate the 4 wrong answers . . . . we ' re told that there are 2 types of boxes : those that hold 12 glasses and those that hold 16 glasses . since the average number of boxes is 15 , we know that there must be at least some of each . we ' re also told that that there are 16 more of the larger boxes . this means , at the minimum , we have . . . 1 small box and 17 large boxes = 1 ( 12 ) + 17 ( 16 ) = 12 + 272 = 284 glasses at the minimum since the question asks for the total number of glasses , we can now eliminate answers a , b and c . . . . the difference in the number of boxes must be 16 though , so we could have . . . . 2 small boxes and 18 large boxes 3 small boxes and 19 large boxes etc . with every additional small box + large box that we add , we add 12 + 16 = 28 more glasses . thus , we can justadd 28 suntil we hit the correct answer . . . . 284 + 28 = 312 312 + 28 = 340 340 + 28 = 368 368 + 28 = 396 at this point , we ' ve ' gone past ' answer d , so the correct answer must be answer e . . . . . but here ' s the proof . . . . 396 + 28 = 424 424 + 28 = 452 452 + 28 = 480 final answer : e\"" + }, + { + "Answer": 501, + "Options": "a ) 171 , b ) 281 , c ) 391 , d ) 501 , e ) 613", + "Correct": "d", + "Explanation": "\"sum s = n / 2 { 2 a + ( n - 1 ) d } = 11 / 2 { 2 * 40 + ( 11 - 1 ) * 1 } = 11 * 45 = 495 = x number of even number = ( 50 - 40 ) / 2 + 1 = 6 = y x + y = 495 + 6 = 501 d\"" + }, + { + "Answer": 44, + "Options": "a ) 44 , b ) 47 , c ) 48 , d ) 49 , e ) 50", + "Correct": "a", + "Explanation": "\"mother + daughter + child = 140 kg daughter + child = 60 kg mother = 140 - 60 = 80 kg child = 1 / 5 th of mother = ( 1 / 5 ) * 80 = 16 kg so now daughter = 140 - ( mother + child ) = 140 - ( 80 + 16 ) = 44 kg answer : a\"" + }, + { + "Answer": 0.2, + "Options": "a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 5 , d ) 1 / 7 , e ) 1 / 8", + "Correct": "c", + "Explanation": "we have total of 8 parts : 3 parts of sand and 5 parts of cement . in order there to be half sand and half cement ( 4 parts of sand and 4 parts of cement ) , we should remove 1 part of cement . with 1 part of cement comes 3 / 5 parts of sand , so we should remove 1 + 3 / 5 = 8 / 5 part of the mixture , which is ( 8 / 5 ) / 8 = 1 / 5 of the mixture . answer : c ." + }, + { + "Answer": 50.000000000000014, + "Options": "a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70", + "Correct": "c", + "Explanation": "\"milk : water = 5 : 2 5 x : 2 x + 10 = 5 : 3 3 [ 5 x ] = 5 [ 2 x + 10 ] 15 x = 10 x + 50 15 x - 10 x = 50 x = 10 the quantity of milk in the original mixture is = 5 : 2 = 5 + 2 = 7 7 x = 70 short cut method : milk : water = 5 : 2 after adding 10 liters of water milk : water = 5 : 3 milk is same but water increse 10 liters then the water ratio is increse 1 parts 1 part - - - - - > 10 liters the quantity of milk in the original mixture is = 5 : 2 = 5 + 2 = 7 7 parts - - - - - > 70 liters ( answer is = 70 ) short cut method - 2 : for only milk problems milk : water 5 : 2 5 : 3 milk ratio same but water ratio 1 part incress per 10 liters 1 part of ratio - - - - - - - > 10 liters 7 part of ratio - - - - - - - > 70 liters c )\"" + }, + { + "Answer": 67, + "Options": "a ) 74 % , b ) 75 % , c ) 67 % , d ) 72 % , e ) none", + "Correct": "c", + "Explanation": "solution : sum of pass students of first , second and third class , = ( 45 % of 10 ) + ( 60 % of 15 ) + ( 80 % of 25 ) = 4.5 + 9 + 20 = 33.5 total students appeared , = 10 + 15 + 25 = 50 pass average , = 33.5 * 100 / 50 = 67 % . answer : option c" + }, + { + "Answer": 298.93600000000004, + "Options": "a ) 298.936 , b ) 298.694 , c ) 289.496 , d ) 289.469 , e ) 298.964", + "Correct": "a", + "Explanation": "34.94 240.016 + 23.98 - - - - - - - - 298.936 answer is a ." + }, + { + "Answer": 1000, + "Options": "a ) 650 , b ) 1000 , c ) 1500 , d ) 800 , e ) 750", + "Correct": "b", + "Explanation": "total cost of items : 2000 / - amount paid : 3000 / - balance receivable : 3000 - 2000 = 1000 / - answer is b" + }, + { + "Answer": 121, + "Options": "a ) 21 , b ) 41 , c ) e = 121 , d ) 241 , e ) 481", + "Correct": "c", + "Explanation": "or u can just use the answer choices here . since the answers are already arranged in ascending order , the first number which gives remainder e as 1 for all three is the correct answer . in the given question , the first number which gives a remainder of 1 for 68 and 10 is 121 . c" + }, + { + "Answer": 49, + "Options": "a ) 49 . , b ) 8 . , c ) 12 . , d ) 16 . , e ) 64 .", + "Correct": "a", + "Explanation": "\"eq 1 : a - b - c + d = 18 eq 2 : a + b - c - d = 4 ( 1 ) subtract eq 1 from eq 2 a - b - c + d = 18 - a + b - c - d = 4 - - - - - - - - - - - - - - - - - - - - - - - - - 2 b + 2 d = 14 ( 2 ) simplify - b + d = 7 b - d = - 7 ( b - d ) ^ 2 = ( - 7 ) ^ 2 = 49 my answer : a\"" + }, + { + "Answer": 10, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 10", + "Correct": "e", + "Explanation": "given that the total purchase of two items cost 800 . so the average purchase of one item will cost 800 / 2 = 400 . its given as total shirt cost 400 $ less . hence total shirt cost = 400 - 200 and total trouser cost = 400 + 200 5 shirts = 200 $ = = > one shirt = 40 $ one trouser = 40 + 20 = 60 $ total trousers = 600 / 60 = 10 . e" + }, + { + "Answer": 48, + "Options": "a ) 40 , b ) 41 , c ) 48 , d ) 52 , e ) 43", + "Correct": "c", + "Explanation": "\"total age of all students = 24 \u00e3 \u2014 23 total age of all students + age of the teacher = 25 \u00e3 \u2014 24 age of the teacher = 25 \u00e3 \u2014 24 \u00e2 \u02c6 \u2019 24 \u00e3 \u2014 23 = 24 ( 25 \u00e2 \u02c6 \u2019 23 ) = 24 \u00e3 \u2014 2 = 48 answer is c .\"" + }, + { + "Answer": 2, + "Options": "a ) 1 , b ) 2 , c ) 4 , d ) 6 , e ) 7", + "Correct": "b", + "Explanation": "\"d = ( d - r ) / q = ( 21 - 1 ) / 10 = 20 / 10 = 2 b\"" + }, + { + "Answer": 192, + "Options": "a ) $ 192 , b ) $ 198 , c ) $ 200 , d ) $ 208 , e ) $ 216", + "Correct": "a", + "Explanation": "\"0.8 * ( 1.2 * 200 ) = $ 192 the answer is a .\"" + }, + { + "Answer": 45, + "Options": "a ) 50 , b ) 52 , c ) 35 , d ) 40 , e ) 45", + "Correct": "e", + "Explanation": "let dravid scored point = x then dhoni scored = x + 30 shewag scored = 2 * ( x + 30 ) = 2 x + 60 as given , x + x + 30 + 2 x + 60 = 150 points 4 x + 90 = 150 x = 150 - 90 / 4 = 15 so dhoni scored = x + 30 i . e ) 15 + 30 = 45 answer : e" + }, + { + "Answer": 0.14285714285714288, + "Options": "a ) 1 / 5 , b ) 1 / 6 , c ) 1 / 4 , d ) 1 / 7 , e ) 1 / 3", + "Correct": "d", + "Explanation": "if s is an integer and we know that the average speed is 2.8 , s must be = 2 . that meanss + 1 = 3 . this implies that the ratio of time for s = 2 is 1 / 4 of the total time . the formula for distance / rate is d = rt . . . so the distance travelled when s = 2 is 2 t . the distance travelled for s + 1 = 3 is 3 * 4 t or 12 t . therefore , total distance covered while the sun was shining over him is 2 / 14 = 1 / 7 . answer : d" + }, + { + "Answer": 378, + "Options": "a ) 378 , b ) 365 , c ) 380 , d ) 456 , e ) 460", + "Correct": "a", + "Explanation": "\"easy solution : n = dq 1 + 245 2 n = 2 dq 1 + 490 - ( 1 ) 2 n = dq 2 + 112 - ( 2 ) as ( 1 ) = ( 2 ) = 2 n d * ( q 2 - 2 q 1 ) = 378 d * some integer = 378 checking all options only ( a ) syncs with it . answer a\"" + }, + { + "Answer": 75, + "Options": "a ) 75 , b ) 80 , c ) 85 , d ) 90 , e ) 95", + "Correct": "a", + "Explanation": "\"answer = a please refer diagram below 85 - 10 = 75\"" + }, + { + "Answer": 0.16666666666666666, + "Options": "a ) 1 / 20 , b ) 1 / 6 , c ) 1 / 5 , d ) 4 / 21 , e ) 5 / 21", + "Correct": "b", + "Explanation": "\"this is how i used to calculate which i think works pretty well : if you let the average of the 20 other numbers equal a , can you write this equation for sum of the list ( s ) n + 20 a = s the question tells us that n = 4 a plug this back into the first equation and you get that the sum is 24 a 4 a + 20 a = 24 a therefore fraction t of n to the total would be 4 a / 24 a or 1 / 6 answer b\"" + }, + { + "Answer": 2, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "a", + "Explanation": "\"2 years answer : a\"" + }, + { + "Answer": 86, + "Options": "a ) 56 , b ) 65 , c ) 75 , d ) 86 , e ) 90", + "Correct": "d", + "Explanation": "\"a + b + c = 3 * 55 = 165 a + b + c + d = 4 * 60 = 240 - - - - ( i ) so , d = 75 & e = 75 + 3 = 78 b + c + d + e = 58 * 4 = 232 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 240 \u2013 232 = 8 a = e + 8 = 78 + 8 = 86 answer : d\"" + }, + { + "Answer": 35, + "Options": "a ) 14 , b ) 21 , c ) 28 , d ) 35 , e ) 42", + "Correct": "d", + "Explanation": "\"in 105 liters of drink a , there are 60 liters of milk and 45 liters of juice . with 60 liters of milk , we need a total of 80 liters of juice to make drink b . we need to add 35 liters of juice . the answer is d .\"" + }, + { + "Answer": 28.57142857142857, + "Options": "a ) 34 % , b ) 36 % , c ) 28.57 % , d ) 30 % , e ) 32 %", + "Correct": "c", + "Explanation": "x * y = constt . let x = y = 100 in beginning i . e . x * y = 100 * 100 = 10000 x ( 100 ) - - - becomes - - - > 1.4 x ( 140 ) i . e . 140 * new ' y ' = 10000 i . e . new ' y ' = 10000 / 140 = 71.43 i . e . y decreases from 100 to 71.43 i . e . decrease of 28.57 % c" + }, + { + "Answer": 23.999999999999993, + "Options": "a ) 36 , b ) 24 , c ) 17 , d ) 6 , e ) 5", + "Correct": "b", + "Explanation": "\"sol . ( b ) the sum of roots = a + b = 6 product of roots = ab = 6 now , a 2 + b 2 = ( a + b ) 2 - 2 ab = 36 - 12 = 24 answer b\"" + }, + { + "Answer": 0.3, + "Options": "a ) 1 / 4 , b ) 1 / 70 , c ) 3 / 14 , d ) 3 / 10 , e ) 11 / 14", + "Correct": "d", + "Explanation": "the fraction is nothing but the probability . . number to choose 3 out of 6 = 6 c 3 number to choose x and y and 2 from remaining 4 = 4 c 2 . . prob of a and b choosen = 4 c 2 / 6 c 3 = 3 / 10 answer : d" + }, + { + "Answer": 22, + "Options": "a ) 28 , b ) 27 , c ) 26 , d ) 22 , e ) 24", + "Correct": "d", + "Explanation": "\"explanation : let the average score of the first 18 innings be n 18 n + 94 = 19 ( n + 4 ) = > n = 18 so , average score after 19 th innings = x + 4 = 22 . answer : d\"" + }, + { + "Answer": 38, + "Options": "a ) 30 , b ) 34 , c ) 38 , d ) 42 , e ) 48", + "Correct": "c", + "Explanation": "\"the cost of annie ' s ride was 2.5 + 5 + ( 0.25 * 18 ) = $ 12 let x be the distance of mike ' s ride . the cost of mike ' s ride is 2.5 + ( 0.25 * x ) = 12 0.25 * x = 9.5 x = 38 miles the answer is c .\"" + }, + { + "Answer": 0.509090909090909, + "Options": "a ) 28 / 55 , b ) 19 / 33 , c ) 7 / 11 , d ) 4 / 7 , e ) 3 / 5", + "Correct": "a", + "Explanation": "\"p ( neither pen is defective ) = 8 / 11 * 7 / 10 = 28 / 55 the answer is a .\"" + }, + { + "Answer": 15, + "Options": "a ) 14 , b ) 17 , c ) 15 , d ) 19 , e ) 99", + "Correct": "c", + "Explanation": "\"let the son ' s present age be x years . then , ( 40 - x ) = x x = 20 . son ' s age 5 years back = ( 20 - 5 ) = 15 years answer : c\"" + }, + { + "Answer": 1.9583333333333335, + "Options": "a ) $ 1.75 , b ) $ 1.96 , c ) $ 2.00 , d ) $ 2.15 , e ) $ 2.30", + "Correct": "b", + "Explanation": "\"this question can be solved with a handful of different algebra approaches ( as has been shown in the various posts ) . since the question asks for the price of the largest pot , and the answers are prices , we can test the answers . we ' re told that there are 6 pots and that each pot costs 25 cents more than the next . the total price of the pots is $ 8.25 . we ' re asked for the price of the largest ( most expensive ) pot . since the total price is $ 8.00 ( a 25 - cent increment ) and the the difference in sequential prices of the pots is 25 cents , the largest pot probably has a price that is a 25 - cent increment . from the answer choices , i would then test answer c first ( since answers b and d are not in 25 - cent increments ) . if . . . . the largest pot = $ 1.958 0.708 0.958 1.208 1.458 1.708 1.958 total = $ 8.00 so this must be the answer . b\"" + }, + { + "Answer": 0.01616, + "Options": "a ) 1.012526 , b ) 0.012625 , c ) 0.12526 , d ) 0.01616 , e ) 0.12725", + "Correct": "d", + "Explanation": "\"25.25 / 2000 = 2525 / 200000 = 0.01616 answer : d\"" + }, + { + "Answer": 22.499999999999996, + "Options": "a ) 25 , b ) 30 , c ) 20 , d ) 22.5 , e ) 12", + "Correct": "d", + "Explanation": "let the amount of money be 200 let cost of 1 orange be 4 let cost of 1 mango be 5 he decides to retain 5 % of 200 = 10 for taxi fare , so he is left with 190 he buys 20 mangoes ( @ 5 ) so he spends 100 money left is 90 ( 190 - 100 ) no of oranges he can buy = 90 / 4 = > 22,5 so , george can buy 20 oranges . d" + }, + { + "Answer": 65.8, + "Options": "a ) 35.67 % , b ) 65.80 % , c ) 68.57 % , d ) 69.57 % , e ) none of these", + "Correct": "b", + "Explanation": "\"girls = 900 , boys = 1100 passed = ( 36 % of 1100 ) + ( 32 % of 900 ) = 396 + 288 = 684 failed = 2000 - 684 = 1316 failed % = [ ( 1316 / 2000 ) x 100 ] % = 65.8 % . answer : b\"" + }, + { + "Answer": 8, + "Options": "a ) $ 8 , b ) $ 12 , c ) $ 6 , d ) $ 21 , e ) $ 10", + "Correct": "a", + "Explanation": "5 x $ 3 = $ 15 for baby - sitting 3 x $ 4 = $ 12 for garden work $ 15 + $ 12 = $ 27 she has $ 35 - $ 27 = $ 8 more needed to buy the game correct answer a" + }, + { + "Answer": 70, + "Options": "a ) 25 , b ) 70 , c ) 90 , d ) 140 , e ) it can not be determined from the information given", + "Correct": "b", + "Explanation": "\"the arithmetic mean of a and b = ( a + b ) / 2 = 45 - - a + b = 90 - - 1 similarly for b + c = 160 - - 2 subtracting 1 from 2 we have c - a = 70 ; answer : b\"" + }, + { + "Answer": 6.559999999999999, + "Options": "a ) 6.56 kg , b ) 6.8 kg , c ) 6.7 kg , d ) 6.9 kg , e ) 7.8 kg", + "Correct": "a", + "Explanation": "\"800 * 8.2 6560.0 gm 6.56 kg answer : a\"" + }, + { + "Answer": 340.90909090909093, + "Options": "a ) s . 200.90 , b ) s . 250.90 , c ) s . 290.90 , d ) s . 300.90 , e ) s . 340.90", + "Correct": "e", + "Explanation": "\"let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 750 but x = 120 % of y = 120 y / 100 = 12 y / 10 \u2234 12 y / 10 + y = 750 \u21d2 y [ 12 / 10 + 1 ] = 750 \u21d2 22 y / 10 = 750 \u21d2 22 y = 7500 \u21d2 y = 7500 / 22 = rs . 340.90 e )\"" + }, + { + "Answer": 1, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5", + "Correct": "b", + "Explanation": "there are several algebraic ways to solve this question , but the easiest way is as follows : since we can not have two correct answers just pick a prime greater than 5 , square it and see what would be the remainder upon division of it by 12 . n = 7 - - > n ^ 2 = 49 - - > remainder upon division 49 by 12 is 1 . answer : b ." + }, + { + "Answer": 4, + "Options": "a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8", + "Correct": "c", + "Explanation": "since there are only 5 integers , another approach is the just list all 5 . we get : - 2 , 0,2 , 4 , 6 range of positive integers = 6 - 2 = 4 answer : c" + }, + { + "Answer": 142, + "Options": "a ) 90 , b ) 100 , c ) 120 , d ) 142 , e ) 200", + "Correct": "d", + "Explanation": "\"solution : let x be the number he chose , then 2 * x * 180 = 104 2 x = 284 x = 142 correct answer d\"" + }, + { + "Answer": 72, + "Options": "a ) 8 , b ) 64 , c ) 72 , d ) 102 , e ) 144", + "Correct": "c", + "Explanation": "\"if 80 % of the packages weigh at least 25 pounds this means that 20 % of the packages weigh less than 25 pounds let t = total number of packages so , 20 % of t = # of packages that weigh less than 25 pounds 48 packages weigh less than 25 pounds great . so , 20 % of t = 48 rewrite to get : 0.2 t = 48 solve : t = 240 50 % of the packages weigh less than 75 pounds so , 50 % oft = number of packages that weigh less than 75 pounds 50 % of 240 = 120 , so 120 packages weigh less than 75 pounds of those 120 packages that weigh less than 75 pounds , 48 packages weigh less than 25 pounds . so , the number of packages that weight between 25 and 75 pounds = 120 - 48 = 72 = c\"" + }, + { + "Answer": 30, + "Options": "a ) 21 , b ) 30 , c ) 11 , d ) 10 , e ) 9", + "Correct": "b", + "Explanation": "\"number start between 20 to 80 is 60 numbers half of them is even . . which is 30 answer : b\"" + }, + { + "Answer": 6, + "Options": "a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 10", + "Correct": "d", + "Explanation": "if b is 2 , 4 , 5 , or 10 , then gcd of a and b is 2 , 4 , 5 , and 10 respectively . so , by poe the answer must be d . still : if b is a multiple of 6 , then a is 20 greater than a multiple of 6 , so not a multiple of 6 , so both of them can not be divisive by 6 . answer : d ." + }, + { + "Answer": 115, + "Options": "a ) 75 , b ) 100 , c ) 115 , d ) 175 , e ) 225", + "Correct": "c", + "Explanation": "female = x male = 690 - x x / 2 + 690 - x / 4 = 1 / 3 * ( 690 ) = 230 x = 230 x / 2 = 115 is supposed to be the answer m is missing something correct option c" + }, + { + "Answer": 3, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "b", + "Explanation": "akar has = ram + rahul + john after evenly distribution each has 11 . so , total no . is 44 so , akar has = 22 & ram + rahul + john = 22 also ram = rahul - 4 & john - 3 = 3 * ram solving these we get the sol . answer : b" + }, + { + "Answer": 192, + "Options": "a ) 190 , b ) 191 , c ) 192 , d ) 193 , e ) 194", + "Correct": "c", + "Explanation": "divide as ( 1 - 100 ) ( 100 - 200 ) . . . . ( 900 - 1000 ) total 192 answer : c" + }, + { + "Answer": 50, + "Options": "a ) 50 % , b ) 12 % , c ) 8 % , d ) 6 % , e ) 5 %", + "Correct": "a", + "Explanation": "let the annual bonus be x . a corporation double its annual bonus . so new bonus = 2 x . increase = 2 x - x = x the increase is what percent of the employees \u2019 new bonus = ( x / 2 x ) * 100 = 50 % hence a ." + }, + { + "Answer": 0.3333333333333333, + "Options": "a ) 4 / 12 , b ) 4 / 17 , c ) 4 / 15 , d ) 4 / 11 , e ) 4 / 03", + "Correct": "a", + "Explanation": "\"explanation : let the positive number be x . then , 2 / 3 x = 16 / 216 * 1 / x x 2 = 16 / 216 * 3 / 2 = 16 / 144 x = \u221a 16 / 144 = 4 / 12 . answer : a\"" + }, + { + "Answer": 0.375, + "Options": "a ) 1 / 8 , b ) 1 / 4 , c ) 1 / 2 , d ) 3 / 8 , e ) 5 / 8", + "Correct": "d", + "Explanation": "one possible case is : girl - boy - boy the probability of this is 1 / 2 * 1 / 2 * 1 / 2 = 1 / 8 there are 3 c 2 = 3 such cases so we should multiply by 3 . p ( one girl and two boys ) = 3 / 8 the answer is d ." + }, + { + "Answer": 85, + "Options": "a ) 17 , b ) 98 , c ) 88 , d ) 85 , e ) 83", + "Correct": "d", + "Explanation": "let the number of wickets taken till the last match be x . then , ( 12.4 x + 26 ) / ( x + 5 ) = 12 = 12.4 x + 26 = 12 x + 60 = 0.4 x = 34 = x = 340 / 4 = 85 . answer : d" + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 10 , c ) 15 , d ) 25 , e ) 35", + "Correct": "a", + "Explanation": "\"total applicants = 40 political science = 15 and non political science = 40 - 15 = 25 gpa > 3.0 = 20 and gpa < = 3.0 = 20 10 non political science students had gpa < = 3.0 - - > 15 non political science students had gpa > 3.0 gpa > 3.0 in political science = total - ( gpa > 3.0 in non political science ) t = 20 - 15 = 5 answer : a\"" + }, + { + "Answer": 3600.000000000001, + "Options": "a ) rs . 2400 , b ) rs . 3000 , c ) rs . 3600 , d ) rs . 4800 , e ) none of these", + "Correct": "c", + "Explanation": "solution a : b : c = ( 16000 x 3 + 11000 x 9 ) : ( 12000 x 3 + 17000 x 9 ) : ( 21000 x 6 ) = 147 : 180 : 126 = 7 : 9 : 6 . \u2234 difference of b and c \u2019 s shares = rs . ( 26400 x 9 / 22 - 26400 x 6 / 22 ) = rs . 3600 . answer c" + }, + { + "Answer": 80, + "Options": "a ) 70 , b ) 80 , c ) 85 , d ) 90 , e ) 95", + "Correct": "b", + "Explanation": "\"if on a test three people answered 90 % of the questions correctly and two people answered 80 % correctly , then the average for the group is not 85 % but rather 3 \u00d7 90 + 2 \u00d7 805 = 4305 = 86.3 \u00d7 90 + 2 \u00d7 805 = 4305 = 86 . here , 90 has a weight of 3 = > it occurs 3 times . whereas 80 has a weight of 2 = > it occurs 2 times . so the average is closer to 90 than to 80 as we have just calculated . b\"" + }, + { + "Answer": 18, + "Options": "a ) 22 , b ) 18 , c ) 99 , d ) 77 , e ) 24", + "Correct": "b", + "Explanation": "a : b = 2 : 3 b : c = 2 : 5 a : b : c = 4 : 6 : 15 6 / 25 * 75 = 18 answer : b" + }, + { + "Answer": 56.99999999999999, + "Options": "a ) 40 % , b ) 45 % , c ) 57 % , d ) 58 % , e ) 60 %", + "Correct": "c", + "Explanation": "tot no of votes = ( 1136 + 7636 + 11628 ) = 20400 req = > ( 11628 / 20400 * 100 ) = > 57 % answer c" + }, + { + "Answer": 28000, + "Options": "a ) 23477 , b ) 28000 , c ) 28877 , d ) 1987 , e ) 1771", + "Correct": "b", + "Explanation": "\"explanation : suppose b invested rs . x for y months . then , a invested rs . 3 x for 2 y months . so , a : b = ( 3 x * 2 y ) : ( x * y ) = 6 xy : xy = 6 : 1 . b ' s profit : total profit = 1 : 7 . let the total profit be rs . x then , 1 / 7 = 4000 / x or x = 28000 . answer : b ) 28000\"" + }, + { + "Answer": 0.041666666666666664, + "Options": "a ) 2 / 5 , b ) 1 / 4 , c ) 1 / 2 , d ) 1 / 24 , e ) 1 / 25", + "Correct": "d", + "Explanation": "ped = 3 / 5 = 12 / 20 sur = 1 / 4 = 4 / 20 gp = 1 - ( 12 / 20 + 4 / 20 ) = 1 - 16 / 20 = 4 / 20 hsur = ( 1 / 4 ) ( 4 / 20 ) = 1 / 20 if gp doubled = > ( 2 ) ( 4 ) = 8 ; then , total = 12 + 4 + 8 = 24 , and 1 is hsur = > proportion = 1 / 24 . answer : d" + }, + { + "Answer": 80, + "Options": "a ) 12 % , b ) 18 % , c ) 80 % , d ) 20 % , e ) 15 %", + "Correct": "c", + "Explanation": "let the annual bonus be x . a corporation triples its annual bonus . so new bonus = 5 x . increase = 5 x - x = 4 x the increase is what percent of the employees \u2019 new bonus = ( 4 x / 5 x ) * 100 = 80 % hence c ." + }, + { + "Answer": 175, + "Options": "a ) 174 , b ) 150 , c ) 180 , d ) 175 , e ) 190", + "Correct": "a", + "Explanation": "each set has 12 even and 13 odd numbered questions leading to total 96 even and 104 odd questions . 96 + 3 / 4 \u00e2 \u02c6 \u2014 104 = 96 + 78 = 17496 + 3 / 4 \u00e2 \u02c6 \u2014 104 = 96 + 78 = 174 answer : a" + }, + { + "Answer": 20, + "Options": "a ) 8 , b ) 12 , c ) 16 , d ) 20 , e ) 24", + "Correct": "d", + "Explanation": "we ' re asked how old jim is now . we ' re given three facts to work with : 1 ) today , jim is twice as old as fred 2 ) today , sam is 4 years younger than fred 3 ) four years ago , jim was 8 times as old as sam . let ' s test answer d : 20 if . . . . jim is currently 20 years old . . . . fred is 10 years old sam is 6 years old 4 years ago , jim was 16 and sam was 2 , so jim was 8 times sam ' s age . this is an exact match for what we were told , so this must be the answer . d" + }, + { + "Answer": 10.000000000000009, + "Options": "a ) 5 , b ) 6 , c ) 8 , d ) 9 , e ) 10", + "Correct": "e", + "Explanation": "a has 10 yellows 20 reds total = 30 so b has 1.2 x 20 = 24 reds 0.9 x 10 = 9 yellows total = 33 difference = 3 / 30 = 10 % answer : e" + }, + { + "Answer": 12800, + "Options": "a ) 12800 , b ) 13000 , c ) 11500 , d ) 12500 , e ) 12000", + "Correct": "a", + "Explanation": "b claims 2 / 7 of the profit a claims remaining 5 / 7 of the profit = > a : b = 5 / 7 : 2 / 7 = 5 : 2 let the money contributed by b = b then a : b = 16000 \u00d7 8 : b \u00d7 4 therefore , 16000 \u00d7 8 : b \u00d7 4 = 5 : 2 16000 \u00d7 8 \u00d7 2 = b \u00d7 4 \u00d7 5 16000 \u00d7 2 \u00d7 2 = b \u00d7 5 3200 \u00d7 2 \u00d7 2 = b b = 12800 answer is a ." + }, + { + "Answer": 3, + "Options": "a ) b / 2 , b ) b , c ) 3 b / 2 , d ) 2 b , e ) 3 b", + "Correct": "e", + "Explanation": "lets do it by picking up numbers . let arthur carry 2 crumbs per trip , this means amy carries 3 crumbs per trip . also let arthur make 2 trips and so amy makes 4 trips . thus total crumbs carried by arthur ( b ) = 2 x 2 = 4 , total crumbs carried by amy = 3 x 4 = 12 . 12 is 3 times 4 , so e" + }, + { + "Answer": 26, + "Options": "a ) 30 , b ) 26 , c ) 11 , d ) 31 , e ) 32", + "Correct": "b", + "Explanation": "detailed solution let the total students be ( n + 1 ) let total badges be x let the average of \u2018 n \u2019 students be y the student who got 1 / 6 th of x = 5 y or y = x / 30 therefore \u2018 n \u2019 students got 1 / 30 th of total share each or n * x / 30 + 1 * x / 6 = x nx + 5 x = 30 x n + 5 = 30 or n = 25 total = n + 1 = 26 correct answer : b" + }, + { + "Answer": 14, + "Options": "a ) 14 , b ) 10 , c ) 9 , d ) 6 , e ) 5", + "Correct": "a", + "Explanation": "# of people times the # of hours : 4 * 7 = 28 - - > 4 lawyers do 28 worksin 7 hours . 3 * 14 / 3 = 14 - - > 3 assistants do 14 worksin 4 hours so , since the amount of work the assistants do is half the work the lawyers do , the time will be double , soans a" + }, + { + "Answer": 9, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", + "Correct": "c", + "Explanation": "let x be the larger number and y be the smaller number . x - y = 6 x + 2 ( y ) = 15 solve by substitution : y = x - 6 x + 2 ( x - 6 ) = 15 x + 2 x - 12 = 15 3 x = 27 x = 9 the larger number is 9 , so answer c is correct ." + }, + { + "Answer": 120, + "Options": "a ) 10 , b ) 45 , c ) 95 , d ) 120 , e ) none of these", + "Correct": "d", + "Explanation": "explanation : 3 prize among 10 students can be distributed in 10 c 3 ways = 120 ways . answer : d" + }, + { + "Answer": 0.0625, + "Options": "a ) 1 / 8 , b ) 1 / 4 , c ) 1 / 16 , d ) 1 / 32 , e ) 1 / 2", + "Correct": "c", + "Explanation": "must be twice on heads and twice on tails 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 16 answer : c" + }, + { + "Answer": 24, + "Options": "a ) 18 metres , b ) 16 metres , c ) 38 metres , d ) 42 metres , e ) 24 metres", + "Correct": "e", + "Explanation": "a little reflection will show that chalk marks will touch the ground together for the first time after the wheels have passed over a distance which is the lcm of 2 2 / 5 metres and 3 3 / 7 metres . lcm of 12 / 5 metres and 24 / 7 metres = 24 metres . answer is e" + }, + { + "Answer": 40.20000000000002, + "Options": "a ) 60.2 degrees c , b ) 50.2 degrees c , c ) 40.2 degrees c , d ) 70.2 degrees c , e ) none of these", + "Correct": "c", + "Explanation": "explanation : mon + tue + wed temperature = 3 x 36.3 = 108.9 tue + wed temperature = 108.9 \u2013 39 = 69.9 tue + wed + thu temperature = 3 x 36.7 = 110.1 so , thursday \u2019 s temperature = 110.1 \u2013 69.9 = 40.2 degrees c answer : c" + }, + { + "Answer": 36000, + "Options": "a ) 240000 , b ) 300000 , c ) 168000 , d ) 36000 , e ) 24,000", + "Correct": "d", + "Explanation": "explanatory answer let the percentage of the total votes secured by party d be x % then the percentage of total votes secured by party r = ( x - 12 ) % as there are only two parties contesting in the election , the sum total of the votes secured by the two parties should total up to 100 % i . e . , x + x - 12 = 100 2 x - 12 = 100 or 2 x = 112 or x = 56 % . if party d got 56 % of the votes , then party got ( 56 - 12 ) = 44 % of the total votes . 44 % of the total votes = 132,000 i . e . , 44 / 100 * t = 132,000 = > t = 132000 * 100 / 44 = 300,000 votes . the margin by which party r lost the election = 12 % of the total votes = 12 % of 300,000 = 36,000 . the correct choice is ( d )" + }, + { + "Answer": 625, + "Options": "a ) 24 , b ) 120 , c ) 625 , d ) 720 , e ) 1024", + "Correct": "c", + "Explanation": "\"5 choices for each of the 4 questions , thus total e of 5 * 5 * 5 * 5 = 5 ^ 4 = 625 ways to answer all of them . answer : c .\"" + }, + { + "Answer": 350, + "Options": "a ) a ) 350 , b ) b ) 346 , c ) c ) 358 , d ) d ) 336 , e ) e ) 364", + "Correct": "a", + "Explanation": "x + x ( xx ) put the value of x = 7 in the above expression we get , 7 + 7 ( 77 ) = 7 + 7 ( 7 \u00e3 \u2014 7 ) = 7 + 7 ( 49 ) = 7 + 343 = 350 the answer is ( a )" + }, + { + "Answer": 140, + "Options": "a ) 130 , b ) 155 , c ) 490 , d ) 140 , e ) 160", + "Correct": "d", + "Explanation": "explanation : x - 35 = 80 x / 100 = > x = 175 = > 4 x / 5 = 4 x 175 / 5 = 140 . answer d" + }, + { + "Answer": 0.16666666666666666, + "Options": "a ) 1 / 20 , b ) 1 / 6 , c ) 1 / 5 , d ) 4 / 21 , e ) 5 / 21", + "Correct": "b", + "Explanation": "this is how i used to calculate which i think works pretty well : if you let the average of the 20 other numbers equal a , can you write this equation for sum of the list ( s ) n + 20 a = s the question tells us that n = 4 a plug this back into the first equation and you get that the sum is 24 a 4 a + 20 a = 24 a therefore fraction q of n to the total would be 4 a / 24 a or 1 / 6 answer b" + }, + { + "Answer": 250, + "Options": "a ) $ 240 , b ) $ 350 , c ) $ 217 , d ) $ 250 , e ) $ 340", + "Correct": "d", + "Explanation": "answer is ( d ) . if mathew is left with about $ 350 after all expenses each month , he would need to divide the total expense budget to london ( $ 3000 ) by 12 months to determine how much he would need to put away every single month to hit his target . $ 3000 / 12 = $ 250 ." + }, + { + "Answer": 8.4, + "Options": "a ) 3 , b ) 3.75 , c ) 4.5 , d ) 8.4 , e ) 9", + "Correct": "d", + "Explanation": "05 grass seed contains 5 % herbicide and its amount is 3 pound 20 grass seed contains 20 % herbicide and its amount is x when these two types of grass seeds are mixed , their average becomes 15 % thus we have 3 ( 1 ) + x ( 20 ) / ( x + 3 ) = 15 3 + 20 x = 15 x + 45 5 x = 42 or x = 8.4 d" + }, + { + "Answer": 2013, + "Options": "a ) 222 , b ) 2787 , c ) 2013 , d ) 2778 , e ) 10222", + "Correct": "c", + "Explanation": "\"put n = 0 then f ( f ( 0 ) ) + f ( 0 ) = 2 ( 0 ) + 3 \u21d2 \u21d2 f ( 1 ) + 1 = 3 \u21d2 \u21d2 f ( 1 ) = 2 put n = 1 f ( f ( 1 ) ) + f ( 1 ) = 2 ( 1 ) + 3 \u21d2 \u21d2 f ( 2 ) + 2 = 5 \u21d2 \u21d2 f ( 2 ) = 3 put n = 2 f ( f ( 2 ) ) + f ( 2 ) = 2 ( 2 ) + 3 \u21d2 \u21d2 f ( 3 ) + 3 = 7 \u21d2 \u21d2 f ( 3 ) = 4 . . . . . . f ( 2012 ) = 2013 answer : c\"" + }, + { + "Answer": 40, + "Options": "a ) 87 , b ) 40 , c ) 37 , d ) 28 , e ) 26", + "Correct": "b", + "Explanation": "a . m . of 75 numbers = 35 sum of 75 numbers = 75 * 35 = 2625 total increase = 75 * 5 = 375 increased sum = 2625 + 375 = 3000 increased average = 3000 / 75 = 40 . answer : b" + }, + { + "Answer": 1200, + "Options": "a ) 1200 , b ) 380 , c ) 3800 , d ) 2180 , e ) 3180", + "Correct": "a", + "Explanation": "let the number of boys = x , number of girls = y 40 y / 100 = 120 y = 300 120 = 2 / 3 * 20 x / 100 = 2 x / 15 x = 900 total = x + y = 300 + 900 = 1200 answer : a" + }, + { + "Answer": 1.25, + "Options": "a ) 2 hours , b ) 2.25 hours , c ) 1 hour , d ) 1.25 hours , e ) not enough information", + "Correct": "d", + "Explanation": "each train is averaging 40 km / hour in an opposite direction . after 1 hour , they will be 80 km apart , and after 1.25 hours , they will be 100 km apart . ( 80 * 1.25 = 100 ) answer is d" + }, + { + "Answer": 27.638888888888896, + "Options": "a ) 25.7 miles , b ) 26.2 miles , c ) 27.6 miles , d ) 27.9 miles , e ) 29.9 miles", + "Correct": "c", + "Explanation": "for sad : saddaily = $ 34.95 / day sadmile = $ 0.23 / mile for ral : raldaily = $ 25.00 / day ralmile = $ 1.31 / mile we want the raltotal = sadtotal , so we get ( raldaily * days ) + ( ralmile * miles ) = ( saddaily * days ) + ( sadmile * miles ) = > miles = ( ( saddaily * days ) - ( raldaily * days ) ) / ( ralmiles - sadmiles ) = ( ( saddaily - raldaily ) * days ) / ( ralmiles - sadmiles ) miles = ( ( $ 34.95 * 3 ) - ( $ 25.00 * 3 ) ) / ( $ 1.31 - $ 0.23 ) = 27.6 miles c . 27.6 miles" + }, + { + "Answer": 43, + "Options": "a ) 41 , b ) 39 , c ) 43 , d ) 45 , e ) 47", + "Correct": "c", + "Explanation": "option ' c '" + }, + { + "Answer": 34, + "Options": "a ) 30 , b ) 34 , c ) 40 , d ) 50 , e ) 60", + "Correct": "b", + "Explanation": "explanation : ( a + b ) , five years ago = ( 15 * 2 ) = 30 years . ( a + b ) , now = ( 30 + 5 * 2 ) years = 40 years . ( a + b + c ) , now = ( 20 x 3 ) years = 60 years . c , now = ( 60 - 40 ) years = 20 years . c , after 14 years = ( 20 + 14 ) years = 34 years . answer : b" + }, + { + "Answer": 6, + "Options": "a ) 12 , b ) 18 , c ) 15 , d ) 6 , e ) 9", + "Correct": "d", + "Explanation": "explanation : = > y = x ^ 2 + 5 x + 6 = > y = ( x + 2 ) ( x + 3 ) = > x = - 2 , x = - 3 product x = ( - 2 ) ( - 3 ) = 6 answer option 6 answer : d" + }, + { + "Answer": 90, + "Options": "a ) 50 , b ) 60 , c ) 90 , d ) 48 , e ) 67", + "Correct": "c", + "Explanation": "c $ 90 let number of notes of each denomination be x . then x + 5 x + 10 x = 480 16 x = 480 x = 30 . hence , total number of notes = 3 x = 90 ." + }, + { + "Answer": 10, + "Options": "a ) 12 years , b ) 10 years , c ) 8 years , d ) 14 years , e ) 16 years", + "Correct": "b", + "Explanation": "\"c age x , then b age is 2 x so a age is 2 x + 2 . ( 2 x + 2 ) + 2 x + x = 27 5 x = 25 x = 5 so b is 2 x = 2 ( 5 ) 2 x 5 = 10 answer : b\"" + }, + { + "Answer": 6, + "Options": "a ) 10 , b ) 6 , c ) 4 , d ) 0 , e ) it can not be determined", + "Correct": "b", + "Explanation": "it is essential to recognize that the remainder when an integer is divided by 10 is simply the units digit of that integer . to help see this , consider the following examples : 4 / 10 is 0 with a remainder of 4 14 / 10 is 1 with a remainder of 4 5 / 10 is 0 with a remainder of 5 105 / 10 is 10 with a remainder of 5 it is also essential to remember that the s is a positive integer and multiple of 2 . any integer that is a multiple of 2 is an even number . so , s must be a positive even integer . with these two observations , the question can be simplified to : what is the units digit of 4 raised to an even positive integer ? the units digit of 4 raised to an integer follows a specific repeating pattern : 4 ^ 1 = 4 4 ^ 2 = 16 4 ^ 3 = 64 4 ^ 4 = 256 4 ^ ( odd number ) - - > units digit of 4 4 ^ ( even number ) - - > units digit of 6 there is a clear pattern regarding the units digit . 4 raised to any odd integer has a units digit of 4 while 4 raised to any even integer has a units digit of 6 . since s must be an even integer , the units digit of p = 4 ^ s will always be 6 . consequently , the remainder when p = 4 ^ s is divided by 10 will always be 6 . in case this is too theoretical , consider the following examples : s = 2 - - > p = 4 ^ z = 16 - - > s / 10 = 1 with a remainder of 6 s = 4 - - > p = 4 ^ z = 256 - - > s / 10 = 25 with a remainder of 6 s = 6 - - > p = 4 ^ z = 4096 - - > s / 10 = 409 with a remainder of 6 s = 8 - - > p = 4 ^ z = 65536 - - > s / 10 = 6553 with a remainder of 6 answer : b ." + }, + { + "Answer": 248, + "Options": "a ) 248 , b ) 120 , c ) 252 , d ) 250 , e ) 350", + "Correct": "a", + "Explanation": "amount left = 0.5 x \u2212 4 for fifth store this is zero . so x = 8 . that means he entered fifth store with 8 . now for fourth store , amount left = 8 so 0.5 x \u2212 4 = 8 \u21d2 x = 24 for third store , amount left = 24 so 12 x \u2212 4 = 24 \u21d2 x = 56 for second store , amount left = 56 so 0.5 x \u2212 4 = 56 \u21d2 x = 120 for first store , amount left = 120 so 0.5 x \u2212 4 = 120 \u21d2 x = 248 so he entered first store with 248 . answer : a" + }, + { + "Answer": 0.5000000000000001, + "Options": "a ) 1 / 2 , b ) 2 / 7 , c ) 3 / 2 , d ) 4 / 7 , e ) none of them", + "Correct": "a", + "Explanation": "original share of 1 person = 1 / 3 new share of 1 person = 1 / 2 increase = ( 1 / 2 - 1 / 3 = 1 / 6 ) therefore , required fraction = ( 1 / 6 ) / ( 1 / 3 ) = ( 1 / 6 ) x ( 3 / 1 ) = 1 / 2 answer is a ." + }, + { + "Answer": 159, + "Options": "a ) 79 , b ) 80 , c ) 81 , d ) 157 , e ) 159", + "Correct": "e", + "Explanation": "\"the number of terms in this set would be : n = ( k - 1 ) / 2 ( as k is odd ) last term : k - 1 average would be first term + last term / 2 = ( 2 + k - 1 ) / 2 = ( k + 1 ) / 2 also average : sum / number of terms = 79 * 80 / ( ( k - 1 ) / 2 ) = 158 * 80 / ( k - 1 ) ( k + 1 ) / 2 = 158 * 80 / ( k - 1 ) - - > ( k - 1 ) ( k + 1 ) = 158 * 160 - - > k = 159 answer e .\"" + }, + { + "Answer": 45, + "Options": "a ) 40 , b ) 48 , c ) 43 , d ) 45 , e ) 41", + "Correct": "d", + "Explanation": "ele , the circus elephant , is currently three times older than lyn , the circus lion . ele = 3 * lyn usually , ages are integers so there is a good possibility that the age of ele is 45 ( the only option that is a multiple of 3 ) . then age of lyn would be 15 . in 15 yrs , ele would be 60 and lyn would be 30 - so lyn would be half as old as ele . answer ( d )" + }, + { + "Answer": 110.00000000000001, + "Options": "a ) $ 50 , b ) $ 100 , c ) $ 110 , d ) $ 600 , e ) $ 300", + "Correct": "c", + "Explanation": "let the lowest price be x . therefore , highest price is x + 100 . now price of each variety is increased by 10 % . therefore the price will remain arranged in the same order as before . or lowest price = 1.1 x and highest = 1.1 * ( x + 100 ) or range = highest - lowest = 1.1 * ( x + 100 ) - 1.1 x = 110 , hence , c" + }, + { + "Answer": 89.6, + "Options": "a ) 90 % , b ) 80 % , c ) 70 % , d ) 60 % , e ) 40 %", + "Correct": "a", + "Explanation": "the problem asks for the approximate chance that no more than 1 / 3 of the original investment is lost . we can apply the \u201c 1 \u2013 x \u201d technique : what \u2019 s the chance that more than 1 / 3 of the original investment is lost ? there are two outcomes we have to separately measure : ( a ) all 3 investments become worthless . ( b ) 2 of the 3 investments become worthless , while 1 doesn \u2019 t . outcome ( a ) : the probability is ( 0.2 ) ( 0.2 ) ( 0.2 ) = 0.008 , or a little less than 1 % . outcome ( b ) : call the investments x , y , and z . the probability that x retains value , while y and z become worthless , is ( 0.8 ) ( 0.2 ) ( 0.2 ) = 0.032 . now , we have to do the same thing for the specific scenarios in which y retains value ( while x and z don \u2019 t ) and in which z retains value ( while x and y don \u2019 t ) . each of those scenarios results in the same math : 0.032 . thus , we can simply multiply 0.032 by 3 to get 0.096 , or a little less than 10 % . the sum of these two probabilities is 0.008 + 0.096 = 0.104 , or a little more than 10 % . finally , subtracting from 100 % and rounding , we find that the probability we were looking for is approximately 90 % . the correct answer is a . this problem illustrates the power of diversification in financial investments . all else being equal , it \u2019 s less risky to hold a third of your money in three uncorrelated ( independent ) but otherwise equivalent investments than to put all your eggs in one of the baskets . that said , be wary of historical correlations ! housing price changes in different us cities were not so correlated \u2014 and then they became highly correlated during the recent housing crisis ( they all fell together ) , fatally undermining spreadsheet models that assumed that these price changes were independent ." + }, + { + "Answer": 25400, + "Options": "a ) 2840 , b ) 5680 , c ) 6840 , d ) 25400 , e ) 28400", + "Correct": "d", + "Explanation": "bank balance is doubled with accumulation of interest tp 5080 . . this means interest is 5080 / 2 = 2540 for entire year . . although since interest is 10 % of avg monthly balance , it becomes 25400 . . d" + }, + { + "Answer": 7.4074074074074066, + "Options": "a ) 7.5 % , b ) 7.41 % , c ) 10.9 % , d ) 12.6 % , e ) 15 %", + "Correct": "b", + "Explanation": "reduce in consumption = r / ( 100 + r ) * 100 % = 8 / 108 * 100 = 7.41 % answer is b" + }, + { + "Answer": 0.16666666666666666, + "Options": "a ) 1 / 20 , b ) 1 / 6 , c ) 1 / 5 , d ) 4 / 21 , e ) 5 / 21", + "Correct": "b", + "Explanation": "\"this is how i used to calculate which i think works pretty well : if you let the average of the 20 other numbers equal a , can you write this equation for sum of the list ( s ) n + 20 a = s the question tells us that n = 4 a plug this back into the first equation and you get that the sum is 24 a 4 a + 20 a = 24 a therefore fraction e of n to the total would be 4 a / 24 a or 1 / 6 answer b\"" + }, + { + "Answer": 7028, + "Options": "a ) 7028 , b ) 4028 , c ) 3128 , d ) 3256 , e ) 5264", + "Correct": "a", + "Explanation": "( 7000 + 28 ) / 100 * 100 = 7028 answer : a" + }, + { + "Answer": 0.5714285714285715, + "Options": "a ) 3 / 7 , b ) 4 / 7 , c ) 5 / 7 , d ) 7 / 11 , e ) 9 / 11", + "Correct": "b", + "Explanation": "let a be the event \u2018 the number on the card drawn is even \u2019 and b be the event \u2018 the number on the card drawn is greater than 3 \u2019 . we have to find p ( a | b ) . now , the sample space of the experiment is s = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 } then a = { 2 , 4 , 6 , 8 , 10 } , b = { 4 , 5 , 6 , 7 , 8 , 9 , 10 } and a n b = { 4 , 6 , 8 , 10 } also p ( a ) = 5 / 2 , p ( b ) = 7 / 10 and p ( a n b ) = 4 / 10 then p ( a | b ) = p ( a n b ) / p ( b ) = ( 4 / 10 ) / ( 7 / 10 ) = 4 / 7 b )" + }, + { + "Answer": 74, + "Options": "a ) 74 , b ) 76 , c ) 78 , d ) 80 , e ) 82", + "Correct": "a", + "Explanation": "\"a score of 58 was 2 standard deviations below the mean - - > 58 = mean - 2 d a score of 98 was 3 standard deviations above the mean - - > 98 = mean + 3 d solving above for mean w = 74 . answer : a .\"" + }, + { + "Answer": 855220, + "Options": "a ) 854542 , b ) 856945 , c ) 758965 , d ) 855220 , e ) 826450", + "Correct": "d", + "Explanation": "\"( 855000 + 220 ) / 900 * 900 = 855000 + 220 = 855220 answer : d\"" + }, + { + "Answer": 3, + "Options": "a ) 3 , b ) 5 , c ) 6 , d ) 10 , e ) 18", + "Correct": "a", + "Explanation": "# of boxes of cookies mary sold = x ann sold 5 times more = 5 x x + 5 x = 18 6 x = 18 x = 18 / 6 = 3 answer : a" + }, + { + "Answer": 9, + "Options": "a ) 3 , b ) 4 , c ) 8 , d ) 9 , e ) 13", + "Correct": "d", + "Explanation": "let number of packs of four = f let number of packs of nine = n 4 f + 9 n = 97 now , we need to test for values of n . since sum 97 is odd and 4 f will always be even , n ca n ' t be even . now , we can test for values e = 2 , 4 and 6 4 * 4 + 9 * 9 = 16 + 81 = 97 answer d" + }, + { + "Answer": 600, + "Options": "a ) rs . 500 , b ) rs . 600 , c ) rs . 650 , d ) rs . 760 , e ) rs . 800", + "Correct": "b", + "Explanation": "first selling price = 110 % - - - - - > x rupees = sold at for rs . 60 / - = 120 % - - - - - > x + 60 rupees ~ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 10 % - - - - - - - - > 60 100 % - - - - - - - > rs . 600 / - option ' b '" + }, + { + "Answer": 65500, + "Options": "a ) 65500 $ , b ) 125800 $ , c ) 125900 $ , d ) 6500 $ , e ) 122500 $", + "Correct": "a", + "Explanation": "solution c ( 100 ) = 600 * 100 + 5500 = 125500 $ answer a" + }, + { + "Answer": 74, + "Options": "a ) 12 , b ) 18 , c ) 25 , d ) 74 , e ) 88", + "Correct": "d", + "Explanation": "number of runs scored more to increase the ratio by 1 is 26 - 14 = 12 to raise the average by one ( from 14 to 15 ) , he scored 12 more than the existing average . therefore , to raise the average by five ( from 14 to 19 ) , he should score 12 x 5 = 60 more than the existing average . thus he should score 14 + 60 = 74 . answer d" + }, + { + "Answer": 518.984375, + "Options": "a ) 511 , b ) 519 , c ) 256 , d ) 255 , e ) 1023", + "Correct": "b", + "Explanation": "there are 520 players , only 1 person wins , 519 players lose . in order to lose , you must have lost a game . 519 games . ans - b" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "c", + "Explanation": "( 7 w + 6 ) / 6 + ( 9 w + 8 ) / 2 = 22 or , [ 7 w + 6 + 3 ( 9 w + 8 ) ] / 6 = 22 or , 7 w + 6 + 27 w + 24 = 132 or , 34 w + 30 = 132 or , 34 w = 132 - 30 or , 34 w = 102 or , w = 102 / 34 therefore , w = 3 answer : c" + }, + { + "Answer": 11, + "Options": "a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14", + "Correct": "b", + "Explanation": "we can determine quickly that total number should range between 49 / 8 < = n < = 49 / 1.5 , so ans should be between 6 and 33 . now solving the expression 8 a + 1.5 b = 49 decreasing 49 in multiple of 8 and checking divisibility of that number by 1.5 . this way we get 2 red giants , 22 white dwarfs we get 49 , but 2 + 22 = 24 and 24 is not an option . next we get 5 red giants and 6 white dwarfs to get 49 , 5 * 8 + 6 * 1.5 = 49 hence total number is 5 + 6 = 11 ans b" + }, + { + "Answer": 900, + "Options": "a ) 900 , b ) 1000 , c ) 1100 , d ) 1200 , e ) 1300", + "Correct": "a", + "Explanation": "a = b + 300 . a = 4 ( b - 600 ) . 4 ( b - 600 ) = b + 300 . 3 b = 2700 . b = 900 . the answer is a ." + }, + { + "Answer": 84, + "Options": "a ) 84 , b ) 68 , c ) 85 , d ) 75 , e ) 42", + "Correct": "a", + "Explanation": "explanation total marks of 5 students = ( 65 + 75 + 55 + 72 + 69 ) = 336 required marks = [ ( 70 x 6 ) \u2013 336 ] = ( 420 \u2013 336 ) = 84 answer a" + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14", + "Correct": "a", + "Explanation": "t 7 + t 23 = t 8 + t 15 + t 13 = > a + 6 d + a + 22 d = a + 7 d + a + 14 d + a + 12 d = > a + 5 d = 0 = > t 6 = 0 i . e . 6 th term is zero . answer : a" + }, + { + "Answer": 15, + "Options": "a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16", + "Correct": "d", + "Explanation": "w + b + c + 14 + 15 = 12 * 5 = 60 = > w + b + c = 60 - 29 = 31 w + b + c + 29 = 31 + 29 = 60 average = 60 / 4 = 15 answer d" + }, + { + "Answer": 6, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 11 , e ) 12", + "Correct": "b", + "Explanation": "since - 4 is the least integer in list a , then 7 is the largest integer in that list . thus the range of the positive integers in the list is 7 - 1 = 6 . answer : b ." + }, + { + "Answer": 40, + "Options": "a ) 25 litres , b ) 35 litres , c ) 30 litres , d ) 40 litres , e ) none of these", + "Correct": "d", + "Explanation": "x / 5 + 22 = 3 x / 4 = > x = 40 litres answer : d" + }, + { + "Answer": 786858, + "Options": "a ) 786845 , b ) 786857 , c ) 786858 , d ) 786859 , e ) 786860", + "Correct": "c", + "Explanation": "\"( 875 233 / 899 ) \u00d7 899 ( 786625 + 233 ) / 899 \u00d7 899 786858 / 899 \u00d7 899 786858 c\"" + }, + { + "Answer": 180, + "Options": "a ) 120 , b ) 150 , c ) 180 , d ) 210 , e ) 240", + "Correct": "c", + "Explanation": "they can make a team of 3 men and 2 women . the number of ways to do this is 6 c 3 * 4 c 2 = 20 * 6 = 120 they can make a team of 2 men and 3 women . the number of ways to do this is 6 c 2 * 4 c 3 = 15 * 4 = 60 the total number of distinct groups is 180 . the answer is c ." + }, + { + "Answer": 540, + "Options": "a ) 540 , b ) 570 , c ) 619 , d ) 649 , e ) 700", + "Correct": "a", + "Explanation": "\"before price increase price = a after 30 % price increase price = a + ( 30 / 100 ) * a = 1.3 a = 351 ( given ) i . e . a = 351 / 1.3 = $ 270 i . e . 2 a = 2 * 270 = 540 answer : option a\"" + }, + { + "Answer": 30, + "Options": "a ) 30 , 10 , b ) 2010 , c ) 3515 , d ) 5117 , e ) 20,17", + "Correct": "a", + "Explanation": "let their ages be x and ( x + 20 ) years ( x - 5 ) * 5 = ( x + 20 - 5 ) after solving this we get x = 10 years the age of elder one = 10 + 20 = 30 years so the present ages are 30 and 10 years answer : a" + }, + { + "Answer": 1.5200000000000102, + "Options": "a ) 0.2 % , b ) 0.8 % , c ) 1.2 % , d ) 1.52 % , e ) 2 %", + "Correct": "d", + "Explanation": "( 100 % + 8 % ) * ( 100 % - 6 % ) = 1.08 * 0.94 = 1.0152 = 101.52 % . the net percentage change in the price of the stock is ( + ) 1.52 % the answer is d" + }, + { + "Answer": 8, + "Options": "a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12", + "Correct": "d", + "Explanation": "there are twice as many girls as boys in the class - - > g = 2 b . each girl writes 3 more letters than each boy - - > boys write x letters , girls write x + 3 letters . boys write 24 letters - - > bx = 24 . girls write 90 - 24 = 66 letters - - > ( 2 b ) ( x + 3 ) = 66 - - > 2 bx + 6 b = 66 - - > 2 * 24 + 6 b = 66 - - > b = 3 . bx = 24 - - > 3 x = 24 - - > x = 8 . answer : d ." + }, + { + "Answer": 98.56, + "Options": "a ) rs . 48 , b ) rs . 98.56 , c ) rs . 66.56 , d ) rs . 66.58 , e ) none of these", + "Correct": "b", + "Explanation": "explanation : given that simple interest for 2 years is rs . 800 i . e . , simple interest for 1 st year is rs . 400 and simple interest for 2 nd year is also rs . 400 compound interest for 1 st year will be 400 and compound interest for 2 nd year will be 832 - 400 = 432 you can see that compound interest for 2 nd year is more than simple interest for 2 nd year by 432 - 400 = rs . 32 i . e , rs . 32 is the interest obtained for rs . 400 for 1 year rate , r = 100 \u00d7 si / pt = ( 100 \u00d7 32 ) / ( 400 \u00d7 1 ) = 8 % difference between compound and simple interest for the 3 rd year = simple interest obtained for rs . 832 = prt / 100 = ( 832 \u00d7 8 \u00d7 1 ) / 100 = rs . 66.56 total difference between the compound and simple interest for 3 years = 32 + 66.56 = rs . 98.56 answer : option b" + }, + { + "Answer": 3, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "b", + "Explanation": "25 ^ 5 \u00d7 5 ^ ( - 1 ) = ( 125 ) ^ x ( 5 ^ 2 ) ^ 5 \u00d7 5 ^ ( - 1 ) = 5 ^ 3 x 5 ^ 10 x 5 ^ ( - 1 ) = 5 ^ 3 x ; since all of the bases are the same now , we can equate the exponents in the next step 10 - 1 = 3 x 9 = 3 x x = 3 ans . b ) 3" + }, + { + "Answer": 80, + "Options": "a ) 80 , b ) 81 , c ) 82 , d ) 83 , e ) 84", + "Correct": "a", + "Explanation": "explanation : if n = 1 , then the set t 1 = { 1 , 23 , 45 } , and it does not have 6 or any multiples . n = 2 to n = 6 has 6 in the set . n = 7 , has the set t 7 = { 7 , 89 , 1011 } , and no 6 or multiples . so 1 in every 6 members do not have 6 or multiples of 6 . so , till n = 96 , there are 16 sets of \u201c 6 members \u201d ( 16 * 6 = 96 ) and 16 sets do not have 6 or its multiples , while the remaining 80 sets have . answer : a" + }, + { + "Answer": 22000, + "Options": "a ) $ 27000 , b ) $ 22000 , c ) $ 33000 , d ) $ 16000 , e ) $ 43000", + "Correct": "b", + "Explanation": "let the lowest bonus be x . therefore , highest bonus is x + 20000 . now bonus of each employee is increased by 10 % . therefore the bonus will remain arranged in the same order as before . or lowest bonus = 1.1 x and highest = 1.1 * ( x + 20000 ) or range = highest - lowest = 1.1 * ( x + 20000 ) - 1.1 x = 22000 , hence , b" + }, + { + "Answer": 0.8888888888888888, + "Options": "a ) 8 / 9 , b ) 11 / 12 , c ) 8 / 13 , d ) 11 / 13 , e ) 12 / 13", + "Correct": "a", + "Explanation": "we can take some easy numbers and make calculations simpler . let r ( rex ' s income ) = 100 q ( niall ' s income ) = 40 % r = 40 s ( sam ' s income ) = 75 % q = ( 3 / 4 ) * 40 = 30 now , if rex gives 40 % to niall - - > q = 40 + 40 = 80 60 % given to sam - - > s = 30 + 60 = 90 the ratio is : q / s = 80 / 90 = 8 / 9 = a" + }, + { + "Answer": 6, + "Options": "a ) 9 , b ) 12 , c ) 20 , d ) 10 , e ) 0", + "Correct": "d", + "Explanation": "d" + }, + { + "Answer": 1.7999999999999998, + "Options": "a ) $ 1.80 , b ) $ 2.00 , c ) $ 2.40 , d ) $ 2.70 , e ) $ 3.00", + "Correct": "a", + "Explanation": "the price in 1970 was 150 percent of its price in 1960 , means that the percent increase was 50 % from 1960 to 1970 ( and from 1970 to 1980 ) . therefore the price in 1980 = $ 1.2 * 1.5 = $ 1.8 . answer : a ." + }, + { + "Answer": 6, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9", + "Correct": "b", + "Explanation": "let ct + t + c = x add 1 on both sides : ct + t + c + 1 = x + 1 t ( c + 1 ) + c + 1 = x + 1 ( c + 1 ) ( t + 1 ) = x + 1 minimum value of ( c + 1 ) = 2 minimum value of ( t + 1 ) = 2 hence x + 1 can not be prime substitute x from the given options : 6 + 1 = 7 - - > prime - - > ct + t + s can not be 6 answer : b" + }, + { + "Answer": 665, + "Options": "a ) 665 , b ) 376 , c ) 998 , d ) 1277 , e ) 1991", + "Correct": "a", + "Explanation": "explanation : let the total score be x . ( x + 92 - 85 ) / 8 = 84 . so , x + 7 = 672 = > x = 665 . answer : a ) 665" + }, + { + "Answer": 13, + "Options": "a ) 5 , b ) 8 , c ) 10 , d ) 13 , e ) 17", + "Correct": "d", + "Explanation": "official solution : ( b ) we know that a # b = 100 and a # b = 4 a \u00b2 + 4 b \u00b2 + 8 ab . so 4 a \u00b2 + 4 b \u00b2 + 8 ab = 100 we can see that 4 a \u00b2 + 4 b \u00b2 + 8 ab is a well - known formula for ( 2 a + 2 b ) \u00b2 . therefore ( 2 a + 2 b ) \u00b2 = 100 . ( 2 a + 2 b ) is non - negative number , since both a and b are non - negative numbers . so we can conclude that 2 ( a + b ) = 10 . ( a + b ) + 8 = 10 / 2 + 8 = 13 . the correct answer is d" + }, + { + "Answer": 5, + "Options": "a ) 2 , b ) 6 , c ) 7 , d ) 8 , e ) 5", + "Correct": "e", + "Explanation": "let amount of 10 $ be x . then amount of 5 $ be 2 x . now 5 * 2 x + 10 * x = 100 . thus x = 5 . answer : e" + }, + { + "Answer": 200, + "Options": "a ) 240 , b ) 300 , c ) 200 , d ) 400 , e ) 480", + "Correct": "c", + "Explanation": "{ total } = { retirees } + { bridge players } - { both } + { neither } x = 5 / 20 * x + x / 2 - 3 / 20 * x + 120 20 x = 5 x + 10 x - 3 x + 120 * 20 ( multiply by 20 ) 12 x = 120 * 20 x = 200 . answer : c" + }, + { + "Answer": 84, + "Options": "a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %", + "Correct": "d", + "Explanation": "d the prompt says that 68 % of the population lies between m - d and m + d . thus , 32 % of the population is less than m - d or greater than m + d . since the population is symmetric , half of this 32 % is less than m - d and half is greater than m + d . thus , e = ( 68 + 16 ) % or ( 100 - 16 ) % of the population is less than m + d . d" + }, + { + "Answer": 81, + "Options": "a ) 78 , b ) 79 , c ) 80 , d ) 81 , e ) 82", + "Correct": "d", + "Explanation": "if ramesh attempts ' x ' questions correct and ' y ' questions wrong , then x + y = 108 - - - ( i ) & x - ( 1 / 3 ) y = 0 - - - ( ii ) on solving x = 27 , y = 81 answer : d" + }, + { + "Answer": 14999.99999999999, + "Options": "a ) 15000 , b ) 25000 , c ) 7500 , d ) 14500 , e ) none of these", + "Correct": "a", + "Explanation": "let the amount be x . from the question , x \u00d7 14 \u00d7 6 / 1200 \u2212 x \u00d7 8 \u00d7 8 / 1200 = 250 \u2234 x = 15000 answer a" + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9", + "Correct": "a", + "Explanation": "explanation : number of questions attempted correctly = ( 70 % of 10 + 40 % of 30 + 60 % of 35 ) = 7 + 12 + 21 = 40 . questions to be answered correctly for 60 % = 60 % of total quotations = 60 % of 75 = 45 . he would have to answer 45 - 40 = 5 answer : a" + }, + { + "Answer": 1.161290322580645, + "Options": "a ) 32 / 31 , b ) 33 / 31 , c ) 34 / 31 , d ) 36 / 31 , e ) 0 / 31", + "Correct": "d", + "Explanation": "connie has a 1 6 chance of winning 6 dollars her first turn . she has a 5 / 6 1 / 6 chance of winning 1 dollar her second turn . next , she has a 25 36 1 / 6 chance of winning 1 / 6 dollars her third turn . generalizing , connie ' s expected earnings form a geometric series with initial term 1 / 6 * 6 = 1 and common ratio 5 / 6 * 1 / 6 = 5 / 36 . hence , connie ' s expected earnings are 1 / 1 - 5 / 36 = 36 / 31 correct answer d" + }, + { + "Answer": 2, + "Options": "a ) 3 , b ) 5 , c ) 4 , d ) 2 , e ) 1", + "Correct": "d", + "Explanation": "because a + b = 1 , 2 a + 2 b = 2 ( a + b ) = 2 \u00d7 1 = 2 . correct answer d" + }, + { + "Answer": 40.5, + "Options": "a ) 43.25 , b ) 43 , c ) 38 , d ) 40.5 , e ) 36", + "Correct": "d", + "Explanation": "sum of last 4 matches = ( ( 10 \u00d7 45 ) \u2013 ( 6 \u00d7 48 ) = 162 average = 162 / 4 = 40.5 answer : d" + }, + { + "Answer": 4, + "Options": "a ) 5 , b ) 8 , c ) 10 , d ) 4 , e ) 17", + "Correct": "d", + "Explanation": "chicken - ch cows - c sheep - s ch + c = 6 s c > ch and c > s each cow has 4 legs and 1 head each chicken has 2 legs and 1 head so 5 c + 3 ch = 100 ( sum of legs and head ) there are 2 possible solutions to this equation c = 11 and ch = 9 or c = 14 and ch = 10 since from first equation where ch + c = 6 s the sum of ch and c should be divisbile by 6 . 20 is not so the only possible solution is c = 14 and ch = 10 . so s = 4 answer : d" + }, + { + "Answer": 80.76923076923075, + "Options": "a ) 80.78 % , b ) 80.76 % , c ) 80.72 % , d ) 80.79 % , e ) 80.74 %", + "Correct": "b", + "Explanation": "explanation : number of students appeared from school ' p ' = 100 , say number of students qualified from school ' p ' = 70 and number of students appeared from school ' q ' = 130 number of students qualified from school ' q ' = 50 % more than those qualified from school ' p ' . = 70 + 35 = 105 % of students qualified to the number of students appeared from school b = 105 / 130 * 100 = 80.76 % answer : b" + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) 16 , c ) 18 , d ) 24 , e ) 26", + "Correct": "a", + "Explanation": "\"log 8 x + log 8 ( 1 / 6 ) = 1 / 3 = > ( log x / log 8 ) + ( log 1 / 6 / log 8 ) = log ( 81 / 3 ) = log 2 = > log x = log 2 \u2013 log 1 / 6 = log ( 2 * 6 / 1 ) = log 12 answer : a\"" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "c", + "Explanation": "30 , 870,000 = 2 ^ 4 * 5 ^ 4 * 3087 = 2 ^ 4 * 3 * 5 ^ 4 * 1029 = 2 ^ 4 * 3 ^ 2 * 5 ^ 4 * 343 = 2 ^ 4 * 3 ^ 2 * 5 ^ 4 * 7 ^ 3 the answer is c ." + }, + { + "Answer": 28, + "Options": "a ) 16 , b ) 28 , c ) 41 , d ) 54 , e ) 65", + "Correct": "b", + "Explanation": "you can just write out the pattern and count : rgwbyrgwbyrgwby . . . but to save time a good test taker will just look for a pattern . min # is 3 , because w is the third one . then every 5 beads another white comes , so it must be 3 + 5 + 5 + 5 . . and so on . . . 3 + 5 = 8 3 + 5 + 5 = 13 3 + 5 + 5 + 5 = 18 3 + 5 + 5 + 5 + 5 = 23 so you see it ends in either 8 or 3 . pick an answer that ends in either 8 or 3 . only one answer does , b ." + }, + { + "Answer": 30, + "Options": "a ) 29 , b ) 30 , c ) 31 , d ) 32 , e ) 33", + "Correct": "b", + "Explanation": "solution : 3 ! + 15 + 9 = 30 explanation : 3 ! = 3 * 2 * 1 = 6 6 + 15 + 9 = 30 answer b" + }, + { + "Answer": 10, + "Options": "a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16", + "Correct": "b", + "Explanation": "explanation : let the number of articles of types p , q and r be 3 a , 2 a and 3 a respectively . thus , we get , ( 200 x 3 a ) + ( 90 x 2 a ) + ( 60 x 3 a ) = 4800 960 a = 4800 a = 5 hence , the number of articles of type \u201c q \u201d = 2 x 5 = 10 answer b" + }, + { + "Answer": 45, + "Options": "a ) 45 , b ) 46 , c ) 47 , d ) 48 , e ) 49", + "Correct": "a", + "Explanation": "weight of the teacher = ( 35.4 x 25 - 35 x 24 ) kg = 45 kg . answer : a" + }, + { + "Answer": 24, + "Options": "a ) 6 , b ) 7 , c ) 12 , d ) 16 , e ) 24", + "Correct": "e", + "Explanation": "number of ways first - place medal can be awarded to four contestants = 8 number of ways second - place medal can be awarded to contestants after awarding first - place medal = 3 therefore number of possibilities = 8 * 3 = 24 answer : e" + }, + { + "Answer": 2, + "Options": "a ) 2 . , b ) 4 . , c ) 5 . , d ) 6 . , e ) 7 .", + "Correct": "a", + "Explanation": "let x be the number of guests . number of muffins prepared = 5 x + 2 number of muffins eaten + number of muffins remaining = number of muffins prepared 6 ( x - 1 ) + 6 = 5 x + 2 6 x = 5 x + 2 x = 2 answer : a" + }, + { + "Answer": 48, + "Options": "a ) 20 , b ) 36 , c ) 48 , d ) 60 , e ) 84", + "Correct": "c", + "Explanation": "first , we have to understand what linearly means . it ' s not a straight ratio ( since 6 : 30 does not equal 24 : 60 ) . we need to look at the increases in each measurement to see what the scalar actually is . from 6 to 24 we have an increase of 18 . from 30 to 60 we have an increase of 30 . therefore , the increase ratio is 18 : 30 or 3 : 5 . in other words , for every 3 that t increases , s increases by 5 . we know that s is 100 . to get from 60 to 100 , we went up by 40 , or 8 jumps of 5 ; therefore , t will go up by 8 jumps of 3 . 24 + 8 ( 3 ) = 24 + 24 = 48 = c" + }, + { + "Answer": 72, + "Options": "a ) 72 , b ) 64 , c ) 84 , d ) 12 , e ) 92", + "Correct": "a", + "Explanation": "let the numbers be x and ( 184 - x ) . then , ( x / 3 ) - ( 184 - x ) / 7 = 8 7 x - 3 ( 184 - x ) = 168 10 x = 720 , x = 72 . hence the correct answer is option a ) 72 ." + }, + { + "Answer": 1, + "Options": "a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 2", + "Correct": "a", + "Explanation": "case 1 n = 5,8 , 11,14 , 17,20 case 2 m = 5 , 9,13 , 17,21 therefore n = 17 remainder of 17 / 16 will be 1 a" + }, + { + "Answer": 67, + "Options": "a ) 66 kg , b ) 67 kg , c ) 68 kg , d ) 69 kg , e ) none of these", + "Correct": "b", + "Explanation": "explanation : let arun \u2019 s weight by x kg . according to arun , 65 < x < 72 according to arun \u2019 s brother , 60 < x < 70 . according to arun \u2019 s mother , x < = 68 the values satisfying all the above conditions are 66 , 67 and 68 . required average = [ 66 + 67 + 68 / 3 ] = [ 201 / 3 ] = 67 kg answer b" + }, + { + "Answer": 30, + "Options": "a ) 23 minutes , b ) 30 minutes , c ) 43 minutes , d ) 23 minutes , e ) 33 minutes", + "Correct": "b", + "Explanation": "distance travelled by ramu = 45 * 4 = 180 km somu travelled the same distance in 6 hours . his speed = 180 / 6 = 30 km / hr hence in the conditional case , ramu ' s speed = 45 - 9 = 36 km / hr and somu ' s speed = 30 + 10 = 40 km / hr . therefore travel time of ramu and somu would be 5 hours and 4.5 hours respectively . hence difference in the time taken = 0.5 hours = 30 minutes . answer : b" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9", + "Correct": "b", + "Explanation": "\"we have equation 2 n + 5 m = 50 we have factor 2 in first number and we have factor 5 in second number . lcm ( 2 , 5 ) = 10 so we can try some numbers and we should start from 5 because it will be less list than for 2 2 * 5 = 10 and n should be equal 20 4 * 5 = 20 and n should be equal 15 6 * 5 = 30 and n should be equal 10 8 * 5 = 40 and n should be equal 5 10 * 5 = 50 and n should be equal 0 third variant give us the mininal difference n - m = 10 - 6 = 4 and there is some mistake in my way of thinking because we do n ' t have such answer ) if we change the task and will seek for difference between m and n than minimal result r will be 8 - 5 = 3 and answer b\"" + }, + { + "Answer": 285, + "Options": "a ) 250 , b ) 276 , c ) 280 , d ) 285 , e ) none", + "Correct": "d", + "Explanation": "sol . since the month begins with a sunday , so there will be five sundays in the month . \u2234 required average = [ 510 x 5 + 240 x 25 / 30 ] = 8550 / 30 = 285 answer d" + }, + { + "Answer": 11, + "Options": "a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13", + "Correct": "c", + "Explanation": "7 m - 20 = 2 m so , 5 m = 20 so , m + 7 = 11 answer : c" + }, + { + "Answer": 20, + "Options": "a ) 20 % , b ) 25 % , c ) 40 % , d ) 50 % , e ) 80 %", + "Correct": "a", + "Explanation": "two hundred multiples of seven will have 100 even and 100 odd numbers 300 multiples of eight will have all even ( being multiple of 8 ) probability of number selected being odd = total odd numbers / total available numbers probability = 100 / 500 = 0.2 = 20 % answer : option a" + }, + { + "Answer": 6.25, + "Options": "a ) 93.5 , b ) 90 , c ) 6.75 , d ) 6.25 , e ) 2", + "Correct": "d", + "Explanation": "\"let , p = 400 then j = ( 75 / 100 ) * 400 = 300 also j = ( 80 / 100 ) * t i . e . t = 300 * 100 / 80 = 375 and t = [ 1 - ( x / 100 ) ] * p i . e . 100 - x = 100 * t / p = 100 * 375 / 400 = 93.75 i . e . x = 6.25 answer : option d\"" + }, + { + "Answer": 44, + "Options": "a ) 0.33 , b ) 0.44 , c ) 0.55 , d ) 44 , e ) 55", + "Correct": "d", + "Explanation": "\"main thing to remember is answer is asked in cents , however when we calculate , it comes up as 0.44 $ just multiply by 100 , answer q = 44 . d\"" + }, + { + "Answer": 15, + "Options": "a ) 14 , b ) 12 , c ) 13 , d ) 15 , e ) 16", + "Correct": "d", + "Explanation": "\"let n be the number of persons in the party . number of hands shake = 105 ; total number of hands shake is given by nc 2 . now , according to the question , nc 2 = 105 ; or , n ! / [ 2 ! * ( n - 2 ) ! ] = 105 ; or , n * ( n - 1 ) / 2 = 105 ; or , n 2 - n = 210 ; or , n 2 - n - 210 = 0 ; or , n = 15 , - 14 ; but , we can not take negative value of n . so , n = 15 i . e . number of persons in the party = 15 . option d\"" + }, + { + "Answer": 40, + "Options": "a ) 22 , b ) 88 , c ) 40 , d ) 87 , e ) 17", + "Correct": "c", + "Explanation": "explanation : sum of the present ages of a , b and c = ( 27 \u00d7 3 + 3 \u00d7 3 ) years = 90 years . sum of the present ages of b and c = ( 20 \u00d7 2 + 5 \u00d7 2 ) years = 50 years . a ' s present age = 90 \u2013 50 = 40 years . answer : c" + }, + { + "Answer": 91.66666666666666, + "Options": "a ) 90.1 , b ) 91.7 , c ) 97.1 , d ) 101.1 , e ) 107.1", + "Correct": "b", + "Explanation": "explanation : in such a case the middle number ( c ) is the average \u2234 c = 20 and d = 22 and e = 24 required percentage = 22 / 24 x 100 = 91.7 answer : option b" + }, + { + "Answer": 0.39999999999999997, + "Options": "a ) $ 015 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45", + "Correct": "d", + "Explanation": "\"on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.6 = 3 * x - - > x = $ 0.4 . answer : d .\"" + }, + { + "Answer": 50, + "Options": "a ) 50 . , b ) 45 . , c ) 40 . , d ) 30 . , e ) 25 .", + "Correct": "a", + "Explanation": "given there are 50 students in the seaside summer camp , 90 % of 50 = 45 boys and remaining 5 girls . now here 90 % are boys and 10 % are girls . now question is asking about how many boys do we need to add , to make the girls percentage to 5 or 5 % . . if we add 50 to existing 45 then the count will be 95 and the girls number will be 5 as it . now boys are 95 % and girls are 5 % . ( out of 100 students = 95 boys + 5 girls ) . imo option a is correct ." + }, + { + "Answer": 5625, + "Options": "a ) 2379 , b ) 2889 , c ) 5625 , d ) 9000 , e ) 28311", + "Correct": "c", + "Explanation": "let their prices be 3 x , 5 x and 7 x . then , 2 x + 6 x + 8 x = ( 15000 * 3 ) or x = 2812.5 . cost of cheapest item = 2 x = rs . 5625 . answer : c" + }, + { + "Answer": 0.6666666666666666, + "Options": "a ) 5 / 3 , b ) 4 / 3 , c ) 2 / 3 , d ) 1 / 3 , e ) 1 / 5", + "Correct": "c", + "Explanation": "explanation : 1 \u00f7 [ 1 + 1 \u00f7 { 1 + 1 \u00f7 ( 1 \u00f7 1 ) } ] = 1 \u00f7 [ 1 + 1 \u00f7 { 1 + 1 \u00f7 1 } ] = 1 \u00f7 [ 1 + 1 \u00f7 { 1 + 1 } ] = 1 \u00f7 [ 1 + 1 \u00f7 2 ] = 1 \u00f7 [ 1 + ( 1 / 2 ) ] = 1 \u00f7 3 / 2 = 1 \u00d7 3 / 2 = 1 \u00d7 2 / 3 = 2 / 3 answer : option c" + }, + { + "Answer": 7, + "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", + "Correct": "a", + "Explanation": "\"a simple and elegant solution . as addition of 39 , shifts mean by 2 , and addition of 15 , shifts mean by 1 to the other side , we have the mean lying between 3915 , and in a ratio of 2 : 1 39 - 15 = 24 24 divide by 3 is 8 . meaning mean of the n terms is 15 + 8 = 39 - 16 = 23 now , from first statement , when a person aged 39 is added to a group of n people , the average age increases by 2 . t * 23 + 39 = 25 * ( t + 1 ) t = 7 ans . ( a )\"" + }, + { + "Answer": 20, + "Options": "a ) rs 18.95 , b ) rs 16 , c ) rs 20 , d ) rs 25.71 , e ) none of these", + "Correct": "c", + "Explanation": "total earning for the week = rs ( 4 \u00d7 18 + 4 \u00d7 22 - 20 ) = rs 140 average earning = rs 140 / 7 = rs 20 . answer : c" + }, + { + "Answer": 1.5, + "Options": "a ) 3 / 2 , b ) 3 / 3 , c ) 2 / 4 , d ) 4 / 4 , e ) 4 / 5", + "Correct": "a", + "Explanation": "if we substitute y = 4 x , we have y 2 + 4 y - 96 = 0 , so y = - 4 or y = 8 . the first does not map to a real solution , while the second maps to x = 3 / 2 correct answer a" + }, + { + "Answer": 100, + "Options": "a ) 90 , b ) 100 , c ) 110 , d ) 120 , e ) 130", + "Correct": "b", + "Explanation": "x / 2 + 6 + 3 + 1 + 4 sqrt ( x ) = x x / 2 + 10 + 4 sqrt ( x ) = x 4 sqrt ( x ) = x / 2 - 10 squaring on both sides 16 x = x \u00b2 / 4 + 100 - 10 x simplifying x \u00b2 - 104 x + 400 = 0 x = 100 , 4 x = 4 is not possible therefore x = 100 answer : b" + }, + { + "Answer": 12, + "Options": "a ) 8 , b ) 7 , c ) 12 , d ) 9 , e ) none of the above", + "Correct": "c", + "Explanation": "ans is c : 39 pounds - - > 6 days 117 pounds - - > x days x = 117 * 6 / 39 = 18 the animal has already consumed food in 6 days so the the number of days for it ' s total consumption be 117 pounds is 18 - 6 = 12" + }, + { + "Answer": 7, + "Options": "a ) 7 , b ) 8 , c ) 6 , d ) 5 , e ) 4", + "Correct": "a", + "Explanation": "explanation : let the higher number be n and x be the number erased . then ( ( n ( n + 1 ) / 2 ) + x ) / ( n + 1 ) = 35 * 7 / 17 = 602 / 17 hence , n = 69 and x = 7 satisfy the above conditions . answer : a" + }, + { + "Answer": 24, + "Options": "a ) 15 , b ) 18 , c ) 21 , d ) 24 , e ) 27", + "Correct": "d", + "Explanation": "let x be the rainfall in the first week . then 1.5 x was the rainfall in the second week . 2.5 x = 40 x = 16 the rainfall during the second week was 1.5 * 16 = 24 inches the answer is d ." + }, + { + "Answer": 37.5, + "Options": "a ) a : 45 , b ) b : 25 , c ) c : 37.5 , d ) d : 36 , e ) e : 42", + "Correct": "c", + "Explanation": "if you have a 37.5 liter capacity , you start with 37.5 l of a and 0 l of b . 1 st replacement after the first replacement you have 37.5 - 15 = 22.5 l of a and 15 l of b . the key is figuring out how many liters of a and b , respectively , are contained in the next 15 liters of mixture to be removed . the current ratio of a to total mixture is 22.5 / 37.5 ; expressed as a fraction this becomes ( 45 / 2 ) / ( 75 / 2 ) , or 45 / 2 * 2 / 75 . canceling the 2 s and factoring out a 5 leaves the ratio as 9 / 15 . note , no need to reduce further as we ' re trying to figure out the amount of a and b in 15 l of solution . 9 / 15 of a means there must be 6 / 15 of b . multiply each respective ratio by 15 to get 9 l of a and 6 l of b in the next 15 l removal . final replacement the next 15 l removal means 9 liters of a and 6 liters of b are removed and replaced with 15 liters of b . 22.5 - 9 = 13.5 liters of a . 15 liters of b - 6 liters + 15 more liters = 24 liters of b . test to the see if the final ratio = 9 / 16 ; 13.5 / 24 = ( 27 / 2 ) * ( 1 / 24 ) = 9 / 16 . choice c is correct ." + }, + { + "Answer": 6000, + "Options": "a ) 6500 , b ) 2000 , c ) 4500 , d ) 3000 , e ) 6000", + "Correct": "e", + "Explanation": "let the amounts be x , y , z in ascending order of value . as the interest rate and interest accrued are same for 2 years 6 years and 11 years i . e . 2 x = 6 y = 11 z = k . l . c . m . of 2 , 611 = 66 so x : y : z : = 33000 : 11000 : 6000 the amount deposited for 11 years = 6000 answer : e" + }, + { + "Answer": 25.00000000000001, + "Options": "a ) 50 % , b ) 40 % , c ) 25 % , d ) 20 % , e ) 10 %", + "Correct": "c", + "Explanation": "looking at the ratio we can take total number of people = 20 . . ans 5 / 20 or 25 % c" + }, + { + "Answer": 10.4, + "Options": "a ) 15.5 , b ) 15.4 , c ) 15.25 , d ) 10.4 , e ) 15.6", + "Correct": "d", + "Explanation": "total age of 20 men = 15.6 x 20 = 312 now , total age of 25 men = 364 . total age of five men added later = 364 - 312 = 52 . hence , the total average of five men = 52 / 5 = 10.4 answer : d" + }, + { + "Answer": 0.4117647058823529, + "Options": "a ) 5 / 17 , b ) 7 / 17 , c ) 4 / 17 , d ) 3 / 17 , e ) 5", + "Correct": "b", + "Explanation": "# of basic stereos was 2 / 3 of total and # of deluxe stereos was 1 / 3 of total , let ' s assume total = 15 , then basic = 10 and deluxe = 5 . now , if time needed to produce one deluxe stereo is 1 unit than time needed to produce one basic stereo would be 7 / 5 units . total time for basic would be 10 * 1 = 10 and total time for deluxe would be 5 * 7 / 5 = 7 - - > total time for both of them would be 10 + 7 = 17 - - > deluxe / total = 7 / 17 . b" + }, + { + "Answer": 49.9, + "Options": "a ) 40.9 kg , b ) 42.9 kg , c ) 49.9 kg , d ) 39.9 kg , e ) none of these", + "Correct": "c", + "Explanation": "here one boy is excluded and final average of the group decreases . \u2234 change in average is ( \u2013 ) ve = \u2013 0.1 kg . using the formula sum of the quantities excluded = ( changein no . ofquantities \u00d7 origina laverage ) + ( changeinaverage \u00d7 final no . ofquantities ) \u21d2 weight of the boy who left = ( 1 \u00d7 45 ) \u2013 ( \u2013 0.1 \u00d7 49 ) = 49.9 kg answer c" + }, + { + "Answer": 36, + "Options": "a ) 4 , b ) 8 , c ) 12 , d ) 36 , e ) 32", + "Correct": "d", + "Explanation": "6 flavours * 6 choices = 6 c 1 * 6 c 1 = 6 * 6 = 36 = d" + }, + { + "Answer": 25300, + "Options": "a ) 10000 , b ) 12000 , c ) 23000 , d ) 25300 , e ) 45000", + "Correct": "d", + "Explanation": "explanation : salary of the manager = ( 56 * 8800 - 55 * 8500 ) = 25300 answer : d" + }, + { + "Answer": 0.4166666666666667, + "Options": "a ) 5 / 7 , b ) 4 / 7 , c ) 5 / 12 , d ) 4 / 7 , e ) 1 / 6", + "Correct": "c", + "Explanation": "here n ( s ) = ( 6 * 6 ) = 36 let e = event of getting a total more than 7 = { ( 2,6 ) , ( 3,5 ) , ( 3,6 ) , ( 4,4 ) , ( 4,5 ) , ( 4,6 ) , ( 5,3 ) , ( 5,4 ) , ( 5,5 ) , ( 5,6 ) , ( 6,2 ) , ( 6,3 ) , ( 6,4 ) , ( 6,5 ) , ( 6,6 ) } p ( e ) = n ( e ) / n ( s ) = 15 / 36 = 5 / 12 option c" + }, + { + "Answer": 10, + "Options": "a ) a ) 9 , b ) b ) 5 , c ) c ) 7 , d ) d ) 10 , e ) e ) none of the above", + "Correct": "d", + "Explanation": "sol . apples 250 each carries 25 = 250 / 25 = 10 answer : d" + }, + { + "Answer": 0.18, + "Options": "a ) 0.52 , b ) 0.42 , c ) 0.18 , d ) 0.64 , e ) 0.46", + "Correct": "c", + "Explanation": "\"given exp . = 0.3 * 0.3 + ( 0.3 * 0.3 ) = 0.09 + 0.09 = 0.18 answer is c .\"" + }, + { + "Answer": 0.08333333333333333, + "Options": "a ) 1 / 12 , b ) 1 / 6 , c ) 1 / 4 , d ) 1 / 3 , e ) 1 / 2", + "Correct": "a", + "Explanation": "x = - 2.5 prob = 1 / 12 answer - a" + }, + { + "Answer": 15, + "Options": "a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16", + "Correct": "d", + "Explanation": "r + b + c + 14 + 15 = 12 * 5 = 60 = > r + b + c = 60 - 29 = 31 r + b + c + 29 = 31 + 29 = 60 average = 60 / 4 = 15 answer d" + }, + { + "Answer": 10, + "Options": "a ) 5 , b ) 6 , c ) 9 , d ) 10 , e ) 15", + "Correct": "d", + "Explanation": "since the starting point is given as the $ 4000 scholarship , assume $ 4000 scholarships to be x by the given information , $ 2500 scholarships = 2 x and $ 1250 scholarships = 6 x gievn : total $ 1250 scholarships = $ 75000 6 x * 1250 = 75000 solve for x = 10 option d" + }, + { + "Answer": 2, + "Options": "a ) 3 : 2 , b ) 4 : 3 , c ) 8 : 7 , d ) 5 : 8 , e ) 2 : 1", + "Correct": "e", + "Explanation": "let the two numbers be x and y . ( 1 / 10 ) * x + y = ( 6 / 5 ) * y ( 1 / 10 ) * x = ( 1 / 5 ) * y x / y = 2 / 1 = 2 / 1 the answer is e ." + }, + { + "Answer": 25, + "Options": "a ) 23 , b ) 28 , c ) 25 , d ) 19 , e ) 11", + "Correct": "c", + "Explanation": "explanation : given r \u2013 q = q \u2013 t and r + t = 50 which gives q = 25 as the difference between r & q and q & t is same so answer is 25 years answer : c" + }, + { + "Answer": 130, + "Options": "a ) 120 , b ) 130 , c ) 110 , d ) 150 , e ) 180", + "Correct": "b", + "Explanation": "let x be the correct answer and y be the wrong answer so the total number of questions is ( x + y ) = 150 = > 4 x - 2 y = 480 = > 6 x = 780 hence x = 130 answer : b" + }, + { + "Answer": 6, + "Options": "a ) 4.37 % , b ) 5 % , c ) 6 % , d ) 8.75 % , e ) none of these", + "Correct": "c", + "Explanation": "solution increase in 10 year = ( 80000 - 50000 ) = 30000 . increase % = ( 30000 / 50000 x 100 ) % = 60 % \u00e2 \u02c6 \u00b4 required average = ( 60 / 10 ) % = 6 % answer c" + }, + { + "Answer": 96, + "Options": "a ) 96 % , b ) 95 % , c ) 2400 % , d ) 200 % , e ) 400 %", + "Correct": "a", + "Explanation": "lets take a number 20 20 / 5 = 4 20 * 5 = 100 diff = 100 - 4 = 96 % answer : a" + }, + { + "Answer": 4.870967741935484, + "Options": "a ) 0 , b ) 156 / 31 , c ) 123 / 31 , d ) 151 / 31 , e ) none", + "Correct": "d", + "Explanation": "solution : both fractions should be reduced before performing arithmetic operations . we get 3 * 27 / 31 + 3.27 / 3.31 = 3 * 27 / 31 + 27 / 31 = 4 * 27 / 31 = 151 / 31 answer d" + }, + { + "Answer": 35, + "Options": "a ) 25 % , b ) 35 % , c ) 45 % , d ) 70 % , e ) 80 %", + "Correct": "b", + "Explanation": "\"1 . we are given the following percentages : 30 ( 70 ) , 40 ( 60 ) , 25 ( 75 ) . there are two threads from here . first starts at 30 % and finishes there . second one starts at 70 , then 40 , and then 25 . we need a value that is divisible by 7 , 2 , and 5 at least once . lets pick a number now , say 700 . so say if non hawks are 700 ( this is 70 % of the total , so total = 1000 ) , then paddy warbs are 2 / 5 x 700 = 1400 / 5 = 280 . kingfishers , therefore , are 280 / 4 = 70 . lets add them up . 300 hawks + 280 peddy warbs + 70 kingsifhers = 650 . so all others are 1000 - 650 = 350 or 35 % of total birds . the main job here to to identify the smart number to start the question with . this can be time consuming , but once identified , this question can be solved fairly quickly . 2 . another method : if x is total - - > non hawks = 0.7 x - - > warbs = 0.4 ( 0.7 x ) - - > kfs = 0.25 ( 0.4 ( 0.7 x ) ) . our job is to find out e : ( 0.3 x + 0.28 x + 0.07 x ) / x . or 0.65 x / x = 0.65 . we need to find 1 - 0.65 = 0.35 or 35 % . b\"" + }, + { + "Answer": 121, + "Options": "a ) 21 , b ) 41 , c ) t = 121 , d ) 241 , e ) 481", + "Correct": "c", + "Explanation": "or u can just use the answer choices here . since the answers are already arranged in ascending order , the first number which gives remainder t as 1 for all three is the correct answer . in the given question , the first number which gives a remainder of 1 for 6,8 and 10 is 121 . c" + }, + { + "Answer": 40, + "Options": "a ) 20 , b ) 25 , c ) 30 , d ) 40 , e ) 50", + "Correct": "d", + "Explanation": "\"let the list price be 2 x for min sale price , the first discount given should be 50 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 40 and 0.8 x = 32 so lowest sale price is 32 , which w is 40 % of 80 hence , d is the answer\"" + }, + { + "Answer": 50, + "Options": "a ) 50 , b ) 47 , c ) 48 , d ) 49 , e ) 46", + "Correct": "a", + "Explanation": "solution 5 years ago average age of a , b , c , d = 45 years = > 5 years ago total age of a , b , c , d = 45 x 4 = 180 years = > total present age of a , b , c , d = 180 + 5 x 4 = 200 years if e ' s present age is x years = 200 + x / 5 = 50 x = 50 years . answer a" + }, + { + "Answer": 13.99999999999999, + "Options": "a ) 14 , b ) 24 , c ) 34 , d ) 12 , e ) 13", + "Correct": "a", + "Explanation": "\"required difference = [ 3 1 / 2 % of $ 8400 ] \u2013 [ 3 1 / 3 % of $ 8400 ] = [ ( 7 / 20 ) - ( 10 / 3 ) ] % of $ 8400 = 1 / 6 % of $ 8400 = $ [ ( 1 / 6 ) * ( 1 / 100 ) * 8400 ] = $ 14 . answer a .\"" + }, + { + "Answer": 1600, + "Options": "a ) q = 200 , b ) q = 600 , c ) q = 800 , d ) q = 1600 , e ) q = 50", + "Correct": "d", + "Explanation": "\"original cost c 1 = t 1 * b 1 ^ 4 new cost c 2 = t 2 * b 2 ^ 4 . . . . only b is doubled so t 2 = t 1 and b 2 = 2 b 1 c 2 = t 2 * ( 2 b 1 ) ^ 4 = 16 ( t 1 * b 1 ^ 4 ) = 16 c 1 16 times c 1 = > 1600 % of c 1 ans d = 1600\"" + }, + { + "Answer": 1200, + "Options": "a ) 1250 , b ) 1300 , c ) 1375 , d ) 1200 , e ) none of them", + "Correct": "d", + "Explanation": "let 4207 - x = 3007 then x = 4207 - 3007 = 1200 answer is d" + }, + { + "Answer": 39, + "Options": "a ) 39 , b ) 88 , c ) 266 , d ) 278 , e ) 221", + "Correct": "a", + "Explanation": "explanation : assume his initial average = xx his total runs after 16 innings = 16 xx after scoring 87 runs his average got increased by 3 to xx + 3 so his total runs after 17 innings = 17 \u00d7 ( xx + 3 ) but it was given that the difference in the total scores after 16 innings and 17 innings = 87 therefore 17 \u00d7 ( x + 3 ) \u2212 16 x = 87 \u21d2 x = 3617 \u00d7 ( x + 3 ) \u2212 16 x = 87 \u21d2 x = 36 his new average = 36 + 3 = 39 answer : a" + }, + { + "Answer": 615, + "Options": "a ) $ 600 , b ) $ 575 , c ) $ 550 , d ) $ 580 , e ) $ 615", + "Correct": "e", + "Explanation": "a + b + c = 1230 given ratio 9 : 10 : 11 let us say the shares of a , b , c deducting 5 , 1015 be a , b , c a + b + c = 1230 - 30 = 1200 = 30 k c share = ( 1200 x 30 ) / 60 = 600 c = charlie share = 600 + 15 = 615 option e" + }, + { + "Answer": 40, + "Options": "a ) 29 , b ) 88 , c ) 40 , d ) 28 , e ) 27", + "Correct": "c", + "Explanation": "explanation : 3 / 4 x = 30 = > x = 40 answer : c" + }, + { + "Answer": 19, + "Options": "a ) 19 min , b ) 19 hrs , c ) 52 min , d ) 126 min , e ) 52 min", + "Correct": "a", + "Explanation": "let the correct time to complete the journey be x min distance covered in ( x + 11 ) min . at 40 kmph distance covered in ( x + 5 ) min . at 50 kmph ( x + 11 ) / 60 * 40 = ( x + 5 ) / 60 * 50 x = 19 min answer ( a )" + }, + { + "Answer": 750, + "Options": "a ) $ 450 , b ) $ 500 , c ) $ 750 , d ) $ 800 , e ) $ 840", + "Correct": "c", + "Explanation": "let the shares of a , b , c , d are x , 3 x , 4 x , 2 x 4 x - 2 x = 500 x = 250 b ' s share = 3 x = $ 750 answer is c" + }, + { + "Answer": 60, + "Options": "a ) 200 km , b ) 50 km , c ) 20 km , d ) 60 km , e ) 80 km", + "Correct": "d", + "Explanation": "not really . when you solve the 2 equation above , you get , 6 t - 4 / 3 = 5 r / 6 from simplifying equation 1 4 t - 2 = r / 2 from simplifying equation 2 you can now multiply equation 2 by 5 to get 5 ( 4 t - 2 = r / 2 ) = 20 t - 10 = 5 r / 2 and then subtract this new equation from equation 1 to get t = 3 , followed by r = 20 to give you distance q = r * t = 20 * 3 = 60 km . d" + }, + { + "Answer": 35, + "Options": "a ) q = 20 , b ) q = 25 , c ) q = 30 , d ) q = 35 , e ) 40", + "Correct": "d", + "Explanation": "suppose the population of the country in current year is 1000 . so annual increase is 1000 + 39.4 - 19.4 = 1020 hence every year there is an increase of 2 % . 2000 = 1000 ( 1 + ( 2 / 100 ) ) ^ n n = 35 answer is d" + }, + { + "Answer": 126, + "Options": "a ) rs . 126 , b ) rs . 132 , c ) rs . 120 , d ) rs . 114 , e ) none of these", + "Correct": "a", + "Explanation": "let the train fare between the two places for one person be rs . t bus fare between the two places for two persons rs . 4 / 3 t = > 6 / 2 ( 4 / 3 t ) + 8 ( t ) = 1512 = > 12 t = 1512 = > t = 126 . answer : a" + }, + { + "Answer": 0.358, + "Options": "a ) 0.853 , b ) 0.358 , c ) 3.58 , d ) 8.35 , e ) none", + "Correct": "b", + "Explanation": "answer 3 / 10 + 5 / 100 + 8 / 1000 = 0.3 + 0.05 + 0.008 = 0.358 correct option : b" + }, + { + "Answer": 3.694512960621597, + "Options": "a ) 3.6 kg , b ) 3.696 kg , c ) 36 kg , d ) 36.9 kg , e ) 3.06 kg", + "Correct": "b", + "Explanation": "\"external radius = 4 cm , internal radius = 3 cm . volume of iron = ( 22 / 7 x [ ( 4 ) ^ 2 - ( 3 ) ^ 2 ] x 21 ) cm ^ 3 ( 22 / 7 x 7 x 1 x 21 ) cm ^ 3 462 cm ^ 3 . weight of iron = ( 462 x 8 ) gm = 3696 gm = 3.696 kg . answer b\"" + }, + { + "Answer": 57.14285714285714, + "Options": "a ) 30 % , b ) 50 % , c ) 57 % , d ) 62 % , e ) 75 %", + "Correct": "c", + "Explanation": "total number of votes polled = ( 1000 + 2000 + 4000 ) = 7000 required percentage = 4000 / 7000 * 100 = 57 % ( approximately ) answer : option c" + }, + { + "Answer": 74, + "Options": "a ) 74 , b ) 76 , c ) 78 , d ) 80 , e ) 82", + "Correct": "a", + "Explanation": "\"a score of 58 was 2 standard deviations below the mean - - > 58 = mean - 2 d a score of 98 was 3 standard deviations above the mean - - > 98 = mean + 3 d solving above for mean r = 74 . answer : a .\"" + }, + { + "Answer": 480, + "Options": "a ) 96 , b ) 240 , c ) w = 256 , d ) w = 384 , e ) w = 480", + "Correct": "e", + "Explanation": "\"most test takers would recognize thesystemof equations in this prompt and just do algebra to get to the solution ( and that ' s fine ) . the wording of the prompt and the ' spread ' of the answer choices actually provide an interesting ' brute force ' shortcut that you can take advantage of to eliminate the 4 wrong answers . . . . we ' re told that there are 2 types of boxes : those that hold 12 glasses and those that hold 16 glasses . since the average number of boxes is 15 , we know that there must be at least some of each . we ' re also told that that there are 16 more of the larger boxes . this means , at the minimum , we have . . . 1 small box and 17 large boxes = 1 ( 12 ) + 17 ( 16 ) = 12 + 272 = 284 glasses at the minimum since the question asks for the total number of glasses , we can now eliminate answers a , b and c . . . . the difference in the number of boxes must be 16 though , so we could have . . . . 2 small boxes and 18 large boxes 3 small boxes and 19 large boxes etc . with every additional small box + large box that we add , we add 12 + 16 = 28 more glasses . thus , we can justadd 28 suntil we hit the correct answer . . . . 284 + 28 = 312 312 + 28 = 340 340 + 28 = 368 368 + 28 = 396 at this point , we ' ve ' gone past ' answer d , so the correct answer must be answer e . . . . . but here ' s the proof . . . . 396 + 28 = 424 424 + 28 = 452 452 + 28 = 480 final answer : e\"" + }, + { + "Answer": 0.2, + "Options": "a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 5 , d ) 1 / 7 , e ) 1 / 8", + "Correct": "c", + "Explanation": "we have total of 8 parts : 3 parts of sand and 5 parts of cement . in order there to be half sand and half cement ( 4 parts of sand and 4 parts of cement ) , we should remove 1 part of cement . with 1 part of cement comes 3 / 5 parts of sand , so we should remove 1 + 3 / 5 = 8 / 5 part of the mixture , which is ( 8 / 5 ) / 8 = 1 / 5 of the mixture . answer : c ." + }, + { + "Answer": 50.000000000000014, + "Options": "a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70", + "Correct": "c", + "Explanation": "\"milk : water = 5 : 2 5 x : 2 x + 10 = 5 : 3 3 [ 5 x ] = 5 [ 2 x + 10 ] 15 x = 10 x + 50 15 x - 10 x = 50 x = 10 the quantity of milk in the original mixture is = 5 : 2 = 5 + 2 = 7 7 x = 70 short cut method : milk : water = 5 : 2 after adding 10 liters of water milk : water = 5 : 3 milk is same but water increse 10 liters then the water ratio is increse 1 parts 1 part - - - - - > 10 liters the quantity of milk in the original mixture is = 5 : 2 = 5 + 2 = 7 7 parts - - - - - > 70 liters ( answer is = 70 ) short cut method - 2 : for only milk problems milk : water 5 : 2 5 : 3 milk ratio same but water ratio 1 part incress per 10 liters 1 part of ratio - - - - - - - > 10 liters 7 part of ratio - - - - - - - > 70 liters c )\"" + }, + { + "Answer": 67, + "Options": "a ) 74 % , b ) 75 % , c ) 67 % , d ) 72 % , e ) none", + "Correct": "c", + "Explanation": "solution : sum of pass students of first , second and third class , = ( 45 % of 10 ) + ( 60 % of 15 ) + ( 80 % of 25 ) = 4.5 + 9 + 20 = 33.5 total students appeared , = 10 + 15 + 25 = 50 pass average , = 33.5 * 100 / 50 = 67 % . answer : option c" + }, + { + "Answer": 298.93600000000004, + "Options": "a ) 298.936 , b ) 298.694 , c ) 289.496 , d ) 289.469 , e ) 298.964", + "Correct": "a", + "Explanation": "34.94 240.016 + 23.98 - - - - - - - - 298.936 answer is a ." + }, + { + "Answer": 1000, + "Options": "a ) 650 , b ) 1000 , c ) 1500 , d ) 800 , e ) 750", + "Correct": "b", + "Explanation": "total cost of items : 2000 / - amount paid : 3000 / - balance receivable : 3000 - 2000 = 1000 / - answer is b" + }, + { + "Answer": 121, + "Options": "a ) 21 , b ) 41 , c ) e = 121 , d ) 241 , e ) 481", + "Correct": "c", + "Explanation": "or u can just use the answer choices here . since the answers are already arranged in ascending order , the first number which gives remainder e as 1 for all three is the correct answer . in the given question , the first number which gives a remainder of 1 for 68 and 10 is 121 . c" + }, + { + "Answer": 45, + "Options": "a ) 50 , b ) 52 , c ) 35 , d ) 40 , e ) 45", + "Correct": "e", + "Explanation": "let dravid scored point = x then dhoni scored = x + 30 shewag scored = 2 * ( x + 30 ) = 2 x + 60 as given , x + x + 30 + 2 x + 60 = 150 points 4 x + 90 = 150 x = 150 - 90 / 4 = 15 so dhoni scored = x + 30 i . e ) 15 + 30 = 45 answer : e" + }, + { + "Answer": 0.14285714285714288, + "Options": "a ) 1 / 5 , b ) 1 / 6 , c ) 1 / 4 , d ) 1 / 7 , e ) 1 / 3", + "Correct": "d", + "Explanation": "if s is an integer and we know that the average speed is 2.8 , s must be = 2 . that meanss + 1 = 3 . this implies that the ratio of time for s = 2 is 1 / 4 of the total time . the formula for distance / rate is d = rt . . . so the distance travelled when s = 2 is 2 t . the distance travelled for s + 1 = 3 is 3 * 4 t or 12 t . therefore , total distance covered while the sun was shining over him is 2 / 14 = 1 / 7 . answer : d" + }, + { + "Answer": 0.16666666666666666, + "Options": "a ) 1 / 20 , b ) 1 / 6 , c ) 1 / 5 , d ) 4 / 21 , e ) 5 / 21", + "Correct": "b", + "Explanation": "\"this is how i used to calculate which i think works pretty well : if you let the average of the 20 other numbers equal a , can you write this equation for sum of the list ( s ) n + 20 a = s the question tells us that n = 4 a plug this back into the first equation and you get that the sum is 24 a 4 a + 20 a = 24 a therefore fraction t of n to the total would be 4 a / 24 a or 1 / 6 answer b\"" + }, + { + "Answer": 8, + "Options": "a ) $ 8 , b ) $ 12 , c ) $ 6 , d ) $ 21 , e ) $ 10", + "Correct": "a", + "Explanation": "5 x $ 3 = $ 15 for baby - sitting 3 x $ 4 = $ 12 for garden work $ 15 + $ 12 = $ 27 she has $ 35 - $ 27 = $ 8 more needed to buy the game correct answer a" + }, + { + "Answer": 3, + "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", + "Correct": "b", + "Explanation": "akar has = ram + rahul + john after evenly distribution each has 11 . so , total no . is 44 so , akar has = 22 & ram + rahul + john = 22 also ram = rahul - 4 & john - 3 = 3 * ram solving these we get the sol . answer : b" + } + ] +} \ No newline at end of file