diff --git "a/all/mathqa_other.json" "b/all/mathqa_other.json" deleted file mode 100644--- "a/all/mathqa_other.json" +++ /dev/null @@ -1,19798 +0,0 @@ -{ - "Source": "https://arxiv.org/pdf/2108.07732.pdf", - "Categories": [ - { - "Math complexity": 3, - "Language complexity": 7, - "Domain knowledge complexity": 0 - } - ], - "Instances": [ - { - "Input": "there are 10 girls and 20 boys in a classroom . what is the ratio of girls to boys ?", - "Output Program": [ - "n0 = 10.0\nn1 = 20.0\n\nanswer = n0 / n1\nprint(answer)" - ], - "Output Answer": [ - "0.5" - ], - "split": "train" - }, - { - "Input": "in a family 13 people eat only vegetarian , 7 people eat only non veg . , 8 people eat both veg and non veg . . how many people eat veg in the family ?", - "Output Program": [ - "n0 = 13.0\nn1 = 7.0\nn2 = 8.0\n\nanswer = n0 + n2\nprint(answer)" - ], - "Output Answer": [ - "21" - ], - "split": "train" - }, - { - "Input": "the salaries of a , b , and c are in the ratio of 1 : 2 : 3 . the salary of b and c together is rs . 6000 . by what percent is the salary of c more than that of a ?", - "Output Program": [ - "n0 = 1.0\nn1 = 2.0\nn2 = 3.0\nn3 = 6000.0\nt0 = n1 + n2\nt1 = n3 / t0\nt2 = n2 * t1\nt3 = t2 / t1\nt4 = t3 - 1.0\nanswer = t4 * 100.0\nprint(answer)" - ], - "Output Answer": [ - "200" - ], - "split": "train" - }, - { - "Input": "there are 2 available positions and 50 candidates , one half of whom are democrats and another half are republicans . if it was decided that the positions would be filled at random , then what is the probability e that the both positions will be taken by members of just one party ?", - "Output Program": [ - "n0 = 2.0\nn1 = 50.0\nt0 = n1 / 2.0\nt1 = n1 - 1.0\nt2 = t0 / n1\nt3 = t0 - 1.0\nt4 = t3 / t1\nt5 = t4 * t2\nanswer = n0 * t5\nprint(answer)" - ], - "Output Answer": [ - "0.4897959183673469" - ], - "split": "train" - }, - { - "Input": "in a class of 60 children , 30 % children can speak only english , 20 % hindi and english both and the rest of the children can speak only hindi . how many children can speak hindi ?", - "Output Program": [ - "n0 = 60.0\nn1 = 30.0\nn2 = 20.0\nt0 = n0 * n2\nt1 = n0 - n1\nt2 = t0 / 100.0\nanswer = t2 + t1\nprint(answer)" - ], - "Output Answer": [ - "42" - ], - "split": "train" - }, - { - "Input": "in a certain town , the ratio of ny yankees fans to ny mets fans is 3 : 2 , and the ratio of ny mets fans to boston red sox fans is 4 : 5 . if there are 330 baseball fans in the town , each of whom is a fan of exactly one of those three teams , how many ny mets fans are there in this town ?", - "Output Program": [ - "n0 = 3.0\nn1 = 2.0\nn2 = 4.0\nn3 = 5.0\nn4 = 330.0\nt0 = n0 * n1\nt1 = n2 + t0\nt2 = n3 + t1\nt3 = n4 / t2\nanswer = n2 * t3\nprint(answer)" - ], - "Output Answer": [ - "88" - ], - "split": "train" - }, - { - "Input": "the ratio of a and b is 5 : 3 . after 2 years their ratio is 3 : 2 . what is the age of b ?", - "Output Program": [ - "n0 = 5.0\nn1 = 3.0\nn2 = 2.0\nn3 = 3.0\nn4 = 2.0\nt0 = n0 * n2\nt1 = n1 * n1\nt2 = n1 * t0\nt3 = t2 / n2\nanswer = t3 - t1\nprint(answer)" - ], - "Output Answer": [ - "6" - ], - "split": "train" - }, - { - "Input": "if the ratio of the sum of the first 6 terms of a g . p . to the sum of the first 3 terms of the g . p . is 217 , what is the common ratio of the g . p ?", - "Output Program": [ - "n0 = 6.0\nn1 = 3.0\nn2 = 217.0\nt0 = 1.0 / n1\nt1 = n2 - 1.0\nanswer = t1**min(t0, 5)\nprint(answer)" - ], - "Output Answer": [ - "5.999999999999999" - ], - "split": "train" - }, - { - "Input": "a 50 kg metal bar made of alloy of tin and silver lost 5 kg of its weight in the water . 10 kg of tin loses 1.375 kg in the water ; 5 kg of silver loses 0.375 kg . what is the ratio of tin to silver in the bar ?", - "Output Program": [ - "n0 = 50.0\nn1 = 5.0\nn2 = 10.0\nn3 = 1.375\nn4 = 5.0\nn5 = 0.375\nt0 = n5 / n4\nt1 = n3 / n2\nt2 = n0 * t0\nt3 = t1 - t0\nt4 = n1 - t2\nt5 = t4 / t3\nt6 = n0 - t5\nanswer = t5 / t6\nprint(answer)" - ], - "Output Answer": [ - "0.6666666666666665" - ], - "split": "train" - }, - { - "Input": "6 years ago , the ratio of the ages of vimal and saroj was 6 : 5 . 4 years hence , the ratio of their ages will be 11 : 10 . what is saroj ' s age at present ?", - "Output Program": [ - "n0 = 6.0\nn1 = 6.0\nn2 = 5.0\nn3 = 4.0\nn4 = 11.0\nn5 = 10.0\nt0 = n4 * n5\nt1 = n5 * 10.0\nt2 = n0 * n5\nt3 = n2 * n4\nt4 = t0 - t1\nt5 = t2 - t3\nt6 = t4 / t5\nt7 = n2 * t6\nanswer = n0 + t7\nprint(answer)" - ], - "Output Answer": [ - "16" - ], - "split": "train" - }, - { - "Input": "ratio between rahul and deepak is 5 : 2 , after 6 years rahul age will be 26 years . what is deepak present age .", - "Output Program": [ - "n0 = 5.0\nn1 = 2.0\nn2 = 6.0\nn3 = 26.0\nt0 = n3 - n2\nt1 = n1 * t0\nanswer = t1 / n0\nprint(answer)" - ], - "Output Answer": [ - "8" - ], - "split": "train" - }, - { - "Input": "in a group of 650 readers who read science fiction or literacy works or both , 250 read science fiction and 550 read literacy works . how many read both science fiction and literacy works ?", - "Output Program": [ - "n0 = 650.0\nn1 = 250.0\nn2 = 550.0\nt0 = n1 + n2\nanswer = t0 - n0\nprint(answer)" - ], - "Output Answer": [ - "150" - ], - "split": "train" - }, - { - "Input": "if 50 % of the 880 students at a certain college are enrolled in biology classes , how many students at the college are not enrolled in a biology class ?", - "Output Program": [ - "n0 = 50.0\nn1 = 880.0\nt0 = n1 / 100.0\nt1 = 100.0 - n0\nanswer = t0 * t1\nprint(answer)" - ], - "Output Answer": [ - "440.00000000000006" - ], - "split": "train" - }, - { - "Input": "the probability that event a occurs is 0.4 , and the probability that events a and b both occur is 0.25 . if the probability that either event a or event b occurs is 0.6 , what is the probability that event b will occur ?", - "Output Program": [ - "n0 = 0.4\nn1 = 0.25\nn2 = 0.6\nt0 = n1 + n2\nanswer = t0 - n0\nprint(answer)" - ], - "Output Answer": [ - "0.44999999999999996" - ], - "split": "train" - }, - { - "Input": "the ratio of sum of squares of first n natural numbers to square of sum of first n natural numbers is 17 : 325 . the value of n is", - "Output Program": [ - "n0 = 17.0\nn1 = 325.0\nt0 = n1 + 100.0\nanswer = t0 / n0\nprint(answer)" - ], - "Output Answer": [ - "25" - ], - "split": "train" - }, - { - "Input": "the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 10 and 12 . the larger of the two numbers is :", - "Output Program": [ - "n0 = 23.0\nn1 = 10.0\nn2 = 12.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "276" - ], - "split": "train" - }, - { - "Input": "the ratio of pens to pencils is 5 to 6 . there are 4 more pencils than pens . how many pencils are there ?", - "Output Program": [ - "n0 = 5.0\nn1 = 6.0\nn2 = 4.0\nt0 = n0 * n2\nanswer = n2 + t0\nprint(answer)" - ], - "Output Answer": [ - "24" - ], - "split": "train" - }, - { - "Input": "in what ratio mental a at rs . 68 per kg be mixed with another metal at rs . 96 per kg so that cost of alloy ( mixture ) is rs . 75 per kg ?", - "Output Program": [ - "n0 = 68.0\nn1 = 96.0\nn2 = 75.0\nt0 = n1 - n2\nt1 = n1 - n0\nt2 = t0 / t1\nt3 = 1.0 - t2\nanswer = t2 / t3\nprint(answer)" - ], - "Output Answer": [ - "3" - ], - "split": "train" - }, - { - "Input": "how many different positive integers are factors of 40 ?", - "Output Program": [ - "n0 = 40.0\nt0 = 2.0**min(2.0, 5)\nanswer = t0 + 2.0\nprint(answer)" - ], - "Output Answer": [ - "6" - ], - "split": "train" - }, - { - "Input": "in a college the ratio of the numbers of boys to the girls is 8 : 5 . if there are 175 girls , the total number of students in the college is ?", - "Output Program": [ - "n0 = 8.0\nn1 = 5.0\nn2 = 175.0\nt0 = n0 / n1\nt1 = n2 * t0\nanswer = n2 + t1\nprint(answer)" - ], - "Output Answer": [ - "455" - ], - "split": "train" - }, - { - "Input": "a bag contains 6 red , 5 blue and 2 green balls . if 2 ballsare picked at random , what is the probability that both are red ?", - "Output Program": [ - "import scipy\nn0 = 6.0\nn1 = 5.0\nn2 = 2.0\nn3 = 2.0\nt0 = n0 + n1\nt1 = scipy.special.comb(n0, n3)\nt2 = n2 + t0\nt3 = scipy.special.comb(t2, n3)\nanswer = t1 / t3\nprint(answer)" - ], - "Output Answer": [ - "0.19230769230769232" - ], - "split": "train" - }, - { - "Input": "a girl scout was selling boxes of cookies . in a month , she sold both boxes of chocolate chip cookies ( $ 1.25 each ) and boxes of plain cookies ( $ 0.75 each ) . altogether , she sold 1,585 boxes for a combined value of $ 1 , 586.25 . how many boxes of plain cookies did she sell ?", - "Output Program": [ - "n0 = 1.25\nn1 = 0.75\nn2 = 1585.0\nn3 = 1.0\nn4 = 586.25\nt0 = n4 + 1000.0\nanswer = t0 / 2.0\nprint(answer)" - ], - "Output Answer": [ - "793.125" - ], - "split": "train" - }, - { - "Input": "out of 460 students of a school , 325 play football , 175 play cricket and 50 neither play football nor cricket . how many students play both football and cricket ?", - "Output Program": [ - "n0 = 460.0\nn1 = 325.0\nn2 = 175.0\nn3 = 50.0\nt0 = n1 + n2\nt1 = n0 - n3\nanswer = t0 - t1\nprint(answer)" - ], - "Output Answer": [ - "90" - ], - "split": "train" - }, - { - "Input": "a person want to give his money of $ 15800 to his 4 children a , b , c , d in the ratio 5 : 9 : 6 : 5 . what is the a + c share ?", - "Output Program": [ - "n0 = 15800.0\nn1 = 4.0\nn2 = 5.0\nn3 = 9.0\nn4 = 6.0\nn5 = 5.0\nt0 = 3.0 + 2.0\nt1 = 4.0 + t0\nt2 = n1 / t1\nanswer = n0 * t2\nprint(answer)" - ], - "Output Answer": [ - "7022.222222222222" - ], - "split": "train" - }, - { - "Input": "a college has classes from 10 : 00 am until 1 : 40 pm . in this duration , there are 5 periods . if 5 minutes are provided between each period to leave one class and enter the next class , how many minutes long is each period ?", - "Output Program": [ - "n0 = 10.0\nn1 = 0.0\nn2 = 1.0\nn3 = 40.0\nn4 = 5.0\nn5 = 5.0\nt0 = 3.0 * 60.0\nt1 = n4 * 4.0\nt2 = n3 + t0\nt3 = t2 - t1\nanswer = t3 / n4\nprint(answer)" - ], - "Output Answer": [ - "40" - ], - "split": "train" - }, - { - "Input": "set a consists of the integers from 4 to 15 , inclusive , while set b consists of the integers from 6 to 20 , inclusive . how many distinct integers do belong to the both sets at the same time ?", - "Output Program": [ - "n0 = 4.0\nn1 = 15.0\nn2 = 6.0\nn3 = 20.0\n\nanswer = n0 + n2\nprint(answer)" - ], - "Output Answer": [ - "10" - ], - "split": "train" - }, - { - "Input": "share rs . 4800 among john , jose & binoy in the ration 2 : 4 : 6 . find the amount received by john ?", - "Output Program": [ - "n0 = 4800.0\nn1 = 2.0\nn2 = 4.0\nn3 = 6.0\nt0 = n0 / n1\nt1 = n0 / n3\nanswer = t0 - t1\nprint(answer)" - ], - "Output Answer": [ - "1600" - ], - "split": "train" - }, - { - "Input": "if the numbers 1 to 95 are written on 95 pieces of paper , ( one on each ) and one piece is picked at random , then what is the probability that the number drawn is neither prime nor composite ?", - "Output Program": [ - "n0 = 1.0\nn1 = 95.0\nn2 = 95.0\n\nanswer = n0 / n1\nprint(answer)" - ], - "Output Answer": [ - "0.010526315789473684" - ], - "split": "train" - }, - { - "Input": "if x and y are both odd prime numbers and x < y , how many distinct positive integer w factors does 2 xy have ?", - "Output Program": [ - "n0 = 2.0\nt0 = 1.0 + 1.0\nt1 = n0 * t0\nanswer = t0 * t1\nprint(answer)" - ], - "Output Answer": [ - "8" - ], - "split": "train" - }, - { - "Input": "compound x contains elements a and b at an approximate ratio , by weight , of 2 : 10 . approximately how many grams of element b are there in 330 grams of compound x ?", - "Output Program": [ - "n0 = 2.0\nn1 = 10.0\nn2 = 330.0\nt0 = n0 + n1\nt1 = n1 * n2\nanswer = t1 / t0\nprint(answer)" - ], - "Output Answer": [ - "275" - ], - "split": "train" - }, - { - "Input": "the monthly incomes of a and b are in the ratio 5 : 2 . b ' s monthly income is 12 % more than c ' s monthly income . if c ' s monthly income is rs . 17000 , then find the annual income of a ?", - "Output Program": [ - "n0 = 5.0\nn1 = 2.0\nn2 = 12.0\nn3 = 17000.0\nt0 = n0 / n1\nt1 = n2 / 100.0\nt2 = t1 + 1.0\nt3 = n3 * t2\nt4 = t0 * t3\nanswer = n2 * t4\nprint(answer)" - ], - "Output Answer": [ - "571200" - ], - "split": "train" - }, - { - "Input": "at the faculty of aerospace engineering , 302 students study random - processing methods , 232 students study scramjet rocket engines and 112 students study them both . if every student in the faculty has to study one of the two subjects , how many students are there in the faculty of aerospace engineering ?", - "Output Program": [ - "n0 = 302.0\nn1 = 232.0\nn2 = 112.0\nt0 = n2 / 2.0\nt1 = n0 - t0\nt2 = n1 - t0\nanswer = t1 + t2\nprint(answer)" - ], - "Output Answer": [ - "422" - ], - "split": "train" - }, - { - "Input": "in a group of 100 people , 55 have visited iceland and 43 have visited norway . if 61 people have visited both iceland and norway , how many people have visited neither country ?", - "Output Program": [ - "n0 = 100.0\nn1 = 55.0\nn2 = 43.0\nn3 = 61.0\nt0 = n1 + n2\nt1 = t0 - n3\nanswer = n0 - t1\nprint(answer)" - ], - "Output Answer": [ - "63" - ], - "split": "train" - }, - { - "Input": "into a room you store 38 black bottles and 4 green bottles , and you turn off the light . if you ask to someone look for 2 bottles without turn on the light , what is the probability of both the selected bottles will be green ?", - "Output Program": [ - "n0 = 38.0\nn1 = 4.0\nn2 = 2.0\nt0 = n0 + n1\nt1 = n1 - 1.0\nt2 = n1 * t1\nt3 = t0 - 1.0\nt4 = t0 * t3\nanswer = t2 / t4\nprint(answer)" - ], - "Output Answer": [ - "0.006968641114982578" - ], - "split": "train" - }, - { - "Input": "kul is 22 years old and saras is 33 years . find the ratio of saras ' s age to kul ' s age .", - "Output Program": [ - "n0 = 22.0\nn1 = 33.0\n\nanswer = n1 / n0\nprint(answer)" - ], - "Output Answer": [ - "1.5" - ], - "split": "train" - }, - { - "Input": "the ratio of boarders to day students at a school was originally 5 to 12 . however , after a number of new boarders join the initial 220 boarders , the ratio changed to 1 to 2 . if no boarders became day students and vice versa , and no students left the school , how many new boarders joined the school ?", - "Output Program": [ - "n0 = 5.0\nn1 = 12.0\nn2 = 220.0\nn3 = 1.0\nn4 = 2.0\nt0 = n2 / n0\nt1 = n1 * t0\nt2 = t1 / n4\nanswer = t2 - n2\nprint(answer)" - ], - "Output Answer": [ - "44" - ], - "split": "train" - }, - { - "Input": "in a group of 90 students , 36 are taking history , and 32 are taking statistics . if 57 students are taking history or statistics or both , then how many students are taking history but not statistics ?", - "Output Program": [ - "n0 = 90.0\nn1 = 36.0\nn2 = 32.0\nn3 = 57.0\nt0 = n1 + n2\nt1 = t0 - n3\nanswer = n1 - t1\nprint(answer)" - ], - "Output Answer": [ - "25" - ], - "split": "train" - }, - { - "Input": "apple costs l rupees per kilogram for first 30 kgs and q rupees per kilogram for each additional kilogram . if the price of 33 kilograms is 168 and for 36 kgs of apples is 186 then the cost of first 20 kgs of apples is", - "Output Program": [ - "n0 = 30.0\nn1 = 33.0\nn2 = 168.0\nn3 = 36.0\nn4 = 186.0\nn5 = 20.0\nt0 = n4 - n2\nt1 = n3 - n1\nt2 = n1 - n0\nt3 = t0 / t1\nt4 = t3 * t2\nt5 = n2 - t4\nt6 = t5 / n0\nanswer = n5 * t6\nprint(answer)" - ], - "Output Answer": [ - "100" - ], - "split": "train" - }, - { - "Input": "the number of stamps that p and q had were in the ratio of 7 : 4 respectively . after p gave q 8 stamps , the ratio of the number of p ' s stamps to the number of q ' s stamps was 6 : 5 . as a result of the gift , p had how many more stamps than q ?", - "Output Program": [ - "n0 = 7.0\nn1 = 4.0\nn2 = 8.0\nn3 = 6.0\nn4 = 5.0\nt0 = n3 + n4\nt1 = n2 * n3\nt2 = n2 * n4\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" - ], - "Output Answer": [ - "8" - ], - "split": "train" - }, - { - "Input": "there are 14 slate rocks , 20 pumice rocks , and 10 granite rocks randomly distributed in a certain field . if 2 rocks are chosen at random and without replacement , what is the probability that both rocks will be slate rocks ?", - "Output Program": [ - "n0 = 14.0\nn1 = 20.0\nn2 = 10.0\nn3 = 2.0\nt0 = n0 + n1\nt1 = n0 - 1.0\nt2 = n2 + t0\nt3 = n0 / t2\nt4 = t2 - 1.0\nt5 = t1 / t4\nanswer = t3 * t5\nprint(answer)" - ], - "Output Answer": [ - "0.09619450317124735" - ], - "split": "train" - }, - { - "Input": "in a class of 36 students 26 play football and play 20 long tennis , if 17 play above , many play neither ?", - "Output Program": [ - "n0 = 36.0\nn1 = 26.0\nn2 = 20.0\nn3 = 17.0\nt0 = n1 + n2\nt1 = t0 - n3\nanswer = n0 - t1\nprint(answer)" - ], - "Output Answer": [ - "7" - ], - "split": "train" - }, - { - "Input": "in a group of 10 doctors , 3 doctors are only pediatricians ; the others are surgeons or general practitioners - but not both . a team of 3 doctors is to be chosen which must have at least 1 pediatrician , how many different teams can be chosen ?", - "Output Program": [ - "import math\nn0 = 10.0\nn1 = 3.0\nn2 = 3.0\nn3 = 1.0\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 = n0 * t2\nt5 = t4 / 2.0\nt6 = t3 * t1\nt7 = t0 / t6\nanswer = t7 - t5\nprint(answer)" - ], - "Output Answer": [ - "85" - ], - "split": "train" - }, - { - "Input": "find the fraction which has the same ratio to 2 / 6 that 3 / 4 has to 1 / 2", - "Output Program": [ - "n0 = 2.0\nn1 = 6.0\nn2 = 3.0\nn3 = 4.0\nn4 = 1.0\nn5 = 2.0\nt0 = n2 / n3\nt1 = n4 / n5\nt2 = n0 / n1\nt3 = t0 / t1\nanswer = t3 * t2\nprint(answer)" - ], - "Output Answer": [ - "0.5" - ], - "split": "train" - }, - { - "Input": "if m = 3 ^ n , what is the greatest value of n for which m is a factor of 19 !", - "Output Program": [ - "import math\nn0 = 3.0\nn1 = 19.0\nt0 = n1 / n0\nt1 = n0**min(2.0, 5)\nt2 = n1 / t1\nt3 = math.floor(t0)\nt4 = math.floor(t2)\nanswer = t3 + t4\nprint(answer)" - ], - "Output Answer": [ - "8" - ], - "split": "train" - }, - { - "Input": "two family reunions are happening at the leela hotel , the oates reunion and the hall reunion . all 100 guests at the hotel attend at least one of the reunions . if 50 people attend the oates reunion and 62 people attend the hall reunion , how many people attend both reunions ?", - "Output Program": [ - "n0 = 100.0\nn1 = 50.0\nn2 = 62.0\n\nanswer = n2 - n1\nprint(answer)" - ], - "Output Answer": [ - "12" - ], - "split": "train" - }, - { - "Input": "if 75 percent of a class answered the first question on a certain test correctly , 35 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?", - "Output Program": [ - "n0 = 75.0\nn1 = 35.0\nn2 = 20.0\nt0 = n0 + n1\nt1 = n2 + t0\nanswer = t1 - 100.0\nprint(answer)" - ], - "Output Answer": [ - "30" - ], - "split": "train" - }, - { - "Input": "in a class , 7 students like to play basketball and 5 like to play cricket . 3 students like to play on both basketball and cricket . how many students like to play basketball or cricket or both ?", - "Output Program": [ - "n0 = 7.0\nn1 = 5.0\nn2 = 3.0\nt0 = n0 + n1\nanswer = t0 - n2\nprint(answer)" - ], - "Output Answer": [ - "9" - ], - "split": "train" - }, - { - "Input": "13 different biology books and 8 different chemistry books lie on a shelf . in how many ways can a student pick 2 books of each type ?", - "Output Program": [ - "import math\nn0 = 13.0\nn1 = 8.0\nn2 = 2.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(n1)))\nt2 = n0 - n2\nt3 = n1 - n2\nt4 = math.factorial(min(15, int(t2)))\nt5 = math.factorial(min(15, int(t3)))\nt6 = t0 / t4\nt7 = t1 / t5\nt8 = t6 / n2\nt9 = t7 / n2\nanswer = t8 * t9\nprint(answer)" - ], - "Output Answer": [ - "2184" - ], - "split": "train" - }, - { - "Input": "the ratio of three numbers is 1 : 2 : 4 and the sum of their squares is 4725 . the sum of the numbers is ?", - "Output Program": [ - "import math\nn0 = 1.0\nn1 = 2.0\nn2 = 4.0\nn3 = 4725.0\nt0 = n0**min(2.0, 5)\nt1 = n1**min(2.0, 5)\nt2 = n2**min(2.0, 5)\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n3 / t4\nanswer = math.sqrt(max(0, t5))\nprint(answer)" - ], - "Output Answer": [ - "15" - ], - "split": "train" - }, - { - "Input": "madhav ranks seventeenth in a class of thirtyone . what is his rank from the last ?", - "Output Program": [ - "t0 = 3.0 * 4.0\nt1 = t0 + 4.0\nt2 = t1 + 1.0\nt3 = t2 + t0\nt4 = t3 + 2.0\nt5 = t4 - t2\nanswer = t5 + 1.0\nprint(answer)" - ], - "Output Answer": [ - "15" - ], - "split": "train" - }, - { - "Input": "at a garage sale , all of the items were sold at different prices . if the price of a radio sold at the garage sale was both the 16 th highest price and the 23 rd lowest price among the prices of the items sold , how many items were sold at the garage sale ?", - "Output Program": [ - "n0 = 16.0\nn1 = 23.0\nt0 = n0 + n1\nanswer = t0 - 1.0\nprint(answer)" - ], - "Output Answer": [ - "38" - ], - "split": "train" - }, - { - "Input": "jill ' s favorite number is even and has some repeating prime factors . john is guessing jills favorite number , and the only hint she gives is that 7 is a prime factor . what is johns best guess ?", - "Output Program": [ - "n0 = 7.0\nt0 = n0 * 3.0\nt1 = 2.0**min(2.0, 5)\nanswer = t0 * t1\nprint(answer)" - ], - "Output Answer": [ - "84" - ], - "split": "train" - }, - { - "Input": "assisants are needed to prepare for preparation . each helper can make either 2 large cakes or 35 small cakes / hour . the kitchen is available for 3 hours and 20 large cakes and 700 small cakes are needed . how many helpers are required ?", - "Output Program": [ - "n0 = 2.0\nn1 = 35.0\nn2 = 3.0\nn3 = 20.0\nn4 = 700.0\nt0 = n3 / n0\nt1 = n4 / n1\nt2 = t0 + t1\nanswer = t2 / n2\nprint(answer)" - ], - "Output Answer": [ - "10" - ], - "split": "train" - }, - { - "Input": "at the faculty of aerospace engineering , 312 students study random - processing methods , 222 students study scramjet rocket engines and 112 students study them both . if every student in the faculty has to study one of the two subjects , how many students are there in the faculty of aerospace engineering ?", - "Output Program": [ - "n0 = 312.0\nn1 = 222.0\nn2 = 112.0\nt0 = n2 / 2.0\nt1 = n0 - t0\nt2 = n1 - t0\nanswer = t1 + t2\nprint(answer)" - ], - "Output Answer": [ - "422" - ], - "split": "train" - }, - { - "Input": "the marks obtained by polly and sandy are in the ratio 4 : 5 and those obtained by sandy and willy are in the ratio of 5 : 2 . the marks obtained by polly and willy are in the ratio of . . . ?", - "Output Program": [ - "n0 = 4.0\nn1 = 5.0\nn2 = 5.0\nn3 = 2.0\nt0 = n0 * n2\nt1 = n1 * n3\nanswer = t0 / t1\nprint(answer)" - ], - "Output Answer": [ - "2" - ], - "split": "train" - }, - { - "Input": "a bag contains 6 green and 8 white balls . if two balls are drawn simultaneously , the probability that both are of the same colour is", - "Output Program": [ - "n0 = 6.0\nn1 = 8.0\nt0 = n0 + n1\nt1 = n1 - 1.0\nt2 = n0 - 1.0\nt3 = n1 / t0\nt4 = n0 / t0\nt5 = t0 - 1.0\nt6 = t1 / t5\nt7 = t2 / t5\nt8 = t3 * t6\nt9 = t4 * t7\nanswer = t8 + t9\nprint(answer)" - ], - "Output Answer": [ - "0.4725274725274725" - ], - "split": "train" - }, - { - "Input": "if the numbers 1 to 97 are written on 97 pieces of paper , ( one on each ) and one piece is picked at random , then what is the probability that the number drawn is neither prime nor composite ?", - "Output Program": [ - "n0 = 1.0\nn1 = 97.0\nn2 = 97.0\n\nanswer = n0 / n1\nprint(answer)" - ], - "Output Answer": [ - "0.010309278350515464" - ], - "split": "train" - }, - { - "Input": "the ratio of pens to pencils is 5 to 6 . there are 9 more pencils than pens . how many pencils are there ?", - "Output Program": [ - "n0 = 5.0\nn1 = 6.0\nn2 = 9.0\nt0 = n0 * n2\nanswer = n2 + t0\nprint(answer)" - ], - "Output Answer": [ - "54" - ], - "split": "train" - }, - { - "Input": "compound x contains elements a and b at an approximate ratio , by weight , of 2 : 10 . approximately how many grams of element b are there in 222 grams of compound x ?", - "Output Program": [ - "n0 = 2.0\nn1 = 10.0\nn2 = 222.0\nt0 = n0 + n1\nt1 = n1 * n2\nanswer = t1 / t0\nprint(answer)" - ], - "Output Answer": [ - "185" - ], - "split": "train" - }, - { - "Input": "a starts business with rs . 35000 and after 5 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b \u2019 s contribution in the capital ?", - "Output Program": [ - "n0 = 35000.0\nn1 = 5.0\nn2 = 2.0\nn3 = 3.0\nt0 = n0 * 12.0\nt1 = 12.0 - n1\nt2 = n3 * t0\nt3 = n2 * t1\nt4 = t2 / t3\nanswer = t4 / 10.0\nprint(answer)" - ], - "Output Answer": [ - "9000" - ], - "split": "train" - }, - { - "Input": "find the fraction which has the same ratio to 2 / 5 that 3 / 8 has to 1 / 5", - "Output Program": [ - "n0 = 2.0\nn1 = 5.0\nn2 = 3.0\nn3 = 8.0\nn4 = 1.0\nn5 = 5.0\nt0 = n2 / n3\nt1 = n4 / n5\nt2 = n0 / n1\nt3 = t0 / t1\nanswer = t3 * t2\nprint(answer)" - ], - "Output Answer": [ - "0.75" - ], - "split": "train" - }, - { - "Input": "how many zeros does 1000 ! end with ?", - "Output Program": [ - "n0 = 1000.0\nt0 = 1.0 + 4.0\nt1 = n0 / t0\nt2 = t0**min(2.0, 5)\nt3 = t0**min(3.0, 5)\nt4 = n0 - t0\nt5 = t4 / t2\nt6 = t4 / t3\nt7 = t1 + t5\nanswer = t7 + t6\nprint(answer)" - ], - "Output Answer": [ - "247.76000000000002" - ], - "split": "train" - }, - { - "Input": "in a college , the ratio of the number of boys to girls is 8 : 5 . if there are 400 girls , the total number of students in the college is", - "Output Program": [ - "n0 = 8.0\nn1 = 5.0\nn2 = 400.0\nt0 = n2 / n1\nt1 = n0 * t0\nanswer = n2 + t1\nprint(answer)" - ], - "Output Answer": [ - "1040" - ], - "split": "train" - }, - { - "Input": "a bag contains 7 green balls and 7 white balls . if two balls are drawn simultaneously , what is the probability that both balls are the same colour ?", - "Output Program": [ - "n0 = 7.0\nn1 = 7.0\nt0 = n0 + n1\nt1 = n1 - 1.0\nt2 = n0 - 1.0\nt3 = n1 / t0\nt4 = n0 / t0\nt5 = t0 - 1.0\nt6 = t1 / t5\nt7 = t2 / t5\nt8 = t3 * t6\nt9 = t7 * t4\nanswer = t8 + t9\nprint(answer)" - ], - "Output Answer": [ - "0.46153846153846156" - ], - "split": "train" - }, - { - "Input": "in a neighborhood having 90 households , 11 did not have either a car or a bike . if 22 households had a both a car and a bike and 44 had a car , how many had bike only ?", - "Output Program": [ - "n0 = 90.0\nn1 = 11.0\nn2 = 22.0\nn3 = 44.0\nt0 = n0 - n1\nt1 = n2 + t0\nt2 = t1 - n3\nanswer = t2 - n2\nprint(answer)" - ], - "Output Answer": [ - "35" - ], - "split": "train" - }, - { - "Input": "uba capital recently bought brand new vehicles for office use . uba capital only went for toyota and honda and bought more of toyota than honda at the ratio of 8 : 2 . if 80 % of the toyota bought and 20 % of the honda bought were suv \u00e2 \u20ac \u2122 s . how many suv \u00e2 \u20ac \u2122 s did uba capital buy in the aforementioned purchase ?", - "Output Program": [ - "n0 = 8.0\nn1 = 2.0\nn2 = 80.0\nn3 = 20.0\nt0 = n0 * n1\nt1 = t0 + t0\nanswer = 100.0 - t1\nprint(answer)" - ], - "Output Answer": [ - "68" - ], - "split": "train" - }, - { - "Input": "right now , the ratio between the ages of sandy and molly is 4 : 3 . after 6 years , sandy \u2019 s age will be 30 years . what is molly ' s age right now ?", - "Output Program": [ - "n0 = 4.0\nn1 = 3.0\nn2 = 6.0\nn3 = 30.0\nt0 = n3 - n2\nt1 = t0 / n0\nanswer = n1 * t1\nprint(answer)" - ], - "Output Answer": [ - "18" - ], - "split": "train" - }, - { - "Input": "in a colony of 50 residents , the ratio of the number of men and women is 3 : 2 . among the women , the ratio of the educated to the uneducated is 1 : 3 . if the ratio of the number of education to uneducated persons is 4 : 6 , then find the ratio of the number of educated and uneducated men in the colony ?", - "Output Program": [ - "n0 = 50.0\nn1 = 3.0\nn2 = 2.0\nn3 = 1.0\nn4 = 3.0\nn5 = 4.0\nn6 = 6.0\nt0 = n5 + n6\nt1 = n1 + n2\nt2 = n1 + n3\nt3 = n0 / t0\nt4 = n0 / t1\nt5 = n5 * t3\nt6 = n2 * t4\nt7 = n6 * t3\nt8 = t6 / t2\nt9 = n1 * t8\nt10 = t5 - t8\nt11 = t7 - t9\nanswer = t10 / t11\nprint(answer)" - ], - "Output Answer": [ - "1" - ], - "split": "train" - }, - { - "Input": "the ratio of the number of females to males at a party was 1 : 2 but when 3 females and 3 males left , the ratio became 1 : 3 . how many people were at the party originally ?", - "Output Program": [ - "n0 = 1.0\nn1 = 2.0\nn2 = 3.0\nn3 = 3.0\nn4 = 1.0\nn5 = 3.0\nt0 = n1 * n2\nt1 = n5 * t0\nt2 = t1 - t0\nt3 = t2 / n1\nanswer = t3 + t2\nprint(answer)" - ], - "Output Answer": [ - "18" - ], - "split": "train" - }, - { - "Input": "the ratio of spinsters to cats is 2 to 9 . if there are 63 more cats than spinsters , how many spinsters are there ?", - "Output Program": [ - "n0 = 2.0\nn1 = 9.0\nn2 = 63.0\nt0 = n1 - n0\nt1 = n2 / t0\nanswer = n0 * t1\nprint(answer)" - ], - "Output Answer": [ - "18" - ], - "split": "train" - }, - { - "Input": "the h . c . f . of two numbers is 60 and the other two factors of their l . c . m . are 11 and 15 . the larger of the two numbers is :", - "Output Program": [ - "n0 = 60.0\nn1 = 11.0\nn2 = 15.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "900" - ], - "split": "train" - }, - { - "Input": "the number of even factors of 21600 is", - "Output Program": [ - "n0 = 21600.0\nt0 = 1.0 + 2.0\nt1 = 2.0 + 3.0\nt2 = 1.0 + 3.0\nt3 = t1 + 1.0\nt4 = t2 * t0\nt5 = t3 * t2\nt6 = t0 * t5\nanswer = t6 - t4\nprint(answer)" - ], - "Output Answer": [ - "60" - ], - "split": "train" - }, - { - "Input": "a consignment of 20 picture tubes contains 5 defectives . two tubes are selected one after the other at random . the probability that both are defective assuming that the first tube is not replaced before drawing the second , would be :", - "Output Program": [ - "import scipy\nn0 = 20.0\nn1 = 5.0\nt0 = scipy.special.comb(5.0, 2.0)\nt1 = scipy.special.comb(n0, 2.0)\nanswer = t0 / t1\nprint(answer)" - ], - "Output Answer": [ - "0.05263157894736842" - ], - "split": "train" - }, - { - "Input": "teas worth rs . 126 per kg and rs . 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs 154 per kg , the price of the third variety per kg will be ?", - "Output Program": [ - "n0 = 126.0\nn1 = 135.0\nn2 = 1.0\nn3 = 1.0\nn4 = 2.0\nn5 = 154.0\nt0 = n2 + n2\nt1 = n0 + n1\nt2 = n4 + t0\nt3 = n5 * t2\nt4 = t3 - t1\nanswer = t4 / n4\nprint(answer)" - ], - "Output Answer": [ - "177.5" - ], - "split": "train" - }, - { - "Input": "the hcf of two numbers is 52 and the other two factors of their lcm are 11 and 12 . what is the largest number .", - "Output Program": [ - "n0 = 52.0\nn1 = 11.0\nn2 = 12.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "624" - ], - "split": "train" - }, - { - "Input": "if the radii of umbra and penumbra cast by an object on a wall are of the ratio 2 : 6 , what is the area of the penumbra ring around the umbra of the latter \u2019 s radius is 40 cms ?", - "Output Program": [ - "n0 = 2.0\nn1 = 6.0\nn2 = 40.0\nt0 = n1 * n2\nt1 = n2 * 2.0\nt2 = t0 * t0\nt3 = t1 * t1\nt4 = t2 * 3.141592653589793\nt5 = t3 * 3.141592653589793\nt6 = t4 - t5\nt7 = t6 / n0\nanswer = t7 / n0\nprint(answer)" - ], - "Output Answer": [ - "40212.385965949354" - ], - "split": "train" - }, - { - "Input": "the ratio between the number of sheep and the number of horses at the stewar farm is 2 to 7 . if each of horse is fed 230 ounces of horse food per day and the farm needs a total 12880 ounces of horse food per day . what is number sheep in the form ? ?", - "Output Program": [ - "n0 = 2.0\nn1 = 7.0\nn2 = 230.0\nn3 = 12880.0\nt0 = n3 / n2\nt1 = t0 / n1\nanswer = n0 * t1\nprint(answer)" - ], - "Output Answer": [ - "16" - ], - "split": "train" - }, - { - "Input": "a certain university will select 1 of 4 candidates eligible to fill a position in the mathematics department and 2 of 7 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?", - "Output Program": [ - "n0 = 1.0\nn1 = 4.0\nn2 = 2.0\nn3 = 7.0\nn4 = 2.0\nn5 = 3.0\nn6 = 3.0\nt0 = n3 * n5\nanswer = n1 * t0\nprint(answer)" - ], - "Output Answer": [ - "84" - ], - "split": "train" - }, - { - "Input": "a class has a ratio of 3 : 6 : 7 of children with red hair , blonde hair and black hair respectively . if the class has 9 kids with red hair , how many kids are in the class ?", - "Output Program": [ - "n0 = 3.0\nn1 = 6.0\nn2 = 7.0\nn3 = 9.0\nt0 = n1 + n2\nt1 = n0 + t0\nanswer = n0 * t1\nprint(answer)" - ], - "Output Answer": [ - "48" - ], - "split": "train" - }, - { - "Input": "the probability that a computer company will get a computer hardware contract is 3 / 4 and the probability that it will not get a software contract is 3 / 5 . if the probability of getting at least one contract is 5 / 6 , what is the probability that it will get both the contracts ?", - "Output Program": [ - "n0 = 3.0\nn1 = 4.0\nn2 = 3.0\nn3 = 5.0\nn4 = 5.0\nn5 = 6.0\nt0 = n0 / n1\nt1 = n0 / n3\nt2 = n3 / n5\nt3 = 1.0 - t1\nt4 = t0 + t3\nanswer = t4 - t2\nprint(answer)" - ], - "Output Answer": [ - "0.31666666666666654" - ], - "split": "train" - }, - { - "Input": "the monthly incomes of a and b are in the ratio 5 : 2 . b ' s monthly income is 12 % more than c ' s monthly income . if c ' s monthly income is rs . 13000 , then find the annual income of a ?", - "Output Program": [ - "n0 = 5.0\nn1 = 2.0\nn2 = 12.0\nn3 = 13000.0\nt0 = n0 / n1\nt1 = n2 / 100.0\nt2 = t1 + 1.0\nt3 = n3 * t2\nt4 = t0 * t3\nanswer = n2 * t4\nprint(answer)" - ], - "Output Answer": [ - "436800.0000000001" - ], - "split": "train" - }, - { - "Input": "a technology company made a $ 5 million profit on its first $ 15 million in sales and a $ 12 million profit on its next $ 30 million in sales . by what percent did the ratio of profit to sales increase from the first $ 15 million in sales to the next $ 30 million in sales ?", - "Output Program": [ - "n0 = 5.0\nn1 = 15.0\nn2 = 12.0\nn3 = 30.0\nn4 = 15.0\nn5 = 30.0\nt0 = n2 / n3\nt1 = n0 / n1\nt2 = t0 - t1\nt3 = t2 / t1\nanswer = t3 * 100.0\nprint(answer)" - ], - "Output Answer": [ - "20.00000000000001" - ], - "split": "train" - }, - { - "Input": "in a neighborhood having 90 households , 11 did not have either a car or a bike . if 20 households had a both a car and a bike and 44 had a car , how many had bike only ?", - "Output Program": [ - "n0 = 90.0\nn1 = 11.0\nn2 = 20.0\nn3 = 44.0\nt0 = n0 - n1\nt1 = n2 + t0\nt2 = t1 - n3\nanswer = t2 - n2\nprint(answer)" - ], - "Output Answer": [ - "35" - ], - "split": "train" - }, - { - "Input": "75 persons major in physics , 83 major in chemistry , 10 not at major in these subjects u want to find number of students majoring in both subjects", - "Output Program": [ - "n0 = 75.0\nn1 = 83.0\nn2 = 10.0\nt0 = n0 + n1\nt1 = 100.0 - n2\nanswer = t0 - t1\nprint(answer)" - ], - "Output Answer": [ - "68" - ], - "split": "train" - }, - { - "Input": "the ratio of number of boys and girls in a school is 1 : 2 . if there are 90 students in the school , find the number of girls in the school ?", - "Output Program": [ - "n0 = 1.0\nn1 = 2.0\nn2 = 90.0\nt0 = n2 / 3.0\nanswer = n1 * t0\nprint(answer)" - ], - "Output Answer": [ - "60" - ], - "split": "train" - }, - { - "Input": "mangoes , oranges and apples in a fruit shop are in the ratio of 10 : 2 : 3 . if there are 120 mangoes , the number of apples in the shop is : .", - "Output Program": [ - "n0 = 10.0\nn1 = 2.0\nn2 = 3.0\nn3 = 120.0\nt0 = n3 / n0\nanswer = n2 * t0\nprint(answer)" - ], - "Output Answer": [ - "36" - ], - "split": "train" - }, - { - "Input": "there 3 kinds of books in the library physics , chemistry and biology . ratio of physics to chemistry is 3 to 2 ; ratio of chemistry to biology is 4 to 3 , and the total of the books is more than 3000 . which one of following can be the total e of the book ?", - "Output Program": [ - "n0 = 3.0\nn1 = 3.0\nn2 = 2.0\nn3 = 4.0\nn4 = 3.0\nn5 = 3000.0\n\nanswer = n0 + n5\nprint(answer)" - ], - "Output Answer": [ - "3003" - ], - "split": "train" - }, - { - "Input": "a farmer with 1350 acres of land had planted his fields with corn , sugar cane , and tobacco in the ratio of 5 : 2 : 2 , respectively , but he wanted to make more money , so he shifted the ratio to 2 : 2 : 5 , respectively . how many more acres of land were planted with tobacco under the new system ?", - "Output Program": [ - "n0 = 1350.0\nn1 = 5.0\nn2 = 2.0\nn3 = 2.0\nn4 = 2.0\nn5 = 2.0\nn6 = 5.0\nt0 = n1 + n2\nt1 = n0 * 3.0\nt2 = n2 + t0\nanswer = t1 / t2\nprint(answer)" - ], - "Output Answer": [ - "450" - ], - "split": "train" - }, - { - "Input": "the ratio by weight , measured in pounds , of books to clothes to electronics in a suitcase initially stands at 5 : 4 : 2 . someone removes 9 pounds of clothing from the suitcase , thereby doubling the ratio of books to clothes . how many pounds do the electronics in the suitcase weigh ?", - "Output Program": [ - "n0 = 5.0\nn1 = 4.0\nn2 = 2.0\nn3 = 9.0\nt0 = n0 + n1\nt1 = n2 + t0\nt2 = n3 * t1\nt3 = t1 * 2.0\nt4 = n1 * t1\nt5 = -t2\nt6 = t3 - t4\nt7 = t5 / t6\nanswer = n2 * t7\nprint(answer)" - ], - "Output Answer": [ - "9" - ], - "split": "train" - }, - { - "Input": "in a certain alphabet , 8 letters contain a dot and a straight line . 24 letters contain a straight line but do not contain a dot . if that alphabet has 40 letters , all of which contain either a dot or a straight line or both , how many letters contain a dot but do not contain a straight line ?", - "Output Program": [ - "n0 = 8.0\nn1 = 24.0\nn2 = 40.0\nt0 = n0 + n1\nanswer = n2 - t0\nprint(answer)" - ], - "Output Answer": [ - "8" - ], - "split": "train" - }, - { - "Input": "a bag contains 6 green balls and 8 white balls . if two balls are drawn simultaneously , what is the probability that both balls are the same colour ?", - "Output Program": [ - "n0 = 6.0\nn1 = 8.0\nt0 = n0 + n1\nt1 = n1 - 1.0\nt2 = n0 - 1.0\nt3 = n1 / t0\nt4 = n0 / t0\nt5 = t0 - 1.0\nt6 = t1 / t5\nt7 = t2 / t5\nt8 = t3 * t6\nt9 = t7 * t4\nanswer = t8 + t9\nprint(answer)" - ], - "Output Answer": [ - "0.4725274725274725" - ], - "split": "train" - }, - { - "Input": "the ratio of the incomes of rajan and balan is 7 : 6 and the ratio of their expenditure is 6 : 5 . if at the end of the year , each saves $ 1000 then the income of rajan is ?", - "Output Program": [ - "n0 = 7.0\nn1 = 6.0\nn2 = 6.0\nn3 = 5.0\nn4 = 1000.0\nt0 = n0 / n1\nt1 = n1 / n3\nt2 = n4 * t0\nt3 = t0 - t1\nt4 = n4 - t2\nt5 = t4 / t3\nt6 = n4 + t5\nt7 = n0 * t6\nanswer = t7 / n1\nprint(answer)" - ], - "Output Answer": [ - "7000.000000000023" - ], - "split": "train" - }, - { - "Input": "a certain quantity of 40 % solution is replaced with 25 % solution such that the new concentration is 35 % . what is the fraction of the solution that was replaced ?", - "Output Program": [ - "n0 = 40.0\nn1 = 25.0\nn2 = 35.0\nt0 = n2 - n1\nt1 = n0 - n2\nt2 = t0 / t1\nt3 = t2 + 1.0\nanswer = 1 / t3\nprint(answer)" - ], - "Output Answer": [ - "0.3333333333333333" - ], - "split": "train" - }, - { - "Input": "pencils , pens and exercise books in a shop are in the ratio of 14 : 4 : 3 . if there are 140 pencils , the number of exercise books in the shop is :", - "Output Program": [ - "n0 = 14.0\nn1 = 4.0\nn2 = 3.0\nn3 = 140.0\nt0 = n3 / n0\nanswer = n2 * t0\nprint(answer)" - ], - "Output Answer": [ - "30" - ], - "split": "train" - }, - { - "Input": "a person want to give his money of $ 4500 to his 4 children a , b , c , d in the ratio 2 : 4 : 5 : 4 . what is the a + b share ?", - "Output Program": [ - "n0 = 4500.0\nn1 = 4.0\nn2 = 2.0\nn3 = 4.0\nn4 = 5.0\nn5 = 4.0\nt0 = 3.0 + n2\nt1 = n4 + t0\nt2 = n1 / t1\nanswer = n0 * t2\nprint(answer)" - ], - "Output Answer": [ - "1800" - ], - "split": "train" - }, - { - "Input": "if the ratio of a to b is 4 to 3 and the ratio of b to c is 1 to 5 , what is the ratio of a to c ?", - "Output Program": [ - "n0 = 4.0\nn1 = 3.0\nn2 = 1.0\nn3 = 5.0\nt0 = n0 * n2\nt1 = n1 * n3\nanswer = t0 / t1\nprint(answer)" - ], - "Output Answer": [ - "0.26666666666666666" - ], - "split": "train" - }, - { - "Input": "the h . c . f . of two numbers is 63 and the other two factors of their l . c . m . are 11 and 17 . the larger of the two numbers is :", - "Output Program": [ - "n0 = 63.0\nn1 = 11.0\nn2 = 17.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "1071" - ], - "split": "train" - }, - { - "Input": "integer m has 4 different prime factors and n has 3 different prime factors . if m and n has the greatest common factor of 15 , how many different prime factors does mn have ?", - "Output Program": [ - "n0 = 4.0\nn1 = 3.0\nn2 = 15.0\n\nanswer = n0 + 1.0\nprint(answer)" - ], - "Output Answer": [ - "5" - ], - "split": "train" - }, - { - "Input": "if both 5 ^ 2 and 3 ^ 3 are factors of n x ( 2 ^ 5 ) x ( 6 ^ 2 ) x ( 7 ^ 3 ) , what is the smallest possible positive value of n ? .", - "Output Program": [ - "n0 = 5.0\nn1 = 2.0\nn2 = 3.0\nn3 = 3.0\nn4 = 2.0\nn5 = 5.0\nn6 = 6.0\nn7 = 2.0\nn8 = 7.0\nn9 = 3.0\nt0 = n0**min(n1, 5)\nanswer = n2 * t0\nprint(answer)" - ], - "Output Answer": [ - "75" - ], - "split": "train" - }, - { - "Input": "in a college students can play cricket or basketball . 500 play cricket . 220 played both and 600 played basketball . what is the total strength of college ?", - "Output Program": [ - "n0 = 500.0\nn1 = 220.0\nn2 = 600.0\nt0 = n0 + n2\nanswer = t0 - n1\nprint(answer)" - ], - "Output Answer": [ - "880" - ], - "split": "train" - }, - { - "Input": "the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 19 . the larger of the two numbers is :", - "Output Program": [ - "n0 = 23.0\nn1 = 13.0\nn2 = 19.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "437" - ], - "split": "train" - }, - { - "Input": "the ratio of flour to water to sugar in a recipe is 10 : 6 : 3 . the ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar . if the new recipe calls for 2 cups of water , how much sugar is required ?", - "Output Program": [ - "n0 = 10.0\nn1 = 6.0\nn2 = 3.0\nn3 = 2.0\nt0 = n3 / n1\nt1 = n2 * 4.0\nanswer = t0 * t1\nprint(answer)" - ], - "Output Answer": [ - "4" - ], - "split": "train" - }, - { - "Input": "two family reunions are happening at the taj hotel , the oates reunion and the hall reunion . all 150 guests at the hotel attend at least one of the reunions . if 70 people attend the oates reunion and 52 people attend the hall reunion , how many people attend both reunions ?", - "Output Program": [ - "n0 = 150.0\nn1 = 70.0\nn2 = 52.0\nt0 = n1 + n2\nanswer = n0 - t0\nprint(answer)" - ], - "Output Answer": [ - "28" - ], - "split": "train" - }, - { - "Input": "what is the prime factors \u2019 number of 48 ?", - "Output Program": [ - "n0 = 48.0\nt0 = 1.0 + 1.0\nt1 = t0 + 1.0\nt2 = t1 + 1.0\nanswer = t2 + 1.0\nprint(answer)" - ], - "Output Answer": [ - "5" - ], - "split": "train" - }, - { - "Input": "the ratio of the number of females to males at a party was 1 : 2 but when 5 females and 5 males left , the ratio became 1 : 3 . how many people were at the party originally ?", - "Output Program": [ - "n0 = 1.0\nn1 = 2.0\nn2 = 5.0\nn3 = 5.0\nn4 = 1.0\nn5 = 3.0\nt0 = n1 * n2\nt1 = n5 * t0\nt2 = t1 - t0\nt3 = t2 / n1\nanswer = t3 + t2\nprint(answer)" - ], - "Output Answer": [ - "30" - ], - "split": "train" - }, - { - "Input": "there 3 kinds of books in the library physics , chemistry and biology . ratio of physics to chemistry is 3 to 2 ; ratio of chemistry to biology is 4 to 3 , and the total of the books is more than 3000 . which one of following can be the total r of the book ?", - "Output Program": [ - "n0 = 3.0\nn1 = 3.0\nn2 = 2.0\nn3 = 4.0\nn4 = 3.0\nn5 = 3000.0\n\nanswer = n0 + n5\nprint(answer)" - ], - "Output Answer": [ - "3003" - ], - "split": "train" - }, - { - "Input": "a person want to give his money of $ 5400 to his 3 children a , b , c in the ratio 2 : 3 : 4 . what is the b ' s share ?", - "Output Program": [ - "n0 = 5400.0\nn1 = 3.0\nn2 = 2.0\nn3 = 3.0\nn4 = 4.0\nt0 = n1 + n2\nt1 = n4 + t0\nt2 = n1 / t1\nanswer = n0 * t2\nprint(answer)" - ], - "Output Answer": [ - "1800" - ], - "split": "train" - }, - { - "Input": "income and expenditure of a person are in the ratio 10 : 7 . if the income of the person is rs . 10000 , then find his savings ?", - "Output Program": [ - "n0 = 10.0\nn1 = 7.0\nn2 = 10000.0\nt0 = n1 / n0\nt1 = n2 * t0\nanswer = n2 - t1\nprint(answer)" - ], - "Output Answer": [ - "3000" - ], - "split": "train" - }, - { - "Input": "in a graduating class of 232 students , 144 took geometry and 119 took biology . what is the difference between the greatest possible number i and the smallest possible number of students that could have taken both geometry and biology ?", - "Output Program": [ - "n0 = 232.0\nn1 = 144.0\nn2 = 119.0\nt0 = n1 + n2\nt1 = t0 - n0\nanswer = n2 - t1\nprint(answer)" - ], - "Output Answer": [ - "88" - ], - "split": "train" - }, - { - "Input": "in a class of 38 students 26 play football and play 20 long tennis , if 17 play above , many play neither ?", - "Output Program": [ - "n0 = 38.0\nn1 = 26.0\nn2 = 20.0\nn3 = 17.0\nt0 = n1 + n2\nt1 = t0 - n3\nanswer = n0 - t1\nprint(answer)" - ], - "Output Answer": [ - "9" - ], - "split": "train" - }, - { - "Input": "a number is said to be prime saturated if the product of all the different positive prime factors of d is less than the square root of d . what is the greatest two digit prime saturated integer ?", - "Output Program": [ - "t0 = 2.0 * 3.0\nt1 = 100.0 - 10.0\nanswer = t0 + t1\nprint(answer)" - ], - "Output Answer": [ - "96" - ], - "split": "train" - }, - { - "Input": "in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of thesportformulation contains 5 ounces of corn syrup , how many ounces of water does it contain ?", - "Output Program": [ - "n0 = 1.0\nn1 = 12.0\nn2 = 30.0\nn3 = 5.0\nt0 = n0 / n1\nt1 = n0 / n2\nt2 = t1 / 2.0\nt3 = t0 * 3.0\nt4 = t3 / t2\nanswer = n3 * t4\nprint(answer)" - ], - "Output Answer": [ - "75" - ], - "split": "train" - }, - { - "Input": "a certain business school has 500 students , and the law school at the same university has 800 students . among these students , there are 30 sibling pairs consisting of 1 business student and 1 law student . if 1 student is selected at random from both schools , what is the probability that a sibling pair is selected ?", - "Output Program": [ - "n0 = 500.0\nn1 = 800.0\nn2 = 30.0\nn3 = 1.0\nn4 = 1.0\nn5 = 1.0\nt0 = n3 / n0\nt1 = n3 / n1\nt2 = t0 * t1\nanswer = n2 * t2\nprint(answer)" - ], - "Output Answer": [ - "7.500000000000001e-05" - ], - "split": "train" - }, - { - "Input": "if a student loses 5 kilograms , he will weigh twice as much as his sister . together they now weigh 116 kilograms . what is the student ' s present weight in kilograms ?", - "Output Program": [ - "n0 = 5.0\nn1 = 116.0\nt0 = n1 - n0\nt1 = t0 / 3.0\nanswer = n1 - t1\nprint(answer)" - ], - "Output Answer": [ - "79" - ], - "split": "train" - }, - { - "Input": "uba capital recently bought brand new vehicles for office use . uba capital only went for toyota and honda and bought less of toyota than honda at the ratio of 4 : 6 . if 40 % of the toyota bought and 60 % of the honda bought were suv \u00e3 \u00a2 \u00e2 \u201a \u00ac \u00e2 \u201e \u00a2 s . how many suv \u00e3 \u00a2 \u00e2 \u201a \u00ac \u00e2 \u201e \u00a2 s did uba capital buy in the aforementioned purchase ?", - "Output Program": [ - "n0 = 4.0\nn1 = 6.0\nn2 = 40.0\nn3 = 60.0\nt0 = n0 * n1\nt1 = t0 + t0\nanswer = 100.0 - t1\nprint(answer)" - ], - "Output Answer": [ - "52" - ], - "split": "train" - }, - { - "Input": "if a and b are both odd prime numbers and a < b , then how many different positive integer factors does 2 ab have ?", - "Output Program": [ - "n0 = 2.0\n\nanswer = n0 * 4.0\nprint(answer)" - ], - "Output Answer": [ - "8" - ], - "split": "train" - }, - { - "Input": "a bag contains 3 red , 2 blue and 3 green balls . if 2 ballsare picked at random , what is the probability that both are red ?", - "Output Program": [ - "import scipy\nn0 = 3.0\nn1 = 2.0\nn2 = 3.0\nn3 = 2.0\nt0 = n0 + n1\nt1 = scipy.special.comb(n0, n3)\nt2 = n2 + t0\nt3 = scipy.special.comb(t2, n3)\nanswer = t1 / t3\nprint(answer)" - ], - "Output Answer": [ - "0.10714285714285714" - ], - "split": "train" - }, - { - "Input": "in a sports club with 40 members , 20 play badminton and 18 play tennis and 5 do not play either . how many members play both badminton and tennis ?", - "Output Program": [ - "n0 = 40.0\nn1 = 20.0\nn2 = 18.0\nn3 = 5.0\nt0 = n1 + n2\nt1 = n3 + t0\nanswer = t1 - n0\nprint(answer)" - ], - "Output Answer": [ - "3" - ], - "split": "train" - }, - { - "Input": "how many multiples of 10 are there between 100 and 10000 ( both are inclusive ) ?", - "Output Program": [ - "n0 = 10.0\nn1 = 100.0\nn2 = 10000.0\nt0 = n2 - n1\nt1 = t0 / n0\nanswer = t1 + 1.0\nprint(answer)" - ], - "Output Answer": [ - "991" - ], - "split": "train" - }, - { - "Input": "a baseball team played 10 games and won 5 . what is the ratio of the number of games played to the number of losses ?", - "Output Program": [ - "n0 = 10.0\nn1 = 5.0\n\nanswer = n0 / n1\nprint(answer)" - ], - "Output Answer": [ - "2" - ], - "split": "train" - }, - { - "Input": "q - 1 ) of the 84 parents who attended a meeting at a school , 25 volunteered to supervise children during the school picnic and 11 volunteered both to supervise children during the picnic and to bring refreshments to the picnic . if the number of parents who volunteered to bring refreshments was 1.5 times the number of parents who neither volunteered to supervise children during the picnic nor volunteered to bring refreshments , how many of the parents volunteered to bring refreshments ?", - "Output Program": [ - "n0 = 1.0\nn1 = 84.0\nn2 = 25.0\nn3 = 11.0\nn4 = 1.5\nt0 = n4 + 1.0\nt1 = n1 - n2\nt2 = n4 * t1\nt3 = t2 - n3\nt4 = t3 / t0\nanswer = n3 + t4\nprint(answer)" - ], - "Output Answer": [ - "42" - ], - "split": "train" - }, - { - "Input": "the ratio between the sale price and the cost price of an article is 6 : 2 . what is the ratio between the profit and the cost price of that article ?", - "Output Program": [ - "n0 = 6.0\nn1 = 2.0\nt0 = n0 - n1\nanswer = t0 / n1\nprint(answer)" - ], - "Output Answer": [ - "2" - ], - "split": "train" - }, - { - "Input": "in a class of 94 students 41 are taking french , 22 are taking german . of the students taking french or german , 9 are taking both courses . how many students are not enrolled in either course ?", - "Output Program": [ - "n0 = 94.0\nn1 = 41.0\nn2 = 22.0\nn3 = 9.0\nt0 = n1 + n2\nt1 = t0 - n3\nanswer = n0 - t1\nprint(answer)" - ], - "Output Answer": [ - "40" - ], - "split": "train" - }, - { - "Input": "at a certain zoo , the ratio of sea lions to penguins is 4 to 11 . if there are 84 more penguins than sea lions at the zoo , how many sea lions are there ?", - "Output Program": [ - "n0 = 4.0\nn1 = 11.0\nn2 = 84.0\nt0 = n1 - n0\nt1 = t0 / n0\nanswer = n2 / t1\nprint(answer)" - ], - "Output Answer": [ - "48" - ], - "split": "train" - }, - { - "Input": "two family reunions are happening at the same hotel , the dates reunion and the hall reunion . all 50 guests at the hotel attend at least one of the reunions . if 50 people attend the dates reunion and 60 people attend the hall reunion , how many people attend both reunions ?", - "Output Program": [ - "n0 = 50.0\nn1 = 50.0\nn2 = 60.0\nt0 = n0 + n2\nanswer = t0 - n0\nprint(answer)" - ], - "Output Answer": [ - "60" - ], - "split": "train" - }, - { - "Input": "a certain store sold pens for $ 0.35 each and pencils for $ 0.25 each . if a customer purchased both pens and pencils from the store for a total of $ 3.00 , what total number of pens and pencils did the customer purchase ?", - "Output Program": [ - "n0 = 0.35\nn1 = 0.25\nn2 = 3.0\nt0 = n0 + n1\nt1 = n2 / t0\nanswer = t1 * 2.0\nprint(answer)" - ], - "Output Answer": [ - "10" - ], - "split": "train" - }, - { - "Input": "sachin is younger than rahul by 18 years . if the ratio of their ages is 7 : 9 , find the age of sachin", - "Output Program": [ - "n0 = 18.0\nn1 = 7.0\nn2 = 9.0\nt0 = n2 - n1\nt1 = n0 / t0\nanswer = n1 * t1\nprint(answer)" - ], - "Output Answer": [ - "63" - ], - "split": "train" - }, - { - "Input": "in a corporation , 50 percent of the male employees and 40 percent of the female employees are at least 35 years old . if 42 percent of all the employees are at least 35 years old , what fraction of the employees in the corporation are females ?", - "Output Program": [ - "n0 = 50.0\nn1 = 40.0\nn2 = 35.0\nn3 = 42.0\nn4 = 35.0\nt0 = n0 - n3\nt1 = n0 - n1\nanswer = t0 / t1\nprint(answer)" - ], - "Output Answer": [ - "0.8" - ], - "split": "train" - }, - { - "Input": "in a class there are 55 pupil , out of them 10 are in debate only and 18 in singing only . then how many in both ?", - "Output Program": [ - "n0 = 55.0\nn1 = 10.0\nn2 = 18.0\nt0 = n0 - n2\nt1 = t0 - n1\nanswer = t1 - n1\nprint(answer)" - ], - "Output Answer": [ - "17" - ], - "split": "train" - }, - { - "Input": "if 70 percent of a class answered the first question on a certain test correctly , 55 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?", - "Output Program": [ - "n0 = 70.0\nn1 = 55.0\nn2 = 20.0\nt0 = n0 + n1\nt1 = n2 + t0\nanswer = t1 - 100.0\nprint(answer)" - ], - "Output Answer": [ - "45" - ], - "split": "train" - }, - { - "Input": "a company conducted a survey about its two brands , a and b . x percent of respondents liked product a , ( x \u2013 20 ) percent liked product b , 23 percent liked both products , and 23 percent liked neither product . what is the minimum number q of people surveyed by the company ?", - "Output Program": [ - "n0 = 20.0\nn1 = 23.0\nn2 = 23.0\nt0 = 100.0 - n1\nt1 = n1 + t0\nt2 = n0 + t1\nt3 = t2 / 2.0\nt4 = t3 - n0\nanswer = t3 + t4\nprint(answer)" - ], - "Output Answer": [ - "100" - ], - "split": "train" - }, - { - "Input": "on multiplying a number a by 153 , the result obtained was 102325 . however , it is found that both the 2 ' s are wrong . find the correct result .", - "Output Program": [ - "n0 = 153.0\nn1 = 102325.0\nn2 = 2.0\nt0 = 3.0 + 4.0\nt1 = 10.0 * 100.0\nt2 = t0 * 10.0\nt3 = t0 * t1\nt4 = t2 + t3\nanswer = n1 + t4\nprint(answer)" - ], - "Output Answer": [ - "109395" - ], - "split": "train" - }, - { - "Input": "at a certain restaurant , the ratio of the number of cooks to the number of waiters is 3 to 10 . when 12 more waiters are hired , the ratio of the number of cooks to the number of waiters changes to 3 to 14 . how many cooks does the restaurant have ?", - "Output Program": [ - "n0 = 3.0\nn1 = 10.0\nn2 = 12.0\nn3 = 3.0\nn4 = 14.0\nt0 = n2 / 4.0\nanswer = t0 * t0\nprint(answer)" - ], - "Output Answer": [ - "9" - ], - "split": "train" - }, - { - "Input": "an amount of money is to be distributed among faruk , vasim and ranjith in the ratio 3 : 5 : 6 . if vasims share is rs . 1500 , what is the difference between faruk ' s and ranjith ' s shares ?", - "Output Program": [ - "n0 = 3.0\nn1 = 5.0\nn2 = 6.0\nn3 = 1500.0\nt0 = n3 / n1\nt1 = n2 - n0\nanswer = t0 * t1\nprint(answer)" - ], - "Output Answer": [ - "900" - ], - "split": "train" - }, - { - "Input": "if x and y are sets of integers , x # y denotes the set of integers that belong to set x or set y , but not both . if x consists of 12 integers , y consists of 18 integers , and 6 of the integers are in both x and y , then x # y consists of how many integers ?", - "Output Program": [ - "n0 = 12.0\nn1 = 18.0\nn2 = 6.0\nt0 = n1 - n2\nt1 = n0 - n2\nanswer = t0 + t1\nprint(answer)" - ], - "Output Answer": [ - "18" - ], - "split": "train" - }, - { - "Input": "at a certain company , two - thirds of the employees had cell phones and two - fifths had pagers . if one - third of the employees had neither cell phones nor pagers then what fraction of the employees had both cell phones and pagers ?", - "Output Program": [ - "t0 = 1.0 + 4.0\nt1 = 1.0 / 3.0\nt2 = 2.0 / t0\nt3 = 1.0 - t1\nt4 = t2 + t3\nanswer = t4 - t3\nprint(answer)" - ], - "Output Answer": [ - "0.40000000000000013" - ], - "split": "train" - }, - { - "Input": "a bag contains 4 red , 4 blue and 2 green balls . if 2 ballsare picked at random , what is the probability that both are red ?", - "Output Program": [ - "import scipy\nn0 = 4.0\nn1 = 4.0\nn2 = 2.0\nn3 = 2.0\nt0 = n0 + n1\nt1 = scipy.special.comb(n0, n3)\nt2 = n2 + t0\nt3 = scipy.special.comb(t2, n3)\nanswer = t1 / t3\nprint(answer)" - ], - "Output Answer": [ - "0.13333333333333333" - ], - "split": "train" - }, - { - "Input": "log 3 n + log 15 n what is 3 digit number n that will be whole number", - "Output Program": [ - "n0 = 3.0\nn1 = 15.0\nn2 = 3.0\n\nanswer = n1**min(n0, 5)\nprint(answer)" - ], - "Output Answer": [ - "3375" - ], - "split": "train" - }, - { - "Input": "in a class , 30 students pass in english and 20 students in math , while some students among these pass in both . how many more students do only english as compared to those doing only maths ?", - "Output Program": [ - "n0 = 30.0\nn1 = 20.0\n\nanswer = n0 - n1\nprint(answer)" - ], - "Output Answer": [ - "10" - ], - "split": "train" - }, - { - "Input": "log 3 n + log 6 n what is 3 digit number n that will be whole number", - "Output Program": [ - "n0 = 3.0\nn1 = 6.0\nn2 = 3.0\n\nanswer = n1**min(n0, 5)\nprint(answer)" - ], - "Output Answer": [ - "216" - ], - "split": "train" - }, - { - "Input": "in a class of 79 students 41 are taking french , 22 are taking german . of the students taking french or german , 9 are taking both courses . how many students are not enrolled in either course ?", - "Output Program": [ - "n0 = 79.0\nn1 = 41.0\nn2 = 22.0\nn3 = 9.0\nt0 = n1 + n2\nt1 = t0 - n3\nanswer = n0 - t1\nprint(answer)" - ], - "Output Answer": [ - "25" - ], - "split": "train" - }, - { - "Input": "in a class , 7 students like to play basketball and 8 like to play cricket . 5 students like to play on both basketball and cricket . how many students like to play basketball or cricket or both ?", - "Output Program": [ - "n0 = 7.0\nn1 = 8.0\nn2 = 5.0\nt0 = n0 + n1\nanswer = t0 - n2\nprint(answer)" - ], - "Output Answer": [ - "10" - ], - "split": "train" - }, - { - "Input": "find the fraction which has the same ratio to 1 / 2 that 2 / 5 has to 3 / 7", - "Output Program": [ - "n0 = 1.0\nn1 = 2.0\nn2 = 2.0\nn3 = 5.0\nn4 = 3.0\nn5 = 7.0\nt0 = n2 / n3\nt1 = n4 / n5\nt2 = n0 / n1\nt3 = t0 / t1\nanswer = t3 * t2\nprint(answer)" - ], - "Output Answer": [ - "0.46666666666666673" - ], - "split": "train" - }, - { - "Input": "a hen leaps 6 leaps for every 8 leaps of a duck , but 4 leaps of the duck are equal to 3 leaps of the hen . what is the ratio of the speed of the hen to that of the duck ?", - "Output Program": [ - "n0 = 6.0\nn1 = 8.0\nn2 = 4.0\nn3 = 3.0\nt0 = n0 / n1\nt1 = n3 / n2\nanswer = t0 / t1\nprint(answer)" - ], - "Output Answer": [ - "1" - ], - "split": "train" - }, - { - "Input": "a company conducted a survey about its two brands , a and b . x percent of respondents liked product a , ( x \u2013 20 ) percent liked product b , 23 percent liked both products , and 23 percent liked neither product . what is the minimum number d of people surveyed by the company ?", - "Output Program": [ - "n0 = 20.0\nn1 = 23.0\nn2 = 23.0\nt0 = 100.0 - n1\nt1 = n1 + t0\nt2 = n0 + t1\nt3 = t2 / 2.0\nt4 = t3 - n0\nanswer = t3 + t4\nprint(answer)" - ], - "Output Answer": [ - "100" - ], - "split": "train" - }, - { - "Input": "bhatia , ashtikar and singh begin to play with rs 70 each . at the end the ratio of the amounts left with ashtikar and singh is 1 : 2 and of those with singh and bhatia is 4 : 1 . what is singh ' s gain ( in rs ) ?", - "Output Program": [ - "n0 = 70.0\nn1 = 1.0\nn2 = 2.0\nn3 = 4.0\nn4 = 1.0\nt0 = n1 + n3\nt1 = n0 * 3.0\nt2 = n2 + t0\nt3 = n3 * t1\nt4 = t3 / t2\nanswer = t4 - n0\nprint(answer)" - ], - "Output Answer": [ - "50" - ], - "split": "train" - }, - { - "Input": "if a student loses 5 kilograms , he will weigh twice as much as his sister . together they now weigh 110 kilograms . what is the student ' s present weight in kilograms ?", - "Output Program": [ - "n0 = 5.0\nn1 = 110.0\nt0 = n1 - n0\nt1 = t0 / 3.0\nanswer = n1 - t1\nprint(answer)" - ], - "Output Answer": [ - "75" - ], - "split": "train" - }, - { - "Input": "ashley paid 5 dollars for 1 notebook and 1 pencil . if both prices were integers , how many pencils did ashley buy if she paid 93 dollars for the pencils and for 15 notebooks ?", - "Output Program": [ - "n0 = 5.0\nn1 = 1.0\nn2 = 1.0\nn3 = 93.0\nn4 = 15.0\nt0 = n0 + n4\nanswer = t0 + 1.0\nprint(answer)" - ], - "Output Answer": [ - "21" - ], - "split": "train" - }, - { - "Input": "how many integers from 1 to 100 ( both inclusive ) have odd number of factors ?", - "Output Program": [ - "n0 = 1.0\nn1 = 100.0\n\nanswer = n1 / 10.0\nprint(answer)" - ], - "Output Answer": [ - "10" - ], - "split": "train" - }, - { - "Input": "a certain music store stocks 800 cellos and 600 violas . of these instruments , there are 70 cello - viola pairs , such that a cello and a viola were both made with wood from the same tree ( each tree can make at most one viola and one cello , so there are no pairs other than these 90 ) . if one viola and one cello are chosen at random , what is the probability that the two instruments are made with wood from the same tree ?", - "Output Program": [ - "n0 = 800.0\nn1 = 600.0\nn2 = 70.0\nn3 = 90.0\nt0 = n2 / n0\nt1 = 1.0 / n1\nanswer = t0 * t1\nprint(answer)" - ], - "Output Answer": [ - "0.00014583333333333335" - ], - "split": "train" - }, - { - "Input": "apple costs l rupees per kilogram for first 30 kgs and q rupees per kilogram for each additional kilogram . if the price of 33 kilograms is 333 and for 36 kgs of apples is 366 then the cost of first 15 kgs of apples is", - "Output Program": [ - "n0 = 30.0\nn1 = 33.0\nn2 = 333.0\nn3 = 36.0\nn4 = 366.0\nn5 = 15.0\nt0 = n4 - n2\nt1 = n3 - n1\nt2 = n1 - n0\nt3 = t0 / t1\nt4 = t3 * t2\nt5 = n2 - t4\nt6 = t5 / n0\nanswer = n5 * t6\nprint(answer)" - ], - "Output Answer": [ - "150" - ], - "split": "train" - }, - { - "Input": "a group of people participate in some curriculum , 35 of them practice yoga , 20 study cooking , 15 study weaving , 7 of them study cooking only , 5 of them study both the cooking and yoga , 3 of them participate all curriculums . how many people study both cooking and weaving ?", - "Output Program": [ - "n0 = 35.0\nn1 = 20.0\nn2 = 15.0\nn3 = 7.0\nn4 = 5.0\nn5 = 3.0\nt0 = n1 - n4\nt1 = t0 - n5\nanswer = t1 - n3\nprint(answer)" - ], - "Output Answer": [ - "5" - ], - "split": "train" - }, - { - "Input": "a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 9 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many liter q of liquid a was contained by the can initially ?", - "Output Program": [ - "n0 = 7.0\nn1 = 5.0\nn2 = 9.0\nn3 = 7.0\nn4 = 9.0\nt0 = n0 + n2\nt1 = n0 + n1\nt2 = n0 * n2\nt3 = n0 * n1\nt4 = n1 / t1\nt5 = t2 - t3\nt6 = n2 * t4\nt7 = n2 - t6\nt8 = t0 * t7\nt9 = t8 / t5\nanswer = n0 * t9\nprint(answer)" - ], - "Output Answer": [ - "21" - ], - "split": "train" - }, - { - "Input": "a farmer used 1,034 acres of land for beans , wheat , and corn in the ratio of 5 : 2 : 4 , respectively . how many r acres were used for corn ?", - "Output Program": [ - "n0 = 1034.0\nn1 = 5.0\nn2 = 2.0\nn3 = 4.0\nt0 = n1 + n2\nt1 = 10.0 * 3.0\nt2 = 1.0 * 1000.0\nt3 = n3 + t1\nt4 = n3 + t0\nt5 = t3 + t2\nt6 = t5 / t4\nanswer = n3 * t6\nprint(answer)" - ], - "Output Answer": [ - "376" - ], - "split": "train" - }, - { - "Input": "in a group of 25 , 13 can speak latin , 15 can speak french , and 6 do n ' t speak either . how many of these speak both latin and french ?", - "Output Program": [ - "n0 = 25.0\nn1 = 13.0\nn2 = 15.0\nn3 = 6.0\nt0 = n1 + n2\nt1 = n3 + t0\nanswer = t1 - n0\nprint(answer)" - ], - "Output Answer": [ - "9" - ], - "split": "train" - }, - { - "Input": "24 oz of juice p and 25 oz of juice v are mixed to make smothies m and y . the ratio of p to v in smothie m is 4 is to 1 and that in y is 1 is to 5 . how many ounces of juice p are contained in the smothie m ?", - "Output Program": [ - "n0 = 24.0\nn1 = 25.0\nn2 = 4.0\nn3 = 1.0\nn4 = 1.0\nn5 = 5.0\nt0 = n0 * n5\nt1 = n2 * n5\nt2 = t0 - n1\nt3 = t1 - n3\nt4 = t2 / t3\nanswer = n2 * t4\nprint(answer)" - ], - "Output Answer": [ - "20" - ], - "split": "train" - }, - { - "Input": "there are two names given johnson and jones . if one letter is picked from both simultaneously at random , then find the probability that the letter is same ?", - "Output Program": [ - "t0 = 3.0 + 4.0\nt1 = 1.0 / 5.0\nt2 = 1.0 / t0\nt3 = 2.0 / t0\nt4 = t2 * t1\nt5 = t3 * t1\nt6 = t4 + t5\nanswer = t6 * 2.0\nprint(answer)" - ], - "Output Answer": [ - "0.17142857142857143" - ], - "split": "train" - }, - { - "Input": "a firm is comprised of partners and associates in a ratio of 2 : 63 . if 45 more associates were hired , the ratio of partners to associates would be 1 : 34 . how many partners are currently in the firm ?", - "Output Program": [ - "n0 = 2.0\nn1 = 63.0\nn2 = 45.0\nn3 = 1.0\nn4 = 34.0\nt0 = n0 * n4\nt1 = t0 - n1\nt2 = n2 / t1\nanswer = n0 * t2\nprint(answer)" - ], - "Output Answer": [ - "18" - ], - "split": "train" - }, - { - "Input": "how many trailing zeroes does 53 ! + 54 ! have ?", - "Output Program": [ - "n0 = 53.0\nn1 = 54.0\nt0 = n1 + 1.0\nt1 = 1.0 + 4.0\nt2 = t0 / t1\nanswer = t2 + 2.0\nprint(answer)" - ], - "Output Answer": [ - "13" - ], - "split": "train" - }, - { - "Input": "in a class , 12 students like to play basketball and 8 like to play cricket . 3 students like to play on both basketball and cricket . how many students like to play basketball or cricket or both ?", - "Output Program": [ - "n0 = 12.0\nn1 = 8.0\nn2 = 3.0\nt0 = n0 + n1\nanswer = t0 - n2\nprint(answer)" - ], - "Output Answer": [ - "17" - ], - "split": "train" - }, - { - "Input": "the ratio between the number of sheep and the number of horses at the stewar farm is 6 to 7 . if each of horse is fed 230 ounces of horse food per day and the farm needs a total 12880 ounces of horse food per day . what is number sheep in the form ? ?", - "Output Program": [ - "n0 = 6.0\nn1 = 7.0\nn2 = 230.0\nn3 = 12880.0\nt0 = n3 / n2\nt1 = t0 / n1\nanswer = n0 * t1\nprint(answer)" - ], - "Output Answer": [ - "48" - ], - "split": "train" - }, - { - "Input": "how many zeros does 500 ! end with ?", - "Output Program": [ - "n0 = 500.0\nt0 = 1.0 + 4.0\nt1 = n0 / t0\nt2 = t0**min(2.0, 5)\nt3 = t0**min(3.0, 5)\nt4 = n0 - t0\nt5 = t4 / t2\nt6 = t4 / t3\nt7 = t1 + t5\nanswer = t7 + t6\nprint(answer)" - ], - "Output Answer": [ - "123.75999999999999" - ], - "split": "train" - }, - { - "Input": "a dog breeder currently has 9 breeding dogs . 6 of the dogs have exactly 1 littermate , and 3 of the dogs have exactly 2 littermates . if 2 dogs are selected at random , what is the probability w that both selected dogs are not littermates ?", - "Output Program": [ - "n0 = 9.0\nn1 = 6.0\nn2 = 1.0\nn3 = 3.0\nn4 = 2.0\nn5 = 2.0\n\nanswer = 5.0 / n1\nprint(answer)" - ], - "Output Answer": [ - "0.8333333333333334" - ], - "split": "train" - }, - { - "Input": "sandy is younger than molly by 18 years . if the ratio of their ages is 7 : 9 , how old is sandy ?", - "Output Program": [ - "n0 = 18.0\nn1 = 7.0\nn2 = 9.0\nt0 = n2 - n1\nt1 = n1 / t0\nanswer = n0 * t1\nprint(answer)" - ], - "Output Answer": [ - "63" - ], - "split": "train" - }, - { - "Input": "one bacterium splits into 8 bacteria of the next generation . but due to environment , only 50 % of one generation can produced the next generation . if the seventh generation number is 4096 million , what is the number in first generation ?", - "Output Program": [ - "n0 = 8.0\nn1 = 50.0\nn2 = 4096.0\nt0 = n0 / 2.0\nt1 = n0 - 2.0\nt2 = t0**min(t1, 5)\nanswer = t2 / t2\nprint(answer)" - ], - "Output Answer": [ - "1" - ], - "split": "train" - }, - { - "Input": "if m = 3 ^ n , what is the greatest value of n for which m is a factor of 25 !", - "Output Program": [ - "import math\nn0 = 3.0\nn1 = 25.0\nt0 = n1 / n0\nt1 = n0**min(2.0, 5)\nt2 = n1 / t1\nt3 = math.floor(t0)\nt4 = math.floor(t2)\nanswer = t3 + t4\nprint(answer)" - ], - "Output Answer": [ - "10" - ], - "split": "train" - }, - { - "Input": "the ratio of money with ram and gopal is 7 : 17 and that with gopal and krishan is 7 : 17 . if ram has rs . 539 , krishan has ?", - "Output Program": [ - "n0 = 7.0\nn1 = 17.0\nn2 = 7.0\nn3 = 17.0\nn4 = 539.0\nt0 = n4 / n0\nt1 = n1 * t0\nt2 = t1 / n0\nanswer = n1 * t2\nprint(answer)" - ], - "Output Answer": [ - "3179" - ], - "split": "train" - }, - { - "Input": "the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 17 . the larger of the two numbers is :", - "Output Program": [ - "n0 = 23.0\nn1 = 13.0\nn2 = 17.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "391" - ], - "split": "train" - }, - { - "Input": "the h . c . f . of two numbers is 40 and the other two factors of their l . c . m . are 11 and 15 . the larger of the two numbers is :", - "Output Program": [ - "n0 = 40.0\nn1 = 11.0\nn2 = 15.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "600" - ], - "split": "train" - }, - { - "Input": "a bag contains 5 red , 6 blue and 2 green balls . if 2 ballsare picked at random , what is the probability that both are red ?", - "Output Program": [ - "import scipy\nn0 = 5.0\nn1 = 6.0\nn2 = 2.0\nn3 = 2.0\nt0 = n0 + n1\nt1 = scipy.special.comb(n0, n3)\nt2 = n2 + t0\nt3 = scipy.special.comb(t2, n3)\nanswer = t1 / t3\nprint(answer)" - ], - "Output Answer": [ - "0.1282051282051282" - ], - "split": "train" - }, - { - "Input": "a family has two children . find the probability that both the children are girls given that at least one of them is a girl ?", - "Output Program": [ - "t0 = 0.25 * 3.0\nanswer = 0.25 / t0\nprint(answer)" - ], - "Output Answer": [ - "0.3333333333333333" - ], - "split": "train" - }, - { - "Input": "a certain hobby shop sold model cars for $ 5.00 each and model trains for $ 8.00 each . if a customer purchased both cars and trains from the store for a total of $ 31.00 , what total number of cars and trains did the customer purchase ?", - "Output Program": [ - "n0 = 5.0\nn1 = 8.0\nn2 = 31.0\nt0 = n0 * 3.0\nt1 = t0 / n0\nt2 = n2 - t0\nt3 = t2 / n1\nanswer = t3 + t1\nprint(answer)" - ], - "Output Answer": [ - "5" - ], - "split": "train" - }, - { - "Input": "mrs . evans gave a test to her freshmen economics class , which has 30 students enrolled and 25 of them answered question 1 correctly . if 22 answered question 2 correctly and 5 did not take the test then how many answered both questions correctly ?", - "Output Program": [ - "n0 = 30.0\nn1 = 25.0\nn2 = 1.0\nn3 = 22.0\nn4 = 2.0\nn5 = 5.0\nt0 = n1 + n3\nt1 = n5 + t0\nanswer = t1 - n0\nprint(answer)" - ], - "Output Answer": [ - "22" - ], - "split": "train" - }, - { - "Input": "there are 200 doctors and nurses at a hospital . if the ratio of doctors to nurses is 4 to 6 , how many nurses are at the hospital ?", - "Output Program": [ - "n0 = 200.0\nn1 = 4.0\nn2 = 6.0\nt0 = n1 + n2\nt1 = n0 / t0\nanswer = n2 * t1\nprint(answer)" - ], - "Output Answer": [ - "120" - ], - "split": "train" - }, - { - "Input": "the ratio of three numbers is 1 : 2 : 4 and the sum of their squares is 1701 . the sum of the numbers is ?", - "Output Program": [ - "import math\nn0 = 1.0\nn1 = 2.0\nn2 = 4.0\nn3 = 1701.0\nt0 = n0**min(n1, 5)\nt1 = n1**min(n1, 5)\nt2 = n2**min(n1, 5)\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n3 / t4\nanswer = math.sqrt(max(0, t5))\nprint(answer)" - ], - "Output Answer": [ - "9" - ], - "split": "train" - }, - { - "Input": "in a group of 400 players some are outdoor players , some are indoor players and some plays both . 350 plays outdoors and 110 plays indoor . how many plays indoor as well as outdoor games .", - "Output Program": [ - "n0 = 400.0\nn1 = 350.0\nn2 = 110.0\nt0 = n1 + n2\nanswer = t0 - n0\nprint(answer)" - ], - "Output Answer": [ - "60" - ], - "split": "train" - }, - { - "Input": "if 75 percent of a class answered the first question on a certain test correctly , 25 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?", - "Output Program": [ - "n0 = 75.0\nn1 = 25.0\nn2 = 20.0\nt0 = n0 + n1\nt1 = n2 + t0\nanswer = t1 - 100.0\nprint(answer)" - ], - "Output Answer": [ - "20" - ], - "split": "train" - }, - { - "Input": "each man in a gang of 100 investors has investments ineither equities or securities or both . exactly 2525 of the investors in equities haveinvestments in securities , exactly 4040 of the investorsin securities have investments inequities . how many have investmentsin equities ?", - "Output Program": [ - "n0 = 100.0\nn1 = 2525.0\nn2 = 4040.0\nt0 = n0 + 10.0\nt1 = 2.0 + 3.0\nt2 = 10.0 * 4.0\nt3 = t2 / 100.0\nt4 = t1 * t1\nt5 = t4 / 100.0\nt6 = t3 / t5\nt7 = t6 + 1.0\nt8 = t7 - t3\nt9 = t0 / t8\nanswer = t9 * t6\nprint(answer)" - ], - "Output Answer": [ - "80" - ], - "split": "train" - }, - { - "Input": "at a certain zoo , the ratio of lions to penguins is 3 to 11 . if there are 82 more penguins than lions at the zoo , how many lions are there ?", - "Output Program": [ - "import math\nn0 = 3.0\nn1 = 11.0\nn2 = 82.0\nt0 = n1 - n0\nt1 = n2 / t0\nt2 = n0 * t1\nanswer = math.floor(t2)\nprint(answer)" - ], - "Output Answer": [ - "30" - ], - "split": "train" - }, - { - "Input": "out of 420 students of a school , 325 play football , 175 play cricket and 50 neither play football nor cricket . how many students play both football and cricket ?", - "Output Program": [ - "n0 = 420.0\nn1 = 325.0\nn2 = 175.0\nn3 = 50.0\nt0 = n1 + n2\nt1 = n0 - n3\nanswer = t0 - t1\nprint(answer)" - ], - "Output Answer": [ - "130" - ], - "split": "train" - }, - { - "Input": "if the ratio of a to b is 2 to 3 and the ratio of b to c is 1 to 5 , what is the ratio of a to c ?", - "Output Program": [ - "n0 = 2.0\nn1 = 3.0\nn2 = 1.0\nn3 = 5.0\nt0 = n0 * n2\nt1 = n1 * n3\nanswer = t0 / t1\nprint(answer)" - ], - "Output Answer": [ - "0.13333333333333333" - ], - "split": "train" - }, - { - "Input": "if 75 % of a boys answered the first question on a certain test correctly , 55 % answered the second question on the test correctly , and 20 % answered neither of the questions correctly , what % answered both correctly ?", - "Output Program": [ - "n0 = 75.0\nn1 = 55.0\nn2 = 20.0\nt0 = n0 + n1\nt1 = n2 + t0\nanswer = t1 - 100.0\nprint(answer)" - ], - "Output Answer": [ - "50" - ], - "split": "train" - }, - { - "Input": "of the diplomats who attended a summit conference : 20 spoke latin , 32 did not speak russian and 20 % of the diplomats spoke neither latin nor russian . if 10 % of the diplomats spoke both latin and russian , then how many diplomats attended the conference ?", - "Output Program": [ - "n0 = 20.0\nn1 = 32.0\nn2 = 20.0\nn3 = 10.0\nt0 = n0 / 100.0\nt1 = n3 / 100.0\nt2 = n1 - n0\nt3 = t0 - t1\nanswer = t2 / t3\nprint(answer)" - ], - "Output Answer": [ - "120" - ], - "split": "train" - }, - { - "Input": "the ratio of flour to water to sugar in a recipe is 11 : 5 : 2 . the ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar . if the new recipe calls for 7.5 cups of water , how much sugar is required ?", - "Output Program": [ - "n0 = 11.0\nn1 = 5.0\nn2 = 2.0\nn3 = 7.5\nt0 = n3 / n1\nt1 = n2 * 4.0\nanswer = t0 * t1\nprint(answer)" - ], - "Output Answer": [ - "12" - ], - "split": "train" - }, - { - "Input": "if a student loses 5 kilograms , he will weigh twice as much as his sister . together they now weigh 104 kilograms . what is the student ' s present weight in kilograms ?", - "Output Program": [ - "n0 = 5.0\nn1 = 104.0\nt0 = n1 - n0\nt1 = t0 / 3.0\nanswer = n1 - t1\nprint(answer)" - ], - "Output Answer": [ - "71" - ], - "split": "train" - }, - { - "Input": "a group of people participate in some curriculum , 25 of them practice yoga , 18 study cooking , 10 study weaving , 4 of them study cooking only , 5 of them study both the cooking and yoga , 4 of them participate all curriculums . how many people study both cooking and weaving ?", - "Output Program": [ - "n0 = 25.0\nn1 = 18.0\nn2 = 10.0\nn3 = 4.0\nn4 = 5.0\nn5 = 4.0\nt0 = n1 - n4\nt1 = t0 - n5\nanswer = t1 - n3\nprint(answer)" - ], - "Output Answer": [ - "5" - ], - "split": "train" - }, - { - "Input": "a boy multiplied 987 by a certain number and obtained 559981 as his answer . if in the answer both 98 are wrong and other digits are correct , then the correct answer would be :", - "Output Program": [ - "n0 = 987.0\nn1 = 559981.0\nn2 = 98.0\nt0 = n1 / n0\nt1 = t0 - 4.0\nt2 = t1 - 0.33\nanswer = n0 * t2\nprint(answer)" - ], - "Output Answer": [ - "555707.2899999999" - ], - "split": "train" - }, - { - "Input": "three numbers are in the ratio of 3 : 4 : 6 and their product is 1944 . the largest of these numbers is", - "Output Program": [ - "n0 = 3.0\nn1 = 4.0\nn2 = 6.0\nn3 = 1944.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "18" - ], - "split": "train" - }, - { - "Input": "if 75 percent of a class answered the first question on a certain test correctly , 30 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?", - "Output Program": [ - "n0 = 75.0\nn1 = 30.0\nn2 = 20.0\nt0 = n0 + n1\nt1 = n2 + t0\nanswer = t1 - 100.0\nprint(answer)" - ], - "Output Answer": [ - "25" - ], - "split": "train" - }, - { - "Input": "if 85 percent of the test takers taking an old paper and pencil gmat exam answered the first question on a given math section correctly , and 80 percent of the test takers answered the second question correctly , and 5 percent of the test takers answered neither question correctly , what percent answered both correctly ?", - "Output Program": [ - "n0 = 85.0\nn1 = 80.0\nn2 = 5.0\nt0 = n0 + n1\nt1 = n2 + t0\nanswer = t1 - 100.0\nprint(answer)" - ], - "Output Answer": [ - "70" - ], - "split": "train" - }, - { - "Input": "what is the square root of 625 , divided by 5 ?", - "Output Program": [ - "import math\nn0 = 625.0\nn1 = 5.0\nt0 = math.sqrt(max(0, n0))\nanswer = t0 / n1\nprint(answer)" - ], - "Output Answer": [ - "5" - ], - "split": "train" - }, - { - "Input": "if x and y are both odd prime numbers and x < y , how many distinct positive integer factors does 2 xy have ?", - "Output Program": [ - "n0 = 2.0\nt0 = 1.0 + 1.0\nt1 = n0 * t0\nanswer = t0 * t1\nprint(answer)" - ], - "Output Answer": [ - "8" - ], - "split": "train" - }, - { - "Input": "a certain quantity of 80 % solution is replaced with 25 % solution such that the new concentration is 35 % . what is the fraction of the solution that was replaced ?", - "Output Program": [ - "n0 = 80.0\nn1 = 25.0\nn2 = 35.0\nt0 = n2 - n1\nt1 = n0 - n2\nt2 = t0 / t1\nt3 = t2 + 1.0\nanswer = 1 / t3\nprint(answer)" - ], - "Output Answer": [ - "0.8181818181818181" - ], - "split": "train" - }, - { - "Input": "in a bag , there are 2400 ball , and their colors are red , green blue . . the ratio of the balls are 15 : 13 : 17 . then how many red color balls are available in the bag ?", - "Output Program": [ - "n0 = 2400.0\nn1 = 15.0\nn2 = 13.0\nn3 = 17.0\nt0 = n1 + n2\nt1 = n3 + t0\nt2 = n3 / t1\nanswer = n0 * t2\nprint(answer)" - ], - "Output Answer": [ - "906.6666666666666" - ], - "split": "train" - }, - { - "Input": "an alloy is to contain copper and zinc in the ratio 9 : 4 . the zinc required to be melted with 24 kg of copper is ?", - "Output Program": [ - "n0 = 9.0\nn1 = 4.0\nn2 = 24.0\nt0 = n1 * n2\nanswer = t0 / n0\nprint(answer)" - ], - "Output Answer": [ - "10.666666666666666" - ], - "split": "train" - }, - { - "Input": "a marketing survey of anytown found that the ratio of trucks to sedans to motorcycles was 3 : 7 : 2 , respectively . given that there are 9,100 sedans in anytown , how many motorcycles are there ?", - "Output Program": [ - "n0 = 3.0\nn1 = 7.0\nn2 = 2.0\nn3 = 9100.0\nt0 = 3.0 * 3.0\nt1 = t0 * 1000.0\nt2 = t1 + 100.0\nt3 = t2 / n1\nanswer = n2 * t3\nprint(answer)" - ], - "Output Answer": [ - "2600" - ], - "split": "train" - }, - { - "Input": "income and expenditure of a person are in the ratio 4 : 3 . if the income of the person is rs . 20000 , then find his savings ?", - "Output Program": [ - "n0 = 4.0\nn1 = 3.0\nn2 = 20000.0\nt0 = n1 / n0\nt1 = n2 * t0\nanswer = n2 - t1\nprint(answer)" - ], - "Output Answer": [ - "5000" - ], - "split": "train" - }, - { - "Input": "a certain manufacturer of cake , muffin , and bread mixes has 100 buyers , of whom 50 purchases cake mix , 40 purchase muffin mix , and 19 purchase both cake mix and muffin mix . if a buyer is to be selected at random from the 100 buyers , what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix ?", - "Output Program": [ - "n0 = 100.0\nn1 = 50.0\nn2 = 40.0\nn3 = 19.0\nn4 = 100.0\nt0 = n1 + n2\nt1 = t0 - n3\nt2 = n0 - t1\nanswer = t2 / n0\nprint(answer)" - ], - "Output Answer": [ - "0.29" - ], - "split": "train" - }, - { - "Input": "a jar contains a mixture of two liquids acid ( nitric acid ) and base ( ammonium chloride ) in the ratio 4 : 1 . when 10 litres of the mixture is taken out and 10 litres of liquid base is poured into the jar , the ratio becomes 2 : 3 . how many litres of liquid acid was contained in the jar ?", - "Output Program": [ - "n0 = 4.0\nn1 = 1.0\nn2 = 10.0\nn3 = 10.0\nn4 = 2.0\nn5 = 3.0\nt0 = n2 + n2\nt1 = n0 + n1\nt2 = n0 * t0\nanswer = t2 / t1\nprint(answer)" - ], - "Output Answer": [ - "16" - ], - "split": "train" - }, - { - "Input": "praveen starts business with rs . 3500 and after 5 months , hari joins with praveen as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is hari \u2019 s contribution in the capital ?", - "Output Program": [ - "n0 = 3500.0\nn1 = 5.0\nn2 = 2.0\nn3 = 3.0\nt0 = n1 / 12.0\nt1 = n2 / n3\nt2 = 1.0 - t0\nt3 = n0 / t2\nanswer = t3 / t1\nprint(answer)" - ], - "Output Answer": [ - "9000.000000000002" - ], - "split": "train" - }, - { - "Input": "in a group of 250 readers who read science fiction or literacy works or both , 180 read science fiction and 88 read literacy works . how many read both science fiction and literacy works ?", - "Output Program": [ - "n0 = 250.0\nn1 = 180.0\nn2 = 88.0\nt0 = n1 + n2\nanswer = t0 - n0\nprint(answer)" - ], - "Output Answer": [ - "18" - ], - "split": "train" - }, - { - "Input": "if a positive integer n has 211 factors , then how many prime factors does n have ?", - "Output Program": [ - "n0 = 211.0\n\nanswer = n0 / n0\nprint(answer)" - ], - "Output Answer": [ - "1" - ], - "split": "train" - }, - { - "Input": "which number is a factor of 20 ?", - "Output Program": [ - "n0 = 20.0\n\nanswer = 2.0**min(2.0, 5)\nprint(answer)" - ], - "Output Answer": [ - "4" - ], - "split": "train" - }, - { - "Input": "the ratio , by volume , of bleach to detergent to water in a certain solution is 2 : 25 : 100 . the solution will be altered so that the ratio of bleach to detergent is tripled while the ratio of detergent to water is halved . if the altered solution will contain 300 liters of water , how many liters of detergent will it contain ?", - "Output Program": [ - "n0 = 2.0\nn1 = 25.0\nn2 = 100.0\nn3 = 300.0\nt0 = n3 / n2\nt1 = n1 / 2.0\nanswer = t0 * t1\nprint(answer)" - ], - "Output Answer": [ - "37.5" - ], - "split": "train" - }, - { - "Input": "income and expenditure of a person are in the ratio 5 : 4 . if the income of the person is rs . 19000 , then find his savings ?", - "Output Program": [ - "n0 = 5.0\nn1 = 4.0\nn2 = 19000.0\nt0 = n1 / n0\nt1 = n2 * t0\nanswer = n2 - t1\nprint(answer)" - ], - "Output Answer": [ - "3800" - ], - "split": "train" - }, - { - "Input": "how many multiples of 3 are there between 100 and 300 ( both are inclusive ) ?", - "Output Program": [ - "n0 = 3.0\nn1 = 100.0\nn2 = 300.0\nt0 = n2 - n1\nt1 = t0 / n0\nanswer = t1 + 1.0\nprint(answer)" - ], - "Output Answer": [ - "67.66666666666667" - ], - "split": "train" - }, - { - "Input": "a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 6 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many liter of liquid a was contained by the can initially ?", - "Output Program": [ - "n0 = 7.0\nn1 = 5.0\nn2 = 6.0\nn3 = 7.0\nn4 = 9.0\nt0 = n0 + n4\nt1 = n0 + n1\nt2 = n0 * n4\nt3 = n0 * n1\nt4 = n1 / t1\nt5 = t2 - t3\nt6 = n2 * t4\nt7 = n2 - t6\nt8 = t0 * t7\nt9 = t8 / t5\nanswer = n0 * t9\nprint(answer)" - ], - "Output Answer": [ - "14" - ], - "split": "train" - }, - { - "Input": "there are 4 red books and 4 blue books on a shelf . if 2 books are selected at random from the shelf , what is the probability that both books selected are red books ?", - "Output Program": [ - "n0 = 4.0\nn1 = 4.0\nn2 = 2.0\nt0 = n0 + n0\nt1 = n0 - 1.0\nt2 = n0 / t0\nt3 = t0 - 1.0\nt4 = t1 / t3\nanswer = t2 * t4\nprint(answer)" - ], - "Output Answer": [ - "0.21428571428571427" - ], - "split": "train" - }, - { - "Input": "in a neighborhood having 90 households , 11 did not have either a car or a bike . if 14 households had a both a car and a bike and 44 had a car , how many had bike only ?", - "Output Program": [ - "n0 = 90.0\nn1 = 11.0\nn2 = 14.0\nn3 = 44.0\nt0 = n0 - n1\nt1 = n2 + t0\nt2 = t1 - n3\nanswer = t2 - n2\nprint(answer)" - ], - "Output Answer": [ - "35" - ], - "split": "train" - }, - { - "Input": "income and expenditure of a person are in the ratio 5 : 4 . if the income of the person is rs . 20000 , then find his savings ?", - "Output Program": [ - "n0 = 5.0\nn1 = 4.0\nn2 = 20000.0\nt0 = n1 / n0\nt1 = n2 * t0\nanswer = n2 - t1\nprint(answer)" - ], - "Output Answer": [ - "4000" - ], - "split": "train" - }, - { - "Input": "sachin is younger than rahul by 8 years . if the ratio of their ages is 7 : 9 , find the age of sachin", - "Output Program": [ - "n0 = 8.0\nn1 = 7.0\nn2 = 9.0\nt0 = n2 - n1\nt1 = n0 / t0\nanswer = n1 * t1\nprint(answer)" - ], - "Output Answer": [ - "28" - ], - "split": "train" - }, - { - "Input": "the h . c . f . of two numbers is 25 and the other two factors of their l . c . m . are 14 and 16 . the larger of the two numbers is", - "Output Program": [ - "n0 = 25.0\nn1 = 14.0\nn2 = 16.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "400" - ], - "split": "train" - }, - { - "Input": "if 40 % of the 880 students at a certain college are enrolled in biology classes , how many students at the college are not enrolled in a biology class ?", - "Output Program": [ - "n0 = 40.0\nn1 = 880.0\nt0 = n1 / 100.0\nt1 = 100.0 - n0\nanswer = t0 * t1\nprint(answer)" - ], - "Output Answer": [ - "528" - ], - "split": "train" - }, - { - "Input": "ramesh , xyz and rajeev put a partnership . profit is 36000 , if ramesh and xyz ratio is 5 : 4 and xyz and rajeev 8 : 9 . find rajeev ' s share .", - "Output Program": [ - "n0 = 36000.0\nn1 = 5.0\nn2 = 4.0\nn3 = 8.0\nn4 = 9.0\nt0 = n1 * n3\nt1 = t0 / n2\nt2 = n3 + t1\nt3 = n4 + t2\nt4 = n4 / t3\nanswer = n0 * t4\nprint(answer)" - ], - "Output Answer": [ - "12000" - ], - "split": "train" - }, - { - "Input": "the probability that event b occurs is 0.4 , and the probability that events a and b both occur is 0.25 . if the probability that either event a or event b occurs is 0.6 , what is the probability that event a will occur ?", - "Output Program": [ - "n0 = 0.4\nn1 = 0.25\nn2 = 0.6\nt0 = n1 + n2\nanswer = t0 - n0\nprint(answer)" - ], - "Output Answer": [ - "0.44999999999999996" - ], - "split": "train" - }, - { - "Input": "a marketing firm determined that , of 200 households surveyed , 80 used neither brand e nor brand b soap , 60 used only brand e soap , and for every household that used both brands of soap , 3 used only brand b soap . how many of the 200 households surveyed used both brands of soap ?", - "Output Program": [ - "n0 = 200.0\nn1 = 80.0\nn2 = 60.0\nn3 = 3.0\nn4 = 200.0\nt0 = n0 - n1\nanswer = t0 / n3\nprint(answer)" - ], - "Output Answer": [ - "40" - ], - "split": "train" - }, - { - "Input": "how many odd integers from 1 to 100 ( both inclusive ) have odd number of factors ?", - "Output Program": [ - "n0 = 1.0\nn1 = 100.0\nt0 = n1 / 2.0\nt1 = t0 / 2.0\nt2 = t1 - 10.0\nanswer = t2 - 10.0\nprint(answer)" - ], - "Output Answer": [ - "5" - ], - "split": "train" - }, - { - "Input": "135 kg of an alloy a is mixed with 145 kg of alloy b . if alloy a has lead and tin in the ratio 3 : 5 and alloy b has tin and copper in the ratio 2 : 3 , then the amount of tin in the new alloy is ?", - "Output Program": [ - "n0 = 135.0\nn1 = 145.0\nn2 = 3.0\nn3 = 5.0\nn4 = 2.0\nn5 = 3.0\nt0 = n2 + n3\nt1 = n4 + n5\nt2 = n0 / t0\nt3 = n1 / t1\nt4 = n3 * t2\nt5 = n4 * t3\nanswer = t4 + t5\nprint(answer)" - ], - "Output Answer": [ - "142.375" - ], - "split": "train" - }, - { - "Input": "what is the square root of 16 , divided by 2 ?", - "Output Program": [ - "import math\nn0 = 16.0\nn1 = 2.0\nt0 = math.sqrt(max(0, n0))\nanswer = t0 / n1\nprint(answer)" - ], - "Output Answer": [ - "2" - ], - "split": "train" - }, - { - "Input": "sandy is younger than molly by 14 years . if the ratio of their ages is 7 : 9 , how old is sandy ?", - "Output Program": [ - "n0 = 14.0\nn1 = 7.0\nn2 = 9.0\nt0 = n2 - n1\nt1 = n1 / t0\nanswer = n0 * t1\nprint(answer)" - ], - "Output Answer": [ - "49" - ], - "split": "train" - }, - { - "Input": "70 students are required to paint a picture . 52 use green color and some children use red , 38 students use both the colors . how many students use red color ?", - "Output Program": [ - "n0 = 70.0\nn1 = 52.0\nn2 = 38.0\nt0 = n0 - n1\nanswer = n2 + t0\nprint(answer)" - ], - "Output Answer": [ - "56" - ], - "split": "train" - }, - { - "Input": "there are 2 available positions and 50 candidates , one half of whom are democrats and another half are republicans . if it was decided that the positions would be filled at random , then what is the probability r that the both positions will be taken by members of just one party ?", - "Output Program": [ - "n0 = 2.0\nn1 = 50.0\nt0 = n1 / n0\nt1 = n1 - 1.0\nt2 = t0 / n1\nt3 = t0 - 1.0\nt4 = t3 / t1\nt5 = t4 * t2\nanswer = n0 * t5\nprint(answer)" - ], - "Output Answer": [ - "0.4897959183673469" - ], - "split": "train" - }, - { - "Input": "if x and y are sets of integers , x # y denotes the set of integers that belong to set x or set y , but not both . if x consists of 8 integers , y consists of 18 integers , and 6 of the integers are in both x and y , then x # y consists of how many integers ?", - "Output Program": [ - "n0 = 8.0\nn1 = 18.0\nn2 = 6.0\nt0 = n1 - n2\nt1 = n0 - n2\nanswer = t0 + t1\nprint(answer)" - ], - "Output Answer": [ - "14" - ], - "split": "train" - }, - { - "Input": "if the ratio of a to b is 8 to 3 and the ratio of b to c is 1 to 5 , what is the ratio of a to c ?", - "Output Program": [ - "n0 = 8.0\nn1 = 3.0\nn2 = 1.0\nn3 = 5.0\nt0 = n0 * n2\nt1 = n1 * n3\nanswer = t0 / t1\nprint(answer)" - ], - "Output Answer": [ - "0.5333333333333333" - ], - "split": "train" - }, - { - "Input": "the monthly incomes of a and b are in the ratio 5 : 2 . b ' s monthly income is 12 % more than c ' s monthly income . if c ' s monthly income is rs . 16000 , then find the annual income of a ?", - "Output Program": [ - "n0 = 5.0\nn1 = 2.0\nn2 = 12.0\nn3 = 16000.0\nt0 = n0 / n1\nt1 = n2 / 100.0\nt2 = t1 + 1.0\nt3 = n3 * t2\nt4 = t0 * t3\nanswer = n2 * t4\nprint(answer)" - ], - "Output Answer": [ - "537600" - ], - "split": "train" - }, - { - "Input": "in a sports club with 30 members , 17 play badminton and 21 play tennis and 2 do not play either . how many members play both badminton and tennis ?", - "Output Program": [ - "n0 = 30.0\nn1 = 17.0\nn2 = 21.0\nn3 = 2.0\nt0 = n1 + n2\nt1 = n3 + t0\nanswer = t1 - n0\nprint(answer)" - ], - "Output Answer": [ - "10" - ], - "split": "train" - }, - { - "Input": "a person want to give his money of $ 12000 to his 5 children a , b , c , d , e in the ratio 2 : 4 : 3 : 1 : 5 . what is the d + e share ?", - "Output Program": [ - "n0 = 12000.0\nn1 = 5.0\nn2 = 2.0\nn3 = 4.0\nn4 = 3.0\nn5 = 1.0\nn6 = 5.0\nt0 = n1 + n2\nt1 = n4 + t0\nt2 = n3 / t1\nanswer = n0 * t2\nprint(answer)" - ], - "Output Answer": [ - "4800" - ], - "split": "train" - }, - { - "Input": "the ratio , by volume , of bleach to detergent to water in a certain solution is 2 : 40 : 100 . the solution will be altered so that the ratio of bleach to detergent is tripled while the ratio of detergent to water is halved . if the altered solution will contain 200 liters of water , how many liters of detergent will it contain ?", - "Output Program": [ - "n0 = 2.0\nn1 = 40.0\nn2 = 100.0\nn3 = 200.0\nt0 = n3 / n2\nt1 = n1 / 2.0\nanswer = t0 * t1\nprint(answer)" - ], - "Output Answer": [ - "40" - ], - "split": "train" - }, - { - "Input": "solution a is made up of alcohol and water mixed in the ratio of 21 : 4 by volume ; solution b is made up of alcohol and water mixed in the ratio of 2 : 3 by volume . if solution a and solution b are mixed in the ratio of 5 : 6 by volume , what percent of the resultant mixture is alcohol ?", - "Output Program": [ - "n0 = 21.0\nn1 = 4.0\nn2 = 2.0\nn3 = 3.0\nn4 = 5.0\nn5 = 6.0\nt0 = n0 + n1\nt1 = n4 + n5\nt2 = n2 + n3\nt3 = n0 / t0\nt4 = n4 / t1\nt5 = n2 / t2\nt6 = n5 / t1\nt7 = t3 * t4\nt8 = t5 * t6\nt9 = t7 + t8\nanswer = t9 * 100.0\nprint(answer)" - ], - "Output Answer": [ - "60" - ], - "split": "train" - }, - { - "Input": "if 47.5 % of the 880 students at a certain college are enrolled in biology classes , how many students at the college are not enrolled in a biology class ?", - "Output Program": [ - "n0 = 47.5\nn1 = 880.0\nt0 = n1 / 100.0\nt1 = 100.0 - n0\nanswer = t0 * t1\nprint(answer)" - ], - "Output Answer": [ - "462.00000000000006" - ], - "split": "train" - }, - { - "Input": "the ratio of the incomes of uma and bala is 4 : 3 and the ratio of their expenditure is 3 : 2 . if at the end of the year , each saves $ 5000 then the income of uma is ?", - "Output Program": [ - "n0 = 4.0\nn1 = 3.0\nn2 = 3.0\nn3 = 2.0\nn4 = 5000.0\n\nanswer = n0 * n4\nprint(answer)" - ], - "Output Answer": [ - "20000" - ], - "split": "train" - }, - { - "Input": "a bag contains 12 red marbles . if someone were to remove 2 marbles from the bag , one at a time , and replace the first marble after it was removed , the probability that neither marble would be red is 9 / 16 . how many marbles are in the bag ?", - "Output Program": [ - "import math\nn0 = 12.0\nn1 = 2.0\nn2 = 9.0\nn3 = 16.0\nt0 = n2 / n3\nt1 = math.sqrt(max(0, t0))\nt2 = 1.0 - t1\nanswer = n0 / t2\nprint(answer)" - ], - "Output Answer": [ - "48" - ], - "split": "train" - }, - { - "Input": "a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 9 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many liter w of liquid a was contained by the can initially ?", - "Output Program": [ - "n0 = 7.0\nn1 = 5.0\nn2 = 9.0\nn3 = 7.0\nn4 = 9.0\nt0 = n0 + n2\nt1 = n0 + n1\nt2 = n0 * n2\nt3 = n0 * n1\nt4 = n1 / t1\nt5 = t2 - t3\nt6 = n2 * t4\nt7 = n2 - t6\nt8 = t0 * t7\nt9 = t8 / t5\nanswer = n0 * t9\nprint(answer)" - ], - "Output Answer": [ - "21" - ], - "split": "train" - }, - { - "Input": "income and expenditure of a person are in the ratio 7 : 6 . if the income of the person is rs . 21000 , then find his savings ?", - "Output Program": [ - "n0 = 7.0\nn1 = 6.0\nn2 = 21000.0\nt0 = n1 / n0\nt1 = n2 * t0\nanswer = n2 - t1\nprint(answer)" - ], - "Output Answer": [ - "3000" - ], - "split": "train" - }, - { - "Input": "the weights of one liter vegetable ghee packet of two brands \u2018 a \u2019 and \u2018 b \u2019 are 900 gm and 700 gm respectively . if they are mixed in the ratio of 3 : 2 by volumes to form a mixture of 4 liters , what is the weight ( in kg ) of the mixture ?", - "Output Program": [ - "n0 = 900.0\nn1 = 700.0\nn2 = 3.0\nn3 = 2.0\nn4 = 4.0\nt0 = n2 + n3\nt1 = n0 * n2\nt2 = n1 * n3\nt3 = t1 + t2\nt4 = n4 * t3\nt5 = t4 / t0\nanswer = t5 / 1000.0\nprint(answer)" - ], - "Output Answer": [ - "3.28" - ], - "split": "train" - }, - { - "Input": "there are 190 items that are members of set u . of these items , 49 are members of set b , 59 are not members of either of set a or set b , and 23 are members of both sets a and b . how many of the members of set u are members of set a ?", - "Output Program": [ - "n0 = 190.0\nn1 = 49.0\nn2 = 59.0\nn3 = 23.0\nt0 = n0 - n2\nt1 = n3 + t0\nanswer = t1 - n1\nprint(answer)" - ], - "Output Answer": [ - "105" - ], - "split": "train" - }, - { - "Input": "a certain music store stocks 800 cellos and 600 violas . of these instruments , there are 100 cello - viola pairs , such that a cello and a viola were both made with wood from the same tree ( each tree can make at most one viola and one cello , so there are no pairs other than these 90 ) . if one viola and one cello are chosen at random , what is the probability that the two instruments are made with wood from the same tree ?", - "Output Program": [ - "n0 = 800.0\nn1 = 600.0\nn2 = 100.0\nn3 = 90.0\nt0 = n2 / n0\nt1 = 1.0 / n1\nanswer = t0 * t1\nprint(answer)" - ], - "Output Answer": [ - "0.00020833333333333335" - ], - "split": "train" - }, - { - "Input": "how many numbers up to 200 are divisible by 2 and 3 both ?", - "Output Program": [ - "import math\nn0 = 200.0\nn1 = 2.0\nn2 = 3.0\nt0 = n1 * n2\nt1 = n0 / t0\nanswer = math.floor(t1)\nprint(answer)" - ], - "Output Answer": [ - "33" - ], - "split": "train" - }, - { - "Input": "on a certain farm the ratio of horses to cows is 5 : 1 . if the farm were to sell 15 horses and buy 15 cows , the ratio of horses to cows would then be 17 : 7 . after the transaction , how many more horses than cows would the farm own ?", - "Output Program": [ - "n0 = 5.0\nn1 = 1.0\nn2 = 15.0\nn3 = 15.0\nn4 = 17.0\nn5 = 7.0\nt0 = n2 * n4\nt1 = n2 * n5\nt2 = n0 * n5\nt3 = t0 + t1\nt4 = t2 - n4\nt5 = t3 / t4\nt6 = n2 + t5\nt7 = n0 * t5\nt8 = t7 - n2\nanswer = t8 - t6\nprint(answer)" - ], - "Output Answer": [ - "50" - ], - "split": "train" - }, - { - "Input": "a can contains a mixture of two liquids a and b in the ratio 7 : 5 . when 9 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many litres of liquid a was contained by the can initially ?", - "Output Program": [ - "import math\nn0 = 7.0\nn1 = 5.0\nn2 = 9.0\nn3 = 7.0\nn4 = 9.0\nt0 = math.sqrt(max(0, n2))\nanswer = n0 * t0\nprint(answer)" - ], - "Output Answer": [ - "21" - ], - "split": "train" - }, - { - "Input": "tea worth rs . 126 per kg and rs . 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs . 153 per kg , the price of the third variety per kg will be :", - "Output Program": [ - "n0 = 126.0\nn1 = 135.0\nn2 = 1.0\nn3 = 1.0\nn4 = 2.0\nn5 = 153.0\nt0 = n5 + 10.0\nt1 = 0.25 + 0.25\nt2 = t0 + 10.0\nt3 = n4 + t2\nanswer = t3 + t1\nprint(answer)" - ], - "Output Answer": [ - "175.5" - ], - "split": "train" - }, - { - "Input": "the h . c . f . of two numbers is 59 and the other two factors of their l . c . m . are 13 and 16 . the larger of the two numbers is :", - "Output Program": [ - "n0 = 59.0\nn1 = 13.0\nn2 = 16.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "944" - ], - "split": "train" - }, - { - "Input": "two vessels contains equal number of mixtures milk and water in the ratio 7 : 2 and 8 : 1 . both the mixtures are now mixed thoroughly . find the ratio of milk to water in the new mixture so obtained ?", - "Output Program": [ - "n0 = 7.0\nn1 = 2.0\nn2 = 8.0\nn3 = 1.0\nt0 = n2 + n3\nt1 = n0 + n1\nt2 = t0 / t1\nt3 = n0 * t2\nt4 = n1 * t2\nt5 = n2 + t3\nt6 = n3 + t4\nanswer = t5 / t6\nprint(answer)" - ], - "Output Answer": [ - "5" - ], - "split": "train" - }, - { - "Input": "a 30 kg metal bar made of alloy of tin and silver lost 3 kg of its weight in the water . 10 kg of tin loses 1.375 kg in the water ; 5 kg of silver loses 0.375 kg . what is the ratio of tin to silver in the bar ?", - "Output Program": [ - "n0 = 30.0\nn1 = 3.0\nn2 = 10.0\nn3 = 1.375\nn4 = 5.0\nn5 = 0.375\nt0 = n5 / n4\nt1 = n3 / n2\nt2 = n0 * t0\nt3 = t1 - t0\nt4 = n1 - t2\nt5 = t4 / t3\nt6 = n0 - t5\nanswer = t5 / t6\nprint(answer)" - ], - "Output Answer": [ - "0.6666666666666665" - ], - "split": "train" - }, - { - "Input": "a jar contains a mixture of ab in the ratio 4 : 1 . when 20 l of mixture is replaced with liquid b , ratio becomes 2 : 3 . how many liters of liquid a was present in mixture initially .", - "Output Program": [ - "n0 = 4.0\nn1 = 1.0\nn2 = 20.0\nn3 = 2.0\nn4 = 3.0\nt0 = n0 + n1\nt1 = n4 * n3\nt2 = n3 * n3\nt3 = t1 + t2\nt4 = t1 - n1\nt5 = n2 / t4\nt6 = t3 * t5\nt7 = t6 / t0\nanswer = n0 * t7\nprint(answer)" - ], - "Output Answer": [ - "32" - ], - "split": "train" - }, - { - "Input": "in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is 3 times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the sport formulation contains 2 ounces of corn syrup , how many ounces of water does it contain ?", - "Output Program": [ - "n0 = 1.0\nn1 = 12.0\nn2 = 30.0\nn3 = 3.0\nn4 = 2.0\nt0 = n0 / n1\nt1 = n2 * n4\nt2 = n3 * t0\nt3 = t2 * 2.0\nanswer = t3 * t1\nprint(answer)" - ], - "Output Answer": [ - "30" - ], - "split": "train" - }, - { - "Input": "a certain bag contains 60 balls \u2014 22 white , 18 green , 17 yellow , 3 red , and 1 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?", - "Output Program": [ - "n0 = 60.0\nn1 = 22.0\nn2 = 18.0\nn3 = 17.0\nn4 = 3.0\nn5 = 1.0\nt0 = n1 + n2\nt1 = n3 + t0\nanswer = t1 / n0\nprint(answer)" - ], - "Output Answer": [ - "0.95" - ], - "split": "train" - }, - { - "Input": "two integers are in the ratio of 1 to 4 . if 12 is added to the smaller number , the ratio becomes 1 to 1 . find the larger integer .", - "Output Program": [ - "n0 = 1.0\nn1 = 4.0\nn2 = 12.0\nn3 = 1.0\nn4 = 1.0\nt0 = n2 * n4\nt1 = n1 - n4\nt2 = t0 / t1\nanswer = n1 * t2\nprint(answer)" - ], - "Output Answer": [ - "16" - ], - "split": "train" - }, - { - "Input": "divide rs . 116000 among 3 persons a , b and c such that the ratio of the shares of a and b is 3 : 4 and that of b : c is 5 : 6 . find the share of a ?", - "Output Program": [ - "n0 = 116000.0\nn1 = 3.0\nn2 = 3.0\nn3 = 4.0\nn4 = 5.0\nn5 = 6.0\nt0 = n1 * n4\nt1 = n3 * n4\nt2 = n3 * n5\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = t0 / t4\nanswer = n0 * t5\nprint(answer)" - ], - "Output Answer": [ - "29491.525423728814" - ], - "split": "train" - }, - { - "Input": "in a class of 50 students , 12 enrolled for both english and german . 22 enrolled for german . if the students of the class enrolled for at least one of the two subjects , then how many students enrolled for only english and not german ?", - "Output Program": [ - "n0 = 50.0\nn1 = 12.0\nn2 = 22.0\nt0 = n0 + n1\nt1 = t0 - n2\nanswer = t1 - n1\nprint(answer)" - ], - "Output Answer": [ - "28" - ], - "split": "train" - }, - { - "Input": "a bag contains 7 red , 5 blue and 4 green balls . if 2 ballsare picked at random , what is the probability that both are red ?", - "Output Program": [ - "import scipy\nn0 = 7.0\nn1 = 5.0\nn2 = 4.0\nn3 = 2.0\nt0 = n0 + n1\nt1 = scipy.special.comb(n0, n3)\nt2 = n2 + t0\nt3 = scipy.special.comb(t2, n3)\nanswer = t1 / t3\nprint(answer)" - ], - "Output Answer": [ - "0.175" - ], - "split": "train" - }, - { - "Input": "kelly and chris are moving into a new city . both of them love books and thus packed several boxes with books . if chris packed 60 % of the total number of boxes , what was the ratio of the number of boxes kelly packed to the number of boxes chris packed ?", - "Output Program": [ - "n0 = 60.0\nt0 = 100.0 - n0\nanswer = t0 / n0\nprint(answer)" - ], - "Output Answer": [ - "0.6666666666666666" - ], - "split": "train" - }, - { - "Input": "profits in the partnership of bess , bill and bob are shared in the ratio 1 : 2 : 3 . if bill ' s share of the profits is $ 300 , what is bob ' s share ?", - "Output Program": [ - "n0 = 1.0\nn1 = 2.0\nn2 = 3.0\nn3 = 300.0\nt0 = n3 / n0\nt1 = n3 / n1\nt2 = t0 + t1\nt3 = t2 + t1\nanswer = t3 + t0\nprint(answer)" - ], - "Output Answer": [ - "900" - ], - "split": "train" - }, - { - "Input": "if w is the set of all the integers between 10 and 332 , inclusive , that are either multiples of 3 or multiples of 2 or multiples of both , then w contains how many numbers ?", - "Output Program": [ - "import math\nn0 = 10.0\nn1 = 332.0\nn2 = 3.0\nn3 = 2.0\nt0 = n3 * n2\nt1 = n1 - n0\nt2 = t1 / n3\nt3 = t1 / n2\nt4 = t1 / t0\nt5 = math.floor(t3)\nt6 = math.floor(t4)\nt7 = t2 + t5\nanswer = t7 - t6\nprint(answer)" - ], - "Output Answer": [ - "215" - ], - "split": "train" - }, - { - "Input": "how many positive integers d between 200 and 300 ( both inclusive ) are not divisible by 2 , 3 or 5 ?", - "Output Program": [ - "import math\nn0 = 200.0\nn1 = 300.0\nn2 = 2.0\nn3 = 3.0\nn4 = 5.0\nt0 = n3 * n4\nt1 = n1 - n0\nt2 = t1 + 1.0\nt3 = n2 + t0\nt4 = t1 / n2\nt5 = t1 / n3\nt6 = t1 / n4\nt7 = t4 + 1.0\nt8 = t5 + 1.0\nt9 = t6 + 1.0\nt10 = t8 - t3\nt11 = t9 - t0\nt12 = math.floor(t10)\nt13 = t12 + 1.0\nt14 = t7 + t13\nt15 = t14 + t11\nanswer = t2 - t15\nprint(answer)" - ], - "Output Answer": [ - "26" - ], - "split": "train" - }, - { - "Input": "the ratio of boarders to day students at a school was originally 2 to 5 . however , after a number of new boarders join the initial 120 boarders , the ratio changed to 1 to 2 . if no boarders became day students and vice versa , and no students left the school , how many new boarders joined the school ?", - "Output Program": [ - "n0 = 2.0\nn1 = 5.0\nn2 = 120.0\nn3 = 1.0\nn4 = 2.0\nt0 = n2 / n0\nt1 = n1 * t0\nt2 = t1 / n4\nanswer = t2 - n2\nprint(answer)" - ], - "Output Answer": [ - "30" - ], - "split": "train" - }, - { - "Input": "a 20 kg metal bar made of alloy of tin and silver lost 2 kg of its weight in the water . 10 kg of tin loses 1.375 kg in the water ; 5 kg of silver loses 0.375 kg . what is the ratio of tin to silver in the bar ?", - "Output Program": [ - "n0 = 20.0\nn1 = 2.0\nn2 = 10.0\nn3 = 1.375\nn4 = 5.0\nn5 = 0.375\nt0 = n5 / n4\nt1 = n3 / n2\nt2 = n0 * t0\nt3 = t1 - t0\nt4 = n1 - t2\nt5 = t4 / t3\nt6 = n0 - t5\nanswer = t5 / t6\nprint(answer)" - ], - "Output Answer": [ - "0.6666666666666664" - ], - "split": "train" - }, - { - "Input": "there are 2 available positions and 50 candidates , one half of whom are democrats and another half are republicans . if it was decided that the positions would be filled at random , then what is the probability q that the both positions will be taken by members of just one party ?", - "Output Program": [ - "n0 = 2.0\nn1 = 50.0\nt0 = n1 / n0\nt1 = n1 - 1.0\nt2 = t0 / n1\nt3 = t0 - 1.0\nt4 = t3 / t1\nt5 = t4 * t2\nanswer = n0 * t5\nprint(answer)" - ], - "Output Answer": [ - "0.4897959183673469" - ], - "split": "train" - }, - { - "Input": "what is the square root of 144 , divided by 6 ?", - "Output Program": [ - "import math\nn0 = 144.0\nn1 = 6.0\nt0 = math.sqrt(max(0, n0))\nanswer = t0 / n1\nprint(answer)" - ], - "Output Answer": [ - "2" - ], - "split": "train" - }, - { - "Input": "from a container having pure milk , 20 % is replaced by water and the process is repeated thrice . at the end of the third operation , the milk is", - "Output Program": [ - "n0 = 20.0\nt0 = 100.0 - n0\nt1 = t0 / 100.0\nt2 = t1**min(3.0, 5)\nanswer = t2 * 100.0\nprint(answer)" - ], - "Output Answer": [ - "51.20000000000001" - ], - "split": "train" - }, - { - "Input": "the l . c . m . of two numbers is 30 . the numbers are in the ratio 2 : 3 . then sum of the number is :", - "Output Program": [ - "n0 = 30.0\nn1 = 2.0\nn2 = 3.0\nt0 = n1 * n2\nt1 = n0 / t0\nt2 = n2 * t1\nt3 = n1 * t1\nanswer = t2 + t3\nprint(answer)" - ], - "Output Answer": [ - "25" - ], - "split": "train" - }, - { - "Input": "in a sports club with 35 members , 15 play badminton and 18 play tennis and 5 do not play either . how many members play both badminton and tennis ?", - "Output Program": [ - "n0 = 35.0\nn1 = 15.0\nn2 = 18.0\nn3 = 5.0\nt0 = n1 + n2\nt1 = n3 + t0\nanswer = t1 - n0\nprint(answer)" - ], - "Output Answer": [ - "3" - ], - "split": "train" - }, - { - "Input": "john , james and jim ' investment ratio in a business is 4 : 7 : 9 . if total total investment is 80000 . find jim ' s investment ?", - "Output Program": [ - "n0 = 4.0\nn1 = 7.0\nn2 = 9.0\nn3 = 80000.0\nt0 = n0 + n1\nt1 = n2 + t0\nt2 = n3 / t1\nanswer = n2 * t2\nprint(answer)" - ], - "Output Answer": [ - "36000" - ], - "split": "train" - }, - { - "Input": "the ratio of money with ram and gopal is 7 : 17 and that with gopal and krishan is 7 : 17 . if ram has rs . 637 , krishan has ?", - "Output Program": [ - "n0 = 7.0\nn1 = 17.0\nn2 = 7.0\nn3 = 17.0\nn4 = 637.0\nt0 = n4 / n0\nt1 = n1 * t0\nt2 = t1 / n0\nanswer = n1 * t2\nprint(answer)" - ], - "Output Answer": [ - "3757" - ], - "split": "train" - }, - { - "Input": "the ratio of 3 numbers is 1 : 2 : 4 and the sum of their squares is 1701 . the sum of the numbers is ?", - "Output Program": [ - "import math\nn0 = 3.0\nn1 = 1.0\nn2 = 2.0\nn3 = 4.0\nn4 = 1701.0\nt0 = n1**min(n2, 5)\nt1 = n2**min(n2, 5)\nt2 = n3**min(n2, 5)\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n4 / t4\nanswer = math.sqrt(max(0, t5))\nprint(answer)" - ], - "Output Answer": [ - "9" - ], - "split": "train" - }, - { - "Input": "in assembling a bluetooth device , a factory uses one of two kinds of modules . one module costs $ 10 and the other one , that is cheaper , costs $ 3.5 . the factory holds a $ 45 worth stock of 11 modules . how many of the modules in the stock are of the cheaper kind ?", - "Output Program": [ - "n0 = 10.0\nn1 = 3.5\nn2 = 45.0\nn3 = 11.0\nt0 = n2 - n0\nanswer = t0 / n1\nprint(answer)" - ], - "Output Answer": [ - "10" - ], - "split": "train" - }, - { - "Input": "the ratio of incomes of two person p 1 and p 2 is 5 : 4 and the ratio of their expenditures is 3 : 2 . if at the end of the year , each saves rs . 1200 , then what is the income of p 1 ?", - "Output Program": [ - "n0 = 1.0\nn1 = 2.0\nn2 = 5.0\nn3 = 4.0\nn4 = 3.0\nn5 = 2.0\nn6 = 1200.0\nn7 = 1.0\nt0 = n6 / n1\nt1 = n4 * t0\nt2 = t1 - n6\nanswer = n2 * t2\nprint(answer)" - ], - "Output Answer": [ - "3000" - ], - "split": "train" - }, - { - "Input": "in a ratio which is equal to 4 : 6 , if the antecedent is 50 , then the consequent is ?", - "Output Program": [ - "n0 = 4.0\nn1 = 6.0\nn2 = 50.0\nt0 = n2 / 2.0\nanswer = n2 + t0\nprint(answer)" - ], - "Output Answer": [ - "75" - ], - "split": "train" - }, - { - "Input": "there are 192 items that are members of set u . of these items , 49 are members of set b , 59 are not members of either of set a or set b , and 23 are members of both sets a and b . how many of the members of set u are members of set a ?", - "Output Program": [ - "n0 = 192.0\nn1 = 49.0\nn2 = 59.0\nn3 = 23.0\nt0 = n0 - n2\nt1 = n3 + t0\nanswer = t1 - n1\nprint(answer)" - ], - "Output Answer": [ - "107" - ], - "split": "train" - }, - { - "Input": "find the fraction which has the same ratio to 2 / 13 that 5 / 34 has to 7 / 48 ?", - "Output Program": [ - "n0 = 2.0\nn1 = 13.0\nn2 = 5.0\nn3 = 34.0\nn4 = 7.0\nn5 = 48.0\nt0 = n2 / n3\nt1 = n4 / n5\nt2 = n0 / n1\nt3 = t0 / t1\nanswer = t3 * t2\nprint(answer)" - ], - "Output Answer": [ - "0.15513897866839044" - ], - "split": "train" - }, - { - "Input": "how many multiples of 2 are there between 10 and 100 ( both are inclusive ) ?", - "Output Program": [ - "n0 = 2.0\nn1 = 10.0\nn2 = 100.0\nt0 = n2 - n1\nt1 = t0 / n0\nanswer = t1 + 1.0\nprint(answer)" - ], - "Output Answer": [ - "46" - ], - "split": "train" - }, - { - "Input": "a certain quantity of 45 % solution is replaced with 25 % solution such that the new concentration is 35 % . what is the fraction of the solution that was replaced ?", - "Output Program": [ - "n0 = 45.0\nn1 = 25.0\nn2 = 35.0\nt0 = n2 - n1\nt1 = n0 - n2\nt2 = t0 / t1\nt3 = t2 + 1.0\nanswer = 1 / t3\nprint(answer)" - ], - "Output Answer": [ - "0.5" - ], - "split": "train" - }, - { - "Input": "if 27.5 % of the 880 students at a certain college are enrolled in biology classes , how many students at the college are not enrolled in a biology class ?", - "Output Program": [ - "n0 = 27.5\nn1 = 880.0\nt0 = n1 / 100.0\nt1 = 100.0 - n0\nanswer = t0 * t1\nprint(answer)" - ], - "Output Answer": [ - "638" - ], - "split": "train" - }, - { - "Input": "the ratio of local and international calls made by amy this week is 5 to 2 . if the ratio changes to 5 to 3 after amy makes 3 more international calls , how many local calls did amy make this week ?", - "Output Program": [ - "n0 = 5.0\nn1 = 2.0\nn2 = 5.0\nn3 = 3.0\nn4 = 3.0\nt0 = n3 - n1\nt1 = n3 / t0\nanswer = n0 * t1\nprint(answer)" - ], - "Output Answer": [ - "15" - ], - "split": "train" - }, - { - "Input": "the ratio between the present ages of a and b is 6 : 3 respectively . the ratio between a ' s age 4 years ago and b ' s age 4 years hence is 1 : 1 . what is the ratio between a ' s age 4 years hence and b ' s age 4 years ago ?", - "Output Program": [ - "n0 = 6.0\nn1 = 3.0\nn2 = 4.0\nn3 = 4.0\nn4 = 1.0\nn5 = 1.0\nn6 = 4.0\nn7 = 4.0\nt0 = n0 + n0\nt1 = n0 - n1\nt2 = t0 / t1\nt3 = n0 * t2\nt4 = n1 * t2\nt5 = n0 + t3\nt6 = t4 - n0\nanswer = t5 / t6\nprint(answer)" - ], - "Output Answer": [ - "5" - ], - "split": "train" - }, - { - "Input": "in a certain state , the ratio of registered republicans to registered democrats is 3 to 2 , and every registered voter is either a republican or a democrat . if 80 percent of the republicans and 25 percent of the democrats are expected to vote for candidate x , and everyone else is expected to vote for candidate y , by what percent is candidate x expected to win the election ?", - "Output Program": [ - "n0 = 3.0\nn1 = 2.0\nn2 = 80.0\nn3 = 25.0\nt0 = n0 + n1\nt1 = n3 / 100.0\nt2 = n2 / 100.0\nt3 = n1 * t1\nt4 = n0 * t2\nt5 = t3 + t4\nt6 = n0 - t4\nt7 = n1 - t3\nt8 = t6 + t7\nt9 = t5 - t8\nt10 = t9 / t0\nanswer = t10 * 100.0\nprint(answer)" - ], - "Output Answer": [ - "16.000000000000014" - ], - "split": "train" - }, - { - "Input": "the ratio of pens to pencils is 5 to 6 . there are 6 more pencils than pens . how many pencils are there ?", - "Output Program": [ - "n0 = 5.0\nn1 = 6.0\nn2 = 6.0\nt0 = n0 * n2\nanswer = n2 + t0\nprint(answer)" - ], - "Output Answer": [ - "36" - ], - "split": "train" - }, - { - "Input": "how many kilograms of pure water is to be added to 100 kilograms of a 30 % saline solution to make it a 10 % saline solution .", - "Output Program": [ - "n0 = 100.0\nn1 = 30.0\nn2 = 10.0\nt0 = n1 / 100.0\nt1 = n2 / 100.0\nt2 = n0 * t0\nt3 = t2 / t1\nanswer = t3 - n0\nprint(answer)" - ], - "Output Answer": [ - "200" - ], - "split": "train" - }, - { - "Input": "an alloy of zinc and copper contains the metals in the ratio 5 : 3 . the quantity of zinc to be added to 6 kg of the alloy so that the ratio of the metal may be 3 : 1 is :", - "Output Program": [ - "n0 = 5.0\nn1 = 3.0\nn2 = 6.0\nn3 = 3.0\nn4 = 1.0\nt0 = n2 + 10.0\nt1 = n0 + n1\nt2 = n1 / t1\nt3 = n0 / t1\nt4 = t0 * t2\nt5 = t0 * t3\nt6 = n1 * t4\nanswer = t6 - t5\nprint(answer)" - ], - "Output Answer": [ - "8" - ], - "split": "train" - }, - { - "Input": "a number is said to be prime saturated if the product of all the different positive prime factors of r is less than the square root of r . what is the greatest two digit prime saturated integer ?", - "Output Program": [ - "t0 = 2.0 * 3.0\nt1 = 100.0 - 10.0\nanswer = t0 + t1\nprint(answer)" - ], - "Output Answer": [ - "96" - ], - "split": "train" - }, - { - "Input": "the ratio of buses to cars on river road is 1 to 13 . if there are 60 fewer buses than cars on river road , how many cars are on river road ?", - "Output Program": [ - "n0 = 1.0\nn1 = 13.0\nn2 = 60.0\nt0 = n1 - n0\nt1 = n2 / t0\nanswer = n1 * t1\nprint(answer)" - ], - "Output Answer": [ - "65" - ], - "split": "train" - }, - { - "Input": "the h . c . f and l . c . m of two numbers are 84 and 21 respectively . if the ratio of the two numbers is 1 : 4 , then the larger of the two numbers is :", - "Output Program": [ - "import math\nn0 = 84.0\nn1 = 21.0\nn2 = 1.0\nn3 = 4.0\nt0 = n0 * n1\nt1 = t0 / n3\nt2 = math.sqrt(max(0, t1))\nanswer = n3 * t2\nprint(answer)" - ], - "Output Answer": [ - "84" - ], - "split": "train" - }, - { - "Input": "a dog breeder currently has 9 breeding dogs . 6 of the dogs have exactly 1 littermate , and 3 of the dogs have exactly 2 littermates . if 2 dogs are selected at random , what is the probability t that both selected dogs are not littermates ?", - "Output Program": [ - "n0 = 9.0\nn1 = 6.0\nn2 = 1.0\nn3 = 3.0\nn4 = 2.0\nn5 = 2.0\n\nanswer = 5.0 / n1\nprint(answer)" - ], - "Output Answer": [ - "0.8333333333333334" - ], - "split": "train" - }, - { - "Input": "the ratio of buses to cars on river road is 1 to 3 . if there are 40 fewer buses than cars on river road , how many cars are on river road ?", - "Output Program": [ - "n0 = 1.0\nn1 = 3.0\nn2 = 40.0\nt0 = n1 - n0\nt1 = n2 / t0\nanswer = n1 * t1\nprint(answer)" - ], - "Output Answer": [ - "60" - ], - "split": "train" - }, - { - "Input": "at a certain zoo , the ratio of sea horse to penguins is 5 to 11 . if there are 85 more penguins than sea horses at the zoo , how many sea horses are there ?", - "Output Program": [ - "import math\nn0 = 5.0\nn1 = 11.0\nn2 = 85.0\nt0 = n0 + 1.0\nt1 = n2 / t0\nt2 = n0 * t1\nanswer = math.floor(t2)\nprint(answer)" - ], - "Output Answer": [ - "70" - ], - "split": "train" - }, - { - "Input": "the ratio of numbers is 3 : 4 and their h . c . f is 4 . their l . c . m is :", - "Output Program": [ - "import scipy\nn0 = 3.0\nn1 = 4.0\nn2 = 4.0\nt0 = n0 * n2\nt1 = n1 * n2\nanswer = scipy.lcm(int(t0), int(t1))\nprint(answer)" - ], - "Output Answer": [ - "48" - ], - "split": "train" - }, - { - "Input": "bucket p has thrice the capacity as bucket q . it takes 80 turns for bucket p to fill the empty drum . how many turns it will take for both the buckets p and q , having each turn together to fill the empty drum ?", - "Output Program": [ - "n0 = 80.0\nt0 = 1.0 / n0\nt1 = n0 * 3.0\nt2 = 1.0 / t1\nt3 = t0 + t2\nanswer = 1.0 / t3\nprint(answer)" - ], - "Output Answer": [ - "60" - ], - "split": "train" - }, - { - "Input": "if x and y are both odd prime numbers and x < y , how many distinct positive integer q factors does 2 xy have ?", - "Output Program": [ - "n0 = 2.0\nt0 = 1.0 + 1.0\nt1 = n0 * t0\nanswer = t0 * t1\nprint(answer)" - ], - "Output Answer": [ - "8" - ], - "split": "train" - }, - { - "Input": "in a college the ratio of the numbers of boys to the girls is 8 : 5 . if there are 190 girls , the total number of students in the college is ?", - "Output Program": [ - "n0 = 8.0\nn1 = 5.0\nn2 = 190.0\nt0 = n0 / n1\nt1 = n2 * t0\nanswer = n2 + t1\nprint(answer)" - ], - "Output Answer": [ - "494" - ], - "split": "train" - }, - { - "Input": "of the 90 house in a development , 50 have a two - car garage , 40 have an in - the - ground swimming pool , and 35 have both a two - car garage and an in - the - ground swimming pool . how many houses in the development have neither a two - car garage nor an in - the - ground swimming pool ?", - "Output Program": [ - "n0 = 90.0\nn1 = 50.0\nn2 = 40.0\nn3 = 35.0\nt0 = n1 - n3\nt1 = n2 - n3\nt2 = t0 + t1\nt3 = n3 + t2\nanswer = n0 - t3\nprint(answer)" - ], - "Output Answer": [ - "35" - ], - "split": "train" - }, - { - "Input": "in a family 11 people eat only vegetarian , 6 people eat only non veg . , 9 people eat both veg and non veg . . how many people eat veg in the family ?", - "Output Program": [ - "n0 = 11.0\nn1 = 6.0\nn2 = 9.0\n\nanswer = n0 + n2\nprint(answer)" - ], - "Output Answer": [ - "20" - ], - "split": "train" - }, - { - "Input": "the ratio between the number of sheep and the number of horses at the stewart farm is 6 to 7 , if each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day , what is the number of sheep in the farm ?", - "Output Program": [ - "n0 = 6.0\nn1 = 7.0\nn2 = 230.0\nn3 = 12880.0\nt0 = 2.0 * 4.0\nt1 = 1000.0 * 12.0\nt2 = t0 * 10.0\nt3 = t0 * 100.0\nt4 = t2 + t3\nt5 = t4 + t1\nt6 = t5 / n2\nt7 = t6 / n1\nanswer = n0 * t7\nprint(answer)" - ], - "Output Answer": [ - "48" - ], - "split": "train" - }, - { - "Input": "a firm is comprised of partners and associates in a ratio of 2 : 63 . if 50 more associates were hired , the ratio of partners to associates would be 1 : 34 . how many partners are currently in the firm ?", - "Output Program": [ - "n0 = 2.0\nn1 = 63.0\nn2 = 50.0\nn3 = 1.0\nn4 = 34.0\nt0 = n0 * n4\nt1 = t0 - n1\nt2 = n2 / t1\nanswer = n0 * t2\nprint(answer)" - ], - "Output Answer": [ - "20" - ], - "split": "train" - }, - { - "Input": "the ratio between the number of sheep and the number of horses at the stewar farm is 5 to 7 . if each of horse is fed 230 ounces of horse food per day and the farm needs a total 12880 ounces of horse food per day . what is number sheep in the form ? ?", - "Output Program": [ - "n0 = 5.0\nn1 = 7.0\nn2 = 230.0\nn3 = 12880.0\nt0 = n3 / n2\nt1 = t0 / n1\nanswer = n0 * t1\nprint(answer)" - ], - "Output Answer": [ - "40" - ], - "split": "train" - }, - { - "Input": "of the people who responded to a market survey , 360 preferred brand x and the rest preferred brand y . if the respondents indicated a preference for brand x over brand y by ratio of 9 to 1 , how many people responded to the survey ?", - "Output Program": [ - "n0 = 360.0\nn1 = 9.0\nn2 = 1.0\nt0 = n0 / n1\nanswer = n0 + t0\nprint(answer)" - ], - "Output Answer": [ - "400" - ], - "split": "train" - }, - { - "Input": "the ratio between the number of sheep and the number of horses at the stewar farm is 7 to 7 . if each of horse is fed 230 ounces of horse food per day and the farm needs a total 12880 ounces of horse food per day . what is number sheep in the form ? ?", - "Output Program": [ - "n0 = 7.0\nn1 = 7.0\nn2 = 230.0\nn3 = 12880.0\nt0 = n3 / n2\nt1 = t0 / n1\nanswer = n0 * t1\nprint(answer)" - ], - "Output Answer": [ - "56" - ], - "split": "train" - }, - { - "Input": "in a certain town , the ratio of ny yankees fans to ny mets fans is 3 : 2 , and the ratio of ny mets fans to boston red sox fans is 4 : 5 . if there are 330 baseball fans in the town , each of whom is a fan of exactly one of those 3 teams , how many ny mets fans are there in this town ?", - "Output Program": [ - "n0 = 3.0\nn1 = 2.0\nn2 = 4.0\nn3 = 5.0\nn4 = 330.0\nn5 = 3.0\nt0 = n0 * n3\nt1 = n4 / t0\nanswer = n2 * t1\nprint(answer)" - ], - "Output Answer": [ - "88" - ], - "split": "train" - }, - { - "Input": "ratio between rahul and deepak is 4 : 3 , after 10 years rahul age will be 26 years . what is deepak present age .", - "Output Program": [ - "n0 = 4.0\nn1 = 3.0\nn2 = 10.0\nn3 = 26.0\nt0 = n3 - n2\nt1 = n1 * t0\nanswer = t1 / n0\nprint(answer)" - ], - "Output Answer": [ - "12" - ], - "split": "train" - }, - { - "Input": "the ratio of buses to cars on river road is 1 to 10 . if there are 90 fewer buses than cars on river road , how many cars are on river road ?", - "Output Program": [ - "n0 = 1.0\nn1 = 10.0\nn2 = 90.0\nt0 = n1 - n0\nt1 = n2 / t0\nanswer = n1 * t1\nprint(answer)" - ], - "Output Answer": [ - "100" - ], - "split": "train" - }, - { - "Input": "in a certain alphabet , 16 letters contain a dot and a straight line . 30 letters contain a straight line but do not contain a dot . if that alphabet has 50 letters , all of which contain either a dot or a straight line or both , how many letters contain a dot but do not contain a straight line ?", - "Output Program": [ - "n0 = 16.0\nn1 = 30.0\nn2 = 50.0\nt0 = n0 + n1\nanswer = n2 - t0\nprint(answer)" - ], - "Output Answer": [ - "4" - ], - "split": "train" - }, - { - "Input": "in what ratio must tea at rs . 65 per kg be mixed with tea at rs . 70 per kg so that the mixture must be worth rs . 6 per kg ?", - "Output Program": [ - "n0 = 64.0\nn1 = 74.0\nn2 = 69.0\nt0 = n1 - n2\nt1 = n2 - n0\nanswer = t0 / t1\nprint(answer)" - ], - "Output Answer": [ - "1" - ], - "split": "train" - }, - { - "Input": "share rs . 4320 among john , jose & binoy in the ration 2 : 4 : 6 . find the amount received by john ?", - "Output Program": [ - "n0 = 4320.0\nn1 = 2.0\nn2 = 4.0\nn3 = 6.0\nt0 = n0 / n1\nt1 = n0 / n3\nanswer = t0 - t1\nprint(answer)" - ], - "Output Answer": [ - "1440" - ], - "split": "train" - }, - { - "Input": "in a group of cheerleaders , the group made of 10 males and 16 females . every cheerleader gets to choose between a coke or malt . the number of those that choose malt is double the number that chose coke , if all the 6 males choose malt , how many females chose malt ?", - "Output Program": [ - "import math\nn0 = 10.0\nn1 = 16.0\nn2 = 6.0\nt0 = n0 + n1\nt1 = 1.0 + 2.0\nt2 = t0 / t1\nt3 = math.floor(t2)\nanswer = n1 - t3\nprint(answer)" - ], - "Output Answer": [ - "8" - ], - "split": "train" - }, - { - "Input": "the ratio of spinsters to cats is 2 to 7 . if there are 35 more cats than spinsters , how many spinsters are there ?", - "Output Program": [ - "n0 = 2.0\nn1 = 7.0\nn2 = 35.0\nt0 = n1 - n0\nt1 = n2 / t0\nanswer = n0 * t1\nprint(answer)" - ], - "Output Answer": [ - "14" - ], - "split": "train" - }, - { - "Input": "two vessels p and q contain 62.5 % and 87.5 % of alcohol respectively . if 4 litres from vessel p is mixed with 4 litres from vessel q , the ratio of alcohol and water in the resulting mixture is ?", - "Output Program": [ - "n0 = 62.5\nn1 = 87.5\nn2 = 4.0\nn3 = 4.0\nt0 = n0 * n2\nt1 = n1 * n3\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nt4 = t2 + t3\nt5 = n2 - t2\nt6 = n3 - t3\nt7 = t5 + t6\nanswer = t4 / t7\nprint(answer)" - ], - "Output Answer": [ - "3" - ], - "split": "train" - }, - { - "Input": "in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the sport formulation contains 2 ounces of corn syrup , how many ounces of water does it contain ?", - "Output Program": [ - "n0 = 1.0\nn1 = 12.0\nn2 = 30.0\nn3 = 2.0\nt0 = n0 / n1\nt1 = n0 / n2\nt2 = t1 / 2.0\nt3 = t0 * 3.0\nt4 = t3 / t2\nanswer = n3 * t4\nprint(answer)" - ], - "Output Answer": [ - "30" - ], - "split": "train" - }, - { - "Input": "the ratio , by volume , of bleach to detergent to water in a certain solution is 2 : 40 : 100 . the solution will be altered so that the ratio of bleach ( b ) to detergent is tripled while the ratio of detergent to water is halved . if the altered solution will contain 300 liters of water , how many liters of detergent will it contain ?", - "Output Program": [ - "n0 = 2.0\nn1 = 40.0\nn2 = 100.0\nn3 = 300.0\nt0 = n3 / n2\nt1 = n1 / 2.0\nanswer = t0 * t1\nprint(answer)" - ], - "Output Answer": [ - "60" - ], - "split": "train" - }, - { - "Input": "the sum of 3 numbers is 98 . if the ratio between first and second be 2 : 3 and that between second and third be 5 : 8 , then 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 = n2 / n0\nt1 = n5 / n4\nt2 = t0 + 1.0\nt3 = t2 + t1\nanswer = n1 / t3\nprint(answer)" - ], - "Output Answer": [ - "30" - ], - "split": "train" - }, - { - "Input": "a certain bag contains 60 balls \u2014 22 white , 18 green , 8 yellow , 5 red , and 7 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?", - "Output Program": [ - "n0 = 60.0\nn1 = 22.0\nn2 = 18.0\nn3 = 8.0\nn4 = 5.0\nn5 = 7.0\nt0 = n1 + n2\nt1 = n3 + t0\nanswer = t1 / n0\nprint(answer)" - ], - "Output Answer": [ - "0.8" - ], - "split": "train" - }, - { - "Input": "in a college , the ratio of the number of boys to girls is 8 : 5 . if there are 160 girls , the total number of students in the college is", - "Output Program": [ - "n0 = 8.0\nn1 = 5.0\nn2 = 160.0\nt0 = n2 / n1\nt1 = n0 * t0\nanswer = n2 + t1\nprint(answer)" - ], - "Output Answer": [ - "416" - ], - "split": "train" - }, - { - "Input": "how many factors of 220 are odd numbers greater than 1 ?", - "Output Program": [ - "n0 = 220.0\nn1 = 1.0\nt0 = 10.0 * 2.0\nanswer = 60.0 / t0\nprint(answer)" - ], - "Output Answer": [ - "3" - ], - "split": "train" - }, - { - "Input": "a group of people participate in some curriculum , 25 of them practice yoga , 15 study cooking , 8 study weaving , 2 of them study cooking only , 7 of them study both the cooking and yoga , 3 of them participate all curriculums . how many people study both cooking and weaving ?", - "Output Program": [ - "n0 = 25.0\nn1 = 15.0\nn2 = 8.0\nn3 = 2.0\nn4 = 7.0\nn5 = 3.0\nt0 = n1 - n4\nt1 = t0 - n5\nanswer = t1 - n3\nprint(answer)" - ], - "Output Answer": [ - "3" - ], - "split": "train" - }, - { - "Input": "income and expenditure of a person are in the ratio 5 : 4 . if the income of the person is rs . 16000 , then find his savings ?", - "Output Program": [ - "n0 = 5.0\nn1 = 4.0\nn2 = 16000.0\nt0 = n1 / n0\nt1 = n2 * t0\nanswer = n2 - t1\nprint(answer)" - ], - "Output Answer": [ - "3200" - ], - "split": "train" - }, - { - "Input": "a ratio between two numbers is 5 : 4 and their l . c . m . is 80 . the first number is", - "Output Program": [ - "n0 = 5.0\nn1 = 4.0\nn2 = 80.0\nt0 = n0 * n1\nt1 = n2 / t0\nanswer = n0 * t1\nprint(answer)" - ], - "Output Answer": [ - "20" - ], - "split": "train" - }, - { - "Input": "in a sports club with 30 members , 17 play badminton and 17 play tennis and 2 do not play either . how many members play both badminton and tennis ?", - "Output Program": [ - "n0 = 30.0\nn1 = 17.0\nn2 = 17.0\nn3 = 2.0\nt0 = n1 + n2\nt1 = n3 + t0\nanswer = t1 - n0\nprint(answer)" - ], - "Output Answer": [ - "6" - ], - "split": "train" - }, - { - "Input": "in a certain large company , the ratio of college graduates with a graduate degree to non - college graduates is 1 : 8 , and ratio of college graduates without a graduate degree to non - college graduates is 2 : 3 . if one picks a random college graduate at this large company , what is the probability r this college graduate has a graduate degree ?", - "Output Program": [ - "n0 = 1.0\nn1 = 8.0\nn2 = 2.0\nn3 = 3.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = t0 / t1\nt3 = t2 + n0\nanswer = t2 / t3\nprint(answer)" - ], - "Output Answer": [ - "0.15789473684210525" - ], - "split": "train" - }, - { - "Input": "the ratio of incomes of two person p 1 and p 2 is 5 : 4 and the ratio of their expenditures is 3 : 2 . if at the end of the year , each saves rs . 2000 , then what is the income of p 1 ?", - "Output Program": [ - "n0 = 1.0\nn1 = 2.0\nn2 = 5.0\nn3 = 4.0\nn4 = 3.0\nn5 = 2.0\nn6 = 2000.0\nn7 = 1.0\nt0 = n6 / n1\nt1 = n4 * t0\nt2 = t1 - n6\nanswer = n2 * t2\nprint(answer)" - ], - "Output Answer": [ - "5000" - ], - "split": "train" - }, - { - "Input": "there are 193 items that are members of set u . of these items , 49 are members of set b , 59 are not members of either of set a or set b , and 25 are members of both sets a and b . how many of the members of set u are members of set a ?", - "Output Program": [ - "n0 = 193.0\nn1 = 49.0\nn2 = 59.0\nn3 = 25.0\nt0 = n0 - n2\nt1 = n3 + t0\nanswer = t1 - n1\nprint(answer)" - ], - "Output Answer": [ - "110" - ], - "split": "train" - }, - { - "Input": "if the ratio of the sum of the first 6 terms of a g . p . to the sum of the first 3 terms of the g . p . is 126 , what is the common ratio of the g . p ?", - "Output Program": [ - "n0 = 6.0\nn1 = 3.0\nn2 = 126.0\nt0 = 1.0 / n1\nt1 = n2 - 1.0\nanswer = t1**min(t0, 5)\nprint(answer)" - ], - "Output Answer": [ - "4.999999999999999" - ], - "split": "train" - }, - { - "Input": "100 people are attending a newspaper conference . 40 of them are writers and more than 38 are editors . of the people at the conference , x are both writers and editors and 2 x are neither . what is the largest possible number of people who are both writers and editors ?", - "Output Program": [ - "n0 = 100.0\nn1 = 40.0\nn2 = 38.0\nn3 = 2.0\nt0 = n2 + 1.0\nt1 = n1 + t0\nanswer = n0 - t1\nprint(answer)" - ], - "Output Answer": [ - "21" - ], - "split": "train" - }, - { - "Input": "what number has a 20 : 1 ratio to the number 10 ?", - "Output Program": [ - "n0 = 20.0\nn1 = 1.0\nn2 = 10.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "200" - ], - "split": "train" - }, - { - "Input": "if n is the greatest positive integer for which 4 ^ n is a factor of 10 ! , then n = ?", - "Output Program": [ - "n0 = 4.0\nn1 = 10.0\nt0 = n1 / 2.0\nanswer = t0 - 1.0\nprint(answer)" - ], - "Output Answer": [ - "4" - ], - "split": "train" - }, - { - "Input": "two sacks together contained 40 kilograms of sugar . if after 1 kilogram of sugar was taken from the first sack and poured into the second the weight of the sugar in the first sack became 60 % the weight of the sugar in the second , what was the original difference in the weights of the sacks ?", - "Output Program": [ - "n0 = 40.0\nn1 = 1.0\nn2 = 60.0\nt0 = n2 / 100.0\nt1 = t0 + 1.0\nt2 = n0 / t1\nt3 = t2 - n1\nt4 = n0 - t3\nanswer = t3 - t4\nprint(answer)" - ], - "Output Answer": [ - "8" - ], - "split": "train" - }, - { - "Input": "a starts business with rs . 3500 and after 6 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b \u00e2 \u20ac \u2122 s contribution in the capital ?", - "Output Program": [ - "n0 = 3500.0\nn1 = 6.0\nn2 = 2.0\nn3 = 3.0\nt0 = n0 * 12.0\nt1 = 12.0 - n1\nt2 = n3 * t0\nt3 = n2 * t1\nanswer = t2 / t3\nprint(answer)" - ], - "Output Answer": [ - "10500" - ], - "split": "train" - }, - { - "Input": "a certain telephone company offers two plans , a and b . under plan a , the company charges a total of $ 0.60 for the first 4 minutes of each call and $ 0.06 per minute thereafter . under plan b , the company charges $ 0.08 per minute of each call . what is the duration of a call , in minutes , for which the company charges the same amount under plan a and under plan b ?", - "Output Program": [ - "n0 = 0.6\nn1 = 4.0\nn2 = 0.06\nn3 = 0.08\nt0 = n1 * n2\nt1 = n3 - n2\nt2 = n0 - t0\nanswer = t2 / t1\nprint(answer)" - ], - "Output Answer": [ - "17.999999999999996" - ], - "split": "train" - }, - { - "Input": "in a class of 69 students 41 are taking french , 22 are taking german . of the students taking french or german , 9 are taking both courses . how many students are not enrolled in either course ?", - "Output Program": [ - "n0 = 69.0\nn1 = 41.0\nn2 = 22.0\nn3 = 9.0\nt0 = n1 + n2\nt1 = t0 - n3\nanswer = n0 - t1\nprint(answer)" - ], - "Output Answer": [ - "15" - ], - "split": "train" - }, - { - "Input": "the h . c . f . of two numbers is 42 and the other two factors of their l . c . m . are 12 and 14 . the larger of the two numbers is :", - "Output Program": [ - "n0 = 42.0\nn1 = 12.0\nn2 = 14.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "588" - ], - "split": "train" - }, - { - "Input": "in assembling a bluetooth device , a factory uses one of two kinds of modules . one module costs $ 10 and the other one , that is cheaper , costs $ 2.5 . the factory holds a $ 62.50 worth stock of 22 modules . how many of the modules in the stock are of the cheaper kind ?", - "Output Program": [ - "n0 = 10.0\nn1 = 2.5\nn2 = 62.5\nn3 = 22.0\nt0 = n2 - n0\nanswer = t0 / n1\nprint(answer)" - ], - "Output Answer": [ - "21" - ], - "split": "train" - }, - { - "Input": "if the ratio of a to b is 11 to 3 and the ratio of b to c is 1 to 5 , what is the ratio of a to c ?", - "Output Program": [ - "n0 = 11.0\nn1 = 3.0\nn2 = 1.0\nn3 = 5.0\nt0 = n0 * n2\nt1 = n1 * n3\nanswer = t0 / t1\nprint(answer)" - ], - "Output Answer": [ - "0.7333333333333333" - ], - "split": "train" - }, - { - "Input": "out of 410 students of a school , 325 play football , 175 play cricket and 50 neither play football nor cricket . how many students play both football and cricket ?", - "Output Program": [ - "n0 = 410.0\nn1 = 325.0\nn2 = 175.0\nn3 = 50.0\nt0 = n1 + n2\nt1 = n0 - n3\nanswer = t0 - t1\nprint(answer)" - ], - "Output Answer": [ - "140" - ], - "split": "train" - }, - { - "Input": "among 600 students , 56 % study sociology , 44 % study mathematics and 40 % study biology . if 30 % of students study both mathematics and sociology , what is the largest possible number of students who study biology but do not study either mathematics or sociology ?", - "Output Program": [ - "n0 = 600.0\nn1 = 56.0\nn2 = 44.0\nn3 = 40.0\nn4 = 30.0\nt0 = n0 / 100.0\nt1 = n1 * t0\nt2 = n2 * t0\nt3 = n4 * t0\nt4 = t1 + t2\nt5 = t4 - t3\nanswer = n0 - t5\nprint(answer)" - ], - "Output Answer": [ - "180" - ], - "split": "train" - }, - { - "Input": "of 60 children , 30 are happy , 10 are sad , and 20 are neither happy nor sad . there are 18 boys and 42 girls . if there are 6 happy boys and 4 sad girls , how many boys are neither happy nor sad ?", - "Output Program": [ - "n0 = 60.0\nn1 = 30.0\nn2 = 10.0\nn3 = 20.0\nn4 = 18.0\nn5 = 42.0\nn6 = 6.0\nn7 = 4.0\nt0 = n2 - n7\nt1 = n4 - t0\nanswer = t1 - n6\nprint(answer)" - ], - "Output Answer": [ - "6" - ], - "split": "train" - }, - { - "Input": "if w is the set of all the integers between 29 and 99 , inclusive , that are either multiples of 3 or multiples of 2 or multiples of both , then w contains how many numbers ?", - "Output Program": [ - "import math\nn0 = 29.0\nn1 = 99.0\nn2 = 3.0\nn3 = 2.0\nt0 = n3 * n2\nt1 = n1 - n0\nt2 = t1 / n3\nt3 = t1 / n2\nt4 = t1 / t0\nt5 = math.floor(t3)\nt6 = math.floor(t4)\nt7 = t2 + t5\nanswer = t7 - t6\nprint(answer)" - ], - "Output Answer": [ - "47" - ], - "split": "train" - }, - { - "Input": "from a container , 6 liters milk was drawn out and was replaced by water . again 6 liters of mixture was drawn out and was replaced by the water . thus the quantity of milk and water in the container after these two operations is 9 : 16 . the quantity of mixture is :", - "Output Program": [ - "import math\nn0 = 6.0\nn1 = 6.0\nn2 = 9.0\nn3 = 16.0\nt0 = n2 + n3\nt1 = math.sqrt(max(0, t0))\nt2 = n0 * t1\nanswer = t2 / 2.0\nprint(answer)" - ], - "Output Answer": [ - "15" - ], - "split": "train" - }, - { - "Input": "there 3 kinds of books in the library physics , chemistry and biology . ratio of physics to chemistry is 3 to 2 ; ratio of chemistry to biology is 4 to 3 , and the total of the books is more than 3000 . which one of following can be the total q of the book ?", - "Output Program": [ - "n0 = 3.0\nn1 = 3.0\nn2 = 2.0\nn3 = 4.0\nn4 = 3.0\nn5 = 3000.0\n\nanswer = n0 + n5\nprint(answer)" - ], - "Output Answer": [ - "3003" - ], - "split": "train" - }, - { - "Input": "the h . c . f of two numbers is 23 and the other two factors of their l . c . m are 12 and 13 . the larger of the two numbers is :", - "Output Program": [ - "n0 = 23.0\nn1 = 12.0\nn2 = 13.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "299" - ], - "split": "train" - }, - { - "Input": "in a certain large company , the ratio of college graduates with a graduate degree to non - college graduates is 1 : 8 , and ratio of college graduates without a graduate degree to non - college graduates is 2 : 3 . if one picks a random college graduate at this large company , what is the probability t this college graduate has a graduate degree ?", - "Output Program": [ - "n0 = 1.0\nn1 = 8.0\nn2 = 2.0\nn3 = 3.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = t0 / t1\nt3 = t2 + n0\nanswer = t2 / t3\nprint(answer)" - ], - "Output Answer": [ - "0.15789473684210525" - ], - "split": "train" - }, - { - "Input": "in a group of 100 people , 50 like reading books , 20 like both reading books and listening songs . how many like listening songs ?", - "Output Program": [ - "n0 = 100.0\nn1 = 50.0\nn2 = 20.0\nt0 = n1 - n2\nt1 = n2 + t0\nanswer = n2 + t1\nprint(answer)" - ], - "Output Answer": [ - "70" - ], - "split": "train" - }, - { - "Input": "there are 97 lights which are functional and each is controlled by a separate on / off switch . two children a and b start playing with the switches . a starts by pressing every third switch till he reaches the end . b , 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": [ - "import math\nn0 = 97.0\nt0 = 1.0 + 4.0\nt1 = n0 / 3.0\nt2 = n0 / t0\nt3 = math.floor(t1)\nt4 = t0 * 3.0\nt5 = n0 / t4\nt6 = math.floor(t2)\nt7 = t3 + t6\nt8 = math.floor(t5)\nt9 = t8 * 2.0\nanswer = t7 - t9\nprint(answer)" - ], - "Output Answer": [ - "39" - ], - "split": "train" - }, - { - "Input": "a business finds that their ratio of spending to income is 5 to 9 . their total profit is $ 48000 . what is their total income ?", - "Output Program": [ - "n0 = 5.0\nn1 = 9.0\nn2 = 48000.0\nt0 = n1 - n0\nt1 = n2 / t0\nanswer = n1 * t1\nprint(answer)" - ], - "Output Answer": [ - "108000" - ], - "split": "train" - }, - { - "Input": "in a bag , there are 5 green , 6 black and 7 red pens . one pen is picked up randomly . what is the probability that it is neither red nor green ?", - "Output Program": [ - "n0 = 5.0\nn1 = 6.0\nn2 = 7.0\nt0 = n0 + n1\nt1 = n2 + t0\nanswer = n1 / t1\nprint(answer)" - ], - "Output Answer": [ - "0.3333333333333333" - ], - "split": "train" - }, - { - "Input": "of the 85 house in a development , 50 have a two - car garage , 40 have an in - the - ground swimming pool , and 35 have both a two - car garage and an in - the - ground swimming pool . how many houses in the development have neither a two - car garage nor an in - the - ground swimming pool ?", - "Output Program": [ - "n0 = 85.0\nn1 = 50.0\nn2 = 40.0\nn3 = 35.0\nt0 = n1 - n3\nt1 = n2 - n3\nt2 = t0 + t1\nt3 = n3 + t2\nanswer = n0 - t3\nprint(answer)" - ], - "Output Answer": [ - "30" - ], - "split": "train" - }, - { - "Input": "the ratio of pens to pencils is 5 to 6 . there are 5 more pencils than pens . how many pencils are there ?", - "Output Program": [ - "n0 = 5.0\nn1 = 6.0\nn2 = 5.0\nt0 = n0 * n2\nanswer = n2 + t0\nprint(answer)" - ], - "Output Answer": [ - "30" - ], - "split": "train" - }, - { - "Input": "if the ratio of the sum of the first 6 terms of a g . p . to the sum of the first 3 terms of the g . p . is 28 , what is the common ratio of the g . p ?", - "Output Program": [ - "n0 = 6.0\nn1 = 3.0\nn2 = 28.0\nt0 = 1.0 / n1\nt1 = n2 - 1.0\nanswer = t1**min(t0, 5)\nprint(answer)" - ], - "Output Answer": [ - "3" - ], - "split": "train" - }, - { - "Input": "a bag contains 5 red , 4 blue and 3 green balls . if 2 ballsare picked at random , what is the probability that both are red ?", - "Output Program": [ - "import scipy\nn0 = 5.0\nn1 = 4.0\nn2 = 3.0\nn3 = 2.0\nt0 = n0 + n1\nt1 = scipy.special.comb(n0, n3)\nt2 = n2 + t0\nt3 = scipy.special.comb(t2, n3)\nanswer = t1 / t3\nprint(answer)" - ], - "Output Answer": [ - "0.15151515151515152" - ], - "split": "train" - }, - { - "Input": "puzzle ! ! ! \ud83d\ude42 if 111 = 09 444 = 12 777 = 15 then 888 = ? ? ?", - "Output Program": [ - "n0 = 111.0\nn1 = 9.0\nn2 = 444.0\nn3 = 12.0\nn4 = 777.0\nn5 = 15.0\nn6 = 888.0\n\nanswer = n5 * 1.0\nprint(answer)" - ], - "Output Answer": [ - "15" - ], - "split": "train" - }, - { - "Input": "on a certain farm the ratio of horses to cows is 3 : 1 . if the farm were to sell 15 horses and buy 15 cows , the ratio of horses to cows would then be 5 : 3 . after the transaction , how many more horses than cows would the farm own ?", - "Output Program": [ - "n0 = 3.0\nn1 = 1.0\nn2 = 15.0\nn3 = 15.0\nn4 = 5.0\nn5 = 3.0\nt0 = n2 * n4\nt1 = n2 * n5\nt2 = n0 * n5\nt3 = t0 + t1\nt4 = t2 - n4\nt5 = t3 / t4\nt6 = n2 + t5\nt7 = n0 * t5\nt8 = t7 - n2\nanswer = t8 - t6\nprint(answer)" - ], - "Output Answer": [ - "30" - ], - "split": "train" - }, - { - "Input": "the ratio , by volume , of bleach ( b ) to detergent ( d ) to water in a certain solution is 2 : 40 : 100 . the solution will be altered so that the ratio of bleach to detergent is tripled while the ratio of detergent to water is halved . if the altered solution will contain 300 liters of water , how many liters of detergent will it contain ?", - "Output Program": [ - "n0 = 2.0\nn1 = 40.0\nn2 = 100.0\nn3 = 300.0\nt0 = n1 / n2\nt1 = t0 / 2.0\nanswer = n3 * t1\nprint(answer)" - ], - "Output Answer": [ - "60" - ], - "split": "train" - }, - { - "Input": "210 reputed college students were asked in a survey if they preferred windows or mac brand computers . 60 students claimed that they preferred mac to windows brand computers . one third as many of the students who preferred mac to windows , equally preferred both brands . 90 of the students had no preference . how many of the students in the survey preferred windows to mac brand computers ?", - "Output Program": [ - "n0 = 210.0\nn1 = 60.0\nn2 = 90.0\nt0 = n1 + n2\nt1 = n1 / 3.0\nt2 = t0 + t1\nanswer = n0 - t2\nprint(answer)" - ], - "Output Answer": [ - "40" - ], - "split": "train" - }, - { - "Input": "ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 18 years . what is deepak present age ?", - "Output Program": [ - "n0 = 4.0\nn1 = 3.0\nn2 = 6.0\nn3 = 18.0\nt0 = n3 - n2\nt1 = n1 * t0\nanswer = t1 / n0\nprint(answer)" - ], - "Output Answer": [ - "9" - ], - "split": "train" - }, - { - "Input": "the l . c . m . of two numbers is 36 . the numbers are in the ratio 2 : 3 . then sum of the number is :", - "Output Program": [ - "n0 = 36.0\nn1 = 2.0\nn2 = 3.0\nt0 = n1 * n2\nt1 = n0 / t0\nt2 = n2 * t1\nt3 = n1 * t1\nanswer = t2 + t3\nprint(answer)" - ], - "Output Answer": [ - "30" - ], - "split": "train" - }, - { - "Input": "in a certain corporation , there are 300 male employees and 150 female employees . it is known that 10 % of the male employees have advanced degrees and 40 % of the females have advanced degrees . if one of the 450 employees is chosen at random , what is the probability this employee has an advanced degree or is female ?", - "Output Program": [ - "n0 = 300.0\nn1 = 150.0\nn2 = 10.0\nn3 = 40.0\nn4 = 450.0\nt0 = n2 * n2\nt1 = n3 / t0\nt2 = n2 / t0\nt3 = n0 * t2\nt4 = n1 * t1\nt5 = 1.0 - t1\nt6 = t3 + t4\nt7 = n1 * t5\nt8 = t7 / n4\nt9 = t6 / n4\nanswer = t8 + t9\nprint(answer)" - ], - "Output Answer": [ - "0.4" - ], - "split": "train" - }, - { - "Input": "in a neighborhood having 90 households , 11 did not have either a car or a bike . if 18 households had a both a car and a bike and 44 had a car , how many had bike only ?", - "Output Program": [ - "n0 = 90.0\nn1 = 11.0\nn2 = 18.0\nn3 = 44.0\nt0 = n0 - n1\nt1 = n2 + t0\nt2 = t1 - n3\nanswer = t2 - n2\nprint(answer)" - ], - "Output Answer": [ - "35" - ], - "split": "train" - }, - { - "Input": "in a college the ratio of the numbers of boys to the girls is 5 : 7 . if there are 140 girls , the total number of students in the college is ?", - "Output Program": [ - "n0 = 5.0\nn1 = 7.0\nn2 = 140.0\nt0 = n0 / n1\nt1 = n2 * t0\nanswer = n2 + t1\nprint(answer)" - ], - "Output Answer": [ - "240" - ], - "split": "train" - }, - { - "Input": "if m = 3 ^ n , what is the greatest value of n for which m is a factor of 16 !", - "Output Program": [ - "import math\nn0 = 3.0\nn1 = 16.0\nt0 = n1 / n0\nt1 = n0**min(2.0, 5)\nt2 = n1 / t1\nt3 = math.floor(t0)\nt4 = math.floor(t2)\nanswer = t3 + t4\nprint(answer)" - ], - "Output Answer": [ - "6" - ], - "split": "train" - }, - { - "Input": "income and expenditure of a person are in the ratio 5 : 4 . if the income of the person is rs . 17000 , then find his savings ?", - "Output Program": [ - "n0 = 5.0\nn1 = 4.0\nn2 = 17000.0\nt0 = n1 / n0\nt1 = n2 * t0\nanswer = n2 - t1\nprint(answer)" - ], - "Output Answer": [ - "3400" - ], - "split": "train" - }, - { - "Input": "out of 470 students of a school , 325 play football , 175 play cricket and 50 neither play football nor cricket . how many students play both football and cricket ?", - "Output Program": [ - "n0 = 470.0\nn1 = 325.0\nn2 = 175.0\nn3 = 50.0\nt0 = n1 + n2\nt1 = n0 - n3\nanswer = t0 - t1\nprint(answer)" - ], - "Output Answer": [ - "80" - ], - "split": "train" - }, - { - "Input": "in a class of 60 students 41 are taking french , 22 are taking german . of the students taking french or german , 9 are taking both courses . how many students are not enrolled in either course ?", - "Output Program": [ - "n0 = 60.0\nn1 = 41.0\nn2 = 22.0\nn3 = 9.0\nt0 = n1 + n2\nt1 = t0 - n3\nanswer = n0 - t1\nprint(answer)" - ], - "Output Answer": [ - "6" - ], - "split": "train" - }, - { - "Input": "in a certain alphabet , 10 letters contain a dot and a straight line . 24 letters contain a straight line but do not contain a dot . if that alphabet has 40 letters , all of which contain either a dot or a straight line or both , how many letters contain a dot but do not contain a straight line ?", - "Output Program": [ - "n0 = 10.0\nn1 = 24.0\nn2 = 40.0\nt0 = n0 + n1\nanswer = n2 - t0\nprint(answer)" - ], - "Output Answer": [ - "6" - ], - "split": "train" - }, - { - "Input": "a salesman sold twice as much pears in the afternoon than in the morning . if he sold $ 480 kilograms of pears that day , how many kilograms did he sell in the afternoon ?", - "Output Program": [ - "n0 = 480.0\nt0 = n0 / 3.0\nanswer = t0 * 2.0\nprint(answer)" - ], - "Output Answer": [ - "320" - ], - "split": "train" - }, - { - "Input": "a number is said to be prime saturated if the product of all the different positive prime factors of w is less than the square root of w . what is the greatest two digit prime saturated integer ?", - "Output Program": [ - "t0 = 2.0 * 3.0\nt1 = 100.0 - 10.0\nanswer = t0 + t1\nprint(answer)" - ], - "Output Answer": [ - "96" - ], - "split": "train" - }, - { - "Input": "at an international conference , \u201c red \u201d world countries and \u201c blue \u201d world countries are the only participants . the ratio of \u201c red \u201d world participants to \u201c blue \u201d world participants is 10 : 5 . if one - third of \u201c red \u201d world participants are left - handed and two - thirds of \u201c blue \u201d world participants are left - handed , then what is the fraction of the participants who are left - handed ?", - "Output Program": [ - "n0 = 10.0\nn1 = 5.0\nt0 = n0 + n1\nt1 = 2.0 / 3.0\nt2 = n0 * 0.33\nt3 = n1 * t1\nt4 = t2 + t3\nanswer = t4 / t0\nprint(answer)" - ], - "Output Answer": [ - "0.4422222222222222" - ], - "split": "train" - }, - { - "Input": "the ratio of boys to girl in a school is 5 : 4 . if there are 1500 boys in the school , how many girls are there ?", - "Output Program": [ - "n0 = 5.0\nn1 = 4.0\nn2 = 1500.0\nt0 = n2 / n0\nanswer = n1 * t0\nprint(answer)" - ], - "Output Answer": [ - "1200" - ], - "split": "train" - }, - { - "Input": "the ratio of flour to water to sugar in a recipe is 7 : 2 : 1 . the ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar . if the new recipe calls for 2 cups of water , how much sugar is required ?", - "Output Program": [ - "n0 = 7.0\nn1 = 2.0\nn2 = 1.0\nn3 = 2.0\nt0 = n3 / n1\nt1 = n2 * 4.0\nanswer = t0 * t1\nprint(answer)" - ], - "Output Answer": [ - "4" - ], - "split": "train" - }, - { - "Input": "in a class of 78 students 41 are taking french , 22 are taking german . of the students taking french or german , 9 are taking both courses . how many students are not enrolled in either course ?", - "Output Program": [ - "n0 = 78.0\nn1 = 41.0\nn2 = 22.0\nn3 = 9.0\nt0 = n1 + n2\nt1 = t0 - n3\nanswer = n0 - t1\nprint(answer)" - ], - "Output Answer": [ - "24" - ], - "split": "train" - }, - { - "Input": "in what ratio must tea at rs . 64 per kg be mixed with tea at rs . 74 per kg so that the mixture must be worth rs . 69 per kg ?", - "Output Program": [ - "n0 = 64.0\nn1 = 74.0\nn2 = 69.0\nt0 = n1 - n2\nt1 = n2 - n0\nanswer = t0 / t1\nprint(answer)" - ], - "Output Answer": [ - "1" - ], - "split": "train" - }, - { - "Input": "in gabriel ' s sheep herd , every sheep has either fleas or lice or both . half of the sheep have lice , and 84 sheep have both pests . if 94 sheep have lice , how many sheep have only fleas ?", - "Output Program": [ - "n0 = 84.0\nn1 = 94.0\n\nanswer = n1 - n0\nprint(answer)" - ], - "Output Answer": [ - "10" - ], - "split": "train" - }, - { - "Input": "log 3 n + log 7 n what is 3 digit number n that will be whole number", - "Output Program": [ - "n0 = 3.0\nn1 = 7.0\nn2 = 3.0\n\nanswer = n1**min(n0, 5)\nprint(answer)" - ], - "Output Answer": [ - "343" - ], - "split": "train" - }, - { - "Input": "an alloy is to contain steel and iron in the ratio 5 : 2 . the iron required to be melted with 35 kg of steel is ?", - "Output Program": [ - "n0 = 5.0\nn1 = 2.0\nn2 = 35.0\nt0 = n2 / n0\nanswer = n1 * t0\nprint(answer)" - ], - "Output Answer": [ - "14" - ], - "split": "train" - }, - { - "Input": "the ratio of flour to water to sugar in a recipe is 11 : 8 : 1 . the ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar . if the new recipe calls for 4 cups of water , how much sugar is required ?", - "Output Program": [ - "n0 = 11.0\nn1 = 8.0\nn2 = 1.0\nn3 = 4.0\nt0 = n3 / n1\nt1 = n2 * 4.0\nanswer = t0 * t1\nprint(answer)" - ], - "Output Answer": [ - "2" - ], - "split": "train" - }, - { - "Input": "in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the sport formulation contains 1 ounces of corn syrup , how many ounces of water does it contain ?", - "Output Program": [ - "n0 = 1.0\nn1 = 12.0\nn2 = 30.0\nn3 = 1.0\nt0 = n0 / n1\nt1 = n0 / n2\nt2 = t1 / 2.0\nt3 = t0 * 3.0\nt4 = t3 / t2\nanswer = n3 * t4\nprint(answer)" - ], - "Output Answer": [ - "15" - ], - "split": "train" - }, - { - "Input": "in a certain animal shelter , the ratio of the number of dogs to the number of cats is 15 to 7 . if 8 additional cats were to be taken in by the shelter , the ratio of the number of dogs to the number of cats would be 15 to 11 . how many dogs are in the shelter ?", - "Output Program": [ - "n0 = 15.0\nn1 = 7.0\nn2 = 8.0\nn3 = 15.0\nn4 = 11.0\nt0 = n1 * n2\nt1 = n4 - n1\nt2 = t0 / t1\nt3 = t2 / n1\nanswer = n0 * t3\nprint(answer)" - ], - "Output Answer": [ - "30" - ], - "split": "train" - }, - { - "Input": "what number has a 15 : 1 ratio to the number 10 ?", - "Output Program": [ - "n0 = 15.0\nn1 = 1.0\nn2 = 10.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "150" - ], - "split": "train" - }, - { - "Input": "of 60 children , 30 are happy , 10 are sad , and 20 are neither happy nor sad . there are 17 boys and 43 girls . if there are 6 happy boys and 4 sad girls , how many boys are neither happy nor sad ?", - "Output Program": [ - "n0 = 60.0\nn1 = 30.0\nn2 = 10.0\nn3 = 20.0\nn4 = 17.0\nn5 = 43.0\nn6 = 6.0\nn7 = 4.0\nt0 = n2 - n7\nt1 = n4 - t0\nanswer = t1 - n6\nprint(answer)" - ], - "Output Answer": [ - "5" - ], - "split": "train" - }, - { - "Input": "of the diplomats attending a summit conference , 14 speak french , 32 do not speak russian , and 20 % of the diplomats speak neither french nor russian . if 10 % of the diplomats speak both languages , then how many diplomats attended the conference ?", - "Output Program": [ - "n0 = 14.0\nn1 = 32.0\nn2 = 20.0\nn3 = 10.0\nt0 = n2 / 100.0\nt1 = n3 / 100.0\nt2 = n1 - n0\nt3 = t0 - t1\nanswer = t2 / t3\nprint(answer)" - ], - "Output Answer": [ - "180" - ], - "split": "train" - }, - { - "Input": "the cost of 3 pens and 5 pencils is rs . 240 . also the cost of one pen and one pencil is in the ratio of 5 : 1 respectively . what is the cost of one dozen pens ?", - "Output Program": [ - "n0 = 3.0\nn1 = 5.0\nn2 = 240.0\nn3 = 5.0\nn4 = 1.0\nt0 = n0 + n4\nt1 = n0 * 4.0\nt2 = n2 / t0\nanswer = t2 * t1\nprint(answer)" - ], - "Output Answer": [ - "720" - ], - "split": "train" - }, - { - "Input": "the ratio between the number of sheep and the number of horses at the stewart farm is 2 to 7 , if each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day , what is the number of sheep in the farm ?", - "Output Program": [ - "n0 = 2.0\nn1 = 7.0\nn2 = 230.0\nn3 = 12880.0\nt0 = 2.0 * 4.0\nt1 = 1000.0 * 12.0\nt2 = t0 * 10.0\nt3 = t0 * 100.0\nt4 = t2 + t3\nt5 = t4 + t1\nt6 = t5 / n2\nt7 = t6 / n1\nanswer = n0 * t7\nprint(answer)" - ], - "Output Answer": [ - "16" - ], - "split": "train" - }, - { - "Input": "praveen starts business with rs . 3220 and after 5 months , hari joins with praveen as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is hari \u2019 s contribution in the capital ?", - "Output Program": [ - "n0 = 3220.0\nn1 = 5.0\nn2 = 2.0\nn3 = 3.0\nt0 = n1 / 12.0\nt1 = n2 / n3\nt2 = 1.0 - t0\nt3 = n0 / t2\nanswer = t3 / t1\nprint(answer)" - ], - "Output Answer": [ - "8280.000000000002" - ], - "split": "train" - }, - { - "Input": "what is the square root of 81 , divided by 3 ?", - "Output Program": [ - "import math\nn0 = 81.0\nn1 = 3.0\nt0 = math.sqrt(max(0, n0))\nanswer = t0 / n1\nprint(answer)" - ], - "Output Answer": [ - "3" - ], - "split": "train" - }, - { - "Input": "in a group of 60 people , 35 have visited iceland and 23 have visited norway . if 31 people have visited both iceland and norway , how many people have visited neither country ?", - "Output Program": [ - "n0 = 60.0\nn1 = 35.0\nn2 = 23.0\nn3 = 31.0\nt0 = n1 + n2\nt1 = t0 - n3\nanswer = n0 - t1\nprint(answer)" - ], - "Output Answer": [ - "33" - ], - "split": "train" - }, - { - "Input": "the cost of 3 pens and 5 pencils is rs . 200 . also the cost of one pen and one pencil is in the ratio of 5 : 1 respectively . what is the cost of one dozen pens ?", - "Output Program": [ - "n0 = 3.0\nn1 = 5.0\nn2 = 200.0\nn3 = 5.0\nn4 = 1.0\nt0 = n0 + n4\nt1 = n0 * 4.0\nt2 = n2 / t0\nanswer = t2 * t1\nprint(answer)" - ], - "Output Answer": [ - "600" - ], - "split": "train" - }, - { - "Input": "if 85 percent of the test takers taking an old paper and pencil gmat exam answered the first question on a given math section correctly , and 65 percent of the test takers answered the second question correctly , and 5 percent of the test takers answered neither question correctly , what percent answered both correctly ?", - "Output Program": [ - "n0 = 85.0\nn1 = 65.0\nn2 = 5.0\nt0 = n0 + n1\nt1 = n2 + t0\nanswer = t1 - 100.0\nprint(answer)" - ], - "Output Answer": [ - "55" - ], - "split": "train" - }, - { - "Input": "a bag contains 3 red , 4 blue and 4 green balls . if 2 ballsare picked at random , what is the probability that both are red ?", - "Output Program": [ - "import scipy\nn0 = 3.0\nn1 = 4.0\nn2 = 4.0\nn3 = 2.0\nt0 = n0 + n1\nt1 = scipy.special.comb(n0, n3)\nt2 = n2 + t0\nt3 = scipy.special.comb(t2, n3)\nanswer = t1 / t3\nprint(answer)" - ], - "Output Answer": [ - "0.05454545454545454" - ], - "split": "train" - }, - { - "Input": "how many multiples of 5 are there between 1 and 100 ( both are inclusive ) ?", - "Output Program": [ - "n0 = 5.0\nn1 = 1.0\nn2 = 100.0\nt0 = n2 - n1\nt1 = t0 / n0\nanswer = t1 + 1.0\nprint(answer)" - ], - "Output Answer": [ - "20.8" - ], - "split": "train" - }, - { - "Input": "for a positive integer n , if 5 ^ n is a factor of 20 ! , but 5 ^ n + 1 is not a factor of 20 ! , what is the value of n ?", - "Output Program": [ - "n0 = 5.0\nn1 = 20.0\nn2 = 5.0\nn3 = 1.0\nn4 = 20.0\nt0 = n0 * n0\nt1 = t0 - n1\nanswer = t1 - n3\nprint(answer)" - ], - "Output Answer": [ - "4" - ], - "split": "train" - }, - { - "Input": "in a class of 25 students , 15 play hockey and 16 play basketball . if there are 4 students who play neither sport , determine the number of students who play both hockey and basketball ?", - "Output Program": [ - "n0 = 25.0\nn1 = 15.0\nn2 = 16.0\nn3 = 4.0\nt0 = n1 + n2\nt1 = n0 - n3\nanswer = t0 - t1\nprint(answer)" - ], - "Output Answer": [ - "10" - ], - "split": "train" - }, - { - "Input": "a bag contains 5 red , 6 blue and 4 green balls . if 2 ballsare picked at random , what is the probability that both are red ?", - "Output Program": [ - "import scipy\nn0 = 5.0\nn1 = 6.0\nn2 = 4.0\nn3 = 2.0\nt0 = n0 + n1\nt1 = scipy.special.comb(n0, n3)\nt2 = n2 + t0\nt3 = scipy.special.comb(t2, n3)\nanswer = t1 / t3\nprint(answer)" - ], - "Output Answer": [ - "0.09523809523809523" - ], - "split": "train" - }, - { - "Input": "the ratio of pens to pencils is 5 to 6 . there are 7 more pencils than pens . how many pencils are there ?", - "Output Program": [ - "n0 = 5.0\nn1 = 6.0\nn2 = 7.0\nt0 = n0 * n2\nanswer = n2 + t0\nprint(answer)" - ], - "Output Answer": [ - "42" - ], - "split": "train" - }, - { - "Input": "a person want to give his money of $ 900 to his 3 children a , b , c in the ratio 2 : 3 : 4 . what is the b ' s share ?", - "Output Program": [ - "n0 = 900.0\nn1 = 3.0\nn2 = 2.0\nn3 = 3.0\nn4 = 4.0\nt0 = n1 + n2\nt1 = n4 + t0\nt2 = n1 / t1\nanswer = n0 * t2\nprint(answer)" - ], - "Output Answer": [ - "300" - ], - "split": "train" - }, - { - "Input": "the ratio between the number of sheep and the number of horses at the stewar farm is 3 to 7 . if each of horse is fed 230 ounces of horse food per day and the farm needs a total 12880 ounces of horse food per day . what is number sheep in the form ? ?", - "Output Program": [ - "n0 = 3.0\nn1 = 7.0\nn2 = 230.0\nn3 = 12880.0\nt0 = n3 / n2\nt1 = t0 / n1\nanswer = n0 * t1\nprint(answer)" - ], - "Output Answer": [ - "24" - ], - "split": "train" - }, - { - "Input": "in a college the ratio of the numbers of boys to the girls is 8 : 5 . if there are 160 girls , the total number of students in the college is ?", - "Output Program": [ - "n0 = 8.0\nn1 = 5.0\nn2 = 160.0\nt0 = n0 / n1\nt1 = n2 * t0\nanswer = n2 + t1\nprint(answer)" - ], - "Output Answer": [ - "416" - ], - "split": "train" - }, - { - "Input": "two vessels contains equal number of mixtures milk and water in the ratio 4 : 2 and 5 : 1 . both the mixtures are now mixed thoroughly . find the ratio of milk to water in the new mixture so obtained ?", - "Output Program": [ - "n0 = 4.0\nn1 = 2.0\nn2 = 5.0\nn3 = 1.0\nt0 = n2 + n3\nt1 = n0 + n1\nt2 = t0 / t1\nt3 = n0 * t2\nt4 = n1 * t2\nt5 = n2 + t3\nt6 = n3 + t4\nanswer = t5 / t6\nprint(answer)" - ], - "Output Answer": [ - "3" - ], - "split": "train" - }, - { - "Input": "the ratio of numbers is 3 : 4 and their h . c . f is 3 . their l . c . m is :", - "Output Program": [ - "import scipy\nn0 = 3.0\nn1 = 4.0\nn2 = 3.0\nt0 = n0 * n2\nt1 = n1 * n2\nanswer = scipy.lcm(int(t0), int(t1))\nprint(answer)" - ], - "Output Answer": [ - "36" - ], - "split": "train" - }, - { - "Input": "each of the dogs in a certain kennel is a single color . each of the dogs in the kennel either has long fur or does not . of the 45 dogs in the kennel , 36 have long fur , 27 are brown , and 8 are neither long - furred nor brown . how many long - furred dogs are brown ?", - "Output Program": [ - "n0 = 45.0\nn1 = 36.0\nn2 = 27.0\nn3 = 8.0\nt0 = n1 + n2\nt1 = n0 - n3\nanswer = t0 - t1\nprint(answer)" - ], - "Output Answer": [ - "26" - ], - "split": "train" - }, - { - "Input": "a ratio between two numbers is 8 : 9 and their l . c . m . is 432 . the first number is", - "Output Program": [ - "n0 = 8.0\nn1 = 9.0\nn2 = 432.0\nt0 = n0 * n1\nt1 = n2 / t0\nanswer = n0 * t1\nprint(answer)" - ], - "Output Answer": [ - "48" - ], - "split": "train" - }, - { - "Input": "there 3 kinds of books in the library physics , chemistry and biology . ratio of physics to chemistry is 3 to 2 ; ratio of chemistry to biology is 4 to 3 , and the total of the books is more than 3000 . which one of following can be the total t of the book ?", - "Output Program": [ - "n0 = 3.0\nn1 = 3.0\nn2 = 2.0\nn3 = 4.0\nn4 = 3.0\nn5 = 3000.0\n\nanswer = n0 + n5\nprint(answer)" - ], - "Output Answer": [ - "3003" - ], - "split": "train" - }, - { - "Input": "if log 0.318 = 0.3364 and log 0.317 = 0.33320 then log 0.319 = ?", - "Output Program": [ - "n0 = 0.318\nn1 = 0.3364\nn2 = 0.317\nn3 = 0.3332\nn4 = 0.319\nt0 = n1 / n3\nanswer = n1 * t0\nprint(answer)" - ], - "Output Answer": [ - "0.3396307322929171" - ], - "split": "train" - }, - { - "Input": "in a class of 52 students , 12 enrolled for both english and german . 22 enrolled for german . if the students of the class enrolled for at least one of the two subjects , then how many students enrolled for only english and not german ?", - "Output Program": [ - "n0 = 52.0\nn1 = 12.0\nn2 = 22.0\nt0 = n0 + n1\nt1 = t0 - n2\nanswer = t1 - n1\nprint(answer)" - ], - "Output Answer": [ - "30" - ], - "split": "train" - }, - { - "Input": "the compounded ratio of ( 2 : 3 ) , ( 6 : 11 ) and ( 11 : 2 ) is :", - "Output Program": [ - "n0 = 2.0\nn1 = 3.0\nn2 = 6.0\nn3 = 11.0\nn4 = 11.0\nn5 = 2.0\nt0 = n3 / n0\nt1 = n0 / n1\nt2 = n2 / n3\nt3 = t1 * t2\nanswer = t0 * t3\nprint(answer)" - ], - "Output Answer": [ - "1.9999999999999998" - ], - "split": "train" - }, - { - "Input": "in a graduating class of 232 students , 144 took geometry and 119 took biology . what is the difference between the greatest possible number p and the smallest possible number of students that could have taken both geometry and biology ?", - "Output Program": [ - "n0 = 232.0\nn1 = 144.0\nn2 = 119.0\nt0 = n1 + n2\nt1 = t0 - n0\nanswer = n2 - t1\nprint(answer)" - ], - "Output Answer": [ - "88" - ], - "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 v 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": "pencils , pens and exercise books in a shop are in the ratio of 10 : 2 : 3 . if there are 120 pencils , the number of exercise books in the shop is :", - "Output Program": [ - "n0 = 10.0\nn1 = 2.0\nn2 = 3.0\nn3 = 120.0\nt0 = n3 / n0\nanswer = n2 * t0\nprint(answer)" - ], - "Output Answer": [ - "36" - ], - "split": "train" - }, - { - "Input": "12 different biology books and 8 different chemistry books lie on a shelf . in how many ways can a student pick 2 books of each type ?", - "Output Program": [ - "import math\nn0 = 12.0\nn1 = 8.0\nn2 = 2.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(n1)))\nt2 = n0 - n2\nt3 = n1 - n2\nt4 = math.factorial(min(15, int(t2)))\nt5 = math.factorial(min(15, int(t3)))\nt6 = t0 / t4\nt7 = t1 / t5\nt8 = t6 / n2\nt9 = t7 / n2\nanswer = t8 * t9\nprint(answer)" - ], - "Output Answer": [ - "1848" - ], - "split": "train" - }, - { - "Input": "a student committee on academic integrity has 72 ways to select a president and vice president from a group of candidates . the same person can not be both president and vice president . how many candidates are there ?", - "Output Program": [ - "import math\nn0 = 72.0\nt0 = n0 * 4.0\nt1 = -1.0\nt2 = t1**min(2.0, 5)\nt3 = t0 + t2\nt4 = math.sqrt(max(0, t3))\nt5 = t4 + 1.0\nanswer = t5 / 2.0\nprint(answer)" - ], - "Output Answer": [ - "9" - ], - "split": "train" - }, - { - "Input": "there are 35 kids in a play school . 26 kids play with white color balls and some kids play with yellow color balls and 19 kids play with both color balls . how many kids use yellow color balls ?", - "Output Program": [ - "n0 = 35.0\nn1 = 26.0\nn2 = 19.0\nt0 = n1 - n2\nanswer = n0 - t0\nprint(answer)" - ], - "Output Answer": [ - "28" - ], - "split": "train" - }, - { - "Input": "sachin is younger than rahul by 7 years . if their ages are in the respective ratio of 7 : 9 , how old is sachin ?", - "Output Program": [ - "n0 = 7.0\nn1 = 7.0\nn2 = 9.0\nt0 = n2 - n1\nt1 = n0 / t0\nanswer = n1 * t1\nprint(answer)" - ], - "Output Answer": [ - "24.5" - ], - "split": "train" - }, - { - "Input": "a box contains 4 black , 3 red and 6 green marbles . 2 marbles are drawn from the box at random . what is the probability that both the marbles are of the same color ?", - "Output Program": [ - "n0 = 4.0\nn1 = 3.0\nn2 = 6.0\nn3 = 2.0\nt0 = n1 + n2\nt1 = n1 + n3\nt2 = 10.0 + 3.0\nt3 = t1 + 10.0\nt4 = n2 * t2\nt5 = t0 + t3\nanswer = t5 / t4\nprint(answer)" - ], - "Output Answer": [ - "0.3076923076923077" - ], - "split": "train" - }, - { - "Input": "the probability that a computer company will get a computer hardware contract is 4 / 5 and the probability that it will not get a software contract is 3 / 5 . if the probability of getting at least one contract is 5 / 6 , what is the probability that it will get both the contracts ?", - "Output Program": [ - "n0 = 4.0\nn1 = 5.0\nn2 = 3.0\nn3 = 5.0\nn4 = 5.0\nn5 = 6.0\nt0 = n0 / 4.0\nt1 = n0 / n3\nt2 = n3 / n5\nt3 = 1.0 - t1\nt4 = t0 + t3\nanswer = t4 - t2\nprint(answer)" - ], - "Output Answer": [ - "0.3666666666666666" - ], - "split": "train" - }, - { - "Input": "the probability that a computer company will get a computer hardware contract is 4 / 5 and the probability that it will not get a software contract is 3 / 5 . if the probability of getting at least one contract is 9 / 10 , what is the probability that it will get both the contracts ?", - "Output Program": [ - "n0 = 4.0\nn1 = 5.0\nn2 = 3.0\nn3 = 5.0\nn4 = 9.0\nn5 = 10.0\nt0 = n2 / n1\nt1 = n0 / n3\nt2 = n3 / n5\nt3 = 1.0 - t1\nt4 = t0 + t3\nanswer = t4 - t2\nprint(answer)" - ], - "Output Answer": [ - "0.29999999999999993" - ], - "split": "train" - }, - { - "Input": "two vessels having volumes in the ratio 3 : 5 are filled with water and milk solutions . the ratio of milk and water in the two vessels are 1 : 2 and 3 : 2 respectively . if the contents of both the vessel are empties into a larger vessel , find the ratio of milk and water in the larger vessel .", - "Output Program": [ - "n0 = 3.0\nn1 = 5.0\nn2 = 1.0\nn3 = 2.0\nn4 = 3.0\nn5 = 2.0\n\nanswer = n2**min(n0, 5)\nprint(answer)" - ], - "Output Answer": [ - "1" - ], - "split": "train" - }, - { - "Input": "what number has a 5 : 1 ratio to the number 8 ?", - "Output Program": [ - "n0 = 5.0\nn1 = 1.0\nn2 = 8.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "40" - ], - "split": "train" - }, - { - "Input": "the ratio of the adjacent angles of a parallelogram is 4 : 11 . also , the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12 . what is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral ?", - "Output Program": [ - "n0 = 4.0\nn1 = 11.0\nn2 = 5.0\nn3 = 6.0\nn4 = 7.0\nn5 = 12.0\nt0 = n2 + n3\nt1 = 2.0 * 4.0\nt2 = n4 + t0\nt3 = t1 * 10.0\nt4 = t3 + 100.0\nt5 = n5 + t2\nt6 = t4 * 2.0\nt7 = t6 / t5\nanswer = n1 * t7\nprint(answer)" - ], - "Output Answer": [ - "132" - ], - "split": "train" - }, - { - "Input": "a began business with rs . 27000 and was joined afterwards by b with rs . 36000 . when did b join if the profits at the end of the year were divided in the ratio of 2 : 1 ?", - "Output Program": [ - "n0 = 27000.0\nn1 = 36000.0\nn2 = 2.0\nn3 = 1.0\nt0 = 3.0 * 4.0\nt1 = n0 * t0\nt2 = t1 / n1\nt3 = t2 / n2\nanswer = t0 - t3\nprint(answer)" - ], - "Output Answer": [ - "7.5" - ], - "split": "train" - }, - { - "Input": "find the probability in a group of 10 students sitting in a row , two of them always sit next to each other", - "Output Program": [ - "import math\nn0 = 10.0\nt0 = math.factorial(min(15, int(2.0)))\nt1 = math.factorial(min(15, int(n0)))\nt2 = n0 - 1.0\nt3 = math.factorial(min(15, int(t2)))\nt4 = t3 * t0\nanswer = t4 / t1\nprint(answer)" - ], - "Output Answer": [ - "0.2" - ], - "split": "train" - }, - { - "Input": "a farmer used 1,034 acres of land for beans , wheat , and corn in the ratio of 5 : 2 : 4 , respectively . how many e acres were used for corn ?", - "Output Program": [ - "n0 = 1034.0\nn1 = 5.0\nn2 = 2.0\nn3 = 4.0\nt0 = n1 + n2\nt1 = 10.0 * 3.0\nt2 = 1.0 * 1000.0\nt3 = n3 + t1\nt4 = n3 + t0\nt5 = t3 + t2\nt6 = t5 / t4\nanswer = n3 * t6\nprint(answer)" - ], - "Output Answer": [ - "376" - ], - "split": "train" - }, - { - "Input": "in a class of 50 students , 3 / 5 went away do painting , 1 / 5 went to play in the field . how many students are left in the classroom ?", - "Output Program": [ - "n0 = 50.0\nn1 = 3.0\nn2 = 5.0\nn3 = 1.0\nn4 = 5.0\nt0 = n1 / n2\nt1 = n3 / n2\nt2 = n0 * t0\nt3 = n0 * t1\nt4 = t2 + t3\nanswer = n0 - t4\nprint(answer)" - ], - "Output Answer": [ - "10" - ], - "split": "train" - }, - { - "Input": "if the ratio of a to b is 7 to 3 and the ratio of b to c is 1 to 5 , what is the ratio of a to c ?", - "Output Program": [ - "n0 = 7.0\nn1 = 3.0\nn2 = 1.0\nn3 = 5.0\nt0 = n0 * n2\nt1 = n1 * n3\nanswer = t0 / t1\nprint(answer)" - ], - "Output Answer": [ - "0.4666666666666667" - ], - "split": "train" - }, - { - "Input": "a shipment of 250 smartphones contains 76 that are defective . if a customer buys two smartphones at random from the shipment , what is the approximate probability that both phones are defective ?", - "Output Program": [ - "n0 = 250.0\nn1 = 76.0\nt0 = n1 - 1.0\nt1 = n0 - 1.0\nt2 = n1 * t0\nt3 = n0 * t1\nanswer = t2 / t3\nprint(answer)" - ], - "Output Answer": [ - "0.09156626506024096" - ], - "split": "train" - }, - { - "Input": "at a kennel with 80 dogs , 45 of the dogs wear tags and 40 wear flea collars . if 6 of the dogs wear both , then how many of the dogs wear neither a collar nor tags ?", - "Output Program": [ - "n0 = 80.0\nn1 = 45.0\nn2 = 40.0\nn3 = 6.0\nt0 = n1 + n2\nt1 = t0 - n3\nanswer = n0 - t1\nprint(answer)" - ], - "Output Answer": [ - "1" - ], - "split": "train" - }, - { - "Input": "two numbers are in the ratio of 2 : 3 . if 4 is added in both numbers the ratio becomes 5 : 7 . find the difference between numbers .", - "Output Program": [ - "n0 = 2.0\nn1 = 3.0\nn2 = 4.0\nn3 = 5.0\nn4 = 7.0\nt0 = n1 / n0\nt1 = n2 * n4\nt2 = n2 * n3\nt3 = t1 - t2\nt4 = n0 * t3\nt5 = t0 * t4\nanswer = t5 - t4\nprint(answer)" - ], - "Output Answer": [ - "8" - ], - "split": "train" - }, - { - "Input": "the ratio of football players , baseball players , soccer players , and basketball players in a school is 10 : 7 : 5 : 4 . how many athletes are in the school if 16 players are on the basketball team ?", - "Output Program": [ - "n0 = 10.0\nn1 = 7.0\nn2 = 5.0\nn3 = 4.0\nn4 = 16.0\nt0 = n2 * n4\nt1 = n1 * n4\nt2 = n0 * n4\nt3 = t0 / n3\nt4 = t1 / n3\nt5 = t2 / n3\nt6 = n4 + t3\nt7 = t6 + t4\nanswer = t7 + t5\nprint(answer)" - ], - "Output Answer": [ - "104" - ], - "split": "train" - }, - { - "Input": "susan finds that she spends her free time during summer vacation between swimming , reading , and hanging out with friends in a ratio of 1 : 4 : 10 . how many hours did she spend reading if she hung out with her friends for 20 hours ?", - "Output Program": [ - "n0 = 1.0\nn1 = 4.0\nn2 = 10.0\nn3 = 20.0\nt0 = n0 + n1\nt1 = n2 + t0\nt2 = n3 * t1\nt3 = t2 / n2\nt4 = n1 * t3\nanswer = t4 / t1\nprint(answer)" - ], - "Output Answer": [ - "8" - ], - "split": "train" - }, - { - "Input": "the ratio of toddlers to infants at a day care center is 7 to 3 . if 12 more infants join the day care to change the ratio to 7 to 5 , how many toddlers are there at this day care center ?", - "Output Program": [ - "n0 = 7.0\nn1 = 3.0\nn2 = 12.0\nn3 = 7.0\nn4 = 5.0\nt0 = n0 * n0\nt1 = n1 * n4\nt2 = t0 - t1\nt3 = n2 + t2\nanswer = t3 - 4.0\nprint(answer)" - ], - "Output Answer": [ - "42" - ], - "split": "train" - }, - { - "Input": "of the diplomats attending a summit conference , 22 speak french , 32 do not speak russian , and 20 % of the diplomats speak neither french nor russian . if 10 % of the diplomats speak both languages , then how many diplomats attended the conference ?", - "Output Program": [ - "n0 = 22.0\nn1 = 32.0\nn2 = 20.0\nn3 = 10.0\nt0 = n2 / 100.0\nt1 = n3 / 100.0\nt2 = n1 - n0\nt3 = t0 - t1\nanswer = t2 / t3\nprint(answer)" - ], - "Output Answer": [ - "100" - ], - "split": "train" - }, - { - "Input": "sandy is younger than molly by 16 years . if the ratio of their ages is 7 : 9 , how old is sandy ?", - "Output Program": [ - "n0 = 16.0\nn1 = 7.0\nn2 = 9.0\nt0 = n2 - n1\nt1 = n1 / t0\nanswer = n0 * t1\nprint(answer)" - ], - "Output Answer": [ - "56" - ], - "split": "train" - }, - { - "Input": "mrs . evans gave a test to her freshmen economics class , which has 40 students enrolled and 30 of them answered question 1 correctly . if 29 answered question 2 correctly and 10 did not take the test then how many answered both questions correctly ?", - "Output Program": [ - "n0 = 40.0\nn1 = 30.0\nn2 = 1.0\nn3 = 29.0\nn4 = 2.0\nn5 = 10.0\nt0 = n1 + n3\nt1 = n5 + t0\nanswer = t1 - n0\nprint(answer)" - ], - "Output Answer": [ - "29" - ], - "split": "train" - }, - { - "Input": "the h . c . f . of two numbers is 20 and the other two factors of their l . c . m . are 21 and 23 . the larger of the two numbers is", - "Output Program": [ - "n0 = 20.0\nn1 = 21.0\nn2 = 23.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "460" - ], - "split": "train" - }, - { - "Input": "the ratio of the number of red cars in a certain parking lot to the number of black cars is 3 to 8 . if there are 70 black cars in the lot , how many red cars are there in the lot ?", - "Output Program": [ - "import math\nn0 = 3.0\nn1 = 8.0\nn2 = 70.0\nt0 = n0 / n1\nt1 = n2 * t0\nanswer = math.floor(t1)\nprint(answer)" - ], - "Output Answer": [ - "26" - ], - "split": "train" - }, - { - "Input": "the ratio between the number of sheep and the number of horses at the stewar farm is 4 to 7 . if each of horse is fed 230 ounces of horse food per day and the farm needs a total 12880 ounces of horse food per day . what is number sheep in the form ? ?", - "Output Program": [ - "n0 = 4.0\nn1 = 7.0\nn2 = 230.0\nn3 = 12880.0\nt0 = n3 / n2\nt1 = t0 / n1\nanswer = n0 * t1\nprint(answer)" - ], - "Output Answer": [ - "32" - ], - "split": "train" - }, - { - "Input": "what is the number of integers from 1 to 1000 ( inclusive ) that are divisible by neither 11 nor by 30 ?", - "Output Program": [ - "n0 = 1.0\nn1 = 1000.0\nn2 = 11.0\nn3 = 30.0\nt0 = n1 / n2\nt1 = n1 / n3\nt2 = n2 * n3\nt3 = t0 + t1\nt4 = n1 / t2\nt5 = t3 - t4\nanswer = n1 - t5\nprint(answer)" - ], - "Output Answer": [ - "878.7878787878788" - ], - "split": "train" - }, - { - "Input": "the probability that a computer company will get a computer hardware contract is 3 / 4 and the probability that it will not get a software contract is 5 / 9 . if the probability of getting at least one contract is 4 / 5 , what is the probability that it will get both the contracts ?", - "Output Program": [ - "n0 = 3.0\nn1 = 4.0\nn2 = 5.0\nn3 = 9.0\nn4 = 4.0\nn5 = 5.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = n4 / n5\nt3 = 1.0 - t1\nt4 = t0 + t3\nanswer = t4 - t2\nprint(answer)" - ], - "Output Answer": [ - "0.3944444444444444" - ], - "split": "train" - }, - { - "Input": "each of the dogs in a certain kennel is a single color . each of the dogs in the kennel either has long fur or does not . of the 45 dogs in the kennel , 26 have long fur , 30 are brown , and 8 are neither long - furred nor brown . how many long - furred dogs are brown ?", - "Output Program": [ - "n0 = 45.0\nn1 = 26.0\nn2 = 30.0\nn3 = 8.0\nt0 = n1 + n2\nt1 = n0 - n3\nanswer = t0 - t1\nprint(answer)" - ], - "Output Answer": [ - "19" - ], - "split": "train" - }, - { - "Input": "income and expenditure of a person are in the ratio 15 : 8 . if the income of the person is rs . 15000 , then find his savings ?", - "Output Program": [ - "n0 = 15.0\nn1 = 8.0\nn2 = 15000.0\nt0 = n1 / n0\nt1 = n2 * t0\nanswer = n2 - t1\nprint(answer)" - ], - "Output Answer": [ - "7000" - ], - "split": "train" - }, - { - "Input": "the rational number for recurring decimal 0.125125 . . . . is :", - "Output Program": [ - "import math\nn0 = 0.125125\nt0 = 1.0 + 10.0\nt1 = n0 * 1000.0\nt2 = math.floor(t1)\nt3 = t0 * 10.0\nt4 = t3 + 1.0\nt5 = t4 * 3.0\nt6 = t5 * 3.0\nanswer = t2 / t6\nprint(answer)" - ], - "Output Answer": [ - "0.12512512512512514" - ], - "split": "train" - }, - { - "Input": "in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the sport formulation contains 6 ounces of corn syrup , how many ounces of water does it contain ?", - "Output Program": [ - "n0 = 1.0\nn1 = 12.0\nn2 = 30.0\nn3 = 6.0\nt0 = n0 / n1\nt1 = n0 / n2\nt2 = t1 / 2.0\nt3 = t0 * 3.0\nt4 = t3 / t2\nanswer = n3 * t4\nprint(answer)" - ], - "Output Answer": [ - "90" - ], - "split": "train" - }, - { - "Input": "if both 112 and 33 are factors of the number a * 43 * 62 * 1311 , then what is the smallest possible value of a ?", - "Output Program": [ - "import scipy\nn0 = 112.0\nn1 = 33.0\nn2 = 43.0\nn3 = 62.0\nn4 = 1311.0\nt0 = 1.0 + 10.0\nt1 = n1 - 3.0\nt2 = t1 / 10.0\nt3 = t0**min(2.0, 5)\nanswer = scipy.lcm(int(t2), int(t3))\nprint(answer)" - ], - "Output Answer": [ - "363" - ], - "split": "train" - }, - { - "Input": "a ratio between two numbers is 3 : 4 and their l . c . m . is 180 . the first number is", - "Output Program": [ - "n0 = 3.0\nn1 = 4.0\nn2 = 180.0\nt0 = n0 * n1\nt1 = n2 / t0\nanswer = n0 * t1\nprint(answer)" - ], - "Output Answer": [ - "45" - ], - "split": "train" - }, - { - "Input": "ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 22 years . what is deepak present age ?", - "Output Program": [ - "n0 = 4.0\nn1 = 3.0\nn2 = 6.0\nn3 = 22.0\nt0 = n3 - n2\nt1 = n1 * t0\nanswer = t1 / n0\nprint(answer)" - ], - "Output Answer": [ - "12" - ], - "split": "train" - }, - { - "Input": "if g and f are both odd prime numbers andg < f , then how many different positive integer factors does 2 gfhave ?", - "Output Program": [ - "n0 = 2.0\nt0 = n0 * n0\nanswer = n0 * t0\nprint(answer)" - ], - "Output Answer": [ - "8" - ], - "split": "train" - }, - { - "Input": "3 numbers are in the ratio 3 : 5 : 7 . the largest number is 56 . what is the difference between smallest and largest number ?", - "Output Program": [ - "n0 = 3.0\nn1 = 3.0\nn2 = 5.0\nn3 = 7.0\nn4 = 56.0\nt0 = n4 / n3\nt1 = n0 * t0\nanswer = n4 - t1\nprint(answer)" - ], - "Output Answer": [ - "32" - ], - "split": "train" - }, - { - "Input": "each factor of 200 is inscribed on its own plastic ball , and all of the balls are placed in a jar . if a ball is randomly selected from the jar , what is the probability that the ball is inscribed with a multiple of 42 ?", - "Output Program": [ - "import scipy\nn0 = 200.0\nn1 = 42.0\nt0 = scipy.special.comb(n1, 1.0)\nt1 = 3.0**min(2.0, 5)\nt2 = t0 / n1\nanswer = t2 / t1\nprint(answer)" - ], - "Output Answer": [ - "0.1111111111111111" - ], - "split": "train" - }, - { - "Input": "the ratio between the number of sheep and the number of horses at the stewart farm is 3 to 7 , if each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day , what is the number of sheep in the farm ?", - "Output Program": [ - "n0 = 3.0\nn1 = 7.0\nn2 = 230.0\nn3 = 12880.0\nt0 = 2.0 * 4.0\nt1 = 1000.0 * 12.0\nt2 = t0 * 10.0\nt3 = t0 * 100.0\nt4 = t2 + t3\nt5 = t4 + t1\nt6 = t5 / n2\nt7 = t6 / n1\nanswer = n0 * t7\nprint(answer)" - ], - "Output Answer": [ - "24" - ], - "split": "train" - }, - { - "Input": "income and expenditure of a person are in the ratio 3 : 2 . if the income of the person is rs . 21000 , then find his savings ?", - "Output Program": [ - "n0 = 3.0\nn1 = 2.0\nn2 = 21000.0\nt0 = n1 / n0\nt1 = n2 * t0\nanswer = n2 - t1\nprint(answer)" - ], - "Output Answer": [ - "7000" - ], - "split": "train" - }, - { - "Input": "at the faculty of aerospace engineering , 312 students study random - processing methods , 232 students study scramjet rocket engines and 114 students study them both . if every student in the faculty has to study one of the two subjects , how many students are there in the faculty of aerospace engineering ?", - "Output Program": [ - "n0 = 312.0\nn1 = 232.0\nn2 = 114.0\nt0 = n2 / 2.0\nt1 = n0 - t0\nt2 = n1 - t0\nanswer = t1 + t2\nprint(answer)" - ], - "Output Answer": [ - "430" - ], - "split": "train" - }, - { - "Input": "there are 193 items that are members of set u . of these items , 41 are members of set b , 59 are not members of either of set a or set b , and 23 are members of both sets a and b . how many of the members of set u are members of set a ?", - "Output Program": [ - "n0 = 193.0\nn1 = 41.0\nn2 = 59.0\nn3 = 23.0\nt0 = n0 - n2\nt1 = n3 + t0\nanswer = t1 - n1\nprint(answer)" - ], - "Output Answer": [ - "116" - ], - "split": "train" - }, - { - "Input": "at an international conference , \u201c red \u201d world countries and \u201c blue \u201d world countries are the only participants . the ratio of \u201c red \u201d world participants to \u201c blue \u201d world participants is 5 : 5 . if one - third of \u201c red \u201d world participants are left - handed and two - thirds of \u201c blue \u201d world participants are left - handed , then what is the fraction of the participants who are left - handed ?", - "Output Program": [ - "n0 = 5.0\nn1 = 5.0\nt0 = n0 + n1\nt1 = 2.0 / 3.0\nt2 = n0 * 0.33\nt3 = n1 * t1\nt4 = t2 + t3\nanswer = t4 / t0\nprint(answer)" - ], - "Output Answer": [ - "0.49833333333333335" - ], - "split": "train" - }, - { - "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 numbers will be 3 ?", - "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 = 3.0\nt0 = 1.0 / n0\nt1 = 1.0 / n7\nanswer = t0 * t1\nprint(answer)" - ], - "Output Answer": [ - "0.023809523809523808" - ], - "split": "train" - }, - { - "Input": "a certain fruit stand sold apples for $ 0.70 each and cherry for $ 0.50 each . if a customer purchased both apples and bananas from the stand for a total of $ 6.30 , what total number of apples and bananas did the customer purchase ?", - "Output Program": [ - "n0 = 0.7\nn1 = 0.5\nn2 = 6.3\nt0 = n0 * 10.0\nanswer = t0 + 4.0\nprint(answer)" - ], - "Output Answer": [ - "11" - ], - "split": "train" - }, - { - "Input": "in a graduating class of 232 students , 144 took geometry and 119 took biology . what is the difference between the greatest possible number t and the smallest possible number of students that could have taken both geometry and biology ?", - "Output Program": [ - "n0 = 232.0\nn1 = 144.0\nn2 = 119.0\nt0 = n1 + n2\nt1 = t0 - n0\nanswer = n2 - t1\nprint(answer)" - ], - "Output Answer": [ - "88" - ], - "split": "train" - }, - { - "Input": "a certain fruit stand sold apples for $ 0.80 each and bananas for $ 0.70 each . if a customer purchased both apples and bananas from the stand for a total of $ 6.50 , what total number of apples and bananas did the customer purchase ?", - "Output Program": [ - "n0 = 0.8\nn1 = 0.7\nn2 = 6.5\nt0 = n0 * 2.0\nt1 = n2 - t0\nt2 = t1 / n1\nanswer = t2 + 2.0\nprint(answer)" - ], - "Output Answer": [ - "9" - ], - "split": "train" - }, - { - "Input": "if the numbers 1 to 98 are written on 98 pieces of paper , ( one on each ) and one piece is picked at random , then what is the probability that the number drawn is neither prime nor composite ?", - "Output Program": [ - "n0 = 1.0\nn1 = 98.0\nn2 = 98.0\n\nanswer = n0 / n1\nprint(answer)" - ], - "Output Answer": [ - "0.01020408163265306" - ], - "split": "train" - }, - { - "Input": "in a class of 35 students 26 play football and play 20 long tennis , if 17 play above , many play neither ?", - "Output Program": [ - "n0 = 35.0\nn1 = 26.0\nn2 = 20.0\nn3 = 17.0\nt0 = n1 + n2\nt1 = t0 - n3\nanswer = n0 - t1\nprint(answer)" - ], - "Output Answer": [ - "6" - ], - "split": "train" - }, - { - "Input": "the least whole number which when subtracted from both the terms of the ratio 6 : 7 to give a ratio less than 16 : 21 , is ?", - "Output Program": [ - "n0 = 6.0\nn1 = 7.0\nn2 = 16.0\nn3 = 21.0\nt0 = 2.0 / 10.0\nt1 = n0 * n3\nt2 = n1 * n2\nt3 = n3 - n2\nt4 = t1 - t2\nt5 = t4 / t3\nanswer = t5 + t0\nprint(answer)" - ], - "Output Answer": [ - "3" - ], - "split": "train" - }, - { - "Input": "a certain manufacturer of cake , muffin , and bread mixes has 100 buyers , of whom 50 purchases cake mix , 40 purchase muffin mix , and 17 purchase both cake mix and muffin mix . if a buyer is to be selected at random from the 100 buyers , what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix ?", - "Output Program": [ - "n0 = 100.0\nn1 = 50.0\nn2 = 40.0\nn3 = 17.0\nn4 = 100.0\nt0 = n1 + n2\nt1 = t0 - n3\nt2 = n0 - t1\nanswer = t2 / n0\nprint(answer)" - ], - "Output Answer": [ - "0.27" - ], - "split": "train" - }, - { - "Input": "an amount of money is to be distributed among faruk , vasim and ranjith in the ratio 3 : 5 : 8 . if vasims share is rs . 1500 , what is the difference between faruk ' s and ranjith ' s shares ?", - "Output Program": [ - "n0 = 3.0\nn1 = 5.0\nn2 = 8.0\nn3 = 1500.0\nt0 = n3 / n1\nt1 = n2 - n0\nanswer = t0 * t1\nprint(answer)" - ], - "Output Answer": [ - "1500" - ], - "split": "train" - }, - { - "Input": "the ratio between the number of passengers travelling by i and ii class between the two railway stations is 1 : 50 , whereas the ratio of i and ii class fares between the same stations is 3 : 1 . if on a particular day rs . 1,325 were collected from the passengers travelling between these stations , then what was the amount collected from the ii class passengers ?", - "Output Program": [ - "n0 = 1.0\nn1 = 50.0\nn2 = 3.0\nn3 = 1.0\nn4 = 1325.0\nt0 = 2.0 + 3.0\nt1 = 10.0 * 100.0\nt2 = 100.0 * 3.0\nt3 = 10.0 * 2.0\nt4 = n0 * n2\nt5 = n0 * n1\nt6 = t1 + t2\nt7 = t4 + t5\nt8 = t6 + t3\nt9 = t8 + t0\nt10 = t9 / t7\nanswer = t10 * t5\nprint(answer)" - ], - "Output Answer": [ - "1250" - ], - "split": "train" - }, - { - "Input": "the ratio by weight , measured in pounds , of books to clothes to electronics in a suitcase initially stands at 7 : 4 : 3 . someone removes 6 pounds of clothing from the suitcase , thereby doubling the ratio of books to clothes . how many pounds do the electronics in the suitcase weigh ?", - "Output Program": [ - "n0 = 7.0\nn1 = 4.0\nn2 = 3.0\nn3 = 6.0\nt0 = n0 + n1\nt1 = n2 + t0\nt2 = n3 * t1\nt3 = t1 * 2.0\nt4 = n1 * t1\nt5 = -t2\nt6 = t3 - t4\nt7 = t5 / t6\nanswer = n2 * t7\nprint(answer)" - ], - "Output Answer": [ - "9" - ], - "split": "train" - }, - { - "Input": "there are 12 slate rocks , 17 pumice rocks , and 8 granite rocks randomly distributed in a certain field . if 2 rocks are chosen at random and without replacement , what is the probability that both rocks will be slate rocks ?", - "Output Program": [ - "n0 = 12.0\nn1 = 17.0\nn2 = 8.0\nn3 = 2.0\nt0 = n0 + n1\nt1 = n0 - 1.0\nt2 = n2 + t0\nt3 = n0 / t2\nt4 = t2 - 1.0\nt5 = t1 / t4\nanswer = t3 * t5\nprint(answer)" - ], - "Output Answer": [ - "0.09909909909909911" - ], - "split": "train" - }, - { - "Input": "100 kg of an alloy a is mixed with 200 kg of alloy b . if alloy a has lead and tin in the ratio 5 : 3 and alloy b has tin and copper in the ratio 2 : 3 , then the amount of tin in the new alloy is ?", - "Output Program": [ - "n0 = 100.0\nn1 = 200.0\nn2 = 5.0\nn3 = 3.0\nn4 = 2.0\nn5 = 3.0\nt0 = n2 + n3\nt1 = n4 + n5\nt2 = n0 / t0\nt3 = n1 / t1\nt4 = n3 * t2\nt5 = n4 * t3\nanswer = t4 + t5\nprint(answer)" - ], - "Output Answer": [ - "117.5" - ], - "split": "train" - }, - { - "Input": "the price of a car and ac are in the ratio 3 : 2 . if the scooter costs $ 500 more than the ac . then the price of the ac ?", - "Output Program": [ - "n0 = 3.0\nn1 = 2.0\nn2 = 500.0\n\nanswer = n2 * 3.0\nprint(answer)" - ], - "Output Answer": [ - "1500" - ], - "split": "train" - }, - { - "Input": "a company sells pens and pencils . the revenue from pens in 2007 was up 5 % from 2006 . the revenue from pencils declined 13 % over the same period . overall revenue was down 1 % from 06 to 07 . what was the ratio of pencil revenue to pen revenue in 2006", - "Output Program": [ - "n0 = 2007.0\nn1 = 5.0\nn2 = 2006.0\nn3 = 13.0\nn4 = 1.0\nn5 = 6.0\nn6 = 7.0\nn7 = 2006.0\nt0 = n1 + 100.0\nt1 = 100.0 - n4\nt2 = 100.0 - n3\nt3 = t0 - t1\nt4 = t1 - t2\nanswer = t3 / t4\nprint(answer)" - ], - "Output Answer": [ - "0.5" - ], - "split": "train" - }, - { - "Input": "if x and y are both odd prime numbers andx < y , then how many different positive integer factors does 2 xyhave ?", - "Output Program": [ - "n0 = 2.0\nt0 = 1.0 + 1.0\nt1 = n0 * t0\nanswer = t0 * t1\nprint(answer)" - ], - "Output Answer": [ - "8" - ], - "split": "train" - }, - { - "Input": "there are 30 students in a classroom . the ratio of the # of girls to boys was 1 : 2 , how many boys are there ?", - "Output Program": [ - "n0 = 30.0\nn1 = 1.0\nn2 = 2.0\nt0 = n1 + n2\nt1 = n2 / t0\nanswer = n0 * t1\nprint(answer)" - ], - "Output Answer": [ - "20" - ], - "split": "train" - }, - { - "Input": "99 ! how many zero ' s ?", - "Output Program": [ - "import math\nn0 = 99.0\nt0 = 1.0 + 4.0\nt1 = n0 / t0\nt2 = t0**min(2.0, 5)\nt3 = n0 / t2\nt4 = math.floor(t1)\nt5 = math.floor(t3)\nanswer = t4 + t5\nprint(answer)" - ], - "Output Answer": [ - "22" - ], - "split": "train" - }, - { - "Input": "two integers are in the ratio of 1 to 4 . if 12 is added to the smaller number , the ratio becomes 1 to 2 . find the larger integer .", - "Output Program": [ - "n0 = 1.0\nn1 = 4.0\nn2 = 12.0\nn3 = 1.0\nn4 = 2.0\nt0 = n2 * n4\nt1 = n1 - n4\nt2 = t0 / t1\nanswer = n1 * t2\nprint(answer)" - ], - "Output Answer": [ - "48" - ], - "split": "train" - }, - { - "Input": "a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 9 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many liter of liquid a was contained by the can initially ?", - "Output Program": [ - "n0 = 7.0\nn1 = 5.0\nn2 = 9.0\nn3 = 7.0\nn4 = 9.0\nt0 = n0 + n2\nt1 = n0 + n1\nt2 = n0 * n2\nt3 = n0 * n1\nt4 = n1 / t1\nt5 = t2 - t3\nt6 = n2 * t4\nt7 = n2 - t6\nt8 = t0 * t7\nt9 = t8 / t5\nanswer = n0 * t9\nprint(answer)" - ], - "Output Answer": [ - "21" - ], - "split": "train" - }, - { - "Input": "at an international conference , \u201c red \u201d world countries and \u201c blue \u201d world countries are the only participants . the ratio of \u201c red \u201d world participants to \u201c blue \u201d world participants is 2 : 1 . if one - third of \u201c red \u201d world participants are left - handed and two - thirds of \u201c blue \u201d world participants are left - handed , then what is the fraction of the participants who are left - handed ?", - "Output Program": [ - "n0 = 2.0\nn1 = 1.0\nt0 = n0 + n1\nt1 = 2.0 / 3.0\nt2 = n0 * 0.33\nt3 = n1 * t1\nt4 = t2 + t3\nanswer = t4 / t0\nprint(answer)" - ], - "Output Answer": [ - "0.44222222222222224" - ], - "split": "train" - }, - { - "Input": "15 different biology books and 8 different chemistry books lie on a shelf . in how many ways can a student pick 2 books of each type ?", - "Output Program": [ - "import math\nn0 = 15.0\nn1 = 8.0\nn2 = 2.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(n1)))\nt2 = n0 - n2\nt3 = n1 - n2\nt4 = math.factorial(min(15, int(t2)))\nt5 = math.factorial(min(15, int(t3)))\nt6 = t0 / t4\nt7 = t1 / t5\nt8 = t6 / n2\nt9 = t7 / n2\nanswer = t8 * t9\nprint(answer)" - ], - "Output Answer": [ - "2940" - ], - "split": "train" - }, - { - "Input": "what is the ratio of arun ' s monthly income in the year 2006 , suman ' s monthly income in the year 2007 and jyothi ' s monthly income in the year 2005 ?", - "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": "the ratio of red balls to blue balls is 3 : 7 . 70 % of the red balls and 30 % of the blue balls are tennis balls . how many of the balls are tennis balls ?", - "Output Program": [ - "n0 = 3.0\nn1 = 7.0\nn2 = 70.0\nn3 = 30.0\nt0 = n0 + n1\nt1 = n0 * n2\nt2 = n1 * n3\nt3 = t1 + t2\nanswer = t3 / t0\nprint(answer)" - ], - "Output Answer": [ - "42" - ], - "split": "train" - }, - { - "Input": "find the fraction which has the same ratio to 2 / 5 that 3 / 7 has to 6 / 5", - "Output Program": [ - "n0 = 2.0\nn1 = 5.0\nn2 = 3.0\nn3 = 7.0\nn4 = 6.0\nn5 = 5.0\nt0 = n2 / n3\nt1 = n4 / n5\nt2 = n0 / n1\nt3 = t0 / t1\nanswer = t3 * t2\nprint(answer)" - ], - "Output Answer": [ - "0.14285714285714288" - ], - "split": "train" - }, - { - "Input": "a certain store sold pens for $ 0.35 each and pencils for $ 0.25 each . if a customer purchased both pens and pencils from the store for a total of $ 1.80 , what total number of pens and pencils did the customer purchase ?", - "Output Program": [ - "n0 = 0.35\nn1 = 0.25\nn2 = 1.8\nt0 = n0 + n1\nt1 = n2 / t0\nanswer = t1 * 2.0\nprint(answer)" - ], - "Output Answer": [ - "6" - ], - "split": "train" - }, - { - "Input": "in a certain pet shop , the ratio of dogs to cats to bunnies in stock is 7 : 7 : 8 . if the shop carries 330 dogs and bunnies total in stock , how many dogs are there ?", - "Output Program": [ - "n0 = 7.0\nn1 = 7.0\nn2 = 8.0\nn3 = 330.0\nt0 = n0 + n2\nt1 = n3 / t0\nanswer = n0 * t1\nprint(answer)" - ], - "Output Answer": [ - "154" - ], - "split": "train" - }, - { - "Input": "the probability of two events a and b are 0.15 and 0.40 respectively . the probability that both a and b occur is 0.15 . the probability that neither a nor b occur is _________", - "Output Program": [ - "n0 = 0.15\nn1 = 0.4\nn2 = 0.15\nt0 = n0 + n1\nt1 = t0 - n2\nanswer = 1.0 - t1\nprint(answer)" - ], - "Output Answer": [ - "0.6" - ], - "split": "train" - }, - { - "Input": "if 12 ounces of a strong vinegar solution are diluted with 50 ounces of water to form a 7 - percent vinegar solution , what was the concentration of the original solution ?", - "Output Program": [ - "n0 = 12.0\nn1 = 50.0\nn2 = 7.0\nt0 = n0 + n1\nt1 = n2 * t0\nanswer = t1 / n0\nprint(answer)" - ], - "Output Answer": [ - "36.166666666666664" - ], - "split": "train" - }, - { - "Input": "a garrison of 400 men had a provision for 31 days . after 27 days 200 persons re - enforcement leave the garrison . find the number of days for which the remaining ration will be sufficient ?", - "Output Program": [ - "n0 = 400.0\nn1 = 31.0\nn2 = 27.0\nn3 = 200.0\nt0 = n1 - n2\nt1 = n0 * t0\nanswer = t1 / n3\nprint(answer)" - ], - "Output Answer": [ - "8" - ], - "split": "train" - }, - { - "Input": "170 kg of an alloy a is mixed with 250 kg of alloy b . if alloy a has lead and tin in the ratio 1 : 3 and alloy b has tin and copper in the ratio 3 : 5 , then the amount of tin in the new alloy is ?", - "Output Program": [ - "n0 = 170.0\nn1 = 250.0\nn2 = 1.0\nn3 = 3.0\nn4 = 3.0\nn5 = 5.0\nt0 = n2 + n3\nt1 = n4 + n5\nt2 = n0 / t0\nt3 = n1 / t1\nt4 = n3 * t2\nt5 = n4 * t3\nanswer = t4 + t5\nprint(answer)" - ], - "Output Answer": [ - "221.25" - ], - "split": "train" - }, - { - "Input": "in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the sport formulation contains 7 ounces of corn syrup , how many ounces of water does it contain ?", - "Output Program": [ - "n0 = 1.0\nn1 = 12.0\nn2 = 30.0\nn3 = 7.0\nt0 = n0 / n1\nt1 = n0 / n2\nt2 = t1 / 2.0\nt3 = t0 * 3.0\nt4 = t3 / t2\nanswer = n3 * t4\nprint(answer)" - ], - "Output Answer": [ - "105" - ], - "split": "train" - }, - { - "Input": "praveen starts business with rs . 3360 and after 5 months , hari joins with praveen as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is hari \u2019 s contribution in the capital ?", - "Output Program": [ - "n0 = 3360.0\nn1 = 5.0\nn2 = 2.0\nn3 = 3.0\nt0 = n1 / 12.0\nt1 = n2 / n3\nt2 = 1.0 - t0\nt3 = n0 / t2\nanswer = t3 / t1\nprint(answer)" - ], - "Output Answer": [ - "8640.000000000002" - ], - "split": "train" - }, - { - "Input": "each of the dogs in a certain kennel is a single color . each of the dogs in the kennel either has long fur or does not . of the 45 dogs in the kennel , 29 have long fur , 17 are brown , and 8 are neither long - furred nor brown . how many long - furred dogs are brown ?", - "Output Program": [ - "n0 = 45.0\nn1 = 29.0\nn2 = 17.0\nn3 = 8.0\nt0 = n1 + n2\nt1 = n0 - n3\nanswer = t0 - t1\nprint(answer)" - ], - "Output Answer": [ - "9" - ], - "split": "train" - }, - { - "Input": "if the numbers 1 to 96 are written on 96 pieces of paper , ( one on each ) and one piece is picked at random , then what is the probability that the number drawn is neither prime nor composite ?", - "Output Program": [ - "n0 = 1.0\nn1 = 96.0\nn2 = 96.0\n\nanswer = n0 / n1\nprint(answer)" - ], - "Output Answer": [ - "0.010416666666666666" - ], - "split": "train" - }, - { - "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 numbers will be even ?", - "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\nt0 = n2 * n7\nanswer = n3 / t0\nprint(answer)" - ], - "Output Answer": [ - "0.21428571428571427" - ], - "split": "train" - }, - { - "Input": "log 3 n + log 9 n what is 3 digit number n that will be whole number", - "Output Program": [ - "n0 = 3.0\nn1 = 9.0\nn2 = 3.0\n\nanswer = n1**min(n0, 5)\nprint(answer)" - ], - "Output Answer": [ - "729" - ], - "split": "train" - }, - { - "Input": "the ratio of the number of red cars in a certain parking lot to the number of black cars is 3 to 8 . if there are 75 black cars in the lot , how many red cars are there in the lot ?", - "Output Program": [ - "import math\nn0 = 3.0\nn1 = 8.0\nn2 = 75.0\nt0 = n0 / n1\nt1 = n2 * t0\nanswer = math.floor(t1)\nprint(answer)" - ], - "Output Answer": [ - "28" - ], - "split": "train" - }, - { - "Input": "a number is said to be prime saturated if the product of all the different positive prime factors of a is less than the square root of a . what is the greatest two digit prime saturated integer ?", - "Output Program": [ - "t0 = 2.0 * 3.0\nt1 = 100.0 - 10.0\nanswer = t0 + t1\nprint(answer)" - ], - "Output Answer": [ - "96" - ], - "split": "train" - }, - { - "Input": "a number is said to be prime saturated if the product of all the different positive prime factors of n is less than the square root of n . what is the greatest two digit prime saturated integer ?", - "Output Program": [ - "t0 = 2.0 * 3.0\nt1 = 100.0 - 10.0\nanswer = t0 + t1\nprint(answer)" - ], - "Output Answer": [ - "96" - ], - "split": "train" - }, - { - "Input": "sachin is younger than rahul by 7 years . if the ratio of their ages is 7 : 9 , find the age of sachin", - "Output Program": [ - "n0 = 7.0\nn1 = 7.0\nn2 = 9.0\nt0 = n2 - n1\nt1 = n0 / t0\nanswer = n1 * t1\nprint(answer)" - ], - "Output Answer": [ - "24.5" - ], - "split": "train" - }, - { - "Input": "share rs . 6000 among john , jose & binoy in the ration 2 : 4 : 6 . find the amount received by john ?", - "Output Program": [ - "n0 = 6000.0\nn1 = 2.0\nn2 = 4.0\nn3 = 6.0\nt0 = n0 / n1\nt1 = n0 / n3\nanswer = t0 - t1\nprint(answer)" - ], - "Output Answer": [ - "2000" - ], - "split": "train" - }, - { - "Input": "in a group of 89 students , 36 are taking history , and 32 are taking statistics . if 59 students are taking history or statistics or both , then how many students are taking history but not statistics ?", - "Output Program": [ - "n0 = 89.0\nn1 = 36.0\nn2 = 32.0\nn3 = 59.0\nt0 = n1 + n2\nt1 = t0 - n3\nanswer = n1 - t1\nprint(answer)" - ], - "Output Answer": [ - "27" - ], - "split": "train" - }, - { - "Input": "in township k , 1 / 5 of the housing units are equiped with cable tv . if 1 / 10 of the housing units , including 1 / 4 of those that are equiped with cable tv , are equipped with videocassette recorders , what fraction of the housing units have neither cable tv nor videocassette recorders ?", - "Output Program": [ - "n0 = 1.0\nn1 = 5.0\nn2 = 1.0\nn3 = 10.0\nn4 = 1.0\nn5 = 4.0\nt0 = n1 + n3\nt1 = n3 * 2.0\nanswer = t0 / t1\nprint(answer)" - ], - "Output Answer": [ - "0.75" - ], - "split": "train" - }, - { - "Input": "local kennel has cats and dogs in the ratio of 2 : 3 . if there are 6 fewer cats than dogs , how many dogs are in the kennel ?", - "Output Program": [ - "n0 = 2.0\nn1 = 3.0\nn2 = 6.0\n\nanswer = n1 * n2\nprint(answer)" - ], - "Output Answer": [ - "18" - ], - "split": "train" - }, - { - "Input": "the ratio of the number of females to males at a party was 1 : 2 but when 6 females and 6 males left , the ratio became 1 : 3 . how many people were at the party originally ?", - "Output Program": [ - "n0 = 1.0\nn1 = 2.0\nn2 = 6.0\nn3 = 6.0\nn4 = 1.0\nn5 = 3.0\nt0 = n1 * n2\nt1 = n5 * t0\nt2 = t1 - t0\nt3 = t2 / n1\nanswer = t3 + t2\nprint(answer)" - ], - "Output Answer": [ - "36" - ], - "split": "train" - }, - { - "Input": "a and b have monthly incomes in the ratio 5 : 6 and monthly expenditures in the ratio 3 : 4 . if they save rs . 1800 and rs . 1600 respectively , find the monthly income of b", - "Output Program": [ - "n0 = 5.0\nn1 = 6.0\nn2 = 3.0\nn3 = 4.0\nn4 = 1800.0\nn5 = 1600.0\nt0 = n3 * n4\nt1 = n0 * n3\nt2 = t0 / n2\nt3 = t1 / n2\nt4 = t2 - n5\nt5 = t3 - n1\nt6 = t4 / t5\nanswer = n1 * t6\nprint(answer)" - ], - "Output Answer": [ - "7199.999999999997" - ], - "split": "train" - }, - { - "Input": "a certain manufacturer of cake , muffin , and bread mixes has 100 buyers , of whom 50 purchases cake mix , 40 purchase muffin mix , and 16 purchase both cake mix and muffin mix . if a buyer is to be selected at random from the 100 buyers , what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix ?", - "Output Program": [ - "n0 = 100.0\nn1 = 50.0\nn2 = 40.0\nn3 = 16.0\nn4 = 100.0\nt0 = n1 + n2\nt1 = t0 - n3\nt2 = n0 - t1\nanswer = t2 / n0\nprint(answer)" - ], - "Output Answer": [ - "0.26" - ], - "split": "train" - }, - { - "Input": "a 60 kg metal bar made of alloy of tin and silver lost 6 kg of its weight in the water . 10 kg of tin loses 1.375 kg in the water ; 5 kg of silver loses 0.375 kg . what is the ratio of tin to silver in the bar ?", - "Output Program": [ - "n0 = 60.0\nn1 = 6.0\nn2 = 10.0\nn3 = 1.375\nn4 = 5.0\nn5 = 0.375\nt0 = n5 / n4\nt1 = n3 / n2\nt2 = n0 * t0\nt3 = t1 - t0\nt4 = n1 - t2\nt5 = t4 / t3\nt6 = n0 - t5\nanswer = t5 / t6\nprint(answer)" - ], - "Output Answer": [ - "0.6666666666666665" - ], - "split": "train" - }, - { - "Input": "6 ) a marketing firm determined that , of 240 households surveyed , 80 used neither brand a nor brand b soap . 60 used only brand a soap and for every household that used both brands of soap , 3 used only brand b soap . how many of the 200 household surveyed used both brands of soap ?", - "Output Program": [ - "n0 = 6.0\nn1 = 240.0\nn2 = 80.0\nn3 = 60.0\nn4 = 3.0\nn5 = 200.0\nt0 = n1 - n2\nt1 = t0 - n3\nanswer = t1 / 4.0\nprint(answer)" - ], - "Output Answer": [ - "25" - ], - "split": "train" - }, - { - "Input": "in a class of 87 students 41 are taking french , 22 are taking german . of the students taking french or german , 9 are taking both courses . how many students are not enrolled in either course ?", - "Output Program": [ - "n0 = 87.0\nn1 = 41.0\nn2 = 22.0\nn3 = 9.0\nt0 = n1 + n2\nt1 = t0 - n3\nanswer = n0 - t1\nprint(answer)" - ], - "Output Answer": [ - "33" - ], - "split": "train" - }, - { - "Input": "the hcf of two numbers is 62 and the other two factors of their lcm are 11 and 12 . what is the largest number .", - "Output Program": [ - "n0 = 62.0\nn1 = 11.0\nn2 = 12.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "744" - ], - "split": "train" - }, - { - "Input": "teas worth rs . 126 per kg and rs . 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs 152 per kg , the price of the third variety per kg will be ?", - "Output Program": [ - "n0 = 126.0\nn1 = 135.0\nn2 = 1.0\nn3 = 1.0\nn4 = 2.0\nn5 = 152.0\nt0 = n2 + n2\nt1 = n0 + n1\nt2 = n4 + t0\nt3 = n5 * t2\nt4 = t3 - t1\nanswer = t4 / n4\nprint(answer)" - ], - "Output Answer": [ - "173.5" - ], - "split": "train" - }, - { - "Input": "the ratio of type of pen and type of notebook is 5 : 4 . and in 80 ways one can start writing . tell me the no . of pen and no . of notebook .", - "Output Program": [ - "n0 = 5.0\nn1 = 4.0\nn2 = 80.0\nt0 = n0 * n2\nt1 = t0 / n1\nanswer = t1 / 10.0\nprint(answer)" - ], - "Output Answer": [ - "10" - ], - "split": "train" - }, - { - "Input": "the ratio of the incomes of uma and bala is 8 : 7 and the ratio of their expenditure is 7 : 6 . if at the end of the year , each saves $ 2000 then the income of uma is ?", - "Output Program": [ - "n0 = 8.0\nn1 = 7.0\nn2 = 7.0\nn3 = 6.0\nn4 = 2000.0\n\nanswer = n0 * n4\nprint(answer)" - ], - "Output Answer": [ - "16000" - ], - "split": "train" - }, - { - "Input": "how many of the positive factors of 15 , 45 and how many common factors are there in numbers ?", - "Output Program": [ - "n0 = 15.0\nn1 = 45.0\n\nanswer = n1 / n0\nprint(answer)" - ], - "Output Answer": [ - "3" - ], - "split": "train" - }, - { - "Input": "how many positive integers between 20 and 2000 ( both are inclusive ) are there such that they are multiples of 10 ?", - "Output Program": [ - "n0 = 20.0\nn1 = 2000.0\nn2 = 10.0\nt0 = n1 - n0\nanswer = t0 / n2\nprint(answer)" - ], - "Output Answer": [ - "198" - ], - "split": "train" - }, - { - "Input": "water consists of hydrogen and oxygen , and the approximate ratio , by mass , of hydrogen to oxygen is 2 : 16 . approximately how many grams of hydrogen are there in 171 grams of water ?", - "Output Program": [ - "n0 = 2.0\nn1 = 16.0\nn2 = 171.0\nt0 = n0 + n1\nt1 = n2 / t0\nanswer = n0 * t1\nprint(answer)" - ], - "Output Answer": [ - "19" - ], - "split": "train" - }, - { - "Input": "in what ratio should a variety of rice costing rs . 6 per kg be mixed with another variety of rice costing rs . 8.75 per kg to obtain a mixture costing rs . 7.50 per kg ?", - "Output Program": [ - "n0 = 6.0\nn1 = 8.75\nn2 = 7.5\nt0 = n1 - n2\nt1 = n1 - n0\nt2 = t0 / t1\nt3 = 1.0 - t2\nanswer = t2 / t3\nprint(answer)" - ], - "Output Answer": [ - "0.8333333333333334" - ], - "split": "train" - }, - { - "Input": "what is log 3 ( 4 ) log 4 ( 5 ) . . . log 80 ( 81 ) ?", - "Output Program": [ - "import math\nn0 = 3.0\nn1 = 4.0\nn2 = 4.0\nn3 = 5.0\nn4 = 80.0\nn5 = 81.0\nt0 = math.log(max(1e-5, n5), 2)\nt1 = math.log(max(1e-5, n0), 2)\nanswer = t0 / t1\nprint(answer)" - ], - "Output Answer": [ - "4" - ], - "split": "train" - }, - { - "Input": "rajat , vikas and abhishek are submitting questions in the ratio 7 : 3 : 2 . if total number of questions submitted by them is 24 . find the number of questions submitted by vikas .", - "Output Program": [ - "n0 = 7.0\nn1 = 3.0\nn2 = 2.0\nn3 = 24.0\n\nanswer = n3 / 4.0\nprint(answer)" - ], - "Output Answer": [ - "6" - ], - "split": "train" - }, - { - "Input": "each of the dogs in a certain kennel is a single color . each of the dogs in the kennel either has long fur or does not . of the 45 dogs in the kennel , 26 have long fur , 22 are brown , and 8 are neither long - furred nor brown . how many long - furred dogs are brown ?", - "Output Program": [ - "n0 = 45.0\nn1 = 26.0\nn2 = 22.0\nn3 = 8.0\nt0 = n1 + n2\nt1 = n0 - n3\nanswer = t0 - t1\nprint(answer)" - ], - "Output Answer": [ - "11" - ], - "split": "train" - }, - { - "Input": "how many multiples of 8 are there between 100 and 200 ( both are inclusive ) ?", - "Output Program": [ - "n0 = 8.0\nn1 = 100.0\nn2 = 200.0\nt0 = n2 - n1\nt1 = t0 / n0\nanswer = t1 + 1.0\nprint(answer)" - ], - "Output Answer": [ - "13.5" - ], - "split": "train" - }, - { - "Input": "the ratio of incomes of two person p 1 and p 2 is 5 : 4 and the ratio of their expenditures is 3 : 2 . if at the end of the year , each saves rs . 1600 , then what is the income of p 1 ?", - "Output Program": [ - "n0 = 1.0\nn1 = 2.0\nn2 = 5.0\nn3 = 4.0\nn4 = 3.0\nn5 = 2.0\nn6 = 1600.0\nn7 = 1.0\nt0 = n6 / n1\nt1 = n4 * t0\nt2 = t1 - n6\nanswer = n2 * t2\nprint(answer)" - ], - "Output Answer": [ - "4000" - ], - "split": "train" - }, - { - "Input": "the ratio of 3 numbers is 5 : 3 : 4 and their sum is 108 . the second number of the 3 numbers is ?", - "Output Program": [ - "n0 = 3.0\nn1 = 5.0\nn2 = 3.0\nn3 = 4.0\nn4 = 108.0\nn5 = 3.0\nt0 = n0 + n1\nt1 = n3 + t0\nt2 = n0 / t1\nanswer = n4 * t2\nprint(answer)" - ], - "Output Answer": [ - "27" - ], - "split": "train" - }, - { - "Input": "in a college the ratio of the numbers of boys to the girls is 8 : 5 . if there are 120 girls , the total number of students in the college is ?", - "Output Program": [ - "n0 = 8.0\nn1 = 5.0\nn2 = 120.0\nt0 = n0 / n1\nt1 = n2 * t0\nanswer = n2 + t1\nprint(answer)" - ], - "Output Answer": [ - "312" - ], - "split": "train" - }, - { - "Input": "if 75 percent of a class answered the first question on a certain test correctly , 65 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?", - "Output Program": [ - "n0 = 75.0\nn1 = 65.0\nn2 = 20.0\nt0 = n0 + n1\nt1 = n2 + t0\nanswer = t1 - 100.0\nprint(answer)" - ], - "Output Answer": [ - "60" - ], - "split": "train" - }, - { - "Input": "if 80 percent of the test takers taking an old paper and pencil gmat exam answered the first question on a given math section correctly , and 75 percent of the test takers answered the second question correctly , and 5 percent of the test takers answered neither question correctly , what percent answered both correctly ?", - "Output Program": [ - "n0 = 80.0\nn1 = 75.0\nn2 = 5.0\nt0 = n0 + n1\nt1 = n2 + t0\nanswer = t1 - 100.0\nprint(answer)" - ], - "Output Answer": [ - "60" - ], - "split": "train" - }, - { - "Input": "compound x contains elements a and b at an approximate ratio , by weight , of 2 : 10 . approximately how many grams of element b are there in 324 grams of compound x ?", - "Output Program": [ - "n0 = 2.0\nn1 = 10.0\nn2 = 324.0\nt0 = n0 + n1\nt1 = n1 * n2\nanswer = t1 / t0\nprint(answer)" - ], - "Output Answer": [ - "270" - ], - "split": "train" - }, - { - "Input": "in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the ` ` sport ' ' formulation , the ratio of flavoring to corn syrup is 3 times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the ` ` sport ' ' formulation contains 3 ounces of corn syrup , how many ounces of water does it contain ?", - "Output Program": [ - "n0 = 1.0\nn1 = 12.0\nn2 = 30.0\nn3 = 3.0\nn4 = 3.0\nt0 = n1 / 3.0\nt1 = n2 * 2.0\nt2 = n3 / t0\nanswer = t2 * t1\nprint(answer)" - ], - "Output Answer": [ - "45" - ], - "split": "train" - }, - { - "Input": "of the diplomats who attended a summit conference : 20 spoke french , 32 did not speak english and 20 % of the diplomats spoke neither french nor english . if 10 % of the diplomats spoke both french and english , then how many diplomats attended the conference ?", - "Output Program": [ - "n0 = 20.0\nn1 = 32.0\nn2 = 20.0\nn3 = 10.0\nt0 = n0 / 100.0\nt1 = n3 / 100.0\nt2 = n1 - n0\nt3 = t0 - t1\nanswer = t2 / t3\nprint(answer)" - ], - "Output Answer": [ - "120" - ], - "split": "train" - }, - { - "Input": "the diluted wine contains only 8 liters of wine and the rest is water . a new mixture whose concentration is 30 % , is to be formed by replacing wine . how many liters of mixture shall be replaced with pure wine if there was initially 32 liters of water in the mixture ?", - "Output Program": [ - "n0 = 8.0\nn1 = 30.0\nn2 = 32.0\nt0 = n0 + n2\nt1 = 3.0 + 4.0\nt2 = t1 / n0\nt3 = 1.0 - t2\nanswer = t0 * t3\nprint(answer)" - ], - "Output Answer": [ - "5" - ], - "split": "train" - }, - { - "Input": "in what ratio should a variety of rice costing rs . 7 per kg be mixed with another variety of rice costing rs . 8.75 per kg to obtain a mixture costing rs . 7.50 per kg ?", - "Output Program": [ - "n0 = 7.0\nn1 = 8.75\nn2 = 7.5\nt0 = n1 - n2\nt1 = n1 - n0\nt2 = t0 / t1\nt3 = 1.0 - t2\nanswer = t2 / t3\nprint(answer)" - ], - "Output Answer": [ - "2.5" - ], - "split": "train" - }, - { - "Input": "if the ratio of two number is 2 : 5 and lcm of the number is 160 then what is the number .", - "Output Program": [ - "n0 = 2.0\nn1 = 5.0\nn2 = 160.0\nt0 = n0 * n1\nanswer = n2 / t0\nprint(answer)" - ], - "Output Answer": [ - "16" - ], - "split": "train" - }, - { - "Input": "income and expenditure of a person are in the ratio 5 : 4 . if the income of the person is rs . 15000 , then find his savings ?", - "Output Program": [ - "n0 = 5.0\nn1 = 4.0\nn2 = 15000.0\nt0 = n1 / n0\nt1 = n2 * t0\nanswer = n2 - t1\nprint(answer)" - ], - "Output Answer": [ - "3000" - ], - "split": "train" - }, - { - "Input": "solution a is 40 % salt and solution b is 80 % salt . if you have 30 ounces of solution a and 60 ounces of solution b , in what ratio could you mix solution a with solution b to produce 50 ounces of a 50 % salt solution ?", - "Output Program": [ - "n0 = 40.0\nn1 = 80.0\nn2 = 30.0\nn3 = 60.0\nn4 = 50.0\nn5 = 50.0\nt0 = n1 / 100.0\nt1 = n4 / 100.0\nt2 = n0 / 100.0\nt3 = n4 * t0\nt4 = n4 * t1\nt5 = t0 - t2\nt6 = t3 - t4\nt7 = t6 / t5\nt8 = n4 - t7\nanswer = t7 / t8\nprint(answer)" - ], - "Output Answer": [ - "3" - ], - "split": "train" - }, - { - "Input": "in a class of 38 children , 19 play tennis , 21 play squash and 10 play neither sport . ( 1 ) how many children play both sports ?", - "Output Program": [ - "n0 = 38.0\nn1 = 19.0\nn2 = 21.0\nn3 = 10.0\nn4 = 1.0\nt0 = n1 + n2\nt1 = n0 - n3\nanswer = t0 - t1\nprint(answer)" - ], - "Output Answer": [ - "12" - ], - "split": "train" - }, - { - "Input": "of the 200 stamps in a collection , 90 are foreign and 70 are more than 10 years old . if 20 stamps are both foreign and more than 10 years old , how many stamps are neither foreign nor more than 10 years old ?", - "Output Program": [ - "n0 = 200.0\nn1 = 90.0\nn2 = 70.0\nn3 = 10.0\nn4 = 20.0\nn5 = 10.0\nn6 = 10.0\nt0 = n1 + n2\nt1 = t0 - n4\nanswer = n0 - t1\nprint(answer)" - ], - "Output Answer": [ - "60" - ], - "split": "train" - }, - { - "Input": "the ratio of spinsters to cats is 2 to 9 . if there are 42 more cats than spinsters , how many spinsters are there ?", - "Output Program": [ - "n0 = 2.0\nn1 = 9.0\nn2 = 42.0\nt0 = n1 - n0\nt1 = n2 / t0\nanswer = n0 * t1\nprint(answer)" - ], - "Output Answer": [ - "12" - ], - "split": "train" - }, - { - "Input": "a certain bag contains 100 balls \u00e2 \u20ac \u201d 20 white , 30 green , 10 yellow , 37 red , and 3 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?", - "Output Program": [ - "n0 = 100.0\nn1 = 20.0\nn2 = 30.0\nn3 = 10.0\nn4 = 37.0\nn5 = 3.0\nt0 = n4 + n5\nt1 = n0 - t0\nanswer = t1 / n0\nprint(answer)" - ], - "Output Answer": [ - "0.6" - ], - "split": "train" - }, - { - "Input": "in a ratio which is equal to 4 : 6 , if the antecedent is 20 , then the consequent is ?", - "Output Program": [ - "n0 = 4.0\nn1 = 6.0\nn2 = 20.0\nt0 = n2 / 2.0\nanswer = n2 + t0\nprint(answer)" - ], - "Output Answer": [ - "30" - ], - "split": "train" - }, - { - "Input": "sandy is younger than molly by 20 years . if the ratio of their ages is 7 : 9 , how old is sandy ?", - "Output Program": [ - "n0 = 20.0\nn1 = 7.0\nn2 = 9.0\nt0 = n2 - n1\nt1 = n1 / t0\nanswer = n0 * t1\nprint(answer)" - ], - "Output Answer": [ - "70" - ], - "split": "train" - }, - { - "Input": "on a certain farm the ratio of horses to cows is 6 : 1 . if the farm were to sell 15 horses and buy 15 cows , the ratio of horses to cows would then be 3 : 1 . after the transaction , how many more horses than cows would the farm own ?", - "Output Program": [ - "n0 = 6.0\nn1 = 1.0\nn2 = 15.0\nn3 = 15.0\nn4 = 3.0\nn5 = 1.0\nt0 = n2 * n4\nt1 = n2 * n5\nt2 = n0 * n5\nt3 = t0 + t1\nt4 = t2 - n4\nt5 = t3 / t4\nt6 = n2 + t5\nt7 = n0 * t5\nt8 = t7 - n2\nanswer = t8 - t6\nprint(answer)" - ], - "Output Answer": [ - "70" - ], - "split": "train" - }, - { - "Input": "a bag holds 2 red marbles and 3 green marbles . if you removed two randomly selected marbles from the bag , without replacement , what is the probability that both would be red ?", - "Output Program": [ - "import scipy\nn0 = 2.0\nn1 = 3.0\nt0 = n0 + n1\nt1 = scipy.special.comb(n0, n0)\nt2 = scipy.special.comb(t0, 2.0)\nanswer = t1 / t2\nprint(answer)" - ], - "Output Answer": [ - "0.1" - ], - "split": "train" - }, - { - "Input": "income and expenditure of a person are in the ratio 10 : 4 . if the income of the person is rs . 19000 , then find his savings ?", - "Output Program": [ - "n0 = 10.0\nn1 = 4.0\nn2 = 19000.0\nt0 = n1 / n0\nt1 = n2 * t0\nanswer = n2 - t1\nprint(answer)" - ], - "Output Answer": [ - "11400" - ], - "split": "train" - }, - { - "Input": "the ratio of numbers is 4 : 5 and their h . c . f is 4 . their l . c . m is :", - "Output Program": [ - "import scipy\nn0 = 4.0\nn1 = 5.0\nn2 = 4.0\nt0 = n0 * n2\nt1 = n1 * n2\nanswer = scipy.lcm(int(t0), int(t1))\nprint(answer)" - ], - "Output Answer": [ - "80" - ], - "split": "train" - }, - { - "Input": "a boy multiplied 987 by a certain number and obtained 559981 as his answer . if in the answer both 98 are wrong and the other digits are correct , then the correct answer would be :", - "Output Program": [ - "n0 = 987.0\nn1 = 559981.0\nn2 = 98.0\nt0 = n1 / n0\nt1 = t0 - 4.0\nt2 = t1 - 0.33\nanswer = n0 * t2\nprint(answer)" - ], - "Output Answer": [ - "555707.2899999999" - ], - "split": "train" - }, - { - "Input": "a number is said to be prime saturated if the product of all the different positive prime factors of q is less than the square root of q . what is the greatest two digit prime saturated integer ?", - "Output Program": [ - "t0 = 2.0 * 3.0\nt1 = 100.0 - 10.0\nanswer = t0 + t1\nprint(answer)" - ], - "Output Answer": [ - "96" - ], - "split": "train" - }, - { - "Input": "sachin is younger than rahul by 7 years . if the ratio of their ages is 5 : 12 , find the age of sachin", - "Output Program": [ - "n0 = 7.0\nn1 = 5.0\nn2 = 12.0\nt0 = n2 - n1\nt1 = n0 / t0\nanswer = n1 * t1\nprint(answer)" - ], - "Output Answer": [ - "5" - ], - "split": "train" - }, - { - "Input": "a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 9 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many liter e of liquid a was contained by the can initially ?", - "Output Program": [ - "n0 = 7.0\nn1 = 5.0\nn2 = 9.0\nn3 = 7.0\nn4 = 9.0\nt0 = n0 + n2\nt1 = n0 + n1\nt2 = n0 * n2\nt3 = n0 * n1\nt4 = n1 / t1\nt5 = t2 - t3\nt6 = n2 * t4\nt7 = n2 - t6\nt8 = t0 * t7\nt9 = t8 / t5\nanswer = n0 * t9\nprint(answer)" - ], - "Output Answer": [ - "21" - ], - "split": "train" - }, - { - "Input": "hree number are in the ratio of 3 : 4 : 5 and their l . c . m . is 2400 . their h . c . f . is :", - "Output Program": [ - "n0 = 3.0\nn1 = 4.0\nn2 = 5.0\nn3 = 2400.0\nt0 = n0 * n1\nt1 = n2 * t0\nanswer = n3 / t1\nprint(answer)" - ], - "Output Answer": [ - "40" - ], - "split": "train" - }, - { - "Input": "a factory produces 1 defective bulb out of 10 bulbs a yr . if it produces 870 bulbs a yr , how many defective bulbs are produced ?", - "Output Program": [ - "n0 = 1.0\nn1 = 10.0\nn2 = 870.0\n\nanswer = n2 / n1\nprint(answer)" - ], - "Output Answer": [ - "87" - ], - "split": "train" - }, - { - "Input": "if w and y are both odd prime numbers and w < y , how many distinct positive integer factors does 2 wy have ?", - "Output Program": [ - "n0 = 2.0\nt0 = n0 + 3.0\nanswer = t0 + 3.0\nprint(answer)" - ], - "Output Answer": [ - "8" - ], - "split": "train" - }, - { - "Input": "out of 450 students of a school , 325 play football , 175 play cricket and 50 neither play football nor cricket . how many students play both football and cricket ?", - "Output Program": [ - "n0 = 450.0\nn1 = 325.0\nn2 = 175.0\nn3 = 50.0\nt0 = n1 + n2\nt1 = n0 - n3\nanswer = t0 - t1\nprint(answer)" - ], - "Output Answer": [ - "100" - ], - "split": "train" - }, - { - "Input": "210 school students were asked in a survey if they preferred windows or mac brand computers . 60 students claimed that they preferred mac to windows brand computers . one third as many of the students who preferred mac to windows , equally preferred both brands . 90 of the students had no preference . how many of the students in the survey preferred windows to mac brand computers ?", - "Output Program": [ - "n0 = 210.0\nn1 = 60.0\nn2 = 90.0\nt0 = n1 + n2\nt1 = n1 / 3.0\nt2 = t0 + t1\nanswer = n0 - t2\nprint(answer)" - ], - "Output Answer": [ - "40" - ], - "split": "train" - }, - { - "Input": "a certain bag contains 100 balls \u00e2 \u20ac \u201d 10 white , 30 green , 10 yellow , 47 red , and 3 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?", - "Output Program": [ - "n0 = 100.0\nn1 = 10.0\nn2 = 30.0\nn3 = 10.0\nn4 = 47.0\nn5 = 3.0\nt0 = n4 + n5\nt1 = n0 - t0\nanswer = t1 / n0\nprint(answer)" - ], - "Output Answer": [ - "0.5" - ], - "split": "train" - }, - { - "Input": "among 400 students , 51 % study sociology , 46 % study mathematics and 40 % study biology . if 34 % of students study both mathematics and sociology , what is the largest possible number of students who study biology but do not study either mathematics or sociology ?", - "Output Program": [ - "n0 = 400.0\nn1 = 51.0\nn2 = 46.0\nn3 = 40.0\nn4 = 34.0\nt0 = n0 / 100.0\nt1 = n1 * t0\nt2 = n2 * t0\nt3 = n4 * t0\nt4 = t1 + t2\nt5 = t4 - t3\nanswer = n0 - t5\nprint(answer)" - ], - "Output Answer": [ - "148" - ], - "split": "train" - }, - { - "Input": "a certain bag contains 60 balls \u2014 22 white , 10 green , 7 yellow , 15 red , and 6 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?", - "Output Program": [ - "n0 = 60.0\nn1 = 22.0\nn2 = 10.0\nn3 = 7.0\nn4 = 15.0\nn5 = 6.0\nt0 = n1 + n2\nt1 = n3 + t0\nanswer = t1 / n0\nprint(answer)" - ], - "Output Answer": [ - "0.65" - ], - "split": "train" - }, - { - "Input": "in a group of 90 people , 55 have visited iceland and 33 have visited norway . if 51 people have visited both iceland and norway , how many people have visited neither country ?", - "Output Program": [ - "n0 = 90.0\nn1 = 55.0\nn2 = 33.0\nn3 = 51.0\nt0 = n1 + n2\nt1 = t0 - n3\nanswer = n0 - t1\nprint(answer)" - ], - "Output Answer": [ - "53" - ], - "split": "train" - }, - { - "Input": "the ratio of income of anand to that of balu is 5 : 4 and the expenditure of anand to that of balu is 3 : 2 . if at the end of the year , each saves rs , 800 , the income of anand is :", - "Output Program": [ - "n0 = 5.0\nn1 = 4.0\nn2 = 3.0\nn3 = 2.0\nn4 = 800.0\nt0 = n0 * n4\nt1 = n1 * n4\nt2 = n1 * n2\nt3 = n0 * n3\nt4 = t0 - t1\nt5 = t2 - t3\nt6 = t4 / t5\nt7 = n2 * t6\nanswer = n4 + t7\nprint(answer)" - ], - "Output Answer": [ - "2000" - ], - "split": "train" - }, - { - "Input": "income and expenditure of a person are in the ratio 10 : 8 . if the income of the person is rs . 10000 , then find his savings ?", - "Output Program": [ - "n0 = 10.0\nn1 = 8.0\nn2 = 10000.0\nt0 = n1 / n0\nt1 = n2 * t0\nanswer = n2 - t1\nprint(answer)" - ], - "Output Answer": [ - "2000" - ], - "split": "train" - }, - { - "Input": "in a class of 150 students 55 speak english \u037e 85 speak telugu and 30 speak neither english nor telugu how many speak both english and telugu ?", - "Output Program": [ - "n0 = 150.0\nn1 = 55.0\nn2 = 85.0\nn3 = 30.0\nt0 = n1 + n2\nt1 = n0 - n3\nanswer = t0 - t1\nprint(answer)" - ], - "Output Answer": [ - "20" - ], - "split": "train" - }, - { - "Input": "the h . c . f . of two numbers is 28 and the other two factors of their l . c . m . are 12 and 15 . the larger of the two numbers is", - "Output Program": [ - "n0 = 28.0\nn1 = 12.0\nn2 = 15.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "420" - ], - "split": "train" - }, - { - "Input": "find the fraction which has the same ratio to 2 / 13 that 5 / 34 has to 7 / 48 .", - "Output Program": [ - "n0 = 2.0\nn1 = 13.0\nn2 = 5.0\nn3 = 34.0\nn4 = 7.0\nn5 = 48.0\nt0 = n2 / n3\nt1 = n4 / n5\nt2 = n0 / n1\nt3 = t0 / t1\nanswer = t3 * t2\nprint(answer)" - ], - "Output Answer": [ - "0.15513897866839044" - ], - "split": "train" - }, - { - "Input": "p starts a business with rs . 4000 . after 4 months , q joins with p as his partner . after a year , the profit is divided in the ratio 2 : 3 . q ' s contribution in the capital is ?", - "Output Program": [ - "n0 = 4000.0\nn1 = 4.0\nn2 = 2.0\nn3 = 3.0\nt0 = n0 * 12.0\nt1 = 12.0 - n1\nt2 = n3 * t0\nt3 = t2 / n2\nanswer = t3 / t1\nprint(answer)" - ], - "Output Answer": [ - "9000" - ], - "split": "train" - }, - { - "Input": "two integers are in the ratio of 1 to 3 . if 10 is added to the smaller number , the ratio becomes 1 to 1 . find the larger integer .", - "Output Program": [ - "n0 = 1.0\nn1 = 3.0\nn2 = 10.0\nn3 = 1.0\nn4 = 1.0\nt0 = n2 * n4\nt1 = n1 - n4\nt2 = t0 / t1\nanswer = n1 * t2\nprint(answer)" - ], - "Output Answer": [ - "15" - ], - "split": "train" - }, - { - "Input": "a shipment of 220 smartphones contains 84 that are defective . if a customer buys two smartphones at random from the shipment , what is the approximate probability that both phones are defective ?", - "Output Program": [ - "n0 = 220.0\nn1 = 84.0\nt0 = n1 - 1.0\nt1 = n0 - 1.0\nt2 = n1 * t0\nt3 = n0 * t1\nanswer = t2 / t3\nprint(answer)" - ], - "Output Answer": [ - "0.14470734744707348" - ], - "split": "train" - }, - { - "Input": "the ratio of the money with ravi and giri is 6 : 7 and that with giri and kiran is 6 : 15 . if ravi has $ 36 , how much money does kiran have ?", - "Output Program": [ - "n0 = 6.0\nn1 = 7.0\nn2 = 6.0\nn3 = 15.0\nn4 = 36.0\nt0 = n4 / n0\nt1 = n1 * t0\nt2 = t1 / t0\nanswer = n3 * t2\nprint(answer)" - ], - "Output Answer": [ - "105" - ], - "split": "train" - }, - { - "Input": "how many positive integers h between 200 and 300 ( both inclusive ) are not divisible by 2 , 3 or 5 ?", - "Output Program": [ - "import math\nn0 = 200.0\nn1 = 300.0\nn2 = 2.0\nn3 = 3.0\nn4 = 5.0\nt0 = n3 * n4\nt1 = n1 - n0\nt2 = t1 + 1.0\nt3 = n2 + t0\nt4 = t1 / n2\nt5 = t1 / n3\nt6 = t1 / n4\nt7 = t4 + 1.0\nt8 = t5 + 1.0\nt9 = t6 + 1.0\nt10 = t8 - t3\nt11 = t9 - t0\nt12 = math.floor(t10)\nt13 = t12 + 1.0\nt14 = t7 + t13\nt15 = t14 + t11\nanswer = t2 - t15\nprint(answer)" - ], - "Output Answer": [ - "26" - ], - "split": "train" - }, - { - "Input": "in a certain school , the ratio of boys to girls is 5 to 13 . if there are 128 more girls than boys , how many boys are there ?", - "Output Program": [ - "n0 = 5.0\nn1 = 13.0\nn2 = 128.0\nt0 = n0 / n1\nt1 = 1.0 - t0\nt2 = n2 / t1\nanswer = t2 - n2\nprint(answer)" - ], - "Output Answer": [ - "80" - ], - "split": "train" - }, - { - "Input": "a certain telephone company offers two plans , a and b . under plan a , the company charges a total of $ 0.60 for the first 5 minutes of each call and $ 0.06 per minute thereafter . under plan b , the company charges $ 0.08 per minute of each call . what is the duration of a call , in minutes , for which the company charges the same amount under plan a and under plan b ?", - "Output Program": [ - "n0 = 0.6\nn1 = 5.0\nn2 = 0.06\nn3 = 0.08\nt0 = n1 * n2\nt1 = n3 - n2\nt2 = n0 - t0\nanswer = t2 / t1\nprint(answer)" - ], - "Output Answer": [ - "14.999999999999996" - ], - "split": "train" - }, - { - "Input": "the ratio , by volume , of bleach to detergent to water in a certain solution is 4 : 40 : 100 . the solution will be altered so that the ratio of bleach to detergent is tripled while the ratio of detergent to water is halved . if the altered solution will contain 300 liters of water , how many liters of detergent will it contain ?", - "Output Program": [ - "n0 = 4.0\nn1 = 40.0\nn2 = 100.0\nn3 = 300.0\nt0 = n3 / n2\nt1 = n1 / 2.0\nanswer = t0 * t1\nprint(answer)" - ], - "Output Answer": [ - "60" - ], - "split": "train" - }, - { - "Input": "in the biotechnology class of 2000 , there were x graduates . 32 of the graduates found a job , 45 continued on to their second degree and 13 did both . if only 9 people did n ' t do both , what is x equal to ?", - "Output Program": [ - "n0 = 2000.0\nn1 = 32.0\nn2 = 45.0\nn3 = 13.0\nn4 = 9.0\nt0 = n1 + n2\nt1 = t0 - n3\nanswer = n4 + t1\nprint(answer)" - ], - "Output Answer": [ - "73" - ], - "split": "train" - }, - { - "Input": "in what ratio should a variety of rice costing rs . 5.5 per kg be mixed with another variety of rice costing rs . 8.75 per kg to obtain a mixture costing rs . 7.50 per kg ?", - "Output Program": [ - "n0 = 5.5\nn1 = 8.75\nn2 = 7.5\nt0 = n1 - n2\nt1 = n1 - n0\nt2 = t0 / t1\nt3 = 1.0 - t2\nanswer = t2 / t3\nprint(answer)" - ], - "Output Answer": [ - "0.625" - ], - "split": "train" - }, - { - "Input": "what is the least positive integer that is not a factor of 30 ! and is not a prime number ?", - "Output Program": [ - "n0 = 30.0\nt0 = n0 + 1.0\nanswer = t0 * 2.0\nprint(answer)" - ], - "Output Answer": [ - "62" - ], - "split": "train" - }, - { - "Input": "in a certain pet shop , the ratio of dogs to cats to bunnies in stock is 3 : 7 : 12 . if the shop carries 375 dogs and bunnies total in stock , how many dogs are there ?", - "Output Program": [ - "n0 = 3.0\nn1 = 7.0\nn2 = 12.0\nn3 = 375.0\nt0 = n0 + n2\nt1 = n3 / t0\nanswer = n0 * t1\nprint(answer)" - ], - "Output Answer": [ - "75" - ], - "split": "train" - }, - { - "Input": "income and expenditure of a person are in the ratio 8 : 7 . if the income of the person is rs . 40000 , then find his savings ?", - "Output Program": [ - "n0 = 8.0\nn1 = 7.0\nn2 = 40000.0\nt0 = n1 / n0\nt1 = n2 * t0\nanswer = n2 - t1\nprint(answer)" - ], - "Output Answer": [ - "5000" - ], - "split": "train" - }, - { - "Input": "present ages of abi and suji are in the ratio of 5 : 4 respectively . 3 years hence , the ratio of their ages will become 11 : 9 respectively . what is suji ' s present age in years ?", - "Output Program": [ - "n0 = 5.0\nn1 = 4.0\nn2 = 3.0\nn3 = 11.0\nn4 = 9.0\nt0 = n0 + n1\nt1 = t0 - n2\nanswer = n1 * t1\nprint(answer)" - ], - "Output Answer": [ - "24" - ], - "split": "train" - }, - { - "Input": "the ratio of flour to water to sugar in a recipe is 8 : 4 : 3 . the ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar . if the new recipe calls for 2 cups of water , how much sugar is required ?", - "Output Program": [ - "n0 = 8.0\nn1 = 4.0\nn2 = 3.0\nn3 = 2.0\nt0 = n3 / n1\nt1 = n2 * 4.0\nanswer = t0 * t1\nprint(answer)" - ], - "Output Answer": [ - "6" - ], - "split": "train" - }, - { - "Input": "ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 26 years . what is deepak present age", - "Output Program": [ - "n0 = 4.0\nn1 = 3.0\nn2 = 6.0\nn3 = 26.0\nt0 = n3 - n2\nt1 = n1 * t0\nanswer = t1 / n0\nprint(answer)" - ], - "Output Answer": [ - "15" - ], - "split": "train" - }, - { - "Input": "the weights of one liter vegetable ghee packet of two brands \u2018 a \u2019 and \u2018 b \u2019 are 900 gm and 800 gm respectively . if they are mixed in the ratio of 3 : 2 by volumes to form a mixture of 4 liters , what is the weight ( in kg ) of the mixture ?", - "Output Program": [ - "n0 = 900.0\nn1 = 800.0\nn2 = 3.0\nn3 = 2.0\nn4 = 4.0\nt0 = n2 + n3\nt1 = n0 * n2\nt2 = n1 * n3\nt3 = t1 + t2\nt4 = n4 * t3\nt5 = t4 / t0\nanswer = t5 / 1000.0\nprint(answer)" - ], - "Output Answer": [ - "3.44" - ], - "split": "train" - }, - { - "Input": "right now , the ratio between the ages of sandy and molly is 4 : 3 . after 6 years , sandy \u2019 s age will be 34 years . what is molly ' s age right now ?", - "Output Program": [ - "n0 = 4.0\nn1 = 3.0\nn2 = 6.0\nn3 = 34.0\nt0 = n3 - n2\nt1 = t0 / n0\nanswer = n1 * t1\nprint(answer)" - ], - "Output Answer": [ - "21" - ], - "split": "train" - }, - { - "Input": "what is the square root of 400 , divided by 2 ?", - "Output Program": [ - "import math\nn0 = 400.0\nn1 = 2.0\nt0 = math.sqrt(max(0, n0))\nanswer = t0 / n1\nprint(answer)" - ], - "Output Answer": [ - "10" - ], - "split": "train" - }, - { - "Input": "a starts business with rs . 3500 and after 5 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b \u2019 s contribution in the capital ?", - "Output Program": [ - "n0 = 3500.0\nn1 = 5.0\nn2 = 2.0\nn3 = 3.0\nt0 = n0 * 12.0\nt1 = 12.0 - n1\nt2 = n3 * t0\nt3 = n2 * t1\nanswer = t2 / t3\nprint(answer)" - ], - "Output Answer": [ - "9000" - ], - "split": "train" - }, - { - "Input": "how many consecutive zeros are there at the end of 100 ! ( 100 factorial ) ?", - "Output Program": [ - "n0 = 100.0\nn1 = 100.0\nt0 = 1.0 + 4.0\nt1 = n0 / t0\nt2 = t0 * t0\nt3 = n0 / t2\nanswer = t1 + t3\nprint(answer)" - ], - "Output Answer": [ - "24" - ], - "split": "train" - }, - { - "Input": "the ratio of spinsters to cats is 2 to 7 . if there are 55 more cats than spinsters , how many spinsters are there ?", - "Output Program": [ - "n0 = 2.0\nn1 = 7.0\nn2 = 55.0\nt0 = n1 - n0\nt1 = n2 / t0\nanswer = n0 * t1\nprint(answer)" - ], - "Output Answer": [ - "22" - ], - "split": "train" - }, - { - "Input": "in what ratio should a variety of rice costing rs . 5 per kg be mixed with another variety of rice costing rs . 8.75 per kg to obtain a mixture costing rs . 7.50 per kg ?", - "Output Program": [ - "n0 = 5.0\nn1 = 8.75\nn2 = 7.5\nt0 = n1 - n2\nt1 = n1 - n0\nt2 = t0 / t1\nt3 = 1.0 - t2\nanswer = t2 / t3\nprint(answer)" - ], - "Output Answer": [ - "0.49999999999999994" - ], - "split": "train" - }, - { - "Input": "if 65 percent of a class answered the first question on a certain test correctly , 55 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?", - "Output Program": [ - "n0 = 65.0\nn1 = 55.0\nn2 = 20.0\nt0 = n0 + n1\nt1 = n2 + t0\nanswer = t1 - 100.0\nprint(answer)" - ], - "Output Answer": [ - "40" - ], - "split": "train" - }, - { - "Input": "among 300 students , 56 % study sociology , 44 % study mathematics and 40 % study biology . if 30 % of students study both mathematics and sociology , what is the largest possible number of students who study biology but do not study either mathematics or sociology ?", - "Output Program": [ - "n0 = 300.0\nn1 = 56.0\nn2 = 44.0\nn3 = 40.0\nn4 = 30.0\nt0 = n0 / 100.0\nt1 = n1 * t0\nt2 = n2 * t0\nt3 = n4 * t0\nt4 = t1 + t2\nt5 = t4 - t3\nanswer = n0 - t5\nprint(answer)" - ], - "Output Answer": [ - "90" - ], - "split": "train" - }, - { - "Input": "in a group of 90 students , 36 are taking history , and 30 are taking statistics . if 59 students are taking history or statistics or both , then how many students are taking history but not statistics ?", - "Output Program": [ - "n0 = 90.0\nn1 = 36.0\nn2 = 30.0\nn3 = 59.0\nt0 = n1 + n2\nt1 = t0 - n3\nanswer = n1 - t1\nprint(answer)" - ], - "Output Answer": [ - "29" - ], - "split": "train" - }, - { - "Input": "in a school of 320 students , 85 students are in the band , 200 students are on sports teams , and 60 students participate in both activities . how many students are involved in either band or sports ?", - "Output Program": [ - "n0 = 320.0\nn1 = 85.0\nn2 = 200.0\nn3 = 60.0\nt0 = n1 - n3\nt1 = n2 - n3\nt2 = t0 + t1\nanswer = n3 + t2\nprint(answer)" - ], - "Output Answer": [ - "225" - ], - "split": "train" - }, - { - "Input": "if ramola ranks 14 th in a class of 26 , what is her rank from the last ?", - "Output Program": [ - "n0 = 14.0\nn1 = 26.0\nt0 = n1 - n0\nanswer = t0 + 1.0\nprint(answer)" - ], - "Output Answer": [ - "13" - ], - "split": "train" - }, - { - "Input": "the ratio of three numbers is 1 : 2 : 5 and the sum of their squares is 4320 . the sum of the numbers is ?", - "Output Program": [ - "import math\nn0 = 1.0\nn1 = 2.0\nn2 = 5.0\nn3 = 4320.0\nt0 = n0**min(n1, 5)\nt1 = n1**min(n1, 5)\nt2 = n2**min(n1, 5)\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n3 / t4\nanswer = math.sqrt(max(0, t5))\nprint(answer)" - ], - "Output Answer": [ - "12" - ], - "split": "train" - }, - { - "Input": "how many multiples of 100 are there between 100 and 1000 ( both are inclusive ) ?", - "Output Program": [ - "n0 = 100.0\nn1 = 100.0\nn2 = 1000.0\nt0 = n2 - n1\nt1 = t0 / n0\nanswer = t1 + 1.0\nprint(answer)" - ], - "Output Answer": [ - "10" - ], - "split": "train" - }, - { - "Input": "the h . c . f and l . c . m of two numbers are 84 and 21 respectively . if the ratio of the two numbers is 1 : 4 , then the larger of the two numbers is", - "Output Program": [ - "import math\nn0 = 84.0\nn1 = 21.0\nn2 = 1.0\nn3 = 4.0\nt0 = n0 * n1\nt1 = t0 / n3\nt2 = math.sqrt(max(0, t1))\nanswer = n3 * t2\nprint(answer)" - ], - "Output Answer": [ - "84" - ], - "split": "train" - }, - { - "Input": "half of the workers in palabras bookstore have read the latest book by j . saramago , and 1 / 6 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 150 workers in the palabras bookstore , how many of them have read both books ?", - "Output Program": [ - "n0 = 1.0\nn1 = 6.0\nn2 = 150.0\nt0 = n2 / 2.0\nt1 = n2 / n1\nt2 = t0 + t1\nt3 = t0 - n0\nt4 = n2 - t2\nt5 = t3 - t4\nanswer = t5 / 2.0\nprint(answer)" - ], - "Output Answer": [ - "12" - ], - "split": "train" - }, - { - "Input": "a certain bag contains 100 balls \u00e2 \u20ac \u201d 50 white , 20 green , 10 yellow , 17 red , and 3 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?", - "Output Program": [ - "n0 = 100.0\nn1 = 50.0\nn2 = 20.0\nn3 = 10.0\nn4 = 17.0\nn5 = 3.0\nt0 = n4 + n5\nt1 = n0 - t0\nanswer = t1 / n0\nprint(answer)" - ], - "Output Answer": [ - "0.8" - ], - "split": "train" - }, - { - "Input": "a starts business with rs . 3500 and after 9 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b \u00e2 \u20ac \u2122 s contribution in the capital ?", - "Output Program": [ - "n0 = 3500.0\nn1 = 9.0\nn2 = 2.0\nn3 = 3.0\nt0 = n0 * 12.0\nt1 = 12.0 - n1\nt2 = n3 * t0\nt3 = n2 * t1\nanswer = t2 / t3\nprint(answer)" - ], - "Output Answer": [ - "21000" - ], - "split": "train" - }, - { - "Input": "if w is the set of all the integers between 39 and 99 , inclusive , that are either multiples of 3 or multiples of 2 or multiples of both , then w contains how many numbers ?", - "Output Program": [ - "import math\nn0 = 39.0\nn1 = 99.0\nn2 = 3.0\nn3 = 2.0\nt0 = n3 * n2\nt1 = n1 - n0\nt2 = t1 / n3\nt3 = t1 / n2\nt4 = t1 / t0\nt5 = math.floor(t3)\nt6 = math.floor(t4)\nt7 = t2 + t5\nanswer = t7 - t6\nprint(answer)" - ], - "Output Answer": [ - "40" - ], - "split": "train" - }, - { - "Input": "the sum of the numbers is 98 . if the ratio between the first and the second be 2 : 3 and that between the second and third be 5 : 8 , then find the second number ?", - "Output Program": [ - "import scipy\nn0 = 98.0\nn1 = 2.0\nn2 = 3.0\nn3 = 5.0\nn4 = 8.0\nt0 = scipy.lcm(int(n2), int(n3))\nt1 = n1 * n3\nt2 = n2 * n3\nt3 = n2 * n4\nt4 = t1 + t2\nt5 = n0 * t0\nt6 = t4 + t3\nanswer = t5 / t6\nprint(answer)" - ], - "Output Answer": [ - "30" - ], - "split": "train" - }, - { - "Input": "a marketing firm determined that , of 200 households surveyed , 80 used neither brand w nor brand b soap , 60 used only brand w soap , and for every household that used both brands of soap , 3 used only brand b soap . how many of the 200 households surveyed used both brands of soap ?", - "Output Program": [ - "n0 = 200.0\nn1 = 80.0\nn2 = 60.0\nn3 = 3.0\nn4 = 200.0\nt0 = n0 - n1\nt1 = t0 - n2\nt2 = t1 / n3\nanswer = t1 - t2\nprint(answer)" - ], - "Output Answer": [ - "40" - ], - "split": "train" - }, - { - "Input": "there are 12 slate rocks , 16 pumice rocks , and 8 granite rocks randomly distributed in a certain field . if 2 rocks are chosen at random and without replacement , what is the probability that both rocks will be slate rocks ?", - "Output Program": [ - "n0 = 12.0\nn1 = 16.0\nn2 = 8.0\nn3 = 2.0\nt0 = n0 + n1\nt1 = n0 - 1.0\nt2 = n2 + t0\nt3 = n0 / t2\nt4 = t2 - 1.0\nt5 = t1 / t4\nanswer = t3 * t5\nprint(answer)" - ], - "Output Answer": [ - "0.10476190476190475" - ], - "split": "train" - }, - { - "Input": "if number divisible by both 3 and 2 , then the same number divisible by which number ?", - "Output Program": [ - "n0 = 3.0\nn1 = 2.0\nt0 = n0 * n1\nanswer = t0 * 1.0\nprint(answer)" - ], - "Output Answer": [ - "6" - ], - "split": "train" - }, - { - "Input": "a bag contains 4 green and 8 white balls . if two balls are drawn simultaneously , the probability that both are of the same colour is", - "Output Program": [ - "n0 = 4.0\nn1 = 8.0\nt0 = n0 + n1\nt1 = n1 - 1.0\nt2 = n0 - 1.0\nt3 = n1 / t0\nt4 = n0 / t0\nt5 = t0 - 1.0\nt6 = t1 / t5\nt7 = t2 / t5\nt8 = t3 * t6\nt9 = t4 * t7\nanswer = t8 + t9\nprint(answer)" - ], - "Output Answer": [ - "0.5151515151515151" - ], - "split": "train" - }, - { - "Input": "a student committee on academic integrity has 42 ways to select a president and vice president from a group of candidates . the same person can not be both president and vice president . how many candidates are there ?", - "Output Program": [ - "import math\nn0 = 42.0\nt0 = n0 * 4.0\nt1 = -1.0\nt2 = t1**min(2.0, 5)\nt3 = t0 + t2\nt4 = math.sqrt(max(0, t3))\nt5 = t4 + 1.0\nanswer = t5 / 2.0\nprint(answer)" - ], - "Output Answer": [ - "7" - ], - "split": "train" - }, - { - "Input": "a number is said to be prime saturated if the product of all the different positive prime factors of g is less than the square root of g . what is the greatest two digit prime saturated integer ?", - "Output Program": [ - "t0 = 2.0 * 3.0\nt1 = 100.0 - 10.0\nanswer = t0 + t1\nprint(answer)" - ], - "Output Answer": [ - "96" - ], - "split": "train" - }, - { - "Input": "find the highest common factor of 36 and 84 ?", - "Output Program": [ - "import scipy\nn0 = 36.0\nn1 = 84.0\n\nanswer = scipy.gcd(int(n0), int(n1))\nprint(answer)" - ], - "Output Answer": [ - "12" - ], - "split": "train" - }, - { - "Input": "the ratio of two numbers is 2 : 3 and their h . c . f . is 6 . their l . c . m . is", - "Output Program": [ - "n0 = 2.0\nn1 = 3.0\nn2 = 6.0\nt0 = n0 * n1\nanswer = n2 * t0\nprint(answer)" - ], - "Output Answer": [ - "36" - ], - "split": "train" - }, - { - "Input": "at present , the ratio between the ages of shekhar and shobha is 4 : 3 . after 6 years , shekhar ' s age will be 26 years . find out the age of shobha at present ?", - "Output Program": [ - "n0 = 4.0\nn1 = 3.0\nn2 = 6.0\nn3 = 26.0\nt0 = n3 - n2\nt1 = t0 / n0\nanswer = n1 * t1\nprint(answer)" - ], - "Output Answer": [ - "15" - ], - "split": "train" - }, - { - "Input": "at present the ratio between the ages of arun and deepak is 4 : 3 . after 6 years arun ' s age will be 26 years . what is the age of the deepak ?", - "Output Program": [ - "n0 = 4.0\nn1 = 3.0\nn2 = 6.0\nn3 = 26.0\nt0 = n3 - n2\nt1 = n1 * t0\nanswer = t1 / n0\nprint(answer)" - ], - "Output Answer": [ - "15" - ], - "split": "train" - }, - { - "Input": "uba capital recently bought brand new vehicles for office use . uba capital only went for toyota and honda and bought more of toyota than honda at the ratio of 9 : 1 . if 90 % of the toyota bought and 10 % of the honda bought were suv \u00e3 \u00a2 \u00e2 \u201a \u00ac \u00e2 \u201e \u00a2 s . how many suv \u00e3 \u00a2 \u00e2 \u201a \u00ac \u00e2 \u201e \u00a2 s did uba capital buy in the aforementioned purchase ?", - "Output Program": [ - "n0 = 9.0\nn1 = 1.0\nn2 = 90.0\nn3 = 10.0\nt0 = n0 * n1\nt1 = t0 + t0\nanswer = 100.0 - t1\nprint(answer)" - ], - "Output Answer": [ - "82" - ], - "split": "train" - }, - { - "Input": "among 400 students , 56 % study sociology , 44 % study mathematics and 40 % study biology . if 42 % of students study both mathematics and sociology , what is the largest possible number of students who study biology but do not study either mathematics or sociology ?", - "Output Program": [ - "n0 = 400.0\nn1 = 56.0\nn2 = 44.0\nn3 = 40.0\nn4 = 42.0\nt0 = n0 / 100.0\nt1 = n1 * t0\nt2 = n2 * t0\nt3 = n4 * t0\nt4 = t1 + t2\nt5 = t4 - t3\nanswer = n0 - t5\nprint(answer)" - ], - "Output Answer": [ - "168" - ], - "split": "train" - }, - { - "Input": "a precious stone weighing 35 grams worth rs . 12,250 is accidentally dropped and gets broken into two pieces having weights in the ratio of 2 : 5 . if the price varies as the square of the weight then find the loss incurred .", - "Output Program": [ - "n0 = 35.0\nn1 = 12250.0\nn2 = 2.0\nn3 = 5.0\nt0 = 100.0 / 2.0\nt1 = 100.0 * 100.0\nt2 = n2 * n3\nt3 = n3 * n3\nt4 = n0**min(2.0, 5)\nt5 = t1 / 2.0\nt6 = t2**min(2.0, 5)\nt7 = t3**min(2.0, 5)\nt8 = t5 / n2\nt9 = t8 + t1\nt10 = t9 - 100.0\nt11 = t10 - 100.0\nt12 = t11 - t0\nt13 = t12 / t4\nt14 = t13 * t6\nt15 = t13 * t7\nt16 = t14 + t15\nanswer = t12 - t16\nprint(answer)" - ], - "Output Answer": [ - "5000" - ], - "split": "train" - }, - { - "Input": "an amount of money is to be distributed among faruk , vasim and ranjith in the ratio 3 : 5 : 9 . if vasims share is rs . 1500 , what is the difference between faruk ' s and ranjith ' s shares ?", - "Output Program": [ - "n0 = 3.0\nn1 = 5.0\nn2 = 9.0\nn3 = 1500.0\nt0 = n3 / n1\nt1 = n2 - n0\nanswer = t0 * t1\nprint(answer)" - ], - "Output Answer": [ - "1800" - ], - "split": "train" - }, - { - "Input": "a bag contains 3 red , 2 blue and 4 green balls . if 2 balls are picked at random , what is the probability that both are red ?", - "Output Program": [ - "import scipy\nn0 = 3.0\nn1 = 2.0\nn2 = 4.0\nn3 = 2.0\nt0 = n0 + n1\nt1 = scipy.special.comb(n0, n3)\nt2 = n2 + t0\nt3 = scipy.special.comb(t2, n3)\nanswer = t1 / t3\nprint(answer)" - ], - "Output Answer": [ - "0.08333333333333333" - ], - "split": "train" - }, - { - "Input": "in a graduating class of 232 students , 144 took geometry and 119 took biology . what is the difference between the greatest possible number r and the smallest possible number of students that could have taken both geometry and biology ?", - "Output Program": [ - "n0 = 232.0\nn1 = 144.0\nn2 = 119.0\nt0 = n1 + n2\nt1 = t0 - n0\nanswer = n2 - t1\nprint(answer)" - ], - "Output Answer": [ - "88" - ], - "split": "train" - }, - { - "Input": "a shipment of 250 smartphones contains 67 that are defective . if a customer buys two smartphones at random from the shipment , what is the approximate probability that both phones are defective ?", - "Output Program": [ - "n0 = 250.0\nn1 = 67.0\nt0 = n1 - 1.0\nt1 = n0 - 1.0\nt2 = n1 * t0\nt3 = n0 * t1\nanswer = t2 / t3\nprint(answer)" - ], - "Output Answer": [ - "0.07103614457831325" - ], - "split": "train" - }, - { - "Input": "one fast typist type some matter in 2 hrs and another slow typist type the same matter in 3 hrs . if both do combine in how much time they will take to finish .", - "Output Program": [ - "n0 = 2.0\nn1 = 3.0\nt0 = 1.0 / n0\nt1 = 1.0 / n1\nt2 = t0 + t1\nt3 = 1.0 / t2\nanswer = t3 * 10.0\nprint(answer)" - ], - "Output Answer": [ - "12.000000000000002" - ], - "split": "train" - }, - { - "Input": "in a sports club with 30 members , 16 play badminton and 19 play tennis and 2 do not play either . how many members play both badminton and tennis ?", - "Output Program": [ - "n0 = 30.0\nn1 = 16.0\nn2 = 19.0\nn3 = 2.0\nt0 = n1 + n2\nt1 = n3 + t0\nanswer = t1 - n0\nprint(answer)" - ], - "Output Answer": [ - "7" - ], - "split": "train" - }, - { - "Input": "a salesman sold twice as much pears in the afternoon than in the morning . if he sold 360 kilograms of pears that day , how many kilograms did he sell in the morning and how many in the afternoon ?", - "Output Program": [ - "n0 = 360.0\nt0 = n0 / 3.0\nanswer = t0 * 2.0\nprint(answer)" - ], - "Output Answer": [ - "240" - ], - "split": "train" - }, - { - "Input": "a company conducted a survey about its two brands , a and b . x percent of respondents liked product a , ( x \u2013 20 ) percent liked product b , 23 percent liked both products , and 23 percent liked neither product . what is the minimum number f of people surveyed by the company ?", - "Output Program": [ - "n0 = 20.0\nn1 = 23.0\nn2 = 23.0\nt0 = 100.0 - n1\nt1 = n1 + t0\nt2 = n0 + t1\nt3 = t2 / 2.0\nt4 = t3 - n0\nanswer = t3 + t4\nprint(answer)" - ], - "Output Answer": [ - "100" - ], - "split": "train" - }, - { - "Input": "the ratio of boarders to day students at a school was originally 5 to 12 . however , after a number of new boarders join the initial 330 boarders , the ratio changed to 1 to 2 . if no boarders became day students and vice versa , and no students left the school , how many new boarders joined the school ?", - "Output Program": [ - "n0 = 5.0\nn1 = 12.0\nn2 = 330.0\nn3 = 1.0\nn4 = 2.0\nt0 = n2 / n0\nt1 = n1 * t0\nt2 = t1 / n4\nanswer = t2 - n2\nprint(answer)" - ], - "Output Answer": [ - "66" - ], - "split": "train" - }, - { - "Input": "presently the ratio between the ages of dan and james is 6 : 5 . after 4 years dan will be 28 . what is the present age of james ?", - "Output Program": [ - "n0 = 6.0\nn1 = 5.0\nn2 = 4.0\nn3 = 28.0\nt0 = 2.0 * 4.0\nanswer = n3 - t0\nprint(answer)" - ], - "Output Answer": [ - "20" - ], - "split": "train" - }, - { - "Input": "a certain high school has 500 students . of these students , 30 are taking music , 20 are taking art , and 10 are taking both music and art . how many students are taking neither music nor art ?", - "Output Program": [ - "n0 = 500.0\nn1 = 30.0\nn2 = 20.0\nn3 = 10.0\nt0 = n1 + n2\nt1 = t0 - n3\nanswer = n0 - t1\nprint(answer)" - ], - "Output Answer": [ - "460" - ], - "split": "train" - }, - { - "Input": "among 200 students , 56 % study sociology , 44 % study mathematics and 40 % study biology . if 30 % of students study both mathematics and sociology , what is the largest possible number of students who study biology but do not study either mathematics or sociology ?", - "Output Program": [ - "n0 = 200.0\nn1 = 56.0\nn2 = 44.0\nn3 = 40.0\nn4 = 30.0\nt0 = n0 / 100.0\nt1 = n1 * t0\nt2 = n2 * t0\nt3 = n4 * t0\nt4 = t1 + t2\nt5 = t4 - t3\nanswer = n0 - t5\nprint(answer)" - ], - "Output Answer": [ - "60" - ], - "split": "train" - }, - { - "Input": "there are 456 doctors and nurses in a hospital . if the ratio of the doctors to the nurses is 8 : 11 , then how many nurses are there in the hospital ?", - "Output Program": [ - "n0 = 456.0\nn1 = 8.0\nn2 = 11.0\nt0 = n2 - n1\nt1 = n1 * t0\nanswer = n2 * t1\nprint(answer)" - ], - "Output Answer": [ - "264" - ], - "split": "train" - }, - { - "Input": "a movie buff buys movies on dvd and on blu - ray in a ratio of 17 : 4 . if she returns 4 blu - ray movies , that ratio would change to 9 : 2 . if she buys movies on no other medium , what was the original number of movies purchased ?", - "Output Program": [ - "n0 = 17.0\nn1 = 4.0\nn2 = 4.0\nn3 = 9.0\nn4 = 2.0\nt0 = n0 + n1\nt1 = n1 * n3\nt2 = t1 / n4\nanswer = t0 * t2\nprint(answer)" - ], - "Output Answer": [ - "378" - ], - "split": "train" - }, - { - "Input": "find the two digit number , such that the ratio is 7 / 4 of original number to the number formed by reversing the digits .", - "Output Program": [ - "n0 = 7.0\nn1 = 4.0\nt0 = n0 * n1\nanswer = t0 - n0\nprint(answer)" - ], - "Output Answer": [ - "21" - ], - "split": "train" - }, - { - "Input": "in a group of 100 cars , 37 cars do not have air conditioning . if at least 51 cars have racing stripes , what is the greatest number of cars that could have air conditioning but not racing stripes ?", - "Output Program": [ - "n0 = 100.0\nn1 = 37.0\nn2 = 51.0\n\nanswer = n0 - n2\nprint(answer)" - ], - "Output Answer": [ - "49" - ], - "split": "train" - }, - { - "Input": "a salesman sold twice as much pears in the afternoon than in the morning . if he sold $ 420 kilograms of pears that day , how many kilograms did he sell in the afternoon ?", - "Output Program": [ - "n0 = 420.0\nt0 = n0 / 3.0\nanswer = t0 * 2.0\nprint(answer)" - ], - "Output Answer": [ - "280" - ], - "split": "train" - }, - { - "Input": "the probability that a can solve the problem is 2 / 3 and b can solve it is 3 / 4 . if both of them attemp the problem , then what is the probability that the problem get solved ?", - "Output Program": [ - "n0 = 2.0\nn1 = 3.0\nn2 = 3.0\nn3 = 4.0\nt0 = n0 / n1\nt1 = n1 / n3\nt2 = 1.0 - t0\nt3 = 1.0 - t1\nt4 = t2 * t3\nanswer = 1.0 - t4\nprint(answer)" - ], - "Output Answer": [ - "0.9166666666666666" - ], - "split": "train" - }, - { - "Input": "a bag contains 9 green and 8 white balls . if two balls are drawn simultaneously , the probability that both are of the same colour is", - "Output Program": [ - "n0 = 9.0\nn1 = 8.0\nt0 = n0 + n1\nt1 = n1 - 1.0\nt2 = n0 - 1.0\nt3 = n1 / t0\nt4 = n0 / t0\nt5 = t0 - 1.0\nt6 = t1 / t5\nt7 = t2 / t5\nt8 = t3 * t6\nt9 = t4 * t7\nanswer = t8 + t9\nprint(answer)" - ], - "Output Answer": [ - "0.47058823529411764" - ], - "split": "train" - }, - { - "Input": "how many trailing zeros will be there after the rightmost non - zero digit in the value of 25 ! ( factorial 25 ) ?", - "Output Program": [ - "import math\nn0 = 25.0\nn1 = 25.0\nt0 = math.sqrt(max(0, n0))\nanswer = t0 + 1.0\nprint(answer)" - ], - "Output Answer": [ - "6" - ], - "split": "train" - }, - { - "Input": "in a class , 7 students like to play basketball and 8 like to play cricket . 3 students like to play on both basketball and cricket . how many students like to play basketball or cricket or both ?", - "Output Program": [ - "n0 = 7.0\nn1 = 8.0\nn2 = 3.0\nt0 = n0 + n1\nanswer = t0 - n2\nprint(answer)" - ], - "Output Answer": [ - "12" - ], - "split": "train" - }, - { - "Input": "ratio of girl and boys in class is 5 : 6 . if 20 girl leave the class and ratio become 2 : 3 . calculate the no . of boys ?", - "Output Program": [ - "n0 = 5.0\nn1 = 6.0\nn2 = 20.0\nn3 = 2.0\nn4 = 3.0\nt0 = n2 * n4\nt1 = n0 * n4\nt2 = n1 * n3\nt3 = t1 - t2\nt4 = t0 / t3\nanswer = n1 * t4\nprint(answer)" - ], - "Output Answer": [ - "120" - ], - "split": "train" - }, - { - "Input": "in a factory , each day the expected number of accidents is related to the number of overtime hour by linear equation . suppose that on one day there were 1000 overtime hours logged and 8 accidents reported and on another day there were 400 overtime hours logged and 5 accidents . what is the expected number of accidents when no overtime hours are logged ?", - "Output Program": [ - "n0 = 1000.0\nn1 = 8.0\nn2 = 400.0\nn3 = 5.0\nt0 = n1 - n3\nt1 = n0 - n2\nt2 = t0 / t1\nt3 = n0 * t2\nanswer = n1 - t3\nprint(answer)" - ], - "Output Answer": [ - "3" - ], - "split": "train" - }, - { - "Input": "the ratio of pens to pencils is 5 to 6 . there are 8 more pencils than pens . how many pencils are there ?", - "Output Program": [ - "n0 = 5.0\nn1 = 6.0\nn2 = 8.0\nt0 = n0 * n2\nanswer = n2 + t0\nprint(answer)" - ], - "Output Answer": [ - "48" - ], - "split": "train" - }, - { - "Input": "in a certain animal shelter , the ratio of the number of dogs to the number of cats is 15 to 7 . if 16 additional cats were to be taken in by the shelter , the ratio of the number of dogs to the number of cats would be 15 to 11 . how many dogs are in the shelter ?", - "Output Program": [ - "n0 = 15.0\nn1 = 7.0\nn2 = 16.0\nn3 = 15.0\nn4 = 11.0\nt0 = n1 * n2\nt1 = n4 - n1\nt2 = t0 / t1\nt3 = t2 / n1\nanswer = n0 * t3\nprint(answer)" - ], - "Output Answer": [ - "60" - ], - "split": "train" - }, - { - "Input": "of the 200 stamps in a collection , 90 are foreign and 60 are more than 10 years old . if 20 stamps are both foreign and more than 10 years old , how many stamps are neither foreign nor more than 10 years old ?", - "Output Program": [ - "n0 = 200.0\nn1 = 90.0\nn2 = 60.0\nn3 = 10.0\nn4 = 20.0\nn5 = 10.0\nn6 = 10.0\nt0 = n1 + n2\nt1 = t0 - n4\nanswer = n0 - t1\nprint(answer)" - ], - "Output Answer": [ - "70" - ], - "split": "train" - }, - { - "Input": "the weights of one liter vegetable ghee packet of two brands \u2018 a \u2019 and \u2018 b \u2019 are 900 gm and 750 gm respectively . if they are mixed in the ratio of 3 : 2 by volumes to form a mixture of 4 liters , what is the weight ( in kg ) of the mixture ?", - "Output Program": [ - "n0 = 900.0\nn1 = 750.0\nn2 = 3.0\nn3 = 2.0\nn4 = 4.0\nt0 = n2 + n3\nt1 = n0 * n2\nt2 = n1 * n3\nt3 = t1 + t2\nt4 = n4 * t3\nt5 = t4 / t0\nanswer = t5 / 1000.0\nprint(answer)" - ], - "Output Answer": [ - "3.36" - ], - "split": "train" - }, - { - "Input": "find the common factors of 15 and 18 .", - "Output Program": [ - "import scipy\nn0 = 15.0\nn1 = 18.0\n\nanswer = scipy.lcm(int(n0), int(n1))\nprint(answer)" - ], - "Output Answer": [ - "90" - ], - "split": "train" - }, - { - "Input": "half of the workers in palabras bookstore have read the latest book by j . saramago , and 1 / 6 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 42 workers in the palabras bookstore , how many of them have read both books ?", - "Output Program": [ - "n0 = 1.0\nn1 = 6.0\nn2 = 42.0\nt0 = n2 / 2.0\nt1 = n2 / n1\nt2 = t0 + t1\nt3 = t0 - 1.0\nt4 = n2 - t2\nt5 = t3 - t4\nanswer = t5 / 2.0\nprint(answer)" - ], - "Output Answer": [ - "3" - ], - "split": "train" - }, - { - "Input": "sachin is younger than rahul by 14 years . if the ratio of their ages is 7 : 9 , find the age of sachin", - "Output Program": [ - "n0 = 14.0\nn1 = 7.0\nn2 = 9.0\nt0 = n2 - n1\nt1 = n0 / t0\nanswer = n1 * t1\nprint(answer)" - ], - "Output Answer": [ - "49" - ], - "split": "train" - }, - { - "Input": "the hcf of two numbers is 40 and the other two factors of their lcm are 11 and 12 . what is the largest number .", - "Output Program": [ - "n0 = 40.0\nn1 = 11.0\nn2 = 12.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "480" - ], - "split": "train" - }, - { - "Input": "if a student loses 6 kilograms , he will weigh twice as much as his sister . together they now weigh 132 kilograms . what is the student ' s present weight in kilograms ?", - "Output Program": [ - "n0 = 6.0\nn1 = 132.0\nt0 = n1 - n0\nt1 = t0 / 3.0\nanswer = n1 - t1\nprint(answer)" - ], - "Output Answer": [ - "90" - ], - "split": "train" - }, - { - "Input": "if x and y are sets of integers , x # y denotes the set of integers that belong to set x or set y , but not both . if x consists of 8 integers , y consists of 10 integers , and 6 of the integers are in both x and y , then x # y consists of how many integers ?", - "Output Program": [ - "n0 = 8.0\nn1 = 10.0\nn2 = 6.0\nt0 = n1 - n2\nt1 = n0 - n2\nanswer = t0 + t1\nprint(answer)" - ], - "Output Answer": [ - "6" - ], - "split": "train" - }, - { - "Input": "a began business with rs . 45000 and was joined afterwards by b with rs . 27000 . when did b join if the profits at the end of the year were divided in the ratio of 2 : 1 ?", - "Output Program": [ - "n0 = 45000.0\nn1 = 27000.0\nn2 = 2.0\nn3 = 1.0\nt0 = 3.0 * 4.0\nt1 = n0 * t0\nt2 = t1 / n1\nt3 = t2 / n2\nanswer = t0 - t3\nprint(answer)" - ], - "Output Answer": [ - "2" - ], - "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": "in a group of houses , 40 had dogs , 30 had cats and 10 houses having both dogs and cats . what is the number of houses ?", - "Output Program": [ - "n0 = 40.0\nn1 = 30.0\nn2 = 10.0\nt0 = n0 + n1\nanswer = t0 - n2\nprint(answer)" - ], - "Output Answer": [ - "60" - ], - "split": "train" - }, - { - "Input": "in a class of 40 students , 12 enrolled for both english and german . 22 enrolled for german . if the students of the class enrolled for at least one of the two subjects , then how many students enrolled for only english and not german ?", - "Output Program": [ - "n0 = 40.0\nn1 = 12.0\nn2 = 22.0\nt0 = n0 + n1\nt1 = t0 - n2\nanswer = t1 - n1\nprint(answer)" - ], - "Output Answer": [ - "18" - ], - "split": "train" - }, - { - "Input": "the ratio of money with ram and gopal is 7 : 17 and that with gopal and krishan is 7 : 17 . if ram has rs . 686 , krishan has ?", - "Output Program": [ - "n0 = 7.0\nn1 = 17.0\nn2 = 7.0\nn3 = 17.0\nn4 = 686.0\nt0 = n4 / n0\nt1 = n1 * t0\nt2 = t1 / n0\nanswer = n1 * t2\nprint(answer)" - ], - "Output Answer": [ - "4046" - ], - "split": "train" - }, - { - "Input": "a farmer with 1,350 acres of land had planted his fields with corn , sugar cane , and tobacco in the ratio of 5 : 2 : 2 , respectively , but he wanted to make more money , so he shifted the ratio to 2 : 2 : 5 , respectively . how many more acres of land were planted with tobacco under the new system ?", - "Output Program": [ - "n0 = 1350.0\nn1 = 5.0\nn2 = 2.0\nn3 = 2.0\nn4 = 2.0\nn5 = 2.0\nn6 = 5.0\nt0 = n1 + n2\nt1 = n0 * 3.0\nt2 = n2 + t0\nanswer = t1 / t2\nprint(answer)" - ], - "Output Answer": [ - "450" - ], - "split": "train" - }, - { - "Input": "if w is the set of all the integers between 59 and 99 , inclusive , that are either multiples of 3 or multiples of 2 or multiples of both , then w contains how many numbers ?", - "Output Program": [ - "import math\nn0 = 59.0\nn1 = 99.0\nn2 = 3.0\nn3 = 2.0\nt0 = 2.0 * 3.0\nt1 = n1 - n0\nt2 = t1 / n3\nt3 = t1 / n2\nt4 = t1 / t0\nt5 = math.floor(t3)\nt6 = math.floor(t4)\nt7 = t2 + t5\nanswer = t7 - t6\nprint(answer)" - ], - "Output Answer": [ - "27" - ], - "split": "train" - }, - { - "Input": "income and expenditure of a person are in the ratio 5 : 3 . if the income of the person is rs . 10000 , then find his savings ?", - "Output Program": [ - "n0 = 5.0\nn1 = 3.0\nn2 = 10000.0\nt0 = n1 / n0\nt1 = n2 * t0\nanswer = n2 - t1\nprint(answer)" - ], - "Output Answer": [ - "4000" - ], - "split": "train" - }, - { - "Input": "in 50 l can , milk and water in the ratio of 3 : 1 . if the ratio has made 1 : 3 then the quantity of water that has to be added further is ?", - "Output Program": [ - "n0 = 50.0\nn1 = 3.0\nn2 = 1.0\nn3 = 1.0\nn4 = 3.0\nt0 = n1 + n2\nt1 = n0 / t0\nt2 = n1 * t1\nt3 = n2 * t1\nt4 = n1 * t2\nanswer = t4 - t3\nprint(answer)" - ], - "Output Answer": [ - "100" - ], - "split": "train" - }, - { - "Input": "a bag contains 7 red , 9 blue and 5 green balls . if 3 balls are picked at random , what is the probability that both are red ?", - "Output Program": [ - "import scipy\nn0 = 7.0\nn1 = 9.0\nn2 = 5.0\nn3 = 3.0\nt0 = n0 + n1\nt1 = scipy.special.comb(n0, n3)\nt2 = n2 + t0\nt3 = scipy.special.comb(t2, n3)\nanswer = t1 / t3\nprint(answer)" - ], - "Output Answer": [ - "0.02631578947368421" - ], - "split": "train" - }, - { - "Input": "in a certain school , the ratio of boys to girls is 5 to 13 . if there are 80 more girls than boys , how many boys are there ?", - "Output Program": [ - "n0 = 5.0\nn1 = 13.0\nn2 = 80.0\nt0 = n0 / n1\nt1 = 1.0 - t0\nt2 = n2 / t1\nanswer = t2 - n2\nprint(answer)" - ], - "Output Answer": [ - "50" - ], - "split": "train" - }, - { - "Input": "the ratio of numbers is 3 : 4 and their h . c . f is 5 . their l . c . m is :", - "Output Program": [ - "import scipy\nn0 = 3.0\nn1 = 4.0\nn2 = 5.0\nt0 = n0 * n2\nt1 = n1 * n2\nanswer = scipy.lcm(int(t0), int(t1))\nprint(answer)" - ], - "Output Answer": [ - "60" - ], - "split": "train" - }, - { - "Input": "if 85 percent of the test takers taking an old paper and pencil gmat exam answered the first question on a given math section correctly , and 70 percent of the test takers answered the second question correctly , and 5 percent of the test takers answered neither question correctly , what percent answered both correctly ?", - "Output Program": [ - "n0 = 85.0\nn1 = 70.0\nn2 = 5.0\nt0 = n0 + n1\nt1 = n2 + t0\nanswer = t1 - 100.0\nprint(answer)" - ], - "Output Answer": [ - "60" - ], - "split": "train" - }, - { - "Input": "in a family 15 people eat only vegetarian , 8 people eat only non veg . , 11 people eat both veg and non veg . . how many people eat veg in the family ?", - "Output Program": [ - "n0 = 15.0\nn1 = 8.0\nn2 = 11.0\n\nanswer = n0 + n2\nprint(answer)" - ], - "Output Answer": [ - "26" - ], - "split": "train" - }, - { - "Input": "in a certain state , the ratio of registered republicans to registered democrats is 3 to 2 , and every registered voter is either a republican or a democrat . if 70 percent of the republicans and 25 percent of the democrats are expected to vote for candidate x , and everyone else is expected to vote for candidate y , by what percent is candidate x expected to win the election ?", - "Output Program": [ - "n0 = 3.0\nn1 = 2.0\nn2 = 70.0\nn3 = 25.0\nt0 = n0 + n1\nt1 = n3 / 100.0\nt2 = n2 / 100.0\nt3 = n1 * t1\nt4 = n0 * t2\nt5 = t3 + t4\nt6 = n0 - t4\nt7 = n1 - t3\nt8 = t6 + t7\nt9 = t5 - t8\nt10 = t9 / t0\nanswer = t10 * 100.0\nprint(answer)" - ], - "Output Answer": [ - "3.9999999999999853" - ], - "split": "train" - }, - { - "Input": "the ratio between the number of sheep and the number of horses at the stewart farm is 1 to 7 , if each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day , what is the number of sheep in the farm ?", - "Output Program": [ - "n0 = 1.0\nn1 = 7.0\nn2 = 230.0\nn3 = 12880.0\nt0 = 2.0 * 4.0\nt1 = 1000.0 * 12.0\nt2 = t0 * 10.0\nt3 = t0 * 100.0\nt4 = t2 + t3\nt5 = t4 + t1\nt6 = t5 / n2\nt7 = t6 / n1\nanswer = n0 * t7\nprint(answer)" - ], - "Output Answer": [ - "8" - ], - "split": "train" - }, - { - "Input": "up to 20 , how many no . are odd and prime both ?", - "Output Program": [ - "n0 = 20.0\nt0 = n0 / 4.0\nanswer = t0 + 2.0\nprint(answer)" - ], - "Output Answer": [ - "7" - ], - "split": "train" - }, - { - "Input": "the ratio of boarders to day students at a school was originally 2 to 5 . however , after a number of new boarders join the initial 60 boarders , the ratio changed to 1 to 2 . if no boarders became day students and vice versa , and no students left the school , how many new boarders joined the school ?", - "Output Program": [ - "n0 = 2.0\nn1 = 5.0\nn2 = 60.0\nn3 = 1.0\nn4 = 2.0\nt0 = n2 / n0\nt1 = n1 * t0\nt2 = t1 / n4\nanswer = t2 - n2\nprint(answer)" - ], - "Output Answer": [ - "15" - ], - "split": "train" - }, - { - "Input": "in a primary school , the ratio of the number of girls to boys is 5 : 8 . if there are 160 girls , the total number of students in the college is :", - "Output Program": [ - "n0 = 5.0\nn1 = 8.0\nn2 = 160.0\nt0 = n2 / n1\nt1 = n0 * n1\nt2 = n2 + t1\nt3 = n0 * t0\nanswer = t2 + t3\nprint(answer)" - ], - "Output Answer": [ - "300" - ], - "split": "train" - }, - { - "Input": "of 60 children , 30 are happy , 10 are sad , and 20 are neither happy nor sad . there are 16 boys and 44 girls . if there are 6 happy boys and 4 sad girls , how many boys are neither happy nor sad ?", - "Output Program": [ - "n0 = 60.0\nn1 = 30.0\nn2 = 10.0\nn3 = 20.0\nn4 = 16.0\nn5 = 44.0\nn6 = 6.0\nn7 = 4.0\nt0 = n2 - n7\nt1 = n4 - t0\nanswer = t1 - n6\nprint(answer)" - ], - "Output Answer": [ - "4" - ], - "split": "train" - }, - { - "Input": "ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 38 years . what is deepak present age ?", - "Output Program": [ - "n0 = 4.0\nn1 = 3.0\nn2 = 6.0\nn3 = 38.0\nt0 = n3 - n2\nt1 = n1 * t0\nanswer = t1 / n0\nprint(answer)" - ], - "Output Answer": [ - "24" - ], - "split": "train" - }, - { - "Input": "the cost of 3 pens and 5 pencils is rs . 100 . also the cost of one pen and one pencil is in the ratio of 5 : 1 respectively . what is the cost of one dozen pens ?", - "Output Program": [ - "n0 = 3.0\nn1 = 5.0\nn2 = 100.0\nn3 = 5.0\nn4 = 1.0\nt0 = n0 + n4\nt1 = n0 * 4.0\nt2 = n2 / t0\nanswer = t2 * t1\nprint(answer)" - ], - "Output Answer": [ - "300" - ], - "split": "train" - }, - { - "Input": "how many even integers from 1 to 100 ( both inclusive ) have even number of factors ?", - "Output Program": [ - "import math\nn0 = 1.0\nn1 = 100.0\nt0 = math.sqrt(max(0, n1))\nanswer = t0 / 2.0\nprint(answer)" - ], - "Output Answer": [ - "5" - ], - "split": "train" - }, - { - "Input": "the ratio of the number of females to males at a party was 1 : 2 but when 4 females and 4 males left , the ratio became 1 : 3 . how many people were at the party originally ?", - "Output Program": [ - "n0 = 1.0\nn1 = 2.0\nn2 = 4.0\nn3 = 4.0\nn4 = 1.0\nn5 = 3.0\nt0 = n1 * n2\nt1 = n5 * t0\nt2 = t1 - t0\nt3 = t2 / n1\nanswer = t3 + t2\nprint(answer)" - ], - "Output Answer": [ - "24" - ], - "split": "train" - }, - { - "Input": "a bag contains 6 green balls and 7 white balls . if two balls are drawn simultaneously , what is the probability that both balls are the same colour ?", - "Output Program": [ - "n0 = 6.0\nn1 = 7.0\nt0 = n0 + n1\nt1 = n1 - 1.0\nt2 = n0 - 1.0\nt3 = n1 / t0\nt4 = n0 / t0\nt5 = t0 - 1.0\nt6 = t1 / t5\nt7 = t2 / t5\nt8 = t3 * t6\nt9 = t7 * t4\nanswer = t8 + t9\nprint(answer)" - ], - "Output Answer": [ - "0.46153846153846156" - ], - "split": "train" - }, - { - "Input": "set x consists of the integers from 1 to 12 , inclusive , while set y consists of the integers from 0 to 20 , inclusive . how many distinct integers do belong to the both sets at the same time ?", - "Output Program": [ - "n0 = 1.0\nn1 = 12.0\nn2 = 0.0\nn3 = 20.0\nt0 = n1 - n0\nanswer = t0 + 1.0\nprint(answer)" - ], - "Output Answer": [ - "12" - ], - "split": "train" - }, - { - "Input": "if w is the set of all the integers between 69 and 99 , inclusive , that are either multiples of 3 or multiples of 2 or multiples of both , then w contains how many numbers ?", - "Output Program": [ - "import math\nn0 = 69.0\nn1 = 99.0\nn2 = 3.0\nn3 = 2.0\nt0 = n3 * n2\nt1 = n1 - n0\nt2 = t1 / n3\nt3 = t1 / n2\nt4 = t1 / t0\nt5 = math.floor(t3)\nt6 = math.floor(t4)\nt7 = t2 + t5\nanswer = t7 - t6\nprint(answer)" - ], - "Output Answer": [ - "20" - ], - "split": "train" - }, - { - "Input": "in a sports club with 30 members , 18 play badminton and 19 play tennis and 2 do not play either . how many members play both badminton and tennis ?", - "Output Program": [ - "n0 = 30.0\nn1 = 18.0\nn2 = 19.0\nn3 = 2.0\nt0 = n1 + n2\nt1 = n3 + t0\nanswer = t1 - n0\nprint(answer)" - ], - "Output Answer": [ - "9" - ], - "split": "train" - }, - { - "Input": "at a garage sale , all of the items were sold at different prices . if the price of a radio sold at the garage sale was both the 17 th highest price and the 24 th lowest price among the prices of the items sold , how many items were sold at the garage sale ?", - "Output Program": [ - "n0 = 17.0\nn1 = 24.0\nt0 = n0 + n1\nanswer = t0 - 1.0\nprint(answer)" - ], - "Output Answer": [ - "40" - ], - "split": "train" - }, - { - "Input": "the ratio of incomes of two person p 1 and p 2 is 5 : 4 and the ratio of their expenditures is 3 : 2 . if at the end of the year , each saves rs . 1800 , then what is the income of p 1 ?", - "Output Program": [ - "n0 = 1.0\nn1 = 2.0\nn2 = 5.0\nn3 = 4.0\nn4 = 3.0\nn5 = 2.0\nn6 = 1800.0\nn7 = 1.0\nt0 = n6 / n1\nt1 = n4 * t0\nt2 = t1 - n6\nanswer = n2 * t2\nprint(answer)" - ], - "Output Answer": [ - "4500" - ], - "split": "train" - }, - { - "Input": "in a group of 22 boys , 13 play basketball and 15 play football . 3 of the boys play neither . how many play both ?", - "Output Program": [ - "n0 = 22.0\nn1 = 13.0\nn2 = 15.0\nn3 = 3.0\nt0 = n1 + n2\nt1 = n0 - n3\nt2 = t1 - n2\nt3 = t1 - n1\nt4 = t2 + t3\nanswer = t0 - t4\nprint(answer)" - ], - "Output Answer": [ - "18" - ], - "split": "train" - }, - { - "Input": "in a group of 6 boys & 4 girls a committee of 4 persons is to be formed . in how many different ways can it be done so that the committee has at least 1 girl ?", - "Output Program": [ - "import math\nn0 = 6.0\nn1 = 4.0\nn2 = 4.0\nn3 = 1.0\nt0 = n0 + n1\nt1 = math.factorial(min(15, int(n1)))\nt2 = math.factorial(min(15, int(n0)))\nt3 = math.factorial(min(15, int(2.0)))\nt4 = math.factorial(min(15, int(t0)))\nt5 = t1 * t2\nt6 = t3 * t1\nt7 = t4 / t5\nt8 = t2 / t6\nanswer = t7 - t8\nprint(answer)" - ], - "Output Answer": [ - "195" - ], - "split": "train" - }, - { - "Input": "at an international conference , \u201c red \u201d world countries and \u201c blue \u201d world countries are the only participants . the ratio of \u201c red \u201d world participants to \u201c blue \u201d world participants is 7 : 3 . if one - third of \u201c red \u201d world participants are left - handed and two - thirds of \u201c blue \u201d world participants are left - handed , then what is the fraction of the participants who are left - handed ?", - "Output Program": [ - "n0 = 7.0\nn1 = 3.0\nt0 = n0 + n1\nt1 = 2.0 / 3.0\nt2 = n0 * 0.33\nt3 = n1 * t1\nt4 = t2 + t3\nanswer = t4 / t0\nprint(answer)" - ], - "Output Answer": [ - "0.43100000000000005" - ], - "split": "train" - }, - { - "Input": "in a classroom , 12 students brought apples and 8 students brought bananas . if exactly 10 students brought only one of the two types of fruits , how many students brought both types of fruits ?", - "Output Program": [ - "n0 = 12.0\nn1 = 8.0\nn2 = 10.0\nt0 = n0 + n1\nanswer = t0 / 4.0\nprint(answer)" - ], - "Output Answer": [ - "5" - ], - "split": "train" - }, - { - "Input": "ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 26 years . what is deepak present age .", - "Output Program": [ - "n0 = 4.0\nn1 = 3.0\nn2 = 6.0\nn3 = 26.0\nt0 = n3 - n2\nt1 = n1 * t0\nanswer = t1 / n0\nprint(answer)" - ], - "Output Answer": [ - "15" - ], - "split": "train" - }, - { - "Input": "a and b play a game where each is asked to select a number from 1 to 16 . if the two numbers match , both of them win a prize . find the probability that they will not win a prize in a single trial .", - "Output Program": [ - "n0 = 1.0\nn1 = 16.0\nt0 = n1 - n0\nanswer = t0 / n1\nprint(answer)" - ], - "Output Answer": [ - "0.9375" - ], - "split": "train" - }, - { - "Input": "the ratio of boarders to day students at a school was originally 5 to 12 . however , after a number of new boarders join the initial 150 boarders , the ratio changed to 1 to 2 . if no boarders became day students and vice versa , and no students left the school , how many new boarders joined the school ?", - "Output Program": [ - "n0 = 5.0\nn1 = 12.0\nn2 = 150.0\nn3 = 1.0\nn4 = 2.0\nt0 = n2 / n0\nt1 = n1 * t0\nt2 = t1 / n4\nanswer = t2 - n2\nprint(answer)" - ], - "Output Answer": [ - "30" - ], - "split": "train" - }, - { - "Input": "two numbers are in ratio 4 : 5 and their lcm is 180 . the smaller number is", - "Output Program": [ - "n0 = 4.0\nn1 = 5.0\nn2 = 180.0\nt0 = n0 * n1\nt1 = n2 / t0\nanswer = n0 * t1\nprint(answer)" - ], - "Output Answer": [ - "36" - ], - "split": "train" - }, - { - "Input": "a bag contains 12 red marbles . if someone were to remove 2 marbles from the bag , one at a time , and replace the first marble after it was removed , the probability that neither marble would be red is 36 / 49 . how many marbles are in the bag ?", - "Output Program": [ - "import math\nn0 = 12.0\nn1 = 2.0\nn2 = 36.0\nn3 = 49.0\nt0 = n2 / n3\nt1 = math.sqrt(max(0, t0))\nt2 = 1.0 - t1\nanswer = n0 / t2\nprint(answer)" - ], - "Output Answer": [ - "84.00000000000004" - ], - "split": "train" - }, - { - "Input": "what is the value of ( log 2 3 ) ( log 3 4 ) ( log 4 5 ) . . . ( log 63 64 ) ?", - "Output Program": [ - "import math\nn0 = 2.0\nn1 = 3.0\nn2 = 3.0\nn3 = 4.0\nn4 = 4.0\nn5 = 5.0\nn6 = 63.0\nn7 = 64.0\nt0 = n5 + 1.0\nt1 = math.log(max(1e-5, n0), 2)\nt2 = t1 / t1\nanswer = t0 * t2\nprint(answer)" - ], - "Output Answer": [ - "6" - ], - "split": "train" - }, - { - "Input": "if 35 % of the 880 students at a certain college are enrolled in biology classes , how many students at the college are not enrolled in a biology class ?", - "Output Program": [ - "n0 = 35.0\nn1 = 880.0\nt0 = n1 / 100.0\nt1 = 100.0 - n0\nanswer = t0 * t1\nprint(answer)" - ], - "Output Answer": [ - "572" - ], - "split": "train" - }, - { - "Input": "at a certain restaurant , the ratio of the number of cooks to the number of waiters is 3 to 11 . when 12 more waiters are hired , the ratio of the number of cooks to the number of waiters changes to 1 to 5 . how many cooks does the restaurant have ?", - "Output Program": [ - "n0 = 3.0\nn1 = 11.0\nn2 = 12.0\nn3 = 1.0\nn4 = 5.0\nt0 = n2 / 4.0\nanswer = t0 * t0\nprint(answer)" - ], - "Output Answer": [ - "9" - ], - "split": "train" - }, - { - "Input": "the ratio of money with ram and gopal is 7 : 17 and that with gopal and krishan is 7 : 17 . if ram has rs . 588 , krishan has ?", - "Output Program": [ - "n0 = 7.0\nn1 = 17.0\nn2 = 7.0\nn3 = 17.0\nn4 = 588.0\nt0 = n4 / n0\nt1 = n1 * t0\nt2 = t1 / n0\nanswer = n1 * t2\nprint(answer)" - ], - "Output Answer": [ - "3468" - ], - "split": "train" - }, - { - "Input": "a certain fruit stand sold apples for $ 0.70 each and bananas for $ 0.60 each . if a customer purchased both apples and bananas from the stand for a total of $ 5.60 , what total number of apples and bananas did the customer purchase ?", - "Output Program": [ - "n0 = 0.7\nn1 = 0.6\nn2 = 5.6\nt0 = n0 * 2.0\nt1 = n2 - t0\nt2 = t1 / n1\nanswer = t2 + 2.0\nprint(answer)" - ], - "Output Answer": [ - "9" - ], - "split": "train" - }, - { - "Input": "of the 65 cars on a car lot , 45 have air - bag , 30 have power windows , and 12 have both air - bag and power windows . how many of the cars on the lot have neither air - bag nor power windows ?", - "Output Program": [ - "n0 = 65.0\nn1 = 45.0\nn2 = 30.0\nn3 = 12.0\nt0 = n1 + n2\nt1 = t0 - n3\nanswer = n0 - t1\nprint(answer)" - ], - "Output Answer": [ - "2" - ], - "split": "train" - }, - { - "Input": "the probability that event a occurs is 0.4 , and the probability that events a and b both occur is 0.25 . if the probability that either event a or event b occurs is 0.8 , what is the probability that event b will occur ?", - "Output Program": [ - "n0 = 0.4\nn1 = 0.25\nn2 = 0.8\nt0 = n1 + n2\nanswer = t0 - n0\nprint(answer)" - ], - "Output Answer": [ - "0.65" - ], - "split": "train" - }, - { - "Input": "a certain quantity of 60 % solution is replaced with 25 % solution such that the new concentration is 35 % . what is the fraction of the solution that was replaced ?", - "Output Program": [ - "n0 = 60.0\nn1 = 25.0\nn2 = 35.0\nt0 = n2 - n1\nt1 = n0 - n2\nt2 = t0 / t1\nt3 = t2 + 1.0\nanswer = 1 / t3\nprint(answer)" - ], - "Output Answer": [ - "0.7142857142857143" - ], - "split": "train" - }, - { - "Input": "in a certain state , the ratio of registered republicans to registered democrats is 3 to 2 , and every registered voter is either a republican or a democrat . if 90 percent of the republicans and 15 percent of the democrats are expected to vote for candidate x , and everyone else is expected to vote for candidate y , by what percent is candidate x expected to win the election ?", - "Output Program": [ - "n0 = 3.0\nn1 = 2.0\nn2 = 90.0\nn3 = 15.0\nt0 = n0 + n1\nt1 = n3 / 100.0\nt2 = n2 / 100.0\nt3 = n1 * t1\nt4 = n0 * t2\nt5 = t3 + t4\nt6 = n0 - t4\nt7 = n1 - t3\nt8 = t6 + t7\nt9 = t5 - t8\nt10 = t9 / t0\nanswer = t10 * 100.0\nprint(answer)" - ], - "Output Answer": [ - "20.000000000000004" - ], - "split": "train" - }, - { - "Input": "an ore contains 25 % of an alloy that has 90 % iron . other than this , in the remaining 75 % of the ore , there is no iron . how many kilograms of the ore are needed to obtain 60 kg of pure iron ?", - "Output Program": [ - "n0 = 25.0\nn1 = 90.0\nn2 = 75.0\nn3 = 60.0\nt0 = n3 * 100.0\nt1 = n0 * n1\nt2 = t1 / 100.0\nanswer = t0 / t2\nprint(answer)" - ], - "Output Answer": [ - "266.6666666666667" - ], - "split": "train" - }, - { - "Input": "what is the number of integers from 1 to 500 ( inclusive ) that are divisible by neither 10 nor by 15 ?", - "Output Program": [ - "n0 = 1.0\nn1 = 500.0\nn2 = 10.0\nn3 = 15.0\nt0 = n1 / n2\nt1 = n1 / n3\nt2 = n2 * n3\nt3 = t0 + t1\nt4 = n1 / t2\nt5 = t3 - t4\nanswer = n1 - t5\nprint(answer)" - ], - "Output Answer": [ - "420" - ], - "split": "train" - }, - { - "Input": "what is the number of integers from 11 to 1010 ( inclusive ) that are divisible by neither 12 nor by 15 ?", - "Output Program": [ - "n0 = 11.0\nn1 = 1010.0\nn2 = 12.0\nn3 = 15.0\nt0 = n1 / n2\nt1 = n1 / n3\nt2 = n2 * n3\nt3 = t0 + t1\nt4 = n1 / t2\nt5 = t3 - t4\nanswer = n1 - t5\nprint(answer)" - ], - "Output Answer": [ - "864.1111111111111" - ], - "split": "train" - }, - { - "Input": "two family reunions are happening at the park avenue hotel , the oates reunion and the hall reunion . all 100 guests at the hotel attend at least one of the reunions . if 40 people attend the oates reunion and 70 people attend the hall reunion , how many people attend both reunions", - "Output Program": [ - "n0 = 100.0\nn1 = 40.0\nn2 = 70.0\nt0 = n1 + n2\nanswer = t0 - n0\nprint(answer)" - ], - "Output Answer": [ - "10" - ], - "split": "train" - }, - { - "Input": "at a certain restaurant , the ratio of the number of cooks to the number of waiters is 3 to 8 . when 12 more waiters are hired , the ratio of the number of cooks to the number of waiters changes to 1 to 4 . how many cooks does the restaurant have ?", - "Output Program": [ - "n0 = 3.0\nn1 = 8.0\nn2 = 12.0\nn3 = 1.0\nn4 = 4.0\nt0 = n2 / n4\nanswer = t0 * t0\nprint(answer)" - ], - "Output Answer": [ - "9" - ], - "split": "train" - }, - { - "Input": "a bag contains 5 green balls and 8 white balls . if two balls are drawn simultaneously , what is the probability that both balls are the same colour ?", - "Output Program": [ - "n0 = 5.0\nn1 = 8.0\nt0 = n0 + n1\nt1 = n1 - 1.0\nt2 = n0 - 1.0\nt3 = n1 / t0\nt4 = n0 / t0\nt5 = t0 - 1.0\nt6 = t1 / t5\nt7 = t2 / t5\nt8 = t3 * t6\nt9 = t7 * t4\nanswer = t8 + t9\nprint(answer)" - ], - "Output Answer": [ - "0.4871794871794872" - ], - "split": "train" - }, - { - "Input": "the ratio of the two natural numbers is 6 : 5 . if a certain number is subtracted to both the numbers , the ratio becomes 5 : 4 . if the larger number exceeds the smaller number by 5 , find the number subtracted ?", - "Output Program": [ - "n0 = 6.0\nn1 = 5.0\nn2 = 5.0\nn3 = 4.0\nn4 = 5.0\nt0 = n1 * n1\nt1 = n1 + t0\nt2 = n1 * t0\nt3 = n3 * t1\nanswer = t2 - t3\nprint(answer)" - ], - "Output Answer": [ - "5" - ], - "split": "train" - }, - { - "Input": "a starts business with rs . 3500 and after 10 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b \u00e2 \u20ac \u2122 s contribution in the capital ?", - "Output Program": [ - "n0 = 3500.0\nn1 = 10.0\nn2 = 2.0\nn3 = 3.0\nt0 = n0 * 12.0\nt1 = 12.0 - n1\nt2 = n3 * t0\nt3 = n2 * t1\nanswer = t2 / t3\nprint(answer)" - ], - "Output Answer": [ - "31500" - ], - "split": "train" - }, - { - "Input": "log 3 n + log 12 n what is 3 digit number n that will be whole number", - "Output Program": [ - "n0 = 3.0\nn1 = 12.0\nn2 = 3.0\n\nanswer = n1**min(n0, 5)\nprint(answer)" - ], - "Output Answer": [ - "1728" - ], - "split": "train" - }, - { - "Input": "of the people who responded to a market survey , 150 preferred brand x and the rest preferred brand y . if the respondents indicated a preference for brand x over brand y by ratio of 5 to 1 , how many people responded to the survey ?", - "Output Program": [ - "n0 = 150.0\nn1 = 5.0\nn2 = 1.0\nt0 = n0 / n1\nanswer = n0 + t0\nprint(answer)" - ], - "Output Answer": [ - "180" - ], - "split": "train" - }, - { - "Input": "the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 9 and 10 . the larger of the two numbers is :", - "Output Program": [ - "n0 = 23.0\nn1 = 9.0\nn2 = 10.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "230" - ], - "split": "train" - }, - { - "Input": "the weights of one liter vegetable ghee packet of two brands \u2018 a \u2019 and \u2018 b \u2019 are 950 gm and 850 gm respectively . if they are mixed in the ratio of 3 : 2 by volumes to form a mixture of 4 liters , what is the weight ( in kg ) of the mixture ?", - "Output Program": [ - "n0 = 950.0\nn1 = 850.0\nn2 = 3.0\nn3 = 2.0\nn4 = 4.0\nt0 = n2 + n3\nt1 = n0 * n2\nt2 = n1 * n3\nt3 = t1 + t2\nt4 = n4 * t3\nt5 = t4 / t0\nanswer = t5 / 1000.0\nprint(answer)" - ], - "Output Answer": [ - "3.64" - ], - "split": "train" - }, - { - "Input": "local kennel has cats and dogs in the ratio of 3 : 4 . if there are 8 fewer cats than dogs , how many dogs are in the kennel ?", - "Output Program": [ - "n0 = 3.0\nn1 = 4.0\nn2 = 8.0\n\nanswer = n1 * n2\nprint(answer)" - ], - "Output Answer": [ - "32" - ], - "split": "train" - }, - { - "Input": "a student committee on academic integrity has 90 ways to select a president and vice president from a group of candidates . the same person can not be both president and vice president . how many candidates are there ?", - "Output Program": [ - "import math\nn0 = 90.0\nt0 = n0 * 4.0\nt1 = -1.0\nt2 = t1**min(2.0, 5)\nt3 = t0 + t2\nt4 = math.sqrt(max(0, t3))\nt5 = t4 + 1.0\nanswer = t5 / 2.0\nprint(answer)" - ], - "Output Answer": [ - "10" - ], - "split": "train" - }, - { - "Input": "a 40 kg metal bar made of alloy of tin and silver lost 4 kg of its weight in the water . 10 kg of tin loses 1.375 kg in the water ; 5 kg of silver loses 0.375 kg . what is the ratio of tin to silver in the bar ?", - "Output Program": [ - "n0 = 40.0\nn1 = 4.0\nn2 = 10.0\nn3 = 1.375\nn4 = 5.0\nn5 = 0.375\nt0 = n5 / n4\nt1 = n3 / n2\nt2 = n0 * t0\nt3 = t1 - t0\nt4 = n1 - t2\nt5 = t4 / t3\nt6 = n0 - t5\nanswer = t5 / t6\nprint(answer)" - ], - "Output Answer": [ - "0.6666666666666664" - ], - "split": "train" - }, - { - "Input": "in a sports club with 28 members , 17 play badminton and 19 play tennis and 2 do not play either . how many members play both badminton and tennis ?", - "Output Program": [ - "n0 = 28.0\nn1 = 17.0\nn2 = 19.0\nn3 = 2.0\nt0 = n1 + n2\nt1 = n3 + t0\nanswer = t1 - n0\nprint(answer)" - ], - "Output Answer": [ - "10" - ], - "split": "train" - }, - { - "Input": "two family reunions are happening at the same hotel , the oates reunion and the yellow reunion . all 100 guests at the hotel attend at least one of the reunions . if 42 people attend the oates reunion and 65 people attend the yellow reunion , how many people attend both reunions ?", - "Output Program": [ - "n0 = 100.0\nn1 = 42.0\nn2 = 65.0\nt0 = n1 + n2\nanswer = t0 - n0\nprint(answer)" - ], - "Output Answer": [ - "7" - ], - "split": "train" - }, - { - "Input": "a certain quantity of 70 % solution is replaced with 25 % solution such that the new concentration is 35 % . what is the fraction of the solution that was replaced ?", - "Output Program": [ - "n0 = 70.0\nn1 = 25.0\nn2 = 35.0\nt0 = n2 - n1\nt1 = n0 - n2\nt2 = t0 / t1\nt3 = t2 + 1.0\nanswer = 1 / t3\nprint(answer)" - ], - "Output Answer": [ - "0.7777777777777779" - ], - "split": "train" - }, - { - "Input": "of 60 children , 30 are happy , 10 are sad , and 20 are neither happy nor sad . there are 22 boys and 38 girls . if there are 6 happy boys and 4 sad girls , how many boys are neither happy nor sad ?", - "Output Program": [ - "n0 = 60.0\nn1 = 30.0\nn2 = 10.0\nn3 = 20.0\nn4 = 22.0\nn5 = 38.0\nn6 = 6.0\nn7 = 4.0\nt0 = n2 - n7\nt1 = n4 - t0\nanswer = t1 - n6\nprint(answer)" - ], - "Output Answer": [ - "10" - ], - "split": "train" - }, - { - "Input": "ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 34 years . what is deepak present age ?", - "Output Program": [ - "n0 = 4.0\nn1 = 3.0\nn2 = 6.0\nn3 = 34.0\nt0 = n3 - n2\nt1 = n1 * t0\nanswer = t1 / n0\nprint(answer)" - ], - "Output Answer": [ - "21" - ], - "split": "train" - }, - { - "Input": "in a certain alphabet , 20 letters contain a dot and a straight line . 36 letters contain a straight line but do not contain a dot . if that alphabet has 60 letters , all of which contain either a dot or a straight line or both , how many letters contain a dot but do not contain a straight line ?", - "Output Program": [ - "n0 = 20.0\nn1 = 36.0\nn2 = 60.0\nt0 = n0 + n1\nanswer = n2 - t0\nprint(answer)" - ], - "Output Answer": [ - "4" - ], - "split": "train" - }, - { - "Input": "the present ratio of students to teachers at a certain school is 50 to 1 . if the student enrollment were to increase by 50 students and the number of teachers were to increase by 5 , the ratio of students to teachers would then be 25 to 1 . what is the present number of teachers ?", - "Output Program": [ - "n0 = 50.0\nn1 = 1.0\nn2 = 50.0\nn3 = 5.0\nn4 = 25.0\nn5 = 1.0\nt0 = n0 + n4\nanswer = t0 / n4\nprint(answer)" - ], - "Output Answer": [ - "3" - ], - "split": "train" - }, - { - "Input": "how many zeros are the end of 380 ! ?", - "Output Program": [ - "n0 = 380.0\nt0 = 1.0 + 4.0\nt1 = n0 / t0\nt2 = t0**min(2.0, 5)\nt3 = t0**min(3.0, 5)\nt4 = n0 - t0\nt5 = t4 / t2\nt6 = t4 / t3\nt7 = t1 + t5\nanswer = t7 + t6\nprint(answer)" - ], - "Output Answer": [ - "94" - ], - "split": "train" - }, - { - "Input": "6 ) a marketing firm determined that , of 160 households surveyed , 80 used neither brand a nor brand b soap . 60 used only brand a soap and for every household that used both brands of soap , 3 used only brand b soap . how many of the 200 household surveyed used both brands of soap ?", - "Output Program": [ - "n0 = 6.0\nn1 = 160.0\nn2 = 80.0\nn3 = 60.0\nn4 = 3.0\nn5 = 200.0\nt0 = n1 - n2\nt1 = t0 - n3\nanswer = t1 / 4.0\nprint(answer)" - ], - "Output Answer": [ - "5" - ], - "split": "train" - }, - { - "Input": "ratio between rahul and deepak is 4 : 3 , after 22 years rahul age will be 26 years . what is deepak present age", - "Output Program": [ - "n0 = 4.0\nn1 = 3.0\nn2 = 22.0\nn3 = 26.0\nt0 = n3 - n2\nt1 = n1 * t0\nanswer = t1 / n0\nprint(answer)" - ], - "Output Answer": [ - "3" - ], - "split": "train" - }, - { - "Input": "the ratio of three numbers is 1 : 2 : 3 and the sum of their squares is 2744 . the sum of the numbers is ?", - "Output Program": [ - "import math\nn0 = 1.0\nn1 = 2.0\nn2 = 3.0\nn3 = 2744.0\nt0 = n0**min(n1, 5)\nt1 = n1**min(n1, 5)\nt2 = n2**min(n1, 5)\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n3 / t4\nanswer = math.sqrt(max(0, t5))\nprint(answer)" - ], - "Output Answer": [ - "14" - ], - "split": "train" - }, - { - "Input": "a certain manufacturer of cake , muffin , and bread mixes has 100 buyers , of whom 50 purchases cake mix , 40 purchase muffin mix , and 18 purchase both cake mix and muffin mix . if a buyer is to be selected at random from the 100 buyers , what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix ?", - "Output Program": [ - "n0 = 100.0\nn1 = 50.0\nn2 = 40.0\nn3 = 18.0\nn4 = 100.0\nt0 = n1 + n2\nt1 = t0 - n3\nt2 = n0 - t1\nanswer = t2 / n0\nprint(answer)" - ], - "Output Answer": [ - "0.28" - ], - "split": "train" - }, - { - "Input": "income and expenditure of a person are in the ratio 9 : 8 . if the income of the person is rs . 18000 , then find his savings ?", - "Output Program": [ - "n0 = 9.0\nn1 = 8.0\nn2 = 18000.0\nt0 = n1 / n0\nt1 = n2 * t0\nanswer = n2 - t1\nprint(answer)" - ], - "Output Answer": [ - "2000" - ], - "split": "train" - }, - { - "Input": "in a class of 39 students 26 play football and play 20 long tennis , if 17 play above , many play neither ?", - "Output Program": [ - "n0 = 39.0\nn1 = 26.0\nn2 = 20.0\nn3 = 17.0\nt0 = n1 + n2\nt1 = t0 - n3\nanswer = n0 - t1\nprint(answer)" - ], - "Output Answer": [ - "10" - ], - "split": "train" - }, - { - "Input": "the ratio of incomes of two person p 1 and p 2 is 5 : 4 and the ratio of their expenditures is 3 : 2 . if at the end of the year , each saves rs . 2200 , then what is the income of p 1 ?", - "Output Program": [ - "n0 = 1.0\nn1 = 2.0\nn2 = 5.0\nn3 = 4.0\nn4 = 3.0\nn5 = 2.0\nn6 = 2200.0\nn7 = 1.0\nt0 = n6 / n1\nt1 = n4 * t0\nt2 = t1 - n6\nanswer = n2 * t2\nprint(answer)" - ], - "Output Answer": [ - "5500" - ], - "split": "train" - }, - { - "Input": "the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is", - "Output Program": [ - "n0 = 23.0\nn1 = 13.0\nn2 = 14.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "322" - ], - "split": "train" - }, - { - "Input": "the 7 th grade french and spanish classes each have 21 students in them , and there are 6 students in the 7 th grade taking both languages . if everyone in the 7 th grade is in at least one of the two language classes , how many students are taking just one of the two classes ?", - "Output Program": [ - "n0 = 7.0\nn1 = 21.0\nn2 = 6.0\nn3 = 7.0\nn4 = 7.0\nt0 = n1 - n2\nanswer = t0 + t0\nprint(answer)" - ], - "Output Answer": [ - "30" - ], - "split": "train" - }, - { - "Input": "what number has a 5 : 1 ratio to the number 9 ?", - "Output Program": [ - "n0 = 5.0\nn1 = 1.0\nn2 = 9.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "45" - ], - "split": "train" - }, - { - "Input": "an amount of money is to be distributed among faruk , vasim and ranjith in the ratio 3 : 3 : 7 . if vasims share is rs . 1500 , what is the difference between faruk ' s and ranjith ' s shares ?", - "Output Program": [ - "n0 = 3.0\nn1 = 3.0\nn2 = 7.0\nn3 = 1500.0\nt0 = n3 / n1\nt1 = n2 - n0\nanswer = t0 * t1\nprint(answer)" - ], - "Output Answer": [ - "2000" - ], - "split": "train" - }, - { - "Input": "the length of the ribbon was originally 55 cm . it was reduced in the ratio 11 : 7 . what is its length now ?", - "Output Program": [ - "n0 = 55.0\nn1 = 11.0\nn2 = 7.0\nt0 = n2 / n1\nanswer = n0 * t0\nprint(answer)" - ], - "Output Answer": [ - "35" - ], - "split": "train" - }, - { - "Input": "the probability of two events a and b are 0.25 and 0.30 respectively . the probability that both a and b occur is 0.15 . the probability that neither a nor b occur is _________", - "Output Program": [ - "n0 = 0.25\nn1 = 0.3\nn2 = 0.15\nt0 = n0 + n1\nt1 = t0 - n2\nanswer = 1.0 - t1\nprint(answer)" - ], - "Output Answer": [ - "0.6" - ], - "split": "train" - }, - { - "Input": "90 people are attending a newspaper conference . 45 of them are writers and more than 38 are editors . of the people at the conference , x are both writers and editors and 2 x are neither . what is the largest possible number of people who are both writers and editors ?", - "Output Program": [ - "n0 = 90.0\nn1 = 45.0\nn2 = 38.0\nn3 = 2.0\nt0 = n2 + 1.0\nt1 = n1 + t0\nanswer = n0 - t1\nprint(answer)" - ], - "Output Answer": [ - "6" - ], - "split": "train" - }, - { - "Input": "two integers are in the ratio of 1 to 4 . if 6 is added to the smaller number , the ratio becomes 1 to 2 . find the larger integer .", - "Output Program": [ - "n0 = 1.0\nn1 = 4.0\nn2 = 6.0\nn3 = 1.0\nn4 = 2.0\nt0 = n2 * n4\nt1 = n1 - n4\nt2 = t0 / t1\nanswer = n1 * t2\nprint(answer)" - ], - "Output Answer": [ - "24" - ], - "split": "train" - }, - { - "Input": "find the number of different prime factors of 6440", - "Output Program": [ - "n0 = 6440.0\n\nanswer = 2.0 + 2.0\nprint(answer)" - ], - "Output Answer": [ - "4" - ], - "split": "train" - }, - { - "Input": "one lady has 2 children , one of her child is boy , what is the probability of having both are boys", - "Output Program": [ - "n0 = 2.0\n\nanswer = 1.0 / n0\nprint(answer)" - ], - "Output Answer": [ - "0.5" - ], - "split": "train" - }, - { - "Input": "apple costs l rupees per kilogram for first 30 kgs and q rupees per kilogram for each additional kilogram . if the price of 33 kilograms is 11.67 and for 36 kgs of apples is 12.48 then the cost of first 10 kgs of apples is", - "Output Program": [ - "n0 = 30.0\nn1 = 33.0\nn2 = 11.67\nn3 = 36.0\nn4 = 12.48\nn5 = 10.0\nt0 = n4 - n2\nt1 = n3 - n1\nt2 = n1 - n0\nt3 = t0 / t1\nt4 = t3 * t2\nt5 = n2 - t4\nt6 = t5 / n0\nanswer = n5 * t6\nprint(answer)" - ], - "Output Answer": [ - "3.62" - ], - "split": "train" - }, - { - "Input": "at the faculty of aerospace engineering , 312 students study random - processing methods , 234 students study scramjet rocket engines and 112 students study them both . if every student in the faculty has to study one of the two subjects , how many students are there in the faculty of aerospace engineering ?", - "Output Program": [ - "n0 = 312.0\nn1 = 234.0\nn2 = 112.0\nt0 = n2 / 2.0\nt1 = n0 - t0\nt2 = n1 - t0\nanswer = t1 + t2\nprint(answer)" - ], - "Output Answer": [ - "434" - ], - "split": "train" - }, - { - "Input": "if m = 3 ^ n , what is the greatest value of n for which m is a factor of 22 !", - "Output Program": [ - "import math\nn0 = 3.0\nn1 = 22.0\nt0 = n1 / n0\nt1 = n0**min(2.0, 5)\nt2 = n1 / t1\nt3 = math.floor(t0)\nt4 = math.floor(t2)\nanswer = t3 + t4\nprint(answer)" - ], - "Output Answer": [ - "9" - ], - "split": "train" - }, - { - "Input": "the ratio of money with ram and gopal is 7 : 17 and that with gopal and krishan is 7 : 17 . if ram has rs . 735 , krishan has ?", - "Output Program": [ - "n0 = 7.0\nn1 = 17.0\nn2 = 7.0\nn3 = 17.0\nn4 = 735.0\nt0 = n4 / n0\nt1 = n1 * t0\nt2 = t1 / n0\nanswer = n1 * t2\nprint(answer)" - ], - "Output Answer": [ - "4335" - ], - "split": "train" - }, - { - "Input": "1024 people in village 720 speak tamil , 562 speak english while 346 speak both . person who don not speack english or tamil speak hindi . what is probibility that person speak hindi", - "Output Program": [ - "n0 = 1024.0\nn1 = 720.0\nn2 = 562.0\nn3 = 346.0\nt0 = n2 - n3\nt1 = n1 - n3\nt2 = t0 + t1\nt3 = n3 + t2\nt4 = n0 - t3\nanswer = t4 / n0\nprint(answer)" - ], - "Output Answer": [ - "0.0859375" - ], - "split": "train" - }, - { - "Input": "on multiplying a number f by 153 , the result obtained was 102325 . however , it is found that both the 2 ' s are wrong . find the correct result .", - "Output Program": [ - "n0 = 153.0\nn1 = 102325.0\nn2 = 2.0\nt0 = 3.0 + 4.0\nt1 = t0 * 10.0\nt2 = t0 * 100.0\nt3 = t2 * 10.0\nt4 = t1 + t3\nanswer = n1 + t4\nprint(answer)" - ], - "Output Answer": [ - "109395" - ], - "split": "train" - }, - { - "Input": "60 kg of an alloy a is mixed with 100 kg of alloy b . if alloy a has lead and tin in the ratio 3 : 2 and alloy b has tin and copper in the ratio 1 : 4 , then the amount of tin in the new alloy is ?", - "Output Program": [ - "n0 = 60.0\nn1 = 100.0\nn2 = 3.0\nn3 = 2.0\nn4 = 1.0\nn5 = 4.0\nt0 = n2 + n3\nt1 = n4 + n5\nt2 = n0 / t0\nt3 = n1 / t1\nt4 = n3 * t2\nt5 = n4 * t3\nanswer = t4 + t5\nprint(answer)" - ], - "Output Answer": [ - "44" - ], - "split": "train" - }, - { - "Input": "in a certain town , the ratio of ny yankees fans to ny mets fans is 3 : 2 , and the ratio of ny mets fans to boston red sox fans is 4 : 5 . if there are 390 baseball fans in the town , each of whom is a fan of exactly one of those three teams , how many ny mets fans are there in this town ?", - "Output Program": [ - "n0 = 3.0\nn1 = 2.0\nn2 = 4.0\nn3 = 5.0\nn4 = 390.0\nt0 = n0 * n1\nt1 = n2 + t0\nt2 = n3 + t1\nt3 = n4 / t2\nanswer = n2 * t3\nprint(answer)" - ], - "Output Answer": [ - "104" - ], - "split": "train" - }, - { - "Input": "there are 100 lights which are functional and each is controlled by a separate on / off switch . two children a and b start playing with the switches . a starts by pressing every third switch till he reaches the end . b , 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": [ - "import math\nn0 = 100.0\nt0 = 1.0 + 4.0\nt1 = n0 / 3.0\nt2 = n0 / t0\nt3 = math.floor(t1)\nt4 = t0 * 3.0\nt5 = n0 / t4\nt6 = math.floor(t2)\nt7 = t3 + t6\nt8 = math.floor(t5)\nt9 = t8 * 2.0\nanswer = t7 - t9\nprint(answer)" - ], - "Output Answer": [ - "41" - ], - "split": "train" - }, - { - "Input": "how many two digit prime numbers are there in which both digits are prime numbers ? ( for example , 23 is one of these numbers but 31 is not , since 1 is not a prime number . )", - "Output Program": [ - "n0 = 23.0\nn1 = 31.0\nn2 = 1.0\nt0 = n1 % n0\nanswer = t0 / 2.0\nprint(answer)" - ], - "Output Answer": [ - "4" - ], - "split": "train" - }, - { - "Input": "the h . c . f of two numbers is 23 and the other two factors of their l . c . m are 11 and 12 . the larger of the two numbers is :", - "Output Program": [ - "n0 = 23.0\nn1 = 11.0\nn2 = 12.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "276" - ], - "split": "train" - }, - { - "Input": "16 balls are numbered 1 to 16 . a ball is drawn and then another ball is drawn without replacement . what is the probability that both balls have even numbers ?", - "Output Program": [ - "n0 = 16.0\nn1 = 1.0\nn2 = 16.0\nt0 = 4.0 + 4.0\nt1 = n0 - n1\nt2 = t0 / n0\nt3 = t0 - n1\nt4 = t3 / t1\nanswer = t2 * t4\nprint(answer)" - ], - "Output Answer": [ - "0.23333333333333334" - ], - "split": "train" - }, - { - "Input": "pens , pencils and markers in a jenna ' s desk are in the ratio of 2 : 2 : 5 . if there are 10 pens , the number of markers in jenna ' s desk is :", - "Output Program": [ - "n0 = 2.0\nn1 = 2.0\nn2 = 5.0\nn3 = 10.0\nt0 = n2 * n3\nanswer = t0 / n0\nprint(answer)" - ], - "Output Answer": [ - "25" - ], - "split": "train" - }, - { - "Input": "in a class of boys and girls vikas ' s rank is 9 th and tanvi ' s rank is 17 th . vikas ' s rank among the boys in that class is 4 th from the top and 18 th from the bottom and tanvi ' s rank among the girls is 8 th from top and 21 st from bottom . in the order of rank , how many girls are there between tanvi and vikas ?", - "Output Program": [ - "n0 = 9.0\nn1 = 17.0\nn2 = 4.0\nn3 = 18.0\nn4 = 8.0\nn5 = 21.0\nt0 = n4 - 1.0\nt1 = n0 - 1.0\nt2 = n2 - 1.0\nt3 = t1 - t2\nanswer = t0 - t3\nprint(answer)" - ], - "Output Answer": [ - "2" - ], - "split": "train" - }, - { - "Input": "what is the square root of 36 , divided by 6 ?", - "Output Program": [ - "import math\nn0 = 36.0\nn1 = 6.0\nt0 = math.sqrt(max(0, n0))\nanswer = t0 / n1\nprint(answer)" - ], - "Output Answer": [ - "1" - ], - "split": "train" - }, - { - "Input": "in a college , the ratio of the number of boys to girls is 6 : 5 . if there are 200 girls , the total number of students in the college is", - "Output Program": [ - "n0 = 6.0\nn1 = 5.0\nn2 = 200.0\nt0 = n2 / n1\nt1 = n0 * t0\nanswer = n2 + t1\nprint(answer)" - ], - "Output Answer": [ - "440" - ], - "split": "train" - }, - { - "Input": "the hcf of two numbers is 50 and the other two factors of their lcm are 11 and 12 . what is the largest number .", - "Output Program": [ - "n0 = 50.0\nn1 = 11.0\nn2 = 12.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "600" - ], - "split": "train" - }, - { - "Input": "the least whole number which when subtracted from both the terms of the ratio 6 : 7 to give a ratio less than 16 : 21 , is", - "Output Program": [ - "n0 = 6.0\nn1 = 7.0\nn2 = 16.0\nn3 = 21.0\nt0 = 2.0 / 10.0\nt1 = n0 * n3\nt2 = n1 * n2\nt3 = n3 - n2\nt4 = t1 - t2\nt5 = t4 / t3\nanswer = t5 + t0\nprint(answer)" - ], - "Output Answer": [ - "3" - ], - "split": "train" - }, - { - "Input": "there are 2 available positions and 50 candidates , one half of whom are democrats and another half are republicans . if it was decided that the positions would be filled at random , then what is the probability w that the both positions will be taken by members of just one party ?", - "Output Program": [ - "n0 = 2.0\nn1 = 50.0\nt0 = n1 / n0\nt1 = n1 - 1.0\nt2 = t0 / n1\nt3 = t0 - 1.0\nt4 = t3 / t1\nt5 = t4 * t2\nanswer = n0 * t5\nprint(answer)" - ], - "Output Answer": [ - "0.4897959183673469" - ], - "split": "train" - }, - { - "Input": "in a group of 400 readers who read science fiction or literacy works or both , 250 read science fiction and 230 read literacy works . how many read both science fiction and literacy works ?", - "Output Program": [ - "n0 = 400.0\nn1 = 250.0\nn2 = 230.0\nt0 = n1 + n2\nanswer = t0 - n0\nprint(answer)" - ], - "Output Answer": [ - "80" - ], - "split": "train" - }, - { - "Input": "the h . c . f . of two numbers is 16 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is :", - "Output Program": [ - "n0 = 16.0\nn1 = 13.0\nn2 = 14.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "224" - ], - "split": "train" - }, - { - "Input": "income and expenditure of a person are in the ratio 9 : 8 . if the income of the person is rs . 36000 , then find his savings ?", - "Output Program": [ - "n0 = 9.0\nn1 = 8.0\nn2 = 36000.0\nt0 = n1 / n0\nt1 = n2 * t0\nanswer = n2 - t1\nprint(answer)" - ], - "Output Answer": [ - "4000" - ], - "split": "train" - }, - { - "Input": "a dog takes 10 leaps for every 2 leaps of a hare . if one leap of the dog is equal to 2 leaps of the hare , the ratio of the speed of the dog to that of the hare is :", - "Output Program": [ - "n0 = 10.0\nn1 = 2.0\nn2 = 2.0\nt0 = n0 * n2\nanswer = t0 / n1\nprint(answer)" - ], - "Output Answer": [ - "10" - ], - "split": "train" - }, - { - "Input": "at a party , 13 guests brought wine and 14 guests brought beer . if exactly 11 guests brought only one of the two types of drinks , how many guests brought both types of drinks ?", - "Output Program": [ - "n0 = 13.0\nn1 = 14.0\nn2 = 11.0\nt0 = n0 + n1\nt1 = t0 - n2\nanswer = t1 / 2.0\nprint(answer)" - ], - "Output Answer": [ - "8" - ], - "split": "train" - }, - { - "Input": "the ratio of incomes of two person p 1 and p 2 is 5 : 4 and the ratio of their expenditures is 3 : 2 . if at the end of the year , each saves rs . 1400 , then what is the income of p 1 ?", - "Output Program": [ - "n0 = 1.0\nn1 = 2.0\nn2 = 5.0\nn3 = 4.0\nn4 = 3.0\nn5 = 2.0\nn6 = 1400.0\nn7 = 1.0\nt0 = n6 / n1\nt1 = n4 * t0\nt2 = t1 - n6\nanswer = n2 * t2\nprint(answer)" - ], - "Output Answer": [ - "3500" - ], - "split": "train" - }, - { - "Input": "4 dice are thrown and the sum of the numbers noted is 10 . find the probability that all the numbers lie between 2 and 5 ( both inclusive ) ?", - "Output Program": [ - "n0 = 4.0\nn1 = 10.0\nn2 = 2.0\nn3 = 5.0\nt0 = n0 * n2\nt1 = n1 * t0\nt2 = t1 - 1.0\nanswer = n1 / t2\nprint(answer)" - ], - "Output Answer": [ - "0.12658227848101267" - ], - "split": "train" - }, - { - "Input": "there are 10 slate rocks , 11 pumice rocks , and 4 granite rocks randomly distributed in a certain field . if 2 rocks are chosen at random and without replacement , what is the probability that both rocks will be slate rocks ?", - "Output Program": [ - "n0 = 10.0\nn1 = 11.0\nn2 = 4.0\nn3 = 2.0\nt0 = n0 + n1\nt1 = n0 - 1.0\nt2 = n2 + t0\nt3 = n0 / t2\nt4 = t2 - 1.0\nt5 = t1 / t4\nanswer = t3 * t5\nprint(answer)" - ], - "Output Answer": [ - "0.15000000000000002" - ], - "split": "train" - }, - { - "Input": "a farmer used 1,034 acres of land for beans , wheat , and corn in the ratio of 5 : 2 : 4 , respectively . how many y acres were used for corn ?", - "Output Program": [ - "n0 = 1034.0\nn1 = 5.0\nn2 = 2.0\nn3 = 4.0\nt0 = n1 + n2\nt1 = 10.0 * 3.0\nt2 = 1.0 * 1000.0\nt3 = n3 + t1\nt4 = n3 + t0\nt5 = t3 + t2\nt6 = t5 / t4\nanswer = n3 * t6\nprint(answer)" - ], - "Output Answer": [ - "376" - ], - "split": "train" - }, - { - "Input": "if x and y are sets of integers , x # y denotes the set of integers that belong to set x or set y , but not both . if x consists of 16 integers , y consists of 18 integers , and 6 of the integers are in both x and y , then x # y consists of how many integers ?", - "Output Program": [ - "n0 = 16.0\nn1 = 18.0\nn2 = 6.0\nt0 = n1 - n2\nt1 = n0 - n2\nanswer = t0 + t1\nprint(answer)" - ], - "Output Answer": [ - "22" - ], - "split": "train" - }, - { - "Input": "in a family 19 people eat only vegetarian , 9 people eat only non veg . , 12 people eat both veg and non veg . . how many people eat veg in the family ?", - "Output Program": [ - "n0 = 19.0\nn1 = 9.0\nn2 = 12.0\n\nanswer = n0 + n2\nprint(answer)" - ], - "Output Answer": [ - "31" - ], - "split": "train" - }, - { - "Input": "how many prime numbers between 1 and 100 are factors of 210 ?", - "Output Program": [ - "n0 = 1.0\nn1 = 100.0\nn2 = 210.0\n\nanswer = 1.0 * 4.0\nprint(answer)" - ], - "Output Answer": [ - "4" - ], - "split": "train" - }, - { - "Input": "if 4 and 8 are factors of 60 n , what is the minimum value of n ?", - "Output Program": [ - "import scipy\nn0 = 4.0\nn1 = 8.0\nn2 = 60.0\n\nanswer = scipy.lcm(int(n0), int(n1))\nprint(answer)" - ], - "Output Answer": [ - "8" - ], - "split": "train" - }, - { - "Input": "the compound ratio of 2 / 3 , 6 / 7 , 1 / 3 and 3 / 8 is given by ?", - "Output Program": [ - "n0 = 2.0\nn1 = 3.0\nn2 = 6.0\nn3 = 7.0\nn4 = 1.0\nn5 = 3.0\nn6 = 3.0\nn7 = 8.0\nt0 = n0 * n3\nanswer = 1 / t0\nprint(answer)" - ], - "Output Answer": [ - "0.07142857142857142" - ], - "split": "train" - }, - { - "Input": "in a group of 50 people , 25 have visited iceland and 23 have visited norway . if 21 people have visited both iceland and norway , how many people have visited neither country ?", - "Output Program": [ - "n0 = 50.0\nn1 = 25.0\nn2 = 23.0\nn3 = 21.0\nt0 = n1 + n2\nt1 = t0 - n3\nanswer = n0 - t1\nprint(answer)" - ], - "Output Answer": [ - "23" - ], - "split": "train" - }, - { - "Input": "in a college , the ratio of the number of boys to girls is 8 : 5 . if there are 200 girls , the total number of students in the college is", - "Output Program": [ - "n0 = 8.0\nn1 = 5.0\nn2 = 200.0\nt0 = n2 / n1\nt1 = n0 * t0\nanswer = n2 + t1\nprint(answer)" - ], - "Output Answer": [ - "520" - ], - "split": "train" - }, - { - "Input": "a king has 1000 bottles of wine , a queen wants to kill the king and sends a servant to poison the wine . fortunately the king ' s guard ' s catch d servant after he has only poisoned one bottle and the guard do n ' t know which bottle is poisoned . furthermore it takes one month to have an effect , and there is an anniversary party coming up in 5 weeks time ! the king decides he will get some of the prisoners in his vast dungeons to drink the wine . how many minimum prisoners does it required to sample the wine to find out the poisoned bottle so that the guests will still be able to drink the rest of the wine at his anniversary party in 5 weeks time ?", - "Output Program": [ - "n0 = 1000.0\nn1 = 5.0\nn2 = 5.0\n\nanswer = n0 / 100.0\nprint(answer)" - ], - "Output Answer": [ - "10" - ], - "split": "train" - }, - { - "Input": "a number is said to be prime saturated if the product of all the different positive prime factors of e is less than the square root of e . what is the greatest two digit prime saturated integer ?", - "Output Program": [ - "t0 = 2.0 * 3.0\nt1 = 100.0 - 10.0\nanswer = t0 + t1\nprint(answer)" - ], - "Output Answer": [ - "96" - ], - "split": "train" - }, - { - "Input": "14 different biology books and 8 different chemistry books lie on a shelf . in how many ways can a student pick 2 books of each type ?", - "Output Program": [ - "import math\nn0 = 14.0\nn1 = 8.0\nn2 = 2.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(n1)))\nt2 = n0 - n2\nt3 = n1 - n2\nt4 = math.factorial(min(15, int(t2)))\nt5 = math.factorial(min(15, int(t3)))\nt6 = t0 / t4\nt7 = t1 / t5\nt8 = t6 / n2\nt9 = t7 / n2\nanswer = t8 * t9\nprint(answer)" - ], - "Output Answer": [ - "2548" - ], - "split": "train" - }, - { - "Input": "the weights of one liter vegetable ghee packet of two brands \u2018 a \u2019 and \u2018 b \u2019 are 900 gm and 850 gm respectively . if they are mixed in the ratio of 3 : 2 by volumes to form a mixture of 4 liters , what is the weight ( in kg ) of the mixture ?", - "Output Program": [ - "n0 = 900.0\nn1 = 850.0\nn2 = 3.0\nn3 = 2.0\nn4 = 4.0\nt0 = n2 + n3\nt1 = n0 * n2\nt2 = n1 * n3\nt3 = t1 + t2\nt4 = n4 * t3\nt5 = t4 / t0\nanswer = t5 / 1000.0\nprint(answer)" - ], - "Output Answer": [ - "3.52" - ], - "split": "train" - }, - { - "Input": "in a certain kindergarten , every child has got either a dog or a cat or both . 18 children have got dogs only and 6 children have got both dogs and cats . if there are 30 children in the kindergarten , how many of them have cats ?", - "Output Program": [ - "n0 = 18.0\nn1 = 6.0\nn2 = 30.0\n\nanswer = n2 - n0\nprint(answer)" - ], - "Output Answer": [ - "12" - ], - "split": "train" - }, - { - "Input": "a dog breeder currently has 9 breeding dogs . 6 of the dogs have exactly 1 littermate , and 3 of the dogs have exactly 2 littermates . if 2 dogs are selected at random , what is the probability r that both selected dogs are not littermates ?", - "Output Program": [ - "n0 = 9.0\nn1 = 6.0\nn2 = 1.0\nn3 = 3.0\nn4 = 2.0\nn5 = 2.0\n\nanswer = 5.0 / n1\nprint(answer)" - ], - "Output Answer": [ - "0.8333333333333334" - ], - "split": "train" - }, - { - "Input": "a certain high school has 500 students . of these students , 40 are taking music , 20 are taking art , and 10 are taking both music and art . how many students are taking neither music nor art ?", - "Output Program": [ - "n0 = 500.0\nn1 = 40.0\nn2 = 20.0\nn3 = 10.0\nt0 = n1 + n2\nt1 = t0 - n3\nanswer = n0 - t1\nprint(answer)" - ], - "Output Answer": [ - "450" - ], - "split": "train" - }, - { - "Input": "a certain manufacturer of cake , muffin , and bread mixes has 100 buyers , of whom 50 purchases cake mix , 40 purchase muffin mix , and 15 purchase both cake mix and muffin mix . if a buyer is to be selected at random from the 100 buyers , what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix ?", - "Output Program": [ - "n0 = 100.0\nn1 = 50.0\nn2 = 40.0\nn3 = 15.0\nn4 = 100.0\nt0 = n1 + n2\nt1 = t0 - n3\nt2 = n0 - t1\nanswer = t2 / n0\nprint(answer)" - ], - "Output Answer": [ - "0.25" - ], - "split": "train" - }, - { - "Input": "in a group of people , if 30 people were made to stand in each column , 16 columns could be formed . if 48 people were made to stand in a column , how many columns could be formed ?", - "Output Program": [ - "n0 = 30.0\nn1 = 16.0\nn2 = 48.0\nt0 = n2 / n1\nanswer = n0 / t0\nprint(answer)" - ], - "Output Answer": [ - "10" - ], - "split": "train" - }, - { - "Input": "in a college , the ratio of the number of boys to girls is 8 : 4 . if there are 200 girls , the total number of students in the college is", - "Output Program": [ - "n0 = 8.0\nn1 = 4.0\nn2 = 200.0\nt0 = n2 / n1\nt1 = n0 * t0\nanswer = n2 + t1\nprint(answer)" - ], - "Output Answer": [ - "600" - ], - "split": "train" - }, - { - "Input": "a certain bag contains 60 balls \u2014 22 white , 18 green , 5 yellow , 6 red , and 9 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?", - "Output Program": [ - "n0 = 60.0\nn1 = 22.0\nn2 = 18.0\nn3 = 5.0\nn4 = 6.0\nn5 = 9.0\nt0 = n1 + n2\nt1 = n3 + t0\nanswer = t1 / n0\nprint(answer)" - ], - "Output Answer": [ - "0.75" - ], - "split": "train" - }, - { - "Input": "an alloy is to contain copper and zinc in the ratio 5 : 3 . the zinc required to be melted with 40 kg of copper is ?", - "Output Program": [ - "n0 = 5.0\nn1 = 3.0\nn2 = 40.0\nt0 = n1 * n2\nanswer = t0 / n0\nprint(answer)" - ], - "Output Answer": [ - "24" - ], - "split": "train" - }, - { - "Input": "in a circuit board factory , all circuit boards that pass a verification process are certified . every board that fails the verification process is indeed faulty , but 1 / 8 of those that pass are also faulty . approximately how many faulty circuit boards exist in a group of 3200 circuit boards where 64 fail inspection ?", - "Output Program": [ - "n0 = 1.0\nn1 = 8.0\nn2 = 3200.0\nn3 = 64.0\nt0 = n0 / n1\nt1 = n2 - n3\nt2 = t0 * t1\nanswer = n3 + t2\nprint(answer)" - ], - "Output Answer": [ - "456" - ], - "split": "train" - }, - { - "Input": "in a sports club with 30 members , 17 play badminton and 19 play tennis and 2 do not play either . how many members play both badminton and tennis ?", - "Output Program": [ - "n0 = 30.0\nn1 = 17.0\nn2 = 19.0\nn3 = 2.0\nt0 = n1 + n2\nt1 = n3 + t0\nanswer = t1 - n0\nprint(answer)" - ], - "Output Answer": [ - "8" - ], - "split": "train" - }, - { - "Input": "in a certain alphabet , 13 letters contain a dot and a straight line . 24 letters contain a straight line but do not contain a dot . if that alphabet has 40 letters , all of which contain either a dot or a straight line or both , how many letters contain a dot but do not contain a straight line ?", - "Output Program": [ - "n0 = 13.0\nn1 = 24.0\nn2 = 40.0\nt0 = n0 + n1\nanswer = n2 - t0\nprint(answer)" - ], - "Output Answer": [ - "3" - ], - "split": "train" - }, - { - "Input": "in a group of 6 boys and 4 girls are to be selected . in how many different ways can they be selected such that at least one boy should be there ?", - "Output Program": [ - "import math\nn0 = 6.0\nn1 = 4.0\nt0 = n0 + n1\nt1 = math.factorial(min(15, int(n1)))\nt2 = math.factorial(min(15, int(n0)))\nt3 = math.factorial(min(15, int(t0)))\nt4 = t1 * t2\nanswer = t3 / t4\nprint(answer)" - ], - "Output Answer": [ - "210" - ], - "split": "train" - }, - { - "Input": "the ratio of the incomes of a and b is 5 : 4 and the ratio of their expenditure is 3 : 2 . if at the end of the year , each saves $ 1600 then the income of a is ?", - "Output Program": [ - "n0 = 5.0\nn1 = 4.0\nn2 = 3.0\nn3 = 2.0\nn4 = 1600.0\nt0 = n0 / n3\nanswer = n4 * t0\nprint(answer)" - ], - "Output Answer": [ - "4000" - ], - "split": "train" - }, - { - "Input": "in a group of 8 engineers , 3 engineers have a phd degree ; the others have only an ms or bs degree . a team of 3 engineers is to be chosen which must have at least 1 engineer with a phd , how many different teams can be chosen ?", - "Output Program": [ - "n0 = 8.0\nn1 = 3.0\nn2 = 3.0\nn3 = 1.0\nt0 = n0 - n1\nt1 = n1 * t0\nt2 = n1 * t1\nanswer = n3 + t2\nprint(answer)" - ], - "Output Answer": [ - "46" - ], - "split": "train" - }, - { - "Input": "in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the sport formulation contains 4 ounces of corn syrup , how many ounces of water does it contain ?", - "Output Program": [ - "n0 = 1.0\nn1 = 12.0\nn2 = 30.0\nn3 = 4.0\nt0 = n0 / n1\nt1 = n0 / n2\nt2 = t1 / 2.0\nt3 = t0 * 3.0\nt4 = t3 / t2\nanswer = n3 * t4\nprint(answer)" - ], - "Output Answer": [ - "60" - ], - "split": "train" - }, - { - "Input": "in a class of 50 students , 18 take chorus , 26 take band , and 2 take both chorus and band . how many students in the class are not enrolled in either chorus or band ?", - "Output Program": [ - "n0 = 50.0\nn1 = 18.0\nn2 = 26.0\nn3 = 2.0\nt0 = n1 - n3\nt1 = n2 - n3\nt2 = t0 + t1\nt3 = n3 + t2\nanswer = n0 - t3\nprint(answer)" - ], - "Output Answer": [ - "8" - ], - "split": "train" - }, - { - "Input": "if 30 % of the 880 students at a certain college are enrolled in biology classes , how many students at the college are not enrolled in a biology class ?", - "Output Program": [ - "n0 = 30.0\nn1 = 880.0\nt0 = n1 / 100.0\nt1 = 100.0 - n0\nanswer = t0 * t1\nprint(answer)" - ], - "Output Answer": [ - "616" - ], - "split": "train" - }, - { - "Input": "ratio between rahul and deepak is 4 : 3 , after 10 years rahul age will be 26 years . what is deepak present age", - "Output Program": [ - "n0 = 4.0\nn1 = 3.0\nn2 = 10.0\nn3 = 26.0\nt0 = n3 - n2\nt1 = n1 * t0\nanswer = t1 / n0\nprint(answer)" - ], - "Output Answer": [ - "12" - ], - "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 z 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": "if all the 6 are replaced by 9 , then the algebraic sum of all the numbers from 1 to 100 ( both inclusive ) varies by", - "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 the ratio of two number is 3 : 4 and lcm of the number is 180 then what is the number .", - "Output Program": [ - "n0 = 3.0\nn1 = 4.0\nn2 = 180.0\nt0 = n0 * n1\nanswer = n2 / t0\nprint(answer)" - ], - "Output Answer": [ - "15" - ], - "split": "train" - }, - { - "Input": "the h . c . f of two numbers is 23 and the other two factors of their l . c . m are 15 and 16 . the larger of the two numbers is :", - "Output Program": [ - "n0 = 23.0\nn1 = 15.0\nn2 = 16.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "368" - ], - "split": "train" - }, - { - "Input": "initially , the men and women in a room were in the ratio of 4 : 5 . then , 2 men entered the room and 3 women left the room . then , the number of women doubled . now there are 14 men in the room . how many r women are currently in the room ?", - "Output Program": [ - "n0 = 4.0\nn1 = 5.0\nn2 = 2.0\nn3 = 3.0\nn4 = 14.0\nt0 = n4 - n2\nt1 = n1 * t0\nt2 = t1 / n0\nt3 = t2 - n3\nanswer = n2 * t3\nprint(answer)" - ], - "Output Answer": [ - "24" - ], - "split": "train" - }, - { - "Input": "find the fraction which has the same ratio to 2 / 3 that 3 / 5 has to 6 / 7", - "Output Program": [ - "n0 = 2.0\nn1 = 3.0\nn2 = 3.0\nn3 = 5.0\nn4 = 6.0\nn5 = 7.0\nt0 = n2 / n3\nt1 = n4 / n5\nt2 = n0 / n1\nt3 = t0 / t1\nanswer = t3 * t2\nprint(answer)" - ], - "Output Answer": [ - "0.4666666666666667" - ], - "split": "train" - }, - { - "Input": "a survey was taken among 100 brainiacs . of those surveyed , twice as many brainiacs likerebus teasers as math teasers . if 18 brainiacs like both rebus teasers and math teasers and 4 like neither kind of teaser , how many brainiacs like math teasers but not rebus teasers ?", - "Output Program": [ - "n0 = 100.0\nn1 = 18.0\nn2 = 4.0\nt0 = 1.0 + 2.0\nt1 = n0 - n2\nt2 = n1 + t1\nt3 = t2 / t0\nanswer = t3 - n1\nprint(answer)" - ], - "Output Answer": [ - "20" - ], - "split": "train" - }, - { - "Input": "a jar contains a mixture of a & b in the ratio 4 : 1 . when 10 l of mixture is replaced with liquid b , ratio becomes 2 : 3 . how many liters of liquid a was present in mixture initially .", - "Output Program": [ - "n0 = 4.0\nn1 = 1.0\nn2 = 10.0\nn3 = 2.0\nn4 = 3.0\nt0 = n0 + n1\nt1 = n3 + n4\nt2 = n0 / t0\nt3 = n3 / t1\nt4 = n2 * t2\nt5 = t2 - t3\nt6 = t4 / t5\nanswer = t2 * t6\nprint(answer)" - ], - "Output Answer": [ - "16" - ], - "split": "train" - }, - { - "Input": "at an m & m factory , two types of m & ms are produced , red and blue . the m & ms are transported individually on a conveyor belt . anna is watching the conveyor belt , and has determined that 4 out of every 5 red m & ms are followed by a blue one , while one out of every 6 blue m & ms is followed by a red one . what proportion of the m & ms are red ?", - "Output Program": [ - "n0 = 4.0\nn1 = 5.0\nn2 = 6.0\nt0 = n0 + n1\nt1 = n0 * n1\nt2 = t0 + t1\nanswer = n1 / t2\nprint(answer)" - ], - "Output Answer": [ - "0.1724137931034483" - ], - "split": "train" - }, - { - "Input": "a firm is comprised of partners and associates in a ratio of 2 : 63 . if 35 more associates were hired , the ratio of partners to associates would be 1 : 34 . how many partners are currently in the firm ?", - "Output Program": [ - "n0 = 2.0\nn1 = 63.0\nn2 = 35.0\nn3 = 1.0\nn4 = 34.0\nt0 = n0 * n4\nt1 = t0 - n1\nt2 = n2 / t1\nanswer = n0 * t2\nprint(answer)" - ], - "Output Answer": [ - "14" - ], - "split": "train" - }, - { - "Input": "the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 16 . the larger of the two numbers is :", - "Output Program": [ - "n0 = 23.0\nn1 = 13.0\nn2 = 16.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "368" - ], - "split": "train" - }, - { - "Input": "how many positive factors do 150 and 90 have in common ?", - "Output Program": [ - "n0 = 150.0\nn1 = 90.0\nt0 = n1 - 10.0\nanswer = t0 / 10.0\nprint(answer)" - ], - "Output Answer": [ - "8" - ], - "split": "train" - }, - { - "Input": "a certain telephone company offers two plans , a and b . under plan a , the company charges a total of $ 0.60 for the first 8 minutes of each call and $ 0.06 per minute thereafter . under plan b , the company charges $ 0.08 per minute of each call . what is the duration of a call , in minutes , for which the company charges the same amount under plan a and under plan b ?", - "Output Program": [ - "n0 = 0.6\nn1 = 8.0\nn2 = 0.06\nn3 = 0.08\nt0 = n1 * n2\nt1 = n3 - n2\nt2 = n0 - t0\nanswer = t2 / t1\nprint(answer)" - ], - "Output Answer": [ - "5.999999999999998" - ], - "split": "train" - }, - { - "Input": "sachin is younger than rahul by 9 years . if the ratio of their ages is 7 : 9 , find the age of sachin", - "Output Program": [ - "n0 = 9.0\nn1 = 7.0\nn2 = 9.0\nt0 = n2 - n1\nt1 = n0 / t0\nanswer = n1 * t1\nprint(answer)" - ], - "Output Answer": [ - "31.5" - ], - "split": "train" - }, - { - "Input": "in a class of 40 students , 10 did not opt for math . 15 did not opt for science and 2 did not opt for either . how many students of the class opted for both math and science ?", - "Output Program": [ - "n0 = 40.0\nn1 = 10.0\nn2 = 15.0\nn3 = 2.0\nt0 = n0 - n1\nt1 = n0 - n2\nt2 = t1 - n3\nanswer = t0 - t2\nprint(answer)" - ], - "Output Answer": [ - "7" - ], - "split": "train" - }, - { - "Input": "in a certain animal shelter , the ratio of the number of dogs to the number of cats is 15 to 7 . if 20 additional cats were to be taken in by the shelter , the ratio of the number of dogs to the number of cats would be 15 to 11 . how many dogs are in the shelter ?", - "Output Program": [ - "n0 = 15.0\nn1 = 7.0\nn2 = 20.0\nn3 = 15.0\nn4 = 11.0\nt0 = n1 * n2\nt1 = n4 - n1\nt2 = t0 / t1\nt3 = t2 / n1\nanswer = n0 * t3\nprint(answer)" - ], - "Output Answer": [ - "75" - ], - "split": "train" - }, - { - "Input": "a study group consists of 4 english majors , 6 biological sciences majors , and 5 engineers . in how many ways can 3 english majors , 3 biological science majors and 3 engineers selected from the given group ?", - "Output Program": [ - "import math\nn0 = 4.0\nn1 = 6.0\nn2 = 5.0\nn3 = 3.0\nn4 = 3.0\nn5 = 3.0\nt0 = math.factorial(min(15, int(n1)))\nt1 = math.factorial(min(15, int(n3)))\nt2 = math.factorial(min(15, int(n2)))\nt3 = t1 * t1\nt4 = t1 * 2.0\nt5 = t0 / t3\nt6 = t2 / t4\nanswer = t5 * t6\nprint(answer)" - ], - "Output Answer": [ - "200" - ], - "split": "train" - }, - { - "Input": "in a certain large company , the ratio of college graduates with a graduate degree to non - college graduates is 1 : 8 , and ratio of college graduates without a graduate degree to non - college graduates is 2 : 3 . if one picks a random college graduate at this large company , what is the probability e this college graduate has a graduate degree ?", - "Output Program": [ - "n0 = 1.0\nn1 = 8.0\nn2 = 2.0\nn3 = 3.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = t0 / t1\nt3 = t2 + 1.0\nanswer = t2 / t3\nprint(answer)" - ], - "Output Answer": [ - "0.15789473684210525" - ], - "split": "train" - }, - { - "Input": "a certain bag contains 100 balls \u00e2 \u20ac \u201d 50 white , 30 green , 8 yellow , 9 red , and 3 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?", - "Output Program": [ - "n0 = 100.0\nn1 = 50.0\nn2 = 30.0\nn3 = 8.0\nn4 = 9.0\nn5 = 3.0\nt0 = n4 + n5\nt1 = n0 - t0\nanswer = t1 / n0\nprint(answer)" - ], - "Output Answer": [ - "0.88" - ], - "split": "train" - }, - { - "Input": "if neha is 10 both sonali and priyanka is 15 both sadaf and tanu is 10 . how much is prinka by the same system ?", - "Output Program": [ - "n0 = 10.0\nn1 = 15.0\nn2 = 10.0\nt0 = n1 - n0\nanswer = t0 * 2.0\nprint(answer)" - ], - "Output Answer": [ - "10" - ], - "split": "train" - }, - { - "Input": "what number has a 5 : 1 ratio to the number 12 ?", - "Output Program": [ - "n0 = 5.0\nn1 = 1.0\nn2 = 12.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "60" - ], - "split": "train" - }, - { - "Input": "there are 10 slate rocks , 15 pumice rocks , and 6 granite rocks randomly distributed in a certain field . if 2 rocks are chosen at random and without replacement , what is the probability that both rocks will be slate rocks ?", - "Output Program": [ - "n0 = 10.0\nn1 = 15.0\nn2 = 6.0\nn3 = 2.0\nt0 = n0 + n1\nt1 = n0 - 1.0\nt2 = n2 + t0\nt3 = n0 / t2\nt4 = t2 - 1.0\nt5 = t1 / t4\nanswer = t3 * t5\nprint(answer)" - ], - "Output Answer": [ - "0.0967741935483871" - ], - "split": "train" - }, - { - "Input": "ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 42 years . what is deepak present age .", - "Output Program": [ - "n0 = 4.0\nn1 = 3.0\nn2 = 6.0\nn3 = 42.0\nt0 = n3 - n2\nt1 = n1 * t0\nanswer = t1 / n0\nprint(answer)" - ], - "Output Answer": [ - "27" - ], - "split": "train" - }, - { - "Input": "a bag contains 4 red , 5 blue and 3 green balls . if 3 ballsare picked at random , what is the probability that both are red ?", - "Output Program": [ - "import scipy\nn0 = 4.0\nn1 = 5.0\nn2 = 3.0\nn3 = 3.0\nt0 = n0 + n1\nt1 = scipy.special.comb(n0, n3)\nt2 = n2 + t0\nt3 = scipy.special.comb(t2, n3)\nanswer = t1 / t3\nprint(answer)" - ], - "Output Answer": [ - "0.01818181818181818" - ], - "split": "train" - }, - { - "Input": "at a meeting , 25 attendants used a pencil and 15 attendants used a pen . if exactly 20 attendants used only one of the two types of writing tools , how many attendants wrote with both types of writing tools ?", - "Output Program": [ - "n0 = 25.0\nn1 = 15.0\nn2 = 20.0\nt0 = n0 + n1\nt1 = t0 - n2\nanswer = t1 / 2.0\nprint(answer)" - ], - "Output Answer": [ - "10" - ], - "split": "train" - }, - { - "Input": "of the 200 stamps in a collection , 90 are foreign and 50 are more than 10 years old . if 20 stamps are both foreign and more than 10 years old , how many stamps are neither foreign nor more than 10 years old ?", - "Output Program": [ - "n0 = 200.0\nn1 = 90.0\nn2 = 50.0\nn3 = 10.0\nn4 = 20.0\nn5 = 10.0\nn6 = 10.0\nt0 = n1 + n2\nt1 = t0 - n4\nanswer = n0 - t1\nprint(answer)" - ], - "Output Answer": [ - "80" - ], - "split": "train" - }, - { - "Input": "how many positive integers between 5 and 5000 ( both are inclusive ) are there such that they are multiples of 5 ?", - "Output Program": [ - "n0 = 5.0\nn1 = 5000.0\nn2 = 5.0\nt0 = n1 - n0\nanswer = t0 / n2\nprint(answer)" - ], - "Output Answer": [ - "999" - ], - "split": "train" - }, - { - "Input": "in a certain pet shop , the ratio of dogs to cats to bunnies in stock is 3 : 5 : 9 . if the shop carries 204 dogs and bunnies total in stock , how many dogs are there ?", - "Output Program": [ - "n0 = 3.0\nn1 = 5.0\nn2 = 9.0\nn3 = 204.0\nt0 = n0 + n2\nt1 = n3 / t0\nanswer = n0 * t1\nprint(answer)" - ], - "Output Answer": [ - "51" - ], - "split": "train" - }, - { - "Input": "there are 9 executives , including the ceo and cfo , that are asked to form a small team of 4 members . however , the ceo and cfo may not both be assigned to the team . given this constraint , how many ways are there to form the team ?", - "Output Program": [ - "import math\nn0 = 9.0\nn1 = 4.0\nt0 = n1 * 3.0\nt1 = n0 - n1\nt2 = t0 + 3.0\nt3 = math.factorial(min(15, int(t1)))\nanswer = t3 - t2\nprint(answer)" - ], - "Output Answer": [ - "105" - ], - "split": "train" - }, - { - "Input": "if the numbers 1 to 100 are written on 100 pieces of paper , ( one on each ) and one piece is picked at random , then what is the probability that the number drawn is neither prime nor composite ?", - "Output Program": [ - "n0 = 1.0\nn1 = 100.0\nn2 = 100.0\n\nanswer = n0 / n1\nprint(answer)" - ], - "Output Answer": [ - "0.01" - ], - "split": "train" - }, - { - "Input": "what is the number of integers from 1 to 1000 ( inclusive ) that are divisible by neither 11 nor by 34 ?", - "Output Program": [ - "n0 = 1.0\nn1 = 1000.0\nn2 = 11.0\nn3 = 34.0\nt0 = n1 / n2\nt1 = n1 / n3\nt2 = n2 * n3\nt3 = t0 + t1\nt4 = n1 / t2\nt5 = t3 - t4\nanswer = n1 - t5\nprint(answer)" - ], - "Output Answer": [ - "882.3529411764706" - ], - "split": "train" - }, - { - "Input": "total num of pupiles in 3 grades of scholl is 333 . the no of pupiles in grades 1 and 2 are un 3 : 5 ratio and 2 and 3 grades are 7 : 11 ratio . what is the strength of class that has highest no of pupils", - "Output Program": [ - "n0 = 3.0\nn1 = 333.0\nn2 = 1.0\nn3 = 2.0\nn4 = 3.0\nn5 = 5.0\nn6 = 2.0\nn7 = 3.0\nn8 = 7.0\nn9 = 11.0\nt0 = n8 / n9\nt1 = n0 / n5\nt2 = t1 * t0\nt3 = t0 + t2\nt4 = t3 + 1.0\nanswer = n1 / t4\nprint(answer)" - ], - "Output Answer": [ - "165" - ], - "split": "train" - }, - { - "Input": "initially , the men and women in a room were in the ratio of 4 : 5 . then , 2 men entered the room and 3 women left the room . then , the number of women doubled . now there are 14 men in the room . how many d women are currently in the room ?", - "Output Program": [ - "n0 = 4.0\nn1 = 5.0\nn2 = 2.0\nn3 = 3.0\nn4 = 14.0\nt0 = n4 - n2\nt1 = n1 * t0\nt2 = t1 / n0\nt3 = t2 - n3\nanswer = n2 * t3\nprint(answer)" - ], - "Output Answer": [ - "24" - ], - "split": "train" - }, - { - "Input": "a girl scout was selling boxes of cookies . in a month , she sold both boxes of chocolate chip cookies ( $ 1.25 each ) and boxes of plain cookies ( $ 0.75 each ) . altogether , she sold 1,585 boxes for a combined value of $ 1 , 586.75 . how many boxes of plain cookies did she sell ?", - "Output Program": [ - "n0 = 1.25\nn1 = 0.75\nn2 = 1585.0\nn3 = 1.0\nn4 = 586.75\nt0 = n4 + 1000.0\nanswer = t0 / 2.0\nprint(answer)" - ], - "Output Answer": [ - "793.375" - ], - "split": "train" - }, - { - "Input": "110 people are attending a newspaper conference . 45 of them are writers and more than 38 are editors . of the people at the conference , x are both writers and editors and 2 x are neither . what is the largest possible number of people who are both writers and editors ?", - "Output Program": [ - "n0 = 110.0\nn1 = 45.0\nn2 = 38.0\nn3 = 2.0\nt0 = n2 + 1.0\nt1 = n1 + t0\nanswer = n0 - t1\nprint(answer)" - ], - "Output Answer": [ - "26" - ], - "split": "train" - }, - { - "Input": "one year ago , the ratio of roonie \u2019 s and ronaldo \u2019 s age was 6 : 7 respectively . 4 years hence , this ratio would become 7 : 8 . how old is ronaldo ?", - "Output Program": [ - "n0 = 6.0\nn1 = 7.0\nn2 = 4.0\nn3 = 7.0\nn4 = 8.0\nt0 = n2 + 1.0\nt1 = n1 * n1\nt2 = n0 * n4\nt3 = n4 * t0\nt4 = n1 * t0\nt5 = t1 - t2\nt6 = t3 - t4\nt7 = n1 * t6\nt8 = t7 / t5\nanswer = t8 + 1.0\nprint(answer)" - ], - "Output Answer": [ - "36" - ], - "split": "train" - }, - { - "Input": "6 ) a marketing firm determined that , of 180 households surveyed , 80 used neither brand a nor brand b soap . 60 used only brand a soap and for every household that used both brands of soap , 3 used only brand b soap . how many of the 200 household surveyed used both brands of soap ?", - "Output Program": [ - "n0 = 6.0\nn1 = 180.0\nn2 = 80.0\nn3 = 60.0\nn4 = 3.0\nn5 = 200.0\nt0 = n1 - n2\nt1 = t0 - n3\nanswer = t1 / 4.0\nprint(answer)" - ], - "Output Answer": [ - "10" - ], - "split": "train" - }, - { - "Input": "a pizzeria in castroville creates its own special blend of shredded cheese at a cost of $ 696.05 per kilogram . the blend includes mozzarella , at $ 504.35 per kilogram , and romano cheese , at $ 887.75 per kilogram . if the employees have already shredded 19 kilograms of mozzarella cheese , how many kilograms of romano cheese will they need to shred now ?", - "Output Program": [ - "n0 = 696.05\nn1 = 504.35\nn2 = 887.75\nn3 = 19.0\nt0 = n0 - n1\nt1 = n2 - n1\nt2 = t0 / t1\nt3 = 1.0 - t2\nt4 = t2 / t3\nanswer = n3 * t4\nprint(answer)" - ], - "Output Answer": [ - "18.999999999999986" - ], - "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 b 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": "ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 50 years . what is deepak present age", - "Output Program": [ - "n0 = 4.0\nn1 = 3.0\nn2 = 6.0\nn3 = 50.0\nt0 = n3 - n2\nt1 = n1 * t0\nanswer = t1 / n0\nprint(answer)" - ], - "Output Answer": [ - "33" - ], - "split": "train" - }, - { - "Input": "how many factors of 880 are odd numbers greater than 1 ?", - "Output Program": [ - "n0 = 880.0\nn1 = 1.0\nt0 = 10.0 * 2.0\nanswer = 60.0 / t0\nprint(answer)" - ], - "Output Answer": [ - "3" - ], - "split": "train" - }, - { - "Input": "in what ratio must tea at rs . 62 per kg be mixed with tea at rs . 72 per kg so that the mixture must be worth rs . 67 per kg ?", - "Output Program": [ - "n0 = 62.0\nn1 = 72.0\nn2 = 67.0\nt0 = n1 - n2\nt1 = n2 - n0\nanswer = t0 / t1\nprint(answer)" - ], - "Output Answer": [ - "1" - ], - "split": "train" - }, - { - "Input": "in a group of people , if 30 people were made to stand in each column , 16 columns could be formed . if 12 people were made to stand in a column , how many columns could be formed ?", - "Output Program": [ - "n0 = 30.0\nn1 = 16.0\nn2 = 12.0\nt0 = n2 / n1\nanswer = n0 / t0\nprint(answer)" - ], - "Output Answer": [ - "40" - ], - "split": "train" - }, - { - "Input": "log 3 n + log 5 n what is 3 digit number n that will be whole number", - "Output Program": [ - "n0 = 3.0\nn1 = 5.0\nn2 = 3.0\n\nanswer = n1**min(n0, 5)\nprint(answer)" - ], - "Output Answer": [ - "125" - ], - "split": "train" - }, - { - "Input": "at a garage sale , all of the items were sold at different prices . if the price of a radio sold at the garage sale was both the 18 th highest price and the 25 th lowest price among the prices of the items sold , how many items were sold at the garage sale ?", - "Output Program": [ - "n0 = 18.0\nn1 = 25.0\nt0 = n0 + n1\nanswer = t0 - 1.0\nprint(answer)" - ], - "Output Answer": [ - "42" - ], - "split": "train" - }, - { - "Input": "if x and y are both odd prime numbers and x < y , how many distinct positive integer t factors does 2 xy have ?", - "Output Program": [ - "n0 = 2.0\nt0 = 1.0 + 1.0\nt1 = n0 * t0\nanswer = t0 * t1\nprint(answer)" - ], - "Output Answer": [ - "8" - ], - "split": "train" - }, - { - "Input": "in a sports club with 27 members , 17 play badminton and 19 play tennis and 2 do not play either . how many members play both badminton and tennis ?", - "Output Program": [ - "n0 = 27.0\nn1 = 17.0\nn2 = 19.0\nn3 = 2.0\nt0 = n1 + n2\nt1 = n3 + t0\nanswer = t1 - n0\nprint(answer)" - ], - "Output Answer": [ - "11" - ], - "split": "train" - }, - { - "Input": "a certain bag contains 100 balls \u2014 50 white , 30 green , 10 yellow , 7 red , and 3 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?", - "Output Program": [ - "n0 = 100.0\nn1 = 50.0\nn2 = 30.0\nn3 = 10.0\nn4 = 7.0\nn5 = 3.0\nt0 = n1 + n2\nt1 = n3 + t0\nanswer = t1 / n0\nprint(answer)" - ], - "Output Answer": [ - "0.9" - ], - "split": "train" - }, - { - "Input": "bag a contains red , white and blue marbles such that the red to white marble ratio is 1 : 3 and the white to blue marble ratio is 2 : 3 . bag b contains red and white marbles in the ratio of 1 : 4 . together , the two bags contain 50 white marbles . how many red marbles could be in bag a ?", - "Output Program": [ - "n0 = 1.0\nn1 = 3.0\nn2 = 2.0\nn3 = 3.0\nn4 = 1.0\nn5 = 4.0\nn6 = 50.0\nt0 = n1 * n2\nt1 = n5 + t0\nanswer = n6 / t1\nprint(answer)" - ], - "Output Answer": [ - "5" - ], - "split": "train" - }, - { - "Input": "the number of stamps that kaye and alberto had were in the ration of 5 : 3 respectively . after kaye gave alberto 12 of her stamps , the ration of the number of kaye had to the number of alberto had was 8 : 6 . as a result of the gift , kaye had how many more stamps than alberto ?", - "Output Program": [ - "import scipy\nn0 = 5.0\nn1 = 3.0\nn2 = 12.0\nn3 = 8.0\nn4 = 6.0\nt0 = n0 + n1\nt1 = n3 + n4\nt2 = scipy.lcm(int(t0), int(t1))\nt3 = t2 / t1\nanswer = n3 * t3\nprint(answer)" - ], - "Output Answer": [ - "32" - ], - "split": "train" - }, - { - "Input": "at a garage sale , all of the items were sold at different prices . if the price of a radio sold at the garage sale was both the 14 th highest price and the 21 st lowest price among the prices of the items sold , how many items were sold at the garage sale ?", - "Output Program": [ - "n0 = 14.0\nn1 = 21.0\nt0 = n0 + n1\nanswer = t0 - 1.0\nprint(answer)" - ], - "Output Answer": [ - "34" - ], - "split": "train" - }, - { - "Input": "the cost of 3 pens and 5 pencils is rs . 260 . also the cost of one pen and one pencil is in the ratio of 5 : 1 respectively . what is the cost of one dozen pens ?", - "Output Program": [ - "n0 = 3.0\nn1 = 5.0\nn2 = 260.0\nn3 = 5.0\nn4 = 1.0\nt0 = n0 + n4\nt1 = 3.0 * 4.0\nt2 = n2 / t0\nanswer = t2 * t1\nprint(answer)" - ], - "Output Answer": [ - "780" - ], - "split": "train" - }, - { - "Input": "right now , the ratio between the ages of sandy and molly is 4 : 3 . after 6 years , sandy \u2019 s age will be 42 years . what is molly ' s age right now ?", - "Output Program": [ - "n0 = 4.0\nn1 = 3.0\nn2 = 6.0\nn3 = 42.0\nt0 = n3 - n2\nt1 = t0 / n0\nanswer = n1 * t1\nprint(answer)" - ], - "Output Answer": [ - "27" - ], - "split": "train" - }, - { - "Input": "tea worth rs . 126 per kg and rs . 135 per kg are mixed with a third variety of tea in the ratio 1 : 1 : 2 . if the mixture is worth rs . 153 per kg , what is the price of the third variety per kg ?", - "Output Program": [ - "n0 = 126.0\nn1 = 135.0\nn2 = 1.0\nn3 = 1.0\nn4 = 2.0\nn5 = 153.0\nt0 = n5 + 10.0\nt1 = 0.25 + 0.25\nt2 = t0 + 10.0\nt3 = n4 + t2\nanswer = t3 + t1\nprint(answer)" - ], - "Output Answer": [ - "175.5" - ], - "split": "train" - }, - { - "Input": "a shipment of 250 smartphones contains 84 that are defective . if a customer buys two smartphones at random from the shipment , what is the approximate probability that both phones are defective ? a . b . c . d . e .", - "Output Program": [ - "n0 = 250.0\nn1 = 84.0\nt0 = n0 + 1.0\nt1 = n1 / n0\nt2 = n1 - 1.0\nt3 = t2 / t0\nanswer = t1 * t3\nprint(answer)" - ], - "Output Answer": [ - "0.11110756972111555" - ], - "split": "train" - }, - { - "Input": "the ratio of numbers is 3 : 4 and their h . c . f is 4 . their l . c . m is ?", - "Output Program": [ - "import scipy\nn0 = 3.0\nn1 = 4.0\nn2 = 4.0\nt0 = n0 * n2\nt1 = n1 * n2\nanswer = scipy.lcm(int(t0), int(t1))\nprint(answer)" - ], - "Output Answer": [ - "48" - ], - "split": "train" - }, - { - "Input": "in a certain alphabet , 11 letters contain a dot and a straight line . 24 letters contain a straight line but do not contain a dot . if that alphabet has 40 letters , all of which contain either a dot or a straight line or both , how many letters contain a dot but do not contain a straight line ?", - "Output Program": [ - "n0 = 11.0\nn1 = 24.0\nn2 = 40.0\nt0 = n0 + n1\nanswer = n2 - t0\nprint(answer)" - ], - "Output Answer": [ - "5" - ], - "split": "train" - }, - { - "Input": "a certain car dealership sells economy cars , luxury cars , and sport utility vehicles . the ratio of economy to luxury cars is 3 : 2 . the ratio of economy cars to sport utility vehicles is 4 : 1 . what is the ratio of luxury cars to sport utility vehicles ?", - "Output Program": [ - "n0 = 3.0\nn1 = 2.0\nn2 = 4.0\nn3 = 1.0\nt0 = n3 * 4.0\nt1 = n3 * n3\nt2 = n1 * 4.0\nt3 = t0 / t1\nt4 = t0 / t2\nanswer = t3 / t4\nprint(answer)" - ], - "Output Answer": [ - "8" - ], - "split": "train" - }, - { - "Input": "income and expenditure of a person are in the ratio 5 : 4 . if the income of the person is rs . 18000 , then find his savings ?", - "Output Program": [ - "n0 = 5.0\nn1 = 4.0\nn2 = 18000.0\nt0 = n1 / n0\nt1 = n2 * t0\nanswer = n2 - t1\nprint(answer)" - ], - "Output Answer": [ - "3600" - ], - "split": "train" - }, - { - "Input": "at the faculty of aerospace engineering , 310 students study random - processing methods , 232 students study scramjet rocket engines and 112 students study them both . if every student in the faculty has to study one of the two subjects , how many students are there in the faculty of aerospace engineering ?", - "Output Program": [ - "n0 = 310.0\nn1 = 232.0\nn2 = 112.0\nt0 = n2 / 2.0\nt1 = n0 - t0\nt2 = n1 - t0\nanswer = t1 + t2\nprint(answer)" - ], - "Output Answer": [ - "430" - ], - "split": "train" - }, - { - "Input": "the l . c . m . of two numbers is 48 . the numbers are in the ratio 2 : 3 . then sum of the number is :", - "Output Program": [ - "n0 = 48.0\nn1 = 2.0\nn2 = 3.0\nt0 = n1 * n2\nt1 = n0 / t0\nt2 = n2 * t1\nt3 = n1 * t1\nanswer = t2 + t3\nprint(answer)" - ], - "Output Answer": [ - "40" - ], - "split": "train" - }, - { - "Input": "how many positive integers e between 200 and 300 ( both inclusive ) are not divisible by 2 , 3 or 5 ?", - "Output Program": [ - "import math\nn0 = 200.0\nn1 = 300.0\nn2 = 2.0\nn3 = 3.0\nn4 = 5.0\nt0 = n3 * n4\nt1 = n1 - n0\nt2 = t1 + 1.0\nt3 = n2 + t0\nt4 = t1 / n2\nt5 = t1 / n3\nt6 = t1 / n4\nt7 = t4 + 1.0\nt8 = t5 + 1.0\nt9 = t6 + 1.0\nt10 = t8 - t3\nt11 = t9 - t0\nt12 = math.floor(t10)\nt13 = t12 + 1.0\nt14 = t7 + t13\nt15 = t14 + t11\nanswer = t2 - t15\nprint(answer)" - ], - "Output Answer": [ - "26" - ], - "split": "train" - }, - { - "Input": "the hcf of two numbers is 23 and the other two factors of their lcm are 13 and 14 . what is the largest number ?", - "Output Program": [ - "n0 = 23.0\nn1 = 13.0\nn2 = 14.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "322" - ], - "split": "train" - }, - { - "Input": "the school soccer team looks at their record and finds that they win , lose , and tie games in a ratio of 4 : 3 : 1 . how many games did they play if they lost 9 games ?", - "Output Program": [ - "n0 = 4.0\nn1 = 3.0\nn2 = 1.0\nn3 = 9.0\nt0 = n0 + n1\nt1 = n3 / n1\nt2 = n2 + t0\nanswer = t2 * t1\nprint(answer)" - ], - "Output Answer": [ - "24" - ], - "split": "train" - }, - { - "Input": "at a garage sale , all of the items were sold at different prices . if the price of a radio sold at the garage sale was both the 15 th highest price and the 22 nd lowest price among the prices of the items sold , how many items were sold at the garage sale ?", - "Output Program": [ - "n0 = 15.0\nn1 = 22.0\nt0 = n0 + n1\nanswer = t0 - 1.0\nprint(answer)" - ], - "Output Answer": [ - "36" - ], - "split": "train" - }, - { - "Input": "of the people who responded to a market survey , 60 preferred brand x and the rest preferred brand y . if the respondents indicated a preference for brand x over brand y by ratio of 3 to 1 , how many people responded to the survey ?", - "Output Program": [ - "n0 = 60.0\nn1 = 3.0\nn2 = 1.0\nt0 = n0 / n1\nanswer = n0 + t0\nprint(answer)" - ], - "Output Answer": [ - "80" - ], - "split": "train" - }, - { - "Input": "what number has a 5 : 1 ratio to the number 13 ?", - "Output Program": [ - "n0 = 5.0\nn1 = 1.0\nn2 = 13.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "65" - ], - "split": "train" - }, - { - "Input": "ratio between rahul and deepak is 4 : 3 , after 2 years rahul age will be 26 years . what is deepak present age .", - "Output Program": [ - "n0 = 4.0\nn1 = 3.0\nn2 = 2.0\nn3 = 26.0\nt0 = n3 - n2\nt1 = n1 * t0\nanswer = t1 / n0\nprint(answer)" - ], - "Output Answer": [ - "18" - ], - "split": "train" - }, - { - "Input": "a farmer used 1,034 acres of land for beans , wheat , and corn in the ratio of 5 : 2 : 4 , respectively . how many acres q were used for corn ?", - "Output Program": [ - "n0 = 1034.0\nn1 = 5.0\nn2 = 2.0\nn3 = 4.0\nt0 = n1 + n2\nt1 = 10.0 * 3.0\nt2 = 1.0 * 1000.0\nt3 = n3 + t1\nt4 = n3 + t0\nt5 = t3 + t2\nt6 = t5 / t4\nanswer = n3 * t6\nprint(answer)" - ], - "Output Answer": [ - "376" - ], - "split": "train" - }, - { - "Input": "in a college , the ratio of the number of boys to girls is 8 : 5 . if there are 300 girls , the total number of students in the college is", - "Output Program": [ - "n0 = 8.0\nn1 = 5.0\nn2 = 300.0\nt0 = n2 / n1\nt1 = n0 * t0\nanswer = n2 + t1\nprint(answer)" - ], - "Output Answer": [ - "780" - ], - "split": "train" - }, - { - "Input": "in a club with 310 peopl , 138 play tennis , 255 play baseball , and 94 people play both sports . how many people do not pla a sport ?", - "Output Program": [ - "n0 = 310.0\nn1 = 138.0\nn2 = 255.0\nn3 = 94.0\nt0 = n0 - n1\nt1 = n2 - n3\nanswer = t0 - t1\nprint(answer)" - ], - "Output Answer": [ - "11" - ], - "split": "train" - }, - { - "Input": "at present the ratio between the ages of arun and deepak is 4 : 3 . after 6 years , arun ' s age will be 26 years . what is the age of deepak at present ?", - "Output Program": [ - "n0 = 4.0\nn1 = 3.0\nn2 = 6.0\nn3 = 26.0\nt0 = n3 - n2\nt1 = n1 * t0\nanswer = t1 / n0\nprint(answer)" - ], - "Output Answer": [ - "15" - ], - "split": "train" - }, - { - "Input": "a bag contains 5 green balls and 9 white balls . if two balls are drawn simultaneously , what is the probability that both balls are the same colour ?", - "Output Program": [ - "n0 = 5.0\nn1 = 9.0\nt0 = n0 + n1\nt1 = n1 - 1.0\nt2 = n0 - 1.0\nt3 = n1 / t0\nt4 = n0 / t0\nt5 = t0 - 1.0\nt6 = t1 / t5\nt7 = t2 / t5\nt8 = t3 * t6\nt9 = t7 * t4\nanswer = t8 + t9\nprint(answer)" - ], - "Output Answer": [ - "0.5054945054945056" - ], - "split": "train" - }, - { - "Input": "the sum of 3 numbers is 98 . if the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8 , then 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 + n2\nt1 = n0 * n5\nt2 = t1 / n4\nt3 = t0 + t2\nt4 = n1 / t3\nanswer = n0 * t4\nprint(answer)" - ], - "Output Answer": [ - "30" - ], - "split": "train" - }, - { - "Input": "24 oz of juice p and 25 oz of juice v are mixed to make smothies a and y . the ratio of p to v in smothie a is 4 is to 1 and that in y is 1 is to 5 . how many ounces of juice p are contained in the smothie a ?", - "Output Program": [ - "n0 = 24.0\nn1 = 25.0\nn2 = 4.0\nn3 = 1.0\nn4 = 1.0\nn5 = 5.0\nt0 = n3 / n2\nt1 = n0 * n5\nt2 = t1 - n1\nt3 = n5 - t0\nanswer = t2 / t3\nprint(answer)" - ], - "Output Answer": [ - "20" - ], - "split": "train" - }, - { - "Input": "a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 9 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many liter t of liquid a was contained by the can initially ?", - "Output Program": [ - "n0 = 7.0\nn1 = 5.0\nn2 = 9.0\nn3 = 7.0\nn4 = 9.0\nt0 = n0 + n2\nt1 = n0 + n1\nt2 = n0 * n2\nt3 = n0 * n1\nt4 = n1 / t1\nt5 = t2 - t3\nt6 = n2 * t4\nt7 = n2 - t6\nt8 = t0 * t7\nt9 = t8 / t5\nanswer = n0 * t9\nprint(answer)" - ], - "Output Answer": [ - "21" - ], - "split": "train" - }, - { - "Input": "on a certain farm the ratio of horses to cows is 4 : 1 . if the farm were to sell 15 horses and buy 15 cows , the ratio of horses to cows would then be 7 : 3 . after the transaction , how many more horses than cows would the farm own ?", - "Output Program": [ - "n0 = 4.0\nn1 = 1.0\nn2 = 15.0\nn3 = 15.0\nn4 = 7.0\nn5 = 3.0\nt0 = n2 * n4\nt1 = n2 * n5\nt2 = n0 * n5\nt3 = t0 + t1\nt4 = t2 - n4\nt5 = t3 / t4\nt6 = n2 + t5\nt7 = n0 * t5\nt8 = t7 - n2\nanswer = t8 - t6\nprint(answer)" - ], - "Output Answer": [ - "60" - ], - "split": "train" - }, - { - "Input": "a bag contains 6 red , 4 blue and 2 green balls . if 2 ballsare picked at random , what is the probability that both are red ?", - "Output Program": [ - "import scipy\nn0 = 6.0\nn1 = 4.0\nn2 = 2.0\nn3 = 2.0\nt0 = n0 + n1\nt1 = scipy.special.comb(n0, n3)\nt2 = n2 + t0\nt3 = scipy.special.comb(t2, n3)\nanswer = t1 / t3\nprint(answer)" - ], - "Output Answer": [ - "0.22727272727272727" - ], - "split": "train" - }, - { - "Input": "a jar contains a mixture of ab in the ratio 4 : 1 . when 30 l of mixture is replaced with liquid b , ratio becomes 2 : 3 . how many liters of liquid a was present in mixture initially .", - "Output Program": [ - "n0 = 4.0\nn1 = 1.0\nn2 = 30.0\nn3 = 2.0\nn4 = 3.0\nt0 = n0 + n1\nt1 = n4 * n3\nt2 = n3 * n3\nt3 = t1 + t2\nt4 = t1 - n1\nt5 = n2 / t4\nt6 = t3 * t5\nt7 = t6 / t0\nanswer = n0 * t7\nprint(answer)" - ], - "Output Answer": [ - "48" - ], - "split": "train" - }, - { - "Input": "in a graduating class of 232 students , 144 took geometry and 119 took biology . what is the difference between the greatest possible number w and the smallest possible number of students that could have taken both geometry and biology ?", - "Output Program": [ - "n0 = 232.0\nn1 = 144.0\nn2 = 119.0\nt0 = n1 + n2\nt1 = t0 - n0\nanswer = n2 - t1\nprint(answer)" - ], - "Output Answer": [ - "88" - ], - "split": "train" - }, - { - "Input": "in a ratio which is equal to 4 : 6 , if the antecedent is 30 , then the consequent is ?", - "Output Program": [ - "n0 = 4.0\nn1 = 6.0\nn2 = 30.0\nt0 = n2 / 2.0\nanswer = n2 + t0\nprint(answer)" - ], - "Output Answer": [ - "45" - ], - "split": "train" - }, - { - "Input": "3 years ago , the ratio of ages of p and q was 4 : 3 . 6 years from now , the ratio of their ages will be 7 : 6 . what is p ' s age at present ?", - "Output Program": [ - "n0 = 3.0\nn1 = 4.0\nn2 = 3.0\nn3 = 6.0\nn4 = 7.0\nn5 = 6.0\nt0 = n0 + n3\nt1 = n0 / n1\nt2 = n4 * t0\nt3 = n3 * t0\nt4 = n4 * t1\nt5 = t2 - t3\nt6 = n3 - t4\nt7 = t5 / t6\nanswer = n0 + t7\nprint(answer)" - ], - "Output Answer": [ - "15" - ], - "split": "train" - }, - { - "Input": "the ratio between the number of sheep and the number of horses at the stewart farm is 4 to 7 , if each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day , what is the number of sheep in the farm ?", - "Output Program": [ - "n0 = 4.0\nn1 = 7.0\nn2 = 230.0\nn3 = 12880.0\nt0 = 2.0 * 4.0\nt1 = 1000.0 * 12.0\nt2 = t0 * 10.0\nt3 = t0 * 100.0\nt4 = t2 + t3\nt5 = t4 + t1\nt6 = t5 / n2\nt7 = t6 / n1\nanswer = n0 * t7\nprint(answer)" - ], - "Output Answer": [ - "32" - ], - "split": "train" - }, - { - "Input": "the h . c . f . of two numbers is 10 and the other two factors of their l . c . m . are 11 and 15 . the larger of the two numbers is :", - "Output Program": [ - "n0 = 10.0\nn1 = 11.0\nn2 = 15.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "150" - ], - "split": "train" - }, - { - "Input": "compound x contains elements a and b at an approximate ratio , by weight , of 2 : 10 . approximately how many grams of element b are there in 300 grams of compound x ?", - "Output Program": [ - "n0 = 2.0\nn1 = 10.0\nn2 = 300.0\nt0 = n0 + n1\nt1 = n1 * n2\nanswer = t1 / t0\nprint(answer)" - ], - "Output Answer": [ - "250" - ], - "split": "train" - }, - { - "Input": "if log 102 = 0.3010 , what is the value of log 101600 ?", - "Output Program": [ - "import math\nn0 = 102.0\nn1 = 0.301\nn2 = 101600.0\nt0 = math.log(max(1e-5, 100.0), 2)\nt1 = math.log(max(1e-5, 10.0), 2)\nt2 = n1 * 4.0\nt3 = t0 / t1\nanswer = t3 + t2\nprint(answer)" - ], - "Output Answer": [ - "3.2039999999999997" - ], - "split": "train" - }, - { - "Input": "a starts business with rs . 4500 and after 7 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b \u00e2 \u20ac \u2122 s contribution in the capital ?", - "Output Program": [ - "n0 = 4500.0\nn1 = 7.0\nn2 = 2.0\nn3 = 3.0\nt0 = n0 * 12.0\nt1 = 12.0 - n1\nt2 = n3 * t0\nt3 = n2 * t1\nanswer = t2 / t3\nprint(answer)" - ], - "Output Answer": [ - "16200" - ], - "split": "train" - }, - { - "Input": "find the number of zero \u2019 s in 173 ! ( 173 factorial ) ?", - "Output Program": [ - "import math\nn0 = 173.0\nn1 = 173.0\nt0 = 1.0 + 4.0\nt1 = n0 / t0\nt2 = t0**min(2.0, 5)\nt3 = t0**min(3.0, 5)\nt4 = n0 / t2\nt5 = n0 / t3\nt6 = math.floor(t1)\nt7 = math.floor(t4)\nt8 = math.floor(t5)\nt9 = t6 + t7\nanswer = t9 + t8\nprint(answer)" - ], - "Output Answer": [ - "41" - ], - "split": "train" - }, - { - "Input": "janet invited her boy and girl friends to her party at the ratio of 3 : 7 . if 30 % of the boys and 70 % of the girls will be coming for the party from texas , how many janet invited friends will be coming from texas .", - "Output Program": [ - "n0 = 3.0\nn1 = 7.0\nn2 = 30.0\nn3 = 70.0\nt0 = n3 / 100.0\nt1 = n2 / 100.0\nt2 = n1 * t0\nt3 = n0 * t1\nt4 = t2 + t3\nanswer = t4 * 10.0\nprint(answer)" - ], - "Output Answer": [ - "57.999999999999986" - ], - "split": "train" - }, - { - "Input": "a polling company found that , of 300 households surveyed , 120 spent at least $ 100 per month on both gasoline and electricity , 60 spent at least $ 100 per month on gasoline but not on electricity , and for every household that did not spend at least $ 100 per month on gasoline or electricity , 4 spent at least $ 100 per month on electricity but not on gasoline . how many of the 300 households did not spend at least $ 100 per month on either gasoline or electricity ?", - "Output Program": [ - "n0 = 300.0\nn1 = 120.0\nn2 = 100.0\nn3 = 60.0\nn4 = 100.0\nn5 = 100.0\nn6 = 4.0\nn7 = 100.0\nn8 = 300.0\nn9 = 100.0\nt0 = n1 + n3\nt1 = n6 + 1.0\nt2 = n0 - t0\nanswer = t2 / t1\nprint(answer)" - ], - "Output Answer": [ - "24" - ], - "split": "train" - }, - { - "Input": "the price of rice is reduced by 2 % . how many kilograms of rice can now be bought for the money which was sufficient to buy 49 kg of rice earlier ?", - "Output Program": [ - "n0 = 2.0\nn1 = 49.0\nt0 = n1 * 100.0\nt1 = 100.0 - 2.0\nanswer = t0 / t1\nprint(answer)" - ], - "Output Answer": [ - "50" - ], - "split": "train" - }, - { - "Input": "what is the number of integers from 1 to 1000 ( inclusive ) that are divisible by neither 15 nor by 20 ?", - "Output Program": [ - "n0 = 1.0\nn1 = 1000.0\nn2 = 15.0\nn3 = 20.0\nt0 = n1 / n2\nt1 = n1 / n3\nt2 = n2 * n3\nt3 = t0 + t1\nt4 = n1 / t2\nt5 = t3 - t4\nanswer = n1 - t5\nprint(answer)" - ], - "Output Answer": [ - "886.6666666666666" - ], - "split": "train" - }, - { - "Input": "mrs . evans gave a test to her freshmen economics class , which has 25 students enrolled and 22 of them answered question 1 correctly . if 20 answered question 2 correctly and 3 did not take the test then how many answered both questions correctly ?", - "Output Program": [ - "n0 = 25.0\nn1 = 22.0\nn2 = 1.0\nn3 = 20.0\nn4 = 2.0\nn5 = 3.0\nt0 = n1 + n3\nt1 = n5 + t0\nanswer = t1 - n0\nprint(answer)" - ], - "Output Answer": [ - "20" - ], - "split": "train" - }, - { - "Input": "in two alloys , copper and tin are related in the ratios of 4 : 1 and 1 : 3 . 10 kg of ist alloy , 16 kg of 2 nd alloy and some pure copper melted together . an alloy obtained in which the ratio of copper and tin was 3 : 2 . find the weight of the new alloy .", - "Output Program": [ - "n0 = 4.0\nn1 = 1.0\nn2 = 1.0\nn3 = 3.0\nn4 = 10.0\nn5 = 16.0\nn6 = 2.0\nn7 = 3.0\nn8 = 2.0\nt0 = n4 + n5\nt1 = n0 + n1\nt2 = n3 / n0\nt3 = n4 / t1\nt4 = n5 * t2\nt5 = t3 + t4\nt6 = n3 * t5\nt7 = t6 / n6\nt8 = t7 - t4\nanswer = t0 + t8\nprint(answer)" - ], - "Output Answer": [ - "35" - ], - "split": "train" - }, - { - "Input": "find the highest common factor of 36 and 84 .", - "Output Program": [ - "import scipy\nn0 = 36.0\nn1 = 84.0\n\nanswer = scipy.gcd(int(n0), int(n1))\nprint(answer)" - ], - "Output Answer": [ - "12" - ], - "split": "train" - }, - { - "Input": "in a class , 9 students like to play basketball and 8 like to play cricket . 6 students like to play on both basketball and cricket . how many students like to play basketball or cricket or both ?", - "Output Program": [ - "n0 = 9.0\nn1 = 8.0\nn2 = 6.0\nt0 = n0 + n1\nanswer = t0 - n2\nprint(answer)" - ], - "Output Answer": [ - "11" - ], - "split": "train" - }, - { - "Input": "two numbers are in the ratio of 3 : 8 . if 24 be subtracted from each , they are in the ratio of 4 : 9 . find the numbers ?", - "Output Program": [ - "n0 = 3.0\nn1 = 8.0\nn2 = 24.0\nn3 = 4.0\nn4 = 9.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "72" - ], - "split": "train" - }, - { - "Input": "in a group of people , if 30 people were made to stand in each column , 16 columns could be formed . if 60 people were made to stand in a column , how many columns could be formed ?", - "Output Program": [ - "n0 = 30.0\nn1 = 16.0\nn2 = 60.0\nt0 = n2 / n1\nanswer = n0 / t0\nprint(answer)" - ], - "Output Answer": [ - "8" - ], - "split": "train" - }, - { - "Input": "a small island country of 5000 people has an emigration and immigration statistic per 500 persons of 50.4 and 15.4 respectively . how long will it take for the population to be half of its current number .", - "Output Program": [ - "n0 = 5000.0\nn1 = 500.0\nn2 = 50.4\nn3 = 15.4\nt0 = n0 / 2.0\nt1 = n0 / n1\nt2 = n2 - n3\nt3 = t1 * t2\nanswer = t0 / t3\nprint(answer)" - ], - "Output Answer": [ - "7.142857142857143" - ], - "split": "train" - }, - { - "Input": "the h . c . f . of two numbers is 30 and the other two factors of their l . c . m . are 10 and 15 . the larger of the two numbers is :", - "Output Program": [ - "n0 = 30.0\nn1 = 10.0\nn2 = 15.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "450" - ], - "split": "train" - }, - { - "Input": "if 35 % of the 840 students at a certain college are enrolled in biology classes , how many students at the college are not enrolled in a biology class ?", - "Output Program": [ - "n0 = 35.0\nn1 = 840.0\nt0 = n1 / 100.0\nt1 = 100.0 - n0\nanswer = t0 * t1\nprint(answer)" - ], - "Output Answer": [ - "546" - ], - "split": "train" - }, - { - "Input": "of the diplomats who attended a summit conference : 20 spoke french , 32 did not speak hindi and 20 % of the diplomats spoke neither french nor hindi . if 10 % of the diplomats spoke both french and hindi , then how many diplomats attended the conference ?", - "Output Program": [ - "n0 = 20.0\nn1 = 32.0\nn2 = 20.0\nn3 = 10.0\nt0 = n3 / 100.0\nt1 = n1 - n0\nanswer = t1 / t0\nprint(answer)" - ], - "Output Answer": [ - "120" - ], - "split": "train" - }, - { - "Input": "if below equation are true 24 $ 6 = 64 35 $ 5 = 87 63 $ 7 = 99 by using same logic what is the value of the below question 88 $ 8 = ?", - "Output Program": [ - "n0 = 24.0\nn1 = 6.0\nn2 = 64.0\nn3 = 35.0\nn4 = 5.0\nn5 = 87.0\nn6 = 63.0\nn7 = 7.0\nn8 = 99.0\nn9 = 88.0\nn10 = 8.0\nt0 = n10 + n10\nt1 = n9 / n10\nt2 = t0 * 100.0\nanswer = t1 + t2\nprint(answer)" - ], - "Output Answer": [ - "1611" - ], - "split": "train" - }, - { - "Input": "in a certain kindergarten , half of the children are allergic to peanuts , 10 children are not allergic to cashew nuts , 10 children are allergic to both peanuts and cashew nuts , and 18 children are allergic to cashew nuts . how many of the kindergarten ' s children are not allergic to peanuts and are not allergic to cashew nuts ?", - "Output Program": [ - "n0 = 10.0\nn1 = 10.0\nn2 = 18.0\nt0 = n0 + n2\nt1 = t0 / 2.0\nt2 = n2 + t1\nt3 = t2 - n0\nanswer = t0 - t3\nprint(answer)" - ], - "Output Answer": [ - "6" - ], - "split": "train" - }, - { - "Input": "if 63 percent of a class answered the first question on a certain test correctly , 49 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?", - "Output Program": [ - "n0 = 63.0\nn1 = 49.0\nn2 = 20.0\nt0 = n0 + n1\nt1 = n2 + t0\nanswer = t1 - 100.0\nprint(answer)" - ], - "Output Answer": [ - "32" - ], - "split": "train" - }, - { - "Input": "at present the ratio between the ages of arun and deepak is 2 : 3 . after 5 years , arun ' s age will be 25 years . what is the age of deepak at present ?", - "Output Program": [ - "n0 = 2.0\nn1 = 3.0\nn2 = 5.0\nn3 = 25.0\nt0 = n3 - n2\nt1 = n1 * t0\nanswer = t1 / n0\nprint(answer)" - ], - "Output Answer": [ - "30" - ], - "split": "train" - }, - { - "Input": "ratio between rahul and deepak is 4 : 3 , after 4 years rahul age will be 32 years . what is deepak present age .", - "Output Program": [ - "n0 = 4.0\nn1 = 3.0\nn2 = 4.0\nn3 = 32.0\nt0 = n3 - n2\nt1 = n1 * t0\nanswer = t1 / n0\nprint(answer)" - ], - "Output Answer": [ - "21" - ], - "split": "train" - }, - { - "Input": "in what ratio should a variety of rice costing rs . 4.5 per kg be mixed with another variety of rice costing rs . 8.75 per kg to obtain a mixture costing rs . 7.50 per kg ?", - "Output Program": [ - "n0 = 4.5\nn1 = 8.75\nn2 = 7.5\nt0 = n1 - n2\nt1 = n1 - n0\nt2 = t0 / t1\nt3 = 1.0 - t2\nanswer = t2 / t3\nprint(answer)" - ], - "Output Answer": [ - "0.41666666666666674" - ], - "split": "train" - }, - { - "Input": "the ratio of buses to cars on river road is 1 to 17 . if there are 80 fewer buses than cars on river road , how many cars are on river road ?", - "Output Program": [ - "n0 = 1.0\nn1 = 17.0\nn2 = 80.0\nt0 = n1 - n0\nt1 = n2 / t0\nanswer = n1 * t1\nprint(answer)" - ], - "Output Answer": [ - "85" - ], - "split": "train" - }, - { - "Input": "two brother x and y appeared for an exam . let a be the event that x is selected and b is the event that y is selected . the probability of a is 17 and that of b is 29 . find the probability that both of them are selected .", - "Output Program": [ - "n0 = 17.0\nn1 = 29.0\nt0 = n0 % 10.0\nt1 = n1 % 10.0\nt2 = 1.0 / t0\nt3 = 2.0 / t1\nanswer = t2 * t3\nprint(answer)" - ], - "Output Answer": [ - "0.031746031746031744" - ], - "split": "train" - }, - { - "Input": "sandy is younger than molly by 12 years . if the ratio of their ages is 7 : 9 , how old is sandy ?", - "Output Program": [ - "n0 = 12.0\nn1 = 7.0\nn2 = 9.0\nt0 = n2 - n1\nt1 = n1 / t0\nanswer = n0 * t1\nprint(answer)" - ], - "Output Answer": [ - "42" - ], - "split": "train" - }, - { - "Input": "if three numbers in the ratio 3 : 2 : 5 be such that the sum of their squares is 1862 , the middle number will be", - "Output Program": [ - "import math\nn0 = 3.0\nn1 = 2.0\nn2 = 5.0\nn3 = 1862.0\nt0 = n0 * n0\nt1 = n1 * n1\nt2 = n2 * n2\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n3 / t4\nt6 = math.sqrt(max(0, t5))\nanswer = n1 * t6\nprint(answer)" - ], - "Output Answer": [ - "14" - ], - "split": "train" - }, - { - "Input": "what is the greatest value of x such that 4 ^ x is a factor of 21 ! ?", - "Output Program": [ - "n0 = 4.0\nn1 = 21.0\nt0 = n1 - 1.0\nt1 = t0 / n0\nanswer = t1 + 1.0\nprint(answer)" - ], - "Output Answer": [ - "6" - ], - "split": "train" - }, - { - "Input": "what number has a 150 : 1 ratio to the number 2 ?", - "Output Program": [ - "n0 = 150.0\nn1 = 1.0\nn2 = 2.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "300" - ], - "split": "train" - }, - { - "Input": "if 73 ! has 16 zeroes at the end , how many zeroes will 80 ! have at the end ?", - "Output Program": [ - "n0 = 73.0\nn1 = 16.0\nn2 = 80.0\nt0 = 10.0 / 2.0\nt1 = n2 / t0\nanswer = t1 + 3.0\nprint(answer)" - ], - "Output Answer": [ - "19" - ], - "split": "train" - }, - { - "Input": "doughnuts , cookies and muffins in a pastry shop are in the ratio of 5 : 3 : 1 . if there are 50 doughnuts , the number of muffins in the shop is : .", - "Output Program": [ - "n0 = 5.0\nn1 = 3.0\nn2 = 1.0\nn3 = 50.0\n\nanswer = n3 / n0\nprint(answer)" - ], - "Output Answer": [ - "10" - ], - "split": "train" - }, - { - "Input": "if the ratio of a to b is 5 to 3 and the ratio of b to c is 1 to 5 , what is the ratio of a to c ?", - "Output Program": [ - "n0 = 5.0\nn1 = 3.0\nn2 = 1.0\nn3 = 5.0\nt0 = n0 * n2\nt1 = n1 * n3\nanswer = t0 / t1\nprint(answer)" - ], - "Output Answer": [ - "0.3333333333333333" - ], - "split": "train" - }, - { - "Input": "the fisherman sale , all of the prices of the fishes sold were different . if the price of a radio sold at the fisherman sale was both the 4 th highest price and the 13 th lowest price among the prices of the fishes sold , how many fishes were sold at the fisherman sale ?", - "Output Program": [ - "n0 = 4.0\nn1 = 13.0\nt0 = n0 + n1\nanswer = t0 - 1.0\nprint(answer)" - ], - "Output Answer": [ - "16" - ], - "split": "train" - }, - { - "Input": "the l . c . m . of two numbers is 42 . the numbers are in the ratio 2 : 3 . then sum of the number is :", - "Output Program": [ - "n0 = 42.0\nn1 = 2.0\nn2 = 3.0\nt0 = n1 * n2\nt1 = n0 / t0\nt2 = n2 * t1\nt3 = n1 * t1\nanswer = t2 + t3\nprint(answer)" - ], - "Output Answer": [ - "35" - ], - "split": "train" - }, - { - "Input": "the h . c . f . of two numbers is 32 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is :", - "Output Program": [ - "n0 = 32.0\nn1 = 13.0\nn2 = 14.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "448" - ], - "split": "train" - }, - { - "Input": "the monthly incomes of a and b are in the ratio 5 : 2 . b ' s monthly income is 12 % more than c ' s monthly income . if c ' s monthly income is rs . 15000 , then find the annual income of a ?", - "Output Program": [ - "n0 = 5.0\nn1 = 2.0\nn2 = 12.0\nn3 = 15000.0\nt0 = n0 / n1\nt1 = n2 / 100.0\nt2 = t1 + 1.0\nt3 = n3 * t2\nt4 = t0 * t3\nanswer = n2 * t4\nprint(answer)" - ], - "Output Answer": [ - "504000" - ], - "split": "train" - }, - { - "Input": "of the people who responded to a market survey , 200 preferred brand x and the rest preferred brand y . if the respondents indicated a preference for brand x over brand y by ratio of 4 to 1 , how many people responded to the survey ?", - "Output Program": [ - "n0 = 200.0\nn1 = 4.0\nn2 = 1.0\nt0 = n0 / n1\nanswer = n0 + t0\nprint(answer)" - ], - "Output Answer": [ - "250" - ], - "split": "train" - }, - { - "Input": "a student committee on academic integrity has 30 ways to select a president and vice president from a group of candidates . the same person can not be both president and vice president . how many candidates are there ?", - "Output Program": [ - "import math\nn0 = 30.0\nt0 = n0 * 4.0\nt1 = -1.0\nt2 = t1**min(2.0, 5)\nt3 = t0 + t2\nt4 = math.sqrt(max(0, t3))\nt5 = t4 + 1.0\nanswer = t5 / 2.0\nprint(answer)" - ], - "Output Answer": [ - "6" - ], - "split": "train" - }, - { - "Input": "a bag contains 4 red , 3 blue and 2 green balls . if 2 ballsare picked at random , what is the probability that both are red ?", - "Output Program": [ - "import scipy\nn0 = 4.0\nn1 = 3.0\nn2 = 2.0\nn3 = 2.0\nt0 = n0 + n1\nt1 = scipy.special.comb(n0, n3)\nt2 = n2 + t0\nt3 = scipy.special.comb(t2, n3)\nanswer = t1 / t3\nprint(answer)" - ], - "Output Answer": [ - "0.16666666666666666" - ], - "split": "train" - }, - { - "Input": "there are two positive numbers in the ratio 7 : 11 . if the larger number exceeds the smaller by 16 , then find the smaller number ?", - "Output Program": [ - "n0 = 7.0\nn1 = 11.0\nn2 = 16.0\nt0 = n0 * n2\nanswer = t0 / 4.0\nprint(answer)" - ], - "Output Answer": [ - "28" - ], - "split": "train" - }, - { - "Input": "in a group of 100 cars , 37 cars do not have air conditioning . if at least 41 cars have racing stripes , what is the greatest number of cars that could have air conditioning but not racing stripes ?", - "Output Program": [ - "n0 = 100.0\nn1 = 37.0\nn2 = 41.0\n\nanswer = n0 - n2\nprint(answer)" - ], - "Output Answer": [ - "59" - ], - "split": "train" - }, - { - "Input": "in a college the ratio of the numbers of boys to the girls is 8 : 5 . if there are 135 girls , the total number of students in the college is ?", - "Output Program": [ - "n0 = 8.0\nn1 = 5.0\nn2 = 135.0\nt0 = n0 / n1\nt1 = n2 * t0\nanswer = n2 + t1\nprint(answer)" - ], - "Output Answer": [ - "351" - ], - "split": "train" - }, - { - "Input": "in a class , 30 % of the students speaks truth , 20 % speaks lie and 10 % speaks both . if a student is selected at random , what is the probability that he has speak truth or lie ?", - "Output Program": [ - "n0 = 30.0\nn1 = 20.0\nn2 = 10.0\nt0 = 5.0 * 5.0\nt1 = t0 * 4.0\nt2 = n0 / t1\nt3 = n1 / t1\nt4 = n2 / t1\nt5 = t2 + t3\nt6 = t5 + t4\nanswer = 1.0 - t6\nprint(answer)" - ], - "Output Answer": [ - "0.4" - ], - "split": "train" - }, - { - "Input": "100 students appeared in 2 tests . 60 students passed 1 st test . 40 students passed in the 2 nd test . 20 students passed in both 1 and 2 tests . what is the probability of the students who failed in both tests ?", - "Output Program": [ - "n0 = 100.0\nn1 = 2.0\nn2 = 60.0\nn3 = 1.0\nn4 = 40.0\nn5 = 2.0\nn6 = 20.0\nn7 = 1.0\nn8 = 2.0\nt0 = n2 + n4\nt1 = t0 - n6\nanswer = 100.0 - t1\nprint(answer)" - ], - "Output Answer": [ - "20" - ], - "split": "train" - }, - { - "Input": "the ratio of 3 numbers is 5 : 1 : 4 and their sum is 1000 . the last number of the 3 numbers is ?", - "Output Program": [ - "n0 = 3.0\nn1 = 5.0\nn2 = 1.0\nn3 = 4.0\nn4 = 1000.0\nn5 = 3.0\nt0 = n1 / n3\nt1 = n2 / n3\nt2 = t0 + t1\nt3 = n2 + t2\nanswer = n4 / t3\nprint(answer)" - ], - "Output Answer": [ - "400" - ], - "split": "train" - }, - { - "Input": "a certain telephone company offers two plans , a and b . under plan a , the company charges a total of $ 0.60 for the first 6 minutes of each call and $ 0.06 per minute thereafter . under plan b , the company charges $ 0.08 per minute of each call . what is the duration of a call , in minutes , for which the company charges the same amount under plan a and under plan b ?", - "Output Program": [ - "n0 = 0.6\nn1 = 6.0\nn2 = 0.06\nn3 = 0.08\nt0 = n1 * n2\nt1 = n3 - n2\nt2 = n0 - t0\nanswer = t2 / t1\nprint(answer)" - ], - "Output Answer": [ - "11.999999999999996" - ], - "split": "train" - }, - { - "Input": "the flowerman sale , all of the prices of the flowers sold were different . if the price of a radio sold at the flowerman sale was both the 17 th highest price and the 42 th lowest price among the prices of the slowers sold , how many flowers were sold at the flowerman sale ?", - "Output Program": [ - "n0 = 17.0\nn1 = 42.0\nt0 = n0 + n1\nanswer = t0 - 1.0\nprint(answer)" - ], - "Output Answer": [ - "58" - ], - "split": "train" - }, - { - "Input": "the monthly incomes of a and b are in the ratio 5 : 2 . b ' s monthly income is 12 % more than c ' s monthly income . if c ' s monthly income is rs . 14000 , then find the annual income of a ?", - "Output Program": [ - "n0 = 5.0\nn1 = 2.0\nn2 = 12.0\nn3 = 14000.0\nt0 = n0 / n1\nt1 = n2 / 100.0\nt2 = t1 + 1.0\nt3 = n3 * t2\nt4 = t0 * t3\nanswer = n2 * t4\nprint(answer)" - ], - "Output Answer": [ - "470400.0000000001" - ], - "split": "train" - }, - { - "Input": "uba capital recently bought brand new vehicles for office use . uba capital only went for toyota and honda and bought more of toyota than honda at the ratio of 6 : 4 . if 60 % of the toyota bought and 40 % of the honda bought were suv \u00e3 \u00a2 \u00e2 \u201a \u00ac \u00e2 \u201e \u00a2 s . how many suv \u00e3 \u00a2 \u00e2 \u201a \u00ac \u00e2 \u201e \u00a2 s did uba capital buy in the aforementioned purchase ?", - "Output Program": [ - "n0 = 6.0\nn1 = 4.0\nn2 = 60.0\nn3 = 40.0\nt0 = n0 * n1\nt1 = t0 + t0\nanswer = 100.0 - t1\nprint(answer)" - ], - "Output Answer": [ - "52" - ], - "split": "train" - }, - { - "Input": "at present the ratio between the ages of arun and deepak is 2 : 5 . after 10 years arun ' s age will be 30 years . what is the age of the deepak ?", - "Output Program": [ - "n0 = 2.0\nn1 = 5.0\nn2 = 10.0\nn3 = 30.0\nt0 = n3 - n2\nt1 = n1 * t0\nanswer = t1 / n0\nprint(answer)" - ], - "Output Answer": [ - "50" - ], - "split": "train" - }, - { - "Input": "on multiplying a numberz by 153 , the result obtained was 102325 . however , it is found that both the 2 ' s are wrong . find the correct result .", - "Output Program": [ - "n0 = 153.0\nn1 = 102325.0\nn2 = 2.0\nt0 = 3.0 * 4.0\nt1 = 100.0 * 4.0\nt2 = t0 + 3.0\nt3 = t1 + t1\nt4 = t3 - 100.0\nt5 = t2 + t4\nanswer = n0 * t5\nprint(answer)" - ], - "Output Answer": [ - "109395" - ], - "split": "train" - }, - { - "Input": "the l . c . m . of two numbers is 54 . the numbers are in the ratio 2 : 3 . then sum of the number is :", - "Output Program": [ - "n0 = 54.0\nn1 = 2.0\nn2 = 3.0\nt0 = n1 * n2\nt1 = n0 / t0\nt2 = n2 * t1\nt3 = n1 * t1\nanswer = t2 + t3\nprint(answer)" - ], - "Output Answer": [ - "45" - ], - "split": "train" - }, - { - "Input": "divide $ 2000 among b , c in the ratio 4 : 16 . how many $ that c get ?", - "Output Program": [ - "n0 = 2000.0\nn1 = 4.0\nn2 = 16.0\nt0 = n1 + n2\nt1 = n2 / t0\nanswer = n0 * t1\nprint(answer)" - ], - "Output Answer": [ - "1600" - ], - "split": "train" - }, - { - "Input": "the ratio of two numbers is 3 : 4 and their sum is 21 . the greater of the two numbers is ?", - "Output Program": [ - "n0 = 3.0\nn1 = 4.0\nn2 = 21.0\nt0 = n0 + n1\nt1 = n0 * n2\nt2 = t1 / t0\nanswer = n2 - t2\nprint(answer)" - ], - "Output Answer": [ - "12" - ], - "split": "train" - }, - { - "Input": "the ratio by weight , measured in pounds , of books to clothes to electronics in a suitcase initially stands at 5 : 4 : 2 . someone removes 7 pounds of clothing from the suitcase , thereby doubling the ratio of books to clothes . how many pounds do the electronics in the suitcase weigh ?", - "Output Program": [ - "n0 = 5.0\nn1 = 4.0\nn2 = 2.0\nn3 = 7.0\nt0 = n0 + n1\nt1 = n2 + t0\nt2 = n3 * t1\nt3 = t1 * 2.0\nt4 = n1 * t1\nt5 = -t2\nt6 = t3 - t4\nt7 = t5 / t6\nanswer = n2 * t7\nprint(answer)" - ], - "Output Answer": [ - "7" - ], - "split": "train" - }, - { - "Input": "share rs . 4200 among john , jose & binoy in the ration 2 : 4 : 6 . find the amount received by john ?", - "Output Program": [ - "n0 = 4200.0\nn1 = 2.0\nn2 = 4.0\nn3 = 6.0\nt0 = n0 / n1\nt1 = n0 / n3\nanswer = t0 - t1\nprint(answer)" - ], - "Output Answer": [ - "1400" - ], - "split": "train" - }, - { - "Input": "in a group of people , if 30 people were made to stand in each column , 16 columns could be formed . if 40 people were made to stand in a column , how many columns could be formed ?", - "Output Program": [ - "n0 = 30.0\nn1 = 16.0\nn2 = 40.0\nt0 = n2 / n1\nanswer = n0 / t0\nprint(answer)" - ], - "Output Answer": [ - "12" - ], - "split": "train" - }, - { - "Input": "the monthly incomes of a and b are in the ratio 5 : 2 . b ' s monthly income is 12 % more than c ' s monthly income . if c ' s monthly income is rs . 12000 , then find the annual income of a ?", - "Output Program": [ - "n0 = 5.0\nn1 = 2.0\nn2 = 12.0\nn3 = 12000.0\nt0 = n0 / n1\nt1 = n2 / 100.0\nt2 = t1 + 1.0\nt3 = n3 * t2\nt4 = t0 * t3\nanswer = n2 * t4\nprint(answer)" - ], - "Output Answer": [ - "403200.0000000001" - ], - "split": "train" - }, - { - "Input": "pants , shorts and shirts in a dresser are in the ratio of 7 : 7 : 10 . if there are 14 pants , the number of shirts in the dresser is :", - "Output Program": [ - "n0 = 7.0\nn1 = 7.0\nn2 = 10.0\nn3 = 14.0\nt0 = n2 * n3\nanswer = t0 / n0\nprint(answer)" - ], - "Output Answer": [ - "20" - ], - "split": "train" - }, - { - "Input": "in a certain animal shelter , the ratio of the number of catsto the number of dogs is 15 to 7 . if 12 additional dogs were to be taken in by the shelter , the ratio of the number of cats to the number of dogs would be 15 to 11 . how many cats are in the shelter ?", - "Output Program": [ - "n0 = 15.0\nn1 = 7.0\nn2 = 12.0\nn3 = 15.0\nn4 = 11.0\nt0 = n4 - n1\nt1 = n2 / t0\nanswer = n0 * t1\nprint(answer)" - ], - "Output Answer": [ - "45" - ], - "split": "train" - }, - { - "Input": "of the 65 house in a development , 50 have a two - car garage , 40 have an in - the - ground swimming pool , and 35 have both a two - car garage and an in - the - ground swimming pool . how many houses in the development have neither a two - car garage nor an in - the - ground swimming pool ?", - "Output Program": [ - "n0 = 65.0\nn1 = 50.0\nn2 = 40.0\nn3 = 35.0\nt0 = n1 - n3\nt1 = n2 - n3\nt2 = t0 + t1\nt3 = n3 + t2\nanswer = n0 - t3\nprint(answer)" - ], - "Output Answer": [ - "10" - ], - "split": "train" - }, - { - "Input": "the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is :", - "Output Program": [ - "n0 = 23.0\nn1 = 13.0\nn2 = 14.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "322" - ], - "split": "train" - }, - { - "Input": "in a group of people , if 30 people were made to stand in each column , 16 columns could be formed . if 32 people were made to stand in a column , how many columns could be formed ?", - "Output Program": [ - "n0 = 30.0\nn1 = 16.0\nn2 = 32.0\nt0 = n2 / n1\nanswer = n0 / t0\nprint(answer)" - ], - "Output Answer": [ - "15" - ], - "split": "train" - }, - { - "Input": "ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 26 years . what is deepak present age ?", - "Output Program": [ - "n0 = 4.0\nn1 = 3.0\nn2 = 6.0\nn3 = 26.0\nt0 = n3 - n2\nt1 = n1 * t0\nanswer = t1 / n0\nprint(answer)" - ], - "Output Answer": [ - "15" - ], - "split": "train" - }, - { - "Input": "divide $ 600 among a , b in the ratio 1 : 2 . how many $ that a get ?", - "Output Program": [ - "n0 = 600.0\nn1 = 1.0\nn2 = 2.0\n\nanswer = n0 / n1\nprint(answer)" - ], - "Output Answer": [ - "600" - ], - "split": "train" - }, - { - "Input": "in a certain state , the ratio of registered republicans to registered democrats is 3 to 2 , and every registered voter is either a republican or a democrat . if 75 percent of the republicans and 15 percent of the democrats are expected to vote for candidate x , and everyone else is expected to vote for candidate y , by what percent is candidate x expected to win the election ?", - "Output Program": [ - "n0 = 3.0\nn1 = 2.0\nn2 = 75.0\nn3 = 15.0\nt0 = n0 + n1\nt1 = n3 / 100.0\nt2 = n2 / 100.0\nt3 = n1 * t1\nt4 = n0 * t2\nt5 = t3 + t4\nt6 = n0 - t4\nt7 = n1 - t3\nt8 = t6 + t7\nt9 = t5 - t8\nt10 = t9 / t0\nanswer = t10 * 100.0\nprint(answer)" - ], - "Output Answer": [ - "1.9999999999999927" - ], - "split": "train" - }, - { - "Input": "in a zoo , the ratio of the number of cheetahs to the number of pandas is 1 : 3 and was the same 5 years ago . if the increase in the number of cheetahs in the zoo since then is 2 , then what is the increase in the number of pandas ?", - "Output Program": [ - "import scipy\nn0 = 1.0\nn1 = 3.0\nn2 = 5.0\nn3 = 2.0\nt0 = scipy.lcm(int(n0), int(n1))\nanswer = n3 * t0\nprint(answer)" - ], - "Output Answer": [ - "6" - ], - "split": "train" - }, - { - "Input": "ratio and proportion 215 : 474 : : 537 : ?", - "Output Program": [ - "n0 = 215.0\nn1 = 474.0\nn2 = 537.0\nt0 = 2.0 + 4.0\nt1 = 10.0 + 10.0\nanswer = t0 + t1\nprint(answer)" - ], - "Output Answer": [ - "26" - ], - "split": "train" - }, - { - "Input": "in what ratio mental a at rs . 68 per kg be mixed with another metal at rs . 96 per kg so that cost of alloy ( mixture ) is rs . 72 per kg ?", - "Output Program": [ - "n0 = 68.0\nn1 = 96.0\nn2 = 72.0\nt0 = n1 - n2\nt1 = n1 - n0\nt2 = t0 / t1\nt3 = 1.0 - t2\nanswer = t2 / t3\nprint(answer)" - ], - "Output Answer": [ - "5.999999999999997" - ], - "split": "train" - }, - { - "Input": "two vessels contains equal number of mixtures milk and water in the ratio 4 : 1 and 7 : 3 . both the mixtures are now mixed thoroughly . find the ratio of milk to water in the new mixture so obtained ?", - "Output Program": [ - "n0 = 4.0\nn1 = 1.0\nn2 = 7.0\nn3 = 3.0\nt0 = n2 + n3\nt1 = n0 + n1\nt2 = t0 / t1\nt3 = n0 * t2\nt4 = n1 * t2\nt5 = n2 + t3\nt6 = n3 + t4\nanswer = t5 / t6\nprint(answer)" - ], - "Output Answer": [ - "3" - ], - "split": "train" - }, - { - "Input": "jaya ranks 5 th in a class of 53 . what is her rank from the bottom in the class ?", - "Output Program": [ - "n0 = 5.0\nn1 = 53.0\nt0 = n1 - n0\nanswer = t0 + 1.0\nprint(answer)" - ], - "Output Answer": [ - "49" - ], - "split": "train" - }, - { - "Input": "of the 70 house in a development , 50 have a two - car garage , 40 have an in - the - ground swimming pool , and 35 have both a two - car garage and an in - the - ground swimming pool . how many houses in the development have neither a two - car garage nor an in - the - ground swimming pool ?", - "Output Program": [ - "n0 = 70.0\nn1 = 50.0\nn2 = 40.0\nn3 = 35.0\nt0 = n1 - n3\nt1 = n2 - n3\nt2 = t0 + t1\nt3 = n3 + t2\nanswer = n0 - t3\nprint(answer)" - ], - "Output Answer": [ - "15" - ], - "split": "train" - }, - { - "Input": "a person want to give his money of $ 3600 to his 3 children a , b , c in the ratio 2 : 3 : 4 . what is the b ' s share ?", - "Output Program": [ - "n0 = 3600.0\nn1 = 3.0\nn2 = 2.0\nn3 = 3.0\nn4 = 4.0\nt0 = n1 + n2\nt1 = n4 + t0\nt2 = n1 / t1\nanswer = n0 * t2\nprint(answer)" - ], - "Output Answer": [ - "1200" - ], - "split": "train" - }, - { - "Input": "at present the ratio between the ages of arun and deepak is 5 : 7 . after 6 years , arun ' s age will be 36 years . what is the age of deepak at present ?", - "Output Program": [ - "n0 = 5.0\nn1 = 7.0\nn2 = 6.0\nn3 = 36.0\nt0 = n3 - n2\nt1 = n1 * t0\nanswer = t1 / n0\nprint(answer)" - ], - "Output Answer": [ - "42" - ], - "split": "train" - }, - { - "Input": "a farmer used 1,034 acres of land for beans , wheat , and corn in the ratio of 5 : 2 : 4 , respectively . how many w acres were used for corn ?", - "Output Program": [ - "n0 = 1034.0\nn1 = 5.0\nn2 = 2.0\nn3 = 4.0\nt0 = n1 + n2\nt1 = 10.0 * 3.0\nt2 = 1.0 * 1000.0\nt3 = n3 + t1\nt4 = n3 + t0\nt5 = t3 + t2\nt6 = t5 / t4\nanswer = n3 * t6\nprint(answer)" - ], - "Output Answer": [ - "376" - ], - "split": "train" - }, - { - "Input": "a began business with rs . 36000 and was joined afterwards by b with rs . 54000 . when did b join if the profits at the end of the year were divided in the ratio of 2 : 1 ?", - "Output Program": [ - "n0 = 36000.0\nn1 = 54000.0\nn2 = 2.0\nn3 = 1.0\nt0 = 3.0 * 4.0\nt1 = n0 * t0\nt2 = t1 / n1\nt3 = t2 / n2\nanswer = t0 - t3\nprint(answer)" - ], - "Output Answer": [ - "8" - ], - "split": "train" - }, - { - "Input": "sachin is younger than rahul by 7 years . if the ratio of their ages is 6 : 9 , find the age of sachin", - "Output Program": [ - "n0 = 7.0\nn1 = 6.0\nn2 = 9.0\nt0 = n2 - n1\nt1 = n0 / t0\nanswer = n1 * t1\nprint(answer)" - ], - "Output Answer": [ - "14" - ], - "split": "train" - }, - { - "Input": "the probability of two events a and b are 0.25 and 0.35 respectively . the probability that both a and b occur is 0.15 . the probability that neither a nor b occur is _________", - "Output Program": [ - "n0 = 0.25\nn1 = 0.35\nn2 = 0.15\nt0 = n0 + n1\nt1 = t0 - n2\nanswer = 1.0 - t1\nprint(answer)" - ], - "Output Answer": [ - "0.55" - ], - "split": "train" - }, - { - "Input": "if the numbers 1 to 99 are written on 99 pieces of paper , ( one on each ) and one piece is picked at random , then what is the probability that the number drawn is neither prime nor composite ?", - "Output Program": [ - "n0 = 1.0\nn1 = 99.0\nn2 = 99.0\n\nanswer = n0 / n1\nprint(answer)" - ], - "Output Answer": [ - "0.010101010101010102" - ], - "split": "train" - }, - { - "Input": "the value of ( log 9 27 + log 8 32 ) is :", - "Output Program": [ - "import math\nn0 = 9.0\nn1 = 27.0\nn2 = 8.0\nn3 = 32.0\nt0 = math.log(max(1e-5, n3), 2)\nt1 = math.log(max(1e-5, n2), 2)\nanswer = t0 / t1\nprint(answer)" - ], - "Output Answer": [ - "1.6666666666666667" - ], - "split": "train" - }, - { - "Input": "the ratio of boarders to day scholars at a school is 7 to 16 . however , after a few new students join the initial 560 boarders , the ratio changed to 1 to 2 , respectively . if no boarders became day scholars and vice versa , and no students left the school , how many boarders joined the school ?", - "Output Program": [ - "n0 = 7.0\nn1 = 16.0\nn2 = 560.0\nn3 = 1.0\nn4 = 2.0\nt0 = n3 + n4\nt1 = n2 / n0\nt2 = n4 / t0\nt3 = n1 * t1\nt4 = n2 + t3\nt5 = t3 / t2\nanswer = t5 - t4\nprint(answer)" - ], - "Output Answer": [ - "80" - ], - "split": "train" - }, - { - "Input": "the ratio of numbers is 3 : 4 and their h . c . f is 8 . their l . c . m is :", - "Output Program": [ - "import scipy\nn0 = 3.0\nn1 = 4.0\nn2 = 8.0\nt0 = n0 * n2\nt1 = n1 * n2\nanswer = scipy.lcm(int(t0), int(t1))\nprint(answer)" - ], - "Output Answer": [ - "96" - ], - "split": "train" - }, - { - "Input": "6 ) a marketing firm determined that , of 300 households surveyed , 80 used neither brand a nor brand b soap . 60 used only brand a soap and for every household that used both brands of soap , 3 used only brand b soap . how many of the 200 household surveyed used both brands of soap ?", - "Output Program": [ - "n0 = 6.0\nn1 = 300.0\nn2 = 80.0\nn3 = 60.0\nn4 = 3.0\nn5 = 200.0\nt0 = n1 - n2\nt1 = t0 - n3\nanswer = t1 / 4.0\nprint(answer)" - ], - "Output Answer": [ - "40" - ], - "split": "train" - }, - { - "Input": "what number has a 5 : 1 ratio to the number 11 ?", - "Output Program": [ - "n0 = 5.0\nn1 = 1.0\nn2 = 11.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "55" - ], - "split": "train" - }, - { - "Input": "in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the sport formulation contains 5 ounces of corn syrup , how many ounces of water does it contain ?", - "Output Program": [ - "n0 = 1.0\nn1 = 12.0\nn2 = 30.0\nn3 = 5.0\nt0 = n0 / n1\nt1 = n0 / n2\nt2 = t1 / 2.0\nt3 = t0 * 3.0\nt4 = t3 / t2\nanswer = n3 * t4\nprint(answer)" - ], - "Output Answer": [ - "75" - ], - "split": "train" - }, - { - "Input": "find the fraction which has the same ratio to 1 / 13 that 5 / 34 has to 7 / 48 .", - "Output Program": [ - "n0 = 1.0\nn1 = 13.0\nn2 = 5.0\nn3 = 34.0\nn4 = 7.0\nn5 = 48.0\nt0 = n2 / n3\nt1 = n4 / n5\nt2 = n0 / n1\nt3 = t0 / t1\nanswer = t3 * t2\nprint(answer)" - ], - "Output Answer": [ - "0.07756948933419522" - ], - "split": "train" - }, - { - "Input": "the least whole number which when subtracted from both the terms of the ratio 6 : 7 to give a ra \u0275 o less than 16 : 21 , is", - "Output Program": [ - "import math\nn0 = 6.0\nn1 = 7.0\nn2 = 16.0\nn3 = 21.0\nt0 = n0 * n3\nt1 = n1 * n2\nt2 = n3 - n2\nt3 = t0 - t1\nt4 = t3 / t2\nt5 = math.floor(t4)\nanswer = t5 + 1.0\nprint(answer)" - ], - "Output Answer": [ - "3" - ], - "split": "train" - }, - { - "Input": "the ratio by weight , measured in pounds , of books to clothes to electronics in a suitcase initially stands at 7 : 4 : 3 . someone removes 8 pounds of clothing from the suitcase , thereby doubling the ratio of books to clothes . how many pounds do the electronics in the suitcase weigh ?", - "Output Program": [ - "n0 = 7.0\nn1 = 4.0\nn2 = 3.0\nn3 = 8.0\nt0 = n0 + n1\nt1 = n2 + t0\nt2 = n3 * t1\nt3 = t1 * 2.0\nt4 = n1 * t1\nt5 = -t2\nt6 = t3 - t4\nt7 = t5 / t6\nanswer = n2 * t7\nprint(answer)" - ], - "Output Answer": [ - "12" - ], - "split": "train" - }, - { - "Input": "a dog breeder currently has 9 breeding dogs . 6 of the dogs have exactly 1 littermate , and 3 of the dogs have exactly 2 littermates . if 2 dogs are selected at random , what is the probability q that both selected dogs are not littermates ?", - "Output Program": [ - "n0 = 9.0\nn1 = 6.0\nn2 = 1.0\nn3 = 3.0\nn4 = 2.0\nn5 = 2.0\n\nanswer = 5.0 / n1\nprint(answer)" - ], - "Output Answer": [ - "0.8333333333333334" - ], - "split": "train" - }, - { - "Input": "210 college students were asked in a survey if they preferred windows or mac brand computers . 60 students claimed that they preferred mac to windows brand computers . one third as many of the students who preferred mac to windows , equally preferred both brands . 90 of the students had no preference . how many of the students in the survey preferred windows to mac brand computers ?", - "Output Program": [ - "n0 = 210.0\nn1 = 60.0\nn2 = 90.0\nt0 = n0 - n2\nt1 = t0 - n1\nt2 = t1 / 3.0\nanswer = t1 - t2\nprint(answer)" - ], - "Output Answer": [ - "40" - ], - "split": "train" - }, - { - "Input": "a certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 7 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?", - "Output Program": [ - "n0 = 1.0\nn1 = 7.0\nn2 = 2.0\nn3 = 7.0\nn4 = 2.0\nn5 = 3.0\nn6 = 3.0\nt0 = n3 * n5\nanswer = n1 * t0\nprint(answer)" - ], - "Output Answer": [ - "147" - ], - "split": "train" - }, - { - "Input": "two vessels having volumes in the ratio 3 : 5 are filled with water and milk solutions . the ratio of milk and water in the two vessels are 1 : 2 and 6 : 4 respectively . if the contents of both the vessel are empties into a larger vessel , find the ratio of milk and water in the larger vessel .", - "Output Program": [ - "n0 = 3.0\nn1 = 5.0\nn2 = 1.0\nn3 = 2.0\nn4 = 6.0\nn5 = 4.0\n\nanswer = n2**min(n0, 5)\nprint(answer)" - ], - "Output Answer": [ - "1" - ], - "split": "train" - }, - { - "Input": "how many positive integers w between 200 and 300 ( both inclusive ) are not divisible by 2 , 3 or 5 ?", - "Output Program": [ - "import math\nn0 = 200.0\nn1 = 300.0\nn2 = 2.0\nn3 = 3.0\nn4 = 5.0\nt0 = n3 * n4\nt1 = n1 - n0\nt2 = t1 + 1.0\nt3 = n2 + t0\nt4 = t1 / n2\nt5 = t1 / n3\nt6 = t1 / n4\nt7 = t4 + 1.0\nt8 = t5 + 1.0\nt9 = t6 + 1.0\nt10 = t8 - t3\nt11 = t9 - t0\nt12 = math.floor(t10)\nt13 = t12 + 1.0\nt14 = t7 + t13\nt15 = t14 + t11\nanswer = t2 - t15\nprint(answer)" - ], - "Output Answer": [ - "26" - ], - "split": "train" - }, - { - "Input": "a person want to give his money of $ 4500 to his 3 children a , b , c in the ratio 2 : 3 : 4 . what is the b ' s share ?", - "Output Program": [ - "n0 = 4500.0\nn1 = 3.0\nn2 = 2.0\nn3 = 3.0\nn4 = 4.0\nt0 = n1 + n2\nt1 = n4 + t0\nt2 = n1 / t1\nanswer = n0 * t2\nprint(answer)" - ], - "Output Answer": [ - "1500" - ], - "split": "train" - }, - { - "Input": "7 machines at a certain factory operate at the same constant rate . if 6 of these machines , operating simultaneously , take 42 hours to fill a certain production order , how many fewer hours does it take all 7 machines , operating simultaneously , to fill the same production order ?", - "Output Program": [ - "n0 = 7.0\nn1 = 6.0\nn2 = 42.0\nn3 = 7.0\nt0 = n1 * n2\nt1 = t0 / n0\nanswer = n2 - t1\nprint(answer)" - ], - "Output Answer": [ - "6" - ], - "split": "train" - }, - { - "Input": "uba capital recently bought brand new vehicles for office use . uba capital only went for toyota and honda and bought more of toyota than honda at the ratio of 4 : 6 . if 40 % of the toyota bought and 60 % of the honda bought were suv \u00e3 \u00a2 \u00e2 \u201a \u00ac \u00e2 \u201e \u00a2 s . how many suv \u00e3 \u00a2 \u00e2 \u201a \u00ac \u00e2 \u201e \u00a2 s did uba capital buy in the aforementioned purchase ?", - "Output Program": [ - "n0 = 4.0\nn1 = 6.0\nn2 = 40.0\nn3 = 60.0\nt0 = n0 * n1\nt1 = t0 + t0\nanswer = 100.0 - t1\nprint(answer)" - ], - "Output Answer": [ - "52" - ], - "split": "train" - }, - { - "Input": "in the year 1990 there are 5000 men 3000 women 2000 boys . in 1994 men are increased by 20 % women are increased by ratio of boys and women ?", - "Output Program": [ - "n0 = 1990.0\nn1 = 5000.0\nn2 = 3000.0\nn3 = 2000.0\nn4 = 1994.0\nn5 = 20.0\nt0 = n5 / 100.0\nt1 = n3 / n2\nt2 = t0 + 1.0\nt3 = t1 + 1.0\nt4 = n1 * t2\nt5 = n2 * t3\nt6 = t4 + t5\nanswer = n3 + t6\nprint(answer)" - ], - "Output Answer": [ - "13000" - ], - "split": "train" - }, - { - "Input": "apple costs l rupees per kilogram for first 30 kgs and q rupees per kilogram for each additional kilogram . if the price of 33 kilograms is 360 and for 36 kgs of apples is 420 then the cost of first 25 kgs of apples is", - "Output Program": [ - "n0 = 30.0\nn1 = 33.0\nn2 = 360.0\nn3 = 36.0\nn4 = 420.0\nn5 = 25.0\nt0 = n4 - n2\nt1 = n3 - n1\nt2 = n1 - n0\nt3 = t0 / t1\nt4 = t3 * t2\nt5 = n2 - t4\nt6 = t5 / n0\nanswer = n5 * t6\nprint(answer)" - ], - "Output Answer": [ - "250" - ], - "split": "train" - }, - { - "Input": "initially , the men and women in a room were in the ratio of 4 : 5 . then , 2 men entered the room and 3 women left the room . then , the number of women doubled . now there are 14 men in the room . how many e women are currently in the room ?", - "Output Program": [ - "n0 = 4.0\nn1 = 5.0\nn2 = 2.0\nn3 = 3.0\nn4 = 14.0\nt0 = n4 - n2\nt1 = n1 * t0\nt2 = t1 / n0\nt3 = t2 - n3\nanswer = n2 * t3\nprint(answer)" - ], - "Output Answer": [ - "24" - ], - "split": "train" - }, - { - "Input": "in a neighborhood having 90 households , 11 did not have either a car or a bike . if 16 households had a both a car and a bike and 44 had a car , how many had bike only ?", - "Output Program": [ - "n0 = 90.0\nn1 = 11.0\nn2 = 16.0\nn3 = 44.0\nt0 = n0 - n1\nt1 = n2 + t0\nt2 = t1 - n3\nanswer = t2 - n2\nprint(answer)" - ], - "Output Answer": [ - "35" - ], - "split": "train" - }, - { - "Input": "at garage sale , all of the prices of the items sold were different . if the price of a radio sold at the garage sale was both the 15 th highest price and the 25 th lowest price among the prices of the items sold , how many items were sold at the garage sale ?", - "Output Program": [ - "n0 = 15.0\nn1 = 25.0\nt0 = n0 + n1\nanswer = t0 - 1.0\nprint(answer)" - ], - "Output Answer": [ - "39" - ], - "split": "train" - }, - { - "Input": "10 different biology books and 8 different chemistry books lie on a shelf . in how many ways can a student pick 2 books of each type ?", - "Output Program": [ - "import math\nn0 = 10.0\nn1 = 8.0\nn2 = 2.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(n1)))\nt2 = n0 - n2\nt3 = n1 - n2\nt4 = math.factorial(min(15, int(t2)))\nt5 = math.factorial(min(15, int(t3)))\nt6 = t0 / t4\nt7 = t1 / t5\nt8 = t6 / n2\nt9 = t7 / n2\nanswer = t8 * t9\nprint(answer)" - ], - "Output Answer": [ - "1260" - ], - "split": "train" - }, - { - "Input": "if the ratio of two number is 2 : 3 and lcm of the number is 120 then what is the number .", - "Output Program": [ - "n0 = 2.0\nn1 = 3.0\nn2 = 120.0\nt0 = n0 * n1\nanswer = n2 / t0\nprint(answer)" - ], - "Output Answer": [ - "20" - ], - "split": "train" - }, - { - "Input": "a marketing firm determined that , of 200 households surveyed , 80 used neither brand r nor brand b soap , 60 used only brand r soap , and for every household that used both brands of soap , 3 used only brand b soap . how many of the 200 households surveyed used both brands of soap ?", - "Output Program": [ - "n0 = 200.0\nn1 = 80.0\nn2 = 60.0\nn3 = 3.0\nn4 = 200.0\nt0 = n1 + n2\nt1 = n3 + 1.0\nt2 = n0 - t0\nt3 = t2 / t1\nt4 = t3 + t3\nanswer = t4 + 10.0\nprint(answer)" - ], - "Output Answer": [ - "40" - ], - "split": "train" - }, - { - "Input": "a certain bag contains 60 balls \u2014 22 white , 18 green , 2 yellow , 15 red , and 3 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?", - "Output Program": [ - "n0 = 60.0\nn1 = 22.0\nn2 = 18.0\nn3 = 2.0\nn4 = 15.0\nn5 = 3.0\nt0 = n1 + n2\nt1 = n3 + t0\nanswer = t1 / n0\nprint(answer)" - ], - "Output Answer": [ - "0.7" - ], - "split": "train" - }, - { - "Input": "if x and y are sets of integers , x # y denotes the set of integers that belong to set x or set y , but not both . if x consists of 14 integers , y consists of 18 integers , and 6 of the integers are in both x and y , then x # y consists of how many integers ?", - "Output Program": [ - "n0 = 14.0\nn1 = 18.0\nn2 = 6.0\nt0 = n1 - n2\nt1 = n0 - n2\nanswer = t0 + t1\nprint(answer)" - ], - "Output Answer": [ - "20" - ], - "split": "train" - }, - { - "Input": "a person want to give his money of $ 2700 to his 3 children a , b , c in the ratio 2 : 3 : 4 . what is the b ' s share ?", - "Output Program": [ - "n0 = 2700.0\nn1 = 3.0\nn2 = 2.0\nn3 = 3.0\nn4 = 4.0\nt0 = n1 + n2\nt1 = n4 + t0\nt2 = n1 / t1\nanswer = n0 * t2\nprint(answer)" - ], - "Output Answer": [ - "900" - ], - "split": "train" - }, - { - "Input": "the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 18 . the larger of the two numbers is :", - "Output Program": [ - "n0 = 23.0\nn1 = 13.0\nn2 = 18.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "414" - ], - "split": "train" - }, - { - "Input": "the value of log 2 ( log 5625 ) is", - "Output Program": [ - "import math\nn0 = 2.0\nn1 = 5625.0\nt0 = 1.0 + 4.0\nt1 = math.log(max(1e-5, t0), 2)\nt2 = t0 * 1000.0\nt3 = n1 - t2\nt4 = math.log(max(1e-5, t3), 2)\nt5 = t4 / t1\nanswer = math.log(max(1e-5, t5), 2)\nprint(answer)" - ], - "Output Answer": [ - "2" - ], - "split": "train" - }, - { - "Input": "the ratio of the number of females to males at a party was 1 : 2 but when 7 females and 7 males left , the ratio became 1 : 3 . how many people were at the party originally ?", - "Output Program": [ - "n0 = 1.0\nn1 = 2.0\nn2 = 7.0\nn3 = 7.0\nn4 = 1.0\nn5 = 3.0\nt0 = n1 * n2\nt1 = n5 * t0\nt2 = t1 - t0\nt3 = t2 / 2.0\nanswer = t3 + t2\nprint(answer)" - ], - "Output Answer": [ - "42" - ], - "split": "dev" - }, - { - "Input": "the price of precious stone is directly proportional to square of its weight . what will be the loss incurred if a stone weighing 28 gm and costing 28,000 breaks into two pieces whose weights are in the ratio 15 : 13 ?", - "Output Program": [ - "n0 = 28.0\nn1 = 28000.0\nn2 = 15.0\nn3 = 13.0\nt0 = 10.0 * 100.0\nt1 = n0 * n0\nt2 = n3 * n3\nt3 = n2 * n2\nt4 = n0 * t0\nt5 = t4 / t1\nt6 = t5 * t2\nt7 = t5 * t3\nt8 = t6 + t7\nanswer = t4 - t8\nprint(answer)" - ], - "Output Answer": [ - "13928.571428571428" - ], - "split": "dev" - }, - { - "Input": "in a sports club with 80 members , 48 play badminton and 46 play tennis and 7 do not play either . how many members play both badminton and tennis ?", - "Output Program": [ - "n0 = 80.0\nn1 = 48.0\nn2 = 46.0\nn3 = 7.0\nt0 = n1 + n2\nt1 = n3 + t0\nanswer = t1 - n0\nprint(answer)" - ], - "Output Answer": [ - "21" - ], - "split": "dev" - }, - { - "Input": "if the ratio of the sum of the first 6 terms of a g . p . to the sum of the first 3 terms of the g . p . is 343 , what is the common ratio of the g . p ?", - "Output Program": [ - "n0 = 6.0\nn1 = 3.0\nn2 = 343.0\nt0 = 1.0 / n1\nt1 = n2 - 1.0\nanswer = t1**min(t0, 5)\nprint(answer)" - ], - "Output Answer": [ - "6.993190657180867" - ], - "split": "dev" - }, - { - "Input": "in the class of 40 students , 30 speak hindi and 20 speak english . what is the lowest possible number of students who speak both the languages ?", - "Output Program": [ - "n0 = 40.0\nn1 = 30.0\nn2 = 20.0\nt0 = n1 + n2\nanswer = t0 - n0\nprint(answer)" - ], - "Output Answer": [ - "10" - ], - "split": "dev" - }, - { - "Input": "a class consists of 15 biology students and 10 chemistry students . if you pick two students at the same time , what ' s the probability that one is maths and one is chemistry ?", - "Output Program": [ - "n0 = 15.0\nn1 = 10.0\nt0 = n0 + n1\nt1 = n0 / t0\nt2 = n1 / t0\nt3 = t0 - 1.0\nt4 = n1 / t3\nt5 = n0 / t3\nt6 = t1 * t4\nt7 = t5 * t2\nanswer = t6 + t7\nprint(answer)" - ], - "Output Answer": [ - "0.5" - ], - "split": "dev" - }, - { - "Input": "in a class , 5 people like baseball and football , 2 people only like baseball , 3 people only like football , and 6 people like neither . how many people are in the class ?", - "Output Program": [ - "n0 = 5.0\nn1 = 2.0\nn2 = 3.0\nn3 = 6.0\nt0 = n0 + n1\nt1 = n2 + t0\nanswer = n3 + t1\nprint(answer)" - ], - "Output Answer": [ - "16" - ], - "split": "dev" - }, - { - "Input": "share rs . 6600 among john , jose & binoy in the ration 2 : 4 : 6 . find the amount received by john ?", - "Output Program": [ - "n0 = 6600.0\nn1 = 2.0\nn2 = 4.0\nn3 = 6.0\nt0 = n0 / n1\nt1 = n0 / n3\nanswer = t0 - t1\nprint(answer)" - ], - "Output Answer": [ - "2200" - ], - "split": "dev" - }, - { - "Input": "the h . c . f of two numbers is 23 and the other two factors of their l . c . m are 13 and 14 . the larger of the two numbers is :", - "Output Program": [ - "n0 = 23.0\nn1 = 13.0\nn2 = 14.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "322" - ], - "split": "dev" - }, - { - "Input": "there are 280 doctors and nurses at a hospital . if the ratio of doctors to nurses is 5 to 9 , how many nurses are at the hospital ?", - "Output Program": [ - "n0 = 280.0\nn1 = 5.0\nn2 = 9.0\nt0 = n1 + n2\nt1 = n0 / t0\nanswer = n2 * t1\nprint(answer)" - ], - "Output Answer": [ - "180" - ], - "split": "dev" - }, - { - "Input": "in what ratio must tea at rs . 62 per kg be mixed with tea at rs . 72 per kg so that the mixture must be worth rs . 64.50 per kg ?", - "Output Program": [ - "n0 = 62.0\nn1 = 72.0\nn2 = 64.5\nt0 = n1 - n2\nt1 = n2 - n0\nanswer = t0 / t1\nprint(answer)" - ], - "Output Answer": [ - "3" - ], - "split": "dev" - }, - { - "Input": "if p and q are both odd prime numbers andp < q , then how many different positive integer factors does 2 pqhave ?", - "Output Program": [ - "n0 = 2.0\n\nanswer = n0**min(3.0, 5)\nprint(answer)" - ], - "Output Answer": [ - "8" - ], - "split": "dev" - }, - { - "Input": "a starts a business with $ 3500 . after 5 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . b ' s contribution in the capital is", - "Output Program": [ - "n0 = 3500.0\nn1 = 5.0\nn2 = 2.0\nn3 = 3.0\nt0 = n0 * 12.0\nt1 = 12.0 - n1\nt2 = n3 * t0\nt3 = t2 / n2\nanswer = t3 / t1\nprint(answer)" - ], - "Output Answer": [ - "9000" - ], - "split": "dev" - }, - { - "Input": "a bag contains 21 toys numbered 1 to 21 . a toy is drawn and then another toy is drawn without replacement . find the probability that both toys will show even numbers .", - "Output Program": [ - "import math\nn0 = 21.0\nn1 = 1.0\nn2 = 21.0\nt0 = n0 / 2.0\nt1 = n0 - 1.0\nt2 = math.floor(t0)\nt3 = t2 / n0\nt4 = t2 - 1.0\nt5 = t4 / t1\nanswer = t5 * t3\nprint(answer)" - ], - "Output Answer": [ - "0.21428571428571427" - ], - "split": "dev" - }, - { - "Input": "a number is said to be prime saturated if the product of all the different positive prime factors of z is less than the square root of z . what is the greatest two digit prime saturated integer ?", - "Output Program": [ - "t0 = 2.0 * 3.0\nt1 = 100.0 - 10.0\nanswer = t0 + t1\nprint(answer)" - ], - "Output Answer": [ - "96" - ], - "split": "dev" - }, - { - "Input": "1 blue dice and 2 red dice are thrown . . . . what is the probability that the no . appeared on blue dice is always greater than both the no . appeared on the 2 red dice . .", - "Output Program": [ - "n0 = 1.0\nn1 = 2.0\nn2 = 2.0\nt0 = 2.0 + 3.0\nt1 = 2.0 * 3.0\nt2 = n0**min(2.0, 5)\nt3 = n1**min(2.0, 5)\nt4 = 3.0**min(2.0, 5)\nt5 = 4.0**min(2.0, 5)\nt6 = t2 + t3\nt7 = t1 * 2.0\nt8 = t0**min(2.0, 5)\nt9 = t6 + t4\nt10 = t6 * t7\nt11 = t7**min(2.0, 5)\nt12 = t9 + t5\nt13 = t10 + t7\nt14 = t12 + t8\nt15 = t13 + t11\nanswer = t14 / t15\nprint(answer)" - ], - "Output Answer": [ - "0.25462962962962965" - ], - "split": "dev" - }, - { - "Input": "a jar contains a mixture of ab in the ratio 4 : 1 . when 40 l of mixture is replaced with liquid b , ratio becomes 2 : 3 . how many liters of liquid a was present in mixture initially .", - "Output Program": [ - "n0 = 4.0\nn1 = 1.0\nn2 = 40.0\nn3 = 2.0\nn4 = 3.0\nt0 = n0 + n1\nt1 = n4 * 2.0\nt2 = n3 * 2.0\nt3 = t1 + t2\nt4 = t1 - n1\nt5 = n2 / t4\nt6 = t3 * t5\nt7 = t6 / t0\nanswer = n0 * t7\nprint(answer)" - ], - "Output Answer": [ - "64" - ], - "split": "dev" - }, - { - "Input": "if x and y are both odd prime numbers and x < y , how many distinct positive r integer factors does 2 xy have ?", - "Output Program": [ - "n0 = 2.0\nt0 = 1.0 + 1.0\nt1 = n0 * t0\nanswer = t0 * t1\nprint(answer)" - ], - "Output Answer": [ - "8" - ], - "split": "dev" - }, - { - "Input": "a certain telephone company offers two plans , a and b . under plan a , the company charges a total of $ 0.60 for the first 9 minutes of each call and $ 0.06 per minute thereafter . under plan b , the company charges $ 0.08 per minute of each call . what is the duration of a call , in minutes , for which the company charges the same amount under plan a and under plan b ?", - "Output Program": [ - "n0 = 0.6\nn1 = 9.0\nn2 = 0.06\nn3 = 0.08\nt0 = n1 * n2\nt1 = n3 - n2\nt2 = n0 - t0\nanswer = t2 / t1\nprint(answer)" - ], - "Output Answer": [ - "2.9999999999999964" - ], - "split": "dev" - }, - { - "Input": "on a certain farm the ratio of horses to cows is 4 : 1 . if the farm were to sell 15 horses and buy 15 cows , the ratio of horses to cows would then be 13 : 7 . after the transaction , how many more horses than cows would the farm own ?", - "Output Program": [ - "n0 = 4.0\nn1 = 1.0\nn2 = 15.0\nn3 = 15.0\nn4 = 13.0\nn5 = 7.0\nt0 = n2 * n4\nt1 = n2 * n5\nt2 = n0 * n5\nt3 = t0 + t1\nt4 = t2 - n4\nt5 = t3 / t4\nt6 = n2 + t5\nt7 = n0 * t5\nt8 = t7 - n2\nanswer = t8 - t6\nprint(answer)" - ], - "Output Answer": [ - "30" - ], - "split": "dev" - }, - { - "Input": "if s and t are both odd prime numbers ands < t , then how many different positive integer factors does 2 sthave ?", - "Output Program": [ - "n0 = 2.0\nt0 = n0 + n0\nanswer = n0 * t0\nprint(answer)" - ], - "Output Answer": [ - "8" - ], - "split": "dev" - }, - { - "Input": "teas worth rs . 126 per kg and rs . 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs 153 per kg , the price of the third variety per kg will be ?", - "Output Program": [ - "n0 = 126.0\nn1 = 135.0\nn2 = 1.0\nn3 = 1.0\nn4 = 2.0\nn5 = 153.0\nt0 = n2 + n2\nt1 = n0 + n1\nt2 = n4 + t0\nt3 = n5 * t2\nt4 = t3 - t1\nanswer = t4 / n4\nprint(answer)" - ], - "Output Answer": [ - "175.5" - ], - "split": "dev" - }, - { - "Input": "in what ratio mental a at rs . 68 per kg be mixed with another metal at rs . 96 per kg so that cost of alloy ( mixture ) is rs . 82 per kg ?", - "Output Program": [ - "n0 = 68.0\nn1 = 96.0\nn2 = 82.0\nt0 = n1 - n2\nt1 = n1 - n0\nt2 = t0 / t1\nt3 = 1.0 - t2\nanswer = t2 / t3\nprint(answer)" - ], - "Output Answer": [ - "1" - ], - "split": "dev" - }, - { - "Input": "initially , the men and women in a room were in the ratio of 4 : 5 . then , 2 men entered the room and 3 women left the room . then , the number of women doubled . now there are 14 men in the room . how many w women are currently in the room ?", - "Output Program": [ - "n0 = 4.0\nn1 = 5.0\nn2 = 2.0\nn3 = 3.0\nn4 = 14.0\nt0 = n4 - n2\nt1 = n1 * t0\nt2 = t1 / n0\nt3 = t2 - n3\nanswer = n2 * t3\nprint(answer)" - ], - "Output Answer": [ - "24" - ], - "split": "dev" - }, - { - "Input": "two dice are rolled . what is the probability that the sum on the top face of both the dice will be greater than 9 ?", - "Output Program": [ - "n0 = 9.0\nt0 = 2.0 * 3.0\nt1 = 1.0 / t0\nt2 = t1 * t1\nanswer = t2 * t0\nprint(answer)" - ], - "Output Answer": [ - "0.16666666666666666" - ], - "split": "dev" - }, - { - "Input": "130 kg of an alloy a is mixed with 160 kg of alloy b . if alloy a has lead and tin in the ratio 2 : 3 and alloy b has tin and copper in the ratio 3 : 4 , then the amount of tin in the new alloy is ?", - "Output Program": [ - "n0 = 130.0\nn1 = 160.0\nn2 = 2.0\nn3 = 3.0\nn4 = 3.0\nn5 = 4.0\nt0 = n2 + n3\nt1 = n4 + n5\nt2 = n0 / t0\nt3 = n1 / t1\nt4 = n3 * t2\nt5 = n4 * t3\nanswer = t4 + t5\nprint(answer)" - ], - "Output Answer": [ - "146.57142857142856" - ], - "split": "dev" - }, - { - "Input": "the hcf of two numbers is 42 and the other two factors of their lcm are 11 and 12 . what is the largest number .", - "Output Program": [ - "n0 = 42.0\nn1 = 11.0\nn2 = 12.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "504" - ], - "split": "dev" - }, - { - "Input": "17 balls are numbered 1 to 17 . a ball is drawn and then another ball is drawn without replacement . what is the probability that both balls have even numbers ?", - "Output Program": [ - "n0 = 17.0\nn1 = 1.0\nn2 = 17.0\nt0 = 4.0 + 4.0\nt1 = n0 - n1\nt2 = t0 / n0\nt3 = t0 - n1\nt4 = t3 / t1\nanswer = t2 * t4\nprint(answer)" - ], - "Output Answer": [ - "0.20588235294117646" - ], - "split": "dev" - }, - { - "Input": "the h . c . f . of two numbers is 20 and the other two factors of their l . c . m . are 11 and 15 . the larger of the two numbers is :", - "Output Program": [ - "n0 = 20.0\nn1 = 11.0\nn2 = 15.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "300" - ], - "split": "dev" - }, - { - "Input": "the ratio between the present ages of a and b is 5 : 3 respectively . the ratio between a ' s age 4 years ago and b ' s age 4 years hence is 1 : 1 . what is the ratio between a ' s age 4 years hence and b ' s age 4 years ago ?", - "Output Program": [ - "n0 = 5.0\nn1 = 3.0\nn2 = 4.0\nn3 = 4.0\nn4 = 1.0\nn5 = 1.0\nn6 = 4.0\nn7 = 4.0\nt0 = n0 + n0\nt1 = n0 - n1\nt2 = t0 / t1\nt3 = n0 * t2\nt4 = n1 * t2\nt5 = n0 + t3\nt6 = t4 - n0\nanswer = t5 / t6\nprint(answer)" - ], - "Output Answer": [ - "3" - ], - "split": "dev" - }, - { - "Input": "a shipment of 240 smartphones contains 84 that are defective . if a customer buys two smartphones at random from the shipment , what is the approximate probability that both phones are defective ?", - "Output Program": [ - "n0 = 240.0\nn1 = 84.0\nt0 = n1 - 1.0\nt1 = n0 - 1.0\nt2 = n1 * t0\nt3 = n0 * t1\nanswer = t2 / t3\nprint(answer)" - ], - "Output Answer": [ - "0.12154811715481172" - ], - "split": "dev" - }, - { - "Input": "200 pupil total , out of 125 like pizza , 115 like burger , then how many like both ?", - "Output Program": [ - "n0 = 200.0\nn1 = 125.0\nn2 = 115.0\nt0 = n1 + n2\nanswer = t0 - n0\nprint(answer)" - ], - "Output Answer": [ - "40" - ], - "split": "dev" - }, - { - "Input": "a starts business with rs . 3500 and after 8 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b \u00e2 \u20ac \u2122 s contribution in the capital ?", - "Output Program": [ - "n0 = 3500.0\nn1 = 8.0\nn2 = 2.0\nn3 = 3.0\nt0 = n0 * 12.0\nt1 = 12.0 - n1\nt2 = n3 * t0\nt3 = n2 * t1\nanswer = t2 / t3\nprint(answer)" - ], - "Output Answer": [ - "15750" - ], - "split": "dev" - }, - { - "Input": "the h . c . f . of two numbers is 20 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is :", - "Output Program": [ - "n0 = 20.0\nn1 = 13.0\nn2 = 14.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "280" - ], - "split": "dev" - }, - { - "Input": "in a group of 6 boys and 4 girls , four children are to be selected . in how many different ways can they be selected ?", - "Output Program": [ - "import math\nn0 = 6.0\nn1 = 4.0\nt0 = n0 + n1\nt1 = math.factorial(min(15, int(n1)))\nt2 = math.factorial(min(15, int(n0)))\nt3 = math.factorial(min(15, int(t0)))\nt4 = t1 * t2\nanswer = t3 / t4\nprint(answer)" - ], - "Output Answer": [ - "210" - ], - "split": "dev" - }, - { - "Input": "in a certain town , the ratio of ny yankees fans to ny mets fans is 3 : 2 , and the ratio of ny mets fans to boston red sox fans is 4 : 5 . if there are 360 baseball fans in the town , each of whom is a fan of exactly one of those three teams , how many ny mets fans are there in this town ?", - "Output Program": [ - "n0 = 3.0\nn1 = 2.0\nn2 = 4.0\nn3 = 5.0\nn4 = 360.0\nt0 = n0 * n1\nt1 = n2 + t0\nt2 = n3 + t1\nt3 = n4 / t2\nanswer = n2 * t3\nprint(answer)" - ], - "Output Answer": [ - "96" - ], - "split": "dev" - }, - { - "Input": "water consists of hydrogen and oxygen , and the approximate ratio , by mass , of hydrogen to oxygen is 2 : 16 . approximately how many grams of hydrogen are there in 117 grams of water ?", - "Output Program": [ - "n0 = 2.0\nn1 = 16.0\nn2 = 117.0\nt0 = n0 + n1\nt1 = n2 / t0\nanswer = n0 * t1\nprint(answer)" - ], - "Output Answer": [ - "13" - ], - "split": "dev" - }, - { - "Input": "in a group of 100 cars , 47 cars do not have air conditioning . if at least 55 cars have racing stripes , what is the greatest number of cars that could have air conditioning but not racing stripes ?", - "Output Program": [ - "n0 = 100.0\nn1 = 47.0\nn2 = 55.0\n\nanswer = n0 - n2\nprint(answer)" - ], - "Output Answer": [ - "45" - ], - "split": "dev" - }, - { - "Input": "in a class of 32 students , 12 enrolled for both english and german . 22 enrolled for german . if the students of the class enrolled for at least one of the two subjects , then how many students enrolled for only english and not german ?", - "Output Program": [ - "n0 = 32.0\nn1 = 12.0\nn2 = 22.0\nt0 = n0 + n1\nt1 = t0 - n2\nanswer = t1 - n1\nprint(answer)" - ], - "Output Answer": [ - "10" - ], - "split": "dev" - }, - { - "Input": "a ratio between two numbers is 3 : 4 and their l . c . m . is 84 . the first number is", - "Output Program": [ - "n0 = 3.0\nn1 = 4.0\nn2 = 84.0\nt0 = n0 * n1\nt1 = n2 / t0\nanswer = n0 * t1\nprint(answer)" - ], - "Output Answer": [ - "21" - ], - "split": "dev" - }, - { - "Input": "6 ) a marketing firm determined that , of 260 households surveyed , 80 used neither brand a nor brand b soap . 60 used only brand a soap and for every household that used both brands of soap , 3 used only brand b soap . how many of the 200 household surveyed used both brands of soap ?", - "Output Program": [ - "n0 = 6.0\nn1 = 260.0\nn2 = 80.0\nn3 = 60.0\nn4 = 3.0\nn5 = 200.0\nt0 = n1 - n2\nt1 = t0 - n3\nanswer = t1 / 4.0\nprint(answer)" - ], - "Output Answer": [ - "30" - ], - "split": "dev" - }, - { - "Input": "a 70 kg metal bar made of alloy of tin and silver lost 7 kg of its weight in the water . 10 kg of tin loses 1.375 kg in the water ; 5 kg of silver loses 0.375 kg . what is the ratio of tin to silver in the bar ?", - "Output Program": [ - "n0 = 70.0\nn1 = 7.0\nn2 = 10.0\nn3 = 1.375\nn4 = 5.0\nn5 = 0.375\nt0 = n5 / n4\nt1 = n3 / n2\nt2 = n0 * t0\nt3 = t1 - t0\nt4 = n1 - t2\nt5 = t4 / t3\nt6 = n0 - t5\nanswer = t5 / t6\nprint(answer)" - ], - "Output Answer": [ - "0.6666666666666664" - ], - "split": "dev" - }, - { - "Input": "the probability of two events a and b are 0.25 and 0.40 respectively . the probability that both a and b occur is 0.20 . the probability that neither a nor b occur is _________", - "Output Program": [ - "n0 = 0.25\nn1 = 0.4\nn2 = 0.2\nt0 = n0 + n1\nt1 = t0 - n2\nanswer = 1.0 - t1\nprint(answer)" - ], - "Output Answer": [ - "0.55" - ], - "split": "dev" - }, - { - "Input": "the ratio between the number of sheep and the number of horses at the stewart farm is 5 to 7 , if each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day , what is the number of sheep in the farm ?", - "Output Program": [ - "n0 = 5.0\nn1 = 7.0\nn2 = 230.0\nn3 = 12880.0\nt0 = 2.0 * 4.0\nt1 = 1000.0 * 12.0\nt2 = t0 * 10.0\nt3 = t0 * 100.0\nt4 = t2 + t3\nt5 = t4 + t1\nt6 = t5 / n2\nt7 = t6 / n1\nanswer = n0 * t7\nprint(answer)" - ], - "Output Answer": [ - "40" - ], - "split": "dev" - }, - { - "Input": "the dimensions of a field are 20 m by 10 m . a pit 8 m long , 5 m wide and 2 m deep is dug in one corner of the field and the earth removed has been evenly spread over the remaining area of the field . what will be the rise in the height of field as a result of this operation ?", - "Output Program": [ - "n0 = 20.0\nn1 = 10.0\nn2 = 8.0\nn3 = 5.0\nn4 = 2.0\nt0 = n1 * n2\nt1 = n0 * n1 # area of rectangle\nt2 = n2 * n3 # area of rectangle\nt3 = t1 - t2\nanswer = t0 / t3\nprint(answer)" - ], - "Output Answer": [ - "0.5" - ], - "split": "dev" - }, - { - "Input": "what is the number of integers from 1 to 1000 ( inclusive ) that are divisible by neither 11 nor by 35 ?", - "Output Program": [ - "n0 = 1.0\nn1 = 1000.0\nn2 = 11.0\nn3 = 35.0\nt0 = n1 / n2\nt1 = n1 / n3\nt2 = n2 * n3\nt3 = t0 + t1\nt4 = n1 / t2\nt5 = t3 - t4\nanswer = n1 - t5\nprint(answer)" - ], - "Output Answer": [ - "883.1168831168832" - ], - "split": "dev" - }, - { - "Input": "a certain high school has 500 students . of these students , 30 are taking music , 10 are taking art , and 10 are taking both music and art . how many students are taking neither music nor art ?", - "Output Program": [ - "n0 = 500.0\nn1 = 30.0\nn2 = 10.0\nn3 = 10.0\nt0 = n1 + n2\nt1 = t0 - n3\nanswer = n0 - t1\nprint(answer)" - ], - "Output Answer": [ - "470" - ], - "split": "dev" - }, - { - "Input": "a salesman sold twice as much pears in the afternoon than in the morning . if he sold $ 390 kilograms of pears that day , how many kilograms did he sell in the afternoon ?", - "Output Program": [ - "n0 = 390.0\nt0 = n0 / 3.0\nanswer = t0 * 2.0\nprint(answer)" - ], - "Output Answer": [ - "260" - ], - "split": "dev" - }, - { - "Input": "a certain high school has 500 students . of these students , 20 are taking music , 20 are taking art , and 10 are taking both music and art . how many students are taking neither music nor art ?", - "Output Program": [ - "n0 = 500.0\nn1 = 20.0\nn2 = 20.0\nn3 = 10.0\nt0 = n1 + n2\nt1 = t0 - n3\nanswer = n0 - t1\nprint(answer)" - ], - "Output Answer": [ - "470" - ], - "split": "dev" - }, - { - "Input": "the h . c . f . of two numbers is 15 and the other two factors of their l . c . m . are 11 and 15 . the larger of the two numbers is :", - "Output Program": [ - "n0 = 15.0\nn1 = 11.0\nn2 = 15.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "225" - ], - "split": "dev" - }, - { - "Input": "the concentration of spirit in 3 different vessels a , b and c are 45 % , 30 % and 10 % respectively . if 4 litres from vessel a , 5 litres from vessel b and 6 litres from vessel c are mixed , find the concentration of spirit in the resultant solution .", - "Output Program": [ - "n0 = 3.0\nn1 = 45.0\nn2 = 30.0\nn3 = 10.0\nn4 = 4.0\nn5 = 5.0\nn6 = 6.0\nt0 = n3 + n5\nt1 = n1 * n4\nt2 = n2 * n5\nt3 = n3 * n6\nt4 = t1 / 100.0\nt5 = t2 / 100.0\nt6 = t3 / 100.0\nt7 = t4 + t5\nt8 = t7 + t6\nt9 = t8 * 100.0\nanswer = t9 / t0\nprint(answer)" - ], - "Output Answer": [ - "26" - ], - "split": "dev" - }, - { - "Input": "a class of boys stands in a single line , one boy is 19 th in order from both the ends , how many boys are there in the class ?", - "Output Program": [ - "n0 = 19.0\nt0 = n0 * 2.0\nanswer = t0 - 1.0\nprint(answer)" - ], - "Output Answer": [ - "37" - ], - "split": "dev" - }, - { - "Input": "a student committee on academic integrity has 132 ways to select a president and vice president from a group of candidates . the same person can not be both president and vice president . how many candidates are there ?", - "Output Program": [ - "import math\nn0 = 132.0\nt0 = n0 * 4.0\nt1 = -1.0\nt2 = t1**min(2.0, 5)\nt3 = t0 + t2\nt4 = math.sqrt(max(0, t3))\nt5 = t4 + 1.0\nanswer = t5 / 2.0\nprint(answer)" - ], - "Output Answer": [ - "12" - ], - "split": "dev" - }, - { - "Input": "of 60 children , 30 are happy , 10 are sad , and 20 are neither happy nor sad . there are 19 boys and 41 girls . if there are 6 happy boys and 4 sad girls , how many boys are neither happy nor sad ?", - "Output Program": [ - "n0 = 60.0\nn1 = 30.0\nn2 = 10.0\nn3 = 20.0\nn4 = 19.0\nn5 = 41.0\nn6 = 6.0\nn7 = 4.0\nt0 = n2 - n7\nt1 = n4 - t0\nanswer = t1 - n6\nprint(answer)" - ], - "Output Answer": [ - "7" - ], - "split": "dev" - }, - { - "Input": "an amount of money is to be distributed among faruk , vasim and ranjith in the ratio 3 : 5 : 7 . if vasims share is rs . 1500 , what is the difference between faruk ' s and ranjith ' s shares ?", - "Output Program": [ - "n0 = 3.0\nn1 = 5.0\nn2 = 7.0\nn3 = 1500.0\nt0 = n3 / n1\nt1 = n2 - n0\nanswer = t0 * t1\nprint(answer)" - ], - "Output Answer": [ - "1200" - ], - "split": "dev" - }, - { - "Input": "the probability of two events a and b are 0.25 and 0.40 respectively . the probability that both a and b occur is 0.15 . the probability that neither a nor b occur is _________", - "Output Program": [ - "n0 = 0.25\nn1 = 0.4\nn2 = 0.15\nt0 = n0 + n1\nt1 = t0 - n2\nanswer = 1.0 - t1\nprint(answer)" - ], - "Output Answer": [ - "0.5" - ], - "split": "dev" - }, - { - "Input": "ratio between rahul and deepak is 4 : 2 , after 10 years rahul age will be 26 years . what is deepak present age", - "Output Program": [ - "n0 = 4.0\nn1 = 2.0\nn2 = 10.0\nn3 = 26.0\nt0 = n3 - n2\nt1 = n1 * t0\nanswer = t1 / n0\nprint(answer)" - ], - "Output Answer": [ - "8" - ], - "split": "dev" - }, - { - "Input": "the ratio of three numbers is 1 : 2 : 3 and the sum of their squares is 2016 . the sum of the numbers is ?", - "Output Program": [ - "import math\nn0 = 1.0\nn1 = 2.0\nn2 = 3.0\nn3 = 2016.0\nt0 = n0**min(n1, 5)\nt1 = n1**min(n1, 5)\nt2 = n2**min(n1, 5)\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n3 / t4\nanswer = math.sqrt(max(0, t5))\nprint(answer)" - ], - "Output Answer": [ - "12" - ], - "split": "dev" - }, - { - "Input": "100 people are attending a newspaper conference . 45 of them are writers and more than 36 are editors . of the people at the conference , x are both writers and editors and 2 x are neither . what is the largest possible number of people who are both writers and editors ?", - "Output Program": [ - "n0 = 100.0\nn1 = 45.0\nn2 = 36.0\nn3 = 2.0\nt0 = n2 + 1.0\nt1 = n1 + t0\nanswer = n0 - t1\nprint(answer)" - ], - "Output Answer": [ - "18" - ], - "split": "dev" - }, - { - "Input": "if 63 percent of a class answered the first question on a certain test correctly , 50 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?", - "Output Program": [ - "n0 = 63.0\nn1 = 50.0\nn2 = 20.0\nt0 = n0 + n1\nt1 = n2 + t0\nanswer = t1 - 100.0\nprint(answer)" - ], - "Output Answer": [ - "33" - ], - "split": "dev" - }, - { - "Input": "a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 18 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many liter of liquid a was contained by the can initially ?", - "Output Program": [ - "n0 = 7.0\nn1 = 5.0\nn2 = 18.0\nn3 = 7.0\nn4 = 9.0\nt0 = n0 + n4\nt1 = n0 + n1\nt2 = n0 * n4\nt3 = n0 * n1\nt4 = n1 / t1\nt5 = t2 - t3\nt6 = n2 * t4\nt7 = n2 - t6\nt8 = t0 * t7\nt9 = t8 / t5\nanswer = n0 * t9\nprint(answer)" - ], - "Output Answer": [ - "42" - ], - "split": "dev" - }, - { - "Input": "of the 200 stamps in a collection , 80 are foreign and 50 are more than 10 years old . if 20 stamps are both foreign and more than 10 years old , how many stamps are neither foreign nor more than 10 years old ?", - "Output Program": [ - "n0 = 200.0\nn1 = 80.0\nn2 = 50.0\nn3 = 10.0\nn4 = 20.0\nn5 = 10.0\nn6 = 10.0\nt0 = n1 + n2\nt1 = t0 - n4\nanswer = n0 - t1\nprint(answer)" - ], - "Output Answer": [ - "90" - ], - "split": "dev" - }, - { - "Input": "the ratio of money with ram and gopal is 7 : 17 and that with gopal and krishan is 7 : 17 . if ram has rs . 490 , krishan has ?", - "Output Program": [ - "n0 = 7.0\nn1 = 17.0\nn2 = 7.0\nn3 = 17.0\nn4 = 490.0\nt0 = n4 / n0\nt1 = n1 * t0\nt2 = t1 / n0\nanswer = n1 * t2\nprint(answer)" - ], - "Output Answer": [ - "2890" - ], - "split": "dev" - }, - { - "Input": "3 numbers are in the ratio 3 : 5 : 7 . the largest number value is 70 . find difference between smallest & largest number is ?", - "Output Program": [ - "n0 = 3.0\nn1 = 3.0\nn2 = 5.0\nn3 = 7.0\nn4 = 70.0\nt0 = n4 / n3\nt1 = n0 * t0\nanswer = n4 - t1\nprint(answer)" - ], - "Output Answer": [ - "40" - ], - "split": "dev" - }, - { - "Input": "an amount of money is to be distributed among faruk , vasim and ranjith in the ratio 3 : 5 : 11 . if vasims share is rs . 1500 , what is the difference between faruk ' s and ranjith ' s shares ?", - "Output Program": [ - "n0 = 3.0\nn1 = 5.0\nn2 = 11.0\nn3 = 1500.0\nt0 = n3 / n1\nt1 = n2 - n0\nanswer = t0 * t1\nprint(answer)" - ], - "Output Answer": [ - "2400" - ], - "split": "dev" - }, - { - "Input": "a shipment of 230 smartphones contains 84 that are defective . if a customer buys two smartphones at random from the shipment , what is the approximate probability that both phones are defective ?", - "Output Program": [ - "n0 = 230.0\nn1 = 84.0\nt0 = n1 - 1.0\nt1 = n0 - 1.0\nt2 = n1 * t0\nt3 = n0 * t1\nanswer = t2 / t3\nprint(answer)" - ], - "Output Answer": [ - "0.13237136890070247" - ], - "split": "dev" - }, - { - "Input": "in a group of 28 junior high school students , 5 take french , 10 take spanish , and 4 take both languages . the students taking both french and spanish are not counted with the 7 taking french or the 10 taking spanish . how many students are not taking either french or spanish ?", - "Output Program": [ - "n0 = 28.0\nn1 = 5.0\nn2 = 10.0\nn3 = 4.0\nn4 = 7.0\nn5 = 10.0\nt0 = n1 + n2\nanswer = n0 - t0\nprint(answer)" - ], - "Output Answer": [ - "13" - ], - "split": "dev" - }, - { - "Input": "a person want to give his money of $ 1800 to his 3 children a , b , c in the ratio 2 : 3 : 4 . what is the b ' s share ?", - "Output Program": [ - "n0 = 1800.0\nn1 = 3.0\nn2 = 2.0\nn3 = 3.0\nn4 = 4.0\nt0 = n1 + n2\nt1 = n4 + t0\nt2 = n1 / t1\nanswer = n0 * t2\nprint(answer)" - ], - "Output Answer": [ - "600" - ], - "split": "dev" - }, - { - "Input": "mala and usha shared their water from a bottle . if mala and usha both drank for the same amount of time , but usha only drank 2 / 10 of the total bottle , what was the ratio of mala and usha speed ?", - "Output Program": [ - "n0 = 2.0\nn1 = 10.0\nt0 = n1 - n0\nanswer = t0 / n0\nprint(answer)" - ], - "Output Answer": [ - "4" - ], - "split": "dev" - }, - { - "Input": "in township k , 1 / 5 of the housing units are equipped with cable television . if 1 / 10 of the housing units , including 1 / 3 of those that are equipped with cable television , are equipped with videocassette recorders , what fraction of the housing units have neither cable television nor videocassette recorders ?", - "Output Program": [ - "n0 = 1.0\nn1 = 5.0\nn2 = 1.0\nn3 = 10.0\nn4 = 1.0\nn5 = 3.0\nt0 = n0 / n1\nt1 = n0 / n5\nt2 = n0 / n3\nt3 = t0 * t1\nt4 = 1.0 - t0\nt5 = t4 - t2\nanswer = t3 + t5\nprint(answer)" - ], - "Output Answer": [ - "0.7666666666666667" - ], - "split": "dev" - }, - { - "Input": "in a certain school , the ratio of boys to girls is 5 to 13 . if there are 64 more girls than boys , how many boys are there ?", - "Output Program": [ - "n0 = 5.0\nn1 = 13.0\nn2 = 64.0\nt0 = n0 / n1\nt1 = 1.0 - t0\nt2 = n2 / t1\nanswer = t2 - n2\nprint(answer)" - ], - "Output Answer": [ - "40" - ], - "split": "dev" - }, - { - "Input": "a salesman sold twice as much pears in the afternoon than in the morning . if he sold $ 510 kilograms of pears that day , how many kilograms did he sell in the afternoon ?", - "Output Program": [ - "n0 = 510.0\nt0 = n0 / 3.0\nanswer = t0 * 2.0\nprint(answer)" - ], - "Output Answer": [ - "340" - ], - "split": "dev" - }, - { - "Input": "if 80 percent of a class answered the first question on a certain test correctly , 55 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?", - "Output Program": [ - "n0 = 80.0\nn1 = 55.0\nn2 = 20.0\nt0 = n0 + n1\nt1 = n2 + t0\nanswer = t1 - 100.0\nprint(answer)" - ], - "Output Answer": [ - "55" - ], - "split": "dev" - }, - { - "Input": "how many numbers are divisible by both 2 and 3 up to 300 ?", - "Output Program": [ - "n0 = 2.0\nn1 = 3.0\nn2 = 300.0\nt0 = n0 * n1\nanswer = n2 / t0\nprint(answer)" - ], - "Output Answer": [ - "50" - ], - "split": "dev" - }, - { - "Input": "how many numbers up to 300 and 700 are divisible by 2 , 3 and 7 both together ?", - "Output Program": [ - "import scipy\nn0 = 300.0\nn1 = 700.0\nn2 = 2.0\nn3 = 3.0\nn4 = 7.0\nt0 = scipy.lcm(int(n2), int(n3))\nt1 = 10.0 * 2.0\nt2 = n1 - n0\nt3 = n2 + t1\nt4 = scipy.lcm(int(n4), int(t0))\nt5 = t2 / t4\nt6 = t3 / t4\nanswer = t5 - t6\nprint(answer)" - ], - "Output Answer": [ - "9" - ], - "split": "dev" - }, - { - "Input": "in a family 16 people eat only vegetarian , 9 people eat only non veg . , 12 people eat both veg and non veg . . how many people eat veg in the family ?", - "Output Program": [ - "n0 = 16.0\nn1 = 9.0\nn2 = 12.0\n\nanswer = n0 + n2\nprint(answer)" - ], - "Output Answer": [ - "28" - ], - "split": "dev" - }, - { - "Input": "in a certain alphabet , 9 letters contain a dot and a straight line . 24 letters contain a straight line but do not contain a dot . if that alphabet has 40 letters , all of which contain either a dot or a straight line or both , how many letters contain a dot but do not contain a straight line ?", - "Output Program": [ - "n0 = 9.0\nn1 = 24.0\nn2 = 40.0\nt0 = n0 + n1\nanswer = n2 - t0\nprint(answer)" - ], - "Output Answer": [ - "7" - ], - "split": "dev" - }, - { - "Input": "in a group of 100 cars , 47 cars do not have air conditioning . if at least 53 cars have racing stripes , what is the greatest number of cars that could have air conditioning but not racing stripes ?", - "Output Program": [ - "n0 = 100.0\nn1 = 47.0\nn2 = 53.0\n\nanswer = n0 - n2\nprint(answer)" - ], - "Output Answer": [ - "47" - ], - "split": "dev" - }, - { - "Input": "sachin is younger than rahul by 4 years . if the ratio of their ages is 7 : 9 , find the age of sachin", - "Output Program": [ - "n0 = 4.0\nn1 = 7.0\nn2 = 9.0\nt0 = n2 - n1\nt1 = n0 / t0\nanswer = n1 * t1\nprint(answer)" - ], - "Output Answer": [ - "14" - ], - "split": "dev" - }, - { - "Input": "in a class , 10 students like to play basketball and 8 like to play cricket . 4 students like to play on both basketball and cricket . how many students like to play basketball or cricket or both ?", - "Output Program": [ - "n0 = 10.0\nn1 = 8.0\nn2 = 4.0\nt0 = n0 + n1\nanswer = t0 - n2\nprint(answer)" - ], - "Output Answer": [ - "14" - ], - "split": "dev" - }, - { - "Input": "of the 65 cars on a car lot , 45 have power steering , 25 have power windows , and 17 have both power steering and power windows . how many of the cars on the lot have neither power steering nor power windows ?", - "Output Program": [ - "n0 = 65.0\nn1 = 45.0\nn2 = 25.0\nn3 = 17.0\nt0 = n1 + n2\nt1 = t0 - n3\nanswer = n0 - t1\nprint(answer)" - ], - "Output Answer": [ - "12" - ], - "split": "dev" - }, - { - "Input": "the l . c . m . of two numbers is 60 . the numbers are in the ratio 2 : 3 . then sum of the number is :", - "Output Program": [ - "n0 = 60.0\nn1 = 2.0\nn2 = 3.0\nt0 = n1 * n2\nt1 = n0 / t0\nt2 = n2 * t1\nt3 = n1 * t1\nanswer = t2 + t3\nprint(answer)" - ], - "Output Answer": [ - "50" - ], - "split": "dev" - }, - { - "Input": "the ratio of the present age of viju to that of aju is 7 : 2 . 4 years from now , the ratio of the ages of viju to aju will be 5 : 2 . what was viju age 5 years ago ? ( rbi assistant 2015 )", - "Output Program": [ - "n0 = 7.0\nn1 = 2.0\nn2 = 4.0\nn3 = 5.0\nn4 = 2.0\nn5 = 5.0\nn6 = 2015.0\nt0 = n2 * n3\nt1 = n1 * n2\nt2 = n0 - n3\nt3 = t0 - t1\nt4 = t3 / t2\nt5 = n0 * t4\nt6 = t5 / n1\nanswer = t6 - n3\nprint(answer)" - ], - "Output Answer": [ - "16" - ], - "split": "dev" - }, - { - "Input": "if all 6 are replaced by 9 , the algebric sum of all numbers from 1 to 100 ( both inclusive ) varies by ,", - "Output Program": [ - "n0 = 6.0\nn1 = 9.0\nn2 = 1.0\nn3 = 100.0\nt0 = n1 - n0\nt1 = t0 * 10.0\nt2 = t0 * 100.0\nanswer = t1 + t2\nprint(answer)" - ], - "Output Answer": [ - "330" - ], - "split": "dev" - }, - { - "Input": "the ratio between speed of the two trains is 7 : 8 . if the 2 nd train runs 400 km in 4 hrs , what is the speed of the 1 st train ?", - "Output Program": [ - "n0 = 7.0\nn1 = 8.0\nn2 = 2.0\nn3 = 400.0\nn4 = 4.0\nn5 = 1.0\nt0 = n3 / n4\nt1 = n0 / n1\nanswer = t0 * t1\nprint(answer)" - ], - "Output Answer": [ - "87.5" - ], - "split": "dev" - }, - { - "Input": "if 32.5 % of the 880 students at a certain college are enrolled in biology classes , how many students at the college are not enrolled in a biology class ?", - "Output Program": [ - "n0 = 32.5\nn1 = 880.0\nt0 = n1 / 100.0\nt1 = 100.0 - n0\nanswer = t0 * t1\nprint(answer)" - ], - "Output Answer": [ - "594" - ], - "split": "dev" - }, - { - "Input": "irin , ingrid and nell bake chocolate chip cookies in the ratio of 9.18 : 5.17 : 2.05 . if altogether they baked a batch of 148 cookies , what percent of the cookies did ingrid bake ?", - "Output Program": [ - "n0 = 9.18\nn1 = 5.17\nn2 = 2.05\nn3 = 148.0\nt0 = n0 + n1\nt1 = n1 * n3\nt2 = n2 + t0\nt3 = t1 / t2\nt4 = t3 / n3\nanswer = t4 * 100.0\nprint(answer)" - ], - "Output Answer": [ - "31.524390243902438" - ], - "split": "dev" - }, - { - "Input": "two integers are in the ratio of 1 to 4 . if 6 is added to the smaller number , the ratio becomes 1 to 3 . find the larger integer .", - "Output Program": [ - "n0 = 1.0\nn1 = 4.0\nn2 = 6.0\nn3 = 1.0\nn4 = 3.0\nt0 = n2 * n4\nt1 = n1 - n4\nt2 = t0 / t1\nanswer = n1 * t2\nprint(answer)" - ], - "Output Answer": [ - "72" - ], - "split": "dev" - }, - { - "Input": "in a group of 7 boys and 8 girls , 5 members are to be selected . in how many different ways can they be selected such that at least 3 boys should be there ?", - "Output Program": [ - "import math\nn0 = 7.0\nn1 = 8.0\nn2 = 5.0\nn3 = 3.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(n1)))\nt2 = n0 * n3\nt3 = t0 * t0\nt4 = t3 / t1\nt5 = t4 * 2.0\nanswer = t5 + t2\nprint(answer)" - ], - "Output Answer": [ - "1281" - ], - "split": "dev" - }, - { - "Input": "initially , the men and women in a room were in the ratio of 4 : 5 . then , 2 men entered the room and 3 women left the room . then , the number of women doubled . now there are 14 men in the room . how many q women are currently in the room ?", - "Output Program": [ - "n0 = 4.0\nn1 = 5.0\nn2 = 2.0\nn3 = 3.0\nn4 = 14.0\nt0 = n4 - n2\nt1 = n1 * t0\nt2 = t1 / n0\nt3 = t2 - n3\nanswer = n2 * t3\nprint(answer)" - ], - "Output Answer": [ - "24" - ], - "split": "dev" - }, - { - "Input": "apple costs l rupees per kilogram for first 30 kgs and q rupees per kilogram for each additional kilogram . if the price of 33 kilograms is 663 and for 36 kgs of apples is 726 then the cost of first 10 kgs of apples is", - "Output Program": [ - "n0 = 30.0\nn1 = 33.0\nn2 = 663.0\nn3 = 36.0\nn4 = 726.0\nn5 = 10.0\nt0 = n4 - n2\nt1 = n3 - n1\nt2 = n1 - n0\nt3 = t0 / t1\nt4 = t3 * t2\nt5 = n2 - t4\nt6 = t5 / n0\nanswer = n5 * t6\nprint(answer)" - ], - "Output Answer": [ - "200" - ], - "split": "dev" - }, - { - "Input": "if ( log 5 5 ) ( log 4 9 ) ( log 3 2 ) is equal to", - "Output Program": [ - "import math\nn0 = 5.0\nn1 = 5.0\nn2 = 4.0\nn3 = 9.0\nn4 = 3.0\nn5 = 2.0\nt0 = math.log(max(1e-5, n0), 2)\nanswer = t0 / t0\nprint(answer)" - ], - "Output Answer": [ - "1" - ], - "split": "dev" - }, - { - "Input": "in a class of 40 students 26 play football and play 20 long tennis , if 17 play above , many play neither ?", - "Output Program": [ - "n0 = 40.0\nn1 = 26.0\nn2 = 20.0\nn3 = 17.0\nt0 = n1 + n2\nt1 = t0 - n3\nanswer = n0 - t1\nprint(answer)" - ], - "Output Answer": [ - "11" - ], - "split": "dev" - }, - { - "Input": "the hcf of two numbers is 42 and the other two factors of their lcm are 10 and 20 . what is the largest number .", - "Output Program": [ - "n0 = 42.0\nn1 = 10.0\nn2 = 20.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "840" - ], - "split": "dev" - }, - { - "Input": "a dog have birth to 12 puppies , 2 female and 10 male . what is the ratio of the female puppies to the male ?", - "Output Program": [ - "n0 = 12.0\nn1 = 2.0\nn2 = 10.0\n\nanswer = n1 / n2\nprint(answer)" - ], - "Output Answer": [ - "0.2" - ], - "split": "dev" - }, - { - "Input": "there are 250 doctors and nurses at a hospital . if the ratio of doctors to nurses is 2 to 3 , how many nurses are at the hospital ?", - "Output Program": [ - "n0 = 250.0\nn1 = 2.0\nn2 = 3.0\nt0 = n1 + n2\nt1 = n0 / t0\nanswer = n2 * t1\nprint(answer)" - ], - "Output Answer": [ - "150" - ], - "split": "dev" - }, - { - "Input": "in a chess competition involving some men and women , every player needs to play exactly one game with every other player . it was found that in 45 games , both the players were women and in 190 games , both players were men . what is the number of games in which one person was a man and other person was a woman ?", - "Output Program": [ - "import math\nn0 = 45.0\nn1 = 190.0\nt0 = n0 * 2.0\nt1 = n1 * 2.0\nt2 = t0 * 4.0\nt3 = t1 * 4.0\nt4 = t2 + 1.0\nt5 = t3 + 1.0\nt6 = math.sqrt(max(0, t4))\nt7 = math.sqrt(max(0, t5))\nt8 = t6 + 1.0\nt9 = t7 + 1.0\nt10 = t8 / 2.0\nt11 = t9 / 2.0\nanswer = t10 * t11\nprint(answer)" - ], - "Output Answer": [ - "200" - ], - "split": "dev" - }, - { - "Input": "praveen starts business with rs . 3780 and after 5 months , hari joins with praveen as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is hari \u2019 s contribution in the capital ?", - "Output Program": [ - "n0 = 3780.0\nn1 = 5.0\nn2 = 2.0\nn3 = 3.0\nt0 = n1 / 12.0\nt1 = n2 / n3\nt2 = 1.0 - t0\nt3 = n0 / t2\nanswer = t3 / t1\nprint(answer)" - ], - "Output Answer": [ - "9720.000000000002" - ], - "split": "dev" - }, - { - "Input": "in a certain pet shop , the ratio of dogs to cats to bunnies in stock is 4 : 7 : 9 . if the shop carries 364 dogs and bunnies total in stock , how many dogs are there ?", - "Output Program": [ - "n0 = 4.0\nn1 = 7.0\nn2 = 9.0\nn3 = 364.0\nt0 = n0 + n2\nt1 = n3 / t0\nanswer = n0 * t1\nprint(answer)" - ], - "Output Answer": [ - "112" - ], - "split": "dev" - }, - { - "Input": "the h . c . f of two numbers is 23 and the other two factors of their l . c . m are 16 and 17 . the larger of the two numbers is :", - "Output Program": [ - "n0 = 23.0\nn1 = 16.0\nn2 = 17.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "391" - ], - "split": "dev" - }, - { - "Input": "the cost of 3 pens and 5 pencils is rs . 150 . also the cost of one pen and one pencil is in the ratio of 5 : 1 respectively . what is the cost of one dozen pens ?", - "Output Program": [ - "n0 = 3.0\nn1 = 5.0\nn2 = 150.0\nn3 = 5.0\nn4 = 1.0\nt0 = n0 + n4\nt1 = n0 * 4.0\nt2 = n2 / t0\nanswer = t2 * t1\nprint(answer)" - ], - "Output Answer": [ - "450" - ], - "split": "dev" - }, - { - "Input": "out of 250 students of a college , 160 play football , 90 play cricket and 50 neither play football nor cricket . how many students play both football and cricket ?", - "Output Program": [ - "n0 = 250.0\nn1 = 160.0\nn2 = 90.0\nn3 = 50.0\nt0 = n1 + n2\nt1 = n3 + t0\nanswer = t1 - n0\nprint(answer)" - ], - "Output Answer": [ - "50" - ], - "split": "dev" - }, - { - "Input": "if 75 percent of a class answered the first question on a certain test correctly , 70 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?", - "Output Program": [ - "n0 = 75.0\nn1 = 70.0\nn2 = 20.0\nt0 = n0 + n1\nt1 = n2 + t0\nanswer = t1 - 100.0\nprint(answer)" - ], - "Output Answer": [ - "65" - ], - "split": "dev" - }, - { - "Input": "compound x contains elements a and b at an approximate ratio , by weight , of 2 : 10 . approximately how many grams of element b are there in 108 grams of compound x ?", - "Output Program": [ - "n0 = 2.0\nn1 = 10.0\nn2 = 108.0\nt0 = n0 + n1\nt1 = n1 * n2\nanswer = t1 / t0\nprint(answer)" - ], - "Output Answer": [ - "90" - ], - "split": "dev" - }, - { - "Input": "tough and tricky questions : ratios 4 / 5 of a certain class left on a field trip . 1 / 3 of the students who stayed behind did not want to go on the field trip ( all the others did want to go ) . when another vehicle was located , 1 / 2 of the students who did want to go on the field trip but had been left behind were able to join . what fraction of the class ended up going on the field trip ?", - "Output Program": [ - "import scipy\nn0 = 4.0\nn1 = 5.0\nn2 = 1.0\nn3 = 3.0\nn4 = 1.0\nn5 = 2.0\nt0 = n2 / n5\nt1 = n0 / n1\nt2 = n2 / n3\nt3 = scipy.lcm(int(n1), int(n3))\nt4 = scipy.lcm(int(n5), int(t3))\nt5 = t1 * t4\nt6 = t4 - t5\nt7 = t2 * t6\nt8 = t6 - t7\nt9 = t0 * t8\nt10 = t9 + t5\nanswer = t10 / t4\nprint(answer)" - ], - "Output Answer": [ - "0.8666666666666667" - ], - "split": "dev" - }, - { - "Input": "a bag contains 5 green and 8 white balls . if two balls are drawn simultaneously , the probability that both are of the same colour is", - "Output Program": [ - "n0 = 5.0\nn1 = 8.0\nt0 = n0 + n1\nt1 = n1 - 1.0\nt2 = n0 - 1.0\nt3 = n1 / t0\nt4 = n0 / t0\nt5 = t0 - 1.0\nt6 = t1 / t5\nt7 = t2 / t5\nt8 = t3 * t6\nt9 = t4 * t7\nanswer = t8 + t9\nprint(answer)" - ], - "Output Answer": [ - "0.4871794871794872" - ], - "split": "dev" - }, - { - "Input": "of the diplomats attending a summit conference , 17 speak french , 32 do not speak russian , and 20 % of the diplomats speak neither french nor russian . if 10 % of the diplomats speak both languages , then how many diplomats attended the conference ?", - "Output Program": [ - "n0 = 17.0\nn1 = 32.0\nn2 = 20.0\nn3 = 10.0\nt0 = n2 / 100.0\nt1 = n3 / 100.0\nt2 = n1 - n0\nt3 = t0 - t1\nanswer = t2 / t3\nprint(answer)" - ], - "Output Answer": [ - "150" - ], - "split": "dev" - }, - { - "Input": "in a sports club with 30 members , 17 play badminton and 19 play tennis and 3 do not play either . how many members play both badminton and tennis ?", - "Output Program": [ - "n0 = 30.0\nn1 = 17.0\nn2 = 19.0\nn3 = 3.0\nt0 = n1 + n2\nt1 = n3 + t0\nanswer = t1 - n0\nprint(answer)" - ], - "Output Answer": [ - "9" - ], - "split": "dev" - }, - { - "Input": "income and expenditure of a person are in the ratio 7 : 6 . if the income of the person is rs . 14000 , then find his savings ?", - "Output Program": [ - "n0 = 7.0\nn1 = 6.0\nn2 = 14000.0\nt0 = n1 / n0\nt1 = n2 * t0\nanswer = n2 - t1\nprint(answer)" - ], - "Output Answer": [ - "2000" - ], - "split": "dev" - }, - { - "Input": "in a group of 8 semifinalists , all but 2 will advance to the final round . if in the final round only the top 3 will be awarded medals , then how many groups of medal winners are possible ?", - "Output Program": [ - "import math\nn0 = 8.0\nn1 = 2.0\nn2 = 3.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(n2)))\nt2 = n0 - n1\nt3 = math.factorial(min(15, int(t2)))\nt4 = t1 * t1\nt5 = t3 / t4\nt6 = n1 * t3\nt7 = t0 / t6\nt8 = t7 * t5\nanswer = t8 / 10.0\nprint(answer)" - ], - "Output Answer": [ - "56" - ], - "split": "dev" - }, - { - "Input": "the ratio of the number of red cars in a certain parking lot to the number of black cars is 3 to 8 . if there are 90 black cars in the lot , how many red cars are there in the lot ?", - "Output Program": [ - "import math\nn0 = 3.0\nn1 = 8.0\nn2 = 90.0\nt0 = n0 / n1\nt1 = n2 * t0\nanswer = math.floor(t1)\nprint(answer)" - ], - "Output Answer": [ - "33" - ], - "split": "dev" - }, - { - "Input": "a set of pictures of butterflies contains 10 pictures . jim bought 3 of the pictures . if 2 pictures are to be picked out from the 10 pictures , what is the probability that both pictures are not those that were already bought by jim ?", - "Output Program": [ - "import math\nn0 = 10.0\nn1 = 3.0\nn2 = 2.0\nn3 = 10.0\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 = t1 / t5\nt8 = math.factorial(min(15, int(t6)))\nt9 = t4 / t8\nt10 = t7 / t0\nt11 = t9 / t0\nanswer = t11 / t10\nprint(answer)" - ], - "Output Answer": [ - "0.4666666666666667" - ], - "split": "dev" - }, - { - "Input": "120 kg of an alloy a is mixed with 180 kg of alloy b . if alloy a has lead and tin in the ratio 2 : 3 and alloy b has tin and copper in the ratio 3 : 5 , then the amount of tin in the new alloy is ?", - "Output Program": [ - "n0 = 120.0\nn1 = 180.0\nn2 = 2.0\nn3 = 3.0\nn4 = 3.0\nn5 = 5.0\nt0 = n2 + n3\nt1 = n4 + n5\nt2 = n0 / t0\nt3 = n1 / t1\nt4 = n3 * t2\nt5 = n4 * t3\nanswer = t4 + t5\nprint(answer)" - ], - "Output Answer": [ - "139.5" - ], - "split": "dev" - }, - { - "Input": "a bag contains 7 black and 8 white balls . if two balls are drawn simultaneously , what is the probability that both are of the same color is ?", - "Output Program": [ - "import math\nn0 = 7.0\nn1 = 8.0\nt0 = n0 + n1\nt1 = math.factorial(min(15, int(n1)))\nt2 = math.factorial(min(15, int(2.0)))\nt3 = math.factorial(min(15, int(n0)))\nt4 = n1 - 2.0\nt5 = n0 - 2.0\nt6 = math.factorial(min(15, int(t4)))\nt7 = math.factorial(min(15, int(t5)))\nt8 = math.factorial(min(15, int(t0)))\nt9 = t0 - 2.0\nt10 = t1 / t6\nt11 = t3 / t7\nt12 = math.factorial(min(15, int(t9)))\nt13 = t10 / t2\nt14 = t11 / t2\nt15 = t8 / t12\nt16 = t13 + t14\nt17 = t15 / t2\nanswer = t16 / t17\nprint(answer)" - ], - "Output Answer": [ - "0.4666666666666667" - ], - "split": "dev" - }, - { - "Input": "the h . c . f of two numbers is 23 and the other two factors of their l . c . m are 14 and 15 . the larger of the two numbers is :", - "Output Program": [ - "n0 = 23.0\nn1 = 14.0\nn2 = 15.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "345" - ], - "split": "dev" - }, - { - "Input": "in a group of 100 cars , 49 cars do not have air conditioning . if at least 51 cars have racing stripes , what is the greatest number of cars that could have air conditioning but not racing stripes ?", - "Output Program": [ - "n0 = 100.0\nn1 = 49.0\nn2 = 51.0\n\nanswer = n0 - n2\nprint(answer)" - ], - "Output Answer": [ - "49" - ], - "split": "dev" - }, - { - "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 c 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": "dev" - }, - { - "Input": "in what ratio must rice of rs . 16 per kg be mixed with rice of rs . 24 per kg so that cost of mixture is rs . 18 per kg ?", - "Output Program": [ - "n0 = 16.0\nn1 = 24.0\nn2 = 18.0\nt0 = n2 - n1\nt1 = n0 - n1\nt2 = t0 / t1\nt3 = 1.0 - t2\nanswer = t2 / t3\nprint(answer)" - ], - "Output Answer": [ - "3" - ], - "split": "dev" - }, - { - "Input": "sachin is older than rahul by 7 years . if the ratio of their ages is 11 : 9 , find the age of sachin", - "Output Program": [ - "n0 = 7.0\nn1 = 11.0\nn2 = 9.0\nt0 = n0 * n1\nt1 = n1 - n2\nanswer = t0 / t1\nprint(answer)" - ], - "Output Answer": [ - "38.5" - ], - "split": "dev" - }, - { - "Input": "in a circuit board factory , all circuit boards that pass a verification process are certified . every board that fails the verification process is indeed faulty , but 1 / 8 of those that pass are also faulty . approximately how many faulty circuit boards exist in a group of 3,200 circuit boards where 64 fail inspection ?", - "Output Program": [ - "n0 = 1.0\nn1 = 8.0\nn2 = 3200.0\nn3 = 64.0\nt0 = n0 / n1\nt1 = n2 - n3\nt2 = t0 * t1\nanswer = n3 + t2\nprint(answer)" - ], - "Output Answer": [ - "456" - ], - "split": "dev" - }, - { - "Input": "a girl multiplies 987 by a certain number and obtains 559981 as her answer . if in the answer , both 9 \u2019 s are wrong but the other digits are correct , then the correct answer will be", - "Output Program": [ - "n0 = 987.0\nn1 = 559981.0\nn2 = 9.0\nt0 = 1.0 + 4.0\nt1 = 2.0 * 3.0\nt2 = n2 * 10.0\nt3 = n2 + t2\nt4 = t0 * 10.0\nt5 = t1 + t4\nt6 = t3 * 100.0\nt7 = t5 * 100.0\nt8 = n1 - t6\nanswer = t7 + t8\nprint(answer)" - ], - "Output Answer": [ - "555681" - ], - "split": "dev" - }, - { - "Input": "a bag has 9 green balls and 23 pink balls . how many green balls should be added to the bag so that the ratio of green balls and pink balls in the bag becomes 1 : 1 ?", - "Output Program": [ - "n0 = 9.0\nn1 = 23.0\nn2 = 1.0\nn3 = 1.0\n\nanswer = n1 - n0\nprint(answer)" - ], - "Output Answer": [ - "14" - ], - "split": "dev" - }, - { - "Input": "in a family 13 people eat only vegetarian , 8 people eat only non veg . , 6 people eat both veg and non veg . . how many people eat veg in the family ?", - "Output Program": [ - "n0 = 13.0\nn1 = 8.0\nn2 = 6.0\n\nanswer = n0 + n2\nprint(answer)" - ], - "Output Answer": [ - "19" - ], - "split": "dev" - }, - { - "Input": "a number is said to be prime saturated if the product of all the different positive prime factors of t is less than the square root of t . what is the greatest two digit prime saturated integer ?", - "Output Program": [ - "t0 = 2.0 * 3.0\nt1 = 100.0 - 10.0\nanswer = t0 + t1\nprint(answer)" - ], - "Output Answer": [ - "96" - ], - "split": "dev" - }, - { - "Input": "right now , the ratio between the ages of sandy and molly is 4 : 3 . after 6 years , sandy \u2019 s age will be 66 years . what is molly ' s age right now ?", - "Output Program": [ - "n0 = 4.0\nn1 = 3.0\nn2 = 6.0\nn3 = 66.0\nt0 = n3 - n2\nt1 = t0 / n0\nanswer = n1 * t1\nprint(answer)" - ], - "Output Answer": [ - "45" - ], - "split": "dev" - }, - { - "Input": "the ratio of boys to girls is 6 : 4.60 % of the boys and 40 % of girls take lunch in the canteen . what % of class takes lunch ?", - "Output Program": [ - "n0 = 6.0\nn1 = 4.6\nn2 = 40.0\nt0 = n0 / 10.0\nt1 = 4.0 / 10.0\nt2 = 100.0 - n2\nt3 = t0 * t2\nt4 = n2 * t1\nanswer = t3 + t4\nprint(answer)" - ], - "Output Answer": [ - "52" - ], - "split": "dev" - }, - { - "Input": "there 3 kinds of books in the library physics , chemistry and biology . ratio of physics to chemistry is 3 to 2 ; ratio of chemistry to biology is 4 to 3 , and the total of the books is more than 3000 . which one of following can be the total w of the book ?", - "Output Program": [ - "n0 = 3.0\nn1 = 3.0\nn2 = 2.0\nn3 = 4.0\nn4 = 3.0\nn5 = 3000.0\n\nanswer = n0 + n5\nprint(answer)" - ], - "Output Answer": [ - "3003" - ], - "split": "dev" - }, - { - "Input": "a salesman sold twice as much pears in the afternoon than in the morning . if he sold $ 360 kilograms of pears that day , how many kilograms did he sell in the morning and how many in the afternoon ?", - "Output Program": [ - "n0 = 360.0\nt0 = n0 / 3.0\nanswer = t0 * 2.0\nprint(answer)" - ], - "Output Answer": [ - "240" - ], - "split": "dev" - }, - { - "Input": "cheese , bologna , and peanut butter sandwiches were made for a picnic in a ratio of 1 to 7 to 8 . if a total of 80 sandwiches were made , how many bologna sandwiches were made ?", - "Output Program": [ - "n0 = 1.0\nn1 = 7.0\nn2 = 8.0\nn3 = 80.0\nt0 = n0 + n1\nt1 = n2 + t0\nt2 = n3 / t1\nanswer = n1 * t2\nprint(answer)" - ], - "Output Answer": [ - "35" - ], - "split": "dev" - }, - { - "Input": "the compounded ratio of ( 2 : 3 ) , ( 6 : 11 ) and ( 11 : 2 ) is", - "Output Program": [ - "n0 = 2.0\nn1 = 3.0\nn2 = 6.0\nn3 = 11.0\nn4 = 11.0\nn5 = 2.0\nt0 = n3 / n0\nt1 = n0 / n1\nt2 = n2 / n3\nt3 = t1 * t2\nanswer = t0 * t3\nprint(answer)" - ], - "Output Answer": [ - "1.9999999999999998" - ], - "split": "dev" - }, - { - "Input": "90 kg of an alloy a is mixed with 140 kg of alloy b . if alloy a has lead and tin in the ratio 3 : 4 and alloy b has tin and copper in the ratio 2 : 5 , then the amount of tin in the new alloy is ?", - "Output Program": [ - "n0 = 90.0\nn1 = 140.0\nn2 = 3.0\nn3 = 4.0\nn4 = 2.0\nn5 = 5.0\nt0 = n2 + n3\nt1 = n4 + n5\nt2 = n0 / t0\nt3 = n1 / t1\nt4 = n3 * t2\nt5 = n4 * t3\nanswer = t4 + t5\nprint(answer)" - ], - "Output Answer": [ - "91.42857142857143" - ], - "split": "dev" - }, - { - "Input": "bucket p has thrice the capacity as bucket q . it takes 60 turns for bucket p to fill the empty drum . how many turns it will take for both the buckets p and q , having each turn together to fill the empty drum ?", - "Output Program": [ - "n0 = 60.0\nt0 = 1.0 / n0\nt1 = n0 * 3.0\nt2 = 1.0 / t1\nt3 = t0 + t2\nanswer = 1.0 / t3\nprint(answer)" - ], - "Output Answer": [ - "45" - ], - "split": "dev" - }, - { - "Input": "a certain high school has 500 students . of these students , 50 are taking music , 20 are taking art , and 10 are taking both music and art . how many students are taking neither music nor art ?", - "Output Program": [ - "n0 = 500.0\nn1 = 50.0\nn2 = 20.0\nn3 = 10.0\nt0 = n1 + n2\nt1 = t0 - n3\nanswer = n0 - t1\nprint(answer)" - ], - "Output Answer": [ - "440" - ], - "split": "dev" - }, - { - "Input": "praveen starts business with rs . 3920 and after 5 months , hari joins with praveen as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is hari \u2019 s contribution in the capital ?", - "Output Program": [ - "n0 = 3920.0\nn1 = 5.0\nn2 = 2.0\nn3 = 3.0\nt0 = n1 / 12.0\nt1 = n2 / n3\nt2 = 1.0 - t0\nt3 = n0 / t2\nanswer = t3 / t1\nprint(answer)" - ], - "Output Answer": [ - "10080.000000000002" - ], - "split": "dev" - }, - { - "Input": "100 people are attending a newspaper conference . 35 of them are writers and more than 38 are editors . of the people at the conference , x are both writers and editors and 2 x are neither . what is the largest possible number of people who are both writers and editors ?", - "Output Program": [ - "n0 = 100.0\nn1 = 35.0\nn2 = 38.0\nn3 = 2.0\nt0 = n2 + 1.0\nt1 = n1 + t0\nanswer = n0 - t1\nprint(answer)" - ], - "Output Answer": [ - "26" - ], - "split": "dev" - }, - { - "Input": "in a class of 45 students , 12 enrolled for both english and german . 22 enrolled for german . if the students of the class enrolled for at least one of the two subjects , then how many students enrolled for only english and not german ?", - "Output Program": [ - "n0 = 45.0\nn1 = 12.0\nn2 = 22.0\nt0 = n0 + n1\nt1 = t0 - n2\nanswer = t1 - n1\nprint(answer)" - ], - "Output Answer": [ - "23" - ], - "split": "dev" - }, - { - "Input": "there are 22 kids in a classroom . 12 kids are wearing socks and 8 are wearing shoes . 6 kids are wearing both . how many are bare feet ?", - "Output Program": [ - "n0 = 22.0\nn1 = 12.0\nn2 = 8.0\nn3 = 6.0\nt0 = n1 - n3\nt1 = n2 - n3\nt2 = t0 + t1\nt3 = n3 + t2\nanswer = n0 - t3\nprint(answer)" - ], - "Output Answer": [ - "8" - ], - "split": "dev" - }, - { - "Input": "ketchup , mustard and mayo bottles at a hot dog stand are in the ratio of 3 : 3 : 2 . if there are 6 ketchup bottles , the number of mayo bottles at the hot dog stand is :", - "Output Program": [ - "n0 = 3.0\nn1 = 3.0\nn2 = 2.0\nn3 = 6.0\nt0 = n3 / n0\nanswer = n2 * t0\nprint(answer)" - ], - "Output Answer": [ - "4" - ], - "split": "dev" - }, - { - "Input": "of the 200 stamps in a collection , 90 are foreign and 80 are more than 10 years old . if 20 stamps are both foreign and more than 10 years old , how many stamps are neither foreign nor more than 10 years old ?", - "Output Program": [ - "n0 = 200.0\nn1 = 90.0\nn2 = 80.0\nn3 = 10.0\nn4 = 20.0\nn5 = 10.0\nn6 = 10.0\nt0 = n1 + n2\nt1 = t0 - n4\nanswer = n0 - t1\nprint(answer)" - ], - "Output Answer": [ - "50" - ], - "split": "dev" - }, - { - "Input": "nitin ranks 24 th in a class of 58 students . what is rank from the last ?", - "Output Program": [ - "n0 = 24.0\nn1 = 58.0\n\nanswer = n1 - n0\nprint(answer)" - ], - "Output Answer": [ - "34" - ], - "split": "dev" - }, - { - "Input": "an urn contains 10 black and 5 white balls . two balls are drawn from the urn one after the other without replacement . what is the probability that both drawn balls are black ?", - "Output Program": [ - "n0 = 10.0\nn1 = 5.0\nt0 = n0 + n1\nt1 = n0 - 1.0\nt2 = n0 / t0\nt3 = t0 - 1.0\nt4 = t1 / t3\nanswer = t2 * t4\nprint(answer)" - ], - "Output Answer": [ - "0.4285714285714286" - ], - "split": "dev" - }, - { - "Input": "the probability of two events a and b are 0.20 and 0.40 respectively . the probability that both a and b occur is 0.15 . the probability that neither a nor b occur is _________", - "Output Program": [ - "n0 = 0.2\nn1 = 0.4\nn2 = 0.15\nt0 = n0 + n1\nt1 = t0 - n2\nanswer = 1.0 - t1\nprint(answer)" - ], - "Output Answer": [ - "0.5499999999999999" - ], - "split": "dev" - }, - { - "Input": "of the diplomats who attended a summit conference : 20 spoke japanese , 32 did not speak russian and 20 % of the diplomats spoke neither japanese nor russian . if 10 % of the diplomats spoke both japanese and russian , then how many diplomats attended the conference ?", - "Output Program": [ - "n0 = 20.0\nn1 = 32.0\nn2 = 20.0\nn3 = 10.0\nt0 = n0 / 100.0\nt1 = n3 / 100.0\nt2 = n1 - n0\nt3 = t0 - t1\nanswer = t2 / t3\nprint(answer)" - ], - "Output Answer": [ - "120" - ], - "split": "dev" - }, - { - "Input": "ratio between two numbers is 3 : 4 and their sum is 420 . find the smaller number ?", - "Output Program": [ - "n0 = 3.0\nn1 = 4.0\nn2 = 420.0\nt0 = n0 + n1\nt1 = n2 / t0\nanswer = n0 * t1\nprint(answer)" - ], - "Output Answer": [ - "180" - ], - "split": "dev" - }, - { - "Input": "uba capital recently bought brand new vehicles for office use . uba capital only went for toyota and honda and bought less of toyota than honda at the ratio of 7 : 3 . if 70 % of the toyota bought and 30 % of the honda bought were suv \u00e3 \u00a2 \u00e2 \u201a \u00ac \u00e2 \u201e \u00a2 s . how many suv \u00e3 \u00a2 \u00e2 \u201a \u00ac \u00e2 \u201e \u00a2 s did uba capital buy in the aforementioned purchase ?", - "Output Program": [ - "n0 = 7.0\nn1 = 3.0\nn2 = 70.0\nn3 = 30.0\nt0 = n0 * n1\nt1 = t0 + t0\nanswer = 100.0 - t1\nprint(answer)" - ], - "Output Answer": [ - "58" - ], - "split": "dev" - }, - { - "Input": "( 4 ! ) ^ n is a factor of 12 ! , but ( 4 ! ) ^ ( n + 1 ) is not factor of 12 ! . what is the value of n ?", - "Output Program": [ - "n0 = 4.0\nn1 = 12.0\nn2 = 4.0\nn3 = 1.0\nn4 = 12.0\nt0 = n0 + n3\nt1 = n1 / n1\nt2 = t0 + t1\nanswer = t2 - 3.0\nprint(answer)" - ], - "Output Answer": [ - "3" - ], - "split": "dev" - }, - { - "Input": "in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the sport formulation contains 8 ounces of corn syrup , how many ounces of water does it contain ?", - "Output Program": [ - "n0 = 1.0\nn1 = 12.0\nn2 = 30.0\nn3 = 8.0\nt0 = n0 / n1\nt1 = n0 / n2\nt2 = t1 / 2.0\nt3 = t0 * 3.0\nt4 = t3 / t2\nanswer = n3 * t4\nprint(answer)" - ], - "Output Answer": [ - "120" - ], - "split": "dev" - }, - { - "Input": "in a certain large company , the ratio of college graduates with a graduate degree to non - college graduates is 1 : 8 , and ratio of college graduates without a graduate degree to non - college graduates is 2 : 3 . if one picks a random college graduate at this large company , what is the probability q this college graduate has a graduate degree ?", - "Output Program": [ - "n0 = 1.0\nn1 = 8.0\nn2 = 2.0\nn3 = 3.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = t0 / t1\nt3 = t2 + n0\nanswer = t2 / t3\nprint(answer)" - ], - "Output Answer": [ - "0.15789473684210525" - ], - "split": "dev" - }, - { - "Input": "the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 15 . the larger of the two numbers is :", - "Output Program": [ - "n0 = 23.0\nn1 = 13.0\nn2 = 15.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "345" - ], - "split": "dev" - }, - { - "Input": "210 students were asked in a survey if they preferred windows or mac brand computers . 60 students claimed that they preferred mac to windows brand computers . one third as many of the students who preferred mac to windows , equally preferred both brands . 90 of the students had no preference . how many of the students in the survey preferred windows to mac brand computers ?", - "Output Program": [ - "n0 = 210.0\nn1 = 60.0\nn2 = 90.0\nt0 = n1 + n2\nt1 = n1 / 3.0\nt2 = t0 + t1\nanswer = n0 - t2\nprint(answer)" - ], - "Output Answer": [ - "40" - ], - "split": "dev" - }, - { - "Input": "the h . c . f . of two numbers is 25 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is :", - "Output Program": [ - "n0 = 25.0\nn1 = 13.0\nn2 = 14.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "350" - ], - "split": "dev" - }, - { - "Input": "in a sports club with 42 members , 20 play badminton and 23 play tennis and 6 do not play either . how many members play both badminton and tennis ?", - "Output Program": [ - "n0 = 42.0\nn1 = 20.0\nn2 = 23.0\nn3 = 6.0\nt0 = n1 + n2\nt1 = n3 + t0\nanswer = t1 - n0\nprint(answer)" - ], - "Output Answer": [ - "7" - ], - "split": "dev" - }, - { - "Input": "mrs . evans gave a test to her freshmen economics class , which has 29 students enrolled and 19 of them answered question 1 correctly . if 24 answered question 2 correctly and 5 did not take the test then how many answered both questions correctly ?", - "Output Program": [ - "n0 = 29.0\nn1 = 19.0\nn2 = 1.0\nn3 = 24.0\nn4 = 2.0\nn5 = 5.0\nt0 = n1 + n3\nt1 = n5 + t0\nanswer = t1 - n0\nprint(answer)" - ], - "Output Answer": [ - "19" - ], - "split": "dev" - }, - { - "Input": "in a school the ratio of boys and girls are in the ration 5 : 6 . 25 % of boys will get scholar ship and 20 % of girls will get scholar ship what % of students wont get scholarship ?", - "Output Program": [ - "n0 = 5.0\nn1 = 6.0\nn2 = 25.0\nn3 = 20.0\nt0 = n0 + n1\nt1 = 100.0 - n2\nt2 = 100.0 - n3\nt3 = t1 / 100.0\nt4 = n0 / t0\nt5 = t2 / 100.0\nt6 = n1 / t0\nt7 = t3 * t4\nt8 = t5 * t6\nt9 = t7 + t8\nanswer = t9 * 100.0\nprint(answer)" - ], - "Output Answer": [ - "77.72727272727272" - ], - "split": "dev" - }, - { - "Input": "right now , the ratio between the ages of sandy and molly is 4 : 3 . after 6 years , sandy \u2019 s age will be 38 years . what is molly ' s age right now ?", - "Output Program": [ - "n0 = 4.0\nn1 = 3.0\nn2 = 6.0\nn3 = 38.0\nt0 = n3 - n2\nt1 = t0 / n0\nanswer = n1 * t1\nprint(answer)" - ], - "Output Answer": [ - "24" - ], - "split": "dev" - }, - { - "Input": "from a container having pure milk , 20 % is replaced by water and the process is repeated thrice . at the end of the third operation , the milk is ?", - "Output Program": [ - "n0 = 20.0\nt0 = 100.0 - n0\nt1 = t0 / 100.0\nt2 = t1**min(3.0, 5)\nanswer = t2 * 100.0\nprint(answer)" - ], - "Output Answer": [ - "51.20000000000001" - ], - "split": "dev" - }, - { - "Input": "a bag contains 10 green and 8 white balls . if two balls are drawn simultaneously , the probability that both are of the same colour is", - "Output Program": [ - "n0 = 10.0\nn1 = 8.0\nt0 = n0 + n1\nt1 = n1 - 1.0\nt2 = n0 - 1.0\nt3 = n1 / t0\nt4 = n0 / t0\nt5 = t0 - 1.0\nt6 = t1 / t5\nt7 = t2 / t5\nt8 = t3 * t6\nt9 = t4 * t7\nanswer = t8 + t9\nprint(answer)" - ], - "Output Answer": [ - "0.4771241830065359" - ], - "split": "dev" - }, - { - "Input": "of the diplomats attending a summit conference , 25 speak french , 32 do not speak russian , and 20 % of the diplomats speak neither french nor russian . if 10 % of the diplomats speak both languages , then how many diplomats attended the conference ?", - "Output Program": [ - "n0 = 25.0\nn1 = 32.0\nn2 = 20.0\nn3 = 10.0\nt0 = n2 / 100.0\nt1 = n3 / 100.0\nt2 = n1 - n0\nt3 = t0 - t1\nanswer = t2 / t3\nprint(answer)" - ], - "Output Answer": [ - "70" - ], - "split": "dev" - }, - { - "Input": "in a group of 150 readers who read science fiction or literacy works or both , 120 read science fiction and 90 read literacy works . how many read both science fiction and literacy works ?", - "Output Program": [ - "n0 = 150.0\nn1 = 120.0\nn2 = 90.0\nt0 = n1 + n2\nanswer = t0 - n0\nprint(answer)" - ], - "Output Answer": [ - "60" - ], - "split": "dev" - }, - { - "Input": "at garage sale , all of the prices of the items sold were different . if the price of a radio sold at the garage sale was both the 9 th highest price and the 35 th lowest price among the prices of the items sold , how many items were sold at the garage sale ?", - "Output Program": [ - "n0 = 9.0\nn1 = 35.0\nt0 = n0 + n1\nanswer = t0 - 1.0\nprint(answer)" - ], - "Output Answer": [ - "43" - ], - "split": "dev" - }, - { - "Input": "a company conducted a survey about its two brands , a and b . x percent of respondents liked product a , ( x \u2013 20 ) percent liked product b , 23 percent liked both products , and 23 percent liked neither product . what is the minimum number g of people surveyed by the company ?", - "Output Program": [ - "n0 = 20.0\nn1 = 23.0\nn2 = 23.0\nt0 = 100.0 - n1\nt1 = n1 + t0\nt2 = n0 + t1\nt3 = t2 / 2.0\nt4 = t3 - n0\nanswer = t3 + t4\nprint(answer)" - ], - "Output Answer": [ - "100" - ], - "split": "dev" - }, - { - "Input": "the weights of one liter vegetable ghee packet of two brands \u2018 a \u2019 and \u2018 b \u2019 are 800 gm and 850 gm respectively . if they are mixed in the ratio of 3 : 2 by volumes to form a mixture of 3 liters , what is the weight ( in kg ) of the mixture ?", - "Output Program": [ - "n0 = 800.0\nn1 = 850.0\nn2 = 3.0\nn3 = 2.0\nn4 = 3.0\nt0 = n2 + n3\nt1 = n0 * n2\nt2 = n1 * n3\nt3 = t1 + t2\nt4 = n4 * t3\nt5 = t4 / t0\nanswer = t5 / 1000.0\nprint(answer)" - ], - "Output Answer": [ - "2.46" - ], - "split": "dev" - }, - { - "Input": "in a college the ratio of the numbers of boys to the girls is 8 : 5 . if there are 210 girls , the total number of students in the college is ?", - "Output Program": [ - "n0 = 8.0\nn1 = 5.0\nn2 = 210.0\nt0 = n0 / n1\nt1 = n2 * t0\nanswer = n2 + t1\nprint(answer)" - ], - "Output Answer": [ - "546" - ], - "split": "dev" - }, - { - "Input": "a woman bought a pack of 36 eggs , but the seller told her that there were 3 rotten eggs in the pack . she forgot it and begun to prepare a recipe that needs 2 eggs . what is the probability that both choosen eggs will be rotten ?", - "Output Program": [ - "n0 = 36.0\nn1 = 3.0\nn2 = 2.0\nt0 = n1 / n0\nt1 = n0 - 1.0\nt2 = n2 / t1\nanswer = t2 * t0\nprint(answer)" - ], - "Output Answer": [ - "0.0047619047619047615" - ], - "split": "dev" - }, - { - "Input": "if a student loses 6 kilograms , he will weigh twice as much as his sister . together they now weigh 126 kilograms . what is the student ' s present weight in kilograms ?", - "Output Program": [ - "n0 = 6.0\nn1 = 126.0\nt0 = n1 - n0\nt1 = t0 / 3.0\nanswer = n1 - t1\nprint(answer)" - ], - "Output Answer": [ - "86" - ], - "split": "test" - }, - { - "Input": "the ratio between the present ages of a and b is 7 : 3 respectively . the ratio between a ' s age 4 years ago and b ' s age 4 years hence is 1 : 1 . what is the ratio between a ' s age 4 years hence and b ' s age 4 years ago ?", - "Output Program": [ - "n0 = 7.0\nn1 = 3.0\nn2 = 4.0\nn3 = 4.0\nn4 = 1.0\nn5 = 1.0\nn6 = 4.0\nn7 = 4.0\nt0 = n0 + n0\nt1 = n0 - n1\nt2 = t0 / t1\nt3 = n0 * t2\nt4 = n1 * t2\nt5 = n0 + t3\nt6 = t4 - n0\nanswer = t5 / t6\nprint(answer)" - ], - "Output Answer": [ - "9" - ], - "split": "test" - }, - { - "Input": "at the faculty of aerospace engineering , 312 students study random - processing methods , 232 students study scramjet rocket engines and 112 students study them both . if every student in the faculty has to study one of the two subjects , how many students are there in the faculty of aerospace engineering ?", - "Output Program": [ - "n0 = 312.0\nn1 = 232.0\nn2 = 112.0\nt0 = n2 / 2.0\nt1 = n0 - t0\nt2 = n1 - t0\nanswer = t1 + t2\nprint(answer)" - ], - "Output Answer": [ - "432" - ], - "split": "test" - }, - { - "Input": "the h . c . f . of two numbers is 10 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is :", - "Output Program": [ - "n0 = 10.0\nn1 = 13.0\nn2 = 14.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "140" - ], - "split": "test" - }, - { - "Input": "a began business with rs . 27000 and was joined afterwards by b with rs . 54000 . when did b join if the profits at the end of the year were divided in the ratio of 2 : 1 ?", - "Output Program": [ - "n0 = 27000.0\nn1 = 54000.0\nn2 = 2.0\nn3 = 1.0\nt0 = 3.0 * 4.0\nt1 = n0 * t0\nt2 = t1 / n1\nt3 = t2 / n2\nanswer = t0 - t3\nprint(answer)" - ], - "Output Answer": [ - "9" - ], - "split": "test" - }, - { - "Input": "if 65 percent of a class answered the first question on a certain test correctly , 50 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?", - "Output Program": [ - "n0 = 65.0\nn1 = 50.0\nn2 = 20.0\nt0 = n0 + n1\nt1 = n2 + t0\nanswer = t1 - 100.0\nprint(answer)" - ], - "Output Answer": [ - "35" - ], - "split": "test" - }, - { - "Input": "in the class of 50 students , 30 speak tamil and 40 speak telugu . what is the lowest possible number of students who speak both the languages ?", - "Output Program": [ - "n0 = 50.0\nn1 = 30.0\nn2 = 40.0\nt0 = n1 + n2\nanswer = t0 - n0\nprint(answer)" - ], - "Output Answer": [ - "20" - ], - "split": "test" - }, - { - "Input": "a ratio between two numbers is 4 : 5 and their l . c . m . is 200 . the first number is", - "Output Program": [ - "n0 = 4.0\nn1 = 5.0\nn2 = 200.0\nt0 = n0 * n1\nt1 = n2 / t0\nanswer = n0 * t1\nprint(answer)" - ], - "Output Answer": [ - "40" - ], - "split": "test" - }, - { - "Input": "45 pupil , out of them 12 in debate only and 22 in singing only . then how many in both ?", - "Output Program": [ - "n0 = 45.0\nn1 = 12.0\nn2 = 22.0\nt0 = n1 + n2\nanswer = n0 - t0\nprint(answer)" - ], - "Output Answer": [ - "11" - ], - "split": "test" - }, - { - "Input": "of the 75 cars on a car lot , 45 have air - conditioning , 35 have power steering , and 12 have both air - conditioning and power steering . how many of the cars on the lot have neither air - conditioning nor power steering ?", - "Output Program": [ - "n0 = 75.0\nn1 = 45.0\nn2 = 35.0\nn3 = 12.0\nt0 = n1 + n2\nt1 = t0 - n3\nanswer = n0 - t1\nprint(answer)" - ], - "Output Answer": [ - "7" - ], - "split": "test" - }, - { - "Input": "in a sports club with 55 members , 23 play badminton and 29 play tennis and 7 do not play either . how many members play both badminton and tennis ?", - "Output Program": [ - "n0 = 55.0\nn1 = 23.0\nn2 = 29.0\nn3 = 7.0\nt0 = n1 + n2\nt1 = n3 + t0\nanswer = t1 - n0\nprint(answer)" - ], - "Output Answer": [ - "4" - ], - "split": "test" - }, - { - "Input": "find the greatest common factor ( gfc ) of 24 , 40 and 60 .", - "Output Program": [ - "import scipy\nn0 = 24.0\nn1 = 40.0\nn2 = 60.0\nt0 = scipy.gcd(int(n0), int(n1))\nanswer = scipy.gcd(int(n2), int(t0))\nprint(answer)" - ], - "Output Answer": [ - "4" - ], - "split": "test" - }, - { - "Input": "in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the ` ` sport ' ' formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the ` ` sport ' ' formulation contains 3 ounces of corn syrup , how many ounces of water does it contain ?", - "Output Program": [ - "n0 = 1.0\nn1 = 12.0\nn2 = 30.0\nn3 = 3.0\nn4 = 3.0\nt0 = n1 / 3.0\nt1 = n2 * 2.0\nt2 = n3 / t0\nanswer = t2 * t1\nprint(answer)" - ], - "Output Answer": [ - "45" - ], - "split": "test" - }, - { - "Input": "a group of people participate in some curriculum , 30 of them practice yoga , 20 study cooking , 15 study weaving , 5 of them study cooking only , 8 of them study both the cooking and yoga , 5 of them participate all curriculums . how many people study both cooking and weaving ?", - "Output Program": [ - "n0 = 30.0\nn1 = 20.0\nn2 = 15.0\nn3 = 5.0\nn4 = 8.0\nn5 = 5.0\nt0 = n1 - n4\nt1 = t0 - n5\nanswer = t1 - n3\nprint(answer)" - ], - "Output Answer": [ - "2" - ], - "split": "test" - }, - { - "Input": "a starts business with rs . 3500 and after 5 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b ' s contribution in the capital ?", - "Output Program": [ - "n0 = 3500.0\nn1 = 5.0\nn2 = 2.0\nn3 = 3.0\nt0 = n0 * 12.0\nt1 = 12.0 - n1\nt2 = n3 * t0\nt3 = n2 * t1\nanswer = t2 / t3\nprint(answer)" - ], - "Output Answer": [ - "9000" - ], - "split": "test" - }, - { - "Input": "a bag contains 7 green and 8 white balls . if two balls are drawn simultaneously , the probability that both are of the same colour is - .", - "Output Program": [ - "n0 = 7.0\nn1 = 8.0\nt0 = n0 + n1\nt1 = n1 - 1.0\nt2 = n0 - 1.0\nt3 = n1 / t0\nt4 = n0 / t0\nt5 = t0 - 1.0\nt6 = t1 / t5\nt7 = t2 / t5\nt8 = t3 * t6\nt9 = t4 * t7\nanswer = t8 + t9\nprint(answer)" - ], - "Output Answer": [ - "0.4666666666666667" - ], - "split": "test" - }, - { - "Input": "a group of people participate in some curriculum , 30 of them practice yoga , 25 study cooking , 15 study weaving , 6 of them study cooking only , 8 of them study both the cooking and yoga , 7 of them participate all curriculums . how many people study both cooking and weaving ?", - "Output Program": [ - "n0 = 30.0\nn1 = 25.0\nn2 = 15.0\nn3 = 6.0\nn4 = 8.0\nn5 = 7.0\nt0 = n1 - n4\nt1 = t0 - n5\nanswer = t1 - n3\nprint(answer)" - ], - "Output Answer": [ - "4" - ], - "split": "test" - }, - { - "Input": "each of the dogs in a certain kennel is a single color . each of the dogs in the kennel either has long fur or does not . of the 45 dogs in the kennel , 28 have long fur , 17 are brown , and 8 are neither long - furred nor brown . how many long - furred dogs are brown ?", - "Output Program": [ - "n0 = 45.0\nn1 = 28.0\nn2 = 17.0\nn3 = 8.0\nt0 = n1 + n2\nt1 = n0 - n3\nanswer = t0 - t1\nprint(answer)" - ], - "Output Answer": [ - "8" - ], - "split": "test" - }, - { - "Input": "at a wedding reception , 125 guests ate chicken and 75 guests ate beef . if exactly 100 guests ate only one of the two types of meat , how many guests ate both types of meat ?", - "Output Program": [ - "n0 = 125.0\nn1 = 75.0\nn2 = 100.0\nt0 = n0 - n2\nt1 = n2 - n1\nanswer = t0 + t1\nprint(answer)" - ], - "Output Answer": [ - "50" - ], - "split": "test" - }, - { - "Input": "a starts business with rs . 3500 and after 5 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b ' s contribution in the capital", - "Output Program": [ - "n0 = 3500.0\nn1 = 5.0\nn2 = 2.0\nn3 = 3.0\nt0 = n0 * 12.0\nt1 = 12.0 - n1\nt2 = n3 * t0\nt3 = n2 * t1\nanswer = t2 / t3\nprint(answer)" - ], - "Output Answer": [ - "9000" - ], - "split": "test" - }, - { - "Input": "you need to print a document of the area 216 sq cm . condition is 3 cm margin is to be left at both top & bottom and 2 cm at the sides . what is the optimized size of your paper ?", - "Output Program": [ - "n0 = 216.0\nn1 = 3.0\nn2 = 2.0\nt0 = n1 * 2.0\nt1 = n2 * 2.0\nt2 = 3.0**min(2.0, 5)\nt3 = n0 / t2\nt4 = t2 - t1\nt5 = t3 - t0\nanswer = t5 * t4\nprint(answer)" - ], - "Output Answer": [ - "90" - ], - "split": "test" - }, - { - "Input": "24 oz of juice p and 25 oz of juice v are mixed to make smothies x and y . the ratio of p to v in smothie x is 4 is to 1 and that in y is 1 is to 5 . how many ounces of juice p are contained in the smothie x ?", - "Output Program": [ - "n0 = 24.0\nn1 = 25.0\nn2 = 4.0\nn3 = 1.0\nn4 = 1.0\nn5 = 5.0\n\nanswer = n1 * n3\nprint(answer)" - ], - "Output Answer": [ - "25" - ], - "split": "test" - }, - { - "Input": "the h . c . f . of two numbers is 18 and the other two factors of their l . c . m . are 11 and 15 . the larger of the two numbers is :", - "Output Program": [ - "n0 = 18.0\nn1 = 11.0\nn2 = 15.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "270" - ], - "split": "test" - }, - { - "Input": "the ratio of buses to cars on river road is 1 to 3 . if there are 20 fewer buses than cars on river road , how many cars are on river road ?", - "Output Program": [ - "n0 = 1.0\nn1 = 3.0\nn2 = 20.0\nt0 = n1 - n0\nt1 = n2 / t0\nanswer = n1 * t1\nprint(answer)" - ], - "Output Answer": [ - "30" - ], - "split": "test" - }, - { - "Input": "a bag contains 12 red marbles . if someone were to remove 2 marbles from the bag , one at a time , and replace the first marble after it was removed , the probability that neither marble would be red is 49 / 64 . how many marbles are in the bag ?", - "Output Program": [ - "import math\nn0 = 12.0\nn1 = 2.0\nn2 = 49.0\nn3 = 64.0\nt0 = n2 / n3\nt1 = math.sqrt(max(0, t0))\nt2 = 1.0 - t1\nanswer = n0 / t2\nprint(answer)" - ], - "Output Answer": [ - "96" - ], - "split": "test" - }, - { - "Input": "in a certain pet shop , the ratio of dogs to cats to bunnies in stock is 3 : 7 : 13 . if the shop carries 352 dogs and bunnies total in stock , how many dogs are there ?", - "Output Program": [ - "n0 = 3.0\nn1 = 7.0\nn2 = 13.0\nn3 = 352.0\nt0 = n0 + n2\nt1 = n3 / t0\nanswer = n0 * t1\nprint(answer)" - ], - "Output Answer": [ - "66" - ], - "split": "test" - }, - { - "Input": "in a certain state , the ratio of registered republicans to registered democrats is 3 to 2 , and every registered voter is either a republican or a democrat . if 80 percent of the republicans and 20 percent of the democrats are expected to vote for candidate x , and everyone else is expected to vote for candidate y , by what percent is candidate x expected to win the election ?", - "Output Program": [ - "n0 = 3.0\nn1 = 2.0\nn2 = 80.0\nn3 = 20.0\nt0 = n0 + n1\nt1 = n3 / 100.0\nt2 = n2 / 100.0\nt3 = n1 * t1\nt4 = n0 * t2\nt5 = t3 + t4\nt6 = n0 - t4\nt7 = n1 - t3\nt8 = t6 + t7\nt9 = t5 - t8\nt10 = t9 / t0\nanswer = t10 * 100.0\nprint(answer)" - ], - "Output Answer": [ - "12.00000000000001" - ], - "split": "test" - }, - { - "Input": "how many odd factors does 210 have ?", - "Output Program": [ - "n0 = 210.0\nt0 = 2.0 + 4.0\nt1 = t0 + 1.0\nanswer = t1 + 1.0\nprint(answer)" - ], - "Output Answer": [ - "8" - ], - "split": "test" - }, - { - "Input": "the ratio of numbers is 5 : 6 and their h . c . f is 4 . their l . c . m is :", - "Output Program": [ - "import scipy\nn0 = 5.0\nn1 = 6.0\nn2 = 4.0\nt0 = n0 * n2\nt1 = n1 * n2\nanswer = scipy.lcm(int(t0), int(t1))\nprint(answer)" - ], - "Output Answer": [ - "120" - ], - "split": "test" - }, - { - "Input": "a certain quantity of 50 % solution is replaced with 25 % solution such that the new concentration is 35 % . what is the fraction of the solution that was replaced ?", - "Output Program": [ - "n0 = 50.0\nn1 = 25.0\nn2 = 35.0\nt0 = n2 - n1\nt1 = n0 - n2\nt2 = t0 / t1\nt3 = t2 + 1.0\nanswer = 1 / t3\nprint(answer)" - ], - "Output Answer": [ - "0.6000000000000001" - ], - "split": "test" - }, - { - "Input": "11 different biology books and 8 different chemistry books lie on a shelf . in how many ways can a student pick 2 books of each type ?", - "Output Program": [ - "import math\nn0 = 11.0\nn1 = 8.0\nn2 = 2.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(n1)))\nt2 = n0 - n2\nt3 = n1 - n2\nt4 = math.factorial(min(15, int(t2)))\nt5 = math.factorial(min(15, int(t3)))\nt6 = t0 / t4\nt7 = t1 / t5\nt8 = t6 / n2\nt9 = t7 / n2\nanswer = t8 * t9\nprint(answer)" - ], - "Output Answer": [ - "1540" - ], - "split": "test" - }, - { - "Input": "a certain bag contains 100 balls \u00e2 \u20ac \u201d 50 white , 25 green , 10 yellow , 7 red , and 8 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?", - "Output Program": [ - "n0 = 100.0\nn1 = 50.0\nn2 = 25.0\nn3 = 10.0\nn4 = 7.0\nn5 = 8.0\nt0 = n4 + n5\nt1 = n0 - t0\nanswer = t1 / n0\nprint(answer)" - ], - "Output Answer": [ - "0.85" - ], - "split": "test" - }, - { - "Input": "ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 30 years . what is deepak present age ?", - "Output Program": [ - "n0 = 4.0\nn1 = 3.0\nn2 = 6.0\nn3 = 30.0\nt0 = n3 - n2\nt1 = n1 * t0\nanswer = t1 / n0\nprint(answer)" - ], - "Output Answer": [ - "18" - ], - "split": "test" - }, - { - "Input": "of the diplomats attending a summit conference , 30 speak french , 32 do not speak russian , and 20 % of the diplomats speak neither french nor russian . if 10 % of the diplomats speak both languages , then how many diplomats attended the conference ?", - "Output Program": [ - "n0 = 30.0\nn1 = 32.0\nn2 = 20.0\nn3 = 10.0\nt0 = n2 / 100.0\nt1 = n3 / 100.0\nt2 = n1 - n0\nt3 = t0 - t1\nanswer = t2 / t3\nprint(answer)" - ], - "Output Answer": [ - "20" - ], - "split": "test" - }, - { - "Input": "a salesman sold twice as much pears in the afternoon than in the morning . if he sold $ 450 kilograms of pears that day , how many kilograms did he sell in the afternoon ?", - "Output Program": [ - "n0 = 450.0\nt0 = n0 / 3.0\nanswer = t0 * 2.0\nprint(answer)" - ], - "Output Answer": [ - "300" - ], - "split": "test" - }, - { - "Input": "in a class of 54 students , 12 enrolled for both english and german . 22 enrolled for german . if the students of the class enrolled for at least one of the two subjects , then how many students enrolled for only english and not german ?", - "Output Program": [ - "n0 = 54.0\nn1 = 12.0\nn2 = 22.0\nt0 = n0 + n1\nt1 = t0 - n2\nanswer = t1 - n1\nprint(answer)" - ], - "Output Answer": [ - "32" - ], - "split": "test" - }, - { - "Input": "forks , spoons , and knives in drawer are in the ratio of 4 : 4 : 3 . if there are 16 forks , the number of knives in the drawer is :", - "Output Program": [ - "n0 = 4.0\nn1 = 4.0\nn2 = 3.0\nn3 = 16.0\nt0 = n3 / n0\nanswer = n2 * t0\nprint(answer)" - ], - "Output Answer": [ - "12" - ], - "split": "test" - }, - { - "Input": "of the 75 house in a development , 50 have a two - car garage , 40 have an in - the - ground swimming pool , and 35 have both a two - car garage and an in - the - ground swimming pool . how many houses in the development have neither a two - car garage nor an in - the - ground swimming pool ?", - "Output Program": [ - "n0 = 75.0\nn1 = 50.0\nn2 = 40.0\nn3 = 35.0\nt0 = n1 - n3\nt1 = n2 - n3\nt2 = t0 + t1\nt3 = n3 + t2\nanswer = n0 - t3\nprint(answer)" - ], - "Output Answer": [ - "20" - ], - "split": "test" - }, - { - "Input": "in a certain large company , the ratio of college graduates with a graduate degree to non - college graduates is 1 : 8 , and ratio of college graduates without a graduate degree to non - college graduates is 2 : 3 . if one picks a random college graduate at this large company , what is the probability w this college graduate has a graduate degree ?", - "Output Program": [ - "n0 = 1.0\nn1 = 8.0\nn2 = 2.0\nn3 = 3.0\nt0 = n0 / n1\nt1 = n2 / n3\nt2 = t0 / t1\nt3 = t2 + n0\nanswer = t2 / t3\nprint(answer)" - ], - "Output Answer": [ - "0.15789473684210525" - ], - "split": "test" - }, - { - "Input": "what number has a 4 : 1 ratio to the number 100 ?", - "Output Program": [ - "n0 = 4.0\nn1 = 1.0\nn2 = 100.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "400" - ], - "split": "test" - }, - { - "Input": "a certain fruit stand sold apples for $ 0.70 each and guava for $ 0.50 each . if a customer purchased both apples and bananas from the stand for a total of $ 6.30 , what total number of apples and bananas did the customer purchase ?", - "Output Program": [ - "n0 = 0.7\nn1 = 0.5\nn2 = 6.3\nt0 = n0 * 4.0\nt1 = n2 - t0\nt2 = t1 / n1\nanswer = t2 + 4.0\nprint(answer)" - ], - "Output Answer": [ - "11" - ], - "split": "test" - }, - { - "Input": "if 25 % of the 880 students at a certain college are enrolled in biology classes , how many students at the college are not enrolled in a biology class ?", - "Output Program": [ - "n0 = 25.0\nn1 = 880.0\nt0 = n1 / 100.0\nt1 = 100.0 - n0\nanswer = t0 * t1\nprint(answer)" - ], - "Output Answer": [ - "660" - ], - "split": "test" - }, - { - "Input": "find the number of different prime factors of 25650", - "Output Program": [ - "n0 = 25650.0\n\nanswer = 2.0 + 2.0\nprint(answer)" - ], - "Output Answer": [ - "4" - ], - "split": "test" - }, - { - "Input": "in a group of 95 students , 36 are taking history , and 32 are taking statistics . if 59 students are taking history or statistics or both , then how many students are taking history but not statistics ?", - "Output Program": [ - "n0 = 95.0\nn1 = 36.0\nn2 = 32.0\nn3 = 59.0\nt0 = n1 + n2\nt1 = t0 - n3\nanswer = n1 - t1\nprint(answer)" - ], - "Output Answer": [ - "27" - ], - "split": "test" - }, - { - "Input": "how many factors of 60 are odd numbers greater than 1 ?", - "Output Program": [ - "n0 = 60.0\nn1 = 1.0\nt0 = 10.0 * 2.0\nanswer = n0 / t0\nprint(answer)" - ], - "Output Answer": [ - "3" - ], - "split": "test" - }, - { - "Input": "in a certain school , the ratio of boys to girls is 5 to 13 . if there are 160 more girls than boys , how many boys are there ?", - "Output Program": [ - "n0 = 5.0\nn1 = 13.0\nn2 = 160.0\nt0 = n0 / n1\nt1 = 1.0 - t0\nt2 = n2 / t1\nanswer = t2 - n2\nprint(answer)" - ], - "Output Answer": [ - "100" - ], - "split": "test" - }, - { - "Input": "out of 400 students of a school , 325 play football , 175 play cricket and 50 neither play football nor cricket . how many students play both football and cricket ?", - "Output Program": [ - "n0 = 400.0\nn1 = 325.0\nn2 = 175.0\nn3 = 50.0\nt0 = n1 + n2\nt1 = n0 - n3\nanswer = t0 - t1\nprint(answer)" - ], - "Output Answer": [ - "150" - ], - "split": "test" - }, - { - "Input": "a boy multiplied 987 by a certain number and obtained 559981 as his answer . if in the answer both 9 are wrong and the other digits are correct , then the correct answer would be :", - "Output Program": [ - "n0 = 987.0\nn1 = 559981.0\nn2 = 9.0\nt0 = n1 / n0\nt1 = t0 - 4.0\nt2 = t1 - 0.33\nanswer = n0 * t2\nprint(answer)" - ], - "Output Answer": [ - "555707.2899999999" - ], - "split": "test" - }, - { - "Input": "if the ratio of the sum of the first 6 terms of a g . p . to the sum of the first 3 terms of the g . p . is 65 , what is the common ratio of the g . p ?", - "Output Program": [ - "n0 = 6.0\nn1 = 3.0\nn2 = 65.0\nt0 = 1.0 / 3.0\nt1 = n2 - 1.0\nanswer = t1**min(t0, 5)\nprint(answer)" - ], - "Output Answer": [ - "3.9999999999999996" - ], - "split": "test" - }, - { - "Input": "a girl scout was selling boxes of cookies . in a month , she sold both boxes of chocolate chip cookies ( $ 1.25 each ) and boxes of plain cookies ( $ 0.75 each ) . altogether , she sold 1,585 boxes for a combined value of $ 1 , 585.75 . how many boxes of plain cookies did she sell ?", - "Output Program": [ - "n0 = 1.25\nn1 = 0.75\nn2 = 1585.0\nn3 = 1.0\nn4 = 585.75\nt0 = n4 + 1000.0\nanswer = t0 / 2.0\nprint(answer)" - ], - "Output Answer": [ - "792.875" - ], - "split": "test" - }, - { - "Input": "the ratio of spinsters to cats is 2 to 7 . if there are 40 more cats than spinsters , how many spinsters are there ?", - "Output Program": [ - "n0 = 2.0\nn1 = 7.0\nn2 = 40.0\nt0 = n1 - n0\nt1 = n2 / t0\nanswer = n0 * t1\nprint(answer)" - ], - "Output Answer": [ - "16" - ], - "split": "test" - }, - { - "Input": "in a sports club with 30 members , 17 play badminton and 18 play tennis and 2 do not play either . how many members play both badminton and tennis ?", - "Output Program": [ - "n0 = 30.0\nn1 = 17.0\nn2 = 18.0\nn3 = 2.0\nt0 = n1 + n2\nt1 = n3 + t0\nanswer = t1 - n0\nprint(answer)" - ], - "Output Answer": [ - "7" - ], - "split": "test" - }, - { - "Input": "24 oz of juice p and 25 oz of juice t are mixed to make smothies x and y . the ratio of p to t in smothie x is 4 is to 1 and that in y is 1 is to 5 . how many ounces of juice p are contained in the smothie x ?", - "Output Program": [ - "n0 = 24.0\nn1 = 25.0\nn2 = 4.0\nn3 = 1.0\nn4 = 1.0\nn5 = 5.0\nt0 = n1 * n2\nt1 = n2 * n5\nt2 = t0 - n0\nt3 = t1 - n3\nt4 = t2 / t3\nanswer = n0 - t4\nprint(answer)" - ], - "Output Answer": [ - "20" - ], - "split": "test" - }, - { - "Input": "if 85 percent of the test takers taking an old paper and pencil gmat exam answered the first question on a given math section correctly , and 75 percent of the test takers answered the second question correctly , and 15 percent of the test takers answered neither question correctly , what percent answered both correctly ?", - "Output Program": [ - "n0 = 85.0\nn1 = 75.0\nn2 = 15.0\nt0 = n0 + n1\nt1 = n2 + t0\nanswer = t1 - 100.0\nprint(answer)" - ], - "Output Answer": [ - "75" - ], - "split": "test" - }, - { - "Input": "mrs . evans gave a test to her freshmen economics class , which has 29 students enrolled and 24 of them answered question 1 correctly . if 22 answered question 2 correctly and 5 did not take the test then how many answered both questions correctly ?", - "Output Program": [ - "n0 = 29.0\nn1 = 24.0\nn2 = 1.0\nn3 = 22.0\nn4 = 2.0\nn5 = 5.0\nt0 = n1 + n3\nt1 = n5 + t0\nanswer = t1 - n0\nprint(answer)" - ], - "Output Answer": [ - "22" - ], - "split": "test" - }, - { - "Input": "there are 240 doctors and nurses at a hospital . if the ratio of doctors to nurses is 3 to 7 , how many nurses are at the hospital ?", - "Output Program": [ - "n0 = 240.0\nn1 = 3.0\nn2 = 7.0\nt0 = n1 + n2\nt1 = n0 / t0\nanswer = n2 * t1\nprint(answer)" - ], - "Output Answer": [ - "168" - ], - "split": "test" - }, - { - "Input": "in a group of 15 people , 8 read english , 7 read french while 3 of them read none of these two . how many of them read french and english both ?", - "Output Program": [ - "n0 = 15.0\nn1 = 8.0\nn2 = 7.0\nn3 = 3.0\nt0 = n1 + n2\nt1 = n0 - n3\nanswer = t0 - t1\nprint(answer)" - ], - "Output Answer": [ - "3" - ], - "split": "test" - }, - { - "Input": "in a class total 34 students , 16 are have a brother , 15 are have sisters , 9 students do n ' t have either brothers or sisters . find the number of students having both brother and sisters .", - "Output Program": [ - "n0 = 34.0\nn1 = 16.0\nn2 = 15.0\nn3 = 9.0\nt0 = n1 + n2\nt1 = n0 - n3\nanswer = t0 - t1\nprint(answer)" - ], - "Output Answer": [ - "6" - ], - "split": "test" - }, - { - "Input": "a company conducted a survey about its two brands , a and b . x percent of respondents liked product a , ( x \u2013 20 ) percent liked product b , 23 percent liked both products , and 23 percent liked neither product . what is the minimum number w of people surveyed by the company ?", - "Output Program": [ - "n0 = 20.0\nn1 = 23.0\nn2 = 23.0\nt0 = 100.0 - n1\nt1 = n1 + t0\nt2 = n0 + t1\nt3 = t2 / 2.0\nt4 = t3 - n0\nanswer = t3 + t4\nprint(answer)" - ], - "Output Answer": [ - "100" - ], - "split": "test" - }, - { - "Input": "what is the number of integers from 1 to 1000 ( inclusive ) that are divisible by neither 20 nor by 35 ?", - "Output Program": [ - "n0 = 1.0\nn1 = 1000.0\nn2 = 20.0\nn3 = 35.0\nt0 = n1 / n2\nt1 = n1 / n3\nt2 = n2 * n3\nt3 = t0 + t1\nt4 = n1 / t2\nt5 = t3 - t4\nanswer = n1 - t5\nprint(answer)" - ], - "Output Answer": [ - "922.8571428571429" - ], - "split": "test" - }, - { - "Input": "each person in a group of 110 investors has investments in either equities or securities or both . exactly 25 of the investors in equities have investments in securities , and exactly 40 of the investors in securities have investments in equities . how many have investments in equities ?", - "Output Program": [ - "n0 = 110.0\nn1 = 25.0\nn2 = 40.0\nt0 = n2 / 100.0\nt1 = n1 / 100.0\nt2 = t0 / t1\nt3 = t2 * t1\nt4 = 1.0 - t3\nt5 = t2 - t3\nt6 = t3 + t4\nt7 = t6 + t5\nt8 = n0 / t7\nanswer = t8 * t2\nprint(answer)" - ], - "Output Answer": [ - "80" - ], - "split": "test" - }, - { - "Input": "a dog breeder currently has 9 breeding dogs . 6 of the dogs have exactly 1 littermate , and 3 of the dogs have exactly 2 littermates . if 2 dogs are selected at random , what is the probability e that both selected dogs are not littermates ?", - "Output Program": [ - "n0 = 9.0\nn1 = 6.0\nn2 = 1.0\nn3 = 3.0\nn4 = 2.0\nn5 = 2.0\n\nanswer = 5.0 / n1\nprint(answer)" - ], - "Output Answer": [ - "0.8333333333333334" - ], - "split": "test" - }, - { - "Input": "a student committee on academic integrity has 56 ways to select a president and vice president from a group of candidates . the same person can not be both president and vice president . how many candidates are there ?", - "Output Program": [ - "import math\nn0 = 56.0\nt0 = n0 * 4.0\nt1 = -1.0\nt2 = t1**min(2.0, 5)\nt3 = t0 + t2\nt4 = math.sqrt(max(0, t3))\nt5 = t4 + 1.0\nanswer = t5 / 2.0\nprint(answer)" - ], - "Output Answer": [ - "8" - ], - "split": "test" - }, - { - "Input": "in a zoo , the ratio of the number of cheetahs to the number 4 then what is the increase in the number of pandas ?", - "Output Program": [ - "n0 = 4.0\nt0 = n0 * n0\nanswer = t0 - 4.0\nprint(answer)" - ], - "Output Answer": [ - "12" - ], - "split": "test" - }, - { - "Input": "if shares of two persons in profits are rs . 600 and rs . 300 then ratio of their capitals is", - "Output Program": [ - "n0 = 600.0\nn1 = 300.0\n\nanswer = n0 / n1\nprint(answer)" - ], - "Output Answer": [ - "2" - ], - "split": "test" - }, - { - "Input": "in what ratio should a variety of rice costing rs . 6.5 per kg be mixed with another variety of rice costing rs . 8.75 per kg to obtain a mixture costing rs . 7.50 per kg ?", - "Output Program": [ - "n0 = 6.5\nn1 = 8.75\nn2 = 7.5\nt0 = n1 - n2\nt1 = n1 - n0\nt2 = t0 / t1\nt3 = 1.0 - t2\nanswer = t2 / t3\nprint(answer)" - ], - "Output Answer": [ - "1.2500000000000002" - ], - "split": "test" - }, - { - "Input": "a bag contains 7 green and 8 white balls . if two balls are drawn simultaneously , the probability that both are of the same colour is", - "Output Program": [ - "n0 = 7.0\nn1 = 8.0\nt0 = n0 + n1\nt1 = n1 - 1.0\nt2 = n0 - 1.0\nt3 = n1 / t0\nt4 = n0 / t0\nt5 = t0 - 1.0\nt6 = t1 / t5\nt7 = t2 / t5\nt8 = t3 * t6\nt9 = t4 * t7\nanswer = t8 + t9\nprint(answer)" - ], - "Output Answer": [ - "0.4666666666666667" - ], - "split": "test" - }, - { - "Input": "in a class of 50 students , 20 play baseball , 15 play cricket and 11 play football . 7 play both baseball and cricket , 4 play cricket and football and 5 play baseball and football . if 18 students do not play any of these given sports , how many students play exactly two of these sports ?", - "Output Program": [ - "n0 = 50.0\nn1 = 20.0\nn2 = 15.0\nn3 = 11.0\nn4 = 7.0\nn5 = 4.0\nn6 = 5.0\nn7 = 18.0\nt0 = n1 + n2\nt1 = n4 + n5\nt2 = n3 + t0\nt3 = n6 + t1\nt4 = t2 - t3\nt5 = n7 + t4\nt6 = n0 - t5\nt7 = n4 - t6\nt8 = n5 - t6\nt9 = n6 - t6\nt10 = t7 + t8\nanswer = t10 + t9\nprint(answer)" - ], - "Output Answer": [ - "10" - ], - "split": "test" - }, - { - "Input": "a hen leaps 3 leaps for every 2 leaps of a duck , but 4 leaps of the duck are equal to 3 leaps of the hen . what is the ratio of the speed of the hen to that of the duck ?", - "Output Program": [ - "n0 = 3.0\nn1 = 2.0\nn2 = 4.0\nn3 = 3.0\nt0 = n0 / n1\nt1 = n3 / n2\nanswer = t0 / t1\nprint(answer)" - ], - "Output Answer": [ - "2" - ], - "split": "test" - }, - { - "Input": "praveen starts business with rs . 3640 and after 5 months , hari joins with praveen as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is hari \u2019 s contribution in the capital ?", - "Output Program": [ - "n0 = 3640.0\nn1 = 5.0\nn2 = 2.0\nn3 = 3.0\nt0 = n1 / 12.0\nt1 = n2 / n3\nt2 = 1.0 - t0\nt3 = n0 / t2\nanswer = t3 / t1\nprint(answer)" - ], - "Output Answer": [ - "9360.000000000002" - ], - "split": "test" - }, - { - "Input": "how many positive integers q between 200 and 300 ( both inclusive ) are not divisible by 2 , 3 or 5 ?", - "Output Program": [ - "import math\nn0 = 200.0\nn1 = 300.0\nn2 = 2.0\nn3 = 3.0\nn4 = 5.0\nt0 = n3 * n4\nt1 = n1 - n0\nt2 = t1 + 1.0\nt3 = n2 + t0\nt4 = t1 / n2\nt5 = t1 / n3\nt6 = t1 / n4\nt7 = t4 + 1.0\nt8 = t5 + 1.0\nt9 = t6 + 1.0\nt10 = t8 - t3\nt11 = t9 - t0\nt12 = math.floor(t10)\nt13 = t12 + 1.0\nt14 = t7 + t13\nt15 = t14 + t11\nanswer = t2 - t15\nprint(answer)" - ], - "Output Answer": [ - "26" - ], - "split": "test" - }, - { - "Input": "the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 10 and 11 . the larger of the two numbers is :", - "Output Program": [ - "n0 = 23.0\nn1 = 10.0\nn2 = 11.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "253" - ], - "split": "test" - }, - { - "Input": "all numbers from 1 to 200 ( in decimal system ) are written in base 6 and base 7 systems . how many of the numbers will have a non - zero units digit in both base 6 and base 7 notations ?", - "Output Program": [ - "n0 = 1.0\nn1 = 200.0\nn2 = 6.0\nn3 = 7.0\nn4 = 6.0\nn5 = 7.0\nt0 = n1 / n2\nt1 = n1 / n3\nt2 = n2 * n3\nt3 = t0 + t1\nt4 = n1 / t2\nt5 = t3 - t4\nanswer = n1 - t5\nprint(answer)" - ], - "Output Answer": [ - "142.85714285714283" - ], - "split": "test" - }, - { - "Input": "an urn contains 6 red , 5 blue and 2 green marbles . if 2 marbles are picked at random , what is the probability that both are red ?", - "Output Program": [ - "n0 = 6.0\nn1 = 5.0\nn2 = 2.0\nn3 = 2.0\nt0 = n0 + n1\nt1 = n0 * n1\nt2 = n2 + t0\nt3 = t1 / 2.0\nt4 = t2 - 1.0\nt5 = t2 * t4\nt6 = t5 / 2.0\nanswer = t3 / t6\nprint(answer)" - ], - "Output Answer": [ - "0.19230769230769232" - ], - "split": "test" - }, - { - "Input": "if both 5 ^ 2 and 3 ^ 3 are factors of n x ( 2 ^ 5 ) x ( 6 ) x ( 7 ^ 3 ) , what is the smallest possible positive value of n ?", - "Output Program": [ - "n0 = 5.0\nn1 = 2.0\nn2 = 3.0\nn3 = 3.0\nn4 = 2.0\nn5 = 5.0\nn6 = 6.0\nn7 = 7.0\nn8 = 3.0\nt0 = n0 * n7\nt1 = n1 * t0\nt2 = t1 + t1\nt3 = t2 + t1\nt4 = n7 + t3\nt5 = t4 + 4.0\nanswer = t5 + 4.0\nprint(answer)" - ], - "Output Answer": [ - "225" - ], - "split": "test" - }, - { - "Input": "the probability that event b occurs is 0.6 , and the probability that events a and b both occur is 0.25 . if the probability that either event a or event b occurs is 0.4 , what is the probability that event a will occur ?", - "Output Program": [ - "n0 = 0.6\nn1 = 0.25\nn2 = 0.4\nt0 = n1 + n2\nanswer = t0 - n0\nprint(answer)" - ], - "Output Answer": [ - "0.050000000000000044" - ], - "split": "test" - }, - { - "Input": "if x and y are both odd prime numbers and x < y , how many distinct positive integer e factors does 2 xy have ?", - "Output Program": [ - "n0 = 2.0\nt0 = 1.0 + 1.0\nt1 = n0 * t0\nanswer = t0 * t1\nprint(answer)" - ], - "Output Answer": [ - "8" - ], - "split": "test" - }, - { - "Input": "in a certain group of 10 developers , 4 developers code only in python and the rest program in either ruby on rails or php - but not both . if a developer organization is to choose a 3 - member team , which must have at least 1 developer who codes in python , how many different programming teams can be chosen ?", - "Output Program": [ - "import math\nn0 = 10.0\nn1 = 4.0\nn2 = 3.0\nn3 = 1.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(n2)))\nt2 = n0 - n2\nt3 = n0 - n1\nt4 = math.factorial(min(15, int(t2)))\nt5 = math.factorial(min(15, int(t3)))\nt6 = t1 * t1\nt7 = t5 / t6\nt8 = t4 * t1\nt9 = t0 / t8\nanswer = t9 - t7\nprint(answer)" - ], - "Output Answer": [ - "100" - ], - "split": "test" - }, - { - "Input": "there are 15 slate rocks , 20 pumice rocks , and 10 granite rocks randomly distributed in a certain field . if 2 rocks are to be chosen at random and without replacement , what is the probability that both rocks will be slate rocks ?", - "Output Program": [ - "n0 = 15.0\nn1 = 20.0\nn2 = 10.0\nn3 = 2.0\nt0 = n0 + n1\nt1 = n0 - 1.0\nt2 = n2 + t0\nt3 = n0 / t2\nt4 = t2 - 1.0\nt5 = t1 / t4\nanswer = t3 * t5\nprint(answer)" - ], - "Output Answer": [ - "0.10606060606060605" - ], - "split": "test" - }, - { - "Input": "a girl scout was selling boxes of cookies . in a month , she sold both boxes of chocolate chip cookies ( $ 1.25 each ) and boxes of plain cookies ( $ 0.75 each ) . altogether , she sold 1,585 boxes for a combined value of $ 1 , 587.75 . how many boxes of plain cookies did she sell ?", - "Output Program": [ - "n0 = 1.25\nn1 = 0.75\nn2 = 1585.0\nn3 = 1.0\nn4 = 587.75\nt0 = n4 + 1000.0\nanswer = t0 / 2.0\nprint(answer)" - ], - "Output Answer": [ - "793.875" - ], - "split": "test" - }, - { - "Input": "a certain music store stocks 800 cellos and 600 violas . of these instruments , there are 110 cello - viola pairs , such that a cello and a viola were both made with wood from the same tree ( each tree can make at most one viola and one cello , so there are no pairs other than these 90 ) . if one viola and one cello are chosen at random , what is the probability that the two instruments are made with wood from the same tree ?", - "Output Program": [ - "n0 = 800.0\nn1 = 600.0\nn2 = 110.0\nn3 = 90.0\nt0 = n2 / n0\nt1 = 1.0 / n1\nanswer = t0 * t1\nprint(answer)" - ], - "Output Answer": [ - "0.0002291666666666667" - ], - "split": "test" - }, - { - "Input": "there are 180 doctors and nurses at a hospital . if the ratio of doctors to nurses is 2 to 3 , how many nurses are at the hospital ?", - "Output Program": [ - "n0 = 180.0\nn1 = 2.0\nn2 = 3.0\nt0 = n1 + n2\nt1 = n0 / t0\nanswer = n2 * t1\nprint(answer)" - ], - "Output Answer": [ - "108" - ], - "split": "test" - }, - { - "Input": "bag contains 7 green and 8 white balls . if two balls are drawn simultaneously , the probability that both are of the same colour is - .", - "Output Program": [ - "import math\nn0 = 7.0\nn1 = 8.0\nt0 = n0 + n1\nt1 = math.factorial(min(15, int(n0)))\nt2 = math.factorial(min(15, int(2.0)))\nt3 = math.factorial(min(15, int(n1)))\nt4 = n0 - 2.0\nt5 = n1 - 2.0\nt6 = math.factorial(min(15, int(t4)))\nt7 = math.factorial(min(15, int(t5)))\nt8 = math.factorial(min(15, int(t0)))\nt9 = t0 - 2.0\nt10 = math.factorial(min(15, int(t9)))\nt11 = t6 * t2\nt12 = t7 * t2\nt13 = t1 / t11\nt14 = t3 / t12\nt15 = t10 * t2\nt16 = t13 + t14\nt17 = t8 / t15\nanswer = t16 / t17\nprint(answer)" - ], - "Output Answer": [ - "0.4666666666666667" - ], - "split": "test" - }, - { - "Input": "share rs . 5400 among john , jose & binoy in the ration 2 : 4 : 6 . find the amount received by john ?", - "Output Program": [ - "n0 = 5400.0\nn1 = 2.0\nn2 = 4.0\nn3 = 6.0\nt0 = n0 / n1\nt1 = n0 / n3\nanswer = t0 - t1\nprint(answer)" - ], - "Output Answer": [ - "1800" - ], - "split": "test" - }, - { - "Input": "of the people who responded to a market survey , 240 preferred brand x and the rest preferred brand y . if the respondents indicated a preference for brand x over brand y by ratio of 6 to 1 , how many people responded to the survey ?", - "Output Program": [ - "n0 = 240.0\nn1 = 6.0\nn2 = 1.0\nt0 = n0 / n1\nanswer = n0 + t0\nprint(answer)" - ], - "Output Answer": [ - "280" - ], - "split": "test" - }, - { - "Input": "what number has a 5 : 1 ratio to the number 10 ?", - "Output Program": [ - "n0 = 5.0\nn1 = 1.0\nn2 = 10.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "50" - ], - "split": "test" - }, - { - "Input": "of the 55 cars on a car lot , 40 have air - conditioning , 25 have power windows , and 12 have both air - conditioning and power windows . how many of the cars on the lot have neither air - conditioning nor power windows ?", - "Output Program": [ - "n0 = 55.0\nn1 = 40.0\nn2 = 25.0\nn3 = 12.0\nt0 = n1 + n2\nt1 = t0 - n3\nanswer = n0 - t1\nprint(answer)" - ], - "Output Answer": [ - "2" - ], - "split": "test" - }, - { - "Input": "in a class of 37 students 26 play football and play 20 long tennis , if 17 play above , many play neither ?", - "Output Program": [ - "n0 = 37.0\nn1 = 26.0\nn2 = 20.0\nn3 = 17.0\nt0 = n1 + n2\nt1 = t0 - n3\nanswer = n0 - t1\nprint(answer)" - ], - "Output Answer": [ - "8" - ], - "split": "test" - }, - { - "Input": "bucket p has thrice the capacity as bucket q . it takes 60 turns for bucket p to fill the empty drum . how many turns it will take for both the buckets p & q , having each turn together to fill the empty drum ?", - "Output Program": [ - "n0 = 60.0\nt0 = 1.0 / n0\nt1 = n0 * 3.0\nt2 = 1.0 / t1\nt3 = t0 + t2\nanswer = 1.0 / t3\nprint(answer)" - ], - "Output Answer": [ - "45" - ], - "split": "test" - }, - { - "Input": "the h . c . f . of two numbers is 30 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is :", - "Output Program": [ - "n0 = 30.0\nn1 = 13.0\nn2 = 14.0\n\nanswer = n0 * n2\nprint(answer)" - ], - "Output Answer": [ - "420" - ], - "split": "test" - }, - { - "Input": "income and expenditure of a person are in the ratio 5 : 4 . if the income of the person is rs . 14000 , then find his savings ?", - "Output Program": [ - "n0 = 5.0\nn1 = 4.0\nn2 = 14000.0\nt0 = n1 / n0\nt1 = n2 * t0\nanswer = n2 - t1\nprint(answer)" - ], - "Output Answer": [ - "2800" - ], - "split": "test" - } - ], - "Metadata": [ - { - "Answer": 0.5, - "Options": "a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 5 , d ) 10 / 30 , e ) 2 / 5", - "Correct": "a", - "Explanation": "if girls is 10 and boys is 20 , then 10 / 20 . so ratio of girls to boys is = 10 / 20 = 1 / 2 answer : a" - }, - { - "Answer": 21, - "Options": "a ) 20 , b ) 11 , c ) 9 , d ) 31 , e ) 21", - "Correct": "e", - "Explanation": "\"total people eat veg = only veg + both veg and non veg total = 13 + 8 = 21 answer = e\"" - }, - { - "Answer": 200, - "Options": "a ) 209 % , b ) 200 % , c ) 290 % , d ) 600 % , e ) 100 %", - "Correct": "b", - "Explanation": "explanation : let the salaries of a , b , c be x , 2 x and 3 x respectively . then , 2 x + 3 x = 6000 = > x = 1200 . a ' s salary = rs . 1200 , b ' s salary = rs . 2400 , and cs salary rs . 3600 . excess of c ' s salary over a ' s = [ ( 2400 / 1200 ) x 100 ] = 200 % . answer : b ) 200 %" - }, - { - "Answer": 0.4897959183673469, - "Options": "a ) 1 / 25 , b ) 12 / 49 , c ) 1 / 4 , d ) 24 / 49 , e ) 1 / 2", - "Correct": "d", - "Explanation": "e probability of one party having both spots : ( 1 / 2 ) * ( 24 / 49 ) = 12 / 49 ( 1 / 2 ) or ( 25 / 50 ) because it does not matter which party or which person gets the first spot . ( 24 / 49 ) because after one person from a particular party is chosen , there are 24 members of the same party left out of 49 total candidates . since this result can happen for both parties , ( 12 / 49 ) + ( 12 / 49 ) = ( 24 / 49 ) answer : d" - }, - { - "Answer": 42, - "Options": "a ) 42 , b ) 36 , c ) 30 , d ) 48 , e ) none of these", - "Correct": "a", - "Explanation": "number of students who speak only english = 30 % of 60 = 18 \u2235 number of students who speak hindi and english = 20 % of 60 = 12 \u2235 number of students who speak only hindi = ( 60 \u2013 30 = ) 30 \u2235 no . of students who speak hindi = 30 + 12 = 42 answer a" - }, - { - "Answer": 88, - "Options": "a ) 72 , b ) 88 , c ) 95 , d ) 120 , e ) 135", - "Correct": "b", - "Explanation": "\"the ratio of yankees : mets : red sox = 6 : 4 : 5 the mets fans are 4 / 15 of the population . ( 4 / 15 ) * 330 = 88 the answer is b .\"" - }, - { - "Answer": 6, - "Options": "a ) 5 , b ) 3 , c ) 6 , d ) 7 , e ) 8", - "Correct": "c", - "Explanation": "the ratio of a and b is 5 x and 3 x years . after 2 years , their ratio will be 3 and 2 . ( i . e ) ( 5 x + 2 ) / ( 3 x + 2 ) = 3 / 2 10 x + 4 = 9 x + 6 x = 2 b ' s age = 3 x = 3 ( 2 ) = 6 years answer is option c" - }, - { - "Answer": 5.999999999999999, - "Options": "a ) 3 , b ) 1 / 3 , c ) 2 , d ) 6 , e ) 1 / 6", - "Correct": "d", - "Explanation": "\"217 = ( a 1 + a 2 + a 3 + a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) factorize the same terms 217 = 1 + ( a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) write every term with respect to r a 1 = a 1 a 2 = a 1 * r ^ 1 a 3 = a 1 * r ^ 2 . . . . . . . . . 217 = 1 + ( a 1 ( r ^ 3 + r ^ 4 + r ^ 5 ) ) / ( a 1 ( 1 + r ^ 1 + r ^ 2 ) ) 216 = ( r ^ 3 ( 1 + r ^ 1 + r ^ 2 ) ) / ( ( 1 + r ^ 1 + r ^ 2 ) ) 216 = r ^ 3 r = 6 d\"" - }, - { - "Answer": 0.6666666666666665, - "Options": "a ) 1 / 4 , b ) 2 / 5 , c ) 1 / 2 , d ) 3 / 5 , e ) 2 / 3", - "Correct": "e", - "Explanation": "\"you can simply use this formula to avoid confusion : w 1 / w 2 = ( a 2 - aavg ) / ( avg - a 1 ) here is how you will find the values of a 1 an a 2 . we have an overall loss ( average loss ) . the average loss is 5 kg when 50 kg alloy is immersed . this is a loss of ( 5 / 50 ) * 100 = 10 % . this is aavg the loss of tin is 1.375 kg for every 10 kg . this means it loses ( 1.375 / 10 ) * 100 = 13.75 % of its weight in water . this is a 1 . the loss of silver is . 375 kg for every 5 kg . this means it loses ( . 375 / 5 ) * 100 = 7.5 % of its weight in water . this is a 2 . weight of tin / weight of silver = ( silver ' s loss - avg loss ) / ( avg loss - tin ' s loss ) x / y = ( 7.5 - 10 ) / ( 10 - 13.75 ) = 2 / 3 e\"" - }, - { - "Answer": 16, - "Options": "a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 15", - "Correct": "c", - "Explanation": "given that , six years ago , the ratio of the ages of vimal and saroj = 6 : 5 hence we can assume that age of vimal six years ago = 6 x age of saroj six years ago = 5 x after 4 years , the ratio of their ages = 11 : 10 \u21d2 ( 6 x + 10 ) : ( 5 x + 10 ) = 11 : 10 \u21d2 10 ( 6 x + 10 ) = 11 ( 5 x + 10 ) \u21d2 5 x = 10 \u21d2 x = 105 = 2 saroj ' s present age = ( 5 x + 6 ) = 5 \u00d7 2 + 6 = 16 answer is c ." - }, - { - "Answer": 8, - "Options": "a ) 14 , b ) 15 , c ) 8 , d ) 22 , e ) 24", - "Correct": "c", - "Explanation": "\"explanation : present age is 5 x and 2 x , = > 5 x + 6 = 26 = > x = 4 so deepak age is = 2 ( 4 ) = 8 option c\"" - }, - { - "Answer": 150, - "Options": "a ) 650 , b ) 250 , c ) 150 , d ) 100 , e ) 400", - "Correct": "c", - "Explanation": "\"consider total number of reader n ( s u l ) = 650 people who read science fiction n ( s ) = 250 people who read literacy works n ( l ) = 550 both science fiction and literacy n ( s \u00e2 \u02c6 \u00a9 l ) = ? n ( s u l ) = n ( s ) + n ( l ) - n ( s \u00e2 \u02c6 \u00a9 l ) 650 = 250 + 550 - n ( s \u00e2 \u02c6 \u00a9 l ) n ( s \u00e2 \u02c6 \u00a9 l ) = 800 - 650 n ( s \u00e2 \u02c6 \u00a9 l ) = 150 so people read both science fiction and literacy works are 150 answer : c\"" - }, - { - "Answer": 440.00000000000006, - "Options": "a ) 560 , b ) 540 , c ) 520 , d ) 440 , e ) 500", - "Correct": "d", - "Explanation": "we know 50 % people study biology , therefore the no of people not studying = 100 - 50 = 50 % > therefore the people not studying biology out of a total 880 people are = 50 % of 880 > ( 50 / 100 ) * 880 = 440 people d" - }, - { - "Answer": 0.44999999999999996, - "Options": "a ) 0.05 , b ) 0.15 , c ) 0.45 , d ) 0.5 , e ) 0.55", - "Correct": "c", - "Explanation": "p ( a or b ) = p ( a ) + p ( b ) - p ( a n b ) 0.6 = 0.4 + p ( b ) - 0.25 p ( b ) = 0.45 answer : c" - }, - { - "Answer": 25, - "Options": "['a ) 15', 'b ) 25', 'c ) 35', 'd ) 30', 'e ) none of these']", - "Correct": "b", - "Explanation": "sum of 1 st n natural no . s is n ( n + 1 ) / 2 , sum of sqaures of 1 st n natural no . s is n ( n + 1 ) ( 2 n + 1 ) / 6 , the ratio of sum of squares of first n natural numbers to square of sum of first n natural numbers = n ( n + 1 ) ( 2 n + 1 ) * 2 * 2 / ( n * n * ( n + 1 ) * ( n + 1 ) ) = 2 ( 2 n + 1 ) / ( 3 n ( n + 1 ) ) now by hit and trial for the given options , if we put 25 then this will give 17 / 325 therefore the answer is 25 answer : b" - }, - { - "Answer": 276, - "Options": "a ) 276 , b ) 295 , c ) 322 , d ) 345 , e ) 354", - "Correct": "a", - "Explanation": "\"clearly , the numbers are ( 23 x 10 ) and ( 23 x 12 ) . larger number = ( 23 x 12 ) = 276 . answer : option a\"" - }, - { - "Answer": 24, - "Options": "a ) 12 , b ) 16 , c ) 20 , d ) 24 , e ) 28", - "Correct": "d", - "Explanation": "\"let the number of pens be 5 x and the number of pencils be 6 x . 6 x - 5 x = 4 x = 4 the number of pencils is 24 . the answer is d .\"" - }, - { - "Answer": 3, - "Options": "a ) 5 : 8 , b ) 3 : 1 , c ) 3 : 7 , d ) 9 : 5 , e ) 9 : 8", - "Correct": "b", - "Explanation": "\"( 96 - 75 ) / ( 75 - 68 ) = 21 / 7 = 3 / 1 answer : b\"" - }, - { - "Answer": 6, - "Options": "a ) 3 , b ) 2 , c ) 1 , d ) 6 , e ) 4", - "Correct": "d", - "Explanation": "2 * 20 4 * 10 8 * 5 answer : d" - }, - { - "Answer": 455, - "Options": "a ) 562 , b ) 356 , c ) 455 , d ) 416 , e ) 512", - "Correct": "c", - "Explanation": "\"let the number of boys and girls be 8 x and 5 x then , 5 x = 175 x = 35 total number of students = 13 x = 13 * 35 = 455 answer is c\"" - }, - { - "Answer": 0.19230769230769232, - "Options": "a ) 2 / 13 , b ) 3 / 17 , c ) 5 / 26 , d ) 5 / 21 , e ) 7 / 15", - "Correct": "c", - "Explanation": "\"p ( both are red ) , = 6 c 213 c 2 = 6 c 213 c 2 = 5 / 26 c\"" - }, - { - "Answer": 793.125, - "Options": "a ) 0 , b ) 233 , c ) 500 , d ) 695 , e ) 790", - "Correct": "e", - "Explanation": "let # plain cookies sold be x then # chocolate cookies = ( total cookies - x ) equating for x ( 0.75 ) * x + ( 1.25 ) * ( 1585 - x ) = 1586.25 = > x = 790 e" - }, - { - "Answer": 90, - "Options": "a ) 120 , b ) 150 , c ) 100 , d ) 180 , e ) 90", - "Correct": "e", - "Explanation": "\"n ( a ) = 325 , n ( b ) = 175 , n ( aub ) = 460 - 50 = 410 . required number = n ( anb ) = n ( a ) + n ( b ) - n ( aub ) = 325 + 175 - 410 = 90 . answer is e\"" - }, - { - "Answer": 7022.222222222222, - "Options": "a ) $ 4000 , b ) $ 2890 , c ) $ 3005 , d ) $ 6952 , e ) $ 6003", - "Correct": "d", - "Explanation": "\"a ' s share = 15800 * 5 / 25 = $ 3160 c ' s share = 15800 * 6 / 25 = $ 3792 a + c = $ 6952 answer is d\"" - }, - { - "Answer": 40, - "Options": "a ) 38 min , b ) 41 min , c ) 40 min , d ) 42 min , e ) 52 min", - "Correct": "c", - "Explanation": "the total time is 220 minutes . there are four breaks of five minutes between the classes for a total of 20 minutes . the total class time is 200 minutes . 200 / 5 classes = 40 minutes per class the answer is c ." - }, - { - "Answer": 10, - "Options": "a ) 5 , b ) 7 , c ) 8 , d ) 9 , e ) 10", - "Correct": "e", - "Explanation": "a = { 4,5 , 6,7 , 8,9 , 10,11 , 12,13 , 14,15 } b = { 6 , 7,8 , 9,10 , 11,12 . . . 20 } thus we see that there are 10 distinct integers that are common to both . e is the correct answer ." - }, - { - "Answer": 1600, - "Options": "a ) 900 , b ) 980 , c ) 1600 , d ) 1240 , e ) 1400", - "Correct": "c", - "Explanation": "amount received by sanjay . 4 / 12 x 4800 = 1600 = ( related ratio / sum of ratio ) x total amount so , the amount received by sanjay is 1600 . c" - }, - { - "Answer": 0.010526315789473684, - "Options": "a ) 1 / 50 , b ) 1 / 25 , c ) 1 / 95 , d ) 1 , e ) 2", - "Correct": "c", - "Explanation": "\"there are 25 primes , 69 composite numbers from 1 to 95 . the number which is neither prime nor composite is 1 . therefore , required probability = 1 / 95 . answer : c\"" - }, - { - "Answer": 8, - "Options": "a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12", - "Correct": "d", - "Explanation": "since 2 xy prime w factors are x ^ 1 * y ^ 1 * 2 ^ 1 , its total number or factors must be ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 2 ^ 3 = 8 . thus , i think d would be the correct answer ." - }, - { - "Answer": 275, - "Options": "a ) 54 , b ) 162 , c ) 250 , d ) 275 , e ) 322", - "Correct": "d", - "Explanation": "total number of fractions = 2 + 10 = 12 element b constitutes = 10 out of 12 parts of x so in 330 gms of x have 330 * 10 / 12 = 275 gms of b and 330 - 275 = 55 gms of a . cross check : - a / b = 55 / 275 = 2 / 10 ( as given ) ans d" - }, - { - "Answer": 571200, - "Options": "a ) rs . 571200 , b ) rs . 180000 , c ) rs . 201600 , d ) rs . 504000 , e ) none of these", - "Correct": "a", - "Explanation": "\"b ' s monthly income = 17000 * 112 / 100 = rs . 19040 b ' s monthly income = 2 parts - - - - > rs . 19040 a ' s monthly income = 5 parts = 5 / 2 * 19040 = rs . 47600 a ' s annual income = rs . 47600 * 12 = rs . 571200 answer : a\"" - }, - { - "Answer": 422, - "Options": "a ) 444 , b ) 432 , c ) 346 , d ) 422 , e ) 448", - "Correct": "d", - "Explanation": "\"302 + 232 - 112 ( since 112 is counted twice ) = 422 d is the answer\"" - }, - { - "Answer": 63, - "Options": "a ) 60 , b ) 61 , c ) 62 , d ) 63 , e ) 64", - "Correct": "d", - "Explanation": "\"this is an example of a standard overlapping sets question . it has no ' twists ' to it , so you ' ll likely find using the overlapping sets formula to be a fairly easy approach . if you ' re not familiar with it , then here is the formula : 100 = 55 + 43 - 61 + ( # in neither group ) = 63 the prompt gives you all of the numbers you need to get to the correct answer . just plug in and solve . d\"" - }, - { - "Answer": 0.006968641114982578, - "Options": "a ) 1 / 574 , b ) 2 / 574 , c ) 1 / 287 , d ) 2 / 287 , e ) 3 / 287", - "Correct": "d", - "Explanation": "there are 4 green bottles in a group of 38 + 4 that is 42 . thus the probability of picking 2 green bottles is : ( 4 / 42 ) ( 3 / 41 ) = 2 / 287 . the correct answer is d ." - }, - { - "Answer": 1.5, - "Options": "a ) 3 / 1 , b ) 3 / 2 , c ) 5 / 2 , d ) 5 / 3 , e ) none of these", - "Correct": "b", - "Explanation": "explanation : kul is 22 years old . saras is 33 years old . saras ' s age : kul ' s age = 33 : 22 = 3 : 2 answer : b" - }, - { - "Answer": 44, - "Options": "a ) 44 , b ) 64 , c ) 70 , d ) 80 , e ) 84", - "Correct": "a", - "Explanation": "\"let x be the number of new boarders . the ratio changed from 5 : 12 up to 1 : 2 = 6 : 12 . 220 / ( 220 + x ) = 5 / 6 x = 44 the answer is a .\"" - }, - { - "Answer": 25, - "Options": "a ) 9 , b ) 19 , c ) 25 , d ) 27 , e ) 31", - "Correct": "c", - "Explanation": "number of students taking history = h = 36 number of students taking statistics = s = 32 total number of students = t = 90 number of students taking history or statistics or both = b = 57 number of students taking neither history nor statistics = n = 90 - 57 = 33 letxbe the number of students taking both history and statistics . then t = h + s + n - x or 90 = 36 + 32 + 33 - x or x = 11 now , number of students taking only history will be h - x or 36 - 11 = 25 answer : - c" - }, - { - "Answer": 100, - "Options": "a ) 3.69 , b ) 3.66 , c ) 3.6 , d ) 100 , e ) 3.61", - "Correct": "d", - "Explanation": "\"ans : by framing equations we get 30 l + 3 q = 168 30 l + 6 q = 186 eliminate q by multiplying the first equation by 2 and subtracting second equation from the first 30 l = 150 = > l = 5 then we get l = 5 cost of 20 kgs of apples = 20 x 5 = 100 answer : d\"" - }, - { - "Answer": 8, - "Options": "a ) 4 , b ) 8 , c ) 12 , d ) 16 , e ) 20", - "Correct": "b", - "Explanation": "p started with 7 k stamps and q started with 4 k stamps . ( 7 k - 8 ) / ( 4 k + 8 ) = 6 / 5 35 k - 24 k = 48 + 40 11 k = 88 k = 8 p has 7 ( 8 ) - 8 = 48 stamps and q has 4 ( 8 ) + 8 = 40 stamps . the answer is b ." - }, - { - "Answer": 0.09619450317124735, - "Options": "a ) 1 / 5 , b ) 11 / 22 , c ) 81 / 724 , d ) 91 / 946 , e ) 101 / 987", - "Correct": "d", - "Explanation": "\"14 / 44 * 13 / 43 = 91 / 946 the answer is d .\"" - }, - { - "Answer": 7, - "Options": "a ) 7 , b ) 8 , c ) 10 , d ) 12 , e ) 14", - "Correct": "a", - "Explanation": "\"26 + 20 - 17 = 29 36 - 29 = 7 play neither answer is a\"" - }, - { - "Answer": 85, - "Options": "a ) 85 , b ) 140 , c ) 60 , d ) 80 , e ) 75", - "Correct": "a", - "Explanation": "the problem asks for a combination , since order does n ' t matter . now , selecting r items from a set of n gives the combination formula : ncr = n ! / r ! ( n - r ) ! n = 10 r = 3 so , total teams is 10 c 3 = 10 ! / ( 3 ! ( 10 - 3 ) ! ) = 120 , and n = 10 - 3 = 7 r = 3 for teams without a pediatrician is 7 c 3 = 7 ! / ( 3 ! ( 7 - 3 ) ! ) = 35 , so , teams with at least 1 pediatrician = 120 - 35 = 85 answer : a" - }, - { - "Answer": 0.5, - "Options": "a ) 1 / 2 , b ) 2 / 5 , c ) 6 / 8 , d ) 9 / 4 , e ) 7 / 5", - "Correct": "a", - "Explanation": "\"p : 2 / 6 = 3 / 4 : 1 / 2 as the product of the means is equal to the product of the extremes . p * 1 / 2 = 2 / 6 * 3 / 4 p * 1 / 2 = 6 / 24 p = 1 / 2 = > p = 1 / 2 answer : a\"" - }, - { - "Answer": 8, - "Options": "a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16", - "Correct": "a", - "Explanation": "solution - consider multiples of 25 ! = > 3,6 , 9,12 , 15,18 count no . of 3 in each multiple . 3 = 3 x 1 - > 1 6 = 3 x 2 - > 1 9 = 3 x 3 - > 2 12 = 3 x 4 - > 1 15 = 3 x 5 - > 1 18 = 3 x 3 x 2 - > 2 - - - - count 3 ' s = 8 so answer is 8 answer : a" - }, - { - "Answer": 12, - "Options": "a ) 2 , b ) 5 , c ) 12 , d ) 16 , e ) 22", - "Correct": "c", - "Explanation": "no of people in oates reunion = 50 no of people in hall reunion = 62 attending both = x all guests attend at least one . therefore , 100 = 50 + 62 - ( both ) both = 12 answer c" - }, - { - "Answer": 30, - "Options": "a ) 10 % , b ) ( 8 ) 20 % , c ) 30 % , d ) 50 % , e ) 65 %", - "Correct": "c", - "Explanation": "\"i did n ' t understand how to connect 20 percent with the whole equation . why 20 is out of the percentile diagram ( circles ) but inside of 100 ? 20 % appeared in the exam ; however did not answer question aquestion b correctly so they are out of the two circles , however as they have appeared in the exam , they have to be taken into consideration for calculation purpose i am doing it this way : suppose the total class size is 100 , then 20 percent of the class answered incorrectly and rest 80 percent answered correctly in question 1 or 2 or both . now , 100 - [ ( 75 - x ) + x + ( 35 - x ) ] = 20 . . . . . . . . . . values are in percent x = 20 - 100 + 110 x = 30 ans : c\"" - }, - { - "Answer": 9, - "Options": "a ) 12 , b ) 15 , c ) 16 , d ) 9 , e ) 22", - "Correct": "d", - "Explanation": "\"draw a venn diagram yourself ! b + c - bc = number of students that play either basketball or cricket 7 + 5 - 3 = 9 d )\"" - }, - { - "Answer": 2184, - "Options": "a ) 80 , b ) 160 , c ) 720 , d ) 1100 , e ) 2184", - "Correct": "e", - "Explanation": "\"no . of ways of picking 2 biology books ( from 13 books ) = 13 c 2 = ( 13 * 12 ) / 2 = 78 no . of ways of picking 2 chemistry books ( from 8 books ) = 8 c 2 = ( 8 * 7 ) / 2 = 28 total ways of picking 2 books of each type = 78 * 28 = 2184 ( option e )\"" - }, - { - "Answer": 15, - "Options": "['a ) a ) 10', 'b ) b ) 12', 'c ) c ) 15', 'd ) d ) 14', 'e ) e ) 9']", - "Correct": "c", - "Explanation": "let the numbers be x , 2 x , 4 x then , x ^ 2 + 4 x ^ 2 + 16 x ^ 2 = 4725 21 x ^ 2 = 4725 x ^ 2 = 225 x = 15 answer is c" - }, - { - "Answer": 15, - "Options": "a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17", - "Correct": "c", - "Explanation": "( rank from top ) + ( rank from bottom ) - 1 = total students 17 + x - 1 = 31 x = 15 answer : c" - }, - { - "Answer": 38, - "Options": "a ) 35 , b ) 36 , c ) 37 , d ) 38 , e ) 39", - "Correct": "d", - "Explanation": "\"there were 15 items sold at a higher price than the radio and 22 items sold at a lower price than the radio . including the radio , there were 15 + 22 + 1 = 38 items sold . the answer is d .\"" - }, - { - "Answer": 84, - "Options": "a ) 84 , b ) 105 , c ) 54 , d ) 42 , e ) 70", - "Correct": "a", - "Explanation": "a 84 = 2 * 2 * 2 * 7 b 105 is odd c 54 = 2 * 3 * 3 d 42 = 2 * 3 * 7 e 70 = 2 * 5 * 7 the answer must meet three criteria : odd , have repeating prime factors , and 7 is a prime factor . a is the only answer that meets all criteria" - }, - { - "Answer": 10, - "Options": "a ) 9 , b ) 10 , c ) 13 , d ) 16 , e ) 18", - "Correct": "b", - "Explanation": "20 large cakes will require the equivalent of 10 helpers working for one hour . 700 small cakes will require the equivalent of 20 helpers working for one hour . this means if only one hour were available we would need 30 helpers . but since three hours are available we can use 10 helpers . b" - }, - { - "Answer": 422, - "Options": "a ) 404 , b ) 452 , c ) 444 , d ) 468 , e ) 422", - "Correct": "e", - "Explanation": "\"312 + 222 - 112 ( since 112 is counted twice ) = 422 e is the answer\"" - }, - { - "Answer": 2, - "Options": "a ) 2 : 1 , b ) 3 : 2 , c ) 4 : 3 , d ) 5 : 4 , e ) 6 : 5", - "Correct": "a", - "Explanation": "\"polly : sandy = 4 : 5 sandy : willy = 5 : 2 polly : sandy : willy = 4 : 5 : 2 polly : willy = 4 : 2 = 2 : 1 the answer is a .\"" - }, - { - "Answer": 0.4725274725274725, - "Options": "a ) 8 / 15 , b ) 2 / 5 , c ) 3 / 5 , d ) 11 / 15 , e ) 43 / 91", - "Correct": "e", - "Explanation": "\"drawing two balls of same color from six green balls can be done in 6 c \u2082 ways . similarly from eight white balls two can be drawn in \u2078 c \u2082 ways . p = 6 c \u2082 / \u00b9 \u2075 c \u2082 + \u2078 c \u2082 / \u00b9 \u2075 c \u2082 = 43 / 91 answer : e\"" - }, - { - "Answer": 0.010309278350515464, - "Options": "a ) 1 / 50 , b ) 1 / 25 , c ) 1 / 97 , d ) 1 , e ) 2", - "Correct": "c", - "Explanation": "\"there are 25 primes , 71 composite numbers from 1 to 97 . the number which is neither prime nor composite is 1 . therefore , required probability = 1 / 97 . answer : c\"" - }, - { - "Answer": 54, - "Options": "a ) 36 , b ) 42 , c ) 48 , d ) 54 , e ) 60", - "Correct": "d", - "Explanation": "let the number of pens be 5 x and the number of pencils be 6 x . 6 x - 5 x = 9 x = 9 the number of pencils is 54 . the answer is d ." - }, - { - "Answer": 185, - "Options": "a ) 54 , b ) 185 , c ) 250 , d ) 270 , e ) 322", - "Correct": "b", - "Explanation": "\"total number of fractions = 2 + 10 = 12 element b constitutes = 10 out of 12 parts of x so in 222 gms of x have 222 * 10 / 12 = 185 gms of b and 222 - 185 = 37 gms of a . cross check : - a / b = 37 / 185 = 2 / 10 ( as given ) ans b\"" - }, - { - "Answer": 9000, - "Options": "a ) 22378 , b ) 279889 , c ) 2788 , d ) 9000 , e ) 2882", - "Correct": "d", - "Explanation": "explanation : ratio in which profit is to be divided = 2 : 3 assume that b ' s contribution to the capital = b \u21d2 3500 \u00d7 12 : b \u00d7 7 = 2 : 3 \u21d2 3500 \u00d7 12 / 7 b = 2 / 3 \u21d2 b = ( 3500 \u00d7 12 \u00d7 3 ) / ( 2 \u00d7 7 ) = 500 \u00d7 6 \u00d7 3 = 9000 answer : d" - }, - { - "Answer": 0.75, - "Options": "a ) 1 / 15 , b ) 3 / 4 , c ) 5 / 8 , d ) 9 / 6 , e ) 8 / 7", - "Correct": "b", - "Explanation": "\"p : 2 / 5 = 3 / 8 : 1 / 5 as the product of the means is equal to the product of the extremes . p * 1 / 5 = 2 / 5 * 3 / 8 p * 1 / 5 = 6 / 40 p = 3 / 4 = > p = 3 / 4 answer : b\"" - }, - { - "Answer": 247.76000000000002, - "Options": "a ) 20 o , b ) 24 o , c ) 249 , d ) 30 o , e ) 325", - "Correct": "c", - "Explanation": "\"according to above 1000 ! has 1000 / 5 + 1000 / 25 + 1000 / 125 + 1000 / 625 = 200 + 40 + 8 + 1 = 249 trailing zeros . answer : c\"" - }, - { - "Answer": 1040, - "Options": "a ) 1040 , b ) 920 , c ) 980 , d ) 720 , e ) 820", - "Correct": "a", - "Explanation": "\"explanation : let the boy are 8 x and girls are 5 x = > 5 x = 400 = > x = 80 total students = 8 x + 5 x = 13 x = 13 ( 80 ) = 1040 option a\"" - }, - { - "Answer": 0.46153846153846156, - "Options": "a ) 4 / 13 , b ) 6 / 13 , c ) 8 / 21 , d ) 11 / 21 , e ) 17 / 42", - "Correct": "b", - "Explanation": "\"the total number of ways to draw two balls is 14 c 2 = 91 the number of ways to draw two green balls is 7 c 2 = 21 the number of ways to draw two white balls is 7 c 2 = 21 p ( two balls of the same colour ) = 42 / 91 = 6 / 13 the answer is b .\"" - }, - { - "Answer": 35, - "Options": "a ) 30 , b ) 35 , c ) 20 , d ) 18 , e ) 10", - "Correct": "b", - "Explanation": "{ total } = { car } + { bike } - { both } + { neither } - - > 90 = 44 + { bike } - 22 + 11 - - > { bike } = 57 - - > # those who have bike only is { bike } - { both } = 57 - 22 = 35 . answer : b ." - }, - { - "Answer": 68, - "Options": "a ) 66 % , b ) 64 % , c ) 68 % , d ) 69 % , e ) 72 %", - "Correct": "c", - "Explanation": "\"let total no of vehicles bought be 100 , toyota 80 and honda 20 , so total number of suv ' s bought for toyota and honda respectively 80 * 80 / 100 = 64 and 20 * 20 / 100 = 4 so total 68 suv ' s were bought out of 100 vehicles bought . . so required % is 68 % answer : c\"" - }, - { - "Answer": 18, - "Options": "a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20", - "Correct": "d", - "Explanation": "\"now , sandy is 30 - 6 = 24 molly ' s age is ( 3 / 4 ) * 24 = 18 the answer is d .\"" - }, - { - "Answer": 1, - "Options": "a ) 1 : 1 , b ) 3 : 2 , c ) 1 : 3 , d ) 2 : 5 , e ) 5 : 7", - "Correct": "a", - "Explanation": "\"number of men in the colony = 3 / 5 ( 50 ) = 30 number of women in the colony = 2 / 5 ( 50 ) = 20 number of educated women in the colony = 1 / 4 ( 20 ) = 5 number of uneducated women in the colony = 3 / 4 ( 20 ) = 15 number of educated persons in the colony = 4 / 10 ( 50 ) = 20 as 5 females are educated , remaining 15 educated persons must be men . number of uneducated men in the colony = 30 - 15 = 15 number of educated men and uneducated men are in the ratio 15 : 15 = > 1 : 1 answer : a\"" - }, - { - "Answer": 18, - "Options": "a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22", - "Correct": "c", - "Explanation": "\"the total number of people are x females + 2 x males . 3 * ( x - 3 ) = 2 x - 3 x = 6 there were 3 x = 18 people at the party originally . the answer is c .\"" - }, - { - "Answer": 18, - "Options": "a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18", - "Correct": "e", - "Explanation": "\"let 2 x be the number of spinsters . then 9 x is the number of cats . 9 x - 2 x = 63 x = 9 and the number of spinsters is 2 ( 9 ) = 18 . the answer is e .\"" - }, - { - "Answer": 900, - "Options": "a ) 276 , b ) 300 , c ) 500 , d ) 700 , e ) 900", - "Correct": "e", - "Explanation": "\"the numbers are ( 60 x 11 ) and ( 60 x 15 ) . larger number = ( 60 x 15 ) = 900 . answer : e\"" - }, - { - "Answer": 60, - "Options": "a ) 32 , b ) 42 , c ) 60 , d ) 25 , e ) 52", - "Correct": "c", - "Explanation": "make a prime factorization of the number : 21,600 = 25 \u2217 33 \u2217 52 according to the above the number of factors is ( 5 + 1 ) ( 3 + 1 ) ( 2 + 1 ) = 72 now , get rid of powers of 2 as they give even factors - - > you ' ll have 33 \u2217 52 which has ( 3 + 1 ) ( 2 + 1 ) = 12 factors . all the remaining factors will be odd , therefore 21,600 has 72 - 12 = 60 even factors . answer : c ." - }, - { - "Answer": 0.05263157894736842, - "Options": "a ) 1 / 16 , b ) 1 / 19 , c ) 1 / 4 , d ) 1 / 3 , e ) none of these", - "Correct": "b", - "Explanation": "probability of drawing a defective tube in first draw is 5 / 20 probability of drawing a defective tube in second draw ( without replacing first tube ) is 4 / 19 . therefore probability of getting both defective is = ( 5 / 20 ) * ( 4 / 19 ) = 1 / 19 answer : b" - }, - { - "Answer": 177.5, - "Options": "a ) rs . 147.50 , b ) rs . 785.50 , c ) rs . 176.50 , d ) rs . 258.50 , e ) none of these", - "Correct": "c", - "Explanation": "\"explanation : since first and second varieties are mixed in equal proportions . so , their average price = rs . ( 126 + 135 ) / 2 . = > rs . 130.50 . so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . by the rule of alligation , we have : cost of 1 kg cost of 1 kg of 1 st kind of 2 nd kind ( rs . 130.50 ) ( rs . x ) \\ / mean price ( rs . 154 ) / \\ x \u00e2 \u02c6 \u2019 154 22.50 = > x \u00e2 \u02c6 \u2019 ( 154 / 22.50 ) = 1 . = > x \u00e2 \u02c6 \u2019 154 = 22.50 . = > x = 176.50 rs . answer : c\"" - }, - { - "Answer": 624, - "Options": "a ) 624 , b ) 450 , c ) 480 , d ) 504 , e ) 555", - "Correct": "a", - "Explanation": "\"explanation : hcf of the two numbers = 52 hcf will be always a factor of lcm 52 is factor of lcm other two factors are 11 & 12 then the numbers are ( 52 * 11 ) and ( 52 x 12 ) = 572 and 624 answer : option a\"" - }, - { - "Answer": 40212.385965949354, - "Options": "['a ) 40288.57 cm ^ 2', 'b ) 40388.57 cm ^ 2', 'c ) 40488.57 cm ^ 2', 'd ) 40588.57 cm ^ 2', 'e ) 40688.57 cm ^ 2']", - "Correct": "a", - "Explanation": "et the radius of umbra and penumbra are 2 k and 6 k . then as given radius of umbra = 40 cm so 2 k = 40 k = 20 radius of penumbra = 20 * 6 = 120 area of penumbra ring around the umbra = area of penumbra - area of umbra 22 / 7 * [ ( 120 ) ^ 2 - ( 40 ) ^ 2 ] = 40288.57 cm ^ 2 answer : a" - }, - { - "Answer": 16, - "Options": "a ) 18 , b ) 16 , c ) 32 , d ) 56 , e ) 58", - "Correct": "b", - "Explanation": "\"et no of sheep and horses are 2 k and 7 k no of horses = 12880 / 230 = 56 now 7 k = 56 and k = 8 no of sheep = ( 2 * 8 ) = 16 answer : b\"" - }, - { - "Answer": 84, - "Options": "a ) 81 , b ) 82 , c ) 84 , d ) 86 , e ) 88", - "Correct": "c", - "Explanation": "1 c 4 * 2 c 7 = 4 * 21 = 84 the answer is ( c )" - }, - { - "Answer": 48, - "Options": "a ) 99 , b ) 48 , c ) 16 , d ) 22 , e ) 60", - "Correct": "b", - "Explanation": "since there are 9 children with red hair , and the class exists in a 3 : 6 : 7 ratio , there are 3 times more children than the unit ratio . therefore 9 red - haired children 3 * ( 6 ) blonde - haired children 3 * ( 7 ) black - haired children 9 + 18 + 21 = 48 alternatively , a part - to - whole ratio can be set up . since the whole is 3 + 6 + 7 = 16 , 9 / 3 = x / 16 3 * 16 = 48 answer : b )" - }, - { - "Answer": 0.31666666666666654, - "Options": "a ) 7 / 30 , b ) 11 / 40 , c ) 17 / 50 , d ) 19 / 60 , e ) 33 / 80", - "Correct": "d", - "Explanation": "let , a \u2261 event of getting hardware contract b \u2261 event of getting software contract ab \u2261 event of getting both hardware and software contract . p ( a ) = 3 / 4 , p ( ~ b ) = 5 / 9 = > p ( b ) = 1 - ( 3 / 5 ) = 2 / 5 . a and b are not mutually exclusive events but independent events . so , p ( at least one of a and b ) = p ( a ) + p ( b ) - p ( ab ) . = > 5 / 6 = ( 3 / 4 ) + ( 2 / 5 ) - p ( ab ) . = > p ( ab ) = 19 / 60 . hence , the required probability is 19 / 60 . the answer is d ." - }, - { - "Answer": 436800.0000000001, - "Options": "a ) rs . 420000 , b ) rs . 180000 , c ) rs . 436800 , d ) rs . 504000 , e ) none of these", - "Correct": "c", - "Explanation": "\"b ' s monthly income = 13000 * 112 / 100 = rs . 14560 b ' s monthly income = 2 parts - - - - > rs . 14560 a ' s monthly income = 5 parts = 5 / 2 * 14560 = rs . 36400 a ' s annual income = rs . 36400 * 12 = rs . 436800 answer : c\"" - }, - { - "Answer": 20.00000000000001, - "Options": "a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 50 %", - "Correct": "b", - "Explanation": "solution : this is a percent increase 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 profits to sales . the first ratio will be for the first 15 million in sales , and the second ratio will be for the next 30 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 15 million profit / sales = 5 / 15 = 1 / 3 next 30 million profit / sales = 12 / 30 = 2 / 5 we can simplify each ratio by multiplying each by the lcm of the two denominators , which is 15 . keep in mind that we are able to do this only because our answer choices are expressed in percents . first 15 million royalties / sales = ( 1 / 3 ) x 15 = 5 next 30 million royalties / sales = ( 2 / 5 ) x 15 = 6 we can plug 5 and 6 into our percent change formula : ( new \u2013 old ) / old x 100 [ ( 6 \u2013 5 ) / 5 ] x 100 1 / 5 x 100 , so a 20 % increase . answer b ." - }, - { - "Answer": 35, - "Options": "a ) 30 , b ) 35 , c ) 20 , d ) 18 , e ) 10", - "Correct": "b", - "Explanation": "\"{ total } = { car } + { bike } - { both } + { neither } - - > 90 = 44 + { bike } - 20 + 11 - - > { bike } = 55 - - > # those who have bike only is { bike } - { both } = 55 - 20 = 35 . answer : b .\"" - }, - { - "Answer": 68, - "Options": "a ) 65 , b ) 66 , c ) 67 , d ) 68 , e ) 69", - "Correct": "d", - "Explanation": "consider the number of total students = n ( t ) = 100 number of persons major in physics = n ( p ) = 75 number of persons major in chemistry = n ( c ) = 83 according to the question ; 10 not at major in these subjects = n ( p ' \u2229 c ' ) = 10 n ( p ' \u2229 c ' ) = n ( p u c ) ' = 10 n ( p u c ) ' = n ( t ) - n ( p u c ) 10 = 100 - n ( p u c ) n ( p u c ) = 90 n ( p u c ) = n ( p ) + n ( c ) - n ( p \u2229 c ) 90 = 75 + 83 - n ( p \u2229 c ) n ( p \u2229 c ) = 158 - 90 n ( p \u2229 c ) = 68 number of students majoring in both subjects will be 68 answer : d" - }, - { - "Answer": 60, - "Options": "a ) 45 , b ) 50 , c ) 60 , d ) 75 , e ) 90", - "Correct": "c", - "Explanation": "let the number of boys and girls be x and 2 x total students = 100 number of girls in the school = 2 * 90 / 3 = 60 answer is c" - }, - { - "Answer": 36, - "Options": "a ) 36 , b ) 42 , c ) 72 , d ) 400 , e ) 56", - "Correct": "a", - "Explanation": "explanation : let mangoes = 10 x , oranges = 2 x & apples = 3 x . now , 10 x = 120 hence x = 12 . number of apples = 3 x = 36 . answer : a" - }, - { - "Answer": 3003, - "Options": "a ) 3003 , b ) 3027 , c ) 3024 , d ) 3021 , e ) 3018", - "Correct": "a", - "Explanation": "\"first , you have to find the common ratio for all 3 books . you have : p : c : b 3 : 2 - - > multiply by 2 ( gives you row 3 ) 4 : 6 6 : 4 : 3 hence : p : c : b : t ( total ) 6 : 4 : 3 : 13 - - - - > this means , the total number e must be a multiple of 13 . answer a is correct since 299 is divisible by 13 , hence is 2990 and so is 3003 ( 2990 + 13 ) .\"" - }, - { - "Answer": 450, - "Options": "a ) 90 , b ) 150 , c ) 270 , d ) 300 , e ) 450", - "Correct": "e", - "Explanation": "originally ( 2 / 9 ) * 1350 = 300 acres were planted with tobacco . in the new system ( 5 / 9 ) * 1350 = 750 acres were planted with tobacco . thus 750 - 300 = 450 more acres were planted with tobacco . the answer is e ." - }, - { - "Answer": 9, - "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", - "Correct": "c", - "Explanation": "\"the weights of the items in the suitcase are 5 k , 4 k , and 2 k . if removing 9 pounds of clothes doubles the ratio of books to clothes , then 9 pounds represents half the weight of the clothes . 2 k = 9 pounds and then k = 4.5 pounds . the electronics weigh 2 ( 4.5 ) = 9 pounds . the answer is c .\"" - }, - { - "Answer": 8, - "Options": "a ) 4 , b ) 8 , c ) 14 , d ) 20 , e ) 28", - "Correct": "b", - "Explanation": "\"we are told that all of the letters contain either a dot or a straight line or both , which implies that there are no letters without a dot and a line ( no line / no dot box = 0 ) . first we find the total # of letters with lines : 8 + 24 = 32 ; next , we find the total # of letters without line : 40 - 32 = 8 ; finally , we find the # of letters that contain a dot but do not contain a straight line : 8 - 0 = 8 . b\"" - }, - { - "Answer": 0.4725274725274725, - "Options": "a ) 5 / 14 , b ) 8 / 21 , c ) 12 / 21 , d ) 43 / 91 , e ) 47 / 91", - "Correct": "d", - "Explanation": "the total number of ways to draw two balls is 14 c 2 = 91 the number of ways to draw two green balls is 6 c 2 = 15 the number of ways to draw two white balls is 8 c 2 = 28 p ( two balls of the same colour ) = 43 / 91 the answer is d ." - }, - { - "Answer": 7000.000000000023, - "Options": "a ) $ 7600 , b ) $ 7000 , c ) $ 8000 , d ) $ 9000 , e ) $ 5000", - "Correct": "b", - "Explanation": "let the income of rajan and balan be $ 7 x and $ 6 x let their expenditures be $ 6 y and $ 5 y 7 x - 6 y = 1000 - - - - - - - 1 ) 6 x - 5 y = 1000 - - - - - - - 2 ) from 1 ) and 2 ) x = 1000 rajan ' s income = 7 x = 7 * 1000 = $ 7000 answer is b" - }, - { - "Answer": 0.3333333333333333, - "Options": "a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4", - "Correct": "b", - "Explanation": "\"original quantity = a substituted quantity = b then : ( a * 0.4 + 0.25 * b \u0442 \u0430 \u0443 0.4 * b ) / a = 0.35 0.4 + ( b / a ) * ( - 0.15 ) = 0.35 b / a = - 0.05 / - 0.15 = 1 / 3 answer : b\"" - }, - { - "Answer": 30, - "Options": "a ) 30 , b ) 27 , c ) 35 , d ) 33 , e ) 37", - "Correct": "a", - "Explanation": "explanation : let pencils = 14 x , pens = 4 x & exercise books = 3 x . now , 14 x = 140 hence x = 10 number of exercise books = 3 x = 30 answer : a" - }, - { - "Answer": 1800, - "Options": "a ) $ 1000 , b ) $ 2000 , c ) $ 1800 , d ) $ 1500 , e ) $ 1600", - "Correct": "c", - "Explanation": "\"a ' s share = 4500 * 2 / 15 = $ 600 b ' s share = 4500 * 4 / 15 = $ 1200 a + b = $ 1800 answer is c\"" - }, - { - "Answer": 0.26666666666666666, - "Options": "a ) 4 / 15 , b ) 1 / 3 , c ) 2 / 5 , d ) 4 / 5 , e ) 7 / 6", - "Correct": "a", - "Explanation": "a : b = 4 : 3 - - 1 b : c = 1 : 5 = > b : c = 3 : 15 - - 2 from 1 and 2 , we get a : c = 4 : 15 answer a" - }, - { - "Answer": 1071, - "Options": "a ) 3421 , b ) 2132 , c ) 1111 , d ) 4323 , e ) 1071", - "Correct": "e", - "Explanation": "\": explanation : clearly , the numbers are ( 63 x 11 ) and ( 63 x 17 ) . { \\ color { blue } \\ therefore } larger number = ( 63 x 17 ) = 1071 . answer : e ) 1071\"" - }, - { - "Answer": 5, - "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8", - "Correct": "b", - "Explanation": "as m and n has gcf of 15 , 3 * 5 should be common factor for both m and n . m = 3 * 5 * p 1 * p 2 n = 3 * 5 * p 3 mn = 3 ^ 2 * 5 ^ 2 * p 1 * p 2 * p 3 mn has prime numbers of 3,5 , p 1 , p 2 p 3 b" - }, - { - "Answer": 75, - "Options": "a ) 25 , b ) 27 , c ) 45 , d ) 75 , e ) 125", - "Correct": "d", - "Explanation": "if both 5 ^ 2 & 3 ^ 3 are factors , then they must be present in the number . leaving rest of the prime factors and splitting 6 ^ 2 into 3 ^ 2 * 2 ^ 3 . the number is lacking 5 ^ 2 & a 3 , so that 5 ^ 2 and 3 ^ 3 is a factor . hence the smallest number is 5 ^ 2 * 3 = 75 answer : d" - }, - { - "Answer": 880, - "Options": "a ) 800 , b ) 880 , c ) 920 , d ) 950 , e ) 980", - "Correct": "b", - "Explanation": "p ( c ) = 500 p ( b ) = 600 p ( c n b ) = 220 p ( c u b ) = p ( c ) + p ( b ) - p ( c n b ) = 500 + 600 - 220 = 880 answer : b" - }, - { - "Answer": 437, - "Options": "a ) 437 , b ) 299 , c ) 322 , d ) 345 , e ) 355", - "Correct": "a", - "Explanation": "\"clearly , the numbers are ( 23 x 13 ) and ( 23 x 19 ) . larger number = ( 23 x 19 ) = 437 . answer : option a\"" - }, - { - "Answer": 4, - "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", - "Correct": "b", - "Explanation": "\"the ratio of flour to water is 10 : 3 . the ratio of flour to sugar is 5 : 3 = 10 : 6 . the new ratio of flour to water to sugar is 10 : 3 : 6 if we need 2 cups of water , then we need 4 cups of sugar . the answer is b .\"" - }, - { - "Answer": 28, - "Options": "a ) 2 , b ) 5 , c ) 10 , d ) 16 , e ) 28", - "Correct": "e", - "Explanation": "no of people in oates reunion = 70 no of people in hall reunion = 52 attending both = x all guests attend at least one . therefore , 150 = 70 + 52 - ( both ) both = 28 answer e" - }, - { - "Answer": 5, - "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", - "Correct": "d", - "Explanation": "prime factors \u2019 number , as i assume , for a number x = a ^ n * b ^ m * c ^ o * d ^ p . . . is = n + m + o + p . . . so , 24 = 2 ^ 4 * 3 ^ 1 prime factors \u2019 number will be 4 + 1 = 5 . hence , answer is d ." - }, - { - "Answer": 30, - "Options": "a ) 26 , b ) 28 , c ) 30 , d ) 32 , e ) 34", - "Correct": "c", - "Explanation": "\"the total number of people are x females + 2 x males . 3 * ( x - 5 ) = 2 x - 5 x = 10 there were 3 x = 30 people at the party originally . the answer is c .\"" - }, - { - "Answer": 3003, - "Options": "a ) 3003 , b ) 3027 , c ) 3024 , d ) 3021 , e ) 3018", - "Correct": "a", - "Explanation": "\"first , you have to find the common ratio for all 3 books . you have : p : c : b 3 : 2 - - > multiply by 2 ( gives you row 3 ) 4 : 6 6 : 4 : 3 hence : p : c : b : t ( total ) r 6 : 4 : 3 : 13 - - - - > this means , the total number must be a multiple of 13 . answer a is correct since 299 is divisible by 13 , hence is 2990 and so is 3003 ( 2990 + 13 ) .\"" - }, - { - "Answer": 1800, - "Options": "a ) $ 2000 , b ) $ 1800 , c ) $ 2500 , d ) $ 1500 , e ) $ 1600", - "Correct": "b", - "Explanation": "\"b ' s share = 5400 * 3 / 9 = $ 1800 answer is b\"" - }, - { - "Answer": 3000, - "Options": "a ) 3005 , b ) 3098 , c ) 3300 , d ) 3010 , e ) 3000", - "Correct": "e", - "Explanation": "\"let the income and the expenditure of the person be rs . 10 x and rs . 7 x respectively . income , 10 x = 10000 = > x = 1000 savings = income - expenditure = 10 x - 7 x = 3 x = 3 ( 1000 ) so , savings = rs . 3000 . answer : e\"" - }, - { - "Answer": 88, - "Options": "a ) 144 , b ) 119 , c ) 113 , d ) 88 , e ) 31", - "Correct": "d", - "Explanation": "official solution : first of all , notice that since 144 took geometry and 119 took biology , then the number of students who took both geometry and biology can not be greater than 119 . { total } = { geometry } + { biology } - { both } + { neither } ; 232 = 144 + 119 - { both } + { neither } ; { both } = 31 + { neither } . { both } is minimized when { neither } is 0 . in this case { both } = 31 . the greatest possible number i of students that could have taken both geometry and biology , is 119 . thus , the answer is 119 - 31 = 88 . answer : d ." - }, - { - "Answer": 9, - "Options": "a ) 6 , b ) 8 , c ) 9 , d ) 12 , e ) 14", - "Correct": "c", - "Explanation": "\"26 + 20 - 17 = 29 38 - 29 = 9 play neither answer is c\"" - }, - { - "Answer": 96, - "Options": "a ) 99 , b ) 98 , c ) 97 , d ) 96 , e ) 95", - "Correct": "d", - "Explanation": "\"clearly d a number is said to be prime saturated if the product of all the different positive prime factors of d is less than the square root of d . 96 has more number of smaller prime factor thats the clue ! ! = d\"" - }, - { - "Answer": 75, - "Options": "['a ) 15', 'b ) 30', 'c ) 45', 'd ) 75', 'e ) 90']", - "Correct": "d", - "Explanation": "standard : fl : corn s : water = 1 : 12 : 30 sport : fl : corn s : water = 3 : 12 : 180 this simplifies to 1 : 4 : 60 if the large bottle has a capacity of x ounces , then 4 x / 65 = 5 . so , x = 325 / 4 ounces . water = ( 60 / 65 ) * ( 325 / 4 ) = 60 * 3 / 4 = 75 ounces . ans d" - }, - { - "Answer": 7.500000000000001e-05, - "Options": "a ) 3 / 40000 , b ) 3 / 20000 , c ) 3 / 4000 , d ) 9 / 400 , e ) 6 / 130", - "Correct": "a", - "Explanation": "probability of selecting 1 student from harvard ' s business school - - - 1 / 500 probability of selecting 1 student from harvard ' s law school - - - - - - - - - 1 / 800 probability that these two students are siblings - - - - ( 1 / 500 * 1 / 800 ) since there are 30 siblings , hence ( 1 / 500 * 1 / 800 ) * 30 . 3 / 40000 answer : a" - }, - { - "Answer": 79, - "Options": "a ) 76 , b ) 77 , c ) 78 , d ) 79 , e ) 80", - "Correct": "d", - "Explanation": "\"let x be the weight of the sister . then the student ' s weight is 2 x + 5 . x + ( 2 x + 5 ) = 116 3 x = 111 x = 37 kg then the student ' s weight is 79 kg . the answer is d .\"" - }, - { - "Answer": 52, - "Options": "a ) 66 % , b ) 64 % , c ) 68 % , d ) 52 % , e ) 72 %", - "Correct": "d", - "Explanation": "\"let total no of vehicles bought be 100 , toyota 40 and honda 60 , so total number of suv ' s bought for toyota and honda respectively 40 * 40 / 100 = 16 and 60 * 60 / 100 = 36 so total 52 suv ' s were bought out of 100 vehicles bought . . so required % is 52 % answer : d\"" - }, - { - "Answer": 8, - "Options": "a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12", - "Correct": "d", - "Explanation": "a and b are both odd prime numbers - it means either a or b is not 2 and since prime numbers have only two factors - 1 and the number itself a and b each will have ( 1 + 1 ) = 2 factors hence 2 ab will have ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 8 factors d is the answer" - }, - { - "Answer": 0.10714285714285714, - "Options": "a ) 2 / 21 , b ) 3 / 41 , c ) 3 / 28 , d ) 3 / 31 , e ) 5 / 32", - "Correct": "c", - "Explanation": "\"p ( both are red ) , = 3 c 2 / 8 c 2 = 6 c 213 c 2 = 3 / 28 c\"" - }, - { - "Answer": 3, - "Options": "a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 3", - "Correct": "e", - "Explanation": "\"20 + 18 = 38 but where as total number is 40 - 5 = 35 therefore answer is 38 - 35 = 3 hence answer is e\"" - }, - { - "Answer": 991, - "Options": "a ) 456 , b ) 789 , c ) 991 , d ) 1020 , e ) 1100", - "Correct": "c", - "Explanation": "\"the answer is ( 10000 - 100 ) / 10 + 1 = 991 answer is c\"" - }, - { - "Answer": 2, - "Options": "a ) 5 : 1 , b ) 1 : 1 , c ) 20 : 4 , d ) 10 : 3 , e ) 2 : 1", - "Correct": "e", - "Explanation": "the number of games played is 10 . the number of games won is 5 , so 10 - 5 = 5 = number of game losses . answer = ! 0 : 5 = 2 : 1 answer is e" - }, - { - "Answer": 42, - "Options": "a ) 25 , b ) 36 , c ) 38 , d ) 45 , e ) 42", - "Correct": "e", - "Explanation": "i used the following formula : total = group 1 + group 2 + neither - both using the information from the question stem , we have : 84 total people 25 who supervise ( group 1 ) x who neither supervise nor bring refreshments 1.5 x people who bring refreshments ( group 2 ) 11 who supervise and bring refreshments ( both ) therefore . . . 84 = 25 + 1.5 x + x - 11 solving , we get x = 28 since we want the value of those who bring refreshments and supervise : 1.5 ( 28 ) = 42 answer is e" - }, - { - "Answer": 2, - "Options": "a ) 23 , b ) 1 : 2 , c ) 2 : 5 , d ) 3 : 5 , e ) 2 : 1", - "Correct": "e", - "Explanation": "\"c . p . = rs . 2 x and s . p . = rs . 6 x . then , gain = rs . 4 x required ratio = 4 x : 2 x = 2 : 1 e\"" - }, - { - "Answer": 40, - "Options": "a ) 6 , b ) 15 , c ) 24 , d ) 33 , e ) 40", - "Correct": "e", - "Explanation": "\"formula for calculating two overlapping sets : a + b - both + not ( a or b ) = total so in our task we have equation : 41 ( french ) + 22 ( german ) - 9 ( both ) + not = 94 54 + not = 94 not = 94 - 54 = 40 so answer is e\"" - }, - { - "Answer": 48, - "Options": "a ) 24 , b ) 36 , c ) 48 , d ) 72 , e ) 132", - "Correct": "c", - "Explanation": "the ratio as mentioned = 4 / 11 also sea lion + 84 = penguins or , 4 x + 84 = 11 x x = 84 / 7 = 12 number of sea lions = 12 * 4 = 48 answer : c" - }, - { - "Answer": 60, - "Options": "a ) 2 , b ) 5 , c ) 10 , d ) 16 , e ) 60", - "Correct": "e", - "Explanation": "no of people in dates reunion = 50 no of people in hall reunion = 60 attending both = x all guests attend at least one . therefore , 50 = 50 + 60 - ( both ) both = 60 answer e" - }, - { - "Answer": 10, - "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12", - "Correct": "c", - "Explanation": "answer : algebraically , the question looks like this : 3.0 = 0.35 x + 0.25 y there are six possible numbers of pens that fit that requirement : 1 pen : $ 0.35 2 pens : $ 0.70 3 pens : $ 1.05 4 pens : $ 1.40 5 pens : $ 1.75 balance 1.25 5 pencils cost $ 1.25 that ' s 5 pens and 5 pencils choice ( c ) is correct ." - }, - { - "Answer": 63, - "Options": "a ) 24.5 , b ) 63 , c ) 65 , d ) 36 , e ) 24.19", - "Correct": "b", - "Explanation": "\"explanation : if rahul age is x , then sachin age is x - 18 , so , 9 x - 162 = 7 x 2 x = 162 x = 81 so sachin age is 81 - 18 = 63 answer : b ) 63\"" - }, - { - "Answer": 0.8, - "Options": "a ) 3 / 5 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 5 , e ) 5 / 6", - "Correct": "d", - "Explanation": "you can use the weighted averages formula for a 10 sec solution . no of females / no of males = ( 50 - 42 ) / ( 42 - 40 ) = 4 / 1 no of females as a fraction of total employees = 4 / ( 4 + 1 ) = 4 / 5 ; answer : d" - }, - { - "Answer": 17, - "Options": "a ) 132 , b ) 26 , c ) 17 , d ) 11 , e ) 12", - "Correct": "c", - "Explanation": "explanation : total pupil = 55 debate + singing = 10 + 18 = 28 the intersection for two = 55 \u00e2 \u20ac \u201c 10 \u00e2 \u20ac \u201c 28 = 17 play both games . answer : c" - }, - { - "Answer": 45, - "Options": "a ) 45 % , b ) 40 % , c ) 35 % , d ) 30 % , e ) 25 %", - "Correct": "a", - "Explanation": "\"70 % answered the first question correctly and 20 % answered neither correctly . then 10 % missed the first question but answered the second question correctly . then the percent who answered both correctly is 55 % - 10 % = 45 % . the answer is a .\"" - }, - { - "Answer": 100, - "Options": "a ) 46 , b ) q . 80 , c ) q . 90 , d ) q . 100 , e ) 200", - "Correct": "d", - "Explanation": "\"100 = x + x - 20 + 23 - 23 x = 60 , so , product a = 60 % , product b = 40 % , both = 23 % , neither = 23 % 23 % of the total no . of people should be an integer . so , a , bc are out . 60 % of d and 40 % of d are both integers . so , d satisfies all conditions . so , answer is d .\"" - }, - { - "Answer": 109395, - "Options": "a ) 104345 , b ) 107375 , c ) 108385 , d ) 109395 , e ) 105355", - "Correct": "d", - "Explanation": "the only thing you actually know about the correct number a is that it is divisible by 153 and has 5 as a factor . you should immediately try to find the factors of 153 and look for them in the options . 153 = 9 * 17 divisibility by 9 is easy to check . only ( d ) satisfies ." - }, - { - "Answer": 9, - "Options": "a ) 4 , b ) 6 , c ) 9 , d ) 12 , e ) 15", - "Correct": "c", - "Explanation": "\"originally there were 3 k cooks and 10 k waiters . 14 k = 10 k + 12 k = 3 there are 9 cooks . the answer is c .\"" - }, - { - "Answer": 900, - "Options": "a ) s 1200 , b ) s 1500 , c ) s 1600 , d ) s 1900 , e ) s 900", - "Correct": "e", - "Explanation": "explanation : let p = faruk , q = vasim , r = ranjith let p = 3 x , q = 5 x and r = 6 x . then , 5 x = 1500 ? x = 300 . p = 900 , q = 1500 and r = 1800 . hence , ( r - p ) = ( 1800 - 900 ) = 900 answer : e" - }, - { - "Answer": 18, - "Options": "a ) 6 , b ) 16 , c ) 18 , d ) 30 , e ) 174", - "Correct": "c", - "Explanation": "\"the number of integers that belong to set x only is 12 - 6 = 6 ; the number of integers that belong to set y only is 18 - 6 = 12 ; the number of integers that belong to set x or set y , but not both is 6 + 12 = 18 . answer : c .\"" - }, - { - "Answer": 0.40000000000000013, - "Options": "a ) 7 / 5 , b ) 6 / 11 , c ) 2 / 5 , d ) 1 / 3 , e ) 4 / 15", - "Correct": "c", - "Explanation": "let there be 15 employees cell phone = 10 pagers = 6 neither pager nor cell phone = 5 so , 10 = 10 + 6 - x or , x = 6 so , fraction of the employees had both cell phones and pagers = 6 / 15 = > 2 / 5 answer : c" - }, - { - "Answer": 0.13333333333333333, - "Options": "a ) 2 / 15 , b ) 2 / 21 , c ) 5 / 26 , d ) 3 / 29 , e ) 4 / 27", - "Correct": "a", - "Explanation": "\"p ( both are red ) , = 4 c 210 c 2 = 4 c 210 c 2 = 6 / 45 = 2 / 15 a\"" - }, - { - "Answer": 3375, - "Options": "a ) 3375 , b ) 7292 , c ) 8291 , d ) 3929 , e ) 2727", - "Correct": "a", - "Explanation": "\"no of values n can take is 1 15 ^ 3 = 3375 answer : a\"" - }, - { - "Answer": 10, - "Options": "a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) indeterminate", - "Correct": "a", - "Explanation": "let us consider tht x student are tohse who passed in both english and maths . . . so first we remove x student from both of them therefore , english = 30 - x maths = 20 - x now , number of students more in english = ( 30 - x ) - ( 20 - x ) = 30 - x - 20 + x = 10 answer : a" - }, - { - "Answer": 216, - "Options": "a ) 629 , b ) 729 , c ) 829 , d ) 929 , e ) 216", - "Correct": "e", - "Explanation": "\"no of values n can take is 1 6 ^ 3 = 216 answer : e\"" - }, - { - "Answer": 25, - "Options": "a ) 6 , b ) 15 , c ) 25 , d ) 33 , e ) 54", - "Correct": "c", - "Explanation": "\"formula for calculating two overlapping sets : a + b - both + not ( a or b ) = total so in our task we have equation : 41 ( french ) + 22 ( german ) - 9 ( both ) + not = 79 54 + not = 79 not = 79 - 54 = 25 so answer is c\"" - }, - { - "Answer": 10, - "Options": "a ) 10 , b ) 15 , c ) 16 , d ) 18 , e ) 22", - "Correct": "a", - "Explanation": "draw a venn diagram yourself ! b + c - bc = number of students that play either basketball or cricket 7 + 8 - 5 = 10 a )" - }, - { - "Answer": 0.46666666666666673, - "Options": "a ) 1 / 2 , b ) 2 / 12 , c ) 14 / 30 , d ) 3 / 8 , e ) 7 / 9", - "Correct": "c", - "Explanation": "\"a : 1 / 2 = 2 / 5 : 3 / 7 as the product of the means is equal to the product of the extremes . a * 3 / 7 = 1 / 2 * 2 / 5 a * 3 / 7 = 2 / 10 a = 14 / 30 = > a = 14 / 30 answer : c\"" - }, - { - "Answer": 1, - "Options": "a ) 1 : 1 , b ) 3 : 8 , c ) 4 : 3 , d ) 8 : 9 , e ) 1 : 3", - "Correct": "a", - "Explanation": "given ; 4 duck = 3 hen ; or , duck / hen = 3 / 4 ; let hen ' s 1 leap = 4 meter and ducks 1 leap = 3 meter . then , ratio of speed of hen and duck = 4 * 6 / 3 * 8 = 1 : 1 ' ' answer : 1 : 1 ;" - }, - { - "Answer": 100, - "Options": "a ) 46 , b ) 80 , c ) d . 90 , d ) d . 100 , e ) 200", - "Correct": "d", - "Explanation": "100 = x + x - 20 + 23 - 23 x = 60 , so , product a = 60 % , product b = 40 % , both = 23 % , neither = 23 % 23 % of the total no . of people should be an integer . so , a , bc are out . 60 % of d and 40 % of d are both integers . so , d satisfies all conditions . so , answer is d ." - }, - { - "Answer": 50, - "Options": "a ) 40 , b ) 45 , c ) 48 , d ) 50 , e ) 53", - "Correct": "d", - "Explanation": "we have b + a + s = 210 and s = 2 a , s = 4 b and a = 2 b solving these eqs we got that singh have rs . 120 in the end bhatia have 30 and astikar have 60 . so singh ' s profit is 120 - 70 = 50 answer : d" - }, - { - "Answer": 75, - "Options": "a ) 71 , b ) 72 , c ) 73 , d ) 74 , e ) 75", - "Correct": "e", - "Explanation": "let x be the weight of the sister . then the student ' s weight is 2 x + 5 . x + ( 2 x + 5 ) = 110 3 x = 105 x = 35 kg then the student ' s weight is 75 kg . the answer is e ." - }, - { - "Answer": 21, - "Options": "a ) 6 . , b ) 16 . , c ) 18 , d ) 21 , e ) 26", - "Correct": "d", - "Explanation": "5 = 1 p + 1 n 93 = xp + 15 n , where x is the number of pencils possible prices for 1 p & 1 n ( integers ) : n = 1 p = 4 then 15 n = 15 , 4 x = 93 - 15 = 78 , x = 19.5 ( not an integer ) n = 2 p = 3 then 15 n = 30 , 3 x = 93 - 30 = 63 , x = 21 ( the answer we were looking for , no need to continue calculations ) n = 3 p = 2 n = 4 p = 1 answer : d" - }, - { - "Answer": 10, - "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) greater than 10", - "Correct": "d", - "Explanation": "all perfect squares have odd # of factors . squaring integers 1 - 10 produces 1 , 4 , 9 , 16 , . . . 100 which all have odd # of factors . answer is d" - }, - { - "Answer": 0.00014583333333333335, - "Options": "a ) 3 / 16,000 , b ) 1 / 8,100 , c ) 7 / 48,000 , d ) 1 / 90 , e ) 2 / 45", - "Correct": "c", - "Explanation": "\"solution provided by stanford 2012 is correct : 70 / 800 choosing one of the cellos which has a pair viola , 1 / 600 choosing the viola which is the pair of chosen cello - - > p = 70 / 800 * 1 / 600 = 7 / 48,000 . answer : c .\"" - }, - { - "Answer": 150, - "Options": "a ) 3.69 , b ) 3.66 , c ) 3.6 , d ) 150 , e ) 3.61", - "Correct": "d", - "Explanation": "\"ans : by framing equations we get 30 l + 3 q = 333 30 l + 6 q = 366 eliminate q by multiplying the first equation by 2 and subtracting second equation from the first 60 l + 6 q = 666 30 l + 6 q = 366 30 l = 300 = > l = 10 then we get l = 10 cost of 15 kgs of apples = 15 x 10 = 150 answer : d\"" - }, - { - "Answer": 5, - "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", - "Correct": "e", - "Explanation": "\"both cooking and weaving = 20 - ( 7 + 5 + 3 ) = 5 so , the correct answer is e .\"" - }, - { - "Answer": 21, - "Options": "a ) 10 , b ) 20 , c ) 21 , d ) 25 , e ) 27", - "Correct": "c", - "Explanation": "\"as a : b : : 7 : 5 - - - > only option c is a multiple of 7 and hence it is a good place to start . also a : b : : 7 : 5 means that , a = ( 712 ) * total and b = ( 5 / 12 ) * total if a = 21 , b = 15 - - - > remove 9 litres - - - > you remove ( 7 / 12 ) * 9 of a - - - > a remaining = 21 - ( 7 / 12 ) * 9 = 63 / 4 similarly , for b , you remove ( 5 / 12 ) * 9 - - - > b remaining = 15 - ( 5 / 12 ) * 9 = 45 / 4 and then add 9 more litres of b - - - > 9 + 45 / 4 = 81 / 4 thus a / b ( final ratio ) = ( 45 / 4 ) / ( 81 / 4 ) = 7 : 9 , the same as the final ratio mentioned in the question . hence c is the correct answer . a / b = 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) , where 7 x and 5 x are initial quantities of a and b respectively . thus , 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) - - - > giving you x = 3 . thus a ( original ) q = 7 * 3 = 21 . c\"" - }, - { - "Answer": 376, - "Options": "a ) 188 , b ) 258 , c ) 376 , d ) 470 , e ) 517", - "Correct": "c", - "Explanation": "\"consider 5 x acres of land used for bean consider 2 x acres of land used for wheat consider 4 x acres of land used for corn total given is 1034 acres 11 x = 1034 x = 94 land used for corn r = 4 * 94 = 376 correct option - c\"" - }, - { - "Answer": 9, - "Options": "a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 8", - "Correct": "a", - "Explanation": "let no . of persons who speeks booth latin and french = x so , no . of persons who speeks only latin = 13 - x no . of persons who speeks only french = 15 - x no . of persons who speeks dont speek any lag = 6 therefore ( 13 - x ) + ( 15 - x ) + x + 6 = 25 34 - x = 25 x = 9 answer : a" - }, - { - "Answer": 20, - "Options": "a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25", - "Correct": "d", - "Explanation": "the ratio of p to v in smothie m is 4 is to 1 and that in y is 1 is to 5 . p 1 + p 2 = 24 v 1 + v 2 = 25 p 1 = 4 v 1 p 2 = v 2 / 5 4 v 1 + v 2 / 5 = 24 v 1 + v 2 = 25 4 v 2 - v 2 / 5 = 76 19 v 2 / 5 = 76 = > v 2 = 20 = > v 1 = 5 = > p 1 = 20 answer - d" - }, - { - "Answer": 0.17142857142857143, - "Options": "a ) 24 / 35 , b ) 17 / 35 , c ) 8 / 25 , d ) 6 / 35 , e ) 1 / 25", - "Correct": "d", - "Explanation": "this question can also be solved by using ' brute force ' - you just have to ' map out ' the possibilities . the namejohnsonhas 7 letters and the namejoneshas 5 letters , so there are ( 7 ) ( 5 ) = 35 possible pairings of letters that can occur . of those 35 , the pairings that include the same letter both times are : j and j 1 st o and o 1 st n and n s and s 2 nd o and o 2 nd n and n total : 6 so the probability that the two randomly selected letters will match is 6 / 35 . d" - }, - { - "Answer": 18, - "Options": "a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20", - "Correct": "d", - "Explanation": "\"the ratio 1 : 34 = 2 : 68 so the ratio changed from 2 : 63 to 2 : 68 . 68 - 63 = 5 which is 1 / 9 of the increase in 45 associates . the ratio changed from 18 : 567 to 18 : 612 . thus the number of partners is 18 . the answer is d .\"" - }, - { - "Answer": 13, - "Options": "a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16", - "Correct": "b", - "Explanation": "53 ! + 54 ! = 53 ! + 54 * 53 ! = 53 ! ( 1 + 54 ) = 53 ! * 55 number of trailing 0 s in 53 ! = number of 5 s in the expansion of 53 ! = 10 + 2 = 12 there is 1 more 5 in 55 . hence , total number of trailing 0 s = 12 + 1 = 13 answer ( b ) . in most cases , when we are adding multiple terms , all of which have trailing 0 s , the sum will have as many trailing 0 s as that in the lowest term . example : 20 + 2300 + 34210000 = 34212320 - > one 0 because lowest term 20 has one 0 . this case has an exception because of an additional 5 in 55 . answer is b" - }, - { - "Answer": 17, - "Options": "a ) 12 , b ) 15 , c ) 17 , d ) 18 , e ) 22", - "Correct": "c", - "Explanation": "\"draw a venn diagram yourself ! b + c - bc = number of students that play either basketball or cricket 12 + 8 - 3 = 17 c )\"" - }, - { - "Answer": 48, - "Options": "a ) 18 , b ) 28 , c ) 32 , d ) 48 , e ) 58", - "Correct": "d", - "Explanation": "\"et no of sheep and horses are 6 k and 7 k no of horses = 12880 / 230 = 56 now 7 k = 56 and k = 8 no of sheep = ( 6 * 8 ) = 48 answer : d\"" - }, - { - "Answer": 123.75999999999999, - "Options": "a ) 201 , b ) 240 , c ) 124 , d ) 125 , e ) 180", - "Correct": "c", - "Explanation": "\"according to above 500 ! has 500 / 5 + 500 / 25 + 500 / 125 = 100 + 20 + 4 = 124 trailing zeros . answer : c .\"" - }, - { - "Answer": 0.8333333333333334, - "Options": "a ) 1 / 6 , b ) 2 / 9 , c ) 5 / 6 , d ) 7 / 9 , e ) 8 / 9", - "Correct": "c", - "Explanation": "we have three pairs of dogs for the 6 with exactly one littermate , and one triplet , with each having exactly two littermates . so , in fact there are two types of dogs : those with one littermate - say a , and the others with two littermates - b . work with probabilities : choosing two dogs , we can have either one dog of type b or none ( we can not have two dogs both of type b ) . the probability of choosing one dog of type b and one of type a is 3 / 9 * 6 / 8 * 2 = 1 / 2 ( the factor of 2 for the two possibilities ba and ab ) . the probability of choosing two dogs of type a which are not littermates is 6 / 9 * 4 / 8 = 1 / 3 ( choose one a , then another a which is n ' t the previous one ' s littermate ) . the required probability is 1 / 2 + 1 / 3 = 5 / 6 . find the probability for the complementary event : choose aa or bb . probability of choosing two dogs of type a who are littermates is 6 / 9 * 1 / 8 = 1 / 12 . probability of choosing two dogs of type b ( who necessarily are littermates ) is 3 / 9 * 2 / 8 = 1 / 12 . again , we obtain 1 - ( 1 / 12 + 1 / 12 ) w = 5 / 6 . answer : c" - }, - { - "Answer": 63, - "Options": "a ) 42 , b ) 49 , c ) 56 , d ) 63 , e ) 70", - "Correct": "d", - "Explanation": "\"let sandy ' s age be 7 x and let molly ' s age be 9 x . 9 x - 7 x = 18 x = 9 sandy is 63 years old . the answer is d .\"" - }, - { - "Answer": 1, - "Options": "a ) 1 million , b ) 2 million , c ) 4 million , d ) 8 million , e ) none of these", - "Correct": "a", - "Explanation": "solution : let the number of bacteria in the 1 st generation be x , then number of bacteria in 2 nd , 3 rd , 4 th . . . . . generation would be 8 ( x / 2 ) , 8 ( 4 x / 2 ) , 8 ( 16 x / 2 ) . . . . and so on . as x , 4 x , 16 x , 64 x . . . . . it is in gp with common ratio 4 . hence , 7 th term of gp , x ( 4 ) 6 = 4096 or , x = 1 or 1 million . answer : option a" - }, - { - "Answer": 10, - "Options": "a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16", - "Correct": "b", - "Explanation": "\"we should find the highest power of 3 in 25 ! : 25 / 3 + 25 / 3 ^ 2 = 8 + 2 = 10 ( take only the quotient into account ) . . so the highest power of 3 in 25 ! is 10 . answer : b .\"" - }, - { - "Answer": 3179, - "Options": "a ) s . 2890 , b ) s . 2330 , c ) s . 1190 , d ) s . 1620 , e ) s . 3179", - "Correct": "e", - "Explanation": "\"ram : gopal = 7 : 17 = 49 : 119 gopal : krishan = 7 : 17 = 119 : 289 ram : gopal : krishan = 49 : 119 : 289 ram : krishan = 49 : 289 thus , 49 : 289 = 539 : n & there n = 289 x 539 / 49 = rs . 3179 answer : e\"" - }, - { - "Answer": 391, - "Options": "a ) 276 , b ) 299 , c ) 391 , d ) 345 , e ) 355", - "Correct": "c", - "Explanation": "\"clearly , the numbers are ( 23 x 13 ) and ( 23 x 17 ) . larger number = ( 23 x 17 ) = 391 . answer : option c\"" - }, - { - "Answer": 600, - "Options": "a ) 276 , b ) 600 , c ) 699 , d ) 722 , e ) 745", - "Correct": "b", - "Explanation": "\"the numbers are ( 40 x 11 ) and ( 40 x 15 ) . larger number = ( 40 x 15 ) = 600 . answer : b\"" - }, - { - "Answer": 0.1282051282051282, - "Options": "a ) 1 / 13 , b ) 2 / 23 , c ) 5 / 39 , d ) 4 / 27 , e ) 3 / 23", - "Correct": "c", - "Explanation": "\"p ( both are red ) , 5 c 213 c 2 = 6 c 213 c 2 = 10 / 78 = 5 / 39 c\"" - }, - { - "Answer": 0.3333333333333333, - "Options": "a ) 1 / 5 , b ) 1 / 3 , c ) 3 / 7 , d ) 2 / 7 , e ) 3 / 7", - "Correct": "b", - "Explanation": "let b stand for boy and g for girl . the sample space of the experiment is s = { ( g , g ) , ( g , b ) , ( b , g ) , ( b , b ) } let e and f denote the following events : e : \u2018 both the children are girls \u2019 f : \u2018 at least one of the child is a girl \u2019 then e = { ( g , g ) } and f = { ( g , g ) , ( g , b ) , ( b , g ) } now e n f = { ( g , g ) } thus p ( f ) = 3 / 4 and p ( e n f ) = 1 / 4 therefore p ( e | f ) = p ( e \u2229 f ) / p ( f ) = ( 1 / 4 ) / ( 3 / 4 ) = 1 / 3 b )" - }, - { - "Answer": 5, - "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", - "Correct": "c", - "Explanation": "we can take numbers , as price of car 5 , 8 for train and 31 total for ease . now we can determine quickly that total number should range between 31 / 8 < = n < = 31 / 5 , so ans should be between 3 and 7 . now solving the expression 5 a + 8 b = 31 decreasing 31 in multiple of 5 and checking divisibility of that number by 8 . this way we get 3 cars , 2 trains we get $ 31.00 total 3 * 5 + 2 * 8 = 31 hence total number is 3 + 2 = 5 ans c" - }, - { - "Answer": 22, - "Options": "a ) 30 , b ) 28 , c ) 26 , d ) 22 , e ) 19", - "Correct": "d", - "Explanation": "total number of enrolled students = 30 number of students who did not take test = 5 hence , number of students who took test = 30 - 5 = 25 number of students who answered q 2 correctly = 22 , therefore , all students who took test answered q 2 correctly . so , number of students who answered q 1 correctly , also answered q 2 correctly = 22 . number of students who answered both q 1 & q 2 correctly = 22 . answer : d" - }, - { - "Answer": 120, - "Options": "a ) 110 , b ) 120 , c ) 130 , d ) 140 , e ) 150", - "Correct": "b", - "Explanation": "\"the number of nurses at the hospital is ( 6 / 10 ) * 200 = 120 . the answer is b .\"" - }, - { - "Answer": 9, - "Options": "a ) a ) 10 , b ) b ) 12 , c ) c ) 15 , d ) d ) 14 , e ) e ) 9", - "Correct": "e", - "Explanation": "\"let the numbers be x , 2 x , 4 x then , x ^ 2 + 4 x ^ 2 + 16 x ^ 2 = 1701 21 x ^ 2 = 1701 x ^ 2 = 81 x = 9 answer is e\"" - }, - { - "Answer": 60, - "Options": "a ) 70 , b ) 60 , c ) 90 , d ) 100 , e ) 110", - "Correct": "b", - "Explanation": "consider total number of players n ( o u i ) = 400 players who plays outdoors n ( o ) = 350 players who plays indoors n ( i ) = 110 players who plays both n ( o \u00e2 \u02c6 \u00a9 i ) = ? n ( o u i ) = n ( o ) + n ( i ) - n ( o \u00e2 \u02c6 \u00a9 i ) 400 = 350 + 110 - n ( o \u00e2 \u02c6 \u00a9 i ) n ( o \u00e2 \u02c6 \u00a9 i ) = 460 - 400 n ( o \u00e2 \u02c6 \u00a9 i ) = 60 so people read both science fiction and literacy works are 60 answer : b" - }, - { - "Answer": 20, - "Options": "a ) 10 % , b ) 20 % , c ) 30 % , d ) 50 % , e ) 65 %", - "Correct": "b", - "Explanation": "\"{ total } = { first } + { second } - { both } + { neither } 100 % = 75 % + 25 % - { both } + 20 % - - > { both } = 20 % . answer : b .\"" - }, - { - "Answer": 80, - "Options": "a ) 70 , b ) 80 , c ) 90 , d ) 100 , e ) 120", - "Correct": "b", - "Explanation": "the investors can be categorized into three groups : ( 1 ) those who have investments in equities only . ( 2 ) those who have investments in securities only . ( 3 ) those who have investments in both equities and securities . let xx , yy , and zz denote the number of people in the respective categories . since the total number of investors is 110 , we have x + y + z = 110 x + y + z = 110 - - - - - - - - - - - - - ( 1 ) also , the number of people with investments in equities is x + zx + z and the number of people with investments in securities is y + zy + z . since exactly 25 % 25 % of the investors in equities have investments in securities , we have the equation 25100 \u00d7 ( x + z ) = z 25100 \u00d7 ( x + z ) = z 25100 \u00d7 x = 25100 \u00d7 z 25100 \u00d7 x = 25100 \u00d7 z x = 3 zx = 3 z - - - - - - - - - - - - - - - - - - - ( 2 ) since exactly 40 % 40 % of the investors in securities have investments in equities , we have the equation 40100 \u00d7 ( y + z ) = z 40100 \u00d7 ( y + z ) = z ( y + z ) = 5 z 2 ( y + z ) = 5 z 2 y = 3 z 2 y = 3 z 2 substituting equations ( 2 ) and ( 3 ) into equation ( 1 ) yields 3 z + 3 z 2 + z = 1103 z + 3 z 2 + z = 110 11 z 2 = 11011 z 2 = 110 z = 110 \u00d7 211 = 20 z = 110 \u00d7 211 = 20 hence , the number of people with investments in equities is : x + z = 3 z + z = 3 \u00d7 20 + 20 = 60 + 20 x + z = 3 z + z = 3 \u00d7 20 + 20 = 60 + 20 = 80 b" - }, - { - "Answer": 30, - "Options": "a ) 24 , b ) 30 , c ) 48 , d ) 72 , e ) 132", - "Correct": "b", - "Explanation": "3 / 11 = x / x + 82 3 * 82 = 8 x x = 30 b . 30" - }, - { - "Answer": 130, - "Options": "a ) 120 , b ) 150 , c ) 130 , d ) 180 , e ) 220", - "Correct": "c", - "Explanation": "\"n ( a ) = 325 , n ( b ) = 175 , n ( aub ) = 420 - 50 = 370 . required number = n ( anb ) = n ( a ) + n ( b ) - n ( aub ) = 325 + 175 - 370 = 130 . answer is c\"" - }, - { - "Answer": 0.13333333333333333, - "Options": "a ) 4 / 15 , b ) 1 / 3 , c ) 2 / 15 , d ) 4 / 5 , e ) 7 / 6", - "Correct": "c", - "Explanation": "\"a : b = 2 : 3 - - 1 b : c = 1 : 5 = > b : c = 3 : 15 - - 2 from 1 and 2 , we get a : c = 2 : 15 answer c\"" - }, - { - "Answer": 50, - "Options": "a ) 10 % , b ) ( 8 ) 20 % , c ) 50 % , d ) 60 % , e ) 65 %", - "Correct": "c", - "Explanation": "{ total } = { first } + { second } - { both } + { neither } 100 % = 75 % + 55 % - { both } + 20 % - - > { both } = 50 % . answer : c" - }, - { - "Answer": 120, - "Options": "a ) 70 , b ) 96 , c ) 108 , d ) 120 , e ) 150", - "Correct": "d", - "Explanation": "2 x 2 matrix will be the easiest way to calculate this . text in black : given statements text in red : calculated values thus d = 120 is the correct answer" - }, - { - "Answer": 12, - "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12", - "Correct": "e", - "Explanation": "the ratio of flour to water is 22 : 5 . the ratio of flour to sugar is 5.5 : 2 = 22 : 8 . the new ratio of flour to water to sugar is 22 : 5 : 8 if we need 7.5 cups of water , then we need 12 cups of sugar . the answer is e ." - }, - { - "Answer": 71, - "Options": "a ) 70 , b ) 71 , c ) 72 , d ) 73 , e ) 74", - "Correct": "b", - "Explanation": "\"let x be the weight of the sister . then the student ' s weight is 2 x + 5 . x + ( 2 x + 5 ) = 104 3 x = 99 x = 33 kg then the student ' s weight is 71 kg . the answer is b .\"" - }, - { - "Answer": 5, - "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", - "Correct": "e", - "Explanation": "\"both cooking and weaving = 18 - ( 4 + 4 + 5 ) = 5 so , the correct answer is e .\"" - }, - { - "Answer": 555707.2899999999, - "Options": "a ) 553681 , b ) 555181 , c ) 555681 , d ) 556581 , e ) 555581", - "Correct": "c", - "Explanation": "\"987 = 3 x 7 x 47 . so , the required number must be divisible by each one of 3 , 7 , 47 553681 - - > sum of digits = 28 , not divisible by 3 555181 sum of digits = 25 , not divisible by 3 555681 is divisible by each one of 3 , 7 , 47 . 556581 sum of digits = 30 , not divisible by 7 555581 sum of digits = 29 , not divisible by 3 so the answer is c .\"" - }, - { - "Answer": 18, - "Options": "a ) 6 , b ) 12 , c ) 18 , d ) 26 , e ) 28", - "Correct": "c", - "Explanation": "\"solution let the numbers be 3 x , 4 x and 6 x . then , 3 x \u00d7 4 x \u00d7 6 x = 1944 \u2039 = \u203a 72 x 3 = 1944 \u2039 = \u203a x 3 = 27 \u2039 = \u203a x = 3 therefore , largest number = 6 x = 18 . answer c\"" - }, - { - "Answer": 25, - "Options": "a ) 25 % , b ) ( 8 ) 20 % , c ) 30 % , d ) 50 % , e ) 65 %", - "Correct": "a", - "Explanation": "\"i did n ' t understand how to connect 20 percent with the whole equation . why 20 is out of the percentile diagram ( circles ) but inside of 100 ? 20 % appeared in the exam ; however did not answer question aquestion b correctly so they are out of the two circles , however as they have appeared in the exam , they have to be taken into consideration for calculation purpose i am doing it this way : suppose the total class size is 100 , then 20 percent of the class answered incorrectly and rest 80 percent answered correctly in question 1 or 2 or both . now , 100 - [ ( 75 - x ) + x + ( 30 - x ) ] = 20 . . . . . . . . . . values are in percent x = 20 - 100 + 105 x = 25 ans : a\"" - }, - { - "Answer": 70, - "Options": "a ) 60 % , b ) 65 % , c ) 70 % , d ) 75 % , e ) 80 %", - "Correct": "c", - "Explanation": "\"{ total } = { first correctly } + { second correctly } - { both correctly } + { neither correctly } 100 = 85 + 80 - { both correctly } + 5 { both correctly } = 70 . answer : c .\"" - }, - { - "Answer": 5, - "Options": "a ) 9 , b ) 36 , c ) 5 , d ) 6 , e ) 1", - "Correct": "c", - "Explanation": "square root is a number times itself square root of 625 = 25 , 25 / 5 = 5 ( c ) 5" - }, - { - "Answer": 8, - "Options": "a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12", - "Correct": "d", - "Explanation": "the solution should be the same for all numbers that fulfill the condition above . as x and y are odd prime numbers , they must be > 2 . also , they must be distinct as x < y . i choose x = 3 and y = 5 : how many factors does 2 x 3 x 5 = 30 have : 1 , 2 , 3 , 5 , 6 , 10 , 15 , 30 = 8 distinct positive integer factors . hence , the correct answer is d ." - }, - { - "Answer": 0.8181818181818181, - "Options": "a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 9 / 11", - "Correct": "e", - "Explanation": "\"let ' s say that the total original mixture a is 100 ml the original mixture a thus has 50 ml of alcohol out of 100 ml of solution you want to replace some of that original mixture a with another mixture b that contains 25 ml of alcohol per 100 ml . thus , the difference between 80 ml and 25 ml is 55 ml per 100 ml of mixture . this means that every time you replace 100 ml of the original mixture a by 100 ml of mixture b , the original alcohol concentration will decrease by 25 % . the question says that the new mixture , let ' s call it c , must be 35 % alcohol , a decrease of only 45 % . therefore , 45 out of 55 is 9 / 11 and e is the answer .\"" - }, - { - "Answer": 906.6666666666666, - "Options": "a ) 900 , b ) 1600 , c ) 750 , d ) 890 , e ) 1010", - "Correct": "a", - "Explanation": "red : green : blue = 15 + 13 + 17 = 45 ; ratio of the red balls = 15 / 40 simplify = 3 / 8 * 2400 = 900 . answer = a" - }, - { - "Answer": 10.666666666666666, - "Options": "a ) 12 kg , b ) 8.3 kg , c ) 10.7 kg , d ) 15.5 kg , e ) 7 kg", - "Correct": "c", - "Explanation": "\"let the required quantity of copper be x kg 9 : 4 : : 24 : x 9 x = 4 * 24 x = 10 2 / 3 kg = 32 / 3 = 10.7 kg answer is c\"" - }, - { - "Answer": 2600, - "Options": "a ) 1260 , b ) 2600 , c ) 3600 , d ) 4200 , e ) 5200", - "Correct": "b", - "Explanation": "let the total number of trucks = 3 x total number of sedans = 7 x total number of motorcycles = 2 x total number of sedans = 9100 = > 7 x = 9100 = > x = 1300 total number of motorcycles = 2 x = 2 * 1300 = 2600 answer b" - }, - { - "Answer": 5000, - "Options": "a ) rs . 3600 , b ) rs . 3603 , c ) rs . 3639 , d ) rs . 3632 , e ) rs . 5000", - "Correct": "e", - "Explanation": "\"let the income and the expenditure of the person be rs . 4 x and rs . 3 x respectively . income , 4 x = 20000 = > x = 5000 savings = income - expenditure = 4 x - 3 x = x so , savings = rs . 5000 answer : e\"" - }, - { - "Answer": 0.29, - "Options": "a ) 1 / 10 , b ) 3 / 10 , c ) 1 / 2 , d ) 7 / 10 , e ) 29 / 100", - "Correct": "e", - "Explanation": "\"c + m + b - cm - mb - cb - 2 cmb = 100 c - cake buyers , m - muffin and b - bread buyers . cm , mb , cb and cmb are intersecting regions . the question asks for people who have bought only bread mixes = b - cb - mb - 2 cmb has to be found out . 50 + 40 + b - cb - mb - 19 - 2 cmb = 100 b - cb - mb - 2 cmb = 29 hence the probability = 29 / 100 . e\"" - }, - { - "Answer": 16, - "Options": "a ) 14 lts , b ) 18 lts , c ) 20 lts , d ) 16 lts , e ) 26 lts", - "Correct": "d", - "Explanation": "% age of liquid base in the original mixture = 1 / 5 x 100 = 20 % in the final mixture % of the liquid base = 3 / 5 x 100 = 60 % now using the rule of allegation hence reduced quantity of the first mixture and the quantity of mixture b which is to be added are the same . total mixture = 10 + 10 = 20 liters and quantity of liquid a = 20 / 5 x 4 = 16 lts answer : d" - }, - { - "Answer": 9000.000000000002, - "Options": "a ) rs . 7500 , b ) rs . 8000 , c ) rs . 8500 , d ) rs . 9000 , e ) rs . 6000", - "Correct": "d", - "Explanation": "\"let hari \u2019 s capital be rs . x . then , 3500 * 12 / 7 x = 2 / 3 = > 14 x = 126000 = > x = 9000 . answer : d\"" - }, - { - "Answer": 18, - "Options": "a ) 268 , b ) 180 , c ) 150 , d ) 18 , e ) 88", - "Correct": "d", - "Explanation": "\"consider total number of reader n ( s u l ) = 250 people who read science fiction n ( s ) = 180 people who read literacy works n ( l ) = 88 both science fiction and literacy n ( s \u00e2 \u02c6 \u00a9 l ) = ? n ( s u l ) = n ( s ) + n ( l ) - n ( s \u00e2 \u02c6 \u00a9 l ) 250 = 180 + 88 - n ( s \u00e2 \u02c6 \u00a9 l ) n ( s \u00e2 \u02c6 \u00a9 l ) = 268 - 250 n ( s \u00e2 \u02c6 \u00a9 l ) = 18 so people read both science fiction and literacy works are 18 answer : d\"" - }, - { - "Answer": 1, - "Options": "a ) 3 , b ) 2 , c ) can not be determined , d ) 4 , e ) 1", - "Correct": "e", - "Explanation": "let the factor be a ^ x * b ^ y . . . . . so ( x + 1 ) ( y + 1 ) . . . . . = 211 . . now 211 is a prime number . . . so only one variable x or y is 210 and the others are 0 . . ( 210 + 1 ) ( 0 + 1 ) . . . so the number becomes a ^ 210 . . thus only one prime factor is there ." - }, - { - "Answer": 4, - "Options": "a ) 3 , b ) 4 , c ) 7 , d ) 18 , e ) 9", - "Correct": "b", - "Explanation": "a whole number that divides exactly into another whole number is called a factor 20 / 5 = 4 answer b" - }, - { - "Answer": 37.5, - "Options": "a ) 40 , b ) 45 , c ) 50 , d ) 75 / 2 , e ) 35", - "Correct": "d", - "Explanation": "\"b : d : w = 2 : 25 : 100 bnew / dnew = ( 1 / 3 ) * ( 2 / 25 ) = ( 2 / 75 ) dnew / wnew = ( 1 / 2 ) * ( 25 / 100 ) = ( 1 / 8 ) wnew = 300 dnew = wnew / 5 = 300 / 8 = 75 / 2 so , answer will be d\"" - }, - { - "Answer": 3800, - "Options": "a ) 3800 , b ) 3607 , c ) 3608 , d ) 3602 , e ) 3603", - "Correct": "a", - "Explanation": "\"let the income and the expenditure of the person be rs . 5 x and rs . 4 x respectively . income , 5 x = 19000 = > x = 3800 savings = income - expenditure = 5 x - 4 x = x so , savings = rs . 3800 . answer : a\"" - }, - { - "Answer": 67.66666666666667, - "Options": "a ) 67.6 , b ) 1.58 , c ) 2.47 , d ) 3.54 , e ) 6.51", - "Correct": "a", - "Explanation": "\"the answer is ( 300 - 100 ) / 3 + 1 = 67.6 answer is a\"" - }, - { - "Answer": 14, - "Options": "a ) 12 , b ) 18 , c ) 14 , d ) 20 , e ) 22", - "Correct": "c", - "Explanation": "\"ci * vi = cf * vf ( 7 / 12 ) * ( v 1 - 6 ) = ( 7 / 16 ) * v 1 ( v 1 - 6 ) / v 1 = 3 / 4 6 accounts for the difference of 1 on ratio scale so initial volume = v 1 = 4 * 6 = 24 litres . 7 / 12 of the initial mixture was liquid a so liquid a was ( 7 / 12 ) * 24 = 14 litres . answer : c\"" - }, - { - "Answer": 0.21428571428571427, - "Options": "a ) 2 / 7 , b ) 3 / 7 , c ) 3 / 14 , d ) 5 / 28 , e ) 9 / 28", - "Correct": "c", - "Explanation": "the number of ways of choosing 2 books from the shelf is 8 c 2 = 28 . the number of ways of choosing 2 red books is 4 c 2 = 6 . p ( 2 red books ) = 6 / 28 = 3 / 14 . the answer is c ." - }, - { - "Answer": 35, - "Options": "a ) 30 , b ) 35 , c ) 20 , d ) 18 , e ) 10", - "Correct": "b", - "Explanation": "\"{ total } = { car } + { bike } - { both } + { neither } - - > 90 = 44 + { bike } - 14 + 11 - - > { bike } = 49 - - > # those who have bike only is { bike } - { both } = 49 - 14 = 35 . answer : b .\"" - }, - { - "Answer": 4000, - "Options": "a ) rs . 3600 , b ) rs . 4000 , c ) rs . 3639 , d ) rs . 3632 , e ) rs . 3602", - "Correct": "b", - "Explanation": "\"let the income and the expenditure of the person be rs . 5 x and rs . 4 x respectively . income , 5 x = 20000 = > x = 4000 savings = income - expenditure = 5 x - 4 x = x so , savings = rs . 4000 answer : b\"" - }, - { - "Answer": 28, - "Options": "a ) 24.58 , b ) 24.5 , c ) 26 , d ) 27 , e ) 28", - "Correct": "e", - "Explanation": "\"if rahul age is x , then sachin age is x - 8 , so ( x - 8 ) / x = 7 / 9 = > 9 x - 72 = 7 x = > 2 x = 72 = > x = 36 so sachin age is 36 - 8 = 28 answer : e\"" - }, - { - "Answer": 400, - "Options": "a ) 276 , b ) 299 , c ) 312 , d ) 400 , e ) none", - "Correct": "d", - "Explanation": "\"solution clearly , the numbers are ( 25 x 14 ) and ( 25 x 16 ) . larger number = ( 25 x 16 ) = 400 . answer d\"" - }, - { - "Answer": 528, - "Options": "a ) 540 , b ) 528 , c ) 530 , d ) 520 , e ) 510", - "Correct": "b", - "Explanation": "\"we know 37.5 % people study biology , therefore the no of people not studying = 100 - 40 = 60 % > therefore the people not studying biology out of a total 880 people are = 60 % of 880 > ( 60 / 100 ) * 880 = 528 people b\"" - }, - { - "Answer": 12000, - "Options": "a ) 14000 , b ) 15000 , c ) 16000 , d ) 12000 , e ) 17000", - "Correct": "d", - "Explanation": "ramesh : xyz = 5 : 4 xyz : rajeev = 8 : 9 then ramesh : xyz / rajeev : xyz = 5 : 4 / 9 : 8 ramesh / rajeev = 10 / 9 therefore ramesh : xyz : rajeev = 10 : 8 : 9 then rajeev share = ( 9 / 27 ) * 36000 = 12000 answer : d" - }, - { - "Answer": 0.44999999999999996, - "Options": "a ) 0.05 , b ) 0.45 , c ) 0.15 , d ) 0.5 , e ) 0.55", - "Correct": "b", - "Explanation": "\"p ( a or b ) = p ( a ) + p ( b ) - p ( a n b ) 0.6 = 0.4 + p ( a ) - 0.25 p ( a ) = 0.45 ans : b\"" - }, - { - "Answer": 40, - "Options": "a ) 15 , b ) 20 , c ) 30 , d ) 40 , e ) 45", - "Correct": "d", - "Explanation": "solution for soap e and soap b ( d ) 40" - }, - { - "Answer": 5, - "Options": "a ) 13 , b ) 14 , c ) 5 , d ) 6 , e ) 7", - "Correct": "c", - "Explanation": "integers having odd number of factors will be perfect squares . odd numbers will have odd perfect squares . thus , the possible values for the perfect squares are : 1 , 9,25 , 49,81 and the corresponding integers are 1 , 3,5 , 7,9 ( more than 4 ) . thus c is the correct answer ." - }, - { - "Answer": 142.375, - "Options": "a ) 100.6 kg , b ) 142 kg , c ) 135 kg , d ) 110.8 kg , e ) 114 kg", - "Correct": "b", - "Explanation": "\"quantity of tin in 135 kg of a = 135 * 5 / 8 = 84 kg quantity of tin in 145 kg of b = 145 * 2 / 5 = 58 kg quantity of tin in the new alloy = 84 + 58 = 142 kg answer is b\"" - }, - { - "Answer": 2, - "Options": "a ) 9 , b ) 2 , c ) 122 , d ) 6 , e ) 1", - "Correct": "b", - "Explanation": "\"square root is a number times itself square root of 16 = 4 , 4 / 2 = 2 ( b ) 2\"" - }, - { - "Answer": 49, - "Options": "a ) 42 , b ) 49 , c ) 56 , d ) 63 , e ) 70", - "Correct": "b", - "Explanation": "\"let sandy ' s age be 7 x and let molly ' s age be 9 x . 9 x - 7 x = 14 x = 7 sandy is 49 years old . the answer is b .\"" - }, - { - "Answer": 56, - "Options": "a ) 53 , b ) 54 , c ) 55 , d ) 56 , e ) 57", - "Correct": "d", - "Explanation": "70 = red + green - both red = 70 - green + both = 70 - 52 + 38 = 56 answer : d" - }, - { - "Answer": 0.4897959183673469, - "Options": "a ) 1 / 25 , b ) 12 / 49 , c ) 1 / 4 , d ) 24 / 49 , e ) 1 / 2", - "Correct": "d", - "Explanation": "\"r probability of one party having both spots : ( 1 / 2 ) * ( 24 / 49 ) = 12 / 49 ( 1 / 2 ) or ( 25 / 50 ) because it does not matter which party or which person gets the first spot . ( 24 / 49 ) because after one person from a particular party is chosen , there are 24 members of the same party left out of 49 total candidates . since this result can happen for both parties , ( 12 / 49 ) + ( 12 / 49 ) = ( 24 / 49 ) answer : d\"" - }, - { - "Answer": 14, - "Options": "a ) 6 , b ) 14 , c ) 22 , d ) 30 , e ) 174", - "Correct": "b", - "Explanation": "\"the number of integers that belong to set x only is 8 - 6 = 2 ; the number of integers that belong to set y only is 18 - 6 = 12 ; the number of integers that belong to set x or set y , but not both is 2 + 12 = 14 . answer : b .\"" - }, - { - "Answer": 0.5333333333333333, - "Options": "a ) 8 / 15 , b ) 1 / 3 , c ) 2 / 5 , d ) 4 / 5 , e ) 7 / 6", - "Correct": "a", - "Explanation": "\"a : b = 8 : 3 - - 1 b : c = 1 : 5 = > b : c = 3 : 15 - - 2 from 1 and 2 , we get a : c = 8 : 15 answer a\"" - }, - { - "Answer": 537600, - "Options": "a ) rs . 537600 , b ) rs . 180000 , c ) rs . 201600 , d ) rs . 504000 , e ) none of these", - "Correct": "a", - "Explanation": "b ' s monthly income = 16000 * 112 / 100 = rs . 17920 b ' s monthly income = 2 parts - - - - > rs . 17920 a ' s monthly income = 5 parts = 5 / 2 * 17920 = rs . 44800 a ' s annual income = rs . 44800 * 12 = rs . 537600 answer : a" - }, - { - "Answer": 10, - "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", - "Correct": "d", - "Explanation": "\"let x play both badminton and tennis so 17 - x play only badminton and 19 - x play only tennis . 2 play none and there are total 30 students . hence , ( 17 - x ) + ( 21 - x ) + x + 2 = 30 40 - 2 x + x = 30 40 - x = 30 x = 10 so 10 members play both badminton and tennis . d\"" - }, - { - "Answer": 4800, - "Options": "a ) $ 1800 , b ) $ 2800 , c ) $ 3800 , d ) $ 5800 , e ) $ 4800", - "Correct": "e", - "Explanation": "\"d ' s share = 12000 * 1 / 15 = $ 800 d ' s share = 12000 * 5 / 15 = $ 4000 a + d = $ 4800 answer is e\"" - }, - { - "Answer": 40, - "Options": "a ) 60 , b ) 55 , c ) 50 , d ) 45 , e ) 40", - "Correct": "e", - "Explanation": "\"b : d : w = 2 : 40 : 100 bnew / dnew = ( 1 / 3 ) * ( 2 / 40 ) = ( 1 / 60 ) dnew / wnew = ( 1 / 2 ) * ( 40 / 100 ) = ( 1 / 5 ) wnew = 200 dnew = wnew / 5 = 200 / 5 = 40 so , answer will be e\"" - }, - { - "Answer": 60, - "Options": "a ) 32.5 % , b ) 40 % , c ) 60 % , d ) 65 % , e ) can not be determined", - "Correct": "c", - "Explanation": "let mixture after mixing a and b is 110 ml ( number assumed for calculation because of 5 : 6 ) now solution a is 50 ml and solu b is 60 ml further in a 100 ml a contains 84 ml alch so 50 ml contain 42 ml in mix b 100 ml solution contain 40 ml alc , 60 ml of b , it will be 24 ml alcohol . so 42 + 24 = 66 in 110 ml solution which is 60 % answer : c" - }, - { - "Answer": 462.00000000000006, - "Options": "a ) 110 , b ) 330 , c ) 550 , d ) 462 , e ) 880", - "Correct": "d", - "Explanation": "\"students enrolled in biology are 47.5 % and therefore not enrolled are 52.5 % . so of 880 is 880 * . 525 = 462 answer is d 462\"" - }, - { - "Answer": 20000, - "Options": "a ) $ 24000 , b ) $ 23000 , c ) $ 22000 , d ) $ 21000 , e ) $ 20000", - "Correct": "e", - "Explanation": "\"let the income of uma and bala be $ 4 x and $ 3 x let their expenditures be $ 3 y and $ 2 y 4 x - 3 y = 5000 - - - - - - - 1 ) 3 x - 2 y = 5000 - - - - - - - 2 ) from 1 ) and 2 ) x = 5000 uma ' s income = 4 x = 4 * 5000 = $ 20000 answer is e\"" - }, - { - "Answer": 48, - "Options": "a ) 48 , b ) 24 , c ) 60 , d ) 72 , e ) 84", - "Correct": "a", - "Explanation": "\"ok let me see if i can explain what went on in the previous post lets say i have x marbles in the bag in total - - > out of them 12 are red so the probability of pulling a non - red marble is ( x - 12 ) / x now the marble is placed back in the bag and we have x marbles again , of which again 12 are red . so the probability of pulling a non - red marble out is ( x - 12 ) / x probability theorm states that if the probability of event a occuring is m and the probability of event b occuring is n then the probability of both a and b occuring is m * n so therefore the probability of 2 non - red marbles getting pulled out is [ ( x - 12 ) / x ] * [ ( x - 12 ) / x ] this is given as 9 / 16 - - > ( x - 12 ) ^ 2 = 16 / 25 x ^ 2 a square rooting u have x - 12 / x = 3 / 4 or 4 x - 48 = 3 x or x = 48\"" - }, - { - "Answer": 21, - "Options": "a ) 10 , b ) 20 , c ) 21 , d ) 25 , e ) 27", - "Correct": "c", - "Explanation": "\"as a : b : : 7 : 5 - - - > only option c is a multiple of 7 and hence it is a good place to start . also a : b : : 7 : 5 means that , a = ( 712 ) * total and b = ( 5 / 12 ) * total if a = 21 , b = 15 - - - > remove 9 litres - - - > you remove ( 7 / 12 ) * 9 of a - - - > a remaining = 21 - ( 7 / 12 ) * 9 = 63 / 4 similarly , for b , you remove ( 5 / 12 ) * 9 - - - > b remaining = 15 - ( 5 / 12 ) * 9 = 45 / 4 and then add 9 more litres of b - - - > 9 + 45 / 4 = 81 / 4 thus a / b ( final ratio ) = ( 45 / 4 ) / ( 81 / 4 ) = 7 : 9 , the same as the final ratio mentioned in the question . hence c is the correct answer . a / b = 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) , where 7 x and 5 x are initial quantities of a and b respectively . thus , 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) - - - > giving you x = 3 . thus a ( original ) w = 7 * 3 = 21 . c\"" - }, - { - "Answer": 3000, - "Options": "a ) rs . 3600 , b ) rs . 3603 , c ) rs . 3639 , d ) rs . 3000 , e ) rs . 3602", - "Correct": "d", - "Explanation": "\"let the income and the expenditure of the person be rs . 7 x and rs . 6 x respectively . income , 7 x = 21000 = > x = 3000 savings = income - expenditure = 7 x - 6 x = x so , savings = rs . 3000 answer : d\"" - }, - { - "Answer": 3.28, - "Options": "a ) 3.84 , b ) 1.75 , c ) 3.28 , d ) 2.72 , e ) none of these", - "Correct": "c", - "Explanation": "\"here ' s how i did it . my notes from reading the problem were : 1 l a = 900 gm 1 l b = 700 gm we are mixing five parts ( 3 parts a plus 2 parts b , 5 parts total ) to get 4 l , so 5 x = 4 - - - > x = 4 / 5 . each part is 4 / 5 of a liter . so if we have 3 parts a , we have 900 * 3 * ( 4 / 5 ) = 2160 if we have 2 parts b , we have 700 * 2 * ( 4 / 5 ) = 1120 2160 + 1120 = 3280 solving for units gives us 3.28 so the answer is c\"" - }, - { - "Answer": 105, - "Options": "a ) 72 , b ) 85 , c ) 94 , d ) 105 , e ) 108", - "Correct": "d", - "Explanation": "\"you had the answer almost right . the x = 82 refers to only set a . however what ' s being asked is how many members are part of set a . this will include : 1 . only set a 2 . set a and set b so the answer is set a = 82 + set ab = 82 + 23 = 105 d\"" - }, - { - "Answer": 0.00020833333333333335, - "Options": "a ) 3 / 16,000 , b ) 1 / 4,800 , c ) 3 / 1,600 , d ) 1 / 90 , e ) 2 / 45", - "Correct": "b", - "Explanation": "solution provided by stanford 2012 is correct : 100 / 800 choosing one of the cellos which has a pair viola , 1 / 600 choosing the viola which is the pair of chosen cello - - > p = 100 / 800 * 1 / 600 = 1 / 4,800 . answer : b ." - }, - { - "Answer": 33, - "Options": "a ) 22 , b ) 33 , c ) 77 , d ) 28 , e ) 22", - "Correct": "b", - "Explanation": "explanation : 200 / 6 = 33 2 / 6 = > 33 numbers answer : b" - }, - { - "Answer": 50, - "Options": "a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70", - "Correct": "c", - "Explanation": "originally , there were 5 k horses and k cows . 7 ( 5 k - 15 ) = 17 ( k + 15 ) 35 k - 17 k = 255 + 105 18 k = 360 k = 20 the difference between horses and cows is ( 5 k - 15 ) - ( k + 15 ) = 4 k - 30 = 50 the answer is c ." - }, - { - "Answer": 21, - "Options": "a ) 25 , b ) 21 , c ) 20 , d ) 10 , e ) 15", - "Correct": "b", - "Explanation": "suppose the can initially contains 7 x and 5 x litres mixtures a and b respectively quantity of a in mix . left = [ 7 x \u2013 7 / 12 * 9 ] = [ 7 x \u2013 21 / 4 ] quantity of b in mix . left = [ 5 x \u2013 5 / 12 * 9 ] = [ 5 x - 15 / 4 ] therefore [ 7 x - 21 / 4 ] = 7 / 9 or 28 x - 21 = 7 / 9 [ 5 x - 15 / 4 ] + 9 20 x + 21 252 x - 189 = 140 x + 147 or 112 x = 336 , x = 3 . quantity of a in the can initially = 7 * 3 = 21 answer : b" - }, - { - "Answer": 175.5, - "Options": "a ) rs . 169.50 , b ) rs . 170 , c ) rs . 175.50 , d ) rs . 180 , e ) rs . 190", - "Correct": "c", - "Explanation": "explanation : since first and second varieties are mixed in equal proportions . so , their average price = rs . 126 + 135 = rs . 130.50 2 so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . x - 153 / 22.50 = 1 x - 153 = 22.50 x = 175.50 answer is c" - }, - { - "Answer": 944, - "Options": "a ) 678 , b ) 944 , c ) 456 , d ) 323 , e ) 899", - "Correct": "b", - "Explanation": ": explanation : clearly , the numbers are ( 59 x 13 ) and ( 59 x 16 ) . { \\ color { blue } \\ therefore } larger number = ( 59 x 16 ) = 944 . answer : b ) 944" - }, - { - "Answer": 5, - "Options": "a ) 1 : 3 , b ) 9 : 13 , c ) 5 : 1 , d ) 11 : 3 , e ) 15 : 4", - "Correct": "c", - "Explanation": "\"the ratio of milk and water in the new vessel is = ( 7 / 9 + 8 / 9 ) : ( 2 / 9 + 1 / 9 ) = 15 / 9 : 3 / 9 = 5 : 1 answer is c\"" - }, - { - "Answer": 0.6666666666666665, - "Options": "a ) 1 / 4 , b ) 2 / 5 , c ) 1 / 2 , d ) 3 / 5 , e ) 2 / 3", - "Correct": "e", - "Explanation": "\"you can simply use this formula to avoid confusion : w 1 / w 2 = ( a 2 - aavg ) / ( avg - a 1 ) here is how you will find the values of a 1 an a 2 . we have an overall loss ( average loss ) . the average loss is 3 kg when 30 kg alloy is immersed . this is a loss of ( 3 / 30 ) * 100 = 10 % . this is aavg the loss of tin is 1.375 kg for every 10 kg . this means it loses ( 1.375 / 10 ) * 100 = 13.75 % of its weight in water . this is a 1 . the loss of silver is . 375 kg for every 5 kg . this means it loses ( . 375 / 5 ) * 100 = 7.5 % of its weight in water . this is a 2 . weight of tin / weight of silver = ( silver ' s loss - avg loss ) / ( avg loss - tin ' s loss ) x / y = ( 7.5 - 10 ) / ( 10 - 13.75 ) = 2 / 3 e\"" - }, - { - "Answer": 32, - "Options": "a ) 12 , b ) 15 , c ) 32 , d ) 20 , e ) 25", - "Correct": "c", - "Explanation": "\"20 litres of mixture that is replaced will contain 16 litres of a and 4 litres of b ( as a : b = 4 : 1 ) let the initial volume of the mixture be 4 k + 1 k = 5 k so by condition , [ 4 k - 16 ] / [ k - 4 + 20 ] = 2 / 3 = > 12 k - 48 = 2 k - 8 + 40 = > 10 k = 80 solve for k which is k = 8 so initial volume of liquid a = 4 k = 32 litres answer : c\"" - }, - { - "Answer": 30, - "Options": "a ) 15 , b ) 30 , c ) 45 , d ) 60 , e ) 90", - "Correct": "b", - "Explanation": "standard : fl : corn s : water = 1 : 12 : 30 sport : fl : corn s : water = 3 : 12 : 180 this simplifies to 1 : 4 : 60 if the large bottle has a capacity of x ounces , then 4 x / 65 = 2 . so , x = 32.5 ounces . water = ( 60 / 65 ) * ( 65 / 2 ) = = 30 ounces . ans b" - }, - { - "Answer": 0.95, - "Options": "a ) 0.09 , b ) 0.15 , c ) 0.54 , d ) 0.85 , e ) 0.95", - "Correct": "e", - "Explanation": "\"according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 22 + 18 + 17 ) / 60 = 57 / 60 = 0.95 . answer : e .\"" - }, - { - "Answer": 16, - "Options": "a ) 8 , b ) 16 , c ) 32 , d ) 48 , e ) 54", - "Correct": "b", - "Explanation": "\"one option is to set up the equations and solve : if the ratio of two integers x and y is 1 to 4 , then 4 x = y , where x is the smaller integer . if adding 12 to the smaller integer makes the ratio 1 to 1 , then x + 12 = y . substituting y = 4 x into the second equation yields x + 12 = 4 x . so , x = 4 ( smaller integer ) and , y = 4 x = 16 ( larger integer ) so b is the correct answer . another option is to test the answer choices . a ) the larger number is 8 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 2 if 12 is added to the smaller number , the ratio becomes 1 to 1 if we add 12 to the smaller number ( 2 ) , we get 14 . so , the new ratio is 14 to 8 which is the same as 7 to 4 . no good . we want a resulting ratio of 1 to 1 eliminate a b ) the larger number is 16 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 4 if 12 is added to the smaller number , the ratio becomes 1 to 1 if we add 12 to the smaller number ( 4 ) , we get 16 so , the new ratio is 16 to 16 which is 1 to 1 . therefore ( b ) is correct . c ) the larger number is 32 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 8 if 12 is added to the smaller number , the ratio becomes 1 to 1 if we add 12 to the smaller number ( 8 ) , we get 20 so , the new ratio is 20 to 32 which is 5 to 8 . no good . we want a resulting ratio of 1 to 1 eliminate c d ) the larger number is 48 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 12 if 12 is added to the smaller number , the ratio becomes 1 to 1 if we add 12 to the smaller number ( 12 ) , we get 24 so , the new ratio is 24 to 48 . this is the same as the ratio of 1 to 2 no good . we want a resulting ratio of 1 to 1 eliminate d e ) the larger number is 54 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 13.5 ( which is not an integer ) since both numbers are integers , the larger number can not be 54 . eliminate e therefore b is the only correct choice .\"" - }, - { - "Answer": 29491.525423728814, - "Options": "a ) 29491 , b ) 28491 , c ) 39491 , d ) 49491 , e ) 59491", - "Correct": "a", - "Explanation": "compound ratio of a : b : c a : b = 3 : 4 b : c = 5 : 6 - - - - - - - - - - a : b : c = 15 : 20 : 24 we can divide rs . 116000 in this ratio . share of a = 15 / 59 * 116000 = 29491 answer : a" - }, - { - "Answer": 28, - "Options": "a ) 30 , b ) 10 , c ) 18 , d ) 28 , e ) 32", - "Correct": "d", - "Explanation": "\"total = english + german - both + neither - - > 50 = english + 22 - 12 + 0 - - > english = 40 - - > only english = english - both = 40 - 12 = 28 . answer : d .\"" - }, - { - "Answer": 0.175, - "Options": "a ) 2 / 15 , b ) 2 / 21 , c ) 7 / 40 , d ) 3 / 29 , e ) 4 / 27", - "Correct": "c", - "Explanation": "\"p ( both are red ) , = 7 c 216 c 2 = 7 c 216 c 2 = 21 / 120 = 7 / 40 c\"" - }, - { - "Answer": 0.6666666666666666, - "Options": "a ) 4 / 3 , b ) 2 / 3 , c ) 1 / 3 , d ) 3 / 4 , e ) 1 / 4", - "Correct": "b", - "Explanation": "the ratio of the number of boxes kelly packed to the number of boxes chris packed = 40 / 60 = 2 / 3 answer : b" - }, - { - "Answer": 900, - "Options": "a ) $ 150 , b ) $ 900 , c ) $ 600 , d ) $ 450 , e ) none", - "Correct": "b", - "Explanation": "ans is d given profit ratio , bess : bill : bob = 1 : 2 : 3 to make bill ' s portion $ 300 , multiply by $ 150 = > bess : bill : bob = $ 150 : $ 300 : $ 450 = > bob ' s share = $ 450" - }, - { - "Answer": 215, - "Options": "a ) 111 , b ) 28 , c ) 160 , d ) 213 , e ) 107", - "Correct": "d", - "Explanation": "\"official solution : number of multiples of 3 step 1 . subtract the extreme multiples of 3 within the range ( the greatest is 330 , the smallest is 12 ) : 330 - 12 = 318 step 2 . divide by 3 : 318 / 3 = 106 step 3 . add 1 : 106 + 1 = 107 . so there are 107 multiples of 3 within the range : examples are 51 , 54 , 57 , 60 , etc . number of multiples of 2 step 1 . subtract the extreme multiples of 2 within the range ( the greatest is 330 , the smallest is 12 ) : 330 - 12 = 318 step 2 . divide by 2 : 318 / 2 = 159 step 3 . add 1 : 159 + 1 = 160 . so there are 160 multiples of 2 within the range : examples are 50 , 52 , 54 , 56 , 58 , 60 etc . add the 107 multiples of 3 and the 160 multiples of 2 : 107 + 160 = 267 . however , by adding the multiples of 2 and the multiples of 3 , we are effectively counting several numbers twice : for example , 54 and 60 are parts of both the lists above . so we ca n ' t just take 107 + 160 = 267 . find the number of multiples of 6 ( which are the double counted , as 6 is divisible by both 2 and 3 ) , and subtract it from 25 : step 1 . subtract the extreme multiples of 6 within the range ( the greatest is 72 , the smallest is 54 ) : 330 - 12 = 318 step 2 . divide by 6 : 318 / 6 = 53 step 3 . add 1 : 53 + 1 = 54 . so there are 54 multiples of 6 within the range : we counted 54 numbers twice . subtract the 54 multiples of 6 from the sum of the multiples of 2 and 3 : = 107 + 160 - 54 = 267 - 54 = 213 therefore , the final number of multiples of 2 , 3 or 6 is 213 . hence , this is the correct answer . ( d )\"" - }, - { - "Answer": 26, - "Options": "a ) 3 , b ) 16 , c ) 75 , d ) 24 , e ) 26", - "Correct": "e", - "Explanation": "1 ) i figured there are 101 integers ( 300 - 200 + 1 = 101 ) . since the set begins with an even and ends with an even , there are 51 evens . 2 ) question says integers are not divisible by 2 , leaving all of the odds ( 101 - 51 = 50 integers ) . 3 ) question says integers are not divisible by 5 , removing all the integers ending in 5 ( already took out those ending in 0 ) . take out 10 integers ( 2 ? 5 , ? = 0 to 9 ) , leaving us with 40 integers . 4 ) now the painstaking part . we have to remove the remaining numbers that are multiples of 3 . those are 201 , 207 , 213 , 219 , 231 , 237 , 243 , 249 , 261 , 267 , 273 , 279 , 291 , and 297 . . . a total of 14 numbers . 26 numbers left ! 6 ) answer choice e ." - }, - { - "Answer": 30, - "Options": "a ) 30 , b ) 50 , c ) 70 , d ) 80 , e ) 90", - "Correct": "a", - "Explanation": "\"let x be the number of new boarders . the ratio changed from 2 : 5 = 4 : 10 up to 1 : 2 = 5 : 10 . 120 / ( 120 + x ) = 4 / 5 x = 30 the answer is a .\"" - }, - { - "Answer": 0.6666666666666664, - "Options": "a ) 1 / 4 , b ) 2 / 5 , c ) 1 / 2 , d ) 3 / 5 , e ) 2 / 3", - "Correct": "e", - "Explanation": "\"the bar lost certain percentage of its weight . we do n ' t know how much tin was lost and how much silver was lost but in all 2 kg was lost with is 10 % of its overall weight . tin loses 1.375 kg in 10 kg so 13.75 % of its weight when it is put in water . silver loses . 375 kg in 5 kg so . 375 / 5 * 100 = 7.5 % of its weight in water . now , we just need to use weighted averages : wt / ws = ( 7.5 - 10 ) / ( 10 - 13.75 ) = 2.5 / 3.75 = 2 / 3 answer ( e )\"" - }, - { - "Answer": 0.4897959183673469, - "Options": "a ) 1 / 25 , b ) 12 / 49 , c ) 1 / 4 , d ) 24 / 49 , e ) 1 / 2", - "Correct": "d", - "Explanation": "\"q probability of one party having both spots : ( 1 / 2 ) * ( 24 / 49 ) = 12 / 49 ( 1 / 2 ) or ( 25 / 50 ) because it does not matter which party or which person gets the first spot . ( 24 / 49 ) because after one person from a particular party is chosen , there are 24 members of the same party left out of 49 total candidates . since this result can happen for both parties , ( 12 / 49 ) + ( 12 / 49 ) = ( 24 / 49 ) answer : d\"" - }, - { - "Answer": 2, - "Options": "a ) 9 , b ) 36 , c ) 2 , d ) 6 , e ) 1", - "Correct": "c", - "Explanation": "\"square root is a number times itself square root of 144 = 12 , 12 / 6 = 2 ( c ) 2\"" - }, - { - "Answer": 51.20000000000001, - "Options": "a ) 40 % pure , b ) 50 % pure , c ) 51.2 % pure , d ) 58.8 % pure , e ) none", - "Correct": "c", - "Explanation": "\"solution let total quantity of original milk = 100 gm . milk after first operation = 80 % of 1000 \u2039 = \u203a 800 gm . milk after second operation = 80 % of 800 \u2039 = \u203a 640 gm . milk after third operation = 80 % of 640 \u2039 = \u203a 512 gm . strength of final mixtures = 51.2 % . answer c\"" - }, - { - "Answer": 25, - "Options": "a ) 25 , b ) 32 , c ) 40 , d ) 53 , e ) 54", - "Correct": "a", - "Explanation": "\"let the numbers be 2 x and 3 x . then , their l . c . m . = 6 x . so , 6 x = 30 or x = 5 . the numbers are 10 and 15 . hence , required sum = ( 10 + 15 ) = 25 . answer : option a\"" - }, - { - "Answer": 3, - "Options": "a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8", - "Correct": "a", - "Explanation": "\"15 + 18 = 33 but where as total number is 35 - 5 = 30 therefore answer is 33 - 30 = 3 hence answer is a\"" - }, - { - "Answer": 36000, - "Options": "a ) 35000 , b ) 40000 , c ) 16000 , d ) 36000 , e ) 60000", - "Correct": "d", - "Explanation": "let the investment of john james and jim is 4 x 7 x and 9 x 4 x + 7 x + 9 x = 80000 20 x = 80000 x = 4000 jim ' investment = 9 * 4000 = 36000 answer : d" - }, - { - "Answer": 3757, - "Options": "a ) s . 2890 , b ) s . 2330 , c ) s . 3757 , d ) s . 1620 , e ) s . 2680", - "Correct": "c", - "Explanation": "\"ram : gopal = 7 : 17 = 49 : 119 gopal : krishan = 7 : 17 = 119 : 289 ram : gopal : krishan = 49 : 119 : 289 ram : krishan = 49 : 289 thus , 49 : 289 = 637 : n & there n = 289 x 637 / 49 = rs . 3757 answer : c\"" - }, - { - "Answer": 9, - "Options": "a ) a ) 10 , b ) b ) 12 , c ) c ) 15 , d ) d ) 14 , e ) e ) 9", - "Correct": "e", - "Explanation": "let the numbers be x , 2 x , 4 x then , x ^ 2 + 4 x ^ 2 + 16 x ^ 2 = 1701 21 x ^ 2 = 1701 x ^ 2 = 81 x = 9 answer is e" - }, - { - "Answer": 10, - "Options": "a ) 30 , b ) 28 , c ) 25 , d ) 20 , e ) 10", - "Correct": "e", - "Explanation": "so the number of $ 3.50 modules must be 10 so that the leftover 1 modules are of $ 10 which will give a total value $ 45 . 10 * 3.50 + 1 * 10 = 35 + 10 = 45 answer : e" - }, - { - "Answer": 3000, - "Options": "a ) s . 800 , b ) s . 2400 , c ) s . 3000 , d ) s . 3200 , e ) s . 4200", - "Correct": "c", - "Explanation": "\"let the income of p 1 and p 2 be rs . 5 x and rs . 4 x respectively and let their expenditures be rs . 3 y and 2 y respectively . then , 5 x \u2013 3 y = 1200 \u2026 ( i ) and 4 x \u2013 2 y = 1200 \u2026 \u2026 . . ( ii ) on multiplying ( i ) by 2 , ( ii ) by 3 and subtracting , we get : 2 x = 1200 - > x = 600 p 1 \u2019 s income = rs 5 * 600 = rs . 3000 answer : c\"" - }, - { - "Answer": 75, - "Options": "a ) 75 , b ) 85 , c ) 64 , d ) 51 , e ) 45", - "Correct": "a", - "Explanation": "we have 4 / 6 = 50 / x 4 x = 50 * 6 x = 75 consequent = 75 answer is a" - }, - { - "Answer": 107, - "Options": "a ) 72 , b ) 85 , c ) 107 , d ) 98 , e ) 108", - "Correct": "c", - "Explanation": "\"you had the answer almost right . the x = 84 refers to only set a . however what ' s being asked is how many members are part of set a . this will include : 1 . only set a 2 . set a and set b so the answer is set a = 84 + set ab = 84 + 23 = 17 c\"" - }, - { - "Answer": 0.15513897866839044, - "Options": "a ) 240 / 1576 , b ) 240 / 1542 , c ) 240 / 1547 , d ) 240 / 1528 , e ) 240 / 1529", - "Correct": "c", - "Explanation": "\"p : 2 / 13 = 5 / 34 : 7 / 48 as the product of the means is equal to the product of the extremes . p * 7 / 48 = 2 / 13 * 5 / 34 p * 7 / 48 = 10 / 442 p = 480 / 3094 = > p = 240 / 1547 answer : c\"" - }, - { - "Answer": 46, - "Options": "a ) 2 , b ) 7 , c ) 6 , d ) 46 , e ) 3", - "Correct": "d", - "Explanation": "the answer is ( 100 - 10 ) / 2 + 1 = 46 answer is d" - }, - { - "Answer": 0.5, - "Options": "a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4", - "Correct": "c", - "Explanation": "\"let ' s say that the total original mixture a is 100 ml the original mixture a thus has 45 ml of alcohol out of 100 ml of solution you want to replace some of that original mixture a with another mixture b that contains 25 ml of alcohol per 100 ml . thus , the difference between 45 ml and 25 ml is 20 ml per 100 ml of mixture . this means that every time you replace 100 ml of the original mixture a by 100 ml of mixture b , the original alcohol concentration will decrease by 20 % . the question says that the new mixture , let ' s call it c , must be 35 % alcohol , a decrease of only 10 % . therefore , 10 out of 20 is 1 / 2 and c is the answer .\"" - }, - { - "Answer": 638, - "Options": "a ) 638 , b ) 330 , c ) 550 , d ) 430 , e ) 880", - "Correct": "a", - "Explanation": "\"students enrolled in biology are 27.5 % and therefore not enrolled are 72.5 % . so of 880 is 880 * . 225 = 638 answer is a 638\"" - }, - { - "Answer": 15, - "Options": "a ) 3 , b ) 5 , c ) 10 , d ) 15 , e ) 21", - "Correct": "d", - "Explanation": "the ratio of local and international calls made by amy this week is 5 to 2 let the current ratio be 5 x / 2 x the ratio changes to 5 to 3 after amy makes three more international calls 5 x / ( 2 x + 3 ) = 5 / 3 solving we get x = 3 initial ratio 15 : 6 ( 5 : 2 ) final ratio 15 : ( 6 + 3 ) = 15 : 9 = 5 : 3 so total number of local calls = 15 answer : d" - }, - { - "Answer": 5, - "Options": "a ) 5 : 4 , b ) 3 : 0 , c ) 5 : 1 , d ) 3 : 2 , e ) 3 : 7", - "Correct": "c", - "Explanation": "\"let the present ages of a and b be 6 x and 3 x years respectively . then , ( 6 x - 4 ) / ( 3 x + 4 ) = 1 / 1 3 x = 8 = > x = 2.67 required ratio = ( 5 x + 4 ) : ( 3 x - 4 ) = 20 : 4 = 5 : 1 . answer : c\"" - }, - { - "Answer": 16.000000000000014, - "Options": "a ) 2 % , b ) 5 % , c ) 16 % , d ) 20 % , e ) 25 %", - "Correct": "c", - "Explanation": "\"since we were expected to find a percentage figure - it thought that it might be easier to pick a ' smart number ' to represent the total number of voters ( republicans and democrats ) . therefore , i picked 100 ( as the total number of voters ) and thus 30 : 20 represents the number ratio of republicans : democrats . if 80 % of republicans ( which is ( 60 * 0.8 ) = 48 ) and 25 % of democrats ( 40 * 0.25 = 10 ) voted for candidate x , means that out of total of 100 voters ; 58 ( 48 + 10 ) voters voted for candidate x and 42 voted for candidate y . thus we can infer that candidate x is expected to win the election by 16 ( 58 - 42 ) votes . therefore candidate x is expected to win the election by ( 16 / 100 ) votes which is equivalent to 16 % . i think the answer is c .\"" - }, - { - "Answer": 36, - "Options": "a ) 32 , b ) 36 , c ) 40 , d ) 44 , e ) 48", - "Correct": "b", - "Explanation": "\"let the number of pens be 5 x and the number of pencils be 6 x . 6 x - 5 x = 6 x = 6 the number of pencils is 36 . the answer is b .\"" - }, - { - "Answer": 200, - "Options": "a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500", - "Correct": "b", - "Explanation": "let x be the weights , in kilograms , of pure water to be added . let y be the weight , in kilograms , of the 10 % solution . hence x + 100 = y x = 200 kilograms . answer b" - }, - { - "Answer": 8, - "Options": "a ) 2 , b ) 9 , c ) 8 , d ) 7 , e ) 4", - "Correct": "c", - "Explanation": "explanation : in sixteen kg of alloy 10 kg of zinc and 6 kg copper is present to make the ratio 3 : 1 we must add 8 kg of zinc to make it 18 kg of zinc and 6 kg copper so answer is 8 . answer : c" - }, - { - "Answer": 96, - "Options": "a ) 99 , b ) 98 , c ) 97 , d ) 96 , e ) 95", - "Correct": "d", - "Explanation": "clearly d a number is said to be prime saturated if the product of all the different positive prime factors of r is less than the square root of r . 96 has more number of smaller prime factor thats the clue ! ! = d" - }, - { - "Answer": 65, - "Options": "a ) 65 , b ) 60 , c ) 55 , d ) 40 , e ) 45", - "Correct": "a", - "Explanation": "\"b / c = 1 / 13 c - b = 60 . . . . . . . . . > b = c - 60 ( c - 60 ) / c = 1 / 13 testing answers . clearly eliminate bcde put c = 65 . . . . . . . . . > ( 65 - 60 ) / 65 = 5 / 65 = 1 / 13 answer : a\"" - }, - { - "Answer": 84, - "Options": "a ) 12 , b ) 24 , c ) 84 , d ) 48 , e ) 42", - "Correct": "c", - "Explanation": "\"let the numbers be x and 4 x . then , x * 4 x = 84 * 21 x 2 = ( 84 * 21 ) / 4 = x = 21 . hence , larger number = 4 x = 84 . answer : c\"" - }, - { - "Answer": 0.8333333333333334, - "Options": "a ) 1 / 6 , b ) 2 / 9 , c ) 5 / 6 , d ) 7 / 9 , e ) 8 / 9", - "Correct": "c", - "Explanation": "\"we have three pairs of dogs for the 6 with exactly one littermate , and one triplet , with each having exactly two littermates . so , in fact there are two types of dogs : those with one littermate - say a , and the others with two littermates - b . work with probabilities : choosing two dogs , we can have either one dog of type b or none ( we can not have two dogs both of type b ) . the probability of choosing one dog of type b and one of type a is 3 / 9 * 6 / 8 * 2 = 1 / 2 ( the factor of 2 for the two possibilities ba and ab ) . the probability of choosing two dogs of type a which are not littermates is 6 / 9 * 4 / 8 = 1 / 3 ( choose one a , then another a which is n ' t the previous one ' s littermate ) . the required probability is 1 / 2 + 1 / 3 = 5 / 6 . find the probability for the complementary event : choose aa or bb . probability of choosing two dogs of type a who are littermates is 6 / 9 * 1 / 8 = 1 / 12 . probability of choosing two dogs of type b ( who necessarily are littermates ) is 3 / 9 * 2 / 8 = 1 / 12 . again , we obtain 1 - ( 1 / 12 + 1 / 12 ) t = 5 / 6 . answer : c\"" - }, - { - "Answer": 60, - "Options": "a ) 60 , b ) 75 , c ) 85 , d ) 95 , e ) 105", - "Correct": "a", - "Explanation": "\"b / c = 1 / 3 c - b = 40 . . . . . . . . . > b = c - 40 ( c - 40 ) / c = 1 / 3 testing answers . clearly eliminate bcde put c = 60 . . . . . . . . . > ( 60 - 40 ) / 60 = 20 / 60 = 1 / 3 answer : a\"" - }, - { - "Answer": 70, - "Options": "a ) 24 , b ) 36 , c ) 48 , d ) 70 , e ) 132", - "Correct": "d", - "Explanation": "5 / 11 = x / x + 85 5 * 85 = 6 x x = 70 d . 70" - }, - { - "Answer": 48, - "Options": "a ) 12 , b ) 16 , c ) 24 , d ) 48 , e ) 98", - "Correct": "d", - "Explanation": "\"let the numbers be 3 x and 4 x . then their h . c . f = x . so , x = 4 . so , the numbers are 12 and 16 . l . c . m of 12 and 16 = 48 . answer : d\"" - }, - { - "Answer": 60, - "Options": "a ) 30 , b ) 45 , c ) 60 , d ) 80 , e ) 100", - "Correct": "c", - "Explanation": "\"explanation : let capacity of q = 1 litre . then , capacity of p = 3 litre . given that it takes 80 turns for bucket p to fill the empty drum . = > capacity of the drum = 80 \u00d7 3 = 240 litre . number of turns required if both p and q are used having each turn together 240 / 3 + 1 = 60 litre . answer : option c\"" - }, - { - "Answer": 8, - "Options": "a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12", - "Correct": "d", - "Explanation": "since 2 xy prime q factors are x ^ 1 * y ^ 1 * 2 ^ 1 , its total number or factors must be ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 2 ^ 3 = 8 . thus , i think d would be the correct answer ." - }, - { - "Answer": 494, - "Options": "a ) 562 , b ) 356 , c ) 452 , d ) 494 , e ) 512", - "Correct": "d", - "Explanation": "\"let the number of boys and girls be 8 x and 5 x then , 5 x = 190 x = 38 total number of students = 13 x = 13 * 38 = 494 answer is d\"" - }, - { - "Answer": 35, - "Options": "a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 35", - "Correct": "e", - "Explanation": "\"neither car nor garage = total - garage - ( swim - common ) = 90 - 50 - ( 40 - 35 ) = 90 - 55 = 35 answer e\"" - }, - { - "Answer": 20, - "Options": "a ) 20 , b ) 11 , c ) 9 , d ) 31 , e ) 21", - "Correct": "a", - "Explanation": "\"total people eat veg = only veg + both veg and non veg total = 11 + 9 = 20 answer = a\"" - }, - { - "Answer": 48, - "Options": "a ) 18 , b ) 28 , c ) 48 , d ) 56 , e ) 60", - "Correct": "c", - "Explanation": "\"let the number of sheeps and horses be 4 x and 7 x . now total number of horses = total consumption of horse food / consumption per horse = 12880 / 230 = 56 , which is equal to 7 x . = > x = 8 sheeps = 6 x = 6 * 8 = 48 . hence c .\"" - }, - { - "Answer": 20, - "Options": "a ) 5 , b ) 10 , c ) 12 , d ) 20 , e ) 25", - "Correct": "d", - "Explanation": "the ratio 1 : 34 = 2 : 68 so the ratio changed from 2 : 63 to 2 : 68 . 68 - 63 = 5 which is 1 / 10 of the increase in 50 associates . the ratio changed from 20 : 630 to 20 : 680 . thus the number of partners is 20 . the answer is d ." - }, - { - "Answer": 40, - "Options": "a ) 18 , b ) 28 , c ) 40 , d ) 56 , e ) 58", - "Correct": "c", - "Explanation": "\"et no of sheep and horses are 5 k and 7 k no of horses = 12880 / 230 = 56 now 7 k = 56 and k = 8 no of sheep = ( 5 * 8 ) = 40 answer : c\"" - }, - { - "Answer": 400, - "Options": "a ) 80 , b ) 160 , c ) 240 , d ) 360 , e ) 400", - "Correct": "e", - "Explanation": "\"ratio = 9 : 1 = > 9 x respondents preferred brand x and x preferred brand y since , no . of respondents who preferred brand x = 360 = > 9 x = 360 = > x = 40 hence total no . of respondents = 360 + 40 = 400 hence e is the answer .\"" - }, - { - "Answer": 56, - "Options": "a ) 18 , b ) 28 , c ) 32 , d ) 56 , e ) 58", - "Correct": "d", - "Explanation": "\"et no of sheep and horses are 7 k and 7 k no of horses = 12880 / 230 = 56 now 7 k = 56 and k = 8 no of sheep = ( 7 * 8 ) = 56 answer : d\"" - }, - { - "Answer": 88, - "Options": "a ) 72 , b ) 88 , c ) 95 , d ) 120 , e ) 135", - "Correct": "b", - "Explanation": "the ratio of yankees : mets : red sox = 6 : 4 : 5 the mets fans are 4 / 15 of the population . ( 4 / 15 ) * 330 = 88 the answer is b ." - }, - { - "Answer": 12, - "Options": "a ) 12 , b ) 15 , c ) 20 , d ) 22 , e ) 24", - "Correct": "a", - "Explanation": "explanation : present age is 4 x and 3 x , = > 4 x + 10 = 26 = > x = 16 so deepak age is = 3 ( 4 ) = 12 option a" - }, - { - "Answer": 100, - "Options": "a ) 50 , b ) 40 , c ) 100 , d ) 30 , e ) 20", - "Correct": "c", - "Explanation": "\"b / c = 1 / 10 c - b = 90 . . . . . . . . . > b = c - 90 ( c - 90 ) / c = 1 / 10 testing answers . clearly eliminate abde put c = 100 . . . . . . . . . > ( 100 - 90 ) / 100 = 10 / 100 = 1 / 10 answer : c\"" - }, - { - "Answer": 4, - "Options": "a ) 4 , b ) 8 , c ) 12 , d ) 16 , e ) 20", - "Correct": "a", - "Explanation": "\"we are told that all of the letters contain either a dot or a straight line or both , which implies that there are no letters without a dot and a line ( no line / no dot box = 0 ) . first we find the total # of letters with lines : 16 + 30 = 46 ; next , we find the total # of letters without line : 50 - 46 = 4 ; finally , we find the # of letters that contain a dot but do not contain a straight line : 4 - 0 = 4 . answer : a\"" - }, - { - "Answer": 1, - "Options": "a ) 1 : 1 , b ) 3 : 2 , c ) 4 : 3 , d ) 5 : 3 , e ) none", - "Correct": "a", - "Explanation": "\"required ratio = 500 : 500 = 1 : 1 answer a\"" - }, - { - "Answer": 1440, - "Options": "a ) 900 , b ) 980 , c ) 1200 , d ) 1240 , e ) 1440", - "Correct": "e", - "Explanation": "\"amount received by sanjay . 4 / 12 x 4320 = 1440 = ( related ratio / sum of ratio ) x total amount so , the amount received by sanjay is 1440 . e\"" - }, - { - "Answer": 8, - "Options": "a ) 30 , b ) 5 , c ) 8 , d ) 20 , e ) 10", - "Correct": "c", - "Explanation": "number of cheerleaders = 27 number of male = 10 number of female = 17 coke = 9 maly = 17 female who chose malt = 17 - 9 = 8 answer = c" - }, - { - "Answer": 14, - "Options": "a ) 14 , b ) 21 , c ) 28 , d ) 35 , e ) 42", - "Correct": "a", - "Explanation": "let 2 x be the number of spinsters . then 7 x is the number of cats . 7 x - 2 x = 35 x = 7 and the number of spinsters is 2 ( 7 ) = 14 . the answer is a ." - }, - { - "Answer": 3, - "Options": "a ) 1 : 2 , b ) 1 : 3 , c ) 3 : 1 , d ) 1 : 5 , e ) 1 : 4", - "Correct": "c", - "Explanation": "\"quantity of alcohol in vessel p = 62.5 / 100 * 4 = 5 / 2 litres quantity of alcohol in vessel q = 87.5 / 100 * 4 = 7 / 2 litres quantity of alcohol in the mixture formed = 5 / 2 + 7 / 2 = 6 litres as 8 litres of mixture is formed , ratio of alcohol and water in the mixture formed = 6 : 2 = 3 : 1 . answer : c\"" - }, - { - "Answer": 30, - "Options": "a ) 15 , b ) 30 , c ) 45 , d ) 60 , e ) 90", - "Correct": "b", - "Explanation": "\"standard : fl : corn s : water = 1 : 12 : 30 sport : fl : corn s : water = 3 : 12 : 180 this simplifies to 1 : 4 : 60 if the large bottle has a capacity of x ounces , then 4 x / 65 = 2 . so , x = 32.5 ounces . water = ( 60 / 65 ) * ( 65 / 2 ) = = 30 ounces . ans b\"" - }, - { - "Answer": 60, - "Options": "a ) 40 , b ) 60 , c ) 50 , d ) 30 , e ) 70", - "Correct": "b", - "Explanation": "\"b : d : w = 2 : 40 : 100 bnew / dnew = ( 1 / 3 ) * ( 2 / 40 ) = ( 1 / 60 ) dnew / wnew = ( 1 / 2 ) * ( 40 / 100 ) = ( 1 / 5 ) wnew = 300 dnew = wnew / 5 = 300 / 5 = 60 so , answer will be b b\"" - }, - { - "Answer": 30, - "Options": "a ) 30 , b ) 20 , c ) 58 , d ) 48 , e ) 68", - "Correct": "a", - "Explanation": "let the numbers be x , y and z . then , x + y + z = 98 , x / y = 2 / 3 and y / z = 5 / 8 therefore , x = 2 y / 3 and z = 8 y / 5 . so , 2 y / 3 + y + 8 y / 5 = 98 . 49 y / 15 = 98 y = 30 . answer : a" - }, - { - "Answer": 0.8, - "Options": "a ) 0.09 , b ) 0.15 , c ) 0.54 , d ) 0.8 , e ) 0.91", - "Correct": "d", - "Explanation": "\"according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 22 + 18 + 8 ) / 60 = 48 / 60 = 0.8 . answer : d .\"" - }, - { - "Answer": 416, - "Options": "a ) 2447 , b ) 377 , c ) 667 , d ) 416 , e ) 871", - "Correct": "d", - "Explanation": "\"explanation : let the number of boys and girls be 8 x and 5 x . total number of students = 13 x = 13 * 32 = 416 . answer : d\"" - }, - { - "Answer": 3, - "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", - "Correct": "a", - "Explanation": "when factorized , 220 has 4 prime factors . of these prime factors 2 are odd and 2 are even . hence total number of odd factors is 2 * 2 ( 4 ) , which includes 1 . the total number of odd factors greater than 1 are 3 . ( option a )" - }, - { - "Answer": 3, - "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", - "Correct": "c", - "Explanation": "both cooking and weaving = 15 - ( 2 + 3 + 7 ) = 3 so , the correct answer is c ." - }, - { - "Answer": 3200, - "Options": "a ) 3600 , b ) 3607 , c ) 3200 , d ) 3602 , e ) 3603", - "Correct": "c", - "Explanation": "\"let the income and the expenditure of the person be rs . 5 x and rs . 4 x respectively . income , 5 x = 16000 = > x = 3200 savings = income - expenditure = 5 x - 4 x = x so , savings = rs . 3200 . answer : c\"" - }, - { - "Answer": 20, - "Options": "a ) 60 , b ) 45 , c ) 20 , d ) 15 , e ) none", - "Correct": "c", - "Explanation": "\"sol . let the required numbers be 5 x and 4 x . then , their l . c . m . is 20 x . \u2234 20 x = 80 \u21d4 x = 4 . hence , the first number is 20 . answer c\"" - }, - { - "Answer": 6, - "Options": "a ) 7 , b ) 6 , c ) 9 , d ) 10 , e ) 11", - "Correct": "b", - "Explanation": "\"let x play both badminton and tennis so 17 - x play only badminton and 17 - x play only tennis . 2 play none and there are total 30 students . hence , ( 17 - x ) + ( 17 - x ) + x + 2 = 30 36 - 2 x + x = 30 36 - x = 30 x = 6 so 6 members play both badminton and tennis . b\"" - }, - { - "Answer": 0.15789473684210525, - "Options": "a ) 1 / 11 , b ) 1 / 12 , c ) 1 / 13 , d ) 3 / 19 , e ) 3 / 43", - "Correct": "d", - "Explanation": "\"in believe the answer is d . please see below for explanation . 0 ) we are told the following ratios cgd - college graduate with degree ncg - non college graduate cgn - college graduate no degree cgd ncg cgn 1 8 3 2 in order to make cgd and cgn comparable we need to find the least common multiple of 8 and 3 and that is 24 multiplying the first ratio by 3 and the second ratio by 8 we get cgd ncg cgn 3 24 16 if one picks a random college graduate at this large company , what is the probability this college graduate has a graduate degree ? nr of cgd = 3 nr of cg = 3 + 16 = 19 probability r of cgd / ( cg ) - > 3 / 19 answer d\"" - }, - { - "Answer": 5000, - "Options": "a ) s . 5000 , b ) s . 2400 , c ) s . 4000 , d ) s . 3200 , e ) s . 4200", - "Correct": "a", - "Explanation": "\"let the income of p 1 and p 2 be rs . 5 x and rs . 4 x respectively and let their expenditures be rs . 3 y and 2 y respectively . then , 5 x \u2013 3 y = 2000 \u2026 ( i ) and 4 x \u2013 2 y = 2000 \u2026 \u2026 . . ( ii ) on multiplying ( i ) by 2 , ( ii ) by 3 and subtracting , we get : 2 x = 2000 - > x = 1000 p 1 \u2019 s income = rs 5 * 1000 = rs . 5000 answer : a\"" - }, - { - "Answer": 110, - "Options": "a ) 72 , b ) 85 , c ) 110 , d ) 98 , e ) 108", - "Correct": "c", - "Explanation": "you had the answer almost right . the x = 85 refers to only set a . however what ' s being asked is how many members are part of set a . this will include : 1 . only set a 2 . set a and set b so the answer is set a = 85 + set ab = 85 + 25 = 110 c" - }, - { - "Answer": 4.999999999999999, - "Options": "a ) 3 , b ) 1 / 3 , c ) 2 , d ) 5 , e ) 1 / 5", - "Correct": "d", - "Explanation": "\"126 = ( a 1 + a 2 + a 3 + a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) factorize the same terms 126 = 1 + ( a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) write every term with respect to r a 1 = a 1 a 2 = a 1 * r ^ 1 a 3 = a 1 * r ^ 2 . . . . . . . . . 126 = 1 + ( a 1 ( r ^ 3 + r ^ 4 + r ^ 5 ) ) / ( a 1 ( 1 + r ^ 1 + r ^ 2 ) ) 125 = ( r ^ 3 ( 1 + r ^ 1 + r ^ 2 ) ) / ( ( 1 + r ^ 1 + r ^ 2 ) ) 125 = r ^ 3 r = 5 d\"" - }, - { - "Answer": 21, - "Options": "a ) 21 , b ) 24 , c ) 28 , d ) 30 , e ) 32", - "Correct": "a", - "Explanation": "\"{ total } = { writers } + { editors } - { both } + { neither } . { total } = 100 ; { writers } = 40 ; { editors } > 38 ; { both } = x ; { neither } = 2 x ; 100 = 40 + { editors } - x + 2 x - - > x = 60 - { editors } . we want to maximize x , thus we should minimize { editors } , minimum possible value of { editors } is 39 , thus x = { both } = 60 - 39 = 21 . answer : a .\"" - }, - { - "Answer": 200, - "Options": "a ) 130 , b ) 100 , c ) 200 , d ) 150 , e ) 120", - "Correct": "c", - "Explanation": "\"20 : 1 = x : 10 x = 10 * 20 x = 150 answer : c\"" - }, - { - "Answer": 4, - "Options": "a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10", - "Correct": "b", - "Explanation": "10 ! = 3628800 e . 4 ^ 10 = 1048576 ( 3628800 / 1048576 ) - this is not a factor of 10 ! d . 4 ^ 8 = 65536 ( 3628800 / 65536 ) - this is not a factor of 10 ! c . 4 ^ 6 = 4096 ( 3628800 / 4096 ) - this is not a factor of 10 ! b . 4 ^ 4 = 256 ( 3628800 / 256 ) - this is a factor of 10 ! b is answer" - }, - { - "Answer": 8, - "Options": "a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12", - "Correct": "c", - "Explanation": "say the weight of the second sack after change is x kilograms , then the weight of the first sack after change would be 0.6 x . since the total weight of sugar in both sacks remained the same then x + 0.6 x = 40 , which gives x = 25 . now , if the weight of the second sack after change is 25 kilograms then initially it was 25 \u2212 1 = 24 kilograms and the initial weight of the first sack was 40 \u2212 24 = 16 kilograms , so the difference was 24 \u2212 16 = 8 kilograms . answer : c" - }, - { - "Answer": 10500, - "Options": "a ) 24887 , b ) 20778 , c ) 23788 , d ) 10500 , e ) 2811", - "Correct": "d", - "Explanation": "\"explanation : a invested rs . 3500 for 12 months . let b joined with investment x . and he invested for 12 - 6 = 6 months . so there profit ratio = ( 3500 \u00e3 \u2014 12 ) : ( 6 x ) = 2 : 3 \u00e2 \u2021 \u2019 x = 10500 answer : d\"" - }, - { - "Answer": 17.999999999999996, - "Options": "a ) 2 , b ) 9 , c ) 15 , d ) 18 , e ) 30", - "Correct": "d", - "Explanation": "\"let the duration , in minutes , for which the company charges the same under plan a and plan b be t minutes . then under plan a the cost would be $ 0.6 + 0.06 ( t - 4 ) and under plan b the cost would be $ 0.08 t . we want these amount to be equal : 0.6 + 0.06 ( t - 4 ) = 0.08 t - - > 60 + 6 ( t - 4 ) = 8 t - - > t = 18 . answer : d .\"" - }, - { - "Answer": 15, - "Options": "a ) 6 , b ) 15 , c ) 24 , d ) 33 , e ) 54", - "Correct": "b", - "Explanation": "\"formula for calculating two overlapping sets : a + b - both + not ( a or b ) = total so in our task we have equation : 41 ( french ) + 22 ( german ) - 9 ( both ) + not = 69 54 + not = 69 not = 69 - 54 = 15 so answer is b\"" - }, - { - "Answer": 588, - "Options": "a ) 588 , b ) 642 , c ) 567 , d ) 344 , e ) 789", - "Correct": "a", - "Explanation": "\"explanation : clearly , the numbers are ( 42 x 12 ) and ( 42 x 14 ) . { \\ color { blue } \\ therefore } larger number = ( 42 x 14 ) = 588 . answer : a ) 588\"" - }, - { - "Answer": 21, - "Options": "a ) 31 , b ) 35 , c ) 21 , d ) 40 , e ) 45", - "Correct": "c", - "Explanation": "\"so the number of $ 2.50 modules must be 21 so that the leftover 1 modules are of $ 10 which will give a total value $ 62.50 . 21 * 2.50 + 1 * 10 = 52.50 + 10 = 62.50 answer : c\"" - }, - { - "Answer": 0.7333333333333333, - "Options": "a ) 4 / 15 , b ) 11 / 15 , c ) 2 / 5 , d ) 4 / 5 , e ) 7 / 6", - "Correct": "b", - "Explanation": "\"a : b = 11 : 3 - - 1 b : c = 1 : 5 = > b : c = 3 : 15 - - 2 from 1 and 2 , we get a : c = 11 : 15 answer b\"" - }, - { - "Answer": 140, - "Options": "a ) 120 , b ) 150 , c ) 100 , d ) 140 , e ) 220", - "Correct": "d", - "Explanation": "n ( a ) = 325 , n ( b ) = 175 , n ( aub ) = 410 - 50 = 360 . required number = n ( anb ) = n ( a ) + n ( b ) - n ( aub ) = 325 + 175 - 360 = 140 . answer is d" - }, - { - "Answer": 180, - "Options": "a ) 30 , b ) 90 , c ) 120 , d ) 172 , e ) 180", - "Correct": "e", - "Explanation": "\"i would just like to add a bit of explanation after the step where you calculate that the number of students studying both m and s = 180 using your analysis : we see that the total number of students who study either maths or sociology = 264 + 336 - 180 = 420 so , in the image we know that the number of students in the zone with the black boundary = 420 let ' s assume the number of students who studyonlybiology to beb ( this is the number that we have to maximize ) and , let ' s assume the number of students who study none of the three subjects , that is the number of students in the white space = w since the total number of students = 600 , we can write : 420 + b + w = 600 or , b + w = 600 - 420 = 180 that is , b = 180 - w so , the maximum value ofbwill happen forw = 0 this is how we get , the maximum value ofb = 180 e\"" - }, - { - "Answer": 6, - "Options": "a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10", - "Correct": "c", - "Explanation": "\"venn diagrams are useful for multiple values of a single variable e . g . state of mind - happy / sad / neither . when you have two or more variables such as here where you have gender - boy / girl too , it becomes unwieldy . in this case , either use the table or logic . table method is shown above ; here is how you will use logic : there are 6 happy boys . there are 4 sad girls but total 10 sad children . so rest 6 sad children must be sad boys . we have 6 happy boys and 6 sad boys . total we have 18 boys . so 18 - 6 - 6 = 6 boys must be neither happy nor sad . answer ( c )\"" - }, - { - "Answer": 47, - "Options": "a ) 26 , b ) 32 , c ) 33 , d ) 34 , e ) 47", - "Correct": "e", - "Explanation": "\"multiples of 2 from 29 to 99 = multiples of 2 from 1 to 99 - multiples of 2 from 1 to 28 = [ 99 / 2 ] - [ 28 / 2 ] = 49 - 14 = 35 multiples of 3 from 29 to 99 = multiples of 3 from 1 to 99 - multiples of 3 from 1 to 28 = [ 99 / 3 ] - [ 28 / 3 ] = 33 - 9 = 24 multiples of 2 and 3 bothi . e . 6 from 29 to 99 = multiples of 6 from 1 to 99 - multiples of 6 from 1 to 28 = [ 99 / 6 ] - [ 28 / 6 ] = 16 - 4 = 12 these 8 numbers have been counted twice in both the above calculation while calculating multiples of 2 and 3 i . e . total numbers in w = 35 + 24 - 12 = 47 answer option e\"" - }, - { - "Answer": 15, - "Options": "a ) 15 , b ) 26 , c ) 22 , d ) 27 , e ) 11", - "Correct": "a", - "Explanation": "explanation : let quantity of mixture be x liters . suppose a container contains x units of liquid from which y units are taken out and replaced by water . after operations , the quantity of pure liquid = units , where n = no of operations . so , quantity of milk = given that , milk : water = 9 : 16 milk : ( milk + water ) = 9 : ( 9 + 16 ) milk : mixture = 9 : 25 answer : a ) 15" - }, - { - "Answer": 3003, - "Options": "a ) 3003 , b ) 3027 , c ) 3024 , d ) 3021 , e ) 3018", - "Correct": "a", - "Explanation": "first , you have to find the common ratio for all 3 books . you have : p : c : b 3 : 2 - - > multiply by 2 ( gives you row 3 ) 4 : 6 6 : 4 : 3 hence : p : c : b : t ( total ) = q 6 : 4 : 3 : 13 - - - - > this means , the total number must be a multiple of 13 . answer a is correct since 299 is divisible by 13 , hence is 2990 and so is 3003 ( 2990 + 13 ) ." - }, - { - "Answer": 299, - "Options": "a ) 299 , b ) 278 , c ) 322 , d ) 231 , e ) 121", - "Correct": "a", - "Explanation": "\"clearly , the numbers are ( 23 * 12 ) and ( 23 * 13 ) . larger number = ( 23 * 13 ) = 299 . answer : a\"" - }, - { - "Answer": 0.15789473684210525, - "Options": "a ) 1 / 11 , b ) 1 / 12 , c ) 1 / 13 , d ) 3 / 19 , e ) 3 / 43", - "Correct": "d", - "Explanation": "\"in believe the answer is d . please see below for explanation . 0 ) we are told the following ratios cgd - college graduate with degree ncg - non college graduate cgn - college graduate no degree cgd ncg cgn 1 8 3 2 in order to make cgd and cgn comparable we need to find the least common multiple of 8 and 3 and that is 24 multiplying the first ratio by 3 and the second ratio by 8 we get cgd ncg cgn 3 24 16 if one picks a random college graduate at this large company , what is the probability this college graduate has a graduate degree ? nr of cgd = 3 nr of cg = 3 + 16 = 19 probability t of cgd / ( cg ) - > 3 / 19 answer d\"" - }, - { - "Answer": 70, - "Options": "a ) 40 , b ) 50 , c ) 70 , d ) 60 , e ) none", - "Correct": "c", - "Explanation": "make a venn diagram , and enter your data . let the number of people who like listening songs be x x + 20 + 30 = 100 x = 50 so number who like listening songs = 20 + 50 = 70 answer c" - }, - { - "Answer": 39, - "Options": "a ) 29 , b ) 49 , c ) 39 , d ) 59 , e ) 69", - "Correct": "c", - "Explanation": "editing my solution : number of switches = 97 number of switches turned on by a : 3 , 6 , . . . 96 = 32 number of switches turned on by b : 5 , 10 , . . . . 95 = 19 few switches are turned on by a and later turned off by b : lcm ( 3,5 ) = 15 x = 15 , 30 , . . . . 90 = 6 . subtract the above 6 switches from both a and b as they are turned off . number of switches that are turned on = ( 32 - 6 ) + ( 19 - 6 ) = 39 answer : c" - }, - { - "Answer": 108000, - "Options": "a ) $ 90000 , b ) $ 108000 , c ) $ 119000 , d ) $ 126000 , e ) $ 140000", - "Correct": "b", - "Explanation": "let x equal the amount of spending , and y equal the amount of income . we know that x = 5 / 9 y we also know that x = y - 48000 therefore we can simplify to : y - 48000 = 5 / 9 y we isolate y , and get : 4 / 9 y = 48000 and to solve for y , we get : y = 48000 answer : b" - }, - { - "Answer": 0.3333333333333333, - "Options": "a ) 5 / 18 , b ) 7 / 18 , c ) 1 / 3 , d ) 1 / 2 , e ) 1 / 5", - "Correct": "c", - "Explanation": "explanation : neither red nor green means the pen drawn is black . total number of outcomes = ( 5 + 6 + 7 ) = 18 . number of favourable outcomes = 6 = number of black pens . hence , probability of the event = 6 / 18 = 1 / 3 . answer : c" - }, - { - "Answer": 30, - "Options": "a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30", - "Correct": "e", - "Explanation": "\"neither car nor garage = total - garage - ( swim - common ) = 85 - 50 - ( 40 - 35 ) = 85 - 55 = 30 answer e\"" - }, - { - "Answer": 30, - "Options": "a ) 24 , b ) 30 , c ) 36 , d ) 42 , e ) 48", - "Correct": "b", - "Explanation": "\"let the number of pens be 5 x and the number of pencils be 6 x . 6 x - 5 x = 5 x = 5 the number of pencils is 30 . the answer is b .\"" - }, - { - "Answer": 3, - "Options": "a ) 3 , b ) 1 / 3 , c ) 2 , d ) 9 , e ) 1 / 9", - "Correct": "a", - "Explanation": "\"28 = ( a 1 + a 2 + a 3 + a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) factorize the same terms 28 = 1 + ( a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) write every term with respect to r a 1 = a 1 a 2 = a 1 * r ^ 1 a 3 = a 1 * r ^ 2 . . . . . . . . . 28 = 1 + ( a 1 ( r ^ 3 + r ^ 4 + r ^ 5 ) ) / ( a 1 ( 1 + r ^ 1 + r ^ 2 ) ) 27 = ( r ^ 3 ( 1 + r ^ 1 + r ^ 2 ) ) / ( ( 1 + r ^ 1 + r ^ 2 ) ) 27 = r ^ 3 r = 3 a\"" - }, - { - "Answer": 0.15151515151515152, - "Options": "a ) 1 / 13 , b ) 2 / 23 , c ) 5 / 33 , d ) 4 / 27 , e ) 3 / 23", - "Correct": "c", - "Explanation": "\"p ( both are red ) , = 5 c 212 c 2 = 5 c 212 c 2 = 10 / 66 = 5 / 33 c\"" - }, - { - "Answer": 15, - "Options": "a ) 13 , b ) 17 , c ) 18 , d ) 11 , e ) 15", - "Correct": "e", - "Explanation": "e 15 one + one + one ( 3 + 3 + 3 ) = 09 four + four + four ( 4 + 4 + 4 ) = 12 seven + seven + seven ( 5 + 5 + 5 ) = 15 therefore eight + eight + eight ( 5 + 5 + 5 ) = 15" - }, - { - "Answer": 30, - "Options": "a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60", - "Correct": "b", - "Explanation": "\"originally , there were 3 k horses and k cows . 3 ( 3 k - 15 ) = 5 ( k + 15 ) 9 k - 5 k = 75 + 45 4 k = 120 k = 30 the difference between horses and cows is ( 3 k - 15 ) - ( k + 15 ) = 2 k - 30 = 30 the answer is b .\"" - }, - { - "Answer": 60, - "Options": "['a ) 60', 'b ) 50', 'c ) 40', 'd ) 80', 'e ) 70']", - "Correct": "a", - "Explanation": "b : d : w = 2 : 40 : 100 bnew / dnew = ( 1 / 3 ) * ( 2 / 40 ) = ( 1 / 60 ) dnew / wnew = ( 1 / 2 ) * ( 40 / 100 ) = ( 1 / 5 ) wnew = 300 dnew = wnew / 5 = 300 / 5 = 60 so , answer will be a" - }, - { - "Answer": 40, - "Options": "a ) 25 , b ) 40 , c ) 50 , d ) 60 , e ) 75", - "Correct": "b", - "Explanation": "we are told that 60 students claimed that they preferred mac to windows , which means that 60 preferred mac but not windows , so # of students who preferred mac ( p ( a ) as you wrote ) , does not equal to 60 , it equals to 60 + 20 ( 20 is # of students who equally preferred both brands ) . also we are asked to find # of the students who preferred windows to mac , so if you denote x as those who prefer windows then you should calculate x - 20 . so , if we use your formula it should be : 210 = { mac } + { windows } - { both } + { neither } = ( 60 + 20 ) + x - 20 + 90 - - > x = 60 ( # of student who prefer windows ) - - > # of the students who preferred windows to mac is x - 20 = 40 ." - }, - { - "Answer": 9, - "Options": "a ) 22 , b ) 15 , c ) 77 , d ) 9 , e ) 182", - "Correct": "d", - "Explanation": "\"present age is 4 x and 3 x , = > 4 x + 6 = 18 = > x = 3 so deepak age is = 3 ( 3 ) = 9 answer : d\"" - }, - { - "Answer": 30, - "Options": "a ) 28 , b ) 30 , c ) 40 , d ) 53 , e ) 54", - "Correct": "b", - "Explanation": "\"let the numbers be 2 x and 3 x . then , their l . c . m . = 6 x . so , 6 x = 36 or x = 6 . the numbers are 12 and 18 . hence , required sum = ( 12 + 18 ) = 30 . answer : option b\"" - }, - { - "Answer": 0.4, - "Options": "a ) 1 / 5 , b ) 5 / 15 , c ) 6 / 15 , d ) 3 / 10 , e ) 4 / 15", - "Correct": "c", - "Explanation": "p ( female ) = 150 / 450 = 1 / 3 p ( male with advanced degree ) = 0.1 * 300 / 450 = 30 / 450 = 1 / 15 the sum of the probabilities is 6 / 15 = 2 / 5 the answer is c ." - }, - { - "Answer": 35, - "Options": "a ) 30 , b ) 35 , c ) 20 , d ) 18 , e ) 10", - "Correct": "b", - "Explanation": "\"{ total } = { car } + { bike } - { both } + { neither } - - > 90 = 44 + { bike } - 18 + 11 - - > { bike } = 53 - - > # those who have bike only is { bike } - { both } = 53 - 18 = 35 . answer : b .\"" - }, - { - "Answer": 240, - "Options": "a ) 200 , b ) 240 , c ) 160 , d ) 250 , e ) 310", - "Correct": "b", - "Explanation": "\"let the number of boys and girls be 5 x and 7 x then , 7 x = 140 x = 20 total number of students = 12 x = 12 * 20 = 240 answer is b\"" - }, - { - "Answer": 6, - "Options": "a ) 8 , b ) 10 , c ) 6 , d ) 14 , e ) 16", - "Correct": "c", - "Explanation": "\"solution - consider multiples of 25 ! = > 3 , 6,9 , 12,15 count no . of 3 in each multiple . 3 = 3 x 1 - > 1 6 = 3 x 2 - > 1 9 = 3 x 3 - > 2 12 = 3 x 4 - > 1 15 = 3 x 5 - > 1 - - - - count 3 ' s = 6 so answer is 6\"" - }, - { - "Answer": 3400, - "Options": "a ) 3600 , b ) 3400 , c ) 3608 , d ) 3602 , e ) 3603", - "Correct": "b", - "Explanation": "\"let the income and the expenditure of the person be rs . 5 x and rs . 4 x respectively . income , 5 x = 17000 = > x = 3400 savings = income - expenditure = 5 x - 4 x = x so , savings = rs . 3400 . answer : b\"" - }, - { - "Answer": 80, - "Options": "a ) 80 , b ) 150 , c ) 100 , d ) 180 , e ) 220", - "Correct": "a", - "Explanation": "\"n ( a ) = 325 , n ( b ) = 175 , n ( aub ) = 470 - 50 = 420 . required number = n ( anb ) = n ( a ) + n ( b ) - n ( aub ) = 325 + 175 - 420 = 80 . answer is a\"" - }, - { - "Answer": 6, - "Options": "a ) 6 , b ) 15 , c ) 24 , d ) 33 , e ) 54", - "Correct": "a", - "Explanation": "\"formula for calculating two overlapping sets : a + b - both + not ( a or b ) = total so in our task we have equation : 41 ( french ) + 22 ( german ) - 9 ( both ) + not = 60 54 + not = 60 not = 60 - 54 = 6 so answer is a\"" - }, - { - "Answer": 6, - "Options": "a ) 6 , b ) 8 , c ) 14 , d ) 20 , e ) 28", - "Correct": "a", - "Explanation": "we are told that all of the letters contain either a dot or a straight line or both , which implies that there are no letters without a dot and a line ( no line / no dot box = 0 ) . first we find the total # of letters with lines : 10 + 24 = 34 ; next , we find the total # of letters without line : 40 - 34 = 6 ; finally , we find the # of letters that contain a dot but do not contain a straight line : 6 - 0 = 6 . a" - }, - { - "Answer": 320, - "Options": "a ) 120 , b ) 180 , c ) 240 , d ) 280 , e ) 320", - "Correct": "e", - "Explanation": "\"3 x = 480 x = 160 therefore , the salesman sold 160 kg in the morning and 2 \u22c5 160 = 320 kg in the afternoon . so answer is e .\"" - }, - { - "Answer": 96, - "Options": "a ) 99 , b ) 98 , c ) 97 , d ) 96 , e ) 95", - "Correct": "d", - "Explanation": "\"w 96 = 3 * 32 = 3 * 2 ^ 5 answer is d .\"" - }, - { - "Answer": 0.4422222222222222, - "Options": "a ) 4 / 10 , b ) 4 / 9 , c ) 6 / 5 , d ) 9 / 2 , e ) 6 / 4", - "Correct": "b", - "Explanation": "red : blue = 10 : 5 let red = 10 x and blue = 5 x 1 / 3 of red are left handed = > 1 / 3 * 10 x = 10 x / 3 red left handed 2 / 3 of blue are left handed = > 2 / 3 * 5 x = 10 x / 3 blue left handed fraction of participants who are left handed = total left handed / total participants = ( red left handed + blue left handed ) / total participants = ( 10 x / 3 + 10 x / 3 ) / ( 10 x + 5 x ) = 20 / 45 = 4 / 9 answer : b" - }, - { - "Answer": 1200, - "Options": "a ) 300 , b ) 1200 , c ) 1500 , d ) 1800 , e ) 2000", - "Correct": "b", - "Explanation": "think of the ratio as 5 parts : 4 parts . divide 1500 by 5 to find 1 ` ` part ' ' of the ratio . 1500 / 5 = 300 multiply this by 4 to get 4 ` ` parts ' ' of the ratio . 300 * 4 = 1200 there are 1200 girls in the school . the answer is b" - }, - { - "Answer": 4, - "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", - "Correct": "c", - "Explanation": "\"the ratio of flour to water is 14 : 2 . the ratio of flour to sugar is 3.5 : 1 = 14 : 4 . the new ratio of flour to water to sugar is 14 : 2 : 4 if we need 2 cups of water , then we need 4 cups of sugar . the answer is c .\"" - }, - { - "Answer": 24, - "Options": "a ) 26 , b ) 27 , c ) 24 , d ) 18 , e ) 11", - "Correct": "c", - "Explanation": "\"explanation : you could solve this by drawing a venn diagram . a simpler way is to realize that you can subtract the number of students taking both languages from the numbers taking french to find the number taking only french . likewise find those taking only german . then we have : total = only french + only german + both + neither 78 = ( 41 - 9 ) + ( 22 - 9 ) + 9 + neither . not enrolled students = 24 answer : c\"" - }, - { - "Answer": 1, - "Options": "a ) 1 : 1 , b ) 3 : 2 , c ) 4 : 3 , d ) 5 : 3 , e ) none", - "Correct": "a", - "Explanation": "\"required ratio = 500 : 500 = 1 : 1 answer a\"" - }, - { - "Answer": 10, - "Options": "a ) 10 , b ) 20 , c ) 84 , d ) 94 , e ) 178", - "Correct": "a", - "Explanation": "n ( lice ) = n ( only lice ) + n ( both lice and fleas ) n ( both lice and fleas ) = 84 n ( lice ) = 94 n ( only lice ) = 94 - 84 = 10 since , it is also said that exactly half the sheep have lice , it can be inferred that half the number of sheep is 94 . therefore , the total number of sheep having only fleas is 10 ans : ( option a )" - }, - { - "Answer": 343, - "Options": "a ) 343 , b ) 729 , c ) 829 , d ) 929 , e ) 727", - "Correct": "a", - "Explanation": "no of values n can take is 1 7 ^ 3 = 343 answer : a" - }, - { - "Answer": 14, - "Options": "a ) 12 kg , b ) 14 kg , c ) 15 kg , d ) 20 kg , e ) 18 kg", - "Correct": "b", - "Explanation": "let the required quantity of steel be x kg 5 : 2 : : 35 : x 5 x = 2 * 35 x = 14 kg answer is b" - }, - { - "Answer": 2, - "Options": "a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1", - "Correct": "d", - "Explanation": "\"the ratio of flour to water is 22 : 8 = 11 : 4 . the ratio of flour to sugar is 5.5 : 1 = 11 : 2 . the new ratio of flour to water to sugar is 11 : 4 : 2 if we need 4 cups of water , then we need 2 cups of sugar . the answer is d .\"" - }, - { - "Answer": 15, - "Options": "a ) 15 , b ) 30 , c ) 45 , d ) 60 , e ) 90", - "Correct": "a", - "Explanation": "\"standard : fl : corn s : water = 1 : 12 : 30 sport : fl : corn s : water = 3 : 12 : 180 this simplifies to 1 : 4 : 60 if the large bottle has a capacity of x ounces , then 4 x / 65 = 1 . so , x = 65 / 4 ounces . water = ( 60 / 65 ) * ( 65 / 4 ) = 15 ounces . ans a\"" - }, - { - "Answer": 30, - "Options": "a ) 15 , b ) 25 , c ) 30 , d ) 45 , e ) 60", - "Correct": "c", - "Explanation": "\"this ratio question can be solved in a couple of different ways . here ' s an algebraic approach . . . we ' re told that the ratio of the number of dogs to the number of cats is 15 : 7 . we ' re then told that 8 more cats are added to this group and the ratio becomes 15 : 11 . we ' re asked for the number of dogs . algebraically , since the number of dogs is a multiple of 15 and the number of cats is a multiple of 7 , we can write this initial relationship as . . . 15 x / 7 x when we add the 18 cats and factor in the ' ending ratio ' , we have an equation . . . . 15 x / ( 7 x + 8 ) = 15 / 11 here we have 1 variable and 1 equation , so we can solve for x . . . . ( 15 x ) ( 11 ) = ( 7 x + 8 ) ( 15 ) ( x ) ( 11 ) = ( 7 x + 8 ) ( 1 ) 11 x = 7 x + 8 4 x = 8 x = 2 with this x , we can figure out the initial number of dogs and cats . . . initial dogs = 15 x = 15 ( 2 ) = 30 final answer : c\"" - }, - { - "Answer": 150, - "Options": "a ) 130 , b ) 100 , c ) 200 , d ) 150 , e ) 120", - "Correct": "d", - "Explanation": "\"15 : 1 = x : 10 x = 10 * 15 x = 150 answer : d\"" - }, - { - "Answer": 5, - "Options": "a ) 5 , b ) 4 , c ) 6 , d ) 8 , e ) 10", - "Correct": "a", - "Explanation": "\"venn diagrams are useful for multiple values of a single variable e . g . state of mind - happy / sad / neither . when you have two or more variables such as here where you have gender - boy / girl too , it becomes unwieldy . in this case , either use the table or logic . table method is shown above ; here is how you will use logic : there are 6 happy boys . there are 4 sad girls but total 10 sad children . so rest 6 sad children must be sad boys . we have 6 happy boys and 6 sad boys . total we have 17 boys . so 17 - 6 - 6 = 5 boys must be neither happy nor sad . answer ( a )\"" - }, - { - "Answer": 180, - "Options": "a ) 72 , b ) 96 , c ) 108 , d ) 120 , e ) 180", - "Correct": "e", - "Explanation": "{ total } = { french } + { russian } - { both } + { neither } { total } = 14 + ( { total } - 32 ) - ( 0.1 * { total } ) + 0.2 * { total } solving gives { total } = 180 . answer : e ." - }, - { - "Answer": 720, - "Options": "a ) rs . 200 , b ) rs . 720 , c ) rs . 300 , d ) rs . 150 , e ) none of these", - "Correct": "b", - "Explanation": "\"explanation : let the cost of one pen is \u2018 5 x \u2019 and pencil is \u2018 x \u2019 3 x 5 x + 5 x = rs . 240 15 x + 5 x = rs . 240 x = 240 / 20 = 12 : . cost of 1 pen = 5 x = 5 x 12 = 60 : . cost of 12 pens , i . e . ( one dozen ) = 60 x 12 = rs . 720 answer : option b\"" - }, - { - "Answer": 16, - "Options": "a ) 18 , b ) 16 , c ) 32 , d ) 56 , e ) 60", - "Correct": "b", - "Explanation": "\"let the number of sheeps and horses be 4 x and 7 x . now total number of horses = total consumption of horse food / consumption per horse = 12880 / 230 = 56 , which is equal to 7 x . = > x = 8 sheeps = 2 x = 2 * 8 = 16 . hence b\"" - }, - { - "Answer": 8280.000000000002, - "Options": "a ) s . 7500 , b ) s . 8000 , c ) s . 8280 , d ) s . 9000 , e ) s . 6000", - "Correct": "c", - "Explanation": "\"let hari \u2019 s capital be rs . x . then , 3220 * 12 / 7 x = 2 / 3 = > 14 x = 115920 = > x = 8280 . answer : c\"" - }, - { - "Answer": 3, - "Options": "a ) 9 , b ) 36 , c ) 122 , d ) 3 , e ) 1", - "Correct": "d", - "Explanation": "\"square root is a number times itself square root of 81 = 6 , 9 / 3 = 3 ( d ) 3\"" - }, - { - "Answer": 33, - "Options": "a ) 30 , b ) 31 , c ) 32 , d ) 33 , e ) 34", - "Correct": "d", - "Explanation": "this is an example of a standard overlapping sets question . it has no ' twists ' to it , so you ' ll likely find using the overlapping sets formula to be a fairly easy approach . if you ' re not familiar with it , then here is the formula : 60 = 35 + 23 - 31 + ( # in neither group ) = 33 the prompt gives you all of the numbers you need to get to the correct answer . just plug in and solve . d" - }, - { - "Answer": 600, - "Options": "a ) rs . 200 , b ) rs . 250 , c ) rs . 300 , d ) rs . 150 , e ) rs . 600", - "Correct": "e", - "Explanation": "\"explanation : let the cost of one pen is \u2018 5 x \u2019 and pencil is \u2018 x \u2019 3 x 5 x + 5 x = rs . 200 15 x + 5 x = rs . 200 x = 200 / 20 = 10 : . cost of 1 pen = 5 x = 5 x 10 = 50 : . cost of 12 pens , i . e . ( one dozen ) = 50 x 12 = rs . 600 answer : option e\"" - }, - { - "Answer": 55, - "Options": "a ) 60 % , b ) 55 % , c ) 70 % , d ) 75 % , e ) 80 %", - "Correct": "b", - "Explanation": "\"{ total } = { first correctly } + { second correctly } - { both correctly } + { neither correctly } 100 = 85 + 65 - { both correctly } + 5 { both correctly } = 55 . answer : b .\"" - }, - { - "Answer": 0.05454545454545454, - "Options": "a ) 2 / 15 , b ) 2 / 21 , c ) 3 / 55 , d ) 3 / 29 , e ) 4 / 27", - "Correct": "c", - "Explanation": "\"p ( both are red ) , = 3 c 211 c 2 = 3 c 211 c 2 = 3 / 55 c\"" - }, - { - "Answer": 20.8, - "Options": "a ) 1.2 , b ) 20.8 , c ) 2.3 , d ) 6.7 , e ) 8.2", - "Correct": "b", - "Explanation": "\"the answer is ( 100 - 1 ) / 5 + 1 = 20.8 answer is b\"" - }, - { - "Answer": 4, - "Options": "a ) 4 , b ) 6 , c ) 7 , d ) 8 , e ) 9", - "Correct": "a", - "Explanation": "20 ! has four 5 ' s 20 / 5 = 4 thus 5 ^ 4 can completely divide 20 ! and 5 ^ 5 can not divide 20 ! so , answer will be ( a ) 4" - }, - { - "Answer": 10, - "Options": "a ) 10 , b ) 11 , c ) 13 , d ) 14 , e ) 15", - "Correct": "a", - "Explanation": "let the number of who play both be x number of students who play sports 25 - 4 = 21 use venn diagram ( 15 - x ) + x + ( 16 - x ) = 21 which gives x = 10 answer is a 10 play both sport" - }, - { - "Answer": 0.09523809523809523, - "Options": "a ) 2 / 15 , b ) 2 / 21 , c ) 5 / 26 , d ) 3 / 29 , e ) 4 / 27", - "Correct": "b", - "Explanation": "p ( both are red ) , = 5 c 215 c 2 = 5 c 215 c 2 = 10 / 105 = 2 / 21 b" - }, - { - "Answer": 42, - "Options": "a ) 36 , b ) 42 , c ) 48 , d ) 55 , e ) 64", - "Correct": "b", - "Explanation": "\"let the number of pens be 5 x and the number of pencils be 6 x . 6 x - 5 x = 7 x = 7 the number of pencils is 42 . the answer is b .\"" - }, - { - "Answer": 300, - "Options": "a ) $ 400 , b ) $ 300 , c ) $ 500 , d ) $ 180 , e ) $ 200", - "Correct": "b", - "Explanation": "\"b ' s share = 900 * 3 / 9 = $ 300 answer is b\"" - }, - { - "Answer": 24, - "Options": "a ) 24 , b ) 28 , c ) 32 , d ) 56 , e ) 58", - "Correct": "a", - "Explanation": "et no of sheep and horses are 3 k and 7 k no of horses = 12880 / 230 = 56 now 7 k = 56 and k = 8 no of sheep = ( 3 * 8 ) = 24 answer : a" - }, - { - "Answer": 416, - "Options": "a ) 562 , b ) 356 , c ) 452 , d ) 416 , e ) 512", - "Correct": "d", - "Explanation": "\"let the number of boys and girls be 8 x and 5 x then , 5 x = 160 x = 32 total number of students = 13 x = 13 * 32 = 416 answer is d\"" - }, - { - "Answer": 3, - "Options": "a ) 3 : 1 , b ) 9 : 13 , c ) 5 : 11 , d ) 11 : 3 , e ) 15 : 4", - "Correct": "a", - "Explanation": "\"the ratio of milk and water in the new vessel is = ( 4 / 6 + 5 / 6 ) : ( 2 / 6 + 1 / 6 ) = 9 / 6 : 3 / 6 = 3 : 1 answer is a\"" - }, - { - "Answer": 36, - "Options": "a ) 12 , b ) 16 , c ) 36 , d ) 48 , e ) 98", - "Correct": "c", - "Explanation": "\"let the numbers be 3 x and 4 x . then their h . c . f = x . so , x = 3 . so , the numbers are 9 and 12 . l . c . m of 9 and 12 = 36 . answer : c\"" - }, - { - "Answer": 26, - "Options": "a ) 26 , b ) 19 , c ) 11 , d ) 8 , e ) 6", - "Correct": "a", - "Explanation": "\"no of dogs = 45 long fur = 36 brown = 27 neither long fur nor brown = 8 therefore , either long fur or brown = 45 - 8 = 37 37 = 36 + 27 - both both = 26 answer a\"" - }, - { - "Answer": 48, - "Options": "a ) 60 , b ) 45 , c ) 50 , d ) 48 , e ) none", - "Correct": "d", - "Explanation": "sol . let the required numbers be 8 x and 9 x . then , their l . c . m . is 72 x . \u2234 72 x = 432 \u21d4 x = 6 . hence , the first number is 48 . answer d" - }, - { - "Answer": 3003, - "Options": "a ) 3003 , b ) 3027 , c ) 3024 , d ) 3021 , e ) 3018", - "Correct": "a", - "Explanation": "\"first , you have to find the common ratio for all 3 books . you have : p : c : b 3 : 2 - - > multiply by 2 ( gives you row 3 ) 4 : 6 6 : 4 : 3 hence : p : c : b : t ( total ) t 6 : 4 : 3 : 13 - - - - > this means , the total number must be a multiple of 13 . answer a is correct since 299 is divisible by 13 , hence is 2990 and so is 3003 ( 2990 + 13 ) .\"" - }, - { - "Answer": 0.3396307322929171, - "Options": "a ) 0.33365 , b ) 0.3368 , c ) 0.3396 , d ) 0.3369 , e ) 0.3469", - "Correct": "c", - "Explanation": "log 0.318 / log 0.317 = log ( 0.318 - 0.317 ) = log 0.001 = 0.3364 / 0.33320 = 1.0096 now , log 0.318 * log 0.001 = log ( 0.318 + 0.001 ) = log 0.319 = 0.3364 * 1.0096 = 0.3396 so option c answer : c" - }, - { - "Answer": 30, - "Options": "a ) 30 , b ) 10 , c ) 18 , d ) 28 , e ) 32", - "Correct": "a", - "Explanation": "total = english + german - both + neither - - > 52 = english + 22 - 12 + 0 - - > english = 42 - - > only english = english - both = 42 - 12 = 30 answer : a ." - }, - { - "Answer": 1.9999999999999998, - "Options": "a ) 1 : 2 , b ) 5 : 9 , c ) 2 : 1 , d ) 11 : 24 , e ) none", - "Correct": "c", - "Explanation": "answer : option c 2 / 3 : 6 / 11 : 11 / 2 = 2 : 1" - }, - { - "Answer": 88, - "Options": "a ) 144 , b ) 119 , c ) 113 , d ) 88 , e ) 31", - "Correct": "d", - "Explanation": "\"official solution : first of all , notice that since 144 took geometry and 119 took biology , then the number of students who took both geometry and biology can not be greater than 119 . { total } = { geometry } + { biology } - { both } + { neither } ; 232 = 144 + 119 - { both } + { neither } ; { both } = 31 + { neither } . { both } is minimized when { neither } is 0 . in this case { both } = 31 . the greatest possible number of students p that could have taken both geometry and biology , is 119 . thus , the answer is 119 - 31 = 88 . answer : d .\"" - }, - { - "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 , v = 1000 purchased a only . ( this is much simpler to solve using the venn diagram ) . correct answer is d . 1000\"" - }, - { - "Answer": 36, - "Options": "a ) 26 , b ) 36 , c ) 46 , d ) 56 , e ) 66", - "Correct": "b", - "Explanation": "\"explanation : let pencils = 10 x , pens = 2 x & exercise books = 3 x . now , 10 x = 120 hence x = 12 . number of exercise books = 3 x = 36 . answer : b\"" - }, - { - "Answer": 1848, - "Options": "a ) 80 , b ) 160 , c ) 720 , d ) 1600 , e ) 1848", - "Correct": "e", - "Explanation": "no . of ways of picking 2 biology books ( from 12 books ) = 12 c 2 = ( 12 * 11 ) / 2 = 66 no . of ways of picking 2 chemistry books ( from 8 books ) = 8 c 2 = ( 8 * 7 ) / 2 = 28 total ways of picking 2 books of each type = 66 * 28 = 1848 ( option e )" - }, - { - "Answer": 9, - "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", - "Correct": "c", - "Explanation": "\"xc 1 * ( x - 1 ) c 1 = 72 x ^ 2 - x - 72 = 0 ( x - 9 ) ( x + 8 ) = 0 x = 9 , - 8 - 8 ca n ' t possible . c\"" - }, - { - "Answer": 28, - "Options": "a ) 12 , b ) 32 , c ) 5 , d ) 28 , e ) 35", - "Correct": "d", - "Explanation": "explanation : n ( aub ) = n ( a ) + n ( b ) - n ( anb ) . . . . ( 1 ) n ( a ) = number of kids playing with white color balls = 26 n ( aub ) = total number of kids in the play school = 35 n ( anb ) = number of kids playing with both white and yellow color balls = 19 we have to find , n ( b ) = number of kids playing with yellow color balls from ( 1 ) , 35 = 26 + n ( b ) - 19 n ( b ) = 35 + 19 - 26 = 28 hence , answer is 28 kids play with yellow color balls . answer : d" - }, - { - "Answer": 24.5, - "Options": "a ) 22.5 years , b ) 24.5 years , c ) 12.5 years , d ) 28.5 years , e ) 29.5 years", - "Correct": "b", - "Explanation": "\"let rahul ' s age be x years . then , sachin ' s age = ( x - 7 ) years . therefore ( x - 7 ) / x = 7 / 9 9 x - 63 = 7 x 2 x = 63 x = 31.5 hence , sachin ' s age = ( x - 7 ) = 24.5 years . answer : b\"" - }, - { - "Answer": 0.3076923076923077, - "Options": "a ) 24 / 78 , b ) 24 / 709 , c ) 24 / 76 , d ) 24 / 71 , e ) 24 / 72", - "Correct": "a", - "Explanation": "explanation : total marbles in a box = 4 black + 3 red + 6 green marbles = 13 marbles 2 marbles are drawn from 13 marbles at random . therefore , n ( s ) = 13 c 2 = 78 ways let a be the event that 2 marbles drawn at random are of the same color . number of cases favorable to the event a is n ( a ) = 4 c 2 + 3 c 2 + 6 c 2 = 6 + 3 + 15 = 24 therefore , by definition of probability of event a , p ( a ) = n ( a ) / n ( s ) = 24 / 78 answer : a" - }, - { - "Answer": 0.3666666666666666, - "Options": "a ) 7 / 20 , b ) 9 / 25 , c ) 11 / 30 , d ) 13 / 35 , e ) 17 / 40", - "Correct": "c", - "Explanation": "\"let , a \u2261 event of getting hardware contract b \u2261 event of getting software contract ab \u2261 event of getting both hardware and software contract . p ( a ) = 4 / 5 , p ( ~ b ) = 5 / 9 = > p ( b ) = 1 - ( 3 / 5 ) = 2 / 5 . a and b are not mutually exclusive events but independent events . so , p ( at least one of a and b ) = p ( a ) + p ( b ) - p ( ab ) . = > 5 / 6 = ( 4 / 5 ) + ( 2 / 5 ) - p ( ab ) . = > p ( ab ) = 11 / 30 . hence , the required probability is 11 / 30 . the answer is c .\"" - }, - { - "Answer": 0.29999999999999993, - "Options": "a ) 1 / 8 , b ) 2 / 9 , c ) 3 / 10 , d ) 4 / 11 , e ) 5 / 12", - "Correct": "c", - "Explanation": "\"let , a \u2261 event of getting hardware contract b \u2261 event of getting software contract ab \u2261 event of getting both hardware and software contract . p ( a ) = 4 / 5 , p ( ~ b ) = 5 / 9 = > p ( b ) = 1 - ( 3 / 5 ) = 2 / 5 . a and b are not mutually exclusive events but independent events . so , p ( at least one of a and b ) = p ( a ) + p ( b ) - p ( ab ) . = > 9 / 10 = ( 4 / 5 ) + ( 2 / 5 ) - p ( ab ) . = > p ( ab ) = 3 / 10 . hence , the required probability is 3 / 10 . the answer is c .\"" - }, - { - "Answer": 1, - "Options": "['a ) 99 : 61', 'b ) 1 : 1', 'c ) 61 : 160', 'd ) 61 : 99', 'e ) 99 : 160']", - "Correct": "b", - "Explanation": "vessel a = 300 gallons - - > milk = 100 , water = 200 ; vessel b = 500 gallons - - > milk = 300 , water = 200 ; vessel a + b = 800 gallons - - > milk = 400 , water 400 . the ratio = 400 / 400 - - > 1 : 1 answer : b" - }, - { - "Answer": 40, - "Options": "a ) 22 , b ) 40 , c ) 88 , d ) 52 , e ) 12", - "Correct": "b", - "Explanation": "5 : 1 = x : 8 x = 40 answer : b" - }, - { - "Answer": 132, - "Options": "a ) 132 \u00b0 , b ) 228 \u00b0 , c ) 156 \u00b0 , d ) 224 \u00b0 , e ) none of these", - "Correct": "a", - "Explanation": "the measures of the adjacent angles of a parallelogram add up to be 180 \u00b0 given so , 4 x + 11 x = 180 \u00b0 or , 15 x = 180 \u00b0 or , x = 12 \u00b0 hence the angles of the parallelogram are 48 \u00b0 and 132 \u00b0 further it is given we know sum of all the four angles of a quadrilateral is 360 \u00b0 so , 5 y + 6 y + 7 y + 12 y = 360 \u00b0 or , 5 y + 6 y + 7 y + 12 y = 360 \u00b0 or , 30 y = 360 \u00b0 or , y = 12 \u00b0 hence the angles of the quadrilateral are 60 \u00b0 , 72 , 84 \u00b0 and 144 \u00b0 will be 48 \u00b0 + 84 \u00b0 = 132 \u00b0 answer : a" - }, - { - "Answer": 7.5, - "Options": "a ) 1.5 , b ) 6.5 , c ) 7.5 , d ) 8 , e ) 2", - "Correct": "c", - "Explanation": "\"27 * 12 : 36 * x = 2 : 1 x = 4.5 12 - 4.5 = 7.5 answer : c\"" - }, - { - "Answer": 0.2, - "Options": "a ) 0.5 , b ) 0.4 , c ) 0.3 , d ) 0.2 , e ) 0.1", - "Correct": "d", - "Explanation": "assume that these 2 students are 1 and then u can sit is 9 ! and these 2 students can sit by 2 ways then total ways are 9 ! * 2 and the probability is 9 ! * 2 / 10 ! = 1 / 5 = 0.2 answer : d" - }, - { - "Answer": 376, - "Options": "a ) 188 , b ) 258 , c ) 376 , d ) 470 , e ) 517", - "Correct": "c", - "Explanation": "\"consider 5 x acres of land used for bean consider 2 x acres of land used for wheat consider 4 x acres of land used for corn total given is 1034 acres 11 x = 1034 x = 94 land used for corn e = 4 * 94 = 376 correct option - c\"" - }, - { - "Answer": 10, - "Options": "a ) 20 , b ) 30 , c ) 5 , d ) 8 , e ) 10", - "Correct": "e", - "Explanation": "3 / 5 + 1 / 5 are the students who have left the classroom 3 / 5 + 1 / 5 = ( 3 + 1 ) / 5 , since denominator is same for both fractions = 4 / 5 remaining students in the classroom = 1 - 4 / 5 = 5 / 5 - 4 / 5 = ( 5 - 4 ) / 5 = 1 / 5 1 / 5 of 50 = 10 ans : e" - }, - { - "Answer": 0.4666666666666667, - "Options": "a ) 4 / 15 , b ) 1 / 3 , c ) 2 / 5 , d ) 4 / 5 , e ) 7 / 15", - "Correct": "e", - "Explanation": "\"a : b = 7 : 3 - - 1 b : c = 1 : 5 = > b : c = 3 : 15 - - 2 from 1 and 2 , we get a : c = 7 : 15 answer e\"" - }, - { - "Answer": 0.09156626506024096, - "Options": "a ) 1 / 250 , b ) 1 / 84 , c ) 1 / 11 , d ) 1 / 9 , e ) 1 / 3", - "Correct": "c", - "Explanation": "\"probability of chosing one defective phone from a lot of 250 which ontains 76 defective phones is = ( 76 / 250 ) probability of chosing one defective phone from a lot of 249 ( we already picked one ) which ontains 75 ( we already picked one ) defective phones is = ( 75 / 249 ) combined probability of series of events = product of the probabilities = ( 76 / 250 ) * ( 75 / 249 ) 76 / 250 is close to ( 7 / 23 ) and ( 75 / 249 ) = ( 25 / 83 ) so answer is ( 7 / 23 ) * ( 25 / 83 ) = ( 1 / 11 ) so , answer will be c\"" - }, - { - "Answer": 1, - "Options": "a ) 1 , b ) 6 , c ) 34 , d ) 79 , e ) 85", - "Correct": "a", - "Explanation": "dogs wear neither a collar nor tags = 80 - ( 45 + 40 - 6 ) dogs wear neither a collar nor tags = 80 - 79 dogs wear neither a collar nor tags = 80 - 79 hence , answer will be 1 answer : a" - }, - { - "Answer": 8, - "Options": "a ) 8 , b ) 6 , c ) 4 , d ) 2 , e ) 10", - "Correct": "a", - "Explanation": "we ' re told that two numbers are in the ratio of 2 : 3 . thus , the two numbers could be . . . 2 and 3 4 and 6 6 and 9 8 and 12 10 and 15 etc . we ' re told that adding 4 to each number changes the ratio of the numbers to 5 : 7 . we ' re asked for the difference between the original numbers . since adding 4 makes the first number a multiple of 5 , this limits the possibilities . . . . 2 + 4 = 6 not possible 4 + 4 = 8 not possible 6 + 4 = 10 this is possible . . . using this example , we would have . . . 6 and 9 , after adding 4 to each , becomes 10 and 13 . . . this is not a ratio of 5 to 7 though ( even though it ' s pretty close ) , so we have to keep looking . . . . the next value that becomes a multiple of 5 when you add 4 to it is . . . 16 . . . 16 + 4 = 20 with 16 and 24 , after adding 4 to each , we have 20 and 28 . this is a ratio of 5 to 7 , so we have our pair of original numbers . the difference between them is 8 . final answer : a" - }, - { - "Answer": 104, - "Options": "a ) 40 , b ) 92 , c ) 104 , d ) 208 , e ) 80", - "Correct": "c", - "Explanation": "the ratio is 10 football players : 7 baseball players : 5 soccer players : 4 basketball players . divide 16 by 4 to find 1 ` ` part ' ' of the ratio . 16 / 4 = 4 multiply 4 by 5 to find the number of soccer players . 4 * 5 = 20 multiply 4 by 7 to find the number of baseball players . 4 * 7 = 28 multiply 4 by 10 to find the number of football players . 4 * 10 = 40 . add them all up to find total athletes . 16 + 20 + 28 + 40 = 104 the answer is c ." - }, - { - "Answer": 8, - "Options": "a ) 2 , b ) 4 , c ) 5 , d ) 8 , e ) 10", - "Correct": "d", - "Explanation": "the ratio is 1 hour swimming : 4 hours reading : 10 hours hanging out with friends . divide 20 by 10 to find 1 ` ` part ' ' of the ratio . 20 / 10 = 2 multiply this by 4 to find the hours spent reading . 2 * 4 = 8 the answer is d ." - }, - { - "Answer": 42, - "Options": "a ) 24 , b ) 36 , c ) 42 , d ) 72 , e ) 120", - "Correct": "c", - "Explanation": "5 x - 3 x = 12 so , 2 x = 6 hence no of toddlers is 6 * 7 = 42 answer will be ( c ) 42" - }, - { - "Answer": 100, - "Options": "a ) 72 , b ) 96 , c ) 100 , d ) 120 , e ) 150", - "Correct": "c", - "Explanation": "\"{ total } = { french } + { russian } - { both } + { neither } { total } = 22 + ( { total } - 32 ) - ( 0.1 * { total } ) + 0.2 * { total } solving gives { total } = 100 . answer : c .\"" - }, - { - "Answer": 56, - "Options": "a ) 42 , b ) 49 , c ) 56 , d ) 63 , e ) 70", - "Correct": "c", - "Explanation": "\"let sandy ' s age be 7 x and let molly ' s age be 9 x . 9 x - 7 x = 16 x = 8 sandy is 56 years old . the answer is c .\"" - }, - { - "Answer": 29, - "Options": "a ) 24 , b ) 27 , c ) 29 , d ) 31 , e ) 33", - "Correct": "c", - "Explanation": "\"total number of enrolled students = 40 number of students who did not take test = 10 hence , number of students who took test = 40 - 10 = 30 number of students who answered q 2 correctly = 29 , therefore , all students who took test answered q 2 correctly . so , number of students who answered q 1 correctly , also answered q 2 correctly = 29 . number of students who answered both q 1 & q 2 correctly = 29 . answer : c\"" - }, - { - "Answer": 460, - "Options": "a ) 276 , b ) 299 , c ) 312 , d ) 460 , e ) none", - "Correct": "d", - "Explanation": "\"solution clearly , the numbers are ( 20 x 21 ) and ( 20 x 23 ) . larger number = ( 20 x 23 ) = 460 . answer d\"" - }, - { - "Answer": 26, - "Options": "a ) 11 , b ) 26 , c ) 24 , d ) 27 , e ) 32", - "Correct": "b", - "Explanation": "\"b is correct r / b = 3 / 8 and b = 70 r = 70 * 3 / 8 = 26\"" - }, - { - "Answer": 32, - "Options": "a ) 18 , b ) 28 , c ) 32 , d ) 56 , e ) 58", - "Correct": "c", - "Explanation": "\"et no of sheep and horses are 4 k and 7 k no of horses = 12880 / 230 = 56 now 7 k = 56 and k = 8 no of sheep = ( 4 * 8 ) = 32 answer : c\"" - }, - { - "Answer": 878.7878787878788, - "Options": "a ) 884 , b ) 890 , c ) 892 , d ) 910 , e ) 945", - "Correct": "a", - "Explanation": "\"normally , i would use the method used by bunuel . it ' s the most accurate . but if you are looking for a speedy solution , you can use another method which will sometimes give you an estimate . looking at the options ( most of them are spread out ) , i wont mind trying it . ( mind you , the method is accurate here since the numbers start from 1 . ) in 1000 consecutive numbers , number of multiples of 11 = 1000 / 11 = 90 ( ignore decimals ) in 1000 consecutive numbers , number of multiples of 35 = 1000 / 35 = 28 number of multiples of 11 * 35 i . e . 385 = 1000 / 385 = 2 number of integers from 1 to 1000 that are divisible by neither 11 nor by 35 = 1000 - ( 90 + 28 - 2 ) { using the concept of sets here ) = 884 think : why did i say the method is approximate in some cases ? think what happens if the given range is 11 to 1010 both inclusive ( again 1000 numbers ) what is the number of multiples in this case ? a\"" - }, - { - "Answer": 0.3944444444444444, - "Options": "a ) 11 / 30 , b ) 31 / 60 , c ) 41 / 80 , d ) 51 / 120 , e ) 71 / 180", - "Correct": "e", - "Explanation": "\"let , a \u2261 event of getting hardware contract b \u2261 event of getting software contract ab \u2261 event of getting both hardware and software contract . p ( a ) = 3 / 4 , p ( ~ b ) = 5 / 9 = > p ( b ) = 1 - ( 5 / 9 ) = 4 / 9 . a and b are not mutually exclusive events but independent events . so , p ( at least one of a and b ) = p ( a ) + p ( b ) - p ( ab ) . = > 4 / 5 = ( 3 / 4 ) + ( 4 / 9 ) - p ( ab ) . = > p ( ab ) = 71 / 180 . hence , the required probability is 71 / 180 . the answer is e .\"" - }, - { - "Answer": 19, - "Options": "a ) 26 , b ) 19 , c ) 11 , d ) 8 , e ) 6", - "Correct": "b", - "Explanation": "\"no of dogs = 45 long fur = 26 brown = 30 neither long fur nor brown = 8 therefore , either long fur or brown = 45 - 8 = 37 37 = 26 + 30 - both both = 19 answer b\"" - }, - { - "Answer": 7000, - "Options": "a ) 6999 , b ) 7000 , c ) 7001 , d ) 7002 , e ) 7003", - "Correct": "b", - "Explanation": "\"let the income and the expenditure of the person be rs . 15 x and rs . 8 x respectively . income , 15 x = 15000 = > x = 1000 savings = income - expenditure = 15 x - 8 x = 7 x = 7 ( 1000 ) so , savings = rs . 7000 . answer : b\"" - }, - { - "Answer": 0.12512512512512514, - "Options": "a ) 125 / 990 , b ) 125 / 999 , c ) 125 / 900 , d ) 12 / 999 , e ) 12 / 990", - "Correct": "b", - "Explanation": "0.125125 . . . = 0.125 = 125 / 999 answer is b ." - }, - { - "Answer": 90, - "Options": "a ) 45 , b ) 50 , c ) 55 , d ) 60 , e ) 90", - "Correct": "e", - "Explanation": "\"f : c : w 1 : 12 : 30 sport version : f : c 3 : 12 f : w 1 : 60 or 3 : 180 so c : f : w = 12 : 3 : 180 c / w = 12 / 180 = 3 ounces / x ounces x = 6 * 180 / 12 = 90 ounces of water e\"" - }, - { - "Answer": 363, - "Options": "a ) 121 , b ) 3267 , c ) 363 , d ) 33 , e ) none of the above", - "Correct": "c", - "Explanation": "explanatory answer step 1 : prime factorize the given expression a * 43 * 62 * 1311 can be expressed in terms of its prime factors as a * 28 * 32 * 1311 step 2 : find factors missing after excluding ' a ' to make the number divisible by both 112 and 33 112 is a factor of the given number . if we do not include ' a ' , 11 is not a prime factor of the given number . if 112 is a factor of the number , 112 should have been in ' a ' 33 is a factor of the given number . if we do not include ' a ' , the number has only 32 in it . therefore , if 33 has to be a factor of the given number ' a ' has to contain 31 in it . therefore , ' a ' should be at least 112 * 3 = 363 if the given number has 112 and 33 as its factors . the smallest value that ` ` a ' ' can take is 363 . choice c is the correct answer ." - }, - { - "Answer": 45, - "Options": "a ) 60 , b ) 45 , c ) 20 , d ) 15 , e ) none", - "Correct": "b", - "Explanation": "\"sol . let the required numbers be 3 x and 4 x . then , their l . c . m . is 12 x . \u2234 12 x = 180 \u21d4 x = 15 . hence , the first number is 45 . answer b\"" - }, - { - "Answer": 12, - "Options": "a ) 22 , b ) 15 , c ) 77 , d ) 266 , e ) 12", - "Correct": "e", - "Explanation": "\"present age is 4 x and 3 x , = > 4 x + 6 = 22 = > x = 4 so deepak age is = 3 ( 4 ) = 12 answer : e\"" - }, - { - "Answer": 8, - "Options": "a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12", - "Correct": "d", - "Explanation": "g and f are both odd prime numbers - it means either g or f is not 2 and since prime numbers have only two factors - 1 and the number itself g and f each will have ( 1 + 1 ) = 2 factors hence 2 gf will have ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 8 factors d is the answer" - }, - { - "Answer": 32, - "Options": "a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36", - "Correct": "d", - "Explanation": "the three numbers are 3 x , 5 x , and 7 x . the largest number is 56 = 7 * 8 , so x = 8 . the smallest number is 3 * 8 = 24 . 56 - 24 = 32 the answer is d ." - }, - { - "Answer": 0.1111111111111111, - "Options": "a ) 1 / 16 , b ) 5 / 42 , c ) 1 / 8 , d ) 3 / 16 , e ) 1 / 9", - "Correct": "e", - "Explanation": "200 = 2 * 3 * 5 * 7 , so the # of factors 210 has is ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 16 ( see below ) ; 42 = 2 * 3 * 7 , so out of 16 factors only two are multiples of 42 : 42 and 210 , itself ; so , the probability is 2 / 16 = 1 / 9 . answer : e ." - }, - { - "Answer": 24, - "Options": "a ) 24 , b ) 28 , c ) 32 , d ) 56 , e ) 60", - "Correct": "a", - "Explanation": "let the number of sheeps and horses be 3 x and 7 x . now total number of horses = total consumption of horse food / consumption per horse = 12880 / 230 = 56 , which is equal to 7 x . = > x = 8 sheeps = 3 x = 3 * 8 = 24 . hence a" - }, - { - "Answer": 7000, - "Options": "a ) 6000 , b ) 7000 , c ) 8000 , d ) 9000 , e ) 10000", - "Correct": "b", - "Explanation": "let the income and the expenditure of the person be rs . 3 x and rs . 2 x respectively . income , 3 x = 21000 = > x = 7000 savings = income - expenditure = 3 x - 2 x = x so , savings = rs . 7000 . answer : b" - }, - { - "Answer": 430, - "Options": "a ) 438 , b ) 436 , c ) 430 , d ) 442 , e ) 444", - "Correct": "c", - "Explanation": "312 + 232 - 114 ( since 112 is counted twice ) = 430 c is the answer" - }, - { - "Answer": 116, - "Options": "a ) 116 , b ) 85 , c ) 94 , d ) 98 , e ) 108", - "Correct": "a", - "Explanation": "\"you had the answer almost right . the x = 93 refers to only set a . however what ' s being asked is how many members are part of set a . this will include : 1 . only set a 2 . set a and set b so the answer is set a = 93 + set ab = 93 + 23 = 116 a\"" - }, - { - "Answer": 0.49833333333333335, - "Options": "a ) 1 / 4 , b ) 1 / 8 , c ) 1 / 6 , d ) 1 / 2 , e ) 1", - "Correct": "d", - "Explanation": "\"red : blue = 5 : 5 let red = 5 x and blue = 5 x 1 / 3 of red are left handed = > 1 / 3 * 5 x = 5 x / 3 red left handed 2 / 3 of blue are left handed = > 2 / 3 * 5 x = 10 x / 3 blue left handed fraction of participants who are left handed = total left handed / total participants = ( red left handed + blue left handed ) / total participants = ( 5 x / 3 + 10 x / 3 ) / ( 5 x + 5 x ) = ( 15 x / 30 x ) = 1 / 2 answer : d\"" - }, - { - "Answer": 0.023809523809523808, - "Options": "a ) 3 / 14 , b ) 2 / 7 , c ) 1 / 3 , d ) 1 / 42 , e ) 12 / 21", - "Correct": "d", - "Explanation": "method - 1 probability that the number on first die is 3 = 1 / 6 probability that the number on second die is 3 = 1 / 7 probability that both dice result in odd numbers = ( 1 / 6 ) * ( 1 / 7 ) = 1 / 42 answer : option d" - }, - { - "Answer": 11, - "Options": "a ) 12 , b ) 11 , c ) 13 , d ) 14 , e ) 15", - "Correct": "b", - "Explanation": "some multiple of 7 + some multiple of 5 should yield 63 . to get to a some multiple of 5 , we should ensure that a 3 or 8 ( 5 + 3 ) should be a multiple of 7 . 63 is a direct multiple of 7 , however in this case there wo n ' t be any cherry . hence the next option is to look for a multiple of 7 that has 8 as the unit digit . 28 satisfies this hence no . of apples is 4 and no of bananas is 7 b" - }, - { - "Answer": 88, - "Options": "a ) 144 , b ) 119 , c ) 113 , d ) 88 , e ) 31", - "Correct": "d", - "Explanation": "\"official solution : first of all , notice that since 144 took geometry and 119 took biology , then the number of students who took both geometry and biology can not be greater than 119 . { total } = { geometry } + { biology } - { both } + { neither } ; 232 = 144 + 119 - { both } + { neither } ; { both } = 31 + { neither } . { both } is minimized when { neither } is 0 . in this case { both } = 31 . the greatest possible number t of students that could have taken both geometry and biology , is 119 . thus , the answer is 119 - 31 = 88 . answer : d .\"" - }, - { - "Answer": 9, - "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12", - "Correct": "b", - "Explanation": "let ' s start with 1 apple for $ 0.80 . let ' s subtract $ 0.80 from $ 6.50 until we get a multiple of $ 0.70 . $ 6.50 , $ 5.70 , $ 4.90 = 7 * $ 0.70 the customer purchased 7 bananas and 2 apples . the answer is b ." - }, - { - "Answer": 0.01020408163265306, - "Options": "a ) 1 / 50 , b ) 1 / 25 , c ) 1 / 98 , d ) 1 , e ) 2", - "Correct": "c", - "Explanation": "\"there are 25 primes , 72 composite numbers from 1 to 98 . the number which is neither prime nor composite is 1 . therefore , required probability = 1 / 98 . answer : c\"" - }, - { - "Answer": 6, - "Options": "a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14", - "Correct": "a", - "Explanation": "\"26 + 20 - 17 = 29 35 - 29 = 6 play neither answer is a\"" - }, - { - "Answer": 3, - "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", - "Correct": "a", - "Explanation": "let x be subtracted . then , 6 - x 7 - x < 16 21 21 ( 6 - x ) < 16 ( 7 - x ) 5 x > 14 x > 2.8 least such whole number is 3 . answer : a" - }, - { - "Answer": 0.27, - "Options": "a ) 1 / 10 , b ) 3 / 10 , c ) 1 / 2 , d ) 27 / 100 , e ) 9 / 100", - "Correct": "d", - "Explanation": "c + m + b - cm - mb - cb - 2 cmb = 100 c - cake buyers , m - muffin and b - bread buyers . cm , mb , cb and cmb are intersecting regions . the question asks for people who have bought only bread mixes = b - cb - mb - 2 cmb has to be found out . 50 + 40 + b - cb - mb - 17 - 2 cmb = 100 b - cb - mb - 2 cmb = 27 hence the probability = 27 / 100 d" - }, - { - "Answer": 1500, - "Options": "a ) s 1200 , b ) s 1500 , c ) s 1600 , d ) s 1900 , e ) s 1700", - "Correct": "b", - "Explanation": "\"explanation : let p = faruk , q = vasim , r = ranjith let p = 3 x , q = 5 x and r = 8 x . then , 5 x = 1500 ? x = 300 . p = 900 , q = 1500 and r = 2400 . hence , ( r - p ) = ( 2400 - 900 ) = 1500 answer : b\"" - }, - { - "Answer": 1250, - "Options": "a ) rs . 750 , b ) rs . 1000 , c ) rs . 850 , d ) rs . 1250 , e ) none of these", - "Correct": "d", - "Explanation": "let x be the number of passengers and y be the fare taken from passengers . 3 xy + 50 xy = 1325 = > xy = 25 amount collected from ii class passengers = 25 \u00d7 50 = rs . 1250 . answer : d" - }, - { - "Answer": 9, - "Options": "a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9", - "Correct": "e", - "Explanation": "\"the weights of the items in the suitcase are 7 k , 4 k , and 3 k . if removing 6 pounds of clothes doubles the ratio of books to clothes , then 6 pounds represents half the weight of the clothes . 2 k = 6 pounds and then k = 3 pounds . the electronics weigh 3 ( 3 ) = 9 pounds . the answer is e .\"" - }, - { - "Answer": 0.09909909909909911, - "Options": "a ) 5 / 36 , b ) 7 / 64 , c ) 9 / 83 , d ) 11 / 111 , e ) 13 / 135", - "Correct": "d", - "Explanation": "\"12 / 37 * 11 / 36 = 11 / 111 the answer is d .\"" - }, - { - "Answer": 117.5, - "Options": "a ) 100.6 kg , b ) 120.3 kg , c ) 117.5 kg , d ) 110.8 kg , e ) 114 kg", - "Correct": "c", - "Explanation": "\"quantity of tin in 100 kg of a = 100 * 3 / 8 = 37.5 kg quantity of tin in 200 kg of b = 200 * 2 / 5 = 80 kg quantity of tin in the new alloy = 37.5 + 80 = 117.5 kg answer is c\"" - }, - { - "Answer": 1500, - "Options": "a ) 1500 , b ) 200 , c ) 1700 , d ) 2000 , e ) 2500", - "Correct": "a", - "Explanation": "let the price of the car and ac is 3 x and 2 x 3 x - 2 x = 500 x = 500 price of ac = 3 * 500 = $ 1500 answer is a" - }, - { - "Answer": 0.5, - "Options": "a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6", - "Correct": "a", - "Explanation": "let the revenue of pens be ' x ' let the revenue of pencils be ' y ' the revenue of pens up from 2006 by 5 % = > 105 % the revenue of pencils down from 2006 by 13 % = > 87 % overall revenue down by 1 % = > 99 % hence the ratio of pencils to pens = 6 / 12 = 1 / 2 answer : a" - }, - { - "Answer": 8, - "Options": "a ) 3 , b ) 4 , c ) 6 , d ) 12 , e ) 8", - "Correct": "e", - "Explanation": "\"x and y are both odd prime numbers - it means either x or y is not 2 and since prime numbers have only two factors - 1 and the number itself x and y each will have ( 1 + 1 ) = 2 factors hence 2 xy will have ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 8 factors e is the answer\"" - }, - { - "Answer": 20, - "Options": "a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30", - "Correct": "c", - "Explanation": "# of girls = x # of boys = 2 x x + 2 x = 30 3 x = 30 x = 30 / 3 = 10 boys = 2 x = 2 * 10 = 20 answer : c" - }, - { - "Answer": 22, - "Options": "a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24", - "Correct": "c", - "Explanation": "99 ! = 99 / 5 = 19 = 19 / 5 = 3 so 99 ! has ( 19 + 3 = 22 zeroes ) answer : c" - }, - { - "Answer": 48, - "Options": "a ) 8 , b ) 16 , c ) 32 , d ) 48 , e ) 54", - "Correct": "d", - "Explanation": "one option is to set up the equations and solve : if the ratio of two integers x and y is 1 to 4 , then 4 x = y , where x is the smaller integer . if adding 12 to the smaller integer makes the ratio 1 to 2 , then 2 ( x + 12 ) = y . substituting y = 4 x into the second equation yields 2 x + 24 = 4 x . so , x = 12 ( smaller integer ) and , y = 4 x = 48 ( larger integer ) so d is the correct answer . another option is to test the answer choices . a ) the larger number is 8 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 2 if 12 is added to the smaller number , the ratio becomes 1 to 2 if we add 12 to the smaller number ( 2 ) , we get 14 . so , the new ratio is 14 to 8 which is the same as 7 to 4 . no good . we want a resulting ratio of 1 to 2 eliminate a b ) the larger number is 16 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 4 if 12 is added to the smaller number , the ratio becomes 1 to 2 if we add 12 to the smaller number ( 4 ) , we get 16 so , the new ratio is 16 to 16 which is 1 to 1 . no good . we want a resulting ratio of 1 to 2 eliminate b c ) the larger number is 32 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 8 if 12 is added to the smaller number , the ratio becomes 1 to 2 if we add 12 to the smaller number ( 8 ) , we get 20 so , the new ratio is 20 to 32 which is 5 to 8 . no good . we want a resulting ratio of 1 to 2 eliminate c d ) the larger number is 48 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 12 if 12 is added to the smaller number , the ratio becomes 1 to 2 if we add 12 to the smaller number ( 12 ) , we get 24 so , the new ratio is 24 to 48 . this is the same as the ratio of 1 to 2 therefore ( d ) is correct e ) the larger number is 54 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 13.5 ( which is not an integer ) since both numbers are integers , the larger number can not be 54 . eliminate e therefore d is the only correct choice ." - }, - { - "Answer": 21, - "Options": "a ) 10 , b ) 20 , c ) 21 , d ) 25 , e ) 27", - "Correct": "c", - "Explanation": "using the values here might be the most straightforward way for this question . as a : b : : 7 : 5 - - - > only option c is a multiple of 7 and hence it is a good place to start . also a : b : : 7 : 5 means that , a = ( 712 ) * total and b = ( 5 / 12 ) * total if a = 21 , b = 15 - - - > remove 9 litres - - - > you remove ( 7 / 12 ) * 9 of a - - - > a remaining = 21 - ( 7 / 12 ) * 9 = 63 / 4 similarly , for b , you remove ( 5 / 12 ) * 9 - - - > b remaining = 15 - ( 5 / 12 ) * 9 = 45 / 4 and then add 9 more litres of b - - - > 9 + 45 / 4 = 81 / 4 thus a / b ( final ratio ) = ( 45 / 4 ) / ( 81 / 4 ) = 7 : 9 , the same as the final ratio mentioned in the question . hence c is the correct answer . fyi , the algebraic equations will become : a / b = 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) , where 7 x and 5 x are initial quantities of a and b respectively . thus , 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) - - - > giving you x = 3 . thus a ( original ) = 7 * 3 = 21 . answer : c" - }, - { - "Answer": 0.44222222222222224, - "Options": "a ) 2 / 3 , b ) 4 / 5 , c ) 6 / 2 , d ) 5 / 2 , e ) 4 / 9", - "Correct": "e", - "Explanation": "\"red : blue = 2 : 1 let red = 2 x and blue = 1 x 1 / 3 of red are left handed = > 1 / 3 * 2 x = 2 x / 3 red left handed 2 / 3 of blue are left handed = > 2 / 3 * 1 x = 2 x / 3 blue left handed fraction of participants who are left handed = total left handed / total participants = ( red left handed + blue left handed ) / total participants = ( 2 x / 3 + 2 x / 3 ) / ( 2 x + 1 x ) = 4 / 9 answer : e\"" - }, - { - "Answer": 2940, - "Options": "a ) 80 , b ) 160 , c ) 720 , d ) 2100 , e ) 2940", - "Correct": "e", - "Explanation": "\"no . of ways of picking 2 biology books ( from 15 books ) = 15 c 2 = ( 15 * 14 ) / 2 = 105 no . of ways of picking 2 chemistry books ( from 8 books ) = 8 c 2 = ( 8 * 7 ) / 2 = 28 total ways of picking 2 books of each type = 105 * 28 = 2940 ( option e )\"" - }, - { - "Answer": 33, - "Options": "a ) 22 , b ) 67 , c ) 26 , d ) 18 , e ) 16", - "Correct": "a", - "Explanation": "answer : a" - }, - { - "Answer": 42, - "Options": "a ) 44 % , b ) 40 % , c ) 45 % , d ) 42 % , e ) 48 %", - "Correct": "d", - "Explanation": "let total no of balls 100 , red ball 30 and blue ball 70 , so tennis ball for red and blue ball respectively 30 * 70 / 100 = 21 and 70 * 30 / 100 = 21 so total 42 tennis balls out of 100 balls . . so required % is 42 % answer : d" - }, - { - "Answer": 0.14285714285714288, - "Options": "a ) 2 / 4 , b ) 6 / 78 , c ) 4 / 7 , d ) 3 / 5 , e ) 1 / 7", - "Correct": "e", - "Explanation": "\"p : 2 / 5 = 3 / 7 : 6 / 5 as the product of the means is equal to the product of the extremes . p * 6 / 5 = 2 / 5 * 3 / 7 p * 6 / 5 = 6 / 35 p = 1 / 7 = > p = 1 / 7 answer : e\"" - }, - { - "Answer": 6, - "Options": "a ) 6 , b ) 9 , c ) 10 , d ) 11 , e ) 12", - "Correct": "a", - "Explanation": "\"answer : algebraically , the question looks like this : 2.5 = 0.35 x + 0.25 y there are three possible numbers of pens that fit that requirement : 1 pen : $ 0.35 2 pens : $ 0.70 3 pens : $ 1.05 and 3 pencils for $ 0.25 each . that ' s 3 pens and 3 pencils for a total of 6 pens and pencils . choice ( a ) is correct .\"" - }, - { - "Answer": 154, - "Options": "a ) 42 , b ) 66 , c ) 98 , d ) 112 , e ) 154", - "Correct": "e", - "Explanation": "\"let us assume the number of dogs , cats and bunnies to be 7 x , 7 x and 8 x total dogs and bunnies = 15 x . and we are given that 15 x = 330 . hence x = 22 . dogs = 7 x = 7 * 22 = 154 ( option e )\"" - }, - { - "Answer": 0.6, - "Options": "a ) 0.45 , b ) 0.4 , c ) 0.5 , d ) 0.05 , e ) 0.6", - "Correct": "e", - "Explanation": "\"we are apply that formula . . . . . . . . . . . . . . p ( aorb ) = p ( a ) + p ( b ) - p ( a and b ) = . 15 + . 40 - . 15 = . 40 but the probability of neither a nor b = 1 - . 40 = 0.60 answer : e\"" - }, - { - "Answer": 36.166666666666664, - "Options": "a ) 19.3 % , b ) 17 % , c ) 36.17 % , d ) 15.5 % , e ) 12.5 %", - "Correct": "c", - "Explanation": "let x be the quantity of non - vinegar in the strong vinegar solution thus vinegar quantity will be 12 - x when 50 ounces of water were added the percentage of vinegar becomes 7 % , thus ( 12 - x ) / 62 = 7 / 100 from this equation x = 7.66 answer ( 12 - 7.66 ) / 12 = 36.17 % answer : c" - }, - { - "Answer": 8, - "Options": "a ) 65 days , b ) 45 days , c ) 8 days , d ) 16 days , e ) 18 days", - "Correct": "c", - "Explanation": "400 - - - 31 400 - - - 4 200 - - - ? 400 * 4 = 200 * x = > x = 8 days . answer : c" - }, - { - "Answer": 221.25, - "Options": "a ) 210.6 kg , b ) 221.3 kg , c ) 229.5 kg , d ) 110.8 kg , e ) 114 kg", - "Correct": "b", - "Explanation": "\"quantity of tin in 170 kg of a = 170 * 3 / 4 = 127.5 kg quantity of tin in 250 kg of b = 250 * 3 / 8 = 93.75 kg quantity of tin in the new alloy = 127.5 + 93.75 = 221.25 kg answer is b\"" - }, - { - "Answer": 105, - "Options": "a ) 45 , b ) 50 , c ) 55 , d ) 60 , e ) 105", - "Correct": "e", - "Explanation": "\"f : c : w 1 : 12 : 30 sport version : f : c 3 : 12 f : w 1 : 60 or 3 : 180 so c : f : w = 12 : 3 : 180 c / w = 12 / 180 = 3 ounces / x ounces x = 7 * 180 / 12 = 105 ounces of water e\"" - }, - { - "Answer": 8640.000000000002, - "Options": "a ) s . 7500 , b ) s . 8640 , c ) s . 8500 , d ) s . 9000 , e ) s . 6000", - "Correct": "b", - "Explanation": "let hari \u2019 s capital be rs . x . then , 3360 * 12 / 7 x = 2 / 3 = > 14 x = 120960 = > x = 8640 . answer : b" - }, - { - "Answer": 9, - "Options": "a ) 26 , b ) 19 , c ) 11 , d ) 8 , e ) 9", - "Correct": "e", - "Explanation": "no of dogs = 45 long fur = 29 brown = 17 neither long fur nor brown = 8 therefore , either long fur or brown = 45 - 8 = 37 37 = 29 + 17 - both both = 9 answer e" - }, - { - "Answer": 0.010416666666666666, - "Options": "a ) 1 / 50 , b ) 1 / 25 , c ) 1 / 96 , d ) 1 , e ) 2", - "Correct": "c", - "Explanation": "there are 25 primes , 70 composite numbers from 1 to 96 . the number which is neither prime nor composite is 1 . therefore , required probability = 1 / 96 . answer : c" - }, - { - "Answer": 0.21428571428571427, - "Options": "a ) 3 / 14 , b ) 2 / 7 , c ) 1 / 3 , d ) 1 / 2 , e ) 12 / 21", - "Correct": "a", - "Explanation": "probability that the number on first die is even = 3 / 6 [ because 3 out of 6 faces are even ] probability that the number on second die is even = 3 / 7 [ because 3 out of 7 faces are even ] probability that both dice result in odd numbers = ( 3 / 6 ) * ( 3 / 7 ) = 3 / 14 answer : option a" - }, - { - "Answer": 729, - "Options": "a ) 629 , b ) 729 , c ) 829 , d ) 929 , e ) 727", - "Correct": "b", - "Explanation": "\"no of values n can take is 1 9 ^ 3 = 729 answer : b\"" - }, - { - "Answer": 28, - "Options": "a ) 11 , b ) 28 , c ) 24 , d ) 29 , e ) 32", - "Correct": "b", - "Explanation": "\"b is correct r / b = 3 / 8 and b = 75 r = 75 * 3 / 8 = 28\"" - }, - { - "Answer": 96, - "Options": "a ) 99 , b ) 98 , c ) 97 , d ) 96 , e ) 95", - "Correct": "d", - "Explanation": "\"clearly d a number is said to be prime saturated if the product of all the different positive prime factors of a is less than the square root of a . 96 has more number of smaller prime factor thats the clue ! ! = d\"" - }, - { - "Answer": 96, - "Options": "a ) 99 , b ) 98 , c ) 97 , d ) 96 answer , e ) 95", - "Correct": "d", - "Explanation": "\"the square roots of all numbers from answer choices are between 9 and 10 , so the product of primes of the number we are looking should be less then 9 , so this number should have only 2 - s , only 3 - s , only 5 - s , or only 2 - s and 3 - s as its primes . only 96 satisfies this . answer : d .\"" - }, - { - "Answer": 24.5, - "Options": "a ) 24.58 , b ) 24.5 , c ) 24.3 , d ) 24.9 , e ) 24.1", - "Correct": "b", - "Explanation": "\"if rahul age is x , then sachin age is x - 7 , so ( x - 7 ) / x = 7 / 9 = > 9 x - 63 = 7 x = > 2 x = 63 = > x = 31.5 so sachin age is 31.5 - 7 = 24.5 answer : b\"" - }, - { - "Answer": 2000, - "Options": "a ) 900 , b ) 980 , c ) 1200 , d ) 1240 , e ) 2000", - "Correct": "e", - "Explanation": "\"amount received by sanjay . 4 / 12 x 6000 = 2000 = ( related ratio / sum of ratio ) x total amount so , the amount received by sanjay is 2000 . e\"" - }, - { - "Answer": 27, - "Options": "a ) 9 , b ) 19 , c ) 27 , d ) 26 , e ) 31", - "Correct": "c", - "Explanation": "\"number of students taking history = h = 36 number of students taking statistics = s = 32 total number of students = t = 89 number of students taking history or statistics or both = b = 59 number of students taking neither history nor statistics = n = 89 - 59 = 30 letxbe the number of students taking both history and statistics . then t = h + s + n - x or 89 = 36 + 32 + 30 - x or x = 9 now , number of students taking only history will be h - x or 36 - 9 = 27 answer : - c\"" - }, - { - "Answer": 0.75, - "Options": "a ) 3 / 4 , b ) 11 / 15 , c ) 7 / 10 , d ) 1 / 6 , e ) 2 / 15", - "Correct": "a", - "Explanation": "1 / 5 - - cable tv ( this includes some data from video cassette recorder ) 1 / 10 - - video cassette recorder including 1 / 4 ( equiped with cable tv ) i . e . 1 / 4 ( 1 / 5 ) = 1 / 20 therefore only video cassette recorder = 1 / 10 - 1 / 20 = 1 / 20 total = 1 / 5 + 1 / 20 + neither cable tv nor videocassette recorders 1 = 1 / 4 + neither cable tv nor videocassette recorders therefore neither cable tv nor videocassette recorders = 1 - 1 / 4 = 3 / 4 hence a ." - }, - { - "Answer": 18, - "Options": "a ) 24 , b ) 18 , c ) 30 , d ) 15 , e ) 12", - "Correct": "b", - "Explanation": "lets work with the data given to us . we know that there ratio of cats to dogs is 2 : 3 or cats 2 dogs 3 we can write number of cats as 2 x and number of dogs as 3 x and we know that 3 x - 2 x = 6 ( therefore x = 6 ) then # of dogs = 3 x 6 = 18 answer is b" - }, - { - "Answer": 36, - "Options": "a ) 24 , b ) 28 , c ) 32 , d ) 36 , e ) 40", - "Correct": "d", - "Explanation": "\"the total number of people are x females + 2 x males . 3 * ( x - 6 ) = 2 x - 6 x = 12 there were 3 x = 36 people at the party originally . the answer is d .\"" - }, - { - "Answer": 7199.999999999997, - "Options": "a ) rs . 3400 , b ) rs . 2700 , c ) rs . 1720 , d ) rs . 7200 , e ) rs . 8200", - "Correct": "d", - "Explanation": "explanation : incomes of a and b = 5 x and 6 x and expenses of a and b = 3 y and 4 y then , savings of a = 5 x - 3 y = 1800 \u2014 ? ( 1 ) savings of b = 6 x - 4 y = 1600 \u2014 ? ( 2 ) by solving equations ( 1 ) and ( 2 ) y = 1400 monthly income of b = expenses of b + savings of b = 4 y + 1600 = 4 ( 1400 ) + 1600 = rs . 7200 answer : d" - }, - { - "Answer": 0.26, - "Options": "a ) 1 / 10 , b ) 13 / 50 , c ) 1 / 2 , d ) 7 / 10 , e ) 9 / 10", - "Correct": "b", - "Explanation": "\"c + m + b - cm - mb - cb - 2 cmb = 100 c - cake buyers , m - muffin and b - bread buyers . cm , mb , cb and cmb are intersecting regions . the question asks for people who have bought only bread mixes = b - cb - mb - 2 cmb has to be found out . 50 + 40 + b - cb - mb - 16 - 2 cmb = 100 b - cb - mb - 2 cmb = 26 hence the probability = 26 / 100 = 13 / 50 . b\"" - }, - { - "Answer": 0.6666666666666665, - "Options": "a ) 1 / 4 , b ) 2 / 5 , c ) 1 / 2 , d ) 3 / 5 , e ) 2 / 3", - "Correct": "e", - "Explanation": "\"you can simply use this formula to avoid confusion : w 1 / w 2 = ( a 2 - aavg ) / ( avg - a 1 ) here is how you will find the values of a 1 an a 2 . we have an overall loss ( average loss ) . the average loss is 6 kg when 60 kg alloy is immersed . this is a loss of ( 6 / 60 ) * 100 = 10 % . this is aavg the loss of tin is 1.375 kg for every 10 kg . this means it loses ( 1.375 / 10 ) * 100 = 13.75 % of its weight in water . this is a 1 . the loss of silver is . 375 kg for every 5 kg . this means it loses ( . 375 / 5 ) * 100 = 7.5 % of its weight in water . this is a 2 . weight of tin / weight of silver = ( silver ' s loss - avg loss ) / ( avg loss - tin ' s loss ) x / y = ( 7.5 - 10 ) / ( 10 - 13.75 ) = 2 / 3 e\"" - }, - { - "Answer": 25, - "Options": "a ) a ) 15 , b ) b ) 20 , c ) c ) 25 , d ) d ) 40 , e ) e ) 45", - "Correct": "c", - "Explanation": "\"160 = at least one of soap a or b both brands = x brand b = 3 x = > 60 + x + 3 x = 160 = > 4 x = 100 = > x = 25 answer - c\"" - }, - { - "Answer": 33, - "Options": "a ) 6 , b ) 15 , c ) 24 , d ) 33 , e ) 54", - "Correct": "d", - "Explanation": "formula for calculating two overlapping sets : a + b - both + not ( a or b ) = total so in our task we have equation : 41 ( french ) + 22 ( german ) - 9 ( both ) + not = 87 54 + not = 87 not = 87 - 54 = 33 so answer is d" - }, - { - "Answer": 744, - "Options": "a ) 462 , b ) 744 , c ) 480 , d ) 504 , e ) 555", - "Correct": "b", - "Explanation": "\"explanation : hcf of the two numbers = 62 hcf will be always a factor of lcm 62 is factor of lcm other two factors are 11 & 12 then the numbers are ( 62 * 11 ) and ( 62 x 12 ) = 682 and 744 answer : option b\"" - }, - { - "Answer": 173.5, - "Options": "a ) rs . 147.50 , b ) rs . 785.50 , c ) rs . 174.50 , d ) rs . 258.50 , e ) none of these", - "Correct": "c", - "Explanation": "\"explanation : since first and second varieties are mixed in equal proportions . so , their average price = rs . ( 126 + 135 ) / 2 . = > rs . 130.50 . so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . by the rule of alligation , we have : cost of 1 kg cost of 1 kg of 1 st kind of 2 nd kind ( rs . 130.50 ) ( rs . x ) \\ / mean price ( rs . 152 ) / \\ x \u00e2 \u02c6 \u2019 152 22.50 = > x \u00e2 \u02c6 \u2019 ( 152 / 22.50 ) = 1 . = > x \u00e2 \u02c6 \u2019 152 = 22.50 . = > x = 174.50 rs . answer : c\"" - }, - { - "Answer": 10, - "Options": "a ) 6,12 , b ) 10,6 , c ) 10,8 , d ) 8,4 , e ) 6,8", - "Correct": "c", - "Explanation": "let the ratio constant be x . no . of pen = 5 x , no . of notebook = 4 x . total no . of ways of start writing = 5 x * 4 x = 20 ( square of x ) = 80 x = \u00e2 \u02c6 \u0161 4 = 2 pen = 10 , notebook = 8 answer c" - }, - { - "Answer": 16000, - "Options": "a ) $ 16800 , b ) $ 16500 , c ) $ 16000 , d ) $ 16300 , e ) $ 16200", - "Correct": "c", - "Explanation": "let the income of uma and bala be $ 8 x and $ 7 x let their expenditures be $ 7 y and $ 6 y 8 x - 7 y = 2000 - - - - - - - 1 ) 7 x - 6 y = 2000 - - - - - - - 2 ) from 1 ) and 2 ) x = 1000 uma ' s income = 8 x = 8 * 2000 = $ 16000 answer is c" - }, - { - "Answer": 3, - "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", - "Correct": "c", - "Explanation": "factors of 15 - 1 , 3 , 5 , and 15 factors of 45 - 1 , 3 , 9 , 15 and 45 comparing both , we have three common factors of 45,16 - 3 answer c" - }, - { - "Answer": 198, - "Options": "a ) 201 , b ) 193 , c ) 200 , d ) 199 , e ) 195", - "Correct": "d", - "Explanation": "\"multiples of 10 = 20 , 30,40 - - - - - , 1990,2000 number of multiples of 10 = > 2000 - 20 / 10 + 1 = 199 answer is d\"" - }, - { - "Answer": 19, - "Options": "a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 19", - "Correct": "e", - "Explanation": "\"( 2 / 18 ) * 171 = 19 grams the answer is e .\"" - }, - { - "Answer": 0.8333333333333334, - "Options": "a ) 1 / 68 , b ) 62 / 89 , c ) 12 / 68 , d ) 11 / 84 , e ) 5 / 6", - "Correct": "e", - "Explanation": "\"explanation : let us say the ratio of the quantities of cheaper and dearer varieties = x : y by the rule of allegation , x / y = ( 87.5 - 7.50 ) / ( 7.50 - 6 ) = 5 / 6 answer : e\"" - }, - { - "Answer": 4, - "Options": "a ) 1 , b ) 4 , c ) 81 , d ) log 80 243 , e ) e 81", - "Correct": "b", - "Explanation": "recall the change of base formula logb ( a ) = ln ( a ) ln ( b ) : ( alternatively , we can substitute logc for ln on the right , as long as the base is the same on the top and on the bottom . ) using this , we can rewrite the entire expression using natural logarithms , as ln ( 4 ) ln ( 3 ) ln ( 5 ) ln ( 4 ) ln ( 81 ) ln ( 80 ) = ln ( 81 ) ln ( 3 ) = log 3 ( 81 ) = log 3 ( 34 ) = 4 : correct answer b" - }, - { - "Answer": 6, - "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", - "Correct": "d", - "Explanation": "explanation : number of questions submitted by vikas = ( 24 * 3 ) / ( 7 + 3 + 2 ) = 6 answer : d" - }, - { - "Answer": 11, - "Options": "a ) 26 , b ) 19 , c ) 11 , d ) 8 , e ) 6", - "Correct": "c", - "Explanation": "\"no of dogs = 45 long fur = 26 brown = 22 neither long fur nor brown = 8 therefore , either long fur or brown = 45 - 8 = 37 37 = 26 + 22 - both both = 11 answer c\"" - }, - { - "Answer": 13.5, - "Options": "a ) 27 , b ) 4 , c ) 6 , d ) 13.5 , e ) 8", - "Correct": "d", - "Explanation": "\"the answer is ( 200 - 100 ) / 8 + 1 = 13.5 answer is d\"" - }, - { - "Answer": 4000, - "Options": "a ) rs . 800 , b ) rs . 2400 , c ) rs . 4000 , d ) rs . 3200 , e ) rs . 4200", - "Correct": "c", - "Explanation": "let the income of p 1 and p 2 be rs . 5 x and rs . 4 x respectively and let their expenditures be rs . 3 y and 2 y respectively . then , 5 x \u2013 3 y = 1600 \u2026 ( i ) and 4 x \u2013 2 y = 1600 \u2026 \u2026 . . ( ii ) on multiplying ( i ) by 2 , ( ii ) by 3 and subtracting , we get : 2 x = 1600 - > x = 800 p 1 \u2019 s income = rs 5 * 800 = rs . 4000 answer : c" - }, - { - "Answer": 27, - "Options": "a ) 23 , b ) 27 , c ) 30 , d ) 32 , e ) 34", - "Correct": "b", - "Explanation": "5 : 3 : 4 total parts = 12 12 parts - - > 108 1 part - - - - > 9 the second number of the three numbers is = 3 3 parts - - - - > 27 b )" - }, - { - "Answer": 312, - "Options": "a ) 312 , b ) 356 , c ) 452 , d ) 416 , e ) 512", - "Correct": "a", - "Explanation": "let the number of boys and girls be 8 x and 5 x then , 5 x = 120 x = 24 total number of students = 13 x = 13 * 24 = 312 answer is a" - }, - { - "Answer": 60, - "Options": "a ) 10 % , b ) ( 8 ) 20 % , c ) 30 % , d ) 50 % , e ) 60 %", - "Correct": "e", - "Explanation": "\"{ total } = { first } + { second } - { both } + { neither } 100 % = 75 % + 65 % - { both } + 20 % - - > { both } = 60 % . answer : e .\"" - }, - { - "Answer": 60, - "Options": "a ) 60 % , b ) 65 % , c ) 70 % , d ) 75 % , e ) 80 %", - "Correct": "a", - "Explanation": "\"{ total } = { first correctly } + { second correctly } - { both correctly } + { neither correctly } 100 = 80 + 75 - { both correctly } + 5 { both correctly } = 60 . answer : a .\"" - }, - { - "Answer": 270, - "Options": "a ) 54 , b ) 162 , c ) 250 , d ) 270 , e ) 322", - "Correct": "d", - "Explanation": "\"total number of fractions = 2 + 10 = 12 element b constitutes = 10 out of 12 parts of x so in 324 gms of x have 324 * 10 / 12 = 270 gms of b and 324 - 270 = 54 gms of a . cross check : - a / b = 54 / 270 = 2 / 10 ( as given ) ans d\"" - }, - { - "Answer": 45, - "Options": "a ) 45 , b ) 50 , c ) 55 , d ) 60 , e ) 63", - "Correct": "a", - "Explanation": "f : c : w 1 : 12 : 30 sport version : f : c 3 : 12 f : w 1 : 60 or 3 : 180 so c : f : w = 12 : 3 : 180 c / w = 12 / 180 = 3 ounces / x ounces x = 3 * 180 / 12 = 45 ounces of water answer : a" - }, - { - "Answer": 120, - "Options": "a ) 70 , b ) 96 , c ) 108 , d ) 120 , e ) 150", - "Correct": "d", - "Explanation": "2 x 2 matrix will be the easiest way to calculate this . text in black : given statements text in red : calculated values thus d = 120 is the correct answer" - }, - { - "Answer": 5, - "Options": "a ) 2 , b ) 5 , c ) 6 , d ) 7 , e ) 8", - "Correct": "b", - "Explanation": "explanation : wine water 8 l 32 l 1 : 4 20 % 80 % ( original ratio ) 30 % 70 % ( required ratio ) in ths case , the percentage of water being reduced when the mixture is being replaced with wine . so the ratio of left quantity to the initial quantity is 7 : 8 therefore , \\ frac { 7 } { 8 } = \\ left [ 1 - \\ frac { k } { 40 } \\ right ] \\ rightarrow \\ frac { 7 } { 8 } = \\ left [ \\ frac { 40 - k } { 40 } \\ right ] \\ rightarrow k = 5 l answer : b ) 5" - }, - { - "Answer": 2.5, - "Options": "a ) 5 / 6 , b ) 5 / 2 , c ) 5 / 1 , d ) 5 / 3 , e ) 7 / 6", - "Correct": "b", - "Explanation": "\"let us say the ratio of the quantities of cheaper and dearer varieties = x : y by the rule of allegation , x / y = ( 8.75 - 7.50 ) / ( 7.50 - 7 ) = 5 / 2 answer : b\"" - }, - { - "Answer": 16, - "Options": "a ) 15 , b ) 20 , c ) 16 , d ) 30 , e ) 35", - "Correct": "c", - "Explanation": "\"product of two no = lcm * hcf 2 x * 5 x = 160 * x x = 16 answer : c\"" - }, - { - "Answer": 3000, - "Options": "a ) 3600 , b ) 3607 , c ) 3608 , d ) 3602 , e ) 3000", - "Correct": "e", - "Explanation": "\"let the income and the expenditure of the person be rs . 5 x and rs . 4 x respectively . income , 5 x = 15000 = > x = 3000 savings = income - expenditure = 5 x - 4 x = x so , savings = rs . 3000 . answer : e\"" - }, - { - "Answer": 3, - "Options": "a ) 6 : 4 , b ) 6 : 14 , c ) 4 : 4 , d ) 4 : 6 , e ) 3 : 1", - "Correct": "e", - "Explanation": "forget the volumes for the time being . you have to mix 20 % and 80 % solutions to get 50 % . this is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities . if this does n ' t strike , use w 1 / w 2 = ( a 2 - aavg ) / ( aavg - a 1 ) w 1 / w 2 = ( 80 - 50 ) / ( 50 - 40 ) = 3 / 1 so the volume of the two solutions will be equal . answer has to be 3 : 1 . e" - }, - { - "Answer": 12, - "Options": "a ) 11 , b ) 12 , c ) 14 , d ) 15 , e ) 19", - "Correct": "b", - "Explanation": "28 play some sport 19 + 21 - both = 28 both = 12 answer is b" - }, - { - "Answer": 60, - "Options": "a ) 60 , b ) 80 , c ) 100 , d ) 130 , e ) 150", - "Correct": "a", - "Explanation": "20 stamps are both foreign and more than 10 years old . 70 stamps are foreign only . 50 stamps are 10 years old only . the number of remaining stamps is 200 - ( 20 + 70 + 50 ) = 60 the answer is a ." - }, - { - "Answer": 12, - "Options": "a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13", - "Correct": "d", - "Explanation": "\"let 2 x be the number of spinsters . then 9 x is the number of cats . 9 x - 2 x = 42 x = 6 and the number of spinsters is 2 ( 6 ) = 12 . the answer is d .\"" - }, - { - "Answer": 0.6, - "Options": "a ) 0.9 , b ) 0.75 , c ) 0.6 , d ) 0.8 , e ) 0.5", - "Correct": "c", - "Explanation": "\"according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 20 + 30 + 10 ) / 100 = 60 / 100 = 0.6 . answer is c\"" - }, - { - "Answer": 30, - "Options": "a ) 72 , b ) 85 , c ) 30 , d ) 51 , e ) 45", - "Correct": "c", - "Explanation": "\"we have 4 / 6 = 20 / x 4 x = 20 * 6 x = 30 consequent = 30 answer is c\"" - }, - { - "Answer": 70, - "Options": "a ) 42 , b ) 49 , c ) 56 , d ) 63 , e ) 70", - "Correct": "e", - "Explanation": "\"let sandy ' s age be 7 x and let molly ' s age be 9 x . 9 x - 7 x = 20 x = 10 sandy is 70 years old . the answer is e .\"" - }, - { - "Answer": 70, - "Options": "a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80", - "Correct": "d", - "Explanation": "\"originally , there were 6 k horses and k cows . ( 6 k - 15 ) = 3 ( k + 15 ) 6 k - 3 k = 45 + 15 3 k = 60 k = 20 the difference between horses and cows is ( 6 k - 15 ) - ( k + 15 ) = 5 k - 30 = 70 the answer is d .\"" - }, - { - "Answer": 0.1, - "Options": "a ) 1 / 10 , b ) 1 / 5 , c ) 3 / 10 , d ) 2 / 5 , e ) 1 / 2", - "Correct": "a", - "Explanation": "probability of selecting first red marble = 2 / 5 probability of selecting second red marble without replacement = 1 / 4 final probability = 2 / 5 * 1 / 4 = 1 / 10 correct answer - a" - }, - { - "Answer": 11400, - "Options": "a ) 79754 , b ) 87689 , c ) 59875 , d ) 11400 , e ) 87648", - "Correct": "d", - "Explanation": "\"let the income and the expenditure of the person be rs . 10 x and rs . 4 x respectively . income , 10 x = 19000 = > x = 1900 savings = income - expenditure = 10 x - 4 x = 6 x = 6 ( 1900 ) so , savings = rs . 11400 . answer : d\"" - }, - { - "Answer": 80, - "Options": "a ) 80 , b ) 16 , c ) 24 , d ) 48 , e ) 98", - "Correct": "a", - "Explanation": "\"let the numbers be 4 x and 5 x . then their h . c . f = x . so , x = 4 . so , the numbers are 16 and 20 . l . c . m of 16 and 20 = 80 . answer : a\"" - }, - { - "Answer": 555707.2899999999, - "Options": "a ) 288889 , b ) 556677 , c ) 555681 , d ) 267788 , e ) 268811", - "Correct": "c", - "Explanation": "\"explanation : 987 = 3 * 7 * 47 . so , the required number must be divisible by each one of 3 , 7 , 47 553681 = > ( sum of digits = 28 , not divisible by 3 ) 555181 = > ( sum of digits = 25 , not divisible by 3 ) 555681 is divisible by each one of 3 , 7 , 47 . answer : c ) 555681\"" - }, - { - "Answer": 96, - "Options": "a ) 99 , b ) 98 , c ) 97 , d ) 96 , e ) 95", - "Correct": "d", - "Explanation": "\"q 96 = 3 * 32 = 3 * 2 ^ 5 answer is d .\"" - }, - { - "Answer": 5, - "Options": "a ) 9 , b ) 24.8 , c ) 2 , d ) 3 , e ) 5", - "Correct": "e", - "Explanation": "explanation : if rahul age is x , then sachin age is x - 7 , so , 12 x - 84 = 5 x 7 x = 84 x = 12 so sachin age is 12 - 7 = 5 answer : e ) 5" - }, - { - "Answer": 21, - "Options": "a ) 10 , b ) 20 , c ) 21 , d ) 25 , e ) 27", - "Correct": "c", - "Explanation": "\"as a : b : : 7 : 5 - - - > only option c is a multiple of 7 and hence it is a good place to start . also a : b : : 7 : 5 means that , a = ( 712 ) * total and b = ( 5 / 12 ) * total if a = 21 , b = 15 - - - > remove 9 litres - - - > you remove ( 7 / 12 ) * 9 of a - - - > a remaining = 21 - ( 7 / 12 ) * 9 = 63 / 4 similarly , for b , you remove ( 5 / 12 ) * 9 - - - > b remaining = 15 - ( 5 / 12 ) * 9 = 45 / 4 and then add 9 more litres of b - - - > 9 + 45 / 4 = 81 / 4 thus a / b ( final ratio ) = ( 45 / 4 ) / ( 81 / 4 ) = 7 : 9 , the same as the final ratio mentioned in the question . hence c is the correct answer . a / b = 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) , where 7 x and 5 x are initial quantities of a and b respectively . thus , 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) - - - > giving you x = 3 . thus a ( original ) e = 7 * 3 = 21 . c\"" - }, - { - "Answer": 40, - "Options": "a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80", - "Correct": "a", - "Explanation": "let the numbers be 3 x , 4 x and 5 x . then , their l . c . m . = 60 x . so , 60 x = 2400 or x = 40 . the numbers are ( 3 x 40 ) , ( 4 x 40 ) and ( 5 x 40 ) . hence , required h . c . f . = 40 . answer : a" - }, - { - "Answer": 87, - "Options": "a ) 84 , b ) 85 , c ) 86 , d ) 87 , e ) 88", - "Correct": "d", - "Explanation": "10 out of 1 is defective 20 out of 2 is defective 100 out of 10 is defective and so on 800 out of 80 is defective 70 out of 7 is defective 80 + 7 = 87 answer : d" - }, - { - "Answer": 8, - "Options": "a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12", - "Correct": "d", - "Explanation": "since 2 wy prime factors are w ^ 1 * y ^ 1 * 2 ^ 1 , its total number or factors must be ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 2 ^ 3 = 8 . thus , i think d would be the correct answer . d" - }, - { - "Answer": 100, - "Options": "a ) 75 , b ) 100 , c ) 125 , d ) 150 , e ) none of these", - "Correct": "b", - "Explanation": "\"explanation : students who play cricket , n ( a ) = 325 students who play football , n ( b ) = 175 total students who play either or both games , = n ( a \u222a b ) = 450 \u2212 50 = 400 required number , n ( a \u2229 b ) = n ( a ) + n ( b ) \u2212 n ( a \u222a b ) = 325 + 175 \u2212 400 = 100 option b\"" - }, - { - "Answer": 40, - "Options": "a ) 25 , b ) 40 , c ) 50 , d ) 60 , e ) 75", - "Correct": "b", - "Explanation": "we are told that 60 students claimed that they preferred mac to windows , which means that 60 preferred mac but not windows , so # of students who preferred mac ( p ( a ) as you wrote ) , does not equal to 60 , it equals to 60 + 20 ( 20 is # of students who equally preferred both brands ) . also we are asked to find # of the students who preferred windows to mac , so if you denote x as those who prefer windows then you should calculate x - 20 . so , if we use your formula it should be : 210 = { mac } + { windows } - { both } + { neither } = ( 60 + 20 ) + x - 20 + 90 - - > x = 60 ( # of student who prefer windows ) - - > # of the students who preferred windows to mac is x - 20 = 40 ." - }, - { - "Answer": 0.5, - "Options": "a ) 0.9 , b ) 0.75 , c ) 0.6 , d ) 0.8 , e ) 0.5", - "Correct": "e", - "Explanation": "\"according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 10 + 30 + 10 ) / 100 = 50 / 100 = 0.5 . answer is e\"" - }, - { - "Answer": 148, - "Options": "a ) 30 , b ) 90 , c ) 148 , d ) 172 , e ) 188", - "Correct": "c", - "Explanation": "i would just like to add a bit of explanation after the step where you calculate that the number of students studying both m and s = 136 using your analysis : we see that the total number of students who study either maths or sociology = 184 + 204 - 136 = 252 so , in the image we know that the number of students in the zone with the black boundary = 252 let ' s assume the number of students who studyonlybiology to beb ( this is the number that we have to maximize ) and , let ' s assume the number of students who study none of the three subjects , that is the number of students in the white space = w since the total number of students = 400 , we can write : 252 + b + w = 400 or , b + w = 400 - 252 = 148 that is , b = 148 - w so , the maximum value ofbwill happen forw = 0 this is how we get , the maximum value ofb = 148 c" - }, - { - "Answer": 0.65, - "Options": "a ) 0.09 , b ) 0.65 , c ) 0.54 , d ) 0.85 , e ) 0.91", - "Correct": "b", - "Explanation": "\"according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 22 + 10 + 17 ) / 60 = 39 / 60 = 0.65 . answer : b .\"" - }, - { - "Answer": 53, - "Options": "a ) 50 , b ) 51 , c ) 52 , d ) 53 , e ) 54", - "Correct": "d", - "Explanation": "\"this is an example of a standard overlapping sets question . it has no ' twists ' to it , so you ' ll likely find using the overlapping sets formula to be a fairly easy approach . if you ' re not familiar with it , then here is the formula : 90 = 55 + 33 - 51 + ( # in neither group ) = 53 the prompt gives you all of the numbers you need to get to the correct answer . just plug in and solve . d\"" - }, - { - "Answer": 2000, - "Options": "a ) rs 1600 , b ) rs 1800 , c ) rs 2000 , d ) rs 2200 , e ) none of these", - "Correct": "c", - "Explanation": "explanation : let the income of anand and balu be 5 x and 4 x and . the expenditures of anand and balu be 3 y and 2 y . then , 5 x 3 y = 800 and 4 x 2 y = 800 . on solving we get : x = 400 . as income = 5 x = rs . 2000 . answer : c" - }, - { - "Answer": 2000, - "Options": "a ) 2003 , b ) 2002 , c ) 2000 , d ) 2001 , e ) 2004", - "Correct": "c", - "Explanation": "\"let the income and the expenditure of the person be rs . 10 x and rs . 8 x respectively . income , 10 x = 10000 = > x = 1000 savings = income - expenditure = 10 x - 8 x = 2 x = 2 ( 1000 ) so , savings = rs . 2000 . answer : c\"" - }, - { - "Answer": 20, - "Options": "a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50", - "Correct": "b", - "Explanation": "total = 150 english = 55 telugu = 85 none / neither english nor telugu = 30 no . of students who speak only one or both = 150 - 30 = 120 so , 120 stud ' s can speak english or telugu or both . then , no . of stud ' s speak only english = 120 - 85 ( telugu ) = 35 ` ` ` ` ` ` ` ` ` ` telugu = 120 - 55 = 65 remaining 120 - ( 65 + 35 ) = 20 stud ' s can speak both . b )" - }, - { - "Answer": 420, - "Options": "a ) 420 , b ) 430 , c ) 312 , d ) 322 , e ) none", - "Correct": "a", - "Explanation": "\"solution clearly , the numbers are ( 28 x 12 ) and ( 28 x 15 ) . larger number = ( 28 x 15 ) = 420 . answer a\"" - }, - { - "Answer": 0.15513897866839044, - "Options": "a ) 240 / 1587 , b ) 240 / 1545 , c ) 240 / 1547 , d ) 240 / 1542 , e ) 240 / 1512", - "Correct": "c", - "Explanation": "\"p : 2 / 13 = 5 / 34 : 7 / 48 as the product of the means is equal to the product of the extremes . p * 7 / 48 = 2 / 13 * 5 / 34 p * 7 / 48 = 10 / 442 p = 480 / 3094 = > p = 240 / 1547 answer : c\"" - }, - { - "Answer": 9000, - "Options": "a ) rs . 7000 , b ) rs . 11000 , c ) rs . 8000 , d ) rs . 10000 , e ) rs . 9000", - "Correct": "e", - "Explanation": "solution : let ' s q ' s capital is x . p : q = ( 4000 * 12 ) : ( x : 8 ) = 2 : 3 . so q ' s share = ( 4000 * 12 / 8 x ) = 2 / 3 = > x = ( 4000 * 12 * 3 ) / ( 2 * 8 ) = rs . 9000 answer : option e" - }, - { - "Answer": 15, - "Options": "a ) 6 , b ) 9 , c ) 10 , d ) 12 , e ) 15", - "Correct": "e", - "Explanation": "\"one option is to set up the equations and solve : if the ratio of two integers x and y is 1 to 3 , then 3 x = y , where x is the smaller integer . if adding 10 to the smaller integer makes the ratio 1 to 1 , then x + 10 = y . substituting y = 3 x into the second equation yields x + 10 = 3 x . so , x = 5 ( smaller integer ) and , y = 3 x = 15 ( larger integer ) so e is the correct answer . another option is to test the answer choices . a ) the larger number is 6 given : the two integers are in the ratio of 1 to 3 so , the smaller number must be 2 if 10 is added to the smaller number , the ratio becomes 1 to 1 if we add 10 to the smaller number ( 2 ) , we get 12 . so , the new ratio is 12 to 6 which is the same as 2 to 1 . no good . we want a resulting ratio of 1 to 1 eliminate a b ) the larger number is 9 given : the two integers are in the ratio of 1 to 3 so , the smaller number must be 3 if 10 is added to the smaller number , the ratio becomes 1 to 1 if we add 10 to the smaller number ( 3 ) , we get 13 so , the new ratio is 13 to 9 . no good . we want a resulting ratio of 1 to 1 eliminate b c ) the larger number is 10 given : the two integers are in the ratio of 1 to 3 so , the smaller number must be 3.33 ( which is not an integer ) since both numbers are integers , the larger number can not be 10 . eliminate c d ) the larger number is 12 given : the two integers are in the ratio of 1 to 3 so , the smaller number must be 4 if 10 is added to the smaller number , the ratio becomes 1 to 1 if we add 10 to the smaller number ( 4 ) , we get 14 so , the new ratio is 14 to 12 which is 7 to 6 . no good . we want a resulting ratio of 1 to 1 eliminate d e ) the larger number is 15 given : the two integers are in the ratio of 1 to 3 so , the smaller number must be 5 if 10 is added to the smaller number , the ratio becomes 1 to 1 if we add 10 to the smaller number ( 5 ) , we get 15 so , the new ratio is 15 to 15 . this is the same as the ratio of 1 to 1 therefore e is the only correct choice .\"" - }, - { - "Answer": 0.14470734744707348, - "Options": "a ) 1 / 250 , b ) 1 / 84 , c ) 11 / 76 , d ) 1 / 9 , e ) 1 / 3", - "Correct": "c", - "Explanation": "\"probability of chosing one defective phone from a lot of 220 which ontains 84 defective phones is = ( 84 / 220 ) probability of chosing one defective phone from a lot of 219 ( we already picked one ) which ontains 83 ( we already picked one ) defective phones is = ( 83 / 219 ) combined probability of series of events = product of the probabilities = ( 84 / 220 ) * ( 83 / 219 ) 84 / 220 is close to ( 21 / 55 ) and ( 83 / 219 ) = ( 36 / 95 ) so answer is ( 21 / 55 ) * ( 36 / 95 ) = ( 11 / 76 ) so , answer will be c\"" - }, - { - "Answer": 105, - "Options": "a ) $ 36 , b ) $ 42 , c ) $ 60 , d ) $ 75 , e ) $ 105", - "Correct": "e", - "Explanation": "rita : sita : kavita 6 : 7 6 : 15 36 : 42 : 105 the ratio of money with ravi , giri and kiran is 36 : 42 : 105 we see that 36 = $ 36 then 105 = $ 105 answer is e" - }, - { - "Answer": 26, - "Options": "a ) 3 , b ) 16 , c ) 75 , d ) 24 , e ) 26", - "Correct": "e", - "Explanation": "1 ) i figured there are 101 integers ( 300 - 200 + 1 = 101 ) . since the set begins with an even and ends with an even , there are 51 evens . 2 ) question says integers are not divisible by 2 , leaving all of the odds ( 101 - 51 = 50 integers ) . 3 ) question says integers are not divisible by 5 , removing all the integers ending in 5 ( already took out those ending in 0 ) . take out 10 integers ( 2 ? 5 , ? = 0 to 9 ) , leaving us with 40 integers . 4 ) now the painstaking part . we have to remove the remaining numbers that are multiples of 3 . those are 201 , 207 , 213 , 219 , 231 , 237 , 243 , 249 , 261 , 267 , 273 , 279 , 291 , and 297 . . . a total of 14 numbers . 26 numbers left ! 6 ) answer choice e ." - }, - { - "Answer": 80, - "Options": "a ) 27 , b ) 36 , c ) 45 , d ) 72 , e ) 80", - "Correct": "e", - "Explanation": "\"the ratio of b to g is 5 : 13 and the other data point is g are more than boys by 128 . . . looking at the ratio we can say that the 8 ( 13 - 5 ) extra parts caused this diff of 128 . so 1 part corresponds to 128 / 8 = 16 and so 5 parts correspond to 5 * 16 = 80 . e\"" - }, - { - "Answer": 14.999999999999996, - "Options": "a ) 2 , b ) 9 , c ) 15 , d ) 21 , e ) 30", - "Correct": "c", - "Explanation": "\"let the duration , in minutes , for which the company charges the same under plan a and plan b be t minutes . then under plan a the cost would be $ 0.6 + 0.06 ( t - 5 ) and under plan b the cost would be $ 0.08 t . we want these amount to be equal : 0.6 + 0.06 ( t - 5 ) = 0.08 t - - > 60 + 6 ( t - 5 ) = 8 t - - > t = 15 . answer : c .\"" - }, - { - "Answer": 60, - "Options": "['a ) 80', 'b ) 70', 'c ) 60', 'd ) 40', 'e ) 50']", - "Correct": "c", - "Explanation": "b : d : w = 4 : 40 : 100 bnew / dnew = ( 1 / 3 ) * ( 4 / 40 ) = ( 1 / 30 ) dnew / wnew = ( 1 / 2 ) * ( 40 / 100 ) = ( 1 / 5 ) wnew = 300 dnew = wnew / 5 = 300 / 5 = 60 so , answer will be c" - }, - { - "Answer": 73, - "Options": "a ) 69 . , b ) 71 , c ) 73 , d ) 75 , e ) 76", - "Correct": "c", - "Explanation": "graduates got job = 32 graduates continued to second degree = 45 graduates got job and continued to second degree = 13 graduates did n ' t get job and did n ' t continue to second degree = 9 job no job total second degree 13 32 45 no second degree 19 9 28 total 32 41 x therefore x = 73 answer c" - }, - { - "Answer": 0.625, - "Options": "a ) 5 / 6 , b ) 5 / 9 , c ) 5 / 1 , d ) 5 / 8 , e ) 7 / 6", - "Correct": "d", - "Explanation": "\"let us say the ratio of the quantities of cheaper and dearer varieties = x : y by the rule of allegation , x / y = ( 8.75 - 7.50 ) / ( 7.50 - 5.5 ) = 5 / 8 answer : d\"" - }, - { - "Answer": 62, - "Options": "a ) 31 , b ) 32 , c ) 33 , d ) 62 , e ) 64", - "Correct": "d", - "Explanation": "a ) 31 is prime and per the question stem we can not use this b ) 32 = 2 * 16 - within 30 ! we have a 2 and 16 so 32 will be a factor of 30 ! c ) 33 = 3 * 11 - again within 30 ! we have a 3 and an 11 so 33 will be a factor of 30 ! d ) 62 = 31 * 2 - bingo 31 is not included in 30 ! e ) 64 = 16 * 4 - both 16 and 4 are multiplied in 30 ! answer is d !" - }, - { - "Answer": 75, - "Options": "a ) 42 , b ) 66 , c ) 75 , d ) 112 , e ) 154", - "Correct": "c", - "Explanation": "\"let us assume the number of dogs , cats and bunnies to be 3 x , 7 x and 12 x total dogs and bunnies = 15 x . and we are given that 15 x = 375 . hence x = 25 . dogs = 3 x = 3 * 25 = 75 ( option c )\"" - }, - { - "Answer": 5000, - "Options": "a ) 5000 , b ) 6000 , c ) 7000 , d ) 8000 , e ) 9000", - "Correct": "a", - "Explanation": "\"let the income and the expenditure of the person be rs . 8 x and rs . 7 x respectively . income , 8 x = 40000 = > x = 5000 savings = income - expenditure = 8 x - 7 x = x so , savings = rs . 5000 . answer : a\"" - }, - { - "Answer": 24, - "Options": "a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24", - "Correct": "e", - "Explanation": "present ages = 5 x : 4 x three hence = 5 x + 3 : 4 x + 3 5 x + 3 : 4 x + 3 = 11 : 9 weget x = 6 suji age is = 4 x = 4 * 6 = 24 answer : e" - }, - { - "Answer": 6, - "Options": "a ) 6 , b ) 5 , c ) 4 , d ) 3 , e ) 2", - "Correct": "a", - "Explanation": "\"the ratio of flour to water is 16 : 4 = 4 : 1 . the ratio of flour to sugar is 4 : 3 . the new ratio of flour to water to sugar is 4 : 1 : 3 if we need 2 cups of water , then we need 6 cups of sugar . the answer is a .\"" - }, - { - "Answer": 15, - "Options": "a ) 14 , b ) 15 , c ) 20 , d ) 22 , e ) 23", - "Correct": "b", - "Explanation": "\"explanation : present age is 4 x and 3 x , = > 4 x + 6 = 26 = > x = 5 so deepak age is = 3 ( 5 ) = 15 answer : option b\"" - }, - { - "Answer": 3.44, - "Options": "a ) 3.84 , b ) 1.75 , c ) 3.44 , d ) 2.72 , e ) none of these", - "Correct": "c", - "Explanation": "\"here ' s how i did it . my notes from reading the problem were : 1 l a = 900 gm 1 l b = 800 gm we are mixing five parts ( 3 parts a plus 2 parts b , 5 parts total ) to get 4 l , so 5 x = 4 - - - > x = 4 / 5 . each part is 4 / 5 of a liter . so if we have 3 parts a , we have 900 * 3 * ( 4 / 5 ) = 2160 if we have 2 parts b , we have 800 * 2 * ( 4 / 5 ) = 1280 2160 + 1280 = 3440 solving for units gives us 3.44 so the answer is c\"" - }, - { - "Answer": 21, - "Options": "a ) 12 , b ) 15 , c ) 18 , d ) 21 , e ) 24", - "Correct": "d", - "Explanation": "\"now , sandy is 34 - 6 = 28 molly ' s age is ( 3 / 4 ) * 28 = 21 the answer is d .\"" - }, - { - "Answer": 10, - "Options": "a ) 9 , b ) 36 , c ) 122 , d ) 6 , e ) 10", - "Correct": "e", - "Explanation": "\"square root is a number times itself square root of 400 = 20 , 20 / 2 = 10 ( e ) 1\"" - }, - { - "Answer": 9000, - "Options": "a ) 6000 , b ) 9000 , c ) 9500 , d ) 12000 , e ) none", - "Correct": "b", - "Explanation": "\"sol . let b \u2019 s capital be rs . x . then , 3500 * 12 / 7 x = 2 / 3 \u21d4 14 x = 126000 \u21d4 x = 9000 . answer b\"" - }, - { - "Answer": 24, - "Options": "a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25", - "Correct": "d", - "Explanation": "number of zeros will be 24 reason 100 / 5 = 20 20 / 5 = 4 so the total number of 5 will be 20 + 4 = 24 answer : d" - }, - { - "Answer": 22, - "Options": "a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24", - "Correct": "c", - "Explanation": "\"let 2 x be the number of spinsters . then 7 x is the number of cats . 7 x - 2 x = 55 x = 11 and the number of spinsters is 2 ( 11 ) = 22 . the answer is c .\"" - }, - { - "Answer": 0.49999999999999994, - "Options": "a ) 1 / 2 , b ) 5 / 9 , c ) 5 / 1 , d ) 5 / 3 , e ) 7 / 6", - "Correct": "a", - "Explanation": "let us say the ratio of the quantities of cheaper and dearer varieties = x : y by the rule of allegation , x / y = ( 8.75 - 7.50 ) / ( 7.50 - 5 ) = 1 / 2 answer : a" - }, - { - "Answer": 40, - "Options": "a ) 45 % , b ) 40 % , c ) 35 % , d ) 30 % , e ) 25 %", - "Correct": "b", - "Explanation": "\"65 % answered the first question correctly and 20 % answered neither correctly . then 15 % missed the first question but answered the second question correctly . then the percent who answered both correctly is 55 % - 15 % = 40 % . the answer is b .\"" - }, - { - "Answer": 90, - "Options": "a ) 30 , b ) 90 , c ) 120 , d ) 172 , e ) 188", - "Correct": "b", - "Explanation": "\"i would just like to add a bit of explanation after the step where you calculate that the number of students studying both m and s = 90 using your analysis : we see that the total number of students who study either maths or sociology = 132 + 168 - 90 = 210 so , in the image we know that the number of students in the zone with the black boundary = 210 let ' s assume the number of students who studyonlybiology to beb ( this is the number that we have to maximize ) and , let ' s assume the number of students who study none of the three subjects , that is the number of students in the white space = w since the total number of students = 300 , we can write : 210 + b + w = 300 or , b + w = 300 - 210 = 90 that is , b = 90 - w so , the maximum value ofbwill happen forw = 0 this is how we get , the maximum value ofb = 90 b\"" - }, - { - "Answer": 29, - "Options": "a ) 9 , b ) 19 , c ) 23 , d ) 27 , e ) 29", - "Correct": "e", - "Explanation": "\"number of students taking history = h = 36 number of students taking statistics = s = 30 total number of students = t = 90 number of students taking history or statistics or both = b = 59 number of students taking neither history nor statistics = n = 90 - 59 = 31 letxbe the number of students taking both history and statistics . then t = h + s + n - x or 90 = 36 + 30 + 31 - x or x = 7 now , number of students taking only history will be h - x or 36 - 7 = 29 answer : - e\"" - }, - { - "Answer": 225, - "Options": "a ) 220 , b ) 225 , c ) 230 , d ) 240 , e ) 245", - "Correct": "b", - "Explanation": "25 + 60 + 140 = 225 there are 225 students involved in either band or sports . b )" - }, - { - "Answer": 13, - "Options": "a ) 11 th , b ) 13 th , c ) 12 th , d ) 14 th , e ) 15 th", - "Correct": "b", - "Explanation": "when considered from last , 12 ( i . e 26 - 14 ) students are ranked before her . so she is 13 th rank from last . answer : b" - }, - { - "Answer": 12, - "Options": "a ) a ) 10 , b ) b ) 12 , c ) c ) 15 , d ) d ) 14 , e ) e ) 9", - "Correct": "b", - "Explanation": "\"let the numbers be x , 2 x , 5 x then , x ^ 2 + 4 x ^ 2 + 25 x ^ 2 = 4320 30 x ^ 2 = 4320 x ^ 2 = 144 x = 12 answer is b\"" - }, - { - "Answer": 10, - "Options": "a ) 2 , b ) 8 , c ) 4 , d ) 5 , e ) 10", - "Correct": "e", - "Explanation": "\"the answer is ( 1000 - 100 ) / 100 + 1 = 10 answer is e\"" - }, - { - "Answer": 84, - "Options": "a ) 32 , b ) 37 , c ) 84 , d ) 29 , e ) 21", - "Correct": "c", - "Explanation": "explanation : let the numbers be x and 4 x . then , \\ inline \\ fn _ jvn x \\ times 4 x = 84 \\ times 21 \\ : \\ : \\ leftrightarrow \\ : \\ : x ^ { 2 } = \\ frac { 84 \\ times 21 } { 4 } \\ : \\ : \\ leftrightarrow \\ : \\ : x = 21 hence larger number = 4 x = 84 answer : c ) 84" - }, - { - "Answer": 12, - "Options": "a ) 13 , b ) 12 , c ) 9 , d ) 8 , e ) 7", - "Correct": "b", - "Explanation": "\"there are total 150 workers . half of the workers in palabras bookstore have read the latest book by j . saramago , so 75 have read saramago . 1 / 6 of the workers have read the latest book by h . kureishi . so ( 1 / 6 ) * 150 = 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 , ( 75 - b - 1 ) have read neither . total = n ( a ) + n ( b ) - both + neither 150 = 75 + 25 - b + ( 75 - b - 1 ) b = 12 answer ( b )\"" - }, - { - "Answer": 0.8, - "Options": "a ) 0.9 , b ) 0.75 , c ) 0.6 , d ) 0.8 , e ) 0.5", - "Correct": "d", - "Explanation": "\"according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 50 + 20 + 10 ) / 100 = 80 / 100 = 0.8 . answer is d\"" - }, - { - "Answer": 21000, - "Options": "a ) 24887 , b ) 20778 , c ) 23788 , d ) 21000 , e ) 2811", - "Correct": "d", - "Explanation": "\"explanation : a invested rs . 3500 for 12 months . let b joined with investment x . and he invested for 12 - 9 = 3 months . so there profit ratio = ( 3500 \u00e3 \u2014 12 ) : ( 3 x ) = 2 : 3 \u00e2 \u2021 \u2019 x = 21000 answer : d\"" - }, - { - "Answer": 40, - "Options": "a ) 26 , b ) 32 , c ) 33 , d ) 34 , e ) 40", - "Correct": "e", - "Explanation": "\"multiples of 2 from 39 to 99 = multiples of 2 from 1 to 99 - multiples of 2 from 1 to 38 = [ 99 / 2 ] - [ 38 / 2 ] = 49 - 19 = 30 multiples of 3 from 39 to 99 = multiples of 3 from 1 to 99 - multiples of 3 from 1 to 38 = [ 99 / 3 ] - [ 38 / 3 ] = 33 - 13 = 20 multiples of 2 and 3 bothi . e . 6 from 39 to 99 = multiples of 6 from 1 to 99 - multiples of 6 from 1 to 38 = [ 99 / 6 ] - [ 38 / 6 ] = 16 - 6 = 10 these 8 numbers have been counted twice in both the above calculation while calculating multiples of 2 and 3 i . e . total numbers in w = 30 + 20 - 10 = 40 answer option e\"" - }, - { - "Answer": 30, - "Options": "a ) 24 , b ) 30 , c ) 36 , d ) 42 , e ) 50", - "Correct": "b", - "Explanation": "given ratios 2 : 3 5 : 8 10 : 15 : 24 the second number = 98 / ( 10 + 15 + 24 ) * 15 = 30 answer is b" - }, - { - "Answer": 40, - "Options": "a ) 15 , b ) 20 , c ) 30 , d ) 40 , e ) 45", - "Correct": "d", - "Explanation": "solution for soap w and soap b ( d ) 40" - }, - { - "Answer": 0.10476190476190475, - "Options": "a ) 3 / 32 , b ) 7 / 64 , c ) 11 / 105 , d ) 15 / 127 , e ) 19 / 134", - "Correct": "c", - "Explanation": "12 / 36 * 11 / 35 = 11 / 105 the answer is c ." - }, - { - "Answer": 6, - "Options": "a ) 4 , b ) 5 , c ) 8 , d ) 6 , e ) 9", - "Correct": "d", - "Explanation": "obviously , the answer is 6 option d" - }, - { - "Answer": 0.5151515151515151, - "Options": "a ) 8 / 15 , b ) 2 / 5 , c ) 3 / 5 , d ) 11 / 15 , e ) 17 / 33", - "Correct": "e", - "Explanation": "\"drawing two balls of same color from four green balls can be done in 4 c \u2082 ways . similarly from eight white balls two can be drawn in \u2078 c \u2082 ways . p = 4 c \u2082 / \u00b9 \u2075 c \u2082 + \u2078 c \u2082 / \u00b9 \u2075 c \u2082 = 17 / 33 answer : e\"" - }, - { - "Answer": 7, - "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", - "Correct": "a", - "Explanation": "\"xc 1 * ( x - 1 ) c 1 = 42 x ^ 2 - x - 42 = 0 ( x - 7 ( x + 6 ) = 0 x = 7 , - 6 - 6 ca n ' t possible . hence 7 should be the answer a\"" - }, - { - "Answer": 96, - "Options": "a ) 99 , b ) 98 , c ) 97 , d ) 96 , e ) 95", - "Correct": "d", - "Explanation": "\"g = 96 = 3 * 32 = 3 * 2 ^ 5 answer is d .\"" - }, - { - "Answer": 12, - "Options": "a ) 4 , b ) 6 , c ) 12 , d ) 18 , e ) none of these", - "Correct": "c", - "Explanation": "36 = 2 ^ 2 * 3 ^ 2 ; 84 = 2 ^ 2 * 3 * 7 h . c . f = 2 ^ 2 * 3 = 12 . correct option : c" - }, - { - "Answer": 36, - "Options": "a ) 48 , b ) 22 , c ) 36 , d ) 27 , e ) 67", - "Correct": "c", - "Explanation": "explanation : let the numbers be 2 x and 3 x . then , their h . c . f . = x . so , x = 6 . so , the numbers 12 and 18 l . c . m . of 12 and 18 = 36 option c" - }, - { - "Answer": 15, - "Options": "a ) 10 , b ) 12 , c ) 14 , d ) 15 , e ) 20", - "Correct": "d", - "Explanation": "after 6 years , shekhar ' s age will be 26 years therefore , present age of shekhar = 26 \u2212 6 = 20 let present age of shobha = x then , 20 x = 43 x = 20 \u00d7 34 = 15 answer is d ." - }, - { - "Answer": 15, - "Options": "a ) 15 , b ) 20 , c ) 18 , d ) 22 , e ) 35", - "Correct": "a", - "Explanation": "\"let the present age of arun and deepak be 4 x and 3 x 4 x + 6 = 26 4 x = 20 x = 5 deepak ' s age = 3 x = 15 years answer is a\"" - }, - { - "Answer": 82, - "Options": "a ) 82 % , b ) 64 % , c ) 28 % , d ) 69 % , e ) 80 %", - "Correct": "a", - "Explanation": "\"let total no of vehicles bought be 100 , toyota 90 and honda 10 , so total number of suv ' s bought for toyota and honda respectively 90 * 90 / 100 = 81 and 10 * 10 / 100 = 1 so total 82 suv ' s were bought out of 100 vehicles bought . . so required % is 82 % answer : a\"" - }, - { - "Answer": 168, - "Options": "a ) 30 , b ) 90 , c ) 120 , d ) 168 , e ) 188", - "Correct": "d", - "Explanation": "\"i would just like to add a bit of explanation after the step where you calculate that the number of students studying both m and s = 168 using your analysis : we see that the total number of students who study either maths or sociology = 176 + 224 - 168 = 232 so , in the image we know that the number of students in the zone with the black boundary = 232 let ' s assume the number of students who studyonlybiology to beb ( this is the number that we have to maximize ) and , let ' s assume the number of students who study none of the three subjects , that is the number of students in the white space = w since the total number of students = 400 , we can write : 232 + b + w = 400 or , b + w = 400 - 232 = 168 that is , b = 168 - w so , the maximum value ofbwill happen forw = 0 this is how we get , the maximum value ofb = 168 d\"" - }, - { - "Answer": 5000, - "Options": "a ) rs . 5750 , b ) rs . 6000 , c ) rs . 5500 , d ) rs . 5000 , e ) rs . 7000", - "Correct": "d", - "Explanation": "the price varies as the square of the weight , p = k x w 2 12250 = k x 352 k = 10 thus , p = 10 w 2 when the two pieces are in the ratio 2 : 5 ( weight wise ) then we know that their weights must be 10 g and 25 g respectively . their values should be : 10 g piece : 10 x 102 = rs . 1000 ; 25 g piece : 10 x 252 = rs . 6250 . total value of stone now , = 1000 + 6250 = rs . 7250 loss incurred = 12250 - 7250 = rs . 5000 answer : d" - }, - { - "Answer": 1800, - "Options": "a ) s 1800 , b ) s 1500 , c ) s 1600 , d ) s 1900 , e ) s 1700", - "Correct": "a", - "Explanation": "\"explanation : let p = faruk , q = vasim , r = ranjith let p = 3 x , q = 5 x and r = 9 x . then , 5 x = 1500 ? x = 300 . p = 900 , q = 1500 and r = 2700 . hence , ( r - p ) = ( 2700 - 900 ) = 1800 answer : a\"" - }, - { - "Answer": 0.08333333333333333, - "Options": "a ) 1 / 12 , b ) 1 / 13 , c ) 1 / 14 , d ) 1 / 15 , e ) 1 / 18", - "Correct": "a", - "Explanation": "\"p ( both are red ) , = 3 c 2 / 9 c 2 = 1 / 12 a\"" - }, - { - "Answer": 88, - "Options": "a ) 144 , b ) 119 , c ) 113 , d ) 88 , e ) 31", - "Correct": "d", - "Explanation": "\"official solution : first of all , notice that since 144 took geometry and 119 took biology , then the number of students who took both geometry and biology can not be greater than 119 . { total } = { geometry } + { biology } - { both } + { neither } ; 232 = 144 + 119 - { both } + { neither } ; { both } = 31 + { neither } . { both } is minimized when { neither } is 0 . in this case { both } = 31 . the greatest possible number r of students that could have taken both geometry and biology , is 119 . thus , the answer is 119 - 31 = 88 . answer : d .\"" - }, - { - "Answer": 0.07103614457831325, - "Options": "a ) 1 / 250 , b ) 1 / 14 , c ) 1 / 11 , d ) 1 / 9 , e ) 1 / 3", - "Correct": "b", - "Explanation": "probability of chosing one defective phone from a lot of 250 which ontains 67 defective phones is = ( 67 / 250 ) probability of chosing one defective phone from a lot of 249 ( we already picked one ) which ontains 66 ( we already picked one ) defective phones is = ( 66 / 249 ) combined probability of series of events = product of the probabilities = ( 67 / 250 ) * ( 66 / 249 ) 67 / 250 is close to ( 26 / 97 ) and ( 66 / 249 ) = ( 22 / 83 ) so answer is ( 26 / 97 ) * ( 22 / 83 ) = ( 1 / 14 ) so , answer will be b" - }, - { - "Answer": 12.000000000000002, - "Options": "a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14", - "Correct": "c", - "Explanation": "fast ' s 1 hr work = 1 / 2 slow ' s 1 hr work = 1 / 3 1 / 2 + 1 / 3 = 5 / 6 they ll finish in 6 / 5 hrs = 1 1 / 5 = = > 1 hr 12 mins answer : c" - }, - { - "Answer": 7, - "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", - "Correct": "a", - "Explanation": "\"let x play both badminton and tennis so 16 - x play only badminton and 19 - x play only tennis . 2 play none and there are total 30 students . hence , ( 16 - x ) + ( 19 - x ) + x + 2 = 30 37 - 2 x + x = 30 37 - x = 30 x = 7 so 7 members play both badminton and tennis . a\"" - }, - { - "Answer": 240, - "Options": "a ) 560 , b ) 240 , c ) 329 , d ) 443 , e ) 544", - "Correct": "b", - "Explanation": "\"let x be the number of kilograms he sold in the morning . then in the afternoon he sold 2 xkilograms . so , the total is x + 2 x = 3 x this must be equal to 360 . 3 x = 360 x = 360 / 3 x = 120 therefore , the salesman sold 120 kg in the morning and 2 \u22c5 120 = 240 kg in the afternoon .\"" - }, - { - "Answer": 100, - "Options": "a ) 46 , b ) 80 , c ) f = 90 , d ) f = 100 , e ) 200", - "Correct": "d", - "Explanation": "\"100 = x + x - 20 + 23 - 23 x = 60 , so , product a = 60 % , product b = 40 % , both = 23 % , neither = 23 % 23 % of the total no . of people should be an integer . so , a , bc are out . 60 % of d and 40 % of d are both integers . so , d satisfies all conditions . so , answer is d .\"" - }, - { - "Answer": 66, - "Options": "a ) 48 , b ) 66 , c ) 72 , d ) 80 , e ) 84", - "Correct": "b", - "Explanation": "let x be the number of new boarders . the ratio changed from 5 : 12 up to 1 : 2 = 6 : 12 . 330 / ( 330 + x ) = 5 / 6 x = 66 the answer is b ." - }, - { - "Answer": 20, - "Options": "a ) 20 , b ) 19 , c ) 21 , d ) 18 , e ) 22", - "Correct": "a", - "Explanation": "let the present ages dan and james be 6 x years and 5 x years respectively 6 x + 4 = 28 6 x = 24 x = 4 kim ' s age = 5 x = 20 years answer is a" - }, - { - "Answer": 460, - "Options": "a ) 430 , b ) 440 , c ) 450 , d ) 460 , e ) 470", - "Correct": "d", - "Explanation": "\"we ' re given a series of facts to work with : 1 ) a certain high school has 500 students . 2 ) of these students : x are taking music , y are taking art , and z are taking both music and art . we ' re asked how many students are taking neither music nor art ? let ' s test x = 30 y = 20 z = 10 so , we have 30 students taking music , 20 taking art and 10 taking both music and art . 20 student taking just music 10 student taking just art 10 student taking both music and art total = 40 students we ' re asked for the total number of students who are taking neither course . that is 500 - 40 = 460 . d\"" - }, - { - "Answer": 60, - "Options": "a ) 60 , b ) 90 , c ) 120 , d ) 172 , e ) 188", - "Correct": "a", - "Explanation": "\"i would just like to add a bit of explanation after the step where you calculate that the number of students studying both m and s = 60 using your analysis : we see that the total number of students who study either maths or sociology = 88 + 112 - 60 = 140 so , in the image we know that the number of students in the zone with the black boundary = 140 let ' s assume the number of students who studyonlybiology to beb ( this is the number that we have to maximize ) and , let ' s assume the number of students who study none of the three subjects , that is the number of students in the white space = w since the total number of students = 200 , we can write : 140 + b + w = 200 or , b + w = 200 - 140 = 60 that is , b = 60 - w so , the maximum value ofbwill happen forw = 0 this is how we get , the maximum value ofb = 60 a\"" - }, - { - "Answer": 264, - "Options": "a ) 264 , b ) 209 , c ) 57 , d ) 171 , e ) 181", - "Correct": "a", - "Explanation": "given , the ratio of the doctors to the nurses is 8 : 11 number of nurses = 11 / 19 x 456 = 264 answer : a" - }, - { - "Answer": 378, - "Options": "a ) 22 , b ) 28 , c ) 77 , d ) 99 , e ) 378", - "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 ) = 17 x and b ( d ) = 4 x now from the next line the new eqn becomes 17 x / ( 4 x - 4 ) = 9 / 2 solving it 34 x = 36 x - 36 x = 18 which means m ( d ) = 306 and b ( d ) = 72 so total initially is m ( d ) + b ( d ) = 378 e" - }, - { - "Answer": 21, - "Options": "a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24", - "Correct": "b", - "Explanation": "here ratio is 7 / 4 . so lets check one by one . for 1 : 7 * 1 / 4 * 1 = 7 / 4 for 2 : 7 * 2 / 4 * 2 = 14 / 8 , which does n ' t satisfy the conditions . for 3 : 7 * 3 / 4 * 3 = 21 / 12 answer : b" - }, - { - "Answer": 49, - "Options": "a ) 45 , b ) 47 , c ) 48 , d ) 49 , e ) 53", - "Correct": "d", - "Explanation": "\"lets assume ac = 63 ( includesonly ac carsandcars with ac and racing stripes ) lets assume rs ( racing stripes ) > = 51 ( includescars with ac and racing stripesandonly racing stripes ) . now since we want to maximize ( only ac ) we have to see to it thatcars with ac and racing stripesis minimal ( assume 0 ) but since rs > = 51 . . we have to assign atleast 14 tocars with ac and racing stripes . hence ac = 63 - 14 = 49 . the answer is d\"" - }, - { - "Answer": 280, - "Options": "a ) 120 , b ) 180 , c ) 240 , d ) 280 , e ) 320", - "Correct": "d", - "Explanation": "\"3 x = 420 x = 140 therefore , the salesman sold 140 kg in the morning and 2 \u22c5 140 = 280 kg in the afternoon . so answer is d .\"" - }, - { - "Answer": 0.9166666666666666, - "Options": "a ) 9 / 12 , b ) 10 / 12 , c ) 11 / 12 , d ) 1 , e ) 2", - "Correct": "c", - "Explanation": "explanation : the event is defined as : a solves the problem and b does not solve the problem or a does n ' t solve the problem and b solves the problem or a solves the problem and b solves the problem numerically this is equivalent to : ( 2 / 3 ) x ( 1 / 4 ) + ( 1 / 3 ) x ( 3 / 4 ) + ( 2 / 3 ) x ( 3 / 4 ) = 11 / 12 answer : c" - }, - { - "Answer": 0.47058823529411764, - "Options": "a ) 8 / 17 , b ) 2 / 5 , c ) 3 / 5 , d ) 11 / 15 , e ) 7 / 15", - "Correct": "a", - "Explanation": "\"drawing two balls of same color from nine green balls can be done in 9 c \u2082 ways . similarly from eight white balls two can be drawn in \u2078 c \u2082 ways . p = 9 c \u2082 / \u00b9 \u2075 c \u2082 + \u2078 c \u2082 / \u00b9 \u2075 c \u2082 = 8 / 17 answer : a\"" - }, - { - "Answer": 6, - "Options": "a ) 25 , b ) 8 , c ) 6 , d ) 5 , e ) 2", - "Correct": "c", - "Explanation": "explanatory answer 25 ! means factorial 25 whose value = 25 * 24 * 23 * 22 * . . . . * 1 when a number that has 5 as its factor is multiplied by an even number , it results in a trailing zero . ( product of 5 and 2 is 10 and any number when multiplied with 10 or a power of 10 will have one or as many zeroes as the power of 10 with which it has been multiplied ) in 25 ! , the following numbers have 5 as their factor : 5 , 10 , 15 , 20 , and 25 . 25 is the square of 5 and hence it has two 5 s in it . in toto , it is equivalent of having six 5 s . there are at least 6 even numbers in 25 ! hence , the number 25 ! will have 6 trailing zeroes in it . choice c" - }, - { - "Answer": 12, - "Options": "a ) 12 , b ) 15 , c ) 16 , d ) 18 , e ) 22", - "Correct": "a", - "Explanation": "\"draw a venn diagram yourself ! b + c - bc = number of students that play either basketball or cricket 7 + 8 - 3 = 12 a )\"" - }, - { - "Answer": 120, - "Options": "a ) 100 , b ) 120 , c ) 80 , d ) 90 , e ) none of the above", - "Correct": "b", - "Explanation": "girl 5 x and boys 6 x 5 x - 20 / 6 x = 2 / 3,15 x - 60 = 12 x , 3 x = 60 , x = 20 boys = 6 x = 120 answer b" - }, - { - "Answer": 3, - "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6", - "Correct": "b", - "Explanation": "explanation : let , the number of over time hours be x and expected number of accidents be y . we will use the equation y = mx + c , where m and c are constant . now , according to the question , if x = 1000 , then y = 8 i . e 8 = 1000 x + c - - - - ( i ) and , if x = 400 , then y = 5 i . e 5 = 400 x + c . - - - - ( ii ) on solving these equations , we get m = 1 / 200 and c = 3 . hence , in case , no overtime is there i . e x = 0 , then the number of expected accident will be 3 . answer : b" - }, - { - "Answer": 48, - "Options": "a ) 30 , b ) 32 , c ) 48 , d ) 55 , e ) 64", - "Correct": "c", - "Explanation": "\"let x equal the number of pens , and y the number of pencils . then , x = 5 / 6 y . we also know that x = y - 8 . and so , we can substitute : y - 8 = 5 / 6 y so to isolate y , we get : 1 / 6 y = 8 and therefore : y = 48 answer : c\"" - }, - { - "Answer": 60, - "Options": "a ) 15 , b ) 25 , c ) 30 , d ) 45 , e ) 60", - "Correct": "e", - "Explanation": "\"this ratio question can be solved in a couple of different ways . here ' s an algebraic approach . . . we ' re told that the ratio of the number of dogs to the number of cats is 15 : 7 . we ' re then told that 16 more cats are added to this group and the ratio becomes 15 : 11 . we ' re asked for the number of dogs . algebraically , since the number of dogs is a multiple of 15 and the number of cats is a multiple of 7 , we can write this initial relationship as . . . 15 x / 7 x when we add the 12 cats and factor in the ' ending ratio ' , we have an equation . . . . 15 x / ( 7 x + 16 ) = 15 / 11 here we have 1 variable and 1 equation , so we can solve for x . . . . ( 15 x ) ( 11 ) = ( 7 x + 16 ) ( 15 ) ( x ) ( 11 ) = ( 7 x + 16 ) ( 1 ) 11 x = 7 x + 16 4 x = 16 x = 4 with this x , we can figure out the initial number of dogs and cats . . . initial dogs = 15 x = 15 ( 4 ) = 60 final answer : e\"" - }, - { - "Answer": 70, - "Options": "a ) 50 , b ) 70 , c ) 100 , d ) 130 , e ) 150", - "Correct": "b", - "Explanation": "\"20 stamps are both foreign and more than 10 years old . 70 stamps are foreign only . 40 stamps are 10 years old only . the number of remaining stamps is 200 - ( 20 + 70 + 40 ) = 70 the answer is b .\"" - }, - { - "Answer": 3.36, - "Options": "['a ) 3.84', 'b ) 1.75', 'c ) 3.36', 'd ) 2.72', 'e ) none of these']", - "Correct": "c", - "Explanation": "here ' s how i did it . my notes from reading the problem were : 1 l a = 900 gm 1 l b = 850 gm we are mixing five parts ( 3 parts a plus 2 parts b , 5 parts total ) to get 4 l , so 5 x = 4 - - - > x = 4 / 5 . eachpartis 4 / 5 of a liter . so if we have 3 parts a , we have 900 * 3 * ( 4 / 5 ) = 2160 if we have 2 parts b , we have 750 * 2 * ( 4 / 5 ) = 1200 2160 + 1200 = 3360 solving for units gives us 3.36 so the answer is c" - }, - { - "Answer": 90, - "Options": "a ) 50 , b ) 55 , c ) 60 , d ) 70 , e ) 90", - "Correct": "e", - "Explanation": "first of all we need to find the prime factors of 15 and 18 15 = 5 x 3 18 = 3 x 3 x 2 lcm is the product of highest exponent of all the factors . lcm ( 15,18 ) = 5 x 3 ^ 2 x 2 = 90 answer : 90" - }, - { - "Answer": 3, - "Options": "a ) 3 , b ) 12 , c ) 9 , d ) 8 , e ) 7", - "Correct": "a", - "Explanation": "there are total 42 workers . half of the workers in palabras bookstore have read the latest book by j . saramago , so 21 have read saramago . 1 / 6 of the workers have read the latest book by h . kureishi . so ( 1 / 6 ) * 42 = 7 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 , ( 21 - b - 1 ) have read neither . total = n ( a ) + n ( b ) - both + neither 42 = 21 + 7 - b + ( 21 - b - 1 ) b = 3 answer ( a )" - }, - { - "Answer": 49, - "Options": "a ) 48 , b ) 24.8 , c ) 24.21 , d ) 24.88 , e ) 49", - "Correct": "e", - "Explanation": "\"explanation : if rahul age is x , then sachin age is x - 14 , so , 9 x - 126 = 7 x 2 x = 126 x = 63 so sachin age is 63 - 14 = 49 answer : e ) 49\"" - }, - { - "Answer": 480, - "Options": "a ) 462 , b ) 450 , c ) 488 , d ) 480 , e ) 555", - "Correct": "d", - "Explanation": "\"explanation : hcf of the two numbers = 40 hcf will be always a factor of lcm 40 is factor of lcm other two factors are 11 & 12 then the numbers are ( 40 * 11 ) and ( 40 x 12 ) = 440 and 480 answer : option d\"" - }, - { - "Answer": 90, - "Options": "a ) 82 , b ) 84 , c ) 86 , d ) 88 , e ) 90", - "Correct": "e", - "Explanation": "\"let x be the weight of the sister . then the student ' s weight is 2 x + 6 . x + ( 2 x + 6 ) = 132 3 x = 126 x = 42 kg then the student ' s weight is 90 kg . the answer is e .\"" - }, - { - "Answer": 6, - "Options": "a ) 6 , b ) 16 , c ) 22 , d ) 30 , e ) 174", - "Correct": "a", - "Explanation": "\"the number of integers that belong to set x only is 8 - 6 = 2 ; the number of integers that belong to set y only is 10 - 6 = 4 ; the number of integers that belong to set x or set y , but not both is 2 + 4 = 6 . answer : a .\"" - }, - { - "Answer": 2, - "Options": "a ) 1 , b ) 6 , c ) 7 , d ) 8 , e ) 2", - "Correct": "e", - "Explanation": "\"45 * 12 : 27 * x = 2 : 1 x = 10 12 - 10 = 2 answer : e\"" - }, - { - "Answer": 4, - "Options": "a ) 4,0 , b ) 0,4 , c ) 4,4 , d ) 0,0 , e ) none", - "Correct": "a", - "Explanation": "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 : a" - }, - { - "Answer": 60, - "Options": "a ) 30 , b ) 60 , c ) 40 , d ) 45 , e ) 50", - "Correct": "b", - "Explanation": "make a venn diagram , and enter your data . let the number of houses be x 30 + 10 + 20 = x x = 60 so number of houses were = 60 answer b" - }, - { - "Answer": 18, - "Options": "a ) 30 , b ) 10 , c ) 18 , d ) 28 , e ) 32", - "Correct": "c", - "Explanation": "\"answer let a be the set of students who have enrolled for english and b be the set of students who have enrolled for german . then , ( a u b ) is the set of students who have enrolled at least one of the two subjects . as the students of the class have enrolled for at least one of the two subjects , a u b = 40 we know a u b = a + b - ( a n b ) i . e , 40 = a + 22 - 12 or a = 30 which is the set of students who have enrolled for english and includes those who have enrolled for both the subjects . however , we need to find out the number of students who have enrolled for only english = students enrolled for english - students enrolled for both german and english = 30 - 12 = 18 . choice is ( c )\"" - }, - { - "Answer": 4046, - "Options": "a ) s . 2890 , b ) s . 4046 , c ) s . 1190 , d ) s . 1620 , e ) s . 2680", - "Correct": "b", - "Explanation": "\"ram : gopal = 7 : 17 = 49 : 119 gopal : krishan = 7 : 17 = 119 : 289 ram : gopal : krishan = 49 : 119 : 289 ram : krishan = 49 : 289 thus , 49 : 289 = 686 : n & there n = 289 x 686 / 49 = rs . 4046 answer : b\"" - }, - { - "Answer": 450, - "Options": "a ) 90 , b ) 150 , c ) 270 , d ) 300 , e ) 450", - "Correct": "e", - "Explanation": "originally ( 2 / 9 ) * 1350 = 300 acres were planted with tobacco . in the new system ( 5 / 9 ) * 1350 = 750 acres were planted with tobacco . thus 750 - 300 = 450 more acres were planted with tobacco . the answer is e ." - }, - { - "Answer": 27, - "Options": "a ) 27 , b ) 32 , c ) 33 , d ) 34 , e ) 35", - "Correct": "a", - "Explanation": "multiples of 2 from 59 to 99 = multiples of 2 from 1 to 99 - multiples of 2 from 1 to 58 = [ 99 / 2 ] - [ 58 / 2 ] = 49 - 29 = 20 multiples of 3 from 59 to 99 = multiples of 3 from 1 to 99 - multiples of 3 from 1 to 58 = [ 99 / 3 ] - [ 58 / 3 ] = 33 - 169 = 14 multiples of 2 and 3 bothi . e . 6 from 59 to 99 = multiples of 6 from 1 to 99 - multiples of 6 from 1 to 58 = [ 99 / 6 ] - [ 58 / 6 ] = 16 - 9 = 7 these 8 numbers have been counted twice in both the above calculation while calculating multiples of 2 and 3 i . e . total numbers in w = 20 + 14 - 7 = 27 answer option a" - }, - { - "Answer": 4000, - "Options": "a ) rs . 4000 , b ) rs . 3603 , c ) rs . 3639 , d ) rs . 3632 , e ) rs . 3602", - "Correct": "a", - "Explanation": "\"let the income and the expenditure of the person be rs . 5 x and rs . 3 x respectively . income , 5 x = 10000 = > x = 2000 savings = income - expenditure = 5 x - 3 x = 2 x so , savings = rs . 2 * 2000 = rs . 4000 answer : a\"" - }, - { - "Answer": 100, - "Options": "a ) 100 , b ) 120 , c ) 90 , d ) 80 , e ) 70", - "Correct": "a", - "Explanation": "100 litre water is to be added . let ' x ' liter water is to be added more . then 1 / 3 = 37.5 / ( 12.5 + x ) x = 100 answer : a" - }, - { - "Answer": 0.02631578947368421, - "Options": "a ) 2 / 21 , b ) 3 / 41 , c ) 5 / 26 , d ) 1 / 38 , e ) 5 / 32", - "Correct": "d", - "Explanation": "\"p ( both are red ) , = 7 c 3 / 21 c 3 = ( 7 * 6 * 5 ) / 21 * 20 * 19 = 1 / 38 d\"" - }, - { - "Answer": 50, - "Options": "a ) 27 , b ) 36 , c ) 45 , d ) 50 , e ) 117", - "Correct": "d", - "Explanation": "\"the ratio of b to g is 5 : 13 and the other data point is g are more than boys by 80 . . . looking at the ratio we can say that the 8 ( 13 - 5 ) extra parts caused this diff of 80 . so 1 part corresponds to 80 / 8 = 10 and so 5 parts correspond to 5 * 10 = 50 . d\"" - }, - { - "Answer": 60, - "Options": "a ) 12 , b ) 16 , c ) 24 , d ) 60 , e ) 98", - "Correct": "d", - "Explanation": "\"let the numbers be 3 x and 4 x . then their h . c . f = x . so , x = 5 . so , the numbers are 15 and 20 . l . c . m of 15 and 20 = 60 . answer : d\"" - }, - { - "Answer": 60, - "Options": "a ) 60 % , b ) 65 % , c ) 70 % , d ) 75 % , e ) 80 %", - "Correct": "a", - "Explanation": "\"{ total } = { first correctly } + { second correctly } - { both correctly } + { neither correctly } 100 = 85 + 70 - { both correctly } + 5 { both correctly } = 60 . answer : a .\"" - }, - { - "Answer": 26, - "Options": "a ) 20 , b ) 11 , c ) 23 , d ) 26 , e ) 21", - "Correct": "d", - "Explanation": "\"total people eat veg = only veg + both veg and non veg total = 15 + 11 = 26 answer = d\"" - }, - { - "Answer": 3.9999999999999853, - "Options": "a ) 2 % , b ) 4 % , c ) 8 % , d ) 10 % , e ) 15 %", - "Correct": "b", - "Explanation": "since we were expected to find a percentage figure - it thought that it might be easier to pick a ' smart number ' to represent the total number of voters ( republicans and democrats ) . therefore , i picked 100 ( as the total number of voters ) and thus 60 : 40 represents the number ratio of republicans : democrats . if 70 % of republicans ( which is ( 60 * 0.7 ) = 42 ) and 25 % of democrats ( 40 * 0.25 = 10 ) voted for candidate x , means that out of total of 100 voters ; 52 ( 42 + 10 ) voters voted for candidate x and 48 voted for candidate y . thus we can infer that candidate x is expected to win the election by 4 ( 52 - 48 ) votes . therefore candidate x is expected to win the election by ( 4 / 100 ) votes which is equivalent to 4 % . i think the answer is b ." - }, - { - "Answer": 8, - "Options": "a ) 18 , b ) 28 , c ) 32 , d ) 56 , e ) 8", - "Correct": "e", - "Explanation": "\"let the number of sheeps and horses be 1 x and 7 x . now total number of horses = total consumption of horse food / consumption per horse = 12880 / 230 = 56 , which is equal to 7 x . = > x = 8 sheeps = 1 x = 1 * 8 = 8 . hence e\"" - }, - { - "Answer": 7, - "Options": "a ) 9 , b ) 5 , c ) 6 , d ) 7 , e ) 8", - "Correct": "d", - "Explanation": "we have to calculate it manually . odd 1,3 , 5,7 , 9,11 , 13,15 , 17,19 prime 2,3 , 5,7 , 11,13 , 17,19 common 3 , 5,7 , 11,13 , 17,19 total no . 7 answer d" - }, - { - "Answer": 15, - "Options": "a ) 12 , b ) 15 , c ) 20 , d ) 24 , e ) 30", - "Correct": "b", - "Explanation": "\"let x be the number of new boarders . the ratio changed from 2 : 5 = 4 : 10 up to 1 : 2 = 5 : 10 . 60 / ( 60 + x ) = 4 / 5 x = 15 the answer is b .\"" - }, - { - "Answer": 300, - "Options": "a ) 100 , b ) 250 , c ) 260 , d ) 300 , e ) 350", - "Correct": "d", - "Explanation": "let the number of girls and boys be 5 x and 8 x . total number of students = 13 x = 13 x 32 = 416 . answer : d" - }, - { - "Answer": 4, - "Options": "a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10", - "Correct": "b", - "Explanation": "venn diagrams are useful for multiple values of a single variable e . g . state of mind - happy / sad / neither . when you have two or more variables such as here where you have gender - boy / girl too , it becomes unwieldy . in this case , either use the table or logic . table method is shown above ; here is how you will use logic : there are 6 happy boys . there are 4 sad girls but total 10 sad children . so rest 6 sad children must be sad boys . we have 6 happy boys and 6 sad boys . total we have 16 boys . so 16 - 6 - 6 = 4 boys must be neither happy nor sad . answer ( b )" - }, - { - "Answer": 24, - "Options": "a ) 22 , b ) 24 , c ) 77 , d ) 266 , e ) 182", - "Correct": "b", - "Explanation": "\"present age is 4 x and 3 x , = > 4 x + 6 = 38 = > x = 8 so deepak age is = 3 ( 8 ) = 24 answer : b\"" - }, - { - "Answer": 300, - "Options": "a ) rs . 200 , b ) rs . 250 , c ) rs . 300 , d ) rs . 150 , e ) none of these", - "Correct": "c", - "Explanation": "\"explanation : let the cost of one pen is \u2018 5 x \u2019 and pencil is \u2018 x \u2019 3 x 5 x + 5 x = rs . 100 15 x + 5 x = rs . 100 x = 100 / 20 = 5 : . cost of 1 pen = 5 x = 5 x 5 = 25 : . cost of 12 pens , i . e . ( one dozen ) = 25 x 12 = rs . 300 answer : option c\"" - }, - { - "Answer": 5, - "Options": "a ) 13 , b ) 14 , c ) 5 , d ) 6 , e ) 7", - "Correct": "c", - "Explanation": "integers having even number of factors will be perfect squares . even numbers will have even perfect squares . thus , the possible values for the perfect squares are : 4 , 16,36 , 64,100 and the corresponding integers are 2 , 4,6 , 8,10 ( more than 4 ) . thus c is the correct answer ." - }, - { - "Answer": 24, - "Options": "a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28", - "Correct": "c", - "Explanation": "\"the total number of people are x females + 2 x males . 3 * ( x - 4 ) = 2 x - 4 x = 8 there were 3 x = 24 people at the party originally . the answer is c .\"" - }, - { - "Answer": 0.46153846153846156, - "Options": "a ) 2 / 7 , b ) 3 / 10 , c ) 5 / 11 , d ) 6 / 13 , e ) 11 / 21", - "Correct": "d", - "Explanation": "\"the total number of ways to draw two balls is 13 c 2 = 78 the number of ways to draw two green balls is 6 c 2 = 15 the number of ways to draw two white balls is 7 c 2 = 21 p ( two balls of the same colour ) = 36 / 78 = 6 / 13 the answer is d .\"" - }, - { - "Answer": 12, - "Options": "a ) 12 , b ) 15 , c ) 10 , d ) 20 , e ) 8", - "Correct": "a", - "Explanation": "x = { 1,2 , 3,4 , 5,6 , 7 , 8 , 9 , 10 , 11 , 12 } y = { 0 , 1,2 , 3,4 , 5,6 , 7 , 8 , 9 , 10 , 11,12 , 13,14 , 15,16 , 17,18 , 19,20 } common elements = { 1,2 , 3,4 , 5,6 , 7,8 , 9,10 , 11,12 } = 12 elements answer : option a ." - }, - { - "Answer": 20, - "Options": "a ) 20 , b ) 32 , c ) 33 , d ) 34 , e ) 35", - "Correct": "a", - "Explanation": "\"multiples of 2 from 69 to 99 = multiples of 2 from 1 to 99 - multiples of 2 from 1 to 68 = [ 99 / 2 ] - [ 68 / 2 ] = 49 - 34 = 15 multiples of 3 from 69 to 99 = multiples of 3 from 1 to 99 - multiples of 3 from 1 to 68 = [ 99 / 3 ] - [ 68 / 3 ] = 33 - 23 = 10 multiples of 2 and 3 bothi . e . 6 from 69 to 99 = multiples of 6 from 1 to 99 - multiples of 6 from 1 to 68 = [ 99 / 6 ] - [ 68 / 6 ] = 16 - 11 = 5 these 8 numbers have been counted twice in both the above calculation while calculating multiples of 2 and 3 i . e . total numbers in w = 15 + 10 - 5 = 20 answer option a\"" - }, - { - "Answer": 9, - "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", - "Correct": "c", - "Explanation": "\"let x play both badminton and tennis so 18 - x play only badminton and 19 - x play only tennis . 2 play none and there are total 30 students . hence , ( 18 - x ) + ( 19 - x ) + x + 2 = 30 39 - 2 x + x = 30 39 - x = 30 x = 9 so 9 members play both badminton and tennis . c\"" - }, - { - "Answer": 40, - "Options": "a ) 38 , b ) 39 , c ) 40 , d ) 41 , e ) 42", - "Correct": "c", - "Explanation": "\"there were 16 items sold at a higher price than the radio and 23 items sold at a lower price than the radio . including the radio , there were 16 + 23 + 1 = 40 items sold . the answer is c .\"" - }, - { - "Answer": 4500, - "Options": "a ) s . 800 , b ) s . 2400 , c ) s . 4000 , d ) s . 3200 , e ) s . 4500", - "Correct": "e", - "Explanation": "\"let the income of p 1 and p 2 be rs . 5 x and rs . 4 x respectively and let their expenditures be rs . 3 y and 2 y respectively . then , 5 x \u2013 3 y = 1800 \u2026 ( i ) and 4 x \u2013 2 y = 1800 \u2026 \u2026 . . ( ii ) on multiplying ( i ) by 2 , ( ii ) by 3 and subtracting , we get : 2 x = 1800 - > x = 900 p 1 \u2019 s income = rs 5 * 900 = rs . 4500 answer : e\"" - }, - { - "Answer": 18, - "Options": "a ) 18 , b ) 20 , c ) 21 , d ) 22 , e ) 25", - "Correct": "a", - "Explanation": "18 boys play something . if b play both , then 13 + 15 - b = 18 answer is a" - }, - { - "Answer": 195, - "Options": "a ) 187 , b ) 190 , c ) 192 , d ) 195 , e ) 213", - "Correct": "d", - "Explanation": "the committee of 4 persons is to be so formed that it has at least 1 woman the different ways that we can choose to form such a committee are : ( i ) lw . 3 m in t 6 x 5 x 4 ' x 6 c 3 = 4 x \u2014 \u2014 80 3 x 2 x 1 x 6 c 2 = 42 : : x 26 : : = 90 ( ii ) 2 w . 2 m in \u00b0 c 2 ( iii ) 3 w . 1 m in 4 c 3 x 6 c 1 = 4 x 6 = 24 ( iv ) 4 w in 6 c 4 = 1 total no . of different ways in which a committee of 4 persons can be formed so that it has at least one woman . = 80 + 90 + 24 + 1 = 195 d" - }, - { - "Answer": 0.43100000000000005, - "Options": "a ) 45 / 21 , b ) 46 / 2 , c ) 13 / 30 , d ) 23 / 6 , e ) 4 / 6", - "Correct": "c", - "Explanation": "\"red : blue = 7 : 3 let red = 7 x and blue = 3 x 1 / 3 of red are left handed = > 1 / 3 * 7 x = 7 x / 3 red left handed 2 / 3 of blue are left handed = > 2 / 3 * 3 x = 6 x / 3 blue left handed fraction of participants who are left handed = total left handed / total participants = ( red left handed + blue left handed ) / total participants = ( 7 x / 3 + 6 x / 3 ) / ( 7 x + 3 x ) = 13 / 30 answer : c\"" - }, - { - "Answer": 5, - "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 12 , e ) 14", - "Correct": "a", - "Explanation": "say x students brought both fruits . ( 12 - x ) + ( 8 - x ) = 10 - - > x = 5 . answer : a ." - }, - { - "Answer": 15, - "Options": "a ) 14 , b ) 15 , c ) 20 , d ) 22 , e ) 24", - "Correct": "b", - "Explanation": "\"explanation : present age is 4 x and 3 x , = > 4 x + 6 = 26 = > x = 5 so deepak age is = 3 ( 5 ) = 15 option b\"" - }, - { - "Answer": 0.9375, - "Options": "a ) 15 / 16 , b ) 1 / 16 , c ) 7 / 8 , d ) 9 / 8 , e ) none of these", - "Correct": "a", - "Explanation": "explanation : a and b win a prize , only if both a and b select the number . so , if a chooses a number , b has to select the same number . hence , it is problem on dependent event . let a select a number . , then p ( a ) = 1 / 16 = probability of a . now , b selects the same number after a has already selected that number . then , p ( b / a ) = 1 / 1 = dependent probability of b given a has occurred . p ( ab ) = probability of winning a prize by both a and b is : - = > p ( a ) x p ( ab ) . = > ( 1 / 16 ) x 1 = 1 / 16 . hence , the probability of not winning a prize is : - = 1 - ( 1 / 16 ) . = 15 / 16 . answer : a" - }, - { - "Answer": 30, - "Options": "a ) 30 , b ) 50 , c ) 70 , d ) 80 , e ) 90", - "Correct": "a", - "Explanation": "\"let x be the number of new boarders . the ratio changed from 5 : 12 up to 1 : 2 = 6 : 12 . 150 / ( 150 + x ) = 5 / 6 x = 30 the answer is a .\"" - }, - { - "Answer": 36, - "Options": "a ) 9 , b ) 15 , c ) 36 , d ) 45 , e ) none", - "Correct": "c", - "Explanation": "solution : let two numbers be 4 x and 5 x ; their lcm = 180 and hcf = x ; now , 1 st number * 2 nd number = lcm * hcf or , 4 x * 5 x = 180 * x ; or , 20 x = 180 ; or , x = 9 ; then , the smaller number = 4 * 9 = 36 . answer : option c" - }, - { - "Answer": 84.00000000000004, - "Options": "a ) 24 , b ) 48 , c ) 84 , d ) 72 , e ) 80", - "Correct": "c", - "Explanation": "ok let me see if i can explain what went on in the previous post lets say i have x marbles in the bag in total - - > out of them 12 are red so the probability of pulling a non - red marble is ( x - 12 ) / x now the marble is placed back in the bag and we have x marbles again , of which again 12 are red . so the probability of pulling a non - red marble out is ( x - 12 ) / x probability theorm states that if the probability of event a occuring is m and the probability of event b occuring is n then the probability of both a and b occuring is m * n so therefore the probability of 2 non - red marbles getting pulled out is [ ( x - 12 ) / x ] * [ ( x - 12 ) / x ] this is given as 36 / 49 - - > ( x - 12 ) ^ 2 = 36 / 49 x ^ 2 square rooting u have x - 12 / x = 6 / 7 or 7 x - 6 x = 84 or x = 84 c" - }, - { - "Answer": 6, - "Options": "a ) 1 / 6 , b ) 2 , c ) 5 / 2 , d ) 6 , e ) 32", - "Correct": "d", - "Explanation": "using the identity ( loga b ) ( logb c ) = loga c repeatedly , we obtain ( log 2 3 ) ( log 3 4 ) ( log 4 5 ) . . . ( log 63 64 ) = log 2 64 = 6 correct answer d" - }, - { - "Answer": 572, - "Options": "a ) 110 , b ) 330 , c ) 572 , d ) 430 , e ) 880", - "Correct": "c", - "Explanation": "\"students enrolled in biology are 35 % and therefore not enrolled are 65 % . so of 880 is 880 * . 65 = 572 answer is c 572\"" - }, - { - "Answer": 9, - "Options": "a ) 4 , b ) 6 , c ) 9 , d ) 12 , e ) 15", - "Correct": "c", - "Explanation": "\"originally there were 3 k cooks and 11 k waiters . the new ratio is 1 : 5 which equals 3 : 15 . 15 k = 11 k + 12 k = 3 there are 9 cooks . the answer is c .\"" - }, - { - "Answer": 3468, - "Options": "a ) s . 2890 , b ) s . 2330 , c ) s . 1190 , d ) s . 3468 , e ) s . 2680", - "Correct": "d", - "Explanation": "\"ram : gopal = 7 : 17 = 49 : 119 gopal : krishan = 7 : 17 = 119 : 289 ram : gopal : krishan = 49 : 119 : 289 ram : krishan = 49 : 289 thus , 49 : 289 = 588 : n & there n = 289 x 588 / 49 = rs . 3468 answer : d\"" - }, - { - "Answer": 9, - "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12", - "Correct": "b", - "Explanation": "\"let ' s start with 1 apple for $ 0.70 . let ' s subtract $ 0.70 from $ 5.60 until we get a multiple of $ 0.60 . $ 5.60 , $ 4.90 , $ 4.20 = 7 * $ 0.60 the customer purchased 7 bananas and 2 apples . the answer is b .\"" - }, - { - "Answer": 2, - "Options": "a ) 8 , b ) 2 , c ) 10 , d ) 15 , e ) 18", - "Correct": "b", - "Explanation": "total - neither = all air bag + all power windows - both or 65 - neither = 45 + 30 - 12 = 63 . = > neither = 2 , hence b . answer : b" - }, - { - "Answer": 0.65, - "Options": "a ) 0.05 , b ) 0.15 , c ) 0.45 , d ) 0.5 , e ) 0.65", - "Correct": "e", - "Explanation": "\"p ( a or b ) = p ( a ) + p ( b ) - p ( a n b ) 0.8 = 0.4 + p ( b ) - 0.25 p ( b ) = 0.65 ans : e\"" - }, - { - "Answer": 0.7142857142857143, - "Options": "a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 7", - "Correct": "e", - "Explanation": "\"let ' s say that the total original mixture a is 100 ml the original mixture a thus has 60 ml of alcohol out of 100 ml of solution you want to replace some of that original mixture a with another mixture b that contains 25 ml of alcohol per 100 ml . thus , the difference between 60 ml and 25 ml is 35 ml per 100 ml of mixture . this means that every time you replace 100 ml of the original mixture a by 100 ml of mixture b , the original alcohol concentration will decrease by 35 % . the question says that the new mixture , let ' s call it c , must be 35 % alcohol , a decrease of only 25 % . therefore , 25 out of 35 is 5 / 7 and e is the answer .\"" - }, - { - "Answer": 20.000000000000004, - "Options": "a ) 2 % , b ) 5 % , c ) 8 % , d ) 10 % , e ) 20 %", - "Correct": "e", - "Explanation": "\"since we were expected to find a percentage figure - it thought that it might be easier to pick a ' smart number ' to represent the total number of voters ( republicans and democrats ) . therefore , i picked 100 ( as the total number of voters ) and thus 30 : 20 represents the number ratio of republicans : democrats . if 90 % of republicans ( which is ( 60 * 0.9 ) = 54 ) and 15 % of democrats ( 40 * 0.15 = 6 ) voted for candidate x , means that out of total of 100 voters ; 60 ( 54 + 6 ) voters voted for candidate x and 40 voted for candidate y . thus we can infer that candidate x is expected to win the election by 20 ( 60 - 40 ) votes . therefore candidate x is expected to win the election by ( 20 / 100 ) votes which is equivalent to 20 % . i think the answer is e .\"" - }, - { - "Answer": 266.6666666666667, - "Options": "a ) 250 kg , b ) 275 kg , c ) 300 kg , d ) 266.66 kg , e ) none", - "Correct": "d", - "Explanation": "solution : let there is 100 kg of ore . 25 % ore contains 90 % off iron that means 25 kg contains ; 25 * 90 / 100 = 22.5 kg iron . 22.5 kg iron contains 100 kg of ore . then , 1 kg of iron contains = 25 / 100 kg ore ; hence , 60 kg iron contains = 100 * 60 / 22.5 = 266.66 kg ore . answer : option d" - }, - { - "Answer": 420, - "Options": "a ) 170 , b ) 250 , c ) 300 , d ) 560 , e ) 420", - "Correct": "e", - "Explanation": "in 500 consecutive numbers , number of multiples of 10 = 500 / 10 = 50 ( ignore decimals ) in 500 consecutive numbers , number of multiples of 15 = 500 / 15 = 33 number of multiples of 10 * 15 i . e . 150 = 500 / 150 = 3 number of integers from 1 to 500 that are divisible by neither 10 nor by 15 = 500 - ( 50 + 33 - 3 ) { using the concept of sets here ) = 420 answer is e" - }, - { - "Answer": 864.1111111111111, - "Options": "a ) 565 , b ) 856 , c ) 783 , d ) 590 , e ) 300", - "Correct": "b", - "Explanation": "\"in 1000 consecutive numbers , number of multiples of 12 = 1000 / 12 = 83 ( ignore decimals ) in 1000 consecutive numbers , number of multiples of 15 = 1000 / 15 = 66 number of multiples of 12 * 15 i . e . 180 = 1000 / 180 = 5 number of integers from 11 to 1010 that are divisible by neither 12 nor by 15 = 1000 - ( 83 + 66 - 5 ) { using the concept of sets here ) = 856 answer is b\"" - }, - { - "Answer": 10, - "Options": "a ) 2 , b ) 5 , c ) 10 , d ) 16 , e ) 22", - "Correct": "c", - "Explanation": "no of people in oates reunion = 40 no of people in hall reunion = 70 attending both = x all guests attend at least one . therefore , 100 = 40 + 70 - ( both ) both = 10 answer c" - }, - { - "Answer": 9, - "Options": "a ) 4 , b ) 6 , c ) 9 , d ) 12 , e ) 15", - "Correct": "c", - "Explanation": "originally there were 3 k cooks and 8 k waiters . the new ratio is 1 : 4 which equals 3 : 12 . 12 k = 8 k + 12 k = 3 there are 9 cooks . the answer is c ." - }, - { - "Answer": 0.4871794871794872, - "Options": "a ) 3 / 7 , b ) 6 / 11 , c ) 12 / 21 , d ) 19 / 39 , e ) 29 / 49", - "Correct": "d", - "Explanation": "\"the total number of ways to draw two balls is 13 c 2 = 78 the number of ways to draw two green balls is 5 c 2 = 10 the number of ways to draw two white balls is 8 c 2 = 28 p ( two balls of the same colour ) = 38 / 78 = 19 / 39 the answer is d .\"" - }, - { - "Answer": 5, - "Options": "a ) 8 , b ) 5 , c ) 15 , d ) 22 , e ) 6", - "Correct": "b", - "Explanation": "let the two numbers be 6 x and 5 x . let the numbers subtracted to both so that their ratio becomes 5 : 4 be k . ( 6 x - k ) / ( 5 x - k ) = 5 / 4 = > 24 x - 4 k = 25 x - 5 k = > k = x . 6 x - 5 x = 5 = > x = 5 k = x = 5 . answer : b" - }, - { - "Answer": 31500, - "Options": "a ) 24887 , b ) 20778 , c ) 23788 , d ) 31500 , e ) 2811", - "Correct": "d", - "Explanation": "\"explanation : a invested rs . 3500 for 12 months . let b joined with investment x . and he invested for 12 - 10 = 2 months . so there profit ratio = ( 3500 \u00e3 \u2014 12 ) : ( 2 x ) = 2 : 3 \u00e2 \u2021 \u2019 x = 31500 answer : d\"" - }, - { - "Answer": 1728, - "Options": "a ) 6291 , b ) 7292 , c ) 1728 , d ) 1929 , e ) 1727", - "Correct": "c", - "Explanation": "\"no of values n can take is 1 12 ^ 3 = 1728 answer : c\"" - }, - { - "Answer": 180, - "Options": "a ) 80 , b ) 180 , c ) 240 , d ) 360 , e ) 480", - "Correct": "b", - "Explanation": "ratio = 5 : 1 = > 5 x respondents preferred brand x and x preferred brand y since , no . of respondents who preferred brand x = 150 = > 5 x = 150 = > x = 30 hence total no . of respondents = 150 + 30 = 180 hence b is the answer ." - }, - { - "Answer": 230, - "Options": "a ) 276 , b ) 299 , c ) 230 , d ) 345 , e ) 395", - "Correct": "c", - "Explanation": "\"clearly , the numbers are ( 23 x 9 ) and ( 23 x 10 ) . larger number = ( 23 x 10 ) = 230 . answer : option c\"" - }, - { - "Answer": 3.64, - "Options": "a ) 3.64 , b ) 1.75 , c ) 3.52 , d ) 2.72 , e ) none of these", - "Correct": "a", - "Explanation": "\"here ' s how i did it . my notes from reading the problem were : 1 l a = 950 gm 1 l b = 850 gm we are mixing five parts ( 3 parts a plus 2 parts b , 5 parts total ) to get 4 l , so 5 x = 4 - - - > x = 4 / 5 . each part is 4 / 5 of a liter . so if we have 3 parts a , we have 950 * 3 * ( 4 / 5 ) = 2280 if we have 2 parts b , we have 850 * 2 * ( 4 / 5 ) = 1360 2280 + 1360 = 3640 solving for units gives us 3.64 so the answer is a\"" - }, - { - "Answer": 32, - "Options": "a ) 28 , b ) 26 , c ) 24 , d ) 32 , e ) 30", - "Correct": "d", - "Explanation": "\"lets work with the data given to us . we know that there ratio of cats to dogs is 3 : 4 or cats 3 dogs 4 we can write number of cats as 3 x and number of dogs as 4 x and we know that 4 x - 3 x = 8 ( therefore x = 8 ) then # of dogs = 4 x 8 = 32 answer is d\"" - }, - { - "Answer": 10, - "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", - "Correct": "d", - "Explanation": "\"let the number of people to choose from = n no of people to be chosen = 2 the number of ways 2 people can be chosen from n people = nc 2 now , the two people selected can be arranged in 2 ! ways hence nc 2 * 2 ! = 90 which gives n = 10 answer : d\"" - }, - { - "Answer": 0.6666666666666664, - "Options": "a ) 1 / 4 , b ) 2 / 5 , c ) 1 / 2 , d ) 3 / 5 , e ) 2 / 3", - "Correct": "e", - "Explanation": "you can simply use this formula to avoid confusion : w 1 / w 2 = ( a 2 - aavg ) / ( avg - a 1 ) here is how you will find the values of a 1 an a 2 . we have an overall loss ( average loss ) . the average loss is 4 kg when 40 kg alloy is immersed . this is a loss of ( 4 / 40 ) * 100 = 10 % . this is aavg the loss of tin is 1.375 kg for every 10 kg . this means it loses ( 1.375 / 10 ) * 100 = 13.75 % of its weight in water . this is a 1 . the loss of silver is . 375 kg for every 5 kg . this means it loses ( . 375 / 5 ) * 100 = 7.5 % of its weight in water . this is a 2 . weight of tin / weight of silver = ( silver ' s loss - avg loss ) / ( avg loss - tin ' s loss ) x / y = ( 7.5 - 10 ) / ( 10 - 13.75 ) = 2 / 3 e" - }, - { - "Answer": 10, - "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", - "Correct": "d", - "Explanation": "\"let x play both badminton and tennis so 17 - x play only badminton and 19 - x play only tennis . 2 play none and there are total 30 students . hence , ( 17 - x ) + ( 19 - x ) + x + 2 = 28 38 - 2 x + x = 28 38 - x = 28 x = 10 so 8 members play both badminton and tennis . d\"" - }, - { - "Answer": 7, - "Options": "a ) 2 , b ) 7 , c ) 10 , d ) 16 , e ) 22", - "Correct": "b", - "Explanation": "no of people in oates reunion = 42 no of people in yellow reunion = 65 attending both = x all guests attend at least one . therefore , 100 = 42 + 65 - ( both ) both = 7 answer b" - }, - { - "Answer": 0.7777777777777779, - "Options": "a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 7 / 9", - "Correct": "e", - "Explanation": "let ' s say that the total original mixture a is 100 ml the original mixture a thus has 70 ml of alcohol out of 100 ml of solution you want to replace some of that original mixture a with another mixture b that contains 25 ml of alcohol per 100 ml . thus , the difference between 70 ml and 25 ml is 45 ml per 100 ml of mixture . this means that every time you replace 100 ml of the original mixture a by 100 ml of mixture b , the original alcohol concentration will decrease by 45 % . the question says that the new mixture , let ' s call it c , must be 35 % alcohol , a decrease of only 35 % . therefore , 35 out of 45 is 7 / 9 and e is the answer ." - }, - { - "Answer": 10, - "Options": "a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10", - "Correct": "e", - "Explanation": "\"venn diagrams are useful for multiple values of a single variable e . g . state of mind - happy / sad / neither . when you have two or more variables such as here where you have gender - boy / girl too , it becomes unwieldy . in this case , either use the table or logic . table method is shown above ; here is how you will use logic : there are 6 happy boys . there are 4 sad girls but total 10 sad children . so rest 6 sad children must be sad boys . we have 6 happy boys and 6 sad boys . total we have 22 boys . so 22 - 6 - 6 = 10 boys must be neither happy nor sad . answer ( e )\"" - }, - { - "Answer": 21, - "Options": "a ) 22 , b ) 15 , c ) 77 , d ) 21 , e ) 182", - "Correct": "d", - "Explanation": "\"present age is 4 x and 3 x , = > 4 x + 6 = 34 = > x = 7 so deepak age is = 3 ( 7 ) = 21 answer : d\"" - }, - { - "Answer": 4, - "Options": "a ) 4 , b ) 3 , c ) 14 , d ) 20 , e ) 28", - "Correct": "a", - "Explanation": "\"we are told that all of the letters contain either a dot or a straight line or both , which implies that there are no letters without a dot and a line ( no line / no dot box = 0 ) . first we find the total # of letters with lines : 20 + 36 = 56 ; next , we find the total # of letters without line : 60 - 56 = 4 ; finally , we find the # of letters that contain a dot but do not contain a straight line : 4 - 0 = 4 .\"" - }, - { - "Answer": 3, - "Options": "a ) 3 , b ) 8 , c ) 10 , d ) 12 , e ) 15", - "Correct": "a", - "Explanation": "we are given that the ratio of students to teacher is 50 to 1 . we can rewrite this using variable multipliers . students : teachers = 50 x : x we are next given that student enrollment increases by 50 and the number of teachers increases by 5 . with this change the new ratio becomes 25 to 1 . we can put all this into an equation : students / teachers \uf0e0 25 / 1 = ( 30 x + 50 ) / ( x + 5 ) if we cross multiply we have : 25 ( x + 5 ) = 50 x + 50 25 x + 125 = 50 x + 50 3 = x since x is the present number of teachers , currently there are 3 teachers . answer a ." - }, - { - "Answer": 94, - "Options": "a ) 90 , b ) 91 , c ) 94 , d ) none , e ) 95", - "Correct": "c", - "Explanation": "380 ! has 380 / 5 + 380 / 5 ^ 2 + 380 / 5 ^ 3 = 76 + 15 + 3 = 94 trailing zeros ( take only the quotient into account ) . answer : c ." - }, - { - "Answer": 5, - "Options": "a ) a ) 15 , b ) b ) 20 , c ) c ) 30 , d ) d ) 40 , e ) e ) 5", - "Correct": "e", - "Explanation": "\"80 = at least one of soap a or b both brands = x brand b = 3 x = > 60 + x + 3 x = 120 = > 4 x = 20 = > x = 5 answer - e\"" - }, - { - "Answer": 3, - "Options": "a ) 10 , b ) 3 , c ) 5 , d ) 7 , e ) 8", - "Correct": "b", - "Explanation": "\"explanation : present age is 4 x and 3 x , = > 4 x + 22 = 26 = > x = 1 so deepak age is = 3 ( 1 ) = 3 answer : option b\"" - }, - { - "Answer": 14, - "Options": "a ) 10 , b ) 12 , c ) 15 , d ) 14 , e ) 9", - "Correct": "d", - "Explanation": "\"let the numbers be x , 2 x , 3 x then , x ^ 2 + 4 x ^ 2 + 9 x ^ 2 = 2744 14 x ^ 2 = 2744 x ^ 2 = 196 x = 14 answer is d\"" - }, - { - "Answer": 0.28, - "Options": "a ) 1 / 10 , b ) 3 / 10 , c ) 1 / 2 , d ) 7 / 25 , e ) 9 / 10", - "Correct": "d", - "Explanation": "\"c + m + b - cm - mb - cb - 2 cmb = 100 c - cake buyers , m - muffin and b - bread buyers . cm , mb , cb and cmb are intersecting regions . the question asks for people who have bought only bread mixes = b - cb - mb - 2 cmb has to be found out . 50 + 40 + b - cb - mb - 18 - 2 cmb = 100 b - cb - mb - 2 cmb = 28 hence the probability = 28 / 100 = 7 / 25 . d\"" - }, - { - "Answer": 2000, - "Options": "a ) rs . 3600 , b ) rs . 3603 , c ) rs . 2000 , d ) rs . 3632 , e ) rs . 3602", - "Correct": "c", - "Explanation": "\"let the income and the expenditure of the person be rs . 9 x and rs . 8 x respectively . income , 9 x = 18000 = > x = 2000 savings = income - expenditure = 9 x - 8 x = x so , savings = rs . 2000 answer : c\"" - }, - { - "Answer": 10, - "Options": "a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14", - "Correct": "c", - "Explanation": "\"26 + 20 - 17 = 29 39 - 29 = 10 play neither answer is c\"" - }, - { - "Answer": 5500, - "Options": "a ) s . 800 , b ) s . 2400 , c ) s . 4000 , d ) s . 5500 , e ) s . 4200", - "Correct": "d", - "Explanation": "\"let the income of p 1 and p 2 be rs . 5 x and rs . 4 x respectively and let their expenditures be rs . 3 y and 2 y respectively . then , 5 x \u2013 3 y = 2200 \u2026 ( i ) and 4 x \u2013 2 y = 2200 \u2026 \u2026 . . ( ii ) on multiplying ( i ) by 2 , ( ii ) by 3 and subtracting , we get : 2 x = 2200 - > x = 1100 p 1 \u2019 s income = rs 5 * 1100 = rs . 5500 answer : d\"" - }, - { - "Answer": 322, - "Options": "a ) 276 , b ) 299 , c ) 312 , d ) 322 , e ) none", - "Correct": "d", - "Explanation": "\"solution clearly , the numbers are ( 23 x 13 ) and ( 23 x 14 ) . larger number = ( 23 x 14 ) = 322 . answer d\"" - }, - { - "Answer": 30, - "Options": "a ) 24 , b ) 28 , c ) 30 , d ) 32 , e ) 34", - "Correct": "c", - "Explanation": "french class + spanish class = 42 students . six students are in both classes so they were counted twice . the number of students taking just one class is 42 - 2 ( 6 ) = 30 . the answer is c ." - }, - { - "Answer": 45, - "Options": "a ) 45 , b ) 50 , c ) 88 , d ) 52 , e ) 12", - "Correct": "a", - "Explanation": "\"5 : 1 = x : 9 x = 45 answer : a\"" - }, - { - "Answer": 2000, - "Options": "a ) s 1200 , b ) s 1500 , c ) s 1600 , d ) s 2000 , e ) s 1700", - "Correct": "d", - "Explanation": "\"explanation : let p = faruk , q = vasim , r = ranjith let p = 3 x , q = 3 x and r = 7 x . then , 5 x = 1500 ? x = 500 . p = 1500 , q = 1500 and r = 3500 . hence , ( r - p ) = ( 3500 - 1500 ) = 2000 answer : d\"" - }, - { - "Answer": 35, - "Options": "a ) 6 cm , b ) 12 cm , c ) 35 cm , d ) 44 cm , e ) none of these", - "Correct": "c", - "Explanation": "explanation : length of ribbon originally = 55 cm let the original length be 11 x and reduced length be 7 x . but 11 x = 55 cm x = 55 / 11 cm = 5 cm therefore , reduced length = 7 x cm = 7 5 cm = 35 cm answer : c" - }, - { - "Answer": 0.6, - "Options": "a ) 0.45 , b ) 0.4 , c ) 0.5 , d ) 0.05 , e ) 0.6", - "Correct": "e", - "Explanation": "we are apply that formula . . . . . . . . . . . . . . p ( aorb ) = p ( a ) + p ( b ) - p ( a and b ) = . 25 + . 30 - . 15 = . 40 but the probability of neither a nor b = 1 - . 40 = 0.60 answer : e" - }, - { - "Answer": 6, - "Options": "a ) 18 , b ) 16 , c ) 12 , d ) 10 , e ) 6", - "Correct": "e", - "Explanation": "{ total } = { writers } + { editors } - { both } + { neither } . { total } = 90 ; { writers } = 45 ; { editors } > 38 ; { both } = x ; { neither } = 2 x ; 90 = 45 + { editors } - x + 2 x - - > x = 45 - { editors } . we want to maximize x , thus we should minimize { editors } , minimum possible value of { editors } is 39 , thus x = { both } = 45 - 39 = 6 . answer : e ." - }, - { - "Answer": 24, - "Options": "a ) 4 , b ) 6 , c ) 12 , d ) 24 , e ) 30", - "Correct": "d", - "Explanation": "\"assume the integers to be x and y , where x < y given x / y = 1 / 4 - ( i ) or y = 4 x and x + 6 / y = 1 / 2 - ( ii ) or y = 2 x + 12 substituting the value of y from ( i ) , 4 x = 2 x + 12 x = 6 hence y = 4 * 6 = 24 answer d\"" - }, - { - "Answer": 4, - "Options": "a ) 4 , b ) 2 , c ) 3 , d ) 5 , e ) 6", - "Correct": "a", - "Explanation": "\"explanation : l . c . m of 6440 = 2 x 2 x 2 x 5 x 7 x 23 2 , 5 , 7,23 number of different prime factors is 4 . answer : option a\"" - }, - { - "Answer": 0.5, - "Options": "a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 3 / 4", - "Correct": "a", - "Explanation": "n ( s ) = one of her child is boy out of 2 children = bb , bg = 2 n ( e ) = both are boys = bb = 1 so p = n ( e ) / n ( s ) = 1 / 2 answer : a" - }, - { - "Answer": 3.62, - "Options": "a ) 3.69 , b ) 3.66 , c ) 3.6 , d ) 3.62 , e ) 3.61", - "Correct": "d", - "Explanation": "\"ans : by framing equations we get 30 l + 3 q = 11.67 30 l + 6 q = 12.48 eliminate q by multiplying the first equation by 2 and subtracting second equation from the first then we get l = 0.362 cost of 10 kgs of apples = 0.362 x 10 = 3.62 answer : d\"" - }, - { - "Answer": 434, - "Options": "a ) 430 , b ) 434 , c ) 438 , d ) 444 , e ) 446", - "Correct": "b", - "Explanation": "\"312 + 234 - 112 ( since 112 is counted twice ) = 434 b is the answer\"" - }, - { - "Answer": 9, - "Options": "a ) 8 , b ) 10 , c ) 9 , d ) 14 , e ) 16", - "Correct": "c", - "Explanation": "\"solution - consider multiples of 25 ! = > 3 , 6,9 , 12,15 , 18,21 count no . of 3 in each multiple . 3 = 3 x 1 - > 1 6 = 3 x 2 - > 1 9 = 3 x 3 - > 2 12 = 3 x 4 - > 1 15 = 3 x 5 - > 1 18 = 3 x 3 x 2 - > 2 21 = 3 x 7 - > 1 - - - - count 3 ' s = 9 so answer is 9 answer : c\"" - }, - { - "Answer": 4335, - "Options": "a ) s . 4335 , b ) s . 2330 , c ) s . 1190 , d ) s . 1620 , e ) s . 2680", - "Correct": "a", - "Explanation": "ram : gopal = 7 : 17 = 49 : 119 gopal : krishan = 7 : 17 = 119 : 289 ram : gopal : krishan = 49 : 119 : 289 ram : krishan = 49 : 289 thus , 49 : 289 = 735 : n & there n = 289 x 735 / 49 = rs . 4335 answer : a" - }, - { - "Answer": 0.0859375, - "Options": "a ) 13 / 128 , b ) 12 / 128 , c ) 11 / 126 , d ) 11 / 127 , e ) 11 / 128", - "Correct": "e", - "Explanation": "n ( t ) = 720 n ( e ) = 562 n ( t ^ e ) = 346 n ( tue ) = 720 + 562 - 346 = 936 now , n ( h ) = 1024 - 936 = 88 p ( h ) = 88 / 1024 = 11 / 128 = 0.085 answer : e" - }, - { - "Answer": 109395, - "Options": "a ) 104345 , b ) 107375 , c ) 108385 , d ) 109395 , e ) 105355", - "Correct": "d", - "Explanation": "the only thing you actually know about the correct number f is that it is divisible by 153 and has 5 as a factor . you should immediately try to find the factors of 153 and look for them in the options . 153 = 9 * 17 divisibility by 9 is easy to check . only ( d ) satisfies ." - }, - { - "Answer": 44, - "Options": "a ) 24 kg , b ) 44 kg , c ) 20 kg , d ) 30 kg , e ) 52 kg", - "Correct": "b", - "Explanation": "quantity of tin in 60 kg of a = 60 * 2 / 5 = 24 kg quantity of tin in 100 kg of b = 100 * 1 / 5 = 20 kg quantity of tin in the new alloy = 24 + 20 = 44 kg answer is b" - }, - { - "Answer": 104, - "Options": "a ) 84 , b ) 96 , c ) 104 , d ) 112 , e ) 120", - "Correct": "c", - "Explanation": "\"the ratio of yankees : mets : red sox = 6 : 4 : 5 the mets fans are 4 / 15 of the population . ( 4 / 15 ) * 390 = 104 the answer is c .\"" - }, - { - "Answer": 41, - "Options": "a ) 13 , b ) 41 , c ) 47 , d ) 48 , e ) 53", - "Correct": "b", - "Explanation": "\"number of switches = 100 number of switches turned on by a : 3 , 6 , . . . 99 = 33 number of switches turned on by b : 5 , 10 , . . . . 100 = 20 few switches are turned on by a and later turned off by b : lcm ( 3,5 ) = 15 x = 15 , 30 , . . . . 90 = 6 . subtract the above 6 switches from both a and b as they are turned off . number of switches that are turned on = ( 33 - 6 ) + ( 20 - 6 ) = 41 answer : b\"" - }, - { - "Answer": 4, - "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 8 , e ) 15", - "Correct": "b", - "Explanation": "the second digit can only be 3 or 7 , so the choice quickly narrows down to 23 , 27 , 33 , 37 , 53 , 57 , 73 , and 77 . of these , 27 , 33 , and 57 are divisible by 3 , and 77 by 7 , leaving 23 , 37 , 53 , and 73 . it is easy to see that none of these is divisible by 2 , 3 , 5 , or 7 , and there is no need to look at greater prime divisors since root 77 < 11 . correct answer b" - }, - { - "Answer": 276, - "Options": "a ) 338 , b ) 276 , c ) 322 , d ) 231 , e ) 121", - "Correct": "b", - "Explanation": "\"clearly , the numbers are ( 23 * 11 ) and ( 23 * 12 ) . larger number = ( 23 * 12 ) = 276 . answer : b\"" - }, - { - "Answer": 0.23333333333333334, - "Options": "a ) 4 / 11 , b ) 5 / 17 , c ) 6 / 25 , d ) 7 / 30 , e ) 8 / 37", - "Correct": "d", - "Explanation": "\"p ( 1 st ball is even ) = 8 / 16 p ( 2 nd ball is also even ) = 7 / 15 p ( both balls are even ) = 8 / 16 * 7 / 15 = 7 / 30 the answer is d .\"" - }, - { - "Answer": 25, - "Options": "a ) 30 , b ) 22 , c ) 20 , d ) 25 , e ) 100", - "Correct": "d", - "Explanation": "explanation : let pens = 2 x , pencils = 2 x & markers = 5 x . now , 2 x = 10 hence x = 5 . number of markers = 5 x which is 25 . answer : d" - }, - { - "Answer": 2, - "Options": "a ) 29 , b ) 8 , c ) 2 , d ) 4 , e ) 6", - "Correct": "c", - "Explanation": "explanation : vikas ' s rank in the class is 9 . so there are 8 people before him . his rank among boys is 4 . so 3 boys are before him . so there are 8 \u2013 3 = 5 girls before him . tanvi ' s rank among the girls is 8 . so there are 7 girls before her . so number of girls between vikas and tanvi is 7 \u2013 5 = 2 answer : c" - }, - { - "Answer": 1, - "Options": "a ) 9 , b ) 36 , c ) 122 , d ) 6 , e ) 1", - "Correct": "e", - "Explanation": "\"square root is a number times itself square root of 36 = 6 , 6 / 6 = 1 ( e ) 1\"" - }, - { - "Answer": 440, - "Options": "a ) 440 , b ) 520 , c ) 620 , d ) 720 , e ) 820", - "Correct": "a", - "Explanation": "\"explanation : let the boy are 6 x and girls are 5 x = > 5 x = 200 = > x = 40 total students = 6 x + 5 x = 11 x = 11 ( 40 ) = 440 option a\"" - }, - { - "Answer": 600, - "Options": "a ) 462 , b ) 450 , c ) 480 , d ) 504 , e ) 600", - "Correct": "e", - "Explanation": "\"explanation : hcf of the two numbers = 50 hcf will be always a factor of lcm 50 is factor of lcm other two factors are 11 & 12 then the numbers are ( 50 * 11 ) and ( 50 x 12 ) = 550 and 600 answer : option e\"" - }, - { - "Answer": 3, - "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", - "Correct": "a", - "Explanation": "\"explanation : let x is subtracted . then , ( 6 \u2212 x ) / ( 7 \u2212 x ) < 16 / 21 21 ( 6 \u2014 x ) < 16 ( 7 \u2014 x ) = > 5 x > 14 = x > 2.8 least such number is 3 option a\"" - }, - { - "Answer": 0.4897959183673469, - "Options": "a ) 1 / 25 , b ) 12 / 49 , c ) 1 / 4 , d ) 24 / 49 , e ) 1 / 2", - "Correct": "d", - "Explanation": "\"w probability of one party having both spots : ( 1 / 2 ) * ( 24 / 49 ) = 12 / 49 ( 1 / 2 ) or ( 25 / 50 ) because it does not matter which party or which person gets the first spot . ( 24 / 49 ) because after one person from a particular party is chosen , there are 24 members of the same party left out of 49 total candidates . since this result can happen for both parties , ( 12 / 49 ) + ( 12 / 49 ) = ( 24 / 49 ) answer : d\"" - }, - { - "Answer": 80, - "Options": "a ) 70 , b ) 80 , c ) 90 , d ) 100 , e ) 110", - "Correct": "b", - "Explanation": "\"consider total number of reader n ( s u l ) = 400 people who read science fiction n ( s ) = 250 people who read literacy works n ( l ) = 230 both science fiction and literacy n ( s \u2229 l ) = ? n ( s u l ) = n ( s ) + n ( l ) - n ( s \u2229 l ) 400 = 250 + 230 - n ( s \u2229 l ) n ( s \u2229 l ) = 480 - 400 n ( s \u2229 l ) = 80 so people read both science fiction and literacy works are 80 answer : b\"" - }, - { - "Answer": 224, - "Options": "a ) 276 , b ) 299 , c ) 224 , d ) 345 , e ) 365", - "Correct": "c", - "Explanation": "\"clearly , the numbers are ( 16 x 13 ) and ( 16 x 14 ) . larger number = ( 23 x 14 ) = 224 . answer : option c\"" - }, - { - "Answer": 4000, - "Options": "a ) 2000 , b ) 3000 , c ) 4000 , d ) 5000 , e ) 6000", - "Correct": "c", - "Explanation": "\"let the income and the expenditure of the person be rs . 9 x and rs . 7 x respectively . income , 9 x = 36000 = > x = 4000 savings = income - expenditure = 9 x - 8 x = x so , savings = rs . 4000 . answer : c\"" - }, - { - "Answer": 10, - "Options": "a ) 5 : 1 , b ) 10 : 1 , c ) 15 : 1 , d ) 20 : 1 , e ) 25 : 1", - "Correct": "b", - "Explanation": "\"explanation : dog : hare = ( 10 * 2 ) leaps of hare : 2 leaps of hare = 20 : 2 . answer : b ) 10 : 1\"" - }, - { - "Answer": 8, - "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 14", - "Correct": "d", - "Explanation": "say x guests brought both drinks . ( 13 - x ) + ( 14 - x ) = 11 - - > x = 8 . answer : d ." - }, - { - "Answer": 3500, - "Options": "a ) s . 800 , b ) s . 2400 , c ) s . 4000 , d ) s . 3500 , e ) s . 4200", - "Correct": "d", - "Explanation": "\"let the income of p 1 and p 2 be rs . 5 x and rs . 4 x respectively and let their expenditures be rs . 3 y and 2 y respectively . then , 5 x \u2013 3 y = 1400 \u2026 ( i ) and 4 x \u2013 2 y = 1400 \u2026 \u2026 . . ( ii ) on multiplying ( i ) by 2 , ( ii ) by 3 and subtracting , we get : 2 x = 1400 - > x = 700 p 1 \u2019 s income = rs 5 * 700 = rs . 3500 answer : d\"" - }, - { - "Answer": 0.12658227848101267, - "Options": "a ) 11 / 79 , b ) 10 / 79 , c ) 12 / 79 , d ) 13 / 79 , e ) 14 / 79", - "Correct": "b", - "Explanation": "sum of numbers noted on 4 dice ( with six faces ) to be 10 will include combinations : ( 1,1 , 2,6 ) ( 1,1 , 3,5 ) ( 1,1 , 4,4 ) ( 1,1 , 5,3 ) ( 1,1 , 6,2 ) ( 1,2 , 1,6 ) ( 1,2 , 2,5 ) ( 1,2 , 3,4 ) ( 1,2 , 4,3 ) ( 1,2 , 5,2 ) ( 1,2 , 6,1 ) ( 1,3 , 1,5 ) ( 1,3 , 2,4 ) ( 1,3 , 3,3 ) ( 1,3 , 4,2 ) ( 1,3 , 5,1 ) ( 1,4 , 1,4 ) ( 1,4 , 2,3 ) ( 1,4 , 3,2 ) ( 1,4 , 4,1 ) ( 1,5 , 1,3 ) ( 1,5 , 2,2 ) ( 1,5 , 3,1 ) ( 1,6 , 1,2 ) ( 1,6 , 2,1 ) ( 2,1 , 1,6 ) ( 2,1 , 2,5 ) ( 2,1 , 3,4 ) ( 2,1 , 4,3 ) ( 2,1 , 5,2 ) ( 2,1 , 6,1 ) ( 2,2 , 1,5 ) ( 2,2 , 2,4 ) ( 2,2 , 3,3 ) ( 2,2 , 4,2 ) ( 2,2 , 5,1 ) ( 2,3 , 1,4 ) ( 2,3 , 2,3 ) ( 2,3 , 3,2 ) ( 2,3 , 4,1 ) ( 2,4 , 1,3 ) ( 2,4 , 2,2 ) ( 2,4 , 3,1 ) ( 2,5 , 1,2 ) ( 2,5 , 2,1 ) ( 2,6 , 1,1 ) ( 3,1 , 1,5 ) ( 3,1 , 2,4 ) ( 3,1 , 3,3 ) ( 3,1 , 4,2 ) ( 3,1 , 5,1 ) ( 3,2 , 1,4 ) ( 3,2 , 2,3 ) ( 3,2 , 3,2 ) ( 3,2 , 4,1 ) ( 3,3 , 1,3 ) ( 3,3 , 2,2 ) ( 3,3 , 3,1 ) ( 3,4 , 1,2 ) ( 3,4 , 2,1 ) ( 3,5 , 1,1 ) ( 4,1 , 1,4 ) ( 4,1 , 2,3 ) ( 4,1 , 3,2 ) ( 4,1 , 4,1 ) ( 4,2 , 1,3 ) ( 4,2 , 2,2 ) ( 4,2 , 3,1 ) ( 4,3 , 1,2 ) ( 4,3 , 2,1 ) ( 4,4 , 1,1 ) ( 5,1 , 1,3 ) ( 5,1 , 2,2 ) ( 5,1 , 3,1 ) ( 5,2 , 1,2 ) ( 5,2 , 2,1 ) ( 5,3 , 1,1 ) ( 6,1 , 1,2 ) ( 6,1 , 2,1 ) - - - - - - - total 79 combinations with all the numbers lie between 2 and 5 are ( 2,2 , 2,4 ) ( 2,2 , 3,3 ) ( 2,2 , 4,2 ) ( 2,3 , 2,3 ) ( 2,3 , 3,2 ) ( 2,4 , 2,2 ) ( 3,2 , 2,3 ) ( 3,2 , 3,2 ) ( 3,3 , 2,2 ) ( 4,2 , 2,2 ) - - - - - - total 10 so probability = 10 / 79 answer : b" - }, - { - "Answer": 0.15000000000000002, - "Options": "a ) 3 / 20 , b ) 5 / 26 , c ) 7 / 34 , d ) 9 / 37 , e ) 11 / 49", - "Correct": "a", - "Explanation": "\"10 / 25 * 9 / 24 = 3 / 20 the answer is a .\"" - }, - { - "Answer": 376, - "Options": "a ) 188 , b ) 258 , c ) 376 , d ) 470 , e ) 517", - "Correct": "c", - "Explanation": "\"consider 5 x acres of land used for bean consider 2 x acres of land used for wheat consider 4 x acres of land used for corn total given is 1034 acres 11 x = 1034 x = 94 land used for corn y = 4 * 94 = 376 correct option - c\"" - }, - { - "Answer": 22, - "Options": "a ) 6 , b ) 16 , c ) 22 , d ) 30 , e ) 174", - "Correct": "c", - "Explanation": "\"the number of integers that belong to set x only is 16 - 6 = 10 ; the number of integers that belong to set y only is 18 - 6 = 12 ; the number of integers that belong to set x or set y , but not both is 10 + 12 = 22 . answer : c\"" - }, - { - "Answer": 31, - "Options": "a ) 20 , b ) 31 , c ) 9 , d ) 31 , e ) 21", - "Correct": "b", - "Explanation": "\"total people eat veg = only veg + both veg and non veg total = 19 + 12 = 31 answer = b\"" - }, - { - "Answer": 4, - "Options": "a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1", - "Correct": "b", - "Explanation": "factor of 210 = 2 * 3 * 5 * 7 - - - 4 prime numbers b" - }, - { - "Answer": 8, - "Options": "a ) 2 , b ) 3 , c ) 8 , d ) 14 , e ) 56", - "Correct": "c", - "Explanation": "60 n / 4 * 8 should be integer = > 2 * 2 * 3 * 5 * n / 2 * 2 * 2 * 2 * 2 = 3 * 5 * n / 8 must be an integer for this to be true n must multiple of 8 , thus min of n = 8 hence c" - }, - { - "Answer": 0.07142857142857142, - "Options": "a ) 7 / 98 , b ) 1 / 48 , c ) 1 / 98 , d ) 1 / 96 , e ) 3 / 42", - "Correct": "e", - "Explanation": "2 / 3 * 6 / 7 * 1 / 3 * 3 / 8 = 36 / 504 = 3 / 42 answer : e" - }, - { - "Answer": 23, - "Options": "a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24", - "Correct": "d", - "Explanation": "\"this is an example of a standard overlapping sets question . it has no ' twists ' to it , so you ' ll likely find using the overlapping sets formula to be a fairly easy approach . if you ' re not familiar with it , then here is the formula : 50 = 25 + 23 - 21 + ( # in neither group ) = 23 the prompt gives you all of the numbers you need to get to the correct answer . just plug in and solve . d\"" - }, - { - "Answer": 520, - "Options": "a ) 420 , b ) 520 , c ) 620 , d ) 620 , e ) none of these", - "Correct": "b", - "Explanation": "explanation : let the boy are 8 x and girls are 5 x = > 5 x = 200 = > x = 40 total students = 8 x + 5 x = 13 x = 13 ( 40 ) = 520 answer : b" - }, - { - "Answer": 10, - "Options": "a ) 1 , b ) 499 , c ) 500 , d ) 999 , e ) 10", - "Correct": "e", - "Explanation": "since you need 10 digits to represent 1000 numbers in binary , you will need 10 prisoners . now the logic is this : every bottle has a unique number from 1 to 1000 and a unique binary representation from 0000000001 to 1111101000 . now you have 10 prisoners . each bottle will be tasted by the prisoners depending on the binary representation of the bottle . wherever there is 1 , the bottle will be tasted by that prisoner ( assuming units digit represents the 1 st prisoner , tens digit the 2 nd prisoner and so on . . . ) 1 st bottle is 0000000001 so it will be tasted by only the 1 st prisoner . 2 nd bottle is 0000000010 so it will be tasted by only the 2 nd prisoner . 3 rd bottle is 0000000011 so it will be tasted by the 1 st and 2 nd prisoners . and so on . . . 1000 th bottle is 1111101000 so it will be tasted by 4 th , 6 th , 7 th , 8 th , 9 th and 10 th prisoners . at the end of a month , we see which prisoners die . say , only the 3 rd prisoner dies . this means the poisoned bottle number is 0000000100 = 3 . say 1 st , 7 th and 9 th prisoners die . this means the poisoned bottle number is 0101000001 = 321 ans : e" - }, - { - "Answer": 96, - "Options": "a ) 99 , b ) 98 , c ) 97 , d ) 96 , e ) 95", - "Correct": "d", - "Explanation": "\"e = 96 = 3 * 32 = 3 * 2 ^ 5 answer is d .\"" - }, - { - "Answer": 2548, - "Options": "a ) 80 , b ) 160 , c ) 720 , d ) 1100 , e ) 2548", - "Correct": "e", - "Explanation": "\"no . of ways of picking 2 biology books ( from 14 books ) = 14 c 2 = ( 14 * 13 ) / 2 = 91 no . of ways of picking 2 chemistry books ( from 8 books ) = 8 c 2 = ( 8 * 7 ) / 2 = 28 total ways of picking 2 books of each type = 91 * 28 = 2548 ( option e )\"" - }, - { - "Answer": 3.52, - "Options": "a ) 3.84 , b ) 1.75 , c ) 3.52 , d ) 2.72 , e ) none of these", - "Correct": "c", - "Explanation": "\"1 l a = 900 gm 1 l b = 850 gm we are mixing five parts ( 3 parts a plus 2 parts b , 5 parts total ) to get 4 l , so 5 x = 4 - - - > x = 4 / 5 . each ` ` part ' ' is 4 / 5 of a liter . so if we have 3 parts a , we have 900 * 3 * ( 4 / 5 ) = 2160 if we have 2 parts b , we have 850 * 2 * ( 4 / 5 ) = 1360 2160 + 1360 = 3520 solving for units gives us 3.52 so the answer is c\"" - }, - { - "Answer": 12, - "Options": "a ) 6 , b ) 12 , c ) 14 , d ) 16 , e ) 20", - "Correct": "b", - "Explanation": "a : only cats b : both cats and dogs c : only dogs as per question , a + b + c = 30 c = 18 b = 6 , so a = 6 . hence , a + b = 12 . answer is b" - }, - { - "Answer": 0.8333333333333334, - "Options": "a ) 1 / 6 , b ) 2 / 9 , c ) 5 / 6 , d ) 7 / 9 , e ) 8 / 9", - "Correct": "c", - "Explanation": "\"we have three pairs of dogs for the 6 with exactly one littermate , and one triplet , with each having exactly two littermates . so , in fact there are two types of dogs : those with one littermate - say a , and the others with two littermates - b . work with probabilities : choosing two dogs , we can have either one dog of type b or none ( we can not have two dogs both of type b ) . the probability of choosing one dog of type b and one of type a is 3 / 9 * 6 / 8 * 2 = 1 / 2 ( the factor of 2 for the two possibilities ba and ab ) . the probability r of choosing two dogs of type a which are not littermates is 6 / 9 * 4 / 8 = 1 / 3 ( choose one a , then another a which is n ' t the previous one ' s littermate ) . the required probability is 1 / 2 + 1 / 3 = 5 / 6 . find the probability for the complementary event : choose aa or bb . probability of choosing two dogs of type a who are littermates is 6 / 9 * 1 / 8 = 1 / 12 . probability of choosing two dogs of type b ( who necessarily are littermates ) is 3 / 9 * 2 / 8 = 1 / 12 . again , we obtain 1 - ( 1 / 12 + 1 / 12 ) = 5 / 6 . answer : c\"" - }, - { - "Answer": 450, - "Options": "a ) 430 , b ) 440 , c ) 450 , d ) 460 , e ) 470", - "Correct": "c", - "Explanation": "we ' re given a series of facts to work with : 1 ) a certain high school has 500 students . 2 ) of these students : x are taking music , y are taking art , and z are taking both music and art . we ' re asked how many students are taking neither music nor art ? let ' s test x = 40 y = 20 z = 10 so , we have 40 students taking music , 20 taking art and 10 taking both music and art . 30 student taking just music 10 student taking just art 10 student taking both music and art total = 50 students we ' re asked for the total number of students who are taking neither course . that is 500 - 50 = 450 . c" - }, - { - "Answer": 0.25, - "Options": "a ) 1 / 10 , b ) 3 / 10 , c ) 1 / 4 , d ) 7 / 10 , e ) 9 / 10", - "Correct": "c", - "Explanation": "\"c + m + b - cm - mb - cb - 2 cmb = 100 c - cake buyers , m - muffin and b - bread buyers . cm , mb , cb and cmb are intersecting regions . the question asks for people who have bought only bread mixes = b - cb - mb - 2 cmb has to be found out . 50 + 40 + b - cb - mb - 15 - 2 cmb = 100 b - cb - mb - 2 cmb = 25 hence the probability = 25 / 100 = 1 / 4 . c\"" - }, - { - "Answer": 10, - "Options": "a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18", - "Correct": "a", - "Explanation": "16 * 30 = 48 * n n = 10 the answer is a ." - }, - { - "Answer": 600, - "Options": "a ) 420 , b ) 520 , c ) 600 , d ) 720 , e ) 820", - "Correct": "c", - "Explanation": "\"explanation : let the boy are 8 x and girls are 4 x = > 4 x = 200 = > x = 50 total students = 8 x + 4 x = 12 x = 12 ( 50 ) = 600 option c\"" - }, - { - "Answer": 0.75, - "Options": "a ) 0.09 , b ) 0.15 , c ) 0.54 , d ) 0.75 , e ) 0.91", - "Correct": "d", - "Explanation": "according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 22 + 18 + 5 ) / 60 = 45 / 60 = 0.75 . answer : d ." - }, - { - "Answer": 24, - "Options": "a ) 15 kg , b ) 20 kg , c ) 8 kg , d ) 24 kg , e ) 32 kg", - "Correct": "d", - "Explanation": "let the required quantity of copper be x kg 5 : 3 : : 40 : x 5 x = 40 * 3 x = 24 kg answer is d" - }, - { - "Answer": 456, - "Options": "a ) 72 , b ) 192 , c ) 456 , d ) 256 , e ) 264", - "Correct": "c", - "Explanation": "total of 3,200 boards . all that fail verification are indeed faulty . so the 64 are indeed faulty . 1 / 8 those that pass are also faulty . from the 3,200 we know 64 fail . so 3,136 must pass . of these 1 / 8 are faulty . 3,136 divided by 8 gives you 392 . what one must do now is to add to the 392 which were not detected the actually detected faulty ones , namely the 64 . total faulty : 456 . answer : c" - }, - { - "Answer": 8, - "Options": "a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8", - "Correct": "e", - "Explanation": "\"17 + 19 = 36 but where as total number is 30 - 2 = 28 therefore answer is 36 - 28 = 8 hence answer is e\"" - }, - { - "Answer": 3, - "Options": "a ) 3 , b ) 8 , c ) 14 , d ) 20 , e ) 28", - "Correct": "a", - "Explanation": "\"we are told that all of the letters contain either a dot or a straight line or both , which implies that there are no letters without a dot and a line ( no line / no dot box = 0 ) . first we find the total # of letters with lines : 13 + 24 = 37 ; next , we find the total # of letters without line : 40 - 37 = 3 ; finally , we find the # of letters that contain a dot but do not contain a straight line : 3 - 0 = 3 . a\"" - }, - { - "Answer": 210, - "Options": "a ) 209 , b ) 200 , c ) 210 , d ) 225 , e ) 221", - "Correct": "a", - "Explanation": "no of boys = 6 no of girls = 4 therefore , no of ways at least 1 boy can be selected = 6 c 4 * 4 c 0 + 6 c 3 * 4 c 1 + 6 c 2 * 4 c 2 + 6 c 1 * 4 c 3 = 15 + 80 + 90 + 24 = 209 ans - a" - }, - { - "Answer": 4000, - "Options": "a ) $ 1500 , b ) $ 4000 , c ) $ 2000 , d ) $ 2500 , e ) $ 3200", - "Correct": "b", - "Explanation": "let the income of a and b be $ 5 x and $ 4 x let their expenditures be $ 3 y and $ 2 y 5 x - 3 y = 1600 - - - - - - - 1 ) 4 x - 2 y = 1600 - - - - - - - 2 ) from 1 ) and 2 ) x = 800 a ' s income = 5 x = 5 * 800 = $ 4000 answer is b" - }, - { - "Answer": 46, - "Options": "a ) 56 , b ) 46 , c ) 64 , d ) 65 , e ) 10", - "Correct": "b", - "Explanation": "the problem asks for a combination , since order does n ' t matter . now , selecting r items from a set of n gives the combination formula : ncr = n ! / r ! ( n - r ) ! n = 8 r = 3 so , total teams is 8 c 3 = 8 ! / ( 3 ! ( 8 - 3 ) ! ) = 56 , and n = 8 - 3 = 5 r = 3 for teams without a phd is 5 c 3 = 5 ! / ( 3 ! ( 5 - 3 ) ! ) = 10 , so , teams with at least 1 phd = 56 - 10 = 46 answer : b" - }, - { - "Answer": 60, - "Options": "a ) 45 , b ) 50 , c ) 55 , d ) 60 , e ) 63", - "Correct": "d", - "Explanation": "\"f : c : w 1 : 12 : 30 sport version : f : c 3 : 12 f : w 1 : 60 or 3 : 180 so c : f : w = 12 : 3 : 180 c / w = 12 / 180 = 3 ounces / x ounces x = 4 * 180 / 12 = 60 ounces of water d\"" - }, - { - "Answer": 8, - "Options": "a ) 8 , b ) 12 , c ) 15 , d ) 16 , e ) 18", - "Correct": "a", - "Explanation": "16 + 2 + 24 + x = 50 42 + x = 50 x = 8 students a )" - }, - { - "Answer": 616, - "Options": "a ) 620 , b ) 630 , c ) 616 , d ) 600 , e ) 650", - "Correct": "c", - "Explanation": "\"we know 37.5 % people study biology , therefore the no of people not studying = 100 - 30 = 70 % > therefore the people not studying biology out of a total 880 people are = 70 % of 880 > ( 70 / 100 ) * 880 = 616 people c\"" - }, - { - "Answer": 12, - "Options": "a ) 12 , b ) 15 , c ) 20 , d ) 22 , e ) 23", - "Correct": "a", - "Explanation": "\"explanation : present age is 4 x and 3 x , = > 4 x + 10 = 26 = > x = 4 so deepak age is = 3 ( 4 ) = 12 answer : option 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 , z = 1000 purchased a only . ( this is much simpler to solve using the venn diagram ) . correct answer is d . 1000\"" - }, - { - "Answer": 330, - "Options": "a ) 330 , b ) 340 , c ) 350 , d ) 360 , e ) 370", - "Correct": "a", - "Explanation": "1 11 21 . . . . . . . 91 2 12 22 . . . . . . . . 92 3 13 23 . . . . . . . . 93 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . there are total 20 occurrence of 6 . once place at 6 th row in every column and tens place in 6 th column and diff of 6 and 9 is 3 so 3 * 1 * 10 + 3 * 10 * 10 = 330 answer : a" - }, - { - "Answer": 15, - "Options": "a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 35", - "Correct": "a", - "Explanation": "\"product of two no = lcm * hcf 3 x * 4 x = 180 * x x = 15 answer : a\"" - }, - { - "Answer": 368, - "Options": "a ) 338 , b ) 278 , c ) 322 , d ) 368 , e ) 121", - "Correct": "d", - "Explanation": "clearly , the numbers are ( 23 * 15 ) and ( 23 * 16 ) . larger number = ( 23 * 16 ) = 368 . answer : d" - }, - { - "Answer": 24, - "Options": "a ) 12 , b ) 14 , c ) 15 , d ) 24 , e ) 36", - "Correct": "d", - "Explanation": "\"the number of women doubled means that they have become 24 from 12 . . and we have to tell the current strength so 24 is the answer . . let the number be 4 x and 5 x . . given 4 x + 2 = 14 . . so x = 3 . . women number = 5 * 3 - 3 = 12 , then doubled = 24 . . ans d\"" - }, - { - "Answer": 0.4666666666666667, - "Options": "a ) 1 / 5 , b ) 2 / 22 , c ) 3 / 4 , d ) 7 / 15 , e ) 5 / 6", - "Correct": "d", - "Explanation": "\"p : 2 / 3 = 3 / 5 : 6 / 7 as the product of the means is equal to the product of the extremes . p * 6 / 7 = 2 / 3 * 3 / 5 p * 6 / 7 = 6 / 15 p = 7 / 15 = > p = 7 / 15 answer : d\"" - }, - { - "Answer": 20, - "Options": "a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 21", - "Correct": "d", - "Explanation": "let x brainiacs like only rebus teasers and y brainiacs like only math teasers . now , x + y = 100 - 18 - 4 = 78 . also given that , x + 18 = 2 ( y + 18 ) x = 2 y + 18 . 78 - y = 2 y + 18 3 y = 60 y = 20 so 20 brainiacs like math teasers but not rebus teasers answer : d" - }, - { - "Answer": 16, - "Options": "a ) 12 , b ) 15 , c ) 16 , d ) 20 , e ) 25", - "Correct": "c", - "Explanation": "10 litres of mixture that is replaced will contain 8 litres of a and 2 litres of b ( as a : b = 4 : 1 ) let the initial volume of the mixture be 4 k + 1 k = 5 k so by condition , [ 4 k - 8 ] / [ k - 2 + 10 ] = 2 / 3 solve for k which is k = 4 so initial volume of liquid a = 4 k = 16 litres answer : c" - }, - { - "Answer": 0.1724137931034483, - "Options": "a ) 1 / 29 , b ) 2 / 29 , c ) 3 / 29 , d ) 4 / 29 , e ) 5 / 29", - "Correct": "e", - "Explanation": "suppose that the fraction of red m & ms is fr and the fraction of blue m & ms is fb . then the probability that anna sees a red one emerge next is fr . this probabil - ity can also be expressed using conditional probabilities as fr = p ( blue ) p ( red after blue ) + p ( red ) p ( red after red ) , or fr = fb ( 1 = 6 ) + fr ( 1 = 5 ) . likewise , we find fb = fr ( 4 = 5 ) + fb ( 5 = 6 ) . solving the system of equations gives fb = 24 29 and fr = 5 / 29 correct answer e" - }, - { - "Answer": 14, - "Options": "a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20", - "Correct": "b", - "Explanation": "\"the ratio 1 : 34 = 2 : 68 so the ratio changed from 2 : 63 to 2 : 68 . 68 - 63 = 5 which is 1 / 7 of the increase in 35 associates . the ratio changed from 14 : 441 to 14 : 476 . thus the number of partners is 14 . the answer is b .\"" - }, - { - "Answer": 368, - "Options": "a ) 276 , b ) 299 , c ) 322 , d ) 345 , e ) 368", - "Correct": "e", - "Explanation": "\"clearly , the numbers are ( 23 x 13 ) and ( 23 x 16 ) . larger number = ( 23 x 16 ) = 368 . answer : option e\"" - }, - { - "Answer": 8, - "Options": "a ) 8 , b ) 12 , c ) 16 , d ) 18 , e ) 24", - "Correct": "a", - "Explanation": "the number of common factors will be same as number of factors of the highest common factor ( hcf ) hcf of 150 and 90 is 30 number of factors of 30 = 8 answer : a" - }, - { - "Answer": 5.999999999999998, - "Options": "a ) 2 , b ) 9 , c ) 6 , d ) 21 , e ) 30", - "Correct": "c", - "Explanation": "let the duration , in minutes , for which the company charges the same under plan a and plan b be t minutes . then under plan a the cost would be $ 0.6 + 0.06 ( t - 8 ) and under plan b the cost would be $ 0.08 t . we want these amount to be equal : 0.6 + 0.06 ( t - 8 ) = 0.08 t - - > 60 + 6 ( t - 8 ) = 8 t - - > t = 6 . answer : c ." - }, - { - "Answer": 31.5, - "Options": "a ) 31.5 , b ) 24.5 , c ) 24.3 , d ) 24.9 , e ) 24.1", - "Correct": "a", - "Explanation": "\"if rahul age is x , then sachin age is x - 9 , so ( x - 9 ) / x = 7 / 9 = > 9 x - 81 = 7 x = > 2 x = 81 = > x = 40.5 so sachin age is 40.5 - 9 = 31.5 answer : a\"" - }, - { - "Answer": 7, - "Options": "a ) 13 , b ) 15 , c ) 7 , d ) 17 , e ) 18", - "Correct": "c", - "Explanation": "40 students total 10 did not opt for math 15 did not opt for science 2 did not opt for either total of 30 students in math and 13 did not opt for sci but did for math 30 - 13 = 7 7 students of the class opted for both math and science answer : c . 7" - }, - { - "Answer": 75, - "Options": "a ) 75 , b ) 25 , c ) 30 , d ) 45 , e ) 60", - "Correct": "a", - "Explanation": "this ratio question can be solved in a couple of different ways . here ' s an algebraic approach . . . we ' re told that the ratio of the number of dogs to the number of cats is 15 : 7 . we ' re then told that 20 more cats are added to this group and the ratio becomes 15 : 11 . we ' re asked for the number of dogs . algebraically , since the number of dogs is a multiple of 15 and the number of cats is a multiple of 7 , we can write this initial relationship as . . . 15 x / 7 x when we add the 20 cats and factor in the ' ending ratio ' , we have an equation . . . . 15 x / ( 7 x + 20 ) = 15 / 11 here we have 1 variable and 1 equation , so we can solve for x . . . . ( 15 x ) ( 11 ) = ( 7 x + 20 ) ( 15 ) ( x ) ( 11 ) = ( 7 x + 20 ) ( 1 ) 11 x = 7 x + 20 4 x = 20 x = 5 with this x , we can figure out the initial number of dogs and cats . . . initial dogs = 15 x = 15 ( 5 ) = 75 final answer : a" - }, - { - "Answer": 200, - "Options": "a ) 987 ways , b ) 346 ways , c ) 600 ways , d ) 200 ways , e ) 134 ways", - "Correct": "d", - "Explanation": "the number of ways of selecting three english majors , two biological science majors and three engineers is : = \u2074 c \u2083 * \u2076 c \u2082 * \u2075 c \u2083 = ( 4 * 3 * 2 ) / ( 3 * 2 * 1 ) * ( 6 * 5 ) / ( 3 * 2 * 1 ) * ( 5 * 4 * 3 ) / ( 3 * 2 * 1 ) = 4 * 5 * 10 = 200 ways . answer : d" - }, - { - "Answer": 0.15789473684210525, - "Options": "a ) 1 / 11 , b ) 1 / 12 , c ) 1 / 13 , d ) 3 / 19 , e ) 3 / 43", - "Correct": "d", - "Explanation": "in believe the answer is d . please see below for explanation . 0 ) we are told the following ratios cgd - college graduate with degree ncg - non college graduate cgn - college graduate no degree cgd ncg cgn 1 8 3 2 in order to make cgd and cgn comparable we need to find the least common multiple of 8 and 3 and that is 24 multiplying the first ratio by 3 and the second ratio by 8 we get cgd ncg cgn 3 24 16 if one picks a random college graduate at this large company , what is the probability this college graduate has a graduate degree ? nr of cgd = 3 nr of cg = 3 + 16 = 19 probability e of cgd / ( cg ) - > 3 / 19 answer d" - }, - { - "Answer": 0.88, - "Options": "a ) 0.9 , b ) 0.75 , c ) 0.6 , d ) 0.88 , e ) 0.5", - "Correct": "d", - "Explanation": "\"according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 50 + 30 + 8 ) / 100 = 88 / 100 = 0.88 . answer is d\"" - }, - { - "Answer": 10, - "Options": "a ) 8 , b ) 11 , c ) 10 , d ) 15 , e ) 6", - "Correct": "c", - "Explanation": "c prinka is 10 , in a system that awards five for each vowel ." - }, - { - "Answer": 60, - "Options": "a ) 22 , b ) 50 , c ) 88 , d ) 52 , e ) 60", - "Correct": "e", - "Explanation": "\"5 : 1 = x : 12 x = 60 answer : e\"" - }, - { - "Answer": 0.0967741935483871, - "Options": "a ) 2 / 19 , b ) 3 / 31 , c ) 4 / 37 , d ) 5 / 41 , e ) 6 / 53", - "Correct": "b", - "Explanation": "\"10 / 31 * 9 / 30 = 3 / 31 the answer is b .\"" - }, - { - "Answer": 27, - "Options": "a ) 14 , b ) 15 , c ) 20 , d ) 22 , e ) 27", - "Correct": "e", - "Explanation": "\"explanation : present age is 4 x and 3 x , = > 4 x + 6 = 42 = > x = 9 so deepak age is = 3 ( 9 ) = 27 option e\"" - }, - { - "Answer": 0.01818181818181818, - "Options": "a ) 1 / 33 , b ) 1 / 22 , c ) 1 / 12 , d ) 1 / 44 , e ) 1 / 55", - "Correct": "e", - "Explanation": "\"p ( both are red ) , = 4 c 3 / 12 c 3 = 1 / 55 e\"" - }, - { - "Answer": 10, - "Options": "a ) 10 , b ) 6 , c ) 7 , d ) 4 , e ) 14", - "Correct": "a", - "Explanation": "say x attendants wrote with both writing tools . ( 25 - x ) + ( 15 - x ) = 20 - - > x = 10 . answer : a ." - }, - { - "Answer": 80, - "Options": "a ) 30 , b ) 80 , c ) 100 , d ) 130 , e ) 150", - "Correct": "b", - "Explanation": "\"20 stamps are both foreign and more than 10 years old . 70 stamps are foreign only . 30 stamps are 10 years old only . the number of remaining stamps is 200 - ( 20 + 70 + 30 ) = 80 the answer is b .\"" - }, - { - "Answer": 999, - "Options": "a ) 1500 , b ) 1000 , c ) 999 , d ) 1001 , e ) 1005", - "Correct": "b", - "Explanation": "\"multiples of 5 = 5 , 10,15 - - - - - , 5000 number of multiples of 5 = > 5000 - 5 / 5 + 1 = 1000 answer is b\"" - }, - { - "Answer": 51, - "Options": "a ) 51 , b ) 66 , c ) 98 , d ) 112 , e ) 154", - "Correct": "a", - "Explanation": "let us assume the number of dogs , cats and bunnies to be 3 x , 5 x and 9 x total dogs and bunnies = 12 x . and we are given that 12 x = 204 . hence x = 17 . dogs = 3 x = 3 * 17 = 51 ( option a )" - }, - { - "Answer": 105, - "Options": "a ) 97 , b ) 99 , c ) 101 , d ) 103 , e ) 105", - "Correct": "e", - "Explanation": "the total number of ways to form a team of 4 is 9 c 4 = 126 . we need to subtract the number of teams that have both the ceo and the cfo . the number of teams with both the ceo and cfo is 7 c 2 = 21 . the number of ways to form an acceptable team is 126 - 21 = 105 . the answer is e ." - }, - { - "Answer": 0.01, - "Options": "a ) 1 / 50 , b ) 1 / 25 , c ) 1 / 100 , d ) 1 , e ) 2", - "Correct": "c", - "Explanation": "\"there are 25 primes , 74 composite numbers from 1 to 100 . the number which is neither prime nor composite is 1 . therefore , required probability = 1 / 100 . answer : c\"" - }, - { - "Answer": 882.3529411764706, - "Options": "a ) 884 , b ) 890 , c ) 892 , d ) 910 , e ) 945", - "Correct": "b", - "Explanation": "\"normally , i would use the method used by bunuel . it ' s the most accurate . but if you are looking for a speedy solution , you can use another method which will sometimes give you an estimate . looking at the options ( most of them are spread out ) , i wont mind trying it . ( mind you , the method is accurate here since the numbers start from 1 . ) in 1000 consecutive numbers , number of multiples of 11 = 1000 / 11 = 90 ( ignore decimals ) in 1000 consecutive numbers , number of multiples of 35 = 1000 / 35 = 28 number of multiples of 11 * 35 i . e . 385 = 1000 / 385 = 2 number of integers from 1 to 1000 that are divisible by neither 11 nor by 35 = 1000 - ( 90 + 28 - 2 ) { using the concept of sets here ) = 890 think : why did i say the method is approximate in some cases ? think what happens if the given range is 11 to 1010 both inclusive ( again 1000 numbers ) what is the number of multiples in this case ? b\"" - }, - { - "Answer": 165, - "Options": "a ) 145 , b ) 155 , c ) 165 , d ) 175 , e ) 185", - "Correct": "c", - "Explanation": "ratio g 1 : g 2 = 3 : 5 and g 2 : g 3 = 7 : 11 so g 1 : g 2 : g 3 = 21 : 35 : 55 let the strength of three classes are 21 x , 35 x and 55 x respectively , then 21 x + 35 x + 55 x = 333 = > 111 x = 333 or x = 3 so strength of the class with highest number of pupils = 55 x = 55 * 3 = 165 answer : c" - }, - { - "Answer": 24, - "Options": "a ) 12 , b ) 14 , c ) 15 , d ) 24 , e ) 36", - "Correct": "d", - "Explanation": "the number of women doubled means that they have become 24 from 12 . . and we have to tell the current strength so 24 is the answer . . let the number be 4 x and 5 x . . given 4 x + 2 = 14 . . so x = 3 . . women number = 5 * 3 - 3 = 12 , then doubled = 24 . . ans d" - }, - { - "Answer": 793.375, - "Options": "a ) 0 , b ) 233 , c ) 500 , d ) 695 , e ) 789", - "Correct": "e", - "Explanation": "\"let # plain cookies sold be x then # chocolate cookies = ( total cookies - x ) equating for x ( 0.75 ) * x + ( 1.25 ) * ( 1585 - x ) = 1586.75 = > x = 789\"" - }, - { - "Answer": 26, - "Options": "a ) 34 , b ) 32 , c ) 30 , d ) 26 , e ) 28", - "Correct": "d", - "Explanation": "\"{ total } = { writers } + { editors } - { both } + { neither } . { total } = 110 ; { writers } = 45 ; { editors } > 38 ; { both } = x ; { neither } = 2 x ; 110 = 45 + { editors } - x + 2 x - - > x = 65 - { editors } . we want to maximize x , thus we should minimize { editors } , minimum possible value of { editors } is 39 , thus x = { both } = 65 - 39 = 26 . answer : d .\"" - }, - { - "Answer": 36, - "Options": "a ) 32 , b ) 33 , c ) 34 , d ) 35 , e ) 36", - "Correct": "e", - "Explanation": "7 ( x - 1 ) = 6 ( y - 1 ) = > 7 x - 6 y - 1 = 0 - - - - eq 1 8 ( x + 4 ) = 7 ( y + 4 ) = > 8 x - 7 y + 4 = 0 - - - - eq 2 on solving eq 1 n eq 2 y = 36 answer : e" - }, - { - "Answer": 10, - "Options": "a ) a ) 15 , b ) b ) 20 , c ) c ) 30 , d ) d ) 10 , e ) e ) 45", - "Correct": "d", - "Explanation": "100 = at least one of soap a or b both brands = x brand b = 3 x = > 60 + x + 3 x = 100 = > 4 x = 40 = > x = 10 answer - d" - }, - { - "Answer": 18.999999999999986, - "Options": "a ) 19 kg , b ) 13 kg , c ) 10 kg , d ) 23 kg , e ) 15 kg", - "Correct": "a", - "Explanation": "504.35 ( 19 ) + 887.75 x = 696.05 ( 19 + x ) solve the equation . 504.35 ( 19 ) + 887.75 x = 696.05 ( 19 + x ) 9 , 582.65 + 887.75 x = 13 , 224.95 + 696.05 x 9 , 582.65 + 191.7 x = 13 , 224.95 191.7 x = 3 , 642.3 x = 19 . answer is 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 , b = 1000 purchased a only . ( this is much simpler to solve using the venn diagram ) . correct answer is d . 1000" - }, - { - "Answer": 33, - "Options": "a ) 14 , b ) 15 , c ) 33 , d ) 22 , e ) 23", - "Correct": "c", - "Explanation": "\"explanation : present age is 4 x and 3 x , = > 4 x + 6 = 50 = > x = 11 so deepak age is = 3 ( 11 ) = 33 answer : option c\"" - }, - { - "Answer": 3, - "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", - "Correct": "a", - "Explanation": "when factorized , 880 has 6 prime factors . of these prime factors 2 are odd and 4 are even . hence total number of odd factors is 2 * 2 ( 4 ) , which includes 4 . the total number of odd factors greater than 1 are 3 . ( option a )" - }, - { - "Answer": 1, - "Options": "a ) 3 : 1 , b ) 3 : 2 , c ) 4 : 3 , d ) 5 : 3 , e ) 1 : 1", - "Correct": "e", - "Explanation": "\"required ratio = 500 : 500 = 3 : 1 answer e\"" - }, - { - "Answer": 40, - "Options": "a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60", - "Correct": "c", - "Explanation": "\"16 * 30 = 12 * n n = 40 the answer is c .\"" - }, - { - "Answer": 125, - "Options": "a ) 629 , b ) 729 , c ) 829 , d ) 125 , e ) 727", - "Correct": "d", - "Explanation": "\"no of values n can take is 1 5 ^ 3 = 125 answer : d\"" - }, - { - "Answer": 42, - "Options": "a ) 41 , b ) 42 , c ) 43 , d ) 44 , e ) 45", - "Correct": "b", - "Explanation": "\"there were 17 items sold at a higher price than the radio and 24 items sold at a lower price than the radio . including the radio , there were 17 + 24 + 1 = 42 items sold . the answer is b .\"" - }, - { - "Answer": 8, - "Options": "a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12", - "Correct": "d", - "Explanation": "since 2 xy prime t factors are x ^ 1 * y ^ 1 * 2 ^ 1 , its total number or factors must be ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 2 ^ 3 = 8 . thus , i think d would be the correct answer ." - }, - { - "Answer": 11, - "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", - "Correct": "e", - "Explanation": "\"let x play both badminton and tennis so 17 - x play only badminton and 19 - x play only tennis . 2 play none and there are total 30 students . hence , ( 17 - x ) + ( 19 - x ) + x + 2 = 27 38 - 2 x + x = 27 38 - x = 27 x = 11 so 8 members play both badminton and tennis . e\"" - }, - { - "Answer": 0.9, - "Options": "a ) 0.9 , b ) 0.75 , c ) 0.6 , d ) 0.8 , e ) 0.5", - "Correct": "a", - "Explanation": "\"according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 50 + 30 + 10 ) / 100 = 90 / 100 = 0.9 . answer is a\"" - }, - { - "Answer": 5, - "Options": "a ) 1 , b ) 5 , c ) 4 , d ) 6 , e ) 8", - "Correct": "b", - "Explanation": "6 is the answer . bag a - r : w : b = 2 : 6 : 9 let w in bag a be 6 k bab b - r : w = 1 : 4 let w in bag b be 4 k w = 50 = 6 k + 4 k = > k = 5 total red ' s in bag a will be 2 k = 10 b" - }, - { - "Answer": 32, - "Options": "a ) 20 , b ) 30 , c ) 40 , d ) 32 , e ) 90", - "Correct": "d", - "Explanation": "c k 1 = 5 x a 1 = 3 x k 2 = 5 x - 12 a 2 = 3 x + 12 k 2 / a 2 = 8 / 6 ( 5 x - 12 ) / ( 3 x + 12 ) = 8 / 6 6 * ( 5 x - 12 ) = 8 * ( 3 x + 12 ) 30 x - 72 = 24 x + 96 6 x = 168 x = 28 k 2 = 5 * 28 - 12 = 128 a 2 = 3 * 28 + 12 = 96 k 2 - a 2 = 32 answer : d" - }, - { - "Answer": 34, - "Options": "a ) 33 , b ) 34 , c ) 35 , d ) 36 , e ) 37", - "Correct": "b", - "Explanation": "there were 13 items sold at a higher price than the radio and 20 items sold at a lower price than the radio . including the radio , there were 13 + 20 + 1 = 34 items sold . the answer is b ." - }, - { - "Answer": 780, - "Options": "a ) rs . 200 , b ) rs . 250 , c ) rs . 300 , d ) rs . 780 , e ) none of these", - "Correct": "d", - "Explanation": "explanation : let the cost of one pen is \u2018 5 x \u2019 and pencil is \u2018 x \u2019 3 x 5 x + 5 x = rs . 260 15 x + 5 x = rs . 260 x = 260 / 20 = 13 : . cost of 1 pen = 5 x = 5 x 13 = 65 : . cost of 12 pens , i . e . ( one dozen ) = 65 x 12 = rs . 780 answer : option d" - }, - { - "Answer": 27, - "Options": "a ) 24 , b ) 27 , c ) 30 , d ) 33 , e ) 36", - "Correct": "b", - "Explanation": "\"now , sandy is 42 - 6 = 36 molly ' s age is ( 3 / 4 ) * 36 = 27 the answer is b .\"" - }, - { - "Answer": 175.5, - "Options": "a ) 175.5 , b ) 182.5 , c ) 170.0 , d ) 180.0 , e ) 190.0", - "Correct": "a", - "Explanation": "\"tea worth rs . 126 ratio 1 : 1 average price = ( 126 + 135 ) / 2 = 130.5 mean price = ( x - 153 ) : 22.50 = > x - 153 = 22.50 x = 175.5 answer a\"" - }, - { - "Answer": 0.11110756972111555, - "Options": "a ) 1 / 250 , b ) 1 / 84 , c ) 1 / 11 , d ) 1 / 9 , e ) 1 / 3", - "Correct": "d", - "Explanation": "probability of choosing one defective phone from a lot of 250 which ontains 84 defective phones is = ( 84 / 250 ) probability of choosing one defective phone from a lot of 249 ( we already picked one ) which ontains 83 ( we already picked one ) defective phones is = ( 83 / 249 ) combined probability of series of events = product of the probabilities = ( 84 / 250 ) * ( 83 / 249 ) 84 / 250 is close to ( 1 / 3 ) and ( 83 / 249 ) = ( 1 / 3 ) so answer is ( 1 / 3 ) * ( 1 / 3 ) = ( 1 / 9 ) answer : d" - }, - { - "Answer": 48, - "Options": "a ) 23 , b ) 77 , c ) 88 , d ) 48 , e ) 11", - "Correct": "d", - "Explanation": "\"let the numbers be 3 x and 4 x . then their h . c . f = x . so , x = 4 . so , the numbers are 12 and 16 . l . c . m of 12 and 16 = 48 . answer : d\"" - }, - { - "Answer": 5, - "Options": "a ) 5 , b ) 8 , c ) 14 , d ) 20 , e ) 28", - "Correct": "a", - "Explanation": "\"we are told that all of the letters contain either a dot or a straight line or both , which implies that there are no letters without a dot and a line ( no line / no dot box = 0 ) . first we find the total # of letters with lines : 11 + 24 = 35 ; next , we find the total # of letters without line : 40 - 35 = 5 ; finally , we find the # of letters that contain a dot but do not contain a straight line : 5 - 0 = 5 . a\"" - }, - { - "Answer": 8, - "Options": "a ) 9 : 8 , b ) 8 : 3 , c ) 3 : 2 , d ) 2 : 3 , e ) 1 : 2", - "Correct": "b", - "Explanation": "\"the ratio of economy to luxury cars is 3 : 2 - - > e : l = 3 : 2 = 12 : 8 . the ratio of economy cars to sport utility vehicles is 4 : 1 - - > e : s = 4 : 1 = 12 : 3 . thus , l : s = 8 : 3 . answer : b .\"" - }, - { - "Answer": 3600, - "Options": "a ) rs . 3600 , b ) rs . 3629 , c ) rs . 3279 , d ) rs . 3629 , e ) rs . 3283", - "Correct": "a", - "Explanation": "\"let the income and the expenditure of the person be rs . 5 x and rs . 4 x respectively . income , 5 x = 18000 = > x = 3600 savings = income - expenditure = 5 x - 4 x = x so , savings = rs . 3600 . answer : a\"" - }, - { - "Answer": 430, - "Options": "a ) 430 , b ) 432 , c ) 440 , d ) 442 , e ) 446", - "Correct": "a", - "Explanation": "\"310 + 232 - 112 ( since 112 is counted twice ) = 430 a is the answer\"" - }, - { - "Answer": 40, - "Options": "a ) 28 , b ) 32 , c ) 40 , d ) 53 , e ) 54", - "Correct": "c", - "Explanation": "\"let the numbers be 2 x and 3 x . then , their l . c . m . = 6 x . so , 6 x = 48 or x = 8 . the numbers are 16 and 24 . hence , required sum = ( 16 + 24 ) = 40 . answer : option c\"" - }, - { - "Answer": 26, - "Options": "a ) 3 , b ) 16 , c ) 75 , d ) 24 , e ) 26", - "Correct": "e", - "Explanation": "1 ) i figured there are 101 integers ( 300 - 200 + 1 = 101 ) . since the set begins with an even and ends with an even , there are 51 evens . 2 ) question says integers are not divisible by 2 , leaving all of the odds ( 101 - 51 = 50 integers ) . 3 ) question says integers are not divisible by 5 , removing all the integers ending in 5 ( already took out those ending in 0 ) . take out 10 integers ( 2 ? 5 , ? = 0 to 9 ) , leaving us with 40 integers . 4 ) now the painstaking part . we have to remove the remaining numbers that are multiples of 3 . those are 201 , 207 , 213 , 219 , 231 , 237 , 243 , 249 , 261 , 267 , 273 , 279 , 291 , and 297 . . . a total of 14 numbers . 26 numbers left ! 6 ) answer choice e ." - }, - { - "Answer": 322, - "Options": "a ) 280 , b ) 284 , c ) 292 , d ) 320 , e ) 322", - "Correct": "e", - "Explanation": "hcf of the two numbers = 23 since hcf will be always a factor of lcm , 23 is a factor of the lcm . given that other two factors in the lcm are 13 and 14 . hence factors of the lcm are 23 , 13 , 14 so , numbers can be taken as ( 23 \u00d7 13 ) and ( 23 \u00d7 14 ) = 299 and 322 hence , largest number = 322 e )" - }, - { - "Answer": 24, - "Options": "a ) 3 , b ) 9 , c ) 12 , d ) 18 , e ) 24", - "Correct": "e", - "Explanation": "the ratio is 4 wins : 3 losses : 1 tie . think of ratio as ` ` parts . ' ' divide 9 ( total losses ) by 3 ( ratio losses ) to find 1 ` ` part ' ' of the ratio . 9 / 3 = 3 this means the team tied 3 games . multiply 3 ( 1 ` ` part ' ' of ratio ) by 4 ( ratio wins ) to find total wins . 3 * 4 = 12 . this mean the team won 12 games . add up wins , losses , and ties . 12 + 9 + 3 = 24 the answer is e" - }, - { - "Answer": 36, - "Options": "a ) 34 , b ) 35 , c ) 36 , d ) 37 , e ) 38", - "Correct": "c", - "Explanation": "\"there were 14 items sold at a higher price than the radio and 21 items sold at a lower price than the radio . including the radio , there were 14 + 21 + 1 = 36 items sold . the answer is c .\"" - }, - { - "Answer": 80, - "Options": "a ) 80 , b ) 150 , c ) 240 , d ) 360 , e ) 480", - "Correct": "a", - "Explanation": "\"ratio = 3 : 1 = > 3 x respondents preferred brand x and x preferred brand y since , no . of respondents who preferred brand x = 60 = > 3 x = 60 = > x = 20 hence total no . of respondents = 60 + 20 = 80 hence a is the answer .\"" - }, - { - "Answer": 65, - "Options": "a ) 22 , b ) 50 , c ) 88 , d ) 65 , e ) 12", - "Correct": "d", - "Explanation": "\"5 : 1 = x : 13 x = 65 answer : d\"" - }, - { - "Answer": 18, - "Options": "a ) 14 , b ) 18 , c ) 20 , d ) 22 , e ) 24", - "Correct": "b", - "Explanation": "\"explanation : present age is 4 x and 3 x , = > 4 x + 2 = 26 = > x = 6 so deepak age is = 3 ( 6 ) = 18 option b\"" - }, - { - "Answer": 376, - "Options": "a ) 188 , b ) 258 , c ) 376 , d ) 470 , e ) 517", - "Correct": "c", - "Explanation": "consider 5 x acres of land used for bean consider 2 x acres of land used for wheat consider 4 x acres of land used for corn total given is 1034 acres 11 x = 1034 x = 94 land used for corn q = 4 * 94 = 376 correct option - c" - }, - { - "Answer": 780, - "Options": "a ) 420 , b ) 520 , c ) 620 , d ) 780 , e ) 820", - "Correct": "d", - "Explanation": "\"explanation : let the boy are 8 x and girls are 5 x = > 5 x = 300 = > x = 60 total students = 8 x + 5 x = 13 x = 13 ( 60 ) = 780 option d\"" - }, - { - "Answer": 11, - "Options": "['a ) 9', 'b ) 8', 'c ) 4', 'd ) 10', 'e ) 11']", - "Correct": "e", - "Explanation": "take 94 off the baseball players - - > 161 then 161 + 138 = 299 play either baseball or tennis 310 - 299 = 11 answer is e" - }, - { - "Answer": 15, - "Options": "a ) 15 , b ) 21 , c ) 23 , d ) 12 , e ) 25", - "Correct": "a", - "Explanation": "let the present ages of arun and deepak be 4 x years and 3 x years respectively 4 x + 6 = 26 4 x = 20 x = 5 deepak ' s age = 3 x = 15 years answer is a" - }, - { - "Answer": 0.5054945054945056, - "Options": "a ) 11 / 21 , b ) 17 / 42 , c ) 23 / 42 , d ) 46 / 91 , e ) 51 / 91", - "Correct": "d", - "Explanation": "\"the total number of ways to draw two balls is 14 c 2 = 91 the number of ways to draw two green balls is 5 c 2 = 10 the number of ways to draw two white balls is 9 c 2 = 36 p ( two balls of the same colour ) = 46 / 91 the answer is d .\"" - }, - { - "Answer": 30, - "Options": "a ) 20 , b ) 30 , c ) 38 , d ) 48 , e ) none of these", - "Correct": "b", - "Explanation": "a : b = 2 : 3 = 2 \u00d7 5 : 3 \u00d7 5 = 10 : 15 and b : c = 5 : 8 = 5 \u00d7 3 : 8 \u00d7 3 = 15 : 24 therefore , a : b : c = 10 : 15 : 24 \u2234 a : b : c = 10 : 15 : 24 let the number be 10 x , 15 x and 24 x . then , 10 x + 15 x + 24 x = 98 or 49 x = 98 or x = 2 \u21d2 second number = 15 x = 15 \u00d7 2 = 30 answer b" - }, - { - "Answer": 20, - "Options": "a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25", - "Correct": "d", - "Explanation": "the ratio of p to v in smothie x is 4 is to 1 and that in y is 1 is to 5 . p 1 + p 2 = 24 v 1 + v 2 = 25 p 1 = 4 v 1 p 2 = v 2 / 5 4 v 1 + v 2 / 5 = 24 v 1 + v 2 = 25 4 v 2 - v 2 / 5 = 76 19 v 2 / 5 = 76 = > v 2 = 20 = > v 1 = 5 = > p 1 = 20 answer - d" - }, - { - "Answer": 21, - "Options": "a ) 10 , b ) 20 , c ) 21 , d ) 25 , e ) 27", - "Correct": "c", - "Explanation": "\"as a : b : : 7 : 5 - - - > only option c is a multiple of 7 and hence it is a good place to start . also a : b : : 7 : 5 means that , a = ( 712 ) * total and b = ( 5 / 12 ) * total if a = 21 , b = 15 - - - > remove 9 litres - - - > you remove ( 7 / 12 ) * 9 of a - - - > a remaining = 21 - ( 7 / 12 ) * 9 = 63 / 4 similarly , for b , you remove ( 5 / 12 ) * 9 - - - > b remaining = 15 - ( 5 / 12 ) * 9 = 45 / 4 and then add 9 more litres of b - - - > 9 + 45 / 4 = 81 / 4 thus a / b ( final ratio ) = ( 45 / 4 ) / ( 81 / 4 ) = 7 : 9 , the same as the final ratio mentioned in the question . hence c is the correct answer . a / b = 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) , where 7 x and 5 x are initial quantities of a and b respectively . thus , 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) - - - > giving you x = 3 . thus a ( original ) t = 7 * 3 = 21 . c\"" - }, - { - "Answer": 60, - "Options": "a ) 20 , b ) 40 , c ) 50 , d ) 60 , e ) 80", - "Correct": "d", - "Explanation": "\"originally , there were 4 k horses and k cows . 3 ( 4 k - 15 ) = 7 ( k + 15 ) 12 k - 7 k = 105 + 45 5 k = 150 k = 30 the difference between horses and cows is ( 4 k - 15 ) - ( k + 15 ) = 3 k - 30 = 60 the answer is d .\"" - }, - { - "Answer": 0.22727272727272727, - "Options": "a ) 1 / 13 , b ) 2 / 23 , c ) 5 / 26 , d ) 5 / 22 , e ) 3 / 23", - "Correct": "d", - "Explanation": "\"p ( both are red ) , = 6 c 212 c 2 = 6 c 212 c 2 = 15 / 66 = 5 / 22 d\"" - }, - { - "Answer": 48, - "Options": "a ) 12 , b ) 48 , c ) 16 , d ) 20 , e ) 25", - "Correct": "b", - "Explanation": "\"30 litres of mixture that is replaced will contain 24 litres of a and 6 litres of b ( as a : b = 4 : 1 ) let the initial volume of the mixture be 4 k + 1 k = 5 k so by condition , [ 4 k - 24 ] / [ k - 6 + 30 ] = 2 / 3 = > 12 k - 72 = 2 k - 12 + 60 = > 10 k = 120 solve for k which is k = 12 so initial volume of liquid a = 4 k = 48 litres answer : b\"" - }, - { - "Answer": 88, - "Options": "a ) 144 , b ) 119 , c ) 113 , d ) 88 , e ) 31", - "Correct": "d", - "Explanation": "\"official solution : first of all , notice that since 144 took geometry and 119 took biology , then the number of students who took both geometry and biology can not be greater than 119 . { total } = { geometry } + { biology } - { both } + { neither } ; 232 = 144 + 119 - { both } + { neither } ; { both } = 31 + { neither } . { both } is minimized when { neither } is 0 . in this case { both } = 31 . the greatest possible number w of students that could have taken both geometry and biology , is 119 . thus , the answer is 119 - 31 = 88 . answer : d .\"" - }, - { - "Answer": 45, - "Options": "a ) 72 , b ) 85 , c ) 64 , d ) 51 , e ) 45", - "Correct": "e", - "Explanation": "\"we have 4 / 6 = 30 / x 4 x = 30 * 6 x = 45 consequent = 45 answer is e\"" - }, - { - "Answer": 15, - "Options": "a ) 9 , b ) 12 , c ) 15 , d ) 18 , e ) 21", - "Correct": "c", - "Explanation": "3 ( p - 3 ) / 4 = ( q - 3 ) . then q = 3 ( p - 3 ) / 4 + 3 6 ( p + 6 ) / 7 = q + 6 6 ( p + 6 ) / 7 = 3 ( p - 3 ) / 4 + 9 24 p + 144 = 21 p + 189 3 p = 45 p = 15 the answer is c ." - }, - { - "Answer": 32, - "Options": "a ) 18 , b ) 28 , c ) 32 , d ) 56 , e ) 60", - "Correct": "c", - "Explanation": "\"actual number of horses = 12,880 / 230 ( hold it since it is a harder calculation ) ratio multiplier = 1288 / ( 23 * 7 ) actual number of sheep = 1288 / ( 23 * 7 ) * 4 . first divide 1288 by 7 to get : 184 * 4 / 23 use the last digit to figure out that 23 will go 8 times into 184 . confirm . 8 * 4 = 32 answer ( c )\"" - }, - { - "Answer": 150, - "Options": "a ) 150 , b ) 300 , c ) 299 , d ) 322 , e ) 345", - "Correct": "a", - "Explanation": "\"the numbers are ( 10 x 11 ) and ( 10 x 15 ) . larger number = ( 10 x 15 ) = 150 . answer : a\"" - }, - { - "Answer": 250, - "Options": "a ) 54 , b ) 162 , c ) 250 , d ) 270 , e ) 322", - "Correct": "c", - "Explanation": "\"total number of fractions = 2 + 10 = 12 element b constitutes = 10 out of 12 parts of x so in 300 gms of x have 300 * 10 / 12 = 250 gms of b and 300 - 250 = 50 gms of a . cross check : - a / b = 50 / 250 = 2 / 10 ( as given ) ans c\"" - }, - { - "Answer": 3.2039999999999997, - "Options": "a ) 3.208 , b ) 3.202 , c ) 3.209 , d ) 3.204 , e ) 3.2112", - "Correct": "d", - "Explanation": "explanation : log 101600 = log 10 ( 16 \u00d7 100 ) = log 10 ( 16 ) + log 10 ( 100 ) = log 10 ( 24 ) + log 10 ( 102 ) = 4 log 10 ( 2 ) + 2 = ( 4 \u00d7 0.3010 ) + 2 = 1.204 + 2 = 3.204 answer : option d" - }, - { - "Answer": 16200, - "Options": "a ) 24887 , b ) 20778 , c ) 16200 , d ) 9000 , e ) 2811", - "Correct": "c", - "Explanation": "\"explanation : a invested rs . 3500 for 12 months . let b joined with investment x . and he invested for 12 - 7 = 5 months . so there profit ratio = ( 4500 \u00e3 \u2014 12 ) : ( 5 x ) = 2 : 3 \u00e2 \u2021 \u2019 x = 16200 answer : c\"" - }, - { - "Answer": 41, - "Options": "a ) 38 , b ) 39 , c ) 40 , d ) 41 , e ) 42", - "Correct": "d", - "Explanation": "no of zeroes in 173 ! is 173 / 5 = 34 ( quotient ) 34 / 5 = 6 ( quotient ) 6 / 5 = 1 ( quotient ) 34 + 6 + 1 = 41 ans 41 zeroes answer : d" - }, - { - "Answer": 57.999999999999986, - "Options": "a ) 62 % , b ) 52 % , c ) 57 % , d ) 56 % , e ) 58 %", - "Correct": "e", - "Explanation": "let total no of janet invited friends be 100 , boys 30 and girls 70 , so total number of janet ' s invited guests coming from texas for both boys and girls respectively 30 * 30 / 100 = 9 and 70 * 70 / 100 = 49 so total 58 of janet ' s invited guest out of the 100 invited guests will be coming from texas . . so required % is 58 % answer : e" - }, - { - "Answer": 24, - "Options": "a ) 24 , b ) 30 , c ) 36 , d ) 90 , e ) 96", - "Correct": "a", - "Explanation": "120 spend $ 100 on gas & electricity 60 spend $ 100 on gas but not on electricity for every one that spent < $ 100 on both there are 4 that spent $ 100 on electricity not gas let the ones that spent on neither be x the ones that spent on just electricity will be 4 x total households = those who spend > $ 100 on both + those who spend > $ 100 on just one + those who spend < $ 100 on both = 120 + 60 + 4 x + x 300 = 180 + 5 x implies x = 24 answer is ( a )" - }, - { - "Answer": 50, - "Options": "a ) 48 kg , b ) 49 kg , c ) 50 kg , d ) 51 kg , e ) none", - "Correct": "c", - "Explanation": "sol . let the original price be rs . 100 per kg . money required to buy 49 kg of rice = rs . ( 100 x 49 ) = rs . 4900 . new price = rs . 98 per kg . \u2234 quantity of rice bought = [ 4900 / 98 ] kg = 50 kg . answer c" - }, - { - "Answer": 886.6666666666666, - "Options": "a ) 887 , b ) 678 , c ) 765 , d ) 345 , e ) 256", - "Correct": "a", - "Explanation": "\"in 1000 consecutive numbers , number of multiples of 15 = 1000 / 15 = 66 ( ignore decimals ) in 1000 consecutive numbers , number of multiples of 20 = 1000 / 20 = 50 number of multiples of 15 * 20 i . e . 300 = 1000 / 300 = 3 number of integers from 1 to 1000 that are divisible by neither 15 nor by 20 = 1000 - ( 66 + 50 - 3 ) { using the concept of sets here ) = 887 answer is a\"" - }, - { - "Answer": 20, - "Options": "a ) 30 , b ) 20 , c ) 23 , d ) 17 , e ) 19", - "Correct": "b", - "Explanation": "\"total number of enrolled students = 25 number of students who did not take test = 3 hence , number of students who took test = 25 - 3 = 22 number of students who answered q 2 correctly = 20 , therefore , all students who took test answered q 2 correctly . so , number of students who answered q 1 correctly , also answered q 2 correctly = 20 . number of students who answered both q 1 & q 2 correctly = 20 . answer : b\"" - }, - { - "Answer": 35, - "Options": "a ) 34 kg , b ) 35 kg , c ) 36 kg , d ) 30 kg , e ) 32 kg", - "Correct": "b", - "Explanation": "suppose x kg of pure copper is melted with 10 kg of ist alloy and 16 kg of 2 nd alloy , then pure cooper in new alloy = 10 * 4 / 5 + 16 * 1 / 4 + x = 12 + x kg pure tin in new alloy = 10 * 1 / 5 + 16 * 3 / 4 = 14 kg as per given condition ( 12 + x ) / 14 = 3 / 2 24 + 2 x = 42 x = 9 kg total weight of new alloy = 10 + 16 + 9 = 35 kg answer : b" - }, - { - "Answer": 12, - "Options": "a ) 12 , b ) 10 , c ) 16 , d ) 19 , e ) 18", - "Correct": "a", - "Explanation": "\"36 = 2 ^ 2 x 3 ^ 2 84 = 2 ^ 2 x 3 x 7 h . c . f . = 2 ^ 2 x 3 = 12 . answer : option a\"" - }, - { - "Answer": 11, - "Options": "a ) 12 , b ) 11 , c ) 16 , d ) 18 , e ) 22", - "Correct": "b", - "Explanation": "\"draw a venn diagram yourself ! b + c - bc = number of students that play either basketball or cricket 9 + 8 - 6 = 11 b )\"" - }, - { - "Answer": 72, - "Options": "a ) 60,89 , b ) 60,88 , c ) - 27 , - 128 , d ) 60,84 , e ) - 72 , - 192", - "Correct": "e", - "Explanation": "\"( 3 x - 24 ) : ( 8 x - 24 ) = 4 : 9 x = - 24 = > - 72 , - 192 answer : e\"" - }, - { - "Answer": 8, - "Options": "a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14", - "Correct": "b", - "Explanation": "\"16 * 30 = 60 * n n = 8 the answer is b .\"" - }, - { - "Answer": 7.142857142857143, - "Options": "a ) 6.8 , b ) 8.5 , c ) 6.1 , d ) 9.1 , e ) 7.14", - "Correct": "e", - "Explanation": "annual decrease is ( 500 + 15.4 - 50.4 ) * 10 = 4650 hence every year there is a decrease of 350 for the population to become half 2500 must emigrate therefore 2500 / 350 = 133.3 correct option is e ) 7.14" - }, - { - "Answer": 450, - "Options": "a ) 350 , b ) 250 , c ) 450 , d ) 500 , e ) 620", - "Correct": "c", - "Explanation": "\"explanation : clearly , the numbers are ( 30 x 10 ) and ( 30 x 15 ) . { \\ color { blue } \\ therefore } larger number = ( 30 x 15 ) = 450 . answer : c ) 450\"" - }, - { - "Answer": 546, - "Options": "a ) 546 , b ) 550 , c ) 555 , d ) 532 , e ) 515", - "Correct": "a", - "Explanation": "\"we know 35 % people study biology , therefore the no of people not studying = 100 - 35 = 65 % > therefore the people not studying biology out of a total 840 people are = 65 % of 840 > ( 65 / 100 ) * 840 = 546 people a\"" - }, - { - "Answer": 120, - "Options": "a ) 70 , b ) 96 , c ) 108 , d ) 120 , e ) 150", - "Correct": "d", - "Explanation": "\"2 x 2 matrix will be the easiest way to calculate this . text in black : given statements text in red : calculated values thus d = 120 is the correct answer\"" - }, - { - "Answer": 1611, - "Options": "a ) 1621 , b ) 1711 , c ) 1611 , d ) 1511 , e ) 1311", - "Correct": "c", - "Explanation": "correct answer : c the number on the right side is formed as ( sum of digits of the 1 st number ) no 1 / no 2 ex : 35 $ 5 = 87 ( 3 + 5 = 8 ) ( 35 / 5 = 7 ) 63 $ 7 = 99 ( 6 + 3 = 9 ) ( 63 / 7 = 9 )" - }, - { - "Answer": 6, - "Options": "a ) 14 , b ) 10 , c ) 8 , d ) 6 , e ) 4", - "Correct": "d", - "Explanation": "we are given children allergic to cashew nuts as 18 and not allergic to cashew nuts as 10 , so total = 10 + 18 = 28 . . . children allergic to both are 10 . . . 18 are allergic to cashew nuts , so and half or 28 / 2 = 14 are allergic to peanuts . . so children allergic to at least one of the two are 18 + 14 - 10 = 22 . . therefore children not allergic to any of the two are 28 - 22 = 6 answer : d" - }, - { - "Answer": 32, - "Options": "a ) 22 % , b ) 24 % , c ) 26 % , d ) 28 % , e ) 32 %", - "Correct": "e", - "Explanation": "\"63 % answered the first question correctly and 20 % answered neither correctly . then 17 % missed the first question but answered the second question correctly . then the percent who answered both correctly is 49 % - 17 % = 32 % . the answer is e .\"" - }, - { - "Answer": 30, - "Options": "a ) 20 years , b ) 30 years , c ) 15 years , d ) 25 years , e ) 28 years", - "Correct": "b", - "Explanation": "\"let the present ages of arun and deepak be 2 x years and 3 x years respectively 2 x + 5 = 25 2 x = 20 x = 10 deepak ' s age = 3 x = 30 years answer is b\"" - }, - { - "Answer": 21, - "Options": "a ) 14 , b ) 15 , c ) 20 , d ) 21 , e ) 24", - "Correct": "d", - "Explanation": "\"explanation : present age is 4 x and 3 x , = > 4 x + 4 = 32 = > x = 7 so deepak age is = 3 ( 7 ) = 21 option d\"" - }, - { - "Answer": 0.41666666666666674, - "Options": "a ) 5 / 6 , b ) 5 / 9 , c ) 5 / 1 , d ) 5 / 3 , e ) 5 / 12", - "Correct": "e", - "Explanation": "\"let us say the ratio of the quantities of cheaper and dearer varieties = x : y by the rule of allegation , x / y = ( 8.75 - 7.50 ) / ( 7.50 - 4.5 ) = 5 / 12 answer : e\"" - }, - { - "Answer": 85, - "Options": "a ) 40 , b ) 85 , c ) 60 , d ) 30 , e ) 20", - "Correct": "b", - "Explanation": "b / c = 1 / 17 c - b = 80 . . . . . . . . . > b = c - 80 ( c - 80 ) / c = 1 / 17 testing answers . clearly eliminate acde put c = 85 . . . . . . . . . > ( 85 - 80 ) / 85 = 5 / 85 = 1 / 17 answer : b" - }, - { - "Answer": 0.031746031746031744, - "Options": "a ) 2 / 63 , b ) 2 / 67 , c ) 2 , d ) 3 / 31 , e ) 4", - "Correct": "a", - "Explanation": "given , a be the event that x is selected and b is the event that y is selected . p ( a ) = 17 , p ( b ) = 29 . let c be the event that both are selected . p ( c ) = p ( a ) \u00d7 p ( b ) as a and b are independent events : = ( 17 ) \u00d7 ( 29 ) = 2 / 63 answer is a" - }, - { - "Answer": 42, - "Options": "a ) 42 , b ) 49 , c ) 56 , d ) 63 , e ) 70", - "Correct": "a", - "Explanation": "let sandy ' s age be 7 x and let molly ' s age be 9 x . 9 x - 7 x = 12 x = 6 sandy is 42 years old . the answer is a ." - }, - { - "Answer": 14, - "Options": "['a ) 10', 'b ) 14', 'c ) 18', 'd ) 22', 'e ) 24']", - "Correct": "b", - "Explanation": "explanation : let the numbers be 3 x , 2 x and 5 x . then , 9 x + 4 x + 25 x = 1862 \u21d2 38 x = 1862 \u21d2 x = 49 \u21d2 x = 7 . middle number = 2 x = 14 option b" - }, - { - "Answer": 6, - "Options": "a ) 5 , b ) 6 , c ) 3 , d ) 2 , e ) 4", - "Correct": "b", - "Explanation": "pretty simple , really . if m = 6 , then 4 m = 24 , which is 12 x 2 , both of which are included in 21 ! since 6 is the largest number here , its the answer . answer is b" - }, - { - "Answer": 300, - "Options": "a ) 130 , b ) 300 , c ) 200 , d ) 30 , e ) 75", - "Correct": "b", - "Explanation": "\"150 : 1 = x : 2 x = 150 * 2 x = 300 answer : b\"" - }, - { - "Answer": 19, - "Options": "a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20", - "Correct": "d", - "Explanation": "prime factoring : you need a 2 and a 5 to make a 10 ( a ` ` zero ' ' ) , and there are tons of 2 ' s so let ' s skip these and focus on the ( rarer ) 5 s : 80 ! = 1 * 2 * 3 * 4 * 5 * 6 . . . * 78 * 79 * 80 since there are 80 consecutive numbers , there are 16 multiples of 5 in there , but if we ' re prime factoring , we need to remember that some multiples of 5 actually contain more than just one 5 . which ? 25 comes to mind - - it ' s got two of them ! so all the multiples of 25 actually contain two 5 ' s ( ie : 50 and 75 ) so , to recap , we have 16 of them , plus 3 more ( the additional 5 ' s in 25 , 50 , and 75 ) , so that makes 19 , and since we have more than enough 2 ' s , we know our number will have exactly 19 zeros at the end . answer : d" - }, - { - "Answer": 10, - "Options": "a ) 25 , b ) 30 , c ) 10 , d ) 15 , e ) 20", - "Correct": "c", - "Explanation": "explanation : let doughnuts = 5 x , cookies = 3 x & muffins = 1 x . now , 5 x = 50 hence x = 10 . number of muffins = 1 x which is 10 . answer : c" - }, - { - "Answer": 0.3333333333333333, - "Options": "a ) 4 / 15 , b ) 1 / 3 , c ) 2 / 5 , d ) 4 / 5 , e ) 7 / 6", - "Correct": "b", - "Explanation": "\"a : b = 5 : 3 - - 1 b : c = 1 : 5 = > b : c = 3 : 15 - - 2 from 1 and 2 , we get a : c = 4 : 15 answer b\"" - }, - { - "Answer": 16, - "Options": "a ) 13 , b ) 14 , c ) 15 , d ) 41 , e ) 16", - "Correct": "e", - "Explanation": "3 + 12 + 1 = 16 answer : e" - }, - { - "Answer": 35, - "Options": "a ) 28 , b ) 32 , c ) 35 , d ) 53 , e ) 54", - "Correct": "c", - "Explanation": "let the numbers be 2 x and 3 x . then , their l . c . m . = 6 x . so , 6 x = 42 or x = 7 . the numbers are 14 and 21 . hence , required sum = ( 14 + 21 ) = 35 . answer : option c" - }, - { - "Answer": 448, - "Options": "a ) 448 , b ) 299 , c ) 421 , d ) 460 , e ) 365", - "Correct": "a", - "Explanation": "\"clearly , the numbers are ( 32 x 13 ) and ( 32 x 14 ) . larger number = ( 32 x 14 ) = 448 . answer : option a\"" - }, - { - "Answer": 504000, - "Options": "a ) 187888 , b ) 276889 , c ) 267777 , d ) 504000 , e ) 297112", - "Correct": "d", - "Explanation": "\"b ' s monthly income = 15000 * 112 / 100 = rs . 16800 b ' s monthly income = 2 parts - - - - > rs . 16800 a ' s monthly income = 5 parts = 5 / 2 * 16800 = rs . 42000 a ' s annual income = rs . 42000 * 12 = rs . 504000 answer : d\"" - }, - { - "Answer": 250, - "Options": "a ) 80 , b ) 160 , c ) 250 , d ) 350 , e ) 480", - "Correct": "c", - "Explanation": "\"ratio = 4 : 1 = > 4 x respondents preferred brand x and x preferred brand y since , no . of respondents who preferred brand x = 200 = > 4 x = 200 = > x = 50 hence total no . of respondents = 200 + 50 = 250 hence c is the answer .\"" - }, - { - "Answer": 6, - "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 6 , e ) 11", - "Correct": "d", - "Explanation": "\"xc 1 * ( x - 1 ) c 1 = 30 x ^ 2 - x - 30 = 0 ( x - 6 ) ( x + 5 ) = 0 x = 6 , - 5 - 5 ca n ' t possible . d\"" - }, - { - "Answer": 0.16666666666666666, - "Options": "a ) 1 / 13 , b ) 2 / 23 , c ) 1 / 6 , d ) 4 / 27 , e ) 3 / 23", - "Correct": "c", - "Explanation": "\"p ( both are red ) , = 4 c 29 c 2 = 4 c 29 c 2 = 6 / 36 = 1 / 6 c\"" - }, - { - "Answer": 28, - "Options": "a ) 25 , b ) 26 , c ) 30 , d ) 24 , e ) 28", - "Correct": "e", - "Explanation": "let the two positive numbers be 7 x and 11 x respectively . 11 x - 7 x = 16 4 x = 16 = > x = 4 = > smaller number = 7 x = 28 . answer : e" - }, - { - "Answer": 59, - "Options": "a ) 45 , b ) 47 , c ) 59 , d ) 51 , e ) 53", - "Correct": "c", - "Explanation": "\"lets assume ac = 63 ( includesonly ac carsandcars with ac and racing stripes ) lets assume rs ( racing stripes ) > = 41 ( includescars with ac and racing stripesandonly racing stripes ) . now since we want to maximize ( only ac ) we have to see to it thatcars with ac and racing stripesis minimal ( assume 0 ) but since rs > = 41 . . we have to assign atleast 4 tocars with ac and racing stripes . hence ac = 63 - 4 = 59 . the answer is\"" - }, - { - "Answer": 351, - "Options": "a ) 562 , b ) 351 , c ) 452 , d ) 416 , e ) 512", - "Correct": "b", - "Explanation": "\"let the number of boys and girls be 8 x and 5 x then , 5 x = 135 x = 27 total number of students = 13 x = 13 * 27 = 351 answer is b\"" - }, - { - "Answer": 0.4, - "Options": "a ) 1 / 4 , b ) 2 / 3 , c ) 3 / 5 , d ) 2 / 5 , e ) 2 / 7", - "Correct": "d", - "Explanation": "d ) 2 / 5" - }, - { - "Answer": 20, - "Options": "a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 30 %", - "Correct": "c", - "Explanation": "20 student passed both two test 40 student passed only 1 st test 20 student passed only 2 nd test so 100 - ( 20 + 40 + 20 ) = 20 student failed in both sub so ans is 20 % answer : c" - }, - { - "Answer": 400, - "Options": "a ) 24 , b ) 26 , c ) 27 , d ) 400 , e ) 30", - "Correct": "d", - "Explanation": "5 : 1 : 4 total parts = 10 10 parts - - > 1000 1 part - - - - > 100 the last number of the three numbers is = 4 * 100 = 400 answer : d" - }, - { - "Answer": 11.999999999999996, - "Options": "a ) 12 , b ) 9 , c ) 15 , d ) 21 , e ) 30", - "Correct": "a", - "Explanation": "\"let the duration , in minutes , for which the company charges the same under plan a and plan b be t minutes . then under plan a the cost would be $ 0.6 + 0.06 ( t - 6 ) and under plan b the cost would be $ 0.08 t . we want these amount to be equal : 0.6 + 0.06 ( t - 6 ) = 0.08 t - - > 60 + 6 ( t - 6 ) = 8 t - - > t = 12 . answer : a .\"" - }, - { - "Answer": 58, - "Options": "a ) 38 , b ) 34 , c ) 58 , d ) 63 , e ) 73", - "Correct": "c", - "Explanation": "16 + 41 + 1 = 58 answer : c" - }, - { - "Answer": 470400.0000000001, - "Options": "a ) rs . 420000 , b ) rs . 180000 , c ) rs . 201600 , d ) rs . 470400 , e ) none of these", - "Correct": "d", - "Explanation": "\"b ' s monthly income = 14000 * 112 / 100 = rs . 15680 b ' s monthly income = 2 parts - - - - > rs . 15680 a ' s monthly income = 5 parts = 5 / 2 * 15680 = rs . 39200 a ' s annual income = rs . 39200 * 12 = rs . 470400 answer : d\"" - }, - { - "Answer": 52, - "Options": "a ) 66 % , b ) 64 % , c ) 68 % , d ) 52 % , e ) 72 %", - "Correct": "d", - "Explanation": "\"let total no of vehicles bought be 100 , toyota 60 and honda 40 , so total number of suv ' s bought for toyota and honda respectively 60 * 60 / 100 = 36 and 40 * 40 / 100 = 16 so total 52 suv ' s were bought out of 100 vehicles bought . . so required % is 52 % answer : d\"" - }, - { - "Answer": 50, - "Options": "a ) 20 , b ) 40 , c ) 50 , d ) 60 , e ) 45", - "Correct": "c", - "Explanation": "\"let the present age of arun and deepak be 4 x and 3 x 2 x + 10 = 30 2 x = 20 x = 10 deepak ' s age = 5 x = 50 years answer is c\"" - }, - { - "Answer": 109395, - "Options": "a ) 104345 , b ) 107375 , c ) 108385 , d ) 109395 , e ) 105355", - "Correct": "d", - "Explanation": "the only thing you actually know about the correct number z is that it is divisible by 153 and has 5 as a factor . you should immediately try to find the factors of 153 and look for them in the options . 153 = 9 * 17 divisibility by 9 is easy to check . only ( d ) satisfies ." - }, - { - "Answer": 45, - "Options": "a ) 28 , b ) 32 , c ) 40 , d ) 45 , e ) 54", - "Correct": "d", - "Explanation": "\"let the numbers be 2 x and 3 x . then , their l . c . m . = 6 x . so , 6 x = 54 or x = 9 . the numbers are 18 and 27 . hence , required sum = ( 18 + 27 ) = 45 . answer : option d\"" - }, - { - "Answer": 1600, - "Options": "a ) $ 1200 , b ) $ 1400 , c ) $ 1600 , d ) $ 1800 , e ) $ 2000", - "Correct": "c", - "Explanation": "sum of ratio terms = 4 + 16 = 20 c = 2000 * 16 / 20 = $ 1600 answer is c" - }, - { - "Answer": 12, - "Options": "a ) 12 , b ) 14 , c ) 16 , d ) 17 , e ) 19", - "Correct": "a", - "Explanation": "3 : 4 total parts = 7 = 7 parts - - > 21 ( 7 \u00e3 \u2014 3 = 21 ) = 1 part - - - - > 3 ( 1 \u00e3 \u2014 3 = 4 ) = the greater of the two number is = 4 = 4 parts - - - - > 12 ( 4 \u00e3 \u2014 3 = 12 ) a" - }, - { - "Answer": 7, - "Options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10", - "Correct": "b", - "Explanation": "\"the weights of the items in the suitcase are 5 k , 4 k , and 2 k . if removing 7 pounds of clothes doubles the ratio of books to clothes , then 7 pounds represents half the weight of the clothes . 2 k = 7 pounds and then k = 3.5 pounds . the electronics weigh 2 ( 3.5 ) = 7 pounds . the answer is b .\"" - }, - { - "Answer": 1400, - "Options": "a ) 900 , b ) 980 , c ) 1200 , d ) 1240 , e ) 1400", - "Correct": "e", - "Explanation": "\"amount received by sanjay . 4 / 12 x 4200 = 1400 = ( related ratio / sum of ratio ) x total amount so , the amount received by sanjay is 1400 . e\"" - }, - { - "Answer": 12, - "Options": "a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20", - "Correct": "a", - "Explanation": "\"16 * 30 = 40 * n n = 12 the answer is a .\"" - }, - { - "Answer": 403200.0000000001, - "Options": "a ) rs . 420000 , b ) rs . 403200 , c ) rs . 201600 , d ) rs . 504000 , e ) none of these", - "Correct": "b", - "Explanation": "\"b ' s monthly income = 12000 * 112 / 100 = rs . 13440 b ' s monthly income = 2 parts - - - - > rs . 13440 a ' s monthly income = 5 parts = 5 / 2 * 13440 = rs . 33600 a ' s annual income = rs . 33600 * 12 = rs . 403200 answer : b\"" - }, - { - "Answer": 20, - "Options": "a ) 14 , b ) 7 , c ) 20 , d ) 70 , e ) 35", - "Correct": "c", - "Explanation": "explanation : let pants = 7 x , shorts = 7 x & shirts = 10 x . now , 7 x = 14 hence x = 2 . number of apples = 10 x = 20 . answer : c" - }, - { - "Answer": 45, - "Options": "a ) 15 , b ) 45 , c ) 30 , d ) 45 , e ) 60", - "Correct": "b", - "Explanation": "this ratio question can be solved in a couple of different ways . here ' s an algebraic approach . . . we ' re told that the ratio of the number of cats to the number of dogs is 15 : 7 . we ' re then told that 12 more dogs are added to this group and the ratio becomes 15 : 11 . we ' re asked for the number of cats . algebraically , since the number of cats is a multiple of 15 and the number of dogs is a multiple of 7 , we can write this initial relationship as . . . 15 x / 7 x when we add the 12 cats and factor in the ' ending ratio ' , we have an equation . . . . 15 x / ( 7 x + 12 ) = 15 / 11 here we have 1 variable and 1 equation , so we can solve for x . . . . ( 15 x ) ( 11 ) = ( 7 x + 12 ) ( 15 ) ( x ) ( 11 ) = ( 7 x + 12 ) ( 1 ) 11 x = 7 x + 12 4 x = 12 x = 3 with this x , we can figure out the initial number of dogs and cats . . . initial dogs = 15 x = 15 ( 3 ) = 45 final answer : b" - }, - { - "Answer": 10, - "Options": "a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30", - "Correct": "a", - "Explanation": "neither car nor garage = total - garage - ( swim - common ) = 65 - 50 - ( 40 - 35 ) = 65 - 55 = 10 answer a" - }, - { - "Answer": 322, - "Options": "a ) 276 , b ) 299 , c ) 322 , d ) 345 , e ) 355", - "Correct": "c", - "Explanation": "\"clearly , the numbers are ( 23 x 13 ) and ( 23 x 14 ) . larger number = ( 23 x 14 ) = 322 . answer : option c\"" - }, - { - "Answer": 15, - "Options": "a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 35", - "Correct": "a", - "Explanation": "\"16 * 30 = 32 * n n = 15 the answer is a .\"" - }, - { - "Answer": 15, - "Options": "a ) 22 , b ) 15 , c ) 77 , d ) 266 , e ) 182", - "Correct": "b", - "Explanation": "\"present age is 4 x and 3 x , = > 4 x + 6 = 26 = > x = 5 so deepak age is = 3 ( 5 ) = 15 answer : b\"" - }, - { - "Answer": 600, - "Options": "a ) $ 50 , b ) $ 500 , c ) $ 150 , d ) $ 250 , e ) $ 600", - "Correct": "e", - "Explanation": "sum of ratio terms = 1 + 2 = 3 a = 600 * 1 / 3 = $ 200 answer is e" - }, - { - "Answer": 1.9999999999999927, - "Options": "a ) 2 % , b ) 5 % , c ) 8 % , d ) 10 % , e ) 15 %", - "Correct": "a", - "Explanation": "\"since we were expected to find a percentage figure - it thought that it might be easier to pick a ' smart number ' to represent the total number of voters ( republicans and democrats ) . therefore , i picked 100 ( as the total number of voters ) and thus 3 : 2 = = 60 : 40 represents the number ratio of republicans : democrats . if 75 % of republicans ( which is ( 60 * 0.75 ) = 45 ) and 15 % of democrats ( 40 * 0.15 = 6 ) voted for candidate x , means that out of total of 100 voters ; 51 ( 45 + 6 ) voters voted for candidate x and 49 voted for candidate y . thus we can infer that candidate x is expected to win the election by 2 ( 51 - 49 ) votes . therefore candidate x is expected to win the election by ( 2 / 100 ) votes which is equivalent to 2 % . i think the answer is a .\"" - }, - { - "Answer": 6, - "Options": "a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 15", - "Correct": "d", - "Explanation": "one short cut to solve the problem is c : p = 1 : 3 c increased to 3 = > 1 : 3 = 3 : x = > x = 9 = > p increased by 6 d is the answer" - }, - { - "Answer": 26, - "Options": "a ) 26 , b ) 27 , c ) 25 , d ) 22 , e ) 23", - "Correct": "a", - "Explanation": "2 + 1 + 5 + 4 + 7 + 4 = 23 5 + 3 + 7 + x = 23 = > x = 8 combination that match 8 is 26 since 2 + 6 = 8 answer : a" - }, - { - "Answer": 5.999999999999997, - "Options": "a ) 6 : 1 , b ) 4 : 7 , c ) 3 : 7 , d ) 9 : 5 , e ) 9 : 8", - "Correct": "a", - "Explanation": "\"( 96 - 72 ) / ( 72 - 68 ) = 24 / 4 = 6 / 1 answer : a\"" - }, - { - "Answer": 3, - "Options": "a ) 2 : 1 , b ) 4 : 1 , c ) 3 : 1 , d ) 2 : 3 , e ) 4 : 3", - "Correct": "c", - "Explanation": "the ratio of milk and water in the new vessel is = ( 4 / 5 + 7 / 10 ) : ( 1 / 5 + 3 / 10 ) = 3 / 2 : 1 / 2 = 3 : 1 answer is c" - }, - { - "Answer": 49, - "Options": "a ) 49 th , b ) 48 th , c ) 47 th , d ) 50 th , e ) none of these", - "Correct": "a", - "Explanation": "there are 4 students above her . when takan from bottom there are 4 students below her rank . so her rank wud be 53 - 4 i . e . 49 th . answer : a" - }, - { - "Answer": 15, - "Options": "a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30", - "Correct": "b", - "Explanation": "\"neither car nor garage = total - garage - ( swim - common ) = 70 - 50 - ( 40 - 35 ) = 70 - 55 = 15 answer b\"" - }, - { - "Answer": 1200, - "Options": "a ) $ 2000 , b ) $ 1200 , c ) $ 2500 , d ) $ 1800 , e ) $ 1600", - "Correct": "b", - "Explanation": "\"b ' s share = 3600 * 3 / 9 = $ 1200 answer is b\"" - }, - { - "Answer": 42, - "Options": "a ) 35 years , b ) 25 years , c ) 42 years , d ) 39 years , e ) 40 years", - "Correct": "c", - "Explanation": "\"let the present ages of arun and deepak be 5 x years and 7 x years respectively 5 x + 6 = 36 5 x = 30 x = 6 deepak ' s age = 7 x = 42 years answer is c\"" - }, - { - "Answer": 376, - "Options": "a ) 188 , b ) 258 , c ) 376 , d ) 470 , e ) 517", - "Correct": "c", - "Explanation": "\"consider 5 x acres of land used for bean consider 2 x acres of land used for wheat consider 4 x acres of land used for corn total given is 1034 acres 11 x = 1034 x = 94 land used for corn w = 4 * 94 = 376 correct option - c\"" - }, - { - "Answer": 8, - "Options": "a ) 1 , b ) 6 , c ) 7 , d ) 8 , e ) 2", - "Correct": "d", - "Explanation": "\"36 * 12 : 54 * x = 2 : 1 x = 4 12 - 4 = 8 answer : d\"" - }, - { - "Answer": 14, - "Options": "a ) 24.5 , b ) 14 , c ) 24.21 , d ) 27 , e ) 25", - "Correct": "b", - "Explanation": "\"explanation : if rahul age is x , then sachin age is x - 7 , so , 9 x - 63 = 6 x 3 x = 63 x = 21 so sachin age is 21 - 7 = 14 answer : b ) 14\"" - }, - { - "Answer": 0.55, - "Options": "a ) 0.55 , b ) 0.4 , c ) 0.5 , d ) 0.05 , e ) 0.6", - "Correct": "a", - "Explanation": "\"we are apply that formula . . . . . . . . . . . . . . p ( aorb ) = p ( a ) + p ( b ) - p ( a and b ) = . 25 + . 35 - . 15 = . 45 but the probability of neither a nor b = 1 - . 45 = 0.55 answer : a\"" - }, - { - "Answer": 0.010101010101010102, - "Options": "a ) 1 / 50 , b ) 1 / 25 , c ) 1 / 99 , d ) 1 , e ) 2", - "Correct": "c", - "Explanation": "\"there are 25 primes , 73 composite numbers from 1 to 100 . the number which is neither prime nor composite is 1 . therefore , required probability = 1 / 99 . answer : c\"" - }, - { - "Answer": 1.6666666666666667, - "Options": "a ) 7 / 2 , b ) 19 / 6 , c ) 5 / 3 , d ) 7 , e ) 8", - "Correct": "c", - "Explanation": "let log 9 27 = x . then , 9 x = 27 = > ( 32 ) x = 33 = > 2 x = 3 = > x = 3 / 2 let log 8 32 = y . then 8 y = 32 = > ( 23 ) y = 25 = > 3 y = 5 = > y = 5 / 3 answer : c" - }, - { - "Answer": 80, - "Options": "a ) 48 , b ) 64 , c ) 70 , d ) 80 , e ) 84", - "Correct": "d", - "Explanation": "let day scholars be ds and boarders be b given b / ds = 7 / 16 - - - > eq 1 initially b = 560 and x be new boarders joined then from eq 1 , we get ds = 16 / 7 * 560 = 1280 now , new ration is 560 + x / ds = 1 / 2 560 + x / 1280 = 1 / 2 = > 1120 + 2 x = 1280 = > 2 x = 160 = > x = 80 ans option d" - }, - { - "Answer": 96, - "Options": "a ) 12 , b ) 96 , c ) 24 , d ) 48 , e ) 98", - "Correct": "b", - "Explanation": "let the numbers be 3 x and 4 x . then their h . c . f = x . so , x = 8 . so , the numbers are 24 and 32 . l . c . m of 24 and 32 = 96 . answer : b" - }, - { - "Answer": 40, - "Options": "a ) a ) 15 , b ) b ) 20 , c ) c ) 30 , d ) d ) 40 , e ) e ) 45", - "Correct": "d", - "Explanation": "\"220 = at least one of soap a or b both brands = x brand b = 3 x = > 60 + x + 3 x = 220 = > 4 x = 160 = > x = 40 answer - d\"" - }, - { - "Answer": 55, - "Options": "a ) 22 , b ) 50 , c ) 55 , d ) 52 , e ) 12", - "Correct": "c", - "Explanation": "\"5 : 1 = x : 10 x = 55 answer : c\"" - }, - { - "Answer": 75, - "Options": "a ) 45 , b ) 50 , c ) 55 , d ) 60 , e ) 75", - "Correct": "e", - "Explanation": "\"f : c : w 1 : 12 : 30 sport version : f : c 3 : 12 f : w 1 : 60 or 3 : 180 so c : f : w = 12 : 3 : 180 c / w = 12 / 180 = 3 ounces / x ounces x = 5 * 180 / 12 = 75 ounces of water e\"" - }, - { - "Answer": 0.07756948933419522, - "Options": "a ) 110 / 1547 , b ) 120 / 1547 , c ) 140 / 1547 , d ) 160 / 1547 , e ) 220 / 1547", - "Correct": "b", - "Explanation": "p : 1 / 13 = 5 / 34 : 7 / 48 as the product of the means is equal to the product of the extremes . p * 7 / 48 = 1 / 13 * 5 / 34 p * 7 / 48 = 5 / 442 p = 240 / 3094 = > p = 120 / 1547 answer : b" - }, - { - "Answer": 3, - "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", - "Correct": "a", - "Explanation": "explanation : let x is subtracted . then , ( 6 \u2212 x ) ( 7 \u2212 x ) < 162121 ( 6 \ufffd x ) < 16 ( 7 \ufffd x ) = > 5 x > 14 = x > 2.8 least such number is 3 answer : a" - }, - { - "Answer": 12, - "Options": "a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14", - "Correct": "d", - "Explanation": "the weights of the items in the suitcase are 7 k , 4 k , and 3 k . if removing 8 pounds of clothes doubles the ratio of books to clothes , then 8 pounds represents half the weight of the clothes . 2 k = 8 pounds and then k = 4 pounds . the electronics weigh 3 ( 4 ) = 12 pounds . the answer is d ." - }, - { - "Answer": 0.8333333333333334, - "Options": "a ) 1 / 6 , b ) 2 / 9 , c ) 5 / 6 , d ) 7 / 9 , e ) 8 / 9", - "Correct": "c", - "Explanation": "\"we have three pairs of dogs for the 6 with exactly one littermate , and one triplet , with each having exactly two littermates . so , in fact there are two types of dogs : those with one littermate - say a , and the others with two littermates - b . work with probabilities : choosing two dogs , we can have either one dog of type b or none ( we can not have two dogs both of type b ) . the probability of choosing one dog of type b and one of type a is 3 / 9 * 6 / 8 * 2 = 1 / 2 ( the factor of 2 for the two possibilities ba and ab ) . the probability of choosing two dogs of type a which are not littermates is 6 / 9 * 4 / 8 = 1 / 3 ( choose one a , then another a which is n ' t the previous one ' s littermate ) . the required probability is 1 / 2 + 1 / 3 = 5 / 6 . find the probability for the complementary event : choose aa or bb . probability of choosing two dogs of type a who are littermates is 6 / 9 * 1 / 8 = 1 / 12 . probability of choosing two dogs of type b ( who necessarily are littermates ) is 3 / 9 * 2 / 8 q = 1 / 12 . again , we obtain 1 - ( 1 / 12 + 1 / 12 ) = 5 / 6 . answer : c\"" - }, - { - "Answer": 40, - "Options": "a ) 25 , b ) 40 , c ) 50 , d ) 60 , e ) 75", - "Correct": "b", - "Explanation": "120 = 60 ( mac ) + x ( window ) + 20 ( both ) = > x = 40 answer : b" - }, - { - "Answer": 147, - "Options": "a ) 42 , b ) 70 , c ) 147 , d ) 165 , e ) 315", - "Correct": "c", - "Explanation": "\"ans : 147 7 c 1 * 7 c 2 answer c )\"" - }, - { - "Answer": 1, - "Options": "a ) 1 : 1 , b ) 2 : 1 , c ) 3 : 1 , d ) 5 : 1 , e ) 6 : 1", - "Correct": "a", - "Explanation": "\"vessel a = 300 gallons - - > milk = 100 , water = 200 ; vessel b = 500 gallons - - > milk = 300 , water = 200 ; vessel a + b = 800 gallons - - > milk = 400 , water 400 the ratio = 400 / 400 - - > 1 : 1 answer : a\"" - }, - { - "Answer": 26, - "Options": "a ) 3 , b ) 16 , c ) 75 , d ) 24 , e ) 26", - "Correct": "e", - "Explanation": "1 ) i figured there are 101 integers ( 300 - 200 + 1 = 101 ) . since the set begins with an even and ends with an even , there are 51 evens . 2 ) question says integers are not divisible by 2 , leaving all of the odds ( 101 - 51 = 50 integers ) . 3 ) question says integers are not divisible by 5 , removing all the integers ending in 5 ( already took out those ending in 0 ) . take out 10 integers ( 2 ? 5 , ? = 0 to 9 ) , leaving us with 40 integers . 4 ) now the painstaking part . we have to remove the remaining numbers that are multiples of 3 . those are 201 , 207 , 213 , 219 , 231 , 237 , 243 , 249 , 261 , 267 , 273 , 279 , 291 , and 297 . . . a total of 14 numbers . 26 numbers left ! 6 ) answer choice e ." - }, - { - "Answer": 1500, - "Options": "a ) $ 2000 , b ) $ 1500 , c ) $ 2500 , d ) $ 1800 , e ) $ 1600", - "Correct": "b", - "Explanation": "b ' s share = 4500 * 3 / 9 = $ 1500 answer is b" - }, - { - "Answer": 6, - "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", - "Correct": "d", - "Explanation": "the total work is 6 * 42 = 252 machine hours the time required for seven machines is 252 / 7 = 36 hours , thus 6 fewer hours . the answer is d ." - }, - { - "Answer": 52, - "Options": "a ) 66 % , b ) 64 % , c ) 68 % , d ) 69 % , e ) 52 %", - "Correct": "e", - "Explanation": "\"let total no of vehicles bought be 100 , toyota 40 and honda 60 , so total number of suv ' s bought for toyota and honda respectively 40 * 40 / 100 = 16 and 60 * 60 / 100 = 36 so total 52 suv ' s were bought out of 100 vehicles bought . . so required % is 52 % answer : e\"" - }, - { - "Answer": 13000, - "Options": "a ) 11000 , b ) 12000 , c ) 13000 , d ) 14000 , e ) 15000", - "Correct": "c", - "Explanation": "total population in year 1990 = 5000 + 3000 + 2000 = 10000 total population in year 1994 = ( ( 5000 * 120 / 100 ) + ( 3000 + ( 3000 * 2 / 3 ) ) + ( 2000 ) ) = 13000 answer : c" - }, - { - "Answer": 250, - "Options": "a ) 100 , b ) 250 , c ) 125 , d ) 110 , e ) 115", - "Correct": "b", - "Explanation": "\"ans : by framing equations we get 30 l + 3 q = 360 30 l + 6 q = 420 eliminate q by multiplying the first equation by 2 and subtracting second equation from the first then we get l = 10 cost of 10 kgs of apples = 25 x 10 = 250 answer : b\"" - }, - { - "Answer": 24, - "Options": "a ) 12 , b ) 14 , c ) 15 , d ) 24 , e ) 36", - "Correct": "d", - "Explanation": "\"the number of women doubled means that they have become 24 from 12 . . and we have to tell the current strength so 24 is the answer . . let the number be 4 x and 5 x . . given 4 x + 2 = 14 . . so x = 3 . . women number = 5 * 3 - 3 = 12 , then doubled = 24 . . ans d\"" - }, - { - "Answer": 35, - "Options": "a ) 30 , b ) 35 , c ) 20 , d ) 18 , e ) 10", - "Correct": "b", - "Explanation": "\"{ total } = { car } + { bike } - { both } + { neither } - - > 90 = 44 + { bike } - 16 + 11 - - > { bike } = 51 - - > # those who have bike only is { bike } - { both } = 51 - 16 = 35 . answer : b .\"" - }, - { - "Answer": 39, - "Options": "a ) 33 , b ) 34 , c ) 35 , d ) 39 , e ) 37", - "Correct": "d", - "Explanation": "\"14 + 24 + 1 = 39 answer : d\"" - }, - { - "Answer": 1260, - "Options": "a ) 80 , b ) 160 , c ) 720 , d ) 1100 , e ) 1260", - "Correct": "e", - "Explanation": "\"no . of ways of picking 2 biology books ( from 10 books ) = 10 c 2 = ( 10 * 9 ) / 2 = 45 no . of ways of picking 2 chemistry books ( from 8 books ) = 8 c 2 = ( 8 * 7 ) / 2 = 28 total ways of picking 2 books of each type = 45 * 28 = 1260 ( option e )\"" - }, - { - "Answer": 20, - "Options": "a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 35", - "Correct": "b", - "Explanation": "\"product of two no = lcm * hcf 2 x * 3 x = 120 * x x = 20 answer : b\"" - }, - { - "Answer": 40, - "Options": "a ) 15 , b ) 20 , c ) 30 , d ) 40 , e ) 45", - "Correct": "d", - "Explanation": "solution for soap r and soap b ( d ) 40" - }, - { - "Answer": 0.7, - "Options": "a ) 0.7 , b ) 0.15 , c ) 0.54 , d ) 0.85 , e ) 0.91", - "Correct": "a", - "Explanation": "\"according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 22 + 18 + 2 ) / 60 = 42 / 60 = 0.7 . answer : a .\"" - }, - { - "Answer": 20, - "Options": "a ) 6 , b ) 16 , c ) 20 , d ) 30 , e ) 174", - "Correct": "c", - "Explanation": "the number of integers that belong to set x only is 14 - 6 = 8 ; the number of integers that belong to set y only is 18 - 6 = 12 ; the number of integers that belong to set x or set y , but not both is 8 + 12 = 20 . answer : c ." - }, - { - "Answer": 900, - "Options": "a ) $ 200 , b ) $ 900 , c ) $ 700 , d ) $ 600 , e ) $ 400", - "Correct": "b", - "Explanation": "\"b ' s share = 2700 * 3 / 9 = $ 900 answer is b\"" - }, - { - "Answer": 414, - "Options": "a ) 276 , b ) 414 , c ) 322 , d ) 345 , e ) 355", - "Correct": "b", - "Explanation": "\"clearly , the numbers are ( 23 x 13 ) and ( 23 x 18 ) . larger number = ( 23 x 18 ) = 414 . answer : option b\"" - }, - { - "Answer": 2, - "Options": "a ) 2 , b ) 5 , c ) 10 , d ) 15 , e ) 20", - "Correct": "a", - "Explanation": "solution let log 5625 = x . then , 5 x = 625 = 54 \u2039 = \u203a x = 4 . let log 2 ( log 5625 ) = y . then , log 24 = y \u2039 = \u203a 2 y = 4 y ; 2 . answer a" - }, - { - "Answer": 42, - "Options": "a ) 28 , b ) 32 , c ) 36 , d ) 42 , e ) 50", - "Correct": "d", - "Explanation": "the total number of people are x females + 2 x males . 3 * ( x - 7 ) = 2 x - 7 x = 14 there were 3 x = 42 people at the party originally . the answer is d ." - }, - { - "Answer": 13928.571428571428, - "Options": "a ) no loss , b ) 10,000 , c ) 28,000 , d ) 9,500 , e ) 14,000", - "Correct": "e", - "Explanation": "x = 28000 / 28 ^ 2 = 35.71 cost of 15 g = 35.71 * 15 ^ 2 = 8035.714 cost of 13 g = 35.71 * 13 ^ 2 = 6035.714 total cost = 14071.428 loss = 28000 - 14071.428 = 13928.5 = 14000 answer : e" - }, - { - "Answer": 21, - "Options": "['a ) 23', 'b ) 21', 'c ) 20', 'd ) 26', 'e ) 27']", - "Correct": "b", - "Explanation": "48 + 46 = 94 but where as total number is 80 - 7 = 73 therefore answer is 94 - 73 = 21 hence answer is b" - }, - { - "Answer": 6.993190657180867, - "Options": "a ) 3 , b ) 1 / 3 , c ) 2 , d ) 7 , e ) 1 / 7", - "Correct": "d", - "Explanation": "\"343 = ( a 1 + a 2 + a 3 + a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) factorize the same terms 343 = 1 + ( a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) write every term with respect to r a 1 = a 1 a 2 = a 1 * r ^ 1 a 3 = a 1 * r ^ 2 . . . . . . . . . 343 = 1 + ( a 1 ( r ^ 3 + r ^ 4 + r ^ 5 ) ) / ( a 1 ( 1 + r ^ 1 + r ^ 2 ) ) 342 = ( r ^ 3 ( 1 + r ^ 1 + r ^ 2 ) ) / ( ( 1 + r ^ 1 + r ^ 2 ) ) 342 = r ^ 3 r = 7 d\"" - }, - { - "Answer": 10, - "Options": "a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30", - "Correct": "a", - "Explanation": "let the student who speaks hindi - x let the student who speaks english - y as ( xuy ) - ( xny ) = total 30 + 20 - ( xny ) = 40 = 10 a )" - }, - { - "Answer": 0.5, - "Options": "a ) 2 / 7 , b ) 5 / 7 , c ) 1 / 2 , d ) 3 / 7 , e ) 1 / 2", - "Correct": "c", - "Explanation": "p ( 1 st b , 2 nd c ) = 15 / 25 * 10 / 24 = 150 / 600 = 1 / 4 ; p ( 1 st c , 2 nd b ) = 10 / 25 * 15 / 24 = 150 / 600 = 1 / 4 . p = 1 / 4 + 1 / 4 = 1 / 2 . answer : c ." - }, - { - "Answer": 16, - "Options": "['a ) 10', 'b ) 14', 'c ) 16', 'd ) 20', 'e ) 22']", - "Correct": "c", - "Explanation": "16 . to get the answer , you can simply add the different types of students , as there are no overlaps in the categories : 5 + 2 + 3 + 6 = 16 . as such , the correct answer is c : 16 ." - }, - { - "Answer": 2200, - "Options": "a ) 2200 , b ) 980 , c ) 1200 , d ) 1240 , e ) 1400", - "Correct": "a", - "Explanation": "\"amount received by sanjay . 4 / 12 x 6600 = 2200 = ( related ratio / sum of ratio ) x total amount so , the amount received by sanjay is 2200 . a\"" - }, - { - "Answer": 322, - "Options": "a ) 338 , b ) 278 , c ) 322 , d ) 231 , e ) 121", - "Correct": "c", - "Explanation": "\"clearly , the numbers are ( 23 * 13 ) and ( 23 * 14 ) . larger number = ( 23 * 14 ) = 322 . answer : c\"" - }, - { - "Answer": 180, - "Options": "a ) 165 , b ) 170 , c ) 175 , d ) 180 , e ) 185", - "Correct": "d", - "Explanation": "the number of nurses at the hospital is ( 9 / 14 ) * 280 = 180 . the answer is d ." - }, - { - "Answer": 3, - "Options": "a ) 3 : 1 , b ) 2 : 1 , c ) 5 : 2 , d ) 3 : 2 , e ) 3 : 4", - "Correct": "a", - "Explanation": "mean price = ( 72 - 64.5 = 7.5 ) ( 64.5 - 62 = 2.5 ) req ratio = 7.5 : 2.5 = 3 : 1 answer a" - }, - { - "Answer": 8, - "Options": "a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12", - "Correct": "d", - "Explanation": "p and q are both odd prime numbers - it means either p or q is not 2 and since prime numbers have only two factors - 1 and the number itself p and q each will have ( 1 + 1 ) = 2 factors hence 2 pq will have ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 8 factors d is the answer" - }, - { - "Answer": 9000, - "Options": "a ) 7000 , b ) 9000 , c ) 8000 , d ) 9900 , e ) 7900", - "Correct": "b", - "Explanation": "ratio in which profit is divided = 2 : 3 assume that b ' s contribution to the capital = b 3500 \u00d7 12 : b \u00d7 7 = 2 : 3 \u21d2 3500 \u00d7 12 \u00d7 3 = 2 \u00d7 b \u00d7 7 \u21d2 b = 3500 \u00d7 12 \u00d7 3 / 2 \u00d7 7 = 500 \u00d7 6 \u00d7 3 = 9000 answer : b" - }, - { - "Answer": 0.21428571428571427, - "Options": "a ) 5 / 21 , b ) 9 / 42 , c ) 6 / 22 , d ) 4 / 21 , e ) 3 / 21", - "Correct": "b", - "Explanation": "since there are 10 even numbers in the given range , the probability that the first toy shows an even number = 10 / 21 since the toy is not replaced , there are now 9 even numbered toys and total 20 toys left . hence , probability that the second toy shows an even number = 9 / 20 . required probability = 10 / 21 x 9 / 20 = 9 / 42 . answer : b" - }, - { - "Answer": 96, - "Options": "a ) 99 , b ) 98 , c ) 97 , d ) 96 , e ) 95", - "Correct": "d", - "Explanation": "\"clearly d a number is said to be prime saturated if the product of all the different positive prime factors of z is less than the square root of z . 96 has more number of smaller prime factor thats the clue ! ! = d\"" - }, - { - "Answer": 0.25462962962962965, - "Options": "a ) 55 / 216 , b ) 56 / 216 , c ) 57 / 216 , d ) 54 / 216 , e ) 53 / 216", - "Correct": "a", - "Explanation": "if the no . on blue dice is 2 then 2 red dice can take ( 1,1 ) value = 1 ^ 2 if the no . on blue dice is 3 then 2 red dice can take ( 1,1 ) ( 1,2 ) ( 2,1 ) ( 2,2 ) = 2 ^ 2 if the no . on blue dice is 4 then 2 red dice can take ( 1,1 ) ( 1,2 ) ( 2,1 ) ( 2,2 ) ( 1,3 ) ( 2,3 ) ( 3,2 ) ( 3,1 ) ( 3,3 ) = 3 ^ 2 similarly , if the no . on blue dice is 5 then 2 red dice can take = 4 ^ 2 and if the no . on blue dice is 6 then 2 red dice can take = 5 ^ 2 therefor , probability = total no . of favourable outcome / total no . of possible outcome = 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + 4 ^ 2 + 5 ^ 2 / 216 = 55 / 216 answer : a" - }, - { - "Answer": 64, - "Options": "a ) 12 , b ) 15 , c ) 16 , d ) 64 , e ) 25", - "Correct": "d", - "Explanation": "40 litres of mixture that is replaced will contain 32 litres of a and 8 litres of b ( as a : b = 4 : 1 ) let the initial volume of the mixture be 4 k + 1 k = 5 k so by condition , [ 4 k - 32 ] / [ k - 8 + 40 ] = 2 / 3 = > 12 k - 96 = 2 k - 16 + 80 = > 10 k = 160 solve for k which is k = 16 so initial volume of liquid a = 4 k = 64 litres answer : d" - }, - { - "Answer": 8, - "Options": "a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12", - "Correct": "d", - "Explanation": "since 2 xy prime r factors are x ^ 1 * y ^ 1 * 2 ^ 1 , its total number or factors must be ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 2 ^ 3 = 8 . thus , i think d would be the correct answer ." - }, - { - "Answer": 2.9999999999999964, - "Options": "a ) 3 , b ) 9 , c ) 15 , d ) 21 , e ) 30", - "Correct": "a", - "Explanation": "\"let the duration , in minutes , for which the company charges the same under plan a and plan b be t minutes . then under plan a the cost would be $ 0.6 + 0.06 ( t - 9 ) and under plan b the cost would be $ 0.08 t . we want these amount to be equal : 0.6 + 0.06 ( t - 9 ) = 0.08 t - - > 60 + 6 ( t - 9 ) = 8 t - - > t = 3 . answer : a .\"" - }, - { - "Answer": 30, - "Options": "a ) 30 , b ) 60 , c ) 75 , d ) 90 , e ) 105", - "Correct": "a", - "Explanation": "\"originally , there were 4 k horses and k cows . 7 ( 4 k - 15 ) = 13 ( k + 15 ) 28 k - 13 k = 195 + 105 15 k = 300 k = 20 the difference between horses and cows is ( 4 k - 15 ) - ( k + 15 ) = 3 k - 30 = 30 the answer is a .\"" - }, - { - "Answer": 8, - "Options": "a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12", - "Correct": "d", - "Explanation": "s and t are both odd prime numbers - it means either s or t is not 2 and since prime numbers have only two factors - 1 and the number itself s and t each will have ( 1 + 1 ) = 2 factors hence 2 st will have ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 8 factors d is the answer" - }, - { - "Answer": 175.5, - "Options": "a ) rs . 147.50 , b ) rs . 785.50 , c ) rs . 175.50 , d ) rs . 258.50 , e ) none of these", - "Correct": "c", - "Explanation": "\"explanation : since first and second varieties are mixed in equal proportions . so , their average price = rs . ( 126 + 135 ) / 2 . = > rs . 130.50 . so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . by the rule of alligation , we have : cost of 1 kg cost of 1 kg of 1 st kind of 2 nd kind ( rs . 130.50 ) ( rs . x ) \\ / mean price ( rs . 153 ) / \\ x \u2212 153 22.50 = > x \u2212 ( 153 / 22.50 ) = 1 . = > x \u2212 153 = 22.50 . = > x = 175.50 rs . answer : c\"" - }, - { - "Answer": 1, - "Options": "a ) 5 : 8 , b ) 4 : 7 , c ) 3 : 7 , d ) 1 : 1 , e ) 9 : 8", - "Correct": "d", - "Explanation": "\"( 96 - 82 ) / ( 82 - 68 ) = 14 / 14 = 1 / 1 answer : d\"" - }, - { - "Answer": 24, - "Options": "a ) 12 , b ) 14 , c ) 15 , d ) 24 , e ) 36", - "Correct": "d", - "Explanation": "\"the number of women doubled means that they have become 24 from 12 . . and we have to tell the current strength so 24 is the answer . . let the number be 4 x and 5 x . . given 4 x + 2 = 14 . . so x = 3 . . women number = 5 * 3 - 3 = 12 , then doubled = 24 . . ans d\"" - }, - { - "Answer": 0.16666666666666666, - "Options": "a ) 3 / 8 , b ) 2 / 3 , c ) 1 / 2 , d ) 1 / 3 , e ) 1 / 6", - "Correct": "e", - "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 two dice are rolled , n ( s ) = 6 \u00d7 6 = 36 e = getting a sum greater than 9 when the two dice are rolled = { ( 4 , 6 ) , { 5 , 5 } , { 5 , 6 } , { 6 , 4 } , { 6 , 5 } , ( 6 , 6 ) } hence , n ( e ) = 6 p ( e ) = n ( e ) / n ( s ) = 6 / 36 = 1 / 6" - }, - { - "Answer": 146.57142857142856, - "Options": "a ) 140.6 kg , b ) 145.3 kg , c ) 146.5 kg , d ) 110.8 kg , e ) 114 kg", - "Correct": "c", - "Explanation": "\"quantity of tin in 130 kg of a = 130 * 3 / 5 = 78 kg quantity of tin in 160 kg of b = 160 * 3 / 7 = 68.5 kg quantity of tin in the new alloy = 78 + 68.5 = 146.5 kg answer is c\"" - }, - { - "Answer": 504, - "Options": "a ) 462 , b ) 450 , c ) 480 , d ) 504 , e ) 555", - "Correct": "d", - "Explanation": "\"explanation : hcf of the two numbers = 42 hcf will be always a factor of lcm 42 is factor of lcm other two factors are 11 & 12 then the numbers are ( 42 11 ) and ( 42 x 12 ) = 462 and 504 answer : option d\"" - }, - { - "Answer": 0.20588235294117646, - "Options": "a ) 1 / 7 , b ) 3 / 14 , c ) 5 / 23 , d ) 7 / 34 , e ) 9 / 41", - "Correct": "d", - "Explanation": "p ( 1 st ball is even ) = 8 / 17 p ( 2 nd ball is also even ) = 7 / 16 p ( both balls are even ) = 8 / 17 * 7 / 16 = 7 / 34 the answer is d ." - }, - { - "Answer": 300, - "Options": "a ) 276 , b ) 300 , c ) 299 , d ) 322 , e ) 345", - "Correct": "b", - "Explanation": "\"the numbers are ( 20 x 11 ) and ( 20 x 15 ) . larger number = ( 20 x 15 ) = 300 . answer : b\"" - }, - { - "Answer": 3, - "Options": "a ) 3 : 9 , b ) 3 : 6 , c ) 3 : 1 , d ) 3 : 4 , e ) 3 : 2", - "Correct": "c", - "Explanation": "\"let the present ages of a and b be 5 x and 3 x years respectively . then , ( 5 x - 4 ) / ( 3 x + 4 ) = 1 / 1 2 x = 8 = > x = 4 required ratio = ( 5 x + 4 ) : ( 3 x - 4 ) = 24 : 8 = 3 : 1 answer : c\"" - }, - { - "Answer": 0.12154811715481172, - "Options": "a ) 1 / 250 , b ) 9 / 74 , c ) 1 / 11 , d ) 1 / 9 , e ) 1 / 3", - "Correct": "b", - "Explanation": "\"probability of chosing one defective phone from a lot of 240 which ontains 84 defective phones is = ( 84 / 240 ) probability of chosing one defective phone from a lot of 239 ( we already picked one ) which ontains 83 ( we already picked one ) defective phones is = ( 83 / 239 ) combined probability of series of events = product of the probabilities = ( 84 / 240 ) * ( 83 / 239 ) 84 / 240 is close to ( 7 / 20 ) and ( 83 / 239 ) = ( 25 / 72 ) so answer is ( 7 / 20 ) * ( 25 / 72 ) ( 9 / 74 ) so , answer will be b\"" - }, - { - "Answer": 40, - "Options": "a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80", - "Correct": "a", - "Explanation": "n ( a u b ) = n ( a ) + n ( b ) - n ( a intersection b ) 200 = 125 + 115 - both both = 240 - 200 = 40 . answer : a" - }, - { - "Answer": 15750, - "Options": "a ) 24887 , b ) 20778 , c ) 23788 , d ) 15750 , e ) 2811", - "Correct": "d", - "Explanation": "\"explanation : a invested rs . 3500 for 12 months . let b joined with investment x . and he invested for 12 - 8 = 4 months . so there profit ratio = ( 3500 \u00e3 \u2014 12 ) : ( 4 x ) = 2 : 3 \u00e2 \u2021 \u2019 x = 15750 answer : d\"" - }, - { - "Answer": 280, - "Options": "a ) 276 , b ) 280 , c ) 322 , d ) 345 , e ) 354", - "Correct": "b", - "Explanation": "\"clearly , the numbers are ( 20 x 13 ) and ( 20 x 14 ) . larger number = ( 20 x 14 ) = 280 . answer : option b\"" - }, - { - "Answer": 210, - "Options": "a ) 159 , b ) 194 , c ) 210 , d ) 209 , e ) 166", - "Correct": "c", - "Explanation": "\"out of 10 students 4 children should to be selected . so the combination will be 10 c 4 . 10 c 4 = 10 ! / 6 ! * 4 ! = 10 * 9 * 8 * 7 * 6 ! / 6 ! * ( 4 * 3 * 2 * 1 ) 10 c 4 = 210 there are 210 differect possible ways to select 4 children out of 10 students .\"" - }, - { - "Answer": 96, - "Options": "['a ) 96', 'b ) 108', 'c ) 120', 'd ) 132', 'e ) 140']", - "Correct": "a", - "Explanation": "the ratio of yankees : mets : red sox = 6 : 4 : 5 the mets fans are 4 / 15 of the population . ( 4 / 15 ) * 360 = 96 the answer is a ." - }, - { - "Answer": 13, - "Options": "a ) 7 , b ) 9 , c ) 11 , d ) 13 , e ) 15", - "Correct": "d", - "Explanation": "( 2 / 18 ) * 117 = 13 grams the answer is d ." - }, - { - "Answer": 45, - "Options": "a ) 45 , b ) 47 , c ) 49 , d ) 51 , e ) 53", - "Correct": "a", - "Explanation": "\"lets assume ac = 53 ( includesonly ac carsandcars with ac and racing stripes ) lets assume rs ( racing stripes ) > = 55 ( includescars with ac and racing stripesandonly racing stripes ) . now since we want to maximize ( only ac ) we have to see to it thatcars with ac and racing stripesis minimal ( assume 0 ) but since rs > = 55 . . we have to assign atleast 8 tocars with ac and racing stripes . hence ac = 53 - 8 = 45 . the answer is a\"" - }, - { - "Answer": 10, - "Options": "a ) 30 , b ) 10 , c ) 18 , d ) 28 , e ) 32", - "Correct": "b", - "Explanation": "\"total = english + german - both + neither - - > 40 = english + 22 - 12 + 0 - - > english = 22 - - > only english = english - both = 22 - 12 = 10 . answer : b .\"" - }, - { - "Answer": 21, - "Options": "a ) 60 , b ) 45 , c ) 21 , d ) 15 , e ) none", - "Correct": "c", - "Explanation": "\"sol . let the required numbers be 3 x and 4 x . then , their l . c . m . is 12 x . \u2234 12 x = 84 \u21d4 x = 7 . hence , the first number is 21 . answer c\"" - }, - { - "Answer": 30, - "Options": "a ) a ) 15 , b ) b ) 20 , c ) c ) 30 , d ) d ) 40 , e ) e ) 45", - "Correct": "c", - "Explanation": "\"180 = at least one of soap a or b both brands = x brand b = 3 x = > 60 + x + 3 x = 180 = > 4 x = 120 = > x = 30 answer - c\"" - }, - { - "Answer": 0.6666666666666664, - "Options": "a ) 1 / 4 , b ) 2 / 5 , c ) 1 / 2 , d ) 3 / 5 , e ) 2 / 3", - "Correct": "e", - "Explanation": "\"you can simply use this formula to avoid confusion : w 1 / w 2 = ( a 2 - aavg ) / ( avg - a 1 ) here is how you will find the values of a 1 an a 2 . we have an overall loss ( average loss ) . the average loss is 7 kg when 70 kg alloy is immersed . this is a loss of ( 7 / 70 ) * 100 = 10 % . this is aavg the loss of tin is 1.375 kg for every 10 kg . this means it loses ( 1.375 / 10 ) * 100 = 13.75 % of its weight in water . this is a 1 . the loss of silver is . 375 kg for every 5 kg . this means it loses ( . 375 / 5 ) * 100 = 7.5 % of its weight in water . this is a 2 . weight of tin / weight of silver = ( silver ' s loss - avg loss ) / ( avg loss - tin ' s loss ) x / y = ( 7.5 - 10 ) / ( 10 - 13.75 ) = 2 / 3 e\"" - }, - { - "Answer": 0.55, - "Options": "a ) 0.45 , b ) 0.4 , c ) 0.55 , d ) 0.05 , e ) 0.6", - "Correct": "c", - "Explanation": "\"we are apply that formula . . . . . . . . . . . . . . p ( aorb ) = p ( a ) + p ( b ) - p ( a and b ) = . 25 + . 40 - . 20 = . 45 but the probability of neither a nor b = 1 - . 45 = 0.55 answer : c\"" - }, - { - "Answer": 40, - "Options": "a ) 18 , b ) 28 , c ) 40 , d ) 56 , e ) 60", - "Correct": "c", - "Explanation": "\"let the number of sheeps and horses be 4 x and 7 x . now total number of horses = total consumption of horse food / consumption per horse = 12880 / 230 = 56 , which is equal to 7 x . = > x = 8 sheeps = 5 x = 5 * 8 = 40 . hence c .\"" - }, - { - "Answer": 0.5, - "Options": "['a ) 1 m', 'b ) 2 m', 'c ) 0.5 m', 'd ) 0.75 m', 'e ) 1.5 m']", - "Correct": "c", - "Explanation": "the volume of the earth removed is 8 * 5 * 2 = 80 m ^ 3 . the remaining area of the field is 20 * 10 - 8 * 5 = 160 m ^ 2 . 80 m ^ 3 of the earth evenly spread over the area of 160 m ^ 2 will rise the height by ( height ) = ( volume ) / ( area ) = 80 / 160 = 0.5 m . answer : c" - }, - { - "Answer": 883.1168831168832, - "Options": "a ) 884 , b ) 890 , c ) 892 , d ) 910 , e ) 945", - "Correct": "a", - "Explanation": "\"number divisible by 11 : - 1000 / 11 = 90 numbers divisible by 35 : - 1000 / 35 = 28 numbers divisible by both 11 and 35 = 2 total numbers divisible by both 11 and 28 = 90 + 28 - 2 = 116 ( because we counted 2 in both 90 and 28 ) total numbers not divisible by 11 or 35 = 1000 - 116 = 884 answer : a\"" - }, - { - "Answer": 470, - "Options": "a ) 430 , b ) 440 , c ) 450 , d ) 460 , e ) 470", - "Correct": "e", - "Explanation": "\"we ' re given a series of facts to work with : 1 ) a certain high school has 500 students . 2 ) of these students : x are taking music , y are taking art , and z are taking both music and art . we ' re asked how many students are taking neither music nor art ? let ' s test x = 30 y = 10 z = 10 so , we have 30 students taking music , 10 taking art and 10 taking both music and art . 20 student taking just music 0 student taking just art 10 student taking both music and art total = 30 students we ' re asked for the total number of students who are taking neither course . that is 500 - 30 = 470 . e\"" - }, - { - "Answer": 260, - "Options": "a ) 120 , b ) 180 , c ) 260 , d ) 280 , e ) 320", - "Correct": "c", - "Explanation": "\"3 x = 390 x = 130 therefore , the salesman sold 130 kg in the morning and 2 \u22c5 130 = 260 kg in the afternoon . so answer is c .\"" - }, - { - "Answer": 470, - "Options": "a ) 430 , b ) 440 , c ) 450 , d ) 460 , e ) 470", - "Correct": "e", - "Explanation": "\"we ' re given a series of facts to work with : 1 ) a certain high school has 500 students . 2 ) of these students : x are taking music , y are taking art , and z are taking both music and art . we ' re asked how many students are taking neither music nor art ? let ' s test x = 20 y = 20 z = 10 so , we have 20 students taking music , 20 taking art and 10 taking both music and art . that 10 person has been counted twice though ( once in the music ' group ' and once in the art ' group ' ) , so what we really have is . . . 10 student taking just music 10 student taking just art 10 student taking both music and art total = 30 students we ' re asked for the total number of students who are taking neither course . that is 5000 - 30 = 470 . e\"" - }, - { - "Answer": 225, - "Options": "a ) 225 , b ) 300 , c ) 299 , d ) 322 , e ) 345", - "Correct": "a", - "Explanation": "\"the numbers are ( 15 x 11 ) and ( 15 x 15 ) . larger number = ( 15 x 15 ) = 225 . answer : a\"" - }, - { - "Answer": 26, - "Options": "a ) 26 % , b ) 33 % , c ) 34 % , d ) 35 % , e ) 24 %", - "Correct": "a", - "Explanation": "quantity of spirit in new solution = ( 4 * 45 / 100 ) + ( 5 * 30 / 100 ) + ( 6 * 10 / 100 ) = 1.8 + 1.5 + 0.6 = 3.9 liters so % concentration of spirit = 100 * 3.9 / ( 4 + 5 + 6 ) = 26 % answer : a" - }, - { - "Answer": 37, - "Options": "a ) 37 , b ) 38 , c ) 27 , d ) 29 , e ) 11", - "Correct": "a", - "Explanation": "explanation : number of boys in the class = ( 18 + 1 + 18 ) = 37 answer : a ) 37" - }, - { - "Answer": 12, - "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 12", - "Correct": "e", - "Explanation": "\"xc 1 * ( x - 1 ) c 1 = 132 x ^ 2 - x - 132 = 0 ( x - 12 ) ( x + 11 ) = 0 x = 12 , - 11 - 11 ca n ' t possible . hence 12 should be the answer e\"" - }, - { - "Answer": 7, - "Options": "a ) 2 , b ) 7 , c ) 6 , d ) 8 , e ) 10", - "Correct": "b", - "Explanation": "\"venn diagrams are useful for multiple values of a single variable e . g . state of mind - happy / sad / neither . when you have two or more variables such as here where you have gender - boy / girl too , it becomes unwieldy . in this case , either use the table or logic . table method is shown above ; here is how you will use logic : there are 6 happy boys . there are 4 sad girls but total 10 sad children . so rest 6 sad children must be sad boys . we have 6 happy boys and 6 sad boys . total we have 19 boys . so 19 - 6 - 6 = 7 boys must be neither happy nor sad . answer ( b )\"" - }, - { - "Answer": 1200, - "Options": "a ) rs 1200 , b ) rs 1500 , c ) rs 1600 , d ) rs 1900 , e ) rs 1700", - "Correct": "a", - "Explanation": "\"explanation : let p = faruk , q = vasim , r = ranjith let p = 3 x , q = 5 x and r = 7 x . then , 5 x = 1500 ? x = 300 . p = 900 , q = 1500 and r = 2100 . hence , ( r - p ) = ( 2100 - 900 ) = 1200 answer : a\"" - }, - { - "Answer": 0.5, - "Options": "a ) 0.45 , b ) 0.4 , c ) 0.5 , d ) 0.05 , e ) 0.6", - "Correct": "c", - "Explanation": "\"we are apply that formula . . . . . . . . . . . . . . p ( aorb ) = p ( a ) + p ( b ) - p ( a and b ) = . 25 + . 40 - . 15 = . 50 but the probability of neither a nor b = 1 - . 50 = 0.50 answer : c\"" - }, - { - "Answer": 8, - "Options": "a ) 14 , b ) 15 , c ) 12 , d ) 22 , e ) 8", - "Correct": "e", - "Explanation": "\"explanation : present age is 4 x and 3 x , = > 4 x + 10 = 26 = > x = 4 so deepak age is = 2 ( 4 ) = 8 answer : option e\"" - }, - { - "Answer": 12, - "Options": "a ) a ) 10 , b ) b ) 12 , c ) c ) 15 , d ) d ) 14 , e ) e ) 9", - "Correct": "b", - "Explanation": "\"let the numbers be x , 2 x , 3 x then , x ^ 2 + 4 x ^ 2 + 9 x ^ 2 = 2016 14 x ^ 2 = 2016 x ^ 2 = 144 x = 12 answer is b\"" - }, - { - "Answer": 18, - "Options": "a ) 26 , b ) 24 , c ) 18 , d ) 20 , e ) 22", - "Correct": "c", - "Explanation": "\"{ total } = { writers } + { editors } - { both } + { neither } . { total } = 100 ; { writers } = 45 ; { editors } > 38 ; { both } = x ; { neither } = 2 x ; 100 = 45 + { editors } - x + 2 x - - > x = 55 - { editors } . we want to maximize x , thus we should minimize { editors } , minimum possible value of { editors } is 37 , thus x = { both } = 55 - 37 = 18 . answer : c .\"" - }, - { - "Answer": 33, - "Options": "a ) 24 % , b ) 27 % , c ) 30 % , d ) 33 % , e ) 36 %", - "Correct": "d", - "Explanation": "\"63 % answered the first question correctly and 20 % answered neither correctly . then 17 % missed the first question but answered the second question correctly . then the percent who answered both correctly is 50 % - 17 % = 33 % . the answer is d .\"" - }, - { - "Answer": 42, - "Options": "a ) 32 , b ) 52 , c ) 62 , d ) 42 , e ) 48", - "Correct": "d", - "Explanation": "\"ci * vi = cf * vf ( 7 / 12 ) * ( v 1 - 18 ) = ( 7 / 16 ) * v 1 ( v 1 - 18 ) / v 1 = 3 / 4 18 accounts for the difference of 1 on ratio scale so initial volume = v 1 = 4 * 18 = 72 litres . 7 / 12 of the initial mixture was liquid a so liquid a was ( 7 / 12 ) * 72 = 42 litres . answer : d\"" - }, - { - "Answer": 90, - "Options": "a ) 60 , b ) 90 , c ) 100 , d ) 130 , e ) 150", - "Correct": "b", - "Explanation": "\"20 stamps are both foreign and more than 10 years old . 60 stamps are foreign only . 30 stamps are 10 years old only . the number of remaining stamps is 200 - ( 20 + 60 + 30 ) = 90 the answer is b .\"" - }, - { - "Answer": 2890, - "Options": "a ) rs . 2890 , b ) rs . 2330 , c ) rs . 1190 , d ) rs . 1620 , e ) rs . 2680", - "Correct": "a", - "Explanation": "\"ram : gopal = 7 : 17 = 49 : 119 gopal : krishan = 7 : 17 = 119 : 289 ram : gopal : krishan = 49 : 119 : 289 ram : krishan = 49 : 289 thus , 49 : 289 = 490 : n & there n = 289 x 490 / 49 = rs . 2890 answer : a\"" - }, - { - "Answer": 40, - "Options": "a ) 40 , b ) 45 , c ) 35 , d ) 30 , e ) 50", - "Correct": "a", - "Explanation": "= = 3 : 5 : 7 total parts = 15 = the largest number value is 70 = the largest number is = 7 = then 7 parts - - - - - > 70 ( 7 * 10 = 70 ) = smallest number = 3 & largest number = 7 = difference between smallest number & largest number is = 7 - 3 = 4 = then 4 parts - - - - - > 40 ( 4 * 10 = 40 ) a" - }, - { - "Answer": 2400, - "Options": "a ) s 1200 , b ) s 1500 , c ) s 1600 , d ) s 1900 , e ) s 2400", - "Correct": "e", - "Explanation": "\"explanation : let p = faruk , q = vasim , r = ranjith let p = 3 x , q = 5 x and r = 11 x . then , 5 x = 1500 ? x = 300 . p = 900 , q = 1500 and r = 3300 . hence , ( r - p ) = ( 3300 - 900 ) = 2400 answer : e\"" - }, - { - "Answer": 0.13237136890070247, - "Options": "a ) 1 / 250 , b ) 1 / 84 , c ) 1 / 11 , d ) 9 / 68 , e ) 1 / 3", - "Correct": "d", - "Explanation": "\"probability of chosing one defective phone from a lot of 230 which ontains 84 defective phones is = ( 84 / 230 ) probability of chosing one defective phone from a lot of 229 ( we already picked one ) which ontains 83 ( we already picked one ) defective phones is = ( 83 / 229 ) combined probability of series of events = product of the probabilities = ( 84 / 230 ) * ( 83 / 229 ) 84 / 230 is close to ( 23 / 63 ) and ( 83 / 229 ) = ( 29 / 80 ) so answer is ( 23 / 63 ) * ( 29 / 80 ) = ( 9 / 68 ) so , answer will be d\"" - }, - { - "Answer": 13, - "Options": "a ) 7 , b ) 13 , c ) 9 , d ) 12 , e ) 10", - "Correct": "b", - "Explanation": "b 13 add 1 + 10 + 4 to get 15 . then subtract 21 from the total students \u21d2 28 \u2013 15 = 13 . answer is b" - }, - { - "Answer": 600, - "Options": "a ) $ 700 , b ) $ 600 , c ) $ 900 , d ) $ 500 , e ) $ 400", - "Correct": "b", - "Explanation": "\"b ' s share = 1800 * 3 / 9 = $ 600 answer is b\"" - }, - { - "Answer": 4, - "Options": "a ) 1 : 4 , b ) 2 : 5 , c ) 4 : 1 , d ) 3 : 5 , e ) 2 : 3", - "Correct": "c", - "Explanation": "the answer is suppose to be c . 4 : 1 . it ' s from the gmatprep answer : option c" - }, - { - "Answer": 0.7666666666666667, - "Options": "a ) 23 / 30 , b ) 11 / 15 , c ) 7 / 10 , d ) 1 / 6 , e ) 2 / 15", - "Correct": "a", - "Explanation": "let total housing units = 5 x . as per question , equipped with cable tv = x equipped with vcr = x / 2 , which includes x / 3 ctv . so , only vcr = x / 2 - x / 3 = x / 6 . so , cable tv + vcr = x + x / 6 = 7 x / 6 no cable tv and vcr = 5 x - 7 x / 6 = 23 x / 6 . fraction = 23 x / ( 6 * 5 x ) = 23 / 30 . hence , a" - }, - { - "Answer": 40, - "Options": "a ) 27 , b ) 40 , c ) 45 , d ) 72 , e ) 117", - "Correct": "b", - "Explanation": "the ratio of b to g is 5 : 13 and the other data point is g are more than boys by 64 . . . looking at the ratio we can say that the 8 ( 13 - 5 ) extra parts caused this diff of 64 . so 1 part corresponds to 64 / 8 = 8 and so 5 parts correspond to 5 * 8 = 40 . b" - }, - { - "Answer": 340, - "Options": "a ) 120 , b ) 180 , c ) 340 , d ) 280 , e ) 320", - "Correct": "c", - "Explanation": "\"3 x = 510 x = 170 therefore , the salesman sold 170 kg in the morning and 2 \u22c5 170 = 340 kg in the afternoon . so answer is c .\"" - }, - { - "Answer": 55, - "Options": "a ) 10 % , b ) ( 8 ) 20 % , c ) 30 % , d ) 50 % , e ) 55 %", - "Correct": "e", - "Explanation": "\"i did n ' t understand how to connect 20 percent with the whole equation . why 20 is out of the percentile diagram ( circles ) but inside of 100 ? 20 % appeared in the exam ; however did not answer question aquestion b correctly so they are out of the two circles , however as they have appeared in the exam , they have to be taken into consideration for calculation purpose i am doing it this way : suppose the total class size is 100 , then 20 percent of the class answered incorrectly and rest 80 percent answered correctly in question 1 or 2 or both . now , 100 - [ ( 80 - x ) + x + ( 55 - x ) ] = 20 . . . . . . . . . . values are in percent x = 20 - 100 + 135 x = 55 ans : e\"" - }, - { - "Answer": 50, - "Options": "a ) 50 , b ) 100 , c ) 150 , d ) 200 , e ) 250", - "Correct": "a", - "Explanation": "divide 300 by 6 , as the numbers which are divisible by both 2 and 3 are also divisible by 6 . the quotient obtained after dividing 300 by 6 is 50 , hence answer is 50 . option a" - }, - { - "Answer": 9, - "Options": "a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13", - "Correct": "a", - "Explanation": "( 700 \u2013 300 ) / 42 = 9 22 / 42 = > 9 numbers answer : a" - }, - { - "Answer": 28, - "Options": "a ) 28 , b ) 26 , c ) 22 , d ) 31 , e ) 21", - "Correct": "a", - "Explanation": "total people eat veg = only veg + both veg and non veg total = 16 + 12 = 28 answer = a" - }, - { - "Answer": 7, - "Options": "a ) 7 , b ) 8 , c ) 14 , d ) 20 , e ) 28", - "Correct": "a", - "Explanation": "\"we are told that all of the letters contain either a dot or a straight line or both , which implies that there are no letters without a dot and a line ( no line / no dot box = 0 ) . first we find the total # of letters with lines : 9 + 24 = 33 ; next , we find the total # of letters without line : 40 - 33 = 7 ; finally , we find the # of letters that contain a dot but do not contain a straight line : 7 - 0 = 7 . a\"" - }, - { - "Answer": 47, - "Options": "a ) 45 , b ) 47 , c ) 49 , d ) 51 , e ) 53", - "Correct": "b", - "Explanation": "\"lets assume ac = 53 ( includesonly ac carsandcars with ac and racing stripes ) lets assume rs ( racing stripes ) > = 53 ( includescars with ac and racing stripesandonly racing stripes ) . now since we want to maximize ( only ac ) we have to see to it thatcars with ac and racing stripesis minimal ( assume 0 ) but since rs > = 53 . . we have to assign atleast 6 tocars with ac and racing stripes . hence ac = 53 - 6 = 47 . the answer is b\"" - }, - { - "Answer": 14, - "Options": "a ) 24.58 , b ) 24.5 , c ) 24.3 , d ) 24.9 , e ) 14", - "Correct": "e", - "Explanation": "\"if rahul age is x , then sachin age is x - 4 , so ( x - 4 ) / x = 7 / 9 = > 9 x - 36 = 7 x = > 2 x = 36 = > x = 18 so sachin age is 18 - 4 = 14 answer : e\"" - }, - { - "Answer": 14, - "Options": "a ) 12 , b ) 15 , c ) 16 , d ) 18 , e ) 14", - "Correct": "e", - "Explanation": "\"draw a venn diagram yourself ! b + c - bc = number of students that play either basketball or cricket 10 + 8 - 4 = 14 e )\"" - }, - { - "Answer": 12, - "Options": "a ) 2 , b ) 8 , c ) 12 , d ) 15 , e ) 18", - "Correct": "c", - "Explanation": "total - neither = all power steering + all power windows - both or 65 - neither = 45 + 25 - 17 = 53 . = > neither = 12 , hence c . answer : c" - }, - { - "Answer": 50, - "Options": "a ) 28 , b ) 32 , c ) 40 , d ) 53 , e ) 50", - "Correct": "e", - "Explanation": "\"let the numbers be 2 x and 3 x . then , their l . c . m . = 6 x . so , 6 x = 60 or x = 10 . the numbers are 20 and 30 . hence , required sum = ( 20 + 30 ) = 50 . answer : option e\"" - }, - { - "Answer": 16, - "Options": "a ) 24 , b ) 18 , c ) 12 , d ) 16 , e ) 13", - "Correct": "d", - "Explanation": "let the present age of viju be 7 x years and that of aju be 2 x years . then , 4 years from now 7 x + 4 / 2 x + 4 = 5 / 2 or 4 x = 12 or x = 3 viju present age = 7 * 3 = 21 years viju age 5 years ago = 21 - 5 = 16 years answer : d" - }, - { - "Answer": 330, - "Options": "a ) 980 , b ) 330 , c ) 660 , d ) 990 , e ) 300", - "Correct": "b", - "Explanation": "6 , 16,26 , 36,46 , 56,76 , 86,96 replace by 9 then 3 * 9 = 27 60,61 , 62,63 , 64,65 , 66,67 , 68,69 then increase by 30 i . e , 30 * 10 = 300 + 3 99 - 66 = 33 - 30 it will be 330 answer : b" - }, - { - "Answer": 87.5, - "Options": "a ) 87.9 , b ) 87.5 , c ) 87.7 , d ) 87.6 , e ) 43.3", - "Correct": "b", - "Explanation": "answer : b explanation : speed of 2 nd train = 400 / 4 = 100 kmph since the ratios are in 7 : 8 speed of first train = 7 / 8 \u00d7 100 = 87.5 kmph answer : b" - }, - { - "Answer": 594, - "Options": "a ) 110 , b ) 330 , c ) 550 , d ) 594 , e ) 880", - "Correct": "d", - "Explanation": "\"students enrolled in biology are 32.5 % and therefore not enrolled are 67.5 % . so of 880 is 880 * . 675 = 594 answer is d 594\"" - }, - { - "Answer": 31.524390243902438, - "Options": "a ) 0.125 % , b ) 1.25 % , c ) 31.7 % , d ) 125 % , e ) 0.152 %", - "Correct": "c", - "Explanation": "9.18 x + 5.17 x + 2.05 x = 16.4 x = 148 cookies x = 148 / 16.4 = 9 ( approx ) so , ingrid baked 9 * 5.17 cookies or 47 cookies ( approx ) % share = 47 / 148 = 31.7 approx hence , answer is c ." - }, - { - "Answer": 72, - "Options": "a ) 4 , b ) 24 , c ) 30 , d ) 72 , e ) 80", - "Correct": "d", - "Explanation": "\"one option is to set up the equations and solve : if the ratio of two integers x and y is 1 to 4 , then 4 x = y , where x is the smaller integer . if adding 6 to the smaller integer makes the ratio 1 to 3 , then 3 ( x + 6 ) = y . substituting y = 4 x into the second equation yields 3 x + 18 = 4 x . so , x = 18 ( smaller integer ) and , y = 4 x = 72 ( larger integer ) so d is the correct answer . another option is to test the answer choices . a ) the larger number is 4 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 1 if 6 is added to the smaller number , the ratio becomes 1 to 3 if we add 6 to the smaller number ( 1 ) , we get 7 . so , the new ratio is 7 to 4 . no good . we want a resulting ratio of 1 to 3 eliminate a b ) the larger number is 24 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 6 if 6 is added to the smaller number , the ratio becomes 1 to 3 if we add 6 to the smaller number ( 6 ) , we get 12 so , the new ratio is 12 to 24 which is 1 to 2 . no good . we want a resulting ratio of 1 to 3 eliminate b c ) the larger number is 30 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 7.5 ( which is not an integer ) since both numbers are integers , the larger number can not be 30 . eliminate c d ) the larger number is 72 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 18 if 6 is added to the smaller number , the ratio becomes 1 to 3 if we add 6 to the smaller number ( 18 ) , we get 24 so , the new ratio is 24 to 72 . this is the same as the ratio of 1 to 3 therefore ( d ) is correct e ) the larger number is 80 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 20 if 6 is added to the smaller number , the ratio becomes 1 to 3 if we add 6 to the smaller number ( 20 ) , we get 26 so , the new ratio is 26 to 80 which is 13 to 40 . no good . we want a resulting ratio of 1 to 3 eliminate e therefore d is the only correct choice .\"" - }, - { - "Answer": 1281, - "Options": "a ) 1200 , b ) 1500 , c ) 1281 , d ) 1339 , e ) 1296", - "Correct": "c", - "Explanation": "no of boys = 7 no of girls = 8 therefore , no of ways at least 3 boy can be selected = 7 c 5 * 8 c 0 + 7 c 4 * 8 c 1 + 7 c 3 * 8 c 2 = 1281 ans - c" - }, - { - "Answer": 24, - "Options": "a ) 12 , b ) 14 , c ) 15 , d ) 24 , e ) 36", - "Correct": "d", - "Explanation": "\"the number of women doubled means that they have become 24 from 12 . . and we have to tell the current strength so 24 is the answer . . let the number be 4 x and 5 x . . given 4 x + 2 = 14 . . so x = 3 . . women number q = 5 * 3 - 3 = 12 , then doubled = 24 . . ans d\"" - }, - { - "Answer": 200, - "Options": "a ) 100 , b ) 150 , c ) 200 , d ) 350 , e ) 450", - "Correct": "c", - "Explanation": "ans : by framing equations we get 30 l + 3 q = 663 30 l + 6 q = 726 eliminate q by multiplying the first equation by 2 and subtracting second equation from the first then we get l = 20 cost of 10 kgs of apples = 10 x 20 = 200 answer : c" - }, - { - "Answer": 1, - "Options": "a ) 1 , b ) 3 / 2 , c ) 2 , d ) 5 , e ) 7", - "Correct": "a", - "Explanation": "solution given expression = log 9 / log 4 \u00d7 log 2 / log 3 \u2039 = \u203a log 3 \u00b2 / log 2 \u00b2 \u00d7 log 2 / log 3 = 2 log 3 / 2 log 2 \u00d7 log 2 / log 3 = 1 . answer a" - }, - { - "Answer": 11, - "Options": "a ) 6 , b ) 8 , c ) 10 , d ) 11 , e ) 14", - "Correct": "d", - "Explanation": "26 + 20 - 17 = 29 40 - 29 = 11 play neither answer is d" - }, - { - "Answer": 840, - "Options": "a ) 462 , b ) 450 , c ) 840 , d ) 504 , e ) 555", - "Correct": "c", - "Explanation": "\"explanation : hcf of the two numbers = 42 hcf will be always a factor of lcm 42 is factor of lcm other two factors are 10 & 20 then the numbers are ( 42 * 10 ) and ( 42 x 20 ) = 420 and 840 answer : option c\"" - }, - { - "Answer": 0.2, - "Options": "a ) 1 / 5 , b ) 1 / 6 , c ) 1 / 10 , d ) 2 / 12 , e ) 1 / 8", - "Correct": "a", - "Explanation": "if female is 2 and male is 10 , then 1 / 5 . so ratio of female to male is = 2 / 10 = 1 / 5 answer : a" - }, - { - "Answer": 150, - "Options": "a ) 134 , b ) 138 , c ) 142 , d ) 146 , e ) 150", - "Correct": "e", - "Explanation": "\"the number of nurses at the hospital is ( 3 / 5 ) * 250 = 150 . the answer is e .\"" - }, - { - "Answer": 200, - "Options": "a ) 40 , b ) 120 , c ) 180 , d ) 200 , e ) 220", - "Correct": "d", - "Explanation": "this is similar to handshake problem , if there are nn people , then number of handshakes = 1 + 2 + . . . n = n \u2217 ( n \u2212 1 ) / 2 no . of women be xx and given x \u2217 ( x \u2212 1 ) / 2 = 45 this gives x = 10 | | | y no . of men : solve y \u2217 ( y \u2212 1 ) / 2 = 190 . this gives y = 20 so total men vs . women = 10 * 20 = 200 . answer is d" - }, - { - "Answer": 9720.000000000002, - "Options": "a ) s . 7500 , b ) s . 8000 , c ) s . 8500 , d ) s . 9720 , e ) s . 6000", - "Correct": "d", - "Explanation": "\"let hari \u2019 s capital be rs . x . then , 3780 * 12 / 7 x = 2 / 3 = > 14 x = 136080 = > x = 9720 . answer : d\"" - }, - { - "Answer": 112, - "Options": "a ) 42 , b ) 66 , c ) 98 , d ) 112 , e ) 154", - "Correct": "d", - "Explanation": "\"let us assume the number of dogs , cats and bunnies to be 4 x , 7 x and 9 x total dogs and bunnies = 13 x . and we are given that 13 x = 364 . hence x = 28 . dogs = 4 x = 4 * 28 = 112 ( option d )\"" - }, - { - "Answer": 391, - "Options": "a ) 338 , b ) 278 , c ) 322 , d ) 231 , e ) 391", - "Correct": "e", - "Explanation": "\"clearly , the numbers are ( 23 * 16 ) and ( 23 * 17 ) . larger number = ( 23 * 17 ) = 391 . answer : e\"" - }, - { - "Answer": 450, - "Options": "a ) rs . 200 , b ) rs . 250 , c ) rs . 300 , d ) rs . 450 , e ) none of these", - "Correct": "d", - "Explanation": "\"explanation : let the cost of one pen is \u2018 5 x \u2019 and pencil is \u2018 x \u2019 3 x 5 x + 5 x = rs . 150 15 x + 5 x = rs . 150 x = 150 / 20 = 7.50 : . cost of 1 pen = 5 x = 5 x 7.50 = 37.50 : . cost of 12 pens , i . e . ( one dozen ) = 37.50 x 12 = rs . 450 answer : option d\"" - }, - { - "Answer": 50, - "Options": "a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70", - "Correct": "c", - "Explanation": "explanation : solution : n ( a ) = 160 , n ( b ) = 90 , n ( a u b ) = 250 - 50 = 200 . required number = > n ( a ^ b ) = n ( a ) + n ( b ) - n ( a u b ) = 160 + 90 - 200 = 250 - 200 = 50 . answer : c" - }, - { - "Answer": 65, - "Options": "a ) 10 % , b ) ( 8 ) 20 % , c ) 30 % , d ) 50 % , e ) 65 %", - "Correct": "e", - "Explanation": "{ total } = { first } + { second } - { both } + { neither } 100 % = 75 % + 70 % - { both } + 20 % - - > { both } = 65 % . answer : e ." - }, - { - "Answer": 90, - "Options": "a ) 90 , b ) 162 , c ) 250 , d ) 270 , e ) 322", - "Correct": "a", - "Explanation": "\"total number of fractions = 2 + 10 = 12 element b constitutes = 10 out of 12 parts of x so in 108 gms of x have 108 * 10 / 12 = 90 gms of b and 108 - 90 = 18 gms of a . cross check : - a / b = 18 / 90 = 2 / 10 ( as given ) ans a\"" - }, - { - "Answer": 0.8666666666666667, - "Options": "a ) 1 / 2 , b ) 2 / 3 , c ) 13 / 15 , d ) 23 / 30 , e ) 4 / 5", - "Correct": "c", - "Explanation": "let total no . of students be 30 students left on a field trip = 4 / 5 ( 30 ) = 24 thus 6 students left behind 1 / 3 ( 6 ) = 2 students did not want to go . thus 4 students want to go on the trip 1 / 2 ( 4 ) = 2 were able to join the other students on the field trip . thus total number of students that went on a field trip = 24 + 2 = 26 thus required fraction = 26 / 30 = 13 / 15 c" - }, - { - "Answer": 0.4871794871794872, - "Options": "a ) 8 / 15 , b ) 2 / 5 , c ) 3 / 5 , d ) 11 / 15 , e ) 19 / 39", - "Correct": "e", - "Explanation": "\"drawing two balls of same color from five green balls can be done in 5 c \u2082 ways . similarly from eight white balls two can be drawn in \u2078 c \u2082 ways . p = 5 c \u2082 / \u00b9 \u2075 c \u2082 + \u2078 c \u2082 / \u00b9 \u2075 c \u2082 = 19 / 39 answer : e\"" - }, - { - "Answer": 150, - "Options": "a ) 72 , b ) 96 , c ) 108 , d ) 120 , e ) 150", - "Correct": "e", - "Explanation": "\"{ total } = { french } + { russian } - { both } + { neither } { total } = 17 + ( { total } - 32 ) - ( 0.1 * { total } ) + 0.2 * { total } solving gives { total } = 150 . answer : e .\"" - }, - { - "Answer": 9, - "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", - "Correct": "c", - "Explanation": "\"let x play both badminton and tennis so 17 - x play only badminton and 19 - x play only tennis . 2 play none and there are total 30 students . hence , ( 17 - x ) + ( 19 - x ) + x + 3 = 30 39 - 2 x + x = 30 39 - x = 30 x = 9 so 9 members play both badminton and tennis . c\"" - }, - { - "Answer": 2000, - "Options": "a ) 500 , b ) 1000 , c ) 1500 , d ) 2000 , e ) 2500", - "Correct": "d", - "Explanation": "\"let the income and the expenditure of the person be rs . 7 x and rs . 6 x respectively . income , 7 x = 14000 = > x = 2000 savings = income - expenditure = 7 x - 6 x = x so , savings = rs . 2000 . answer : d\"" - }, - { - "Answer": 56, - "Options": "a ) 20 , b ) 56 , c ) 120 , d ) 560 , e ) 720", - "Correct": "b", - "Explanation": "1 ) is it important here that how many go into finals . . . no . . . . what is important is how many get medals . . 3 finally these 3 can be any of the 8 - 8 c 3 = 8 ! 5 ! 3 ! = 8 \u2217 7 \u2217 63 \u2217 2 = 568 c 3 = 8 ! 5 ! 3 ! = 8 \u2217 7 \u2217 63 \u2217 2 = 56 2 ) is order important . . . no we are looking for groups only . . ans 56 answer : b" - }, - { - "Answer": 33, - "Options": "a ) 11 , b ) 33 , c ) 24 , d ) 27 , e ) 32", - "Correct": "b", - "Explanation": "b is correct r / b = 3 / 8 and b = 90 r = 90 * 3 / 8 = 33" - }, - { - "Answer": 0.4666666666666667, - "Options": "a ) 14 / 15 , b ) 3 / 5 , c ) 6 / 13 , d ) 7 / 15 , e ) 7 / 10", - "Correct": "d", - "Explanation": "probability of first pick not one of the jim ' s picture is = 7 / 10 ( except for 3 which jim purchased ) probability of second pick not one of the jim ' s picture is = 6 / 9 total = 7 / 10 \u2217 6 / 9 = 7 / 15 answer is d option d" - }, - { - "Answer": 139.5, - "Options": "a ) 100.6 kg , b ) 120.3 kg , c ) 139.5 kg , d ) 140.8 kg , e ) 114.5 kg", - "Correct": "c", - "Explanation": "\"quantity of tin in 120 kg of a = 120 * 3 / 5 = 72 kg quantity of tin in 180 kg of b = 180 * 3 / 8 = 67.5 kg quantity of tin in the new alloy = 72 + 67.5 = 139.5 kg answer is c\"" - }, - { - "Answer": 0.4666666666666667, - "Options": "a ) 1 / 2 , b ) 1 / 3 , c ) 2 / 3 , d ) 3 / 5 , e ) 7 / 15", - "Correct": "e", - "Explanation": "drawing two balls of same color from seven black balls can be done in \u2077 c \u2082 ways . similarly from eight white balls two can be drawn in \u2078 c \u2082 ways . p = \u2077 c \u2082 / \u00b9 \u2075 c \u2082 + \u2078 c \u2082 / \u00b9 \u2075 c \u2082 = 7 / 15 answer is e" - }, - { - "Answer": 345, - "Options": "a ) 338 , b ) 278 , c ) 345 , d ) 231 , e ) 121", - "Correct": "c", - "Explanation": "\"clearly , the numbers are ( 23 * 14 ) and ( 23 * 15 ) . larger number = ( 23 * 15 ) = 345 . answer : c\"" - }, - { - "Answer": 49, - "Options": "a ) 49 , b ) 47 , c ) 48 , d ) 51 , e ) 53", - "Correct": "a", - "Explanation": "lets assume ac = 51 ( includesonly ac carsandcars with ac and racing stripes ) lets assume rs ( racing stripes ) > = 51 ( includescars with ac and racing stripesandonly racing stripes ) . now since we want to maximize ( only ac ) we have to see to it thatcars with ac and racing stripesis minimal ( assume 0 ) but since rs > = 51 . . we have to assign atleast 2 tocars with ac and racing stripes . hence ac = 51 - 2 = 49 . the answer is 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 , c = 1000 purchased a only . ( this is much simpler to solve using the venn diagram ) . correct answer is d . 1000\"" - }, - { - "Answer": 3, - "Options": "a ) 4 : 1 , b ) 2 : 1 , c ) 3 : 1 , d ) 4 : 3 , e ) 4 : 5", - "Correct": "c", - "Explanation": "\"( 18 - 24 ) / ( 16 - 18 ) = 6 / 2 = 3 : 1 answer : c\"" - }, - { - "Answer": 38.5, - "Options": "a ) 24.5 , b ) 24.8 , c ) 38.5 , d ) 24.88 , e ) 24.19", - "Correct": "c", - "Explanation": "explanation : if rahul age is x , then sachin age is x + 7 , so , 9 x + 63 = 11 x 2 x = 63 x = 31.5 so sachin age is 31.5 + 7 = 38.5 answer : c ) 38.5" - }, - { - "Answer": 456, - "Options": "a ) 72 , b ) 192 , c ) 456 , d ) 256 , e ) 264", - "Correct": "c", - "Explanation": "total of 3,200 boards . all that fail verification are indeed faulty . so the 64 are indeed faulty . 1 / 8 those that pass are also faulty . from the 3,200 we know 64 fail . so 3,136 must pass . of these 1 / 8 are faulty . 3,136 divided by 8 gives you 392 . what one must do now is to add to the 392 which were not detected the actually detected faulty ones , namely the 64 . total faulty : 456 . answer : c" - }, - { - "Answer": 555681, - "Options": "a ) 553681 , b ) 555181 , c ) 555681 , d ) 556581 , e ) none of these", - "Correct": "c", - "Explanation": "987 = 3 x 7 x 47 . so , required number must be divisible by each one of 3 , 7 , 47 . none of the numbers in 553681 and 555181 are divisible by 3 . while 556581 is not divisible by 7 . correct answer is 555681 . answer : c" - }, - { - "Answer": 14, - "Options": "a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14", - "Correct": "e", - "Explanation": "suppose x green balls need to be added . then , the number of green balls becomes 9 + x , and the number of pink balls remains the same , 23 . but now the ratio of green and pink balls is 1 : 1 this means , ( 9 + x ) / 23 = 1 / 1 solving this we get x = 14 . ans e" - }, - { - "Answer": 19, - "Options": "a ) 20 , b ) 11 , c ) 19 , d ) 31 , e ) 21", - "Correct": "c", - "Explanation": "\"total people eat veg = only veg + both veg and non veg total = 13 + 6 = 19 answer = c\"" - }, - { - "Answer": 96, - "Options": "a ) 99 , b ) 98 , c ) 97 , d ) 96 , e ) 95", - "Correct": "d", - "Explanation": "\"t = 96 = 3 * 32 = 3 * 2 ^ 5 answer is d .\"" - }, - { - "Answer": 45, - "Options": "a ) 15 years , b ) 35 years , c ) 25 years , d ) 45 years , e ) 55 years", - "Correct": "d", - "Explanation": "\"now , sandy is 66 - 6 = 60 molly ' s age is ( 3 / 4 ) * 60 = 45 the answer is d .\"" - }, - { - "Answer": 52, - "Options": "a ) 51 % , b ) 52 % , c ) 53 % , d ) 54 % , e ) 55 %", - "Correct": "b", - "Explanation": "let total no of students 100 , boy 60 and girl 40 , so lunch taken by boy and girl respectively 60 * 60 / 100 = 36 and 40 * 40 / 100 = 16 so total 52 students takes lunch out of 100 students . . so required % is 52 % answer : b" - }, - { - "Answer": 3003, - "Options": "a ) 3003 , b ) 3027 , c ) 3024 , d ) 3021 , e ) 3018", - "Correct": "a", - "Explanation": "\"first , you have to find the common ratio for all 3 books . you have : p : c : b 3 : 2 - - > multiply by 2 ( gives you row 3 ) 4 : 6 6 : 4 : 3 hence : p : c : b : t ( total ) w 6 : 4 : 3 : 13 - - - - > this means , the total number must be a multiple of 13 . answer a is correct since 299 is divisible by 13 , hence is 2990 and so is 3003 ( 2990 + 13 ) .\"" - }, - { - "Answer": 240, - "Options": "a ) 120 , b ) 180 , c ) 240 , d ) 280 , e ) 320", - "Correct": "c", - "Explanation": "\"let x be the number of kilograms he sold in the morning . then in the afternoon he sold 2 x kilograms . so , the total is x + 2 x = 3 x . this must be equal to 360 . 3 x = 360 x = 3603 x = 120 therefore , the salesman sold 120 kg in the morning and 2 \u22c5 120 = 240 kg in the afternoon . so answer is c .\"" - }, - { - "Answer": 35, - "Options": "a ) 15 , b ) 30 , c ) 35 , d ) 42 , e ) 48", - "Correct": "c", - "Explanation": "for deciding such task we should calculate all parts 1 + 7 + 8 = 16 parts and we should calculate how many sandwiches holds 1 part : 80 / 16 = 5 sandwiches in one part for bologna we have 7 parts so : 7 * 5 = 35 answer is c" - }, - { - "Answer": 1.9999999999999998, - "Options": "a ) 2 : 0 , b ) 2 : 1 , c ) 2 : 9 , d ) 2 : 2 , e ) 2 : 5", - "Correct": "b", - "Explanation": "answer : b ) 2 : 1" - }, - { - "Answer": 91.42857142857143, - "Options": "a ) 100.6 kg , b ) 95.4 kg , c ) 117.5 kg , d ) 91.4 kg , e ) 92 kg", - "Correct": "d", - "Explanation": "\"quantity of tin in 90 kg of a = 90 * 4 / 7 = 51.4 kg quantity of tin in 140 kg of b = 140 * 2 / 7 = 40 kg quantity of tin in the new alloy = 51.4 + 40 = 91.4 kg answer is d\"" - }, - { - "Answer": 45, - "Options": "a ) 30 , b ) 45 , c ) 50 , d ) 25 , e ) 60", - "Correct": "b", - "Explanation": "\"let capacity of p be x liters then capacity of q = x / 3 liters capacity of the drum = 60 x required number of turns = 60 x / ( x + x / 3 ) = 60 x * 3 / 4 x = 45 answer is b\"" - }, - { - "Answer": 440, - "Options": "a ) 430 , b ) 440 , c ) 450 , d ) 460 , e ) 470", - "Correct": "b", - "Explanation": "\"we ' re given a series of facts to work with : 1 ) a certain high school has 500 students . 2 ) of these students : x are taking music , y are taking art , and z are taking both music and art . we ' re asked how many students are taking neither music nor art ? let ' s test x = 50 y = 20 z = 10 so , we have 50 students taking music , 20 taking art and 10 taking both music and art . 40 student taking just music 10 student taking just art 10 student taking both music and art total = 60 students we ' re asked for the total number of students who are taking neither course . that is 500 - 60 = 440 . b\"" - }, - { - "Answer": 10080.000000000002, - "Options": "a ) s . 10080 , b ) s . 8000 , c ) s . 8500 , d ) s . 9000 , e ) s . 6000", - "Correct": "a", - "Explanation": "\"let hari \u2019 s capital be rs . x . then , 3920 * 12 / 7 x = 2 / 3 = > 14 x = 141120 = > x = 10080 . answer : a\"" - }, - { - "Answer": 26, - "Options": "a ) 21 , b ) 26 , c ) 28 , d ) 30 , e ) 32", - "Correct": "b", - "Explanation": "\"{ total } = { writers } + { editors } - { both } + { neither } . { total } = 100 ; { writers } = 35 ; { editors } > 38 ; { both } = x ; { neither } = 2 x ; 100 = 35 + { editors } - x + 2 x - - > x = 65 - { editors } . we want to maximize x , thus we should minimize { editors } , minimum possible value of { editors } is 39 , thus x = { both } = 65 - 39 = 26 . answer : b .\"" - }, - { - "Answer": 23, - "Options": "a ) 30 , b ) 10 , c ) 18 , d ) 23 , e ) 32", - "Correct": "d", - "Explanation": "\"total = english + german - both + neither - - > 45 = english + 22 - 12 + 0 - - > english = 35 - - > only english = english - both = 35 - 12 = 23 . answer : d .\"" - }, - { - "Answer": 8, - "Options": "a ) 10 , b ) 2 , c ) 4 , d ) 5 , e ) 8", - "Correct": "e", - "Explanation": "12 kids wear socks 8 kids wear shoes 6 wear both . 12 \u00e2 \u20ac \u201c 6 = 6 ( wear only socks ) 8 \u00e2 \u20ac \u201c 6 = 2 ( wear only shoes ) 6 ( wear both ) hence , 22 - 14 = 8 8 kids are with bare feet . e" - }, - { - "Answer": 4, - "Options": "a ) 12 , b ) 6 , c ) 3 , d ) 1 , e ) 4", - "Correct": "e", - "Explanation": "explanation : let ketchup = 3 x , mustard = 3 x & mayo = 2 x . now , 3 x = 6 hence x = 2 . number of mayo bottles = 2 x which is 4 . answer : e" - }, - { - "Answer": 50, - "Options": "a ) 50 , b ) 80 , c ) 100 , d ) 130 , e ) 150", - "Correct": "a", - "Explanation": "\"20 stamps are both foreign and more than 10 years old . 70 stamps are foreign only . 60 stamps are 10 years old only . the number of remaining stamps is 200 - ( 20 + 70 + 60 ) = 50 the answer is a .\"" - }, - { - "Answer": 34, - "Options": "a ) 33 , b ) 34 , c ) 32 , d ) 28 , e ) 19", - "Correct": "b", - "Explanation": "\"explanation : number students behind the nitin in rank = ( 58 - 24 ) = 34 nitin is 34 nd from the last answer : b ) 34\"" - }, - { - "Answer": 0.4285714285714286, - "Options": "a ) 1 / 5 , b ) 3 / 7 , c ) 2 / 5 , d ) 3 / 5 , e ) 2 / 7", - "Correct": "b", - "Explanation": "let e and f denote respectively the events that first and second ball drawn are black . we have to find p ( e n f ) or p ( ef ) . now p ( e ) = p ( black ball in first draw ) = 10 / 15 also given that the first ball drawn is black , i . e . , event e has occurred , now there are 9 black balls and five white balls left in the urn . therefore , the probability that the second ball drawn is black , given that the ball in the first draw is black , is nothing but the conditional probability of f given that e has occurred . that is p ( f | e ) = 9 / 14 by multiplication rule of probability , we have p ( e n f ) = p ( e ) p ( f | e ) = 10 / 15 \u00d7 9 / 14 = 3 / 7 b" - }, - { - "Answer": 0.5499999999999999, - "Options": "a ) 0.45 , b ) 0.4 , c ) 0.5 , d ) 0.55 , e ) 0.6", - "Correct": "d", - "Explanation": "\"we are apply that formula . . . . . . . . . . . . . . p ( aorb ) = p ( a ) + p ( b ) - p ( a and b ) = . 20 + . 40 - . 15 = . 45 but the probability of neither a nor b = 1 - . 45 = 0.55 answer : d\"" - }, - { - "Answer": 120, - "Options": "a ) 70 , b ) 96 , c ) 108 , d ) 120 , e ) 150", - "Correct": "d", - "Explanation": "2 x 2 matrix will be the easiest way to calculate this . text in black : given statements text in red : calculated values thus d = 120 is the correct answer" - }, - { - "Answer": 180, - "Options": "a ) 378 , b ) 180 , c ) 820 , d ) 734 , e ) 840", - "Correct": "b", - "Explanation": "explanation : 3 x + 4 x = 420 x = 60 = > 3 x = 180 answer : option b" - }, - { - "Answer": 58, - "Options": "a ) 76 % , b ) 58 % , c ) 68 % , d ) 89 % , e ) 49 %", - "Correct": "b", - "Explanation": "let total no of vehicles bought be 100 , toyota 70 and honda 30 , so total number of suv ' s bought for toyota and honda respectively 70 * 70 / 100 = 49 and 30 * 30 / 100 = 9 so total 58 suv ' s were bought out of 100 vehicles bought . . so required % is 58 % answer : b" - }, - { - "Answer": 3, - "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", - "Correct": "c", - "Explanation": "12 ! = 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 4 ! = 24 question can be rephrased as how many 24 ' s are there in 12 ! 12 * 2 = 24 4 * 6 = 24 3 * 8 = 24 value of n = 3 answer : c" - }, - { - "Answer": 120, - "Options": "a ) 45 , b ) 50 , c ) 55 , d ) 60 , e ) 120", - "Correct": "e", - "Explanation": "\"f : c : w 1 : 12 : 30 sport version : f : c 3 : 12 f : w 1 : 60 or 3 : 180 so c : f : w = 12 : 3 : 180 c / w = 12 / 180 = 3 ounces / x ounces x = 8 * 180 / 12 = 120 ounces of water e\"" - }, - { - "Answer": 0.15789473684210525, - "Options": "a ) 1 / 11 , b ) 1 / 12 , c ) 1 / 13 , d ) 3 / 19 , e ) 3 / 43", - "Correct": "d", - "Explanation": "\"in believe the answer is d . please see below for explanation . 0 ) we are told the following ratios cgd - college graduate with degree ncg - non college graduate cgn - college graduate no degree cgd ncg cgn 1 8 3 2 in order to make cgd and cgn comparable we need to find the least common multiple of 8 and 3 and that is 24 multiplying the first ratio by 3 and the second ratio by 8 we get cgd ncg cgn 3 24 16 if one picks a random college graduate at this large company , what is the probability this college graduate has a graduate degree ? nr of cgd = 3 nr of cg = 3 + 16 = 19 probability of cgd / ( cg ) q - > 3 / 19 answer d\"" - }, - { - "Answer": 345, - "Options": "a ) 276 , b ) 299 , c ) 322 , d ) 345 , e ) 354", - "Correct": "d", - "Explanation": "\"clearly , the numbers are ( 23 x 13 ) and ( 23 x 15 ) . larger number = ( 23 x 15 ) = 345 . answer : option d\"" - }, - { - "Answer": 40, - "Options": "a ) 25 , b ) 40 , c ) 50 , d ) 60 , e ) 75", - "Correct": "b", - "Explanation": "we are told that 60 students claimed that they preferred mac to windows , which means that 60 preferred mac but not windows , so # of students who preferred mac ( p ( a ) as you wrote ) , does not equal to 60 , it equals to 60 + 20 ( 20 is # of students who equally preferred both brands ) . also we are asked to find # of the students who preferred windows to mac , so if you denote x as those who prefer windows then you should calculate x - 20 . so , if we use your formula it should be : 210 = { mac } + { windows } - { both } + { neither } = ( 60 + 20 ) + x - 20 + 90 - - > x = 60 ( # of student who prefer windows ) - - > # of the students who preferred windows to mac is x - 20 = 40 ." - }, - { - "Answer": 350, - "Options": "a ) 276 , b ) 299 , c ) 322 , d ) 345 , e ) 350", - "Correct": "e", - "Explanation": "\"clearly , the numbers are ( 25 x 13 ) and ( 25 x 14 ) . larger number = ( 25 x 14 ) = 350 . answer : option e\"" - }, - { - "Answer": 7, - "Options": "a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8", - "Correct": "d", - "Explanation": "\"20 + 23 = 43 but where as total number is 42 - 6 = 36 therefore answer is 43 - 36 = 7 hence answer is d\"" - }, - { - "Answer": 19, - "Options": "a ) 3 , b ) 9 , c ) 11 , d ) 17 , e ) 19", - "Correct": "e", - "Explanation": "\"total number of enrolled students = 29 number of students who did not take test = 5 hence , number of students who took test = 29 - 5 = 24 number of students who answered q 2 correctly = 24 , therefore , all students who took test answered q 2 correctly . so , number of students who answered q 1 correctly , also answered q 2 correctly = 19 . number of students who answered both q 1 & q 2 correctly = 19 . answer : e\"" - }, - { - "Answer": 77.72727272727272, - "Options": "a ) 60 % , b ) 78 % , c ) 88 % , d ) 98 % , e ) 99 %", - "Correct": "b", - "Explanation": "boys : girls = > 5 x : 6 x total no . of students including boys nd girls = 5 x + 6 x = 11 x 25 % of boys = > 5 x * 25 / 100 = 5 x / 4 20 % of girls = > 6 x * 20 / 100 = 6 x / 5 no . of students who are getting scholarship = > 5 x / 4 + 6 x / 5 = 49 x / 20 no . of students who are not getting scholarship = 11 x - 49 x / 20 = 171 x / 20 % of students not getting scolorship = > 171 x / 20 / 11 x * 100 = > 100 * 171 x / 220 x = 77.7 % answer : b" - }, - { - "Answer": 24, - "Options": "a ) 15 , b ) 18 , c ) 21 , d ) 24 , e ) 27", - "Correct": "d", - "Explanation": "now , sandy is 38 - 6 = 32 molly ' s age is ( 3 / 4 ) * 32 = 24 the answer is d ." - }, - { - "Answer": 51.20000000000001, - "Options": "a ) 45 % , b ) 49.6 % , c ) 51.2 % , d ) 55 % , e ) 60.3 %", - "Correct": "c", - "Explanation": "let the total quantity of original milk = 1000 gm milk after 1 st operation = 80 % of 1000 = 800 gm milk after second operation = 80 % of 800 = 640 gm milk after third operation = 80 % of 640 = 512 gm strength of final mixture = 51.2 % answer is c" - }, - { - "Answer": 0.4771241830065359, - "Options": "a ) 8 / 15 , b ) 21 / 44 , c ) 3 / 5 , d ) 11 / 15 , e ) 7 / 15", - "Correct": "b", - "Explanation": "drawing two balls of same color from ten green balls can be done in 10 c \u2082 ways . similarly from eight white balls two can be drawn in \u2078 c \u2082 ways . p = 10 c \u2082 / \u00b9 \u2075 c \u2082 + \u2078 c \u2082 / \u00b9 \u2075 c \u2082 = 21 / 44 answer : b" - }, - { - "Answer": 70, - "Options": "a ) 72 , b ) 70 , c ) 108 , d ) 120 , e ) 150", - "Correct": "b", - "Explanation": "\"{ total } = { french } + { russian } - { both } + { neither } { total } = 25 + ( { total } - 32 ) - ( 0.1 * { total } ) + 0.2 * { total } solving gives { total } = 70 . answer : b .\"" - }, - { - "Answer": 60, - "Options": "a ) 70 , b ) 60 , c ) 90 , d ) 100 , e ) 110", - "Correct": "b", - "Explanation": "consider total number of reader n ( s u l ) = 150 people who read science fiction n ( s ) = 120 people who read literacy works n ( l ) = 90 both science fiction and literacy n ( s \u00e2 \u02c6 \u00a9 l ) = ? n ( s u l ) = n ( s ) + n ( l ) - n ( s \u00e2 \u02c6 \u00a9 l ) 150 = 120 + 90 - n ( s \u00e2 \u02c6 \u00a9 l ) n ( s \u00e2 \u02c6 \u00a9 l ) = 210 - 150 n ( s \u00e2 \u02c6 \u00a9 l ) = 60 so people read both science fiction and literacy works are 160 answer : b" - }, - { - "Answer": 43, - "Options": "a ) 43 , b ) 28 , c ) 44 , d ) 49 , e ) 46", - "Correct": "a", - "Explanation": "8 + 34 + 1 = 43 answer : a" - }, - { - "Answer": 100, - "Options": "a ) 46 , b ) g = 80 , c ) g = 90 , d ) g = 100 , e ) 200", - "Correct": "d", - "Explanation": "\"100 = x + x - 20 + 23 - 23 x = 60 , so , product a = 60 % , product b = 40 % , both = 23 % , neither = 23 % 23 % of the total no . of people should be an integer . so , a , bc are out . 60 % of d and 40 % of d are both integers . so , d satisfies all conditions . so , answer is d .\"" - }, - { - "Answer": 2.46, - "Options": "a ) 3.84 , b ) 1.75 , c ) 3.52 , d ) 2.46 , e ) none of these", - "Correct": "d", - "Explanation": "\"here ' s how i did it . my notes from reading the problem were : 1 l a = 800 gm 1 l b = 850 gm we are mixing five parts ( 3 parts a plus 2 parts b , 5 parts total ) to get 3 l , so 5 x = 3 - - - > x = 3 / 5 . each part is 3 / 5 of a liter . so if we have 3 parts a , we have 800 * 3 * ( 3 / 5 ) = 1440 if we have 2 parts b , we have 850 * 2 * ( 3 / 5 ) = 1020 1440 + 1020 = 2460 solving for units gives us 2.46 so the answer is d\"" - }, - { - "Answer": 546, - "Options": "a ) 562 , b ) 356 , c ) 452 , d ) 416 , e ) 546", - "Correct": "e", - "Explanation": "\"let the number of boys and girls be 8 x and 5 x then , 5 x = 210 x = 42 total number of students = 13 x = 13 * 42 = 546 answer is e\"" - }, - { - "Answer": 0.0047619047619047615, - "Options": "a ) 1 / 210 , b ) 2 / 210 , c ) 3 / 210 , d ) 1 / 119 , e ) 2 / 119", - "Correct": "a", - "Explanation": "there are 3 rotten eggs in a pack of 36 . thus the probability of picking 2 rotten eggs is : ( 3 / 36 ) ( 2 / 35 ) = 1 / 210 . the correct answer is a ." - }, - { - "Answer": 86, - "Options": "a ) 82 , b ) 84 , c ) 86 , d ) 88 , e ) 90", - "Correct": "c", - "Explanation": "\"let x be the weight of the sister . then the student ' s weight is 2 x + 6 . x + ( 2 x + 6 ) = 126 3 x = 120 x = 40 kg then the student ' s weight is 86 kg . the answer is c .\"" - }, - { - "Answer": 9, - "Options": "a ) 3 : 4 , b ) 3 : 0 , c ) 9 : 1 , d ) 9 : 2 , e ) 3 : 9", - "Correct": "c", - "Explanation": "\"let the present ages of a and b be 7 x and 3 x years respectively . then , ( 7 x - 4 ) / ( 3 x + 4 ) = 1 / 1 4 x = 8 = > x = 2 required ratio = ( 5 x + 4 ) : ( 3 x - 4 ) = 18 : 2 = 9 : 1 . answer : c\"" - }, - { - "Answer": 432, - "Options": "a ) 424 . , b ) 428 . , c ) 430 . , d ) 432 . , e ) 436", - "Correct": "d", - "Explanation": "\"students studying random - processing methods = 312 students studying scramjet rocket engines = 232 students studying them both = 112 therefore ; students studying only random processing methods = 312 - 112 = 200 students studying only scramjet rocket engines = 232 - 112 = 120 students studying both = 112 students studying none = 0 ( as mentioned in question that every student in the faculty has to study one of the two subjects ) total students in faculty of aerospace engineering = students of only random processing methods + students of only scramjet rocket engines + both + none total number of students = 200 + 120 + 112 + 0 = 432 . . . . answer d\"" - }, - { - "Answer": 140, - "Options": "a ) 100 , b ) 120 , c ) 180 , d ) 140 , e ) 60", - "Correct": "d", - "Explanation": "\"clearly , the numbers are ( 10 x 13 ) and ( 10 x 14 ) . larger number = ( 10 x 14 ) = 140 . answer : option d\"" - }, - { - "Answer": 9, - "Options": "a ) 9 , b ) 6 , c ) 7 , d ) 8 , e ) 2", - "Correct": "a", - "Explanation": "27 * 12 : 54 * x = 2 : 1 x = 3 12 - 3 = 9 answer : a" - }, - { - "Answer": 35, - "Options": "a ) 25 % , b ) 30 % , c ) 35 % , d ) 40 % , e ) 45 %", - "Correct": "c", - "Explanation": "\"65 % answered the first question correctly and 20 % answered neither correctly . then 15 % missed the first question but answered the second question correctly . then the percent who answered both correctly is 50 % - 15 % = 35 % . the answer is c .\"" - }, - { - "Answer": 20, - "Options": "a ) a ) 8 , b ) b ) 10 , c ) c ) 20 , d ) d ) 30 , e ) e ) 32", - "Correct": "c", - "Explanation": "let the student who speaks tamil - x let the student who speaks telugu - y as ( xuy ) - ( xny ) = total 30 + 40 - ( xny ) = 50 = 20 c )" - }, - { - "Answer": 40, - "Options": "a ) 60 , b ) 40 , c ) 20 , d ) 15 , e ) none", - "Correct": "b", - "Explanation": "\"sol . let the required numbers be 4 x and 5 x . then , their l . c . m . is 20 x . \u2234 20 x = 200 \u21d4 x = 10 . hence , the first number is 40 . answer b\"" - }, - { - "Answer": 11, - "Options": "a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13", - "Correct": "c", - "Explanation": "the intersection for two = 45 - 12 - 22 = 11 play both games . answer : c" - }, - { - "Answer": 7, - "Options": "a ) 7 , b ) 8 , c ) 10 , d ) 15 , e ) 18", - "Correct": "a", - "Explanation": "\"total - neither = all air conditioning + all power steering - both or 75 - neither = 45 + 35 - 12 = 68 . = > neither = 7 , hence a . answer : a\"" - }, - { - "Answer": 4, - "Options": "a ) 3 , b ) 5 , c ) 4 , d ) 7 , e ) 8", - "Correct": "c", - "Explanation": "\"23 + 29 = 52 but where as total number is 55 - 7 = 48 therefore answer is 52 - 48 = 4 hence answer is c\"" - }, - { - "Answer": 4, - "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", - "Correct": "d", - "Explanation": "we first write the prime factorization of each given number 24 = 2 \u00d7 2 \u00d7 2 \u00d7 3 = 23 * cubic * \u00d7 3 40 = 2 \u00d7 2 \u00d7 2 \u00d7 5 = 23 * cubic * \u00d7 5 60 = 2 \u00d7 2 \u00d7 3 \u00d7 5 = 22 * square * \u00d7 3 \u00d7 5 gfc = 22 * square * = 4 corect answer is d ) 4" - }, - { - "Answer": 45, - "Options": "['a ) 45', 'b ) 50', 'c ) 55', 'd ) 60', 'e ) 63']", - "Correct": "a", - "Explanation": "f : c : w 1 : 12 : 30 sport version : f : c 3 : 12 f : w 1 : 60 or 3 : 180 so c : f : w = 12 : 3 : 180 c / w = 12 / 180 = 3 ounces / x ounces x = 3 * 180 / 12 = 45 ounces of water answer : a" - }, - { - "Answer": 2, - "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", - "Correct": "b", - "Explanation": "\"both cooking and weaving = 20 - ( 5 + 8 + 5 ) = 2 so , the correct answer is b .\"" - }, - { - "Answer": 9000, - "Options": "a ) rs . 9228 , b ) rs . 9129 , c ) rs . 9120 , d ) rs . 9000 , e ) rs . 1922", - "Correct": "d", - "Explanation": "let b ' s capital be rs . x . { 3500 \\ 12 } / { 7 x } = { 2 } / { 3 } = > x = 9000 . answer : d" - }, - { - "Answer": 0.4666666666666667, - "Options": "a ) 7 / 18 , b ) 7 / 19 , c ) 7 / 11 , d ) 7 / 12 , e ) 7 / 15", - "Correct": "e", - "Explanation": "\"drawing two balls of same color from seven green balls can be done in \u2077 c \u2082 ways . similarly from eight white balls two can be drawn in ways . 7 / 15 answer : e\"" - }, - { - "Answer": 4, - "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", - "Correct": "d", - "Explanation": "\"both cooking and weaving = 25 - ( 6 + 8 + 7 ) = 4 so , the correct answer is d .\"" - }, - { - "Answer": 8, - "Options": "a ) 26 , b ) 19 , c ) 11 , d ) 8 , e ) 6", - "Correct": "d", - "Explanation": "\"no of dogs = 45 long fur = 28 brown = 17 neither long fur nor brown = 8 therefore , either long fur or brown = 45 - 8 = 37 37 = 28 + 17 - both both = 8 answer d\"" - }, - { - "Answer": 50, - "Options": "a ) 5 , b ) 100 , c ) 7 , d ) 4 , e ) 50", - "Correct": "e", - "Explanation": "say x guests ate both types of meat . ( 125 - x ) + ( 75 - x ) = 100 - - > x = 50 . answer : e ." - }, - { - "Answer": 9000, - "Options": "a ) rs 9000 , b ) rs 7000 , c ) rs 5000 , d ) rs 4000 , e ) none of these", - "Correct": "a", - "Explanation": "\"explanation : let b contribution is x . 3500 * 12 / 7 x = 2 / 3 = > 14 x = 126000 = > x = rs 9000 option a\"" - }, - { - "Answer": 90, - "Options": "['a ) 60 sq . cm', 'b ) 70 sq . cm', 'c ) 95 sq . cm', 'd ) 80 sq . cm', 'e ) 90 sq . cm']", - "Correct": "e", - "Explanation": "let us consider it is a rectangle . so area = 24 * 9 = 216 sq . cm now ( 24 - 3 * 2 ) * ( 9 - 2 * 2 ) = 18 * 5 = 90 sq . cm answer : e" - }, - { - "Answer": 25, - "Options": "a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25", - "Correct": "e", - "Explanation": "let us now solve for x : ( 4 / 5 ) x + ( 1 / 6 ) ( 49 - x ) = 24 24 x + 5 ( 49 - x ) = ( 24 ) ( 30 ) 24 x + 245 - 5 x = ( 24 ) ( 30 ) 19 x = 720 - 245 19 x = 475 x = 25 answer : e" - }, - { - "Answer": 270, - "Options": "a ) 270 , b ) 300 , c ) 299 , d ) 322 , e ) 345", - "Correct": "a", - "Explanation": "\"the numbers are ( 18 x 11 ) and ( 18 x 15 ) . larger number = ( 18 x 15 ) = 270 . answer : a\"" - }, - { - "Answer": 30, - "Options": "a ) 100 , b ) 120 , c ) 140 , d ) 30 , e ) 150", - "Correct": "d", - "Explanation": "\"b / c = 1 / 3 c - b = 20 . . . . . . . . . > b = c - 20 ( c - 20 ) / c = 1 / 3 testing answers . clearly eliminate abce put c = 30 . . . . . . . . . > ( 30 - 20 ) / 30 = 10 / 30 = 1 / 3 answer : d\"" - }, - { - "Answer": 96, - "Options": "a ) 24 , b ) 48 , c ) 60 , d ) 96 , e ) 84", - "Correct": "d", - "Explanation": "\"ok let me see if i can explain what went on in the previous post lets say i have x marbles in the bag in total - - > out of them 12 are red so the probability of pulling a non - red marble is ( x - 12 ) / x now the marble is placed back in the bag and we have x marbles again , of which again 12 are red . so the probability of pulling a non - red marble out is ( x - 12 ) / x probability theorm states that if the probability of event a occuring is m and the probability of event b occuring is n then the probability of both a and b occuring is m * n so therefore the probability of 2 non - red marbles getting pulled out is [ ( x - 12 ) / x ] * [ ( x - 12 ) / x ] this is given as 49 / 64 - - > ( x - 12 ) ^ 2 = 49 / 64 x ^ 2 square rooting u have x - 12 / x = 7 / 8 or x = 96 d\"" - }, - { - "Answer": 66, - "Options": "a ) 42 , b ) 66 , c ) 98 , d ) 112 , e ) 154", - "Correct": "b", - "Explanation": "\"let us assume the number of dogs , cats and bunnies to be 3 x , 7 x and 13 x total dogs and bunnies = 16 x . and we are given that 16 x = 352 . hence x = 22 . dogs = 3 x = 3 * 22 = 66 ( option b )\"" - }, - { - "Answer": 12.00000000000001, - "Options": "a ) 2 % , b ) 5 % , c ) 8 % , d ) 10 % , e ) 12 %", - "Correct": "e", - "Explanation": "\"since we were expected to find a percentage figure - it thought that it might be easier to pick a ' smart number ' to represent the total number of voters ( republicans and democrats ) . therefore , i picked 100 ( as the total number of voters ) and thus 30 : 20 represents the number ratio of republicans : democrats . if 80 % of republicans ( which is ( 60 * 0.8 ) = 48 ) and 20 % of democrats ( 40 * 0.2 = 8 ) voted for candidate x , means that out of total of 100 voters ; 56 ( 48 + 8 ) voters voted for candidate x and 44 voted for candidate y . thus we can infer that candidate x is expected to win the election by 12 ( 56 - 44 ) votes . therefore candidate x is expected to win the election by ( 12 / 100 ) votes which is equivalent to 12 % . i think the answer is e .\"" - }, - { - "Answer": 8, - "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8", - "Correct": "e", - "Explanation": "start with the prime factorization : 210 = 2 * 3 * 5 * 7 for odd factors , we put aside the factor of two , and look at the other prime factors . set of exponents = { 1 , 1 , 1 } plus 1 to each = { 2 , 2 , 2 } product = 2 * 2 * 2 = 8 therefore , there are 8 odd factors of 210 . in case you are curious , they are { 1 , 3 , 5 , 7 , 15 , 21 , 35 , and 105 } answer : e ." - }, - { - "Answer": 120, - "Options": "a ) 12 , b ) 16 , c ) 24 , d ) 48 , e ) 120", - "Correct": "e", - "Explanation": "\"let the numbers be 5 x and 6 x . then their h . c . f = x . so , x = 4 . so , the numbers are 20 and 24 . l . c . m of 20 and 24 = 120 . answer : e\"" - }, - { - "Answer": 0.6000000000000001, - "Options": "a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 5", - "Correct": "e", - "Explanation": "\"let ' s say that the total original mixture a is 100 ml the original mixture a thus has 50 ml of alcohol out of 100 ml of solution you want to replace some of that original mixture a with another mixture b that contains 25 ml of alcohol per 100 ml . thus , the difference between 50 ml and 25 ml is 25 ml per 100 ml of mixture . this means that every time you replace 100 ml of the original mixture a by 100 ml of mixture b , the original alcohol concentration will decrease by 25 % . the question says that the new mixture , let ' s call it c , must be 35 % alcohol , a decrease of only 15 % . therefore , 15 out of 25 is 3 / 5 and e is the answer .\"" - }, - { - "Answer": 1540, - "Options": "a ) 80 , b ) 160 , c ) 720 , d ) 1100 , e ) 1540", - "Correct": "e", - "Explanation": "\"no . of ways of picking 2 biology books ( from 11 books ) = 11 c 2 = ( 11 * 10 ) / 2 = 55 no . of ways of picking 2 chemistry books ( from 8 books ) = 8 c 2 = ( 8 * 7 ) / 2 = 28 total ways of picking 2 books of each type = 55 * 28 = 1540 ( option e )\"" - }, - { - "Answer": 0.85, - "Options": "a ) 0.9 , b ) 0.85 , c ) 0.6 , d ) 0.8 , e ) 0.5", - "Correct": "b", - "Explanation": "according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 50 + 25 + 10 ) / 100 = 85 / 100 = 0.85 . answer is b" - }, - { - "Answer": 18, - "Options": "a ) 18 , b ) 15 , c ) 77 , d ) 266 , e ) 182", - "Correct": "a", - "Explanation": "\"present age is 4 x and 3 x , = > 4 x + 6 = 30 = > x = 6 so deepak age is = 3 ( 6 ) = 18 answer : a\"" - }, - { - "Answer": 20, - "Options": "a ) 20 , b ) 96 , c ) 108 , d ) 120 , e ) 150", - "Correct": "a", - "Explanation": "\"{ total } = { french } + { russian } - { both } + { neither } { total } = 30 + ( { total } - 32 ) - ( 0.1 * { total } ) + 0.2 * { total } solving gives { total } = 20 . answer : a .\"" - }, - { - "Answer": 300, - "Options": "a ) 120 , b ) 180 , c ) 300 , d ) 280 , e ) 320", - "Correct": "c", - "Explanation": "3 x = 450 x = 150 therefore , the salesman sold 150 kg in the morning and 2 \u22c5 150 = 300 kg in the afternoon . so answer is c ." - }, - { - "Answer": 32, - "Options": "a ) 30 , b ) 10 , c ) 18 , d ) 28 , e ) 32", - "Correct": "e", - "Explanation": "\"total = english + german - both + neither - - > 54 = english + 22 - 12 + 0 - - > english = 44 - - > only english = english - both = 44 - 12 = 32 . answer : e .\"" - }, - { - "Answer": 12, - "Options": "a ) 8 , b ) 4 , c ) 12 , d ) 16 , e ) 14", - "Correct": "c", - "Explanation": "explanation : let forks = 4 x , spoons = 4 x & knives = 3 x . now , 4 x = 16 hence x = 4 . number of knives = 3 x = 12 . answer : c" - }, - { - "Answer": 20, - "Options": "a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30", - "Correct": "c", - "Explanation": "\"neither car nor garage = total - garage - ( swim - common ) = 75 - 50 - ( 40 - 35 ) = 75 - 55 = 20 answer c\"" - }, - { - "Answer": 0.15789473684210525, - "Options": "a ) 1 / 11 , b ) 1 / 12 , c ) 1 / 13 , d ) 3 / 19 , e ) 3 / 43", - "Correct": "d", - "Explanation": "\"in believe the answer is d . please see below for explanation . 0 ) we are told the following ratios cgd - college graduate with degree ncg - non college graduate cgn - college graduate no degree cgd ncg cgn 1 8 3 2 in order to make cgd and cgn comparable we need to find the least common multiple of 8 and 3 and that is 24 multiplying the first ratio by 3 and the second ratio by 8 we get cgd ncg cgn 3 24 16 if one picks a random college graduate at this large company , what is the probability this college graduate has a graduate degree ? nr of cgd = 3 nr of cg = 3 + 16 = 19 probability w of cgd / ( cg ) - > 3 / 19 answer d\"" - }, - { - "Answer": 400, - "Options": "a ) 40 , b ) 200 , c ) 400 , d ) 800 , e ) 4000", - "Correct": "c", - "Explanation": "\"4 : 1 = x : 100 x = 4 * 100 x = 400 answer : c\"" - }, - { - "Answer": 11, - "Options": "a ) 12 , b ) 13 , c ) 11 , d ) 14 , e ) 5", - "Correct": "c", - "Explanation": "some multiple of 7 + some multiple of 5 should yield 63 . to get to a some multiple of 5 , we should ensure that a 3 or 8 ( 5 + 3 ) should be a multiple of 7 . 63 is a direct multiple of 7 , however in this case there wo n ' t be any guava . hence the next option is to look for a multiple of 7 that has 8 as the unit digit . 28 satisfies this hence no . of apples is 4 and no of bananas is 7 . c" - }, - { - "Answer": 660, - "Options": "a ) 500 , b ) 600 , c ) 620 , d ) 640 , e ) 660", - "Correct": "e", - "Explanation": "\"we know 25 % people study biology , therefore the no of people not studying = 100 - 25 = 75 % > therefore the people not studying biology out of a total 880 people are = 75 % of 880 > ( 75 / 100 ) * 880 = 660 people e\"" - }, - { - "Answer": 4, - "Options": "a ) 4 , b ) 2 , c ) 3 , d ) 5 , e ) 6", - "Correct": "a", - "Explanation": "explanation : l . c . m of 25650 = 2 x 3 x 3 x 3 x 5 x 5 x 19 3 , 2 , 5,19 number of different prime factors is 4 . answer : option a" - }, - { - "Answer": 27, - "Options": "a ) 9 , b ) 19 , c ) 23 , d ) 45 , e ) 27", - "Correct": "e", - "Explanation": "\"number of students taking history = h = 36 number of students taking statistics = s = 32 total number of students = t = 90 number of students taking history or statistics or both = b = 59 number of students taking neither history nor statistics = n = 95 - 59 = 36 letxbe the number of students taking both history and statistics . then t = h + s + n - x or 95 = 36 + 32 + 36 - x or x = 9 now , number of students taking only history will be h - x or 36 - 9 = 27 answer : - e\"" - }, - { - "Answer": 3, - "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 3 , e ) 7", - "Correct": "d", - "Explanation": "prime factors of 60 are 2 ^ 2,3 ^ 1,5 ^ 1 total divisors = ( power if a prime factor + 1 ) total no . of odd factors ( 3,5 , ) = ( 1 + 1 ) ( 1 + 1 ) = 4 since we need odd divisors other than 1 = > 4 - 1 = 3 odd divisors d is the answer" - }, - { - "Answer": 100, - "Options": "a ) 100 , b ) 36 , c ) 45 , d ) 72 , e ) 117", - "Correct": "a", - "Explanation": "\"the ratio of b to g is 5 : 13 and the other data point is g are more than boys by 160 . . . looking at the ratio we can say that the 8 ( 13 - 5 ) extra parts caused this diff of 160 . so 1 part corresponds to 160 / 8 = 20 and so 5 parts correspond to 5 * 10 = 100 . a\"" - }, - { - "Answer": 150, - "Options": "a ) 120 , b ) 150 , c ) 100 , d ) 180 , e ) 220", - "Correct": "b", - "Explanation": "\"n ( a ) = 325 , n ( b ) = 175 , n ( aub ) = 400 - 50 = 350 . required number = n ( anb ) = n ( a ) + n ( b ) - n ( aub ) = 325 + 175 - 350 = 150 . answer is b\"" - }, - { - "Answer": 555707.2899999999, - "Options": "a ) 553681 , b ) 555181 , c ) 555681 , d ) 556581 , e ) 556881", - "Correct": "c", - "Explanation": "987 = 3 x 7 x 47 so , the required number must be divisible by each one of 3 , 7 , 47 553681 - > ( sum of digits = 28 , not divisible by 3 ) 555181 - > ( sum of digits = 25 , not divisible by 3 ) 555681 is divisible by 3 , 7 , 47 answer c" - }, - { - "Answer": 3.9999999999999996, - "Options": "a ) 4 , b ) 1 / 4 , c ) 2 , d ) 9 , e ) 1 / 9", - "Correct": "a", - "Explanation": "65 = ( a 1 + a 2 + a 3 + a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) factorize the same terms 65 = 1 + ( a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) write every term with respect to r a 1 = a 1 a 2 = a 1 * r ^ 1 a 3 = a 1 * r ^ 2 . . . . . . . . . 65 = 1 + ( a 1 ( r ^ 3 + r ^ 4 + r ^ 5 ) ) / ( a 1 ( 1 + r ^ 1 + r ^ 2 ) ) 64 = ( r ^ 3 ( 1 + r ^ 1 + r ^ 2 ) ) / ( ( 1 + r ^ 1 + r ^ 2 ) ) 64 = r ^ 3 r = 4 a" - }, - { - "Answer": 792.875, - "Options": "a ) 0 , b ) 233 , c ) 500 , d ) 695 , e ) 791", - "Correct": "e", - "Explanation": "\"let # plain cookies sold be x then # chocolate cookies = ( total cookies - x ) equating for x ( 0.75 ) * x + ( 1.25 ) * ( 1585 - x ) = 1585.75 = > x = 791 e\"" - }, - { - "Answer": 16, - "Options": "a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22", - "Correct": "b", - "Explanation": "\"let 2 x be the number of spinsters . then 7 x is the number of cats . 7 x - 2 x = 40 x = 8 and the number of spinsters is 2 ( 8 ) = 16 . the answer is b .\"" - }, - { - "Answer": 7, - "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", - "Correct": "a", - "Explanation": "\"let x play both badminton and tennis so 17 - x play only badminton and 19 - x play only tennis . 2 play none and there are total 30 students . hence , ( 17 - x ) + ( 18 - x ) + x + 2 = 30 37 - 2 x + x = 30 37 - x = 30 x = 7 so 7 members play both badminton and tennis . a\"" - }, - { - "Answer": 20, - "Options": "a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25", - "Correct": "d", - "Explanation": "easy way to solve this question is start from the answer and then conform the information provided in the question . we can start from option d i . e 20 . . . as a quantity of juice p in x because it is the only one option that gets divided by 4 is 20 . . . since in the x the juice p to t ratio is 4 : 1 this gives us that quantity of juice p in x = 20 therefore quantity of juice t will be 5 . . . hence ratio = 4 : 1 this will lead to quantity of juice p in x = 4 and quantity of juice t = 20 . . . hence ratio 1 : 5 if we calculate total juice p = 24 and total of juice v = 25 it fits because totals are same as what mentioned in the question . . . thus ans is d" - }, - { - "Answer": 75, - "Options": "a ) 60 % , b ) 65 % , c ) 70 % , d ) 75 % , e ) 80 %", - "Correct": "d", - "Explanation": "{ total } = { first correctly } + { second correctly } - { both correctly } + { neither correctly } 100 = 85 + 75 - { both correctly } + 15 { both correctly } = 75 . answer : d ." - }, - { - "Answer": 22, - "Options": "a ) 18 , b ) 19 , c ) 22 , d ) 20 , e ) 19", - "Correct": "c", - "Explanation": "\"total number of enrolled students = 29 number of students who did not take test = 5 hence , number of students who took test = 29 - 5 = 24 number of students who answered q 2 correctly = 24 , therefore , all students who took test answered q 2 correctly . so , number of students who answered q 1 correctly , also answered q 2 correctly = 22 . number of students who answered both q 1 & q 2 correctly = 22 . answer : c\"" - }, - { - "Answer": 168, - "Options": "a ) 168 , b ) 172 , c ) 176 , d ) 180 , e ) 184", - "Correct": "a", - "Explanation": "\"the number of nurses at the hospital is ( 7 / 10 ) * 240 = 168 . the answer is a .\"" - }, - { - "Answer": 3, - "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 7 , e ) 5", - "Correct": "b", - "Explanation": "in the following venn diagram , f and e represent people who read french and english respectively . now , [ f + ( { f \u2229 e } ) + e ] = 15 - 3 ( or ) f + e + ( f \u2229 e ) = 12 . . . . . . ( 1 ) also , f + ( f \u2229 e ) = 7 ; e + ( f \u2229 e ) = 8 . by adding , f + e + 2 ( f \u2229 e ) = 15 - - - - - - - - - - ( 2 ) by subtracting ( 1 ) from ( 2 ) , we get ( f \u2229 e ) = 3 . \u2234 3 of them read both french and english . answer : b" - }, - { - "Answer": 6, - "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8", - "Correct": "c", - "Explanation": "total number of students = 34 let a be the number of students have a brothers . let b be the number of students have a sisters . aub = number of students have either brothers or sisters = 34 - 9 = 25 n ( aub ) = n ( a ) + n ( b ) - n ( anb ) 25 = 16 + 15 - n ( anb ) n ( anb ) = 31 - 25 n ( anb ) = 6 the number of students having both brother and sisters = 6 answer : c" - }, - { - "Answer": 100, - "Options": "a ) 46 , b ) 80 , c ) w . 90 , d ) w . 100 , e ) 200", - "Correct": "d", - "Explanation": "\"100 = x + x - 20 + 23 - 23 x = 60 , so , product a = 60 % , product b = 40 % , both = 23 % , neither = 23 % 23 % of the total no . of people should be an integer . so , a , bc are out . 60 % of d and 40 % of d are both integers . so , d satisfies all conditions . so , answer is d .\"" - }, - { - "Answer": 922.8571428571429, - "Options": "a ) 567 , b ) 850 , c ) 560 , d ) 923 , e ) 240", - "Correct": "d", - "Explanation": "\"in 1000 consecutive numbers , number of multiples of 20 = 1000 / 20 = 50 ( ignore decimals ) in 1000 consecutive numbers , number of multiples of 35 = 1000 / 35 = 28 number of multiples of 20 * 35 i . e . 700 = 1000 / 700 = 1 number of integers from 1 to 1000 that are divisible by neither 20 nor by 35 = 1000 - ( 50 + 28 - 1 ) { using the concept of sets here ) = 923 answer is d\"" - }, - { - "Answer": 80, - "Options": "a ) 65 , b ) 80 , c ) 120 , d ) 180 , e ) 190", - "Correct": "b", - "Explanation": "explanation : the investors can be categorized into three groups : ( 1 ) those who have investments in equities only . ( 2 ) those who have investments in securities only . ( 3 ) those who have investments in both equities and securities . let x , y , and z denote the number of people in the respective categories . since the total number of investors is 110 , we have : - = > x + y + z = 110 - - - - - - - - - - - - - ( 1 ) . also , the number of people with investments in equities is x + z and the number of people with investments in securities is y + z . since exactly 25 % of the investors in equities have investments in securities , we have the equation = > ( 25 / 100 ) \u00d7 ( x + z ) = z . = > ( 25 / 100 ) \u00d7 x = 75 z / 100 . = > x = 3 z . - - - - - - - - - - - - - - ( 2 ) since exactly 40 % of the investors in securities have investments in equities , we have the equation = > ( 40 / 100 ) \u00d7 ( y + z ) = z . = > ( y + z ) = 5 z / 2 . = > y = 3 z / 2 . - - - - - - - - - - - - - - - - - ( 3 ) substituting equations ( 2 ) and ( 3 ) into equation ( 1 ) gives : - = > 3 z + ( 3 z / 2 ) + z = 110 . = > 11 z / 2 = 110 . = > z = 110 \u00d7 2 / 11 = 20 . hence , the number of people with investments in equities is : = > x + z = 3 z + z = 3 \u00d7 20 + 20 = 60 + 20 = 80 . answer : b" - }, - { - "Answer": 0.8333333333333334, - "Options": "a ) 1 / 6 , b ) 2 / 9 , c ) 5 / 6 , d ) 7 / 9 , e ) 8 / 9", - "Correct": "c", - "Explanation": "\"we have three pairs of dogs for the 6 with exactly one littermate , and one triplet , with each having exactly two littermates . so , in fact there are two types of dogs : those with one littermate - say a , and the others with two littermates - b . work with probabilities : choosing two dogs , we can have either one dog of type b or none ( we can not have two dogs both of type b ) . the probability of choosing one dog of type b and one of type a is 3 / 9 * 6 / 8 * 2 = 1 / 2 ( the factor of 2 for the two possibilities ba and ab ) . the probability e of choosing two dogs of type a which are not littermates is 6 / 9 * 4 / 8 = 1 / 3 ( choose one a , then another a which is n ' t the previous one ' s littermate ) . the required probability is 1 / 2 + 1 / 3 = 5 / 6 . find the probability for the complementary event : choose aa or bb . probability of choosing two dogs of type a who are littermates is 6 / 9 * 1 / 8 = 1 / 12 . probability of choosing two dogs of type b ( who necessarily are littermates ) is 3 / 9 * 2 / 8 = 1 / 12 . again , we obtain 1 - ( 1 / 12 + 1 / 12 ) = 5 / 6 . answer : c\"" - }, - { - "Answer": 8, - "Options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11", - "Correct": "b", - "Explanation": "xc 1 * ( x - 1 ) c 1 = 56 x ^ 2 - x - 56 = 0 ( x - 8 ) ( x + 7 ) = 0 x = 8 , - 7 - 7 ca n ' t possible . hence 8 should be the answer b" - }, - { - "Answer": 12, - "Options": "a ) 2 , b ) 12 , c ) 5 , d ) 10 , e ) 15", - "Correct": "b", - "Explanation": "one short cut to solve the problem is c : p = 1 : 3 c increased to 5 = > 1 : 3 = 5 : x = > x = 15 = > p increased by 12 b is the answer" - }, - { - "Answer": 2, - "Options": "a ) 3 : 4 , b ) 2 : 3 , c ) 4 : 3 , d ) 1 : 3 , e ) 2 : 1", - "Correct": "e", - "Explanation": "\"total profit = 1000 ratio = 600 / 300 = 2 : 1 answer : e\"" - }, - { - "Answer": 1.2500000000000002, - "Options": "a ) 5 / 6 , b ) 5 / 9 , c ) 5 / 4 , d ) 5 / 3 , e ) 7 / 6", - "Correct": "c", - "Explanation": "\"let us say the ratio of the quantities of cheaper and dearer varieties = x : y by the rule of allegation , x / y = ( 8.75 - 7.50 ) / ( 7.50 - 6.5 ) = 5 / 4 answer : c\"" - }, - { - "Answer": 0.4666666666666667, - "Options": "a ) 7 / 16 , b ) 7 / 12 , c ) 7 / 19 , d ) 7 / 12 , e ) 7 / 15", - "Correct": "e", - "Explanation": "\"drawing two balls of same color from seven green balls can be done in \u2077 c \u2082 ways . similarly from eight white balls two can be drawn in \u2078 c \u2082 ways . p = \u2077 c \u2082 / \u00b9 \u2075 c \u2082 + \u2078 c \u2082 / \u00b9 \u2075 c \u2082 = 7 / 15 answer : e\"" - }, - { - "Answer": 10, - "Options": "a ) 10 , b ) 46 , c ) 67 , d ) 68 , e ) 446", - "Correct": "a", - "Explanation": "notice that 7 play both baseball and cricket does not mean that out of those 7 , some does not play football too . the same for cricket / football and baseball / football . [ color = # ffff 00 ] { total } = { baseball } + { cricket } + { football } - { hc + ch + hf } + { all three } + { neither } for more checkadvanced overlapping sets problems [ / color ] 50 = 20 + 15 + 11 - ( 7 + 4 + 5 ) + { all three } + 18 - - > { all three } = 2 ; those who play only baseball and cricket are 7 - 2 = 5 ; those who play only cricket and football are 4 - 2 = 2 ; those who play only baseball and football are 5 - 2 = 3 ; hence , 5 + 2 + 3 = 10 students play exactly two of these sports . answer : a ." - }, - { - "Answer": 2, - "Options": "a ) 2 : 1 , b ) 3 : 4 , c ) 4 : 3 , d ) 1 : 4 , e ) 5 : 6", - "Correct": "a", - "Explanation": "\"given ; 4 duck = 3 hen ; or , duck / hen = 3 / 4 ; let hen ' s 1 leap = 4 meter and ducks 1 leap = 3 meter . then , ratio of speed of hen and duck = 4 * 3 / 3 * 2 = 2 : 1 ' ' answer : 2 : 1 ;\"" - }, - { - "Answer": 9360.000000000002, - "Options": "a ) s . 7500 , b ) s . 8000 , c ) s . 8500 , d ) s . 9000 , e ) s . 9360", - "Correct": "e", - "Explanation": "\"let hari \u2019 s capital be rs . x . then , 3640 * 12 / 7 x = 2 / 3 = > 14 x = 131040 = > x = 9360 . answer : e\"" - }, - { - "Answer": 26, - "Options": "a ) 3 , b ) 16 , c ) 75 , d ) 24 , e ) 26", - "Correct": "e", - "Explanation": "1 ) i figured there are 101 integers ( 300 - 200 + 1 = 101 ) . since the set begins with an even and ends with an even , there are 51 evens . 2 ) question says integers are not divisible by 2 , leaving all of the odds ( 101 - 51 = 50 integers ) . 3 ) question says integers are not divisible by 5 , removing all the integers ending in 5 ( already took out those ending in 0 ) . take out 10 integers ( 2 ? 5 , ? = 0 to 9 ) , leaving us with 40 integers . 4 ) now the painstaking part . we have to remove the remaining numbers that are multiples of 3 . those are 201 , 207 , 213 , 219 , 231 , 237 , 243 , 249 , 261 , 267 , 273 , 279 , 291 , and 297 . . . a total of 14 numbers . 26 numbers left ! 6 ) answer choice e ." - }, - { - "Answer": 253, - "Options": "a ) 276 , b ) 253 , c ) 322 , d ) 345 , e ) 395", - "Correct": "b", - "Explanation": "\"clearly , the numbers are ( 23 x 10 ) and ( 23 x 11 ) . larger number = ( 23 x 11 ) = 253 . answer : option b\"" - }, - { - "Answer": 142.85714285714283, - "Options": "['a ) 143', 'b ) 200', 'c ) 157', 'd ) 122', 'e ) 132']", - "Correct": "a", - "Explanation": "detailed solution if a number written in base 6 ends with a zero , it should be a multiple of 6 . in other words , the question wants us to find all numbers from 1 to 200 that are not multiples of 6 or 7 . there are 33 multiples of 6 less than 201 . there are 28 multiples of 7 less than 201 . there are 4 multiples of 6 & 7 ( or multiple of 42 ) from 1 to 200 . so , total multiples of 6 or 7 less than 201 = 33 + 28 - 4 = 57 . number of numbers with non - zero units digit = 200 - 57 = 143 . correct answer : a" - }, - { - "Answer": 0.19230769230769232, - "Options": "a ) 6 / 13 , b ) 5 / 26 , c ) 6 / 26 , d ) 9 / 26 , e ) 10 / 27", - "Correct": "b", - "Explanation": "option ( b ) is correct p ( both are red ) , 6 c 2 / 13 c 2 = 5 / 26 answer b" - }, - { - "Answer": 225, - "Options": "a ) 75 , b ) 125 , c ) 145 , d ) 175 , e ) 225", - "Correct": "e", - "Explanation": "( 2 ^ 5 ) x ( 6 ) x ( 7 ^ 3 ) has one appearance of 3 ( in the 6 ) and no appearances of 5 . thus n must include at least 3 ^ 2 * 5 ^ 2 = 9 * 25 = 225 the answer is e ." - }, - { - "Answer": 0.050000000000000044, - "Options": "a ) 0.05 , b ) 0.15 , c ) 0.45 , d ) 0.5 , e ) 0.55", - "Correct": "a", - "Explanation": "p ( a or b ) = p ( a ) + p ( b ) - p ( a n b ) 0.4 = 0.6 + p ( a ) - 0.25 p ( a ) = 0.05 ans : a" - }, - { - "Answer": 8, - "Options": "a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12", - "Correct": "d", - "Explanation": "since 2 xy prime e factors are x ^ 1 * y ^ 1 * 2 ^ 1 , its total number or factors must be ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 2 ^ 3 = 8 . thus , i think d would be the correct answer ." - }, - { - "Answer": 100, - "Options": "a ) 100 , b ) 40 , c ) 66 , d ) 80 , e ) 75", - "Correct": "a", - "Explanation": "two ways . . . 1 ) total ways = 10 c 3 = 10 ! / 7 ! 3 ! = 120 . . ways without python developer = 6 c 3 = 6 ! / 3 ! 3 ! = 20 . . ways of at least one python developer = 120 - 20 = 100 . . 2 ) ways of selecting only one = 4 * 6 c 2 = 4 * 15 = 60 . . ways of selecting only two = 4 c 2 * 6 c 1 = 6 * 6 = 36 . . ways of selecting all three = 4 c 3 = 4 = 4 . . total = 60 + 36 + 4 = 100 . . . answer : a" - }, - { - "Answer": 0.10606060606060605, - "Options": "a ) 1 / 3 , b ) 7 / 22 , c ) 1 / 9 , d ) 7 / 66 , e ) 2 / 45", - "Correct": "d", - "Explanation": "\"total no of rocks = 45 probability of choosing 1 st slate rock = 15 / 45 probability of choosing 2 nd slate rock = 14 / 44 ( without replacement ) so combined probability = 15 / 45 * 14 / 44 = 7 / 66 so , answer d .\"" - }, - { - "Answer": 793.875, - "Options": "a ) 0 , b ) 233 , c ) 500 , d ) 695 , e ) 787", - "Correct": "e", - "Explanation": "\"let # plain cookies sold be x then # chocolate cookies = ( total cookies - x ) equating for x ( 0.75 ) * x + ( 1.25 ) * ( 1585 - x ) = 1587.75 = > x = 787 e\"" - }, - { - "Answer": 0.0002291666666666667, - "Options": "a ) 11 / 48,000 , b ) 1 / 8,100 , c ) 3 / 1,600 , d ) 1 / 90 , e ) 2 / 45", - "Correct": "a", - "Explanation": "\"solution provided by stanford 2012 is correct : 110 / 800 choosing one of the cellos which has a pair viola , 1 / 600 choosing the viola which is the pair of chosen cello - - > p = 110 / 800 * 1 / 600 = 311 / 48,000 . answer : a .\"" - }, - { - "Answer": 108, - "Options": "a ) 100 , b ) 104 , c ) 108 , d ) 112 , e ) 116", - "Correct": "c", - "Explanation": "\"the number of nurses at the hospital is ( 3 / 5 ) * 180 = 108 . the answer is c .\"" - }, - { - "Answer": 0.4666666666666667, - "Options": "a ) 7 / 15 , b ) 2 / 8 , c ) 7 / 11 , d ) 13 / 5 , e ) 87", - "Correct": "a", - "Explanation": "explanation : drawing two balls of same color from seven green balls can be done in \u00e2 \u0081 \u00b7 c \u00e2 \u201a \u201a ways . similarly from eight white balls two can be drawn in \u00e2 \u0081 \u00b8 c \u00e2 \u201a \u201a ways . p = \u00e2 \u0081 \u00b7 c \u00e2 \u201a \u201a / \u00e2 \u00b9 \u00e2 \u0081 \u00b5 c \u00e2 \u201a \u201a + \u00e2 \u0081 \u00b8 c \u00e2 \u201a \u201a / \u00e2 \u00b9 \u00e2 \u0081 \u00b5 c \u00e2 \u201a \u201a = 7 / 15 a" - }, - { - "Answer": 1800, - "Options": "a ) 1800 , b ) 980 , c ) 1200 , d ) 1240 , e ) 1400", - "Correct": "a", - "Explanation": "\"amount received by sanjay . 4 / 12 x 5400 = 1800 = ( related ratio / sum of ratio ) x total amount so , the amount received by sanjay is 1800 . a\"" - }, - { - "Answer": 280, - "Options": "a ) 80 , b ) 160 , c ) 280 , d ) 360 , e ) 480", - "Correct": "c", - "Explanation": "\"ratio = 6 : 1 = > 6 x respondents preferred brand x and x preferred brand y since , no . of respondents who preferred brand x = 240 = > 6 x = 240 = > x = 40 hence total no . of respondents = 240 + 40 = 280 hence c is the answer .\"" - }, - { - "Answer": 50, - "Options": "a ) 74 , b ) 50 , c ) 94 , d ) 59 , e ) 48", - "Correct": "b", - "Explanation": "\"answer : option b explanation : 5 : 1 = x : 10 x = 50 answer : option b\"" - }, - { - "Answer": 2, - "Options": "a ) 15 , b ) 8 , c ) 10 , d ) 2 , e ) 18", - "Correct": "d", - "Explanation": "total - neither = all air conditioning + all power windows - both or 55 - neither = 40 + 25 - 12 = 53 . = > neither = 2 , hence d . answer : d" - }, - { - "Answer": 8, - "Options": "a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14", - "Correct": "b", - "Explanation": "\"26 + 20 - 17 = 29 37 - 29 = 8 play neither answer is b\"" - }, - { - "Answer": 45, - "Options": "a ) 45 , b ) 53 , c ) 54 , d ) 46 , e ) 63", - "Correct": "a", - "Explanation": "if caoacity of q is x units , then capacity of p is 3 x and capacity of drum is 60 * 3 x = 180 x . it will take 180 x / 4 x = 45 turns it will take for both the buckets p & q , having each turn together to fill the empty drum . answer : a" - }, - { - "Answer": 420, - "Options": "a ) 276 , b ) 299 , c ) 420 , d ) 345 , e ) 365", - "Correct": "c", - "Explanation": "\"clearly , the numbers are ( 30 x 13 ) and ( 30 x 14 ) . larger number = ( 30 x 14 ) = 420 . answer : option c\"" - }, - { - "Answer": 2800, - "Options": "a ) 3600 , b ) 2800 , c ) 3608 , d ) 3602 , e ) 3603", - "Correct": "b", - "Explanation": "\"let the income and the expenditure of the person be rs . 5 x and rs . 4 x respectively . income , 5 x = 14000 = > x = 2800 savings = income - expenditure = 5 x - 4 x = x so , savings = rs . 2800 . answer : b\"" - }, - { - "Answer": 20, - "Options": "a ) a ) 8 , b ) b ) 10 , c ) c ) 20 , d ) d ) 30 , e ) e ) 32", - "Correct": "c", - "Explanation": "let the student who speaks tamil - x let the student who speaks telugu - y as ( xuy ) - ( xny ) = total 30 + 40 - ( xny ) = 50 = 20 c )" - }, - { - "Answer": 11, - "Options": "a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13", - "Correct": "c", - "Explanation": "the intersection for two = 45 - 12 - 22 = 11 play both games . answer : c" - }, - { - "Answer": 7, - "Options": "a ) 7 , b ) 8 , c ) 10 , d ) 15 , e ) 18", - "Correct": "a", - "Explanation": "\"total - neither = all air conditioning + all power steering - both or 75 - neither = 45 + 35 - 12 = 68 . = > neither = 7 , hence a . answer : a\"" - }, - { - "Answer": 4, - "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", - "Correct": "d", - "Explanation": "we first write the prime factorization of each given number 24 = 2 \u00d7 2 \u00d7 2 \u00d7 3 = 23 * cubic * \u00d7 3 40 = 2 \u00d7 2 \u00d7 2 \u00d7 5 = 23 * cubic * \u00d7 5 60 = 2 \u00d7 2 \u00d7 3 \u00d7 5 = 22 * square * \u00d7 3 \u00d7 5 gfc = 22 * square * = 4 corect answer is d ) 4" - }, - { - "Answer": 45, - "Options": "['a ) 45', 'b ) 50', 'c ) 55', 'd ) 60', 'e ) 63']", - "Correct": "a", - "Explanation": "f : c : w 1 : 12 : 30 sport version : f : c 3 : 12 f : w 1 : 60 or 3 : 180 so c : f : w = 12 : 3 : 180 c / w = 12 / 180 = 3 ounces / x ounces x = 3 * 180 / 12 = 45 ounces of water answer : a" - }, - { - "Answer": 9000, - "Options": "a ) rs . 9228 , b ) rs . 9129 , c ) rs . 9120 , d ) rs . 9000 , e ) rs . 1922", - "Correct": "d", - "Explanation": "let b ' s capital be rs . x . { 3500 \\ 12 } / { 7 x } = { 2 } / { 3 } = > x = 9000 . answer : d" - }, - { - "Answer": 0.4666666666666667, - "Options": "a ) 7 / 18 , b ) 7 / 19 , c ) 7 / 11 , d ) 7 / 12 , e ) 7 / 15", - "Correct": "e", - "Explanation": "\"drawing two balls of same color from seven green balls can be done in \u2077 c \u2082 ways . similarly from eight white balls two can be drawn in ways . 7 / 15 answer : e\"" - }, - { - "Answer": 50, - "Options": "a ) 5 , b ) 100 , c ) 7 , d ) 4 , e ) 50", - "Correct": "e", - "Explanation": "say x guests ate both types of meat . ( 125 - x ) + ( 75 - x ) = 100 - - > x = 50 . answer : e ." - }, - { - "Answer": 9000, - "Options": "a ) rs 9000 , b ) rs 7000 , c ) rs 5000 , d ) rs 4000 , e ) none of these", - "Correct": "a", - "Explanation": "\"explanation : let b contribution is x . 3500 * 12 / 7 x = 2 / 3 = > 14 x = 126000 = > x = rs 9000 option a\"" - }, - { - "Answer": 90, - "Options": "['a ) 60 sq . cm', 'b ) 70 sq . cm', 'c ) 95 sq . cm', 'd ) 80 sq . cm', 'e ) 90 sq . cm']", - "Correct": "e", - "Explanation": "let us consider it is a rectangle . so area = 24 * 9 = 216 sq . cm now ( 24 - 3 * 2 ) * ( 9 - 2 * 2 ) = 18 * 5 = 90 sq . cm answer : e" - }, - { - "Answer": 12, - "Options": "a ) 8 , b ) 4 , c ) 12 , d ) 16 , e ) 14", - "Correct": "c", - "Explanation": "explanation : let forks = 4 x , spoons = 4 x & knives = 3 x . now , 4 x = 16 hence x = 4 . number of knives = 3 x = 12 . answer : c" - }, - { - "Answer": 0.15789473684210525, - "Options": "a ) 1 / 11 , b ) 1 / 12 , c ) 1 / 13 , d ) 3 / 19 , e ) 3 / 43", - "Correct": "d", - "Explanation": "\"in believe the answer is d . please see below for explanation . 0 ) we are told the following ratios cgd - college graduate with degree ncg - non college graduate cgn - college graduate no degree cgd ncg cgn 1 8 3 2 in order to make cgd and cgn comparable we need to find the least common multiple of 8 and 3 and that is 24 multiplying the first ratio by 3 and the second ratio by 8 we get cgd ncg cgn 3 24 16 if one picks a random college graduate at this large company , what is the probability this college graduate has a graduate degree ? nr of cgd = 3 nr of cg = 3 + 16 = 19 probability w of cgd / ( cg ) - > 3 / 19 answer d\"" - }, - { - "Answer": 11, - "Options": "a ) 12 , b ) 13 , c ) 11 , d ) 14 , e ) 5", - "Correct": "c", - "Explanation": "some multiple of 7 + some multiple of 5 should yield 63 . to get to a some multiple of 5 , we should ensure that a 3 or 8 ( 5 + 3 ) should be a multiple of 7 . 63 is a direct multiple of 7 , however in this case there wo n ' t be any guava . hence the next option is to look for a multiple of 7 that has 8 as the unit digit . 28 satisfies this hence no . of apples is 4 and no of bananas is 7 . c" - }, - { - "Answer": 3, - "Options": "a ) 2 , b ) 3 , c ) 4 , d ) 7 , e ) 5", - "Correct": "b", - "Explanation": "in the following venn diagram , f and e represent people who read french and english respectively . now , [ f + ( { f \u2229 e } ) + e ] = 15 - 3 ( or ) f + e + ( f \u2229 e ) = 12 . . . . . . ( 1 ) also , f + ( f \u2229 e ) = 7 ; e + ( f \u2229 e ) = 8 . by adding , f + e + 2 ( f \u2229 e ) = 15 - - - - - - - - - - ( 2 ) by subtracting ( 1 ) from ( 2 ) , we get ( f \u2229 e ) = 3 . \u2234 3 of them read both french and english . answer : b" - }, - { - "Answer": 6, - "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8", - "Correct": "c", - "Explanation": "total number of students = 34 let a be the number of students have a brothers . let b be the number of students have a sisters . aub = number of students have either brothers or sisters = 34 - 9 = 25 n ( aub ) = n ( a ) + n ( b ) - n ( anb ) 25 = 16 + 15 - n ( anb ) n ( anb ) = 31 - 25 n ( anb ) = 6 the number of students having both brother and sisters = 6 answer : c" - }, - { - "Answer": 100, - "Options": "a ) 46 , b ) 80 , c ) w . 90 , d ) w . 100 , e ) 200", - "Correct": "d", - "Explanation": "\"100 = x + x - 20 + 23 - 23 x = 60 , so , product a = 60 % , product b = 40 % , both = 23 % , neither = 23 % 23 % of the total no . of people should be an integer . so , a , bc are out . 60 % of d and 40 % of d are both integers . so , d satisfies all conditions . so , answer is d .\"" - }, - { - "Answer": 80, - "Options": "a ) 65 , b ) 80 , c ) 120 , d ) 180 , e ) 190", - "Correct": "b", - "Explanation": "explanation : the investors can be categorized into three groups : ( 1 ) those who have investments in equities only . ( 2 ) those who have investments in securities only . ( 3 ) those who have investments in both equities and securities . let x , y , and z denote the number of people in the respective categories . since the total number of investors is 110 , we have : - = > x + y + z = 110 - - - - - - - - - - - - - ( 1 ) . also , the number of people with investments in equities is x + z and the number of people with investments in securities is y + z . since exactly 25 % of the investors in equities have investments in securities , we have the equation = > ( 25 / 100 ) \u00d7 ( x + z ) = z . = > ( 25 / 100 ) \u00d7 x = 75 z / 100 . = > x = 3 z . - - - - - - - - - - - - - - ( 2 ) since exactly 40 % of the investors in securities have investments in equities , we have the equation = > ( 40 / 100 ) \u00d7 ( y + z ) = z . = > ( y + z ) = 5 z / 2 . = > y = 3 z / 2 . - - - - - - - - - - - - - - - - - ( 3 ) substituting equations ( 2 ) and ( 3 ) into equation ( 1 ) gives : - = > 3 z + ( 3 z / 2 ) + z = 110 . = > 11 z / 2 = 110 . = > z = 110 \u00d7 2 / 11 = 20 . hence , the number of people with investments in equities is : = > x + z = 3 z + z = 3 \u00d7 20 + 20 = 60 + 20 = 80 . answer : b" - }, - { - "Answer": 0.8333333333333334, - "Options": "a ) 1 / 6 , b ) 2 / 9 , c ) 5 / 6 , d ) 7 / 9 , e ) 8 / 9", - "Correct": "c", - "Explanation": "\"we have three pairs of dogs for the 6 with exactly one littermate , and one triplet , with each having exactly two littermates . so , in fact there are two types of dogs : those with one littermate - say a , and the others with two littermates - b . work with probabilities : choosing two dogs , we can have either one dog of type b or none ( we can not have two dogs both of type b ) . the probability of choosing one dog of type b and one of type a is 3 / 9 * 6 / 8 * 2 = 1 / 2 ( the factor of 2 for the two possibilities ba and ab ) . the probability e of choosing two dogs of type a which are not littermates is 6 / 9 * 4 / 8 = 1 / 3 ( choose one a , then another a which is n ' t the previous one ' s littermate ) . the required probability is 1 / 2 + 1 / 3 = 5 / 6 . find the probability for the complementary event : choose aa or bb . probability of choosing two dogs of type a who are littermates is 6 / 9 * 1 / 8 = 1 / 12 . probability of choosing two dogs of type b ( who necessarily are littermates ) is 3 / 9 * 2 / 8 = 1 / 12 . again , we obtain 1 - ( 1 / 12 + 1 / 12 ) = 5 / 6 . answer : c\"" - }, - { - "Answer": 12, - "Options": "a ) 2 , b ) 12 , c ) 5 , d ) 10 , e ) 15", - "Correct": "b", - "Explanation": "one short cut to solve the problem is c : p = 1 : 3 c increased to 5 = > 1 : 3 = 5 : x = > x = 15 = > p increased by 12 b is the answer" - }, - { - "Answer": 10, - "Options": "a ) 10 , b ) 46 , c ) 67 , d ) 68 , e ) 446", - "Correct": "a", - "Explanation": "notice that 7 play both baseball and cricket does not mean that out of those 7 , some does not play football too . the same for cricket / football and baseball / football . [ color = # ffff 00 ] { total } = { baseball } + { cricket } + { football } - { hc + ch + hf } + { all three } + { neither } for more checkadvanced overlapping sets problems [ / color ] 50 = 20 + 15 + 11 - ( 7 + 4 + 5 ) + { all three } + 18 - - > { all three } = 2 ; those who play only baseball and cricket are 7 - 2 = 5 ; those who play only cricket and football are 4 - 2 = 2 ; those who play only baseball and football are 5 - 2 = 3 ; hence , 5 + 2 + 3 = 10 students play exactly two of these sports . answer : a ." - }, - { - "Answer": 142.85714285714283, - "Options": "['a ) 143', 'b ) 200', 'c ) 157', 'd ) 122', 'e ) 132']", - "Correct": "a", - "Explanation": "detailed solution if a number written in base 6 ends with a zero , it should be a multiple of 6 . in other words , the question wants us to find all numbers from 1 to 200 that are not multiples of 6 or 7 . there are 33 multiples of 6 less than 201 . there are 28 multiples of 7 less than 201 . there are 4 multiples of 6 & 7 ( or multiple of 42 ) from 1 to 200 . so , total multiples of 6 or 7 less than 201 = 33 + 28 - 4 = 57 . number of numbers with non - zero units digit = 200 - 57 = 143 . correct answer : a" - }, - { - "Answer": 0.19230769230769232, - "Options": "a ) 6 / 13 , b ) 5 / 26 , c ) 6 / 26 , d ) 9 / 26 , e ) 10 / 27", - "Correct": "b", - "Explanation": "option ( b ) is correct p ( both are red ) , 6 c 2 / 13 c 2 = 5 / 26 answer b" - }, - { - "Answer": 225, - "Options": "a ) 75 , b ) 125 , c ) 145 , d ) 175 , e ) 225", - "Correct": "e", - "Explanation": "( 2 ^ 5 ) x ( 6 ) x ( 7 ^ 3 ) has one appearance of 3 ( in the 6 ) and no appearances of 5 . thus n must include at least 3 ^ 2 * 5 ^ 2 = 9 * 25 = 225 the answer is e ." - }, - { - "Answer": 100, - "Options": "a ) 100 , b ) 40 , c ) 66 , d ) 80 , e ) 75", - "Correct": "a", - "Explanation": "two ways . . . 1 ) total ways = 10 c 3 = 10 ! / 7 ! 3 ! = 120 . . ways without python developer = 6 c 3 = 6 ! / 3 ! 3 ! = 20 . . ways of at least one python developer = 120 - 20 = 100 . . 2 ) ways of selecting only one = 4 * 6 c 2 = 4 * 15 = 60 . . ways of selecting only two = 4 c 2 * 6 c 1 = 6 * 6 = 36 . . ways of selecting all three = 4 c 3 = 4 = 4 . . total = 60 + 36 + 4 = 100 . . . answer : a" - }, - { - "Answer": 0.10606060606060605, - "Options": "a ) 1 / 3 , b ) 7 / 22 , c ) 1 / 9 , d ) 7 / 66 , e ) 2 / 45", - "Correct": "d", - "Explanation": "\"total no of rocks = 45 probability of choosing 1 st slate rock = 15 / 45 probability of choosing 2 nd slate rock = 14 / 44 ( without replacement ) so combined probability = 15 / 45 * 14 / 44 = 7 / 66 so , answer d .\"" - }, - { - "Answer": 0.4666666666666667, - "Options": "a ) 7 / 15 , b ) 2 / 8 , c ) 7 / 11 , d ) 13 / 5 , e ) 87", - "Correct": "a", - "Explanation": "explanation : drawing two balls of same color from seven green balls can be done in \u00e2 \u0081 \u00b7 c \u00e2 \u201a \u201a ways . similarly from eight white balls two can be drawn in \u00e2 \u0081 \u00b8 c \u00e2 \u201a \u201a ways . p = \u00e2 \u0081 \u00b7 c \u00e2 \u201a \u201a / \u00e2 \u00b9 \u00e2 \u0081 \u00b5 c \u00e2 \u201a \u201a + \u00e2 \u0081 \u00b8 c \u00e2 \u201a \u201a / \u00e2 \u00b9 \u00e2 \u0081 \u00b5 c \u00e2 \u201a \u201a = 7 / 15 a" - }, - { - "Answer": 2, - "Options": "a ) 15 , b ) 8 , c ) 10 , d ) 2 , e ) 18", - "Correct": "d", - "Explanation": "total - neither = all air conditioning + all power windows - both or 55 - neither = 40 + 25 - 12 = 53 . = > neither = 2 , hence d . answer : d" - }, - { - "Answer": 45, - "Options": "a ) 45 , b ) 53 , c ) 54 , d ) 46 , e ) 63", - "Correct": "a", - "Explanation": "if caoacity of q is x units , then capacity of p is 3 x and capacity of drum is 60 * 3 x = 180 x . it will take 180 x / 4 x = 45 turns it will take for both the buckets p & q , having each turn together to fill the empty drum . answer : a" - } - ] -} \ No newline at end of file