Cheukting/mathqa huggingface dataset:
Question (general): find the value of 2.5 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ]
Options: a ) 2000 , b ) 500 , c ) 900 , d ) 1600 , e ) none
Rationale: "answer 2.5 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ] = 2.5 x [ ( 36 x 48 x 250 ) / ( 12 x 9 x 5 ) ] = 2.5 x 4 x 4 x 50 = 2000 correct option : a"
Answer: a
Question (general): on an order of 3 dozen boxes of a consumer product , a retailer receives an extra dozen free . this is equivalent to allowing him a discount of :
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 40 %
Rationale: clearly , the retailer gets 1 dozen out of 4 dozens free . equivalent discount = 1 / 4 * 100 = 25 % . answer b ) 25 %
Answer: b
Question (general): if bill can buy 3 pairs of jeans and 2 shirts for $ 69 or 2 pairs of jeans and 3 shirts for $ 61 , how much does one shirt cost ?
Options: a ) $ 9 , b ) $ 12 , c ) $ 13.20 , d ) $ 15 , e ) $ 16.80
Rationale: 3 j + 2 s = 69 2 j + 3 s = 61 - - - - - - - - - - - - - - - - 5 j + 5 s = 130 - - - - ( divide by 5 ) - - - > j + s = 26 3 j + 2 s = j + 2 ( j + s ) = j + 52 = 69 - - - > j = 17 3 * 17 + 2 s = 69 51 + 2 s = 69 2 s = 18 s = 9 answer : a
Answer: a
Question (geometry): 30 square stone slabs of equal size were needed to cover a floor area of 50.7 sq . m . find the length of each stone slab ?
Options: a ) 130 cm , b ) 767 cm , c ) 88 cm , d ) 666 cm , e ) 776 cm
Rationale: "area of each slab = 50.7 / 30 m 2 = 1.69 m 2 length of each slab √ 1.69 = 1.3 m = 130 cm"
Answer: a
Question (general): the cost of 10 kg of apples is equal to the cost of 24 kg of rice . the cost of 6 kg of flour equals the cost of 2 kg of rice . the cost of each kg of flour is rs . 20.50 . find the total cost of 4 kg of apples , 3 kg of rice and 5 kg of flour ?
Options: a ) rs . 849.40 , b ) rs . 877.40 , c ) rs . 901.60 , d ) rs . 815.20 , e ) none of these
Rationale: let the costs of each kg of apples and each kg of rice be rs . a and rs . r respectively . 10 a = 24 r and 6 * 20.50 = 2 r a = 12 / 5 r and r = 61.5 a = 147.6 required total cost = 4 * 147.6 + 3 * 61.5 + 5 * 20.5 = 590.4 + 184.5 + 102.5 = rs . 877.40 answer : b
Answer: b
Question (general): the shopkeeper increased the price of a product by 25 % so that customer finds it difficult to purchase the required amount . but somehow the customer managed to purchase only 70 % of the required amount . what is the net difference in the expenditure on that product ?
Options: a ) 12.5 % , b ) 13 % , c ) 13.15 % , d ) 14 % , e ) 15 %
Rationale: "quantity x rate = price 1 x 1 = 1 0.7 x 1.25 = 0.875 decrease in price = ( 0.125 / 1 ) × 100 = 12.5 % a )"
Answer: a
Question (general): how many positive integers less than 100 have a remainder of 5 when divided by 13 ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "we have to include 5 also . as 13 * 0 + 5 = 5 if somebody says to divide 5 by 13 , we will be telling we have 0 quotient and remainder as 5 . answer is a"
Answer: a
Question (geometry): a spirit and water solution is sold in a market . the cost per liter of the solution is directly proportional to the part ( fraction ) of spirit ( by volume ) the solution has . a solution of 1 liter of spirit and 1 liter of water costs 80 cents . how many cents does a solution of 1 liter of spirit and 2 liters of water cost ?
Options: a ) 53 , b ) 66 , c ) 60 , d ) 85 , e ) 80
Rationale: "yes , ensure that you understand the relation thoroughly ! cost per liter = k * fraction of spirit 80 cents is the cost of 2 liters of solution ( 1 part water , 1 part spirit ) . so cost per liter is 40 cents . fraction of spirit is 1 / 2 . 40 = k * ( 1 / 2 ) k = 80 cost per liter = 80 * ( 1 / 3 ) ( 1 part spirit , 2 parts water ) cost for 3 liters = 80 * ( 1 / 3 ) * 3 = 80 cents e . 80 cents"
Answer: e
Question (physics): two pipes can fill a tank in 10 minutes and 15 minutes . an outlet pipe can empty the tank in 45 minutes . if all the pipes are opened when the tank is empty , then how many minutes will it take to fill the tank ?
Options: a ) 30 minutes , b ) 8 minutes , c ) 15 minutes , d ) 10 minutes , e ) 12 minutes
Rationale: "part of the filled by all the three pipes in one minute = 1 / 10 + 1 / 15 - 1 / 45 = ( 9 + 6 - 2 ) / 90 = 13 / 90 so , the tank becomes full in 8 minutes . answer : b"
Answer: b
Question (physics): dean winchester has got a long wooden stock of size 60 feet , he need to cut small stock of size 1 feet long using his axe . he takes 5 minutes to cut one small stock ( 1 feet ) , how long will he take to make 60 such small stocks ?
Options: a ) 296 minutes . , b ) 297 minutes . , c ) 295 minutes . , d ) 294 minutes . , e ) none
Rationale: solution : 295 minutes . when he cut 59 stocks , the 60 th stock will remain . 59 * 5 = 295 minutes . answer c
Answer: c
Question (general): the difference between the squares of two consecutive odd integers is a square < 1000 whose root equals the combined sum of the digits of the two integers . what is the sum of the digits x of the larger integer ?
Options: a ) x = 2 , b ) x = 5 , c ) x = 8 , d ) 10 , e ) 11
Rationale: really hard . but let ' s start with few concepts : 1 . square of an odd integer will be odd . 2 . difference of odd and odd will be even . 3 . any odd integer can be expressed as difference of two squares . 4 . an even integer can be expressed as difference of two squares only if that even integer is a multiple of 4 . assume two odd integers to be ( 2 x - 1 ) and ( 2 x + 1 ) . difference of their squares = ( 2 x + 1 ) ^ 2 - ( 2 x - 1 ) ^ 2 = 4 x ^ 2 + 1 + 4 x - ( 4 x ^ 2 + 1 - 4 x ) = 4 x ^ 2 + 1 + 4 x - 4 x ^ 2 - 1 + 4 x = 8 x now root of 8 x needs to be an integer such that it is equal to the sum of the digits of the two odd integers . 8 = 2 ^ 3 , so x needs to be such that itcompletesa perfect square . if we find x , we can find the value of 2 x + 1 ( larger integer ) and then sum of its digits . let ' s check the options , starting with c . for sum to be 8 , few possibilities are : 17 , 35 , 53 , 71 if we take 17 , the pair is 15 and 17 , meaning x = 8 . 8 x = 64 root of 64 = 4 but 4 is not equal to 1 + 5 + 1 + 7 . reject . if we take 35 , the pair is 33 and 35 , meaning x = 17 . 8 x = 8 * 17 reject since perfect square is not possible . if we take 53 , the pair is 51 and 53 , meaning x = 26 . 8 x = 8 * 26 reject since perfect square is not possible . if we take 71 , the pair is 69 and 71 , meaning x = 35 . 8 x = 8 * 35 reject since perfect square is not possible . i tried each option and the possibilities and then got lost . then , it occurred to me that i was only checking 2 - digit integers . what about 3 - digits ? starting with option a , only 2 - digit odd integer whose sum is 2 is 101 . if we take 101 , the pair is 99 and 101 , meaning x = 50 . 8 x = 8 * 50 = 400 root of 400 = 20 which is indeed equal to 9 + 9 + 1 + 1 . answer ( a ) .
Answer: a
Question (gain): if c is 25 % of a and 50 % of b , what percent of a is b ?
Options: a ) 2.5 % , b ) 50 % , c ) 25 % , d ) 35 % , e ) 250 %
Rationale: "answer = b 25 a / 100 = 50 b / 100 b = 25 a / 50 = 50 a / 100 = 50 %"
Answer: b
Question (physics): a metallic cuboid of dimensions 27 x 18 x 12 m is melted . find the minimum amount of the volume of molten metal which should be added to mould it into a cube whose edge is ' a ' cm where a is an integer .
Options: a ) 16 m
b ) 17 m
c ) 18 m
d ) 19 m
e ) 15 m
Rationale: volume of cuboid = 27 * 18 * 12 = ( 27 * 27 * 8 ) = ( 3 * 3 * 2 ) ^ 3 = 18 ^ 3 so no amount of the volume of molten metal should be added to mould it into a cube whose edge is ' a ' cm where a is 18 m . answer : c
Answer: c
Question (general): a teacher grades students ’ tests by subtracting twice the number of incorrect responses from the number of correct responses . if student a answers each of the 100 questions on her test and receives a score of 61 , how many questions did student a answer correctly ?
Options: a ) 55 , b ) 60 , c ) 73 , d ) 81 , e ) 87
Rationale: "let the number of correct responses be x then the number of incorrect responses = 100 - x according to question x - 2 ( 100 - x ) = 61 ( subtracting twice of incorrect from correct ) 3 x = 261 x = 87 answer : e"
Answer: e
Question (gain): if x is invested in a bank at a rate of simple interest of y % p . a . for two years , then the interest earned is 600 . if x is invested at y % p . a . , for two years when the interest is compounded annually , the interest is 615 . what is the value of x ?
Options: a ) 8000 , b ) 6000 , c ) 5000 , d ) 4000 , e ) 3000
Rationale: "simple way to solve this question is to use options . from si , we know that x * y = 30,000 . now , put the value of x = 6000 , we will have y = 5 % to calculate ci , now , we know 1 st year amount = 6000 + 5 % of 6000 = 6300 . 2 nd year , amount = 6300 + 5 % of 6300 = 6615 we can see after 2 years interest = 6615 - 6000 = 615 . hence , it satisfies the question . hence b is the correct answer"
Answer: b
Question (general): a store purchased a pair of pants for $ 210 and was selling it at a price that equaled the purchase price of the pants plus a markup that was 25 percent of the selling price . after some time a store owner decided to decrease the selling price by 20 percent . what was the store ' s gross profit on this sale ?
Options: a ) $ 14 , b ) $ 2 , c ) $ 10 , d ) $ 6 , e ) $ 8
Rationale: sale price ( sp ) = 210 + markup ( mp ) - - > mp = sp - 210 and given mp = sp / 4 ( 25 % is 1 / 4 th ) so sp / 4 = sp - 210 3 sp / 4 = 210 sp = 280 now a discount of 20 % is given so new sp is . 8 * 280 = 224 profit = 224 - 210 = 14 answer is a
Answer: a
Question (physics): the length of a room is 5.5 m and width is 3.75 m . find the cost of paving the floor by slabs at the rate of rs . 400 per sq . metre .
Options: a ) rs . 15000 , b ) rs . 8250 , c ) rs . 15600 , d ) rs . 16500 , e ) none of these
Rationale: "solution area of the floor = ( 5.5 × 3.75 ) m 2 = 20.625 m 2 ∴ cost of paving = rs . ( 400 × 20.625 ) = 8250 . answer b"
Answer: b
Question (general): find 125 / 14 * 6
Options: a ) 2.4658 , b ) 6.398 , c ) 1.488 , d ) 5.687 , e ) 9.652
Rationale: "answer = 125 / 14 * 6 = 125 / 84 = 1.488 option c is correct"
Answer: c
Question (general): if a 2 - b 2 = 5 and a * b = 2 , find a 4 + b 4 .
Options: a ) 50 , b ) 72 , c ) 25 , d ) 92 , e ) 33
Rationale: "a 2 - b 2 = 5 : given a 4 + b 4 - 2 a 2 b 2 = 52 : square both sides and expand . a * b = 2 : given a 2 b 2 = 22 : square both sides . a 4 + b 4 - 2 ( 4 ) = 25 : substitute a 4 + b 4 = 33 correct answer e"
Answer: e
Question (general): if 1 + 2 + 3 + . . . + n = n ( n + 1 ) , then 3 ( 1 + 3 + 5 + . . . . + 79 ) = ?
Options: a ) 4500 , b ) 4250 , c ) 4350 , d ) 4800 , e ) 4150
Rationale: "explanation : to solve this use the formula of ap , sn = ( n / 2 ) ( a + l ) . . . . . . . . . . . . . . . . ( 1 ) to find n , use = > tn = a + ( n - 1 ) d = > 79 = 1 + ( n - 1 ) 2 = > n = 40 use value of n in ( 1 ) then , sn = ( 40 / 2 ) ( 1 + 79 ) = 1600 ans : - 3 ( sn ) = 4800 answer : d"
Answer: d
Question (physics): a river boat leaves silver town and travels upstream to gold town at an average speed of 4 kilometers per hour . it returns by the same route at an average speed of 7 kilometers per hour . what is the average speed for the round - trip in kilometers per hour ?
Options: a ) 5.1 , b ) 7.1 , c ) 7.2 , d ) 7.5 , e ) 8.0
Rationale: "pick a number which is lcm of 7 and 4 = 18 . upstream time = 28 / 4 = 7 hrs downstream time = 28 / 7 = 4 hrs total time = 11 hrs total distance = 56 average speed = 56 / 11 = 5.1 km / hr"
Answer: a
Question (general): a certain car traveled twice as many miles from town a to town b as it did from town b to town c . from town a to town b , the car averaged 25 miles per gallon , and from town b to town c , the car averaged 30 miles per gallon . what is the average miles per gallon that the car achieved on its trip from town a through town b to town c ?
Options: a ) 24 , b ) 25 , c ) 23 , d ) 22 , e ) 26.5
Rationale: step 1 ) took lcm of 25 and 30 . . came as 150 . step 2 ) 150 distance between b to c . . . do 150 / 30 hence 5 gallons used step 3 ) twice distance . . hence 150 * 2 = 300 . . . do as above . . 300 / 25 = 12 gallons used step 4 ) total gallons . . 5 + 12 = 17 gallons step ) total miles = 150 + 300 = 450 miles hence . . average of whole journey = 450 / 17 which comes to 26.5 answer : e
Answer: e
Question (general): if w , x , y and z are distinct odd positive integers , then the maximum value of the expression ( w ^ 2 + x ^ 2 ) * ( y ^ 2 + z ^ 2 ) can be divisible by ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 8 , e ) 10
Rationale: any odd number square will give odd number only . . similarly wen we add 2 odd numbers we will get even number . . wen we multiply 2 even owe will get even nuber . . so the result of the above expression is an even number only . . hence it is divisible by 2 . . . answer : a
Answer: a
Question (general): john found that the average of 15 numbers is 40 . if 10 is added to each number then the mean of number is ?
Options: a ) 50 , b ) 60 , c ) 75 , d ) 80 , e ) 85
Rationale: "( x + x 1 + . . . x 14 ) / 15 = 40 50 option a"
Answer: a
Question (general): if a ' s salary is 20 % less than b ' s salary , by how much percent is b ' s salary more than a ' s ?
Options: a ) 5 % , b ) 10 % , c ) 15 % , d ) 25 % , e ) none
Rationale: solution required percentage ‹ = › [ 20 / ( 100 - 20 ) x 100 ] % ‹ = › 25 % answer d
Answer: d
Question (gain): what will be the difference between simple interest and compound interest @ 10 % per annum on a sum of rs . 1000 after 3 years ?
Options: a ) 22 , b ) 77 , c ) 26 , d ) 19 , e ) 31
Rationale: "explanation : s . i . = rs . [ ( 1000 x 10 x 3 ) / 100 ] = rs . 300 c . i . = rs . [ 1000 x ( 1 + ( 10 / 100 ) ) 3 - 1000 ] = rs . 331 difference = rs . ( 331 - 300 ) = rs . 31 answer : e"
Answer: e
Question (general): the mean of 25 values was 190 . it was detected on rechecking that one value 165 was wrongly copied as 130 for the computation of the mean . find the correct mean .
Options: a ) 151 , b ) 149 , c ) 152 , d ) 191.4 , e ) none of the above
Rationale: "corrected mean = 190 × 25 − 130 + 165 / 25 = 4750 + 35 / 25 = 4785 / 25 = 191.4 answer d"
Answer: d
Question (general): a man can swim in still water at 5 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ?
Options: a ) 1.78 , b ) 1.667 , c ) 1.15 , d ) 1.5 , e ) 1.2
Rationale: m = 5 s = x ds = 5 + x us = 5 - x 5 + x = ( 5 - x ) 2 5 + x = 10 - 2 x 3 x = 5 x = 1.667 answer : b
Answer: b
Question (gain): in an office , 10 percent of the workers have at least 5 years of service , and a total of 16 workers have at least 10 years of service . if 90 percent of the workers have fewer than 10 years of service , how many of the workers have at least 5 but fewer than 10 years of service ?
Options: a ) 16 , b ) 64 , c ) 50 , d ) 144 , e ) 160
Rationale: "( 10 / 100 ) workers = 16 = > number of workers = 160 ( 10 / 100 ) * workers = x + 16 = > x = 16 answer a"
Answer: a
Question (physics): micheal and adam can do together a piece of work in 20 days . after they have worked together for 11 days micheal stops and adam completes the remaining work in 10 days . in how many days micheal complete the work separately .
Options: a ) 80 days , b ) 100 days , c ) 120 days , d ) 110 days , e ) 200 days
Rationale: rate of both = 1 / 20 together they do = 1 / 20 * 11 = 11 / 20 left work = 1 - 11 / 20 = 9 / 20 adam completes 9 / 20 work in 10 day so he took 10 * 20 / 9 = 200 / 9 days to complete the left work alone . thus the rate of adam is 9 / 200 rate of micheal = 1 / 20 - 9 / 200 = 1 / 200 thus micheal takes 200 days to complete the whole work . ans . e .
Answer: e
Question (physics): a train crosses a platform of 250 m in 20 sec , same train crosses another platform of length 640 m in 40 sec . then find the length of the train ?
Options: a ) 150 m , b ) 180 m , c ) 152 m , d ) 140 m , e ) 160 m
Rationale: "length of the train be ‘ x ’ x + 250 / 20 = x + 640 / 40 2 x + 500 = x + 640 x = 140 m answer : d"
Answer: d
Question (general): the difference between the ages of two persons is 11 years . ten years ago , the elder one was twice as old as the younger one . the present age of the elder person is
Options: a ) 18 , b ) 19 , c ) 20 , d ) 17 , e ) 16
Rationale: "let their ages of x years and ( x + 11 ) years respectively . then , ( x + 11 ) - 10 = 2 ( x - 10 ) ⇔ x + 1 = 2 x - 20 ⇔ 3 x = 21 . ∴ present age of the elder person = ( 7 + 11 ) = 18 years . answer : 18 years"
Answer: a
Question (physics): a walks at 10 kmph and 3 hours after his start , b cycles after him at 20 kmph . how far from the start does b catch up with a ?
Options: a ) 100 km , b ) 150 km , c ) 60 km , d ) 120 km , e ) 200 km
Rationale: "suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 3 hours . x / 10 - x / 20 = 3 x = 60 km answer is c"
Answer: c
Question (geometry): what would be the length of the diagonal of a square plot whose area is equal to the area of a rectangular plot of 45 m length and 40 m width ?
Options: a ) 42.5 m
b ) 60 m
c ) 4800 m
d ) data inadequate
e ) none of these
Rationale: a 2 = 45 × 40 = 1800 ∴ a = √ 1800 = 30 √ 2 ∴ diagonal of the square = √ 2 a = √ 2 × 30 √ 2 = 30 × 2 = 60 m answer b
Answer: b
Question (physics): a goods train runs at the speed of 72 km / hr and crosses a 80 m long platform in 26 sec . what is the length of the goods train ?
Options: a ) 382 , b ) 440 , c ) 278 , d ) 270 , e ) 881
Rationale: "speed = 72 * 5 / 18 = 20 m / sec . time = 26 sec . let the length of the train be x meters . then , ( x + 80 ) / 26 = 20 x = 440 m . answer : b"
Answer: b
Question (general): what is the total cost of 2 sandwiches at $ 1.49 each and 4 sodas at $ 0.87 each ?
Options: a ) $ 3.36 , b ) $ 6.46 , c ) $ 8.46 , d ) $ 10.08 , e ) $ 11.85
Rationale: answer = b 2 * 1.49 + 4 * 0.87 = 2 ( 1.50 - 0.01 ) + 4 ( 1.00 - 0.13 ) = 3 + 4 - 0.02 - 0.52 = 7 - 0.54 = 6.46
Answer: b
Question (gain): population of a city in 20004 was 1500000 . if in 2005 there isan increment of 15 % , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45 % , then find the population of city atthe end of the year 2007
Options: a ) 354354 , b ) 545454 , c ) 465785 , d ) 456573 , e ) 3251625 / 2
Rationale: "required population = p ( 1 + r 1 / 100 ) ( 1 - r 2 / 100 ) ( 1 + r 3 / 100 ) = p ( 1 + 15 / 100 ) ( 1 - 35 / 100 ) ( 1 + 45 / 100 ) = 3251625 / 2 e"
Answer: e
Question (other): how many prime numbers between 1 and 100 are factors of 7,150 ?
Options: a ) one , b ) two , c ) three , d ) four , e ) five
Rationale: "make prime factorization of 7,150 - - > 7,150 = 2 ∗ 5 ^ 2 ∗ 11 ∗ 13 so , 4 prime numbers between 1 and 100 ( namely 2 , 5 , 11 , and 13 ) are factors of 7,150 . answer : d ."
Answer: d
Question (other): a firm is comprised of partners and associates in a ratio of 2 : 61 . if 60 more associates were hired , the ratio of partners to associates would be 4 : 137 . how many partners are currently in the firm ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "the ratio 2 : 61 = 4 : 122 so the ratio changed from 4 : 122 to 4 : 137 . 137 - 122 = 15 which is 1 / 4 of the increase in 60 associates . the ratio changed from 16 : 488 to 16 : 548 . thus the number of partners is 16 . the answer is c ."
Answer: c
Question (general): 5 , 7 , 11 , 18 , 33 , ( . . . )
Options: a ) 22 , b ) 35 , c ) 27 , d ) 63 , e ) 25
Rationale: "explanation : 5 5 × 2 - 3 = 7 7 × 2 - 3 = 11 11 × 2 - 3 = 18 18 × 2 - 3 = 33 33 × 2 - 3 = 63 answer : option d"
Answer: d
Question (geometry): if the radius of a circle that centers at the origin is 5 , how many w points on the circle have integer coordinates ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 15 , e ) 20
Rationale: "i understand this might not be required but i used the equation of a circle . since the origin is at 0 , x ^ 2 + y ^ 2 = 5 ^ 2 . x , y could be + / - ( 0,5 or 5,0 ) - 4 possibilities . x , y could be + / - ( 3,4 or 4,3 ) - 8 possibilities . ans : w = c"
Answer: c
Question (general): how many multiples of 7 are there between 14 and 252 ?
Options: a ) 33 , b ) 46 , c ) 59 , d ) 66 , e ) 80
Rationale: "it should be mentioned whether 14 and 252 are inclusive . if 14 and 252 are inclusive , then the answer is ( 252 - 14 ) / 7 + 1 = 35 . if 14 and 252 are not inclusive , then the answer is ( 245 - 21 ) / 7 + 1 = 33 . since oa is a , then we have not inclusive case ."
Answer: a
Question (general): solve x 2 â € “ 3 x â € “ 4 = 0 .
Options: a ) 14 , b ) - 14 , c ) 23 , d ) 2 , - 3 , e ) 34
Rationale: this one factors easily : x 2 â € “ 3 x â € “ 4 = 0 ( x + 1 ) ( x â € “ 4 ) = 0 x + 1 = 0 or x â € “ 4 = 0 x = â € “ 1 or x = 4 the solution is x = â € “ 1 , 4 answer b
Answer: b
Question (geometry): the height of two right circular cones are in the ratio 1 : 2 and their perimeters of their bases are in the ratio 3 : 4 , the ratio of their volume is ?
Options: a ) 9 : 38
b ) 9 : 31
c ) 9 : 32
d ) 9 : 39
e ) 9 : 35
Rationale: 9 : 32 answer : c
Answer: c
Question (gain): ? % of 360 = 93.6
Options: a ) 277 , b ) 36 , c ) 26 , d ) 72 , e ) none of these
Rationale: "? % of 360 = 93.6 or , ? = 93.6 × 100 / 360 = 26 answer c"
Answer: c
Question (general): linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 450 , what were her original savings ?
Options: a ) $ 1500 , b ) $ 1600 , c ) $ 1700 , d ) $ 1800 , e ) $ 1900
Rationale: "if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 450 . so 1 / 4 of her savings is $ 450 . so her original savings are 4 times $ 450 = $ 1800 correct answer d"
Answer: d
Question (general): a man purchased 1 blankets @ rs . 100 each , 5 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ?
Options: a ) 278 , b ) 277 , c ) 278 , d ) 450 , e ) 650
Rationale: "10 * 150 = 1500 1 * 100 + 5 * 150 = 850 1500 – 850 = 650 answer : e"
Answer: e
Question (general): rice weighing 29 / 4 pounds was divided equally and placed in 4 containers . how many ounces of rice were in each container ? ( note that 1 pound = 16 ounces )
Options: a ) 21 , b ) 25 , c ) 29 , d ) 33 , e ) 37
Rationale: "29 / 4 ÷ 4 = 29 / 16 pounds in each container 29 / 16 pounds * 16 ounces / pound = 29 ounces in each container the answer is c ."
Answer: c
Question (physics): the speed at which a man can row a boat in still water is 15 km / hr . if he rows downstream , where the speed of current is 3 km / hr , how many seconds will he take to cover 90 meters ?
Options: a ) 12 , b ) 16 , c ) 17 , d ) 18 , e ) 20
Rationale: "the speed of the boat downstream = 15 + 3 = 18 km / hr 18 km / hr * 5 / 18 = 5 m / s the time taken to cover 90 meters = 90 / 5 = 18 seconds . the answer is d ."
Answer: d
Question (general): for all positive integers m , [ m ] = 3 m when m is odd and [ m ] = ( 1 / 2 ) * m when m is even . what is [ 9 ] * [ 10 ] equivalent to ?
Options: a ) [ 25 ] , b ) [ 135 ] , c ) [ 30 ] , d ) [ 90 ] , e ) [ 45 ]
Rationale: [ 9 ] * [ 10 ] = 27 * 5 = 135 = 3 * 45 = [ 45 ] the answer is e .
Answer: e
Question (general): a cube with its sides numbered 1 through 6 is rolled twice , first landing on a and then landing on b . if any roll of the cube yields an equal chance of landing on any of the numbers 1 through 6 , what is the probability q that a + b is prime ?
Options: a ) 0 , b ) 1 / 12 , c ) 5 / 12 , d ) 7 / 18 , e ) 4 / 9
Rationale: "total # of outcomes is 6 * 6 = 36 ; favorable outcomes : a - b - - > prime 1 - 1 - - > 2 ; 1 - 2 - - > 3 ; 2 - 1 - - > 3 ; 1 - 4 - - > 5 ; 4 - 1 - - > 5 ; 2 - 3 - - > 5 ; 3 - 2 - - > 5 ; 1 - 6 - - > 7 ; 6 - 1 - - > 7 ; 2 - 5 - - > 7 ; 5 - 2 - - > 7 ; 3 - 4 - - > 7 ; 4 - 3 - - > 7 ; 6 - 5 - - > 11 ; 5 - 6 - - > 11 . total of 15 favorable outcomes q = 15 / 36 . answer : c ."
Answer: c