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load_in_math_allenai_math

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if k ^ 3 is divisible by 162 , what is the least possible value of integer k ?
"k ^ 3 = 162 * x = 2 * 3 ^ 4 * x the factors of k must at minimum include 2 * 3 ^ 2 = 18 . the answer is c ."
a ) 12 , b ) 15 , c ) 18 , d ) 24 , e ) 36
c
divide(divide(162, const_2), const_2)
divide(n1,const_2)|divide(#0,const_2)|
general
allenai/math_qa
what is the sum of all digits for the number 10 ^ 26 - 51 ?
"10 ^ 26 is a 27 - digit number : 1 followed by 26 zeros . 10 ^ 26 - 51 is a 26 - digit number : 24 9 ' s and 49 at the end . the sum of the digits is 24 * 9 + 4 + 9 = 229 . the answer is d ."
a ) 199 , b ) 209 , c ) 219 , d ) 229 , e ) 239
d
multiply(add(divide(subtract(subtract(26, 10), const_2), const_2), 10), divide(add(subtract(26, 10), const_2), const_2))
subtract(n1,n0)|add(#0,const_2)|subtract(#0,const_2)|divide(#2,const_2)|divide(#1,const_2)|add(n0,#3)|multiply(#5,#4)|
general
allenai/math_qa
the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 18000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is
"solution let the toatl number of workers be x . then 8000 x = ( 18000 x 7 ) + 6000 ( x - 7 ) x = 42 answer c"
a ) 20 , b ) 21 , c ) 42 , d ) 23 , e ) 24
c
add(7, divide(multiply(7, subtract(18000, 8000)), subtract(8000, 6000)))
subtract(n2,n0)|subtract(n0,n3)|multiply(n1,#0)|divide(#2,#1)|add(n1,#3)|
general
allenai/math_qa
a man can row upstream at 8 kmph and downstream at 13 kmph . the speed of the stream is ?
"speed of stream = 1 / 2 ( 13 - 8 ) = 2.5 kmph answer is b"
a ) 3 kmph , b ) 2.5 kmph , c ) 3.5 kmph , d ) 4.3 kmph , e ) 5 kmph
b
divide(add(8, 13), const_2)
add(n0,n1)|divide(#0,const_2)|
physics
allenai/math_qa
if 4 men can colour 48 m long cloth in 2 days , then 6 men can colour 72 m long cloth in
"the length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m no . of days required to paint 36 m cloth by 6 men = 72 / 6 × 6 = 2 day . b"
a ) 1 day , b ) 2 days , c ) 3 days , d ) 4 days , e ) 5 days
b
divide(72, multiply(divide(48, multiply(4, 2)), 6))
multiply(n0,n2)|divide(n1,#0)|multiply(n3,#1)|divide(n4,#2)|
physics
allenai/math_qa
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 ?
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
a ) 4 / 15 , b ) 1 / 3 , c ) 2 / 5 , d ) 4 / 5 , e ) 7 / 6
a
divide(multiply(4, 1), multiply(3, 5))
multiply(n0,n2)|multiply(n1,n3)|divide(#0,#1)
other
allenai/math_qa
jack and christina are standing 270 feet apart on a level surface . their dog , lindy , is standing next to christina . at the same time , they all begin moving toward each other . jack walks in a straight line toward christina at a constant speed of 4 feet per second and christina walks in a straight line toward jack at a constant speed of 5 feet per second . lindy runs at a constant speed of 8 feet per second from christina to jack , back to christina , back to jack , and so forth . what is the total distance , in feet , that lindy has traveled when the three meet at one place ?
"the relative speed of jack and christina is 4 + 5 = 9 feet per second . the distance between them is 210 feet , hence they will meet in ( time ) = ( distance ) / ( relative speed ) = 270 / 7 = 30 seconds . for all this time lindy was running back and forth , so it covered ( distance ) = ( speed ) * ( time ) = 8 * 30 = 240 feet . answer : d ."
a ) 150 , b ) 180 , c ) 210 , d ) 240 , e ) 270
d
multiply(divide(270, add(4, 5)), 8)
add(n1,n2)|divide(n0,#0)|multiply(n3,#1)|
physics
allenai/math_qa
the difference between the ages of two persons is 20 years . fifteen years ago , the elder one was twice as old as the younger one . the present age of the younger person is ?
let their ages be x years and ( x + 20 ) years then , ( x + 20 ) - 15 = 2 ( x - 15 ) x + 5 = 2 x - 30 x = 35 answer is b
a ) 30 , b ) 35 , c ) 25 , d ) 28 , e ) 32
b
add(subtract(20, subtract(20, add(const_3, const_2))), multiply(subtract(20, add(const_3, const_2)), const_2))
add(const_2,const_3)|subtract(n0,#0)|multiply(#1,const_2)|subtract(n0,#1)|add(#2,#3)
general
allenai/math_qa
two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post . if the length of each train be 160 m , in what time will they cross other travelling in opposite direction ?
"speed of the first train = 120 / 10 = 12 m / sec . speed of the second train = 120 / 5 = 8 m / sec . relative speed = 12 + 8 = 20 m / sec . required time = ( 160 + 160 ) / 20 = 16 sec . answer : c"
a ) 17 sec , b ) 12 sec , c ) 16 sec , d ) 15 sec , e ) 18 sec
c
divide(multiply(160, const_2), add(speed(160, 15), speed(160, 10)))
multiply(n2,const_2)|speed(n2,n1)|speed(n2,n0)|add(#1,#2)|divide(#0,#3)|
physics
allenai/math_qa
a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets $ 500 more than d , what is a ' s share ?
"let the shares of a , b , c and d be 5 x , 2 x , 4 x and 3 x respectively . then , 4 x - 3 x = 500 x = $ 500 a ' s share = 5 x = 5 * $ 500 = $ 2500 the answer is d ."
a ) $ 1200 , b ) $ 1600 , c ) $ 2000 , d ) $ 2500 , e ) $ 3000
d
multiply(multiply(subtract(4, 3), 500), 3)
subtract(n2,n3)|multiply(n4,#0)|multiply(n3,#1)|
general
allenai/math_qa
a certain farmer pays $ 60 per acre per month to rent farmland . how much does the farmer pay per month to rent a rectangular plot of farmland that is 360 feet by 1210 feet ? ( 43,560 square feet = 1 acre )
basically the question an error . 1 acre = 43,560 square feet and if it is then the answer is 600 ( d )
a ) $ 5,330 , b ) $ 3,360 , c ) $ 1,350 , d ) $ 600 , e ) $ 150
d
multiply(60, divide(multiply(360, 1210), divide(multiply(360, 1210), const_10)))
multiply(n1,n2)|divide(#0,const_10)|divide(#0,#1)|multiply(n0,#2)|
geometry
allenai/math_qa
the racing magic takes 50 seconds to circle the racing track once . the charging bull makes 40 rounds of the track in an hour . if they left the starting point together , how many minutes will it take for them to meet at the starting point for the second time ?
"time taken by racing magic to make one circle = 50 seconds time taken bycharging bullto make one circle = 60 mins / 40 = 1.5 mins = 90 seconds lcm of 90 and 50 seconds = 450 seconds time taken for them to meet at the starting point for the second time = 450 * 2 = 900 seconds = 15 mins answer e"
a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
e
multiply(divide(multiply(multiply(50, divide(50, 40)), const_2), 50), const_2)
divide(n0,n1)|multiply(#0,n0)|multiply(#1,const_2)|divide(#2,n0)|multiply(#3,const_2)|
physics
allenai/math_qa
what is the average ( arithmetic mean ) of the numbers 2 , 4 , 6 , 8 , 10 , 12 , 14 and 16 ?
"avg = sum of observations / number of observations avg = ( 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 ) / 8 = 9 answer is a"
a ) 9 , b ) 10 , c ) 15 , d ) 12 , e ) 14
a
divide(divide(multiply(add(2, 6), add(divide(subtract(6, 2), 2), const_1)), const_2), add(divide(subtract(6, 2), 2), const_1))
add(n0,n2)|subtract(n2,n0)|divide(#1,n0)|add(#2,const_1)|multiply(#0,#3)|divide(#4,const_2)|divide(#5,#3)|
general
allenai/math_qa
the smallest number which when diminished by 7 , is divisible 12 , 16 , 18 , 21 and 28 is :
"explanation required number = ( l . c . m . of 12,16 , 18 , 21 , 28 ) + 7 = 1008 + 7 = 1015 answer b"
a ) 1008 , b ) 1015 , c ) 1022 , d ) 1032 , e ) none of these
b
add(multiply(multiply(power(const_3, const_2.0), power(const_2.0, const_4)), add(const_3, const_4)), 7)
add(const_3,const_4)|power(const_3,const_2.0)|power(const_2.0,const_4)|multiply(#1,#2)|multiply(#0,#3)|add(#4,n0)|
general
allenai/math_qa
in what ratio p : q should the mixture p of milk and water in the ratio of 5 : 4 be mixed with another mixture q of milk and water in the ratio 2 : 7 so that the resultant mixture contains equal quantities of milk and water ?
( 5 / 9 ) * p + ( 2 / 9 ) * q = ( 4 / 9 ) * p + ( 7 / 9 ) * q p = 5 q p / q = 5 / 1 the answer is e .
a ) 3 : 2 , b ) 2 : 1 , c ) 4 : 3 , d ) 4 : 1 , e ) 5 : 1
e
add(subtract(add(4, 7), add(5, 2)), const_1)
add(n1,n3)|add(n0,n2)|subtract(#0,#1)|add(#2,const_1)
general
allenai/math_qa
the population of locusts in a certain swarm doubles every two hours . if 4 hours ago there were 1,000 locusts in the swarm , in approximately how many hours will the swarm population exceed 512,000 locusts ?
"- 4 hours : 1,000 - 2 hours : 2,000 now : 4,000 + 2 hours : 8,000 + 4 hours : 16,000 + 6 hours : 32,000 + 8 hours : 64,000 + 10 hours : 128,000 + 12 hours : 256,000 + 14 hours : 512,000 answer : d"
a ) 18 , b ) 15 , c ) 13 , d ) 14 , e ) 12
d
subtract(multiply(log(divide(power(4, 4), const_2)), const_2), 4)
power(n0,n0)|divide(#0,const_2)|log(#1)|multiply(#2,const_2)|subtract(#3,n0)|
general
allenai/math_qa
if a person cover 3 / 5 part of his journey by train , 7 / 20 part of his journey by bus and rest 6.5 km . by walk . what is total distance of his journey ?
let total distance be = x km . then , 3 x / 5 + 7 x / 20 + 6.5 = x ; 12 x + 7 x + 130 = 20 x ; x = 130 hence total distance = 130 km . answer d
a ) 65 km , b ) 100 km , c ) 120 km , d ) 130 km , e ) 75 km
d
divide(6.5, subtract(const_1, add(divide(3, 5), divide(7, 20))))
divide(n0,n1)|divide(n2,n3)|add(#0,#1)|subtract(const_1,#2)|divide(n4,#3)
general
allenai/math_qa
what sum of money put at c . i amounts in 2 years to rs . 8800 and in 3 years to rs . 9261 ?
"8800 - - - - 461 100 - - - - ? = > 5.238 % x * 105.238 / 100 * 105.238 / 100 = 8800 x * 1.1075 = 8800 x = 8800 / 1.1075 = > 7945.70 answer : a"
a ) 7945 , b ) 8877 , c ) 2877 , d ) 2678 , e ) 1011
a
divide(8800, power(add(subtract(divide(9261, 8800), const_1), const_1), 2))
divide(n3,n1)|subtract(#0,const_1)|add(#1,const_1)|power(#2,n0)|divide(n1,#3)|
general
allenai/math_qa
in the xy - plane , a triangle has vertices ( 0,0 ) , ( 4,0 ) and ( 4,6 ) . if a point ( a , b ) is selected at random from the triangular region , what is the probability that a - b > 0 ?
"the area of the right triangle is ( 1 / 2 ) * 4 * 6 = 12 . only the points ( a , b ) below the line y = x satisfy a - b > 0 . the part of the triangle which is below the line y = x has an area of ( 1 / 2 ) ( 4 ) ( 4 ) = 8 . p ( a - b > 0 ) = 8 / 12 = 2 / 3 the answer is d ."
a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 4 / 5
d
divide(const_4, add(0,0, const_10))
add(n0,const_10)|divide(const_4,#0)|
geometry
allenai/math_qa
the length of the rectangular field is double its width . inside the field there is square shaped pond 8 m long . if the area of the pond is 1 / 8 of the area of the field . what is the length of the field ?
"explanation : a / 8 = 8 * 8 = > a = 8 * 8 * 8 x * 2 x = 8 * 8 * 8 x = 16 = > 2 x = 32 answer : option b"
a ) 73 , b ) 32 , c ) 34 , d ) 43 , e ) 42
b
sqrt(divide(multiply(square_area(8), 8), inverse(const_2)))
inverse(const_2)|square_area(n0)|multiply(n2,#1)|divide(#2,#0)|sqrt(#3)|
geometry
allenai/math_qa
if the mean of numbers 38 , x , 70 , 88 and 110 is 69 , what is the mean of 50 , 72 , 97 , 125,147 and x ?
"mean = ( sum of all no . in series ) / ( no . in series ) m 1 = 69 = ( x + 38 + 70 + 88 + 110 ) / ( 5 ) 69 x 5 = 290 + x x = 39 therefore mean of 2 nd series m 2 = ( x + 50 + 62 + 97 + 125 + 147 ) / 6 m 2 = 86.67 answer = c"
a ) 73.5 , b ) 77.86 , c ) 86.67 , d ) 66.69 , e ) 70.56
c
divide(add(add(add(add(subtract(multiply(69, add(const_4, const_1)), add(add(add(38, 70), 88), 110)), 50), 72), 97), 125,147), add(const_4, const_1))
add(const_1,const_4)|add(n0,n1)|add(n2,#1)|multiply(n4,#0)|add(n3,#2)|subtract(#3,#4)|add(n5,#5)|add(n6,#6)|add(n7,#7)|add(n8,#8)|divide(#9,#0)|
general
allenai/math_qa
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 ?
"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 )"
a ) 13 , b ) 12 , c ) 9 , d ) 8 , e ) 7
b
divide(subtract(subtract(divide(150, const_2), 1), subtract(150, add(divide(150, const_2), divide(150, 6)))), const_2)
divide(n2,const_2)|divide(n2,n1)|add(#0,#1)|subtract(#0,n0)|subtract(n2,#2)|subtract(#3,#4)|divide(#5,const_2)|
other
allenai/math_qa
the simple form of the ratio 2 / 3 : 2 / 5 is ?
"2 / 3 : 2 / 5 = 10 : 6 = 5 : 3 answer : d"
a ) 5 : 0 , b ) 5 : 3 , c ) 5 : 1 , d ) 5 : 2 , e ) 5 : 7
d
divide(2, 5)
divide(n2,n3)|
other
allenai/math_qa
mike earns $ 17.5 per hour and phil earns $ 10.5 per hour . approximately how much less , as a percentage , does phil earn than mike per hour ?
"what % less of 17.5 is 10.5 let it be x % less , then = 17.5 ( 1 - x / 100 ) = 10.5 1 - x / 100 = 10.5 / 17.5 x = 200 / 5 x = 40 % ans e"
a ) 25 % , b ) 32.5 % , c ) 37 % , d ) 37.5 % , e ) 40 %
e
multiply(divide(10.5, 17.5), const_100)
divide(n1,n0)|multiply(#0,const_100)|
general
allenai/math_qa
the angle between two hands at 3.45 is
"theta degree = 11 / 2 m - 30 h = 11 / 2 ( 45 ) - 30 ( 3 ) = 247.5 - 90 = 157.5 or 157 1 / 2 degree answer : e"
a ) 110 degree , b ) 115 degree , c ) 112 1 / 2 degree , d ) 117 degree , e ) 157 1 / 2 degree
e
divide(multiply(subtract(multiply(divide(multiply(const_3, const_4), subtract(multiply(const_3, const_4), const_1)), multiply(add(const_4, const_1), subtract(multiply(const_3, const_4), const_1))), divide(const_60, const_2)), subtract(multiply(const_3, const_4), const_1)), const_2)
add(const_1,const_4)|divide(const_60,const_2)|multiply(const_3,const_4)|subtract(#2,const_1)|divide(#2,#3)|multiply(#0,#3)|multiply(#4,#5)|subtract(#6,#1)|multiply(#7,#3)|divide(#8,const_2)|
geometry
allenai/math_qa
a man took a loan from a bank at the rate of 9 % p . a . simple interest . after 3 years he had to pay rs . 5400 interest only for the period . the principal amount borrowed by him was :
"solution principal = rs . ( 100 x 5400 / 9 x 3 ) = rs . 20000 . answer d"
a ) rs . 2000 , b ) rs . 10,000 , c ) rs . 15,000 , d ) rs . 20,000 , e ) none
d
divide(divide(multiply(5400, const_100), multiply(3, 9)), multiply(divide(const_60, const_4), const_100))
divide(const_60,const_4)|multiply(n2,const_100)|multiply(n0,n1)|divide(#1,#2)|multiply(#0,const_100)|divide(#3,#4)|
gain
allenai/math_qa
what will be the fraction of 12 %
"explanation : 12 * 1 / 100 = 3 / 25 . option d"
a ) 1 / 20 , b ) 1 / 50 , c ) 1 / 75 , d ) 3 / 25 , e ) none of these
d
divide(circle_area(divide(12, const_2)), const_2)
divide(n0,const_2)|circle_area(#0)|divide(#1,const_2)|
gain
allenai/math_qa
an item is being sold for $ 10 each . however , if a customer will “ buy at least 3 ” they have a promo discount of 12 % . also , if a customer will “ buy at least 10 ” items they will deduct an additional 8 % to their “ buy at least 3 ” promo price . if sam buys 10 pcs of that item how much should he pay ?
"without any discount sam should pay 10 * 10 = $ 100 . now , the overall discount would be slightly less than 20 % , thus he must pay slightly more than $ 80 . only answer choice d fits . answer : d ."
a ) $ 92.00 , b ) $ 88.00 , c ) $ 87.04 , d ) $ 80.96 , e ) $ 80.00
d
multiply(subtract(10, divide(multiply(12, 8), const_100)), 10)
multiply(n2,n4)|divide(#0,const_100)|subtract(n0,#1)|multiply(#2,n0)|
gain
allenai/math_qa
if the digits 35 in the decimal 0.00035 repeat indefinitely , what is the value of ( 10 ^ 5 - 10 ^ 3 ) ( 0.00035 ) ?
"99 * 0.35 = 34.65 approx . 35 answer : b"
a ) 37 , b ) 41 , c ) 3.5 e - 05 , d ) 35 , e ) 3.5 e - 07
b
multiply(divide(multiply(multiply(multiply(10, 10), subtract(multiply(10, 10), const_1)), divide(35, subtract(multiply(10, 10), const_1))), const_1000), 10)
multiply(n2,n2)|subtract(#0,const_1)|divide(n0,#1)|multiply(#0,#1)|multiply(#2,#3)|divide(#4,const_1000)|multiply(n2,#5)|
general
allenai/math_qa
mr . john used to purchase certain number of mangoes for $ 360 since the price of mangoes is reduced by 10 % he got 12 more mangoes today . find the original price of 115 mangoes .
"mr . john used to purchase certain number of mangoes for $ 360 since the price of mangoes is reduced by 10 % he got 12 more mangoes today . find the original price of 120 mangoes . method 1 : let price per mango = x . let number of mangoes be n . then , nx = 360 . now price = 0.9 x ; number of mangoes = n + 12 . total amount = 0.9 x * ( n + 12 ) = 360 . nx = 0.9 nx + 10.8 x = > 0.1 nx = 10.8 x = > n = 108 = > x = 360 / 108 = 3.33 original price of 115 mangoes = 115 * 3.33 = 383 . answer b"
a ) 360 , b ) 383 , c ) 400 , d ) 406 , e ) 412
b
multiply(divide(subtract(divide(360, subtract(const_1, divide(const_1, 10))), 360), 12), 115)
divide(const_1,n1)|subtract(const_1,#0)|divide(n0,#1)|subtract(#2,n0)|divide(#3,n2)|multiply(n3,#4)|
gain
allenai/math_qa
a van takes 6 hours to cover a distance of 378 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
"time = 6 distence = 378 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 378 / 9 = 42 kmph d"
a ) 50 kmph , b ) 60 kmph , c ) 70 kmph , d ) 42 kmph , e ) 90 kmph
d
divide(378, multiply(divide(3, 2), 6))
divide(n2,n3)|multiply(n0,#0)|divide(n1,#1)|
physics
allenai/math_qa
a particular store purchased a stock of turtleneck sweaters and marked up its cost by 20 % . during the new year season , it further marked up its prices by 25 % of the original retail price . in february , the store then offered a discount of 9 % . what was its profit on the items sold in february ?
"assume the total price = 100 x price after 20 % markup = 120 x price after 25 % further markup = 1.25 * 120 x = 150 x price after the discount = 0.91 * 150 x = 136.5 x hence total profit = 36.5 % option d"
a ) 27.5 % , b ) 30 % , c ) 35 % , d ) 36.5 % , e ) 40 %
d
subtract(multiply(divide(subtract(const_100, 9), const_100), multiply(add(const_100, 20), divide(add(const_100, 25), const_100))), const_100)
add(n0,const_100)|add(n1,const_100)|subtract(const_100,n2)|divide(#2,const_100)|divide(#1,const_100)|multiply(#0,#4)|multiply(#3,#5)|subtract(#6,const_100)|
gain
allenai/math_qa
the area of a triangle will be when a = 2 m , b = 5 m , c = 7 m , a , b , c being lengths of respective sides ?
"s = ( 2 + 5 + 7 ) / 2 = 7 answer : b"
a ) 2 , b ) 7 , c ) 5 , d ) 3 , e ) 4
b
divide(add(add(2, 5), 7), 5)
add(n0,n1)|add(n2,#0)|divide(#1,n1)|
geometry
allenai/math_qa
a dog takes 2 leaps for every 3 leaps of a hare . if one leap of the dog is equal to 5 leaps of the hare , the ratio of the speed of the dog to that of the hare is :
"explanation : dog : hare = ( 2 * 5 ) leaps of hare : 3 leaps of hare = 10 : 3 answer : e"
a ) 9 : 3 , b ) 3 : 10 , c ) 2 : 3 , d ) 6 : 3 , e ) 10 : 3
e
divide(multiply(2, 5), 3)
multiply(n0,n2)|divide(#0,n1)|
other
allenai/math_qa
if ( m - 8 ) is a factor of m ^ 2 - km - 24 , then k =
"( m - 8 ) ( m - a ) = m ^ 2 - km - 24 a = - 3 k = 8 + a = 5 = b"
a ) 3 , b ) 5 , c ) 6 , d ) 11 , e ) 16
b
subtract(8, divide(24, 8))
divide(n2,n0)|subtract(n0,#0)|
general
allenai/math_qa
find the value of 4 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ]
"answer 4 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ] = 4 x [ ( 36 x 48 x 250 ) / ( 12 x 9 x 5 ) ] = 4 x 4 x 4 x 50 = 3200 correct option : b"
a ) 800 , b ) 3200 , c ) 900 , d ) 1600 , e ) none
b
multiply(divide(multiply(multiply(3.6, 0.48), 2.50), multiply(multiply(0.12, 0.09), 0.5)), 4)
multiply(n1,n2)|multiply(n4,n5)|multiply(n3,#0)|multiply(n6,#1)|divide(#2,#3)|multiply(n0,#4)|
general
allenai/math_qa
p alone can complete a job in 5 days . the work done by q alone in one day is equal to one - fourth of the work done by p alone in one day . in how many days can the work be completed if p and q work together ?
"p ' s rate is 1 / 5 q ' s rate is 1 / 20 the combined rate is 1 / 5 + 1 / 20 = 1 / 4 if they work together , the job will take 4 days . the answer is d ."
a ) 2.5 , b ) 3.0 , c ) 3.5 , d ) 4.0 , e ) 4.5
d
divide(const_1, add(divide(const_1, 5), divide(divide(const_1, 5), const_3)))
divide(const_1,n0)|divide(#0,const_3)|add(#0,#1)|divide(const_1,#2)|
physics
allenai/math_qa
how many different positive integers are factors of 36 ?
"6 × 6 = 3 ^ 2 × 2 ^ 2 so total factors = ( 2 + 1 ) ( 2 + 1 ) = 9 answer : d"
a ) 4 , b ) 6 , c ) 7 , d ) 9 , e ) 11
d
add(power(const_2, const_2), const_2)
power(const_2,const_2)|add(#0,const_2)|
other
allenai/math_qa
a and b start a business , with a investing the total capital of rs . 50000 , on the condition that b pays a interest @ 10 % per annum on his half of the capital . a is a working partner and receives rs . 1500 per month from the total profit and any profit remaining is equally shared by both of them . at the end of the year , it was found that the income of a is twice that of b . find the total profit for the year ?
"interest received by a from b = 10 % of half of rs . 50000 = 10 % * 25000 = 2500 . amount received by a per annum for being a working partner = 1500 * 12 = rs . 18000 . let ' p ' be the part of the remaining profit that a receives as his share . total income of a = ( 2500 + 18000 + p ) total income of b = only his share from the remaining profit = ' p ' , as a and b share the remaining profit equally . income of a = twice the income of b ( 2500 + 18000 + p ) = 2 ( p ) p = 20500 total profit = 2 p + 18000 = 2 * 20500 + 18000 = 59000 . answer : d"
a ) 59028 , b ) 27777 , c ) 29999 , d ) 59000 , e ) 27772
d
add(multiply(multiply(divide(divide(50000, const_2), 10), const_3), const_4), 1500)
divide(n0,const_2)|divide(#0,n1)|multiply(#1,const_3)|multiply(#2,const_4)|add(n2,#3)|
gain
allenai/math_qa
a batch of cookies was divided amomg 4 tins : 2 / 3 of all the cookies were placed in either the blue or the green tin , and the rest were placed in the red tin . if 1 / 4 of all the cookies were placed in the blue tin , what fraction of the cookies that were placed in the other tins were placed in the green tin
"this will help reduce the number of variables you have to deal with : g + b = 2 / 3 r = 1 / 4 b = 1 / 4 we can solve for g which is 5 / 12 what fraction ( let it equal x ) of the cookies that were placed in the other tins were placed in the green tin ? so . . x * ( g + r ) = g x * ( 5 / 12 + 1 / 4 ) = 5 / 12 x = 5 / 8 answer : e"
a ) 15 / 2 , b ) 9 / 4 , c ) 5 / 9 , d ) 7 / 5 , e ) 5 / 8
e
add(subtract(1, divide(2, 3)), subtract(divide(2, 3), divide(1, 4)))
divide(n1,n2)|divide(n3,n4)|subtract(n3,#0)|subtract(#0,#1)|add(#2,#3)|
general
allenai/math_qa
3 * 14 + 3 * 15 + 3 * 18 + 11 = ?
"3 * 14 + 3 * 15 + 3 * 18 + 11 = 42 + 45 + 54 + 11 = 152 the answer is e ."
a ) 125 , b ) 126 , c ) 130 , d ) 148 , e ) 152
e
add(add(add(multiply(3, 14), multiply(3, 15)), multiply(3, 18)), 11)
multiply(n0,n1)|multiply(n0,n3)|multiply(n0,n5)|add(#0,#1)|add(#3,#2)|add(n6,#4)|
general
allenai/math_qa
when a certain number x is divided by 63 , the remainder is 11 . what is the remainder when x is divided by 9 ?
"when a certain number x is divided by 63 , the remainder is 11 . what is the remainder when x is divided by 9 ? putting a value say x = 11 we get remainder as 11 when divided by 63 . when 11 divided by 9 we get 2 as remainder . a is the answer ."
a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
a
reminder(11, 9)
reminder(n1,n2)|
general
allenai/math_qa
in a dairy farm , 46 cows eat 46 bags of husk in 46 days . in how many days one cow will eat one bag of husk ?
"explanation : one bag of husk = 46 cows per day ⇒ 46 × 1 × 46 = 1 × 46 × x for one cow = 46 days answer : b"
a ) 1 , b ) 46 , c ) 20 , d ) 26 , e ) 30
b
multiply(divide(46, 46), 46)
divide(n0,n0)|multiply(n0,#0)|
physics
allenai/math_qa
if y ¤ w = y ^ ( 2 w ) for all positive integers , then ( 3 ¤ 4 ) ¤ 2 =
y ¤ w = y ^ ( 2 w ) 3 ¤ 4 = 3 ^ ( 8 ) ( 3 ¤ 4 ) ¤ 2 = ( 3 ^ 8 ) ¤ 2 = ( 3 ^ 8 ) ^ 4 = 3 ^ 32 correct option : e
a ) 3 ^ 8 , b ) 3 ^ 12 , c ) 3 ^ 16 , d ) 3 ^ 24 , e ) 3 ^ 32
e
power(power(3, multiply(2, 4)), multiply(2, 2))
multiply(n0,n2)|multiply(n0,n0)|power(n1,#0)|power(#2,#1)
general
allenai/math_qa
45 men took a dip in a water tank 40 m long and 20 m broad on a religious day . if the average displacement of water by a man is 4 m 3 , then the rise in the water level in the tank will be :
explanation : total volume of water displaced = ( 4 x 45 ) m 3 = 180 m 3 rise in water level = 180 / 40 ã — 20 = 0.225 m = 22.5 cm answer : e
a ) 20 cm , b ) 25 cm , c ) 35 cm , d ) 50 cm , e ) none of these
e
divide(multiply(4, 45), multiply(40, 20))
multiply(n0,n3)|multiply(n1,n2)|divide(#0,#1)
physics
allenai/math_qa
one hour before john started walking from p to q , a distance of 13 miles , ann had started walking along the same road from q to p . ann walked at a constant speed of 3 miles per hour and john at 2 miles per hour . how many miles had ann walked when they met ?
"ann walks from q to p at a speed of 3 miles / hr for one hour . she covers 3 miles in 1 hour and now distance between john and ann is 13 - 3 = 10 miles . ann walks at 3 mph and john at 2 mph so their relative speed is 3 + 2 = 5 mph . they have to cover 10 miles so it will take them 10 / 5 = 2 hours to meet . in 2 hrs , ann would have covered 2 hrs * 3 miles per hour = 6 miles . adding this to the 3 miles she covered before john , ann covered a total of 3 + 6 = 9 miles . answer ( c )"
a ) 6 miles , b ) 8,4 miles , c ) 9 miles , d ) 9,6 miles , e ) 12 miles
c
multiply(divide(13, add(3, 2)), 2)
add(n1,n2)|divide(n0,#0)|multiply(n2,#1)|
physics
allenai/math_qa
what is the remainder when the number r = 14 ^ 2 * 15 ^ 8 is divided by 5 ?
"14 ^ 2 has units digit 6 15 ^ 8 has units digit 5 thus r = 14 ^ 2 * 15 ^ 8 has units digit 0 and will be divisible by 5 . the remainder will be zero answer : ( a )"
a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 5
a
divide(5, 5)
divide(n4,n4)|
general
allenai/math_qa
a man walking at a rate of 10 km / hr crosses a bridge in 10 minutes . the length of the bridge is ?
"speed = 10 * 5 / 18 = 50 / 18 m / sec distance covered in 10 minutes = 50 / 18 * 10 * 60 = 1667 m answer is c"
a ) 1521 , b ) 1492 , c ) 1667 , d ) 1254 , e ) 1112
c
multiply(divide(multiply(10, const_1000), const_60), 10)
multiply(n0,const_1000)|divide(#0,const_60)|multiply(n1,#1)|
gain
allenai/math_qa
in a recent head - to - head run - off election , 12000 absentee ballets were cast . 1 / 6 of the absentee ballets were thrown out and 3 / 5 of the remaining absentee ballets were cast for candidate a . how many absentee votes did candidate b receive ?
5 / 6 * 2 / 5 ( total absentee votes ) = 1 / 3 ( total votes ) = 1 / 3 * 12000 = 4000 answer is c
a ) 2,000 , b ) 3,000 , c ) 4,000 , d ) 8,000 , e ) 9,000
c
subtract(divide(subtract(multiply(divide(multiply(divide(12000, 6), 5), 5), 3), divide(multiply(divide(12000, 6), 5), 5)), const_1000), 1)
divide(n0,n2)|multiply(n4,#0)|divide(#1,n4)|multiply(n3,#2)|subtract(#3,#2)|divide(#4,const_1000)|subtract(#5,n1)
general
allenai/math_qa
a rectangular circuit board is designed to have width w inches , perimeter p inches , and area x square inches . which of the following equations must be true ?
notice that we can discard options a , and c right away . the sum of 3 positive values can not be 0 . now , assume : width = w = 1 inchand length = 1 inch ; perimeter = p = 4 inches ; area = x = 1 square inches . plug the values of w , p , and x into the answer choices : only for e 2 w ^ 2 - pw + 2 x = 2 - 4 + 2 = 0 . answer : e .
['a ) w ^ 2 + pw + x = 0', 'b ) w ^ 2 - pw + 2 x = 0', 'c ) 2 w ^ 2 + pw + 2 x = 0', 'd ) 2 w ^ 2 - pw - 2 x = 0', 'e ) 2 w ^ 2 - pw + 2 x = 0']
e
add(subtract(multiply(const_2, const_1), add(multiply(const_2, power(const_1, const_2)), multiply(const_2, power(const_1, const_2)))), multiply(const_2, power(const_1, const_2)))
multiply(const_1,const_2)|power(const_1,const_2)|multiply(#1,const_2)|add(#2,#2)|subtract(#0,#3)|add(#2,#4)
geometry
allenai/math_qa
machine t can produce x units in 3 / 4 of the time it takes machine n to produce x units . machine n can produce x units in 2 / 3 the time it takes machine o to produce x units . if all 3 machines are working simultaneously , what fraction of the total output is produced by machine n ?
let the following be true : t makes x in time t then the following follows : n makes x in 4 t / 3 o makes x in 3 / 2 ( 4 t / 3 ) = 2 t m : n : o = 1 : 4 / 3 : 2 = 3 : 4 : 6 so n = 4 / ( 3 + 4 + 6 ) = 4 / 13 = c
a ) 1 / 2 , b ) 1 / 3 , c ) 4 / 13 , d ) 8 / 29 , e ) 6 / 33
c
multiply(inverse(add(divide(2, 3), add(const_1, multiply(divide(2, 3), divide(3, 4))))), divide(2, 3))
divide(n2,n0)|divide(n0,n1)|multiply(#0,#1)|add(#2,const_1)|add(#3,#0)|inverse(#4)|multiply(#0,#5)
general
allenai/math_qa
a man buys an article for $ 100 . and sells it for $ 110 . find the gain percent ?
"c . p . = $ 100 s . p . = $ 110 gain = $ 10 gain % = 10 / 100 * 100 = 10 % answer is a"
a ) 10 % , b ) 15 % , c ) 25 % , d ) 20 % , e ) 30 %
a
subtract(divide(110, divide(100, const_100)), const_100)
divide(n0,const_100)|divide(n1,#0)|subtract(#1,const_100)|
gain
allenai/math_qa
a man can row downstream at 24 kmph and upstream at 10 kmph . find the speed of the man in still water and the speed of stream respectively ?
"let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 24 - - - ( 1 ) and x - y = 10 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 34 = > x = 17 , y = 7 answer : e"
a ) 2 , 7 , b ) 7 , 4 , c ) 8 , 7 , d ) 4 , 7 , e ) 17 , 7
e
divide(divide(add(24, 10), const_2), const_2)
add(n0,n1)|divide(#0,const_2)|divide(#1,const_2)|
physics
allenai/math_qa
how many numbers from 10 to 10000 are exactly divisible by 9 ?
"10 / 9 = 1 and 10000 / 9 = 1111 = = > 1111 - 1 = 1110 . therefore 1110 answer : c"
a ) 900 , b ) 1000 , c ) 1110 , d ) 1200 , e ) 1400
c
add(divide(subtract(multiply(floor(divide(10000, 9)), 9), multiply(add(floor(divide(10, 9)), const_1), 9)), 9), const_1)
divide(n1,n2)|divide(n0,n2)|floor(#0)|floor(#1)|add(#3,const_1)|multiply(n2,#2)|multiply(n2,#4)|subtract(#5,#6)|divide(#7,n2)|add(#8,const_1)|
general
allenai/math_qa
the difference between compound interest and simple interest on a certain amount of money at 5 % per annum for 2 years is 16 . find the sum :
"sol . ( d ) let the sum be 100 . therefore , si = 100 × 5 × 2 / 100 = 10 and ci = 100 ( 1 + 5 / 100 ) 2 − 100 ∴ = 100 × 21 × 21 / 20 × 20 − 100 = 41 / 4 difference of ci and si = 41 ⁄ 4 - 10 = 1 ⁄ 4 if the difference is 1 ⁄ 4 , the sum = 100 = > if the difference is 16 , the sum = 400 × 16 = 6400 answer d"
a ) 4500 , b ) 7500 , c ) 5000 , d ) 6400 , e ) none of these
d
divide(16, subtract(power(add(const_1, divide(5, const_100)), 2), add(const_1, multiply(2, divide(5, const_100)))))
divide(n0,const_100)|add(#0,const_1)|multiply(n1,#0)|add(#2,const_1)|power(#1,n1)|subtract(#4,#3)|divide(n2,#5)|
gain
allenai/math_qa
if the sides of a triangle are 36 cm , 34 cm and 20 cm , what is its area ?
"the triangle with sides 36 cm , 34 cm and 20 cm is right angled , where the hypotenuse is 36 cm . area of the triangle = 1 / 2 * 34 * 20 = 340 cm 2 answer : c"
a ) 320 cm 2 , b ) 360 cm 2 , c ) 340 cm 2 , d ) 310 cm 2 , e ) 300 cm 2
c
divide(multiply(34, 20), const_2)
multiply(n1,n2)|divide(#0,const_2)|
geometry
allenai/math_qa
laura took out a charge account at the general store and agreed to pay 4 % simple annual interest . if she charges $ 35 on her account in january , how much will she owe a year later , assuming she does not make any additional charges or payments ?
"principal that is amount taken by laura at year beginning = 35 $ rate of interest = 4 % interest = ( 4 / 100 ) * 35 = 1.4 $ total amount that laura owes a year later = 35 + 1.4 = 36.4 $ answer a"
a ) $ 36.4 , b ) $ 37.10 , c ) $ 37.16 , d ) $ 38.10 , e ) $ 38.80
a
add(multiply(divide(4, const_100), 35), 35)
divide(n0,const_100)|multiply(n1,#0)|add(n1,#1)|
general
allenai/math_qa
two trains of equal length are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train catches and completely passes the slower train in 54 seconds . what is the length of each train ( in meters ) ?
"the relative speed = 46 - 36 = 10 km / hr = 10 * 5 / 18 = 25 / 9 m / s in 54 seconds , the relative difference in distance traveled is 54 * 25 / 9 = 150 meters this distance is twice the length of each train . the length of each train is 150 / 2 = 75 meters the answer is d ."
a ) 45 , b ) 55 , c ) 65 , d ) 75 , e ) 85
d
divide(multiply(divide(multiply(subtract(46, 36), const_1000), const_3600), 54), const_2)
subtract(n0,n1)|multiply(#0,const_1000)|divide(#1,const_3600)|multiply(n2,#2)|divide(#3,const_2)|
physics
allenai/math_qa
instead of multiplying a number by 2 , the number is divided by 10 . what is the percentage of error obtained ?
let the number be x the right number is 2 x the wrong number is x / 10 error is ( 2 x - x / 10 ) = 19 x / 10 percentage of error is ( ( 19 x / 10 ) / 2 x ) * 100 = 95 % answer : c
a ) 94 % , b ) 92 % , c ) 95 % , d ) 93 % , e ) 97 %
c
subtract(const_100, multiply(divide(divide(10, 10), multiply(2, const_10)), const_100))
divide(n1,n1)|multiply(n0,const_10)|divide(#0,#1)|multiply(#2,const_100)|subtract(const_100,#3)
general
allenai/math_qa
david works at a resort from the beginning of march to the end of september . during the month of august this past year , he made 2 times the average ( arithmetic mean ) of his monthly totals in tips for the other months . his total tips for august were what fraction of his total tips for all of the months he worked ?
"first notice the number of months for which he worked - march to sept i . e . 7 months avg of monthly totals in tips for months other than august = x tips in august = 2 x total tips for all months = 6 * x + 2 x = 8 x tips for august / total tips for all months = 2 x / 8 x = 1 / 4 answer : d"
a ) 1 / 6 , b ) 1 / 7 , c ) 1 / 8 , d ) 1 / 4 , e ) 1 / 3
d
divide(const_4.0, add(subtract(const_10, 2), 2))
subtract(const_10,const_4.0)|add(n0,#0)|divide(n0,#1)|
general
allenai/math_qa
how many of the positive divisors of 480 are also multiples of 4 not including 480 ?
"480 = 2 ^ 6 * 3 * 5 = ( 4 ) * 2 ^ 3 * 3 * 5 besides ( 4 ) , the exponents of 2 , 3 , and 5 are 3 , 1 , and 1 . there are ( 3 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 16 ways to make multiples of 4 . we must subtract 1 because one of these multiples is 480 . the answer is a ."
a ) 15 , b ) 16 , c ) 19 , d ) 20 , e ) 24
a
divide(divide(divide(480, 4), const_2), const_3)
divide(n0,n1)|divide(#0,const_2)|divide(#1,const_3)|
general
allenai/math_qa
in what time will a train 120 m long cross an electric pole , it its speed be 185 km / hr ?
"speed = 185 * 5 / 18 = 51 m / sec time taken = 120 / 51 = 2.3 sec . answer : a"
a ) 2.3 sec , b ) 2.9 sec , c ) 2.7 sec , d ) 8.7 sec , e ) 8.5 sec
a
divide(120, multiply(185, const_0_2778))
multiply(n1,const_0_2778)|divide(n0,#0)|
physics
allenai/math_qa
sum of the squares of 3 no . ' s is 267 and the sum of their products taken two at a time is 131 . find the sum ?
"( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 267 + 2 * 131 a + b + c = √ 529 = 23 d"
a ) 20 , b ) 24 , c ) 26 , d ) 23 , e ) 30
d
sqrt(add(multiply(131, const_2), 267))
multiply(n2,const_2)|add(n1,#0)|sqrt(#1)|
general
allenai/math_qa
walking 4 / 3 of his usual rate , a boy reaches his school 4 min early . find his usual time to reach the school ?
"speed ratio = 1 : 4 / 3 = 3 : 4 time ratio = 4 : 3 1 - - - - - - - - 4 4 - - - - - - - - - ? 16 m . answer : b"
a ) 22 , b ) 16 , c ) 27 , d ) 28 , e ) 20
b
multiply(4, 4)
multiply(n0,n2)|
gain
allenai/math_qa
there are two positive numbers in the ratio 5 : 8 . if the larger number exceeds the smaller by 18 , then find the smaller number ?
"let the two positive numbers be 5 x and 8 x respectively . 8 x - 5 x = 18 3 x = 18 = > x = 6 = > smaller number = 5 x = 30 . answer : a"
a ) 30 , b ) 66 , c ) 77 , d ) 88 , e ) 44
a
divide(multiply(18, 5), const_4)
multiply(n0,n2)|divide(#0,const_4)|
other
allenai/math_qa
a , b and c completed a piece of work , a worked for 6 days , b for 9 days and c for 4 days . their daily wages were in the ratio of 3 : 4 : 5 . find the daily wages of c , if their total earning was rs . 1702 ?
"3 x 4 x 5 x 6 9 4 18 x + 36 x + 20 x = 1702 74 x = 1702 = > x = 23 5 x = 115 rs . answer : b"
a ) s . 109 , b ) s . 115 , c ) s . 100 , d ) s . 103 , e ) s . 102
b
multiply(5, divide(1702, add(add(multiply(6, 3), multiply(9, 4)), multiply(4, 5))))
multiply(n0,n3)|multiply(n1,n2)|multiply(n2,n5)|add(#0,#1)|add(#3,#2)|divide(n6,#4)|multiply(n5,#5)|
physics
allenai/math_qa
find the area of a parallelogram with base 24 cm and height 16 cm ?
"area of a parallelogram = base * height = 24 * 16 = 384 cm 2 answer : b"
a ) 298 cm 2 , b ) 384 cm 2 , c ) 279 cm 2 , d ) 297 cm 2 , e ) 278 cm 2
b
multiply(24, 16)
multiply(n0,n1)|
geometry
allenai/math_qa
if a = 105 and a ^ 3 = 21 × 25 × 45 × w , what is the value of w ?
"a = 105 = 3 * 5 * 7 a ^ 3 = 21 × 25 × 45 × w = > a ^ 3 = ( 7 * 3 ) x ( 5 * 5 ) x ( 3 ^ 2 * 5 ) x w = > a ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x w = > ( 3 * 5 * 7 ) ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x w w = 7 ^ 2 = 49 answer d"
a ) 35 , b ) 42 , c ) 45 , d ) 49 , e ) 54
d
divide(power(105, 3), multiply(multiply(21, 25), 45))
multiply(n2,n3)|power(n0,n1)|multiply(n4,#0)|divide(#1,#2)|
general
allenai/math_qa
find the last digit of 322 ^ 369
for calculating the unit place of these type of question ( exponent ) as the power of 2 repeats after 4 , so we will divide the exponent by 4 e . g , 2 ^ 1 = 2 and 2 ^ ( 4 + 1 ) = 32 , both have same unit place 369 / 4 gives the remainder as 1 so we can write 322 ^ 369 = 2 ^ 1 = 2 so , the unit place will be 2 answer : b
a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
b
reminder(power(reminder(322, const_10), reminder(369, const_10)), const_10)
reminder(n0,const_10)|reminder(n1,const_10)|power(#0,#1)|reminder(#2,const_10)
general
allenai/math_qa
the center of a circle lies on the origin of the coordinate plane . if a point ( x , y ) is randomly selected inside of the circle , what is the probability that y > 0 and y > x ?
the line y = x divides the circle into two equal areas . all the points above the line y = x satisfy the condition that y > x . all the points above the x - axis satisfy the condition that y > 0 . the intersection of these two areas is 3 / 8 of the circle . the answer is c .
a ) 1 / 8 , b ) 1 / 6 , c ) 3 / 8 , d ) 1 / 2 , e ) 3 / 4
c
divide(const_3, multiply(const_2, const_4))
multiply(const_2,const_4)|divide(const_3,#0)
physics
allenai/math_qa
if 15 % of 30 % of 50 % of a number is 90 , then what is the number ?
"let the number be a given , 15 / 100 * 30 / 100 * 50 / 100 * a = 90 = > 3 / 20 * 3 / 10 * 1 / 2 * a = 90 = > a = 10 * 20 * 10 * 2 = 4000 . answer : a"
a ) 4000 , b ) 3050 , c ) 4400 , d ) 4500 , e ) none of these
a
divide(90, multiply(multiply(divide(50, const_100), divide(30, const_100)), divide(15, const_100)))
divide(n0,const_100)|divide(n2,const_100)|divide(n1,const_100)|multiply(#1,#2)|multiply(#0,#3)|divide(n3,#4)|
gain
allenai/math_qa
a man can row his boat with the stream at 6 km / h and against the stream in 4 km / h . the man ' s rate is ?
"ds = 6 us = 4 s = ? s = ( 6 - 4 ) / 2 = 1 kmph answer : a"
a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 7
a
divide(subtract(6, 4), const_2)
subtract(n0,n1)|divide(#0,const_2)|
gain
allenai/math_qa
a cyclist rides a bicycle 8 km at an average speed of 10 km / hr and again travels 10 km at an average speed of 8 km / hr . what is the average speed for the entire trip ?
"distance = 18 km time = 8 / 10 + 10 / 8 = ( 64 + 100 ) / 80 = 164 / 80 = 41 / 20 hours average speed = ( 18 * 20 ) / 41 = 8.78 km / h the answer is c ."
a ) 9.28 , b ) 8.48 , c ) 8.78 , d ) 8.98 , e ) 9.18
c
divide(add(8, 10), add(divide(8, 10), divide(10, 8)))
add(n0,n1)|divide(n0,n1)|divide(n1,n0)|add(#1,#2)|divide(#0,#3)|
general
allenai/math_qa
what is the compound interest paid on a sum of rs . 700 for the period of 2 years at 10 % per annum .
"solution = interest % for 1 st year = 10 interest % for 2 nd year = 10 + 10 % of 10 = 10 + 10 * 10 / 100 = 11 total % of interest = 10 + 11 = 21 total interest = 21 % 700 = 700 * ( 21 / 100 ) = 147 answer c"
a ) 130 , b ) 620 , c ) 147 , d ) 120 , e ) none of these
c
subtract(multiply(700, power(add(const_1, divide(10, const_100)), 2)), 700)
divide(n2,const_100)|add(#0,const_1)|power(#1,n1)|multiply(n0,#2)|subtract(#3,n0)|
gain
allenai/math_qa
if a , b , c , d , e and f are integers and ( ab + cdef ) < 0 , then what is the maximum number a of integers that can be negative ?
minimuum should be 1 maximum should be 4 : 1 out of a or b to make the multiplication negative 3 out of c , d , e or f to make the multiplication negative . negative + negative < 0 answer : c maximum will be 5 . . you dont require both the multiplicatin to be negative for entire equation to be negative . . . any one a or b can be negative to make ab negative and it can still be more ( away from 0 ) than the multiplication of 4 other - ve numbers . . . actually by writing minimum required as 1 out of 6 , you are actually meaning 5 out of 6 also possible as you will see a = 5 or 1 will give you same equation . . ans d
a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
d
add(divide(const_10, const_2), 0)
divide(const_10,const_2)|add(n0,#0)
general
allenai/math_qa
the average height of 35 boys in a class was calculated as 183 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ) . ?
"calculated average height of 35 boys = 183 cm . wrong total height of 35 boys = 183 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 183 cm - ( 166 cm - 106 cm ) / 35 = 183 cm - 60 / 35 cm = 183 cm - 1.71 cm = 181.29 cm . answer : b"
a ) 178.27 cm , b ) 181.29 cm , c ) 978.29 cm , d ) 178.89 cm , e ) 176.29 cm
b
floor(divide(add(subtract(multiply(35, 183), 166), 106), 35))
multiply(n0,n1)|subtract(#0,n2)|add(n3,#1)|divide(#2,n0)|floor(#3)|
general
allenai/math_qa
the cross - section of a stream is a trapezium in shape . if the stream is 10 m wide at the top and the area of cross - section is 640 sq m , the depth of stream is 80 m and width at the bottom is ?
1 / 2 * 80 ( 10 + b ) = 640 b = 6 m answer : b
a ) 2 m , b ) 6 m , c ) 4 m , d ) 8 m , e ) 9 m
b
divide(subtract(640, multiply(multiply(80, divide(const_1, const_2)), 10)), multiply(80, divide(const_1, const_2)))
divide(const_1,const_2)|multiply(n2,#0)|multiply(n0,#1)|subtract(n1,#2)|divide(#3,#1)
physics
allenai/math_qa
an engineer undertakes a project to build a road 15 km long in 300 days and employs 35 men for the purpose . after 100 days , he finds only 2.5 km of the road has been completed . find the ( approximate ) number of extra men he must employ to finish the work in time .
"35 workers working already let x be the total men required to finish the task in next 200 days 2.5 km done hence remaining is 12.5 km also , work has to be completed in next 200 days ( 300 - 100 = 200 ) we know that , proportion of men to distance is direct proportion and , proportion of men to days is inverse proportion hence , x = ( 35 * 12.5 * 100 ) / ( 2.5 * 200 ) thus , x = 87.5 that is approximately 88 thus , more men needed to finish the task = 88 - 35 = 53 hence answer is b"
a ) a . 43 , b ) b . 53 , c ) c . 55 , d ) d . 68 , e ) e . 60
b
subtract(divide(multiply(multiply(35, subtract(15, 2.5)), 100), multiply(2.5, subtract(300, 100))), 35)
subtract(n0,n4)|subtract(n1,n3)|multiply(n2,#0)|multiply(n4,#1)|multiply(n3,#2)|divide(#4,#3)|subtract(#5,n2)|
physics
allenai/math_qa
what is the median of a set of consecutive integers if the sum of nth number from the beginning and nth number from the end is 200 ?
"surprisingly no one answered this easy one . property of a set of consecutive integerz . mean = median = ( first element + last element ) / 2 = ( second element + last but one element ) / 2 = ( third element + third last element ) / 2 etc . etc . so mean = median = 200 / 2 = 100 answer is e"
a ) 10 , b ) 25 , c ) 50 , d ) 75 , e ) 100
e
divide(200, const_2)
divide(n0,const_2)|
general
allenai/math_qa
a 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2 . 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more . at the end of the two removal and replacement , what is the ratio r of milk and water in the resultant mixture ?
"he 20 litre mixture contains milk and water in the ratio of 3 : 2 . therefore , there will be 12 litres of milk in the mixture and 8 litres of water in the mixture . step 1 . when 10 litres of the mixture is removed , 6 litres of milk is removed and 4 litres of water is removed . therefore , there will be 6 litres of milk and 4 litres of water left in the container . it is then replaced with pure milk of 10 litres . now the container will have 16 litres of milk and 4 litres of water . step 2 . when 10 litres of the new mixture is removed , 8 litres of milk and 2 litres of water is removed . the container will have 8 litres of milk and 2 litres of water in it . now 10 litres of pure milk is added . therefore , the container will have 18 litres of milk and 2 litres of water in it at the end of the second step . therefore , the ratio of milk and water is 18 : 2 or 9 : 1 . shortcut . we are essentially replacing water in the mixture with pure milk . let w _ o be the amount of water in the mixture originally = 8 litres . let w _ r be the amount of water in the mixture after the replacements have taken place . then , { w _ r } / { w _ o } = ( 1 - r / m ) ^ n where r is the amount of the mixture replaced by milk in each of the steps , m is the total volume of the mixture and n is the number of times the cycle is repeated . hence , { w _ r } / { w _ o }   = ( 1 / 2 ) ^ 2   = 1 / 4 therefore r , w _ r   = { w _ o } / 4 = 8 / 4   = 2 litres . b"
a ) 17 : 3 , b ) 9 : 1 , c ) 3 : 17 , d ) 5 : 3 , e ) 11 : 2
b
divide(add(multiply(divide(add(multiply(divide(3, add(3, 2)), subtract(20, 10)), 10), 20), subtract(20, 10)), 10), multiply(divide(multiply(divide(2, add(3, 2)), subtract(20, 10)), 20), subtract(20, 10)))
add(n1,n2)|subtract(n0,n3)|divide(n1,#0)|divide(n2,#0)|multiply(#2,#1)|multiply(#3,#1)|add(n3,#4)|divide(#5,n0)|divide(#6,n0)|multiply(#7,#1)|multiply(#8,#1)|add(n3,#10)|divide(#11,#9)|
general
allenai/math_qa
in an election between the two candidates , the candidates who gets 70 % of votes polled is winned by 360 vote ’ s majority . what is the total number of votes polled ?
"explanation : note : majority ( 40 % ) = difference in votes polled to win ( 70 % ) & defeated candidates ( 30 % ) 40 % = 70 % - 30 % 40 % - - - - - > 360 ( 40 * 9 = 360 ) 100 % - - - - - > 900 ( 100 * 9 = 900 ) answer : option c"
a ) 750 , b ) 700 , c ) 900 , d ) 850 , e ) none of these
c
divide(multiply(const_100, 360), subtract(70, subtract(const_100, 70)))
multiply(n1,const_100)|subtract(const_100,n0)|subtract(n0,#1)|divide(#0,#2)|
gain
allenai/math_qa
a searchlight on top of the watchtower makes 4 revolutions per minute . what is the probability that a man appearing near the tower will stay in the dark for at least 12 seconds ?
"the searchlight completes one revolution every 15 seconds . the probability that the man ' s area will be lit up is 12 / 15 = 4 / 5 . the probability that he will stay in the dark is 1 - 4 / 5 = 1 / 5 the answer is e ."
a ) 1 / 2 , b ) 2 / 3 , c ) 1 / 3 , d ) 1 / 4 , e ) 1 / 5
e
subtract(const_1, divide(12, multiply(12, const_3)))
multiply(n1,const_3)|divide(n1,#0)|subtract(const_1,#1)|
physics
allenai/math_qa
if m and n are positive integers and m ^ 2 + n ^ 2 = 20 , what is the value of m ^ 3 + n ^ 3 ?
"you need to integers which squared are equal 20 . which could it be ? let ' s start with the first integer : 1 ^ 2 = 1 2 ^ 2 = 4 3 ^ 2 = 9 4 ^ 2 = 16 stop . the integers ca n ' t be greater than 4 or we will score above 20 . the second integer need to be picked up the same way . 1 ^ 2 = 1 2 ^ 2 = 4 3 ^ 2 = 9 4 ^ 2 = 16 the only pair that matches is 4 ^ 2 + 2 ^ 2 = 20 . so 4 ^ 3 + 2 ^ 3 = 72 . answer a . )"
a ) 72 , b ) 224 , c ) 320 , d ) 512 , e ) 1,600
a
gcd(20, const_4)
gcd(n2,const_4)|
general
allenai/math_qa
if 25 % of a number is subtracted from a second number , the second number reduces to its 4 - sixth . what is the ratio of the first number to the second number ?
explanation : let the numbers be p & q q - p / 4 = 4 q / 6 = > q - 4 q / 6 = p / 4 = > 2 q / 6 = p / 4 = > p / q = 4 / 3 answer b
a ) 5 : 3 , b ) 4 : 3 , c ) 6 : 3 , d ) 3 : 4 , e ) 5 : 4
b
divide(subtract(const_1, divide(4, multiply(const_3, const_2))), divide(25, const_100))
divide(n0,const_100)|multiply(const_2,const_3)|divide(n1,#1)|subtract(const_1,#2)|divide(#3,#0)
general
allenai/math_qa
three machines , each working at the same constant rate , together can complete a certain job in 18 days . how many additional machines , each working at the same constant rate , will be needed to complete the job in 9 days ?
"rate of one machine = 1 job / ( 18 * 3 ) days let x = number of machines needed to complete the job in 9 days 1 / ( 3 * 18 ) * 9 * x = 1 job x = 6 6 - 3 = 3 answer : a"
a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 8
a
subtract(divide(multiply(18, add(const_4, const_1)), 9), add(const_4, const_1))
add(const_1,const_4)|multiply(n0,#0)|divide(#1,n1)|subtract(#2,#0)|
physics
allenai/math_qa
before leaving home for the town of madison , pete checks a map which shows that madison is 5 inches from his current location , gardensquare . pete arrives in madison 6.5 hours later and drove at an average speed of 60 miles per hour . at what scale , in inches per mile , is the map drawn ?
"pete covered 6.5 * 60 = 390 miles which correspond to 5 inches on the map - - > scale in inches per mile is 5 / 390 = 1 / 78 . answer : d ."
a ) 1 / 3 , b ) 1 / 30 , c ) 1 / 10 , d ) 1 / 78 , e ) 30
d
divide(const_1, multiply(divide(6.5, 5), 60))
divide(n1,n0)|multiply(#0,n2)|divide(const_1,#1)|
physics
allenai/math_qa
if it is assumed that 62 percent of those who receive a questionnaire by mail will respond and 300 responses are needed , what is the minimum number of questionnaires that should be mailed ?
"minimum no of mail to be sent for getting 300 responses at 62 % = 300 / 0.62 = 483.8 option d"
a ) 400 , b ) 420 , c ) 480 , d ) 483.8 , e ) 600
d
divide(300, divide(62, const_100))
divide(n0,const_100)|divide(n1,#0)|
gain
allenai/math_qa
the average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 65 kg . what is the correct weight ?
"actual total weight is ( 20 ã — 58.4 - 56 + 65 ) = 1177 kgs actual average weight is 1177 / 20 = 58.85 kgs answer is c"
a ) 67.4 kg , b ) 57.75 kg , c ) 58.85 kg , d ) 49.4 kg , e ) none of these
c
divide(add(multiply(58.4, 20), subtract(65, 56)), 20)
multiply(n0,n1)|subtract(n3,n2)|add(#0,#1)|divide(#2,n0)|
general
allenai/math_qa
a certain number of men complete a piece of work in 60 days . if there were 8 men more , the work could be finished in 10 days less . how many men were originally there ?
originally 1 et there be x men . more men , less days ( x + 8 ) : x ∷ 60 : 50 so , x + 8 / x = 60 / 50 or x = 40 . answer : d
a ) 30 , b ) 32 , c ) 36 , d ) 40 , e ) 45
d
divide(multiply(8, subtract(60, 10)), 10)
subtract(n0,n2)|multiply(n1,#0)|divide(#1,n2)
physics
allenai/math_qa
solve the equation for x : 6 x - 87 + 3 x = 4 + 9 - x
"c 10 9 x + x = 13 + 87 10 x = 100 = > x = 10"
a ) 12 , b ) 5 , c ) 10 , d ) 9 , e ) 3
c
divide(add(87, 4), add(3, 6))
add(n1,n3)|add(n2,n0)|divide(#0,#1)|
general
allenai/math_qa
the radius of the base of cone is 3 cm and height is 4 cm . find the volume of the cone ?
1 / 3 * π * 3 * 3 * 4 = 12 π answer : a
['a ) 12', 'b ) 75', 'c ) 97', 'd ) 15', 'e ) 91']
a
rectangle_area(3, 4)
rectangle_area(n0,n1)
geometry
allenai/math_qa
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 ?
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
a ) 11000 , b ) 12000 , c ) 13000 , d ) 14000 , e ) 15000
c
add(add(multiply(5000, add(const_1, divide(20, const_100))), multiply(3000, add(const_1, divide(2000, 3000)))), 2000)
divide(n5,const_100)|divide(n3,n2)|add(#0,const_1)|add(#1,const_1)|multiply(n1,#2)|multiply(n2,#3)|add(#4,#5)|add(n3,#6)
other
allenai/math_qa
a work as fast as b . if b can complete a work in 36 days independently , the number of days in which a and b can together finish the work in ?
"ratio of rates of working of a and b = 2 : 1 ratio of times taken = 1 : 2 a ' s 1 day work = 1 / 18 b ' s 1 day work = 1 / 36 a + b 1 day work = 1 / 18 + 1 / 36 = 3 / 36 = 1 / 12 a and b can finish the work in 12 days answer is a"
a ) 12 days , b ) 3 days , c ) 4 days , d ) 5 days , e ) 6 days
a
inverse(add(inverse(36), multiply(const_2, inverse(36))))
inverse(n0)|multiply(#0,const_2)|add(#0,#1)|inverse(#2)|
physics
allenai/math_qa
a and b can do a work in 12 days and 36 days respectively . if they work on alternate days beginning with b , in how many days will the work be completed ?
the work done in the first two days = 1 / 12 + 1 / 36 = 1 / 9 so , 9 such two days are required to finish the work . i . e . , 18 days are required to finish the work . answer : e
a ) 11 , b ) 17 , c ) 10 , d ) 17 , e ) 18
e
subtract(add(inverse(add(inverse(36), inverse(12))), 12), const_3)
inverse(n1)|inverse(n0)|add(#0,#1)|inverse(#2)|add(n0,#3)|subtract(#4,const_3)
physics
allenai/math_qa
the speed at which a man can row a boat in still water is 25 kmph . if he rows downstream , where the speed of current is 11 kmph , what time will he take to cover 80 metres ?
"speed of the boat downstream = 25 + 11 = 36 kmph = 36 * 5 / 18 = 10 m / s hence time taken to cover 80 m = 80 / 10 = 8 seconds . answer : e"
a ) 18 seconds , b ) 27 seconds , c ) 26 seconds , d ) 12 seconds , e ) 8 seconds
e
divide(80, multiply(add(25, 11), const_0_2778))
add(n0,n1)|multiply(#0,const_0_2778)|divide(n2,#1)|
physics
allenai/math_qa
the ratio of the present age of sandy to that of molly is 7 : 2 . eight years from now , the ratio of the ages of sandy to molly will be 5 : 2 . what was sandy ' s age 6 years ago ?
"let the present age of sandy be 7 x years and that of molly be 2 x years . ( 7 x + 8 ) / ( 2 x + 8 ) = 5 / 2 4 x = 24 x = 6 six years ago , sandy ' s age was 7 ( 6 ) - 6 = 36 the answer is d ."
a ) 18 , b ) 24 , c ) 30 , d ) 36 , e ) 42
d
subtract(divide(multiply(subtract(multiply(5, add(const_10, 6)), multiply(2, add(const_10, 6))), 7), add(2, 2)), 6)
add(n4,const_10)|add(n1,n1)|multiply(n2,#0)|multiply(n1,#0)|subtract(#2,#3)|multiply(n0,#4)|divide(#5,#1)|subtract(#6,n4)|
other
allenai/math_qa
the price of an item is discounted 10 percent on day 1 of a sale . on day 2 , the item is discounted another 10 percent , and on day 3 , it is discounted an additional 20 percent . the price of the item on day 3 is what percentage of the sale price on day 1 ?
"let initial price be 1000 price in day 1 after 10 % discount = 900 price in day 2 after 10 % discount = 810 price in day 3 after 20 % discount = 648 so , price in day 3 as percentage of the sale price on day 1 will be = 648 / 900 * 100 = > 72 % answer will definitely be ( e )"
a ) 28 % , b ) 40 % , c ) 64.8 % , d ) 70 % , e ) 72 %
e
add(multiply(divide(divide(20, const_100), subtract(1, divide(1, 10))), const_100), 2)
divide(n5,const_100)|divide(n1,n0)|subtract(n1,#1)|divide(#0,#2)|multiply(#3,const_100)|add(n2,#4)|
gain
allenai/math_qa
how many integers are between 5 and 74 / 5 , inclusive ?
"74 / 5 = 14 . xx we are not concerned about the exact value of 74 / 5 as we just need the integers . the different integers between 5 and 74 / 5 would be 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13,14 . total number of integers = 10 option e"
a ) 4 , b ) 5 , c ) 7 , d ) 8 , e ) 10
e
add(subtract(divide(74, 5), 5), const_1)
divide(n1,n2)|subtract(#0,n0)|add(#1,const_1)|
general
allenai/math_qa
divide rs . 1300 among a , b and c so that a receives 1 / 3 as much as b and c together and b receives 2 / 3 as a and c together . a ' s share is ?
"a + b + c = 1300 a = 1 / 3 ( b + c ) ; b = 2 / 3 ( a + c ) a / ( b + c ) = 1 / 3 a = 1 / 4 * 1300 = > 325 answer : e"
a ) 346 , b ) 368 , c ) 375 , d ) 337 , e ) 325
e
divide(1300, const_3)
divide(n0,const_3)|
general
allenai/math_qa
( 700 + 200 ) ã — 4 ã — ( 4 + 2 ) = ?
"( 700 + 200 ) ã — 4 ã — ( 4 + 2 ) = ? or , ? = 900 ã — 4 ã — 6 = 21600 answer b"
a ) 24500 , b ) 21600 , c ) 36600 , d ) 22400 , e ) 12500
b
divide(add(700, 200), 4)
add(n0,n1)|divide(#0,n2)|
general
allenai/math_qa